Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,9,Mod(21,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.21");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.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: | \(8.96232942134\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7944x^{6} + 15215349x^{4} + 1757611988x^{2} + 38177252100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 11^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.5 | ||
Root | \(9.64354i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.21 |
Dual form | 22.9.b.a.21.1 |
$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.3137i | 0.707107i | ||||||||
\(3\) | −143.261 | −1.76865 | −0.884326 | − | 0.466871i | \(-0.845381\pi\) | ||||
−0.884326 | + | 0.466871i | \(0.845381\pi\) | |||||||
\(4\) | −128.000 | −0.500000 | ||||||||
\(5\) | −309.991 | −0.495986 | −0.247993 | − | 0.968762i | \(-0.579771\pi\) | ||||
−0.247993 | + | 0.968762i | \(0.579771\pi\) | |||||||
\(6\) | − | 1620.81i | − | 1.25063i | ||||||
\(7\) | 1256.92i | 0.523500i | 0.965136 | + | 0.261750i | \(0.0842997\pi\) | ||||
−0.965136 | + | 0.261750i | \(0.915700\pi\) | |||||||
\(8\) | − | 1448.15i | − | 0.353553i | ||||||
\(9\) | 13962.6 | 2.12813 | ||||||||
\(10\) | − | 3507.15i | − | 0.350715i | ||||||
\(11\) | 2859.33 | − | 14359.1i | 0.195296 | − | 0.980744i | ||||
\(12\) | 18337.4 | 0.884326 | ||||||||
\(13\) | 38587.8i | 1.35107i | 0.737330 | + | 0.675533i | \(0.236086\pi\) | ||||
−0.737330 | + | 0.675533i | \(0.763914\pi\) | |||||||
\(14\) | −14220.5 | −0.370171 | ||||||||
\(15\) | 44409.6 | 0.877226 | ||||||||
\(16\) | 16384.0 | 0.250000 | ||||||||
\(17\) | − | 31930.4i | − | 0.382304i | −0.981560 | − | 0.191152i | \(-0.938778\pi\) | ||
0.981560 | − | 0.191152i | \(-0.0612224\pi\) | |||||||
\(18\) | 157969.i | 1.50481i | ||||||||
\(19\) | − | 196632.i | − | 1.50882i | −0.656401 | − | 0.754412i | \(-0.727922\pi\) | ||
0.656401 | − | 0.754412i | \(-0.272078\pi\) | |||||||
\(20\) | 39678.9 | 0.247993 | ||||||||
\(21\) | − | 180068.i | − | 0.925890i | ||||||
\(22\) | 162454. | + | 32349.6i | 0.693491 | + | 0.138095i | ||||
\(23\) | 293331. | 1.04821 | 0.524104 | − | 0.851654i | \(-0.324400\pi\) | ||||
0.524104 | + | 0.851654i | \(0.324400\pi\) | |||||||
\(24\) | 207464.i | 0.625313i | ||||||||
\(25\) | −294530. | −0.753998 | ||||||||
\(26\) | −436571. | −0.955348 | ||||||||
\(27\) | −1.06036e6 | −1.99526 | ||||||||
\(28\) | − | 160886.i | − | 0.261750i | ||||||
\(29\) | − | 368541.i | − | 0.521067i | −0.965465 | − | 0.260533i | \(-0.916102\pi\) | ||
0.965465 | − | 0.260533i | \(-0.0838984\pi\) | |||||||
\(30\) | 502437.i | 0.620292i | ||||||||
\(31\) | −433548. | −0.469451 | −0.234725 | − | 0.972062i | \(-0.575419\pi\) | ||||
−0.234725 | + | 0.972062i | \(0.575419\pi\) | |||||||
\(32\) | 185364.i | 0.176777i | ||||||||
\(33\) | −409629. | + | 2.05709e6i | −0.345410 | + | 1.73459i | ||||
\(34\) | 361252. | 0.270330 | ||||||||
\(35\) | − | 389635.i | − | 0.259649i | ||||||
\(36\) | −1.78722e6 | −1.06406 | ||||||||
\(37\) | 2.92200e6 | 1.55910 | 0.779550 | − | 0.626340i | \(-0.215448\pi\) | ||||
0.779550 | + | 0.626340i | \(0.215448\pi\) | |||||||
\(38\) | 2.22463e6 | 1.06690 | ||||||||
\(39\) | − | 5.52812e6i | − | 2.38956i | ||||||
\(40\) | 448915.i | 0.175357i | ||||||||
\(41\) | 3.66432e6i | 1.29675i | 0.761319 | + | 0.648377i | \(0.224552\pi\) | ||||
−0.761319 | + | 0.648377i | \(0.775448\pi\) | |||||||
\(42\) | 2.03724e6 | 0.654703 | ||||||||
\(43\) | − | 5.40993e6i | − | 1.58240i | −0.611555 | − | 0.791202i | \(-0.709455\pi\) | ||
0.611555 | − | 0.791202i | \(-0.290545\pi\) | |||||||
\(44\) | −365994. | + | 1.83796e6i | −0.0976479 | + | 0.490372i | ||||
\(45\) | −4.32829e6 | −1.05552 | ||||||||
\(46\) | 3.31867e6i | 0.741195i | ||||||||
\(47\) | 3.98014e6 | 0.815656 | 0.407828 | − | 0.913059i | \(-0.366286\pi\) | ||||
0.407828 | + | 0.913059i | \(0.366286\pi\) | |||||||
\(48\) | −2.34718e6 | −0.442163 | ||||||||
\(49\) | 4.18494e6 | 0.725947 | ||||||||
\(50\) | − | 3.33223e6i | − | 0.533157i | ||||||
\(51\) | 4.57438e6i | 0.676163i | ||||||||
\(52\) | − | 4.93924e6i | − | 0.675533i | ||||||
\(53\) | 4.85507e6 | 0.615307 | 0.307654 | − | 0.951498i | \(-0.400456\pi\) | ||||
0.307654 | + | 0.951498i | \(0.400456\pi\) | |||||||
\(54\) | − | 1.19967e7i | − | 1.41086i | ||||||
\(55\) | −886366. | + | 4.45119e6i | −0.0968640 | + | 0.486435i | ||||
\(56\) | 1.82022e6 | 0.185085 | ||||||||
\(57\) | 2.81696e7i | 2.66858i | ||||||||
\(58\) | 4.16956e6 | 0.368450 | ||||||||
\(59\) | 761371. | 0.0628330 | 0.0314165 | − | 0.999506i | \(-0.489998\pi\) | ||||
0.0314165 | + | 0.999506i | \(0.489998\pi\) | |||||||
\(60\) | −5.68442e6 | −0.438613 | ||||||||
\(61\) | − | 1.65487e7i | − | 1.19521i | −0.801789 | − | 0.597607i | \(-0.796118\pi\) | ||
0.801789 | − | 0.597607i | \(-0.203882\pi\) | |||||||
\(62\) | − | 4.90503e6i | − | 0.331952i | ||||||
\(63\) | 1.75500e7i | 1.11408i | ||||||||
\(64\) | −2.09715e6 | −0.125000 | ||||||||
\(65\) | − | 1.19619e7i | − | 0.670110i | ||||||
\(66\) | −2.32733e7 | − | 4.63443e6i | −1.22654 | − | 0.244242i | ||||
\(67\) | −3.56044e7 | −1.76687 | −0.883434 | − | 0.468555i | \(-0.844775\pi\) | ||||
−0.883434 | + | 0.468555i | \(0.844775\pi\) | |||||||
\(68\) | 4.08710e6i | 0.191152i | ||||||||
\(69\) | −4.20229e7 | −1.85391 | ||||||||
\(70\) | 4.40822e6 | 0.183599 | ||||||||
\(71\) | 6.40846e6 | 0.252186 | 0.126093 | − | 0.992018i | \(-0.459756\pi\) | ||||
0.126093 | + | 0.992018i | \(0.459756\pi\) | |||||||
\(72\) | − | 2.02201e7i | − | 0.752406i | ||||||
\(73\) | − | 1.18845e7i | − | 0.418493i | −0.977863 | − | 0.209246i | \(-0.932899\pi\) | ||
0.977863 | − | 0.209246i | \(-0.0671011\pi\) | |||||||
\(74\) | 3.30587e7i | 1.10245i | ||||||||
\(75\) | 4.21947e7 | 1.33356 | ||||||||
\(76\) | 2.51688e7i | 0.754412i | ||||||||
\(77\) | 1.80483e7 | + | 3.59396e6i | 0.513420 | + | 0.102237i | ||||
\(78\) | 6.25435e7 | 1.68968 | ||||||||
\(79\) | − | 5.34827e7i | − | 1.37311i | −0.727079 | − | 0.686554i | \(-0.759123\pi\) | ||
0.727079 | − | 0.686554i | \(-0.240877\pi\) | |||||||
\(80\) | −5.07889e6 | −0.123996 | ||||||||
\(81\) | 6.02997e7 | 1.40080 | ||||||||
\(82\) | −4.14570e7 | −0.916944 | ||||||||
\(83\) | − | 1.61252e7i | − | 0.339776i | −0.985463 | − | 0.169888i | \(-0.945659\pi\) | ||
0.985463 | − | 0.169888i | \(-0.0543406\pi\) | |||||||
\(84\) | 2.30487e7i | 0.462945i | ||||||||
\(85\) | 9.89815e6i | 0.189618i | ||||||||
\(86\) | 6.12063e7 | 1.11893 | ||||||||
\(87\) | 5.27974e7i | 0.921585i | ||||||||
\(88\) | −2.07942e7 | − | 4.14075e6i | −0.346746 | − | 0.0690475i | ||||
\(89\) | −1.55356e6 | −0.0247610 | −0.0123805 | − | 0.999923i | \(-0.503941\pi\) | ||||
−0.0123805 | + | 0.999923i | \(0.503941\pi\) | |||||||
\(90\) | − | 4.89691e7i | − | 0.746366i | ||||||
\(91\) | −4.85019e7 | −0.707284 | ||||||||
\(92\) | −3.75464e7 | −0.524104 | ||||||||
\(93\) | 6.21104e7 | 0.830295 | ||||||||
\(94\) | 4.50302e7i | 0.576756i | ||||||||
\(95\) | 6.09540e7i | 0.748356i | ||||||||
\(96\) | − | 2.65554e7i | − | 0.312656i | ||||||
\(97\) | −1.42492e8 | −1.60955 | −0.804776 | − | 0.593579i | \(-0.797714\pi\) | ||||
−0.804776 | + | 0.593579i | \(0.797714\pi\) | |||||||
\(98\) | 4.73472e7i | 0.513322i | ||||||||
\(99\) | 3.99237e7 | − | 2.00491e8i | 0.415614 | − | 2.08715i | ||||
\(100\) | 3.76999e7 | 0.376999 | ||||||||
\(101\) | − | 5.11231e7i | − | 0.491283i | −0.969361 | − | 0.245642i | \(-0.921001\pi\) | ||
0.969361 | − | 0.245642i | \(-0.0789986\pi\) | |||||||
\(102\) | −5.17532e7 | −0.478119 | ||||||||
\(103\) | 1.62007e8 | 1.43942 | 0.719708 | − | 0.694277i | \(-0.244276\pi\) | ||||
0.719708 | + | 0.694277i | \(0.244276\pi\) | |||||||
\(104\) | 5.58811e7 | 0.477674 | ||||||||
\(105\) | 5.58195e7i | 0.459228i | ||||||||
\(106\) | 5.49288e7i | 0.435088i | ||||||||
\(107\) | − | 1.98786e8i | − | 1.51653i | −0.651946 | − | 0.758266i | \(-0.726047\pi\) | ||
0.651946 | − | 0.758266i | \(-0.273953\pi\) | |||||||
\(108\) | 1.35727e8 | 0.997631 | ||||||||
\(109\) | 1.49606e8i | 1.05984i | 0.848046 | + | 0.529922i | \(0.177779\pi\) | ||||
−0.848046 | + | 0.529922i | \(0.822221\pi\) | |||||||
\(110\) | −5.03594e7 | − | 1.00281e7i | −0.343962 | − | 0.0684932i | ||||
\(111\) | −4.18609e8 | −2.75750 | ||||||||
\(112\) | 2.05935e7i | 0.130875i | ||||||||
\(113\) | 9.52975e7 | 0.584477 | 0.292239 | − | 0.956345i | \(-0.405600\pi\) | ||||
0.292239 | + | 0.956345i | \(0.405600\pi\) | |||||||
\(114\) | −3.18702e8 | −1.88697 | ||||||||
\(115\) | −9.09301e7 | −0.519896 | ||||||||
\(116\) | 4.71732e7i | 0.260533i | ||||||||
\(117\) | 5.38788e8i | 2.87524i | ||||||||
\(118\) | 8.61393e6i | 0.0444297i | ||||||||
\(119\) | 4.01342e7 | 0.200136 | ||||||||
\(120\) | − | 6.43119e7i | − | 0.310146i | ||||||
\(121\) | −1.98007e8 | − | 8.21146e7i | −0.923719 | − | 0.383071i | ||||
\(122\) | 1.87228e8 | 0.845144 | ||||||||
\(123\) | − | 5.24953e8i | − | 2.29351i | ||||||
\(124\) | 5.54941e7 | 0.234725 | ||||||||
\(125\) | 2.12392e8 | 0.869958 | ||||||||
\(126\) | −1.98555e8 | −0.787770 | ||||||||
\(127\) | − | 8.11193e7i | − | 0.311824i | −0.987771 | − | 0.155912i | \(-0.950168\pi\) | ||
0.987771 | − | 0.155912i | \(-0.0498316\pi\) | |||||||
\(128\) | − | 2.37266e7i | − | 0.0883883i | ||||||
\(129\) | 7.75030e8i | 2.79872i | ||||||||
\(130\) | 1.35333e8 | 0.473839 | ||||||||
\(131\) | 2.71103e7i | 0.0920553i | 0.998940 | + | 0.0460276i | \(0.0146562\pi\) | ||||
−0.998940 | + | 0.0460276i | \(0.985344\pi\) | |||||||
\(132\) | 5.24325e7 | − | 2.63308e8i | 0.172705 | − | 0.867297i | ||||
\(133\) | 2.47151e8 | 0.789870 | ||||||||
\(134\) | − | 4.02818e8i | − | 1.24936i | ||||||
\(135\) | 3.28704e8 | 0.989622 | ||||||||
\(136\) | −4.62402e7 | −0.135165 | ||||||||
\(137\) | 6.89037e8 | 1.95596 | 0.977981 | − | 0.208692i | \(-0.0669207\pi\) | ||||
0.977981 | + | 0.208692i | \(0.0669207\pi\) | |||||||
\(138\) | − | 4.75435e8i | − | 1.31091i | ||||||
\(139\) | − | 3.22285e7i | − | 0.0863339i | −0.999068 | − | 0.0431669i | \(-0.986255\pi\) | ||
0.999068 | − | 0.0431669i | \(-0.0137447\pi\) | |||||||
\(140\) | 4.98733e7i | 0.129824i | ||||||||
\(141\) | −5.70198e8 | −1.44261 | ||||||||
\(142\) | 7.25035e7i | 0.178322i | ||||||||
\(143\) | 5.54085e8 | + | 1.10335e8i | 1.32505 | + | 0.263858i | ||||
\(144\) | 2.28764e8 | 0.532032 | ||||||||
\(145\) | 1.14244e8i | 0.258442i | ||||||||
\(146\) | 1.34457e8 | 0.295919 | ||||||||
\(147\) | −5.99538e8 | −1.28395 | ||||||||
\(148\) | −3.74017e8 | −0.779550 | ||||||||
\(149\) | − | 7.59825e8i | − | 1.54159i | −0.637084 | − | 0.770794i | \(-0.719860\pi\) | ||
0.637084 | − | 0.770794i | \(-0.280140\pi\) | |||||||
\(150\) | 4.77378e8i | 0.942969i | ||||||||
\(151\) | 4.11446e8i | 0.791416i | 0.918376 | + | 0.395708i | \(0.129501\pi\) | ||||
−0.918376 | + | 0.395708i | \(0.870499\pi\) | |||||||
\(152\) | −2.84753e8 | −0.533450 | ||||||||
\(153\) | − | 4.45833e8i | − | 0.813592i | ||||||
\(154\) | −4.06610e7 | + | 2.04193e8i | −0.0722928 | + | 0.363043i | ||||
\(155\) | 1.34396e8 | 0.232841 | ||||||||
\(156\) | 7.07599e8i | 1.19478i | ||||||||
\(157\) | −4.67385e8 | −0.769265 | −0.384632 | − | 0.923070i | \(-0.625672\pi\) | ||||
−0.384632 | + | 0.923070i | \(0.625672\pi\) | |||||||
\(158\) | 6.05087e8 | 0.970934 | ||||||||
\(159\) | −6.95541e8 | −1.08826 | ||||||||
\(160\) | − | 5.74611e7i | − | 0.0876787i | ||||||
\(161\) | 3.68695e8i | 0.548737i | ||||||||
\(162\) | 6.82213e8i | 0.990513i | ||||||||
\(163\) | 2.51220e8 | 0.355880 | 0.177940 | − | 0.984041i | \(-0.443057\pi\) | ||||
0.177940 | + | 0.984041i | \(0.443057\pi\) | |||||||
\(164\) | − | 4.69033e8i | − | 0.648377i | ||||||
\(165\) | 1.26981e8 | − | 6.37680e8i | 0.171319 | − | 0.860334i | ||||
\(166\) | 1.82436e8 | 0.240258 | ||||||||
\(167\) | 1.37596e9i | 1.76905i | 0.466490 | + | 0.884526i | \(0.345518\pi\) | ||||
−0.466490 | + | 0.884526i | \(0.654482\pi\) | |||||||
\(168\) | −2.60766e8 | −0.327351 | ||||||||
\(169\) | −6.73287e8 | −0.825379 | ||||||||
\(170\) | −1.11985e8 | −0.134080 | ||||||||
\(171\) | − | 2.74550e9i | − | 3.21097i | ||||||
\(172\) | 6.92471e8i | 0.791202i | ||||||||
\(173\) | 2.76459e8i | 0.308636i | 0.988021 | + | 0.154318i | \(0.0493181\pi\) | ||||
−0.988021 | + | 0.154318i | \(0.950682\pi\) | |||||||
\(174\) | −5.97334e8 | −0.651659 | ||||||||
\(175\) | − | 3.70203e8i | − | 0.394718i | ||||||
\(176\) | 4.68472e7 | − | 2.35259e8i | 0.0488240 | − | 0.245186i | ||||
\(177\) | −1.09075e8 | −0.111130 | ||||||||
\(178\) | − | 1.75765e7i | − | 0.0175087i | ||||||
\(179\) | 4.07962e8 | 0.397381 | 0.198690 | − | 0.980062i | \(-0.436331\pi\) | ||||
0.198690 | + | 0.980062i | \(0.436331\pi\) | |||||||
\(180\) | 5.54022e8 | 0.527760 | ||||||||
\(181\) | 3.39618e8 | 0.316429 | 0.158215 | − | 0.987405i | \(-0.449426\pi\) | ||||
0.158215 | + | 0.987405i | \(0.449426\pi\) | |||||||
\(182\) | − | 5.48737e8i | − | 0.500125i | ||||||
\(183\) | 2.37078e9i | 2.11392i | ||||||||
\(184\) | − | 4.24789e8i | − | 0.370597i | ||||||
\(185\) | −9.05796e8 | −0.773292 | ||||||||
\(186\) | 7.02699e8i | 0.587107i | ||||||||
\(187\) | −4.58492e8 | − | 9.12995e7i | −0.374943 | − | 0.0746624i | ||||
\(188\) | −5.09458e8 | −0.407828 | ||||||||
\(189\) | − | 1.33280e9i | − | 1.04452i | ||||||
\(190\) | −6.89616e8 | −0.529167 | ||||||||
\(191\) | −7.22044e8 | −0.542538 | −0.271269 | − | 0.962504i | \(-0.587443\pi\) | ||||
−0.271269 | + | 0.962504i | \(0.587443\pi\) | |||||||
\(192\) | 3.00440e8 | 0.221081 | ||||||||
\(193\) | − | 1.18124e9i | − | 0.851354i | −0.904875 | − | 0.425677i | \(-0.860036\pi\) | ||
0.904875 | − | 0.425677i | \(-0.139964\pi\) | |||||||
\(194\) | − | 1.61212e9i | − | 1.13812i | ||||||
\(195\) | 1.71367e9i | 1.18519i | ||||||||
\(196\) | −5.35673e8 | −0.362974 | ||||||||
\(197\) | 8.48888e8i | 0.563619i | 0.959470 | + | 0.281809i | \(0.0909346\pi\) | ||||
−0.959470 | + | 0.281809i | \(0.909065\pi\) | |||||||
\(198\) | 2.26829e9 | + | 4.51686e8i | 1.47584 | + | 0.293884i | ||||
\(199\) | −7.90352e7 | −0.0503974 | −0.0251987 | − | 0.999682i | \(-0.508022\pi\) | ||||
−0.0251987 | + | 0.999682i | \(0.508022\pi\) | |||||||
\(200\) | 4.26526e8i | 0.266579i | ||||||||
\(201\) | 5.10071e9 | 3.12497 | ||||||||
\(202\) | 5.78392e8 | 0.347390 | ||||||||
\(203\) | 4.63228e8 | 0.272779 | ||||||||
\(204\) | − | 5.85520e8i | − | 0.338081i | ||||||
\(205\) | − | 1.13591e9i | − | 0.643172i | ||||||
\(206\) | 1.83291e9i | 1.01782i | ||||||||
\(207\) | 4.09568e9 | 2.23072 | ||||||||
\(208\) | 6.32222e8i | 0.337767i | ||||||||
\(209\) | −2.82345e9 | − | 5.62234e8i | −1.47977 | − | 0.294667i | ||||
\(210\) | −6.31525e8 | −0.324723 | ||||||||
\(211\) | − | 1.77494e9i | − | 0.895477i | −0.894165 | − | 0.447738i | \(-0.852230\pi\) | ||
0.894165 | − | 0.447738i | \(-0.147770\pi\) | |||||||
\(212\) | −6.21449e8 | −0.307654 | ||||||||
\(213\) | −9.18081e8 | −0.446028 | ||||||||
\(214\) | 2.24901e9 | 1.07235 | ||||||||
\(215\) | 1.67703e9i | 0.784850i | ||||||||
\(216\) | 1.53557e9i | 0.705432i | ||||||||
\(217\) | − | 5.44937e8i | − | 0.245758i | ||||||
\(218\) | −1.69260e9 | −0.749423 | ||||||||
\(219\) | 1.70258e9i | 0.740168i | ||||||||
\(220\) | 1.13455e8 | − | 5.69752e8i | 0.0484320 | − | 0.243218i | ||||
\(221\) | 1.23213e9 | 0.516518 | ||||||||
\(222\) | − | 4.73601e9i | − | 1.94985i | ||||||
\(223\) | −2.44670e9 | −0.989374 | −0.494687 | − | 0.869071i | \(-0.664717\pi\) | ||||
−0.494687 | + | 0.869071i | \(0.664717\pi\) | |||||||
\(224\) | −2.32988e8 | −0.0925427 | ||||||||
\(225\) | −4.11242e9 | −1.60460 | ||||||||
\(226\) | 1.07817e9i | 0.413288i | ||||||||
\(227\) | 2.04022e9i | 0.768377i | 0.923255 | + | 0.384188i | \(0.125519\pi\) | ||||
−0.923255 | + | 0.384188i | \(0.874481\pi\) | |||||||
\(228\) | − | 3.60571e9i | − | 1.33429i | ||||||
\(229\) | 1.18977e9 | 0.432635 | 0.216317 | − | 0.976323i | \(-0.430595\pi\) | ||||
0.216317 | + | 0.976323i | \(0.430595\pi\) | |||||||
\(230\) | − | 1.02876e9i | − | 0.367622i | ||||||
\(231\) | −2.58561e9 | − | 5.14873e8i | −0.908061 | − | 0.180822i | ||||
\(232\) | −5.33704e8 | −0.184225 | ||||||||
\(233\) | − | 2.48427e7i | − | 0.00842898i | −0.999991 | − | 0.00421449i | \(-0.998658\pi\) | ||
0.999991 | − | 0.00421449i | \(-0.00134152\pi\) | |||||||
\(234\) | −6.09568e9 | −2.03310 | ||||||||
\(235\) | −1.23381e9 | −0.404554 | ||||||||
\(236\) | −9.74554e7 | −0.0314165 | ||||||||
\(237\) | 7.66197e9i | 2.42855i | ||||||||
\(238\) | 4.54066e8i | 0.141518i | ||||||||
\(239\) | − | 2.28556e9i | − | 0.700487i | −0.936659 | − | 0.350244i | \(-0.886099\pi\) | ||
0.936659 | − | 0.350244i | \(-0.113901\pi\) | |||||||
\(240\) | 7.27606e8 | 0.219306 | ||||||||
\(241\) | − | 4.44393e8i | − | 0.131734i | −0.997828 | − | 0.0658672i | \(-0.979019\pi\) | ||
0.997828 | − | 0.0658672i | \(-0.0209814\pi\) | |||||||
\(242\) | 9.29020e8 | − | 2.24020e9i | 0.270872 | − | 0.653168i | ||||
\(243\) | −1.68153e9 | −0.482258 | ||||||||
\(244\) | 2.11824e9i | 0.597607i | ||||||||
\(245\) | −1.29729e9 | −0.360060 | ||||||||
\(246\) | 5.93917e9 | 1.62175 | ||||||||
\(247\) | 7.58758e9 | 2.03852 | ||||||||
\(248\) | 6.27844e8i | 0.165976i | ||||||||
\(249\) | 2.31011e9i | 0.600945i | ||||||||
\(250\) | 2.40294e9i | 0.615153i | ||||||||
\(251\) | −1.07101e9 | −0.269834 | −0.134917 | − | 0.990857i | \(-0.543077\pi\) | ||||
−0.134917 | + | 0.990857i | \(0.543077\pi\) | |||||||
\(252\) | − | 2.24640e9i | − | 0.557038i | ||||||
\(253\) | 8.38730e8 | − | 4.21197e9i | 0.204711 | − | 1.02802i | ||||
\(254\) | 9.17760e8 | 0.220493 | ||||||||
\(255\) | − | 1.41802e9i | − | 0.335367i | ||||||
\(256\) | 2.68435e8 | 0.0625000 | ||||||||
\(257\) | 1.65767e9 | 0.379983 | 0.189992 | − | 0.981786i | \(-0.439154\pi\) | ||||
0.189992 | + | 0.981786i | \(0.439154\pi\) | |||||||
\(258\) | −8.76846e9 | −1.97900 | ||||||||
\(259\) | 3.67274e9i | 0.816190i | ||||||||
\(260\) | 1.53112e9i | 0.335055i | ||||||||
\(261\) | − | 5.14580e9i | − | 1.10890i | ||||||
\(262\) | −3.06718e8 | −0.0650929 | ||||||||
\(263\) | 2.52475e9i | 0.527711i | 0.964562 | + | 0.263855i | \(0.0849942\pi\) | ||||
−0.964562 | + | 0.263855i | \(0.915006\pi\) | |||||||
\(264\) | 2.97899e9 | + | 5.93206e8i | 0.613272 | + | 0.122121i | ||||
\(265\) | −1.50503e9 | −0.305184 | ||||||||
\(266\) | 2.79619e9i | 0.558523i | ||||||||
\(267\) | 2.22564e8 | 0.0437935 | ||||||||
\(268\) | 4.55736e9 | 0.883434 | ||||||||
\(269\) | −3.95184e9 | −0.754728 | −0.377364 | − | 0.926065i | \(-0.623169\pi\) | ||||
−0.377364 | + | 0.926065i | \(0.623169\pi\) | |||||||
\(270\) | 3.71886e9i | 0.699768i | ||||||||
\(271\) | − | 8.79271e9i | − | 1.63022i | −0.579308 | − | 0.815109i | \(-0.696677\pi\) | ||
0.579308 | − | 0.815109i | \(-0.303323\pi\) | |||||||
\(272\) | − | 5.23148e8i | − | 0.0955761i | ||||||
\(273\) | 6.94842e9 | 1.25094 | ||||||||
\(274\) | 7.79557e9i | 1.38307i | ||||||||
\(275\) | −8.42159e8 | + | 4.22919e9i | −0.147253 | + | 0.739479i | ||||
\(276\) | 5.37893e9 | 0.926957 | ||||||||
\(277\) | − | 6.17521e9i | − | 1.04890i | −0.851442 | − | 0.524449i | \(-0.824272\pi\) | ||
0.851442 | − | 0.524449i | \(-0.175728\pi\) | |||||||
\(278\) | 3.64624e8 | 0.0610473 | ||||||||
\(279\) | −6.05347e9 | −0.999051 | ||||||||
\(280\) | −5.64252e8 | −0.0917997 | ||||||||
\(281\) | − | 8.95370e9i | − | 1.43607i | −0.696005 | − | 0.718037i | \(-0.745041\pi\) | ||
0.696005 | − | 0.718037i | \(-0.254959\pi\) | |||||||
\(282\) | − | 6.45106e9i | − | 1.02008i | ||||||
\(283\) | 2.92082e9i | 0.455364i | 0.973736 | + | 0.227682i | \(0.0731146\pi\) | ||||
−0.973736 | + | 0.227682i | \(0.926885\pi\) | |||||||
\(284\) | −8.20283e8 | −0.126093 | ||||||||
\(285\) | − | 8.73232e9i | − | 1.32358i | ||||||
\(286\) | −1.24830e9 | + | 6.26876e9i | −0.186575 | + | 0.936952i | ||||
\(287\) | −4.60577e9 | −0.678852 | ||||||||
\(288\) | 2.58817e9i | 0.376203i | ||||||||
\(289\) | 5.95620e9 | 0.853843 | ||||||||
\(290\) | −1.29253e9 | −0.182746 | ||||||||
\(291\) | 2.04136e10 | 2.84673 | ||||||||
\(292\) | 1.52121e9i | 0.209246i | ||||||||
\(293\) | − | 1.20314e10i | − | 1.63248i | −0.577714 | − | 0.816239i | \(-0.696055\pi\) | ||
0.577714 | − | 0.816239i | \(-0.303945\pi\) | |||||||
\(294\) | − | 6.78300e9i | − | 0.907888i | ||||||
\(295\) | −2.36018e8 | −0.0311643 | ||||||||
\(296\) | − | 4.23151e9i | − | 0.551225i | ||||||
\(297\) | −3.03193e9 | + | 1.52259e10i | −0.389666 | + | 1.95684i | ||||
\(298\) | 8.59644e9 | 1.09007 | ||||||||
\(299\) | 1.13190e10i | 1.41620i | ||||||||
\(300\) | −5.40092e9 | −0.666780 | ||||||||
\(301\) | 6.79987e9 | 0.828389 | ||||||||
\(302\) | −4.65498e9 | −0.559616 | ||||||||
\(303\) | 7.32394e9i | 0.868909i | ||||||||
\(304\) | − | 3.22161e9i | − | 0.377206i | ||||||
\(305\) | 5.12996e9i | 0.592809i | ||||||||
\(306\) | 5.04403e9 | 0.575296 | ||||||||
\(307\) | 3.80612e9i | 0.428478i | 0.976781 | + | 0.214239i | \(0.0687272\pi\) | ||||
−0.976781 | + | 0.214239i | \(0.931273\pi\) | |||||||
\(308\) | −2.31018e9 | − | 4.60027e8i | −0.256710 | − | 0.0511187i | ||||
\(309\) | −2.32093e10 | −2.54582 | ||||||||
\(310\) | 1.52052e9i | 0.164643i | ||||||||
\(311\) | −4.35112e9 | −0.465114 | −0.232557 | − | 0.972583i | \(-0.574709\pi\) | ||||
−0.232557 | + | 0.972583i | \(0.574709\pi\) | |||||||
\(312\) | −8.00557e9 | −0.844839 | ||||||||
\(313\) | −7.40132e9 | −0.771137 | −0.385569 | − | 0.922679i | \(-0.625995\pi\) | ||||
−0.385569 | + | 0.922679i | \(0.625995\pi\) | |||||||
\(314\) | − | 5.28785e9i | − | 0.543952i | ||||||
\(315\) | − | 5.44034e9i | − | 0.552565i | ||||||
\(316\) | 6.84578e9i | 0.686554i | ||||||||
\(317\) | −1.24891e10 | −1.23678 | −0.618392 | − | 0.785870i | \(-0.712215\pi\) | ||||
−0.618392 | + | 0.785870i | \(0.712215\pi\) | |||||||
\(318\) | − | 7.86915e9i | − | 0.769519i | ||||||
\(319\) | −5.29190e9 | − | 1.05378e9i | −0.511033 | − | 0.101762i | ||||
\(320\) | 6.50099e8 | 0.0619982 | ||||||||
\(321\) | 2.84783e10i | 2.68221i | ||||||||
\(322\) | −4.17131e9 | −0.388016 | ||||||||
\(323\) | −6.27853e9 | −0.576830 | ||||||||
\(324\) | −7.71836e9 | −0.700398 | ||||||||
\(325\) | − | 1.13653e10i | − | 1.01870i | ||||||
\(326\) | 2.84223e9i | 0.251645i | ||||||||
\(327\) | − | 2.14326e10i | − | 1.87450i | ||||||
\(328\) | 5.30650e9 | 0.458472 | ||||||||
\(329\) | 5.00274e9i | 0.426996i | ||||||||
\(330\) | 7.21453e9 | + | 1.43663e9i | 0.608348 | + | 0.121141i | ||||
\(331\) | −2.09868e9 | −0.174837 | −0.0874187 | − | 0.996172i | \(-0.527862\pi\) | ||||
−0.0874187 | + | 0.996172i | \(0.527862\pi\) | |||||||
\(332\) | 2.06403e9i | 0.169888i | ||||||||
\(333\) | 4.07989e10 | 3.31796 | ||||||||
\(334\) | −1.55672e10 | −1.25091 | ||||||||
\(335\) | 1.10370e10 | 0.876342 | ||||||||
\(336\) | − | 2.95023e9i | − | 0.231472i | ||||||
\(337\) | − | 3.34750e9i | − | 0.259538i | −0.991544 | − | 0.129769i | \(-0.958576\pi\) | ||
0.991544 | − | 0.129769i | \(-0.0414235\pi\) | |||||||
\(338\) | − | 7.61738e9i | − | 0.583631i | ||||||
\(339\) | −1.36524e10 | −1.03374 | ||||||||
\(340\) | − | 1.26696e9i | − | 0.0948088i | ||||||
\(341\) | −1.23965e9 | + | 6.22535e9i | −0.0916818 | + | 0.460411i | ||||
\(342\) | 3.10617e10 | 2.27050 | ||||||||
\(343\) | 1.25061e10i | 0.903534i | ||||||||
\(344\) | −7.83441e9 | −0.559465 | ||||||||
\(345\) | 1.30267e10 | 0.919515 | ||||||||
\(346\) | −3.12778e9 | −0.218239 | ||||||||
\(347\) | 9.26936e9i | 0.639340i | 0.947529 | + | 0.319670i | \(0.103572\pi\) | ||||
−0.947529 | + | 0.319670i | \(0.896428\pi\) | |||||||
\(348\) | − | 6.75807e9i | − | 0.460793i | ||||||
\(349\) | − | 4.31190e9i | − | 0.290648i | −0.989384 | − | 0.145324i | \(-0.953578\pi\) | ||
0.989384 | − | 0.145324i | \(-0.0464224\pi\) | |||||||
\(350\) | 4.18836e9 | 0.279108 | ||||||||
\(351\) | − | 4.09171e10i | − | 2.69573i | ||||||
\(352\) | 2.66165e9 | + | 5.30016e8i | 0.173373 | + | 0.0345238i | ||||
\(353\) | 1.11945e10 | 0.720954 | 0.360477 | − | 0.932768i | \(-0.382614\pi\) | ||||
0.360477 | + | 0.932768i | \(0.382614\pi\) | |||||||
\(354\) | − | 1.23404e9i | − | 0.0785806i | ||||||
\(355\) | −1.98657e9 | −0.125081 | ||||||||
\(356\) | 1.98856e8 | 0.0123805 | ||||||||
\(357\) | −5.74965e9 | −0.353972 | ||||||||
\(358\) | 4.61556e9i | 0.280991i | ||||||||
\(359\) | − | 1.51798e10i | − | 0.913877i | −0.889498 | − | 0.456939i | \(-0.848946\pi\) | ||
0.889498 | − | 0.456939i | \(-0.151054\pi\) | |||||||
\(360\) | 6.26804e9i | 0.373183i | ||||||||
\(361\) | −2.16804e10 | −1.27655 | ||||||||
\(362\) | 3.84234e9i | 0.223749i | ||||||||
\(363\) | 2.83667e10 | + | 1.17638e10i | 1.63374 | + | 0.677518i | ||||
\(364\) | 6.20825e9 | 0.353642 | ||||||||
\(365\) | 3.68408e9i | 0.207567i | ||||||||
\(366\) | −2.68224e10 | −1.49476 | ||||||||
\(367\) | −1.69081e9 | −0.0932034 | −0.0466017 | − | 0.998914i | \(-0.514839\pi\) | ||||
−0.0466017 | + | 0.998914i | \(0.514839\pi\) | |||||||
\(368\) | 4.80594e9 | 0.262052 | ||||||||
\(369\) | 5.11636e10i | 2.75966i | ||||||||
\(370\) | − | 1.02479e10i | − | 0.546800i | ||||||
\(371\) | 6.10246e9i | 0.322114i | ||||||||
\(372\) | −7.95013e9 | −0.415147 | ||||||||
\(373\) | 2.28601e10i | 1.18098i | 0.807044 | + | 0.590491i | \(0.201066\pi\) | ||||
−0.807044 | + | 0.590491i | \(0.798934\pi\) | |||||||
\(374\) | 1.03294e9 | − | 5.18724e9i | 0.0527943 | − | 0.265125i | ||||
\(375\) | −3.04275e10 | −1.53865 | ||||||||
\(376\) | − | 5.76386e9i | − | 0.288378i | ||||||
\(377\) | 1.42212e10 | 0.703995 | ||||||||
\(378\) | 1.50789e10 | 0.738588 | ||||||||
\(379\) | 2.27992e9 | 0.110500 | 0.0552500 | − | 0.998473i | \(-0.482404\pi\) | ||||
0.0552500 | + | 0.998473i | \(0.482404\pi\) | |||||||
\(380\) | − | 7.80212e9i | − | 0.374178i | ||||||
\(381\) | 1.16212e10i | 0.551507i | ||||||||
\(382\) | − | 8.16899e9i | − | 0.383632i | ||||||
\(383\) | 3.47039e10 | 1.61281 | 0.806405 | − | 0.591364i | \(-0.201410\pi\) | ||||
0.806405 | + | 0.591364i | \(0.201410\pi\) | |||||||
\(384\) | 3.39909e9i | 0.156328i | ||||||||
\(385\) | −5.59481e9 | − | 1.11409e9i | −0.254649 | − | 0.0507083i | ||||
\(386\) | 1.33642e10 | 0.601998 | ||||||||
\(387\) | − | 7.55369e10i | − | 3.36756i | ||||||
\(388\) | 1.82390e10 | 0.804776 | ||||||||
\(389\) | 2.33533e10 | 1.01988 | 0.509942 | − | 0.860209i | \(-0.329667\pi\) | ||||
0.509942 | + | 0.860209i | \(0.329667\pi\) | |||||||
\(390\) | −1.93879e10 | −0.838056 | ||||||||
\(391\) | − | 9.36620e9i | − | 0.400734i | ||||||
\(392\) | − | 6.06044e9i | − | 0.256661i | ||||||
\(393\) | − | 3.88384e9i | − | 0.162814i | ||||||
\(394\) | −9.60407e9 | −0.398539 | ||||||||
\(395\) | 1.65792e10i | 0.681042i | ||||||||
\(396\) | −5.11024e9 | + | 2.56628e10i | −0.207807 | + | 1.04357i | ||||
\(397\) | −1.07914e10 | −0.434427 | −0.217213 | − | 0.976124i | \(-0.569697\pi\) | ||||
−0.217213 | + | 0.976124i | \(0.569697\pi\) | |||||||
\(398\) | − | 8.94181e8i | − | 0.0356363i | ||||||
\(399\) | −3.54070e10 | −1.39701 | ||||||||
\(400\) | −4.82559e9 | −0.188500 | ||||||||
\(401\) | −5.21695e9 | −0.201762 | −0.100881 | − | 0.994898i | \(-0.532166\pi\) | ||||
−0.100881 | + | 0.994898i | \(0.532166\pi\) | |||||||
\(402\) | 5.77079e10i | 2.20969i | ||||||||
\(403\) | − | 1.67297e10i | − | 0.634259i | ||||||
\(404\) | 6.54376e9i | 0.245642i | ||||||||
\(405\) | −1.86924e10 | −0.694775 | ||||||||
\(406\) | 5.24082e9i | 0.192884i | ||||||||
\(407\) | 8.35496e9 | − | 4.19573e10i | 0.304486 | − | 1.52908i | ||||
\(408\) | 6.62441e9 | 0.239060 | ||||||||
\(409\) | − | 2.36701e10i | − | 0.845877i | −0.906158 | − | 0.422939i | \(-0.860999\pi\) | ||
0.906158 | − | 0.422939i | \(-0.139001\pi\) | |||||||
\(410\) | 1.28513e10 | 0.454791 | ||||||||
\(411\) | −9.87120e10 | −3.45942 | ||||||||
\(412\) | −2.07370e10 | −0.719708 | ||||||||
\(413\) | 9.56985e8i | 0.0328931i | ||||||||
\(414\) | 4.63373e10i | 1.57736i | ||||||||
\(415\) | 4.99867e9i | 0.168524i | ||||||||
\(416\) | −7.15278e9 | −0.238837 | ||||||||
\(417\) | 4.61708e9i | 0.152695i | ||||||||
\(418\) | 6.36095e9 | − | 3.19437e10i | 0.208361 | − | 1.04636i | ||||
\(419\) | −1.41556e10 | −0.459273 | −0.229637 | − | 0.973276i | \(-0.573754\pi\) | ||||
−0.229637 | + | 0.973276i | \(0.573754\pi\) | |||||||
\(420\) | − | 7.14489e9i | − | 0.229614i | ||||||
\(421\) | 1.60760e10 | 0.511742 | 0.255871 | − | 0.966711i | \(-0.417638\pi\) | ||||
0.255871 | + | 0.966711i | \(0.417638\pi\) | |||||||
\(422\) | 2.00812e10 | 0.633198 | ||||||||
\(423\) | 5.55733e10 | 1.73582 | ||||||||
\(424\) | − | 7.03089e9i | − | 0.217544i | ||||||
\(425\) | 9.40449e9i | 0.288257i | ||||||||
\(426\) | − | 1.03869e10i | − | 0.315390i | ||||||
\(427\) | 2.08005e10 | 0.625695 | ||||||||
\(428\) | 2.54447e10i | 0.758266i | ||||||||
\(429\) | −7.93787e10 | − | 1.58067e10i | −2.34355 | − | 0.466672i | ||||
\(430\) | −1.89734e10 | −0.554973 | ||||||||
\(431\) | 5.69466e10i | 1.65028i | 0.564926 | + | 0.825142i | \(0.308905\pi\) | ||||
−0.564926 | + | 0.825142i | \(0.691095\pi\) | |||||||
\(432\) | −1.73730e10 | −0.498816 | ||||||||
\(433\) | 3.63016e9 | 0.103270 | 0.0516350 | − | 0.998666i | \(-0.483557\pi\) | ||||
0.0516350 | + | 0.998666i | \(0.483557\pi\) | |||||||
\(434\) | 6.16526e9 | 0.173777 | ||||||||
\(435\) | − | 1.63667e10i | − | 0.457093i | ||||||
\(436\) | − | 1.91495e10i | − | 0.529922i | ||||||
\(437\) | − | 5.76782e10i | − | 1.58156i | ||||||
\(438\) | −1.92625e10 | −0.523378 | ||||||||
\(439\) | 4.75630e10i | 1.28059i | 0.768128 | + | 0.640296i | \(0.221188\pi\) | ||||
−0.768128 | + | 0.640296i | \(0.778812\pi\) | |||||||
\(440\) | 6.44601e9 | + | 1.28359e9i | 0.171981 | + | 0.0342466i | ||||
\(441\) | 5.84328e10 | 1.54491 | ||||||||
\(442\) | 1.39399e10i | 0.365234i | ||||||||
\(443\) | 6.68171e10 | 1.73489 | 0.867446 | − | 0.497531i | \(-0.165760\pi\) | ||||
0.867446 | + | 0.497531i | \(0.165760\pi\) | |||||||
\(444\) | 5.35819e10 | 1.37875 | ||||||||
\(445\) | 4.81590e8 | 0.0122811 | ||||||||
\(446\) | − | 2.76812e10i | − | 0.699593i | ||||||
\(447\) | 1.08853e11i | 2.72653i | ||||||||
\(448\) | − | 2.63596e9i | − | 0.0654375i | ||||||
\(449\) | 3.66527e10 | 0.901822 | 0.450911 | − | 0.892569i | \(-0.351099\pi\) | ||||
0.450911 | + | 0.892569i | \(0.351099\pi\) | |||||||
\(450\) | − | 4.65268e10i | − | 1.13463i | ||||||
\(451\) | 5.26162e10 | + | 1.04775e10i | 1.27179 | + | 0.253251i | ||||
\(452\) | −1.21981e10 | −0.292239 | ||||||||
\(453\) | − | 5.89441e10i | − | 1.39974i | ||||||
\(454\) | −2.30825e10 | −0.543324 | ||||||||
\(455\) | 1.50352e10 | 0.350803 | ||||||||
\(456\) | 4.07939e10 | 0.943487 | ||||||||
\(457\) | 8.74858e9i | 0.200573i | 0.994959 | + | 0.100287i | \(0.0319759\pi\) | ||||
−0.994959 | + | 0.100287i | \(0.968024\pi\) | |||||||
\(458\) | 1.34607e10i | 0.305919i | ||||||||
\(459\) | 3.38579e10i | 0.762798i | ||||||||
\(460\) | 1.16391e10 | 0.259948 | ||||||||
\(461\) | − | 7.45105e9i | − | 0.164973i | −0.996592 | − | 0.0824867i | \(-0.973714\pi\) | ||
0.996592 | − | 0.0824867i | \(-0.0262862\pi\) | |||||||
\(462\) | 5.82512e9 | − | 2.92528e10i | 0.127861 | − | 0.642096i | ||||
\(463\) | −2.66604e10 | −0.580153 | −0.290077 | − | 0.957003i | \(-0.593681\pi\) | ||||
−0.290077 | + | 0.957003i | \(0.593681\pi\) | |||||||
\(464\) | − | 6.03817e9i | − | 0.130267i | ||||||
\(465\) | −1.92537e10 | −0.411815 | ||||||||
\(466\) | 2.81063e8 | 0.00596019 | ||||||||
\(467\) | −5.56014e10 | −1.16901 | −0.584504 | − | 0.811390i | \(-0.698711\pi\) | ||||
−0.584504 | + | 0.811390i | \(0.698711\pi\) | |||||||
\(468\) | − | 6.89648e10i | − | 1.43762i | ||||||
\(469\) | − | 4.47520e10i | − | 0.924956i | ||||||
\(470\) | − | 1.39590e10i | − | 0.286063i | ||||||
\(471\) | 6.69579e10 | 1.36056 | ||||||||
\(472\) | − | 1.10258e9i | − | 0.0222148i | ||||||
\(473\) | −7.76816e10 | − | 1.54687e10i | −1.55193 | − | 0.309037i | ||||
\(474\) | −8.66853e10 | −1.71724 | ||||||||
\(475\) | 5.79140e10i | 1.13765i | ||||||||
\(476\) | −5.13717e9 | −0.100068 | ||||||||
\(477\) | 6.77896e10 | 1.30945 | ||||||||
\(478\) | 2.58581e10 | 0.495319 | ||||||||
\(479\) | − | 3.43852e10i | − | 0.653175i | −0.945167 | − | 0.326588i | \(-0.894101\pi\) | ||
0.945167 | − | 0.326588i | \(-0.105899\pi\) | |||||||
\(480\) | 8.23192e9i | 0.155073i | ||||||||
\(481\) | 1.12754e11i | 2.10645i | ||||||||
\(482\) | 5.02773e9 | 0.0931503 | ||||||||
\(483\) | − | 5.28196e10i | − | 0.970524i | ||||||
\(484\) | 2.53449e10 | + | 1.05107e10i | 0.461860 | + | 0.191535i | ||||
\(485\) | 4.41714e10 | 0.798315 | ||||||||
\(486\) | − | 1.90243e10i | − | 0.341008i | ||||||
\(487\) | −9.31385e10 | −1.65582 | −0.827911 | − | 0.560860i | \(-0.810471\pi\) | ||||
−0.827911 | + | 0.560860i | \(0.810471\pi\) | |||||||
\(488\) | −2.39651e10 | −0.422572 | ||||||||
\(489\) | −3.59899e10 | −0.629428 | ||||||||
\(490\) | − | 1.46772e10i | − | 0.254601i | ||||||
\(491\) | − | 7.76972e10i | − | 1.33684i | −0.743784 | − | 0.668420i | \(-0.766971\pi\) | ||
0.743784 | − | 0.668420i | \(-0.233029\pi\) | |||||||
\(492\) | 6.71940e10i | 1.14675i | ||||||||
\(493\) | −1.17677e10 | −0.199206 | ||||||||
\(494\) | 8.58437e10i | 1.44145i | ||||||||
\(495\) | −1.23760e10 | + | 6.21503e10i | −0.206139 | + | 1.03520i | ||||
\(496\) | −7.10325e9 | −0.117363 | ||||||||
\(497\) | 8.05495e9i | 0.132019i | ||||||||
\(498\) | −2.61359e10 | −0.424933 | ||||||||
\(499\) | −5.94257e10 | −0.958457 | −0.479228 | − | 0.877690i | \(-0.659083\pi\) | ||||
−0.479228 | + | 0.877690i | \(0.659083\pi\) | |||||||
\(500\) | −2.71862e10 | −0.434979 | ||||||||
\(501\) | − | 1.97121e11i | − | 3.12884i | ||||||
\(502\) | − | 1.21170e10i | − | 0.190801i | ||||||
\(503\) | 8.94434e10i | 1.39726i | 0.715485 | + | 0.698629i | \(0.246206\pi\) | ||||
−0.715485 | + | 0.698629i | \(0.753794\pi\) | |||||||
\(504\) | 2.54151e10 | 0.393885 | ||||||||
\(505\) | 1.58477e10i | 0.243670i | ||||||||
\(506\) | 4.76530e10 | + | 9.48915e9i | 0.726922 | + | 0.144752i | ||||
\(507\) | 9.64557e10 | 1.45981 | ||||||||
\(508\) | 1.03833e10i | 0.155912i | ||||||||
\(509\) | −5.73817e10 | −0.854875 | −0.427437 | − | 0.904045i | \(-0.640584\pi\) | ||||
−0.427437 | + | 0.904045i | \(0.640584\pi\) | |||||||
\(510\) | 1.60430e10 | 0.237140 | ||||||||
\(511\) | 1.49379e10 | 0.219081 | ||||||||
\(512\) | 3.03700e9i | 0.0441942i | ||||||||
\(513\) | 2.08501e11i | 3.01050i | ||||||||
\(514\) | 1.87544e10i | 0.268689i | ||||||||
\(515\) | −5.02209e10 | −0.713930 | ||||||||
\(516\) | − | 9.92038e10i | − | 1.39936i | ||||||
\(517\) | 1.13805e10 | − | 5.71512e10i | 0.159294 | − | 0.799950i | ||||
\(518\) | −4.15523e10 | −0.577133 | ||||||||
\(519\) | − | 3.96058e10i | − | 0.545870i | ||||||
\(520\) | −1.73226e10 | −0.236920 | ||||||||
\(521\) | 8.04784e10 | 1.09227 | 0.546133 | − | 0.837698i | \(-0.316099\pi\) | ||||
0.546133 | + | 0.837698i | \(0.316099\pi\) | |||||||
\(522\) | 5.82181e10 | 0.784108 | ||||||||
\(523\) | − | 7.86300e10i | − | 1.05095i | −0.850809 | − | 0.525475i | \(-0.823888\pi\) | ||
0.850809 | − | 0.525475i | \(-0.176112\pi\) | |||||||
\(524\) | − | 3.47011e9i | − | 0.0460276i | ||||||
\(525\) | 5.30355e10i | 0.698119i | ||||||||
\(526\) | −2.85643e10 | −0.373148 | ||||||||
\(527\) | 1.38434e10i | 0.179473i | ||||||||
\(528\) | −6.71136e9 | + | 3.37034e10i | −0.0863525 | + | 0.433649i | ||||
\(529\) | 7.73235e9 | 0.0987390 | ||||||||
\(530\) | − | 1.70275e10i | − | 0.215797i | ||||||
\(531\) | 1.06307e10 | 0.133717 | ||||||||
\(532\) | −3.16353e10 | −0.394935 | ||||||||
\(533\) | −1.41398e11 | −1.75200 | ||||||||
\(534\) | 2.51803e9i | 0.0309667i | ||||||||
\(535\) | 6.16220e10i | 0.752178i | ||||||||
\(536\) | 5.15607e10i | 0.624682i | ||||||||
\(537\) | −5.84449e10 | −0.702828 | ||||||||
\(538\) | − | 4.47100e10i | − | 0.533673i | ||||||
\(539\) | 1.19661e10 | − | 6.00919e10i | 0.141774 | − | 0.711969i | ||||
\(540\) | −4.20741e10 | −0.494811 | ||||||||
\(541\) | 1.17136e11i | 1.36741i | 0.729756 | + | 0.683707i | \(0.239633\pi\) | ||||
−0.729756 | + | 0.683707i | \(0.760367\pi\) | |||||||
\(542\) | 9.94781e10 | 1.15274 | ||||||||
\(543\) | −4.86539e10 | −0.559653 | ||||||||
\(544\) | 5.91875e9 | 0.0675825 | ||||||||
\(545\) | − | 4.63764e10i | − | 0.525668i | ||||||
\(546\) | 7.86125e10i | 0.884547i | ||||||||
\(547\) | − | 4.84298e10i | − | 0.540958i | −0.962726 | − | 0.270479i | \(-0.912818\pi\) | ||
0.962726 | − | 0.270479i | \(-0.0871821\pi\) | |||||||
\(548\) | −8.81968e10 | −0.977981 | ||||||||
\(549\) | − | 2.31064e11i | − | 2.54357i | ||||||
\(550\) | −4.78478e10 | − | 9.52794e9i | −0.522891 | − | 0.104123i | ||||
\(551\) | −7.24667e10 | −0.786198 | ||||||||
\(552\) | 6.08556e10i | 0.655457i | ||||||||
\(553\) | 6.72237e10 | 0.718823 | ||||||||
\(554\) | 6.98646e10 | 0.741682 | ||||||||
\(555\) | 1.29765e11 | 1.36768 | ||||||||
\(556\) | 4.12525e9i | 0.0431669i | ||||||||
\(557\) | − | 6.78924e10i | − | 0.705343i | −0.935747 | − | 0.352671i | \(-0.885273\pi\) | ||
0.935747 | − | 0.352671i | \(-0.114727\pi\) | |||||||
\(558\) | − | 6.84872e10i | − | 0.706436i | ||||||
\(559\) | 2.08757e11 | 2.13793 | ||||||||
\(560\) | − | 6.38379e9i | − | 0.0649122i | ||||||
\(561\) | 6.56839e10 | + | 1.30796e10i | 0.663143 | + | 0.132052i | ||||
\(562\) | 1.01300e11 | 1.01546 | ||||||||
\(563\) | − | 4.05432e10i | − | 0.403538i | −0.979433 | − | 0.201769i | \(-0.935331\pi\) | ||
0.979433 | − | 0.201769i | \(-0.0646691\pi\) | |||||||
\(564\) | 7.29854e10 | 0.721306 | ||||||||
\(565\) | −2.95414e10 | −0.289892 | ||||||||
\(566\) | −3.30453e10 | −0.321991 | ||||||||
\(567\) | 7.57922e10i | 0.733318i | ||||||||
\(568\) | − | 9.28044e9i | − | 0.0891611i | ||||||
\(569\) | − | 8.62637e10i | − | 0.822961i | −0.911419 | − | 0.411480i | \(-0.865012\pi\) | ||
0.911419 | − | 0.411480i | \(-0.134988\pi\) | |||||||
\(570\) | 9.87949e10 | 0.935913 | ||||||||
\(571\) | 4.01160e10i | 0.377375i | 0.982037 | + | 0.188688i | \(0.0604234\pi\) | ||||
−0.982037 | + | 0.188688i | \(0.939577\pi\) | |||||||
\(572\) | −7.09229e10 | − | 1.41229e10i | −0.662525 | − | 0.131929i | ||||
\(573\) | 1.03441e11 | 0.959560 | ||||||||
\(574\) | − | 5.21084e10i | − | 0.480021i | ||||||
\(575\) | −8.63951e10 | −0.790346 | ||||||||
\(576\) | −2.92818e10 | −0.266016 | ||||||||
\(577\) | 5.13949e10 | 0.463679 | 0.231839 | − | 0.972754i | \(-0.425526\pi\) | ||||
0.231839 | + | 0.972754i | \(0.425526\pi\) | |||||||
\(578\) | 6.73868e10i | 0.603758i | ||||||||
\(579\) | 1.69226e11i | 1.50575i | ||||||||
\(580\) | − | 1.46233e10i | − | 0.129221i | ||||||
\(581\) | 2.02682e10 | 0.177873 | ||||||||
\(582\) | 2.30953e11i | 2.01295i | ||||||||
\(583\) | 1.38822e10 | − | 6.97143e10i | 0.120167 | − | 0.603459i | ||||
\(584\) | −1.72105e10 | −0.147960 | ||||||||
\(585\) | − | 1.67019e11i | − | 1.42608i | ||||||
\(586\) | 1.36120e11 | 1.15434 | ||||||||
\(587\) | −4.03753e10 | −0.340066 | −0.170033 | − | 0.985438i | \(-0.554387\pi\) | ||||
−0.170033 | + | 0.985438i | \(0.554387\pi\) | |||||||
\(588\) | 7.67408e10 | 0.641974 | ||||||||
\(589\) | 8.52492e10i | 0.708319i | ||||||||
\(590\) | − | 2.67024e9i | − | 0.0220365i | ||||||
\(591\) | − | 1.21612e11i | − | 0.996845i | ||||||
\(592\) | 4.78741e10 | 0.389775 | ||||||||
\(593\) | 1.97480e11i | 1.59700i | 0.601996 | + | 0.798499i | \(0.294372\pi\) | ||||
−0.601996 | + | 0.798499i | \(0.705628\pi\) | |||||||
\(594\) | −1.72261e11 | − | 3.43023e10i | −1.38370 | − | 0.275536i | ||||
\(595\) | −1.24412e10 | −0.0992648 | ||||||||
\(596\) | 9.72576e10i | 0.770794i | ||||||||
\(597\) | 1.13226e10 | 0.0891354 | ||||||||
\(598\) | −1.28060e11 | −1.00140 | ||||||||
\(599\) | 9.12212e10 | 0.708580 | 0.354290 | − | 0.935136i | \(-0.384723\pi\) | ||||
0.354290 | + | 0.935136i | \(0.384723\pi\) | |||||||
\(600\) | − | 6.11044e10i | − | 0.471484i | ||||||
\(601\) | − | 1.40799e11i | − | 1.07920i | −0.841922 | − | 0.539599i | \(-0.818576\pi\) | ||
0.841922 | − | 0.539599i | \(-0.181424\pi\) | |||||||
\(602\) | 7.69317e10i | 0.585760i | ||||||||
\(603\) | −4.97131e11 | −3.76012 | ||||||||
\(604\) | − | 5.26651e10i | − | 0.395708i | ||||||
\(605\) | 6.13805e10 | + | 2.54548e10i | 0.458152 | + | 0.189998i | ||||
\(606\) | −8.28609e10 | −0.614411 | ||||||||
\(607\) | − | 1.46613e11i | − | 1.07999i | −0.841669 | − | 0.539994i | \(-0.818427\pi\) | ||
0.841669 | − | 0.539994i | \(-0.181573\pi\) | |||||||
\(608\) | 3.64484e10 | 0.266725 | ||||||||
\(609\) | −6.63623e10 | −0.482450 | ||||||||
\(610\) | −5.80389e10 | −0.419179 | ||||||||
\(611\) | 1.53585e11i | 1.10201i | ||||||||
\(612\) | 5.70667e10i | 0.406796i | ||||||||
\(613\) | 1.42880e11i | 1.01188i | 0.862569 | + | 0.505939i | \(0.168854\pi\) | ||||
−0.862569 | + | 0.505939i | \(0.831146\pi\) | |||||||
\(614\) | −4.30613e10 | −0.302980 | ||||||||
\(615\) | 1.62731e11i | 1.13755i | ||||||||
\(616\) | 5.20461e9 | − | 2.61367e10i | 0.0361464 | − | 0.181521i | ||||
\(617\) | −1.69764e11 | −1.17140 | −0.585700 | − | 0.810528i | \(-0.699180\pi\) | ||||
−0.585700 | + | 0.810528i | \(0.699180\pi\) | |||||||
\(618\) | − | 2.62583e11i | − | 1.80017i | ||||||
\(619\) | −7.20916e10 | −0.491046 | −0.245523 | − | 0.969391i | \(-0.578960\pi\) | ||||
−0.245523 | + | 0.969391i | \(0.578960\pi\) | |||||||
\(620\) | −1.72027e10 | −0.116421 | ||||||||
\(621\) | −3.11038e11 | −2.09145 | ||||||||
\(622\) | − | 4.92273e10i | − | 0.328885i | ||||||
\(623\) | − | 1.95271e9i | − | 0.0129624i | ||||||
\(624\) | − | 9.05727e10i | − | 0.597391i | ||||||
\(625\) | 4.92113e10 | 0.322511 | ||||||||
\(626\) | − | 8.37364e10i | − | 0.545277i | ||||||
\(627\) | 4.04489e11 | + | 8.05460e10i | 2.61720 | + | 0.521163i | ||||
\(628\) | 5.98252e10 | 0.384632 | ||||||||
\(629\) | − | 9.33009e10i | − | 0.596051i | ||||||
\(630\) | 6.15504e10 | 0.390723 | ||||||||
\(631\) | 2.64546e11 | 1.66872 | 0.834362 | − | 0.551218i | \(-0.185837\pi\) | ||||
0.834362 | + | 0.551218i | \(0.185837\pi\) | |||||||
\(632\) | −7.74512e10 | −0.485467 | ||||||||
\(633\) | 2.54279e11i | 1.58379i | ||||||||
\(634\) | − | 1.41298e11i | − | 0.874538i | ||||||
\(635\) | 2.51463e10i | 0.154660i | ||||||||
\(636\) | 8.90292e10 | 0.544132 | ||||||||
\(637\) | 1.61488e11i | 0.980803i | ||||||||
\(638\) | 1.19221e10 | − | 5.98710e10i | 0.0719567 | − | 0.361355i | ||||
\(639\) | 8.94790e10 | 0.536683 | ||||||||
\(640\) | 7.35503e9i | 0.0438394i | ||||||||
\(641\) | 7.40418e10 | 0.438576 | 0.219288 | − | 0.975660i | \(-0.429627\pi\) | ||||
0.219288 | + | 0.975660i | \(0.429627\pi\) | |||||||
\(642\) | −3.22195e11 | −1.89661 | ||||||||
\(643\) | −7.98961e9 | −0.0467393 | −0.0233696 | − | 0.999727i | \(-0.507439\pi\) | ||||
−0.0233696 | + | 0.999727i | \(0.507439\pi\) | |||||||
\(644\) | − | 4.71930e10i | − | 0.274369i | ||||||
\(645\) | − | 2.40252e11i | − | 1.38813i | ||||||
\(646\) | − | 7.10335e10i | − | 0.407881i | ||||||
\(647\) | −1.94844e11 | −1.11191 | −0.555957 | − | 0.831211i | \(-0.687648\pi\) | ||||
−0.555957 | + | 0.831211i | \(0.687648\pi\) | |||||||
\(648\) | − | 8.73233e10i | − | 0.495256i | ||||||
\(649\) | 2.17701e9 | − | 1.09326e10i | 0.0122710 | − | 0.0616232i | ||||
\(650\) | 1.28584e11 | 0.720331 | ||||||||
\(651\) | 7.80681e10i | 0.434660i | ||||||||
\(652\) | −3.21561e10 | −0.177940 | ||||||||
\(653\) | 1.05032e11 | 0.577657 | 0.288828 | − | 0.957381i | \(-0.406734\pi\) | ||||
0.288828 | + | 0.957381i | \(0.406734\pi\) | |||||||
\(654\) | 2.42482e11 | 1.32547 | ||||||||
\(655\) | − | 8.40394e9i | − | 0.0456581i | ||||||
\(656\) | 6.00362e10i | 0.324189i | ||||||||
\(657\) | − | 1.65938e11i | − | 0.890606i | ||||||
\(658\) | −5.65995e10 | −0.301932 | ||||||||
\(659\) | 1.21988e11i | 0.646810i | 0.946261 | + | 0.323405i | \(0.104828\pi\) | ||||
−0.946261 | + | 0.323405i | \(0.895172\pi\) | |||||||
\(660\) | −1.62536e10 | + | 8.16231e10i | −0.0856593 | + | 0.430167i | ||||
\(661\) | −4.46559e10 | −0.233923 | −0.116962 | − | 0.993136i | \(-0.537315\pi\) | ||||
−0.116962 | + | 0.993136i | \(0.537315\pi\) | |||||||
\(662\) | − | 2.37439e10i | − | 0.123629i | ||||||
\(663\) | −1.76515e11 | −0.913541 | ||||||||
\(664\) | −2.33518e10 | −0.120129 | ||||||||
\(665\) | −7.66146e10 | −0.391765 | ||||||||
\(666\) | 4.61587e11i | 2.34615i | ||||||||
\(667\) | − | 1.08105e11i | − | 0.546186i | ||||||
\(668\) | − | 1.76123e11i | − | 0.884526i | ||||||
\(669\) | 3.50515e11 | 1.74986 | ||||||||
\(670\) | 1.24870e11i | 0.619667i | ||||||||
\(671\) | −2.37625e11 | − | 4.73182e10i | −1.17220 | − | 0.233420i | ||||
\(672\) | 3.33781e10 | 0.163676 | ||||||||
\(673\) | 3.68652e11i | 1.79703i | 0.438941 | + | 0.898516i | \(0.355354\pi\) | ||||
−0.438941 | + | 0.898516i | \(0.644646\pi\) | |||||||
\(674\) | 3.78726e10 | 0.183521 | ||||||||
\(675\) | 3.12310e11 | 1.50442 | ||||||||
\(676\) | 8.61808e10 | 0.412690 | ||||||||
\(677\) | 1.82453e10i | 0.0868554i | 0.999057 | + | 0.0434277i | \(0.0138278\pi\) | ||||
−0.999057 | + | 0.0434277i | \(0.986172\pi\) | |||||||
\(678\) | − | 1.54459e11i | − | 0.730962i | ||||||
\(679\) | − | 1.79102e11i | − | 0.842601i | ||||||
\(680\) | 1.43341e10 | 0.0670399 | ||||||||
\(681\) | − | 2.92284e11i | − | 1.35899i | ||||||
\(682\) | −7.04318e10 | − | 1.40251e10i | −0.325560 | − | 0.0648288i | ||||
\(683\) | 3.48602e11 | 1.60194 | 0.800972 | − | 0.598702i | \(-0.204317\pi\) | ||||
0.800972 | + | 0.598702i | \(0.204317\pi\) | |||||||
\(684\) | 3.51423e11i | 1.60549i | ||||||||
\(685\) | −2.13595e11 | −0.970130 | ||||||||
\(686\) | −1.41490e11 | −0.638895 | ||||||||
\(687\) | −1.70447e11 | −0.765180 | ||||||||
\(688\) | − | 8.86362e10i | − | 0.395601i | ||||||
\(689\) | 1.87346e11i | 0.831321i | ||||||||
\(690\) | 1.47381e11i | 0.650195i | ||||||||
\(691\) | −2.99034e11 | −1.31162 | −0.655811 | − | 0.754925i | \(-0.727673\pi\) | ||||
−0.655811 | + | 0.754925i | \(0.727673\pi\) | |||||||
\(692\) | − | 3.53868e10i | − | 0.154318i | ||||||
\(693\) | 2.52002e11 | + | 5.01811e10i | 1.09262 | + | 0.217574i | ||||
\(694\) | −1.04871e11 | −0.452082 | ||||||||
\(695\) | 9.99056e9i | 0.0428204i | ||||||||
\(696\) | 7.64588e10 | 0.325830 | ||||||||
\(697\) | 1.17003e11 | 0.495755 | ||||||||
\(698\) | 4.87836e10 | 0.205519 | ||||||||
\(699\) | 3.55898e9i | 0.0149079i | ||||||||
\(700\) | 4.73859e10i | 0.197359i | ||||||||
\(701\) | − | 1.73386e11i | − | 0.718030i | −0.933332 | − | 0.359015i | \(-0.883113\pi\) | ||
0.933332 | − | 0.359015i | \(-0.116887\pi\) | |||||||
\(702\) | 4.62924e11 | 1.90617 | ||||||||
\(703\) | − | 5.74558e11i | − | 2.35241i | ||||||
\(704\) | −5.99644e9 | + | 3.01132e10i | −0.0244120 | + | 0.122593i | ||||
\(705\) | 1.76756e11 | 0.715515 | ||||||||
\(706\) | 1.26652e11i | 0.509791i | ||||||||
\(707\) | 6.42579e10 | 0.257187 | ||||||||
\(708\) | 1.39615e10 | 0.0555649 | ||||||||
\(709\) | 2.62470e11 | 1.03871 | 0.519356 | − | 0.854558i | \(-0.326172\pi\) | ||||
0.519356 | + | 0.854558i | \(0.326172\pi\) | |||||||
\(710\) | − | 2.24754e10i | − | 0.0884453i | ||||||
\(711\) | − | 7.46759e11i | − | 2.92215i | ||||||
\(712\) | 2.24979e9i | 0.00875433i | ||||||||
\(713\) | −1.27173e11 | −0.492082 | ||||||||
\(714\) | − | 6.50498e10i | − | 0.250296i | ||||||
\(715\) | −1.71762e11 | − | 3.42029e10i | −0.657206 | − | 0.130870i | ||||
\(716\) | −5.22191e10 | −0.198690 | ||||||||
\(717\) | 3.27430e11i | 1.23892i | ||||||||
\(718\) | 1.71740e11 | 0.646209 | ||||||||
\(719\) | 3.75789e11 | 1.40614 | 0.703069 | − | 0.711121i | \(-0.251812\pi\) | ||||
0.703069 | + | 0.711121i | \(0.251812\pi\) | |||||||
\(720\) | −7.09148e10 | −0.263880 | ||||||||
\(721\) | 2.03631e11i | 0.753535i | ||||||||
\(722\) | − | 2.45286e11i | − | 0.902659i | ||||||
\(723\) | 6.36641e10i | 0.232992i | ||||||||
\(724\) | −4.34711e10 | −0.158215 | ||||||||
\(725\) | 1.08546e11i | 0.392883i | ||||||||
\(726\) | −1.33092e11 | + | 3.20932e11i | −0.479078 | + | 1.15523i | ||||
\(727\) | −5.04234e11 | −1.80507 | −0.902536 | − | 0.430613i | \(-0.858297\pi\) | ||||
−0.902536 | + | 0.430613i | \(0.858297\pi\) | |||||||
\(728\) | 7.02383e10i | 0.250063i | ||||||||
\(729\) | −1.54729e11 | −0.547851 | ||||||||
\(730\) | −4.16806e10 | −0.146772 | ||||||||
\(731\) | −1.72741e11 | −0.604960 | ||||||||
\(732\) | − | 3.03460e11i | − | 1.05696i | ||||||
\(733\) | 2.95479e11i | 1.02355i | 0.859119 | + | 0.511776i | \(0.171012\pi\) | ||||
−0.859119 | + | 0.511776i | \(0.828988\pi\) | |||||||
\(734\) | − | 1.91294e10i | − | 0.0659047i | ||||||
\(735\) | 1.85851e11 | 0.636820 | ||||||||
\(736\) | 5.43730e10i | 0.185299i | ||||||||
\(737\) | −1.01805e11 | + | 5.11246e11i | −0.345062 | + | 1.73285i | ||||
\(738\) | −5.78850e11 | −1.95137 | ||||||||
\(739\) | 1.70289e11i | 0.570964i | 0.958384 | + | 0.285482i | \(0.0921536\pi\) | ||||
−0.958384 | + | 0.285482i | \(0.907846\pi\) | |||||||
\(740\) | 1.15942e11 | 0.386646 | ||||||||
\(741\) | −1.08700e12 | −3.60543 | ||||||||
\(742\) | −6.90414e10 | −0.227769 | ||||||||
\(743\) | − | 5.05484e11i | − | 1.65864i | −0.558774 | − | 0.829320i | \(-0.688728\pi\) | ||
0.558774 | − | 0.829320i | \(-0.311272\pi\) | |||||||
\(744\) | − | 8.99454e10i | − | 0.293554i | ||||||
\(745\) | 2.35539e11i | 0.764606i | ||||||||
\(746\) | −2.58633e11 | −0.835080 | ||||||||
\(747\) | − | 2.25150e11i | − | 0.723087i | ||||||
\(748\) | 5.86869e10 | + | 1.16863e10i | 0.187471 | + | 0.0373312i | ||||
\(749\) | 2.49859e11 | 0.793905 | ||||||||
\(750\) | − | 3.44247e11i | − | 1.08799i | ||||||
\(751\) | −1.53665e11 | −0.483077 | −0.241538 | − | 0.970391i | \(-0.577652\pi\) | ||||
−0.241538 | + | 0.970391i | \(0.577652\pi\) | |||||||
\(752\) | 6.52107e10 | 0.203914 | ||||||||
\(753\) | 1.53433e11 | 0.477242 | ||||||||
\(754\) | 1.60894e11i | 0.497800i | ||||||||
\(755\) | − | 1.27545e11i | − | 0.392531i | ||||||
\(756\) | 1.70598e11i | 0.522260i | ||||||||
\(757\) | 1.98576e11 | 0.604703 | 0.302352 | − | 0.953196i | \(-0.402228\pi\) | ||||
0.302352 | + | 0.953196i | \(0.402228\pi\) | |||||||
\(758\) | 2.57943e10i | 0.0781353i | ||||||||
\(759\) | −1.20157e11 | + | 6.03410e11i | −0.362062 | + | 1.81822i | ||||
\(760\) | 8.82709e10 | 0.264584 | ||||||||
\(761\) | − | 2.65735e11i | − | 0.792338i | −0.918178 | − | 0.396169i | \(-0.870339\pi\) | ||
0.918178 | − | 0.396169i | \(-0.129661\pi\) | |||||||
\(762\) | −1.31479e11 | −0.389975 | ||||||||
\(763\) | −1.88043e11 | −0.554829 | ||||||||
\(764\) | 9.24216e10 | 0.271269 | ||||||||
\(765\) | 1.38204e11i | 0.403530i | ||||||||
\(766\) | 3.92630e11i | 1.14043i | ||||||||
\(767\) | 2.93796e10i | 0.0848916i | ||||||||
\(768\) | −3.84563e10 | −0.110541 | ||||||||
\(769\) | − | 3.30229e11i | − | 0.944299i | −0.881518 | − | 0.472150i | \(-0.843478\pi\) | ||
0.881518 | − | 0.472150i | \(-0.156522\pi\) | |||||||
\(770\) | 1.26045e10 | − | 6.32980e10i | 0.0358562 | − | 0.180064i | ||||
\(771\) | −2.37478e11 | −0.672058 | ||||||||
\(772\) | 1.51199e11i | 0.425677i | ||||||||
\(773\) | −8.90645e9 | −0.0249452 | −0.0124726 | − | 0.999922i | \(-0.503970\pi\) | ||||
−0.0124726 | + | 0.999922i | \(0.503970\pi\) | |||||||
\(774\) | 8.54602e11 | 2.38122 | ||||||||
\(775\) | 1.27693e11 | 0.353965 | ||||||||
\(776\) | 2.06351e11i | 0.569062i | ||||||||
\(777\) | − | 5.26159e11i | − | 1.44355i | ||||||
\(778\) | 2.64213e11i | 0.721166i | ||||||||
\(779\) | 7.20521e11 | 1.95658 | ||||||||
\(780\) | − | 2.19349e11i | − | 0.592595i | ||||||
\(781\) | 1.83239e10 | − | 9.20196e10i | 0.0492508 | − | 0.247330i | ||||
\(782\) | 1.05966e11 | 0.283362 | ||||||||
\(783\) | 3.90787e11i | 1.03966i | ||||||||
\(784\) | 6.85661e10 | 0.181487 | ||||||||
\(785\) | 1.44885e11 | 0.381544 | ||||||||
\(786\) | 4.39406e10 | 0.115127 | ||||||||
\(787\) | 2.31980e11i | 0.604717i | 0.953194 | + | 0.302358i | \(0.0977740\pi\) | ||||
−0.953194 | + | 0.302358i | \(0.902226\pi\) | |||||||
\(788\) | − | 1.08658e11i | − | 0.281809i | ||||||
\(789\) | − | 3.61698e11i | − | 0.933336i | ||||||
\(790\) | −1.87572e11 | −0.481570 | ||||||||
\(791\) | 1.19782e11i | 0.305974i | ||||||||
\(792\) | −2.90341e11 | − | 5.78158e10i | −0.737918 | − | 0.146942i | ||||
\(793\) | 6.38579e11 | 1.61481 | ||||||||
\(794\) | − | 1.22091e11i | − | 0.307186i | ||||||
\(795\) | 2.15611e11 | 0.539763 | ||||||||
\(796\) | 1.01165e10 | 0.0251987 | ||||||||
\(797\) | 2.60242e11 | 0.644976 | 0.322488 | − | 0.946574i | \(-0.395481\pi\) | ||||
0.322488 | + | 0.946574i | \(0.395481\pi\) | |||||||
\(798\) | − | 4.00585e11i | − | 0.987832i | ||||||
\(799\) | − | 1.27088e11i | − | 0.311829i | ||||||
\(800\) | − | 5.45953e10i | − | 0.133289i | ||||||
\(801\) | −2.16918e10 | −0.0526945 | ||||||||
\(802\) | − | 5.90231e10i | − | 0.142667i | ||||||
\(803\) | −1.70650e11 | − | 3.39816e10i | −0.410435 | − | 0.0817299i | ||||
\(804\) | −6.52891e11 | −1.56249 | ||||||||
\(805\) | − | 1.14292e11i | − | 0.272166i | ||||||
\(806\) | 1.89274e11 | 0.448489 | ||||||||
\(807\) | 5.66144e11 | 1.33485 | ||||||||
\(808\) | −7.40342e10 | −0.173695 | ||||||||
\(809\) | − | 2.68336e11i | − | 0.626448i | −0.949679 | − | 0.313224i | \(-0.898591\pi\) | ||
0.949679 | − | 0.313224i | \(-0.101409\pi\) | |||||||
\(810\) | − | 2.11480e11i | − | 0.491280i | ||||||
\(811\) | − | 5.22878e11i | − | 1.20870i | −0.796721 | − | 0.604348i | \(-0.793434\pi\) | ||
0.796721 | − | 0.604348i | \(-0.206566\pi\) | |||||||
\(812\) | −5.92931e10 | −0.136389 | ||||||||
\(813\) | 1.25965e12i | 2.88329i | ||||||||
\(814\) | 4.74693e11 | + | 9.45256e10i | 1.08122 | + | 0.215304i | ||||
\(815\) | −7.78759e10 | −0.176511 | ||||||||
\(816\) | 7.49466e10i | 0.169041i | ||||||||
\(817\) | −1.06376e12 | −2.38757 | ||||||||
\(818\) | 2.67797e11 | 0.598125 | ||||||||
\(819\) | −6.77215e11 | −1.50519 | ||||||||
\(820\) | 1.45396e11i | 0.321586i | ||||||||
\(821\) | 2.21311e11i | 0.487115i | 0.969887 | + | 0.243557i | \(0.0783144\pi\) | ||||
−0.969887 | + | 0.243557i | \(0.921686\pi\) | |||||||
\(822\) | − | 1.11680e12i | − | 2.44618i | ||||||
\(823\) | 2.08544e11 | 0.454568 | 0.227284 | − | 0.973829i | \(-0.427015\pi\) | ||||
0.227284 | + | 0.973829i | \(0.427015\pi\) | |||||||
\(824\) | − | 2.34612e11i | − | 0.508910i | ||||||
\(825\) | 1.20648e11 | − | 6.05876e11i | 0.260439 | − | 1.30788i | ||||
\(826\) | −1.08271e10 | −0.0232590 | ||||||||
\(827\) | 5.24626e11i | 1.12157i | 0.827960 | + | 0.560786i | \(0.189501\pi\) | ||||
−0.827960 | + | 0.560786i | \(0.810499\pi\) | |||||||
\(828\) | −5.24247e11 | −1.11536 | ||||||||
\(829\) | −3.55424e11 | −0.752538 | −0.376269 | − | 0.926511i | \(-0.622793\pi\) | ||||
−0.376269 | + | 0.926511i | \(0.622793\pi\) | |||||||
\(830\) | −5.65535e10 | −0.119165 | ||||||||
\(831\) | 8.84666e11i | 1.85513i | ||||||||
\(832\) | − | 8.09245e10i | − | 0.168883i | ||||||
\(833\) | − | 1.33627e11i | − | 0.277533i | ||||||
\(834\) | −5.22363e10 | −0.107971 | ||||||||
\(835\) | − | 4.26536e11i | − | 0.877425i | ||||||
\(836\) | 3.61401e11 | + | 7.19659e10i | 0.739886 | + | 0.147334i | ||||
\(837\) | 4.59719e11 | 0.936678 | ||||||||
\(838\) | − | 1.60152e11i | − | 0.324755i | ||||||
\(839\) | 3.96702e11 | 0.800603 | 0.400301 | − | 0.916384i | \(-0.368905\pi\) | ||||
0.400301 | + | 0.916384i | \(0.368905\pi\) | |||||||
\(840\) | 8.08352e10 | 0.162362 | ||||||||
\(841\) | 3.64424e11 | 0.728490 | ||||||||
\(842\) | 1.81880e11i | 0.361856i | ||||||||
\(843\) | 1.28271e12i | 2.53992i | ||||||||
\(844\) | 2.27193e11i | 0.447738i | ||||||||
\(845\) | 2.08713e11 | 0.409377 | ||||||||
\(846\) | 6.28740e11i | 1.22741i | ||||||||
\(847\) | 1.03212e11 | − | 2.48880e11i | 0.200538 | − | 0.483567i | ||||
\(848\) | 7.95455e10 | 0.153827 | ||||||||
\(849\) | − | 4.18438e11i | − | 0.805380i | ||||||
\(850\) | −1.06400e11 | −0.203828 | ||||||||
\(851\) | 8.57116e11 | 1.63426 | ||||||||
\(852\) | 1.17514e11 | 0.223014 | ||||||||
\(853\) | 1.59147e11i | 0.300609i | 0.988640 | + | 0.150304i | \(0.0480254\pi\) | ||||
−0.988640 | + | 0.150304i | \(0.951975\pi\) | |||||||
\(854\) | 2.35331e11i | 0.442433i | ||||||||
\(855\) | 8.51079e11i | 1.59260i | ||||||||
\(856\) | −2.87873e11 | −0.536175 | ||||||||
\(857\) | − | 7.79199e11i | − | 1.44453i | −0.691619 | − | 0.722263i | \(-0.743102\pi\) | ||
0.691619 | − | 0.722263i | \(-0.256898\pi\) | |||||||
\(858\) | 1.78832e11 | − | 8.98067e11i | 0.329987 | − | 1.65714i | ||||
\(859\) | 1.95693e11 | 0.359420 | 0.179710 | − | 0.983720i | \(-0.442484\pi\) | ||||
0.179710 | + | 0.983720i | \(0.442484\pi\) | |||||||
\(860\) | − | 2.14660e11i | − | 0.392425i | ||||||
\(861\) | 6.59826e11 | 1.20065 | ||||||||
\(862\) | −6.44277e11 | −1.16693 | ||||||||
\(863\) | −9.26945e11 | −1.67113 | −0.835566 | − | 0.549390i | \(-0.814860\pi\) | ||||
−0.835566 | + | 0.549390i | \(0.814860\pi\) | |||||||
\(864\) | − | 1.96553e11i | − | 0.352716i | ||||||
\(865\) | − | 8.56999e10i | − | 0.153079i | ||||||
\(866\) | 4.10706e10i | 0.0730229i | ||||||||
\(867\) | −8.53290e11 | −1.51015 | ||||||||
\(868\) | 6.97519e10i | 0.122879i | ||||||||
\(869\) | −7.67962e11 | − | 1.52924e11i | −1.34667 | − | 0.268162i | ||||
\(870\) | 1.85168e11 | 0.323214 | ||||||||
\(871\) | − | 1.37389e12i | − | 2.38716i | ||||||
\(872\) | 2.16652e11 | 0.374712 | ||||||||
\(873\) | −1.98957e12 | −3.42533 | ||||||||
\(874\) | 6.52555e11 | 1.11833 | ||||||||
\(875\) | 2.66961e11i | 0.455423i | ||||||||
\(876\) | − | 2.17930e11i | − | 0.370084i | ||||||
\(877\) | 3.79925e11i | 0.642244i | 0.947038 | + | 0.321122i | \(0.104060\pi\) | ||||
−0.947038 | + | 0.321122i | \(0.895940\pi\) | |||||||
\(878\) | −5.38114e11 | −0.905516 | ||||||||
\(879\) | 1.72363e12i | 2.88728i | ||||||||
\(880\) | −1.45222e10 | + | 7.29282e10i | −0.0242160 | + | 0.121609i | ||||
\(881\) | 5.59727e11 | 0.929122 | 0.464561 | − | 0.885541i | \(-0.346212\pi\) | ||||
0.464561 | + | 0.885541i | \(0.346212\pi\) | |||||||
\(882\) | 6.61092e11i | 1.09241i | ||||||||
\(883\) | 6.16215e11 | 1.01365 | 0.506827 | − | 0.862048i | \(-0.330818\pi\) | ||||
0.506827 | + | 0.862048i | \(0.330818\pi\) | |||||||
\(884\) | −1.57712e11 | −0.258259 | ||||||||
\(885\) | 3.38121e10 | 0.0551188 | ||||||||
\(886\) | 7.55949e11i | 1.22675i | ||||||||
\(887\) | 2.94445e11i | 0.475675i | 0.971305 | + | 0.237838i | \(0.0764386\pi\) | ||||
−0.971305 | + | 0.237838i | \(0.923561\pi\) | |||||||
\(888\) | 6.06210e11i | 0.974925i | ||||||||
\(889\) | 1.01961e11 | 0.163240 | ||||||||
\(890\) | 5.44857e9i | 0.00868405i | ||||||||
\(891\) | 1.72417e11 | − | 8.65848e11i | 0.273570 | − | 1.37382i | ||||
\(892\) | 3.13177e11 | 0.494687 | ||||||||
\(893\) | − | 7.82622e11i | − | 1.23068i | ||||||
\(894\) | −1.23153e12 | −1.92795 | ||||||||
\(895\) | −1.26464e11 | −0.197095 | ||||||||
\(896\) | 2.98225e10 | 0.0462713 | ||||||||
\(897\) | − | 1.62157e12i | − | 2.50476i | ||||||
\(898\) | 4.14678e11i | 0.637685i | ||||||||
\(899\) | 1.59780e11i | 0.244615i | ||||||||
\(900\) | 5.26390e11 | 0.802302 | ||||||||
\(901\) | − | 1.55024e11i | − | 0.235235i | ||||||
\(902\) | −1.18539e11 | + | 5.95285e11i | −0.179075 | + | 0.899288i | ||||
\(903\) | −9.74154e11 | −1.46513 | ||||||||
\(904\) | − | 1.38005e11i | − | 0.206644i | ||||||
\(905\) | −1.05279e11 | −0.156944 | ||||||||
\(906\) | 6.66876e11 | 0.989765 | ||||||||
\(907\) | −6.09734e11 | −0.900972 | −0.450486 | − | 0.892784i | \(-0.648749\pi\) | ||||
−0.450486 | + | 0.892784i | \(0.648749\pi\) | |||||||
\(908\) | − | 2.61149e11i | − | 0.384188i | ||||||
\(909\) | − | 7.13814e11i | − | 1.04551i | ||||||
\(910\) | 1.70104e11i | 0.248055i | ||||||||
\(911\) | −5.64111e11 | −0.819013 | −0.409507 | − | 0.912307i | \(-0.634299\pi\) | ||||
−0.409507 | + | 0.912307i | \(0.634299\pi\) | |||||||
\(912\) | 4.61530e11i | 0.667146i | ||||||||
\(913\) | −2.31543e11 | − | 4.61072e10i | −0.333233 | − | 0.0663568i | ||||
\(914\) | −9.89788e10 | −0.141827 | ||||||||
\(915\) | − | 7.34922e11i | − | 1.04847i | ||||||
\(916\) | −1.52291e11 | −0.216317 | ||||||||
\(917\) | −3.40756e10 | −0.0481910 | ||||||||
\(918\) | −3.83058e11 | −0.539379 | ||||||||
\(919\) | 4.06554e11i | 0.569975i | 0.958531 | + | 0.284988i | \(0.0919895\pi\) | ||||
−0.958531 | + | 0.284988i | \(0.908011\pi\) | |||||||
\(920\) | 1.31681e11i | 0.183811i | ||||||||
\(921\) | − | 5.45267e11i | − | 0.757829i | ||||||
\(922\) | 8.42990e10 | 0.116654 | ||||||||
\(923\) | 2.47288e11i | 0.340719i | ||||||||
\(924\) | 3.30958e11 | + | 6.59037e10i | 0.454030 | + | 0.0904112i | ||||
\(925\) | −8.60619e11 | −1.17556 | ||||||||
\(926\) | − | 3.01628e11i | − | 0.410230i | ||||||
\(927\) | 2.26205e12 | 3.06326 | ||||||||
\(928\) | 6.83141e10 | 0.0921124 | ||||||||
\(929\) | 9.63039e11 | 1.29295 | 0.646474 | − | 0.762936i | \(-0.276243\pi\) | ||||
0.646474 | + | 0.762936i | \(0.276243\pi\) | |||||||
\(930\) | − | 2.17830e11i | − | 0.291197i | ||||||
\(931\) | − | 8.22892e11i | − | 1.09533i | ||||||
\(932\) | 3.17987e9i | 0.00421449i | ||||||||
\(933\) | 6.23345e11 | 0.822624 | ||||||||
\(934\) | − | 6.29058e11i | − | 0.826614i | ||||||
\(935\) | 1.42128e11 | + | 2.83021e10i | 0.185966 | + | 0.0370315i | ||||
\(936\) | 7.80248e11 | 1.01655 | ||||||||
\(937\) | 2.62286e11i | 0.340264i | 0.985421 | + | 0.170132i | \(0.0544194\pi\) | ||||
−0.985421 | + | 0.170132i | \(0.945581\pi\) | |||||||
\(938\) | 5.06311e11 | 0.654043 | ||||||||
\(939\) | 1.06032e12 | 1.36387 | ||||||||
\(940\) | 1.57928e11 | 0.202277 | ||||||||
\(941\) | 9.14087e11i | 1.16581i | 0.812539 | + | 0.582907i | \(0.198085\pi\) | ||||
−0.812539 | + | 0.582907i | \(0.801915\pi\) | |||||||
\(942\) | 7.57542e11i | 0.962062i | ||||||||
\(943\) | 1.07486e12i | 1.35927i | ||||||||
\(944\) | 1.24743e10 | 0.0157083 | ||||||||
\(945\) | 4.13156e11i | 0.518067i | ||||||||
\(946\) | 1.75009e11 | − | 8.78867e11i | 0.218522 | − | 1.09738i | ||||
\(947\) | −1.46362e12 | −1.81983 | −0.909913 | − | 0.414800i | \(-0.863852\pi\) | ||||
−0.909913 | + | 0.414800i | \(0.863852\pi\) | |||||||
\(948\) | − | 9.80732e11i | − | 1.21427i | ||||||
\(949\) | 4.58595e11 | 0.565412 | ||||||||
\(950\) | −6.55222e11 | −0.804441 | ||||||||
\(951\) | 1.78920e12 | 2.18744 | ||||||||
\(952\) | − | 5.81205e10i | − | 0.0707589i | ||||||
\(953\) | 1.45117e12i | 1.75933i | 0.475593 | + | 0.879665i | \(0.342233\pi\) | ||||
−0.475593 | + | 0.879665i | \(0.657767\pi\) | |||||||
\(954\) | 7.66952e11i | 0.925922i | ||||||||
\(955\) | 2.23827e11 | 0.269091 | ||||||||
\(956\) | 2.92551e11i | 0.350244i | ||||||||
\(957\) | 7.58122e11 | + | 1.50965e11i | 0.903839 | + | 0.179982i | ||||
\(958\) | 3.89024e11 | 0.461865 | ||||||||
\(959\) | 8.66068e11i | 1.02395i | ||||||||
\(960\) | −9.31336e10 | −0.109653 | ||||||||
\(961\) | −6.64927e11 | −0.779616 | ||||||||
\(962\) | −1.27566e12 | −1.48948 | ||||||||
\(963\) | − | 2.77558e12i | − | 3.22737i | ||||||
\(964\) | 5.68823e10i | 0.0658672i | ||||||||
\(965\) | 3.66175e11i | 0.422260i | ||||||||
\(966\) | 5.97585e11 | 0.686264 | ||||||||
\(967\) | − | 1.58102e12i | − | 1.80814i | −0.427386 | − | 0.904069i | \(-0.640566\pi\) | ||
0.427386 | − | 0.904069i | \(-0.359434\pi\) | |||||||
\(968\) | −1.18915e11 | + | 2.86745e11i | −0.135436 | + | 0.326584i | ||||
\(969\) | 8.99467e11 | 1.02021 | ||||||||
\(970\) | 4.99742e11i | 0.564494i | ||||||||
\(971\) | −1.32322e12 | −1.48852 | −0.744258 | − | 0.667892i | \(-0.767197\pi\) | ||||
−0.744258 | + | 0.667892i | \(0.767197\pi\) | |||||||
\(972\) | 2.15236e11 | 0.241129 | ||||||||
\(973\) | 4.05088e10 | 0.0451958 | ||||||||
\(974\) | − | 1.05374e12i | − | 1.17084i | ||||||
\(975\) | 1.62820e12i | 1.80173i | ||||||||
\(976\) | − | 2.71134e11i | − | 0.298803i | ||||||
\(977\) | −4.93380e11 | −0.541506 | −0.270753 | − | 0.962649i | \(-0.587273\pi\) | ||||
−0.270753 | + | 0.962649i | \(0.587273\pi\) | |||||||
\(978\) | − | 4.07180e11i | − | 0.445072i | ||||||
\(979\) | −4.44213e9 | + | 2.23077e10i | −0.00483572 | + | 0.0242842i | ||||
\(980\) | 1.66054e11 | 0.180030 | ||||||||
\(981\) | 2.08889e12i | 2.25548i | ||||||||
\(982\) | 8.79044e11 | 0.945289 | ||||||||
\(983\) | 3.86926e11 | 0.414394 | 0.207197 | − | 0.978299i | \(-0.433566\pi\) | ||||
0.207197 | + | 0.978299i | \(0.433566\pi\) | |||||||
\(984\) | −7.60213e11 | −0.810877 | ||||||||
\(985\) | − | 2.63148e11i | − | 0.279547i | ||||||
\(986\) | − | 1.33136e11i | − | 0.140860i | ||||||
\(987\) | − | 7.16696e11i | − | 0.755208i | ||||||
\(988\) | −9.71210e11 | −1.01926 | ||||||||
\(989\) | − | 1.58690e12i | − | 1.65869i | ||||||
\(990\) | −7.03151e11 | − | 1.40019e11i | −0.731994 | − | 0.145762i | ||||
\(991\) | −5.12465e10 | −0.0531337 | −0.0265668 | − | 0.999647i | \(-0.508457\pi\) | ||||
−0.0265668 | + | 0.999647i | \(0.508457\pi\) | |||||||
\(992\) | − | 8.03641e10i | − | 0.0829880i | ||||||
\(993\) | 3.00659e11 | 0.309226 | ||||||||
\(994\) | −9.11314e10 | −0.0933517 | ||||||||
\(995\) | 2.45002e10 | 0.0249964 | ||||||||
\(996\) | − | 2.95694e11i | − | 0.300473i | ||||||
\(997\) | 1.50058e12i | 1.51872i | 0.650670 | + | 0.759361i | \(0.274488\pi\) | ||||
−0.650670 | + | 0.759361i | \(0.725512\pi\) | |||||||
\(998\) | − | 6.72326e11i | − | 0.677731i | ||||||
\(999\) | −3.09839e12 | −3.11081 |
(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 | 22.9.b.a.21.5 | yes | 8 | |
3.2 | odd | 2 | 198.9.d.a.109.3 | 8 | |||
4.3 | odd | 2 | 176.9.h.e.65.7 | 8 | |||
11.10 | odd | 2 | inner | 22.9.b.a.21.1 | ✓ | 8 | |
33.32 | even | 2 | 198.9.d.a.109.7 | 8 | |||
44.43 | even | 2 | 176.9.h.e.65.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.9.b.a.21.1 | ✓ | 8 | 11.10 | odd | 2 | inner | |
22.9.b.a.21.5 | yes | 8 | 1.1 | even | 1 | trivial | |
176.9.h.e.65.7 | 8 | 4.3 | odd | 2 | |||
176.9.h.e.65.8 | 8 | 44.43 | even | 2 | |||
198.9.d.a.109.3 | 8 | 3.2 | odd | 2 | |||
198.9.d.a.109.7 | 8 | 33.32 | even | 2 |