Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,13,Mod(13,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.13");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.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: | \(12.7959134419\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 154710x^{6} + 8245426887x^{4} + 174724076278260x^{2} + 1264170035276291934 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{2}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.7 | ||
Root | \(-149.422i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.13 |
Dual form | 14.13.b.a.13.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 45.2548 | 0.707107 | ||||||||
\(3\) | 321.888i | 0.441548i | 0.975325 | + | 0.220774i | \(0.0708583\pi\) | ||||
−0.975325 | + | 0.220774i | \(0.929142\pi\) | |||||||
\(4\) | 2048.00 | 0.500000 | ||||||||
\(5\) | − | 17149.5i | − | 1.09757i | −0.835964 | − | 0.548785i | \(-0.815091\pi\) | ||
0.835964 | − | 0.548785i | \(-0.184909\pi\) | |||||||
\(6\) | 14567.0i | 0.312221i | ||||||||
\(7\) | −71756.5 | − | 93232.5i | −0.609920 | − | 0.792463i | ||||
\(8\) | 92681.9 | 0.353553 | ||||||||
\(9\) | 427829. | 0.805036 | ||||||||
\(10\) | − | 776099.i | − | 0.776099i | ||||||
\(11\) | 1.62995e6 | 0.920062 | 0.460031 | − | 0.887903i | \(-0.347838\pi\) | ||||
0.460031 | + | 0.887903i | \(0.347838\pi\) | |||||||
\(12\) | 659227.i | 0.220774i | ||||||||
\(13\) | − | 4.55860e6i | − | 0.944434i | −0.881482 | − | 0.472217i | \(-0.843454\pi\) | ||
0.881482 | − | 0.472217i | \(-0.156546\pi\) | |||||||
\(14\) | −3.24733e6 | − | 4.21922e6i | −0.431279 | − | 0.560356i | ||||
\(15\) | 5.52023e6 | 0.484630 | ||||||||
\(16\) | 4.19430e6 | 0.250000 | ||||||||
\(17\) | 1.51452e7i | 0.627455i | 0.949513 | + | 0.313727i | \(0.101578\pi\) | ||||
−0.949513 | + | 0.313727i | \(0.898422\pi\) | |||||||
\(18\) | 1.93613e7 | 0.569246 | ||||||||
\(19\) | − | 8.19846e7i | − | 1.74265i | −0.490704 | − | 0.871326i | \(-0.663261\pi\) | ||
0.490704 | − | 0.871326i | \(-0.336739\pi\) | |||||||
\(20\) | − | 3.51222e7i | − | 0.548785i | ||||||
\(21\) | 3.00104e7 | − | 2.30976e7i | 0.349910 | − | 0.269309i | ||||
\(22\) | 7.37629e7 | 0.650582 | ||||||||
\(23\) | 8.57392e7 | 0.579179 | 0.289589 | − | 0.957151i | \(-0.406481\pi\) | ||||
0.289589 | + | 0.957151i | \(0.406481\pi\) | |||||||
\(24\) | 2.98332e7i | 0.156111i | ||||||||
\(25\) | −4.99658e7 | −0.204660 | ||||||||
\(26\) | − | 2.06299e8i | − | 0.667816i | ||||||
\(27\) | 3.08778e8i | 0.797009i | ||||||||
\(28\) | −1.46957e8 | − | 1.90940e8i | −0.304960 | − | 0.396231i | ||||
\(29\) | −9.60080e8 | −1.61406 | −0.807029 | − | 0.590512i | \(-0.798926\pi\) | ||||
−0.807029 | + | 0.590512i | \(0.798926\pi\) | |||||||
\(30\) | 2.49817e8 | 0.342685 | ||||||||
\(31\) | 1.52654e9i | 1.72003i | 0.510267 | + | 0.860016i | \(0.329547\pi\) | ||||
−0.510267 | + | 0.860016i | \(0.670453\pi\) | |||||||
\(32\) | 1.89813e8 | 0.176777 | ||||||||
\(33\) | 5.24661e8i | 0.406251i | ||||||||
\(34\) | 6.85395e8i | 0.443677i | ||||||||
\(35\) | −1.59889e9 | + | 1.23059e9i | −0.869783 | + | 0.669430i | ||||
\(36\) | 8.76194e8 | 0.402518 | ||||||||
\(37\) | −1.82147e9 | −0.709926 | −0.354963 | − | 0.934880i | \(-0.615506\pi\) | ||||
−0.354963 | + | 0.934880i | \(0.615506\pi\) | |||||||
\(38\) | − | 3.71020e9i | − | 1.23224i | ||||||
\(39\) | 1.46736e9 | 0.417013 | ||||||||
\(40\) | − | 1.58945e9i | − | 0.388050i | ||||||
\(41\) | 6.08045e8i | 0.128007i | 0.997950 | + | 0.0640033i | \(0.0203868\pi\) | ||||
−0.997950 | + | 0.0640033i | \(0.979613\pi\) | |||||||
\(42\) | 1.35812e9 | − | 1.04528e9i | 0.247424 | − | 0.190430i | ||||
\(43\) | 3.59485e9 | 0.568683 | 0.284341 | − | 0.958723i | \(-0.408225\pi\) | ||||
0.284341 | + | 0.958723i | \(0.408225\pi\) | |||||||
\(44\) | 3.33813e9 | 0.460031 | ||||||||
\(45\) | − | 7.33706e9i | − | 0.883583i | ||||||
\(46\) | 3.88011e9 | 0.409541 | ||||||||
\(47\) | − | 6.65675e9i | − | 0.617554i | −0.951134 | − | 0.308777i | \(-0.900080\pi\) | ||
0.951134 | − | 0.308777i | \(-0.0999197\pi\) | |||||||
\(48\) | 1.35010e9i | 0.110387i | ||||||||
\(49\) | −3.54330e9 | + | 1.33801e10i | −0.255995 | + | 0.966678i | ||||
\(50\) | −2.26119e9 | −0.144716 | ||||||||
\(51\) | −4.87507e9 | −0.277051 | ||||||||
\(52\) | − | 9.33602e9i | − | 0.472217i | ||||||
\(53\) | 1.15079e10 | 0.519208 | 0.259604 | − | 0.965715i | \(-0.416408\pi\) | ||||
0.259604 | + | 0.965715i | \(0.416408\pi\) | |||||||
\(54\) | 1.39737e10i | 0.563571i | ||||||||
\(55\) | − | 2.79528e10i | − | 1.00983i | ||||||
\(56\) | −6.65053e9 | − | 8.64096e9i | −0.215639 | − | 0.280178i | ||||
\(57\) | 2.63899e10 | 0.769464 | ||||||||
\(58\) | −4.34482e10 | −1.14131 | ||||||||
\(59\) | 5.91993e10i | 1.40347i | 0.712436 | + | 0.701737i | \(0.247592\pi\) | ||||
−0.712436 | + | 0.701737i | \(0.752408\pi\) | |||||||
\(60\) | 1.13054e10 | 0.242315 | ||||||||
\(61\) | − | 2.23715e10i | − | 0.434226i | −0.976146 | − | 0.217113i | \(-0.930336\pi\) | ||
0.976146 | − | 0.217113i | \(-0.0696641\pi\) | |||||||
\(62\) | 6.90831e10i | 1.21625i | ||||||||
\(63\) | −3.06995e10 | − | 3.98875e10i | −0.491007 | − | 0.637961i | ||||
\(64\) | 8.58993e9 | 0.125000 | ||||||||
\(65\) | −7.81779e10 | −1.03658 | ||||||||
\(66\) | 2.37434e10i | 0.287263i | ||||||||
\(67\) | 5.96155e10 | 0.659037 | 0.329519 | − | 0.944149i | \(-0.393114\pi\) | ||||
0.329519 | + | 0.944149i | \(0.393114\pi\) | |||||||
\(68\) | 3.10174e10i | 0.313727i | ||||||||
\(69\) | 2.75985e10i | 0.255735i | ||||||||
\(70\) | −7.23576e10 | + | 5.56902e10i | −0.615030 | + | 0.473359i | ||||
\(71\) | 6.47737e10 | 0.505648 | 0.252824 | − | 0.967512i | \(-0.418641\pi\) | ||||
0.252824 | + | 0.967512i | \(0.418641\pi\) | |||||||
\(72\) | 3.96520e10 | 0.284623 | ||||||||
\(73\) | − | 1.47593e10i | − | 0.0975278i | −0.998810 | − | 0.0487639i | \(-0.984472\pi\) | ||
0.998810 | − | 0.0487639i | \(-0.0155282\pi\) | |||||||
\(74\) | −8.24305e10 | −0.501993 | ||||||||
\(75\) | − | 1.60834e10i | − | 0.0903671i | ||||||
\(76\) | − | 1.67904e11i | − | 0.871326i | ||||||
\(77\) | −1.16959e11 | − | 1.51964e11i | −0.561164 | − | 0.729115i | ||||
\(78\) | 6.64052e10 | 0.294873 | ||||||||
\(79\) | 2.34078e11 | 0.962936 | 0.481468 | − | 0.876464i | \(-0.340104\pi\) | ||||
0.481468 | + | 0.876464i | \(0.340104\pi\) | |||||||
\(80\) | − | 7.19303e10i | − | 0.274392i | ||||||
\(81\) | 1.27974e11 | 0.453118 | ||||||||
\(82\) | 2.75170e10i | 0.0905143i | ||||||||
\(83\) | − | 1.33751e11i | − | 0.409098i | −0.978856 | − | 0.204549i | \(-0.934427\pi\) | ||
0.978856 | − | 0.204549i | \(-0.0655727\pi\) | |||||||
\(84\) | 6.14614e10 | − | 4.73038e10i | 0.174955 | − | 0.134654i | ||||
\(85\) | 2.59734e11 | 0.688675 | ||||||||
\(86\) | 1.62684e11 | 0.402119 | ||||||||
\(87\) | − | 3.09038e11i | − | 0.712684i | ||||||
\(88\) | 1.51066e11 | 0.325291 | ||||||||
\(89\) | 3.77427e11i | 0.759440i | 0.925101 | + | 0.379720i | \(0.123980\pi\) | ||||
−0.925101 | + | 0.379720i | \(0.876020\pi\) | |||||||
\(90\) | − | 3.32038e11i | − | 0.624787i | ||||||
\(91\) | −4.25010e11 | + | 3.27109e11i | −0.748429 | + | 0.576030i | ||||
\(92\) | 1.75594e11 | 0.289589 | ||||||||
\(93\) | −4.91374e11 | −0.759476 | ||||||||
\(94\) | − | 3.01250e11i | − | 0.436677i | ||||||
\(95\) | −1.40600e12 | −1.91268 | ||||||||
\(96\) | 6.10984e10i | 0.0780554i | ||||||||
\(97\) | 1.35962e12i | 1.63225i | 0.577874 | + | 0.816126i | \(0.303883\pi\) | ||||
−0.577874 | + | 0.816126i | \(0.696117\pi\) | |||||||
\(98\) | −1.60351e11 | + | 6.05513e11i | −0.181016 | + | 0.683545i | ||||
\(99\) | 6.97338e11 | 0.740683 | ||||||||
\(100\) | −1.02330e11 | −0.102330 | ||||||||
\(101\) | 1.34633e12i | 1.26831i | 0.773208 | + | 0.634153i | \(0.218651\pi\) | ||||
−0.773208 | + | 0.634153i | \(0.781349\pi\) | |||||||
\(102\) | −2.20621e11 | −0.195905 | ||||||||
\(103\) | − | 4.74121e11i | − | 0.397069i | −0.980094 | − | 0.198535i | \(-0.936382\pi\) | ||
0.980094 | − | 0.198535i | \(-0.0636182\pi\) | |||||||
\(104\) | − | 4.22500e11i | − | 0.333908i | ||||||
\(105\) | −3.96113e11 | − | 5.14665e11i | −0.295585 | − | 0.384051i | ||||
\(106\) | 5.20789e11 | 0.367136 | ||||||||
\(107\) | 2.10200e12 | 1.40065 | 0.700327 | − | 0.713822i | \(-0.253038\pi\) | ||||
0.700327 | + | 0.713822i | \(0.253038\pi\) | |||||||
\(108\) | 6.32377e11i | 0.398505i | ||||||||
\(109\) | −3.32488e12 | −1.98252 | −0.991258 | − | 0.131935i | \(-0.957881\pi\) | ||||
−0.991258 | + | 0.131935i | \(0.957881\pi\) | |||||||
\(110\) | − | 1.26500e12i | − | 0.714059i | ||||||
\(111\) | − | 5.86312e11i | − | 0.313466i | ||||||
\(112\) | −3.00969e11 | − | 3.91045e11i | −0.152480 | − | 0.198116i | ||||
\(113\) | 3.62455e12 | 1.74094 | 0.870470 | − | 0.492222i | \(-0.163815\pi\) | ||||
0.870470 | + | 0.492222i | \(0.163815\pi\) | |||||||
\(114\) | 1.19427e12 | 0.544093 | ||||||||
\(115\) | − | 1.47039e12i | − | 0.635689i | ||||||
\(116\) | −1.96624e12 | −0.807029 | ||||||||
\(117\) | − | 1.95030e12i | − | 0.760303i | ||||||
\(118\) | 2.67905e12i | 0.992406i | ||||||||
\(119\) | 1.41203e12 | − | 1.08677e12i | 0.497234 | − | 0.382697i | ||||
\(120\) | 5.11626e11 | 0.171342 | ||||||||
\(121\) | −4.81704e11 | −0.153486 | ||||||||
\(122\) | − | 1.01242e12i | − | 0.307044i | ||||||
\(123\) | −1.95722e11 | −0.0565210 | ||||||||
\(124\) | 3.12634e12i | 0.860016i | ||||||||
\(125\) | − | 3.33001e12i | − | 0.872941i | ||||||
\(126\) | −1.38930e12 | − | 1.80510e12i | −0.347195 | − | 0.451106i | ||||
\(127\) | 6.01653e12 | 1.43392 | 0.716958 | − | 0.697117i | \(-0.245534\pi\) | ||||
0.716958 | + | 0.697117i | \(0.245534\pi\) | |||||||
\(128\) | 3.88736e11 | 0.0883883 | ||||||||
\(129\) | 1.15714e12i | 0.251101i | ||||||||
\(130\) | −3.53793e12 | −0.732975 | ||||||||
\(131\) | − | 2.12789e12i | − | 0.421038i | −0.977590 | − | 0.210519i | \(-0.932485\pi\) | ||
0.977590 | − | 0.210519i | \(-0.0675154\pi\) | |||||||
\(132\) | 1.07450e12i | 0.203126i | ||||||||
\(133\) | −7.64363e12 | + | 5.88293e12i | −1.38099 | + | 1.06288i | ||||
\(134\) | 2.69789e12 | 0.466010 | ||||||||
\(135\) | 5.29539e12 | 0.874774 | ||||||||
\(136\) | 1.40369e12i | 0.221839i | ||||||||
\(137\) | −5.40066e12 | −0.816814 | −0.408407 | − | 0.912800i | \(-0.633916\pi\) | ||||
−0.408407 | + | 0.912800i | \(0.633916\pi\) | |||||||
\(138\) | 1.24896e12i | 0.180832i | ||||||||
\(139\) | − | 3.07261e12i | − | 0.426009i | −0.977051 | − | 0.213005i | \(-0.931675\pi\) | ||
0.977051 | − | 0.213005i | \(-0.0683250\pi\) | |||||||
\(140\) | −3.27453e12 | + | 2.52025e12i | −0.434892 | + | 0.334715i | ||||
\(141\) | 2.14273e12 | 0.272680 | ||||||||
\(142\) | 2.93132e12 | 0.357547 | ||||||||
\(143\) | − | 7.43028e12i | − | 0.868938i | ||||||
\(144\) | 1.79444e12 | 0.201259 | ||||||||
\(145\) | 1.64649e13i | 1.77154i | ||||||||
\(146\) | − | 6.67929e11i | − | 0.0689626i | ||||||
\(147\) | −4.30689e12 | − | 1.14055e12i | −0.426835 | − | 0.113034i | ||||
\(148\) | −3.73038e12 | −0.354963 | ||||||||
\(149\) | −4.81326e12 | −0.439867 | −0.219934 | − | 0.975515i | \(-0.570584\pi\) | ||||
−0.219934 | + | 0.975515i | \(0.570584\pi\) | |||||||
\(150\) | − | 7.27852e11i | − | 0.0638992i | ||||||
\(151\) | −1.38146e13 | −1.16541 | −0.582704 | − | 0.812684i | \(-0.698005\pi\) | ||||
−0.582704 | + | 0.812684i | \(0.698005\pi\) | |||||||
\(152\) | − | 7.59849e12i | − | 0.616121i | ||||||
\(153\) | 6.47957e12i | 0.505123i | ||||||||
\(154\) | −5.29297e12 | − | 6.87710e12i | −0.396803 | − | 0.515562i | ||||
\(155\) | 2.61794e13 | 1.88786 | ||||||||
\(156\) | 3.00516e12 | 0.208506 | ||||||||
\(157\) | 2.01680e13i | 1.34668i | 0.739332 | + | 0.673341i | \(0.235141\pi\) | ||||
−0.739332 | + | 0.673341i | \(0.764859\pi\) | |||||||
\(158\) | 1.05931e13 | 0.680899 | ||||||||
\(159\) | 3.70426e12i | 0.229255i | ||||||||
\(160\) | − | 3.25520e12i | − | 0.194025i | ||||||
\(161\) | −6.15235e12 | − | 7.99368e12i | −0.353253 | − | 0.458978i | ||||
\(162\) | 5.79144e12 | 0.320403 | ||||||||
\(163\) | −2.02503e13 | −1.07971 | −0.539853 | − | 0.841759i | \(-0.681520\pi\) | ||||
−0.539853 | + | 0.841759i | \(0.681520\pi\) | |||||||
\(164\) | 1.24528e12i | 0.0640033i | ||||||||
\(165\) | 8.99768e12 | 0.445889 | ||||||||
\(166\) | − | 6.05286e12i | − | 0.289276i | ||||||
\(167\) | − | 1.09922e13i | − | 0.506741i | −0.967369 | − | 0.253370i | \(-0.918461\pi\) | ||
0.967369 | − | 0.253370i | \(-0.0815391\pi\) | |||||||
\(168\) | 2.78142e12 | − | 2.14073e12i | 0.123712 | − | 0.0952151i | ||||
\(169\) | 2.51721e12 | 0.108044 | ||||||||
\(170\) | 1.17542e13 | 0.486967 | ||||||||
\(171\) | − | 3.50754e13i | − | 1.40290i | ||||||
\(172\) | 7.36225e12 | 0.284341 | ||||||||
\(173\) | − | 3.94980e13i | − | 1.47333i | −0.676260 | − | 0.736663i | \(-0.736401\pi\) | ||
0.676260 | − | 0.736663i | \(-0.263599\pi\) | |||||||
\(174\) | − | 1.39855e13i | − | 0.503944i | ||||||
\(175\) | 3.58537e12 | + | 4.65843e12i | 0.124826 | + | 0.162185i | ||||
\(176\) | 6.83649e12 | 0.230016 | ||||||||
\(177\) | −1.90556e13 | −0.619701 | ||||||||
\(178\) | 1.70804e13i | 0.537005i | ||||||||
\(179\) | 4.48619e13 | 1.36383 | 0.681914 | − | 0.731433i | \(-0.261148\pi\) | ||||
0.681914 | + | 0.731433i | \(0.261148\pi\) | |||||||
\(180\) | − | 1.50263e13i | − | 0.441791i | ||||||
\(181\) | 6.52144e13i | 1.85469i | 0.374205 | + | 0.927346i | \(0.377916\pi\) | ||||
−0.374205 | + | 0.927346i | \(0.622084\pi\) | |||||||
\(182\) | −1.92338e13 | + | 1.48033e13i | −0.529219 | + | 0.407314i | ||||
\(183\) | 7.20113e12 | 0.191732 | ||||||||
\(184\) | 7.94647e12 | 0.204771 | ||||||||
\(185\) | 3.12374e13i | 0.779193i | ||||||||
\(186\) | −2.22370e13 | −0.537031 | ||||||||
\(187\) | 2.46859e13i | 0.577297i | ||||||||
\(188\) | − | 1.36330e13i | − | 0.308777i | ||||||
\(189\) | 2.87881e13 | − | 2.21568e13i | 0.631600 | − | 0.486112i | ||||
\(190\) | −6.36282e13 | −1.35247 | ||||||||
\(191\) | −3.95085e13 | −0.813749 | −0.406874 | − | 0.913484i | \(-0.633381\pi\) | ||||
−0.406874 | + | 0.913484i | \(0.633381\pi\) | |||||||
\(192\) | 2.76500e12i | 0.0551935i | ||||||||
\(193\) | −5.42202e13 | −1.04910 | −0.524551 | − | 0.851379i | \(-0.675767\pi\) | ||||
−0.524551 | + | 0.851379i | \(0.675767\pi\) | |||||||
\(194\) | 6.15294e13i | 1.15418i | ||||||||
\(195\) | − | 2.51646e13i | − | 0.457701i | ||||||
\(196\) | −7.25667e12 | + | 2.74024e13i | −0.127997 | + | 0.483339i | ||||
\(197\) | −3.53646e13 | −0.605023 | −0.302511 | − | 0.953146i | \(-0.597825\pi\) | ||||
−0.302511 | + | 0.953146i | \(0.597825\pi\) | |||||||
\(198\) | 3.15579e13 | 0.523742 | ||||||||
\(199\) | − | 5.93934e13i | − | 0.956357i | −0.878263 | − | 0.478178i | \(-0.841297\pi\) | ||
0.878263 | − | 0.478178i | \(-0.158703\pi\) | |||||||
\(200\) | −4.63092e12 | −0.0723582 | ||||||||
\(201\) | 1.91895e13i | 0.290997i | ||||||||
\(202\) | 6.09280e13i | 0.896827i | ||||||||
\(203\) | 6.88919e13 | + | 8.95106e13i | 0.984447 | + | 1.27908i | ||||
\(204\) | −9.98415e12 | −0.138526 | ||||||||
\(205\) | 1.04277e13 | 0.140496 | ||||||||
\(206\) | − | 2.14563e13i | − | 0.280770i | ||||||
\(207\) | 3.66817e13 | 0.466259 | ||||||||
\(208\) | − | 1.91202e13i | − | 0.236109i | ||||||
\(209\) | − | 1.33630e14i | − | 1.60335i | ||||||
\(210\) | −1.79260e13 | − | 2.32911e13i | −0.209010 | − | 0.271565i | ||||
\(211\) | −6.27775e13 | −0.711393 | −0.355696 | − | 0.934602i | \(-0.615756\pi\) | ||||
−0.355696 | + | 0.934602i | \(0.615756\pi\) | |||||||
\(212\) | 2.35682e13 | 0.259604 | ||||||||
\(213\) | 2.08499e13i | 0.223268i | ||||||||
\(214\) | 9.51258e13 | 0.990412 | ||||||||
\(215\) | − | 6.16500e13i | − | 0.624169i | ||||||
\(216\) | 2.86181e13i | 0.281785i | ||||||||
\(217\) | 1.42323e14 | − | 1.09539e14i | 1.36306 | − | 1.04908i | ||||
\(218\) | −1.50467e14 | −1.40185 | ||||||||
\(219\) | 4.75084e12 | 0.0430632 | ||||||||
\(220\) | − | 5.72474e13i | − | 0.504916i | ||||||
\(221\) | 6.90411e13 | 0.592590 | ||||||||
\(222\) | − | 2.65334e13i | − | 0.221654i | ||||||
\(223\) | 6.75460e13i | 0.549250i | 0.961551 | + | 0.274625i | \(0.0885538\pi\) | ||||
−0.961551 | + | 0.274625i | \(0.911446\pi\) | |||||||
\(224\) | −1.36203e13 | − | 1.76967e13i | −0.107820 | − | 0.140089i | ||||
\(225\) | −2.13768e13 | −0.164758 | ||||||||
\(226\) | 1.64029e14 | 1.23103 | ||||||||
\(227\) | 1.22559e14i | 0.895758i | 0.894094 | + | 0.447879i | \(0.147821\pi\) | ||||
−0.894094 | + | 0.447879i | \(0.852179\pi\) | |||||||
\(228\) | 5.40465e13 | 0.384732 | ||||||||
\(229\) | − | 7.10590e13i | − | 0.492727i | −0.969178 | − | 0.246363i | \(-0.920764\pi\) | ||
0.969178 | − | 0.246363i | \(-0.0792357\pi\) | |||||||
\(230\) | − | 6.65421e13i | − | 0.449500i | ||||||
\(231\) | 4.89154e13 | − | 3.76478e13i | 0.321939 | − | 0.247781i | ||||
\(232\) | −8.89820e13 | −0.570656 | ||||||||
\(233\) | −1.45093e14 | −0.906798 | −0.453399 | − | 0.891308i | \(-0.649789\pi\) | ||||
−0.453399 | + | 0.891308i | \(0.649789\pi\) | |||||||
\(234\) | − | 8.82606e13i | − | 0.537616i | ||||||
\(235\) | −1.14160e14 | −0.677809 | ||||||||
\(236\) | 1.21240e14i | 0.701737i | ||||||||
\(237\) | 7.53469e13i | 0.425182i | ||||||||
\(238\) | 6.39010e13 | − | 4.91815e13i | 0.351598 | − | 0.270608i | ||||
\(239\) | −1.73085e14 | −0.928692 | −0.464346 | − | 0.885654i | \(-0.653711\pi\) | ||||
−0.464346 | + | 0.885654i | \(0.653711\pi\) | |||||||
\(240\) | 2.31535e13 | 0.121157 | ||||||||
\(241\) | 1.55030e14i | 0.791251i | 0.918412 | + | 0.395625i | \(0.129472\pi\) | ||||
−0.918412 | + | 0.395625i | \(0.870528\pi\) | |||||||
\(242\) | −2.17994e13 | −0.108531 | ||||||||
\(243\) | 2.05290e14i | 0.997083i | ||||||||
\(244\) | − | 4.58168e13i | − | 0.217113i | ||||||
\(245\) | 2.29462e14 | + | 6.07659e13i | 1.06100 | + | 0.280972i | ||||
\(246\) | −8.85739e12 | −0.0399664 | ||||||||
\(247\) | −3.73735e14 | −1.64582 | ||||||||
\(248\) | 1.41482e14i | 0.608123i | ||||||||
\(249\) | 4.30527e13 | 0.180636 | ||||||||
\(250\) | − | 1.50699e14i | − | 0.617263i | ||||||
\(251\) | − | 2.64148e13i | − | 0.105634i | −0.998604 | − | 0.0528171i | \(-0.983180\pi\) | ||
0.998604 | − | 0.0528171i | \(-0.0168200\pi\) | |||||||
\(252\) | −6.28726e13 | − | 8.16897e13i | −0.245504 | − | 0.318980i | ||||
\(253\) | 1.39750e14 | 0.532880 | ||||||||
\(254\) | 2.72277e14 | 1.01393 | ||||||||
\(255\) | 8.36052e13i | 0.304083i | ||||||||
\(256\) | 1.75922e13 | 0.0625000 | ||||||||
\(257\) | − | 3.96591e13i | − | 0.137640i | −0.997629 | − | 0.0688200i | \(-0.978077\pi\) | ||
0.997629 | − | 0.0688200i | \(-0.0219234\pi\) | |||||||
\(258\) | 5.23662e13i | 0.177555i | ||||||||
\(259\) | 1.30703e14 | + | 1.69821e14i | 0.432998 | + | 0.562590i | ||||
\(260\) | −1.60108e14 | −0.518291 | ||||||||
\(261\) | −4.10750e14 | −1.29937 | ||||||||
\(262\) | − | 9.62973e13i | − | 0.297719i | ||||||
\(263\) | 1.78810e14 | 0.540327 | 0.270164 | − | 0.962814i | \(-0.412922\pi\) | ||||
0.270164 | + | 0.962814i | \(0.412922\pi\) | |||||||
\(264\) | 4.86265e13i | 0.143632i | ||||||||
\(265\) | − | 1.97355e14i | − | 0.569867i | ||||||
\(266\) | −3.45911e14 | + | 2.66231e14i | −0.976505 | + | 0.751569i | ||||
\(267\) | −1.21489e14 | −0.335329 | ||||||||
\(268\) | 1.22092e14 | 0.329519 | ||||||||
\(269\) | − | 5.00560e14i | − | 1.32112i | −0.750773 | − | 0.660560i | \(-0.770319\pi\) | ||
0.750773 | − | 0.660560i | \(-0.229681\pi\) | |||||||
\(270\) | 2.39642e14 | 0.618558 | ||||||||
\(271\) | 1.94816e14i | 0.491822i | 0.969292 | + | 0.245911i | \(0.0790872\pi\) | ||||
−0.969292 | + | 0.245911i | \(0.920913\pi\) | |||||||
\(272\) | 6.35237e13i | 0.156864i | ||||||||
\(273\) | −1.05293e14 | − | 1.36806e14i | −0.254345 | − | 0.330467i | ||||
\(274\) | −2.44406e14 | −0.577575 | ||||||||
\(275\) | −8.14415e13 | −0.188300 | ||||||||
\(276\) | 5.65216e13i | 0.127868i | ||||||||
\(277\) | 4.77604e14 | 1.05728 | 0.528640 | − | 0.848846i | \(-0.322702\pi\) | ||||
0.528640 | + | 0.848846i | \(0.322702\pi\) | |||||||
\(278\) | − | 1.39051e14i | − | 0.301234i | ||||||
\(279\) | 6.53096e14i | 1.38469i | ||||||||
\(280\) | −1.48188e14 | + | 1.14053e14i | −0.307515 | + | 0.236679i | ||||
\(281\) | 6.92339e14 | 1.40631 | 0.703155 | − | 0.711037i | \(-0.251774\pi\) | ||||
0.703155 | + | 0.711037i | \(0.251774\pi\) | |||||||
\(282\) | 9.69689e13 | 0.192814 | ||||||||
\(283\) | − | 9.19667e14i | − | 1.79024i | −0.445823 | − | 0.895121i | \(-0.647089\pi\) | ||
0.445823 | − | 0.895121i | \(-0.352911\pi\) | |||||||
\(284\) | 1.32657e14 | 0.252824 | ||||||||
\(285\) | − | 4.52574e14i | − | 0.844541i | ||||||
\(286\) | − | 3.36256e14i | − | 0.614432i | ||||||
\(287\) | 5.66895e13 | − | 4.36312e13i | 0.101440 | − | 0.0780738i | ||||
\(288\) | 8.12073e13 | 0.142312 | ||||||||
\(289\) | 3.53244e14 | 0.606301 | ||||||||
\(290\) | 7.45117e14i | 1.25267i | ||||||||
\(291\) | −4.37646e14 | −0.720717 | ||||||||
\(292\) | − | 3.02270e13i | − | 0.0487639i | ||||||
\(293\) | − | 5.68183e14i | − | 0.898013i | −0.893528 | − | 0.449007i | \(-0.851778\pi\) | ||
0.893528 | − | 0.449007i | \(-0.148222\pi\) | |||||||
\(294\) | −1.94908e14 | − | 5.16152e13i | −0.301818 | − | 0.0799270i | ||||
\(295\) | 1.01524e15 | 1.54041 | ||||||||
\(296\) | −1.68818e14 | −0.250997 | ||||||||
\(297\) | 5.03291e14i | 0.733298i | ||||||||
\(298\) | −2.17823e14 | −0.311033 | ||||||||
\(299\) | − | 3.90851e14i | − | 0.546996i | ||||||
\(300\) | − | 3.29388e13i | − | 0.0451835i | ||||||
\(301\) | −2.57954e14 | − | 3.35157e14i | −0.346851 | − | 0.450660i | ||||
\(302\) | −6.25180e14 | −0.824068 | ||||||||
\(303\) | −4.33368e14 | −0.560017 | ||||||||
\(304\) | − | 3.43868e14i | − | 0.435663i | ||||||
\(305\) | −3.83661e14 | −0.476594 | ||||||||
\(306\) | 2.93232e14i | 0.357176i | ||||||||
\(307\) | 1.42572e14i | 0.170295i | 0.996368 | + | 0.0851477i | \(0.0271362\pi\) | ||||
−0.996368 | + | 0.0851477i | \(0.972864\pi\) | |||||||
\(308\) | −2.39532e14 | − | 3.11222e14i | −0.280582 | − | 0.364558i | ||||
\(309\) | 1.52614e14 | 0.175325 | ||||||||
\(310\) | 1.18474e15 | 1.33492 | ||||||||
\(311\) | 9.22041e14i | 1.01903i | 0.860461 | + | 0.509516i | \(0.170176\pi\) | ||||
−0.860461 | + | 0.509516i | \(0.829824\pi\) | |||||||
\(312\) | 1.35998e14 | 0.147436 | ||||||||
\(313\) | 1.10750e15i | 1.17781i | 0.808201 | + | 0.588907i | \(0.200441\pi\) | ||||
−0.808201 | + | 0.588907i | \(0.799559\pi\) | |||||||
\(314\) | 9.12700e14i | 0.952248i | ||||||||
\(315\) | −6.84053e14 | + | 5.26482e14i | −0.700207 | + | 0.538915i | ||||
\(316\) | 4.79391e14 | 0.481468 | ||||||||
\(317\) | −6.06894e14 | −0.598077 | −0.299038 | − | 0.954241i | \(-0.596666\pi\) | ||||
−0.299038 | + | 0.954241i | \(0.596666\pi\) | |||||||
\(318\) | 1.67636e14i | 0.162108i | ||||||||
\(319\) | −1.56488e15 | −1.48503 | ||||||||
\(320\) | − | 1.47313e14i | − | 0.137196i | ||||||
\(321\) | 6.76610e14i | 0.618455i | ||||||||
\(322\) | −2.78423e14 | − | 3.61753e14i | −0.249787 | − | 0.324546i | ||||
\(323\) | 1.24168e15 | 1.09344 | ||||||||
\(324\) | 2.62090e14 | 0.226559 | ||||||||
\(325\) | 2.27774e14i | 0.193288i | ||||||||
\(326\) | −9.16424e14 | −0.763468 | ||||||||
\(327\) | − | 1.07024e15i | − | 0.875376i | ||||||
\(328\) | 5.63547e13i | 0.0452572i | ||||||||
\(329\) | −6.20625e14 | + | 4.77665e14i | −0.489389 | + | 0.376659i | ||||
\(330\) | 4.07189e14 | 0.315291 | ||||||||
\(331\) | −5.43125e12 | −0.00412982 | −0.00206491 | − | 0.999998i | \(-0.500657\pi\) | ||||
−0.00206491 | + | 0.999998i | \(0.500657\pi\) | |||||||
\(332\) | − | 2.73921e14i | − | 0.204549i | ||||||
\(333\) | −7.79280e14 | −0.571515 | ||||||||
\(334\) | − | 4.97450e14i | − | 0.358320i | ||||||
\(335\) | − | 1.02238e15i | − | 0.723340i | ||||||
\(336\) | 1.25873e14 | − | 9.68783e13i | 0.0874776 | − | 0.0673272i | ||||
\(337\) | 5.72107e14 | 0.390569 | 0.195284 | − | 0.980747i | \(-0.437437\pi\) | ||||
0.195284 | + | 0.980747i | \(0.437437\pi\) | |||||||
\(338\) | 1.13916e14 | 0.0763984 | ||||||||
\(339\) | 1.16670e15i | 0.768708i | ||||||||
\(340\) | 5.31934e14 | 0.344338 | ||||||||
\(341\) | 2.48817e15i | 1.58254i | ||||||||
\(342\) | − | 1.58733e15i | − | 0.991998i | ||||||
\(343\) | 1.50171e15 | − | 6.29757e14i | 0.922193 | − | 0.386730i | ||||
\(344\) | 3.33178e14 | 0.201060 | ||||||||
\(345\) | 4.73301e14 | 0.280687 | ||||||||
\(346\) | − | 1.78748e15i | − | 1.04180i | ||||||
\(347\) | 2.48442e14 | 0.142314 | 0.0711572 | − | 0.997465i | \(-0.477331\pi\) | ||||
0.0711572 | + | 0.997465i | \(0.477331\pi\) | |||||||
\(348\) | − | 6.32911e14i | − | 0.356342i | ||||||
\(349\) | − | 1.93344e15i | − | 1.06999i | −0.844856 | − | 0.534994i | \(-0.820314\pi\) | ||
0.844856 | − | 0.534994i | \(-0.179686\pi\) | |||||||
\(350\) | 1.62255e14 | + | 2.10817e14i | 0.0882654 | + | 0.114682i | ||||
\(351\) | 1.40760e15 | 0.752723 | ||||||||
\(352\) | 3.09384e14 | 0.162646 | ||||||||
\(353\) | − | 3.51317e15i | − | 1.81573i | −0.419261 | − | 0.907866i | \(-0.637711\pi\) | ||
0.419261 | − | 0.907866i | \(-0.362289\pi\) | |||||||
\(354\) | −8.62356e14 | −0.438195 | ||||||||
\(355\) | − | 1.11084e15i | − | 0.554985i | ||||||
\(356\) | 7.72971e14i | 0.379720i | ||||||||
\(357\) | 3.49818e14 | + | 4.54515e14i | 0.168979 | + | 0.219553i | ||||
\(358\) | 2.03022e15 | 0.964371 | ||||||||
\(359\) | 1.80389e15 | 0.842644 | 0.421322 | − | 0.906911i | \(-0.361566\pi\) | ||||
0.421322 | + | 0.906911i | \(0.361566\pi\) | |||||||
\(360\) | − | 6.80013e14i | − | 0.312394i | ||||||
\(361\) | −4.50816e15 | −2.03684 | ||||||||
\(362\) | 2.95127e15i | 1.31147i | ||||||||
\(363\) | − | 1.55055e14i | − | 0.0677713i | ||||||
\(364\) | −8.70420e14 | + | 6.69920e14i | −0.374215 | + | 0.288015i | ||||
\(365\) | −2.53115e14 | −0.107044 | ||||||||
\(366\) | 3.25886e14 | 0.135575 | ||||||||
\(367\) | 1.98525e15i | 0.812491i | 0.913764 | + | 0.406245i | \(0.133162\pi\) | ||||
−0.913764 | + | 0.406245i | \(0.866838\pi\) | |||||||
\(368\) | 3.59616e14 | 0.144795 | ||||||||
\(369\) | 2.60139e14i | 0.103050i | ||||||||
\(370\) | 1.41365e15i | 0.550973i | ||||||||
\(371\) | −8.25768e14 | − | 1.07291e15i | −0.316676 | − | 0.411453i | ||||
\(372\) | −1.00633e15 | −0.379738 | ||||||||
\(373\) | 1.67605e15 | 0.622348 | 0.311174 | − | 0.950353i | \(-0.399278\pi\) | ||||
0.311174 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(374\) | 1.11716e15i | 0.408211i | ||||||||
\(375\) | 1.07189e15 | 0.385445 | ||||||||
\(376\) | − | 6.16960e14i | − | 0.218338i | ||||||
\(377\) | 4.37662e15i | 1.52437i | ||||||||
\(378\) | 1.30280e15 | − | 1.00270e15i | 0.446609 | − | 0.343733i | ||||
\(379\) | −2.71186e15 | −0.915024 | −0.457512 | − | 0.889204i | \(-0.651259\pi\) | ||||
−0.457512 | + | 0.889204i | \(0.651259\pi\) | |||||||
\(380\) | −2.87948e15 | −0.956341 | ||||||||
\(381\) | 1.93665e15i | 0.633142i | ||||||||
\(382\) | −1.78795e15 | −0.575407 | ||||||||
\(383\) | − | 5.49836e15i | − | 1.74197i | −0.491310 | − | 0.870985i | \(-0.663482\pi\) | ||
0.491310 | − | 0.870985i | \(-0.336518\pi\) | |||||||
\(384\) | 1.25130e14i | 0.0390277i | ||||||||
\(385\) | −2.60611e15 | + | 2.00580e15i | −0.800255 | + | 0.615917i | ||||
\(386\) | −2.45373e15 | −0.741827 | ||||||||
\(387\) | 1.53798e15 | 0.457810 | ||||||||
\(388\) | 2.78450e15i | 0.816126i | ||||||||
\(389\) | 3.52503e15 | 1.01734 | 0.508668 | − | 0.860963i | \(-0.330138\pi\) | ||||
0.508668 | + | 0.860963i | \(0.330138\pi\) | |||||||
\(390\) | − | 1.13882e15i | − | 0.323643i | ||||||
\(391\) | 1.29854e15i | 0.363408i | ||||||||
\(392\) | −3.28399e14 | + | 1.24009e15i | −0.0905078 | + | 0.341772i | ||||
\(393\) | 6.84943e14 | 0.185908 | ||||||||
\(394\) | −1.60042e15 | −0.427816 | ||||||||
\(395\) | − | 4.01432e15i | − | 1.05689i | ||||||
\(396\) | 1.42815e15 | 0.370341 | ||||||||
\(397\) | 2.66362e15i | 0.680345i | 0.940363 | + | 0.340173i | \(0.110486\pi\) | ||||
−0.940363 | + | 0.340173i | \(0.889514\pi\) | |||||||
\(398\) | − | 2.68784e15i | − | 0.676246i | ||||||
\(399\) | −1.89365e15 | − | 2.46039e15i | −0.469312 | − | 0.609772i | ||||
\(400\) | −2.09572e14 | −0.0511650 | ||||||||
\(401\) | −2.18901e15 | −0.526480 | −0.263240 | − | 0.964730i | \(-0.584791\pi\) | ||||
−0.263240 | + | 0.964730i | \(0.584791\pi\) | |||||||
\(402\) | 8.68419e14i | 0.205766i | ||||||||
\(403\) | 6.95887e15 | 1.62446 | ||||||||
\(404\) | 2.75729e15i | 0.634153i | ||||||||
\(405\) | − | 2.19469e15i | − | 0.497329i | ||||||
\(406\) | 3.11769e15 | + | 4.05079e15i | 0.696109 | + | 0.904447i | ||||
\(407\) | −2.96891e15 | −0.653176 | ||||||||
\(408\) | −4.51831e14 | −0.0979524 | ||||||||
\(409\) | 5.27335e15i | 1.12654i | 0.826273 | + | 0.563270i | \(0.190457\pi\) | ||||
−0.826273 | + | 0.563270i | \(0.809543\pi\) | |||||||
\(410\) | 4.71903e14 | 0.0993458 | ||||||||
\(411\) | − | 1.73841e15i | − | 0.360662i | ||||||
\(412\) | − | 9.71001e14i | − | 0.198535i | ||||||
\(413\) | 5.51929e15 | − | 4.24793e15i | 1.11220 | − | 0.856007i | ||||
\(414\) | 1.66003e15 | 0.329695 | ||||||||
\(415\) | −2.29376e15 | −0.449013 | ||||||||
\(416\) | − | 8.65280e14i | − | 0.166954i | ||||||
\(417\) | 9.89039e14 | 0.188103 | ||||||||
\(418\) | − | 6.04743e15i | − | 1.13374i | ||||||
\(419\) | 2.34826e15i | 0.433973i | 0.976175 | + | 0.216986i | \(0.0696227\pi\) | ||||
−0.976175 | + | 0.216986i | \(0.930377\pi\) | |||||||
\(420\) | −8.11239e14 | − | 1.05403e15i | −0.147793 | − | 0.192025i | ||||
\(421\) | −7.08816e15 | −1.27304 | −0.636519 | − | 0.771261i | \(-0.719626\pi\) | ||||
−0.636519 | + | 0.771261i | \(0.719626\pi\) | |||||||
\(422\) | −2.84099e15 | −0.503031 | ||||||||
\(423\) | − | 2.84795e15i | − | 0.497153i | ||||||
\(424\) | 1.06658e15 | 0.183568 | ||||||||
\(425\) | − | 7.56743e14i | − | 0.128415i | ||||||
\(426\) | 9.43559e14i | 0.157874i | ||||||||
\(427\) | −2.08575e15 | + | 1.60530e15i | −0.344108 | + | 0.264843i | ||||
\(428\) | 4.30490e15 | 0.700327 | ||||||||
\(429\) | 2.39172e15 | 0.383678 | ||||||||
\(430\) | − | 2.78996e15i | − | 0.441354i | ||||||
\(431\) | 6.46463e15 | 1.00851 | 0.504255 | − | 0.863555i | \(-0.331767\pi\) | ||||
0.504255 | + | 0.863555i | \(0.331767\pi\) | |||||||
\(432\) | 1.29511e15i | 0.199252i | ||||||||
\(433\) | − | 4.42035e15i | − | 0.670701i | −0.942093 | − | 0.335351i | \(-0.891145\pi\) | ||
0.942093 | − | 0.335351i | \(-0.108855\pi\) | |||||||
\(434\) | 6.44079e15 | − | 4.95716e15i | 0.963830 | − | 0.741813i | ||||
\(435\) | −5.29986e15 | −0.782220 | ||||||||
\(436\) | −6.80935e15 | −0.991258 | ||||||||
\(437\) | − | 7.02930e15i | − | 1.00931i | ||||||
\(438\) | 2.14999e14 | 0.0304503 | ||||||||
\(439\) | 1.32566e16i | 1.85202i | 0.377501 | + | 0.926009i | \(0.376783\pi\) | ||||
−0.377501 | + | 0.926009i | \(0.623217\pi\) | |||||||
\(440\) | − | 2.59072e15i | − | 0.357030i | ||||||
\(441\) | −1.51592e15 | + | 5.72438e15i | −0.206085 | + | 0.778210i | ||||
\(442\) | 3.12444e15 | 0.419024 | ||||||||
\(443\) | 6.84771e15 | 0.905989 | 0.452995 | − | 0.891513i | \(-0.350356\pi\) | ||||
0.452995 | + | 0.891513i | \(0.350356\pi\) | |||||||
\(444\) | − | 1.20077e15i | − | 0.156733i | ||||||
\(445\) | 6.47270e15 | 0.833538 | ||||||||
\(446\) | 3.05678e15i | 0.388379i | ||||||||
\(447\) | − | 1.54933e15i | − | 0.194222i | ||||||
\(448\) | −6.16384e14 | − | 8.00861e14i | −0.0762400 | − | 0.0990579i | ||||
\(449\) | −1.39377e16 | −1.70103 | −0.850515 | − | 0.525950i | \(-0.823710\pi\) | ||||
−0.850515 | + | 0.525950i | \(0.823710\pi\) | |||||||
\(450\) | −9.67404e14 | −0.116502 | ||||||||
\(451\) | 9.91080e14i | 0.117774i | ||||||||
\(452\) | 7.42308e15 | 0.870470 | ||||||||
\(453\) | − | 4.44677e15i | − | 0.514584i | ||||||
\(454\) | 5.54640e15i | 0.633397i | ||||||||
\(455\) | 5.60977e15 | + | 7.28872e15i | 0.632233 | + | 0.821453i | ||||
\(456\) | 2.44587e15 | 0.272047 | ||||||||
\(457\) | −7.42405e15 | −0.814974 | −0.407487 | − | 0.913211i | \(-0.633595\pi\) | ||||
−0.407487 | + | 0.913211i | \(0.633595\pi\) | |||||||
\(458\) | − | 3.21576e15i | − | 0.348410i | ||||||
\(459\) | −4.67651e15 | −0.500087 | ||||||||
\(460\) | − | 3.01135e15i | − | 0.317845i | ||||||
\(461\) | 1.49069e15i | 0.155304i | 0.996981 | + | 0.0776521i | \(0.0247423\pi\) | ||||
−0.996981 | + | 0.0776521i | \(0.975258\pi\) | |||||||
\(462\) | 2.21366e15 | − | 1.70375e15i | 0.227645 | − | 0.175208i | ||||
\(463\) | −5.08405e15 | −0.516088 | −0.258044 | − | 0.966133i | \(-0.583078\pi\) | ||||
−0.258044 | + | 0.966133i | \(0.583078\pi\) | |||||||
\(464\) | −4.02687e15 | −0.403515 | ||||||||
\(465\) | 8.42683e15i | 0.833579i | ||||||||
\(466\) | −6.56615e15 | −0.641203 | ||||||||
\(467\) | 1.01578e15i | 0.0979256i | 0.998801 | + | 0.0489628i | \(0.0155916\pi\) | ||||
−0.998801 | + | 0.0489628i | \(0.984408\pi\) | |||||||
\(468\) | − | 3.99422e15i | − | 0.380152i | ||||||
\(469\) | −4.27780e15 | − | 5.55810e15i | −0.401960 | − | 0.522263i | ||||
\(470\) | −5.16630e15 | −0.479283 | ||||||||
\(471\) | −6.49184e15 | −0.594624 | ||||||||
\(472\) | 5.48670e15i | 0.496203i | ||||||||
\(473\) | 5.85941e15 | 0.523223 | ||||||||
\(474\) | 3.40981e15i | 0.300649i | ||||||||
\(475\) | 4.09642e15i | 0.356651i | ||||||||
\(476\) | 2.89183e15 | − | 2.22570e15i | 0.248617 | − | 0.191349i | ||||
\(477\) | 4.92342e15 | 0.417981 | ||||||||
\(478\) | −7.83293e15 | −0.656684 | ||||||||
\(479\) | 9.98479e15i | 0.826658i | 0.910582 | + | 0.413329i | \(0.135634\pi\) | ||||
−0.910582 | + | 0.413329i | \(0.864366\pi\) | |||||||
\(480\) | 1.04781e15 | 0.0856712 | ||||||||
\(481\) | 8.30338e15i | 0.670478i | ||||||||
\(482\) | 7.01587e15i | 0.559499i | ||||||||
\(483\) | 2.57307e15 | − | 1.98037e15i | 0.202661 | − | 0.155978i | ||||
\(484\) | −9.86530e14 | −0.0767429 | ||||||||
\(485\) | 2.33169e16 | 1.79151 | ||||||||
\(486\) | 9.29039e15i | 0.705044i | ||||||||
\(487\) | −6.94006e15 | −0.520223 | −0.260111 | − | 0.965579i | \(-0.583759\pi\) | ||||
−0.260111 | + | 0.965579i | \(0.583759\pi\) | |||||||
\(488\) | − | 2.07343e15i | − | 0.153522i | ||||||
\(489\) | − | 6.51834e15i | − | 0.476742i | ||||||
\(490\) | 1.03843e16 | + | 2.74995e15i | 0.750238 | + | 0.198677i | ||||
\(491\) | −2.58155e16 | −1.84244 | −0.921218 | − | 0.389048i | \(-0.872804\pi\) | ||||
−0.921218 | + | 0.389048i | \(0.872804\pi\) | |||||||
\(492\) | −4.00840e14 | −0.0282605 | ||||||||
\(493\) | − | 1.45406e16i | − | 1.01275i | ||||||
\(494\) | −1.69133e16 | −1.16377 | ||||||||
\(495\) | − | 1.19590e16i | − | 0.812951i | ||||||
\(496\) | 6.40275e15i | 0.430008i | ||||||||
\(497\) | −4.64793e15 | − | 6.03901e15i | −0.308405 | − | 0.400708i | ||||
\(498\) | 1.94834e15 | 0.127729 | ||||||||
\(499\) | 2.21490e16 | 1.43467 | 0.717334 | − | 0.696730i | \(-0.245362\pi\) | ||||
0.717334 | + | 0.696730i | \(0.245362\pi\) | |||||||
\(500\) | − | 6.81986e15i | − | 0.436471i | ||||||
\(501\) | 3.53826e15 | 0.223750 | ||||||||
\(502\) | − | 1.19540e15i | − | 0.0746947i | ||||||
\(503\) | − | 1.32694e16i | − | 0.819301i | −0.912243 | − | 0.409651i | \(-0.865651\pi\) | ||
0.912243 | − | 0.409651i | \(-0.134349\pi\) | |||||||
\(504\) | −2.84529e15 | − | 3.69685e15i | −0.173597 | − | 0.225553i | ||||
\(505\) | 2.30890e16 | 1.39205 | ||||||||
\(506\) | 6.32438e15 | 0.376803 | ||||||||
\(507\) | 8.10261e14i | 0.0477065i | ||||||||
\(508\) | 1.23218e16 | 0.716958 | ||||||||
\(509\) | − | 3.04670e16i | − | 1.75195i | −0.482352 | − | 0.875977i | \(-0.660218\pi\) | ||
0.482352 | − | 0.875977i | \(-0.339782\pi\) | |||||||
\(510\) | 3.78354e15i | 0.215019i | ||||||||
\(511\) | −1.37604e15 | + | 1.05908e15i | −0.0772871 | + | 0.0594842i | ||||
\(512\) | 7.96131e14 | 0.0441942 | ||||||||
\(513\) | 2.53150e16 | 1.38891 | ||||||||
\(514\) | − | 1.79477e15i | − | 0.0973261i | ||||||
\(515\) | −8.13096e15 | −0.435811 | ||||||||
\(516\) | 2.36982e15i | 0.125550i | ||||||||
\(517\) | − | 1.08501e16i | − | 0.568188i | ||||||
\(518\) | 5.91493e15 | + | 7.68520e15i | 0.306176 | + | 0.397811i | ||||
\(519\) | 1.27140e16 | 0.650544 | ||||||||
\(520\) | −7.24568e15 | −0.366487 | ||||||||
\(521\) | 8.65982e15i | 0.432995i | 0.976283 | + | 0.216497i | \(0.0694633\pi\) | ||||
−0.976283 | + | 0.216497i | \(0.930537\pi\) | |||||||
\(522\) | −1.85884e16 | −0.918796 | ||||||||
\(523\) | 1.27985e15i | 0.0625388i | 0.999511 | + | 0.0312694i | \(0.00995498\pi\) | ||||
−0.999511 | + | 0.0312694i | \(0.990045\pi\) | |||||||
\(524\) | − | 4.35792e15i | − | 0.210519i | ||||||
\(525\) | −1.49950e15 | + | 1.15409e15i | −0.0716126 | + | 0.0551167i | ||||
\(526\) | 8.09201e15 | 0.382069 | ||||||||
\(527\) | −2.31197e16 | −1.07924 | ||||||||
\(528\) | 2.20059e15i | 0.101563i | ||||||||
\(529\) | −1.45634e16 | −0.664552 | ||||||||
\(530\) | − | 8.93128e15i | − | 0.402957i | ||||||
\(531\) | 2.53272e16i | 1.12985i | ||||||||
\(532\) | −1.56541e16 | + | 1.20482e16i | −0.690494 | + | 0.531439i | ||||
\(533\) | 2.77183e15 | 0.120894 | ||||||||
\(534\) | −5.49799e15 | −0.237113 | ||||||||
\(535\) | − | 3.60484e16i | − | 1.53732i | ||||||
\(536\) | 5.52527e15 | 0.233005 | ||||||||
\(537\) | 1.44405e16i | 0.602195i | ||||||||
\(538\) | − | 2.26528e16i | − | 0.934173i | ||||||
\(539\) | −5.77538e15 | + | 2.18088e16i | −0.235531 | + | 0.889404i | ||||
\(540\) | 1.08450e16 | 0.437387 | ||||||||
\(541\) | −6.76645e15 | −0.269884 | −0.134942 | − | 0.990854i | \(-0.543085\pi\) | ||||
−0.134942 | + | 0.990854i | \(0.543085\pi\) | |||||||
\(542\) | 8.81636e15i | 0.347771i | ||||||||
\(543\) | −2.09917e16 | −0.818935 | ||||||||
\(544\) | 2.87475e15i | 0.110919i | ||||||||
\(545\) | 5.70201e16i | 2.17595i | ||||||||
\(546\) | −4.76500e15 | − | 6.19112e15i | −0.179849 | − | 0.233676i | ||||
\(547\) | 3.11128e16 | 1.16149 | 0.580745 | − | 0.814086i | \(-0.302761\pi\) | ||||
0.580745 | + | 0.814086i | \(0.302761\pi\) | |||||||
\(548\) | −1.10605e16 | −0.408407 | ||||||||
\(549\) | − | 9.57117e15i | − | 0.349568i | ||||||
\(550\) | −3.68562e15 | −0.133148 | ||||||||
\(551\) | 7.87117e16i | 2.81274i | ||||||||
\(552\) | 2.55788e15i | 0.0904160i | ||||||||
\(553\) | −1.67966e16 | − | 2.18236e16i | −0.587314 | − | 0.763091i | ||||
\(554\) | 2.16139e16 | 0.747609 | ||||||||
\(555\) | −1.00550e16 | −0.344051 | ||||||||
\(556\) | − | 6.29271e15i | − | 0.213005i | ||||||
\(557\) | −1.20078e16 | −0.402098 | −0.201049 | − | 0.979581i | \(-0.564435\pi\) | ||||
−0.201049 | + | 0.979581i | \(0.564435\pi\) | |||||||
\(558\) | 2.95557e16i | 0.979122i | ||||||||
\(559\) | − | 1.63875e16i | − | 0.537084i | ||||||
\(560\) | −6.70624e15 | + | 5.16147e15i | −0.217446 | + | 0.167358i | ||||
\(561\) | −7.94610e15 | −0.254904 | ||||||||
\(562\) | 3.13317e16 | 0.994411 | ||||||||
\(563\) | 2.90442e16i | 0.912030i | 0.889972 | + | 0.456015i | \(0.150724\pi\) | ||||
−0.889972 | + | 0.456015i | \(0.849276\pi\) | |||||||
\(564\) | 4.38831e15 | 0.136340 | ||||||||
\(565\) | − | 6.21594e16i | − | 1.91080i | ||||||
\(566\) | − | 4.16194e16i | − | 1.26589i | ||||||
\(567\) | −9.18296e15 | − | 1.19313e16i | −0.276366 | − | 0.359079i | ||||
\(568\) | 6.00335e15 | 0.178774 | ||||||||
\(569\) | −3.98456e16 | −1.17411 | −0.587053 | − | 0.809549i | \(-0.699712\pi\) | ||||
−0.587053 | + | 0.809549i | \(0.699712\pi\) | |||||||
\(570\) | − | 2.04812e16i | − | 0.597181i | ||||||
\(571\) | 1.06745e16 | 0.307986 | 0.153993 | − | 0.988072i | \(-0.450787\pi\) | ||||
0.153993 | + | 0.988072i | \(0.450787\pi\) | |||||||
\(572\) | − | 1.52172e16i | − | 0.434469i | ||||||
\(573\) | − | 1.27173e16i | − | 0.359309i | ||||||
\(574\) | 2.56547e15 | − | 1.97452e15i | 0.0717292 | − | 0.0552065i | ||||
\(575\) | −4.28403e15 | −0.118535 | ||||||||
\(576\) | 3.67502e15 | 0.100629 | ||||||||
\(577\) | 5.69176e16i | 1.54238i | 0.636604 | + | 0.771191i | \(0.280339\pi\) | ||||
−0.636604 | + | 0.771191i | \(0.719661\pi\) | |||||||
\(578\) | 1.59860e16 | 0.428719 | ||||||||
\(579\) | − | 1.74529e16i | − | 0.463228i | ||||||
\(580\) | 3.37201e16i | 0.885771i | ||||||||
\(581\) | −1.24699e16 | + | 9.59747e15i | −0.324195 | + | 0.249517i | ||||
\(582\) | −1.98056e16 | −0.509624 | ||||||||
\(583\) | 1.87573e16 | 0.477704 | ||||||||
\(584\) | − | 1.36792e15i | − | 0.0344813i | ||||||
\(585\) | −3.34468e16 | −0.834486 | ||||||||
\(586\) | − | 2.57130e16i | − | 0.634991i | ||||||
\(587\) | − | 4.51143e16i | − | 1.10277i | −0.834250 | − | 0.551386i | \(-0.814099\pi\) | ||
0.834250 | − | 0.551386i | \(-0.185901\pi\) | |||||||
\(588\) | −8.82051e15 | − | 2.33584e15i | −0.213417 | − | 0.0565170i | ||||
\(589\) | 1.25152e17 | 2.99742 | ||||||||
\(590\) | 4.59445e16 | 1.08923 | ||||||||
\(591\) | − | 1.13835e16i | − | 0.267147i | ||||||
\(592\) | −7.63982e15 | −0.177481 | ||||||||
\(593\) | 1.11718e16i | 0.256917i | 0.991715 | + | 0.128459i | \(0.0410030\pi\) | ||||
−0.991715 | + | 0.128459i | \(0.958997\pi\) | |||||||
\(594\) | 2.27764e16i | 0.518520i | ||||||||
\(595\) | −1.86376e16 | − | 2.42156e16i | −0.420037 | − | 0.545750i | ||||
\(596\) | −9.85756e15 | −0.219934 | ||||||||
\(597\) | 1.91180e16 | 0.422277 | ||||||||
\(598\) | − | 1.76879e16i | − | 0.386785i | ||||||
\(599\) | 5.04237e16 | 1.09163 | 0.545813 | − | 0.837907i | \(-0.316221\pi\) | ||||
0.545813 | + | 0.837907i | \(0.316221\pi\) | |||||||
\(600\) | − | 1.49064e15i | − | 0.0319496i | ||||||
\(601\) | − | 6.11133e15i | − | 0.129685i | −0.997896 | − | 0.0648424i | \(-0.979346\pi\) | ||
0.997896 | − | 0.0648424i | \(-0.0206545\pi\) | |||||||
\(602\) | −1.16737e16 | − | 1.51675e16i | −0.245261 | − | 0.318665i | ||||
\(603\) | 2.55052e16 | 0.530549 | ||||||||
\(604\) | −2.82924e16 | −0.582704 | ||||||||
\(605\) | 8.26100e15i | 0.168461i | ||||||||
\(606\) | −1.96120e16 | −0.395992 | ||||||||
\(607\) | − | 5.40145e15i | − | 0.107989i | −0.998541 | − | 0.0539943i | \(-0.982805\pi\) | ||
0.998541 | − | 0.0539943i | \(-0.0171953\pi\) | |||||||
\(608\) | − | 1.55617e16i | − | 0.308060i | ||||||
\(609\) | −2.88124e16 | + | 2.21755e16i | −0.564775 | + | 0.434680i | ||||
\(610\) | −1.73625e16 | −0.337003 | ||||||||
\(611\) | −3.03455e16 | −0.583240 | ||||||||
\(612\) | 1.32702e16i | 0.252562i | ||||||||
\(613\) | −1.04841e16 | −0.197592 | −0.0987961 | − | 0.995108i | \(-0.531499\pi\) | ||||
−0.0987961 | + | 0.995108i | \(0.531499\pi\) | |||||||
\(614\) | 6.45206e15i | 0.120417i | ||||||||
\(615\) | 3.35655e15i | 0.0620358i | ||||||||
\(616\) | −1.08400e16 | − | 1.40843e16i | −0.198402 | − | 0.257781i | ||||
\(617\) | −3.78397e16 | −0.685862 | −0.342931 | − | 0.939361i | \(-0.611420\pi\) | ||||
−0.342931 | + | 0.939361i | \(0.611420\pi\) | |||||||
\(618\) | 6.90653e15 | 0.123974 | ||||||||
\(619\) | − | 2.62642e16i | − | 0.466896i | −0.972369 | − | 0.233448i | \(-0.924999\pi\) | ||
0.972369 | − | 0.233448i | \(-0.0750008\pi\) | |||||||
\(620\) | 5.36153e16 | 0.943928 | ||||||||
\(621\) | 2.64744e16i | 0.461611i | ||||||||
\(622\) | 4.17268e16i | 0.720565i | ||||||||
\(623\) | 3.51885e16 | − | 2.70829e16i | 0.601828 | − | 0.463198i | ||||
\(624\) | 6.15456e15 | 0.104253 | ||||||||
\(625\) | −6.93067e16 | −1.16277 | ||||||||
\(626\) | 5.01196e16i | 0.832840i | ||||||||
\(627\) | 4.30141e16 | 0.707955 | ||||||||
\(628\) | 4.13041e16i | 0.673341i | ||||||||
\(629\) | − | 2.75867e16i | − | 0.445446i | ||||||
\(630\) | −3.09567e16 | + | 2.38259e16i | −0.495121 | + | 0.381070i | ||||
\(631\) | −9.67799e15 | −0.153324 | −0.0766618 | − | 0.997057i | \(-0.524426\pi\) | ||||
−0.0766618 | + | 0.997057i | \(0.524426\pi\) | |||||||
\(632\) | 2.16948e16 | 0.340449 | ||||||||
\(633\) | − | 2.02073e16i | − | 0.314114i | ||||||
\(634\) | −2.74649e16 | −0.422904 | ||||||||
\(635\) | − | 1.03181e17i | − | 1.57382i | ||||||
\(636\) | 7.58633e15i | 0.114628i | ||||||||
\(637\) | 6.09944e16 | + | 1.61525e16i | 0.912964 | + | 0.241770i | ||||
\(638\) | −7.08183e16 | −1.05008 | ||||||||
\(639\) | 2.77121e16 | 0.407065 | ||||||||
\(640\) | − | 6.66664e15i | − | 0.0970124i | ||||||
\(641\) | −5.73035e16 | −0.826101 | −0.413050 | − | 0.910708i | \(-0.635537\pi\) | ||||
−0.413050 | + | 0.910708i | \(0.635537\pi\) | |||||||
\(642\) | 3.06199e16i | 0.437314i | ||||||||
\(643\) | 4.27668e16i | 0.605119i | 0.953131 | + | 0.302559i | \(0.0978410\pi\) | ||||
−0.953131 | + | 0.302559i | \(0.902159\pi\) | |||||||
\(644\) | −1.26000e16 | − | 1.63711e16i | −0.176626 | − | 0.229489i | ||||
\(645\) | 1.98444e16 | 0.275601 | ||||||||
\(646\) | 5.61918e16 | 0.773175 | ||||||||
\(647\) | 7.05664e15i | 0.0961994i | 0.998843 | + | 0.0480997i | \(0.0153165\pi\) | ||||
−0.998843 | + | 0.0480997i | \(0.984683\pi\) | |||||||
\(648\) | 1.18609e16 | 0.160201 | ||||||||
\(649\) | 9.64916e16i | 1.29128i | ||||||||
\(650\) | 1.03079e16i | 0.136675i | ||||||||
\(651\) | 3.52593e16 | + | 4.58120e16i | 0.463220 | + | 0.601857i | ||||
\(652\) | −4.14726e16 | −0.539853 | ||||||||
\(653\) | 5.13577e15 | 0.0662410 | 0.0331205 | − | 0.999451i | \(-0.489455\pi\) | ||||
0.0331205 | + | 0.999451i | \(0.489455\pi\) | |||||||
\(654\) | − | 4.84335e16i | − | 0.618984i | ||||||
\(655\) | −3.64923e16 | −0.462119 | ||||||||
\(656\) | 2.55032e15i | 0.0320016i | ||||||||
\(657\) | − | 6.31445e15i | − | 0.0785133i | ||||||
\(658\) | −2.80863e16 | + | 2.16167e16i | −0.346050 | + | 0.266338i | ||||
\(659\) | −7.30365e16 | −0.891718 | −0.445859 | − | 0.895103i | \(-0.647102\pi\) | ||||
−0.445859 | + | 0.895103i | \(0.647102\pi\) | |||||||
\(660\) | 1.84273e16 | 0.222945 | ||||||||
\(661\) | − | 5.83643e16i | − | 0.699743i | −0.936798 | − | 0.349871i | \(-0.886225\pi\) | ||
0.936798 | − | 0.349871i | \(-0.113775\pi\) | |||||||
\(662\) | −2.45790e14 | −0.00292023 | ||||||||
\(663\) | 2.22235e16i | 0.261657i | ||||||||
\(664\) | − | 1.23963e16i | − | 0.144638i | ||||||
\(665\) | 1.00889e17 | + | 1.31085e17i | 1.16658 | + | 1.51573i | ||||
\(666\) | −3.52662e16 | −0.404122 | ||||||||
\(667\) | −8.23165e16 | −0.934828 | ||||||||
\(668\) | − | 2.25120e16i | − | 0.253370i | ||||||
\(669\) | −2.17423e16 | −0.242520 | ||||||||
\(670\) | − | 4.62675e16i | − | 0.511478i | ||||||
\(671\) | − | 3.64643e16i | − | 0.399515i | ||||||
\(672\) | 5.69636e15 | − | 4.38421e15i | 0.0618560 | − | 0.0476075i | ||||
\(673\) | −1.02330e17 | −1.10131 | −0.550656 | − | 0.834732i | \(-0.685623\pi\) | ||||
−0.550656 | + | 0.834732i | \(0.685623\pi\) | |||||||
\(674\) | 2.58906e16 | 0.276174 | ||||||||
\(675\) | − | 1.54283e16i | − | 0.163116i | ||||||
\(676\) | 5.15525e15 | 0.0540219 | ||||||||
\(677\) | − | 1.61708e16i | − | 0.167957i | −0.996468 | − | 0.0839787i | \(-0.973237\pi\) | ||
0.996468 | − | 0.0839787i | \(-0.0267628\pi\) | |||||||
\(678\) | 5.27989e16i | 0.543559i | ||||||||
\(679\) | 1.26761e17 | − | 9.75616e16i | 1.29350 | − | 0.995544i | ||||
\(680\) | 2.40726e16 | 0.243483 | ||||||||
\(681\) | −3.94504e16 | −0.395520 | ||||||||
\(682\) | 1.12602e17i | 1.11902i | ||||||||
\(683\) | 8.92961e16 | 0.879646 | 0.439823 | − | 0.898084i | \(-0.355041\pi\) | ||||
0.439823 | + | 0.898084i | \(0.355041\pi\) | |||||||
\(684\) | − | 7.18344e16i | − | 0.701448i | ||||||
\(685\) | 9.26187e16i | 0.896511i | ||||||||
\(686\) | 6.79597e16 | − | 2.84995e16i | 0.652089 | − | 0.273460i | ||||
\(687\) | 2.28731e16 | 0.217562 | ||||||||
\(688\) | 1.50779e16 | 0.142171 | ||||||||
\(689\) | − | 5.24600e16i | − | 0.490358i | ||||||
\(690\) | 2.14191e16 | 0.198476 | ||||||||
\(691\) | − | 5.19820e16i | − | 0.477512i | −0.971080 | − | 0.238756i | \(-0.923260\pi\) | ||
0.971080 | − | 0.238756i | \(-0.0767397\pi\) | |||||||
\(692\) | − | 8.08919e16i | − | 0.736663i | ||||||
\(693\) | −5.00385e16 | − | 6.50145e16i | −0.451757 | − | 0.586964i | ||||
\(694\) | 1.12432e16 | 0.100631 | ||||||||
\(695\) | −5.26939e16 | −0.467575 | ||||||||
\(696\) | − | 2.86423e16i | − | 0.251972i | ||||||
\(697\) | −9.20897e15 | −0.0803183 | ||||||||
\(698\) | − | 8.74977e16i | − | 0.756596i | ||||||
\(699\) | − | 4.67037e16i | − | 0.400395i | ||||||
\(700\) | 7.34284e15 | + | 9.54047e15i | 0.0624131 | + | 0.0810927i | ||||
\(701\) | 5.55849e16 | 0.468435 | 0.234217 | − | 0.972184i | \(-0.424747\pi\) | ||||
0.234217 | + | 0.972184i | \(0.424747\pi\) | |||||||
\(702\) | 6.37005e16 | 0.532256 | ||||||||
\(703\) | 1.49333e17i | 1.23715i | ||||||||
\(704\) | 1.40011e16 | 0.115008 | ||||||||
\(705\) | − | 3.67468e16i | − | 0.299285i | ||||||
\(706\) | − | 1.58988e17i | − | 1.28392i | ||||||
\(707\) | 1.25522e17 | − | 9.66080e16i | 1.00508 | − | 0.773565i | ||||
\(708\) | −3.90258e16 | −0.309850 | ||||||||
\(709\) | −5.06204e16 | −0.398518 | −0.199259 | − | 0.979947i | \(-0.563854\pi\) | ||||
−0.199259 | + | 0.979947i | \(0.563854\pi\) | |||||||
\(710\) | − | 5.02708e16i | − | 0.392433i | ||||||
\(711\) | 1.00145e17 | 0.775198 | ||||||||
\(712\) | 3.49807e16i | 0.268503i | ||||||||
\(713\) | 1.30884e17i | 0.996206i | ||||||||
\(714\) | 1.58310e16 | + | 2.05690e16i | 0.119486 | + | 0.155247i | ||||
\(715\) | −1.27426e17 | −0.953721 | ||||||||
\(716\) | 9.18771e16 | 0.681914 | ||||||||
\(717\) | − | 5.57140e16i | − | 0.410062i | ||||||
\(718\) | 8.16349e16 | 0.595839 | ||||||||
\(719\) | 1.49143e17i | 1.07951i | 0.841821 | + | 0.539757i | \(0.181484\pi\) | ||||
−0.841821 | + | 0.539757i | \(0.818516\pi\) | |||||||
\(720\) | − | 3.07739e16i | − | 0.220896i | ||||||
\(721\) | −4.42035e16 | + | 3.40213e16i | −0.314663 | + | 0.242181i | ||||
\(722\) | −2.04016e17 | −1.44026 | ||||||||
\(723\) | −4.99024e16 | −0.349375 | ||||||||
\(724\) | 1.33559e17i | 0.927346i | ||||||||
\(725\) | 4.79711e16 | 0.330333 | ||||||||
\(726\) | − | 7.01699e15i | − | 0.0479216i | ||||||
\(727\) | − | 4.70655e16i | − | 0.318784i | −0.987215 | − | 0.159392i | \(-0.949047\pi\) | ||
0.987215 | − | 0.159392i | \(-0.0509533\pi\) | |||||||
\(728\) | −3.93907e16 | + | 3.03171e16i | −0.264610 | + | 0.203657i | ||||
\(729\) | 1.92995e15 | 0.0128582 | ||||||||
\(730\) | −1.14547e16 | −0.0756912 | ||||||||
\(731\) | 5.44448e16i | 0.356823i | ||||||||
\(732\) | 1.47479e16 | 0.0958658 | ||||||||
\(733\) | 9.08600e16i | 0.585799i | 0.956143 | + | 0.292900i | \(0.0946202\pi\) | ||||
−0.956143 | + | 0.292900i | \(0.905380\pi\) | |||||||
\(734\) | 8.98421e16i | 0.574518i | ||||||||
\(735\) | −1.95598e16 | + | 7.38611e16i | −0.124063 | + | 0.468481i | ||||
\(736\) | 1.62744e16 | 0.102385 | ||||||||
\(737\) | 9.71700e16 | 0.606355 | ||||||||
\(738\) | 1.17726e16i | 0.0728672i | ||||||||
\(739\) | −1.57582e17 | −0.967473 | −0.483737 | − | 0.875214i | \(-0.660721\pi\) | ||||
−0.483737 | + | 0.875214i | \(0.660721\pi\) | |||||||
\(740\) | 6.39743e16i | 0.389597i | ||||||||
\(741\) | − | 1.20301e17i | − | 0.726708i | ||||||
\(742\) | −3.73700e16 | − | 4.85544e16i | −0.223923 | − | 0.290941i | ||||
\(743\) | −3.29081e17 | −1.95600 | −0.978002 | − | 0.208597i | \(-0.933110\pi\) | ||||
−0.978002 | + | 0.208597i | \(0.933110\pi\) | |||||||
\(744\) | −4.55415e16 | −0.268515 | ||||||||
\(745\) | 8.25452e16i | 0.482785i | ||||||||
\(746\) | 7.58493e16 | 0.440067 | ||||||||
\(747\) | − | 5.72223e16i | − | 0.329338i | ||||||
\(748\) | 5.05567e16i | 0.288649i | ||||||||
\(749\) | −1.50832e17 | − | 1.95975e17i | −0.854287 | − | 1.10997i | ||||
\(750\) | 4.85082e16 | 0.272551 | ||||||||
\(751\) | −1.25278e17 | −0.698291 | −0.349146 | − | 0.937068i | \(-0.613528\pi\) | ||||
−0.349146 | + | 0.937068i | \(0.613528\pi\) | |||||||
\(752\) | − | 2.79204e16i | − | 0.154389i | ||||||
\(753\) | 8.50261e15 | 0.0466426 | ||||||||
\(754\) | 1.98063e17i | 1.07789i | ||||||||
\(755\) | 2.36915e17i | 1.27912i | ||||||||
\(756\) | 5.89581e16 | − | 4.53772e16i | 0.315800 | − | 0.243056i | ||||
\(757\) | 2.14020e17 | 1.13731 | 0.568655 | − | 0.822576i | \(-0.307464\pi\) | ||||
0.568655 | + | 0.822576i | \(0.307464\pi\) | |||||||
\(758\) | −1.22725e17 | −0.647020 | ||||||||
\(759\) | 4.49840e16i | 0.235292i | ||||||||
\(760\) | −1.30311e17 | −0.676235 | ||||||||
\(761\) | − | 9.85642e16i | − | 0.507471i | −0.967274 | − | 0.253736i | \(-0.918341\pi\) | ||
0.967274 | − | 0.253736i | \(-0.0816593\pi\) | |||||||
\(762\) | 8.76427e16i | 0.447699i | ||||||||
\(763\) | 2.38582e17 | + | 3.09987e17i | 1.20918 | + | 1.57107i | ||||
\(764\) | −8.09134e16 | −0.406874 | ||||||||
\(765\) | 1.11122e17 | 0.554408 | ||||||||
\(766\) | − | 2.48827e17i | − | 1.23176i | ||||||
\(767\) | 2.69866e17 | 1.32549 | ||||||||
\(768\) | 5.66272e15i | 0.0275967i | ||||||||
\(769\) | − | 5.66365e16i | − | 0.273866i | −0.990580 | − | 0.136933i | \(-0.956275\pi\) | ||
0.990580 | − | 0.136933i | \(-0.0437245\pi\) | |||||||
\(770\) | −1.17939e17 | + | 9.07720e16i | −0.565866 | + | 0.435519i | ||||
\(771\) | 1.27658e16 | 0.0607746 | ||||||||
\(772\) | −1.11043e17 | −0.524551 | ||||||||
\(773\) | − | 2.50006e17i | − | 1.17185i | −0.810364 | − | 0.585927i | \(-0.800730\pi\) | ||
0.810364 | − | 0.585927i | \(-0.199270\pi\) | |||||||
\(774\) | 6.96011e16 | 0.323720 | ||||||||
\(775\) | − | 7.62745e16i | − | 0.352022i | ||||||
\(776\) | 1.26012e17i | 0.577088i | ||||||||
\(777\) | −5.46633e16 | + | 4.20717e16i | −0.248410 | + | 0.191189i | ||||
\(778\) | 1.59524e17 | 0.719366 | ||||||||
\(779\) | 4.98503e16 | 0.223071 | ||||||||
\(780\) | − | 5.15370e16i | − | 0.228850i | ||||||
\(781\) | 1.05578e17 | 0.465228 | ||||||||
\(782\) | 5.87652e16i | 0.256968i | ||||||||
\(783\) | − | 2.96451e17i | − | 1.28642i | ||||||
\(784\) | −1.48617e16 | + | 5.61201e16i | −0.0639987 | + | 0.241670i | ||||
\(785\) | 3.45872e17 | 1.47808 | ||||||||
\(786\) | 3.09970e16 | 0.131457 | ||||||||
\(787\) | − | 2.38004e17i | − | 1.00169i | −0.865536 | − | 0.500847i | \(-0.833022\pi\) | ||
0.865536 | − | 0.500847i | \(-0.166978\pi\) | |||||||
\(788\) | −7.24268e16 | −0.302511 | ||||||||
\(789\) | 5.75568e16i | 0.238580i | ||||||||
\(790\) | − | 1.81668e17i | − | 0.747334i | ||||||
\(791\) | −2.60085e17 | − | 3.37926e17i | −1.06183 | − | 1.37963i | ||||
\(792\) | 6.46306e16 | 0.261871 | ||||||||
\(793\) | −1.01983e17 | −0.410098 | ||||||||
\(794\) | 1.20542e17i | 0.481077i | ||||||||
\(795\) | 6.35264e16 | 0.251624 | ||||||||
\(796\) | − | 1.21638e17i | − | 0.478178i | ||||||
\(797\) | − | 4.63716e17i | − | 1.80926i | −0.426193 | − | 0.904632i | \(-0.640145\pi\) | ||
0.426193 | − | 0.904632i | \(-0.359855\pi\) | |||||||
\(798\) | −8.56966e16 | − | 1.11345e17i | −0.331854 | − | 0.431174i | ||||
\(799\) | 1.00818e17 | 0.387487 | ||||||||
\(800\) | −9.48413e15 | −0.0361791 | ||||||||
\(801\) | 1.61474e17i | 0.611376i | ||||||||
\(802\) | −9.90634e16 | −0.372278 | ||||||||
\(803\) | − | 2.40568e16i | − | 0.0897316i | ||||||
\(804\) | 3.93001e16i | 0.145498i | ||||||||
\(805\) | −1.37088e17 | + | 1.05510e17i | −0.503760 | + | 0.387720i | ||||
\(806\) | 3.14922e17 | 1.14867 | ||||||||
\(807\) | 1.61124e17 | 0.583338 | ||||||||
\(808\) | 1.24781e17i | 0.448414i | ||||||||
\(809\) | 6.94137e15 | 0.0247602 | 0.0123801 | − | 0.999923i | \(-0.496059\pi\) | ||||
0.0123801 | + | 0.999923i | \(0.496059\pi\) | |||||||
\(810\) | − | 9.93204e16i | − | 0.351664i | ||||||
\(811\) | 3.87199e17i | 1.36085i | 0.732819 | + | 0.680424i | \(0.238204\pi\) | ||||
−0.732819 | + | 0.680424i | \(0.761796\pi\) | |||||||
\(812\) | 1.41091e17 | + | 1.83318e17i | 0.492223 | + | 0.639541i | ||||
\(813\) | −6.27089e16 | −0.217163 | ||||||||
\(814\) | −1.34357e17 | −0.461865 | ||||||||
\(815\) | 3.47283e17i | 1.18505i | ||||||||
\(816\) | −2.04475e16 | −0.0692628 | ||||||||
\(817\) | − | 2.94722e17i | − | 0.991016i | ||||||
\(818\) | 2.38644e17i | 0.796584i | ||||||||
\(819\) | −1.81832e17 | + | 1.39947e17i | −0.602512 | + | 0.463724i | ||||
\(820\) | 2.13559e16 | 0.0702481 | ||||||||
\(821\) | 1.91848e17 | 0.626467 | 0.313233 | − | 0.949676i | \(-0.398588\pi\) | ||||
0.313233 | + | 0.949676i | \(0.398588\pi\) | |||||||
\(822\) | − | 7.86714e16i | − | 0.255027i | ||||||
\(823\) | −2.54026e17 | −0.817485 | −0.408742 | − | 0.912650i | \(-0.634033\pi\) | ||||
−0.408742 | + | 0.912650i | \(0.634033\pi\) | |||||||
\(824\) | − | 4.39425e16i | − | 0.140385i | ||||||
\(825\) | − | 2.62151e16i | − | 0.0831433i | ||||||
\(826\) | 2.49775e17 | − | 1.92240e17i | 0.786445 | − | 0.605288i | ||||
\(827\) | −2.42292e16 | −0.0757367 | −0.0378683 | − | 0.999283i | \(-0.512057\pi\) | ||||
−0.0378683 | + | 0.999283i | \(0.512057\pi\) | |||||||
\(828\) | 7.51242e16 | 0.233130 | ||||||||
\(829\) | 1.45965e17i | 0.449698i | 0.974394 | + | 0.224849i | \(0.0721889\pi\) | ||||
−0.974394 | + | 0.224849i | \(0.927811\pi\) | |||||||
\(830\) | −1.03804e17 | −0.317500 | ||||||||
\(831\) | 1.53735e17i | 0.466839i | ||||||||
\(832\) | − | 3.91581e16i | − | 0.118054i | ||||||
\(833\) | −2.02644e17 | − | 5.36640e16i | −0.606547 | − | 0.160625i | ||||
\(834\) | 4.47588e16 | 0.133009 | ||||||||
\(835\) | −1.88511e17 | −0.556183 | ||||||||
\(836\) | − | 2.73675e17i | − | 0.801674i | ||||||
\(837\) | −4.71360e17 | −1.37088 | ||||||||
\(838\) | 1.06270e17i | 0.306865i | ||||||||
\(839\) | 4.16440e17i | 1.19393i | 0.802266 | + | 0.596967i | \(0.203628\pi\) | ||||
−0.802266 | + | 0.596967i | \(0.796372\pi\) | |||||||
\(840\) | −3.67125e16 | − | 4.77001e16i | −0.104505 | − | 0.135783i | ||||
\(841\) | 5.67938e17 | 1.60518 | ||||||||
\(842\) | −3.20774e17 | −0.900173 | ||||||||
\(843\) | 2.22856e17i | 0.620953i | ||||||||
\(844\) | −1.28568e17 | −0.355696 | ||||||||
\(845\) | − | 4.31690e16i | − | 0.118586i | ||||||
\(846\) | − | 1.28884e17i | − | 0.351540i | ||||||
\(847\) | 3.45654e16 | + | 4.49105e16i | 0.0936141 | + | 0.121632i | ||||
\(848\) | 4.82677e16 | 0.129802 | ||||||||
\(849\) | 2.96030e17 | 0.790478 | ||||||||
\(850\) | − | 3.42463e16i | − | 0.0908029i | ||||||
\(851\) | −1.56172e17 | −0.411174 | ||||||||
\(852\) | 4.27006e16i | 0.111634i | ||||||||
\(853\) | 4.06359e17i | 1.05491i | 0.849583 | + | 0.527455i | \(0.176854\pi\) | ||||
−0.849583 | + | 0.527455i | \(0.823146\pi\) | |||||||
\(854\) | −9.43903e16 | + | 7.26476e16i | −0.243321 | + | 0.187273i | ||||
\(855\) | −6.01526e17 | −1.53978 | ||||||||
\(856\) | 1.94818e17 | 0.495206 | ||||||||
\(857\) | − | 1.14470e17i | − | 0.288939i | −0.989509 | − | 0.144470i | \(-0.953852\pi\) | ||
0.989509 | − | 0.144470i | \(-0.0461476\pi\) | |||||||
\(858\) | 1.08237e17 | 0.271301 | ||||||||
\(859\) | − | 3.66056e17i | − | 0.911148i | −0.890198 | − | 0.455574i | \(-0.849434\pi\) | ||
0.890198 | − | 0.455574i | \(-0.150566\pi\) | |||||||
\(860\) | − | 1.26259e17i | − | 0.312085i | ||||||
\(861\) | 1.40444e16 | + | 1.82477e16i | 0.0344733 | + | 0.0447908i | ||||
\(862\) | 2.92556e17 | 0.713124 | ||||||||
\(863\) | 4.37768e17 | 1.05969 | 0.529845 | − | 0.848095i | \(-0.322250\pi\) | ||||
0.529845 | + | 0.848095i | \(0.322250\pi\) | |||||||
\(864\) | 5.86099e16i | 0.140893i | ||||||||
\(865\) | −6.77372e17 | −1.61708 | ||||||||
\(866\) | − | 2.00042e17i | − | 0.474257i | ||||||
\(867\) | 1.13705e17i | 0.267711i | ||||||||
\(868\) | 2.91477e17 | − | 2.24335e17i | 0.681531 | − | 0.524541i | ||||
\(869\) | 3.81534e17 | 0.885961 | ||||||||
\(870\) | −2.39844e17 | −0.553113 | ||||||||
\(871\) | − | 2.71763e17i | − | 0.622418i | ||||||
\(872\) | −3.08156e17 | −0.700926 | ||||||||
\(873\) | 5.81685e17i | 1.31402i | ||||||||
\(874\) | − | 3.18110e17i | − | 0.713688i | ||||||
\(875\) | −3.10465e17 | + | 2.38950e17i | −0.691774 | + | 0.532425i | ||||
\(876\) | 9.72973e15 | 0.0215316 | ||||||||
\(877\) | 2.71033e17 | 0.595696 | 0.297848 | − | 0.954613i | \(-0.403731\pi\) | ||||
0.297848 | + | 0.954613i | \(0.403731\pi\) | |||||||
\(878\) | 5.99926e17i | 1.30957i | ||||||||
\(879\) | 1.82892e17 | 0.396516 | ||||||||
\(880\) | − | 1.17243e17i | − | 0.252458i | ||||||
\(881\) | − | 2.64245e17i | − | 0.565134i | −0.959248 | − | 0.282567i | \(-0.908814\pi\) | ||
0.959248 | − | 0.282567i | \(-0.0911860\pi\) | |||||||
\(882\) | −6.86029e16 | + | 2.59056e17i | −0.145724 | + | 0.550278i | ||||
\(883\) | −1.41964e17 | −0.299511 | −0.149756 | − | 0.988723i | \(-0.547849\pi\) | ||||
−0.149756 | + | 0.988723i | \(0.547849\pi\) | |||||||
\(884\) | 1.41396e17 | 0.296295 | ||||||||
\(885\) | 3.26794e17i | 0.680165i | ||||||||
\(886\) | 3.09892e17 | 0.640631 | ||||||||
\(887\) | 6.27004e17i | 1.28745i | 0.765259 | + | 0.643723i | \(0.222611\pi\) | ||||
−0.765259 | + | 0.643723i | \(0.777389\pi\) | |||||||
\(888\) | − | 5.43405e16i | − | 0.110827i | ||||||
\(889\) | −4.31725e17 | − | 5.60935e17i | −0.874574 | − | 1.13632i | ||||
\(890\) | 2.92921e17 | 0.589401 | ||||||||
\(891\) | 2.08590e17 | 0.416897 | ||||||||
\(892\) | 1.38334e17i | 0.274625i | ||||||||
\(893\) | −5.45751e17 | −1.07618 | ||||||||
\(894\) | − | 7.01148e16i | − | 0.137336i | ||||||
\(895\) | − | 7.69360e17i | − | 1.49690i | ||||||
\(896\) | −2.78943e16 | − | 3.62428e16i | −0.0539098 | − | 0.0700445i | ||||
\(897\) | 1.25810e17 | 0.241525 | ||||||||
\(898\) | −6.30747e17 | −1.20281 | ||||||||
\(899\) | − | 1.46560e18i | − | 2.77623i | ||||||
\(900\) | −4.37797e16 | −0.0823792 | ||||||||
\(901\) | 1.74290e17i | 0.325779i | ||||||||
\(902\) | 4.48512e16i | 0.0832788i | ||||||||
\(903\) | 1.07883e17 | − | 8.30323e16i | 0.198988 | − | 0.153151i | ||||
\(904\) | 3.35930e17 | 0.615515 | ||||||||
\(905\) | 1.11840e18 | 2.03565 | ||||||||
\(906\) | − | 2.01238e17i | − | 0.363866i | ||||||
\(907\) | 1.03608e18 | 1.86101 | 0.930504 | − | 0.366281i | \(-0.119369\pi\) | ||||
0.930504 | + | 0.366281i | \(0.119369\pi\) | |||||||
\(908\) | 2.51001e17i | 0.447879i | ||||||||
\(909\) | 5.76000e17i | 1.02103i | ||||||||
\(910\) | 2.53869e17 | + | 3.29850e17i | 0.447056 | + | 0.580855i | ||||
\(911\) | −6.25946e17 | −1.09503 | −0.547516 | − | 0.836795i | \(-0.684426\pi\) | ||||
−0.547516 | + | 0.836795i | \(0.684426\pi\) | |||||||
\(912\) | 1.10687e17 | 0.192366 | ||||||||
\(913\) | − | 2.18006e17i | − | 0.376395i | ||||||
\(914\) | −3.35974e17 | −0.576274 | ||||||||
\(915\) | − | 1.23496e17i | − | 0.210439i | ||||||
\(916\) | − | 1.45529e17i | − | 0.246363i | ||||||
\(917\) | −1.98388e17 | + | 1.52690e17i | −0.333657 | + | 0.256800i | ||||
\(918\) | −2.11635e17 | −0.353615 | ||||||||
\(919\) | 1.26202e17 | 0.209495 | 0.104748 | − | 0.994499i | \(-0.466597\pi\) | ||||
0.104748 | + | 0.994499i | \(0.466597\pi\) | |||||||
\(920\) | − | 1.36278e17i | − | 0.224750i | ||||||
\(921\) | −4.58922e16 | −0.0751936 | ||||||||
\(922\) | 6.74611e16i | 0.109817i | ||||||||
\(923\) | − | 2.95278e17i | − | 0.477552i | ||||||
\(924\) | 1.00179e17 | − | 7.71027e16i | 0.160970 | − | 0.123890i | ||||
\(925\) | 9.10114e16 | 0.145293 | ||||||||
\(926\) | −2.30078e17 | −0.364929 | ||||||||
\(927\) | − | 2.02843e17i | − | 0.319655i | ||||||
\(928\) | −1.82235e17 | −0.285328 | ||||||||
\(929\) | − | 5.28504e17i | − | 0.822155i | −0.911600 | − | 0.411078i | \(-0.865153\pi\) | ||
0.911600 | − | 0.411078i | \(-0.134847\pi\) | |||||||
\(930\) | 3.81355e17i | 0.589429i | ||||||||
\(931\) | 1.09696e18 | + | 2.90496e17i | 1.68458 | + | 0.446110i | ||||
\(932\) | −2.97150e17 | −0.453399 | ||||||||
\(933\) | −2.96794e17 | −0.449952 | ||||||||
\(934\) | 4.59687e16i | 0.0692439i | ||||||||
\(935\) | 4.23352e17 | 0.633624 | ||||||||
\(936\) | − | 1.80758e17i | − | 0.268808i | ||||||
\(937\) | − | 7.15104e17i | − | 1.05665i | −0.849042 | − | 0.528325i | \(-0.822820\pi\) | ||
0.849042 | − | 0.528325i | \(-0.177180\pi\) | |||||||
\(938\) | −1.93591e17 | − | 2.51531e17i | −0.284229 | − | 0.369295i | ||||
\(939\) | −3.56490e17 | −0.520061 | ||||||||
\(940\) | −2.33800e17 | −0.338905 | ||||||||
\(941\) | 1.08977e18i | 1.56963i | 0.619727 | + | 0.784817i | \(0.287243\pi\) | ||||
−0.619727 | + | 0.784817i | \(0.712757\pi\) | |||||||
\(942\) | −2.93787e17 | −0.420463 | ||||||||
\(943\) | 5.21333e16i | 0.0741387i | ||||||||
\(944\) | 2.48300e17i | 0.350868i | ||||||||
\(945\) | −3.79979e17 | − | 4.93703e17i | −0.533542 | − | 0.693226i | ||||
\(946\) | 2.65167e17 | 0.369975 | ||||||||
\(947\) | −3.24790e17 | −0.450300 | −0.225150 | − | 0.974324i | \(-0.572287\pi\) | ||||
−0.225150 | + | 0.974324i | \(0.572287\pi\) | |||||||
\(948\) | 1.54310e17i | 0.212591i | ||||||||
\(949\) | −6.72818e16 | −0.0921086 | ||||||||
\(950\) | 1.85383e17i | 0.252190i | ||||||||
\(951\) | − | 1.95352e17i | − | 0.264080i | ||||||
\(952\) | 1.30869e17 | − | 1.00724e17i | 0.175799 | − | 0.135304i | ||||
\(953\) | 9.80184e16 | 0.130843 | 0.0654215 | − | 0.997858i | \(-0.479161\pi\) | ||||
0.0654215 | + | 0.997858i | \(0.479161\pi\) | |||||||
\(954\) | 2.22809e17 | 0.295557 | ||||||||
\(955\) | 6.77552e17i | 0.893146i | ||||||||
\(956\) | −3.54478e17 | −0.464346 | ||||||||
\(957\) | − | 5.03716e17i | − | 0.655713i | ||||||
\(958\) | 4.51860e17i | 0.584535i | ||||||||
\(959\) | 3.87532e17 | + | 5.03517e17i | 0.498191 | + | 0.647295i | ||||
\(960\) | 4.74184e16 | 0.0605787 | ||||||||
\(961\) | −1.54265e18 | −1.95851 | ||||||||
\(962\) | 3.75768e17i | 0.474100i | ||||||||
\(963\) | 8.99298e17 | 1.12758 | ||||||||
\(964\) | 3.17502e17i | 0.395625i | ||||||||
\(965\) | 9.29851e17i | 1.15146i | ||||||||
\(966\) | 1.16444e17 | − | 8.96213e16i | 0.143303 | − | 0.110293i | ||||
\(967\) | −2.08918e17 | −0.255515 | −0.127757 | − | 0.991805i | \(-0.540778\pi\) | ||||
−0.127757 | + | 0.991805i | \(0.540778\pi\) | |||||||
\(968\) | −4.46453e16 | −0.0542654 | ||||||||
\(969\) | 3.99681e17i | 0.482804i | ||||||||
\(970\) | 1.05520e18 | 1.26679 | ||||||||
\(971\) | − | 2.81318e17i | − | 0.335647i | −0.985817 | − | 0.167824i | \(-0.946326\pi\) | ||
0.985817 | − | 0.167824i | \(-0.0536739\pi\) | |||||||
\(972\) | 4.20435e17i | 0.498541i | ||||||||
\(973\) | −2.86467e17 | + | 2.20480e17i | −0.337597 | + | 0.259832i | ||||
\(974\) | −3.14071e17 | −0.367853 | ||||||||
\(975\) | −7.33179e16 | −0.0853458 | ||||||||
\(976\) | − | 9.38329e16i | − | 0.108557i | ||||||
\(977\) | 1.86043e17 | 0.213918 | 0.106959 | − | 0.994263i | \(-0.465889\pi\) | ||||
0.106959 | + | 0.994263i | \(0.465889\pi\) | |||||||
\(978\) | − | 2.94986e17i | − | 0.337108i | ||||||
\(979\) | 6.15186e17i | 0.698732i | ||||||||
\(980\) | 4.69938e17 | + | 1.24449e17i | 0.530498 | + | 0.140486i | ||||
\(981\) | −1.42248e18 | −1.59600 | ||||||||
\(982\) | −1.16828e18 | −1.30280 | ||||||||
\(983\) | 7.20268e16i | 0.0798313i | 0.999203 | + | 0.0399156i | \(0.0127089\pi\) | ||||
−0.999203 | + | 0.0399156i | \(0.987291\pi\) | |||||||
\(984\) | −1.81399e16 | −0.0199832 | ||||||||
\(985\) | 6.06487e17i | 0.664055i | ||||||||
\(986\) | − | 6.58033e17i | − | 0.716121i | ||||||
\(987\) | −1.53755e17 | − | 1.99772e17i | −0.166313 | − | 0.216089i | ||||
\(988\) | −7.65410e17 | −0.822910 | ||||||||
\(989\) | 3.08220e17 | 0.329369 | ||||||||
\(990\) | − | 5.41203e17i | − | 0.574843i | ||||||
\(991\) | 8.33698e17 | 0.880171 | 0.440085 | − | 0.897956i | \(-0.354948\pi\) | ||||
0.440085 | + | 0.897956i | \(0.354948\pi\) | |||||||
\(992\) | 2.89755e17i | 0.304062i | ||||||||
\(993\) | − | 1.74825e15i | − | 0.00182351i | ||||||
\(994\) | −2.10342e17 | − | 2.73295e17i | −0.218075 | − | 0.283343i | ||||
\(995\) | −1.01857e18 | −1.04967 | ||||||||
\(996\) | 8.81720e16 | 0.0903181 | ||||||||
\(997\) | − | 5.85320e17i | − | 0.595968i | −0.954571 | − | 0.297984i | \(-0.903686\pi\) | ||
0.954571 | − | 0.297984i | \(-0.0963142\pi\) | |||||||
\(998\) | 1.00235e18 | 1.01446 | ||||||||
\(999\) | − | 5.62431e17i | − | 0.565817i |
(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 | 14.13.b.a.13.7 | yes | 8 | |
3.2 | odd | 2 | 126.13.c.a.55.4 | 8 | |||
4.3 | odd | 2 | 112.13.c.c.97.3 | 8 | |||
7.2 | even | 3 | 98.13.d.b.31.2 | 16 | |||
7.3 | odd | 6 | 98.13.d.b.19.2 | 16 | |||
7.4 | even | 3 | 98.13.d.b.19.3 | 16 | |||
7.5 | odd | 6 | 98.13.d.b.31.3 | 16 | |||
7.6 | odd | 2 | inner | 14.13.b.a.13.6 | ✓ | 8 | |
21.20 | even | 2 | 126.13.c.a.55.1 | 8 | |||
28.27 | even | 2 | 112.13.c.c.97.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.13.b.a.13.6 | ✓ | 8 | 7.6 | odd | 2 | inner | |
14.13.b.a.13.7 | yes | 8 | 1.1 | even | 1 | trivial | |
98.13.d.b.19.2 | 16 | 7.3 | odd | 6 | |||
98.13.d.b.19.3 | 16 | 7.4 | even | 3 | |||
98.13.d.b.31.2 | 16 | 7.2 | even | 3 | |||
98.13.d.b.31.3 | 16 | 7.5 | odd | 6 | |||
112.13.c.c.97.3 | 8 | 4.3 | odd | 2 | |||
112.13.c.c.97.6 | 8 | 28.27 | even | 2 | |||
126.13.c.a.55.1 | 8 | 21.20 | even | 2 | |||
126.13.c.a.55.4 | 8 | 3.2 | odd | 2 |