Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,90,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 90, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 90);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 90 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(451.461862736\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3 x^{6} + \cdots + 56\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{43}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.01484e12\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.42254e13 | −1.77761 | −0.888805 | − | 0.458285i | \(-0.848464\pi\) | ||||
−0.888805 | + | 0.458285i | \(0.848464\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.33691e27 | 2.15990 | ||||||||
\(5\) | −3.67006e30 | −0.288741 | −0.144370 | − | 0.989524i | \(-0.546116\pi\) | ||||
−0.144370 | + | 0.989524i | \(0.546116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.35255e37 | −1.07617 | −0.538085 | − | 0.842891i | \(-0.680852\pi\) | ||||
−0.538085 | + | 0.842891i | \(0.680852\pi\) | |||||||
\(8\) | −3.17513e40 | −2.06185 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.62310e44 | 0.513269 | ||||||||
\(11\) | 2.45458e46 | 1.11687 | 0.558435 | − | 0.829548i | \(-0.311402\pi\) | ||||
0.558435 | + | 0.829548i | \(0.311402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.70001e49 | −1.80134 | −0.900672 | − | 0.434501i | \(-0.856925\pi\) | ||||
−0.900672 | + | 0.434501i | \(0.856925\pi\) | |||||||
\(14\) | 1.92493e51 | 1.91301 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.76705e53 | 1.50527 | ||||||||
\(17\) | −4.97159e54 | −0.874014 | −0.437007 | − | 0.899458i | \(-0.643962\pi\) | ||||
−0.437007 | + | 0.899458i | \(0.643962\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.54728e56 | 0.566522 | 0.283261 | − | 0.959043i | \(-0.408584\pi\) | ||||
0.283261 | + | 0.959043i | \(0.408584\pi\) | |||||||
\(20\) | −4.90655e57 | −0.623651 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.08555e60 | −1.98536 | ||||||||
\(23\) | −2.88267e60 | −0.729301 | −0.364650 | − | 0.931144i | \(-0.618812\pi\) | ||||
−0.364650 | + | 0.931144i | \(0.618812\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.48089e62 | −0.916629 | ||||||||
\(26\) | 2.96311e63 | 3.20209 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.81898e64 | −2.32442 | ||||||||
\(29\) | 1.57790e65 | 1.32242 | 0.661208 | − | 0.750203i | \(-0.270044\pi\) | ||||
0.661208 | + | 0.750203i | \(0.270044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.07570e66 | 1.75633 | 0.878166 | − | 0.478356i | \(-0.158767\pi\) | ||||
0.878166 | + | 0.478356i | \(0.158767\pi\) | |||||||
\(32\) | −5.85187e66 | −0.613932 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.19871e68 | 1.55366 | ||||||||
\(35\) | 1.59741e68 | 0.310734 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.75996e69 | −1.27316 | −0.636580 | − | 0.771211i | \(-0.719651\pi\) | ||||
−0.636580 | + | 0.771211i | \(0.719651\pi\) | |||||||
\(38\) | −2.01105e70 | −1.00706 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.16529e71 | 0.595340 | ||||||||
\(41\) | −2.95976e71 | −0.503936 | −0.251968 | − | 0.967736i | \(-0.581078\pi\) | ||||
−0.251968 | + | 0.967736i | \(0.581078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.81368e72 | −0.370863 | −0.185431 | − | 0.982657i | \(-0.559368\pi\) | ||||
−0.185431 | + | 0.982657i | \(0.559368\pi\) | |||||||
\(44\) | 3.28156e73 | 2.41233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.27487e74 | 1.29641 | ||||||||
\(47\) | −1.54316e73 | −0.0602636 | −0.0301318 | − | 0.999546i | \(-0.509593\pi\) | ||||
−0.0301318 | + | 0.999546i | \(0.509593\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.58682e74 | 0.158140 | ||||||||
\(50\) | 6.54931e75 | 1.62941 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.95734e76 | −3.89072 | ||||||||
\(53\) | −3.79389e76 | −0.706005 | −0.353003 | − | 0.935622i | \(-0.614839\pi\) | ||||
−0.353003 | + | 0.935622i | \(0.614839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.00846e76 | −0.322486 | ||||||||
\(56\) | 1.38199e78 | 2.21890 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.97831e78 | −2.35074 | ||||||||
\(59\) | −4.03039e78 | −0.634502 | −0.317251 | − | 0.948342i | \(-0.602760\pi\) | ||||
−0.317251 | + | 0.948342i | \(0.602760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.95660e79 | −1.05588 | −0.527940 | − | 0.849282i | \(-0.677035\pi\) | ||||
−0.527940 | + | 0.849282i | \(0.677035\pi\) | |||||||
\(62\) | −1.80249e80 | −3.12207 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.81620e79 | −0.413937 | ||||||||
\(65\) | 2.45894e80 | 0.520121 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.44278e80 | 0.298877 | 0.149438 | − | 0.988771i | \(-0.452253\pi\) | ||||
0.149438 | + | 0.988771i | \(0.452253\pi\) | |||||||
\(68\) | −6.64659e81 | −1.88778 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.06461e81 | −0.552364 | ||||||||
\(71\) | −6.75644e81 | −0.281010 | −0.140505 | − | 0.990080i | \(-0.544873\pi\) | ||||
−0.140505 | + | 0.990080i | \(0.544873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.55795e82 | −0.188229 | −0.0941146 | − | 0.995561i | \(-0.530002\pi\) | ||||
−0.0941146 | + | 0.995561i | \(0.530002\pi\) | |||||||
\(74\) | 3.43187e83 | 2.26318 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.07933e83 | 1.22363 | ||||||||
\(77\) | −1.06837e84 | −1.20194 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.89294e84 | −1.75859 | −0.879294 | − | 0.476280i | \(-0.841985\pi\) | ||||
−0.879294 | + | 0.476280i | \(0.841985\pi\) | |||||||
\(80\) | −2.11654e84 | −0.434633 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.30897e85 | 0.895802 | ||||||||
\(83\) | 5.34367e84 | 0.213238 | 0.106619 | − | 0.994300i | \(-0.465997\pi\) | ||||
0.106619 | + | 0.994300i | \(0.465997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.82460e85 | 0.252363 | ||||||||
\(86\) | 8.02105e85 | 0.659250 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.79362e86 | −2.30282 | ||||||||
\(89\) | 7.65546e86 | 1.36809 | 0.684047 | − | 0.729438i | \(-0.260218\pi\) | ||||
0.684047 | + | 0.729438i | \(0.260218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.91621e87 | 1.93855 | ||||||||
\(92\) | −3.85389e87 | −1.57522 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.82466e86 | 0.107125 | ||||||||
\(95\) | −1.66888e87 | −0.163578 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.46156e87 | −0.0566859 | −0.0283430 | − | 0.999598i | \(-0.509023\pi\) | ||||
−0.0283430 | + | 0.999598i | \(0.509023\pi\) | |||||||
\(98\) | −1.14403e88 | −0.281111 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.97983e89 | −1.97983 | ||||||||
\(101\) | −1.76473e89 | −1.13338 | −0.566691 | − | 0.823931i | \(-0.691777\pi\) | ||||
−0.566691 | + | 0.823931i | \(0.691777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.57477e89 | 0.422632 | 0.211316 | − | 0.977418i | \(-0.432225\pi\) | ||||
0.211316 | + | 0.977418i | \(0.432225\pi\) | |||||||
\(104\) | 2.12734e90 | 3.71410 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.67786e90 | 1.25500 | ||||||||
\(107\) | −1.57684e90 | −0.776621 | −0.388311 | − | 0.921529i | \(-0.626941\pi\) | ||||
−0.388311 | + | 0.921529i | \(0.626941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.09287e90 | 1.74833 | 0.874164 | − | 0.485630i | \(-0.161410\pi\) | ||||
0.874164 | + | 0.485630i | \(0.161410\pi\) | |||||||
\(110\) | 3.98402e90 | 0.573255 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.51013e91 | −1.61992 | ||||||||
\(113\) | −1.43205e91 | −0.622255 | −0.311128 | − | 0.950368i | \(-0.600707\pi\) | ||||
−0.311128 | + | 0.950368i | \(0.600707\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.05796e91 | 0.210579 | ||||||||
\(116\) | 2.10951e92 | 2.85629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.78246e92 | 1.12790 | ||||||||
\(119\) | 2.16391e92 | 0.940587 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.19495e92 | 0.247400 | ||||||||
\(122\) | 1.30757e93 | 1.87694 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.44886e93 | 3.79350 | ||||||||
\(125\) | 1.13643e93 | 0.553409 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.89751e93 | −1.17682 | −0.588409 | − | 0.808563i | \(-0.700246\pi\) | ||||
−0.588409 | + | 0.808563i | \(0.700246\pi\) | |||||||
\(128\) | 7.96338e93 | 1.34975 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.08748e94 | −0.924573 | ||||||||
\(131\) | 1.69999e94 | 1.02772 | 0.513858 | − | 0.857875i | \(-0.328216\pi\) | ||||
0.513858 | + | 0.857875i | \(0.328216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.97923e94 | −0.609674 | ||||||||
\(134\) | −2.40709e94 | −0.531287 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.57855e95 | 1.80209 | ||||||||
\(137\) | −6.04210e94 | −0.497878 | −0.248939 | − | 0.968519i | \(-0.580082\pi\) | ||||
−0.248939 | + | 0.968519i | \(0.580082\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.73639e95 | −0.750739 | −0.375370 | − | 0.926875i | \(-0.622484\pi\) | ||||
−0.375370 | + | 0.926875i | \(0.622484\pi\) | |||||||
\(140\) | 2.13560e95 | 0.671154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.98806e95 | 0.499526 | ||||||||
\(143\) | −1.64457e96 | −2.01187 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.79098e95 | −0.381835 | ||||||||
\(146\) | 6.89010e95 | 0.334598 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.03744e97 | −2.74990 | ||||||||
\(149\) | −8.32082e96 | −1.63447 | −0.817236 | − | 0.576304i | \(-0.804494\pi\) | ||||
−0.817236 | + | 0.576304i | \(0.804494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.01165e96 | −0.109788 | −0.0548942 | − | 0.998492i | \(-0.517482\pi\) | ||||
−0.0548942 | + | 0.998492i | \(0.517482\pi\) | |||||||
\(152\) | −1.44382e97 | −1.16808 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.72490e97 | 2.13658 | ||||||||
\(155\) | −1.49581e97 | −0.507124 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.72359e97 | −0.713554 | −0.356777 | − | 0.934190i | \(-0.616124\pi\) | ||||
−0.356777 | + | 0.934190i | \(0.616124\pi\) | |||||||
\(158\) | 2.16392e98 | 3.12608 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.14767e97 | 0.177267 | ||||||||
\(161\) | 1.25470e98 | 0.784851 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.03319e98 | −0.373107 | −0.186554 | − | 0.982445i | \(-0.559732\pi\) | ||||
−0.186554 | + | 0.982445i | \(0.559732\pi\) | |||||||
\(164\) | −3.95695e98 | −1.08845 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.36326e98 | −0.379054 | ||||||||
\(167\) | 1.50110e99 | 1.84301 | 0.921503 | − | 0.388372i | \(-0.126962\pi\) | ||||
0.921503 | + | 0.388372i | \(0.126962\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.10558e99 | 2.24484 | ||||||||
\(170\) | −8.06938e98 | −0.448604 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.42473e99 | −0.801027 | ||||||||
\(173\) | −1.10447e99 | −0.281906 | −0.140953 | − | 0.990016i | \(-0.545017\pi\) | ||||
−0.140953 | + | 0.990016i | \(0.545017\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.44566e99 | 0.986448 | ||||||||
\(176\) | 1.41557e100 | 1.68119 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.38566e100 | −2.43194 | ||||||||
\(179\) | −1.69588e100 | −0.949372 | −0.474686 | − | 0.880155i | \(-0.657438\pi\) | ||||
−0.474686 | + | 0.880155i | \(0.657438\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.52788e100 | −0.863099 | −0.431549 | − | 0.902089i | \(-0.642033\pi\) | ||||
−0.431549 | + | 0.902089i | \(0.642033\pi\) | |||||||
\(182\) | −1.28971e101 | −3.44599 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.15287e100 | 1.50371 | ||||||||
\(185\) | 2.84795e100 | 0.367613 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.22032e101 | −0.976161 | ||||||||
\(188\) | −2.06307e100 | −0.130163 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.38069e100 | 0.290778 | ||||||||
\(191\) | 3.78547e101 | 1.18069 | 0.590344 | − | 0.807152i | \(-0.298992\pi\) | ||||
0.590344 | + | 0.807152i | \(0.298992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.50651e101 | 0.295578 | 0.147789 | − | 0.989019i | \(-0.452784\pi\) | ||||
0.147789 | + | 0.989019i | \(0.452784\pi\) | |||||||
\(194\) | 6.46382e100 | 0.100766 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.45836e101 | 0.341566 | ||||||||
\(197\) | 6.14218e101 | 0.483700 | 0.241850 | − | 0.970314i | \(-0.422246\pi\) | ||||
0.241850 | + | 0.970314i | \(0.422246\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.92526e102 | −0.967223 | −0.483611 | − | 0.875283i | \(-0.660675\pi\) | ||||
−0.483611 | + | 0.875283i | \(0.660675\pi\) | |||||||
\(200\) | 4.70203e102 | 1.88995 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.80456e102 | 2.01471 | ||||||||
\(203\) | −6.86787e102 | −1.42314 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.08625e102 | 0.145507 | ||||||||
\(206\) | −6.96450e102 | −0.751275 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.86393e103 | −2.71151 | ||||||||
\(209\) | 1.11617e103 | 0.632732 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.45026e103 | −0.909166 | −0.454583 | − | 0.890704i | \(-0.650212\pi\) | ||||
−0.454583 | + | 0.890704i | \(0.650212\pi\) | |||||||
\(212\) | −5.07210e103 | −1.52490 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.97363e103 | 1.38053 | ||||||||
\(215\) | 6.65630e102 | 0.107083 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.77397e104 | −1.89011 | ||||||||
\(218\) | −3.57910e104 | −3.10785 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.20435e104 | −0.696538 | ||||||||
\(221\) | 3.33097e104 | 1.57440 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.73510e104 | −1.49887 | −0.749434 | − | 0.662079i | \(-0.769674\pi\) | ||||
−0.749434 | + | 0.662079i | \(0.769674\pi\) | |||||||
\(224\) | 2.54705e104 | 0.660695 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.33331e104 | 1.10613 | ||||||||
\(227\) | 1.36699e104 | 0.196161 | 0.0980807 | − | 0.995178i | \(-0.468730\pi\) | ||||
0.0980807 | + | 0.995178i | \(0.468730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.84461e104 | 0.276276 | 0.138138 | − | 0.990413i | \(-0.455888\pi\) | ||||
0.138138 | + | 0.990413i | \(0.455888\pi\) | |||||||
\(230\) | −4.67886e104 | −0.374327 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.01003e105 | −2.72662 | ||||||||
\(233\) | 1.32351e104 | 0.0594823 | 0.0297411 | − | 0.999558i | \(-0.490532\pi\) | ||||
0.0297411 | + | 0.999558i | \(0.490532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.66347e103 | 0.0174005 | ||||||||
\(236\) | −5.38829e105 | −1.37046 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.56997e105 | −1.67200 | ||||||||
\(239\) | −1.73403e105 | −0.251391 | −0.125696 | − | 0.992069i | \(-0.540116\pi\) | ||||
−0.125696 | + | 0.992069i | \(0.540116\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.77326e105 | −0.377536 | −0.188768 | − | 0.982022i | \(-0.560449\pi\) | ||||
−0.188768 | + | 0.982022i | \(0.560449\pi\) | |||||||
\(242\) | −5.28470e105 | −0.439781 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.95271e106 | −2.28059 | ||||||||
\(245\) | −9.49380e104 | −0.0456614 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.04669e106 | −1.02050 | ||||||||
\(248\) | −1.29409e107 | −3.62130 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.02589e106 | −0.983745 | ||||||||
\(251\) | −1.00216e107 | −1.64231 | −0.821155 | − | 0.570705i | \(-0.806670\pi\) | ||||
−0.821155 | + | 0.570705i | \(0.806670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.07576e106 | −0.814535 | ||||||||
\(254\) | 2.16594e107 | 2.09192 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.91424e107 | −1.98540 | ||||||||
\(257\) | −1.47865e107 | −0.846920 | −0.423460 | − | 0.905915i | \(-0.639185\pi\) | ||||
−0.423460 | + | 0.905915i | \(0.639185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.37756e107 | 1.37014 | ||||||||
\(260\) | 3.28740e107 | 1.12341 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.51826e107 | −1.82688 | ||||||||
\(263\) | −5.33852e106 | −0.109494 | −0.0547469 | − | 0.998500i | \(-0.517435\pi\) | ||||
−0.0547469 | + | 0.998500i | \(0.517435\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.39238e107 | 0.203852 | ||||||||
\(266\) | 8.75320e107 | 1.08376 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.27653e107 | 0.645544 | ||||||||
\(269\) | −1.15813e108 | −0.870524 | −0.435262 | − | 0.900304i | \(-0.643344\pi\) | ||||
−0.435262 | + | 0.900304i | \(0.643344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.64602e108 | −1.43041 | −0.715203 | − | 0.698917i | \(-0.753666\pi\) | ||||
−0.715203 | + | 0.698917i | \(0.753666\pi\) | |||||||
\(272\) | −2.86714e108 | −1.31563 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.67214e108 | 0.885033 | ||||||||
\(275\) | −3.63497e108 | −1.02376 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.07845e108 | −0.220015 | −0.110007 | − | 0.993931i | \(-0.535087\pi\) | ||||
−0.110007 | + | 0.993931i | \(0.535087\pi\) | |||||||
\(278\) | 7.67926e108 | 1.33452 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.07199e108 | −0.640687 | ||||||||
\(281\) | 4.97309e108 | 0.536037 | 0.268019 | − | 0.963414i | \(-0.413631\pi\) | ||||
0.268019 | + | 0.963414i | \(0.413631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.20179e109 | 0.944785 | 0.472392 | − | 0.881388i | \(-0.343391\pi\) | ||||
0.472392 | + | 0.881388i | \(0.343391\pi\) | |||||||
\(284\) | −9.03278e108 | −0.606953 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.27318e109 | 3.57632 | ||||||||
\(287\) | 1.28825e109 | 0.542320 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.63920e108 | −0.236099 | ||||||||
\(290\) | 2.56108e109 | 0.678754 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.08285e109 | −0.406556 | ||||||||
\(293\) | −3.43775e109 | −0.576322 | −0.288161 | − | 0.957582i | \(-0.593044\pi\) | ||||
−0.288161 | + | 0.957582i | \(0.593044\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.47918e109 | 0.183206 | ||||||||
\(296\) | 2.46389e110 | 2.62507 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.67991e110 | 2.90545 | ||||||||
\(299\) | 1.93140e110 | 1.31372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.89410e109 | 0.399111 | ||||||||
\(302\) | 4.47407e109 | 0.195161 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.62244e110 | 0.852769 | ||||||||
\(305\) | 1.08509e110 | 0.304875 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.58639e110 | −1.17347 | −0.586737 | − | 0.809778i | \(-0.699588\pi\) | ||||
−0.586737 | + | 0.809778i | \(0.699588\pi\) | |||||||
\(308\) | −1.42832e111 | −2.59607 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.61525e110 | 0.901470 | ||||||||
\(311\) | −9.96934e110 | −1.17714 | −0.588572 | − | 0.808445i | \(-0.700309\pi\) | ||||
−0.588572 | + | 0.808445i | \(0.700309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.36331e110 | −0.653657 | −0.326828 | − | 0.945084i | \(-0.605980\pi\) | ||||
−0.326828 | + | 0.945084i | \(0.605980\pi\) | |||||||
\(314\) | 1.64677e111 | 1.26842 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.54143e111 | −3.79837 | ||||||||
\(317\) | −1.40479e111 | −0.708721 | −0.354361 | − | 0.935109i | \(-0.615302\pi\) | ||||
−0.354361 | + | 0.935109i | \(0.615302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.87308e111 | 1.47697 | ||||||||
\(320\) | 3.60260e110 | 0.119520 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.54894e111 | −1.39516 | ||||||||
\(323\) | −2.26072e111 | −0.495148 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.92201e111 | 1.65116 | ||||||||
\(326\) | 4.56934e111 | 0.663239 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.39764e111 | 1.03904 | ||||||||
\(329\) | 6.71665e110 | 0.0648538 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.93674e112 | −1.42799 | −0.713997 | − | 0.700149i | \(-0.753117\pi\) | ||||
−0.713997 | + | 0.700149i | \(0.753117\pi\) | |||||||
\(332\) | 7.14403e111 | 0.460573 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.63867e112 | −3.27615 | ||||||||
\(335\) | −1.99753e111 | −0.0862979 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.04243e112 | −1.00853 | −0.504266 | − | 0.863548i | \(-0.668237\pi\) | ||||
−0.504266 | + | 0.863548i | \(0.668237\pi\) | |||||||
\(338\) | −1.37346e113 | −3.99045 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.43934e112 | 0.545080 | ||||||||
\(341\) | 1.00041e113 | 1.96160 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.99389e112 | 0.905984 | ||||||||
\(344\) | 5.75866e112 | 0.764664 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.88458e112 | 0.501119 | ||||||||
\(347\) | −5.62569e112 | −0.507591 | −0.253796 | − | 0.967258i | \(-0.581679\pi\) | ||||
−0.253796 | + | 0.967258i | \(0.581679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.27631e111 | −0.0298771 | −0.0149385 | − | 0.999888i | \(-0.504755\pi\) | ||||
−0.0149385 | + | 0.999888i | \(0.504755\pi\) | |||||||
\(350\) | −2.85062e113 | −1.75352 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.43639e113 | −0.685683 | ||||||||
\(353\) | −1.17997e113 | −0.496473 | −0.248236 | − | 0.968699i | \(-0.579851\pi\) | ||||
−0.248236 | + | 0.968699i | \(0.579851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.47965e112 | 0.0811390 | ||||||||
\(356\) | 1.02347e114 | 2.95495 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.50011e113 | 1.68761 | ||||||||
\(359\) | 3.09309e113 | 0.614738 | 0.307369 | − | 0.951590i | \(-0.400551\pi\) | ||||
0.307369 | + | 0.951590i | \(0.400551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.37496e113 | −0.679053 | ||||||||
\(362\) | 1.11797e114 | 1.53425 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.89872e114 | 4.18707 | ||||||||
\(365\) | 5.71778e112 | 0.0543494 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.47042e113 | 0.631342 | 0.315671 | − | 0.948869i | \(-0.397770\pi\) | ||||
0.315671 | + | 0.948869i | \(0.397770\pi\) | |||||||
\(368\) | −1.66245e114 | −1.09779 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.25952e114 | −0.653473 | ||||||||
\(371\) | 1.65131e114 | 0.759781 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.26483e114 | −0.458131 | −0.229066 | − | 0.973411i | \(-0.573567\pi\) | ||||
−0.229066 | + | 0.973411i | \(0.573567\pi\) | |||||||
\(374\) | 5.39690e114 | 1.73523 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.89972e113 | 0.124255 | ||||||||
\(377\) | −1.05719e115 | −2.38212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.05579e114 | −0.187989 | −0.0939943 | − | 0.995573i | \(-0.529964\pi\) | ||||
−0.0939943 | + | 0.995573i | \(0.529964\pi\) | |||||||
\(380\) | −2.23115e114 | −0.353312 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.67414e115 | −2.09880 | ||||||||
\(383\) | −1.02001e115 | −1.13831 | −0.569155 | − | 0.822230i | \(-0.692730\pi\) | ||||
−0.569155 | + | 0.822230i | \(0.692730\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.92097e114 | 0.347049 | ||||||||
\(386\) | −6.66260e114 | −0.525422 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.95398e114 | −0.122436 | ||||||||
\(389\) | 2.00350e115 | 1.11952 | 0.559760 | − | 0.828655i | \(-0.310893\pi\) | ||||
0.559760 | + | 0.828655i | \(0.310893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.43315e115 | 0.637420 | ||||||||
\(392\) | −8.21351e114 | −0.326061 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.71640e115 | −0.859830 | ||||||||
\(395\) | 1.79574e115 | 0.507776 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.43963e115 | 0.325142 | 0.162571 | − | 0.986697i | \(-0.448021\pi\) | ||||
0.162571 | + | 0.986697i | \(0.448021\pi\) | |||||||
\(398\) | 8.51452e115 | 1.71935 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.54039e115 | −1.37977 | ||||||||
\(401\) | 6.32353e115 | 0.914187 | 0.457093 | − | 0.889419i | \(-0.348890\pi\) | ||||
0.457093 | + | 0.889419i | \(0.348890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.73072e116 | −3.16376 | ||||||||
\(404\) | −2.35929e116 | −2.44799 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.03734e116 | 2.52979 | ||||||||
\(407\) | −1.90475e116 | −1.42195 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.70354e114 | 0.0342339 | 0.0171170 | − | 0.999853i | \(-0.494551\pi\) | ||||
0.0171170 | + | 0.999853i | \(0.494551\pi\) | |||||||
\(410\) | −4.80399e115 | −0.258654 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.10534e116 | 0.912842 | ||||||||
\(413\) | 1.75425e116 | 0.682831 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.96116e115 | −0.0615705 | ||||||||
\(416\) | 3.92076e116 | 1.10590 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.93629e116 | −1.12475 | ||||||||
\(419\) | −2.82318e116 | −0.578382 | −0.289191 | − | 0.957271i | \(-0.593386\pi\) | ||||
−0.289191 | + | 0.957271i | \(0.593386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.04056e116 | 1.00121 | 0.500604 | − | 0.865676i | \(-0.333111\pi\) | ||||
0.500604 | + | 0.865676i | \(0.333111\pi\) | |||||||
\(422\) | 1.08364e117 | 1.61614 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.20461e117 | 1.45568 | ||||||||
\(425\) | 7.36240e116 | 0.801147 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.28687e117 | 1.13630 | ||||||||
\(428\) | −2.10810e117 | −1.67742 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.94377e116 | −0.190352 | ||||||||
\(431\) | 2.26583e117 | 1.32126 | 0.660632 | − | 0.750710i | \(-0.270288\pi\) | ||||
0.660632 | + | 0.750710i | \(0.270288\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.27088e116 | 0.345045 | 0.172522 | − | 0.985006i | \(-0.444808\pi\) | ||||
0.172522 | + | 0.985006i | \(0.444808\pi\) | |||||||
\(434\) | 7.84543e117 | 3.35988 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.08195e118 | 3.77622 | ||||||||
\(437\) | −1.31083e117 | −0.413165 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.51676e116 | 0.116187 | 0.0580933 | − | 0.998311i | \(-0.481498\pi\) | ||||
0.0580933 | + | 0.998311i | \(0.481498\pi\) | |||||||
\(440\) | 2.86031e117 | 0.664918 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.47314e118 | −2.79867 | ||||||||
\(443\) | −8.00727e117 | −1.37568 | −0.687842 | − | 0.725860i | \(-0.741442\pi\) | ||||
−0.687842 | + | 0.725860i | \(0.741442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.80960e117 | −0.395024 | ||||||||
\(446\) | 2.09412e118 | 2.66440 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.27254e117 | 0.445466 | ||||||||
\(449\) | −1.58652e118 | −1.49790 | −0.748949 | − | 0.662627i | \(-0.769441\pi\) | ||||
−0.748949 | + | 0.662627i | \(0.769441\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.26498e117 | −0.562831 | ||||||||
\(452\) | −1.91453e118 | −1.34401 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.04555e117 | −0.348699 | ||||||||
\(455\) | −1.07027e118 | −0.559738 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.01717e117 | −0.0437644 | −0.0218822 | − | 0.999761i | \(-0.506966\pi\) | ||||
−0.0218822 | + | 0.999761i | \(0.506966\pi\) | |||||||
\(458\) | −1.25804e118 | −0.491111 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.41440e118 | 0.454829 | ||||||||
\(461\) | 5.67592e118 | 1.65709 | 0.828543 | − | 0.559926i | \(-0.189170\pi\) | ||||
0.828543 | + | 0.559926i | \(0.189170\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.42212e118 | −0.824028 | −0.412014 | − | 0.911178i | \(-0.635174\pi\) | ||||
−0.412014 | + | 0.911178i | \(0.635174\pi\) | |||||||
\(464\) | 9.09981e118 | 1.99059 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.85326e117 | −0.105736 | ||||||||
\(467\) | 5.74060e118 | 0.942662 | 0.471331 | − | 0.881956i | \(-0.343774\pi\) | ||||
0.471331 | + | 0.881956i | \(0.343774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.36900e118 | −0.321642 | ||||||||
\(470\) | −2.50469e117 | −0.0309314 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.27970e119 | 1.30825 | ||||||||
\(473\) | −4.45181e118 | −0.414206 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.73405e118 | −0.519291 | ||||||||
\(476\) | 2.89296e119 | 2.03157 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.66882e118 | 0.446876 | ||||||||
\(479\) | 7.35495e118 | 0.390526 | 0.195263 | − | 0.980751i | \(-0.437444\pi\) | ||||
0.195263 | + | 0.980751i | \(0.437444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.19918e119 | 2.29340 | ||||||||
\(482\) | 1.66874e119 | 0.671112 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.59754e119 | 0.534360 | ||||||||
\(485\) | 5.36402e117 | 0.0163675 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.73116e119 | 0.439843 | 0.219922 | − | 0.975518i | \(-0.429420\pi\) | ||||
0.219922 | + | 0.975518i | \(0.429420\pi\) | |||||||
\(488\) | 9.38758e119 | 2.17707 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.19867e118 | 0.0811682 | ||||||||
\(491\) | −9.48426e119 | −1.67447 | −0.837234 | − | 0.546845i | \(-0.815829\pi\) | ||||
−0.837234 | + | 0.546845i | \(0.815829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.84466e119 | −1.15581 | ||||||||
\(494\) | 1.34741e120 | 1.81405 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.35047e120 | 2.64375 | ||||||||
\(497\) | 2.94077e119 | 0.302414 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.96564e119 | 0.255061 | 0.127530 | − | 0.991835i | \(-0.459295\pi\) | ||||
0.127530 | + | 0.991835i | \(0.459295\pi\) | |||||||
\(500\) | 1.51930e120 | 1.19531 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.43208e120 | 2.91939 | ||||||||
\(503\) | 1.72800e120 | 1.04176 | 0.520881 | − | 0.853630i | \(-0.325604\pi\) | ||||
0.520881 | + | 0.853630i | \(0.325604\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.47665e119 | 0.327253 | ||||||||
\(506\) | 3.12928e120 | 1.44793 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.54754e120 | −2.54181 | ||||||||
\(509\) | 1.24174e120 | 0.441661 | 0.220830 | − | 0.975312i | \(-0.429123\pi\) | ||||
0.220830 | + | 0.975312i | \(0.429123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.78106e119 | 0.202566 | ||||||||
\(512\) | 7.95925e120 | 2.17951 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.53940e120 | 1.50549 | ||||||||
\(515\) | −5.77952e119 | −0.122031 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.78780e119 | −0.0673066 | ||||||||
\(518\) | −1.49374e121 | −2.43557 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.80748e120 | −1.07241 | ||||||||
\(521\) | −6.02844e120 | −0.760197 | −0.380099 | − | 0.924946i | \(-0.624110\pi\) | ||||
−0.380099 | + | 0.924946i | \(0.624110\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.30371e121 | −1.38630 | −0.693148 | − | 0.720796i | \(-0.743777\pi\) | ||||
−0.693148 | + | 0.720796i | \(0.743777\pi\) | |||||||
\(524\) | 2.27274e121 | 2.21976 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.36098e120 | 0.194638 | ||||||||
\(527\) | −2.02627e121 | −1.53506 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.31366e120 | −0.468120 | ||||||||
\(530\) | −6.15785e120 | −0.362370 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.64605e121 | −1.31683 | ||||||||
\(533\) | 1.98305e121 | 0.907762 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.78709e120 | 0.224242 | ||||||||
\(536\) | −1.72816e121 | −0.616240 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.12187e121 | 1.54745 | ||||||||
\(539\) | 6.34957e120 | 0.176622 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.02509e121 | −0.713609 | −0.356804 | − | 0.934179i | \(-0.616134\pi\) | ||||
−0.356804 | + | 0.934179i | \(0.616134\pi\) | |||||||
\(542\) | 1.17021e122 | 2.54270 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.90931e121 | 0.536586 | ||||||||
\(545\) | −2.97013e121 | −0.504814 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.07810e120 | 0.0877671 | 0.0438836 | − | 0.999037i | \(-0.486027\pi\) | ||||
0.0438836 | + | 0.999037i | \(0.486027\pi\) | |||||||
\(548\) | −8.07777e121 | −1.07537 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.60758e122 | 1.81984 | ||||||||
\(551\) | 7.17515e121 | 0.749178 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.12967e122 | 1.89254 | ||||||||
\(554\) | 4.76950e121 | 0.391101 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.32141e122 | −1.62152 | ||||||||
\(557\) | 9.48715e121 | 0.611758 | 0.305879 | − | 0.952070i | \(-0.401050\pi\) | ||||
0.305879 | + | 0.952070i | \(0.401050\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.21516e122 | 0.668051 | ||||||||
\(560\) | 9.21234e121 | 0.467738 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.19937e122 | −0.952866 | ||||||||
\(563\) | −3.99353e122 | −1.59858 | −0.799288 | − | 0.600949i | \(-0.794790\pi\) | ||||
−0.799288 | + | 0.600949i | \(0.794790\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.25572e121 | 0.179670 | ||||||||
\(566\) | −5.31497e122 | −1.67946 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.14526e122 | 0.579401 | ||||||||
\(569\) | 4.99506e122 | 1.24751 | 0.623756 | − | 0.781619i | \(-0.285606\pi\) | ||||
0.623756 | + | 0.781619i | \(0.285606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.98755e121 | −0.170650 | −0.0853251 | − | 0.996353i | \(-0.527193\pi\) | ||||
−0.0853251 | + | 0.996353i | \(0.527193\pi\) | |||||||
\(572\) | −2.19865e123 | −4.34543 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.69734e122 | −0.964035 | ||||||||
\(575\) | 4.26893e122 | 0.668498 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.20737e123 | −1.62000 | −0.810001 | − | 0.586429i | \(-0.800533\pi\) | ||||
−0.810001 | + | 0.586429i | \(0.800533\pi\) | |||||||
\(578\) | 3.37847e122 | 0.419692 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.74204e122 | −0.824726 | ||||||||
\(581\) | −2.32586e122 | −0.229480 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.31240e122 | −0.788517 | ||||||||
\(584\) | 4.94671e122 | 0.388101 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.52036e123 | 1.02448 | ||||||||
\(587\) | −6.63777e122 | −0.414597 | −0.207299 | − | 0.978278i | \(-0.566467\pi\) | ||||
−0.207299 | + | 0.978278i | \(0.566467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.85334e123 | 0.995001 | ||||||||
\(590\) | −6.54172e122 | −0.325670 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.47521e123 | −1.91645 | ||||||||
\(593\) | 3.67636e123 | 1.46044 | 0.730221 | − | 0.683211i | \(-0.239417\pi\) | ||||
0.730221 | + | 0.683211i | \(0.239417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.94167e122 | −0.271586 | ||||||||
\(596\) | −1.11242e124 | −3.53029 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.54167e123 | −2.33529 | ||||||||
\(599\) | −7.52276e123 | −1.90934 | −0.954671 | − | 0.297663i | \(-0.903793\pi\) | ||||
−0.954671 | + | 0.297663i | \(0.903793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.62225e123 | 0.573798 | 0.286899 | − | 0.957961i | \(-0.407376\pi\) | ||||
0.286899 | + | 0.957961i | \(0.407376\pi\) | |||||||
\(602\) | −3.49120e123 | −0.709464 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.35249e123 | −0.237132 | ||||||||
\(605\) | −4.38553e122 | −0.0714345 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.96123e123 | −0.838377 | −0.419188 | − | 0.907899i | \(-0.637685\pi\) | ||||
−0.419188 | + | 0.907899i | \(0.637685\pi\) | |||||||
\(608\) | −2.66101e123 | −0.347806 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.79884e123 | −0.541950 | ||||||||
\(611\) | 1.03392e123 | 0.108555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.49430e124 | 1.35659 | 0.678293 | − | 0.734792i | \(-0.262720\pi\) | ||||
0.678293 | + | 0.734792i | \(0.262720\pi\) | |||||||
\(614\) | 2.47060e124 | 2.08598 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.39221e124 | 2.47823 | ||||||||
\(617\) | 1.42286e124 | 0.967101 | 0.483551 | − | 0.875316i | \(-0.339347\pi\) | ||||
0.483551 | + | 0.875316i | \(0.339347\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.75124e124 | −1.03065 | −0.515327 | − | 0.856994i | \(-0.672329\pi\) | ||||
−0.515327 | + | 0.856994i | \(0.672329\pi\) | |||||||
\(620\) | −1.99976e124 | −1.09534 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.40898e124 | 2.09250 | ||||||||
\(623\) | −3.33207e124 | −1.47230 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.97544e124 | 0.756837 | ||||||||
\(626\) | 3.25645e124 | 1.16195 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.97811e124 | −1.54121 | ||||||||
\(629\) | 3.85794e124 | 1.11276 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.10999e124 | 0.528413 | 0.264207 | − | 0.964466i | \(-0.414890\pi\) | ||||
0.264207 | + | 0.964466i | \(0.414890\pi\) | |||||||
\(632\) | 1.55357e125 | 3.62595 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.21276e124 | 1.25983 | ||||||||
\(635\) | 1.79741e124 | 0.339795 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.73317e124 | −0.284864 | ||||||||
\(638\) | −1.71288e125 | −2.62547 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.92261e124 | −0.389728 | ||||||||
\(641\) | −9.40134e124 | −1.16952 | −0.584759 | − | 0.811207i | \(-0.698811\pi\) | ||||
−0.584759 | + | 0.811207i | \(0.698811\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.35874e124 | −0.580330 | −0.290165 | − | 0.956977i | \(-0.593710\pi\) | ||||
−0.290165 | + | 0.956977i | \(0.593710\pi\) | |||||||
\(644\) | 1.67742e125 | 1.69520 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.99814e124 | 0.880181 | ||||||||
\(647\) | 1.76192e125 | 1.44792 | 0.723962 | − | 0.689840i | \(-0.242319\pi\) | ||||
0.723962 | + | 0.689840i | \(0.242319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.89293e124 | −0.708657 | ||||||||
\(650\) | −4.38804e125 | −2.93513 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.38129e125 | −0.805874 | ||||||||
\(653\) | 2.70255e125 | 1.47278 | 0.736388 | − | 0.676560i | \(-0.236530\pi\) | ||||
0.736388 | + | 0.676560i | \(0.236530\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.23906e124 | −0.296743 | ||||||||
\(656\) | −1.70691e125 | −0.758560 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.97047e124 | −0.115285 | ||||||||
\(659\) | −4.92460e125 | −1.78636 | −0.893182 | − | 0.449696i | \(-0.851532\pi\) | ||||
−0.893182 | + | 0.449696i | \(0.851532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.53102e123 | 0.00485306 | 0.00242653 | − | 0.999997i | \(-0.499228\pi\) | ||||
0.00242653 | + | 0.999997i | \(0.499228\pi\) | |||||||
\(662\) | 8.56532e125 | 2.53842 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.69669e125 | −0.439665 | ||||||||
\(665\) | 7.26388e124 | 0.176038 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.54856e125 | −0.964439 | ||||||||
\(668\) | 2.00684e126 | 3.98071 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.83417e124 | 0.153404 | ||||||||
\(671\) | −7.25720e125 | −1.17928 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.14314e126 | 1.62716 | 0.813579 | − | 0.581455i | \(-0.197516\pi\) | ||||
0.813579 | + | 0.581455i | \(0.197516\pi\) | |||||||
\(674\) | 1.34553e126 | 1.79278 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.15190e126 | 4.84862 | ||||||||
\(677\) | −8.57614e125 | −0.937770 | −0.468885 | − | 0.883259i | \(-0.655344\pi\) | ||||
−0.468885 | + | 0.883259i | \(0.655344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.36152e124 | 0.0610036 | ||||||||
\(680\) | −5.79336e125 | −0.520336 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.42436e126 | −3.48695 | ||||||||
\(683\) | 8.28357e125 | 0.611641 | 0.305820 | − | 0.952089i | \(-0.401069\pi\) | ||||
0.305820 | + | 0.952089i | \(0.401069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.21749e125 | 0.143758 | ||||||||
\(686\) | −2.65082e126 | −1.61049 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.04596e126 | −0.558249 | ||||||||
\(689\) | 2.54191e126 | 1.27176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.99715e125 | 0.219760 | 0.109880 | − | 0.993945i | \(-0.464953\pi\) | ||||
0.109880 | + | 0.993945i | \(0.464953\pi\) | |||||||
\(692\) | −1.47659e126 | −0.608889 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.48798e126 | 0.902299 | ||||||||
\(695\) | 6.37266e125 | 0.216769 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.47147e126 | 0.440447 | ||||||||
\(698\) | 1.89121e125 | 0.0531098 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.61729e126 | 2.13063 | ||||||||
\(701\) | −1.20764e126 | −0.280212 | −0.140106 | − | 0.990137i | \(-0.544744\pi\) | ||||
−0.140106 | + | 0.990137i | \(0.544744\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.52868e126 | −0.721273 | ||||||||
\(704\) | −2.40947e126 | −0.462314 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.21845e126 | 0.882535 | ||||||||
\(707\) | 7.68105e126 | 1.21971 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.71841e126 | −0.660751 | −0.330376 | − | 0.943850i | \(-0.607175\pi\) | ||||
−0.330376 | + | 0.943850i | \(0.607175\pi\) | |||||||
\(710\) | −1.09664e126 | −0.144234 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.43071e127 | −2.82081 | ||||||||
\(713\) | −1.17489e127 | −1.28089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.03568e126 | 0.580908 | ||||||||
\(716\) | −2.26725e127 | −2.05055 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.36793e127 | −1.09276 | ||||||||
\(719\) | 1.53894e127 | 1.15554 | 0.577770 | − | 0.816200i | \(-0.303923\pi\) | ||||
0.577770 | + | 0.816200i | \(0.303923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.85428e126 | −0.454823 | ||||||||
\(722\) | 1.93484e127 | 1.20709 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.37956e127 | −1.86421 | ||||||||
\(725\) | −2.33670e127 | −1.21216 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.29984e126 | −0.426770 | −0.213385 | − | 0.976968i | \(-0.568449\pi\) | ||||
−0.213385 | + | 0.976968i | \(0.568449\pi\) | |||||||
\(728\) | −9.25936e127 | −3.99700 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.52871e126 | −0.0966121 | ||||||||
\(731\) | 9.01685e126 | 0.324139 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.90574e127 | 0.924974 | 0.462487 | − | 0.886626i | \(-0.346957\pi\) | ||||
0.462487 | + | 0.886626i | \(0.346957\pi\) | |||||||
\(734\) | −3.74607e127 | −1.12228 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.68690e127 | 0.447741 | ||||||||
\(737\) | 1.33598e127 | 0.333807 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.49478e127 | −0.774002 | −0.387001 | − | 0.922079i | \(-0.626489\pi\) | ||||
−0.387001 | + | 0.922079i | \(0.626489\pi\) | |||||||
\(740\) | 3.80747e127 | 0.794008 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.30296e127 | −1.35060 | ||||||||
\(743\) | −8.90897e127 | −1.55176 | −0.775882 | − | 0.630879i | \(-0.782695\pi\) | ||||
−0.775882 | + | 0.630879i | \(0.782695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.05379e127 | 0.471938 | ||||||||
\(746\) | 5.59377e127 | 0.814379 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.63146e128 | −2.10841 | ||||||||
\(749\) | 6.86326e127 | 0.835776 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.71982e127 | 0.618594 | 0.309297 | − | 0.950966i | \(-0.399906\pi\) | ||||
0.309297 | + | 0.950966i | \(0.399906\pi\) | |||||||
\(752\) | −8.89945e126 | −0.0907130 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.67548e128 | 4.23449 | ||||||||
\(755\) | 3.71282e126 | 0.0317004 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.03779e128 | 1.54665 | 0.773325 | − | 0.634010i | \(-0.218592\pi\) | ||||
0.773325 | + | 0.634010i | \(0.218592\pi\) | |||||||
\(758\) | 4.66926e127 | 0.334171 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.29892e127 | 0.337274 | ||||||||
\(761\) | 1.17204e126 | 0.00703599 | 0.00351799 | − | 0.999994i | \(-0.498880\pi\) | ||||
0.00351799 | + | 0.999994i | \(0.498880\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.52246e128 | −1.88150 | ||||||||
\(764\) | 5.06085e128 | 2.55017 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.51105e128 | 2.02347 | ||||||||
\(767\) | 2.70037e128 | 1.14296 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.19825e127 | 0.120556 | 0.0602782 | − | 0.998182i | \(-0.480801\pi\) | ||||
0.0602782 | + | 0.998182i | \(0.480801\pi\) | |||||||
\(770\) | −1.73406e128 | −0.616919 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.01407e128 | 0.638419 | ||||||||
\(773\) | −3.28146e128 | −0.981929 | −0.490965 | − | 0.871179i | \(-0.663356\pi\) | ||||
−0.490965 | + | 0.871179i | \(0.663356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.03567e128 | −1.60990 | ||||||||
\(776\) | 4.64066e127 | 0.116878 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.86055e128 | −1.99007 | ||||||||
\(779\) | −1.34589e128 | −0.285491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.65842e128 | −0.313852 | ||||||||
\(782\) | −6.33815e128 | −1.13308 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.49183e128 | 0.238043 | ||||||||
\(785\) | 1.36658e128 | 0.206032 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.37748e129 | 1.85443 | 0.927214 | − | 0.374532i | \(-0.122197\pi\) | ||||
0.927214 | + | 0.374532i | \(0.122197\pi\) | |||||||
\(788\) | 8.21157e128 | 1.04474 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.94171e128 | −0.902628 | ||||||||
\(791\) | 6.23308e128 | 0.669652 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.98092e129 | 1.90200 | ||||||||
\(794\) | −6.36681e128 | −0.577976 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.57390e129 | −2.08910 | ||||||||
\(797\) | 4.39500e128 | 0.337337 | 0.168668 | − | 0.985673i | \(-0.446053\pi\) | ||||
0.168668 | + | 0.985673i | \(0.446053\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.67194e127 | 0.0526712 | ||||||||
\(800\) | 8.66599e128 | 0.562748 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.79660e129 | −1.62507 | ||||||||
\(803\) | −3.82412e128 | −0.210228 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.60481e128 | −0.226618 | ||||||||
\(806\) | 1.20767e130 | 5.62393 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.60324e129 | 2.33686 | ||||||||
\(809\) | −3.31962e129 | −1.31032 | −0.655162 | − | 0.755488i | \(-0.727400\pi\) | ||||
−0.655162 | + | 0.755488i | \(0.727400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.97411e129 | −1.40544 | −0.702720 | − | 0.711467i | \(-0.748031\pi\) | ||||
−0.702720 | + | 0.711467i | \(0.748031\pi\) | |||||||
\(812\) | −9.18175e129 | −3.07385 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.42381e129 | 2.52768 | ||||||||
\(815\) | 3.79188e128 | 0.107731 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.24730e128 | −0.210102 | ||||||||
\(818\) | −2.52241e128 | −0.0608546 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.45222e129 | 0.314280 | ||||||||
\(821\) | 1.35805e129 | 0.278386 | 0.139193 | − | 0.990265i | \(-0.455549\pi\) | ||||
0.139193 | + | 0.990265i | \(0.455549\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.64457e129 | 0.302524 | 0.151262 | − | 0.988494i | \(-0.451666\pi\) | ||||
0.151262 | + | 0.988494i | \(0.451666\pi\) | |||||||
\(824\) | −5.00012e129 | −0.871404 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.75822e129 | −1.21381 | ||||||||
\(827\) | −6.57180e127 | −0.00974292 | −0.00487146 | − | 0.999988i | \(-0.501551\pi\) | ||||
−0.00487146 | + | 0.999988i | \(0.501551\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.74673e129 | 0.632001 | 0.316000 | − | 0.948759i | \(-0.397660\pi\) | ||||
0.316000 | + | 0.948759i | \(0.397660\pi\) | |||||||
\(830\) | 8.67330e128 | 0.109448 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.57686e129 | 0.745643 | ||||||||
\(833\) | −1.28606e129 | −0.138216 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.50913e129 | −0.532151 | ||||||||
\(836\) | 1.49222e130 | 1.36664 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.24856e130 | 1.02814 | ||||||||
\(839\) | 1.79965e130 | 1.40533 | 0.702667 | − | 0.711518i | \(-0.251992\pi\) | ||||
0.702667 | + | 0.711518i | \(0.251992\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.06605e130 | 0.748782 | ||||||||
\(842\) | −2.67146e130 | −1.77976 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.27579e130 | −1.96371 | ||||||||
\(845\) | −1.13977e130 | −0.648176 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.20106e129 | −0.266244 | ||||||||
\(848\) | −2.18795e130 | −1.06273 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.25605e130 | −1.42413 | ||||||||
\(851\) | 2.23694e130 | 0.928517 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.67965e130 | 1.37586 | 0.687930 | − | 0.725777i | \(-0.258519\pi\) | ||||
0.687930 | + | 0.725777i | \(0.258519\pi\) | |||||||
\(854\) | −5.69124e130 | −2.01991 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.00667e130 | 1.60128 | ||||||||
\(857\) | −7.78814e129 | −0.236476 | −0.118238 | − | 0.992985i | \(-0.537725\pi\) | ||||
−0.118238 | + | 0.992985i | \(0.537725\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.94984e129 | −0.272346 | −0.136173 | − | 0.990685i | \(-0.543480\pi\) | ||||
−0.136173 | + | 0.990685i | \(0.543480\pi\) | |||||||
\(860\) | 8.89889e129 | 0.231289 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.00207e131 | −2.34869 | ||||||||
\(863\) | 8.18207e130 | 1.82131 | 0.910653 | − | 0.413172i | \(-0.135579\pi\) | ||||
0.910653 | + | 0.413172i | \(0.135579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.05349e129 | 0.0813977 | ||||||||
\(866\) | −3.21557e130 | −0.613356 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.37164e131 | −4.08245 | ||||||||
\(869\) | −1.20101e131 | −1.96411 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.64667e130 | −0.538380 | ||||||||
\(872\) | −2.56959e131 | −3.60480 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.79721e130 | 0.734447 | ||||||||
\(875\) | −4.94635e130 | −0.595561 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.51544e130 | 0.273610 | 0.136805 | − | 0.990598i | \(-0.456317\pi\) | ||||
0.136805 | + | 0.990598i | \(0.456317\pi\) | |||||||
\(878\) | −1.99756e130 | −0.206535 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.19522e130 | −0.485428 | ||||||||
\(881\) | −9.16844e130 | −0.814456 | −0.407228 | − | 0.913327i | \(-0.633505\pi\) | ||||
−0.407228 | + | 0.913327i | \(0.633505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.89867e130 | 0.714618 | 0.357309 | − | 0.933986i | \(-0.383694\pi\) | ||||
0.357309 | + | 0.933986i | \(0.383694\pi\) | |||||||
\(884\) | 4.45322e131 | 3.40055 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.54125e131 | 2.44543 | ||||||||
\(887\) | 2.22905e131 | 1.46393 | 0.731963 | − | 0.681344i | \(-0.238604\pi\) | ||||
0.731963 | + | 0.681344i | \(0.238604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.13166e131 | 1.26646 | ||||||||
\(890\) | 1.24256e131 | 0.702200 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.33043e131 | −3.23740 | ||||||||
\(893\) | −7.01717e129 | −0.0341407 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.22400e130 | 0.274122 | ||||||||
\(896\) | −3.46610e131 | −1.45256 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.01643e131 | 2.66268 | ||||||||
\(899\) | 6.43103e131 | 2.32260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.88617e131 | 0.617059 | ||||||||
\(902\) | 3.21296e131 | 1.00050 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.54696e131 | 1.28300 | ||||||||
\(905\) | 9.27749e130 | 0.249212 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.83857e131 | −0.934642 | −0.467321 | − | 0.884088i | \(-0.654781\pi\) | ||||
−0.467321 | + | 0.884088i | \(0.654781\pi\) | |||||||
\(908\) | 1.82754e131 | 0.423689 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.73329e131 | 0.994997 | ||||||||
\(911\) | 1.57548e131 | 0.315387 | 0.157694 | − | 0.987488i | \(-0.449594\pi\) | ||||
0.157694 | + | 0.987488i | \(0.449594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.31165e131 | 0.238159 | ||||||||
\(914\) | 4.49845e130 | 0.0777960 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.80299e131 | 0.596729 | ||||||||
\(917\) | −7.39928e131 | −1.10600 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.76660e131 | 0.510987 | 0.255493 | − | 0.966811i | \(-0.417762\pi\) | ||||
0.255493 | + | 0.966811i | \(0.417762\pi\) | |||||||
\(920\) | −3.35916e131 | −0.434182 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.51020e132 | −2.94565 | ||||||||
\(923\) | 4.52682e131 | 0.506195 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.14917e132 | 1.16701 | ||||||||
\(926\) | 1.51345e132 | 1.46480 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.23365e131 | −0.811873 | ||||||||
\(929\) | −1.74031e132 | −1.45857 | −0.729286 | − | 0.684209i | \(-0.760147\pi\) | ||||
−0.729286 | + | 0.684209i | \(0.760147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.17630e131 | 0.0895897 | ||||||||
\(932\) | 1.76941e131 | 0.128476 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.53880e132 | −1.67569 | ||||||||
\(935\) | 4.47864e131 | 0.281857 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.51226e132 | 0.865397 | 0.432698 | − | 0.901539i | \(-0.357562\pi\) | ||||
0.432698 | + | 0.901539i | \(0.357562\pi\) | |||||||
\(938\) | 1.04770e132 | 0.571754 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.57157e130 | 0.0375835 | ||||||||
\(941\) | 6.31705e131 | 0.299072 | 0.149536 | − | 0.988756i | \(-0.452222\pi\) | ||||
0.149536 | + | 0.988756i | \(0.452222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.53203e131 | 0.367521 | ||||||||
\(944\) | −2.32435e132 | −0.955097 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.96883e132 | 0.736297 | ||||||||
\(947\) | 1.15806e132 | 0.413196 | 0.206598 | − | 0.978426i | \(-0.433761\pi\) | ||||
0.206598 | + | 0.978426i | \(0.433761\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.04383e132 | 0.339065 | ||||||||
\(950\) | 2.97816e132 | 0.923097 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.87070e132 | −1.93935 | ||||||||
\(953\) | 6.23693e132 | 1.68011 | 0.840053 | − | 0.542504i | \(-0.182524\pi\) | ||||
0.840053 | + | 0.542504i | \(0.182524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.38929e132 | −0.340913 | ||||||||
\(956\) | −2.31825e132 | −0.542980 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.25276e132 | −0.694203 | ||||||||
\(959\) | 2.62985e132 | 0.535801 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.12262e133 | 2.08470 | ||||||||
\(962\) | −2.29936e133 | −4.07677 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.04452e132 | −0.815440 | ||||||||
\(965\) | −5.52898e131 | −0.0853454 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.82355e132 | −0.397482 | −0.198741 | − | 0.980052i | \(-0.563685\pi\) | ||||
−0.198741 | + | 0.980052i | \(0.563685\pi\) | |||||||
\(968\) | −3.79412e132 | −0.510102 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.37226e131 | −0.0290951 | ||||||||
\(971\) | −1.37580e132 | −0.161176 | −0.0805879 | − | 0.996748i | \(-0.525680\pi\) | ||||
−0.0805879 | + | 0.996748i | \(0.525680\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.55772e132 | 0.807922 | ||||||||
\(974\) | −7.65611e132 | −0.781870 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.70508e133 | −1.58938 | ||||||||
\(977\) | 1.36516e133 | 1.21584 | 0.607920 | − | 0.793998i | \(-0.292004\pi\) | ||||
0.607920 | + | 0.793998i | \(0.292004\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.87909e133 | 1.52798 | ||||||||
\(980\) | −1.26924e132 | −0.0986241 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.19445e133 | 2.97655 | ||||||||
\(983\) | −1.70343e133 | −1.15530 | −0.577649 | − | 0.816285i | \(-0.696030\pi\) | ||||
−0.577649 | + | 0.816285i | \(0.696030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.25422e132 | −0.139664 | ||||||||
\(986\) | 3.46933e133 | 2.05458 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.07316e133 | −2.20418 | ||||||||
\(989\) | 5.22823e132 | 0.270471 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.06033e133 | 0.501375 | 0.250687 | − | 0.968068i | \(-0.419343\pi\) | ||||
0.250687 | + | 0.968068i | \(0.419343\pi\) | |||||||
\(992\) | −2.38504e133 | −1.07827 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.30057e133 | −0.537575 | ||||||||
\(995\) | 7.06580e132 | 0.279277 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.46285e133 | 0.528768 | 0.264384 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264384 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(998\) | −1.31156e133 | −0.453399 | ||||||||
\(999\) | 0 | 0 |
(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 | 9.90.a.b.1.1 | 7 | ||
3.2 | odd | 2 | 1.90.a.a.1.7 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.90.a.a.1.7 | ✓ | 7 | 3.2 | odd | 2 | ||
9.90.a.b.1.1 | 7 | 1.1 | even | 1 | trivial |