Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,13,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (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: | \(7.31195053821\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} + 468 x^{8} + 1496 x^{7} + 710096 x^{6} + 29155008 x^{5} + 143571008 x^{4} + 28213427840 x^{3} + 1335549648384 x^{2} + \cdots + 824967906703360 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{3}\cdot 23 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.8 | ||
Root | \(17.4695 - 29.8739i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.13.d.b.3.7 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.9390 | + | 59.7478i | 0.358422 | + | 0.933560i | ||||
\(3\) | 271.191 | 0.372005 | 0.186002 | − | 0.982549i | \(-0.440447\pi\) | ||||
0.186002 | + | 0.982549i | \(0.440447\pi\) | |||||||
\(4\) | −3043.60 | + | 2741.11i | −0.743067 | + | 0.669217i | ||||
\(5\) | 11036.2i | 0.706316i | 0.935564 | + | 0.353158i | \(0.114892\pi\) | ||||
−0.935564 | + | 0.353158i | \(0.885108\pi\) | |||||||
\(6\) | 6220.87 | + | 16203.1i | 0.133335 | + | 0.347289i | ||||
\(7\) | 58770.2i | 0.499539i | 0.968305 | + | 0.249769i | \(0.0803548\pi\) | ||||
−0.968305 | + | 0.249769i | \(0.919645\pi\) | |||||||
\(8\) | −233593. | − | 118970.i | −0.891086 | − | 0.453835i | ||||
\(9\) | −457896. | −0.861613 | ||||||||
\(10\) | −659388. | + | 253159.i | −0.659388 | + | 0.253159i | ||||
\(11\) | −146799. | −0.0828640 | −0.0414320 | − | 0.999141i | \(-0.513192\pi\) | ||||
−0.0414320 | + | 0.999141i | \(0.513192\pi\) | |||||||
\(12\) | −825399. | + | 743367.i | −0.276424 | + | 0.248952i | ||||
\(13\) | 4.26288e6i | 0.883167i | 0.897220 | + | 0.441583i | \(0.145583\pi\) | ||||
−0.897220 | + | 0.441583i | \(0.854417\pi\) | |||||||
\(14\) | −3.51139e6 | + | 1.34813e6i | −0.466349 | + | 0.179046i | ||||
\(15\) | 2.99292e6i | 0.262753i | ||||||||
\(16\) | 1.74980e6 | − | 1.66857e7i | 0.104296 | − | 0.994546i | ||||
\(17\) | 2.95267e7 | 1.22327 | 0.611634 | − | 0.791141i | \(-0.290513\pi\) | ||||
0.611634 | + | 0.791141i | \(0.290513\pi\) | |||||||
\(18\) | −1.05037e7 | − | 2.73583e7i | −0.308821 | − | 0.804367i | ||||
\(19\) | 6.17776e7 | 1.31313 | 0.656567 | − | 0.754268i | \(-0.272008\pi\) | ||||
0.656567 | + | 0.754268i | \(0.272008\pi\) | |||||||
\(20\) | −3.02514e7 | − | 3.35897e7i | −0.472679 | − | 0.524840i | ||||
\(21\) | 1.59380e7i | 0.185831i | ||||||||
\(22\) | −3.36742e6 | − | 8.77090e6i | −0.0297003 | − | 0.0773585i | ||||
\(23\) | 2.07436e8i | 1.40126i | 0.713526 | + | 0.700629i | \(0.247097\pi\) | ||||
−0.713526 | + | 0.700629i | \(0.752903\pi\) | |||||||
\(24\) | −6.33484e7 | − | 3.22636e7i | −0.331488 | − | 0.168829i | ||||
\(25\) | 1.22343e8 | 0.501118 | ||||||||
\(26\) | −2.54698e8 | + | 9.77863e7i | −0.824489 | + | 0.316547i | ||||
\(27\) | −2.68300e8 | −0.692529 | ||||||||
\(28\) | −1.61096e8 | − | 1.78873e8i | −0.334300 | − | 0.371191i | ||||
\(29\) | − | 4.01062e8i | − | 0.674255i | −0.941459 | − | 0.337127i | \(-0.890545\pi\) | ||
0.941459 | − | 0.337127i | \(-0.109455\pi\) | |||||||
\(30\) | −1.78820e8 | + | 6.86547e7i | −0.245295 | + | 0.0941765i | ||||
\(31\) | 4.64456e8i | 0.523329i | 0.965159 | + | 0.261664i | \(0.0842714\pi\) | ||||
−0.965159 | + | 0.261664i | \(0.915729\pi\) | |||||||
\(32\) | 1.03707e9 | − | 2.78207e8i | 0.965850 | − | 0.259101i | ||||
\(33\) | −3.98105e7 | −0.0308258 | ||||||||
\(34\) | 6.77314e8 | + | 1.76416e9i | 0.438446 | + | 1.14199i | ||||
\(35\) | −6.48599e8 | −0.352832 | ||||||||
\(36\) | 1.39365e9 | − | 1.25515e9i | 0.640236 | − | 0.576606i | ||||
\(37\) | − | 4.99972e9i | − | 1.94866i | −0.225132 | − | 0.974328i | \(-0.572281\pi\) | ||
0.225132 | − | 0.974328i | \(-0.427719\pi\) | |||||||
\(38\) | 1.41712e9 | + | 3.69107e9i | 0.470657 | + | 1.22589i | ||||
\(39\) | 1.15606e9i | 0.328542i | ||||||||
\(40\) | 1.31298e9 | − | 2.57797e9i | 0.320551 | − | 0.629388i | ||||
\(41\) | 7.68376e7 | 0.0161760 | 0.00808799 | − | 0.999967i | \(-0.497425\pi\) | ||||
0.00808799 | + | 0.999967i | \(0.497425\pi\) | |||||||
\(42\) | −9.52260e8 | + | 3.65602e8i | −0.173484 | + | 0.0666059i | ||||
\(43\) | −7.15914e9 | −1.13253 | −0.566266 | − | 0.824223i | \(-0.691612\pi\) | ||||
−0.566266 | + | 0.824223i | \(0.691612\pi\) | |||||||
\(44\) | 4.46797e8 | − | 4.02392e8i | 0.0615735 | − | 0.0554540i | ||||
\(45\) | − | 5.05343e9i | − | 0.608571i | ||||||
\(46\) | −1.23939e10 | + | 4.75839e9i | −1.30816 | + | 0.502242i | ||||
\(47\) | 2.06601e10i | 1.91666i | 0.285666 | + | 0.958329i | \(0.407785\pi\) | ||||
−0.285666 | + | 0.958329i | \(0.592215\pi\) | |||||||
\(48\) | 4.74532e8 | − | 4.52502e9i | 0.0387988 | − | 0.369976i | ||||
\(49\) | 1.03873e10 | 0.750461 | ||||||||
\(50\) | 2.80644e9 | + | 7.30974e9i | 0.179612 | + | 0.467823i | ||||
\(51\) | 8.00739e9 | 0.455061 | ||||||||
\(52\) | −1.16850e10 | − | 1.29745e10i | −0.591030 | − | 0.656252i | ||||
\(53\) | − | 5.81907e9i | − | 0.262542i | −0.991347 | − | 0.131271i | \(-0.958094\pi\) | ||
0.991347 | − | 0.131271i | \(-0.0419058\pi\) | |||||||
\(54\) | −6.15454e9 | − | 1.60303e10i | −0.248218 | − | 0.646517i | ||||
\(55\) | − | 1.62010e9i | − | 0.0585282i | ||||||
\(56\) | 6.99190e9 | − | 1.37283e10i | 0.226708 | − | 0.445132i | ||||
\(57\) | 1.67535e10 | 0.488492 | ||||||||
\(58\) | 2.39626e10 | − | 9.19998e9i | 0.629457 | − | 0.241668i | ||||
\(59\) | 3.59188e10 | 0.851549 | 0.425775 | − | 0.904829i | \(-0.360002\pi\) | ||||
0.425775 | + | 0.904829i | \(0.360002\pi\) | |||||||
\(60\) | −8.20393e9 | − | 9.10925e9i | −0.175839 | − | 0.195243i | ||||
\(61\) | 3.83534e10i | 0.744432i | 0.928146 | + | 0.372216i | \(0.121402\pi\) | ||||
−0.928146 | + | 0.372216i | \(0.878598\pi\) | |||||||
\(62\) | −2.77502e10 | + | 1.06542e10i | −0.488559 | + | 0.187573i | ||||
\(63\) | − | 2.69107e10i | − | 0.430409i | ||||||
\(64\) | 4.04117e10 | + | 5.55811e10i | 0.588068 | + | 0.808811i | ||||
\(65\) | −4.70459e10 | −0.623795 | ||||||||
\(66\) | −9.13215e8 | − | 2.37859e9i | −0.0110487 | − | 0.0287777i | ||||
\(67\) | −8.74298e10 | −0.966520 | −0.483260 | − | 0.875477i | \(-0.660547\pi\) | ||||
−0.483260 | + | 0.875477i | \(0.660547\pi\) | |||||||
\(68\) | −8.98675e10 | + | 8.09360e10i | −0.908969 | + | 0.818631i | ||||
\(69\) | 5.62550e10i | 0.521275i | ||||||||
\(70\) | −1.48782e10 | − | 3.87524e10i | −0.126463 | − | 0.329390i | ||||
\(71\) | − | 1.98703e11i | − | 1.55115i | −0.631255 | − | 0.775576i | \(-0.717460\pi\) | ||
0.631255 | − | 0.775576i | \(-0.282540\pi\) | |||||||
\(72\) | 1.06961e11 | + | 5.44759e10i | 0.767771 | + | 0.391030i | ||||
\(73\) | −1.90567e11 | −1.25924 | −0.629622 | − | 0.776902i | \(-0.716790\pi\) | ||||
−0.629622 | + | 0.776902i | \(0.716790\pi\) | |||||||
\(74\) | 2.98722e11 | − | 1.14689e11i | 1.81919 | − | 0.698442i | ||||
\(75\) | 3.31784e10 | 0.186418 | ||||||||
\(76\) | −1.88026e11 | + | 1.69339e11i | −0.975746 | + | 0.878772i | ||||
\(77\) | − | 8.62739e9i | − | 0.0413938i | ||||||
\(78\) | −6.90718e10 | + | 2.65188e10i | −0.306714 | + | 0.117757i | ||||
\(79\) | − | 4.39590e10i | − | 0.180836i | −0.995904 | − | 0.0904181i | \(-0.971180\pi\) | ||
0.995904 | − | 0.0904181i | \(-0.0288204\pi\) | |||||||
\(80\) | 1.84147e11 | + | 1.93112e10i | 0.702464 | + | 0.0736663i | ||||
\(81\) | 1.70584e11 | 0.603989 | ||||||||
\(82\) | 1.76258e9 | + | 4.59088e9i | 0.00579783 | + | 0.0151012i | ||||
\(83\) | 3.26303e11 | 0.998049 | 0.499025 | − | 0.866588i | \(-0.333692\pi\) | ||||
0.499025 | + | 0.866588i | \(0.333692\pi\) | |||||||
\(84\) | −4.36878e10 | − | 4.85089e10i | −0.124361 | − | 0.138085i | ||||
\(85\) | 3.25862e11i | 0.864013i | ||||||||
\(86\) | −1.64224e11 | − | 4.27743e11i | −0.405925 | − | 1.05729i | ||||
\(87\) | − | 1.08765e11i | − | 0.250826i | ||||||
\(88\) | 3.42911e10 | + | 1.74646e10i | 0.0738390 | + | 0.0376066i | ||||
\(89\) | 1.81425e11 | 0.365054 | 0.182527 | − | 0.983201i | \(-0.441572\pi\) | ||||
0.182527 | + | 0.983201i | \(0.441572\pi\) | |||||||
\(90\) | 3.01931e11 | − | 1.15921e11i | 0.568137 | − | 0.218125i | ||||
\(91\) | −2.50530e11 | −0.441176 | ||||||||
\(92\) | −5.68607e11 | − | 6.31354e11i | −0.937746 | − | 1.04123i | ||||
\(93\) | 1.25957e11i | 0.194681i | ||||||||
\(94\) | −1.23439e12 | + | 4.73922e11i | −1.78931 | + | 0.686973i | ||||
\(95\) | 6.81788e11i | 0.927487i | ||||||||
\(96\) | 2.81246e11 | − | 7.54474e10i | 0.359301 | − | 0.0963867i | ||||
\(97\) | 4.70836e10 | 0.0565249 | 0.0282624 | − | 0.999601i | \(-0.491003\pi\) | ||||
0.0282624 | + | 0.999601i | \(0.491003\pi\) | |||||||
\(98\) | 2.38276e11 | + | 6.20621e11i | 0.268982 | + | 0.700600i | ||||
\(99\) | 6.72186e10 | 0.0713967 | ||||||||
\(100\) | −3.72364e11 | + | 3.35357e11i | −0.372364 | + | 0.335357i | ||||
\(101\) | − | 8.79652e11i | − | 0.828672i | −0.910124 | − | 0.414336i | \(-0.864014\pi\) | ||
0.910124 | − | 0.414336i | \(-0.135986\pi\) | |||||||
\(102\) | 1.83682e11 | + | 4.78424e11i | 0.163104 | + | 0.424827i | ||||
\(103\) | 1.45548e12i | 1.21895i | 0.792807 | + | 0.609473i | \(0.208619\pi\) | ||||
−0.792807 | + | 0.609473i | \(0.791381\pi\) | |||||||
\(104\) | 5.07155e11 | − | 9.95778e11i | 0.400812 | − | 0.786978i | ||||
\(105\) | −1.75895e11 | −0.131255 | ||||||||
\(106\) | 3.47677e11 | − | 1.33484e11i | 0.245098 | − | 0.0941008i | ||||
\(107\) | −3.55167e11 | −0.236663 | −0.118331 | − | 0.992974i | \(-0.537755\pi\) | ||||
−0.118331 | + | 0.992974i | \(0.537755\pi\) | |||||||
\(108\) | 8.16598e11 | − | 7.35440e11i | 0.514595 | − | 0.463452i | ||||
\(109\) | − | 2.28440e12i | − | 1.36211i | −0.732231 | − | 0.681056i | \(-0.761521\pi\) | ||
0.732231 | − | 0.681056i | \(-0.238479\pi\) | |||||||
\(110\) | 9.67973e10 | − | 3.71635e10i | 0.0546395 | − | 0.0209778i | ||||
\(111\) | − | 1.35588e12i | − | 0.724909i | ||||||
\(112\) | 9.80624e11 | + | 1.02836e11i | 0.496815 | + | 0.0521001i | ||||
\(113\) | 1.95500e12 | 0.939021 | 0.469511 | − | 0.882927i | \(-0.344430\pi\) | ||||
0.469511 | + | 0.882927i | \(0.344430\pi\) | |||||||
\(114\) | 3.84310e11 | + | 1.00099e12i | 0.175086 | + | 0.456036i | ||||
\(115\) | −2.28931e12 | −0.989731 | ||||||||
\(116\) | 1.09936e12 | + | 1.22067e12i | 0.451223 | + | 0.501016i | ||||
\(117\) | − | 1.95196e12i | − | 0.760948i | ||||||
\(118\) | 8.23943e11 | + | 2.14607e12i | 0.305214 | + | 0.794972i | ||||
\(119\) | 1.73529e12i | 0.611069i | ||||||||
\(120\) | 3.56068e11 | − | 6.99124e11i | 0.119246 | − | 0.234135i | ||||
\(121\) | −3.11688e12 | −0.993134 | ||||||||
\(122\) | −2.29153e12 | + | 8.79790e11i | −0.694972 | + | 0.266821i | ||||
\(123\) | 2.08377e10 | 0.00601754 | ||||||||
\(124\) | −1.27313e12 | − | 1.41362e12i | −0.350221 | − | 0.388868i | ||||
\(125\) | 4.04458e12i | 1.06026i | ||||||||
\(126\) | 1.60785e12 | − | 6.17305e11i | 0.401812 | − | 0.154268i | ||||
\(127\) | − | 1.24761e12i | − | 0.297341i | −0.988887 | − | 0.148671i | \(-0.952501\pi\) | ||
0.988887 | − | 0.148671i | \(-0.0474994\pi\) | |||||||
\(128\) | −2.39384e12 | + | 3.68949e12i | −0.544297 | + | 0.838893i | ||||
\(129\) | −1.94150e12 | −0.421307 | ||||||||
\(130\) | −1.07919e12 | − | 2.81089e12i | −0.223582 | − | 0.582349i | ||||
\(131\) | 3.97920e12 | 0.787350 | 0.393675 | − | 0.919250i | \(-0.371204\pi\) | ||||
0.393675 | + | 0.919250i | \(0.371204\pi\) | |||||||
\(132\) | 1.21167e11 | − | 1.09125e11i | 0.0229056 | − | 0.0206292i | ||||
\(133\) | 3.63068e12i | 0.655962i | ||||||||
\(134\) | −2.00555e12 | − | 5.22374e12i | −0.346422 | − | 0.902304i | ||||
\(135\) | − | 2.96101e12i | − | 0.489144i | ||||||
\(136\) | −6.89722e12 | − | 3.51279e12i | −1.09004 | − | 0.555161i | ||||
\(137\) | 5.76362e12 | 0.871710 | 0.435855 | − | 0.900017i | \(-0.356446\pi\) | ||||
0.435855 | + | 0.900017i | \(0.356446\pi\) | |||||||
\(138\) | −3.36111e12 | + | 1.29044e12i | −0.486641 | + | 0.186836i | ||||
\(139\) | 4.37090e12 | 0.606013 | 0.303006 | − | 0.952989i | \(-0.402010\pi\) | ||||
0.303006 | + | 0.952989i | \(0.402010\pi\) | |||||||
\(140\) | 1.97408e12 | − | 1.77788e12i | 0.262178 | − | 0.236121i | ||||
\(141\) | 5.60283e12i | 0.713006i | ||||||||
\(142\) | 1.18721e13 | − | 4.55805e12i | 1.44809 | − | 0.555967i | ||||
\(143\) | − | 6.25785e11i | − | 0.0731828i | ||||||
\(144\) | −8.01229e11 | + | 7.64033e12i | −0.0898632 | + | 0.856913i | ||||
\(145\) | 4.42620e12 | 0.476237 | ||||||||
\(146\) | −4.37142e12 | − | 1.13859e13i | −0.451341 | − | 1.17558i | ||||
\(147\) | 2.81696e12 | 0.279175 | ||||||||
\(148\) | 1.37048e13 | + | 1.52172e13i | 1.30407 | + | 1.44798i | ||||
\(149\) | 7.63175e12i | 0.697440i | 0.937227 | + | 0.348720i | \(0.113384\pi\) | ||||
−0.937227 | + | 0.348720i | \(0.886616\pi\) | |||||||
\(150\) | 7.61081e11 | + | 1.98234e12i | 0.0668165 | + | 0.174033i | ||||
\(151\) | − | 1.05853e13i | − | 0.892978i | −0.894789 | − | 0.446489i | \(-0.852674\pi\) | ||
0.894789 | − | 0.446489i | \(-0.147326\pi\) | |||||||
\(152\) | −1.44308e13 | − | 7.34968e12i | −1.17012 | − | 0.595946i | ||||
\(153\) | −1.35202e13 | −1.05398 | ||||||||
\(154\) | 5.15468e11 | − | 1.97904e11i | 0.0386436 | − | 0.0148365i | ||||
\(155\) | −5.12583e12 | −0.369635 | ||||||||
\(156\) | −3.16888e12 | − | 3.51857e12i | −0.219866 | − | 0.244129i | ||||
\(157\) | − | 1.18606e13i | − | 0.791971i | −0.918257 | − | 0.395986i | \(-0.870403\pi\) | ||
0.918257 | − | 0.395986i | \(-0.129597\pi\) | |||||||
\(158\) | 2.62646e12 | − | 1.00838e12i | 0.168821 | − | 0.0648158i | ||||
\(159\) | − | 1.57808e12i | − | 0.0976668i | ||||||
\(160\) | 3.07035e12 | + | 1.14453e13i | 0.183007 | + | 0.682195i | ||||
\(161\) | −1.21911e13 | −0.699983 | ||||||||
\(162\) | 3.91304e12 | + | 1.01920e13i | 0.216483 | + | 0.563859i | ||||
\(163\) | −4.52743e12 | −0.241394 | −0.120697 | − | 0.992689i | \(-0.538513\pi\) | ||||
−0.120697 | + | 0.992689i | \(0.538513\pi\) | |||||||
\(164\) | −2.33863e11 | + | 2.10621e11i | −0.0120198 | + | 0.0108252i | ||||
\(165\) | − | 4.39356e11i | − | 0.0217728i | ||||||
\(166\) | 7.48507e12 | + | 1.94959e13i | 0.357723 | + | 0.931738i | ||||
\(167\) | 5.64186e12i | 0.260090i | 0.991508 | + | 0.130045i | \(0.0415122\pi\) | ||||
−0.991508 | + | 0.130045i | \(0.958488\pi\) | |||||||
\(168\) | 1.89614e12 | − | 3.72300e12i | 0.0843365 | − | 0.165591i | ||||
\(169\) | 5.12596e12 | 0.220016 | ||||||||
\(170\) | −1.94695e13 | + | 7.47496e12i | −0.806607 | + | 0.309682i | ||||
\(171\) | −2.82877e13 | −1.13141 | ||||||||
\(172\) | 2.17896e13 | − | 1.96240e13i | 0.841547 | − | 0.757910i | ||||
\(173\) | − | 3.48709e12i | − | 0.130073i | −0.997883 | − | 0.0650364i | \(-0.979284\pi\) | ||
0.997883 | − | 0.0650364i | \(-0.0207163\pi\) | |||||||
\(174\) | 6.49845e12 | − | 2.49496e12i | 0.234161 | − | 0.0899016i | ||||
\(175\) | 7.19014e12i | 0.250328i | ||||||||
\(176\) | −2.56869e11 | + | 2.44944e12i | −0.00864243 | + | 0.0824121i | ||||
\(177\) | 9.74087e12 | 0.316780 | ||||||||
\(178\) | 4.16171e12 | + | 1.08397e13i | 0.130844 | + | 0.340800i | ||||
\(179\) | 3.52407e13 | 1.07134 | 0.535668 | − | 0.844428i | \(-0.320060\pi\) | ||||
0.535668 | + | 0.844428i | \(0.320060\pi\) | |||||||
\(180\) | 1.38520e13 | + | 1.53806e13i | 0.407266 | + | 0.452209i | ||||
\(181\) | − | 4.56757e13i | − | 1.29901i | −0.760356 | − | 0.649507i | \(-0.774975\pi\) | ||
0.760356 | − | 0.649507i | \(-0.225025\pi\) | |||||||
\(182\) | −5.74692e12 | − | 1.49686e13i | −0.158127 | − | 0.411864i | ||||
\(183\) | 1.04011e13i | 0.276932i | ||||||||
\(184\) | 2.46787e13 | − | 4.84557e13i | 0.635939 | − | 1.24864i | ||||
\(185\) | 5.51778e13 | 1.37637 | ||||||||
\(186\) | −7.52563e12 | + | 2.88932e12i | −0.181746 | + | 0.0697780i | ||||
\(187\) | −4.33448e12 | −0.101365 | ||||||||
\(188\) | −5.66316e13 | − | 6.28810e13i | −1.28266 | − | 1.42421i | ||||
\(189\) | − | 1.57680e13i | − | 0.345945i | ||||||
\(190\) | −4.07354e13 | + | 1.56396e13i | −0.865865 | + | 0.332432i | ||||
\(191\) | 9.20825e13i | 1.89661i | 0.317367 | + | 0.948303i | \(0.397201\pi\) | ||||
−0.317367 | + | 0.948303i | \(0.602799\pi\) | |||||||
\(192\) | 1.09593e13 | + | 1.50731e13i | 0.218764 | + | 0.300882i | ||||
\(193\) | −9.14371e12 | −0.176921 | −0.0884603 | − | 0.996080i | \(-0.528195\pi\) | ||||
−0.0884603 | + | 0.996080i | \(0.528195\pi\) | |||||||
\(194\) | 1.08005e12 | + | 2.81314e12i | 0.0202598 | + | 0.0527693i | ||||
\(195\) | −1.27584e13 | −0.232055 | ||||||||
\(196\) | −3.16149e13 | + | 2.84729e13i | −0.557643 | + | 0.502221i | ||||
\(197\) | 5.41898e13i | 0.927087i | 0.886074 | + | 0.463544i | \(0.153422\pi\) | ||||
−0.886074 | + | 0.463544i | \(0.846578\pi\) | |||||||
\(198\) | 1.54193e12 | + | 4.01616e12i | 0.0255902 | + | 0.0666531i | ||||
\(199\) | 2.40613e13i | 0.387436i | 0.981057 | + | 0.193718i | \(0.0620547\pi\) | ||||
−0.981057 | + | 0.193718i | \(0.937945\pi\) | |||||||
\(200\) | −2.85785e13 | − | 1.45552e13i | −0.446539 | − | 0.227425i | ||||
\(201\) | −2.37102e13 | −0.359550 | ||||||||
\(202\) | 5.25573e13 | − | 2.01784e13i | 0.773615 | − | 0.297015i | ||||
\(203\) | 2.35705e13 | 0.336816 | ||||||||
\(204\) | −2.43713e13 | + | 2.19492e13i | −0.338141 | + | 0.304535i | ||||
\(205\) | 8.47993e11i | 0.0114253i | ||||||||
\(206\) | −8.69620e13 | + | 3.33874e13i | −1.13796 | + | 0.436897i | ||||
\(207\) | − | 9.49844e13i | − | 1.20734i | ||||||
\(208\) | 7.11292e13 | + | 7.45920e12i | 0.878350 | + | 0.0921112i | ||||
\(209\) | −9.06886e12 | −0.108812 | ||||||||
\(210\) | −4.03485e12 | − | 1.05093e13i | −0.0470448 | − | 0.122535i | ||||
\(211\) | −3.69601e13 | −0.418831 | −0.209415 | − | 0.977827i | \(-0.567156\pi\) | ||||
−0.209415 | + | 0.977827i | \(0.567156\pi\) | |||||||
\(212\) | 1.59507e13 | + | 1.77109e13i | 0.175697 | + | 0.195086i | ||||
\(213\) | − | 5.38865e13i | − | 0.577035i | ||||||
\(214\) | −8.14719e12 | − | 2.12205e13i | −0.0848252 | − | 0.220939i | ||||
\(215\) | − | 7.90096e13i | − | 0.799925i | ||||||
\(216\) | 6.26729e13 | + | 3.19196e13i | 0.617102 | + | 0.314293i | ||||
\(217\) | −2.72962e13 | −0.261423 | ||||||||
\(218\) | 1.36488e14 | − | 5.24019e13i | 1.27161 | − | 0.488211i | ||||
\(219\) | −5.16801e13 | −0.468445 | ||||||||
\(220\) | 4.44087e12 | + | 4.93093e12i | 0.0391681 | + | 0.0434903i | ||||
\(221\) | 1.25869e14i | 1.08035i | ||||||||
\(222\) | 8.10109e13 | − | 3.11026e13i | 0.676746 | − | 0.259824i | ||||
\(223\) | − | 1.37554e14i | − | 1.11852i | −0.828993 | − | 0.559259i | \(-0.811086\pi\) | ||
0.828993 | − | 0.559259i | \(-0.188914\pi\) | |||||||
\(224\) | 1.63503e13 | + | 6.09491e13i | 0.129431 | + | 0.482480i | ||||
\(225\) | −5.60205e13 | −0.431770 | ||||||||
\(226\) | 4.48457e13 | + | 1.16807e14i | 0.336566 | + | 0.876632i | ||||
\(227\) | 2.35297e14 | 1.71973 | 0.859867 | − | 0.510518i | \(-0.170546\pi\) | ||||
0.859867 | + | 0.510518i | \(0.170546\pi\) | |||||||
\(228\) | −5.09911e13 | + | 4.59234e13i | −0.362982 | + | 0.326907i | ||||
\(229\) | 4.10302e13i | 0.284506i | 0.989830 | + | 0.142253i | \(0.0454346\pi\) | ||||
−0.989830 | + | 0.142253i | \(0.954565\pi\) | |||||||
\(230\) | −5.25145e13 | − | 1.36781e14i | −0.354742 | − | 0.923973i | ||||
\(231\) | − | 2.33968e12i | − | 0.0153987i | ||||||
\(232\) | −4.77144e13 | + | 9.36853e13i | −0.306000 | + | 0.600819i | ||||
\(233\) | −1.76573e13 | −0.110354 | −0.0551770 | − | 0.998477i | \(-0.517572\pi\) | ||||
−0.0551770 | + | 0.998477i | \(0.517572\pi\) | |||||||
\(234\) | 1.16625e14 | − | 4.47760e13i | 0.710390 | − | 0.272741i | ||||
\(235\) | −2.28008e14 | −1.35377 | ||||||||
\(236\) | −1.09323e14 | + | 9.84575e13i | −0.632758 | + | 0.569871i | ||||
\(237\) | − | 1.19213e13i | − | 0.0672719i | ||||||
\(238\) | −1.03680e14 | + | 3.98059e13i | −0.570470 | + | 0.219021i | ||||
\(239\) | − | 8.88181e13i | − | 0.476556i | −0.971197 | − | 0.238278i | \(-0.923417\pi\) | ||
0.971197 | − | 0.238278i | \(-0.0765830\pi\) | |||||||
\(240\) | 4.99390e13 | + | 5.23702e12i | 0.261320 | + | 0.0274042i | ||||
\(241\) | −1.16450e14 | −0.594345 | −0.297172 | − | 0.954824i | \(-0.596044\pi\) | ||||
−0.297172 | + | 0.954824i | \(0.596044\pi\) | |||||||
\(242\) | −7.14982e13 | − | 1.86227e14i | −0.355961 | − | 0.927149i | ||||
\(243\) | 1.88846e14 | 0.917215 | ||||||||
\(244\) | −1.05131e14 | − | 1.16733e14i | −0.498187 | − | 0.553163i | ||||
\(245\) | 1.14637e14i | 0.530062i | ||||||||
\(246\) | 4.77996e11 | + | 1.24501e12i | 0.00215682 | + | 0.00561773i | ||||
\(247\) | 2.63350e14i | 1.15972i | ||||||||
\(248\) | 5.52564e13 | − | 1.08494e14i | 0.237505 | − | 0.466331i | ||||
\(249\) | 8.84905e13 | 0.371279 | ||||||||
\(250\) | −2.41655e14 | + | 9.27788e13i | −0.989819 | + | 0.380022i | ||||
\(251\) | −2.12179e14 | −0.848517 | −0.424258 | − | 0.905541i | \(-0.639465\pi\) | ||||
−0.424258 | + | 0.905541i | \(0.639465\pi\) | |||||||
\(252\) | 7.37652e13 | + | 8.19054e13i | 0.288037 | + | 0.319823i | ||||
\(253\) | − | 3.04514e13i | − | 0.116114i | ||||||
\(254\) | 7.45417e13 | − | 2.86189e13i | 0.277586 | − | 0.106574i | ||||
\(255\) | 8.83710e13i | 0.321417i | ||||||||
\(256\) | −2.75351e14 | − | 5.83935e13i | −0.978244 | − | 0.207455i | ||||
\(257\) | 3.91679e14 | 1.35935 | 0.679675 | − | 0.733513i | \(-0.262121\pi\) | ||||
0.679675 | + | 0.733513i | \(0.262121\pi\) | |||||||
\(258\) | −4.45361e13 | − | 1.16000e14i | −0.151006 | − | 0.393315i | ||||
\(259\) | 2.93835e14 | 0.973430 | ||||||||
\(260\) | 1.43189e14 | − | 1.28958e14i | 0.463521 | − | 0.417454i | ||||
\(261\) | 1.83645e14i | 0.580946i | ||||||||
\(262\) | 9.12790e13 | + | 2.37748e14i | 0.282204 | + | 0.735038i | ||||
\(263\) | − | 1.40060e14i | − | 0.423234i | −0.977353 | − | 0.211617i | \(-0.932127\pi\) | ||
0.977353 | − | 0.211617i | \(-0.0678729\pi\) | |||||||
\(264\) | 9.29946e12 | + | 4.73626e12i | 0.0274684 | + | 0.0139898i | ||||
\(265\) | 6.42203e13 | 0.185437 | ||||||||
\(266\) | −2.16925e14 | + | 8.32843e13i | −0.612379 | + | 0.235111i | ||||
\(267\) | 4.92009e13 | 0.135802 | ||||||||
\(268\) | 2.66101e14 | − | 2.39655e14i | 0.718189 | − | 0.646812i | ||||
\(269\) | − | 4.24104e14i | − | 1.11933i | −0.828718 | − | 0.559666i | \(-0.810929\pi\) | ||
0.828718 | − | 0.559666i | \(-0.189071\pi\) | |||||||
\(270\) | 1.76914e14 | − | 6.79226e13i | 0.456645 | − | 0.175320i | ||||
\(271\) | 5.78260e14i | 1.45985i | 0.683529 | + | 0.729923i | \(0.260444\pi\) | ||||
−0.683529 | + | 0.729923i | \(0.739556\pi\) | |||||||
\(272\) | 5.16659e13 | − | 4.92674e14i | 0.127582 | − | 1.21660i | ||||
\(273\) | −6.79417e13 | −0.164120 | ||||||||
\(274\) | 1.32212e14 | + | 3.44364e14i | 0.312440 | + | 0.813793i | ||||
\(275\) | −1.79598e13 | −0.0415247 | ||||||||
\(276\) | −1.54201e14 | − | 1.71218e14i | −0.348846 | − | 0.387342i | ||||
\(277\) | − | 8.12211e14i | − | 1.79800i | −0.437946 | − | 0.899001i | \(-0.644294\pi\) | ||
0.437946 | − | 0.899001i | \(-0.355706\pi\) | |||||||
\(278\) | 1.00264e14 | + | 2.61151e14i | 0.217208 | + | 0.565749i | ||||
\(279\) | − | 2.12673e14i | − | 0.450907i | ||||||
\(280\) | 1.51508e14 | + | 7.71639e13i | 0.314404 | + | 0.160127i | ||||
\(281\) | −5.48235e14 | −1.11360 | −0.556800 | − | 0.830647i | \(-0.687971\pi\) | ||||
−0.556800 | + | 0.830647i | \(0.687971\pi\) | |||||||
\(282\) | −3.34757e14 | + | 1.28524e14i | −0.665633 | + | 0.255557i | ||||
\(283\) | −8.25508e14 | −1.60695 | −0.803476 | − | 0.595338i | \(-0.797018\pi\) | ||||
−0.803476 | + | 0.595338i | \(0.797018\pi\) | |||||||
\(284\) | 5.44667e14 | + | 6.04772e14i | 1.03806 | + | 1.15261i | ||||
\(285\) | 1.84895e14i | 0.345030i | ||||||||
\(286\) | 3.73893e13 | − | 1.43549e13i | 0.0683205 | − | 0.0262303i | ||||
\(287\) | 4.51576e12i | 0.00808053i | ||||||||
\(288\) | −4.74872e14 | + | 1.27390e14i | −0.832189 | + | 0.223244i | ||||
\(289\) | 2.89203e14 | 0.496382 | ||||||||
\(290\) | 1.01533e14 | + | 2.64456e14i | 0.170694 | + | 0.444595i | ||||
\(291\) | 1.27687e13 | 0.0210275 | ||||||||
\(292\) | 5.80009e14 | − | 5.22365e14i | 0.935702 | − | 0.842708i | ||||
\(293\) | 1.43564e14i | 0.226902i | 0.993544 | + | 0.113451i | \(0.0361905\pi\) | ||||
−0.993544 | + | 0.113451i | \(0.963809\pi\) | |||||||
\(294\) | 6.46183e13 | + | 1.68307e14i | 0.100063 | + | 0.260626i | ||||
\(295\) | 3.96407e14i | 0.601463i | ||||||||
\(296\) | −5.94817e14 | + | 1.16790e15i | −0.884368 | + | 1.73642i | ||||
\(297\) | 3.93861e13 | 0.0573857 | ||||||||
\(298\) | −4.55980e14 | + | 1.75065e14i | −0.651101 | + | 0.249978i | ||||
\(299\) | −8.84276e14 | −1.23754 | ||||||||
\(300\) | −1.00982e14 | + | 9.09459e13i | −0.138521 | + | 0.124754i | ||||
\(301\) | − | 4.20745e14i | − | 0.565744i | ||||||
\(302\) | 6.32447e14 | − | 2.42816e14i | 0.833648 | − | 0.320063i | ||||
\(303\) | − | 2.38554e14i | − | 0.308270i | ||||||
\(304\) | 1.08099e14 | − | 1.03080e15i | 0.136955 | − | 1.30597i | ||||
\(305\) | −4.23275e14 | −0.525804 | ||||||||
\(306\) | −3.10139e14 | − | 8.07800e14i | −0.377771 | − | 0.983955i | ||||
\(307\) | 1.53573e15 | 1.83437 | 0.917183 | − | 0.398467i | \(-0.130458\pi\) | ||||
0.917183 | + | 0.398467i | \(0.130458\pi\) | |||||||
\(308\) | 2.36487e13 | + | 2.62584e13i | 0.0277014 | + | 0.0307584i | ||||
\(309\) | 3.94715e14i | 0.453453i | ||||||||
\(310\) | −1.17581e14 | − | 3.06257e14i | −0.132486 | − | 0.345077i | ||||
\(311\) | − | 7.26434e14i | − | 0.802848i | −0.915892 | − | 0.401424i | \(-0.868515\pi\) | ||
0.915892 | − | 0.401424i | \(-0.131485\pi\) | |||||||
\(312\) | 1.37536e14 | − | 2.70046e14i | 0.149104 | − | 0.292759i | ||||
\(313\) | 8.78186e14 | 0.933943 | 0.466972 | − | 0.884272i | \(-0.345345\pi\) | ||||
0.466972 | + | 0.884272i | \(0.345345\pi\) | |||||||
\(314\) | 7.08646e14 | − | 2.72071e14i | 0.739352 | − | 0.283860i | ||||
\(315\) | 2.96991e14 | 0.304005 | ||||||||
\(316\) | 1.20497e14 | + | 1.33794e14i | 0.121019 | + | 0.134373i | ||||
\(317\) | 1.03708e15i | 1.02202i | 0.859576 | + | 0.511008i | \(0.170728\pi\) | ||||
−0.859576 | + | 0.511008i | \(0.829272\pi\) | |||||||
\(318\) | 9.42869e13 | − | 3.61997e13i | 0.0911777 | − | 0.0350060i | ||||
\(319\) | 5.88754e13i | 0.0558715i | ||||||||
\(320\) | −6.13403e14 | + | 4.45991e14i | −0.571276 | + | 0.415362i | ||||
\(321\) | −9.63183e13 | −0.0880397 | ||||||||
\(322\) | −2.79652e14 | − | 7.28391e14i | −0.250890 | − | 0.653476i | ||||
\(323\) | 1.82409e15 | 1.60631 | ||||||||
\(324\) | −5.19190e14 | + | 4.67591e14i | −0.448804 | + | 0.404200i | ||||
\(325\) | 5.21534e14i | 0.442571i | ||||||||
\(326\) | −1.03855e14 | − | 2.70504e14i | −0.0865210 | − | 0.225356i | ||||
\(327\) | − | 6.19509e14i | − | 0.506712i | ||||||
\(328\) | −1.79487e13 | − | 9.14137e12i | −0.0144142 | − | 0.00734122i | ||||
\(329\) | −1.21420e15 | −0.957445 | ||||||||
\(330\) | 2.62506e13 | − | 1.00784e13i | 0.0203262 | − | 0.00780384i | ||||
\(331\) | −1.44918e15 | −1.10193 | −0.550964 | − | 0.834529i | \(-0.685740\pi\) | ||||
−0.550964 | + | 0.834529i | \(0.685740\pi\) | |||||||
\(332\) | −9.93135e14 | + | 8.94433e14i | −0.741617 | + | 0.667912i | ||||
\(333\) | 2.28935e15i | 1.67899i | ||||||||
\(334\) | −3.37089e14 | + | 1.29419e14i | −0.242809 | + | 0.0932220i | ||||
\(335\) | − | 9.64891e14i | − | 0.682668i | ||||||
\(336\) | 2.65937e14 | + | 2.78884e13i | 0.184817 | + | 0.0193815i | ||||
\(337\) | 1.51299e15 | 1.03290 | 0.516449 | − | 0.856318i | \(-0.327254\pi\) | ||||
0.516449 | + | 0.856318i | \(0.327254\pi\) | |||||||
\(338\) | 1.17585e14 | + | 3.06265e14i | 0.0788588 | + | 0.205398i | ||||
\(339\) | 5.30178e14 | 0.349320 | ||||||||
\(340\) | −8.93225e14 | − | 9.91794e14i | −0.578212 | − | 0.642019i | ||||
\(341\) | − | 6.81816e13i | − | 0.0433651i | ||||||
\(342\) | −6.48893e14 | − | 1.69013e15i | −0.405524 | − | 1.05624i | ||||
\(343\) | 1.42392e15i | 0.874423i | ||||||||
\(344\) | 1.67232e15 | + | 8.51724e14i | 1.00918 | + | 0.513982i | ||||
\(345\) | −6.20840e14 | −0.368184 | ||||||||
\(346\) | 2.08346e14 | − | 7.99904e13i | 0.121431 | − | 0.0466210i | ||||
\(347\) | −2.67016e15 | −1.52954 | −0.764769 | − | 0.644305i | \(-0.777147\pi\) | ||||
−0.764769 | + | 0.644305i | \(0.777147\pi\) | |||||||
\(348\) | 2.98136e14 | + | 3.31036e14i | 0.167857 | + | 0.186380i | ||||
\(349\) | − | 2.60277e15i | − | 1.44040i | −0.693767 | − | 0.720199i | \(-0.744050\pi\) | ||
0.693767 | − | 0.720199i | \(-0.255950\pi\) | |||||||
\(350\) | −4.29595e14 | + | 1.64935e14i | −0.233696 | + | 0.0897231i | ||||
\(351\) | − | 1.14373e15i | − | 0.611618i | ||||||
\(352\) | −1.52241e14 | + | 4.08405e13i | −0.0800342 | + | 0.0214701i | ||||
\(353\) | −2.63038e15 | −1.35947 | −0.679737 | − | 0.733456i | \(-0.737906\pi\) | ||||
−0.679737 | + | 0.733456i | \(0.737906\pi\) | |||||||
\(354\) | 2.23446e14 | + | 5.81996e14i | 0.113541 | + | 0.295733i | ||||
\(355\) | 2.19292e15 | 1.09560 | ||||||||
\(356\) | −5.52185e14 | + | 4.97307e14i | −0.271260 | + | 0.244300i | ||||
\(357\) | 4.70596e14i | 0.227321i | ||||||||
\(358\) | 8.08387e14 | + | 2.10555e15i | 0.383991 | + | 1.00016i | ||||
\(359\) | − | 1.33956e15i | − | 0.625742i | −0.949796 | − | 0.312871i | \(-0.898709\pi\) | ||
0.949796 | − | 0.312871i | \(-0.101291\pi\) | |||||||
\(360\) | −6.01206e14 | + | 1.18044e15i | −0.276190 | + | 0.542289i | ||||
\(361\) | 1.60315e15 | 0.724321 | ||||||||
\(362\) | 2.72902e15 | − | 1.04776e15i | 1.21271 | − | 0.465596i | ||||
\(363\) | −8.45271e14 | −0.369450 | ||||||||
\(364\) | 7.62515e14 | − | 6.86732e14i | 0.327823 | − | 0.295243i | ||||
\(365\) | − | 2.10313e15i | − | 0.889424i | ||||||
\(366\) | −6.21444e14 | + | 2.38592e14i | −0.258533 | + | 0.0992587i | ||||
\(367\) | 2.93675e15i | 1.20191i | 0.799285 | + | 0.600953i | \(0.205212\pi\) | ||||
−0.799285 | + | 0.600953i | \(0.794788\pi\) | |||||||
\(368\) | 3.46123e15 | + | 3.62973e14i | 1.39362 | + | 0.146146i | ||||
\(369\) | −3.51836e13 | −0.0139374 | ||||||||
\(370\) | 1.26573e15 | + | 3.29675e15i | 0.493321 | + | 1.28492i | ||||
\(371\) | 3.41988e14 | 0.131150 | ||||||||
\(372\) | −3.45261e14 | − | 3.83362e14i | −0.130284 | − | 0.144661i | ||||
\(373\) | − | 2.60686e15i | − | 0.967977i | −0.875074 | − | 0.483989i | \(-0.839188\pi\) | ||
0.875074 | − | 0.483989i | \(-0.160812\pi\) | |||||||
\(374\) | −9.94288e13 | − | 2.58976e14i | −0.0363314 | − | 0.0946301i | ||||
\(375\) | 1.09686e15i | 0.394423i | ||||||||
\(376\) | 2.45793e15 | − | 4.82605e15i | 0.869846 | − | 1.70791i | ||||
\(377\) | 1.70968e15 | 0.595479 | ||||||||
\(378\) | 9.42106e14 | − | 3.61704e14i | 0.322960 | − | 0.123994i | ||||
\(379\) | −4.34547e15 | −1.46623 | −0.733115 | − | 0.680105i | \(-0.761934\pi\) | ||||
−0.733115 | + | 0.680105i | \(0.761934\pi\) | |||||||
\(380\) | −1.86886e15 | − | 2.07509e15i | −0.620691 | − | 0.689185i | ||||
\(381\) | − | 3.38340e14i | − | 0.110612i | ||||||
\(382\) | −5.50173e15 | + | 2.11228e15i | −1.77059 | + | 0.679786i | ||||
\(383\) | − | 2.23766e15i | − | 0.708926i | −0.935070 | − | 0.354463i | \(-0.884664\pi\) | ||
0.935070 | − | 0.354463i | \(-0.115336\pi\) | |||||||
\(384\) | −6.49189e14 | + | 1.00056e15i | −0.202481 | + | 0.312072i | ||||
\(385\) | 9.52135e13 | 0.0292371 | ||||||||
\(386\) | −2.09748e14 | − | 5.46316e14i | −0.0634123 | − | 0.165166i | ||||
\(387\) | 3.27815e15 | 0.975804 | ||||||||
\(388\) | −1.43304e14 | + | 1.29062e14i | −0.0420017 | + | 0.0378274i | ||||
\(389\) | 9.97389e14i | 0.287851i | 0.989589 | + | 0.143925i | \(0.0459725\pi\) | ||||
−0.989589 | + | 0.143925i | \(0.954028\pi\) | |||||||
\(390\) | −2.92666e14 | − | 7.62289e14i | −0.0831735 | − | 0.216637i | ||||
\(391\) | 6.12491e15i | 1.71411i | ||||||||
\(392\) | −2.42641e15 | − | 1.23578e15i | −0.668725 | − | 0.340585i | ||||
\(393\) | 1.07912e15 | 0.292898 | ||||||||
\(394\) | −3.23772e15 | + | 1.24306e15i | −0.865491 | + | 0.332289i | ||||
\(395\) | 4.85140e14 | 0.127728 | ||||||||
\(396\) | −2.04587e14 | + | 1.84254e14i | −0.0530525 | + | 0.0477799i | ||||
\(397\) | 6.25341e14i | 0.159725i | 0.996806 | + | 0.0798627i | \(0.0254482\pi\) | ||||
−0.996806 | + | 0.0798627i | \(0.974552\pi\) | |||||||
\(398\) | −1.43761e15 | + | 5.51943e14i | −0.361695 | + | 0.138866i | ||||
\(399\) | 9.84610e14i | 0.244021i | ||||||||
\(400\) | 2.14077e14 | − | 2.04139e15i | 0.0522648 | − | 0.498385i | ||||
\(401\) | 1.75229e15 | 0.421445 | 0.210722 | − | 0.977546i | \(-0.432418\pi\) | ||||
0.210722 | + | 0.977546i | \(0.432418\pi\) | |||||||
\(402\) | −5.43889e14 | − | 1.41663e15i | −0.128871 | − | 0.335661i | ||||
\(403\) | −1.97992e15 | −0.462187 | ||||||||
\(404\) | 2.41123e15 | + | 2.67731e15i | 0.554562 | + | 0.615759i | ||||
\(405\) | 1.88260e15i | 0.426607i | ||||||||
\(406\) | 5.40685e14 | + | 1.40829e15i | 0.120723 | + | 0.314438i | ||||
\(407\) | 7.33952e14i | 0.161474i | ||||||||
\(408\) | −1.87047e15 | − | 9.52639e14i | −0.405499 | − | 0.206522i | ||||
\(409\) | −2.66611e15 | −0.569559 | −0.284779 | − | 0.958593i | \(-0.591920\pi\) | ||||
−0.284779 | + | 0.958593i | \(0.591920\pi\) | |||||||
\(410\) | −5.06658e13 | + | 1.94521e13i | −0.0106662 | + | 0.00409510i | ||||
\(411\) | 1.56304e15 | 0.324280 | ||||||||
\(412\) | −3.98965e15 | − | 4.42991e15i | −0.815739 | − | 0.905758i | ||||
\(413\) | 2.11096e15i | 0.425382i | ||||||||
\(414\) | 5.67511e15 | − | 2.17885e15i | 1.12713 | − | 0.432738i | ||||
\(415\) | 3.60114e15i | 0.704938i | ||||||||
\(416\) | 1.18596e15 | + | 4.42092e15i | 0.228829 | + | 0.853007i | ||||
\(417\) | 1.18535e15 | 0.225440 | ||||||||
\(418\) | −2.08031e14 | − | 5.41845e14i | −0.0390005 | − | 0.101582i | ||||
\(419\) | 4.88044e15 | 0.901934 | 0.450967 | − | 0.892541i | \(-0.351079\pi\) | ||||
0.450967 | + | 0.892541i | \(0.351079\pi\) | |||||||
\(420\) | 5.35353e14 | − | 4.82147e14i | 0.0975314 | − | 0.0878383i | ||||
\(421\) | − | 7.51831e15i | − | 1.35029i | −0.737685 | − | 0.675146i | \(-0.764081\pi\) | ||
0.737685 | − | 0.675146i | \(-0.235919\pi\) | |||||||
\(422\) | −8.47829e14 | − | 2.20829e15i | −0.150118 | − | 0.391003i | ||||
\(423\) | − | 9.46017e15i | − | 1.65142i | ||||||
\(424\) | −6.92295e14 | + | 1.35929e15i | −0.119151 | + | 0.233947i | ||||
\(425\) | 3.61239e15 | 0.613001 | ||||||||
\(426\) | 3.21960e15 | − | 1.23610e15i | 0.538697 | − | 0.206822i | ||||
\(427\) | −2.25404e15 | −0.371873 | ||||||||
\(428\) | 1.08099e15 | − | 9.73553e14i | 0.175856 | − | 0.158379i | ||||
\(429\) | − | 1.69707e14i | − | 0.0272243i | ||||||
\(430\) | 4.72065e15 | − | 1.81240e15i | 0.746778 | − | 0.286711i | ||||
\(431\) | − | 4.80009e15i | − | 0.748834i | −0.927260 | − | 0.374417i | \(-0.877843\pi\) | ||
0.927260 | − | 0.374417i | \(-0.122157\pi\) | |||||||
\(432\) | −4.69472e14 | + | 4.47677e15i | −0.0722283 | + | 0.688752i | ||||
\(433\) | −4.81144e15 | −0.730042 | −0.365021 | − | 0.930999i | \(-0.618938\pi\) | ||||
−0.365021 | + | 0.930999i | \(0.618938\pi\) | |||||||
\(434\) | −6.26149e14 | − | 1.63089e15i | −0.0936999 | − | 0.244054i | ||||
\(435\) | 1.20035e15 | 0.177162 | ||||||||
\(436\) | 6.26180e15 | + | 6.95280e15i | 0.911549 | + | 1.01214i | ||||
\(437\) | 1.28149e16i | 1.84004i | ||||||||
\(438\) | −1.18549e15 | − | 3.08777e15i | −0.167901 | − | 0.437321i | ||||
\(439\) | − | 7.01559e15i | − | 0.980115i | −0.871690 | − | 0.490057i | \(-0.836976\pi\) | ||
0.871690 | − | 0.490057i | \(-0.163024\pi\) | |||||||
\(440\) | −1.92743e14 | + | 3.78443e14i | −0.0265621 | + | 0.0521536i | ||||
\(441\) | −4.75633e15 | −0.646607 | ||||||||
\(442\) | −7.52038e15 | + | 2.88731e15i | −1.00857 | + | 0.387221i | ||||
\(443\) | −4.37539e15 | −0.578888 | −0.289444 | − | 0.957195i | \(-0.593470\pi\) | ||||
−0.289444 | + | 0.957195i | \(0.593470\pi\) | |||||||
\(444\) | 3.71662e15 | + | 4.12676e15i | 0.485122 | + | 0.538656i | ||||
\(445\) | 2.00224e15i | 0.257843i | ||||||||
\(446\) | 8.21853e15 | − | 3.15535e15i | 1.04420 | − | 0.400902i | ||||
\(447\) | 2.06967e15i | 0.259451i | ||||||||
\(448\) | −3.26651e15 | + | 2.37501e15i | −0.404033 | + | 0.293763i | ||||
\(449\) | −4.57989e15 | −0.558956 | −0.279478 | − | 0.960152i | \(-0.590161\pi\) | ||||
−0.279478 | + | 0.960152i | \(0.590161\pi\) | |||||||
\(450\) | −1.28506e15 | − | 3.34710e15i | −0.154756 | − | 0.403083i | ||||
\(451\) | −1.12797e13 | −0.00134041 | ||||||||
\(452\) | −5.95023e15 | + | 5.35887e15i | −0.697756 | + | 0.628409i | ||||
\(453\) | − | 2.87064e15i | − | 0.332192i | ||||||
\(454\) | 5.39749e15 | + | 1.40585e16i | 0.616391 | + | 1.60547i | ||||
\(455\) | − | 2.76490e15i | − | 0.311610i | ||||||
\(456\) | −3.91351e15 | − | 1.99317e15i | −0.435288 | − | 0.221695i | ||||
\(457\) | −3.73761e15 | −0.410295 | −0.205148 | − | 0.978731i | \(-0.565767\pi\) | ||||
−0.205148 | + | 0.978731i | \(0.565767\pi\) | |||||||
\(458\) | −2.45147e15 | + | 9.41194e14i | −0.265603 | + | 0.101973i | ||||
\(459\) | −7.92200e15 | −0.847147 | ||||||||
\(460\) | 6.96774e15 | − | 6.27525e15i | 0.735436 | − | 0.662345i | ||||
\(461\) | 5.99757e15i | 0.624841i | 0.949944 | + | 0.312421i | \(0.101140\pi\) | ||||
−0.949944 | + | 0.312421i | \(0.898860\pi\) | |||||||
\(462\) | 1.39790e14 | − | 5.36699e13i | 0.0143756 | − | 0.00551923i | ||||
\(463\) | − | 4.85727e15i | − | 0.493067i | −0.969134 | − | 0.246534i | \(-0.920708\pi\) | ||
0.969134 | − | 0.246534i | \(-0.0792916\pi\) | |||||||
\(464\) | −6.69201e15 | − | 7.01781e14i | −0.670577 | − | 0.0703224i | ||||
\(465\) | −1.39008e15 | −0.137506 | ||||||||
\(466\) | −4.05041e14 | − | 1.05498e15i | −0.0395534 | − | 0.103022i | ||||
\(467\) | 1.02535e16 | 0.988486 | 0.494243 | − | 0.869324i | \(-0.335445\pi\) | ||||
0.494243 | + | 0.869324i | \(0.335445\pi\) | |||||||
\(468\) | 5.35053e15 | + | 5.94097e15i | 0.509239 | + | 0.565435i | ||||
\(469\) | − | 5.13827e15i | − | 0.482814i | ||||||
\(470\) | −5.23029e15 | − | 1.36230e16i | −0.485220 | − | 1.26382i | ||||
\(471\) | − | 3.21650e15i | − | 0.294617i | ||||||
\(472\) | −8.39037e15 | − | 4.27326e15i | −0.758804 | − | 0.386463i | ||||
\(473\) | 1.05095e15 | 0.0938461 | ||||||||
\(474\) | 7.12272e14 | − | 2.73463e14i | 0.0628024 | − | 0.0241118i | ||||
\(475\) | 7.55807e15 | 0.658035 | ||||||||
\(476\) | −4.75663e15 | − | 5.28153e15i | −0.408938 | − | 0.454065i | ||||
\(477\) | 2.66453e15i | 0.226209i | ||||||||
\(478\) | 5.30669e15 | − | 2.03740e15i | 0.444894 | − | 0.170808i | ||||
\(479\) | 1.01603e16i | 0.841190i | 0.907248 | + | 0.420595i | \(0.138179\pi\) | ||||
−0.907248 | + | 0.420595i | \(0.861821\pi\) | |||||||
\(480\) | 8.32652e14 | + | 3.10388e15i | 0.0680794 | + | 0.253780i | ||||
\(481\) | 2.13132e16 | 1.72099 | ||||||||
\(482\) | −2.67126e15 | − | 6.95765e15i | −0.213026 | − | 0.554856i | ||||
\(483\) | −3.30612e15 | −0.260397 | ||||||||
\(484\) | 9.48654e15 | − | 8.54372e15i | 0.737965 | − | 0.664622i | ||||
\(485\) | 5.19624e14i | 0.0399244i | ||||||||
\(486\) | 4.33196e15 | + | 1.12832e16i | 0.328750 | + | 0.856275i | ||||
\(487\) | 2.34412e16i | 1.75714i | 0.477617 | + | 0.878568i | \(0.341501\pi\) | ||||
−0.477617 | + | 0.878568i | \(0.658499\pi\) | |||||||
\(488\) | 4.56291e15 | − | 8.95908e15i | 0.337849 | − | 0.663353i | ||||
\(489\) | −1.22780e15 | −0.0897997 | ||||||||
\(490\) | −6.84929e15 | + | 2.62965e15i | −0.494845 | + | 0.189986i | ||||
\(491\) | 2.04090e16 | 1.45657 | 0.728286 | − | 0.685273i | \(-0.240317\pi\) | ||||
0.728286 | + | 0.685273i | \(0.240317\pi\) | |||||||
\(492\) | −6.34216e13 | + | 5.71185e13i | −0.00447143 | + | 0.00402704i | ||||
\(493\) | − | 1.18420e16i | − | 0.824794i | ||||||
\(494\) | −1.57346e16 | + | 6.04100e15i | −1.08266 | + | 0.415668i | ||||
\(495\) | 7.41836e14i | 0.0504286i | ||||||||
\(496\) | 7.74979e15 | + | 8.12708e14i | 0.520475 | + | 0.0545814i | ||||
\(497\) | 1.16778e16 | 0.774860 | ||||||||
\(498\) | 2.02989e15 | + | 5.28711e15i | 0.133075 | + | 0.346611i | ||||
\(499\) | −2.95094e16 | −1.91143 | −0.955714 | − | 0.294298i | \(-0.904914\pi\) | ||||
−0.955714 | + | 0.294298i | \(0.904914\pi\) | |||||||
\(500\) | −1.10867e16 | − | 1.23101e16i | −0.709547 | − | 0.787846i | ||||
\(501\) | 1.53002e15i | 0.0967546i | ||||||||
\(502\) | −4.86719e15 | − | 1.26772e16i | −0.304127 | − | 0.792141i | ||||
\(503\) | 1.23276e16i | 0.761148i | 0.924750 | + | 0.380574i | \(0.124274\pi\) | ||||
−0.924750 | + | 0.380574i | \(0.875726\pi\) | |||||||
\(504\) | −3.20156e15 | + | 6.28614e15i | −0.195334 | + | 0.383531i | ||||
\(505\) | 9.70801e15 | 0.585304 | ||||||||
\(506\) | 1.81940e15 | − | 6.98526e14i | 0.108399 | − | 0.0416178i | ||||
\(507\) | 1.39012e15 | 0.0818471 | ||||||||
\(508\) | 3.41983e15 | + | 3.79721e15i | 0.198986 | + | 0.220944i | ||||
\(509\) | − | 2.08634e16i | − | 1.19972i | −0.800106 | − | 0.599859i | \(-0.795223\pi\) | ||
0.800106 | − | 0.599859i | \(-0.204777\pi\) | |||||||
\(510\) | −5.27997e15 | + | 2.02714e15i | −0.300062 | + | 0.115203i | ||||
\(511\) | − | 1.11997e16i | − | 0.629041i | ||||||
\(512\) | −2.82741e15 | − | 1.77911e16i | −0.156953 | − | 0.987606i | ||||
\(513\) | −1.65749e16 | −0.909383 | ||||||||
\(514\) | 8.98474e15 | + | 2.34020e16i | 0.487222 | + | 1.26903i | ||||
\(515\) | −1.60630e16 | −0.860960 | ||||||||
\(516\) | 5.90915e15 | − | 5.32187e15i | 0.313059 | − | 0.281946i | ||||
\(517\) | − | 3.03287e15i | − | 0.158822i | ||||||
\(518\) | 6.74028e15 | + | 1.75560e16i | 0.348899 | + | 0.908755i | ||||
\(519\) | − | 9.45669e14i | − | 0.0483877i | ||||||
\(520\) | 1.09896e16 | + | 5.59705e15i | 0.555855 | + | 0.283100i | ||||
\(521\) | −1.72320e16 | −0.861607 | −0.430803 | − | 0.902446i | \(-0.641770\pi\) | ||||
−0.430803 | + | 0.902446i | \(0.641770\pi\) | |||||||
\(522\) | −1.09724e16 | + | 4.21264e15i | −0.542348 | + | 0.208224i | ||||
\(523\) | 1.15450e16 | 0.564137 | 0.282068 | − | 0.959394i | \(-0.408980\pi\) | ||||
0.282068 | + | 0.959394i | \(0.408980\pi\) | |||||||
\(524\) | −1.21111e16 | + | 1.09074e16i | −0.585054 | + | 0.526908i | ||||
\(525\) | 1.94991e15i | 0.0931232i | ||||||||
\(526\) | 8.36830e15 | − | 3.21285e15i | 0.395114 | − | 0.151697i | ||||
\(527\) | 1.37139e16i | 0.640171i | ||||||||
\(528\) | −6.96607e13 | + | 6.64267e14i | −0.00321502 | + | 0.0306577i | ||||
\(529\) | −2.11153e16 | −0.963524 | ||||||||
\(530\) | 1.47315e15 | + | 3.83702e15i | 0.0664649 | + | 0.173117i | ||||
\(531\) | −1.64471e16 | −0.733706 | ||||||||
\(532\) | −9.95211e15 | − | 1.10503e16i | −0.438981 | − | 0.487423i | ||||
\(533\) | 3.27549e14i | 0.0142861i | ||||||||
\(534\) | 1.12862e15 | + | 2.93965e15i | 0.0486744 | + | 0.126779i | ||||
\(535\) | − | 3.91969e15i | − | 0.167159i | ||||||
\(536\) | 2.04230e16 | + | 1.04015e16i | 0.861252 | + | 0.438640i | ||||
\(537\) | 9.55697e15 | 0.398542 | ||||||||
\(538\) | 2.53393e16 | − | 9.72854e15i | 1.04496 | − | 0.401194i | ||||
\(539\) | −1.52485e15 | −0.0621862 | ||||||||
\(540\) | 8.11645e15 | + | 9.01212e15i | 0.327344 | + | 0.363467i | ||||
\(541\) | − | 2.22285e15i | − | 0.0886598i | −0.999017 | − | 0.0443299i | \(-0.985885\pi\) | ||
0.999017 | − | 0.0443299i | \(-0.0141153\pi\) | |||||||
\(542\) | −3.45497e16 | + | 1.32647e16i | −1.36285 | + | 0.523242i | ||||
\(543\) | − | 1.23869e16i | − | 0.483239i | ||||||
\(544\) | 3.06214e16 | − | 8.21454e15i | 1.18149 | − | 0.316949i | ||||
\(545\) | 2.52110e16 | 0.962081 | ||||||||
\(546\) | −1.55852e15 | − | 4.05937e15i | −0.0588241 | − | 0.153215i | ||||
\(547\) | 1.84557e16 | 0.688981 | 0.344490 | − | 0.938790i | \(-0.388052\pi\) | ||||
0.344490 | + | 0.938790i | \(0.388052\pi\) | |||||||
\(548\) | −1.75422e16 | + | 1.57987e16i | −0.647739 | + | 0.583363i | ||||
\(549\) | − | 1.75619e16i | − | 0.641412i | ||||||
\(550\) | −4.11981e14 | − | 1.07306e15i | −0.0148834 | − | 0.0387657i | ||||
\(551\) | − | 2.47767e16i | − | 0.885387i | ||||||
\(552\) | 6.69266e15 | − | 1.31408e16i | 0.236572 | − | 0.464500i | ||||
\(553\) | 2.58348e15 | 0.0903348 | ||||||||
\(554\) | 4.85278e16 | − | 1.86313e16i | 1.67854 | − | 0.644444i | ||||
\(555\) | 1.49638e16 | 0.512015 | ||||||||
\(556\) | −1.33033e16 | + | 1.19811e16i | −0.450308 | + | 0.405554i | ||||
\(557\) | 2.98593e16i | 0.999881i | 0.866060 | + | 0.499940i | \(0.166645\pi\) | ||||
−0.866060 | + | 0.499940i | \(0.833355\pi\) | |||||||
\(558\) | 1.27067e16 | − | 4.87851e15i | 0.420948 | − | 0.161615i | ||||
\(559\) | − | 3.05186e16i | − | 1.00021i | ||||||
\(560\) | −1.13492e15 | + | 1.08223e16i | −0.0367992 | + | 0.350908i | ||||
\(561\) | −1.17547e15 | −0.0377082 | ||||||||
\(562\) | −1.25760e16 | − | 3.27559e16i | −0.399139 | − | 1.03961i | ||||
\(563\) | −2.83523e16 | −0.890305 | −0.445152 | − | 0.895455i | \(-0.646850\pi\) | ||||
−0.445152 | + | 0.895455i | \(0.646850\pi\) | |||||||
\(564\) | −1.53580e16 | − | 1.70528e16i | −0.477156 | − | 0.529811i | ||||
\(565\) | 2.15757e16i | 0.663246i | ||||||||
\(566\) | −1.89364e16 | − | 4.93223e16i | −0.575967 | − | 1.50018i | ||||
\(567\) | 1.00253e16i | 0.301716i | ||||||||
\(568\) | −2.36397e16 | + | 4.64156e16i | −0.703966 | + | 1.38221i | ||||
\(569\) | −1.48709e16 | −0.438190 | −0.219095 | − | 0.975704i | \(-0.570310\pi\) | ||||
−0.219095 | + | 0.975704i | \(0.570310\pi\) | |||||||
\(570\) | −1.10471e16 | + | 4.24132e15i | −0.322106 | + | 0.123666i | ||||
\(571\) | 3.35787e16 | 0.968830 | 0.484415 | − | 0.874838i | \(-0.339033\pi\) | ||||
0.484415 | + | 0.874838i | \(0.339033\pi\) | |||||||
\(572\) | 1.71535e15 | + | 1.90464e15i | 0.0489752 | + | 0.0543797i | ||||
\(573\) | 2.49720e16i | 0.705546i | ||||||||
\(574\) | −2.69807e14 | + | 1.03587e14i | −0.00754365 | + | 0.00289624i | ||||
\(575\) | 2.53785e16i | 0.702196i | ||||||||
\(576\) | −1.85044e16 | − | 2.54504e16i | −0.506687 | − | 0.696882i | ||||
\(577\) | −1.51145e16 | −0.409581 | −0.204790 | − | 0.978806i | \(-0.565651\pi\) | ||||
−0.204790 | + | 0.978806i | \(0.565651\pi\) | |||||||
\(578\) | 6.63404e15 | + | 1.72793e16i | 0.177914 | + | 0.463402i | ||||
\(579\) | −2.47969e15 | −0.0658153 | ||||||||
\(580\) | −1.34716e16 | + | 1.21327e16i | −0.353876 | + | 0.318706i | ||||
\(581\) | 1.91769e16i | 0.498564i | ||||||||
\(582\) | 2.92901e14 | + | 7.62900e14i | 0.00753673 | + | 0.0196304i | ||||
\(583\) | 8.54232e14i | 0.0217553i | ||||||||
\(584\) | 4.45150e16 | + | 2.26717e16i | 1.12209 | + | 0.571488i | ||||
\(585\) | 2.15421e16 | 0.537469 | ||||||||
\(586\) | −8.57761e15 | + | 3.29321e15i | −0.211827 | + | 0.0813268i | ||||
\(587\) | 4.64906e16 | 1.13641 | 0.568207 | − | 0.822886i | \(-0.307637\pi\) | ||||
0.568207 | + | 0.822886i | \(0.307637\pi\) | |||||||
\(588\) | −8.57370e15 | + | 7.72161e15i | −0.207446 | + | 0.186829i | ||||
\(589\) | 2.86930e16i | 0.687201i | ||||||||
\(590\) | −2.36844e16 | + | 9.09318e15i | −0.561501 | + | 0.215578i | ||||
\(591\) | 1.46958e16i | 0.344881i | ||||||||
\(592\) | −8.34239e16 | − | 8.74853e15i | −1.93803 | − | 0.203238i | ||||
\(593\) | −9.55760e15 | −0.219796 | −0.109898 | − | 0.993943i | \(-0.535052\pi\) | ||||
−0.109898 | + | 0.993943i | \(0.535052\pi\) | |||||||
\(594\) | 9.03478e14 | + | 2.35323e15i | 0.0205683 | + | 0.0535730i | ||||
\(595\) | −1.91510e16 | −0.431608 | ||||||||
\(596\) | −2.09195e16 | − | 2.32280e16i | −0.466739 | − | 0.518244i | ||||
\(597\) | 6.52521e15i | 0.144128i | ||||||||
\(598\) | −2.02844e16 | − | 5.28336e16i | −0.443564 | − | 1.15532i | ||||
\(599\) | − | 3.48480e16i | − | 0.754427i | −0.926126 | − | 0.377214i | \(-0.876882\pi\) | ||
0.926126 | − | 0.377214i | \(-0.123118\pi\) | |||||||
\(600\) | −7.75025e15 | − | 3.94724e15i | −0.166115 | − | 0.0846031i | ||||
\(601\) | −2.82379e16 | −0.599218 | −0.299609 | − | 0.954062i | \(-0.596856\pi\) | ||||
−0.299609 | + | 0.954062i | \(0.596856\pi\) | |||||||
\(602\) | 2.51386e16 | − | 9.65148e15i | 0.528155 | − | 0.202775i | ||||
\(603\) | 4.00338e16 | 0.832765 | ||||||||
\(604\) | 2.90155e16 | + | 3.22174e16i | 0.597596 | + | 0.663542i | ||||
\(605\) | − | 3.43984e16i | − | 0.701466i | ||||||
\(606\) | 1.42531e16 | − | 5.47220e15i | 0.287788 | − | 0.110491i | ||||
\(607\) | − | 4.04099e16i | − | 0.807897i | −0.914782 | − | 0.403948i | \(-0.867638\pi\) | ||
0.914782 | − | 0.403948i | \(-0.132362\pi\) | |||||||
\(608\) | 6.40679e16 | − | 1.71870e16i | 1.26829 | − | 0.340234i | ||||
\(609\) | 6.39213e15 | 0.125297 | ||||||||
\(610\) | −9.70953e15 | − | 2.52898e16i | −0.188460 | − | 0.490869i | ||||
\(611\) | −8.80714e16 | −1.69273 | ||||||||
\(612\) | 4.11500e16 | − | 3.70603e16i | 0.783179 | − | 0.705343i | ||||
\(613\) | 4.16832e16i | 0.785595i | 0.919625 | + | 0.392797i | \(0.128493\pi\) | ||||
−0.919625 | + | 0.392797i | \(0.871507\pi\) | |||||||
\(614\) | 3.52283e16 | + | 9.17568e16i | 0.657478 | + | 1.71249i | ||||
\(615\) | 2.29969e14i | 0.00425028i | ||||||||
\(616\) | −1.02640e15 | + | 2.01530e15i | −0.0187859 | + | 0.0368854i | ||||
\(617\) | 7.05658e16 | 1.27904 | 0.639519 | − | 0.768775i | \(-0.279134\pi\) | ||||
0.639519 | + | 0.768775i | \(0.279134\pi\) | |||||||
\(618\) | −2.35834e16 | + | 9.05438e15i | −0.423326 | + | 0.162528i | ||||
\(619\) | 7.32448e14 | 0.0130207 | 0.00651033 | − | 0.999979i | \(-0.497928\pi\) | ||||
0.00651033 | + | 0.999979i | \(0.497928\pi\) | |||||||
\(620\) | 1.56010e16 | − | 1.40505e16i | 0.274664 | − | 0.247366i | ||||
\(621\) | − | 5.56552e16i | − | 0.970411i | ||||||
\(622\) | 4.34028e16 | − | 1.66637e16i | 0.749507 | − | 0.287759i | ||||
\(623\) | 1.06624e16i | 0.182359i | ||||||||
\(624\) | 1.92896e16 | + | 2.02287e15i | 0.326750 | + | 0.0342658i | ||||
\(625\) | −1.47678e16 | −0.247763 | ||||||||
\(626\) | 2.01447e16 | + | 5.24697e16i | 0.334746 | + | 0.871892i | ||||
\(627\) | −2.45940e15 | −0.0404784 | ||||||||
\(628\) | 3.25113e16 | + | 3.60990e16i | 0.530001 | + | 0.588487i | ||||
\(629\) | − | 1.47625e17i | − | 2.38373i | ||||||
\(630\) | 6.81269e15 | + | 1.77446e16i | 0.108962 | + | 0.283806i | ||||
\(631\) | 1.39747e16i | 0.221394i | 0.993854 | + | 0.110697i | \(0.0353083\pi\) | ||||
−0.993854 | + | 0.110697i | \(0.964692\pi\) | |||||||
\(632\) | −5.22981e15 | + | 1.02685e16i | −0.0820698 | + | 0.161141i | ||||
\(633\) | −1.00233e16 | −0.155807 | ||||||||
\(634\) | −6.19634e16 | + | 2.37897e16i | −0.954113 | + | 0.366314i | ||||
\(635\) | 1.37688e16 | 0.210017 | ||||||||
\(636\) | 4.32570e15 | + | 4.80305e15i | 0.0653603 | + | 0.0725729i | ||||
\(637\) | 4.42800e16i | 0.662782i | ||||||||
\(638\) | −3.51768e15 | + | 1.35055e15i | −0.0521593 | + | 0.0200256i | ||||
\(639\) | 9.09853e16i | 1.33649i | ||||||||
\(640\) | −4.07179e16 | − | 2.64189e16i | −0.592523 | − | 0.384445i | ||||
\(641\) | −7.70870e16 | −1.11130 | −0.555652 | − | 0.831415i | \(-0.687531\pi\) | ||||
−0.555652 | + | 0.831415i | \(0.687531\pi\) | |||||||
\(642\) | −2.20945e15 | − | 5.75480e15i | −0.0315554 | − | 0.0821903i | ||||
\(643\) | −5.78604e16 | −0.818683 | −0.409341 | − | 0.912381i | \(-0.634242\pi\) | ||||
−0.409341 | + | 0.912381i | \(0.634242\pi\) | |||||||
\(644\) | 3.71048e16 | − | 3.34172e16i | 0.520134 | − | 0.468441i | ||||
\(645\) | − | 2.14267e16i | − | 0.297576i | ||||||
\(646\) | 4.18428e16 | + | 1.08985e17i | 0.575739 | + | 1.49959i | ||||
\(647\) | 2.38112e15i | 0.0324605i | 0.999868 | + | 0.0162303i | \(0.00516648\pi\) | ||||
−0.999868 | + | 0.0162303i | \(0.994834\pi\) | |||||||
\(648\) | −3.98473e16 | − | 2.02944e16i | −0.538206 | − | 0.274111i | ||||
\(649\) | −5.27283e15 | −0.0705628 | ||||||||
\(650\) | −3.11605e16 | + | 1.19635e16i | −0.413166 | + | 0.158627i | ||||
\(651\) | −7.40250e15 | −0.0972506 | ||||||||
\(652\) | 1.37797e16 | − | 1.24102e16i | 0.179372 | − | 0.161545i | ||||
\(653\) | − | 9.86680e16i | − | 1.27262i | −0.771435 | − | 0.636308i | \(-0.780461\pi\) | ||
0.771435 | − | 0.636308i | \(-0.219539\pi\) | |||||||
\(654\) | 3.70143e16 | − | 1.42109e16i | 0.473046 | − | 0.181617i | ||||
\(655\) | 4.39152e16i | 0.556118i | ||||||||
\(656\) | 1.34451e14 | − | 1.28209e15i | 0.00168710 | − | 0.0160878i | ||||
\(657\) | 8.72598e16 | 1.08498 | ||||||||
\(658\) | −2.78525e16 | − | 7.25456e16i | −0.343170 | − | 0.893832i | ||||
\(659\) | −6.67559e16 | −0.815037 | −0.407518 | − | 0.913197i | \(-0.633606\pi\) | ||||
−0.407518 | + | 0.913197i | \(0.633606\pi\) | |||||||
\(660\) | 1.20433e15 | + | 1.33723e15i | 0.0145707 | + | 0.0161786i | ||||
\(661\) | 9.72864e16i | 1.16639i | 0.812333 | + | 0.583194i | \(0.198197\pi\) | ||||
−0.812333 | + | 0.583194i | \(0.801803\pi\) | |||||||
\(662\) | −3.32427e16 | − | 8.65851e16i | −0.394956 | − | 1.02872i | ||||
\(663\) | 3.41345e16i | 0.401895i | ||||||||
\(664\) | −7.62219e16 | − | 3.88202e16i | −0.889348 | − | 0.452949i | ||||
\(665\) | −4.00689e16 | −0.463316 | ||||||||
\(666\) | −1.36784e17 | + | 5.25155e16i | −1.56743 | + | 0.601786i | ||||
\(667\) | 8.31950e16 | 0.944805 | ||||||||
\(668\) | −1.54650e16 | − | 1.71716e16i | −0.174057 | − | 0.193264i | ||||
\(669\) | − | 3.73034e16i | − | 0.416094i | ||||||
\(670\) | 5.76501e16 | − | 2.21337e16i | 0.637311 | − | 0.244684i | ||||
\(671\) | − | 5.63023e15i | − | 0.0616866i | ||||||
\(672\) | 4.43406e15 | + | 1.65289e16i | 0.0481489 | + | 0.179485i | ||||
\(673\) | 6.78970e16 | 0.730735 | 0.365368 | − | 0.930863i | \(-0.380943\pi\) | ||||
0.365368 | + | 0.930863i | \(0.380943\pi\) | |||||||
\(674\) | 3.47066e16 | + | 9.03980e16i | 0.370214 | + | 0.964272i | ||||
\(675\) | −3.28247e16 | −0.347039 | ||||||||
\(676\) | −1.56014e16 | + | 1.40508e16i | −0.163487 | + | 0.147239i | ||||
\(677\) | 3.44804e16i | 0.358130i | 0.983837 | + | 0.179065i | \(0.0573073\pi\) | ||||
−0.983837 | + | 0.179065i | \(0.942693\pi\) | |||||||
\(678\) | 1.21618e16 | + | 3.16770e16i | 0.125204 | + | 0.326111i | ||||
\(679\) | 2.76712e15i | 0.0282364i | ||||||||
\(680\) | 3.87678e16 | − | 7.61190e16i | 0.392119 | − | 0.769910i | ||||
\(681\) | 6.38105e16 | 0.639749 | ||||||||
\(682\) | 4.07370e15 | − | 1.56402e15i | 0.0404839 | − | 0.0155430i | ||||
\(683\) | 5.65913e16 | 0.557475 | 0.278738 | − | 0.960367i | \(-0.410084\pi\) | ||||
0.278738 | + | 0.960367i | \(0.410084\pi\) | |||||||
\(684\) | 8.60965e16 | − | 7.75398e16i | 0.840715 | − | 0.757161i | ||||
\(685\) | 6.36084e16i | 0.615702i | ||||||||
\(686\) | −8.50763e16 | + | 3.26634e16i | −0.816326 | + | 0.313413i | ||||
\(687\) | 1.11270e16i | 0.105837i | ||||||||
\(688\) | −1.25271e16 | + | 1.19455e17i | −0.118119 | + | 1.12636i | ||||
\(689\) | 2.48060e16 | 0.231868 | ||||||||
\(690\) | −1.42415e16 | − | 3.70939e16i | −0.131966 | − | 0.343722i | ||||
\(691\) | 1.15097e17 | 1.05730 | 0.528648 | − | 0.848841i | \(-0.322699\pi\) | ||||
0.528648 | + | 0.848841i | \(0.322699\pi\) | |||||||
\(692\) | 9.55851e15 | + | 1.06133e16i | 0.0870469 | + | 0.0966528i | ||||
\(693\) | 3.95045e15i | 0.0356654i | ||||||||
\(694\) | −6.12509e16 | − | 1.59536e17i | −0.548221 | − | 1.42791i | ||||
\(695\) | 4.82380e16i | 0.428036i | ||||||||
\(696\) | −1.29397e16 | + | 2.54067e16i | −0.113833 | + | 0.223507i | ||||
\(697\) | 2.26876e15 | 0.0197875 | ||||||||
\(698\) | 1.55510e17 | − | 5.97050e16i | 1.34470 | − | 0.516271i | ||||
\(699\) | −4.78850e15 | −0.0410522 | ||||||||
\(700\) | −1.97090e16 | − | 2.18839e16i | −0.167524 | − | 0.186010i | ||||
\(701\) | 1.29467e17i | 1.09107i | 0.838089 | + | 0.545533i | \(0.183673\pi\) | ||||
−0.838089 | + | 0.545533i | \(0.816327\pi\) | |||||||
\(702\) | 6.83353e16 | − | 2.62360e16i | 0.570982 | − | 0.219218i | ||||
\(703\) | − | 3.08870e17i | − | 2.55885i | ||||||
\(704\) | −5.93239e15 | − | 8.15923e15i | −0.0487297 | − | 0.0670214i | ||||
\(705\) | −6.18339e16 | −0.503607 | ||||||||
\(706\) | −6.03384e16 | − | 1.57160e17i | −0.487266 | − | 1.26915i | ||||
\(707\) | 5.16974e16 | 0.413954 | ||||||||
\(708\) | −2.96473e16 | + | 2.67008e16i | −0.235389 | + | 0.211995i | ||||
\(709\) | 1.13514e16i | 0.0893657i | 0.999001 | + | 0.0446829i | \(0.0142277\pi\) | ||||
−0.999001 | + | 0.0446829i | \(0.985772\pi\) | |||||||
\(710\) | 5.03035e16 | + | 1.31022e17i | 0.392688 | + | 1.02281i | ||||
\(711\) | 2.01287e16i | 0.155811i | ||||||||
\(712\) | −4.23796e16 | − | 2.15841e16i | −0.325295 | − | 0.165674i | ||||
\(713\) | −9.63452e16 | −0.733319 | ||||||||
\(714\) | −2.81171e16 | + | 1.07950e16i | −0.212217 | + | 0.0814768i | ||||
\(715\) | 6.90628e15 | 0.0516901 | ||||||||
\(716\) | −1.07259e17 | + | 9.65987e16i | −0.796075 | + | 0.716957i | ||||
\(717\) | − | 2.40867e16i | − | 0.177281i | ||||||
\(718\) | 8.00357e16 | − | 3.07282e16i | 0.584167 | − | 0.224280i | ||||
\(719\) | 3.34950e16i | 0.242441i | 0.992626 | + | 0.121221i | \(0.0386809\pi\) | ||||
−0.992626 | + | 0.121221i | \(0.961319\pi\) | |||||||
\(720\) | −8.43201e16 | − | 8.84251e15i | −0.605252 | − | 0.0634718i | ||||
\(721\) | −8.55392e16 | −0.608911 | ||||||||
\(722\) | 3.67747e16 | + | 9.57848e16i | 0.259613 | + | 0.676197i | ||||
\(723\) | −3.15803e16 | −0.221099 | ||||||||
\(724\) | 1.25202e17 | + | 1.39019e17i | 0.869322 | + | 0.965254i | ||||
\(725\) | − | 4.90673e16i | − | 0.337881i | ||||||
\(726\) | −1.93897e16 | − | 5.05031e16i | −0.132419 | − | 0.344904i | ||||
\(727\) | − | 9.28323e16i | − | 0.628771i | −0.949295 | − | 0.314386i | \(-0.898202\pi\) | ||
0.949295 | − | 0.314386i | \(-0.101798\pi\) | |||||||
\(728\) | 5.85221e16 | + | 2.98056e16i | 0.393126 | + | 0.200221i | ||||
\(729\) | −3.94419e16 | −0.262780 | ||||||||
\(730\) | 1.25657e17 | − | 4.82437e16i | 0.830330 | − | 0.318789i | ||||
\(731\) | −2.11386e17 | −1.38539 | ||||||||
\(732\) | −2.85106e16 | − | 3.16569e16i | −0.185328 | − | 0.205779i | ||||
\(733\) | 1.02514e17i | 0.660939i | 0.943817 | + | 0.330469i | \(0.107207\pi\) | ||||
−0.943817 | + | 0.330469i | \(0.892793\pi\) | |||||||
\(734\) | −1.75464e17 | + | 6.73662e16i | −1.12205 | + | 0.430790i | ||||
\(735\) | 3.10885e16i | 0.197186i | ||||||||
\(736\) | 5.77103e16 | + | 2.15127e17i | 0.363067 | + | 1.35341i | ||||
\(737\) | 1.28346e16 | 0.0800897 | ||||||||
\(738\) | −8.07078e14 | − | 2.10214e15i | −0.00499548 | − | 0.0130114i | ||||
\(739\) | 3.10260e16 | 0.190484 | 0.0952421 | − | 0.995454i | \(-0.469637\pi\) | ||||
0.0952421 | + | 0.995454i | \(0.469637\pi\) | |||||||
\(740\) | −1.67939e17 | + | 1.51249e17i | −1.02273 | + | 0.921088i | ||||
\(741\) | 7.14183e16i | 0.431420i | ||||||||
\(742\) | 7.84488e15 | + | 2.04330e16i | 0.0470070 | + | 0.122436i | ||||
\(743\) | − | 6.07618e16i | − | 0.361158i | −0.983560 | − | 0.180579i | \(-0.942203\pi\) | ||
0.983560 | − | 0.180579i | \(-0.0577972\pi\) | |||||||
\(744\) | 1.49851e16 | − | 2.94225e16i | 0.0883529 | − | 0.173477i | ||||
\(745\) | −8.42254e16 | −0.492613 | ||||||||
\(746\) | 1.55754e17 | − | 5.97989e16i | 0.903664 | − | 0.346945i | ||||
\(747\) | −1.49413e17 | −0.859932 | ||||||||
\(748\) | 1.31924e16 | − | 1.18813e16i | 0.0753208 | − | 0.0678351i | ||||
\(749\) | − | 2.08733e16i | − | 0.118222i | ||||||
\(750\) | −6.55348e16 | + | 2.51608e16i | −0.368217 | + | 0.141370i | ||||
\(751\) | − | 1.70978e17i | − | 0.953018i | −0.879170 | − | 0.476509i | \(-0.841902\pi\) | ||
0.879170 | − | 0.476509i | \(-0.158098\pi\) | |||||||
\(752\) | 3.44728e17 | + | 3.61511e16i | 1.90621 | + | 0.199901i | ||||
\(753\) | −5.75412e16 | −0.315652 | ||||||||
\(754\) | 3.92184e16 | + | 1.02150e17i | 0.213433 | + | 0.555915i | ||||
\(755\) | 1.16821e17 | 0.630724 | ||||||||
\(756\) | 4.32220e16 | + | 4.79916e16i | 0.231512 | + | 0.257060i | ||||
\(757\) | − | 1.08916e17i | − | 0.578785i | −0.957211 | − | 0.289393i | \(-0.906547\pi\) | ||
0.957211 | − | 0.289393i | \(-0.0934533\pi\) | |||||||
\(758\) | −9.96810e16 | − | 2.59633e17i | −0.525529 | − | 1.36881i | ||||
\(759\) | − | 8.25816e15i | − | 0.0431949i | ||||||
\(760\) | 8.11124e16 | − | 1.59261e17i | 0.420926 | − | 0.826471i | ||||
\(761\) | 1.35235e16 | 0.0696275 | 0.0348138 | − | 0.999394i | \(-0.488916\pi\) | ||||
0.0348138 | + | 0.999394i | \(0.488916\pi\) | |||||||
\(762\) | 2.02151e16 | − | 7.76119e15i | 0.103263 | − | 0.0396459i | ||||
\(763\) | 1.34255e17 | 0.680428 | ||||||||
\(764\) | −2.52409e17 | − | 2.80262e17i | −1.26924 | − | 1.40930i | ||||
\(765\) | − | 1.49211e17i | − | 0.744444i | ||||||
\(766\) | 1.33695e17 | − | 5.13297e16i | 0.661824 | − | 0.254095i | ||||
\(767\) | 1.53117e17i | 0.752060i | ||||||||
\(768\) | −7.46729e16 | − | 1.58358e16i | −0.363912 | − | 0.0771744i | ||||
\(769\) | 3.05550e17 | 1.47749 | 0.738745 | − | 0.673986i | \(-0.235419\pi\) | ||||
0.738745 | + | 0.673986i | \(0.235419\pi\) | |||||||
\(770\) | 2.18411e15 | + | 5.68880e15i | 0.0104792 | + | 0.0272946i | ||||
\(771\) | 1.06220e17 | 0.505685 | ||||||||
\(772\) | 2.78298e16 | − | 2.50639e16i | 0.131464 | − | 0.118398i | ||||
\(773\) | 9.17640e16i | 0.430126i | 0.976600 | + | 0.215063i | \(0.0689956\pi\) | ||||
−0.976600 | + | 0.215063i | \(0.931004\pi\) | |||||||
\(774\) | 7.51975e16 | + | 1.95862e17i | 0.349750 | + | 0.910971i | ||||
\(775\) | 5.68231e16i | 0.262250i | ||||||||
\(776\) | −1.09984e16 | − | 5.60154e15i | −0.0503685 | − | 0.0256529i | ||||
\(777\) | 7.96855e16 | 0.362120 | ||||||||
\(778\) | −5.95918e16 | + | 2.28791e16i | −0.268726 | + | 0.103172i | ||||
\(779\) | 4.74684e15 | 0.0212412 | ||||||||
\(780\) | 3.88316e16 | − | 3.49724e16i | 0.172432 | − | 0.155295i | ||||
\(781\) | 2.91693e16i | 0.128535i | ||||||||
\(782\) | −3.65950e17 | + | 1.40500e17i | −1.60023 | + | 0.614376i | ||||
\(783\) | 1.07605e17i | 0.466941i | ||||||||
\(784\) | 1.81758e16 | − | 1.73320e17i | 0.0782704 | − | 0.746368i | ||||
\(785\) | 1.30896e17 | 0.559382 | ||||||||
\(786\) | 2.47541e16 | + | 6.44753e16i | 0.104981 | + | 0.273438i | ||||
\(787\) | −1.56040e16 | −0.0656733 | −0.0328366 | − | 0.999461i | \(-0.510454\pi\) | ||||
−0.0328366 | + | 0.999461i | \(0.510454\pi\) | |||||||
\(788\) | −1.48541e17 | − | 1.64932e17i | −0.620423 | − | 0.688888i | ||||
\(789\) | − | 3.79832e16i | − | 0.157445i | ||||||
\(790\) | 1.11286e16 | + | 2.89861e16i | 0.0457804 | + | 0.119241i | ||||
\(791\) | 1.14896e17i | 0.469078i | ||||||||
\(792\) | −1.57018e16 | − | 7.99699e15i | −0.0636206 | − | 0.0324023i | ||||
\(793\) | −1.63496e17 | −0.657458 | ||||||||
\(794\) | −3.73628e16 | + | 1.43447e16i | −0.149113 | + | 0.0572492i | ||||
\(795\) | 1.74160e16 | 0.0689836 | ||||||||
\(796\) | −6.59547e16 | − | 7.32330e16i | −0.259279 | − | 0.287891i | ||||
\(797\) | − | 4.85611e16i | − | 0.189469i | −0.995503 | − | 0.0947347i | \(-0.969800\pi\) | ||
0.995503 | − | 0.0947347i | \(-0.0302003\pi\) | |||||||
\(798\) | −5.88283e16 | + | 2.25860e16i | −0.227808 | + | 0.0874625i | ||||
\(799\) | 6.10024e17i | 2.34458i | ||||||||
\(800\) | 1.26879e17 | − | 3.40368e16i | 0.484005 | − | 0.129840i | ||||
\(801\) | −8.30738e16 | −0.314535 | ||||||||
\(802\) | 4.01959e16 | + | 1.04696e17i | 0.151055 | + | 0.393444i | ||||
\(803\) | 2.79749e16 | 0.104346 | ||||||||
\(804\) | 7.21644e16 | − | 6.49924e16i | 0.267170 | − | 0.240617i | ||||
\(805\) | − | 1.34543e17i | − | 0.494409i | ||||||
\(806\) | −4.54175e16 | − | 1.18296e17i | −0.165658 | − | 0.431479i | ||||
\(807\) | − | 1.15013e17i | − | 0.416397i | ||||||
\(808\) | −1.04652e17 | + | 2.05480e17i | −0.376080 | + | 0.738418i | ||||
\(809\) | 4.40284e17 | 1.57051 | 0.785257 | − | 0.619170i | \(-0.212531\pi\) | ||||
0.785257 | + | 0.619170i | \(0.212531\pi\) | |||||||
\(810\) | −1.12481e17 | + | 4.31850e16i | −0.398263 | + | 0.152905i | ||||
\(811\) | −3.50936e17 | −1.23340 | −0.616698 | − | 0.787200i | \(-0.711530\pi\) | ||||
−0.616698 | + | 0.787200i | \(0.711530\pi\) | |||||||
\(812\) | −7.17393e16 | + | 6.46095e16i | −0.250277 | + | 0.225403i | ||||
\(813\) | 1.56819e17i | 0.543070i | ||||||||
\(814\) | −4.38520e16 | + | 1.68362e16i | −0.150745 | + | 0.0578757i | ||||
\(815\) | − | 4.99656e16i | − | 0.170500i | ||||||
\(816\) | 1.40114e16 | − | 1.33609e17i | 0.0474613 | − | 0.452579i | ||||
\(817\) | −4.42274e17 | −1.48717 | ||||||||
\(818\) | −6.11580e16 | − | 1.59294e17i | −0.204143 | − | 0.531717i | ||||
\(819\) | 1.14717e17 | 0.380123 | ||||||||
\(820\) | −2.32445e15 | − | 2.58095e15i | −0.00764604 | − | 0.00848979i | ||||
\(821\) | − | 1.05121e17i | − | 0.343267i | −0.985161 | − | 0.171633i | \(-0.945096\pi\) | ||
0.985161 | − | 0.171633i | \(-0.0549044\pi\) | |||||||
\(822\) | 3.58547e16 | + | 9.33885e16i | 0.116229 | + | 0.302735i | ||||
\(823\) | − | 6.15349e16i | − | 0.198026i | −0.995086 | − | 0.0990130i | \(-0.968431\pi\) | ||
0.995086 | − | 0.0990130i | \(-0.0315686\pi\) | |||||||
\(824\) | 1.73159e17 | − | 3.39991e17i | 0.553200 | − | 1.08619i | ||||
\(825\) | −4.87055e15 | −0.0154474 | ||||||||
\(826\) | −1.26125e17 | + | 4.84233e16i | −0.397119 | + | 0.152466i | ||||
\(827\) | −3.00278e17 | −0.938622 | −0.469311 | − | 0.883033i | \(-0.655498\pi\) | ||||
−0.469311 | + | 0.883033i | \(0.655498\pi\) | |||||||
\(828\) | 2.60363e17 | + | 2.89095e17i | 0.807974 | + | 0.897135i | ||||
\(829\) | − | 5.15625e17i | − | 1.58857i | −0.607544 | − | 0.794286i | \(-0.707845\pi\) | ||
0.607544 | − | 0.794286i | \(-0.292155\pi\) | |||||||
\(830\) | −2.15160e17 | + | 8.26066e16i | −0.658102 | + | 0.252666i | ||||
\(831\) | − | 2.20265e17i | − | 0.668865i | ||||||
\(832\) | −2.36935e17 | + | 1.72270e17i | −0.714315 | + | 0.519362i | ||||
\(833\) | 3.06704e17 | 0.918014 | ||||||||
\(834\) | 2.71908e16 | + | 7.08220e16i | 0.0808026 | + | 0.210461i | ||||
\(835\) | −6.22646e16 | −0.183706 | ||||||||
\(836\) | 2.76020e16 | − | 2.48588e16i | 0.0808543 | − | 0.0728186i | ||||
\(837\) | − | 1.24614e17i | − | 0.362420i | ||||||
\(838\) | 1.11953e17 | + | 2.91596e17i | 0.323273 | + | 0.842009i | ||||
\(839\) | 4.16410e17i | 1.19385i | 0.802297 | + | 0.596925i | \(0.203611\pi\) | ||||
−0.802297 | + | 0.596925i | \(0.796389\pi\) | |||||||
\(840\) | 4.10877e16 | + | 2.09262e16i | 0.116960 | + | 0.0595682i | ||||
\(841\) | 1.92964e17 | 0.545381 | ||||||||
\(842\) | 4.49202e17 | − | 1.72463e17i | 1.26058 | − | 0.483975i | ||||
\(843\) | −1.48677e17 | −0.414264 | ||||||||
\(844\) | 1.12492e17 | − | 1.01312e17i | 0.311219 | − | 0.280289i | ||||
\(845\) | 5.65710e16i | 0.155401i | ||||||||
\(846\) | 5.65224e17 | − | 2.17007e17i | 1.54170 | − | 0.591905i | ||||
\(847\) | − | 1.83180e17i | − | 0.496109i | ||||||
\(848\) | −9.70954e16 | − | 1.01822e16i | −0.261110 | − | 0.0273822i | ||||
\(849\) | −2.23871e17 | −0.597793 | ||||||||
\(850\) | 8.28648e16 | + | 2.15832e17i | 0.219713 | + | 0.572273i | ||||
\(851\) | 1.03712e18 | 2.73057 | ||||||||
\(852\) | 1.47709e17 | + | 1.64009e17i | 0.386162 | + | 0.428776i | ||||
\(853\) | 5.70676e17i | 1.48148i | 0.671792 | + | 0.740740i | \(0.265525\pi\) | ||||
−0.671792 | + | 0.740740i | \(0.734475\pi\) | |||||||
\(854\) | −5.17055e16 | − | 1.34674e17i | −0.133287 | − | 0.347165i | ||||
\(855\) | − | 3.12188e17i | − | 0.799135i | ||||||
\(856\) | 8.29645e16 | + | 4.22542e16i | 0.210887 | + | 0.107406i | ||||
\(857\) | −6.68524e17 | −1.68746 | −0.843728 | − | 0.536772i | \(-0.819644\pi\) | ||||
−0.843728 | + | 0.536772i | \(0.819644\pi\) | |||||||
\(858\) | 1.01396e16 | − | 3.89293e15i | 0.0254155 | − | 0.00975781i | ||||
\(859\) | −5.56346e17 | −1.38480 | −0.692399 | − | 0.721515i | \(-0.743446\pi\) | ||||
−0.692399 | + | 0.721515i | \(0.743446\pi\) | |||||||
\(860\) | 2.16574e17 | + | 2.40474e17i | 0.535324 | + | 0.594398i | ||||
\(861\) | 1.22464e15i | 0.00300599i | ||||||||
\(862\) | 2.86795e17 | − | 1.10109e17i | 0.699081 | − | 0.268399i | ||||
\(863\) | − | 4.97736e17i | − | 1.20485i | −0.798174 | − | 0.602427i | \(-0.794201\pi\) | ||
0.798174 | − | 0.602427i | \(-0.205799\pi\) | |||||||
\(864\) | −2.78247e17 | + | 7.46429e16i | −0.668879 | + | 0.179435i | ||||
\(865\) | 3.84842e16 | 0.0918725 | ||||||||
\(866\) | −1.10370e17 | − | 2.87473e17i | −0.261663 | − | 0.681537i | ||||
\(867\) | 7.84295e16 | 0.184657 | ||||||||
\(868\) | 8.30788e16 | − | 7.48220e16i | 0.194255 | − | 0.174949i | ||||
\(869\) | 6.45313e15i | 0.0149848i | ||||||||
\(870\) | 2.75348e16 | + | 7.17181e16i | 0.0634989 | + | 0.165392i | ||||
\(871\) | − | 3.72703e17i | − | 0.853598i | ||||||
\(872\) | −2.71775e17 | + | 5.33619e17i | −0.618174 | + | 1.21376i | ||||
\(873\) | −2.15594e16 | −0.0487025 | ||||||||
\(874\) | −7.65663e17 | + | 2.93962e17i | −1.71779 | + | 0.659511i | ||||
\(875\) | −2.37701e17 | −0.529643 | ||||||||
\(876\) | 1.57293e17 | − | 1.41661e17i | 0.348086 | − | 0.313491i | ||||
\(877\) | − | 1.21940e17i | − | 0.268008i | −0.990981 | − | 0.134004i | \(-0.957216\pi\) | ||
0.990981 | − | 0.134004i | \(-0.0427836\pi\) | |||||||
\(878\) | 4.19166e17 | − | 1.60931e17i | 0.914996 | − | 0.351295i | ||||
\(879\) | 3.89332e16i | 0.0844087i | ||||||||
\(880\) | −2.70325e16 | − | 2.83485e15i | −0.0582090 | − | 0.00610428i | ||||
\(881\) | −1.61506e16 | −0.0345410 | −0.0172705 | − | 0.999851i | \(-0.505498\pi\) | ||||
−0.0172705 | + | 0.999851i | \(0.505498\pi\) | |||||||
\(882\) | −1.09106e17 | − | 2.84180e17i | −0.231758 | − | 0.603646i | ||||
\(883\) | 3.48909e17 | 0.736118 | 0.368059 | − | 0.929802i | \(-0.380022\pi\) | ||||
0.368059 | + | 0.929802i | \(0.380022\pi\) | |||||||
\(884\) | −3.45020e17 | − | 3.83094e17i | −0.722988 | − | 0.802771i | ||||
\(885\) | 1.07502e17i | 0.223747i | ||||||||
\(886\) | −1.00367e17 | − | 2.61420e17i | −0.207486 | − | 0.540426i | ||||
\(887\) | − | 1.79060e17i | − | 0.367668i | −0.982957 | − | 0.183834i | \(-0.941149\pi\) | ||
0.982957 | − | 0.183834i | \(-0.0588509\pi\) | |||||||
\(888\) | −1.61309e17 | + | 3.16724e17i | −0.328989 | + | 0.645957i | ||||
\(889\) | 7.33221e16 | 0.148533 | ||||||||
\(890\) | −1.19629e17 | + | 4.59295e16i | −0.240712 | + | 0.0924169i | ||||
\(891\) | −2.50415e16 | −0.0500489 | ||||||||
\(892\) | 3.77050e17 | + | 4.18659e17i | 0.748532 | + | 0.831134i | ||||
\(893\) | 1.27633e18i | 2.51683i | ||||||||
\(894\) | −1.23658e17 | + | 4.74761e16i | −0.242213 | + | 0.0929930i | ||||
\(895\) | 3.88923e17i | 0.756702i | ||||||||
\(896\) | −2.16832e17 | − | 1.40687e17i | −0.419060 | − | 0.271897i | ||||
\(897\) | −2.39808e17 | −0.460372 | ||||||||
\(898\) | −1.05058e17 | − | 2.73639e17i | −0.200342 | − | 0.521818i | ||||
\(899\) | 1.86276e17 | 0.352857 | ||||||||
\(900\) | 1.70504e17 | − | 1.53559e17i | 0.320834 | − | 0.288948i | ||||
\(901\) | − | 1.71818e17i | − | 0.321159i | ||||||
\(902\) | −2.58744e14 | − | 6.73934e14i | −0.000480432 | − | 0.00125135i | ||||
\(903\) | − | 1.14102e17i | − | 0.210459i | ||||||
\(904\) | −4.56673e17 | − | 2.32586e17i | −0.836749 | − | 0.426160i | ||||
\(905\) | 5.04085e17 | 0.917514 | ||||||||
\(906\) | 1.71514e17 | − | 6.58497e16i | 0.310121 | − | 0.119065i | ||||
\(907\) | −2.91685e17 | −0.523927 | −0.261963 | − | 0.965078i | \(-0.584370\pi\) | ||||
−0.261963 | + | 0.965078i | \(0.584370\pi\) | |||||||
\(908\) | −7.16151e17 | + | 6.44976e17i | −1.27788 | + | 1.15088i | ||||
\(909\) | 4.02789e17i | 0.713994i | ||||||||
\(910\) | 1.65197e17 | − | 6.34241e16i | 0.290906 | − | 0.111688i | ||||
\(911\) | 3.15264e15i | 0.00551523i | 0.999996 | + | 0.00275761i | \(0.000877777\pi\) | ||||
−0.999996 | + | 0.00275761i | \(0.999122\pi\) | |||||||
\(912\) | 2.93154e16 | − | 2.79545e17i | 0.0509480 | − | 0.485828i | ||||
\(913\) | −4.79008e16 | −0.0827024 | ||||||||
\(914\) | −8.57371e16 | − | 2.23314e17i | −0.147059 | − | 0.383035i | ||||
\(915\) | −1.14789e17 | −0.195602 | ||||||||
\(916\) | −1.12469e17 | − | 1.24880e17i | −0.190396 | − | 0.211407i | ||||
\(917\) | 2.33858e17i | 0.393312i | ||||||||
\(918\) | −1.81723e17 | − | 4.73322e17i | −0.303637 | − | 0.790863i | ||||
\(919\) | 9.27348e17i | 1.53939i | 0.638409 | + | 0.769697i | \(0.279593\pi\) | ||||
−0.638409 | + | 0.769697i | \(0.720407\pi\) | |||||||
\(920\) | 5.34766e17 | + | 2.72359e17i | 0.881935 | + | 0.449174i | ||||
\(921\) | 4.16478e17 | 0.682393 | ||||||||
\(922\) | −3.58342e17 | + | 1.37578e17i | −0.583327 | + | 0.223957i | ||||
\(923\) | 8.47046e17 | 1.36993 | ||||||||
\(924\) | 6.41332e15 | + | 7.12104e15i | 0.0103051 | + | 0.0114423i | ||||
\(925\) | − | 6.11682e17i | − | 0.976507i | ||||||
\(926\) | 2.90211e17 | − | 1.11421e17i | 0.460308 | − | 0.176726i | ||||
\(927\) | − | 6.66461e17i | − | 1.05026i | ||||||
\(928\) | −1.11578e17 | − | 4.15931e17i | −0.174700 | − | 0.651229i | ||||
\(929\) | −9.18415e16 | −0.142871 | −0.0714356 | − | 0.997445i | \(-0.522758\pi\) | ||||
−0.0714356 | + | 0.997445i | \(0.522758\pi\) | |||||||
\(930\) | −3.18871e16 | − | 8.30542e16i | −0.0492853 | − | 0.128370i | ||||
\(931\) | 6.41705e17 | 0.985456 | ||||||||
\(932\) | 5.37417e16 | − | 4.84006e16i | 0.0820005 | − | 0.0738509i | ||||
\(933\) | − | 1.97003e17i | − | 0.298663i | ||||||
\(934\) | 2.35205e17 | + | 6.12624e17i | 0.354296 | + | 0.922811i | ||||
\(935\) | − | 4.78361e16i | − | 0.0715956i | ||||||
\(936\) | −2.32224e17 | + | 4.55963e17i | −0.345344 | + | 0.678070i | ||||
\(937\) | 1.41341e17 | 0.208848 | 0.104424 | − | 0.994533i | \(-0.466700\pi\) | ||||
0.104424 | + | 0.994533i | \(0.466700\pi\) | |||||||
\(938\) | 3.07000e17 | − | 1.17867e17i | 0.450736 | − | 0.173051i | ||||
\(939\) | 2.38157e17 | 0.347431 | ||||||||
\(940\) | 6.93967e17 | − | 6.24997e17i | 1.00594 | − | 0.905964i | ||||
\(941\) | − | 7.67731e17i | − | 1.10579i | −0.833252 | − | 0.552893i | \(-0.813524\pi\) | ||
0.833252 | − | 0.552893i | \(-0.186476\pi\) | |||||||
\(942\) | 1.92179e17 | − | 7.37833e16i | 0.275042 | − | 0.105597i | ||||
\(943\) | 1.59389e16i | 0.0226667i | ||||||||
\(944\) | 6.28509e16 | − | 5.99331e17i | 0.0888136 | − | 0.846905i | ||||
\(945\) | 1.74019e17 | 0.244346 | ||||||||
\(946\) | 2.41078e16 | + | 6.27921e16i | 0.0336366 | + | 0.0876110i | ||||
\(947\) | −9.75819e17 | −1.35291 | −0.676456 | − | 0.736483i | \(-0.736485\pi\) | ||||
−0.676456 | + | 0.736483i | \(0.736485\pi\) | |||||||
\(948\) | 3.26777e16 | + | 3.62837e16i | 0.0450195 | + | 0.0499876i | ||||
\(949\) | − | 8.12362e17i | − | 1.11212i | ||||||
\(950\) | 1.73375e17 | + | 4.51578e17i | 0.235855 | + | 0.614315i | ||||
\(951\) | 2.81248e17i | 0.380195i | ||||||||
\(952\) | 2.06448e17 | − | 4.05352e17i | 0.277324 | − | 0.544515i | ||||
\(953\) | −1.09905e18 | −1.46710 | −0.733552 | − | 0.679633i | \(-0.762139\pi\) | ||||
−0.733552 | + | 0.679633i | \(0.762139\pi\) | |||||||
\(954\) | −1.59200e17 | + | 6.11217e16i | −0.211180 | + | 0.0810785i | ||||
\(955\) | −1.01624e18 | −1.33960 | ||||||||
\(956\) | 2.43461e17 | + | 2.70327e17i | 0.318920 | + | 0.354113i | ||||
\(957\) | 1.59665e16i | 0.0207844i | ||||||||
\(958\) | −6.07057e17 | + | 2.33068e17i | −0.785301 | + | 0.301501i | ||||
\(959\) | 3.38729e17i | 0.435453i | ||||||||
\(960\) | −1.66350e17 | + | 1.20949e17i | −0.212517 | + | 0.154517i | ||||
\(961\) | 5.71943e17 | 0.726127 | ||||||||
\(962\) | 4.88904e17 | + | 1.27342e18i | 0.616841 | + | 1.60665i | ||||
\(963\) | 1.62630e17 | 0.203912 | ||||||||
\(964\) | 3.54428e17 | − | 3.19204e17i | 0.441638 | − | 0.397746i | ||||
\(965\) | − | 1.00912e17i | − | 0.124962i | ||||||
\(966\) | −7.58392e16 | − | 1.97533e17i | −0.0933321 | − | 0.243096i | ||||
\(967\) | 4.86043e17i | 0.594451i | 0.954807 | + | 0.297226i | \(0.0960613\pi\) | ||||
−0.954807 | + | 0.297226i | \(0.903939\pi\) | |||||||
\(968\) | 7.28080e17 | + | 3.70815e17i | 0.884967 | + | 0.450718i | ||||
\(969\) | 4.94677e17 | 0.597556 | ||||||||
\(970\) | −3.10464e16 | + | 1.19197e16i | −0.0372718 | + | 0.0143098i | ||||
\(971\) | −9.53000e17 | −1.13704 | −0.568522 | − | 0.822668i | \(-0.692485\pi\) | ||||
−0.568522 | + | 0.822668i | \(0.692485\pi\) | |||||||
\(972\) | −5.74773e17 | + | 5.17650e17i | −0.681552 | + | 0.613816i | ||||
\(973\) | 2.56879e17i | 0.302727i | ||||||||
\(974\) | −1.40056e18 | + | 5.37718e17i | −1.64039 | + | 0.629797i | ||||
\(975\) | 1.41436e17i | 0.164638i | ||||||||
\(976\) | 6.39954e17 | + | 6.71110e16i | 0.740372 | + | 0.0776416i | ||||
\(977\) | −3.17247e17 | −0.364780 | −0.182390 | − | 0.983226i | \(-0.558383\pi\) | ||||
−0.182390 | + | 0.983226i | \(0.558383\pi\) | |||||||
\(978\) | −2.81646e16 | − | 7.33584e16i | −0.0321862 | − | 0.0838334i | ||||
\(979\) | −2.66330e16 | −0.0302498 | ||||||||
\(980\) | −3.14232e17 | − | 3.48908e17i | −0.354727 | − | 0.393872i | ||||
\(981\) | 1.04602e18i | 1.17361i | ||||||||
\(982\) | 4.68162e17 | + | 1.21939e18i | 0.522068 | + | 1.35980i | ||||
\(983\) | − | 1.23563e18i | − | 1.36952i | −0.728770 | − | 0.684759i | \(-0.759907\pi\) | ||
0.728770 | − | 0.684759i | \(-0.240093\pi\) | |||||||
\(984\) | −4.86753e15 | − | 2.47906e15i | −0.00536214 | − | 0.00273097i | ||||
\(985\) | −5.98049e17 | −0.654816 | ||||||||
\(986\) | 7.07536e17 | − | 2.71645e17i | 0.769994 | − | 0.295624i | ||||
\(987\) | −3.29280e17 | −0.356174 | ||||||||
\(988\) | −7.21873e17 | − | 8.01533e17i | −0.776102 | − | 0.861747i | ||||
\(989\) | − | 1.48507e18i | − | 1.58697i | ||||||
\(990\) | −4.43231e16 | + | 1.70170e16i | −0.0470781 | + | 0.0180747i | ||||
\(991\) | 5.61949e17i | 0.593274i | 0.954990 | + | 0.296637i | \(0.0958651\pi\) | ||||
−0.954990 | + | 0.296637i | \(0.904135\pi\) | |||||||
\(992\) | 1.29215e17 | + | 4.81675e17i | 0.135595 | + | 0.505457i | ||||
\(993\) | −3.93004e17 | −0.409922 | ||||||||
\(994\) | 2.67878e17 | + | 6.97724e17i | 0.277727 | + | 0.723378i | ||||
\(995\) | −2.65545e17 | −0.273652 | ||||||||
\(996\) | −2.69330e17 | + | 2.42562e17i | −0.275885 | + | 0.248466i | ||||
\(997\) | − | 1.39731e18i | − | 1.42272i | −0.702826 | − | 0.711361i | \(-0.748079\pi\) | ||
0.702826 | − | 0.711361i | \(-0.251921\pi\) | |||||||
\(998\) | −6.76918e17 | − | 1.76312e18i | −0.685098 | − | 1.78443i | ||||
\(999\) | 1.34142e18i | 1.34950i |
(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 | 8.13.d.b.3.8 | yes | 10 | |
3.2 | odd | 2 | 72.13.b.b.19.3 | 10 | |||
4.3 | odd | 2 | 32.13.d.b.15.4 | 10 | |||
8.3 | odd | 2 | inner | 8.13.d.b.3.7 | ✓ | 10 | |
8.5 | even | 2 | 32.13.d.b.15.3 | 10 | |||
24.11 | even | 2 | 72.13.b.b.19.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.13.d.b.3.7 | ✓ | 10 | 8.3 | odd | 2 | inner | |
8.13.d.b.3.8 | yes | 10 | 1.1 | even | 1 | trivial | |
32.13.d.b.15.3 | 10 | 8.5 | even | 2 | |||
32.13.d.b.15.4 | 10 | 4.3 | odd | 2 | |||
72.13.b.b.19.3 | 10 | 3.2 | odd | 2 | |||
72.13.b.b.19.4 | 10 | 24.11 | even | 2 |