Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,20,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
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: | yes |
Analytic conductor: | \(20.5935026901\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{87481}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 21870 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(148.386\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1238.32 | −1.71020 | −0.855099 | − | 0.518465i | \(-0.826504\pi\) | ||||
−0.855099 | + | 0.518465i | \(0.826504\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00914e6 | 1.92478 | ||||||||
\(5\) | −6.69930e6 | −1.53396 | −0.766981 | − | 0.641670i | \(-0.778242\pi\) | ||||
−0.766981 | + | 0.641670i | \(0.778242\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 214621. | 0.00201021 | 0.00100510 | − | 0.999999i | \(-0.499680\pi\) | ||||
0.00100510 | + | 0.999999i | \(0.499680\pi\) | |||||||
\(8\) | −6.00397e8 | −1.58155 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.29585e9 | 2.62338 | ||||||||
\(11\) | 1.30816e10 | 1.67275 | 0.836373 | − | 0.548161i | \(-0.184672\pi\) | ||||
0.836373 | + | 0.548161i | \(0.184672\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.34409e10 | 0.351533 | 0.175766 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175766 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(14\) | −2.65768e8 | −0.00343785 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.14402e11 | 0.779990 | ||||||||
\(17\) | 3.48802e11 | 0.713368 | 0.356684 | − | 0.934225i | \(-0.383907\pi\) | ||||
0.356684 | + | 0.934225i | \(0.383907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.20630e11 | −0.441238 | −0.220619 | − | 0.975360i | \(-0.570808\pi\) | ||||
−0.220619 | + | 0.975360i | \(0.570808\pi\) | |||||||
\(20\) | −6.76052e12 | −2.95253 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.61991e13 | −2.86073 | ||||||||
\(23\) | 2.65405e12 | 0.307252 | 0.153626 | − | 0.988129i | \(-0.450905\pi\) | ||||
0.153626 | + | 0.988129i | \(0.450905\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.58072e13 | 1.35304 | ||||||||
\(26\) | −1.66441e13 | −0.601191 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.16582e11 | 0.00386920 | ||||||||
\(29\) | −1.27229e14 | −1.62857 | −0.814286 | − | 0.580464i | \(-0.802871\pi\) | ||||
−0.814286 | + | 0.580464i | \(0.802871\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32290e12 | 0.0157795 | 0.00788977 | − | 0.999969i | \(-0.497489\pi\) | ||||
0.00788977 | + | 0.999969i | \(0.497489\pi\) | |||||||
\(32\) | 4.92835e13 | 0.247615 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.31927e14 | −1.22000 | ||||||||
\(35\) | −1.43781e12 | −0.00308358 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.19096e14 | −0.909642 | −0.454821 | − | 0.890583i | \(-0.650297\pi\) | ||||
−0.454821 | + | 0.890583i | \(0.650297\pi\) | |||||||
\(38\) | 7.68535e14 | 0.754605 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.02224e15 | 2.42604 | ||||||||
\(41\) | −1.72545e15 | −0.823105 | −0.411553 | − | 0.911386i | \(-0.635013\pi\) | ||||
−0.411553 | + | 0.911386i | \(0.635013\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.48385e15 | 0.753660 | 0.376830 | − | 0.926282i | \(-0.377014\pi\) | ||||
0.376830 | + | 0.926282i | \(0.377014\pi\) | |||||||
\(44\) | 1.32011e16 | 3.21966 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.28655e15 | −0.525462 | ||||||||
\(47\) | −1.39689e15 | −0.182067 | −0.0910336 | − | 0.995848i | \(-0.529017\pi\) | ||||
−0.0910336 | + | 0.995848i | \(0.529017\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.13988e16 | −0.999996 | ||||||||
\(50\) | −3.19574e16 | −2.31396 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.35637e16 | 0.676623 | ||||||||
\(53\) | −1.05483e16 | −0.439099 | −0.219550 | − | 0.975601i | \(-0.570459\pi\) | ||||
−0.219550 | + | 0.975601i | \(0.570459\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.76375e16 | −2.56593 | ||||||||
\(56\) | −1.28858e14 | −0.00317925 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.57550e17 | 2.78518 | ||||||||
\(59\) | 2.80846e16 | 0.422060 | 0.211030 | − | 0.977480i | \(-0.432318\pi\) | ||||
0.211030 | + | 0.977480i | \(0.432318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.60392e16 | −0.394586 | −0.197293 | − | 0.980345i | \(-0.563215\pi\) | ||||
−0.197293 | + | 0.980345i | \(0.563215\pi\) | |||||||
\(62\) | −2.87648e15 | −0.0269861 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.73437e17 | −1.20346 | ||||||||
\(65\) | −9.00446e16 | −0.539238 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.91862e17 | 1.31059 | 0.655296 | − | 0.755373i | \(-0.272544\pi\) | ||||
0.655296 | + | 0.755373i | \(0.272544\pi\) | |||||||
\(68\) | 3.51989e17 | 1.37308 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.78046e15 | 0.00527353 | ||||||||
\(71\) | −3.20038e17 | −0.828414 | −0.414207 | − | 0.910183i | \(-0.635941\pi\) | ||||
−0.414207 | + | 0.910183i | \(0.635941\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.15819e17 | −0.627873 | −0.313936 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313936 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(74\) | 8.90467e17 | 1.55567 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.26301e17 | −0.849286 | ||||||||
\(77\) | 2.80758e15 | 0.00336256 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.83029e18 | 1.71815 | 0.859077 | − | 0.511846i | \(-0.171038\pi\) | ||||
0.859077 | + | 0.511846i | \(0.171038\pi\) | |||||||
\(80\) | −1.43634e18 | −1.19647 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.13665e18 | 1.40767 | ||||||||
\(83\) | 1.64758e18 | 0.967397 | 0.483698 | − | 0.875235i | \(-0.339293\pi\) | ||||
0.483698 | + | 0.875235i | \(0.339293\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.33673e18 | −1.09428 | ||||||||
\(86\) | −3.07579e18 | −1.28891 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.85414e18 | −2.64553 | ||||||||
\(89\) | −5.75855e18 | −1.74224 | −0.871120 | − | 0.491069i | \(-0.836606\pi\) | ||||
−0.871120 | + | 0.491069i | \(0.836606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.88469e15 | 0.000706654 0 | ||||||||
\(92\) | 2.67830e18 | 0.591392 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.72979e18 | 0.311371 | ||||||||
\(95\) | 4.15779e18 | 0.676843 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.23309e18 | 0.832477 | 0.416238 | − | 0.909256i | \(-0.363348\pi\) | ||||
0.416238 | + | 0.909256i | \(0.363348\pi\) | |||||||
\(98\) | 1.41154e19 | 1.71019 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.60430e19 | 2.60430 | ||||||||
\(101\) | −8.80411e17 | −0.0801000 | −0.0400500 | − | 0.999198i | \(-0.512752\pi\) | ||||
−0.0400500 | + | 0.999198i | \(0.512752\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.96998e19 | −1.48767 | −0.743837 | − | 0.668361i | \(-0.766996\pi\) | ||||
−0.743837 | + | 0.668361i | \(0.766996\pi\) | |||||||
\(104\) | −8.06987e18 | −0.555968 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.30622e19 | 0.750946 | ||||||||
\(107\) | −2.58893e19 | −1.36136 | −0.680682 | − | 0.732579i | \(-0.738316\pi\) | ||||
−0.680682 | + | 0.732579i | \(0.738316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.42533e19 | −1.51060 | −0.755302 | − | 0.655377i | \(-0.772510\pi\) | ||||
−0.755302 | + | 0.655377i | \(0.772510\pi\) | |||||||
\(110\) | 1.08523e20 | 4.38825 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.60151e16 | 0.00156794 | ||||||||
\(113\) | −5.49844e19 | −1.72185 | −0.860923 | − | 0.508735i | \(-0.830113\pi\) | ||||
−0.860923 | + | 0.508735i | \(0.830113\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.77803e19 | −0.471313 | ||||||||
\(116\) | −1.28392e20 | −3.13464 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.47776e19 | −0.721806 | ||||||||
\(119\) | 7.48601e16 | 0.00143402 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.09969e20 | 1.79808 | ||||||||
\(122\) | 4.46279e19 | 0.674821 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.34412e18 | 0.0303721 | ||||||||
\(125\) | −4.51110e19 | −0.541549 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.76640e19 | −0.905078 | −0.452539 | − | 0.891745i | \(-0.649482\pi\) | ||||
−0.452539 | + | 0.891745i | \(0.649482\pi\) | |||||||
\(128\) | 1.88931e20 | 1.81054 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.11504e20 | 0.922204 | ||||||||
\(131\) | 1.23083e20 | 0.946497 | 0.473249 | − | 0.880929i | \(-0.343081\pi\) | ||||
0.473249 | + | 0.880929i | \(0.343081\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.33200e17 | −0.000886980 0 | ||||||||
\(134\) | −3.61418e20 | −2.24137 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.09419e20 | −1.12823 | ||||||||
\(137\) | 1.10729e20 | 0.556435 | 0.278218 | − | 0.960518i | \(-0.410256\pi\) | ||||
0.278218 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.36141e20 | −1.03402 | −0.517012 | − | 0.855978i | \(-0.672956\pi\) | ||||
−0.517012 | + | 0.855978i | \(0.672956\pi\) | |||||||
\(140\) | −1.45095e18 | −0.00593520 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.96308e20 | 1.41675 | ||||||||
\(143\) | 1.75828e20 | 0.588025 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.52349e20 | 2.49817 | ||||||||
\(146\) | 3.91084e20 | 1.07379 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.25666e20 | −1.75086 | ||||||||
\(149\) | −2.05810e20 | −0.465796 | −0.232898 | − | 0.972501i | \(-0.574821\pi\) | ||||
−0.232898 | + | 0.972501i | \(0.574821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.24449e20 | −0.447546 | −0.223773 | − | 0.974641i | \(-0.571837\pi\) | ||||
−0.223773 | + | 0.974641i | \(0.571837\pi\) | |||||||
\(152\) | 3.72624e20 | 0.697842 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.47667e18 | −0.00575065 | ||||||||
\(155\) | −1.55618e19 | −0.0242052 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.13212e20 | 0.431312 | 0.215656 | − | 0.976469i | \(-0.430811\pi\) | ||||
0.215656 | + | 0.976469i | \(0.430811\pi\) | |||||||
\(158\) | −2.26647e21 | −2.93838 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.30165e20 | −0.379832 | ||||||||
\(161\) | 5.69615e17 | 0.000617640 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00591e20 | 0.193432 | 0.0967160 | − | 0.995312i | \(-0.469166\pi\) | ||||
0.0967160 | + | 0.995312i | \(0.469166\pi\) | |||||||
\(164\) | −1.74122e21 | −1.58429 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.04022e21 | −1.65444 | ||||||||
\(167\) | 2.56060e21 | 1.96126 | 0.980632 | − | 0.195860i | \(-0.0627497\pi\) | ||||
0.980632 | + | 0.195860i | \(0.0627497\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.28126e21 | −0.876425 | ||||||||
\(170\) | 2.89361e21 | 1.87144 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.50655e21 | 1.45063 | ||||||||
\(173\) | −2.86308e21 | −1.56818 | −0.784089 | − | 0.620649i | \(-0.786869\pi\) | ||||
−0.784089 | + | 0.620649i | \(0.786869\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.53876e18 | 0.00271989 | ||||||||
\(176\) | 2.80472e21 | 1.30472 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.13090e21 | 2.97958 | ||||||||
\(179\) | −3.79065e20 | −0.150179 | −0.0750896 | − | 0.997177i | \(-0.523924\pi\) | ||||
−0.0750896 | + | 0.997177i | \(0.523924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.15578e21 | −1.12502 | −0.562510 | − | 0.826790i | \(-0.690164\pi\) | ||||
−0.562510 | + | 0.826790i | \(0.690164\pi\) | |||||||
\(182\) | −3.57216e18 | −0.00120852 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.59348e21 | −0.485935 | ||||||||
\(185\) | 4.81744e21 | 1.39536 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.56288e21 | 1.19328 | ||||||||
\(188\) | −1.40965e21 | −0.350439 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.14865e21 | −1.15754 | ||||||||
\(191\) | −2.79667e21 | −0.598170 | −0.299085 | − | 0.954226i | \(-0.596681\pi\) | ||||
−0.299085 | + | 0.954226i | \(0.596681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.34293e20 | −0.142257 | −0.0711287 | − | 0.997467i | \(-0.522660\pi\) | ||||
−0.0711287 | + | 0.997467i | \(0.522660\pi\) | |||||||
\(194\) | −7.71854e21 | −1.42370 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.15030e22 | −1.92477 | ||||||||
\(197\) | 5.32518e21 | 0.848995 | 0.424498 | − | 0.905429i | \(-0.360451\pi\) | ||||
0.424498 | + | 0.905429i | \(0.360451\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.54553e21 | −0.368701 | −0.184350 | − | 0.982861i | \(-0.559018\pi\) | ||||
−0.184350 | + | 0.982861i | \(0.559018\pi\) | |||||||
\(200\) | −1.54945e22 | −2.13990 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.09023e21 | 0.136987 | ||||||||
\(203\) | −2.73061e19 | −0.00327376 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.15593e22 | 1.26261 | ||||||||
\(206\) | 2.43945e22 | 2.54422 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.88175e21 | 0.274192 | ||||||||
\(209\) | −8.11882e21 | −0.738080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.77610e21 | 0.645771 | 0.322886 | − | 0.946438i | \(-0.395347\pi\) | ||||
0.322886 | + | 0.946438i | \(0.395347\pi\) | |||||||
\(212\) | −1.06447e22 | −0.845168 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.20591e22 | 2.32820 | ||||||||
\(215\) | −1.66401e22 | −1.15609 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.98543e17 | 3.17201e−5 0 | ||||||||
\(218\) | 4.24164e22 | 2.58343 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.84383e22 | −4.93884 | ||||||||
\(221\) | 4.68820e21 | 0.250772 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.89249e22 | −0.929259 | −0.464629 | − | 0.885505i | \(-0.653812\pi\) | ||||
−0.464629 | + | 0.885505i | \(0.653812\pi\) | |||||||
\(224\) | 1.05773e19 | 0.000497757 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.80881e22 | 2.94470 | ||||||||
\(227\) | −2.42145e22 | −1.00422 | −0.502111 | − | 0.864803i | \(-0.667443\pi\) | ||||
−0.502111 | + | 0.864803i | \(0.667443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.29966e22 | −1.25902 | −0.629510 | − | 0.776992i | \(-0.716744\pi\) | ||||
−0.629510 | + | 0.776992i | \(0.716744\pi\) | |||||||
\(230\) | 2.20176e22 | 0.806039 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.63882e22 | 2.57567 | ||||||||
\(233\) | 8.99479e21 | 0.291145 | 0.145573 | − | 0.989348i | \(-0.453498\pi\) | ||||
0.145573 | + | 0.989348i | \(0.453498\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.35817e21 | 0.279284 | ||||||||
\(236\) | 2.83412e22 | 0.812371 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.27005e19 | −0.00245245 | ||||||||
\(239\) | −1.22851e22 | −0.312319 | −0.156159 | − | 0.987732i | \(-0.549911\pi\) | ||||
−0.156159 | + | 0.987732i | \(0.549911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.48313e22 | −1.05298 | −0.526489 | − | 0.850182i | \(-0.676492\pi\) | ||||
−0.526489 | + | 0.850182i | \(0.676492\pi\) | |||||||
\(242\) | −1.36176e23 | −3.07507 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.63685e22 | −0.759491 | ||||||||
\(245\) | 7.63643e22 | 1.53396 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.34181e21 | −0.155110 | ||||||||
\(248\) | −1.39466e21 | −0.0249562 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.58617e22 | 0.926155 | ||||||||
\(251\) | −3.85123e22 | −0.614750 | −0.307375 | − | 0.951588i | \(-0.599451\pi\) | ||||
−0.307375 | + | 0.951588i | \(0.599451\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.47192e22 | 0.513955 | ||||||||
\(254\) | 1.08556e23 | 1.54786 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.43025e23 | −1.89292 | ||||||||
\(257\) | −9.07321e22 | −1.15717 | −0.578584 | − | 0.815623i | \(-0.696394\pi\) | ||||
−0.578584 | + | 0.815623i | \(0.696394\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.54333e20 | −0.00182857 | ||||||||
\(260\) | −9.08674e22 | −1.03791 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.52415e23 | −1.61870 | ||||||||
\(263\) | 2.56086e21 | 0.0262305 | 0.0131152 | − | 0.999914i | \(-0.495825\pi\) | ||||
0.0131152 | + | 0.999914i | \(0.495825\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.06664e22 | 0.673561 | ||||||||
\(266\) | 1.64944e20 | 0.00151691 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.94529e23 | 2.52260 | ||||||||
\(269\) | −3.82577e22 | −0.316281 | −0.158140 | − | 0.987417i | \(-0.550550\pi\) | ||||
−0.158140 | + | 0.987417i | \(0.550550\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.64857e22 | 0.281135 | 0.140567 | − | 0.990071i | \(-0.455107\pi\) | ||||
0.140567 | + | 0.990071i | \(0.455107\pi\) | |||||||
\(272\) | 7.47838e22 | 0.556420 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.37117e23 | −0.951615 | ||||||||
\(275\) | 3.37599e23 | 2.26329 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.78571e23 | 1.11752 | 0.558758 | − | 0.829331i | \(-0.311278\pi\) | ||||
0.558758 | + | 0.829331i | \(0.311278\pi\) | |||||||
\(278\) | 2.92417e23 | 1.76839 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.63257e20 | 0.00487684 | ||||||||
\(281\) | 2.28261e23 | 1.24659 | 0.623293 | − | 0.781989i | \(-0.285795\pi\) | ||||
0.623293 | + | 0.781989i | \(0.285795\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.87538e23 | 0.957453 | 0.478727 | − | 0.877964i | \(-0.341098\pi\) | ||||
0.478727 | + | 0.877964i | \(0.341098\pi\) | |||||||
\(284\) | −3.22962e23 | −1.59451 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.17731e23 | −1.00564 | ||||||||
\(287\) | −3.70317e20 | −0.00165461 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.17410e23 | −0.491106 | ||||||||
\(290\) | −1.05548e24 | −4.27236 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.18705e23 | −1.20852 | ||||||||
\(293\) | −2.82617e23 | −1.03742 | −0.518711 | − | 0.854950i | \(-0.673588\pi\) | ||||
−0.518711 | + | 0.854950i | \(0.673588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.88147e23 | −0.647424 | ||||||||
\(296\) | 4.31743e23 | 1.43865 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.54857e23 | 0.796604 | ||||||||
\(299\) | 3.56728e22 | 0.108009 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.33087e20 | 0.00151501 | ||||||||
\(302\) | 2.77939e23 | 0.765392 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.33064e23 | −0.344162 | ||||||||
\(305\) | 2.41438e23 | 0.605280 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.47019e23 | −0.581991 | −0.290996 | − | 0.956724i | \(-0.593986\pi\) | ||||
−0.290996 | + | 0.956724i | \(0.593986\pi\) | |||||||
\(308\) | 2.83324e21 | 0.00647219 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.92704e22 | 0.0413957 | ||||||||
\(311\) | −3.27126e23 | −0.681539 | −0.340770 | − | 0.940147i | \(-0.610688\pi\) | ||||
−0.340770 | + | 0.940147i | \(0.610688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.73412e23 | 0.732011 | 0.366005 | − | 0.930613i | \(-0.380725\pi\) | ||||
0.366005 | + | 0.930613i | \(0.380725\pi\) | |||||||
\(314\) | −3.87855e23 | −0.737628 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.84701e24 | 3.30706 | ||||||||
\(317\) | 5.83518e22 | 0.101389 | 0.0506945 | − | 0.998714i | \(-0.483857\pi\) | ||||
0.0506945 | + | 0.998714i | \(0.483857\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.66436e24 | −2.72419 | ||||||||
\(320\) | 1.16191e24 | 1.84606 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.05363e20 | −0.00105629 | ||||||||
\(323\) | −2.16477e23 | −0.314766 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.46871e23 | 0.475638 | ||||||||
\(326\) | −2.48394e23 | −0.330807 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.03595e24 | 1.30178 | ||||||||
\(329\) | −2.99801e20 | −0.000365993 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.84253e23 | 0.442845 | 0.221422 | − | 0.975178i | \(-0.428930\pi\) | ||||
0.221422 | + | 0.975178i | \(0.428930\pi\) | |||||||
\(332\) | 1.66263e24 | 1.86202 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.17084e24 | −3.35415 | ||||||||
\(335\) | −1.95527e24 | −2.01040 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.30128e24 | 1.26440 | 0.632202 | − | 0.774803i | \(-0.282151\pi\) | ||||
0.632202 | + | 0.774803i | \(0.282151\pi\) | |||||||
\(338\) | 1.58661e24 | 1.49886 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.35808e24 | −2.10624 | ||||||||
\(341\) | 3.03872e22 | 0.0263952 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.89287e21 | −0.00402040 | ||||||||
\(344\) | −1.49130e24 | −1.19195 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.54539e24 | 2.68189 | ||||||||
\(347\) | 8.56826e22 | 0.0630613 | 0.0315306 | − | 0.999503i | \(-0.489962\pi\) | ||||
0.0315306 | + | 0.999503i | \(0.489962\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.11294e24 | −0.775586 | −0.387793 | − | 0.921746i | \(-0.626763\pi\) | ||||
−0.387793 | + | 0.921746i | \(0.626763\pi\) | |||||||
\(350\) | −6.85873e21 | −0.00465155 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.44706e23 | 0.414197 | ||||||||
\(353\) | 2.23748e24 | 1.39926 | 0.699631 | − | 0.714505i | \(-0.253348\pi\) | ||||
0.699631 | + | 0.714505i | \(0.253348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.14403e24 | 1.27076 | ||||||||
\(356\) | −5.81117e24 | −3.35343 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.69402e23 | 0.256836 | ||||||||
\(359\) | −2.02884e24 | −1.08106 | −0.540531 | − | 0.841324i | \(-0.681777\pi\) | ||||
−0.540531 | + | 0.841324i | \(0.681777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.59324e24 | −0.805309 | ||||||||
\(362\) | 3.90785e24 | 1.92401 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.91105e21 | 0.00136015 | ||||||||
\(365\) | 2.11577e24 | 0.963133 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.03395e24 | −0.879049 | −0.439525 | − | 0.898230i | \(-0.644853\pi\) | ||||
−0.439525 | + | 0.898230i | \(0.644853\pi\) | |||||||
\(368\) | 5.69034e23 | 0.239654 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.96551e24 | −2.38633 | ||||||||
\(371\) | −2.26389e21 | −0.000882680 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.78333e23 | −0.288358 | −0.144179 | − | 0.989552i | \(-0.546054\pi\) | ||||
−0.144179 | + | 0.989552i | \(0.546054\pi\) | |||||||
\(374\) | −5.65029e24 | −2.04075 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.38687e23 | 0.287949 | ||||||||
\(377\) | −1.71008e24 | −0.572497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.15677e24 | 1.00501 | 0.502505 | − | 0.864575i | \(-0.332412\pi\) | ||||
0.502505 | + | 0.864575i | \(0.332412\pi\) | |||||||
\(380\) | 4.19578e24 | 1.30277 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.46316e24 | 1.02299 | ||||||||
\(383\) | 3.09305e24 | 0.891249 | 0.445625 | − | 0.895220i | \(-0.352982\pi\) | ||||
0.445625 | + | 0.895220i | \(0.352982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.88088e22 | −0.00515804 | ||||||||
\(386\) | 9.09286e23 | 0.243288 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.29005e24 | 1.60233 | ||||||||
\(389\) | 4.58505e24 | 1.13978 | 0.569892 | − | 0.821719i | \(-0.306985\pi\) | ||||
0.569892 | + | 0.821719i | \(0.306985\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.25738e23 | 0.219184 | ||||||||
\(392\) | 6.84383e24 | 1.58155 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.59426e24 | −1.45195 | ||||||||
\(395\) | −1.22617e25 | −2.63558 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.62169e24 | 1.15175 | 0.575873 | − | 0.817539i | \(-0.304662\pi\) | ||||
0.575873 | + | 0.817539i | \(0.304662\pi\) | |||||||
\(398\) | 3.15217e24 | 0.630551 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.53311e24 | 1.05536 | ||||||||
\(401\) | 8.34521e24 | 1.55441 | 0.777206 | − | 0.629247i | \(-0.216636\pi\) | ||||
0.777206 | + | 0.629247i | \(0.216636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.12218e22 | 0.00554703 | ||||||||
\(404\) | −8.88456e23 | −0.154175 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.38136e22 | 0.00559878 | ||||||||
\(407\) | −9.40691e24 | −1.52160 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.09120e25 | −1.68474 | −0.842370 | − | 0.538900i | \(-0.818840\pi\) | ||||
−0.842370 | + | 0.538900i | \(0.818840\pi\) | |||||||
\(410\) | −1.43141e25 | −2.15932 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.98798e25 | −2.86344 | ||||||||
\(413\) | 6.02754e21 | 0.000848427 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.10376e25 | −1.48395 | ||||||||
\(416\) | 6.62414e23 | 0.0870448 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.00537e25 | 1.26226 | ||||||||
\(419\) | 1.35175e25 | 1.65906 | 0.829529 | − | 0.558463i | \(-0.188609\pi\) | ||||
0.829529 | + | 0.558463i | \(0.188609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.91185e24 | 1.16272 | 0.581360 | − | 0.813647i | \(-0.302521\pi\) | ||||
0.581360 | + | 0.813647i | \(0.302521\pi\) | |||||||
\(422\) | −9.62927e24 | −1.10440 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.33318e24 | 0.694458 | ||||||||
\(425\) | 9.00159e24 | 0.965215 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.73477e21 | −0.000793200 0 | ||||||||
\(428\) | −2.61259e25 | −2.62032 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.06057e25 | 1.97714 | ||||||||
\(431\) | −1.91272e24 | −0.179522 | −0.0897610 | − | 0.995963i | \(-0.528610\pi\) | ||||
−0.0897610 | + | 0.995963i | \(0.528610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.77174e24 | 0.518408 | 0.259204 | − | 0.965823i | \(-0.416540\pi\) | ||||
0.259204 | + | 0.965823i | \(0.416540\pi\) | |||||||
\(434\) | −6.17353e20 | −5.42477e−5 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.45663e25 | −2.90758 | ||||||||
\(437\) | −1.64718e24 | −0.135571 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.11473e21 | 0.000639530 0 | 0.000319765 | − | 1.00000i | \(-0.499898\pi\) | ||||
0.000319765 | 1.00000i | \(0.499898\pi\) | ||||||||
\(440\) | 5.26173e25 | 4.05815 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.80548e24 | −0.428871 | ||||||||
\(443\) | −2.51728e24 | −0.182010 | −0.0910051 | − | 0.995850i | \(-0.529008\pi\) | ||||
−0.0910051 | + | 0.995850i | \(0.529008\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.85783e25 | 2.67253 | ||||||||
\(446\) | 2.34350e25 | 1.58922 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.72232e22 | −0.00241920 | ||||||||
\(449\) | 1.07451e25 | 0.683706 | 0.341853 | − | 0.939753i | \(-0.388945\pi\) | ||||
0.341853 | + | 0.939753i | \(0.388945\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.25716e25 | −1.37685 | ||||||||
\(452\) | −5.54869e25 | −3.31417 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.99852e25 | 1.71742 | ||||||||
\(455\) | −1.93254e22 | −0.00108398 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.09140e24 | 0.435331 | 0.217665 | − | 0.976023i | \(-0.430156\pi\) | ||||
0.217665 | + | 0.976023i | \(0.430156\pi\) | |||||||
\(458\) | 4.08603e25 | 2.15317 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.79428e25 | −0.907173 | ||||||||
\(461\) | −1.48075e25 | −0.733368 | −0.366684 | − | 0.930346i | \(-0.619507\pi\) | ||||
−0.366684 | + | 0.930346i | \(0.619507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.65292e25 | −1.26097 | −0.630485 | − | 0.776202i | \(-0.717144\pi\) | ||||
−0.630485 | + | 0.776202i | \(0.717144\pi\) | |||||||
\(464\) | −2.72783e25 | −1.27027 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.11384e25 | −0.497916 | ||||||||
\(467\) | −3.57468e25 | −1.56576 | −0.782882 | − | 0.622170i | \(-0.786251\pi\) | ||||
−0.782882 | + | 0.622170i | \(0.786251\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.26397e22 | 0.00263456 | ||||||||
\(470\) | −1.15884e25 | −0.477631 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.68619e25 | −0.667510 | ||||||||
\(473\) | 3.24927e25 | 1.26068 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.60167e25 | −0.597013 | ||||||||
\(476\) | 7.55442e22 | 0.00276016 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.52128e25 | 0.534127 | ||||||||
\(479\) | 2.88220e24 | 0.0992056 | 0.0496028 | − | 0.998769i | \(-0.484204\pi\) | ||||
0.0496028 | + | 0.998769i | \(0.484204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.66528e24 | −0.319769 | ||||||||
\(482\) | 5.55152e25 | 1.80080 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.10974e26 | 3.46090 | ||||||||
\(485\) | −4.17574e25 | −1.27699 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.03233e25 | 1.77403 | 0.887014 | − | 0.461743i | \(-0.152776\pi\) | ||||
0.887014 | + | 0.461743i | \(0.152776\pi\) | |||||||
\(488\) | 2.16378e25 | 0.624059 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.45632e25 | −2.62337 | ||||||||
\(491\) | −4.20599e25 | −1.14444 | −0.572222 | − | 0.820099i | \(-0.693918\pi\) | ||||
−0.572222 | + | 0.820099i | \(0.693918\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.43779e25 | −1.16177 | ||||||||
\(494\) | 1.03298e25 | 0.265269 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.98034e23 | 0.0123079 | ||||||||
\(497\) | −6.86869e22 | −0.00166528 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.96358e25 | −0.924979 | −0.462490 | − | 0.886625i | \(-0.653044\pi\) | ||||
−0.462490 | + | 0.886625i | \(0.653044\pi\) | |||||||
\(500\) | −4.55232e25 | −1.04236 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.76904e25 | 1.05134 | ||||||||
\(503\) | −5.09940e25 | −1.10312 | −0.551561 | − | 0.834135i | \(-0.685968\pi\) | ||||
−0.551561 | + | 0.834135i | \(0.685968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.89814e24 | 0.122870 | ||||||||
\(506\) | −4.29933e25 | −0.878965 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.84651e25 | −1.74207 | ||||||||
\(509\) | 4.45056e25 | 0.860193 | 0.430096 | − | 0.902783i | \(-0.358480\pi\) | ||||
0.430096 | + | 0.902783i | \(0.358480\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.77814e22 | −0.00126215 | ||||||||
\(512\) | 7.80561e25 | 1.42673 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.12355e26 | 1.97899 | ||||||||
\(515\) | 1.31975e26 | 2.28204 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.82735e25 | −0.304552 | ||||||||
\(518\) | 1.91113e23 | 0.00312721 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.40625e25 | 0.852833 | ||||||||
\(521\) | 1.65819e24 | 0.0256847 | 0.0128424 | − | 0.999918i | \(-0.495912\pi\) | ||||
0.0128424 | + | 0.999918i | \(0.495912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.69898e25 | −0.701839 | −0.350920 | − | 0.936406i | \(-0.614131\pi\) | ||||
−0.350920 | + | 0.936406i | \(0.614131\pi\) | |||||||
\(524\) | 1.24207e26 | 1.82180 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.17115e24 | −0.0448593 | ||||||||
\(527\) | 8.10231e23 | 0.0112566 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.75715e25 | −0.905596 | ||||||||
\(530\) | −8.75073e25 | −1.15192 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.34417e23 | −0.00170724 | ||||||||
\(533\) | −2.31916e25 | −0.289349 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.73440e26 | 2.08828 | ||||||||
\(536\) | −1.75233e26 | −2.07277 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.73752e25 | 0.540903 | ||||||||
\(539\) | −1.49115e26 | −1.67274 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.20242e25 | 0.671718 | 0.335859 | − | 0.941912i | \(-0.390973\pi\) | ||||
0.335859 | + | 0.941912i | \(0.390973\pi\) | |||||||
\(542\) | −4.51808e25 | −0.480796 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.71902e25 | 0.176641 | ||||||||
\(545\) | 2.29473e26 | 2.31721 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.76624e25 | 0.757410 | 0.378705 | − | 0.925517i | \(-0.376370\pi\) | ||||
0.378705 | + | 0.925517i | \(0.376370\pi\) | |||||||
\(548\) | 1.11740e26 | 1.07101 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.18054e26 | −3.87068 | ||||||||
\(551\) | 7.89624e25 | 0.718588 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.92818e23 | 0.00345384 | ||||||||
\(554\) | −2.21128e26 | −1.91117 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.38299e26 | −1.99027 | ||||||||
\(557\) | −3.67420e25 | −0.301675 | −0.150837 | − | 0.988559i | \(-0.548197\pi\) | ||||
−0.150837 | + | 0.988559i | \(0.548197\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.33852e25 | 0.264936 | ||||||||
\(560\) | −3.08269e23 | −0.00240516 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.82659e26 | −2.13191 | ||||||||
\(563\) | −1.24531e26 | −0.923526 | −0.461763 | − | 0.887003i | \(-0.652783\pi\) | ||||
−0.461763 | + | 0.887003i | \(0.652783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.68357e26 | 2.64125 | ||||||||
\(566\) | −2.32231e26 | −1.63743 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.92150e26 | 1.31018 | ||||||||
\(569\) | 5.63513e25 | 0.377866 | 0.188933 | − | 0.981990i | \(-0.439497\pi\) | ||||
0.188933 | + | 0.981990i | \(0.439497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.23813e26 | −0.803012 | −0.401506 | − | 0.915856i | \(-0.631513\pi\) | ||||
−0.401506 | + | 0.915856i | \(0.631513\pi\) | |||||||
\(572\) | 1.77435e26 | 1.13182 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.58570e23 | 0.00282971 | ||||||||
\(575\) | 6.84936e25 | 0.415724 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.01722e26 | −1.77189 | −0.885945 | − | 0.463790i | \(-0.846489\pi\) | ||||
−0.885945 | + | 0.463790i | \(0.846489\pi\) | |||||||
\(578\) | 1.45390e26 | 0.839888 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.60137e26 | 4.80841 | ||||||||
\(581\) | 3.53605e23 | 0.00194467 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.37989e26 | −0.734501 | ||||||||
\(584\) | 1.89617e26 | 0.993014 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.49968e26 | 1.77420 | ||||||||
\(587\) | 6.00743e25 | 0.299659 | 0.149829 | − | 0.988712i | \(-0.452128\pi\) | ||||
0.149829 | + | 0.988712i | \(0.452128\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.44166e24 | −0.00696254 | ||||||||
\(590\) | 2.32986e26 | 1.10722 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.54176e26 | −0.709511 | ||||||||
\(593\) | 9.94196e25 | 0.450248 | 0.225124 | − | 0.974330i | \(-0.427721\pi\) | ||||
0.225124 | + | 0.974330i | \(0.427721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.01511e23 | −0.00219973 | ||||||||
\(596\) | −2.07690e26 | −0.896554 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.41742e25 | −0.184717 | ||||||||
\(599\) | 1.95677e26 | 0.805350 | 0.402675 | − | 0.915343i | \(-0.368080\pi\) | ||||
0.402675 | + | 0.915343i | \(0.368080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.73445e26 | −1.88782 | −0.943912 | − | 0.330197i | \(-0.892885\pi\) | ||||
−0.943912 | + | 0.330197i | \(0.892885\pi\) | |||||||
\(602\) | −6.60129e23 | −0.00259097 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.26500e26 | −0.861426 | ||||||||
\(605\) | −7.36715e26 | −2.75818 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.22707e26 | −0.445222 | −0.222611 | − | 0.974907i | \(-0.571458\pi\) | ||||
−0.222611 | + | 0.974907i | \(0.571458\pi\) | |||||||
\(608\) | −3.05868e25 | −0.109257 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.98976e26 | −1.03515 | ||||||||
\(611\) | −1.87754e25 | −0.0640026 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.20354e26 | 1.05866 | 0.529329 | − | 0.848417i | \(-0.322444\pi\) | ||||
0.529329 | + | 0.848417i | \(0.322444\pi\) | |||||||
\(614\) | 3.05888e26 | 0.995320 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.68566e24 | −0.00531807 | ||||||||
\(617\) | −9.79781e25 | −0.304383 | −0.152191 | − | 0.988351i | \(-0.548633\pi\) | ||||
−0.152191 | + | 0.988351i | \(0.548633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.22713e25 | −0.0369682 | −0.0184841 | − | 0.999829i | \(-0.505884\pi\) | ||||
−0.0184841 | + | 0.999829i | \(0.505884\pi\) | |||||||
\(620\) | −1.57040e25 | −0.0465896 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.05085e26 | 1.16557 | ||||||||
\(623\) | −1.23591e24 | −0.00350226 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.90020e26 | −0.522324 | ||||||||
\(626\) | −4.62402e26 | −1.25188 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.16074e26 | 0.830179 | ||||||||
\(629\) | −2.50822e26 | −0.648909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.30803e26 | 1.08143 | 0.540716 | − | 0.841205i | \(-0.318153\pi\) | ||||
0.540716 | + | 0.841205i | \(0.318153\pi\) | |||||||
\(632\) | −1.09890e27 | −2.71735 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.22579e25 | −0.173395 | ||||||||
\(635\) | 5.87288e26 | 1.38836 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.53211e26 | −0.351532 | ||||||||
\(638\) | 2.06101e27 | 4.65890 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.26571e27 | −2.77730 | ||||||||
\(641\) | −5.54923e26 | −1.19972 | −0.599862 | − | 0.800104i | \(-0.704778\pi\) | ||||
−0.599862 | + | 0.800104i | \(0.704778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.72911e26 | 1.41239 | 0.706193 | − | 0.708019i | \(-0.250411\pi\) | ||||
0.706193 | + | 0.708019i | \(0.250411\pi\) | |||||||
\(644\) | 5.74820e23 | 0.00118882 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.68066e26 | 0.538311 | ||||||||
\(647\) | 3.57860e26 | 0.708146 | 0.354073 | − | 0.935218i | \(-0.384796\pi\) | ||||
0.354073 | + | 0.935218i | \(0.384796\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.67391e26 | 0.705999 | ||||||||
\(650\) | −4.29536e26 | −0.813435 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.02423e26 | 0.372313 | ||||||||
\(653\) | −5.10990e26 | −0.926269 | −0.463135 | − | 0.886288i | \(-0.653275\pi\) | ||||
−0.463135 | + | 0.886288i | \(0.653275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.24568e26 | −1.45189 | ||||||||
\(656\) | −3.69940e26 | −0.642014 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.71249e23 | 0.000625920 0 | ||||||||
\(659\) | 6.67000e26 | 1.10844 | 0.554222 | − | 0.832369i | \(-0.313016\pi\) | ||||
0.554222 | + | 0.832369i | \(0.313016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.27178e26 | 0.366819 | 0.183410 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183410 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(662\) | −4.75827e26 | −0.757352 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.89202e26 | −1.52999 | ||||||||
\(665\) | 8.92348e23 | 0.00136059 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.37674e26 | −0.500382 | ||||||||
\(668\) | 2.58400e27 | 3.77500 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.42125e27 | 3.43818 | ||||||||
\(671\) | −4.71450e26 | −0.660043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.72017e26 | 0.370214 | 0.185107 | − | 0.982718i | \(-0.440737\pi\) | ||||
0.185107 | + | 0.982718i | \(0.440737\pi\) | |||||||
\(674\) | −1.61139e27 | −2.16238 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.29297e27 | −1.68692 | ||||||||
\(677\) | −4.27674e26 | −0.550200 | −0.275100 | − | 0.961416i | \(-0.588711\pi\) | ||||
−0.275100 | + | 0.961416i | \(0.588711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.33775e24 | 0.00167345 | ||||||||
\(680\) | 1.40296e27 | 1.73066 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.76290e25 | −0.0451409 | ||||||||
\(683\) | 1.11866e26 | 0.132344 | 0.0661719 | − | 0.997808i | \(-0.478921\pi\) | ||||
0.0661719 | + | 0.997808i | \(0.478921\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.41805e26 | −0.853551 | ||||||||
\(686\) | 6.05892e24 | 0.00687569 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.32543e26 | 0.587847 | ||||||||
\(689\) | −1.41779e26 | −0.154358 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.82536e27 | 1.93333 | 0.966667 | − | 0.256037i | \(-0.0824171\pi\) | ||||
0.966667 | + | 0.256037i | \(0.0824171\pi\) | |||||||
\(692\) | −2.88924e27 | −3.01839 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.06102e26 | −0.107847 | ||||||||
\(695\) | 1.58198e27 | 1.58615 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.01839e26 | −0.587177 | ||||||||
\(698\) | 1.37817e27 | 1.32641 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.58937e24 | 0.00523518 | ||||||||
\(701\) | 2.03227e27 | 1.87785 | 0.938924 | − | 0.344125i | \(-0.111824\pi\) | ||||
0.938924 | + | 0.344125i | \(0.111824\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.46292e26 | 0.401369 | ||||||||
\(704\) | −2.26883e27 | −2.01308 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.77070e27 | −2.39301 | ||||||||
\(707\) | −1.88955e23 | −0.000161017 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.86039e27 | −1.54335 | −0.771675 | − | 0.636017i | \(-0.780581\pi\) | ||||
−0.771675 | + | 0.636017i | \(0.780581\pi\) | |||||||
\(710\) | −2.65499e27 | −2.17324 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.45742e27 | 2.75544 | ||||||||
\(713\) | 6.16510e24 | 0.00484830 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.17793e27 | −0.902009 | ||||||||
\(716\) | −3.82529e26 | −0.289062 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.51234e27 | 1.84883 | ||||||||
\(719\) | −1.92780e27 | −1.40003 | −0.700014 | − | 0.714129i | \(-0.746823\pi\) | ||||
−0.700014 | + | 0.714129i | \(0.746823\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.22798e24 | −0.00299053 | ||||||||
\(722\) | 1.97293e27 | 1.37724 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.18462e27 | −2.16541 | ||||||||
\(725\) | −3.28343e27 | −2.20352 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.11559e27 | −0.729339 | −0.364670 | − | 0.931137i | \(-0.618818\pi\) | ||||
−0.364670 | + | 0.931137i | \(0.618818\pi\) | |||||||
\(728\) | −1.73196e24 | −0.00111761 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.61999e27 | −1.64715 | ||||||||
\(731\) | 8.66372e26 | 0.537637 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.04762e27 | 1.23812 | 0.619059 | − | 0.785344i | \(-0.287514\pi\) | ||||
0.619059 | + | 0.785344i | \(0.287514\pi\) | |||||||
\(734\) | 2.51868e27 | 1.50335 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.30801e26 | 0.0760802 | ||||||||
\(737\) | 3.81802e27 | 2.19229 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.50373e27 | 0.841486 | 0.420743 | − | 0.907180i | \(-0.361769\pi\) | ||||
0.420743 | + | 0.907180i | \(0.361769\pi\) | |||||||
\(740\) | 4.86146e27 | 2.68575 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.80341e24 | 0.00150956 | ||||||||
\(743\) | −1.88836e27 | −1.00390 | −0.501950 | − | 0.864897i | \(-0.667384\pi\) | ||||
−0.501950 | + | 0.864897i | \(0.667384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.37878e27 | 0.714514 | ||||||||
\(746\) | 9.63821e26 | 0.493149 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.60457e27 | 2.29681 | ||||||||
\(749\) | −5.55638e24 | −0.00273662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.19244e26 | 0.393400 | 0.196700 | − | 0.980464i | \(-0.436978\pi\) | ||||
0.196700 | + | 0.980464i | \(0.436978\pi\) | |||||||
\(752\) | −2.99495e26 | −0.142011 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.11762e27 | 0.979082 | ||||||||
\(755\) | 1.50365e27 | 0.686518 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.94096e27 | 0.864184 | 0.432092 | − | 0.901829i | \(-0.357776\pi\) | ||||
0.432092 | + | 0.901829i | \(0.357776\pi\) | |||||||
\(758\) | −3.90907e27 | −1.71876 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.49632e27 | −1.07046 | ||||||||
\(761\) | −2.40135e27 | −1.01695 | −0.508477 | − | 0.861076i | \(-0.669791\pi\) | ||||
−0.508477 | + | 0.861076i | \(0.669791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.35147e24 | −0.00303663 | ||||||||
\(764\) | −2.82223e27 | −1.15134 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.83018e27 | −1.52421 | ||||||||
\(767\) | 3.77482e26 | 0.148368 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.49979e27 | −1.34197 | −0.670984 | − | 0.741472i | \(-0.734128\pi\) | ||||
−0.670984 | + | 0.741472i | \(0.734128\pi\) | |||||||
\(770\) | 2.32913e25 | 0.00882128 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.41002e26 | −0.273814 | ||||||||
\(773\) | 3.84483e27 | 1.40337 | 0.701685 | − | 0.712487i | \(-0.252431\pi\) | ||||
0.701685 | + | 0.712487i | \(0.252431\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.99475e25 | 0.0213503 | ||||||||
\(776\) | −3.74233e27 | −1.31661 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.67774e27 | −1.94926 | ||||||||
\(779\) | 1.07086e27 | 0.363186 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.18661e27 | −1.38573 | ||||||||
\(782\) | −1.14636e27 | −0.374848 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.44394e27 | −0.779987 | ||||||||
\(785\) | −2.09830e27 | −0.661615 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.22212e27 | 1.29948 | 0.649741 | − | 0.760155i | \(-0.274877\pi\) | ||||
0.649741 | + | 0.760155i | \(0.274877\pi\) | |||||||
\(788\) | 5.37384e27 | 1.63413 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.51838e28 | 4.50737 | ||||||||
\(791\) | −1.18008e25 | −0.00346127 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.84399e26 | −0.138710 | ||||||||
\(794\) | −6.96142e27 | −1.96971 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.56879e27 | −0.709667 | ||||||||
\(797\) | 2.10706e27 | 0.575205 | 0.287602 | − | 0.957750i | \(-0.407142\pi\) | ||||
0.287602 | + | 0.957750i | \(0.407142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.87237e26 | −0.129881 | ||||||||
\(800\) | 1.27187e27 | 0.335033 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.03340e28 | −2.65835 | ||||||||
\(803\) | −4.13142e27 | −1.05027 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.81602e24 | −0.000947436 0 | ||||||||
\(806\) | −3.86625e25 | −0.00948652 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.28596e26 | 0.126682 | ||||||||
\(809\) | −2.31386e27 | −0.548056 | −0.274028 | − | 0.961722i | \(-0.588356\pi\) | ||||
−0.274028 | + | 0.961722i | \(0.588356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.32427e27 | 0.537760 | 0.268880 | − | 0.963174i | \(-0.413347\pi\) | ||||
0.268880 | + | 0.963174i | \(0.413347\pi\) | |||||||
\(812\) | −2.75556e25 | −0.00630127 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.16487e28 | 2.60224 | ||||||||
\(815\) | −1.34382e27 | −0.296717 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.54155e27 | −0.332544 | ||||||||
\(818\) | 1.35125e28 | 2.88124 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.16649e28 | 2.43025 | ||||||||
\(821\) | −6.08231e27 | −1.25259 | −0.626295 | − | 0.779587i | \(-0.715429\pi\) | ||||
−0.626295 | + | 0.779587i | \(0.715429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.84390e27 | −0.773523 | −0.386762 | − | 0.922180i | \(-0.626406\pi\) | ||||
−0.386762 | + | 0.922180i | \(0.626406\pi\) | |||||||
\(824\) | 1.18277e28 | 2.35283 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.46400e24 | −0.00145098 | ||||||||
\(827\) | −5.47093e27 | −1.05138 | −0.525689 | − | 0.850677i | \(-0.676193\pi\) | ||||
−0.525689 | + | 0.850677i | \(0.676193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.53655e26 | 0.160330 | 0.0801649 | − | 0.996782i | \(-0.474455\pi\) | ||||
0.0801649 | + | 0.996782i | \(0.474455\pi\) | |||||||
\(830\) | 1.36681e28 | 2.53785 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.33115e27 | −0.423056 | ||||||||
\(833\) | −3.97594e27 | −0.713365 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.71543e28 | −3.00850 | ||||||||
\(836\) | −8.19301e27 | −1.42064 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.67389e28 | −2.83732 | ||||||||
\(839\) | 8.76504e27 | 1.46898 | 0.734489 | − | 0.678621i | \(-0.237422\pi\) | ||||
0.734489 | + | 0.678621i | \(0.237422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00841e28 | 1.65224 | ||||||||
\(842\) | −1.22740e28 | −1.98848 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.84716e27 | 1.24297 | ||||||||
\(845\) | 8.58357e27 | 1.34440 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.36016e25 | 0.00361451 | ||||||||
\(848\) | −2.26158e27 | −0.342493 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.11468e28 | −1.65071 | ||||||||
\(851\) | −1.90852e27 | −0.279489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.55754e27 | 0.652702 | 0.326351 | − | 0.945249i | \(-0.394181\pi\) | ||||
0.326351 | + | 0.945249i | \(0.394181\pi\) | |||||||
\(854\) | 9.57809e24 | 0.00135653 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.55438e28 | 2.15307 | ||||||||
\(857\) | −8.72531e27 | −1.19526 | −0.597631 | − | 0.801771i | \(-0.703891\pi\) | ||||
−0.597631 | + | 0.801771i | \(0.703891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.82608e27 | −0.914610 | −0.457305 | − | 0.889310i | \(-0.651185\pi\) | ||||
−0.457305 | + | 0.889310i | \(0.651185\pi\) | |||||||
\(860\) | −1.67921e28 | −2.22521 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.36855e27 | 0.307018 | ||||||||
\(863\) | −1.70088e27 | −0.218058 | −0.109029 | − | 0.994039i | \(-0.534774\pi\) | ||||
−0.109029 | + | 0.994039i | \(0.534774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.91806e28 | 2.40552 | ||||||||
\(866\) | −7.14723e27 | −0.886580 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.03098e23 | 6.10542e−5 0 | ||||||||
\(869\) | 2.39431e28 | 2.87404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.92289e27 | 0.460716 | ||||||||
\(872\) | 2.05656e28 | 2.38910 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.03973e27 | 0.231854 | ||||||||
\(875\) | −9.68176e24 | −0.00108862 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.69466e27 | −1.06669 | −0.533343 | − | 0.845899i | \(-0.679064\pi\) | ||||
−0.533343 | + | 0.845899i | \(0.679064\pi\) | |||||||
\(878\) | −1.00486e25 | −0.00109372 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.87897e28 | −2.00140 | ||||||||
\(881\) | 2.20901e27 | 0.232769 | 0.116385 | − | 0.993204i | \(-0.462869\pi\) | ||||
0.116385 | + | 0.993204i | \(0.462869\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.45945e27 | −0.563018 | −0.281509 | − | 0.959559i | \(-0.590835\pi\) | ||||
−0.281509 | + | 0.959559i | \(0.590835\pi\) | |||||||
\(884\) | 4.73104e27 | 0.482681 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.11718e27 | 0.311273 | ||||||||
\(887\) | −1.69664e28 | −1.67616 | −0.838081 | − | 0.545546i | \(-0.816322\pi\) | ||||
−0.838081 | + | 0.545546i | \(0.816322\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.88145e25 | −0.00181939 | ||||||||
\(890\) | −4.77721e28 | −4.57056 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.90978e28 | −1.78862 | ||||||||
\(893\) | 8.66950e26 | 0.0803351 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.53947e27 | 0.230369 | ||||||||
\(896\) | 4.05485e25 | 0.00363956 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.33058e28 | −1.16927 | ||||||||
\(899\) | −2.95541e26 | −0.0256981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.67927e27 | −0.313239 | ||||||||
\(902\) | 2.79508e28 | 2.35468 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.30125e28 | 2.72319 | ||||||||
\(905\) | 2.11415e28 | 1.72574 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.06963e28 | 0.854996 | 0.427498 | − | 0.904016i | \(-0.359395\pi\) | ||||
0.427498 | + | 0.904016i | \(0.359395\pi\) | |||||||
\(908\) | −2.44357e28 | −1.93290 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.39310e25 | 0.00185382 | ||||||||
\(911\) | 2.36272e28 | 1.81129 | 0.905645 | − | 0.424036i | \(-0.139387\pi\) | ||||
0.905645 | + | 0.424036i | \(0.139387\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.15530e28 | 1.61821 | ||||||||
\(914\) | −1.00197e28 | −0.744502 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.32982e28 | −2.42333 | ||||||||
\(917\) | 2.64161e25 | 0.00190265 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.79736e27 | 0.338458 | 0.169229 | − | 0.985577i | \(-0.445872\pi\) | ||||
0.169229 | + | 0.985577i | \(0.445872\pi\) | |||||||
\(920\) | 1.06752e28 | 0.745406 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.83363e28 | 1.25420 | ||||||||
\(923\) | −4.30160e27 | −0.291215 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.85578e28 | −1.23078 | ||||||||
\(926\) | 3.28515e28 | 2.15651 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.27031e27 | −0.403258 | ||||||||
\(929\) | 4.77499e27 | 0.303965 | 0.151982 | − | 0.988383i | \(-0.451434\pi\) | ||||
0.151982 | + | 0.988383i | \(0.451434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.07446e27 | 0.441237 | ||||||||
\(932\) | 9.07699e27 | 0.560390 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.42658e28 | 2.67777 | ||||||||
\(935\) | −3.05681e28 | −1.83045 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.08658e27 | −0.181114 | −0.0905568 | − | 0.995891i | \(-0.528865\pi\) | ||||
−0.0905568 | + | 0.995891i | \(0.528865\pi\) | |||||||
\(938\) | −7.75677e25 | −0.00450562 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.44368e27 | 0.537560 | ||||||||
\(941\) | −2.51804e27 | −0.141893 | −0.0709466 | − | 0.997480i | \(-0.522602\pi\) | ||||
−0.0709466 | + | 0.997480i | \(0.522602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.57943e27 | −0.252901 | ||||||||
\(944\) | 6.02139e27 | 0.329202 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.02363e28 | −2.15602 | ||||||||
\(947\) | −8.85552e27 | −0.469774 | −0.234887 | − | 0.972023i | \(-0.575472\pi\) | ||||
−0.234887 | + | 0.972023i | \(0.575472\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.24489e27 | −0.220718 | ||||||||
\(950\) | 1.98337e28 | 1.02101 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.49458e25 | −0.00226797 | ||||||||
\(953\) | −1.35516e28 | −0.677030 | −0.338515 | − | 0.940961i | \(-0.609925\pi\) | ||||
−0.338515 | + | 0.940961i | \(0.609925\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.87358e28 | 0.917570 | ||||||||
\(956\) | −1.23973e28 | −0.601144 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.56907e27 | −0.169661 | ||||||||
\(959\) | 2.37647e25 | 0.00111855 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.16653e28 | −0.999751 | ||||||||
\(962\) | 1.19687e28 | 0.546868 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.52409e28 | −2.02675 | ||||||||
\(965\) | 4.91925e27 | 0.218217 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.51108e27 | 0.239710 | 0.119855 | − | 0.992791i | \(-0.461757\pi\) | ||||
0.119855 | + | 0.992791i | \(0.461757\pi\) | |||||||
\(968\) | −6.60250e28 | −2.84376 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.17088e28 | 2.18390 | ||||||||
\(971\) | −2.37023e28 | −0.991308 | −0.495654 | − | 0.868520i | \(-0.665072\pi\) | ||||
−0.495654 | + | 0.868520i | \(0.665072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.06808e25 | −0.00207860 | ||||||||
\(974\) | −7.46993e28 | −3.03394 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.72688e27 | −0.307773 | ||||||||
\(977\) | 6.97540e27 | 0.275151 | 0.137575 | − | 0.990491i | \(-0.456069\pi\) | ||||
0.137575 | + | 0.990491i | \(0.456069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.53310e28 | −2.91433 | ||||||||
\(980\) | 7.70621e28 | 2.95252 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.20835e28 | 1.95722 | ||||||||
\(983\) | −1.96330e28 | −0.730683 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.56750e28 | −1.30233 | ||||||||
\(986\) | 5.49538e28 | 1.98686 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.41804e27 | −0.298552 | ||||||||
\(989\) | 6.59227e27 | 0.231564 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.20556e28 | 1.44918 | 0.724592 | − | 0.689178i | \(-0.242028\pi\) | ||||
0.724592 | + | 0.689178i | \(0.242028\pi\) | |||||||
\(992\) | 1.14481e26 | 0.00390725 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.50560e25 | 0.00284796 | ||||||||
\(995\) | 1.70533e28 | 0.565573 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.15418e28 | −0.375551 | −0.187776 | − | 0.982212i | \(-0.560128\pi\) | ||||
−0.187776 | + | 0.982212i | \(0.560128\pi\) | |||||||
\(998\) | 4.90816e28 | 1.58190 | ||||||||
\(999\) | 0 | 0 |
(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 | 9.20.a.c.1.1 | 2 | ||
3.2 | odd | 2 | 3.20.a.b.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 48.20.a.j.1.2 | 2 | |||
15.2 | even | 4 | 75.20.b.b.49.4 | 4 | |||
15.8 | even | 4 | 75.20.b.b.49.1 | 4 | |||
15.14 | odd | 2 | 75.20.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.20.a.b.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
9.20.a.c.1.1 | 2 | 1.1 | even | 1 | trivial | ||
48.20.a.j.1.2 | 2 | 12.11 | even | 2 | |||
75.20.a.b.1.1 | 2 | 15.14 | odd | 2 | |||
75.20.b.b.49.1 | 4 | 15.8 | even | 4 | |||
75.20.b.b.49.4 | 4 | 15.2 | even | 4 |