Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [242,10,Mod(1,242)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(242, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("242.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 242 = 2 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 242.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: | \(124.638672352\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{889}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 222 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-14.4081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 242.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0000 | 0.707107 | ||||||||
\(3\) | 123.672 | 0.881510 | 0.440755 | − | 0.897627i | \(-0.354711\pi\) | ||||
0.440755 | + | 0.897627i | \(0.354711\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 1185.58 | 0.848333 | 0.424166 | − | 0.905584i | \(-0.360567\pi\) | ||||
0.424166 | + | 0.905584i | \(0.360567\pi\) | |||||||
\(6\) | 1978.76 | 0.623322 | ||||||||
\(7\) | −1174.66 | −0.184914 | −0.0924570 | − | 0.995717i | \(-0.529472\pi\) | ||||
−0.0924570 | + | 0.995717i | \(0.529472\pi\) | |||||||
\(8\) | 4096.00 | 0.353553 | ||||||||
\(9\) | −4388.12 | −0.222940 | ||||||||
\(10\) | 18969.3 | 0.599862 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 31660.2 | 0.440755 | ||||||||
\(13\) | −82461.9 | −0.800771 | −0.400386 | − | 0.916347i | \(-0.631124\pi\) | ||||
−0.400386 | + | 0.916347i | \(0.631124\pi\) | |||||||
\(14\) | −18794.5 | −0.130754 | ||||||||
\(15\) | 146624. | 0.747814 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | −440826. | −1.28011 | −0.640055 | − | 0.768329i | \(-0.721089\pi\) | ||||
−0.640055 | + | 0.768329i | \(0.721089\pi\) | |||||||
\(18\) | −70209.9 | −0.157642 | ||||||||
\(19\) | −804401. | −1.41606 | −0.708030 | − | 0.706183i | \(-0.750416\pi\) | ||||
−0.708030 | + | 0.706183i | \(0.750416\pi\) | |||||||
\(20\) | 303509. | 0.424166 | ||||||||
\(21\) | −145273. | −0.163004 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −228403. | −0.170187 | −0.0850936 | − | 0.996373i | \(-0.527119\pi\) | ||||
−0.0850936 | + | 0.996373i | \(0.527119\pi\) | |||||||
\(24\) | 506562. | 0.311661 | ||||||||
\(25\) | −547523. | −0.280332 | ||||||||
\(26\) | −1.31939e6 | −0.566231 | ||||||||
\(27\) | −2.97693e6 | −1.07803 | ||||||||
\(28\) | −300712. | −0.0924570 | ||||||||
\(29\) | −2.28497e6 | −0.599914 | −0.299957 | − | 0.953953i | \(-0.596972\pi\) | ||||
−0.299957 | + | 0.953953i | \(0.596972\pi\) | |||||||
\(30\) | 2.34598e6 | 0.528784 | ||||||||
\(31\) | 2.56508e6 | 0.498853 | 0.249427 | − | 0.968394i | \(-0.419758\pi\) | ||||
0.249427 | + | 0.968394i | \(0.419758\pi\) | |||||||
\(32\) | 1.04858e6 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.05322e6 | −0.905175 | ||||||||
\(35\) | −1.39265e6 | −0.156869 | ||||||||
\(36\) | −1.12336e6 | −0.111470 | ||||||||
\(37\) | −4.68709e6 | −0.411146 | −0.205573 | − | 0.978642i | \(-0.565906\pi\) | ||||
−0.205573 | + | 0.978642i | \(0.565906\pi\) | |||||||
\(38\) | −1.28704e7 | −1.00131 | ||||||||
\(39\) | −1.01983e7 | −0.705888 | ||||||||
\(40\) | 4.85614e6 | 0.299931 | ||||||||
\(41\) | −3.30235e6 | −0.182514 | −0.0912569 | − | 0.995827i | \(-0.529088\pi\) | ||||
−0.0912569 | + | 0.995827i | \(0.529088\pi\) | |||||||
\(42\) | −2.32436e6 | −0.115261 | ||||||||
\(43\) | −7.81398e6 | −0.348549 | −0.174275 | − | 0.984697i | \(-0.555758\pi\) | ||||
−0.174275 | + | 0.984697i | \(0.555758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.20247e6 | −0.189127 | ||||||||
\(46\) | −3.65445e6 | −0.120341 | ||||||||
\(47\) | −2.85515e6 | −0.0853470 | −0.0426735 | − | 0.999089i | \(-0.513588\pi\) | ||||
−0.0426735 | + | 0.999089i | \(0.513588\pi\) | |||||||
\(48\) | 8.10500e6 | 0.220378 | ||||||||
\(49\) | −3.89738e7 | −0.965807 | ||||||||
\(50\) | −8.76036e6 | −0.198224 | ||||||||
\(51\) | −5.45181e7 | −1.12843 | ||||||||
\(52\) | −2.11103e7 | −0.400386 | ||||||||
\(53\) | 9.97047e6 | 0.173570 | 0.0867849 | − | 0.996227i | \(-0.472341\pi\) | ||||
0.0867849 | + | 0.996227i | \(0.472341\pi\) | |||||||
\(54\) | −4.76310e7 | −0.762285 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.81140e6 | −0.0653770 | ||||||||
\(57\) | −9.94823e7 | −1.24827 | ||||||||
\(58\) | −3.65595e7 | −0.424203 | ||||||||
\(59\) | 6.31658e7 | 0.678653 | 0.339326 | − | 0.940669i | \(-0.389801\pi\) | ||||
0.339326 | + | 0.940669i | \(0.389801\pi\) | |||||||
\(60\) | 3.75357e7 | 0.373907 | ||||||||
\(61\) | 2.12529e8 | 1.96532 | 0.982660 | − | 0.185414i | \(-0.0593627\pi\) | ||||
0.982660 | + | 0.185414i | \(0.0593627\pi\) | |||||||
\(62\) | 4.10412e7 | 0.352743 | ||||||||
\(63\) | 5.15454e6 | 0.0412247 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −9.77653e7 | −0.679320 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.27892e8 | −1.38163 | −0.690815 | − | 0.723031i | \(-0.742748\pi\) | ||||
−0.690815 | + | 0.723031i | \(0.742748\pi\) | |||||||
\(68\) | −1.12852e8 | −0.640055 | ||||||||
\(69\) | −2.82472e7 | −0.150022 | ||||||||
\(70\) | −2.22824e7 | −0.110923 | ||||||||
\(71\) | −1.55605e8 | −0.726708 | −0.363354 | − | 0.931651i | \(-0.618368\pi\) | ||||
−0.363354 | + | 0.931651i | \(0.618368\pi\) | |||||||
\(72\) | −1.79737e7 | −0.0788211 | ||||||||
\(73\) | 1.04177e8 | 0.429357 | 0.214679 | − | 0.976685i | \(-0.431130\pi\) | ||||
0.214679 | + | 0.976685i | \(0.431130\pi\) | |||||||
\(74\) | −7.49935e7 | −0.290724 | ||||||||
\(75\) | −6.77135e7 | −0.247115 | ||||||||
\(76\) | −2.05927e8 | −0.708030 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.63172e8 | −0.499138 | ||||||||
\(79\) | 2.96624e8 | 0.856811 | 0.428405 | − | 0.903587i | \(-0.359076\pi\) | ||||
0.428405 | + | 0.903587i | \(0.359076\pi\) | |||||||
\(80\) | 7.76982e7 | 0.212083 | ||||||||
\(81\) | −2.81793e8 | −0.727358 | ||||||||
\(82\) | −5.28376e7 | −0.129057 | ||||||||
\(83\) | 7.38793e8 | 1.70872 | 0.854361 | − | 0.519680i | \(-0.173949\pi\) | ||||
0.854361 | + | 0.519680i | \(0.173949\pi\) | |||||||
\(84\) | −3.71898e7 | −0.0815018 | ||||||||
\(85\) | −5.22635e8 | −1.08596 | ||||||||
\(86\) | −1.25024e8 | −0.246462 | ||||||||
\(87\) | −2.82588e8 | −0.528830 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00049e8 | 1.52059 | 0.760293 | − | 0.649580i | \(-0.225055\pi\) | ||||
0.760293 | + | 0.649580i | \(0.225055\pi\) | |||||||
\(90\) | −8.32396e7 | −0.133733 | ||||||||
\(91\) | 9.68645e7 | 0.148074 | ||||||||
\(92\) | −5.84712e7 | −0.0850936 | ||||||||
\(93\) | 3.17229e8 | 0.439744 | ||||||||
\(94\) | −4.56823e7 | −0.0603494 | ||||||||
\(95\) | −9.53683e8 | −1.20129 | ||||||||
\(96\) | 1.29680e8 | 0.155830 | ||||||||
\(97\) | 1.29157e9 | 1.48131 | 0.740653 | − | 0.671888i | \(-0.234516\pi\) | ||||
0.740653 | + | 0.671888i | \(0.234516\pi\) | |||||||
\(98\) | −6.23581e8 | −0.682929 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.40166e8 | −0.140166 | ||||||||
\(101\) | −1.45652e9 | −1.39275 | −0.696373 | − | 0.717681i | \(-0.745204\pi\) | ||||
−0.696373 | + | 0.717681i | \(0.745204\pi\) | |||||||
\(102\) | −8.72289e8 | −0.797921 | ||||||||
\(103\) | −1.95971e9 | −1.71563 | −0.857814 | − | 0.513960i | \(-0.828178\pi\) | ||||
−0.857814 | + | 0.513960i | \(0.828178\pi\) | |||||||
\(104\) | −3.37764e8 | −0.283115 | ||||||||
\(105\) | −1.72233e8 | −0.138281 | ||||||||
\(106\) | 1.59528e8 | 0.122732 | ||||||||
\(107\) | −6.07627e8 | −0.448136 | −0.224068 | − | 0.974573i | \(-0.571934\pi\) | ||||
−0.224068 | + | 0.974573i | \(0.571934\pi\) | |||||||
\(108\) | −7.62095e8 | −0.539017 | ||||||||
\(109\) | 1.14761e9 | 0.778708 | 0.389354 | − | 0.921088i | \(-0.372698\pi\) | ||||
0.389354 | + | 0.921088i | \(0.372698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.79664e8 | −0.362429 | ||||||||
\(112\) | −7.69823e7 | −0.0462285 | ||||||||
\(113\) | −2.54053e8 | −0.146579 | −0.0732895 | − | 0.997311i | \(-0.523350\pi\) | ||||
−0.0732895 | + | 0.997311i | \(0.523350\pi\) | |||||||
\(114\) | −1.59172e9 | −0.882661 | ||||||||
\(115\) | −2.70790e8 | −0.144375 | ||||||||
\(116\) | −5.84952e8 | −0.299957 | ||||||||
\(117\) | 3.61853e8 | 0.178524 | ||||||||
\(118\) | 1.01065e9 | 0.479880 | ||||||||
\(119\) | 5.17820e8 | 0.236710 | ||||||||
\(120\) | 6.00571e8 | 0.264392 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.40046e9 | 1.38969 | ||||||||
\(123\) | −4.08410e8 | −0.160888 | ||||||||
\(124\) | 6.56660e8 | 0.249427 | ||||||||
\(125\) | −2.96472e9 | −1.08615 | ||||||||
\(126\) | 8.24726e7 | 0.0291502 | ||||||||
\(127\) | 1.26227e8 | 0.0430561 | 0.0215280 | − | 0.999768i | \(-0.493147\pi\) | ||||
0.0215280 | + | 0.999768i | \(0.493147\pi\) | |||||||
\(128\) | 2.68435e8 | 0.0883883 | ||||||||
\(129\) | −9.66374e8 | −0.307250 | ||||||||
\(130\) | −1.56425e9 | −0.480352 | ||||||||
\(131\) | 1.87859e9 | 0.557328 | 0.278664 | − | 0.960389i | \(-0.410108\pi\) | ||||
0.278664 | + | 0.960389i | \(0.410108\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.44895e8 | 0.261849 | ||||||||
\(134\) | −3.64627e9 | −0.976960 | ||||||||
\(135\) | −3.52940e9 | −0.914531 | ||||||||
\(136\) | −1.80563e9 | −0.452587 | ||||||||
\(137\) | 6.32338e9 | 1.53358 | 0.766791 | − | 0.641897i | \(-0.221852\pi\) | ||||
0.766791 | + | 0.641897i | \(0.221852\pi\) | |||||||
\(138\) | −4.51955e8 | −0.106081 | ||||||||
\(139\) | 7.82379e9 | 1.77767 | 0.888833 | − | 0.458230i | \(-0.151517\pi\) | ||||
0.888833 | + | 0.458230i | \(0.151517\pi\) | |||||||
\(140\) | −3.56519e8 | −0.0784343 | ||||||||
\(141\) | −3.53103e8 | −0.0752342 | ||||||||
\(142\) | −2.48967e9 | −0.513860 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.87580e8 | −0.0557349 | ||||||||
\(145\) | −2.70901e9 | −0.508927 | ||||||||
\(146\) | 1.66683e9 | 0.303602 | ||||||||
\(147\) | −4.81998e9 | −0.851369 | ||||||||
\(148\) | −1.19990e9 | −0.205573 | ||||||||
\(149\) | 2.69524e8 | 0.0447981 | 0.0223991 | − | 0.999749i | \(-0.492870\pi\) | ||||
0.0223991 | + | 0.999749i | \(0.492870\pi\) | |||||||
\(150\) | −1.08342e9 | −0.174737 | ||||||||
\(151\) | −1.18223e10 | −1.85057 | −0.925286 | − | 0.379270i | \(-0.876175\pi\) | ||||
−0.925286 | + | 0.379270i | \(0.876175\pi\) | |||||||
\(152\) | −3.29483e9 | −0.500653 | ||||||||
\(153\) | 1.93440e9 | 0.285387 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.04111e9 | 0.423194 | ||||||||
\(156\) | −2.61076e9 | −0.352944 | ||||||||
\(157\) | 3.66990e9 | 0.482065 | 0.241032 | − | 0.970517i | \(-0.422514\pi\) | ||||
0.241032 | + | 0.970517i | \(0.422514\pi\) | |||||||
\(158\) | 4.74599e9 | 0.605857 | ||||||||
\(159\) | 1.23307e9 | 0.153004 | ||||||||
\(160\) | 1.24317e9 | 0.149965 | ||||||||
\(161\) | 2.68295e8 | 0.0314700 | ||||||||
\(162\) | −4.50870e9 | −0.514320 | ||||||||
\(163\) | −1.30610e10 | −1.44921 | −0.724605 | − | 0.689165i | \(-0.757978\pi\) | ||||
−0.724605 | + | 0.689165i | \(0.757978\pi\) | |||||||
\(164\) | −8.45401e8 | −0.0912569 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.18207e10 | 1.20825 | ||||||||
\(167\) | 1.16911e9 | 0.116314 | 0.0581571 | − | 0.998307i | \(-0.481478\pi\) | ||||
0.0581571 | + | 0.998307i | \(0.481478\pi\) | |||||||
\(168\) | −5.95037e8 | −0.0576305 | ||||||||
\(169\) | −3.80453e9 | −0.358765 | ||||||||
\(170\) | −8.36217e9 | −0.767889 | ||||||||
\(171\) | 3.52981e9 | 0.315696 | ||||||||
\(172\) | −2.00038e9 | −0.174275 | ||||||||
\(173\) | −1.90893e10 | −1.62025 | −0.810124 | − | 0.586258i | \(-0.800601\pi\) | ||||
−0.810124 | + | 0.586258i | \(0.800601\pi\) | |||||||
\(174\) | −4.52140e9 | −0.373940 | ||||||||
\(175\) | 6.43151e8 | 0.0518373 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.81187e9 | 0.598240 | ||||||||
\(178\) | 1.44008e10 | 1.07522 | ||||||||
\(179\) | −1.99470e10 | −1.45224 | −0.726122 | − | 0.687566i | \(-0.758679\pi\) | ||||
−0.726122 | + | 0.687566i | \(0.758679\pi\) | |||||||
\(180\) | −1.33183e9 | −0.0945635 | ||||||||
\(181\) | −8.20947e9 | −0.568541 | −0.284270 | − | 0.958744i | \(-0.591751\pi\) | ||||
−0.284270 | + | 0.958744i | \(0.591751\pi\) | |||||||
\(182\) | 1.54983e9 | 0.104704 | ||||||||
\(183\) | 2.62840e10 | 1.73245 | ||||||||
\(184\) | −9.35539e8 | −0.0601703 | ||||||||
\(185\) | −5.55693e9 | −0.348788 | ||||||||
\(186\) | 5.07567e9 | 0.310946 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.30918e8 | −0.0426735 | ||||||||
\(189\) | 3.49688e9 | 0.199344 | ||||||||
\(190\) | −1.52589e10 | −0.849440 | ||||||||
\(191\) | 1.24525e10 | 0.677027 | 0.338513 | − | 0.940962i | \(-0.390076\pi\) | ||||
0.338513 | + | 0.940962i | \(0.390076\pi\) | |||||||
\(192\) | 2.07488e9 | 0.110189 | ||||||||
\(193\) | −1.60846e9 | −0.0834456 | −0.0417228 | − | 0.999129i | \(-0.513285\pi\) | ||||
−0.0417228 | + | 0.999129i | \(0.513285\pi\) | |||||||
\(194\) | 2.06651e10 | 1.04744 | ||||||||
\(195\) | −1.20909e10 | −0.598828 | ||||||||
\(196\) | −9.97729e9 | −0.482903 | ||||||||
\(197\) | −4.02780e10 | −1.90533 | −0.952664 | − | 0.304024i | \(-0.901670\pi\) | ||||
−0.952664 | + | 0.304024i | \(0.901670\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.22083e10 | 1.45589 | 0.727945 | − | 0.685636i | \(-0.240476\pi\) | ||||
0.727945 | + | 0.685636i | \(0.240476\pi\) | |||||||
\(200\) | −2.24265e9 | −0.0991122 | ||||||||
\(201\) | −2.81839e10 | −1.21792 | ||||||||
\(202\) | −2.33044e10 | −0.984819 | ||||||||
\(203\) | 2.68405e9 | 0.110933 | ||||||||
\(204\) | −1.39566e10 | −0.564215 | ||||||||
\(205\) | −3.91520e9 | −0.154832 | ||||||||
\(206\) | −3.13553e10 | −1.21313 | ||||||||
\(207\) | 1.00226e9 | 0.0379415 | ||||||||
\(208\) | −5.40423e9 | −0.200193 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.75572e9 | −0.0977796 | ||||||||
\(211\) | −1.06111e10 | −0.368544 | −0.184272 | − | 0.982875i | \(-0.558993\pi\) | ||||
−0.184272 | + | 0.982875i | \(0.558993\pi\) | |||||||
\(212\) | 2.55244e9 | 0.0867849 | ||||||||
\(213\) | −1.92440e10 | −0.640601 | ||||||||
\(214\) | −9.72203e9 | −0.316880 | ||||||||
\(215\) | −9.26410e9 | −0.295686 | ||||||||
\(216\) | −1.21935e10 | −0.381143 | ||||||||
\(217\) | −3.01309e9 | −0.0922450 | ||||||||
\(218\) | 1.83618e10 | 0.550630 | ||||||||
\(219\) | 1.28838e10 | 0.378483 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.63514e10 | 1.02508 | ||||||||
\(222\) | −9.27463e9 | −0.256276 | ||||||||
\(223\) | −2.11175e10 | −0.571835 | −0.285918 | − | 0.958254i | \(-0.592298\pi\) | ||||
−0.285918 | + | 0.958254i | \(0.592298\pi\) | |||||||
\(224\) | −1.23172e9 | −0.0326885 | ||||||||
\(225\) | 2.40260e9 | 0.0624970 | ||||||||
\(226\) | −4.06485e9 | −0.103647 | ||||||||
\(227\) | 5.33286e9 | 0.133304 | 0.0666521 | − | 0.997776i | \(-0.478768\pi\) | ||||
0.0666521 | + | 0.997776i | \(0.478768\pi\) | |||||||
\(228\) | −2.54675e10 | −0.624135 | ||||||||
\(229\) | −2.62407e10 | −0.630545 | −0.315272 | − | 0.949001i | \(-0.602096\pi\) | ||||
−0.315272 | + | 0.949001i | \(0.602096\pi\) | |||||||
\(230\) | −4.33265e9 | −0.102089 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.35923e9 | −0.212102 | ||||||||
\(233\) | −4.77174e10 | −1.06066 | −0.530329 | − | 0.847792i | \(-0.677932\pi\) | ||||
−0.530329 | + | 0.847792i | \(0.677932\pi\) | |||||||
\(234\) | 5.78965e9 | 0.126235 | ||||||||
\(235\) | −3.38501e9 | −0.0724026 | ||||||||
\(236\) | 1.61704e10 | 0.339326 | ||||||||
\(237\) | 3.66843e10 | 0.755287 | ||||||||
\(238\) | 8.28512e9 | 0.167380 | ||||||||
\(239\) | 2.64340e10 | 0.524050 | 0.262025 | − | 0.965061i | \(-0.415610\pi\) | ||||
0.262025 | + | 0.965061i | \(0.415610\pi\) | |||||||
\(240\) | 9.60913e9 | 0.186953 | ||||||||
\(241\) | 4.95287e10 | 0.945758 | 0.472879 | − | 0.881127i | \(-0.343215\pi\) | ||||
0.472879 | + | 0.881127i | \(0.343215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.37449e10 | 0.436860 | ||||||||
\(244\) | 5.44074e10 | 0.982660 | ||||||||
\(245\) | −4.62066e10 | −0.819325 | ||||||||
\(246\) | −6.53455e9 | −0.113765 | ||||||||
\(247\) | 6.63325e10 | 1.13394 | ||||||||
\(248\) | 1.05066e10 | 0.176371 | ||||||||
\(249\) | 9.13683e10 | 1.50626 | ||||||||
\(250\) | −4.74355e10 | −0.768022 | ||||||||
\(251\) | −8.76978e10 | −1.39462 | −0.697311 | − | 0.716768i | \(-0.745620\pi\) | ||||
−0.697311 | + | 0.716768i | \(0.745620\pi\) | |||||||
\(252\) | 1.31956e9 | 0.0206123 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.01963e9 | 0.0304453 | ||||||||
\(255\) | −6.46356e10 | −0.957285 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | −1.09539e11 | −1.56628 | −0.783140 | − | 0.621846i | \(-0.786383\pi\) | ||||
−0.783140 | + | 0.621846i | \(0.786383\pi\) | |||||||
\(258\) | −1.54620e10 | −0.217258 | ||||||||
\(259\) | 5.50573e9 | 0.0760266 | ||||||||
\(260\) | −2.50279e10 | −0.339660 | ||||||||
\(261\) | 1.00267e10 | 0.133745 | ||||||||
\(262\) | 3.00574e10 | 0.394091 | ||||||||
\(263\) | −4.08592e9 | −0.0526610 | −0.0263305 | − | 0.999653i | \(-0.508382\pi\) | ||||
−0.0263305 | + | 0.999653i | \(0.508382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.18208e10 | 0.147245 | ||||||||
\(266\) | 1.51183e10 | 0.185155 | ||||||||
\(267\) | 1.11311e11 | 1.34041 | ||||||||
\(268\) | −5.83403e10 | −0.690815 | ||||||||
\(269\) | −8.48247e10 | −0.987727 | −0.493864 | − | 0.869539i | \(-0.664416\pi\) | ||||
−0.493864 | + | 0.869539i | \(0.664416\pi\) | |||||||
\(270\) | −5.64704e10 | −0.646671 | ||||||||
\(271\) | −6.76455e10 | −0.761864 | −0.380932 | − | 0.924603i | \(-0.624397\pi\) | ||||
−0.380932 | + | 0.924603i | \(0.624397\pi\) | |||||||
\(272\) | −2.88900e10 | −0.320028 | ||||||||
\(273\) | 1.19795e10 | 0.130529 | ||||||||
\(274\) | 1.01174e11 | 1.08441 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.23128e9 | −0.0750109 | ||||||||
\(277\) | −1.22944e11 | −1.25472 | −0.627361 | − | 0.778728i | \(-0.715865\pi\) | ||||
−0.627361 | + | 0.778728i | \(0.715865\pi\) | |||||||
\(278\) | 1.25181e11 | 1.25700 | ||||||||
\(279\) | −1.12559e10 | −0.111214 | ||||||||
\(280\) | −5.70430e9 | −0.0554614 | ||||||||
\(281\) | 1.28901e11 | 1.23333 | 0.616664 | − | 0.787226i | \(-0.288484\pi\) | ||||
0.616664 | + | 0.787226i | \(0.288484\pi\) | |||||||
\(282\) | −5.64965e9 | −0.0531986 | ||||||||
\(283\) | −2.08828e10 | −0.193530 | −0.0967651 | − | 0.995307i | \(-0.530850\pi\) | ||||
−0.0967651 | + | 0.995307i | \(0.530850\pi\) | |||||||
\(284\) | −3.98348e10 | −0.363354 | ||||||||
\(285\) | −1.17944e11 | −1.05895 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.87913e9 | 0.0337494 | ||||||||
\(288\) | −4.60128e9 | −0.0394105 | ||||||||
\(289\) | 7.57401e10 | 0.638683 | ||||||||
\(290\) | −4.33442e10 | −0.359866 | ||||||||
\(291\) | 1.59731e11 | 1.30579 | ||||||||
\(292\) | 2.66693e10 | 0.214679 | ||||||||
\(293\) | −3.85968e9 | −0.0305948 | −0.0152974 | − | 0.999883i | \(-0.504869\pi\) | ||||
−0.0152974 | + | 0.999883i | \(0.504869\pi\) | |||||||
\(294\) | −7.71197e10 | −0.602009 | ||||||||
\(295\) | 7.48881e10 | 0.575723 | ||||||||
\(296\) | −1.91983e10 | −0.145362 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.31239e9 | 0.0316770 | ||||||||
\(299\) | 1.88346e10 | 0.136281 | ||||||||
\(300\) | −1.73347e10 | −0.123558 | ||||||||
\(301\) | 9.17874e9 | 0.0644516 | ||||||||
\(302\) | −1.89157e11 | −1.30855 | ||||||||
\(303\) | −1.80132e11 | −1.22772 | ||||||||
\(304\) | −5.27172e10 | −0.354015 | ||||||||
\(305\) | 2.51970e11 | 1.66725 | ||||||||
\(306\) | 3.09504e10 | 0.201799 | ||||||||
\(307\) | −4.11326e10 | −0.264279 | −0.132140 | − | 0.991231i | \(-0.542185\pi\) | ||||
−0.132140 | + | 0.991231i | \(0.542185\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.42362e11 | −1.51234 | ||||||||
\(310\) | 4.86577e10 | 0.299243 | ||||||||
\(311\) | −2.75638e11 | −1.67078 | −0.835388 | − | 0.549661i | \(-0.814757\pi\) | ||||
−0.835388 | + | 0.549661i | \(0.814757\pi\) | |||||||
\(312\) | −4.17721e10 | −0.249569 | ||||||||
\(313\) | 3.14160e11 | 1.85013 | 0.925064 | − | 0.379810i | \(-0.124011\pi\) | ||||
0.925064 | + | 0.379810i | \(0.124011\pi\) | |||||||
\(314\) | 5.87183e10 | 0.340871 | ||||||||
\(315\) | 6.11112e9 | 0.0349722 | ||||||||
\(316\) | 7.59358e10 | 0.428405 | ||||||||
\(317\) | 2.58171e11 | 1.43595 | 0.717977 | − | 0.696067i | \(-0.245068\pi\) | ||||
0.717977 | + | 0.696067i | \(0.245068\pi\) | |||||||
\(318\) | 1.97292e10 | 0.108190 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.98907e10 | 0.106042 | ||||||||
\(321\) | −7.51467e10 | −0.395037 | ||||||||
\(322\) | 4.29273e9 | 0.0222527 | ||||||||
\(323\) | 3.54601e11 | 1.81271 | ||||||||
\(324\) | −7.21391e10 | −0.363679 | ||||||||
\(325\) | 4.51498e10 | 0.224482 | ||||||||
\(326\) | −2.08975e11 | −1.02475 | ||||||||
\(327\) | 1.41928e11 | 0.686440 | ||||||||
\(328\) | −1.35264e10 | −0.0645284 | ||||||||
\(329\) | 3.35382e9 | 0.0157819 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.94811e10 | −0.272366 | −0.136183 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136183 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(332\) | 1.89131e11 | 0.854361 | ||||||||
\(333\) | 2.05675e10 | 0.0916607 | ||||||||
\(334\) | 1.87058e10 | 0.0822466 | ||||||||
\(335\) | −2.70184e11 | −1.17208 | ||||||||
\(336\) | −9.52059e9 | −0.0407509 | ||||||||
\(337\) | −9.61669e10 | −0.406154 | −0.203077 | − | 0.979163i | \(-0.565094\pi\) | ||||
−0.203077 | + | 0.979163i | \(0.565094\pi\) | |||||||
\(338\) | −6.08724e10 | −0.253685 | ||||||||
\(339\) | −3.14194e10 | −0.129211 | ||||||||
\(340\) | −1.33795e11 | −0.542980 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.64770e10 | 0.223231 | ||||||||
\(343\) | 9.31825e10 | 0.363505 | ||||||||
\(344\) | −3.20061e10 | −0.123231 | ||||||||
\(345\) | −3.34893e10 | −0.127268 | ||||||||
\(346\) | −3.05428e11 | −1.14569 | ||||||||
\(347\) | 3.65974e11 | 1.35509 | 0.677543 | − | 0.735483i | \(-0.263045\pi\) | ||||
0.677543 | + | 0.735483i | \(0.263045\pi\) | |||||||
\(348\) | −7.23424e10 | −0.264415 | ||||||||
\(349\) | 4.32258e11 | 1.55966 | 0.779828 | − | 0.625993i | \(-0.215306\pi\) | ||||
0.779828 | + | 0.625993i | \(0.215306\pi\) | |||||||
\(350\) | 1.02904e10 | 0.0366545 | ||||||||
\(351\) | 2.45484e11 | 0.863259 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.67882e11 | −1.26102 | −0.630511 | − | 0.776180i | \(-0.717155\pi\) | ||||
−0.630511 | + | 0.776180i | \(0.717155\pi\) | |||||||
\(354\) | 1.24990e11 | 0.423019 | ||||||||
\(355\) | −1.84482e11 | −0.616490 | ||||||||
\(356\) | 2.30413e11 | 0.760293 | ||||||||
\(357\) | 6.40401e10 | 0.208663 | ||||||||
\(358\) | −3.19152e11 | −1.02689 | ||||||||
\(359\) | 1.25751e11 | 0.399564 | 0.199782 | − | 0.979840i | \(-0.435977\pi\) | ||||
0.199782 | + | 0.979840i | \(0.435977\pi\) | |||||||
\(360\) | −2.13093e10 | −0.0668665 | ||||||||
\(361\) | 3.24374e11 | 1.00522 | ||||||||
\(362\) | −1.31352e11 | −0.402019 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.47973e10 | 0.0740369 | ||||||||
\(365\) | 1.23510e11 | 0.364238 | ||||||||
\(366\) | 4.20543e11 | 1.22503 | ||||||||
\(367\) | 5.19603e11 | 1.49511 | 0.747557 | − | 0.664197i | \(-0.231227\pi\) | ||||
0.747557 | + | 0.664197i | \(0.231227\pi\) | |||||||
\(368\) | −1.49686e10 | −0.0425468 | ||||||||
\(369\) | 1.44911e10 | 0.0406896 | ||||||||
\(370\) | −8.89109e10 | −0.246631 | ||||||||
\(371\) | −1.17119e10 | −0.0320955 | ||||||||
\(372\) | 8.12108e10 | 0.219872 | ||||||||
\(373\) | −4.65238e11 | −1.24447 | −0.622237 | − | 0.782829i | \(-0.713776\pi\) | ||||
−0.622237 | + | 0.782829i | \(0.713776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.66654e11 | −0.957450 | ||||||||
\(376\) | −1.16947e10 | −0.0301747 | ||||||||
\(377\) | 1.88423e11 | 0.480394 | ||||||||
\(378\) | 5.59500e10 | 0.140957 | ||||||||
\(379\) | 4.48793e11 | 1.11730 | 0.558650 | − | 0.829404i | \(-0.311320\pi\) | ||||
0.558650 | + | 0.829404i | \(0.311320\pi\) | |||||||
\(380\) | −2.44143e11 | −0.600645 | ||||||||
\(381\) | 1.56108e10 | 0.0379544 | ||||||||
\(382\) | 1.99240e11 | 0.478730 | ||||||||
\(383\) | 2.75704e11 | 0.654710 | 0.327355 | − | 0.944901i | \(-0.393843\pi\) | ||||
0.327355 | + | 0.944901i | \(0.393843\pi\) | |||||||
\(384\) | 3.31981e10 | 0.0779152 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.57354e10 | −0.0590049 | ||||||||
\(387\) | 3.42887e10 | 0.0777055 | ||||||||
\(388\) | 3.30641e11 | 0.740653 | ||||||||
\(389\) | 8.29663e11 | 1.83708 | 0.918540 | − | 0.395327i | \(-0.129369\pi\) | ||||
0.918540 | + | 0.395327i | \(0.129369\pi\) | |||||||
\(390\) | −1.93454e11 | −0.423435 | ||||||||
\(391\) | 1.00686e11 | 0.217858 | ||||||||
\(392\) | −1.59637e11 | −0.341464 | ||||||||
\(393\) | 2.32330e11 | 0.491290 | ||||||||
\(394\) | −6.44448e11 | −1.34727 | ||||||||
\(395\) | 3.51672e11 | 0.726861 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.53152e11 | 0.309432 | 0.154716 | − | 0.987959i | \(-0.450554\pi\) | ||||
0.154716 | + | 0.987959i | \(0.450554\pi\) | |||||||
\(398\) | 5.15332e11 | 1.02947 | ||||||||
\(399\) | 1.16858e11 | 0.230823 | ||||||||
\(400\) | −3.58824e10 | −0.0700829 | ||||||||
\(401\) | 2.05461e11 | 0.396807 | 0.198404 | − | 0.980120i | \(-0.436424\pi\) | ||||
0.198404 | + | 0.980120i | \(0.436424\pi\) | |||||||
\(402\) | −4.50943e11 | −0.861200 | ||||||||
\(403\) | −2.11521e11 | −0.399467 | ||||||||
\(404\) | −3.72870e11 | −0.696373 | ||||||||
\(405\) | −3.34089e11 | −0.617042 | ||||||||
\(406\) | 4.29448e10 | 0.0784411 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −2.23306e11 | −0.398960 | ||||||||
\(409\) | 6.57635e11 | 1.16206 | 0.581032 | − | 0.813880i | \(-0.302649\pi\) | ||||
0.581032 | + | 0.813880i | \(0.302649\pi\) | |||||||
\(410\) | −6.26432e10 | −0.109483 | ||||||||
\(411\) | 7.82029e11 | 1.35187 | ||||||||
\(412\) | −5.01685e11 | −0.857814 | ||||||||
\(413\) | −7.41981e10 | −0.125492 | ||||||||
\(414\) | 1.60362e10 | 0.0268287 | ||||||||
\(415\) | 8.75899e11 | 1.44956 | ||||||||
\(416\) | −8.64676e10 | −0.141558 | ||||||||
\(417\) | 9.67587e11 | 1.56703 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.79470e11 | −0.601471 | −0.300735 | − | 0.953708i | \(-0.597232\pi\) | ||||
−0.300735 | + | 0.953708i | \(0.597232\pi\) | |||||||
\(420\) | −4.40915e10 | −0.0691407 | ||||||||
\(421\) | 9.15367e11 | 1.42012 | 0.710061 | − | 0.704140i | \(-0.248667\pi\) | ||||
0.710061 | + | 0.704140i | \(0.248667\pi\) | |||||||
\(422\) | −1.69778e11 | −0.260600 | ||||||||
\(423\) | 1.25287e10 | 0.0190272 | ||||||||
\(424\) | 4.08390e10 | 0.0613662 | ||||||||
\(425\) | 2.41362e11 | 0.358855 | ||||||||
\(426\) | −3.07904e11 | −0.452973 | ||||||||
\(427\) | −2.49648e11 | −0.363415 | ||||||||
\(428\) | −1.55553e11 | −0.224068 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.48226e11 | −0.209081 | ||||||||
\(431\) | −4.90485e11 | −0.684664 | −0.342332 | − | 0.939579i | \(-0.611217\pi\) | ||||
−0.342332 | + | 0.939579i | \(0.611217\pi\) | |||||||
\(432\) | −1.95096e11 | −0.269508 | ||||||||
\(433\) | −5.67227e11 | −0.775464 | −0.387732 | − | 0.921772i | \(-0.626741\pi\) | ||||
−0.387732 | + | 0.921772i | \(0.626741\pi\) | |||||||
\(434\) | −4.82094e10 | −0.0652271 | ||||||||
\(435\) | −3.35030e11 | −0.448624 | ||||||||
\(436\) | 2.93788e11 | 0.389354 | ||||||||
\(437\) | 1.83728e11 | 0.240995 | ||||||||
\(438\) | 2.06141e11 | 0.267628 | ||||||||
\(439\) | 1.15068e12 | 1.47865 | 0.739323 | − | 0.673351i | \(-0.235146\pi\) | ||||
0.739323 | + | 0.673351i | \(0.235146\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.71022e11 | 0.215317 | ||||||||
\(442\) | 5.81622e11 | 0.724838 | ||||||||
\(443\) | −4.44419e11 | −0.548247 | −0.274123 | − | 0.961695i | \(-0.588388\pi\) | ||||
−0.274123 | + | 0.961695i | \(0.588388\pi\) | |||||||
\(444\) | −1.48394e11 | −0.181215 | ||||||||
\(445\) | 1.06708e12 | 1.28996 | ||||||||
\(446\) | −3.37880e11 | −0.404349 | ||||||||
\(447\) | 3.33327e10 | 0.0394900 | ||||||||
\(448\) | −1.97075e10 | −0.0231143 | ||||||||
\(449\) | 6.03886e11 | 0.701208 | 0.350604 | − | 0.936524i | \(-0.385976\pi\) | ||||
0.350604 | + | 0.936524i | \(0.385976\pi\) | |||||||
\(450\) | 3.84415e10 | 0.0441921 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.50377e10 | −0.0732895 | ||||||||
\(453\) | −1.46209e12 | −1.63130 | ||||||||
\(454\) | 8.53258e10 | 0.0942603 | ||||||||
\(455\) | 1.14841e11 | 0.125616 | ||||||||
\(456\) | −4.07479e11 | −0.441330 | ||||||||
\(457\) | 2.80219e11 | 0.300521 | 0.150260 | − | 0.988646i | \(-0.451989\pi\) | ||||
0.150260 | + | 0.988646i | \(0.451989\pi\) | |||||||
\(458\) | −4.19851e11 | −0.445862 | ||||||||
\(459\) | 1.31231e12 | 1.38000 | ||||||||
\(460\) | −6.93224e10 | −0.0721877 | ||||||||
\(461\) | −1.25259e12 | −1.29168 | −0.645838 | − | 0.763475i | \(-0.723492\pi\) | ||||
−0.645838 | + | 0.763475i | \(0.723492\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.46886e11 | 0.148548 | 0.0742739 | − | 0.997238i | \(-0.476336\pi\) | ||||
0.0742739 | + | 0.997238i | \(0.476336\pi\) | |||||||
\(464\) | −1.49748e11 | −0.149979 | ||||||||
\(465\) | 3.76101e11 | 0.373050 | ||||||||
\(466\) | −7.63479e11 | −0.749999 | ||||||||
\(467\) | 1.49431e12 | 1.45383 | 0.726916 | − | 0.686726i | \(-0.240953\pi\) | ||||
0.726916 | + | 0.686726i | \(0.240953\pi\) | |||||||
\(468\) | 9.26344e10 | 0.0892618 | ||||||||
\(469\) | 2.67695e11 | 0.255483 | ||||||||
\(470\) | −5.41601e10 | −0.0511964 | ||||||||
\(471\) | 4.53865e11 | 0.424945 | ||||||||
\(472\) | 2.58727e11 | 0.239940 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 5.86948e11 | 0.534069 | ||||||||
\(475\) | 4.40428e11 | 0.396966 | ||||||||
\(476\) | 1.32562e11 | 0.118355 | ||||||||
\(477\) | −4.37516e10 | −0.0386956 | ||||||||
\(478\) | 4.22944e11 | 0.370559 | ||||||||
\(479\) | 1.58007e11 | 0.137140 | 0.0685702 | − | 0.997646i | \(-0.478156\pi\) | ||||
0.0685702 | + | 0.997646i | \(0.478156\pi\) | |||||||
\(480\) | 1.53746e11 | 0.132196 | ||||||||
\(481\) | 3.86507e11 | 0.329234 | ||||||||
\(482\) | 7.92459e11 | 0.668752 | ||||||||
\(483\) | 3.31808e10 | 0.0277411 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.53126e12 | 1.25664 | ||||||||
\(486\) | 3.79919e11 | 0.308907 | ||||||||
\(487\) | −1.99896e12 | −1.61036 | −0.805181 | − | 0.593029i | \(-0.797932\pi\) | ||||
−0.805181 | + | 0.593029i | \(0.797932\pi\) | |||||||
\(488\) | 8.70518e11 | 0.694846 | ||||||||
\(489\) | −1.61528e12 | −1.27749 | ||||||||
\(490\) | −7.39305e11 | −0.579351 | ||||||||
\(491\) | −9.33204e11 | −0.724619 | −0.362310 | − | 0.932058i | \(-0.618012\pi\) | ||||
−0.362310 | + | 0.932058i | \(0.618012\pi\) | |||||||
\(492\) | −1.04553e11 | −0.0804439 | ||||||||
\(493\) | 1.00727e12 | 0.767956 | ||||||||
\(494\) | 1.06132e12 | 0.801817 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.68105e11 | 0.124713 | ||||||||
\(497\) | 1.82782e11 | 0.134379 | ||||||||
\(498\) | 1.46189e12 | 1.06508 | ||||||||
\(499\) | −1.93508e12 | −1.39716 | −0.698580 | − | 0.715532i | \(-0.746184\pi\) | ||||
−0.698580 | + | 0.715532i | \(0.746184\pi\) | |||||||
\(500\) | −7.58968e11 | −0.543074 | ||||||||
\(501\) | 1.44587e11 | 0.102532 | ||||||||
\(502\) | −1.40316e12 | −0.986147 | ||||||||
\(503\) | −1.50533e12 | −1.04852 | −0.524260 | − | 0.851558i | \(-0.675658\pi\) | ||||
−0.524260 | + | 0.851558i | \(0.675658\pi\) | |||||||
\(504\) | 2.11130e10 | 0.0145751 | ||||||||
\(505\) | −1.72683e12 | −1.18151 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.70515e11 | −0.316255 | ||||||||
\(508\) | 3.23140e10 | 0.0215280 | ||||||||
\(509\) | −1.56888e12 | −1.03600 | −0.518001 | − | 0.855380i | \(-0.673324\pi\) | ||||
−0.518001 | + | 0.855380i | \(0.673324\pi\) | |||||||
\(510\) | −1.03417e12 | −0.676902 | ||||||||
\(511\) | −1.22372e11 | −0.0793942 | ||||||||
\(512\) | 6.87195e10 | 0.0441942 | ||||||||
\(513\) | 2.39465e12 | 1.52656 | ||||||||
\(514\) | −1.75262e12 | −1.10753 | ||||||||
\(515\) | −2.32339e12 | −1.45542 | ||||||||
\(516\) | −2.47392e11 | −0.153625 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.80916e10 | 0.0537590 | ||||||||
\(519\) | −2.36082e12 | −1.42827 | ||||||||
\(520\) | −4.00447e11 | −0.240176 | ||||||||
\(521\) | −8.36119e11 | −0.497163 | −0.248581 | − | 0.968611i | \(-0.579964\pi\) | ||||
−0.248581 | + | 0.968611i | \(0.579964\pi\) | |||||||
\(522\) | 1.60427e11 | 0.0945717 | ||||||||
\(523\) | 1.04380e12 | 0.610043 | 0.305021 | − | 0.952345i | \(-0.401336\pi\) | ||||
0.305021 | + | 0.952345i | \(0.401336\pi\) | |||||||
\(524\) | 4.80919e11 | 0.278664 | ||||||||
\(525\) | 7.95401e10 | 0.0456951 | ||||||||
\(526\) | −6.53748e10 | −0.0372370 | ||||||||
\(527\) | −1.13075e12 | −0.638587 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.74898e12 | −0.971036 | ||||||||
\(530\) | 1.89133e11 | 0.104118 | ||||||||
\(531\) | −2.77179e11 | −0.151299 | ||||||||
\(532\) | 2.41893e11 | 0.130925 | ||||||||
\(533\) | 2.72318e11 | 0.146152 | ||||||||
\(534\) | 1.78098e12 | 0.947815 | ||||||||
\(535\) | −7.20391e11 | −0.380169 | ||||||||
\(536\) | −9.33444e11 | −0.488480 | ||||||||
\(537\) | −2.46690e12 | −1.28017 | ||||||||
\(538\) | −1.35719e12 | −0.698428 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.03526e11 | −0.457266 | ||||||||
\(541\) | 2.61498e11 | 0.131245 | 0.0656223 | − | 0.997845i | \(-0.479097\pi\) | ||||
0.0656223 | + | 0.997845i | \(0.479097\pi\) | |||||||
\(542\) | −1.08233e12 | −0.538719 | ||||||||
\(543\) | −1.01529e12 | −0.501175 | ||||||||
\(544\) | −4.62240e11 | −0.226294 | ||||||||
\(545\) | 1.36058e12 | 0.660604 | ||||||||
\(546\) | 1.91672e11 | 0.0922977 | ||||||||
\(547\) | −3.97347e12 | −1.89770 | −0.948848 | − | 0.315734i | \(-0.897749\pi\) | ||||
−0.948848 | + | 0.315734i | \(0.897749\pi\) | |||||||
\(548\) | 1.61879e12 | 0.766791 | ||||||||
\(549\) | −9.32602e11 | −0.438148 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.83803e12 | 0.849514 | ||||||||
\(552\) | −1.15700e11 | −0.0530407 | ||||||||
\(553\) | −3.48432e11 | −0.158436 | ||||||||
\(554\) | −1.96710e12 | −0.887223 | ||||||||
\(555\) | −6.87239e11 | −0.307461 | ||||||||
\(556\) | 2.00289e12 | 0.888833 | ||||||||
\(557\) | 1.26345e12 | 0.556175 | 0.278087 | − | 0.960556i | \(-0.410300\pi\) | ||||
0.278087 | + | 0.960556i | \(0.410300\pi\) | |||||||
\(558\) | −1.80094e11 | −0.0786403 | ||||||||
\(559\) | 6.44356e11 | 0.279108 | ||||||||
\(560\) | −9.12688e10 | −0.0392172 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.06242e12 | 0.872095 | ||||||||
\(563\) | −2.98705e12 | −1.25301 | −0.626505 | − | 0.779417i | \(-0.715515\pi\) | ||||
−0.626505 | + | 0.779417i | \(0.715515\pi\) | |||||||
\(564\) | −9.03944e10 | −0.0376171 | ||||||||
\(565\) | −3.01201e11 | −0.124348 | ||||||||
\(566\) | −3.34124e11 | −0.136847 | ||||||||
\(567\) | 3.31011e11 | 0.134499 | ||||||||
\(568\) | −6.37357e11 | −0.256930 | ||||||||
\(569\) | 4.48345e11 | 0.179311 | 0.0896555 | − | 0.995973i | \(-0.471423\pi\) | ||||
0.0896555 | + | 0.995973i | \(0.471423\pi\) | |||||||
\(570\) | −1.88711e12 | −0.748790 | ||||||||
\(571\) | −1.93797e12 | −0.762931 | −0.381466 | − | 0.924383i | \(-0.624580\pi\) | ||||
−0.381466 | + | 0.924383i | \(0.624580\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.54003e12 | 0.596806 | ||||||||
\(574\) | 6.20660e10 | 0.0238644 | ||||||||
\(575\) | 1.25056e11 | 0.0477089 | ||||||||
\(576\) | −7.36205e10 | −0.0278675 | ||||||||
\(577\) | −1.54518e12 | −0.580347 | −0.290174 | − | 0.956974i | \(-0.593713\pi\) | ||||
−0.290174 | + | 0.956974i | \(0.593713\pi\) | |||||||
\(578\) | 1.21184e12 | 0.451617 | ||||||||
\(579\) | −1.98923e11 | −0.0735581 | ||||||||
\(580\) | −6.93508e11 | −0.254463 | ||||||||
\(581\) | −8.67828e11 | −0.315967 | ||||||||
\(582\) | 2.55570e12 | 0.923330 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.26709e11 | 0.151801 | ||||||||
\(585\) | 4.29006e11 | 0.151447 | ||||||||
\(586\) | −6.17549e10 | −0.0216338 | ||||||||
\(587\) | −1.73985e10 | −0.00604841 | −0.00302421 | − | 0.999995i | \(-0.500963\pi\) | ||||
−0.00302421 | + | 0.999995i | \(0.500963\pi\) | |||||||
\(588\) | −1.23392e12 | −0.425684 | ||||||||
\(589\) | −2.06335e12 | −0.706406 | ||||||||
\(590\) | 1.19821e12 | 0.407098 | ||||||||
\(591\) | −4.98128e12 | −1.67957 | ||||||||
\(592\) | −3.07173e11 | −0.102786 | ||||||||
\(593\) | −8.05756e10 | −0.0267582 | −0.0133791 | − | 0.999910i | \(-0.504259\pi\) | ||||
−0.0133791 | + | 0.999910i | \(0.504259\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.13917e11 | 0.200809 | ||||||||
\(596\) | 6.89982e10 | 0.0223991 | ||||||||
\(597\) | 3.98327e12 | 1.28338 | ||||||||
\(598\) | 3.01353e11 | 0.0963652 | ||||||||
\(599\) | 4.11009e11 | 0.130446 | 0.0652229 | − | 0.997871i | \(-0.479224\pi\) | ||||
0.0652229 | + | 0.997871i | \(0.479224\pi\) | |||||||
\(600\) | −2.77354e11 | −0.0873684 | ||||||||
\(601\) | 3.07127e12 | 0.960246 | 0.480123 | − | 0.877201i | \(-0.340592\pi\) | ||||
0.480123 | + | 0.877201i | \(0.340592\pi\) | |||||||
\(602\) | 1.46860e11 | 0.0455742 | ||||||||
\(603\) | 1.00002e12 | 0.308020 | ||||||||
\(604\) | −3.02651e12 | −0.925286 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.88211e12 | −0.868128 | ||||||||
\(607\) | −1.67239e12 | −0.500021 | −0.250010 | − | 0.968243i | \(-0.580434\pi\) | ||||
−0.250010 | + | 0.968243i | \(0.580434\pi\) | |||||||
\(608\) | −8.43476e11 | −0.250326 | ||||||||
\(609\) | 3.31943e11 | 0.0977882 | ||||||||
\(610\) | 4.03152e12 | 1.17892 | ||||||||
\(611\) | 2.35441e11 | 0.0683434 | ||||||||
\(612\) | 4.95206e11 | 0.142694 | ||||||||
\(613\) | 2.38637e11 | 0.0682598 | 0.0341299 | − | 0.999417i | \(-0.489134\pi\) | ||||
0.0341299 | + | 0.999417i | \(0.489134\pi\) | |||||||
\(614\) | −6.58121e11 | −0.186874 | ||||||||
\(615\) | −4.84203e11 | −0.136486 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.55970e12 | 0.711060 | 0.355530 | − | 0.934665i | \(-0.384300\pi\) | ||||
0.355530 | + | 0.934665i | \(0.384300\pi\) | |||||||
\(618\) | −3.87779e12 | −1.06939 | ||||||||
\(619\) | −4.65350e12 | −1.27401 | −0.637004 | − | 0.770860i | \(-0.719827\pi\) | ||||
−0.637004 | + | 0.770860i | \(0.719827\pi\) | |||||||
\(620\) | 7.78524e11 | 0.211597 | ||||||||
\(621\) | 6.79941e11 | 0.183468 | ||||||||
\(622\) | −4.41022e12 | −1.18142 | ||||||||
\(623\) | −1.05725e12 | −0.281178 | ||||||||
\(624\) | −6.68354e11 | −0.176472 | ||||||||
\(625\) | −2.44554e12 | −0.641083 | ||||||||
\(626\) | 5.02657e12 | 1.30824 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.39493e11 | 0.241032 | ||||||||
\(629\) | 2.06619e12 | 0.526312 | ||||||||
\(630\) | 9.77780e10 | 0.0247291 | ||||||||
\(631\) | −2.86910e12 | −0.720466 | −0.360233 | − | 0.932862i | \(-0.617303\pi\) | ||||
−0.360233 | + | 0.932862i | \(0.617303\pi\) | |||||||
\(632\) | 1.21497e12 | 0.302928 | ||||||||
\(633\) | −1.31230e12 | −0.324875 | ||||||||
\(634\) | 4.13073e12 | 1.01537 | ||||||||
\(635\) | 1.49652e11 | 0.0365259 | ||||||||
\(636\) | 3.15667e11 | 0.0765018 | ||||||||
\(637\) | 3.21385e12 | 0.773390 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.82812e11 | 0.162012 | ||||||||
\(640\) | 3.18252e11 | 0.0749827 | ||||||||
\(641\) | −6.45940e12 | −1.51123 | −0.755615 | − | 0.655016i | \(-0.772662\pi\) | ||||
−0.755615 | + | 0.655016i | \(0.772662\pi\) | |||||||
\(642\) | −1.20235e12 | −0.279333 | ||||||||
\(643\) | −2.55823e12 | −0.590188 | −0.295094 | − | 0.955468i | \(-0.595351\pi\) | ||||
−0.295094 | + | 0.955468i | \(0.595351\pi\) | |||||||
\(644\) | 6.86836e10 | 0.0157350 | ||||||||
\(645\) | −1.14571e12 | −0.260650 | ||||||||
\(646\) | 5.67362e12 | 1.28178 | ||||||||
\(647\) | −9.97781e11 | −0.223855 | −0.111927 | − | 0.993716i | \(-0.535702\pi\) | ||||
−0.111927 | + | 0.993716i | \(0.535702\pi\) | |||||||
\(648\) | −1.15423e12 | −0.257160 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 7.22397e11 | 0.158732 | ||||||||
\(651\) | −3.72636e11 | −0.0813149 | ||||||||
\(652\) | −3.34361e12 | −0.724605 | ||||||||
\(653\) | −7.53538e12 | −1.62179 | −0.810897 | − | 0.585188i | \(-0.801021\pi\) | ||||
−0.810897 | + | 0.585188i | \(0.801021\pi\) | |||||||
\(654\) | 2.27084e12 | 0.485386 | ||||||||
\(655\) | 2.22722e12 | 0.472800 | ||||||||
\(656\) | −2.16423e11 | −0.0456284 | ||||||||
\(657\) | −4.57141e11 | −0.0957208 | ||||||||
\(658\) | 5.36611e10 | 0.0111595 | ||||||||
\(659\) | 8.67293e12 | 1.79135 | 0.895677 | − | 0.444706i | \(-0.146692\pi\) | ||||
0.895677 | + | 0.444706i | \(0.146692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.77055e12 | 0.971991 | 0.485995 | − | 0.873961i | \(-0.338457\pi\) | ||||
0.485995 | + | 0.873961i | \(0.338457\pi\) | |||||||
\(662\) | −9.51697e11 | −0.192592 | ||||||||
\(663\) | 4.49567e12 | 0.903615 | ||||||||
\(664\) | 3.02610e12 | 0.604124 | ||||||||
\(665\) | 1.12025e12 | 0.222135 | ||||||||
\(666\) | 3.29081e11 | 0.0648139 | ||||||||
\(667\) | 5.21894e11 | 0.102098 | ||||||||
\(668\) | 2.99293e11 | 0.0581571 | ||||||||
\(669\) | −2.61166e12 | −0.504079 | ||||||||
\(670\) | −4.32294e12 | −0.828787 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.52329e11 | −0.0288152 | ||||||||
\(673\) | 7.71533e12 | 1.44973 | 0.724864 | − | 0.688892i | \(-0.241902\pi\) | ||||
0.724864 | + | 0.688892i | \(0.241902\pi\) | |||||||
\(674\) | −1.53867e12 | −0.287194 | ||||||||
\(675\) | 1.62994e12 | 0.302207 | ||||||||
\(676\) | −9.73959e11 | −0.179383 | ||||||||
\(677\) | −9.14395e12 | −1.67296 | −0.836479 | − | 0.548000i | \(-0.815389\pi\) | ||||
−0.836479 | + | 0.548000i | \(0.815389\pi\) | |||||||
\(678\) | −5.02711e11 | −0.0913659 | ||||||||
\(679\) | −1.51715e12 | −0.273914 | ||||||||
\(680\) | −2.14071e12 | −0.383945 | ||||||||
\(681\) | 6.59528e11 | 0.117509 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.83407e11 | 0.155334 | 0.0776672 | − | 0.996979i | \(-0.475253\pi\) | ||||
0.0776672 | + | 0.996979i | \(0.475253\pi\) | |||||||
\(684\) | 9.03631e11 | 0.157848 | ||||||||
\(685\) | 7.49688e12 | 1.30099 | ||||||||
\(686\) | 1.49092e12 | 0.257037 | ||||||||
\(687\) | −3.24525e12 | −0.555832 | ||||||||
\(688\) | −5.12097e11 | −0.0871373 | ||||||||
\(689\) | −8.22184e11 | −0.138990 | ||||||||
\(690\) | −5.35829e11 | −0.0899923 | ||||||||
\(691\) | 6.58731e12 | 1.09915 | 0.549575 | − | 0.835445i | \(-0.314790\pi\) | ||||
0.549575 | + | 0.835445i | \(0.314790\pi\) | |||||||
\(692\) | −4.88685e12 | −0.810124 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.85558e12 | 0.958191 | ||||||||
\(695\) | 9.27573e12 | 1.50805 | ||||||||
\(696\) | −1.15748e12 | −0.186970 | ||||||||
\(697\) | 1.45576e12 | 0.233638 | ||||||||
\(698\) | 6.91613e12 | 1.10284 | ||||||||
\(699\) | −5.90133e12 | −0.934981 | ||||||||
\(700\) | 1.64647e11 | 0.0259186 | ||||||||
\(701\) | −6.57894e12 | −1.02902 | −0.514512 | − | 0.857483i | \(-0.672027\pi\) | ||||
−0.514512 | + | 0.857483i | \(0.672027\pi\) | |||||||
\(702\) | 3.92774e12 | 0.610416 | ||||||||
\(703\) | 3.77030e12 | 0.582207 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.18632e11 | −0.0638236 | ||||||||
\(706\) | −5.88612e12 | −0.891678 | ||||||||
\(707\) | 1.71092e12 | 0.257538 | ||||||||
\(708\) | 1.99984e12 | 0.299120 | ||||||||
\(709\) | 8.74938e11 | 0.130038 | 0.0650188 | − | 0.997884i | \(-0.479289\pi\) | ||||
0.0650188 | + | 0.997884i | \(0.479289\pi\) | |||||||
\(710\) | −2.95171e12 | −0.435924 | ||||||||
\(711\) | −1.30162e12 | −0.191017 | ||||||||
\(712\) | 3.68660e12 | 0.537609 | ||||||||
\(713\) | −5.85872e11 | −0.0848985 | ||||||||
\(714\) | 1.02464e12 | 0.147547 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.10644e12 | −0.726122 | ||||||||
\(717\) | 3.26916e12 | 0.461955 | ||||||||
\(718\) | 2.01202e12 | 0.282535 | ||||||||
\(719\) | 8.46541e12 | 1.18132 | 0.590660 | − | 0.806920i | \(-0.298867\pi\) | ||||
0.590660 | + | 0.806920i | \(0.298867\pi\) | |||||||
\(720\) | −3.40949e11 | −0.0472818 | ||||||||
\(721\) | 2.30198e12 | 0.317244 | ||||||||
\(722\) | 5.18998e12 | 0.710801 | ||||||||
\(723\) | 6.12534e12 | 0.833696 | ||||||||
\(724\) | −2.10163e12 | −0.284270 | ||||||||
\(725\) | 1.25107e12 | 0.168175 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.57971e12 | −0.608042 | −0.304021 | − | 0.952665i | \(-0.598329\pi\) | ||||
−0.304021 | + | 0.952665i | \(0.598329\pi\) | |||||||
\(728\) | 3.96757e11 | 0.0523520 | ||||||||
\(729\) | 8.48313e12 | 1.11245 | ||||||||
\(730\) | 1.97616e12 | 0.257555 | ||||||||
\(731\) | 3.44461e12 | 0.446182 | ||||||||
\(732\) | 6.72869e12 | 0.866225 | ||||||||
\(733\) | −2.48940e12 | −0.318512 | −0.159256 | − | 0.987237i | \(-0.550910\pi\) | ||||
−0.159256 | + | 0.987237i | \(0.550910\pi\) | |||||||
\(734\) | 8.31365e12 | 1.05721 | ||||||||
\(735\) | −5.71448e12 | −0.722244 | ||||||||
\(736\) | −2.39498e11 | −0.0300851 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.31858e11 | 0.0287719 | ||||||||
\(739\) | 8.85822e12 | 1.09256 | 0.546282 | − | 0.837602i | \(-0.316043\pi\) | ||||
0.546282 | + | 0.837602i | \(0.316043\pi\) | |||||||
\(740\) | −1.42257e12 | −0.174394 | ||||||||
\(741\) | 8.20350e12 | 0.999580 | ||||||||
\(742\) | −1.87390e11 | −0.0226949 | ||||||||
\(743\) | 1.02362e13 | 1.23222 | 0.616112 | − | 0.787659i | \(-0.288707\pi\) | ||||
0.616112 | + | 0.787659i | \(0.288707\pi\) | |||||||
\(744\) | 1.29937e12 | 0.155473 | ||||||||
\(745\) | 3.19543e11 | 0.0380037 | ||||||||
\(746\) | −7.44381e12 | −0.879975 | ||||||||
\(747\) | −3.24191e12 | −0.380942 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.13753e11 | 0.0828667 | ||||||||
\(750\) | −5.86647e12 | −0.677019 | ||||||||
\(751\) | 3.19150e12 | 0.366113 | 0.183056 | − | 0.983102i | \(-0.441401\pi\) | ||||
0.183056 | + | 0.983102i | \(0.441401\pi\) | |||||||
\(752\) | −1.87115e11 | −0.0213367 | ||||||||
\(753\) | −1.08458e13 | −1.22937 | ||||||||
\(754\) | 3.01477e12 | 0.339690 | ||||||||
\(755\) | −1.40163e13 | −1.56990 | ||||||||
\(756\) | 8.95201e11 | 0.0996718 | ||||||||
\(757\) | 1.65793e13 | 1.83499 | 0.917496 | − | 0.397746i | \(-0.130207\pi\) | ||||
0.917496 | + | 0.397746i | \(0.130207\pi\) | |||||||
\(758\) | 7.18069e12 | 0.790050 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.90628e12 | −0.424720 | ||||||||
\(761\) | −8.76788e12 | −0.947685 | −0.473842 | − | 0.880610i | \(-0.657133\pi\) | ||||
−0.473842 | + | 0.880610i | \(0.657133\pi\) | |||||||
\(762\) | 2.49772e11 | 0.0268378 | ||||||||
\(763\) | −1.34805e12 | −0.143994 | ||||||||
\(764\) | 3.18784e12 | 0.338513 | ||||||||
\(765\) | 2.29339e12 | 0.242103 | ||||||||
\(766\) | 4.41127e12 | 0.462950 | ||||||||
\(767\) | −5.20877e12 | −0.543446 | ||||||||
\(768\) | 5.31169e11 | 0.0550944 | ||||||||
\(769\) | −1.02168e13 | −1.05353 | −0.526764 | − | 0.850011i | \(-0.676595\pi\) | ||||
−0.526764 | + | 0.850011i | \(0.676595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.35469e13 | −1.38069 | ||||||||
\(772\) | −4.11767e11 | −0.0417228 | ||||||||
\(773\) | −4.77737e12 | −0.481262 | −0.240631 | − | 0.970617i | \(-0.577354\pi\) | ||||
−0.240631 | + | 0.970617i | \(0.577354\pi\) | |||||||
\(774\) | 5.48619e11 | 0.0549461 | ||||||||
\(775\) | −1.40444e12 | −0.139844 | ||||||||
\(776\) | 5.29026e12 | 0.523720 | ||||||||
\(777\) | 6.80907e11 | 0.0670183 | ||||||||
\(778\) | 1.32746e13 | 1.29901 | ||||||||
\(779\) | 2.65641e12 | 0.258450 | ||||||||
\(780\) | −3.09526e12 | −0.299414 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.61098e12 | 0.154049 | ||||||||
\(783\) | 6.80220e12 | 0.646728 | ||||||||
\(784\) | −2.55419e12 | −0.241452 | ||||||||
\(785\) | 4.35096e12 | 0.408951 | ||||||||
\(786\) | 3.71728e12 | 0.347395 | ||||||||
\(787\) | 1.03319e11 | 0.00960053 | 0.00480026 | − | 0.999988i | \(-0.498472\pi\) | ||||
0.00480026 | + | 0.999988i | \(0.498472\pi\) | |||||||
\(788\) | −1.03112e13 | −0.952664 | ||||||||
\(789\) | −5.05316e11 | −0.0464212 | ||||||||
\(790\) | 5.62676e12 | 0.513968 | ||||||||
\(791\) | 2.98426e11 | 0.0271045 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.75255e13 | −1.57377 | ||||||||
\(794\) | 2.45043e12 | 0.218801 | ||||||||
\(795\) | 1.46191e12 | 0.129798 | ||||||||
\(796\) | 8.24531e12 | 0.727945 | ||||||||
\(797\) | −1.18659e13 | −1.04169 | −0.520844 | − | 0.853652i | \(-0.674383\pi\) | ||||
−0.520844 | + | 0.853652i | \(0.674383\pi\) | |||||||
\(798\) | 1.86972e12 | 0.163216 | ||||||||
\(799\) | 1.25862e12 | 0.109254 | ||||||||
\(800\) | −5.74119e11 | −0.0495561 | ||||||||
\(801\) | −3.94953e12 | −0.338999 | ||||||||
\(802\) | 3.28738e12 | 0.280585 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −7.21508e12 | −0.608961 | ||||||||
\(805\) | 3.18086e11 | 0.0266970 | ||||||||
\(806\) | −3.38434e12 | −0.282466 | ||||||||
\(807\) | −1.04905e13 | −0.870691 | ||||||||
\(808\) | −5.96592e12 | −0.492410 | ||||||||
\(809\) | −1.31694e13 | −1.08093 | −0.540465 | − | 0.841367i | \(-0.681751\pi\) | ||||
−0.540465 | + | 0.841367i | \(0.681751\pi\) | |||||||
\(810\) | −5.34542e12 | −0.436314 | ||||||||
\(811\) | 3.03385e12 | 0.246263 | 0.123132 | − | 0.992390i | \(-0.460706\pi\) | ||||
0.123132 | + | 0.992390i | \(0.460706\pi\) | |||||||
\(812\) | 6.87118e11 | 0.0554663 | ||||||||
\(813\) | −8.36589e12 | −0.671591 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.54848e13 | −1.22941 | ||||||||
\(816\) | −3.57290e12 | −0.282108 | ||||||||
\(817\) | 6.28557e12 | 0.493566 | ||||||||
\(818\) | 1.05222e13 | 0.821704 | ||||||||
\(819\) | −4.25053e11 | −0.0330115 | ||||||||
\(820\) | −1.00229e12 | −0.0774162 | ||||||||
\(821\) | −1.60816e13 | −1.23534 | −0.617670 | − | 0.786438i | \(-0.711923\pi\) | ||||
−0.617670 | + | 0.786438i | \(0.711923\pi\) | |||||||
\(822\) | 1.25125e13 | 0.955915 | ||||||||
\(823\) | 9.77833e12 | 0.742960 | 0.371480 | − | 0.928441i | \(-0.378850\pi\) | ||||
0.371480 | + | 0.928441i | \(0.378850\pi\) | |||||||
\(824\) | −8.02695e12 | −0.606566 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.18717e12 | −0.0887366 | ||||||||
\(827\) | −1.19955e13 | −0.891749 | −0.445874 | − | 0.895096i | \(-0.647107\pi\) | ||||
−0.445874 | + | 0.895096i | \(0.647107\pi\) | |||||||
\(828\) | 2.56579e11 | 0.0189707 | ||||||||
\(829\) | 1.25391e13 | 0.922085 | 0.461043 | − | 0.887378i | \(-0.347475\pi\) | ||||
0.461043 | + | 0.887378i | \(0.347475\pi\) | |||||||
\(830\) | 1.40144e13 | 1.02500 | ||||||||
\(831\) | −1.52048e13 | −1.10605 | ||||||||
\(832\) | −1.38348e12 | −0.100096 | ||||||||
\(833\) | 1.71807e13 | 1.23634 | ||||||||
\(834\) | 1.54814e13 | 1.10806 | ||||||||
\(835\) | 1.38608e12 | 0.0986732 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.63607e12 | −0.537781 | ||||||||
\(838\) | −6.07152e12 | −0.425304 | ||||||||
\(839\) | 1.36095e13 | 0.948233 | 0.474116 | − | 0.880462i | \(-0.342768\pi\) | ||||
0.474116 | + | 0.880462i | \(0.342768\pi\) | |||||||
\(840\) | −7.05465e11 | −0.0488898 | ||||||||
\(841\) | −9.28607e12 | −0.640103 | ||||||||
\(842\) | 1.46459e13 | 1.00418 | ||||||||
\(843\) | 1.59415e13 | 1.08719 | ||||||||
\(844\) | −2.71644e12 | −0.184272 | ||||||||
\(845\) | −4.51057e12 | −0.304352 | ||||||||
\(846\) | 2.00460e11 | 0.0134543 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.53425e11 | 0.0433925 | ||||||||
\(849\) | −2.58262e12 | −0.170599 | ||||||||
\(850\) | 3.86180e12 | 0.253749 | ||||||||
\(851\) | 1.07055e12 | 0.0699718 | ||||||||
\(852\) | −4.92647e12 | −0.320300 | ||||||||
\(853\) | 5.86443e12 | 0.379276 | 0.189638 | − | 0.981854i | \(-0.439269\pi\) | ||||
0.189638 | + | 0.981854i | \(0.439269\pi\) | |||||||
\(854\) | −3.99437e12 | −0.256974 | ||||||||
\(855\) | 4.18488e12 | 0.267815 | ||||||||
\(856\) | −2.48884e12 | −0.158440 | ||||||||
\(857\) | 1.19243e12 | 0.0755128 | 0.0377564 | − | 0.999287i | \(-0.487979\pi\) | ||||
0.0377564 | + | 0.999287i | \(0.487979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.96633e13 | 1.23222 | 0.616108 | − | 0.787662i | \(-0.288709\pi\) | ||||
0.616108 | + | 0.787662i | \(0.288709\pi\) | |||||||
\(860\) | −2.37161e12 | −0.147843 | ||||||||
\(861\) | 4.79741e11 | 0.0297504 | ||||||||
\(862\) | −7.84775e12 | −0.484131 | ||||||||
\(863\) | −1.56800e13 | −0.962271 | −0.481135 | − | 0.876646i | \(-0.659775\pi\) | ||||
−0.481135 | + | 0.876646i | \(0.659775\pi\) | |||||||
\(864\) | −3.12154e12 | −0.190571 | ||||||||
\(865\) | −2.26319e13 | −1.37451 | ||||||||
\(866\) | −9.07564e12 | −0.548336 | ||||||||
\(867\) | 9.36696e12 | 0.563006 | ||||||||
\(868\) | −7.71350e11 | −0.0461225 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −5.36049e12 | −0.317225 | ||||||||
\(871\) | 1.87924e13 | 1.10637 | ||||||||
\(872\) | 4.70061e12 | 0.275315 | ||||||||
\(873\) | −5.66756e12 | −0.330242 | ||||||||
\(874\) | 2.93964e12 | 0.170409 | ||||||||
\(875\) | 3.48253e12 | 0.200844 | ||||||||
\(876\) | 3.29826e12 | 0.189241 | ||||||||
\(877\) | 1.56274e13 | 0.892047 | 0.446023 | − | 0.895021i | \(-0.352840\pi\) | ||||
0.446023 | + | 0.895021i | \(0.352840\pi\) | |||||||
\(878\) | 1.84109e13 | 1.04556 | ||||||||
\(879\) | −4.77336e11 | −0.0269696 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.19215e12 | 0.402223 | 0.201112 | − | 0.979568i | \(-0.435545\pi\) | ||||
0.201112 | + | 0.979568i | \(0.435545\pi\) | |||||||
\(882\) | 2.73635e12 | 0.152252 | ||||||||
\(883\) | 8.94240e11 | 0.0495029 | 0.0247515 | − | 0.999694i | \(-0.492121\pi\) | ||||
0.0247515 | + | 0.999694i | \(0.492121\pi\) | |||||||
\(884\) | 9.30596e12 | 0.512538 | ||||||||
\(885\) | 9.26160e12 | 0.507506 | ||||||||
\(886\) | −7.11071e12 | −0.387669 | ||||||||
\(887\) | −1.98339e13 | −1.07585 | −0.537926 | − | 0.842992i | \(-0.680792\pi\) | ||||
−0.537926 | + | 0.842992i | \(0.680792\pi\) | |||||||
\(888\) | −2.37431e12 | −0.128138 | ||||||||
\(889\) | −1.48273e11 | −0.00796168 | ||||||||
\(890\) | 1.70733e13 | 0.912142 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.40609e12 | −0.285918 | ||||||||
\(893\) | 2.29668e12 | 0.120856 | ||||||||
\(894\) | 5.33324e11 | 0.0279236 | ||||||||
\(895\) | −2.36488e13 | −1.23199 | ||||||||
\(896\) | −3.15320e11 | −0.0163442 | ||||||||
\(897\) | 2.32932e12 | 0.120133 | ||||||||
\(898\) | 9.66218e12 | 0.495829 | ||||||||
\(899\) | −5.86112e12 | −0.299269 | ||||||||
\(900\) | 6.15065e11 | 0.0312485 | ||||||||
\(901\) | −4.39525e12 | −0.222189 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.13516e12 | 0.0568148 | ||||||||
\(904\) | −1.04060e12 | −0.0518235 | ||||||||
\(905\) | −9.73300e12 | −0.482312 | ||||||||
\(906\) | −2.33935e13 | −1.15350 | ||||||||
\(907\) | −1.02442e13 | −0.502625 | −0.251313 | − | 0.967906i | \(-0.580862\pi\) | ||||
−0.251313 | + | 0.967906i | \(0.580862\pi\) | |||||||
\(908\) | 1.36521e12 | 0.0666521 | ||||||||
\(909\) | 6.39141e12 | 0.310498 | ||||||||
\(910\) | 1.83745e12 | 0.0888239 | ||||||||
\(911\) | −7.68070e12 | −0.369461 | −0.184730 | − | 0.982789i | \(-0.559141\pi\) | ||||
−0.184730 | + | 0.982789i | \(0.559141\pi\) | |||||||
\(912\) | −6.51967e12 | −0.312068 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 4.48350e12 | 0.212500 | ||||||||
\(915\) | 3.11618e13 | 1.46969 | ||||||||
\(916\) | −6.71762e12 | −0.315272 | ||||||||
\(917\) | −2.20670e12 | −0.103058 | ||||||||
\(918\) | 2.09970e13 | 0.975809 | ||||||||
\(919\) | −1.89989e13 | −0.878633 | −0.439317 | − | 0.898332i | \(-0.644779\pi\) | ||||
−0.439317 | + | 0.898332i | \(0.644779\pi\) | |||||||
\(920\) | −1.10916e12 | −0.0510444 | ||||||||
\(921\) | −5.08697e12 | −0.232965 | ||||||||
\(922\) | −2.00414e13 | −0.913352 | ||||||||
\(923\) | 1.28315e13 | 0.581927 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.56629e12 | 0.115257 | ||||||||
\(926\) | 2.35018e12 | 0.105039 | ||||||||
\(927\) | 8.59943e12 | 0.382482 | ||||||||
\(928\) | −2.39596e12 | −0.106051 | ||||||||
\(929\) | 2.17473e13 | 0.957931 | 0.478966 | − | 0.877834i | \(-0.341012\pi\) | ||||
0.478966 | + | 0.877834i | \(0.341012\pi\) | |||||||
\(930\) | 6.01762e12 | 0.263786 | ||||||||
\(931\) | 3.13506e13 | 1.36764 | ||||||||
\(932\) | −1.22157e13 | −0.530329 | ||||||||
\(933\) | −3.40889e13 | −1.47281 | ||||||||
\(934\) | 2.39089e13 | 1.02802 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.48215e12 | 0.0631177 | ||||||||
\(937\) | −3.95881e13 | −1.67779 | −0.838893 | − | 0.544297i | \(-0.816797\pi\) | ||||
−0.838893 | + | 0.544297i | \(0.816797\pi\) | |||||||
\(938\) | 4.28311e12 | 0.180654 | ||||||||
\(939\) | 3.88530e13 | 1.63091 | ||||||||
\(940\) | −8.66562e11 | −0.0362013 | ||||||||
\(941\) | 4.13659e13 | 1.71985 | 0.859923 | − | 0.510424i | \(-0.170512\pi\) | ||||
0.859923 | + | 0.510424i | \(0.170512\pi\) | |||||||
\(942\) | 7.26184e12 | 0.300481 | ||||||||
\(943\) | 7.54267e11 | 0.0310615 | ||||||||
\(944\) | 4.13963e12 | 0.169663 | ||||||||
\(945\) | 4.14583e12 | 0.169110 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.78696e12 | 0.314625 | 0.157313 | − | 0.987549i | \(-0.449717\pi\) | ||||
0.157313 | + | 0.987549i | \(0.449717\pi\) | |||||||
\(948\) | 9.39117e12 | 0.377644 | ||||||||
\(949\) | −8.59064e12 | −0.343817 | ||||||||
\(950\) | 7.04685e12 | 0.280698 | ||||||||
\(951\) | 3.19286e13 | 1.26581 | ||||||||
\(952\) | 2.12099e12 | 0.0836898 | ||||||||
\(953\) | −1.26501e13 | −0.496794 | −0.248397 | − | 0.968658i | \(-0.579904\pi\) | ||||
−0.248397 | + | 0.968658i | \(0.579904\pi\) | |||||||
\(954\) | −7.00026e11 | −0.0273619 | ||||||||
\(955\) | 1.47634e13 | 0.574344 | ||||||||
\(956\) | 6.76710e12 | 0.262025 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.52810e12 | 0.0969729 | ||||||||
\(959\) | −7.42781e12 | −0.283581 | ||||||||
\(960\) | 2.45994e12 | 0.0934767 | ||||||||
\(961\) | −1.98600e13 | −0.751145 | ||||||||
\(962\) | 6.18411e12 | 0.232803 | ||||||||
\(963\) | 2.66634e12 | 0.0999074 | ||||||||
\(964\) | 1.26793e13 | 0.472879 | ||||||||
\(965\) | −1.90696e12 | −0.0707896 | ||||||||
\(966\) | 5.30892e11 | 0.0196159 | ||||||||
\(967\) | 6.51628e12 | 0.239652 | 0.119826 | − | 0.992795i | \(-0.461766\pi\) | ||||
0.119826 | + | 0.992795i | \(0.461766\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.38544e13 | 1.59792 | ||||||||
\(970\) | 2.45001e13 | 0.888578 | ||||||||
\(971\) | 2.06099e13 | 0.744028 | 0.372014 | − | 0.928227i | \(-0.378667\pi\) | ||||
0.372014 | + | 0.928227i | \(0.378667\pi\) | |||||||
\(972\) | 6.07870e12 | 0.218430 | ||||||||
\(973\) | −9.19027e12 | −0.328716 | ||||||||
\(974\) | −3.19833e13 | −1.13870 | ||||||||
\(975\) | 5.58379e12 | 0.197883 | ||||||||
\(976\) | 1.39283e13 | 0.491330 | ||||||||
\(977\) | −3.23219e13 | −1.13494 | −0.567468 | − | 0.823395i | \(-0.692077\pi\) | ||||
−0.567468 | + | 0.823395i | \(0.692077\pi\) | |||||||
\(978\) | −2.58445e13 | −0.903324 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.18289e13 | −0.409663 | ||||||||
\(981\) | −5.03585e12 | −0.173605 | ||||||||
\(982\) | −1.49313e13 | −0.512383 | ||||||||
\(983\) | 2.94079e13 | 1.00455 | 0.502277 | − | 0.864707i | \(-0.332496\pi\) | ||||
0.502277 | + | 0.864707i | \(0.332496\pi\) | |||||||
\(984\) | −1.67285e12 | −0.0568824 | ||||||||
\(985\) | −4.77528e13 | −1.61635 | ||||||||
\(986\) | 1.61164e13 | 0.543027 | ||||||||
\(987\) | 4.14775e11 | 0.0139119 | ||||||||
\(988\) | 1.69811e13 | 0.566970 | ||||||||
\(989\) | 1.78474e12 | 0.0593186 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.67690e13 | 1.21102 | 0.605508 | − | 0.795839i | \(-0.292970\pi\) | ||||
0.605508 | + | 0.795839i | \(0.292970\pi\) | |||||||
\(992\) | 2.68968e12 | 0.0881857 | ||||||||
\(993\) | −7.35617e12 | −0.240093 | ||||||||
\(994\) | 2.92451e12 | 0.0950200 | ||||||||
\(995\) | 3.81855e13 | 1.23508 | ||||||||
\(996\) | 2.33903e13 | 0.753128 | ||||||||
\(997\) | 7.67620e12 | 0.246047 | 0.123024 | − | 0.992404i | \(-0.460741\pi\) | ||||
0.123024 | + | 0.992404i | \(0.460741\pi\) | |||||||
\(998\) | −3.09613e13 | −0.987941 | ||||||||
\(999\) | 1.39532e13 | 0.443229 |
(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 | 242.10.a.e.1.2 | 2 | ||
11.10 | odd | 2 | 22.10.a.d.1.2 | ✓ | 2 | ||
33.32 | even | 2 | 198.10.a.n.1.1 | 2 | |||
44.43 | even | 2 | 176.10.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.10.a.d.1.2 | ✓ | 2 | 11.10 | odd | 2 | ||
176.10.a.e.1.1 | 2 | 44.43 | even | 2 | |||
198.10.a.n.1.1 | 2 | 33.32 | even | 2 | |||
242.10.a.e.1.2 | 2 | 1.1 | even | 1 | trivial |