Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,92,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, 92, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 92);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 92 \) |
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: | \(52.4421558310\) |
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: | \( x^{7} - 2 x^{6} + \cdots + 37\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{31}\cdot 5^{8}\cdot 7^{6}\cdot 11\cdot 13^{3}\cdot 23 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.36516e12\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.62150e13 | −1.12976 | −0.564881 | − | 0.825172i | \(-0.691078\pi\) | ||||
−0.564881 | + | 0.825172i | \(0.691078\pi\) | |||||||
\(3\) | −7.69269e21 | −1.50335 | −0.751677 | − | 0.659531i | \(-0.770755\pi\) | ||||
−0.751677 | + | 0.659531i | \(0.770755\pi\) | |||||||
\(4\) | 6.84242e26 | 0.276363 | ||||||||
\(5\) | −3.78165e31 | −0.595040 | −0.297520 | − | 0.954716i | \(-0.596160\pi\) | ||||
−0.297520 | + | 0.954716i | \(0.596160\pi\) | |||||||
\(6\) | 4.32444e35 | 1.69843 | ||||||||
\(7\) | 1.92974e38 | 0.681614 | 0.340807 | − | 0.940133i | \(-0.389300\pi\) | ||||
0.340807 | + | 0.940133i | \(0.389300\pi\) | |||||||
\(8\) | 1.00717e41 | 0.817538 | ||||||||
\(9\) | 3.29936e43 | 1.26007 | ||||||||
\(10\) | 2.12585e45 | 0.672254 | ||||||||
\(11\) | −3.23035e47 | −1.33623 | −0.668117 | − | 0.744056i | \(-0.732899\pi\) | ||||
−0.668117 | + | 0.744056i | \(0.732899\pi\) | |||||||
\(12\) | −5.26366e48 | −0.415472 | ||||||||
\(13\) | 6.38412e50 | 1.32032 | 0.660159 | − | 0.751126i | \(-0.270489\pi\) | ||||
0.660159 | + | 0.751126i | \(0.270489\pi\) | |||||||
\(14\) | −1.08480e52 | −0.770061 | ||||||||
\(15\) | 2.90911e53 | 0.894556 | ||||||||
\(16\) | −7.35590e54 | −1.19999 | ||||||||
\(17\) | −2.02934e55 | −0.209859 | −0.104930 | − | 0.994480i | \(-0.533462\pi\) | ||||
−0.104930 | + | 0.994480i | \(0.533462\pi\) | |||||||
\(18\) | −1.85474e57 | −1.42358 | ||||||||
\(19\) | −2.40506e58 | −1.57702 | −0.788510 | − | 0.615022i | \(-0.789147\pi\) | ||||
−0.788510 | + | 0.615022i | \(0.789147\pi\) | |||||||
\(20\) | −2.58756e58 | −0.164447 | ||||||||
\(21\) | −1.48449e60 | −1.02471 | ||||||||
\(22\) | 1.81594e61 | 1.50963 | ||||||||
\(23\) | 9.50903e61 | 1.04597 | 0.522986 | − | 0.852342i | \(-0.324818\pi\) | ||||
0.522986 | + | 0.852342i | \(0.324818\pi\) | |||||||
\(24\) | −7.74784e62 | −1.22905 | ||||||||
\(25\) | −2.60888e63 | −0.645927 | ||||||||
\(26\) | −3.58883e64 | −1.49165 | ||||||||
\(27\) | −5.23853e64 | −0.390983 | ||||||||
\(28\) | 1.32041e65 | 0.188373 | ||||||||
\(29\) | −5.71159e66 | −1.65062 | −0.825312 | − | 0.564677i | \(-0.809001\pi\) | ||||
−0.825312 | + | 0.564677i | \(0.809001\pi\) | |||||||
\(30\) | −1.63535e67 | −1.01064 | ||||||||
\(31\) | −5.62988e67 | −0.782604 | −0.391302 | − | 0.920262i | \(-0.627975\pi\) | ||||
−0.391302 | + | 0.920262i | \(0.627975\pi\) | |||||||
\(32\) | 1.64148e68 | 0.538162 | ||||||||
\(33\) | 2.48501e69 | 2.00883 | ||||||||
\(34\) | 1.14079e69 | 0.237091 | ||||||||
\(35\) | −7.29761e69 | −0.405587 | ||||||||
\(36\) | 2.25756e70 | 0.348238 | ||||||||
\(37\) | −3.40807e71 | −1.51123 | −0.755613 | − | 0.655018i | \(-0.772661\pi\) | ||||
−0.755613 | + | 0.655018i | \(0.772661\pi\) | |||||||
\(38\) | 1.35200e72 | 1.78166 | ||||||||
\(39\) | −4.91111e72 | −1.98490 | ||||||||
\(40\) | −3.80876e72 | −0.486468 | ||||||||
\(41\) | 2.61368e73 | 1.08539 | 0.542696 | − | 0.839929i | \(-0.317404\pi\) | ||||
0.542696 | + | 0.839929i | \(0.317404\pi\) | |||||||
\(42\) | 8.34506e73 | 1.15768 | ||||||||
\(43\) | 6.31280e73 | 0.300198 | 0.150099 | − | 0.988671i | \(-0.452041\pi\) | ||||
0.150099 | + | 0.988671i | \(0.452041\pi\) | |||||||
\(44\) | −2.21034e74 | −0.369286 | ||||||||
\(45\) | −1.24770e75 | −0.749795 | ||||||||
\(46\) | −5.34550e75 | −1.18170 | ||||||||
\(47\) | 1.01518e76 | 0.843515 | 0.421757 | − | 0.906709i | \(-0.361413\pi\) | ||||
0.421757 | + | 0.906709i | \(0.361413\pi\) | |||||||
\(48\) | 5.65867e76 | 1.80400 | ||||||||
\(49\) | −4.29143e76 | −0.535403 | ||||||||
\(50\) | 1.46658e77 | 0.729744 | ||||||||
\(51\) | 1.56111e77 | 0.315493 | ||||||||
\(52\) | 4.36828e77 | 0.364887 | ||||||||
\(53\) | 1.79595e78 | 0.630583 | 0.315291 | − | 0.948995i | \(-0.397898\pi\) | ||||
0.315291 | + | 0.948995i | \(0.397898\pi\) | |||||||
\(54\) | 2.94484e78 | 0.441718 | ||||||||
\(55\) | 1.22161e79 | 0.795113 | ||||||||
\(56\) | 1.94358e79 | 0.557245 | ||||||||
\(57\) | 1.85014e80 | 2.37082 | ||||||||
\(58\) | 3.21077e80 | 1.86481 | ||||||||
\(59\) | −2.69860e80 | −0.720066 | −0.360033 | − | 0.932940i | \(-0.617234\pi\) | ||||
−0.360033 | + | 0.932940i | \(0.617234\pi\) | |||||||
\(60\) | 1.99053e80 | 0.247222 | ||||||||
\(61\) | −9.80050e80 | −0.573774 | −0.286887 | − | 0.957964i | \(-0.592620\pi\) | ||||
−0.286887 | + | 0.957964i | \(0.592620\pi\) | |||||||
\(62\) | 3.16483e81 | 0.884156 | ||||||||
\(63\) | 6.36692e81 | 0.858883 | ||||||||
\(64\) | 8.98472e81 | 0.591992 | ||||||||
\(65\) | −2.41425e82 | −0.785642 | ||||||||
\(66\) | −1.39695e83 | −2.26950 | ||||||||
\(67\) | −4.61723e82 | −0.378423 | −0.189212 | − | 0.981936i | \(-0.560593\pi\) | ||||
−0.189212 | + | 0.981936i | \(0.560593\pi\) | |||||||
\(68\) | −1.38856e82 | −0.0579973 | ||||||||
\(69\) | −7.31500e83 | −1.57246 | ||||||||
\(70\) | 4.10235e83 | 0.458217 | ||||||||
\(71\) | −2.60022e83 | −0.152320 | −0.0761598 | − | 0.997096i | \(-0.524266\pi\) | ||||
−0.0761598 | + | 0.997096i | \(0.524266\pi\) | |||||||
\(72\) | 3.32302e84 | 1.03016 | ||||||||
\(73\) | −8.39038e84 | −1.38865 | −0.694323 | − | 0.719663i | \(-0.744296\pi\) | ||||
−0.694323 | + | 0.719663i | \(0.744296\pi\) | |||||||
\(74\) | 1.91584e85 | 1.70733 | ||||||||
\(75\) | 2.00693e85 | 0.971057 | ||||||||
\(76\) | −1.64564e85 | −0.435830 | ||||||||
\(77\) | −6.23374e85 | −0.910795 | ||||||||
\(78\) | 2.76078e86 | 2.24247 | ||||||||
\(79\) | 4.28257e85 | 0.194837 | 0.0974185 | − | 0.995244i | \(-0.468941\pi\) | ||||
0.0974185 | + | 0.995244i | \(0.468941\pi\) | |||||||
\(80\) | 2.78174e86 | 0.714040 | ||||||||
\(81\) | −4.60918e86 | −0.672288 | ||||||||
\(82\) | −1.46928e87 | −1.22623 | ||||||||
\(83\) | −3.77027e87 | −1.81267 | −0.906336 | − | 0.422559i | \(-0.861132\pi\) | ||||
−0.906336 | + | 0.422559i | \(0.861132\pi\) | |||||||
\(84\) | −1.01575e87 | −0.283191 | ||||||||
\(85\) | 7.67424e86 | 0.124875 | ||||||||
\(86\) | −3.54874e87 | −0.339152 | ||||||||
\(87\) | 4.39375e88 | 2.48147 | ||||||||
\(88\) | −3.25351e88 | −1.09242 | ||||||||
\(89\) | −5.46272e88 | −1.09689 | −0.548445 | − | 0.836186i | \(-0.684780\pi\) | ||||
−0.548445 | + | 0.836186i | \(0.684780\pi\) | |||||||
\(90\) | 7.01397e88 | 0.847090 | ||||||||
\(91\) | 1.23197e89 | 0.899946 | ||||||||
\(92\) | 6.50647e88 | 0.289068 | ||||||||
\(93\) | 4.33089e89 | 1.17653 | ||||||||
\(94\) | −5.70686e89 | −0.952971 | ||||||||
\(95\) | 9.09510e89 | 0.938390 | ||||||||
\(96\) | −1.26274e90 | −0.809048 | ||||||||
\(97\) | −2.52770e90 | −1.01067 | −0.505337 | − | 0.862922i | \(-0.668632\pi\) | ||||
−0.505337 | + | 0.862922i | \(0.668632\pi\) | |||||||
\(98\) | 2.41243e90 | 0.604878 | ||||||||
\(99\) | −1.06581e91 | −1.68375 | ||||||||
\(100\) | −1.78510e90 | −0.178510 | ||||||||
\(101\) | −5.55608e90 | −0.353302 | −0.176651 | − | 0.984274i | \(-0.556526\pi\) | ||||
−0.176651 | + | 0.984274i | \(0.556526\pi\) | |||||||
\(102\) | −8.77575e90 | −0.356432 | ||||||||
\(103\) | 6.03016e91 | 1.57121 | 0.785607 | − | 0.618726i | \(-0.212351\pi\) | ||||
0.785607 | + | 0.618726i | \(0.212351\pi\) | |||||||
\(104\) | 6.42988e91 | 1.07941 | ||||||||
\(105\) | 5.61383e91 | 0.609742 | ||||||||
\(106\) | −1.00959e92 | −0.712408 | ||||||||
\(107\) | 7.40024e91 | 0.340631 | 0.170315 | − | 0.985390i | \(-0.445521\pi\) | ||||
0.170315 | + | 0.985390i | \(0.445521\pi\) | |||||||
\(108\) | −3.58442e91 | −0.108053 | ||||||||
\(109\) | −2.17456e92 | −0.430988 | −0.215494 | − | 0.976505i | \(-0.569136\pi\) | ||||
−0.215494 | + | 0.976505i | \(0.569136\pi\) | |||||||
\(110\) | −6.86726e92 | −0.898289 | ||||||||
\(111\) | 2.62172e93 | 2.27191 | ||||||||
\(112\) | −1.41950e93 | −0.817927 | ||||||||
\(113\) | 1.03543e93 | 0.398153 | 0.199076 | − | 0.979984i | \(-0.436206\pi\) | ||||
0.199076 | + | 0.979984i | \(0.436206\pi\) | |||||||
\(114\) | −1.04005e94 | −2.67846 | ||||||||
\(115\) | −3.59598e93 | −0.622395 | ||||||||
\(116\) | −3.90811e93 | −0.456171 | ||||||||
\(117\) | 2.10635e94 | 1.66370 | ||||||||
\(118\) | 1.51702e94 | 0.813503 | ||||||||
\(119\) | −3.91609e93 | −0.143043 | ||||||||
\(120\) | 2.92996e94 | 0.731334 | ||||||||
\(121\) | 4.59085e94 | 0.785522 | ||||||||
\(122\) | 5.50935e94 | 0.648228 | ||||||||
\(123\) | −2.01062e95 | −1.63173 | ||||||||
\(124\) | −3.85220e94 | −0.216283 | ||||||||
\(125\) | 2.51398e95 | 0.979393 | ||||||||
\(126\) | −3.57916e95 | −0.970334 | ||||||||
\(127\) | −6.88314e94 | −0.130232 | −0.0651160 | − | 0.997878i | \(-0.520742\pi\) | ||||
−0.0651160 | + | 0.997878i | \(0.520742\pi\) | |||||||
\(128\) | −9.11487e95 | −1.20697 | ||||||||
\(129\) | −4.85624e95 | −0.451303 | ||||||||
\(130\) | 1.35717e96 | 0.887589 | ||||||||
\(131\) | 1.10101e96 | 0.508098 | 0.254049 | − | 0.967191i | \(-0.418238\pi\) | ||||
0.254049 | + | 0.967191i | \(0.418238\pi\) | |||||||
\(132\) | 1.70035e96 | 0.555167 | ||||||||
\(133\) | −4.64114e96 | −1.07492 | ||||||||
\(134\) | 2.59557e96 | 0.427529 | ||||||||
\(135\) | 1.98103e96 | 0.232651 | ||||||||
\(136\) | −2.04388e96 | −0.171568 | ||||||||
\(137\) | 1.30170e97 | 0.782933 | 0.391466 | − | 0.920192i | \(-0.371968\pi\) | ||||
0.391466 | + | 0.920192i | \(0.371968\pi\) | |||||||
\(138\) | 4.11213e97 | 1.77651 | ||||||||
\(139\) | −2.37924e97 | −0.740058 | −0.370029 | − | 0.929020i | \(-0.620652\pi\) | ||||
−0.370029 | + | 0.929020i | \(0.620652\pi\) | |||||||
\(140\) | −4.99333e96 | −0.112089 | ||||||||
\(141\) | −7.80951e97 | −1.26810 | ||||||||
\(142\) | 1.46172e97 | 0.172085 | ||||||||
\(143\) | −2.06229e98 | −1.76425 | ||||||||
\(144\) | −2.42698e98 | −1.51207 | ||||||||
\(145\) | 2.15992e98 | 0.982187 | ||||||||
\(146\) | 4.71665e98 | 1.56884 | ||||||||
\(147\) | 3.30127e98 | 0.804900 | ||||||||
\(148\) | −2.33194e98 | −0.417647 | ||||||||
\(149\) | 7.78787e98 | 1.02670 | 0.513350 | − | 0.858179i | \(-0.328404\pi\) | ||||
0.513350 | + | 0.858179i | \(0.328404\pi\) | |||||||
\(150\) | −1.12820e99 | −1.09706 | ||||||||
\(151\) | 1.97778e99 | 1.42144 | 0.710718 | − | 0.703477i | \(-0.248370\pi\) | ||||
0.710718 | + | 0.703477i | \(0.248370\pi\) | |||||||
\(152\) | −2.42230e99 | −1.28927 | ||||||||
\(153\) | −6.69551e98 | −0.264438 | ||||||||
\(154\) | 3.50430e99 | 1.02898 | ||||||||
\(155\) | 2.12902e99 | 0.465681 | ||||||||
\(156\) | −3.36038e99 | −0.548554 | ||||||||
\(157\) | −6.55275e99 | −0.799815 | −0.399907 | − | 0.916556i | \(-0.630958\pi\) | ||||
−0.399907 | + | 0.916556i | \(0.630958\pi\) | |||||||
\(158\) | −2.40744e99 | −0.220119 | ||||||||
\(159\) | −1.38157e100 | −0.947989 | ||||||||
\(160\) | −6.20752e99 | −0.320228 | ||||||||
\(161\) | 1.83500e100 | 0.712948 | ||||||||
\(162\) | 2.59105e100 | 0.759525 | ||||||||
\(163\) | −2.29210e100 | −0.507805 | −0.253903 | − | 0.967230i | \(-0.581714\pi\) | ||||
−0.253903 | + | 0.967230i | \(0.581714\pi\) | |||||||
\(164\) | 1.78839e100 | 0.299962 | ||||||||
\(165\) | −9.39744e100 | −1.19534 | ||||||||
\(166\) | 2.11945e101 | 2.04789 | ||||||||
\(167\) | 1.88522e101 | 1.38600 | 0.692999 | − | 0.720939i | \(-0.256289\pi\) | ||||
0.692999 | + | 0.720939i | \(0.256289\pi\) | |||||||
\(168\) | −1.49513e101 | −0.837736 | ||||||||
\(169\) | 1.73769e101 | 0.743238 | ||||||||
\(170\) | −4.31407e100 | −0.141079 | ||||||||
\(171\) | −7.93517e101 | −1.98716 | ||||||||
\(172\) | 4.31948e100 | 0.0829635 | ||||||||
\(173\) | 4.26354e101 | 0.629032 | 0.314516 | − | 0.949252i | \(-0.398158\pi\) | ||||
0.314516 | + | 0.949252i | \(0.398158\pi\) | |||||||
\(174\) | −2.46995e102 | −2.80347 | ||||||||
\(175\) | −5.03446e101 | −0.440273 | ||||||||
\(176\) | 2.37621e102 | 1.60346 | ||||||||
\(177\) | 2.07595e102 | 1.08251 | ||||||||
\(178\) | 3.07086e102 | 1.23923 | ||||||||
\(179\) | −1.69826e102 | −0.531117 | −0.265558 | − | 0.964095i | \(-0.585556\pi\) | ||||
−0.265558 | + | 0.964095i | \(0.585556\pi\) | |||||||
\(180\) | −8.53731e101 | −0.207216 | ||||||||
\(181\) | −1.51134e102 | −0.285094 | −0.142547 | − | 0.989788i | \(-0.545529\pi\) | ||||
−0.142547 | + | 0.989788i | \(0.545529\pi\) | |||||||
\(182\) | −6.92551e102 | −1.01673 | ||||||||
\(183\) | 7.53923e102 | 0.862586 | ||||||||
\(184\) | 9.57720e102 | 0.855121 | ||||||||
\(185\) | 1.28881e103 | 0.899241 | ||||||||
\(186\) | −2.43461e103 | −1.32920 | ||||||||
\(187\) | 6.55547e102 | 0.280421 | ||||||||
\(188\) | 6.94632e102 | 0.233116 | ||||||||
\(189\) | −1.01090e103 | −0.266499 | ||||||||
\(190\) | −5.11281e103 | −1.06016 | ||||||||
\(191\) | −5.22518e103 | −0.853263 | −0.426632 | − | 0.904425i | \(-0.640300\pi\) | ||||
−0.426632 | + | 0.904425i | \(0.640300\pi\) | |||||||
\(192\) | −6.91167e103 | −0.889973 | ||||||||
\(193\) | 1.28561e103 | 0.130693 | 0.0653464 | − | 0.997863i | \(-0.479185\pi\) | ||||
0.0653464 | + | 0.997863i | \(0.479185\pi\) | |||||||
\(194\) | 1.42094e104 | 1.14182 | ||||||||
\(195\) | 1.85721e104 | 1.18110 | ||||||||
\(196\) | −2.93638e103 | −0.147966 | ||||||||
\(197\) | −6.74933e103 | −0.269803 | −0.134902 | − | 0.990859i | \(-0.543072\pi\) | ||||
−0.134902 | + | 0.990859i | \(0.543072\pi\) | |||||||
\(198\) | 5.99145e104 | 1.90224 | ||||||||
\(199\) | −2.90888e104 | −0.734362 | −0.367181 | − | 0.930150i | \(-0.619677\pi\) | ||||
−0.367181 | + | 0.930150i | \(0.619677\pi\) | |||||||
\(200\) | −2.62758e104 | −0.528070 | ||||||||
\(201\) | 3.55189e104 | 0.568904 | ||||||||
\(202\) | 3.12335e104 | 0.399148 | ||||||||
\(203\) | −1.10219e105 | −1.12509 | ||||||||
\(204\) | 1.06817e104 | 0.0871905 | ||||||||
\(205\) | −9.88401e104 | −0.645852 | ||||||||
\(206\) | −3.38985e105 | −1.77510 | ||||||||
\(207\) | 3.13737e105 | 1.31800 | ||||||||
\(208\) | −4.69609e105 | −1.58436 | ||||||||
\(209\) | 7.76919e105 | 2.10727 | ||||||||
\(210\) | −3.15581e105 | −0.688863 | ||||||||
\(211\) | 6.80099e105 | 1.19597 | 0.597985 | − | 0.801507i | \(-0.295968\pi\) | ||||
0.597985 | + | 0.801507i | \(0.295968\pi\) | |||||||
\(212\) | 1.22886e105 | 0.174270 | ||||||||
\(213\) | 2.00027e105 | 0.228990 | ||||||||
\(214\) | −4.16004e105 | −0.384832 | ||||||||
\(215\) | −2.38728e105 | −0.178630 | ||||||||
\(216\) | −5.27608e105 | −0.319644 | ||||||||
\(217\) | −1.08642e106 | −0.533433 | ||||||||
\(218\) | 1.22243e106 | 0.486914 | ||||||||
\(219\) | 6.45447e106 | 2.08763 | ||||||||
\(220\) | 8.35874e105 | 0.219740 | ||||||||
\(221\) | −1.29555e106 | −0.277081 | ||||||||
\(222\) | −1.47380e107 | −2.56672 | ||||||||
\(223\) | −1.29916e106 | −0.184413 | −0.0922065 | − | 0.995740i | \(-0.529392\pi\) | ||||
−0.0922065 | + | 0.995740i | \(0.529392\pi\) | |||||||
\(224\) | 3.16764e106 | 0.366818 | ||||||||
\(225\) | −8.60764e106 | −0.813916 | ||||||||
\(226\) | −5.82064e106 | −0.449818 | ||||||||
\(227\) | −8.73941e106 | −0.552466 | −0.276233 | − | 0.961091i | \(-0.589086\pi\) | ||||
−0.276233 | + | 0.961091i | \(0.589086\pi\) | |||||||
\(228\) | 1.26594e107 | 0.655207 | ||||||||
\(229\) | 4.00186e107 | 1.69726 | 0.848629 | − | 0.528988i | \(-0.177429\pi\) | ||||
0.848629 | + | 0.528988i | \(0.177429\pi\) | |||||||
\(230\) | 2.02148e107 | 0.703158 | ||||||||
\(231\) | 4.79543e107 | 1.36925 | ||||||||
\(232\) | −5.75253e107 | −1.34945 | ||||||||
\(233\) | 9.51391e107 | 1.83512 | 0.917560 | − | 0.397597i | \(-0.130156\pi\) | ||||
0.917560 | + | 0.397597i | \(0.130156\pi\) | |||||||
\(234\) | −1.18409e108 | −1.87958 | ||||||||
\(235\) | −3.83908e107 | −0.501925 | ||||||||
\(236\) | −1.84649e107 | −0.198999 | ||||||||
\(237\) | −3.29445e107 | −0.292909 | ||||||||
\(238\) | 2.20143e107 | 0.161604 | ||||||||
\(239\) | 1.76907e108 | 1.07310 | 0.536551 | − | 0.843868i | \(-0.319727\pi\) | ||||
0.536551 | + | 0.843868i | \(0.319727\pi\) | |||||||
\(240\) | −2.13991e108 | −1.07346 | ||||||||
\(241\) | −2.39870e108 | −0.995867 | −0.497933 | − | 0.867215i | \(-0.665908\pi\) | ||||
−0.497933 | + | 0.867215i | \(0.665908\pi\) | |||||||
\(242\) | −2.58074e108 | −0.887453 | ||||||||
\(243\) | 4.91735e108 | 1.40167 | ||||||||
\(244\) | −6.70591e107 | −0.158570 | ||||||||
\(245\) | 1.62287e108 | 0.318586 | ||||||||
\(246\) | 1.13027e109 | 1.84346 | ||||||||
\(247\) | −1.53542e109 | −2.08217 | ||||||||
\(248\) | −5.67024e108 | −0.639808 | ||||||||
\(249\) | 2.90035e109 | 2.72509 | ||||||||
\(250\) | −1.41324e109 | −1.10648 | ||||||||
\(251\) | 1.43365e109 | 0.936029 | 0.468014 | − | 0.883721i | \(-0.344970\pi\) | ||||
0.468014 | + | 0.883721i | \(0.344970\pi\) | |||||||
\(252\) | 4.35651e108 | 0.237364 | ||||||||
\(253\) | −3.07175e109 | −1.39766 | ||||||||
\(254\) | 3.86936e108 | 0.147131 | ||||||||
\(255\) | −5.90356e108 | −0.187731 | ||||||||
\(256\) | 2.89941e109 | 0.771600 | ||||||||
\(257\) | −1.79396e109 | −0.399812 | −0.199906 | − | 0.979815i | \(-0.564064\pi\) | ||||
−0.199906 | + | 0.979815i | \(0.564064\pi\) | |||||||
\(258\) | 2.72993e109 | 0.509866 | ||||||||
\(259\) | −6.57669e109 | −1.03007 | ||||||||
\(260\) | −1.65193e109 | −0.217122 | ||||||||
\(261\) | −1.88446e110 | −2.07991 | ||||||||
\(262\) | −6.18933e109 | −0.574030 | ||||||||
\(263\) | 1.38443e110 | 1.07965 | 0.539826 | − | 0.841777i | \(-0.318490\pi\) | ||||
0.539826 | + | 0.841777i | \(0.318490\pi\) | |||||||
\(264\) | 2.50282e110 | 1.64230 | ||||||||
\(265\) | −6.79165e109 | −0.375222 | ||||||||
\(266\) | 2.60902e110 | 1.21440 | ||||||||
\(267\) | 4.20230e110 | 1.64902 | ||||||||
\(268\) | −3.15930e109 | −0.104582 | ||||||||
\(269\) | −6.03377e109 | −0.168601 | −0.0843005 | − | 0.996440i | \(-0.526866\pi\) | ||||
−0.0843005 | + | 0.996440i | \(0.526866\pi\) | |||||||
\(270\) | −1.11363e110 | −0.262840 | ||||||||
\(271\) | −6.44449e110 | −1.28554 | −0.642770 | − | 0.766059i | \(-0.722215\pi\) | ||||
−0.642770 | + | 0.766059i | \(0.722215\pi\) | |||||||
\(272\) | 1.49276e110 | 0.251828 | ||||||||
\(273\) | −9.47716e110 | −1.35294 | ||||||||
\(274\) | −7.31749e110 | −0.884528 | ||||||||
\(275\) | 8.42760e110 | 0.863110 | ||||||||
\(276\) | −5.00523e110 | −0.434571 | ||||||||
\(277\) | 1.49744e111 | 1.10286 | 0.551429 | − | 0.834222i | \(-0.314083\pi\) | ||||
0.551429 | + | 0.834222i | \(0.314083\pi\) | |||||||
\(278\) | 1.33749e111 | 0.836089 | ||||||||
\(279\) | −1.85750e111 | −0.986139 | ||||||||
\(280\) | −7.34992e110 | −0.331583 | ||||||||
\(281\) | −2.59225e111 | −0.994348 | −0.497174 | − | 0.867651i | \(-0.665629\pi\) | ||||
−0.497174 | + | 0.867651i | \(0.665629\pi\) | |||||||
\(282\) | 4.39011e111 | 1.43265 | ||||||||
\(283\) | 3.11823e110 | 0.0866213 | 0.0433107 | − | 0.999062i | \(-0.486209\pi\) | ||||
0.0433107 | + | 0.999062i | \(0.486209\pi\) | |||||||
\(284\) | −1.77918e110 | −0.0420955 | ||||||||
\(285\) | −6.99658e111 | −1.41073 | ||||||||
\(286\) | 1.15932e112 | 1.99319 | ||||||||
\(287\) | 5.04372e111 | 0.739818 | ||||||||
\(288\) | 5.41586e111 | 0.678124 | ||||||||
\(289\) | −8.93905e111 | −0.955959 | ||||||||
\(290\) | −1.21420e112 | −1.10964 | ||||||||
\(291\) | 1.94448e112 | 1.51940 | ||||||||
\(292\) | −5.74105e111 | −0.383771 | ||||||||
\(293\) | −1.10509e112 | −0.632298 | −0.316149 | − | 0.948710i | \(-0.602390\pi\) | ||||
−0.316149 | + | 0.948710i | \(0.602390\pi\) | |||||||
\(294\) | −1.85581e112 | −0.909346 | ||||||||
\(295\) | 1.02052e112 | 0.428468 | ||||||||
\(296\) | −3.43250e112 | −1.23548 | ||||||||
\(297\) | 1.69223e112 | 0.522445 | ||||||||
\(298\) | −4.37795e112 | −1.15993 | ||||||||
\(299\) | 6.07068e112 | 1.38101 | ||||||||
\(300\) | 1.37323e112 | 0.268364 | ||||||||
\(301\) | 1.21821e112 | 0.204619 | ||||||||
\(302\) | −1.11181e113 | −1.60588 | ||||||||
\(303\) | 4.27413e112 | 0.531138 | ||||||||
\(304\) | 1.76914e113 | 1.89240 | ||||||||
\(305\) | 3.70621e112 | 0.341419 | ||||||||
\(306\) | 3.76388e112 | 0.298752 | ||||||||
\(307\) | 2.66068e113 | 1.82053 | 0.910263 | − | 0.414031i | \(-0.135879\pi\) | ||||
0.910263 | + | 0.414031i | \(0.135879\pi\) | |||||||
\(308\) | −4.26539e112 | −0.251710 | ||||||||
\(309\) | −4.63882e113 | −2.36209 | ||||||||
\(310\) | −1.19683e113 | −0.526109 | ||||||||
\(311\) | 2.35637e112 | 0.0894634 | 0.0447317 | − | 0.998999i | \(-0.485757\pi\) | ||||
0.0447317 | + | 0.998999i | \(0.485757\pi\) | |||||||
\(312\) | −4.94631e113 | −1.62273 | ||||||||
\(313\) | 6.11078e112 | 0.173312 | 0.0866562 | − | 0.996238i | \(-0.472382\pi\) | ||||
0.0866562 | + | 0.996238i | \(0.472382\pi\) | |||||||
\(314\) | 3.68363e113 | 0.903601 | ||||||||
\(315\) | −2.40775e113 | −0.511070 | ||||||||
\(316\) | 2.93031e112 | 0.0538457 | ||||||||
\(317\) | −6.37657e113 | −1.01482 | −0.507412 | − | 0.861704i | \(-0.669398\pi\) | ||||
−0.507412 | + | 0.861704i | \(0.669398\pi\) | |||||||
\(318\) | 7.76648e113 | 1.07100 | ||||||||
\(319\) | 1.84504e114 | 2.20562 | ||||||||
\(320\) | −3.39771e113 | −0.352259 | ||||||||
\(321\) | −5.69278e113 | −0.512089 | ||||||||
\(322\) | −1.03154e114 | −0.805462 | ||||||||
\(323\) | 4.88067e113 | 0.330952 | ||||||||
\(324\) | −3.15379e113 | −0.185795 | ||||||||
\(325\) | −1.66554e114 | −0.852829 | ||||||||
\(326\) | 1.28850e114 | 0.573699 | ||||||||
\(327\) | 1.67282e114 | 0.647928 | ||||||||
\(328\) | 2.63241e114 | 0.887349 | ||||||||
\(329\) | 1.95904e114 | 0.574951 | ||||||||
\(330\) | 5.28277e114 | 1.35045 | ||||||||
\(331\) | −6.21240e114 | −1.38384 | −0.691919 | − | 0.721975i | \(-0.743235\pi\) | ||||
−0.691919 | + | 0.721975i | \(0.743235\pi\) | |||||||
\(332\) | −2.57977e114 | −0.500955 | ||||||||
\(333\) | −1.12445e115 | −1.90426 | ||||||||
\(334\) | −1.05978e115 | −1.56585 | ||||||||
\(335\) | 1.74608e114 | 0.225177 | ||||||||
\(336\) | 1.09198e115 | 1.22963 | ||||||||
\(337\) | 6.30404e114 | 0.620095 | 0.310048 | − | 0.950721i | \(-0.399655\pi\) | ||||
0.310048 | + | 0.950721i | \(0.399655\pi\) | |||||||
\(338\) | −9.76844e114 | −0.839683 | ||||||||
\(339\) | −7.96521e114 | −0.598564 | ||||||||
\(340\) | 5.25103e113 | 0.0345107 | ||||||||
\(341\) | 1.81865e115 | 1.04574 | ||||||||
\(342\) | 4.46075e115 | 2.24502 | ||||||||
\(343\) | −2.37489e115 | −1.04655 | ||||||||
\(344\) | 6.35805e114 | 0.245423 | ||||||||
\(345\) | 2.76628e115 | 0.935680 | ||||||||
\(346\) | −2.39675e115 | −0.710657 | ||||||||
\(347\) | −2.09181e115 | −0.543916 | −0.271958 | − | 0.962309i | \(-0.587671\pi\) | ||||
−0.271958 | + | 0.962309i | \(0.587671\pi\) | |||||||
\(348\) | 3.00639e115 | 0.685787 | ||||||||
\(349\) | −2.95833e115 | −0.592229 | −0.296115 | − | 0.955152i | \(-0.595691\pi\) | ||||
−0.296115 | + | 0.955152i | \(0.595691\pi\) | |||||||
\(350\) | 2.83012e115 | 0.497404 | ||||||||
\(351\) | −3.34434e115 | −0.516222 | ||||||||
\(352\) | −5.30257e115 | −0.719110 | ||||||||
\(353\) | −1.07870e115 | −0.128573 | −0.0642865 | − | 0.997931i | \(-0.520477\pi\) | ||||
−0.0642865 | + | 0.997931i | \(0.520477\pi\) | |||||||
\(354\) | −1.16699e116 | −1.22298 | ||||||||
\(355\) | 9.83314e114 | 0.0906363 | ||||||||
\(356\) | −3.73782e115 | −0.303140 | ||||||||
\(357\) | 3.01253e115 | 0.215044 | ||||||||
\(358\) | 9.54674e115 | 0.600036 | ||||||||
\(359\) | 1.64225e116 | 0.909166 | 0.454583 | − | 0.890704i | \(-0.349788\pi\) | ||||
0.454583 | + | 0.890704i | \(0.349788\pi\) | |||||||
\(360\) | −1.25665e116 | −0.612985 | ||||||||
\(361\) | 3.45849e116 | 1.48699 | ||||||||
\(362\) | 8.49600e115 | 0.322088 | ||||||||
\(363\) | −3.53160e116 | −1.18092 | ||||||||
\(364\) | 8.42965e115 | 0.248712 | ||||||||
\(365\) | 3.17295e116 | 0.826301 | ||||||||
\(366\) | −4.23817e116 | −0.974517 | ||||||||
\(367\) | 2.76048e116 | 0.560633 | 0.280317 | − | 0.959908i | \(-0.409561\pi\) | ||||
0.280317 | + | 0.959908i | \(0.409561\pi\) | |||||||
\(368\) | −6.99474e116 | −1.25515 | ||||||||
\(369\) | 8.62347e116 | 1.36767 | ||||||||
\(370\) | −7.24505e116 | −1.01593 | ||||||||
\(371\) | 3.46572e116 | 0.429814 | ||||||||
\(372\) | 2.96338e116 | 0.325150 | ||||||||
\(373\) | 1.11360e117 | 1.08138 | 0.540691 | − | 0.841221i | \(-0.318163\pi\) | ||||
0.540691 | + | 0.841221i | \(0.318163\pi\) | |||||||
\(374\) | −3.68515e116 | −0.316809 | ||||||||
\(375\) | −1.93393e117 | −1.47237 | ||||||||
\(376\) | 1.02246e117 | 0.689605 | ||||||||
\(377\) | −3.64635e117 | −2.17935 | ||||||||
\(378\) | 5.68277e116 | 0.301081 | ||||||||
\(379\) | −2.45909e117 | −1.15529 | −0.577644 | − | 0.816289i | \(-0.696028\pi\) | ||||
−0.577644 | + | 0.816289i | \(0.696028\pi\) | |||||||
\(380\) | 6.22325e116 | 0.259336 | ||||||||
\(381\) | 5.29499e116 | 0.195785 | ||||||||
\(382\) | 2.93733e117 | 0.963985 | ||||||||
\(383\) | 1.93839e117 | 0.564802 | 0.282401 | − | 0.959296i | \(-0.408869\pi\) | ||||
0.282401 | + | 0.959296i | \(0.408869\pi\) | |||||||
\(384\) | 7.01179e117 | 1.81451 | ||||||||
\(385\) | 2.35738e117 | 0.541960 | ||||||||
\(386\) | −7.22705e116 | −0.147652 | ||||||||
\(387\) | 2.08282e117 | 0.378271 | ||||||||
\(388\) | −1.72956e117 | −0.279313 | ||||||||
\(389\) | 9.57143e116 | 0.137490 | 0.0687448 | − | 0.997634i | \(-0.478101\pi\) | ||||
0.0687448 | + | 0.997634i | \(0.478101\pi\) | |||||||
\(390\) | −1.04403e118 | −1.33436 | ||||||||
\(391\) | −1.92970e117 | −0.219507 | ||||||||
\(392\) | −4.32220e117 | −0.437712 | ||||||||
\(393\) | −8.46974e117 | −0.763851 | ||||||||
\(394\) | 3.79413e117 | 0.304814 | ||||||||
\(395\) | −1.61952e117 | −0.115936 | ||||||||
\(396\) | −7.29272e117 | −0.465327 | ||||||||
\(397\) | −1.97371e118 | −1.12284 | −0.561418 | − | 0.827533i | \(-0.689744\pi\) | ||||
−0.561418 | + | 0.827533i | \(0.689744\pi\) | |||||||
\(398\) | 1.63522e118 | 0.829654 | ||||||||
\(399\) | 3.57029e118 | 1.61598 | ||||||||
\(400\) | 1.91906e118 | 0.775104 | ||||||||
\(401\) | −1.80007e118 | −0.648965 | −0.324483 | − | 0.945892i | \(-0.605190\pi\) | ||||
−0.324483 | + | 0.945892i | \(0.605190\pi\) | |||||||
\(402\) | −1.99670e118 | −0.642727 | ||||||||
\(403\) | −3.59418e118 | −1.03329 | ||||||||
\(404\) | −3.80170e117 | −0.0976397 | ||||||||
\(405\) | 1.74303e118 | 0.400038 | ||||||||
\(406\) | 6.19595e118 | 1.27108 | ||||||||
\(407\) | 1.10093e119 | 2.01935 | ||||||||
\(408\) | 1.57230e118 | 0.257927 | ||||||||
\(409\) | −1.29259e119 | −1.89693 | −0.948466 | − | 0.316879i | \(-0.897365\pi\) | ||||
−0.948466 | + | 0.316879i | \(0.897365\pi\) | |||||||
\(410\) | 5.55629e118 | 0.729659 | ||||||||
\(411\) | −1.00136e119 | −1.17703 | ||||||||
\(412\) | 4.12609e118 | 0.434225 | ||||||||
\(413\) | −5.20760e118 | −0.490806 | ||||||||
\(414\) | −1.76367e119 | −1.48903 | ||||||||
\(415\) | 1.42578e119 | 1.07861 | ||||||||
\(416\) | 1.04794e119 | 0.710544 | ||||||||
\(417\) | 1.83028e119 | 1.11257 | ||||||||
\(418\) | −4.36745e119 | −2.38071 | ||||||||
\(419\) | 1.38548e119 | 0.677426 | 0.338713 | − | 0.940890i | \(-0.390008\pi\) | ||||
0.338713 | + | 0.940890i | \(0.390008\pi\) | |||||||
\(420\) | 3.84121e118 | 0.168510 | ||||||||
\(421\) | −2.14976e119 | −0.846359 | −0.423179 | − | 0.906046i | \(-0.639086\pi\) | ||||
−0.423179 | + | 0.906046i | \(0.639086\pi\) | |||||||
\(422\) | −3.82317e119 | −1.35116 | ||||||||
\(423\) | 3.34946e119 | 1.06289 | ||||||||
\(424\) | 1.80882e119 | 0.515525 | ||||||||
\(425\) | 5.29429e118 | 0.135554 | ||||||||
\(426\) | −1.12445e119 | −0.258705 | ||||||||
\(427\) | −1.89124e119 | −0.391092 | ||||||||
\(428\) | 5.06355e118 | 0.0941377 | ||||||||
\(429\) | 1.58646e120 | 2.65230 | ||||||||
\(430\) | 1.34201e119 | 0.201809 | ||||||||
\(431\) | −6.16830e119 | −0.834545 | −0.417272 | − | 0.908781i | \(-0.637014\pi\) | ||||
−0.417272 | + | 0.908781i | \(0.637014\pi\) | |||||||
\(432\) | 3.85341e119 | 0.469175 | ||||||||
\(433\) | 8.81345e119 | 0.965932 | 0.482966 | − | 0.875639i | \(-0.339559\pi\) | ||||
0.482966 | + | 0.875639i | \(0.339559\pi\) | |||||||
\(434\) | 6.10731e119 | 0.602653 | ||||||||
\(435\) | −1.66156e120 | −1.47658 | ||||||||
\(436\) | −1.48792e119 | −0.119109 | ||||||||
\(437\) | −2.28698e120 | −1.64952 | ||||||||
\(438\) | −3.62838e120 | −2.35852 | ||||||||
\(439\) | 5.21639e119 | 0.305657 | 0.152828 | − | 0.988253i | \(-0.451162\pi\) | ||||
0.152828 | + | 0.988253i | \(0.451162\pi\) | |||||||
\(440\) | 1.23036e120 | 0.650035 | ||||||||
\(441\) | −1.41590e120 | −0.674647 | ||||||||
\(442\) | 7.28294e119 | 0.313035 | ||||||||
\(443\) | 3.27234e120 | 1.26908 | 0.634540 | − | 0.772890i | \(-0.281190\pi\) | ||||
0.634540 | + | 0.772890i | \(0.281190\pi\) | |||||||
\(444\) | 1.79389e120 | 0.627872 | ||||||||
\(445\) | 2.06581e120 | 0.652694 | ||||||||
\(446\) | 7.30322e119 | 0.208343 | ||||||||
\(447\) | −5.99097e120 | −1.54349 | ||||||||
\(448\) | 1.73382e120 | 0.403509 | ||||||||
\(449\) | 8.16505e120 | 1.71692 | 0.858460 | − | 0.512880i | \(-0.171421\pi\) | ||||
0.858460 | + | 0.512880i | \(0.171421\pi\) | |||||||
\(450\) | 4.83878e120 | 0.919532 | ||||||||
\(451\) | −8.44309e120 | −1.45034 | ||||||||
\(452\) | 7.08481e119 | 0.110035 | ||||||||
\(453\) | −1.52145e121 | −2.13692 | ||||||||
\(454\) | 4.91285e120 | 0.624155 | ||||||||
\(455\) | −4.65888e120 | −0.535504 | ||||||||
\(456\) | 1.86340e121 | 1.93823 | ||||||||
\(457\) | 1.92588e121 | 1.81318 | 0.906591 | − | 0.422011i | \(-0.138676\pi\) | ||||
0.906591 | + | 0.422011i | \(0.138676\pi\) | |||||||
\(458\) | −2.24965e121 | −1.91750 | ||||||||
\(459\) | 1.06307e120 | 0.0820514 | ||||||||
\(460\) | −2.46052e120 | −0.172007 | ||||||||
\(461\) | 4.05866e120 | 0.257034 | 0.128517 | − | 0.991707i | \(-0.458978\pi\) | ||||
0.128517 | + | 0.991707i | \(0.458978\pi\) | |||||||
\(462\) | −2.69575e121 | −1.54692 | ||||||||
\(463\) | −2.28579e121 | −1.18878 | −0.594389 | − | 0.804178i | \(-0.702606\pi\) | ||||
−0.594389 | + | 0.804178i | \(0.702606\pi\) | |||||||
\(464\) | 4.20139e121 | 1.98073 | ||||||||
\(465\) | −1.63779e121 | −0.700083 | ||||||||
\(466\) | −5.34824e121 | −2.07325 | ||||||||
\(467\) | 4.07747e121 | 1.43375 | 0.716873 | − | 0.697203i | \(-0.245573\pi\) | ||||
0.716873 | + | 0.697203i | \(0.245573\pi\) | |||||||
\(468\) | 1.44125e121 | 0.459785 | ||||||||
\(469\) | −8.91006e120 | −0.257939 | ||||||||
\(470\) | 2.15813e121 | 0.567056 | ||||||||
\(471\) | 5.04083e121 | 1.20240 | ||||||||
\(472\) | −2.71795e121 | −0.588681 | ||||||||
\(473\) | −2.03926e121 | −0.401134 | ||||||||
\(474\) | 1.85197e121 | 0.330918 | ||||||||
\(475\) | 6.27451e121 | 1.01864 | ||||||||
\(476\) | −2.67955e120 | −0.0395317 | ||||||||
\(477\) | 5.92549e121 | 0.794581 | ||||||||
\(478\) | −9.94483e121 | −1.21235 | ||||||||
\(479\) | 6.44914e121 | 0.714885 | 0.357443 | − | 0.933935i | \(-0.383649\pi\) | ||||
0.357443 | + | 0.933935i | \(0.383649\pi\) | |||||||
\(480\) | 4.77526e121 | 0.481416 | ||||||||
\(481\) | −2.17575e122 | −1.99530 | ||||||||
\(482\) | 1.34843e122 | 1.12509 | ||||||||
\(483\) | −1.41161e122 | −1.07181 | ||||||||
\(484\) | 3.14125e121 | 0.217089 | ||||||||
\(485\) | 9.55887e121 | 0.601392 | ||||||||
\(486\) | −2.76429e122 | −1.58355 | ||||||||
\(487\) | −2.38886e122 | −1.24630 | −0.623152 | − | 0.782101i | \(-0.714148\pi\) | ||||
−0.623152 | + | 0.782101i | \(0.714148\pi\) | |||||||
\(488\) | −9.87076e121 | −0.469082 | ||||||||
\(489\) | 1.76324e122 | 0.763411 | ||||||||
\(490\) | −9.12296e121 | −0.359927 | ||||||||
\(491\) | 2.74613e122 | 0.987446 | 0.493723 | − | 0.869619i | \(-0.335636\pi\) | ||||
0.493723 | + | 0.869619i | \(0.335636\pi\) | |||||||
\(492\) | −1.37575e122 | −0.450949 | ||||||||
\(493\) | 1.15907e122 | 0.346398 | ||||||||
\(494\) | 8.63135e122 | 2.35235 | ||||||||
\(495\) | 4.03052e122 | 1.00190 | ||||||||
\(496\) | 4.14128e122 | 0.939114 | ||||||||
\(497\) | −5.01776e121 | −0.103823 | ||||||||
\(498\) | −1.63043e123 | −3.07870 | ||||||||
\(499\) | 1.02145e123 | 1.76053 | 0.880266 | − | 0.474481i | \(-0.157364\pi\) | ||||
0.880266 | + | 0.474481i | \(0.157364\pi\) | |||||||
\(500\) | 1.72017e122 | 0.270668 | ||||||||
\(501\) | −1.45024e123 | −2.08365 | ||||||||
\(502\) | −8.05927e122 | −1.05749 | ||||||||
\(503\) | 1.17607e122 | 0.140958 | 0.0704789 | − | 0.997513i | \(-0.477547\pi\) | ||||
0.0704789 | + | 0.997513i | \(0.477547\pi\) | |||||||
\(504\) | 6.41256e122 | 0.702170 | ||||||||
\(505\) | 2.10112e122 | 0.210229 | ||||||||
\(506\) | 1.72678e123 | 1.57903 | ||||||||
\(507\) | −1.33675e123 | −1.11735 | ||||||||
\(508\) | −4.70973e121 | −0.0359913 | ||||||||
\(509\) | −7.10848e122 | −0.496727 | −0.248363 | − | 0.968667i | \(-0.579893\pi\) | ||||
−0.248363 | + | 0.968667i | \(0.579893\pi\) | |||||||
\(510\) | 3.31868e122 | 0.212091 | ||||||||
\(511\) | −1.61913e123 | −0.946520 | ||||||||
\(512\) | 6.26829e122 | 0.335247 | ||||||||
\(513\) | 1.25990e123 | 0.616588 | ||||||||
\(514\) | 1.00847e123 | 0.451692 | ||||||||
\(515\) | −2.28040e123 | −0.934936 | ||||||||
\(516\) | −3.32284e122 | −0.124724 | ||||||||
\(517\) | −3.27940e123 | −1.12713 | ||||||||
\(518\) | 3.69708e123 | 1.16374 | ||||||||
\(519\) | −3.27981e123 | −0.945659 | ||||||||
\(520\) | −2.43156e123 | −0.642292 | ||||||||
\(521\) | 7.73667e123 | 1.87257 | 0.936285 | − | 0.351242i | \(-0.114241\pi\) | ||||
0.936285 | + | 0.351242i | \(0.114241\pi\) | |||||||
\(522\) | 1.05935e124 | 2.34980 | ||||||||
\(523\) | 1.56809e123 | 0.318819 | 0.159410 | − | 0.987213i | \(-0.449041\pi\) | ||||
0.159410 | + | 0.987213i | \(0.449041\pi\) | |||||||
\(524\) | 7.53357e122 | 0.140420 | ||||||||
\(525\) | 3.87286e123 | 0.661886 | ||||||||
\(526\) | −7.78256e123 | −1.21975 | ||||||||
\(527\) | 1.14249e123 | 0.164237 | ||||||||
\(528\) | −1.82795e124 | −2.41057 | ||||||||
\(529\) | 7.77350e122 | 0.0940554 | ||||||||
\(530\) | 3.81793e123 | 0.423912 | ||||||||
\(531\) | −8.90366e123 | −0.907336 | ||||||||
\(532\) | −3.17566e123 | −0.297068 | ||||||||
\(533\) | 1.66860e124 | 1.43306 | ||||||||
\(534\) | −2.36232e124 | −1.86300 | ||||||||
\(535\) | −2.79851e123 | −0.202689 | ||||||||
\(536\) | −4.65033e123 | −0.309375 | ||||||||
\(537\) | 1.30642e124 | 0.798457 | ||||||||
\(538\) | 3.39188e123 | 0.190479 | ||||||||
\(539\) | 1.38628e124 | 0.715424 | ||||||||
\(540\) | 1.35550e123 | 0.0642961 | ||||||||
\(541\) | −2.69933e124 | −1.17701 | −0.588506 | − | 0.808493i | \(-0.700284\pi\) | ||||
−0.588506 | + | 0.808493i | \(0.700284\pi\) | |||||||
\(542\) | 3.62277e124 | 1.45236 | ||||||||
\(543\) | 1.16263e124 | 0.428597 | ||||||||
\(544\) | −3.33112e123 | −0.112938 | ||||||||
\(545\) | 8.22342e123 | 0.256455 | ||||||||
\(546\) | 5.32758e124 | 1.52850 | ||||||||
\(547\) | −3.22227e124 | −0.850627 | −0.425313 | − | 0.905046i | \(-0.639836\pi\) | ||||
−0.425313 | + | 0.905046i | \(0.639836\pi\) | |||||||
\(548\) | 8.90676e123 | 0.216374 | ||||||||
\(549\) | −3.23354e124 | −0.722998 | ||||||||
\(550\) | −4.73757e124 | −0.975109 | ||||||||
\(551\) | 1.37367e125 | 2.60307 | ||||||||
\(552\) | −7.36744e124 | −1.28555 | ||||||||
\(553\) | 8.26424e123 | 0.132804 | ||||||||
\(554\) | −8.41785e124 | −1.24597 | ||||||||
\(555\) | −9.91443e124 | −1.35188 | ||||||||
\(556\) | −1.62798e124 | −0.204525 | ||||||||
\(557\) | −8.11888e124 | −0.939906 | −0.469953 | − | 0.882691i | \(-0.655729\pi\) | ||||
−0.469953 | + | 0.882691i | \(0.655729\pi\) | |||||||
\(558\) | 1.04419e125 | 1.11410 | ||||||||
\(559\) | 4.03017e124 | 0.396356 | ||||||||
\(560\) | 5.36804e124 | 0.486699 | ||||||||
\(561\) | −5.04292e124 | −0.421572 | ||||||||
\(562\) | 1.45723e125 | 1.12338 | ||||||||
\(563\) | 8.74092e124 | 0.621477 | 0.310738 | − | 0.950495i | \(-0.399424\pi\) | ||||
0.310738 | + | 0.950495i | \(0.399424\pi\) | |||||||
\(564\) | −5.34359e124 | −0.350456 | ||||||||
\(565\) | −3.91562e124 | −0.236917 | ||||||||
\(566\) | −1.75291e124 | −0.0978615 | ||||||||
\(567\) | −8.89452e124 | −0.458240 | ||||||||
\(568\) | −2.61887e124 | −0.124527 | ||||||||
\(569\) | −3.58712e125 | −1.57448 | −0.787242 | − | 0.616644i | \(-0.788492\pi\) | ||||
−0.787242 | + | 0.616644i | \(0.788492\pi\) | |||||||
\(570\) | 3.93313e125 | 1.59379 | ||||||||
\(571\) | 2.83528e125 | 1.06085 | 0.530424 | − | 0.847732i | \(-0.322033\pi\) | ||||
0.530424 | + | 0.847732i | \(0.322033\pi\) | |||||||
\(572\) | −1.41111e125 | −0.487574 | ||||||||
\(573\) | 4.01957e125 | 1.28276 | ||||||||
\(574\) | −2.83532e125 | −0.835818 | ||||||||
\(575\) | −2.48079e125 | −0.675621 | ||||||||
\(576\) | 2.96438e125 | 0.745953 | ||||||||
\(577\) | 2.80174e125 | 0.651521 | 0.325760 | − | 0.945452i | \(-0.394380\pi\) | ||||
0.325760 | + | 0.945452i | \(0.394380\pi\) | |||||||
\(578\) | 5.02508e125 | 1.08001 | ||||||||
\(579\) | −9.88980e124 | −0.196478 | ||||||||
\(580\) | 1.47791e125 | 0.271440 | ||||||||
\(581\) | −7.27564e125 | −1.23554 | ||||||||
\(582\) | −1.09309e126 | −1.71656 | ||||||||
\(583\) | −5.80155e125 | −0.842606 | ||||||||
\(584\) | −8.45053e125 | −1.13527 | ||||||||
\(585\) | −7.96549e125 | −0.989967 | ||||||||
\(586\) | 6.21227e125 | 0.714347 | ||||||||
\(587\) | 5.66199e125 | 0.602470 | 0.301235 | − | 0.953550i | \(-0.402601\pi\) | ||||
0.301235 | + | 0.953550i | \(0.402601\pi\) | |||||||
\(588\) | 2.25887e125 | 0.222445 | ||||||||
\(589\) | 1.35402e126 | 1.23418 | ||||||||
\(590\) | −5.73683e125 | −0.484067 | ||||||||
\(591\) | 5.19205e125 | 0.405610 | ||||||||
\(592\) | 2.50694e126 | 1.81345 | ||||||||
\(593\) | 8.91060e125 | 0.596923 | 0.298461 | − | 0.954422i | \(-0.403527\pi\) | ||||
0.298461 | + | 0.954422i | \(0.403527\pi\) | |||||||
\(594\) | −9.51286e125 | −0.590239 | ||||||||
\(595\) | 1.48093e125 | 0.0851162 | ||||||||
\(596\) | 5.32879e125 | 0.283742 | ||||||||
\(597\) | 2.23771e126 | 1.10401 | ||||||||
\(598\) | −3.41263e126 | −1.56022 | ||||||||
\(599\) | −2.42971e126 | −1.02952 | −0.514760 | − | 0.857334i | \(-0.672119\pi\) | ||||
−0.514760 | + | 0.857334i | \(0.672119\pi\) | |||||||
\(600\) | 2.02132e126 | 0.793876 | ||||||||
\(601\) | 3.04722e125 | 0.110947 | 0.0554734 | − | 0.998460i | \(-0.482333\pi\) | ||||
0.0554734 | + | 0.998460i | \(0.482333\pi\) | |||||||
\(602\) | −6.84814e125 | −0.231171 | ||||||||
\(603\) | −1.52339e126 | −0.476841 | ||||||||
\(604\) | 1.35328e126 | 0.392832 | ||||||||
\(605\) | −1.73610e126 | −0.467417 | ||||||||
\(606\) | −2.40270e126 | −0.600060 | ||||||||
\(607\) | −3.83401e126 | −0.888316 | −0.444158 | − | 0.895948i | \(-0.646497\pi\) | ||||
−0.444158 | + | 0.895948i | \(0.646497\pi\) | |||||||
\(608\) | −3.94787e126 | −0.848692 | ||||||||
\(609\) | 8.47880e126 | 1.69141 | ||||||||
\(610\) | −2.08344e126 | −0.385722 | ||||||||
\(611\) | 6.48106e126 | 1.11371 | ||||||||
\(612\) | −4.58135e125 | −0.0730809 | ||||||||
\(613\) | 2.58389e126 | 0.382668 | 0.191334 | − | 0.981525i | \(-0.438719\pi\) | ||||
0.191334 | + | 0.981525i | \(0.438719\pi\) | |||||||
\(614\) | −1.49570e127 | −2.05676 | ||||||||
\(615\) | 7.60347e126 | 0.970944 | ||||||||
\(616\) | −6.27843e126 | −0.744610 | ||||||||
\(617\) | −8.49357e126 | −0.935654 | −0.467827 | − | 0.883820i | \(-0.654963\pi\) | ||||
−0.467827 | + | 0.883820i | \(0.654963\pi\) | |||||||
\(618\) | 2.60771e127 | 2.66860 | ||||||||
\(619\) | 6.34151e126 | 0.602932 | 0.301466 | − | 0.953477i | \(-0.402524\pi\) | ||||
0.301466 | + | 0.953477i | \(0.402524\pi\) | |||||||
\(620\) | 1.45677e126 | 0.128697 | ||||||||
\(621\) | −4.98133e126 | −0.408957 | ||||||||
\(622\) | −1.32463e126 | −0.101072 | ||||||||
\(623\) | −1.05416e127 | −0.747655 | ||||||||
\(624\) | 3.61256e127 | 2.38186 | ||||||||
\(625\) | 1.03017e126 | 0.0631490 | ||||||||
\(626\) | −3.43518e126 | −0.195802 | ||||||||
\(627\) | −5.97660e127 | −3.16797 | ||||||||
\(628\) | −4.48366e126 | −0.221039 | ||||||||
\(629\) | 6.91611e126 | 0.317145 | ||||||||
\(630\) | 1.35351e127 | 0.577388 | ||||||||
\(631\) | 4.33929e127 | 1.72220 | 0.861098 | − | 0.508439i | \(-0.169777\pi\) | ||||
0.861098 | + | 0.508439i | \(0.169777\pi\) | |||||||
\(632\) | 4.31327e126 | 0.159287 | ||||||||
\(633\) | −5.23179e127 | −1.79797 | ||||||||
\(634\) | 3.58459e127 | 1.14651 | ||||||||
\(635\) | 2.60296e126 | 0.0774932 | ||||||||
\(636\) | −9.45327e126 | −0.261989 | ||||||||
\(637\) | −2.73970e127 | −0.706902 | ||||||||
\(638\) | −1.03719e128 | −2.49183 | ||||||||
\(639\) | −8.57909e126 | −0.191934 | ||||||||
\(640\) | 3.44693e127 | 0.718197 | ||||||||
\(641\) | −2.44604e126 | −0.0474705 | −0.0237353 | − | 0.999718i | \(-0.507556\pi\) | ||||
−0.0237353 | + | 0.999718i | \(0.507556\pi\) | |||||||
\(642\) | 3.20019e127 | 0.578539 | ||||||||
\(643\) | 4.22084e127 | 0.710886 | 0.355443 | − | 0.934698i | \(-0.384330\pi\) | ||||
0.355443 | + | 0.934698i | \(0.384330\pi\) | |||||||
\(644\) | 1.25558e127 | 0.197032 | ||||||||
\(645\) | 1.83646e127 | 0.268544 | ||||||||
\(646\) | −2.74367e127 | −0.373897 | ||||||||
\(647\) | 1.31481e128 | 1.67000 | 0.835001 | − | 0.550249i | \(-0.185467\pi\) | ||||
0.835001 | + | 0.550249i | \(0.185467\pi\) | |||||||
\(648\) | −4.64222e127 | −0.549621 | ||||||||
\(649\) | 8.71743e127 | 0.962176 | ||||||||
\(650\) | 9.36282e127 | 0.963494 | ||||||||
\(651\) | 8.35750e127 | 0.801939 | ||||||||
\(652\) | −1.56835e127 | −0.140339 | ||||||||
\(653\) | −4.67831e127 | −0.390426 | −0.195213 | − | 0.980761i | \(-0.562540\pi\) | ||||
−0.195213 | + | 0.980761i | \(0.562540\pi\) | |||||||
\(654\) | −9.40376e127 | −0.732005 | ||||||||
\(655\) | −4.16364e127 | −0.302339 | ||||||||
\(656\) | −1.92259e128 | −1.30246 | ||||||||
\(657\) | −2.76829e128 | −1.74980 | ||||||||
\(658\) | −1.10128e128 | −0.649558 | ||||||||
\(659\) | −9.77042e127 | −0.537808 | −0.268904 | − | 0.963167i | \(-0.586661\pi\) | ||||
−0.268904 | + | 0.963167i | \(0.586661\pi\) | |||||||
\(660\) | −6.43012e127 | −0.330347 | ||||||||
\(661\) | 2.06865e128 | 0.992018 | 0.496009 | − | 0.868317i | \(-0.334798\pi\) | ||||
0.496009 | + | 0.868317i | \(0.334798\pi\) | |||||||
\(662\) | 3.49230e128 | 1.56341 | ||||||||
\(663\) | 9.96628e127 | 0.416550 | ||||||||
\(664\) | −3.79730e128 | −1.48193 | ||||||||
\(665\) | 1.75512e128 | 0.639619 | ||||||||
\(666\) | 6.32106e128 | 2.15136 | ||||||||
\(667\) | −5.43117e128 | −1.72650 | ||||||||
\(668\) | 1.28995e128 | 0.383039 | ||||||||
\(669\) | 9.99404e127 | 0.277238 | ||||||||
\(670\) | −9.81556e127 | −0.254397 | ||||||||
\(671\) | 3.16591e128 | 0.766697 | ||||||||
\(672\) | −2.43677e128 | −0.551458 | ||||||||
\(673\) | 2.75253e127 | 0.0582167 | 0.0291083 | − | 0.999576i | \(-0.490733\pi\) | ||||
0.0291083 | + | 0.999576i | \(0.490733\pi\) | |||||||
\(674\) | −3.54381e128 | −0.700560 | ||||||||
\(675\) | 1.36667e128 | 0.252547 | ||||||||
\(676\) | 1.18900e128 | 0.205404 | ||||||||
\(677\) | 3.28446e128 | 0.530493 | 0.265246 | − | 0.964181i | \(-0.414547\pi\) | ||||
0.265246 | + | 0.964181i | \(0.414547\pi\) | |||||||
\(678\) | 4.47764e128 | 0.676236 | ||||||||
\(679\) | −4.87780e128 | −0.688889 | ||||||||
\(680\) | 7.72925e127 | 0.102090 | ||||||||
\(681\) | 6.72296e128 | 0.830552 | ||||||||
\(682\) | −1.02235e129 | −1.18144 | ||||||||
\(683\) | 1.04661e129 | 1.13147 | 0.565736 | − | 0.824587i | \(-0.308592\pi\) | ||||
0.565736 | + | 0.824587i | \(0.308592\pi\) | |||||||
\(684\) | −5.42957e128 | −0.549178 | ||||||||
\(685\) | −4.92257e128 | −0.465877 | ||||||||
\(686\) | 1.33504e129 | 1.18235 | ||||||||
\(687\) | −3.07851e129 | −2.55158 | ||||||||
\(688\) | −4.64363e128 | −0.360233 | ||||||||
\(689\) | 1.14656e129 | 0.832569 | ||||||||
\(690\) | −1.55506e129 | −1.05710 | ||||||||
\(691\) | 4.76039e128 | 0.302964 | 0.151482 | − | 0.988460i | \(-0.451595\pi\) | ||||
0.151482 | + | 0.988460i | \(0.451595\pi\) | |||||||
\(692\) | 2.91729e128 | 0.173841 | ||||||||
\(693\) | −2.05674e129 | −1.14767 | ||||||||
\(694\) | 1.17591e129 | 0.614496 | ||||||||
\(695\) | 8.99747e128 | 0.440364 | ||||||||
\(696\) | 4.42525e129 | 2.02870 | ||||||||
\(697\) | −5.30403e128 | −0.227779 | ||||||||
\(698\) | 1.66302e129 | 0.669078 | ||||||||
\(699\) | −7.31876e129 | −2.75884 | ||||||||
\(700\) | −3.44479e128 | −0.121675 | ||||||||
\(701\) | 1.83996e129 | 0.609029 | 0.304515 | − | 0.952508i | \(-0.401506\pi\) | ||||
0.304515 | + | 0.952508i | \(0.401506\pi\) | |||||||
\(702\) | 1.88002e129 | 0.583208 | ||||||||
\(703\) | 8.19660e129 | 2.38323 | ||||||||
\(704\) | −2.90238e129 | −0.791039 | ||||||||
\(705\) | 2.95328e129 | 0.754571 | ||||||||
\(706\) | 6.06388e128 | 0.145257 | ||||||||
\(707\) | −1.07218e129 | −0.240816 | ||||||||
\(708\) | 1.42045e129 | 0.299167 | ||||||||
\(709\) | −6.54379e129 | −1.29248 | −0.646242 | − | 0.763132i | \(-0.723660\pi\) | ||||
−0.646242 | + | 0.763132i | \(0.723660\pi\) | |||||||
\(710\) | −5.52770e128 | −0.102398 | ||||||||
\(711\) | 1.41297e129 | 0.245509 | ||||||||
\(712\) | −5.50188e129 | −0.896750 | ||||||||
\(713\) | −5.35347e129 | −0.818581 | ||||||||
\(714\) | −1.69349e129 | −0.242949 | ||||||||
\(715\) | 7.79888e129 | 1.04980 | ||||||||
\(716\) | −1.16202e129 | −0.146781 | ||||||||
\(717\) | −1.36089e130 | −1.61325 | ||||||||
\(718\) | −9.23193e129 | −1.02714 | ||||||||
\(719\) | −2.08574e129 | −0.217819 | −0.108909 | − | 0.994052i | \(-0.534736\pi\) | ||||
−0.108909 | + | 0.994052i | \(0.534736\pi\) | |||||||
\(720\) | 9.17798e129 | 0.899743 | ||||||||
\(721\) | 1.16367e130 | 1.07096 | ||||||||
\(722\) | −1.94419e130 | −1.67995 | ||||||||
\(723\) | 1.84525e130 | 1.49714 | ||||||||
\(724\) | −1.03412e129 | −0.0787893 | ||||||||
\(725\) | 1.49008e130 | 1.06618 | ||||||||
\(726\) | 1.98529e130 | 1.33416 | ||||||||
\(727\) | 2.57362e130 | 1.62453 | 0.812267 | − | 0.583286i | \(-0.198233\pi\) | ||||
0.812267 | + | 0.583286i | \(0.198233\pi\) | |||||||
\(728\) | 1.24080e130 | 0.735740 | ||||||||
\(729\) | −2.57590e130 | −1.43492 | ||||||||
\(730\) | −1.78367e130 | −0.933523 | ||||||||
\(731\) | −1.28108e129 | −0.0629992 | ||||||||
\(732\) | 5.15865e129 | 0.238387 | ||||||||
\(733\) | −2.63415e130 | −1.14396 | −0.571978 | − | 0.820269i | \(-0.693824\pi\) | ||||
−0.571978 | + | 0.820269i | \(0.693824\pi\) | |||||||
\(734\) | −1.55180e130 | −0.633382 | ||||||||
\(735\) | −1.24842e130 | −0.478948 | ||||||||
\(736\) | 1.56089e130 | 0.562902 | ||||||||
\(737\) | 1.49153e130 | 0.505662 | ||||||||
\(738\) | −4.84768e130 | −1.54515 | ||||||||
\(739\) | −3.11762e129 | −0.0934331 | −0.0467166 | − | 0.998908i | \(-0.514876\pi\) | ||||
−0.0467166 | + | 0.998908i | \(0.514876\pi\) | |||||||
\(740\) | 8.81859e129 | 0.248517 | ||||||||
\(741\) | 1.18115e131 | 3.13023 | ||||||||
\(742\) | −1.94825e130 | −0.485587 | ||||||||
\(743\) | −3.03372e130 | −0.711189 | −0.355595 | − | 0.934640i | \(-0.615722\pi\) | ||||
−0.355595 | + | 0.934640i | \(0.615722\pi\) | |||||||
\(744\) | 4.36194e130 | 0.961858 | ||||||||
\(745\) | −2.94510e130 | −0.610928 | ||||||||
\(746\) | −6.26012e130 | −1.22170 | ||||||||
\(747\) | −1.24395e131 | −2.28410 | ||||||||
\(748\) | 4.48552e129 | 0.0774980 | ||||||||
\(749\) | 1.42805e130 | 0.232179 | ||||||||
\(750\) | 1.08716e131 | 1.66343 | ||||||||
\(751\) | 3.69393e130 | 0.531951 | 0.265976 | − | 0.963980i | \(-0.414306\pi\) | ||||
0.265976 | + | 0.963980i | \(0.414306\pi\) | |||||||
\(752\) | −7.46760e130 | −1.01221 | ||||||||
\(753\) | −1.10286e131 | −1.40718 | ||||||||
\(754\) | 2.04979e131 | 2.46214 | ||||||||
\(755\) | −7.47928e130 | −0.845811 | ||||||||
\(756\) | −6.91700e129 | −0.0736506 | ||||||||
\(757\) | −8.74343e130 | −0.876636 | −0.438318 | − | 0.898820i | \(-0.644426\pi\) | ||||
−0.438318 | + | 0.898820i | \(0.644426\pi\) | |||||||
\(758\) | 1.38238e131 | 1.30520 | ||||||||
\(759\) | 2.36300e131 | 2.10118 | ||||||||
\(760\) | 9.16030e130 | 0.767169 | ||||||||
\(761\) | 1.23497e130 | 0.0974213 | 0.0487106 | − | 0.998813i | \(-0.484489\pi\) | ||||
0.0487106 | + | 0.998813i | \(0.484489\pi\) | |||||||
\(762\) | −2.97658e130 | −0.221190 | ||||||||
\(763\) | −4.19633e130 | −0.293767 | ||||||||
\(764\) | −3.57529e130 | −0.235810 | ||||||||
\(765\) | 2.53201e130 | 0.157351 | ||||||||
\(766\) | −1.08966e131 | −0.638092 | ||||||||
\(767\) | −1.72282e131 | −0.950715 | ||||||||
\(768\) | −2.23043e131 | −1.15999 | ||||||||
\(769\) | −4.35333e130 | −0.213390 | −0.106695 | − | 0.994292i | \(-0.534027\pi\) | ||||
−0.106695 | + | 0.994292i | \(0.534027\pi\) | |||||||
\(770\) | −1.32520e131 | −0.612286 | ||||||||
\(771\) | 1.38004e131 | 0.601059 | ||||||||
\(772\) | 8.79668e129 | 0.0361187 | ||||||||
\(773\) | 1.74484e130 | 0.0675441 | 0.0337721 | − | 0.999430i | \(-0.489248\pi\) | ||||
0.0337721 | + | 0.999430i | \(0.489248\pi\) | |||||||
\(774\) | −1.17086e131 | −0.427357 | ||||||||
\(775\) | 1.46877e131 | 0.505505 | ||||||||
\(776\) | −2.54582e131 | −0.826264 | ||||||||
\(777\) | 5.05924e131 | 1.54856 | ||||||||
\(778\) | −5.38058e130 | −0.155331 | ||||||||
\(779\) | −6.28605e131 | −1.71168 | ||||||||
\(780\) | 1.27078e131 | 0.326412 | ||||||||
\(781\) | 8.39964e130 | 0.203535 | ||||||||
\(782\) | 1.08478e131 | 0.247990 | ||||||||
\(783\) | 2.99203e131 | 0.645366 | ||||||||
\(784\) | 3.15673e131 | 0.642476 | ||||||||
\(785\) | 2.47802e131 | 0.475922 | ||||||||
\(786\) | 4.76126e131 | 0.862971 | ||||||||
\(787\) | 8.46104e131 | 1.44735 | 0.723675 | − | 0.690141i | \(-0.242452\pi\) | ||||
0.723675 | + | 0.690141i | \(0.242452\pi\) | |||||||
\(788\) | −4.61817e130 | −0.0745637 | ||||||||
\(789\) | −1.06500e132 | −1.62310 | ||||||||
\(790\) | 9.10411e130 | 0.130980 | ||||||||
\(791\) | 1.99810e131 | 0.271386 | ||||||||
\(792\) | −1.07345e132 | −1.37653 | ||||||||
\(793\) | −6.25676e131 | −0.757564 | ||||||||
\(794\) | 1.10952e132 | 1.26854 | ||||||||
\(795\) | 5.22461e131 | 0.564092 | ||||||||
\(796\) | −1.99037e131 | −0.202950 | ||||||||
\(797\) | −4.56377e131 | −0.439511 | −0.219756 | − | 0.975555i | \(-0.570526\pi\) | ||||
−0.219756 | + | 0.975555i | \(0.570526\pi\) | |||||||
\(798\) | −2.00704e132 | −1.82568 | ||||||||
\(799\) | −2.06015e131 | −0.177019 | ||||||||
\(800\) | −4.28244e131 | −0.347613 | ||||||||
\(801\) | −1.80235e132 | −1.38216 | ||||||||
\(802\) | 1.01191e132 | 0.733176 | ||||||||
\(803\) | 2.71039e132 | 1.85556 | ||||||||
\(804\) | 2.43035e131 | 0.157224 | ||||||||
\(805\) | −6.93932e131 | −0.424233 | ||||||||
\(806\) | 2.02047e132 | 1.16737 | ||||||||
\(807\) | 4.64159e131 | 0.253467 | ||||||||
\(808\) | −5.59591e131 | −0.288838 | ||||||||
\(809\) | 1.78159e131 | 0.0869260 | 0.0434630 | − | 0.999055i | \(-0.486161\pi\) | ||||
0.0434630 | + | 0.999055i | \(0.486161\pi\) | |||||||
\(810\) | −9.79844e131 | −0.451948 | ||||||||
\(811\) | −1.01353e132 | −0.441966 | −0.220983 | − | 0.975278i | \(-0.570926\pi\) | ||||
−0.220983 | + | 0.975278i | \(0.570926\pi\) | |||||||
\(812\) | −7.54164e131 | −0.310933 | ||||||||
\(813\) | 4.95755e132 | 1.93262 | ||||||||
\(814\) | −6.18885e132 | −2.28139 | ||||||||
\(815\) | 8.66791e131 | 0.302164 | ||||||||
\(816\) | −1.14833e132 | −0.378587 | ||||||||
\(817\) | −1.51827e132 | −0.473418 | ||||||||
\(818\) | 7.26631e132 | 2.14308 | ||||||||
\(819\) | 4.06472e132 | 1.13400 | ||||||||
\(820\) | −6.76306e131 | −0.178489 | ||||||||
\(821\) | −5.58073e132 | −1.39341 | −0.696703 | − | 0.717360i | \(-0.745350\pi\) | ||||
−0.696703 | + | 0.717360i | \(0.745350\pi\) | |||||||
\(822\) | 5.62912e132 | 1.32976 | ||||||||
\(823\) | −1.66879e132 | −0.373000 | −0.186500 | − | 0.982455i | \(-0.559714\pi\) | ||||
−0.186500 | + | 0.982455i | \(0.559714\pi\) | |||||||
\(824\) | 6.07339e132 | 1.28453 | ||||||||
\(825\) | −6.48309e132 | −1.29756 | ||||||||
\(826\) | 2.92745e132 | 0.554495 | ||||||||
\(827\) | 7.08680e131 | 0.127043 | 0.0635213 | − | 0.997980i | \(-0.479767\pi\) | ||||
0.0635213 | + | 0.997980i | \(0.479767\pi\) | |||||||
\(828\) | 2.14672e132 | 0.364247 | ||||||||
\(829\) | −7.66881e132 | −1.23168 | −0.615838 | − | 0.787873i | \(-0.711183\pi\) | ||||
−0.615838 | + | 0.787873i | \(0.711183\pi\) | |||||||
\(830\) | −8.01504e132 | −1.21858 | ||||||||
\(831\) | −1.15193e133 | −1.65799 | ||||||||
\(832\) | 5.73595e132 | 0.781617 | ||||||||
\(833\) | 8.70876e131 | 0.112359 | ||||||||
\(834\) | −1.02889e133 | −1.25694 | ||||||||
\(835\) | −7.12925e132 | −0.824725 | ||||||||
\(836\) | 5.31600e132 | 0.582371 | ||||||||
\(837\) | 2.94923e132 | 0.305985 | ||||||||
\(838\) | −7.78846e132 | −0.765330 | ||||||||
\(839\) | 1.18559e133 | 1.10349 | 0.551743 | − | 0.834014i | \(-0.313963\pi\) | ||||
0.551743 | + | 0.834014i | \(0.313963\pi\) | |||||||
\(840\) | 5.65407e132 | 0.498487 | ||||||||
\(841\) | 2.06488e133 | 1.72456 | ||||||||
\(842\) | 1.20849e133 | 0.956184 | ||||||||
\(843\) | 1.99413e133 | 1.49486 | ||||||||
\(844\) | 4.65352e132 | 0.330522 | ||||||||
\(845\) | −6.57135e132 | −0.442257 | ||||||||
\(846\) | −1.88290e133 | −1.20081 | ||||||||
\(847\) | 8.85914e132 | 0.535422 | ||||||||
\(848\) | −1.32108e133 | −0.756691 | ||||||||
\(849\) | −2.39876e132 | −0.130223 | ||||||||
\(850\) | −2.97618e132 | −0.153143 | ||||||||
\(851\) | −3.24074e133 | −1.58070 | ||||||||
\(852\) | 1.36867e132 | 0.0632845 | ||||||||
\(853\) | 1.11576e133 | 0.489090 | 0.244545 | − | 0.969638i | \(-0.421361\pi\) | ||||
0.244545 | + | 0.969638i | \(0.421361\pi\) | |||||||
\(854\) | 1.06316e133 | 0.441841 | ||||||||
\(855\) | 3.00080e133 | 1.18244 | ||||||||
\(856\) | 7.45329e132 | 0.278479 | ||||||||
\(857\) | −1.41529e132 | −0.0501438 | −0.0250719 | − | 0.999686i | \(-0.507981\pi\) | ||||
−0.0250719 | + | 0.999686i | \(0.507981\pi\) | |||||||
\(858\) | −8.91828e133 | −2.99647 | ||||||||
\(859\) | 4.54822e132 | 0.144928 | 0.0724641 | − | 0.997371i | \(-0.476914\pi\) | ||||
0.0724641 | + | 0.997371i | \(0.476914\pi\) | |||||||
\(860\) | −1.63348e132 | −0.0493666 | ||||||||
\(861\) | −3.87998e133 | −1.11221 | ||||||||
\(862\) | 3.46751e133 | 0.942837 | ||||||||
\(863\) | 4.19992e133 | 1.08330 | 0.541652 | − | 0.840603i | \(-0.317799\pi\) | ||||
0.541652 | + | 0.840603i | \(0.317799\pi\) | |||||||
\(864\) | −8.59897e132 | −0.210412 | ||||||||
\(865\) | −1.61232e133 | −0.374300 | ||||||||
\(866\) | −4.95448e133 | −1.09127 | ||||||||
\(867\) | 6.87653e133 | 1.43715 | ||||||||
\(868\) | −7.43374e132 | −0.147421 | ||||||||
\(869\) | −1.38342e133 | −0.260348 | ||||||||
\(870\) | 9.34047e133 | 1.66818 | ||||||||
\(871\) | −2.94769e133 | −0.499639 | ||||||||
\(872\) | −2.19015e133 | −0.352349 | ||||||||
\(873\) | −8.33979e133 | −1.27352 | ||||||||
\(874\) | 1.28562e134 | 1.86356 | ||||||||
\(875\) | 4.85134e133 | 0.667567 | ||||||||
\(876\) | 4.41641e133 | 0.576943 | ||||||||
\(877\) | −5.09327e133 | −0.631706 | −0.315853 | − | 0.948808i | \(-0.602291\pi\) | ||||
−0.315853 | + | 0.948808i | \(0.602291\pi\) | |||||||
\(878\) | −2.93239e133 | −0.345320 | ||||||||
\(879\) | 8.50114e133 | 0.950568 | ||||||||
\(880\) | −8.98601e133 | −0.954125 | ||||||||
\(881\) | −1.28135e134 | −1.29201 | −0.646003 | − | 0.763335i | \(-0.723561\pi\) | ||||
−0.646003 | + | 0.763335i | \(0.723561\pi\) | |||||||
\(882\) | 7.95948e133 | 0.762191 | ||||||||
\(883\) | 1.34221e134 | 1.22070 | 0.610351 | − | 0.792131i | \(-0.291028\pi\) | ||||
0.610351 | + | 0.792131i | \(0.291028\pi\) | |||||||
\(884\) | −8.86470e132 | −0.0765748 | ||||||||
\(885\) | −7.85052e133 | −0.644139 | ||||||||
\(886\) | −1.83955e134 | −1.43376 | ||||||||
\(887\) | −9.27028e133 | −0.686386 | −0.343193 | − | 0.939265i | \(-0.611508\pi\) | ||||
−0.343193 | + | 0.939265i | \(0.611508\pi\) | |||||||
\(888\) | 2.64052e134 | 1.85737 | ||||||||
\(889\) | −1.32827e133 | −0.0887679 | ||||||||
\(890\) | −1.16129e134 | −0.737389 | ||||||||
\(891\) | 1.48893e134 | 0.898334 | ||||||||
\(892\) | −8.88940e132 | −0.0509649 | ||||||||
\(893\) | −2.44158e134 | −1.33024 | ||||||||
\(894\) | 3.36782e134 | 1.74378 | ||||||||
\(895\) | 6.42221e133 | 0.316036 | ||||||||
\(896\) | −1.75893e134 | −0.822688 | ||||||||
\(897\) | −4.66999e134 | −2.07615 | ||||||||
\(898\) | −4.58998e134 | −1.93971 | ||||||||
\(899\) | 3.21556e134 | 1.29178 | ||||||||
\(900\) | −5.88971e133 | −0.224936 | ||||||||
\(901\) | −3.64458e133 | −0.132334 | ||||||||
\(902\) | 4.74628e134 | 1.63854 | ||||||||
\(903\) | −9.37129e133 | −0.307614 | ||||||||
\(904\) | 1.04285e134 | 0.325505 | ||||||||
\(905\) | 5.71537e133 | 0.169642 | ||||||||
\(906\) | 8.55281e134 | 2.41421 | ||||||||
\(907\) | 4.24923e134 | 1.14072 | 0.570360 | − | 0.821395i | \(-0.306804\pi\) | ||||
0.570360 | + | 0.821395i | \(0.306804\pi\) | |||||||
\(908\) | −5.97987e133 | −0.152681 | ||||||||
\(909\) | −1.83315e134 | −0.445187 | ||||||||
\(910\) | 2.61899e134 | 0.604993 | ||||||||
\(911\) | 3.15914e134 | 0.694198 | 0.347099 | − | 0.937828i | \(-0.387167\pi\) | ||||
0.347099 | + | 0.937828i | \(0.387167\pi\) | |||||||
\(912\) | −1.36094e135 | −2.84495 | ||||||||
\(913\) | 1.21793e135 | 2.42215 | ||||||||
\(914\) | −1.08263e135 | −2.04846 | ||||||||
\(915\) | −2.85107e134 | −0.513273 | ||||||||
\(916\) | 2.73824e134 | 0.469059 | ||||||||
\(917\) | 2.12467e134 | 0.346327 | ||||||||
\(918\) | −5.97606e133 | −0.0926986 | ||||||||
\(919\) | −7.04232e134 | −1.03958 | −0.519792 | − | 0.854293i | \(-0.673991\pi\) | ||||
−0.519792 | + | 0.854293i | \(0.673991\pi\) | |||||||
\(920\) | −3.62176e134 | −0.508831 | ||||||||
\(921\) | −2.04678e135 | −2.73690 | ||||||||
\(922\) | −2.28157e134 | −0.290387 | ||||||||
\(923\) | −1.66001e134 | −0.201110 | ||||||||
\(924\) | 3.28123e134 | 0.378410 | ||||||||
\(925\) | 8.89123e134 | 0.976142 | ||||||||
\(926\) | 1.28495e135 | 1.34304 | ||||||||
\(927\) | 1.98957e135 | 1.97985 | ||||||||
\(928\) | −9.37549e134 | −0.888303 | ||||||||
\(929\) | −8.78763e134 | −0.792788 | −0.396394 | − | 0.918081i | \(-0.629739\pi\) | ||||
−0.396394 | + | 0.918081i | \(0.629739\pi\) | |||||||
\(930\) | 9.20685e134 | 0.790928 | ||||||||
\(931\) | 1.03212e135 | 0.844341 | ||||||||
\(932\) | 6.50981e134 | 0.507159 | ||||||||
\(933\) | −1.81268e134 | −0.134495 | ||||||||
\(934\) | −2.29215e135 | −1.61979 | ||||||||
\(935\) | −2.47905e134 | −0.166862 | ||||||||
\(936\) | 2.12145e135 | 1.36014 | ||||||||
\(937\) | −1.33059e135 | −0.812633 | −0.406316 | − | 0.913733i | \(-0.633187\pi\) | ||||
−0.406316 | + | 0.913733i | \(0.633187\pi\) | |||||||
\(938\) | 5.00879e134 | 0.291409 | ||||||||
\(939\) | −4.70084e134 | −0.260550 | ||||||||
\(940\) | −2.62686e134 | −0.138714 | ||||||||
\(941\) | 1.15538e135 | 0.581295 | 0.290648 | − | 0.956830i | \(-0.406129\pi\) | ||||
0.290648 | + | 0.956830i | \(0.406129\pi\) | |||||||
\(942\) | −2.83370e135 | −1.35843 | ||||||||
\(943\) | 2.48535e135 | 1.13529 | ||||||||
\(944\) | 1.98506e135 | 0.864069 | ||||||||
\(945\) | 3.82287e134 | 0.158578 | ||||||||
\(946\) | 1.14637e135 | 0.453186 | ||||||||
\(947\) | −6.75941e134 | −0.254674 | −0.127337 | − | 0.991859i | \(-0.540643\pi\) | ||||
−0.127337 | + | 0.991859i | \(0.540643\pi\) | |||||||
\(948\) | −2.25420e134 | −0.0809492 | ||||||||
\(949\) | −5.35652e135 | −1.83345 | ||||||||
\(950\) | −3.52721e135 | −1.15082 | ||||||||
\(951\) | 4.90530e135 | 1.52564 | ||||||||
\(952\) | −3.94416e134 | −0.116943 | ||||||||
\(953\) | 3.89093e135 | 1.09983 | 0.549915 | − | 0.835220i | \(-0.314660\pi\) | ||||
0.549915 | + | 0.835220i | \(0.314660\pi\) | |||||||
\(954\) | −3.33101e135 | −0.897687 | ||||||||
\(955\) | 1.97598e135 | 0.507726 | ||||||||
\(956\) | 1.21047e135 | 0.296566 | ||||||||
\(957\) | −1.41934e136 | −3.31583 | ||||||||
\(958\) | −3.62538e135 | −0.807650 | ||||||||
\(959\) | 2.51194e135 | 0.533658 | ||||||||
\(960\) | 2.61375e135 | 0.529570 | ||||||||
\(961\) | −2.00549e135 | −0.387531 | ||||||||
\(962\) | 1.22310e136 | 2.25421 | ||||||||
\(963\) | 2.44161e135 | 0.429220 | ||||||||
\(964\) | −1.64129e135 | −0.275221 | ||||||||
\(965\) | −4.86173e134 | −0.0777675 | ||||||||
\(966\) | 7.93534e135 | 1.21089 | ||||||||
\(967\) | −2.80342e135 | −0.408116 | −0.204058 | − | 0.978959i | \(-0.565413\pi\) | ||||
−0.204058 | + | 0.978959i | \(0.565413\pi\) | |||||||
\(968\) | 4.62376e135 | 0.642194 | ||||||||
\(969\) | −3.75455e135 | −0.497538 | ||||||||
\(970\) | −5.37351e135 | −0.679430 | ||||||||
\(971\) | −6.04055e135 | −0.728789 | −0.364394 | − | 0.931245i | \(-0.618724\pi\) | ||||
−0.364394 | + | 0.931245i | \(0.618724\pi\) | |||||||
\(972\) | 3.36466e135 | 0.387370 | ||||||||
\(973\) | −4.59133e135 | −0.504433 | ||||||||
\(974\) | 1.34290e136 | 1.40803 | ||||||||
\(975\) | 1.28125e136 | 1.28210 | ||||||||
\(976\) | 7.20915e135 | 0.688521 | ||||||||
\(977\) | −9.72367e135 | −0.886396 | −0.443198 | − | 0.896424i | \(-0.646156\pi\) | ||||
−0.443198 | + | 0.896424i | \(0.646156\pi\) | |||||||
\(978\) | −9.91205e135 | −0.862473 | ||||||||
\(979\) | 1.76465e136 | 1.46570 | ||||||||
\(980\) | 1.11044e135 | 0.0880455 | ||||||||
\(981\) | −7.17466e135 | −0.543077 | ||||||||
\(982\) | −1.54374e136 | −1.11558 | ||||||||
\(983\) | −3.38448e135 | −0.233511 | −0.116755 | − | 0.993161i | \(-0.537249\pi\) | ||||
−0.116755 | + | 0.993161i | \(0.537249\pi\) | |||||||
\(984\) | −2.02504e136 | −1.33400 | ||||||||
\(985\) | 2.55236e135 | 0.160544 | ||||||||
\(986\) | −6.51572e135 | −0.391348 | ||||||||
\(987\) | −1.50703e136 | −0.864355 | ||||||||
\(988\) | −1.05060e136 | −0.575434 | ||||||||
\(989\) | 6.00286e135 | 0.313998 | ||||||||
\(990\) | −2.26576e136 | −1.13191 | ||||||||
\(991\) | 1.21030e136 | 0.577486 | 0.288743 | − | 0.957407i | \(-0.406763\pi\) | ||||
0.288743 | + | 0.957407i | \(0.406763\pi\) | |||||||
\(992\) | −9.24136e135 | −0.421167 | ||||||||
\(993\) | 4.77901e136 | 2.08040 | ||||||||
\(994\) | 2.82073e135 | 0.117295 | ||||||||
\(995\) | 1.10004e136 | 0.436975 | ||||||||
\(996\) | 1.98454e136 | 0.753113 | ||||||||
\(997\) | 4.44306e136 | 1.61084 | 0.805419 | − | 0.592705i | \(-0.201940\pi\) | ||||
0.805419 | + | 0.592705i | \(0.201940\pi\) | |||||||
\(998\) | −5.74210e136 | −1.98898 | ||||||||
\(999\) | 1.78533e136 | 0.590864 |
(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 | 1.92.a.a.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 9.92.a.b.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.92.a.a.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.92.a.b.1.6 | 7 | 3.2 | odd | 2 |