Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,35,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 35, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 35);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 35 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(21.9676962128\) |
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: | \( x^{10} + 789518143 x^{8} + \cdots + 50\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{54}\cdot 3^{65}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.2 | ||
Root | \(-16987.2i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.35.b.a.2.9 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 203846.i | − | 1.55522i | −0.628746 | − | 0.777611i | \(-0.716432\pi\) | ||
0.628746 | − | 0.777611i | \(-0.283568\pi\) | |||||||
\(3\) | −1.15096e8 | − | 5.85668e7i | −0.891249 | − | 0.453513i | ||||
\(4\) | −2.43733e10 | −1.41871 | ||||||||
\(5\) | − | 1.79877e11i | − | 0.235768i | −0.993027 | − | 0.117884i | \(-0.962389\pi\) | ||
0.993027 | − | 0.117884i | \(-0.0376111\pi\) | |||||||
\(6\) | −1.19386e13 | + | 2.34619e13i | −0.705313 | + | 1.38609i | ||||
\(7\) | −2.97937e14 | −1.28073 | −0.640365 | − | 0.768070i | \(-0.721217\pi\) | ||||
−0.640365 | + | 0.768070i | \(0.721217\pi\) | |||||||
\(8\) | 1.46635e15i | 0.651190i | ||||||||
\(9\) | 9.81704e15 | + | 1.34816e16i | 0.588651 | + | 0.808387i | ||||
\(10\) | −3.66671e16 | −0.366671 | ||||||||
\(11\) | 5.45809e17i | 1.07985i | 0.841712 | + | 0.539927i | \(0.181548\pi\) | ||||
−0.841712 | + | 0.539927i | \(0.818452\pi\) | |||||||
\(12\) | 2.80527e18 | + | 1.42747e18i | 1.26443 | + | 0.643405i | ||||
\(13\) | 6.76117e18 | 0.781601 | 0.390800 | − | 0.920475i | \(-0.372198\pi\) | ||||
0.390800 | + | 0.920475i | \(0.372198\pi\) | |||||||
\(14\) | 6.07333e19i | 1.99182i | ||||||||
\(15\) | −1.05348e19 | + | 2.07031e19i | −0.106924 | + | 0.210128i | ||||
\(16\) | −1.19820e20 | −0.405968 | ||||||||
\(17\) | − | 1.38305e21i | − | 1.67188i | −0.548821 | − | 0.835940i | \(-0.684923\pi\) | ||
0.548821 | − | 0.835940i | \(-0.315077\pi\) | |||||||
\(18\) | 2.74817e21 | − | 2.00116e21i | 1.25722 | − | 0.915483i | ||||
\(19\) | −8.87671e21 | −1.61972 | −0.809862 | − | 0.586621i | \(-0.800458\pi\) | ||||
−0.809862 | + | 0.586621i | \(0.800458\pi\) | |||||||
\(20\) | 4.38419e21i | 0.334487i | ||||||||
\(21\) | 3.42914e22 | + | 1.74492e22i | 1.14145 | + | 0.580829i | ||||
\(22\) | 1.11261e23 | 1.67941 | ||||||||
\(23\) | − | 2.99358e22i | − | 0.212235i | −0.994354 | − | 0.106118i | \(-0.966158\pi\) | ||
0.994354 | − | 0.106118i | \(-0.0338420\pi\) | |||||||
\(24\) | 8.58794e22 | − | 1.68771e23i | 0.295323 | − | 0.580373i | ||||
\(25\) | 5.49721e23 | 0.944413 | ||||||||
\(26\) | − | 1.37824e24i | − | 1.21556i | ||||||
\(27\) | −3.40329e23 | − | 2.12663e24i | −0.158021 | − | 0.987436i | ||||
\(28\) | 7.26171e24 | 1.81699 | ||||||||
\(29\) | 3.17183e24i | 0.437063i | 0.975830 | + | 0.218532i | \(0.0701267\pi\) | ||||
−0.975830 | + | 0.218532i | \(0.929873\pi\) | |||||||
\(30\) | 4.22024e24 | + | 2.14748e24i | 0.326796 | + | 0.166290i | ||||
\(31\) | 1.17602e24 | 0.0521514 | 0.0260757 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260757 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(32\) | 4.96166e25i | 1.28256i | ||||||||
\(33\) | 3.19663e25 | − | 6.28205e25i | 0.489728 | − | 0.962420i | ||||
\(34\) | −2.81928e26 | −2.60014 | ||||||||
\(35\) | 5.35919e25i | 0.301955i | ||||||||
\(36\) | −2.39274e26 | − | 3.28591e26i | −0.835127 | − | 1.14687i | ||||
\(37\) | 3.74912e26 | 0.821296 | 0.410648 | − | 0.911794i | \(-0.365302\pi\) | ||||
0.410648 | + | 0.911794i | \(0.365302\pi\) | |||||||
\(38\) | 1.80948e27i | 2.51903i | ||||||||
\(39\) | −7.78185e26 | − | 3.95980e26i | −0.696601 | − | 0.354466i | ||||
\(40\) | 2.63762e26 | 0.153530 | ||||||||
\(41\) | 2.13908e27i | 0.818281i | 0.912471 | + | 0.409140i | \(0.134171\pi\) | ||||
−0.912471 | + | 0.409140i | \(0.865829\pi\) | |||||||
\(42\) | 3.55695e27 | − | 6.99016e27i | 0.903317 | − | 1.77521i | ||||
\(43\) | 4.08388e27 | 0.695200 | 0.347600 | − | 0.937643i | \(-0.386997\pi\) | ||||
0.347600 | + | 0.937643i | \(0.386997\pi\) | |||||||
\(44\) | − | 1.33032e28i | − | 1.53200i | ||||||
\(45\) | 2.42503e27 | − | 1.76586e27i | 0.190592 | − | 0.138785i | ||||
\(46\) | −6.10229e27 | −0.330073 | ||||||||
\(47\) | 4.95016e28i | 1.85761i | 0.370564 | + | 0.928807i | \(0.379164\pi\) | ||||
−0.370564 | + | 0.928807i | \(0.620836\pi\) | |||||||
\(48\) | 1.37909e28 | + | 7.01750e27i | 0.361818 | + | 0.184112i | ||||
\(49\) | 3.46495e28 | 0.640272 | ||||||||
\(50\) | − | 1.12058e29i | − | 1.46877i | ||||||
\(51\) | −8.10006e28 | + | 1.59183e29i | −0.758220 | + | 1.49006i | ||||
\(52\) | −1.64792e29 | −1.10887 | ||||||||
\(53\) | − | 9.35752e28i | − | 0.455482i | −0.973722 | − | 0.227741i | \(-0.926866\pi\) | ||
0.973722 | − | 0.227741i | \(-0.0731339\pi\) | |||||||
\(54\) | −4.33506e29 | + | 6.93746e28i | −1.53568 | + | 0.245757i | ||||
\(55\) | 9.81784e28 | 0.254595 | ||||||||
\(56\) | − | 4.36880e29i | − | 0.833999i | ||||||
\(57\) | 1.02167e30 | + | 5.19881e29i | 1.44358 | + | 0.734566i | ||||
\(58\) | 6.46565e29 | 0.679730 | ||||||||
\(59\) | 6.32368e29i | 0.497148i | 0.968613 | + | 0.248574i | \(0.0799619\pi\) | ||||
−0.968613 | + | 0.248574i | \(0.920038\pi\) | |||||||
\(60\) | 2.56768e29 | − | 5.04603e29i | 0.151694 | − | 0.298111i | ||||
\(61\) | 4.42775e29 | 0.197504 | 0.0987519 | − | 0.995112i | \(-0.468515\pi\) | ||||
0.0987519 | + | 0.995112i | \(0.468515\pi\) | |||||||
\(62\) | − | 2.39727e29i | − | 0.0811069i | ||||||
\(63\) | −2.92486e30 | − | 4.01667e30i | −0.753904 | − | 1.03533i | ||||
\(64\) | 8.05565e30 | 1.58870 | ||||||||
\(65\) | − | 1.21618e30i | − | 0.184276i | ||||||
\(66\) | −1.28057e31 | − | 6.51620e30i | −1.49678 | − | 0.761636i | ||||
\(67\) | −4.63018e30 | −0.419108 | −0.209554 | − | 0.977797i | \(-0.567201\pi\) | ||||
−0.209554 | + | 0.977797i | \(0.567201\pi\) | |||||||
\(68\) | 3.37094e31i | 2.37192i | ||||||||
\(69\) | −1.75324e30 | + | 3.44549e30i | −0.0962516 | + | 0.189155i | ||||
\(70\) | 1.09245e31 | 0.469607 | ||||||||
\(71\) | 2.74044e30i | 0.0925611i | 0.998928 | + | 0.0462805i | \(0.0147368\pi\) | ||||
−0.998928 | + | 0.0462805i | \(0.985263\pi\) | |||||||
\(72\) | −1.97688e31 | + | 1.43952e31i | −0.526414 | + | 0.383324i | ||||
\(73\) | −2.72565e31 | −0.574092 | −0.287046 | − | 0.957917i | \(-0.592673\pi\) | ||||
−0.287046 | + | 0.957917i | \(0.592673\pi\) | |||||||
\(74\) | − | 7.64242e31i | − | 1.27730i | ||||||
\(75\) | −6.32707e31 | − | 3.21954e31i | −0.841708 | − | 0.428304i | ||||
\(76\) | 2.16355e32 | 2.29792 | ||||||||
\(77\) | − | 1.62617e32i | − | 1.38300i | ||||||
\(78\) | −8.07189e31 | + | 1.58630e32i | −0.551274 | + | 1.08337i | ||||
\(79\) | 1.93130e32 | 1.06216 | 0.531080 | − | 0.847322i | \(-0.321787\pi\) | ||||
0.531080 | + | 0.847322i | \(0.321787\pi\) | |||||||
\(80\) | 2.15529e31i | 0.0957142i | ||||||||
\(81\) | −8.53797e31 | + | 2.64699e32i | −0.306979 | + | 0.951716i | ||||
\(82\) | 4.36044e32 | 1.27261 | ||||||||
\(83\) | 2.76431e32i | 0.656537i | 0.944584 | + | 0.328269i | \(0.106465\pi\) | ||||
−0.944584 | + | 0.328269i | \(0.893535\pi\) | |||||||
\(84\) | −8.35794e32 | − | 4.25295e32i | −1.61939 | − | 0.824029i | ||||
\(85\) | −2.48778e32 | −0.394176 | ||||||||
\(86\) | − | 8.32483e32i | − | 1.08119i | ||||||
\(87\) | 1.85764e32 | − | 3.65065e32i | 0.198214 | − | 0.389532i | ||||
\(88\) | −8.00347e32 | −0.703191 | ||||||||
\(89\) | 2.71501e33i | 1.96853i | 0.176706 | + | 0.984264i | \(0.443456\pi\) | ||||
−0.176706 | + | 0.984264i | \(0.556544\pi\) | |||||||
\(90\) | −3.59963e32 | − | 4.94332e32i | −0.215842 | − | 0.296412i | ||||
\(91\) | −2.01440e33 | −1.00102 | ||||||||
\(92\) | 7.29634e32i | 0.301101i | ||||||||
\(93\) | −1.35355e32 | − | 6.88757e31i | −0.0464799 | − | 0.0236513i | ||||
\(94\) | 1.00907e34 | 2.88900 | ||||||||
\(95\) | 1.59671e33i | 0.381879i | ||||||||
\(96\) | 2.90589e33 | − | 5.71068e33i | 0.581658 | − | 1.14308i | ||||
\(97\) | −1.23468e33 | −0.207222 | −0.103611 | − | 0.994618i | \(-0.533040\pi\) | ||||
−0.103611 | + | 0.994618i | \(0.533040\pi\) | |||||||
\(98\) | − | 7.06317e33i | − | 0.995764i | ||||||
\(99\) | −7.35839e33 | + | 5.35823e33i | −0.872940 | + | 0.635658i | ||||
\(100\) | −1.33985e34 | −1.33985 | ||||||||
\(101\) | − | 1.60999e34i | − | 1.35944i | −0.733473 | − | 0.679718i | \(-0.762102\pi\) | ||
0.733473 | − | 0.679718i | \(-0.237898\pi\) | |||||||
\(102\) | 3.24489e34 | + | 1.65116e34i | 2.31738 | + | 1.17920i | ||||
\(103\) | −1.43441e34 | −0.867841 | −0.433920 | − | 0.900951i | \(-0.642870\pi\) | ||||
−0.433920 | + | 0.900951i | \(0.642870\pi\) | |||||||
\(104\) | 9.91424e33i | 0.508971i | ||||||||
\(105\) | 3.13871e33 | − | 6.16822e33i | 0.136941 | − | 0.269118i | ||||
\(106\) | −1.90749e34 | −0.708375 | ||||||||
\(107\) | 1.60322e34i | 0.507537i | 0.967265 | + | 0.253768i | \(0.0816701\pi\) | ||||
−0.967265 | + | 0.253768i | \(0.918330\pi\) | |||||||
\(108\) | 8.29493e33 | + | 5.18331e34i | 0.224186 | + | 1.40089i | ||||
\(109\) | −5.19945e34 | −1.20145 | −0.600727 | − | 0.799454i | \(-0.705122\pi\) | ||||
−0.600727 | + | 0.799454i | \(0.705122\pi\) | |||||||
\(110\) | − | 2.00133e34i | − | 0.395952i | ||||||
\(111\) | −4.31509e34 | − | 2.19574e34i | −0.731980 | − | 0.372469i | ||||
\(112\) | 3.56990e34 | 0.519935 | ||||||||
\(113\) | 1.59663e34i | 0.199927i | 0.994991 | + | 0.0999633i | \(0.0318725\pi\) | ||||
−0.994991 | + | 0.0999633i | \(0.968127\pi\) | |||||||
\(114\) | 1.05976e35 | − | 2.08264e35i | 1.14241 | − | 2.24508i | ||||
\(115\) | −5.38475e33 | −0.0500383 | ||||||||
\(116\) | − | 7.73080e34i | − | 0.620067i | ||||||
\(117\) | 6.63747e34 | + | 9.11515e34i | 0.460090 | + | 0.631836i | ||||
\(118\) | 1.28906e35 | 0.773175 | ||||||||
\(119\) | 4.12061e35i | 2.14123i | ||||||||
\(120\) | −3.03580e34 | − | 1.54477e34i | −0.136833 | − | 0.0696278i | ||||
\(121\) | −4.24310e34 | −0.166086 | ||||||||
\(122\) | − | 9.02578e34i | − | 0.307162i | ||||||
\(123\) | 1.25279e35 | − | 2.46200e35i | 0.371101 | − | 0.729292i | ||||
\(124\) | −2.86635e34 | −0.0739878 | ||||||||
\(125\) | − | 2.03584e35i | − | 0.458430i | ||||||
\(126\) | −8.18783e35 | + | 5.96221e35i | −1.61016 | + | 1.17249i | ||||
\(127\) | −6.17065e34 | −0.106088 | −0.0530442 | − | 0.998592i | \(-0.516892\pi\) | ||||
−0.0530442 | + | 0.998592i | \(0.516892\pi\) | |||||||
\(128\) | − | 7.89704e35i | − | 1.18821i | ||||||
\(129\) | −4.70039e35 | − | 2.39180e35i | −0.619596 | − | 0.315282i | ||||
\(130\) | −2.47913e35 | −0.286591 | ||||||||
\(131\) | 3.37852e35i | 0.342858i | 0.985196 | + | 0.171429i | \(0.0548385\pi\) | ||||
−0.985196 | + | 0.171429i | \(0.945162\pi\) | |||||||
\(132\) | −7.79124e35 | + | 1.53114e36i | −0.694784 | + | 1.36540i | ||||
\(133\) | 2.64470e36 | 2.07443 | ||||||||
\(134\) | 9.43843e35i | 0.651806i | ||||||||
\(135\) | −3.82532e35 | + | 6.12172e34i | −0.232806 | + | 0.0372563i | ||||
\(136\) | 2.02803e36 | 1.08871 | ||||||||
\(137\) | − | 2.58108e36i | − | 1.22335i | −0.791107 | − | 0.611677i | \(-0.790495\pi\) | ||
0.791107 | − | 0.611677i | \(-0.209505\pi\) | |||||||
\(138\) | 7.02350e35 | + | 3.57392e35i | 0.294177 | + | 0.149692i | ||||
\(139\) | −2.72993e36 | −1.01135 | −0.505673 | − | 0.862725i | \(-0.668756\pi\) | ||||
−0.505673 | + | 0.862725i | \(0.668756\pi\) | |||||||
\(140\) | − | 1.30621e36i | − | 0.428388i | ||||||
\(141\) | 2.89915e36 | − | 5.69744e36i | 0.842453 | − | 1.65560i | ||||
\(142\) | 5.58628e35 | 0.143953 | ||||||||
\(143\) | 3.69031e36i | 0.844015i | ||||||||
\(144\) | −1.17628e36 | − | 1.61537e36i | −0.238973 | − | 0.328179i | ||||
\(145\) | 5.70539e35 | 0.103045 | ||||||||
\(146\) | 5.55613e36i | 0.892841i | ||||||||
\(147\) | −3.98803e36 | − | 2.02931e36i | −0.570642 | − | 0.290372i | ||||
\(148\) | −9.13783e36 | −1.16518 | ||||||||
\(149\) | 1.30238e37i | 1.48105i | 0.672026 | + | 0.740527i | \(0.265424\pi\) | ||||
−0.672026 | + | 0.740527i | \(0.734576\pi\) | |||||||
\(150\) | −6.56290e36 | + | 1.28975e37i | −0.666108 | + | 1.30904i | ||||
\(151\) | 1.53327e37 | 1.38998 | 0.694992 | − | 0.719017i | \(-0.255408\pi\) | ||||
0.694992 | + | 0.719017i | \(0.255408\pi\) | |||||||
\(152\) | − | 1.30164e37i | − | 1.05475i | ||||||
\(153\) | 1.86457e37 | − | 1.35774e37i | 1.35153 | − | 0.984154i | ||||
\(154\) | −3.31488e37 | −2.15088 | ||||||||
\(155\) | − | 2.11538e35i | − | 0.0122956i | ||||||
\(156\) | 1.89669e37 | + | 9.65134e36i | 0.988277 | + | 0.502886i | ||||
\(157\) | −2.25738e37 | −1.05514 | −0.527570 | − | 0.849512i | \(-0.676897\pi\) | ||||
−0.527570 | + | 0.849512i | \(0.676897\pi\) | |||||||
\(158\) | − | 3.93688e37i | − | 1.65189i | ||||||
\(159\) | −5.48040e36 | + | 1.07701e37i | −0.206567 | + | 0.405948i | ||||
\(160\) | 8.92487e36 | 0.302386 | ||||||||
\(161\) | 8.91899e36i | 0.271816i | ||||||||
\(162\) | 5.39579e37 | + | 1.74043e37i | 1.48013 | + | 0.477421i | ||||
\(163\) | 2.51834e37 | 0.622194 | 0.311097 | − | 0.950378i | \(-0.399304\pi\) | ||||
0.311097 | + | 0.950378i | \(0.399304\pi\) | |||||||
\(164\) | − | 5.21365e37i | − | 1.16091i | ||||||
\(165\) | −1.12999e37 | − | 5.74999e36i | −0.226908 | − | 0.115462i | ||||
\(166\) | 5.63494e37 | 1.02106 | ||||||||
\(167\) | 6.73804e37i | 1.10244i | 0.834361 | + | 0.551218i | \(0.185837\pi\) | ||||
−0.834361 | + | 0.551218i | \(0.814163\pi\) | |||||||
\(168\) | −2.55867e37 | + | 5.02832e37i | −0.378230 | + | 0.743302i | ||||
\(169\) | −2.91163e37 | −0.389100 | ||||||||
\(170\) | 5.07123e37i | 0.613030i | ||||||||
\(171\) | −8.71431e37 | − | 1.19672e38i | −0.953452 | − | 1.30936i | ||||
\(172\) | −9.95377e37 | −0.986288 | ||||||||
\(173\) | 4.60014e37i | 0.413036i | 0.978443 | + | 0.206518i | \(0.0662131\pi\) | ||||
−0.978443 | + | 0.206518i | \(0.933787\pi\) | |||||||
\(174\) | −7.44171e37 | − | 3.78672e37i | −0.605809 | − | 0.308267i | ||||
\(175\) | −1.63782e38 | −1.20954 | ||||||||
\(176\) | − | 6.53991e37i | − | 0.438386i | ||||||
\(177\) | 3.70358e37 | − | 7.27831e37i | 0.225463 | − | 0.443083i | ||||
\(178\) | 5.53444e38 | 3.06150 | ||||||||
\(179\) | 7.46180e37i | 0.375269i | 0.982239 | + | 0.187634i | \(0.0600820\pi\) | ||||
−0.982239 | + | 0.187634i | \(0.939918\pi\) | |||||||
\(180\) | −5.91059e37 | + | 4.30398e37i | −0.270395 | + | 0.196896i | ||||
\(181\) | −2.13615e38 | −0.889396 | −0.444698 | − | 0.895681i | \(-0.646689\pi\) | ||||
−0.444698 | + | 0.895681i | \(0.646689\pi\) | |||||||
\(182\) | 4.10628e38i | 1.55681i | ||||||||
\(183\) | −5.09616e37 | − | 2.59319e37i | −0.176025 | − | 0.0895706i | ||||
\(184\) | 4.38964e37 | 0.138206 | ||||||||
\(185\) | − | 6.74379e37i | − | 0.193635i | ||||||
\(186\) | −1.40400e37 | + | 2.75916e37i | −0.0367831 | + | 0.0722865i | ||||
\(187\) | 7.54880e38 | 1.80539 | ||||||||
\(188\) | − | 1.20652e39i | − | 2.63542i | ||||||
\(189\) | 1.01396e38 | + | 6.33603e38i | 0.202382 | + | 1.26464i | ||||
\(190\) | 3.25484e38 | 0.593906 | ||||||||
\(191\) | − | 5.98739e38i | − | 0.999242i | −0.866244 | − | 0.499621i | \(-0.833473\pi\) | ||
0.866244 | − | 0.499621i | \(-0.166527\pi\) | |||||||
\(192\) | −9.27173e38 | − | 4.71793e38i | −1.41592 | − | 0.720495i | ||||
\(193\) | −5.27026e38 | −0.736814 | −0.368407 | − | 0.929665i | \(-0.620097\pi\) | ||||
−0.368407 | + | 0.929665i | \(0.620097\pi\) | |||||||
\(194\) | 2.51685e38i | 0.322276i | ||||||||
\(195\) | −7.12276e37 | + | 1.39977e38i | −0.0835718 | + | 0.164236i | ||||
\(196\) | −8.44524e38 | −0.908361 | ||||||||
\(197\) | 1.44438e39i | 1.42480i | 0.701772 | + | 0.712402i | \(0.252393\pi\) | ||||
−0.701772 | + | 0.712402i | \(0.747607\pi\) | |||||||
\(198\) | 1.09225e39 | + | 1.49998e39i | 0.988588 | + | 1.35762i | ||||
\(199\) | 2.12251e38 | 0.176338 | 0.0881691 | − | 0.996106i | \(-0.471898\pi\) | ||||
0.0881691 | + | 0.996106i | \(0.471898\pi\) | |||||||
\(200\) | 8.06083e38i | 0.614993i | ||||||||
\(201\) | 5.32915e38 | + | 2.71175e38i | 0.373530 | + | 0.190071i | ||||
\(202\) | −3.28189e39 | −2.11422 | ||||||||
\(203\) | − | 9.45006e38i | − | 0.559760i | ||||||
\(204\) | 1.97425e39 | − | 3.87982e39i | 1.07570 | − | 2.11397i | ||||
\(205\) | 3.84771e38 | 0.192924 | ||||||||
\(206\) | 2.92398e39i | 1.34968i | ||||||||
\(207\) | 4.03583e38 | − | 2.93881e38i | 0.171568 | − | 0.124933i | ||||
\(208\) | −8.10127e38 | −0.317305 | ||||||||
\(209\) | − | 4.84499e39i | − | 1.74907i | ||||||
\(210\) | −1.25737e39 | − | 6.39813e38i | −0.418537 | − | 0.212973i | ||||
\(211\) | 2.65596e39 | 0.815491 | 0.407745 | − | 0.913096i | \(-0.366315\pi\) | ||||
0.407745 | + | 0.913096i | \(0.366315\pi\) | |||||||
\(212\) | 2.28074e39i | 0.646198i | ||||||||
\(213\) | 1.60499e38 | − | 3.15414e38i | 0.0419777 | − | 0.0824950i | ||||
\(214\) | 3.26809e39 | 0.789332 | ||||||||
\(215\) | − | 7.34595e38i | − | 0.163906i | ||||||
\(216\) | 3.11839e39 | − | 4.99041e38i | 0.643009 | − | 0.102902i | ||||
\(217\) | −3.50380e38 | −0.0667919 | ||||||||
\(218\) | 1.05989e40i | 1.86853i | ||||||||
\(219\) | 3.13712e39 | + | 1.59633e39i | 0.511660 | + | 0.260359i | ||||
\(220\) | −2.39293e39 | −0.361197 | ||||||||
\(221\) | − | 9.35102e39i | − | 1.30674i | ||||||
\(222\) | −4.47592e39 | + | 8.79613e39i | −0.579271 | + | 1.13839i | ||||
\(223\) | −1.51320e40 | −1.81432 | −0.907160 | − | 0.420787i | \(-0.861754\pi\) | ||||
−0.907160 | + | 0.420787i | \(0.861754\pi\) | |||||||
\(224\) | − | 1.47826e40i | − | 1.64261i | ||||||
\(225\) | 5.39664e39 | + | 7.41113e39i | 0.555930 | + | 0.763452i | ||||
\(226\) | 3.25466e39 | 0.310930 | ||||||||
\(227\) | 6.49041e38i | 0.0575218i | 0.999586 | + | 0.0287609i | \(0.00915614\pi\) | ||||
−0.999586 | + | 0.0287609i | \(0.990844\pi\) | |||||||
\(228\) | −2.49016e40 | − | 1.26712e40i | −2.04802 | − | 1.04214i | ||||
\(229\) | 1.50995e40 | 1.15282 | 0.576408 | − | 0.817162i | \(-0.304454\pi\) | ||||
0.576408 | + | 0.817162i | \(0.304454\pi\) | |||||||
\(230\) | 1.09766e39i | 0.0778206i | ||||||||
\(231\) | −9.52394e39 | + | 1.87166e40i | −0.627210 | + | 1.23260i | ||||
\(232\) | −4.65102e39 | −0.284611 | ||||||||
\(233\) | 1.83862e40i | 1.04578i | 0.852400 | + | 0.522891i | \(0.175147\pi\) | ||||
−0.852400 | + | 0.522891i | \(0.824853\pi\) | |||||||
\(234\) | 1.85809e40 | − | 1.35302e40i | 0.982645 | − | 0.715542i | ||||
\(235\) | 8.90418e39 | 0.437966 | ||||||||
\(236\) | − | 1.54129e40i | − | 0.705310i | ||||||
\(237\) | −2.22285e40 | − | 1.13110e40i | −0.946649 | − | 0.481703i | ||||
\(238\) | 8.39969e40 | 3.33008 | ||||||||
\(239\) | 2.31681e40i | 0.855317i | 0.903940 | + | 0.427658i | \(0.140661\pi\) | ||||
−0.903940 | + | 0.427658i | \(0.859339\pi\) | |||||||
\(240\) | 1.26228e39 | − | 2.48066e39i | 0.0434076 | − | 0.0853052i | ||||
\(241\) | −2.31568e40 | −0.741974 | −0.370987 | − | 0.928638i | \(-0.620980\pi\) | ||||
−0.370987 | + | 0.928638i | \(0.620980\pi\) | |||||||
\(242\) | 8.64939e39i | 0.258300i | ||||||||
\(243\) | 2.53295e40 | − | 2.54654e40i | 0.705211 | − | 0.708997i | ||||
\(244\) | −1.07919e40 | −0.280201 | ||||||||
\(245\) | − | 6.23265e39i | − | 0.150956i | ||||||
\(246\) | −5.01869e40 | − | 2.55377e40i | −1.13421 | − | 0.577144i | ||||
\(247\) | −6.00170e40 | −1.26598 | ||||||||
\(248\) | 1.72446e39i | 0.0339605i | ||||||||
\(249\) | 1.61897e40 | − | 3.18162e40i | 0.297748 | − | 0.585139i | ||||
\(250\) | −4.14998e40 | −0.712961 | ||||||||
\(251\) | 1.45158e39i | 0.0233016i | 0.999932 | + | 0.0116508i | \(0.00370866\pi\) | ||||
−0.999932 | + | 0.0116508i | \(0.996291\pi\) | |||||||
\(252\) | 7.12885e40 | + | 9.78996e40i | 1.06957 | + | 1.46883i | ||||
\(253\) | 1.63392e40 | 0.229183 | ||||||||
\(254\) | 1.25786e40i | 0.164991i | ||||||||
\(255\) | 2.86334e40 | + | 1.45701e40i | 0.351309 | + | 0.178764i | ||||
\(256\) | −2.25829e40 | −0.259239 | ||||||||
\(257\) | − | 2.58352e40i | − | 0.277555i | −0.990324 | − | 0.138778i | \(-0.955683\pi\) | ||
0.990324 | − | 0.138778i | \(-0.0443173\pi\) | |||||||
\(258\) | −4.87559e40 | + | 9.58155e40i | −0.490334 | + | 0.963609i | ||||
\(259\) | −1.11700e41 | −1.05186 | ||||||||
\(260\) | 2.96422e40i | 0.261435i | ||||||||
\(261\) | −4.27614e40 | + | 3.11380e40i | −0.353316 | + | 0.257278i | ||||
\(262\) | 6.88698e40 | 0.533221 | ||||||||
\(263\) | 3.82679e40i | 0.277707i | 0.990313 | + | 0.138853i | \(0.0443417\pi\) | ||||
−0.990313 | + | 0.138853i | \(0.955658\pi\) | |||||||
\(264\) | 9.21169e40 | + | 4.68738e40i | 0.626718 | + | 0.318906i | ||||
\(265\) | −1.68320e40 | −0.107388 | ||||||||
\(266\) | − | 5.39112e41i | − | 3.22620i | ||||||
\(267\) | 1.59009e41 | − | 3.12487e41i | 0.892753 | − | 1.75445i | ||||
\(268\) | 1.12853e41 | 0.594594 | ||||||||
\(269\) | 9.18662e40i | 0.454325i | 0.973857 | + | 0.227163i | \(0.0729449\pi\) | ||||
−0.973857 | + | 0.227163i | \(0.927055\pi\) | |||||||
\(270\) | 1.24789e40 | + | 7.79776e40i | 0.0579417 | + | 0.362064i | ||||
\(271\) | 5.88942e40 | 0.256800 | 0.128400 | − | 0.991722i | \(-0.459016\pi\) | ||||
0.128400 | + | 0.991722i | \(0.459016\pi\) | |||||||
\(272\) | 1.65717e41i | 0.678729i | ||||||||
\(273\) | 2.31850e41 | + | 1.17977e41i | 0.892159 | + | 0.453976i | ||||
\(274\) | −5.26143e41 | −1.90259 | ||||||||
\(275\) | 3.00043e41i | 1.01983i | ||||||||
\(276\) | 4.27323e40 | − | 8.39781e40i | 0.136553 | − | 0.268356i | ||||
\(277\) | 2.24409e41 | 0.674348 | 0.337174 | − | 0.941442i | \(-0.390529\pi\) | ||||
0.337174 | + | 0.941442i | \(0.390529\pi\) | |||||||
\(278\) | 5.56485e41i | 1.57287i | ||||||||
\(279\) | 1.15450e40 | + | 1.58546e40i | 0.0306990 | + | 0.0421585i | ||||
\(280\) | −7.85845e40 | −0.196630 | ||||||||
\(281\) | 8.35899e40i | 0.196855i | 0.995144 | + | 0.0984275i | \(0.0313813\pi\) | ||||
−0.995144 | + | 0.0984275i | \(0.968619\pi\) | |||||||
\(282\) | −1.16140e42 | − | 5.90980e41i | −2.57482 | − | 1.31020i | ||||
\(283\) | 4.36918e41 | 0.912074 | 0.456037 | − | 0.889961i | \(-0.349268\pi\) | ||||
0.456037 | + | 0.889961i | \(0.349268\pi\) | |||||||
\(284\) | − | 6.67936e40i | − | 0.131318i | ||||||
\(285\) | 9.35144e40 | − | 1.83776e41i | 0.173187 | − | 0.340349i | ||||
\(286\) | 7.52255e41 | 1.31263 | ||||||||
\(287\) | − | 6.37313e41i | − | 1.04800i | ||||||
\(288\) | −6.68912e41 | + | 4.87089e41i | −1.03680 | + | 0.754980i | ||||
\(289\) | −1.22849e42 | −1.79518 | ||||||||
\(290\) | − | 1.16302e41i | − | 0.160259i | ||||||
\(291\) | 1.42107e41 | + | 7.23113e40i | 0.184686 | + | 0.0939778i | ||||
\(292\) | 6.64331e41 | 0.814472 | ||||||||
\(293\) | − | 2.32629e41i | − | 0.269100i | −0.990907 | − | 0.134550i | \(-0.957041\pi\) | ||
0.990907 | − | 0.134550i | \(-0.0429590\pi\) | |||||||
\(294\) | −4.13667e41 | + | 8.12943e41i | −0.451592 | + | 0.887474i | ||||
\(295\) | 1.13748e41 | 0.117212 | ||||||||
\(296\) | 5.49752e41i | 0.534820i | ||||||||
\(297\) | 1.16074e42 | − | 1.85754e41i | 1.06629 | − | 0.170640i | ||||
\(298\) | 2.65485e42 | 2.30337 | ||||||||
\(299\) | − | 2.02401e41i | − | 0.165883i | ||||||
\(300\) | 1.54212e42 | + | 7.84708e41i | 1.19414 | + | 0.607640i | ||||
\(301\) | −1.21674e42 | −0.890364 | ||||||||
\(302\) | − | 3.12550e42i | − | 2.16173i | ||||||
\(303\) | −9.42917e41 | + | 1.85303e42i | −0.616523 | + | 1.21160i | ||||
\(304\) | 1.06361e42 | 0.657555 | ||||||||
\(305\) | − | 7.96448e40i | − | 0.0465651i | ||||||
\(306\) | −2.76770e42 | − | 3.80085e42i | −1.53058 | − | 2.10192i | ||||
\(307\) | −3.20258e42 | −1.67551 | −0.837756 | − | 0.546044i | \(-0.816133\pi\) | ||||
−0.837756 | + | 0.546044i | \(0.816133\pi\) | |||||||
\(308\) | 3.96351e42i | 1.96208i | ||||||||
\(309\) | 1.65095e42 | + | 8.40087e41i | 0.773463 | + | 0.393577i | ||||
\(310\) | −4.31212e40 | −0.0191224 | ||||||||
\(311\) | − | 3.41897e42i | − | 1.43538i | −0.696360 | − | 0.717692i | \(-0.745198\pi\) | ||
0.696360 | − | 0.717692i | \(-0.254802\pi\) | |||||||
\(312\) | 5.80645e41 | − | 1.14109e42i | 0.230825 | − | 0.453620i | ||||
\(313\) | 4.76701e41 | 0.179470 | 0.0897350 | − | 0.995966i | \(-0.471398\pi\) | ||||
0.0897350 | + | 0.995966i | \(0.471398\pi\) | |||||||
\(314\) | 4.60157e42i | 1.64097i | ||||||||
\(315\) | −7.22506e41 | + | 5.26114e41i | −0.244097 | + | 0.177746i | ||||
\(316\) | −4.70722e42 | −1.50690 | ||||||||
\(317\) | 1.47092e42i | 0.446254i | 0.974789 | + | 0.223127i | \(0.0716265\pi\) | ||||
−0.974789 | + | 0.223127i | \(0.928373\pi\) | |||||||
\(318\) | 2.19545e42 | + | 1.11716e42i | 0.631339 | + | 0.321257i | ||||
\(319\) | −1.73122e42 | −0.471965 | ||||||||
\(320\) | − | 1.44902e42i | − | 0.374564i | ||||||
\(321\) | 9.38952e41 | − | 1.84524e42i | 0.230175 | − | 0.452342i | ||||
\(322\) | 1.81810e42 | 0.422735 | ||||||||
\(323\) | 1.22769e43i | 2.70798i | ||||||||
\(324\) | 2.08098e42 | − | 6.45159e42i | 0.435515 | − | 1.35021i | ||||
\(325\) | 3.71676e42 | 0.738154 | ||||||||
\(326\) | − | 5.13354e42i | − | 0.967649i | ||||||
\(327\) | 5.98437e42 | + | 3.04515e42i | 1.07080 | + | 0.544875i | ||||
\(328\) | −3.13665e42 | −0.532857 | ||||||||
\(329\) | − | 1.47484e43i | − | 2.37910i | ||||||
\(330\) | −1.17211e42 | + | 2.30345e42i | −0.179569 | + | 0.352892i | ||||
\(331\) | −1.30392e43 | −1.89746 | −0.948732 | − | 0.316081i | \(-0.897633\pi\) | ||||
−0.948732 | + | 0.316081i | \(0.897633\pi\) | |||||||
\(332\) | − | 6.73754e42i | − | 0.931438i | ||||||
\(333\) | 3.68053e42 | + | 5.05442e42i | 0.483457 | + | 0.663925i | ||||
\(334\) | 1.37352e43 | 1.71453 | ||||||||
\(335\) | 8.32861e41i | 0.0988123i | ||||||||
\(336\) | −4.10881e42 | − | 2.09077e42i | −0.463392 | − | 0.235798i | ||||
\(337\) | 3.57010e42 | 0.382800 | 0.191400 | − | 0.981512i | \(-0.438697\pi\) | ||||
0.191400 | + | 0.981512i | \(0.438697\pi\) | |||||||
\(338\) | 5.93523e42i | 0.605137i | ||||||||
\(339\) | 9.35095e41 | − | 1.83766e42i | 0.0906694 | − | 0.178184i | ||||
\(340\) | 6.06354e42 | 0.559222 | ||||||||
\(341\) | 6.41882e41i | 0.0563159i | ||||||||
\(342\) | −2.43947e43 | + | 1.77638e43i | −2.03635 | + | 1.48283i | ||||
\(343\) | 5.80006e42 | 0.460715 | ||||||||
\(344\) | 5.98840e42i | 0.452707i | ||||||||
\(345\) | 6.19764e41 | + | 3.15368e41i | 0.0445966 | + | 0.0226930i | ||||
\(346\) | 9.37720e42 | 0.642362 | ||||||||
\(347\) | − | 2.26027e43i | − | 1.47421i | −0.675777 | − | 0.737106i | \(-0.736192\pi\) | ||
0.675777 | − | 0.737106i | \(-0.263808\pi\) | |||||||
\(348\) | −4.52768e42 | + | 8.89785e42i | −0.281209 | + | 0.552634i | ||||
\(349\) | −1.34307e43 | −0.794450 | −0.397225 | − | 0.917721i | \(-0.630027\pi\) | ||||
−0.397225 | + | 0.917721i | \(0.630027\pi\) | |||||||
\(350\) | 3.33863e43i | 1.88110i | ||||||||
\(351\) | −2.30102e42 | − | 1.43785e43i | −0.123509 | − | 0.771781i | ||||
\(352\) | −2.70812e43 | −1.38498 | ||||||||
\(353\) | 1.97828e43i | 0.964088i | 0.876147 | + | 0.482044i | \(0.160105\pi\) | ||||
−0.876147 | + | 0.482044i | \(0.839895\pi\) | |||||||
\(354\) | −1.48365e43 | − | 7.54959e42i | −0.689092 | − | 0.350645i | ||||
\(355\) | 4.92941e41 | 0.0218229 | ||||||||
\(356\) | − | 6.61738e43i | − | 2.79277i | ||||||
\(357\) | 2.41331e43 | − | 4.74266e43i | 0.971076 | − | 1.90837i | ||||
\(358\) | 1.52106e43 | 0.583626 | ||||||||
\(359\) | 3.01626e43i | 1.10373i | 0.833933 | + | 0.551865i | \(0.186084\pi\) | ||||
−0.833933 | + | 0.551865i | \(0.813916\pi\) | |||||||
\(360\) | 2.58937e42 | + | 3.55594e42i | 0.0903755 | + | 0.124112i | ||||
\(361\) | 4.87614e43 | 1.62350 | ||||||||
\(362\) | 4.35445e43i | 1.38321i | ||||||||
\(363\) | 4.88364e42 | + | 2.48505e42i | 0.148024 | + | 0.0753221i | ||||
\(364\) | 4.90977e43 | 1.42016 | ||||||||
\(365\) | 4.90281e42i | 0.135353i | ||||||||
\(366\) | −5.28611e42 | + | 1.03883e43i | −0.139302 | + | 0.273758i | ||||
\(367\) | −3.90052e43 | −0.981295 | −0.490648 | − | 0.871358i | \(-0.663240\pi\) | ||||
−0.490648 | + | 0.871358i | \(0.663240\pi\) | |||||||
\(368\) | 3.58692e42i | 0.0861607i | ||||||||
\(369\) | −2.88383e43 | + | 2.09995e43i | −0.661488 | + | 0.481682i | ||||
\(370\) | −1.37469e43 | −0.301146 | ||||||||
\(371\) | 2.78795e43i | 0.583350i | ||||||||
\(372\) | 3.29905e42 | + | 1.67873e42i | 0.0659416 | + | 0.0335544i | ||||
\(373\) | 4.80844e43 | 0.918236 | 0.459118 | − | 0.888375i | \(-0.348166\pi\) | ||||
0.459118 | + | 0.888375i | \(0.348166\pi\) | |||||||
\(374\) | − | 1.53879e44i | − | 2.80778i | ||||||
\(375\) | −1.19233e43 | + | 2.34317e43i | −0.207904 | + | 0.408576i | ||||
\(376\) | −7.25866e43 | −1.20966 | ||||||||
\(377\) | 2.14453e43i | 0.341609i | ||||||||
\(378\) | 1.29157e44 | − | 2.06693e43i | 1.96679 | − | 0.314749i | ||||
\(379\) | −1.06583e44 | −1.55175 | −0.775875 | − | 0.630886i | \(-0.782691\pi\) | ||||
−0.775875 | + | 0.630886i | \(0.782691\pi\) | |||||||
\(380\) | − | 3.89172e43i | − | 0.541776i | ||||||
\(381\) | 7.10218e42 | + | 3.61395e42i | 0.0945512 | + | 0.0481125i | ||||
\(382\) | −1.22051e44 | −1.55404 | ||||||||
\(383\) | − | 1.75688e42i | − | 0.0213975i | −0.999943 | − | 0.0106988i | \(-0.996594\pi\) | ||
0.999943 | − | 0.0106988i | \(-0.00340559\pi\) | |||||||
\(384\) | −4.62504e43 | + | 9.08918e43i | −0.538871 | + | 1.05899i | ||||
\(385\) | −2.92510e43 | −0.326068 | ||||||||
\(386\) | 1.07432e44i | 1.14591i | ||||||||
\(387\) | 4.00917e43 | + | 5.50574e43i | 0.409230 | + | 0.561990i | ||||
\(388\) | 3.00932e43 | 0.293988 | ||||||||
\(389\) | − | 5.10095e41i | − | 0.00476988i | −0.999997 | − | 0.00238494i | \(-0.999241\pi\) | ||
0.999997 | − | 0.00238494i | \(-0.000759151\pi\) | |||||||
\(390\) | 2.85338e43 | + | 1.45195e43i | 0.255424 | + | 0.129973i | ||||
\(391\) | −4.14026e43 | −0.354832 | ||||||||
\(392\) | 5.08084e43i | 0.416939i | ||||||||
\(393\) | 1.97869e43 | − | 3.88855e43i | 0.155491 | − | 0.305572i | ||||
\(394\) | 2.94431e44 | 2.21589 | ||||||||
\(395\) | − | 3.47396e43i | − | 0.250423i | ||||||
\(396\) | 1.79348e44 | − | 1.30598e44i | 1.23845 | − | 0.901815i | ||||
\(397\) | 7.73555e43 | 0.511744 | 0.255872 | − | 0.966711i | \(-0.417637\pi\) | ||||
0.255872 | + | 0.966711i | \(0.417637\pi\) | |||||||
\(398\) | − | 4.32664e43i | − | 0.274245i | ||||||
\(399\) | −3.04395e44 | − | 1.54892e44i | −1.84883 | − | 0.940782i | ||||
\(400\) | −6.58678e43 | −0.383401 | ||||||||
\(401\) | − | 2.78483e44i | − | 1.55362i | −0.629737 | − | 0.776808i | \(-0.716837\pi\) | ||
0.629737 | − | 0.776808i | \(-0.283163\pi\) | |||||||
\(402\) | 5.52778e43 | − | 1.08633e44i | 0.295603 | − | 0.580921i | ||||
\(403\) | 7.95127e42 | 0.0407615 | ||||||||
\(404\) | 3.92407e44i | 1.92865i | ||||||||
\(405\) | 4.76132e43 | + | 1.53578e43i | 0.224384 | + | 0.0723759i | ||||
\(406\) | −1.92636e44 | −0.870551 | ||||||||
\(407\) | 2.04630e44i | 0.886880i | ||||||||
\(408\) | −2.33418e44 | − | 1.18775e44i | −0.970314 | − | 0.493745i | ||||
\(409\) | 2.45834e44 | 0.980271 | 0.490136 | − | 0.871646i | \(-0.336947\pi\) | ||||
0.490136 | + | 0.871646i | \(0.336947\pi\) | |||||||
\(410\) | − | 7.84341e43i | − | 0.300040i | ||||||
\(411\) | −1.51166e44 | + | 2.97073e44i | −0.554808 | + | 1.09031i | ||||
\(412\) | 3.49613e44 | 1.23122 | ||||||||
\(413\) | − | 1.88406e44i | − | 0.636713i | ||||||
\(414\) | −5.99065e43 | − | 8.22688e43i | −0.194298 | − | 0.266827i | ||||
\(415\) | 4.97235e43 | 0.154790 | ||||||||
\(416\) | 3.35466e44i | 1.00245i | ||||||||
\(417\) | 3.14204e44 | + | 1.59883e44i | 0.901362 | + | 0.458659i | ||||
\(418\) | −9.87632e44 | −2.72018 | ||||||||
\(419\) | 3.06939e44i | 0.811733i | 0.913932 | + | 0.405866i | \(0.133030\pi\) | ||||
−0.913932 | + | 0.405866i | \(0.866970\pi\) | |||||||
\(420\) | −7.65006e43 | + | 1.50340e44i | −0.194280 | + | 0.381800i | ||||
\(421\) | 5.45542e44 | 1.33055 | 0.665277 | − | 0.746596i | \(-0.268313\pi\) | ||||
0.665277 | + | 0.746596i | \(0.268313\pi\) | |||||||
\(422\) | − | 5.41406e44i | − | 1.26827i | ||||||
\(423\) | −6.67361e44 | + | 4.85959e44i | −1.50167 | + | 1.09349i | ||||
\(424\) | 1.37214e44 | 0.296605 | ||||||||
\(425\) | − | 7.60290e44i | − | 1.57895i | ||||||
\(426\) | −6.42959e43 | − | 3.27170e43i | −0.128298 | − | 0.0652846i | ||||
\(427\) | −1.31919e44 | −0.252949 | ||||||||
\(428\) | − | 3.90756e44i | − | 0.720049i | ||||||
\(429\) | 2.16130e44 | − | 4.24740e44i | 0.382772 | − | 0.752228i | ||||
\(430\) | −1.49744e44 | −0.254910 | ||||||||
\(431\) | 1.40207e44i | 0.229433i | 0.993398 | + | 0.114717i | \(0.0365960\pi\) | ||||
−0.993398 | + | 0.114717i | \(0.963404\pi\) | |||||||
\(432\) | 4.07783e43 | + | 2.54814e44i | 0.0641513 | + | 0.400867i | ||||
\(433\) | 1.02287e45 | 1.54712 | 0.773560 | − | 0.633723i | \(-0.218474\pi\) | ||||
0.773560 | + | 0.633723i | \(0.218474\pi\) | |||||||
\(434\) | 7.14235e43i | 0.103876i | ||||||||
\(435\) | −6.56668e43 | − | 3.34146e43i | −0.0918392 | − | 0.0467325i | ||||
\(436\) | 1.26728e45 | 1.70452 | ||||||||
\(437\) | 2.65732e44i | 0.343763i | ||||||||
\(438\) | 3.25405e44 | − | 6.39489e44i | 0.404915 | − | 0.795744i | ||||
\(439\) | −4.46827e44 | −0.534863 | −0.267432 | − | 0.963577i | \(-0.586175\pi\) | ||||
−0.267432 | + | 0.963577i | \(0.586175\pi\) | |||||||
\(440\) | 1.43964e44i | 0.165790i | ||||||||
\(441\) | 3.40156e44 | + | 4.67132e44i | 0.376897 | + | 0.517587i | ||||
\(442\) | −1.90617e45 | −2.03227 | ||||||||
\(443\) | − | 4.00047e44i | − | 0.410438i | −0.978716 | − | 0.205219i | \(-0.934209\pi\) | ||
0.978716 | − | 0.205219i | \(-0.0657907\pi\) | |||||||
\(444\) | 1.05173e45 | + | 5.35174e44i | 1.03847 | + | 0.528426i | ||||
\(445\) | 4.88367e44 | 0.464116 | ||||||||
\(446\) | 3.08460e45i | 2.82167i | ||||||||
\(447\) | 7.62762e44 | − | 1.49899e45i | 0.671678 | − | 1.31999i | ||||
\(448\) | −2.40008e45 | −2.03469 | ||||||||
\(449\) | − | 3.21986e44i | − | 0.262814i | −0.991328 | − | 0.131407i | \(-0.958051\pi\) | ||
0.991328 | − | 0.131407i | \(-0.0419495\pi\) | |||||||
\(450\) | 1.51073e45 | − | 1.10008e45i | 1.18734 | − | 0.864594i | ||||
\(451\) | −1.16753e45 | −0.883624 | ||||||||
\(452\) | − | 3.89151e44i | − | 0.283638i | ||||||
\(453\) | −1.76473e45 | − | 8.97986e44i | −1.23882 | − | 0.630376i | ||||
\(454\) | 1.32304e44 | 0.0894591 | ||||||||
\(455\) | 3.62344e44i | 0.236008i | ||||||||
\(456\) | −7.62327e44 | + | 1.49813e45i | −0.478342 | + | 0.940044i | ||||
\(457\) | −1.13640e45 | −0.686996 | −0.343498 | − | 0.939153i | \(-0.611612\pi\) | ||||
−0.343498 | + | 0.939153i | \(0.611612\pi\) | |||||||
\(458\) | − | 3.07797e45i | − | 1.79288i | ||||||
\(459\) | −2.94123e45 | + | 4.70690e44i | −1.65087 | + | 0.264192i | ||||
\(460\) | 1.31244e44 | 0.0709900 | ||||||||
\(461\) | 1.29866e45i | 0.676985i | 0.940969 | + | 0.338493i | \(0.109917\pi\) | ||||
−0.940969 | + | 0.338493i | \(0.890083\pi\) | |||||||
\(462\) | 3.81529e45 | + | 1.94142e45i | 1.91697 | + | 0.975451i | ||||
\(463\) | 1.91002e45 | 0.925042 | 0.462521 | − | 0.886608i | \(-0.346945\pi\) | ||||
0.462521 | + | 0.886608i | \(0.346945\pi\) | |||||||
\(464\) | − | 3.80050e44i | − | 0.177433i | ||||||
\(465\) | −1.23891e43 | + | 2.43472e43i | −0.00557623 | + | 0.0109585i | ||||
\(466\) | 3.74795e45 | 1.62642 | ||||||||
\(467\) | 2.71525e45i | 1.13612i | 0.822988 | + | 0.568058i | \(0.192305\pi\) | ||||
−0.822988 | + | 0.568058i | \(0.807695\pi\) | |||||||
\(468\) | −1.61777e45 | − | 2.22166e45i | −0.652736 | − | 0.896393i | ||||
\(469\) | 1.37950e45 | 0.536765 | ||||||||
\(470\) | − | 1.81508e45i | − | 0.681134i | ||||||
\(471\) | 2.59815e45 | + | 1.32207e45i | 0.940392 | + | 0.478520i | ||||
\(472\) | −9.27273e44 | −0.323738 | ||||||||
\(473\) | 2.22902e45i | 0.750714i | ||||||||
\(474\) | −2.30570e45 | + | 4.53120e45i | −0.749155 | + | 1.47225i | ||||
\(475\) | −4.87971e45 | −1.52969 | ||||||||
\(476\) | − | 1.00433e46i | − | 3.03779i | ||||||
\(477\) | 1.26155e45 | − | 9.18632e44i | 0.368206 | − | 0.268120i | ||||
\(478\) | 4.72273e45 | 1.33021 | ||||||||
\(479\) | − | 4.10305e45i | − | 1.11533i | −0.830066 | − | 0.557665i | \(-0.811697\pi\) | ||
0.830066 | − | 0.557665i | \(-0.188303\pi\) | |||||||
\(480\) | −1.02722e45 | − | 5.22701e44i | −0.269502 | − | 0.137136i | ||||
\(481\) | 2.53484e45 | 0.641926 | ||||||||
\(482\) | 4.72042e45i | 1.15393i | ||||||||
\(483\) | 5.22356e44 | − | 1.02654e45i | 0.123272 | − | 0.242256i | ||||
\(484\) | 1.03418e45 | 0.235628 | ||||||||
\(485\) | 2.22090e44i | 0.0488562i | ||||||||
\(486\) | −5.19103e45 | − | 5.16331e45i | −1.10265 | − | 1.09676i | ||||
\(487\) | −2.80093e45 | −0.574527 | −0.287263 | − | 0.957852i | \(-0.592746\pi\) | ||||
−0.287263 | + | 0.957852i | \(0.592746\pi\) | |||||||
\(488\) | 6.49262e44i | 0.128613i | ||||||||
\(489\) | −2.89852e45 | − | 1.47491e45i | −0.554530 | − | 0.282173i | ||||
\(490\) | −1.27050e45 | −0.234769 | ||||||||
\(491\) | 1.01670e46i | 1.81471i | 0.420365 | + | 0.907355i | \(0.361902\pi\) | ||||
−0.420365 | + | 0.907355i | \(0.638098\pi\) | |||||||
\(492\) | −3.05347e45 | + | 6.00071e45i | −0.526486 | + | 1.03466i | ||||
\(493\) | 4.38679e45 | 0.730717 | ||||||||
\(494\) | 1.22342e46i | 1.96887i | ||||||||
\(495\) | 9.63821e44 | + | 1.32360e45i | 0.149868 | + | 0.205811i | ||||
\(496\) | −1.40911e44 | −0.0211718 | ||||||||
\(497\) | − | 8.16479e44i | − | 0.118546i | ||||||
\(498\) | −6.48559e45 | − | 3.30020e45i | −0.910020 | − | 0.463065i | ||||
\(499\) | −8.61330e44 | −0.116805 | −0.0584023 | − | 0.998293i | \(-0.518601\pi\) | ||||
−0.0584023 | + | 0.998293i | \(0.518601\pi\) | |||||||
\(500\) | 4.96201e45i | 0.650381i | ||||||||
\(501\) | 3.94625e45 | − | 7.75522e45i | 0.499970 | − | 0.982546i | ||||
\(502\) | 2.95898e44 | 0.0362392 | ||||||||
\(503\) | − | 1.60755e46i | − | 1.90331i | −0.307173 | − | 0.951654i | \(-0.599383\pi\) | ||
0.307173 | − | 0.951654i | \(-0.400617\pi\) | |||||||
\(504\) | 5.88985e45 | − | 4.28887e45i | 0.674194 | − | 0.490935i | ||||
\(505\) | −2.89599e45 | −0.320512 | ||||||||
\(506\) | − | 3.33069e45i | − | 0.356431i | ||||||
\(507\) | 3.35117e45 | + | 1.70525e45i | 0.346785 | + | 0.176462i | ||||
\(508\) | 1.50399e45 | 0.150509 | ||||||||
\(509\) | − | 7.93372e45i | − | 0.767847i | −0.923365 | − | 0.383923i | \(-0.874573\pi\) | ||
0.923365 | − | 0.383923i | \(-0.125427\pi\) | |||||||
\(510\) | 2.97006e45 | − | 5.83679e45i | 0.278018 | − | 0.546363i | ||||
\(511\) | 8.12073e45 | 0.735258 | ||||||||
\(512\) | − | 8.96357e45i | − | 0.785040i | ||||||
\(513\) | 3.02100e45 | + | 1.88775e46i | 0.255950 | + | 1.59937i | ||||
\(514\) | −5.26641e45 | −0.431660 | ||||||||
\(515\) | 2.58017e45i | 0.204609i | ||||||||
\(516\) | 1.14564e46 | + | 5.82960e45i | 0.879029 | + | 0.447295i | ||||
\(517\) | −2.70184e46 | −2.00595 | ||||||||
\(518\) | 2.27696e46i | 1.63587i | ||||||||
\(519\) | 2.69416e45 | − | 5.29459e45i | 0.187317 | − | 0.368118i | ||||
\(520\) | 1.78334e45 | 0.119999 | ||||||||
\(521\) | − | 1.97184e46i | − | 1.28419i | −0.766623 | − | 0.642097i | \(-0.778064\pi\) | ||
0.766623 | − | 0.642097i | \(-0.221936\pi\) | |||||||
\(522\) | 6.34736e45 | + | 8.71674e45i | 0.400124 | + | 0.549485i | ||||
\(523\) | 6.08625e45 | 0.371382 | 0.185691 | − | 0.982608i | \(-0.440548\pi\) | ||||
0.185691 | + | 0.982608i | \(0.440548\pi\) | |||||||
\(524\) | − | 8.23457e45i | − | 0.486418i | ||||||
\(525\) | 1.88507e46 | + | 9.59220e45i | 1.07800 | + | 0.548542i | ||||
\(526\) | 7.80075e45 | 0.431895 | ||||||||
\(527\) | − | 1.62649e45i | − | 0.0871908i | ||||||
\(528\) | −3.83022e45 | + | 7.52718e45i | −0.198814 | + | 0.390711i | ||||
\(529\) | 1.89990e46 | 0.954956 | ||||||||
\(530\) | 3.43113e45i | 0.167012i | ||||||||
\(531\) | −8.52534e45 | + | 6.20798e45i | −0.401888 | + | 0.292647i | ||||
\(532\) | −6.44601e46 | −2.94302 | ||||||||
\(533\) | 1.44627e46i | 0.639569i | ||||||||
\(534\) | −6.36992e46 | − | 3.24134e46i | −2.72856 | − | 1.38843i | ||||
\(535\) | 2.88381e45 | 0.119661 | ||||||||
\(536\) | − | 6.78946e45i | − | 0.272919i | ||||||
\(537\) | 4.37014e45 | − | 8.58824e45i | 0.170189 | − | 0.334458i | ||||
\(538\) | 1.87265e46 | 0.706576 | ||||||||
\(539\) | 1.89120e46i | 0.691400i | ||||||||
\(540\) | 9.32356e45 | − | 1.49206e45i | 0.330284 | − | 0.0528559i | ||||
\(541\) | −4.44680e46 | −1.52649 | −0.763245 | − | 0.646109i | \(-0.776395\pi\) | ||||
−0.763245 | + | 0.646109i | \(0.776395\pi\) | |||||||
\(542\) | − | 1.20054e46i | − | 0.399381i | ||||||
\(543\) | 2.45862e46 | + | 1.25107e46i | 0.792674 | + | 0.403353i | ||||
\(544\) | 6.86221e46 | 2.14429 | ||||||||
\(545\) | 9.35260e45i | 0.283264i | ||||||||
\(546\) | 2.40492e46 | − | 4.72617e46i | 0.706033 | − | 1.38750i | ||||
\(547\) | −6.87329e45 | −0.195605 | −0.0978026 | − | 0.995206i | \(-0.531181\pi\) | ||||
−0.0978026 | + | 0.995206i | \(0.531181\pi\) | |||||||
\(548\) | 6.29095e46i | 1.73559i | ||||||||
\(549\) | 4.34674e45 | + | 5.96932e45i | 0.116261 | + | 0.159660i | ||||
\(550\) | 6.11625e46 | 1.58606 | ||||||||
\(551\) | − | 2.81554e46i | − | 0.707922i | ||||||
\(552\) | −5.05230e45 | − | 2.57087e45i | −0.123176 | − | 0.0626781i | ||||
\(553\) | −5.75406e46 | −1.36034 | ||||||||
\(554\) | − | 4.57449e46i | − | 1.04876i | ||||||
\(555\) | −3.94962e45 | + | 7.76184e45i | −0.0878162 | + | 0.172577i | ||||
\(556\) | 6.65374e46 | 1.43481 | ||||||||
\(557\) | 7.61000e46i | 1.59164i | 0.605530 | + | 0.795822i | \(0.292961\pi\) | ||||
−0.605530 | + | 0.795822i | \(0.707039\pi\) | |||||||
\(558\) | 3.23190e45 | − | 2.35341e45i | 0.0655658 | − | 0.0477437i | ||||
\(559\) | 2.76118e46 | 0.543369 | ||||||||
\(560\) | − | 6.42141e45i | − | 0.122584i | ||||||
\(561\) | −8.68837e46 | − | 4.42109e46i | −1.60905 | − | 0.818767i | ||||
\(562\) | 1.70395e46 | 0.306153 | ||||||||
\(563\) | − | 7.61164e46i | − | 1.32689i | −0.748225 | − | 0.663446i | \(-0.769093\pi\) | ||
0.748225 | − | 0.663446i | \(-0.230907\pi\) | |||||||
\(564\) | −7.06618e46 | + | 1.38865e47i | −1.19520 | + | 2.34882i | ||||
\(565\) | 2.87196e45 | 0.0471363 | ||||||||
\(566\) | − | 8.90639e46i | − | 1.41848i | ||||||
\(567\) | 2.54378e46 | − | 7.88637e46i | 0.393158 | − | 1.21889i | ||||
\(568\) | −4.01844e45 | −0.0602749 | ||||||||
\(569\) | 5.50884e46i | 0.801958i | 0.916087 | + | 0.400979i | \(0.131330\pi\) | ||||
−0.916087 | + | 0.400979i | \(0.868670\pi\) | |||||||
\(570\) | −3.74619e46 | − | 1.90625e46i | −0.529319 | − | 0.269344i | ||||
\(571\) | 5.77202e46 | 0.791615 | 0.395808 | − | 0.918333i | \(-0.370465\pi\) | ||||
0.395808 | + | 0.918333i | \(0.370465\pi\) | |||||||
\(572\) | − | 8.99450e46i | − | 1.19741i | ||||||
\(573\) | −3.50662e46 | + | 6.89126e46i | −0.453170 | + | 0.890574i | ||||
\(574\) | −1.29914e47 | −1.62987 | ||||||||
\(575\) | − | 1.64563e46i | − | 0.200438i | ||||||
\(576\) | 7.90826e46 | + | 1.08603e47i | 0.935188 | + | 1.28428i | ||||
\(577\) | −8.48789e46 | −0.974565 | −0.487283 | − | 0.873244i | \(-0.662012\pi\) | ||||
−0.487283 | + | 0.873244i | \(0.662012\pi\) | |||||||
\(578\) | 2.50423e47i | 2.79191i | ||||||||
\(579\) | 6.06587e46 | + | 3.08662e46i | 0.656685 | + | 0.334155i | ||||
\(580\) | −1.39059e46 | −0.146192 | ||||||||
\(581\) | − | 8.23591e46i | − | 0.840848i | ||||||
\(582\) | 1.47404e46 | − | 2.89679e46i | 0.146156 | − | 0.287228i | ||||
\(583\) | 5.10742e46 | 0.491854 | ||||||||
\(584\) | − | 3.99676e46i | − | 0.373843i | ||||||
\(585\) | 1.63960e46 | − | 1.19393e46i | 0.148967 | − | 0.108475i | ||||
\(586\) | −4.74205e46 | −0.418511 | ||||||||
\(587\) | 1.53943e46i | 0.131982i | 0.997820 | + | 0.0659908i | \(0.0210208\pi\) | ||||
−0.997820 | + | 0.0659908i | \(0.978979\pi\) | |||||||
\(588\) | 9.72014e46 | + | 4.94610e46i | 0.809576 | + | 0.411954i | ||||
\(589\) | −1.04392e46 | −0.0844708 | ||||||||
\(590\) | − | 2.31871e46i | − | 0.182290i | ||||||
\(591\) | 8.45926e46 | − | 1.66242e47i | 0.646168 | − | 1.26986i | ||||
\(592\) | −4.49221e46 | −0.333420 | ||||||||
\(593\) | 1.56245e47i | 1.12687i | 0.826159 | + | 0.563437i | \(0.190521\pi\) | ||||
−0.826159 | + | 0.563437i | \(0.809479\pi\) | |||||||
\(594\) | −3.78653e46 | − | 2.36611e47i | −0.265382 | − | 1.65831i | ||||
\(595\) | 7.41201e46 | 0.504833 | ||||||||
\(596\) | − | 3.17433e47i | − | 2.10119i | ||||||
\(597\) | −2.44292e46 | − | 1.24308e46i | −0.157161 | − | 0.0799717i | ||||
\(598\) | −4.12586e46 | −0.257985 | ||||||||
\(599\) | 1.40577e47i | 0.854394i | 0.904159 | + | 0.427197i | \(0.140499\pi\) | ||||
−0.904159 | + | 0.427197i | \(0.859501\pi\) | |||||||
\(600\) | 4.72097e46 | − | 9.27771e46i | 0.278907 | − | 0.548112i | ||||
\(601\) | 1.86614e47 | 1.07171 | 0.535856 | − | 0.844309i | \(-0.319989\pi\) | ||||
0.535856 | + | 0.844309i | \(0.319989\pi\) | |||||||
\(602\) | 2.48028e47i | 1.38471i | ||||||||
\(603\) | −4.54547e46 | − | 6.24223e46i | −0.246708 | − | 0.338802i | ||||
\(604\) | −3.73708e47 | −1.97199 | ||||||||
\(605\) | 7.63235e45i | 0.0391577i | ||||||||
\(606\) | 3.77733e47 | + | 1.92210e47i | 1.88430 | + | 0.958829i | ||||
\(607\) | 2.36509e47 | 1.14720 | 0.573600 | − | 0.819135i | \(-0.305546\pi\) | ||||
0.573600 | + | 0.819135i | \(0.305546\pi\) | |||||||
\(608\) | − | 4.40432e47i | − | 2.07739i | ||||||
\(609\) | −5.53460e46 | + | 1.08767e47i | −0.253859 | + | 0.498886i | ||||
\(610\) | −1.62353e46 | −0.0724190 | ||||||||
\(611\) | 3.34689e47i | 1.45191i | ||||||||
\(612\) | −4.54457e47 | + | 3.30927e47i | −1.91743 | + | 1.39623i | ||||
\(613\) | −8.98395e46 | −0.368671 | −0.184336 | − | 0.982863i | \(-0.559013\pi\) | ||||
−0.184336 | + | 0.982863i | \(0.559013\pi\) | |||||||
\(614\) | 6.52833e47i | 2.60579i | ||||||||
\(615\) | −4.42857e46 | − | 2.25348e46i | −0.171944 | − | 0.0874938i | ||||
\(616\) | 2.38453e47 | 0.900598 | ||||||||
\(617\) | − | 3.23338e47i | − | 1.18798i | −0.804472 | − | 0.593990i | \(-0.797552\pi\) | ||
0.804472 | − | 0.593990i | \(-0.202448\pi\) | |||||||
\(618\) | 1.71248e47 | − | 3.36539e47i | 0.612100 | − | 1.20291i | ||||
\(619\) | −4.05876e47 | −1.41141 | −0.705703 | − | 0.708507i | \(-0.749369\pi\) | ||||
−0.705703 | + | 0.708507i | \(0.749369\pi\) | |||||||
\(620\) | 5.15589e45i | 0.0174439i | ||||||||
\(621\) | −6.36625e46 | + | 1.01880e46i | −0.209569 | + | 0.0335376i | ||||
\(622\) | −6.96943e47 | −2.23234 | ||||||||
\(623\) | − | 8.08902e47i | − | 2.52115i | ||||||
\(624\) | 9.32424e46 | + | 4.74465e46i | 0.282798 | + | 0.143902i | ||||
\(625\) | 2.83360e47 | 0.836330 | ||||||||
\(626\) | − | 9.71735e46i | − | 0.279116i | ||||||
\(627\) | −2.83756e47 | + | 5.57640e47i | −0.793225 | + | 1.55885i | ||||
\(628\) | 5.50197e47 | 1.49694 | ||||||||
\(629\) | − | 5.18520e47i | − | 1.37311i | ||||||
\(630\) | 1.07246e47 | + | 1.47280e47i | 0.276435 | + | 0.379624i | ||||
\(631\) | 3.21525e47 | 0.806705 | 0.403353 | − | 0.915045i | \(-0.367845\pi\) | ||||
0.403353 | + | 0.915045i | \(0.367845\pi\) | |||||||
\(632\) | 2.83196e47i | 0.691668i | ||||||||
\(633\) | −3.05690e47 | − | 1.55551e47i | −0.726806 | − | 0.369836i | ||||
\(634\) | 2.99842e47 | 0.694024 | ||||||||
\(635\) | 1.10996e46i | 0.0250122i | ||||||||
\(636\) | 1.33575e47 | − | 2.62504e47i | 0.293059 | − | 0.575923i | ||||
\(637\) | 2.34272e47 | 0.500437 | ||||||||
\(638\) | 3.52901e47i | 0.734009i | ||||||||
\(639\) | −3.69456e46 | + | 2.69030e46i | −0.0748252 | + | 0.0544862i | ||||
\(640\) | −1.42049e47 | −0.280143 | ||||||||
\(641\) | 8.34203e47i | 1.60208i | 0.598608 | + | 0.801042i | \(0.295721\pi\) | ||||
−0.598608 | + | 0.801042i | \(0.704279\pi\) | |||||||
\(642\) | −3.76144e47 | − | 1.91402e47i | −0.703492 | − | 0.357973i | ||||
\(643\) | −2.61463e47 | −0.476237 | −0.238119 | − | 0.971236i | \(-0.576531\pi\) | ||||
−0.238119 | + | 0.971236i | \(0.576531\pi\) | |||||||
\(644\) | − | 2.17385e47i | − | 0.385629i | ||||||
\(645\) | −4.30229e46 | + | 8.45491e46i | −0.0743335 | + | 0.146081i | ||||
\(646\) | 2.50260e48 | 4.21151 | ||||||||
\(647\) | 2.68818e47i | 0.440642i | 0.975427 | + | 0.220321i | \(0.0707105\pi\) | ||||
−0.975427 | + | 0.220321i | \(0.929289\pi\) | |||||||
\(648\) | −3.88142e47 | − | 1.25196e47i | −0.619748 | − | 0.199902i | ||||
\(649\) | −3.45152e47 | −0.536847 | ||||||||
\(650\) | − | 7.57646e47i | − | 1.14799i | ||||||
\(651\) | 4.03273e46 | + | 2.05206e46i | 0.0595282 | + | 0.0302910i | ||||
\(652\) | −6.13803e47 | −0.882714 | ||||||||
\(653\) | 1.04474e47i | 0.146381i | 0.997318 | + | 0.0731907i | \(0.0233182\pi\) | ||||
−0.997318 | + | 0.0731907i | \(0.976682\pi\) | |||||||
\(654\) | 6.20742e47 | − | 1.21989e48i | 0.847402 | − | 1.66532i | ||||
\(655\) | 6.07718e46 | 0.0808350 | ||||||||
\(656\) | − | 2.56306e47i | − | 0.332196i | ||||||
\(657\) | −2.67578e47 | − | 3.67462e47i | −0.337940 | − | 0.464089i | ||||
\(658\) | −3.00639e48 | −3.70003 | ||||||||
\(659\) | 3.02504e47i | 0.362810i | 0.983408 | + | 0.181405i | \(0.0580645\pi\) | ||||
−0.983408 | + | 0.181405i | \(0.941936\pi\) | |||||||
\(660\) | 2.75417e47 | + | 1.40146e47i | 0.321917 | + | 0.163808i | ||||
\(661\) | −8.00100e47 | −0.911422 | −0.455711 | − | 0.890128i | \(-0.650615\pi\) | ||||
−0.455711 | + | 0.890128i | \(0.650615\pi\) | |||||||
\(662\) | 2.65798e48i | 2.95098i | ||||||||
\(663\) | −5.47659e47 | + | 1.07627e48i | −0.592625 | + | 1.16463i | ||||
\(664\) | −4.05345e47 | −0.427531 | ||||||||
\(665\) | − | 4.75720e47i | − | 0.489084i | ||||||
\(666\) | 1.03032e48 | − | 7.50260e47i | 1.03255 | − | 0.751882i | ||||
\(667\) | 9.49514e46 | 0.0927603 | ||||||||
\(668\) | − | 1.64228e48i | − | 1.56404i | ||||||
\(669\) | 1.74163e48 | + | 8.86233e47i | 1.61701 | + | 0.822818i | ||||
\(670\) | 1.69775e47 | 0.153675 | ||||||||
\(671\) | 2.41670e47i | 0.213275i | ||||||||
\(672\) | −8.65771e47 | + | 1.70142e48i | −0.744947 | + | 1.46398i | ||||
\(673\) | 1.44286e48 | 1.21051 | 0.605255 | − | 0.796032i | \(-0.293071\pi\) | ||||
0.605255 | + | 0.796032i | \(0.293071\pi\) | |||||||
\(674\) | − | 7.27750e47i | − | 0.595339i | ||||||
\(675\) | −1.87086e47 | − | 1.16906e48i | −0.149237 | − | 0.932548i | ||||
\(676\) | 7.09659e47 | 0.552021 | ||||||||
\(677\) | 4.98678e47i | 0.378280i | 0.981950 | + | 0.189140i | \(0.0605699\pi\) | ||||
−0.981950 | + | 0.189140i | \(0.939430\pi\) | |||||||
\(678\) | −3.74599e47 | − | 1.90615e47i | −0.277116 | − | 0.141011i | ||||
\(679\) | 3.67857e47 | 0.265395 | ||||||||
\(680\) | − | 3.64795e47i | − | 0.256683i | ||||||
\(681\) | 3.80122e46 | − | 7.47020e46i | 0.0260869 | − | 0.0512662i | ||||
\(682\) | 1.30845e47 | 0.0875836 | ||||||||
\(683\) | − | 1.74664e48i | − | 1.14039i | −0.821511 | − | 0.570193i | \(-0.806868\pi\) | ||
0.821511 | − | 0.570193i | \(-0.193132\pi\) | |||||||
\(684\) | 2.12396e48 | + | 2.91681e48i | 1.35267 | + | 1.85761i | ||||
\(685\) | −4.64277e47 | −0.288428 | ||||||||
\(686\) | − | 1.18232e48i | − | 0.716514i | ||||||
\(687\) | −1.73790e48 | − | 8.84330e47i | −1.02745 | − | 0.522817i | ||||
\(688\) | −4.89333e47 | −0.282229 | ||||||||
\(689\) | − | 6.32678e47i | − | 0.356005i | ||||||
\(690\) | 6.42864e46 | − | 1.26336e47i | 0.0352927 | − | 0.0693576i | ||||
\(691\) | −5.10678e47 | −0.273540 | −0.136770 | − | 0.990603i | \(-0.543672\pi\) | ||||
−0.136770 | + | 0.990603i | \(0.543672\pi\) | |||||||
\(692\) | − | 1.12121e48i | − | 0.585979i | ||||||
\(693\) | 2.19234e48 | − | 1.59642e48i | 1.11800 | − | 0.814106i | ||||
\(694\) | −4.60748e48 | −2.29273 | ||||||||
\(695\) | 4.91051e47i | 0.238443i | ||||||||
\(696\) | 5.35314e47 | + | 2.72395e47i | 0.253660 | + | 0.129075i | ||||
\(697\) | 2.95845e48 | 1.36807 | ||||||||
\(698\) | 2.73779e48i | 1.23554i | ||||||||
\(699\) | 1.07682e48 | − | 2.11618e48i | 0.474276 | − | 0.932053i | ||||
\(700\) | 3.99191e48 | 1.71599 | ||||||||
\(701\) | − | 1.07393e48i | − | 0.450579i | −0.974292 | − | 0.225289i | \(-0.927667\pi\) | ||
0.974292 | − | 0.225289i | \(-0.0723328\pi\) | |||||||
\(702\) | −2.93101e48 | + | 4.69053e47i | −1.20029 | + | 0.192084i | ||||
\(703\) | −3.32798e48 | −1.33027 | ||||||||
\(704\) | 4.39685e48i | 1.71556i | ||||||||
\(705\) | −1.02484e48 | − | 5.21489e47i | −0.390337 | − | 0.198623i | ||||
\(706\) | 4.03263e48 | 1.49937 | ||||||||
\(707\) | 4.79675e48i | 1.74107i | ||||||||
\(708\) | −9.02683e47 | + | 1.77396e48i | −0.319867 | + | 0.628607i | ||||
\(709\) | −3.47364e48 | −1.20171 | −0.600854 | − | 0.799359i | \(-0.705173\pi\) | ||||
−0.600854 | + | 0.799359i | \(0.705173\pi\) | |||||||
\(710\) | − | 1.00484e47i | − | 0.0339395i | ||||||
\(711\) | 1.89597e48 | + | 2.60371e48i | 0.625241 | + | 0.858636i | ||||
\(712\) | −3.98116e48 | −1.28189 | ||||||||
\(713\) | − | 3.52051e46i | − | 0.0110684i | ||||||
\(714\) | −9.66772e48 | − | 4.91943e48i | −2.96794 | − | 1.51024i | ||||
\(715\) | 6.63801e47 | 0.198992 | ||||||||
\(716\) | − | 1.81869e48i | − | 0.532398i | ||||||
\(717\) | 1.35688e48 | − | 2.66656e48i | 0.387898 | − | 0.762301i | ||||
\(718\) | 6.14852e48 | 1.71654 | ||||||||
\(719\) | 3.13338e48i | 0.854321i | 0.904176 | + | 0.427161i | \(0.140486\pi\) | ||||
−0.904176 | + | 0.427161i | \(0.859514\pi\) | |||||||
\(720\) | −2.90568e47 | + | 2.11586e47i | −0.0773741 | + | 0.0563423i | ||||
\(721\) | 4.27363e48 | 1.11147 | ||||||||
\(722\) | − | 9.93981e48i | − | 2.52491i | ||||||
\(723\) | 2.66526e48 | + | 1.35622e48i | 0.661284 | + | 0.336495i | ||||
\(724\) | 5.20649e48 | 1.26180 | ||||||||
\(725\) | 1.74362e48i | 0.412768i | ||||||||
\(726\) | 5.06567e47 | − | 9.95511e47i | 0.117142 | − | 0.230210i | ||||
\(727\) | −6.94524e48 | −1.56893 | −0.784463 | − | 0.620176i | \(-0.787061\pi\) | ||||
−0.784463 | + | 0.620176i | \(0.787061\pi\) | |||||||
\(728\) | − | 2.95382e48i | − | 0.651855i | ||||||
\(729\) | −4.40675e48 | + | 1.44751e48i | −0.950059 | + | 0.312071i | ||||
\(730\) | 9.99418e47 | 0.210503 | ||||||||
\(731\) | − | 5.64820e48i | − | 1.16229i | ||||||
\(732\) | 1.24210e48 | + | 6.32045e47i | 0.249729 | + | 0.127075i | ||||
\(733\) | 5.31469e48 | 1.04402 | 0.522012 | − | 0.852938i | \(-0.325182\pi\) | ||||
0.522012 | + | 0.852938i | \(0.325182\pi\) | |||||||
\(734\) | 7.95106e48i | 1.52613i | ||||||||
\(735\) | −3.65026e47 | + | 7.17353e47i | −0.0684603 | + | 0.134539i | ||||
\(736\) | 1.48531e48 | 0.272205 | ||||||||
\(737\) | − | 2.52719e48i | − | 0.452576i | ||||||
\(738\) | 4.28066e48 | + | 5.87857e48i | 0.749122 | + | 1.02876i | ||||
\(739\) | −4.01720e48 | −0.687017 | −0.343509 | − | 0.939150i | \(-0.611615\pi\) | ||||
−0.343509 | + | 0.939150i | \(0.611615\pi\) | |||||||
\(740\) | 1.64368e48i | 0.274713i | ||||||||
\(741\) | 6.90772e48 | + | 3.51500e48i | 1.12830 | + | 0.574138i | ||||
\(742\) | 5.68313e48 | 0.907238 | ||||||||
\(743\) | 6.75695e48i | 1.05424i | 0.849790 | + | 0.527121i | \(0.176729\pi\) | ||||
−0.849790 | + | 0.527121i | \(0.823271\pi\) | |||||||
\(744\) | 1.00996e47 | − | 1.98478e47i | 0.0154015 | − | 0.0302672i | ||||
\(745\) | 2.34268e48 | 0.349185 | ||||||||
\(746\) | − | 9.80181e48i | − | 1.42806i | ||||||
\(747\) | −3.72674e48 | + | 2.71374e48i | −0.530736 | + | 0.386472i | ||||
\(748\) | −1.83989e49 | −2.56133 | ||||||||
\(749\) | − | 4.77657e48i | − | 0.650018i | ||||||
\(750\) | 4.77646e48 | + | 2.43051e48i | 0.635426 | + | 0.323337i | ||||
\(751\) | −1.38155e49 | −1.79675 | −0.898377 | − | 0.439226i | \(-0.855253\pi\) | ||||
−0.898377 | + | 0.439226i | \(0.855253\pi\) | |||||||
\(752\) | − | 5.93130e48i | − | 0.754131i | ||||||
\(753\) | 8.50142e46 | − | 1.67071e47i | 0.0105676 | − | 0.0207676i | ||||
\(754\) | 4.37154e48 | 0.531277 | ||||||||
\(755\) | − | 2.75799e48i | − | 0.327714i | ||||||
\(756\) | −2.47137e48 | − | 1.54430e49i | −0.287122 | − | 1.79416i | ||||
\(757\) | −9.82606e48 | −1.11622 | −0.558109 | − | 0.829767i | \(-0.688473\pi\) | ||||
−0.558109 | + | 0.829767i | \(0.688473\pi\) | |||||||
\(758\) | 2.17265e49i | 2.41332i | ||||||||
\(759\) | −1.88058e48 | − | 9.56937e47i | −0.204260 | − | 0.103938i | ||||
\(760\) | −2.34134e48 | −0.248676 | ||||||||
\(761\) | − | 8.35952e48i | − | 0.868245i | −0.900854 | − | 0.434122i | \(-0.857059\pi\) | ||
0.900854 | − | 0.434122i | \(-0.142941\pi\) | |||||||
\(762\) | 7.36689e47 | − | 1.44775e48i | 0.0748255 | − | 0.147048i | ||||
\(763\) | 1.54911e49 | 1.53874 | ||||||||
\(764\) | 1.45933e49i | 1.41764i | ||||||||
\(765\) | −2.44226e48 | − | 3.35393e48i | −0.232032 | − | 0.318647i | ||||
\(766\) | −3.58133e47 | −0.0332779 | ||||||||
\(767\) | 4.27555e48i | 0.388571i | ||||||||
\(768\) | 2.59920e48 | + | 1.32261e48i | 0.231047 | + | 0.117568i | ||||
\(769\) | −7.58017e48 | −0.659069 | −0.329535 | − | 0.944144i | \(-0.606892\pi\) | ||||
−0.329535 | + | 0.944144i | \(0.606892\pi\) | |||||||
\(770\) | 5.96269e48i | 0.507107i | ||||||||
\(771\) | −1.51309e48 | + | 2.97353e48i | −0.125875 | + | 0.247371i | ||||
\(772\) | 1.28454e49 | 1.04533 | ||||||||
\(773\) | 6.23870e48i | 0.496641i | 0.968678 | + | 0.248320i | \(0.0798786\pi\) | ||||
−0.968678 | + | 0.248320i | \(0.920121\pi\) | |||||||
\(774\) | 1.12232e49 | − | 8.17252e48i | 0.874019 | − | 0.636443i | ||||
\(775\) | 6.46482e47 | 0.0492524 | ||||||||
\(776\) | − | 1.81047e48i | − | 0.134941i | ||||||
\(777\) | 1.28562e49 | + | 6.54192e48i | 0.937469 | + | 0.477032i | ||||
\(778\) | −1.03981e47 | −0.00741822 | ||||||||
\(779\) | − | 1.89880e49i | − | 1.32539i | ||||||
\(780\) | 1.73605e48 | − | 3.41171e48i | 0.118564 | − | 0.233004i | ||||
\(781\) | −1.49576e48 | −0.0999525 | ||||||||
\(782\) | 8.43976e48i | 0.551842i | ||||||||
\(783\) | 6.74533e48 | − | 1.07946e48i | 0.431572 | − | 0.0690651i | ||||
\(784\) | −4.15173e48 | −0.259930 | ||||||||
\(785\) | 4.06049e48i | 0.248768i | ||||||||
\(786\) | −7.92665e48 | − | 4.03348e48i | −0.475233 | − | 0.241823i | ||||
\(787\) | 3.06475e48 | 0.179814 | 0.0899071 | − | 0.995950i | \(-0.471343\pi\) | ||||
0.0899071 | + | 0.995950i | \(0.471343\pi\) | |||||||
\(788\) | − | 3.52043e49i | − | 2.02139i | ||||||
\(789\) | 2.24123e48 | − | 4.40448e48i | 0.125944 | − | 0.247506i | ||||
\(790\) | −7.08153e48 | −0.389463 | ||||||||
\(791\) | − | 4.75695e48i | − | 0.256052i | ||||||
\(792\) | −7.85705e48 | − | 1.07900e49i | −0.413934 | − | 0.568450i | ||||
\(793\) | 2.99367e48 | 0.154369 | ||||||||
\(794\) | − | 1.57686e49i | − | 0.795875i | ||||||
\(795\) | 1.93730e48 | + | 9.85796e47i | 0.0957095 | + | 0.0487019i | ||||
\(796\) | −5.17324e48 | −0.250173 | ||||||||
\(797\) | 5.47474e48i | 0.259162i | 0.991569 | + | 0.129581i | \(0.0413633\pi\) | ||||
−0.991569 | + | 0.129581i | \(0.958637\pi\) | |||||||
\(798\) | −3.15740e49 | + | 6.20497e49i | −1.46312 | + | 2.87535i | ||||
\(799\) | 6.84630e49 | 3.10571 | ||||||||
\(800\) | 2.72753e49i | 1.21127i | ||||||||
\(801\) | −3.66027e49 | + | 2.66534e49i | −1.59133 | + | 1.15878i | ||||
\(802\) | −5.67676e49 | −2.41622 | ||||||||
\(803\) | − | 1.48769e49i | − | 0.619936i | ||||||
\(804\) | −1.29889e49 | − | 6.60942e48i | −0.529931 | − | 0.269656i | ||||
\(805\) | 1.60432e48 | 0.0640856 | ||||||||
\(806\) | − | 1.62083e48i | − | 0.0633932i | ||||||
\(807\) | 5.38031e48 | − | 1.05734e49i | 0.206043 | − | 0.404917i | ||||
\(808\) | 2.36080e49 | 0.885252 | ||||||||
\(809\) | 2.65490e49i | 0.974818i | 0.873174 | + | 0.487409i | \(0.162058\pi\) | ||||
−0.873174 | + | 0.487409i | \(0.837942\pi\) | |||||||
\(810\) | 3.13063e48 | − | 9.70576e48i | 0.112561 | − | 0.348967i | ||||
\(811\) | 1.59289e49 | 0.560832 | 0.280416 | − | 0.959879i | \(-0.409528\pi\) | ||||
0.280416 | + | 0.959879i | \(0.409528\pi\) | |||||||
\(812\) | 2.30329e49i | 0.794139i | ||||||||
\(813\) | −6.77850e48 | − | 3.44925e48i | −0.228873 | − | 0.116462i | ||||
\(814\) | 4.17131e49 | 1.37929 | ||||||||
\(815\) | − | 4.52991e48i | − | 0.146693i | ||||||
\(816\) | 9.70553e48 | − | 1.90734e49i | 0.307813 | − | 0.604917i | ||||
\(817\) | −3.62515e49 | −1.12603 | ||||||||
\(818\) | − | 5.01123e49i | − | 1.52454i | ||||||
\(819\) | −1.97755e49 | − | 2.71574e49i | −0.589252 | − | 0.809212i | ||||
\(820\) | −9.37815e48 | −0.273704 | ||||||||
\(821\) | 3.21505e49i | 0.919082i | 0.888156 | + | 0.459541i | \(0.151986\pi\) | ||||
−0.888156 | + | 0.459541i | \(0.848014\pi\) | |||||||
\(822\) | 6.05570e49 | + | 3.08145e49i | 1.69568 | + | 0.862848i | ||||
\(823\) | −1.30350e49 | −0.357532 | −0.178766 | − | 0.983892i | \(-0.557210\pi\) | ||||
−0.178766 | + | 0.983892i | \(0.557210\pi\) | |||||||
\(824\) | − | 2.10334e49i | − | 0.565129i | ||||||
\(825\) | 1.75725e49 | − | 3.45338e49i | 0.462506 | − | 0.908922i | ||||
\(826\) | −3.84058e49 | −0.990229 | ||||||||
\(827\) | 1.13125e49i | 0.285736i | 0.989742 | + | 0.142868i | \(0.0456325\pi\) | ||||
−0.989742 | + | 0.142868i | \(0.954367\pi\) | |||||||
\(828\) | −9.83665e48 | + | 7.16285e48i | −0.243406 | + | 0.177243i | ||||
\(829\) | −2.88791e49 | −0.700094 | −0.350047 | − | 0.936732i | \(-0.613834\pi\) | ||||
−0.350047 | + | 0.936732i | \(0.613834\pi\) | |||||||
\(830\) | − | 1.01359e49i | − | 0.240733i | ||||||
\(831\) | −2.58286e49 | − | 1.31429e49i | −0.601013 | − | 0.305826i | ||||
\(832\) | 5.44656e49 | 1.24173 | ||||||||
\(833\) | − | 4.79219e49i | − | 1.07046i | ||||||
\(834\) | 3.25916e49 | − | 6.40493e49i | 0.713317 | − | 1.40182i | ||||
\(835\) | 1.21202e49 | 0.259919 | ||||||||
\(836\) | 1.18088e50i | 2.48142i | ||||||||
\(837\) | −4.00233e47 | − | 2.50096e48i | −0.00824100 | − | 0.0514961i | ||||
\(838\) | 6.25682e49 | 1.26242 | ||||||||
\(839\) | 8.09012e49i | 1.59956i | 0.600290 | + | 0.799782i | \(0.295052\pi\) | ||||
−0.600290 | + | 0.799782i | \(0.704948\pi\) | |||||||
\(840\) | 9.04477e48 | + | 4.60244e48i | 0.175247 | + | 0.0891745i | ||||
\(841\) | 4.26057e49 | 0.808976 | ||||||||
\(842\) | − | 1.11207e50i | − | 2.06931i | ||||||
\(843\) | 4.89559e48 | − | 9.62088e48i | 0.0892764 | − | 0.175447i | ||||
\(844\) | −6.47344e49 | −1.15695 | ||||||||
\(845\) | 5.23734e48i | 0.0917374i | ||||||||
\(846\) | 9.90608e49 | + | 1.36039e50i | 1.70061 | + | 2.33543i | ||||
\(847\) | 1.26418e49 | 0.212711 | ||||||||
\(848\) | 1.12122e49i | 0.184911i | ||||||||
\(849\) | −5.02875e49 | − | 2.55889e49i | −0.812885 | − | 0.413638i | ||||
\(850\) | −1.54982e50 | −2.45561 | ||||||||
\(851\) | − | 1.12233e49i | − | 0.174308i | ||||||
\(852\) | −3.91188e48 | + | 7.68768e48i | −0.0595543 | + | 0.117037i | ||||
\(853\) | −8.15421e49 | −1.21688 | −0.608441 | − | 0.793599i | \(-0.708205\pi\) | ||||
−0.608441 | + | 0.793599i | \(0.708205\pi\) | |||||||
\(854\) | 2.68911e49i | 0.393392i | ||||||||
\(855\) | −2.15263e49 | + | 1.56750e49i | −0.308706 | + | 0.224794i | ||||
\(856\) | −2.35088e49 | −0.330503 | ||||||||
\(857\) | 1.28860e48i | 0.0177600i | 0.999961 | + | 0.00888001i | \(0.00282663\pi\) | ||||
−0.999961 | + | 0.00888001i | \(0.997173\pi\) | |||||||
\(858\) | −8.65816e49 | − | 4.40571e49i | −1.16988 | − | 0.595295i | ||||
\(859\) | −3.27445e48 | −0.0433764 | −0.0216882 | − | 0.999765i | \(-0.506904\pi\) | ||||
−0.0216882 | + | 0.999765i | \(0.506904\pi\) | |||||||
\(860\) | 1.79045e49i | 0.232535i | ||||||||
\(861\) | −3.73254e49 | + | 7.33522e49i | −0.475281 | + | 0.934027i | ||||
\(862\) | 2.85806e49 | 0.356819 | ||||||||
\(863\) | − | 1.42272e50i | − | 1.74155i | −0.491683 | − | 0.870774i | \(-0.663618\pi\) | ||
0.491683 | − | 0.870774i | \(-0.336382\pi\) | |||||||
\(864\) | 1.05516e50 | − | 1.68860e49i | 1.26645 | − | 0.202671i | ||||
\(865\) | 8.27458e48 | 0.0973806 | ||||||||
\(866\) | − | 2.08507e50i | − | 2.40611i | ||||||
\(867\) | 1.41395e50 | + | 7.19488e49i | 1.59996 | + | 0.814140i | ||||
\(868\) | 8.53991e48 | 0.0947584 | ||||||||
\(869\) | 1.05412e50i | 1.14698i | ||||||||
\(870\) | −6.81143e48 | + | 1.33859e49i | −0.0726794 | + | 0.142830i | ||||
\(871\) | −3.13054e49 | −0.327575 | ||||||||
\(872\) | − | 7.62422e49i | − | 0.782375i | ||||||
\(873\) | −1.21209e49 | − | 1.66455e49i | −0.121981 | − | 0.167515i | ||||
\(874\) | 5.41683e49 | 0.534627 | ||||||||
\(875\) | 6.06552e49i | 0.587126i | ||||||||
\(876\) | −7.64619e49 | − | 3.89077e49i | −0.725898 | − | 0.369374i | ||||
\(877\) | 1.15072e50 | 1.07146 | 0.535732 | − | 0.844388i | \(-0.320036\pi\) | ||||
0.535732 | + | 0.844388i | \(0.320036\pi\) | |||||||
\(878\) | 9.10839e49i | 0.831831i | ||||||||
\(879\) | −1.36243e49 | + | 2.67747e49i | −0.122041 | + | 0.239836i | ||||
\(880\) | −1.17638e49 | −0.103357 | ||||||||
\(881\) | 1.73656e50i | 1.49658i | 0.663373 | + | 0.748289i | \(0.269124\pi\) | ||||
−0.663373 | + | 0.748289i | \(0.730876\pi\) | |||||||
\(882\) | 9.52230e49 | − | 6.93394e49i | 0.804963 | − | 0.586158i | ||||
\(883\) | 1.12242e50 | 0.930729 | 0.465364 | − | 0.885119i | \(-0.345923\pi\) | ||||
0.465364 | + | 0.885119i | \(0.345923\pi\) | |||||||
\(884\) | 2.27915e50i | 1.85389i | ||||||||
\(885\) | −1.30920e49 | − | 6.66187e48i | −0.104465 | − | 0.0531570i | ||||
\(886\) | −8.15480e49 | −0.638322 | ||||||||
\(887\) | − | 7.41162e49i | − | 0.569130i | −0.958657 | − | 0.284565i | \(-0.908151\pi\) | ||
0.958657 | − | 0.284565i | \(-0.0918492\pi\) | |||||||
\(888\) | 3.21972e49 | − | 6.32743e49i | 0.242548 | − | 0.476658i | ||||
\(889\) | 1.83847e49 | 0.135871 | ||||||||
\(890\) | − | 9.95517e49i | − | 0.721803i | ||||||
\(891\) | −1.44475e50 | − | 4.66010e49i | −1.02771 | − | 0.331493i | ||||
\(892\) | 3.68817e50 | 2.57400 | ||||||||
\(893\) | − | 4.39411e50i | − | 3.00882i | ||||||
\(894\) | −3.05563e50 | − | 1.55486e50i | −2.05287 | − | 1.04461i | ||||
\(895\) | 1.34220e49 | 0.0884763 | ||||||||
\(896\) | 2.35282e50i | 1.52178i | ||||||||
\(897\) | −1.18540e49 | + | 2.32956e49i | −0.0752303 | + | 0.147843i | ||||
\(898\) | −6.56355e49 | −0.408734 | ||||||||
\(899\) | 3.73014e48i | 0.0227934i | ||||||||
\(900\) | −1.31534e50 | − | 1.80634e50i | −0.788705 | − | 1.08312i | ||||
\(901\) | −1.29419e50 | −0.761511 | ||||||||
\(902\) | 2.37997e50i | 1.37423i | ||||||||
\(903\) | 1.40042e50 | + | 7.12606e49i | 0.793536 | + | 0.403792i | ||||
\(904\) | −2.34122e49 | −0.130190 | ||||||||
\(905\) | 3.84243e49i | 0.209691i | ||||||||
\(906\) | −1.83051e50 | + | 3.59733e50i | −0.980375 | + | 1.92664i | ||||
\(907\) | −8.59889e49 | −0.451979 | −0.225990 | − | 0.974130i | \(-0.572562\pi\) | ||||
−0.225990 | + | 0.974130i | \(0.572562\pi\) | |||||||
\(908\) | − | 1.58193e49i | − | 0.0816068i | ||||||
\(909\) | 2.17052e50 | − | 1.58053e50i | 1.09895 | − | 0.800234i | ||||
\(910\) | 7.38624e49 | 0.367045 | ||||||||
\(911\) | − | 4.93285e49i | − | 0.240594i | −0.992738 | − | 0.120297i | \(-0.961615\pi\) | ||
0.992738 | − | 0.120297i | \(-0.0383847\pi\) | |||||||
\(912\) | −1.22418e50 | − | 6.22923e49i | −0.586046 | − | 0.298210i | ||||
\(913\) | −1.50879e50 | −0.708965 | ||||||||
\(914\) | 2.31650e50i | 1.06843i | ||||||||
\(915\) | −4.66454e48 | + | 9.16681e48i | −0.0211179 | + | 0.0415011i | ||||
\(916\) | −3.68025e50 | −1.63551 | ||||||||
\(917\) | − | 1.00659e50i | − | 0.439109i | ||||||
\(918\) | 9.59483e49 | + | 5.99559e50i | 0.410877 | + | 2.56747i | ||||
\(919\) | 1.25993e50 | 0.529643 | 0.264822 | − | 0.964297i | \(-0.414687\pi\) | ||||
0.264822 | + | 0.964297i | \(0.414687\pi\) | |||||||
\(920\) | − | 7.89593e48i | − | 0.0325845i | ||||||
\(921\) | 3.68605e50 | + | 1.87565e50i | 1.49330 | + | 0.759867i | ||||
\(922\) | 2.64726e50 | 1.05286 | ||||||||
\(923\) | 1.85286e49i | 0.0723458i | ||||||||
\(924\) | 2.32130e50 | − | 4.56184e50i | 0.889831 | − | 1.74871i | ||||
\(925\) | 2.06097e50 | 0.775643 | ||||||||
\(926\) | − | 3.89350e50i | − | 1.43865i | ||||||
\(927\) | −1.40817e50 | − | 1.93381e50i | −0.510856 | − | 0.701551i | ||||
\(928\) | −1.57376e50 | −0.560560 | ||||||||
\(929\) | − | 1.62540e50i | − | 0.568452i | −0.958757 | − | 0.284226i | \(-0.908263\pi\) | ||
0.958757 | − | 0.284226i | \(-0.0917366\pi\) | |||||||
\(930\) | 4.96309e48 | + | 2.52547e48i | 0.0170428 | + | 0.00867227i | ||||
\(931\) | −3.07574e50 | −1.03706 | ||||||||
\(932\) | − | 4.48132e50i | − | 1.48366i | ||||||
\(933\) | −2.00238e50 | + | 3.93510e50i | −0.650966 | + | 1.27929i | ||||
\(934\) | 5.53493e50 | 1.76691 | ||||||||
\(935\) | − | 1.35785e50i | − | 0.425652i | ||||||
\(936\) | −1.33660e50 | + | 9.73286e49i | −0.411445 | + | 0.299606i | ||||
\(937\) | −1.89835e50 | −0.573856 | −0.286928 | − | 0.957952i | \(-0.592634\pi\) | ||||
−0.286928 | + | 0.957952i | \(0.592634\pi\) | |||||||
\(938\) | − | 2.81206e50i | − | 0.834788i | ||||||
\(939\) | −5.48664e49 | − | 2.79188e49i | −0.159953 | − | 0.0813921i | ||||
\(940\) | −2.17024e50 | −0.621348 | ||||||||
\(941\) | 3.83489e50i | 1.07827i | 0.842218 | + | 0.539137i | \(0.181250\pi\) | ||||
−0.842218 | + | 0.539137i | \(0.818750\pi\) | |||||||
\(942\) | 2.69499e50 | − | 5.29623e50i | 0.744204 | − | 1.46252i | ||||
\(943\) | 6.40352e49 | 0.173668 | ||||||||
\(944\) | − | 7.57706e49i | − | 0.201826i | ||||||
\(945\) | 1.13970e50 | − | 1.82389e49i | 0.298161 | − | 0.0477152i | ||||
\(946\) | 4.54377e50 | 1.16753 | ||||||||
\(947\) | 5.14482e50i | 1.29844i | 0.760602 | + | 0.649218i | \(0.224904\pi\) | ||||
−0.760602 | + | 0.649218i | \(0.775096\pi\) | |||||||
\(948\) | 5.41782e50 | + | 2.75687e50i | 1.34302 | + | 0.683398i | ||||
\(949\) | −1.84286e50 | −0.448711 | ||||||||
\(950\) | 9.94710e50i | 2.37900i | ||||||||
\(951\) | 8.61472e49 | − | 1.69297e50i | 0.202382 | − | 0.397724i | ||||
\(952\) | −6.04226e50 | −1.39435 | ||||||||
\(953\) | 2.02536e50i | 0.459116i | 0.973295 | + | 0.229558i | \(0.0737281\pi\) | ||||
−0.973295 | + | 0.229558i | \(0.926272\pi\) | |||||||
\(954\) | −1.87259e50 | − | 2.57161e50i | −0.416986 | − | 0.572641i | ||||
\(955\) | −1.07699e50 | −0.235589 | ||||||||
\(956\) | − | 5.64684e50i | − | 1.21345i | ||||||
\(957\) | 1.99256e50 | + | 1.01392e50i | 0.420638 | + | 0.214042i | ||||
\(958\) | −8.36391e50 | −1.73458 | ||||||||
\(959\) | 7.69000e50i | 1.56679i | ||||||||
\(960\) | −8.48646e49 | + | 1.66777e50i | −0.169870 | + | 0.333830i | ||||
\(961\) | −5.07125e50 | −0.997280 | ||||||||
\(962\) | − | 5.16717e50i | − | 0.998336i | ||||||
\(963\) | −2.16139e50 | + | 1.57388e50i | −0.410286 | + | 0.298762i | ||||
\(964\) | 5.64407e50 | 1.05265 | ||||||||
\(965\) | 9.47998e49i | 0.173717i | ||||||||
\(966\) | −2.09256e50 | − | 1.06480e50i | −0.376762 | − | 0.191716i | ||||
\(967\) | 3.17102e49 | 0.0560983 | 0.0280491 | − | 0.999607i | \(-0.491071\pi\) | ||||
0.0280491 | + | 0.999607i | \(0.491071\pi\) | |||||||
\(968\) | − | 6.22187e49i | − | 0.108153i | ||||||
\(969\) | 7.19019e50 | − | 1.41302e51i | 1.22811 | − | 2.41349i | ||||
\(970\) | 4.52722e49 | 0.0759823 | ||||||||
\(971\) | − | 2.74349e50i | − | 0.452456i | −0.974074 | − | 0.226228i | \(-0.927361\pi\) | ||
0.974074 | − | 0.226228i | \(-0.0726395\pi\) | |||||||
\(972\) | −6.17362e50 | + | 6.20677e50i | −1.00049 | + | 1.00586i | ||||
\(973\) | 8.13348e50 | 1.29526 | ||||||||
\(974\) | 5.70959e50i | 0.893516i | ||||||||
\(975\) | −4.27784e50 | − | 2.17679e50i | −0.657880 | − | 0.334763i | ||||
\(976\) | −5.30535e49 | −0.0801801 | ||||||||
\(977\) | − | 3.91008e50i | − | 0.580735i | −0.956915 | − | 0.290367i | \(-0.906222\pi\) | ||
0.956915 | − | 0.290367i | \(-0.0937775\pi\) | |||||||
\(978\) | −3.00655e50 | + | 5.90851e50i | −0.438842 | + | 0.862417i | ||||
\(979\) | −1.48188e51 | −2.12572 | ||||||||
\(980\) | 1.51910e50i | 0.214162i | ||||||||
\(981\) | −5.10433e50 | − | 7.00970e50i | −0.707237 | − | 0.971240i | ||||
\(982\) | 2.07250e51 | 2.82228 | ||||||||
\(983\) | − | 5.78758e50i | − | 0.774618i | −0.921950 | − | 0.387309i | \(-0.873405\pi\) | ||
0.921950 | − | 0.387309i | \(-0.126595\pi\) | |||||||
\(984\) | 3.61016e50 | + | 1.83703e50i | 0.474908 | + | 0.241658i | ||||
\(985\) | 2.59810e50 | 0.335923 | ||||||||
\(986\) | − | 8.94230e50i | − | 1.13643i | ||||||
\(987\) | −8.63764e50 | + | 1.69748e51i | −1.07896 | + | 2.12037i | ||||
\(988\) | 1.46281e51 | 1.79606 | ||||||||
\(989\) | − | 1.22254e50i | − | 0.147546i | ||||||
\(990\) | 2.69811e50 | − | 1.96471e50i | 0.320082 | − | 0.233077i | ||||
\(991\) | 5.62137e50 | 0.655526 | 0.327763 | − | 0.944760i | \(-0.393705\pi\) | ||||
0.327763 | + | 0.944760i | \(0.393705\pi\) | |||||||
\(992\) | 5.83501e49i | 0.0668872i | ||||||||
\(993\) | 1.50076e51 | + | 7.63661e50i | 1.69111 | + | 0.860525i | ||||
\(994\) | −1.66436e50 | −0.184365 | ||||||||
\(995\) | − | 3.81789e49i | − | 0.0415749i | ||||||
\(996\) | −3.94596e50 | + | 7.75464e50i | −0.422419 | + | 0.830143i | ||||
\(997\) | 4.10467e50 | 0.431977 | 0.215988 | − | 0.976396i | \(-0.430703\pi\) | ||||
0.215988 | + | 0.976396i | \(0.430703\pi\) | |||||||
\(998\) | 1.75579e50i | 0.181657i | ||||||||
\(999\) | −1.27593e50 | − | 7.97300e50i | −0.129782 | − | 0.810977i |
(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 | 3.35.b.a.2.2 | ✓ | 10 | |
3.2 | odd | 2 | inner | 3.35.b.a.2.9 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.35.b.a.2.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
3.35.b.a.2.9 | yes | 10 | 3.2 | odd | 2 | inner |