Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,74,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 74, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 74);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 74 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(33.7483973737\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots + 17\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.10442e9\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 | \(-0.619786\pi\) | ||||
−0.367500 | + | 0.930024i | \(0.619786\pi\) | |||||||
\(3\) | −1.08968e17 | −0.419155 | −0.209577 | − | 0.977792i | \(-0.567209\pi\) | ||||
−0.209577 | + | 0.977792i | \(0.567209\pi\) | |||||||
\(4\) | −4.34246e21 | −0.459775 | ||||||||
\(5\) | −5.37334e25 | −1.65135 | −0.825676 | − | 0.564145i | \(-0.809206\pi\) | ||||
−0.825676 | + | 0.564145i | \(0.809206\pi\) | |||||||
\(6\) | 7.78363e27 | 0.308079 | ||||||||
\(7\) | 1.02465e31 | 1.46049 | 0.730245 | − | 0.683185i | \(-0.239406\pi\) | ||||
0.730245 | + | 0.683185i | \(0.239406\pi\) | |||||||
\(8\) | 9.84822e32 | 1.07293 | ||||||||
\(9\) | −5.57111e34 | −0.824309 | ||||||||
\(10\) | 3.83819e36 | 1.21374 | ||||||||
\(11\) | −4.39076e37 | −0.428260 | −0.214130 | − | 0.976805i | \(-0.568692\pi\) | ||||
−0.214130 | + | 0.976805i | \(0.568692\pi\) | |||||||
\(12\) | 4.73190e38 | 0.192717 | ||||||||
\(13\) | 5.53509e40 | 1.21393 | 0.606963 | − | 0.794730i | \(-0.292388\pi\) | ||||
0.606963 | + | 0.794730i | \(0.292388\pi\) | |||||||
\(14\) | −7.31912e41 | −1.07346 | ||||||||
\(15\) | 5.85525e42 | 0.692172 | ||||||||
\(16\) | −2.93327e43 | −0.328831 | ||||||||
\(17\) | 9.40723e44 | 1.15365 | 0.576827 | − | 0.816866i | \(-0.304290\pi\) | ||||
0.576827 | + | 0.816866i | \(0.304290\pi\) | |||||||
\(18\) | 3.97946e45 | 0.605867 | ||||||||
\(19\) | 1.72590e46 | 0.365182 | 0.182591 | − | 0.983189i | \(-0.441552\pi\) | ||||
0.182591 | + | 0.983189i | \(0.441552\pi\) | |||||||
\(20\) | 2.33335e47 | 0.759251 | ||||||||
\(21\) | −1.11655e48 | −0.612172 | ||||||||
\(22\) | 3.13633e48 | 0.314771 | ||||||||
\(23\) | −5.77480e49 | −1.14412 | −0.572059 | − | 0.820212i | \(-0.693855\pi\) | ||||
−0.572059 | + | 0.820212i | \(0.693855\pi\) | |||||||
\(24\) | −1.07314e50 | −0.449726 | ||||||||
\(25\) | 1.82849e51 | 1.72696 | ||||||||
\(26\) | −3.95373e51 | −0.892236 | ||||||||
\(27\) | 1.34354e52 | 0.764668 | ||||||||
\(28\) | −4.44951e52 | −0.671497 | ||||||||
\(29\) | −8.69385e52 | −0.364490 | −0.182245 | − | 0.983253i | \(-0.558336\pi\) | ||||
−0.182245 | + | 0.983253i | \(0.558336\pi\) | |||||||
\(30\) | −4.18242e53 | −0.508746 | ||||||||
\(31\) | 1.48414e54 | 0.545472 | 0.272736 | − | 0.962089i | \(-0.412071\pi\) | ||||
0.272736 | + | 0.962089i | \(0.412071\pi\) | |||||||
\(32\) | −7.20614e54 | −0.831244 | ||||||||
\(33\) | 4.78454e54 | 0.179507 | ||||||||
\(34\) | −6.71960e55 | −0.847936 | ||||||||
\(35\) | −5.50582e56 | −2.41178 | ||||||||
\(36\) | 2.41923e56 | 0.378997 | ||||||||
\(37\) | −2.64558e57 | −1.52461 | −0.762304 | − | 0.647219i | \(-0.775932\pi\) | ||||
−0.762304 | + | 0.647219i | \(0.775932\pi\) | |||||||
\(38\) | −1.23282e57 | −0.268409 | ||||||||
\(39\) | −6.03150e57 | −0.508823 | ||||||||
\(40\) | −5.29179e58 | −1.77179 | ||||||||
\(41\) | 3.07305e57 | 0.0417791 | 0.0208896 | − | 0.999782i | \(-0.493350\pi\) | ||||
0.0208896 | + | 0.999782i | \(0.493350\pi\) | |||||||
\(42\) | 7.97553e58 | 0.449946 | ||||||||
\(43\) | 3.24223e59 | 0.774900 | 0.387450 | − | 0.921891i | \(-0.373356\pi\) | ||||
0.387450 | + | 0.921891i | \(0.373356\pi\) | |||||||
\(44\) | 1.90667e59 | 0.196903 | ||||||||
\(45\) | 2.99355e60 | 1.36122 | ||||||||
\(46\) | 4.12496e60 | 0.840927 | ||||||||
\(47\) | −8.51145e60 | −0.791465 | −0.395732 | − | 0.918366i | \(-0.629509\pi\) | ||||
−0.395732 | + | 0.918366i | \(0.629509\pi\) | |||||||
\(48\) | 3.19634e60 | 0.137831 | ||||||||
\(49\) | 5.57697e61 | 1.13303 | ||||||||
\(50\) | −1.30610e62 | −1.26932 | ||||||||
\(51\) | −1.02509e62 | −0.483560 | ||||||||
\(52\) | −2.40359e62 | −0.558133 | ||||||||
\(53\) | −8.36780e62 | −0.969488 | −0.484744 | − | 0.874656i | \(-0.661087\pi\) | ||||
−0.484744 | + | 0.874656i | \(0.661087\pi\) | |||||||
\(54\) | −9.59693e62 | −0.562031 | ||||||||
\(55\) | 2.35931e63 | 0.707207 | ||||||||
\(56\) | 1.00910e64 | 1.56701 | ||||||||
\(57\) | −1.88069e63 | −0.153068 | ||||||||
\(58\) | 6.21004e63 | 0.267900 | ||||||||
\(59\) | 2.35468e64 | 0.544293 | 0.272147 | − | 0.962256i | \(-0.412266\pi\) | ||||
0.272147 | + | 0.962256i | \(0.412266\pi\) | |||||||
\(60\) | −2.54261e64 | −0.318244 | ||||||||
\(61\) | 5.89372e64 | 0.403507 | 0.201753 | − | 0.979436i | \(-0.435336\pi\) | ||||
0.201753 | + | 0.979436i | \(0.435336\pi\) | |||||||
\(62\) | −1.06012e65 | −0.400922 | ||||||||
\(63\) | −5.70846e65 | −1.20390 | ||||||||
\(64\) | 7.91776e65 | 0.939795 | ||||||||
\(65\) | −2.97420e66 | −2.00462 | ||||||||
\(66\) | −3.41761e65 | −0.131938 | ||||||||
\(67\) | 6.87121e66 | 1.53216 | 0.766078 | − | 0.642747i | \(-0.222206\pi\) | ||||
0.766078 | + | 0.642747i | \(0.222206\pi\) | |||||||
\(68\) | −4.08505e66 | −0.530422 | ||||||||
\(69\) | 6.29271e66 | 0.479563 | ||||||||
\(70\) | 3.93282e67 | 1.77266 | ||||||||
\(71\) | 8.24197e66 | 0.221361 | 0.110681 | − | 0.993856i | \(-0.464697\pi\) | ||||
0.110681 | + | 0.993856i | \(0.464697\pi\) | |||||||
\(72\) | −5.48655e67 | −0.884430 | ||||||||
\(73\) | −1.53931e68 | −1.49983 | −0.749913 | − | 0.661537i | \(-0.769905\pi\) | ||||
−0.749913 | + | 0.661537i | \(0.769905\pi\) | |||||||
\(74\) | 1.88974e68 | 1.12059 | ||||||||
\(75\) | −1.99248e68 | −0.723865 | ||||||||
\(76\) | −7.49465e67 | −0.167902 | ||||||||
\(77\) | −4.49901e68 | −0.625469 | ||||||||
\(78\) | 4.30831e68 | 0.373985 | ||||||||
\(79\) | −3.64169e68 | −0.198570 | −0.0992850 | − | 0.995059i | \(-0.531656\pi\) | ||||
−0.0992850 | + | 0.995059i | \(0.531656\pi\) | |||||||
\(80\) | 1.57615e69 | 0.543016 | ||||||||
\(81\) | 2.30121e69 | 0.503795 | ||||||||
\(82\) | −2.19509e68 | −0.0307076 | ||||||||
\(83\) | 1.69878e70 | 1.52682 | 0.763409 | − | 0.645915i | \(-0.223524\pi\) | ||||
0.763409 | + | 0.645915i | \(0.223524\pi\) | |||||||
\(84\) | 4.84856e69 | 0.281461 | ||||||||
\(85\) | −5.05483e70 | −1.90509 | ||||||||
\(86\) | −2.31594e70 | −0.569552 | ||||||||
\(87\) | 9.47355e69 | 0.152778 | ||||||||
\(88\) | −4.32412e70 | −0.459495 | ||||||||
\(89\) | 7.76576e69 | 0.0546322 | 0.0273161 | − | 0.999627i | \(-0.491304\pi\) | ||||
0.0273161 | + | 0.999627i | \(0.491304\pi\) | |||||||
\(90\) | −2.13830e71 | −1.00050 | ||||||||
\(91\) | 5.67155e71 | 1.77293 | ||||||||
\(92\) | 2.50768e71 | 0.526038 | ||||||||
\(93\) | −1.61724e71 | −0.228637 | ||||||||
\(94\) | 6.07975e71 | 0.581726 | ||||||||
\(95\) | −9.27387e71 | −0.603044 | ||||||||
\(96\) | 7.85241e71 | 0.348420 | ||||||||
\(97\) | 4.51236e71 | 0.137162 | 0.0685812 | − | 0.997646i | \(-0.478153\pi\) | ||||
0.0685812 | + | 0.997646i | \(0.478153\pi\) | |||||||
\(98\) | −3.98365e72 | −0.832777 | ||||||||
\(99\) | 2.44614e72 | 0.353018 | ||||||||
\(100\) | −7.94014e72 | −0.794014 | ||||||||
\(101\) | −9.01684e72 | −0.627082 | −0.313541 | − | 0.949575i | \(-0.601515\pi\) | ||||
−0.313541 | + | 0.949575i | \(0.601515\pi\) | |||||||
\(102\) | 7.32224e72 | 0.355417 | ||||||||
\(103\) | −2.78483e73 | −0.946762 | −0.473381 | − | 0.880858i | \(-0.656967\pi\) | ||||
−0.473381 | + | 0.880858i | \(0.656967\pi\) | |||||||
\(104\) | 5.45108e73 | 1.30246 | ||||||||
\(105\) | 5.99960e73 | 1.01091 | ||||||||
\(106\) | 5.97714e73 | 0.712573 | ||||||||
\(107\) | 7.06643e72 | 0.0597988 | 0.0298994 | − | 0.999553i | \(-0.490481\pi\) | ||||
0.0298994 | + | 0.999553i | \(0.490481\pi\) | |||||||
\(108\) | −5.83426e73 | −0.351576 | ||||||||
\(109\) | −1.98041e74 | −0.852486 | −0.426243 | − | 0.904609i | \(-0.640163\pi\) | ||||
−0.426243 | + | 0.904609i | \(0.640163\pi\) | |||||||
\(110\) | −1.68526e74 | −0.519797 | ||||||||
\(111\) | 2.88285e74 | 0.639047 | ||||||||
\(112\) | −3.00559e74 | −0.480255 | ||||||||
\(113\) | −1.25005e75 | −1.44400 | −0.721998 | − | 0.691896i | \(-0.756776\pi\) | ||||
−0.721998 | + | 0.691896i | \(0.756776\pi\) | |||||||
\(114\) | 1.34338e74 | 0.112505 | ||||||||
\(115\) | 3.10300e75 | 1.88934 | ||||||||
\(116\) | 3.77527e74 | 0.167583 | ||||||||
\(117\) | −3.08366e75 | −1.00065 | ||||||||
\(118\) | −1.68195e75 | −0.400055 | ||||||||
\(119\) | 9.63915e75 | 1.68490 | ||||||||
\(120\) | 5.76637e75 | 0.742655 | ||||||||
\(121\) | −8.58365e75 | −0.816594 | ||||||||
\(122\) | −4.20990e75 | −0.296577 | ||||||||
\(123\) | −3.34866e74 | −0.0175119 | ||||||||
\(124\) | −6.44481e75 | −0.250795 | ||||||||
\(125\) | −4.13587e76 | −1.20047 | ||||||||
\(126\) | 4.07756e76 | 0.884863 | ||||||||
\(127\) | −7.12034e76 | −1.15788 | −0.578942 | − | 0.815369i | \(-0.696534\pi\) | ||||
−0.578942 | + | 0.815369i | \(0.696534\pi\) | |||||||
\(128\) | 1.15033e76 | 0.140494 | ||||||||
\(129\) | −3.53301e76 | −0.324803 | ||||||||
\(130\) | 2.12447e77 | 1.47339 | ||||||||
\(131\) | 2.45112e77 | 1.28517 | 0.642587 | − | 0.766213i | \(-0.277861\pi\) | ||||
0.642587 | + | 0.766213i | \(0.277861\pi\) | |||||||
\(132\) | −2.07767e76 | −0.0825330 | ||||||||
\(133\) | 1.76845e77 | 0.533345 | ||||||||
\(134\) | −4.90812e77 | −1.12613 | ||||||||
\(135\) | −7.21930e77 | −1.26274 | ||||||||
\(136\) | 9.26444e77 | 1.23780 | ||||||||
\(137\) | −6.33470e77 | −0.647776 | −0.323888 | − | 0.946095i | \(-0.604990\pi\) | ||||
−0.323888 | + | 0.946095i | \(0.604990\pi\) | |||||||
\(138\) | −4.49490e77 | −0.352479 | ||||||||
\(139\) | −1.79078e78 | −1.07895 | −0.539475 | − | 0.842002i | \(-0.681377\pi\) | ||||
−0.539475 | + | 0.842002i | \(0.681377\pi\) | |||||||
\(140\) | 2.39088e78 | 1.10888 | ||||||||
\(141\) | 9.27478e77 | 0.331746 | ||||||||
\(142\) | −5.88726e77 | −0.162700 | ||||||||
\(143\) | −2.43033e78 | −0.519876 | ||||||||
\(144\) | 1.63416e78 | 0.271059 | ||||||||
\(145\) | 4.67151e78 | 0.601901 | ||||||||
\(146\) | 1.09953e79 | 1.10237 | ||||||||
\(147\) | −6.07714e78 | −0.474915 | ||||||||
\(148\) | 1.14883e79 | 0.700977 | ||||||||
\(149\) | −2.55369e79 | −1.21862 | −0.609310 | − | 0.792932i | \(-0.708554\pi\) | ||||
−0.609310 | + | 0.792932i | \(0.708554\pi\) | |||||||
\(150\) | 1.42323e79 | 0.532040 | ||||||||
\(151\) | −4.58400e79 | −1.34458 | −0.672289 | − | 0.740289i | \(-0.734689\pi\) | ||||
−0.672289 | + | 0.740289i | \(0.734689\pi\) | |||||||
\(152\) | 1.69971e79 | 0.391817 | ||||||||
\(153\) | −5.24087e79 | −0.950968 | ||||||||
\(154\) | 3.21365e79 | 0.459719 | ||||||||
\(155\) | −7.97479e79 | −0.900767 | ||||||||
\(156\) | 2.61915e79 | 0.233944 | ||||||||
\(157\) | 2.23717e80 | 1.58257 | 0.791283 | − | 0.611450i | \(-0.209414\pi\) | ||||
0.791283 | + | 0.611450i | \(0.209414\pi\) | |||||||
\(158\) | 2.60126e79 | 0.145949 | ||||||||
\(159\) | 9.11826e79 | 0.406366 | ||||||||
\(160\) | 3.87211e80 | 1.37268 | ||||||||
\(161\) | −5.91717e80 | −1.67097 | ||||||||
\(162\) | −1.64376e80 | −0.370289 | ||||||||
\(163\) | 1.41890e80 | 0.255331 | 0.127665 | − | 0.991817i | \(-0.459252\pi\) | ||||
0.127665 | + | 0.991817i | \(0.459252\pi\) | |||||||
\(164\) | −1.33446e79 | −0.0192090 | ||||||||
\(165\) | −2.57090e80 | −0.296429 | ||||||||
\(166\) | −1.21344e81 | −1.12221 | ||||||||
\(167\) | 5.60731e80 | 0.416489 | 0.208244 | − | 0.978077i | \(-0.433225\pi\) | ||||
0.208244 | + | 0.978077i | \(0.433225\pi\) | |||||||
\(168\) | −1.09960e81 | −0.656820 | ||||||||
\(169\) | 9.84674e80 | 0.473618 | ||||||||
\(170\) | 3.61067e81 | 1.40024 | ||||||||
\(171\) | −9.61519e80 | −0.301023 | ||||||||
\(172\) | −1.40793e81 | −0.356280 | ||||||||
\(173\) | −3.93500e81 | −0.805864 | −0.402932 | − | 0.915230i | \(-0.632009\pi\) | ||||
−0.402932 | + | 0.915230i | \(0.632009\pi\) | |||||||
\(174\) | −6.76698e80 | −0.112292 | ||||||||
\(175\) | 1.87357e82 | 2.52221 | ||||||||
\(176\) | 1.28793e81 | 0.140825 | ||||||||
\(177\) | −2.56585e81 | −0.228143 | ||||||||
\(178\) | −5.54710e80 | −0.0401547 | ||||||||
\(179\) | −3.22411e82 | −1.90228 | −0.951140 | − | 0.308759i | \(-0.900086\pi\) | ||||
−0.951140 | + | 0.308759i | \(0.900086\pi\) | |||||||
\(180\) | −1.29994e82 | −0.625857 | ||||||||
\(181\) | 3.64648e82 | 1.43419 | 0.717095 | − | 0.696976i | \(-0.245472\pi\) | ||||
0.717095 | + | 0.696976i | \(0.245472\pi\) | |||||||
\(182\) | −4.05120e82 | −1.30310 | ||||||||
\(183\) | −6.42229e81 | −0.169132 | ||||||||
\(184\) | −5.68715e82 | −1.22756 | ||||||||
\(185\) | 1.42156e83 | 2.51766 | ||||||||
\(186\) | 1.15520e82 | 0.168048 | ||||||||
\(187\) | −4.13049e82 | −0.494064 | ||||||||
\(188\) | 3.69606e82 | 0.363896 | ||||||||
\(189\) | 1.37666e83 | 1.11679 | ||||||||
\(190\) | 6.62435e82 | 0.443238 | ||||||||
\(191\) | −1.38052e83 | −0.762649 | −0.381325 | − | 0.924441i | \(-0.624532\pi\) | ||||
−0.381325 | + | 0.924441i | \(0.624532\pi\) | |||||||
\(192\) | −8.62785e82 | −0.393920 | ||||||||
\(193\) | −2.46248e83 | −0.930101 | −0.465051 | − | 0.885284i | \(-0.653964\pi\) | ||||
−0.465051 | + | 0.885284i | \(0.653964\pi\) | |||||||
\(194\) | −3.22319e82 | −0.100814 | ||||||||
\(195\) | 3.24093e83 | 0.840246 | ||||||||
\(196\) | −2.42178e83 | −0.520940 | ||||||||
\(197\) | −4.95791e83 | −0.885689 | −0.442844 | − | 0.896598i | \(-0.646031\pi\) | ||||
−0.442844 | + | 0.896598i | \(0.646031\pi\) | |||||||
\(198\) | −1.74729e83 | −0.259468 | ||||||||
\(199\) | −4.06154e82 | −0.0501826 | −0.0250913 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250913 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(200\) | 1.80074e84 | 1.85292 | ||||||||
\(201\) | −7.48745e83 | −0.642211 | ||||||||
\(202\) | 6.44075e83 | 0.460905 | ||||||||
\(203\) | −8.90819e83 | −0.532334 | ||||||||
\(204\) | 4.45141e83 | 0.222329 | ||||||||
\(205\) | −1.65126e83 | −0.0689920 | ||||||||
\(206\) | 1.98921e84 | 0.695870 | ||||||||
\(207\) | 3.21721e84 | 0.943108 | ||||||||
\(208\) | −1.62359e84 | −0.399177 | ||||||||
\(209\) | −7.57803e83 | −0.156393 | ||||||||
\(210\) | −4.28553e84 | −0.743019 | ||||||||
\(211\) | −9.12088e84 | −1.32962 | −0.664810 | − | 0.747013i | \(-0.731487\pi\) | ||||
−0.664810 | + | 0.747013i | \(0.731487\pi\) | |||||||
\(212\) | 3.63368e84 | 0.445747 | ||||||||
\(213\) | −8.98114e83 | −0.0927846 | ||||||||
\(214\) | −5.04757e83 | −0.0439521 | ||||||||
\(215\) | −1.74216e85 | −1.27963 | ||||||||
\(216\) | 1.32315e85 | 0.820439 | ||||||||
\(217\) | 1.52073e85 | 0.796657 | ||||||||
\(218\) | 1.41461e85 | 0.626577 | ||||||||
\(219\) | 1.67736e85 | 0.628659 | ||||||||
\(220\) | −1.02452e85 | −0.325156 | ||||||||
\(221\) | 5.20699e85 | 1.40045 | ||||||||
\(222\) | −2.05922e85 | −0.469699 | ||||||||
\(223\) | −1.10503e85 | −0.213918 | −0.106959 | − | 0.994263i | \(-0.534111\pi\) | ||||
−0.106959 | + | 0.994263i | \(0.534111\pi\) | |||||||
\(224\) | −7.38379e85 | −1.21402 | ||||||||
\(225\) | −1.01867e86 | −1.42355 | ||||||||
\(226\) | 8.92917e85 | 1.06134 | ||||||||
\(227\) | 9.88450e84 | 0.100003 | 0.0500013 | − | 0.998749i | \(-0.484077\pi\) | ||||
0.0500013 | + | 0.998749i | \(0.484077\pi\) | |||||||
\(228\) | 8.16680e84 | 0.0703769 | ||||||||
\(229\) | 6.28394e85 | 0.461569 | 0.230785 | − | 0.973005i | \(-0.425871\pi\) | ||||
0.230785 | + | 0.973005i | \(0.425871\pi\) | |||||||
\(230\) | −2.21648e86 | −1.38867 | ||||||||
\(231\) | 4.90250e85 | 0.262168 | ||||||||
\(232\) | −8.56190e85 | −0.391074 | ||||||||
\(233\) | 7.37366e85 | 0.287867 | 0.143934 | − | 0.989587i | \(-0.454025\pi\) | ||||
0.143934 | + | 0.989587i | \(0.454025\pi\) | |||||||
\(234\) | 2.20267e86 | 0.735478 | ||||||||
\(235\) | 4.57349e86 | 1.30699 | ||||||||
\(236\) | −1.02251e86 | −0.250253 | ||||||||
\(237\) | 3.96828e85 | 0.0832316 | ||||||||
\(238\) | −6.88526e86 | −1.23840 | ||||||||
\(239\) | 5.40038e86 | 0.833491 | 0.416746 | − | 0.909023i | \(-0.363171\pi\) | ||||
0.416746 | + | 0.909023i | \(0.363171\pi\) | |||||||
\(240\) | −1.71750e86 | −0.227608 | ||||||||
\(241\) | 4.43408e86 | 0.504873 | 0.252436 | − | 0.967614i | \(-0.418768\pi\) | ||||
0.252436 | + | 0.967614i | \(0.418768\pi\) | |||||||
\(242\) | 6.13132e86 | 0.600196 | ||||||||
\(243\) | −1.15879e87 | −0.975836 | ||||||||
\(244\) | −2.55932e86 | −0.185522 | ||||||||
\(245\) | −2.99670e87 | −1.87103 | ||||||||
\(246\) | 2.39195e85 | 0.0128713 | ||||||||
\(247\) | 9.55303e86 | 0.443305 | ||||||||
\(248\) | 1.46161e87 | 0.585256 | ||||||||
\(249\) | −1.85113e87 | −0.639973 | ||||||||
\(250\) | 2.95426e87 | 0.882345 | ||||||||
\(251\) | −4.58295e86 | −0.118319 | −0.0591595 | − | 0.998249i | \(-0.518842\pi\) | ||||
−0.0591595 | + | 0.998249i | \(0.518842\pi\) | |||||||
\(252\) | 2.47887e87 | 0.553521 | ||||||||
\(253\) | 2.53558e87 | 0.489980 | ||||||||
\(254\) | 5.08608e87 | 0.851044 | ||||||||
\(255\) | 5.50816e87 | 0.798528 | ||||||||
\(256\) | −8.29980e87 | −1.04306 | ||||||||
\(257\) | −5.46778e87 | −0.596008 | −0.298004 | − | 0.954565i | \(-0.596321\pi\) | ||||
−0.298004 | + | 0.954565i | \(0.596321\pi\) | |||||||
\(258\) | 2.52364e87 | 0.238730 | ||||||||
\(259\) | −2.71080e88 | −2.22667 | ||||||||
\(260\) | 1.29153e88 | 0.921675 | ||||||||
\(261\) | 4.84344e87 | 0.300452 | ||||||||
\(262\) | −1.75084e88 | −0.944603 | ||||||||
\(263\) | −5.24740e87 | −0.246354 | −0.123177 | − | 0.992385i | \(-0.539308\pi\) | ||||
−0.123177 | + | 0.992385i | \(0.539308\pi\) | |||||||
\(264\) | 4.71192e87 | 0.192599 | ||||||||
\(265\) | 4.49631e88 | 1.60096 | ||||||||
\(266\) | −1.26321e88 | −0.392009 | ||||||||
\(267\) | −8.46222e86 | −0.0228994 | ||||||||
\(268\) | −2.98379e88 | −0.704448 | ||||||||
\(269\) | −6.27826e87 | −0.129384 | −0.0646920 | − | 0.997905i | \(-0.520607\pi\) | ||||
−0.0646920 | + | 0.997905i | \(0.520607\pi\) | |||||||
\(270\) | 5.15676e88 | 0.928111 | ||||||||
\(271\) | 8.67497e88 | 1.36423 | 0.682117 | − | 0.731243i | \(-0.261059\pi\) | ||||
0.682117 | + | 0.731243i | \(0.261059\pi\) | |||||||
\(272\) | −2.75940e88 | −0.379358 | ||||||||
\(273\) | −6.18019e88 | −0.743131 | ||||||||
\(274\) | 4.52489e88 | 0.476116 | ||||||||
\(275\) | −8.02848e88 | −0.739588 | ||||||||
\(276\) | −2.73258e88 | −0.220491 | ||||||||
\(277\) | 1.05020e89 | 0.742610 | 0.371305 | − | 0.928511i | \(-0.378910\pi\) | ||||
0.371305 | + | 0.928511i | \(0.378910\pi\) | |||||||
\(278\) | 1.27916e89 | 0.793027 | ||||||||
\(279\) | −8.26830e88 | −0.449638 | ||||||||
\(280\) | −5.42225e89 | −2.58768 | ||||||||
\(281\) | −1.29679e89 | −0.543362 | −0.271681 | − | 0.962387i | \(-0.587580\pi\) | ||||
−0.271681 | + | 0.962387i | \(0.587580\pi\) | |||||||
\(282\) | −6.62500e88 | −0.243833 | ||||||||
\(283\) | 5.99633e89 | 1.93946 | 0.969729 | − | 0.244182i | \(-0.0785194\pi\) | ||||
0.969729 | + | 0.244182i | \(0.0785194\pi\) | |||||||
\(284\) | −3.57904e88 | −0.101776 | ||||||||
\(285\) | 1.01056e89 | 0.252769 | ||||||||
\(286\) | 1.73599e89 | 0.382109 | ||||||||
\(287\) | 3.14881e88 | 0.0610180 | ||||||||
\(288\) | 4.01462e89 | 0.685202 | ||||||||
\(289\) | 2.20036e89 | 0.330920 | ||||||||
\(290\) | −3.33687e89 | −0.442397 | ||||||||
\(291\) | −4.91704e88 | −0.0574923 | ||||||||
\(292\) | 6.68437e89 | 0.689583 | ||||||||
\(293\) | −3.90288e89 | −0.355400 | −0.177700 | − | 0.984085i | \(-0.556866\pi\) | ||||
−0.177700 | + | 0.984085i | \(0.556866\pi\) | |||||||
\(294\) | 4.34091e89 | 0.349063 | ||||||||
\(295\) | −1.26525e90 | −0.898819 | ||||||||
\(296\) | −2.60543e90 | −1.63580 | ||||||||
\(297\) | −5.89917e89 | −0.327477 | ||||||||
\(298\) | 1.82410e90 | 0.895686 | ||||||||
\(299\) | −3.19641e90 | −1.38888 | ||||||||
\(300\) | 8.65225e89 | 0.332815 | ||||||||
\(301\) | 3.32217e90 | 1.13173 | ||||||||
\(302\) | 3.27436e90 | 0.988265 | ||||||||
\(303\) | 9.82550e89 | 0.262844 | ||||||||
\(304\) | −5.06254e89 | −0.120083 | ||||||||
\(305\) | −3.16690e90 | −0.666331 | ||||||||
\(306\) | 3.74356e90 | 0.698962 | ||||||||
\(307\) | −5.03208e90 | −0.834059 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(308\) | 1.95368e90 | 0.287575 | ||||||||
\(309\) | 3.03459e90 | 0.396840 | ||||||||
\(310\) | 5.69641e90 | 0.662063 | ||||||||
\(311\) | 5.56953e90 | 0.575525 | 0.287763 | − | 0.957702i | \(-0.407089\pi\) | ||||
0.287763 | + | 0.957702i | \(0.407089\pi\) | |||||||
\(312\) | −5.93995e90 | −0.545934 | ||||||||
\(313\) | −1.93772e91 | −1.58461 | −0.792305 | − | 0.610125i | \(-0.791119\pi\) | ||||
−0.792305 | + | 0.610125i | \(0.791119\pi\) | |||||||
\(314\) | −1.59802e91 | −1.16319 | ||||||||
\(315\) | 3.06735e91 | 1.98805 | ||||||||
\(316\) | 1.58139e90 | 0.0912976 | ||||||||
\(317\) | −1.45832e91 | −0.750221 | −0.375110 | − | 0.926980i | \(-0.622395\pi\) | ||||
−0.375110 | + | 0.926980i | \(0.622395\pi\) | |||||||
\(318\) | −6.51319e90 | −0.298679 | ||||||||
\(319\) | 3.81727e90 | 0.156096 | ||||||||
\(320\) | −4.25448e91 | −1.55193 | ||||||||
\(321\) | −7.70018e89 | −0.0250650 | ||||||||
\(322\) | 4.22665e91 | 1.22817 | ||||||||
\(323\) | 1.62360e91 | 0.421294 | ||||||||
\(324\) | −9.99291e90 | −0.231632 | ||||||||
\(325\) | 1.01209e92 | 2.09640 | ||||||||
\(326\) | −1.01352e91 | −0.187668 | ||||||||
\(327\) | 2.15802e91 | 0.357324 | ||||||||
\(328\) | 3.02641e90 | 0.0448263 | ||||||||
\(329\) | −8.72128e91 | −1.15593 | ||||||||
\(330\) | 1.83640e91 | 0.217876 | ||||||||
\(331\) | −5.05919e91 | −0.537476 | −0.268738 | − | 0.963213i | \(-0.586607\pi\) | ||||
−0.268738 | + | 0.963213i | \(0.586607\pi\) | |||||||
\(332\) | −7.37688e91 | −0.701993 | ||||||||
\(333\) | 1.47388e92 | 1.25675 | ||||||||
\(334\) | −4.00531e91 | −0.306119 | ||||||||
\(335\) | −3.69214e92 | −2.53013 | ||||||||
\(336\) | 3.27514e91 | 0.201301 | ||||||||
\(337\) | 1.39888e92 | 0.771419 | 0.385710 | − | 0.922620i | \(-0.373957\pi\) | ||||
0.385710 | + | 0.922620i | \(0.373957\pi\) | |||||||
\(338\) | −7.03355e91 | −0.348109 | ||||||||
\(339\) | 1.36216e92 | 0.605258 | ||||||||
\(340\) | 2.19504e92 | 0.875913 | ||||||||
\(341\) | −6.51650e91 | −0.233604 | ||||||||
\(342\) | 6.86815e91 | 0.221252 | ||||||||
\(343\) | 6.70944e91 | 0.194290 | ||||||||
\(344\) | 3.19302e92 | 0.831417 | ||||||||
\(345\) | −3.38129e92 | −0.791927 | ||||||||
\(346\) | 2.81078e92 | 0.592310 | ||||||||
\(347\) | −9.06972e91 | −0.172016 | −0.0860078 | − | 0.996294i | \(-0.527411\pi\) | ||||
−0.0860078 | + | 0.996294i | \(0.527411\pi\) | |||||||
\(348\) | −4.11385e91 | −0.0702434 | ||||||||
\(349\) | 4.50813e92 | 0.693216 | 0.346608 | − | 0.938010i | \(-0.387333\pi\) | ||||
0.346608 | + | 0.938010i | \(0.387333\pi\) | |||||||
\(350\) | −1.33830e93 | −1.85382 | ||||||||
\(351\) | 7.43661e92 | 0.928251 | ||||||||
\(352\) | 3.16405e92 | 0.355988 | ||||||||
\(353\) | −1.31440e93 | −1.33337 | −0.666685 | − | 0.745339i | \(-0.732288\pi\) | ||||
−0.666685 | + | 0.745339i | \(0.732288\pi\) | |||||||
\(354\) | 1.83279e92 | 0.167685 | ||||||||
\(355\) | −4.42869e92 | −0.365545 | ||||||||
\(356\) | −3.37225e91 | −0.0251185 | ||||||||
\(357\) | −1.05036e93 | −0.706235 | ||||||||
\(358\) | 2.30299e93 | 1.39818 | ||||||||
\(359\) | −1.25513e93 | −0.688245 | −0.344122 | − | 0.938925i | \(-0.611824\pi\) | ||||
−0.344122 | + | 0.938925i | \(0.611824\pi\) | |||||||
\(360\) | 2.94811e93 | 1.46050 | ||||||||
\(361\) | −1.93576e93 | −0.866642 | ||||||||
\(362\) | −2.60469e93 | −1.05413 | ||||||||
\(363\) | 9.35346e92 | 0.342279 | ||||||||
\(364\) | −2.46285e93 | −0.815148 | ||||||||
\(365\) | 8.27122e93 | 2.47674 | ||||||||
\(366\) | 4.58746e92 | 0.124312 | ||||||||
\(367\) | 5.71510e93 | 1.40189 | 0.700943 | − | 0.713217i | \(-0.252763\pi\) | ||||
0.700943 | + | 0.713217i | \(0.252763\pi\) | |||||||
\(368\) | 1.69391e93 | 0.376222 | ||||||||
\(369\) | −1.71203e92 | −0.0344389 | ||||||||
\(370\) | −1.01542e94 | −1.85048 | ||||||||
\(371\) | −8.57410e93 | −1.41593 | ||||||||
\(372\) | 7.02280e92 | 0.105122 | ||||||||
\(373\) | −3.74173e93 | −0.507809 | −0.253905 | − | 0.967229i | \(-0.581715\pi\) | ||||
−0.253905 | + | 0.967229i | \(0.581715\pi\) | |||||||
\(374\) | 2.95042e93 | 0.363137 | ||||||||
\(375\) | 4.50679e93 | 0.503183 | ||||||||
\(376\) | −8.38226e93 | −0.849190 | ||||||||
\(377\) | −4.81213e93 | −0.442464 | ||||||||
\(378\) | −9.83353e93 | −0.820841 | ||||||||
\(379\) | 2.02793e94 | 1.53717 | 0.768586 | − | 0.639747i | \(-0.220961\pi\) | ||||
0.768586 | + | 0.639747i | \(0.220961\pi\) | |||||||
\(380\) | 4.02714e93 | 0.277265 | ||||||||
\(381\) | 7.75892e93 | 0.485333 | ||||||||
\(382\) | 9.86109e93 | 0.560547 | ||||||||
\(383\) | −8.75423e93 | −0.452337 | −0.226169 | − | 0.974088i | \(-0.572620\pi\) | ||||
−0.226169 | + | 0.974088i | \(0.572620\pi\) | |||||||
\(384\) | −1.25350e93 | −0.0588889 | ||||||||
\(385\) | 2.41747e94 | 1.03287 | ||||||||
\(386\) | 1.75895e94 | 0.683624 | ||||||||
\(387\) | −1.80628e94 | −0.638757 | ||||||||
\(388\) | −1.95947e93 | −0.0630639 | ||||||||
\(389\) | −1.08943e94 | −0.319182 | −0.159591 | − | 0.987183i | \(-0.551018\pi\) | ||||
−0.159591 | + | 0.987183i | \(0.551018\pi\) | |||||||
\(390\) | −2.31500e94 | −0.617581 | ||||||||
\(391\) | −5.43249e94 | −1.31992 | ||||||||
\(392\) | 5.49233e94 | 1.21567 | ||||||||
\(393\) | −2.67094e94 | −0.538687 | ||||||||
\(394\) | 3.54144e94 | 0.650981 | ||||||||
\(395\) | 1.95680e94 | 0.327909 | ||||||||
\(396\) | −1.06223e94 | −0.162309 | ||||||||
\(397\) | −1.01644e95 | −1.41654 | −0.708268 | − | 0.705944i | \(-0.750523\pi\) | ||||
−0.708268 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(398\) | 2.90116e93 | 0.0368842 | ||||||||
\(399\) | −1.92705e94 | −0.223554 | ||||||||
\(400\) | −5.36347e94 | −0.567879 | ||||||||
\(401\) | 1.22596e95 | 1.18497 | 0.592483 | − | 0.805583i | \(-0.298148\pi\) | ||||
0.592483 | + | 0.805583i | \(0.298148\pi\) | |||||||
\(402\) | 5.34830e94 | 0.472025 | ||||||||
\(403\) | 8.21484e94 | 0.662163 | ||||||||
\(404\) | 3.91552e94 | 0.288317 | ||||||||
\(405\) | −1.23652e95 | −0.831942 | ||||||||
\(406\) | 6.36314e94 | 0.391265 | ||||||||
\(407\) | 1.16161e95 | 0.652928 | ||||||||
\(408\) | −1.00953e95 | −0.518828 | ||||||||
\(409\) | 2.38071e94 | 0.111894 | 0.0559469 | − | 0.998434i | \(-0.482182\pi\) | ||||
0.0559469 | + | 0.998434i | \(0.482182\pi\) | |||||||
\(410\) | 1.17950e94 | 0.0507091 | ||||||||
\(411\) | 6.90281e94 | 0.271519 | ||||||||
\(412\) | 1.20930e95 | 0.435298 | ||||||||
\(413\) | 2.41273e95 | 0.794935 | ||||||||
\(414\) | −2.29806e95 | −0.693184 | ||||||||
\(415\) | −9.12814e95 | −2.52131 | ||||||||
\(416\) | −3.98866e95 | −1.00907 | ||||||||
\(417\) | 1.95138e95 | 0.452247 | ||||||||
\(418\) | 5.41300e94 | 0.114949 | ||||||||
\(419\) | 6.44324e95 | 1.25399 | 0.626993 | − | 0.779025i | \(-0.284286\pi\) | ||||
0.626993 | + | 0.779025i | \(0.284286\pi\) | |||||||
\(420\) | −2.60530e95 | −0.464792 | ||||||||
\(421\) | −6.80537e95 | −1.11315 | −0.556577 | − | 0.830796i | \(-0.687886\pi\) | ||||
−0.556577 | + | 0.830796i | \(0.687886\pi\) | |||||||
\(422\) | 6.51507e95 | 0.977270 | ||||||||
\(423\) | 4.74182e95 | 0.652412 | ||||||||
\(424\) | −8.24080e95 | −1.04020 | ||||||||
\(425\) | 1.72010e96 | 1.99232 | ||||||||
\(426\) | 6.41525e94 | 0.0681966 | ||||||||
\(427\) | 6.03902e95 | 0.589318 | ||||||||
\(428\) | −3.06857e94 | −0.0274940 | ||||||||
\(429\) | 2.64829e95 | 0.217908 | ||||||||
\(430\) | 1.24443e96 | 0.940530 | ||||||||
\(431\) | −2.50780e96 | −1.74130 | −0.870649 | − | 0.491904i | \(-0.836301\pi\) | ||||
−0.870649 | + | 0.491904i | \(0.836301\pi\) | |||||||
\(432\) | −3.94097e95 | −0.251447 | ||||||||
\(433\) | −1.03865e96 | −0.609063 | −0.304531 | − | 0.952502i | \(-0.598500\pi\) | ||||
−0.304531 | + | 0.952502i | \(0.598500\pi\) | |||||||
\(434\) | −1.08626e96 | −0.585543 | ||||||||
\(435\) | −5.09046e95 | −0.252290 | ||||||||
\(436\) | 8.59983e95 | 0.391952 | ||||||||
\(437\) | −9.96675e95 | −0.417812 | ||||||||
\(438\) | −1.19814e96 | −0.462064 | ||||||||
\(439\) | 4.08395e96 | 1.44919 | 0.724596 | − | 0.689174i | \(-0.242027\pi\) | ||||
0.724596 | + | 0.689174i | \(0.242027\pi\) | |||||||
\(440\) | 2.32350e96 | 0.758787 | ||||||||
\(441\) | −3.10699e96 | −0.933968 | ||||||||
\(442\) | −3.71936e96 | −1.02933 | ||||||||
\(443\) | 2.68993e96 | 0.685496 | 0.342748 | − | 0.939427i | \(-0.388642\pi\) | ||||
0.342748 | + | 0.939427i | \(0.388642\pi\) | |||||||
\(444\) | −1.25186e96 | −0.293818 | ||||||||
\(445\) | −4.17281e95 | −0.0902170 | ||||||||
\(446\) | 7.89325e95 | 0.157229 | ||||||||
\(447\) | 2.78271e96 | 0.510791 | ||||||||
\(448\) | 8.11296e96 | 1.37256 | ||||||||
\(449\) | −8.90575e96 | −1.38893 | −0.694463 | − | 0.719528i | \(-0.744358\pi\) | ||||
−0.694463 | + | 0.719528i | \(0.744358\pi\) | |||||||
\(450\) | 7.27640e96 | 1.04631 | ||||||||
\(451\) | −1.34931e95 | −0.0178923 | ||||||||
\(452\) | 5.42831e96 | 0.663913 | ||||||||
\(453\) | 4.99511e96 | 0.563587 | ||||||||
\(454\) | −7.06052e95 | −0.0735019 | ||||||||
\(455\) | −3.04752e97 | −2.92773 | ||||||||
\(456\) | −1.85214e96 | −0.164232 | ||||||||
\(457\) | 1.95894e97 | 1.60354 | 0.801769 | − | 0.597634i | \(-0.203892\pi\) | ||||
0.801769 | + | 0.597634i | \(0.203892\pi\) | |||||||
\(458\) | −4.48863e96 | −0.339253 | ||||||||
\(459\) | 1.26390e97 | 0.882163 | ||||||||
\(460\) | −1.34746e97 | −0.868673 | ||||||||
\(461\) | −1.16420e97 | −0.693335 | −0.346667 | − | 0.937988i | \(-0.612687\pi\) | ||||
−0.346667 | + | 0.937988i | \(0.612687\pi\) | |||||||
\(462\) | −3.50187e96 | −0.192694 | ||||||||
\(463\) | −2.97083e97 | −1.51068 | −0.755338 | − | 0.655336i | \(-0.772527\pi\) | ||||
−0.755338 | + | 0.655336i | \(0.772527\pi\) | |||||||
\(464\) | 2.55014e96 | 0.119856 | ||||||||
\(465\) | 8.69000e96 | 0.377561 | ||||||||
\(466\) | −5.26702e96 | −0.211582 | ||||||||
\(467\) | 3.83937e97 | 1.42624 | 0.713122 | − | 0.701040i | \(-0.247281\pi\) | ||||
0.713122 | + | 0.701040i | \(0.247281\pi\) | |||||||
\(468\) | 1.33907e97 | 0.460075 | ||||||||
\(469\) | 7.04061e97 | 2.23770 | ||||||||
\(470\) | −3.26686e97 | −0.960635 | ||||||||
\(471\) | −2.43781e97 | −0.663340 | ||||||||
\(472\) | 2.31894e97 | 0.583991 | ||||||||
\(473\) | −1.42359e97 | −0.331859 | ||||||||
\(474\) | −2.83455e96 | −0.0611752 | ||||||||
\(475\) | 3.15580e97 | 0.630656 | ||||||||
\(476\) | −4.18576e97 | −0.774676 | ||||||||
\(477\) | 4.66180e97 | 0.799158 | ||||||||
\(478\) | −3.85751e97 | −0.612616 | ||||||||
\(479\) | 7.62727e93 | 0.000112234 0 | 5.61168e−5 | − | 1.00000i | \(-0.499982\pi\) | ||||
5.61168e−5 | 1.00000i | \(0.499982\pi\) | ||||||||
\(480\) | −4.21937e97 | −0.575364 | ||||||||
\(481\) | −1.46435e98 | −1.85076 | ||||||||
\(482\) | −3.16728e97 | −0.371081 | ||||||||
\(483\) | 6.44785e97 | 0.700397 | ||||||||
\(484\) | 3.72741e97 | 0.375450 | ||||||||
\(485\) | −2.42464e97 | −0.226503 | ||||||||
\(486\) | 8.27729e97 | 0.717239 | ||||||||
\(487\) | −7.46183e97 | −0.599844 | −0.299922 | − | 0.953964i | \(-0.596961\pi\) | ||||
−0.299922 | + | 0.953964i | \(0.596961\pi\) | |||||||
\(488\) | 5.80427e97 | 0.432936 | ||||||||
\(489\) | −1.54615e97 | −0.107023 | ||||||||
\(490\) | 2.14055e98 | 1.37521 | ||||||||
\(491\) | 8.28295e97 | 0.493982 | 0.246991 | − | 0.969018i | \(-0.420558\pi\) | ||||
0.246991 | + | 0.969018i | \(0.420558\pi\) | |||||||
\(492\) | 1.45414e96 | 0.00805155 | ||||||||
\(493\) | −8.17850e97 | −0.420495 | ||||||||
\(494\) | −6.82375e97 | −0.325829 | ||||||||
\(495\) | −1.31440e98 | −0.582957 | ||||||||
\(496\) | −4.35338e97 | −0.179368 | ||||||||
\(497\) | 8.44516e97 | 0.323296 | ||||||||
\(498\) | 1.32227e98 | 0.470380 | ||||||||
\(499\) | 1.76754e98 | 0.584387 | 0.292193 | − | 0.956359i | \(-0.405615\pi\) | ||||
0.292193 | + | 0.956359i | \(0.405615\pi\) | |||||||
\(500\) | 1.79598e98 | 0.551946 | ||||||||
\(501\) | −6.11019e97 | −0.174573 | ||||||||
\(502\) | 3.27361e97 | 0.0869644 | ||||||||
\(503\) | −6.60146e98 | −1.63083 | −0.815414 | − | 0.578878i | \(-0.803491\pi\) | ||||
−0.815414 | + | 0.578878i | \(0.803491\pi\) | |||||||
\(504\) | −5.62181e98 | −1.29170 | ||||||||
\(505\) | 4.84506e98 | 1.03553 | ||||||||
\(506\) | −1.81117e98 | −0.360135 | ||||||||
\(507\) | −1.07298e98 | −0.198519 | ||||||||
\(508\) | 3.09198e98 | 0.532366 | ||||||||
\(509\) | 4.28277e98 | 0.686319 | 0.343159 | − | 0.939277i | \(-0.388503\pi\) | ||||
0.343159 | + | 0.939277i | \(0.388503\pi\) | |||||||
\(510\) | −3.93449e98 | −0.586918 | ||||||||
\(511\) | −1.57726e99 | −2.19048 | ||||||||
\(512\) | 4.84211e98 | 0.626153 | ||||||||
\(513\) | 2.31882e98 | 0.279243 | ||||||||
\(514\) | 3.90565e98 | 0.438066 | ||||||||
\(515\) | 1.49639e99 | 1.56344 | ||||||||
\(516\) | 1.53419e98 | 0.149337 | ||||||||
\(517\) | 3.73718e98 | 0.338952 | ||||||||
\(518\) | 1.93633e99 | 1.63661 | ||||||||
\(519\) | 4.28790e98 | 0.337782 | ||||||||
\(520\) | −2.92905e99 | −2.15083 | ||||||||
\(521\) | 9.97828e98 | 0.683091 | 0.341546 | − | 0.939865i | \(-0.389050\pi\) | ||||
0.341546 | + | 0.939865i | \(0.389050\pi\) | |||||||
\(522\) | −3.45968e98 | −0.220832 | ||||||||
\(523\) | −5.97094e98 | −0.355411 | −0.177706 | − | 0.984084i | \(-0.556867\pi\) | ||||
−0.177706 | + | 0.984084i | \(0.556867\pi\) | |||||||
\(524\) | −1.06439e99 | −0.590891 | ||||||||
\(525\) | −2.04160e99 | −1.05720 | ||||||||
\(526\) | 3.74823e98 | 0.181070 | ||||||||
\(527\) | 1.39616e99 | 0.629287 | ||||||||
\(528\) | −1.40344e98 | −0.0590276 | ||||||||
\(529\) | 7.87231e98 | 0.309008 | ||||||||
\(530\) | −3.21172e99 | −1.17671 | ||||||||
\(531\) | −1.31182e99 | −0.448666 | ||||||||
\(532\) | −7.67942e98 | −0.245219 | ||||||||
\(533\) | 1.70096e98 | 0.0507168 | ||||||||
\(534\) | 6.04458e97 | 0.0168310 | ||||||||
\(535\) | −3.79704e98 | −0.0987488 | ||||||||
\(536\) | 6.76692e99 | 1.64390 | ||||||||
\(537\) | 3.51326e99 | 0.797350 | ||||||||
\(538\) | 4.48457e98 | 0.0950973 | ||||||||
\(539\) | −2.44872e99 | −0.485231 | ||||||||
\(540\) | 3.13495e99 | 0.580575 | ||||||||
\(541\) | 6.65195e99 | 1.15146 | 0.575730 | − | 0.817640i | \(-0.304718\pi\) | ||||
0.575730 | + | 0.817640i | \(0.304718\pi\) | |||||||
\(542\) | −6.19655e99 | −1.00271 | ||||||||
\(543\) | −3.97351e99 | −0.601147 | ||||||||
\(544\) | −6.77898e99 | −0.958968 | ||||||||
\(545\) | 1.06414e100 | 1.40775 | ||||||||
\(546\) | 4.41453e99 | 0.546201 | ||||||||
\(547\) | −1.55974e100 | −1.80515 | −0.902576 | − | 0.430531i | \(-0.858326\pi\) | ||||
−0.902576 | + | 0.430531i | \(0.858326\pi\) | |||||||
\(548\) | 2.75081e99 | 0.297832 | ||||||||
\(549\) | −3.28346e99 | −0.332614 | ||||||||
\(550\) | 5.73476e99 | 0.543597 | ||||||||
\(551\) | −1.50047e99 | −0.133105 | ||||||||
\(552\) | 6.19720e99 | 0.514540 | ||||||||
\(553\) | −3.73147e99 | −0.290009 | ||||||||
\(554\) | −7.50161e99 | −0.545818 | ||||||||
\(555\) | −1.54905e100 | −1.05529 | ||||||||
\(556\) | 7.77636e99 | 0.496074 | ||||||||
\(557\) | −2.03966e100 | −1.21855 | −0.609275 | − | 0.792959i | \(-0.708540\pi\) | ||||
−0.609275 | + | 0.792959i | \(0.708540\pi\) | |||||||
\(558\) | 5.90607e99 | 0.330484 | ||||||||
\(559\) | 1.79461e100 | 0.940672 | ||||||||
\(560\) | 1.61501e100 | 0.793070 | ||||||||
\(561\) | 4.50093e99 | 0.207089 | ||||||||
\(562\) | 9.26301e99 | 0.399371 | ||||||||
\(563\) | −3.81014e100 | −1.53952 | −0.769758 | − | 0.638336i | \(-0.779623\pi\) | ||||
−0.769758 | + | 0.638336i | \(0.779623\pi\) | |||||||
\(564\) | −4.02753e99 | −0.152529 | ||||||||
\(565\) | 6.71697e100 | 2.38454 | ||||||||
\(566\) | −4.28319e100 | −1.42550 | ||||||||
\(567\) | 2.35795e100 | 0.735787 | ||||||||
\(568\) | 8.11687e99 | 0.237506 | ||||||||
\(569\) | 2.20282e100 | 0.604480 | 0.302240 | − | 0.953232i | \(-0.402266\pi\) | ||||
0.302240 | + | 0.953232i | \(0.402266\pi\) | |||||||
\(570\) | −7.21844e99 | −0.185785 | ||||||||
\(571\) | 7.36336e99 | 0.177770 | 0.0888850 | − | 0.996042i | \(-0.471670\pi\) | ||||
0.0888850 | + | 0.996042i | \(0.471670\pi\) | |||||||
\(572\) | 1.05536e100 | 0.239026 | ||||||||
\(573\) | 1.50433e100 | 0.319668 | ||||||||
\(574\) | −2.24921e99 | −0.0448482 | ||||||||
\(575\) | −1.05592e101 | −1.97585 | ||||||||
\(576\) | −4.41107e100 | −0.774682 | ||||||||
\(577\) | −1.01125e101 | −1.66702 | −0.833512 | − | 0.552501i | \(-0.813674\pi\) | ||||
−0.833512 | + | 0.552501i | \(0.813674\pi\) | |||||||
\(578\) | −1.57172e100 | −0.243226 | ||||||||
\(579\) | 2.68332e100 | 0.389857 | ||||||||
\(580\) | −2.02858e100 | −0.276739 | ||||||||
\(581\) | 1.74066e101 | 2.22990 | ||||||||
\(582\) | 3.51225e99 | 0.0422568 | ||||||||
\(583\) | 3.67411e100 | 0.415192 | ||||||||
\(584\) | −1.51594e101 | −1.60921 | ||||||||
\(585\) | 1.65696e101 | 1.65243 | ||||||||
\(586\) | 2.78784e100 | 0.261219 | ||||||||
\(587\) | −5.72321e100 | −0.503906 | −0.251953 | − | 0.967740i | \(-0.581073\pi\) | ||||
−0.251953 | + | 0.967740i | \(0.581073\pi\) | |||||||
\(588\) | 2.63897e100 | 0.218354 | ||||||||
\(589\) | 2.56148e100 | 0.199197 | ||||||||
\(590\) | 9.03770e100 | 0.660632 | ||||||||
\(591\) | 5.40255e100 | 0.371241 | ||||||||
\(592\) | 7.76021e100 | 0.501339 | ||||||||
\(593\) | −3.32917e100 | −0.202227 | −0.101114 | − | 0.994875i | \(-0.532241\pi\) | ||||
−0.101114 | + | 0.994875i | \(0.532241\pi\) | |||||||
\(594\) | 4.21379e100 | 0.240695 | ||||||||
\(595\) | −5.17945e101 | −2.78236 | ||||||||
\(596\) | 1.10893e101 | 0.560292 | ||||||||
\(597\) | 4.42579e99 | 0.0210343 | ||||||||
\(598\) | 2.28320e101 | 1.02082 | ||||||||
\(599\) | −2.64261e100 | −0.111162 | −0.0555808 | − | 0.998454i | \(-0.517701\pi\) | ||||
−0.0555808 | + | 0.998454i | \(0.517701\pi\) | |||||||
\(600\) | −1.96224e101 | −0.776659 | ||||||||
\(601\) | 8.61412e100 | 0.320843 | 0.160422 | − | 0.987049i | \(-0.448715\pi\) | ||||
0.160422 | + | 0.987049i | \(0.448715\pi\) | |||||||
\(602\) | −2.37303e101 | −0.831824 | ||||||||
\(603\) | −3.82803e101 | −1.26297 | ||||||||
\(604\) | 1.99058e101 | 0.618204 | ||||||||
\(605\) | 4.61229e101 | 1.34848 | ||||||||
\(606\) | −7.01838e100 | −0.193191 | ||||||||
\(607\) | −1.93297e101 | −0.501001 | −0.250501 | − | 0.968116i | \(-0.580595\pi\) | ||||
−0.250501 | + | 0.968116i | \(0.580595\pi\) | |||||||
\(608\) | −1.24371e101 | −0.303556 | ||||||||
\(609\) | 9.70710e100 | 0.223130 | ||||||||
\(610\) | 2.26212e101 | 0.489753 | ||||||||
\(611\) | −4.71116e101 | −0.960780 | ||||||||
\(612\) | 2.27582e101 | 0.437232 | ||||||||
\(613\) | 4.68691e101 | 0.848358 | 0.424179 | − | 0.905578i | \(-0.360563\pi\) | ||||
0.424179 | + | 0.905578i | \(0.360563\pi\) | |||||||
\(614\) | 3.59443e101 | 0.613033 | ||||||||
\(615\) | 1.79935e100 | 0.0289183 | ||||||||
\(616\) | −4.43073e101 | −0.671087 | ||||||||
\(617\) | 1.24724e102 | 1.78049 | 0.890246 | − | 0.455479i | \(-0.150532\pi\) | ||||
0.890246 | + | 0.455479i | \(0.150532\pi\) | |||||||
\(618\) | −2.16761e101 | −0.291677 | ||||||||
\(619\) | −5.63173e101 | −0.714386 | −0.357193 | − | 0.934031i | \(-0.616266\pi\) | ||||
−0.357193 | + | 0.934031i | \(0.616266\pi\) | |||||||
\(620\) | 3.46302e101 | 0.414150 | ||||||||
\(621\) | −7.75868e101 | −0.874871 | ||||||||
\(622\) | −3.97833e101 | −0.423011 | ||||||||
\(623\) | 7.95721e100 | 0.0797898 | ||||||||
\(624\) | 1.76920e101 | 0.167317 | ||||||||
\(625\) | 2.86353e101 | 0.255436 | ||||||||
\(626\) | 1.38412e102 | 1.16469 | ||||||||
\(627\) | 8.25766e100 | 0.0655528 | ||||||||
\(628\) | −9.71481e101 | −0.727625 | ||||||||
\(629\) | −2.48876e102 | −1.75887 | ||||||||
\(630\) | −2.19102e102 | −1.46122 | ||||||||
\(631\) | −1.04720e102 | −0.659111 | −0.329555 | − | 0.944136i | \(-0.606899\pi\) | ||||
−0.329555 | + | 0.944136i | \(0.606899\pi\) | |||||||
\(632\) | −3.58641e101 | −0.213053 | ||||||||
\(633\) | 9.93888e101 | 0.557316 | ||||||||
\(634\) | 1.04168e102 | 0.551412 | ||||||||
\(635\) | 3.82600e102 | 1.91207 | ||||||||
\(636\) | −3.95956e101 | −0.186837 | ||||||||
\(637\) | 3.08691e102 | 1.37542 | ||||||||
\(638\) | −2.72668e101 | −0.114731 | ||||||||
\(639\) | −4.59169e101 | −0.182470 | ||||||||
\(640\) | −6.18112e101 | −0.232006 | ||||||||
\(641\) | 1.40637e102 | 0.498635 | 0.249317 | − | 0.968422i | \(-0.419794\pi\) | ||||
0.249317 | + | 0.968422i | \(0.419794\pi\) | |||||||
\(642\) | 5.50025e100 | 0.0184227 | ||||||||
\(643\) | −1.43530e102 | −0.454195 | −0.227098 | − | 0.973872i | \(-0.572924\pi\) | ||||
−0.227098 | + | 0.973872i | \(0.572924\pi\) | |||||||
\(644\) | 2.56951e102 | 0.768273 | ||||||||
\(645\) | 1.89841e102 | 0.536364 | ||||||||
\(646\) | −1.15974e102 | −0.309651 | ||||||||
\(647\) | −4.09180e102 | −1.03254 | −0.516271 | − | 0.856425i | \(-0.672680\pi\) | ||||
−0.516271 | + | 0.856425i | \(0.672680\pi\) | |||||||
\(648\) | 2.26629e102 | 0.540539 | ||||||||
\(649\) | −1.03388e102 | −0.233099 | ||||||||
\(650\) | −7.22936e102 | −1.54086 | ||||||||
\(651\) | −1.65711e102 | −0.333923 | ||||||||
\(652\) | −6.16150e101 | −0.117395 | ||||||||
\(653\) | 6.20506e102 | 1.11793 | 0.558965 | − | 0.829191i | \(-0.311198\pi\) | ||||
0.558965 | + | 0.829191i | \(0.311198\pi\) | |||||||
\(654\) | −1.54148e102 | −0.262633 | ||||||||
\(655\) | −1.31707e103 | −2.12227 | ||||||||
\(656\) | −9.01411e100 | −0.0137383 | ||||||||
\(657\) | 8.57564e102 | 1.23632 | ||||||||
\(658\) | 6.22963e102 | 0.849605 | ||||||||
\(659\) | 4.77744e102 | 0.616422 | 0.308211 | − | 0.951318i | \(-0.400270\pi\) | ||||
0.308211 | + | 0.951318i | \(0.400270\pi\) | |||||||
\(660\) | 1.11640e102 | 0.136291 | ||||||||
\(661\) | −6.60511e102 | −0.763004 | −0.381502 | − | 0.924368i | \(-0.624593\pi\) | ||||
−0.381502 | + | 0.924368i | \(0.624593\pi\) | |||||||
\(662\) | 3.61379e102 | 0.395045 | ||||||||
\(663\) | −5.67397e102 | −0.587007 | ||||||||
\(664\) | 1.67300e103 | 1.63818 | ||||||||
\(665\) | −9.50250e102 | −0.880740 | ||||||||
\(666\) | −1.05280e103 | −0.923710 | ||||||||
\(667\) | 5.02053e102 | 0.417020 | ||||||||
\(668\) | −2.43495e102 | −0.191491 | ||||||||
\(669\) | 1.20413e102 | 0.0896646 | ||||||||
\(670\) | 2.63730e103 | 1.85964 | ||||||||
\(671\) | −2.58780e102 | −0.172806 | ||||||||
\(672\) | 8.04600e102 | 0.508864 | ||||||||
\(673\) | −1.40758e103 | −0.843186 | −0.421593 | − | 0.906785i | \(-0.638529\pi\) | ||||
−0.421593 | + | 0.906785i | \(0.638529\pi\) | |||||||
\(674\) | −9.99226e102 | −0.566993 | ||||||||
\(675\) | 2.45665e103 | 1.32055 | ||||||||
\(676\) | −4.27590e102 | −0.217758 | ||||||||
\(677\) | −1.99664e103 | −0.963417 | −0.481708 | − | 0.876332i | \(-0.659984\pi\) | ||||
−0.481708 | + | 0.876332i | \(0.659984\pi\) | |||||||
\(678\) | −9.72997e102 | −0.444864 | ||||||||
\(679\) | 4.62360e102 | 0.200324 | ||||||||
\(680\) | −4.97810e103 | −2.04404 | ||||||||
\(681\) | −1.07710e102 | −0.0419166 | ||||||||
\(682\) | 4.65475e102 | 0.171699 | ||||||||
\(683\) | 9.40230e102 | 0.328760 | 0.164380 | − | 0.986397i | \(-0.447438\pi\) | ||||
0.164380 | + | 0.986397i | \(0.447438\pi\) | |||||||
\(684\) | 4.17535e102 | 0.138403 | ||||||||
\(685\) | 3.40385e103 | 1.06971 | ||||||||
\(686\) | −4.79257e102 | −0.142803 | ||||||||
\(687\) | −6.84751e102 | −0.193469 | ||||||||
\(688\) | −9.51036e102 | −0.254811 | ||||||||
\(689\) | −4.63166e103 | −1.17689 | ||||||||
\(690\) | 2.41526e103 | 0.582066 | ||||||||
\(691\) | 2.43467e103 | 0.556534 | 0.278267 | − | 0.960504i | \(-0.410240\pi\) | ||||
0.278267 | + | 0.960504i | \(0.410240\pi\) | |||||||
\(692\) | 1.70875e103 | 0.370516 | ||||||||
\(693\) | 2.50645e103 | 0.515580 | ||||||||
\(694\) | 6.47852e102 | 0.126431 | ||||||||
\(695\) | 9.62245e103 | 1.78172 | ||||||||
\(696\) | 9.32976e102 | 0.163920 | ||||||||
\(697\) | 2.89089e102 | 0.0481987 | ||||||||
\(698\) | −3.22017e103 | −0.509514 | ||||||||
\(699\) | −8.03495e102 | −0.120661 | ||||||||
\(700\) | −8.13590e103 | −1.15965 | ||||||||
\(701\) | 5.37926e103 | 0.727805 | 0.363902 | − | 0.931437i | \(-0.381444\pi\) | ||||
0.363902 | + | 0.931437i | \(0.381444\pi\) | |||||||
\(702\) | −5.31199e103 | −0.682264 | ||||||||
\(703\) | −4.56602e103 | −0.556760 | ||||||||
\(704\) | −3.47650e103 | −0.402476 | ||||||||
\(705\) | −4.98366e103 | −0.547830 | ||||||||
\(706\) | 9.38879e103 | 0.980027 | ||||||||
\(707\) | −9.23913e103 | −0.915846 | ||||||||
\(708\) | 1.11421e103 | 0.104895 | ||||||||
\(709\) | −1.07535e104 | −0.961530 | −0.480765 | − | 0.876849i | \(-0.659641\pi\) | ||||
−0.480765 | + | 0.876849i | \(0.659641\pi\) | |||||||
\(710\) | 3.16343e103 | 0.268675 | ||||||||
\(711\) | 2.02882e103 | 0.163683 | ||||||||
\(712\) | 7.64789e102 | 0.0586168 | ||||||||
\(713\) | −8.57061e103 | −0.624085 | ||||||||
\(714\) | 7.50276e103 | 0.519082 | ||||||||
\(715\) | 1.30590e104 | 0.858498 | ||||||||
\(716\) | 1.40006e104 | 0.874622 | ||||||||
\(717\) | −5.88471e103 | −0.349362 | ||||||||
\(718\) | 8.96545e103 | 0.505860 | ||||||||
\(719\) | 3.21953e104 | 1.72659 | 0.863293 | − | 0.504703i | \(-0.168398\pi\) | ||||
0.863293 | + | 0.504703i | \(0.168398\pi\) | |||||||
\(720\) | −8.78090e103 | −0.447613 | ||||||||
\(721\) | −2.85349e104 | −1.38274 | ||||||||
\(722\) | 1.38272e104 | 0.636982 | ||||||||
\(723\) | −4.83175e103 | −0.211620 | ||||||||
\(724\) | −1.58347e104 | −0.659405 | ||||||||
\(725\) | −1.58966e104 | −0.629460 | ||||||||
\(726\) | −6.68120e103 | −0.251575 | ||||||||
\(727\) | 1.43449e104 | 0.513678 | 0.256839 | − | 0.966454i | \(-0.417319\pi\) | ||||
0.256839 | + | 0.966454i | \(0.417319\pi\) | |||||||
\(728\) | 5.58547e104 | 1.90224 | ||||||||
\(729\) | −2.92561e103 | −0.0947681 | ||||||||
\(730\) | −5.90815e104 | −1.82040 | ||||||||
\(731\) | 3.05004e104 | 0.893968 | ||||||||
\(732\) | 2.78885e103 | 0.0777627 | ||||||||
\(733\) | −3.44849e104 | −0.914817 | −0.457408 | − | 0.889257i | \(-0.651222\pi\) | ||||
−0.457408 | + | 0.889257i | \(0.651222\pi\) | |||||||
\(734\) | −4.08231e104 | −1.03039 | ||||||||
\(735\) | 3.26546e104 | 0.784252 | ||||||||
\(736\) | 4.16140e104 | 0.951042 | ||||||||
\(737\) | −3.01699e104 | −0.656161 | ||||||||
\(738\) | 1.22291e103 | 0.0253126 | ||||||||
\(739\) | −6.34155e104 | −1.24932 | −0.624660 | − | 0.780897i | \(-0.714762\pi\) | ||||
−0.624660 | + | 0.780897i | \(0.714762\pi\) | |||||||
\(740\) | −6.17307e104 | −1.15756 | ||||||||
\(741\) | −1.04098e104 | −0.185813 | ||||||||
\(742\) | 6.12450e104 | 1.04071 | ||||||||
\(743\) | 4.62751e104 | 0.748611 | 0.374305 | − | 0.927305i | \(-0.377881\pi\) | ||||
0.374305 | + | 0.927305i | \(0.377881\pi\) | |||||||
\(744\) | −1.59270e104 | −0.245313 | ||||||||
\(745\) | 1.37218e105 | 2.01237 | ||||||||
\(746\) | 2.67273e104 | 0.373240 | ||||||||
\(747\) | −9.46410e104 | −1.25857 | ||||||||
\(748\) | 1.79365e104 | 0.227158 | ||||||||
\(749\) | 7.24065e103 | 0.0873355 | ||||||||
\(750\) | −3.21921e104 | −0.369839 | ||||||||
\(751\) | 4.35926e104 | 0.477040 | 0.238520 | − | 0.971138i | \(-0.423338\pi\) | ||||
0.238520 | + | 0.971138i | \(0.423338\pi\) | |||||||
\(752\) | 2.49664e104 | 0.260258 | ||||||||
\(753\) | 4.99397e103 | 0.0495940 | ||||||||
\(754\) | 3.43731e104 | 0.325211 | ||||||||
\(755\) | 2.46314e105 | 2.22037 | ||||||||
\(756\) | −5.97809e104 | −0.513473 | ||||||||
\(757\) | −7.98775e104 | −0.653770 | −0.326885 | − | 0.945064i | \(-0.605999\pi\) | ||||
−0.326885 | + | 0.945064i | \(0.605999\pi\) | |||||||
\(758\) | −1.44856e105 | −1.12982 | ||||||||
\(759\) | −2.76298e104 | −0.205378 | ||||||||
\(760\) | −9.13311e104 | −0.647027 | ||||||||
\(761\) | −2.56065e105 | −1.72906 | −0.864529 | − | 0.502583i | \(-0.832383\pi\) | ||||
−0.864529 | + | 0.502583i | \(0.832383\pi\) | |||||||
\(762\) | −5.54221e104 | −0.356719 | ||||||||
\(763\) | −2.02923e105 | −1.24505 | ||||||||
\(764\) | 5.99485e104 | 0.350647 | ||||||||
\(765\) | 2.81610e105 | 1.57038 | ||||||||
\(766\) | 6.25316e104 | 0.332468 | ||||||||
\(767\) | 1.30333e105 | 0.660732 | ||||||||
\(768\) | 9.04415e104 | 0.437203 | ||||||||
\(769\) | −6.72521e104 | −0.310023 | −0.155012 | − | 0.987913i | \(-0.549542\pi\) | ||||
−0.155012 | + | 0.987913i | \(0.549542\pi\) | |||||||
\(770\) | −1.72681e105 | −0.759158 | ||||||||
\(771\) | 5.95815e104 | 0.249820 | ||||||||
\(772\) | 1.06932e105 | 0.427638 | ||||||||
\(773\) | −2.46049e105 | −0.938578 | −0.469289 | − | 0.883045i | \(-0.655490\pi\) | ||||
−0.469289 | + | 0.883045i | \(0.655490\pi\) | |||||||
\(774\) | 1.29023e105 | 0.469487 | ||||||||
\(775\) | 2.71374e105 | 0.942010 | ||||||||
\(776\) | 4.44387e104 | 0.147166 | ||||||||
\(777\) | 2.95392e105 | 0.933322 | ||||||||
\(778\) | 7.78182e104 | 0.234599 | ||||||||
\(779\) | 5.30379e103 | 0.0152570 | ||||||||
\(780\) | −1.40736e105 | −0.386324 | ||||||||
\(781\) | −3.61885e104 | −0.0948000 | ||||||||
\(782\) | 3.88044e105 | 0.970140 | ||||||||
\(783\) | −1.16805e105 | −0.278714 | ||||||||
\(784\) | −1.63588e105 | −0.372576 | ||||||||
\(785\) | −1.20211e106 | −2.61337 | ||||||||
\(786\) | 1.90786e105 | 0.395935 | ||||||||
\(787\) | 2.71217e105 | 0.537328 | 0.268664 | − | 0.963234i | \(-0.413418\pi\) | ||||
0.268664 | + | 0.963234i | \(0.413418\pi\) | |||||||
\(788\) | 2.15295e105 | 0.407218 | ||||||||
\(789\) | 5.71800e104 | 0.103260 | ||||||||
\(790\) | −1.39775e105 | −0.241013 | ||||||||
\(791\) | −1.28087e106 | −2.10894 | ||||||||
\(792\) | 2.40902e105 | 0.378766 | ||||||||
\(793\) | 3.26223e105 | 0.489828 | ||||||||
\(794\) | 7.26044e105 | 1.04115 | ||||||||
\(795\) | −4.89955e105 | −0.671052 | ||||||||
\(796\) | 1.76370e104 | 0.0230727 | ||||||||
\(797\) | 1.45163e106 | 1.81395 | 0.906977 | − | 0.421179i | \(-0.138384\pi\) | ||||
0.906977 | + | 0.421179i | \(0.138384\pi\) | |||||||
\(798\) | 1.37650e105 | 0.164312 | ||||||||
\(799\) | −8.00691e105 | −0.913077 | ||||||||
\(800\) | −1.31764e106 | −1.43553 | ||||||||
\(801\) | −4.32639e104 | −0.0450338 | ||||||||
\(802\) | −8.75705e105 | −0.870950 | ||||||||
\(803\) | 6.75873e105 | 0.642315 | ||||||||
\(804\) | 3.25139e105 | 0.295273 | ||||||||
\(805\) | 3.17950e106 | 2.75937 | ||||||||
\(806\) | −5.86788e105 | −0.486690 | ||||||||
\(807\) | 6.84131e104 | 0.0542320 | ||||||||
\(808\) | −8.87998e105 | −0.672818 | ||||||||
\(809\) | 3.21507e104 | 0.0232847 | 0.0116423 | − | 0.999932i | \(-0.496294\pi\) | ||||
0.0116423 | + | 0.999932i | \(0.496294\pi\) | |||||||
\(810\) | 8.83250e105 | 0.611477 | ||||||||
\(811\) | 8.87148e105 | 0.587131 | 0.293566 | − | 0.955939i | \(-0.405158\pi\) | ||||
0.293566 | + | 0.955939i | \(0.405158\pi\) | |||||||
\(812\) | 3.86834e105 | 0.244754 | ||||||||
\(813\) | −9.45297e105 | −0.571826 | ||||||||
\(814\) | −8.29742e105 | −0.479902 | ||||||||
\(815\) | −7.62423e105 | −0.421641 | ||||||||
\(816\) | 3.00687e105 | 0.159010 | ||||||||
\(817\) | 5.59578e105 | 0.282980 | ||||||||
\(818\) | −1.70055e105 | −0.0822419 | ||||||||
\(819\) | −3.15968e106 | −1.46144 | ||||||||
\(820\) | 7.17051e104 | 0.0317208 | ||||||||
\(821\) | 1.04180e105 | 0.0440817 | 0.0220409 | − | 0.999757i | \(-0.492984\pi\) | ||||
0.0220409 | + | 0.999757i | \(0.492984\pi\) | |||||||
\(822\) | −4.93070e105 | −0.199566 | ||||||||
\(823\) | −1.21303e106 | −0.469653 | −0.234827 | − | 0.972037i | \(-0.575452\pi\) | ||||
−0.234827 | + | 0.972037i | \(0.575452\pi\) | |||||||
\(824\) | −2.74257e106 | −1.01581 | ||||||||
\(825\) | 8.74850e105 | 0.310002 | ||||||||
\(826\) | −1.72342e106 | −0.584277 | ||||||||
\(827\) | 2.35778e106 | 0.764808 | 0.382404 | − | 0.923995i | \(-0.375096\pi\) | ||||
0.382404 | + | 0.923995i | \(0.375096\pi\) | |||||||
\(828\) | −1.39706e106 | −0.433618 | ||||||||
\(829\) | 1.61461e106 | 0.479543 | 0.239771 | − | 0.970829i | \(-0.422928\pi\) | ||||
0.239771 | + | 0.970829i | \(0.422928\pi\) | |||||||
\(830\) | 6.52025e106 | 1.85316 | ||||||||
\(831\) | −1.14439e106 | −0.311269 | ||||||||
\(832\) | 4.38255e106 | 1.14084 | ||||||||
\(833\) | 5.24639e106 | 1.30713 | ||||||||
\(834\) | −1.39387e106 | −0.332401 | ||||||||
\(835\) | −3.01300e106 | −0.687769 | ||||||||
\(836\) | 3.29073e105 | 0.0719056 | ||||||||
\(837\) | 1.99400e106 | 0.417105 | ||||||||
\(838\) | −4.60242e106 | −0.921679 | ||||||||
\(839\) | −5.26994e106 | −1.01040 | −0.505201 | − | 0.863002i | \(-0.668582\pi\) | ||||
−0.505201 | + | 0.863002i | \(0.668582\pi\) | |||||||
\(840\) | 5.90854e106 | 1.08464 | ||||||||
\(841\) | −4.93340e106 | −0.867147 | ||||||||
\(842\) | 4.86109e106 | 0.818168 | ||||||||
\(843\) | 1.41309e106 | 0.227753 | ||||||||
\(844\) | 3.96070e106 | 0.611326 | ||||||||
\(845\) | −5.29099e106 | −0.782109 | ||||||||
\(846\) | −3.38709e106 | −0.479522 | ||||||||
\(847\) | −8.79527e106 | −1.19263 | ||||||||
\(848\) | 2.45451e106 | 0.318798 | ||||||||
\(849\) | −6.53410e106 | −0.812934 | ||||||||
\(850\) | −1.22867e107 | −1.46435 | ||||||||
\(851\) | 1.52777e107 | 1.74433 | ||||||||
\(852\) | 3.90002e105 | 0.0426601 | ||||||||
\(853\) | 3.38806e105 | 0.0355068 | 0.0177534 | − | 0.999842i | \(-0.494349\pi\) | ||||
0.0177534 | + | 0.999842i | \(0.494349\pi\) | |||||||
\(854\) | −4.31369e106 | −0.433148 | ||||||||
\(855\) | 5.16657e106 | 0.497095 | ||||||||
\(856\) | 6.95918e105 | 0.0641602 | ||||||||
\(857\) | 1.33280e107 | 1.17751 | 0.588754 | − | 0.808313i | \(-0.299619\pi\) | ||||
0.588754 | + | 0.808313i | \(0.299619\pi\) | |||||||
\(858\) | −1.89168e106 | −0.160163 | ||||||||
\(859\) | −1.17251e107 | −0.951405 | −0.475702 | − | 0.879606i | \(-0.657806\pi\) | ||||
−0.475702 | + | 0.879606i | \(0.657806\pi\) | |||||||
\(860\) | 7.56527e106 | 0.588344 | ||||||||
\(861\) | −3.43121e105 | −0.0255760 | ||||||||
\(862\) | 1.79133e107 | 1.27985 | ||||||||
\(863\) | −2.09858e107 | −1.43725 | −0.718623 | − | 0.695400i | \(-0.755227\pi\) | ||||
−0.718623 | + | 0.695400i | \(0.755227\pi\) | |||||||
\(864\) | −9.68173e106 | −0.635626 | ||||||||
\(865\) | 2.11441e107 | 1.33076 | ||||||||
\(866\) | 7.41912e106 | 0.447661 | ||||||||
\(867\) | −2.39770e106 | −0.138707 | ||||||||
\(868\) | −6.60369e106 | −0.366283 | ||||||||
\(869\) | 1.59898e106 | 0.0850395 | ||||||||
\(870\) | 3.63613e106 | 0.185433 | ||||||||
\(871\) | 3.80328e107 | 1.85993 | ||||||||
\(872\) | −1.95035e107 | −0.914661 | ||||||||
\(873\) | −2.51388e106 | −0.113064 | ||||||||
\(874\) | 7.11927e106 | 0.307092 | ||||||||
\(875\) | −4.23783e107 | −1.75327 | ||||||||
\(876\) | −7.28385e106 | −0.289042 | ||||||||
\(877\) | 1.41996e107 | 0.540493 | 0.270246 | − | 0.962791i | \(-0.412895\pi\) | ||||
0.270246 | + | 0.962791i | \(0.412895\pi\) | |||||||
\(878\) | −2.91718e107 | −1.06516 | ||||||||
\(879\) | 4.25291e106 | 0.148968 | ||||||||
\(880\) | −6.92050e106 | −0.232552 | ||||||||
\(881\) | 7.66883e106 | 0.247234 | 0.123617 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123617 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(882\) | 2.21933e107 | 0.686466 | ||||||||
\(883\) | −3.35873e107 | −0.996802 | −0.498401 | − | 0.866947i | \(-0.666079\pi\) | ||||
−0.498401 | + | 0.866947i | \(0.666079\pi\) | |||||||
\(884\) | −2.26111e107 | −0.643893 | ||||||||
\(885\) | 1.37872e107 | 0.376744 | ||||||||
\(886\) | −1.92142e107 | −0.503839 | ||||||||
\(887\) | 6.18714e107 | 1.55696 | 0.778481 | − | 0.627669i | \(-0.215991\pi\) | ||||
0.778481 | + | 0.627669i | \(0.215991\pi\) | |||||||
\(888\) | 2.83909e107 | 0.685656 | ||||||||
\(889\) | −7.29588e107 | −1.69108 | ||||||||
\(890\) | 2.98065e106 | 0.0663094 | ||||||||
\(891\) | −1.01041e107 | −0.215755 | ||||||||
\(892\) | 4.79854e106 | 0.0983540 | ||||||||
\(893\) | −1.46899e107 | −0.289029 | ||||||||
\(894\) | −1.98770e107 | −0.375431 | ||||||||
\(895\) | 1.73243e108 | 3.14133 | ||||||||
\(896\) | 1.17869e107 | 0.205191 | ||||||||
\(897\) | 3.48307e107 | 0.582154 | ||||||||
\(898\) | 6.36140e107 | 1.02086 | ||||||||
\(899\) | −1.29029e107 | −0.198819 | ||||||||
\(900\) | 4.42354e107 | 0.654513 | ||||||||
\(901\) | −7.87178e107 | −1.11845 | ||||||||
\(902\) | 9.63812e105 | 0.0131508 | ||||||||
\(903\) | −3.62011e107 | −0.474372 | ||||||||
\(904\) | −1.23108e108 | −1.54931 | ||||||||
\(905\) | −1.95938e108 | −2.36835 | ||||||||
\(906\) | −3.56802e107 | −0.414236 | ||||||||
\(907\) | 7.84800e107 | 0.875171 | 0.437586 | − | 0.899177i | \(-0.355834\pi\) | ||||
0.437586 | + | 0.899177i | \(0.355834\pi\) | |||||||
\(908\) | −4.29230e106 | −0.0459787 | ||||||||
\(909\) | 5.02338e107 | 0.516909 | ||||||||
\(910\) | 2.17685e108 | 2.15188 | ||||||||
\(911\) | −1.50467e108 | −1.42896 | −0.714482 | − | 0.699653i | \(-0.753338\pi\) | ||||
−0.714482 | + | 0.699653i | \(0.753338\pi\) | |||||||
\(912\) | 5.51657e106 | 0.0503335 | ||||||||
\(913\) | −7.45895e107 | −0.653874 | ||||||||
\(914\) | −1.39927e108 | −1.17860 | ||||||||
\(915\) | 3.45092e107 | 0.279296 | ||||||||
\(916\) | −2.72877e107 | −0.212218 | ||||||||
\(917\) | 2.51155e108 | 1.87698 | ||||||||
\(918\) | −9.02805e107 | −0.648390 | ||||||||
\(919\) | −1.19946e108 | −0.827887 | −0.413944 | − | 0.910303i | \(-0.635849\pi\) | ||||
−0.413944 | + | 0.910303i | \(0.635849\pi\) | |||||||
\(920\) | 3.05590e108 | 2.02714 | ||||||||
\(921\) | 5.48337e107 | 0.349600 | ||||||||
\(922\) | 8.31589e107 | 0.509601 | ||||||||
\(923\) | 4.56200e107 | 0.268716 | ||||||||
\(924\) | −2.12889e107 | −0.120539 | ||||||||
\(925\) | −4.83742e108 | −2.63294 | ||||||||
\(926\) | 2.12207e108 | 1.11035 | ||||||||
\(927\) | 1.55146e108 | 0.780424 | ||||||||
\(928\) | 6.26491e107 | 0.302980 | ||||||||
\(929\) | 3.42076e107 | 0.159056 | 0.0795278 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795278 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(930\) | −6.20728e107 | −0.277507 | ||||||||
\(931\) | 9.62531e107 | 0.413763 | ||||||||
\(932\) | −3.20198e107 | −0.132354 | ||||||||
\(933\) | −6.06903e107 | −0.241234 | ||||||||
\(934\) | −2.74247e108 | −1.04829 | ||||||||
\(935\) | 2.21946e108 | 0.815873 | ||||||||
\(936\) | −3.03686e108 | −1.07363 | ||||||||
\(937\) | 5.24351e108 | 1.78290 | 0.891450 | − | 0.453119i | \(-0.149689\pi\) | ||||
0.891450 | + | 0.453119i | \(0.149689\pi\) | |||||||
\(938\) | −5.02913e108 | −1.64471 | ||||||||
\(939\) | 2.11150e108 | 0.664197 | ||||||||
\(940\) | −1.98602e108 | −0.600920 | ||||||||
\(941\) | −5.99656e107 | −0.174534 | −0.0872672 | − | 0.996185i | \(-0.527813\pi\) | ||||
−0.0872672 | + | 0.996185i | \(0.527813\pi\) | |||||||
\(942\) | 1.74133e108 | 0.487555 | ||||||||
\(943\) | −1.77463e107 | −0.0478003 | ||||||||
\(944\) | −6.90691e107 | −0.178981 | ||||||||
\(945\) | −7.39728e108 | −1.84421 | ||||||||
\(946\) | 1.01687e108 | 0.243916 | ||||||||
\(947\) | 6.02710e108 | 1.39102 | 0.695511 | − | 0.718515i | \(-0.255178\pi\) | ||||
0.695511 | + | 0.718515i | \(0.255178\pi\) | |||||||
\(948\) | −1.72321e107 | −0.0382678 | ||||||||
\(949\) | −8.52020e108 | −1.82068 | ||||||||
\(950\) | −2.25419e108 | −0.463532 | ||||||||
\(951\) | 1.58910e108 | 0.314459 | ||||||||
\(952\) | 9.49284e108 | 1.80779 | ||||||||
\(953\) | 7.10042e108 | 1.30135 | 0.650674 | − | 0.759357i | \(-0.274487\pi\) | ||||
0.650674 | + | 0.759357i | \(0.274487\pi\) | |||||||
\(954\) | −3.32993e108 | −0.587381 | ||||||||
\(955\) | 7.41801e108 | 1.25940 | ||||||||
\(956\) | −2.34509e108 | −0.383219 | ||||||||
\(957\) | −4.15961e107 | −0.0654285 | ||||||||
\(958\) | −5.44818e104 | −8.24916e−5 0 | ||||||||
\(959\) | −6.49087e108 | −0.946071 | ||||||||
\(960\) | 4.63604e108 | 0.650500 | ||||||||
\(961\) | −5.20026e108 | −0.702460 | ||||||||
\(962\) | 1.04599e109 | 1.36031 | ||||||||
\(963\) | −3.93679e107 | −0.0492927 | ||||||||
\(964\) | −1.92548e108 | −0.232128 | ||||||||
\(965\) | 1.32317e109 | 1.53592 | ||||||||
\(966\) | −4.60571e108 | −0.514792 | ||||||||
\(967\) | −3.03350e108 | −0.326495 | −0.163248 | − | 0.986585i | \(-0.552197\pi\) | ||||
−0.163248 | + | 0.986585i | \(0.552197\pi\) | |||||||
\(968\) | −8.45337e108 | −0.876152 | ||||||||
\(969\) | −1.76921e108 | −0.176588 | ||||||||
\(970\) | 1.73193e108 | 0.166480 | ||||||||
\(971\) | −2.07397e109 | −1.91999 | −0.959997 | − | 0.280012i | \(-0.909662\pi\) | ||||
−0.959997 | + | 0.280012i | \(0.909662\pi\) | |||||||
\(972\) | 5.03201e108 | 0.448665 | ||||||||
\(973\) | −1.83492e109 | −1.57579 | ||||||||
\(974\) | 5.33000e108 | 0.440885 | ||||||||
\(975\) | −1.10285e109 | −0.878718 | ||||||||
\(976\) | −1.72879e108 | −0.132686 | ||||||||
\(977\) | 1.80962e109 | 1.33794 | 0.668969 | − | 0.743290i | \(-0.266736\pi\) | ||||
0.668969 | + | 0.743290i | \(0.266736\pi\) | |||||||
\(978\) | 1.10442e108 | 0.0786620 | ||||||||
\(979\) | −3.40976e107 | −0.0233968 | ||||||||
\(980\) | 1.30130e109 | 0.860254 | ||||||||
\(981\) | 1.10331e109 | 0.702712 | ||||||||
\(982\) | −5.91653e108 | −0.363076 | ||||||||
\(983\) | −1.37476e109 | −0.812875 | −0.406438 | − | 0.913679i | \(-0.633229\pi\) | ||||
−0.406438 | + | 0.913679i | \(0.633229\pi\) | |||||||
\(984\) | −3.29783e107 | −0.0187892 | ||||||||
\(985\) | 2.66405e109 | 1.46258 | ||||||||
\(986\) | 5.84192e108 | 0.309064 | ||||||||
\(987\) | 9.50344e108 | 0.484512 | ||||||||
\(988\) | −4.14836e108 | −0.203820 | ||||||||
\(989\) | −1.87233e109 | −0.886578 | ||||||||
\(990\) | 9.38877e108 | 0.428474 | ||||||||
\(991\) | 2.85911e109 | 1.25760 | 0.628800 | − | 0.777567i | \(-0.283546\pi\) | ||||
0.628800 | + | 0.777567i | \(0.283546\pi\) | |||||||
\(992\) | −1.06949e109 | −0.453420 | ||||||||
\(993\) | 5.51292e108 | 0.225286 | ||||||||
\(994\) | −6.03240e108 | −0.237622 | ||||||||
\(995\) | 2.18240e108 | 0.0828691 | ||||||||
\(996\) | 8.03847e108 | 0.294244 | ||||||||
\(997\) | −8.40964e108 | −0.296759 | −0.148380 | − | 0.988930i | \(-0.547406\pi\) | ||||
−0.148380 | + | 0.988930i | \(0.547406\pi\) | |||||||
\(998\) | −1.26256e109 | −0.429524 | ||||||||
\(999\) | −3.55444e109 | −1.16582 |
(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 | 1.74.a.a.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 9.74.a.a.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.74.a.a.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.74.a.a.1.4 | 5 | 3.2 | odd | 2 |