Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,33,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, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
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: | \(19.4599965427\) |
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: | \( x^{10} + 954745942 x^{8} + \cdots + 31\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{61}\cdot 5^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.5 | ||
Root | \(-5429.47i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.33.b.a.2.6 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 32576.8i | − | 0.497082i | −0.968621 | − | 0.248541i | \(-0.920049\pi\) | ||
0.968621 | − | 0.248541i | \(-0.0799511\pi\) | |||||||
\(3\) | −6.54523e6 | − | 4.25462e7i | −0.152049 | − | 0.988373i | ||||
\(4\) | 3.23372e9 | 0.752909 | ||||||||
\(5\) | 1.19330e11i | 0.782042i | 0.920382 | + | 0.391021i | \(0.127878\pi\) | ||||
−0.920382 | + | 0.391021i | \(0.872122\pi\) | |||||||
\(6\) | −1.38602e12 | + | 2.13223e11i | −0.491303 | + | 0.0755811i | ||||
\(7\) | −3.44644e13 | −1.03706 | −0.518529 | − | 0.855060i | \(-0.673520\pi\) | ||||
−0.518529 | + | 0.855060i | \(0.673520\pi\) | |||||||
\(8\) | − | 2.45260e14i | − | 0.871340i | ||||||
\(9\) | −1.76734e15 | + | 5.56949e14i | −0.953762 | + | 0.300563i | ||||
\(10\) | 3.88740e15 | 0.388740 | ||||||||
\(11\) | 2.29269e16i | 0.498957i | 0.968380 | + | 0.249479i | \(0.0802592\pi\) | ||||
−0.968380 | + | 0.249479i | \(0.919741\pi\) | |||||||
\(12\) | −2.11654e16 | − | 1.37583e17i | −0.114479 | − | 0.744155i | ||||
\(13\) | −7.69030e17 | −1.15571 | −0.577856 | − | 0.816139i | \(-0.696110\pi\) | ||||
−0.577856 | + | 0.816139i | \(0.696110\pi\) | |||||||
\(14\) | 1.12274e18i | 0.515503i | ||||||||
\(15\) | 5.07705e18 | − | 7.81044e17i | 0.772950 | − | 0.118909i | ||||
\(16\) | 5.89892e18 | 0.319781 | ||||||||
\(17\) | 2.61771e19i | 0.537947i | 0.963148 | + | 0.268973i | \(0.0866844\pi\) | ||||
−0.963148 | + | 0.268973i | \(0.913316\pi\) | |||||||
\(18\) | 1.81436e19 | + | 5.75743e19i | 0.149405 | + | 0.474098i | ||||
\(19\) | −3.34271e20 | −1.15889 | −0.579443 | − | 0.815013i | \(-0.696730\pi\) | ||||
−0.579443 | + | 0.815013i | \(0.696730\pi\) | |||||||
\(20\) | 3.85880e20i | 0.588807i | ||||||||
\(21\) | 2.25578e20 | + | 1.46633e21i | 0.157684 | + | 1.02500i | ||||
\(22\) | 7.46886e20 | 0.248023 | ||||||||
\(23\) | 1.19887e22i | 1.95491i | 0.211150 | + | 0.977454i | \(0.432279\pi\) | ||||
−0.211150 | + | 0.977454i | \(0.567721\pi\) | |||||||
\(24\) | −1.04349e22 | + | 1.60529e21i | −0.861209 | + | 0.132487i | ||||
\(25\) | 9.04337e21 | 0.388410 | ||||||||
\(26\) | 2.50525e22i | 0.574484i | ||||||||
\(27\) | 3.52637e22 | + | 7.15483e22i | 0.442087 | + | 0.896972i | ||||
\(28\) | −1.11448e23 | −0.780810 | ||||||||
\(29\) | − | 2.90445e23i | − | 1.16064i | −0.814389 | − | 0.580319i | \(-0.802928\pi\) | ||
0.814389 | − | 0.580319i | \(-0.197072\pi\) | |||||||
\(30\) | −2.54439e22 | − | 1.65394e23i | −0.0591076 | − | 0.384220i | ||||
\(31\) | 3.11706e23 | 0.428507 | 0.214254 | − | 0.976778i | \(-0.431268\pi\) | ||||
0.214254 | + | 0.976778i | \(0.431268\pi\) | |||||||
\(32\) | − | 1.24555e24i | − | 1.03030i | ||||||
\(33\) | 9.75454e23 | − | 1.50062e23i | 0.493156 | − | 0.0758661i | ||||
\(34\) | 8.52767e23 | 0.267404 | ||||||||
\(35\) | − | 4.11265e24i | − | 0.811023i | ||||||
\(36\) | −5.71508e24 | + | 1.80102e24i | −0.718096 | + | 0.226297i | ||||
\(37\) | −5.78500e24 | −0.468896 | −0.234448 | − | 0.972129i | \(-0.575328\pi\) | ||||
−0.234448 | + | 0.972129i | \(0.575328\pi\) | |||||||
\(38\) | 1.08895e25i | 0.576062i | ||||||||
\(39\) | 5.03348e24 | + | 3.27193e25i | 0.175725 | + | 1.14227i | ||||
\(40\) | 2.92670e25 | 0.681425 | ||||||||
\(41\) | 3.53959e25i | 0.555152i | 0.960704 | + | 0.277576i | \(0.0895310\pi\) | ||||
−0.960704 | + | 0.277576i | \(0.910469\pi\) | |||||||
\(42\) | 4.77684e25 | − | 7.34860e24i | 0.509509 | − | 0.0783819i | ||||
\(43\) | −1.98562e26 | −1.45345 | −0.726727 | − | 0.686927i | \(-0.758959\pi\) | ||||
−0.726727 | + | 0.686927i | \(0.758959\pi\) | |||||||
\(44\) | 7.41393e25i | 0.375669i | ||||||||
\(45\) | −6.64609e25 | − | 2.10897e26i | −0.235053 | − | 0.745882i | ||||
\(46\) | 3.90553e26 | 0.971750 | ||||||||
\(47\) | − | 5.91452e26i | − | 1.04317i | −0.853200 | − | 0.521583i | \(-0.825342\pi\) | ||
0.853200 | − | 0.521583i | \(-0.174658\pi\) | |||||||
\(48\) | −3.86098e25 | − | 2.50977e26i | −0.0486225 | − | 0.316063i | ||||
\(49\) | 8.33704e25 | 0.0754875 | ||||||||
\(50\) | − | 2.94604e26i | − | 0.193072i | ||||||
\(51\) | 1.11374e27 | − | 1.71335e26i | 0.531692 | − | 0.0817945i | ||||
\(52\) | −2.48683e27 | −0.870146 | ||||||||
\(53\) | 3.37218e27i | 0.869956i | 0.900441 | + | 0.434978i | \(0.143244\pi\) | ||||
−0.900441 | + | 0.434978i | \(0.856756\pi\) | |||||||
\(54\) | 2.33081e27 | − | 1.14878e27i | 0.445869 | − | 0.219754i | ||||
\(55\) | −2.73588e27 | −0.390206 | ||||||||
\(56\) | 8.45277e27i | 0.903630i | ||||||||
\(57\) | 2.18788e27 | + | 1.42219e28i | 0.176208 | + | 1.14541i | ||||
\(58\) | −9.46178e27 | −0.576933 | ||||||||
\(59\) | − | 2.27924e28i | − | 1.05720i | −0.848871 | − | 0.528601i | \(-0.822717\pi\) | ||
0.848871 | − | 0.528601i | \(-0.177283\pi\) | |||||||
\(60\) | 1.64178e28 | − | 2.52568e27i | 0.581961 | − | 0.0895277i | ||||
\(61\) | −1.22762e28 | −0.334032 | −0.167016 | − | 0.985954i | \(-0.553413\pi\) | ||||
−0.167016 | + | 0.985954i | \(0.553413\pi\) | |||||||
\(62\) | − | 1.01544e28i | − | 0.213003i | ||||||
\(63\) | 6.09104e28 | − | 1.91950e28i | 0.989106 | − | 0.311701i | ||||
\(64\) | −1.52405e28 | −0.192362 | ||||||||
\(65\) | − | 9.17685e28i | − | 0.903816i | ||||||
\(66\) | −4.88854e27 | − | 3.17772e28i | −0.0377117 | − | 0.245139i | ||||
\(67\) | −2.88582e29 | −1.75014 | −0.875069 | − | 0.483997i | \(-0.839184\pi\) | ||||
−0.875069 | + | 0.483997i | \(0.839184\pi\) | |||||||
\(68\) | 8.46495e28i | 0.405025i | ||||||||
\(69\) | 5.10073e29 | − | 7.84687e28i | 1.93218 | − | 0.297243i | ||||
\(70\) | −1.33977e29 | −0.403145 | ||||||||
\(71\) | 5.23954e29i | 1.25649i | 0.778015 | + | 0.628245i | \(0.216227\pi\) | ||||
−0.778015 | + | 0.628245i | \(0.783773\pi\) | |||||||
\(72\) | 1.36598e29 | + | 4.33459e29i | 0.261893 | + | 0.831051i | ||||
\(73\) | −2.42194e29 | −0.372390 | −0.186195 | − | 0.982513i | \(-0.559616\pi\) | ||||
−0.186195 | + | 0.982513i | \(0.559616\pi\) | |||||||
\(74\) | 1.88457e29i | 0.233080i | ||||||||
\(75\) | −5.91909e28 | − | 3.84761e29i | −0.0590575 | − | 0.383893i | ||||
\(76\) | −1.08094e30 | −0.872536 | ||||||||
\(77\) | − | 7.90164e29i | − | 0.517447i | ||||||
\(78\) | 1.06589e30 | − | 1.63975e29i | 0.567805 | − | 0.0873500i | ||||
\(79\) | −6.06341e29 | −0.263441 | −0.131720 | − | 0.991287i | \(-0.542050\pi\) | ||||
−0.131720 | + | 0.991287i | \(0.542050\pi\) | |||||||
\(80\) | 7.03919e29i | 0.250082i | ||||||||
\(81\) | 2.81330e30 | − | 1.96864e30i | 0.819324 | − | 0.573331i | ||||
\(82\) | 1.15309e30 | 0.275956 | ||||||||
\(83\) | − | 9.99652e30i | − | 1.97060i | −0.170820 | − | 0.985302i | \(-0.554642\pi\) | ||
0.170820 | − | 0.985302i | \(-0.445358\pi\) | |||||||
\(84\) | 7.29455e29 | + | 4.74171e30i | 0.118722 | + | 0.771731i | ||||
\(85\) | −3.12372e30 | −0.420697 | ||||||||
\(86\) | 6.46852e30i | 0.722486i | ||||||||
\(87\) | −1.23574e31 | + | 1.90103e30i | −1.14714 | + | 0.176474i | ||||
\(88\) | 5.62307e30 | 0.434761 | ||||||||
\(89\) | 6.79334e30i | 0.438372i | 0.975683 | + | 0.219186i | \(0.0703402\pi\) | ||||
−0.975683 | + | 0.219186i | \(0.929660\pi\) | |||||||
\(90\) | −6.87035e30 | + | 2.16508e30i | −0.370765 | + | 0.116841i | ||||
\(91\) | 2.65042e31 | 1.19854 | ||||||||
\(92\) | 3.87681e31i | 1.47187i | ||||||||
\(93\) | −2.04019e30 | − | 1.32619e31i | −0.0651543 | − | 0.423525i | ||||
\(94\) | −1.92676e31 | −0.518540 | ||||||||
\(95\) | − | 3.98886e31i | − | 0.906298i | ||||||
\(96\) | −5.29936e31 | + | 8.15243e30i | −1.01832 | + | 0.156656i | ||||
\(97\) | 8.12346e31 | 1.32249 | 0.661246 | − | 0.750169i | \(-0.270028\pi\) | ||||
0.661246 | + | 0.750169i | \(0.270028\pi\) | |||||||
\(98\) | − | 2.71594e30i | − | 0.0375235i | ||||||
\(99\) | −1.27691e31 | − | 4.05197e31i | −0.149968 | − | 0.475886i | ||||
\(100\) | 2.92437e31 | 0.292437 | ||||||||
\(101\) | − | 1.54385e32i | − | 1.31663i | −0.752742 | − | 0.658315i | \(-0.771269\pi\) | ||
0.752742 | − | 0.658315i | \(-0.228731\pi\) | |||||||
\(102\) | −5.58155e30 | − | 3.62820e31i | −0.0406586 | − | 0.264295i | ||||
\(103\) | −1.71682e31 | −0.106987 | −0.0534933 | − | 0.998568i | \(-0.517036\pi\) | ||||
−0.0534933 | + | 0.998568i | \(0.517036\pi\) | |||||||
\(104\) | 1.88613e32i | 1.00702i | ||||||||
\(105\) | −1.74978e32 | + | 2.69182e31i | −0.801593 | + | 0.123316i | ||||
\(106\) | 1.09855e32 | 0.432440 | ||||||||
\(107\) | − | 1.64949e31i | − | 0.0558738i | −0.999610 | − | 0.0279369i | \(-0.991106\pi\) | ||
0.999610 | − | 0.0279369i | \(-0.00889374\pi\) | |||||||
\(108\) | 1.14033e32 | + | 2.31367e32i | 0.332852 | + | 0.675338i | ||||
\(109\) | 5.26161e31 | 0.132524 | 0.0662620 | − | 0.997802i | \(-0.478893\pi\) | ||||
0.0662620 | + | 0.997802i | \(0.478893\pi\) | |||||||
\(110\) | 8.91261e31i | 0.193964i | ||||||||
\(111\) | 3.78642e31 | + | 2.46130e32i | 0.0712953 | + | 0.463444i | ||||
\(112\) | −2.03303e32 | −0.331631 | ||||||||
\(113\) | 4.55732e32i | 0.644844i | 0.946596 | + | 0.322422i | \(0.104497\pi\) | ||||
−0.946596 | + | 0.322422i | \(0.895503\pi\) | |||||||
\(114\) | 4.63306e32 | − | 7.12740e31i | 0.569364 | − | 0.0875899i | ||||
\(115\) | −1.43061e33 | −1.52882 | ||||||||
\(116\) | − | 9.39219e32i | − | 0.873855i | ||||||
\(117\) | 1.35914e33 | − | 4.28311e32i | 1.10227 | − | 0.347364i | ||||
\(118\) | −7.42503e32 | −0.525516 | ||||||||
\(119\) | − | 9.02180e32i | − | 0.557881i | ||||||
\(120\) | −1.91559e32 | − | 1.24520e33i | −0.103610 | − | 0.673502i | ||||
\(121\) | 1.58573e33 | 0.751042 | ||||||||
\(122\) | 3.99921e32i | 0.166041i | ||||||||
\(123\) | 1.50596e33 | − | 2.31674e32i | 0.548697 | − | 0.0844105i | ||||
\(124\) | 1.00797e33 | 0.322627 | ||||||||
\(125\) | 3.85752e33i | 1.08580i | ||||||||
\(126\) | −6.25310e32 | − | 1.98427e33i | −0.154941 | − | 0.491667i | ||||
\(127\) | −7.91813e33 | −1.72887 | −0.864437 | − | 0.502741i | \(-0.832325\pi\) | ||||
−0.864437 | + | 0.502741i | \(0.832325\pi\) | |||||||
\(128\) | − | 4.85313e33i | − | 0.934678i | ||||||
\(129\) | 1.29963e33 | + | 8.44807e33i | 0.220997 | + | 1.43655i | ||||
\(130\) | −2.98952e33 | −0.449271 | ||||||||
\(131\) | 4.54053e33i | 0.603623i | 0.953368 | + | 0.301812i | \(0.0975914\pi\) | ||||
−0.953368 | + | 0.301812i | \(0.902409\pi\) | |||||||
\(132\) | 3.15435e33 | − | 4.85259e32i | 0.371301 | − | 0.0571203i | ||||
\(133\) | 1.15205e34 | 1.20183 | ||||||||
\(134\) | 9.40108e33i | 0.869963i | ||||||||
\(135\) | −8.53787e33 | + | 4.20803e33i | −0.701470 | + | 0.345731i | ||||
\(136\) | 6.42022e33 | 0.468735 | ||||||||
\(137\) | − | 1.50643e34i | − | 0.978179i | −0.872234 | − | 0.489090i | \(-0.837329\pi\) | ||
0.872234 | − | 0.489090i | \(-0.162671\pi\) | |||||||
\(138\) | −2.55626e33 | − | 1.66165e34i | −0.147754 | − | 0.960451i | ||||
\(139\) | −2.84433e32 | −0.0146468 | −0.00732340 | − | 0.999973i | \(-0.502331\pi\) | ||||
−0.00732340 | + | 0.999973i | \(0.502331\pi\) | |||||||
\(140\) | − | 1.32992e34i | − | 0.610626i | ||||||
\(141\) | −2.51640e34 | + | 3.87119e33i | −1.03104 | + | 0.158613i | ||||
\(142\) | 1.70687e34 | 0.624579 | ||||||||
\(143\) | − | 1.76315e34i | − | 0.576651i | ||||||
\(144\) | −1.04254e34 | + | 3.28540e33i | −0.304995 | + | 0.0961144i | ||||
\(145\) | 3.46589e34 | 0.907668 | ||||||||
\(146\) | 7.88991e33i | 0.185109i | ||||||||
\(147\) | −5.45679e32 | − | 3.54710e33i | −0.0114778 | − | 0.0746098i | ||||
\(148\) | −1.87071e34 | −0.353036 | ||||||||
\(149\) | 3.94968e34i | 0.669240i | 0.942353 | + | 0.334620i | \(0.108608\pi\) | ||||
−0.942353 | + | 0.334620i | \(0.891392\pi\) | |||||||
\(150\) | −1.25343e34 | + | 1.92825e33i | −0.190827 | + | 0.0293564i | ||||
\(151\) | 3.66707e34 | 0.501982 | 0.250991 | − | 0.967989i | \(-0.419244\pi\) | ||||
0.250991 | + | 0.967989i | \(0.419244\pi\) | |||||||
\(152\) | 8.19834e34i | 1.00978i | ||||||||
\(153\) | −1.45793e34 | − | 4.62639e34i | −0.161687 | − | 0.513073i | ||||
\(154\) | −2.57410e34 | −0.257214 | ||||||||
\(155\) | 3.71960e34i | 0.335111i | ||||||||
\(156\) | 1.62769e34 | + | 1.05805e35i | 0.132305 | + | 0.860029i | ||||
\(157\) | −1.58058e35 | −1.15991 | −0.579953 | − | 0.814650i | \(-0.696929\pi\) | ||||
−0.579953 | + | 0.814650i | \(0.696929\pi\) | |||||||
\(158\) | 1.97526e34i | 0.130952i | ||||||||
\(159\) | 1.43474e35 | − | 2.20717e34i | 0.859841 | − | 0.132276i | ||||
\(160\) | 1.48632e35 | 0.805737 | ||||||||
\(161\) | − | 4.13183e35i | − | 2.02735i | ||||||
\(162\) | −6.41319e34 | − | 9.16482e34i | −0.284993 | − | 0.407271i | ||||
\(163\) | −5.09520e34 | −0.205191 | −0.102596 | − | 0.994723i | \(-0.532715\pi\) | ||||
−0.102596 | + | 0.994723i | \(0.532715\pi\) | |||||||
\(164\) | 1.14461e35i | 0.417979i | ||||||||
\(165\) | 1.79069e34 | + | 1.16401e35i | 0.0593305 | + | 0.385669i | ||||
\(166\) | −3.25655e35 | −0.979553 | ||||||||
\(167\) | − | 3.09178e35i | − | 0.844782i | −0.906414 | − | 0.422391i | \(-0.861191\pi\) | ||
0.906414 | − | 0.422391i | \(-0.138809\pi\) | |||||||
\(168\) | 3.59633e35 | − | 5.53253e34i | 0.893123 | − | 0.137396i | ||||
\(169\) | 1.48628e35 | 0.335670 | ||||||||
\(170\) | 1.01761e35i | 0.209121i | ||||||||
\(171\) | 5.90770e35 | − | 1.86172e35i | 1.10530 | − | 0.348318i | ||||
\(172\) | −6.42094e35 | −1.09432 | ||||||||
\(173\) | 6.72781e35i | 1.04505i | 0.852625 | + | 0.522524i | \(0.175009\pi\) | ||||
−0.852625 | + | 0.522524i | \(0.824991\pi\) | |||||||
\(174\) | 6.19295e34 | + | 4.02563e35i | 0.0877223 | + | 0.570224i | ||||
\(175\) | −3.11675e35 | −0.402803 | ||||||||
\(176\) | 1.35244e35i | 0.159557i | ||||||||
\(177\) | −9.69730e35 | + | 1.49181e35i | −1.04491 | + | 0.160747i | ||||
\(178\) | 2.21305e35 | 0.217907 | ||||||||
\(179\) | 1.09444e36i | 0.985244i | 0.870243 | + | 0.492622i | \(0.163961\pi\) | ||||
−0.870243 | + | 0.492622i | \(0.836039\pi\) | |||||||
\(180\) | −2.14916e35 | − | 6.81982e35i | −0.176974 | − | 0.561582i | ||||
\(181\) | 3.24967e35 | 0.244896 | 0.122448 | − | 0.992475i | \(-0.460925\pi\) | ||||
0.122448 | + | 0.992475i | \(0.460925\pi\) | |||||||
\(182\) | − | 8.63422e35i | − | 0.595773i | ||||||
\(183\) | 8.03508e34 | + | 5.22308e35i | 0.0507894 | + | 0.330148i | ||||
\(184\) | 2.94035e36 | 1.70339 | ||||||||
\(185\) | − | 6.90326e35i | − | 0.366696i | ||||||
\(186\) | −4.32031e35 | + | 6.64628e34i | −0.210527 | + | 0.0323871i | ||||
\(187\) | −6.00162e35 | −0.268412 | ||||||||
\(188\) | − | 1.91259e36i | − | 0.785410i | ||||||
\(189\) | −1.21535e36 | − | 2.46587e36i | −0.458470 | − | 0.930211i | ||||
\(190\) | −1.29944e36 | −0.450505 | ||||||||
\(191\) | 1.10939e36i | 0.353632i | 0.984244 | + | 0.176816i | \(0.0565798\pi\) | ||||
−0.984244 | + | 0.176816i | \(0.943420\pi\) | |||||||
\(192\) | 9.97524e34 | + | 6.48424e35i | 0.0292485 | + | 0.190125i | ||||
\(193\) | 1.94146e36 | 0.523855 | 0.261927 | − | 0.965088i | \(-0.415642\pi\) | ||||
0.261927 | + | 0.965088i | \(0.415642\pi\) | |||||||
\(194\) | − | 2.64636e36i | − | 0.657388i | ||||||
\(195\) | −3.90440e36 | + | 6.00646e35i | −0.893307 | + | 0.137425i | ||||
\(196\) | 2.69597e35 | 0.0568352 | ||||||||
\(197\) | 2.96789e36i | 0.576751i | 0.957517 | + | 0.288376i | \(0.0931152\pi\) | ||||
−0.957517 | + | 0.288376i | \(0.906885\pi\) | |||||||
\(198\) | −1.32000e36 | + | 4.15978e35i | −0.236555 | + | 0.0745465i | ||||
\(199\) | 8.87238e36 | 1.46687 | 0.733434 | − | 0.679761i | \(-0.237916\pi\) | ||||
0.733434 | + | 0.679761i | \(0.237916\pi\) | |||||||
\(200\) | − | 2.21798e36i | − | 0.338437i | ||||||
\(201\) | 1.88884e36 | + | 1.22781e37i | 0.266108 | + | 1.72979i | ||||
\(202\) | −5.02938e36 | −0.654474 | ||||||||
\(203\) | 1.00100e37i | 1.20365i | ||||||||
\(204\) | 3.60152e36 | − | 5.54050e35i | 0.400316 | − | 0.0615838i | ||||
\(205\) | −4.22380e36 | −0.434152 | ||||||||
\(206\) | 5.59285e35i | 0.0531812i | ||||||||
\(207\) | −6.67709e36 | − | 2.11881e37i | −0.587573 | − | 1.86452i | ||||
\(208\) | −4.53645e36 | −0.369575 | ||||||||
\(209\) | − | 7.66380e36i | − | 0.578234i | ||||||
\(210\) | 8.76910e35 | + | 5.70021e36i | 0.0612980 | + | 0.398458i | ||||
\(211\) | −5.02459e36 | −0.325523 | −0.162761 | − | 0.986665i | \(-0.552040\pi\) | ||||
−0.162761 | + | 0.986665i | \(0.552040\pi\) | |||||||
\(212\) | 1.09047e37i | 0.654998i | ||||||||
\(213\) | 2.22922e37 | − | 3.42940e36i | 1.24188 | − | 0.191049i | ||||
\(214\) | −5.37349e35 | −0.0277739 | ||||||||
\(215\) | − | 2.36945e37i | − | 1.13666i | ||||||
\(216\) | 1.75480e37 | − | 8.64880e36i | 0.781568 | − | 0.385208i | ||||
\(217\) | −1.07428e37 | −0.444387 | ||||||||
\(218\) | − | 1.71406e36i | − | 0.0658753i | ||||||
\(219\) | 1.58522e36 | + | 1.03045e37i | 0.0566217 | + | 0.368060i | ||||
\(220\) | −8.84706e36 | −0.293789 | ||||||||
\(221\) | − | 2.01310e37i | − | 0.621712i | ||||||
\(222\) | 8.01813e36 | − | 1.23349e36i | 0.230370 | − | 0.0354396i | ||||
\(223\) | −3.13856e37 | −0.839176 | −0.419588 | − | 0.907715i | \(-0.637825\pi\) | ||||
−0.419588 | + | 0.907715i | \(0.637825\pi\) | |||||||
\(224\) | 4.29273e37i | 1.06848i | ||||||||
\(225\) | −1.59827e37 | + | 5.03670e36i | −0.370450 | + | 0.116742i | ||||
\(226\) | 1.48463e37 | 0.320541 | ||||||||
\(227\) | 1.20256e37i | 0.241931i | 0.992657 | + | 0.120966i | \(0.0385991\pi\) | ||||
−0.992657 | + | 0.120966i | \(0.961401\pi\) | |||||||
\(228\) | 7.07498e36 | + | 4.59898e37i | 0.132669 | + | 0.862391i | ||||
\(229\) | 5.75083e37 | 1.00546 | 0.502728 | − | 0.864445i | \(-0.332330\pi\) | ||||
0.502728 | + | 0.864445i | \(0.332330\pi\) | |||||||
\(230\) | 4.66048e37i | 0.759950i | ||||||||
\(231\) | −3.36185e37 | + | 5.17181e36i | −0.511431 | + | 0.0786775i | ||||
\(232\) | −7.12348e37 | −1.01131 | ||||||||
\(233\) | − | 2.85230e37i | − | 0.378007i | −0.981976 | − | 0.189004i | \(-0.939474\pi\) | ||
0.981976 | − | 0.189004i | \(-0.0605258\pi\) | |||||||
\(234\) | −1.39530e37 | − | 4.42763e37i | −0.172669 | − | 0.547921i | ||||
\(235\) | 7.05781e37 | 0.815801 | ||||||||
\(236\) | − | 7.37042e37i | − | 0.795976i | ||||||
\(237\) | 3.96864e36 | + | 2.57975e37i | 0.0400560 | + | 0.260378i | ||||
\(238\) | −2.93901e37 | −0.277313 | ||||||||
\(239\) | − | 2.92964e36i | − | 0.0258492i | −0.999916 | − | 0.0129246i | \(-0.995886\pi\) | ||
0.999916 | − | 0.0129246i | \(-0.00411415\pi\) | |||||||
\(240\) | 2.99491e37 | − | 4.60731e36i | 0.247175 | − | 0.0380249i | ||||
\(241\) | 1.22457e38 | 0.945606 | 0.472803 | − | 0.881168i | \(-0.343242\pi\) | ||||
0.472803 | + | 0.881168i | \(0.343242\pi\) | |||||||
\(242\) | − | 5.16581e37i | − | 0.373330i | ||||||
\(243\) | −1.02172e38 | − | 1.06810e38i | −0.691243 | − | 0.722623i | ||||
\(244\) | −3.96979e37 | −0.251496 | ||||||||
\(245\) | 9.94861e36i | 0.0590344i | ||||||||
\(246\) | −7.54721e36 | − | 4.90594e37i | −0.0419590 | − | 0.272748i | ||||
\(247\) | 2.57064e38 | 1.33934 | ||||||||
\(248\) | − | 7.64492e37i | − | 0.373376i | ||||||
\(249\) | −4.25314e38 | + | 6.54295e37i | −1.94769 | + | 0.299629i | ||||
\(250\) | 1.25666e38 | 0.539730 | ||||||||
\(251\) | 1.63459e38i | 0.658611i | 0.944223 | + | 0.329306i | \(0.106815\pi\) | ||||
−0.944223 | + | 0.329306i | \(0.893185\pi\) | |||||||
\(252\) | 1.96967e38 | − | 6.20711e37i | 0.744707 | − | 0.234683i | ||||
\(253\) | −2.74864e38 | −0.975415 | ||||||||
\(254\) | 2.57947e38i | 0.859393i | ||||||||
\(255\) | 2.04455e37 | + | 1.32903e38i | 0.0639668 | + | 0.415806i | ||||
\(256\) | −2.23557e38 | −0.656974 | ||||||||
\(257\) | 2.96392e38i | 0.818346i | 0.912457 | + | 0.409173i | \(0.134183\pi\) | ||||
−0.912457 | + | 0.409173i | \(0.865817\pi\) | |||||||
\(258\) | 2.75211e38 | − | 4.23379e37i | 0.714086 | − | 0.109854i | ||||
\(259\) | 1.99377e38 | 0.486271 | ||||||||
\(260\) | − | 2.96754e38i | − | 0.680491i | ||||||
\(261\) | 1.61763e38 | + | 5.13316e38i | 0.348845 | + | 1.10697i | ||||
\(262\) | 1.47916e38 | 0.300051 | ||||||||
\(263\) | − | 1.72040e38i | − | 0.328351i | −0.986431 | − | 0.164176i | \(-0.947504\pi\) | ||
0.986431 | − | 0.164176i | \(-0.0524964\pi\) | |||||||
\(264\) | −3.68043e37 | − | 2.39240e38i | −0.0661052 | − | 0.429706i | ||||
\(265\) | −4.02404e38 | −0.680343 | ||||||||
\(266\) | − | 3.75299e38i | − | 0.597409i | ||||||
\(267\) | 2.89031e38 | − | 4.44640e37i | 0.433275 | − | 0.0666543i | ||||
\(268\) | −9.33194e38 | −1.31770 | ||||||||
\(269\) | − | 6.63090e38i | − | 0.882136i | −0.897474 | − | 0.441068i | \(-0.854600\pi\) | ||
0.897474 | − | 0.441068i | \(-0.145400\pi\) | |||||||
\(270\) | 1.37084e38 | + | 2.78136e38i | 0.171857 | + | 0.348689i | ||||
\(271\) | 5.57740e37 | 0.0659057 | 0.0329528 | − | 0.999457i | \(-0.489509\pi\) | ||||
0.0329528 | + | 0.999457i | \(0.489509\pi\) | |||||||
\(272\) | 1.54417e38i | 0.172025i | ||||||||
\(273\) | −1.73476e38 | − | 1.12765e39i | −0.182237 | − | 1.18460i | ||||
\(274\) | −4.90745e38 | −0.486236 | ||||||||
\(275\) | 2.07337e38i | 0.193800i | ||||||||
\(276\) | 1.64943e39 | − | 2.53746e38i | 1.45475 | − | 0.223797i | ||||
\(277\) | 2.01751e39 | 1.67935 | 0.839673 | − | 0.543093i | \(-0.182747\pi\) | ||||
0.839673 | + | 0.543093i | \(0.182747\pi\) | |||||||
\(278\) | 9.26591e36i | 0.00728067i | ||||||||
\(279\) | −5.50891e38 | + | 1.73605e38i | −0.408694 | + | 0.128793i | ||||
\(280\) | −1.00867e39 | −0.706677 | ||||||||
\(281\) | 1.04715e39i | 0.692958i | 0.938058 | + | 0.346479i | \(0.112623\pi\) | ||||
−0.938058 | + | 0.346479i | \(0.887377\pi\) | |||||||
\(282\) | 1.26111e38 | + | 8.19764e38i | 0.0788437 | + | 0.512511i | ||||
\(283\) | −1.34123e39 | −0.792353 | −0.396176 | − | 0.918174i | \(-0.629663\pi\) | ||||
−0.396176 | + | 0.918174i | \(0.629663\pi\) | |||||||
\(284\) | 1.69432e39i | 0.946023i | ||||||||
\(285\) | −1.69711e39 | + | 2.61080e38i | −0.895760 | + | 0.137802i | ||||
\(286\) | −5.74378e38 | −0.286643 | ||||||||
\(287\) | − | 1.21990e39i | − | 0.575724i | ||||||
\(288\) | 6.93710e38 | + | 2.20132e39i | 0.309669 | + | 0.982659i | ||||
\(289\) | 1.68267e39 | 0.710613 | ||||||||
\(290\) | − | 1.12908e39i | − | 0.451186i | ||||||
\(291\) | −5.31699e38 | − | 3.45622e39i | −0.201084 | − | 1.30712i | ||||
\(292\) | −7.83189e38 | −0.280376 | ||||||||
\(293\) | 3.88110e39i | 1.31545i | 0.753260 | + | 0.657723i | \(0.228480\pi\) | ||||
−0.753260 | + | 0.657723i | \(0.771520\pi\) | |||||||
\(294\) | −1.15553e38 | + | 1.77765e37i | −0.0370872 | + | 0.00570542i | ||||
\(295\) | 2.71982e39 | 0.826776 | ||||||||
\(296\) | 1.41883e39i | 0.408568i | ||||||||
\(297\) | −1.64038e39 | + | 8.08490e38i | −0.447550 | + | 0.220583i | ||||
\(298\) | 1.28668e39 | 0.332668 | ||||||||
\(299\) | − | 9.21966e39i | − | 2.25931i | ||||||
\(300\) | −1.91407e38 | − | 1.24421e39i | −0.0444649 | − | 0.289037i | ||||
\(301\) | 6.84333e39 | 1.50731 | ||||||||
\(302\) | − | 1.19461e39i | − | 0.249526i | ||||||
\(303\) | −6.56851e39 | + | 1.01049e39i | −1.30132 | + | 0.200193i | ||||
\(304\) | −1.97184e39 | −0.370590 | ||||||||
\(305\) | − | 1.46493e39i | − | 0.261227i | ||||||
\(306\) | −1.50713e39 | + | 4.74948e38i | −0.255040 | + | 0.0803717i | ||||
\(307\) | 2.20584e38 | 0.0354292 | 0.0177146 | − | 0.999843i | \(-0.494361\pi\) | ||||
0.0177146 | + | 0.999843i | \(0.494361\pi\) | |||||||
\(308\) | − | 2.55517e39i | − | 0.389591i | ||||||
\(309\) | 1.12370e38 | + | 7.30443e38i | 0.0162673 | + | 0.105743i | ||||
\(310\) | 1.21173e39 | 0.166578 | ||||||||
\(311\) | 5.51616e39i | 0.720229i | 0.932908 | + | 0.360115i | \(0.117262\pi\) | ||||
−0.932908 | + | 0.360115i | \(0.882738\pi\) | |||||||
\(312\) | 8.02475e39 | − | 1.23451e39i | 0.995310 | − | 0.153117i | ||||
\(313\) | −8.67278e39 | −1.02200 | −0.510998 | − | 0.859582i | \(-0.670724\pi\) | ||||
−0.510998 | + | 0.859582i | \(0.670724\pi\) | |||||||
\(314\) | 5.14903e39i | 0.576569i | ||||||||
\(315\) | 2.29054e39 | + | 7.26845e39i | 0.243763 | + | 0.773523i | ||||
\(316\) | −1.96074e39 | −0.198347 | ||||||||
\(317\) | 1.41350e40i | 1.35940i | 0.733490 | + | 0.679700i | \(0.237890\pi\) | ||||
−0.733490 | + | 0.679700i | \(0.762110\pi\) | |||||||
\(318\) | −7.19026e38 | − | 4.67391e39i | −0.0657522 | − | 0.427412i | ||||
\(319\) | 6.65903e39 | 0.579108 | ||||||||
\(320\) | − | 1.81865e39i | − | 0.150435i | ||||||
\(321\) | −7.01793e38 | + | 1.07963e38i | −0.0552241 | + | 0.00849557i | ||||
\(322\) | −1.34602e40 | −1.00776 | ||||||||
\(323\) | − | 8.75025e39i | − | 0.623419i | ||||||
\(324\) | 9.09742e39 | − | 6.36602e39i | 0.616876 | − | 0.431666i | ||||
\(325\) | −6.95462e39 | −0.448890 | ||||||||
\(326\) | 1.65985e39i | 0.101997i | ||||||||
\(327\) | −3.44384e38 | − | 2.23861e39i | −0.0201502 | − | 0.130983i | ||||
\(328\) | 8.68122e39 | 0.483726 | ||||||||
\(329\) | 2.03841e40i | 1.08182i | ||||||||
\(330\) | 3.79198e39 | − | 5.83351e38i | 0.191709 | − | 0.0294922i | ||||
\(331\) | 8.27126e39 | 0.398404 | 0.199202 | − | 0.979958i | \(-0.436165\pi\) | ||||
0.199202 | + | 0.979958i | \(0.436165\pi\) | |||||||
\(332\) | − | 3.23260e40i | − | 1.48369i | ||||||
\(333\) | 1.02241e40 | − | 3.22195e39i | 0.447215 | − | 0.140933i | ||||
\(334\) | −1.00720e40 | −0.419926 | ||||||||
\(335\) | − | 3.44366e40i | − | 1.36868i | ||||||
\(336\) | 1.33067e39 | + | 8.64977e39i | 0.0504244 | + | 0.327775i | ||||
\(337\) | −4.31836e40 | −1.56042 | −0.780209 | − | 0.625519i | \(-0.784887\pi\) | ||||
−0.780209 | + | 0.625519i | \(0.784887\pi\) | |||||||
\(338\) | − | 4.84182e39i | − | 0.166856i | ||||||
\(339\) | 1.93897e40 | − | 2.98287e39i | 0.637346 | − | 0.0980481i | ||||
\(340\) | −1.01012e40 | −0.316747 | ||||||||
\(341\) | 7.14647e39i | 0.213807i | ||||||||
\(342\) | −6.06488e39 | − | 1.92454e40i | −0.173143 | − | 0.549426i | ||||
\(343\) | 3.51902e40 | 0.958772 | ||||||||
\(344\) | 4.86994e40i | 1.26645i | ||||||||
\(345\) | 9.36369e39 | + | 6.08671e40i | 0.232456 | + | 1.51104i | ||||
\(346\) | 2.19170e40 | 0.519475 | ||||||||
\(347\) | 4.21051e39i | 0.0952934i | 0.998864 | + | 0.0476467i | \(0.0151722\pi\) | ||||
−0.998864 | + | 0.0476467i | \(0.984828\pi\) | |||||||
\(348\) | −3.99602e40 | + | 6.14741e39i | −0.863694 | + | 0.132869i | ||||
\(349\) | 1.76986e40 | 0.365369 | 0.182685 | − | 0.983172i | \(-0.441521\pi\) | ||||
0.182685 | + | 0.983172i | \(0.441521\pi\) | |||||||
\(350\) | 1.01534e40i | 0.200226i | ||||||||
\(351\) | −2.71189e40 | − | 5.50228e40i | −0.510926 | − | 1.03664i | ||||
\(352\) | 2.85567e40 | 0.514074 | ||||||||
\(353\) | 3.02615e40i | 0.520589i | 0.965529 | + | 0.260295i | \(0.0838197\pi\) | ||||
−0.965529 | + | 0.260295i | \(0.916180\pi\) | |||||||
\(354\) | 4.85985e39 | + | 3.15907e40i | 0.0799044 | + | 0.519406i | ||||
\(355\) | −6.25235e40 | −0.982629 | ||||||||
\(356\) | 2.19678e40i | 0.330055i | ||||||||
\(357\) | −3.83844e40 | + | 5.90498e39i | −0.551395 | + | 0.0848256i | ||||
\(358\) | 3.56534e40 | 0.489747 | ||||||||
\(359\) | − | 9.54033e40i | − | 1.25329i | −0.779304 | − | 0.626646i | \(-0.784427\pi\) | ||
0.779304 | − | 0.626646i | \(-0.215573\pi\) | |||||||
\(360\) | −5.17247e40 | + | 1.63002e40i | −0.649917 | + | 0.204811i | ||||
\(361\) | 2.85384e40 | 0.343016 | ||||||||
\(362\) | − | 1.05864e40i | − | 0.121734i | ||||||
\(363\) | −1.03790e40 | − | 6.74669e40i | −0.114195 | − | 0.742309i | ||||
\(364\) | 8.57071e40 | 0.902391 | ||||||||
\(365\) | − | 2.89011e40i | − | 0.291225i | ||||||
\(366\) | 1.70151e40 | − | 2.61757e39i | 0.164111 | − | 0.0252465i | ||||
\(367\) | 9.31860e40 | 0.860386 | 0.430193 | − | 0.902737i | \(-0.358445\pi\) | ||||
0.430193 | + | 0.902737i | \(0.358445\pi\) | |||||||
\(368\) | 7.07203e40i | 0.625143i | ||||||||
\(369\) | −1.97137e40 | − | 6.25567e40i | −0.166858 | − | 0.529483i | ||||
\(370\) | −2.24886e40 | −0.182278 | ||||||||
\(371\) | − | 1.16220e41i | − | 0.902194i | ||||||
\(372\) | −6.59740e39 | − | 4.28853e40i | −0.0490553 | − | 0.318876i | ||||
\(373\) | −8.60796e39 | −0.0613139 | −0.0306569 | − | 0.999530i | \(-0.509760\pi\) | ||||
−0.0306569 | + | 0.999530i | \(0.509760\pi\) | |||||||
\(374\) | 1.95513e40i | 0.133423i | ||||||||
\(375\) | 1.64123e41 | − | 2.52484e40i | 1.07317 | − | 0.165095i | ||||
\(376\) | −1.45060e41 | −0.908953 | ||||||||
\(377\) | 2.23361e41i | 1.34136i | ||||||||
\(378\) | −8.03302e40 | + | 3.95920e40i | −0.462392 | + | 0.227897i | ||||
\(379\) | −2.58970e41 | −1.42897 | −0.714484 | − | 0.699652i | \(-0.753338\pi\) | ||||
−0.714484 | + | 0.699652i | \(0.753338\pi\) | |||||||
\(380\) | − | 1.28989e41i | − | 0.682360i | ||||||
\(381\) | 5.18260e40 | + | 3.36887e41i | 0.262874 | + | 1.70877i | ||||
\(382\) | 3.61405e40 | 0.175784 | ||||||||
\(383\) | − | 7.99494e39i | − | 0.0372936i | −0.999826 | − | 0.0186468i | \(-0.994064\pi\) | ||
0.999826 | − | 0.0186468i | \(-0.00593581\pi\) | |||||||
\(384\) | −2.06482e41 | + | 3.17648e40i | −0.923811 | + | 0.142117i | ||||
\(385\) | 9.42905e40 | 0.404665 | ||||||||
\(386\) | − | 6.32465e40i | − | 0.260399i | ||||||
\(387\) | 3.50927e41 | − | 1.10589e41i | 1.38625 | − | 0.436854i | ||||
\(388\) | 2.62690e41 | 0.995717 | ||||||||
\(389\) | 2.48022e41i | 0.902189i | 0.892476 | + | 0.451094i | \(0.148966\pi\) | ||||
−0.892476 | + | 0.451094i | \(0.851034\pi\) | |||||||
\(390\) | 1.95671e40 | + | 1.27193e41i | 0.0683114 | + | 0.444047i | ||||
\(391\) | −3.13829e41 | −1.05164 | ||||||||
\(392\) | − | 2.04475e40i | − | 0.0657753i | ||||||
\(393\) | 1.93182e41 | − | 2.97188e40i | 0.596605 | − | 0.0917806i | ||||
\(394\) | 9.66844e40 | 0.286693 | ||||||||
\(395\) | − | 7.23548e40i | − | 0.206022i | ||||||
\(396\) | −4.12918e40 | − | 1.31029e41i | −0.112912 | − | 0.358299i | ||||
\(397\) | −6.34349e41 | −1.66602 | −0.833010 | − | 0.553258i | \(-0.813384\pi\) | ||||
−0.833010 | + | 0.553258i | \(0.813384\pi\) | |||||||
\(398\) | − | 2.89034e41i | − | 0.729154i | ||||||
\(399\) | −7.54040e40 | − | 4.90152e41i | −0.182738 | − | 1.18786i | ||||
\(400\) | 5.33461e40 | 0.124206 | ||||||||
\(401\) | 2.07013e41i | 0.463114i | 0.972821 | + | 0.231557i | \(0.0743820\pi\) | ||||
−0.972821 | + | 0.231557i | \(0.925618\pi\) | |||||||
\(402\) | 3.99980e41 | − | 6.15322e40i | 0.859848 | − | 0.132277i | ||||
\(403\) | −2.39711e41 | −0.495231 | ||||||||
\(404\) | − | 4.99239e41i | − | 0.991303i | ||||||
\(405\) | 2.34918e41 | + | 3.35712e41i | 0.448369 | + | 0.640746i | ||||
\(406\) | 3.26095e41 | 0.598312 | ||||||||
\(407\) | − | 1.32632e41i | − | 0.233959i | ||||||
\(408\) | −4.20218e40 | − | 2.73156e41i | −0.0712708 | − | 0.463285i | ||||
\(409\) | 2.76151e41 | 0.450374 | 0.225187 | − | 0.974316i | \(-0.427701\pi\) | ||||
0.225187 | + | 0.974316i | \(0.427701\pi\) | |||||||
\(410\) | 1.37598e41i | 0.215809i | ||||||||
\(411\) | −6.40927e41 | + | 9.85990e40i | −0.966806 | + | 0.148732i | ||||
\(412\) | −5.55172e40 | −0.0805512 | ||||||||
\(413\) | 7.85527e41i | 1.09638i | ||||||||
\(414\) | −6.90240e41 | + | 2.17518e41i | −0.926818 | + | 0.292072i | ||||
\(415\) | 1.19289e42 | 1.54110 | ||||||||
\(416\) | 9.57868e41i | 1.19073i | ||||||||
\(417\) | 1.86168e39 | + | 1.21015e40i | 0.00222704 | + | 0.0144765i | ||||
\(418\) | −2.49662e41 | −0.287430 | ||||||||
\(419\) | − | 1.00009e42i | − | 1.10819i | −0.832454 | − | 0.554094i | \(-0.813065\pi\) | ||
0.832454 | − | 0.554094i | \(-0.186935\pi\) | |||||||
\(420\) | −5.65829e41 | + | 8.70460e40i | −0.603527 | + | 0.0928454i | ||||
\(421\) | −4.52868e41 | −0.465005 | −0.232503 | − | 0.972596i | \(-0.574691\pi\) | ||||
−0.232503 | + | 0.972596i | \(0.574691\pi\) | |||||||
\(422\) | 1.63685e41i | 0.161812i | ||||||||
\(423\) | 3.29409e41 | + | 1.04530e42i | 0.313537 | + | 0.994933i | ||||
\(424\) | 8.27064e41 | 0.758028 | ||||||||
\(425\) | 2.36729e41i | 0.208944i | ||||||||
\(426\) | −1.11719e41 | − | 7.26210e41i | −0.0949670 | − | 0.617317i | ||||
\(427\) | 4.23094e41 | 0.346410 | ||||||||
\(428\) | − | 5.33397e40i | − | 0.0420679i | ||||||
\(429\) | −7.50154e41 | + | 1.15402e41i | −0.569946 | + | 0.0876794i | ||||
\(430\) | −7.71890e41 | −0.565015 | ||||||||
\(431\) | − | 4.47524e40i | − | 0.0315631i | −0.999875 | − | 0.0157816i | \(-0.994976\pi\) | ||
0.999875 | − | 0.0157816i | \(-0.00502363\pi\) | |||||||
\(432\) | 2.08018e41 | + | 4.22058e41i | 0.141371 | + | 0.286835i | ||||
\(433\) | 5.96801e41 | 0.390862 | 0.195431 | − | 0.980717i | \(-0.437389\pi\) | ||||
0.195431 | + | 0.980717i | \(0.437389\pi\) | |||||||
\(434\) | 3.49965e41i | 0.220897i | ||||||||
\(435\) | −2.26851e41 | − | 1.47461e42i | −0.138010 | − | 0.897114i | ||||
\(436\) | 1.70146e41 | 0.0997785 | ||||||||
\(437\) | − | 4.00747e42i | − | 2.26551i | ||||||
\(438\) | 3.35686e41 | − | 5.16413e40i | 0.182956 | − | 0.0281457i | ||||
\(439\) | 7.27745e41 | 0.382425 | 0.191213 | − | 0.981549i | \(-0.438758\pi\) | ||||
0.191213 | + | 0.981549i | \(0.438758\pi\) | |||||||
\(440\) | 6.71002e41i | 0.340002i | ||||||||
\(441\) | −1.47344e41 | + | 4.64331e40i | −0.0719971 | + | 0.0226887i | ||||
\(442\) | −6.55803e41 | −0.309042 | ||||||||
\(443\) | − | 1.23917e42i | − | 0.563212i | −0.959530 | − | 0.281606i | \(-0.909133\pi\) | ||
0.959530 | − | 0.281606i | \(-0.0908672\pi\) | |||||||
\(444\) | 1.22442e41 | + | 7.95916e41i | 0.0536789 | + | 0.348931i | ||||
\(445\) | −8.10651e41 | −0.342826 | ||||||||
\(446\) | 1.02244e42i | 0.417140i | ||||||||
\(447\) | 1.68044e42 | − | 2.58516e41i | 0.661459 | − | 0.101758i | ||||
\(448\) | 5.25254e41 | 0.199490 | ||||||||
\(449\) | 3.01079e42i | 1.10342i | 0.834037 | + | 0.551708i | \(0.186024\pi\) | ||||
−0.834037 | + | 0.551708i | \(0.813976\pi\) | |||||||
\(450\) | 1.64079e41 | + | 5.20665e41i | 0.0580302 | + | 0.184144i | ||||
\(451\) | −8.11520e41 | −0.276997 | ||||||||
\(452\) | 1.47371e42i | 0.485509i | ||||||||
\(453\) | −2.40018e41 | − | 1.56020e42i | −0.0763261 | − | 0.496145i | ||||
\(454\) | 3.91755e41 | 0.120260 | ||||||||
\(455\) | 3.16275e42i | 0.937309i | ||||||||
\(456\) | 3.48808e42 | − | 5.36600e41i | 0.998043 | − | 0.153537i | ||||
\(457\) | −5.01707e42 | −1.38609 | −0.693044 | − | 0.720895i | \(-0.743731\pi\) | ||||
−0.693044 | + | 0.720895i | \(0.743731\pi\) | |||||||
\(458\) | − | 1.87344e42i | − | 0.499794i | ||||||
\(459\) | −1.87293e42 | + | 9.23103e41i | −0.482523 | + | 0.237819i | ||||
\(460\) | −4.62620e42 | −1.15106 | ||||||||
\(461\) | 3.38629e42i | 0.813785i | 0.913476 | + | 0.406892i | \(0.133388\pi\) | ||||
−0.913476 | + | 0.406892i | \(0.866612\pi\) | |||||||
\(462\) | 1.68481e41 | + | 1.09518e42i | 0.0391092 | + | 0.254223i | ||||
\(463\) | 1.44371e42 | 0.323731 | 0.161865 | − | 0.986813i | \(-0.448249\pi\) | ||||
0.161865 | + | 0.986813i | \(0.448249\pi\) | |||||||
\(464\) | − | 1.71331e42i | − | 0.371150i | ||||||
\(465\) | 1.58255e42 | − | 2.43456e41i | 0.331215 | − | 0.0509534i | ||||
\(466\) | −9.29187e41 | −0.187901 | ||||||||
\(467\) | − | 2.83041e42i | − | 0.553068i | −0.961004 | − | 0.276534i | \(-0.910814\pi\) | ||
0.961004 | − | 0.276534i | \(-0.0891859\pi\) | |||||||
\(468\) | 4.39507e42 | − | 1.38504e42i | 0.829912 | − | 0.261534i | ||||
\(469\) | 9.94582e42 | 1.81499 | ||||||||
\(470\) | − | 2.29921e42i | − | 0.405520i | ||||||
\(471\) | 1.03453e42 | + | 6.72478e42i | 0.176363 | + | 1.14642i | ||||
\(472\) | −5.59007e42 | −0.921182 | ||||||||
\(473\) | − | 4.55242e42i | − | 0.725211i | ||||||
\(474\) | 8.40400e41 | − | 1.29286e41i | 0.129429 | − | 0.0199112i | ||||
\(475\) | −3.02293e42 | −0.450122 | ||||||||
\(476\) | − | 2.91740e42i | − | 0.420034i | ||||||
\(477\) | −1.87814e42 | − | 5.95980e42i | −0.261477 | − | 0.829731i | ||||
\(478\) | −9.54382e40 | −0.0128492 | ||||||||
\(479\) | − | 3.54924e42i | − | 0.462134i | −0.972938 | − | 0.231067i | \(-0.925778\pi\) | ||
0.972938 | − | 0.231067i | \(-0.0742216\pi\) | |||||||
\(480\) | −9.72832e41 | − | 6.32374e42i | −0.122512 | − | 0.796368i | ||||
\(481\) | 4.44884e42 | 0.541908 | ||||||||
\(482\) | − | 3.98925e42i | − | 0.470044i | ||||||
\(483\) | −1.75794e43 | + | 2.70438e42i | −2.00378 | + | 0.308258i | ||||
\(484\) | 5.12782e42 | 0.565466 | ||||||||
\(485\) | 9.69374e42i | 1.03425i | ||||||||
\(486\) | −3.47953e42 | + | 3.32843e42i | −0.359203 | + | 0.343605i | ||||
\(487\) | 6.57145e42 | 0.656444 | 0.328222 | − | 0.944601i | \(-0.393551\pi\) | ||||
0.328222 | + | 0.944601i | \(0.393551\pi\) | |||||||
\(488\) | 3.01088e42i | 0.291056i | ||||||||
\(489\) | 3.33492e41 | + | 2.16781e42i | 0.0311992 | + | 0.202806i | ||||
\(490\) | 3.24094e41 | 0.0293450 | ||||||||
\(491\) | 2.24059e43i | 1.96362i | 0.189864 | + | 0.981810i | \(0.439195\pi\) | ||||
−0.189864 | + | 0.981810i | \(0.560805\pi\) | |||||||
\(492\) | 4.86986e42 | − | 7.49170e41i | 0.413119 | − | 0.0635534i | ||||
\(493\) | 7.60303e42 | 0.624361 | ||||||||
\(494\) | − | 8.37433e42i | − | 0.665761i | ||||||
\(495\) | 4.83522e42 | − | 1.52374e42i | 0.372163 | − | 0.117281i | ||||
\(496\) | 1.83873e42 | 0.137029 | ||||||||
\(497\) | − | 1.80578e43i | − | 1.30305i | ||||||
\(498\) | 2.13148e42 | + | 1.38554e43i | 0.148940 | + | 0.968164i | ||||
\(499\) | −1.68499e43 | −1.14022 | −0.570110 | − | 0.821569i | \(-0.693099\pi\) | ||||
−0.570110 | + | 0.821569i | \(0.693099\pi\) | |||||||
\(500\) | 1.24741e43i | 0.817505i | ||||||||
\(501\) | −1.31543e43 | + | 2.02364e42i | −0.834960 | + | 0.128449i | ||||
\(502\) | 5.32497e42 | 0.327384 | ||||||||
\(503\) | 1.76336e43i | 1.05016i | 0.851054 | + | 0.525078i | \(0.175964\pi\) | ||||
−0.851054 | + | 0.525078i | \(0.824036\pi\) | |||||||
\(504\) | −4.70776e42 | − | 1.49389e43i | −0.271598 | − | 0.861848i | ||||
\(505\) | 1.84228e43 | 1.02966 | ||||||||
\(506\) | 8.95418e42i | 0.484862i | ||||||||
\(507\) | −9.72804e41 | − | 6.32355e42i | −0.0510385 | − | 0.331768i | ||||
\(508\) | −2.56050e43 | −1.30168 | ||||||||
\(509\) | − | 2.95377e43i | − | 1.45510i | −0.686056 | − | 0.727549i | \(-0.740659\pi\) | ||
0.686056 | − | 0.727549i | \(-0.259341\pi\) | |||||||
\(510\) | 4.32954e42 | − | 6.66048e41i | 0.206690 | − | 0.0317968i | ||||
\(511\) | 8.34709e42 | 0.386190 | ||||||||
\(512\) | − | 1.35613e43i | − | 0.608108i | ||||||
\(513\) | −1.17876e43 | − | 2.39165e43i | −0.512329 | − | 1.03949i | ||||
\(514\) | 9.65551e42 | 0.406785 | ||||||||
\(515\) | − | 2.04869e42i | − | 0.0836681i | ||||||
\(516\) | 4.20265e42 | + | 2.73187e43i | 0.166390 | + | 1.08159i | ||||
\(517\) | 1.35602e43 | 0.520495 | ||||||||
\(518\) | − | 6.49506e42i | − | 0.241717i | ||||||
\(519\) | 2.86243e43 | − | 4.40351e42i | 1.03290 | − | 0.158899i | ||||
\(520\) | −2.25072e43 | −0.787531 | ||||||||
\(521\) | − | 2.00817e43i | − | 0.681391i | −0.940174 | − | 0.340696i | \(-0.889337\pi\) | ||
0.940174 | − | 0.340696i | \(-0.110663\pi\) | |||||||
\(522\) | 1.67222e43 | − | 5.26973e42i | 0.550256 | − | 0.173405i | ||||
\(523\) | 5.37535e42 | 0.171546 | 0.0857728 | − | 0.996315i | \(-0.472664\pi\) | ||||
0.0857728 | + | 0.996315i | \(0.472664\pi\) | |||||||
\(524\) | 1.46828e43i | 0.454474i | ||||||||
\(525\) | 2.03998e42 | + | 1.32606e43i | 0.0612460 | + | 0.398119i | ||||
\(526\) | −5.60453e42 | −0.163218 | ||||||||
\(527\) | 8.15957e42i | 0.230514i | ||||||||
\(528\) | 5.75413e42 | − | 8.85204e41i | 0.157702 | − | 0.0242606i | ||||
\(529\) | −1.06120e44 | −2.82166 | ||||||||
\(530\) | 1.31090e43i | 0.338186i | ||||||||
\(531\) | 1.26942e43 | + | 4.02819e43i | 0.317756 | + | 1.00832i | ||||
\(532\) | 3.72539e43 | 0.904869 | ||||||||
\(533\) | − | 2.72205e43i | − | 0.641595i | ||||||
\(534\) | −1.44849e42 | − | 9.41570e42i | −0.0331327 | − | 0.215374i | ||||
\(535\) | 1.96833e42 | 0.0436957 | ||||||||
\(536\) | 7.07778e43i | 1.52497i | ||||||||
\(537\) | 4.65643e43 | − | 7.16336e42i | 0.973788 | − | 0.149806i | ||||
\(538\) | −2.16013e43 | −0.438495 | ||||||||
\(539\) | 1.91143e42i | 0.0376650i | ||||||||
\(540\) | −2.76091e43 | + | 1.36076e43i | −0.528143 | + | 0.260304i | ||||
\(541\) | 1.60260e43 | 0.297625 | 0.148813 | − | 0.988865i | \(-0.452455\pi\) | ||||
0.148813 | + | 0.988865i | \(0.452455\pi\) | |||||||
\(542\) | − | 1.81694e42i | − | 0.0327606i | ||||||
\(543\) | −2.12699e42 | − | 1.38261e43i | −0.0372364 | − | 0.242049i | ||||
\(544\) | 3.26050e43 | 0.554245 | ||||||||
\(545\) | 6.27869e42i | 0.103639i | ||||||||
\(546\) | −3.67353e43 | + | 5.65129e42i | −0.588846 | + | 0.0905869i | ||||
\(547\) | −2.80279e43 | −0.436308 | −0.218154 | − | 0.975914i | \(-0.570003\pi\) | ||||
−0.218154 | + | 0.975914i | \(0.570003\pi\) | |||||||
\(548\) | − | 4.87136e43i | − | 0.736480i | ||||||
\(549\) | 2.16963e43 | − | 6.83725e42i | 0.318587 | − | 0.100398i | ||||
\(550\) | 6.75436e42 | 0.0963344 | ||||||||
\(551\) | 9.70874e43i | 1.34505i | ||||||||
\(552\) | −1.92453e43 | − | 1.25101e44i | −0.258999 | − | 1.68358i | ||||
\(553\) | 2.08972e43 | 0.273203 | ||||||||
\(554\) | − | 6.57241e43i | − | 0.834773i | ||||||
\(555\) | −2.93707e43 | + | 4.51834e42i | −0.362433 | + | 0.0557560i | ||||
\(556\) | −9.19776e41 | −0.0110277 | ||||||||
\(557\) | − | 1.16007e44i | − | 1.35145i | −0.737152 | − | 0.675727i | \(-0.763830\pi\) | ||
0.737152 | − | 0.675727i | \(-0.236170\pi\) | |||||||
\(558\) | 5.65548e42 | + | 1.79463e43i | 0.0640210 | + | 0.203155i | ||||
\(559\) | 1.52700e44 | 1.67977 | ||||||||
\(560\) | − | 2.42602e43i | − | 0.259350i | ||||||
\(561\) | 3.92819e42 | + | 2.55346e43i | 0.0408119 | + | 0.265291i | ||||
\(562\) | 3.41127e43 | 0.344457 | ||||||||
\(563\) | 2.75878e43i | 0.270759i | 0.990794 | + | 0.135379i | \(0.0432253\pi\) | ||||
−0.990794 | + | 0.135379i | \(0.956775\pi\) | |||||||
\(564\) | −8.13735e43 | + | 1.25183e43i | −0.776278 | + | 0.119421i | ||||
\(565\) | −5.43826e43 | −0.504295 | ||||||||
\(566\) | 4.36928e43i | 0.393865i | ||||||||
\(567\) | −9.69588e43 | + | 6.78480e43i | −0.849685 | + | 0.594577i | ||||
\(568\) | 1.28505e44 | 1.09483 | ||||||||
\(569\) | 1.45549e43i | 0.120563i | 0.998181 | + | 0.0602814i | \(0.0191998\pi\) | ||||
−0.998181 | + | 0.0602814i | \(0.980800\pi\) | |||||||
\(570\) | 8.50515e42 | + | 5.52863e43i | 0.0684990 | + | 0.445267i | ||||
\(571\) | −2.49281e44 | −1.95214 | −0.976072 | − | 0.217450i | \(-0.930226\pi\) | ||||
−0.976072 | + | 0.217450i | \(0.930226\pi\) | |||||||
\(572\) | − | 5.70153e43i | − | 0.434166i | ||||||
\(573\) | 4.72005e43 | − | 7.26123e42i | 0.349520 | − | 0.0537696i | ||||
\(574\) | −3.97405e43 | −0.286182 | ||||||||
\(575\) | 1.08418e44i | 0.759305i | ||||||||
\(576\) | 2.69351e43 | − | 8.48817e42i | 0.183467 | − | 0.0578168i | ||||
\(577\) | 1.65085e44 | 1.09369 | 0.546847 | − | 0.837233i | \(-0.315828\pi\) | ||||
0.546847 | + | 0.837233i | \(0.315828\pi\) | |||||||
\(578\) | − | 5.48160e43i | − | 0.353233i | ||||||
\(579\) | −1.27073e43 | − | 8.26017e43i | −0.0796518 | − | 0.517764i | ||||
\(580\) | 1.12077e44 | 0.683391 | ||||||||
\(581\) | 3.44525e44i | 2.04363i | ||||||||
\(582\) | −1.12593e44 | + | 1.73210e43i | −0.649744 | + | 0.0999554i | ||||
\(583\) | −7.73139e43 | −0.434071 | ||||||||
\(584\) | 5.94007e43i | 0.324479i | ||||||||
\(585\) | 5.11104e43 | + | 1.62186e44i | 0.271654 | + | 0.862025i | ||||
\(586\) | 1.26434e44 | 0.653885 | ||||||||
\(587\) | − | 3.84776e44i | − | 1.93642i | −0.250148 | − | 0.968208i | \(-0.580479\pi\) | ||
0.250148 | − | 0.968208i | \(-0.419521\pi\) | |||||||
\(588\) | −1.76457e42 | − | 1.14703e43i | −0.00864176 | − | 0.0561744i | ||||
\(589\) | −1.04194e44 | −0.496591 | ||||||||
\(590\) | − | 8.86030e43i | − | 0.410976i | ||||||
\(591\) | 1.26273e44 | − | 1.94255e43i | 0.570045 | − | 0.0876947i | ||||
\(592\) | −3.41253e43 | −0.149944 | ||||||||
\(593\) | 2.01475e43i | 0.0861682i | 0.999071 | + | 0.0430841i | \(0.0137183\pi\) | ||||
−0.999071 | + | 0.0430841i | \(0.986282\pi\) | |||||||
\(594\) | 2.63380e43 | + | 5.34384e43i | 0.109648 | + | 0.222469i | ||||
\(595\) | 1.07657e44 | 0.436287 | ||||||||
\(596\) | 1.27722e44i | 0.503877i | ||||||||
\(597\) | −5.80718e43 | − | 3.77486e44i | −0.223036 | − | 1.44981i | ||||
\(598\) | −3.00347e44 | −1.12306 | ||||||||
\(599\) | − | 4.08398e44i | − | 1.48681i | −0.668843 | − | 0.743404i | \(-0.733210\pi\) | ||
0.668843 | − | 0.743404i | \(-0.266790\pi\) | |||||||
\(600\) | −9.43667e43 | + | 1.45172e43i | −0.334502 | + | 0.0514591i | ||||
\(601\) | −3.61344e44 | −1.24718 | −0.623590 | − | 0.781751i | \(-0.714327\pi\) | ||||
−0.623590 | + | 0.781751i | \(0.714327\pi\) | |||||||
\(602\) | − | 2.22934e44i | − | 0.749259i | ||||||
\(603\) | 5.10023e44 | − | 1.60726e44i | 1.66922 | − | 0.526027i | ||||
\(604\) | 1.18583e44 | 0.377947 | ||||||||
\(605\) | 1.89226e44i | 0.587347i | ||||||||
\(606\) | 3.29184e43 | + | 2.13981e44i | 0.0995124 | + | 0.646864i | ||||
\(607\) | −3.35513e44 | −0.987847 | −0.493923 | − | 0.869505i | \(-0.664438\pi\) | ||||
−0.493923 | + | 0.869505i | \(0.664438\pi\) | |||||||
\(608\) | 4.16352e44i | 1.19400i | ||||||||
\(609\) | 4.25889e44 | − | 6.55180e43i | 1.18965 | − | 0.183014i | ||||
\(610\) | −4.77226e43 | −0.129852 | ||||||||
\(611\) | 4.54844e44i | 1.20560i | ||||||||
\(612\) | −4.71455e43 | − | 1.49604e44i | −0.121736 | − | 0.386297i | ||||
\(613\) | 5.40629e44 | 1.35998 | 0.679989 | − | 0.733222i | \(-0.261984\pi\) | ||||
0.679989 | + | 0.733222i | \(0.261984\pi\) | |||||||
\(614\) | − | 7.18594e42i | − | 0.0176112i | ||||||
\(615\) | 2.76458e43 | + | 1.79707e44i | 0.0660126 | + | 0.429104i | ||||
\(616\) | −1.93796e44 | −0.450872 | ||||||||
\(617\) | − | 2.60746e44i | − | 0.591091i | −0.955329 | − | 0.295546i | \(-0.904499\pi\) | ||
0.955329 | − | 0.295546i | \(-0.0955015\pi\) | |||||||
\(618\) | 2.37955e43 | − | 3.66065e42i | 0.0525628 | − | 0.00808617i | ||||
\(619\) | −1.43900e43 | −0.0309750 | −0.0154875 | − | 0.999880i | \(-0.504930\pi\) | ||||
−0.0154875 | + | 0.999880i | \(0.504930\pi\) | |||||||
\(620\) | 1.20281e44i | 0.252308i | ||||||||
\(621\) | −8.57770e44 | + | 4.22766e44i | −1.75350 | + | 0.864240i | ||||
\(622\) | 1.79699e44 | 0.358013 | ||||||||
\(623\) | − | 2.34129e44i | − | 0.454617i | ||||||
\(624\) | 2.96921e43 | + | 1.93009e44i | 0.0561937 | + | 0.365278i | ||||
\(625\) | −2.49761e44 | −0.460728 | ||||||||
\(626\) | 2.82531e44i | 0.508016i | ||||||||
\(627\) | −3.26066e44 | + | 5.01613e43i | −0.571511 | + | 0.0879202i | ||||
\(628\) | −5.11116e44 | −0.873304 | ||||||||
\(629\) | − | 1.51435e44i | − | 0.252241i | ||||||
\(630\) | 2.36783e44 | − | 7.46184e43i | 0.384504 | − | 0.121171i | ||||
\(631\) | 6.57169e44 | 1.04042 | 0.520208 | − | 0.854040i | \(-0.325854\pi\) | ||||
0.520208 | + | 0.854040i | \(0.325854\pi\) | |||||||
\(632\) | 1.48711e44i | 0.229547i | ||||||||
\(633\) | 3.28871e43 | + | 2.13777e44i | 0.0494956 | + | 0.321738i | ||||
\(634\) | 4.60473e44 | 0.675734 | ||||||||
\(635\) | − | 9.44872e44i | − | 1.35205i | ||||||
\(636\) | 4.63954e44 | − | 7.13738e43i | 0.647382 | − | 0.0995921i | ||||
\(637\) | −6.41144e43 | −0.0872418 | ||||||||
\(638\) | − | 2.16930e44i | − | 0.287865i | ||||||
\(639\) | −2.91816e44 | − | 9.26004e44i | −0.377655 | − | 1.19839i | ||||
\(640\) | 5.79125e44 | 0.730958 | ||||||||
\(641\) | 1.18680e45i | 1.46100i | 0.682914 | + | 0.730499i | \(0.260712\pi\) | ||||
−0.682914 | + | 0.730499i | \(0.739288\pi\) | |||||||
\(642\) | 3.51707e42 | + | 2.28622e43i | 0.00422300 | + | 0.0274509i | ||||
\(643\) | 4.85455e44 | 0.568556 | 0.284278 | − | 0.958742i | \(-0.408246\pi\) | ||||
0.284278 | + | 0.958742i | \(0.408246\pi\) | |||||||
\(644\) | − | 1.33612e45i | − | 1.52641i | ||||||
\(645\) | −1.00811e45 | + | 1.55086e44i | −1.12345 | + | 0.172829i | ||||
\(646\) | −2.85055e44 | −0.309891 | ||||||||
\(647\) | − | 6.54008e44i | − | 0.693609i | −0.937937 | − | 0.346805i | \(-0.887267\pi\) | ||
0.937937 | − | 0.346805i | \(-0.112733\pi\) | |||||||
\(648\) | −4.82829e44 | − | 6.89991e44i | −0.499567 | − | 0.713910i | ||||
\(649\) | 5.22560e44 | 0.527498 | ||||||||
\(650\) | 2.26559e44i | 0.223135i | ||||||||
\(651\) | 7.03140e43 | + | 4.57065e44i | 0.0675687 | + | 0.439220i | ||||
\(652\) | −1.64764e44 | −0.154490 | ||||||||
\(653\) | 1.22828e45i | 1.12379i | 0.827207 | + | 0.561897i | \(0.189928\pi\) | ||||
−0.827207 | + | 0.561897i | \(0.810072\pi\) | |||||||
\(654\) | −7.29269e43 | + | 1.12189e43i | −0.0651094 | + | 0.0100163i | ||||
\(655\) | −5.41823e44 | −0.472059 | ||||||||
\(656\) | 2.08798e44i | 0.177527i | ||||||||
\(657\) | 4.28040e44 | − | 1.34890e44i | 0.355172 | − | 0.111927i | ||||
\(658\) | 6.64048e44 | 0.537755 | ||||||||
\(659\) | 9.83151e44i | 0.777058i | 0.921436 | + | 0.388529i | \(0.127017\pi\) | ||||
−0.921436 | + | 0.388529i | \(0.872983\pi\) | |||||||
\(660\) | 5.79060e43 | + | 3.76409e44i | 0.0446705 | + | 0.290373i | ||||
\(661\) | 3.07694e44 | 0.231684 | 0.115842 | − | 0.993268i | \(-0.463043\pi\) | ||||
0.115842 | + | 0.993268i | \(0.463043\pi\) | |||||||
\(662\) | − | 2.69451e44i | − | 0.198040i | ||||||
\(663\) | −8.56498e44 | + | 1.31762e44i | −0.614483 | + | 0.0945309i | ||||
\(664\) | −2.45175e45 | −1.71707 | ||||||||
\(665\) | 1.37474e45i | 0.939883i | ||||||||
\(666\) | −1.04961e44 | − | 3.33067e44i | −0.0700552 | − | 0.222303i | ||||
\(667\) | 3.48206e45 | 2.26894 | ||||||||
\(668\) | − | 9.99795e44i | − | 0.636044i | ||||||
\(669\) | 2.05426e44 | + | 1.33534e45i | 0.127596 | + | 0.829419i | ||||
\(670\) | −1.12183e45 | −0.680348 | ||||||||
\(671\) | − | 2.81457e44i | − | 0.166668i | ||||||
\(672\) | 1.82639e45 | − | 2.80969e44i | 1.05605 | − | 0.162461i | ||||
\(673\) | −1.93264e45 | −1.09122 | −0.545608 | − | 0.838041i | \(-0.683701\pi\) | ||||
−0.545608 | + | 0.838041i | \(0.683701\pi\) | |||||||
\(674\) | 1.40678e45i | 0.775656i | ||||||||
\(675\) | 3.18903e44 | + | 6.47037e44i | 0.171711 | + | 0.348393i | ||||
\(676\) | 4.80621e44 | 0.252729 | ||||||||
\(677\) | − | 1.63334e45i | − | 0.838797i | −0.907802 | − | 0.419398i | \(-0.862241\pi\) | ||
0.907802 | − | 0.419398i | \(-0.137759\pi\) | |||||||
\(678\) | −9.71724e43 | − | 6.31653e44i | −0.0487380 | − | 0.316814i | ||||
\(679\) | −2.79971e45 | −1.37150 | ||||||||
\(680\) | 7.66126e44i | 0.366570i | ||||||||
\(681\) | 5.11643e44 | − | 7.87101e43i | 0.239118 | − | 0.0367855i | ||||
\(682\) | 2.32809e44 | 0.106280 | ||||||||
\(683\) | − | 2.16605e45i | − | 0.965912i | −0.875645 | − | 0.482956i | \(-0.839563\pi\) | ||
0.875645 | − | 0.482956i | \(-0.160437\pi\) | |||||||
\(684\) | 1.91038e45 | − | 6.02028e44i | 0.832191 | − | 0.262252i | ||||
\(685\) | 1.79762e45 | 0.764978 | ||||||||
\(686\) | − | 1.14638e45i | − | 0.476589i | ||||||
\(687\) | −3.76405e44 | − | 2.44676e45i | −0.152879 | − | 0.993765i | ||||
\(688\) | −1.17130e45 | −0.464787 | ||||||||
\(689\) | − | 2.59331e45i | − | 1.00542i | ||||||
\(690\) | 1.98286e45 | − | 3.05039e44i | 0.751114 | − | 0.115550i | ||||
\(691\) | −2.09275e45 | −0.774584 | −0.387292 | − | 0.921957i | \(-0.626589\pi\) | ||||
−0.387292 | + | 0.921957i | \(0.626589\pi\) | |||||||
\(692\) | 2.17559e45i | 0.786826i | ||||||||
\(693\) | 4.40082e44 | + | 1.39649e45i | 0.155525 | + | 0.493521i | ||||
\(694\) | 1.37165e44 | 0.0473687 | ||||||||
\(695\) | − | 3.39414e43i | − | 0.0114544i | ||||||
\(696\) | 4.66248e44 | + | 3.03077e45i | 0.153769 | + | 0.999552i | ||||
\(697\) | −9.26564e44 | −0.298642 | ||||||||
\(698\) | − | 5.76563e44i | − | 0.181619i | ||||||
\(699\) | −1.21354e45 | + | 1.86689e44i | −0.373612 | + | 0.0574758i | ||||
\(700\) | −1.00787e45 | −0.303274 | ||||||||
\(701\) | − | 1.28379e45i | − | 0.377578i | −0.982018 | − | 0.188789i | \(-0.939544\pi\) | ||
0.982018 | − | 0.188789i | \(-0.0604562\pi\) | |||||||
\(702\) | −1.79247e45 | + | 8.83446e44i | −0.515296 | + | 0.253972i | ||||
\(703\) | 1.93376e45 | 0.543396 | ||||||||
\(704\) | − | 3.49417e44i | − | 0.0959803i | ||||||
\(705\) | −4.61950e44 | − | 3.00283e45i | −0.124042 | − | 0.806315i | ||||
\(706\) | 9.85823e44 | 0.258776 | ||||||||
\(707\) | 5.32080e45i | 1.36542i | ||||||||
\(708\) | −3.13583e45 | + | 4.82411e44i | −0.786721 | + | 0.121028i | ||||
\(709\) | 3.46980e45 | 0.851068 | 0.425534 | − | 0.904942i | \(-0.360086\pi\) | ||||
0.425534 | + | 0.904942i | \(0.360086\pi\) | |||||||
\(710\) | 2.03682e45i | 0.488448i | ||||||||
\(711\) | 1.07161e45 | − | 3.37701e44i | 0.251260 | − | 0.0791806i | ||||
\(712\) | 1.66614e45 | 0.381972 | ||||||||
\(713\) | 3.73695e45i | 0.837692i | ||||||||
\(714\) | 1.92365e44 | + | 1.25044e45i | 0.0421653 | + | 0.274089i | ||||
\(715\) | 2.10397e45 | 0.450965 | ||||||||
\(716\) | 3.53911e45i | 0.741799i | ||||||||
\(717\) | −1.24645e44 | + | 1.91751e43i | −0.0255487 | + | 0.00393036i | ||||
\(718\) | −3.10793e45 | −0.622990 | ||||||||
\(719\) | − | 3.30156e44i | − | 0.0647227i | −0.999476 | − | 0.0323614i | \(-0.989697\pi\) | ||
0.999476 | − | 0.0323614i | \(-0.0103027\pi\) | |||||||
\(720\) | −3.92048e44 | − | 1.24407e45i | −0.0751655 | − | 0.238519i | ||||
\(721\) | 5.91693e44 | 0.110951 | ||||||||
\(722\) | − | 9.29690e44i | − | 0.170507i | ||||||
\(723\) | −8.01508e44 | − | 5.21007e45i | −0.143779 | − | 0.934611i | ||||
\(724\) | 1.05085e45 | 0.184385 | ||||||||
\(725\) | − | 2.62660e45i | − | 0.450803i | ||||||
\(726\) | −2.19786e45 | + | 3.38114e44i | −0.368989 | + | 0.0567646i | ||||
\(727\) | −7.70469e45 | −1.26533 | −0.632666 | − | 0.774425i | \(-0.718039\pi\) | ||||
−0.632666 | + | 0.774425i | \(0.718039\pi\) | |||||||
\(728\) | − | 6.50043e45i | − | 1.04434i | ||||||
\(729\) | −3.87562e45 | + | 5.04612e45i | −0.609118 | + | 0.793080i | ||||
\(730\) | −9.41505e44 | −0.144763 | ||||||||
\(731\) | − | 5.19779e45i | − | 0.781881i | ||||||
\(732\) | 2.59832e44 | + | 1.68900e45i | 0.0382398 | + | 0.248572i | ||||
\(733\) | 6.90519e45 | 0.994288 | 0.497144 | − | 0.867668i | \(-0.334382\pi\) | ||||
0.497144 | + | 0.867668i | \(0.334382\pi\) | |||||||
\(734\) | − | 3.03570e45i | − | 0.427683i | ||||||
\(735\) | 4.23276e44 | − | 6.51159e43i | 0.0583480 | − | 0.00897615i | ||||
\(736\) | 1.49326e46 | 2.01414 | ||||||||
\(737\) | − | 6.61630e45i | − | 0.873244i | ||||||
\(738\) | −2.03790e45 | + | 6.42211e44i | −0.263196 | + | 0.0829422i | ||||
\(739\) | 7.70771e45 | 0.974125 | 0.487062 | − | 0.873367i | \(-0.338068\pi\) | ||||
0.487062 | + | 0.873367i | \(0.338068\pi\) | |||||||
\(740\) | − | 2.23232e45i | − | 0.276089i | ||||||
\(741\) | −1.68254e45 | − | 1.09371e46i | −0.203646 | − | 1.32377i | ||||
\(742\) | −3.78609e45 | −0.448465 | ||||||||
\(743\) | 1.53205e46i | 1.77604i | 0.459803 | + | 0.888021i | \(0.347920\pi\) | ||||
−0.459803 | + | 0.888021i | \(0.652080\pi\) | |||||||
\(744\) | −3.25262e45 | + | 5.00378e44i | −0.369034 | + | 0.0567716i | ||||
\(745\) | −4.71317e45 | −0.523374 | ||||||||
\(746\) | 2.80420e44i | 0.0304781i | ||||||||
\(747\) | 5.56756e45 | + | 1.76673e46i | 0.592291 | + | 1.87949i | ||||
\(748\) | −1.94075e45 | −0.202090 | ||||||||
\(749\) | 5.68486e44i | 0.0579443i | ||||||||
\(750\) | −8.22510e44 | − | 5.34660e45i | −0.0820656 | − | 0.533454i | ||||
\(751\) | −1.09755e46 | −1.07198 | −0.535988 | − | 0.844226i | \(-0.680061\pi\) | ||||
−0.535988 | + | 0.844226i | \(0.680061\pi\) | |||||||
\(752\) | − | 3.48893e45i | − | 0.333585i | ||||||
\(753\) | 6.95456e45 | − | 1.06988e45i | 0.650954 | − | 0.100141i | ||||
\(754\) | 7.27639e45 | 0.666768 | ||||||||
\(755\) | 4.37592e45i | 0.392571i | ||||||||
\(756\) | −3.93009e45 | − | 7.97394e45i | −0.345186 | − | 0.700364i | ||||
\(757\) | −1.74621e46 | −1.50163 | −0.750816 | − | 0.660511i | \(-0.770340\pi\) | ||||
−0.750816 | + | 0.660511i | \(0.770340\pi\) | |||||||
\(758\) | 8.43642e45i | 0.710315i | ||||||||
\(759\) | 1.79905e45 | + | 1.16944e46i | 0.148311 | + | 0.964074i | ||||
\(760\) | −9.78309e45 | −0.789694 | ||||||||
\(761\) | − | 5.05977e45i | − | 0.399923i | −0.979804 | − | 0.199961i | \(-0.935918\pi\) | ||
0.979804 | − | 0.199961i | \(-0.0640816\pi\) | |||||||
\(762\) | 1.09747e46 | − | 1.68832e45i | 0.849400 | − | 0.130670i | ||||
\(763\) | −1.81338e45 | −0.137435 | ||||||||
\(764\) | 3.58747e45i | 0.266253i | ||||||||
\(765\) | 5.52068e45 | − | 1.73976e45i | 0.401245 | − | 0.126446i | ||||
\(766\) | −2.60450e44 | −0.0185380 | ||||||||
\(767\) | 1.75280e46i | 1.22182i | ||||||||
\(768\) | 1.46323e45 | + | 9.51149e45i | 0.0998925 | + | 0.649335i | ||||
\(769\) | 1.03873e45 | 0.0694514 | 0.0347257 | − | 0.999397i | \(-0.488944\pi\) | ||||
0.0347257 | + | 0.999397i | \(0.488944\pi\) | |||||||
\(770\) | − | 3.07168e45i | − | 0.201152i | ||||||
\(771\) | 1.26104e46 | − | 1.93996e45i | 0.808831 | − | 0.124429i | ||||
\(772\) | 6.27813e45 | 0.394415 | ||||||||
\(773\) | − | 3.24752e45i | − | 0.199839i | −0.994996 | − | 0.0999194i | \(-0.968142\pi\) | ||
0.994996 | − | 0.0999194i | \(-0.0318585\pi\) | |||||||
\(774\) | −3.60264e45 | − | 1.14321e46i | −0.217153 | − | 0.689080i | ||||
\(775\) | 2.81887e45 | 0.166436 | ||||||||
\(776\) | − | 1.99236e46i | − | 1.15234i | ||||||
\(777\) | −1.30497e45 | − | 8.48274e45i | −0.0739373 | − | 0.480618i | ||||
\(778\) | 8.07978e45 | 0.448462 | ||||||||
\(779\) | − | 1.18318e46i | − | 0.643357i | ||||||
\(780\) | −1.26257e46 | + | 1.94232e45i | −0.672579 | + | 0.103468i | ||||
\(781\) | −1.20127e46 | −0.626935 | ||||||||
\(782\) | 1.02236e46i | 0.522750i | ||||||||
\(783\) | 2.07809e46 | − | 1.02422e46i | 1.04106 | − | 0.513103i | ||||
\(784\) | 4.91796e44 | 0.0241395 | ||||||||
\(785\) | − | 1.88611e46i | − | 0.907096i | ||||||
\(786\) | −9.68144e44 | − | 6.29327e45i | −0.0456225 | − | 0.296562i | ||||
\(787\) | −2.75850e46 | −1.27373 | −0.636864 | − | 0.770976i | \(-0.719769\pi\) | ||||
−0.636864 | + | 0.770976i | \(0.719769\pi\) | |||||||
\(788\) | 9.59733e45i | 0.434241i | ||||||||
\(789\) | −7.31967e45 | + | 1.12604e45i | −0.324533 | + | 0.0499256i | ||||
\(790\) | −2.35709e45 | −0.102410 | ||||||||
\(791\) | − | 1.57066e46i | − | 0.668740i | ||||||
\(792\) | −9.93788e45 | + | 3.13177e45i | −0.414659 | + | 0.130673i | ||||
\(793\) | 9.44080e45 | 0.386045 | ||||||||
\(794\) | 2.06651e46i | 0.828149i | ||||||||
\(795\) | 2.63382e45 | + | 1.71207e46i | 0.103446 | + | 0.672432i | ||||
\(796\) | 2.86908e46 | 1.10442 | ||||||||
\(797\) | 1.67857e46i | 0.633294i | 0.948543 | + | 0.316647i | \(0.102557\pi\) | ||||
−0.948543 | + | 0.316647i | \(0.897443\pi\) | |||||||
\(798\) | −1.59676e46 | + | 2.45642e45i | −0.590463 | + | 0.0908357i | ||||
\(799\) | 1.54825e46 | 0.561168 | ||||||||
\(800\) | − | 1.12640e46i | − | 0.400178i | ||||||
\(801\) | −3.78355e45 | − | 1.20061e46i | −0.131759 | − | 0.418103i | ||||
\(802\) | 6.74383e45 | 0.230206 | ||||||||
\(803\) | − | 5.55278e45i | − | 0.185807i | ||||||
\(804\) | 6.10797e45 | + | 3.97039e46i | 0.200355 | + | 1.30237i | ||||
\(805\) | 4.93053e46 | 1.58547 | ||||||||
\(806\) | 7.80903e45i | 0.246171i | ||||||||
\(807\) | −2.82120e46 | + | 4.34007e45i | −0.871880 | + | 0.134128i | ||||
\(808\) | −3.78646e46 | −1.14723 | ||||||||
\(809\) | 6.96435e45i | 0.206873i | 0.994636 | + | 0.103437i | \(0.0329839\pi\) | ||||
−0.994636 | + | 0.103437i | \(0.967016\pi\) | |||||||
\(810\) | 1.09364e46 | − | 7.65288e45i | 0.318504 | − | 0.222877i | ||||
\(811\) | −5.91909e46 | −1.69013 | −0.845067 | − | 0.534660i | \(-0.820440\pi\) | ||||
−0.845067 | + | 0.534660i | \(0.820440\pi\) | |||||||
\(812\) | 3.23697e46i | 0.906237i | ||||||||
\(813\) | −3.65053e44 | − | 2.37297e45i | −0.0100209 | − | 0.0651394i | ||||
\(814\) | −4.32074e45 | −0.116297 | ||||||||
\(815\) | − | 6.08011e45i | − | 0.160468i | ||||||
\(816\) | 6.56985e45 | − | 1.01069e45i | 0.170025 | − | 0.0261563i | ||||
\(817\) | 6.63735e46 | 1.68439 | ||||||||
\(818\) | − | 8.99611e45i | − | 0.223873i | ||||||
\(819\) | −4.68419e46 | + | 1.47615e46i | −1.14312 | + | 0.360237i | ||||
\(820\) | −1.36586e46 | −0.326877 | ||||||||
\(821\) | − | 4.49542e46i | − | 1.05507i | −0.849535 | − | 0.527533i | \(-0.823117\pi\) | ||
0.849535 | − | 0.527533i | \(-0.176883\pi\) | |||||||
\(822\) | 3.21204e45 | + | 2.08793e46i | 0.0739319 | + | 0.480582i | ||||
\(823\) | 6.74191e46 | 1.52190 | 0.760949 | − | 0.648812i | \(-0.224734\pi\) | ||||
0.760949 | + | 0.648812i | \(0.224734\pi\) | |||||||
\(824\) | 4.21069e45i | 0.0932218i | ||||||||
\(825\) | 8.82139e45 | − | 1.35707e45i | 0.191546 | − | 0.0294671i | ||||
\(826\) | 2.55899e46 | 0.544990 | ||||||||
\(827\) | 4.31119e46i | 0.900551i | 0.892890 | + | 0.450276i | \(0.148674\pi\) | ||||
−0.892890 | + | 0.450276i | \(0.851326\pi\) | |||||||
\(828\) | −2.15918e46 | − | 6.85163e46i | −0.442389 | − | 1.40381i | ||||
\(829\) | −6.45320e46 | −1.29689 | −0.648444 | − | 0.761262i | \(-0.724580\pi\) | ||||
−0.648444 | + | 0.761262i | \(0.724580\pi\) | |||||||
\(830\) | − | 3.88604e46i | − | 0.766052i | ||||||
\(831\) | −1.32051e46 | − | 8.58375e46i | −0.255344 | − | 1.65982i | ||||
\(832\) | 1.17204e46 | 0.222315 | ||||||||
\(833\) | 2.18240e45i | 0.0406082i | ||||||||
\(834\) | 3.94229e44 | − | 6.06475e43i | 0.00719602 | − | 0.00110702i | ||||
\(835\) | 3.68943e46 | 0.660656 | ||||||||
\(836\) | − | 2.47826e46i | − | 0.435358i | ||||||
\(837\) | 1.09919e46 | + | 2.23020e46i | 0.189438 | + | 0.384359i | ||||
\(838\) | −3.25796e46 | −0.550861 | ||||||||
\(839\) | − | 8.91849e44i | − | 0.0147945i | −0.999973 | − | 0.00739725i | \(-0.997645\pi\) | ||
0.999973 | − | 0.00739725i | \(-0.00235464\pi\) | |||||||
\(840\) | 6.60198e45 | + | 4.29151e46i | 0.107450 | + | 0.698460i | ||||
\(841\) | −2.17353e46 | −0.347080 | ||||||||
\(842\) | 1.47530e46i | 0.231146i | ||||||||
\(843\) | 4.45522e46 | − | 6.85383e45i | 0.684901 | − | 0.105364i | ||||
\(844\) | −1.62481e46 | −0.245089 | ||||||||
\(845\) | 1.77358e46i | 0.262509i | ||||||||
\(846\) | 3.40524e46 | − | 1.07311e46i | 0.494564 | − | 0.155854i | ||||
\(847\) | −5.46514e46 | −0.778873 | ||||||||
\(848\) | 1.98923e46i | 0.278196i | ||||||||
\(849\) | 8.77863e45 | + | 5.70640e46i | 0.120477 | + | 0.783140i | ||||
\(850\) | 7.71188e45 | 0.103862 | ||||||||
\(851\) | − | 6.93546e46i | − | 0.916647i | ||||||
\(852\) | 7.20869e46 | − | 1.10897e46i | 0.935024 | − | 0.143842i | ||||
\(853\) | −2.65966e46 | −0.338565 | −0.169283 | − | 0.985568i | \(-0.554145\pi\) | ||||
−0.169283 | + | 0.985568i | \(0.554145\pi\) | |||||||
\(854\) | − | 1.37830e46i | − | 0.172195i | ||||||
\(855\) | 2.22159e46 | + | 7.04967e46i | 0.272400 | + | 0.864392i | ||||
\(856\) | −4.04554e45 | −0.0486851 | ||||||||
\(857\) | 1.45906e47i | 1.72338i | 0.507436 | + | 0.861689i | \(0.330593\pi\) | ||||
−0.507436 | + | 0.861689i | \(0.669407\pi\) | |||||||
\(858\) | 3.75944e45 | + | 2.44376e46i | 0.0435839 | + | 0.283310i | ||||
\(859\) | −8.28772e46 | −0.943071 | −0.471536 | − | 0.881847i | \(-0.656300\pi\) | ||||
−0.471536 | + | 0.881847i | \(0.656300\pi\) | |||||||
\(860\) | − | 7.66212e46i | − | 0.855803i | ||||||
\(861\) | −5.19022e46 | + | 7.98453e45i | −0.569030 | + | 0.0875385i | ||||
\(862\) | −1.45789e45 | −0.0156895 | ||||||||
\(863\) | 1.45539e47i | 1.53748i | 0.639564 | + | 0.768738i | \(0.279115\pi\) | ||||
−0.639564 | + | 0.768738i | \(0.720885\pi\) | |||||||
\(864\) | 8.91172e46 | − | 4.39229e46i | 0.924148 | − | 0.455482i | ||||
\(865\) | −8.02831e46 | −0.817272 | ||||||||
\(866\) | − | 1.94419e46i | − | 0.194290i | ||||||
\(867\) | −1.10135e46 | − | 7.15912e46i | −0.108048 | − | 0.702351i | ||||
\(868\) | −3.47391e46 | −0.334583 | ||||||||
\(869\) | − | 1.39015e46i | − | 0.131446i | ||||||
\(870\) | −4.80379e46 | + | 7.39006e45i | −0.445940 | + | 0.0686025i | ||||
\(871\) | 2.21928e47 | 2.02266 | ||||||||
\(872\) | − | 1.29046e46i | − | 0.115473i | ||||||
\(873\) | −1.43569e47 | + | 4.52436e46i | −1.26134 | + | 0.397492i | ||||
\(874\) | −1.30550e47 | −1.12615 | ||||||||
\(875\) | − | 1.32947e47i | − | 1.12603i | ||||||
\(876\) | 5.12615e45 | + | 3.33217e46i | 0.0426310 | + | 0.277116i | ||||
\(877\) | 1.39827e47 | 1.14182 | 0.570911 | − | 0.821012i | \(-0.306590\pi\) | ||||
0.570911 | + | 0.821012i | \(0.306590\pi\) | |||||||
\(878\) | − | 2.37076e46i | − | 0.190097i | ||||||
\(879\) | 1.65126e47 | − | 2.54027e46i | 1.30015 | − | 0.200013i | ||||
\(880\) | −1.61387e46 | −0.124780 | ||||||||
\(881\) | − | 4.31984e46i | − | 0.327984i | −0.986462 | − | 0.163992i | \(-0.947563\pi\) | ||
0.986462 | − | 0.163992i | \(-0.0524372\pi\) | |||||||
\(882\) | 1.51264e45 | + | 4.79999e45i | 0.0112782 | + | 0.0357885i | ||||
\(883\) | −3.15126e46 | −0.230735 | −0.115368 | − | 0.993323i | \(-0.536805\pi\) | ||||
−0.115368 | + | 0.993323i | \(0.536805\pi\) | |||||||
\(884\) | − | 6.50980e46i | − | 0.468092i | ||||||
\(885\) | −1.78018e46 | − | 1.15718e47i | −0.125711 | − | 0.817163i | ||||
\(886\) | −4.03683e46 | −0.279963 | ||||||||
\(887\) | − | 1.48664e47i | − | 1.01258i | −0.862364 | − | 0.506289i | \(-0.831017\pi\) | ||
0.862364 | − | 0.506289i | \(-0.168983\pi\) | |||||||
\(888\) | 6.03660e46 | − | 9.28659e45i | 0.403817 | − | 0.0621225i | ||||
\(889\) | 2.72894e47 | 1.79294 | ||||||||
\(890\) | 2.64084e46i | 0.170413i | ||||||||
\(891\) | 4.51348e46 | + | 6.45003e46i | 0.286068 | + | 0.408807i | ||||
\(892\) | −1.01492e47 | −0.631823 | ||||||||
\(893\) | 1.97705e47i | 1.20891i | ||||||||
\(894\) | −8.42162e45 | − | 5.47434e46i | −0.0505819 | − | 0.328800i | ||||
\(895\) | −1.30600e47 | −0.770502 | ||||||||
\(896\) | 1.67260e47i | 0.969315i | ||||||||
\(897\) | −3.92262e47 | + | 6.03448e46i | −2.23304 | + | 0.343527i | ||||
\(898\) | 9.80820e46 | 0.548489 | ||||||||
\(899\) | − | 9.05336e46i | − | 0.497342i | ||||||
\(900\) | −5.16836e46 | + | 1.62873e46i | −0.278915 | + | 0.0878958i | ||||
\(901\) | −8.82741e46 | −0.467990 | ||||||||
\(902\) | 2.64367e46i | 0.137690i | ||||||||
\(903\) | −4.47912e46 | − | 2.91158e47i | −0.229186 | − | 1.48979i | ||||
\(904\) | 1.11773e47 | 0.561878 | ||||||||
\(905\) | 3.87784e46i | 0.191519i | ||||||||
\(906\) | −5.08263e46 | + | 7.81902e45i | −0.246625 | + | 0.0379404i | ||||
\(907\) | 2.38350e46 | 0.113631 | 0.0568157 | − | 0.998385i | \(-0.481905\pi\) | ||||
0.0568157 | + | 0.998385i | \(0.481905\pi\) | |||||||
\(908\) | 3.88873e46i | 0.182152i | ||||||||
\(909\) | 8.59848e46 | + | 2.72851e47i | 0.395731 | + | 1.25575i | ||||
\(910\) | 1.03032e47 | 0.465920 | ||||||||
\(911\) | 1.76038e47i | 0.782190i | 0.920350 | + | 0.391095i | \(0.127904\pi\) | ||||
−0.920350 | + | 0.391095i | \(0.872096\pi\) | |||||||
\(912\) | 1.29061e46 | + | 8.38942e46i | 0.0563480 | + | 0.366281i | ||||
\(913\) | 2.29190e47 | 0.983247 | ||||||||
\(914\) | 1.63440e47i | 0.689000i | ||||||||
\(915\) | −6.23271e46 | + | 9.58828e45i | −0.258190 | + | 0.0397195i | ||||
\(916\) | 1.85966e47 | 0.757016 | ||||||||
\(917\) | − | 1.56487e47i | − | 0.625992i | ||||||
\(918\) | 3.00717e46 | + | 6.10140e46i | 0.118216 | + | 0.239854i | ||||
\(919\) | −1.98683e47 | −0.767561 | −0.383781 | − | 0.923424i | \(-0.625378\pi\) | ||||
−0.383781 | + | 0.923424i | \(0.625378\pi\) | |||||||
\(920\) | 3.50873e47i | 1.33212i | ||||||||
\(921\) | −1.44378e45 | − | 9.38503e45i | −0.00538698 | − | 0.0350172i | ||||
\(922\) | 1.10315e47 | 0.404518 | ||||||||
\(923\) | − | 4.02936e47i | − | 1.45214i | ||||||
\(924\) | −1.08713e47 | + | 1.67242e46i | −0.385061 | + | 0.0592370i | ||||
\(925\) | −5.23159e46 | −0.182124 | ||||||||
\(926\) | − | 4.70314e46i | − | 0.160921i | ||||||
\(927\) | 3.03421e46 | − | 9.56183e45i | 0.102040 | − | 0.0321562i | ||||
\(928\) | −3.61765e47 | −1.19580 | ||||||||
\(929\) | − | 4.91494e47i | − | 1.59686i | −0.602088 | − | 0.798430i | \(-0.705664\pi\) | ||
0.602088 | − | 0.798430i | \(-0.294336\pi\) | |||||||
\(930\) | −7.93102e45 | − | 5.15543e46i | −0.0253281 | − | 0.164641i | ||||
\(931\) | −2.78683e46 | −0.0874813 | ||||||||
\(932\) | − | 9.22353e46i | − | 0.284605i | ||||||
\(933\) | 2.34692e47 | − | 3.61045e46i | 0.711855 | − | 0.109510i | ||||
\(934\) | −9.22056e46 | −0.274921 | ||||||||
\(935\) | − | 7.16174e46i | − | 0.209910i | ||||||
\(936\) | −1.05048e47 | − | 3.33343e47i | −0.302673 | − | 0.960456i | ||||
\(937\) | 1.90187e46 | 0.0538700 | 0.0269350 | − | 0.999637i | \(-0.491425\pi\) | ||||
0.0269350 | + | 0.999637i | \(0.491425\pi\) | |||||||
\(938\) | − | 3.24003e47i | − | 0.902202i | ||||||
\(939\) | 5.67653e46 | + | 3.68994e47i | 0.155394 | + | 1.01011i | ||||
\(940\) | 2.28230e47 | 0.614224 | ||||||||
\(941\) | 5.88799e47i | 1.55788i | 0.627100 | + | 0.778939i | \(0.284242\pi\) | ||||
−0.627100 | + | 0.778939i | \(0.715758\pi\) | |||||||
\(942\) | 2.19072e47 | − | 3.37016e46i | 0.569865 | − | 0.0876670i | ||||
\(943\) | −4.24351e47 | −1.08527 | ||||||||
\(944\) | − | 1.34450e47i | − | 0.338073i | ||||||
\(945\) | 2.94253e47 | − | 1.45027e47i | 0.727465 | − | 0.358543i | ||||
\(946\) | −1.48303e47 | −0.360490 | ||||||||
\(947\) | − | 3.72450e47i | − | 0.890161i | −0.895491 | − | 0.445080i | \(-0.853175\pi\) | ||
0.895491 | − | 0.445080i | \(-0.146825\pi\) | |||||||
\(948\) | 1.28335e46 | + | 8.34219e46i | 0.0301586 | + | 0.196041i | ||||
\(949\) | 1.86255e47 | 0.430376 | ||||||||
\(950\) | 9.84774e46i | 0.223748i | ||||||||
\(951\) | 6.01391e47 | − | 9.25168e46i | 1.34360 | − | 0.206696i | ||||
\(952\) | −2.21269e47 | −0.486105 | ||||||||
\(953\) | 7.63371e47i | 1.64911i | 0.565783 | + | 0.824554i | \(0.308574\pi\) | ||||
−0.565783 | + | 0.824554i | \(0.691426\pi\) | |||||||
\(954\) | −1.94151e47 | + | 6.11837e46i | −0.412445 | + | 0.129975i | ||||
\(955\) | −1.32384e47 | −0.276555 | ||||||||
\(956\) | − | 9.47363e45i | − | 0.0194621i | ||||||
\(957\) | −4.35848e46 | − | 2.83316e47i | −0.0880531 | − | 0.572375i | ||||
\(958\) | −1.15623e47 | −0.229719 | ||||||||
\(959\) | 5.19181e47i | 1.01443i | ||||||||
\(960\) | −7.73766e46 | + | 1.19035e46i | −0.148686 | + | 0.0228736i | ||||
\(961\) | −4.31984e47 | −0.816381 | ||||||||
\(962\) | − | 1.44929e47i | − | 0.269373i | ||||||
\(963\) | 9.18680e45 | + | 2.91520e46i | 0.0167936 | + | 0.0532903i | ||||
\(964\) | 3.95991e47 | 0.711955 | ||||||||
\(965\) | 2.31675e47i | 0.409677i | ||||||||
\(966\) | 8.81000e46 | + | 5.72680e47i | 0.153229 | + | 0.996043i | ||||
\(967\) | −1.08220e47 | −0.185134 | −0.0925669 | − | 0.995706i | \(-0.529507\pi\) | ||||
−0.0925669 | + | 0.995706i | \(0.529507\pi\) | |||||||
\(968\) | − | 3.88918e47i | − | 0.654413i | ||||||
\(969\) | −3.72290e47 | + | 5.72724e46i | −0.616170 | + | 0.0947905i | ||||
\(970\) | 3.15791e47 | 0.514105 | ||||||||
\(971\) | 4.75830e47i | 0.761982i | 0.924579 | + | 0.380991i | \(0.124417\pi\) | ||||
−0.924579 | + | 0.380991i | \(0.875583\pi\) | |||||||
\(972\) | −3.30395e47 | − | 3.45394e47i | −0.520443 | − | 0.544069i | ||||
\(973\) | 9.80282e45 | 0.0151896 | ||||||||
\(974\) | − | 2.14077e47i | − | 0.326307i | ||||||
\(975\) | 4.55196e46 | + | 2.95893e47i | 0.0682534 | + | 0.443670i | ||||
\(976\) | −7.24166e46 | −0.106817 | ||||||||
\(977\) | 3.83901e46i | 0.0557065i | 0.999612 | + | 0.0278532i | \(0.00886711\pi\) | ||||
−0.999612 | + | 0.0278532i | \(0.991133\pi\) | |||||||
\(978\) | 7.06204e46 | − | 1.08641e46i | 0.100811 | − | 0.0155086i | ||||
\(979\) | −1.55750e47 | −0.218729 | ||||||||
\(980\) | 3.21710e46i | 0.0444475i | ||||||||
\(981\) | −9.29905e46 | + | 2.93045e46i | −0.126396 | + | 0.0398318i | ||||
\(982\) | 7.29911e47 | 0.976081 | ||||||||
\(983\) | 1.04363e47i | 0.137306i | 0.997641 | + | 0.0686531i | \(0.0218702\pi\) | ||||
−0.997641 | + | 0.0686531i | \(0.978130\pi\) | |||||||
\(984\) | −5.68206e46 | − | 3.69353e47i | −0.0735503 | − | 0.478102i | ||||
\(985\) | −3.54159e47 | −0.451044 | ||||||||
\(986\) | − | 2.47682e47i | − | 0.310359i | ||||||
\(987\) | 8.67265e47 | − | 1.33418e47i | 1.06925 | − | 0.164491i | ||||
\(988\) | 8.31273e47 | 1.00840 | ||||||||
\(989\) | − | 2.38050e48i | − | 2.84137i | ||||||
\(990\) | −4.96387e46 | − | 1.57516e47i | −0.0582985 | − | 0.184996i | ||||
\(991\) | −6.69689e47 | −0.773917 | −0.386959 | − | 0.922097i | \(-0.626474\pi\) | ||||
−0.386959 | + | 0.922097i | \(0.626474\pi\) | |||||||
\(992\) | − | 3.88247e47i | − | 0.441490i | ||||||
\(993\) | −5.41373e46 | − | 3.51911e47i | −0.0605771 | − | 0.393772i | ||||
\(994\) | −5.88264e47 | −0.647725 | ||||||||
\(995\) | 1.05874e48i | 1.14715i | ||||||||
\(996\) | −1.37535e48 | + | 2.11581e47i | −1.46644 | + | 0.225594i | ||||
\(997\) | 6.01354e47 | 0.630968 | 0.315484 | − | 0.948931i | \(-0.397833\pi\) | ||||
0.315484 | + | 0.948931i | \(0.397833\pi\) | |||||||
\(998\) | 5.48916e47i | 0.566783i | ||||||||
\(999\) | −2.04001e47 | − | 4.13907e47i | −0.207293 | − | 0.420586i |
(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 | 3.33.b.a.2.5 | ✓ | 10 | |
3.2 | odd | 2 | inner | 3.33.b.a.2.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.33.b.a.2.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
3.33.b.a.2.6 | yes | 10 | 3.2 | odd | 2 | inner |