Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,54,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, 54, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 54);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 54 \) |
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: | \(160.112796847\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2315873743412x^{2} - 421178019174503472x + 612167648493870378955584 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{27}\cdot 3^{11}\cdot 5^{3}\cdot 7\cdot 13 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.26509e6\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38568e8 | 1.46005 | 0.730024 | − | 0.683421i | \(-0.239509\pi\) | ||||
0.730024 | + | 0.683421i | \(0.239509\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.01938e16 | 1.13174 | ||||||||
\(5\) | 5.35900e18 | 1.60834 | 0.804172 | − | 0.594397i | \(-0.202609\pi\) | ||||
0.804172 | + | 0.594397i | \(0.202609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55363e22 | 1.02816 | 0.514080 | − | 0.857742i | \(-0.328134\pi\) | ||||
0.514080 | + | 0.857742i | \(0.328134\pi\) | |||||||
\(8\) | 1.64427e23 | 0.192348 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.42585e26 | 2.34826 | ||||||||
\(11\) | −2.25708e27 | −0.571006 | −0.285503 | − | 0.958378i | \(-0.592161\pi\) | ||||
−0.285503 | + | 0.958378i | \(0.592161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.44397e29 | 0.436576 | 0.218288 | − | 0.975884i | \(-0.429953\pi\) | ||||
0.218288 | + | 0.975884i | \(0.429953\pi\) | |||||||
\(14\) | 3.53851e30 | 1.50116 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.90335e31 | −0.850903 | ||||||||
\(17\) | 6.08256e32 | 1.50380 | 0.751899 | − | 0.659278i | \(-0.229138\pi\) | ||||
0.751899 | + | 0.659278i | \(0.229138\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.84282e33 | 0.757970 | 0.378985 | − | 0.925403i | \(-0.376273\pi\) | ||||
0.378985 | + | 0.925403i | \(0.376273\pi\) | |||||||
\(20\) | 5.46287e34 | 1.82023 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.12758e35 | −0.833696 | ||||||||
\(23\) | −9.54096e35 | −0.783077 | −0.391538 | − | 0.920162i | \(-0.628057\pi\) | ||||
−0.391538 | + | 0.920162i | \(0.628057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.76167e37 | 1.58677 | ||||||||
\(26\) | 2.00088e37 | 0.637422 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.60313e38 | 1.16361 | ||||||||
\(29\) | 4.38838e37 | 0.0774029 | 0.0387015 | − | 0.999251i | \(-0.487678\pi\) | ||||
0.0387015 | + | 0.999251i | \(0.487678\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.43957e38 | 0.254235 | 0.127118 | − | 0.991888i | \(-0.459427\pi\) | ||||
0.127118 | + | 0.991888i | \(0.459427\pi\) | |||||||
\(32\) | −1.10468e40 | −1.43471 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.42846e40 | 2.19562 | ||||||||
\(35\) | 1.36849e41 | 1.65363 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.19964e41 | 0.332433 | 0.166216 | − | 0.986089i | \(-0.446845\pi\) | ||||
0.166216 | + | 0.986089i | \(0.446845\pi\) | |||||||
\(38\) | 8.09626e41 | 1.10667 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.81165e41 | 0.309362 | ||||||||
\(41\) | 8.08650e42 | 1.47567 | 0.737834 | − | 0.674983i | \(-0.235849\pi\) | ||||
0.737834 | + | 0.674983i | \(0.235849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.66354e43 | 0.859249 | 0.429624 | − | 0.903008i | \(-0.358646\pi\) | ||||
0.429624 | + | 0.903008i | \(0.358646\pi\) | |||||||
\(44\) | −2.30083e43 | −0.646231 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.32207e44 | −1.14333 | ||||||||
\(47\) | 7.16487e42 | 0.0350441 | 0.0175220 | − | 0.999846i | \(-0.494422\pi\) | ||||
0.0175220 | + | 0.999846i | \(0.494422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.52310e43 | 0.0571122 | ||||||||
\(50\) | 2.44110e45 | 2.31676 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.47196e45 | 0.494091 | ||||||||
\(53\) | −3.19144e45 | −0.646660 | −0.323330 | − | 0.946286i | \(-0.604802\pi\) | ||||
−0.323330 | + | 0.946286i | \(0.604802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.20957e46 | −0.918374 | ||||||||
\(56\) | 4.19887e45 | 0.197765 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.08088e45 | 0.113012 | ||||||||
\(59\) | −3.07882e46 | −0.363752 | −0.181876 | − | 0.983321i | \(-0.558217\pi\) | ||||
−0.181876 | + | 0.983321i | \(0.558217\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.46965e47 | −1.20613 | −0.603066 | − | 0.797691i | \(-0.706054\pi\) | ||||
−0.603066 | + | 0.797691i | \(0.706054\pi\) | |||||||
\(62\) | 1.16945e47 | 0.371195 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.08937e47 | −1.24384 | ||||||||
\(65\) | 7.73825e47 | 0.702164 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.37146e48 | 0.557445 | 0.278723 | − | 0.960372i | \(-0.410089\pi\) | ||||
0.278723 | + | 0.960372i | \(0.410089\pi\) | |||||||
\(68\) | 6.20045e48 | 1.70191 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.89629e49 | 2.41439 | ||||||||
\(71\) | −1.40028e49 | −1.22424 | −0.612122 | − | 0.790763i | \(-0.709684\pi\) | ||||
−0.612122 | + | 0.790763i | \(0.709684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.59560e49 | −0.668140 | −0.334070 | − | 0.942548i | \(-0.608422\pi\) | ||||
−0.334070 | + | 0.942548i | \(0.608422\pi\) | |||||||
\(74\) | 1.66231e49 | 0.485368 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.95606e49 | 0.857825 | ||||||||
\(77\) | −5.76375e49 | −0.587085 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.73480e50 | −0.895635 | −0.447818 | − | 0.894125i | \(-0.647799\pi\) | ||||
−0.447818 | + | 0.894125i | \(0.647799\pi\) | |||||||
\(80\) | −3.69950e50 | −1.36854 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.12053e51 | 2.15455 | ||||||||
\(83\) | 1.32890e51 | 1.85320 | 0.926600 | − | 0.376048i | \(-0.122717\pi\) | ||||
0.926600 | + | 0.376048i | \(0.122717\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.25964e51 | 2.41862 | ||||||||
\(86\) | 2.30513e51 | 1.25454 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.71125e50 | −0.109832 | ||||||||
\(89\) | 6.74530e51 | 1.47967 | 0.739837 | − | 0.672786i | \(-0.234902\pi\) | ||||
0.739837 | + | 0.672786i | \(0.234902\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.68737e51 | 0.448870 | ||||||||
\(92\) | −9.72588e51 | −0.886240 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.92819e50 | 0.0511661 | ||||||||
\(95\) | 3.13117e52 | 1.21908 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.44346e52 | 0.996025 | 0.498012 | − | 0.867170i | \(-0.334063\pi\) | ||||
0.498012 | + | 0.867170i | \(0.334063\pi\) | |||||||
\(98\) | 4.88188e51 | 0.0833866 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.79581e53 | 1.79581 | ||||||||
\(101\) | −1.33654e53 | −1.02675 | −0.513377 | − | 0.858163i | \(-0.671606\pi\) | ||||
−0.513377 | + | 0.858163i | \(0.671606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.98514e52 | 0.364835 | 0.182417 | − | 0.983221i | \(-0.441608\pi\) | ||||
0.182417 | + | 0.983221i | \(0.441608\pi\) | |||||||
\(104\) | 2.37428e52 | 0.0839747 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.42230e53 | −0.944155 | ||||||||
\(107\) | 1.04658e54 | 1.74222 | 0.871108 | − | 0.491092i | \(-0.163402\pi\) | ||||
0.871108 | + | 0.491092i | \(0.163402\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.02767e53 | −0.512348 | −0.256174 | − | 0.966631i | \(-0.582462\pi\) | ||||
−0.256174 | + | 0.966631i | \(0.582462\pi\) | |||||||
\(110\) | −1.67607e54 | −1.34087 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.76286e54 | −0.874864 | ||||||||
\(113\) | −3.92048e54 | −1.53731 | −0.768654 | − | 0.639665i | \(-0.779073\pi\) | ||||
−0.768654 | + | 0.639665i | \(0.779073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.11300e54 | −1.25946 | ||||||||
\(116\) | 4.47344e53 | 0.0876001 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.26625e54 | −0.531096 | ||||||||
\(119\) | 1.55326e55 | 1.54615 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.05303e55 | −0.673952 | ||||||||
\(122\) | −3.42214e55 | −1.76101 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.60314e54 | 0.287728 | ||||||||
\(125\) | 3.49109e55 | 0.943726 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.95271e55 | 0.524110 | 0.262055 | − | 0.965053i | \(-0.415600\pi\) | ||||
0.262055 | + | 0.965053i | \(0.415600\pi\) | |||||||
\(128\) | −2.64483e55 | −0.381359 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.07227e56 | 1.02519 | ||||||||
\(131\) | 1.59227e55 | 0.124259 | 0.0621296 | − | 0.998068i | \(-0.480211\pi\) | ||||
0.0621296 | + | 0.998068i | \(0.480211\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.49204e56 | 0.779314 | ||||||||
\(134\) | 1.90041e56 | 0.813897 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.00014e56 | 0.289253 | ||||||||
\(137\) | −1.20350e56 | −0.286650 | −0.143325 | − | 0.989676i | \(-0.545779\pi\) | ||||
−0.143325 | + | 0.989676i | \(0.545779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.03961e57 | 1.68647 | 0.843235 | − | 0.537546i | \(-0.180648\pi\) | ||||
0.843235 | + | 0.537546i | \(0.180648\pi\) | |||||||
\(140\) | 1.39502e57 | 1.87149 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.94033e57 | −1.78745 | ||||||||
\(143\) | −3.25916e56 | −0.249287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.35173e56 | 0.124490 | ||||||||
\(146\) | −2.21098e57 | −0.975516 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.22289e57 | 0.376228 | ||||||||
\(149\) | 5.27498e57 | 1.35764 | 0.678820 | − | 0.734305i | \(-0.262492\pi\) | ||||
0.678820 | + | 0.734305i | \(0.262492\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.14345e57 | −0.206695 | −0.103347 | − | 0.994645i | \(-0.532955\pi\) | ||||
−0.103347 | + | 0.994645i | \(0.532955\pi\) | |||||||
\(152\) | 9.60717e56 | 0.145794 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.98670e57 | −0.857173 | ||||||||
\(155\) | 4.52277e57 | 0.408897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.71579e58 | 1.74806 | 0.874030 | − | 0.485873i | \(-0.161498\pi\) | ||||
0.874030 | + | 0.485873i | \(0.161498\pi\) | |||||||
\(158\) | −2.40387e58 | −1.30767 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.92000e58 | −2.30750 | ||||||||
\(161\) | −2.43641e58 | −0.805128 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.18765e58 | −0.282955 | −0.141478 | − | 0.989941i | \(-0.545185\pi\) | ||||
−0.141478 | + | 0.989941i | \(0.545185\pi\) | |||||||
\(164\) | 8.24323e58 | 1.67007 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.84142e59 | 2.70576 | ||||||||
\(167\) | 1.03522e59 | 1.29732 | 0.648661 | − | 0.761078i | \(-0.275329\pi\) | ||||
0.648661 | + | 0.761078i | \(0.275329\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.85445e58 | −0.809402 | ||||||||
\(170\) | 4.51681e59 | 3.53131 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.69578e59 | 0.972447 | ||||||||
\(173\) | −1.05509e59 | −0.518881 | −0.259441 | − | 0.965759i | \(-0.583538\pi\) | ||||
−0.259441 | + | 0.965759i | \(0.583538\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.49865e59 | 1.63145 | ||||||||
\(176\) | 1.55814e59 | 0.485871 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.34681e59 | 2.16040 | ||||||||
\(179\) | 8.35545e58 | 0.166481 | 0.0832405 | − | 0.996529i | \(-0.473473\pi\) | ||||
0.0832405 | + | 0.996529i | \(0.473473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.95749e59 | −1.18112 | −0.590559 | − | 0.806994i | \(-0.701093\pi\) | ||||
−0.590559 | + | 0.806994i | \(0.701093\pi\) | |||||||
\(182\) | 5.10951e59 | 0.655371 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.56879e59 | −0.150624 | ||||||||
\(185\) | 6.42885e59 | 0.534666 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.37288e60 | −0.858678 | ||||||||
\(188\) | 7.30373e58 | 0.0396608 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.33879e60 | 1.77991 | ||||||||
\(191\) | 3.99509e60 | 1.42607 | 0.713037 | − | 0.701126i | \(-0.247319\pi\) | ||||
0.713037 | + | 0.701126i | \(0.247319\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.31728e60 | −0.627638 | −0.313819 | − | 0.949483i | \(-0.601609\pi\) | ||||
−0.313819 | + | 0.949483i | \(0.601609\pi\) | |||||||
\(194\) | 6.15720e60 | 1.45424 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.59139e59 | 0.0646362 | ||||||||
\(197\) | −6.97303e60 | −1.09665 | −0.548323 | − | 0.836267i | \(-0.684733\pi\) | ||||
−0.548323 | + | 0.836267i | \(0.684733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.01618e60 | −0.844295 | −0.422148 | − | 0.906527i | \(-0.638724\pi\) | ||||
−0.422148 | + | 0.906527i | \(0.638724\pi\) | |||||||
\(200\) | 2.89666e60 | 0.305213 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.85202e61 | −1.49911 | ||||||||
\(203\) | 1.12063e60 | 0.0795826 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.33356e61 | 2.37338 | ||||||||
\(206\) | 1.10648e61 | 0.532676 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.96823e60 | −0.371484 | ||||||||
\(209\) | −1.31877e61 | −0.432805 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.11365e60 | 0.181388 | 0.0906938 | − | 0.995879i | \(-0.471092\pi\) | ||||
0.0906938 | + | 0.995879i | \(0.471092\pi\) | |||||||
\(212\) | −3.25329e61 | −0.731852 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.45022e62 | 2.54372 | ||||||||
\(215\) | 8.91491e61 | 1.38197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.15516e61 | 0.261394 | ||||||||
\(218\) | −6.96673e61 | −0.748052 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.23301e62 | −1.03936 | ||||||||
\(221\) | 8.78304e61 | 0.656522 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.07039e62 | −0.630176 | −0.315088 | − | 0.949062i | \(-0.602034\pi\) | ||||
−0.315088 | + | 0.949062i | \(0.602034\pi\) | |||||||
\(224\) | −2.82096e62 | −1.47511 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.43252e62 | −2.24454 | ||||||||
\(227\) | −2.87663e62 | −1.05730 | −0.528651 | − | 0.848840i | \(-0.677302\pi\) | ||||
−0.528651 | + | 0.848840i | \(0.677302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.16513e62 | −1.50467 | −0.752334 | − | 0.658782i | \(-0.771072\pi\) | ||||
−0.752334 | + | 0.658782i | \(0.771072\pi\) | |||||||
\(230\) | −7.08497e62 | −1.83887 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.21569e60 | 0.0148883 | ||||||||
\(233\) | 1.10244e62 | 0.202965 | 0.101483 | − | 0.994837i | \(-0.467641\pi\) | ||||
0.101483 | + | 0.994837i | \(0.467641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.83965e61 | 0.0563629 | ||||||||
\(236\) | −3.13849e62 | −0.411673 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.15232e63 | 2.25745 | ||||||||
\(239\) | −4.32058e61 | −0.0405507 | −0.0202753 | − | 0.999794i | \(-0.506454\pi\) | ||||
−0.0202753 | + | 0.999794i | \(0.506454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.12916e63 | −1.60235 | −0.801175 | − | 0.598431i | \(-0.795791\pi\) | ||||
−0.801175 | + | 0.598431i | \(0.795791\pi\) | |||||||
\(242\) | −1.45916e63 | −0.984003 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.51752e63 | −1.36503 | ||||||||
\(245\) | 1.88803e62 | 0.0918561 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.43686e62 | 0.330911 | ||||||||
\(248\) | 1.38769e62 | 0.0489017 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.83753e63 | 1.37789 | ||||||||
\(251\) | 2.49739e63 | 0.639930 | 0.319965 | − | 0.947429i | \(-0.396329\pi\) | ||||
0.319965 | + | 0.947429i | \(0.396329\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.15347e63 | 0.447141 | ||||||||
\(254\) | 4.09150e63 | 0.765226 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.52210e63 | 0.687038 | ||||||||
\(257\) | −3.80580e63 | −0.521457 | −0.260728 | − | 0.965412i | \(-0.583963\pi\) | ||||
−0.260728 | + | 0.965412i | \(0.583963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.06343e63 | 0.341794 | ||||||||
\(260\) | 7.88823e63 | 0.794668 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.20638e63 | 0.181425 | ||||||||
\(263\) | 1.69696e64 | 1.26137 | 0.630687 | − | 0.776037i | \(-0.282773\pi\) | ||||
0.630687 | + | 0.776037i | \(0.282773\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.71029e64 | −1.04005 | ||||||||
\(266\) | 2.06749e64 | 1.13784 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.39805e64 | 0.630884 | ||||||||
\(269\) | −6.10982e63 | −0.249800 | −0.124900 | − | 0.992169i | \(-0.539861\pi\) | ||||
−0.124900 | + | 0.992169i | \(0.539861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.96186e63 | −0.334699 | −0.167350 | − | 0.985898i | \(-0.553521\pi\) | ||||
−0.167350 | + | 0.985898i | \(0.553521\pi\) | |||||||
\(272\) | −4.19900e64 | −1.27959 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.66767e64 | −0.418523 | ||||||||
\(275\) | −3.97622e64 | −0.906055 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.47062e64 | 0.464615 | 0.232307 | − | 0.972642i | \(-0.425372\pi\) | ||||
0.232307 | + | 0.972642i | \(0.425372\pi\) | |||||||
\(278\) | 1.44056e65 | 2.46233 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.25017e64 | 0.318074 | ||||||||
\(281\) | 1.25270e64 | 0.161113 | 0.0805564 | − | 0.996750i | \(-0.474330\pi\) | ||||
0.0805564 | + | 0.996750i | \(0.474330\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.70393e64 | −0.288174 | −0.144087 | − | 0.989565i | \(-0.546025\pi\) | ||||
−0.144087 | + | 0.989565i | \(0.546025\pi\) | |||||||
\(284\) | −1.42742e65 | −1.38553 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.51614e64 | −0.363972 | ||||||||
\(287\) | 2.06500e65 | 1.51722 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.06371e65 | 1.26141 | ||||||||
\(290\) | 3.25874e64 | 0.181762 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.62652e65 | −0.756161 | ||||||||
\(293\) | 6.85669e64 | 0.291154 | 0.145577 | − | 0.989347i | \(-0.453496\pi\) | ||||
0.145577 | + | 0.989347i | \(0.453496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.64994e65 | −0.585039 | ||||||||
\(296\) | 1.97253e64 | 0.0639429 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.30942e65 | 1.98222 | ||||||||
\(299\) | −1.37769e65 | −0.341872 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.24807e65 | 0.883445 | ||||||||
\(302\) | −1.58446e65 | −0.301784 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.03350e65 | −0.644959 | ||||||||
\(305\) | −1.32349e66 | −1.93987 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.46437e66 | −1.80502 | −0.902512 | − | 0.430664i | \(-0.858279\pi\) | ||||
−0.902512 | + | 0.430664i | \(0.858279\pi\) | |||||||
\(308\) | −5.87547e65 | −0.664429 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.26710e65 | 0.597010 | ||||||||
\(311\) | −2.08500e66 | −1.82371 | −0.911856 | − | 0.410511i | \(-0.865350\pi\) | ||||
−0.911856 | + | 0.410511i | \(0.865350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.88530e66 | −1.39141 | −0.695706 | − | 0.718327i | \(-0.744908\pi\) | ||||
−0.695706 | + | 0.718327i | \(0.744908\pi\) | |||||||
\(314\) | 3.76322e66 | 2.55225 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.76842e66 | −1.01363 | ||||||||
\(317\) | −1.84865e66 | −0.974503 | −0.487252 | − | 0.873262i | \(-0.662001\pi\) | ||||
−0.487252 | + | 0.873262i | \(0.662001\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.90492e64 | −0.0441975 | ||||||||
\(320\) | −4.87100e66 | −2.00052 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.37608e66 | −1.17553 | ||||||||
\(323\) | 3.55393e66 | 1.13983 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.54380e66 | 0.692745 | ||||||||
\(326\) | −1.64570e66 | −0.413129 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.32964e66 | 0.283842 | ||||||||
\(329\) | 1.82964e65 | 0.0360309 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.90131e66 | 0.318867 | 0.159434 | − | 0.987209i | \(-0.449033\pi\) | ||||
0.159434 | + | 0.987209i | \(0.449033\pi\) | |||||||
\(332\) | 1.35466e67 | 2.09734 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.43449e67 | 1.89415 | ||||||||
\(335\) | 7.34968e66 | 0.896564 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.17803e66 | −0.956218 | −0.478109 | − | 0.878300i | \(-0.658678\pi\) | ||||
−0.478109 | + | 0.878300i | \(0.658678\pi\) | |||||||
\(338\) | −1.22694e67 | −1.18177 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.32282e67 | 2.73726 | ||||||||
\(341\) | −1.90488e66 | −0.145170 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.48530e67 | −0.969439 | ||||||||
\(344\) | 2.73531e66 | 0.165275 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.46202e67 | −0.757592 | ||||||||
\(347\) | −1.14278e67 | −0.548569 | −0.274285 | − | 0.961649i | \(-0.588441\pi\) | ||||
−0.274285 | + | 0.961649i | \(0.588441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.72467e67 | 1.12316 | 0.561578 | − | 0.827424i | \(-0.310195\pi\) | ||||
0.561578 | + | 0.827424i | \(0.310195\pi\) | |||||||
\(350\) | 6.23368e67 | 2.38200 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.49336e67 | 0.819227 | ||||||||
\(353\) | 3.17343e67 | 0.967163 | 0.483582 | − | 0.875299i | \(-0.339336\pi\) | ||||
0.483582 | + | 0.875299i | \(0.339336\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.50409e67 | −1.96900 | ||||||||
\(356\) | 6.87604e67 | 1.67461 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.15780e67 | 0.243070 | ||||||||
\(359\) | −3.93676e67 | −0.767601 | −0.383801 | − | 0.923416i | \(-0.625385\pi\) | ||||
−0.383801 | + | 0.923416i | \(0.625385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.52826e67 | −0.425482 | ||||||||
\(362\) | −1.10265e68 | −1.72449 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.75884e67 | 0.508004 | ||||||||
\(365\) | −8.55081e67 | −1.07460 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.53609e68 | −1.67020 | −0.835098 | − | 0.550101i | \(-0.814589\pi\) | ||||
−0.835098 | + | 0.550101i | \(0.814589\pi\) | |||||||
\(368\) | 6.58645e67 | 0.666322 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.90831e67 | 0.780638 | ||||||||
\(371\) | −8.14977e67 | −0.664870 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.29701e68 | −0.917611 | −0.458805 | − | 0.888537i | \(-0.651722\pi\) | ||||
−0.458805 | + | 0.888537i | \(0.651722\pi\) | |||||||
\(374\) | −1.90237e68 | −1.25371 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.17810e66 | 0.00674068 | ||||||||
\(377\) | 6.33670e66 | 0.0337922 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.95972e68 | 0.908354 | 0.454177 | − | 0.890911i | \(-0.349933\pi\) | ||||
0.454177 | + | 0.890911i | \(0.349933\pi\) | |||||||
\(380\) | 3.19185e68 | 1.37968 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.53590e68 | 2.08214 | ||||||||
\(383\) | 7.90039e67 | 0.277256 | 0.138628 | − | 0.990345i | \(-0.455731\pi\) | ||||
0.138628 | + | 0.990345i | \(0.455731\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.08880e68 | −0.944235 | ||||||||
\(386\) | −3.21100e68 | −0.916382 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.52958e68 | 1.12724 | ||||||||
\(389\) | 2.30262e68 | 0.535252 | 0.267626 | − | 0.963523i | \(-0.413761\pi\) | ||||
0.267626 | + | 0.963523i | \(0.413761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.80334e68 | −1.17759 | ||||||||
\(392\) | 5.79293e66 | 0.0109854 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.66236e68 | −1.60116 | ||||||||
\(395\) | −9.29679e68 | −1.44049 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.76387e68 | 0.645671 | 0.322835 | − | 0.946455i | \(-0.395364\pi\) | ||||
0.322835 | + | 0.946455i | \(0.395364\pi\) | |||||||
\(398\) | −9.72217e68 | −1.23271 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.21614e69 | −1.35019 | ||||||||
\(401\) | 5.31851e68 | 0.552668 | 0.276334 | − | 0.961062i | \(-0.410880\pi\) | ||||
0.276334 | + | 0.961062i | \(0.410880\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.21865e68 | 0.110993 | ||||||||
\(404\) | −1.36245e69 | −1.16202 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.55283e68 | 0.116194 | ||||||||
\(407\) | −2.70767e68 | −0.189821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.07340e69 | −1.27649 | −0.638243 | − | 0.769835i | \(-0.720338\pi\) | ||||
−0.638243 | + | 0.769835i | \(0.720338\pi\) | |||||||
\(410\) | 6.00491e69 | 3.46525 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.13991e68 | 0.412898 | ||||||||
\(413\) | −7.86217e68 | −0.373995 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.12157e69 | 2.98058 | ||||||||
\(416\) | −1.59513e69 | −0.626359 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.82739e69 | −0.631916 | ||||||||
\(419\) | −4.81874e69 | −1.56409 | −0.782045 | − | 0.623221i | \(-0.785824\pi\) | ||||
−0.782045 | + | 0.623221i | \(0.785824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.17794e68 | −0.119533 | −0.0597664 | − | 0.998212i | \(-0.519036\pi\) | ||||
−0.0597664 | + | 0.998212i | \(0.519036\pi\) | |||||||
\(422\) | 9.85723e68 | 0.264835 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.24759e68 | −0.124384 | ||||||||
\(425\) | 1.07154e70 | 2.38618 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.30658e69 | −1.24010 | ||||||||
\(428\) | 1.06686e70 | 1.97174 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.23532e70 | 2.01774 | ||||||||
\(431\) | −2.97872e69 | −0.457490 | −0.228745 | − | 0.973486i | \(-0.573462\pi\) | ||||
−0.228745 | + | 0.973486i | \(0.573462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.69910e69 | 0.366682 | 0.183341 | − | 0.983049i | \(-0.441309\pi\) | ||||
0.183341 | + | 0.983049i | \(0.441309\pi\) | |||||||
\(434\) | 2.98635e69 | 0.381648 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.12512e69 | −0.579845 | ||||||||
\(437\) | −5.57460e69 | −0.593548 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.57805e68 | −0.0337549 | −0.0168774 | − | 0.999858i | \(-0.505373\pi\) | ||||
−0.0168774 | + | 0.999858i | \(0.505373\pi\) | |||||||
\(440\) | −1.98886e69 | −0.176648 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.21705e70 | 0.958554 | ||||||||
\(443\) | 9.79799e69 | 0.726839 | 0.363419 | − | 0.931626i | \(-0.381609\pi\) | ||||
0.363419 | + | 0.931626i | \(0.381609\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.61481e70 | 2.37983 | ||||||||
\(446\) | −1.48321e70 | −0.920088 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.32109e70 | −1.27887 | ||||||||
\(449\) | 2.01028e70 | 1.04407 | 0.522033 | − | 0.852925i | \(-0.325174\pi\) | ||||
0.522033 | + | 0.852925i | \(0.325174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.82519e70 | −0.842615 | ||||||||
\(452\) | −3.99647e70 | −1.73983 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.98608e70 | −1.54371 | ||||||||
\(455\) | 1.97606e70 | 0.721937 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.35756e70 | −1.09205 | −0.546027 | − | 0.837768i | \(-0.683860\pi\) | ||||
−0.546027 | + | 0.837768i | \(0.683860\pi\) | |||||||
\(458\) | −7.15720e70 | −2.19689 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.21210e70 | −1.42538 | ||||||||
\(461\) | −4.09546e70 | −1.05737 | −0.528686 | − | 0.848817i | \(-0.677315\pi\) | ||||
−0.528686 | + | 0.848817i | \(0.677315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.86380e69 | 0.0429045 | 0.0214523 | − | 0.999770i | \(-0.493171\pi\) | ||||
0.0214523 | + | 0.999770i | \(0.493171\pi\) | |||||||
\(464\) | −3.02945e69 | −0.0658624 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.52762e70 | 0.296339 | ||||||||
\(467\) | −4.04901e69 | −0.0742081 | −0.0371040 | − | 0.999311i | \(-0.511813\pi\) | ||||
−0.0371040 | + | 0.999311i | \(0.511813\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.50222e70 | 0.573143 | ||||||||
\(470\) | 5.32052e69 | 0.0822926 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.06241e69 | −0.0699672 | ||||||||
\(473\) | −3.75474e70 | −0.490636 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.02931e71 | 1.20272 | ||||||||
\(476\) | 1.58337e71 | 1.74984 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.98694e69 | −0.0592059 | ||||||||
\(479\) | 1.14957e71 | 1.07558 | 0.537790 | − | 0.843079i | \(-0.319259\pi\) | ||||
0.537790 | + | 0.843079i | \(0.319259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.73224e70 | 0.145132 | ||||||||
\(482\) | −2.95033e71 | −2.33951 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.07344e71 | −0.762739 | ||||||||
\(485\) | 2.38125e71 | 1.60195 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.40380e71 | 1.45004 | 0.725022 | − | 0.688726i | \(-0.241830\pi\) | ||||
0.725022 | + | 0.688726i | \(0.241830\pi\) | |||||||
\(488\) | −4.06077e70 | −0.231998 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.61620e70 | 0.134114 | ||||||||
\(491\) | −4.81194e70 | −0.233701 | −0.116850 | − | 0.993150i | \(-0.537280\pi\) | ||||
−0.116850 | + | 0.993150i | \(0.537280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.66926e70 | 0.116398 | ||||||||
\(494\) | 1.16908e71 | 0.483146 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.82613e70 | −0.216329 | ||||||||
\(497\) | −3.57580e71 | −1.25872 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.07670e69 | 0.0129016 | 0.00645082 | − | 0.999979i | \(-0.497947\pi\) | ||||
0.00645082 | + | 0.999979i | \(0.497947\pi\) | |||||||
\(500\) | 3.55875e71 | 1.06805 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.46057e71 | 0.934329 | ||||||||
\(503\) | 2.27736e71 | 0.583284 | 0.291642 | − | 0.956527i | \(-0.405798\pi\) | ||||
0.291642 | + | 0.956527i | \(0.405798\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.16254e71 | −1.65137 | ||||||||
\(506\) | 2.98401e71 | 0.652848 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.00994e71 | 0.593157 | ||||||||
\(509\) | −3.77057e71 | −0.705319 | −0.352659 | − | 0.935752i | \(-0.614723\pi\) | ||||
−0.352659 | + | 0.935752i | \(0.614723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.07457e71 | −0.686954 | ||||||||
\(512\) | 8.64842e71 | 1.38447 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.27361e71 | −0.761352 | ||||||||
\(515\) | 4.27924e71 | 0.586779 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.61717e70 | −0.0200104 | ||||||||
\(518\) | 4.24492e71 | 0.499035 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.27238e71 | 0.135060 | ||||||||
\(521\) | −1.53660e72 | −1.55011 | −0.775055 | − | 0.631894i | \(-0.782278\pi\) | ||||
−0.775055 | + | 0.631894i | \(0.782278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.24951e71 | −0.478436 | −0.239218 | − | 0.970966i | \(-0.576891\pi\) | ||||
−0.239218 | + | 0.970966i | \(0.576891\pi\) | |||||||
\(524\) | 1.62314e71 | 0.140629 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.35144e72 | 1.84167 | ||||||||
\(527\) | 5.13342e71 | 0.382318 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.74185e71 | −0.386791 | ||||||||
\(530\) | −2.36991e72 | −1.51853 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.52096e72 | 0.881981 | ||||||||
\(533\) | 1.16767e72 | 0.644241 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.60862e72 | 2.80208 | ||||||||
\(536\) | 2.25506e71 | 0.107224 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.46624e71 | −0.364721 | ||||||||
\(539\) | −7.95192e70 | −0.0326114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.62761e72 | −1.72040 | −0.860200 | − | 0.509956i | \(-0.829662\pi\) | ||||
−0.860200 | + | 0.509956i | \(0.829662\pi\) | |||||||
\(542\) | −1.38039e72 | −0.488677 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.71930e72 | −2.15751 | ||||||||
\(545\) | −2.69433e72 | −0.824031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.78991e72 | 0.496782 | 0.248391 | − | 0.968660i | \(-0.420098\pi\) | ||||
0.248391 | + | 0.968660i | \(0.420098\pi\) | |||||||
\(548\) | −1.22683e72 | −0.324413 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.50976e72 | −1.32288 | ||||||||
\(551\) | 2.56405e71 | 0.0586691 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.43004e72 | −0.920856 | ||||||||
\(554\) | 3.42349e72 | 0.678360 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.05976e73 | 1.90865 | ||||||||
\(557\) | −2.84794e72 | −0.489067 | −0.244533 | − | 0.969641i | \(-0.578635\pi\) | ||||
−0.244533 | + | 0.969641i | \(0.578635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.40210e72 | 0.375127 | ||||||||
\(560\) | −9.44718e72 | −1.40708 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.73584e72 | 0.235232 | ||||||||
\(563\) | 8.39092e72 | 1.08477 | 0.542385 | − | 0.840130i | \(-0.317522\pi\) | ||||
0.542385 | + | 0.840130i | \(0.317522\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.10099e73 | −2.47252 | ||||||||
\(566\) | −3.74678e72 | −0.420748 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.30244e72 | −0.235481 | ||||||||
\(569\) | −6.11471e72 | −0.596899 | −0.298450 | − | 0.954425i | \(-0.596469\pi\) | ||||
−0.298450 | + | 0.954425i | \(0.596469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.26705e73 | −1.12703 | −0.563515 | − | 0.826106i | \(-0.690551\pi\) | ||||
−0.563515 | + | 0.826106i | \(0.690551\pi\) | |||||||
\(572\) | −3.32233e72 | −0.282129 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.86142e73 | 2.21522 | ||||||||
\(575\) | −1.68080e73 | −1.24256 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.54639e73 | 1.04270 | 0.521350 | − | 0.853343i | \(-0.325429\pi\) | ||||
0.521350 | + | 0.853343i | \(0.325429\pi\) | |||||||
\(578\) | 2.85964e73 | 1.84172 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.39732e72 | 0.140891 | ||||||||
\(581\) | 3.39352e73 | 1.90539 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.20333e72 | 0.369247 | ||||||||
\(584\) | −2.62359e72 | −0.128516 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.50116e72 | 0.425099 | ||||||||
\(587\) | 2.89131e73 | 1.23647 | 0.618237 | − | 0.785992i | \(-0.287847\pi\) | ||||
0.618237 | + | 0.785992i | \(0.287847\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.93109e72 | 0.192702 | ||||||||
\(590\) | −2.28628e73 | −0.854185 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.28150e72 | −0.282868 | ||||||||
\(593\) | 1.35508e73 | 0.442606 | 0.221303 | − | 0.975205i | \(-0.428969\pi\) | ||||
0.221303 | + | 0.975205i | \(0.428969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.32393e73 | 2.48673 | ||||||||
\(596\) | 5.37722e73 | 1.53650 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.90903e73 | −0.499150 | ||||||||
\(599\) | 1.38679e73 | 0.346897 | 0.173448 | − | 0.984843i | \(-0.444509\pi\) | ||||
0.173448 | + | 0.984843i | \(0.444509\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.98700e73 | −1.14200 | −0.571000 | − | 0.820950i | \(-0.693444\pi\) | ||||
−0.571000 | + | 0.820950i | \(0.693444\pi\) | |||||||
\(602\) | 5.88645e73 | 1.28987 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.16561e73 | −0.233925 | ||||||||
\(605\) | −5.64320e73 | −1.08395 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.33744e73 | 0.763367 | 0.381683 | − | 0.924293i | \(-0.375344\pi\) | ||||
0.381683 | + | 0.924293i | \(0.375344\pi\) | |||||||
\(608\) | −6.45446e73 | −1.08747 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.83392e74 | −2.83231 | ||||||||
\(611\) | 1.03459e72 | 0.0152994 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.11056e74 | 1.50605 | 0.753027 | − | 0.657990i | \(-0.228593\pi\) | ||||
0.753027 | + | 0.657990i | \(0.228593\pi\) | |||||||
\(614\) | −2.02914e74 | −2.63542 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.47717e72 | −0.112925 | ||||||||
\(617\) | −6.32555e73 | −0.722007 | −0.361004 | − | 0.932564i | \(-0.617566\pi\) | ||||
−0.361004 | + | 0.932564i | \(0.617566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.98152e73 | −0.312345 | −0.156173 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156173 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(620\) | 4.61043e73 | 0.462766 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.88914e74 | −2.66271 | ||||||||
\(623\) | 1.72250e74 | 1.52134 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.49672e72 | −0.0689336 | ||||||||
\(626\) | −2.61242e74 | −2.03153 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.76843e74 | 1.97835 | ||||||||
\(629\) | 7.29685e73 | 0.499912 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.66754e74 | 1.68009 | 0.840046 | − | 0.542515i | \(-0.182528\pi\) | ||||
0.840046 | + | 0.542515i | \(0.182528\pi\) | |||||||
\(632\) | −2.85248e73 | −0.172274 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.56163e74 | −1.42282 | ||||||||
\(635\) | 1.58236e74 | 0.842949 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.08726e72 | 0.0249338 | ||||||||
\(638\) | −1.37250e73 | −0.0645305 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.41736e74 | −0.613356 | ||||||||
\(641\) | 7.34082e72 | 0.0304794 | 0.0152397 | − | 0.999884i | \(-0.495149\pi\) | ||||
0.0152397 | + | 0.999884i | \(0.495149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.35192e74 | −0.899150 | −0.449575 | − | 0.893243i | \(-0.648425\pi\) | ||||
−0.449575 | + | 0.893243i | \(0.648425\pi\) | |||||||
\(644\) | −2.48363e74 | −0.911196 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.92459e74 | 1.66421 | ||||||||
\(647\) | −1.32555e74 | −0.429963 | −0.214981 | − | 0.976618i | \(-0.568969\pi\) | ||||
−0.214981 | + | 0.976618i | \(0.568969\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.94914e73 | 0.207705 | ||||||||
\(650\) | 3.52488e74 | 1.01144 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.21067e74 | −0.320232 | ||||||||
\(653\) | 8.70965e73 | 0.221208 | 0.110604 | − | 0.993865i | \(-0.464721\pi\) | ||||
0.110604 | + | 0.993865i | \(0.464721\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.53300e73 | 0.199852 | ||||||||
\(656\) | −5.58239e74 | −1.25565 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.53530e73 | 0.0526069 | ||||||||
\(659\) | −2.94646e74 | −0.587270 | −0.293635 | − | 0.955918i | \(-0.594865\pi\) | ||||
−0.293635 | + | 0.955918i | \(0.594865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.59089e73 | −0.0292618 | −0.0146309 | − | 0.999893i | \(-0.504657\pi\) | ||||
−0.0146309 | + | 0.999893i | \(0.504657\pi\) | |||||||
\(662\) | 2.63460e74 | 0.465562 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.18507e74 | 0.356460 | ||||||||
\(665\) | 7.99585e74 | 1.25340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.18693e73 | −0.0606124 | ||||||||
\(668\) | 1.05529e75 | 1.46823 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.01843e75 | 1.30903 | ||||||||
\(671\) | 5.57420e74 | 0.688708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.05609e75 | −1.20587 | −0.602935 | − | 0.797790i | \(-0.706002\pi\) | ||||
−0.602935 | + | 0.797790i | \(0.706002\pi\) | |||||||
\(674\) | −1.27178e75 | −1.39612 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.02607e74 | −0.916033 | ||||||||
\(677\) | 1.20175e75 | 1.17277 | 0.586386 | − | 0.810032i | \(-0.300550\pi\) | ||||
0.586386 | + | 0.810032i | \(0.300550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.13470e75 | 1.02407 | ||||||||
\(680\) | 5.35974e74 | 0.465219 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.63955e74 | −0.211955 | ||||||||
\(683\) | −1.42292e75 | −1.09909 | −0.549543 | − | 0.835466i | \(-0.685198\pi\) | ||||
−0.549543 | + | 0.835466i | \(0.685198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.44957e74 | −0.461031 | ||||||||
\(686\) | −2.05815e75 | −1.41543 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.14840e75 | −0.731138 | ||||||||
\(689\) | −4.60835e74 | −0.282316 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.83314e75 | −1.03998 | −0.519992 | − | 0.854171i | \(-0.674065\pi\) | ||||
−0.519992 | + | 0.854171i | \(0.674065\pi\) | |||||||
\(692\) | −1.07554e75 | −0.587239 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.58352e75 | −0.800938 | ||||||||
\(695\) | 5.57127e75 | 2.71242 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.91866e75 | 2.21911 | ||||||||
\(698\) | 3.77551e75 | 1.63986 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.58584e75 | 1.84638 | ||||||||
\(701\) | 1.33614e75 | 0.517992 | 0.258996 | − | 0.965878i | \(-0.416608\pi\) | ||||
0.258996 | + | 0.965878i | \(0.416608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.00925e74 | 0.251974 | ||||||||
\(704\) | 2.05154e75 | 0.710240 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.39736e75 | 1.41211 | ||||||||
\(707\) | −3.41304e75 | −1.05567 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.59964e75 | −0.746084 | −0.373042 | − | 0.927815i | \(-0.621685\pi\) | ||||
−0.373042 | + | 0.927815i | \(0.621685\pi\) | |||||||
\(710\) | −1.03982e76 | −2.87484 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.10911e75 | 0.284613 | ||||||||
\(713\) | −8.05216e74 | −0.199086 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.74658e75 | −0.400940 | ||||||||
\(716\) | 8.51739e74 | 0.188413 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.45508e75 | −1.12074 | ||||||||
\(719\) | −5.36453e75 | −1.06222 | −0.531112 | − | 0.847302i | \(-0.678226\pi\) | ||||
−0.531112 | + | 0.847302i | \(0.678226\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.03911e75 | 0.375108 | ||||||||
\(722\) | −3.50336e75 | −0.621225 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.11172e75 | −1.33672 | ||||||||
\(725\) | 7.73087e74 | 0.122821 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.93191e75 | −0.728373 | −0.364186 | − | 0.931326i | \(-0.618653\pi\) | ||||
−0.364186 | + | 0.931326i | \(0.618653\pi\) | |||||||
\(728\) | 6.06304e74 | 0.0863394 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.18487e76 | −1.56897 | ||||||||
\(731\) | 1.01186e76 | 1.29214 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.00902e75 | −1.07010 | −0.535048 | − | 0.844822i | \(-0.679706\pi\) | ||||
−0.535048 | + | 0.844822i | \(0.679706\pi\) | |||||||
\(734\) | −2.12853e76 | −2.43857 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.05397e76 | 1.12349 | ||||||||
\(737\) | −3.09550e75 | −0.318305 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.93120e75 | 0.471927 | 0.235964 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235964 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(740\) | 6.55345e75 | 0.605103 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.12929e76 | −0.970742 | ||||||||
\(743\) | 1.49779e76 | 1.24236 | 0.621181 | − | 0.783667i | \(-0.286653\pi\) | ||||
0.621181 | + | 0.783667i | \(0.286653\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.82686e76 | 2.18355 | ||||||||
\(746\) | −1.79723e76 | −1.33976 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.39949e76 | −0.971801 | ||||||||
\(749\) | 2.67258e76 | 1.79128 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.11227e75 | 0.256817 | 0.128408 | − | 0.991721i | \(-0.459013\pi\) | ||||
0.128408 | + | 0.991721i | \(0.459013\pi\) | |||||||
\(752\) | −4.94616e74 | −0.0298191 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.78062e74 | 0.0493383 | ||||||||
\(755\) | −6.12777e75 | −0.332436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.57142e76 | 1.80634 | 0.903172 | − | 0.429278i | \(-0.141232\pi\) | ||||
0.903172 | + | 0.429278i | \(0.141232\pi\) | |||||||
\(758\) | 2.71554e76 | 1.32624 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.14848e75 | 0.234487 | ||||||||
\(761\) | −2.38006e76 | −1.04687 | −0.523437 | − | 0.852064i | \(-0.675351\pi\) | ||||
−0.523437 | + | 0.852064i | \(0.675351\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.28388e76 | −0.526775 | ||||||||
\(764\) | 4.07252e76 | 1.61395 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.09474e76 | 0.404807 | ||||||||
\(767\) | −4.44572e75 | −0.158805 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.37124e76 | 0.790546 | 0.395273 | − | 0.918564i | \(-0.370650\pi\) | ||||
0.395273 | + | 0.918564i | \(0.370650\pi\) | |||||||
\(770\) | −4.28008e76 | −1.37863 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.36219e76 | −0.710324 | ||||||||
\(773\) | 6.25079e76 | 1.81626 | 0.908131 | − | 0.418686i | \(-0.137509\pi\) | ||||
0.908131 | + | 0.418686i | \(0.137509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.48677e76 | 0.403412 | ||||||||
\(776\) | 7.30625e75 | 0.191584 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.19069e76 | 0.781494 | ||||||||
\(779\) | 4.72479e76 | 1.11851 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.16054e76 | 0.699051 | ||||||||
\(782\) | −8.04156e76 | −1.71934 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.43212e75 | −0.0485970 | ||||||||
\(785\) | 1.45540e77 | 2.81148 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.33252e76 | −0.240627 | −0.120314 | − | 0.992736i | \(-0.538390\pi\) | ||||
−0.120314 | + | 0.992736i | \(0.538390\pi\) | |||||||
\(788\) | −7.10818e76 | −1.24112 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.28824e77 | −2.10318 | ||||||||
\(791\) | −1.00115e77 | −1.58060 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.56610e76 | −0.526568 | ||||||||
\(794\) | 6.60118e76 | 0.942710 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.15217e76 | −0.955524 | ||||||||
\(797\) | 2.10248e76 | 0.271698 | 0.135849 | − | 0.990730i | \(-0.456624\pi\) | ||||
0.135849 | + | 0.990730i | \(0.456624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.35807e75 | 0.0526993 | ||||||||
\(800\) | −1.94609e77 | −2.27655 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.36975e76 | 0.806922 | ||||||||
\(803\) | 3.60139e76 | 0.381512 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.30567e77 | −1.29492 | ||||||||
\(806\) | 1.68866e76 | 0.162055 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.19764e76 | −0.197495 | ||||||||
\(809\) | −1.17401e77 | −1.02103 | −0.510514 | − | 0.859870i | \(-0.670545\pi\) | ||||
−0.510514 | + | 0.859870i | \(0.670545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.03233e75 | 0.0735779 | 0.0367889 | − | 0.999323i | \(-0.488287\pi\) | ||||
0.0367889 | + | 0.999323i | \(0.488287\pi\) | |||||||
\(812\) | 1.14235e76 | 0.0900669 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.75196e76 | −0.277148 | ||||||||
\(815\) | −6.36464e76 | −0.455090 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.71975e76 | 0.651285 | ||||||||
\(818\) | −2.87307e77 | −1.86373 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.41755e77 | 2.68605 | ||||||||
\(821\) | −8.19852e76 | −0.482660 | −0.241330 | − | 0.970443i | \(-0.577584\pi\) | ||||
−0.241330 | + | 0.970443i | \(0.577584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.15061e76 | 0.0635088 | 0.0317544 | − | 0.999496i | \(-0.489891\pi\) | ||||
0.0317544 | + | 0.999496i | \(0.489891\pi\) | |||||||
\(824\) | 1.31297e76 | 0.0701754 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.08944e77 | −0.546051 | ||||||||
\(827\) | −4.29383e76 | −0.208425 | −0.104212 | − | 0.994555i | \(-0.533232\pi\) | ||||
−0.104212 | + | 0.994555i | \(0.533232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.25368e77 | −0.570808 | −0.285404 | − | 0.958407i | \(-0.592128\pi\) | ||||
−0.285404 | + | 0.958407i | \(0.592128\pi\) | |||||||
\(830\) | 9.86820e77 | 4.35180 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.31248e77 | −0.543031 | ||||||||
\(833\) | 2.14295e76 | 0.0858853 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.54776e77 | 2.08654 | ||||||||
\(836\) | −1.34433e77 | −0.489823 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.67722e77 | −2.28365 | ||||||||
\(839\) | 1.07457e77 | 0.356075 | 0.178038 | − | 0.984024i | \(-0.443025\pi\) | ||||
0.178038 | + | 0.984024i | \(0.443025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.19510e77 | −0.994009 | ||||||||
\(842\) | −5.78928e76 | −0.174524 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.25153e76 | 0.205284 | ||||||||
\(845\) | −4.74510e77 | −1.30180 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.68906e77 | −0.692930 | ||||||||
\(848\) | 2.20316e77 | 0.550245 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.48481e78 | 3.48394 | ||||||||
\(851\) | −1.14457e77 | −0.260320 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.22678e77 | −1.54453 | −0.772263 | − | 0.635303i | \(-0.780875\pi\) | ||||
−0.772263 | + | 0.635303i | \(0.780875\pi\) | |||||||
\(854\) | −8.73889e77 | −1.81060 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.72086e77 | 0.335113 | ||||||||
\(857\) | 6.80686e77 | 1.28515 | 0.642577 | − | 0.766221i | \(-0.277865\pi\) | ||||
0.642577 | + | 0.766221i | \(0.277865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.28760e77 | 0.761019 | 0.380510 | − | 0.924777i | \(-0.375749\pi\) | ||||
0.380510 | + | 0.924777i | \(0.375749\pi\) | |||||||
\(860\) | 9.08770e77 | 1.56403 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.12755e77 | −0.667958 | ||||||||
\(863\) | −6.31202e77 | −0.990564 | −0.495282 | − | 0.868732i | \(-0.664935\pi\) | ||||
−0.495282 | + | 0.868732i | \(0.664935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.65423e77 | −0.834539 | ||||||||
\(866\) | 3.74009e77 | 0.535374 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.19693e77 | 0.295831 | ||||||||
\(869\) | 3.91558e77 | 0.511413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.98036e77 | 0.243367 | ||||||||
\(872\) | −8.26685e76 | −0.0985493 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.72460e77 | −0.866609 | ||||||||
\(875\) | 8.91497e77 | 0.970301 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.46824e77 | −0.867569 | −0.433785 | − | 0.901017i | \(-0.642822\pi\) | ||||
−0.433785 | + | 0.901017i | \(0.642822\pi\) | |||||||
\(878\) | −4.95802e76 | −0.0492837 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.35008e77 | 0.781447 | ||||||||
\(881\) | −1.78575e78 | −1.62166 | −0.810830 | − | 0.585281i | \(-0.800984\pi\) | ||||
−0.810830 | + | 0.585281i | \(0.800984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.63389e77 | 0.738325 | 0.369163 | − | 0.929365i | \(-0.379645\pi\) | ||||
0.369163 | + | 0.929365i | \(0.379645\pi\) | |||||||
\(884\) | 8.95327e77 | 0.743013 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.35768e78 | 1.06122 | ||||||||
\(887\) | −1.09908e78 | −0.833785 | −0.416893 | − | 0.908956i | \(-0.636881\pi\) | ||||
−0.416893 | + | 0.908956i | \(0.636881\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.54014e77 | 0.538869 | ||||||||
\(890\) | 5.00896e78 | 3.47466 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.09113e78 | −0.713197 | ||||||||
\(893\) | 4.18630e76 | 0.0265624 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.47769e77 | 0.267759 | ||||||||
\(896\) | −6.75393e77 | −0.392097 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.78560e78 | 1.52439 | ||||||||
\(899\) | 3.70360e76 | 0.0196785 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.94121e78 | −0.972446 | ||||||||
\(902\) | −2.52912e78 | −1.23026 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.44633e77 | −0.295699 | ||||||||
\(905\) | −4.26442e78 | −1.89964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.67275e78 | −0.702812 | −0.351406 | − | 0.936223i | \(-0.614296\pi\) | ||||
−0.351406 | + | 0.936223i | \(0.614296\pi\) | |||||||
\(908\) | −2.93238e78 | −1.19659 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.73819e78 | 1.05406 | ||||||||
\(911\) | 3.79500e78 | 1.41898 | 0.709488 | − | 0.704718i | \(-0.248926\pi\) | ||||
0.709488 | + | 0.704718i | \(0.248926\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.99943e78 | −1.05819 | ||||||||
\(914\) | −4.65249e78 | −1.59445 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.26524e78 | −1.70289 | ||||||||
\(917\) | 4.06609e77 | 0.127758 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.27887e78 | 0.675863 | 0.337932 | − | 0.941171i | \(-0.390273\pi\) | ||||
0.337932 | + | 0.941171i | \(0.390273\pi\) | |||||||
\(920\) | −8.40716e77 | −0.242254 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.67499e78 | −1.54382 | ||||||||
\(923\) | −2.02196e78 | −0.534475 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.11336e78 | 0.527494 | ||||||||
\(926\) | 2.58263e77 | 0.0626427 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.84777e77 | −0.111051 | ||||||||
\(929\) | 1.94979e78 | 0.434082 | 0.217041 | − | 0.976162i | \(-0.430359\pi\) | ||||
0.217041 | + | 0.976162i | \(0.430359\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.05848e77 | 0.0432893 | ||||||||
\(932\) | 1.12380e78 | 0.229704 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.61062e77 | −0.108347 | ||||||||
\(935\) | −7.35727e78 | −1.38105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.29807e78 | 1.29452 | 0.647260 | − | 0.762269i | \(-0.275915\pi\) | ||||
0.647260 | + | 0.762269i | \(0.275915\pi\) | |||||||
\(938\) | 4.85295e78 | 0.836816 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.91407e77 | 0.0637883 | ||||||||
\(941\) | 8.24697e78 | 1.30668 | 0.653341 | − | 0.757064i | \(-0.273367\pi\) | ||||
0.653341 | + | 0.757064i | \(0.273367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.71529e78 | −1.15556 | ||||||||
\(944\) | 2.12541e78 | 0.309518 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.20286e78 | −0.716353 | ||||||||
\(947\) | −1.41218e79 | −1.89067 | −0.945335 | − | 0.326100i | \(-0.894266\pi\) | ||||
−0.945335 | + | 0.326100i | \(0.894266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.30400e78 | −0.291694 | ||||||||
\(950\) | 1.42629e79 | 1.75603 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.55398e78 | 0.297399 | ||||||||
\(953\) | 1.39912e79 | 1.58451 | 0.792253 | − | 0.610192i | \(-0.208908\pi\) | ||||
0.792253 | + | 0.610192i | \(0.208908\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.14097e79 | 2.29362 | ||||||||
\(956\) | −4.40432e77 | −0.0458929 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.59293e79 | 1.57040 | ||||||||
\(959\) | −3.07330e78 | −0.294722 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.03074e79 | −0.935365 | ||||||||
\(962\) | 2.40032e78 | 0.211900 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.17043e79 | −1.81344 | ||||||||
\(965\) | −1.24183e79 | −1.00946 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.89301e78 | 0.376508 | 0.188254 | − | 0.982120i | \(-0.439717\pi\) | ||||
0.188254 | + | 0.982120i | \(0.439717\pi\) | |||||||
\(968\) | −1.73147e78 | −0.129634 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.29964e79 | 2.33892 | ||||||||
\(971\) | 5.58018e78 | 0.384892 | 0.192446 | − | 0.981308i | \(-0.438358\pi\) | ||||
0.192446 | + | 0.981308i | \(0.438358\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.65478e79 | 1.73396 | ||||||||
\(974\) | 3.33089e79 | 2.11713 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.70488e79 | 1.02630 | ||||||||
\(977\) | 2.57199e79 | 1.50683 | 0.753414 | − | 0.657546i | \(-0.228406\pi\) | ||||
0.753414 | + | 0.657546i | \(0.228406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.52247e79 | −0.844903 | ||||||||
\(980\) | 1.92462e78 | 0.103957 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.66779e78 | −0.341215 | ||||||||
\(983\) | −3.41218e79 | −1.69967 | −0.849833 | − | 0.527051i | \(-0.823298\pi\) | ||||
−0.849833 | + | 0.527051i | \(0.823298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.73685e79 | −1.76378 | ||||||||
\(986\) | 3.69873e78 | 0.169947 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.60038e78 | 0.374506 | ||||||||
\(989\) | −1.58718e79 | −0.672858 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.88433e79 | −1.15902 | −0.579512 | − | 0.814964i | \(-0.696757\pi\) | ||||
−0.579512 | + | 0.814964i | \(0.696757\pi\) | |||||||
\(992\) | −9.32306e78 | −0.364753 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.95490e79 | −1.83779 | ||||||||
\(995\) | −3.75997e79 | −1.35792 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.11454e79 | −1.06653 | −0.533264 | − | 0.845949i | \(-0.679035\pi\) | ||||
−0.533264 | + | 0.845949i | \(0.679035\pi\) | |||||||
\(998\) | 5.64900e77 | 0.0188370 | ||||||||
\(999\) | 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 | 9.54.a.b.1.4 | 4 | ||
3.2 | odd | 2 | 1.54.a.a.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.54.a.a.1.1 | ✓ | 4 | 3.2 | odd | 2 | ||
9.54.a.b.1.4 | 4 | 1.1 | even | 1 | trivial |