Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,46,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 46, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 46);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 46 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(25.6511452149\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 200169772272162 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.41481e7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.19430e6 | 0.707107 | ||||||||
\(3\) | −2.43982e10 | −0.448880 | −0.224440 | − | 0.974488i | \(-0.572055\pi\) | ||||
−0.224440 | + | 0.974488i | \(0.572055\pi\) | |||||||
\(4\) | 1.75922e13 | 0.500000 | ||||||||
\(5\) | −4.75445e15 | −0.891816 | −0.445908 | − | 0.895079i | \(-0.647119\pi\) | ||||
−0.445908 | + | 0.895079i | \(0.647119\pi\) | |||||||
\(6\) | −1.02334e17 | −0.317406 | ||||||||
\(7\) | 5.49745e18 | 0.531441 | 0.265720 | − | 0.964050i | \(-0.414390\pi\) | ||||
0.265720 | + | 0.964050i | \(0.414390\pi\) | |||||||
\(8\) | 7.37870e19 | 0.353553 | ||||||||
\(9\) | −2.35904e21 | −0.798507 | ||||||||
\(10\) | −1.99416e22 | −0.630609 | ||||||||
\(11\) | 2.16058e23 | 0.800268 | 0.400134 | − | 0.916457i | \(-0.368964\pi\) | ||||
0.400134 | + | 0.916457i | \(0.368964\pi\) | |||||||
\(12\) | −4.29218e23 | −0.224440 | ||||||||
\(13\) | 1.18584e25 | 1.02400 | 0.512001 | − | 0.858985i | \(-0.328904\pi\) | ||||
0.512001 | + | 0.858985i | \(0.328904\pi\) | |||||||
\(14\) | 2.30580e25 | 0.375786 | ||||||||
\(15\) | 1.16000e26 | 0.400318 | ||||||||
\(16\) | 3.09485e26 | 0.250000 | ||||||||
\(17\) | 1.71231e27 | 0.353574 | 0.176787 | − | 0.984249i | \(-0.443430\pi\) | ||||
0.176787 | + | 0.984249i | \(0.443430\pi\) | |||||||
\(18\) | −9.89453e27 | −0.564630 | ||||||||
\(19\) | −7.20975e26 | −0.0121889 | −0.00609444 | − | 0.999981i | \(-0.501940\pi\) | ||||
−0.00609444 | + | 0.999981i | \(0.501940\pi\) | |||||||
\(20\) | −8.36411e28 | −0.445908 | ||||||||
\(21\) | −1.34128e29 | −0.238553 | ||||||||
\(22\) | 9.06215e29 | 0.565875 | ||||||||
\(23\) | 6.93777e30 | 1.59347 | 0.796735 | − | 0.604329i | \(-0.206559\pi\) | ||||
0.796735 | + | 0.604329i | \(0.206559\pi\) | |||||||
\(24\) | −1.80027e30 | −0.158703 | ||||||||
\(25\) | −5.81693e30 | −0.204665 | ||||||||
\(26\) | 4.97377e31 | 0.724079 | ||||||||
\(27\) | 1.29636e32 | 0.807314 | ||||||||
\(28\) | 9.67121e31 | 0.265720 | ||||||||
\(29\) | 1.23261e33 | 1.53770 | 0.768850 | − | 0.639429i | \(-0.220829\pi\) | ||||
0.768850 | + | 0.639429i | \(0.220829\pi\) | |||||||
\(30\) | 4.86540e32 | 0.283068 | ||||||||
\(31\) | 6.35535e33 | 1.76808 | 0.884039 | − | 0.467413i | \(-0.154814\pi\) | ||||
0.884039 | + | 0.467413i | \(0.154814\pi\) | |||||||
\(32\) | 1.29807e33 | 0.176777 | ||||||||
\(33\) | −5.27144e33 | −0.359224 | ||||||||
\(34\) | 7.18193e33 | 0.250015 | ||||||||
\(35\) | −2.61373e34 | −0.473947 | ||||||||
\(36\) | −4.15006e34 | −0.399253 | ||||||||
\(37\) | −1.13513e35 | −0.589531 | −0.294765 | − | 0.955570i | \(-0.595242\pi\) | ||||
−0.294765 | + | 0.955570i | \(0.595242\pi\) | |||||||
\(38\) | −3.02399e33 | −0.00861884 | ||||||||
\(39\) | −2.89324e35 | −0.459654 | ||||||||
\(40\) | −3.50816e35 | −0.315304 | ||||||||
\(41\) | −2.36419e36 | −1.21912 | −0.609560 | − | 0.792740i | \(-0.708654\pi\) | ||||
−0.609560 | + | 0.792740i | \(0.708654\pi\) | |||||||
\(42\) | −5.62573e35 | −0.168683 | ||||||||
\(43\) | 4.96460e36 | 0.876686 | 0.438343 | − | 0.898808i | \(-0.355566\pi\) | ||||
0.438343 | + | 0.898808i | \(0.355566\pi\) | |||||||
\(44\) | 3.80094e36 | 0.400134 | ||||||||
\(45\) | 1.12159e37 | 0.712121 | ||||||||
\(46\) | 2.90991e37 | 1.12675 | ||||||||
\(47\) | 1.34643e37 | 0.321352 | 0.160676 | − | 0.987007i | \(-0.448633\pi\) | ||||
0.160676 | + | 0.987007i | \(0.448633\pi\) | |||||||
\(48\) | −7.55089e36 | −0.112220 | ||||||||
\(49\) | −7.67850e37 | −0.717571 | ||||||||
\(50\) | −2.43980e37 | −0.144720 | ||||||||
\(51\) | −4.17773e37 | −0.158712 | ||||||||
\(52\) | 2.08615e38 | 0.512001 | ||||||||
\(53\) | −1.16156e39 | −1.85710 | −0.928551 | − | 0.371205i | \(-0.878945\pi\) | ||||
−0.928551 | + | 0.371205i | \(0.878945\pi\) | |||||||
\(54\) | 5.43734e38 | 0.570857 | ||||||||
\(55\) | −1.02724e39 | −0.713692 | ||||||||
\(56\) | 4.05640e38 | 0.187893 | ||||||||
\(57\) | 1.75905e37 | 0.00547135 | ||||||||
\(58\) | 5.16995e39 | 1.08732 | ||||||||
\(59\) | −6.70116e39 | −0.959356 | −0.479678 | − | 0.877444i | \(-0.659247\pi\) | ||||
−0.479678 | + | 0.877444i | \(0.659247\pi\) | |||||||
\(60\) | 2.04070e39 | 0.200159 | ||||||||
\(61\) | 1.77152e40 | 1.19791 | 0.598954 | − | 0.800783i | \(-0.295583\pi\) | ||||
0.598954 | + | 0.800783i | \(0.295583\pi\) | |||||||
\(62\) | 2.66563e40 | 1.25022 | ||||||||
\(63\) | −1.29687e40 | −0.424359 | ||||||||
\(64\) | 5.44452e39 | 0.125000 | ||||||||
\(65\) | −5.63802e40 | −0.913221 | ||||||||
\(66\) | −2.21100e40 | −0.254010 | ||||||||
\(67\) | −1.34297e41 | −1.09997 | −0.549987 | − | 0.835174i | \(-0.685367\pi\) | ||||
−0.549987 | + | 0.835174i | \(0.685367\pi\) | |||||||
\(68\) | 3.01232e40 | 0.176787 | ||||||||
\(69\) | −1.69269e41 | −0.715277 | ||||||||
\(70\) | −1.09628e41 | −0.335131 | ||||||||
\(71\) | 4.73439e41 | 1.05184 | 0.525922 | − | 0.850533i | \(-0.323720\pi\) | ||||
0.525922 | + | 0.850533i | \(0.323720\pi\) | |||||||
\(72\) | −1.74066e41 | −0.282315 | ||||||||
\(73\) | 1.25402e42 | 1.49122 | 0.745609 | − | 0.666384i | \(-0.232159\pi\) | ||||
0.745609 | + | 0.666384i | \(0.232159\pi\) | |||||||
\(74\) | −4.76108e41 | −0.416861 | ||||||||
\(75\) | 1.41923e41 | 0.0918700 | ||||||||
\(76\) | −1.26835e40 | −0.00609444 | ||||||||
\(77\) | 1.18777e42 | 0.425295 | ||||||||
\(78\) | −1.21351e42 | −0.325024 | ||||||||
\(79\) | 2.71951e42 | 0.546866 | 0.273433 | − | 0.961891i | \(-0.411841\pi\) | ||||
0.273433 | + | 0.961891i | \(0.411841\pi\) | |||||||
\(80\) | −1.47143e42 | −0.222954 | ||||||||
\(81\) | 3.80644e42 | 0.436120 | ||||||||
\(82\) | −9.91615e42 | −0.862048 | ||||||||
\(83\) | −1.70726e43 | −1.12991 | −0.564955 | − | 0.825122i | \(-0.691106\pi\) | ||||
−0.564955 | + | 0.825122i | \(0.691106\pi\) | |||||||
\(84\) | −2.35960e42 | −0.119277 | ||||||||
\(85\) | −8.14107e42 | −0.315323 | ||||||||
\(86\) | 2.08230e43 | 0.619911 | ||||||||
\(87\) | −3.00736e43 | −0.690243 | ||||||||
\(88\) | 1.59423e43 | 0.282938 | ||||||||
\(89\) | 5.81345e43 | 0.800127 | 0.400063 | − | 0.916487i | \(-0.368988\pi\) | ||||
0.400063 | + | 0.916487i | \(0.368988\pi\) | |||||||
\(90\) | 4.70430e43 | 0.503545 | ||||||||
\(91\) | 6.51909e43 | 0.544197 | ||||||||
\(92\) | 1.22051e44 | 0.796735 | ||||||||
\(93\) | −1.55059e44 | −0.793655 | ||||||||
\(94\) | 5.64732e43 | 0.227230 | ||||||||
\(95\) | 3.42784e42 | 0.0108702 | ||||||||
\(96\) | −3.16707e43 | −0.0793515 | ||||||||
\(97\) | −4.76787e44 | −0.946150 | −0.473075 | − | 0.881022i | \(-0.656856\pi\) | ||||
−0.473075 | + | 0.881022i | \(0.656856\pi\) | |||||||
\(98\) | −3.22060e44 | −0.507399 | ||||||||
\(99\) | −5.09690e44 | −0.639020 | ||||||||
\(100\) | −1.02332e44 | −0.102332 | ||||||||
\(101\) | 1.26653e44 | 0.101248 | 0.0506238 | − | 0.998718i | \(-0.483879\pi\) | ||||
0.0506238 | + | 0.998718i | \(0.483879\pi\) | |||||||
\(102\) | −1.75227e44 | −0.112227 | ||||||||
\(103\) | 2.48579e45 | 1.27828 | 0.639141 | − | 0.769089i | \(-0.279290\pi\) | ||||
0.639141 | + | 0.769089i | \(0.279290\pi\) | |||||||
\(104\) | 8.74996e44 | 0.362039 | ||||||||
\(105\) | 6.37705e44 | 0.212745 | ||||||||
\(106\) | −4.87195e45 | −1.31317 | ||||||||
\(107\) | 1.38278e45 | 0.301729 | 0.150864 | − | 0.988554i | \(-0.451794\pi\) | ||||
0.150864 | + | 0.988554i | \(0.451794\pi\) | |||||||
\(108\) | 2.28059e45 | 0.403657 | ||||||||
\(109\) | 8.73749e45 | 1.25687 | 0.628435 | − | 0.777862i | \(-0.283696\pi\) | ||||
0.628435 | + | 0.777862i | \(0.283696\pi\) | |||||||
\(110\) | −4.30855e45 | −0.504656 | ||||||||
\(111\) | 2.76952e45 | 0.264629 | ||||||||
\(112\) | 1.70138e45 | 0.132860 | ||||||||
\(113\) | −7.03342e45 | −0.449678 | −0.224839 | − | 0.974396i | \(-0.572186\pi\) | ||||
−0.224839 | + | 0.974396i | \(0.572186\pi\) | |||||||
\(114\) | 7.37799e43 | 0.00386883 | ||||||||
\(115\) | −3.29853e46 | −1.42108 | ||||||||
\(116\) | 2.16843e46 | 0.768850 | ||||||||
\(117\) | −2.79744e46 | −0.817672 | ||||||||
\(118\) | −2.81067e46 | −0.678367 | ||||||||
\(119\) | 9.41331e45 | 0.187904 | ||||||||
\(120\) | 8.55930e45 | 0.141534 | ||||||||
\(121\) | −2.62093e46 | −0.359570 | ||||||||
\(122\) | 7.43027e46 | 0.847049 | ||||||||
\(123\) | 5.76822e46 | 0.547238 | ||||||||
\(124\) | 1.11805e47 | 0.884039 | ||||||||
\(125\) | 1.62786e47 | 1.07434 | ||||||||
\(126\) | −5.43946e46 | −0.300067 | ||||||||
\(127\) | −1.52817e47 | −0.705649 | −0.352824 | − | 0.935690i | \(-0.614779\pi\) | ||||
−0.352824 | + | 0.935690i | \(0.614779\pi\) | |||||||
\(128\) | 2.28360e46 | 0.0883883 | ||||||||
\(129\) | −1.21127e47 | −0.393527 | ||||||||
\(130\) | −2.36476e47 | −0.645745 | ||||||||
\(131\) | 1.24762e47 | 0.286734 | 0.143367 | − | 0.989670i | \(-0.454207\pi\) | ||||
0.143367 | + | 0.989670i | \(0.454207\pi\) | |||||||
\(132\) | −9.27362e46 | −0.179612 | ||||||||
\(133\) | −3.96352e45 | −0.00647767 | ||||||||
\(134\) | −5.63281e47 | −0.777798 | ||||||||
\(135\) | −6.16350e47 | −0.719975 | ||||||||
\(136\) | 1.26346e47 | 0.125007 | ||||||||
\(137\) | 1.15687e48 | 0.970670 | 0.485335 | − | 0.874328i | \(-0.338698\pi\) | ||||
0.485335 | + | 0.874328i | \(0.338698\pi\) | |||||||
\(138\) | −7.09968e47 | −0.505777 | ||||||||
\(139\) | 1.44859e48 | 0.877226 | 0.438613 | − | 0.898676i | \(-0.355470\pi\) | ||||
0.438613 | + | 0.898676i | \(0.355470\pi\) | |||||||
\(140\) | −4.59813e47 | −0.236974 | ||||||||
\(141\) | −3.28504e47 | −0.144248 | ||||||||
\(142\) | 1.98575e48 | 0.743766 | ||||||||
\(143\) | 2.56211e48 | 0.819476 | ||||||||
\(144\) | −7.30087e47 | −0.199627 | ||||||||
\(145\) | −5.86039e48 | −1.37134 | ||||||||
\(146\) | 5.25975e48 | 1.05445 | ||||||||
\(147\) | 1.87342e48 | 0.322103 | ||||||||
\(148\) | −1.99694e48 | −0.294765 | ||||||||
\(149\) | 1.96992e48 | 0.249895 | 0.124947 | − | 0.992163i | \(-0.460124\pi\) | ||||
0.124947 | + | 0.992163i | \(0.460124\pi\) | |||||||
\(150\) | 5.95267e47 | 0.0649619 | ||||||||
\(151\) | −1.22959e49 | −1.15553 | −0.577764 | − | 0.816204i | \(-0.696075\pi\) | ||||
−0.577764 | + | 0.816204i | \(0.696075\pi\) | |||||||
\(152\) | −5.31985e46 | −0.00430942 | ||||||||
\(153\) | −4.03940e48 | −0.282332 | ||||||||
\(154\) | 4.98186e48 | 0.300729 | ||||||||
\(155\) | −3.02162e49 | −1.57680 | ||||||||
\(156\) | −5.08984e48 | −0.229827 | ||||||||
\(157\) | 1.07839e49 | 0.421729 | 0.210865 | − | 0.977515i | \(-0.432372\pi\) | ||||
0.210865 | + | 0.977515i | \(0.432372\pi\) | |||||||
\(158\) | 1.14065e49 | 0.386693 | ||||||||
\(159\) | 2.83401e49 | 0.833616 | ||||||||
\(160\) | −6.17163e48 | −0.157652 | ||||||||
\(161\) | 3.81400e49 | 0.846835 | ||||||||
\(162\) | 1.59654e49 | 0.308383 | ||||||||
\(163\) | 9.21779e49 | 1.55026 | 0.775132 | − | 0.631799i | \(-0.217683\pi\) | ||||
0.775132 | + | 0.631799i | \(0.217683\pi\) | |||||||
\(164\) | −4.15913e49 | −0.609560 | ||||||||
\(165\) | 2.50628e49 | 0.320362 | ||||||||
\(166\) | −7.16078e49 | −0.798966 | ||||||||
\(167\) | −1.28707e50 | −1.25453 | −0.627266 | − | 0.778805i | \(-0.715826\pi\) | ||||
−0.627266 | + | 0.778805i | \(0.715826\pi\) | |||||||
\(168\) | −9.89690e48 | −0.0843413 | ||||||||
\(169\) | 6.51488e48 | 0.0485798 | ||||||||
\(170\) | −3.41461e49 | −0.222967 | ||||||||
\(171\) | 1.70081e48 | 0.00973291 | ||||||||
\(172\) | 8.73382e49 | 0.438343 | ||||||||
\(173\) | −1.85770e50 | −0.818350 | −0.409175 | − | 0.912456i | \(-0.634183\pi\) | ||||
−0.409175 | + | 0.912456i | \(0.634183\pi\) | |||||||
\(174\) | −1.26138e50 | −0.488075 | ||||||||
\(175\) | −3.19782e49 | −0.108767 | ||||||||
\(176\) | 6.68668e49 | 0.200067 | ||||||||
\(177\) | 1.63497e50 | 0.430636 | ||||||||
\(178\) | 2.43834e50 | 0.565775 | ||||||||
\(179\) | 1.41352e50 | 0.289141 | 0.144571 | − | 0.989494i | \(-0.453820\pi\) | ||||
0.144571 | + | 0.989494i | \(0.453820\pi\) | |||||||
\(180\) | 1.97313e50 | 0.356060 | ||||||||
\(181\) | −2.62197e50 | −0.417695 | −0.208848 | − | 0.977948i | \(-0.566971\pi\) | ||||
−0.208848 | + | 0.977948i | \(0.566971\pi\) | |||||||
\(182\) | 2.73431e50 | 0.384805 | ||||||||
\(183\) | −4.32219e50 | −0.537717 | ||||||||
\(184\) | 5.11917e50 | 0.563377 | ||||||||
\(185\) | 5.39691e50 | 0.525753 | ||||||||
\(186\) | −6.50366e50 | −0.561199 | ||||||||
\(187\) | 3.69958e50 | 0.282954 | ||||||||
\(188\) | 2.36866e50 | 0.160676 | ||||||||
\(189\) | 7.12669e50 | 0.429040 | ||||||||
\(190\) | 1.43774e49 | 0.00768642 | ||||||||
\(191\) | −3.56974e51 | −1.69584 | −0.847922 | − | 0.530121i | \(-0.822146\pi\) | ||||
−0.847922 | + | 0.530121i | \(0.822146\pi\) | |||||||
\(192\) | −1.32837e50 | −0.0561100 | ||||||||
\(193\) | −9.65667e50 | −0.362901 | −0.181450 | − | 0.983400i | \(-0.558079\pi\) | ||||
−0.181450 | + | 0.983400i | \(0.558079\pi\) | |||||||
\(194\) | −1.99979e51 | −0.669029 | ||||||||
\(195\) | 1.37558e51 | 0.409927 | ||||||||
\(196\) | −1.35082e51 | −0.358785 | ||||||||
\(197\) | 4.05849e51 | 0.961335 | 0.480668 | − | 0.876903i | \(-0.340394\pi\) | ||||
0.480668 | + | 0.876903i | \(0.340394\pi\) | |||||||
\(198\) | −2.13780e51 | −0.451855 | ||||||||
\(199\) | 3.22222e50 | 0.0608081 | 0.0304040 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304040 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(200\) | −4.29214e50 | −0.0723600 | ||||||||
\(201\) | 3.27660e51 | 0.493756 | ||||||||
\(202\) | 5.31221e50 | 0.0715928 | ||||||||
\(203\) | 6.77622e51 | 0.817197 | ||||||||
\(204\) | −7.34953e50 | −0.0793562 | ||||||||
\(205\) | 1.12404e52 | 1.08723 | ||||||||
\(206\) | 1.04262e52 | 0.903882 | ||||||||
\(207\) | −1.63665e52 | −1.27240 | ||||||||
\(208\) | 3.67000e51 | 0.256000 | ||||||||
\(209\) | −1.55773e50 | −0.00975438 | ||||||||
\(210\) | 2.67473e51 | 0.150434 | ||||||||
\(211\) | −2.89921e52 | −1.46529 | −0.732647 | − | 0.680608i | \(-0.761716\pi\) | ||||
−0.732647 | + | 0.680608i | \(0.761716\pi\) | |||||||
\(212\) | −2.04344e52 | −0.928551 | ||||||||
\(213\) | −1.15511e52 | −0.472151 | ||||||||
\(214\) | 5.79978e51 | 0.213355 | ||||||||
\(215\) | −2.36039e52 | −0.781842 | ||||||||
\(216\) | 9.56548e51 | 0.285428 | ||||||||
\(217\) | 3.49382e52 | 0.939629 | ||||||||
\(218\) | 3.66477e52 | 0.888741 | ||||||||
\(219\) | −3.05959e52 | −0.669378 | ||||||||
\(220\) | −1.80714e52 | −0.356846 | ||||||||
\(221\) | 2.03052e52 | 0.362061 | ||||||||
\(222\) | 1.16162e52 | 0.187121 | ||||||||
\(223\) | 5.82693e52 | 0.848360 | 0.424180 | − | 0.905578i | \(-0.360562\pi\) | ||||
0.424180 | + | 0.905578i | \(0.360562\pi\) | |||||||
\(224\) | 7.13609e51 | 0.0939464 | ||||||||
\(225\) | 1.37224e52 | 0.163426 | ||||||||
\(226\) | −2.95003e52 | −0.317970 | ||||||||
\(227\) | −6.91309e52 | −0.674668 | −0.337334 | − | 0.941385i | \(-0.609525\pi\) | ||||
−0.337334 | + | 0.941385i | \(0.609525\pi\) | |||||||
\(228\) | 3.09456e50 | 0.00273567 | ||||||||
\(229\) | 2.12040e53 | 1.69871 | 0.849355 | − | 0.527822i | \(-0.176991\pi\) | ||||
0.849355 | + | 0.527822i | \(0.176991\pi\) | |||||||
\(230\) | −1.38350e53 | −1.00486 | ||||||||
\(231\) | −2.89795e52 | −0.190907 | ||||||||
\(232\) | 9.09507e52 | 0.543659 | ||||||||
\(233\) | 5.96910e52 | 0.323892 | 0.161946 | − | 0.986800i | \(-0.448223\pi\) | ||||
0.161946 | + | 0.986800i | \(0.448223\pi\) | |||||||
\(234\) | −1.17333e53 | −0.578182 | ||||||||
\(235\) | −6.40152e52 | −0.286587 | ||||||||
\(236\) | −1.17888e53 | −0.479678 | ||||||||
\(237\) | −6.63513e52 | −0.245477 | ||||||||
\(238\) | 3.94823e52 | 0.132868 | ||||||||
\(239\) | −5.65103e53 | −1.73051 | −0.865256 | − | 0.501330i | \(-0.832844\pi\) | ||||
−0.865256 | + | 0.501330i | \(0.832844\pi\) | |||||||
\(240\) | 3.59003e52 | 0.100080 | ||||||||
\(241\) | 5.60656e53 | 1.42335 | 0.711677 | − | 0.702507i | \(-0.247936\pi\) | ||||
0.711677 | + | 0.702507i | \(0.247936\pi\) | |||||||
\(242\) | −1.09930e53 | −0.254255 | ||||||||
\(243\) | −4.75857e53 | −1.00308 | ||||||||
\(244\) | 3.11648e53 | 0.598954 | ||||||||
\(245\) | 3.65070e53 | 0.639941 | ||||||||
\(246\) | 2.41937e53 | 0.386956 | ||||||||
\(247\) | −8.54961e51 | −0.0124814 | ||||||||
\(248\) | 4.68942e53 | 0.625110 | ||||||||
\(249\) | 4.16542e53 | 0.507194 | ||||||||
\(250\) | 6.82773e53 | 0.759672 | ||||||||
\(251\) | −1.07353e54 | −1.09183 | −0.545915 | − | 0.837840i | \(-0.683818\pi\) | ||||
−0.545915 | + | 0.837840i | \(0.683818\pi\) | |||||||
\(252\) | −2.28148e53 | −0.212180 | ||||||||
\(253\) | 1.49896e54 | 1.27520 | ||||||||
\(254\) | −6.40962e53 | −0.498969 | ||||||||
\(255\) | 1.98628e53 | 0.141542 | ||||||||
\(256\) | 9.57810e52 | 0.0625000 | ||||||||
\(257\) | −2.16725e54 | −1.29543 | −0.647715 | − | 0.761883i | \(-0.724275\pi\) | ||||
−0.647715 | + | 0.761883i | \(0.724275\pi\) | |||||||
\(258\) | −5.08045e53 | −0.278265 | ||||||||
\(259\) | −6.24031e53 | −0.313301 | ||||||||
\(260\) | −9.91850e53 | −0.456610 | ||||||||
\(261\) | −2.90778e54 | −1.22786 | ||||||||
\(262\) | 5.23292e53 | 0.202752 | ||||||||
\(263\) | 8.56704e53 | 0.304668 | 0.152334 | − | 0.988329i | \(-0.451321\pi\) | ||||
0.152334 | + | 0.988329i | \(0.451321\pi\) | |||||||
\(264\) | −3.88964e53 | −0.127005 | ||||||||
\(265\) | 5.52259e54 | 1.65619 | ||||||||
\(266\) | −1.66242e52 | −0.00458041 | ||||||||
\(267\) | −1.41838e54 | −0.359161 | ||||||||
\(268\) | −2.36257e54 | −0.549987 | ||||||||
\(269\) | 5.69316e54 | 1.21879 | 0.609393 | − | 0.792868i | \(-0.291413\pi\) | ||||
0.609393 | + | 0.792868i | \(0.291413\pi\) | |||||||
\(270\) | −2.58516e54 | −0.509099 | ||||||||
\(271\) | 5.25688e54 | 0.952618 | 0.476309 | − | 0.879278i | \(-0.341974\pi\) | ||||
0.476309 | + | 0.879278i | \(0.341974\pi\) | |||||||
\(272\) | 5.29933e53 | 0.0883936 | ||||||||
\(273\) | −1.59054e54 | −0.244279 | ||||||||
\(274\) | 4.85226e54 | 0.686367 | ||||||||
\(275\) | −1.25680e54 | −0.163787 | ||||||||
\(276\) | −2.97782e54 | −0.357638 | ||||||||
\(277\) | 5.03893e54 | 0.557883 | 0.278942 | − | 0.960308i | \(-0.410016\pi\) | ||||
0.278942 | + | 0.960308i | \(0.410016\pi\) | |||||||
\(278\) | 6.07581e54 | 0.620292 | ||||||||
\(279\) | −1.49925e55 | −1.41182 | ||||||||
\(280\) | −1.92859e54 | −0.167566 | ||||||||
\(281\) | −1.97183e55 | −1.58117 | −0.790584 | − | 0.612354i | \(-0.790223\pi\) | ||||
−0.790584 | + | 0.612354i | \(0.790223\pi\) | |||||||
\(282\) | −1.37785e54 | −0.101999 | ||||||||
\(283\) | 1.50647e55 | 1.02983 | 0.514916 | − | 0.857241i | \(-0.327823\pi\) | ||||
0.514916 | + | 0.857241i | \(0.327823\pi\) | |||||||
\(284\) | 8.32882e54 | 0.525922 | ||||||||
\(285\) | −8.36332e52 | −0.00487943 | ||||||||
\(286\) | 1.07463e55 | 0.579457 | ||||||||
\(287\) | −1.29970e55 | −0.647890 | ||||||||
\(288\) | −3.06221e54 | −0.141157 | ||||||||
\(289\) | −2.05212e55 | −0.874985 | ||||||||
\(290\) | −2.45803e55 | −0.969687 | ||||||||
\(291\) | 1.16328e55 | 0.424708 | ||||||||
\(292\) | 2.20610e55 | 0.745609 | ||||||||
\(293\) | −2.45911e55 | −0.769584 | −0.384792 | − | 0.923003i | \(-0.625727\pi\) | ||||
−0.384792 | + | 0.923003i | \(0.625727\pi\) | |||||||
\(294\) | 7.85769e54 | 0.227761 | ||||||||
\(295\) | 3.18603e55 | 0.855569 | ||||||||
\(296\) | −8.37578e54 | −0.208431 | ||||||||
\(297\) | 2.80090e55 | 0.646068 | ||||||||
\(298\) | 8.26243e54 | 0.176702 | ||||||||
\(299\) | 8.22709e55 | 1.63172 | ||||||||
\(300\) | 2.49673e54 | 0.0459350 | ||||||||
\(301\) | 2.72926e55 | 0.465907 | ||||||||
\(302\) | −5.15729e55 | −0.817081 | ||||||||
\(303\) | −3.09011e54 | −0.0454480 | ||||||||
\(304\) | −2.23131e53 | −0.00304722 | ||||||||
\(305\) | −8.42258e55 | −1.06831 | ||||||||
\(306\) | −1.69425e55 | −0.199639 | ||||||||
\(307\) | −7.26437e54 | −0.0795398 | −0.0397699 | − | 0.999209i | \(-0.512662\pi\) | ||||
−0.0397699 | + | 0.999209i | \(0.512662\pi\) | |||||||
\(308\) | 2.08955e55 | 0.212648 | ||||||||
\(309\) | −6.06489e55 | −0.573795 | ||||||||
\(310\) | −1.26736e56 | −1.11497 | ||||||||
\(311\) | 5.05100e55 | 0.413303 | 0.206652 | − | 0.978415i | \(-0.433743\pi\) | ||||
0.206652 | + | 0.978415i | \(0.433743\pi\) | |||||||
\(312\) | −2.13484e55 | −0.162512 | ||||||||
\(313\) | −1.13054e56 | −0.800827 | −0.400413 | − | 0.916335i | \(-0.631133\pi\) | ||||
−0.400413 | + | 0.916335i | \(0.631133\pi\) | |||||||
\(314\) | 4.52310e55 | 0.298208 | ||||||||
\(315\) | 6.16590e55 | 0.378450 | ||||||||
\(316\) | 4.78421e55 | 0.273433 | ||||||||
\(317\) | −1.02352e56 | −0.544834 | −0.272417 | − | 0.962179i | \(-0.587823\pi\) | ||||
−0.272417 | + | 0.962179i | \(0.587823\pi\) | |||||||
\(318\) | 1.18867e56 | 0.589455 | ||||||||
\(319\) | 2.66316e56 | 1.23057 | ||||||||
\(320\) | −2.58857e55 | −0.111477 | ||||||||
\(321\) | −3.37373e55 | −0.135440 | ||||||||
\(322\) | 1.59971e56 | 0.598803 | ||||||||
\(323\) | −1.23453e54 | −0.00430968 | ||||||||
\(324\) | 6.69636e55 | 0.218060 | ||||||||
\(325\) | −6.89795e55 | −0.209577 | ||||||||
\(326\) | 3.86622e56 | 1.09620 | ||||||||
\(327\) | −2.13179e56 | −0.564184 | ||||||||
\(328\) | −1.74447e56 | −0.431024 | ||||||||
\(329\) | 7.40191e55 | 0.170780 | ||||||||
\(330\) | 1.05121e56 | 0.226530 | ||||||||
\(331\) | −4.11537e56 | −0.828474 | −0.414237 | − | 0.910169i | \(-0.635952\pi\) | ||||
−0.414237 | + | 0.910169i | \(0.635952\pi\) | |||||||
\(332\) | −3.00345e56 | −0.564955 | ||||||||
\(333\) | 2.67781e56 | 0.470744 | ||||||||
\(334\) | −5.39836e56 | −0.887088 | ||||||||
\(335\) | 6.38506e56 | 0.980973 | ||||||||
\(336\) | −4.15106e55 | −0.0596383 | ||||||||
\(337\) | −1.30888e57 | −1.75884 | −0.879422 | − | 0.476044i | \(-0.842070\pi\) | ||||
−0.879422 | + | 0.476044i | \(0.842070\pi\) | |||||||
\(338\) | 2.73254e55 | 0.0343511 | ||||||||
\(339\) | 1.71603e56 | 0.201851 | ||||||||
\(340\) | −1.43219e56 | −0.157662 | ||||||||
\(341\) | 1.37313e57 | 1.41494 | ||||||||
\(342\) | 7.13370e54 | 0.00688220 | ||||||||
\(343\) | −1.01039e57 | −0.912787 | ||||||||
\(344\) | 3.66323e56 | 0.309955 | ||||||||
\(345\) | 8.04783e56 | 0.637895 | ||||||||
\(346\) | −7.79177e56 | −0.578661 | ||||||||
\(347\) | −2.43581e56 | −0.169524 | −0.0847620 | − | 0.996401i | \(-0.527013\pi\) | ||||
−0.0847620 | + | 0.996401i | \(0.527013\pi\) | |||||||
\(348\) | −5.29060e56 | −0.345121 | ||||||||
\(349\) | 9.47821e56 | 0.579634 | 0.289817 | − | 0.957082i | \(-0.406405\pi\) | ||||
0.289817 | + | 0.957082i | \(0.406405\pi\) | |||||||
\(350\) | −1.34126e56 | −0.0769101 | ||||||||
\(351\) | 1.53728e57 | 0.826691 | ||||||||
\(352\) | 2.80460e56 | 0.141469 | ||||||||
\(353\) | 2.19394e57 | 1.03823 | 0.519115 | − | 0.854704i | \(-0.326262\pi\) | ||||
0.519115 | + | 0.854704i | \(0.326262\pi\) | |||||||
\(354\) | 6.85754e56 | 0.304506 | ||||||||
\(355\) | −2.25094e57 | −0.938050 | ||||||||
\(356\) | 1.02271e57 | 0.400063 | ||||||||
\(357\) | −2.29668e56 | −0.0843463 | ||||||||
\(358\) | 5.92875e56 | 0.204454 | ||||||||
\(359\) | −1.03080e57 | −0.333848 | −0.166924 | − | 0.985970i | \(-0.553384\pi\) | ||||
−0.166924 | + | 0.985970i | \(0.553384\pi\) | |||||||
\(360\) | 8.27589e56 | 0.251773 | ||||||||
\(361\) | −3.49822e57 | −0.999851 | ||||||||
\(362\) | −1.09973e57 | −0.295355 | ||||||||
\(363\) | 6.39460e56 | 0.161404 | ||||||||
\(364\) | 1.14685e57 | 0.272098 | ||||||||
\(365\) | −5.96218e57 | −1.32989 | ||||||||
\(366\) | −1.81286e57 | −0.380223 | ||||||||
\(367\) | −6.34847e57 | −1.25223 | −0.626113 | − | 0.779733i | \(-0.715355\pi\) | ||||
−0.626113 | + | 0.779733i | \(0.715355\pi\) | |||||||
\(368\) | 2.14714e57 | 0.398367 | ||||||||
\(369\) | 5.57723e57 | 0.973475 | ||||||||
\(370\) | 2.26363e57 | 0.371763 | ||||||||
\(371\) | −6.38563e57 | −0.986940 | ||||||||
\(372\) | −2.72783e57 | −0.396828 | ||||||||
\(373\) | 1.18275e58 | 1.61974 | 0.809869 | − | 0.586610i | \(-0.199538\pi\) | ||||
0.809869 | + | 0.586610i | \(0.199538\pi\) | |||||||
\(374\) | 1.55172e57 | 0.200079 | ||||||||
\(375\) | −3.97169e57 | −0.482249 | ||||||||
\(376\) | 9.93488e56 | 0.113615 | ||||||||
\(377\) | 1.46168e58 | 1.57461 | ||||||||
\(378\) | 2.98915e57 | 0.303377 | ||||||||
\(379\) | 1.27405e58 | 1.21844 | 0.609219 | − | 0.793002i | \(-0.291483\pi\) | ||||
0.609219 | + | 0.793002i | \(0.291483\pi\) | |||||||
\(380\) | 6.03031e55 | 0.00543512 | ||||||||
\(381\) | 3.72847e57 | 0.316752 | ||||||||
\(382\) | −1.49726e58 | −1.19914 | ||||||||
\(383\) | −7.37288e57 | −0.556756 | −0.278378 | − | 0.960472i | \(-0.589797\pi\) | ||||
−0.278378 | + | 0.960472i | \(0.589797\pi\) | |||||||
\(384\) | −5.57157e56 | −0.0396758 | ||||||||
\(385\) | −5.64719e57 | −0.379285 | ||||||||
\(386\) | −4.05030e57 | −0.256610 | ||||||||
\(387\) | −1.17117e58 | −0.700040 | ||||||||
\(388\) | −8.38772e57 | −0.473075 | ||||||||
\(389\) | 2.64413e57 | 0.140740 | 0.0703699 | − | 0.997521i | \(-0.477582\pi\) | ||||
0.0703699 | + | 0.997521i | \(0.477582\pi\) | |||||||
\(390\) | 5.76959e57 | 0.289862 | ||||||||
\(391\) | 1.18796e58 | 0.563410 | ||||||||
\(392\) | −5.66573e57 | −0.253699 | ||||||||
\(393\) | −3.04398e57 | −0.128709 | ||||||||
\(394\) | 1.70226e58 | 0.679767 | ||||||||
\(395\) | −1.29298e58 | −0.487704 | ||||||||
\(396\) | −8.96656e57 | −0.319510 | ||||||||
\(397\) | −3.15430e58 | −1.06198 | −0.530991 | − | 0.847378i | \(-0.678180\pi\) | ||||
−0.530991 | + | 0.847378i | \(0.678180\pi\) | |||||||
\(398\) | 1.35150e57 | 0.0429978 | ||||||||
\(399\) | 9.67029e55 | 0.00290770 | ||||||||
\(400\) | −1.80025e57 | −0.0511662 | ||||||||
\(401\) | −4.27820e57 | −0.114951 | −0.0574755 | − | 0.998347i | \(-0.518305\pi\) | ||||
−0.0574755 | + | 0.998347i | \(0.518305\pi\) | |||||||
\(402\) | 1.37431e58 | 0.349138 | ||||||||
\(403\) | 7.53643e58 | 1.81052 | ||||||||
\(404\) | 2.22810e57 | 0.0506238 | ||||||||
\(405\) | −1.80975e58 | −0.388939 | ||||||||
\(406\) | 2.84215e58 | 0.577845 | ||||||||
\(407\) | −2.45254e58 | −0.471783 | ||||||||
\(408\) | −3.08262e57 | −0.0561133 | ||||||||
\(409\) | 6.30167e57 | 0.108563 | 0.0542814 | − | 0.998526i | \(-0.482713\pi\) | ||||
0.0542814 | + | 0.998526i | \(0.482713\pi\) | |||||||
\(410\) | 4.71458e58 | 0.768788 | ||||||||
\(411\) | −2.82256e58 | −0.435714 | ||||||||
\(412\) | 4.37305e58 | 0.639141 | ||||||||
\(413\) | −3.68393e58 | −0.509841 | ||||||||
\(414\) | −6.86460e58 | −0.899720 | ||||||||
\(415\) | 8.11710e58 | 1.00767 | ||||||||
\(416\) | 1.53931e58 | 0.181020 | ||||||||
\(417\) | −3.53429e58 | −0.393769 | ||||||||
\(418\) | −6.53358e56 | −0.00689739 | ||||||||
\(419\) | 5.08887e56 | 0.00509104 | 0.00254552 | − | 0.999997i | \(-0.499190\pi\) | ||||
0.00254552 | + | 0.999997i | \(0.499190\pi\) | |||||||
\(420\) | 1.12186e58 | 0.106373 | ||||||||
\(421\) | −2.18083e58 | −0.196009 | −0.0980044 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980044 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(422\) | −1.21602e59 | −1.03612 | ||||||||
\(423\) | −3.17627e58 | −0.256602 | ||||||||
\(424\) | −8.57082e58 | −0.656585 | ||||||||
\(425\) | −9.96036e57 | −0.0723643 | ||||||||
\(426\) | −4.84487e58 | −0.333861 | ||||||||
\(427\) | 9.73881e58 | 0.636618 | ||||||||
\(428\) | 2.43261e58 | 0.150864 | ||||||||
\(429\) | −6.25109e58 | −0.367847 | ||||||||
\(430\) | −9.90021e58 | −0.552846 | ||||||||
\(431\) | 9.32922e58 | 0.494432 | 0.247216 | − | 0.968960i | \(-0.420484\pi\) | ||||
0.247216 | + | 0.968960i | \(0.420484\pi\) | |||||||
\(432\) | 4.01205e58 | 0.201828 | ||||||||
\(433\) | −3.45886e58 | −0.165179 | −0.0825896 | − | 0.996584i | \(-0.526319\pi\) | ||||
−0.0825896 | + | 0.996584i | \(0.526319\pi\) | |||||||
\(434\) | 1.46541e59 | 0.664418 | ||||||||
\(435\) | 1.42983e59 | 0.615569 | ||||||||
\(436\) | 1.53711e59 | 0.628435 | ||||||||
\(437\) | −5.00196e57 | −0.0194226 | ||||||||
\(438\) | −1.28329e59 | −0.473321 | ||||||||
\(439\) | 5.43939e59 | 1.90589 | 0.952946 | − | 0.303139i | \(-0.0980348\pi\) | ||||
0.952946 | + | 0.303139i | \(0.0980348\pi\) | |||||||
\(440\) | −7.57968e58 | −0.252328 | ||||||||
\(441\) | 1.81139e59 | 0.572985 | ||||||||
\(442\) | 8.51663e58 | 0.256016 | ||||||||
\(443\) | −4.79483e59 | −1.36990 | −0.684951 | − | 0.728590i | \(-0.740176\pi\) | ||||
−0.684951 | + | 0.728590i | \(0.740176\pi\) | |||||||
\(444\) | 4.87218e58 | 0.132314 | ||||||||
\(445\) | −2.76398e59 | −0.713566 | ||||||||
\(446\) | 2.44399e59 | 0.599881 | ||||||||
\(447\) | −4.80625e58 | −0.112173 | ||||||||
\(448\) | 2.99309e58 | 0.0664301 | ||||||||
\(449\) | −8.20387e59 | −1.73171 | −0.865857 | − | 0.500292i | \(-0.833226\pi\) | ||||
−0.865857 | + | 0.500292i | \(0.833226\pi\) | |||||||
\(450\) | 5.75557e58 | 0.115560 | ||||||||
\(451\) | −5.10804e59 | −0.975623 | ||||||||
\(452\) | −1.23733e59 | −0.224839 | ||||||||
\(453\) | 2.99999e59 | 0.518693 | ||||||||
\(454\) | −2.89956e59 | −0.477062 | ||||||||
\(455\) | −3.09947e59 | −0.485323 | ||||||||
\(456\) | 1.29795e57 | 0.00193441 | ||||||||
\(457\) | 6.40430e59 | 0.908567 | 0.454284 | − | 0.890857i | \(-0.349895\pi\) | ||||
0.454284 | + | 0.890857i | \(0.349895\pi\) | |||||||
\(458\) | 8.89360e59 | 1.20117 | ||||||||
\(459\) | 2.21977e59 | 0.285445 | ||||||||
\(460\) | −5.80283e59 | −0.710541 | ||||||||
\(461\) | 5.31409e58 | 0.0619667 | 0.0309834 | − | 0.999520i | \(-0.490136\pi\) | ||||
0.0309834 | + | 0.999520i | \(0.490136\pi\) | |||||||
\(462\) | −1.21549e59 | −0.134991 | ||||||||
\(463\) | −6.75536e59 | −0.714622 | −0.357311 | − | 0.933985i | \(-0.616306\pi\) | ||||
−0.357311 | + | 0.933985i | \(0.616306\pi\) | |||||||
\(464\) | 3.81475e59 | 0.384425 | ||||||||
\(465\) | 7.37222e59 | 0.707794 | ||||||||
\(466\) | 2.50362e59 | 0.229027 | ||||||||
\(467\) | 1.81391e60 | 1.58119 | 0.790597 | − | 0.612337i | \(-0.209770\pi\) | ||||
0.790597 | + | 0.612337i | \(0.209770\pi\) | |||||||
\(468\) | −4.92131e59 | −0.408836 | ||||||||
\(469\) | −7.38288e59 | −0.584571 | ||||||||
\(470\) | −2.68499e59 | −0.202647 | ||||||||
\(471\) | −2.63108e59 | −0.189306 | ||||||||
\(472\) | −4.94459e59 | −0.339184 | ||||||||
\(473\) | 1.07264e60 | 0.701584 | ||||||||
\(474\) | −2.78297e59 | −0.173579 | ||||||||
\(475\) | 4.19386e57 | 0.00249464 | ||||||||
\(476\) | 1.65601e59 | 0.0939519 | ||||||||
\(477\) | 2.74017e60 | 1.48291 | ||||||||
\(478\) | −2.37021e60 | −1.22366 | ||||||||
\(479\) | −1.52375e60 | −0.750522 | −0.375261 | − | 0.926919i | \(-0.622447\pi\) | ||||
−0.375261 | + | 0.926919i | \(0.622447\pi\) | |||||||
\(480\) | 1.50577e59 | 0.0707669 | ||||||||
\(481\) | −1.34608e60 | −0.603681 | ||||||||
\(482\) | 2.35156e60 | 1.00646 | ||||||||
\(483\) | −9.30550e59 | −0.380127 | ||||||||
\(484\) | −4.61078e59 | −0.179785 | ||||||||
\(485\) | 2.26686e60 | 0.843791 | ||||||||
\(486\) | −1.99589e60 | −0.709284 | ||||||||
\(487\) | −4.56850e60 | −1.55014 | −0.775072 | − | 0.631873i | \(-0.782287\pi\) | ||||
−0.775072 | + | 0.631873i | \(0.782287\pi\) | |||||||
\(488\) | 1.30715e60 | 0.423525 | ||||||||
\(489\) | −2.24898e60 | −0.695882 | ||||||||
\(490\) | 1.53122e60 | 0.452506 | ||||||||
\(491\) | −4.69070e60 | −1.32405 | −0.662024 | − | 0.749483i | \(-0.730302\pi\) | ||||
−0.662024 | + | 0.749483i | \(0.730302\pi\) | |||||||
\(492\) | 1.01476e60 | 0.273619 | ||||||||
\(493\) | 2.11061e60 | 0.543691 | ||||||||
\(494\) | −3.58597e58 | −0.00882571 | ||||||||
\(495\) | 2.42330e60 | 0.569888 | ||||||||
\(496\) | 1.96689e60 | 0.442020 | ||||||||
\(497\) | 2.60270e60 | 0.558993 | ||||||||
\(498\) | 1.74710e60 | 0.358640 | ||||||||
\(499\) | 2.78439e60 | 0.546347 | 0.273173 | − | 0.961965i | \(-0.411927\pi\) | ||||
0.273173 | + | 0.961965i | \(0.411927\pi\) | |||||||
\(500\) | 2.86376e60 | 0.537169 | ||||||||
\(501\) | 3.14022e60 | 0.563134 | ||||||||
\(502\) | −4.50271e60 | −0.772041 | ||||||||
\(503\) | −3.32687e59 | −0.0545451 | −0.0272726 | − | 0.999628i | \(-0.508682\pi\) | ||||
−0.0272726 | + | 0.999628i | \(0.508682\pi\) | |||||||
\(504\) | −9.56920e59 | −0.150034 | ||||||||
\(505\) | −6.02165e59 | −0.0902941 | ||||||||
\(506\) | 6.28711e60 | 0.901705 | ||||||||
\(507\) | −1.58952e59 | −0.0218065 | ||||||||
\(508\) | −2.68839e60 | −0.352824 | ||||||||
\(509\) | −8.27552e60 | −1.03907 | −0.519535 | − | 0.854449i | \(-0.673895\pi\) | ||||
−0.519535 | + | 0.854449i | \(0.673895\pi\) | |||||||
\(510\) | 8.33105e59 | 0.100085 | ||||||||
\(511\) | 6.89392e60 | 0.792494 | ||||||||
\(512\) | 4.01735e59 | 0.0441942 | ||||||||
\(513\) | −9.34646e58 | −0.00984025 | ||||||||
\(514\) | −9.09011e60 | −0.916007 | ||||||||
\(515\) | −1.18186e61 | −1.13999 | ||||||||
\(516\) | −2.13090e60 | −0.196763 | ||||||||
\(517\) | 2.90907e60 | 0.257168 | ||||||||
\(518\) | −2.61738e60 | −0.221537 | ||||||||
\(519\) | 4.53247e60 | 0.367341 | ||||||||
\(520\) | −4.16012e60 | −0.322872 | ||||||||
\(521\) | −1.78155e61 | −1.32419 | −0.662093 | − | 0.749422i | \(-0.730332\pi\) | ||||
−0.662093 | + | 0.749422i | \(0.730332\pi\) | |||||||
\(522\) | −1.21961e61 | −0.868231 | ||||||||
\(523\) | 1.77356e61 | 1.20937 | 0.604683 | − | 0.796466i | \(-0.293300\pi\) | ||||
0.604683 | + | 0.796466i | \(0.293300\pi\) | |||||||
\(524\) | 2.19484e60 | 0.143367 | ||||||||
\(525\) | 7.80213e59 | 0.0488235 | ||||||||
\(526\) | 3.59328e60 | 0.215433 | ||||||||
\(527\) | 1.08823e61 | 0.625147 | ||||||||
\(528\) | −1.63143e60 | −0.0898061 | ||||||||
\(529\) | 2.91765e61 | 1.53915 | ||||||||
\(530\) | 2.31634e61 | 1.17111 | ||||||||
\(531\) | 1.58083e61 | 0.766053 | ||||||||
\(532\) | −6.97270e58 | −0.00323884 | ||||||||
\(533\) | −2.80356e61 | −1.24838 | ||||||||
\(534\) | −5.94912e60 | −0.253965 | ||||||||
\(535\) | −6.57434e60 | −0.269087 | ||||||||
\(536\) | −9.90934e60 | −0.388899 | ||||||||
\(537\) | −3.44875e60 | −0.129790 | ||||||||
\(538\) | 2.38789e61 | 0.861812 | ||||||||
\(539\) | −1.65900e61 | −0.574249 | ||||||||
\(540\) | −1.08429e61 | −0.359987 | ||||||||
\(541\) | 5.18437e60 | 0.165104 | 0.0825520 | − | 0.996587i | \(-0.473693\pi\) | ||||
0.0825520 | + | 0.996587i | \(0.473693\pi\) | |||||||
\(542\) | 2.20489e61 | 0.673603 | ||||||||
\(543\) | 6.39714e60 | 0.187495 | ||||||||
\(544\) | 2.22270e60 | 0.0625037 | ||||||||
\(545\) | −4.15419e61 | −1.12090 | ||||||||
\(546\) | −6.67122e60 | −0.172731 | ||||||||
\(547\) | −4.57431e60 | −0.113661 | −0.0568304 | − | 0.998384i | \(-0.518099\pi\) | ||||
−0.0568304 | + | 0.998384i | \(0.518099\pi\) | |||||||
\(548\) | 2.03519e61 | 0.485335 | ||||||||
\(549\) | −4.17907e61 | −0.956538 | ||||||||
\(550\) | −5.27138e60 | −0.115815 | ||||||||
\(551\) | −8.88682e59 | −0.0187428 | ||||||||
\(552\) | −1.24899e61 | −0.252889 | ||||||||
\(553\) | 1.49504e61 | 0.290627 | ||||||||
\(554\) | 2.11348e61 | 0.394483 | ||||||||
\(555\) | −1.31675e61 | −0.236000 | ||||||||
\(556\) | 2.54838e61 | 0.438613 | ||||||||
\(557\) | −1.47434e61 | −0.243700 | −0.121850 | − | 0.992549i | \(-0.538883\pi\) | ||||
−0.121850 | + | 0.992549i | \(0.538883\pi\) | |||||||
\(558\) | −6.28832e61 | −0.998309 | ||||||||
\(559\) | 5.88722e61 | 0.897728 | ||||||||
\(560\) | −8.08911e60 | −0.118487 | ||||||||
\(561\) | −9.02633e60 | −0.127013 | ||||||||
\(562\) | −8.27047e61 | −1.11805 | ||||||||
\(563\) | 6.02307e61 | 0.782310 | 0.391155 | − | 0.920325i | \(-0.372076\pi\) | ||||
0.391155 | + | 0.920325i | \(0.372076\pi\) | |||||||
\(564\) | −5.77911e60 | −0.0721242 | ||||||||
\(565\) | 3.34400e61 | 0.401030 | ||||||||
\(566\) | 6.31860e61 | 0.728201 | ||||||||
\(567\) | 2.09257e61 | 0.231772 | ||||||||
\(568\) | 3.49336e61 | 0.371883 | ||||||||
\(569\) | −1.83240e61 | −0.187497 | −0.0937487 | − | 0.995596i | \(-0.529885\pi\) | ||||
−0.0937487 | + | 0.995596i | \(0.529885\pi\) | |||||||
\(570\) | −3.50783e59 | −0.00345028 | ||||||||
\(571\) | 1.05375e62 | 0.996379 | 0.498189 | − | 0.867068i | \(-0.333998\pi\) | ||||
0.498189 | + | 0.867068i | \(0.333998\pi\) | |||||||
\(572\) | 4.50731e61 | 0.409738 | ||||||||
\(573\) | 8.70954e61 | 0.761230 | ||||||||
\(574\) | −5.45135e61 | −0.458128 | ||||||||
\(575\) | −4.03565e61 | −0.326127 | ||||||||
\(576\) | −1.28438e61 | −0.0998133 | ||||||||
\(577\) | 3.46971e60 | 0.0259321 | 0.0129660 | − | 0.999916i | \(-0.495873\pi\) | ||||
0.0129660 | + | 0.999916i | \(0.495873\pi\) | |||||||
\(578\) | −8.60720e61 | −0.618708 | ||||||||
\(579\) | 2.35606e61 | 0.162899 | ||||||||
\(580\) | −1.03097e62 | −0.685672 | ||||||||
\(581\) | −9.38559e61 | −0.600480 | ||||||||
\(582\) | 4.87913e61 | 0.300314 | ||||||||
\(583\) | −2.50965e62 | −1.48618 | ||||||||
\(584\) | 9.25305e61 | 0.527225 | ||||||||
\(585\) | 1.33003e62 | 0.729213 | ||||||||
\(586\) | −1.03142e62 | −0.544178 | ||||||||
\(587\) | −3.47497e62 | −1.76439 | −0.882194 | − | 0.470887i | \(-0.843934\pi\) | ||||
−0.882194 | + | 0.470887i | \(0.843934\pi\) | |||||||
\(588\) | 3.29575e61 | 0.161052 | ||||||||
\(589\) | −4.58205e60 | −0.0215509 | ||||||||
\(590\) | 1.33632e62 | 0.604979 | ||||||||
\(591\) | −9.90201e61 | −0.431524 | ||||||||
\(592\) | −3.51305e61 | −0.147383 | ||||||||
\(593\) | 2.38315e62 | 0.962546 | 0.481273 | − | 0.876571i | \(-0.340175\pi\) | ||||
0.481273 | + | 0.876571i | \(0.340175\pi\) | |||||||
\(594\) | 1.17478e62 | 0.456839 | ||||||||
\(595\) | −4.47551e61 | −0.167576 | ||||||||
\(596\) | 3.46552e61 | 0.124947 | ||||||||
\(597\) | −7.86166e60 | −0.0272955 | ||||||||
\(598\) | 3.45069e62 | 1.15380 | ||||||||
\(599\) | −1.44253e61 | −0.0464539 | −0.0232270 | − | 0.999730i | \(-0.507394\pi\) | ||||
−0.0232270 | + | 0.999730i | \(0.507394\pi\) | |||||||
\(600\) | 1.04721e61 | 0.0324809 | ||||||||
\(601\) | 1.16486e62 | 0.348016 | 0.174008 | − | 0.984744i | \(-0.444328\pi\) | ||||
0.174008 | + | 0.984744i | \(0.444328\pi\) | |||||||
\(602\) | 1.14474e62 | 0.329446 | ||||||||
\(603\) | 3.16811e62 | 0.878336 | ||||||||
\(604\) | −2.16312e62 | −0.577764 | ||||||||
\(605\) | 1.24611e62 | 0.320670 | ||||||||
\(606\) | −1.29609e61 | −0.0321366 | ||||||||
\(607\) | −9.22722e61 | −0.220458 | −0.110229 | − | 0.993906i | \(-0.535158\pi\) | ||||
−0.110229 | + | 0.993906i | \(0.535158\pi\) | |||||||
\(608\) | −9.35879e59 | −0.00215471 | ||||||||
\(609\) | −1.65328e62 | −0.366823 | ||||||||
\(610\) | −3.53269e62 | −0.755412 | ||||||||
\(611\) | 1.59665e62 | 0.329065 | ||||||||
\(612\) | −7.10618e61 | −0.141166 | ||||||||
\(613\) | 6.43322e61 | 0.123188 | 0.0615939 | − | 0.998101i | \(-0.480382\pi\) | ||||
0.0615939 | + | 0.998101i | \(0.480382\pi\) | |||||||
\(614\) | −3.04690e61 | −0.0562431 | ||||||||
\(615\) | −2.74247e62 | −0.488036 | ||||||||
\(616\) | 8.76419e61 | 0.150365 | ||||||||
\(617\) | 3.21910e62 | 0.532498 | 0.266249 | − | 0.963904i | \(-0.414216\pi\) | ||||
0.266249 | + | 0.963904i | \(0.414216\pi\) | |||||||
\(618\) | −2.54380e62 | −0.405735 | ||||||||
\(619\) | −1.15460e63 | −1.77579 | −0.887895 | − | 0.460046i | \(-0.847833\pi\) | ||||
−0.887895 | + | 0.460046i | \(0.847833\pi\) | |||||||
\(620\) | −5.31569e62 | −0.788400 | ||||||||
\(621\) | 8.99388e62 | 1.28643 | ||||||||
\(622\) | 2.11854e62 | 0.292249 | ||||||||
\(623\) | 3.19591e62 | 0.425220 | ||||||||
\(624\) | −8.95415e61 | −0.114913 | ||||||||
\(625\) | −6.08630e62 | −0.753447 | ||||||||
\(626\) | −4.74183e62 | −0.566270 | ||||||||
\(627\) | 3.80058e60 | 0.00437855 | ||||||||
\(628\) | 1.89712e62 | 0.210865 | ||||||||
\(629\) | −1.94369e62 | −0.208443 | ||||||||
\(630\) | 2.58616e62 | 0.267605 | ||||||||
\(631\) | 1.06339e63 | 1.06178 | 0.530889 | − | 0.847441i | \(-0.321858\pi\) | ||||
0.530889 | + | 0.847441i | \(0.321858\pi\) | |||||||
\(632\) | 2.00664e62 | 0.193346 | ||||||||
\(633\) | 7.07357e62 | 0.657741 | ||||||||
\(634\) | −4.29296e62 | −0.385256 | ||||||||
\(635\) | 7.26562e62 | 0.629309 | ||||||||
\(636\) | 4.98564e62 | 0.416808 | ||||||||
\(637\) | −9.10547e62 | −0.734794 | ||||||||
\(638\) | 1.11701e63 | 0.870146 | ||||||||
\(639\) | −1.11686e63 | −0.839904 | ||||||||
\(640\) | −1.08572e62 | −0.0788261 | ||||||||
\(641\) | −1.23129e63 | −0.863085 | −0.431543 | − | 0.902093i | \(-0.642031\pi\) | ||||
−0.431543 | + | 0.902093i | \(0.642031\pi\) | |||||||
\(642\) | −1.41505e62 | −0.0957706 | ||||||||
\(643\) | 6.42176e62 | 0.419669 | 0.209834 | − | 0.977737i | \(-0.432707\pi\) | ||||
0.209834 | + | 0.977737i | \(0.432707\pi\) | |||||||
\(644\) | 6.70967e62 | 0.423418 | ||||||||
\(645\) | 5.75894e62 | 0.350953 | ||||||||
\(646\) | −5.17799e60 | −0.00304740 | ||||||||
\(647\) | 2.16731e63 | 1.23190 | 0.615950 | − | 0.787785i | \(-0.288772\pi\) | ||||
0.615950 | + | 0.787785i | \(0.288772\pi\) | |||||||
\(648\) | 2.80866e62 | 0.154192 | ||||||||
\(649\) | −1.44784e63 | −0.767743 | ||||||||
\(650\) | −2.89321e62 | −0.148194 | ||||||||
\(651\) | −8.52431e62 | −0.421781 | ||||||||
\(652\) | 1.62161e63 | 0.775132 | ||||||||
\(653\) | 5.79373e61 | 0.0267554 | 0.0133777 | − | 0.999911i | \(-0.495742\pi\) | ||||
0.0133777 | + | 0.999911i | \(0.495742\pi\) | |||||||
\(654\) | −8.94139e62 | −0.398938 | ||||||||
\(655\) | −5.93177e62 | −0.255714 | ||||||||
\(656\) | −7.31683e62 | −0.304780 | ||||||||
\(657\) | −2.95829e63 | −1.19075 | ||||||||
\(658\) | 3.10459e62 | 0.120759 | ||||||||
\(659\) | −2.42846e63 | −0.912870 | −0.456435 | − | 0.889757i | \(-0.650874\pi\) | ||||
−0.456435 | + | 0.889757i | \(0.650874\pi\) | |||||||
\(660\) | 4.40910e62 | 0.160181 | ||||||||
\(661\) | −1.52653e63 | −0.536008 | −0.268004 | − | 0.963418i | \(-0.586364\pi\) | ||||
−0.268004 | + | 0.963418i | \(0.586364\pi\) | |||||||
\(662\) | −1.72611e63 | −0.585820 | ||||||||
\(663\) | −4.95411e62 | −0.162522 | ||||||||
\(664\) | −1.25974e63 | −0.399483 | ||||||||
\(665\) | 1.88443e61 | 0.00577689 | ||||||||
\(666\) | 1.12316e63 | 0.332867 | ||||||||
\(667\) | 8.55159e63 | 2.45028 | ||||||||
\(668\) | −2.26424e63 | −0.627266 | ||||||||
\(669\) | −1.42167e63 | −0.380812 | ||||||||
\(670\) | 2.67809e63 | 0.693653 | ||||||||
\(671\) | 3.82751e63 | 0.958648 | ||||||||
\(672\) | −1.74108e62 | −0.0421706 | ||||||||
\(673\) | 6.53256e63 | 1.53019 | 0.765094 | − | 0.643919i | \(-0.222693\pi\) | ||||
0.765094 | + | 0.643919i | \(0.222693\pi\) | |||||||
\(674\) | −5.48984e63 | −1.24369 | ||||||||
\(675\) | −7.54086e62 | −0.165229 | ||||||||
\(676\) | 1.14611e62 | 0.0242899 | ||||||||
\(677\) | 4.70923e63 | 0.965394 | 0.482697 | − | 0.875787i | \(-0.339657\pi\) | ||||
0.482697 | + | 0.875787i | \(0.339657\pi\) | |||||||
\(678\) | 7.19755e62 | 0.142730 | ||||||||
\(679\) | −2.62111e63 | −0.502823 | ||||||||
\(680\) | −6.00705e62 | −0.111484 | ||||||||
\(681\) | 1.68667e63 | 0.302845 | ||||||||
\(682\) | 5.75931e63 | 1.00051 | ||||||||
\(683\) | 4.97563e62 | 0.0836339 | 0.0418169 | − | 0.999125i | \(-0.486685\pi\) | ||||
0.0418169 | + | 0.999125i | \(0.486685\pi\) | |||||||
\(684\) | 2.99209e61 | 0.00486645 | ||||||||
\(685\) | −5.50027e63 | −0.865658 | ||||||||
\(686\) | −4.23787e63 | −0.645438 | ||||||||
\(687\) | −5.17340e63 | −0.762517 | ||||||||
\(688\) | 1.53647e63 | 0.219171 | ||||||||
\(689\) | −1.37743e64 | −1.90168 | ||||||||
\(690\) | 3.37550e63 | 0.451060 | ||||||||
\(691\) | 9.66259e63 | 1.24979 | 0.624896 | − | 0.780708i | \(-0.285142\pi\) | ||||
0.624896 | + | 0.780708i | \(0.285142\pi\) | |||||||
\(692\) | −3.26811e63 | −0.409175 | ||||||||
\(693\) | −2.80199e63 | −0.339601 | ||||||||
\(694\) | −1.02165e63 | −0.119872 | ||||||||
\(695\) | −6.88723e63 | −0.782324 | ||||||||
\(696\) | −2.21904e63 | −0.244038 | ||||||||
\(697\) | −4.04822e63 | −0.431049 | ||||||||
\(698\) | 3.97545e63 | 0.409863 | ||||||||
\(699\) | −1.45636e63 | −0.145389 | ||||||||
\(700\) | −5.62567e62 | −0.0543837 | ||||||||
\(701\) | 1.15174e64 | 1.07819 | 0.539097 | − | 0.842243i | \(-0.318765\pi\) | ||||
0.539097 | + | 0.842243i | \(0.318765\pi\) | |||||||
\(702\) | 6.44782e63 | 0.584559 | ||||||||
\(703\) | 8.18399e61 | 0.00718572 | ||||||||
\(704\) | 1.17633e63 | 0.100034 | ||||||||
\(705\) | 1.56186e63 | 0.128643 | ||||||||
\(706\) | 9.20204e63 | 0.734139 | ||||||||
\(707\) | 6.96268e62 | 0.0538071 | ||||||||
\(708\) | 2.87626e63 | 0.215318 | ||||||||
\(709\) | −2.22559e64 | −1.61401 | −0.807003 | − | 0.590548i | \(-0.798912\pi\) | ||||
−0.807003 | + | 0.590548i | \(0.798912\pi\) | |||||||
\(710\) | −9.44113e63 | −0.663302 | ||||||||
\(711\) | −6.41543e63 | −0.436677 | ||||||||
\(712\) | 4.28957e63 | 0.282888 | ||||||||
\(713\) | 4.40920e64 | 2.81738 | ||||||||
\(714\) | −9.63298e62 | −0.0596418 | ||||||||
\(715\) | −1.21814e64 | −0.730822 | ||||||||
\(716\) | 2.48670e63 | 0.144571 | ||||||||
\(717\) | 1.37875e64 | 0.776793 | ||||||||
\(718\) | −4.32349e63 | −0.236066 | ||||||||
\(719\) | 4.32783e62 | 0.0229018 | 0.0114509 | − | 0.999934i | \(-0.496355\pi\) | ||||
0.0114509 | + | 0.999934i | \(0.496355\pi\) | |||||||
\(720\) | 3.47116e63 | 0.178030 | ||||||||
\(721\) | 1.36655e64 | 0.679332 | ||||||||
\(722\) | −1.46726e64 | −0.707002 | ||||||||
\(723\) | −1.36790e64 | −0.638915 | ||||||||
\(724\) | −4.61261e63 | −0.208848 | ||||||||
\(725\) | −7.17002e63 | −0.314713 | ||||||||
\(726\) | 2.68209e63 | 0.114130 | ||||||||
\(727\) | −7.31606e63 | −0.301824 | −0.150912 | − | 0.988547i | \(-0.548221\pi\) | ||||
−0.150912 | + | 0.988547i | \(0.548221\pi\) | |||||||
\(728\) | 4.81024e63 | 0.192403 | ||||||||
\(729\) | 3.64659e62 | 0.0141422 | ||||||||
\(730\) | −2.50072e64 | −0.940375 | ||||||||
\(731\) | 8.50092e63 | 0.309974 | ||||||||
\(732\) | −7.60367e63 | −0.268859 | ||||||||
\(733\) | 4.17807e64 | 1.43264 | 0.716318 | − | 0.697774i | \(-0.245826\pi\) | ||||
0.716318 | + | 0.697774i | \(0.245826\pi\) | |||||||
\(734\) | −2.66274e64 | −0.885457 | ||||||||
\(735\) | −8.90707e63 | −0.287256 | ||||||||
\(736\) | 9.00575e63 | 0.281688 | ||||||||
\(737\) | −2.90159e64 | −0.880274 | ||||||||
\(738\) | 2.33926e64 | 0.688351 | ||||||||
\(739\) | −6.90768e64 | −1.97166 | −0.985831 | − | 0.167739i | \(-0.946353\pi\) | ||||
−0.985831 | + | 0.167739i | \(0.946353\pi\) | |||||||
\(740\) | 9.49435e63 | 0.262876 | ||||||||
\(741\) | 2.08595e62 | 0.00560267 | ||||||||
\(742\) | −2.67833e64 | −0.697872 | ||||||||
\(743\) | 5.54554e64 | 1.40183 | 0.700916 | − | 0.713244i | \(-0.252775\pi\) | ||||
0.700916 | + | 0.713244i | \(0.252775\pi\) | |||||||
\(744\) | −1.14414e64 | −0.280599 | ||||||||
\(745\) | −9.36587e63 | −0.222860 | ||||||||
\(746\) | 4.96082e64 | 1.14533 | ||||||||
\(747\) | 4.02750e64 | 0.902240 | ||||||||
\(748\) | 6.50837e63 | 0.141477 | ||||||||
\(749\) | 7.60174e63 | 0.160351 | ||||||||
\(750\) | −1.66585e64 | −0.341002 | ||||||||
\(751\) | −5.42200e64 | −1.07711 | −0.538556 | − | 0.842589i | \(-0.681030\pi\) | ||||
−0.538556 | + | 0.842589i | \(0.681030\pi\) | |||||||
\(752\) | 4.16699e63 | 0.0803380 | ||||||||
\(753\) | 2.61922e64 | 0.490101 | ||||||||
\(754\) | 6.13074e64 | 1.11342 | ||||||||
\(755\) | 5.84604e64 | 1.03052 | ||||||||
\(756\) | 1.25374e64 | 0.214520 | ||||||||
\(757\) | −4.84159e64 | −0.804138 | −0.402069 | − | 0.915609i | \(-0.631709\pi\) | ||||
−0.402069 | + | 0.915609i | \(0.631709\pi\) | |||||||
\(758\) | 5.34374e64 | 0.861566 | ||||||||
\(759\) | −3.65721e64 | −0.572413 | ||||||||
\(760\) | 2.52930e62 | 0.00384321 | ||||||||
\(761\) | −6.15512e63 | −0.0907991 | −0.0453995 | − | 0.998969i | \(-0.514456\pi\) | ||||
−0.0453995 | + | 0.998969i | \(0.514456\pi\) | |||||||
\(762\) | 1.56383e64 | 0.223977 | ||||||||
\(763\) | 4.80339e64 | 0.667952 | ||||||||
\(764\) | −6.27995e64 | −0.847922 | ||||||||
\(765\) | 1.92051e64 | 0.251788 | ||||||||
\(766\) | −3.09241e64 | −0.393686 | ||||||||
\(767\) | −7.94651e64 | −0.982383 | ||||||||
\(768\) | −2.33689e63 | −0.0280550 | ||||||||
\(769\) | −8.09959e64 | −0.944322 | −0.472161 | − | 0.881512i | \(-0.656526\pi\) | ||||
−0.472161 | + | 0.881512i | \(0.656526\pi\) | |||||||
\(770\) | −2.36860e64 | −0.268195 | ||||||||
\(771\) | 5.28771e64 | 0.581493 | ||||||||
\(772\) | −1.69882e64 | −0.181450 | ||||||||
\(773\) | −1.09275e65 | −1.13366 | −0.566829 | − | 0.823835i | \(-0.691830\pi\) | ||||
−0.566829 | + | 0.823835i | \(0.691830\pi\) | |||||||
\(774\) | −4.91224e64 | −0.495003 | ||||||||
\(775\) | −3.69686e64 | −0.361864 | ||||||||
\(776\) | −3.51806e64 | −0.334515 | ||||||||
\(777\) | 1.52253e64 | 0.140634 | ||||||||
\(778\) | 1.10903e64 | 0.0995181 | ||||||||
\(779\) | 1.70452e63 | 0.0148597 | ||||||||
\(780\) | 2.41994e64 | 0.204963 | ||||||||
\(781\) | 1.02290e65 | 0.841757 | ||||||||
\(782\) | 4.98266e64 | 0.398391 | ||||||||
\(783\) | 1.59791e65 | 1.24141 | ||||||||
\(784\) | −2.37638e64 | −0.179393 | ||||||||
\(785\) | −5.12715e64 | −0.376105 | ||||||||
\(786\) | −1.27674e64 | −0.0910112 | ||||||||
\(787\) | 2.41478e65 | 1.67281 | 0.836403 | − | 0.548115i | \(-0.184654\pi\) | ||||
0.836403 | + | 0.548115i | \(0.184654\pi\) | |||||||
\(788\) | 7.13978e64 | 0.480668 | ||||||||
\(789\) | −2.09021e64 | −0.136759 | ||||||||
\(790\) | −5.42314e64 | −0.344859 | ||||||||
\(791\) | −3.86658e64 | −0.238977 | ||||||||
\(792\) | −3.76085e64 | −0.225928 | ||||||||
\(793\) | 2.10073e65 | 1.22666 | ||||||||
\(794\) | −1.32301e65 | −0.750934 | ||||||||
\(795\) | −1.34742e65 | −0.743432 | ||||||||
\(796\) | 5.66860e63 | 0.0304040 | ||||||||
\(797\) | −2.14766e64 | −0.111984 | −0.0559918 | − | 0.998431i | \(-0.517832\pi\) | ||||
−0.0559918 | + | 0.998431i | \(0.517832\pi\) | |||||||
\(798\) | 4.05601e62 | 0.00205605 | ||||||||
\(799\) | 2.30550e64 | 0.113622 | ||||||||
\(800\) | −7.55080e63 | −0.0361800 | ||||||||
\(801\) | −1.37142e65 | −0.638907 | ||||||||
\(802\) | −1.79441e64 | −0.0812826 | ||||||||
\(803\) | 2.70942e65 | 1.19337 | ||||||||
\(804\) | 5.76426e64 | 0.246878 | ||||||||
\(805\) | −1.81335e65 | −0.755221 | ||||||||
\(806\) | 3.16101e65 | 1.28023 | ||||||||
\(807\) | −1.38903e65 | −0.547089 | ||||||||
\(808\) | 9.34534e63 | 0.0357964 | ||||||||
\(809\) | −4.54729e65 | −1.69399 | −0.846996 | − | 0.531600i | \(-0.821591\pi\) | ||||
−0.846996 | + | 0.531600i | \(0.821591\pi\) | |||||||
\(810\) | −7.59065e64 | −0.275021 | ||||||||
\(811\) | 2.51365e65 | 0.885801 | 0.442901 | − | 0.896571i | \(-0.353949\pi\) | ||||
0.442901 | + | 0.896571i | \(0.353949\pi\) | |||||||
\(812\) | 1.19209e65 | 0.408598 | ||||||||
\(813\) | −1.28259e65 | −0.427611 | ||||||||
\(814\) | −1.02867e65 | −0.333601 | ||||||||
\(815\) | −4.38255e65 | −1.38255 | ||||||||
\(816\) | −1.29294e64 | −0.0396781 | ||||||||
\(817\) | −3.57935e63 | −0.0106858 | ||||||||
\(818\) | 2.64311e64 | 0.0767656 | ||||||||
\(819\) | −1.53788e65 | −0.434545 | ||||||||
\(820\) | 1.97744e65 | 0.543615 | ||||||||
\(821\) | 3.27797e65 | 0.876765 | 0.438383 | − | 0.898788i | \(-0.355551\pi\) | ||||
0.438383 | + | 0.898788i | \(0.355551\pi\) | |||||||
\(822\) | −1.18387e65 | −0.308096 | ||||||||
\(823\) | −8.90049e63 | −0.0225381 | −0.0112691 | − | 0.999937i | \(-0.503587\pi\) | ||||
−0.0112691 | + | 0.999937i | \(0.503587\pi\) | |||||||
\(824\) | 1.83419e65 | 0.451941 | ||||||||
\(825\) | 3.06636e64 | 0.0735207 | ||||||||
\(826\) | −1.54515e65 | −0.360512 | ||||||||
\(827\) | 1.63577e65 | 0.371405 | 0.185702 | − | 0.982606i | \(-0.440544\pi\) | ||||
0.185702 | + | 0.982606i | \(0.440544\pi\) | |||||||
\(828\) | −2.87922e65 | −0.636198 | ||||||||
\(829\) | 1.84764e65 | 0.397320 | 0.198660 | − | 0.980068i | \(-0.436341\pi\) | ||||
0.198660 | + | 0.980068i | \(0.436341\pi\) | |||||||
\(830\) | 3.40456e65 | 0.712531 | ||||||||
\(831\) | −1.22941e65 | −0.250423 | ||||||||
\(832\) | 6.45633e64 | 0.128000 | ||||||||
\(833\) | −1.31479e65 | −0.253715 | ||||||||
\(834\) | −1.48239e65 | −0.278437 | ||||||||
\(835\) | 6.11931e65 | 1.11881 | ||||||||
\(836\) | −2.74038e63 | −0.00487719 | ||||||||
\(837\) | 8.23885e65 | 1.42739 | ||||||||
\(838\) | 2.13443e63 | 0.00359991 | ||||||||
\(839\) | −7.98160e65 | −1.31053 | −0.655263 | − | 0.755401i | \(-0.727442\pi\) | ||||
−0.655263 | + | 0.755401i | \(0.727442\pi\) | |||||||
\(840\) | 4.70543e64 | 0.0752169 | ||||||||
\(841\) | 8.76779e65 | 1.36452 | ||||||||
\(842\) | −9.14708e64 | −0.138599 | ||||||||
\(843\) | 4.81092e65 | 0.709754 | ||||||||
\(844\) | −5.10035e65 | −0.732647 | ||||||||
\(845\) | −3.09747e64 | −0.0433242 | ||||||||
\(846\) | −1.33223e65 | −0.181445 | ||||||||
\(847\) | −1.44084e65 | −0.191090 | ||||||||
\(848\) | −3.59486e65 | −0.464276 | ||||||||
\(849\) | −3.67553e65 | −0.462271 | ||||||||
\(850\) | −4.17768e64 | −0.0511693 | ||||||||
\(851\) | −7.87527e65 | −0.939400 | ||||||||
\(852\) | −2.03209e65 | −0.236076 | ||||||||
\(853\) | −1.07480e66 | −1.21612 | −0.608058 | − | 0.793892i | \(-0.708051\pi\) | ||||
−0.608058 | + | 0.793892i | \(0.708051\pi\) | |||||||
\(854\) | 4.08475e65 | 0.450157 | ||||||||
\(855\) | −8.08640e63 | −0.00867996 | ||||||||
\(856\) | 1.02031e65 | 0.106677 | ||||||||
\(857\) | 3.80613e65 | 0.387628 | 0.193814 | − | 0.981038i | \(-0.437914\pi\) | ||||
0.193814 | + | 0.981038i | \(0.437914\pi\) | |||||||
\(858\) | −2.62190e65 | −0.260107 | ||||||||
\(859\) | −5.67906e65 | −0.548821 | −0.274410 | − | 0.961613i | \(-0.588483\pi\) | ||||
−0.274410 | + | 0.961613i | \(0.588483\pi\) | |||||||
\(860\) | −4.15245e65 | −0.390921 | ||||||||
\(861\) | 3.17105e65 | 0.290825 | ||||||||
\(862\) | 3.91296e65 | 0.349616 | ||||||||
\(863\) | −6.96770e65 | −0.606522 | −0.303261 | − | 0.952908i | \(-0.598075\pi\) | ||||
−0.303261 | + | 0.952908i | \(0.598075\pi\) | |||||||
\(864\) | 1.68278e65 | 0.142714 | ||||||||
\(865\) | 8.83236e65 | 0.729817 | ||||||||
\(866\) | −1.45075e65 | −0.116799 | ||||||||
\(867\) | 5.00680e65 | 0.392763 | ||||||||
\(868\) | 6.14639e65 | 0.469815 | ||||||||
\(869\) | 5.87573e65 | 0.437640 | ||||||||
\(870\) | 5.99715e65 | 0.435273 | ||||||||
\(871\) | −1.59254e66 | −1.12637 | ||||||||
\(872\) | 6.44713e65 | 0.444371 | ||||||||
\(873\) | 1.12476e66 | 0.755507 | ||||||||
\(874\) | −2.09797e64 | −0.0137339 | ||||||||
\(875\) | 8.94906e65 | 0.570948 | ||||||||
\(876\) | −5.38249e65 | −0.334689 | ||||||||
\(877\) | −3.00025e65 | −0.181830 | −0.0909151 | − | 0.995859i | \(-0.528979\pi\) | ||||
−0.0909151 | + | 0.995859i | \(0.528979\pi\) | |||||||
\(878\) | 2.28144e66 | 1.34767 | ||||||||
\(879\) | 5.99979e65 | 0.345451 | ||||||||
\(880\) | −3.17915e65 | −0.178423 | ||||||||
\(881\) | 7.45578e65 | 0.407882 | 0.203941 | − | 0.978983i | \(-0.434625\pi\) | ||||
0.203941 | + | 0.978983i | \(0.434625\pi\) | |||||||
\(882\) | 7.59751e65 | 0.405162 | ||||||||
\(883\) | −6.77149e65 | −0.352021 | −0.176010 | − | 0.984388i | \(-0.556319\pi\) | ||||
−0.176010 | + | 0.984388i | \(0.556319\pi\) | |||||||
\(884\) | 3.57213e65 | 0.181030 | ||||||||
\(885\) | −7.77336e65 | −0.384048 | ||||||||
\(886\) | −2.01110e66 | −0.968666 | ||||||||
\(887\) | −3.77816e66 | −1.77419 | −0.887093 | − | 0.461592i | \(-0.847279\pi\) | ||||
−0.887093 | + | 0.461592i | \(0.847279\pi\) | |||||||
\(888\) | 2.04354e65 | 0.0935603 | ||||||||
\(889\) | −8.40104e65 | −0.375011 | ||||||||
\(890\) | −1.15930e66 | −0.504567 | ||||||||
\(891\) | 8.22413e65 | 0.349013 | ||||||||
\(892\) | 1.02508e66 | 0.424180 | ||||||||
\(893\) | −9.70740e63 | −0.00391692 | ||||||||
\(894\) | −2.01589e65 | −0.0793181 | ||||||||
\(895\) | −6.72052e65 | −0.257861 | ||||||||
\(896\) | 1.25539e65 | 0.0469732 | ||||||||
\(897\) | −2.00727e66 | −0.732445 | ||||||||
\(898\) | −3.44095e66 | −1.22451 | ||||||||
\(899\) | 7.83369e66 | 2.71877 | ||||||||
\(900\) | 2.41406e65 | 0.0817132 | ||||||||
\(901\) | −1.98895e66 | −0.656624 | ||||||||
\(902\) | −2.14247e66 | −0.689870 | ||||||||
\(903\) | −6.65892e65 | −0.209136 | ||||||||
\(904\) | −5.18975e65 | −0.158985 | ||||||||
\(905\) | 1.24660e66 | 0.372507 | ||||||||
\(906\) | 1.25829e66 | 0.366771 | ||||||||
\(907\) | 5.56448e66 | 1.58220 | 0.791098 | − | 0.611690i | \(-0.209510\pi\) | ||||
0.791098 | + | 0.611690i | \(0.209510\pi\) | |||||||
\(908\) | −1.21616e66 | −0.337334 | ||||||||
\(909\) | −2.98779e65 | −0.0808468 | ||||||||
\(910\) | −1.30001e66 | −0.343175 | ||||||||
\(911\) | −2.38244e66 | −0.613562 | −0.306781 | − | 0.951780i | \(-0.599252\pi\) | ||||
−0.306781 | + | 0.951780i | \(0.599252\pi\) | |||||||
\(912\) | 5.44400e63 | 0.00136784 | ||||||||
\(913\) | −3.68869e66 | −0.904231 | ||||||||
\(914\) | 2.68616e66 | 0.642454 | ||||||||
\(915\) | 2.05496e66 | 0.479544 | ||||||||
\(916\) | 3.73025e66 | 0.849355 | ||||||||
\(917\) | 6.85875e65 | 0.152382 | ||||||||
\(918\) | 9.31040e65 | 0.201840 | ||||||||
\(919\) | −3.52107e65 | −0.0744862 | −0.0372431 | − | 0.999306i | \(-0.511858\pi\) | ||||
−0.0372431 | + | 0.999306i | \(0.511858\pi\) | |||||||
\(920\) | −2.43389e66 | −0.502428 | ||||||||
\(921\) | 1.77238e65 | 0.0357038 | ||||||||
\(922\) | 2.22889e65 | 0.0438171 | ||||||||
\(923\) | 5.61423e66 | 1.07709 | ||||||||
\(924\) | −5.09812e65 | −0.0954533 | ||||||||
\(925\) | 6.60297e65 | 0.120656 | ||||||||
\(926\) | −2.83340e66 | −0.505314 | ||||||||
\(927\) | −5.86407e66 | −1.02072 | ||||||||
\(928\) | 1.60002e66 | 0.271829 | ||||||||
\(929\) | 5.51562e66 | 0.914619 | 0.457310 | − | 0.889308i | \(-0.348813\pi\) | ||||
0.457310 | + | 0.889308i | \(0.348813\pi\) | |||||||
\(930\) | 3.09213e66 | 0.500486 | ||||||||
\(931\) | 5.53600e64 | 0.00874638 | ||||||||
\(932\) | 1.05010e66 | 0.161946 | ||||||||
\(933\) | −1.23236e66 | −0.185524 | ||||||||
\(934\) | 7.60808e66 | 1.11807 | ||||||||
\(935\) | −1.75895e66 | −0.252343 | ||||||||
\(936\) | −2.06415e66 | −0.289091 | ||||||||
\(937\) | −1.16406e67 | −1.59160 | −0.795798 | − | 0.605562i | \(-0.792948\pi\) | ||||
−0.795798 | + | 0.605562i | \(0.792948\pi\) | |||||||
\(938\) | −3.09661e66 | −0.413354 | ||||||||
\(939\) | 2.75832e66 | 0.359475 | ||||||||
\(940\) | −1.12617e66 | −0.143293 | ||||||||
\(941\) | −1.01573e67 | −1.26186 | −0.630931 | − | 0.775839i | \(-0.717327\pi\) | ||||
−0.630931 | + | 0.775839i | \(0.717327\pi\) | |||||||
\(942\) | −1.10356e66 | −0.133859 | ||||||||
\(943\) | −1.64022e67 | −1.94263 | ||||||||
\(944\) | −2.07391e66 | −0.239839 | ||||||||
\(945\) | −3.38835e66 | −0.382624 | ||||||||
\(946\) | 4.49899e66 | 0.496095 | ||||||||
\(947\) | 6.79284e66 | 0.731437 | 0.365718 | − | 0.930726i | \(-0.380823\pi\) | ||||
0.365718 | + | 0.930726i | \(0.380823\pi\) | |||||||
\(948\) | −1.16726e66 | −0.122739 | ||||||||
\(949\) | 1.48707e67 | 1.52701 | ||||||||
\(950\) | 1.75903e64 | 0.00176398 | ||||||||
\(951\) | 2.49721e66 | 0.244565 | ||||||||
\(952\) | 6.94580e65 | 0.0664341 | ||||||||
\(953\) | −1.02194e67 | −0.954626 | −0.477313 | − | 0.878733i | \(-0.658389\pi\) | ||||
−0.477313 | + | 0.878733i | \(0.658389\pi\) | |||||||
\(954\) | 1.14931e67 | 1.04857 | ||||||||
\(955\) | 1.69721e67 | 1.51238 | ||||||||
\(956\) | −9.94140e66 | −0.865256 | ||||||||
\(957\) | −6.49765e66 | −0.552379 | ||||||||
\(958\) | −6.39105e66 | −0.530699 | ||||||||
\(959\) | 6.35982e66 | 0.515854 | ||||||||
\(960\) | 6.31565e65 | 0.0500398 | ||||||||
\(961\) | 2.74701e67 | 2.12610 | ||||||||
\(962\) | −5.64588e66 | −0.426867 | ||||||||
\(963\) | −3.26202e66 | −0.240933 | ||||||||
\(964\) | 9.86316e66 | 0.711677 | ||||||||
\(965\) | 4.59122e66 | 0.323641 | ||||||||
\(966\) | −3.90301e66 | −0.268791 | ||||||||
\(967\) | −2.40504e66 | −0.161818 | −0.0809090 | − | 0.996721i | \(-0.525782\pi\) | ||||
−0.0809090 | + | 0.996721i | \(0.525782\pi\) | |||||||
\(968\) | −1.93390e66 | −0.127127 | ||||||||
\(969\) | 3.01203e64 | 0.00193453 | ||||||||
\(970\) | 9.50789e66 | 0.596651 | ||||||||
\(971\) | −3.51609e66 | −0.215589 | −0.107795 | − | 0.994173i | \(-0.534379\pi\) | ||||
−0.107795 | + | 0.994173i | \(0.534379\pi\) | |||||||
\(972\) | −8.37136e66 | −0.501540 | ||||||||
\(973\) | 7.96352e66 | 0.466194 | ||||||||
\(974\) | −1.91617e67 | −1.09612 | ||||||||
\(975\) | 1.68298e66 | 0.0940750 | ||||||||
\(976\) | 5.48257e66 | 0.299477 | ||||||||
\(977\) | −2.59994e66 | −0.138783 | −0.0693914 | − | 0.997590i | \(-0.522106\pi\) | ||||
−0.0693914 | + | 0.997590i | \(0.522106\pi\) | |||||||
\(978\) | −9.43290e66 | −0.492063 | ||||||||
\(979\) | 1.25604e67 | 0.640316 | ||||||||
\(980\) | 6.42239e66 | 0.319970 | ||||||||
\(981\) | −2.06121e67 | −1.00362 | ||||||||
\(982\) | −1.96742e67 | −0.936243 | ||||||||
\(983\) | −3.00612e67 | −1.39815 | −0.699073 | − | 0.715050i | \(-0.746404\pi\) | ||||
−0.699073 | + | 0.715050i | \(0.746404\pi\) | |||||||
\(984\) | 4.25619e66 | 0.193478 | ||||||||
\(985\) | −1.92959e67 | −0.857334 | ||||||||
\(986\) | 8.85254e66 | 0.384448 | ||||||||
\(987\) | −1.80593e66 | −0.0766595 | ||||||||
\(988\) | −1.50406e65 | −0.00624072 | ||||||||
\(989\) | 3.44433e67 | 1.39697 | ||||||||
\(990\) | 1.01640e67 | 0.402972 | ||||||||
\(991\) | −4.87826e67 | −1.89064 | −0.945318 | − | 0.326149i | \(-0.894249\pi\) | ||||
−0.945318 | + | 0.326149i | \(0.894249\pi\) | |||||||
\(992\) | 8.24972e66 | 0.312555 | ||||||||
\(993\) | 1.00408e67 | 0.371885 | ||||||||
\(994\) | 1.09165e67 | 0.395267 | ||||||||
\(995\) | −1.53199e66 | −0.0542296 | ||||||||
\(996\) | 7.32789e66 | 0.253597 | ||||||||
\(997\) | 3.67161e67 | 1.24227 | 0.621134 | − | 0.783704i | \(-0.286672\pi\) | ||||
0.621134 | + | 0.783704i | \(0.286672\pi\) | |||||||
\(998\) | 1.16786e67 | 0.386325 | ||||||||
\(999\) | −1.47154e67 | −0.475936 |
(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 | 2.46.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 18.46.a.b.1.2 | 2 | |||
4.3 | odd | 2 | 16.46.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.46.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.46.a.a.1.2 | 2 | 4.3 | odd | 2 | |||
18.46.a.b.1.2 | 2 | 3.2 | odd | 2 |