Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,106,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 106, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 106);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 106 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(69.8187388595\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.32050e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.36840e15 | −1.15691 | −0.578453 | − | 0.815715i | \(-0.696344\pi\) | ||||
−0.578453 | + | 0.815715i | \(0.696344\pi\) | |||||||
\(3\) | −8.33754e23 | −0.0745027 | −0.0372514 | − | 0.999306i | \(-0.511860\pi\) | ||||
−0.0372514 | + | 0.999306i | \(0.511860\pi\) | |||||||
\(4\) | 1.37285e31 | 0.338433 | ||||||||
\(5\) | 6.83377e36 | 1.37637 | 0.688185 | − | 0.725535i | \(-0.258408\pi\) | ||||
0.688185 | + | 0.725535i | \(0.258408\pi\) | |||||||
\(6\) | 6.14343e39 | 0.0861927 | ||||||||
\(7\) | 4.41963e44 | 1.89557 | 0.947784 | − | 0.318914i | \(-0.103318\pi\) | ||||
0.947784 | + | 0.318914i | \(0.103318\pi\) | |||||||
\(8\) | 1.97741e47 | 0.765371 | ||||||||
\(9\) | −1.24542e50 | −0.994449 | ||||||||
\(10\) | −5.03539e52 | −1.59233 | ||||||||
\(11\) | −4.48414e54 | −0.951839 | −0.475919 | − | 0.879489i | \(-0.657885\pi\) | ||||
−0.475919 | + | 0.879489i | \(0.657885\pi\) | |||||||
\(12\) | −1.14462e55 | −0.0252142 | ||||||||
\(13\) | 1.91848e58 | 0.632313 | 0.316157 | − | 0.948707i | \(-0.397607\pi\) | ||||
0.316157 | + | 0.948707i | \(0.397607\pi\) | |||||||
\(14\) | −3.25656e60 | −2.19300 | ||||||||
\(15\) | −5.69768e60 | −0.102543 | ||||||||
\(16\) | −2.01393e63 | −1.22390 | ||||||||
\(17\) | 1.58211e64 | 0.398719 | 0.199360 | − | 0.979926i | \(-0.436114\pi\) | ||||
0.199360 | + | 0.979926i | \(0.436114\pi\) | |||||||
\(18\) | 9.17672e65 | 1.15049 | ||||||||
\(19\) | −2.66912e67 | −1.95796 | −0.978979 | − | 0.203960i | \(-0.934619\pi\) | ||||
−0.978979 | + | 0.203960i | \(0.934619\pi\) | |||||||
\(20\) | 9.38173e67 | 0.465809 | ||||||||
\(21\) | −3.68489e68 | −0.141225 | ||||||||
\(22\) | 3.30409e70 | 1.10119 | ||||||||
\(23\) | −2.81725e71 | −0.910151 | −0.455075 | − | 0.890453i | \(-0.650388\pi\) | ||||
−0.455075 | + | 0.890453i | \(0.650388\pi\) | |||||||
\(24\) | −1.64867e71 | −0.0570222 | ||||||||
\(25\) | 2.20485e73 | 0.894394 | ||||||||
\(26\) | −1.41362e74 | −0.731528 | ||||||||
\(27\) | 2.08254e74 | 0.148592 | ||||||||
\(28\) | 6.06749e75 | 0.641523 | ||||||||
\(29\) | −4.39751e76 | −0.736736 | −0.368368 | − | 0.929680i | \(-0.620083\pi\) | ||||
−0.368368 | + | 0.929680i | \(0.620083\pi\) | |||||||
\(30\) | 4.19828e76 | 0.118633 | ||||||||
\(31\) | 4.22496e77 | 0.213468 | 0.106734 | − | 0.994288i | \(-0.465961\pi\) | ||||
0.106734 | + | 0.994288i | \(0.465961\pi\) | |||||||
\(32\) | 6.81810e78 | 0.650563 | ||||||||
\(33\) | 3.73867e78 | 0.0709146 | ||||||||
\(34\) | −1.16576e80 | −0.461281 | ||||||||
\(35\) | 3.02028e81 | 2.60900 | ||||||||
\(36\) | −1.70977e81 | −0.336555 | ||||||||
\(37\) | 1.25411e82 | 0.585792 | 0.292896 | − | 0.956144i | \(-0.405381\pi\) | ||||
0.292896 | + | 0.956144i | \(0.405381\pi\) | |||||||
\(38\) | 1.96671e83 | 2.26518 | ||||||||
\(39\) | −1.59954e82 | −0.0471091 | ||||||||
\(40\) | 1.35132e84 | 1.05343 | ||||||||
\(41\) | −2.50078e84 | −0.533240 | −0.266620 | − | 0.963802i | \(-0.585907\pi\) | ||||
−0.266620 | + | 0.963802i | \(0.585907\pi\) | |||||||
\(42\) | 2.71517e84 | 0.163384 | ||||||||
\(43\) | −6.45716e85 | −1.12966 | −0.564830 | − | 0.825207i | \(-0.691058\pi\) | ||||
−0.564830 | + | 0.825207i | \(0.691058\pi\) | |||||||
\(44\) | −6.15605e85 | −0.322134 | ||||||||
\(45\) | −8.51089e86 | −1.36873 | ||||||||
\(46\) | 2.07586e87 | 1.05296 | ||||||||
\(47\) | −3.82379e87 | −0.627129 | −0.313564 | − | 0.949567i | \(-0.601523\pi\) | ||||
−0.313564 | + | 0.949567i | \(0.601523\pi\) | |||||||
\(48\) | 1.67912e87 | 0.0911836 | ||||||||
\(49\) | 1.40970e89 | 2.59318 | ||||||||
\(50\) | −1.62462e89 | −1.03473 | ||||||||
\(51\) | −1.31909e88 | −0.0297057 | ||||||||
\(52\) | 2.63379e89 | 0.213996 | ||||||||
\(53\) | −3.23348e90 | −0.966467 | −0.483234 | − | 0.875491i | \(-0.660538\pi\) | ||||
−0.483234 | + | 0.875491i | \(0.660538\pi\) | |||||||
\(54\) | −1.53450e90 | −0.171907 | ||||||||
\(55\) | −3.06436e91 | −1.31008 | ||||||||
\(56\) | 8.73942e91 | 1.45081 | ||||||||
\(57\) | 2.22539e91 | 0.145873 | ||||||||
\(58\) | 3.24026e92 | 0.852334 | ||||||||
\(59\) | −3.76398e92 | −0.403568 | −0.201784 | − | 0.979430i | \(-0.564674\pi\) | ||||
−0.201784 | + | 0.979430i | \(0.564674\pi\) | |||||||
\(60\) | −7.82206e91 | −0.0347041 | ||||||||
\(61\) | −9.74654e92 | −0.181566 | −0.0907829 | − | 0.995871i | \(-0.528937\pi\) | ||||
−0.0907829 | + | 0.995871i | \(0.528937\pi\) | |||||||
\(62\) | −3.11312e93 | −0.246963 | ||||||||
\(63\) | −5.50428e94 | −1.88505 | ||||||||
\(64\) | 3.14561e94 | 0.471256 | ||||||||
\(65\) | 1.31105e95 | 0.870297 | ||||||||
\(66\) | −2.75480e94 | −0.0820416 | ||||||||
\(67\) | −4.90505e95 | −0.663309 | −0.331655 | − | 0.943401i | \(-0.607607\pi\) | ||||
−0.331655 | + | 0.943401i | \(0.607607\pi\) | |||||||
\(68\) | 2.17199e95 | 0.134940 | ||||||||
\(69\) | 2.34889e95 | 0.0678087 | ||||||||
\(70\) | −2.22546e97 | −3.01837 | ||||||||
\(71\) | −2.06839e96 | −0.133220 | −0.0666098 | − | 0.997779i | \(-0.521218\pi\) | ||||
−0.0666098 | + | 0.997779i | \(0.521218\pi\) | |||||||
\(72\) | −2.46270e97 | −0.761123 | ||||||||
\(73\) | −4.35765e97 | −0.652833 | −0.326417 | − | 0.945226i | \(-0.605841\pi\) | ||||
−0.326417 | + | 0.945226i | \(0.605841\pi\) | |||||||
\(74\) | −9.24075e97 | −0.677707 | ||||||||
\(75\) | −1.83830e97 | −0.0666348 | ||||||||
\(76\) | −3.66429e98 | −0.662638 | ||||||||
\(77\) | −1.98183e99 | −1.80427 | ||||||||
\(78\) | 1.17861e98 | 0.0545008 | ||||||||
\(79\) | −6.86400e99 | −1.62613 | −0.813064 | − | 0.582174i | \(-0.802202\pi\) | ||||
−0.813064 | + | 0.582174i | \(0.802202\pi\) | |||||||
\(80\) | −1.37627e100 | −1.68453 | ||||||||
\(81\) | 1.54236e100 | 0.983379 | ||||||||
\(82\) | 1.84267e100 | 0.616910 | ||||||||
\(83\) | 1.96175e100 | 0.347572 | 0.173786 | − | 0.984783i | \(-0.444400\pi\) | ||||
0.173786 | + | 0.984783i | \(0.444400\pi\) | |||||||
\(84\) | −5.05880e99 | −0.0477952 | ||||||||
\(85\) | 1.08117e101 | 0.548785 | ||||||||
\(86\) | 4.75790e101 | 1.30691 | ||||||||
\(87\) | 3.66644e100 | 0.0548888 | ||||||||
\(88\) | −8.86698e101 | −0.728510 | ||||||||
\(89\) | 1.19123e102 | 0.540780 | 0.270390 | − | 0.962751i | \(-0.412847\pi\) | ||||
0.270390 | + | 0.962751i | \(0.412847\pi\) | |||||||
\(90\) | 6.27116e102 | 1.58349 | ||||||||
\(91\) | 8.47900e102 | 1.19859 | ||||||||
\(92\) | −3.86765e102 | −0.308025 | ||||||||
\(93\) | −3.52258e101 | −0.0159040 | ||||||||
\(94\) | 2.81752e103 | 0.725530 | ||||||||
\(95\) | −1.82401e104 | −2.69487 | ||||||||
\(96\) | −5.68462e102 | −0.0484687 | ||||||||
\(97\) | 1.02974e104 | 0.509580 | 0.254790 | − | 0.966996i | \(-0.417994\pi\) | ||||
0.254790 | + | 0.966996i | \(0.417994\pi\) | |||||||
\(98\) | −1.03872e105 | −3.00006 | ||||||||
\(99\) | 5.58462e104 | 0.946555 | ||||||||
\(100\) | 3.02693e104 | 0.302693 | ||||||||
\(101\) | 3.13638e104 | 0.186019 | 0.0930094 | − | 0.995665i | \(-0.470351\pi\) | ||||
0.0930094 | + | 0.995665i | \(0.470351\pi\) | |||||||
\(102\) | 9.71956e103 | 0.0343667 | ||||||||
\(103\) | −3.39113e105 | −0.718439 | −0.359219 | − | 0.933253i | \(-0.616957\pi\) | ||||
−0.359219 | + | 0.933253i | \(0.616957\pi\) | |||||||
\(104\) | 3.79363e105 | 0.483954 | ||||||||
\(105\) | −2.51817e105 | −0.194378 | ||||||||
\(106\) | 2.38256e106 | 1.11811 | ||||||||
\(107\) | 1.15787e106 | 0.331904 | 0.165952 | − | 0.986134i | \(-0.446930\pi\) | ||||
0.165952 | + | 0.986134i | \(0.446930\pi\) | |||||||
\(108\) | 2.85901e105 | 0.0502885 | ||||||||
\(109\) | 1.01283e107 | 1.09811 | 0.549055 | − | 0.835786i | \(-0.314988\pi\) | ||||
0.549055 | + | 0.835786i | \(0.314988\pi\) | |||||||
\(110\) | 2.25794e107 | 1.51564 | ||||||||
\(111\) | −1.04562e106 | −0.0436431 | ||||||||
\(112\) | −8.90082e107 | −2.31998 | ||||||||
\(113\) | 4.58630e106 | 0.0749626 | 0.0374813 | − | 0.999297i | \(-0.488067\pi\) | ||||
0.0374813 | + | 0.999297i | \(0.488067\pi\) | |||||||
\(114\) | −1.63975e107 | −0.168762 | ||||||||
\(115\) | −1.92524e108 | −1.25270 | ||||||||
\(116\) | −6.03711e107 | −0.249336 | ||||||||
\(117\) | −2.38931e108 | −0.628804 | ||||||||
\(118\) | 2.77345e108 | 0.466891 | ||||||||
\(119\) | 6.99233e108 | 0.755799 | ||||||||
\(120\) | −1.12666e108 | −0.0784837 | ||||||||
\(121\) | −2.08629e108 | −0.0940030 | ||||||||
\(122\) | 7.18164e108 | 0.210055 | ||||||||
\(123\) | 2.08504e108 | 0.0397279 | ||||||||
\(124\) | 5.80023e108 | 0.0722448 | ||||||||
\(125\) | −1.77910e109 | −0.145353 | ||||||||
\(126\) | 4.05578e110 | 2.18082 | ||||||||
\(127\) | 2.26248e110 | 0.803320 | 0.401660 | − | 0.915789i | \(-0.368433\pi\) | ||||
0.401660 | + | 0.915789i | \(0.368433\pi\) | |||||||
\(128\) | −5.08356e110 | −1.19576 | ||||||||
\(129\) | 5.38369e109 | 0.0841628 | ||||||||
\(130\) | −9.66033e110 | −1.00685 | ||||||||
\(131\) | 9.11375e110 | 0.635264 | 0.317632 | − | 0.948214i | \(-0.397112\pi\) | ||||
0.317632 | + | 0.948214i | \(0.397112\pi\) | |||||||
\(132\) | 5.13263e109 | 0.0239999 | ||||||||
\(133\) | −1.17965e112 | −3.71144 | ||||||||
\(134\) | 3.61424e111 | 0.767387 | ||||||||
\(135\) | 1.42316e111 | 0.204517 | ||||||||
\(136\) | 3.12847e111 | 0.305168 | ||||||||
\(137\) | 1.96095e112 | 1.30208 | 0.651039 | − | 0.759044i | \(-0.274333\pi\) | ||||
0.651039 | + | 0.759044i | \(0.274333\pi\) | |||||||
\(138\) | −1.73076e111 | −0.0784484 | ||||||||
\(139\) | −5.25948e111 | −0.163180 | −0.0815899 | − | 0.996666i | \(-0.526000\pi\) | ||||
−0.0815899 | + | 0.996666i | \(0.526000\pi\) | |||||||
\(140\) | 4.14638e112 | 0.882973 | ||||||||
\(141\) | 3.18810e111 | 0.0467228 | ||||||||
\(142\) | 1.52407e112 | 0.154123 | ||||||||
\(143\) | −8.60276e112 | −0.601860 | ||||||||
\(144\) | 2.50818e113 | 1.21710 | ||||||||
\(145\) | −3.00515e113 | −1.01402 | ||||||||
\(146\) | 3.21089e113 | 0.755267 | ||||||||
\(147\) | −1.17534e113 | −0.193199 | ||||||||
\(148\) | 1.72170e113 | 0.198252 | ||||||||
\(149\) | −1.63050e114 | −1.31838 | −0.659190 | − | 0.751976i | \(-0.729101\pi\) | ||||
−0.659190 | + | 0.751976i | \(0.729101\pi\) | |||||||
\(150\) | 1.35454e113 | 0.0770902 | ||||||||
\(151\) | −1.72555e114 | −0.692846 | −0.346423 | − | 0.938078i | \(-0.612604\pi\) | ||||
−0.346423 | + | 0.938078i | \(0.612604\pi\) | |||||||
\(152\) | −5.27793e114 | −1.49856 | ||||||||
\(153\) | −1.97038e114 | −0.396506 | ||||||||
\(154\) | 1.46029e115 | 2.08738 | ||||||||
\(155\) | 2.88724e114 | 0.293812 | ||||||||
\(156\) | −2.19593e113 | −0.0159433 | ||||||||
\(157\) | 9.78183e113 | 0.0507795 | 0.0253897 | − | 0.999678i | \(-0.491917\pi\) | ||||
0.0253897 | + | 0.999678i | \(0.491917\pi\) | |||||||
\(158\) | 5.05767e115 | 1.88128 | ||||||||
\(159\) | 2.69593e114 | 0.0720044 | ||||||||
\(160\) | 4.65933e115 | 0.895415 | ||||||||
\(161\) | −1.24512e116 | −1.72525 | ||||||||
\(162\) | −1.13647e116 | −1.13768 | ||||||||
\(163\) | 7.23022e115 | 0.523965 | 0.261983 | − | 0.965073i | \(-0.415624\pi\) | ||||
0.261983 | + | 0.965073i | \(0.415624\pi\) | |||||||
\(164\) | −3.43319e115 | −0.180466 | ||||||||
\(165\) | 2.55492e115 | 0.0976047 | ||||||||
\(166\) | −1.44550e116 | −0.402108 | ||||||||
\(167\) | −3.73133e115 | −0.0757268 | −0.0378634 | − | 0.999283i | \(-0.512055\pi\) | ||||
−0.0378634 | + | 0.999283i | \(0.512055\pi\) | |||||||
\(168\) | −7.28653e115 | −0.108089 | ||||||||
\(169\) | −5.52501e116 | −0.600180 | ||||||||
\(170\) | −7.96652e116 | −0.634893 | ||||||||
\(171\) | 3.32416e117 | 1.94709 | ||||||||
\(172\) | −8.86471e116 | −0.382315 | ||||||||
\(173\) | −3.68706e117 | −1.17290 | −0.586449 | − | 0.809986i | \(-0.699474\pi\) | ||||
−0.586449 | + | 0.809986i | \(0.699474\pi\) | |||||||
\(174\) | −2.70158e116 | −0.0635012 | ||||||||
\(175\) | 9.74464e117 | 1.69538 | ||||||||
\(176\) | 9.03073e117 | 1.16495 | ||||||||
\(177\) | 3.13823e116 | 0.0300669 | ||||||||
\(178\) | −8.77746e117 | −0.625632 | ||||||||
\(179\) | 2.91163e118 | 1.54651 | 0.773253 | − | 0.634098i | \(-0.218628\pi\) | ||||
0.773253 | + | 0.634098i | \(0.218628\pi\) | |||||||
\(180\) | −1.16842e118 | −0.463224 | ||||||||
\(181\) | −5.31349e118 | −1.57491 | −0.787454 | − | 0.616374i | \(-0.788601\pi\) | ||||
−0.787454 | + | 0.616374i | \(0.788601\pi\) | |||||||
\(182\) | −6.24767e118 | −1.38666 | ||||||||
\(183\) | 8.12622e116 | 0.0135271 | ||||||||
\(184\) | −5.57085e118 | −0.696603 | ||||||||
\(185\) | 8.57027e118 | 0.806267 | ||||||||
\(186\) | 2.59558e117 | 0.0183994 | ||||||||
\(187\) | −7.09438e118 | −0.379516 | ||||||||
\(188\) | −5.24949e118 | −0.212241 | ||||||||
\(189\) | 9.20405e118 | 0.281666 | ||||||||
\(190\) | 1.34401e120 | 3.11772 | ||||||||
\(191\) | −6.62984e119 | −1.16749 | −0.583743 | − | 0.811939i | \(-0.698412\pi\) | ||||
−0.583743 | + | 0.811939i | \(0.698412\pi\) | |||||||
\(192\) | −2.62267e118 | −0.0351098 | ||||||||
\(193\) | −2.46353e119 | −0.251072 | −0.125536 | − | 0.992089i | \(-0.540065\pi\) | ||||
−0.125536 | + | 0.992089i | \(0.540065\pi\) | |||||||
\(194\) | −7.58756e119 | −0.589537 | ||||||||
\(195\) | −1.09309e119 | −0.0648395 | ||||||||
\(196\) | 1.93530e120 | 0.877617 | ||||||||
\(197\) | 3.61918e120 | 1.25641 | 0.628207 | − | 0.778046i | \(-0.283789\pi\) | ||||
0.628207 | + | 0.778046i | \(0.283789\pi\) | |||||||
\(198\) | −4.11497e120 | −1.09508 | ||||||||
\(199\) | −6.75502e120 | −1.37988 | −0.689938 | − | 0.723868i | \(-0.742362\pi\) | ||||
−0.689938 | + | 0.723868i | \(0.742362\pi\) | |||||||
\(200\) | 4.35989e120 | 0.684543 | ||||||||
\(201\) | 4.08960e119 | 0.0494184 | ||||||||
\(202\) | −2.31101e120 | −0.215206 | ||||||||
\(203\) | −1.94354e121 | −1.39653 | ||||||||
\(204\) | −1.81091e119 | −0.0100534 | ||||||||
\(205\) | −1.70898e121 | −0.733936 | ||||||||
\(206\) | 2.49872e121 | 0.831166 | ||||||||
\(207\) | 3.50864e121 | 0.905099 | ||||||||
\(208\) | −3.86369e121 | −0.773886 | ||||||||
\(209\) | 1.19687e122 | 1.86366 | ||||||||
\(210\) | 1.85549e121 | 0.224877 | ||||||||
\(211\) | 1.13421e122 | 1.07118 | 0.535592 | − | 0.844477i | \(-0.320089\pi\) | ||||
0.535592 | + | 0.844477i | \(0.320089\pi\) | |||||||
\(212\) | −4.43908e121 | −0.327085 | ||||||||
\(213\) | 1.72452e120 | 0.00992522 | ||||||||
\(214\) | −8.53167e121 | −0.383982 | ||||||||
\(215\) | −4.41268e122 | −1.55483 | ||||||||
\(216\) | 4.11803e121 | 0.113728 | ||||||||
\(217\) | 1.86728e122 | 0.404644 | ||||||||
\(218\) | −7.46295e122 | −1.27041 | ||||||||
\(219\) | 3.63321e121 | 0.0486379 | ||||||||
\(220\) | −4.20690e122 | −0.443375 | ||||||||
\(221\) | 3.03524e122 | 0.252115 | ||||||||
\(222\) | 7.70452e121 | 0.0504910 | ||||||||
\(223\) | 1.67124e123 | 0.865035 | 0.432517 | − | 0.901626i | \(-0.357625\pi\) | ||||
0.432517 | + | 0.901626i | \(0.357625\pi\) | |||||||
\(224\) | 3.01335e123 | 1.23319 | ||||||||
\(225\) | −2.74596e123 | −0.889429 | ||||||||
\(226\) | −3.37937e122 | −0.0867247 | ||||||||
\(227\) | −4.72016e123 | −0.960725 | −0.480363 | − | 0.877070i | \(-0.659495\pi\) | ||||
−0.480363 | + | 0.877070i | \(0.659495\pi\) | |||||||
\(228\) | 3.05512e122 | 0.0493684 | ||||||||
\(229\) | 8.23914e123 | 1.05808 | 0.529040 | − | 0.848597i | \(-0.322552\pi\) | ||||
0.529040 | + | 0.848597i | \(0.322552\pi\) | |||||||
\(230\) | 1.41859e124 | 1.44926 | ||||||||
\(231\) | 1.65236e123 | 0.134423 | ||||||||
\(232\) | −8.69567e123 | −0.563876 | ||||||||
\(233\) | −1.55779e124 | −0.805977 | −0.402988 | − | 0.915205i | \(-0.632029\pi\) | ||||
−0.402988 | + | 0.915205i | \(0.632029\pi\) | |||||||
\(234\) | 1.76054e124 | 0.727467 | ||||||||
\(235\) | −2.61309e124 | −0.863161 | ||||||||
\(236\) | −5.16738e123 | −0.136581 | ||||||||
\(237\) | 5.72289e123 | 0.121151 | ||||||||
\(238\) | −5.15223e124 | −0.874389 | ||||||||
\(239\) | −1.18903e125 | −1.61921 | −0.809607 | − | 0.586972i | \(-0.800320\pi\) | ||||
−0.809607 | + | 0.586972i | \(0.800320\pi\) | |||||||
\(240\) | 1.14747e124 | 0.125502 | ||||||||
\(241\) | 1.11462e125 | 0.980017 | 0.490009 | − | 0.871718i | \(-0.336994\pi\) | ||||
0.490009 | + | 0.871718i | \(0.336994\pi\) | |||||||
\(242\) | 1.53726e124 | 0.108753 | ||||||||
\(243\) | −3.89405e124 | −0.221856 | ||||||||
\(244\) | −1.33805e124 | −0.0614479 | ||||||||
\(245\) | 9.63356e125 | 3.56917 | ||||||||
\(246\) | −1.53634e124 | −0.0459614 | ||||||||
\(247\) | −5.12066e125 | −1.23804 | ||||||||
\(248\) | 8.35447e124 | 0.163383 | ||||||||
\(249\) | −1.63562e124 | −0.0258951 | ||||||||
\(250\) | 1.31091e125 | 0.168160 | ||||||||
\(251\) | −1.11133e126 | −1.15604 | −0.578019 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578019 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(252\) | −7.55655e125 | −0.637962 | ||||||||
\(253\) | 1.26329e126 | 0.866317 | ||||||||
\(254\) | −1.66708e126 | −0.929367 | ||||||||
\(255\) | −9.01434e124 | −0.0408860 | ||||||||
\(256\) | 2.46976e126 | 0.912129 | ||||||||
\(257\) | −5.66215e126 | −1.70409 | −0.852044 | − | 0.523470i | \(-0.824637\pi\) | ||||
−0.852044 | + | 0.523470i | \(0.824637\pi\) | |||||||
\(258\) | −3.96692e125 | −0.0973685 | ||||||||
\(259\) | 5.54269e126 | 1.11041 | ||||||||
\(260\) | 1.79987e126 | 0.294537 | ||||||||
\(261\) | 5.47672e126 | 0.732646 | ||||||||
\(262\) | −6.71538e126 | −0.734941 | ||||||||
\(263\) | −9.17187e126 | −0.821828 | −0.410914 | − | 0.911674i | \(-0.634790\pi\) | ||||
−0.410914 | + | 0.911674i | \(0.634790\pi\) | |||||||
\(264\) | 7.39288e125 | 0.0542760 | ||||||||
\(265\) | −2.20969e127 | −1.33022 | ||||||||
\(266\) | 8.69215e127 | 4.29379 | ||||||||
\(267\) | −9.93194e125 | −0.0402896 | ||||||||
\(268\) | −6.73389e126 | −0.224486 | ||||||||
\(269\) | −4.82313e127 | −1.32231 | −0.661156 | − | 0.750248i | \(-0.729934\pi\) | ||||
−0.661156 | + | 0.750248i | \(0.729934\pi\) | |||||||
\(270\) | −1.04864e127 | −0.236608 | ||||||||
\(271\) | 6.98433e127 | 1.29789 | 0.648943 | − | 0.760837i | \(-0.275211\pi\) | ||||
0.648943 | + | 0.760837i | \(0.275211\pi\) | |||||||
\(272\) | −3.18624e127 | −0.487991 | ||||||||
\(273\) | −7.06940e126 | −0.0892984 | ||||||||
\(274\) | −1.44491e128 | −1.50638 | ||||||||
\(275\) | −9.88687e127 | −0.851319 | ||||||||
\(276\) | 3.22467e126 | 0.0229487 | ||||||||
\(277\) | −1.33380e128 | −0.785058 | −0.392529 | − | 0.919740i | \(-0.628400\pi\) | ||||
−0.392529 | + | 0.919740i | \(0.628400\pi\) | |||||||
\(278\) | 3.87540e127 | 0.188784 | ||||||||
\(279\) | −5.26183e127 | −0.212284 | ||||||||
\(280\) | 5.97232e128 | 1.99685 | ||||||||
\(281\) | 1.71423e128 | 0.475321 | 0.237660 | − | 0.971348i | \(-0.423619\pi\) | ||||
0.237660 | + | 0.971348i | \(0.423619\pi\) | |||||||
\(282\) | −2.34912e127 | −0.0540539 | ||||||||
\(283\) | 4.21932e128 | 0.806221 | 0.403111 | − | 0.915151i | \(-0.367929\pi\) | ||||
0.403111 | + | 0.915151i | \(0.367929\pi\) | |||||||
\(284\) | −2.83958e127 | −0.0450859 | ||||||||
\(285\) | 1.52078e128 | 0.200776 | ||||||||
\(286\) | 6.33885e128 | 0.696296 | ||||||||
\(287\) | −1.10525e129 | −1.01079 | ||||||||
\(288\) | −8.49137e128 | −0.646952 | ||||||||
\(289\) | −1.32417e129 | −0.841023 | ||||||||
\(290\) | 2.21432e129 | 1.17313 | ||||||||
\(291\) | −8.58552e127 | −0.0379651 | ||||||||
\(292\) | −5.98239e128 | −0.220941 | ||||||||
\(293\) | −3.79428e129 | −1.17106 | −0.585530 | − | 0.810651i | \(-0.699114\pi\) | ||||
−0.585530 | + | 0.810651i | \(0.699114\pi\) | |||||||
\(294\) | 8.66039e128 | 0.223513 | ||||||||
\(295\) | −2.57222e129 | −0.555459 | ||||||||
\(296\) | 2.47988e129 | 0.448348 | ||||||||
\(297\) | −9.33839e128 | −0.141436 | ||||||||
\(298\) | 1.20141e130 | 1.52524 | ||||||||
\(299\) | −5.40484e129 | −0.575500 | ||||||||
\(300\) | −2.52371e128 | −0.0225514 | ||||||||
\(301\) | −2.85383e130 | −2.14135 | ||||||||
\(302\) | 1.27145e130 | 0.801559 | ||||||||
\(303\) | −2.61497e128 | −0.0138589 | ||||||||
\(304\) | 5.37540e130 | 2.39634 | ||||||||
\(305\) | −6.66056e129 | −0.249902 | ||||||||
\(306\) | 1.45185e130 | 0.458720 | ||||||||
\(307\) | 2.81819e130 | 0.750249 | 0.375125 | − | 0.926974i | \(-0.377600\pi\) | ||||
0.375125 | + | 0.926974i | \(0.377600\pi\) | |||||||
\(308\) | −2.72075e130 | −0.610627 | ||||||||
\(309\) | 2.82737e129 | 0.0535256 | ||||||||
\(310\) | −2.12743e130 | −0.339913 | ||||||||
\(311\) | −1.12349e131 | −1.51583 | −0.757914 | − | 0.652355i | \(-0.773781\pi\) | ||||
−0.757914 | + | 0.652355i | \(0.773781\pi\) | |||||||
\(312\) | −3.16295e129 | −0.0360559 | ||||||||
\(313\) | 9.89355e130 | 0.953398 | 0.476699 | − | 0.879067i | \(-0.341833\pi\) | ||||
0.476699 | + | 0.879067i | \(0.341833\pi\) | |||||||
\(314\) | −7.20764e129 | −0.0587471 | ||||||||
\(315\) | −3.76150e131 | −2.59452 | ||||||||
\(316\) | −9.42323e130 | −0.550336 | ||||||||
\(317\) | 2.02522e131 | 1.00198 | 0.500992 | − | 0.865452i | \(-0.332969\pi\) | ||||
0.500992 | + | 0.865452i | \(0.332969\pi\) | |||||||
\(318\) | −1.98647e130 | −0.0833024 | ||||||||
\(319\) | 1.97190e131 | 0.701253 | ||||||||
\(320\) | 2.14964e131 | 0.648622 | ||||||||
\(321\) | −9.65381e129 | −0.0247278 | ||||||||
\(322\) | 9.17454e131 | 1.99596 | ||||||||
\(323\) | −4.22282e131 | −0.780675 | ||||||||
\(324\) | 2.11742e131 | 0.332808 | ||||||||
\(325\) | 4.22997e131 | 0.565537 | ||||||||
\(326\) | −5.32752e131 | −0.606179 | ||||||||
\(327\) | −8.44453e130 | −0.0818122 | ||||||||
\(328\) | −4.94506e131 | −0.408127 | ||||||||
\(329\) | −1.68998e132 | −1.18876 | ||||||||
\(330\) | −1.88257e131 | −0.112920 | ||||||||
\(331\) | 2.08449e132 | 1.06667 | 0.533336 | − | 0.845904i | \(-0.320938\pi\) | ||||
0.533336 | + | 0.845904i | \(0.320938\pi\) | |||||||
\(332\) | 2.69319e131 | 0.117630 | ||||||||
\(333\) | −1.56188e132 | −0.582541 | ||||||||
\(334\) | 2.74940e131 | 0.0876088 | ||||||||
\(335\) | −3.35200e132 | −0.912959 | ||||||||
\(336\) | 7.42110e131 | 0.172845 | ||||||||
\(337\) | −1.43308e132 | −0.285563 | −0.142781 | − | 0.989754i | \(-0.545605\pi\) | ||||
−0.142781 | + | 0.989754i | \(0.545605\pi\) | |||||||
\(338\) | 4.07105e132 | 0.694352 | ||||||||
\(339\) | −3.82385e130 | −0.00558491 | ||||||||
\(340\) | 1.48429e132 | 0.185727 | ||||||||
\(341\) | −1.89453e132 | −0.203188 | ||||||||
\(342\) | −2.44937e133 | −2.25260 | ||||||||
\(343\) | 3.82776e133 | 3.01997 | ||||||||
\(344\) | −1.27684e133 | −0.864609 | ||||||||
\(345\) | 1.60518e132 | 0.0933299 | ||||||||
\(346\) | 2.71677e133 | 1.35693 | ||||||||
\(347\) | 1.61500e133 | 0.693228 | 0.346614 | − | 0.938008i | \(-0.387331\pi\) | ||||
0.346614 | + | 0.938008i | \(0.387331\pi\) | |||||||
\(348\) | 5.03347e131 | 0.0185762 | ||||||||
\(349\) | 3.42631e133 | 1.08766 | 0.543829 | − | 0.839196i | \(-0.316974\pi\) | ||||
0.543829 | + | 0.839196i | \(0.316974\pi\) | |||||||
\(350\) | −7.18024e133 | −1.96140 | ||||||||
\(351\) | 3.99532e132 | 0.0939566 | ||||||||
\(352\) | −3.05733e133 | −0.619231 | ||||||||
\(353\) | −4.49817e133 | −0.784990 | −0.392495 | − | 0.919754i | \(-0.628388\pi\) | ||||
−0.392495 | + | 0.919754i | \(0.628388\pi\) | |||||||
\(354\) | −2.31238e132 | −0.0347846 | ||||||||
\(355\) | −1.41349e133 | −0.183359 | ||||||||
\(356\) | 1.63538e133 | 0.183018 | ||||||||
\(357\) | −5.82988e132 | −0.0563091 | ||||||||
\(358\) | −2.14540e134 | −1.78916 | ||||||||
\(359\) | −2.93840e132 | −0.0211667 | −0.0105833 | − | 0.999944i | \(-0.503369\pi\) | ||||
−0.0105833 | + | 0.999944i | \(0.503369\pi\) | |||||||
\(360\) | −1.68295e134 | −1.04759 | ||||||||
\(361\) | 5.26583e134 | 2.83360 | ||||||||
\(362\) | 3.91519e134 | 1.82202 | ||||||||
\(363\) | 1.73945e132 | 0.00700348 | ||||||||
\(364\) | 1.16404e134 | 0.405644 | ||||||||
\(365\) | −2.97792e134 | −0.898540 | ||||||||
\(366\) | −5.98772e132 | −0.0156496 | ||||||||
\(367\) | −2.14897e134 | −0.486700 | −0.243350 | − | 0.969939i | \(-0.578246\pi\) | ||||
−0.243350 | + | 0.969939i | \(0.578246\pi\) | |||||||
\(368\) | 5.67373e134 | 1.11393 | ||||||||
\(369\) | 3.11451e134 | 0.530281 | ||||||||
\(370\) | −6.31492e134 | −0.932776 | ||||||||
\(371\) | −1.42908e135 | −1.83200 | ||||||||
\(372\) | −4.83597e132 | −0.00538244 | ||||||||
\(373\) | 8.60799e134 | 0.832124 | 0.416062 | − | 0.909336i | \(-0.363410\pi\) | ||||
0.416062 | + | 0.909336i | \(0.363410\pi\) | |||||||
\(374\) | 5.22743e134 | 0.439065 | ||||||||
\(375\) | 1.48333e133 | 0.0108292 | ||||||||
\(376\) | −7.56120e134 | −0.479986 | ||||||||
\(377\) | −8.43655e134 | −0.465848 | ||||||||
\(378\) | −6.78191e134 | −0.325861 | ||||||||
\(379\) | 9.16019e134 | 0.383130 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(380\) | −2.50409e135 | −0.912035 | ||||||||
\(381\) | −1.88635e134 | −0.0598496 | ||||||||
\(382\) | 4.88513e135 | 1.35067 | ||||||||
\(383\) | 3.16438e135 | 0.762699 | 0.381349 | − | 0.924431i | \(-0.375459\pi\) | ||||
0.381349 | + | 0.924431i | \(0.375459\pi\) | |||||||
\(384\) | 4.23844e134 | 0.0890875 | ||||||||
\(385\) | −1.35434e136 | −2.48335 | ||||||||
\(386\) | 1.81523e135 | 0.290467 | ||||||||
\(387\) | 8.04185e135 | 1.12339 | ||||||||
\(388\) | 1.41368e135 | 0.172459 | ||||||||
\(389\) | 1.36629e136 | 1.45609 | 0.728045 | − | 0.685529i | \(-0.240429\pi\) | ||||
0.728045 | + | 0.685529i | \(0.240429\pi\) | |||||||
\(390\) | 8.05434e134 | 0.0750133 | ||||||||
\(391\) | −4.45718e135 | −0.362895 | ||||||||
\(392\) | 2.78755e136 | 1.98474 | ||||||||
\(393\) | −7.59863e134 | −0.0473289 | ||||||||
\(394\) | −2.66675e136 | −1.45355 | ||||||||
\(395\) | −4.69070e136 | −2.23815 | ||||||||
\(396\) | 7.66684e135 | 0.320346 | ||||||||
\(397\) | −4.44670e136 | −1.62756 | −0.813778 | − | 0.581176i | \(-0.802593\pi\) | ||||
−0.813778 | + | 0.581176i | \(0.802593\pi\) | |||||||
\(398\) | 4.97737e136 | 1.59639 | ||||||||
\(399\) | 9.83540e135 | 0.276513 | ||||||||
\(400\) | −4.44041e136 | −1.09465 | ||||||||
\(401\) | −2.66460e136 | −0.576171 | −0.288086 | − | 0.957605i | \(-0.593019\pi\) | ||||
−0.288086 | + | 0.957605i | \(0.593019\pi\) | |||||||
\(402\) | −3.01338e135 | −0.0571724 | ||||||||
\(403\) | 8.10552e135 | 0.134979 | ||||||||
\(404\) | 4.30578e135 | 0.0629549 | ||||||||
\(405\) | 1.05401e137 | 1.35349 | ||||||||
\(406\) | 1.43208e137 | 1.61566 | ||||||||
\(407\) | −5.62359e136 | −0.557580 | ||||||||
\(408\) | −2.60837e135 | −0.0227358 | ||||||||
\(409\) | 2.73574e136 | 0.209701 | 0.104851 | − | 0.994488i | \(-0.466564\pi\) | ||||
0.104851 | + | 0.994488i | \(0.466564\pi\) | |||||||
\(410\) | 1.25924e137 | 0.849096 | ||||||||
\(411\) | −1.63495e136 | −0.0970084 | ||||||||
\(412\) | −4.65550e136 | −0.243144 | ||||||||
\(413\) | −1.66354e137 | −0.764990 | ||||||||
\(414\) | −2.58531e137 | −1.04712 | ||||||||
\(415\) | 1.34062e137 | 0.478387 | ||||||||
\(416\) | 1.30804e137 | 0.411360 | ||||||||
\(417\) | 4.38512e135 | 0.0121573 | ||||||||
\(418\) | −8.81901e137 | −2.15608 | ||||||||
\(419\) | 6.16363e137 | 1.32923 | 0.664616 | − | 0.747186i | \(-0.268595\pi\) | ||||
0.664616 | + | 0.747186i | \(0.268595\pi\) | |||||||
\(420\) | −3.45706e136 | −0.0657839 | ||||||||
\(421\) | 4.88353e137 | 0.820207 | 0.410104 | − | 0.912039i | \(-0.365492\pi\) | ||||
0.410104 | + | 0.912039i | \(0.365492\pi\) | |||||||
\(422\) | −8.35730e137 | −1.23926 | ||||||||
\(423\) | 4.76221e137 | 0.623648 | ||||||||
\(424\) | −6.39391e137 | −0.739706 | ||||||||
\(425\) | 3.48831e137 | 0.356612 | ||||||||
\(426\) | −1.27070e136 | −0.0114826 | ||||||||
\(427\) | −4.30761e137 | −0.344170 | ||||||||
\(428\) | 1.58958e137 | 0.112327 | ||||||||
\(429\) | 7.17258e136 | 0.0448402 | ||||||||
\(430\) | 3.25144e138 | 1.79879 | ||||||||
\(431\) | −2.78682e138 | −1.36475 | −0.682375 | − | 0.731002i | \(-0.739053\pi\) | ||||
−0.682375 | + | 0.731002i | \(0.739053\pi\) | |||||||
\(432\) | −4.19408e137 | −0.181861 | ||||||||
\(433\) | 3.64338e138 | 1.39923 | 0.699617 | − | 0.714518i | \(-0.253354\pi\) | ||||
0.699617 | + | 0.714518i | \(0.253354\pi\) | |||||||
\(434\) | −1.37589e138 | −0.468135 | ||||||||
\(435\) | 2.50556e137 | 0.0755473 | ||||||||
\(436\) | 1.39046e138 | 0.371637 | ||||||||
\(437\) | 7.51956e138 | 1.78204 | ||||||||
\(438\) | −2.67709e137 | −0.0562695 | ||||||||
\(439\) | −1.56099e138 | −0.291080 | −0.145540 | − | 0.989352i | \(-0.546492\pi\) | ||||
−0.145540 | + | 0.989352i | \(0.546492\pi\) | |||||||
\(440\) | −6.05949e138 | −1.00270 | ||||||||
\(441\) | −1.75566e139 | −2.57878 | ||||||||
\(442\) | −2.23649e138 | −0.291674 | ||||||||
\(443\) | 1.04375e138 | 0.120893 | 0.0604467 | − | 0.998171i | \(-0.480747\pi\) | ||||
0.0604467 | + | 0.998171i | \(0.480747\pi\) | |||||||
\(444\) | −1.43547e137 | −0.0147703 | ||||||||
\(445\) | 8.14060e138 | 0.744313 | ||||||||
\(446\) | −1.23144e139 | −1.00076 | ||||||||
\(447\) | 1.35943e138 | 0.0982229 | ||||||||
\(448\) | 1.39025e139 | 0.893297 | ||||||||
\(449\) | −1.68684e139 | −0.964142 | −0.482071 | − | 0.876132i | \(-0.660115\pi\) | ||||
−0.482071 | + | 0.876132i | \(0.660115\pi\) | |||||||
\(450\) | 2.02333e139 | 1.02899 | ||||||||
\(451\) | 1.12139e139 | 0.507559 | ||||||||
\(452\) | 6.29630e137 | 0.0253698 | ||||||||
\(453\) | 1.43868e138 | 0.0516190 | ||||||||
\(454\) | 3.47800e139 | 1.11147 | ||||||||
\(455\) | 5.79435e139 | 1.64971 | ||||||||
\(456\) | 4.40050e138 | 0.111647 | ||||||||
\(457\) | −4.28923e139 | −0.970015 | −0.485008 | − | 0.874510i | \(-0.661183\pi\) | ||||
−0.485008 | + | 0.874510i | \(0.661183\pi\) | |||||||
\(458\) | −6.07092e139 | −1.22410 | ||||||||
\(459\) | 3.29479e138 | 0.0592464 | ||||||||
\(460\) | −2.64306e139 | −0.423957 | ||||||||
\(461\) | −3.43285e139 | −0.491311 | −0.245656 | − | 0.969357i | \(-0.579003\pi\) | ||||
−0.245656 | + | 0.969357i | \(0.579003\pi\) | |||||||
\(462\) | −1.21752e139 | −0.155515 | ||||||||
\(463\) | −7.65195e139 | −0.872510 | −0.436255 | − | 0.899823i | \(-0.643695\pi\) | ||||
−0.436255 | + | 0.899823i | \(0.643695\pi\) | |||||||
\(464\) | 8.85626e139 | 0.901688 | ||||||||
\(465\) | −2.40725e138 | −0.0218898 | ||||||||
\(466\) | 1.14784e140 | 0.932440 | ||||||||
\(467\) | −7.91580e139 | −0.574590 | −0.287295 | − | 0.957842i | \(-0.592756\pi\) | ||||
−0.287295 | + | 0.957842i | \(0.592756\pi\) | |||||||
\(468\) | −3.28016e139 | −0.212808 | ||||||||
\(469\) | −2.16785e140 | −1.25735 | ||||||||
\(470\) | 1.92543e140 | 0.998597 | ||||||||
\(471\) | −8.15564e137 | −0.00378321 | ||||||||
\(472\) | −7.44293e139 | −0.308879 | ||||||||
\(473\) | 2.89548e140 | 1.07525 | ||||||||
\(474\) | −4.21685e139 | −0.140160 | ||||||||
\(475\) | −5.88500e140 | −1.75119 | ||||||||
\(476\) | 9.59941e139 | 0.255788 | ||||||||
\(477\) | 4.02703e140 | 0.961103 | ||||||||
\(478\) | 8.76127e140 | 1.87328 | ||||||||
\(479\) | −1.70702e140 | −0.327057 | −0.163529 | − | 0.986539i | \(-0.552288\pi\) | ||||
−0.163529 | + | 0.986539i | \(0.552288\pi\) | |||||||
\(480\) | −3.88474e139 | −0.0667109 | ||||||||
\(481\) | 2.40598e140 | 0.370404 | ||||||||
\(482\) | −8.21300e140 | −1.13379 | ||||||||
\(483\) | 1.03812e140 | 0.128536 | ||||||||
\(484\) | −2.86415e139 | −0.0318138 | ||||||||
\(485\) | 7.03703e140 | 0.701371 | ||||||||
\(486\) | 2.86929e140 | 0.256667 | ||||||||
\(487\) | 7.74854e140 | 0.622228 | 0.311114 | − | 0.950373i | \(-0.399298\pi\) | ||||
0.311114 | + | 0.950373i | \(0.399298\pi\) | |||||||
\(488\) | −1.92729e140 | −0.138965 | ||||||||
\(489\) | −6.02823e139 | −0.0390368 | ||||||||
\(490\) | −7.09839e141 | −4.12920 | ||||||||
\(491\) | −6.91335e140 | −0.361335 | −0.180668 | − | 0.983544i | \(-0.557826\pi\) | ||||
−0.180668 | + | 0.983544i | \(0.557826\pi\) | |||||||
\(492\) | 2.86244e139 | 0.0134452 | ||||||||
\(493\) | −6.95732e140 | −0.293750 | ||||||||
\(494\) | 3.77311e141 | 1.43230 | ||||||||
\(495\) | 3.81640e141 | 1.30281 | ||||||||
\(496\) | −8.50876e140 | −0.261263 | ||||||||
\(497\) | −9.14151e140 | −0.252527 | ||||||||
\(498\) | 1.20519e140 | 0.0299582 | ||||||||
\(499\) | 3.99593e141 | 0.894003 | 0.447001 | − | 0.894533i | \(-0.352492\pi\) | ||||
0.447001 | + | 0.894533i | \(0.352492\pi\) | |||||||
\(500\) | −2.44243e140 | −0.0491923 | ||||||||
\(501\) | 3.11102e139 | 0.00564185 | ||||||||
\(502\) | 8.18871e141 | 1.33743 | ||||||||
\(503\) | 1.07217e142 | 1.57741 | 0.788705 | − | 0.614772i | \(-0.210752\pi\) | ||||
0.788705 | + | 0.614772i | \(0.210752\pi\) | |||||||
\(504\) | −1.08842e142 | −1.44276 | ||||||||
\(505\) | 2.14333e141 | 0.256031 | ||||||||
\(506\) | −9.30845e141 | −1.00225 | ||||||||
\(507\) | 4.60650e140 | 0.0447150 | ||||||||
\(508\) | 3.10604e141 | 0.271870 | ||||||||
\(509\) | −1.71358e142 | −1.35276 | −0.676381 | − | 0.736552i | \(-0.736453\pi\) | ||||
−0.676381 | + | 0.736552i | \(0.736453\pi\) | |||||||
\(510\) | 6.64212e140 | 0.0473013 | ||||||||
\(511\) | −1.92592e142 | −1.23749 | ||||||||
\(512\) | 2.42321e141 | 0.140513 | ||||||||
\(513\) | −5.55853e141 | −0.290937 | ||||||||
\(514\) | 4.17210e142 | 1.97147 | ||||||||
\(515\) | −2.31742e142 | −0.988837 | ||||||||
\(516\) | 7.39099e140 | 0.0284835 | ||||||||
\(517\) | 1.71464e142 | 0.596925 | ||||||||
\(518\) | −4.08408e142 | −1.28464 | ||||||||
\(519\) | 3.07410e141 | 0.0873841 | ||||||||
\(520\) | 2.59248e142 | 0.666100 | ||||||||
\(521\) | 5.71915e142 | 1.32847 | 0.664234 | − | 0.747525i | \(-0.268758\pi\) | ||||
0.664234 | + | 0.747525i | \(0.268758\pi\) | |||||||
\(522\) | −4.03547e142 | −0.847603 | ||||||||
\(523\) | −3.96164e142 | −0.752552 | −0.376276 | − | 0.926508i | \(-0.622796\pi\) | ||||
−0.376276 | + | 0.926508i | \(0.622796\pi\) | |||||||
\(524\) | 1.25118e142 | 0.214995 | ||||||||
\(525\) | −8.12463e141 | −0.126311 | ||||||||
\(526\) | 6.75820e142 | 0.950779 | ||||||||
\(527\) | 6.68433e141 | 0.0851139 | ||||||||
\(528\) | −7.52941e141 | −0.0867921 | ||||||||
\(529\) | −1.64439e142 | −0.171625 | ||||||||
\(530\) | 1.62819e143 | 1.53894 | ||||||||
\(531\) | 4.68772e142 | 0.401328 | ||||||||
\(532\) | −1.61948e143 | −1.25608 | ||||||||
\(533\) | −4.79771e142 | −0.337175 | ||||||||
\(534\) | 7.31825e141 | 0.0466113 | ||||||||
\(535\) | 7.91264e142 | 0.456823 | ||||||||
\(536\) | −9.69928e142 | −0.507678 | ||||||||
\(537\) | −2.42758e142 | −0.115219 | ||||||||
\(538\) | 3.55387e143 | 1.52979 | ||||||||
\(539\) | −6.32129e143 | −2.46829 | ||||||||
\(540\) | 1.95378e142 | 0.0692155 | ||||||||
\(541\) | −3.06037e143 | −0.983823 | −0.491912 | − | 0.870645i | \(-0.663702\pi\) | ||||
−0.491912 | + | 0.870645i | \(0.663702\pi\) | |||||||
\(542\) | −5.14633e143 | −1.50153 | ||||||||
\(543\) | 4.43015e142 | 0.117335 | ||||||||
\(544\) | 1.07869e143 | 0.259392 | ||||||||
\(545\) | 6.92146e143 | 1.51141 | ||||||||
\(546\) | 5.20902e142 | 0.103310 | ||||||||
\(547\) | 3.58490e143 | 0.645865 | 0.322933 | − | 0.946422i | \(-0.395331\pi\) | ||||
0.322933 | + | 0.946422i | \(0.395331\pi\) | |||||||
\(548\) | 2.69209e143 | 0.440667 | ||||||||
\(549\) | 1.21385e143 | 0.180558 | ||||||||
\(550\) | 7.28504e143 | 0.984897 | ||||||||
\(551\) | 1.17375e144 | 1.44250 | ||||||||
\(552\) | 4.64472e142 | 0.0518988 | ||||||||
\(553\) | −3.03364e144 | −3.08244 | ||||||||
\(554\) | 9.82795e143 | 0.908239 | ||||||||
\(555\) | −7.14550e142 | −0.0600691 | ||||||||
\(556\) | −7.22048e142 | −0.0552255 | ||||||||
\(557\) | 2.76592e144 | 1.92505 | 0.962524 | − | 0.271198i | \(-0.0874199\pi\) | ||||
0.962524 | + | 0.271198i | \(0.0874199\pi\) | |||||||
\(558\) | 3.87713e143 | 0.245592 | ||||||||
\(559\) | −1.23880e144 | −0.714299 | ||||||||
\(560\) | −6.08262e144 | −3.19315 | ||||||||
\(561\) | 5.91497e142 | 0.0282750 | ||||||||
\(562\) | −1.26311e144 | −0.549902 | ||||||||
\(563\) | 1.21160e144 | 0.480473 | 0.240237 | − | 0.970714i | \(-0.422775\pi\) | ||||
0.240237 | + | 0.970714i | \(0.422775\pi\) | |||||||
\(564\) | 4.37678e142 | 0.0158126 | ||||||||
\(565\) | 3.13417e143 | 0.103176 | ||||||||
\(566\) | −3.10896e144 | −0.932723 | ||||||||
\(567\) | 6.81665e144 | 1.86406 | ||||||||
\(568\) | −4.09004e143 | −0.101962 | ||||||||
\(569\) | 3.93949e144 | 0.895459 | 0.447730 | − | 0.894169i | \(-0.352233\pi\) | ||||
0.447730 | + | 0.894169i | \(0.352233\pi\) | |||||||
\(570\) | −1.12057e144 | −0.232279 | ||||||||
\(571\) | −2.37657e144 | −0.449320 | −0.224660 | − | 0.974437i | \(-0.572127\pi\) | ||||
−0.224660 | + | 0.974437i | \(0.572127\pi\) | |||||||
\(572\) | −1.18103e144 | −0.203690 | ||||||||
\(573\) | 5.52766e143 | 0.0869809 | ||||||||
\(574\) | 8.14395e144 | 1.16939 | ||||||||
\(575\) | −6.21161e144 | −0.814033 | ||||||||
\(576\) | −3.91760e144 | −0.468640 | ||||||||
\(577\) | −6.30933e143 | −0.0689054 | −0.0344527 | − | 0.999406i | \(-0.510969\pi\) | ||||
−0.0344527 | + | 0.999406i | \(0.510969\pi\) | |||||||
\(578\) | 9.75703e144 | 0.972985 | ||||||||
\(579\) | 2.05398e143 | 0.0187056 | ||||||||
\(580\) | −4.12562e144 | −0.343178 | ||||||||
\(581\) | 8.67023e144 | 0.658846 | ||||||||
\(582\) | 6.32616e143 | 0.0439221 | ||||||||
\(583\) | 1.44994e145 | 0.919921 | ||||||||
\(584\) | −8.61685e144 | −0.499660 | ||||||||
\(585\) | −1.63280e145 | −0.865466 | ||||||||
\(586\) | 2.79578e145 | 1.35481 | ||||||||
\(587\) | −4.42324e145 | −1.95993 | −0.979963 | − | 0.199179i | \(-0.936172\pi\) | ||||
−0.979963 | + | 0.199179i | \(0.936172\pi\) | |||||||
\(588\) | −1.61357e144 | −0.0653849 | ||||||||
\(589\) | −1.12769e145 | −0.417962 | ||||||||
\(590\) | 1.89531e145 | 0.642614 | ||||||||
\(591\) | −3.01750e144 | −0.0936063 | ||||||||
\(592\) | −2.52568e145 | −0.716949 | ||||||||
\(593\) | −5.28905e145 | −1.37406 | −0.687031 | − | 0.726628i | \(-0.741086\pi\) | ||||
−0.687031 | + | 0.726628i | \(0.741086\pi\) | |||||||
\(594\) | 6.88090e144 | 0.163628 | ||||||||
\(595\) | 4.77840e145 | 1.04026 | ||||||||
\(596\) | −2.23842e145 | −0.446184 | ||||||||
\(597\) | 5.63203e144 | 0.102805 | ||||||||
\(598\) | 3.98250e145 | 0.665800 | ||||||||
\(599\) | −7.53160e145 | −1.15340 | −0.576699 | − | 0.816957i | \(-0.695659\pi\) | ||||
−0.576699 | + | 0.816957i | \(0.695659\pi\) | |||||||
\(600\) | −3.63508e144 | −0.0510003 | ||||||||
\(601\) | 1.21435e146 | 1.56111 | 0.780553 | − | 0.625090i | \(-0.214938\pi\) | ||||
0.780553 | + | 0.625090i | \(0.214938\pi\) | |||||||
\(602\) | 2.10282e146 | 2.47734 | ||||||||
\(603\) | 6.10883e145 | 0.659628 | ||||||||
\(604\) | −2.36891e145 | −0.234482 | ||||||||
\(605\) | −1.42572e145 | −0.129383 | ||||||||
\(606\) | 1.92681e144 | 0.0160335 | ||||||||
\(607\) | −1.55972e146 | −1.19026 | −0.595130 | − | 0.803630i | \(-0.702899\pi\) | ||||
−0.595130 | + | 0.803630i | \(0.702899\pi\) | |||||||
\(608\) | −1.81983e146 | −1.27377 | ||||||||
\(609\) | 1.62043e145 | 0.104045 | ||||||||
\(610\) | 4.90777e145 | 0.289113 | ||||||||
\(611\) | −7.33589e145 | −0.396542 | ||||||||
\(612\) | −2.70503e145 | −0.134191 | ||||||||
\(613\) | 1.58307e146 | 0.720816 | 0.360408 | − | 0.932795i | \(-0.382638\pi\) | ||||
0.360408 | + | 0.932795i | \(0.382638\pi\) | |||||||
\(614\) | −2.07655e146 | −0.867968 | ||||||||
\(615\) | 1.42487e145 | 0.0546802 | ||||||||
\(616\) | −3.91888e146 | −1.38094 | ||||||||
\(617\) | −4.02502e146 | −1.30256 | −0.651279 | − | 0.758838i | \(-0.725767\pi\) | ||||
−0.651279 | + | 0.758838i | \(0.725767\pi\) | |||||||
\(618\) | −2.08332e145 | −0.0619242 | ||||||||
\(619\) | 6.53348e146 | 1.78396 | 0.891981 | − | 0.452073i | \(-0.149315\pi\) | ||||
0.891981 | + | 0.452073i | \(0.149315\pi\) | |||||||
\(620\) | 3.96374e145 | 0.0994356 | ||||||||
\(621\) | −5.86702e145 | −0.135241 | ||||||||
\(622\) | 8.27834e146 | 1.75367 | ||||||||
\(623\) | 5.26480e146 | 1.02508 | ||||||||
\(624\) | 3.22137e145 | 0.0576566 | ||||||||
\(625\) | −6.65117e146 | −1.09445 | ||||||||
\(626\) | −7.28996e146 | −1.10299 | ||||||||
\(627\) | −9.97895e145 | −0.138848 | ||||||||
\(628\) | 1.34290e145 | 0.0171855 | ||||||||
\(629\) | 1.98413e146 | 0.233567 | ||||||||
\(630\) | 2.77162e147 | 3.00162 | ||||||||
\(631\) | −9.04534e146 | −0.901329 | −0.450664 | − | 0.892693i | \(-0.648813\pi\) | ||||
−0.450664 | + | 0.892693i | \(0.648813\pi\) | |||||||
\(632\) | −1.35729e147 | −1.24459 | ||||||||
\(633\) | −9.45651e145 | −0.0798061 | ||||||||
\(634\) | −1.49226e147 | −1.15920 | ||||||||
\(635\) | 1.54612e147 | 1.10567 | ||||||||
\(636\) | 3.70110e145 | 0.0243687 | ||||||||
\(637\) | 2.70449e147 | 1.63970 | ||||||||
\(638\) | −1.45298e147 | −0.811285 | ||||||||
\(639\) | 2.57600e146 | 0.132480 | ||||||||
\(640\) | −3.47399e147 | −1.64581 | ||||||||
\(641\) | 1.32664e147 | 0.579039 | 0.289520 | − | 0.957172i | \(-0.406504\pi\) | ||||
0.289520 | + | 0.957172i | \(0.406504\pi\) | |||||||
\(642\) | 7.11331e145 | 0.0286077 | ||||||||
\(643\) | −2.59325e147 | −0.961100 | −0.480550 | − | 0.876967i | \(-0.659563\pi\) | ||||
−0.480550 | + | 0.876967i | \(0.659563\pi\) | |||||||
\(644\) | −1.70936e147 | −0.583883 | ||||||||
\(645\) | 3.67909e146 | 0.115839 | ||||||||
\(646\) | 3.11154e147 | 0.903169 | ||||||||
\(647\) | −5.34417e147 | −1.43023 | −0.715115 | − | 0.699007i | \(-0.753626\pi\) | ||||
−0.715115 | + | 0.699007i | \(0.753626\pi\) | |||||||
\(648\) | 3.04987e147 | 0.752650 | ||||||||
\(649\) | 1.68782e147 | 0.384132 | ||||||||
\(650\) | −3.11681e147 | −0.654274 | ||||||||
\(651\) | −1.55685e146 | −0.0301471 | ||||||||
\(652\) | 9.92600e146 | 0.177327 | ||||||||
\(653\) | 6.55280e146 | 0.108015 | 0.0540076 | − | 0.998541i | \(-0.482800\pi\) | ||||
0.0540076 | + | 0.998541i | \(0.482800\pi\) | |||||||
\(654\) | 6.22226e146 | 0.0946491 | ||||||||
\(655\) | 6.22813e147 | 0.874358 | ||||||||
\(656\) | 5.03639e147 | 0.652631 | ||||||||
\(657\) | 5.42709e147 | 0.649210 | ||||||||
\(658\) | 1.24524e148 | 1.37529 | ||||||||
\(659\) | −6.28428e147 | −0.640872 | −0.320436 | − | 0.947270i | \(-0.603829\pi\) | ||||
−0.320436 | + | 0.947270i | \(0.603829\pi\) | |||||||
\(660\) | 3.50752e146 | 0.0330327 | ||||||||
\(661\) | 1.52889e148 | 1.32984 | 0.664920 | − | 0.746914i | \(-0.268465\pi\) | ||||
0.664920 | + | 0.746914i | \(0.268465\pi\) | |||||||
\(662\) | −1.53594e148 | −1.23404 | ||||||||
\(663\) | −2.53065e146 | −0.0187833 | ||||||||
\(664\) | 3.87919e147 | 0.266021 | ||||||||
\(665\) | −8.06147e148 | −5.10832 | ||||||||
\(666\) | 1.15086e148 | 0.673945 | ||||||||
\(667\) | 1.23889e148 | 0.670540 | ||||||||
\(668\) | −5.12256e146 | −0.0256285 | ||||||||
\(669\) | −1.39340e147 | −0.0644474 | ||||||||
\(670\) | 2.46989e148 | 1.05621 | ||||||||
\(671\) | 4.37049e147 | 0.172821 | ||||||||
\(672\) | −2.51239e147 | −0.0918757 | ||||||||
\(673\) | −4.68333e148 | −1.58403 | −0.792016 | − | 0.610501i | \(-0.790968\pi\) | ||||
−0.792016 | + | 0.610501i | \(0.790968\pi\) | |||||||
\(674\) | 1.05595e148 | 0.330370 | ||||||||
\(675\) | 4.59169e147 | 0.132900 | ||||||||
\(676\) | −7.58501e147 | −0.203121 | ||||||||
\(677\) | 5.48314e148 | 1.35870 | 0.679351 | − | 0.733814i | \(-0.262261\pi\) | ||||
0.679351 | + | 0.733814i | \(0.262261\pi\) | |||||||
\(678\) | 2.81756e146 | 0.00646123 | ||||||||
\(679\) | 4.55109e148 | 0.965944 | ||||||||
\(680\) | 2.13792e148 | 0.420024 | ||||||||
\(681\) | 3.93545e147 | 0.0715766 | ||||||||
\(682\) | 1.39597e148 | 0.235069 | ||||||||
\(683\) | −5.85471e148 | −0.912890 | −0.456445 | − | 0.889752i | \(-0.650877\pi\) | ||||
−0.456445 | + | 0.889752i | \(0.650877\pi\) | |||||||
\(684\) | 4.56357e148 | 0.658960 | ||||||||
\(685\) | 1.34007e149 | 1.79214 | ||||||||
\(686\) | −2.82045e149 | −3.49383 | ||||||||
\(687\) | −6.86942e147 | −0.0788299 | ||||||||
\(688\) | 1.30043e149 | 1.38259 | ||||||||
\(689\) | −6.20338e148 | −0.611110 | ||||||||
\(690\) | −1.18276e148 | −0.107974 | ||||||||
\(691\) | −5.99911e147 | −0.0507562 | −0.0253781 | − | 0.999678i | \(-0.508079\pi\) | ||||
−0.0253781 | + | 0.999678i | \(0.508079\pi\) | |||||||
\(692\) | −5.06178e148 | −0.396948 | ||||||||
\(693\) | 2.46820e149 | 1.79426 | ||||||||
\(694\) | −1.19000e149 | −0.802000 | ||||||||
\(695\) | −3.59421e148 | −0.224596 | ||||||||
\(696\) | 7.25005e147 | 0.0420103 | ||||||||
\(697\) | −3.95650e148 | −0.212613 | ||||||||
\(698\) | −2.52464e149 | −1.25832 | ||||||||
\(699\) | 1.29881e148 | 0.0600475 | ||||||||
\(700\) | 1.33779e149 | 0.573775 | ||||||||
\(701\) | 5.70124e148 | 0.226868 | 0.113434 | − | 0.993546i | \(-0.463815\pi\) | ||||
0.113434 | + | 0.993546i | \(0.463815\pi\) | |||||||
\(702\) | −2.94391e148 | −0.108699 | ||||||||
\(703\) | −3.34735e149 | −1.14696 | ||||||||
\(704\) | −1.41054e149 | −0.448559 | ||||||||
\(705\) | 2.17868e148 | 0.0643079 | ||||||||
\(706\) | 3.31443e149 | 0.908161 | ||||||||
\(707\) | 1.38617e149 | 0.352611 | ||||||||
\(708\) | 4.30832e147 | 0.0101756 | ||||||||
\(709\) | −6.68298e146 | −0.00146569 | −0.000732846 | − | 1.00000i | \(-0.500233\pi\) | ||||
−0.000732846 | 1.00000i | \(0.500233\pi\) | ||||||||
\(710\) | 1.04151e149 | 0.212130 | ||||||||
\(711\) | 8.54853e149 | 1.61710 | ||||||||
\(712\) | 2.35555e149 | 0.413897 | ||||||||
\(713\) | −1.19028e149 | −0.194289 | ||||||||
\(714\) | 4.29569e148 | 0.0651444 | ||||||||
\(715\) | −5.87893e149 | −0.828382 | ||||||||
\(716\) | 3.99722e149 | 0.523389 | ||||||||
\(717\) | 9.91362e148 | 0.120636 | ||||||||
\(718\) | 2.16513e148 | 0.0244879 | ||||||||
\(719\) | 5.00706e149 | 0.526400 | 0.263200 | − | 0.964741i | \(-0.415222\pi\) | ||||
0.263200 | + | 0.964741i | \(0.415222\pi\) | |||||||
\(720\) | 1.71403e150 | 1.67518 | ||||||||
\(721\) | −1.49875e150 | −1.36185 | ||||||||
\(722\) | −3.88007e150 | −3.27821 | ||||||||
\(723\) | −9.29323e148 | −0.0730140 | ||||||||
\(724\) | −7.29462e149 | −0.533001 | ||||||||
\(725\) | −9.69585e149 | −0.658932 | ||||||||
\(726\) | −1.28170e148 | −0.00810237 | ||||||||
\(727\) | 6.05190e149 | 0.355906 | 0.177953 | − | 0.984039i | \(-0.443053\pi\) | ||||
0.177953 | + | 0.984039i | \(0.443053\pi\) | |||||||
\(728\) | 1.67664e150 | 0.917368 | ||||||||
\(729\) | −1.89913e150 | −0.966850 | ||||||||
\(730\) | 2.19425e150 | 1.03953 | ||||||||
\(731\) | −1.02159e150 | −0.450417 | ||||||||
\(732\) | 1.11561e148 | 0.00457804 | ||||||||
\(733\) | 4.46401e150 | 1.70516 | 0.852582 | − | 0.522594i | \(-0.175036\pi\) | ||||
0.852582 | + | 0.522594i | \(0.175036\pi\) | |||||||
\(734\) | 1.58344e150 | 0.563066 | ||||||||
\(735\) | −8.03202e149 | −0.265913 | ||||||||
\(736\) | −1.92083e150 | −0.592110 | ||||||||
\(737\) | 2.19949e150 | 0.631364 | ||||||||
\(738\) | −2.29490e150 | −0.613485 | ||||||||
\(739\) | 3.56099e150 | 0.886621 | 0.443311 | − | 0.896368i | \(-0.353804\pi\) | ||||
0.443311 | + | 0.896368i | \(0.353804\pi\) | |||||||
\(740\) | 1.17657e150 | 0.272868 | ||||||||
\(741\) | 4.26937e149 | 0.0922376 | ||||||||
\(742\) | 1.05300e151 | 2.11946 | ||||||||
\(743\) | −6.98622e150 | −1.31018 | −0.655088 | − | 0.755553i | \(-0.727368\pi\) | ||||
−0.655088 | + | 0.755553i | \(0.727368\pi\) | |||||||
\(744\) | −6.96558e148 | −0.0121724 | ||||||||
\(745\) | −1.11424e151 | −1.81458 | ||||||||
\(746\) | −6.34271e150 | −0.962690 | ||||||||
\(747\) | −2.44320e150 | −0.345643 | ||||||||
\(748\) | −9.73952e149 | −0.128441 | ||||||||
\(749\) | 5.11737e150 | 0.629146 | ||||||||
\(750\) | −1.09298e149 | −0.0125284 | ||||||||
\(751\) | 1.18621e150 | 0.126784 | 0.0633920 | − | 0.997989i | \(-0.479808\pi\) | ||||
0.0633920 | + | 0.997989i | \(0.479808\pi\) | |||||||
\(752\) | 7.70084e150 | 0.767541 | ||||||||
\(753\) | 9.26575e149 | 0.0861280 | ||||||||
\(754\) | 6.21639e150 | 0.538942 | ||||||||
\(755\) | −1.17920e151 | −0.953613 | ||||||||
\(756\) | 1.26358e150 | 0.0953252 | ||||||||
\(757\) | −5.00625e150 | −0.352354 | −0.176177 | − | 0.984359i | \(-0.556373\pi\) | ||||
−0.176177 | + | 0.984359i | \(0.556373\pi\) | |||||||
\(758\) | −6.74959e150 | −0.443245 | ||||||||
\(759\) | −1.05328e150 | −0.0645430 | ||||||||
\(760\) | −3.60682e151 | −2.06258 | ||||||||
\(761\) | 2.83818e151 | 1.51476 | 0.757382 | − | 0.652972i | \(-0.226478\pi\) | ||||
0.757382 | + | 0.652972i | \(0.226478\pi\) | |||||||
\(762\) | 1.38994e150 | 0.0692404 | ||||||||
\(763\) | 4.47635e151 | 2.08154 | ||||||||
\(764\) | −9.10177e150 | −0.395116 | ||||||||
\(765\) | −1.34651e151 | −0.545739 | ||||||||
\(766\) | −2.33164e151 | −0.882371 | ||||||||
\(767\) | −7.22114e150 | −0.255181 | ||||||||
\(768\) | −2.05917e150 | −0.0679561 | ||||||||
\(769\) | 3.01681e151 | 0.929853 | 0.464927 | − | 0.885349i | \(-0.346081\pi\) | ||||
0.464927 | + | 0.885349i | \(0.346081\pi\) | |||||||
\(770\) | 9.97928e151 | 2.87300 | ||||||||
\(771\) | 4.72084e150 | 0.126959 | ||||||||
\(772\) | −3.38205e150 | −0.0849713 | ||||||||
\(773\) | −2.17459e151 | −0.510452 | −0.255226 | − | 0.966881i | \(-0.582150\pi\) | ||||
−0.255226 | + | 0.966881i | \(0.582150\pi\) | |||||||
\(774\) | −5.92556e151 | −1.29966 | ||||||||
\(775\) | 9.31541e150 | 0.190925 | ||||||||
\(776\) | 2.03622e151 | 0.390018 | ||||||||
\(777\) | −4.62124e150 | −0.0827285 | ||||||||
\(778\) | −1.00674e152 | −1.68456 | ||||||||
\(779\) | 6.67487e151 | 1.04406 | ||||||||
\(780\) | −1.50065e150 | −0.0219438 | ||||||||
\(781\) | 9.27493e150 | 0.126804 | ||||||||
\(782\) | 3.28423e151 | 0.419835 | ||||||||
\(783\) | −9.15797e150 | −0.109473 | ||||||||
\(784\) | −2.83903e152 | −3.17378 | ||||||||
\(785\) | 6.68468e150 | 0.0698914 | ||||||||
\(786\) | 5.59897e150 | 0.0547551 | ||||||||
\(787\) | −1.84640e152 | −1.68909 | −0.844544 | − | 0.535486i | \(-0.820128\pi\) | ||||
−0.844544 | + | 0.535486i | \(0.820128\pi\) | |||||||
\(788\) | 4.96858e151 | 0.425212 | ||||||||
\(789\) | 7.64708e150 | 0.0612284 | ||||||||
\(790\) | 3.45629e152 | 2.58933 | ||||||||
\(791\) | 2.02698e151 | 0.142097 | ||||||||
\(792\) | 1.10431e152 | 0.724466 | ||||||||
\(793\) | −1.86986e151 | −0.114806 | ||||||||
\(794\) | 3.27650e152 | 1.88293 | ||||||||
\(795\) | 1.84234e151 | 0.0991047 | ||||||||
\(796\) | −9.27362e151 | −0.466996 | ||||||||
\(797\) | −7.49684e151 | −0.353440 | −0.176720 | − | 0.984261i | \(-0.556549\pi\) | ||||
−0.176720 | + | 0.984261i | \(0.556549\pi\) | |||||||
\(798\) | −7.24711e151 | −0.319899 | ||||||||
\(799\) | −6.04964e151 | −0.250048 | ||||||||
\(800\) | 1.50329e152 | 0.581859 | ||||||||
\(801\) | −1.48358e152 | −0.537778 | ||||||||
\(802\) | 1.96338e152 | 0.666577 | ||||||||
\(803\) | 1.95403e152 | 0.621392 | ||||||||
\(804\) | 5.61441e150 | 0.0167248 | ||||||||
\(805\) | −8.50886e152 | −2.37459 | ||||||||
\(806\) | −5.97247e151 | −0.156158 | ||||||||
\(807\) | 4.02130e151 | 0.0985159 | ||||||||
\(808\) | 6.20190e151 | 0.142373 | ||||||||
\(809\) | 7.83353e152 | 1.68523 | 0.842617 | − | 0.538513i | \(-0.181014\pi\) | ||||
0.842617 | + | 0.538513i | \(0.181014\pi\) | |||||||
\(810\) | −7.76637e152 | −1.56587 | ||||||||
\(811\) | −7.46411e152 | −1.41053 | −0.705267 | − | 0.708942i | \(-0.749173\pi\) | ||||
−0.705267 | + | 0.708942i | \(0.749173\pi\) | |||||||
\(812\) | −2.66818e152 | −0.472633 | ||||||||
\(813\) | −5.82321e151 | −0.0966961 | ||||||||
\(814\) | 4.14368e152 | 0.645068 | ||||||||
\(815\) | 4.94097e152 | 0.721170 | ||||||||
\(816\) | 2.65654e151 | 0.0363566 | ||||||||
\(817\) | 1.72349e153 | 2.21183 | ||||||||
\(818\) | −2.01580e152 | −0.242605 | ||||||||
\(819\) | −1.05599e153 | −1.19194 | ||||||||
\(820\) | −2.34617e152 | −0.248388 | ||||||||
\(821\) | −1.02758e153 | −1.02047 | −0.510233 | − | 0.860036i | \(-0.670441\pi\) | ||||
−0.510233 | + | 0.860036i | \(0.670441\pi\) | |||||||
\(822\) | 1.20470e152 | 0.112230 | ||||||||
\(823\) | 9.91017e152 | 0.866143 | 0.433072 | − | 0.901359i | \(-0.357430\pi\) | ||||
0.433072 | + | 0.901359i | \(0.357430\pi\) | |||||||
\(824\) | −6.70564e152 | −0.549872 | ||||||||
\(825\) | 8.24322e151 | 0.0634256 | ||||||||
\(826\) | 1.22576e153 | 0.885023 | ||||||||
\(827\) | 5.69334e152 | 0.385770 | 0.192885 | − | 0.981221i | \(-0.438216\pi\) | ||||
0.192885 | + | 0.981221i | \(0.438216\pi\) | |||||||
\(828\) | 4.81684e152 | 0.306316 | ||||||||
\(829\) | −2.36891e152 | −0.141396 | −0.0706979 | − | 0.997498i | \(-0.522523\pi\) | ||||
−0.0706979 | + | 0.997498i | \(0.522523\pi\) | |||||||
\(830\) | −9.87820e152 | −0.553450 | ||||||||
\(831\) | 1.11206e152 | 0.0584890 | ||||||||
\(832\) | 6.03481e152 | 0.297981 | ||||||||
\(833\) | 2.23029e153 | 1.03395 | ||||||||
\(834\) | −3.23113e151 | −0.0140649 | ||||||||
\(835\) | −2.54991e152 | −0.104228 | ||||||||
\(836\) | 1.64312e153 | 0.630725 | ||||||||
\(837\) | 8.79864e151 | 0.0317197 | ||||||||
\(838\) | −4.54161e153 | −1.53780 | ||||||||
\(839\) | 2.95617e152 | 0.0940214 | 0.0470107 | − | 0.998894i | \(-0.485031\pi\) | ||||
0.0470107 | + | 0.998894i | \(0.485031\pi\) | |||||||
\(840\) | −4.97945e152 | −0.148771 | ||||||||
\(841\) | −1.62898e153 | −0.457221 | ||||||||
\(842\) | −3.59838e153 | −0.948904 | ||||||||
\(843\) | −1.42924e152 | −0.0354127 | ||||||||
\(844\) | 1.55710e153 | 0.362524 | ||||||||
\(845\) | −3.77567e153 | −0.826070 | ||||||||
\(846\) | −3.50899e153 | −0.721502 | ||||||||
\(847\) | −9.22062e152 | −0.178189 | ||||||||
\(848\) | 6.51199e153 | 1.18286 | ||||||||
\(849\) | −3.51787e152 | −0.0600657 | ||||||||
\(850\) | −2.57032e153 | −0.412567 | ||||||||
\(851\) | −3.53312e153 | −0.533159 | ||||||||
\(852\) | 2.36751e151 | 0.00335903 | ||||||||
\(853\) | 6.28821e153 | 0.838886 | 0.419443 | − | 0.907782i | \(-0.362225\pi\) | ||||
0.419443 | + | 0.907782i | \(0.362225\pi\) | |||||||
\(854\) | 3.17402e153 | 0.398173 | ||||||||
\(855\) | 2.27165e154 | 2.67992 | ||||||||
\(856\) | 2.28959e153 | 0.254030 | ||||||||
\(857\) | −3.80402e153 | −0.396962 | −0.198481 | − | 0.980105i | \(-0.563601\pi\) | ||||
−0.198481 | + | 0.980105i | \(0.563601\pi\) | |||||||
\(858\) | −5.28505e152 | −0.0518760 | ||||||||
\(859\) | 6.93239e153 | 0.640091 | 0.320046 | − | 0.947402i | \(-0.396302\pi\) | ||||
0.320046 | + | 0.947402i | \(0.396302\pi\) | |||||||
\(860\) | −6.05794e153 | −0.526206 | ||||||||
\(861\) | 9.21510e152 | 0.0753069 | ||||||||
\(862\) | 2.05344e154 | 1.57889 | ||||||||
\(863\) | −2.25684e154 | −1.63280 | −0.816401 | − | 0.577486i | \(-0.804034\pi\) | ||||
−0.816401 | + | 0.577486i | \(0.804034\pi\) | |||||||
\(864\) | 1.41989e153 | 0.0966684 | ||||||||
\(865\) | −2.51965e154 | −1.61434 | ||||||||
\(866\) | −2.68459e154 | −1.61878 | ||||||||
\(867\) | 1.10403e153 | 0.0626585 | ||||||||
\(868\) | 2.56349e153 | 0.136945 | ||||||||
\(869\) | 3.07791e154 | 1.54781 | ||||||||
\(870\) | −1.84620e153 | −0.0874012 | ||||||||
\(871\) | −9.41026e153 | −0.419419 | ||||||||
\(872\) | 2.00278e154 | 0.840462 | ||||||||
\(873\) | −1.28246e154 | −0.506752 | ||||||||
\(874\) | −5.54071e154 | −2.06165 | ||||||||
\(875\) | −7.86296e153 | −0.275526 | ||||||||
\(876\) | 4.98785e152 | 0.0164607 | ||||||||
\(877\) | 9.58540e153 | 0.297942 | 0.148971 | − | 0.988842i | \(-0.452404\pi\) | ||||
0.148971 | + | 0.988842i | \(0.452404\pi\) | |||||||
\(878\) | 1.15020e154 | 0.336752 | ||||||||
\(879\) | 3.16350e153 | 0.0872472 | ||||||||
\(880\) | 6.17140e154 | 1.60340 | ||||||||
\(881\) | −4.25775e154 | −1.04219 | −0.521093 | − | 0.853500i | \(-0.674475\pi\) | ||||
−0.521093 | + | 0.853500i | \(0.674475\pi\) | |||||||
\(882\) | 1.29364e155 | 2.98341 | ||||||||
\(883\) | −5.65508e154 | −1.22886 | −0.614429 | − | 0.788972i | \(-0.710614\pi\) | ||||
−0.614429 | + | 0.788972i | \(0.710614\pi\) | |||||||
\(884\) | 4.16693e153 | 0.0853242 | ||||||||
\(885\) | 2.14460e153 | 0.0413832 | ||||||||
\(886\) | −7.69079e153 | −0.139862 | ||||||||
\(887\) | −8.11925e154 | −1.39164 | −0.695819 | − | 0.718218i | \(-0.744958\pi\) | ||||
−0.695819 | + | 0.718218i | \(0.744958\pi\) | |||||||
\(888\) | −2.06761e153 | −0.0334032 | ||||||||
\(889\) | 9.99932e154 | 1.52275 | ||||||||
\(890\) | −5.99832e154 | −0.861101 | ||||||||
\(891\) | −6.91614e154 | −0.936018 | ||||||||
\(892\) | 2.29436e154 | 0.292757 | ||||||||
\(893\) | 1.02061e155 | 1.22789 | ||||||||
\(894\) | −1.00168e154 | −0.113635 | ||||||||
\(895\) | 1.98974e155 | 2.12856 | ||||||||
\(896\) | −2.24675e155 | −2.26665 | ||||||||
\(897\) | 4.50631e153 | 0.0428764 | ||||||||
\(898\) | 1.24293e155 | 1.11542 | ||||||||
\(899\) | −1.85793e154 | −0.157270 | ||||||||
\(900\) | −3.76978e154 | −0.301013 | ||||||||
\(901\) | −5.11571e154 | −0.385349 | ||||||||
\(902\) | −8.26282e154 | −0.587198 | ||||||||
\(903\) | 2.37939e154 | 0.159536 | ||||||||
\(904\) | 9.06899e153 | 0.0573742 | ||||||||
\(905\) | −3.63112e155 | −2.16765 | ||||||||
\(906\) | −1.06008e154 | −0.0597183 | ||||||||
\(907\) | 2.73085e155 | 1.45183 | 0.725914 | − | 0.687785i | \(-0.241417\pi\) | ||||
0.725914 | + | 0.687785i | \(0.241417\pi\) | |||||||
\(908\) | −6.48006e154 | −0.325141 | ||||||||
\(909\) | −3.90610e154 | −0.184986 | ||||||||
\(910\) | −4.26951e155 | −1.90856 | ||||||||
\(911\) | 3.00572e155 | 1.26833 | 0.634167 | − | 0.773196i | \(-0.281343\pi\) | ||||
0.634167 | + | 0.773196i | \(0.281343\pi\) | |||||||
\(912\) | −4.48177e154 | −0.178534 | ||||||||
\(913\) | −8.79678e154 | −0.330832 | ||||||||
\(914\) | 3.16047e155 | 1.12222 | ||||||||
\(915\) | 5.55327e153 | 0.0186184 | ||||||||
\(916\) | 1.13111e155 | 0.358090 | ||||||||
\(917\) | 4.02795e155 | 1.20419 | ||||||||
\(918\) | −2.42774e154 | −0.0685426 | ||||||||
\(919\) | 4.20926e155 | 1.12238 | 0.561192 | − | 0.827686i | \(-0.310343\pi\) | ||||
0.561192 | + | 0.827686i | \(0.310343\pi\) | |||||||
\(920\) | −3.80699e155 | −0.958784 | ||||||||
\(921\) | −2.34968e154 | −0.0558956 | ||||||||
\(922\) | 2.52946e155 | 0.568401 | ||||||||
\(923\) | −3.96816e154 | −0.0842365 | ||||||||
\(924\) | 2.26844e154 | 0.0454934 | ||||||||
\(925\) | 2.76512e155 | 0.523929 | ||||||||
\(926\) | 5.63827e155 | 1.00941 | ||||||||
\(927\) | 4.22336e155 | 0.714451 | ||||||||
\(928\) | −2.99826e155 | −0.479293 | ||||||||
\(929\) | −2.46842e155 | −0.372901 | −0.186451 | − | 0.982464i | \(-0.559698\pi\) | ||||
−0.186451 | + | 0.982464i | \(0.559698\pi\) | |||||||
\(930\) | 1.77376e154 | 0.0253244 | ||||||||
\(931\) | −3.76265e156 | −5.07733 | ||||||||
\(932\) | −2.13861e155 | −0.272769 | ||||||||
\(933\) | 9.36717e154 | 0.112933 | ||||||||
\(934\) | 5.83268e155 | 0.664748 | ||||||||
\(935\) | −4.84814e155 | −0.522355 | ||||||||
\(936\) | −4.72464e155 | −0.481268 | ||||||||
\(937\) | 1.82249e156 | 1.75524 | 0.877621 | − | 0.479356i | \(-0.159130\pi\) | ||||
0.877621 | + | 0.479356i | \(0.159130\pi\) | |||||||
\(938\) | 1.59736e156 | 1.45463 | ||||||||
\(939\) | −8.24879e154 | −0.0710308 | ||||||||
\(940\) | −3.58738e155 | −0.292122 | ||||||||
\(941\) | −1.54822e156 | −1.19228 | −0.596138 | − | 0.802882i | \(-0.703299\pi\) | ||||
−0.596138 | + | 0.802882i | \(0.703299\pi\) | |||||||
\(942\) | 6.00940e153 | 0.00437682 | ||||||||
\(943\) | 7.04531e155 | 0.485329 | ||||||||
\(944\) | 7.58038e155 | 0.493925 | ||||||||
\(945\) | 6.28984e155 | 0.387677 | ||||||||
\(946\) | −2.13351e156 | −1.24397 | ||||||||
\(947\) | 2.52207e156 | 1.39118 | 0.695589 | − | 0.718440i | \(-0.255144\pi\) | ||||
0.695589 | + | 0.718440i | \(0.255144\pi\) | |||||||
\(948\) | 7.85666e154 | 0.0410015 | ||||||||
\(949\) | −8.36009e155 | −0.412795 | ||||||||
\(950\) | 4.33631e156 | 2.02596 | ||||||||
\(951\) | −1.68853e155 | −0.0746505 | ||||||||
\(952\) | 1.38267e156 | 0.578467 | ||||||||
\(953\) | −3.92414e155 | −0.155370 | −0.0776850 | − | 0.996978i | \(-0.524753\pi\) | ||||
−0.0776850 | + | 0.996978i | \(0.524753\pi\) | |||||||
\(954\) | −2.96727e156 | −1.11191 | ||||||||
\(955\) | −4.53068e156 | −1.60689 | ||||||||
\(956\) | −1.63236e156 | −0.547996 | ||||||||
\(957\) | −1.64408e155 | −0.0522453 | ||||||||
\(958\) | 1.25780e156 | 0.378375 | ||||||||
\(959\) | 8.66669e156 | 2.46818 | ||||||||
\(960\) | −1.79227e155 | −0.0483241 | ||||||||
\(961\) | −3.73872e156 | −0.954431 | ||||||||
\(962\) | −1.77282e156 | −0.428523 | ||||||||
\(963\) | −1.44203e156 | −0.330062 | ||||||||
\(964\) | 1.53021e156 | 0.331671 | ||||||||
\(965\) | −1.68352e156 | −0.345569 | ||||||||
\(966\) | −7.64931e155 | −0.148704 | ||||||||
\(967\) | 3.51079e156 | 0.646421 | 0.323210 | − | 0.946327i | \(-0.395238\pi\) | ||||
0.323210 | + | 0.946327i | \(0.395238\pi\) | |||||||
\(968\) | −4.12544e155 | −0.0719472 | ||||||||
\(969\) | 3.52080e155 | 0.0581624 | ||||||||
\(970\) | −5.18516e156 | −0.811421 | ||||||||
\(971\) | −4.15598e156 | −0.616118 | −0.308059 | − | 0.951367i | \(-0.599679\pi\) | ||||
−0.308059 | + | 0.951367i | \(0.599679\pi\) | |||||||
\(972\) | −5.34594e155 | −0.0750836 | ||||||||
\(973\) | −2.32450e156 | −0.309318 | ||||||||
\(974\) | −5.70943e156 | −0.719860 | ||||||||
\(975\) | −3.52676e155 | −0.0421341 | ||||||||
\(976\) | 1.96288e156 | 0.222218 | ||||||||
\(977\) | 1.31466e157 | 1.41042 | 0.705209 | − | 0.708999i | \(-0.250853\pi\) | ||||
0.705209 | + | 0.708999i | \(0.250853\pi\) | |||||||
\(978\) | 4.44184e155 | 0.0451620 | ||||||||
\(979\) | −5.34165e156 | −0.514735 | ||||||||
\(980\) | 1.32254e157 | 1.20793 | ||||||||
\(981\) | −1.26140e157 | −1.09202 | ||||||||
\(982\) | 5.09403e156 | 0.418031 | ||||||||
\(983\) | 1.46640e156 | 0.114076 | 0.0570378 | − | 0.998372i | \(-0.481834\pi\) | ||||
0.0570378 | + | 0.998372i | \(0.481834\pi\) | |||||||
\(984\) | 4.12297e155 | 0.0304066 | ||||||||
\(985\) | 2.47326e157 | 1.72929 | ||||||||
\(986\) | 5.12643e156 | 0.339842 | ||||||||
\(987\) | 1.40903e156 | 0.0885662 | ||||||||
\(988\) | −7.02989e156 | −0.418995 | ||||||||
\(989\) | 1.81914e157 | 1.02816 | ||||||||
\(990\) | −2.81208e157 | −1.50723 | ||||||||
\(991\) | 1.77420e157 | 0.901854 | 0.450927 | − | 0.892561i | \(-0.351093\pi\) | ||||
0.450927 | + | 0.892561i | \(0.351093\pi\) | |||||||
\(992\) | 2.88062e156 | 0.138875 | ||||||||
\(993\) | −1.73795e156 | −0.0794699 | ||||||||
\(994\) | 6.73583e156 | 0.292150 | ||||||||
\(995\) | −4.61623e157 | −1.89922 | ||||||||
\(996\) | −2.24546e155 | −0.00876375 | ||||||||
\(997\) | −5.26632e156 | −0.194990 | −0.0974948 | − | 0.995236i | \(-0.531083\pi\) | ||||
−0.0974948 | + | 0.995236i | \(0.531083\pi\) | |||||||
\(998\) | −2.94436e157 | −1.03428 | ||||||||
\(999\) | 2.61172e156 | 0.0870440 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1.106.a.a.1.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.106.a.a.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial |