Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,88,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, 88, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 88);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 88 \) |
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: | \(47.9333631461\) |
Analytic rank: | \(0\) |
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: | \( x^{7} - x^{6} + \cdots - 79\!\cdots\!56 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{76}\cdot 3^{35}\cdot 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 13\cdot 17\cdot 29^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.68228e11\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.19120e13 | 1.76148 | 0.880739 | − | 0.473602i | \(-0.157047\pi\) | ||||
0.880739 | + | 0.473602i | \(0.157047\pi\) | |||||||
\(3\) | 9.03577e20 | 1.58924 | 0.794622 | − | 0.607105i | \(-0.207669\pi\) | ||||
0.794622 | + | 0.607105i | \(0.207669\pi\) | |||||||
\(4\) | 3.25393e26 | 2.10280 | ||||||||
\(5\) | −2.93989e30 | −1.15647 | −0.578236 | − | 0.815869i | \(-0.696259\pi\) | ||||
−0.578236 | + | 0.815869i | \(0.696259\pi\) | |||||||
\(6\) | 1.97992e34 | 2.79942 | ||||||||
\(7\) | 7.30934e36 | 1.26507 | 0.632534 | − | 0.774533i | \(-0.282015\pi\) | ||||
0.632534 | + | 0.774533i | \(0.282015\pi\) | |||||||
\(8\) | 3.73929e39 | 1.94256 | ||||||||
\(9\) | 4.93193e41 | 1.52570 | ||||||||
\(10\) | −6.44188e43 | −2.03710 | ||||||||
\(11\) | −1.23524e45 | −0.618260 | −0.309130 | − | 0.951020i | \(-0.600038\pi\) | ||||
−0.309130 | + | 0.951020i | \(0.600038\pi\) | |||||||
\(12\) | 2.94018e47 | 3.34187 | ||||||||
\(13\) | 1.56397e48 | 0.546629 | 0.273315 | − | 0.961925i | \(-0.411880\pi\) | ||||
0.273315 | + | 0.961925i | \(0.411880\pi\) | |||||||
\(14\) | 1.60162e50 | 2.22839 | ||||||||
\(15\) | −2.65641e51 | −1.83792 | ||||||||
\(16\) | 3.15832e52 | 1.31898 | ||||||||
\(17\) | 4.26647e53 | 1.27509 | 0.637545 | − | 0.770413i | \(-0.279950\pi\) | ||||
0.637545 | + | 0.770413i | \(0.279950\pi\) | |||||||
\(18\) | 1.08069e55 | 2.68748 | ||||||||
\(19\) | −1.72994e55 | −0.409496 | −0.204748 | − | 0.978815i | \(-0.565637\pi\) | ||||
−0.204748 | + | 0.978815i | \(0.565637\pi\) | |||||||
\(20\) | −9.56618e56 | −2.43183 | ||||||||
\(21\) | 6.60456e57 | 2.01050 | ||||||||
\(22\) | −2.70667e58 | −1.08905 | ||||||||
\(23\) | 1.74415e59 | 1.01490 | 0.507451 | − | 0.861681i | \(-0.330588\pi\) | ||||
0.507451 | + | 0.861681i | \(0.330588\pi\) | |||||||
\(24\) | 3.37874e60 | 3.08721 | ||||||||
\(25\) | 2.18058e60 | 0.337428 | ||||||||
\(26\) | 3.42697e61 | 0.962875 | ||||||||
\(27\) | 1.53550e62 | 0.835460 | ||||||||
\(28\) | 2.37841e63 | 2.66019 | ||||||||
\(29\) | 1.40898e63 | 0.342445 | 0.171223 | − | 0.985232i | \(-0.445228\pi\) | ||||
0.171223 | + | 0.985232i | \(0.445228\pi\) | |||||||
\(30\) | −5.82073e64 | −3.23745 | ||||||||
\(31\) | −6.33280e64 | −0.845984 | −0.422992 | − | 0.906134i | \(-0.639020\pi\) | ||||
−0.422992 | + | 0.906134i | \(0.639020\pi\) | |||||||
\(32\) | 1.13424e65 | 0.380786 | ||||||||
\(33\) | −1.11614e66 | −0.982566 | ||||||||
\(34\) | 9.34869e66 | 2.24604 | ||||||||
\(35\) | −2.14886e67 | −1.46302 | ||||||||
\(36\) | 1.60482e68 | 3.20824 | ||||||||
\(37\) | −2.97743e68 | −1.80745 | −0.903727 | − | 0.428110i | \(-0.859180\pi\) | ||||
−0.903727 | + | 0.428110i | \(0.859180\pi\) | |||||||
\(38\) | −3.79065e68 | −0.721318 | ||||||||
\(39\) | 1.41317e69 | 0.868727 | ||||||||
\(40\) | −1.09931e70 | −2.24652 | ||||||||
\(41\) | −4.83288e69 | −0.337371 | −0.168686 | − | 0.985670i | \(-0.553952\pi\) | ||||
−0.168686 | + | 0.985670i | \(0.553952\pi\) | |||||||
\(42\) | 1.44719e71 | 3.54145 | ||||||||
\(43\) | 1.18830e71 | 1.04484 | 0.522419 | − | 0.852689i | \(-0.325030\pi\) | ||||
0.522419 | + | 0.852689i | \(0.325030\pi\) | |||||||
\(44\) | −4.01940e71 | −1.30008 | ||||||||
\(45\) | −1.44993e72 | −1.76443 | ||||||||
\(46\) | 3.82179e72 | 1.78773 | ||||||||
\(47\) | −2.96099e72 | −0.543475 | −0.271737 | − | 0.962371i | \(-0.587598\pi\) | ||||
−0.271737 | + | 0.962371i | \(0.587598\pi\) | |||||||
\(48\) | 2.85379e73 | 2.09618 | ||||||||
\(49\) | 2.00432e73 | 0.600396 | ||||||||
\(50\) | 4.77809e73 | 0.594373 | ||||||||
\(51\) | 3.85509e74 | 2.02643 | ||||||||
\(52\) | 5.08905e74 | 1.14945 | ||||||||
\(53\) | −1.89528e75 | −1.86927 | −0.934635 | − | 0.355609i | \(-0.884273\pi\) | ||||
−0.934635 | + | 0.355609i | \(0.884273\pi\) | |||||||
\(54\) | 3.36458e75 | 1.47164 | ||||||||
\(55\) | 3.63148e75 | 0.715000 | ||||||||
\(56\) | 2.73318e76 | 2.45747 | ||||||||
\(57\) | −1.56313e76 | −0.650789 | ||||||||
\(58\) | 3.08735e76 | 0.603210 | ||||||||
\(59\) | −2.41334e76 | −0.224159 | −0.112080 | − | 0.993699i | \(-0.535751\pi\) | ||||
−0.112080 | + | 0.993699i | \(0.535751\pi\) | |||||||
\(60\) | −8.64378e77 | −3.86478 | ||||||||
\(61\) | 4.87105e77 | 1.06114 | 0.530572 | − | 0.847640i | \(-0.321977\pi\) | ||||
0.530572 | + | 0.847640i | \(0.321977\pi\) | |||||||
\(62\) | −1.38764e78 | −1.49018 | ||||||||
\(63\) | 3.60492e78 | 1.93011 | ||||||||
\(64\) | −2.40192e78 | −0.648231 | ||||||||
\(65\) | −4.59790e78 | −0.632162 | ||||||||
\(66\) | −2.44568e79 | −1.73077 | ||||||||
\(67\) | −1.66474e79 | −0.612482 | −0.306241 | − | 0.951954i | \(-0.599071\pi\) | ||||
−0.306241 | + | 0.951954i | \(0.599071\pi\) | |||||||
\(68\) | 1.38828e80 | 2.68126 | ||||||||
\(69\) | 1.57598e80 | 1.61293 | ||||||||
\(70\) | −4.70859e80 | −2.57707 | ||||||||
\(71\) | 5.91466e80 | 1.74659 | 0.873297 | − | 0.487188i | \(-0.161977\pi\) | ||||
0.873297 | + | 0.487188i | \(0.161977\pi\) | |||||||
\(72\) | 1.84419e81 | 2.96376 | ||||||||
\(73\) | −3.16168e80 | −0.278852 | −0.139426 | − | 0.990233i | \(-0.544526\pi\) | ||||
−0.139426 | + | 0.990233i | \(0.544526\pi\) | |||||||
\(74\) | −6.52415e81 | −3.18379 | ||||||||
\(75\) | 1.97032e81 | 0.536256 | ||||||||
\(76\) | −5.62911e81 | −0.861089 | ||||||||
\(77\) | −9.02883e81 | −0.782140 | ||||||||
\(78\) | 3.09653e82 | 1.53024 | ||||||||
\(79\) | 9.23615e81 | 0.262248 | 0.131124 | − | 0.991366i | \(-0.458141\pi\) | ||||
0.131124 | + | 0.991366i | \(0.458141\pi\) | |||||||
\(80\) | −9.28511e82 | −1.52536 | ||||||||
\(81\) | −2.06846e82 | −0.197947 | ||||||||
\(82\) | −1.05898e83 | −0.594272 | ||||||||
\(83\) | −2.59548e83 | −0.859649 | −0.429824 | − | 0.902912i | \(-0.641425\pi\) | ||||
−0.429824 | + | 0.902912i | \(0.641425\pi\) | |||||||
\(84\) | 2.14908e84 | 4.22769 | ||||||||
\(85\) | −1.25429e84 | −1.47461 | ||||||||
\(86\) | 2.60381e84 | 1.84046 | ||||||||
\(87\) | 1.27312e84 | 0.544229 | ||||||||
\(88\) | −4.61894e84 | −1.20101 | ||||||||
\(89\) | −1.03166e84 | −0.164086 | −0.0820432 | − | 0.996629i | \(-0.526145\pi\) | ||||
−0.0820432 | + | 0.996629i | \(0.526145\pi\) | |||||||
\(90\) | −3.17709e85 | −3.10800 | ||||||||
\(91\) | 1.14316e85 | 0.691523 | ||||||||
\(92\) | 5.67536e85 | 2.13414 | ||||||||
\(93\) | −5.72217e85 | −1.34447 | ||||||||
\(94\) | −6.48811e85 | −0.957319 | ||||||||
\(95\) | 5.08583e85 | 0.473571 | ||||||||
\(96\) | 1.02487e86 | 0.605161 | ||||||||
\(97\) | 1.01460e85 | 0.0381701 | 0.0190851 | − | 0.999818i | \(-0.493925\pi\) | ||||
0.0190851 | + | 0.999818i | \(0.493925\pi\) | |||||||
\(98\) | 4.39187e86 | 1.05758 | ||||||||
\(99\) | −6.09214e86 | −0.943277 | ||||||||
\(100\) | 7.09545e86 | 0.709545 | ||||||||
\(101\) | −1.74397e87 | −1.13125 | −0.565627 | − | 0.824661i | \(-0.691366\pi\) | ||||
−0.565627 | + | 0.824661i | \(0.691366\pi\) | |||||||
\(102\) | 8.44726e87 | 3.56951 | ||||||||
\(103\) | −5.83129e87 | −1.61193 | −0.805964 | − | 0.591965i | \(-0.798352\pi\) | ||||
−0.805964 | + | 0.591965i | \(0.798352\pi\) | |||||||
\(104\) | 5.84815e87 | 1.06186 | ||||||||
\(105\) | −1.94166e88 | −2.32509 | ||||||||
\(106\) | −4.15293e88 | −3.29268 | ||||||||
\(107\) | 2.16890e87 | 0.114300 | 0.0571498 | − | 0.998366i | \(-0.481799\pi\) | ||||
0.0571498 | + | 0.998366i | \(0.481799\pi\) | |||||||
\(108\) | 4.99640e88 | 1.75681 | ||||||||
\(109\) | 7.27972e88 | 1.71420 | 0.857101 | − | 0.515148i | \(-0.172263\pi\) | ||||
0.857101 | + | 0.515148i | \(0.172263\pi\) | |||||||
\(110\) | 7.95729e88 | 1.25946 | ||||||||
\(111\) | −2.69034e89 | −2.87248 | ||||||||
\(112\) | 2.30853e89 | 1.66859 | ||||||||
\(113\) | 2.71121e89 | 1.33122 | 0.665611 | − | 0.746299i | \(-0.268171\pi\) | ||||
0.665611 | + | 0.746299i | \(0.268171\pi\) | |||||||
\(114\) | −3.42514e89 | −1.14635 | ||||||||
\(115\) | −5.12762e89 | −1.17371 | ||||||||
\(116\) | 4.58471e89 | 0.720095 | ||||||||
\(117\) | 7.71340e89 | 0.833991 | ||||||||
\(118\) | −5.28812e89 | −0.394852 | ||||||||
\(119\) | 3.11851e90 | 1.61308 | ||||||||
\(120\) | −9.93310e90 | −3.57027 | ||||||||
\(121\) | −2.46592e90 | −0.617755 | ||||||||
\(122\) | 1.06734e91 | 1.86918 | ||||||||
\(123\) | −4.36688e90 | −0.536165 | ||||||||
\(124\) | −2.06065e91 | −1.77894 | ||||||||
\(125\) | 1.25879e91 | 0.766246 | ||||||||
\(126\) | 7.89910e91 | 3.39984 | ||||||||
\(127\) | −4.43227e89 | −0.0135258 | −0.00676292 | − | 0.999977i | \(-0.502153\pi\) | ||||
−0.00676292 | + | 0.999977i | \(0.502153\pi\) | |||||||
\(128\) | −7.01824e91 | −1.52263 | ||||||||
\(129\) | 1.07372e92 | 1.66050 | ||||||||
\(130\) | −1.00749e92 | −1.11354 | ||||||||
\(131\) | 1.52151e92 | 1.20496 | 0.602482 | − | 0.798133i | \(-0.294179\pi\) | ||||
0.602482 | + | 0.798133i | \(0.294179\pi\) | |||||||
\(132\) | −3.63184e92 | −2.06614 | ||||||||
\(133\) | −1.26447e92 | −0.518040 | ||||||||
\(134\) | −3.64778e92 | −1.07887 | ||||||||
\(135\) | −4.51419e92 | −0.966186 | ||||||||
\(136\) | 1.59536e93 | 2.47694 | ||||||||
\(137\) | −2.51594e92 | −0.284025 | −0.142012 | − | 0.989865i | \(-0.545357\pi\) | ||||
−0.142012 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(138\) | 3.45328e93 | 2.84113 | ||||||||
\(139\) | −1.65051e93 | −0.991912 | −0.495956 | − | 0.868348i | \(-0.665182\pi\) | ||||
−0.495956 | + | 0.868348i | \(0.665182\pi\) | |||||||
\(140\) | −6.99225e93 | −3.07643 | ||||||||
\(141\) | −2.67548e93 | −0.863714 | ||||||||
\(142\) | 1.29602e94 | 3.07659 | ||||||||
\(143\) | −1.93189e93 | −0.337959 | ||||||||
\(144\) | 1.55766e94 | 2.01236 | ||||||||
\(145\) | −4.14223e93 | −0.396029 | ||||||||
\(146\) | −6.92787e93 | −0.491191 | ||||||||
\(147\) | 1.81106e94 | 0.954176 | ||||||||
\(148\) | −9.68836e94 | −3.80072 | ||||||||
\(149\) | −1.58122e94 | −0.462796 | −0.231398 | − | 0.972859i | \(-0.574330\pi\) | ||||
−0.231398 | + | 0.972859i | \(0.574330\pi\) | |||||||
\(150\) | 4.31737e94 | 0.944603 | ||||||||
\(151\) | 8.62448e93 | 0.141330 | 0.0706652 | − | 0.997500i | \(-0.477488\pi\) | ||||
0.0706652 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(152\) | −6.46875e94 | −0.795471 | ||||||||
\(153\) | 2.10420e95 | 1.94540 | ||||||||
\(154\) | −1.97840e95 | −1.37772 | ||||||||
\(155\) | 1.86177e95 | 0.978357 | ||||||||
\(156\) | 4.59835e95 | 1.82676 | ||||||||
\(157\) | 1.43573e95 | 0.431955 | 0.215977 | − | 0.976398i | \(-0.430706\pi\) | ||||
0.215977 | + | 0.976398i | \(0.430706\pi\) | |||||||
\(158\) | 2.02382e95 | 0.461944 | ||||||||
\(159\) | −1.71253e96 | −2.97073 | ||||||||
\(160\) | −3.33453e95 | −0.440368 | ||||||||
\(161\) | 1.27486e96 | 1.28392 | ||||||||
\(162\) | −4.53240e95 | −0.348679 | ||||||||
\(163\) | −3.09568e95 | −0.182220 | −0.0911099 | − | 0.995841i | \(-0.529041\pi\) | ||||
−0.0911099 | + | 0.995841i | \(0.529041\pi\) | |||||||
\(164\) | −1.57259e96 | −0.709425 | ||||||||
\(165\) | 3.28132e96 | 1.13631 | ||||||||
\(166\) | −5.68722e96 | −1.51425 | ||||||||
\(167\) | −4.38882e96 | −0.899873 | −0.449936 | − | 0.893061i | \(-0.648553\pi\) | ||||
−0.449936 | + | 0.893061i | \(0.648553\pi\) | |||||||
\(168\) | 2.46964e97 | 3.90552 | ||||||||
\(169\) | −5.73999e96 | −0.701196 | ||||||||
\(170\) | −2.74841e97 | −2.59749 | ||||||||
\(171\) | −8.53195e96 | −0.624767 | ||||||||
\(172\) | 3.86665e97 | 2.19709 | ||||||||
\(173\) | 1.65137e97 | 0.729187 | 0.364594 | − | 0.931167i | \(-0.381208\pi\) | ||||
0.364594 | + | 0.931167i | \(0.381208\pi\) | |||||||
\(174\) | 2.78966e97 | 0.958647 | ||||||||
\(175\) | 1.59386e97 | 0.426870 | ||||||||
\(176\) | −3.90130e97 | −0.815470 | ||||||||
\(177\) | −2.18064e97 | −0.356244 | ||||||||
\(178\) | −2.26058e97 | −0.289034 | ||||||||
\(179\) | −1.28269e97 | −0.128533 | −0.0642666 | − | 0.997933i | \(-0.520471\pi\) | ||||
−0.0642666 | + | 0.997933i | \(0.520471\pi\) | |||||||
\(180\) | −4.71798e98 | −3.71024 | ||||||||
\(181\) | −9.38672e97 | −0.580091 | −0.290045 | − | 0.957013i | \(-0.593670\pi\) | ||||
−0.290045 | + | 0.957013i | \(0.593670\pi\) | |||||||
\(182\) | 2.50489e98 | 1.21810 | ||||||||
\(183\) | 4.40137e98 | 1.68642 | ||||||||
\(184\) | 6.52190e98 | 1.97151 | ||||||||
\(185\) | 8.75331e98 | 2.09027 | ||||||||
\(186\) | −1.25384e99 | −2.36826 | ||||||||
\(187\) | −5.27014e98 | −0.788337 | ||||||||
\(188\) | −9.63484e98 | −1.14282 | ||||||||
\(189\) | 1.12235e99 | 1.05691 | ||||||||
\(190\) | 1.11441e99 | 0.834184 | ||||||||
\(191\) | 1.32496e99 | 0.789316 | 0.394658 | − | 0.918828i | \(-0.370863\pi\) | ||||
0.394658 | + | 0.918828i | \(0.370863\pi\) | |||||||
\(192\) | −2.17032e99 | −1.03020 | ||||||||
\(193\) | −2.26498e99 | −0.857672 | −0.428836 | − | 0.903382i | \(-0.641076\pi\) | ||||
−0.428836 | + | 0.903382i | \(0.641076\pi\) | |||||||
\(194\) | 2.22319e98 | 0.0672358 | ||||||||
\(195\) | −4.15455e99 | −1.00466 | ||||||||
\(196\) | 6.52192e99 | 1.26251 | ||||||||
\(197\) | −5.25147e98 | −0.0814705 | −0.0407353 | − | 0.999170i | \(-0.512970\pi\) | ||||
−0.0407353 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(198\) | −1.33491e100 | −1.66156 | ||||||||
\(199\) | 1.59307e100 | 1.59267 | 0.796335 | − | 0.604856i | \(-0.206769\pi\) | ||||
0.796335 | + | 0.604856i | \(0.206769\pi\) | |||||||
\(200\) | 8.15383e99 | 0.655476 | ||||||||
\(201\) | −1.50422e100 | −0.973383 | ||||||||
\(202\) | −3.82139e100 | −1.99268 | ||||||||
\(203\) | 1.02987e100 | 0.433216 | ||||||||
\(204\) | 1.25442e101 | 4.26118 | ||||||||
\(205\) | 1.42081e100 | 0.390161 | ||||||||
\(206\) | −1.27775e101 | −2.83937 | ||||||||
\(207\) | 8.60206e100 | 1.54843 | ||||||||
\(208\) | 4.93953e100 | 0.720991 | ||||||||
\(209\) | 2.13690e100 | 0.253175 | ||||||||
\(210\) | −4.25457e101 | −4.09559 | ||||||||
\(211\) | 2.48888e101 | 1.94857 | 0.974287 | − | 0.225311i | \(-0.0723398\pi\) | ||||
0.974287 | + | 0.225311i | \(0.0723398\pi\) | |||||||
\(212\) | −6.16709e101 | −3.93071 | ||||||||
\(213\) | 5.34436e101 | 2.77576 | ||||||||
\(214\) | 4.75249e100 | 0.201336 | ||||||||
\(215\) | −3.49347e101 | −1.20833 | ||||||||
\(216\) | 5.74168e101 | 1.62293 | ||||||||
\(217\) | −4.62886e101 | −1.07023 | ||||||||
\(218\) | 1.59513e102 | 3.01953 | ||||||||
\(219\) | −2.85682e101 | −0.443163 | ||||||||
\(220\) | 1.18166e102 | 1.50350 | ||||||||
\(221\) | 6.67264e101 | 0.697002 | ||||||||
\(222\) | −5.89507e102 | −5.05982 | ||||||||
\(223\) | −3.78800e100 | −0.0267392 | −0.0133696 | − | 0.999911i | \(-0.504256\pi\) | ||||
−0.0133696 | + | 0.999911i | \(0.504256\pi\) | |||||||
\(224\) | 8.29055e101 | 0.481720 | ||||||||
\(225\) | 1.07545e102 | 0.514813 | ||||||||
\(226\) | 5.94079e102 | 2.34492 | ||||||||
\(227\) | −8.50779e101 | −0.277135 | −0.138568 | − | 0.990353i | \(-0.544250\pi\) | ||||
−0.138568 | + | 0.990353i | \(0.544250\pi\) | |||||||
\(228\) | −5.08633e102 | −1.36848 | ||||||||
\(229\) | 6.43959e102 | 1.43224 | 0.716119 | − | 0.697979i | \(-0.245917\pi\) | ||||
0.716119 | + | 0.697979i | \(0.245917\pi\) | |||||||
\(230\) | −1.12356e103 | −2.06746 | ||||||||
\(231\) | −8.15824e102 | −1.24301 | ||||||||
\(232\) | 5.26858e102 | 0.665221 | ||||||||
\(233\) | −9.54865e102 | −0.999907 | −0.499954 | − | 0.866052i | \(-0.666650\pi\) | ||||
−0.499954 | + | 0.866052i | \(0.666650\pi\) | |||||||
\(234\) | 1.69016e103 | 1.46906 | ||||||||
\(235\) | 8.70496e102 | 0.628514 | ||||||||
\(236\) | −7.85285e102 | −0.471363 | ||||||||
\(237\) | 8.34557e102 | 0.416776 | ||||||||
\(238\) | 6.83328e103 | 2.84140 | ||||||||
\(239\) | 4.88897e102 | 0.169398 | 0.0846990 | − | 0.996407i | \(-0.473007\pi\) | ||||
0.0846990 | + | 0.996407i | \(0.473007\pi\) | |||||||
\(240\) | −8.38981e103 | −2.42417 | ||||||||
\(241\) | 3.07268e103 | 0.740927 | 0.370463 | − | 0.928847i | \(-0.379199\pi\) | ||||
0.370463 | + | 0.928847i | \(0.379199\pi\) | |||||||
\(242\) | −5.40333e103 | −1.08816 | ||||||||
\(243\) | −6.83263e103 | −1.15005 | ||||||||
\(244\) | 1.58500e104 | 2.23138 | ||||||||
\(245\) | −5.89247e103 | −0.694341 | ||||||||
\(246\) | −9.56870e103 | −0.944443 | ||||||||
\(247\) | −2.70558e103 | −0.223843 | ||||||||
\(248\) | −2.36802e104 | −1.64338 | ||||||||
\(249\) | −2.34522e104 | −1.36619 | ||||||||
\(250\) | 2.75826e104 | 1.34972 | ||||||||
\(251\) | 3.90400e104 | 1.60584 | 0.802921 | − | 0.596085i | \(-0.203278\pi\) | ||||
0.802921 | + | 0.596085i | \(0.203278\pi\) | |||||||
\(252\) | 1.17302e105 | 4.05864 | ||||||||
\(253\) | −2.15446e104 | −0.627473 | ||||||||
\(254\) | −9.71198e102 | −0.0238255 | ||||||||
\(255\) | −1.13335e105 | −2.34351 | ||||||||
\(256\) | −1.16616e105 | −2.03385 | ||||||||
\(257\) | 7.62729e104 | 1.12274 | 0.561371 | − | 0.827565i | \(-0.310274\pi\) | ||||
0.561371 | + | 0.827565i | \(0.310274\pi\) | |||||||
\(258\) | 2.35274e105 | 2.92494 | ||||||||
\(259\) | −2.17631e105 | −2.28655 | ||||||||
\(260\) | −1.49612e105 | −1.32931 | ||||||||
\(261\) | 6.94899e104 | 0.522468 | ||||||||
\(262\) | 3.33394e105 | 2.12252 | ||||||||
\(263\) | −1.42711e105 | −0.769808 | −0.384904 | − | 0.922957i | \(-0.625765\pi\) | ||||
−0.384904 | + | 0.922957i | \(0.625765\pi\) | |||||||
\(264\) | −4.17357e105 | −1.90869 | ||||||||
\(265\) | 5.57189e105 | 2.16176 | ||||||||
\(266\) | −2.77071e105 | −0.912516 | ||||||||
\(267\) | −9.32187e104 | −0.260773 | ||||||||
\(268\) | −5.41696e105 | −1.28793 | ||||||||
\(269\) | 5.61895e105 | 1.13614 | 0.568069 | − | 0.822981i | \(-0.307691\pi\) | ||||
0.568069 | + | 0.822981i | \(0.307691\pi\) | |||||||
\(270\) | −9.89149e105 | −1.70192 | ||||||||
\(271\) | 4.63708e105 | 0.679330 | 0.339665 | − | 0.940547i | \(-0.389686\pi\) | ||||
0.339665 | + | 0.940547i | \(0.389686\pi\) | |||||||
\(272\) | 1.34749e106 | 1.68181 | ||||||||
\(273\) | 1.03293e106 | 1.09900 | ||||||||
\(274\) | −5.51293e105 | −0.500303 | ||||||||
\(275\) | −2.69355e105 | −0.208618 | ||||||||
\(276\) | 5.12812e106 | 3.39167 | ||||||||
\(277\) | −1.39351e106 | −0.787481 | −0.393741 | − | 0.919222i | \(-0.628819\pi\) | ||||
−0.393741 | + | 0.919222i | \(0.628819\pi\) | |||||||
\(278\) | −3.61659e106 | −1.74723 | ||||||||
\(279\) | −3.12329e106 | −1.29071 | ||||||||
\(280\) | −8.03523e106 | −2.84200 | ||||||||
\(281\) | 6.47868e106 | 1.96228 | 0.981142 | − | 0.193289i | \(-0.0619155\pi\) | ||||
0.981142 | + | 0.193289i | \(0.0619155\pi\) | |||||||
\(282\) | −5.86251e106 | −1.52141 | ||||||||
\(283\) | −6.71456e106 | −1.49385 | −0.746927 | − | 0.664907i | \(-0.768471\pi\) | ||||
−0.746927 | + | 0.664907i | \(0.768471\pi\) | |||||||
\(284\) | 1.92459e107 | 3.67274 | ||||||||
\(285\) | 4.59544e106 | 0.752619 | ||||||||
\(286\) | −4.23315e106 | −0.595307 | ||||||||
\(287\) | −3.53252e106 | −0.426798 | ||||||||
\(288\) | 5.59399e106 | 0.580963 | ||||||||
\(289\) | 7.00697e106 | 0.625855 | ||||||||
\(290\) | −9.07646e106 | −0.697595 | ||||||||
\(291\) | 9.16767e105 | 0.0606616 | ||||||||
\(292\) | −1.02879e107 | −0.586370 | ||||||||
\(293\) | 2.71547e107 | 1.33384 | 0.666918 | − | 0.745131i | \(-0.267613\pi\) | ||||
0.666918 | + | 0.745131i | \(0.267613\pi\) | |||||||
\(294\) | 3.96839e107 | 1.68076 | ||||||||
\(295\) | 7.09496e106 | 0.259234 | ||||||||
\(296\) | −1.11335e108 | −3.51109 | ||||||||
\(297\) | −1.89672e107 | −0.516531 | ||||||||
\(298\) | −3.46477e107 | −0.815205 | ||||||||
\(299\) | 2.72781e107 | 0.554775 | ||||||||
\(300\) | 6.41129e107 | 1.12764 | ||||||||
\(301\) | 8.68571e107 | 1.32179 | ||||||||
\(302\) | 1.88979e107 | 0.248950 | ||||||||
\(303\) | −1.57581e108 | −1.79784 | ||||||||
\(304\) | −5.46371e107 | −0.540116 | ||||||||
\(305\) | −1.43203e108 | −1.22718 | ||||||||
\(306\) | 4.61071e108 | 3.42678 | ||||||||
\(307\) | −3.12996e107 | −0.201846 | −0.100923 | − | 0.994894i | \(-0.532180\pi\) | ||||
−0.100923 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(308\) | −2.93792e108 | −1.64469 | ||||||||
\(309\) | −5.26902e108 | −2.56175 | ||||||||
\(310\) | 4.07951e108 | 1.72335 | ||||||||
\(311\) | 4.07185e108 | 1.49525 | 0.747626 | − | 0.664120i | \(-0.231194\pi\) | ||||
0.747626 | + | 0.664120i | \(0.231194\pi\) | |||||||
\(312\) | 5.28425e108 | 1.68756 | ||||||||
\(313\) | 4.81634e108 | 1.33825 | 0.669126 | − | 0.743149i | \(-0.266668\pi\) | ||||
0.669126 | + | 0.743149i | \(0.266668\pi\) | |||||||
\(314\) | 3.14597e108 | 0.760879 | ||||||||
\(315\) | −1.05981e109 | −2.23212 | ||||||||
\(316\) | 3.00538e108 | 0.551456 | ||||||||
\(317\) | 1.26342e108 | 0.202055 | 0.101028 | − | 0.994884i | \(-0.467787\pi\) | ||||
0.101028 | + | 0.994884i | \(0.467787\pi\) | |||||||
\(318\) | −3.75249e109 | −5.23287 | ||||||||
\(319\) | −1.74043e108 | −0.211720 | ||||||||
\(320\) | 7.06138e108 | 0.749662 | ||||||||
\(321\) | 1.95977e108 | 0.181650 | ||||||||
\(322\) | 2.79348e109 | 2.26160 | ||||||||
\(323\) | −7.38075e108 | −0.522144 | ||||||||
\(324\) | −6.73062e108 | −0.416243 | ||||||||
\(325\) | 3.41036e108 | 0.184448 | ||||||||
\(326\) | −6.78326e108 | −0.320976 | ||||||||
\(327\) | 6.57779e109 | 2.72429 | ||||||||
\(328\) | −1.80715e109 | −0.655365 | ||||||||
\(329\) | −2.16429e109 | −0.687532 | ||||||||
\(330\) | 7.19002e109 | 2.00158 | ||||||||
\(331\) | 4.12697e109 | 1.00720 | 0.503598 | − | 0.863938i | \(-0.332009\pi\) | ||||
0.503598 | + | 0.863938i | \(0.332009\pi\) | |||||||
\(332\) | −8.44552e109 | −1.80767 | ||||||||
\(333\) | −1.46845e110 | −2.75763 | ||||||||
\(334\) | −9.61678e109 | −1.58511 | ||||||||
\(335\) | 4.89416e109 | 0.708319 | ||||||||
\(336\) | 2.08593e110 | 2.65180 | ||||||||
\(337\) | 7.52106e109 | 0.840191 | 0.420096 | − | 0.907480i | \(-0.361997\pi\) | ||||
0.420096 | + | 0.907480i | \(0.361997\pi\) | |||||||
\(338\) | −1.25775e110 | −1.23514 | ||||||||
\(339\) | 2.44978e110 | 2.11564 | ||||||||
\(340\) | −4.08139e110 | −3.10081 | ||||||||
\(341\) | 7.82255e109 | 0.523038 | ||||||||
\(342\) | −1.86952e110 | −1.10051 | ||||||||
\(343\) | −9.75075e109 | −0.505526 | ||||||||
\(344\) | 4.44341e110 | 2.02966 | ||||||||
\(345\) | −4.63320e110 | −1.86531 | ||||||||
\(346\) | 3.61848e110 | 1.28445 | ||||||||
\(347\) | 1.33452e109 | 0.0417823 | 0.0208912 | − | 0.999782i | \(-0.493350\pi\) | ||||
0.0208912 | + | 0.999782i | \(0.493350\pi\) | |||||||
\(348\) | 4.14264e110 | 1.14441 | ||||||||
\(349\) | −3.38813e110 | −0.826141 | −0.413071 | − | 0.910699i | \(-0.635544\pi\) | ||||
−0.413071 | + | 0.910699i | \(0.635544\pi\) | |||||||
\(350\) | 3.49247e110 | 0.751921 | ||||||||
\(351\) | 2.40148e110 | 0.456687 | ||||||||
\(352\) | −1.40106e110 | −0.235424 | ||||||||
\(353\) | 7.71568e110 | 1.14597 | 0.572987 | − | 0.819565i | \(-0.305785\pi\) | ||||
0.572987 | + | 0.819565i | \(0.305785\pi\) | |||||||
\(354\) | −4.77822e110 | −0.627515 | ||||||||
\(355\) | −1.73884e111 | −2.01989 | ||||||||
\(356\) | −3.35696e110 | −0.345041 | ||||||||
\(357\) | 2.81782e111 | 2.56357 | ||||||||
\(358\) | −2.81063e110 | −0.226408 | ||||||||
\(359\) | 1.36407e111 | 0.973261 | 0.486631 | − | 0.873608i | \(-0.338226\pi\) | ||||
0.486631 | + | 0.873608i | \(0.338226\pi\) | |||||||
\(360\) | −5.42172e111 | −3.42751 | ||||||||
\(361\) | −1.48542e111 | −0.832313 | ||||||||
\(362\) | −2.05682e111 | −1.02182 | ||||||||
\(363\) | −2.22815e111 | −0.981763 | ||||||||
\(364\) | 3.71976e111 | 1.45414 | ||||||||
\(365\) | 9.29497e110 | 0.322484 | ||||||||
\(366\) | 9.64427e111 | 2.97059 | ||||||||
\(367\) | −8.73210e110 | −0.238861 | −0.119430 | − | 0.992843i | \(-0.538107\pi\) | ||||
−0.119430 | + | 0.992843i | \(0.538107\pi\) | |||||||
\(368\) | 5.50860e111 | 1.33863 | ||||||||
\(369\) | −2.38354e111 | −0.514726 | ||||||||
\(370\) | 1.91803e112 | 3.68196 | ||||||||
\(371\) | −1.38532e112 | −2.36475 | ||||||||
\(372\) | −1.86195e112 | −2.82716 | ||||||||
\(373\) | 2.10926e110 | 0.0284968 | 0.0142484 | − | 0.999898i | \(-0.495464\pi\) | ||||
0.0142484 | + | 0.999898i | \(0.495464\pi\) | |||||||
\(374\) | −1.15479e112 | −1.38864 | ||||||||
\(375\) | 1.13741e112 | 1.21775 | ||||||||
\(376\) | −1.10720e112 | −1.05573 | ||||||||
\(377\) | 2.20360e111 | 0.187191 | ||||||||
\(378\) | 2.45929e112 | 1.86173 | ||||||||
\(379\) | −2.78355e112 | −1.87842 | −0.939212 | − | 0.343337i | \(-0.888443\pi\) | ||||
−0.939212 | + | 0.343337i | \(0.888443\pi\) | |||||||
\(380\) | 1.65489e112 | 0.995826 | ||||||||
\(381\) | −4.00490e110 | −0.0214959 | ||||||||
\(382\) | 2.90325e112 | 1.39036 | ||||||||
\(383\) | −3.62318e111 | −0.154862 | −0.0774308 | − | 0.996998i | \(-0.524672\pi\) | ||||
−0.0774308 | + | 0.996998i | \(0.524672\pi\) | |||||||
\(384\) | −6.34152e112 | −2.41983 | ||||||||
\(385\) | 2.65437e112 | 0.904524 | ||||||||
\(386\) | −4.96302e112 | −1.51077 | ||||||||
\(387\) | 5.86063e112 | 1.59411 | ||||||||
\(388\) | 3.30143e111 | 0.0802642 | ||||||||
\(389\) | 1.31636e112 | 0.286132 | 0.143066 | − | 0.989713i | \(-0.454304\pi\) | ||||
0.143066 | + | 0.989713i | \(0.454304\pi\) | |||||||
\(390\) | −9.10346e112 | −1.76968 | ||||||||
\(391\) | 7.44139e112 | 1.29409 | ||||||||
\(392\) | 7.49474e112 | 1.16631 | ||||||||
\(393\) | 1.37480e113 | 1.91498 | ||||||||
\(394\) | −1.15070e112 | −0.143508 | ||||||||
\(395\) | −2.71532e112 | −0.303283 | ||||||||
\(396\) | −1.98234e113 | −1.98353 | ||||||||
\(397\) | −1.77777e113 | −1.59400 | −0.797002 | − | 0.603977i | \(-0.793582\pi\) | ||||
−0.797002 | + | 0.603977i | \(0.793582\pi\) | |||||||
\(398\) | 3.49073e113 | 2.80545 | ||||||||
\(399\) | −1.14255e113 | −0.823292 | ||||||||
\(400\) | 6.88697e112 | 0.445060 | ||||||||
\(401\) | −4.38593e112 | −0.254262 | −0.127131 | − | 0.991886i | \(-0.540577\pi\) | ||||
−0.127131 | + | 0.991886i | \(0.540577\pi\) | |||||||
\(402\) | −3.29605e113 | −1.71459 | ||||||||
\(403\) | −9.90431e112 | −0.462439 | ||||||||
\(404\) | −5.67477e113 | −2.37880 | ||||||||
\(405\) | 6.08103e112 | 0.228920 | ||||||||
\(406\) | 2.25665e113 | 0.763101 | ||||||||
\(407\) | 3.67786e113 | 1.11748 | ||||||||
\(408\) | 1.44153e114 | 3.93647 | ||||||||
\(409\) | −1.55796e113 | −0.382466 | −0.191233 | − | 0.981545i | \(-0.561249\pi\) | ||||
−0.191233 | + | 0.981545i | \(0.561249\pi\) | |||||||
\(410\) | 3.11328e113 | 0.687259 | ||||||||
\(411\) | −2.27335e113 | −0.451385 | ||||||||
\(412\) | −1.89746e114 | −3.38957 | ||||||||
\(413\) | −1.76400e113 | −0.283577 | ||||||||
\(414\) | 1.88488e114 | 2.72753 | ||||||||
\(415\) | 7.63042e113 | 0.994160 | ||||||||
\(416\) | 1.77392e113 | 0.208149 | ||||||||
\(417\) | −1.49136e114 | −1.57639 | ||||||||
\(418\) | 4.68237e113 | 0.445962 | ||||||||
\(419\) | 1.49846e114 | 1.28628 | 0.643140 | − | 0.765748i | \(-0.277631\pi\) | ||||
0.643140 | + | 0.765748i | \(0.277631\pi\) | |||||||
\(420\) | −6.31804e114 | −4.88920 | ||||||||
\(421\) | −1.30632e114 | −0.911544 | −0.455772 | − | 0.890096i | \(-0.650637\pi\) | ||||
−0.455772 | + | 0.890096i | \(0.650637\pi\) | |||||||
\(422\) | 5.45363e114 | 3.43237 | ||||||||
\(423\) | −1.46034e114 | −0.829178 | ||||||||
\(424\) | −7.08699e114 | −3.63117 | ||||||||
\(425\) | 9.30339e113 | 0.430252 | ||||||||
\(426\) | 1.17105e115 | 4.88945 | ||||||||
\(427\) | 3.56042e114 | 1.34242 | ||||||||
\(428\) | 7.05744e113 | 0.240349 | ||||||||
\(429\) | −1.74561e114 | −0.537099 | ||||||||
\(430\) | −7.65490e114 | −2.12844 | ||||||||
\(431\) | −5.31720e114 | −1.33635 | −0.668177 | − | 0.744002i | \(-0.732925\pi\) | ||||
−0.668177 | + | 0.744002i | \(0.732925\pi\) | |||||||
\(432\) | 4.84960e114 | 1.10195 | ||||||||
\(433\) | 2.52039e114 | 0.517899 | 0.258949 | − | 0.965891i | \(-0.416624\pi\) | ||||
0.258949 | + | 0.965891i | \(0.416624\pi\) | |||||||
\(434\) | −1.01428e115 | −1.88518 | ||||||||
\(435\) | −3.74283e114 | −0.629386 | ||||||||
\(436\) | 2.36877e115 | 3.60463 | ||||||||
\(437\) | −3.01728e114 | −0.415598 | ||||||||
\(438\) | −6.25986e114 | −0.780622 | ||||||||
\(439\) | 9.43647e113 | 0.106562 | 0.0532811 | − | 0.998580i | \(-0.483032\pi\) | ||||
0.0532811 | + | 0.998580i | \(0.483032\pi\) | |||||||
\(440\) | 1.35792e115 | 1.38893 | ||||||||
\(441\) | 9.88518e114 | 0.916022 | ||||||||
\(442\) | 1.46211e115 | 1.22775 | ||||||||
\(443\) | 2.77028e114 | 0.210844 | 0.105422 | − | 0.994428i | \(-0.466381\pi\) | ||||
0.105422 | + | 0.994428i | \(0.466381\pi\) | |||||||
\(444\) | −8.75418e115 | −6.04027 | ||||||||
\(445\) | 3.03297e114 | 0.189761 | ||||||||
\(446\) | −8.30027e113 | −0.0471005 | ||||||||
\(447\) | −1.42875e115 | −0.735496 | ||||||||
\(448\) | −1.75565e115 | −0.820057 | ||||||||
\(449\) | 2.39383e115 | 1.01479 | 0.507397 | − | 0.861712i | \(-0.330608\pi\) | ||||
0.507397 | + | 0.861712i | \(0.330608\pi\) | |||||||
\(450\) | 2.35652e115 | 0.906832 | ||||||||
\(451\) | 5.96979e114 | 0.208583 | ||||||||
\(452\) | 8.82207e115 | 2.79930 | ||||||||
\(453\) | 7.79288e114 | 0.224608 | ||||||||
\(454\) | −1.86423e115 | −0.488168 | ||||||||
\(455\) | −3.36076e115 | −0.799727 | ||||||||
\(456\) | −5.84502e115 | −1.26420 | ||||||||
\(457\) | 5.47308e115 | 1.07616 | 0.538081 | − | 0.842893i | \(-0.319150\pi\) | ||||
0.538081 | + | 0.842893i | \(0.319150\pi\) | |||||||
\(458\) | 1.41104e116 | 2.52285 | ||||||||
\(459\) | 6.55116e115 | 1.06529 | ||||||||
\(460\) | −1.66849e116 | −2.46807 | ||||||||
\(461\) | 3.15068e115 | 0.424047 | 0.212023 | − | 0.977265i | \(-0.431995\pi\) | ||||
0.212023 | + | 0.977265i | \(0.431995\pi\) | |||||||
\(462\) | −1.78763e116 | −2.18954 | ||||||||
\(463\) | −6.34150e115 | −0.706999 | −0.353500 | − | 0.935435i | \(-0.615008\pi\) | ||||
−0.353500 | + | 0.935435i | \(0.615008\pi\) | |||||||
\(464\) | 4.45001e115 | 0.451677 | ||||||||
\(465\) | 1.68225e116 | 1.55485 | ||||||||
\(466\) | −2.09230e116 | −1.76131 | ||||||||
\(467\) | −2.26650e116 | −1.73808 | −0.869042 | − | 0.494738i | \(-0.835264\pi\) | ||||
−0.869042 | + | 0.494738i | \(0.835264\pi\) | |||||||
\(468\) | 2.50989e116 | 1.75372 | ||||||||
\(469\) | −1.21682e116 | −0.774831 | ||||||||
\(470\) | 1.90743e116 | 1.10711 | ||||||||
\(471\) | 1.29729e116 | 0.686482 | ||||||||
\(472\) | −9.02420e115 | −0.435443 | ||||||||
\(473\) | −1.46784e116 | −0.645982 | ||||||||
\(474\) | 1.82868e116 | 0.734142 | ||||||||
\(475\) | −3.77227e115 | −0.138176 | ||||||||
\(476\) | 1.01474e117 | 3.39198 | ||||||||
\(477\) | −9.34737e116 | −2.85194 | ||||||||
\(478\) | 1.07127e116 | 0.298391 | ||||||||
\(479\) | −2.73182e113 | −0.000694795 0 | −0.000347398 | − | 1.00000i | \(-0.500111\pi\) | ||||
−0.000347398 | 1.00000i | \(0.500111\pi\) | ||||||||
\(480\) | −3.01301e116 | −0.699852 | ||||||||
\(481\) | −4.65662e116 | −0.988007 | ||||||||
\(482\) | 6.73285e116 | 1.30513 | ||||||||
\(483\) | 1.15194e117 | 2.04046 | ||||||||
\(484\) | −8.02394e116 | −1.29902 | ||||||||
\(485\) | −2.98280e115 | −0.0441427 | ||||||||
\(486\) | −1.49717e117 | −2.02578 | ||||||||
\(487\) | 8.24893e116 | 1.02068 | 0.510338 | − | 0.859974i | \(-0.329520\pi\) | ||||
0.510338 | + | 0.859974i | \(0.329520\pi\) | |||||||
\(488\) | 1.82143e117 | 2.06134 | ||||||||
\(489\) | −2.79719e116 | −0.289592 | ||||||||
\(490\) | −1.29116e117 | −1.22307 | ||||||||
\(491\) | −7.22914e116 | −0.626674 | −0.313337 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313337 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(492\) | −1.42095e117 | −1.12745 | ||||||||
\(493\) | 6.01137e116 | 0.436649 | ||||||||
\(494\) | −5.92846e116 | −0.394294 | ||||||||
\(495\) | 1.79102e117 | 1.09087 | ||||||||
\(496\) | −2.00010e117 | −1.11583 | ||||||||
\(497\) | 4.32323e117 | 2.20956 | ||||||||
\(498\) | −5.13884e117 | −2.40652 | ||||||||
\(499\) | −3.07202e117 | −1.31841 | −0.659204 | − | 0.751964i | \(-0.729107\pi\) | ||||
−0.659204 | + | 0.751964i | \(0.729107\pi\) | |||||||
\(500\) | 4.09602e117 | 1.61126 | ||||||||
\(501\) | −3.96564e117 | −1.43012 | ||||||||
\(502\) | 8.55445e117 | 2.82866 | ||||||||
\(503\) | 3.23349e116 | 0.0980538 | 0.0490269 | − | 0.998797i | \(-0.484388\pi\) | ||||
0.0490269 | + | 0.998797i | \(0.484388\pi\) | |||||||
\(504\) | 1.34799e118 | 3.74936 | ||||||||
\(505\) | 5.12708e117 | 1.30826 | ||||||||
\(506\) | −4.72084e117 | −1.10528 | ||||||||
\(507\) | −5.18652e117 | −1.11437 | ||||||||
\(508\) | −1.44223e116 | −0.0284422 | ||||||||
\(509\) | −5.28702e117 | −0.957166 | −0.478583 | − | 0.878042i | \(-0.658849\pi\) | ||||
−0.478583 | + | 0.878042i | \(0.658849\pi\) | |||||||
\(510\) | −2.48340e118 | −4.12804 | ||||||||
\(511\) | −2.31098e117 | −0.352766 | ||||||||
\(512\) | −1.46926e118 | −2.05995 | ||||||||
\(513\) | −2.65632e117 | −0.342117 | ||||||||
\(514\) | 1.67129e118 | 1.97768 | ||||||||
\(515\) | 1.71433e118 | 1.86415 | ||||||||
\(516\) | 3.49382e118 | 3.49171 | ||||||||
\(517\) | 3.65754e117 | 0.336009 | ||||||||
\(518\) | −4.76873e118 | −4.02771 | ||||||||
\(519\) | 1.49214e118 | 1.15886 | ||||||||
\(520\) | −1.71929e118 | −1.22801 | ||||||||
\(521\) | 9.85155e117 | 0.647237 | 0.323619 | − | 0.946188i | \(-0.395101\pi\) | ||||
0.323619 | + | 0.946188i | \(0.395101\pi\) | |||||||
\(522\) | 1.52266e118 | 0.920315 | ||||||||
\(523\) | −2.26194e118 | −1.25793 | −0.628966 | − | 0.777433i | \(-0.716521\pi\) | ||||
−0.628966 | + | 0.777433i | \(0.716521\pi\) | |||||||
\(524\) | 4.95089e118 | 2.53380 | ||||||||
\(525\) | 1.44018e118 | 0.678400 | ||||||||
\(526\) | −3.12708e118 | −1.35600 | ||||||||
\(527\) | −2.70187e118 | −1.07871 | ||||||||
\(528\) | −3.52512e118 | −1.29598 | ||||||||
\(529\) | 8.86796e116 | 0.0300263 | ||||||||
\(530\) | 1.22091e119 | 3.80789 | ||||||||
\(531\) | −1.19025e118 | −0.341999 | ||||||||
\(532\) | −4.11451e118 | −1.08934 | ||||||||
\(533\) | −7.55849e117 | −0.184417 | ||||||||
\(534\) | −2.04261e118 | −0.459346 | ||||||||
\(535\) | −6.37631e117 | −0.132184 | ||||||||
\(536\) | −6.22496e118 | −1.18978 | ||||||||
\(537\) | −1.15901e118 | −0.204271 | ||||||||
\(538\) | 1.23122e119 | 2.00128 | ||||||||
\(539\) | −2.47583e118 | −0.371201 | ||||||||
\(540\) | −1.46889e119 | −2.03170 | ||||||||
\(541\) | 6.77058e118 | 0.864062 | 0.432031 | − | 0.901859i | \(-0.357797\pi\) | ||||
0.432031 | + | 0.901859i | \(0.357797\pi\) | |||||||
\(542\) | 1.01608e119 | 1.19662 | ||||||||
\(543\) | −8.48162e118 | −0.921906 | ||||||||
\(544\) | 4.83920e118 | 0.485536 | ||||||||
\(545\) | −2.14015e119 | −1.98243 | ||||||||
\(546\) | 2.26336e119 | 1.93586 | ||||||||
\(547\) | −1.64167e119 | −1.29669 | −0.648346 | − | 0.761346i | \(-0.724539\pi\) | ||||
−0.648346 | + | 0.761346i | \(0.724539\pi\) | |||||||
\(548\) | −8.18670e118 | −0.597248 | ||||||||
\(549\) | 2.40237e119 | 1.61898 | ||||||||
\(550\) | −5.90210e118 | −0.367477 | ||||||||
\(551\) | −2.43745e118 | −0.140230 | ||||||||
\(552\) | 5.89304e119 | 3.13321 | ||||||||
\(553\) | 6.75102e118 | 0.331762 | ||||||||
\(554\) | −3.05346e119 | −1.38713 | ||||||||
\(555\) | 7.90929e119 | 3.32195 | ||||||||
\(556\) | −5.37063e119 | −2.08580 | ||||||||
\(557\) | −1.22711e119 | −0.440739 | −0.220369 | − | 0.975417i | \(-0.570726\pi\) | ||||
−0.220369 | + | 0.975417i | \(0.570726\pi\) | |||||||
\(558\) | −6.84376e119 | −2.27356 | ||||||||
\(559\) | 1.85847e119 | 0.571139 | ||||||||
\(560\) | −6.78680e119 | −1.92968 | ||||||||
\(561\) | −4.76197e119 | −1.25286 | ||||||||
\(562\) | 1.41961e120 | 3.45652 | ||||||||
\(563\) | 3.15592e119 | 0.711232 | 0.355616 | − | 0.934632i | \(-0.384271\pi\) | ||||
0.355616 | + | 0.934632i | \(0.384271\pi\) | |||||||
\(564\) | −8.70582e119 | −1.81622 | ||||||||
\(565\) | −7.97064e119 | −1.53952 | ||||||||
\(566\) | −1.47129e120 | −2.63139 | ||||||||
\(567\) | −1.51191e119 | −0.250416 | ||||||||
\(568\) | 2.21167e120 | 3.39287 | ||||||||
\(569\) | 7.97402e119 | 1.13317 | 0.566583 | − | 0.824005i | \(-0.308265\pi\) | ||||
0.566583 | + | 0.824005i | \(0.308265\pi\) | |||||||
\(570\) | 1.00695e120 | 1.32572 | ||||||||
\(571\) | 7.69582e119 | 0.938825 | 0.469412 | − | 0.882979i | \(-0.344466\pi\) | ||||
0.469412 | + | 0.882979i | \(0.344466\pi\) | |||||||
\(572\) | −6.28622e119 | −0.710661 | ||||||||
\(573\) | 1.19720e120 | 1.25442 | ||||||||
\(574\) | −7.74045e119 | −0.751794 | ||||||||
\(575\) | 3.80327e119 | 0.342457 | ||||||||
\(576\) | −1.18461e120 | −0.989004 | ||||||||
\(577\) | −3.60188e119 | −0.278857 | −0.139429 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139429 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(578\) | 1.53537e120 | 1.10243 | ||||||||
\(579\) | −2.04658e120 | −1.36305 | ||||||||
\(580\) | −1.34785e120 | −0.832770 | ||||||||
\(581\) | −1.89713e120 | −1.08751 | ||||||||
\(582\) | 2.00882e119 | 0.106854 | ||||||||
\(583\) | 2.34113e120 | 1.15569 | ||||||||
\(584\) | −1.18224e120 | −0.541687 | ||||||||
\(585\) | −2.26765e120 | −0.964487 | ||||||||
\(586\) | 5.95013e120 | 2.34952 | ||||||||
\(587\) | −4.10740e120 | −1.50595 | −0.752973 | − | 0.658052i | \(-0.771381\pi\) | ||||
−0.752973 | + | 0.658052i | \(0.771381\pi\) | |||||||
\(588\) | 5.89306e120 | 2.00644 | ||||||||
\(589\) | 1.09554e120 | 0.346427 | ||||||||
\(590\) | 1.55465e120 | 0.456635 | ||||||||
\(591\) | −4.74511e119 | −0.129477 | ||||||||
\(592\) | −9.40369e120 | −2.38399 | ||||||||
\(593\) | −5.50645e119 | −0.129716 | −0.0648579 | − | 0.997895i | \(-0.520659\pi\) | ||||
−0.0648579 | + | 0.997895i | \(0.520659\pi\) | |||||||
\(594\) | −4.15608e120 | −0.909858 | ||||||||
\(595\) | −9.16807e120 | −1.86548 | ||||||||
\(596\) | −5.14518e120 | −0.973169 | ||||||||
\(597\) | 1.43946e121 | 2.53114 | ||||||||
\(598\) | 5.97717e120 | 0.977224 | ||||||||
\(599\) | 7.02687e120 | 1.06831 | 0.534153 | − | 0.845388i | \(-0.320631\pi\) | ||||
0.534153 | + | 0.845388i | \(0.320631\pi\) | |||||||
\(600\) | 7.36761e120 | 1.04171 | ||||||||
\(601\) | −1.79955e120 | −0.236659 | −0.118330 | − | 0.992974i | \(-0.537754\pi\) | ||||
−0.118330 | + | 0.992974i | \(0.537754\pi\) | |||||||
\(602\) | 1.90321e121 | 2.32831 | ||||||||
\(603\) | −8.21041e120 | −0.934462 | ||||||||
\(604\) | 2.80634e120 | 0.297190 | ||||||||
\(605\) | 7.24954e120 | 0.714416 | ||||||||
\(606\) | −3.45292e121 | −3.16685 | ||||||||
\(607\) | −3.31580e120 | −0.283062 | −0.141531 | − | 0.989934i | \(-0.545202\pi\) | ||||
−0.141531 | + | 0.989934i | \(0.545202\pi\) | |||||||
\(608\) | −1.96217e120 | −0.155930 | ||||||||
\(609\) | 9.30567e120 | 0.688487 | ||||||||
\(610\) | −3.13787e121 | −2.16166 | ||||||||
\(611\) | −4.63090e120 | −0.297079 | ||||||||
\(612\) | 6.84691e121 | 4.09079 | ||||||||
\(613\) | −2.68663e121 | −1.49512 | −0.747562 | − | 0.664192i | \(-0.768776\pi\) | ||||
−0.747562 | + | 0.664192i | \(0.768776\pi\) | |||||||
\(614\) | −6.85838e120 | −0.355547 | ||||||||
\(615\) | 1.28381e121 | 0.620060 | ||||||||
\(616\) | −3.37614e121 | −1.51936 | ||||||||
\(617\) | −9.07733e119 | −0.0380674 | −0.0190337 | − | 0.999819i | \(-0.506059\pi\) | ||||
−0.0190337 | + | 0.999819i | \(0.506059\pi\) | |||||||
\(618\) | −1.15455e122 | −4.51246 | ||||||||
\(619\) | 1.74643e121 | 0.636222 | 0.318111 | − | 0.948053i | \(-0.396952\pi\) | ||||
0.318111 | + | 0.948053i | \(0.396952\pi\) | |||||||
\(620\) | 6.05807e121 | 2.05729 | ||||||||
\(621\) | 2.67815e121 | 0.847910 | ||||||||
\(622\) | 8.92223e121 | 2.63385 | ||||||||
\(623\) | −7.54078e120 | −0.207580 | ||||||||
\(624\) | 4.46324e121 | 1.14583 | ||||||||
\(625\) | −5.10987e121 | −1.22357 | ||||||||
\(626\) | 1.05536e122 | 2.35730 | ||||||||
\(627\) | 1.93085e121 | 0.402357 | ||||||||
\(628\) | 4.67177e121 | 0.908316 | ||||||||
\(629\) | −1.27031e122 | −2.30467 | ||||||||
\(630\) | −2.32225e122 | −3.93183 | ||||||||
\(631\) | 2.91383e121 | 0.460456 | 0.230228 | − | 0.973137i | \(-0.426053\pi\) | ||||
0.230228 | + | 0.973137i | \(0.426053\pi\) | |||||||
\(632\) | 3.45367e121 | 0.509433 | ||||||||
\(633\) | 2.24889e122 | 3.09676 | ||||||||
\(634\) | 2.76841e121 | 0.355916 | ||||||||
\(635\) | 1.30304e120 | 0.0156423 | ||||||||
\(636\) | −5.57244e122 | −6.24685 | ||||||||
\(637\) | 3.13470e121 | 0.328194 | ||||||||
\(638\) | −3.81363e121 | −0.372940 | ||||||||
\(639\) | 2.91707e122 | 2.66477 | ||||||||
\(640\) | 2.06328e122 | 1.76088 | ||||||||
\(641\) | −1.26041e122 | −1.00505 | −0.502524 | − | 0.864563i | \(-0.667595\pi\) | ||||
−0.502524 | + | 0.864563i | \(0.667595\pi\) | |||||||
\(642\) | 4.29424e121 | 0.319972 | ||||||||
\(643\) | −1.27618e121 | −0.0888655 | −0.0444327 | − | 0.999012i | \(-0.514148\pi\) | ||||
−0.0444327 | + | 0.999012i | \(0.514148\pi\) | |||||||
\(644\) | 4.14831e122 | 2.69983 | ||||||||
\(645\) | −3.15662e122 | −1.92033 | ||||||||
\(646\) | −1.61727e122 | −0.919745 | ||||||||
\(647\) | 8.91644e120 | 0.0474084 | 0.0237042 | − | 0.999719i | \(-0.492454\pi\) | ||||
0.0237042 | + | 0.999719i | \(0.492454\pi\) | |||||||
\(648\) | −7.73457e121 | −0.384524 | ||||||||
\(649\) | 2.98107e121 | 0.138589 | ||||||||
\(650\) | 7.47279e121 | 0.324901 | ||||||||
\(651\) | −4.18253e122 | −1.70085 | ||||||||
\(652\) | −1.00731e122 | −0.383172 | ||||||||
\(653\) | 1.51404e122 | 0.538782 | 0.269391 | − | 0.963031i | \(-0.413178\pi\) | ||||
0.269391 | + | 0.963031i | \(0.413178\pi\) | |||||||
\(654\) | 1.44132e123 | 4.79877 | ||||||||
\(655\) | −4.47307e122 | −1.39351 | ||||||||
\(656\) | −1.52638e122 | −0.444985 | ||||||||
\(657\) | −1.55932e122 | −0.425443 | ||||||||
\(658\) | −4.74238e122 | −1.21107 | ||||||||
\(659\) | −2.23773e122 | −0.534924 | −0.267462 | − | 0.963568i | \(-0.586185\pi\) | ||||
−0.267462 | + | 0.963568i | \(0.586185\pi\) | |||||||
\(660\) | 1.06772e123 | 2.38944 | ||||||||
\(661\) | −3.07824e122 | −0.644970 | −0.322485 | − | 0.946575i | \(-0.604518\pi\) | ||||
−0.322485 | + | 0.946575i | \(0.604518\pi\) | |||||||
\(662\) | 9.04302e122 | 1.77415 | ||||||||
\(663\) | 6.02925e122 | 1.10771 | ||||||||
\(664\) | −9.70527e122 | −1.66992 | ||||||||
\(665\) | 3.71741e122 | 0.599099 | ||||||||
\(666\) | −3.21767e123 | −4.85749 | ||||||||
\(667\) | 2.45748e122 | 0.347548 | ||||||||
\(668\) | −1.42809e123 | −1.89226 | ||||||||
\(669\) | −3.42275e121 | −0.0424952 | ||||||||
\(670\) | 1.07241e123 | 1.24769 | ||||||||
\(671\) | −6.01693e122 | −0.656063 | ||||||||
\(672\) | 7.49115e122 | 0.765570 | ||||||||
\(673\) | 9.53095e122 | 0.913022 | 0.456511 | − | 0.889718i | \(-0.349099\pi\) | ||||
0.456511 | + | 0.889718i | \(0.349099\pi\) | |||||||
\(674\) | 1.64801e123 | 1.47998 | ||||||||
\(675\) | 3.34828e122 | 0.281908 | ||||||||
\(676\) | −1.86775e123 | −1.47448 | ||||||||
\(677\) | 2.56578e123 | 1.89938 | 0.949691 | − | 0.313188i | \(-0.101397\pi\) | ||||
0.949691 | + | 0.313188i | \(0.101397\pi\) | |||||||
\(678\) | 5.36796e123 | 3.72664 | ||||||||
\(679\) | 7.41604e121 | 0.0482878 | ||||||||
\(680\) | −4.69017e123 | −2.86452 | ||||||||
\(681\) | −7.68745e122 | −0.440436 | ||||||||
\(682\) | 1.71408e123 | 0.921319 | ||||||||
\(683\) | −2.88998e123 | −1.45745 | −0.728727 | − | 0.684805i | \(-0.759888\pi\) | ||||
−0.728727 | + | 0.684805i | \(0.759888\pi\) | |||||||
\(684\) | −2.77624e123 | −1.31376 | ||||||||
\(685\) | 7.39659e122 | 0.328467 | ||||||||
\(686\) | −2.13658e123 | −0.890473 | ||||||||
\(687\) | 5.81867e123 | 2.27617 | ||||||||
\(688\) | 3.75304e123 | 1.37812 | ||||||||
\(689\) | −2.96416e123 | −1.02180 | ||||||||
\(690\) | −1.01523e124 | −3.28569 | ||||||||
\(691\) | −1.42365e122 | −0.0432621 | −0.0216311 | − | 0.999766i | \(-0.506886\pi\) | ||||
−0.0216311 | + | 0.999766i | \(0.506886\pi\) | |||||||
\(692\) | 5.37344e123 | 1.53334 | ||||||||
\(693\) | −4.45296e123 | −1.19331 | ||||||||
\(694\) | 2.92420e122 | 0.0735986 | ||||||||
\(695\) | 4.85230e123 | 1.14712 | ||||||||
\(696\) | 4.76057e123 | 1.05720 | ||||||||
\(697\) | −2.06194e123 | −0.430179 | ||||||||
\(698\) | −7.42407e123 | −1.45523 | ||||||||
\(699\) | −8.62794e123 | −1.58910 | ||||||||
\(700\) | 5.18631e123 | 0.897623 | ||||||||
\(701\) | 6.07300e123 | 0.987801 | 0.493900 | − | 0.869518i | \(-0.335571\pi\) | ||||
0.493900 | + | 0.869518i | \(0.335571\pi\) | |||||||
\(702\) | 5.26211e123 | 0.804444 | ||||||||
\(703\) | 5.15078e123 | 0.740145 | ||||||||
\(704\) | 2.96696e123 | 0.400775 | ||||||||
\(705\) | 7.86560e123 | 0.998862 | ||||||||
\(706\) | 1.69066e124 | 2.01861 | ||||||||
\(707\) | −1.27473e124 | −1.43111 | ||||||||
\(708\) | −7.09566e123 | −0.749111 | ||||||||
\(709\) | −9.12953e123 | −0.906436 | −0.453218 | − | 0.891400i | \(-0.649724\pi\) | ||||
−0.453218 | + | 0.891400i | \(0.649724\pi\) | |||||||
\(710\) | −3.81015e124 | −3.55799 | ||||||||
\(711\) | 4.55521e123 | 0.400111 | ||||||||
\(712\) | −3.85769e123 | −0.318748 | ||||||||
\(713\) | −1.10454e124 | −0.858591 | ||||||||
\(714\) | 6.17440e124 | 4.51567 | ||||||||
\(715\) | 5.67953e123 | 0.390840 | ||||||||
\(716\) | −4.17379e123 | −0.270280 | ||||||||
\(717\) | 4.41756e123 | 0.269215 | ||||||||
\(718\) | 2.98896e124 | 1.71438 | ||||||||
\(719\) | 1.34804e124 | 0.727771 | 0.363885 | − | 0.931444i | \(-0.381450\pi\) | ||||
0.363885 | + | 0.931444i | \(0.381450\pi\) | |||||||
\(720\) | −4.57935e124 | −2.32724 | ||||||||
\(721\) | −4.26229e124 | −2.03920 | ||||||||
\(722\) | −3.25486e124 | −1.46610 | ||||||||
\(723\) | 2.77640e124 | 1.17751 | ||||||||
\(724\) | −3.05437e124 | −1.21982 | ||||||||
\(725\) | 3.07239e123 | 0.115551 | ||||||||
\(726\) | −4.88233e124 | −1.72935 | ||||||||
\(727\) | 2.45578e124 | 0.819299 | 0.409650 | − | 0.912243i | \(-0.365651\pi\) | ||||
0.409650 | + | 0.912243i | \(0.365651\pi\) | |||||||
\(728\) | 4.27461e124 | 1.34333 | ||||||||
\(729\) | −5.50516e124 | −1.62976 | ||||||||
\(730\) | 2.03671e124 | 0.568049 | ||||||||
\(731\) | 5.06986e124 | 1.33226 | ||||||||
\(732\) | 1.43217e125 | 3.54620 | ||||||||
\(733\) | −6.62584e123 | −0.154603 | −0.0773015 | − | 0.997008i | \(-0.524630\pi\) | ||||
−0.0773015 | + | 0.997008i | \(0.524630\pi\) | |||||||
\(734\) | −1.91338e124 | −0.420748 | ||||||||
\(735\) | −5.32430e124 | −1.10348 | ||||||||
\(736\) | 1.97829e124 | 0.386460 | ||||||||
\(737\) | 2.05636e124 | 0.378673 | ||||||||
\(738\) | −5.22282e124 | −0.906679 | ||||||||
\(739\) | 5.98416e123 | 0.0979422 | 0.0489711 | − | 0.998800i | \(-0.484406\pi\) | ||||
0.0489711 | + | 0.998800i | \(0.484406\pi\) | |||||||
\(740\) | 2.84827e125 | 4.39543 | ||||||||
\(741\) | −2.44470e124 | −0.355740 | ||||||||
\(742\) | −3.03552e125 | −4.16546 | ||||||||
\(743\) | 4.85932e124 | 0.628872 | 0.314436 | − | 0.949279i | \(-0.398185\pi\) | ||||
0.314436 | + | 0.949279i | \(0.398185\pi\) | |||||||
\(744\) | −2.13969e125 | −2.61173 | ||||||||
\(745\) | 4.64861e124 | 0.535211 | ||||||||
\(746\) | 4.62181e123 | 0.0501965 | ||||||||
\(747\) | −1.28007e125 | −1.31156 | ||||||||
\(748\) | −1.71487e125 | −1.65772 | ||||||||
\(749\) | 1.58532e124 | 0.144597 | ||||||||
\(750\) | 2.49230e125 | 2.14504 | ||||||||
\(751\) | −3.85338e124 | −0.312971 | −0.156485 | − | 0.987680i | \(-0.550016\pi\) | ||||
−0.156485 | + | 0.987680i | \(0.550016\pi\) | |||||||
\(752\) | −9.35175e124 | −0.716831 | ||||||||
\(753\) | 3.52757e125 | 2.55208 | ||||||||
\(754\) | 4.82853e124 | 0.329732 | ||||||||
\(755\) | −2.53550e124 | −0.163445 | ||||||||
\(756\) | 3.65204e125 | 2.22248 | ||||||||
\(757\) | 1.30143e125 | 0.747739 | 0.373870 | − | 0.927481i | \(-0.378031\pi\) | ||||
0.373870 | + | 0.927481i | \(0.378031\pi\) | |||||||
\(758\) | −6.09932e125 | −3.30880 | ||||||||
\(759\) | −1.94672e125 | −0.997208 | ||||||||
\(760\) | 1.90174e125 | 0.919941 | ||||||||
\(761\) | −8.62091e124 | −0.393841 | −0.196920 | − | 0.980419i | \(-0.563094\pi\) | ||||
−0.196920 | + | 0.980419i | \(0.563094\pi\) | |||||||
\(762\) | −8.77552e123 | −0.0378645 | ||||||||
\(763\) | 5.32100e125 | 2.16858 | ||||||||
\(764\) | 4.31132e125 | 1.65978 | ||||||||
\(765\) | −6.18610e125 | −2.24980 | ||||||||
\(766\) | −7.93912e124 | −0.272785 | ||||||||
\(767\) | −3.77440e124 | −0.122532 | ||||||||
\(768\) | −1.05371e126 | −3.23228 | ||||||||
\(769\) | 4.22053e125 | 1.22341 | 0.611704 | − | 0.791087i | \(-0.290484\pi\) | ||||
0.611704 | + | 0.791087i | \(0.290484\pi\) | |||||||
\(770\) | 5.81626e125 | 1.59330 | ||||||||
\(771\) | 6.89185e125 | 1.78431 | ||||||||
\(772\) | −7.37008e125 | −1.80351 | ||||||||
\(773\) | −1.70364e125 | −0.394067 | −0.197034 | − | 0.980397i | \(-0.563131\pi\) | ||||
−0.197034 | + | 0.980397i | \(0.563131\pi\) | |||||||
\(774\) | 1.28418e126 | 2.80798 | ||||||||
\(775\) | −1.38092e125 | −0.285459 | ||||||||
\(776\) | 3.79388e124 | 0.0741478 | ||||||||
\(777\) | −1.96646e126 | −3.63389 | ||||||||
\(778\) | 2.88440e125 | 0.504015 | ||||||||
\(779\) | 8.36060e124 | 0.138152 | ||||||||
\(780\) | −1.35186e126 | −2.11260 | ||||||||
\(781\) | −7.30606e125 | −1.07985 | ||||||||
\(782\) | 1.63056e126 | 2.27951 | ||||||||
\(783\) | 2.16348e125 | 0.286099 | ||||||||
\(784\) | 6.33029e125 | 0.791908 | ||||||||
\(785\) | −4.22089e125 | −0.499544 | ||||||||
\(786\) | 3.01247e126 | 3.37320 | ||||||||
\(787\) | −1.36872e126 | −1.45015 | −0.725075 | − | 0.688670i | \(-0.758195\pi\) | ||||
−0.725075 | + | 0.688670i | \(0.758195\pi\) | |||||||
\(788\) | −1.70879e125 | −0.171316 | ||||||||
\(789\) | −1.28950e126 | −1.22341 | ||||||||
\(790\) | −5.94981e125 | −0.534226 | ||||||||
\(791\) | 1.98171e126 | 1.68408 | ||||||||
\(792\) | −2.27803e126 | −1.83237 | ||||||||
\(793\) | 7.61818e125 | 0.580053 | ||||||||
\(794\) | −3.89546e126 | −2.80780 | ||||||||
\(795\) | 5.03463e126 | 3.43556 | ||||||||
\(796\) | 5.18374e126 | 3.34907 | ||||||||
\(797\) | 1.50722e126 | 0.922018 | 0.461009 | − | 0.887396i | \(-0.347488\pi\) | ||||
0.461009 | + | 0.887396i | \(0.347488\pi\) | |||||||
\(798\) | −2.50355e126 | −1.45021 | ||||||||
\(799\) | −1.26330e126 | −0.692980 | ||||||||
\(800\) | 2.47330e125 | 0.128488 | ||||||||
\(801\) | −5.08809e125 | −0.250346 | ||||||||
\(802\) | −9.61044e125 | −0.447877 | ||||||||
\(803\) | 3.90544e125 | 0.172403 | ||||||||
\(804\) | −4.89464e126 | −2.04683 | ||||||||
\(805\) | −3.74795e126 | −1.48482 | ||||||||
\(806\) | −2.17023e126 | −0.814577 | ||||||||
\(807\) | 5.07716e126 | 1.80560 | ||||||||
\(808\) | −6.52122e126 | −2.19753 | ||||||||
\(809\) | −3.29569e126 | −1.05241 | −0.526206 | − | 0.850357i | \(-0.676386\pi\) | ||||
−0.526206 | + | 0.850357i | \(0.676386\pi\) | |||||||
\(810\) | 1.33247e126 | 0.403237 | ||||||||
\(811\) | −1.12128e126 | −0.321595 | −0.160797 | − | 0.986987i | \(-0.551407\pi\) | ||||
−0.160797 | + | 0.986987i | \(0.551407\pi\) | |||||||
\(812\) | 3.35113e126 | 0.910969 | ||||||||
\(813\) | 4.18996e126 | 1.07962 | ||||||||
\(814\) | 8.05892e126 | 1.96841 | ||||||||
\(815\) | 9.10095e125 | 0.210732 | ||||||||
\(816\) | 1.21756e127 | 2.67281 | ||||||||
\(817\) | −2.05569e126 | −0.427857 | ||||||||
\(818\) | −3.41380e126 | −0.673705 | ||||||||
\(819\) | 5.63799e126 | 1.05505 | ||||||||
\(820\) | 4.62322e126 | 0.820431 | ||||||||
\(821\) | −5.03284e126 | −0.847004 | −0.423502 | − | 0.905895i | \(-0.639199\pi\) | ||||
−0.423502 | + | 0.905895i | \(0.639199\pi\) | |||||||
\(822\) | −4.98136e126 | −0.795104 | ||||||||
\(823\) | −2.27045e126 | −0.343732 | −0.171866 | − | 0.985120i | \(-0.554980\pi\) | ||||
−0.171866 | + | 0.985120i | \(0.554980\pi\) | |||||||
\(824\) | −2.18049e127 | −3.13127 | ||||||||
\(825\) | −2.43383e126 | −0.331546 | ||||||||
\(826\) | −3.86527e126 | −0.499514 | ||||||||
\(827\) | −5.03797e126 | −0.617683 | −0.308842 | − | 0.951114i | \(-0.599941\pi\) | ||||
−0.308842 | + | 0.951114i | \(0.599941\pi\) | |||||||
\(828\) | 2.79905e127 | 3.25605 | ||||||||
\(829\) | −1.43049e126 | −0.157893 | −0.0789466 | − | 0.996879i | \(-0.525156\pi\) | ||||
−0.0789466 | + | 0.996879i | \(0.525156\pi\) | |||||||
\(830\) | 1.67198e127 | 1.75119 | ||||||||
\(831\) | −1.25914e127 | −1.25150 | ||||||||
\(832\) | −3.75654e126 | −0.354342 | ||||||||
\(833\) | 8.55138e126 | 0.765559 | ||||||||
\(834\) | −3.26786e127 | −2.77678 | ||||||||
\(835\) | 1.29026e127 | 1.04068 | ||||||||
\(836\) | 6.95332e126 | 0.532377 | ||||||||
\(837\) | −9.72400e126 | −0.706785 | ||||||||
\(838\) | 3.28343e127 | 2.26575 | ||||||||
\(839\) | 1.26937e127 | 0.831654 | 0.415827 | − | 0.909444i | \(-0.363492\pi\) | ||||
0.415827 | + | 0.909444i | \(0.363492\pi\) | |||||||
\(840\) | −7.26045e127 | −4.51663 | ||||||||
\(841\) | −1.49436e127 | −0.882731 | ||||||||
\(842\) | −2.86240e127 | −1.60566 | ||||||||
\(843\) | 5.85399e127 | 3.11855 | ||||||||
\(844\) | 8.09864e127 | 4.09747 | ||||||||
\(845\) | 1.68749e127 | 0.810914 | ||||||||
\(846\) | −3.19989e127 | −1.46058 | ||||||||
\(847\) | −1.80243e127 | −0.781502 | ||||||||
\(848\) | −5.98589e127 | −2.46552 | ||||||||
\(849\) | −6.06713e127 | −2.37410 | ||||||||
\(850\) | 2.03856e127 | 0.757879 | ||||||||
\(851\) | −5.19311e127 | −1.83439 | ||||||||
\(852\) | 1.73902e128 | 5.83688 | ||||||||
\(853\) | −1.54493e127 | −0.492748 | −0.246374 | − | 0.969175i | \(-0.579239\pi\) | ||||
−0.246374 | + | 0.969175i | \(0.579239\pi\) | |||||||
\(854\) | 7.80158e127 | 2.36464 | ||||||||
\(855\) | 2.50830e127 | 0.722525 | ||||||||
\(856\) | 8.11014e126 | 0.222034 | ||||||||
\(857\) | −2.01359e127 | −0.523967 | −0.261984 | − | 0.965072i | \(-0.584377\pi\) | ||||
−0.261984 | + | 0.965072i | \(0.584377\pi\) | |||||||
\(858\) | −3.82498e127 | −0.946088 | ||||||||
\(859\) | 4.07203e127 | 0.957432 | 0.478716 | − | 0.877970i | \(-0.341102\pi\) | ||||
0.478716 | + | 0.877970i | \(0.341102\pi\) | |||||||
\(860\) | −1.13675e128 | −2.54087 | ||||||||
\(861\) | −3.19190e127 | −0.678285 | ||||||||
\(862\) | −1.16510e128 | −2.35396 | ||||||||
\(863\) | 6.84641e127 | 1.31521 | 0.657603 | − | 0.753365i | \(-0.271571\pi\) | ||||
0.657603 | + | 0.753365i | \(0.271571\pi\) | |||||||
\(864\) | 1.74162e127 | 0.318131 | ||||||||
\(865\) | −4.85484e127 | −0.843285 | ||||||||
\(866\) | 5.52268e127 | 0.912267 | ||||||||
\(867\) | 6.33133e127 | 0.994637 | ||||||||
\(868\) | −1.50620e128 | −2.25048 | ||||||||
\(869\) | −1.14089e127 | −0.162138 | ||||||||
\(870\) | −8.20128e127 | −1.10865 | ||||||||
\(871\) | −2.60361e127 | −0.334801 | ||||||||
\(872\) | 2.72210e128 | 3.32994 | ||||||||
\(873\) | 5.00393e126 | 0.0582360 | ||||||||
\(874\) | −6.61147e127 | −0.732067 | ||||||||
\(875\) | 9.20094e127 | 0.969353 | ||||||||
\(876\) | −9.29589e127 | −0.931885 | ||||||||
\(877\) | −6.89675e127 | −0.657904 | −0.328952 | − | 0.944347i | \(-0.606695\pi\) | ||||
−0.328952 | + | 0.944347i | \(0.606695\pi\) | |||||||
\(878\) | 2.06772e127 | 0.187707 | ||||||||
\(879\) | 2.45363e128 | 2.11979 | ||||||||
\(880\) | 1.14694e128 | 0.943069 | ||||||||
\(881\) | −1.42995e128 | −1.11910 | −0.559551 | − | 0.828796i | \(-0.689026\pi\) | ||||
−0.559551 | + | 0.828796i | \(0.689026\pi\) | |||||||
\(882\) | 2.16604e128 | 1.61355 | ||||||||
\(883\) | −1.83260e128 | −1.29950 | −0.649750 | − | 0.760148i | \(-0.725126\pi\) | ||||
−0.649750 | + | 0.760148i | \(0.725126\pi\) | |||||||
\(884\) | 2.17123e128 | 1.46566 | ||||||||
\(885\) | 6.41084e127 | 0.411986 | ||||||||
\(886\) | 6.07023e127 | 0.371397 | ||||||||
\(887\) | 2.22818e128 | 1.29799 | 0.648997 | − | 0.760791i | \(-0.275189\pi\) | ||||
0.648997 | + | 0.760791i | \(0.275189\pi\) | |||||||
\(888\) | −1.00600e129 | −5.57998 | ||||||||
\(889\) | −3.23970e126 | −0.0171111 | ||||||||
\(890\) | 6.64584e127 | 0.334260 | ||||||||
\(891\) | 2.55505e127 | 0.122382 | ||||||||
\(892\) | −1.23259e127 | −0.0562273 | ||||||||
\(893\) | 5.12233e127 | 0.222551 | ||||||||
\(894\) | −3.13069e128 | −1.29556 | ||||||||
\(895\) | 3.77097e127 | 0.148645 | ||||||||
\(896\) | −5.12987e128 | −1.92623 | ||||||||
\(897\) | 2.46478e128 | 0.881673 | ||||||||
\(898\) | 5.24536e128 | 1.78754 | ||||||||
\(899\) | −8.92277e127 | −0.289703 | ||||||||
\(900\) | 3.49943e128 | 1.08255 | ||||||||
\(901\) | −8.08614e128 | −2.38349 | ||||||||
\(902\) | 1.30810e128 | 0.367415 | ||||||||
\(903\) | 7.84821e128 | 2.10065 | ||||||||
\(904\) | 1.01380e129 | 2.58598 | ||||||||
\(905\) | 2.75959e128 | 0.670859 | ||||||||
\(906\) | 1.70757e128 | 0.395643 | ||||||||
\(907\) | −6.58794e128 | −1.45490 | −0.727449 | − | 0.686161i | \(-0.759294\pi\) | ||||
−0.727449 | + | 0.686161i | \(0.759294\pi\) | |||||||
\(908\) | −2.76838e128 | −0.582761 | ||||||||
\(909\) | −8.60116e128 | −1.72595 | ||||||||
\(910\) | −7.36410e128 | −1.40870 | ||||||||
\(911\) | −6.80939e128 | −1.24182 | −0.620910 | − | 0.783882i | \(-0.713237\pi\) | ||||
−0.620910 | + | 0.783882i | \(0.713237\pi\) | |||||||
\(912\) | −4.93688e128 | −0.858376 | ||||||||
\(913\) | 3.20605e128 | 0.531486 | ||||||||
\(914\) | 1.19926e129 | 1.89563 | ||||||||
\(915\) | −1.29395e129 | −1.95030 | ||||||||
\(916\) | 2.09540e129 | 3.01171 | ||||||||
\(917\) | 1.11213e129 | 1.52436 | ||||||||
\(918\) | 1.43549e129 | 1.87648 | ||||||||
\(919\) | 1.02101e129 | 1.27293 | 0.636464 | − | 0.771306i | \(-0.280396\pi\) | ||||
0.636464 | + | 0.771306i | \(0.280396\pi\) | |||||||
\(920\) | −1.91737e129 | −2.28000 | ||||||||
\(921\) | −2.82816e128 | −0.320783 | ||||||||
\(922\) | 6.90376e128 | 0.746949 | ||||||||
\(923\) | 9.25037e128 | 0.954740 | ||||||||
\(924\) | −2.65463e129 | −2.61381 | ||||||||
\(925\) | −6.49253e128 | −0.609886 | ||||||||
\(926\) | −1.38955e129 | −1.24536 | ||||||||
\(927\) | −2.87596e129 | −2.45931 | ||||||||
\(928\) | 1.59812e128 | 0.130398 | ||||||||
\(929\) | 1.05096e128 | 0.0818281 | 0.0409141 | − | 0.999163i | \(-0.486973\pi\) | ||||
0.0409141 | + | 0.999163i | \(0.486973\pi\) | |||||||
\(930\) | 3.68615e129 | 2.73883 | ||||||||
\(931\) | −3.46736e128 | −0.245860 | ||||||||
\(932\) | −3.10707e129 | −2.10261 | ||||||||
\(933\) | 3.67923e129 | 2.37632 | ||||||||
\(934\) | −4.96635e129 | −3.06160 | ||||||||
\(935\) | 1.54936e129 | 0.911690 | ||||||||
\(936\) | 2.88427e129 | 1.62008 | ||||||||
\(937\) | −1.30807e129 | −0.701388 | −0.350694 | − | 0.936490i | \(-0.614054\pi\) | ||||
−0.350694 | + | 0.936490i | \(0.614054\pi\) | |||||||
\(938\) | −2.66629e129 | −1.36485 | ||||||||
\(939\) | 4.35193e129 | 2.12681 | ||||||||
\(940\) | 2.83253e129 | 1.32164 | ||||||||
\(941\) | 3.19454e129 | 1.42318 | 0.711590 | − | 0.702595i | \(-0.247975\pi\) | ||||
0.711590 | + | 0.702595i | \(0.247975\pi\) | |||||||
\(942\) | 2.84263e129 | 1.20922 | ||||||||
\(943\) | −8.42929e128 | −0.342399 | ||||||||
\(944\) | −7.62212e128 | −0.295661 | ||||||||
\(945\) | −3.29958e129 | −1.22229 | ||||||||
\(946\) | −3.21634e129 | −1.13788 | ||||||||
\(947\) | −1.49588e128 | −0.0505442 | −0.0252721 | − | 0.999681i | \(-0.508045\pi\) | ||||
−0.0252721 | + | 0.999681i | \(0.508045\pi\) | |||||||
\(948\) | 2.71559e129 | 0.876398 | ||||||||
\(949\) | −4.94477e128 | −0.152428 | ||||||||
\(950\) | −8.26581e128 | −0.243393 | ||||||||
\(951\) | 1.14160e129 | 0.321115 | ||||||||
\(952\) | 1.16610e130 | 3.13350 | ||||||||
\(953\) | −1.25754e129 | −0.322835 | −0.161417 | − | 0.986886i | \(-0.551607\pi\) | ||||
−0.161417 | + | 0.986886i | \(0.551607\pi\) | |||||||
\(954\) | −2.04820e130 | −5.02362 | ||||||||
\(955\) | −3.89523e129 | −0.912822 | ||||||||
\(956\) | 1.59084e129 | 0.356211 | ||||||||
\(957\) | −1.57261e129 | −0.336475 | ||||||||
\(958\) | −5.98596e126 | −0.00122387 | ||||||||
\(959\) | −1.83899e129 | −0.359311 | ||||||||
\(960\) | 6.38050e129 | 1.19140 | ||||||||
\(961\) | −1.59317e129 | −0.284312 | ||||||||
\(962\) | −1.02036e130 | −1.74035 | ||||||||
\(963\) | 1.06969e129 | 0.174386 | ||||||||
\(964\) | 9.99827e129 | 1.55802 | ||||||||
\(965\) | 6.65878e129 | 0.991874 | ||||||||
\(966\) | 2.52412e130 | 3.59423 | ||||||||
\(967\) | −3.69822e129 | −0.503433 | −0.251717 | − | 0.967801i | \(-0.580995\pi\) | ||||
−0.251717 | + | 0.967801i | \(0.580995\pi\) | |||||||
\(968\) | −9.22081e129 | −1.20003 | ||||||||
\(969\) | −6.66907e129 | −0.829815 | ||||||||
\(970\) | −6.53591e128 | −0.0777563 | ||||||||
\(971\) | 8.38667e129 | 0.954010 | 0.477005 | − | 0.878901i | \(-0.341722\pi\) | ||||
0.477005 | + | 0.878901i | \(0.341722\pi\) | |||||||
\(972\) | −2.22329e130 | −2.41832 | ||||||||
\(973\) | −1.20641e130 | −1.25484 | ||||||||
\(974\) | 1.80750e130 | 1.79790 | ||||||||
\(975\) | 3.08153e129 | 0.293133 | ||||||||
\(976\) | 1.53843e130 | 1.39963 | ||||||||
\(977\) | 8.47225e129 | 0.737200 | 0.368600 | − | 0.929588i | \(-0.379837\pi\) | ||||
0.368600 | + | 0.929588i | \(0.379837\pi\) | |||||||
\(978\) | −6.12920e129 | −0.510109 | ||||||||
\(979\) | 1.27436e129 | 0.101448 | ||||||||
\(980\) | −1.91737e130 | −1.46006 | ||||||||
\(981\) | 3.59031e130 | 2.61535 | ||||||||
\(982\) | −1.58405e130 | −1.10387 | ||||||||
\(983\) | −2.47112e130 | −1.64746 | −0.823732 | − | 0.566979i | \(-0.808112\pi\) | ||||
−0.823732 | + | 0.566979i | \(0.808112\pi\) | |||||||
\(984\) | −1.63290e130 | −1.04153 | ||||||||
\(985\) | 1.54387e129 | 0.0942184 | ||||||||
\(986\) | 1.31721e130 | 0.769147 | ||||||||
\(987\) | −1.95560e130 | −1.09266 | ||||||||
\(988\) | −8.80376e129 | −0.470697 | ||||||||
\(989\) | 2.07258e130 | 1.06041 | ||||||||
\(990\) | 3.92448e130 | 1.92155 | ||||||||
\(991\) | −4.15849e130 | −1.94864 | −0.974319 | − | 0.225171i | \(-0.927706\pi\) | ||||
−0.974319 | + | 0.225171i | \(0.927706\pi\) | |||||||
\(992\) | −7.18291e129 | −0.322138 | ||||||||
\(993\) | 3.72904e130 | 1.60068 | ||||||||
\(994\) | 9.47306e130 | 3.89209 | ||||||||
\(995\) | −4.68344e130 | −1.84188 | ||||||||
\(996\) | −7.63118e130 | −2.87283 | ||||||||
\(997\) | 2.55616e130 | 0.921188 | 0.460594 | − | 0.887611i | \(-0.347636\pi\) | ||||
0.460594 | + | 0.887611i | \(0.347636\pi\) | |||||||
\(998\) | −6.73141e130 | −2.32235 | ||||||||
\(999\) | −4.57184e130 | −1.51005 |
(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 | 1.88.a.a.1.7 | ✓ | 7 | |
3.2 | odd | 2 | 9.88.a.b.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.88.a.a.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.88.a.b.1.1 | 7 | 3.2 | odd | 2 |