Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,20,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(6.86450089669\) |
Analytic rank: | \(0\) |
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: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-147.386\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 | \(-0.173496\pi\) | ||||
0.855099 | + | 0.518465i | \(0.173496\pi\) | |||||||
\(3\) | −19683.0 | −0.577350 | ||||||||
\(4\) | 1.00914e6 | 1.92478 | ||||||||
\(5\) | 6.69930e6 | 1.53396 | 0.766981 | − | 0.641670i | \(-0.221758\pi\) | ||||
0.766981 | + | 0.641670i | \(0.221758\pi\) | |||||||
\(6\) | −2.43738e7 | −0.987383 | ||||||||
\(7\) | 214621. | 0.00201021 | 0.00100510 | − | 0.999999i | \(-0.499680\pi\) | ||||
0.00100510 | + | 0.999999i | \(0.499680\pi\) | |||||||
\(8\) | 6.00397e8 | 1.58155 | ||||||||
\(9\) | 3.87420e8 | 0.333333 | ||||||||
\(10\) | 8.29585e9 | 2.62338 | ||||||||
\(11\) | −1.30816e10 | −1.67275 | −0.836373 | − | 0.548161i | \(-0.815328\pi\) | ||||
−0.836373 | + | 0.548161i | \(0.815328\pi\) | |||||||
\(12\) | −1.98629e10 | −1.11127 | ||||||||
\(13\) | 1.34409e10 | 0.351533 | 0.175766 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175766 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(14\) | 2.65768e8 | 0.00343785 | ||||||||
\(15\) | −1.31862e11 | −0.885633 | ||||||||
\(16\) | 2.14402e11 | 0.779990 | ||||||||
\(17\) | −3.48802e11 | −0.713368 | −0.356684 | − | 0.934225i | \(-0.616093\pi\) | ||||
−0.356684 | + | 0.934225i | \(0.616093\pi\) | |||||||
\(18\) | 4.79749e11 | 0.570066 | ||||||||
\(19\) | −6.20630e11 | −0.441238 | −0.220619 | − | 0.975360i | \(-0.570808\pi\) | ||||
−0.220619 | + | 0.975360i | \(0.570808\pi\) | |||||||
\(20\) | 6.76052e12 | 2.95253 | ||||||||
\(21\) | −4.22438e9 | −0.00116059 | ||||||||
\(22\) | −1.61991e13 | −2.86073 | ||||||||
\(23\) | −2.65405e12 | −0.307252 | −0.153626 | − | 0.988129i | \(-0.549095\pi\) | ||||
−0.153626 | + | 0.988129i | \(0.549095\pi\) | |||||||
\(24\) | −1.18176e13 | −0.913109 | ||||||||
\(25\) | 2.58072e13 | 1.35304 | ||||||||
\(26\) | 1.66441e13 | 0.601191 | ||||||||
\(27\) | −7.62560e12 | −0.192450 | ||||||||
\(28\) | 2.16582e11 | 0.00386920 | ||||||||
\(29\) | 1.27229e14 | 1.62857 | 0.814286 | − | 0.580464i | \(-0.197129\pi\) | ||||
0.814286 | + | 0.580464i | \(0.197129\pi\) | |||||||
\(30\) | −1.63287e14 | −1.51461 | ||||||||
\(31\) | 2.32290e12 | 0.0157795 | 0.00788977 | − | 0.999969i | \(-0.497489\pi\) | ||||
0.00788977 | + | 0.999969i | \(0.497489\pi\) | |||||||
\(32\) | −4.92835e13 | −0.247615 | ||||||||
\(33\) | 2.57485e14 | 0.965760 | ||||||||
\(34\) | −4.31927e14 | −1.22000 | ||||||||
\(35\) | 1.43781e12 | 0.00308358 | ||||||||
\(36\) | 3.90961e14 | 0.641592 | ||||||||
\(37\) | −7.19096e14 | −0.909642 | −0.454821 | − | 0.890583i | \(-0.650297\pi\) | ||||
−0.454821 | + | 0.890583i | \(0.650297\pi\) | |||||||
\(38\) | −7.68535e14 | −0.754605 | ||||||||
\(39\) | −2.64557e14 | −0.202958 | ||||||||
\(40\) | 4.02224e15 | 2.42604 | ||||||||
\(41\) | 1.72545e15 | 0.823105 | 0.411553 | − | 0.911386i | \(-0.364987\pi\) | ||||
0.411553 | + | 0.911386i | \(0.364987\pi\) | |||||||
\(42\) | −5.23112e12 | −0.00198484 | ||||||||
\(43\) | 2.48385e15 | 0.753660 | 0.376830 | − | 0.926282i | \(-0.377014\pi\) | ||||
0.376830 | + | 0.926282i | \(0.377014\pi\) | |||||||
\(44\) | −1.32011e16 | −3.21966 | ||||||||
\(45\) | 2.59545e15 | 0.511321 | ||||||||
\(46\) | −3.28655e15 | −0.525462 | ||||||||
\(47\) | 1.39689e15 | 0.182067 | 0.0910336 | − | 0.995848i | \(-0.470983\pi\) | ||||
0.0910336 | + | 0.995848i | \(0.470983\pi\) | |||||||
\(48\) | −4.22007e15 | −0.450327 | ||||||||
\(49\) | −1.13988e16 | −0.999996 | ||||||||
\(50\) | 3.19574e16 | 2.31396 | ||||||||
\(51\) | 6.86546e15 | 0.411863 | ||||||||
\(52\) | 1.35637e16 | 0.676623 | ||||||||
\(53\) | 1.05483e16 | 0.439099 | 0.219550 | − | 0.975601i | \(-0.429541\pi\) | ||||
0.219550 | + | 0.975601i | \(0.429541\pi\) | |||||||
\(54\) | −9.44290e15 | −0.329128 | ||||||||
\(55\) | −8.76375e16 | −2.56593 | ||||||||
\(56\) | 1.28858e14 | 0.00317925 | ||||||||
\(57\) | 1.22159e16 | 0.254749 | ||||||||
\(58\) | 1.57550e17 | 2.78518 | ||||||||
\(59\) | −2.80846e16 | −0.422060 | −0.211030 | − | 0.977480i | \(-0.567682\pi\) | ||||
−0.211030 | + | 0.977480i | \(0.567682\pi\) | |||||||
\(60\) | −1.33067e17 | −1.70465 | ||||||||
\(61\) | −3.60392e16 | −0.394586 | −0.197293 | − | 0.980345i | \(-0.563215\pi\) | ||||
−0.197293 | + | 0.980345i | \(0.563215\pi\) | |||||||
\(62\) | 2.87648e15 | 0.0269861 | ||||||||
\(63\) | 8.31485e13 | 0.000670069 0 | ||||||||
\(64\) | −1.73437e17 | −1.20346 | ||||||||
\(65\) | 9.00446e16 | 0.539238 | ||||||||
\(66\) | 3.18848e17 | 1.65164 | ||||||||
\(67\) | 2.91862e17 | 1.31059 | 0.655296 | − | 0.755373i | \(-0.272544\pi\) | ||||
0.655296 | + | 0.755373i | \(0.272544\pi\) | |||||||
\(68\) | −3.51989e17 | −1.37308 | ||||||||
\(69\) | 5.22397e16 | 0.177392 | ||||||||
\(70\) | 1.78046e15 | 0.00527353 | ||||||||
\(71\) | 3.20038e17 | 0.828414 | 0.414207 | − | 0.910183i | \(-0.364059\pi\) | ||||
0.414207 | + | 0.910183i | \(0.364059\pi\) | |||||||
\(72\) | 2.32606e17 | 0.527184 | ||||||||
\(73\) | −3.15819e17 | −0.627873 | −0.313936 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313936 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(74\) | −8.90467e17 | −1.55567 | ||||||||
\(75\) | −5.07963e17 | −0.781178 | ||||||||
\(76\) | −6.26301e17 | −0.849286 | ||||||||
\(77\) | −2.80758e15 | −0.00336256 | ||||||||
\(78\) | −3.27605e17 | −0.347098 | ||||||||
\(79\) | 1.83029e18 | 1.71815 | 0.859077 | − | 0.511846i | \(-0.171038\pi\) | ||||
0.859077 | + | 0.511846i | \(0.171038\pi\) | |||||||
\(80\) | 1.43634e18 | 1.19647 | ||||||||
\(81\) | 1.50095e17 | 0.111111 | ||||||||
\(82\) | 2.13665e18 | 1.40767 | ||||||||
\(83\) | −1.64758e18 | −0.967397 | −0.483698 | − | 0.875235i | \(-0.660707\pi\) | ||||
−0.483698 | + | 0.875235i | \(0.660707\pi\) | |||||||
\(84\) | −4.26298e15 | −0.00223388 | ||||||||
\(85\) | −2.33673e18 | −1.09428 | ||||||||
\(86\) | 3.07579e18 | 1.28891 | ||||||||
\(87\) | −2.50426e18 | −0.940256 | ||||||||
\(88\) | −7.85414e18 | −2.64553 | ||||||||
\(89\) | 5.75855e18 | 1.74224 | 0.871120 | − | 0.491069i | \(-0.163394\pi\) | ||||
0.871120 | + | 0.491069i | \(0.163394\pi\) | |||||||
\(90\) | 3.21398e18 | 0.874460 | ||||||||
\(91\) | 2.88469e15 | 0.000706654 0 | ||||||||
\(92\) | −2.67830e18 | −0.591392 | ||||||||
\(93\) | −4.57216e16 | −0.00911032 | ||||||||
\(94\) | 1.72979e18 | 0.311371 | ||||||||
\(95\) | −4.15779e18 | −0.676843 | ||||||||
\(96\) | 9.70047e17 | 0.142960 | ||||||||
\(97\) | 6.23309e18 | 0.832477 | 0.416238 | − | 0.909256i | \(-0.363348\pi\) | ||||
0.416238 | + | 0.909256i | \(0.363348\pi\) | |||||||
\(98\) | −1.41154e19 | −1.71019 | ||||||||
\(99\) | −5.06808e18 | −0.557582 | ||||||||
\(100\) | 2.60430e19 | 2.60430 | ||||||||
\(101\) | 8.80411e17 | 0.0801000 | 0.0400500 | − | 0.999198i | \(-0.487248\pi\) | ||||
0.0400500 | + | 0.999198i | \(0.487248\pi\) | |||||||
\(102\) | 8.50161e18 | 0.704368 | ||||||||
\(103\) | −1.96998e19 | −1.48767 | −0.743837 | − | 0.668361i | \(-0.766996\pi\) | ||||
−0.743837 | + | 0.668361i | \(0.766996\pi\) | |||||||
\(104\) | 8.06987e18 | 0.555968 | ||||||||
\(105\) | −2.83004e16 | −0.00178031 | ||||||||
\(106\) | 1.30622e19 | 0.750946 | ||||||||
\(107\) | 2.58893e19 | 1.36136 | 0.680682 | − | 0.732579i | \(-0.261684\pi\) | ||||
0.680682 | + | 0.732579i | \(0.261684\pi\) | |||||||
\(108\) | −7.69528e18 | −0.370424 | ||||||||
\(109\) | −3.42533e19 | −1.51060 | −0.755302 | − | 0.655377i | \(-0.772510\pi\) | ||||
−0.755302 | + | 0.655377i | \(0.772510\pi\) | |||||||
\(110\) | −1.08523e20 | −4.38825 | ||||||||
\(111\) | 1.41540e19 | 0.525182 | ||||||||
\(112\) | 4.60151e16 | 0.00156794 | ||||||||
\(113\) | 5.49844e19 | 1.72185 | 0.860923 | − | 0.508735i | \(-0.169887\pi\) | ||||
0.860923 | + | 0.508735i | \(0.169887\pi\) | |||||||
\(114\) | 1.51271e19 | 0.435671 | ||||||||
\(115\) | −1.77803e19 | −0.471313 | ||||||||
\(116\) | 1.28392e20 | 3.13464 | ||||||||
\(117\) | 5.20727e18 | 0.117178 | ||||||||
\(118\) | −3.47776e19 | −0.721806 | ||||||||
\(119\) | −7.48601e16 | −0.00143402 | ||||||||
\(120\) | −7.91697e19 | −1.40068 | ||||||||
\(121\) | 1.09969e20 | 1.79808 | ||||||||
\(122\) | −4.46279e19 | −0.674821 | ||||||||
\(123\) | −3.39620e19 | −0.475220 | ||||||||
\(124\) | 2.34412e18 | 0.0303721 | ||||||||
\(125\) | 4.51110e19 | 0.541549 | ||||||||
\(126\) | 1.02964e17 | 0.00114595 | ||||||||
\(127\) | −8.76640e19 | −0.905078 | −0.452539 | − | 0.891745i | \(-0.649482\pi\) | ||||
−0.452539 | + | 0.891745i | \(0.649482\pi\) | |||||||
\(128\) | −1.88931e20 | −1.81054 | ||||||||
\(129\) | −4.88897e19 | −0.435126 | ||||||||
\(130\) | 1.11504e20 | 0.922204 | ||||||||
\(131\) | −1.23083e20 | −0.946497 | −0.473249 | − | 0.880929i | \(-0.656919\pi\) | ||||
−0.473249 | + | 0.880929i | \(0.656919\pi\) | |||||||
\(132\) | 2.59838e20 | 1.85887 | ||||||||
\(133\) | −1.33200e17 | −0.000886980 0 | ||||||||
\(134\) | 3.61418e20 | 2.24137 | ||||||||
\(135\) | −5.10862e19 | −0.295211 | ||||||||
\(136\) | −2.09419e20 | −1.12823 | ||||||||
\(137\) | −1.10729e20 | −0.556435 | −0.278218 | − | 0.960518i | \(-0.589744\pi\) | ||||
−0.278218 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(138\) | 6.46892e19 | 0.303376 | ||||||||
\(139\) | −2.36141e20 | −1.03402 | −0.517012 | − | 0.855978i | \(-0.672956\pi\) | ||||
−0.517012 | + | 0.855978i | \(0.672956\pi\) | |||||||
\(140\) | 1.45095e18 | 0.00593520 | ||||||||
\(141\) | −2.74949e19 | −0.105117 | ||||||||
\(142\) | 3.96308e20 | 1.41675 | ||||||||
\(143\) | −1.75828e20 | −0.588025 | ||||||||
\(144\) | 8.30637e19 | 0.259997 | ||||||||
\(145\) | 8.52349e20 | 2.49817 | ||||||||
\(146\) | −3.91084e20 | −1.07379 | ||||||||
\(147\) | 2.24364e20 | 0.577348 | ||||||||
\(148\) | −7.25666e20 | −1.75086 | ||||||||
\(149\) | 2.05810e20 | 0.465796 | 0.232898 | − | 0.972501i | \(-0.425179\pi\) | ||||
0.232898 | + | 0.972501i | \(0.425179\pi\) | |||||||
\(150\) | −6.29018e20 | −1.33597 | ||||||||
\(151\) | −2.24449e20 | −0.447546 | −0.223773 | − | 0.974641i | \(-0.571837\pi\) | ||||
−0.223773 | + | 0.974641i | \(0.571837\pi\) | |||||||
\(152\) | −3.72624e20 | −0.697842 | ||||||||
\(153\) | −1.35133e20 | −0.237789 | ||||||||
\(154\) | −3.47667e18 | −0.00575065 | ||||||||
\(155\) | 1.55618e19 | 0.0242052 | ||||||||
\(156\) | −2.66974e20 | −0.390648 | ||||||||
\(157\) | 3.13212e20 | 0.431312 | 0.215656 | − | 0.976469i | \(-0.430811\pi\) | ||||
0.215656 | + | 0.976469i | \(0.430811\pi\) | |||||||
\(158\) | 2.26647e21 | 2.93838 | ||||||||
\(159\) | −2.07623e20 | −0.253514 | ||||||||
\(160\) | −3.30165e20 | −0.379832 | ||||||||
\(161\) | −5.69615e17 | −0.000617640 0 | ||||||||
\(162\) | 1.85865e20 | 0.190022 | ||||||||
\(163\) | 2.00591e20 | 0.193432 | 0.0967160 | − | 0.995312i | \(-0.469166\pi\) | ||||
0.0967160 | + | 0.995312i | \(0.469166\pi\) | |||||||
\(164\) | 1.74122e21 | 1.58429 | ||||||||
\(165\) | 1.72497e21 | 1.48144 | ||||||||
\(166\) | −2.04022e21 | −1.65444 | ||||||||
\(167\) | −2.56060e21 | −1.96126 | −0.980632 | − | 0.195860i | \(-0.937250\pi\) | ||||
−0.980632 | + | 0.195860i | \(0.937250\pi\) | |||||||
\(168\) | −2.53631e18 | −0.00183554 | ||||||||
\(169\) | −1.28126e21 | −0.876425 | ||||||||
\(170\) | −2.89361e21 | −1.87144 | ||||||||
\(171\) | −2.40445e20 | −0.147079 | ||||||||
\(172\) | 2.50655e21 | 1.45063 | ||||||||
\(173\) | 2.86308e21 | 1.56818 | 0.784089 | − | 0.620649i | \(-0.213131\pi\) | ||||
0.784089 | + | 0.620649i | \(0.213131\pi\) | |||||||
\(174\) | −3.10106e21 | −1.60802 | ||||||||
\(175\) | 5.53876e18 | 0.00271989 | ||||||||
\(176\) | −2.80472e21 | −1.30472 | ||||||||
\(177\) | 5.52789e20 | 0.243676 | ||||||||
\(178\) | 7.13090e21 | 2.97958 | ||||||||
\(179\) | 3.79065e20 | 0.150179 | 0.0750896 | − | 0.997177i | \(-0.476076\pi\) | ||||
0.0750896 | + | 0.997177i | \(0.476076\pi\) | |||||||
\(180\) | 2.61916e21 | 0.984178 | ||||||||
\(181\) | −3.15578e21 | −1.12502 | −0.562510 | − | 0.826790i | \(-0.690164\pi\) | ||||
−0.562510 | + | 0.826790i | \(0.690164\pi\) | |||||||
\(182\) | 3.57216e18 | 0.00120852 | ||||||||
\(183\) | 7.09360e20 | 0.227814 | ||||||||
\(184\) | −1.59348e21 | −0.485935 | ||||||||
\(185\) | −4.81744e21 | −1.39536 | ||||||||
\(186\) | −5.66178e19 | −0.0155805 | ||||||||
\(187\) | 4.56288e21 | 1.19328 | ||||||||
\(188\) | 1.40965e21 | 0.350439 | ||||||||
\(189\) | −1.63661e18 | −0.000386864 0 | ||||||||
\(190\) | −5.14865e21 | −1.15754 | ||||||||
\(191\) | 2.79667e21 | 0.598170 | 0.299085 | − | 0.954226i | \(-0.403319\pi\) | ||||
0.299085 | + | 0.954226i | \(0.403319\pi\) | |||||||
\(192\) | 3.41376e21 | 0.694818 | ||||||||
\(193\) | −7.34293e20 | −0.142257 | −0.0711287 | − | 0.997467i | \(-0.522660\pi\) | ||||
−0.0711287 | + | 0.997467i | \(0.522660\pi\) | |||||||
\(194\) | 7.71854e21 | 1.42370 | ||||||||
\(195\) | −1.77235e21 | −0.311329 | ||||||||
\(196\) | −1.15030e22 | −1.92477 | ||||||||
\(197\) | −5.32518e21 | −0.848995 | −0.424498 | − | 0.905429i | \(-0.639549\pi\) | ||||
−0.424498 | + | 0.905429i | \(0.639549\pi\) | |||||||
\(198\) | −6.27588e21 | −0.953576 | ||||||||
\(199\) | −2.54553e21 | −0.368701 | −0.184350 | − | 0.982861i | \(-0.559018\pi\) | ||||
−0.184350 | + | 0.982861i | \(0.559018\pi\) | |||||||
\(200\) | 1.54945e22 | 2.13990 | ||||||||
\(201\) | −5.74472e21 | −0.756670 | ||||||||
\(202\) | 1.09023e21 | 0.136987 | ||||||||
\(203\) | 2.73061e19 | 0.00327376 | ||||||||
\(204\) | 6.92820e21 | 0.792745 | ||||||||
\(205\) | 1.15593e22 | 1.26261 | ||||||||
\(206\) | −2.43945e22 | −2.54422 | ||||||||
\(207\) | −1.02823e21 | −0.102417 | ||||||||
\(208\) | 2.88175e21 | 0.274192 | ||||||||
\(209\) | 8.11882e21 | 0.738080 | ||||||||
\(210\) | −3.50448e19 | −0.00304467 | ||||||||
\(211\) | 7.77610e21 | 0.645771 | 0.322886 | − | 0.946438i | \(-0.395347\pi\) | ||||
0.322886 | + | 0.946438i | \(0.395347\pi\) | |||||||
\(212\) | 1.06447e22 | 0.845168 | ||||||||
\(213\) | −6.29931e21 | −0.478285 | ||||||||
\(214\) | 3.20591e22 | 2.32820 | ||||||||
\(215\) | 1.66401e22 | 1.15609 | ||||||||
\(216\) | −4.57838e21 | −0.304370 | ||||||||
\(217\) | 4.98543e17 | 3.17201e−5 0 | ||||||||
\(218\) | −4.24164e22 | −2.58343 | ||||||||
\(219\) | 6.21627e21 | 0.362503 | ||||||||
\(220\) | −8.84383e22 | −4.93884 | ||||||||
\(221\) | −4.68820e21 | −0.250772 | ||||||||
\(222\) | 1.75271e22 | 0.898165 | ||||||||
\(223\) | −1.89249e22 | −0.929259 | −0.464629 | − | 0.885505i | \(-0.653812\pi\) | ||||
−0.464629 | + | 0.885505i | \(0.653812\pi\) | |||||||
\(224\) | −1.05773e19 | −0.000497757 0 | ||||||||
\(225\) | 9.99823e21 | 0.451013 | ||||||||
\(226\) | 6.80881e22 | 2.94470 | ||||||||
\(227\) | 2.42145e22 | 1.00422 | 0.502111 | − | 0.864803i | \(-0.332557\pi\) | ||||
0.502111 | + | 0.864803i | \(0.332557\pi\) | |||||||
\(228\) | 1.23275e22 | 0.490335 | ||||||||
\(229\) | −3.29966e22 | −1.25902 | −0.629510 | − | 0.776992i | \(-0.716744\pi\) | ||||
−0.629510 | + | 0.776992i | \(0.716744\pi\) | |||||||
\(230\) | −2.20176e22 | −0.806039 | ||||||||
\(231\) | 5.52616e19 | 0.00194138 | ||||||||
\(232\) | 7.63882e22 | 2.57567 | ||||||||
\(233\) | −8.99479e21 | −0.291145 | −0.145573 | − | 0.989348i | \(-0.546502\pi\) | ||||
−0.145573 | + | 0.989348i | \(0.546502\pi\) | |||||||
\(234\) | 6.44825e21 | 0.200397 | ||||||||
\(235\) | 9.35817e21 | 0.279284 | ||||||||
\(236\) | −2.83412e22 | −0.812371 | ||||||||
\(237\) | −3.60256e22 | −0.991977 | ||||||||
\(238\) | −9.27005e19 | −0.00245245 | ||||||||
\(239\) | 1.22851e22 | 0.312319 | 0.156159 | − | 0.987732i | \(-0.450089\pi\) | ||||
0.156159 | + | 0.987732i | \(0.450089\pi\) | |||||||
\(240\) | −2.82716e22 | −0.690785 | ||||||||
\(241\) | −4.48313e22 | −1.05298 | −0.526489 | − | 0.850182i | \(-0.676492\pi\) | ||||
−0.526489 | + | 0.850182i | \(0.676492\pi\) | |||||||
\(242\) | 1.36176e23 | 3.07507 | ||||||||
\(243\) | −2.95431e21 | −0.0641500 | ||||||||
\(244\) | −3.63685e22 | −0.759491 | ||||||||
\(245\) | −7.63643e22 | −1.53396 | ||||||||
\(246\) | −4.20557e22 | −0.812720 | ||||||||
\(247\) | −8.34181e21 | −0.155110 | ||||||||
\(248\) | 1.39466e21 | 0.0249562 | ||||||||
\(249\) | 3.24293e22 | 0.558527 | ||||||||
\(250\) | 5.58617e22 | 0.926155 | ||||||||
\(251\) | 3.85123e22 | 0.614750 | 0.307375 | − | 0.951588i | \(-0.400549\pi\) | ||||
0.307375 | + | 0.951588i | \(0.400549\pi\) | |||||||
\(252\) | 8.39083e19 | 0.00128973 | ||||||||
\(253\) | 3.47192e22 | 0.513955 | ||||||||
\(254\) | −1.08556e23 | −1.54786 | ||||||||
\(255\) | 4.59938e22 | 0.631783 | ||||||||
\(256\) | −1.43025e23 | −1.89292 | ||||||||
\(257\) | 9.07321e22 | 1.15717 | 0.578584 | − | 0.815623i | \(-0.303606\pi\) | ||||
0.578584 | + | 0.815623i | \(0.303606\pi\) | |||||||
\(258\) | −6.05408e22 | −0.744151 | ||||||||
\(259\) | −1.54333e20 | −0.00182857 | ||||||||
\(260\) | 9.08674e22 | 1.03791 | ||||||||
\(261\) | 4.92913e22 | 0.542857 | ||||||||
\(262\) | −1.52415e23 | −1.61870 | ||||||||
\(263\) | −2.56086e21 | −0.0262305 | −0.0131152 | − | 0.999914i | \(-0.504175\pi\) | ||||
−0.0131152 | + | 0.999914i | \(0.504175\pi\) | |||||||
\(264\) | 1.54593e23 | 1.52740 | ||||||||
\(265\) | 7.06664e22 | 0.673561 | ||||||||
\(266\) | −1.64944e20 | −0.00151691 | ||||||||
\(267\) | −1.13346e23 | −1.00588 | ||||||||
\(268\) | 2.94529e23 | 2.52260 | ||||||||
\(269\) | 3.82577e22 | 0.316281 | 0.158140 | − | 0.987417i | \(-0.449450\pi\) | ||||
0.158140 | + | 0.987417i | \(0.449450\pi\) | |||||||
\(270\) | −6.32608e22 | −0.504869 | ||||||||
\(271\) | 3.64857e22 | 0.281135 | 0.140567 | − | 0.990071i | \(-0.455107\pi\) | ||||
0.140567 | + | 0.990071i | \(0.455107\pi\) | |||||||
\(272\) | −7.47838e22 | −0.556420 | ||||||||
\(273\) | −5.67794e19 | −0.000407987 0 | ||||||||
\(274\) | −1.37117e23 | −0.951615 | ||||||||
\(275\) | −3.37599e23 | −2.26329 | ||||||||
\(276\) | 5.27170e22 | 0.341440 | ||||||||
\(277\) | 1.78571e23 | 1.11752 | 0.558758 | − | 0.829331i | \(-0.311278\pi\) | ||||
0.558758 | + | 0.829331i | \(0.311278\pi\) | |||||||
\(278\) | −2.92417e23 | −1.76839 | ||||||||
\(279\) | 8.99939e20 | 0.00525985 | ||||||||
\(280\) | 8.63257e20 | 0.00487684 | ||||||||
\(281\) | −2.28261e23 | −1.24659 | −0.623293 | − | 0.781989i | \(-0.714205\pi\) | ||||
−0.623293 | + | 0.781989i | \(0.714205\pi\) | |||||||
\(282\) | −3.40474e22 | −0.179770 | ||||||||
\(283\) | 1.87538e23 | 0.957453 | 0.478727 | − | 0.877964i | \(-0.341098\pi\) | ||||
0.478727 | + | 0.877964i | \(0.341098\pi\) | |||||||
\(284\) | 3.22962e23 | 1.59451 | ||||||||
\(285\) | 8.18377e22 | 0.390775 | ||||||||
\(286\) | −2.17731e23 | −1.00564 | ||||||||
\(287\) | 3.70317e20 | 0.00165461 | ||||||||
\(288\) | −1.90934e22 | −0.0825383 | ||||||||
\(289\) | −1.17410e23 | −0.491106 | ||||||||
\(290\) | 1.05548e24 | 4.27236 | ||||||||
\(291\) | −1.22686e23 | −0.480631 | ||||||||
\(292\) | −3.18705e23 | −1.20852 | ||||||||
\(293\) | 2.82617e23 | 1.03742 | 0.518711 | − | 0.854950i | \(-0.326412\pi\) | ||||
0.518711 | + | 0.854950i | \(0.326412\pi\) | |||||||
\(294\) | 2.77833e23 | 0.987379 | ||||||||
\(295\) | −1.88147e23 | −0.647424 | ||||||||
\(296\) | −4.31743e23 | −1.43865 | ||||||||
\(297\) | 9.97549e22 | 0.321920 | ||||||||
\(298\) | 2.54857e23 | 0.796604 | ||||||||
\(299\) | −3.56728e22 | −0.108009 | ||||||||
\(300\) | −5.12604e23 | −1.50359 | ||||||||
\(301\) | 5.33087e20 | 0.00151501 | ||||||||
\(302\) | −2.77939e23 | −0.765392 | ||||||||
\(303\) | −1.73291e22 | −0.0462457 | ||||||||
\(304\) | −1.33064e23 | −0.344162 | ||||||||
\(305\) | −2.41438e23 | −0.605280 | ||||||||
\(306\) | −1.67337e23 | −0.406667 | ||||||||
\(307\) | −2.47019e23 | −0.581991 | −0.290996 | − | 0.956724i | \(-0.593986\pi\) | ||||
−0.290996 | + | 0.956724i | \(0.593986\pi\) | |||||||
\(308\) | −2.83324e21 | −0.00647219 | ||||||||
\(309\) | 3.87751e23 | 0.858909 | ||||||||
\(310\) | 1.92704e22 | 0.0413957 | ||||||||
\(311\) | 3.27126e23 | 0.681539 | 0.340770 | − | 0.940147i | \(-0.389312\pi\) | ||||
0.340770 | + | 0.940147i | \(0.389312\pi\) | |||||||
\(312\) | −1.58839e23 | −0.320988 | ||||||||
\(313\) | 3.73412e23 | 0.732011 | 0.366005 | − | 0.930613i | \(-0.380725\pi\) | ||||
0.366005 | + | 0.930613i | \(0.380725\pi\) | |||||||
\(314\) | 3.87855e23 | 0.737628 | ||||||||
\(315\) | 5.57037e20 | 0.00102786 | ||||||||
\(316\) | 1.84701e24 | 3.30706 | ||||||||
\(317\) | −5.83518e22 | −0.101389 | −0.0506945 | − | 0.998714i | \(-0.516143\pi\) | ||||
−0.0506945 | + | 0.998714i | \(0.516143\pi\) | |||||||
\(318\) | −2.57102e23 | −0.433559 | ||||||||
\(319\) | −1.66436e24 | −2.72419 | ||||||||
\(320\) | −1.16191e24 | −1.84606 | ||||||||
\(321\) | −5.09579e23 | −0.785984 | ||||||||
\(322\) | −7.05363e20 | −0.00105629 | ||||||||
\(323\) | 2.16477e23 | 0.314766 | ||||||||
\(324\) | 1.51466e23 | 0.213864 | ||||||||
\(325\) | 3.46871e23 | 0.475638 | ||||||||
\(326\) | 2.48394e23 | 0.330807 | ||||||||
\(327\) | 6.74208e23 | 0.872148 | ||||||||
\(328\) | 1.03595e24 | 1.30178 | ||||||||
\(329\) | 2.99801e20 | 0.000365993 0 | ||||||||
\(330\) | 2.13606e24 | 2.53355 | ||||||||
\(331\) | 3.84253e23 | 0.442845 | 0.221422 | − | 0.975178i | \(-0.428930\pi\) | ||||
0.221422 | + | 0.975178i | \(0.428930\pi\) | |||||||
\(332\) | −1.66263e24 | −1.86202 | ||||||||
\(333\) | −2.78592e23 | −0.303214 | ||||||||
\(334\) | −3.17084e24 | −3.35415 | ||||||||
\(335\) | 1.95527e24 | 2.01040 | ||||||||
\(336\) | −9.05716e20 | −0.000905251 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 | ||||||||
\(339\) | −1.08226e24 | −0.994109 | ||||||||
\(340\) | −2.35808e24 | −2.10624 | ||||||||
\(341\) | −3.03872e22 | −0.0263952 | ||||||||
\(342\) | −2.97746e23 | −0.251535 | ||||||||
\(343\) | −4.89287e21 | −0.00402040 | ||||||||
\(344\) | 1.49130e24 | 1.19195 | ||||||||
\(345\) | 3.49970e23 | 0.272113 | ||||||||
\(346\) | 3.54539e24 | 2.68189 | ||||||||
\(347\) | −8.56826e22 | −0.0630613 | −0.0315306 | − | 0.999503i | \(-0.510038\pi\) | ||||
−0.0315306 | + | 0.999503i | \(0.510038\pi\) | |||||||
\(348\) | −2.52714e24 | −1.80978 | ||||||||
\(349\) | −1.11294e24 | −0.775586 | −0.387793 | − | 0.921746i | \(-0.626763\pi\) | ||||
−0.387793 | + | 0.921746i | \(0.626763\pi\) | |||||||
\(350\) | 6.85873e21 | 0.00465155 | ||||||||
\(351\) | −1.02495e23 | −0.0676526 | ||||||||
\(352\) | 6.44706e23 | 0.414197 | ||||||||
\(353\) | −2.23748e24 | −1.39926 | −0.699631 | − | 0.714505i | \(-0.746652\pi\) | ||||
−0.699631 | + | 0.714505i | \(0.746652\pi\) | |||||||
\(354\) | 6.84527e23 | 0.416735 | ||||||||
\(355\) | 2.14403e24 | 1.27076 | ||||||||
\(356\) | 5.81117e24 | 3.35343 | ||||||||
\(357\) | 1.47347e21 | 0.000827930 0 | ||||||||
\(358\) | 4.69402e23 | 0.256836 | ||||||||
\(359\) | 2.02884e24 | 1.08106 | 0.540531 | − | 0.841324i | \(-0.318223\pi\) | ||||
0.540531 | + | 0.841324i | \(0.318223\pi\) | |||||||
\(360\) | 1.55830e24 | 0.808680 | ||||||||
\(361\) | −1.59324e24 | −0.805309 | ||||||||
\(362\) | −3.90785e24 | −1.92401 | ||||||||
\(363\) | −2.16452e24 | −1.03812 | ||||||||
\(364\) | 2.91105e21 | 0.00136015 | ||||||||
\(365\) | −2.11577e24 | −0.963133 | ||||||||
\(366\) | 8.78412e23 | 0.389608 | ||||||||
\(367\) | −2.03395e24 | −0.879049 | −0.439525 | − | 0.898230i | \(-0.644853\pi\) | ||||
−0.439525 | + | 0.898230i | \(0.644853\pi\) | |||||||
\(368\) | −5.69034e23 | −0.239654 | ||||||||
\(369\) | 6.68474e23 | 0.274368 | ||||||||
\(370\) | −5.96551e24 | −2.38633 | ||||||||
\(371\) | 2.26389e21 | 0.000882680 0 | ||||||||
\(372\) | −4.61394e22 | −0.0175353 | ||||||||
\(373\) | −7.78333e23 | −0.288358 | −0.144179 | − | 0.989552i | \(-0.546054\pi\) | ||||
−0.144179 | + | 0.989552i | \(0.546054\pi\) | |||||||
\(374\) | 5.65029e24 | 2.04075 | ||||||||
\(375\) | −8.87920e23 | −0.312663 | ||||||||
\(376\) | 8.38687e23 | 0.287949 | ||||||||
\(377\) | 1.71008e24 | 0.572497 | ||||||||
\(378\) | −2.02664e21 | −0.000661615 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 | ||||||||
\(381\) | 1.72549e24 | 0.522547 | ||||||||
\(382\) | 3.46316e24 | 1.02299 | ||||||||
\(383\) | −3.09305e24 | −0.891249 | −0.445625 | − | 0.895220i | \(-0.647018\pi\) | ||||
−0.445625 | + | 0.895220i | \(0.647018\pi\) | |||||||
\(384\) | 3.71873e24 | 1.04532 | ||||||||
\(385\) | −1.88088e22 | −0.00515804 | ||||||||
\(386\) | −9.09286e23 | −0.243288 | ||||||||
\(387\) | 9.62295e23 | 0.251220 | ||||||||
\(388\) | 6.29005e24 | 1.60233 | ||||||||
\(389\) | −4.58505e24 | −1.13978 | −0.569892 | − | 0.821719i | \(-0.693015\pi\) | ||||
−0.569892 | + | 0.821719i | \(0.693015\pi\) | |||||||
\(390\) | −2.19473e24 | −0.532435 | ||||||||
\(391\) | 9.25738e23 | 0.219184 | ||||||||
\(392\) | −6.84383e24 | −1.58155 | ||||||||
\(393\) | 2.42263e24 | 0.546460 | ||||||||
\(394\) | −6.59426e24 | −1.45195 | ||||||||
\(395\) | 1.22617e25 | 2.63558 | ||||||||
\(396\) | −5.11439e24 | −1.07322 | ||||||||
\(397\) | 5.62169e24 | 1.15175 | 0.575873 | − | 0.817539i | \(-0.304662\pi\) | ||||
0.575873 | + | 0.817539i | \(0.304662\pi\) | |||||||
\(398\) | −3.15217e24 | −0.630551 | ||||||||
\(399\) | 2.62178e21 | 0.000512098 0 | ||||||||
\(400\) | 5.53311e24 | 1.05536 | ||||||||
\(401\) | −8.34521e24 | −1.55441 | −0.777206 | − | 0.629247i | \(-0.783364\pi\) | ||||
−0.777206 | + | 0.629247i | \(0.783364\pi\) | |||||||
\(402\) | −7.11378e24 | −1.29406 | ||||||||
\(403\) | 3.12218e22 | 0.00554703 | ||||||||
\(404\) | 8.88456e23 | 0.154175 | ||||||||
\(405\) | 1.00553e24 | 0.170440 | ||||||||
\(406\) | 3.38136e22 | 0.00559878 | ||||||||
\(407\) | 9.40691e24 | 1.52160 | ||||||||
\(408\) | 4.12200e24 | 0.651383 | ||||||||
\(409\) | −1.09120e25 | −1.68474 | −0.842370 | − | 0.538900i | \(-0.818840\pi\) | ||||
−0.842370 | + | 0.538900i | \(0.818840\pi\) | |||||||
\(410\) | 1.43141e25 | 2.15932 | ||||||||
\(411\) | 2.17947e24 | 0.321258 | ||||||||
\(412\) | −1.98798e25 | −2.86344 | ||||||||
\(413\) | −6.02754e21 | −0.000848427 0 | ||||||||
\(414\) | −1.27328e24 | −0.175154 | ||||||||
\(415\) | −1.10376e25 | −1.48395 | ||||||||
\(416\) | −6.62414e23 | −0.0870448 | ||||||||
\(417\) | 4.64796e24 | 0.596994 | ||||||||
\(418\) | 1.00537e25 | 1.26226 | ||||||||
\(419\) | −1.35175e25 | −1.65906 | −0.829529 | − | 0.558463i | \(-0.811391\pi\) | ||||
−0.829529 | + | 0.558463i | \(0.811391\pi\) | |||||||
\(420\) | −2.85590e22 | −0.00342669 | ||||||||
\(421\) | 9.91185e24 | 1.16272 | 0.581360 | − | 0.813647i | \(-0.302521\pi\) | ||||
0.581360 | + | 0.813647i | \(0.302521\pi\) | |||||||
\(422\) | 9.62927e24 | 1.10440 | ||||||||
\(423\) | 5.41183e23 | 0.0606891 | ||||||||
\(424\) | 6.33318e24 | 0.694458 | ||||||||
\(425\) | −9.00159e24 | −0.965215 | ||||||||
\(426\) | −7.80053e24 | −0.817962 | ||||||||
\(427\) | −7.73477e21 | −0.000793200 0 | ||||||||
\(428\) | 2.61259e25 | 2.62032 | ||||||||
\(429\) | 3.46083e24 | 0.339497 | ||||||||
\(430\) | 2.06057e25 | 1.97714 | ||||||||
\(431\) | 1.91272e24 | 0.179522 | 0.0897610 | − | 0.995963i | \(-0.471390\pi\) | ||||
0.0897610 | + | 0.995963i | \(0.471390\pi\) | |||||||
\(432\) | −1.63494e24 | −0.150109 | ||||||||
\(433\) | 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 | ||||||||
\(435\) | −1.67768e25 | −1.44232 | ||||||||
\(436\) | −3.45663e25 | −2.90758 | ||||||||
\(437\) | 1.64718e24 | 0.135571 | ||||||||
\(438\) | 7.69771e24 | 0.619951 | ||||||||
\(439\) | 8.11473e21 | 0.000639530 0 | 0.000319765 | − | 1.00000i | \(-0.499898\pi\) | ||||
0.000319765 | 1.00000i | \(0.499898\pi\) | ||||||||
\(440\) | −5.26173e25 | −4.05815 | ||||||||
\(441\) | −4.41615e24 | −0.333332 | ||||||||
\(442\) | −5.80548e24 | −0.428871 | ||||||||
\(443\) | 2.51728e24 | 0.182010 | 0.0910051 | − | 0.995850i | \(-0.470992\pi\) | ||||
0.0910051 | + | 0.995850i | \(0.470992\pi\) | |||||||
\(444\) | 1.42833e25 | 1.01086 | ||||||||
\(445\) | 3.85783e25 | 2.67253 | ||||||||
\(446\) | −2.34350e25 | −1.58922 | ||||||||
\(447\) | −4.05095e24 | −0.268928 | ||||||||
\(448\) | −3.72232e22 | −0.00241920 | ||||||||
\(449\) | −1.07451e25 | −0.683706 | −0.341853 | − | 0.939753i | \(-0.611055\pi\) | ||||
−0.341853 | + | 0.939753i | \(0.611055\pi\) | |||||||
\(450\) | 1.23810e25 | 0.771322 | ||||||||
\(451\) | −2.25716e25 | −1.37685 | ||||||||
\(452\) | 5.54869e25 | 3.31417 | ||||||||
\(453\) | 4.41784e24 | 0.258391 | ||||||||
\(454\) | 2.99852e25 | 1.71742 | ||||||||
\(455\) | 1.93254e22 | 0.00108398 | ||||||||
\(456\) | 7.33436e24 | 0.402899 | ||||||||
\(457\) | 8.09140e24 | 0.435331 | 0.217665 | − | 0.976023i | \(-0.430156\pi\) | ||||
0.217665 | + | 0.976023i | \(0.430156\pi\) | |||||||
\(458\) | −4.08603e25 | −2.15317 | ||||||||
\(459\) | 2.65982e24 | 0.137288 | ||||||||
\(460\) | −1.79428e25 | −0.907173 | ||||||||
\(461\) | 1.48075e25 | 0.733368 | 0.366684 | − | 0.930346i | \(-0.380493\pi\) | ||||
0.366684 | + | 0.930346i | \(0.380493\pi\) | |||||||
\(462\) | 6.84313e22 | 0.00332014 | ||||||||
\(463\) | −2.65292e25 | −1.26097 | −0.630485 | − | 0.776202i | \(-0.717144\pi\) | ||||
−0.630485 | + | 0.776202i | \(0.717144\pi\) | |||||||
\(464\) | 2.72783e25 | 1.27027 | ||||||||
\(465\) | −3.06303e23 | −0.0139749 | ||||||||
\(466\) | −1.11384e25 | −0.497916 | ||||||||
\(467\) | 3.57468e25 | 1.56576 | 0.782882 | − | 0.622170i | \(-0.213749\pi\) | ||||
0.782882 | + | 0.622170i | \(0.213749\pi\) | |||||||
\(468\) | 5.25486e24 | 0.225541 | ||||||||
\(469\) | 6.26397e22 | 0.00263456 | ||||||||
\(470\) | 1.15884e25 | 0.477631 | ||||||||
\(471\) | −6.16494e24 | −0.249018 | ||||||||
\(472\) | −1.68619e25 | −0.667510 | ||||||||
\(473\) | −3.24927e25 | −1.26068 | ||||||||
\(474\) | −4.46110e25 | −1.69648 | ||||||||
\(475\) | −1.60167e25 | −0.597013 | ||||||||
\(476\) | −7.55442e22 | −0.00276016 | ||||||||
\(477\) | 4.08664e24 | 0.146366 | ||||||||
\(478\) | 1.52128e25 | 0.534127 | ||||||||
\(479\) | −2.88220e24 | −0.0992056 | −0.0496028 | − | 0.998769i | \(-0.515796\pi\) | ||||
−0.0496028 | + | 0.998769i | \(0.515796\pi\) | |||||||
\(480\) | 6.49864e24 | 0.219296 | ||||||||
\(481\) | −9.66528e24 | −0.319769 | ||||||||
\(482\) | −5.55152e25 | −1.80080 | ||||||||
\(483\) | 1.12117e22 | 0.000356595 0 | ||||||||
\(484\) | 1.10974e26 | 3.46090 | ||||||||
\(485\) | 4.17574e25 | 1.27699 | ||||||||
\(486\) | −3.65837e24 | −0.109709 | ||||||||
\(487\) | 6.03233e25 | 1.77403 | 0.887014 | − | 0.461743i | \(-0.152776\pi\) | ||||
0.887014 | + | 0.461743i | \(0.152776\pi\) | |||||||
\(488\) | −2.16378e25 | −0.624059 | ||||||||
\(489\) | −3.94822e24 | −0.111678 | ||||||||
\(490\) | −9.45632e25 | −2.62337 | ||||||||
\(491\) | 4.20599e25 | 1.14444 | 0.572222 | − | 0.820099i | \(-0.306082\pi\) | ||||
0.572222 | + | 0.820099i | \(0.306082\pi\) | |||||||
\(492\) | −3.42723e25 | −0.914693 | ||||||||
\(493\) | −4.43779e25 | −1.16177 | ||||||||
\(494\) | −1.03298e25 | −0.265269 | ||||||||
\(495\) | −3.39526e25 | −0.855310 | ||||||||
\(496\) | 4.98034e23 | 0.0123079 | ||||||||
\(497\) | 6.86869e22 | 0.00166528 | ||||||||
\(498\) | 4.01577e25 | 0.955191 | ||||||||
\(499\) | −3.96358e25 | −0.924979 | −0.462490 | − | 0.886625i | \(-0.653044\pi\) | ||||
−0.462490 | + | 0.886625i | \(0.653044\pi\) | |||||||
\(500\) | 4.55232e25 | 1.04236 | ||||||||
\(501\) | 5.04004e25 | 1.13234 | ||||||||
\(502\) | 4.76904e25 | 1.05134 | ||||||||
\(503\) | 5.09940e25 | 1.10312 | 0.551561 | − | 0.834135i | \(-0.314032\pi\) | ||||
0.551561 | + | 0.834135i | \(0.314032\pi\) | |||||||
\(504\) | 4.99221e22 | 0.00105975 | ||||||||
\(505\) | 5.89814e24 | 0.122870 | ||||||||
\(506\) | 4.29933e25 | 0.878965 | ||||||||
\(507\) | 2.52191e25 | 0.506004 | ||||||||
\(508\) | −8.84651e25 | −1.74207 | ||||||||
\(509\) | −4.45056e25 | −0.860193 | −0.430096 | − | 0.902783i | \(-0.641520\pi\) | ||||
−0.430096 | + | 0.902783i | \(0.641520\pi\) | |||||||
\(510\) | 5.69549e25 | 1.08047 | ||||||||
\(511\) | −6.77814e22 | −0.00126215 | ||||||||
\(512\) | −7.80561e25 | −1.42673 | ||||||||
\(513\) | 4.73267e24 | 0.0849164 | ||||||||
\(514\) | 1.12355e26 | 1.97899 | ||||||||
\(515\) | −1.31975e26 | −2.28204 | ||||||||
\(516\) | −4.93364e25 | −0.837520 | ||||||||
\(517\) | −1.82735e25 | −0.304552 | ||||||||
\(518\) | −1.91113e23 | −0.00312721 | ||||||||
\(519\) | −5.63540e25 | −0.905388 | ||||||||
\(520\) | 5.40625e25 | 0.852833 | ||||||||
\(521\) | −1.65819e24 | −0.0256847 | −0.0128424 | − | 0.999918i | \(-0.504088\pi\) | ||||
−0.0128424 | + | 0.999918i | \(0.504088\pi\) | |||||||
\(522\) | 6.10382e25 | 0.928393 | ||||||||
\(523\) | −4.69898e25 | −0.701839 | −0.350920 | − | 0.936406i | \(-0.614131\pi\) | ||||
−0.350920 | + | 0.936406i | \(0.614131\pi\) | |||||||
\(524\) | −1.24207e26 | −1.82180 | ||||||||
\(525\) | −1.09019e23 | −0.00157033 | ||||||||
\(526\) | −3.17115e24 | −0.0448593 | ||||||||
\(527\) | −8.10231e23 | −0.0112566 | ||||||||
\(528\) | 5.52053e25 | 0.753283 | ||||||||
\(529\) | −6.75715e25 | −0.905596 | ||||||||
\(530\) | 8.75073e25 | 1.15192 | ||||||||
\(531\) | −1.08805e25 | −0.140687 | ||||||||
\(532\) | −1.34417e23 | −0.00170724 | ||||||||
\(533\) | 2.31916e25 | 0.289349 | ||||||||
\(534\) | −1.40358e26 | −1.72026 | ||||||||
\(535\) | 1.73440e26 | 2.08828 | ||||||||
\(536\) | 1.75233e26 | 2.07277 | ||||||||
\(537\) | −7.46114e24 | −0.0867060 | ||||||||
\(538\) | 4.73752e25 | 0.540903 | ||||||||
\(539\) | 1.49115e26 | 1.67274 | ||||||||
\(540\) | −5.15530e25 | −0.568216 | ||||||||
\(541\) | 6.20242e25 | 0.671718 | 0.335859 | − | 0.941912i | \(-0.390973\pi\) | ||||
0.335859 | + | 0.941912i | \(0.390973\pi\) | |||||||
\(542\) | 4.51808e25 | 0.480796 | ||||||||
\(543\) | 6.21152e25 | 0.649531 | ||||||||
\(544\) | 1.71902e25 | 0.176641 | ||||||||
\(545\) | −2.29473e26 | −2.31721 | ||||||||
\(546\) | −7.03109e22 | −0.000697738 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 | ||||||||
\(549\) | −1.39623e25 | −0.131529 | ||||||||
\(550\) | −4.18054e26 | −3.87068 | ||||||||
\(551\) | −7.89624e25 | −0.718588 | ||||||||
\(552\) | 3.13646e25 | 0.280555 | ||||||||
\(553\) | 3.92818e23 | 0.00345384 | ||||||||
\(554\) | 2.21128e26 | 1.91117 | ||||||||
\(555\) | 9.48217e25 | 0.805609 | ||||||||
\(556\) | −2.38299e26 | −1.99027 | ||||||||
\(557\) | 3.67420e25 | 0.301675 | 0.150837 | − | 0.988559i | \(-0.451803\pi\) | ||||
0.150837 | + | 0.988559i | \(0.451803\pi\) | |||||||
\(558\) | 1.11441e24 | 0.00899538 | ||||||||
\(559\) | 3.33852e25 | 0.264936 | ||||||||
\(560\) | 3.08269e23 | 0.00240516 | ||||||||
\(561\) | −8.98112e25 | −0.688943 | ||||||||
\(562\) | −2.82659e26 | −2.13191 | ||||||||
\(563\) | 1.24531e26 | 0.923526 | 0.461763 | − | 0.887003i | \(-0.347217\pi\) | ||||
0.461763 | + | 0.887003i | \(0.347217\pi\) | |||||||
\(564\) | −2.77462e25 | −0.202326 | ||||||||
\(565\) | 3.68357e26 | 2.64125 | ||||||||
\(566\) | 2.32231e26 | 1.63743 | ||||||||
\(567\) | 3.22134e22 | 0.000223356 0 | ||||||||
\(568\) | 1.92150e26 | 1.31018 | ||||||||
\(569\) | −5.63513e25 | −0.377866 | −0.188933 | − | 0.981990i | \(-0.560503\pi\) | ||||
−0.188933 | + | 0.981990i | \(0.560503\pi\) | |||||||
\(570\) | 1.01341e26 | 0.668303 | ||||||||
\(571\) | −1.23813e26 | −0.803012 | −0.401506 | − | 0.915856i | \(-0.631513\pi\) | ||||
−0.401506 | + | 0.915856i | \(0.631513\pi\) | |||||||
\(572\) | −1.77435e26 | −1.13182 | ||||||||
\(573\) | −5.50469e25 | −0.345354 | ||||||||
\(574\) | 4.58570e23 | 0.00282971 | ||||||||
\(575\) | −6.84936e25 | −0.415724 | ||||||||
\(576\) | −6.71930e25 | −0.401153 | ||||||||
\(577\) | −3.01722e26 | −1.77189 | −0.885945 | − | 0.463790i | \(-0.846489\pi\) | ||||
−0.885945 | + | 0.463790i | \(0.846489\pi\) | |||||||
\(578\) | −1.45390e26 | −0.839888 | ||||||||
\(579\) | 1.44531e25 | 0.0821323 | ||||||||
\(580\) | 8.60137e26 | 4.80841 | ||||||||
\(581\) | −3.53605e23 | −0.00194467 | ||||||||
\(582\) | −1.51924e26 | −0.821974 | ||||||||
\(583\) | −1.37989e26 | −0.734501 | ||||||||
\(584\) | −1.89617e26 | −0.993014 | ||||||||
\(585\) | 3.48851e25 | 0.179746 | ||||||||
\(586\) | 3.49968e26 | 1.77420 | ||||||||
\(587\) | −6.00743e25 | −0.299659 | −0.149829 | − | 0.988712i | \(-0.547872\pi\) | ||||
−0.149829 | + | 0.988712i | \(0.547872\pi\) | |||||||
\(588\) | 2.26414e26 | 1.11127 | ||||||||
\(589\) | −1.44166e24 | −0.00696254 | ||||||||
\(590\) | −2.32986e26 | −1.10722 | ||||||||
\(591\) | 1.04816e26 | 0.490168 | ||||||||
\(592\) | −1.54176e26 | −0.709511 | ||||||||
\(593\) | −9.94196e25 | −0.450248 | −0.225124 | − | 0.974330i | \(-0.572279\pi\) | ||||
−0.225124 | + | 0.974330i | \(0.572279\pi\) | |||||||
\(594\) | 1.23528e26 | 0.550547 | ||||||||
\(595\) | −5.01511e23 | −0.00219973 | ||||||||
\(596\) | 2.07690e26 | 0.896554 | ||||||||
\(597\) | 5.01037e25 | 0.212869 | ||||||||
\(598\) | −4.41742e25 | −0.184717 | ||||||||
\(599\) | −1.95677e26 | −0.805350 | −0.402675 | − | 0.915343i | \(-0.631920\pi\) | ||||
−0.402675 | + | 0.915343i | \(0.631920\pi\) | |||||||
\(600\) | −3.04979e26 | −1.23547 | ||||||||
\(601\) | −4.73445e26 | −1.88782 | −0.943912 | − | 0.330197i | \(-0.892885\pi\) | ||||
−0.943912 | + | 0.330197i | \(0.892885\pi\) | |||||||
\(602\) | 6.60129e23 | 0.00259097 | ||||||||
\(603\) | 1.13073e26 | 0.436864 | ||||||||
\(604\) | −2.26500e26 | −0.861426 | ||||||||
\(605\) | 7.36715e26 | 2.75818 | ||||||||
\(606\) | −2.14589e25 | −0.0790894 | ||||||||
\(607\) | −1.22707e26 | −0.445222 | −0.222611 | − | 0.974907i | \(-0.571458\pi\) | ||||
−0.222611 | + | 0.974907i | \(0.571458\pi\) | |||||||
\(608\) | 3.05868e25 | 0.109257 | ||||||||
\(609\) | −5.37466e23 | −0.00189011 | ||||||||
\(610\) | −2.98976e26 | −1.03515 | ||||||||
\(611\) | 1.87754e25 | 0.0640026 | ||||||||
\(612\) | −1.36368e26 | −0.457692 | ||||||||
\(613\) | 3.20354e26 | 1.05866 | 0.529329 | − | 0.848417i | \(-0.322444\pi\) | ||||
0.529329 | + | 0.848417i | \(0.322444\pi\) | |||||||
\(614\) | −3.05888e26 | −0.995320 | ||||||||
\(615\) | −2.27522e26 | −0.728969 | ||||||||
\(616\) | −1.68566e24 | −0.00531807 | ||||||||
\(617\) | 9.79781e25 | 0.304383 | 0.152191 | − | 0.988351i | \(-0.451367\pi\) | ||||
0.152191 | + | 0.988351i | \(0.451367\pi\) | |||||||
\(618\) | 4.80158e26 | 1.46890 | ||||||||
\(619\) | −1.22713e25 | −0.0369682 | −0.0184841 | − | 0.999829i | \(-0.505884\pi\) | ||||
−0.0184841 | + | 0.999829i | \(0.505884\pi\) | |||||||
\(620\) | 1.57040e25 | 0.0465896 | ||||||||
\(621\) | 2.02387e25 | 0.0591307 | ||||||||
\(622\) | 4.05085e26 | 1.16557 | ||||||||
\(623\) | 1.23591e24 | 0.00350226 | ||||||||
\(624\) | −5.67215e25 | −0.158305 | ||||||||
\(625\) | −1.90020e26 | −0.522324 | ||||||||
\(626\) | 4.62402e26 | 1.25188 | ||||||||
\(627\) | −1.59803e26 | −0.426131 | ||||||||
\(628\) | 3.16074e26 | 0.830179 | ||||||||
\(629\) | 2.50822e26 | 0.648909 | ||||||||
\(630\) | 6.89788e23 | 0.00175784 | ||||||||
\(631\) | 4.30803e26 | 1.08143 | 0.540716 | − | 0.841205i | \(-0.318153\pi\) | ||||
0.540716 | + | 0.841205i | \(0.318153\pi\) | |||||||
\(632\) | 1.09890e27 | 2.71735 | ||||||||
\(633\) | −1.53057e26 | −0.372836 | ||||||||
\(634\) | −7.22579e25 | −0.173395 | ||||||||
\(635\) | −5.87288e26 | −1.38836 | ||||||||
\(636\) | −2.09520e26 | −0.487958 | ||||||||
\(637\) | −1.53211e26 | −0.351532 | ||||||||
\(638\) | −2.06101e27 | −4.65890 | ||||||||
\(639\) | 1.23989e26 | 0.276138 | ||||||||
\(640\) | −1.26571e27 | −2.77730 | ||||||||
\(641\) | 5.54923e26 | 1.19972 | 0.599862 | − | 0.800104i | \(-0.295222\pi\) | ||||
0.599862 | + | 0.800104i | \(0.295222\pi\) | |||||||
\(642\) | −6.31020e26 | −1.34419 | ||||||||
\(643\) | 6.72911e26 | 1.41239 | 0.706193 | − | 0.708019i | \(-0.250411\pi\) | ||||
0.706193 | + | 0.708019i | \(0.250411\pi\) | |||||||
\(644\) | −5.74820e23 | −0.00118882 | ||||||||
\(645\) | −3.27527e26 | −0.667466 | ||||||||
\(646\) | 2.68066e26 | 0.538311 | ||||||||
\(647\) | −3.57860e26 | −0.708146 | −0.354073 | − | 0.935218i | \(-0.615204\pi\) | ||||
−0.354073 | + | 0.935218i | \(0.615204\pi\) | |||||||
\(648\) | 9.01163e25 | 0.175728 | ||||||||
\(649\) | 3.67391e26 | 0.705999 | ||||||||
\(650\) | 4.29536e26 | 0.813435 | ||||||||
\(651\) | −9.81282e21 | −1.83136e−5 0 | ||||||||
\(652\) | 2.02423e26 | 0.372313 | ||||||||
\(653\) | 5.10990e26 | 0.926269 | 0.463135 | − | 0.886288i | \(-0.346725\pi\) | ||||
0.463135 | + | 0.886288i | \(0.346725\pi\) | |||||||
\(654\) | 8.34882e26 | 1.49155 | ||||||||
\(655\) | −8.24568e26 | −1.45189 | ||||||||
\(656\) | 3.69940e26 | 0.642014 | ||||||||
\(657\) | −1.22355e26 | −0.209291 | ||||||||
\(658\) | 3.71249e23 | 0.000625920 0 | ||||||||
\(659\) | −6.67000e26 | −1.10844 | −0.554222 | − | 0.832369i | \(-0.686984\pi\) | ||||
−0.554222 | + | 0.832369i | \(0.686984\pi\) | |||||||
\(660\) | 1.74073e27 | 2.85144 | ||||||||
\(661\) | 2.27178e26 | 0.366819 | 0.183410 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183410 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(662\) | 4.75827e26 | 0.757352 | ||||||||
\(663\) | 9.22779e25 | 0.144784 | ||||||||
\(664\) | −9.89202e26 | −1.52999 | ||||||||
\(665\) | −8.92348e23 | −0.00136059 | ||||||||
\(666\) | −3.44985e26 | −0.518556 | ||||||||
\(667\) | −3.37674e26 | −0.500382 | ||||||||
\(668\) | −2.58400e27 | −3.77500 | ||||||||
\(669\) | 3.72498e26 | 0.536508 | ||||||||
\(670\) | 2.42125e27 | 3.43818 | ||||||||
\(671\) | 4.71450e26 | 0.660043 | ||||||||
\(672\) | 2.08192e23 | 0.000287380 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 | ||||||||
\(675\) | −1.96795e26 | −0.260393 | ||||||||
\(676\) | −1.29297e27 | −1.68692 | ||||||||
\(677\) | 4.27674e26 | 0.550200 | 0.275100 | − | 0.961416i | \(-0.411289\pi\) | ||||
0.275100 | + | 0.961416i | \(0.411289\pi\) | |||||||
\(678\) | −1.34018e27 | −1.70012 | ||||||||
\(679\) | 1.33775e24 | 0.00167345 | ||||||||
\(680\) | −1.40296e27 | −1.73066 | ||||||||
\(681\) | −4.76614e26 | −0.579788 | ||||||||
\(682\) | −3.76290e25 | −0.0451409 | ||||||||
\(683\) | −1.11866e26 | −0.132344 | −0.0661719 | − | 0.997808i | \(-0.521079\pi\) | ||||
−0.0661719 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(684\) | −2.42642e26 | −0.283095 | ||||||||
\(685\) | −7.41805e26 | −0.853551 | ||||||||
\(686\) | −6.05892e24 | −0.00687569 | ||||||||
\(687\) | 6.49473e26 | 0.726896 | ||||||||
\(688\) | 5.32543e26 | 0.587847 | ||||||||
\(689\) | 1.41779e26 | 0.154358 | ||||||||
\(690\) | 4.33373e26 | 0.465367 | ||||||||
\(691\) | 1.82536e27 | 1.93333 | 0.966667 | − | 0.256037i | \(-0.0824171\pi\) | ||||
0.966667 | + | 0.256037i | \(0.0824171\pi\) | |||||||
\(692\) | 2.88924e27 | 3.01839 | ||||||||
\(693\) | −1.08771e24 | −0.00112085 | ||||||||
\(694\) | −1.06102e26 | −0.107847 | ||||||||
\(695\) | −1.58198e27 | −1.58615 | ||||||||
\(696\) | −1.50355e27 | −1.48706 | ||||||||
\(697\) | −6.01839e26 | −0.587177 | ||||||||
\(698\) | −1.37817e27 | −1.32641 | ||||||||
\(699\) | 1.77045e26 | 0.168093 | ||||||||
\(700\) | 5.58937e24 | 0.00523518 | ||||||||
\(701\) | −2.03227e27 | −1.87785 | −0.938924 | − | 0.344125i | \(-0.888176\pi\) | ||||
−0.938924 | + | 0.344125i | \(0.888176\pi\) | |||||||
\(702\) | −1.26921e26 | −0.115699 | ||||||||
\(703\) | 4.46292e26 | 0.401369 | ||||||||
\(704\) | 2.26883e27 | 2.01308 | ||||||||
\(705\) | −1.84197e26 | −0.161245 | ||||||||
\(706\) | −2.77070e27 | −2.39301 | ||||||||
\(707\) | 1.88955e23 | 0.000161017 0 | ||||||||
\(708\) | 5.57840e26 | 0.469023 | ||||||||
\(709\) | −1.86039e27 | −1.54335 | −0.771675 | − | 0.636017i | \(-0.780581\pi\) | ||||
−0.771675 | + | 0.636017i | \(0.780581\pi\) | |||||||
\(710\) | 2.65499e27 | 2.17324 | ||||||||
\(711\) | 7.09091e26 | 0.572718 | ||||||||
\(712\) | 3.45742e27 | 2.75544 | ||||||||
\(713\) | −6.16510e24 | −0.00484830 | ||||||||
\(714\) | 1.82462e24 | 0.00141592 | ||||||||
\(715\) | −1.17793e27 | −0.902009 | ||||||||
\(716\) | 3.82529e26 | 0.289062 | ||||||||
\(717\) | −2.41807e26 | −0.180317 | ||||||||
\(718\) | 2.51234e27 | 1.84883 | ||||||||
\(719\) | 1.92780e27 | 1.40003 | 0.700014 | − | 0.714129i | \(-0.253177\pi\) | ||||
0.700014 | + | 0.714129i | \(0.253177\pi\) | |||||||
\(720\) | 5.56469e26 | 0.398825 | ||||||||
\(721\) | −4.22798e24 | −0.00299053 | ||||||||
\(722\) | −1.97293e27 | −1.37724 | ||||||||
\(723\) | 8.82414e26 | 0.607937 | ||||||||
\(724\) | −3.18462e27 | −2.16541 | ||||||||
\(725\) | 3.28343e27 | 2.20352 | ||||||||
\(726\) | −2.68036e27 | −1.77539 | ||||||||
\(727\) | −1.11559e27 | −0.729339 | −0.364670 | − | 0.931137i | \(-0.618818\pi\) | ||||
−0.364670 | + | 0.931137i | \(0.618818\pi\) | |||||||
\(728\) | 1.73196e24 | 0.00111761 | ||||||||
\(729\) | 5.81497e25 | 0.0370370 | ||||||||
\(730\) | −2.61999e27 | −1.64715 | ||||||||
\(731\) | −8.66372e26 | −0.537637 | ||||||||
\(732\) | 7.15842e26 | 0.438492 | ||||||||
\(733\) | 2.04762e27 | 1.23812 | 0.619059 | − | 0.785344i | \(-0.287514\pi\) | ||||
0.619059 | + | 0.785344i | \(0.287514\pi\) | |||||||
\(734\) | −2.51868e27 | −1.50335 | ||||||||
\(735\) | 1.50308e27 | 0.885630 | ||||||||
\(736\) | 1.30801e26 | 0.0760802 | ||||||||
\(737\) | −3.81802e27 | −2.19229 | ||||||||
\(738\) | 8.27782e26 | 0.469224 | ||||||||
\(739\) | 1.50373e27 | 0.841486 | 0.420743 | − | 0.907180i | \(-0.361769\pi\) | ||||
0.420743 | + | 0.907180i | \(0.361769\pi\) | |||||||
\(740\) | −4.86146e27 | −2.68575 | ||||||||
\(741\) | 1.64192e26 | 0.0895527 | ||||||||
\(742\) | 2.80341e24 | 0.00150956 | ||||||||
\(743\) | 1.88836e27 | 1.00390 | 0.501950 | − | 0.864897i | \(-0.332616\pi\) | ||||
0.501950 | + | 0.864897i | \(0.332616\pi\) | |||||||
\(744\) | −2.74511e25 | −0.0144084 | ||||||||
\(745\) | 1.37878e27 | 0.714514 | ||||||||
\(746\) | −9.63821e26 | −0.493149 | ||||||||
\(747\) | −6.38306e26 | −0.322466 | ||||||||
\(748\) | 4.60457e27 | 2.29681 | ||||||||
\(749\) | 5.55638e24 | 0.00273662 | ||||||||
\(750\) | −1.09953e27 | −0.534716 | ||||||||
\(751\) | 8.19244e26 | 0.393400 | 0.196700 | − | 0.980464i | \(-0.436978\pi\) | ||||
0.196700 | + | 0.980464i | \(0.436978\pi\) | |||||||
\(752\) | 2.99495e26 | 0.142011 | ||||||||
\(753\) | −7.58037e26 | −0.354926 | ||||||||
\(754\) | 2.11762e27 | 0.979082 | ||||||||
\(755\) | −1.50365e27 | −0.686518 | ||||||||
\(756\) | −1.65157e24 | −0.000744628 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 | ||||||||
\(759\) | −6.83378e26 | −0.296732 | ||||||||
\(760\) | −2.49632e27 | −1.07046 | ||||||||
\(761\) | 2.40135e27 | 1.01695 | 0.508477 | − | 0.861076i | \(-0.330209\pi\) | ||||
0.508477 | + | 0.861076i | \(0.330209\pi\) | |||||||
\(762\) | 2.13670e27 | 0.893659 | ||||||||
\(763\) | −7.35147e24 | −0.00303663 | ||||||||
\(764\) | 2.82223e27 | 1.15134 | ||||||||
\(765\) | −9.05296e26 | −0.364760 | ||||||||
\(766\) | −3.83018e27 | −1.52421 | ||||||||
\(767\) | −3.77482e26 | −0.148368 | ||||||||
\(768\) | 2.81516e27 | 1.09288 | ||||||||
\(769\) | −3.49979e27 | −1.34197 | −0.670984 | − | 0.741472i | \(-0.734128\pi\) | ||||
−0.670984 | + | 0.741472i | \(0.734128\pi\) | |||||||
\(770\) | −2.32913e25 | −0.00882128 | ||||||||
\(771\) | −1.78588e27 | −0.668091 | ||||||||
\(772\) | −7.41002e26 | −0.273814 | ||||||||
\(773\) | −3.84483e27 | −1.40337 | −0.701685 | − | 0.712487i | \(-0.747569\pi\) | ||||
−0.701685 | + | 0.712487i | \(0.747569\pi\) | |||||||
\(774\) | 1.19163e27 | 0.429636 | ||||||||
\(775\) | 5.99475e25 | 0.0213503 | ||||||||
\(776\) | 3.74233e27 | 1.31661 | ||||||||
\(777\) | 3.03774e24 | 0.00105572 | ||||||||
\(778\) | −5.67774e27 | −1.94926 | ||||||||
\(779\) | −1.07086e27 | −0.363186 | ||||||||
\(780\) | −1.78854e27 | −0.599240 | ||||||||
\(781\) | −4.18661e27 | −1.38573 | ||||||||
\(782\) | 1.14636e27 | 0.374848 | ||||||||
\(783\) | −9.70201e26 | −0.313419 | ||||||||
\(784\) | −2.44394e27 | −0.779987 | ||||||||
\(785\) | 2.09830e27 | 0.661615 | ||||||||
\(786\) | 2.99999e27 | 0.934556 | ||||||||
\(787\) | 4.22212e27 | 1.29948 | 0.649741 | − | 0.760155i | \(-0.274877\pi\) | ||||
0.649741 | + | 0.760155i | \(0.274877\pi\) | |||||||
\(788\) | −5.37384e27 | −1.63413 | ||||||||
\(789\) | 5.04054e25 | 0.0151442 | ||||||||
\(790\) | 1.51838e28 | 4.50737 | ||||||||
\(791\) | 1.18008e25 | 0.00346127 | ||||||||
\(792\) | −3.04286e27 | −0.881845 | ||||||||
\(793\) | −4.84399e26 | −0.138710 | ||||||||
\(794\) | 6.96142e27 | 1.96971 | ||||||||
\(795\) | −1.39093e27 | −0.388881 | ||||||||
\(796\) | −2.56879e27 | −0.709667 | ||||||||
\(797\) | −2.10706e27 | −0.575205 | −0.287602 | − | 0.957750i | \(-0.592858\pi\) | ||||
−0.287602 | + | 0.957750i | \(0.592858\pi\) | |||||||
\(798\) | 3.24659e24 | 0.000875789 0 | ||||||||
\(799\) | −4.87237e26 | −0.129881 | ||||||||
\(800\) | −1.27187e27 | −0.335033 | ||||||||
\(801\) | 2.23098e27 | 0.580747 | ||||||||
\(802\) | −1.03340e28 | −2.65835 | ||||||||
\(803\) | 4.13142e27 | 1.05027 | ||||||||
\(804\) | −5.79722e27 | −1.45642 | ||||||||
\(805\) | −3.81602e24 | −0.000947436 0 | ||||||||
\(806\) | 3.86625e25 | 0.00948652 | ||||||||
\(807\) | −7.53027e26 | −0.182605 | ||||||||
\(808\) | 5.28596e26 | 0.126682 | ||||||||
\(809\) | 2.31386e27 | 0.548056 | 0.274028 | − | 0.961722i | \(-0.411644\pi\) | ||||
0.274028 | + | 0.961722i | \(0.411644\pi\) | |||||||
\(810\) | 1.24516e27 | 0.291487 | ||||||||
\(811\) | 2.32427e27 | 0.537760 | 0.268880 | − | 0.963174i | \(-0.413347\pi\) | ||||
0.268880 | + | 0.963174i | \(0.413347\pi\) | |||||||
\(812\) | 2.75556e25 | 0.00630127 | ||||||||
\(813\) | −7.18148e26 | −0.162313 | ||||||||
\(814\) | 1.16487e28 | 2.60224 | ||||||||
\(815\) | 1.34382e27 | 0.296717 | ||||||||
\(816\) | 1.47197e27 | 0.321249 | ||||||||
\(817\) | −1.54155e27 | −0.332544 | ||||||||
\(818\) | −1.35125e28 | −2.88124 | ||||||||
\(819\) | 1.11759e24 | 0.000235551 0 | ||||||||
\(820\) | 1.16649e28 | 2.43025 | ||||||||
\(821\) | 6.08231e27 | 1.25259 | 0.626295 | − | 0.779587i | \(-0.284571\pi\) | ||||
0.626295 | + | 0.779587i | \(0.284571\pi\) | |||||||
\(822\) | 2.69888e27 | 0.549415 | ||||||||
\(823\) | −3.84390e27 | −0.773523 | −0.386762 | − | 0.922180i | \(-0.626406\pi\) | ||||
−0.386762 | + | 0.922180i | \(0.626406\pi\) | |||||||
\(824\) | −1.18277e28 | −2.35283 | ||||||||
\(825\) | 6.64496e27 | 1.30671 | ||||||||
\(826\) | −7.46400e24 | −0.00145098 | ||||||||
\(827\) | 5.47093e27 | 1.05138 | 0.525689 | − | 0.850677i | \(-0.323807\pi\) | ||||
0.525689 | + | 0.850677i | \(0.323807\pi\) | |||||||
\(828\) | −1.03763e27 | −0.197131 | ||||||||
\(829\) | 8.53655e26 | 0.160330 | 0.0801649 | − | 0.996782i | \(-0.474455\pi\) | ||||
0.0801649 | + | 0.996782i | \(0.474455\pi\) | |||||||
\(830\) | −1.36681e28 | −2.53785 | ||||||||
\(831\) | −3.51482e27 | −0.645198 | ||||||||
\(832\) | −2.33115e27 | −0.423056 | ||||||||
\(833\) | 3.97594e27 | 0.713365 | ||||||||
\(834\) | 5.75564e27 | 1.02098 | ||||||||
\(835\) | −1.71543e28 | −3.00850 | ||||||||
\(836\) | 8.19301e27 | 1.42064 | ||||||||
\(837\) | −1.77135e25 | −0.00303677 | ||||||||
\(838\) | −1.67389e28 | −2.83732 | ||||||||
\(839\) | −8.76504e27 | −1.46898 | −0.734489 | − | 0.678621i | \(-0.762578\pi\) | ||||
−0.734489 | + | 0.678621i | \(0.762578\pi\) | |||||||
\(840\) | −1.69915e25 | −0.00281565 | ||||||||
\(841\) | 1.00841e28 | 1.65224 | ||||||||
\(842\) | 1.22740e28 | 1.98848 | ||||||||
\(843\) | 4.49287e27 | 0.719716 | ||||||||
\(844\) | 7.84716e27 | 1.24297 | ||||||||
\(845\) | −8.58357e27 | −1.34440 | ||||||||
\(846\) | 6.70155e26 | 0.103790 | ||||||||
\(847\) | 2.36016e25 | 0.00361451 | ||||||||
\(848\) | 2.26158e27 | 0.342493 | ||||||||
\(849\) | −3.69131e27 | −0.552786 | ||||||||
\(850\) | −1.11468e28 | −1.65071 | ||||||||
\(851\) | 1.90852e27 | 0.279489 | ||||||||
\(852\) | −6.35687e27 | −0.920592 | ||||||||
\(853\) | 4.55754e27 | 0.652702 | 0.326351 | − | 0.945249i | \(-0.394181\pi\) | ||||
0.326351 | + | 0.945249i | \(0.394181\pi\) | |||||||
\(854\) | −9.57809e24 | −0.00135653 | ||||||||
\(855\) | −1.61081e27 | −0.225614 | ||||||||
\(856\) | 1.55438e28 | 2.15307 | ||||||||
\(857\) | 8.72531e27 | 1.19526 | 0.597631 | − | 0.801771i | \(-0.296109\pi\) | ||||
0.597631 | + | 0.801771i | \(0.296109\pi\) | |||||||
\(858\) | 4.28559e27 | 0.580606 | ||||||||
\(859\) | −6.82608e27 | −0.914610 | −0.457305 | − | 0.889310i | \(-0.651185\pi\) | ||||
−0.457305 | + | 0.889310i | \(0.651185\pi\) | |||||||
\(860\) | 1.67921e28 | 2.22521 | ||||||||
\(861\) | −7.28895e24 | −0.000955290 0 | ||||||||
\(862\) | 2.36855e27 | 0.307018 | ||||||||
\(863\) | 1.70088e27 | 0.218058 | 0.109029 | − | 0.994039i | \(-0.465226\pi\) | ||||
0.109029 | + | 0.994039i | \(0.465226\pi\) | |||||||
\(864\) | 3.75816e26 | 0.0476535 | ||||||||
\(865\) | 1.91806e28 | 2.40552 | ||||||||
\(866\) | 7.14723e27 | 0.886580 | ||||||||
\(867\) | 2.31098e27 | 0.283540 | ||||||||
\(868\) | 5.03098e23 | 6.10542e−5 0 | ||||||||
\(869\) | −2.39431e28 | −2.87404 | ||||||||
\(870\) | −2.07750e28 | −2.46665 | ||||||||
\(871\) | 3.92289e27 | 0.460716 | ||||||||
\(872\) | −2.05656e28 | −2.38910 | ||||||||
\(873\) | 2.41483e27 | 0.277492 | ||||||||
\(874\) | 2.03973e27 | 0.231854 | ||||||||
\(875\) | 9.68176e24 | 0.00108862 | ||||||||
\(876\) | 6.27308e27 | 0.697737 | ||||||||
\(877\) | −9.69466e27 | −1.06669 | −0.533343 | − | 0.845899i | \(-0.679064\pi\) | ||||
−0.533343 | + | 0.845899i | \(0.679064\pi\) | |||||||
\(878\) | 1.00486e25 | 0.00109372 | ||||||||
\(879\) | −5.56274e27 | −0.598955 | ||||||||
\(880\) | −1.87897e28 | −2.00140 | ||||||||
\(881\) | −2.20901e27 | −0.232769 | −0.116385 | − | 0.993204i | \(-0.537131\pi\) | ||||
−0.116385 | + | 0.993204i | \(0.537131\pi\) | |||||||
\(882\) | −5.46858e27 | −0.570064 | ||||||||
\(883\) | −5.45945e27 | −0.563018 | −0.281509 | − | 0.959559i | \(-0.590835\pi\) | ||||
−0.281509 | + | 0.959559i | \(0.590835\pi\) | |||||||
\(884\) | −4.73104e27 | −0.482681 | ||||||||
\(885\) | 3.70330e27 | 0.373790 | ||||||||
\(886\) | 3.11718e27 | 0.311273 | ||||||||
\(887\) | 1.69664e28 | 1.67616 | 0.838081 | − | 0.545546i | \(-0.183678\pi\) | ||||
0.838081 | + | 0.545546i | \(0.183678\pi\) | |||||||
\(888\) | 8.49799e27 | 0.830602 | ||||||||
\(889\) | −1.88145e25 | −0.00181939 | ||||||||
\(890\) | 4.77721e28 | 4.57056 | ||||||||
\(891\) | −1.96348e27 | −0.185861 | ||||||||
\(892\) | −1.90978e28 | −1.78862 | ||||||||
\(893\) | −8.66950e26 | −0.0803351 | ||||||||
\(894\) | −5.01636e27 | −0.459920 | ||||||||
\(895\) | 2.53947e27 | 0.230369 | ||||||||
\(896\) | −4.05485e25 | −0.00363956 | ||||||||
\(897\) | 7.02148e26 | 0.0623592 | ||||||||
\(898\) | −1.33058e28 | −1.16927 | ||||||||
\(899\) | 2.95541e26 | 0.0256981 | ||||||||
\(900\) | 1.00896e28 | 0.868100 | ||||||||
\(901\) | −3.67927e27 | −0.313239 | ||||||||
\(902\) | −2.79508e28 | −2.35468 | ||||||||
\(903\) | −1.04927e25 | −0.000874692 0 | ||||||||
\(904\) | 3.30125e28 | 2.72319 | ||||||||
\(905\) | −2.11415e28 | −1.72574 | ||||||||
\(906\) | 5.47068e27 | 0.441899 | ||||||||
\(907\) | 1.06963e28 | 0.854996 | 0.427498 | − | 0.904016i | \(-0.359395\pi\) | ||||
0.427498 | + | 0.904016i | \(0.359395\pi\) | |||||||
\(908\) | 2.44357e28 | 1.93290 | ||||||||
\(909\) | 3.41089e26 | 0.0267000 | ||||||||
\(910\) | 2.39310e25 | 0.00185382 | ||||||||
\(911\) | −2.36272e28 | −1.81129 | −0.905645 | − | 0.424036i | \(-0.860613\pi\) | ||||
−0.905645 | + | 0.424036i | \(0.860613\pi\) | |||||||
\(912\) | 2.61910e27 | 0.198702 | ||||||||
\(913\) | 2.15530e28 | 1.61821 | ||||||||
\(914\) | 1.00197e28 | 0.744502 | ||||||||
\(915\) | 4.75222e27 | 0.349459 | ||||||||
\(916\) | −3.32982e28 | −2.42333 | ||||||||
\(917\) | −2.64161e25 | −0.00190265 | ||||||||
\(918\) | 3.29370e27 | 0.234789 | ||||||||
\(919\) | 4.79736e27 | 0.338458 | 0.169229 | − | 0.985577i | \(-0.445872\pi\) | ||||
0.169229 | + | 0.985577i | \(0.445872\pi\) | |||||||
\(920\) | −1.06752e28 | −0.745406 | ||||||||
\(921\) | 4.86208e27 | 0.336013 | ||||||||
\(922\) | 1.83363e28 | 1.25420 | ||||||||
\(923\) | 4.30160e27 | 0.291215 | ||||||||
\(924\) | 5.57666e25 | 0.00373672 | ||||||||
\(925\) | −1.85578e28 | −1.23078 | ||||||||
\(926\) | −3.28515e28 | −2.15651 | ||||||||
\(927\) | −7.63210e27 | −0.495891 | ||||||||
\(928\) | −6.27031e27 | −0.403258 | ||||||||
\(929\) | −4.77499e27 | −0.303965 | −0.151982 | − | 0.988383i | \(-0.548566\pi\) | ||||
−0.151982 | + | 0.988383i | \(0.548566\pi\) | |||||||
\(930\) | −3.79300e26 | −0.0238998 | ||||||||
\(931\) | 7.07446e27 | 0.441237 | ||||||||
\(932\) | −9.07699e27 | −0.560390 | ||||||||
\(933\) | −6.43881e27 | −0.393487 | ||||||||
\(934\) | 4.42658e28 | 2.67777 | ||||||||
\(935\) | 3.05681e28 | 1.83045 | ||||||||
\(936\) | 3.12643e27 | 0.185323 | ||||||||
\(937\) | −3.08658e27 | −0.181114 | −0.0905568 | − | 0.995891i | \(-0.528865\pi\) | ||||
−0.0905568 | + | 0.995891i | \(0.528865\pi\) | |||||||
\(938\) | 7.75677e25 | 0.00450562 | ||||||||
\(939\) | −7.34987e27 | −0.422627 | ||||||||
\(940\) | 9.44368e27 | 0.537560 | ||||||||
\(941\) | 2.51804e27 | 0.141893 | 0.0709466 | − | 0.997480i | \(-0.477398\pi\) | ||||
0.0709466 | + | 0.997480i | \(0.477398\pi\) | |||||||
\(942\) | −7.63414e27 | −0.425870 | ||||||||
\(943\) | −4.57943e27 | −0.252901 | ||||||||
\(944\) | −6.02139e27 | −0.329202 | ||||||||
\(945\) | −1.09642e25 | −0.000593435 0 | ||||||||
\(946\) | −4.02363e28 | −2.15602 | ||||||||
\(947\) | 8.85552e27 | 0.469774 | 0.234887 | − | 0.972023i | \(-0.424528\pi\) | ||||
0.234887 | + | 0.972023i | \(0.424528\pi\) | |||||||
\(948\) | −3.63547e28 | −1.90933 | ||||||||
\(949\) | −4.24489e27 | −0.220718 | ||||||||
\(950\) | −1.98337e28 | −1.02101 | ||||||||
\(951\) | 1.14854e27 | 0.0585370 | ||||||||
\(952\) | −4.49458e25 | −0.00226797 | ||||||||
\(953\) | 1.35516e28 | 0.677030 | 0.338515 | − | 0.940961i | \(-0.390075\pi\) | ||||
0.338515 | + | 0.940961i | \(0.390075\pi\) | |||||||
\(954\) | 5.06055e27 | 0.250315 | ||||||||
\(955\) | 1.87358e28 | 0.917570 | ||||||||
\(956\) | 1.23973e28 | 0.601144 | ||||||||
\(957\) | 3.27597e28 | 1.57281 | ||||||||
\(958\) | −3.56907e27 | −0.169661 | ||||||||
\(959\) | −2.37647e25 | −0.00111855 | ||||||||
\(960\) | 2.28698e28 | 1.06582 | ||||||||
\(961\) | −2.16653e28 | −0.999751 | ||||||||
\(962\) | −1.19687e28 | −0.546868 | ||||||||
\(963\) | 1.00300e28 | 0.453788 | ||||||||
\(964\) | −4.52409e28 | −2.02675 | ||||||||
\(965\) | −4.91925e27 | −0.218217 | ||||||||
\(966\) | 1.38837e25 | 0.000609848 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 | ||||||||
\(969\) | −4.26091e27 | −0.181730 | ||||||||
\(970\) | 5.17088e28 | 2.18390 | ||||||||
\(971\) | 2.37023e28 | 0.991308 | 0.495654 | − | 0.868520i | \(-0.334928\pi\) | ||||
0.495654 | + | 0.868520i | \(0.334928\pi\) | |||||||
\(972\) | −2.98131e27 | −0.123475 | ||||||||
\(973\) | −5.06808e25 | −0.00207860 | ||||||||
\(974\) | 7.46993e28 | 3.03394 | ||||||||
\(975\) | −6.82747e27 | −0.274610 | ||||||||
\(976\) | −7.72688e27 | −0.307773 | ||||||||
\(977\) | −6.97540e27 | −0.275151 | −0.137575 | − | 0.990491i | \(-0.543931\pi\) | ||||
−0.137575 | + | 0.990491i | \(0.543931\pi\) | |||||||
\(978\) | −4.88915e27 | −0.190992 | ||||||||
\(979\) | −7.53310e28 | −2.91433 | ||||||||
\(980\) | −7.70621e28 | −2.95252 | ||||||||
\(981\) | −1.32704e28 | −0.503535 | ||||||||
\(982\) | 5.20835e28 | 1.95722 | ||||||||
\(983\) | 1.96330e28 | 0.730683 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(984\) | −2.03907e28 | −0.751585 | ||||||||
\(985\) | −3.56750e28 | −1.30233 | ||||||||
\(986\) | −5.49538e28 | −1.98686 | ||||||||
\(987\) | −5.90099e24 | −0.000211306 0 | ||||||||
\(988\) | −8.41804e27 | −0.298552 | ||||||||
\(989\) | −6.59227e27 | −0.231564 | ||||||||
\(990\) | −4.20440e28 | −1.46275 | ||||||||
\(991\) | 4.20556e28 | 1.44918 | 0.724592 | − | 0.689178i | \(-0.242028\pi\) | ||||
0.724592 | + | 0.689178i | \(0.242028\pi\) | |||||||
\(992\) | −1.14481e26 | −0.00390725 | ||||||||
\(993\) | −7.56325e27 | −0.255676 | ||||||||
\(994\) | 8.50560e25 | 0.00284796 | ||||||||
\(995\) | −1.70533e28 | −0.565573 | ||||||||
\(996\) | 3.27256e28 | 1.07504 | ||||||||
\(997\) | −1.15418e28 | −0.375551 | −0.187776 | − | 0.982212i | \(-0.560128\pi\) | ||||
−0.187776 | + | 0.982212i | \(0.560128\pi\) | |||||||
\(998\) | −4.90816e28 | −1.58190 | ||||||||
\(999\) | 5.48353e27 | 0.175061 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3.20.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9.20.a.c.1.1 | 2 | |||
4.3 | odd | 2 | 48.20.a.j.1.2 | 2 | |||
5.2 | odd | 4 | 75.20.b.b.49.4 | 4 | |||
5.3 | odd | 4 | 75.20.b.b.49.1 | 4 | |||
5.4 | even | 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 | 1.1 | even | 1 | trivial | |
9.20.a.c.1.1 | 2 | 3.2 | odd | 2 | |||
48.20.a.j.1.2 | 2 | 4.3 | odd | 2 | |||
75.20.a.b.1.1 | 2 | 5.4 | even | 2 | |||
75.20.b.b.49.1 | 4 | 5.3 | odd | 4 | |||
75.20.b.b.49.4 | 4 | 5.2 | odd | 4 |