Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,74,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, 74, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 74);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 74 \) |
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: | \(303.735576363\) |
Analytic rank: | \(0\) |
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: | \( x^{5} - x^{4} + \cdots + 17\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{22}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.10442e9\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.14302e10 | 0.735000 | 0.367500 | − | 0.930024i | \(-0.380214\pi\) | ||||
0.367500 | + | 0.930024i | \(0.380214\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.34246e21 | −0.459775 | ||||||||
\(5\) | 5.37334e25 | 1.65135 | 0.825676 | − | 0.564145i | \(-0.190794\pi\) | ||||
0.825676 | + | 0.564145i | \(0.190794\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.02465e31 | 1.46049 | 0.730245 | − | 0.683185i | \(-0.239406\pi\) | ||||
0.730245 | + | 0.683185i | \(0.239406\pi\) | |||||||
\(8\) | −9.84822e32 | −1.07293 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.83819e36 | 1.21374 | ||||||||
\(11\) | 4.39076e37 | 0.428260 | 0.214130 | − | 0.976805i | \(-0.431308\pi\) | ||||
0.214130 | + | 0.976805i | \(0.431308\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.53509e40 | 1.21393 | 0.606963 | − | 0.794730i | \(-0.292388\pi\) | ||||
0.606963 | + | 0.794730i | \(0.292388\pi\) | |||||||
\(14\) | 7.31912e41 | 1.07346 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.93327e43 | −0.328831 | ||||||||
\(17\) | −9.40723e44 | −1.15365 | −0.576827 | − | 0.816866i | \(-0.695710\pi\) | ||||
−0.576827 | + | 0.816866i | \(0.695710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.72590e46 | 0.365182 | 0.182591 | − | 0.983189i | \(-0.441552\pi\) | ||||
0.182591 | + | 0.983189i | \(0.441552\pi\) | |||||||
\(20\) | −2.33335e47 | −0.759251 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.13633e48 | 0.314771 | ||||||||
\(23\) | 5.77480e49 | 1.14412 | 0.572059 | − | 0.820212i | \(-0.306145\pi\) | ||||
0.572059 | + | 0.820212i | \(0.306145\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.82849e51 | 1.72696 | ||||||||
\(26\) | 3.95373e51 | 0.892236 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.44951e52 | −0.671497 | ||||||||
\(29\) | 8.69385e52 | 0.364490 | 0.182245 | − | 0.983253i | \(-0.441664\pi\) | ||||
0.182245 | + | 0.983253i | \(0.441664\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.48414e54 | 0.545472 | 0.272736 | − | 0.962089i | \(-0.412071\pi\) | ||||
0.272736 | + | 0.962089i | \(0.412071\pi\) | |||||||
\(32\) | 7.20614e54 | 0.831244 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.71960e55 | −0.847936 | ||||||||
\(35\) | 5.50582e56 | 2.41178 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.64558e57 | −1.52461 | −0.762304 | − | 0.647219i | \(-0.775932\pi\) | ||||
−0.762304 | + | 0.647219i | \(0.775932\pi\) | |||||||
\(38\) | 1.23282e57 | 0.268409 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.29179e58 | −1.77179 | ||||||||
\(41\) | −3.07305e57 | −0.0417791 | −0.0208896 | − | 0.999782i | \(-0.506650\pi\) | ||||
−0.0208896 | + | 0.999782i | \(0.506650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24223e59 | 0.774900 | 0.387450 | − | 0.921891i | \(-0.373356\pi\) | ||||
0.387450 | + | 0.921891i | \(0.373356\pi\) | |||||||
\(44\) | −1.90667e59 | −0.196903 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.12496e60 | 0.840927 | ||||||||
\(47\) | 8.51145e60 | 0.791465 | 0.395732 | − | 0.918366i | \(-0.370491\pi\) | ||||
0.395732 | + | 0.918366i | \(0.370491\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.57697e61 | 1.13303 | ||||||||
\(50\) | 1.30610e62 | 1.26932 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.40359e62 | −0.558133 | ||||||||
\(53\) | 8.36780e62 | 0.969488 | 0.484744 | − | 0.874656i | \(-0.338913\pi\) | ||||
0.484744 | + | 0.874656i | \(0.338913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.35931e63 | 0.707207 | ||||||||
\(56\) | −1.00910e64 | −1.56701 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.21004e63 | 0.267900 | ||||||||
\(59\) | −2.35468e64 | −0.544293 | −0.272147 | − | 0.962256i | \(-0.587734\pi\) | ||||
−0.272147 | + | 0.962256i | \(0.587734\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.89372e64 | 0.403507 | 0.201753 | − | 0.979436i | \(-0.435336\pi\) | ||||
0.201753 | + | 0.979436i | \(0.435336\pi\) | |||||||
\(62\) | 1.06012e65 | 0.400922 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.91776e65 | 0.939795 | ||||||||
\(65\) | 2.97420e66 | 2.00462 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.87121e66 | 1.53216 | 0.766078 | − | 0.642747i | \(-0.222206\pi\) | ||||
0.766078 | + | 0.642747i | \(0.222206\pi\) | |||||||
\(68\) | 4.08505e66 | 0.530422 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.93282e67 | 1.77266 | ||||||||
\(71\) | −8.24197e66 | −0.221361 | −0.110681 | − | 0.993856i | \(-0.535303\pi\) | ||||
−0.110681 | + | 0.993856i | \(0.535303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.53931e68 | −1.49983 | −0.749913 | − | 0.661537i | \(-0.769905\pi\) | ||||
−0.749913 | + | 0.661537i | \(0.769905\pi\) | |||||||
\(74\) | −1.88974e68 | −1.12059 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.49465e67 | −0.167902 | ||||||||
\(77\) | 4.49901e68 | 0.625469 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.64169e68 | −0.198570 | −0.0992850 | − | 0.995059i | \(-0.531656\pi\) | ||||
−0.0992850 | + | 0.995059i | \(0.531656\pi\) | |||||||
\(80\) | −1.57615e69 | −0.543016 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.19509e68 | −0.0307076 | ||||||||
\(83\) | −1.69878e70 | −1.52682 | −0.763409 | − | 0.645915i | \(-0.776476\pi\) | ||||
−0.763409 | + | 0.645915i | \(0.776476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.05483e70 | −1.90509 | ||||||||
\(86\) | 2.31594e70 | 0.569552 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.32412e70 | −0.459495 | ||||||||
\(89\) | −7.76576e69 | −0.0546322 | −0.0273161 | − | 0.999627i | \(-0.508696\pi\) | ||||
−0.0273161 | + | 0.999627i | \(0.508696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.67155e71 | 1.77293 | ||||||||
\(92\) | −2.50768e71 | −0.526038 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.07975e71 | 0.581726 | ||||||||
\(95\) | 9.27387e71 | 0.603044 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.51236e71 | 0.137162 | 0.0685812 | − | 0.997646i | \(-0.478153\pi\) | ||||
0.0685812 | + | 0.997646i | \(0.478153\pi\) | |||||||
\(98\) | 3.98365e72 | 0.832777 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.94014e72 | −0.794014 | ||||||||
\(101\) | 9.01684e72 | 0.627082 | 0.313541 | − | 0.949575i | \(-0.398485\pi\) | ||||
0.313541 | + | 0.949575i | \(0.398485\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.78483e73 | −0.946762 | −0.473381 | − | 0.880858i | \(-0.656967\pi\) | ||||
−0.473381 | + | 0.880858i | \(0.656967\pi\) | |||||||
\(104\) | −5.45108e73 | −1.30246 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.97714e73 | 0.712573 | ||||||||
\(107\) | −7.06643e72 | −0.0597988 | −0.0298994 | − | 0.999553i | \(-0.509519\pi\) | ||||
−0.0298994 | + | 0.999553i | \(0.509519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.98041e74 | −0.852486 | −0.426243 | − | 0.904609i | \(-0.640163\pi\) | ||||
−0.426243 | + | 0.904609i | \(0.640163\pi\) | |||||||
\(110\) | 1.68526e74 | 0.519797 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.00559e74 | −0.480255 | ||||||||
\(113\) | 1.25005e75 | 1.44400 | 0.721998 | − | 0.691896i | \(-0.243224\pi\) | ||||
0.721998 | + | 0.691896i | \(0.243224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.10300e75 | 1.88934 | ||||||||
\(116\) | −3.77527e74 | −0.167583 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.68195e75 | −0.400055 | ||||||||
\(119\) | −9.63915e75 | −1.68490 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.58365e75 | −0.816594 | ||||||||
\(122\) | 4.20990e75 | 0.296577 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.44481e75 | −0.250795 | ||||||||
\(125\) | 4.13587e76 | 1.20047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.12034e76 | −1.15788 | −0.578942 | − | 0.815369i | \(-0.696534\pi\) | ||||
−0.578942 | + | 0.815369i | \(0.696534\pi\) | |||||||
\(128\) | −1.15033e76 | −0.140494 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.12447e77 | 1.47339 | ||||||||
\(131\) | −2.45112e77 | −1.28517 | −0.642587 | − | 0.766213i | \(-0.722139\pi\) | ||||
−0.642587 | + | 0.766213i | \(0.722139\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.76845e77 | 0.533345 | ||||||||
\(134\) | 4.90812e77 | 1.12613 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.26444e77 | 1.23780 | ||||||||
\(137\) | 6.33470e77 | 0.647776 | 0.323888 | − | 0.946095i | \(-0.395010\pi\) | ||||
0.323888 | + | 0.946095i | \(0.395010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.79078e78 | −1.07895 | −0.539475 | − | 0.842002i | \(-0.681377\pi\) | ||||
−0.539475 | + | 0.842002i | \(0.681377\pi\) | |||||||
\(140\) | −2.39088e78 | −1.10888 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.88726e77 | −0.162700 | ||||||||
\(143\) | 2.43033e78 | 0.519876 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.67151e78 | 0.601901 | ||||||||
\(146\) | −1.09953e79 | −1.10237 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.14883e79 | 0.700977 | ||||||||
\(149\) | 2.55369e79 | 1.21862 | 0.609310 | − | 0.792932i | \(-0.291446\pi\) | ||||
0.609310 | + | 0.792932i | \(0.291446\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.58400e79 | −1.34458 | −0.672289 | − | 0.740289i | \(-0.734689\pi\) | ||||
−0.672289 | + | 0.740289i | \(0.734689\pi\) | |||||||
\(152\) | −1.69971e79 | −0.391817 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.21365e79 | 0.459719 | ||||||||
\(155\) | 7.97479e79 | 0.900767 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.23717e80 | 1.58257 | 0.791283 | − | 0.611450i | \(-0.209414\pi\) | ||||
0.791283 | + | 0.611450i | \(0.209414\pi\) | |||||||
\(158\) | −2.60126e79 | −0.145949 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.87211e80 | 1.37268 | ||||||||
\(161\) | 5.91717e80 | 1.67097 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.41890e80 | 0.255331 | 0.127665 | − | 0.991817i | \(-0.459252\pi\) | ||||
0.127665 | + | 0.991817i | \(0.459252\pi\) | |||||||
\(164\) | 1.33446e79 | 0.0192090 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.21344e81 | −1.12221 | ||||||||
\(167\) | −5.60731e80 | −0.416489 | −0.208244 | − | 0.978077i | \(-0.566775\pi\) | ||||
−0.208244 | + | 0.978077i | \(0.566775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.84674e80 | 0.473618 | ||||||||
\(170\) | −3.61067e81 | −1.40024 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.40793e81 | −0.356280 | ||||||||
\(173\) | 3.93500e81 | 0.805864 | 0.402932 | − | 0.915230i | \(-0.367991\pi\) | ||||
0.402932 | + | 0.915230i | \(0.367991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.87357e82 | 2.52221 | ||||||||
\(176\) | −1.28793e81 | −0.140825 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.54710e80 | −0.0401547 | ||||||||
\(179\) | 3.22411e82 | 1.90228 | 0.951140 | − | 0.308759i | \(-0.0999138\pi\) | ||||
0.951140 | + | 0.308759i | \(0.0999138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.64648e82 | 1.43419 | 0.717095 | − | 0.696976i | \(-0.245472\pi\) | ||||
0.717095 | + | 0.696976i | \(0.245472\pi\) | |||||||
\(182\) | 4.05120e82 | 1.30310 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.68715e82 | −1.22756 | ||||||||
\(185\) | −1.42156e83 | −2.51766 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.13049e82 | −0.494064 | ||||||||
\(188\) | −3.69606e82 | −0.363896 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.62435e82 | 0.443238 | ||||||||
\(191\) | 1.38052e83 | 0.762649 | 0.381325 | − | 0.924441i | \(-0.375468\pi\) | ||||
0.381325 | + | 0.924441i | \(0.375468\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.46248e83 | −0.930101 | −0.465051 | − | 0.885284i | \(-0.653964\pi\) | ||||
−0.465051 | + | 0.885284i | \(0.653964\pi\) | |||||||
\(194\) | 3.22319e82 | 0.100814 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.42178e83 | −0.520940 | ||||||||
\(197\) | 4.95791e83 | 0.885689 | 0.442844 | − | 0.896598i | \(-0.353969\pi\) | ||||
0.442844 | + | 0.896598i | \(0.353969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.06154e82 | −0.0501826 | −0.0250913 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250913 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(200\) | −1.80074e84 | −1.85292 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.44075e83 | 0.460905 | ||||||||
\(203\) | 8.90819e83 | 0.532334 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.65126e83 | −0.0689920 | ||||||||
\(206\) | −1.98921e84 | −0.695870 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.62359e84 | −0.399177 | ||||||||
\(209\) | 7.57803e83 | 0.156393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.12088e84 | −1.32962 | −0.664810 | − | 0.747013i | \(-0.731487\pi\) | ||||
−0.664810 | + | 0.747013i | \(0.731487\pi\) | |||||||
\(212\) | −3.63368e84 | −0.445747 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.04757e83 | −0.0439521 | ||||||||
\(215\) | 1.74216e85 | 1.27963 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.52073e85 | 0.796657 | ||||||||
\(218\) | −1.41461e85 | −0.626577 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.02452e85 | −0.325156 | ||||||||
\(221\) | −5.20699e85 | −1.40045 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.10503e85 | −0.213918 | −0.106959 | − | 0.994263i | \(-0.534111\pi\) | ||||
−0.106959 | + | 0.994263i | \(0.534111\pi\) | |||||||
\(224\) | 7.38379e85 | 1.21402 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.92917e85 | 1.06134 | ||||||||
\(227\) | −9.88450e84 | −0.100003 | −0.0500013 | − | 0.998749i | \(-0.515923\pi\) | ||||
−0.0500013 | + | 0.998749i | \(0.515923\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.28394e85 | 0.461569 | 0.230785 | − | 0.973005i | \(-0.425871\pi\) | ||||
0.230785 | + | 0.973005i | \(0.425871\pi\) | |||||||
\(230\) | 2.21648e86 | 1.38867 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.56190e85 | −0.391074 | ||||||||
\(233\) | −7.37366e85 | −0.287867 | −0.143934 | − | 0.989587i | \(-0.545975\pi\) | ||||
−0.143934 | + | 0.989587i | \(0.545975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.57349e86 | 1.30699 | ||||||||
\(236\) | 1.02251e86 | 0.250253 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.88526e86 | −1.23840 | ||||||||
\(239\) | −5.40038e86 | −0.833491 | −0.416746 | − | 0.909023i | \(-0.636829\pi\) | ||||
−0.416746 | + | 0.909023i | \(0.636829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.43408e86 | 0.504873 | 0.252436 | − | 0.967614i | \(-0.418768\pi\) | ||||
0.252436 | + | 0.967614i | \(0.418768\pi\) | |||||||
\(242\) | −6.13132e86 | −0.600196 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.55932e86 | −0.185522 | ||||||||
\(245\) | 2.99670e87 | 1.87103 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.55303e86 | 0.443305 | ||||||||
\(248\) | −1.46161e87 | −0.585256 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.95426e87 | 0.882345 | ||||||||
\(251\) | 4.58295e86 | 0.118319 | 0.0591595 | − | 0.998249i | \(-0.481158\pi\) | ||||
0.0591595 | + | 0.998249i | \(0.481158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.53558e87 | 0.489980 | ||||||||
\(254\) | −5.08608e87 | −0.851044 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.29980e87 | −1.04306 | ||||||||
\(257\) | 5.46778e87 | 0.596008 | 0.298004 | − | 0.954565i | \(-0.403679\pi\) | ||||
0.298004 | + | 0.954565i | \(0.403679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.71080e88 | −2.22667 | ||||||||
\(260\) | −1.29153e88 | −0.921675 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.75084e88 | −0.944603 | ||||||||
\(263\) | 5.24740e87 | 0.246354 | 0.123177 | − | 0.992385i | \(-0.460692\pi\) | ||||
0.123177 | + | 0.992385i | \(0.460692\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.49631e88 | 1.60096 | ||||||||
\(266\) | 1.26321e88 | 0.392009 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.98379e88 | −0.704448 | ||||||||
\(269\) | 6.27826e87 | 0.129384 | 0.0646920 | − | 0.997905i | \(-0.479393\pi\) | ||||
0.0646920 | + | 0.997905i | \(0.479393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.67497e88 | 1.36423 | 0.682117 | − | 0.731243i | \(-0.261059\pi\) | ||||
0.682117 | + | 0.731243i | \(0.261059\pi\) | |||||||
\(272\) | 2.75940e88 | 0.379358 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.52489e88 | 0.476116 | ||||||||
\(275\) | 8.02848e88 | 0.739588 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.05020e89 | 0.742610 | 0.371305 | − | 0.928511i | \(-0.378910\pi\) | ||||
0.371305 | + | 0.928511i | \(0.378910\pi\) | |||||||
\(278\) | −1.27916e89 | −0.793027 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.42225e89 | −2.58768 | ||||||||
\(281\) | 1.29679e89 | 0.543362 | 0.271681 | − | 0.962387i | \(-0.412420\pi\) | ||||
0.271681 | + | 0.962387i | \(0.412420\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.99633e89 | 1.93946 | 0.969729 | − | 0.244182i | \(-0.0785194\pi\) | ||||
0.969729 | + | 0.244182i | \(0.0785194\pi\) | |||||||
\(284\) | 3.57904e88 | 0.101776 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.73599e89 | 0.382109 | ||||||||
\(287\) | −3.14881e88 | −0.0610180 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.20036e89 | 0.330920 | ||||||||
\(290\) | 3.33687e89 | 0.442397 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.68437e89 | 0.689583 | ||||||||
\(293\) | 3.90288e89 | 0.355400 | 0.177700 | − | 0.984085i | \(-0.443134\pi\) | ||||
0.177700 | + | 0.984085i | \(0.443134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.26525e90 | −0.898819 | ||||||||
\(296\) | 2.60543e90 | 1.63580 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.82410e90 | 0.895686 | ||||||||
\(299\) | 3.19641e90 | 1.38888 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.32217e90 | 1.13173 | ||||||||
\(302\) | −3.27436e90 | −0.988265 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.06254e89 | −0.120083 | ||||||||
\(305\) | 3.16690e90 | 0.666331 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.03208e90 | −0.834059 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(308\) | −1.95368e90 | −0.287575 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.69641e90 | 0.662063 | ||||||||
\(311\) | −5.56953e90 | −0.575525 | −0.287763 | − | 0.957702i | \(-0.592911\pi\) | ||||
−0.287763 | + | 0.957702i | \(0.592911\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.93772e91 | −1.58461 | −0.792305 | − | 0.610125i | \(-0.791119\pi\) | ||||
−0.792305 | + | 0.610125i | \(0.791119\pi\) | |||||||
\(314\) | 1.59802e91 | 1.16319 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.58139e90 | 0.0912976 | ||||||||
\(317\) | 1.45832e91 | 0.750221 | 0.375110 | − | 0.926980i | \(-0.377605\pi\) | ||||
0.375110 | + | 0.926980i | \(0.377605\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.81727e90 | 0.156096 | ||||||||
\(320\) | 4.25448e91 | 1.55193 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.22665e91 | 1.22817 | ||||||||
\(323\) | −1.62360e91 | −0.421294 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.01209e92 | 2.09640 | ||||||||
\(326\) | 1.01352e91 | 0.187668 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.02641e90 | 0.0448263 | ||||||||
\(329\) | 8.72128e91 | 1.15593 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.05919e91 | −0.537476 | −0.268738 | − | 0.963213i | \(-0.586607\pi\) | ||||
−0.268738 | + | 0.963213i | \(0.586607\pi\) | |||||||
\(332\) | 7.37688e91 | 0.701993 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.00531e91 | −0.306119 | ||||||||
\(335\) | 3.69214e92 | 2.53013 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.39888e92 | 0.771419 | 0.385710 | − | 0.922620i | \(-0.373957\pi\) | ||||
0.385710 | + | 0.922620i | \(0.373957\pi\) | |||||||
\(338\) | 7.03355e91 | 0.348109 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.19504e92 | 0.875913 | ||||||||
\(341\) | 6.51650e91 | 0.233604 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.70944e91 | 0.194290 | ||||||||
\(344\) | −3.19302e92 | −0.831417 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.81078e92 | 0.592310 | ||||||||
\(347\) | 9.06972e91 | 0.172016 | 0.0860078 | − | 0.996294i | \(-0.472589\pi\) | ||||
0.0860078 | + | 0.996294i | \(0.472589\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.50813e92 | 0.693216 | 0.346608 | − | 0.938010i | \(-0.387333\pi\) | ||||
0.346608 | + | 0.938010i | \(0.387333\pi\) | |||||||
\(350\) | 1.33830e93 | 1.85382 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.16405e92 | 0.355988 | ||||||||
\(353\) | 1.31440e93 | 1.33337 | 0.666685 | − | 0.745339i | \(-0.267712\pi\) | ||||
0.666685 | + | 0.745339i | \(0.267712\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.42869e92 | −0.365545 | ||||||||
\(356\) | 3.37225e91 | 0.0251185 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.30299e93 | 1.39818 | ||||||||
\(359\) | 1.25513e93 | 0.688245 | 0.344122 | − | 0.938925i | \(-0.388176\pi\) | ||||
0.344122 | + | 0.938925i | \(0.388176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.93576e93 | −0.866642 | ||||||||
\(362\) | 2.60469e93 | 1.05413 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.46285e93 | −0.815148 | ||||||||
\(365\) | −8.27122e93 | −2.47674 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.71510e93 | 1.40189 | 0.700943 | − | 0.713217i | \(-0.252763\pi\) | ||||
0.700943 | + | 0.713217i | \(0.252763\pi\) | |||||||
\(368\) | −1.69391e93 | −0.376222 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.01542e94 | −1.85048 | ||||||||
\(371\) | 8.57410e93 | 1.41593 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.74173e93 | −0.507809 | −0.253905 | − | 0.967229i | \(-0.581715\pi\) | ||||
−0.253905 | + | 0.967229i | \(0.581715\pi\) | |||||||
\(374\) | −2.95042e93 | −0.363137 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.38226e93 | −0.849190 | ||||||||
\(377\) | 4.81213e93 | 0.442464 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.02793e94 | 1.53717 | 0.768586 | − | 0.639747i | \(-0.220961\pi\) | ||||
0.768586 | + | 0.639747i | \(0.220961\pi\) | |||||||
\(380\) | −4.02714e93 | −0.277265 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.86109e93 | 0.560547 | ||||||||
\(383\) | 8.75423e93 | 0.452337 | 0.226169 | − | 0.974088i | \(-0.427380\pi\) | ||||
0.226169 | + | 0.974088i | \(0.427380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.41747e94 | 1.03287 | ||||||||
\(386\) | −1.75895e94 | −0.683624 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.95947e93 | −0.0630639 | ||||||||
\(389\) | 1.08943e94 | 0.319182 | 0.159591 | − | 0.987183i | \(-0.448982\pi\) | ||||
0.159591 | + | 0.987183i | \(0.448982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.43249e94 | −1.31992 | ||||||||
\(392\) | −5.49233e94 | −1.21567 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.54144e94 | 0.650981 | ||||||||
\(395\) | −1.95680e94 | −0.327909 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.01644e95 | −1.41654 | −0.708268 | − | 0.705944i | \(-0.750523\pi\) | ||||
−0.708268 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(398\) | −2.90116e93 | −0.0368842 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.36347e94 | −0.567879 | ||||||||
\(401\) | −1.22596e95 | −1.18497 | −0.592483 | − | 0.805583i | \(-0.701852\pi\) | ||||
−0.592483 | + | 0.805583i | \(0.701852\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.21484e94 | 0.662163 | ||||||||
\(404\) | −3.91552e94 | −0.288317 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.36314e94 | 0.391265 | ||||||||
\(407\) | −1.16161e95 | −0.652928 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.38071e94 | 0.111894 | 0.0559469 | − | 0.998434i | \(-0.482182\pi\) | ||||
0.0559469 | + | 0.998434i | \(0.482182\pi\) | |||||||
\(410\) | −1.17950e94 | −0.0507091 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.20930e95 | 0.435298 | ||||||||
\(413\) | −2.41273e95 | −0.794935 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.12814e95 | −2.52131 | ||||||||
\(416\) | 3.98866e95 | 1.00907 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.41300e94 | 0.114949 | ||||||||
\(419\) | −6.44324e95 | −1.25399 | −0.626993 | − | 0.779025i | \(-0.715714\pi\) | ||||
−0.626993 | + | 0.779025i | \(0.715714\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.80537e95 | −1.11315 | −0.556577 | − | 0.830796i | \(-0.687886\pi\) | ||||
−0.556577 | + | 0.830796i | \(0.687886\pi\) | |||||||
\(422\) | −6.51507e95 | −0.977270 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.24080e95 | −1.04020 | ||||||||
\(425\) | −1.72010e96 | −1.99232 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.03902e95 | 0.589318 | ||||||||
\(428\) | 3.06857e94 | 0.0274940 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.24443e96 | 0.940530 | ||||||||
\(431\) | 2.50780e96 | 1.74130 | 0.870649 | − | 0.491904i | \(-0.163699\pi\) | ||||
0.870649 | + | 0.491904i | \(0.163699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.03865e96 | −0.609063 | −0.304531 | − | 0.952502i | \(-0.598500\pi\) | ||||
−0.304531 | + | 0.952502i | \(0.598500\pi\) | |||||||
\(434\) | 1.08626e96 | 0.585543 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.59983e95 | 0.391952 | ||||||||
\(437\) | 9.96675e95 | 0.417812 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.08395e96 | 1.44919 | 0.724596 | − | 0.689174i | \(-0.242027\pi\) | ||||
0.724596 | + | 0.689174i | \(0.242027\pi\) | |||||||
\(440\) | −2.32350e96 | −0.758787 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.71936e96 | −1.02933 | ||||||||
\(443\) | −2.68993e96 | −0.685496 | −0.342748 | − | 0.939427i | \(-0.611358\pi\) | ||||
−0.342748 | + | 0.939427i | \(0.611358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.17281e95 | −0.0902170 | ||||||||
\(446\) | −7.89325e95 | −0.157229 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.11296e96 | 1.37256 | ||||||||
\(449\) | 8.90575e96 | 1.38893 | 0.694463 | − | 0.719528i | \(-0.255642\pi\) | ||||
0.694463 | + | 0.719528i | \(0.255642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.34931e95 | −0.0178923 | ||||||||
\(452\) | −5.42831e96 | −0.663913 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.06052e95 | −0.0735019 | ||||||||
\(455\) | 3.04752e97 | 2.92773 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.95894e97 | 1.60354 | 0.801769 | − | 0.597634i | \(-0.203892\pi\) | ||||
0.801769 | + | 0.597634i | \(0.203892\pi\) | |||||||
\(458\) | 4.48863e96 | 0.339253 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.34746e97 | −0.868673 | ||||||||
\(461\) | 1.16420e97 | 0.693335 | 0.346667 | − | 0.937988i | \(-0.387313\pi\) | ||||
0.346667 | + | 0.937988i | \(0.387313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.97083e97 | −1.51068 | −0.755338 | − | 0.655336i | \(-0.772527\pi\) | ||||
−0.755338 | + | 0.655336i | \(0.772527\pi\) | |||||||
\(464\) | −2.55014e96 | −0.119856 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.26702e96 | −0.211582 | ||||||||
\(467\) | −3.83937e97 | −1.42624 | −0.713122 | − | 0.701040i | \(-0.752719\pi\) | ||||
−0.713122 | + | 0.701040i | \(0.752719\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.04061e97 | 2.23770 | ||||||||
\(470\) | 3.26686e97 | 0.960635 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.31894e97 | 0.583991 | ||||||||
\(473\) | 1.42359e97 | 0.331859 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.15580e97 | 0.630656 | ||||||||
\(476\) | 4.18576e97 | 0.774676 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.85751e97 | −0.612616 | ||||||||
\(479\) | −7.62727e93 | −0.000112234 0 | −5.61168e−5 | − | 1.00000i | \(-0.500018\pi\) | ||||
−5.61168e−5 | 1.00000i | \(0.500018\pi\) | ||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.46435e98 | −1.85076 | ||||||||
\(482\) | 3.16728e97 | 0.371081 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.72741e97 | 0.375450 | ||||||||
\(485\) | 2.42464e97 | 0.226503 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.46183e97 | −0.599844 | −0.299922 | − | 0.953964i | \(-0.596961\pi\) | ||||
−0.299922 | + | 0.953964i | \(0.596961\pi\) | |||||||
\(488\) | −5.80427e97 | −0.432936 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.14055e98 | 1.37521 | ||||||||
\(491\) | −8.28295e97 | −0.493982 | −0.246991 | − | 0.969018i | \(-0.579442\pi\) | ||||
−0.246991 | + | 0.969018i | \(0.579442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.17850e97 | −0.420495 | ||||||||
\(494\) | 6.82375e97 | 0.325829 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.35338e97 | −0.179368 | ||||||||
\(497\) | −8.44516e97 | −0.323296 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.76754e98 | 0.584387 | 0.292193 | − | 0.956359i | \(-0.405615\pi\) | ||||
0.292193 | + | 0.956359i | \(0.405615\pi\) | |||||||
\(500\) | −1.79598e98 | −0.551946 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.27361e97 | 0.0869644 | ||||||||
\(503\) | 6.60146e98 | 1.63083 | 0.815414 | − | 0.578878i | \(-0.196509\pi\) | ||||
0.815414 | + | 0.578878i | \(0.196509\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.84506e98 | 1.03553 | ||||||||
\(506\) | 1.81117e98 | 0.360135 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.09198e98 | 0.532366 | ||||||||
\(509\) | −4.28277e98 | −0.686319 | −0.343159 | − | 0.939277i | \(-0.611497\pi\) | ||||
−0.343159 | + | 0.939277i | \(0.611497\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.57726e99 | −2.19048 | ||||||||
\(512\) | −4.84211e98 | −0.626153 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.90565e98 | 0.438066 | ||||||||
\(515\) | −1.49639e99 | −1.56344 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.73718e98 | 0.338952 | ||||||||
\(518\) | −1.93633e99 | −1.63661 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.92905e99 | −2.15083 | ||||||||
\(521\) | −9.97828e98 | −0.683091 | −0.341546 | − | 0.939865i | \(-0.610950\pi\) | ||||
−0.341546 | + | 0.939865i | \(0.610950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.97094e98 | −0.355411 | −0.177706 | − | 0.984084i | \(-0.556867\pi\) | ||||
−0.177706 | + | 0.984084i | \(0.556867\pi\) | |||||||
\(524\) | 1.06439e99 | 0.590891 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.74823e98 | 0.181070 | ||||||||
\(527\) | −1.39616e99 | −0.629287 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.87231e98 | 0.309008 | ||||||||
\(530\) | 3.21172e99 | 1.17671 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.67942e98 | −0.245219 | ||||||||
\(533\) | −1.70096e98 | −0.0507168 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.79704e98 | −0.0987488 | ||||||||
\(536\) | −6.76692e99 | −1.64390 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.48457e98 | 0.0950973 | ||||||||
\(539\) | 2.44872e99 | 0.485231 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.65195e99 | 1.15146 | 0.575730 | − | 0.817640i | \(-0.304718\pi\) | ||||
0.575730 | + | 0.817640i | \(0.304718\pi\) | |||||||
\(542\) | 6.19655e99 | 1.00271 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.77898e99 | −0.958968 | ||||||||
\(545\) | −1.06414e100 | −1.40775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.55974e100 | −1.80515 | −0.902576 | − | 0.430531i | \(-0.858326\pi\) | ||||
−0.902576 | + | 0.430531i | \(0.858326\pi\) | |||||||
\(548\) | −2.75081e99 | −0.297832 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.73476e99 | 0.543597 | ||||||||
\(551\) | 1.50047e99 | 0.133105 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.73147e99 | −0.290009 | ||||||||
\(554\) | 7.50161e99 | 0.545818 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.77636e99 | 0.496074 | ||||||||
\(557\) | 2.03966e100 | 1.21855 | 0.609275 | − | 0.792959i | \(-0.291460\pi\) | ||||
0.609275 | + | 0.792959i | \(0.291460\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.79461e100 | 0.940672 | ||||||||
\(560\) | −1.61501e100 | −0.793070 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.26301e99 | 0.399371 | ||||||||
\(563\) | 3.81014e100 | 1.53952 | 0.769758 | − | 0.638336i | \(-0.220377\pi\) | ||||
0.769758 | + | 0.638336i | \(0.220377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.71697e100 | 2.38454 | ||||||||
\(566\) | 4.28319e100 | 1.42550 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.11687e99 | 0.237506 | ||||||||
\(569\) | −2.20282e100 | −0.604480 | −0.302240 | − | 0.953232i | \(-0.597734\pi\) | ||||
−0.302240 | + | 0.953232i | \(0.597734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.36336e99 | 0.177770 | 0.0888850 | − | 0.996042i | \(-0.471670\pi\) | ||||
0.0888850 | + | 0.996042i | \(0.471670\pi\) | |||||||
\(572\) | −1.05536e100 | −0.239026 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.24921e99 | −0.0448482 | ||||||||
\(575\) | 1.05592e101 | 1.97585 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.01125e101 | −1.66702 | −0.833512 | − | 0.552501i | \(-0.813674\pi\) | ||||
−0.833512 | + | 0.552501i | \(0.813674\pi\) | |||||||
\(578\) | 1.57172e100 | 0.243226 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.02858e100 | −0.276739 | ||||||||
\(581\) | −1.74066e101 | −2.22990 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.67411e100 | 0.415192 | ||||||||
\(584\) | 1.51594e101 | 1.60921 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.78784e100 | 0.261219 | ||||||||
\(587\) | 5.72321e100 | 0.503906 | 0.251953 | − | 0.967740i | \(-0.418927\pi\) | ||||
0.251953 | + | 0.967740i | \(0.418927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.56148e100 | 0.199197 | ||||||||
\(590\) | −9.03770e100 | −0.660632 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.76021e100 | 0.501339 | ||||||||
\(593\) | 3.32917e100 | 0.202227 | 0.101114 | − | 0.994875i | \(-0.467759\pi\) | ||||
0.101114 | + | 0.994875i | \(0.467759\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.17945e101 | −2.78236 | ||||||||
\(596\) | −1.10893e101 | −0.560292 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.28320e101 | 1.02082 | ||||||||
\(599\) | 2.64261e100 | 0.111162 | 0.0555808 | − | 0.998454i | \(-0.482299\pi\) | ||||
0.0555808 | + | 0.998454i | \(0.482299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.61412e100 | 0.320843 | 0.160422 | − | 0.987049i | \(-0.448715\pi\) | ||||
0.160422 | + | 0.987049i | \(0.448715\pi\) | |||||||
\(602\) | 2.37303e101 | 0.831824 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.99058e101 | 0.618204 | ||||||||
\(605\) | −4.61229e101 | −1.34848 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.93297e101 | −0.501001 | −0.250501 | − | 0.968116i | \(-0.580595\pi\) | ||||
−0.250501 | + | 0.968116i | \(0.580595\pi\) | |||||||
\(608\) | 1.24371e101 | 0.303556 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.26212e101 | 0.489753 | ||||||||
\(611\) | 4.71116e101 | 0.960780 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.68691e101 | 0.848358 | 0.424179 | − | 0.905578i | \(-0.360563\pi\) | ||||
0.424179 | + | 0.905578i | \(0.360563\pi\) | |||||||
\(614\) | −3.59443e101 | −0.613033 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.43073e101 | −0.671087 | ||||||||
\(617\) | −1.24724e102 | −1.78049 | −0.890246 | − | 0.455479i | \(-0.849468\pi\) | ||||
−0.890246 | + | 0.455479i | \(0.849468\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.63173e101 | −0.714386 | −0.357193 | − | 0.934031i | \(-0.616266\pi\) | ||||
−0.357193 | + | 0.934031i | \(0.616266\pi\) | |||||||
\(620\) | −3.46302e101 | −0.414150 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.97833e101 | −0.423011 | ||||||||
\(623\) | −7.95721e100 | −0.0797898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.86353e101 | 0.255436 | ||||||||
\(626\) | −1.38412e102 | −1.16469 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.71481e101 | −0.727625 | ||||||||
\(629\) | 2.48876e102 | 1.75887 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.04720e102 | −0.659111 | −0.329555 | − | 0.944136i | \(-0.606899\pi\) | ||||
−0.329555 | + | 0.944136i | \(0.606899\pi\) | |||||||
\(632\) | 3.58641e101 | 0.213053 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.04168e102 | 0.551412 | ||||||||
\(635\) | −3.82600e102 | −1.91207 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.08691e102 | 1.37542 | ||||||||
\(638\) | 2.72668e101 | 0.114731 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.18112e101 | −0.232006 | ||||||||
\(641\) | −1.40637e102 | −0.498635 | −0.249317 | − | 0.968422i | \(-0.580206\pi\) | ||||
−0.249317 | + | 0.968422i | \(0.580206\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.43530e102 | −0.454195 | −0.227098 | − | 0.973872i | \(-0.572924\pi\) | ||||
−0.227098 | + | 0.973872i | \(0.572924\pi\) | |||||||
\(644\) | −2.56951e102 | −0.768273 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.15974e102 | −0.309651 | ||||||||
\(647\) | 4.09180e102 | 1.03254 | 0.516271 | − | 0.856425i | \(-0.327320\pi\) | ||||
0.516271 | + | 0.856425i | \(0.327320\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.03388e102 | −0.233099 | ||||||||
\(650\) | 7.22936e102 | 1.54086 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.16150e101 | −0.117395 | ||||||||
\(653\) | −6.20506e102 | −1.11793 | −0.558965 | − | 0.829191i | \(-0.688802\pi\) | ||||
−0.558965 | + | 0.829191i | \(0.688802\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.31707e103 | −2.12227 | ||||||||
\(656\) | 9.01411e100 | 0.0137383 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.22963e102 | 0.849605 | ||||||||
\(659\) | −4.77744e102 | −0.616422 | −0.308211 | − | 0.951318i | \(-0.599730\pi\) | ||||
−0.308211 | + | 0.951318i | \(0.599730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.60511e102 | −0.763004 | −0.381502 | − | 0.924368i | \(-0.624593\pi\) | ||||
−0.381502 | + | 0.924368i | \(0.624593\pi\) | |||||||
\(662\) | −3.61379e102 | −0.395045 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.67300e103 | 1.63818 | ||||||||
\(665\) | 9.50250e102 | 0.880740 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.02053e102 | 0.417020 | ||||||||
\(668\) | 2.43495e102 | 0.191491 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.63730e103 | 1.85964 | ||||||||
\(671\) | 2.58780e102 | 0.172806 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.40758e103 | −0.843186 | −0.421593 | − | 0.906785i | \(-0.638529\pi\) | ||||
−0.421593 | + | 0.906785i | \(0.638529\pi\) | |||||||
\(674\) | 9.99226e102 | 0.566993 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.27590e102 | −0.217758 | ||||||||
\(677\) | 1.99664e103 | 0.963417 | 0.481708 | − | 0.876332i | \(-0.340016\pi\) | ||||
0.481708 | + | 0.876332i | \(0.340016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.62360e102 | 0.200324 | ||||||||
\(680\) | 4.97810e103 | 2.04404 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.65475e102 | 0.171699 | ||||||||
\(683\) | −9.40230e102 | −0.328760 | −0.164380 | − | 0.986397i | \(-0.552562\pi\) | ||||
−0.164380 | + | 0.986397i | \(0.552562\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.40385e103 | 1.06971 | ||||||||
\(686\) | 4.79257e102 | 0.142803 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.51036e102 | −0.254811 | ||||||||
\(689\) | 4.63166e103 | 1.17689 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.43467e103 | 0.556534 | 0.278267 | − | 0.960504i | \(-0.410240\pi\) | ||||
0.278267 | + | 0.960504i | \(0.410240\pi\) | |||||||
\(692\) | −1.70875e103 | −0.370516 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.47852e102 | 0.126431 | ||||||||
\(695\) | −9.62245e103 | −1.78172 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.89089e102 | 0.0481987 | ||||||||
\(698\) | 3.22017e103 | 0.509514 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.13590e103 | −1.15965 | ||||||||
\(701\) | −5.37926e103 | −0.727805 | −0.363902 | − | 0.931437i | \(-0.618556\pi\) | ||||
−0.363902 | + | 0.931437i | \(0.618556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.56602e103 | −0.556760 | ||||||||
\(704\) | 3.47650e103 | 0.402476 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.38879e103 | 0.980027 | ||||||||
\(707\) | 9.23913e103 | 0.915846 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.07535e104 | −0.961530 | −0.480765 | − | 0.876849i | \(-0.659641\pi\) | ||||
−0.480765 | + | 0.876849i | \(0.659641\pi\) | |||||||
\(710\) | −3.16343e103 | −0.268675 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.64789e102 | 0.0586168 | ||||||||
\(713\) | 8.57061e103 | 0.624085 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.30590e104 | 0.858498 | ||||||||
\(716\) | −1.40006e104 | −0.874622 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.96545e103 | 0.505860 | ||||||||
\(719\) | −3.21953e104 | −1.72659 | −0.863293 | − | 0.504703i | \(-0.831602\pi\) | ||||
−0.863293 | + | 0.504703i | \(0.831602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.85349e104 | −1.38274 | ||||||||
\(722\) | −1.38272e104 | −0.636982 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.58347e104 | −0.659405 | ||||||||
\(725\) | 1.58966e104 | 0.629460 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.43449e104 | 0.513678 | 0.256839 | − | 0.966454i | \(-0.417319\pi\) | ||||
0.256839 | + | 0.966454i | \(0.417319\pi\) | |||||||
\(728\) | −5.58547e104 | −1.90224 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.90815e104 | −1.82040 | ||||||||
\(731\) | −3.05004e104 | −0.893968 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.44849e104 | −0.914817 | −0.457408 | − | 0.889257i | \(-0.651222\pi\) | ||||
−0.457408 | + | 0.889257i | \(0.651222\pi\) | |||||||
\(734\) | 4.08231e104 | 1.03039 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.16140e104 | 0.951042 | ||||||||
\(737\) | 3.01699e104 | 0.656161 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.34155e104 | −1.24932 | −0.624660 | − | 0.780897i | \(-0.714762\pi\) | ||||
−0.624660 | + | 0.780897i | \(0.714762\pi\) | |||||||
\(740\) | 6.17307e104 | 1.15756 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.12450e104 | 1.04071 | ||||||||
\(743\) | −4.62751e104 | −0.748611 | −0.374305 | − | 0.927305i | \(-0.622119\pi\) | ||||
−0.374305 | + | 0.927305i | \(0.622119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.37218e105 | 2.01237 | ||||||||
\(746\) | −2.67273e104 | −0.373240 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.79365e104 | 0.227158 | ||||||||
\(749\) | −7.24065e103 | −0.0873355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.35926e104 | 0.477040 | 0.238520 | − | 0.971138i | \(-0.423338\pi\) | ||||
0.238520 | + | 0.971138i | \(0.423338\pi\) | |||||||
\(752\) | −2.49664e104 | −0.260258 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.43731e104 | 0.325211 | ||||||||
\(755\) | −2.46314e105 | −2.22037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.98775e104 | −0.653770 | −0.326885 | − | 0.945064i | \(-0.605999\pi\) | ||||
−0.326885 | + | 0.945064i | \(0.605999\pi\) | |||||||
\(758\) | 1.44856e105 | 1.12982 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.13311e104 | −0.647027 | ||||||||
\(761\) | 2.56065e105 | 1.72906 | 0.864529 | − | 0.502583i | \(-0.167617\pi\) | ||||
0.864529 | + | 0.502583i | \(0.167617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.02923e105 | −1.24505 | ||||||||
\(764\) | −5.99485e104 | −0.350647 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.25316e104 | 0.332468 | ||||||||
\(767\) | −1.30333e105 | −0.660732 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.72521e104 | −0.310023 | −0.155012 | − | 0.987913i | \(-0.549542\pi\) | ||||
−0.155012 | + | 0.987913i | \(0.549542\pi\) | |||||||
\(770\) | 1.72681e105 | 0.759158 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.06932e105 | 0.427638 | ||||||||
\(773\) | 2.46049e105 | 0.938578 | 0.469289 | − | 0.883045i | \(-0.344510\pi\) | ||||
0.469289 | + | 0.883045i | \(0.344510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.71374e105 | 0.942010 | ||||||||
\(776\) | −4.44387e104 | −0.147166 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.78182e104 | 0.234599 | ||||||||
\(779\) | −5.30379e103 | −0.0152570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.61885e104 | −0.0948000 | ||||||||
\(782\) | −3.88044e105 | −0.970140 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.63588e105 | −0.372576 | ||||||||
\(785\) | 1.20211e106 | 2.61337 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.71217e105 | 0.537328 | 0.268664 | − | 0.963234i | \(-0.413418\pi\) | ||||
0.268664 | + | 0.963234i | \(0.413418\pi\) | |||||||
\(788\) | −2.15295e105 | −0.407218 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.39775e105 | −0.241013 | ||||||||
\(791\) | 1.28087e106 | 2.10894 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.26223e105 | 0.489828 | ||||||||
\(794\) | −7.26044e105 | −1.04115 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.76370e104 | 0.0230727 | ||||||||
\(797\) | −1.45163e106 | −1.81395 | −0.906977 | − | 0.421179i | \(-0.861616\pi\) | ||||
−0.906977 | + | 0.421179i | \(0.861616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00691e105 | −0.913077 | ||||||||
\(800\) | 1.31764e106 | 1.43553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.75705e105 | −0.870950 | ||||||||
\(803\) | −6.75873e105 | −0.642315 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.17950e106 | 2.75937 | ||||||||
\(806\) | 5.86788e105 | 0.486690 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.87998e105 | −0.672818 | ||||||||
\(809\) | −3.21507e104 | −0.0232847 | −0.0116423 | − | 0.999932i | \(-0.503706\pi\) | ||||
−0.0116423 | + | 0.999932i | \(0.503706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.87148e105 | 0.587131 | 0.293566 | − | 0.955939i | \(-0.405158\pi\) | ||||
0.293566 | + | 0.955939i | \(0.405158\pi\) | |||||||
\(812\) | −3.86834e105 | −0.244754 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.29742e105 | −0.479902 | ||||||||
\(815\) | 7.62423e105 | 0.421641 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.59578e105 | 0.282980 | ||||||||
\(818\) | 1.70055e105 | 0.0822419 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.17051e104 | 0.0317208 | ||||||||
\(821\) | −1.04180e105 | −0.0440817 | −0.0220409 | − | 0.999757i | \(-0.507016\pi\) | ||||
−0.0220409 | + | 0.999757i | \(0.507016\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.21303e106 | −0.469653 | −0.234827 | − | 0.972037i | \(-0.575452\pi\) | ||||
−0.234827 | + | 0.972037i | \(0.575452\pi\) | |||||||
\(824\) | 2.74257e106 | 1.01581 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.72342e106 | −0.584277 | ||||||||
\(827\) | −2.35778e106 | −0.764808 | −0.382404 | − | 0.923995i | \(-0.624904\pi\) | ||||
−0.382404 | + | 0.923995i | \(0.624904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.61461e106 | 0.479543 | 0.239771 | − | 0.970829i | \(-0.422928\pi\) | ||||
0.239771 | + | 0.970829i | \(0.422928\pi\) | |||||||
\(830\) | −6.52025e106 | −1.85316 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.38255e106 | 1.14084 | ||||||||
\(833\) | −5.24639e106 | −1.30713 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.01300e106 | −0.687769 | ||||||||
\(836\) | −3.29073e105 | −0.0719056 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.60242e106 | −0.921679 | ||||||||
\(839\) | 5.26994e106 | 1.01040 | 0.505201 | − | 0.863002i | \(-0.331418\pi\) | ||||
0.505201 | + | 0.863002i | \(0.331418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.93340e106 | −0.867147 | ||||||||
\(842\) | −4.86109e106 | −0.818168 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.96070e106 | 0.611326 | ||||||||
\(845\) | 5.29099e106 | 0.782109 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.79527e106 | −1.19263 | ||||||||
\(848\) | −2.45451e106 | −0.318798 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.22867e107 | −1.46435 | ||||||||
\(851\) | −1.52777e107 | −1.74433 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.38806e105 | 0.0355068 | 0.0177534 | − | 0.999842i | \(-0.494349\pi\) | ||||
0.0177534 | + | 0.999842i | \(0.494349\pi\) | |||||||
\(854\) | 4.31369e106 | 0.433148 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.95918e105 | 0.0641602 | ||||||||
\(857\) | −1.33280e107 | −1.17751 | −0.588754 | − | 0.808313i | \(-0.700381\pi\) | ||||
−0.588754 | + | 0.808313i | \(0.700381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.17251e107 | −0.951405 | −0.475702 | − | 0.879606i | \(-0.657806\pi\) | ||||
−0.475702 | + | 0.879606i | \(0.657806\pi\) | |||||||
\(860\) | −7.56527e106 | −0.588344 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.79133e107 | 1.27985 | ||||||||
\(863\) | 2.09858e107 | 1.43725 | 0.718623 | − | 0.695400i | \(-0.244773\pi\) | ||||
0.718623 | + | 0.695400i | \(0.244773\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.11441e107 | 1.33076 | ||||||||
\(866\) | −7.41912e106 | −0.447661 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.60369e106 | −0.366283 | ||||||||
\(869\) | −1.59898e106 | −0.0850395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.80328e107 | 1.85993 | ||||||||
\(872\) | 1.95035e107 | 0.914661 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.11927e106 | 0.307092 | ||||||||
\(875\) | 4.23783e107 | 1.75327 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.41996e107 | 0.540493 | 0.270246 | − | 0.962791i | \(-0.412895\pi\) | ||||
0.270246 | + | 0.962791i | \(0.412895\pi\) | |||||||
\(878\) | 2.91718e107 | 1.06516 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.92050e106 | −0.232552 | ||||||||
\(881\) | −7.66883e106 | −0.247234 | −0.123617 | − | 0.992330i | \(-0.539449\pi\) | ||||
−0.123617 | + | 0.992330i | \(0.539449\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.35873e107 | −0.996802 | −0.498401 | − | 0.866947i | \(-0.666079\pi\) | ||||
−0.498401 | + | 0.866947i | \(0.666079\pi\) | |||||||
\(884\) | 2.26111e107 | 0.643893 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.92142e107 | −0.503839 | ||||||||
\(887\) | −6.18714e107 | −1.55696 | −0.778481 | − | 0.627669i | \(-0.784009\pi\) | ||||
−0.778481 | + | 0.627669i | \(0.784009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.29588e107 | −1.69108 | ||||||||
\(890\) | −2.98065e106 | −0.0663094 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.79854e106 | 0.0983540 | ||||||||
\(893\) | 1.46899e107 | 0.289029 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.73243e108 | 3.14133 | ||||||||
\(896\) | −1.17869e107 | −0.205191 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.36140e107 | 1.02086 | ||||||||
\(899\) | 1.29029e107 | 0.198819 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.87178e107 | −1.11845 | ||||||||
\(902\) | −9.63812e105 | −0.0131508 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.23108e108 | −1.54931 | ||||||||
\(905\) | 1.95938e108 | 2.36835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.84800e107 | 0.875171 | 0.437586 | − | 0.899177i | \(-0.355834\pi\) | ||||
0.437586 | + | 0.899177i | \(0.355834\pi\) | |||||||
\(908\) | 4.29230e106 | 0.0459787 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.17685e108 | 2.15188 | ||||||||
\(911\) | 1.50467e108 | 1.42896 | 0.714482 | − | 0.699653i | \(-0.246662\pi\) | ||||
0.714482 | + | 0.699653i | \(0.246662\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.45895e107 | −0.653874 | ||||||||
\(914\) | 1.39927e108 | 1.17860 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.72877e107 | −0.212218 | ||||||||
\(917\) | −2.51155e108 | −1.87698 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.19946e108 | −0.827887 | −0.413944 | − | 0.910303i | \(-0.635849\pi\) | ||||
−0.413944 | + | 0.910303i | \(0.635849\pi\) | |||||||
\(920\) | −3.05590e108 | −2.02714 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.31589e107 | 0.509601 | ||||||||
\(923\) | −4.56200e107 | −0.268716 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.83742e108 | −2.63294 | ||||||||
\(926\) | −2.12207e108 | −1.11035 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.26491e107 | 0.302980 | ||||||||
\(929\) | −3.42076e107 | −0.159056 | −0.0795278 | − | 0.996833i | \(-0.525341\pi\) | ||||
−0.0795278 | + | 0.996833i | \(0.525341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.62531e107 | 0.413763 | ||||||||
\(932\) | 3.20198e107 | 0.132354 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.74247e108 | −1.04829 | ||||||||
\(935\) | −2.21946e108 | −0.815873 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.24351e108 | 1.78290 | 0.891450 | − | 0.453119i | \(-0.149689\pi\) | ||||
0.891450 | + | 0.453119i | \(0.149689\pi\) | |||||||
\(938\) | 5.02913e108 | 1.64471 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.98602e108 | −0.600920 | ||||||||
\(941\) | 5.99656e107 | 0.174534 | 0.0872672 | − | 0.996185i | \(-0.472187\pi\) | ||||
0.0872672 | + | 0.996185i | \(0.472187\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.77463e107 | −0.0478003 | ||||||||
\(944\) | 6.90691e107 | 0.178981 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.01687e108 | 0.243916 | ||||||||
\(947\) | −6.02710e108 | −1.39102 | −0.695511 | − | 0.718515i | \(-0.744822\pi\) | ||||
−0.695511 | + | 0.718515i | \(0.744822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.52020e108 | −1.82068 | ||||||||
\(950\) | 2.25419e108 | 0.463532 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.49284e108 | 1.80779 | ||||||||
\(953\) | −7.10042e108 | −1.30135 | −0.650674 | − | 0.759357i | \(-0.725513\pi\) | ||||
−0.650674 | + | 0.759357i | \(0.725513\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.41801e108 | 1.25940 | ||||||||
\(956\) | 2.34509e108 | 0.383219 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.44818e104 | −8.24916e−5 0 | ||||||||
\(959\) | 6.49087e108 | 0.946071 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.20026e108 | −0.702460 | ||||||||
\(962\) | −1.04599e109 | −1.36031 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.92548e108 | −0.232128 | ||||||||
\(965\) | −1.32317e109 | −1.53592 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.03350e108 | −0.326495 | −0.163248 | − | 0.986585i | \(-0.552197\pi\) | ||||
−0.163248 | + | 0.986585i | \(0.552197\pi\) | |||||||
\(968\) | 8.45337e108 | 0.876152 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.73193e108 | 0.166480 | ||||||||
\(971\) | 2.07397e109 | 1.91999 | 0.959997 | − | 0.280012i | \(-0.0903384\pi\) | ||||
0.959997 | + | 0.280012i | \(0.0903384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.83492e109 | −1.57579 | ||||||||
\(974\) | −5.33000e108 | −0.440885 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.72879e108 | −0.132686 | ||||||||
\(977\) | −1.80962e109 | −1.33794 | −0.668969 | − | 0.743290i | \(-0.733264\pi\) | ||||
−0.668969 | + | 0.743290i | \(0.733264\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.40976e107 | −0.0233968 | ||||||||
\(980\) | −1.30130e109 | −0.860254 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.91653e108 | −0.363076 | ||||||||
\(983\) | 1.37476e109 | 0.812875 | 0.406438 | − | 0.913679i | \(-0.366771\pi\) | ||||
0.406438 | + | 0.913679i | \(0.366771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.66405e109 | 1.46258 | ||||||||
\(986\) | −5.84192e108 | −0.309064 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.14836e108 | −0.203820 | ||||||||
\(989\) | 1.87233e109 | 0.886578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.85911e109 | 1.25760 | 0.628800 | − | 0.777567i | \(-0.283546\pi\) | ||||
0.628800 | + | 0.777567i | \(0.283546\pi\) | |||||||
\(992\) | 1.06949e109 | 0.453420 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.03240e108 | −0.237622 | ||||||||
\(995\) | −2.18240e108 | −0.0828691 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.40964e108 | −0.296759 | −0.148380 | − | 0.988930i | \(-0.547406\pi\) | ||||
−0.148380 | + | 0.988930i | \(0.547406\pi\) | |||||||
\(998\) | 1.26256e109 | 0.429524 | ||||||||
\(999\) | 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 | 9.74.a.a.1.4 | 5 | ||
3.2 | odd | 2 | 1.74.a.a.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.74.a.a.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
9.74.a.a.1.4 | 5 | 1.1 | even | 1 | trivial |