Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,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, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(91.1613430010\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −39.1029 | −1.72812 | −0.864059 | − | 0.503390i | \(-0.832086\pi\) | ||||
−0.864059 | + | 0.503390i | \(0.832086\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 1017.03 | 1.98639 | ||||||||
\(5\) | 1845.13 | 1.32027 | 0.660134 | − | 0.751148i | \(-0.270500\pi\) | ||||
0.660134 | + | 0.751148i | \(0.270500\pi\) | |||||||
\(6\) | −3167.33 | −0.997730 | ||||||||
\(7\) | 8719.40 | 1.37260 | 0.686302 | − | 0.727317i | \(-0.259233\pi\) | ||||
0.686302 | + | 0.727317i | \(0.259233\pi\) | |||||||
\(8\) | −19748.3 | −1.70461 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −72149.9 | −2.28158 | ||||||||
\(11\) | 11592.4 | 0.238731 | 0.119365 | − | 0.992850i | \(-0.461914\pi\) | ||||
0.119365 | + | 0.992850i | \(0.461914\pi\) | |||||||
\(12\) | 82379.8 | 1.14685 | ||||||||
\(13\) | 8112.04 | 0.0787744 | 0.0393872 | − | 0.999224i | \(-0.487459\pi\) | ||||
0.0393872 | + | 0.999224i | \(0.487459\pi\) | |||||||
\(14\) | −340953. | −2.37202 | ||||||||
\(15\) | 149456. | 0.762257 | ||||||||
\(16\) | 251493. | 0.959370 | ||||||||
\(17\) | −258717. | −0.751284 | −0.375642 | − | 0.926765i | \(-0.622578\pi\) | ||||
−0.375642 | + | 0.926765i | \(0.622578\pi\) | |||||||
\(18\) | −256554. | −0.576040 | ||||||||
\(19\) | −511787. | −0.900944 | −0.450472 | − | 0.892790i | \(-0.648744\pi\) | ||||
−0.450472 | + | 0.892790i | \(0.648744\pi\) | |||||||
\(20\) | 1.87656e6 | 2.62257 | ||||||||
\(21\) | 706271. | 0.792473 | ||||||||
\(22\) | −453298. | −0.412555 | ||||||||
\(23\) | 1.50681e6 | 1.12275 | 0.561376 | − | 0.827561i | \(-0.310272\pi\) | ||||
0.561376 | + | 0.827561i | \(0.310272\pi\) | |||||||
\(24\) | −1.59961e6 | −0.984156 | ||||||||
\(25\) | 1.45138e6 | 0.743107 | ||||||||
\(26\) | −317204. | −0.136132 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 8.86793e6 | 2.72653 | ||||||||
\(29\) | 3.60183e6 | 0.945655 | 0.472827 | − | 0.881155i | \(-0.343233\pi\) | ||||
0.472827 | + | 0.881155i | \(0.343233\pi\) | |||||||
\(30\) | −5.84414e6 | −1.31727 | ||||||||
\(31\) | 517886. | 0.100718 | 0.0503590 | − | 0.998731i | \(-0.483963\pi\) | ||||
0.0503590 | + | 0.998731i | \(0.483963\pi\) | |||||||
\(32\) | 277024. | 0.0467027 | ||||||||
\(33\) | 938988. | 0.137831 | ||||||||
\(34\) | 1.01166e7 | 1.29831 | ||||||||
\(35\) | 1.60884e7 | 1.81220 | ||||||||
\(36\) | 6.67276e6 | 0.662132 | ||||||||
\(37\) | 5.37194e6 | 0.471220 | 0.235610 | − | 0.971848i | \(-0.424291\pi\) | ||||
0.235610 | + | 0.971848i | \(0.424291\pi\) | |||||||
\(38\) | 2.00123e7 | 1.55694 | ||||||||
\(39\) | 657076. | 0.0454804 | ||||||||
\(40\) | −3.64382e7 | −2.25054 | ||||||||
\(41\) | 1.04132e7 | 0.575515 | 0.287757 | − | 0.957703i | \(-0.407090\pi\) | ||||
0.287757 | + | 0.957703i | \(0.407090\pi\) | |||||||
\(42\) | −2.76172e7 | −1.36949 | ||||||||
\(43\) | 1.15939e6 | 0.0517155 | 0.0258577 | − | 0.999666i | \(-0.491768\pi\) | ||||
0.0258577 | + | 0.999666i | \(0.491768\pi\) | |||||||
\(44\) | 1.17899e7 | 0.474213 | ||||||||
\(45\) | 1.21059e7 | 0.440089 | ||||||||
\(46\) | −5.89207e7 | −1.94025 | ||||||||
\(47\) | 2.05249e7 | 0.613535 | 0.306768 | − | 0.951784i | \(-0.400753\pi\) | ||||
0.306768 | + | 0.951784i | \(0.400753\pi\) | |||||||
\(48\) | 2.03709e7 | 0.553892 | ||||||||
\(49\) | 3.56743e7 | 0.884042 | ||||||||
\(50\) | −5.67531e7 | −1.28418 | ||||||||
\(51\) | −2.09560e7 | −0.433754 | ||||||||
\(52\) | 8.25023e6 | 0.156477 | ||||||||
\(53\) | −6.04606e7 | −1.05252 | −0.526260 | − | 0.850323i | \(-0.676406\pi\) | ||||
−0.526260 | + | 0.850323i | \(0.676406\pi\) | |||||||
\(54\) | −2.07809e7 | −0.332577 | ||||||||
\(55\) | 2.13896e7 | 0.315188 | ||||||||
\(56\) | −1.72193e8 | −2.33975 | ||||||||
\(57\) | −4.14547e7 | −0.520160 | ||||||||
\(58\) | −1.40842e8 | −1.63420 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | 1.52001e8 | 1.51414 | ||||||||
\(61\) | 1.74520e8 | 1.61384 | 0.806920 | − | 0.590661i | \(-0.201133\pi\) | ||||
0.806920 | + | 0.590661i | \(0.201133\pi\) | |||||||
\(62\) | −2.02508e7 | −0.174053 | ||||||||
\(63\) | 5.72080e7 | 0.457535 | ||||||||
\(64\) | −1.39597e8 | −1.04008 | ||||||||
\(65\) | 1.49678e7 | 0.104003 | ||||||||
\(66\) | −3.67171e7 | −0.238189 | ||||||||
\(67\) | 7.95827e7 | 0.482483 | 0.241242 | − | 0.970465i | \(-0.422445\pi\) | ||||
0.241242 | + | 0.970465i | \(0.422445\pi\) | |||||||
\(68\) | −2.63124e8 | −1.49235 | ||||||||
\(69\) | 1.22052e8 | 0.648221 | ||||||||
\(70\) | −6.29103e8 | −3.13171 | ||||||||
\(71\) | 1.53469e8 | 0.716736 | 0.358368 | − | 0.933580i | \(-0.383333\pi\) | ||||
0.358368 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(72\) | −1.29568e8 | −0.568203 | ||||||||
\(73\) | −3.49414e8 | −1.44008 | −0.720042 | − | 0.693931i | \(-0.755877\pi\) | ||||
−0.720042 | + | 0.693931i | \(0.755877\pi\) | |||||||
\(74\) | −2.10058e8 | −0.814324 | ||||||||
\(75\) | 1.17562e8 | 0.429033 | ||||||||
\(76\) | −5.20505e8 | −1.78963 | ||||||||
\(77\) | 1.01079e8 | 0.327683 | ||||||||
\(78\) | −2.56935e7 | −0.0785956 | ||||||||
\(79\) | −3.98120e8 | −1.14998 | −0.574992 | − | 0.818159i | \(-0.694995\pi\) | ||||
−0.574992 | + | 0.818159i | \(0.694995\pi\) | |||||||
\(80\) | 4.64037e8 | 1.26662 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −4.07186e8 | −0.994558 | ||||||||
\(83\) | −4.09387e6 | −0.00946852 | −0.00473426 | − | 0.999989i | \(-0.501507\pi\) | ||||
−0.00473426 | + | 0.999989i | \(0.501507\pi\) | |||||||
\(84\) | 7.18302e8 | 1.57417 | ||||||||
\(85\) | −4.77366e8 | −0.991896 | ||||||||
\(86\) | −4.53354e7 | −0.0893705 | ||||||||
\(87\) | 2.91748e8 | 0.545974 | ||||||||
\(88\) | −2.28931e8 | −0.406942 | ||||||||
\(89\) | 2.94766e8 | 0.497992 | 0.248996 | − | 0.968504i | \(-0.419899\pi\) | ||||
0.248996 | + | 0.968504i | \(0.419899\pi\) | |||||||
\(90\) | −4.73375e8 | −0.760526 | ||||||||
\(91\) | 7.07321e7 | 0.108126 | ||||||||
\(92\) | 1.53248e9 | 2.23023 | ||||||||
\(93\) | 4.19488e7 | 0.0581495 | ||||||||
\(94\) | −8.02581e8 | −1.06026 | ||||||||
\(95\) | −9.44313e8 | −1.18949 | ||||||||
\(96\) | 2.24389e7 | 0.0269638 | ||||||||
\(97\) | −4.22911e8 | −0.485039 | −0.242519 | − | 0.970147i | \(-0.577974\pi\) | ||||
−0.242519 | + | 0.970147i | \(0.577974\pi\) | |||||||
\(98\) | −1.39497e9 | −1.52773 | ||||||||
\(99\) | 7.60580e7 | 0.0795768 | ||||||||
\(100\) | 1.47610e9 | 1.47610 | ||||||||
\(101\) | 1.76540e9 | 1.68809 | 0.844046 | − | 0.536271i | \(-0.180167\pi\) | ||||
0.844046 | + | 0.536271i | \(0.180167\pi\) | |||||||
\(102\) | 8.19442e8 | 0.749579 | ||||||||
\(103\) | −8.41804e7 | −0.0736959 | −0.0368480 | − | 0.999321i | \(-0.511732\pi\) | ||||
−0.0368480 | + | 0.999321i | \(0.511732\pi\) | |||||||
\(104\) | −1.60199e8 | −0.134279 | ||||||||
\(105\) | 1.30316e9 | 1.04628 | ||||||||
\(106\) | 2.36418e9 | 1.81888 | ||||||||
\(107\) | 2.00988e9 | 1.48232 | 0.741161 | − | 0.671328i | \(-0.234276\pi\) | ||||
0.741161 | + | 0.671328i | \(0.234276\pi\) | |||||||
\(108\) | 5.40494e8 | 0.382282 | ||||||||
\(109\) | 2.50764e9 | 1.70155 | 0.850776 | − | 0.525529i | \(-0.176132\pi\) | ||||
0.850776 | + | 0.525529i | \(0.176132\pi\) | |||||||
\(110\) | −8.36393e8 | −0.544683 | ||||||||
\(111\) | 4.35127e8 | 0.272059 | ||||||||
\(112\) | 2.19287e9 | 1.31683 | ||||||||
\(113\) | −7.59390e8 | −0.438139 | −0.219069 | − | 0.975709i | \(-0.570302\pi\) | ||||
−0.219069 | + | 0.975709i | \(0.570302\pi\) | |||||||
\(114\) | 1.62100e9 | 0.898899 | ||||||||
\(115\) | 2.78026e9 | 1.48233 | ||||||||
\(116\) | 3.66319e9 | 1.87844 | ||||||||
\(117\) | 5.32231e7 | 0.0262581 | ||||||||
\(118\) | 4.73824e8 | 0.224982 | ||||||||
\(119\) | −2.25585e9 | −1.03122 | ||||||||
\(120\) | −2.95149e9 | −1.29935 | ||||||||
\(121\) | −2.22356e9 | −0.943008 | ||||||||
\(122\) | −6.82422e9 | −2.78891 | ||||||||
\(123\) | 8.43468e8 | 0.332274 | ||||||||
\(124\) | 5.26708e8 | 0.200066 | ||||||||
\(125\) | −9.25785e8 | −0.339168 | ||||||||
\(126\) | −2.23700e9 | −0.790674 | ||||||||
\(127\) | 2.81966e9 | 0.961789 | 0.480895 | − | 0.876778i | \(-0.340312\pi\) | ||||
0.480895 | + | 0.876778i | \(0.340312\pi\) | |||||||
\(128\) | 5.31680e9 | 1.75067 | ||||||||
\(129\) | 9.39103e7 | 0.0298579 | ||||||||
\(130\) | −5.85283e8 | −0.179730 | ||||||||
\(131\) | 3.02532e9 | 0.897533 | 0.448766 | − | 0.893649i | \(-0.351864\pi\) | ||||
0.448766 | + | 0.893649i | \(0.351864\pi\) | |||||||
\(132\) | 9.54983e8 | 0.273787 | ||||||||
\(133\) | −4.46247e9 | −1.23664 | ||||||||
\(134\) | −3.11191e9 | −0.833788 | ||||||||
\(135\) | 9.80578e8 | 0.254086 | ||||||||
\(136\) | 5.10921e9 | 1.28064 | ||||||||
\(137\) | 6.21211e9 | 1.50660 | 0.753298 | − | 0.657680i | \(-0.228462\pi\) | ||||
0.753298 | + | 0.657680i | \(0.228462\pi\) | |||||||
\(138\) | −4.77257e9 | −1.12020 | ||||||||
\(139\) | −7.25432e9 | −1.64828 | −0.824139 | − | 0.566388i | \(-0.808340\pi\) | ||||
−0.824139 | + | 0.566388i | \(0.808340\pi\) | |||||||
\(140\) | 1.63625e10 | 3.59975 | ||||||||
\(141\) | 1.66251e9 | 0.354225 | ||||||||
\(142\) | −6.00109e9 | −1.23860 | ||||||||
\(143\) | 9.40384e7 | 0.0188059 | ||||||||
\(144\) | 1.65005e9 | 0.319790 | ||||||||
\(145\) | 6.64585e9 | 1.24852 | ||||||||
\(146\) | 1.36631e10 | 2.48863 | ||||||||
\(147\) | 2.88962e9 | 0.510402 | ||||||||
\(148\) | 5.46345e9 | 0.936028 | ||||||||
\(149\) | 3.73612e9 | 0.620988 | 0.310494 | − | 0.950575i | \(-0.399506\pi\) | ||||
0.310494 | + | 0.950575i | \(0.399506\pi\) | |||||||
\(150\) | −4.59700e9 | −0.741420 | ||||||||
\(151\) | 3.66181e9 | 0.573192 | 0.286596 | − | 0.958052i | \(-0.407476\pi\) | ||||
0.286596 | + | 0.958052i | \(0.407476\pi\) | |||||||
\(152\) | 1.01069e10 | 1.53576 | ||||||||
\(153\) | −1.69744e9 | −0.250428 | ||||||||
\(154\) | −3.95248e9 | −0.566274 | ||||||||
\(155\) | 9.55568e8 | 0.132975 | ||||||||
\(156\) | 6.68268e8 | 0.0903421 | ||||||||
\(157\) | −8.36523e9 | −1.09883 | −0.549414 | − | 0.835550i | \(-0.685149\pi\) | ||||
−0.549414 | + | 0.835550i | \(0.685149\pi\) | |||||||
\(158\) | 1.55676e10 | 1.98731 | ||||||||
\(159\) | −4.89730e9 | −0.607673 | ||||||||
\(160\) | 5.11145e8 | 0.0616601 | ||||||||
\(161\) | 1.31385e10 | 1.54109 | ||||||||
\(162\) | −1.68325e9 | −0.192013 | ||||||||
\(163\) | −8.59620e9 | −0.953811 | −0.476905 | − | 0.878955i | \(-0.658242\pi\) | ||||
−0.476905 | + | 0.878955i | \(0.658242\pi\) | |||||||
\(164\) | 1.05906e10 | 1.14320 | ||||||||
\(165\) | 1.73256e9 | 0.181974 | ||||||||
\(166\) | 1.60082e8 | 0.0163627 | ||||||||
\(167\) | −1.76924e10 | −1.76020 | −0.880102 | − | 0.474785i | \(-0.842526\pi\) | ||||
−0.880102 | + | 0.474785i | \(0.842526\pi\) | |||||||
\(168\) | −1.39476e10 | −1.35086 | ||||||||
\(169\) | −1.05387e10 | −0.993795 | ||||||||
\(170\) | 1.86664e10 | 1.71411 | ||||||||
\(171\) | −3.35783e9 | −0.300315 | ||||||||
\(172\) | 1.17914e9 | 0.102727 | ||||||||
\(173\) | 1.10926e10 | 0.941516 | 0.470758 | − | 0.882262i | \(-0.343981\pi\) | ||||
0.470758 | + | 0.882262i | \(0.343981\pi\) | |||||||
\(174\) | −1.14082e10 | −0.943508 | ||||||||
\(175\) | 1.26552e10 | 1.01999 | ||||||||
\(176\) | 2.91542e9 | 0.229031 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | −1.15262e10 | −0.860590 | ||||||||
\(179\) | 3.55499e9 | 0.258821 | 0.129411 | − | 0.991591i | \(-0.458691\pi\) | ||||
0.129411 | + | 0.991591i | \(0.458691\pi\) | |||||||
\(180\) | 1.23121e10 | 0.874191 | ||||||||
\(181\) | −1.27355e10 | −0.881986 | −0.440993 | − | 0.897511i | \(-0.645374\pi\) | ||||
−0.440993 | + | 0.897511i | \(0.645374\pi\) | |||||||
\(182\) | −2.76583e9 | −0.186855 | ||||||||
\(183\) | 1.41361e10 | 0.931751 | ||||||||
\(184\) | −2.97569e10 | −1.91385 | ||||||||
\(185\) | 9.91193e9 | 0.622136 | ||||||||
\(186\) | −1.64032e9 | −0.100489 | ||||||||
\(187\) | −2.99916e9 | −0.179354 | ||||||||
\(188\) | 2.08745e10 | 1.21872 | ||||||||
\(189\) | 4.63385e9 | 0.264158 | ||||||||
\(190\) | 3.69254e10 | 2.05558 | ||||||||
\(191\) | −1.21114e10 | −0.658482 | −0.329241 | − | 0.944246i | \(-0.606793\pi\) | ||||
−0.329241 | + | 0.944246i | \(0.606793\pi\) | |||||||
\(192\) | −1.13073e10 | −0.600489 | ||||||||
\(193\) | 1.32381e10 | 0.686781 | 0.343390 | − | 0.939193i | \(-0.388425\pi\) | ||||
0.343390 | + | 0.939193i | \(0.388425\pi\) | |||||||
\(194\) | 1.65370e10 | 0.838205 | ||||||||
\(195\) | 1.21239e9 | 0.0600463 | ||||||||
\(196\) | 3.62820e10 | 1.75606 | ||||||||
\(197\) | −3.74378e9 | −0.177098 | −0.0885488 | − | 0.996072i | \(-0.528223\pi\) | ||||
−0.0885488 | + | 0.996072i | \(0.528223\pi\) | |||||||
\(198\) | −2.97409e9 | −0.137518 | ||||||||
\(199\) | 1.45493e10 | 0.657663 | 0.328831 | − | 0.944389i | \(-0.393345\pi\) | ||||
0.328831 | + | 0.944389i | \(0.393345\pi\) | |||||||
\(200\) | −2.86623e10 | −1.26671 | ||||||||
\(201\) | 6.44620e9 | 0.278562 | ||||||||
\(202\) | −6.90321e10 | −2.91722 | ||||||||
\(203\) | 3.14058e10 | 1.29801 | ||||||||
\(204\) | −2.13130e10 | −0.861607 | ||||||||
\(205\) | 1.92137e10 | 0.759833 | ||||||||
\(206\) | 3.29169e9 | 0.127355 | ||||||||
\(207\) | 9.88619e9 | 0.374251 | ||||||||
\(208\) | 2.04012e9 | 0.0755738 | ||||||||
\(209\) | −5.93286e9 | −0.215083 | ||||||||
\(210\) | −5.09574e10 | −1.80809 | ||||||||
\(211\) | −3.38777e10 | −1.17664 | −0.588319 | − | 0.808629i | \(-0.700210\pi\) | ||||
−0.588319 | + | 0.808629i | \(0.700210\pi\) | |||||||
\(212\) | −6.14904e10 | −2.09072 | ||||||||
\(213\) | 1.24310e10 | 0.413808 | ||||||||
\(214\) | −7.85919e10 | −2.56163 | ||||||||
\(215\) | 2.13922e9 | 0.0682782 | ||||||||
\(216\) | −1.04950e10 | −0.328052 | ||||||||
\(217\) | 4.51566e9 | 0.138246 | ||||||||
\(218\) | −9.80557e10 | −2.94048 | ||||||||
\(219\) | −2.83025e10 | −0.831432 | ||||||||
\(220\) | 2.17539e10 | 0.626088 | ||||||||
\(221\) | −2.09872e9 | −0.0591820 | ||||||||
\(222\) | −1.70147e10 | −0.470150 | ||||||||
\(223\) | −4.03514e10 | −1.09267 | −0.546333 | − | 0.837568i | \(-0.683977\pi\) | ||||
−0.546333 | + | 0.837568i | \(0.683977\pi\) | |||||||
\(224\) | 2.41548e9 | 0.0641044 | ||||||||
\(225\) | 9.52250e9 | 0.247702 | ||||||||
\(226\) | 2.96943e10 | 0.757156 | ||||||||
\(227\) | −1.12508e10 | −0.281234 | −0.140617 | − | 0.990064i | \(-0.544909\pi\) | ||||
−0.140617 | + | 0.990064i | \(0.544909\pi\) | |||||||
\(228\) | −4.21609e10 | −1.03324 | ||||||||
\(229\) | −6.60532e9 | −0.158721 | −0.0793605 | − | 0.996846i | \(-0.525288\pi\) | ||||
−0.0793605 | + | 0.996846i | \(0.525288\pi\) | |||||||
\(230\) | −1.08716e11 | −2.56165 | ||||||||
\(231\) | 8.18741e9 | 0.189188 | ||||||||
\(232\) | −7.11300e10 | −1.61197 | ||||||||
\(233\) | 1.70989e10 | 0.380072 | 0.190036 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190036 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(234\) | −2.08118e9 | −0.0453772 | ||||||||
\(235\) | 3.78710e10 | 0.810031 | ||||||||
\(236\) | −1.23238e10 | −0.258607 | ||||||||
\(237\) | −3.22477e10 | −0.663944 | ||||||||
\(238\) | 8.82103e10 | 1.78206 | ||||||||
\(239\) | 3.34258e10 | 0.662661 | 0.331331 | − | 0.943515i | \(-0.392502\pi\) | ||||
0.331331 | + | 0.943515i | \(0.392502\pi\) | |||||||
\(240\) | 3.75870e10 | 0.731286 | ||||||||
\(241\) | −1.19790e10 | −0.228741 | −0.114370 | − | 0.993438i | \(-0.536485\pi\) | ||||
−0.114370 | + | 0.993438i | \(0.536485\pi\) | |||||||
\(242\) | 8.69477e10 | 1.62963 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 1.77493e11 | 3.20572 | ||||||||
\(245\) | 6.58237e10 | 1.16717 | ||||||||
\(246\) | −3.29820e10 | −0.574208 | ||||||||
\(247\) | −4.15164e9 | −0.0709714 | ||||||||
\(248\) | −1.02274e10 | −0.171685 | ||||||||
\(249\) | −3.31603e8 | −0.00546665 | ||||||||
\(250\) | 3.62008e10 | 0.586123 | ||||||||
\(251\) | 1.78053e10 | 0.283151 | 0.141575 | − | 0.989927i | \(-0.454783\pi\) | ||||
0.141575 | + | 0.989927i | \(0.454783\pi\) | |||||||
\(252\) | 5.81825e10 | 0.908845 | ||||||||
\(253\) | 1.74676e10 | 0.268035 | ||||||||
\(254\) | −1.10257e11 | −1.66209 | ||||||||
\(255\) | −3.86666e10 | −0.572672 | ||||||||
\(256\) | −1.36429e11 | −1.98530 | ||||||||
\(257\) | 3.60577e10 | 0.515583 | 0.257792 | − | 0.966201i | \(-0.417005\pi\) | ||||
0.257792 | + | 0.966201i | \(0.417005\pi\) | |||||||
\(258\) | −3.67216e9 | −0.0515981 | ||||||||
\(259\) | 4.68401e10 | 0.646798 | ||||||||
\(260\) | 1.52227e10 | 0.206592 | ||||||||
\(261\) | 2.36316e10 | 0.315218 | ||||||||
\(262\) | −1.18299e11 | −1.55104 | ||||||||
\(263\) | −3.71011e9 | −0.0478174 | −0.0239087 | − | 0.999714i | \(-0.507611\pi\) | ||||
−0.0239087 | + | 0.999714i | \(0.507611\pi\) | |||||||
\(264\) | −1.85434e10 | −0.234948 | ||||||||
\(265\) | −1.11558e11 | −1.38961 | ||||||||
\(266\) | 1.74496e11 | 2.13706 | ||||||||
\(267\) | 2.38761e10 | 0.287516 | ||||||||
\(268\) | 8.09384e10 | 0.958402 | ||||||||
\(269\) | −4.27276e9 | −0.0497535 | −0.0248767 | − | 0.999691i | \(-0.507919\pi\) | ||||
−0.0248767 | + | 0.999691i | \(0.507919\pi\) | |||||||
\(270\) | −3.83434e10 | −0.439090 | ||||||||
\(271\) | 7.45985e10 | 0.840172 | 0.420086 | − | 0.907484i | \(-0.362000\pi\) | ||||
0.420086 | + | 0.907484i | \(0.362000\pi\) | |||||||
\(272\) | −6.50654e10 | −0.720759 | ||||||||
\(273\) | 5.72930e9 | 0.0624266 | ||||||||
\(274\) | −2.42911e11 | −2.60358 | ||||||||
\(275\) | 1.68250e10 | 0.177402 | ||||||||
\(276\) | 1.24131e11 | 1.28762 | ||||||||
\(277\) | 1.38405e11 | 1.41252 | 0.706258 | − | 0.707955i | \(-0.250382\pi\) | ||||
0.706258 | + | 0.707955i | \(0.250382\pi\) | |||||||
\(278\) | 2.83665e11 | 2.84842 | ||||||||
\(279\) | 3.39785e9 | 0.0335726 | ||||||||
\(280\) | −3.17719e11 | −3.08910 | ||||||||
\(281\) | −6.29759e10 | −0.602554 | −0.301277 | − | 0.953537i | \(-0.597413\pi\) | ||||
−0.301277 | + | 0.953537i | \(0.597413\pi\) | |||||||
\(282\) | −6.50090e10 | −0.612143 | ||||||||
\(283\) | 1.42028e11 | 1.31624 | 0.658121 | − | 0.752912i | \(-0.271352\pi\) | ||||
0.658121 | + | 0.752912i | \(0.271352\pi\) | |||||||
\(284\) | 1.56084e11 | 1.42372 | ||||||||
\(285\) | −7.64894e10 | −0.686751 | ||||||||
\(286\) | −3.67717e9 | −0.0324988 | ||||||||
\(287\) | 9.07967e10 | 0.789954 | ||||||||
\(288\) | 1.81755e9 | 0.0155676 | ||||||||
\(289\) | −5.16536e10 | −0.435572 | ||||||||
\(290\) | −2.59872e11 | −2.15759 | ||||||||
\(291\) | −3.42558e10 | −0.280037 | ||||||||
\(292\) | −3.55366e11 | −2.86057 | ||||||||
\(293\) | 8.04654e10 | 0.637830 | 0.318915 | − | 0.947783i | \(-0.396682\pi\) | ||||
0.318915 | + | 0.947783i | \(0.396682\pi\) | |||||||
\(294\) | −1.12992e11 | −0.882035 | ||||||||
\(295\) | −2.23581e10 | −0.171884 | ||||||||
\(296\) | −1.06087e11 | −0.803245 | ||||||||
\(297\) | 6.16070e9 | 0.0459437 | ||||||||
\(298\) | −1.46093e11 | −1.07314 | ||||||||
\(299\) | 1.22233e10 | 0.0884441 | ||||||||
\(300\) | 1.19564e11 | 0.852229 | ||||||||
\(301\) | 1.01092e10 | 0.0709848 | ||||||||
\(302\) | −1.43187e11 | −0.990544 | ||||||||
\(303\) | 1.42997e11 | 0.974621 | ||||||||
\(304\) | −1.28711e11 | −0.864339 | ||||||||
\(305\) | 3.22012e11 | 2.13070 | ||||||||
\(306\) | 6.63748e10 | 0.432769 | ||||||||
\(307\) | 9.07324e10 | 0.582962 | 0.291481 | − | 0.956577i | \(-0.405852\pi\) | ||||
0.291481 | + | 0.956577i | \(0.405852\pi\) | |||||||
\(308\) | 1.02801e11 | 0.650907 | ||||||||
\(309\) | −6.81861e9 | −0.0425483 | ||||||||
\(310\) | −3.73654e10 | −0.229796 | ||||||||
\(311\) | −1.13266e11 | −0.686556 | −0.343278 | − | 0.939234i | \(-0.611537\pi\) | ||||
−0.343278 | + | 0.939234i | \(0.611537\pi\) | |||||||
\(312\) | −1.29761e10 | −0.0775263 | ||||||||
\(313\) | 3.75570e10 | 0.221178 | 0.110589 | − | 0.993866i | \(-0.464726\pi\) | ||||
0.110589 | + | 0.993866i | \(0.464726\pi\) | |||||||
\(314\) | 3.27105e11 | 1.89890 | ||||||||
\(315\) | 1.05556e11 | 0.604068 | ||||||||
\(316\) | −4.04901e11 | −2.28432 | ||||||||
\(317\) | 9.19099e10 | 0.511206 | 0.255603 | − | 0.966782i | \(-0.417726\pi\) | ||||
0.255603 | + | 0.966782i | \(0.417726\pi\) | |||||||
\(318\) | 1.91499e11 | 1.05013 | ||||||||
\(319\) | 4.17541e10 | 0.225757 | ||||||||
\(320\) | −2.57574e11 | −1.37318 | ||||||||
\(321\) | 1.62800e11 | 0.855819 | ||||||||
\(322\) | −5.13753e11 | −2.66319 | ||||||||
\(323\) | 1.32408e11 | 0.676865 | ||||||||
\(324\) | 4.37800e10 | 0.220711 | ||||||||
\(325\) | 1.17737e10 | 0.0585378 | ||||||||
\(326\) | 3.36136e11 | 1.64830 | ||||||||
\(327\) | 2.03118e11 | 0.982391 | ||||||||
\(328\) | −2.05643e11 | −0.981027 | ||||||||
\(329\) | 1.78964e11 | 0.842141 | ||||||||
\(330\) | −6.77479e10 | −0.314473 | ||||||||
\(331\) | 1.37968e11 | 0.631762 | 0.315881 | − | 0.948799i | \(-0.397700\pi\) | ||||
0.315881 | + | 0.948799i | \(0.397700\pi\) | |||||||
\(332\) | −4.16360e9 | −0.0188082 | ||||||||
\(333\) | 3.52453e10 | 0.157073 | ||||||||
\(334\) | 6.91824e11 | 3.04184 | ||||||||
\(335\) | 1.46840e11 | 0.637007 | ||||||||
\(336\) | 1.77622e11 | 0.760275 | ||||||||
\(337\) | 5.67015e10 | 0.239475 | 0.119738 | − | 0.992806i | \(-0.461795\pi\) | ||||
0.119738 | + | 0.992806i | \(0.461795\pi\) | |||||||
\(338\) | 4.12093e11 | 1.71740 | ||||||||
\(339\) | −6.15106e10 | −0.252960 | ||||||||
\(340\) | −4.85497e11 | −1.97030 | ||||||||
\(341\) | 6.00357e9 | 0.0240444 | ||||||||
\(342\) | 1.31301e11 | 0.518980 | ||||||||
\(343\) | −4.08008e10 | −0.159164 | ||||||||
\(344\) | −2.28959e10 | −0.0881546 | ||||||||
\(345\) | 2.25201e11 | 0.855825 | ||||||||
\(346\) | −4.33754e11 | −1.62705 | ||||||||
\(347\) | −2.48717e11 | −0.920921 | −0.460460 | − | 0.887680i | \(-0.652316\pi\) | ||||
−0.460460 | + | 0.887680i | \(0.652316\pi\) | |||||||
\(348\) | 2.96718e11 | 1.08452 | ||||||||
\(349\) | 4.33331e11 | 1.56353 | 0.781763 | − | 0.623576i | \(-0.214321\pi\) | ||||
0.781763 | + | 0.623576i | \(0.214321\pi\) | |||||||
\(350\) | −4.94853e11 | −1.76267 | ||||||||
\(351\) | 4.31107e9 | 0.0151601 | ||||||||
\(352\) | 3.21138e9 | 0.0111494 | ||||||||
\(353\) | −5.43531e11 | −1.86311 | −0.931554 | − | 0.363604i | \(-0.881546\pi\) | ||||
−0.931554 | + | 0.363604i | \(0.881546\pi\) | |||||||
\(354\) | 3.83797e10 | 0.129893 | ||||||||
\(355\) | 2.83171e11 | 0.946283 | ||||||||
\(356\) | 2.99787e11 | 0.989209 | ||||||||
\(357\) | −1.82724e11 | −0.595373 | ||||||||
\(358\) | −1.39010e11 | −0.447274 | ||||||||
\(359\) | −5.45243e10 | −0.173247 | −0.0866234 | − | 0.996241i | \(-0.527608\pi\) | ||||
−0.0866234 | + | 0.996241i | \(0.527608\pi\) | |||||||
\(360\) | −2.39071e11 | −0.750179 | ||||||||
\(361\) | −6.07619e10 | −0.188299 | ||||||||
\(362\) | 4.97994e11 | 1.52418 | ||||||||
\(363\) | −1.80109e11 | −0.544446 | ||||||||
\(364\) | 7.19370e10 | 0.214781 | ||||||||
\(365\) | −6.44714e11 | −1.90130 | ||||||||
\(366\) | −5.52762e11 | −1.61018 | ||||||||
\(367\) | 2.37654e10 | 0.0683829 | 0.0341914 | − | 0.999415i | \(-0.489114\pi\) | ||||
0.0341914 | + | 0.999415i | \(0.489114\pi\) | |||||||
\(368\) | 3.78953e11 | 1.07713 | ||||||||
\(369\) | 6.83209e10 | 0.191838 | ||||||||
\(370\) | −3.87585e11 | −1.07512 | ||||||||
\(371\) | −5.27180e11 | −1.44469 | ||||||||
\(372\) | 4.26634e10 | 0.115508 | ||||||||
\(373\) | −2.46802e11 | −0.660176 | −0.330088 | − | 0.943950i | \(-0.607078\pi\) | ||||
−0.330088 | + | 0.943950i | \(0.607078\pi\) | |||||||
\(374\) | 1.17276e11 | 0.309946 | ||||||||
\(375\) | −7.49886e10 | −0.195819 | ||||||||
\(376\) | −4.05331e11 | −1.04584 | ||||||||
\(377\) | 2.92182e10 | 0.0744934 | ||||||||
\(378\) | −1.81197e11 | −0.456496 | ||||||||
\(379\) | 5.39891e11 | 1.34409 | 0.672047 | − | 0.740509i | \(-0.265415\pi\) | ||||
0.672047 | + | 0.740509i | \(0.265415\pi\) | |||||||
\(380\) | −9.60399e11 | −2.36279 | ||||||||
\(381\) | 2.28392e11 | 0.555289 | ||||||||
\(382\) | 4.73590e11 | 1.13794 | ||||||||
\(383\) | −6.64007e11 | −1.57681 | −0.788403 | − | 0.615159i | \(-0.789092\pi\) | ||||
−0.788403 | + | 0.615159i | \(0.789092\pi\) | |||||||
\(384\) | 4.30661e11 | 1.01075 | ||||||||
\(385\) | 1.86504e11 | 0.432629 | ||||||||
\(386\) | −5.17648e11 | −1.18684 | ||||||||
\(387\) | 7.60674e9 | 0.0172385 | ||||||||
\(388\) | −4.30115e11 | −0.963479 | ||||||||
\(389\) | −8.92311e10 | −0.197580 | −0.0987900 | − | 0.995108i | \(-0.531497\pi\) | ||||
−0.0987900 | + | 0.995108i | \(0.531497\pi\) | |||||||
\(390\) | −4.74079e10 | −0.103767 | ||||||||
\(391\) | −3.89837e11 | −0.843506 | ||||||||
\(392\) | −7.04506e11 | −1.50695 | ||||||||
\(393\) | 2.45051e11 | 0.518191 | ||||||||
\(394\) | 1.46393e11 | 0.306046 | ||||||||
\(395\) | −7.34583e11 | −1.51829 | ||||||||
\(396\) | 7.73536e10 | 0.158071 | ||||||||
\(397\) | −8.34544e11 | −1.68613 | −0.843067 | − | 0.537808i | \(-0.819252\pi\) | ||||
−0.843067 | + | 0.537808i | \(0.819252\pi\) | |||||||
\(398\) | −5.68919e11 | −1.13652 | ||||||||
\(399\) | −3.61460e11 | −0.713974 | ||||||||
\(400\) | 3.65012e11 | 0.712914 | ||||||||
\(401\) | 6.21503e11 | 1.20031 | 0.600155 | − | 0.799884i | \(-0.295106\pi\) | ||||
0.600155 | + | 0.799884i | \(0.295106\pi\) | |||||||
\(402\) | −2.52065e11 | −0.481388 | ||||||||
\(403\) | 4.20112e9 | 0.00793400 | ||||||||
\(404\) | 1.79547e12 | 3.35322 | ||||||||
\(405\) | 7.94268e10 | 0.146696 | ||||||||
\(406\) | −1.22806e12 | −2.24311 | ||||||||
\(407\) | 6.22739e10 | 0.112495 | ||||||||
\(408\) | 4.13846e11 | 0.739381 | ||||||||
\(409\) | 5.26321e10 | 0.0930028 | 0.0465014 | − | 0.998918i | \(-0.485193\pi\) | ||||
0.0465014 | + | 0.998918i | \(0.485193\pi\) | |||||||
\(410\) | −7.51310e11 | −1.31308 | ||||||||
\(411\) | 5.03181e11 | 0.869833 | ||||||||
\(412\) | −8.56143e10 | −0.146389 | ||||||||
\(413\) | −1.05656e11 | −0.178698 | ||||||||
\(414\) | −3.86578e11 | −0.646749 | ||||||||
\(415\) | −7.55372e9 | −0.0125010 | ||||||||
\(416\) | 2.24723e9 | 0.00367898 | ||||||||
\(417\) | −5.87600e11 | −0.951633 | ||||||||
\(418\) | 2.31992e11 | 0.371689 | ||||||||
\(419\) | 2.70229e11 | 0.428321 | 0.214161 | − | 0.976798i | \(-0.431298\pi\) | ||||
0.214161 | + | 0.976798i | \(0.431298\pi\) | |||||||
\(420\) | 1.32536e12 | 2.07832 | ||||||||
\(421\) | 2.25697e11 | 0.350152 | 0.175076 | − | 0.984555i | \(-0.443983\pi\) | ||||
0.175076 | + | 0.984555i | \(0.443983\pi\) | |||||||
\(422\) | 1.32472e12 | 2.03337 | ||||||||
\(423\) | 1.34664e11 | 0.204512 | ||||||||
\(424\) | 1.19399e12 | 1.79413 | ||||||||
\(425\) | −3.75496e11 | −0.558284 | ||||||||
\(426\) | −4.86089e11 | −0.715109 | ||||||||
\(427\) | 1.52171e12 | 2.21516 | ||||||||
\(428\) | 2.04411e12 | 2.94448 | ||||||||
\(429\) | 7.61711e9 | 0.0108576 | ||||||||
\(430\) | −8.36496e10 | −0.117993 | ||||||||
\(431\) | −1.41241e12 | −1.97158 | −0.985789 | − | 0.167990i | \(-0.946272\pi\) | ||||
−0.985789 | + | 0.167990i | \(0.946272\pi\) | |||||||
\(432\) | 1.33654e11 | 0.184631 | ||||||||
\(433\) | 9.00250e11 | 1.23074 | 0.615372 | − | 0.788237i | \(-0.289006\pi\) | ||||
0.615372 | + | 0.788237i | \(0.289006\pi\) | |||||||
\(434\) | −1.76575e11 | −0.238905 | ||||||||
\(435\) | 5.38314e11 | 0.720832 | ||||||||
\(436\) | 2.55035e12 | 3.37995 | ||||||||
\(437\) | −7.71167e11 | −1.01154 | ||||||||
\(438\) | 1.10671e12 | 1.43681 | ||||||||
\(439\) | 1.91834e11 | 0.246511 | 0.123255 | − | 0.992375i | \(-0.460667\pi\) | ||||
0.123255 | + | 0.992375i | \(0.460667\pi\) | |||||||
\(440\) | −4.22407e11 | −0.537272 | ||||||||
\(441\) | 2.34059e11 | 0.294681 | ||||||||
\(442\) | 8.20660e10 | 0.102273 | ||||||||
\(443\) | 1.26560e12 | 1.56127 | 0.780637 | − | 0.624985i | \(-0.214895\pi\) | ||||
0.780637 | + | 0.624985i | \(0.214895\pi\) | |||||||
\(444\) | 4.42539e11 | 0.540416 | ||||||||
\(445\) | 5.43882e11 | 0.657483 | ||||||||
\(446\) | 1.57786e12 | 1.88826 | ||||||||
\(447\) | 3.02626e11 | 0.358527 | ||||||||
\(448\) | −1.21720e12 | −1.42761 | ||||||||
\(449\) | 3.63594e11 | 0.422190 | 0.211095 | − | 0.977466i | \(-0.432297\pi\) | ||||
0.211095 | + | 0.977466i | \(0.432297\pi\) | |||||||
\(450\) | −3.72357e11 | −0.428059 | ||||||||
\(451\) | 1.20714e11 | 0.137393 | ||||||||
\(452\) | −7.72325e11 | −0.870317 | ||||||||
\(453\) | 2.96607e11 | 0.330933 | ||||||||
\(454\) | 4.39940e11 | 0.486007 | ||||||||
\(455\) | 1.30510e11 | 0.142755 | ||||||||
\(456\) | 8.18660e11 | 0.886669 | ||||||||
\(457\) | −4.51697e11 | −0.484423 | −0.242211 | − | 0.970224i | \(-0.577873\pi\) | ||||
−0.242211 | + | 0.970224i | \(0.577873\pi\) | |||||||
\(458\) | 2.58287e11 | 0.274289 | ||||||||
\(459\) | −1.37493e11 | −0.144585 | ||||||||
\(460\) | 2.82762e12 | 2.94450 | ||||||||
\(461\) | −6.18511e11 | −0.637813 | −0.318906 | − | 0.947786i | \(-0.603316\pi\) | ||||
−0.318906 | + | 0.947786i | \(0.603316\pi\) | |||||||
\(462\) | −3.20151e11 | −0.326939 | ||||||||
\(463\) | 4.03552e10 | 0.0408117 | 0.0204059 | − | 0.999792i | \(-0.493504\pi\) | ||||
0.0204059 | + | 0.999792i | \(0.493504\pi\) | |||||||
\(464\) | 9.05836e11 | 0.907232 | ||||||||
\(465\) | 7.74010e10 | 0.0767729 | ||||||||
\(466\) | −6.68616e11 | −0.656810 | ||||||||
\(467\) | 9.59256e11 | 0.933273 | 0.466637 | − | 0.884449i | \(-0.345466\pi\) | ||||
0.466637 | + | 0.884449i | \(0.345466\pi\) | |||||||
\(468\) | 5.41297e10 | 0.0521590 | ||||||||
\(469\) | 6.93914e11 | 0.662259 | ||||||||
\(470\) | −1.48087e12 | −1.39983 | ||||||||
\(471\) | −6.77584e11 | −0.634408 | ||||||||
\(472\) | 2.39297e11 | 0.221921 | ||||||||
\(473\) | 1.34401e10 | 0.0123461 | ||||||||
\(474\) | 1.26098e12 | 1.14737 | ||||||||
\(475\) | −7.42797e11 | −0.669498 | ||||||||
\(476\) | −2.29428e12 | −2.04840 | ||||||||
\(477\) | −3.96682e11 | −0.350840 | ||||||||
\(478\) | −1.30705e12 | −1.14516 | ||||||||
\(479\) | 8.31520e11 | 0.721711 | 0.360855 | − | 0.932622i | \(-0.382485\pi\) | ||||
0.360855 | + | 0.932622i | \(0.382485\pi\) | |||||||
\(480\) | 4.14028e10 | 0.0355995 | ||||||||
\(481\) | 4.35774e10 | 0.0371201 | ||||||||
\(482\) | 4.68413e11 | 0.395291 | ||||||||
\(483\) | 1.06422e12 | 0.889751 | ||||||||
\(484\) | −2.26144e12 | −1.87319 | ||||||||
\(485\) | −7.80327e11 | −0.640381 | ||||||||
\(486\) | −1.36343e11 | −0.110859 | ||||||||
\(487\) | 1.60466e12 | 1.29271 | 0.646356 | − | 0.763036i | \(-0.276292\pi\) | ||||
0.646356 | + | 0.763036i | \(0.276292\pi\) | |||||||
\(488\) | −3.44647e12 | −2.75096 | ||||||||
\(489\) | −6.96292e11 | −0.550683 | ||||||||
\(490\) | −2.57390e12 | −2.01701 | ||||||||
\(491\) | −9.63225e11 | −0.747930 | −0.373965 | − | 0.927443i | \(-0.622002\pi\) | ||||
−0.373965 | + | 0.927443i | \(0.622002\pi\) | |||||||
\(492\) | 8.57836e11 | 0.660026 | ||||||||
\(493\) | −9.31854e11 | −0.710455 | ||||||||
\(494\) | 1.62341e11 | 0.122647 | ||||||||
\(495\) | 1.40337e11 | 0.105063 | ||||||||
\(496\) | 1.30245e11 | 0.0966257 | ||||||||
\(497\) | 1.33816e12 | 0.983795 | ||||||||
\(498\) | 1.29666e10 | 0.00944703 | ||||||||
\(499\) | −2.21909e12 | −1.60222 | −0.801112 | − | 0.598515i | \(-0.795758\pi\) | ||||
−0.801112 | + | 0.598515i | \(0.795758\pi\) | |||||||
\(500\) | −9.41555e11 | −0.673722 | ||||||||
\(501\) | −1.43309e12 | −1.01625 | ||||||||
\(502\) | −6.96239e11 | −0.489319 | ||||||||
\(503\) | 1.05270e12 | 0.733245 | 0.366622 | − | 0.930370i | \(-0.380514\pi\) | ||||
0.366622 | + | 0.930370i | \(0.380514\pi\) | |||||||
\(504\) | −1.12976e12 | −0.779917 | ||||||||
\(505\) | 3.25739e12 | 2.22873 | ||||||||
\(506\) | −6.83035e11 | −0.463197 | ||||||||
\(507\) | −8.53634e11 | −0.573768 | ||||||||
\(508\) | 2.86769e12 | 1.91049 | ||||||||
\(509\) | −2.21547e11 | −0.146297 | −0.0731486 | − | 0.997321i | \(-0.523305\pi\) | ||||
−0.0731486 | + | 0.997321i | \(0.523305\pi\) | |||||||
\(510\) | 1.51198e12 | 0.989644 | ||||||||
\(511\) | −3.04668e12 | −1.97666 | ||||||||
\(512\) | 2.61255e12 | 1.68015 | ||||||||
\(513\) | −2.71985e11 | −0.173387 | ||||||||
\(514\) | −1.40996e12 | −0.890989 | ||||||||
\(515\) | −1.55324e11 | −0.0972983 | ||||||||
\(516\) | 9.55100e10 | 0.0593096 | ||||||||
\(517\) | 2.37933e11 | 0.146470 | ||||||||
\(518\) | −1.83158e12 | −1.11774 | ||||||||
\(519\) | 8.98504e11 | 0.543584 | ||||||||
\(520\) | −2.95588e11 | −0.177285 | ||||||||
\(521\) | 2.36950e12 | 1.40892 | 0.704460 | − | 0.709743i | \(-0.251189\pi\) | ||||
0.704460 | + | 0.709743i | \(0.251189\pi\) | |||||||
\(522\) | −9.24064e11 | −0.544735 | ||||||||
\(523\) | 2.09943e12 | 1.22700 | 0.613499 | − | 0.789696i | \(-0.289762\pi\) | ||||
0.613499 | + | 0.789696i | \(0.289762\pi\) | |||||||
\(524\) | 3.07685e12 | 1.78285 | ||||||||
\(525\) | 1.02507e12 | 0.588892 | ||||||||
\(526\) | 1.45076e11 | 0.0826342 | ||||||||
\(527\) | −1.33986e11 | −0.0756678 | ||||||||
\(528\) | 2.36149e11 | 0.132231 | ||||||||
\(529\) | 4.69329e11 | 0.260571 | ||||||||
\(530\) | 4.36222e12 | 2.40141 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −4.53849e12 | −2.45646 | ||||||||
\(533\) | 8.44722e10 | 0.0453358 | ||||||||
\(534\) | −9.33622e11 | −0.496862 | ||||||||
\(535\) | 3.70848e12 | 1.95706 | ||||||||
\(536\) | −1.57162e12 | −0.822445 | ||||||||
\(537\) | 2.87954e11 | 0.149431 | ||||||||
\(538\) | 1.67077e11 | 0.0859799 | ||||||||
\(539\) | 4.13552e11 | 0.211048 | ||||||||
\(540\) | 9.97281e11 | 0.504714 | ||||||||
\(541\) | −2.68282e12 | −1.34649 | −0.673245 | − | 0.739419i | \(-0.735100\pi\) | ||||
−0.673245 | + | 0.739419i | \(0.735100\pi\) | |||||||
\(542\) | −2.91701e12 | −1.45192 | ||||||||
\(543\) | −1.03157e12 | −0.509215 | ||||||||
\(544\) | −7.16707e10 | −0.0350870 | ||||||||
\(545\) | 4.62691e12 | 2.24650 | ||||||||
\(546\) | −2.24032e11 | −0.107881 | ||||||||
\(547\) | −1.34648e12 | −0.643066 | −0.321533 | − | 0.946898i | \(-0.604198\pi\) | ||||
−0.321533 | + | 0.946898i | \(0.604198\pi\) | |||||||
\(548\) | 6.31793e12 | 2.99269 | ||||||||
\(549\) | 1.14502e12 | 0.537947 | ||||||||
\(550\) | −6.57907e11 | −0.306572 | ||||||||
\(551\) | −1.84337e12 | −0.851982 | ||||||||
\(552\) | −2.41031e12 | −1.10496 | ||||||||
\(553\) | −3.47136e12 | −1.57847 | ||||||||
\(554\) | −5.41204e12 | −2.44100 | ||||||||
\(555\) | 8.02866e11 | 0.359190 | ||||||||
\(556\) | −7.37789e12 | −3.27413 | ||||||||
\(557\) | −3.58326e12 | −1.57736 | −0.788678 | − | 0.614807i | \(-0.789234\pi\) | ||||
−0.788678 | + | 0.614807i | \(0.789234\pi\) | |||||||
\(558\) | −1.32866e11 | −0.0580175 | ||||||||
\(559\) | 9.40500e9 | 0.00407385 | ||||||||
\(560\) | 4.04613e12 | 1.73857 | ||||||||
\(561\) | −2.42932e11 | −0.103550 | ||||||||
\(562\) | 2.46254e12 | 1.04129 | ||||||||
\(563\) | −1.13265e12 | −0.475125 | −0.237562 | − | 0.971372i | \(-0.576348\pi\) | ||||
−0.237562 | + | 0.971372i | \(0.576348\pi\) | |||||||
\(564\) | 1.69083e12 | 0.703630 | ||||||||
\(565\) | −1.40117e12 | −0.578461 | ||||||||
\(566\) | −5.55371e12 | −2.27462 | ||||||||
\(567\) | 3.75341e11 | 0.152512 | ||||||||
\(568\) | −3.03076e12 | −1.22175 | ||||||||
\(569\) | −4.59730e12 | −1.83865 | −0.919323 | − | 0.393504i | \(-0.871263\pi\) | ||||
−0.919323 | + | 0.393504i | \(0.871263\pi\) | |||||||
\(570\) | 2.99095e12 | 1.18679 | ||||||||
\(571\) | −2.23247e12 | −0.878865 | −0.439433 | − | 0.898276i | \(-0.644821\pi\) | ||||
−0.439433 | + | 0.898276i | \(0.644821\pi\) | |||||||
\(572\) | 9.56403e10 | 0.0373559 | ||||||||
\(573\) | −9.81023e11 | −0.380175 | ||||||||
\(574\) | −3.55041e12 | −1.36513 | ||||||||
\(575\) | 2.18696e12 | 0.834324 | ||||||||
\(576\) | −9.15895e11 | −0.346693 | ||||||||
\(577\) | 1.72653e12 | 0.648461 | 0.324230 | − | 0.945978i | \(-0.394895\pi\) | ||||
0.324230 | + | 0.945978i | \(0.394895\pi\) | |||||||
\(578\) | 2.01980e12 | 0.752720 | ||||||||
\(579\) | 1.07229e12 | 0.396513 | ||||||||
\(580\) | 6.75906e12 | 2.48005 | ||||||||
\(581\) | −3.56960e10 | −0.0129965 | ||||||||
\(582\) | 1.33950e12 | 0.483938 | ||||||||
\(583\) | −7.00886e11 | −0.251269 | ||||||||
\(584\) | 6.90033e12 | 2.45478 | ||||||||
\(585\) | 9.82036e10 | 0.0346678 | ||||||||
\(586\) | −3.14643e12 | −1.10225 | ||||||||
\(587\) | −7.42662e11 | −0.258178 | −0.129089 | − | 0.991633i | \(-0.541205\pi\) | ||||
−0.129089 | + | 0.991633i | \(0.541205\pi\) | |||||||
\(588\) | 2.93884e12 | 1.01386 | ||||||||
\(589\) | −2.65047e11 | −0.0907412 | ||||||||
\(590\) | 8.74266e11 | 0.297036 | ||||||||
\(591\) | −3.03246e11 | −0.102247 | ||||||||
\(592\) | 1.35101e12 | 0.452074 | ||||||||
\(593\) | 1.34284e10 | 0.00445940 | 0.00222970 | − | 0.999998i | \(-0.499290\pi\) | ||||
0.00222970 | + | 0.999998i | \(0.499290\pi\) | |||||||
\(594\) | −2.40901e11 | −0.0793962 | ||||||||
\(595\) | −4.16234e12 | −1.36148 | ||||||||
\(596\) | 3.79976e12 | 1.23353 | ||||||||
\(597\) | 1.17849e12 | 0.379702 | ||||||||
\(598\) | −4.77967e11 | −0.152842 | ||||||||
\(599\) | 3.86405e12 | 1.22637 | 0.613186 | − | 0.789939i | \(-0.289888\pi\) | ||||
0.613186 | + | 0.789939i | \(0.289888\pi\) | |||||||
\(600\) | −2.32164e12 | −0.731333 | ||||||||
\(601\) | 3.04249e12 | 0.951248 | 0.475624 | − | 0.879649i | \(-0.342222\pi\) | ||||
0.475624 | + | 0.879649i | \(0.342222\pi\) | |||||||
\(602\) | −3.95297e11 | −0.122670 | ||||||||
\(603\) | 5.22142e11 | 0.160828 | ||||||||
\(604\) | 3.72419e12 | 1.13859 | ||||||||
\(605\) | −4.10276e12 | −1.24502 | ||||||||
\(606\) | −5.59160e12 | −1.68426 | ||||||||
\(607\) | 2.18130e12 | 0.652179 | 0.326090 | − | 0.945339i | \(-0.394269\pi\) | ||||
0.326090 | + | 0.945339i | \(0.394269\pi\) | |||||||
\(608\) | −1.41777e11 | −0.0420766 | ||||||||
\(609\) | 2.54387e12 | 0.749406 | ||||||||
\(610\) | −1.25916e13 | −3.68210 | ||||||||
\(611\) | 1.66498e11 | 0.0483309 | ||||||||
\(612\) | −1.72635e12 | −0.497449 | ||||||||
\(613\) | −4.85568e12 | −1.38892 | −0.694460 | − | 0.719531i | \(-0.744357\pi\) | ||||
−0.694460 | + | 0.719531i | \(0.744357\pi\) | |||||||
\(614\) | −3.54790e12 | −1.00743 | ||||||||
\(615\) | 1.55631e12 | 0.438690 | ||||||||
\(616\) | −1.99614e12 | −0.558570 | ||||||||
\(617\) | −3.66289e12 | −1.01751 | −0.508757 | − | 0.860910i | \(-0.669895\pi\) | ||||
−0.508757 | + | 0.860910i | \(0.669895\pi\) | |||||||
\(618\) | 2.66627e11 | 0.0735286 | ||||||||
\(619\) | −1.50800e12 | −0.412852 | −0.206426 | − | 0.978462i | \(-0.566183\pi\) | ||||
−0.206426 | + | 0.978462i | \(0.566183\pi\) | |||||||
\(620\) | 9.71845e11 | 0.264140 | ||||||||
\(621\) | 8.00782e11 | 0.216074 | ||||||||
\(622\) | 4.42901e12 | 1.18645 | ||||||||
\(623\) | 2.57018e12 | 0.683546 | ||||||||
\(624\) | 1.65250e11 | 0.0436325 | ||||||||
\(625\) | −4.54292e12 | −1.19090 | ||||||||
\(626\) | −1.46859e12 | −0.382222 | ||||||||
\(627\) | −4.80562e11 | −0.124178 | ||||||||
\(628\) | −8.50773e12 | −2.18271 | ||||||||
\(629\) | −1.38981e12 | −0.354020 | ||||||||
\(630\) | −4.12755e12 | −1.04390 | ||||||||
\(631\) | −5.10589e12 | −1.28215 | −0.641076 | − | 0.767477i | \(-0.721512\pi\) | ||||
−0.641076 | + | 0.767477i | \(0.721512\pi\) | |||||||
\(632\) | 7.86218e12 | 1.96027 | ||||||||
\(633\) | −2.74410e12 | −0.679333 | ||||||||
\(634\) | −3.59394e12 | −0.883424 | ||||||||
\(635\) | 5.20264e12 | 1.26982 | ||||||||
\(636\) | −4.98073e12 | −1.20708 | ||||||||
\(637\) | 2.89391e11 | 0.0696399 | ||||||||
\(638\) | −1.63270e12 | −0.390134 | ||||||||
\(639\) | 1.00691e12 | 0.238912 | ||||||||
\(640\) | 9.81019e12 | 2.31136 | ||||||||
\(641\) | 4.14832e12 | 0.970536 | 0.485268 | − | 0.874365i | \(-0.338722\pi\) | ||||
0.485268 | + | 0.874365i | \(0.338722\pi\) | |||||||
\(642\) | −6.36595e12 | −1.47896 | ||||||||
\(643\) | 6.70027e12 | 1.54576 | 0.772882 | − | 0.634550i | \(-0.218815\pi\) | ||||
0.772882 | + | 0.634550i | \(0.218815\pi\) | |||||||
\(644\) | 1.33623e13 | 3.06122 | ||||||||
\(645\) | 1.73277e11 | 0.0394205 | ||||||||
\(646\) | −5.17752e12 | −1.16970 | ||||||||
\(647\) | 4.57762e12 | 1.02700 | 0.513500 | − | 0.858090i | \(-0.328349\pi\) | ||||
0.513500 | + | 0.858090i | \(0.328349\pi\) | |||||||
\(648\) | −8.50099e11 | −0.189401 | ||||||||
\(649\) | −1.40470e11 | −0.0310801 | ||||||||
\(650\) | −4.60384e11 | −0.101160 | ||||||||
\(651\) | 3.65768e11 | 0.0798163 | ||||||||
\(652\) | −8.74263e12 | −1.89464 | ||||||||
\(653\) | 6.06978e12 | 1.30636 | 0.653181 | − | 0.757201i | \(-0.273434\pi\) | ||||
0.653181 | + | 0.757201i | \(0.273434\pi\) | |||||||
\(654\) | −7.94251e12 | −1.69769 | ||||||||
\(655\) | 5.58211e12 | 1.18498 | ||||||||
\(656\) | 2.61884e12 | 0.552131 | ||||||||
\(657\) | −2.29251e12 | −0.480028 | ||||||||
\(658\) | −6.99802e12 | −1.45532 | ||||||||
\(659\) | 3.83697e12 | 0.792510 | 0.396255 | − | 0.918141i | \(-0.370310\pi\) | ||||
0.396255 | + | 0.918141i | \(0.370310\pi\) | |||||||
\(660\) | 1.76207e12 | 0.361472 | ||||||||
\(661\) | 2.48540e12 | 0.506396 | 0.253198 | − | 0.967415i | \(-0.418518\pi\) | ||||
0.253198 | + | 0.967415i | \(0.418518\pi\) | |||||||
\(662\) | −5.39496e12 | −1.09176 | ||||||||
\(663\) | −1.69996e11 | −0.0341687 | ||||||||
\(664\) | 8.08468e10 | 0.0161401 | ||||||||
\(665\) | −8.23384e12 | −1.63270 | ||||||||
\(666\) | −1.37819e12 | −0.271441 | ||||||||
\(667\) | 5.42728e12 | 1.06174 | ||||||||
\(668\) | −1.79938e13 | −3.49646 | ||||||||
\(669\) | −3.26847e12 | −0.630851 | ||||||||
\(670\) | −5.74188e12 | −1.10082 | ||||||||
\(671\) | 2.02311e12 | 0.385273 | ||||||||
\(672\) | 1.95654e11 | 0.0370107 | ||||||||
\(673\) | 8.77320e12 | 1.64851 | 0.824253 | − | 0.566222i | \(-0.191596\pi\) | ||||
0.824253 | + | 0.566222i | \(0.191596\pi\) | |||||||
\(674\) | −2.21719e12 | −0.413841 | ||||||||
\(675\) | 7.71323e11 | 0.143011 | ||||||||
\(676\) | −1.07182e13 | −1.97407 | ||||||||
\(677\) | −4.36975e12 | −0.799480 | −0.399740 | − | 0.916629i | \(-0.630900\pi\) | ||||
−0.399740 | + | 0.916629i | \(0.630900\pi\) | |||||||
\(678\) | 2.40524e12 | 0.437144 | ||||||||
\(679\) | −3.68753e12 | −0.665766 | ||||||||
\(680\) | 9.42716e12 | 1.69079 | ||||||||
\(681\) | −9.11318e11 | −0.162371 | ||||||||
\(682\) | −2.34757e11 | −0.0415517 | ||||||||
\(683\) | −1.39296e12 | −0.244931 | −0.122466 | − | 0.992473i | \(-0.539080\pi\) | ||||
−0.122466 | + | 0.992473i | \(0.539080\pi\) | |||||||
\(684\) | −3.41503e12 | −0.596544 | ||||||||
\(685\) | 1.14622e13 | 1.98911 | ||||||||
\(686\) | 1.59543e12 | 0.275055 | ||||||||
\(687\) | −5.35031e11 | −0.0916376 | ||||||||
\(688\) | 2.91578e11 | 0.0496142 | ||||||||
\(689\) | −4.90459e11 | −0.0829117 | ||||||||
\(690\) | −8.80602e12 | −1.47897 | ||||||||
\(691\) | −5.40642e12 | −0.902108 | −0.451054 | − | 0.892497i | \(-0.648952\pi\) | ||||
−0.451054 | + | 0.892497i | \(0.648952\pi\) | |||||||
\(692\) | 1.12816e13 | 1.87022 | ||||||||
\(693\) | 6.63180e11 | 0.109228 | ||||||||
\(694\) | 9.72553e12 | 1.59146 | ||||||||
\(695\) | −1.33852e13 | −2.17617 | ||||||||
\(696\) | −5.76153e12 | −0.930671 | ||||||||
\(697\) | −2.69407e12 | −0.432375 | ||||||||
\(698\) | −1.69445e13 | −2.70196 | ||||||||
\(699\) | 1.38501e12 | 0.219435 | ||||||||
\(700\) | 1.28707e13 | 2.02611 | ||||||||
\(701\) | −4.54692e12 | −0.711191 | −0.355596 | − | 0.934640i | \(-0.615722\pi\) | ||||
−0.355596 | + | 0.934640i | \(0.615722\pi\) | |||||||
\(702\) | −1.68575e11 | −0.0261985 | ||||||||
\(703\) | −2.74929e12 | −0.424543 | ||||||||
\(704\) | −1.61827e12 | −0.248298 | ||||||||
\(705\) | 3.06755e12 | 0.467672 | ||||||||
\(706\) | 2.12536e13 | 3.21967 | ||||||||
\(707\) | 1.53932e13 | 2.31708 | ||||||||
\(708\) | −9.98225e11 | −0.149307 | ||||||||
\(709\) | 9.83888e12 | 1.46230 | 0.731152 | − | 0.682215i | \(-0.238983\pi\) | ||||
0.731152 | + | 0.682215i | \(0.238983\pi\) | |||||||
\(710\) | −1.10728e13 | −1.63529 | ||||||||
\(711\) | −2.61206e12 | −0.383328 | ||||||||
\(712\) | −5.82113e12 | −0.848881 | ||||||||
\(713\) | 7.80357e11 | 0.113081 | ||||||||
\(714\) | 7.14504e12 | 1.02887 | ||||||||
\(715\) | 1.73513e11 | 0.0248288 | ||||||||
\(716\) | 3.61555e12 | 0.514121 | ||||||||
\(717\) | 2.70749e12 | 0.382588 | ||||||||
\(718\) | 2.13206e12 | 0.299391 | ||||||||
\(719\) | −1.30734e13 | −1.82435 | −0.912176 | − | 0.409799i | \(-0.865599\pi\) | ||||
−0.912176 | + | 0.409799i | \(0.865599\pi\) | |||||||
\(720\) | 3.04455e12 | 0.422208 | ||||||||
\(721\) | −7.34002e11 | −0.101155 | ||||||||
\(722\) | 2.37596e12 | 0.325403 | ||||||||
\(723\) | −9.70299e11 | −0.132064 | ||||||||
\(724\) | −1.29524e13 | −1.75197 | ||||||||
\(725\) | 5.22763e12 | 0.702722 | ||||||||
\(726\) | 7.04276e12 | 0.940867 | ||||||||
\(727\) | −6.00761e12 | −0.797622 | −0.398811 | − | 0.917033i | \(-0.630577\pi\) | ||||
−0.398811 | + | 0.917033i | \(0.630577\pi\) | |||||||
\(728\) | −1.39684e12 | −0.184313 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 2.52102e13 | 3.28566 | ||||||||
\(731\) | −2.99953e11 | −0.0388530 | ||||||||
\(732\) | 1.43769e13 | 1.85082 | ||||||||
\(733\) | 7.73276e12 | 0.989388 | 0.494694 | − | 0.869067i | \(-0.335280\pi\) | ||||
0.494694 | + | 0.869067i | \(0.335280\pi\) | |||||||
\(734\) | −9.29294e11 | −0.118174 | ||||||||
\(735\) | 5.33172e12 | 0.673867 | ||||||||
\(736\) | 4.17423e11 | 0.0524356 | ||||||||
\(737\) | 9.22558e11 | 0.115183 | ||||||||
\(738\) | −2.67154e12 | −0.331519 | ||||||||
\(739\) | −2.21157e12 | −0.272773 | −0.136386 | − | 0.990656i | \(-0.543549\pi\) | ||||
−0.136386 | + | 0.990656i | \(0.543549\pi\) | |||||||
\(740\) | 1.00808e13 | 1.23581 | ||||||||
\(741\) | −3.36283e11 | −0.0409753 | ||||||||
\(742\) | 2.06142e13 | 2.49660 | ||||||||
\(743\) | 1.19309e12 | 0.143623 | 0.0718113 | − | 0.997418i | \(-0.477122\pi\) | ||||
0.0718113 | + | 0.997418i | \(0.477122\pi\) | |||||||
\(744\) | −8.28417e11 | −0.0991221 | ||||||||
\(745\) | 6.89363e12 | 0.819870 | ||||||||
\(746\) | 9.65068e12 | 1.14086 | ||||||||
\(747\) | −2.68599e10 | −0.00315617 | ||||||||
\(748\) | −3.05025e12 | −0.356269 | ||||||||
\(749\) | 1.75249e13 | 2.03464 | ||||||||
\(750\) | 2.93227e12 | 0.338398 | ||||||||
\(751\) | 1.66285e13 | 1.90754 | 0.953771 | − | 0.300536i | \(-0.0971655\pi\) | ||||
0.953771 | + | 0.300536i | \(0.0971655\pi\) | |||||||
\(752\) | 5.16186e12 | 0.588607 | ||||||||
\(753\) | 1.44223e12 | 0.163477 | ||||||||
\(754\) | −1.14252e12 | −0.128733 | ||||||||
\(755\) | 6.75652e12 | 0.756767 | ||||||||
\(756\) | 4.71278e12 | 0.524722 | ||||||||
\(757\) | −1.66782e13 | −1.84594 | −0.922971 | − | 0.384870i | \(-0.874246\pi\) | ||||
−0.922971 | + | 0.384870i | \(0.874246\pi\) | |||||||
\(758\) | −2.11113e13 | −2.32275 | ||||||||
\(759\) | 1.41488e12 | 0.154750 | ||||||||
\(760\) | 1.86486e13 | 2.02761 | ||||||||
\(761\) | −1.15553e13 | −1.24897 | −0.624483 | − | 0.781039i | \(-0.714690\pi\) | ||||
−0.624483 | + | 0.781039i | \(0.714690\pi\) | |||||||
\(762\) | −8.93080e12 | −0.959606 | ||||||||
\(763\) | 2.18651e13 | 2.33556 | ||||||||
\(764\) | −1.23177e13 | −1.30801 | ||||||||
\(765\) | −3.13200e12 | −0.330632 | ||||||||
\(766\) | 2.59646e13 | 2.72491 | ||||||||
\(767\) | −9.82966e10 | −0.0102556 | ||||||||
\(768\) | −1.10507e13 | −1.14621 | ||||||||
\(769\) | 1.38467e13 | 1.42784 | 0.713918 | − | 0.700229i | \(-0.246919\pi\) | ||||
0.713918 | + | 0.700229i | \(0.246919\pi\) | |||||||
\(770\) | −7.29285e12 | −0.747634 | ||||||||
\(771\) | 2.92067e12 | 0.297672 | ||||||||
\(772\) | 1.34636e13 | 1.36422 | ||||||||
\(773\) | −1.65102e13 | −1.66321 | −0.831603 | − | 0.555371i | \(-0.812576\pi\) | ||||
−0.831603 | + | 0.555371i | \(0.812576\pi\) | |||||||
\(774\) | −2.97445e11 | −0.0297902 | ||||||||
\(775\) | 7.51650e11 | 0.0748442 | ||||||||
\(776\) | 8.35177e12 | 0.826801 | ||||||||
\(777\) | 3.79405e12 | 0.373429 | ||||||||
\(778\) | 3.48919e12 | 0.341442 | ||||||||
\(779\) | −5.32933e12 | −0.518507 | ||||||||
\(780\) | 1.23304e12 | 0.119276 | ||||||||
\(781\) | 1.77909e12 | 0.171107 | ||||||||
\(782\) | 1.52438e13 | 1.45768 | ||||||||
\(783\) | 1.91416e12 | 0.181991 | ||||||||
\(784\) | 8.97183e12 | 0.848123 | ||||||||
\(785\) | −1.54349e13 | −1.45075 | ||||||||
\(786\) | −9.58219e12 | −0.895495 | ||||||||
\(787\) | −1.32806e13 | −1.23405 | −0.617023 | − | 0.786945i | \(-0.711662\pi\) | ||||
−0.617023 | + | 0.786945i | \(0.711662\pi\) | |||||||
\(788\) | −3.80755e12 | −0.351786 | ||||||||
\(789\) | −3.00519e11 | −0.0276074 | ||||||||
\(790\) | 2.87243e13 | 2.62378 | ||||||||
\(791\) | −6.62142e12 | −0.601391 | ||||||||
\(792\) | −1.50202e12 | −0.135647 | ||||||||
\(793\) | 1.41571e12 | 0.127129 | ||||||||
\(794\) | 3.26331e13 | 2.91384 | ||||||||
\(795\) | −9.03616e12 | −0.802291 | ||||||||
\(796\) | 1.47971e13 | 1.30638 | ||||||||
\(797\) | 1.31311e13 | 1.15276 | 0.576380 | − | 0.817182i | \(-0.304465\pi\) | ||||
0.576380 | + | 0.817182i | \(0.304465\pi\) | |||||||
\(798\) | 1.41341e13 | 1.23383 | ||||||||
\(799\) | −5.31012e12 | −0.460939 | ||||||||
\(800\) | 4.02067e11 | 0.0347051 | ||||||||
\(801\) | 1.93396e12 | 0.165997 | ||||||||
\(802\) | −2.43025e13 | −2.07428 | ||||||||
\(803\) | −4.05056e12 | −0.343792 | ||||||||
\(804\) | 6.55601e12 | 0.553334 | ||||||||
\(805\) | 2.42422e13 | 2.03466 | ||||||||
\(806\) | −1.64276e11 | −0.0137109 | ||||||||
\(807\) | −3.46094e11 | −0.0287252 | ||||||||
\(808\) | −3.48636e13 | −2.87753 | ||||||||
\(809\) | 9.61532e12 | 0.789215 | 0.394608 | − | 0.918850i | \(-0.370881\pi\) | ||||
0.394608 | + | 0.918850i | \(0.370881\pi\) | |||||||
\(810\) | −3.10582e12 | −0.253509 | ||||||||
\(811\) | −2.41421e13 | −1.95966 | −0.979830 | − | 0.199831i | \(-0.935961\pi\) | ||||
−0.979830 | + | 0.199831i | \(0.935961\pi\) | |||||||
\(812\) | 3.19408e13 | 2.57836 | ||||||||
\(813\) | 6.04248e12 | 0.485073 | ||||||||
\(814\) | −2.43509e12 | −0.194404 | ||||||||
\(815\) | −1.58611e13 | −1.25929 | ||||||||
\(816\) | −5.27030e12 | −0.416131 | ||||||||
\(817\) | −5.93359e11 | −0.0465927 | ||||||||
\(818\) | −2.05807e12 | −0.160720 | ||||||||
\(819\) | 4.64074e11 | 0.0360420 | ||||||||
\(820\) | 1.95410e13 | 1.50933 | ||||||||
\(821\) | 1.73842e13 | 1.33540 | 0.667698 | − | 0.744432i | \(-0.267280\pi\) | ||||
0.667698 | + | 0.744432i | \(0.267280\pi\) | |||||||
\(822\) | −1.96758e13 | −1.50318 | ||||||||
\(823\) | −9.25703e12 | −0.703352 | −0.351676 | − | 0.936122i | \(-0.614388\pi\) | ||||
−0.351676 | + | 0.936122i | \(0.614388\pi\) | |||||||
\(824\) | 1.66242e12 | 0.125623 | ||||||||
\(825\) | 1.36283e12 | 0.102423 | ||||||||
\(826\) | 4.13146e12 | 0.308811 | ||||||||
\(827\) | −1.05186e12 | −0.0781954 | −0.0390977 | − | 0.999235i | \(-0.512448\pi\) | ||||
−0.0390977 | + | 0.999235i | \(0.512448\pi\) | |||||||
\(828\) | 1.00546e13 | 0.743409 | ||||||||
\(829\) | −2.12061e13 | −1.55943 | −0.779715 | − | 0.626135i | \(-0.784636\pi\) | ||||
−0.779715 | + | 0.626135i | \(0.784636\pi\) | |||||||
\(830\) | 2.95372e11 | 0.0216032 | ||||||||
\(831\) | 1.12108e13 | 0.815516 | ||||||||
\(832\) | −1.13242e12 | −0.0819315 | ||||||||
\(833\) | −9.22953e12 | −0.664167 | ||||||||
\(834\) | 2.29769e13 | 1.64454 | ||||||||
\(835\) | −3.26448e13 | −2.32394 | ||||||||
\(836\) | −6.03392e12 | −0.427240 | ||||||||
\(837\) | 2.75226e11 | 0.0193832 | ||||||||
\(838\) | −1.05667e13 | −0.740190 | ||||||||
\(839\) | −1.87032e13 | −1.30312 | −0.651562 | − | 0.758595i | \(-0.725886\pi\) | ||||
−0.651562 | + | 0.758595i | \(0.725886\pi\) | |||||||
\(840\) | −2.57352e13 | −1.78349 | ||||||||
\(841\) | −1.53394e12 | −0.105737 | ||||||||
\(842\) | −8.82541e12 | −0.605104 | ||||||||
\(843\) | −5.10105e12 | −0.347885 | ||||||||
\(844\) | −3.44548e13 | −2.33727 | ||||||||
\(845\) | −1.94453e13 | −1.31207 | ||||||||
\(846\) | −5.26573e12 | −0.353421 | ||||||||
\(847\) | −1.93881e13 | −1.29438 | ||||||||
\(848\) | −1.52054e13 | −1.00976 | ||||||||
\(849\) | 1.15043e13 | 0.759932 | ||||||||
\(850\) | 1.46830e13 | 0.964781 | ||||||||
\(851\) | 8.09450e12 | 0.529063 | ||||||||
\(852\) | 1.26428e13 | 0.821985 | ||||||||
\(853\) | 2.78903e13 | 1.80378 | 0.901889 | − | 0.431968i | \(-0.142181\pi\) | ||||
0.901889 | + | 0.431968i | \(0.142181\pi\) | |||||||
\(854\) | −5.95031e13 | −3.82807 | ||||||||
\(855\) | −6.19564e12 | −0.396496 | ||||||||
\(856\) | −3.96916e13 | −2.52678 | ||||||||
\(857\) | 2.51339e13 | 1.59164 | 0.795821 | − | 0.605532i | \(-0.207040\pi\) | ||||
0.795821 | + | 0.605532i | \(0.207040\pi\) | |||||||
\(858\) | −2.97851e11 | −0.0187632 | ||||||||
\(859\) | 3.78665e12 | 0.237293 | 0.118647 | − | 0.992937i | \(-0.462144\pi\) | ||||
0.118647 | + | 0.992937i | \(0.462144\pi\) | |||||||
\(860\) | 2.17566e12 | 0.135628 | ||||||||
\(861\) | 7.35454e12 | 0.456080 | ||||||||
\(862\) | 5.52294e13 | 3.40712 | ||||||||
\(863\) | 2.66996e13 | 1.63854 | 0.819268 | − | 0.573410i | \(-0.194380\pi\) | ||||
0.819268 | + | 0.573410i | \(0.194380\pi\) | |||||||
\(864\) | 1.47222e11 | 0.00898795 | ||||||||
\(865\) | 2.04674e13 | 1.24305 | ||||||||
\(866\) | −3.52024e13 | −2.12687 | ||||||||
\(867\) | −4.18394e12 | −0.251478 | ||||||||
\(868\) | 4.59258e12 | 0.274611 | ||||||||
\(869\) | −4.61518e12 | −0.274536 | ||||||||
\(870\) | −2.10496e13 | −1.24568 | ||||||||
\(871\) | 6.45579e11 | 0.0380073 | ||||||||
\(872\) | −4.95215e13 | −2.90048 | ||||||||
\(873\) | −2.77472e12 | −0.161680 | ||||||||
\(874\) | 3.01548e13 | 1.74806 | ||||||||
\(875\) | −8.07229e12 | −0.465543 | ||||||||
\(876\) | −2.87847e13 | −1.65155 | ||||||||
\(877\) | −1.78051e13 | −1.01636 | −0.508179 | − | 0.861252i | \(-0.669681\pi\) | ||||
−0.508179 | + | 0.861252i | \(0.669681\pi\) | |||||||
\(878\) | −7.50126e12 | −0.425999 | ||||||||
\(879\) | 6.51770e12 | 0.368251 | ||||||||
\(880\) | 5.37933e12 | 0.302382 | ||||||||
\(881\) | −8.30442e12 | −0.464427 | −0.232214 | − | 0.972665i | \(-0.574597\pi\) | ||||
−0.232214 | + | 0.972665i | \(0.574597\pi\) | |||||||
\(882\) | −9.15238e12 | −0.509243 | ||||||||
\(883\) | −1.50196e13 | −0.831451 | −0.415725 | − | 0.909490i | \(-0.636472\pi\) | ||||
−0.415725 | + | 0.909490i | \(0.636472\pi\) | |||||||
\(884\) | −2.13447e12 | −0.117559 | ||||||||
\(885\) | −1.81101e12 | −0.0992374 | ||||||||
\(886\) | −4.94885e13 | −2.69807 | ||||||||
\(887\) | 1.96507e13 | 1.06591 | 0.532957 | − | 0.846142i | \(-0.321081\pi\) | ||||
0.532957 | + | 0.846142i | \(0.321081\pi\) | |||||||
\(888\) | −8.59301e12 | −0.463753 | ||||||||
\(889\) | 2.45857e13 | 1.32016 | ||||||||
\(890\) | −2.12673e13 | −1.13621 | ||||||||
\(891\) | 4.99017e11 | 0.0265256 | ||||||||
\(892\) | −4.10388e13 | −2.17046 | ||||||||
\(893\) | −1.05044e13 | −0.552761 | ||||||||
\(894\) | −1.18335e13 | −0.619578 | ||||||||
\(895\) | 6.55942e12 | 0.341713 | ||||||||
\(896\) | 4.63593e13 | 2.40298 | ||||||||
\(897\) | 9.90089e11 | 0.0510632 | ||||||||
\(898\) | −1.42176e13 | −0.729594 | ||||||||
\(899\) | 1.86534e12 | 0.0952444 | ||||||||
\(900\) | 9.68471e12 | 0.492034 | ||||||||
\(901\) | 1.56422e13 | 0.790742 | ||||||||
\(902\) | −4.72028e12 | −0.237431 | ||||||||
\(903\) | 8.18842e11 | 0.0409831 | ||||||||
\(904\) | 1.49966e13 | 0.746855 | ||||||||
\(905\) | −2.34986e13 | −1.16446 | ||||||||
\(906\) | −1.15982e13 | −0.571891 | ||||||||
\(907\) | 2.74590e13 | 1.34726 | 0.673632 | − | 0.739067i | \(-0.264733\pi\) | ||||
0.673632 | + | 0.739067i | \(0.264733\pi\) | |||||||
\(908\) | −1.14425e13 | −0.558643 | ||||||||
\(909\) | 1.15828e13 | 0.562697 | ||||||||
\(910\) | −5.10331e12 | −0.246698 | ||||||||
\(911\) | −1.74124e13 | −0.837580 | −0.418790 | − | 0.908083i | \(-0.637546\pi\) | ||||
−0.418790 | + | 0.908083i | \(0.637546\pi\) | |||||||
\(912\) | −1.04256e13 | −0.499026 | ||||||||
\(913\) | −4.74579e10 | −0.00226043 | ||||||||
\(914\) | 1.76627e13 | 0.837140 | ||||||||
\(915\) | 2.60829e13 | 1.23016 | ||||||||
\(916\) | −6.71784e12 | −0.315282 | ||||||||
\(917\) | 2.63790e13 | 1.23196 | ||||||||
\(918\) | 5.37636e12 | 0.249860 | ||||||||
\(919\) | −2.97047e13 | −1.37374 | −0.686870 | − | 0.726780i | \(-0.741016\pi\) | ||||
−0.686870 | + | 0.726780i | \(0.741016\pi\) | |||||||
\(920\) | −5.49054e13 | −2.52680 | ||||||||
\(921\) | 7.34933e12 | 0.336573 | ||||||||
\(922\) | 2.41855e13 | 1.10222 | ||||||||
\(923\) | 1.24495e12 | 0.0564605 | ||||||||
\(924\) | 8.32688e12 | 0.375801 | ||||||||
\(925\) | 7.79673e12 | 0.350166 | ||||||||
\(926\) | −1.57800e12 | −0.0705275 | ||||||||
\(927\) | −5.52307e11 | −0.0245653 | ||||||||
\(928\) | 9.97794e11 | 0.0441647 | ||||||||
\(929\) | −1.80937e13 | −0.796997 | −0.398499 | − | 0.917169i | \(-0.630469\pi\) | ||||
−0.398499 | + | 0.917169i | \(0.630469\pi\) | |||||||
\(930\) | −3.02660e12 | −0.132673 | ||||||||
\(931\) | −1.82576e13 | −0.796473 | ||||||||
\(932\) | 1.73902e13 | 0.754974 | ||||||||
\(933\) | −9.17451e12 | −0.396383 | ||||||||
\(934\) | −3.75097e13 | −1.61281 | ||||||||
\(935\) | −5.53384e12 | −0.236796 | ||||||||
\(936\) | −1.05107e12 | −0.0447598 | ||||||||
\(937\) | 4.36774e13 | 1.85109 | 0.925546 | − | 0.378634i | \(-0.123606\pi\) | ||||
0.925546 | + | 0.378634i | \(0.123606\pi\) | |||||||
\(938\) | −2.71340e13 | −1.14446 | ||||||||
\(939\) | 3.04212e12 | 0.127697 | ||||||||
\(940\) | 3.85161e13 | 1.60904 | ||||||||
\(941\) | 9.49535e12 | 0.394782 | 0.197391 | − | 0.980325i | \(-0.436753\pi\) | ||||
0.197391 | + | 0.980325i | \(0.436753\pi\) | |||||||
\(942\) | 2.64955e13 | 1.09633 | ||||||||
\(943\) | 1.56907e13 | 0.646160 | ||||||||
\(944\) | −3.04743e12 | −0.124899 | ||||||||
\(945\) | 8.55005e12 | 0.348759 | ||||||||
\(946\) | −5.25548e11 | −0.0213355 | ||||||||
\(947\) | −2.73029e13 | −1.10315 | −0.551574 | − | 0.834126i | \(-0.685973\pi\) | ||||
−0.551574 | + | 0.834126i | \(0.685973\pi\) | |||||||
\(948\) | −3.27970e13 | −1.31885 | ||||||||
\(949\) | −2.83446e12 | −0.113442 | ||||||||
\(950\) | 2.90455e13 | 1.15697 | ||||||||
\(951\) | 7.44470e12 | 0.295145 | ||||||||
\(952\) | 4.45492e13 | 1.75782 | ||||||||
\(953\) | −4.22883e13 | −1.66074 | −0.830372 | − | 0.557210i | \(-0.811872\pi\) | ||||
−0.830372 | + | 0.557210i | \(0.811872\pi\) | |||||||
\(954\) | 1.55114e13 | 0.606294 | ||||||||
\(955\) | −2.23471e13 | −0.869373 | ||||||||
\(956\) | 3.39952e13 | 1.31631 | ||||||||
\(957\) | 3.38208e12 | 0.130341 | ||||||||
\(958\) | −3.25148e13 | −1.24720 | ||||||||
\(959\) | 5.41659e13 | 2.06796 | ||||||||
\(960\) | −2.08635e13 | −0.792806 | ||||||||
\(961\) | −2.61714e13 | −0.989856 | ||||||||
\(962\) | −1.70400e12 | −0.0641479 | ||||||||
\(963\) | 1.31868e13 | 0.494107 | ||||||||
\(964\) | −1.21830e13 | −0.454370 | ||||||||
\(965\) | 2.44260e13 | 0.906734 | ||||||||
\(966\) | −4.16140e13 | −1.53760 | ||||||||
\(967\) | 2.99642e13 | 1.10201 | 0.551003 | − | 0.834504i | \(-0.314245\pi\) | ||||
0.551003 | + | 0.834504i | \(0.314245\pi\) | |||||||
\(968\) | 4.39116e13 | 1.60746 | ||||||||
\(969\) | 1.07250e13 | 0.390788 | ||||||||
\(970\) | 3.05130e13 | 1.10665 | ||||||||
\(971\) | −2.93830e13 | −1.06074 | −0.530371 | − | 0.847766i | \(-0.677947\pi\) | ||||
−0.530371 | + | 0.847766i | \(0.677947\pi\) | |||||||
\(972\) | 3.54618e12 | 0.127427 | ||||||||
\(973\) | −6.32533e13 | −2.26243 | ||||||||
\(974\) | −6.27467e13 | −2.23396 | ||||||||
\(975\) | 9.53666e11 | 0.0337968 | ||||||||
\(976\) | 4.38905e13 | 1.54827 | ||||||||
\(977\) | −6.55846e12 | −0.230291 | −0.115145 | − | 0.993349i | \(-0.536733\pi\) | ||||
−0.115145 | + | 0.993349i | \(0.536733\pi\) | |||||||
\(978\) | 2.72270e13 | 0.951645 | ||||||||
\(979\) | 3.41706e12 | 0.118886 | ||||||||
\(980\) | 6.69450e13 | 2.31847 | ||||||||
\(981\) | 1.64526e13 | 0.567184 | ||||||||
\(982\) | 3.76649e13 | 1.29251 | ||||||||
\(983\) | −2.36158e13 | −0.806698 | −0.403349 | − | 0.915046i | \(-0.632154\pi\) | ||||
−0.403349 | + | 0.915046i | \(0.632154\pi\) | |||||||
\(984\) | −1.66571e13 | −0.566396 | ||||||||
\(985\) | −6.90776e12 | −0.233816 | ||||||||
\(986\) | 3.64382e13 | 1.22775 | ||||||||
\(987\) | 1.44961e13 | 0.486211 | ||||||||
\(988\) | −4.22236e12 | −0.140977 | ||||||||
\(989\) | 1.74698e12 | 0.0580636 | ||||||||
\(990\) | −5.48758e12 | −0.181561 | ||||||||
\(991\) | −2.63307e13 | −0.867223 | −0.433611 | − | 0.901100i | \(-0.642761\pi\) | ||||
−0.433611 | + | 0.901100i | \(0.642761\pi\) | |||||||
\(992\) | 1.43467e11 | 0.00470380 | ||||||||
\(993\) | 1.11754e13 | 0.364748 | ||||||||
\(994\) | −5.23259e13 | −1.70011 | ||||||||
\(995\) | 2.68454e13 | 0.868291 | ||||||||
\(996\) | −3.37252e11 | −0.0108589 | ||||||||
\(997\) | 4.34187e13 | 1.39171 | 0.695855 | − | 0.718182i | \(-0.255025\pi\) | ||||
0.695855 | + | 0.718182i | \(0.255025\pi\) | |||||||
\(998\) | 8.67729e13 | 2.76883 | ||||||||
\(999\) | 2.85487e12 | 0.0906863 |
(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 | 177.10.a.d.1.2 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.d.1.2 | ✓ | 22 | 1.1 | even | 1 | trivial |