Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,94,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, 94, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 94);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 94 \) |
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: | \(54.7725430605\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} + \cdots - 13\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{88}\cdot 3^{34}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-9.86534e10\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.05764e13 | −0.508222 | −0.254111 | − | 0.967175i | \(-0.581783\pi\) | ||||
−0.254111 | + | 0.967175i | \(0.581783\pi\) | |||||||
\(3\) | 2.16277e22 | 1.40887 | 0.704437 | − | 0.709767i | \(-0.251200\pi\) | ||||
0.704437 | + | 0.709767i | \(0.251200\pi\) | |||||||
\(4\) | −7.34554e27 | −0.741710 | ||||||||
\(5\) | 1.20105e32 | 0.377970 | 0.188985 | − | 0.981980i | \(-0.439480\pi\) | ||||
0.188985 | + | 0.981980i | \(0.439480\pi\) | |||||||
\(6\) | −1.09385e36 | −0.716020 | ||||||||
\(7\) | −1.85159e39 | −0.934300 | −0.467150 | − | 0.884178i | \(-0.654719\pi\) | ||||
−0.467150 | + | 0.884178i | \(0.654719\pi\) | |||||||
\(8\) | 8.72396e41 | 0.885176 | ||||||||
\(9\) | 2.32102e44 | 0.984923 | ||||||||
\(10\) | −6.07451e45 | −0.192093 | ||||||||
\(11\) | 6.89038e47 | 0.259110 | 0.129555 | − | 0.991572i | \(-0.458645\pi\) | ||||
0.129555 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(12\) | −1.58867e50 | −1.04498 | ||||||||
\(13\) | 5.57716e51 | 0.887253 | 0.443626 | − | 0.896212i | \(-0.353692\pi\) | ||||
0.443626 | + | 0.896212i | \(0.353692\pi\) | |||||||
\(14\) | 9.36469e52 | 0.474832 | ||||||||
\(15\) | 2.59760e54 | 0.532512 | ||||||||
\(16\) | 2.86240e55 | 0.291845 | ||||||||
\(17\) | −1.91697e57 | −1.16611 | −0.583056 | − | 0.812432i | \(-0.698143\pi\) | ||||
−0.583056 | + | 0.812432i | \(0.698143\pi\) | |||||||
\(18\) | −1.17389e58 | −0.500560 | ||||||||
\(19\) | −4.84589e59 | −1.67237 | −0.836183 | − | 0.548450i | \(-0.815218\pi\) | ||||
−0.836183 | + | 0.548450i | \(0.815218\pi\) | |||||||
\(20\) | −8.82240e59 | −0.280344 | ||||||||
\(21\) | −4.00457e61 | −1.31631 | ||||||||
\(22\) | −3.48491e61 | −0.131685 | ||||||||
\(23\) | 2.71891e63 | 1.30032 | 0.650159 | − | 0.759798i | \(-0.274702\pi\) | ||||
0.650159 | + | 0.759798i | \(0.274702\pi\) | |||||||
\(24\) | 1.88679e64 | 1.24710 | ||||||||
\(25\) | −8.65489e64 | −0.857139 | ||||||||
\(26\) | −2.82073e65 | −0.450921 | ||||||||
\(27\) | −7.68416e64 | −0.0212413 | ||||||||
\(28\) | 1.36009e67 | 0.692980 | ||||||||
\(29\) | 1.52941e68 | 1.52412 | 0.762059 | − | 0.647508i | \(-0.224189\pi\) | ||||
0.762059 | + | 0.647508i | \(0.224189\pi\) | |||||||
\(30\) | −1.31378e68 | −0.270634 | ||||||||
\(31\) | 1.67865e69 | 0.752733 | 0.376367 | − | 0.926471i | \(-0.377173\pi\) | ||||
0.376367 | + | 0.926471i | \(0.377173\pi\) | |||||||
\(32\) | −1.00875e70 | −1.03350 | ||||||||
\(33\) | 1.49023e70 | 0.365052 | ||||||||
\(34\) | 9.69535e70 | 0.592644 | ||||||||
\(35\) | −2.22386e71 | −0.353138 | ||||||||
\(36\) | −1.70492e72 | −0.730528 | ||||||||
\(37\) | −8.48939e72 | −1.01741 | −0.508705 | − | 0.860941i | \(-0.669876\pi\) | ||||
−0.508705 | + | 0.860941i | \(0.669876\pi\) | |||||||
\(38\) | 2.45088e73 | 0.849934 | ||||||||
\(39\) | 1.20621e74 | 1.25003 | ||||||||
\(40\) | 1.04780e74 | 0.334570 | ||||||||
\(41\) | −1.65968e75 | −1.68103 | −0.840516 | − | 0.541787i | \(-0.817748\pi\) | ||||
−0.840516 | + | 0.541787i | \(0.817748\pi\) | |||||||
\(42\) | 2.02537e75 | 0.668978 | ||||||||
\(43\) | −1.12790e75 | −0.124734 | −0.0623672 | − | 0.998053i | \(-0.519865\pi\) | ||||
−0.0623672 | + | 0.998053i | \(0.519865\pi\) | |||||||
\(44\) | −5.06136e75 | −0.192184 | ||||||||
\(45\) | 2.78767e76 | 0.372272 | ||||||||
\(46\) | −1.37513e77 | −0.660851 | ||||||||
\(47\) | 5.85334e76 | 0.103479 | 0.0517396 | − | 0.998661i | \(-0.483523\pi\) | ||||
0.0517396 | + | 0.998661i | \(0.483523\pi\) | |||||||
\(48\) | 6.19072e77 | 0.411172 | ||||||||
\(49\) | −4.99122e77 | −0.127083 | ||||||||
\(50\) | 4.37733e78 | 0.435617 | ||||||||
\(51\) | −4.14596e79 | −1.64290 | ||||||||
\(52\) | −4.09673e79 | −0.658085 | ||||||||
\(53\) | −1.38747e79 | −0.0919173 | −0.0459586 | − | 0.998943i | \(-0.514634\pi\) | ||||
−0.0459586 | + | 0.998943i | \(0.514634\pi\) | |||||||
\(54\) | 3.88637e78 | 0.0107953 | ||||||||
\(55\) | 8.27573e79 | 0.0979357 | ||||||||
\(56\) | −1.61532e81 | −0.827020 | ||||||||
\(57\) | −1.04806e82 | −2.35615 | ||||||||
\(58\) | −7.73524e81 | −0.774590 | ||||||||
\(59\) | −4.69043e81 | −0.212126 | −0.106063 | − | 0.994359i | \(-0.533825\pi\) | ||||
−0.106063 | + | 0.994359i | \(0.533825\pi\) | |||||||
\(60\) | −1.90808e82 | −0.394970 | ||||||||
\(61\) | −1.85512e83 | −1.78047 | −0.890234 | − | 0.455504i | \(-0.849459\pi\) | ||||
−0.890234 | + | 0.455504i | \(0.849459\pi\) | |||||||
\(62\) | −8.49001e82 | −0.382556 | ||||||||
\(63\) | −4.29758e83 | −0.920214 | ||||||||
\(64\) | 2.26711e83 | 0.233402 | ||||||||
\(65\) | 6.69848e83 | 0.335355 | ||||||||
\(66\) | −7.53706e83 | −0.185528 | ||||||||
\(67\) | −7.55695e84 | −0.924417 | −0.462209 | − | 0.886771i | \(-0.652943\pi\) | ||||
−0.462209 | + | 0.886771i | \(0.652943\pi\) | |||||||
\(68\) | 1.40812e85 | 0.864918 | ||||||||
\(69\) | 5.88037e85 | 1.83198 | ||||||||
\(70\) | 1.12475e85 | 0.179472 | ||||||||
\(71\) | 1.37506e86 | 1.13451 | 0.567257 | − | 0.823541i | \(-0.308005\pi\) | ||||
0.567257 | + | 0.823541i | \(0.308005\pi\) | |||||||
\(72\) | 2.02485e86 | 0.871830 | ||||||||
\(73\) | −4.41142e86 | −1.00015 | −0.500076 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500076 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(74\) | 4.29363e86 | 0.517071 | ||||||||
\(75\) | −1.87185e87 | −1.20760 | ||||||||
\(76\) | 3.55957e87 | 1.24041 | ||||||||
\(77\) | −1.27582e87 | −0.242086 | ||||||||
\(78\) | −6.10059e87 | −0.635291 | ||||||||
\(79\) | −3.34870e88 | −1.92849 | −0.964244 | − | 0.265015i | \(-0.914623\pi\) | ||||
−0.964244 | + | 0.265015i | \(0.914623\pi\) | |||||||
\(80\) | 3.43790e87 | 0.110309 | ||||||||
\(81\) | −5.63579e88 | −1.01485 | ||||||||
\(82\) | 8.39409e88 | 0.854337 | ||||||||
\(83\) | −4.06731e88 | −0.235600 | −0.117800 | − | 0.993037i | \(-0.537584\pi\) | ||||
−0.117800 | + | 0.993037i | \(0.537584\pi\) | |||||||
\(84\) | 2.94157e89 | 0.976321 | ||||||||
\(85\) | −2.30239e89 | −0.440756 | ||||||||
\(86\) | 5.70450e88 | 0.0633927 | ||||||||
\(87\) | 3.30777e90 | 2.14729 | ||||||||
\(88\) | 6.01114e89 | 0.229357 | ||||||||
\(89\) | 2.67415e89 | 0.0603324 | 0.0301662 | − | 0.999545i | \(-0.490396\pi\) | ||||
0.0301662 | + | 0.999545i | \(0.490396\pi\) | |||||||
\(90\) | −1.40991e90 | −0.189197 | ||||||||
\(91\) | −1.03266e91 | −0.828960 | ||||||||
\(92\) | −1.99718e91 | −0.964460 | ||||||||
\(93\) | 3.63053e91 | 1.06051 | ||||||||
\(94\) | −2.96041e90 | −0.0525904 | ||||||||
\(95\) | −5.82018e91 | −0.632105 | ||||||||
\(96\) | −2.18169e92 | −1.45607 | ||||||||
\(97\) | −5.40723e91 | −0.222889 | −0.111445 | − | 0.993771i | \(-0.535548\pi\) | ||||
−0.111445 | + | 0.993771i | \(0.535548\pi\) | |||||||
\(98\) | 2.52438e91 | 0.0645866 | ||||||||
\(99\) | 1.59927e92 | 0.255203 | ||||||||
\(100\) | 6.35749e92 | 0.635749 | ||||||||
\(101\) | 2.20531e93 | 1.38844 | 0.694218 | − | 0.719764i | \(-0.255750\pi\) | ||||
0.694218 | + | 0.719764i | \(0.255750\pi\) | |||||||
\(102\) | 2.09688e93 | 0.834960 | ||||||||
\(103\) | −3.68693e93 | −0.932684 | −0.466342 | − | 0.884605i | \(-0.654428\pi\) | ||||
−0.466342 | + | 0.884605i | \(0.654428\pi\) | |||||||
\(104\) | 4.86549e93 | 0.785374 | ||||||||
\(105\) | −4.80970e93 | −0.497526 | ||||||||
\(106\) | 7.01735e92 | 0.0467144 | ||||||||
\(107\) | −1.33971e94 | −0.576321 | −0.288161 | − | 0.957582i | \(-0.593044\pi\) | ||||
−0.288161 | + | 0.957582i | \(0.593044\pi\) | |||||||
\(108\) | 5.64443e92 | 0.0157549 | ||||||||
\(109\) | −2.23851e94 | −0.407031 | −0.203515 | − | 0.979072i | \(-0.565237\pi\) | ||||
−0.203515 | + | 0.979072i | \(0.565237\pi\) | |||||||
\(110\) | −4.18557e93 | −0.0497731 | ||||||||
\(111\) | −1.83606e95 | −1.43340 | ||||||||
\(112\) | −5.30000e94 | −0.272670 | ||||||||
\(113\) | 1.75390e95 | 0.596840 | 0.298420 | − | 0.954435i | \(-0.403540\pi\) | ||||
0.298420 | + | 0.954435i | \(0.403540\pi\) | |||||||
\(114\) | 5.30069e95 | 1.19745 | ||||||||
\(115\) | 3.26556e95 | 0.491482 | ||||||||
\(116\) | −1.12344e96 | −1.13045 | ||||||||
\(117\) | 1.29447e96 | 0.873876 | ||||||||
\(118\) | 2.37225e95 | 0.107807 | ||||||||
\(119\) | 3.54945e96 | 1.08950 | ||||||||
\(120\) | 2.26614e96 | 0.471367 | ||||||||
\(121\) | −6.59686e96 | −0.932862 | ||||||||
\(122\) | 9.38252e96 | 0.904873 | ||||||||
\(123\) | −3.58951e97 | −2.36836 | ||||||||
\(124\) | −1.23306e97 | −0.558310 | ||||||||
\(125\) | −2.25225e97 | −0.701943 | ||||||||
\(126\) | 2.17356e97 | 0.467673 | ||||||||
\(127\) | 3.30674e97 | 0.492637 | 0.246319 | − | 0.969189i | \(-0.420779\pi\) | ||||
0.246319 | + | 0.969189i | \(0.420779\pi\) | |||||||
\(128\) | 8.84355e97 | 0.914878 | ||||||||
\(129\) | −2.43938e97 | −0.175735 | ||||||||
\(130\) | −3.38785e97 | −0.170435 | ||||||||
\(131\) | −7.10571e96 | −0.0250318 | −0.0125159 | − | 0.999922i | \(-0.503984\pi\) | ||||
−0.0125159 | + | 0.999922i | \(0.503984\pi\) | |||||||
\(132\) | −1.09466e98 | −0.270763 | ||||||||
\(133\) | 8.97262e98 | 1.56249 | ||||||||
\(134\) | 3.82204e98 | 0.469809 | ||||||||
\(135\) | −9.22909e96 | −0.00802858 | ||||||||
\(136\) | −1.67236e99 | −1.03221 | ||||||||
\(137\) | 1.91186e99 | 0.839362 | 0.419681 | − | 0.907672i | \(-0.362142\pi\) | ||||
0.419681 | + | 0.907672i | \(0.362142\pi\) | |||||||
\(138\) | −2.97408e99 | −0.931055 | ||||||||
\(139\) | −6.59713e99 | −1.47627 | −0.738136 | − | 0.674652i | \(-0.764294\pi\) | ||||
−0.738136 | + | 0.674652i | \(0.764294\pi\) | |||||||
\(140\) | 1.63355e99 | 0.261926 | ||||||||
\(141\) | 1.26594e99 | 0.145789 | ||||||||
\(142\) | −6.95459e99 | −0.576585 | ||||||||
\(143\) | 3.84288e99 | 0.229896 | ||||||||
\(144\) | 6.64370e99 | 0.287445 | ||||||||
\(145\) | 1.83691e100 | 0.576071 | ||||||||
\(146\) | 2.23114e100 | 0.508299 | ||||||||
\(147\) | −1.07949e100 | −0.179044 | ||||||||
\(148\) | 6.23592e100 | 0.754624 | ||||||||
\(149\) | 1.72761e100 | 0.152857 | 0.0764284 | − | 0.997075i | \(-0.475648\pi\) | ||||
0.0764284 | + | 0.997075i | \(0.475648\pi\) | |||||||
\(150\) | 9.46716e100 | 0.613729 | ||||||||
\(151\) | 2.99143e100 | 0.142381 | 0.0711904 | − | 0.997463i | \(-0.477320\pi\) | ||||
0.0711904 | + | 0.997463i | \(0.477320\pi\) | |||||||
\(152\) | −4.22754e101 | −1.48034 | ||||||||
\(153\) | −4.44933e101 | −1.14853 | ||||||||
\(154\) | 6.45263e100 | 0.123033 | ||||||||
\(155\) | 2.01615e101 | 0.284511 | ||||||||
\(156\) | −8.86028e101 | −0.927158 | ||||||||
\(157\) | 7.17255e101 | 0.557622 | 0.278811 | − | 0.960346i | \(-0.410060\pi\) | ||||
0.278811 | + | 0.960346i | \(0.410060\pi\) | |||||||
\(158\) | 1.69366e102 | 0.980100 | ||||||||
\(159\) | −3.00079e101 | −0.129500 | ||||||||
\(160\) | −1.21156e102 | −0.390631 | ||||||||
\(161\) | −5.03430e102 | −1.21489 | ||||||||
\(162\) | 2.85038e102 | 0.515769 | ||||||||
\(163\) | 1.07628e103 | 1.46285 | 0.731426 | − | 0.681921i | \(-0.238855\pi\) | ||||
0.731426 | + | 0.681921i | \(0.238855\pi\) | |||||||
\(164\) | 1.21913e103 | 1.24684 | ||||||||
\(165\) | 1.78985e102 | 0.137979 | ||||||||
\(166\) | 2.05710e102 | 0.119737 | ||||||||
\(167\) | −1.94781e103 | −0.857492 | −0.428746 | − | 0.903425i | \(-0.641044\pi\) | ||||
−0.428746 | + | 0.903425i | \(0.641044\pi\) | |||||||
\(168\) | −3.49357e103 | −1.16517 | ||||||||
\(169\) | −8.40752e102 | −0.212783 | ||||||||
\(170\) | 1.16446e103 | 0.224002 | ||||||||
\(171\) | −1.12474e104 | −1.64715 | ||||||||
\(172\) | 8.28501e102 | 0.0925168 | ||||||||
\(173\) | 1.97197e104 | 1.68173 | 0.840864 | − | 0.541247i | \(-0.182047\pi\) | ||||
0.840864 | + | 0.541247i | \(0.182047\pi\) | |||||||
\(174\) | −1.67295e104 | −1.09130 | ||||||||
\(175\) | 1.60253e104 | 0.800825 | ||||||||
\(176\) | 1.97231e103 | 0.0756197 | ||||||||
\(177\) | −1.01443e104 | −0.298859 | ||||||||
\(178\) | −1.35249e103 | −0.0306623 | ||||||||
\(179\) | 1.05683e105 | 1.84645 | 0.923224 | − | 0.384262i | \(-0.125544\pi\) | ||||
0.923224 | + | 0.384262i | \(0.125544\pi\) | |||||||
\(180\) | −2.04770e104 | −0.276118 | ||||||||
\(181\) | 3.41629e104 | 0.356042 | 0.178021 | − | 0.984027i | \(-0.443031\pi\) | ||||
0.178021 | + | 0.984027i | \(0.443031\pi\) | |||||||
\(182\) | 5.22284e104 | 0.421296 | ||||||||
\(183\) | −4.01219e105 | −2.50845 | ||||||||
\(184\) | 2.37196e105 | 1.15101 | ||||||||
\(185\) | −1.01962e105 | −0.384551 | ||||||||
\(186\) | −1.83619e105 | −0.538972 | ||||||||
\(187\) | −1.32087e105 | −0.302151 | ||||||||
\(188\) | −4.29959e104 | −0.0767516 | ||||||||
\(189\) | 1.42279e104 | 0.0198458 | ||||||||
\(190\) | 2.94364e105 | 0.321250 | ||||||||
\(191\) | −4.66141e105 | −0.398534 | −0.199267 | − | 0.979945i | \(-0.563856\pi\) | ||||
−0.199267 | + | 0.979945i | \(0.563856\pi\) | |||||||
\(192\) | 4.90323e105 | 0.328833 | ||||||||
\(193\) | 3.64694e105 | 0.192094 | 0.0960471 | − | 0.995377i | \(-0.469380\pi\) | ||||
0.0960471 | + | 0.995377i | \(0.469380\pi\) | |||||||
\(194\) | 2.73478e105 | 0.113277 | ||||||||
\(195\) | 1.44873e106 | 0.472473 | ||||||||
\(196\) | 3.66632e105 | 0.0942591 | ||||||||
\(197\) | 6.37141e106 | 1.29287 | 0.646437 | − | 0.762967i | \(-0.276258\pi\) | ||||
0.646437 | + | 0.762967i | \(0.276258\pi\) | |||||||
\(198\) | −8.08855e105 | −0.129700 | ||||||||
\(199\) | 4.40148e106 | 0.558381 | 0.279190 | − | 0.960236i | \(-0.409934\pi\) | ||||
0.279190 | + | 0.960236i | \(0.409934\pi\) | |||||||
\(200\) | −7.55049e106 | −0.758718 | ||||||||
\(201\) | −1.63439e107 | −1.30239 | ||||||||
\(202\) | −1.11537e107 | −0.705634 | ||||||||
\(203\) | −2.83185e107 | −1.42398 | ||||||||
\(204\) | 3.04544e107 | 1.21856 | ||||||||
\(205\) | −1.99337e107 | −0.635380 | ||||||||
\(206\) | 1.86472e107 | 0.474011 | ||||||||
\(207\) | 6.31064e107 | 1.28071 | ||||||||
\(208\) | 1.59641e107 | 0.258940 | ||||||||
\(209\) | −3.33901e107 | −0.433326 | ||||||||
\(210\) | 2.43258e107 | 0.252854 | ||||||||
\(211\) | −1.08995e108 | −0.908392 | −0.454196 | − | 0.890902i | \(-0.650073\pi\) | ||||
−0.454196 | + | 0.890902i | \(0.650073\pi\) | |||||||
\(212\) | 1.01918e107 | 0.0681760 | ||||||||
\(213\) | 2.97395e108 | 1.59839 | ||||||||
\(214\) | 6.77577e107 | 0.292899 | ||||||||
\(215\) | −1.35467e107 | −0.0471459 | ||||||||
\(216\) | −6.70363e106 | −0.0188023 | ||||||||
\(217\) | −3.10817e108 | −0.703279 | ||||||||
\(218\) | 1.13216e108 | 0.206862 | ||||||||
\(219\) | −9.54089e108 | −1.40909 | ||||||||
\(220\) | −6.07897e107 | −0.0726399 | ||||||||
\(221\) | −1.06912e109 | −1.03464 | ||||||||
\(222\) | 9.28613e108 | 0.728487 | ||||||||
\(223\) | 4.86481e108 | 0.309663 | 0.154832 | − | 0.987941i | \(-0.450517\pi\) | ||||
0.154832 | + | 0.987941i | \(0.450517\pi\) | |||||||
\(224\) | 1.86779e109 | 0.965597 | ||||||||
\(225\) | −2.00882e109 | −0.844216 | ||||||||
\(226\) | −8.87062e108 | −0.303327 | ||||||||
\(227\) | −9.58249e108 | −0.266855 | −0.133428 | − | 0.991059i | \(-0.542598\pi\) | ||||
−0.133428 | + | 0.991059i | \(0.542598\pi\) | |||||||
\(228\) | 7.69854e109 | 1.74758 | ||||||||
\(229\) | 2.66341e109 | 0.493274 | 0.246637 | − | 0.969108i | \(-0.420674\pi\) | ||||
0.246637 | + | 0.969108i | \(0.420674\pi\) | |||||||
\(230\) | −1.65160e109 | −0.249782 | ||||||||
\(231\) | −2.75930e109 | −0.341069 | ||||||||
\(232\) | 1.33426e110 | 1.34911 | ||||||||
\(233\) | −7.83842e109 | −0.648900 | −0.324450 | − | 0.945903i | \(-0.605179\pi\) | ||||
−0.324450 | + | 0.945903i | \(0.605179\pi\) | |||||||
\(234\) | −6.54697e109 | −0.444123 | ||||||||
\(235\) | 7.03018e108 | 0.0391121 | ||||||||
\(236\) | 3.44538e109 | 0.157336 | ||||||||
\(237\) | −7.24247e110 | −2.71700 | ||||||||
\(238\) | −1.79518e110 | −0.553707 | ||||||||
\(239\) | 3.53328e110 | 0.896760 | 0.448380 | − | 0.893843i | \(-0.352001\pi\) | ||||
0.448380 | + | 0.893843i | \(0.352001\pi\) | |||||||
\(240\) | 7.43539e109 | 0.155411 | ||||||||
\(241\) | 6.85756e110 | 1.18135 | 0.590673 | − | 0.806911i | \(-0.298862\pi\) | ||||
0.590673 | + | 0.806911i | \(0.298862\pi\) | |||||||
\(242\) | 3.33646e110 | 0.474101 | ||||||||
\(243\) | −1.20078e111 | −1.40855 | ||||||||
\(244\) | 1.36268e111 | 1.32059 | ||||||||
\(245\) | −5.99473e109 | −0.0480338 | ||||||||
\(246\) | 1.81545e111 | 1.20365 | ||||||||
\(247\) | −2.70263e111 | −1.48381 | ||||||||
\(248\) | 1.46445e111 | 0.666301 | ||||||||
\(249\) | −8.79664e110 | −0.331931 | ||||||||
\(250\) | 1.13911e111 | 0.356743 | ||||||||
\(251\) | −2.00152e111 | −0.520633 | −0.260317 | − | 0.965523i | \(-0.583827\pi\) | ||||
−0.260317 | + | 0.965523i | \(0.583827\pi\) | |||||||
\(252\) | 3.15681e111 | 0.682532 | ||||||||
\(253\) | 1.87343e111 | 0.336925 | ||||||||
\(254\) | −1.67243e111 | −0.250369 | ||||||||
\(255\) | −4.97953e111 | −0.620969 | ||||||||
\(256\) | −6.71799e111 | −0.698362 | ||||||||
\(257\) | −2.15173e112 | −1.86594 | −0.932972 | − | 0.359949i | \(-0.882794\pi\) | ||||
−0.932972 | + | 0.359949i | \(0.882794\pi\) | |||||||
\(258\) | 1.23375e111 | 0.0893123 | ||||||||
\(259\) | 1.57189e112 | 0.950567 | ||||||||
\(260\) | −4.92039e111 | −0.248736 | ||||||||
\(261\) | 3.54980e112 | 1.50114 | ||||||||
\(262\) | 3.59381e110 | 0.0127217 | ||||||||
\(263\) | 2.80215e112 | 0.830899 | 0.415450 | − | 0.909616i | \(-0.363624\pi\) | ||||
0.415450 | + | 0.909616i | \(0.363624\pi\) | |||||||
\(264\) | 1.30007e112 | 0.323136 | ||||||||
\(265\) | −1.66643e111 | −0.0347420 | ||||||||
\(266\) | −4.53803e112 | −0.794093 | ||||||||
\(267\) | 5.78358e111 | 0.0850008 | ||||||||
\(268\) | 5.55099e112 | 0.685650 | ||||||||
\(269\) | −6.54356e112 | −0.679725 | −0.339862 | − | 0.940475i | \(-0.610380\pi\) | ||||
−0.339862 | + | 0.940475i | \(0.610380\pi\) | |||||||
\(270\) | 4.66775e110 | 0.00408030 | ||||||||
\(271\) | 8.26366e112 | 0.608276 | 0.304138 | − | 0.952628i | \(-0.401632\pi\) | ||||
0.304138 | + | 0.952628i | \(0.401632\pi\) | |||||||
\(272\) | −5.48714e112 | −0.340324 | ||||||||
\(273\) | −2.23341e113 | −1.16790 | ||||||||
\(274\) | −9.66950e112 | −0.426582 | ||||||||
\(275\) | −5.96355e112 | −0.222093 | ||||||||
\(276\) | −4.31945e113 | −1.35880 | ||||||||
\(277\) | 3.61986e113 | 0.962460 | 0.481230 | − | 0.876595i | \(-0.340190\pi\) | ||||
0.481230 | + | 0.876595i | \(0.340190\pi\) | |||||||
\(278\) | 3.33659e113 | 0.750274 | ||||||||
\(279\) | 3.89618e113 | 0.741385 | ||||||||
\(280\) | −1.94009e113 | −0.312589 | ||||||||
\(281\) | 8.73104e113 | 1.19185 | 0.595926 | − | 0.803040i | \(-0.296785\pi\) | ||||
0.595926 | + | 0.803040i | \(0.296785\pi\) | |||||||
\(282\) | −6.40268e112 | −0.0740932 | ||||||||
\(283\) | 8.05802e113 | 0.790968 | 0.395484 | − | 0.918473i | \(-0.370577\pi\) | ||||
0.395484 | + | 0.918473i | \(0.370577\pi\) | |||||||
\(284\) | −1.01006e114 | −0.841481 | ||||||||
\(285\) | −1.25877e114 | −0.890555 | ||||||||
\(286\) | −1.94359e113 | −0.116838 | ||||||||
\(287\) | 3.07306e114 | 1.57059 | ||||||||
\(288\) | −2.34133e114 | −1.01792 | ||||||||
\(289\) | 9.72373e113 | 0.359818 | ||||||||
\(290\) | −9.29044e113 | −0.292772 | ||||||||
\(291\) | −1.16946e114 | −0.314023 | ||||||||
\(292\) | 3.24043e114 | 0.741822 | ||||||||
\(293\) | −7.90158e114 | −1.54301 | −0.771507 | − | 0.636221i | \(-0.780497\pi\) | ||||
−0.771507 | + | 0.636221i | \(0.780497\pi\) | |||||||
\(294\) | 5.45965e113 | 0.0909943 | ||||||||
\(295\) | −5.63346e113 | −0.0801773 | ||||||||
\(296\) | −7.40611e114 | −0.900587 | ||||||||
\(297\) | −5.29468e112 | −0.00550383 | ||||||||
\(298\) | −8.73764e113 | −0.0776852 | ||||||||
\(299\) | 1.51638e115 | 1.15371 | ||||||||
\(300\) | 1.37498e115 | 0.895689 | ||||||||
\(301\) | 2.08840e114 | 0.116539 | ||||||||
\(302\) | −1.51296e114 | −0.0723610 | ||||||||
\(303\) | 4.76958e115 | 1.95613 | ||||||||
\(304\) | −1.38709e115 | −0.488071 | ||||||||
\(305\) | −2.22810e115 | −0.672964 | ||||||||
\(306\) | 2.25031e115 | 0.583709 | ||||||||
\(307\) | −7.39463e115 | −1.64809 | −0.824047 | − | 0.566521i | \(-0.808289\pi\) | ||||
−0.824047 | + | 0.566521i | \(0.808289\pi\) | |||||||
\(308\) | 9.37157e114 | 0.179558 | ||||||||
\(309\) | −7.97399e115 | −1.31403 | ||||||||
\(310\) | −1.01970e115 | −0.144595 | ||||||||
\(311\) | 6.85748e115 | 0.837156 | 0.418578 | − | 0.908181i | \(-0.362529\pi\) | ||||
0.418578 | + | 0.908181i | \(0.362529\pi\) | |||||||
\(312\) | 1.05229e116 | 1.10649 | ||||||||
\(313\) | −1.86223e116 | −1.68741 | −0.843706 | − | 0.536805i | \(-0.819631\pi\) | ||||
−0.843706 | + | 0.536805i | \(0.819631\pi\) | |||||||
\(314\) | −3.62762e115 | −0.283396 | ||||||||
\(315\) | −5.16163e115 | −0.347813 | ||||||||
\(316\) | 2.45981e116 | 1.43038 | ||||||||
\(317\) | −6.89517e115 | −0.346170 | −0.173085 | − | 0.984907i | \(-0.555374\pi\) | ||||
−0.173085 | + | 0.984907i | \(0.555374\pi\) | |||||||
\(318\) | 1.51769e115 | 0.0658146 | ||||||||
\(319\) | 1.05383e116 | 0.394913 | ||||||||
\(320\) | 2.72292e115 | 0.0882188 | ||||||||
\(321\) | −2.89748e116 | −0.811964 | ||||||||
\(322\) | 2.54617e116 | 0.617433 | ||||||||
\(323\) | 9.28943e116 | 1.95017 | ||||||||
\(324\) | 4.13980e116 | 0.752724 | ||||||||
\(325\) | −4.82697e116 | −0.760498 | ||||||||
\(326\) | −5.44342e116 | −0.743453 | ||||||||
\(327\) | −4.84139e116 | −0.573455 | ||||||||
\(328\) | −1.44790e117 | −1.48801 | ||||||||
\(329\) | −1.08380e116 | −0.0966806 | ||||||||
\(330\) | −9.05242e115 | −0.0701240 | ||||||||
\(331\) | 2.05417e117 | 1.38240 | 0.691201 | − | 0.722663i | \(-0.257082\pi\) | ||||
0.691201 | + | 0.722663i | \(0.257082\pi\) | |||||||
\(332\) | 2.98766e116 | 0.174747 | ||||||||
\(333\) | −1.97041e117 | −1.00207 | ||||||||
\(334\) | 9.85131e116 | 0.435796 | ||||||||
\(335\) | −9.07631e116 | −0.349402 | ||||||||
\(336\) | −1.14627e117 | −0.384158 | ||||||||
\(337\) | −2.14639e117 | −0.626496 | −0.313248 | − | 0.949671i | \(-0.601417\pi\) | ||||
−0.313248 | + | 0.949671i | \(0.601417\pi\) | |||||||
\(338\) | 4.25223e116 | 0.108141 | ||||||||
\(339\) | 3.79329e117 | 0.840872 | ||||||||
\(340\) | 1.69123e117 | 0.326913 | ||||||||
\(341\) | 1.15665e117 | 0.195040 | ||||||||
\(342\) | 5.68855e117 | 0.837119 | ||||||||
\(343\) | 8.19632e117 | 1.05303 | ||||||||
\(344\) | −9.83973e116 | −0.110412 | ||||||||
\(345\) | 7.06264e117 | 0.692435 | ||||||||
\(346\) | −9.97350e117 | −0.854691 | ||||||||
\(347\) | −2.55511e117 | −0.191465 | −0.0957323 | − | 0.995407i | \(-0.530519\pi\) | ||||
−0.0957323 | + | 0.995407i | \(0.530519\pi\) | |||||||
\(348\) | −2.42974e118 | −1.59267 | ||||||||
\(349\) | −7.79802e117 | −0.447303 | −0.223652 | − | 0.974669i | \(-0.571798\pi\) | ||||
−0.223652 | + | 0.974669i | \(0.571798\pi\) | |||||||
\(350\) | −8.10504e117 | −0.406997 | ||||||||
\(351\) | −4.28558e116 | −0.0188464 | ||||||||
\(352\) | −6.95067e117 | −0.267789 | ||||||||
\(353\) | 4.16579e117 | 0.140661 | 0.0703305 | − | 0.997524i | \(-0.477595\pi\) | ||||
0.0703305 | + | 0.997524i | \(0.477595\pi\) | |||||||
\(354\) | 5.13063e117 | 0.151887 | ||||||||
\(355\) | 1.65153e118 | 0.428812 | ||||||||
\(356\) | −1.96431e117 | −0.0447492 | ||||||||
\(357\) | 7.67663e118 | 1.53497 | ||||||||
\(358\) | −5.34505e118 | −0.938406 | ||||||||
\(359\) | −4.71590e118 | −0.727232 | −0.363616 | − | 0.931549i | \(-0.618458\pi\) | ||||
−0.363616 | + | 0.931549i | \(0.618458\pi\) | |||||||
\(360\) | 2.43196e118 | 0.329526 | ||||||||
\(361\) | 1.50865e119 | 1.79681 | ||||||||
\(362\) | −1.72784e118 | −0.180948 | ||||||||
\(363\) | −1.42675e119 | −1.31428 | ||||||||
\(364\) | 7.58547e118 | 0.614848 | ||||||||
\(365\) | −5.29836e118 | −0.378027 | ||||||||
\(366\) | 2.02922e119 | 1.27485 | ||||||||
\(367\) | −1.13188e118 | −0.0626368 | −0.0313184 | − | 0.999509i | \(-0.509971\pi\) | ||||
−0.0313184 | + | 0.999509i | \(0.509971\pi\) | |||||||
\(368\) | 7.78261e118 | 0.379491 | ||||||||
\(369\) | −3.85216e119 | −1.65569 | ||||||||
\(370\) | 5.15689e118 | 0.195437 | ||||||||
\(371\) | 2.56904e118 | 0.0858783 | ||||||||
\(372\) | −2.66682e119 | −0.786588 | ||||||||
\(373\) | −2.27689e119 | −0.592765 | −0.296382 | − | 0.955069i | \(-0.595780\pi\) | ||||
−0.296382 | + | 0.955069i | \(0.595780\pi\) | |||||||
\(374\) | 6.68047e118 | 0.153560 | ||||||||
\(375\) | −4.87111e119 | −0.988949 | ||||||||
\(376\) | 5.10643e118 | 0.0915973 | ||||||||
\(377\) | 8.52979e119 | 1.35228 | ||||||||
\(378\) | −7.19598e117 | −0.0100860 | ||||||||
\(379\) | 9.67039e118 | 0.119873 | 0.0599364 | − | 0.998202i | \(-0.480910\pi\) | ||||
0.0599364 | + | 0.998202i | \(0.480910\pi\) | |||||||
\(380\) | 4.27524e119 | 0.468839 | ||||||||
\(381\) | 7.15172e119 | 0.694063 | ||||||||
\(382\) | 2.35757e119 | 0.202544 | ||||||||
\(383\) | −1.71702e120 | −1.30627 | −0.653135 | − | 0.757241i | \(-0.726547\pi\) | ||||
−0.653135 | + | 0.757241i | \(0.726547\pi\) | |||||||
\(384\) | 1.91266e120 | 1.28895 | ||||||||
\(385\) | −1.53233e119 | −0.0915013 | ||||||||
\(386\) | −1.84449e119 | −0.0976265 | ||||||||
\(387\) | −2.61787e119 | −0.122854 | ||||||||
\(388\) | 3.97190e119 | 0.165319 | ||||||||
\(389\) | 2.27940e120 | 0.841715 | 0.420857 | − | 0.907127i | \(-0.361729\pi\) | ||||
0.420857 | + | 0.907127i | \(0.361729\pi\) | |||||||
\(390\) | −7.32714e119 | −0.240121 | ||||||||
\(391\) | −5.21206e120 | −1.51632 | ||||||||
\(392\) | −4.35432e119 | −0.112491 | ||||||||
\(393\) | −1.53680e119 | −0.0352666 | ||||||||
\(394\) | −3.22243e120 | −0.657067 | ||||||||
\(395\) | −4.02198e120 | −0.728911 | ||||||||
\(396\) | −1.17475e120 | −0.189287 | ||||||||
\(397\) | −2.02832e120 | −0.290655 | −0.145327 | − | 0.989384i | \(-0.546424\pi\) | ||||
−0.145327 | + | 0.989384i | \(0.546424\pi\) | |||||||
\(398\) | −2.22611e120 | −0.283781 | ||||||||
\(399\) | 1.94057e121 | 2.20135 | ||||||||
\(400\) | −2.47738e120 | −0.250151 | ||||||||
\(401\) | 1.22235e121 | 1.09896 | 0.549480 | − | 0.835507i | \(-0.314826\pi\) | ||||
0.549480 | + | 0.835507i | \(0.314826\pi\) | |||||||
\(402\) | 8.26618e120 | 0.661902 | ||||||||
\(403\) | 9.36210e120 | 0.667865 | ||||||||
\(404\) | −1.61992e121 | −1.02982 | ||||||||
\(405\) | −6.76890e120 | −0.383583 | ||||||||
\(406\) | 1.43225e121 | 0.723699 | ||||||||
\(407\) | −5.84951e120 | −0.263621 | ||||||||
\(408\) | −3.61692e121 | −1.45426 | ||||||||
\(409\) | −1.63408e121 | −0.586326 | −0.293163 | − | 0.956063i | \(-0.594708\pi\) | ||||
−0.293163 | + | 0.956063i | \(0.594708\pi\) | |||||||
\(410\) | 1.00818e121 | 0.322914 | ||||||||
\(411\) | 4.13491e121 | 1.18255 | ||||||||
\(412\) | 2.70825e121 | 0.691781 | ||||||||
\(413\) | 8.68476e120 | 0.198189 | ||||||||
\(414\) | −3.19170e121 | −0.650887 | ||||||||
\(415\) | −4.88506e120 | −0.0890498 | ||||||||
\(416\) | −5.62596e121 | −0.916973 | ||||||||
\(417\) | −1.42681e122 | −2.07988 | ||||||||
\(418\) | 1.68875e121 | 0.220226 | ||||||||
\(419\) | 6.80062e121 | 0.793590 | 0.396795 | − | 0.917907i | \(-0.370122\pi\) | ||||
0.396795 | + | 0.917907i | \(0.370122\pi\) | |||||||
\(420\) | 3.53299e121 | 0.369020 | ||||||||
\(421\) | 9.07457e120 | 0.0848611 | 0.0424306 | − | 0.999099i | \(-0.486490\pi\) | ||||
0.0424306 | + | 0.999099i | \(0.486490\pi\) | |||||||
\(422\) | 5.51259e121 | 0.461665 | ||||||||
\(423\) | 1.35857e121 | 0.101919 | ||||||||
\(424\) | −1.21043e121 | −0.0813629 | ||||||||
\(425\) | 1.65912e122 | 0.999520 | ||||||||
\(426\) | −1.50412e122 | −0.812335 | ||||||||
\(427\) | 3.43492e122 | 1.66349 | ||||||||
\(428\) | 9.84089e121 | 0.427464 | ||||||||
\(429\) | 8.31126e121 | 0.323894 | ||||||||
\(430\) | 6.85142e120 | 0.0239606 | ||||||||
\(431\) | −6.00864e122 | −1.88618 | −0.943090 | − | 0.332537i | \(-0.892096\pi\) | ||||
−0.943090 | + | 0.332537i | \(0.892096\pi\) | |||||||
\(432\) | −2.19952e120 | −0.00619916 | ||||||||
\(433\) | −4.16397e122 | −1.05395 | −0.526976 | − | 0.849880i | \(-0.676674\pi\) | ||||
−0.526976 | + | 0.849880i | \(0.676674\pi\) | |||||||
\(434\) | 1.57200e122 | 0.357422 | ||||||||
\(435\) | 3.97281e122 | 0.811611 | ||||||||
\(436\) | 1.64431e122 | 0.301899 | ||||||||
\(437\) | −1.31755e123 | −2.17461 | ||||||||
\(438\) | 4.82544e122 | 0.716128 | ||||||||
\(439\) | −3.92818e122 | −0.524314 | −0.262157 | − | 0.965025i | \(-0.584434\pi\) | ||||
−0.262157 | + | 0.965025i | \(0.584434\pi\) | |||||||
\(440\) | 7.21971e121 | 0.0866903 | ||||||||
\(441\) | −1.15847e122 | −0.125167 | ||||||||
\(442\) | 5.40725e122 | 0.525825 | ||||||||
\(443\) | −4.72253e122 | −0.413429 | −0.206715 | − | 0.978401i | \(-0.566277\pi\) | ||||
−0.206715 | + | 0.978401i | \(0.566277\pi\) | |||||||
\(444\) | 1.34869e123 | 1.06317 | ||||||||
\(445\) | 3.21180e121 | 0.0228039 | ||||||||
\(446\) | −2.46045e122 | −0.157378 | ||||||||
\(447\) | 3.73643e122 | 0.215356 | ||||||||
\(448\) | −4.19776e122 | −0.218067 | ||||||||
\(449\) | 3.72064e123 | 1.74246 | 0.871230 | − | 0.490875i | \(-0.163323\pi\) | ||||
0.871230 | + | 0.490875i | \(0.163323\pi\) | |||||||
\(450\) | 1.01599e123 | 0.429049 | ||||||||
\(451\) | −1.14359e123 | −0.435571 | ||||||||
\(452\) | −1.28834e123 | −0.442682 | ||||||||
\(453\) | 6.46978e122 | 0.200596 | ||||||||
\(454\) | 4.84648e122 | 0.135622 | ||||||||
\(455\) | −1.24028e123 | −0.313322 | ||||||||
\(456\) | −9.14319e123 | −2.08561 | ||||||||
\(457\) | 1.39159e123 | 0.286687 | 0.143344 | − | 0.989673i | \(-0.454215\pi\) | ||||
0.143344 | + | 0.989673i | \(0.454215\pi\) | |||||||
\(458\) | −1.34706e123 | −0.250693 | ||||||||
\(459\) | 1.47303e122 | 0.0247698 | ||||||||
\(460\) | −2.39873e123 | −0.364537 | ||||||||
\(461\) | 6.88216e123 | 0.945435 | 0.472718 | − | 0.881214i | \(-0.343273\pi\) | ||||
0.472718 | + | 0.881214i | \(0.343273\pi\) | |||||||
\(462\) | 1.39556e123 | 0.173339 | ||||||||
\(463\) | −4.77146e123 | −0.535964 | −0.267982 | − | 0.963424i | \(-0.586357\pi\) | ||||
−0.267982 | + | 0.963424i | \(0.586357\pi\) | |||||||
\(464\) | 4.37780e123 | 0.444805 | ||||||||
\(465\) | 4.36047e123 | 0.400840 | ||||||||
\(466\) | 3.96439e123 | 0.329785 | ||||||||
\(467\) | −1.67559e124 | −1.26163 | −0.630815 | − | 0.775934i | \(-0.717279\pi\) | ||||
−0.630815 | + | 0.775934i | \(0.717279\pi\) | |||||||
\(468\) | −9.50859e123 | −0.648163 | ||||||||
\(469\) | 1.39924e124 | 0.863683 | ||||||||
\(470\) | −3.55561e122 | −0.0198776 | ||||||||
\(471\) | 1.55126e124 | 0.785618 | ||||||||
\(472\) | −4.09191e123 | −0.187769 | ||||||||
\(473\) | −7.77164e122 | −0.0323199 | ||||||||
\(474\) | 3.66299e124 | 1.38084 | ||||||||
\(475\) | 4.19407e124 | 1.43345 | ||||||||
\(476\) | −2.60726e124 | −0.808093 | ||||||||
\(477\) | −3.22036e123 | −0.0905315 | ||||||||
\(478\) | −1.78701e124 | −0.455753 | ||||||||
\(479\) | −1.44179e124 | −0.333656 | −0.166828 | − | 0.985986i | \(-0.553352\pi\) | ||||
−0.166828 | + | 0.985986i | \(0.553352\pi\) | |||||||
\(480\) | −2.62033e124 | −0.550350 | ||||||||
\(481\) | −4.73467e124 | −0.902700 | ||||||||
\(482\) | −3.46831e124 | −0.600386 | ||||||||
\(483\) | −1.08880e125 | −1.71162 | ||||||||
\(484\) | 4.84575e124 | 0.691914 | ||||||||
\(485\) | −6.49438e123 | −0.0842455 | ||||||||
\(486\) | 6.07314e124 | 0.715858 | ||||||||
\(487\) | 1.20536e125 | 1.29128 | 0.645641 | − | 0.763641i | \(-0.276590\pi\) | ||||
0.645641 | + | 0.763641i | \(0.276590\pi\) | |||||||
\(488\) | −1.61840e125 | −1.57603 | ||||||||
\(489\) | 2.32774e125 | 2.06097 | ||||||||
\(490\) | 3.03192e123 | 0.0244118 | ||||||||
\(491\) | −9.38769e124 | −0.687495 | −0.343747 | − | 0.939062i | \(-0.611696\pi\) | ||||
−0.343747 | + | 0.939062i | \(0.611696\pi\) | |||||||
\(492\) | 2.63669e125 | 1.75664 | ||||||||
\(493\) | −2.93184e125 | −1.77729 | ||||||||
\(494\) | 1.36690e125 | 0.754106 | ||||||||
\(495\) | 1.92081e124 | 0.0964591 | ||||||||
\(496\) | 4.80497e124 | 0.219681 | ||||||||
\(497\) | −2.54606e125 | −1.05998 | ||||||||
\(498\) | 4.44903e124 | 0.168694 | ||||||||
\(499\) | 5.48346e125 | 1.89400 | 0.946999 | − | 0.321237i | \(-0.104099\pi\) | ||||
0.946999 | + | 0.321237i | \(0.104099\pi\) | |||||||
\(500\) | 1.65440e125 | 0.520638 | ||||||||
\(501\) | −4.21266e125 | −1.20810 | ||||||||
\(502\) | 1.01230e125 | 0.264597 | ||||||||
\(503\) | −6.31756e125 | −1.50535 | −0.752676 | − | 0.658391i | \(-0.771237\pi\) | ||||
−0.752676 | + | 0.658391i | \(0.771237\pi\) | |||||||
\(504\) | −3.74920e125 | −0.814551 | ||||||||
\(505\) | 2.64870e125 | 0.524788 | ||||||||
\(506\) | −9.47514e124 | −0.171233 | ||||||||
\(507\) | −1.81835e125 | −0.299784 | ||||||||
\(508\) | −2.42898e125 | −0.365394 | ||||||||
\(509\) | −1.89152e125 | −0.259677 | −0.129838 | − | 0.991535i | \(-0.541446\pi\) | ||||
−0.129838 | + | 0.991535i | \(0.541446\pi\) | |||||||
\(510\) | 2.51847e125 | 0.315590 | ||||||||
\(511\) | 8.16815e125 | 0.934441 | ||||||||
\(512\) | −5.36051e125 | −0.559954 | ||||||||
\(513\) | 3.72366e124 | 0.0355233 | ||||||||
\(514\) | 1.08827e126 | 0.948314 | ||||||||
\(515\) | −4.42821e125 | −0.352527 | ||||||||
\(516\) | 1.79186e125 | 0.130344 | ||||||||
\(517\) | 4.03317e124 | 0.0268125 | ||||||||
\(518\) | −7.95005e125 | −0.483099 | ||||||||
\(519\) | 4.26491e126 | 2.36934 | ||||||||
\(520\) | 5.84373e125 | 0.296848 | ||||||||
\(521\) | −2.43131e126 | −1.12950 | −0.564750 | − | 0.825262i | \(-0.691027\pi\) | ||||
−0.564750 | + | 0.825262i | \(0.691027\pi\) | |||||||
\(522\) | −1.79536e126 | −0.762912 | ||||||||
\(523\) | −3.48691e125 | −0.135554 | −0.0677770 | − | 0.997700i | \(-0.521591\pi\) | ||||
−0.0677770 | + | 0.997700i | \(0.521591\pi\) | |||||||
\(524\) | 5.21953e124 | 0.0185663 | ||||||||
\(525\) | 3.46591e126 | 1.12826 | ||||||||
\(526\) | −1.41723e126 | −0.422281 | ||||||||
\(527\) | −3.21792e126 | −0.877772 | ||||||||
\(528\) | 4.26564e125 | 0.106539 | ||||||||
\(529\) | 3.02036e126 | 0.690829 | ||||||||
\(530\) | 8.42822e124 | 0.0176566 | ||||||||
\(531\) | −1.08866e126 | −0.208928 | ||||||||
\(532\) | −6.59088e126 | −1.15892 | ||||||||
\(533\) | −9.25632e126 | −1.49150 | ||||||||
\(534\) | −2.92513e125 | −0.0431993 | ||||||||
\(535\) | −1.60906e126 | −0.217832 | ||||||||
\(536\) | −6.59265e126 | −0.818272 | ||||||||
\(537\) | 2.28567e127 | 2.60141 | ||||||||
\(538\) | 3.30950e126 | 0.345451 | ||||||||
\(539\) | −3.43914e125 | −0.0329285 | ||||||||
\(540\) | 6.77927e124 | 0.00595488 | ||||||||
\(541\) | 1.30995e127 | 1.05580 | 0.527902 | − | 0.849305i | \(-0.322979\pi\) | ||||
0.527902 | + | 0.849305i | \(0.322979\pi\) | |||||||
\(542\) | −4.17947e126 | −0.309139 | ||||||||
\(543\) | 7.38865e126 | 0.501618 | ||||||||
\(544\) | 1.93374e127 | 1.20517 | ||||||||
\(545\) | −2.68858e126 | −0.153846 | ||||||||
\(546\) | 1.12958e127 | 0.593552 | ||||||||
\(547\) | −1.55998e127 | −0.752848 | −0.376424 | − | 0.926447i | \(-0.622846\pi\) | ||||
−0.376424 | + | 0.926447i | \(0.622846\pi\) | |||||||
\(548\) | −1.40436e127 | −0.622563 | ||||||||
\(549\) | −4.30577e127 | −1.75362 | ||||||||
\(550\) | 3.01615e126 | 0.112872 | ||||||||
\(551\) | −7.41138e127 | −2.54888 | ||||||||
\(552\) | 5.13001e127 | 1.62163 | ||||||||
\(553\) | 6.20043e127 | 1.80179 | ||||||||
\(554\) | −1.83080e127 | −0.489143 | ||||||||
\(555\) | −2.20521e127 | −0.541783 | ||||||||
\(556\) | 4.84595e127 | 1.09497 | ||||||||
\(557\) | −3.34419e127 | −0.695063 | −0.347531 | − | 0.937668i | \(-0.612980\pi\) | ||||
−0.347531 | + | 0.937668i | \(0.612980\pi\) | |||||||
\(558\) | −1.97055e127 | −0.376788 | ||||||||
\(559\) | −6.29046e126 | −0.110671 | ||||||||
\(560\) | −6.36559e126 | −0.103061 | ||||||||
\(561\) | −2.85673e127 | −0.425692 | ||||||||
\(562\) | −4.41585e127 | −0.605725 | ||||||||
\(563\) | 1.02212e128 | 1.29080 | 0.645402 | − | 0.763843i | \(-0.276690\pi\) | ||||
0.645402 | + | 0.763843i | \(0.276690\pi\) | |||||||
\(564\) | −9.29903e126 | −0.108133 | ||||||||
\(565\) | 2.10653e127 | 0.225588 | ||||||||
\(566\) | −4.07546e127 | −0.401987 | ||||||||
\(567\) | 1.04352e128 | 0.948174 | ||||||||
\(568\) | 1.19960e128 | 1.00424 | ||||||||
\(569\) | −7.09301e127 | −0.547155 | −0.273577 | − | 0.961850i | \(-0.588207\pi\) | ||||
−0.273577 | + | 0.961850i | \(0.588207\pi\) | |||||||
\(570\) | 6.36642e127 | 0.452600 | ||||||||
\(571\) | 1.97537e128 | 1.29440 | 0.647201 | − | 0.762319i | \(-0.275939\pi\) | ||||
0.647201 | + | 0.762319i | \(0.275939\pi\) | |||||||
\(572\) | −2.82280e127 | −0.170516 | ||||||||
\(573\) | −1.00815e128 | −0.561484 | ||||||||
\(574\) | −1.55424e128 | −0.798208 | ||||||||
\(575\) | −2.35318e128 | −1.11455 | ||||||||
\(576\) | 5.26201e127 | 0.229883 | ||||||||
\(577\) | −1.23481e128 | −0.497652 | −0.248826 | − | 0.968548i | \(-0.580045\pi\) | ||||
−0.248826 | + | 0.968548i | \(0.580045\pi\) | |||||||
\(578\) | −4.91792e127 | −0.182868 | ||||||||
\(579\) | 7.88750e127 | 0.270636 | ||||||||
\(580\) | −1.34931e128 | −0.427278 | ||||||||
\(581\) | 7.53099e127 | 0.220121 | ||||||||
\(582\) | 5.91470e127 | 0.159593 | ||||||||
\(583\) | −9.56023e126 | −0.0238166 | ||||||||
\(584\) | −3.84851e128 | −0.885309 | ||||||||
\(585\) | 1.55473e128 | 0.330299 | ||||||||
\(586\) | 3.99634e128 | 0.784194 | ||||||||
\(587\) | −1.66918e128 | −0.302574 | −0.151287 | − | 0.988490i | \(-0.548342\pi\) | ||||
−0.151287 | + | 0.988490i | \(0.548342\pi\) | |||||||
\(588\) | 7.92941e127 | 0.132799 | ||||||||
\(589\) | −8.13456e128 | −1.25885 | ||||||||
\(590\) | 2.84920e127 | 0.0407479 | ||||||||
\(591\) | 1.37799e129 | 1.82150 | ||||||||
\(592\) | −2.43001e128 | −0.296926 | ||||||||
\(593\) | 1.16393e129 | 1.31487 | 0.657434 | − | 0.753512i | \(-0.271642\pi\) | ||||
0.657434 | + | 0.753512i | \(0.271642\pi\) | |||||||
\(594\) | 2.67786e126 | 0.00279717 | ||||||||
\(595\) | 4.26308e128 | 0.411798 | ||||||||
\(596\) | −1.26902e128 | −0.113375 | ||||||||
\(597\) | 9.51938e128 | 0.786687 | ||||||||
\(598\) | −7.66930e128 | −0.586342 | ||||||||
\(599\) | 1.69191e127 | 0.0119682 | 0.00598412 | − | 0.999982i | \(-0.498095\pi\) | ||||
0.00598412 | + | 0.999982i | \(0.498095\pi\) | |||||||
\(600\) | −1.63300e129 | −1.06894 | ||||||||
\(601\) | −5.01379e128 | −0.303741 | −0.151870 | − | 0.988400i | \(-0.548530\pi\) | ||||
−0.151870 | + | 0.988400i | \(0.548530\pi\) | |||||||
\(602\) | −1.05624e128 | −0.0592278 | ||||||||
\(603\) | −1.75398e129 | −0.910480 | ||||||||
\(604\) | −2.19737e128 | −0.105605 | ||||||||
\(605\) | −7.92319e128 | −0.352594 | ||||||||
\(606\) | −2.41228e129 | −0.994149 | ||||||||
\(607\) | 1.33417e129 | 0.509258 | 0.254629 | − | 0.967039i | \(-0.418047\pi\) | ||||
0.254629 | + | 0.967039i | \(0.418047\pi\) | |||||||
\(608\) | 4.88829e129 | 1.72839 | ||||||||
\(609\) | −6.12464e129 | −2.00621 | ||||||||
\(610\) | 1.12689e129 | 0.342015 | ||||||||
\(611\) | 3.26450e128 | 0.0918122 | ||||||||
\(612\) | 3.26827e129 | 0.851878 | ||||||||
\(613\) | 2.92658e129 | 0.707046 | 0.353523 | − | 0.935426i | \(-0.384984\pi\) | ||||
0.353523 | + | 0.935426i | \(0.384984\pi\) | |||||||
\(614\) | 3.73994e129 | 0.837598 | ||||||||
\(615\) | −4.31120e129 | −0.895170 | ||||||||
\(616\) | −1.11302e129 | −0.214289 | ||||||||
\(617\) | 6.96398e129 | 1.24336 | 0.621681 | − | 0.783270i | \(-0.286450\pi\) | ||||
0.621681 | + | 0.783270i | \(0.286450\pi\) | |||||||
\(618\) | 4.03296e129 | 0.667821 | ||||||||
\(619\) | −8.69061e129 | −1.33486 | −0.667429 | − | 0.744673i | \(-0.732605\pi\) | ||||
−0.667429 | + | 0.744673i | \(0.732605\pi\) | |||||||
\(620\) | −1.48097e129 | −0.211025 | ||||||||
\(621\) | −2.08925e128 | −0.0276205 | ||||||||
\(622\) | −3.46827e129 | −0.425461 | ||||||||
\(623\) | −4.95144e128 | −0.0563686 | ||||||||
\(624\) | 3.45266e129 | 0.364814 | ||||||||
\(625\) | 6.03412e129 | 0.591825 | ||||||||
\(626\) | 9.41849e129 | 0.857580 | ||||||||
\(627\) | −7.22150e129 | −0.610502 | ||||||||
\(628\) | −5.26863e129 | −0.413594 | ||||||||
\(629\) | 1.62739e130 | 1.18642 | ||||||||
\(630\) | 2.61057e129 | 0.176766 | ||||||||
\(631\) | −1.68043e130 | −1.05695 | −0.528475 | − | 0.848949i | \(-0.677236\pi\) | ||||
−0.528475 | + | 0.848949i | \(0.677236\pi\) | |||||||
\(632\) | −2.92140e130 | −1.70705 | ||||||||
\(633\) | −2.35732e130 | −1.27981 | ||||||||
\(634\) | 3.48733e129 | 0.175931 | ||||||||
\(635\) | 3.97158e129 | 0.186202 | ||||||||
\(636\) | 2.20424e129 | 0.0960513 | ||||||||
\(637\) | −2.78368e129 | −0.112755 | ||||||||
\(638\) | −5.32987e129 | −0.200704 | ||||||||
\(639\) | 3.19155e130 | 1.11741 | ||||||||
\(640\) | 1.06216e130 | 0.345797 | ||||||||
\(641\) | 1.12855e130 | 0.341683 | 0.170841 | − | 0.985299i | \(-0.445351\pi\) | ||||
0.170841 | + | 0.985299i | \(0.445351\pi\) | |||||||
\(642\) | 1.46544e130 | 0.412658 | ||||||||
\(643\) | 1.78740e130 | 0.468178 | 0.234089 | − | 0.972215i | \(-0.424789\pi\) | ||||
0.234089 | + | 0.972215i | \(0.424789\pi\) | |||||||
\(644\) | 3.69797e130 | 0.901095 | ||||||||
\(645\) | −2.92983e129 | −0.0664225 | ||||||||
\(646\) | −4.69827e130 | −0.991118 | ||||||||
\(647\) | 7.40078e130 | 1.45288 | 0.726438 | − | 0.687232i | \(-0.241175\pi\) | ||||
0.726438 | + | 0.687232i | \(0.241175\pi\) | |||||||
\(648\) | −4.91664e130 | −0.898320 | ||||||||
\(649\) | −3.23189e129 | −0.0549639 | ||||||||
\(650\) | 2.44131e130 | 0.386502 | ||||||||
\(651\) | −6.72226e130 | −0.990830 | ||||||||
\(652\) | −7.90584e130 | −1.08501 | ||||||||
\(653\) | 8.19216e130 | 1.04697 | 0.523487 | − | 0.852034i | \(-0.324631\pi\) | ||||
0.523487 | + | 0.852034i | \(0.324631\pi\) | |||||||
\(654\) | 2.44860e130 | 0.291442 | ||||||||
\(655\) | −8.53434e128 | −0.00946127 | ||||||||
\(656\) | −4.75069e130 | −0.490600 | ||||||||
\(657\) | −1.02390e131 | −0.985072 | ||||||||
\(658\) | 5.48147e129 | 0.0491352 | ||||||||
\(659\) | 1.38301e131 | 1.15519 | 0.577597 | − | 0.816322i | \(-0.303991\pi\) | ||||
0.577597 | + | 0.816322i | \(0.303991\pi\) | |||||||
\(660\) | −1.31474e130 | −0.102340 | ||||||||
\(661\) | −1.17338e131 | −0.851279 | −0.425640 | − | 0.904893i | \(-0.639951\pi\) | ||||
−0.425640 | + | 0.904893i | \(0.639951\pi\) | |||||||
\(662\) | −1.03892e131 | −0.702567 | ||||||||
\(663\) | −2.31227e131 | −1.45767 | ||||||||
\(664\) | −3.54830e130 | −0.208547 | ||||||||
\(665\) | 1.07766e131 | 0.590576 | ||||||||
\(666\) | 9.96561e130 | 0.509275 | ||||||||
\(667\) | 4.15834e131 | 1.98184 | ||||||||
\(668\) | 1.43077e131 | 0.636010 | ||||||||
\(669\) | 1.05215e131 | 0.436276 | ||||||||
\(670\) | 4.59047e130 | 0.177574 | ||||||||
\(671\) | −1.27825e131 | −0.461336 | ||||||||
\(672\) | 4.03960e131 | 1.36040 | ||||||||
\(673\) | −5.22348e131 | −1.64157 | −0.820786 | − | 0.571236i | \(-0.806464\pi\) | ||||
−0.820786 | + | 0.571236i | \(0.806464\pi\) | |||||||
\(674\) | 1.08557e131 | 0.318399 | ||||||||
\(675\) | 6.65055e129 | 0.0182067 | ||||||||
\(676\) | 6.17578e130 | 0.157823 | ||||||||
\(677\) | −1.57989e131 | −0.376925 | −0.188462 | − | 0.982080i | \(-0.560350\pi\) | ||||
−0.188462 | + | 0.982080i | \(0.560350\pi\) | |||||||
\(678\) | −1.91851e131 | −0.427350 | ||||||||
\(679\) | 1.00120e131 | 0.208245 | ||||||||
\(680\) | −2.00859e131 | −0.390146 | ||||||||
\(681\) | −2.07247e131 | −0.375965 | ||||||||
\(682\) | −5.84994e130 | −0.0991238 | ||||||||
\(683\) | −7.37705e131 | −1.16767 | −0.583834 | − | 0.811873i | \(-0.698448\pi\) | ||||
−0.583834 | + | 0.811873i | \(0.698448\pi\) | |||||||
\(684\) | 8.26184e131 | 1.22171 | ||||||||
\(685\) | 2.29625e131 | 0.317254 | ||||||||
\(686\) | −4.14541e131 | −0.535175 | ||||||||
\(687\) | 5.76034e131 | 0.694961 | ||||||||
\(688\) | −3.22850e130 | −0.0364031 | ||||||||
\(689\) | −7.73817e130 | −0.0815538 | ||||||||
\(690\) | −3.57203e131 | −0.351911 | ||||||||
\(691\) | −3.20174e131 | −0.294888 | −0.147444 | − | 0.989070i | \(-0.547105\pi\) | ||||
−0.147444 | + | 0.989070i | \(0.547105\pi\) | |||||||
\(692\) | −1.44852e132 | −1.24735 | ||||||||
\(693\) | −2.96120e131 | −0.238436 | ||||||||
\(694\) | 1.29228e131 | 0.0973065 | ||||||||
\(695\) | −7.92351e131 | −0.557987 | ||||||||
\(696\) | 2.88569e132 | 1.90073 | ||||||||
\(697\) | 3.18156e132 | 1.96027 | ||||||||
\(698\) | 3.94396e131 | 0.227329 | ||||||||
\(699\) | −1.69527e132 | −0.914218 | ||||||||
\(700\) | −1.17715e132 | −0.593980 | ||||||||
\(701\) | 7.57694e131 | 0.357772 | 0.178886 | − | 0.983870i | \(-0.442751\pi\) | ||||
0.178886 | + | 0.983870i | \(0.442751\pi\) | |||||||
\(702\) | 2.16749e130 | 0.00957816 | ||||||||
\(703\) | 4.11387e132 | 1.70148 | ||||||||
\(704\) | 1.56212e131 | 0.0604766 | ||||||||
\(705\) | 1.52047e131 | 0.0551039 | ||||||||
\(706\) | −2.10691e131 | −0.0714870 | ||||||||
\(707\) | −4.08334e132 | −1.29722 | ||||||||
\(708\) | 7.45155e131 | 0.221667 | ||||||||
\(709\) | −2.69771e132 | −0.751529 | −0.375764 | − | 0.926715i | \(-0.622620\pi\) | ||||
−0.375764 | + | 0.926715i | \(0.622620\pi\) | |||||||
\(710\) | −8.35284e131 | −0.217932 | ||||||||
\(711\) | −7.77241e132 | −1.89941 | ||||||||
\(712\) | 2.33292e131 | 0.0534048 | ||||||||
\(713\) | 4.56409e132 | 0.978793 | ||||||||
\(714\) | −3.88257e132 | −0.780103 | ||||||||
\(715\) | 4.61551e131 | 0.0868937 | ||||||||
\(716\) | −7.76296e132 | −1.36953 | ||||||||
\(717\) | 7.64168e132 | 1.26342 | ||||||||
\(718\) | 2.38514e132 | 0.369595 | ||||||||
\(719\) | 4.75148e132 | 0.690137 | 0.345069 | − | 0.938577i | \(-0.387856\pi\) | ||||
0.345069 | + | 0.938577i | \(0.387856\pi\) | |||||||
\(720\) | 7.97945e131 | 0.108645 | ||||||||
\(721\) | 6.82670e132 | 0.871407 | ||||||||
\(722\) | −7.63019e132 | −0.913179 | ||||||||
\(723\) | 1.48313e133 | 1.66437 | ||||||||
\(724\) | −2.50945e132 | −0.264080 | ||||||||
\(725\) | −1.32369e133 | −1.30638 | ||||||||
\(726\) | 7.21599e132 | 0.667948 | ||||||||
\(727\) | 1.00321e133 | 0.871051 | 0.435526 | − | 0.900176i | \(-0.356563\pi\) | ||||
0.435526 | + | 0.900176i | \(0.356563\pi\) | |||||||
\(728\) | −9.00891e132 | −0.733775 | ||||||||
\(729\) | −1.26892e133 | −0.969623 | ||||||||
\(730\) | 2.67972e132 | 0.192122 | ||||||||
\(731\) | 2.16214e132 | 0.145454 | ||||||||
\(732\) | 2.94717e133 | 1.86055 | ||||||||
\(733\) | 2.91877e132 | 0.172928 | 0.0864640 | − | 0.996255i | \(-0.472443\pi\) | ||||
0.0864640 | + | 0.996255i | \(0.472443\pi\) | |||||||
\(734\) | 5.72467e131 | 0.0318334 | ||||||||
\(735\) | −1.29652e132 | −0.0676735 | ||||||||
\(736\) | −2.74270e133 | −1.34388 | ||||||||
\(737\) | −5.20703e132 | −0.239525 | ||||||||
\(738\) | 1.94829e133 | 0.841457 | ||||||||
\(739\) | −3.91770e133 | −1.58878 | −0.794391 | − | 0.607406i | \(-0.792210\pi\) | ||||
−0.794391 | + | 0.607406i | \(0.792210\pi\) | |||||||
\(740\) | 7.48968e132 | 0.285225 | ||||||||
\(741\) | −5.84517e133 | −2.09050 | ||||||||
\(742\) | −1.29933e132 | −0.0436452 | ||||||||
\(743\) | 6.95679e132 | 0.219497 | 0.109749 | − | 0.993959i | \(-0.464995\pi\) | ||||
0.109749 | + | 0.993959i | \(0.464995\pi\) | |||||||
\(744\) | 3.16726e133 | 0.938734 | ||||||||
\(745\) | 2.07496e132 | 0.0577753 | ||||||||
\(746\) | 1.15157e133 | 0.301256 | ||||||||
\(747\) | −9.44030e132 | −0.232048 | ||||||||
\(748\) | 9.70248e132 | 0.224108 | ||||||||
\(749\) | 2.48059e133 | 0.538457 | ||||||||
\(750\) | 2.46363e133 | 0.502605 | ||||||||
\(751\) | 4.33173e133 | 0.830624 | 0.415312 | − | 0.909679i | \(-0.363672\pi\) | ||||
0.415312 | + | 0.909679i | \(0.363672\pi\) | |||||||
\(752\) | 1.67546e132 | 0.0301999 | ||||||||
\(753\) | −4.32883e133 | −0.733506 | ||||||||
\(754\) | −4.31407e133 | −0.687257 | ||||||||
\(755\) | 3.59287e132 | 0.0538157 | ||||||||
\(756\) | −1.04512e132 | −0.0147198 | ||||||||
\(757\) | 7.50220e133 | 0.993643 | 0.496821 | − | 0.867853i | \(-0.334500\pi\) | ||||
0.496821 | + | 0.867853i | \(0.334500\pi\) | |||||||
\(758\) | −4.89094e132 | −0.0609220 | ||||||||
\(759\) | 4.05180e133 | 0.474685 | ||||||||
\(760\) | −5.07751e133 | −0.559524 | ||||||||
\(761\) | 3.42648e133 | 0.355191 | 0.177595 | − | 0.984104i | \(-0.443168\pi\) | ||||
0.177595 | + | 0.984104i | \(0.443168\pi\) | |||||||
\(762\) | −3.61708e133 | −0.352738 | ||||||||
\(763\) | 4.14481e133 | 0.380289 | ||||||||
\(764\) | 3.42406e133 | 0.295597 | ||||||||
\(765\) | −5.34389e133 | −0.434111 | ||||||||
\(766\) | 8.68409e133 | 0.663875 | ||||||||
\(767\) | −2.61593e133 | −0.188209 | ||||||||
\(768\) | −1.45295e134 | −0.983904 | ||||||||
\(769\) | 4.49538e132 | 0.0286544 | 0.0143272 | − | 0.999897i | \(-0.495439\pi\) | ||||
0.0143272 | + | 0.999897i | \(0.495439\pi\) | |||||||
\(770\) | 7.74996e132 | 0.0465030 | ||||||||
\(771\) | −4.65371e134 | −2.62888 | ||||||||
\(772\) | −2.67888e133 | −0.142478 | ||||||||
\(773\) | 6.94124e133 | 0.347609 | 0.173804 | − | 0.984780i | \(-0.444394\pi\) | ||||
0.173804 | + | 0.984780i | \(0.444394\pi\) | |||||||
\(774\) | 1.32403e133 | 0.0624370 | ||||||||
\(775\) | −1.45285e134 | −0.645197 | ||||||||
\(776\) | −4.71724e133 | −0.197296 | ||||||||
\(777\) | 3.39963e134 | 1.33923 | ||||||||
\(778\) | −1.15284e134 | −0.427778 | ||||||||
\(779\) | 8.04265e134 | 2.81130 | ||||||||
\(780\) | −1.06417e134 | −0.350438 | ||||||||
\(781\) | 9.47472e133 | 0.293963 | ||||||||
\(782\) | 2.63608e134 | 0.770626 | ||||||||
\(783\) | −1.17523e133 | −0.0323742 | ||||||||
\(784\) | −1.42869e133 | −0.0370886 | ||||||||
\(785\) | 8.61462e133 | 0.210764 | ||||||||
\(786\) | 7.77259e132 | 0.0179233 | ||||||||
\(787\) | −4.53355e134 | −0.985401 | −0.492700 | − | 0.870199i | \(-0.663990\pi\) | ||||
−0.492700 | + | 0.870199i | \(0.663990\pi\) | |||||||
\(788\) | −4.68015e134 | −0.958938 | ||||||||
\(789\) | 6.06040e134 | 1.17063 | ||||||||
\(790\) | 2.03417e134 | 0.370449 | ||||||||
\(791\) | −3.24751e134 | −0.557628 | ||||||||
\(792\) | 1.39520e134 | 0.225899 | ||||||||
\(793\) | −1.03463e135 | −1.57972 | ||||||||
\(794\) | 1.02585e134 | 0.147717 | ||||||||
\(795\) | −3.60411e133 | −0.0489471 | ||||||||
\(796\) | −3.23312e134 | −0.414157 | ||||||||
\(797\) | 8.18029e134 | 0.988455 | 0.494228 | − | 0.869333i | \(-0.335451\pi\) | ||||
0.494228 | + | 0.869333i | \(0.335451\pi\) | |||||||
\(798\) | −9.81471e134 | −1.11878 | ||||||||
\(799\) | −1.12207e134 | −0.120668 | ||||||||
\(800\) | 8.73061e134 | 0.885850 | ||||||||
\(801\) | 6.20676e133 | 0.0594228 | ||||||||
\(802\) | −6.18220e134 | −0.558516 | ||||||||
\(803\) | −3.03964e134 | −0.259149 | ||||||||
\(804\) | 1.20055e135 | 0.965994 | ||||||||
\(805\) | −6.04647e134 | −0.459191 | ||||||||
\(806\) | −4.73502e134 | −0.339424 | ||||||||
\(807\) | −1.41522e135 | −0.957646 | ||||||||
\(808\) | 1.92391e135 | 1.22901 | ||||||||
\(809\) | −7.01065e134 | −0.422816 | −0.211408 | − | 0.977398i | \(-0.567805\pi\) | ||||
−0.211408 | + | 0.977398i | \(0.567805\pi\) | |||||||
\(810\) | 3.42347e134 | 0.194945 | ||||||||
\(811\) | −2.27619e134 | −0.122388 | −0.0611940 | − | 0.998126i | \(-0.519491\pi\) | ||||
−0.0611940 | + | 0.998126i | \(0.519491\pi\) | |||||||
\(812\) | 2.08015e135 | 1.05618 | ||||||||
\(813\) | 1.78724e135 | 0.856983 | ||||||||
\(814\) | 2.95848e134 | 0.133978 | ||||||||
\(815\) | 1.29267e135 | 0.552914 | ||||||||
\(816\) | −1.18674e135 | −0.479473 | ||||||||
\(817\) | 5.46567e134 | 0.208602 | ||||||||
\(818\) | 8.26458e134 | 0.297984 | ||||||||
\(819\) | −2.39683e135 | −0.816462 | ||||||||
\(820\) | 1.46424e135 | 0.471268 | ||||||||
\(821\) | −2.38392e135 | −0.724996 | −0.362498 | − | 0.931985i | \(-0.618076\pi\) | ||||
−0.362498 | + | 0.931985i | \(0.618076\pi\) | |||||||
\(822\) | −2.09129e135 | −0.601000 | ||||||||
\(823\) | 4.89963e135 | 1.33067 | 0.665335 | − | 0.746545i | \(-0.268289\pi\) | ||||
0.665335 | + | 0.746545i | \(0.268289\pi\) | |||||||
\(824\) | −3.21647e135 | −0.825589 | ||||||||
\(825\) | −1.28978e135 | −0.312901 | ||||||||
\(826\) | −4.39244e134 | −0.100724 | ||||||||
\(827\) | −2.84246e135 | −0.616152 | −0.308076 | − | 0.951362i | \(-0.599685\pi\) | ||||
−0.308076 | + | 0.951362i | \(0.599685\pi\) | |||||||
\(828\) | −4.63551e135 | −0.949919 | ||||||||
\(829\) | −5.72864e135 | −1.10985 | −0.554927 | − | 0.831899i | \(-0.687254\pi\) | ||||
−0.554927 | + | 0.831899i | \(0.687254\pi\) | |||||||
\(830\) | 2.47069e134 | 0.0452571 | ||||||||
\(831\) | 7.82892e135 | 1.35598 | ||||||||
\(832\) | 1.26440e135 | 0.207086 | ||||||||
\(833\) | 9.56802e134 | 0.148194 | ||||||||
\(834\) | 7.21628e135 | 1.05704 | ||||||||
\(835\) | −2.33942e135 | −0.324106 | ||||||||
\(836\) | 2.45268e135 | 0.321403 | ||||||||
\(837\) | −1.28990e134 | −0.0159890 | ||||||||
\(838\) | −3.43951e135 | −0.403320 | ||||||||
\(839\) | −1.53346e136 | −1.70114 | −0.850571 | − | 0.525860i | \(-0.823743\pi\) | ||||
−0.850571 | + | 0.525860i | \(0.823743\pi\) | |||||||
\(840\) | −4.19597e135 | −0.440398 | ||||||||
\(841\) | 1.33215e136 | 1.32293 | ||||||||
\(842\) | −4.58960e134 | −0.0431283 | ||||||||
\(843\) | 1.88832e136 | 1.67917 | ||||||||
\(844\) | 8.00629e135 | 0.673764 | ||||||||
\(845\) | −1.00979e135 | −0.0804255 | ||||||||
\(846\) | −6.87117e134 | −0.0517975 | ||||||||
\(847\) | 1.22147e136 | 0.871573 | ||||||||
\(848\) | −3.97151e134 | −0.0268256 | ||||||||
\(849\) | 1.74276e136 | 1.11437 | ||||||||
\(850\) | −8.39122e135 | −0.507978 | ||||||||
\(851\) | −2.30819e136 | −1.32296 | ||||||||
\(852\) | −2.18453e136 | −1.18554 | ||||||||
\(853\) | 1.78771e136 | 0.918684 | 0.459342 | − | 0.888260i | \(-0.348085\pi\) | ||||
0.459342 | + | 0.888260i | \(0.348085\pi\) | |||||||
\(854\) | −1.73726e136 | −0.845423 | ||||||||
\(855\) | −1.35088e136 | −0.622575 | ||||||||
\(856\) | −1.16876e136 | −0.510146 | ||||||||
\(857\) | −1.68084e136 | −0.694894 | −0.347447 | − | 0.937700i | \(-0.612951\pi\) | ||||
−0.347447 | + | 0.937700i | \(0.612951\pi\) | |||||||
\(858\) | −4.20354e135 | −0.164610 | ||||||||
\(859\) | −4.56777e136 | −1.69442 | −0.847212 | − | 0.531255i | \(-0.821721\pi\) | ||||
−0.847212 | + | 0.531255i | \(0.821721\pi\) | |||||||
\(860\) | 9.95075e134 | 0.0349686 | ||||||||
\(861\) | 6.64631e136 | 2.21276 | ||||||||
\(862\) | 3.03896e136 | 0.958599 | ||||||||
\(863\) | −2.14397e136 | −0.640791 | −0.320395 | − | 0.947284i | \(-0.603816\pi\) | ||||
−0.320395 | + | 0.947284i | \(0.603816\pi\) | |||||||
\(864\) | 7.75139e134 | 0.0219528 | ||||||||
\(865\) | 2.36844e136 | 0.635643 | ||||||||
\(866\) | 2.10599e136 | 0.535641 | ||||||||
\(867\) | 2.10302e136 | 0.506938 | ||||||||
\(868\) | 2.28312e136 | 0.521629 | ||||||||
\(869\) | −2.30739e136 | −0.499690 | ||||||||
\(870\) | −2.00931e136 | −0.412478 | ||||||||
\(871\) | −4.21463e136 | −0.820192 | ||||||||
\(872\) | −1.95287e136 | −0.360294 | ||||||||
\(873\) | −1.25503e136 | −0.219529 | ||||||||
\(874\) | 6.66372e136 | 1.10518 | ||||||||
\(875\) | 4.17026e136 | 0.655825 | ||||||||
\(876\) | 7.00830e136 | 1.04513 | ||||||||
\(877\) | −4.90563e136 | −0.693767 | −0.346883 | − | 0.937908i | \(-0.612760\pi\) | ||||
−0.346883 | + | 0.937908i | \(0.612760\pi\) | |||||||
\(878\) | 1.98673e136 | 0.266468 | ||||||||
\(879\) | −1.70893e137 | −2.17391 | ||||||||
\(880\) | 2.36885e135 | 0.0285820 | ||||||||
\(881\) | 1.65361e137 | 1.89257 | 0.946287 | − | 0.323328i | \(-0.104802\pi\) | ||||
0.946287 | + | 0.323328i | \(0.104802\pi\) | |||||||
\(882\) | 5.85914e135 | 0.0636128 | ||||||||
\(883\) | −3.55857e136 | −0.366524 | −0.183262 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183262 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(884\) | 7.85330e136 | 0.767401 | ||||||||
\(885\) | −1.21839e136 | −0.112960 | ||||||||
\(886\) | 2.38849e136 | 0.210114 | ||||||||
\(887\) | −1.45980e137 | −1.21856 | −0.609278 | − | 0.792956i | \(-0.708541\pi\) | ||||
−0.609278 | + | 0.792956i | \(0.708541\pi\) | |||||||
\(888\) | −1.60177e137 | −1.26881 | ||||||||
\(889\) | −6.12273e136 | −0.460271 | ||||||||
\(890\) | −1.62442e135 | −0.0115894 | ||||||||
\(891\) | −3.88328e136 | −0.262957 | ||||||||
\(892\) | −3.57346e136 | −0.229680 | ||||||||
\(893\) | −2.83646e136 | −0.173055 | ||||||||
\(894\) | −1.88975e136 | −0.109449 | ||||||||
\(895\) | 1.26930e137 | 0.697903 | ||||||||
\(896\) | −1.63746e137 | −0.854770 | ||||||||
\(897\) | 3.27958e137 | 1.62543 | ||||||||
\(898\) | −1.88177e137 | −0.885556 | ||||||||
\(899\) | 2.56735e137 | 1.14725 | ||||||||
\(900\) | 1.47559e137 | 0.626163 | ||||||||
\(901\) | 2.65975e136 | 0.107186 | ||||||||
\(902\) | 5.78385e136 | 0.221367 | ||||||||
\(903\) | 4.51674e136 | 0.164189 | ||||||||
\(904\) | 1.53010e137 | 0.528308 | ||||||||
\(905\) | 4.10315e136 | 0.134573 | ||||||||
\(906\) | −3.27218e136 | −0.101947 | ||||||||
\(907\) | −4.43491e137 | −1.31264 | −0.656321 | − | 0.754482i | \(-0.727888\pi\) | ||||
−0.656321 | + | 0.754482i | \(0.727888\pi\) | |||||||
\(908\) | 7.03886e136 | 0.197929 | ||||||||
\(909\) | 5.11857e137 | 1.36750 | ||||||||
\(910\) | 6.27292e136 | 0.159237 | ||||||||
\(911\) | −5.56999e136 | −0.134354 | −0.0671769 | − | 0.997741i | \(-0.521399\pi\) | ||||
−0.0671769 | + | 0.997741i | \(0.521399\pi\) | |||||||
\(912\) | −2.99996e137 | −0.687630 | ||||||||
\(913\) | −2.80253e136 | −0.0610463 | ||||||||
\(914\) | −7.03818e136 | −0.145701 | ||||||||
\(915\) | −4.81886e137 | −0.948120 | ||||||||
\(916\) | −1.95642e137 | −0.365867 | ||||||||
\(917\) | 1.31569e136 | 0.0233872 | ||||||||
\(918\) | −7.45006e135 | −0.0125885 | ||||||||
\(919\) | 3.23898e137 | 0.520280 | 0.260140 | − | 0.965571i | \(-0.416231\pi\) | ||||
0.260140 | + | 0.965571i | \(0.416231\pi\) | |||||||
\(920\) | 2.84886e137 | 0.435048 | ||||||||
\(921\) | −1.59929e138 | −2.32196 | ||||||||
\(922\) | −3.48075e137 | −0.480491 | ||||||||
\(923\) | 7.66896e137 | 1.00660 | ||||||||
\(924\) | 2.02686e137 | 0.252974 | ||||||||
\(925\) | 7.34747e137 | 0.872062 | ||||||||
\(926\) | 2.41324e137 | 0.272389 | ||||||||
\(927\) | −8.55745e137 | −0.918622 | ||||||||
\(928\) | −1.54280e138 | −1.57517 | ||||||||
\(929\) | 1.34434e138 | 1.30551 | 0.652753 | − | 0.757571i | \(-0.273614\pi\) | ||||
0.652753 | + | 0.757571i | \(0.273614\pi\) | |||||||
\(930\) | −2.20537e137 | −0.203715 | ||||||||
\(931\) | 2.41869e137 | 0.212530 | ||||||||
\(932\) | 5.75774e137 | 0.481296 | ||||||||
\(933\) | 1.48311e138 | 1.17945 | ||||||||
\(934\) | 8.47452e137 | 0.641188 | ||||||||
\(935\) | −1.58643e137 | −0.114204 | ||||||||
\(936\) | 1.12929e138 | 0.773533 | ||||||||
\(937\) | 2.26993e138 | 1.47952 | 0.739761 | − | 0.672870i | \(-0.234938\pi\) | ||||
0.739761 | + | 0.672870i | \(0.234938\pi\) | |||||||
\(938\) | −7.07685e137 | −0.438943 | ||||||||
\(939\) | −4.02757e138 | −2.37735 | ||||||||
\(940\) | −5.16405e136 | −0.0290098 | ||||||||
\(941\) | 3.49457e138 | 1.86843 | 0.934213 | − | 0.356716i | \(-0.116104\pi\) | ||||
0.934213 | + | 0.356716i | \(0.116104\pi\) | |||||||
\(942\) | −7.84571e137 | −0.399269 | ||||||||
\(943\) | −4.51252e138 | −2.18588 | ||||||||
\(944\) | −1.34259e137 | −0.0619079 | ||||||||
\(945\) | 1.70885e136 | 0.00750110 | ||||||||
\(946\) | 3.93062e136 | 0.0164257 | ||||||||
\(947\) | −3.15534e138 | −1.25537 | −0.627685 | − | 0.778467i | \(-0.715997\pi\) | ||||
−0.627685 | + | 0.778467i | \(0.715997\pi\) | |||||||
\(948\) | 5.31999e138 | 2.01522 | ||||||||
\(949\) | −2.46032e138 | −0.887387 | ||||||||
\(950\) | −2.12121e138 | −0.728511 | ||||||||
\(951\) | −1.49127e138 | −0.487710 | ||||||||
\(952\) | 3.09652e138 | 0.964398 | ||||||||
\(953\) | 2.76357e138 | 0.819692 | 0.409846 | − | 0.912155i | \(-0.365582\pi\) | ||||
0.409846 | + | 0.912155i | \(0.365582\pi\) | |||||||
\(954\) | 1.62874e137 | 0.0460101 | ||||||||
\(955\) | −5.59860e137 | −0.150634 | ||||||||
\(956\) | −2.59539e138 | −0.665136 | ||||||||
\(957\) | 2.27918e138 | 0.556383 | ||||||||
\(958\) | 7.29204e137 | 0.169571 | ||||||||
\(959\) | −3.53998e138 | −0.784216 | ||||||||
\(960\) | 5.88905e137 | 0.124289 | ||||||||
\(961\) | −2.15536e138 | −0.433393 | ||||||||
\(962\) | 2.39463e138 | 0.458772 | ||||||||
\(963\) | −3.10949e138 | −0.567632 | ||||||||
\(964\) | −5.03725e138 | −0.876217 | ||||||||
\(965\) | 4.38018e137 | 0.0726059 | ||||||||
\(966\) | 5.50678e138 | 0.869884 | ||||||||
\(967\) | 6.63903e138 | 0.999479 | 0.499740 | − | 0.866176i | \(-0.333429\pi\) | ||||
0.499740 | + | 0.866176i | \(0.333429\pi\) | |||||||
\(968\) | −5.75508e138 | −0.825747 | ||||||||
\(969\) | 2.00909e139 | 2.74754 | ||||||||
\(970\) | 3.28462e137 | 0.0428154 | ||||||||
\(971\) | −1.84814e138 | −0.229636 | −0.114818 | − | 0.993387i | \(-0.536628\pi\) | ||||
−0.114818 | + | 0.993387i | \(0.536628\pi\) | |||||||
\(972\) | 8.82041e138 | 1.04474 | ||||||||
\(973\) | 1.22152e139 | 1.37928 | ||||||||
\(974\) | −6.09629e138 | −0.656258 | ||||||||
\(975\) | −1.04396e139 | −1.07145 | ||||||||
\(976\) | −5.31009e138 | −0.519620 | ||||||||
\(977\) | −1.80423e139 | −1.68342 | −0.841712 | − | 0.539926i | \(-0.818452\pi\) | ||||
−0.841712 | + | 0.539926i | \(0.818452\pi\) | |||||||
\(978\) | −1.17729e139 | −1.04743 | ||||||||
\(979\) | 1.84259e137 | 0.0156327 | ||||||||
\(980\) | 4.40345e137 | 0.0356271 | ||||||||
\(981\) | −5.19563e138 | −0.400894 | ||||||||
\(982\) | 4.74796e138 | 0.349400 | ||||||||
\(983\) | 5.12719e138 | 0.359866 | 0.179933 | − | 0.983679i | \(-0.442412\pi\) | ||||
0.179933 | + | 0.983679i | \(0.442412\pi\) | |||||||
\(984\) | −3.13148e139 | −2.09641 | ||||||||
\(985\) | 7.65242e138 | 0.488668 | ||||||||
\(986\) | 1.48282e139 | 0.903259 | ||||||||
\(987\) | −2.34401e138 | −0.136211 | ||||||||
\(988\) | 1.98523e139 | 1.10056 | ||||||||
\(989\) | −3.06664e138 | −0.162194 | ||||||||
\(990\) | −9.71479e137 | −0.0490227 | ||||||||
\(991\) | −2.29485e139 | −1.10491 | −0.552457 | − | 0.833541i | \(-0.686310\pi\) | ||||
−0.552457 | + | 0.833541i | \(0.686310\pi\) | |||||||
\(992\) | −1.69334e139 | −0.777948 | ||||||||
\(993\) | 4.44269e139 | 1.94763 | ||||||||
\(994\) | 1.28771e139 | 0.538703 | ||||||||
\(995\) | 5.28641e138 | 0.211051 | ||||||||
\(996\) | 6.46161e138 | 0.246196 | ||||||||
\(997\) | 3.11371e139 | 1.13228 | 0.566139 | − | 0.824310i | \(-0.308436\pi\) | ||||
0.566139 | + | 0.824310i | \(0.308436\pi\) | |||||||
\(998\) | −2.77334e139 | −0.962571 | ||||||||
\(999\) | 6.52338e137 | 0.0216111 |
(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 | 1.94.a.a.1.3 | ✓ | 7 | |
3.2 | odd | 2 | 9.94.a.b.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.94.a.a.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.94.a.b.1.5 | 7 | 3.2 | odd | 2 |