Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −98.0136 | −1.08291 | −0.541454 | − | 0.840731i | \(-0.682126\pi\) | ||||
−0.541454 | + | 0.840731i | \(0.682126\pi\) | |||||||
\(3\) | −729.000 | −0.577350 | ||||||||
\(4\) | 1414.67 | 0.172689 | ||||||||
\(5\) | 43954.8 | 1.25806 | 0.629030 | − | 0.777381i | \(-0.283452\pi\) | ||||
0.629030 | + | 0.777381i | \(0.283452\pi\) | |||||||
\(6\) | 71451.9 | 0.625217 | ||||||||
\(7\) | −396678. | −1.27439 | −0.637193 | − | 0.770704i | \(-0.719905\pi\) | ||||
−0.637193 | + | 0.770704i | \(0.719905\pi\) | |||||||
\(8\) | 664271. | 0.895902 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −4.30817e6 | −1.36236 | ||||||||
\(11\) | −1.79804e6 | −0.306018 | −0.153009 | − | 0.988225i | \(-0.548896\pi\) | ||||
−0.153009 | + | 0.988225i | \(0.548896\pi\) | |||||||
\(12\) | −1.03129e6 | −0.0997019 | ||||||||
\(13\) | 6.51184e6 | 0.374172 | 0.187086 | − | 0.982343i | \(-0.440096\pi\) | ||||
0.187086 | + | 0.982343i | \(0.440096\pi\) | |||||||
\(14\) | 3.88799e7 | 1.38004 | ||||||||
\(15\) | −3.20431e7 | −0.726342 | ||||||||
\(16\) | −7.66965e7 | −1.14287 | ||||||||
\(17\) | 9.76681e7 | 0.981375 | 0.490687 | − | 0.871336i | \(-0.336746\pi\) | ||||
0.490687 | + | 0.871336i | \(0.336746\pi\) | |||||||
\(18\) | −5.20884e7 | −0.360969 | ||||||||
\(19\) | −6.83663e7 | −0.333383 | −0.166692 | − | 0.986009i | \(-0.553308\pi\) | ||||
−0.166692 | + | 0.986009i | \(0.553308\pi\) | |||||||
\(20\) | 6.21814e7 | 0.217253 | ||||||||
\(21\) | 2.89178e8 | 0.735767 | ||||||||
\(22\) | 1.76232e8 | 0.331389 | ||||||||
\(23\) | 1.72252e8 | 0.242624 | 0.121312 | − | 0.992614i | \(-0.461290\pi\) | ||||
0.121312 | + | 0.992614i | \(0.461290\pi\) | |||||||
\(24\) | −4.84253e8 | −0.517249 | ||||||||
\(25\) | 7.11324e8 | 0.582716 | ||||||||
\(26\) | −6.38249e8 | −0.405194 | ||||||||
\(27\) | −3.87420e8 | −0.192450 | ||||||||
\(28\) | −5.61168e8 | −0.220072 | ||||||||
\(29\) | −5.74570e8 | −0.179373 | −0.0896863 | − | 0.995970i | \(-0.528586\pi\) | ||||
−0.0896863 | + | 0.995970i | \(0.528586\pi\) | |||||||
\(30\) | 3.14066e9 | 0.786561 | ||||||||
\(31\) | 3.46020e8 | 0.0700246 | 0.0350123 | − | 0.999387i | \(-0.488853\pi\) | ||||
0.0350123 | + | 0.999387i | \(0.488853\pi\) | |||||||
\(32\) | 2.07560e9 | 0.341718 | ||||||||
\(33\) | 1.31077e9 | 0.176680 | ||||||||
\(34\) | −9.57281e9 | −1.06274 | ||||||||
\(35\) | −1.74359e10 | −1.60326 | ||||||||
\(36\) | 7.51812e8 | 0.0575629 | ||||||||
\(37\) | 2.87382e10 | 1.84140 | 0.920701 | − | 0.390268i | \(-0.127618\pi\) | ||||
0.920701 | + | 0.390268i | \(0.127618\pi\) | |||||||
\(38\) | 6.70083e9 | 0.361023 | ||||||||
\(39\) | −4.74713e9 | −0.216029 | ||||||||
\(40\) | 2.91979e10 | 1.12710 | ||||||||
\(41\) | −3.40879e10 | −1.12074 | −0.560370 | − | 0.828243i | \(-0.689341\pi\) | ||||
−0.560370 | + | 0.828243i | \(0.689341\pi\) | |||||||
\(42\) | −2.83434e10 | −0.796768 | ||||||||
\(43\) | −5.78702e10 | −1.39608 | −0.698040 | − | 0.716059i | \(-0.745944\pi\) | ||||
−0.698040 | + | 0.716059i | \(0.745944\pi\) | |||||||
\(44\) | −2.54363e9 | −0.0528459 | ||||||||
\(45\) | 2.33594e10 | 0.419354 | ||||||||
\(46\) | −1.68830e10 | −0.262739 | ||||||||
\(47\) | −1.12577e11 | −1.52339 | −0.761697 | − | 0.647933i | \(-0.775634\pi\) | ||||
−0.761697 | + | 0.647933i | \(0.775634\pi\) | |||||||
\(48\) | 5.59118e10 | 0.659835 | ||||||||
\(49\) | 6.04647e10 | 0.624061 | ||||||||
\(50\) | −6.97194e10 | −0.631028 | ||||||||
\(51\) | −7.12001e10 | −0.566597 | ||||||||
\(52\) | 9.21208e9 | 0.0646154 | ||||||||
\(53\) | −1.23263e11 | −0.763906 | −0.381953 | − | 0.924182i | \(-0.624748\pi\) | ||||
−0.381953 | + | 0.924182i | \(0.624748\pi\) | |||||||
\(54\) | 3.79725e10 | 0.208406 | ||||||||
\(55\) | −7.90325e10 | −0.384989 | ||||||||
\(56\) | −2.63502e11 | −1.14172 | ||||||||
\(57\) | 4.98390e10 | 0.192479 | ||||||||
\(58\) | 5.63157e10 | 0.194244 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −4.53303e10 | −0.125431 | ||||||||
\(61\) | 5.05675e11 | 1.25669 | 0.628344 | − | 0.777936i | \(-0.283733\pi\) | ||||
0.628344 | + | 0.777936i | \(0.283733\pi\) | |||||||
\(62\) | −3.39147e10 | −0.0758302 | ||||||||
\(63\) | −2.10811e11 | −0.424796 | ||||||||
\(64\) | 4.24861e11 | 0.772818 | ||||||||
\(65\) | 2.86227e11 | 0.470732 | ||||||||
\(66\) | −1.28473e11 | −0.191328 | ||||||||
\(67\) | 1.07434e9 | 0.00145096 | 0.000725482 | − | 1.00000i | \(-0.499769\pi\) | ||||
0.000725482 | 1.00000i | \(0.499769\pi\) | ||||||||
\(68\) | 1.38168e11 | 0.169472 | ||||||||
\(69\) | −1.25572e11 | −0.140079 | ||||||||
\(70\) | 1.70896e12 | 1.73618 | ||||||||
\(71\) | 8.42822e11 | 0.780830 | 0.390415 | − | 0.920639i | \(-0.372332\pi\) | ||||
0.390415 | + | 0.920639i | \(0.372332\pi\) | |||||||
\(72\) | 3.53021e11 | 0.298634 | ||||||||
\(73\) | −6.23496e11 | −0.482208 | −0.241104 | − | 0.970499i | \(-0.577510\pi\) | ||||
−0.241104 | + | 0.970499i | \(0.577510\pi\) | |||||||
\(74\) | −2.81674e12 | −1.99407 | ||||||||
\(75\) | −5.18555e11 | −0.336431 | ||||||||
\(76\) | −9.67155e10 | −0.0575715 | ||||||||
\(77\) | 7.13243e11 | 0.389985 | ||||||||
\(78\) | 4.65283e11 | 0.233939 | ||||||||
\(79\) | −2.92796e12 | −1.35515 | −0.677577 | − | 0.735452i | \(-0.736970\pi\) | ||||
−0.677577 | + | 0.735452i | \(0.736970\pi\) | |||||||
\(80\) | −3.37118e12 | −1.43780 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 3.34107e12 | 1.21366 | ||||||||
\(83\) | 1.48483e12 | 0.498503 | 0.249252 | − | 0.968439i | \(-0.419815\pi\) | ||||
0.249252 | + | 0.968439i | \(0.419815\pi\) | |||||||
\(84\) | 4.09091e11 | 0.127059 | ||||||||
\(85\) | 4.29299e12 | 1.23463 | ||||||||
\(86\) | 5.67207e12 | 1.51183 | ||||||||
\(87\) | 4.18862e11 | 0.103561 | ||||||||
\(88\) | −1.19439e12 | −0.274162 | ||||||||
\(89\) | 8.15790e12 | 1.73998 | 0.869988 | − | 0.493073i | \(-0.164126\pi\) | ||||
0.869988 | + | 0.493073i | \(0.164126\pi\) | |||||||
\(90\) | −2.28954e12 | −0.454121 | ||||||||
\(91\) | −2.58311e12 | −0.476840 | ||||||||
\(92\) | 2.43679e11 | 0.0418984 | ||||||||
\(93\) | −2.52249e11 | −0.0404287 | ||||||||
\(94\) | 1.10341e13 | 1.64970 | ||||||||
\(95\) | −3.00503e12 | −0.419416 | ||||||||
\(96\) | −1.51311e12 | −0.197291 | ||||||||
\(97\) | 1.16685e13 | 1.42233 | 0.711165 | − | 0.703026i | \(-0.248168\pi\) | ||||
0.711165 | + | 0.703026i | \(0.248168\pi\) | |||||||
\(98\) | −5.92636e12 | −0.675801 | ||||||||
\(99\) | −9.55552e11 | −0.102006 | ||||||||
\(100\) | 1.00629e12 | 0.100629 | ||||||||
\(101\) | 5.07705e12 | 0.475908 | 0.237954 | − | 0.971276i | \(-0.423523\pi\) | ||||
0.237954 | + | 0.971276i | \(0.423523\pi\) | |||||||
\(102\) | 6.97858e12 | 0.613572 | ||||||||
\(103\) | 2.23272e13 | 1.84243 | 0.921217 | − | 0.389050i | \(-0.127197\pi\) | ||||
0.921217 | + | 0.389050i | \(0.127197\pi\) | |||||||
\(104\) | 4.32562e12 | 0.335222 | ||||||||
\(105\) | 1.27108e13 | 0.925640 | ||||||||
\(106\) | 1.20815e13 | 0.827239 | ||||||||
\(107\) | −8.65420e12 | −0.557484 | −0.278742 | − | 0.960366i | \(-0.589917\pi\) | ||||
−0.278742 | + | 0.960366i | \(0.589917\pi\) | |||||||
\(108\) | −5.48071e11 | −0.0332340 | ||||||||
\(109\) | 2.16117e13 | 1.23429 | 0.617145 | − | 0.786850i | \(-0.288289\pi\) | ||||
0.617145 | + | 0.786850i | \(0.288289\pi\) | |||||||
\(110\) | 7.74626e12 | 0.416908 | ||||||||
\(111\) | −2.09502e13 | −1.06313 | ||||||||
\(112\) | 3.04239e13 | 1.45645 | ||||||||
\(113\) | −1.90976e12 | −0.0862915 | −0.0431457 | − | 0.999069i | \(-0.513738\pi\) | ||||
−0.0431457 | + | 0.999069i | \(0.513738\pi\) | |||||||
\(114\) | −4.88490e12 | −0.208437 | ||||||||
\(115\) | 7.57131e12 | 0.305235 | ||||||||
\(116\) | −8.12825e11 | −0.0309756 | ||||||||
\(117\) | 3.46066e12 | 0.124724 | ||||||||
\(118\) | 4.13427e12 | 0.140983 | ||||||||
\(119\) | −3.87428e13 | −1.25065 | ||||||||
\(120\) | −2.12853e13 | −0.650731 | ||||||||
\(121\) | −3.12898e13 | −0.906353 | ||||||||
\(122\) | −4.95630e13 | −1.36088 | ||||||||
\(123\) | 2.48501e13 | 0.647059 | ||||||||
\(124\) | 4.89504e11 | 0.0120925 | ||||||||
\(125\) | −2.23897e13 | −0.524968 | ||||||||
\(126\) | 2.06624e13 | 0.460014 | ||||||||
\(127\) | −4.53065e13 | −0.958157 | −0.479079 | − | 0.877772i | \(-0.659029\pi\) | ||||
−0.479079 | + | 0.877772i | \(0.659029\pi\) | |||||||
\(128\) | −5.86455e13 | −1.17861 | ||||||||
\(129\) | 4.21874e13 | 0.806027 | ||||||||
\(130\) | −2.80541e13 | −0.509759 | ||||||||
\(131\) | −1.12857e13 | −0.195103 | −0.0975515 | − | 0.995230i | \(-0.531101\pi\) | ||||
−0.0975515 | + | 0.995230i | \(0.531101\pi\) | |||||||
\(132\) | 1.85430e12 | 0.0305106 | ||||||||
\(133\) | 2.71194e13 | 0.424859 | ||||||||
\(134\) | −1.05300e11 | −0.00157126 | ||||||||
\(135\) | −1.70290e13 | −0.242114 | ||||||||
\(136\) | 6.48781e13 | 0.879215 | ||||||||
\(137\) | 7.67214e13 | 0.991363 | 0.495681 | − | 0.868504i | \(-0.334918\pi\) | ||||
0.495681 | + | 0.868504i | \(0.334918\pi\) | |||||||
\(138\) | 1.23077e13 | 0.151693 | ||||||||
\(139\) | −4.18439e13 | −0.492080 | −0.246040 | − | 0.969260i | \(-0.579129\pi\) | ||||
−0.246040 | + | 0.969260i | \(0.579129\pi\) | |||||||
\(140\) | −2.46660e13 | −0.276864 | ||||||||
\(141\) | 8.20684e13 | 0.879533 | ||||||||
\(142\) | −8.26080e13 | −0.845567 | ||||||||
\(143\) | −1.17085e13 | −0.114503 | ||||||||
\(144\) | −4.07597e13 | −0.380956 | ||||||||
\(145\) | −2.52551e13 | −0.225662 | ||||||||
\(146\) | 6.11111e13 | 0.522187 | ||||||||
\(147\) | −4.40788e13 | −0.360302 | ||||||||
\(148\) | 4.06550e13 | 0.317990 | ||||||||
\(149\) | −8.40108e13 | −0.628962 | −0.314481 | − | 0.949264i | \(-0.601830\pi\) | ||||
−0.314481 | + | 0.949264i | \(0.601830\pi\) | |||||||
\(150\) | 5.08254e13 | 0.364324 | ||||||||
\(151\) | 2.33896e14 | 1.60573 | 0.802865 | − | 0.596161i | \(-0.203308\pi\) | ||||
0.802865 | + | 0.596161i | \(0.203308\pi\) | |||||||
\(152\) | −4.54138e13 | −0.298679 | ||||||||
\(153\) | 5.19049e13 | 0.327125 | ||||||||
\(154\) | −6.99076e13 | −0.422318 | ||||||||
\(155\) | 1.52093e13 | 0.0880952 | ||||||||
\(156\) | −6.71561e12 | −0.0373057 | ||||||||
\(157\) | 1.54696e14 | 0.824385 | 0.412192 | − | 0.911097i | \(-0.364763\pi\) | ||||
0.412192 | + | 0.911097i | \(0.364763\pi\) | |||||||
\(158\) | 2.86980e14 | 1.46751 | ||||||||
\(159\) | 8.98588e13 | 0.441041 | ||||||||
\(160\) | 9.12325e13 | 0.429902 | ||||||||
\(161\) | −6.83286e13 | −0.309197 | ||||||||
\(162\) | −2.76819e13 | −0.120323 | ||||||||
\(163\) | 2.14513e14 | 0.895846 | 0.447923 | − | 0.894072i | \(-0.352164\pi\) | ||||
0.447923 | + | 0.894072i | \(0.352164\pi\) | |||||||
\(164\) | −4.82230e13 | −0.193539 | ||||||||
\(165\) | 5.76147e13 | 0.222274 | ||||||||
\(166\) | −1.45533e14 | −0.539833 | ||||||||
\(167\) | 4.60772e14 | 1.64372 | 0.821862 | − | 0.569687i | \(-0.192936\pi\) | ||||
0.821862 | + | 0.569687i | \(0.192936\pi\) | |||||||
\(168\) | 1.92093e14 | 0.659175 | ||||||||
\(169\) | −2.60471e14 | −0.859995 | ||||||||
\(170\) | −4.20771e14 | −1.33699 | ||||||||
\(171\) | −3.63327e13 | −0.111128 | ||||||||
\(172\) | −8.18671e13 | −0.241087 | ||||||||
\(173\) | −1.40439e14 | −0.398280 | −0.199140 | − | 0.979971i | \(-0.563815\pi\) | ||||
−0.199140 | + | 0.979971i | \(0.563815\pi\) | |||||||
\(174\) | −4.10541e13 | −0.112147 | ||||||||
\(175\) | −2.82167e14 | −0.742606 | ||||||||
\(176\) | 1.37903e14 | 0.349738 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −7.99585e14 | −1.88423 | ||||||||
\(179\) | −3.25729e14 | −0.740136 | −0.370068 | − | 0.929005i | \(-0.620666\pi\) | ||||
−0.370068 | + | 0.929005i | \(0.620666\pi\) | |||||||
\(180\) | 3.30458e13 | 0.0724176 | ||||||||
\(181\) | −6.48931e13 | −0.137179 | −0.0685896 | − | 0.997645i | \(-0.521850\pi\) | ||||
−0.0685896 | + | 0.997645i | \(0.521850\pi\) | |||||||
\(182\) | 2.53179e14 | 0.516374 | ||||||||
\(183\) | −3.68637e14 | −0.725549 | ||||||||
\(184\) | 1.14422e14 | 0.217367 | ||||||||
\(185\) | 1.26318e15 | 2.31660 | ||||||||
\(186\) | 2.47238e13 | 0.0437806 | ||||||||
\(187\) | −1.75611e14 | −0.300318 | ||||||||
\(188\) | −1.59259e14 | −0.263073 | ||||||||
\(189\) | 1.53681e14 | 0.245256 | ||||||||
\(190\) | 2.94534e14 | 0.454189 | ||||||||
\(191\) | −1.25464e15 | −1.86984 | −0.934918 | − | 0.354865i | \(-0.884527\pi\) | ||||
−0.934918 | + | 0.354865i | \(0.884527\pi\) | |||||||
\(192\) | −3.09724e14 | −0.446187 | ||||||||
\(193\) | −1.13796e13 | −0.0158490 | −0.00792452 | − | 0.999969i | \(-0.502522\pi\) | ||||
−0.00792452 | + | 0.999969i | \(0.502522\pi\) | |||||||
\(194\) | −1.14368e15 | −1.54025 | ||||||||
\(195\) | −2.08659e14 | −0.271777 | ||||||||
\(196\) | 8.55374e13 | 0.107768 | ||||||||
\(197\) | 3.13415e14 | 0.382022 | 0.191011 | − | 0.981588i | \(-0.438823\pi\) | ||||
0.191011 | + | 0.981588i | \(0.438823\pi\) | |||||||
\(198\) | 9.36571e13 | 0.110463 | ||||||||
\(199\) | 6.90722e14 | 0.788421 | 0.394211 | − | 0.919020i | \(-0.371018\pi\) | ||||
0.394211 | + | 0.919020i | \(0.371018\pi\) | |||||||
\(200\) | 4.72512e14 | 0.522056 | ||||||||
\(201\) | −7.83196e11 | −0.000837714 0 | ||||||||
\(202\) | −4.97620e14 | −0.515364 | ||||||||
\(203\) | 2.27919e14 | 0.228590 | ||||||||
\(204\) | −1.00724e14 | −0.0978449 | ||||||||
\(205\) | −1.49833e15 | −1.40996 | ||||||||
\(206\) | −2.18837e15 | −1.99518 | ||||||||
\(207\) | 9.15418e13 | 0.0808746 | ||||||||
\(208\) | −4.99435e14 | −0.427630 | ||||||||
\(209\) | 1.22925e14 | 0.102021 | ||||||||
\(210\) | −1.24583e15 | −1.00238 | ||||||||
\(211\) | −1.09845e15 | −0.856925 | −0.428463 | − | 0.903560i | \(-0.640945\pi\) | ||||
−0.428463 | + | 0.903560i | \(0.640945\pi\) | |||||||
\(212\) | −1.74376e14 | −0.131918 | ||||||||
\(213\) | −6.14417e14 | −0.450812 | ||||||||
\(214\) | 8.48230e14 | 0.603704 | ||||||||
\(215\) | −2.54368e15 | −1.75635 | ||||||||
\(216\) | −2.57352e14 | −0.172416 | ||||||||
\(217\) | −1.37259e14 | −0.0892384 | ||||||||
\(218\) | −2.11824e15 | −1.33662 | ||||||||
\(219\) | 4.54528e14 | 0.278403 | ||||||||
\(220\) | −1.11805e14 | −0.0664833 | ||||||||
\(221\) | 6.35999e14 | 0.367203 | ||||||||
\(222\) | 2.05340e15 | 1.15128 | ||||||||
\(223\) | −2.02103e14 | −0.110050 | −0.0550252 | − | 0.998485i | \(-0.517524\pi\) | ||||
−0.0550252 | + | 0.998485i | \(0.517524\pi\) | |||||||
\(224\) | −8.23344e14 | −0.435481 | ||||||||
\(225\) | 3.78026e14 | 0.194239 | ||||||||
\(226\) | 1.87182e14 | 0.0934457 | ||||||||
\(227\) | 3.68958e15 | 1.78982 | 0.894908 | − | 0.446250i | \(-0.147241\pi\) | ||||
0.894908 | + | 0.446250i | \(0.147241\pi\) | |||||||
\(228\) | 7.05056e13 | 0.0332389 | ||||||||
\(229\) | −1.70193e15 | −0.779848 | −0.389924 | − | 0.920847i | \(-0.627499\pi\) | ||||
−0.389924 | + | 0.920847i | \(0.627499\pi\) | |||||||
\(230\) | −7.42091e14 | −0.330542 | ||||||||
\(231\) | −5.19954e14 | −0.225158 | ||||||||
\(232\) | −3.81670e14 | −0.160700 | ||||||||
\(233\) | 1.44631e13 | 0.00592172 | 0.00296086 | − | 0.999996i | \(-0.499058\pi\) | ||||
0.00296086 | + | 0.999996i | \(0.499058\pi\) | |||||||
\(234\) | −3.39192e14 | −0.135065 | ||||||||
\(235\) | −4.94829e15 | −1.91652 | ||||||||
\(236\) | −5.96714e13 | −0.0224822 | ||||||||
\(237\) | 2.13448e15 | 0.782398 | ||||||||
\(238\) | 3.79732e15 | 1.35434 | ||||||||
\(239\) | −1.24049e15 | −0.430534 | −0.215267 | − | 0.976555i | \(-0.569062\pi\) | ||||
−0.215267 | + | 0.976555i | \(0.569062\pi\) | |||||||
\(240\) | 2.45759e15 | 0.830112 | ||||||||
\(241\) | −5.51883e15 | −1.81441 | −0.907207 | − | 0.420685i | \(-0.861790\pi\) | ||||
−0.907207 | + | 0.420685i | \(0.861790\pi\) | |||||||
\(242\) | 3.06682e15 | 0.981497 | ||||||||
\(243\) | −2.05891e14 | −0.0641500 | ||||||||
\(244\) | 7.15361e14 | 0.217016 | ||||||||
\(245\) | 2.65771e15 | 0.785107 | ||||||||
\(246\) | −2.43564e15 | −0.700705 | ||||||||
\(247\) | −4.45190e14 | −0.124743 | ||||||||
\(248\) | 2.29851e14 | 0.0627352 | ||||||||
\(249\) | −1.08244e15 | −0.287811 | ||||||||
\(250\) | 2.19449e15 | 0.568492 | ||||||||
\(251\) | −4.36406e15 | −1.10157 | −0.550784 | − | 0.834648i | \(-0.685671\pi\) | ||||
−0.550784 | + | 0.834648i | \(0.685671\pi\) | |||||||
\(252\) | −2.98227e14 | −0.0733574 | ||||||||
\(253\) | −3.09716e14 | −0.0742472 | ||||||||
\(254\) | 4.44066e15 | 1.03760 | ||||||||
\(255\) | −3.12959e15 | −0.712813 | ||||||||
\(256\) | 2.26759e15 | 0.503506 | ||||||||
\(257\) | −3.31441e15 | −0.717531 | −0.358766 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358766 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(258\) | −4.13494e15 | −0.872853 | ||||||||
\(259\) | −1.13998e16 | −2.34666 | ||||||||
\(260\) | 4.04915e14 | 0.0812901 | ||||||||
\(261\) | −3.05350e14 | −0.0597909 | ||||||||
\(262\) | 1.10615e15 | 0.211279 | ||||||||
\(263\) | −9.91017e15 | −1.84658 | −0.923291 | − | 0.384101i | \(-0.874511\pi\) | ||||
−0.923291 | + | 0.384101i | \(0.874511\pi\) | |||||||
\(264\) | 8.70707e14 | 0.158287 | ||||||||
\(265\) | −5.41801e15 | −0.961040 | ||||||||
\(266\) | −2.65807e15 | −0.460083 | ||||||||
\(267\) | −5.94711e15 | −1.00458 | ||||||||
\(268\) | 1.51984e12 | 0.000250565 0 | ||||||||
\(269\) | 1.08935e15 | 0.175299 | 0.0876495 | − | 0.996151i | \(-0.472064\pi\) | ||||
0.0876495 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(270\) | 1.66907e15 | 0.262187 | ||||||||
\(271\) | −1.62457e13 | −0.00249137 | −0.00124568 | − | 0.999999i | \(-0.500397\pi\) | ||||
−0.00124568 | + | 0.999999i | \(0.500397\pi\) | |||||||
\(272\) | −7.49081e15 | −1.12158 | ||||||||
\(273\) | 1.88308e15 | 0.275304 | ||||||||
\(274\) | −7.51974e15 | −1.07355 | ||||||||
\(275\) | −1.27899e15 | −0.178322 | ||||||||
\(276\) | −1.77642e14 | −0.0241901 | ||||||||
\(277\) | −5.67135e15 | −0.754341 | −0.377171 | − | 0.926144i | \(-0.623103\pi\) | ||||
−0.377171 | + | 0.926144i | \(0.623103\pi\) | |||||||
\(278\) | 4.10127e15 | 0.532877 | ||||||||
\(279\) | 1.83889e14 | 0.0233415 | ||||||||
\(280\) | −1.15822e16 | −1.43636 | ||||||||
\(281\) | 1.53869e15 | 0.186449 | 0.0932243 | − | 0.995645i | \(-0.470283\pi\) | ||||
0.0932243 | + | 0.995645i | \(0.470283\pi\) | |||||||
\(282\) | −8.04382e15 | −0.952452 | ||||||||
\(283\) | −6.94777e15 | −0.803958 | −0.401979 | − | 0.915649i | \(-0.631677\pi\) | ||||
−0.401979 | + | 0.915649i | \(0.631677\pi\) | |||||||
\(284\) | 1.19231e15 | 0.134841 | ||||||||
\(285\) | 2.19067e15 | 0.242150 | ||||||||
\(286\) | 1.14760e15 | 0.123997 | ||||||||
\(287\) | 1.35219e16 | 1.42826 | ||||||||
\(288\) | 1.10306e15 | 0.113906 | ||||||||
\(289\) | −3.65514e14 | −0.0369035 | ||||||||
\(290\) | 2.47535e15 | 0.244371 | ||||||||
\(291\) | −8.50636e15 | −0.821182 | ||||||||
\(292\) | −8.82038e14 | −0.0832720 | ||||||||
\(293\) | −3.05245e15 | −0.281844 | −0.140922 | − | 0.990021i | \(-0.545007\pi\) | ||||
−0.140922 | + | 0.990021i | \(0.545007\pi\) | |||||||
\(294\) | 4.32032e15 | 0.390174 | ||||||||
\(295\) | −1.85404e15 | −0.163786 | ||||||||
\(296\) | 1.90900e16 | 1.64972 | ||||||||
\(297\) | 6.96597e14 | 0.0588932 | ||||||||
\(298\) | 8.23420e15 | 0.681108 | ||||||||
\(299\) | 1.12168e15 | 0.0907832 | ||||||||
\(300\) | −7.33582e14 | −0.0580979 | ||||||||
\(301\) | 2.29559e16 | 1.77915 | ||||||||
\(302\) | −2.29250e16 | −1.73886 | ||||||||
\(303\) | −3.70117e15 | −0.274766 | ||||||||
\(304\) | 5.24346e15 | 0.381013 | ||||||||
\(305\) | 2.22268e16 | 1.58099 | ||||||||
\(306\) | −5.08738e15 | −0.354246 | ||||||||
\(307\) | 5.47480e15 | 0.373223 | 0.186612 | − | 0.982434i | \(-0.440249\pi\) | ||||
0.186612 | + | 0.982434i | \(0.440249\pi\) | |||||||
\(308\) | 1.00900e15 | 0.0673461 | ||||||||
\(309\) | −1.62765e16 | −1.06373 | ||||||||
\(310\) | −1.49072e15 | −0.0953990 | ||||||||
\(311\) | 1.11347e16 | 0.697806 | 0.348903 | − | 0.937159i | \(-0.386554\pi\) | ||||
0.348903 | + | 0.937159i | \(0.386554\pi\) | |||||||
\(312\) | −3.15338e15 | −0.193540 | ||||||||
\(313\) | −6.11381e15 | −0.367514 | −0.183757 | − | 0.982972i | \(-0.558826\pi\) | ||||
−0.183757 | + | 0.982972i | \(0.558826\pi\) | |||||||
\(314\) | −1.51623e16 | −0.892733 | ||||||||
\(315\) | −9.26617e15 | −0.534419 | ||||||||
\(316\) | −4.14208e15 | −0.234020 | ||||||||
\(317\) | 2.22496e15 | 0.123151 | 0.0615753 | − | 0.998102i | \(-0.480388\pi\) | ||||
0.0615753 | + | 0.998102i | \(0.480388\pi\) | |||||||
\(318\) | −8.80738e15 | −0.477607 | ||||||||
\(319\) | 1.03310e15 | 0.0548912 | ||||||||
\(320\) | 1.86747e16 | 0.972252 | ||||||||
\(321\) | 6.30892e15 | 0.321864 | ||||||||
\(322\) | 6.69714e15 | 0.334831 | ||||||||
\(323\) | −6.67721e15 | −0.327174 | ||||||||
\(324\) | 3.99544e14 | 0.0191876 | ||||||||
\(325\) | 4.63202e15 | 0.218036 | ||||||||
\(326\) | −2.10251e16 | −0.970118 | ||||||||
\(327\) | −1.57549e16 | −0.712617 | ||||||||
\(328\) | −2.26436e16 | −1.00407 | ||||||||
\(329\) | 4.46567e16 | 1.94139 | ||||||||
\(330\) | −5.64703e15 | −0.240702 | ||||||||
\(331\) | 1.77998e16 | 0.743934 | 0.371967 | − | 0.928246i | \(-0.378684\pi\) | ||||
0.371967 | + | 0.928246i | \(0.378684\pi\) | |||||||
\(332\) | 2.10053e15 | 0.0860859 | ||||||||
\(333\) | 1.52727e16 | 0.613801 | ||||||||
\(334\) | −4.51619e16 | −1.78000 | ||||||||
\(335\) | 4.72225e13 | 0.00182540 | ||||||||
\(336\) | −2.21790e16 | −0.840885 | ||||||||
\(337\) | −8.05639e14 | −0.0299603 | −0.0149801 | − | 0.999888i | \(-0.504769\pi\) | ||||
−0.0149801 | + | 0.999888i | \(0.504769\pi\) | |||||||
\(338\) | 2.55297e16 | 0.931295 | ||||||||
\(339\) | 1.39221e15 | 0.0498204 | ||||||||
\(340\) | 6.07314e15 | 0.213207 | ||||||||
\(341\) | −6.22158e14 | −0.0214288 | ||||||||
\(342\) | 3.56110e15 | 0.120341 | ||||||||
\(343\) | 1.44487e16 | 0.479091 | ||||||||
\(344\) | −3.84415e16 | −1.25075 | ||||||||
\(345\) | −5.51948e15 | −0.176228 | ||||||||
\(346\) | 1.37649e16 | 0.431300 | ||||||||
\(347\) | −2.01330e16 | −0.619108 | −0.309554 | − | 0.950882i | \(-0.600180\pi\) | ||||
−0.309554 | + | 0.950882i | \(0.600180\pi\) | |||||||
\(348\) | 5.92549e14 | 0.0178838 | ||||||||
\(349\) | −3.93224e15 | −0.116486 | −0.0582431 | − | 0.998302i | \(-0.518550\pi\) | ||||
−0.0582431 | + | 0.998302i | \(0.518550\pi\) | |||||||
\(350\) | 2.76562e16 | 0.804173 | ||||||||
\(351\) | −2.52282e15 | −0.0720095 | ||||||||
\(352\) | −3.73200e15 | −0.104572 | ||||||||
\(353\) | 2.27174e16 | 0.624918 | 0.312459 | − | 0.949931i | \(-0.398847\pi\) | ||||
0.312459 | + | 0.949931i | \(0.398847\pi\) | |||||||
\(354\) | −3.01388e15 | −0.0813963 | ||||||||
\(355\) | 3.70461e16 | 0.982331 | ||||||||
\(356\) | 1.15407e16 | 0.300474 | ||||||||
\(357\) | 2.82435e16 | 0.722064 | ||||||||
\(358\) | 3.19259e16 | 0.801499 | ||||||||
\(359\) | 3.34599e16 | 0.824917 | 0.412458 | − | 0.910976i | \(-0.364670\pi\) | ||||
0.412458 | + | 0.910976i | \(0.364670\pi\) | |||||||
\(360\) | 1.55170e16 | 0.375699 | ||||||||
\(361\) | −3.73790e16 | −0.888856 | ||||||||
\(362\) | 6.36041e15 | 0.148552 | ||||||||
\(363\) | 2.28102e16 | 0.523283 | ||||||||
\(364\) | −3.65423e15 | −0.0823450 | ||||||||
\(365\) | −2.74056e16 | −0.606647 | ||||||||
\(366\) | 3.61314e16 | 0.785702 | ||||||||
\(367\) | −2.96174e16 | −0.632729 | −0.316364 | − | 0.948638i | \(-0.602462\pi\) | ||||
−0.316364 | + | 0.948638i | \(0.602462\pi\) | |||||||
\(368\) | −1.32111e16 | −0.277287 | ||||||||
\(369\) | −1.81157e16 | −0.373580 | ||||||||
\(370\) | −1.23809e17 | −2.50866 | ||||||||
\(371\) | 4.88958e16 | 0.973511 | ||||||||
\(372\) | −3.56848e14 | −0.00698159 | ||||||||
\(373\) | −3.03136e15 | −0.0582814 | −0.0291407 | − | 0.999575i | \(-0.509277\pi\) | ||||
−0.0291407 | + | 0.999575i | \(0.509277\pi\) | |||||||
\(374\) | 1.72123e16 | 0.325217 | ||||||||
\(375\) | 1.63221e16 | 0.303091 | ||||||||
\(376\) | −7.47814e16 | −1.36481 | ||||||||
\(377\) | −3.74151e15 | −0.0671163 | ||||||||
\(378\) | −1.50629e16 | −0.265589 | ||||||||
\(379\) | 1.68088e16 | 0.291329 | 0.145664 | − | 0.989334i | \(-0.453468\pi\) | ||||
0.145664 | + | 0.989334i | \(0.453468\pi\) | |||||||
\(380\) | −4.25111e15 | −0.0724285 | ||||||||
\(381\) | 3.30285e16 | 0.553192 | ||||||||
\(382\) | 1.22972e17 | 2.02486 | ||||||||
\(383\) | 7.39427e16 | 1.19702 | 0.598512 | − | 0.801114i | \(-0.295759\pi\) | ||||
0.598512 | + | 0.801114i | \(0.295759\pi\) | |||||||
\(384\) | 4.27525e16 | 0.680470 | ||||||||
\(385\) | 3.13505e16 | 0.490625 | ||||||||
\(386\) | 1.11535e15 | 0.0171630 | ||||||||
\(387\) | −3.07546e16 | −0.465360 | ||||||||
\(388\) | 1.65071e16 | 0.245620 | ||||||||
\(389\) | 2.70944e16 | 0.396467 | 0.198234 | − | 0.980155i | \(-0.436480\pi\) | ||||
0.198234 | + | 0.980155i | \(0.436480\pi\) | |||||||
\(390\) | 2.04514e16 | 0.294309 | ||||||||
\(391\) | 1.68235e16 | 0.238105 | ||||||||
\(392\) | 4.01649e16 | 0.559098 | ||||||||
\(393\) | 8.22726e15 | 0.112643 | ||||||||
\(394\) | −3.07189e16 | −0.413695 | ||||||||
\(395\) | −1.28698e17 | −1.70487 | ||||||||
\(396\) | −1.35179e15 | −0.0176153 | ||||||||
\(397\) | −1.12309e16 | −0.143971 | −0.0719854 | − | 0.997406i | \(-0.522934\pi\) | ||||
−0.0719854 | + | 0.997406i | \(0.522934\pi\) | |||||||
\(398\) | −6.77002e16 | −0.853787 | ||||||||
\(399\) | −1.97701e16 | −0.245293 | ||||||||
\(400\) | −5.45560e16 | −0.665967 | ||||||||
\(401\) | 2.22390e16 | 0.267101 | 0.133551 | − | 0.991042i | \(-0.457362\pi\) | ||||
0.133551 | + | 0.991042i | \(0.457362\pi\) | |||||||
\(402\) | 7.67638e13 | 0.000907167 0 | ||||||||
\(403\) | 2.25323e15 | 0.0262013 | ||||||||
\(404\) | 7.18234e15 | 0.0821840 | ||||||||
\(405\) | 1.24141e16 | 0.139785 | ||||||||
\(406\) | −2.23392e16 | −0.247542 | ||||||||
\(407\) | −5.16725e16 | −0.563502 | ||||||||
\(408\) | −4.72961e16 | −0.507615 | ||||||||
\(409\) | −1.55417e17 | −1.64172 | −0.820858 | − | 0.571133i | \(-0.806504\pi\) | ||||
−0.820858 | + | 0.571133i | \(0.806504\pi\) | |||||||
\(410\) | 1.46856e17 | 1.52685 | ||||||||
\(411\) | −5.59299e16 | −0.572364 | ||||||||
\(412\) | 3.15855e16 | 0.318168 | ||||||||
\(413\) | 1.67321e16 | 0.165911 | ||||||||
\(414\) | −8.97234e15 | −0.0875797 | ||||||||
\(415\) | 6.52653e16 | 0.627147 | ||||||||
\(416\) | 1.35159e16 | 0.127862 | ||||||||
\(417\) | 3.05042e16 | 0.284103 | ||||||||
\(418\) | −1.20484e16 | −0.110480 | ||||||||
\(419\) | 9.43507e16 | 0.851832 | 0.425916 | − | 0.904763i | \(-0.359952\pi\) | ||||
0.425916 | + | 0.904763i | \(0.359952\pi\) | |||||||
\(420\) | 1.79815e16 | 0.159848 | ||||||||
\(421\) | 2.00336e17 | 1.75358 | 0.876792 | − | 0.480870i | \(-0.159679\pi\) | ||||
0.876792 | + | 0.480870i | \(0.159679\pi\) | |||||||
\(422\) | 1.07663e17 | 0.927971 | ||||||||
\(423\) | −5.98279e16 | −0.507798 | ||||||||
\(424\) | −8.18801e16 | −0.684384 | ||||||||
\(425\) | 6.94736e16 | 0.571863 | ||||||||
\(426\) | 6.02212e16 | 0.488188 | ||||||||
\(427\) | −2.00590e17 | −1.60151 | ||||||||
\(428\) | −1.22428e16 | −0.0962713 | ||||||||
\(429\) | 8.53553e15 | 0.0661086 | ||||||||
\(430\) | 2.49315e17 | 1.90197 | ||||||||
\(431\) | 9.65868e16 | 0.725797 | 0.362899 | − | 0.931829i | \(-0.381787\pi\) | ||||
0.362899 | + | 0.931829i | \(0.381787\pi\) | |||||||
\(432\) | 2.97138e16 | 0.219945 | ||||||||
\(433\) | −6.71250e16 | −0.489455 | −0.244728 | − | 0.969592i | \(-0.578699\pi\) | ||||
−0.244728 | + | 0.969592i | \(0.578699\pi\) | |||||||
\(434\) | 1.34532e16 | 0.0966370 | ||||||||
\(435\) | 1.84110e16 | 0.130286 | ||||||||
\(436\) | 3.05734e16 | 0.213148 | ||||||||
\(437\) | −1.17762e16 | −0.0808867 | ||||||||
\(438\) | −4.45500e16 | −0.301485 | ||||||||
\(439\) | −1.19945e17 | −0.799763 | −0.399881 | − | 0.916567i | \(-0.630949\pi\) | ||||
−0.399881 | + | 0.916567i | \(0.630949\pi\) | |||||||
\(440\) | −5.24990e16 | −0.344912 | ||||||||
\(441\) | 3.21334e16 | 0.208020 | ||||||||
\(442\) | −6.23366e16 | −0.397647 | ||||||||
\(443\) | −1.11001e16 | −0.0697752 | −0.0348876 | − | 0.999391i | \(-0.511107\pi\) | ||||
−0.0348876 | + | 0.999391i | \(0.511107\pi\) | |||||||
\(444\) | −2.96375e16 | −0.183591 | ||||||||
\(445\) | 3.58579e17 | 2.18900 | ||||||||
\(446\) | 1.98089e16 | 0.119174 | ||||||||
\(447\) | 6.12439e16 | 0.363131 | ||||||||
\(448\) | −1.68533e17 | −0.984869 | ||||||||
\(449\) | −2.25580e17 | −1.29927 | −0.649635 | − | 0.760247i | \(-0.725078\pi\) | ||||
−0.649635 | + | 0.760247i | \(0.725078\pi\) | |||||||
\(450\) | −3.70517e16 | −0.210343 | ||||||||
\(451\) | 6.12913e16 | 0.342966 | ||||||||
\(452\) | −2.70167e15 | −0.0149016 | ||||||||
\(453\) | −1.70510e17 | −0.927069 | ||||||||
\(454\) | −3.61629e17 | −1.93821 | ||||||||
\(455\) | −1.13540e17 | −0.599894 | ||||||||
\(456\) | 3.31066e16 | 0.172442 | ||||||||
\(457\) | −2.82152e17 | −1.44886 | −0.724432 | − | 0.689347i | \(-0.757898\pi\) | ||||
−0.724432 | + | 0.689347i | \(0.757898\pi\) | |||||||
\(458\) | 1.66812e17 | 0.844504 | ||||||||
\(459\) | −3.78386e16 | −0.188866 | ||||||||
\(460\) | 1.07109e16 | 0.0527107 | ||||||||
\(461\) | −1.95029e17 | −0.946333 | −0.473167 | − | 0.880973i | \(-0.656889\pi\) | ||||
−0.473167 | + | 0.880973i | \(0.656889\pi\) | |||||||
\(462\) | 5.09626e16 | 0.243825 | ||||||||
\(463\) | 2.97176e17 | 1.40197 | 0.700983 | − | 0.713178i | \(-0.252745\pi\) | ||||
0.700983 | + | 0.713178i | \(0.252745\pi\) | |||||||
\(464\) | 4.40675e16 | 0.204999 | ||||||||
\(465\) | −1.10876e16 | −0.0508618 | ||||||||
\(466\) | −1.41758e15 | −0.00641268 | ||||||||
\(467\) | −3.64073e17 | −1.62416 | −0.812079 | − | 0.583548i | \(-0.801664\pi\) | ||||
−0.812079 | + | 0.583548i | \(0.801664\pi\) | |||||||
\(468\) | 4.89568e15 | 0.0215385 | ||||||||
\(469\) | −4.26168e14 | −0.00184909 | ||||||||
\(470\) | 4.85000e17 | 2.07542 | ||||||||
\(471\) | −1.12773e17 | −0.475959 | ||||||||
\(472\) | −2.80193e16 | −0.116636 | ||||||||
\(473\) | 1.04053e17 | 0.427225 | ||||||||
\(474\) | −2.09208e17 | −0.847265 | ||||||||
\(475\) | −4.86306e16 | −0.194268 | ||||||||
\(476\) | −5.48082e16 | −0.215973 | ||||||||
\(477\) | −6.55071e16 | −0.254635 | ||||||||
\(478\) | 1.21585e17 | 0.466229 | ||||||||
\(479\) | −1.29900e17 | −0.491392 | −0.245696 | − | 0.969347i | \(-0.579016\pi\) | ||||
−0.245696 | + | 0.969347i | \(0.579016\pi\) | |||||||
\(480\) | −6.65085e16 | −0.248204 | ||||||||
\(481\) | 1.87139e17 | 0.689002 | ||||||||
\(482\) | 5.40920e17 | 1.96484 | ||||||||
\(483\) | 4.98116e16 | 0.178515 | ||||||||
\(484\) | −4.42646e16 | −0.156517 | ||||||||
\(485\) | 5.12889e17 | 1.78938 | ||||||||
\(486\) | 2.01801e16 | 0.0694686 | ||||||||
\(487\) | −2.01035e17 | −0.682862 | −0.341431 | − | 0.939907i | \(-0.610912\pi\) | ||||
−0.341431 | + | 0.939907i | \(0.610912\pi\) | |||||||
\(488\) | 3.35905e17 | 1.12587 | ||||||||
\(489\) | −1.56380e17 | −0.517217 | ||||||||
\(490\) | −2.60492e17 | −0.850198 | ||||||||
\(491\) | −3.03144e17 | −0.976382 | −0.488191 | − | 0.872737i | \(-0.662343\pi\) | ||||
−0.488191 | + | 0.872737i | \(0.662343\pi\) | |||||||
\(492\) | 3.51545e16 | 0.111740 | ||||||||
\(493\) | −5.61172e16 | −0.176032 | ||||||||
\(494\) | 4.36347e16 | 0.135085 | ||||||||
\(495\) | −4.20011e16 | −0.128330 | ||||||||
\(496\) | −2.65386e16 | −0.0800289 | ||||||||
\(497\) | −3.34329e17 | −0.995079 | ||||||||
\(498\) | 1.06094e17 | 0.311673 | ||||||||
\(499\) | −6.67583e16 | −0.193576 | −0.0967880 | − | 0.995305i | \(-0.530857\pi\) | ||||
−0.0967880 | + | 0.995305i | \(0.530857\pi\) | |||||||
\(500\) | −3.16739e16 | −0.0906561 | ||||||||
\(501\) | −3.35903e17 | −0.949004 | ||||||||
\(502\) | 4.27737e17 | 1.19290 | ||||||||
\(503\) | −4.65095e17 | −1.28041 | −0.640206 | − | 0.768204i | \(-0.721151\pi\) | ||||
−0.640206 | + | 0.768204i | \(0.721151\pi\) | |||||||
\(504\) | −1.40036e17 | −0.380575 | ||||||||
\(505\) | 2.23161e17 | 0.598721 | ||||||||
\(506\) | 3.03564e16 | 0.0804029 | ||||||||
\(507\) | 1.89883e17 | 0.496518 | ||||||||
\(508\) | −6.40936e16 | −0.165463 | ||||||||
\(509\) | 3.08399e17 | 0.786044 | 0.393022 | − | 0.919529i | \(-0.371430\pi\) | ||||
0.393022 | + | 0.919529i | \(0.371430\pi\) | |||||||
\(510\) | 3.06742e17 | 0.771911 | ||||||||
\(511\) | 2.47327e17 | 0.614520 | ||||||||
\(512\) | 2.58169e17 | 0.633358 | ||||||||
\(513\) | 2.64865e16 | 0.0641596 | ||||||||
\(514\) | 3.24857e17 | 0.777020 | ||||||||
\(515\) | 9.81387e17 | 2.31789 | ||||||||
\(516\) | 5.96811e16 | 0.139192 | ||||||||
\(517\) | 2.02417e17 | 0.466186 | ||||||||
\(518\) | 1.11734e18 | 2.54121 | ||||||||
\(519\) | 1.02380e17 | 0.229947 | ||||||||
\(520\) | 1.90132e17 | 0.421729 | ||||||||
\(521\) | −2.52706e17 | −0.553567 | −0.276784 | − | 0.960932i | \(-0.589269\pi\) | ||||
−0.276784 | + | 0.960932i | \(0.589269\pi\) | |||||||
\(522\) | 2.99285e16 | 0.0647480 | ||||||||
\(523\) | −7.28616e17 | −1.55682 | −0.778409 | − | 0.627757i | \(-0.783973\pi\) | ||||
−0.778409 | + | 0.627757i | \(0.783973\pi\) | |||||||
\(524\) | −1.59655e16 | −0.0336921 | ||||||||
\(525\) | 2.05699e17 | 0.428744 | ||||||||
\(526\) | 9.71331e17 | 1.99968 | ||||||||
\(527\) | 3.37952e16 | 0.0687204 | ||||||||
\(528\) | −1.00532e17 | −0.201921 | ||||||||
\(529\) | −4.74366e17 | −0.941134 | ||||||||
\(530\) | 5.31038e17 | 1.04072 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | 3.83650e16 | 0.0733684 | ||||||||
\(533\) | −2.21975e17 | −0.419350 | ||||||||
\(534\) | 5.82898e17 | 1.08786 | ||||||||
\(535\) | −3.80394e17 | −0.701349 | ||||||||
\(536\) | 7.13654e14 | 0.00129992 | ||||||||
\(537\) | 2.37456e17 | 0.427318 | ||||||||
\(538\) | −1.06772e17 | −0.189833 | ||||||||
\(539\) | −1.08718e17 | −0.190974 | ||||||||
\(540\) | −2.40904e16 | −0.0418103 | ||||||||
\(541\) | 1.03306e17 | 0.177151 | 0.0885756 | − | 0.996069i | \(-0.471769\pi\) | ||||
0.0885756 | + | 0.996069i | \(0.471769\pi\) | |||||||
\(542\) | 1.59230e15 | 0.00269792 | ||||||||
\(543\) | 4.73071e16 | 0.0792004 | ||||||||
\(544\) | 2.02720e17 | 0.335354 | ||||||||
\(545\) | 9.49939e17 | 1.55281 | ||||||||
\(546\) | −1.84568e17 | −0.298129 | ||||||||
\(547\) | −1.17000e18 | −1.86753 | −0.933763 | − | 0.357892i | \(-0.883495\pi\) | ||||
−0.933763 | + | 0.357892i | \(0.883495\pi\) | |||||||
\(548\) | 1.08535e17 | 0.171197 | ||||||||
\(549\) | 2.68736e17 | 0.418896 | ||||||||
\(550\) | 1.25358e17 | 0.193106 | ||||||||
\(551\) | 3.92812e16 | 0.0597998 | ||||||||
\(552\) | −8.34136e16 | −0.125497 | ||||||||
\(553\) | 1.16146e18 | 1.72699 | ||||||||
\(554\) | 5.55869e17 | 0.816882 | ||||||||
\(555\) | −9.20861e17 | −1.33749 | ||||||||
\(556\) | −5.91951e16 | −0.0849767 | ||||||||
\(557\) | 7.54719e16 | 0.107084 | 0.0535422 | − | 0.998566i | \(-0.482949\pi\) | ||||
0.0535422 | + | 0.998566i | \(0.482949\pi\) | |||||||
\(558\) | −1.80237e16 | −0.0252767 | ||||||||
\(559\) | −3.76842e17 | −0.522375 | ||||||||
\(560\) | 1.33728e18 | 1.83231 | ||||||||
\(561\) | 1.28021e17 | 0.173389 | ||||||||
\(562\) | −1.50812e17 | −0.201907 | ||||||||
\(563\) | 4.98148e17 | 0.659256 | 0.329628 | − | 0.944111i | \(-0.393077\pi\) | ||||
0.329628 | + | 0.944111i | \(0.393077\pi\) | |||||||
\(564\) | 1.16099e17 | 0.151885 | ||||||||
\(565\) | −8.39430e16 | −0.108560 | ||||||||
\(566\) | 6.80975e17 | 0.870612 | ||||||||
\(567\) | −1.12034e17 | −0.141599 | ||||||||
\(568\) | 5.59862e17 | 0.699547 | ||||||||
\(569\) | 2.49767e16 | 0.0308535 | 0.0154268 | − | 0.999881i | \(-0.495089\pi\) | ||||
0.0154268 | + | 0.999881i | \(0.495089\pi\) | |||||||
\(570\) | −2.14715e17 | −0.262226 | ||||||||
\(571\) | −3.03773e17 | −0.366787 | −0.183394 | − | 0.983040i | \(-0.558708\pi\) | ||||
−0.183394 | + | 0.983040i | \(0.558708\pi\) | |||||||
\(572\) | −1.65637e16 | −0.0197735 | ||||||||
\(573\) | 9.14635e17 | 1.07955 | ||||||||
\(574\) | −1.32533e18 | −1.54667 | ||||||||
\(575\) | 1.22527e17 | 0.141381 | ||||||||
\(576\) | 2.25789e17 | 0.257606 | ||||||||
\(577\) | −1.35220e18 | −1.52545 | −0.762724 | − | 0.646724i | \(-0.776139\pi\) | ||||
−0.762724 | + | 0.646724i | \(0.776139\pi\) | |||||||
\(578\) | 3.58253e16 | 0.0399631 | ||||||||
\(579\) | 8.29570e15 | 0.00915045 | ||||||||
\(580\) | −3.57276e16 | −0.0389692 | ||||||||
\(581\) | −5.88999e17 | −0.635286 | ||||||||
\(582\) | 8.33739e17 | 0.889264 | ||||||||
\(583\) | 2.21632e17 | 0.233769 | ||||||||
\(584\) | −4.14170e17 | −0.432011 | ||||||||
\(585\) | 1.52113e17 | 0.156911 | ||||||||
\(586\) | 2.99182e17 | 0.305211 | ||||||||
\(587\) | −1.28182e18 | −1.29324 | −0.646619 | − | 0.762813i | \(-0.723818\pi\) | ||||
−0.646619 | + | 0.762813i | \(0.723818\pi\) | |||||||
\(588\) | −6.23567e16 | −0.0622201 | ||||||||
\(589\) | −2.36561e16 | −0.0233450 | ||||||||
\(590\) | 1.81721e17 | 0.177365 | ||||||||
\(591\) | −2.28479e17 | −0.220561 | ||||||||
\(592\) | −2.20412e18 | −2.10448 | ||||||||
\(593\) | 6.39424e17 | 0.603856 | 0.301928 | − | 0.953331i | \(-0.402370\pi\) | ||||
0.301928 | + | 0.953331i | \(0.402370\pi\) | |||||||
\(594\) | −6.82760e16 | −0.0637759 | ||||||||
\(595\) | −1.70293e18 | −1.57339 | ||||||||
\(596\) | −1.18847e17 | −0.108615 | ||||||||
\(597\) | −5.03536e17 | −0.455195 | ||||||||
\(598\) | −1.09940e17 | −0.0983098 | ||||||||
\(599\) | −7.65253e17 | −0.676910 | −0.338455 | − | 0.940983i | \(-0.609904\pi\) | ||||
−0.338455 | + | 0.940983i | \(0.609904\pi\) | |||||||
\(600\) | −3.44461e17 | −0.301409 | ||||||||
\(601\) | 1.09286e18 | 0.945976 | 0.472988 | − | 0.881069i | \(-0.343175\pi\) | ||||
0.472988 | + | 0.881069i | \(0.343175\pi\) | |||||||
\(602\) | −2.24999e18 | −1.92665 | ||||||||
\(603\) | 5.70950e14 | 0.000483655 0 | ||||||||
\(604\) | 3.30885e17 | 0.277292 | ||||||||
\(605\) | −1.37534e18 | −1.14025 | ||||||||
\(606\) | 3.62765e17 | 0.297546 | ||||||||
\(607\) | 6.43496e17 | 0.522179 | 0.261089 | − | 0.965315i | \(-0.415918\pi\) | ||||
0.261089 | + | 0.965315i | \(0.415918\pi\) | |||||||
\(608\) | −1.41901e17 | −0.113923 | ||||||||
\(609\) | −1.66153e17 | −0.131976 | ||||||||
\(610\) | −2.17853e18 | −1.71206 | ||||||||
\(611\) | −7.33081e17 | −0.570013 | ||||||||
\(612\) | 7.34281e16 | 0.0564908 | ||||||||
\(613\) | −1.64149e18 | −1.24953 | −0.624763 | − | 0.780814i | \(-0.714804\pi\) | ||||
−0.624763 | + | 0.780814i | \(0.714804\pi\) | |||||||
\(614\) | −5.36605e17 | −0.404166 | ||||||||
\(615\) | 1.09228e18 | 0.814040 | ||||||||
\(616\) | 4.73787e17 | 0.349388 | ||||||||
\(617\) | −2.19011e18 | −1.59813 | −0.799066 | − | 0.601244i | \(-0.794672\pi\) | ||||
−0.799066 | + | 0.601244i | \(0.794672\pi\) | |||||||
\(618\) | 1.59532e18 | 1.15192 | ||||||||
\(619\) | 2.33506e18 | 1.66843 | 0.834216 | − | 0.551438i | \(-0.185921\pi\) | ||||
0.834216 | + | 0.551438i | \(0.185921\pi\) | |||||||
\(620\) | 2.15160e16 | 0.0152131 | ||||||||
\(621\) | −6.67340e16 | −0.0466930 | ||||||||
\(622\) | −1.09135e18 | −0.755660 | ||||||||
\(623\) | −3.23606e18 | −2.21740 | ||||||||
\(624\) | 3.64088e17 | 0.246892 | ||||||||
\(625\) | −1.85245e18 | −1.24316 | ||||||||
\(626\) | 5.99237e17 | 0.397984 | ||||||||
\(627\) | −8.96126e16 | −0.0589020 | ||||||||
\(628\) | 2.18843e17 | 0.142362 | ||||||||
\(629\) | 2.80681e18 | 1.80711 | ||||||||
\(630\) | 9.08210e17 | 0.578726 | ||||||||
\(631\) | 2.95666e17 | 0.186471 | 0.0932354 | − | 0.995644i | \(-0.470279\pi\) | ||||
0.0932354 | + | 0.995644i | \(0.470279\pi\) | |||||||
\(632\) | −1.94496e18 | −1.21408 | ||||||||
\(633\) | 8.00767e17 | 0.494746 | ||||||||
\(634\) | −2.18076e17 | −0.133361 | ||||||||
\(635\) | −1.99144e18 | −1.20542 | ||||||||
\(636\) | 1.27120e17 | 0.0761629 | ||||||||
\(637\) | 3.93736e17 | 0.233507 | ||||||||
\(638\) | −1.01258e17 | −0.0594421 | ||||||||
\(639\) | 4.47910e17 | 0.260277 | ||||||||
\(640\) | −2.57775e18 | −1.48276 | ||||||||
\(641\) | −1.72246e18 | −0.980780 | −0.490390 | − | 0.871503i | \(-0.663146\pi\) | ||||
−0.490390 | + | 0.871503i | \(0.663146\pi\) | |||||||
\(642\) | −6.18360e17 | −0.348549 | ||||||||
\(643\) | 9.63720e17 | 0.537749 | 0.268875 | − | 0.963175i | \(-0.413348\pi\) | ||||
0.268875 | + | 0.963175i | \(0.413348\pi\) | |||||||
\(644\) | −9.66622e16 | −0.0533948 | ||||||||
\(645\) | 1.85434e18 | 1.01403 | ||||||||
\(646\) | 6.54457e17 | 0.354299 | ||||||||
\(647\) | 1.08203e18 | 0.579909 | 0.289955 | − | 0.957040i | \(-0.406360\pi\) | ||||
0.289955 | + | 0.957040i | \(0.406360\pi\) | |||||||
\(648\) | 1.87610e17 | 0.0995446 | ||||||||
\(649\) | 7.58423e16 | 0.0398401 | ||||||||
\(650\) | −4.54001e17 | −0.236113 | ||||||||
\(651\) | 1.00062e17 | 0.0515218 | ||||||||
\(652\) | 3.03464e17 | 0.154703 | ||||||||
\(653\) | −8.01051e17 | −0.404319 | −0.202160 | − | 0.979353i | \(-0.564796\pi\) | ||||
−0.202160 | + | 0.979353i | \(0.564796\pi\) | |||||||
\(654\) | 1.54420e18 | 0.771699 | ||||||||
\(655\) | −4.96060e17 | −0.245451 | ||||||||
\(656\) | 2.61442e18 | 1.28086 | ||||||||
\(657\) | −3.31351e17 | −0.160736 | ||||||||
\(658\) | −4.37697e18 | −2.10235 | ||||||||
\(659\) | −1.24626e18 | −0.592724 | −0.296362 | − | 0.955076i | \(-0.595773\pi\) | ||||
−0.296362 | + | 0.955076i | \(0.595773\pi\) | |||||||
\(660\) | 8.15056e16 | 0.0383841 | ||||||||
\(661\) | 2.34871e18 | 1.09527 | 0.547633 | − | 0.836719i | \(-0.315529\pi\) | ||||
0.547633 | + | 0.836719i | \(0.315529\pi\) | |||||||
\(662\) | −1.74463e18 | −0.805611 | ||||||||
\(663\) | −4.63643e17 | −0.212005 | ||||||||
\(664\) | 9.86327e17 | 0.446610 | ||||||||
\(665\) | 1.19203e18 | 0.534499 | ||||||||
\(666\) | −1.49693e18 | −0.664690 | ||||||||
\(667\) | −9.89709e16 | −0.0435201 | ||||||||
\(668\) | 6.51838e17 | 0.283853 | ||||||||
\(669\) | 1.47333e17 | 0.0635377 | ||||||||
\(670\) | −4.62845e15 | −0.00197674 | ||||||||
\(671\) | −9.09223e17 | −0.384569 | ||||||||
\(672\) | 6.00218e17 | 0.251425 | ||||||||
\(673\) | 4.08779e18 | 1.69586 | 0.847931 | − | 0.530106i | \(-0.177848\pi\) | ||||
0.847931 | + | 0.530106i | \(0.177848\pi\) | |||||||
\(674\) | 7.89636e16 | 0.0324442 | ||||||||
\(675\) | −2.75581e17 | −0.112144 | ||||||||
\(676\) | −3.68480e17 | −0.148511 | ||||||||
\(677\) | −3.34933e18 | −1.33700 | −0.668500 | − | 0.743712i | \(-0.733063\pi\) | ||||
−0.668500 | + | 0.743712i | \(0.733063\pi\) | |||||||
\(678\) | −1.36456e17 | −0.0539509 | ||||||||
\(679\) | −4.62866e18 | −1.81260 | ||||||||
\(680\) | 2.85171e18 | 1.10611 | ||||||||
\(681\) | −2.68970e18 | −1.03335 | ||||||||
\(682\) | 6.09800e16 | 0.0232054 | ||||||||
\(683\) | −2.32332e18 | −0.875737 | −0.437868 | − | 0.899039i | \(-0.644266\pi\) | ||||
−0.437868 | + | 0.899039i | \(0.644266\pi\) | |||||||
\(684\) | −5.13986e16 | −0.0191905 | ||||||||
\(685\) | 3.37227e18 | 1.24719 | ||||||||
\(686\) | −1.41617e18 | −0.518812 | ||||||||
\(687\) | 1.24070e18 | 0.450246 | ||||||||
\(688\) | 4.43845e18 | 1.59553 | ||||||||
\(689\) | −8.02669e17 | −0.285833 | ||||||||
\(690\) | 5.40984e17 | 0.190838 | ||||||||
\(691\) | 5.87579e17 | 0.205333 | 0.102666 | − | 0.994716i | \(-0.467263\pi\) | ||||
0.102666 | + | 0.994716i | \(0.467263\pi\) | |||||||
\(692\) | −1.98675e17 | −0.0687785 | ||||||||
\(693\) | 3.79047e17 | 0.129995 | ||||||||
\(694\) | 1.97331e18 | 0.670437 | ||||||||
\(695\) | −1.83924e18 | −0.619067 | ||||||||
\(696\) | 2.78238e17 | 0.0927803 | ||||||||
\(697\) | −3.32930e18 | −1.09987 | ||||||||
\(698\) | 3.85413e17 | 0.126144 | ||||||||
\(699\) | −1.05436e16 | −0.00341891 | ||||||||
\(700\) | −3.99172e17 | −0.128240 | ||||||||
\(701\) | −3.77375e18 | −1.20117 | −0.600587 | − | 0.799559i | \(-0.705066\pi\) | ||||
−0.600587 | + | 0.799559i | \(0.705066\pi\) | |||||||
\(702\) | 2.47271e17 | 0.0779797 | ||||||||
\(703\) | −1.96473e18 | −0.613893 | ||||||||
\(704\) | −7.63917e17 | −0.236496 | ||||||||
\(705\) | 3.60730e18 | 1.10651 | ||||||||
\(706\) | −2.22661e18 | −0.676729 | ||||||||
\(707\) | −2.01396e18 | −0.606491 | ||||||||
\(708\) | 4.35004e16 | 0.0129801 | ||||||||
\(709\) | 5.70959e17 | 0.168813 | 0.0844063 | − | 0.996431i | \(-0.473101\pi\) | ||||
0.0844063 | + | 0.996431i | \(0.473101\pi\) | |||||||
\(710\) | −3.63102e18 | −1.06377 | ||||||||
\(711\) | −1.55604e18 | −0.451718 | ||||||||
\(712\) | 5.41905e18 | 1.55885 | ||||||||
\(713\) | 5.96027e16 | 0.0169896 | ||||||||
\(714\) | −2.76825e18 | −0.781928 | ||||||||
\(715\) | −5.14647e17 | −0.144052 | ||||||||
\(716\) | −4.60798e17 | −0.127813 | ||||||||
\(717\) | 9.04318e17 | 0.248569 | ||||||||
\(718\) | −3.27952e18 | −0.893309 | ||||||||
\(719\) | −4.09843e18 | −1.10632 | −0.553159 | − | 0.833076i | \(-0.686578\pi\) | ||||
−0.553159 | + | 0.833076i | \(0.686578\pi\) | |||||||
\(720\) | −1.79158e18 | −0.479265 | ||||||||
\(721\) | −8.85670e18 | −2.34797 | ||||||||
\(722\) | 3.66365e18 | 0.962548 | ||||||||
\(723\) | 4.02323e18 | 1.04755 | ||||||||
\(724\) | −9.18021e16 | −0.0236893 | ||||||||
\(725\) | −4.08705e17 | −0.104523 | ||||||||
\(726\) | −2.23571e18 | −0.566667 | ||||||||
\(727\) | −6.55964e18 | −1.64781 | −0.823904 | − | 0.566729i | \(-0.808209\pi\) | ||||
−0.823904 | + | 0.566729i | \(0.808209\pi\) | |||||||
\(728\) | −1.71588e18 | −0.427202 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 2.68613e18 | 0.656943 | ||||||||
\(731\) | −5.65208e18 | −1.37008 | ||||||||
\(732\) | −5.21498e17 | −0.125294 | ||||||||
\(733\) | 8.63234e17 | 0.205567 | 0.102783 | − | 0.994704i | \(-0.467225\pi\) | ||||
0.102783 | + | 0.994704i | \(0.467225\pi\) | |||||||
\(734\) | 2.90291e18 | 0.685187 | ||||||||
\(735\) | −1.93747e18 | −0.453282 | ||||||||
\(736\) | 3.57526e17 | 0.0829090 | ||||||||
\(737\) | −1.93171e15 | −0.000444021 0 | ||||||||
\(738\) | 1.77558e18 | 0.404552 | ||||||||
\(739\) | 3.66698e18 | 0.828171 | 0.414086 | − | 0.910238i | \(-0.364101\pi\) | ||||
0.414086 | + | 0.910238i | \(0.364101\pi\) | |||||||
\(740\) | 1.78698e18 | 0.400050 | ||||||||
\(741\) | 3.24544e17 | 0.0720203 | ||||||||
\(742\) | −4.79245e18 | −1.05422 | ||||||||
\(743\) | −3.20909e18 | −0.699769 | −0.349885 | − | 0.936793i | \(-0.613779\pi\) | ||||
−0.349885 | + | 0.936793i | \(0.613779\pi\) | |||||||
\(744\) | −1.67562e17 | −0.0362202 | ||||||||
\(745\) | −3.69268e18 | −0.791272 | ||||||||
\(746\) | 2.97114e17 | 0.0631134 | ||||||||
\(747\) | 7.89098e17 | 0.166168 | ||||||||
\(748\) | −2.48431e17 | −0.0518616 | ||||||||
\(749\) | 3.43294e18 | 0.710450 | ||||||||
\(750\) | −1.59979e18 | −0.328219 | ||||||||
\(751\) | −7.66711e18 | −1.55945 | −0.779726 | − | 0.626121i | \(-0.784642\pi\) | ||||
−0.779726 | + | 0.626121i | \(0.784642\pi\) | |||||||
\(752\) | 8.63424e18 | 1.74104 | ||||||||
\(753\) | 3.18140e18 | 0.635991 | ||||||||
\(754\) | 3.66719e17 | 0.0726807 | ||||||||
\(755\) | 1.02809e19 | 2.02011 | ||||||||
\(756\) | 2.17408e17 | 0.0423529 | ||||||||
\(757\) | 3.40955e18 | 0.658528 | 0.329264 | − | 0.944238i | \(-0.393199\pi\) | ||||
0.329264 | + | 0.944238i | \(0.393199\pi\) | |||||||
\(758\) | −1.64750e18 | −0.315482 | ||||||||
\(759\) | 2.25783e17 | 0.0428667 | ||||||||
\(760\) | −1.99615e18 | −0.375756 | ||||||||
\(761\) | 6.05897e18 | 1.13083 | 0.565417 | − | 0.824805i | \(-0.308715\pi\) | ||||
0.565417 | + | 0.824805i | \(0.308715\pi\) | |||||||
\(762\) | −3.23724e18 | −0.599056 | ||||||||
\(763\) | −8.57290e18 | −1.57296 | ||||||||
\(764\) | −1.77490e18 | −0.322900 | ||||||||
\(765\) | 2.28147e18 | 0.411543 | ||||||||
\(766\) | −7.24739e18 | −1.29627 | ||||||||
\(767\) | −2.74673e17 | −0.0487131 | ||||||||
\(768\) | −1.65307e18 | −0.290699 | ||||||||
\(769\) | 7.76829e18 | 1.35458 | 0.677289 | − | 0.735717i | \(-0.263155\pi\) | ||||
0.677289 | + | 0.735717i | \(0.263155\pi\) | |||||||
\(770\) | −3.07277e18 | −0.531301 | ||||||||
\(771\) | 2.41620e18 | 0.414267 | ||||||||
\(772\) | −1.60983e16 | −0.00273695 | ||||||||
\(773\) | 6.22741e18 | 1.04988 | 0.524941 | − | 0.851139i | \(-0.324087\pi\) | ||||
0.524941 | + | 0.851139i | \(0.324087\pi\) | |||||||
\(774\) | 3.01437e18 | 0.503942 | ||||||||
\(775\) | 2.46132e17 | 0.0408045 | ||||||||
\(776\) | 7.75107e18 | 1.27427 | ||||||||
\(777\) | 8.31048e18 | 1.35484 | ||||||||
\(778\) | −2.65562e18 | −0.429337 | ||||||||
\(779\) | 2.33046e18 | 0.373636 | ||||||||
\(780\) | −2.95183e17 | −0.0469328 | ||||||||
\(781\) | −1.51543e18 | −0.238948 | ||||||||
\(782\) | −1.64894e18 | −0.257846 | ||||||||
\(783\) | 2.22600e17 | 0.0345203 | ||||||||
\(784\) | −4.63743e18 | −0.713219 | ||||||||
\(785\) | 6.79961e18 | 1.03713 | ||||||||
\(786\) | −8.06383e17 | −0.121982 | ||||||||
\(787\) | −2.74400e17 | −0.0411670 | −0.0205835 | − | 0.999788i | \(-0.506552\pi\) | ||||
−0.0205835 | + | 0.999788i | \(0.506552\pi\) | |||||||
\(788\) | 4.43377e17 | 0.0659710 | ||||||||
\(789\) | 7.22451e18 | 1.06612 | ||||||||
\(790\) | 1.26141e19 | 1.84621 | ||||||||
\(791\) | 7.57559e17 | 0.109969 | ||||||||
\(792\) | −6.34745e17 | −0.0913873 | ||||||||
\(793\) | 3.29287e18 | 0.470218 | ||||||||
\(794\) | 1.10078e18 | 0.155907 | ||||||||
\(795\) | 3.94973e18 | 0.554857 | ||||||||
\(796\) | 9.77141e17 | 0.136151 | ||||||||
\(797\) | −1.68707e18 | −0.233160 | −0.116580 | − | 0.993181i | \(-0.537193\pi\) | ||||
−0.116580 | + | 0.993181i | \(0.537193\pi\) | |||||||
\(798\) | 1.93774e18 | 0.265629 | ||||||||
\(799\) | −1.09952e19 | −1.49502 | ||||||||
\(800\) | 1.47642e18 | 0.199125 | ||||||||
\(801\) | 4.33544e18 | 0.579992 | ||||||||
\(802\) | −2.17972e18 | −0.289246 | ||||||||
\(803\) | 1.12107e18 | 0.147564 | ||||||||
\(804\) | −1.10796e15 | −0.000144664 0 | ||||||||
\(805\) | −3.00337e18 | −0.388988 | ||||||||
\(806\) | −2.20847e17 | −0.0283736 | ||||||||
\(807\) | −7.94140e17 | −0.101209 | ||||||||
\(808\) | 3.37254e18 | 0.426367 | ||||||||
\(809\) | 8.85570e18 | 1.11060 | 0.555300 | − | 0.831650i | \(-0.312604\pi\) | ||||
0.555300 | + | 0.831650i | \(0.312604\pi\) | |||||||
\(810\) | −1.21675e18 | −0.151374 | ||||||||
\(811\) | −1.43789e18 | −0.177456 | −0.0887280 | − | 0.996056i | \(-0.528280\pi\) | ||||
−0.0887280 | + | 0.996056i | \(0.528280\pi\) | |||||||
\(812\) | 3.22430e17 | 0.0394749 | ||||||||
\(813\) | 1.18431e16 | 0.00143839 | ||||||||
\(814\) | 5.06461e18 | 0.610221 | ||||||||
\(815\) | 9.42886e18 | 1.12703 | ||||||||
\(816\) | 5.46080e18 | 0.647545 | ||||||||
\(817\) | 3.95637e18 | 0.465430 | ||||||||
\(818\) | 1.52330e19 | 1.77783 | ||||||||
\(819\) | −1.37277e18 | −0.158947 | ||||||||
\(820\) | −2.11963e18 | −0.243484 | ||||||||
\(821\) | −7.99413e18 | −0.911046 | −0.455523 | − | 0.890224i | \(-0.650548\pi\) | ||||
−0.455523 | + | 0.890224i | \(0.650548\pi\) | |||||||
\(822\) | 5.48189e18 | 0.619817 | ||||||||
\(823\) | 1.03119e18 | 0.115675 | 0.0578373 | − | 0.998326i | \(-0.481580\pi\) | ||||
0.0578373 | + | 0.998326i | \(0.481580\pi\) | |||||||
\(824\) | 1.48313e19 | 1.65064 | ||||||||
\(825\) | 9.32382e17 | 0.102954 | ||||||||
\(826\) | −1.63997e18 | −0.179666 | ||||||||
\(827\) | −5.41749e17 | −0.0588860 | −0.0294430 | − | 0.999566i | \(-0.509373\pi\) | ||||
−0.0294430 | + | 0.999566i | \(0.509373\pi\) | |||||||
\(828\) | 1.29501e17 | 0.0139661 | ||||||||
\(829\) | 3.08642e18 | 0.330256 | 0.165128 | − | 0.986272i | \(-0.447196\pi\) | ||||
0.165128 | + | 0.986272i | \(0.447196\pi\) | |||||||
\(830\) | −6.39689e18 | −0.679143 | ||||||||
\(831\) | 4.13441e18 | 0.435519 | ||||||||
\(832\) | 2.76663e18 | 0.289167 | ||||||||
\(833\) | 5.90547e18 | 0.612438 | ||||||||
\(834\) | −2.98983e18 | −0.307657 | ||||||||
\(835\) | 2.02531e19 | 2.06790 | ||||||||
\(836\) | 1.73898e17 | 0.0176179 | ||||||||
\(837\) | −1.34055e17 | −0.0134762 | ||||||||
\(838\) | −9.24766e18 | −0.922456 | ||||||||
\(839\) | −5.52405e18 | −0.546771 | −0.273385 | − | 0.961905i | \(-0.588143\pi\) | ||||
−0.273385 | + | 0.961905i | \(0.588143\pi\) | |||||||
\(840\) | 8.44341e18 | 0.829282 | ||||||||
\(841\) | −9.93050e18 | −0.967825 | ||||||||
\(842\) | −1.96357e19 | −1.89897 | ||||||||
\(843\) | −1.12170e18 | −0.107646 | ||||||||
\(844\) | −1.55394e18 | −0.147981 | ||||||||
\(845\) | −1.14490e19 | −1.08193 | ||||||||
\(846\) | 5.86395e18 | 0.549899 | ||||||||
\(847\) | 1.24120e19 | 1.15504 | ||||||||
\(848\) | 9.45385e18 | 0.873043 | ||||||||
\(849\) | 5.06492e18 | 0.464165 | ||||||||
\(850\) | −6.80936e18 | −0.619275 | ||||||||
\(851\) | 4.95022e18 | 0.446768 | ||||||||
\(852\) | −8.69195e17 | −0.0778502 | ||||||||
\(853\) | −1.76911e19 | −1.57248 | −0.786240 | − | 0.617921i | \(-0.787975\pi\) | ||||
−0.786240 | + | 0.617921i | \(0.787975\pi\) | |||||||
\(854\) | 1.96606e19 | 1.73428 | ||||||||
\(855\) | −1.59700e18 | −0.139805 | ||||||||
\(856\) | −5.74874e18 | −0.499451 | ||||||||
\(857\) | −2.92655e18 | −0.252337 | −0.126168 | − | 0.992009i | \(-0.540268\pi\) | ||||
−0.126168 | + | 0.992009i | \(0.540268\pi\) | |||||||
\(858\) | −8.36598e17 | −0.0715895 | ||||||||
\(859\) | 1.31028e19 | 1.11278 | 0.556389 | − | 0.830922i | \(-0.312186\pi\) | ||||
0.556389 | + | 0.830922i | \(0.312186\pi\) | |||||||
\(860\) | −3.59845e18 | −0.303302 | ||||||||
\(861\) | −9.85748e18 | −0.824604 | ||||||||
\(862\) | −9.46682e18 | −0.785972 | ||||||||
\(863\) | 9.80759e18 | 0.808150 | 0.404075 | − | 0.914726i | \(-0.367593\pi\) | ||||
0.404075 | + | 0.914726i | \(0.367593\pi\) | |||||||
\(864\) | −8.04129e17 | −0.0657637 | ||||||||
\(865\) | −6.17298e18 | −0.501060 | ||||||||
\(866\) | 6.57916e18 | 0.530035 | ||||||||
\(867\) | 2.66459e17 | 0.0213062 | ||||||||
\(868\) | −1.94175e17 | −0.0154105 | ||||||||
\(869\) | 5.26458e18 | 0.414701 | ||||||||
\(870\) | −1.80453e18 | −0.141087 | ||||||||
\(871\) | 6.99594e15 | 0.000542911 0 | ||||||||
\(872\) | 1.43560e19 | 1.10580 | ||||||||
\(873\) | 6.20114e18 | 0.474110 | ||||||||
\(874\) | 1.15423e18 | 0.0875928 | ||||||||
\(875\) | 8.88150e18 | 0.669012 | ||||||||
\(876\) | 6.43006e17 | 0.0480771 | ||||||||
\(877\) | −1.77473e19 | −1.31715 | −0.658574 | − | 0.752516i | \(-0.728840\pi\) | ||||
−0.658574 | + | 0.752516i | \(0.728840\pi\) | |||||||
\(878\) | 1.17562e19 | 0.866069 | ||||||||
\(879\) | 2.22524e18 | 0.162723 | ||||||||
\(880\) | 6.06152e18 | 0.439991 | ||||||||
\(881\) | 5.68538e17 | 0.0409653 | 0.0204826 | − | 0.999790i | \(-0.493480\pi\) | ||||
0.0204826 | + | 0.999790i | \(0.493480\pi\) | |||||||
\(882\) | −3.14951e18 | −0.225267 | ||||||||
\(883\) | −1.31235e19 | −0.931765 | −0.465882 | − | 0.884847i | \(-0.654263\pi\) | ||||
−0.465882 | + | 0.884847i | \(0.654263\pi\) | |||||||
\(884\) | 8.99727e17 | 0.0634119 | ||||||||
\(885\) | 1.35159e18 | 0.0945616 | ||||||||
\(886\) | 1.08796e18 | 0.0755601 | ||||||||
\(887\) | −5.67124e18 | −0.390998 | −0.195499 | − | 0.980704i | \(-0.562633\pi\) | ||||
−0.195499 | + | 0.980704i | \(0.562633\pi\) | |||||||
\(888\) | −1.39166e19 | −0.952464 | ||||||||
\(889\) | 1.79721e19 | 1.22106 | ||||||||
\(890\) | −3.51456e19 | −2.37048 | ||||||||
\(891\) | −5.07820e17 | −0.0340020 | ||||||||
\(892\) | −2.85909e17 | −0.0190045 | ||||||||
\(893\) | 7.69646e18 | 0.507874 | ||||||||
\(894\) | −6.00273e18 | −0.393238 | ||||||||
\(895\) | −1.43174e19 | −0.931136 | ||||||||
\(896\) | 2.32634e19 | 1.50200 | ||||||||
\(897\) | −8.17703e17 | −0.0524137 | ||||||||
\(898\) | 2.21099e19 | 1.40699 | ||||||||
\(899\) | −1.98813e17 | −0.0125605 | ||||||||
\(900\) | 5.34781e17 | 0.0335429 | ||||||||
\(901\) | −1.20389e19 | −0.749678 | ||||||||
\(902\) | −6.00738e18 | −0.371401 | ||||||||
\(903\) | −1.67348e19 | −1.02719 | ||||||||
\(904\) | −1.26860e18 | −0.0773087 | ||||||||
\(905\) | −2.85237e18 | −0.172580 | ||||||||
\(906\) | 1.67123e19 | 1.00393 | ||||||||
\(907\) | −2.26476e19 | −1.35075 | −0.675374 | − | 0.737475i | \(-0.736018\pi\) | ||||
−0.675374 | + | 0.737475i | \(0.736018\pi\) | |||||||
\(908\) | 5.21952e18 | 0.309081 | ||||||||
\(909\) | 2.69815e18 | 0.158636 | ||||||||
\(910\) | 1.11285e19 | 0.649630 | ||||||||
\(911\) | 3.19163e19 | 1.84988 | 0.924939 | − | 0.380117i | \(-0.124116\pi\) | ||||
0.924939 | + | 0.380117i | \(0.124116\pi\) | |||||||
\(912\) | −3.82248e18 | −0.219978 | ||||||||
\(913\) | −2.66978e18 | −0.152551 | ||||||||
\(914\) | 2.76547e19 | 1.56898 | ||||||||
\(915\) | −1.62034e19 | −0.912784 | ||||||||
\(916\) | −2.40766e18 | −0.134671 | ||||||||
\(917\) | 4.47678e18 | 0.248637 | ||||||||
\(918\) | 3.70870e18 | 0.204524 | ||||||||
\(919\) | 6.67933e18 | 0.365748 | 0.182874 | − | 0.983136i | \(-0.441460\pi\) | ||||
0.182874 | + | 0.983136i | \(0.441460\pi\) | |||||||
\(920\) | 5.02940e18 | 0.273461 | ||||||||
\(921\) | −3.99113e18 | −0.215481 | ||||||||
\(922\) | 1.91155e19 | 1.02479 | ||||||||
\(923\) | 5.48832e18 | 0.292165 | ||||||||
\(924\) | −7.35562e17 | −0.0388823 | ||||||||
\(925\) | 2.04422e19 | 1.07302 | ||||||||
\(926\) | −2.91273e19 | −1.51820 | ||||||||
\(927\) | 1.18656e19 | 0.614144 | ||||||||
\(928\) | −1.19258e18 | −0.0612949 | ||||||||
\(929\) | −1.94975e19 | −0.995123 | −0.497561 | − | 0.867429i | \(-0.665771\pi\) | ||||
−0.497561 | + | 0.867429i | \(0.665771\pi\) | |||||||
\(930\) | 1.08673e18 | 0.0550786 | ||||||||
\(931\) | −4.13375e18 | −0.208052 | ||||||||
\(932\) | 2.04605e16 | 0.00102262 | ||||||||
\(933\) | −8.11718e18 | −0.402879 | ||||||||
\(934\) | 3.56841e19 | 1.75881 | ||||||||
\(935\) | −7.71896e18 | −0.377819 | ||||||||
\(936\) | 2.29881e18 | 0.111741 | ||||||||
\(937\) | −1.98727e19 | −0.959289 | −0.479645 | − | 0.877463i | \(-0.659234\pi\) | ||||
−0.479645 | + | 0.877463i | \(0.659234\pi\) | |||||||
\(938\) | 4.17703e16 | 0.00200239 | ||||||||
\(939\) | 4.45697e18 | 0.212184 | ||||||||
\(940\) | −7.00018e18 | −0.330962 | ||||||||
\(941\) | −4.48542e18 | −0.210606 | −0.105303 | − | 0.994440i | \(-0.533581\pi\) | ||||
−0.105303 | + | 0.994440i | \(0.533581\pi\) | |||||||
\(942\) | 1.10533e19 | 0.515419 | ||||||||
\(943\) | −5.87170e18 | −0.271918 | ||||||||
\(944\) | 3.23510e18 | 0.148789 | ||||||||
\(945\) | 6.75504e18 | 0.308547 | ||||||||
\(946\) | −1.01986e19 | −0.462646 | ||||||||
\(947\) | −2.27860e18 | −0.102658 | −0.0513290 | − | 0.998682i | \(-0.516346\pi\) | ||||
−0.0513290 | + | 0.998682i | \(0.516346\pi\) | |||||||
\(948\) | 3.01958e18 | 0.135111 | ||||||||
\(949\) | −4.06010e18 | −0.180429 | ||||||||
\(950\) | 4.76646e18 | 0.210374 | ||||||||
\(951\) | −1.62199e18 | −0.0711010 | ||||||||
\(952\) | −2.57357e19 | −1.12046 | ||||||||
\(953\) | 9.30159e18 | 0.402210 | 0.201105 | − | 0.979570i | \(-0.435547\pi\) | ||||
0.201105 | + | 0.979570i | \(0.435547\pi\) | |||||||
\(954\) | 6.42058e18 | 0.275746 | ||||||||
\(955\) | −5.51476e19 | −2.35237 | ||||||||
\(956\) | −1.75488e18 | −0.0743484 | ||||||||
\(957\) | −7.53130e17 | −0.0316915 | ||||||||
\(958\) | 1.27320e19 | 0.532132 | ||||||||
\(959\) | −3.04337e19 | −1.26338 | ||||||||
\(960\) | −1.36139e19 | −0.561330 | ||||||||
\(961\) | −2.42978e19 | −0.995097 | ||||||||
\(962\) | −1.83421e19 | −0.746126 | ||||||||
\(963\) | −4.59920e18 | −0.185828 | ||||||||
\(964\) | −7.80730e18 | −0.313329 | ||||||||
\(965\) | −5.00186e17 | −0.0199390 | ||||||||
\(966\) | −4.88221e18 | −0.193315 | ||||||||
\(967\) | −1.83135e19 | −0.720277 | −0.360139 | − | 0.932899i | \(-0.617271\pi\) | ||||
−0.360139 | + | 0.932899i | \(0.617271\pi\) | |||||||
\(968\) | −2.07849e19 | −0.812003 | ||||||||
\(969\) | 4.86769e18 | 0.188894 | ||||||||
\(970\) | −5.02701e19 | −1.93773 | ||||||||
\(971\) | −1.03164e19 | −0.395005 | −0.197503 | − | 0.980302i | \(-0.563283\pi\) | ||||
−0.197503 | + | 0.980302i | \(0.563283\pi\) | |||||||
\(972\) | −2.91267e17 | −0.0110780 | ||||||||
\(973\) | 1.65986e19 | 0.627100 | ||||||||
\(974\) | 1.97041e19 | 0.739476 | ||||||||
\(975\) | −3.37675e18 | −0.125883 | ||||||||
\(976\) | −3.87835e19 | −1.43623 | ||||||||
\(977\) | 4.89176e19 | 1.79949 | 0.899747 | − | 0.436413i | \(-0.143751\pi\) | ||||
0.899747 | + | 0.436413i | \(0.143751\pi\) | |||||||
\(978\) | 1.53273e19 | 0.560098 | ||||||||
\(979\) | −1.46682e19 | −0.532464 | ||||||||
\(980\) | 3.75978e18 | 0.135579 | ||||||||
\(981\) | 1.14854e19 | 0.411430 | ||||||||
\(982\) | 2.97123e19 | 1.05733 | ||||||||
\(983\) | −1.15301e19 | −0.407600 | −0.203800 | − | 0.979013i | \(-0.565329\pi\) | ||||
−0.203800 | + | 0.979013i | \(0.565329\pi\) | |||||||
\(984\) | 1.65072e19 | 0.579701 | ||||||||
\(985\) | 1.37761e19 | 0.480607 | ||||||||
\(986\) | 5.50025e18 | 0.190626 | ||||||||
\(987\) | −3.25548e19 | −1.12086 | ||||||||
\(988\) | −6.29796e17 | −0.0215417 | ||||||||
\(989\) | −9.96826e18 | −0.338722 | ||||||||
\(990\) | 4.11668e18 | 0.138969 | ||||||||
\(991\) | 2.90894e19 | 0.975565 | 0.487783 | − | 0.872965i | \(-0.337806\pi\) | ||||
0.487783 | + | 0.872965i | \(0.337806\pi\) | |||||||
\(992\) | 7.18199e17 | 0.0239287 | ||||||||
\(993\) | −1.29761e19 | −0.429510 | ||||||||
\(994\) | 3.27688e19 | 1.07758 | ||||||||
\(995\) | 3.03606e19 | 0.991882 | ||||||||
\(996\) | −1.53129e18 | −0.0497017 | ||||||||
\(997\) | 2.78215e19 | 0.897144 | 0.448572 | − | 0.893747i | \(-0.351933\pi\) | ||||
0.448572 | + | 0.893747i | \(0.351933\pi\) | |||||||
\(998\) | 6.54322e18 | 0.209625 | ||||||||
\(999\) | −1.11338e19 | −0.354378 |
(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 | 177.14.a.b.1.8 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.b.1.8 | ✓ | 31 | 1.1 | even | 1 | trivial |