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: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −12.4112 | −0.274251 | −0.137125 | − | 0.990554i | \(-0.543786\pi\) | ||||
−0.137125 | + | 0.990554i | \(0.543786\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −1893.96 | −0.924786 | ||||||||
\(5\) | −2629.42 | −0.376293 | −0.188146 | − | 0.982141i | \(-0.560248\pi\) | ||||
−0.188146 | + | 0.982141i | \(0.560248\pi\) | |||||||
\(6\) | −3015.92 | −0.158339 | ||||||||
\(7\) | 23296.0 | 0.523893 | 0.261947 | − | 0.965082i | \(-0.415636\pi\) | ||||
0.261947 | + | 0.965082i | \(0.415636\pi\) | |||||||
\(8\) | 48924.4 | 0.527874 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 32634.3 | 0.103199 | ||||||||
\(11\) | −219870. | −0.411629 | −0.205815 | − | 0.978591i | \(-0.565984\pi\) | ||||
−0.205815 | + | 0.978591i | \(0.565984\pi\) | |||||||
\(12\) | −460233. | −0.533926 | ||||||||
\(13\) | 1.40491e6 | 1.04945 | 0.524724 | − | 0.851272i | \(-0.324168\pi\) | ||||
0.524724 | + | 0.851272i | \(0.324168\pi\) | |||||||
\(14\) | −289131. | −0.143678 | ||||||||
\(15\) | −638950. | −0.217253 | ||||||||
\(16\) | 3.27163e6 | 0.780016 | ||||||||
\(17\) | −5.70617e6 | −0.974711 | −0.487355 | − | 0.873204i | \(-0.662038\pi\) | ||||
−0.487355 | + | 0.873204i | \(0.662038\pi\) | |||||||
\(18\) | −732868. | −0.0914170 | ||||||||
\(19\) | 820391. | 0.0760109 | 0.0380055 | − | 0.999278i | \(-0.487900\pi\) | ||||
0.0380055 | + | 0.999278i | \(0.487900\pi\) | |||||||
\(20\) | 4.98003e6 | 0.347990 | ||||||||
\(21\) | 5.66094e6 | 0.302470 | ||||||||
\(22\) | 2.72885e6 | 0.112890 | ||||||||
\(23\) | 2.97055e7 | 0.962353 | 0.481176 | − | 0.876624i | \(-0.340210\pi\) | ||||
0.481176 | + | 0.876624i | \(0.340210\pi\) | |||||||
\(24\) | 1.18886e7 | 0.304768 | ||||||||
\(25\) | −4.19143e7 | −0.858404 | ||||||||
\(26\) | −1.74366e7 | −0.287812 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −4.41218e7 | −0.484489 | ||||||||
\(29\) | 9.68327e7 | 0.876664 | 0.438332 | − | 0.898813i | \(-0.355569\pi\) | ||||
0.438332 | + | 0.898813i | \(0.355569\pi\) | |||||||
\(30\) | 7.93012e6 | 0.0595817 | ||||||||
\(31\) | 6.91538e7 | 0.433837 | 0.216919 | − | 0.976190i | \(-0.430399\pi\) | ||||
0.216919 | + | 0.976190i | \(0.430399\pi\) | |||||||
\(32\) | −1.40802e8 | −0.741795 | ||||||||
\(33\) | −5.34284e7 | −0.237654 | ||||||||
\(34\) | 7.08203e7 | 0.267315 | ||||||||
\(35\) | −6.12552e7 | −0.197137 | ||||||||
\(36\) | −1.11837e8 | −0.308262 | ||||||||
\(37\) | −4.51038e8 | −1.06931 | −0.534655 | − | 0.845071i | \(-0.679558\pi\) | ||||
−0.534655 | + | 0.845071i | \(0.679558\pi\) | |||||||
\(38\) | −1.01820e7 | −0.0208461 | ||||||||
\(39\) | 3.41394e8 | 0.605900 | ||||||||
\(40\) | −1.28643e8 | −0.198635 | ||||||||
\(41\) | 4.49616e8 | 0.606081 | 0.303041 | − | 0.952978i | \(-0.401998\pi\) | ||||
0.303041 | + | 0.952978i | \(0.401998\pi\) | |||||||
\(42\) | −7.02589e7 | −0.0829526 | ||||||||
\(43\) | −1.79394e9 | −1.86094 | −0.930469 | − | 0.366371i | \(-0.880600\pi\) | ||||
−0.930469 | + | 0.366371i | \(0.880600\pi\) | |||||||
\(44\) | 4.16426e8 | 0.380669 | ||||||||
\(45\) | −1.55265e8 | −0.125431 | ||||||||
\(46\) | −3.68681e8 | −0.263926 | ||||||||
\(47\) | 5.98279e8 | 0.380509 | 0.190255 | − | 0.981735i | \(-0.439069\pi\) | ||||
0.190255 | + | 0.981735i | \(0.439069\pi\) | |||||||
\(48\) | 7.95005e8 | 0.450343 | ||||||||
\(49\) | −1.43462e9 | −0.725536 | ||||||||
\(50\) | 5.20205e8 | 0.235418 | ||||||||
\(51\) | −1.38660e9 | −0.562750 | ||||||||
\(52\) | −2.66085e9 | −0.970516 | ||||||||
\(53\) | −3.80930e9 | −1.25120 | −0.625602 | − | 0.780143i | \(-0.715146\pi\) | ||||
−0.625602 | + | 0.780143i | \(0.715146\pi\) | |||||||
\(54\) | −1.78087e8 | −0.0527796 | ||||||||
\(55\) | 5.78132e8 | 0.154893 | ||||||||
\(56\) | 1.13974e9 | 0.276550 | ||||||||
\(57\) | 1.99355e8 | 0.0438849 | ||||||||
\(58\) | −1.20181e9 | −0.240426 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 1.21015e9 | 0.200912 | ||||||||
\(61\) | 9.73343e9 | 1.47554 | 0.737772 | − | 0.675050i | \(-0.235878\pi\) | ||||
0.737772 | + | 0.675050i | \(0.235878\pi\) | |||||||
\(62\) | −8.58280e8 | −0.118980 | ||||||||
\(63\) | 1.37561e9 | 0.174631 | ||||||||
\(64\) | −4.95277e9 | −0.576579 | ||||||||
\(65\) | −3.69412e9 | −0.394900 | ||||||||
\(66\) | 6.63109e8 | 0.0651769 | ||||||||
\(67\) | 2.05666e10 | 1.86102 | 0.930511 | − | 0.366265i | \(-0.119364\pi\) | ||||
0.930511 | + | 0.366265i | \(0.119364\pi\) | |||||||
\(68\) | 1.08073e10 | 0.901399 | ||||||||
\(69\) | 7.21845e9 | 0.555615 | ||||||||
\(70\) | 7.60249e8 | 0.0540650 | ||||||||
\(71\) | −1.31509e10 | −0.865038 | −0.432519 | − | 0.901625i | \(-0.642375\pi\) | ||||
−0.432519 | + | 0.901625i | \(0.642375\pi\) | |||||||
\(72\) | 2.88894e9 | 0.175958 | ||||||||
\(73\) | 2.61072e10 | 1.47396 | 0.736978 | − | 0.675917i | \(-0.236252\pi\) | ||||
0.736978 | + | 0.675917i | \(0.236252\pi\) | |||||||
\(74\) | 5.59791e9 | 0.293259 | ||||||||
\(75\) | −1.01852e10 | −0.495600 | ||||||||
\(76\) | −1.55379e9 | −0.0702939 | ||||||||
\(77\) | −5.12210e9 | −0.215650 | ||||||||
\(78\) | −4.23710e9 | −0.166169 | ||||||||
\(79\) | −3.90581e10 | −1.42811 | −0.714056 | − | 0.700089i | \(-0.753144\pi\) | ||||
−0.714056 | + | 0.700089i | \(0.753144\pi\) | |||||||
\(80\) | −8.60249e9 | −0.293514 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −5.58027e9 | −0.166218 | ||||||||
\(83\) | 2.57619e10 | 0.717875 | 0.358938 | − | 0.933362i | \(-0.383139\pi\) | ||||
0.358938 | + | 0.933362i | \(0.383139\pi\) | |||||||
\(84\) | −1.07216e10 | −0.279720 | ||||||||
\(85\) | 1.50039e10 | 0.366776 | ||||||||
\(86\) | 2.22649e10 | 0.510364 | ||||||||
\(87\) | 2.35303e10 | 0.506142 | ||||||||
\(88\) | −1.07570e10 | −0.217289 | ||||||||
\(89\) | 4.36938e10 | 0.829420 | 0.414710 | − | 0.909954i | \(-0.363883\pi\) | ||||
0.414710 | + | 0.909954i | \(0.363883\pi\) | |||||||
\(90\) | 1.92702e9 | 0.0343995 | ||||||||
\(91\) | 3.27289e10 | 0.549799 | ||||||||
\(92\) | −5.62612e10 | −0.889971 | ||||||||
\(93\) | 1.68044e10 | 0.250476 | ||||||||
\(94\) | −7.42534e9 | −0.104355 | ||||||||
\(95\) | −2.15716e9 | −0.0286024 | ||||||||
\(96\) | −3.42149e10 | −0.428275 | ||||||||
\(97\) | −4.40290e10 | −0.520589 | −0.260294 | − | 0.965529i | \(-0.583820\pi\) | ||||
−0.260294 | + | 0.965529i | \(0.583820\pi\) | |||||||
\(98\) | 1.78053e10 | 0.198979 | ||||||||
\(99\) | −1.29831e10 | −0.137210 | ||||||||
\(100\) | 7.93840e10 | 0.793840 | ||||||||
\(101\) | −9.64384e10 | −0.913025 | −0.456512 | − | 0.889717i | \(-0.650902\pi\) | ||||
−0.456512 | + | 0.889717i | \(0.650902\pi\) | |||||||
\(102\) | 1.72093e10 | 0.154335 | ||||||||
\(103\) | −5.45856e10 | −0.463953 | −0.231976 | − | 0.972721i | \(-0.574519\pi\) | ||||
−0.231976 | + | 0.972721i | \(0.574519\pi\) | |||||||
\(104\) | 6.87346e10 | 0.553977 | ||||||||
\(105\) | −1.48850e10 | −0.113817 | ||||||||
\(106\) | 4.72779e10 | 0.343144 | ||||||||
\(107\) | 6.01740e10 | 0.414761 | 0.207381 | − | 0.978260i | \(-0.433506\pi\) | ||||
0.207381 | + | 0.978260i | \(0.433506\pi\) | |||||||
\(108\) | −2.71763e10 | −0.177975 | ||||||||
\(109\) | 1.50982e10 | 0.0939894 | 0.0469947 | − | 0.998895i | \(-0.485036\pi\) | ||||
0.0469947 | + | 0.998895i | \(0.485036\pi\) | |||||||
\(110\) | −7.17529e9 | −0.0424796 | ||||||||
\(111\) | −1.09602e11 | −0.617366 | ||||||||
\(112\) | 7.62159e10 | 0.408645 | ||||||||
\(113\) | 1.65861e11 | 0.846863 | 0.423431 | − | 0.905928i | \(-0.360826\pi\) | ||||
0.423431 | + | 0.905928i | \(0.360826\pi\) | |||||||
\(114\) | −2.47423e9 | −0.0120355 | ||||||||
\(115\) | −7.81085e10 | −0.362126 | ||||||||
\(116\) | −1.83397e11 | −0.810727 | ||||||||
\(117\) | 8.29588e10 | 0.349816 | ||||||||
\(118\) | −8.87305e9 | −0.0357044 | ||||||||
\(119\) | −1.32931e11 | −0.510644 | ||||||||
\(120\) | −3.12603e10 | −0.114682 | ||||||||
\(121\) | −2.36969e11 | −0.830561 | ||||||||
\(122\) | −1.20803e11 | −0.404669 | ||||||||
\(123\) | 1.09257e11 | 0.349921 | ||||||||
\(124\) | −1.30975e11 | −0.401207 | ||||||||
\(125\) | 2.38600e11 | 0.699304 | ||||||||
\(126\) | −1.70729e10 | −0.0478927 | ||||||||
\(127\) | 4.89021e11 | 1.31343 | 0.656715 | − | 0.754139i | \(-0.271945\pi\) | ||||
0.656715 | + | 0.754139i | \(0.271945\pi\) | |||||||
\(128\) | 3.49832e11 | 0.899922 | ||||||||
\(129\) | −4.35928e11 | −1.07441 | ||||||||
\(130\) | 4.58483e10 | 0.108302 | ||||||||
\(131\) | −5.90891e11 | −1.33818 | −0.669091 | − | 0.743181i | \(-0.733316\pi\) | ||||
−0.669091 | + | 0.743181i | \(0.733316\pi\) | |||||||
\(132\) | 1.01191e11 | 0.219779 | ||||||||
\(133\) | 1.91119e10 | 0.0398216 | ||||||||
\(134\) | −2.55256e11 | −0.510387 | ||||||||
\(135\) | −3.77294e10 | −0.0724176 | ||||||||
\(136\) | −2.79171e11 | −0.514525 | ||||||||
\(137\) | 5.20144e11 | 0.920789 | 0.460394 | − | 0.887714i | \(-0.347708\pi\) | ||||
0.460394 | + | 0.887714i | \(0.347708\pi\) | |||||||
\(138\) | −8.95894e10 | −0.152378 | ||||||||
\(139\) | 1.06455e10 | 0.0174014 | 0.00870072 | − | 0.999962i | \(-0.497230\pi\) | ||||
0.00870072 | + | 0.999962i | \(0.497230\pi\) | |||||||
\(140\) | 1.16015e11 | 0.182310 | ||||||||
\(141\) | 1.45382e11 | 0.219687 | ||||||||
\(142\) | 1.63218e11 | 0.237237 | ||||||||
\(143\) | −3.08898e11 | −0.431984 | ||||||||
\(144\) | 1.93186e11 | 0.260005 | ||||||||
\(145\) | −2.54614e11 | −0.329882 | ||||||||
\(146\) | −3.24021e11 | −0.404234 | ||||||||
\(147\) | −3.48613e11 | −0.418888 | ||||||||
\(148\) | 8.54249e11 | 0.988883 | ||||||||
\(149\) | 1.50398e12 | 1.67771 | 0.838856 | − | 0.544353i | \(-0.183225\pi\) | ||||
0.838856 | + | 0.544353i | \(0.183225\pi\) | |||||||
\(150\) | 1.26410e11 | 0.135919 | ||||||||
\(151\) | 1.56843e12 | 1.62590 | 0.812949 | − | 0.582335i | \(-0.197861\pi\) | ||||
0.812949 | + | 0.582335i | \(0.197861\pi\) | |||||||
\(152\) | 4.01371e10 | 0.0401242 | ||||||||
\(153\) | −3.36944e11 | −0.324904 | ||||||||
\(154\) | 6.35713e10 | 0.0591421 | ||||||||
\(155\) | −1.81835e11 | −0.163250 | ||||||||
\(156\) | −6.46588e11 | −0.560328 | ||||||||
\(157\) | 1.64554e12 | 1.37676 | 0.688382 | − | 0.725348i | \(-0.258321\pi\) | ||||
0.688382 | + | 0.725348i | \(0.258321\pi\) | |||||||
\(158\) | 4.84757e11 | 0.391661 | ||||||||
\(159\) | −9.25660e11 | −0.722382 | ||||||||
\(160\) | 3.70228e11 | 0.279132 | ||||||||
\(161\) | 6.92021e11 | 0.504170 | ||||||||
\(162\) | −4.32751e10 | −0.0304723 | ||||||||
\(163\) | −1.67635e11 | −0.114113 | −0.0570563 | − | 0.998371i | \(-0.518171\pi\) | ||||
−0.0570563 | + | 0.998371i | \(0.518171\pi\) | |||||||
\(164\) | −8.51557e11 | −0.560496 | ||||||||
\(165\) | 1.40486e11 | 0.0894275 | ||||||||
\(166\) | −3.19736e11 | −0.196878 | ||||||||
\(167\) | 2.31740e12 | 1.38058 | 0.690289 | − | 0.723534i | \(-0.257483\pi\) | ||||
0.690289 | + | 0.723534i | \(0.257483\pi\) | |||||||
\(168\) | 2.76958e11 | 0.159666 | ||||||||
\(169\) | 1.81623e11 | 0.101343 | ||||||||
\(170\) | −1.86217e11 | −0.100589 | ||||||||
\(171\) | 4.84433e10 | 0.0253370 | ||||||||
\(172\) | 3.39766e12 | 1.72097 | ||||||||
\(173\) | −7.66240e10 | −0.0375934 | −0.0187967 | − | 0.999823i | \(-0.505984\pi\) | ||||
−0.0187967 | + | 0.999823i | \(0.505984\pi\) | |||||||
\(174\) | −2.92039e11 | −0.138810 | ||||||||
\(175\) | −9.76436e11 | −0.449712 | ||||||||
\(176\) | −7.19332e11 | −0.321078 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | −5.42291e11 | −0.227469 | ||||||||
\(179\) | 4.03824e12 | 1.64248 | 0.821240 | − | 0.570582i | \(-0.193282\pi\) | ||||
0.821240 | + | 0.570582i | \(0.193282\pi\) | |||||||
\(180\) | 2.94066e11 | 0.115997 | ||||||||
\(181\) | 4.73737e12 | 1.81261 | 0.906306 | − | 0.422622i | \(-0.138890\pi\) | ||||
0.906306 | + | 0.422622i | \(0.138890\pi\) | |||||||
\(182\) | −4.06205e11 | −0.150783 | ||||||||
\(183\) | 2.36522e12 | 0.851905 | ||||||||
\(184\) | 1.45333e12 | 0.508001 | ||||||||
\(185\) | 1.18597e12 | 0.402373 | ||||||||
\(186\) | −2.08562e11 | −0.0686932 | ||||||||
\(187\) | 1.25462e12 | 0.401219 | ||||||||
\(188\) | −1.13312e12 | −0.351890 | ||||||||
\(189\) | 3.34273e11 | 0.100823 | ||||||||
\(190\) | 2.67729e10 | 0.00784422 | ||||||||
\(191\) | 2.61020e12 | 0.743002 | 0.371501 | − | 0.928433i | \(-0.378843\pi\) | ||||
0.371501 | + | 0.928433i | \(0.378843\pi\) | |||||||
\(192\) | −1.20352e12 | −0.332888 | ||||||||
\(193\) | −2.73486e12 | −0.735139 | −0.367569 | − | 0.929996i | \(-0.619810\pi\) | ||||
−0.367569 | + | 0.929996i | \(0.619810\pi\) | |||||||
\(194\) | 5.46452e11 | 0.142772 | ||||||||
\(195\) | −8.97670e11 | −0.227996 | ||||||||
\(196\) | 2.71712e12 | 0.670966 | ||||||||
\(197\) | −2.98094e12 | −0.715796 | −0.357898 | − | 0.933761i | \(-0.616506\pi\) | ||||
−0.357898 | + | 0.933761i | \(0.616506\pi\) | |||||||
\(198\) | 1.61136e11 | 0.0376299 | ||||||||
\(199\) | 2.64798e12 | 0.601481 | 0.300741 | − | 0.953706i | \(-0.402766\pi\) | ||||
0.300741 | + | 0.953706i | \(0.402766\pi\) | |||||||
\(200\) | −2.05063e12 | −0.453129 | ||||||||
\(201\) | 4.99769e12 | 1.07446 | ||||||||
\(202\) | 1.19691e12 | 0.250398 | ||||||||
\(203\) | 2.25582e12 | 0.459278 | ||||||||
\(204\) | 2.62617e12 | 0.520423 | ||||||||
\(205\) | −1.18223e12 | −0.228064 | ||||||||
\(206\) | 6.77472e11 | 0.127239 | ||||||||
\(207\) | 1.75408e12 | 0.320784 | ||||||||
\(208\) | 4.59635e12 | 0.818587 | ||||||||
\(209\) | −1.80379e11 | −0.0312883 | ||||||||
\(210\) | 1.84740e11 | 0.0312145 | ||||||||
\(211\) | 5.05129e12 | 0.831474 | 0.415737 | − | 0.909485i | \(-0.363524\pi\) | ||||
0.415737 | + | 0.909485i | \(0.363524\pi\) | |||||||
\(212\) | 7.21467e12 | 1.15710 | ||||||||
\(213\) | −3.19567e12 | −0.499430 | ||||||||
\(214\) | −7.46830e11 | −0.113749 | ||||||||
\(215\) | 4.71703e12 | 0.700257 | ||||||||
\(216\) | 7.02012e11 | 0.101589 | ||||||||
\(217\) | 1.61101e12 | 0.227284 | ||||||||
\(218\) | −1.87386e11 | −0.0257767 | ||||||||
\(219\) | 6.34405e12 | 0.850989 | ||||||||
\(220\) | −1.09496e12 | −0.143243 | ||||||||
\(221\) | −8.01668e12 | −1.02291 | ||||||||
\(222\) | 1.36029e12 | 0.169313 | ||||||||
\(223\) | −1.15280e13 | −1.39983 | −0.699917 | − | 0.714224i | \(-0.746780\pi\) | ||||
−0.699917 | + | 0.714224i | \(0.746780\pi\) | |||||||
\(224\) | −3.28013e12 | −0.388621 | ||||||||
\(225\) | −2.47499e12 | −0.286135 | ||||||||
\(226\) | −2.05853e12 | −0.232253 | ||||||||
\(227\) | −1.82623e12 | −0.201101 | −0.100550 | − | 0.994932i | \(-0.532060\pi\) | ||||
−0.100550 | + | 0.994932i | \(0.532060\pi\) | |||||||
\(228\) | −3.77571e11 | −0.0405842 | ||||||||
\(229\) | −1.06757e12 | −0.112022 | −0.0560108 | − | 0.998430i | \(-0.517838\pi\) | ||||
−0.0560108 | + | 0.998430i | \(0.517838\pi\) | |||||||
\(230\) | 9.69418e11 | 0.0993135 | ||||||||
\(231\) | −1.24467e12 | −0.124505 | ||||||||
\(232\) | 4.73748e12 | 0.462768 | ||||||||
\(233\) | 1.52920e13 | 1.45884 | 0.729420 | − | 0.684066i | \(-0.239790\pi\) | ||||
0.729420 | + | 0.684066i | \(0.239790\pi\) | |||||||
\(234\) | −1.02962e12 | −0.0959374 | ||||||||
\(235\) | −1.57313e12 | −0.143183 | ||||||||
\(236\) | −1.35404e12 | −0.120397 | ||||||||
\(237\) | −9.49112e12 | −0.824521 | ||||||||
\(238\) | 1.64983e12 | 0.140045 | ||||||||
\(239\) | −1.01553e13 | −0.842372 | −0.421186 | − | 0.906974i | \(-0.638386\pi\) | ||||
−0.421186 | + | 0.906974i | \(0.638386\pi\) | |||||||
\(240\) | −2.09041e12 | −0.169461 | ||||||||
\(241\) | −1.22766e13 | −0.972714 | −0.486357 | − | 0.873760i | \(-0.661674\pi\) | ||||
−0.486357 | + | 0.873760i | \(0.661674\pi\) | |||||||
\(242\) | 2.94106e12 | 0.227782 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −1.84348e13 | −1.36456 | ||||||||
\(245\) | 3.77223e12 | 0.273014 | ||||||||
\(246\) | −1.35601e12 | −0.0959662 | ||||||||
\(247\) | 1.15258e12 | 0.0797696 | ||||||||
\(248\) | 3.38331e12 | 0.229011 | ||||||||
\(249\) | 6.26015e12 | 0.414465 | ||||||||
\(250\) | −2.96131e12 | −0.191785 | ||||||||
\(251\) | 1.41141e13 | 0.894225 | 0.447112 | − | 0.894478i | \(-0.352452\pi\) | ||||
0.447112 | + | 0.894478i | \(0.352452\pi\) | |||||||
\(252\) | −2.60535e12 | −0.161496 | ||||||||
\(253\) | −6.53136e12 | −0.396133 | ||||||||
\(254\) | −6.06933e12 | −0.360209 | ||||||||
\(255\) | 3.64596e12 | 0.211759 | ||||||||
\(256\) | 5.80145e12 | 0.329774 | ||||||||
\(257\) | 1.81778e13 | 1.01137 | 0.505683 | − | 0.862719i | \(-0.331240\pi\) | ||||
0.505683 | + | 0.862719i | \(0.331240\pi\) | |||||||
\(258\) | 5.41038e12 | 0.294659 | ||||||||
\(259\) | −1.05074e13 | −0.560204 | ||||||||
\(260\) | 6.99652e12 | 0.365198 | ||||||||
\(261\) | 5.71787e12 | 0.292221 | ||||||||
\(262\) | 7.33365e12 | 0.366998 | ||||||||
\(263\) | 1.38536e13 | 0.678902 | 0.339451 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339451 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(264\) | −2.61395e12 | −0.125452 | ||||||||
\(265\) | 1.00163e13 | 0.470819 | ||||||||
\(266\) | −2.37201e11 | −0.0109211 | ||||||||
\(267\) | 1.06176e13 | 0.478866 | ||||||||
\(268\) | −3.89524e13 | −1.72105 | ||||||||
\(269\) | −1.54482e13 | −0.668715 | −0.334357 | − | 0.942446i | \(-0.608519\pi\) | ||||
−0.334357 | + | 0.942446i | \(0.608519\pi\) | |||||||
\(270\) | 4.68266e11 | 0.0198606 | ||||||||
\(271\) | 3.07070e13 | 1.27616 | 0.638082 | − | 0.769969i | \(-0.279728\pi\) | ||||
0.638082 | + | 0.769969i | \(0.279728\pi\) | |||||||
\(272\) | −1.86685e13 | −0.760290 | ||||||||
\(273\) | 7.95313e12 | 0.317427 | ||||||||
\(274\) | −6.45559e12 | −0.252527 | ||||||||
\(275\) | 9.21569e12 | 0.353344 | ||||||||
\(276\) | −1.36715e13 | −0.513825 | ||||||||
\(277\) | 1.11150e13 | 0.409514 | 0.204757 | − | 0.978813i | \(-0.434360\pi\) | ||||
0.204757 | + | 0.978813i | \(0.434360\pi\) | |||||||
\(278\) | −1.32123e11 | −0.00477236 | ||||||||
\(279\) | 4.08346e12 | 0.144612 | ||||||||
\(280\) | −2.99687e12 | −0.104064 | ||||||||
\(281\) | 3.48370e13 | 1.18620 | 0.593098 | − | 0.805130i | \(-0.297905\pi\) | ||||
0.593098 | + | 0.805130i | \(0.297905\pi\) | |||||||
\(282\) | −1.80436e12 | −0.0602494 | ||||||||
\(283\) | 1.58891e13 | 0.520324 | 0.260162 | − | 0.965565i | \(-0.416224\pi\) | ||||
0.260162 | + | 0.965565i | \(0.416224\pi\) | |||||||
\(284\) | 2.49073e13 | 0.799975 | ||||||||
\(285\) | −5.24189e11 | −0.0165136 | ||||||||
\(286\) | 3.83379e12 | 0.118472 | ||||||||
\(287\) | 1.04743e13 | 0.317522 | ||||||||
\(288\) | −8.31421e12 | −0.247265 | ||||||||
\(289\) | −1.71150e12 | −0.0499389 | ||||||||
\(290\) | 3.16006e12 | 0.0904704 | ||||||||
\(291\) | −1.06991e13 | −0.300562 | ||||||||
\(292\) | −4.94461e13 | −1.36309 | ||||||||
\(293\) | −6.51516e13 | −1.76260 | −0.881299 | − | 0.472560i | \(-0.843330\pi\) | ||||
−0.881299 | + | 0.472560i | \(0.843330\pi\) | |||||||
\(294\) | 4.32670e12 | 0.114880 | ||||||||
\(295\) | −1.87984e12 | −0.0489891 | ||||||||
\(296\) | −2.20668e13 | −0.564461 | ||||||||
\(297\) | −3.15489e12 | −0.0792181 | ||||||||
\(298\) | −1.86662e13 | −0.460114 | ||||||||
\(299\) | 4.17337e13 | 1.00994 | ||||||||
\(300\) | 1.92903e13 | 0.458324 | ||||||||
\(301\) | −4.17917e13 | −0.974933 | ||||||||
\(302\) | −1.94661e13 | −0.445904 | ||||||||
\(303\) | −2.34345e13 | −0.527135 | ||||||||
\(304\) | 2.68401e12 | 0.0592898 | ||||||||
\(305\) | −2.55933e13 | −0.555236 | ||||||||
\(306\) | 4.18187e12 | 0.0891051 | ||||||||
\(307\) | −6.94381e12 | −0.145324 | −0.0726619 | − | 0.997357i | \(-0.523149\pi\) | ||||
−0.0726619 | + | 0.997357i | \(0.523149\pi\) | |||||||
\(308\) | 9.70107e12 | 0.199430 | ||||||||
\(309\) | −1.32643e13 | −0.267863 | ||||||||
\(310\) | 2.25678e12 | 0.0447714 | ||||||||
\(311\) | 9.11794e13 | 1.77711 | 0.888555 | − | 0.458770i | \(-0.151710\pi\) | ||||
0.888555 | + | 0.458770i | \(0.151710\pi\) | |||||||
\(312\) | 1.67025e13 | 0.319839 | ||||||||
\(313\) | 4.52842e13 | 0.852026 | 0.426013 | − | 0.904717i | \(-0.359918\pi\) | ||||
0.426013 | + | 0.904717i | \(0.359918\pi\) | |||||||
\(314\) | −2.04230e13 | −0.377579 | ||||||||
\(315\) | −3.61706e12 | −0.0657124 | ||||||||
\(316\) | 7.39746e13 | 1.32070 | ||||||||
\(317\) | 5.55014e13 | 0.973818 | 0.486909 | − | 0.873453i | \(-0.338124\pi\) | ||||
0.486909 | + | 0.873453i | \(0.338124\pi\) | |||||||
\(318\) | 1.14885e13 | 0.198114 | ||||||||
\(319\) | −2.12906e13 | −0.360860 | ||||||||
\(320\) | 1.30229e13 | 0.216962 | ||||||||
\(321\) | 1.46223e13 | 0.239462 | ||||||||
\(322\) | −8.58880e12 | −0.138269 | ||||||||
\(323\) | −4.68129e12 | −0.0740887 | ||||||||
\(324\) | −6.60384e12 | −0.102754 | ||||||||
\(325\) | −5.88859e13 | −0.900851 | ||||||||
\(326\) | 2.08055e12 | 0.0312955 | ||||||||
\(327\) | 3.66886e12 | 0.0542648 | ||||||||
\(328\) | 2.19972e13 | 0.319935 | ||||||||
\(329\) | 1.39375e13 | 0.199346 | ||||||||
\(330\) | −1.74360e12 | −0.0245256 | ||||||||
\(331\) | −1.22787e14 | −1.69862 | −0.849311 | − | 0.527892i | \(-0.822982\pi\) | ||||
−0.849311 | + | 0.527892i | \(0.822982\pi\) | |||||||
\(332\) | −4.87921e13 | −0.663881 | ||||||||
\(333\) | −2.66333e13 | −0.356437 | ||||||||
\(334\) | −2.87617e13 | −0.378625 | ||||||||
\(335\) | −5.40784e13 | −0.700289 | ||||||||
\(336\) | 1.85205e13 | 0.235932 | ||||||||
\(337\) | 1.15972e14 | 1.45341 | 0.726706 | − | 0.686948i | \(-0.241050\pi\) | ||||
0.726706 | + | 0.686948i | \(0.241050\pi\) | |||||||
\(338\) | −2.25416e12 | −0.0277934 | ||||||||
\(339\) | 4.03042e13 | 0.488936 | ||||||||
\(340\) | −2.84169e13 | −0.339190 | ||||||||
\(341\) | −1.52048e13 | −0.178580 | ||||||||
\(342\) | −6.01238e11 | −0.00694869 | ||||||||
\(343\) | −7.94849e13 | −0.903997 | ||||||||
\(344\) | −8.77675e13 | −0.982341 | ||||||||
\(345\) | −1.89804e13 | −0.209074 | ||||||||
\(346\) | 9.50994e11 | 0.0103100 | ||||||||
\(347\) | 8.80751e13 | 0.939812 | 0.469906 | − | 0.882716i | \(-0.344288\pi\) | ||||
0.469906 | + | 0.882716i | \(0.344288\pi\) | |||||||
\(348\) | −4.45656e13 | −0.468073 | ||||||||
\(349\) | −1.17002e14 | −1.20963 | −0.604816 | − | 0.796365i | \(-0.706753\pi\) | ||||
−0.604816 | + | 0.796365i | \(0.706753\pi\) | |||||||
\(350\) | 1.21187e13 | 0.123334 | ||||||||
\(351\) | 2.01590e13 | 0.201967 | ||||||||
\(352\) | 3.09581e13 | 0.305344 | ||||||||
\(353\) | −7.06831e13 | −0.686364 | −0.343182 | − | 0.939269i | \(-0.611505\pi\) | ||||
−0.343182 | + | 0.939269i | \(0.611505\pi\) | |||||||
\(354\) | −2.15615e12 | −0.0206140 | ||||||||
\(355\) | 3.45793e13 | 0.325507 | ||||||||
\(356\) | −8.27544e13 | −0.767037 | ||||||||
\(357\) | −3.23023e13 | −0.294821 | ||||||||
\(358\) | −5.01193e13 | −0.450452 | ||||||||
\(359\) | 3.49060e12 | 0.0308945 | 0.0154472 | − | 0.999881i | \(-0.495083\pi\) | ||||
0.0154472 | + | 0.999881i | \(0.495083\pi\) | |||||||
\(360\) | −7.59624e12 | −0.0662117 | ||||||||
\(361\) | −1.15817e14 | −0.994222 | ||||||||
\(362\) | −5.87963e13 | −0.497110 | ||||||||
\(363\) | −5.75834e13 | −0.479525 | ||||||||
\(364\) | −6.19874e13 | −0.508447 | ||||||||
\(365\) | −6.86469e13 | −0.554639 | ||||||||
\(366\) | −2.93552e13 | −0.233636 | ||||||||
\(367\) | 2.40276e13 | 0.188385 | 0.0941927 | − | 0.995554i | \(-0.469973\pi\) | ||||
0.0941927 | + | 0.995554i | \(0.469973\pi\) | |||||||
\(368\) | 9.71854e13 | 0.750651 | ||||||||
\(369\) | 2.65494e13 | 0.202027 | ||||||||
\(370\) | −1.47193e13 | −0.110351 | ||||||||
\(371\) | −8.87416e13 | −0.655497 | ||||||||
\(372\) | −3.18269e13 | −0.231637 | ||||||||
\(373\) | 4.62694e13 | 0.331814 | 0.165907 | − | 0.986141i | \(-0.446945\pi\) | ||||
0.165907 | + | 0.986141i | \(0.446945\pi\) | |||||||
\(374\) | −1.55713e13 | −0.110035 | ||||||||
\(375\) | 5.79799e13 | 0.403743 | ||||||||
\(376\) | 2.92704e13 | 0.200861 | ||||||||
\(377\) | 1.36042e14 | 0.920014 | ||||||||
\(378\) | −4.14872e12 | −0.0276509 | ||||||||
\(379\) | −1.43879e14 | −0.945110 | −0.472555 | − | 0.881301i | \(-0.656668\pi\) | ||||
−0.472555 | + | 0.881301i | \(0.656668\pi\) | |||||||
\(380\) | 4.08557e12 | 0.0264511 | ||||||||
\(381\) | 1.18832e14 | 0.758309 | ||||||||
\(382\) | −3.23956e13 | −0.203769 | ||||||||
\(383\) | −1.48728e14 | −0.922149 | −0.461074 | − | 0.887362i | \(-0.652536\pi\) | ||||
−0.461074 | + | 0.887362i | \(0.652536\pi\) | |||||||
\(384\) | 8.50092e13 | 0.519570 | ||||||||
\(385\) | 1.34682e13 | 0.0811474 | ||||||||
\(386\) | 3.39428e13 | 0.201612 | ||||||||
\(387\) | −1.05930e14 | −0.620313 | ||||||||
\(388\) | 8.33893e13 | 0.481433 | ||||||||
\(389\) | −1.76673e14 | −1.00565 | −0.502827 | − | 0.864387i | \(-0.667707\pi\) | ||||
−0.502827 | + | 0.864387i | \(0.667707\pi\) | |||||||
\(390\) | 1.11411e13 | 0.0625280 | ||||||||
\(391\) | −1.69505e14 | −0.938016 | ||||||||
\(392\) | −7.01880e13 | −0.382992 | ||||||||
\(393\) | −1.43586e14 | −0.772600 | ||||||||
\(394\) | 3.69970e13 | 0.196308 | ||||||||
\(395\) | 1.02700e14 | 0.537388 | ||||||||
\(396\) | 2.45895e13 | 0.126890 | ||||||||
\(397\) | −6.00013e13 | −0.305361 | −0.152680 | − | 0.988276i | \(-0.548790\pi\) | ||||
−0.152680 | + | 0.988276i | \(0.548790\pi\) | |||||||
\(398\) | −3.28645e13 | −0.164957 | ||||||||
\(399\) | 4.64418e12 | 0.0229910 | ||||||||
\(400\) | −1.37128e14 | −0.669569 | ||||||||
\(401\) | 2.97986e14 | 1.43517 | 0.717583 | − | 0.696473i | \(-0.245248\pi\) | ||||
0.717583 | + | 0.696473i | \(0.245248\pi\) | |||||||
\(402\) | −6.20272e13 | −0.294672 | ||||||||
\(403\) | 9.71551e13 | 0.455290 | ||||||||
\(404\) | 1.82651e14 | 0.844353 | ||||||||
\(405\) | −9.16824e12 | −0.0418103 | ||||||||
\(406\) | −2.79974e13 | −0.125957 | ||||||||
\(407\) | 9.91697e13 | 0.440159 | ||||||||
\(408\) | −6.78386e13 | −0.297061 | ||||||||
\(409\) | −1.83676e14 | −0.793549 | −0.396774 | − | 0.917916i | \(-0.629870\pi\) | ||||
−0.396774 | + | 0.917916i | \(0.629870\pi\) | |||||||
\(410\) | 1.46729e13 | 0.0625467 | ||||||||
\(411\) | 1.26395e14 | 0.531618 | ||||||||
\(412\) | 1.03383e14 | 0.429057 | ||||||||
\(413\) | 1.66549e13 | 0.0682051 | ||||||||
\(414\) | −2.17702e13 | −0.0879754 | ||||||||
\(415\) | −6.77391e13 | −0.270131 | ||||||||
\(416\) | −1.97815e14 | −0.778476 | ||||||||
\(417\) | 2.58686e12 | 0.0100467 | ||||||||
\(418\) | 2.23872e12 | 0.00858085 | ||||||||
\(419\) | −3.37184e14 | −1.27553 | −0.637763 | − | 0.770233i | \(-0.720140\pi\) | ||||
−0.637763 | + | 0.770233i | \(0.720140\pi\) | |||||||
\(420\) | 2.81917e13 | 0.105257 | ||||||||
\(421\) | 4.41343e14 | 1.62639 | 0.813195 | − | 0.581991i | \(-0.197726\pi\) | ||||
0.813195 | + | 0.581991i | \(0.197726\pi\) | |||||||
\(422\) | −6.26924e13 | −0.228032 | ||||||||
\(423\) | 3.53278e13 | 0.126836 | ||||||||
\(424\) | −1.86368e14 | −0.660478 | ||||||||
\(425\) | 2.39170e14 | 0.836695 | ||||||||
\(426\) | 3.96620e13 | 0.136969 | ||||||||
\(427\) | 2.26750e14 | 0.773027 | ||||||||
\(428\) | −1.13967e14 | −0.383565 | ||||||||
\(429\) | −7.50623e13 | −0.249406 | ||||||||
\(430\) | −5.85440e13 | −0.192046 | ||||||||
\(431\) | −4.62208e14 | −1.49697 | −0.748483 | − | 0.663154i | \(-0.769218\pi\) | ||||
−0.748483 | + | 0.663154i | \(0.769218\pi\) | |||||||
\(432\) | 4.69443e13 | 0.150114 | ||||||||
\(433\) | −5.20774e13 | −0.164424 | −0.0822121 | − | 0.996615i | \(-0.526198\pi\) | ||||
−0.0822121 | + | 0.996615i | \(0.526198\pi\) | |||||||
\(434\) | −1.99945e13 | −0.0623329 | ||||||||
\(435\) | −6.18713e13 | −0.190457 | ||||||||
\(436\) | −2.85954e13 | −0.0869202 | ||||||||
\(437\) | 2.43702e13 | 0.0731494 | ||||||||
\(438\) | −7.87371e13 | −0.233384 | ||||||||
\(439\) | −2.17454e14 | −0.636520 | −0.318260 | − | 0.948004i | \(-0.603098\pi\) | ||||
−0.318260 | + | 0.948004i | \(0.603098\pi\) | |||||||
\(440\) | 2.82847e13 | 0.0817641 | ||||||||
\(441\) | −8.47130e13 | −0.241845 | ||||||||
\(442\) | 9.94964e13 | 0.280534 | ||||||||
\(443\) | −2.78979e14 | −0.776875 | −0.388438 | − | 0.921475i | \(-0.626985\pi\) | ||||
−0.388438 | + | 0.921475i | \(0.626985\pi\) | |||||||
\(444\) | 2.07582e14 | 0.570932 | ||||||||
\(445\) | −1.14890e14 | −0.312105 | ||||||||
\(446\) | 1.43076e14 | 0.383906 | ||||||||
\(447\) | 3.65467e14 | 0.968628 | ||||||||
\(448\) | −1.15380e14 | −0.302066 | ||||||||
\(449\) | 6.68167e14 | 1.72795 | 0.863973 | − | 0.503539i | \(-0.167969\pi\) | ||||
0.863973 | + | 0.503539i | \(0.167969\pi\) | |||||||
\(450\) | 3.07176e13 | 0.0784727 | ||||||||
\(451\) | −9.88571e13 | −0.249481 | ||||||||
\(452\) | −3.14135e14 | −0.783167 | ||||||||
\(453\) | 3.81130e14 | 0.938712 | ||||||||
\(454\) | 2.26657e13 | 0.0551521 | ||||||||
\(455\) | −8.60583e13 | −0.206885 | ||||||||
\(456\) | 9.75333e12 | 0.0231657 | ||||||||
\(457\) | 7.36922e13 | 0.172935 | 0.0864674 | − | 0.996255i | \(-0.472442\pi\) | ||||
0.0864674 | + | 0.996255i | \(0.472442\pi\) | |||||||
\(458\) | 1.32498e13 | 0.0307220 | ||||||||
\(459\) | −8.18773e13 | −0.187583 | ||||||||
\(460\) | 1.47935e14 | 0.334890 | ||||||||
\(461\) | 5.66378e13 | 0.126693 | 0.0633463 | − | 0.997992i | \(-0.479823\pi\) | ||||
0.0633463 | + | 0.997992i | \(0.479823\pi\) | |||||||
\(462\) | 1.54478e13 | 0.0341457 | ||||||||
\(463\) | −6.02905e14 | −1.31690 | −0.658451 | − | 0.752624i | \(-0.728788\pi\) | ||||
−0.658451 | + | 0.752624i | \(0.728788\pi\) | |||||||
\(464\) | 3.16800e14 | 0.683812 | ||||||||
\(465\) | −4.41858e13 | −0.0942523 | ||||||||
\(466\) | −1.89792e14 | −0.400088 | ||||||||
\(467\) | 9.34292e14 | 1.94644 | 0.973218 | − | 0.229886i | \(-0.0738354\pi\) | ||||
0.973218 | + | 0.229886i | \(0.0738354\pi\) | |||||||
\(468\) | −1.57121e14 | −0.323505 | ||||||||
\(469\) | 4.79121e14 | 0.974976 | ||||||||
\(470\) | 1.95244e13 | 0.0392680 | ||||||||
\(471\) | 3.99865e14 | 0.794875 | ||||||||
\(472\) | 3.49772e13 | 0.0687234 | ||||||||
\(473\) | 3.94434e14 | 0.766016 | ||||||||
\(474\) | 1.17796e14 | 0.226126 | ||||||||
\(475\) | −3.43861e13 | −0.0652481 | ||||||||
\(476\) | 2.51767e14 | 0.472237 | ||||||||
\(477\) | −2.24935e14 | −0.417068 | ||||||||
\(478\) | 1.26039e14 | 0.231021 | ||||||||
\(479\) | 2.84742e14 | 0.515948 | 0.257974 | − | 0.966152i | \(-0.416945\pi\) | ||||
0.257974 | + | 0.966152i | \(0.416945\pi\) | |||||||
\(480\) | 8.99654e13 | 0.161157 | ||||||||
\(481\) | −6.33669e14 | −1.12219 | ||||||||
\(482\) | 1.52367e14 | 0.266768 | ||||||||
\(483\) | 1.68161e14 | 0.291083 | ||||||||
\(484\) | 4.48810e14 | 0.768092 | ||||||||
\(485\) | 1.15771e14 | 0.195894 | ||||||||
\(486\) | −1.05158e13 | −0.0175932 | ||||||||
\(487\) | −1.18679e15 | −1.96320 | −0.981602 | − | 0.190941i | \(-0.938846\pi\) | ||||
−0.981602 | + | 0.190941i | \(0.938846\pi\) | |||||||
\(488\) | 4.76202e14 | 0.778902 | ||||||||
\(489\) | −4.07354e13 | −0.0658829 | ||||||||
\(490\) | −4.68178e13 | −0.0748743 | ||||||||
\(491\) | −3.24362e14 | −0.512959 | −0.256479 | − | 0.966550i | \(-0.582563\pi\) | ||||
−0.256479 | + | 0.966550i | \(0.582563\pi\) | |||||||
\(492\) | −2.06928e14 | −0.323602 | ||||||||
\(493\) | −5.52544e14 | −0.854493 | ||||||||
\(494\) | −1.43049e13 | −0.0218769 | ||||||||
\(495\) | 3.41381e13 | 0.0516310 | ||||||||
\(496\) | 2.26245e14 | 0.338400 | ||||||||
\(497\) | −3.06364e14 | −0.453187 | ||||||||
\(498\) | −7.76958e13 | −0.113668 | ||||||||
\(499\) | 1.00957e15 | 1.46078 | 0.730388 | − | 0.683033i | \(-0.239339\pi\) | ||||
0.730388 | + | 0.683033i | \(0.239339\pi\) | |||||||
\(500\) | −4.51900e14 | −0.646707 | ||||||||
\(501\) | 5.63129e14 | 0.797077 | ||||||||
\(502\) | −1.75172e14 | −0.245242 | ||||||||
\(503\) | −1.07256e15 | −1.48524 | −0.742619 | − | 0.669714i | \(-0.766416\pi\) | ||||
−0.742619 | + | 0.669714i | \(0.766416\pi\) | |||||||
\(504\) | 6.73008e13 | 0.0921833 | ||||||||
\(505\) | 2.53578e14 | 0.343564 | ||||||||
\(506\) | 8.10618e13 | 0.108640 | ||||||||
\(507\) | 4.41344e13 | 0.0585105 | ||||||||
\(508\) | −9.26187e14 | −1.21464 | ||||||||
\(509\) | 1.40656e15 | 1.82478 | 0.912391 | − | 0.409319i | \(-0.134234\pi\) | ||||
0.912391 | + | 0.409319i | \(0.134234\pi\) | |||||||
\(510\) | −4.52507e13 | −0.0580750 | ||||||||
\(511\) | 6.08194e14 | 0.772196 | ||||||||
\(512\) | −7.88459e14 | −0.990363 | ||||||||
\(513\) | 1.17717e13 | 0.0146283 | ||||||||
\(514\) | −2.25608e14 | −0.277368 | ||||||||
\(515\) | 1.43529e14 | 0.174582 | ||||||||
\(516\) | 8.25631e14 | 0.993602 | ||||||||
\(517\) | −1.31544e14 | −0.156629 | ||||||||
\(518\) | 1.30409e14 | 0.153636 | ||||||||
\(519\) | −1.86196e13 | −0.0217045 | ||||||||
\(520\) | −1.80732e14 | −0.208458 | ||||||||
\(521\) | −9.68497e14 | −1.10533 | −0.552663 | − | 0.833405i | \(-0.686388\pi\) | ||||
−0.552663 | + | 0.833405i | \(0.686388\pi\) | |||||||
\(522\) | −7.09655e13 | −0.0801419 | ||||||||
\(523\) | 5.77418e14 | 0.645254 | 0.322627 | − | 0.946526i | \(-0.395434\pi\) | ||||
0.322627 | + | 0.946526i | \(0.395434\pi\) | |||||||
\(524\) | 1.11913e15 | 1.23753 | ||||||||
\(525\) | −2.37274e14 | −0.259641 | ||||||||
\(526\) | −1.71940e14 | −0.186189 | ||||||||
\(527\) | −3.94603e14 | −0.422866 | ||||||||
\(528\) | −1.74798e14 | −0.185374 | ||||||||
\(529\) | −7.03905e13 | −0.0738767 | ||||||||
\(530\) | −1.24314e14 | −0.129122 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −3.61972e13 | −0.0368265 | ||||||||
\(533\) | 6.31672e14 | 0.636051 | ||||||||
\(534\) | −1.31777e14 | −0.131329 | ||||||||
\(535\) | −1.58223e14 | −0.156072 | ||||||||
\(536\) | 1.00621e15 | 0.982385 | ||||||||
\(537\) | 9.81292e14 | 0.948287 | ||||||||
\(538\) | 1.91731e14 | 0.183396 | ||||||||
\(539\) | 3.15430e14 | 0.298652 | ||||||||
\(540\) | 7.14580e13 | 0.0669708 | ||||||||
\(541\) | −3.42211e14 | −0.317474 | −0.158737 | − | 0.987321i | \(-0.550742\pi\) | ||||
−0.158737 | + | 0.987321i | \(0.550742\pi\) | |||||||
\(542\) | −3.81110e14 | −0.349989 | ||||||||
\(543\) | 1.15118e15 | 1.04651 | ||||||||
\(544\) | 8.03440e14 | 0.723035 | ||||||||
\(545\) | −3.96995e13 | −0.0353675 | ||||||||
\(546\) | −9.87077e13 | −0.0870546 | ||||||||
\(547\) | 1.11343e15 | 0.972148 | 0.486074 | − | 0.873918i | \(-0.338429\pi\) | ||||
0.486074 | + | 0.873918i | \(0.338429\pi\) | |||||||
\(548\) | −9.85132e14 | −0.851533 | ||||||||
\(549\) | 5.74750e14 | 0.491848 | ||||||||
\(550\) | −1.14378e14 | −0.0969049 | ||||||||
\(551\) | 7.94407e13 | 0.0666360 | ||||||||
\(552\) | 3.53158e14 | 0.293295 | ||||||||
\(553\) | −9.09899e14 | −0.748178 | ||||||||
\(554\) | −1.37950e14 | −0.112310 | ||||||||
\(555\) | 2.88191e14 | 0.232310 | ||||||||
\(556\) | −2.01622e13 | −0.0160926 | ||||||||
\(557\) | 1.77163e15 | 1.40013 | 0.700066 | − | 0.714078i | \(-0.253154\pi\) | ||||
0.700066 | + | 0.714078i | \(0.253154\pi\) | |||||||
\(558\) | −5.06806e13 | −0.0396601 | ||||||||
\(559\) | −2.52033e15 | −1.95296 | ||||||||
\(560\) | −2.00404e14 | −0.153770 | ||||||||
\(561\) | 3.04872e14 | 0.231644 | ||||||||
\(562\) | −4.32369e14 | −0.325315 | ||||||||
\(563\) | 1.13752e15 | 0.847542 | 0.423771 | − | 0.905769i | \(-0.360706\pi\) | ||||
0.423771 | + | 0.905769i | \(0.360706\pi\) | |||||||
\(564\) | −2.75348e14 | −0.203164 | ||||||||
\(565\) | −4.36119e14 | −0.318668 | ||||||||
\(566\) | −1.97202e14 | −0.142699 | ||||||||
\(567\) | 8.12283e13 | 0.0582104 | ||||||||
\(568\) | −6.43400e14 | −0.456631 | ||||||||
\(569\) | 2.22030e15 | 1.56061 | 0.780303 | − | 0.625402i | \(-0.215065\pi\) | ||||
0.780303 | + | 0.625402i | \(0.215065\pi\) | |||||||
\(570\) | 6.50580e12 | 0.00452886 | ||||||||
\(571\) | 1.21610e15 | 0.838437 | 0.419218 | − | 0.907885i | \(-0.362304\pi\) | ||||
0.419218 | + | 0.907885i | \(0.362304\pi\) | |||||||
\(572\) | 5.85042e14 | 0.399493 | ||||||||
\(573\) | 6.34278e14 | 0.428972 | ||||||||
\(574\) | −1.29998e14 | −0.0870807 | ||||||||
\(575\) | −1.24509e15 | −0.826088 | ||||||||
\(576\) | −2.92456e14 | −0.192193 | ||||||||
\(577\) | −2.57058e15 | −1.67326 | −0.836631 | − | 0.547767i | \(-0.815478\pi\) | ||||
−0.836631 | + | 0.547767i | \(0.815478\pi\) | |||||||
\(578\) | 2.12417e13 | 0.0136958 | ||||||||
\(579\) | −6.64570e14 | −0.424432 | ||||||||
\(580\) | 4.82230e14 | 0.305070 | ||||||||
\(581\) | 6.00151e14 | 0.376090 | ||||||||
\(582\) | 1.32788e14 | 0.0824294 | ||||||||
\(583\) | 8.37551e14 | 0.515032 | ||||||||
\(584\) | 1.27728e15 | 0.778064 | ||||||||
\(585\) | −2.18134e14 | −0.131633 | ||||||||
\(586\) | 8.08608e14 | 0.483394 | ||||||||
\(587\) | 8.26236e14 | 0.489322 | 0.244661 | − | 0.969609i | \(-0.421323\pi\) | ||||
0.244661 | + | 0.969609i | \(0.421323\pi\) | |||||||
\(588\) | 6.60260e14 | 0.387382 | ||||||||
\(589\) | 5.67332e13 | 0.0329764 | ||||||||
\(590\) | 2.33310e13 | 0.0134353 | ||||||||
\(591\) | −7.24369e14 | −0.413265 | ||||||||
\(592\) | −1.47563e15 | −0.834079 | ||||||||
\(593\) | 2.20813e15 | 1.23659 | 0.618293 | − | 0.785948i | \(-0.287824\pi\) | ||||
0.618293 | + | 0.785948i | \(0.287824\pi\) | |||||||
\(594\) | 3.91560e13 | 0.0217256 | ||||||||
\(595\) | 3.49533e14 | 0.192152 | ||||||||
\(596\) | −2.84848e15 | −1.55153 | ||||||||
\(597\) | 6.43458e14 | 0.347265 | ||||||||
\(598\) | −5.17965e14 | −0.276977 | ||||||||
\(599\) | 2.14568e15 | 1.13689 | 0.568443 | − | 0.822722i | \(-0.307546\pi\) | ||||
0.568443 | + | 0.822722i | \(0.307546\pi\) | |||||||
\(600\) | −4.98303e14 | −0.261614 | ||||||||
\(601\) | 1.03034e15 | 0.536006 | 0.268003 | − | 0.963418i | \(-0.413636\pi\) | ||||
0.268003 | + | 0.963418i | \(0.413636\pi\) | |||||||
\(602\) | 5.18685e14 | 0.267376 | ||||||||
\(603\) | 1.21444e15 | 0.620340 | ||||||||
\(604\) | −2.97056e15 | −1.50361 | ||||||||
\(605\) | 6.23092e14 | 0.312534 | ||||||||
\(606\) | 2.90850e14 | 0.144567 | ||||||||
\(607\) | 6.29663e14 | 0.310149 | 0.155074 | − | 0.987903i | \(-0.450438\pi\) | ||||
0.155074 | + | 0.987903i | \(0.450438\pi\) | |||||||
\(608\) | −1.15513e14 | −0.0563845 | ||||||||
\(609\) | 5.48164e14 | 0.265164 | ||||||||
\(610\) | 3.17643e14 | 0.152274 | ||||||||
\(611\) | 8.40530e14 | 0.399325 | ||||||||
\(612\) | 6.38159e14 | 0.300466 | ||||||||
\(613\) | 4.61880e14 | 0.215524 | 0.107762 | − | 0.994177i | \(-0.465631\pi\) | ||||
0.107762 | + | 0.994177i | \(0.465631\pi\) | |||||||
\(614\) | 8.61808e13 | 0.0398552 | ||||||||
\(615\) | −2.87282e14 | −0.131673 | ||||||||
\(616\) | −2.50596e14 | −0.113836 | ||||||||
\(617\) | 2.25606e15 | 1.01574 | 0.507870 | − | 0.861434i | \(-0.330433\pi\) | ||||
0.507870 | + | 0.861434i | \(0.330433\pi\) | |||||||
\(618\) | 1.64626e14 | 0.0734617 | ||||||||
\(619\) | 3.97848e13 | 0.0175962 | 0.00879810 | − | 0.999961i | \(-0.497199\pi\) | ||||
0.00879810 | + | 0.999961i | \(0.497199\pi\) | |||||||
\(620\) | 3.44388e14 | 0.150971 | ||||||||
\(621\) | 4.26242e14 | 0.185205 | ||||||||
\(622\) | −1.13164e15 | −0.487374 | ||||||||
\(623\) | 1.01789e15 | 0.434528 | ||||||||
\(624\) | 1.11691e15 | 0.472612 | ||||||||
\(625\) | 1.41921e15 | 0.595261 | ||||||||
\(626\) | −5.62030e14 | −0.233669 | ||||||||
\(627\) | −4.38322e13 | −0.0180643 | ||||||||
\(628\) | −3.11658e15 | −1.27321 | ||||||||
\(629\) | 2.57370e15 | 1.04227 | ||||||||
\(630\) | 4.48919e13 | 0.0180217 | ||||||||
\(631\) | −3.85979e15 | −1.53604 | −0.768018 | − | 0.640428i | \(-0.778757\pi\) | ||||
−0.768018 | + | 0.640428i | \(0.778757\pi\) | |||||||
\(632\) | −1.91089e15 | −0.753864 | ||||||||
\(633\) | 1.22746e15 | 0.480052 | ||||||||
\(634\) | −6.88837e14 | −0.267070 | ||||||||
\(635\) | −1.28584e15 | −0.494234 | ||||||||
\(636\) | 1.75316e15 | 0.668050 | ||||||||
\(637\) | −2.01552e15 | −0.761413 | ||||||||
\(638\) | 2.64241e14 | 0.0989663 | ||||||||
\(639\) | −7.76548e14 | −0.288346 | ||||||||
\(640\) | −9.19857e14 | −0.338634 | ||||||||
\(641\) | 3.34095e15 | 1.21941 | 0.609707 | − | 0.792627i | \(-0.291287\pi\) | ||||
0.609707 | + | 0.792627i | \(0.291287\pi\) | |||||||
\(642\) | −1.81480e14 | −0.0656728 | ||||||||
\(643\) | −2.23408e15 | −0.801563 | −0.400781 | − | 0.916174i | \(-0.631261\pi\) | ||||
−0.400781 | + | 0.916174i | \(0.631261\pi\) | |||||||
\(644\) | −1.31066e15 | −0.466250 | ||||||||
\(645\) | 1.14624e15 | 0.404294 | ||||||||
\(646\) | 5.81004e13 | 0.0203189 | ||||||||
\(647\) | −5.72708e15 | −1.98591 | −0.992956 | − | 0.118486i | \(-0.962196\pi\) | ||||
−0.992956 | + | 0.118486i | \(0.962196\pi\) | |||||||
\(648\) | 1.70589e14 | 0.0586527 | ||||||||
\(649\) | −1.57190e14 | −0.0535896 | ||||||||
\(650\) | 7.30844e14 | 0.247059 | ||||||||
\(651\) | 3.91475e14 | 0.131223 | ||||||||
\(652\) | 3.17495e14 | 0.105530 | ||||||||
\(653\) | −5.26368e15 | −1.73487 | −0.867435 | − | 0.497551i | \(-0.834233\pi\) | ||||
−0.867435 | + | 0.497551i | \(0.834233\pi\) | |||||||
\(654\) | −4.55349e13 | −0.0148822 | ||||||||
\(655\) | 1.55370e15 | 0.503548 | ||||||||
\(656\) | 1.47098e15 | 0.472753 | ||||||||
\(657\) | 1.54160e15 | 0.491319 | ||||||||
\(658\) | −1.72981e14 | −0.0546709 | ||||||||
\(659\) | −3.25334e13 | −0.0101967 | −0.00509835 | − | 0.999987i | \(-0.501623\pi\) | ||||
−0.00509835 | + | 0.999987i | \(0.501623\pi\) | |||||||
\(660\) | −2.66075e14 | −0.0827014 | ||||||||
\(661\) | 3.05435e15 | 0.941479 | 0.470739 | − | 0.882272i | \(-0.343987\pi\) | ||||
0.470739 | + | 0.882272i | \(0.343987\pi\) | |||||||
\(662\) | 1.52393e15 | 0.465849 | ||||||||
\(663\) | −1.94805e15 | −0.590577 | ||||||||
\(664\) | 1.26039e15 | 0.378948 | ||||||||
\(665\) | −5.02532e13 | −0.0149846 | ||||||||
\(666\) | 3.30551e14 | 0.0977530 | ||||||||
\(667\) | 2.87647e15 | 0.843660 | ||||||||
\(668\) | −4.38908e15 | −1.27674 | ||||||||
\(669\) | −2.80130e15 | −0.808194 | ||||||||
\(670\) | 6.71176e14 | 0.192055 | ||||||||
\(671\) | −2.14009e15 | −0.607377 | ||||||||
\(672\) | −7.97071e14 | −0.224371 | ||||||||
\(673\) | 7.74289e14 | 0.216182 | 0.108091 | − | 0.994141i | \(-0.465526\pi\) | ||||
0.108091 | + | 0.994141i | \(0.465526\pi\) | |||||||
\(674\) | −1.43935e15 | −0.398600 | ||||||||
\(675\) | −6.01424e14 | −0.165200 | ||||||||
\(676\) | −3.43987e14 | −0.0937208 | ||||||||
\(677\) | −7.12871e14 | −0.192652 | −0.0963260 | − | 0.995350i | \(-0.530709\pi\) | ||||
−0.0963260 | + | 0.995350i | \(0.530709\pi\) | |||||||
\(678\) | −5.00223e14 | −0.134091 | ||||||||
\(679\) | −1.02570e15 | −0.272733 | ||||||||
\(680\) | 7.34059e14 | 0.193612 | ||||||||
\(681\) | −4.43774e14 | −0.116106 | ||||||||
\(682\) | 1.88710e14 | 0.0489757 | ||||||||
\(683\) | 3.21628e15 | 0.828018 | 0.414009 | − | 0.910273i | \(-0.364128\pi\) | ||||
0.414009 | + | 0.910273i | \(0.364128\pi\) | |||||||
\(684\) | −9.17498e13 | −0.0234313 | ||||||||
\(685\) | −1.36768e15 | −0.346486 | ||||||||
\(686\) | 9.86501e14 | 0.247922 | ||||||||
\(687\) | −2.59420e14 | −0.0646757 | ||||||||
\(688\) | −5.86911e15 | −1.45156 | ||||||||
\(689\) | −5.35174e15 | −1.31307 | ||||||||
\(690\) | 2.35569e14 | 0.0573387 | ||||||||
\(691\) | −5.82369e15 | −1.40627 | −0.703135 | − | 0.711056i | \(-0.748217\pi\) | ||||
−0.703135 | + | 0.711056i | \(0.748217\pi\) | |||||||
\(692\) | 1.45123e14 | 0.0347658 | ||||||||
\(693\) | −3.02455e14 | −0.0718833 | ||||||||
\(694\) | −1.09312e15 | −0.257744 | ||||||||
\(695\) | −2.79916e13 | −0.00654804 | ||||||||
\(696\) | 1.15121e15 | 0.267179 | ||||||||
\(697\) | −2.56559e15 | −0.590754 | ||||||||
\(698\) | 1.45213e15 | 0.331743 | ||||||||
\(699\) | 3.71597e15 | 0.842262 | ||||||||
\(700\) | 1.84933e15 | 0.415888 | ||||||||
\(701\) | −5.89396e15 | −1.31510 | −0.657549 | − | 0.753412i | \(-0.728407\pi\) | ||||
−0.657549 | + | 0.753412i | \(0.728407\pi\) | |||||||
\(702\) | −2.50197e14 | −0.0553895 | ||||||||
\(703\) | −3.70027e14 | −0.0812792 | ||||||||
\(704\) | 1.08897e15 | 0.237337 | ||||||||
\(705\) | −3.82270e14 | −0.0826667 | ||||||||
\(706\) | 8.77260e14 | 0.188236 | ||||||||
\(707\) | −2.24663e15 | −0.478328 | ||||||||
\(708\) | −3.29032e14 | −0.0695112 | ||||||||
\(709\) | −4.66229e14 | −0.0977339 | −0.0488669 | − | 0.998805i | \(-0.515561\pi\) | ||||
−0.0488669 | + | 0.998805i | \(0.515561\pi\) | |||||||
\(710\) | −4.29170e14 | −0.0892706 | ||||||||
\(711\) | −2.30634e15 | −0.476037 | ||||||||
\(712\) | 2.13769e15 | 0.437830 | ||||||||
\(713\) | 2.05425e15 | 0.417504 | ||||||||
\(714\) | 4.00909e14 | 0.0808548 | ||||||||
\(715\) | 8.12225e14 | 0.162552 | ||||||||
\(716\) | −7.64827e15 | −1.51894 | ||||||||
\(717\) | −2.46774e15 | −0.486344 | ||||||||
\(718\) | −4.33225e13 | −0.00847284 | ||||||||
\(719\) | 7.59546e15 | 1.47416 | 0.737081 | − | 0.675805i | \(-0.236204\pi\) | ||||
0.737081 | + | 0.675805i | \(0.236204\pi\) | |||||||
\(720\) | −5.07969e14 | −0.0978382 | ||||||||
\(721\) | −1.27163e15 | −0.243062 | ||||||||
\(722\) | 1.43743e15 | 0.272666 | ||||||||
\(723\) | −2.98322e15 | −0.561596 | ||||||||
\(724\) | −8.97240e15 | −1.67628 | ||||||||
\(725\) | −4.05867e15 | −0.752531 | ||||||||
\(726\) | 7.14678e14 | 0.131510 | ||||||||
\(727\) | 6.98199e15 | 1.27509 | 0.637543 | − | 0.770414i | \(-0.279951\pi\) | ||||
0.637543 | + | 0.770414i | \(0.279951\pi\) | |||||||
\(728\) | 1.60124e15 | 0.290225 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 8.51989e14 | 0.152110 | ||||||||
\(731\) | 1.02365e16 | 1.81388 | ||||||||
\(732\) | −4.47965e15 | −0.787831 | ||||||||
\(733\) | −1.14815e15 | −0.200413 | −0.100207 | − | 0.994967i | \(-0.531950\pi\) | ||||
−0.100207 | + | 0.994967i | \(0.531950\pi\) | |||||||
\(734\) | −2.98211e14 | −0.0516649 | ||||||||
\(735\) | 9.16652e14 | 0.157625 | ||||||||
\(736\) | −4.18260e15 | −0.713868 | ||||||||
\(737\) | −4.52198e15 | −0.766051 | ||||||||
\(738\) | −3.29509e14 | −0.0554061 | ||||||||
\(739\) | 8.01991e15 | 1.33852 | 0.669261 | − | 0.743028i | \(-0.266611\pi\) | ||||
0.669261 | + | 0.743028i | \(0.266611\pi\) | |||||||
\(740\) | −2.24618e15 | −0.372109 | ||||||||
\(741\) | 2.80077e14 | 0.0460550 | ||||||||
\(742\) | 1.10139e15 | 0.179771 | ||||||||
\(743\) | −4.20001e15 | −0.680474 | −0.340237 | − | 0.940340i | \(-0.610507\pi\) | ||||
−0.340237 | + | 0.940340i | \(0.610507\pi\) | |||||||
\(744\) | 8.22144e14 | 0.132220 | ||||||||
\(745\) | −3.95460e15 | −0.631311 | ||||||||
\(746\) | −5.74257e14 | −0.0910003 | ||||||||
\(747\) | 1.52122e15 | 0.239292 | ||||||||
\(748\) | −2.37620e15 | −0.371042 | ||||||||
\(749\) | 1.40182e15 | 0.217291 | ||||||||
\(750\) | −7.19598e14 | −0.110727 | ||||||||
\(751\) | 6.91910e15 | 1.05689 | 0.528445 | − | 0.848967i | \(-0.322775\pi\) | ||||
0.528445 | + | 0.848967i | \(0.322775\pi\) | |||||||
\(752\) | 1.95734e15 | 0.296804 | ||||||||
\(753\) | 3.42972e15 | 0.516281 | ||||||||
\(754\) | −1.68844e15 | −0.252315 | ||||||||
\(755\) | −4.12408e15 | −0.611813 | ||||||||
\(756\) | −6.33100e14 | −0.0932400 | ||||||||
\(757\) | −1.00977e16 | −1.47636 | −0.738182 | − | 0.674601i | \(-0.764316\pi\) | ||||
−0.738182 | + | 0.674601i | \(0.764316\pi\) | |||||||
\(758\) | 1.78571e15 | 0.259197 | ||||||||
\(759\) | −1.58712e15 | −0.228707 | ||||||||
\(760\) | −1.05538e14 | −0.0150985 | ||||||||
\(761\) | 3.19854e14 | 0.0454293 | 0.0227146 | − | 0.999742i | \(-0.492769\pi\) | ||||
0.0227146 | + | 0.999742i | \(0.492769\pi\) | |||||||
\(762\) | −1.47485e15 | −0.207967 | ||||||||
\(763\) | 3.51728e14 | 0.0492404 | ||||||||
\(764\) | −4.94362e15 | −0.687118 | ||||||||
\(765\) | 8.85968e14 | 0.122259 | ||||||||
\(766\) | 1.84590e15 | 0.252900 | ||||||||
\(767\) | 1.00441e15 | 0.136627 | ||||||||
\(768\) | 1.40975e15 | 0.190395 | ||||||||
\(769\) | −2.19159e14 | −0.0293876 | −0.0146938 | − | 0.999892i | \(-0.504677\pi\) | ||||
−0.0146938 | + | 0.999892i | \(0.504677\pi\) | |||||||
\(770\) | −1.67156e14 | −0.0222548 | ||||||||
\(771\) | 4.41720e15 | 0.583913 | ||||||||
\(772\) | 5.17971e15 | 0.679846 | ||||||||
\(773\) | 1.29588e16 | 1.68879 | 0.844396 | − | 0.535720i | \(-0.179960\pi\) | ||||
0.844396 | + | 0.535720i | \(0.179960\pi\) | |||||||
\(774\) | 1.31472e15 | 0.170121 | ||||||||
\(775\) | −2.89853e15 | −0.372407 | ||||||||
\(776\) | −2.15409e15 | −0.274805 | ||||||||
\(777\) | −2.55330e15 | −0.323434 | ||||||||
\(778\) | 2.19272e15 | 0.275801 | ||||||||
\(779\) | 3.68861e14 | 0.0460688 | ||||||||
\(780\) | 1.70015e15 | 0.210847 | ||||||||
\(781\) | 2.89149e15 | 0.356075 | ||||||||
\(782\) | 2.10376e15 | 0.257252 | ||||||||
\(783\) | 1.38944e15 | 0.168714 | ||||||||
\(784\) | −4.69354e15 | −0.565930 | ||||||||
\(785\) | −4.32681e15 | −0.518066 | ||||||||
\(786\) | 1.78208e15 | 0.211886 | ||||||||
\(787\) | −1.52401e16 | −1.79939 | −0.899696 | − | 0.436517i | \(-0.856212\pi\) | ||||
−0.899696 | + | 0.436517i | \(0.856212\pi\) | |||||||
\(788\) | 5.64579e15 | 0.661959 | ||||||||
\(789\) | 3.36643e15 | 0.391964 | ||||||||
\(790\) | −1.27463e15 | −0.147379 | ||||||||
\(791\) | 3.86390e15 | 0.443666 | ||||||||
\(792\) | −6.35191e14 | −0.0724295 | ||||||||
\(793\) | 1.36746e16 | 1.54851 | ||||||||
\(794\) | 7.44687e14 | 0.0837454 | ||||||||
\(795\) | 2.43395e15 | 0.271827 | ||||||||
\(796\) | −5.01517e15 | −0.556242 | ||||||||
\(797\) | −1.44420e16 | −1.59077 | −0.795384 | − | 0.606106i | \(-0.792731\pi\) | ||||
−0.795384 | + | 0.606106i | \(0.792731\pi\) | |||||||
\(798\) | −5.76398e13 | −0.00630531 | ||||||||
\(799\) | −3.41388e15 | −0.370887 | ||||||||
\(800\) | 5.90161e15 | 0.636759 | ||||||||
\(801\) | 2.58007e15 | 0.276473 | ||||||||
\(802\) | −3.69836e15 | −0.393595 | ||||||||
\(803\) | −5.74019e15 | −0.606723 | ||||||||
\(804\) | −9.46543e15 | −0.993647 | ||||||||
\(805\) | −1.81962e15 | −0.189716 | ||||||||
\(806\) | −1.20581e15 | −0.124864 | ||||||||
\(807\) | −3.75392e15 | −0.386083 | ||||||||
\(808\) | −4.71819e15 | −0.481962 | ||||||||
\(809\) | −2.52611e15 | −0.256293 | −0.128146 | − | 0.991755i | \(-0.540903\pi\) | ||||
−0.128146 | + | 0.991755i | \(0.540903\pi\) | |||||||
\(810\) | 1.13789e14 | 0.0114665 | ||||||||
\(811\) | −1.71297e16 | −1.71450 | −0.857248 | − | 0.514905i | \(-0.827827\pi\) | ||||
−0.857248 | + | 0.514905i | \(0.827827\pi\) | |||||||
\(812\) | −4.27243e15 | −0.424734 | ||||||||
\(813\) | 7.46180e15 | 0.736793 | ||||||||
\(814\) | −1.23081e15 | −0.120714 | ||||||||
\(815\) | 4.40784e14 | 0.0429397 | ||||||||
\(816\) | −4.53644e15 | −0.438954 | ||||||||
\(817\) | −1.47173e15 | −0.141452 | ||||||||
\(818\) | 2.27963e15 | 0.217631 | ||||||||
\(819\) | 1.93261e15 | 0.183266 | ||||||||
\(820\) | 2.23910e15 | 0.210910 | ||||||||
\(821\) | 1.56247e16 | 1.46192 | 0.730960 | − | 0.682420i | \(-0.239073\pi\) | ||||
0.730960 | + | 0.682420i | \(0.239073\pi\) | |||||||
\(822\) | −1.56871e15 | −0.145797 | ||||||||
\(823\) | −1.41870e15 | −0.130976 | −0.0654881 | − | 0.997853i | \(-0.520860\pi\) | ||||
−0.0654881 | + | 0.997853i | \(0.520860\pi\) | |||||||
\(824\) | −2.67057e15 | −0.244909 | ||||||||
\(825\) | 2.23941e15 | 0.204003 | ||||||||
\(826\) | −2.06707e14 | −0.0187053 | ||||||||
\(827\) | 1.58941e16 | 1.42874 | 0.714372 | − | 0.699766i | \(-0.246713\pi\) | ||||
0.714372 | + | 0.699766i | \(0.246713\pi\) | |||||||
\(828\) | −3.32217e15 | −0.296657 | ||||||||
\(829\) | 9.82076e15 | 0.871154 | 0.435577 | − | 0.900151i | \(-0.356544\pi\) | ||||
0.435577 | + | 0.900151i | \(0.356544\pi\) | |||||||
\(830\) | 8.40722e14 | 0.0740837 | ||||||||
\(831\) | 2.70094e15 | 0.236433 | ||||||||
\(832\) | −6.95822e15 | −0.605090 | ||||||||
\(833\) | 8.18620e15 | 0.707188 | ||||||||
\(834\) | −3.21060e13 | −0.00275532 | ||||||||
\(835\) | −6.09344e15 | −0.519502 | ||||||||
\(836\) | 3.41632e14 | 0.0289350 | ||||||||
\(837\) | 9.92281e14 | 0.0834920 | ||||||||
\(838\) | 4.18485e15 | 0.349814 | ||||||||
\(839\) | −1.39823e16 | −1.16115 | −0.580576 | − | 0.814206i | \(-0.697173\pi\) | ||||
−0.580576 | + | 0.814206i | \(0.697173\pi\) | |||||||
\(840\) | −7.28240e14 | −0.0600812 | ||||||||
\(841\) | −2.82394e15 | −0.231461 | ||||||||
\(842\) | −5.47759e15 | −0.446039 | ||||||||
\(843\) | 8.46540e15 | 0.684851 | ||||||||
\(844\) | −9.56695e15 | −0.768936 | ||||||||
\(845\) | −4.77564e14 | −0.0381347 | ||||||||
\(846\) | −4.38459e14 | −0.0347850 | ||||||||
\(847\) | −5.52044e15 | −0.435126 | ||||||||
\(848\) | −1.24626e16 | −0.975959 | ||||||||
\(849\) | 3.86105e15 | 0.300409 | ||||||||
\(850\) | −2.96838e15 | −0.229464 | ||||||||
\(851\) | −1.33983e16 | −1.02905 | ||||||||
\(852\) | 6.05248e15 | 0.461866 | ||||||||
\(853\) | 2.98160e15 | 0.226063 | 0.113032 | − | 0.993591i | \(-0.463944\pi\) | ||||
0.113032 | + | 0.993591i | \(0.463944\pi\) | |||||||
\(854\) | −2.81424e15 | −0.212003 | ||||||||
\(855\) | −1.27378e14 | −0.00953412 | ||||||||
\(856\) | 2.94398e15 | 0.218942 | ||||||||
\(857\) | 1.96566e16 | 1.45249 | 0.726247 | − | 0.687434i | \(-0.241263\pi\) | ||||
0.726247 | + | 0.687434i | \(0.241263\pi\) | |||||||
\(858\) | 9.31612e14 | 0.0683998 | ||||||||
\(859\) | 2.47331e15 | 0.180433 | 0.0902164 | − | 0.995922i | \(-0.471244\pi\) | ||||
0.0902164 | + | 0.995922i | \(0.471244\pi\) | |||||||
\(860\) | −8.93389e15 | −0.647588 | ||||||||
\(861\) | 2.54525e15 | 0.183321 | ||||||||
\(862\) | 5.73654e15 | 0.410544 | ||||||||
\(863\) | 2.05179e16 | 1.45906 | 0.729530 | − | 0.683949i | \(-0.239739\pi\) | ||||
0.729530 | + | 0.683949i | \(0.239739\pi\) | |||||||
\(864\) | −2.02035e15 | −0.142758 | ||||||||
\(865\) | 2.01477e14 | 0.0141461 | ||||||||
\(866\) | 6.46341e14 | 0.0450935 | ||||||||
\(867\) | −4.15895e14 | −0.0288322 | ||||||||
\(868\) | −3.05119e15 | −0.210189 | ||||||||
\(869\) | 8.58771e15 | 0.587853 | ||||||||
\(870\) | 7.67895e14 | 0.0522331 | ||||||||
\(871\) | 2.88943e16 | 1.95305 | ||||||||
\(872\) | 7.38670e14 | 0.0496146 | ||||||||
\(873\) | −2.59987e15 | −0.173530 | ||||||||
\(874\) | −3.02462e14 | −0.0200613 | ||||||||
\(875\) | 5.55844e15 | 0.366361 | ||||||||
\(876\) | −1.20154e16 | −0.786983 | ||||||||
\(877\) | −1.47558e16 | −0.960428 | −0.480214 | − | 0.877151i | \(-0.659441\pi\) | ||||
−0.480214 | + | 0.877151i | \(0.659441\pi\) | |||||||
\(878\) | 2.69886e15 | 0.174566 | ||||||||
\(879\) | −1.58318e16 | −1.01764 | ||||||||
\(880\) | 1.89143e15 | 0.120819 | ||||||||
\(881\) | 1.32702e16 | 0.842385 | 0.421192 | − | 0.906971i | \(-0.361612\pi\) | ||||
0.421192 | + | 0.906971i | \(0.361612\pi\) | |||||||
\(882\) | 1.05139e15 | 0.0663263 | ||||||||
\(883\) | 1.33127e16 | 0.834608 | 0.417304 | − | 0.908767i | \(-0.362975\pi\) | ||||
0.417304 | + | 0.908767i | \(0.362975\pi\) | |||||||
\(884\) | 1.51833e16 | 0.945973 | ||||||||
\(885\) | −4.56801e14 | −0.0282839 | ||||||||
\(886\) | 3.46246e15 | 0.213059 | ||||||||
\(887\) | 2.10196e16 | 1.28542 | 0.642709 | − | 0.766111i | \(-0.277811\pi\) | ||||
0.642709 | + | 0.766111i | \(0.277811\pi\) | |||||||
\(888\) | −5.36222e15 | −0.325892 | ||||||||
\(889\) | 1.13922e16 | 0.688097 | ||||||||
\(890\) | 1.42591e15 | 0.0855950 | ||||||||
\(891\) | −7.66639e14 | −0.0457366 | ||||||||
\(892\) | 2.18336e16 | 1.29455 | ||||||||
\(893\) | 4.90823e14 | 0.0289229 | ||||||||
\(894\) | −4.53588e15 | −0.265647 | ||||||||
\(895\) | −1.06182e16 | −0.618053 | ||||||||
\(896\) | 8.14970e15 | 0.471463 | ||||||||
\(897\) | 1.01413e16 | 0.583089 | ||||||||
\(898\) | −8.29274e15 | −0.473890 | ||||||||
\(899\) | 6.69635e15 | 0.380329 | ||||||||
\(900\) | 4.68755e15 | 0.264613 | ||||||||
\(901\) | 2.17365e16 | 1.21956 | ||||||||
\(902\) | 1.22693e15 | 0.0684203 | ||||||||
\(903\) | −1.01554e16 | −0.562878 | ||||||||
\(904\) | 8.11465e15 | 0.447037 | ||||||||
\(905\) | −1.24566e16 | −0.682073 | ||||||||
\(906\) | −4.73027e15 | −0.257443 | ||||||||
\(907\) | 1.91783e16 | 1.03745 | 0.518727 | − | 0.854940i | \(-0.326406\pi\) | ||||
0.518727 | + | 0.854940i | \(0.326406\pi\) | |||||||
\(908\) | 3.45882e15 | 0.185975 | ||||||||
\(909\) | −5.69459e15 | −0.304342 | ||||||||
\(910\) | 1.06808e15 | 0.0567385 | ||||||||
\(911\) | −1.43002e16 | −0.755077 | −0.377538 | − | 0.925994i | \(-0.623229\pi\) | ||||
−0.377538 | + | 0.925994i | \(0.623229\pi\) | |||||||
\(912\) | 6.52215e14 | 0.0342310 | ||||||||
\(913\) | −5.66428e15 | −0.295498 | ||||||||
\(914\) | −9.14607e14 | −0.0474275 | ||||||||
\(915\) | −6.21918e15 | −0.320566 | ||||||||
\(916\) | 2.02194e15 | 0.103596 | ||||||||
\(917\) | −1.37654e16 | −0.701065 | ||||||||
\(918\) | 1.01619e15 | 0.0514448 | ||||||||
\(919\) | −1.10785e16 | −0.557501 | −0.278750 | − | 0.960364i | \(-0.589920\pi\) | ||||
−0.278750 | + | 0.960364i | \(0.589920\pi\) | |||||||
\(920\) | −3.82141e15 | −0.191157 | ||||||||
\(921\) | −1.68735e15 | −0.0839027 | ||||||||
\(922\) | −7.02942e14 | −0.0347456 | ||||||||
\(923\) | −1.84759e16 | −0.907813 | ||||||||
\(924\) | 2.35736e15 | 0.115141 | ||||||||
\(925\) | 1.89049e16 | 0.917899 | ||||||||
\(926\) | 7.48276e15 | 0.361161 | ||||||||
\(927\) | −3.22323e15 | −0.154651 | ||||||||
\(928\) | −1.36342e16 | −0.650304 | ||||||||
\(929\) | 3.91778e16 | 1.85761 | 0.928803 | − | 0.370575i | \(-0.120839\pi\) | ||||
0.928803 | + | 0.370575i | \(0.120839\pi\) | |||||||
\(930\) | 5.48398e14 | 0.0258488 | ||||||||
\(931\) | −1.17695e15 | −0.0551487 | ||||||||
\(932\) | −2.89626e16 | −1.34912 | ||||||||
\(933\) | 2.21566e16 | 1.02602 | ||||||||
\(934\) | −1.15957e16 | −0.533811 | ||||||||
\(935\) | −3.29892e15 | −0.150976 | ||||||||
\(936\) | 4.05871e15 | 0.184659 | ||||||||
\(937\) | −5.36663e15 | −0.242736 | −0.121368 | − | 0.992608i | \(-0.538728\pi\) | ||||
−0.121368 | + | 0.992608i | \(0.538728\pi\) | |||||||
\(938\) | −5.94645e15 | −0.267388 | ||||||||
\(939\) | 1.10041e16 | 0.491917 | ||||||||
\(940\) | 2.97945e15 | 0.132414 | ||||||||
\(941\) | 3.20147e16 | 1.41451 | 0.707255 | − | 0.706959i | \(-0.249933\pi\) | ||||
0.707255 | + | 0.706959i | \(0.249933\pi\) | |||||||
\(942\) | −4.96280e15 | −0.217995 | ||||||||
\(943\) | 1.33561e16 | 0.583264 | ||||||||
\(944\) | 2.33897e15 | 0.101549 | ||||||||
\(945\) | −8.78945e14 | −0.0379391 | ||||||||
\(946\) | −4.89539e15 | −0.210081 | ||||||||
\(947\) | 3.95764e16 | 1.68854 | 0.844271 | − | 0.535917i | \(-0.180034\pi\) | ||||
0.844271 | + | 0.535917i | \(0.180034\pi\) | |||||||
\(948\) | 1.79758e16 | 0.762506 | ||||||||
\(949\) | 3.66784e16 | 1.54684 | ||||||||
\(950\) | 4.26772e14 | 0.0178943 | ||||||||
\(951\) | 1.34868e16 | 0.562234 | ||||||||
\(952\) | −6.50358e15 | −0.269556 | ||||||||
\(953\) | −3.58692e15 | −0.147812 | −0.0739061 | − | 0.997265i | \(-0.523547\pi\) | ||||
−0.0739061 | + | 0.997265i | \(0.523547\pi\) | |||||||
\(954\) | 2.79171e15 | 0.114381 | ||||||||
\(955\) | −6.86332e15 | −0.279586 | ||||||||
\(956\) | 1.92337e16 | 0.779014 | ||||||||
\(957\) | −5.17362e15 | −0.208343 | ||||||||
\(958\) | −3.53398e15 | −0.141499 | ||||||||
\(959\) | 1.21173e16 | 0.482395 | ||||||||
\(960\) | 3.16458e15 | 0.125263 | ||||||||
\(961\) | −2.06262e16 | −0.811785 | ||||||||
\(962\) | 7.86458e15 | 0.307760 | ||||||||
\(963\) | 3.55321e15 | 0.138254 | ||||||||
\(964\) | 2.32515e16 | 0.899552 | ||||||||
\(965\) | 7.19110e15 | 0.276627 | ||||||||
\(966\) | −2.08708e15 | −0.0798297 | ||||||||
\(967\) | 6.50498e15 | 0.247400 | 0.123700 | − | 0.992320i | \(-0.460524\pi\) | ||||
0.123700 | + | 0.992320i | \(0.460524\pi\) | |||||||
\(968\) | −1.15936e16 | −0.438432 | ||||||||
\(969\) | −1.13755e15 | −0.0427751 | ||||||||
\(970\) | −1.43685e15 | −0.0537240 | ||||||||
\(971\) | −9.73203e14 | −0.0361824 | −0.0180912 | − | 0.999836i | \(-0.505759\pi\) | ||||
−0.0180912 | + | 0.999836i | \(0.505759\pi\) | |||||||
\(972\) | −1.60473e15 | −0.0593251 | ||||||||
\(973\) | 2.47998e14 | 0.00911650 | ||||||||
\(974\) | 1.47295e16 | 0.538410 | ||||||||
\(975\) | −1.43093e16 | −0.520107 | ||||||||
\(976\) | 3.18442e16 | 1.15095 | ||||||||
\(977\) | −1.99885e16 | −0.718389 | −0.359195 | − | 0.933263i | \(-0.616949\pi\) | ||||
−0.359195 | + | 0.933263i | \(0.616949\pi\) | |||||||
\(978\) | 5.05574e14 | 0.0180685 | ||||||||
\(979\) | −9.60695e15 | −0.341414 | ||||||||
\(980\) | −7.14446e15 | −0.252479 | ||||||||
\(981\) | 8.91533e14 | 0.0313298 | ||||||||
\(982\) | 4.02572e15 | 0.140679 | ||||||||
\(983\) | −4.23850e16 | −1.47288 | −0.736440 | − | 0.676503i | \(-0.763495\pi\) | ||||
−0.736440 | + | 0.676503i | \(0.763495\pi\) | |||||||
\(984\) | 5.34532e15 | 0.184714 | ||||||||
\(985\) | 7.83817e15 | 0.269349 | ||||||||
\(986\) | 6.85772e15 | 0.234346 | ||||||||
\(987\) | 3.38682e15 | 0.115093 | ||||||||
\(988\) | −2.18294e15 | −0.0737699 | ||||||||
\(989\) | −5.32900e16 | −1.79088 | ||||||||
\(990\) | −4.23694e14 | −0.0141599 | ||||||||
\(991\) | 5.09195e16 | 1.69231 | 0.846154 | − | 0.532938i | \(-0.178912\pi\) | ||||
0.846154 | + | 0.532938i | \(0.178912\pi\) | |||||||
\(992\) | −9.73699e15 | −0.321818 | ||||||||
\(993\) | −2.98371e16 | −0.980700 | ||||||||
\(994\) | 3.80234e15 | 0.124287 | ||||||||
\(995\) | −6.96265e15 | −0.226333 | ||||||||
\(996\) | −1.18565e16 | −0.383292 | ||||||||
\(997\) | −3.39819e15 | −0.109251 | −0.0546253 | − | 0.998507i | \(-0.517396\pi\) | ||||
−0.0546253 | + | 0.998507i | \(0.517396\pi\) | |||||||
\(998\) | −1.25300e16 | −0.400619 | ||||||||
\(999\) | −6.47190e15 | −0.205789 |
(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.d.1.12 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.12 | ✓ | 28 | 1.1 | even | 1 | trivial |