Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −35.6107 | −0.786894 | −0.393447 | − | 0.919347i | \(-0.628717\pi\) | ||||
−0.393447 | + | 0.919347i | \(0.628717\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −779.875 | −0.380799 | ||||||||
\(5\) | −1849.70 | −0.264708 | −0.132354 | − | 0.991203i | \(-0.542253\pi\) | ||||
−0.132354 | + | 0.991203i | \(0.542253\pi\) | |||||||
\(6\) | 8653.41 | 0.454313 | ||||||||
\(7\) | 64152.0 | 1.44268 | 0.721342 | − | 0.692579i | \(-0.243526\pi\) | ||||
0.721342 | + | 0.692579i | \(0.243526\pi\) | |||||||
\(8\) | 100703. | 1.08654 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 65869.2 | 0.208297 | ||||||||
\(11\) | −256626. | −0.480443 | −0.240221 | − | 0.970718i | \(-0.577220\pi\) | ||||
−0.240221 | + | 0.970718i | \(0.577220\pi\) | |||||||
\(12\) | 189510. | 0.219854 | ||||||||
\(13\) | 1.02774e6 | 0.767708 | 0.383854 | − | 0.923394i | \(-0.374597\pi\) | ||||
0.383854 | + | 0.923394i | \(0.374597\pi\) | |||||||
\(14\) | −2.28450e6 | −1.13524 | ||||||||
\(15\) | 449477. | 0.152829 | ||||||||
\(16\) | −1.98891e6 | −0.474194 | ||||||||
\(17\) | −1.90460e6 | −0.325338 | −0.162669 | − | 0.986681i | \(-0.552010\pi\) | ||||
−0.162669 | + | 0.986681i | \(0.552010\pi\) | |||||||
\(18\) | −2.10278e6 | −0.262298 | ||||||||
\(19\) | −1.21243e7 | −1.12334 | −0.561672 | − | 0.827360i | \(-0.689842\pi\) | ||||
−0.561672 | + | 0.827360i | \(0.689842\pi\) | |||||||
\(20\) | 1.44254e6 | 0.100800 | ||||||||
\(21\) | −1.55889e7 | −0.832934 | ||||||||
\(22\) | 9.13866e6 | 0.378057 | ||||||||
\(23\) | −3.64620e6 | −0.118124 | −0.0590619 | − | 0.998254i | \(-0.518811\pi\) | ||||
−0.0590619 | + | 0.998254i | \(0.518811\pi\) | |||||||
\(24\) | −2.44708e7 | −0.627315 | ||||||||
\(25\) | −4.54067e7 | −0.929930 | ||||||||
\(26\) | −3.65987e7 | −0.604104 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | −5.00306e7 | −0.549372 | ||||||||
\(29\) | 2.53853e7 | 0.229823 | 0.114911 | − | 0.993376i | \(-0.463342\pi\) | ||||
0.114911 | + | 0.993376i | \(0.463342\pi\) | |||||||
\(30\) | −1.60062e7 | −0.120260 | ||||||||
\(31\) | 5.61268e7 | 0.352112 | 0.176056 | − | 0.984380i | \(-0.443666\pi\) | ||||
0.176056 | + | 0.984380i | \(0.443666\pi\) | |||||||
\(32\) | −1.35412e8 | −0.713401 | ||||||||
\(33\) | 6.23602e7 | 0.277384 | ||||||||
\(34\) | 6.78242e7 | 0.256006 | ||||||||
\(35\) | −1.18662e8 | −0.381889 | ||||||||
\(36\) | −4.60509e7 | −0.126933 | ||||||||
\(37\) | −5.07666e7 | −0.120356 | −0.0601781 | − | 0.998188i | \(-0.519167\pi\) | ||||
−0.0601781 | + | 0.998188i | \(0.519167\pi\) | |||||||
\(38\) | 4.31756e8 | 0.883953 | ||||||||
\(39\) | −2.49742e8 | −0.443236 | ||||||||
\(40\) | −1.86270e8 | −0.287616 | ||||||||
\(41\) | 1.16411e9 | 1.56922 | 0.784608 | − | 0.619992i | \(-0.212864\pi\) | ||||
0.784608 | + | 0.619992i | \(0.212864\pi\) | |||||||
\(42\) | 5.55134e8 | 0.655430 | ||||||||
\(43\) | −1.61126e8 | −0.167144 | −0.0835718 | − | 0.996502i | \(-0.526633\pi\) | ||||
−0.0835718 | + | 0.996502i | \(0.526633\pi\) | |||||||
\(44\) | 2.00137e8 | 0.182952 | ||||||||
\(45\) | −1.09223e8 | −0.0882359 | ||||||||
\(46\) | 1.29844e8 | 0.0929508 | ||||||||
\(47\) | −7.75113e6 | −0.00492977 | −0.00246488 | − | 0.999997i | \(-0.500785\pi\) | ||||
−0.00246488 | + | 0.999997i | \(0.500785\pi\) | |||||||
\(48\) | 4.83306e8 | 0.273776 | ||||||||
\(49\) | 2.13815e9 | 1.08134 | ||||||||
\(50\) | 1.61697e9 | 0.731756 | ||||||||
\(51\) | 4.62818e8 | 0.187834 | ||||||||
\(52\) | −8.01511e8 | −0.292342 | ||||||||
\(53\) | 3.09350e9 | 1.01609 | 0.508046 | − | 0.861330i | \(-0.330368\pi\) | ||||
0.508046 | + | 0.861330i | \(0.330368\pi\) | |||||||
\(54\) | 5.10975e8 | 0.151438 | ||||||||
\(55\) | 4.74682e8 | 0.127177 | ||||||||
\(56\) | 6.46028e9 | 1.56754 | ||||||||
\(57\) | 2.94621e9 | 0.648563 | ||||||||
\(58\) | −9.03990e8 | −0.180846 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | −3.50536e8 | −0.0581970 | ||||||||
\(61\) | −6.22795e9 | −0.944128 | −0.472064 | − | 0.881564i | \(-0.656491\pi\) | ||||
−0.472064 | + | 0.881564i | \(0.656491\pi\) | |||||||
\(62\) | −1.99872e9 | −0.277075 | ||||||||
\(63\) | 3.78811e9 | 0.480894 | ||||||||
\(64\) | 8.89543e9 | 1.03556 | ||||||||
\(65\) | −1.90102e9 | −0.203218 | ||||||||
\(66\) | −2.22069e9 | −0.218271 | ||||||||
\(67\) | −1.55950e10 | −1.41115 | −0.705576 | − | 0.708634i | \(-0.749312\pi\) | ||||
−0.705576 | + | 0.708634i | \(0.749312\pi\) | |||||||
\(68\) | 1.48535e9 | 0.123888 | ||||||||
\(69\) | 8.86026e8 | 0.0681988 | ||||||||
\(70\) | 4.22564e9 | 0.300506 | ||||||||
\(71\) | −2.68594e10 | −1.76675 | −0.883376 | − | 0.468664i | \(-0.844735\pi\) | ||||
−0.883376 | + | 0.468664i | \(0.844735\pi\) | |||||||
\(72\) | 5.94640e9 | 0.362180 | ||||||||
\(73\) | 2.50826e10 | 1.41611 | 0.708056 | − | 0.706157i | \(-0.249573\pi\) | ||||
0.708056 | + | 0.706157i | \(0.249573\pi\) | |||||||
\(74\) | 1.80783e9 | 0.0947075 | ||||||||
\(75\) | 1.10338e10 | 0.536895 | ||||||||
\(76\) | 9.45547e9 | 0.427768 | ||||||||
\(77\) | −1.64631e10 | −0.693127 | ||||||||
\(78\) | 8.89348e9 | 0.348780 | ||||||||
\(79\) | −1.58824e10 | −0.580721 | −0.290361 | − | 0.956917i | \(-0.593775\pi\) | ||||
−0.290361 | + | 0.956917i | \(0.593775\pi\) | |||||||
\(80\) | 3.67889e9 | 0.125523 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −4.14548e10 | −1.23481 | ||||||||
\(83\) | 3.36086e10 | 0.936528 | 0.468264 | − | 0.883589i | \(-0.344880\pi\) | ||||
0.468264 | + | 0.883589i | \(0.344880\pi\) | |||||||
\(84\) | 1.21574e10 | 0.317180 | ||||||||
\(85\) | 3.52294e9 | 0.0861194 | ||||||||
\(86\) | 5.73782e9 | 0.131524 | ||||||||
\(87\) | −6.16863e9 | −0.132688 | ||||||||
\(88\) | −2.58430e10 | −0.522021 | ||||||||
\(89\) | 1.40070e10 | 0.265889 | 0.132944 | − | 0.991123i | \(-0.457557\pi\) | ||||
0.132944 | + | 0.991123i | \(0.457557\pi\) | |||||||
\(90\) | 3.88951e9 | 0.0694322 | ||||||||
\(91\) | 6.59318e10 | 1.10756 | ||||||||
\(92\) | 2.84358e9 | 0.0449814 | ||||||||
\(93\) | −1.36388e10 | −0.203292 | ||||||||
\(94\) | 2.76023e8 | 0.00387920 | ||||||||
\(95\) | 2.24264e10 | 0.297358 | ||||||||
\(96\) | 3.29052e10 | 0.411882 | ||||||||
\(97\) | 7.46648e10 | 0.882818 | 0.441409 | − | 0.897306i | \(-0.354479\pi\) | ||||
0.441409 | + | 0.897306i | \(0.354479\pi\) | |||||||
\(98\) | −7.61412e10 | −0.850896 | ||||||||
\(99\) | −1.51535e10 | −0.160148 | ||||||||
\(100\) | 3.54116e10 | 0.354116 | ||||||||
\(101\) | 2.53766e10 | 0.240251 | 0.120126 | − | 0.992759i | \(-0.461670\pi\) | ||||
0.120126 | + | 0.992759i | \(0.461670\pi\) | |||||||
\(102\) | −1.64813e10 | −0.147805 | ||||||||
\(103\) | 8.90840e10 | 0.757173 | 0.378586 | − | 0.925566i | \(-0.376410\pi\) | ||||
0.378586 | + | 0.925566i | \(0.376410\pi\) | |||||||
\(104\) | 1.03497e11 | 0.834147 | ||||||||
\(105\) | 2.88349e10 | 0.220484 | ||||||||
\(106\) | −1.10162e11 | −0.799557 | ||||||||
\(107\) | 5.21521e10 | 0.359469 | 0.179734 | − | 0.983715i | \(-0.442476\pi\) | ||||
0.179734 | + | 0.983715i | \(0.442476\pi\) | |||||||
\(108\) | 1.11904e10 | 0.0732847 | ||||||||
\(109\) | −3.18182e10 | −0.198075 | −0.0990377 | − | 0.995084i | \(-0.531576\pi\) | ||||
−0.0990377 | + | 0.995084i | \(0.531576\pi\) | |||||||
\(110\) | −1.69038e10 | −0.100075 | ||||||||
\(111\) | 1.23363e10 | 0.0694876 | ||||||||
\(112\) | −1.27593e11 | −0.684112 | ||||||||
\(113\) | 4.14883e9 | 0.0211833 | 0.0105917 | − | 0.999944i | \(-0.496629\pi\) | ||||
0.0105917 | + | 0.999944i | \(0.496629\pi\) | |||||||
\(114\) | −1.04917e11 | −0.510350 | ||||||||
\(115\) | 6.74438e9 | 0.0312683 | ||||||||
\(116\) | −1.97974e10 | −0.0875163 | ||||||||
\(117\) | 6.06872e10 | 0.255903 | ||||||||
\(118\) | −2.54590e10 | −0.102445 | ||||||||
\(119\) | −1.22184e11 | −0.469360 | ||||||||
\(120\) | 4.52636e10 | 0.166055 | ||||||||
\(121\) | −2.19455e11 | −0.769175 | ||||||||
\(122\) | 2.21782e11 | 0.742928 | ||||||||
\(123\) | −2.82879e11 | −0.905987 | ||||||||
\(124\) | −4.37719e10 | −0.134084 | ||||||||
\(125\) | 1.74306e11 | 0.510867 | ||||||||
\(126\) | −1.34897e11 | −0.378413 | ||||||||
\(127\) | −2.47912e11 | −0.665850 | −0.332925 | − | 0.942953i | \(-0.608036\pi\) | ||||
−0.332925 | + | 0.942953i | \(0.608036\pi\) | |||||||
\(128\) | −3.94482e10 | −0.101478 | ||||||||
\(129\) | 3.91537e10 | 0.0965004 | ||||||||
\(130\) | 6.76966e10 | 0.159911 | ||||||||
\(131\) | 1.83558e11 | 0.415700 | 0.207850 | − | 0.978161i | \(-0.433353\pi\) | ||||
0.207850 | + | 0.978161i | \(0.433353\pi\) | |||||||
\(132\) | −4.86332e10 | −0.105627 | ||||||||
\(133\) | −7.77800e11 | −1.62063 | ||||||||
\(134\) | 5.55349e11 | 1.11043 | ||||||||
\(135\) | 2.65412e10 | 0.0509430 | ||||||||
\(136\) | −1.91798e11 | −0.353493 | ||||||||
\(137\) | −1.86742e11 | −0.330582 | −0.165291 | − | 0.986245i | \(-0.552856\pi\) | ||||
−0.165291 | + | 0.986245i | \(0.552856\pi\) | |||||||
\(138\) | −3.15521e10 | −0.0536652 | ||||||||
\(139\) | 6.72902e11 | 1.09994 | 0.549972 | − | 0.835183i | \(-0.314638\pi\) | ||||
0.549972 | + | 0.835183i | \(0.314638\pi\) | |||||||
\(140\) | 9.25416e10 | 0.145423 | ||||||||
\(141\) | 1.88352e9 | 0.00284620 | ||||||||
\(142\) | 9.56484e11 | 1.39025 | ||||||||
\(143\) | −2.63746e11 | −0.368840 | ||||||||
\(144\) | −1.17443e11 | −0.158065 | ||||||||
\(145\) | −4.69552e10 | −0.0608359 | ||||||||
\(146\) | −8.93211e11 | −1.11433 | ||||||||
\(147\) | −5.19571e11 | −0.624309 | ||||||||
\(148\) | 3.95916e10 | 0.0458314 | ||||||||
\(149\) | −1.23789e12 | −1.38089 | −0.690445 | − | 0.723385i | \(-0.742585\pi\) | ||||
−0.690445 | + | 0.723385i | \(0.742585\pi\) | |||||||
\(150\) | −3.92923e11 | −0.422479 | ||||||||
\(151\) | −8.09856e11 | −0.839527 | −0.419763 | − | 0.907634i | \(-0.637887\pi\) | ||||
−0.419763 | + | 0.907634i | \(0.637887\pi\) | |||||||
\(152\) | −1.22095e12 | −1.22056 | ||||||||
\(153\) | −1.12465e11 | −0.108446 | ||||||||
\(154\) | 5.86263e11 | 0.545417 | ||||||||
\(155\) | −1.03818e11 | −0.0932068 | ||||||||
\(156\) | 1.94767e11 | 0.168784 | ||||||||
\(157\) | −2.64498e10 | −0.0221297 | −0.0110648 | − | 0.999939i | \(-0.503522\pi\) | ||||
−0.0110648 | + | 0.999939i | \(0.503522\pi\) | |||||||
\(158\) | 5.65585e11 | 0.456966 | ||||||||
\(159\) | −7.51721e11 | −0.586641 | ||||||||
\(160\) | 2.50473e11 | 0.188843 | ||||||||
\(161\) | −2.33911e11 | −0.170415 | ||||||||
\(162\) | −1.24167e11 | −0.0874326 | ||||||||
\(163\) | 1.81641e12 | 1.23647 | 0.618234 | − | 0.785994i | \(-0.287849\pi\) | ||||
0.618234 | + | 0.785994i | \(0.287849\pi\) | |||||||
\(164\) | −9.07860e11 | −0.597555 | ||||||||
\(165\) | −1.15348e11 | −0.0734256 | ||||||||
\(166\) | −1.19683e12 | −0.736948 | ||||||||
\(167\) | 5.52860e11 | 0.329363 | 0.164681 | − | 0.986347i | \(-0.447340\pi\) | ||||
0.164681 | + | 0.986347i | \(0.447340\pi\) | |||||||
\(168\) | −1.56985e12 | −0.905017 | ||||||||
\(169\) | −7.35905e11 | −0.410625 | ||||||||
\(170\) | −1.25454e11 | −0.0677668 | ||||||||
\(171\) | −7.15930e11 | −0.374448 | ||||||||
\(172\) | 1.25658e11 | 0.0636480 | ||||||||
\(173\) | −6.45797e11 | −0.316842 | −0.158421 | − | 0.987372i | \(-0.550640\pi\) | ||||
−0.158421 | + | 0.987372i | \(0.550640\pi\) | |||||||
\(174\) | 2.19669e11 | 0.104412 | ||||||||
\(175\) | −2.91293e12 | −1.34159 | ||||||||
\(176\) | 5.10408e11 | 0.227823 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | −4.98800e11 | −0.209226 | ||||||||
\(179\) | 6.07973e11 | 0.247282 | 0.123641 | − | 0.992327i | \(-0.460543\pi\) | ||||
0.123641 | + | 0.992327i | \(0.460543\pi\) | |||||||
\(180\) | 8.51803e10 | 0.0336001 | ||||||||
\(181\) | 1.62761e12 | 0.622757 | 0.311378 | − | 0.950286i | \(-0.399209\pi\) | ||||
0.311378 | + | 0.950286i | \(0.399209\pi\) | |||||||
\(182\) | −2.34788e12 | −0.871531 | ||||||||
\(183\) | 1.51339e12 | 0.545093 | ||||||||
\(184\) | −3.67182e11 | −0.128346 | ||||||||
\(185\) | 9.39029e10 | 0.0318592 | ||||||||
\(186\) | 4.85688e11 | 0.159969 | ||||||||
\(187\) | 4.88771e11 | 0.156306 | ||||||||
\(188\) | 6.04491e9 | 0.00187725 | ||||||||
\(189\) | −9.20511e11 | −0.277645 | ||||||||
\(190\) | −7.98620e11 | −0.233989 | ||||||||
\(191\) | −3.35256e12 | −0.954318 | −0.477159 | − | 0.878817i | \(-0.658333\pi\) | ||||
−0.477159 | + | 0.878817i | \(0.658333\pi\) | |||||||
\(192\) | −2.16159e12 | −0.597884 | ||||||||
\(193\) | 6.68094e11 | 0.179586 | 0.0897930 | − | 0.995960i | \(-0.471379\pi\) | ||||
0.0897930 | + | 0.995960i | \(0.471379\pi\) | |||||||
\(194\) | −2.65887e12 | −0.694684 | ||||||||
\(195\) | 4.61947e11 | 0.117328 | ||||||||
\(196\) | −1.66749e12 | −0.411771 | ||||||||
\(197\) | 1.14574e11 | 0.0275120 | 0.0137560 | − | 0.999905i | \(-0.495621\pi\) | ||||
0.0137560 | + | 0.999905i | \(0.495621\pi\) | |||||||
\(198\) | 5.39628e11 | 0.126019 | ||||||||
\(199\) | −7.33403e12 | −1.66591 | −0.832954 | − | 0.553343i | \(-0.813352\pi\) | ||||
−0.832954 | + | 0.553343i | \(0.813352\pi\) | |||||||
\(200\) | −4.57258e12 | −1.01041 | ||||||||
\(201\) | 3.78958e12 | 0.814729 | ||||||||
\(202\) | −9.03678e11 | −0.189052 | ||||||||
\(203\) | 1.62852e12 | 0.331562 | ||||||||
\(204\) | −3.60940e11 | −0.0715269 | ||||||||
\(205\) | −2.15325e12 | −0.415383 | ||||||||
\(206\) | −3.17235e12 | −0.595814 | ||||||||
\(207\) | −2.15304e11 | −0.0393746 | ||||||||
\(208\) | −2.04409e12 | −0.364042 | ||||||||
\(209\) | 3.11142e12 | 0.539703 | ||||||||
\(210\) | −1.02683e12 | −0.173497 | ||||||||
\(211\) | −9.42510e12 | −1.55143 | −0.775716 | − | 0.631082i | \(-0.782611\pi\) | ||||
−0.775716 | + | 0.631082i | \(0.782611\pi\) | |||||||
\(212\) | −2.41255e12 | −0.386927 | ||||||||
\(213\) | 6.52684e12 | 1.02004 | ||||||||
\(214\) | −1.85718e12 | −0.282864 | ||||||||
\(215\) | 2.98035e11 | 0.0442442 | ||||||||
\(216\) | −1.44497e12 | −0.209105 | ||||||||
\(217\) | 3.60065e12 | 0.507986 | ||||||||
\(218\) | 1.13307e12 | 0.155864 | ||||||||
\(219\) | −6.09508e12 | −0.817592 | ||||||||
\(220\) | −3.70193e11 | −0.0484287 | ||||||||
\(221\) | −1.95744e12 | −0.249765 | ||||||||
\(222\) | −4.39304e11 | −0.0546794 | ||||||||
\(223\) | −5.99688e12 | −0.728197 | −0.364098 | − | 0.931361i | \(-0.618623\pi\) | ||||
−0.364098 | + | 0.931361i | \(0.618623\pi\) | |||||||
\(224\) | −8.68698e12 | −1.02921 | ||||||||
\(225\) | −2.68122e12 | −0.309977 | ||||||||
\(226\) | −1.47743e11 | −0.0166690 | ||||||||
\(227\) | 1.12448e13 | 1.23825 | 0.619124 | − | 0.785293i | \(-0.287488\pi\) | ||||
0.619124 | + | 0.785293i | \(0.287488\pi\) | |||||||
\(228\) | −2.29768e12 | −0.246972 | ||||||||
\(229\) | −6.49006e12 | −0.681010 | −0.340505 | − | 0.940243i | \(-0.610598\pi\) | ||||
−0.340505 | + | 0.940243i | \(0.610598\pi\) | |||||||
\(230\) | −2.40172e11 | −0.0246048 | ||||||||
\(231\) | 4.00053e12 | 0.400177 | ||||||||
\(232\) | 2.55637e12 | 0.249712 | ||||||||
\(233\) | −2.50458e12 | −0.238934 | −0.119467 | − | 0.992838i | \(-0.538119\pi\) | ||||
−0.119467 | + | 0.992838i | \(0.538119\pi\) | |||||||
\(234\) | −2.16112e12 | −0.201368 | ||||||||
\(235\) | 1.43373e10 | 0.00130495 | ||||||||
\(236\) | −5.57552e11 | −0.0495757 | ||||||||
\(237\) | 3.85943e12 | 0.335279 | ||||||||
\(238\) | 4.35106e12 | 0.369336 | ||||||||
\(239\) | 6.55750e12 | 0.543938 | 0.271969 | − | 0.962306i | \(-0.412325\pi\) | ||||
0.271969 | + | 0.962306i | \(0.412325\pi\) | |||||||
\(240\) | −8.93971e11 | −0.0724706 | ||||||||
\(241\) | −6.37839e12 | −0.505379 | −0.252690 | − | 0.967547i | \(-0.581315\pi\) | ||||
−0.252690 | + | 0.967547i | \(0.581315\pi\) | |||||||
\(242\) | 7.81494e12 | 0.605259 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 4.85702e12 | 0.359523 | ||||||||
\(245\) | −3.95494e12 | −0.286238 | ||||||||
\(246\) | 1.00735e13 | 0.712916 | ||||||||
\(247\) | −1.24607e13 | −0.862401 | ||||||||
\(248\) | 5.65212e12 | 0.382584 | ||||||||
\(249\) | −8.16688e12 | −0.540705 | ||||||||
\(250\) | −6.20717e12 | −0.401998 | ||||||||
\(251\) | 8.28791e12 | 0.525097 | 0.262548 | − | 0.964919i | \(-0.415437\pi\) | ||||
0.262548 | + | 0.964919i | \(0.415437\pi\) | |||||||
\(252\) | −2.95426e12 | −0.183124 | ||||||||
\(253\) | 9.35711e11 | 0.0567517 | ||||||||
\(254\) | 8.82832e12 | 0.523953 | ||||||||
\(255\) | −8.56074e11 | −0.0497211 | ||||||||
\(256\) | −1.68131e13 | −0.955712 | ||||||||
\(257\) | 1.57395e13 | 0.875707 | 0.437853 | − | 0.899046i | \(-0.355739\pi\) | ||||
0.437853 | + | 0.899046i | \(0.355739\pi\) | |||||||
\(258\) | −1.39429e12 | −0.0759356 | ||||||||
\(259\) | −3.25678e12 | −0.173636 | ||||||||
\(260\) | 1.48256e12 | 0.0773851 | ||||||||
\(261\) | 1.49898e12 | 0.0766077 | ||||||||
\(262\) | −6.53662e12 | −0.327112 | ||||||||
\(263\) | −2.95972e13 | −1.45042 | −0.725211 | − | 0.688527i | \(-0.758258\pi\) | ||||
−0.725211 | + | 0.688527i | \(0.758258\pi\) | |||||||
\(264\) | 6.27984e12 | 0.301389 | ||||||||
\(265\) | −5.72205e12 | −0.268967 | ||||||||
\(266\) | 2.76980e13 | 1.27526 | ||||||||
\(267\) | −3.40370e12 | −0.153511 | ||||||||
\(268\) | 1.21622e13 | 0.537365 | ||||||||
\(269\) | 3.30233e12 | 0.142949 | 0.0714747 | − | 0.997442i | \(-0.477229\pi\) | ||||
0.0714747 | + | 0.997442i | \(0.477229\pi\) | |||||||
\(270\) | −9.45151e11 | −0.0400867 | ||||||||
\(271\) | −2.81967e13 | −1.17184 | −0.585919 | − | 0.810370i | \(-0.699266\pi\) | ||||
−0.585919 | + | 0.810370i | \(0.699266\pi\) | |||||||
\(272\) | 3.78809e12 | 0.154273 | ||||||||
\(273\) | −1.60214e13 | −0.639450 | ||||||||
\(274\) | 6.65003e12 | 0.260133 | ||||||||
\(275\) | 1.16526e13 | 0.446778 | ||||||||
\(276\) | −6.90990e11 | −0.0259700 | ||||||||
\(277\) | 1.63593e13 | 0.602736 | 0.301368 | − | 0.953508i | \(-0.402557\pi\) | ||||
0.301368 | + | 0.953508i | \(0.402557\pi\) | |||||||
\(278\) | −2.39626e13 | −0.865539 | ||||||||
\(279\) | 3.31423e12 | 0.117371 | ||||||||
\(280\) | −1.19496e13 | −0.414938 | ||||||||
\(281\) | −3.16455e13 | −1.07752 | −0.538762 | − | 0.842458i | \(-0.681108\pi\) | ||||
−0.538762 | + | 0.842458i | \(0.681108\pi\) | |||||||
\(282\) | −6.70737e10 | −0.00223966 | ||||||||
\(283\) | 2.01915e13 | 0.661215 | 0.330607 | − | 0.943768i | \(-0.392746\pi\) | ||||
0.330607 | + | 0.943768i | \(0.392746\pi\) | |||||||
\(284\) | 2.09470e13 | 0.672777 | ||||||||
\(285\) | −5.44961e12 | −0.171680 | ||||||||
\(286\) | 9.39219e12 | 0.290238 | ||||||||
\(287\) | 7.46800e13 | 2.26388 | ||||||||
\(288\) | −7.99597e12 | −0.237800 | ||||||||
\(289\) | −3.06444e13 | −0.894155 | ||||||||
\(290\) | 1.67211e12 | 0.0478714 | ||||||||
\(291\) | −1.81435e13 | −0.509695 | ||||||||
\(292\) | −1.95613e13 | −0.539253 | ||||||||
\(293\) | 6.35243e13 | 1.71857 | 0.859287 | − | 0.511494i | \(-0.170908\pi\) | ||||
0.859287 | + | 0.511494i | \(0.170908\pi\) | |||||||
\(294\) | 1.85023e13 | 0.491265 | ||||||||
\(295\) | −1.32240e12 | −0.0344620 | ||||||||
\(296\) | −5.11233e12 | −0.130772 | ||||||||
\(297\) | 3.68231e12 | 0.0924612 | ||||||||
\(298\) | 4.40823e13 | 1.08661 | ||||||||
\(299\) | −3.74736e12 | −0.0906846 | ||||||||
\(300\) | −8.60502e12 | −0.204449 | ||||||||
\(301\) | −1.03366e13 | −0.241135 | ||||||||
\(302\) | 2.88396e13 | 0.660618 | ||||||||
\(303\) | −6.16651e12 | −0.138709 | ||||||||
\(304\) | 2.41143e13 | 0.532683 | ||||||||
\(305\) | 1.15198e13 | 0.249918 | ||||||||
\(306\) | 4.00495e12 | 0.0853355 | ||||||||
\(307\) | 9.58100e12 | 0.200516 | 0.100258 | − | 0.994961i | \(-0.468033\pi\) | ||||
0.100258 | + | 0.994961i | \(0.468033\pi\) | |||||||
\(308\) | 1.28392e13 | 0.263942 | ||||||||
\(309\) | −2.16474e13 | −0.437154 | ||||||||
\(310\) | 3.69703e12 | 0.0733438 | ||||||||
\(311\) | −1.56977e13 | −0.305953 | −0.152976 | − | 0.988230i | \(-0.548886\pi\) | ||||
−0.152976 | + | 0.988230i | \(0.548886\pi\) | |||||||
\(312\) | −2.51497e13 | −0.481595 | ||||||||
\(313\) | 6.24401e13 | 1.17482 | 0.587408 | − | 0.809291i | \(-0.300149\pi\) | ||||
0.587408 | + | 0.809291i | \(0.300149\pi\) | |||||||
\(314\) | 9.41898e11 | 0.0174137 | ||||||||
\(315\) | −7.00687e12 | −0.127296 | ||||||||
\(316\) | 1.23863e13 | 0.221138 | ||||||||
\(317\) | 8.62202e13 | 1.51281 | 0.756403 | − | 0.654106i | \(-0.226955\pi\) | ||||
0.756403 | + | 0.654106i | \(0.226955\pi\) | |||||||
\(318\) | 2.67693e13 | 0.461624 | ||||||||
\(319\) | −6.51454e12 | −0.110417 | ||||||||
\(320\) | −1.64539e13 | −0.274122 | ||||||||
\(321\) | −1.26730e13 | −0.207539 | ||||||||
\(322\) | 8.32974e12 | 0.134099 | ||||||||
\(323\) | 2.30920e13 | 0.365467 | ||||||||
\(324\) | −2.71926e12 | −0.0423109 | ||||||||
\(325\) | −4.66664e13 | −0.713915 | ||||||||
\(326\) | −6.46838e13 | −0.972968 | ||||||||
\(327\) | 7.73183e12 | 0.114359 | ||||||||
\(328\) | 1.17229e14 | 1.70502 | ||||||||
\(329\) | −4.97250e11 | −0.00711210 | ||||||||
\(330\) | 4.10762e12 | 0.0577781 | ||||||||
\(331\) | −1.00373e14 | −1.38855 | −0.694275 | − | 0.719710i | \(-0.744275\pi\) | ||||
−0.694275 | + | 0.719710i | \(0.744275\pi\) | |||||||
\(332\) | −2.62105e13 | −0.356628 | ||||||||
\(333\) | −2.99771e12 | −0.0401187 | ||||||||
\(334\) | −1.96878e13 | −0.259174 | ||||||||
\(335\) | 2.88461e13 | 0.373543 | ||||||||
\(336\) | 3.10051e13 | 0.394972 | ||||||||
\(337\) | −8.43673e13 | −1.05733 | −0.528664 | − | 0.848831i | \(-0.677307\pi\) | ||||
−0.528664 | + | 0.848831i | \(0.677307\pi\) | |||||||
\(338\) | 2.62061e13 | 0.323118 | ||||||||
\(339\) | −1.00817e12 | −0.0122302 | ||||||||
\(340\) | −2.74745e12 | −0.0327941 | ||||||||
\(341\) | −1.44036e13 | −0.169170 | ||||||||
\(342\) | 2.54948e13 | 0.294651 | ||||||||
\(343\) | 1.03174e13 | 0.117341 | ||||||||
\(344\) | −1.62259e13 | −0.181608 | ||||||||
\(345\) | −1.63888e12 | −0.0180527 | ||||||||
\(346\) | 2.29973e13 | 0.249321 | ||||||||
\(347\) | 1.98663e13 | 0.211985 | 0.105992 | − | 0.994367i | \(-0.466198\pi\) | ||||
0.105992 | + | 0.994367i | \(0.466198\pi\) | |||||||
\(348\) | 4.81076e12 | 0.0505275 | ||||||||
\(349\) | −1.08915e13 | −0.112602 | −0.0563012 | − | 0.998414i | \(-0.517931\pi\) | ||||
−0.0563012 | + | 0.998414i | \(0.517931\pi\) | |||||||
\(350\) | 1.03732e14 | 1.05569 | ||||||||
\(351\) | −1.47470e13 | −0.147745 | ||||||||
\(352\) | 3.47504e13 | 0.342748 | ||||||||
\(353\) | −2.77510e13 | −0.269474 | −0.134737 | − | 0.990881i | \(-0.543019\pi\) | ||||
−0.134737 | + | 0.990881i | \(0.543019\pi\) | |||||||
\(354\) | 6.18653e12 | 0.0591465 | ||||||||
\(355\) | 4.96819e13 | 0.467673 | ||||||||
\(356\) | −1.09237e13 | −0.101250 | ||||||||
\(357\) | 2.96907e13 | 0.270985 | ||||||||
\(358\) | −2.16504e13 | −0.194585 | ||||||||
\(359\) | 3.68376e13 | 0.326041 | 0.163020 | − | 0.986623i | \(-0.447876\pi\) | ||||
0.163020 | + | 0.986623i | \(0.447876\pi\) | |||||||
\(360\) | −1.09990e13 | −0.0958719 | ||||||||
\(361\) | 3.05092e13 | 0.261903 | ||||||||
\(362\) | −5.79604e13 | −0.490043 | ||||||||
\(363\) | 5.33275e13 | 0.444083 | ||||||||
\(364\) | −5.14186e13 | −0.421757 | ||||||||
\(365\) | −4.63954e13 | −0.374855 | ||||||||
\(366\) | −5.38930e13 | −0.428930 | ||||||||
\(367\) | 3.19123e13 | 0.250204 | 0.125102 | − | 0.992144i | \(-0.460074\pi\) | ||||
0.125102 | + | 0.992144i | \(0.460074\pi\) | |||||||
\(368\) | 7.25198e12 | 0.0560136 | ||||||||
\(369\) | 6.87395e13 | 0.523072 | ||||||||
\(370\) | −3.34395e12 | −0.0250698 | ||||||||
\(371\) | 1.98454e14 | 1.46590 | ||||||||
\(372\) | 1.06366e13 | 0.0774133 | ||||||||
\(373\) | −1.72704e14 | −1.23852 | −0.619262 | − | 0.785185i | \(-0.712568\pi\) | ||||
−0.619262 | + | 0.785185i | \(0.712568\pi\) | |||||||
\(374\) | −1.74055e13 | −0.122996 | ||||||||
\(375\) | −4.23564e13 | −0.294949 | ||||||||
\(376\) | −7.80560e11 | −0.00535640 | ||||||||
\(377\) | 2.60896e13 | 0.176437 | ||||||||
\(378\) | 3.27801e13 | 0.218477 | ||||||||
\(379\) | −2.30989e13 | −0.151731 | −0.0758657 | − | 0.997118i | \(-0.524172\pi\) | ||||
−0.0758657 | + | 0.997118i | \(0.524172\pi\) | |||||||
\(380\) | −1.74898e13 | −0.113233 | ||||||||
\(381\) | 6.02426e13 | 0.384429 | ||||||||
\(382\) | 1.19387e14 | 0.750947 | ||||||||
\(383\) | −6.49064e13 | −0.402434 | −0.201217 | − | 0.979547i | \(-0.564490\pi\) | ||||
−0.201217 | + | 0.979547i | \(0.564490\pi\) | |||||||
\(384\) | 9.58591e12 | 0.0585884 | ||||||||
\(385\) | 3.04518e13 | 0.183476 | ||||||||
\(386\) | −2.37913e13 | −0.141315 | ||||||||
\(387\) | −9.51434e12 | −0.0557145 | ||||||||
\(388\) | −5.82292e13 | −0.336176 | ||||||||
\(389\) | 2.01526e13 | 0.114712 | 0.0573560 | − | 0.998354i | \(-0.481733\pi\) | ||||
0.0573560 | + | 0.998354i | \(0.481733\pi\) | |||||||
\(390\) | −1.64503e13 | −0.0923247 | ||||||||
\(391\) | 6.94455e12 | 0.0384302 | ||||||||
\(392\) | 2.15318e14 | 1.17492 | ||||||||
\(393\) | −4.46045e13 | −0.240005 | ||||||||
\(394\) | −4.08007e12 | −0.0216490 | ||||||||
\(395\) | 2.93777e13 | 0.153721 | ||||||||
\(396\) | 1.18179e13 | 0.0609839 | ||||||||
\(397\) | −2.26240e14 | −1.15139 | −0.575694 | − | 0.817666i | \(-0.695268\pi\) | ||||
−0.575694 | + | 0.817666i | \(0.695268\pi\) | |||||||
\(398\) | 2.61170e14 | 1.31089 | ||||||||
\(399\) | 1.89005e14 | 0.935672 | ||||||||
\(400\) | 9.03101e13 | 0.440967 | ||||||||
\(401\) | −2.19454e14 | −1.05694 | −0.528468 | − | 0.848953i | \(-0.677233\pi\) | ||||
−0.528468 | + | 0.848953i | \(0.677233\pi\) | |||||||
\(402\) | −1.34950e14 | −0.641105 | ||||||||
\(403\) | 5.76839e13 | 0.270319 | ||||||||
\(404\) | −1.97906e13 | −0.0914872 | ||||||||
\(405\) | −6.44951e12 | −0.0294120 | ||||||||
\(406\) | −5.79927e13 | −0.260904 | ||||||||
\(407\) | 1.30280e13 | 0.0578242 | ||||||||
\(408\) | 4.66070e13 | 0.204089 | ||||||||
\(409\) | −2.37577e14 | −1.02642 | −0.513212 | − | 0.858262i | \(-0.671545\pi\) | ||||
−0.513212 | + | 0.858262i | \(0.671545\pi\) | |||||||
\(410\) | 7.66790e13 | 0.326862 | ||||||||
\(411\) | 4.53784e13 | 0.190862 | ||||||||
\(412\) | −6.94744e13 | −0.288330 | ||||||||
\(413\) | 4.58638e13 | 0.187821 | ||||||||
\(414\) | 7.66715e12 | 0.0309836 | ||||||||
\(415\) | −6.21658e13 | −0.247906 | ||||||||
\(416\) | −1.39169e14 | −0.547684 | ||||||||
\(417\) | −1.63515e14 | −0.635053 | ||||||||
\(418\) | −1.10800e14 | −0.424689 | ||||||||
\(419\) | 8.85726e13 | 0.335060 | 0.167530 | − | 0.985867i | \(-0.446421\pi\) | ||||
0.167530 | + | 0.985867i | \(0.446421\pi\) | |||||||
\(420\) | −2.24876e13 | −0.0839599 | ||||||||
\(421\) | 6.42170e13 | 0.236646 | 0.118323 | − | 0.992975i | \(-0.462248\pi\) | ||||
0.118323 | + | 0.992975i | \(0.462248\pi\) | |||||||
\(422\) | 3.35635e14 | 1.22081 | ||||||||
\(423\) | −4.57696e11 | −0.00164326 | ||||||||
\(424\) | 3.11524e14 | 1.10403 | ||||||||
\(425\) | 8.64817e13 | 0.302542 | ||||||||
\(426\) | −2.32426e14 | −0.802659 | ||||||||
\(427\) | −3.99535e14 | −1.36208 | ||||||||
\(428\) | −4.06722e13 | −0.136885 | ||||||||
\(429\) | 6.40903e13 | 0.212950 | ||||||||
\(430\) | −1.06133e13 | −0.0348155 | ||||||||
\(431\) | −2.80219e14 | −0.907555 | −0.453778 | − | 0.891115i | \(-0.649924\pi\) | ||||
−0.453778 | + | 0.891115i | \(0.649924\pi\) | |||||||
\(432\) | 2.85387e13 | 0.0912587 | ||||||||
\(433\) | −2.24303e13 | −0.0708192 | −0.0354096 | − | 0.999373i | \(-0.511274\pi\) | ||||
−0.0354096 | + | 0.999373i | \(0.511274\pi\) | |||||||
\(434\) | −1.28222e14 | −0.399731 | ||||||||
\(435\) | 1.14101e13 | 0.0351236 | ||||||||
\(436\) | 2.48143e13 | 0.0754268 | ||||||||
\(437\) | 4.42077e13 | 0.132694 | ||||||||
\(438\) | 2.17050e14 | 0.643358 | ||||||||
\(439\) | 9.75244e13 | 0.285469 | 0.142734 | − | 0.989761i | \(-0.454411\pi\) | ||||
0.142734 | + | 0.989761i | \(0.454411\pi\) | |||||||
\(440\) | 4.78018e13 | 0.138183 | ||||||||
\(441\) | 1.26256e14 | 0.360445 | ||||||||
\(442\) | 6.97059e13 | 0.196538 | ||||||||
\(443\) | 4.85637e14 | 1.35236 | 0.676179 | − | 0.736737i | \(-0.263635\pi\) | ||||
0.676179 | + | 0.736737i | \(0.263635\pi\) | |||||||
\(444\) | −9.62076e12 | −0.0264608 | ||||||||
\(445\) | −2.59088e13 | −0.0703828 | ||||||||
\(446\) | 2.13553e14 | 0.573013 | ||||||||
\(447\) | 3.00808e14 | 0.797257 | ||||||||
\(448\) | 5.70660e14 | 1.49399 | ||||||||
\(449\) | 5.64094e14 | 1.45880 | 0.729401 | − | 0.684086i | \(-0.239799\pi\) | ||||
0.729401 | + | 0.684086i | \(0.239799\pi\) | |||||||
\(450\) | 9.54803e13 | 0.243919 | ||||||||
\(451\) | −2.98741e14 | −0.753918 | ||||||||
\(452\) | −3.23557e12 | −0.00806658 | ||||||||
\(453\) | 1.96795e14 | 0.484701 | ||||||||
\(454\) | −4.00434e14 | −0.974370 | ||||||||
\(455\) | −1.21954e14 | −0.293179 | ||||||||
\(456\) | 2.96692e14 | 0.704691 | ||||||||
\(457\) | −6.46165e13 | −0.151637 | −0.0758184 | − | 0.997122i | \(-0.524157\pi\) | ||||
−0.0758184 | + | 0.997122i | \(0.524157\pi\) | |||||||
\(458\) | 2.31116e14 | 0.535882 | ||||||||
\(459\) | 2.73289e13 | 0.0626113 | ||||||||
\(460\) | −5.25977e12 | −0.0119069 | ||||||||
\(461\) | −1.14661e14 | −0.256483 | −0.128242 | − | 0.991743i | \(-0.540933\pi\) | ||||
−0.128242 | + | 0.991743i | \(0.540933\pi\) | |||||||
\(462\) | −1.42462e14 | −0.314897 | ||||||||
\(463\) | −3.67887e14 | −0.803562 | −0.401781 | − | 0.915736i | \(-0.631609\pi\) | ||||
−0.401781 | + | 0.915736i | \(0.631609\pi\) | |||||||
\(464\) | −5.04892e13 | −0.108981 | ||||||||
\(465\) | 2.52277e13 | 0.0538129 | ||||||||
\(466\) | 8.91900e13 | 0.188015 | ||||||||
\(467\) | −6.88247e14 | −1.43384 | −0.716921 | − | 0.697154i | \(-0.754449\pi\) | ||||
−0.716921 | + | 0.697154i | \(0.754449\pi\) | |||||||
\(468\) | −4.73284e13 | −0.0974473 | ||||||||
\(469\) | −1.00045e15 | −2.03585 | ||||||||
\(470\) | −5.10560e11 | −0.00102685 | ||||||||
\(471\) | 6.42731e12 | 0.0127766 | ||||||||
\(472\) | 7.19948e13 | 0.141456 | ||||||||
\(473\) | 4.13493e13 | 0.0803029 | ||||||||
\(474\) | −1.37437e14 | −0.263829 | ||||||||
\(475\) | 5.50526e14 | 1.04463 | ||||||||
\(476\) | 9.52882e13 | 0.178731 | ||||||||
\(477\) | 1.82668e14 | 0.338698 | ||||||||
\(478\) | −2.33517e14 | −0.428022 | ||||||||
\(479\) | 4.85519e13 | 0.0879753 | 0.0439876 | − | 0.999032i | \(-0.485994\pi\) | ||||
0.0439876 | + | 0.999032i | \(0.485994\pi\) | |||||||
\(480\) | −6.08648e13 | −0.109028 | ||||||||
\(481\) | −5.21750e13 | −0.0923984 | ||||||||
\(482\) | 2.27139e14 | 0.397680 | ||||||||
\(483\) | 5.68404e13 | 0.0983893 | ||||||||
\(484\) | 1.71147e14 | 0.292901 | ||||||||
\(485\) | −1.38107e14 | −0.233689 | ||||||||
\(486\) | 3.01726e13 | 0.0504792 | ||||||||
\(487\) | 9.11754e14 | 1.50823 | 0.754116 | − | 0.656741i | \(-0.228066\pi\) | ||||
0.754116 | + | 0.656741i | \(0.228066\pi\) | |||||||
\(488\) | −6.27172e14 | −1.02583 | ||||||||
\(489\) | −4.41388e14 | −0.713875 | ||||||||
\(490\) | 1.40838e14 | 0.225239 | ||||||||
\(491\) | 6.96377e14 | 1.10128 | 0.550638 | − | 0.834744i | \(-0.314384\pi\) | ||||
0.550638 | + | 0.834744i | \(0.314384\pi\) | |||||||
\(492\) | 2.20610e14 | 0.344999 | ||||||||
\(493\) | −4.83489e13 | −0.0747702 | ||||||||
\(494\) | 4.43735e14 | 0.678618 | ||||||||
\(495\) | 2.80295e13 | 0.0423923 | ||||||||
\(496\) | −1.11631e14 | −0.166969 | ||||||||
\(497\) | −1.72309e15 | −2.54886 | ||||||||
\(498\) | 2.90829e14 | 0.425477 | ||||||||
\(499\) | −9.18652e14 | −1.32922 | −0.664612 | − | 0.747189i | \(-0.731403\pi\) | ||||
−0.664612 | + | 0.747189i | \(0.731403\pi\) | |||||||
\(500\) | −1.35937e14 | −0.194537 | ||||||||
\(501\) | −1.34345e14 | −0.190158 | ||||||||
\(502\) | −2.95138e14 | −0.413195 | ||||||||
\(503\) | −4.53959e14 | −0.628627 | −0.314314 | − | 0.949319i | \(-0.601774\pi\) | ||||
−0.314314 | + | 0.949319i | \(0.601774\pi\) | |||||||
\(504\) | 3.81473e14 | 0.522512 | ||||||||
\(505\) | −4.69390e13 | −0.0635963 | ||||||||
\(506\) | −3.33214e13 | −0.0446575 | ||||||||
\(507\) | 1.78825e14 | 0.237074 | ||||||||
\(508\) | 1.93340e14 | 0.253555 | ||||||||
\(509\) | −6.03821e14 | −0.783358 | −0.391679 | − | 0.920102i | \(-0.628106\pi\) | ||||
−0.391679 | + | 0.920102i | \(0.628106\pi\) | |||||||
\(510\) | 3.04854e13 | 0.0391252 | ||||||||
\(511\) | 1.60910e15 | 2.04300 | ||||||||
\(512\) | 6.79516e14 | 0.853522 | ||||||||
\(513\) | 1.73971e14 | 0.216188 | ||||||||
\(514\) | −5.60495e14 | −0.689088 | ||||||||
\(515\) | −1.64779e14 | −0.200429 | ||||||||
\(516\) | −3.05350e13 | −0.0367472 | ||||||||
\(517\) | 1.98914e12 | 0.00236847 | ||||||||
\(518\) | 1.15976e14 | 0.136633 | ||||||||
\(519\) | 1.56929e14 | 0.182929 | ||||||||
\(520\) | −1.91438e14 | −0.220805 | ||||||||
\(521\) | −1.34344e15 | −1.53325 | −0.766624 | − | 0.642097i | \(-0.778065\pi\) | ||||
−0.766624 | + | 0.642097i | \(0.778065\pi\) | |||||||
\(522\) | −5.33797e13 | −0.0602821 | ||||||||
\(523\) | −5.11309e14 | −0.571379 | −0.285690 | − | 0.958322i | \(-0.592223\pi\) | ||||
−0.285690 | + | 0.958322i | \(0.592223\pi\) | |||||||
\(524\) | −1.43152e14 | −0.158298 | ||||||||
\(525\) | 7.07843e14 | 0.774570 | ||||||||
\(526\) | 1.05398e15 | 1.14133 | ||||||||
\(527\) | −1.06899e14 | −0.114555 | ||||||||
\(528\) | −1.24029e14 | −0.131534 | ||||||||
\(529\) | −9.39515e14 | −0.986047 | ||||||||
\(530\) | 2.03767e14 | 0.211649 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | 6.06587e14 | 0.617134 | ||||||||
\(533\) | 1.19641e15 | 1.20470 | ||||||||
\(534\) | 1.21208e14 | 0.120797 | ||||||||
\(535\) | −9.64658e13 | −0.0951541 | ||||||||
\(536\) | −1.57046e15 | −1.53328 | ||||||||
\(537\) | −1.47737e14 | −0.142768 | ||||||||
\(538\) | −1.17598e14 | −0.112486 | ||||||||
\(539\) | −5.48707e14 | −0.519520 | ||||||||
\(540\) | −2.06988e13 | −0.0193990 | ||||||||
\(541\) | −1.49339e15 | −1.38544 | −0.692720 | − | 0.721206i | \(-0.743588\pi\) | ||||
−0.692720 | + | 0.721206i | \(0.743588\pi\) | |||||||
\(542\) | 1.00411e15 | 0.922112 | ||||||||
\(543\) | −3.95509e14 | −0.359549 | ||||||||
\(544\) | 2.57907e14 | 0.232097 | ||||||||
\(545\) | 5.88542e13 | 0.0524320 | ||||||||
\(546\) | 5.70535e14 | 0.503179 | ||||||||
\(547\) | −5.32530e14 | −0.464958 | −0.232479 | − | 0.972601i | \(-0.574684\pi\) | ||||
−0.232479 | + | 0.972601i | \(0.574684\pi\) | |||||||
\(548\) | 1.45636e14 | 0.125885 | ||||||||
\(549\) | −3.67754e14 | −0.314709 | ||||||||
\(550\) | −4.14956e14 | −0.351567 | ||||||||
\(551\) | −3.07780e14 | −0.258170 | ||||||||
\(552\) | 8.92253e13 | 0.0741008 | ||||||||
\(553\) | −1.01889e15 | −0.837797 | ||||||||
\(554\) | −5.82568e14 | −0.474289 | ||||||||
\(555\) | −2.28184e13 | −0.0183939 | ||||||||
\(556\) | −5.24780e14 | −0.418857 | ||||||||
\(557\) | −1.29608e15 | −1.02430 | −0.512151 | − | 0.858896i | \(-0.671151\pi\) | ||||
−0.512151 | + | 0.858896i | \(0.671151\pi\) | |||||||
\(558\) | −1.18022e14 | −0.0923583 | ||||||||
\(559\) | −1.65596e14 | −0.128317 | ||||||||
\(560\) | 2.36008e14 | 0.181090 | ||||||||
\(561\) | −1.18771e14 | −0.0902435 | ||||||||
\(562\) | 1.12692e15 | 0.847897 | ||||||||
\(563\) | −2.22397e15 | −1.65704 | −0.828518 | − | 0.559962i | \(-0.810816\pi\) | ||||
−0.828518 | + | 0.559962i | \(0.810816\pi\) | |||||||
\(564\) | −1.46891e12 | −0.00108383 | ||||||||
\(565\) | −7.67409e12 | −0.00560739 | ||||||||
\(566\) | −7.19033e14 | −0.520306 | ||||||||
\(567\) | 2.23684e14 | 0.160298 | ||||||||
\(568\) | −2.70482e15 | −1.91965 | ||||||||
\(569\) | −1.05219e15 | −0.739569 | −0.369784 | − | 0.929118i | \(-0.620568\pi\) | ||||
−0.369784 | + | 0.929118i | \(0.620568\pi\) | |||||||
\(570\) | 1.94065e14 | 0.135094 | ||||||||
\(571\) | −1.22798e15 | −0.846631 | −0.423316 | − | 0.905982i | \(-0.639134\pi\) | ||||
−0.423316 | + | 0.905982i | \(0.639134\pi\) | |||||||
\(572\) | 2.05689e14 | 0.140454 | ||||||||
\(573\) | 8.14672e14 | 0.550976 | ||||||||
\(574\) | −2.65941e15 | −1.78143 | ||||||||
\(575\) | 1.65562e14 | 0.109847 | ||||||||
\(576\) | 5.25267e14 | 0.345188 | ||||||||
\(577\) | −2.13168e15 | −1.38757 | −0.693786 | − | 0.720182i | \(-0.744058\pi\) | ||||
−0.693786 | + | 0.720182i | \(0.744058\pi\) | |||||||
\(578\) | 1.09127e15 | 0.703605 | ||||||||
\(579\) | −1.62347e14 | −0.103684 | ||||||||
\(580\) | 3.66192e13 | 0.0231662 | ||||||||
\(581\) | 2.15606e15 | 1.35111 | ||||||||
\(582\) | 6.46105e14 | 0.401076 | ||||||||
\(583\) | −7.93875e14 | −0.488174 | ||||||||
\(584\) | 2.52589e15 | 1.53866 | ||||||||
\(585\) | −1.12253e14 | −0.0677394 | ||||||||
\(586\) | −2.26215e15 | −1.35233 | ||||||||
\(587\) | 6.85096e14 | 0.405735 | 0.202867 | − | 0.979206i | \(-0.434974\pi\) | ||||
0.202867 | + | 0.979206i | \(0.434974\pi\) | |||||||
\(588\) | 4.05201e14 | 0.237736 | ||||||||
\(589\) | −6.80500e14 | −0.395543 | ||||||||
\(590\) | 4.70915e13 | 0.0271179 | ||||||||
\(591\) | −2.78415e13 | −0.0158841 | ||||||||
\(592\) | 1.00970e14 | 0.0570722 | ||||||||
\(593\) | 6.09078e14 | 0.341092 | 0.170546 | − | 0.985350i | \(-0.445447\pi\) | ||||
0.170546 | + | 0.985350i | \(0.445447\pi\) | |||||||
\(594\) | −1.31130e14 | −0.0727571 | ||||||||
\(595\) | 2.26004e14 | 0.124243 | ||||||||
\(596\) | 9.65403e14 | 0.525840 | ||||||||
\(597\) | 1.78217e15 | 0.961812 | ||||||||
\(598\) | 1.33446e14 | 0.0713591 | ||||||||
\(599\) | −2.10851e15 | −1.11719 | −0.558596 | − | 0.829440i | \(-0.688660\pi\) | ||||
−0.558596 | + | 0.829440i | \(0.688660\pi\) | |||||||
\(600\) | 1.11114e15 | 0.583359 | ||||||||
\(601\) | −3.51373e15 | −1.82793 | −0.913963 | − | 0.405799i | \(-0.866993\pi\) | ||||
−0.913963 | + | 0.405799i | \(0.866993\pi\) | |||||||
\(602\) | 3.68093e14 | 0.189748 | ||||||||
\(603\) | −9.20869e14 | −0.470384 | ||||||||
\(604\) | 6.31587e14 | 0.319691 | ||||||||
\(605\) | 4.05925e14 | 0.203606 | ||||||||
\(606\) | 2.19594e14 | 0.109149 | ||||||||
\(607\) | −1.15275e15 | −0.567801 | −0.283901 | − | 0.958854i | \(-0.591629\pi\) | ||||
−0.283901 | + | 0.958854i | \(0.591629\pi\) | |||||||
\(608\) | 1.64179e15 | 0.801396 | ||||||||
\(609\) | −3.95730e14 | −0.191427 | ||||||||
\(610\) | −4.10230e14 | −0.196659 | ||||||||
\(611\) | −7.96617e12 | −0.00378462 | ||||||||
\(612\) | 8.77085e13 | 0.0412961 | ||||||||
\(613\) | −3.88504e15 | −1.81286 | −0.906428 | − | 0.422361i | \(-0.861202\pi\) | ||||
−0.906428 | + | 0.422361i | \(0.861202\pi\) | |||||||
\(614\) | −3.41186e14 | −0.157785 | ||||||||
\(615\) | 5.23241e14 | 0.239822 | ||||||||
\(616\) | −1.65788e15 | −0.753111 | ||||||||
\(617\) | −3.26822e15 | −1.47144 | −0.735720 | − | 0.677286i | \(-0.763156\pi\) | ||||
−0.735720 | + | 0.677286i | \(0.763156\pi\) | |||||||
\(618\) | 7.70880e14 | 0.343994 | ||||||||
\(619\) | 1.74251e15 | 0.770683 | 0.385341 | − | 0.922774i | \(-0.374084\pi\) | ||||
0.385341 | + | 0.922774i | \(0.374084\pi\) | |||||||
\(620\) | 8.09649e13 | 0.0354930 | ||||||||
\(621\) | 5.23190e13 | 0.0227329 | ||||||||
\(622\) | 5.59007e14 | 0.240752 | ||||||||
\(623\) | 8.98577e14 | 0.383594 | ||||||||
\(624\) | 4.96714e14 | 0.210180 | ||||||||
\(625\) | 1.89471e15 | 0.794700 | ||||||||
\(626\) | −2.22354e15 | −0.924454 | ||||||||
\(627\) | −7.56076e14 | −0.311598 | ||||||||
\(628\) | 2.06276e13 | 0.00842694 | ||||||||
\(629\) | 9.66900e13 | 0.0391564 | ||||||||
\(630\) | 2.49520e14 | 0.100169 | ||||||||
\(631\) | 1.38785e15 | 0.552307 | 0.276153 | − | 0.961114i | \(-0.410940\pi\) | ||||
0.276153 | + | 0.961114i | \(0.410940\pi\) | |||||||
\(632\) | −1.59940e15 | −0.630978 | ||||||||
\(633\) | 2.29030e15 | 0.895720 | ||||||||
\(634\) | −3.07037e15 | −1.19042 | ||||||||
\(635\) | 4.58562e14 | 0.176256 | ||||||||
\(636\) | 5.86249e14 | 0.223392 | ||||||||
\(637\) | 2.19747e15 | 0.830150 | ||||||||
\(638\) | 2.31988e14 | 0.0868862 | ||||||||
\(639\) | −1.58602e15 | −0.588918 | ||||||||
\(640\) | 7.29673e13 | 0.0268620 | ||||||||
\(641\) | 2.45583e15 | 0.896352 | 0.448176 | − | 0.893945i | \(-0.352074\pi\) | ||||
0.448176 | + | 0.893945i | \(0.352074\pi\) | |||||||
\(642\) | 4.51294e14 | 0.163311 | ||||||||
\(643\) | 1.80437e15 | 0.647388 | 0.323694 | − | 0.946162i | \(-0.395075\pi\) | ||||
0.323694 | + | 0.946162i | \(0.395075\pi\) | |||||||
\(644\) | 1.82421e14 | 0.0648939 | ||||||||
\(645\) | −7.24226e13 | −0.0255444 | ||||||||
\(646\) | −8.22324e14 | −0.287583 | ||||||||
\(647\) | 4.67983e15 | 1.62277 | 0.811384 | − | 0.584514i | \(-0.198715\pi\) | ||||
0.811384 | + | 0.584514i | \(0.198715\pi\) | |||||||
\(648\) | 3.51129e14 | 0.120727 | ||||||||
\(649\) | −1.83468e14 | −0.0625483 | ||||||||
\(650\) | 1.66183e15 | 0.561775 | ||||||||
\(651\) | −8.74957e14 | −0.293286 | ||||||||
\(652\) | −1.41658e15 | −0.470845 | ||||||||
\(653\) | −3.01278e15 | −0.992989 | −0.496494 | − | 0.868040i | \(-0.665380\pi\) | ||||
−0.496494 | + | 0.868040i | \(0.665380\pi\) | |||||||
\(654\) | −2.75336e14 | −0.0899883 | ||||||||
\(655\) | −3.39527e14 | −0.110039 | ||||||||
\(656\) | −2.31531e15 | −0.744113 | ||||||||
\(657\) | 1.48110e15 | 0.472037 | ||||||||
\(658\) | 1.77075e13 | 0.00559646 | ||||||||
\(659\) | −2.52199e15 | −0.790450 | −0.395225 | − | 0.918584i | \(-0.629333\pi\) | ||||
−0.395225 | + | 0.918584i | \(0.629333\pi\) | |||||||
\(660\) | 8.99568e13 | 0.0279603 | ||||||||
\(661\) | 3.09070e15 | 0.952684 | 0.476342 | − | 0.879260i | \(-0.341962\pi\) | ||||
0.476342 | + | 0.879260i | \(0.341962\pi\) | |||||||
\(662\) | 3.57434e15 | 1.09264 | ||||||||
\(663\) | 4.75658e14 | 0.144202 | ||||||||
\(664\) | 3.38448e15 | 1.01758 | ||||||||
\(665\) | 1.43870e15 | 0.428993 | ||||||||
\(666\) | 1.06751e14 | 0.0315692 | ||||||||
\(667\) | −9.25599e13 | −0.0271476 | ||||||||
\(668\) | −4.31162e14 | −0.125421 | ||||||||
\(669\) | 1.45724e15 | 0.420425 | ||||||||
\(670\) | −1.02723e15 | −0.293938 | ||||||||
\(671\) | 1.59826e15 | 0.453599 | ||||||||
\(672\) | 2.11094e15 | 0.594216 | ||||||||
\(673\) | 3.83543e15 | 1.07085 | 0.535427 | − | 0.844581i | \(-0.320151\pi\) | ||||
0.535427 | + | 0.844581i | \(0.320151\pi\) | |||||||
\(674\) | 3.00438e15 | 0.832005 | ||||||||
\(675\) | 6.51537e14 | 0.178965 | ||||||||
\(676\) | 5.73914e14 | 0.156365 | ||||||||
\(677\) | 4.12234e15 | 1.11405 | 0.557027 | − | 0.830494i | \(-0.311942\pi\) | ||||
0.557027 | + | 0.830494i | \(0.311942\pi\) | |||||||
\(678\) | 3.59015e13 | 0.00962387 | ||||||||
\(679\) | 4.78989e15 | 1.27363 | ||||||||
\(680\) | 3.54770e14 | 0.0935723 | ||||||||
\(681\) | −2.73247e15 | −0.714903 | ||||||||
\(682\) | 5.12924e14 | 0.133119 | ||||||||
\(683\) | 6.95455e15 | 1.79042 | 0.895211 | − | 0.445643i | \(-0.147025\pi\) | ||||
0.895211 | + | 0.445643i | \(0.147025\pi\) | |||||||
\(684\) | 5.58336e14 | 0.142589 | ||||||||
\(685\) | 3.45417e14 | 0.0875076 | ||||||||
\(686\) | −3.67409e14 | −0.0923351 | ||||||||
\(687\) | 1.57708e15 | 0.393181 | ||||||||
\(688\) | 3.20466e14 | 0.0792585 | ||||||||
\(689\) | 3.17933e15 | 0.780062 | ||||||||
\(690\) | 5.83618e13 | 0.0142056 | ||||||||
\(691\) | 2.64766e15 | 0.639343 | 0.319671 | − | 0.947528i | \(-0.396427\pi\) | ||||
0.319671 | + | 0.947528i | \(0.396427\pi\) | |||||||
\(692\) | 5.03641e14 | 0.120653 | ||||||||
\(693\) | −9.72130e14 | −0.231042 | ||||||||
\(694\) | −7.07453e14 | −0.166809 | ||||||||
\(695\) | −1.24467e15 | −0.291164 | ||||||||
\(696\) | −6.21198e14 | −0.144171 | ||||||||
\(697\) | −2.21716e15 | −0.510526 | ||||||||
\(698\) | 3.87854e14 | 0.0886061 | ||||||||
\(699\) | 6.08613e14 | 0.137948 | ||||||||
\(700\) | 2.27172e15 | 0.510877 | ||||||||
\(701\) | 3.22140e15 | 0.718779 | 0.359389 | − | 0.933188i | \(-0.382985\pi\) | ||||
0.359389 | + | 0.933188i | \(0.382985\pi\) | |||||||
\(702\) | 5.25151e14 | 0.116260 | ||||||||
\(703\) | 6.15511e14 | 0.135201 | ||||||||
\(704\) | −2.28280e15 | −0.497530 | ||||||||
\(705\) | −3.48395e12 | −0.000753412 0 | ||||||||
\(706\) | 9.88233e14 | 0.212048 | ||||||||
\(707\) | 1.62796e15 | 0.346606 | ||||||||
\(708\) | 1.35485e14 | 0.0286226 | ||||||||
\(709\) | −7.37651e14 | −0.154631 | −0.0773155 | − | 0.997007i | \(-0.524635\pi\) | ||||
−0.0773155 | + | 0.997007i | \(0.524635\pi\) | |||||||
\(710\) | −1.76921e15 | −0.368009 | ||||||||
\(711\) | −9.37841e14 | −0.193574 | ||||||||
\(712\) | 1.41054e15 | 0.288899 | ||||||||
\(713\) | −2.04650e14 | −0.0415928 | ||||||||
\(714\) | −1.05731e15 | −0.213236 | ||||||||
\(715\) | 4.87851e14 | 0.0976346 | ||||||||
\(716\) | −4.74143e14 | −0.0941646 | ||||||||
\(717\) | −1.59347e15 | −0.314043 | ||||||||
\(718\) | −1.31181e15 | −0.256559 | ||||||||
\(719\) | 1.65357e15 | 0.320933 | 0.160467 | − | 0.987041i | \(-0.448700\pi\) | ||||
0.160467 | + | 0.987041i | \(0.448700\pi\) | |||||||
\(720\) | 2.17235e14 | 0.0418409 | ||||||||
\(721\) | 5.71492e15 | 1.09236 | ||||||||
\(722\) | −1.08645e15 | −0.206090 | ||||||||
\(723\) | 1.54995e15 | 0.291781 | ||||||||
\(724\) | −1.26933e15 | −0.237145 | ||||||||
\(725\) | −1.15266e15 | −0.213719 | ||||||||
\(726\) | −1.89903e15 | −0.349446 | ||||||||
\(727\) | −1.93205e15 | −0.352841 | −0.176420 | − | 0.984315i | \(-0.556452\pi\) | ||||
−0.176420 | + | 0.984315i | \(0.556452\pi\) | |||||||
\(728\) | 6.63951e15 | 1.20341 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 1.65217e15 | 0.294971 | ||||||||
\(731\) | 3.06881e14 | 0.0543782 | ||||||||
\(732\) | −1.18026e15 | −0.207570 | ||||||||
\(733\) | −1.52030e15 | −0.265373 | −0.132686 | − | 0.991158i | \(-0.542360\pi\) | ||||
−0.132686 | + | 0.991158i | \(0.542360\pi\) | |||||||
\(734\) | −1.13642e15 | −0.196884 | ||||||||
\(735\) | 9.61051e14 | 0.165259 | ||||||||
\(736\) | 4.93741e14 | 0.0842696 | ||||||||
\(737\) | 4.00209e15 | 0.677978 | ||||||||
\(738\) | −2.44786e15 | −0.411602 | ||||||||
\(739\) | −1.10640e16 | −1.84658 | −0.923291 | − | 0.384100i | \(-0.874512\pi\) | ||||
−0.923291 | + | 0.384100i | \(0.874512\pi\) | |||||||
\(740\) | −7.32326e13 | −0.0121319 | ||||||||
\(741\) | 3.02795e15 | 0.497907 | ||||||||
\(742\) | −7.06711e15 | −1.15351 | ||||||||
\(743\) | −8.63150e15 | −1.39845 | −0.699226 | − | 0.714900i | \(-0.746472\pi\) | ||||
−0.699226 | + | 0.714900i | \(0.746472\pi\) | |||||||
\(744\) | −1.37347e15 | −0.220885 | ||||||||
\(745\) | 2.28973e15 | 0.365532 | ||||||||
\(746\) | 6.15012e15 | 0.974586 | ||||||||
\(747\) | 1.98455e15 | 0.312176 | ||||||||
\(748\) | −3.81180e14 | −0.0595212 | ||||||||
\(749\) | 3.34566e15 | 0.518600 | ||||||||
\(750\) | 1.50834e15 | 0.232094 | ||||||||
\(751\) | −1.80297e15 | −0.275403 | −0.137701 | − | 0.990474i | \(-0.543971\pi\) | ||||
−0.137701 | + | 0.990474i | \(0.543971\pi\) | |||||||
\(752\) | 1.54163e13 | 0.00233767 | ||||||||
\(753\) | −2.01396e15 | −0.303165 | ||||||||
\(754\) | −9.29069e14 | −0.138837 | ||||||||
\(755\) | 1.49799e15 | 0.222229 | ||||||||
\(756\) | 7.17884e14 | 0.105727 | ||||||||
\(757\) | 2.21410e15 | 0.323721 | 0.161860 | − | 0.986814i | \(-0.448251\pi\) | ||||
0.161860 | + | 0.986814i | \(0.448251\pi\) | |||||||
\(758\) | 8.22568e14 | 0.119396 | ||||||||
\(759\) | −2.27378e14 | −0.0327656 | ||||||||
\(760\) | 2.25840e15 | 0.323092 | ||||||||
\(761\) | −8.34704e15 | −1.18554 | −0.592771 | − | 0.805371i | \(-0.701966\pi\) | ||||
−0.592771 | + | 0.805371i | \(0.701966\pi\) | |||||||
\(762\) | −2.14528e15 | −0.302505 | ||||||||
\(763\) | −2.04120e15 | −0.285760 | ||||||||
\(764\) | 2.61458e15 | 0.363403 | ||||||||
\(765\) | 2.08026e14 | 0.0287065 | ||||||||
\(766\) | 2.31136e15 | 0.316672 | ||||||||
\(767\) | 7.34758e14 | 0.0999471 | ||||||||
\(768\) | 4.08558e15 | 0.551781 | ||||||||
\(769\) | 1.19175e16 | 1.59805 | 0.799027 | − | 0.601296i | \(-0.205349\pi\) | ||||
0.799027 | + | 0.601296i | \(0.205349\pi\) | |||||||
\(770\) | −1.08441e15 | −0.144376 | ||||||||
\(771\) | −3.82470e15 | −0.505589 | ||||||||
\(772\) | −5.21030e14 | −0.0683861 | ||||||||
\(773\) | −2.58218e15 | −0.336511 | −0.168256 | − | 0.985743i | \(-0.553813\pi\) | ||||
−0.168256 | + | 0.985743i | \(0.553813\pi\) | |||||||
\(774\) | 3.38813e14 | 0.0438414 | ||||||||
\(775\) | −2.54854e15 | −0.327440 | ||||||||
\(776\) | 7.51894e15 | 0.959218 | ||||||||
\(777\) | 7.91397e14 | 0.100249 | ||||||||
\(778\) | −7.17649e14 | −0.0902661 | ||||||||
\(779\) | −1.41141e16 | −1.76277 | ||||||||
\(780\) | −3.60261e14 | −0.0446783 | ||||||||
\(781\) | 6.89284e15 | 0.848823 | ||||||||
\(782\) | −2.47301e14 | −0.0302404 | ||||||||
\(783\) | −3.64251e14 | −0.0442295 | ||||||||
\(784\) | −4.25260e15 | −0.512763 | ||||||||
\(785\) | 4.89243e13 | 0.00585789 | ||||||||
\(786\) | 1.58840e15 | 0.188858 | ||||||||
\(787\) | −1.06275e16 | −1.25478 | −0.627392 | − | 0.778703i | \(-0.715878\pi\) | ||||
−0.627392 | + | 0.778703i | \(0.715878\pi\) | |||||||
\(788\) | −8.93535e13 | −0.0104765 | ||||||||
\(789\) | 7.19212e15 | 0.837401 | ||||||||
\(790\) | −1.04616e15 | −0.120962 | ||||||||
\(791\) | 2.66156e14 | 0.0305608 | ||||||||
\(792\) | −1.52600e15 | −0.174007 | ||||||||
\(793\) | −6.40073e15 | −0.724815 | ||||||||
\(794\) | 8.05657e15 | 0.906019 | ||||||||
\(795\) | 1.39046e15 | 0.155288 | ||||||||
\(796\) | 5.71963e15 | 0.634375 | ||||||||
\(797\) | 5.37985e15 | 0.592583 | 0.296292 | − | 0.955098i | \(-0.404250\pi\) | ||||
0.296292 | + | 0.955098i | \(0.404250\pi\) | |||||||
\(798\) | −6.73062e15 | −0.736274 | ||||||||
\(799\) | 1.47628e13 | 0.00160384 | ||||||||
\(800\) | 6.14864e15 | 0.663413 | ||||||||
\(801\) | 8.27100e14 | 0.0886296 | ||||||||
\(802\) | 7.81491e15 | 0.831696 | ||||||||
\(803\) | −6.43687e15 | −0.680360 | ||||||||
\(804\) | −2.95540e15 | −0.310248 | ||||||||
\(805\) | 4.32665e14 | 0.0451102 | ||||||||
\(806\) | −2.05417e15 | −0.212713 | ||||||||
\(807\) | −8.02465e14 | −0.0825319 | ||||||||
\(808\) | 2.55549e15 | 0.261043 | ||||||||
\(809\) | 1.16160e16 | 1.17853 | 0.589265 | − | 0.807940i | \(-0.299418\pi\) | ||||
0.589265 | + | 0.807940i | \(0.299418\pi\) | |||||||
\(810\) | 2.29672e14 | 0.0231441 | ||||||||
\(811\) | −1.16748e16 | −1.16851 | −0.584256 | − | 0.811569i | \(-0.698614\pi\) | ||||
−0.584256 | + | 0.811569i | \(0.698614\pi\) | |||||||
\(812\) | −1.27004e15 | −0.126258 | ||||||||
\(813\) | 6.85181e15 | 0.676561 | ||||||||
\(814\) | −4.63938e14 | −0.0455015 | ||||||||
\(815\) | −3.35982e15 | −0.327302 | ||||||||
\(816\) | −9.20505e14 | −0.0890698 | ||||||||
\(817\) | 1.95355e15 | 0.187760 | ||||||||
\(818\) | 8.46030e15 | 0.807686 | ||||||||
\(819\) | 3.89321e15 | 0.369187 | ||||||||
\(820\) | 1.67927e15 | 0.158177 | ||||||||
\(821\) | 2.93787e15 | 0.274881 | 0.137441 | − | 0.990510i | \(-0.456112\pi\) | ||||
0.137441 | + | 0.990510i | \(0.456112\pi\) | |||||||
\(822\) | −1.61596e15 | −0.150188 | ||||||||
\(823\) | −1.24942e16 | −1.15348 | −0.576740 | − | 0.816928i | \(-0.695675\pi\) | ||||
−0.576740 | + | 0.816928i | \(0.695675\pi\) | |||||||
\(824\) | 8.97100e15 | 0.822700 | ||||||||
\(825\) | −2.83157e15 | −0.257947 | ||||||||
\(826\) | −1.63324e15 | −0.147795 | ||||||||
\(827\) | 1.35197e16 | 1.21531 | 0.607654 | − | 0.794202i | \(-0.292111\pi\) | ||||
0.607654 | + | 0.794202i | \(0.292111\pi\) | |||||||
\(828\) | 1.67911e14 | 0.0149938 | ||||||||
\(829\) | −1.02560e16 | −0.909761 | −0.454881 | − | 0.890552i | \(-0.650318\pi\) | ||||
−0.454881 | + | 0.890552i | \(0.650318\pi\) | |||||||
\(830\) | 2.21377e15 | 0.195076 | ||||||||
\(831\) | −3.97532e15 | −0.347990 | ||||||||
\(832\) | 9.14222e15 | 0.795011 | ||||||||
\(833\) | −4.07233e15 | −0.351800 | ||||||||
\(834\) | 5.82290e15 | 0.499719 | ||||||||
\(835\) | −1.02263e15 | −0.0871848 | ||||||||
\(836\) | −2.42652e15 | −0.205518 | ||||||||
\(837\) | −8.05358e14 | −0.0677640 | ||||||||
\(838\) | −3.15414e15 | −0.263656 | ||||||||
\(839\) | −1.43075e16 | −1.18816 | −0.594079 | − | 0.804407i | \(-0.702483\pi\) | ||||
−0.594079 | + | 0.804407i | \(0.702483\pi\) | |||||||
\(840\) | 2.90375e15 | 0.239565 | ||||||||
\(841\) | −1.15561e16 | −0.947181 | ||||||||
\(842\) | −2.28681e15 | −0.186215 | ||||||||
\(843\) | 7.68985e15 | 0.622109 | ||||||||
\(844\) | 7.35041e15 | 0.590783 | ||||||||
\(845\) | 1.36120e15 | 0.108695 | ||||||||
\(846\) | 1.62989e13 | 0.00129307 | ||||||||
\(847\) | −1.40785e16 | −1.10968 | ||||||||
\(848\) | −6.15271e15 | −0.481825 | ||||||||
\(849\) | −4.90653e15 | −0.381753 | ||||||||
\(850\) | −3.07968e15 | −0.238068 | ||||||||
\(851\) | 1.85105e14 | 0.0142169 | ||||||||
\(852\) | −5.09012e15 | −0.388428 | ||||||||
\(853\) | −1.00565e16 | −0.762477 | −0.381239 | − | 0.924477i | \(-0.624502\pi\) | ||||
−0.381239 | + | 0.924477i | \(0.624502\pi\) | |||||||
\(854\) | 1.42278e16 | 1.07181 | ||||||||
\(855\) | 1.32426e15 | 0.0991193 | ||||||||
\(856\) | 5.25186e15 | 0.390578 | ||||||||
\(857\) | −5.67045e15 | −0.419008 | −0.209504 | − | 0.977808i | \(-0.567185\pi\) | ||||
−0.209504 | + | 0.977808i | \(0.567185\pi\) | |||||||
\(858\) | −2.28230e15 | −0.167569 | ||||||||
\(859\) | −3.48425e15 | −0.254183 | −0.127092 | − | 0.991891i | \(-0.540564\pi\) | ||||
−0.127092 | + | 0.991891i | \(0.540564\pi\) | |||||||
\(860\) | −2.32430e14 | −0.0168481 | ||||||||
\(861\) | −1.81472e16 | −1.30705 | ||||||||
\(862\) | 9.97882e15 | 0.714150 | ||||||||
\(863\) | −1.46753e16 | −1.04358 | −0.521791 | − | 0.853074i | \(-0.674736\pi\) | ||||
−0.521791 | + | 0.853074i | \(0.674736\pi\) | |||||||
\(864\) | 1.94302e15 | 0.137294 | ||||||||
\(865\) | 1.19453e15 | 0.0838704 | ||||||||
\(866\) | 7.98758e14 | 0.0557272 | ||||||||
\(867\) | 7.44659e15 | 0.516241 | ||||||||
\(868\) | −2.80806e15 | −0.193440 | ||||||||
\(869\) | 4.07585e15 | 0.279003 | ||||||||
\(870\) | −4.06323e14 | −0.0276385 | ||||||||
\(871\) | −1.60276e16 | −1.08335 | ||||||||
\(872\) | −3.20418e15 | −0.215217 | ||||||||
\(873\) | 4.40888e15 | 0.294273 | ||||||||
\(874\) | −1.57427e15 | −0.104416 | ||||||||
\(875\) | 1.11821e16 | 0.737019 | ||||||||
\(876\) | 4.75340e15 | 0.311338 | ||||||||
\(877\) | 4.80789e15 | 0.312937 | 0.156469 | − | 0.987683i | \(-0.449989\pi\) | ||||
0.156469 | + | 0.987683i | \(0.449989\pi\) | |||||||
\(878\) | −3.47292e15 | −0.224634 | ||||||||
\(879\) | −1.54364e16 | −0.992219 | ||||||||
\(880\) | −9.44101e14 | −0.0603065 | ||||||||
\(881\) | −7.85415e15 | −0.498576 | −0.249288 | − | 0.968429i | \(-0.580197\pi\) | ||||
−0.249288 | + | 0.968429i | \(0.580197\pi\) | |||||||
\(882\) | −4.49606e15 | −0.283632 | ||||||||
\(883\) | −9.07255e15 | −0.568781 | −0.284391 | − | 0.958708i | \(-0.591791\pi\) | ||||
−0.284391 | + | 0.958708i | \(0.591791\pi\) | |||||||
\(884\) | 1.52656e15 | 0.0951100 | ||||||||
\(885\) | 3.21342e14 | 0.0198966 | ||||||||
\(886\) | −1.72939e16 | −1.06416 | ||||||||
\(887\) | 2.32586e16 | 1.42234 | 0.711170 | − | 0.703020i | \(-0.248165\pi\) | ||||
0.711170 | + | 0.703020i | \(0.248165\pi\) | |||||||
\(888\) | 1.24230e15 | 0.0755012 | ||||||||
\(889\) | −1.59040e16 | −0.960611 | ||||||||
\(890\) | 9.22630e14 | 0.0553838 | ||||||||
\(891\) | −8.94801e14 | −0.0533825 | ||||||||
\(892\) | 4.67682e15 | 0.277296 | ||||||||
\(893\) | 9.39772e13 | 0.00553783 | ||||||||
\(894\) | −1.07120e16 | −0.627356 | ||||||||
\(895\) | −1.12457e15 | −0.0654574 | ||||||||
\(896\) | −2.53068e15 | −0.146401 | ||||||||
\(897\) | 9.10607e14 | 0.0523568 | ||||||||
\(898\) | −2.00878e16 | −1.14792 | ||||||||
\(899\) | 1.42480e15 | 0.0809235 | ||||||||
\(900\) | 2.09102e15 | 0.118039 | ||||||||
\(901\) | −5.89189e15 | −0.330574 | ||||||||
\(902\) | 1.06384e16 | 0.593253 | ||||||||
\(903\) | 2.51179e15 | 0.139220 | ||||||||
\(904\) | 4.17799e14 | 0.0230166 | ||||||||
\(905\) | −3.01059e15 | −0.164848 | ||||||||
\(906\) | −7.00802e15 | −0.381408 | ||||||||
\(907\) | 2.26790e16 | 1.22683 | 0.613413 | − | 0.789762i | \(-0.289796\pi\) | ||||
0.613413 | + | 0.789762i | \(0.289796\pi\) | |||||||
\(908\) | −8.76951e15 | −0.471523 | ||||||||
\(909\) | 1.49846e15 | 0.0800837 | ||||||||
\(910\) | 4.34287e15 | 0.230701 | ||||||||
\(911\) | −9.60184e15 | −0.506994 | −0.253497 | − | 0.967336i | \(-0.581581\pi\) | ||||
−0.253497 | + | 0.967336i | \(0.581581\pi\) | |||||||
\(912\) | −5.85976e15 | −0.307545 | ||||||||
\(913\) | −8.62485e15 | −0.449948 | ||||||||
\(914\) | 2.30104e15 | 0.119322 | ||||||||
\(915\) | −2.79932e15 | −0.144290 | ||||||||
\(916\) | 5.06143e15 | 0.259327 | ||||||||
\(917\) | 1.17756e16 | 0.599724 | ||||||||
\(918\) | −9.73204e14 | −0.0492685 | ||||||||
\(919\) | 2.29750e16 | 1.15617 | 0.578084 | − | 0.815978i | \(-0.303801\pi\) | ||||
0.578084 | + | 0.815978i | \(0.303801\pi\) | |||||||
\(920\) | 6.79177e14 | 0.0339743 | ||||||||
\(921\) | −2.32818e15 | −0.115768 | ||||||||
\(922\) | 4.08315e15 | 0.201825 | ||||||||
\(923\) | −2.76046e16 | −1.35635 | ||||||||
\(924\) | −3.11992e15 | −0.152387 | ||||||||
\(925\) | 2.30514e15 | 0.111923 | ||||||||
\(926\) | 1.31007e16 | 0.632318 | ||||||||
\(927\) | 5.26032e15 | 0.252391 | ||||||||
\(928\) | −3.43749e15 | −0.163956 | ||||||||
\(929\) | −1.95032e16 | −0.924740 | −0.462370 | − | 0.886687i | \(-0.653001\pi\) | ||||
−0.462370 | + | 0.886687i | \(0.653001\pi\) | |||||||
\(930\) | −8.98378e14 | −0.0423451 | ||||||||
\(931\) | −2.59237e16 | −1.21471 | ||||||||
\(932\) | 1.95326e15 | 0.0909856 | ||||||||
\(933\) | 3.81454e15 | 0.176642 | ||||||||
\(934\) | 2.45090e16 | 1.12828 | ||||||||
\(935\) | −9.04079e14 | −0.0413754 | ||||||||
\(936\) | 6.11137e15 | 0.278049 | ||||||||
\(937\) | 1.01829e16 | 0.460580 | 0.230290 | − | 0.973122i | \(-0.426033\pi\) | ||||
0.230290 | + | 0.973122i | \(0.426033\pi\) | |||||||
\(938\) | 3.56268e16 | 1.60199 | ||||||||
\(939\) | −1.51729e16 | −0.678280 | ||||||||
\(940\) | −1.11813e13 | −0.000496922 0 | ||||||||
\(941\) | −1.58357e16 | −0.699672 | −0.349836 | − | 0.936811i | \(-0.613763\pi\) | ||||
−0.349836 | + | 0.936811i | \(0.613763\pi\) | |||||||
\(942\) | −2.28881e14 | −0.0100538 | ||||||||
\(943\) | −4.24458e15 | −0.185362 | ||||||||
\(944\) | −1.42192e15 | −0.0617348 | ||||||||
\(945\) | 1.70267e15 | 0.0734946 | ||||||||
\(946\) | −1.47248e15 | −0.0631899 | ||||||||
\(947\) | −2.42419e16 | −1.03429 | −0.517145 | − | 0.855898i | \(-0.673005\pi\) | ||||
−0.517145 | + | 0.855898i | \(0.673005\pi\) | |||||||
\(948\) | −3.00987e15 | −0.127674 | ||||||||
\(949\) | 2.57785e16 | 1.08716 | ||||||||
\(950\) | −1.96046e16 | −0.822014 | ||||||||
\(951\) | −2.09515e16 | −0.873419 | ||||||||
\(952\) | −1.23043e16 | −0.509979 | ||||||||
\(953\) | −2.71994e16 | −1.12085 | −0.560427 | − | 0.828204i | \(-0.689363\pi\) | ||||
−0.560427 | + | 0.828204i | \(0.689363\pi\) | |||||||
\(954\) | −6.50495e15 | −0.266519 | ||||||||
\(955\) | 6.20123e15 | 0.252615 | ||||||||
\(956\) | −5.11403e15 | −0.207131 | ||||||||
\(957\) | 1.58303e15 | 0.0637491 | ||||||||
\(958\) | −1.72897e15 | −0.0692272 | ||||||||
\(959\) | −1.19799e16 | −0.476925 | ||||||||
\(960\) | 3.99829e15 | 0.158264 | ||||||||
\(961\) | −2.22583e16 | −0.876017 | ||||||||
\(962\) | 1.85799e15 | 0.0727077 | ||||||||
\(963\) | 3.07953e15 | 0.119823 | ||||||||
\(964\) | 4.97435e15 | 0.192448 | ||||||||
\(965\) | −1.23577e15 | −0.0475378 | ||||||||
\(966\) | −2.02413e15 | −0.0774219 | ||||||||
\(967\) | −3.21332e16 | −1.22211 | −0.611053 | − | 0.791590i | \(-0.709254\pi\) | ||||
−0.611053 | + | 0.791590i | \(0.709254\pi\) | |||||||
\(968\) | −2.20997e16 | −0.835740 | ||||||||
\(969\) | −5.61136e15 | −0.211002 | ||||||||
\(970\) | 4.91811e15 | 0.183888 | ||||||||
\(971\) | −4.64451e15 | −0.172677 | −0.0863385 | − | 0.996266i | \(-0.527517\pi\) | ||||
−0.0863385 | + | 0.996266i | \(0.527517\pi\) | |||||||
\(972\) | 6.60779e14 | 0.0244282 | ||||||||
\(973\) | 4.31680e16 | 1.58687 | ||||||||
\(974\) | −3.24682e16 | −1.18682 | ||||||||
\(975\) | 1.13399e16 | 0.412179 | ||||||||
\(976\) | 1.23869e16 | 0.447700 | ||||||||
\(977\) | 5.01867e14 | 0.0180372 | 0.00901858 | − | 0.999959i | \(-0.497129\pi\) | ||||
0.00901858 | + | 0.999959i | \(0.497129\pi\) | |||||||
\(978\) | 1.57182e16 | 0.561743 | ||||||||
\(979\) | −3.59457e15 | −0.127744 | ||||||||
\(980\) | 3.08436e15 | 0.108999 | ||||||||
\(981\) | −1.87884e15 | −0.0660251 | ||||||||
\(982\) | −2.47985e16 | −0.866587 | ||||||||
\(983\) | 5.28237e16 | 1.83563 | 0.917813 | − | 0.397013i | \(-0.129953\pi\) | ||||
0.917813 | + | 0.397013i | \(0.129953\pi\) | |||||||
\(984\) | −2.84867e16 | −0.984393 | ||||||||
\(985\) | −2.11928e14 | −0.00728263 | ||||||||
\(986\) | 1.72174e15 | 0.0588362 | ||||||||
\(987\) | 1.20832e14 | 0.00410617 | ||||||||
\(988\) | 9.71779e15 | 0.328401 | ||||||||
\(989\) | 5.87498e14 | 0.0197436 | ||||||||
\(990\) | −9.98151e14 | −0.0333582 | ||||||||
\(991\) | 4.61147e16 | 1.53262 | 0.766310 | − | 0.642471i | \(-0.222091\pi\) | ||||
0.766310 | + | 0.642471i | \(0.222091\pi\) | |||||||
\(992\) | −7.60027e15 | −0.251197 | ||||||||
\(993\) | 2.43905e16 | 0.801679 | ||||||||
\(994\) | 6.13604e16 | 2.00569 | ||||||||
\(995\) | 1.35658e16 | 0.440978 | ||||||||
\(996\) | 6.36915e15 | 0.205899 | ||||||||
\(997\) | 3.25603e16 | 1.04680 | 0.523402 | − | 0.852086i | \(-0.324663\pi\) | ||||
0.523402 | + | 0.852086i | \(0.324663\pi\) | |||||||
\(998\) | 3.27139e16 | 1.04596 | ||||||||
\(999\) | 7.28445e14 | 0.0231625 |
(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 | 177.12.a.a.1.10 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.a.1.10 | ✓ | 26 | 1.1 | even | 1 | trivial |