Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,60,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 60, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 60);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 60 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(198.412204959\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots - 23\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{19}\cdot 5^{3}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.61966e7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25878e9 | −1.65792 | −0.828962 | − | 0.559305i | \(-0.811068\pi\) | ||||
−0.828962 | + | 0.559305i | \(0.811068\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00806e18 | 1.74871 | ||||||||
\(5\) | 4.05126e20 | 0.972691 | 0.486346 | − | 0.873767i | \(-0.338330\pi\) | ||||
0.486346 | + | 0.873767i | \(0.338330\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.66317e24 | 0.312613 | 0.156307 | − | 0.987709i | \(-0.450041\pi\) | ||||
0.156307 | + | 0.987709i | \(0.450041\pi\) | |||||||
\(8\) | −5.43293e26 | −1.24131 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.09964e29 | −1.61265 | ||||||||
\(11\) | −7.79706e30 | −1.48199 | −0.740997 | − | 0.671508i | \(-0.765647\pi\) | ||||
−0.740997 | + | 0.671508i | \(0.765647\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.35975e32 | 0.187124 | 0.0935620 | − | 0.995613i | \(-0.470175\pi\) | ||||
0.0935620 | + | 0.995613i | \(0.470175\pi\) | |||||||
\(14\) | −3.35235e33 | −0.518289 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.02776e35 | 0.309281 | ||||||||
\(17\) | 2.91767e36 | 1.46823 | 0.734113 | − | 0.679027i | \(-0.237598\pi\) | ||||
0.734113 | + | 0.679027i | \(0.237598\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.13079e36 | −0.115954 | −0.0579769 | − | 0.998318i | \(-0.518465\pi\) | ||||
−0.0579769 | + | 0.998318i | \(0.518465\pi\) | |||||||
\(20\) | 4.08393e38 | 1.70096 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.81478e39 | 2.45703 | ||||||||
\(23\) | 2.47627e39 | 0.167042 | 0.0835211 | − | 0.996506i | \(-0.473383\pi\) | ||||
0.0835211 | + | 0.996506i | \(0.473383\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.34524e39 | −0.0538716 | ||||||||
\(26\) | −1.71162e41 | −0.310237 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.68465e42 | 0.546670 | ||||||||
\(29\) | 4.74630e42 | 0.343253 | 0.171626 | − | 0.985162i | \(-0.445098\pi\) | ||||
0.171626 | + | 0.985162i | \(0.445098\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.04997e43 | 0.106172 | 0.0530858 | − | 0.998590i | \(-0.483094\pi\) | ||||
0.0530858 | + | 0.998590i | \(0.483094\pi\) | |||||||
\(32\) | 1.83814e44 | 0.728543 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.67270e45 | −2.43421 | ||||||||
\(35\) | 1.07892e45 | 0.304076 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.35159e45 | −0.402189 | −0.201095 | − | 0.979572i | \(-0.564450\pi\) | ||||
−0.201095 | + | 0.979572i | \(0.564450\pi\) | |||||||
\(38\) | 7.71730e45 | 0.192243 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.20102e47 | −1.20741 | ||||||||
\(41\) | 6.31455e47 | 1.67193 | 0.835965 | − | 0.548782i | \(-0.184908\pi\) | ||||
0.835965 | + | 0.548782i | \(0.184908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.26596e47 | −0.342104 | −0.171052 | − | 0.985262i | \(-0.554717\pi\) | ||||
−0.171052 | + | 0.985262i | \(0.554717\pi\) | |||||||
\(44\) | −7.85993e48 | −2.59158 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.11707e48 | −0.276943 | ||||||||
\(47\) | −3.33197e49 | −1.56969 | −0.784845 | − | 0.619692i | \(-0.787258\pi\) | ||||
−0.784845 | + | 0.619692i | \(0.787258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.54821e49 | −0.902273 | ||||||||
\(50\) | 1.17636e49 | 0.0893151 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.37071e50 | 0.327226 | ||||||||
\(53\) | −7.06726e50 | −0.961863 | −0.480931 | − | 0.876758i | \(-0.659701\pi\) | ||||
−0.480931 | + | 0.876758i | \(0.659701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.15879e51 | −1.44152 | ||||||||
\(56\) | −1.44688e51 | −0.388049 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.97454e51 | −0.569087 | ||||||||
\(59\) | −2.46009e52 | −1.41519 | −0.707597 | − | 0.706616i | \(-0.750221\pi\) | ||||
−0.707597 | + | 0.706616i | \(0.750221\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.32529e52 | 1.14581 | 0.572906 | − | 0.819621i | \(-0.305816\pi\) | ||||
0.572906 | + | 0.819621i | \(0.305816\pi\) | |||||||
\(62\) | −1.32169e52 | −0.176025 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.90628e53 | −1.51715 | ||||||||
\(65\) | 5.50869e52 | 0.182014 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.99074e53 | −0.404178 | −0.202089 | − | 0.979367i | \(-0.564773\pi\) | ||||
−0.202089 | + | 0.979367i | \(0.564773\pi\) | |||||||
\(68\) | 2.94120e54 | 2.56750 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.35812e54 | −0.504135 | ||||||||
\(71\) | 4.94138e54 | 1.20705 | 0.603527 | − | 0.797342i | \(-0.293761\pi\) | ||||
0.603527 | + | 0.797342i | \(0.293761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.41825e54 | 0.798504 | 0.399252 | − | 0.916841i | \(-0.369270\pi\) | ||||
0.399252 | + | 0.916841i | \(0.369270\pi\) | |||||||
\(74\) | 9.25403e54 | 0.666799 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.18022e54 | −0.202770 | ||||||||
\(77\) | −2.07649e55 | −0.463291 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.76516e55 | −0.708400 | −0.354200 | − | 0.935170i | \(-0.615247\pi\) | ||||
−0.354200 | + | 0.935170i | \(0.615247\pi\) | |||||||
\(80\) | 4.16374e55 | 0.300835 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.94862e56 | −2.77193 | ||||||||
\(83\) | −4.29546e56 | −1.04763 | −0.523813 | − | 0.851833i | \(-0.675491\pi\) | ||||
−0.523813 | + | 0.851833i | \(0.675491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18202e57 | 1.42813 | ||||||||
\(86\) | 6.62869e56 | 0.567183 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.23609e57 | 1.83961 | ||||||||
\(89\) | 4.87740e56 | 0.151769 | 0.0758845 | − | 0.997117i | \(-0.475822\pi\) | ||||
0.0758845 | + | 0.997117i | \(0.475822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.62124e56 | 0.0584974 | ||||||||
\(92\) | 2.49623e57 | 0.292109 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.19421e58 | 2.60243 | ||||||||
\(95\) | −2.48374e57 | −0.112787 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.59338e57 | −0.235616 | −0.117808 | − | 0.993036i | \(-0.537587\pi\) | ||||
−0.117808 | + | 0.993036i | \(0.537587\pi\) | |||||||
\(98\) | 8.24274e58 | 1.49590 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.42060e57 | −0.0942060 | ||||||||
\(101\) | −2.04672e59 | −1.52608 | −0.763040 | − | 0.646351i | \(-0.776294\pi\) | ||||
−0.763040 | + | 0.646351i | \(0.776294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.04146e59 | 0.435456 | 0.217728 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217728 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(104\) | −7.38741e58 | −0.232278 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.89612e59 | 1.59470 | ||||||||
\(107\) | 1.19773e60 | 1.62756 | 0.813779 | − | 0.581175i | \(-0.197407\pi\) | ||||
0.813779 | + | 0.581175i | \(0.197407\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.38792e60 | 1.87905 | 0.939526 | − | 0.342478i | \(-0.111266\pi\) | ||||
0.939526 | + | 0.342478i | \(0.111266\pi\) | |||||||
\(110\) | 3.97622e60 | 2.38994 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.73711e59 | 0.0966854 | ||||||||
\(113\) | 1.74667e60 | 0.474674 | 0.237337 | − | 0.971427i | \(-0.423725\pi\) | ||||
0.237337 | + | 0.971427i | \(0.423725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00320e60 | 0.162480 | ||||||||
\(116\) | 4.78457e60 | 0.600250 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.09670e61 | 2.34628 | ||||||||
\(119\) | 7.77026e60 | 0.458987 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.31140e61 | 1.19631 | ||||||||
\(122\) | −6.70336e61 | −1.89967 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.05844e61 | 0.185664 | ||||||||
\(125\) | −7.40642e61 | −1.02509 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.13188e62 | −0.980826 | −0.490413 | − | 0.871490i | \(-0.663154\pi\) | ||||
−0.490413 | + | 0.871490i | \(0.663154\pi\) | |||||||
\(128\) | 2.59875e62 | 1.78678 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.93423e61 | −0.301765 | ||||||||
\(131\) | −1.46816e62 | −0.509646 | −0.254823 | − | 0.966988i | \(-0.582017\pi\) | ||||
−0.254823 | + | 0.966988i | \(0.582017\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.63273e61 | −0.0362487 | ||||||||
\(134\) | 3.76469e62 | 0.670096 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.58515e63 | −1.82252 | ||||||||
\(137\) | −1.25262e63 | −1.16028 | −0.580139 | − | 0.814517i | \(-0.697002\pi\) | ||||
−0.580139 | + | 0.814517i | \(0.697002\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.27386e62 | −0.318560 | −0.159280 | − | 0.987233i | \(-0.550917\pi\) | ||||
−0.159280 | + | 0.987233i | \(0.550917\pi\) | |||||||
\(140\) | 1.08762e63 | 0.531742 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.22011e63 | −2.00121 | ||||||||
\(143\) | −1.06020e63 | −0.277317 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.92285e63 | 0.333879 | ||||||||
\(146\) | −9.33794e63 | −1.32386 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.41087e63 | −0.703313 | ||||||||
\(149\) | −9.39911e63 | −0.731293 | −0.365647 | − | 0.930754i | \(-0.619152\pi\) | ||||
−0.365647 | + | 0.930754i | \(0.619152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.88603e64 | 0.990211 | 0.495105 | − | 0.868833i | \(-0.335129\pi\) | ||||
0.495105 | + | 0.868833i | \(0.335129\pi\) | |||||||
\(152\) | 3.33081e63 | 0.143934 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.61385e64 | 0.768102 | ||||||||
\(155\) | 4.25372e63 | 0.103272 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.92576e64 | 0.819282 | 0.409641 | − | 0.912247i | \(-0.365654\pi\) | ||||
0.409641 | + | 0.912247i | \(0.365654\pi\) | |||||||
\(158\) | 8.51584e64 | 1.17447 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.44680e64 | 0.708647 | ||||||||
\(161\) | 6.59472e63 | 0.0522196 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.13744e64 | −0.447665 | −0.223833 | − | 0.974628i | \(-0.571857\pi\) | ||||
−0.223833 | + | 0.974628i | \(0.571857\pi\) | |||||||
\(164\) | 6.36546e65 | 2.92373 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.40704e65 | 1.73688 | ||||||||
\(167\) | −4.38132e65 | −1.17888 | −0.589439 | − | 0.807813i | \(-0.700651\pi\) | ||||
−0.589439 | + | 0.807813i | \(0.700651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.09540e65 | −0.964985 | ||||||||
\(170\) | −1.48791e66 | −2.36773 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.30843e65 | −0.598242 | ||||||||
\(173\) | 5.55515e65 | 0.527637 | 0.263819 | − | 0.964572i | \(-0.415018\pi\) | ||||
0.263819 | + | 0.964572i | \(0.415018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.48880e64 | −0.0168410 | ||||||||
\(176\) | −8.01353e65 | −0.458353 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.13957e65 | −0.251621 | ||||||||
\(179\) | 1.41303e66 | 0.490893 | 0.245446 | − | 0.969410i | \(-0.421065\pi\) | ||||
0.245446 | + | 0.969410i | \(0.421065\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.80750e65 | −0.0702752 | −0.0351376 | − | 0.999382i | \(-0.511187\pi\) | ||||
−0.0351376 | + | 0.999382i | \(0.511187\pi\) | |||||||
\(182\) | −4.55835e65 | −0.0969843 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.34534e66 | −0.207351 | ||||||||
\(185\) | −2.97832e66 | −0.391206 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.27492e67 | −2.17590 | ||||||||
\(188\) | −3.35884e67 | −2.74494 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.12648e66 | 0.186993 | ||||||||
\(191\) | −3.97971e66 | −0.203876 | −0.101938 | − | 0.994791i | \(-0.532504\pi\) | ||||
−0.101938 | + | 0.994791i | \(0.532504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.02510e66 | 0.189323 | 0.0946616 | − | 0.995510i | \(-0.469823\pi\) | ||||
0.0946616 | + | 0.995510i | \(0.469823\pi\) | |||||||
\(194\) | 1.20759e67 | 0.390634 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.60101e67 | −1.57782 | ||||||||
\(197\) | 1.09574e66 | 0.0225400 | 0.0112700 | − | 0.999936i | \(-0.496413\pi\) | ||||
0.0112700 | + | 0.999936i | \(0.496413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.25782e67 | −1.26096 | −0.630478 | − | 0.776208i | \(-0.717141\pi\) | ||||
−0.630478 | + | 0.776208i | \(0.717141\pi\) | |||||||
\(200\) | 5.07720e66 | 0.0668712 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.57636e68 | 2.53012 | ||||||||
\(203\) | 1.26402e67 | 0.107305 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.55819e68 | 1.62627 | ||||||||
\(206\) | −1.31097e68 | −0.721953 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.39750e67 | 0.0578739 | ||||||||
\(209\) | 4.78021e67 | 0.171843 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.55772e68 | 1.23713 | 0.618565 | − | 0.785734i | \(-0.287714\pi\) | ||||
0.618565 | + | 0.785734i | \(0.287714\pi\) | |||||||
\(212\) | −7.12425e68 | −1.68202 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.50767e69 | −2.69837 | ||||||||
\(215\) | −2.13338e68 | −0.332762 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.79626e67 | 0.0331907 | ||||||||
\(218\) | −3.00587e69 | −3.11532 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.18426e69 | −2.52081 | ||||||||
\(221\) | 3.96729e68 | 0.274740 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.12231e69 | −0.595824 | −0.297912 | − | 0.954593i | \(-0.596290\pi\) | ||||
−0.297912 | + | 0.954593i | \(0.596290\pi\) | |||||||
\(224\) | 4.89529e68 | 0.227752 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.19867e69 | −0.786974 | ||||||||
\(227\) | −3.72597e69 | −1.17078 | −0.585392 | − | 0.810750i | \(-0.699059\pi\) | ||||
−0.585392 | + | 0.810750i | \(0.699059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.90625e69 | 0.704996 | 0.352498 | − | 0.935813i | \(-0.385332\pi\) | ||||
0.352498 | + | 0.935813i | \(0.385332\pi\) | |||||||
\(230\) | −1.26281e69 | −0.269380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.57863e69 | −0.426082 | ||||||||
\(233\) | −2.52938e69 | −0.368141 | −0.184070 | − | 0.982913i | \(-0.558927\pi\) | ||||
−0.184070 | + | 0.982913i | \(0.558927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.34987e70 | −1.52682 | ||||||||
\(236\) | −2.47992e70 | −2.47477 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.78104e69 | −0.760965 | ||||||||
\(239\) | 2.82462e70 | 1.94188 | 0.970940 | − | 0.239322i | \(-0.0769252\pi\) | ||||
0.970940 | + | 0.239322i | \(0.0769252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.56182e69 | 0.406559 | 0.203279 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203279 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(242\) | −4.16832e70 | −1.98339 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.36823e70 | 2.00369 | ||||||||
\(245\) | −2.65285e70 | −0.877633 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.33632e68 | −0.0216977 | ||||||||
\(248\) | −5.70443e69 | −0.131792 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.32304e70 | 1.69952 | ||||||||
\(251\) | 5.62006e70 | 0.910680 | 0.455340 | − | 0.890318i | \(-0.349518\pi\) | ||||
0.455340 | + | 0.890318i | \(0.349518\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.93076e70 | −0.247556 | ||||||||
\(254\) | 1.42479e71 | 1.62614 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.59589e71 | −1.44519 | ||||||||
\(257\) | 1.57080e71 | 1.26792 | 0.633962 | − | 0.773364i | \(-0.281428\pi\) | ||||
0.633962 | + | 0.773364i | \(0.281428\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.95786e70 | −0.125730 | ||||||||
\(260\) | 5.55311e70 | 0.318290 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.84808e71 | 0.844955 | ||||||||
\(263\) | −2.94951e71 | −1.20519 | −0.602595 | − | 0.798047i | \(-0.705867\pi\) | ||||
−0.602595 | + | 0.798047i | \(0.705867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.86313e71 | −0.935596 | ||||||||
\(266\) | 2.05525e70 | 0.0600976 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.01486e71 | −0.706791 | ||||||||
\(269\) | −5.24635e71 | −1.10196 | −0.550979 | − | 0.834519i | \(-0.685745\pi\) | ||||
−0.550979 | + | 0.834519i | \(0.685745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.35272e71 | −0.397170 | −0.198585 | − | 0.980084i | \(-0.563635\pi\) | ||||
−0.198585 | + | 0.980084i | \(0.563635\pi\) | |||||||
\(272\) | 2.99867e71 | 0.454095 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.57677e72 | 1.92365 | ||||||||
\(275\) | 7.28654e70 | 0.0798375 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.69582e71 | −0.238527 | −0.119264 | − | 0.992863i | \(-0.538053\pi\) | ||||
−0.119264 | + | 0.992863i | \(0.538053\pi\) | |||||||
\(278\) | 6.63862e71 | 0.528149 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.86170e71 | −0.377452 | ||||||||
\(281\) | 2.72521e72 | 1.57966 | 0.789831 | − | 0.613325i | \(-0.210168\pi\) | ||||
0.789831 | + | 0.613325i | \(0.210168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.41566e71 | 0.442742 | 0.221371 | − | 0.975190i | \(-0.428947\pi\) | ||||
0.221371 | + | 0.975190i | \(0.428947\pi\) | |||||||
\(284\) | 4.98123e72 | 2.11079 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.33456e72 | 0.459770 | ||||||||
\(287\) | 1.68167e72 | 0.522668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.56380e72 | 1.15569 | ||||||||
\(290\) | −2.42044e72 | −0.553546 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.47807e72 | 1.39635 | ||||||||
\(293\) | 3.41955e72 | 0.577264 | 0.288632 | − | 0.957440i | \(-0.406800\pi\) | ||||
0.288632 | + | 0.957440i | \(0.406800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.96645e72 | −1.37655 | ||||||||
\(296\) | 3.99407e72 | 0.499240 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.18314e73 | 1.21243 | ||||||||
\(299\) | 3.36710e71 | 0.0312576 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.40242e72 | −0.106946 | ||||||||
\(302\) | −2.37409e73 | −1.64169 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.30099e71 | −0.0358623 | ||||||||
\(305\) | 2.15741e73 | 1.11452 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.53220e73 | −1.07874 | −0.539368 | − | 0.842070i | \(-0.681337\pi\) | ||||
−0.539368 | + | 0.842070i | \(0.681337\pi\) | |||||||
\(308\) | −2.09324e73 | −0.810163 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.35449e72 | −0.171218 | ||||||||
\(311\) | −2.94213e73 | −0.855520 | −0.427760 | − | 0.903892i | \(-0.640697\pi\) | ||||
−0.427760 | + | 0.903892i | \(0.640697\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.09875e72 | −0.146785 | −0.0733927 | − | 0.997303i | \(-0.523383\pi\) | ||||
−0.0733927 | + | 0.997303i | \(0.523383\pi\) | |||||||
\(314\) | −6.20044e73 | −1.35831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.81971e73 | −1.23879 | ||||||||
\(317\) | 4.68192e73 | 0.774776 | 0.387388 | − | 0.921917i | \(-0.373377\pi\) | ||||
0.387388 | + | 0.921917i | \(0.373377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.70072e73 | −0.508699 | ||||||||
\(320\) | −1.17741e74 | −1.47572 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.30130e72 | −0.0865761 | ||||||||
\(323\) | −1.78876e73 | −0.170246 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.27072e72 | −0.0100807 | ||||||||
\(326\) | 1.02432e74 | 0.742195 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.43065e74 | −2.07538 | ||||||||
\(329\) | −8.87361e73 | −0.490706 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.18420e74 | −0.547645 | −0.273823 | − | 0.961780i | \(-0.588288\pi\) | ||||
−0.273823 | + | 0.961780i | \(0.588288\pi\) | |||||||
\(332\) | −4.33010e74 | −1.83200 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.51511e74 | 1.95449 | ||||||||
\(335\) | −1.21163e74 | −0.393140 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.43546e74 | 1.20742 | 0.603708 | − | 0.797206i | \(-0.293689\pi\) | ||||
0.603708 | + | 0.797206i | \(0.293689\pi\) | |||||||
\(338\) | 6.41398e74 | 1.59987 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.19156e75 | 2.49739 | ||||||||
\(341\) | −8.18671e73 | −0.157346 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.67669e74 | −0.594676 | ||||||||
\(344\) | 2.86096e74 | 0.424657 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.99270e74 | −0.874783 | ||||||||
\(347\) | 3.30123e74 | 0.379277 | 0.189639 | − | 0.981854i | \(-0.439268\pi\) | ||||
0.189639 | + | 0.981854i | \(0.439268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.57241e74 | −0.249453 | −0.124727 | − | 0.992191i | \(-0.539805\pi\) | ||||
−0.124727 | + | 0.992191i | \(0.539805\pi\) | |||||||
\(350\) | 3.13285e73 | 0.0279211 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.43321e75 | −1.07970 | ||||||||
\(353\) | −5.86179e74 | −0.406141 | −0.203070 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203070 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00188e75 | 1.17409 | ||||||||
\(356\) | 4.91673e74 | 0.265400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.77869e75 | −0.813863 | ||||||||
\(359\) | −6.82502e74 | −0.287619 | −0.143809 | − | 0.989605i | \(-0.545935\pi\) | ||||
−0.143809 | + | 0.989605i | \(0.545935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.75793e75 | −0.986555 | ||||||||
\(362\) | 3.53403e74 | 0.116511 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.65045e74 | 0.102295 | ||||||||
\(365\) | 3.00533e75 | 0.776698 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.95804e75 | −1.31055 | −0.655277 | − | 0.755389i | \(-0.727448\pi\) | ||||
−0.655277 | + | 0.755389i | \(0.727448\pi\) | |||||||
\(368\) | 2.54501e74 | 0.0516630 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.74905e75 | 0.648590 | ||||||||
\(371\) | −1.88214e75 | −0.300691 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.82715e75 | 0.930741 | 0.465370 | − | 0.885116i | \(-0.345921\pi\) | ||||
0.465370 | + | 0.885116i | \(0.345921\pi\) | |||||||
\(374\) | 2.86363e76 | 3.60748 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.81023e76 | 1.94847 | ||||||||
\(377\) | 6.45377e74 | 0.0642308 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.45662e76 | 1.24019 | 0.620097 | − | 0.784525i | \(-0.287093\pi\) | ||||
0.620097 | + | 0.784525i | \(0.287093\pi\) | |||||||
\(380\) | −2.50377e75 | −0.197232 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.00957e75 | 0.338011 | ||||||||
\(383\) | −2.09671e76 | −1.30971 | −0.654854 | − | 0.755756i | \(-0.727270\pi\) | ||||
−0.654854 | + | 0.755756i | \(0.727270\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.41241e75 | −0.450639 | ||||||||
\(386\) | −6.32549e75 | −0.313884 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.67074e75 | −0.412025 | ||||||||
\(389\) | −2.84944e76 | −1.12524 | −0.562621 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562621 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.22492e75 | 0.245256 | ||||||||
\(392\) | 3.55759e76 | 1.12000 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.37930e75 | −0.0373697 | ||||||||
\(395\) | −2.74074e76 | −0.689055 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.03399e76 | −1.52364 | −0.761819 | − | 0.647790i | \(-0.775693\pi\) | ||||
−0.761819 | + | 0.647790i | \(0.775693\pi\) | |||||||
\(398\) | 1.03948e77 | 2.09057 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.60469e74 | −0.0166615 | ||||||||
\(401\) | 3.74569e76 | 0.603633 | 0.301816 | − | 0.953366i | \(-0.402407\pi\) | ||||
0.301816 | + | 0.953366i | \(0.402407\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.42770e75 | 0.0198673 | ||||||||
\(404\) | −2.06322e77 | −2.66867 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.59112e76 | −0.177904 | ||||||||
\(407\) | 5.73208e76 | 0.596042 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.57475e77 | −1.41701 | −0.708507 | − | 0.705703i | \(-0.750631\pi\) | ||||
−0.708507 | + | 0.705703i | \(0.750631\pi\) | |||||||
\(410\) | −3.22019e77 | −2.69624 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.04986e77 | 0.761488 | ||||||||
\(413\) | −6.55163e76 | −0.442408 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.74020e77 | −1.01902 | ||||||||
\(416\) | 2.49941e76 | 0.136328 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.01723e76 | −0.284902 | ||||||||
\(419\) | −1.83449e77 | −0.809474 | −0.404737 | − | 0.914433i | \(-0.632637\pi\) | ||||
−0.404737 | + | 0.914433i | \(0.632637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.33082e77 | −1.27711 | −0.638557 | − | 0.769574i | \(-0.720468\pi\) | ||||
−0.638557 | + | 0.769574i | \(0.720468\pi\) | |||||||
\(422\) | −5.73716e77 | −2.05107 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.83959e77 | 1.19397 | ||||||||
\(425\) | −2.72663e76 | −0.0790957 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.41822e77 | 0.358196 | ||||||||
\(428\) | 1.20738e78 | 2.84613 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.68545e77 | 0.551694 | ||||||||
\(431\) | 7.84833e77 | 1.50556 | 0.752780 | − | 0.658272i | \(-0.228712\pi\) | ||||
0.752780 | + | 0.658272i | \(0.228712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.03006e77 | −1.00909 | −0.504543 | − | 0.863386i | \(-0.668339\pi\) | ||||
−0.504543 | + | 0.863386i | \(0.668339\pi\) | |||||||
\(434\) | −3.51988e76 | −0.0550276 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.40718e78 | 3.28592 | ||||||||
\(437\) | −1.51815e76 | −0.0193692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.29376e77 | 0.478779 | 0.239389 | − | 0.970924i | \(-0.423053\pi\) | ||||
0.239389 | + | 0.970924i | \(0.423053\pi\) | |||||||
\(440\) | 1.71615e78 | 1.78937 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.99395e77 | −0.455499 | ||||||||
\(443\) | −1.51168e78 | −1.28988 | −0.644942 | − | 0.764231i | \(-0.723119\pi\) | ||||
−0.644942 | + | 0.764231i | \(0.723119\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.97596e77 | 0.147624 | ||||||||
\(446\) | 1.41274e78 | 0.987832 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.73993e77 | −0.474281 | ||||||||
\(449\) | −9.96470e77 | −0.571738 | −0.285869 | − | 0.958269i | \(-0.592282\pi\) | ||||
−0.285869 | + | 0.958269i | \(0.592282\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.92349e78 | −2.47779 | ||||||||
\(452\) | 1.76075e78 | 0.830068 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.69017e78 | 1.94107 | ||||||||
\(455\) | 1.46706e77 | 0.0568999 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.29393e77 | −0.146328 | −0.0731640 | − | 0.997320i | \(-0.523310\pi\) | ||||
−0.0731640 | + | 0.997320i | \(0.523310\pi\) | |||||||
\(458\) | −3.65833e78 | −1.16883 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.01129e78 | 0.284131 | ||||||||
\(461\) | −3.37402e78 | −0.889141 | −0.444570 | − | 0.895744i | \(-0.646644\pi\) | ||||
−0.444570 | + | 0.895744i | \(0.646644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.49470e78 | −1.27440 | −0.637199 | − | 0.770700i | \(-0.719907\pi\) | ||||
−0.637199 | + | 0.770700i | \(0.719907\pi\) | |||||||
\(464\) | 4.87807e77 | 0.106162 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.18393e78 | 0.610349 | ||||||||
\(467\) | 1.25571e78 | 0.225965 | 0.112982 | − | 0.993597i | \(-0.463960\pi\) | ||||
0.112982 | + | 0.993597i | \(0.463960\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.96487e77 | −0.126351 | ||||||||
\(470\) | 1.69918e79 | 2.53136 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.33655e79 | 1.75669 | ||||||||
\(473\) | 4.10590e78 | 0.506997 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.72937e76 | 0.00624662 | ||||||||
\(476\) | 7.83292e78 | 0.802636 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.55558e79 | −3.21949 | ||||||||
\(479\) | −1.64131e79 | −1.39731 | −0.698654 | − | 0.715460i | \(-0.746217\pi\) | ||||
−0.698654 | + | 0.715460i | \(0.746217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.99631e77 | −0.0752592 | ||||||||
\(482\) | −9.51866e78 | −0.674044 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.33810e79 | 2.09200 | ||||||||
\(485\) | −3.88653e78 | −0.229182 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.57188e79 | −0.820947 | −0.410473 | − | 0.911873i | \(-0.634637\pi\) | ||||
−0.410473 | + | 0.911873i | \(0.634637\pi\) | |||||||
\(488\) | −2.89319e79 | −1.42230 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.33935e79 | 1.45505 | ||||||||
\(491\) | −9.03820e78 | −0.370833 | −0.185416 | − | 0.982660i | \(-0.559363\pi\) | ||||
−0.185416 | + | 0.982660i | \(0.559363\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.38481e79 | 0.503972 | ||||||||
\(494\) | 1.04936e78 | 0.0359732 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.07912e78 | 0.0328369 | ||||||||
\(497\) | 1.31598e79 | 0.377341 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.86147e79 | 1.23823 | 0.619115 | − | 0.785300i | \(-0.287491\pi\) | ||||
0.619115 | + | 0.785300i | \(0.287491\pi\) | |||||||
\(500\) | −7.46614e79 | −1.79259 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.07441e79 | −1.50984 | ||||||||
\(503\) | 5.22741e79 | 1.05204 | 0.526018 | − | 0.850473i | \(-0.323684\pi\) | ||||
0.526018 | + | 0.850473i | \(0.323684\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.29178e79 | −1.48440 | ||||||||
\(506\) | 2.43040e79 | 0.410428 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.14101e80 | −1.71518 | ||||||||
\(509\) | −1.28179e80 | −1.81821 | −0.909104 | − | 0.416569i | \(-0.863233\pi\) | ||||
−0.909104 | + | 0.416569i | \(0.863233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.97561e79 | 0.249623 | ||||||||
\(512\) | 5.10799e79 | 0.609237 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.97729e80 | −2.10212 | ||||||||
\(515\) | 4.21923e79 | 0.423565 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.59796e80 | 2.32627 | ||||||||
\(518\) | 2.46451e79 | 0.208450 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.99283e79 | −0.225935 | ||||||||
\(521\) | −7.71085e79 | −0.550034 | −0.275017 | − | 0.961439i | \(-0.588683\pi\) | ||||
−0.275017 | + | 0.961439i | \(0.588683\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.72723e80 | −1.10040 | −0.550201 | − | 0.835032i | \(-0.685449\pi\) | ||||
−0.550201 | + | 0.835032i | \(0.685449\pi\) | |||||||
\(524\) | −1.47999e80 | −0.891224 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.71279e80 | 1.99811 | ||||||||
\(527\) | 3.06348e79 | 0.155884 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.13625e80 | −0.972097 | ||||||||
\(530\) | 3.60405e80 | 1.55115 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.64590e79 | −0.0633885 | ||||||||
\(533\) | 8.58619e79 | 0.312858 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.85230e80 | 1.58311 | ||||||||
\(536\) | 1.62485e80 | 0.501709 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.60399e80 | 1.82696 | ||||||||
\(539\) | 5.10568e80 | 1.33716 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.96457e79 | −0.187001 | −0.0935003 | − | 0.995619i | \(-0.529806\pi\) | ||||
−0.0935003 | + | 0.995619i | \(0.529806\pi\) | |||||||
\(542\) | 2.96155e80 | 0.658477 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.36309e80 | 1.06967 | ||||||||
\(545\) | 9.67410e80 | 1.82774 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.46062e80 | 0.417271 | 0.208635 | − | 0.977993i | \(-0.433098\pi\) | ||||
0.208635 | + | 0.977993i | \(0.433098\pi\) | |||||||
\(548\) | −1.26272e81 | −2.02899 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.17214e79 | −0.132364 | ||||||||
\(551\) | −2.90985e79 | −0.0398014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.80168e80 | −0.221455 | ||||||||
\(554\) | 3.39344e80 | 0.395460 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.31638e80 | −0.557070 | ||||||||
\(557\) | −5.11029e80 | −0.507828 | −0.253914 | − | 0.967227i | \(-0.581718\pi\) | ||||
−0.253914 | + | 0.967227i | \(0.581718\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.16038e79 | −0.0640159 | ||||||||
\(560\) | 1.10888e80 | 0.0940450 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.43044e81 | −2.61896 | ||||||||
\(563\) | −5.95243e80 | −0.431218 | −0.215609 | − | 0.976480i | \(-0.569174\pi\) | ||||
−0.215609 | + | 0.976480i | \(0.569174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.07619e80 | 0.461711 | ||||||||
\(566\) | −1.18522e81 | −0.734033 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.68462e81 | −1.49833 | ||||||||
\(569\) | 1.31747e81 | 0.698120 | 0.349060 | − | 0.937100i | \(-0.386501\pi\) | ||||
0.349060 | + | 0.937100i | \(0.386501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.52346e80 | −0.216125 | −0.108063 | − | 0.994144i | \(-0.534465\pi\) | ||||
−0.108063 | + | 0.994144i | \(0.534465\pi\) | |||||||
\(572\) | −1.06875e81 | −0.484947 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.11685e81 | −0.866543 | ||||||||
\(575\) | −2.31413e79 | −0.00899883 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.44759e81 | 1.56113 | 0.780563 | − | 0.625077i | \(-0.214932\pi\) | ||||
0.780563 | + | 0.625077i | \(0.214932\pi\) | |||||||
\(578\) | −5.74482e81 | −1.91604 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.93835e81 | 0.583858 | ||||||||
\(581\) | −1.14396e81 | −0.327502 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.51039e81 | 1.42548 | ||||||||
\(584\) | −4.03028e81 | −0.991189 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.30446e81 | −0.957060 | ||||||||
\(587\) | 8.24445e80 | 0.174316 | 0.0871581 | − | 0.996194i | \(-0.472221\pi\) | ||||
0.0871581 | + | 0.996194i | \(0.472221\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.43716e79 | −0.0123110 | ||||||||
\(590\) | 1.25456e82 | 2.28221 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.55569e80 | −0.124390 | ||||||||
\(593\) | 1.00937e81 | 0.158103 | 0.0790513 | − | 0.996871i | \(-0.474811\pi\) | ||||
0.0790513 | + | 0.996871i | \(0.474811\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.14794e81 | 0.446453 | ||||||||
\(596\) | −9.47490e81 | −1.27882 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.23843e80 | −0.0518227 | ||||||||
\(599\) | −9.57967e81 | −1.11496 | −0.557480 | − | 0.830190i | \(-0.688232\pi\) | ||||
−0.557480 | + | 0.830190i | \(0.688232\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.89987e81 | −0.411390 | −0.205695 | − | 0.978616i | \(-0.565945\pi\) | ||||
−0.205695 | + | 0.978616i | \(0.565945\pi\) | |||||||
\(602\) | 1.76533e81 | 0.177309 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.90123e82 | 1.73159 | ||||||||
\(605\) | 1.34153e82 | 1.16364 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.83298e82 | −1.44242 | −0.721208 | − | 0.692718i | \(-0.756413\pi\) | ||||
−0.721208 | + | 0.692718i | \(0.756413\pi\) | |||||||
\(608\) | −1.12693e81 | −0.0844773 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.71571e82 | −1.84779 | ||||||||
\(611\) | −4.53064e81 | −0.293727 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.18098e82 | 1.28401 | 0.642003 | − | 0.766702i | \(-0.278104\pi\) | ||||
0.642003 | + | 0.766702i | \(0.278104\pi\) | |||||||
\(614\) | 3.18747e82 | 1.78846 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.12814e82 | 0.575087 | ||||||||
\(617\) | −7.94496e81 | −0.386082 | −0.193041 | − | 0.981191i | \(-0.561835\pi\) | ||||
−0.193041 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.42782e82 | −0.630666 | −0.315333 | − | 0.948981i | \(-0.602116\pi\) | ||||
−0.315333 | + | 0.948981i | \(0.602116\pi\) | |||||||
\(620\) | 4.28802e81 | 0.180593 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.70349e82 | 1.41839 | ||||||||
\(623\) | 1.29894e81 | 0.0474450 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.83842e82 | −0.943226 | ||||||||
\(626\) | 7.67698e81 | 0.243359 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.96548e82 | 1.43269 | ||||||||
\(629\) | −2.14495e82 | −0.590505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.26495e82 | −1.57055 | −0.785274 | − | 0.619148i | \(-0.787478\pi\) | ||||
−0.785274 | + | 0.619148i | \(0.787478\pi\) | |||||||
\(632\) | 3.67546e82 | 0.879342 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.89351e82 | −1.28452 | ||||||||
\(635\) | −4.58556e82 | −0.954041 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.90391e81 | −0.168837 | ||||||||
\(638\) | 4.65838e82 | 0.843384 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.05282e83 | 1.73798 | ||||||||
\(641\) | −7.02735e82 | −1.10785 | −0.553923 | − | 0.832568i | \(-0.686870\pi\) | ||||
−0.553923 | + | 0.832568i | \(0.686870\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.72512e81 | −0.139853 | −0.0699264 | − | 0.997552i | \(-0.522276\pi\) | ||||
−0.0699264 | + | 0.997552i | \(0.522276\pi\) | |||||||
\(644\) | 6.64790e81 | 0.0913170 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.25165e82 | 0.282255 | ||||||||
\(647\) | 9.49018e82 | 1.13658 | 0.568288 | − | 0.822830i | \(-0.307606\pi\) | ||||
0.568288 | + | 0.822830i | \(0.307606\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.91814e83 | 2.09731 | ||||||||
\(650\) | 1.59955e81 | 0.0167130 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.20306e82 | −0.782838 | ||||||||
\(653\) | 1.74041e83 | 1.58749 | 0.793746 | − | 0.608249i | \(-0.208128\pi\) | ||||
0.793746 | + | 0.608249i | \(0.208128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.94788e82 | −0.495728 | ||||||||
\(656\) | 6.48986e82 | 0.517097 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.11699e83 | 0.813553 | ||||||||
\(659\) | −2.27995e82 | −0.158784 | −0.0793918 | − | 0.996843i | \(-0.525298\pi\) | ||||
−0.0793918 | + | 0.996843i | \(0.525298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.21921e83 | −1.41337 | −0.706685 | − | 0.707528i | \(-0.749810\pi\) | ||||
−0.706685 | + | 0.707528i | \(0.749810\pi\) | |||||||
\(662\) | 1.49065e83 | 0.907954 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.33369e83 | 1.30043 | ||||||||
\(665\) | −6.61463e81 | −0.0352588 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.17531e82 | 0.0573377 | ||||||||
\(668\) | −4.41665e83 | −2.06152 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.52517e83 | 0.651797 | ||||||||
\(671\) | −4.15216e83 | −1.69809 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.98624e83 | −1.49320 | −0.746602 | − | 0.665271i | \(-0.768316\pi\) | ||||
−0.746602 | + | 0.665271i | \(0.768316\pi\) | |||||||
\(674\) | −5.58326e83 | −2.00180 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.13649e83 | −1.68748 | ||||||||
\(677\) | −2.34092e83 | −0.736242 | −0.368121 | − | 0.929778i | \(-0.619999\pi\) | ||||
−0.368121 | + | 0.929778i | \(0.619999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.55488e82 | −0.0736568 | ||||||||
\(680\) | −6.42185e83 | −1.77275 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.03053e83 | 0.260867 | ||||||||
\(683\) | 4.81642e83 | 1.16765 | 0.583827 | − | 0.811878i | \(-0.301555\pi\) | ||||
0.583827 | + | 0.811878i | \(0.301555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.07469e83 | −1.12859 | ||||||||
\(686\) | 4.62814e83 | 0.985927 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.41216e82 | −0.105806 | ||||||||
\(689\) | −9.60970e82 | −0.179988 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.07164e83 | −1.38790 | −0.693952 | − | 0.720021i | \(-0.744132\pi\) | ||||
−0.693952 | + | 0.720021i | \(0.744132\pi\) | |||||||
\(692\) | 5.59994e83 | 0.922686 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.15552e83 | −0.628813 | ||||||||
\(695\) | −2.13658e83 | −0.309861 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.84238e84 | 2.45477 | ||||||||
\(698\) | 3.23809e83 | 0.413575 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.50887e82 | −0.0294500 | ||||||||
\(701\) | 8.56706e83 | 0.964163 | 0.482082 | − | 0.876126i | \(-0.339881\pi\) | ||||
0.482082 | + | 0.876126i | \(0.339881\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.50710e82 | 0.0466354 | ||||||||
\(704\) | 2.26604e84 | 2.24841 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.37870e83 | 0.673351 | ||||||||
\(707\) | −5.45076e83 | −0.477073 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.41227e84 | 1.94250 | 0.971252 | − | 0.238055i | \(-0.0765100\pi\) | ||||
0.971252 | + | 0.238055i | \(0.0765100\pi\) | |||||||
\(710\) | −2.51993e84 | −1.94655 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.64986e83 | −0.188392 | ||||||||
\(713\) | 2.60001e82 | 0.0177351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.29516e83 | −0.269744 | ||||||||
\(716\) | 1.42442e84 | 0.858430 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.59119e83 | 0.476850 | ||||||||
\(719\) | −1.36154e84 | −0.725315 | −0.362658 | − | 0.931922i | \(-0.618131\pi\) | ||||
−0.362658 | + | 0.931922i | \(0.618131\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.77359e83 | 0.136129 | ||||||||
\(722\) | 3.47163e84 | 1.63563 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.83014e83 | −0.122891 | ||||||||
\(725\) | −4.43553e82 | −0.0184916 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.66201e83 | 0.256059 | 0.128030 | − | 0.991770i | \(-0.459135\pi\) | ||||
0.128030 | + | 0.991770i | \(0.459135\pi\) | |||||||
\(728\) | −1.96740e83 | −0.0726133 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.78304e84 | −1.28771 | ||||||||
\(731\) | −1.53643e84 | −0.502286 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.58371e84 | 1.68405 | 0.842026 | − | 0.539437i | \(-0.181363\pi\) | ||||
0.842026 | + | 0.539437i | \(0.181363\pi\) | |||||||
\(734\) | 7.49986e84 | 2.17280 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.55173e83 | 0.121697 | ||||||||
\(737\) | 2.33190e84 | 0.598990 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.57406e84 | 0.373258 | 0.186629 | − | 0.982430i | \(-0.440244\pi\) | ||||
0.186629 | + | 0.982430i | \(0.440244\pi\) | |||||||
\(740\) | −3.00234e84 | −0.684106 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.36919e84 | 0.498523 | ||||||||
\(743\) | −1.90142e84 | −0.384510 | −0.192255 | − | 0.981345i | \(-0.561580\pi\) | ||||
−0.192255 | + | 0.981345i | \(0.561580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.80782e84 | −0.711323 | ||||||||
\(746\) | −8.59387e84 | −1.54310 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.29327e85 | −3.80503 | ||||||||
\(749\) | 3.18975e84 | 0.508796 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.50454e84 | −1.10649 | −0.553243 | − | 0.833020i | \(-0.686610\pi\) | ||||
−0.553243 | + | 0.833020i | \(0.686610\pi\) | |||||||
\(752\) | −3.42447e84 | −0.485476 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.12387e83 | −0.106490 | ||||||||
\(755\) | 7.64078e84 | 0.963169 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.08215e84 | 0.242764 | 0.121382 | − | 0.992606i | \(-0.461267\pi\) | ||||
0.121382 | + | 0.992606i | \(0.461267\pi\) | |||||||
\(758\) | −1.83356e85 | −2.05615 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.34940e84 | 0.140004 | ||||||||
\(761\) | −1.47227e84 | −0.146940 | −0.0734702 | − | 0.997297i | \(-0.523407\pi\) | ||||
−0.0734702 | + | 0.997297i | \(0.523407\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.35945e84 | 0.587416 | ||||||||
\(764\) | −4.01180e84 | −0.356521 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.63929e85 | 2.17139 | ||||||||
\(767\) | −3.34510e84 | −0.264817 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.22435e84 | −0.0897589 | −0.0448794 | − | 0.998992i | \(-0.514290\pi\) | ||||
−0.0448794 | + | 0.998992i | \(0.514290\pi\) | |||||||
\(770\) | 1.05894e85 | 0.747126 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.06562e84 | 0.331072 | ||||||||
\(773\) | −1.68623e85 | −1.06077 | −0.530385 | − | 0.847757i | \(-0.677953\pi\) | ||||
−0.530385 | + | 0.847757i | \(0.677953\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.81226e82 | −0.00571964 | ||||||||
\(776\) | 5.21202e84 | 0.292472 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.58681e85 | 1.86556 | ||||||||
\(779\) | −3.87131e84 | −0.193867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.85282e85 | −1.78885 | ||||||||
\(782\) | −9.09458e84 | −0.406615 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.73000e84 | −0.279056 | ||||||||
\(785\) | 1.99555e85 | 0.796908 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.38493e85 | 0.513066 | 0.256533 | − | 0.966535i | \(-0.417420\pi\) | ||||
0.256533 | + | 0.966535i | \(0.417420\pi\) | |||||||
\(788\) | 1.10458e84 | 0.0394160 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.44999e85 | 1.14240 | ||||||||
\(791\) | 4.65167e84 | 0.148389 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.24105e84 | 0.214409 | ||||||||
\(794\) | 8.85423e85 | 2.52607 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.32441e85 | −2.20505 | ||||||||
\(797\) | −5.79219e85 | −1.47850 | −0.739251 | − | 0.673430i | \(-0.764820\pi\) | ||||
−0.739251 | + | 0.673430i | \(0.764820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.72158e85 | −2.30466 | ||||||||
\(800\) | −1.71779e84 | −0.0392478 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.71500e85 | −1.00078 | ||||||||
\(803\) | −5.78406e85 | −1.18338 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.67169e84 | 0.0507935 | ||||||||
\(806\) | −1.79716e84 | −0.0329384 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.11197e86 | 1.89433 | ||||||||
\(809\) | −6.11552e85 | −1.00451 | −0.502253 | − | 0.864721i | \(-0.667495\pi\) | ||||
−0.502253 | + | 0.864721i | \(0.667495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.35716e85 | 0.818125 | 0.409062 | − | 0.912506i | \(-0.365856\pi\) | ||||
0.409062 | + | 0.912506i | \(0.365856\pi\) | |||||||
\(812\) | 1.27421e85 | 0.187646 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.21542e85 | −0.988193 | ||||||||
\(815\) | −3.29669e85 | −0.435440 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.22845e84 | 0.0396683 | ||||||||
\(818\) | 1.98226e86 | 2.34930 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.57882e86 | 2.84388 | ||||||||
\(821\) | 1.37690e86 | 1.46480 | 0.732399 | − | 0.680876i | \(-0.238401\pi\) | ||||
0.732399 | + | 0.680876i | \(0.238401\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.30297e86 | −1.29015 | −0.645076 | − | 0.764119i | \(-0.723174\pi\) | ||||
−0.645076 | + | 0.764119i | \(0.723174\pi\) | |||||||
\(824\) | −5.65818e85 | −0.540535 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.24706e85 | 0.733479 | ||||||||
\(827\) | 4.49004e85 | 0.385335 | 0.192667 | − | 0.981264i | \(-0.438286\pi\) | ||||
0.192667 | + | 0.981264i | \(0.438286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.72698e85 | 0.457686 | 0.228843 | − | 0.973463i | \(-0.426506\pi\) | ||||
0.228843 | + | 0.973463i | \(0.426506\pi\) | |||||||
\(830\) | 2.19053e86 | 1.68945 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.95181e85 | −0.283895 | ||||||||
\(833\) | −1.91055e86 | −1.32474 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.77499e86 | −1.14668 | ||||||||
\(836\) | 4.81876e85 | 0.300504 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.30922e86 | 1.34205 | ||||||||
\(839\) | −2.09389e86 | −1.17483 | −0.587415 | − | 0.809286i | \(-0.699854\pi\) | ||||
−0.587415 | + | 0.809286i | \(0.699854\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.68670e86 | −0.882178 | ||||||||
\(842\) | 4.19277e86 | 2.11736 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.59447e86 | 2.16338 | ||||||||
\(845\) | −2.06428e86 | −0.938632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.81884e85 | 0.373982 | ||||||||
\(848\) | −7.26347e85 | −0.297486 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.43223e85 | 0.131135 | ||||||||
\(851\) | −1.82045e85 | −0.0671825 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.65015e86 | −0.568232 | −0.284116 | − | 0.958790i | \(-0.591700\pi\) | ||||
−0.284116 | + | 0.958790i | \(0.591700\pi\) | |||||||
\(854\) | −1.78522e86 | −0.593862 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.50716e86 | −2.02030 | ||||||||
\(857\) | −1.41058e86 | −0.423121 | −0.211560 | − | 0.977365i | \(-0.567855\pi\) | ||||
−0.211560 | + | 0.977365i | \(0.567855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.96519e86 | 0.830337 | 0.415169 | − | 0.909744i | \(-0.363723\pi\) | ||||
0.415169 | + | 0.909744i | \(0.363723\pi\) | |||||||
\(860\) | −2.15058e86 | −0.581905 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.87932e86 | −2.49610 | ||||||||
\(863\) | −4.87041e86 | −1.18918 | −0.594590 | − | 0.804029i | \(-0.702685\pi\) | ||||
−0.594590 | + | 0.804029i | \(0.702685\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.25054e86 | 0.513228 | ||||||||
\(866\) | 7.59051e86 | 1.67299 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.81881e85 | 0.0580409 | ||||||||
\(869\) | 5.27483e86 | 1.04985 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.06666e85 | −0.0756314 | ||||||||
\(872\) | −1.29734e87 | −2.33248 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.91101e85 | 0.0321126 | ||||||||
\(875\) | −1.97246e86 | −0.320457 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.13902e87 | −1.72998 | −0.864992 | − | 0.501786i | \(-0.832677\pi\) | ||||
−0.864992 | + | 0.501786i | \(0.832677\pi\) | |||||||
\(878\) | −5.40490e86 | −0.793779 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.24649e86 | −0.445836 | ||||||||
\(881\) | −1.02118e87 | −1.35617 | −0.678084 | − | 0.734985i | \(-0.737189\pi\) | ||||
−0.678084 | + | 0.734985i | \(0.737189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.55825e86 | 0.814605 | 0.407302 | − | 0.913293i | \(-0.366470\pi\) | ||||
0.407302 | + | 0.913293i | \(0.366470\pi\) | |||||||
\(884\) | 3.99929e86 | 0.480442 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.90287e87 | 2.13853 | ||||||||
\(887\) | −3.31163e86 | −0.359994 | −0.179997 | − | 0.983667i | \(-0.557609\pi\) | ||||
−0.179997 | + | 0.983667i | \(0.557609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.01440e86 | −0.306619 | ||||||||
\(890\) | −2.48730e86 | −0.244750 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.13136e87 | −1.04193 | ||||||||
\(893\) | 2.04276e86 | 0.182012 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.72455e86 | 0.477487 | ||||||||
\(896\) | 6.92092e86 | 0.558570 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.25434e87 | 0.947898 | ||||||||
\(899\) | 4.98349e85 | 0.0364437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.06199e87 | −1.41223 | ||||||||
\(902\) | 6.19758e87 | 4.10799 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.48950e86 | −0.589216 | ||||||||
\(905\) | −1.13739e86 | −0.0683561 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.14918e87 | 1.21020 | 0.605101 | − | 0.796149i | \(-0.293133\pi\) | ||||
0.605101 | + | 0.796149i | \(0.293133\pi\) | |||||||
\(908\) | −3.75602e87 | −2.04736 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.84670e86 | −0.0943358 | ||||||||
\(911\) | 3.84694e87 | 1.90249 | 0.951247 | − | 0.308432i | \(-0.0998041\pi\) | ||||
0.951247 | + | 0.308432i | \(0.0998041\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.34920e87 | 1.55258 | ||||||||
\(914\) | 5.40511e86 | 0.242601 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.92969e87 | 1.23284 | ||||||||
\(917\) | −3.90995e86 | −0.159322 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.17929e87 | −0.832738 | −0.416369 | − | 0.909196i | \(-0.636698\pi\) | ||||
−0.416369 | + | 0.909196i | \(0.636698\pi\) | |||||||
\(920\) | −5.45031e86 | −0.201688 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.24715e87 | 1.47413 | ||||||||
\(923\) | 6.71903e86 | 0.225869 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.87024e85 | 0.0216666 | ||||||||
\(926\) | 6.91661e87 | 2.11285 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.72437e86 | 0.250074 | ||||||||
\(929\) | −7.27755e86 | −0.202079 | −0.101040 | − | 0.994882i | \(-0.532217\pi\) | ||||
−0.101040 | + | 0.994882i | \(0.532217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.01456e86 | 0.104622 | ||||||||
\(932\) | −2.54977e87 | −0.643772 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.58066e87 | −0.374633 | ||||||||
\(935\) | −9.21631e87 | −2.11648 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.04758e87 | −1.08834 | −0.544171 | − | 0.838974i | \(-0.683156\pi\) | ||||
−0.544171 | + | 0.838974i | \(0.683156\pi\) | |||||||
\(938\) | 1.00260e87 | 0.209481 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.36075e88 | −2.66998 | ||||||||
\(941\) | −5.36600e87 | −1.02037 | −0.510184 | − | 0.860065i | \(-0.670423\pi\) | ||||
−0.510184 | + | 0.860065i | \(0.670423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.56365e87 | 0.279283 | ||||||||
\(944\) | −2.52838e87 | −0.437693 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.16843e87 | −0.840562 | ||||||||
\(947\) | 3.04783e87 | 0.480471 | 0.240235 | − | 0.970715i | \(-0.422775\pi\) | ||||
0.240235 | + | 0.970715i | \(0.422775\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00870e87 | 0.149419 | ||||||||
\(950\) | −7.21200e85 | −0.0103564 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.22153e87 | −0.569744 | ||||||||
\(953\) | −1.26501e88 | −1.65522 | −0.827608 | − | 0.561306i | \(-0.810299\pi\) | ||||
−0.827608 | + | 0.561306i | \(0.810299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.61228e87 | −0.198309 | ||||||||
\(956\) | 2.84740e88 | 3.39579 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.06604e88 | 2.31663 | ||||||||
\(959\) | −3.33594e87 | −0.362718 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.66978e87 | −0.988728 | ||||||||
\(962\) | 1.25831e87 | 0.124774 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.62279e87 | 0.710954 | ||||||||
\(965\) | 2.03580e87 | 0.184153 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.77625e87 | 0.151155 | 0.0755776 | − | 0.997140i | \(-0.475920\pi\) | ||||
0.0755776 | + | 0.997140i | \(0.475920\pi\) | |||||||
\(968\) | −1.79906e88 | −1.48499 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.89228e87 | 0.379966 | ||||||||
\(971\) | −2.22991e88 | −1.68004 | −0.840021 | − | 0.542554i | \(-0.817457\pi\) | ||||
−0.840021 | + | 0.542554i | \(0.817457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.40452e87 | −0.0995862 | ||||||||
\(974\) | 1.97865e88 | 1.36107 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.47314e87 | 0.354378 | ||||||||
\(977\) | 1.69730e88 | 1.06627 | 0.533137 | − | 0.846029i | \(-0.321013\pi\) | ||||
0.533137 | + | 0.846029i | \(0.321013\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.80294e87 | −0.224921 | ||||||||
\(980\) | −2.67424e88 | −1.53473 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.13771e88 | 0.614812 | ||||||||
\(983\) | 1.49460e88 | 0.783785 | 0.391893 | − | 0.920011i | \(-0.371821\pi\) | ||||
0.391893 | + | 0.920011i | \(0.371821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.43914e86 | 0.0219245 | ||||||||
\(986\) | −1.74317e88 | −0.835548 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.40354e86 | −0.0379431 | ||||||||
\(989\) | −1.30399e87 | −0.0571458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.20694e88 | −0.498326 | −0.249163 | − | 0.968462i | \(-0.580156\pi\) | ||||
−0.249163 | + | 0.968462i | \(0.580156\pi\) | |||||||
\(992\) | 1.93000e87 | 0.0773506 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.65652e88 | −0.625603 | ||||||||
\(995\) | −3.34546e88 | −1.22652 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.24931e88 | 0.777216 | 0.388608 | − | 0.921403i | \(-0.372956\pi\) | ||||
0.388608 | + | 0.921403i | \(0.372956\pi\) | |||||||
\(998\) | −6.11952e88 | −2.05289 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9.60.a.c.1.1 | 5 | ||
3.2 | odd | 2 | 1.60.a.a.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.60.a.a.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
9.60.a.c.1.1 | 5 | 1.1 | even | 1 | trivial |