Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,94,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, 94, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 94);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 94 \) |
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: | \(492.952887545\) |
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: | \( x^{7} - x^{6} + \cdots - 13\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{88}\cdot 3^{47}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-3.01170e11\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67226e14 | 1.68038 | 0.840192 | − | 0.542290i | \(-0.182442\pi\) | ||||
0.840192 | + | 0.542290i | \(0.182442\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.80609e28 | 1.82369 | ||||||||
\(5\) | 5.69707e32 | 1.79286 | 0.896429 | − | 0.443186i | \(-0.146152\pi\) | ||||
0.896429 | + | 0.443186i | \(0.146152\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.48367e39 | 1.75784 | 0.878918 | − | 0.476973i | \(-0.158266\pi\) | ||||
0.878918 | + | 0.476973i | \(0.158266\pi\) | |||||||
\(8\) | 1.36413e42 | 1.38411 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 9.52696e46 | 3.01269 | ||||||||
\(11\) | 4.56983e47 | 0.171846 | 0.0859231 | − | 0.996302i | \(-0.472616\pi\) | ||||
0.0859231 | + | 0.996302i | \(0.472616\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.65568e49 | −0.00740657 | −0.00370328 | − | 0.999993i | \(-0.501179\pi\) | ||||
−0.00370328 | + | 0.999993i | \(0.501179\pi\) | |||||||
\(14\) | 5.82559e53 | 2.95384 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.92506e55 | 0.502149 | ||||||||
\(17\) | 7.16300e56 | 0.435733 | 0.217866 | − | 0.975979i | \(-0.430090\pi\) | ||||
0.217866 | + | 0.975979i | \(0.430090\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.92840e58 | −0.170084 | −0.0850421 | − | 0.996377i | \(-0.527102\pi\) | ||||
−0.0850421 | + | 0.996377i | \(0.527102\pi\) | |||||||
\(20\) | 1.02894e61 | 3.26961 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.64193e61 | 0.288767 | ||||||||
\(23\) | −1.15698e63 | −0.553328 | −0.276664 | − | 0.960967i | \(-0.589229\pi\) | ||||
−0.276664 | + | 0.960967i | \(0.589229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.23592e65 | 2.21434 | ||||||||
\(26\) | −7.78549e63 | −0.0124459 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.29183e67 | 3.20574 | ||||||||
\(29\) | −1.03850e68 | −1.03490 | −0.517452 | − | 0.855712i | \(-0.673120\pi\) | ||||
−0.517452 | + | 0.855712i | \(0.673120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.93363e67 | −0.0400598 | −0.0200299 | − | 0.999799i | \(-0.506376\pi\) | ||||
−0.0200299 | + | 0.999799i | \(0.506376\pi\) | |||||||
\(32\) | −5.27370e69 | −0.540309 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.19784e71 | 0.732198 | ||||||||
\(35\) | 1.98467e72 | 3.15155 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.91204e72 | 0.708528 | 0.354264 | − | 0.935145i | \(-0.384731\pi\) | ||||
0.354264 | + | 0.935145i | \(0.384731\pi\) | |||||||
\(38\) | −8.24156e72 | −0.285807 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.77153e74 | 2.48152 | ||||||||
\(41\) | −2.38541e74 | −0.241609 | −0.120805 | − | 0.992676i | \(-0.538547\pi\) | ||||
−0.120805 | + | 0.992676i | \(0.538547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.84207e75 | −0.203715 | −0.101857 | − | 0.994799i | \(-0.532479\pi\) | ||||
−0.101857 | + | 0.994799i | \(0.532479\pi\) | |||||||
\(44\) | 8.25353e75 | 0.313394 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.93477e77 | −0.929803 | ||||||||
\(47\) | −5.58584e77 | −0.987502 | −0.493751 | − | 0.869603i | \(-0.664375\pi\) | ||||
−0.493751 | + | 0.869603i | \(0.664375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.20845e78 | 2.08999 | ||||||||
\(50\) | 3.73903e79 | 3.72095 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.40858e77 | −0.0135073 | ||||||||
\(53\) | 2.41979e80 | 1.60306 | 0.801531 | − | 0.597953i | \(-0.204019\pi\) | ||||
0.801531 | + | 0.597953i | \(0.204019\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.60346e80 | 0.308096 | ||||||||
\(56\) | 4.75217e81 | 2.43304 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.73664e82 | −1.73904 | ||||||||
\(59\) | 2.30840e82 | 1.04398 | 0.521990 | − | 0.852951i | \(-0.325190\pi\) | ||||
0.521990 | + | 0.852951i | \(0.325190\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.46410e83 | 1.40518 | 0.702591 | − | 0.711594i | \(-0.252027\pi\) | ||||
0.702591 | + | 0.711594i | \(0.252027\pi\) | |||||||
\(62\) | −1.49393e82 | −0.0673159 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.36965e84 | −1.41007 | ||||||||
\(65\) | −2.65237e82 | −0.0132789 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.40138e84 | 0.171426 | 0.0857131 | − | 0.996320i | \(-0.472683\pi\) | ||||
0.0857131 | + | 0.996320i | \(0.472683\pi\) | |||||||
\(68\) | 1.29370e85 | 0.794640 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.31888e86 | 5.29581 | ||||||||
\(71\) | 1.74082e86 | 1.43628 | 0.718142 | − | 0.695897i | \(-0.244993\pi\) | ||||
0.718142 | + | 0.695897i | \(0.244993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.65018e86 | −1.05428 | −0.527141 | − | 0.849778i | \(-0.676736\pi\) | ||||
−0.527141 | + | 0.849778i | \(0.676736\pi\) | |||||||
\(74\) | 9.88645e86 | 1.19060 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.90115e86 | −0.310180 | ||||||||
\(77\) | 1.59198e87 | 0.302077 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.89450e88 | −1.09103 | −0.545513 | − | 0.838102i | \(-0.683665\pi\) | ||||
−0.545513 | + | 0.838102i | \(0.683665\pi\) | |||||||
\(80\) | 2.80584e88 | 0.900282 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.98902e88 | −0.405996 | ||||||||
\(83\) | 2.23742e89 | 1.29603 | 0.648016 | − | 0.761627i | \(-0.275599\pi\) | ||||
0.648016 | + | 0.761627i | \(0.275599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.08081e89 | 0.781207 | ||||||||
\(86\) | −3.08041e89 | −0.342319 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.23383e89 | 0.237854 | ||||||||
\(89\) | 1.44081e90 | 0.325066 | 0.162533 | − | 0.986703i | \(-0.448034\pi\) | ||||
0.162533 | + | 0.986703i | \(0.448034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.62188e89 | −0.0130195 | ||||||||
\(92\) | −2.08962e91 | −1.00910 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.34096e91 | −1.65938 | ||||||||
\(95\) | −2.80774e91 | −0.304937 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.44825e91 | −0.348242 | −0.174121 | − | 0.984724i | \(-0.555708\pi\) | ||||
−0.174121 | + | 0.984724i | \(0.555708\pi\) | |||||||
\(98\) | 1.37266e93 | 3.51198 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.03827e93 | 4.03827 | ||||||||
\(101\) | −1.31306e93 | −0.826683 | −0.413342 | − | 0.910576i | \(-0.635639\pi\) | ||||
−0.413342 | + | 0.910576i | \(0.635639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.21301e93 | −0.306854 | −0.153427 | − | 0.988160i | \(-0.549031\pi\) | ||||
−0.153427 | + | 0.988160i | \(0.549031\pi\) | |||||||
\(104\) | −6.35094e91 | −0.0102515 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.04652e94 | 2.69376 | ||||||||
\(107\) | 1.56019e94 | 0.671168 | 0.335584 | − | 0.942010i | \(-0.391066\pi\) | ||||
0.335584 | + | 0.942010i | \(0.391066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.90925e94 | 0.528992 | 0.264496 | − | 0.964387i | \(-0.414794\pi\) | ||||
0.264496 | + | 0.964387i | \(0.414794\pi\) | |||||||
\(110\) | 4.35366e94 | 0.517719 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.71573e95 | 0.882695 | ||||||||
\(113\) | 5.02384e95 | 1.70957 | 0.854787 | − | 0.518979i | \(-0.173688\pi\) | ||||
0.854787 | + | 0.518979i | \(0.173688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.59141e95 | −0.992040 | ||||||||
\(116\) | −1.87563e96 | −1.88734 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.86024e96 | 1.75429 | ||||||||
\(119\) | 2.49535e96 | 0.765946 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.86280e96 | −0.970469 | ||||||||
\(122\) | 2.44835e97 | 2.36124 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.61350e96 | −0.0730566 | ||||||||
\(125\) | 6.98559e97 | 2.17715 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.70958e96 | 0.0850611 | 0.0425306 | − | 0.999095i | \(-0.486458\pi\) | ||||
0.0425306 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(128\) | −1.76813e98 | −1.82916 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.43545e96 | −0.0223137 | ||||||||
\(131\) | 6.34511e96 | 0.0223524 | 0.0111762 | − | 0.999938i | \(-0.496442\pi\) | ||||
0.0111762 | + | 0.999938i | \(0.496442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.71689e98 | −0.298980 | ||||||||
\(134\) | 2.34346e98 | 0.288062 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.77125e98 | 0.603102 | ||||||||
\(137\) | 1.94391e99 | 0.853436 | 0.426718 | − | 0.904385i | \(-0.359670\pi\) | ||||
0.426718 | + | 0.904385i | \(0.359670\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.49504e99 | 1.90098 | 0.950489 | − | 0.310758i | \(-0.100583\pi\) | ||||
0.950489 | + | 0.310758i | \(0.100583\pi\) | |||||||
\(140\) | 3.58450e100 | 5.74745 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.91110e100 | 2.41351 | ||||||||
\(143\) | −2.12756e97 | −0.00127279 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.91642e100 | −1.85544 | ||||||||
\(146\) | −7.77630e100 | −1.77160 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.06777e101 | 1.29213 | ||||||||
\(149\) | −1.32597e101 | −1.17320 | −0.586599 | − | 0.809878i | \(-0.699534\pi\) | ||||
−0.586599 | + | 0.809878i | \(0.699534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.45701e101 | −1.64541 | −0.822703 | − | 0.568472i | \(-0.807535\pi\) | ||||
−0.822703 | + | 0.568472i | \(0.807535\pi\) | |||||||
\(152\) | −6.72298e100 | −0.235415 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.66220e101 | 0.507606 | ||||||||
\(155\) | −5.08955e100 | −0.0718216 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50836e102 | −1.17266 | −0.586331 | − | 0.810072i | \(-0.699428\pi\) | ||||
−0.586331 | + | 0.810072i | \(0.699428\pi\) | |||||||
\(158\) | −3.16809e102 | −1.83334 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.00447e102 | −0.968697 | ||||||||
\(161\) | −4.03055e102 | −0.972660 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.68240e102 | −0.364586 | −0.182293 | − | 0.983244i | \(-0.558352\pi\) | ||||
−0.182293 | + | 0.983244i | \(0.558352\pi\) | |||||||
\(164\) | −4.30827e102 | −0.440620 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.74153e103 | 2.17783 | ||||||||
\(167\) | −2.49429e102 | −0.109807 | −0.0549036 | − | 0.998492i | \(-0.517485\pi\) | ||||
−0.0549036 | + | 0.998492i | \(0.517485\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.95101e103 | −0.999945 | ||||||||
\(170\) | 6.82416e103 | 1.31273 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.32695e103 | −0.371512 | ||||||||
\(173\) | −4.59720e103 | −0.392057 | −0.196029 | − | 0.980598i | \(-0.562805\pi\) | ||||
−0.196029 | + | 0.980598i | \(0.562805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.78919e104 | 3.89245 | ||||||||
\(176\) | 2.25067e103 | 0.0862923 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.40941e104 | 0.546236 | ||||||||
\(179\) | 3.50256e104 | 0.611954 | 0.305977 | − | 0.952039i | \(-0.401017\pi\) | ||||
0.305977 | + | 0.952039i | \(0.401017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.14588e105 | −1.19422 | −0.597111 | − | 0.802158i | \(-0.703685\pi\) | ||||
−0.597111 | + | 0.802158i | \(0.703685\pi\) | |||||||
\(182\) | −2.71221e103 | −0.0218778 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.57827e105 | −0.765867 | ||||||||
\(185\) | 3.36813e105 | 1.27029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.27337e104 | 0.0748790 | ||||||||
\(188\) | −1.00885e106 | −1.80089 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.69527e105 | −0.512411 | ||||||||
\(191\) | −1.60846e106 | −1.37518 | −0.687589 | − | 0.726100i | \(-0.741331\pi\) | ||||
−0.687589 | + | 0.726100i | \(0.741331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.70685e106 | −0.899043 | −0.449521 | − | 0.893270i | \(-0.648405\pi\) | ||||
−0.449521 | + | 0.893270i | \(0.648405\pi\) | |||||||
\(194\) | −1.41276e106 | −0.585180 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.48252e107 | 3.81148 | ||||||||
\(197\) | −3.10588e106 | −0.630239 | −0.315119 | − | 0.949052i | \(-0.602045\pi\) | ||||
−0.315119 | + | 0.949052i | \(0.602045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.17602e106 | −0.783504 | −0.391752 | − | 0.920071i | \(-0.628131\pi\) | ||||
−0.391752 | + | 0.920071i | \(0.628131\pi\) | |||||||
\(200\) | 3.05008e107 | 3.06490 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.19577e107 | −1.38915 | ||||||||
\(203\) | −3.61780e107 | −1.81919 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.35898e107 | −0.433172 | ||||||||
\(206\) | −2.02846e107 | −0.515633 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.29295e105 | −0.00371920 | ||||||||
\(209\) | −2.25220e106 | −0.0292283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.25722e107 | −0.688176 | −0.344088 | − | 0.938937i | \(-0.611812\pi\) | ||||
−0.344088 | + | 0.938937i | \(0.611812\pi\) | |||||||
\(212\) | 4.37037e108 | 2.92349 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.60904e108 | 1.12782 | ||||||||
\(215\) | −1.04944e108 | −0.365232 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.11218e107 | −0.0704186 | ||||||||
\(218\) | 4.86502e108 | 0.888909 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.70209e108 | 0.561871 | ||||||||
\(221\) | −3.33486e106 | −0.00322728 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.48798e109 | −1.58369 | −0.791846 | − | 0.610721i | \(-0.790880\pi\) | ||||
−0.791846 | + | 0.610721i | \(0.790880\pi\) | |||||||
\(224\) | −1.83719e109 | −0.949774 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.40115e109 | 2.87274 | ||||||||
\(227\) | 4.23182e109 | 1.17849 | 0.589244 | − | 0.807955i | \(-0.299426\pi\) | ||||
0.589244 | + | 0.807955i | \(0.299426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.89882e109 | 1.09248 | 0.546242 | − | 0.837627i | \(-0.316058\pi\) | ||||
0.546242 | + | 0.837627i | \(0.316058\pi\) | |||||||
\(230\) | −1.10225e110 | −1.66701 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.41665e110 | −1.43242 | ||||||||
\(233\) | −2.13090e110 | −1.76406 | −0.882031 | − | 0.471192i | \(-0.843824\pi\) | ||||
−0.882031 | + | 0.471192i | \(0.843824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.18229e110 | −1.77045 | ||||||||
\(236\) | 4.16918e110 | 1.90389 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.17287e110 | 1.28708 | ||||||||
\(239\) | 8.20500e109 | 0.208246 | 0.104123 | − | 0.994564i | \(-0.466796\pi\) | ||||
0.104123 | + | 0.994564i | \(0.466796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.90307e110 | 0.672378 | 0.336189 | − | 0.941795i | \(-0.390862\pi\) | ||||
0.336189 | + | 0.941795i | \(0.390862\pi\) | |||||||
\(242\) | −1.14764e111 | −1.63076 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.64429e111 | 2.56261 | ||||||||
\(245\) | 4.67641e111 | 3.74705 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.29451e108 | 0.00125974 | ||||||||
\(248\) | −1.21866e110 | −0.0554472 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.16817e112 | 3.65844 | ||||||||
\(251\) | 1.23935e111 | 0.322379 | 0.161190 | − | 0.986923i | \(-0.448467\pi\) | ||||
0.161190 | + | 0.986923i | \(0.448467\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.28721e110 | −0.0950873 | ||||||||
\(254\) | 9.54789e110 | 0.142935 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.60033e112 | −1.66361 | ||||||||
\(257\) | 1.72101e112 | 1.49243 | 0.746213 | − | 0.665707i | \(-0.231870\pi\) | ||||
0.746213 | + | 0.665707i | \(0.231870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.05956e112 | 1.24548 | ||||||||
\(260\) | −4.79043e110 | −0.0242166 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.06107e111 | 0.0375606 | ||||||||
\(263\) | 6.46068e111 | 0.191574 | 0.0957869 | − | 0.995402i | \(-0.469463\pi\) | ||||
0.0957869 | + | 0.995402i | \(0.469463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.37857e113 | 2.87407 | ||||||||
\(266\) | −2.87109e112 | −0.502401 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.53102e112 | 0.312628 | ||||||||
\(269\) | 7.61241e111 | 0.0790753 | 0.0395377 | − | 0.999218i | \(-0.487411\pi\) | ||||
0.0395377 | + | 0.999218i | \(0.487411\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.48308e112 | −0.624427 | −0.312213 | − | 0.950012i | \(-0.601070\pi\) | ||||
−0.312213 | + | 0.950012i | \(0.601070\pi\) | |||||||
\(272\) | 3.52782e112 | 0.218802 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.25073e113 | 1.43410 | ||||||||
\(275\) | 1.02177e113 | 0.380526 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.01098e113 | 0.268802 | 0.134401 | − | 0.990927i | \(-0.457089\pi\) | ||||
0.134401 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(278\) | 1.42059e114 | 3.19437 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.70735e114 | 4.36210 | ||||||||
\(281\) | −2.93864e113 | −0.401146 | −0.200573 | − | 0.979679i | \(-0.564280\pi\) | ||||
−0.200573 | + | 0.979679i | \(0.564280\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.44060e114 | 1.41408 | 0.707042 | − | 0.707172i | \(-0.250029\pi\) | ||||
0.707042 | + | 0.707172i | \(0.250029\pi\) | |||||||
\(284\) | 3.14408e114 | 2.61933 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.55783e111 | −0.00213877 | ||||||||
\(287\) | −8.30999e113 | −0.424710 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.18931e114 | −0.810137 | ||||||||
\(290\) | −9.89377e114 | −3.11785 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.39866e114 | −1.92268 | ||||||||
\(293\) | −2.96400e114 | −0.578807 | −0.289403 | − | 0.957207i | \(-0.593457\pi\) | ||||
−0.289403 | + | 0.957207i | \(0.593457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.31511e115 | 1.87171 | ||||||||
\(296\) | 8.06478e114 | 0.980682 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.21736e115 | −1.97142 | ||||||||
\(299\) | 5.38654e112 | 0.00409826 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.41716e114 | −0.358097 | ||||||||
\(302\) | −5.78102e115 | −2.76491 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.42727e114 | −0.0854075 | ||||||||
\(305\) | 8.34105e115 | 2.51929 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.05946e115 | 0.236129 | 0.118065 | − | 0.993006i | \(-0.462331\pi\) | ||||
0.118065 | + | 0.993006i | \(0.462331\pi\) | |||||||
\(308\) | 2.87526e115 | 0.550895 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.51103e114 | −0.120688 | ||||||||
\(311\) | 9.04218e115 | 1.10386 | 0.551931 | − | 0.833890i | \(-0.313891\pi\) | ||||
0.551931 | + | 0.833890i | \(0.313891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.51474e115 | −0.771542 | −0.385771 | − | 0.922595i | \(-0.626064\pi\) | ||||
−0.385771 | + | 0.922595i | \(0.626064\pi\) | |||||||
\(314\) | −2.52237e116 | −1.97052 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.42164e116 | −1.98969 | ||||||||
\(317\) | 2.02778e116 | 1.01804 | 0.509021 | − | 0.860754i | \(-0.330008\pi\) | ||||
0.509021 | + | 0.860754i | \(0.330008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.74577e115 | −0.177844 | ||||||||
\(320\) | −7.80301e116 | −2.52806 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.74012e116 | −1.63444 | ||||||||
\(323\) | −3.53021e115 | −0.0741112 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.04097e115 | −0.0164007 | ||||||||
\(326\) | −4.48566e116 | −0.612643 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.25401e116 | −0.334414 | ||||||||
\(329\) | −1.94592e117 | −1.73587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.27033e116 | −0.0854901 | −0.0427450 | − | 0.999086i | \(-0.513610\pi\) | ||||
−0.0427450 | + | 0.999086i | \(0.513610\pi\) | |||||||
\(332\) | 4.04098e117 | 2.36356 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.17109e116 | −0.184518 | ||||||||
\(335\) | 7.98374e116 | 0.307343 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.73776e117 | −0.507225 | −0.253612 | − | 0.967306i | \(-0.581619\pi\) | ||||
−0.253612 | + | 0.967306i | \(0.581619\pi\) | |||||||
\(338\) | −6.60710e117 | −1.68029 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.37032e117 | 1.42468 | ||||||||
\(341\) | −4.08251e115 | −0.00688413 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.49134e118 | 1.91602 | ||||||||
\(344\) | −2.51282e117 | −0.281964 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.68770e117 | −0.658806 | ||||||||
\(347\) | −1.27568e118 | −0.955921 | −0.477960 | − | 0.878381i | \(-0.658624\pi\) | ||||
−0.477960 | + | 0.878381i | \(0.658624\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.04561e117 | −0.518866 | −0.259433 | − | 0.965761i | \(-0.583536\pi\) | ||||
−0.259433 | + | 0.965761i | \(0.583536\pi\) | |||||||
\(350\) | 1.30255e119 | 6.54081 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.40999e117 | −0.0928500 | ||||||||
\(353\) | −4.00670e118 | −1.35289 | −0.676447 | − | 0.736492i | \(-0.736481\pi\) | ||||
−0.676447 | + | 0.736492i | \(0.736481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.91756e118 | 2.57505 | ||||||||
\(356\) | 2.60224e118 | 0.592819 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.85717e118 | 1.02832 | ||||||||
\(359\) | 3.72279e118 | 0.574085 | 0.287043 | − | 0.957918i | \(-0.407328\pi\) | ||||
0.287043 | + | 0.957918i | \(0.407328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.15335e118 | −0.971071 | ||||||||
\(362\) | −1.91621e119 | −2.00675 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.92927e117 | −0.0237435 | ||||||||
\(365\) | −2.64924e119 | −1.89018 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.79087e118 | −0.0991043 | −0.0495522 | − | 0.998772i | \(-0.515779\pi\) | ||||
−0.0495522 | + | 0.998772i | \(0.515779\pi\) | |||||||
\(368\) | −5.69821e118 | −0.277853 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.63238e119 | 2.13458 | ||||||||
\(371\) | 8.42977e119 | 2.81792 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.39147e119 | 1.14327 | 0.571635 | − | 0.820508i | \(-0.306309\pi\) | ||||
0.571635 | + | 0.820508i | \(0.306309\pi\) | |||||||
\(374\) | 5.47391e118 | 0.125825 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.61980e119 | −1.36681 | ||||||||
\(377\) | 4.83493e117 | 0.00766509 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.66278e119 | −0.825909 | −0.412954 | − | 0.910752i | \(-0.635503\pi\) | ||||
−0.412954 | + | 0.910752i | \(0.635503\pi\) | |||||||
\(380\) | −5.07105e119 | −0.556110 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.68976e120 | −2.31083 | ||||||||
\(383\) | −1.79657e120 | −1.36679 | −0.683395 | − | 0.730049i | \(-0.739497\pi\) | ||||
−0.683395 | + | 0.730049i | \(0.739497\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.06960e119 | 0.541582 | ||||||||
\(386\) | −2.85429e120 | −1.51074 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.52583e120 | −0.635085 | ||||||||
\(389\) | 3.75042e120 | 1.38492 | 0.692459 | − | 0.721458i | \(-0.256528\pi\) | ||||
0.692459 | + | 0.721458i | \(0.256528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.28747e119 | −0.241103 | ||||||||
\(392\) | 1.11974e121 | 2.89277 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.19383e120 | −1.05904 | ||||||||
\(395\) | −1.07931e121 | −1.95606 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.93819e119 | −0.0994232 | −0.0497116 | − | 0.998764i | \(-0.515830\pi\) | ||||
−0.0497116 | + | 0.998764i | \(0.515830\pi\) | |||||||
\(398\) | −1.03279e121 | −1.31659 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.10120e121 | 1.11193 | ||||||||
\(401\) | 4.38284e120 | 0.394042 | 0.197021 | − | 0.980399i | \(-0.436873\pi\) | ||||
0.197021 | + | 0.980399i | \(0.436873\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.15921e117 | 0.000296706 0 | ||||||||
\(404\) | −2.37150e121 | −1.50761 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.04989e121 | −3.05694 | ||||||||
\(407\) | 2.70170e120 | 0.121758 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.19957e121 | 0.430421 | 0.215210 | − | 0.976568i | \(-0.430956\pi\) | ||||
0.215210 | + | 0.976568i | \(0.430956\pi\) | |||||||
\(410\) | −2.27257e121 | −0.727894 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.19080e121 | −0.559606 | ||||||||
\(413\) | 8.04171e121 | 1.83515 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.27467e122 | 2.32360 | ||||||||
\(416\) | 2.45527e119 | 0.00400183 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.76625e120 | −0.0491148 | ||||||||
\(419\) | 1.55294e122 | 1.81219 | 0.906095 | − | 0.423074i | \(-0.139049\pi\) | ||||
0.906095 | + | 0.423074i | \(0.139049\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.20749e122 | 1.12919 | 0.564595 | − | 0.825368i | \(-0.309032\pi\) | ||||
0.564595 | + | 0.825368i | \(0.309032\pi\) | |||||||
\(422\) | −1.38082e122 | −1.15640 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.30091e122 | 2.21882 | ||||||||
\(425\) | 1.60159e122 | 0.964861 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.10043e122 | 2.47008 | ||||||||
\(428\) | 2.81785e122 | 1.22400 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.75493e122 | −0.613729 | ||||||||
\(431\) | −1.44577e122 | −0.453842 | −0.226921 | − | 0.973913i | \(-0.572866\pi\) | ||||
−0.226921 | + | 0.973913i | \(0.572866\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.73888e122 | −1.70569 | −0.852846 | − | 0.522163i | \(-0.825125\pi\) | ||||
−0.852846 | + | 0.522163i | \(0.825125\pi\) | |||||||
\(434\) | −5.20437e121 | −0.118330 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.25438e122 | 0.964716 | ||||||||
\(437\) | 5.70208e121 | 0.0941124 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.23553e123 | −1.64912 | −0.824560 | − | 0.565775i | \(-0.808577\pi\) | ||||
−0.824560 | + | 0.565775i | \(0.808577\pi\) | |||||||
\(440\) | 3.55145e122 | 0.426439 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.57674e120 | −0.00542307 | ||||||||
\(443\) | −2.19056e122 | −0.191771 | −0.0958854 | − | 0.995392i | \(-0.530568\pi\) | ||||
−0.0958854 | + | 0.995392i | \(0.530568\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.20840e122 | 0.582798 | ||||||||
\(446\) | −4.16054e123 | −2.66121 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.77142e123 | −2.47868 | ||||||||
\(449\) | −7.18526e122 | −0.336502 | −0.168251 | − | 0.985744i | \(-0.553812\pi\) | ||||
−0.168251 | + | 0.985744i | \(0.553812\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.09009e122 | −0.0415197 | ||||||||
\(452\) | 9.07351e123 | 3.11773 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.07670e123 | 1.98031 | ||||||||
\(455\) | −9.23999e121 | −0.0233422 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.72549e123 | 0.973518 | 0.486759 | − | 0.873536i | \(-0.338179\pi\) | ||||
0.486759 | + | 0.873536i | \(0.338179\pi\) | |||||||
\(458\) | 9.86434e123 | 1.83579 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.19047e124 | −1.80917 | ||||||||
\(461\) | −1.23678e124 | −1.69902 | −0.849510 | − | 0.527573i | \(-0.823102\pi\) | ||||
−0.849510 | + | 0.527573i | \(0.823102\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.69925e123 | 0.864833 | 0.432417 | − | 0.901674i | \(-0.357661\pi\) | ||||
0.432417 | + | 0.901674i | \(0.357661\pi\) | |||||||
\(464\) | −5.11468e123 | −0.519676 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.56342e124 | −2.96430 | ||||||||
\(467\) | 1.64477e124 | 1.23843 | 0.619215 | − | 0.785222i | \(-0.287451\pi\) | ||||
0.619215 | + | 0.785222i | \(0.287451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.88194e123 | 0.301339 | ||||||||
\(470\) | −5.32161e124 | −2.97504 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.14895e124 | 1.44498 | ||||||||
\(473\) | −8.41793e122 | −0.0350076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.10195e124 | −0.376625 | ||||||||
\(476\) | 4.50684e124 | 1.39685 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.37209e124 | 0.349933 | ||||||||
\(479\) | 2.79704e124 | 0.647287 | 0.323643 | − | 0.946179i | \(-0.395092\pi\) | ||||
0.323643 | + | 0.946179i | \(0.395092\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.75245e122 | −0.00524776 | ||||||||
\(482\) | 6.52693e124 | 1.12985 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.23949e125 | −1.76983 | ||||||||
\(485\) | −4.81302e124 | −0.624349 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.15017e124 | 0.230343 | 0.115172 | − | 0.993346i | \(-0.463258\pi\) | ||||
0.115172 | + | 0.993346i | \(0.463258\pi\) | |||||||
\(488\) | 1.99721e125 | 1.94493 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.82016e125 | 6.29648 | ||||||||
\(491\) | 2.58184e123 | 0.0189077 | 0.00945387 | − | 0.999955i | \(-0.496991\pi\) | ||||
0.00945387 | + | 0.999955i | \(0.496991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.43879e124 | −0.450942 | ||||||||
\(494\) | 3.83700e122 | 0.00211685 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.39986e123 | −0.0201160 | ||||||||
\(497\) | 6.06444e125 | 2.52475 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.24177e125 | 1.46511 | 0.732557 | − | 0.680706i | \(-0.238327\pi\) | ||||
0.732557 | + | 0.680706i | \(0.238327\pi\) | |||||||
\(500\) | 1.26166e126 | 3.97043 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.07252e125 | 0.541721 | ||||||||
\(503\) | −6.20313e125 | −1.47809 | −0.739043 | − | 0.673658i | \(-0.764722\pi\) | ||||
−0.739043 | + | 0.673658i | \(0.764722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.48057e125 | −1.48213 | ||||||||
\(506\) | −8.84158e124 | −0.159783 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.03120e125 | 0.155125 | ||||||||
\(509\) | −6.21343e125 | −0.853011 | −0.426505 | − | 0.904485i | \(-0.640255\pi\) | ||||
−0.426505 | + | 0.904485i | \(0.640255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.61997e126 | −1.85325 | ||||||||
\(512\) | −9.25092e125 | −0.966344 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.87797e126 | 2.50785 | ||||||||
\(515\) | −6.91058e125 | −0.550146 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.55263e125 | −0.169698 | ||||||||
\(518\) | 3.44412e126 | 2.09288 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.61817e124 | −0.0183795 | ||||||||
\(521\) | −1.08310e126 | −0.503170 | −0.251585 | − | 0.967835i | \(-0.580952\pi\) | ||||
−0.251585 | + | 0.967835i | \(0.580952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.12144e126 | −0.824711 | −0.412356 | − | 0.911023i | \(-0.635294\pi\) | ||||
−0.412356 | + | 0.911023i | \(0.635294\pi\) | |||||||
\(524\) | 1.14599e125 | 0.0407638 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.08039e126 | 0.321917 | ||||||||
\(527\) | −6.39916e124 | −0.0174554 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.03348e126 | −0.693828 | ||||||||
\(530\) | 2.30533e127 | 4.82953 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.10087e126 | −0.545246 | ||||||||
\(533\) | 1.11057e124 | 0.00178950 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.88850e126 | 1.20331 | ||||||||
\(536\) | 1.91166e126 | 0.237273 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.27299e126 | 0.132877 | ||||||||
\(539\) | 3.75112e126 | 0.359156 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.54574e126 | 0.446978 | 0.223489 | − | 0.974706i | \(-0.428255\pi\) | ||||
0.223489 | + | 0.974706i | \(0.428255\pi\) | |||||||
\(542\) | −1.41859e127 | −1.04928 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.77755e126 | −0.235430 | ||||||||
\(545\) | 1.65742e127 | 0.948408 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.32636e127 | 1.12271 | 0.561354 | − | 0.827576i | \(-0.310281\pi\) | ||||
0.561354 | + | 0.827576i | \(0.310281\pi\) | |||||||
\(548\) | 3.51089e127 | 1.55640 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.70867e127 | 0.639430 | ||||||||
\(551\) | 5.11816e126 | 0.176021 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.59982e127 | −1.91784 | ||||||||
\(554\) | 1.69061e127 | 0.451690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.53428e128 | 3.46679 | ||||||||
\(557\) | −5.86328e127 | −1.21864 | −0.609318 | − | 0.792926i | \(-0.708557\pi\) | ||||
−0.609318 | + | 0.792926i | \(0.708557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.57607e124 | 0.00150883 | ||||||||
\(560\) | 9.77462e127 | 1.58255 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.91416e127 | −0.674079 | ||||||||
\(563\) | 6.83447e127 | 0.863107 | 0.431554 | − | 0.902087i | \(-0.357966\pi\) | ||||
0.431554 | + | 0.902087i | \(0.357966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.86211e128 | 3.06502 | ||||||||
\(566\) | 2.40906e128 | 2.37620 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.37470e128 | 1.98797 | ||||||||
\(569\) | 1.82425e128 | 1.40722 | 0.703611 | − | 0.710585i | \(-0.251570\pi\) | ||||
0.703611 | + | 0.710585i | \(0.251570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.22711e127 | 0.539099 | 0.269549 | − | 0.962987i | \(-0.413125\pi\) | ||||
0.269549 | + | 0.962987i | \(0.413125\pi\) | |||||||
\(572\) | −3.84258e125 | −0.00232117 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.38964e128 | −0.713675 | ||||||||
\(575\) | −2.58692e128 | −1.22526 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.15417e128 | −0.465150 | −0.232575 | − | 0.972578i | \(-0.574715\pi\) | ||||
−0.232575 | + | 0.972578i | \(0.574715\pi\) | |||||||
\(578\) | −3.66110e128 | −1.36134 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.06856e129 | −3.38374 | ||||||||
\(581\) | 7.79442e128 | 2.27821 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.10580e128 | 0.275480 | ||||||||
\(584\) | −6.34344e128 | −1.45924 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.95657e128 | −0.972617 | ||||||||
\(587\) | −4.28859e128 | −0.777397 | −0.388699 | − | 0.921365i | \(-0.627075\pi\) | ||||
−0.388699 | + | 0.921365i | \(0.627075\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.40285e126 | 0.00681354 | ||||||||
\(590\) | 2.19920e129 | 3.14519 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.91172e128 | 0.355787 | ||||||||
\(593\) | −8.20747e128 | −0.927184 | −0.463592 | − | 0.886049i | \(-0.653440\pi\) | ||||
−0.463592 | + | 0.886049i | \(0.653440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.42162e129 | 1.37323 | ||||||||
\(596\) | −2.39482e129 | −2.13955 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.00768e126 | 0.00688665 | ||||||||
\(599\) | −4.54499e128 | −0.321504 | −0.160752 | − | 0.986995i | \(-0.551392\pi\) | ||||
−0.160752 | + | 0.986995i | \(0.551392\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.06533e129 | −1.25120 | −0.625599 | − | 0.780145i | \(-0.715145\pi\) | ||||
−0.625599 | + | 0.780145i | \(0.715145\pi\) | |||||||
\(602\) | −1.07311e129 | −0.601740 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.24369e129 | −3.00071 | ||||||||
\(605\) | −3.90978e129 | −1.73991 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.80973e129 | −1.45419 | −0.727094 | − | 0.686538i | \(-0.759130\pi\) | ||||
−0.727094 | + | 0.686538i | \(0.759130\pi\) | |||||||
\(608\) | 2.59909e128 | 0.0918979 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.39484e130 | 4.23338 | ||||||||
\(611\) | 2.60058e127 | 0.00731400 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.21082e129 | −1.01731 | −0.508656 | − | 0.860970i | \(-0.669857\pi\) | ||||
−0.508656 | + | 0.860970i | \(0.669857\pi\) | |||||||
\(614\) | 1.77169e129 | 0.396787 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.17166e129 | 0.418108 | ||||||||
\(617\) | 4.88112e129 | 0.871484 | 0.435742 | − | 0.900072i | \(-0.356486\pi\) | ||||
0.435742 | + | 0.900072i | \(0.356486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.62026e129 | −1.17045 | −0.585227 | − | 0.810869i | \(-0.698995\pi\) | ||||
−0.585227 | + | 0.810869i | \(0.698995\pi\) | |||||||
\(620\) | −9.19219e128 | −0.130980 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.51208e130 | 1.85491 | ||||||||
\(623\) | 5.01931e129 | 0.571413 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.72204e130 | 1.68897 | ||||||||
\(626\) | −1.42388e130 | −1.29649 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.72425e130 | −2.13857 | ||||||||
\(629\) | 4.23479e129 | 0.308729 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.44127e129 | −0.279346 | −0.139673 | − | 0.990198i | \(-0.544605\pi\) | ||||
−0.139673 | + | 0.990198i | \(0.544605\pi\) | |||||||
\(632\) | −2.58434e130 | −1.51010 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.39097e130 | 1.71070 | ||||||||
\(635\) | 3.25279e129 | 0.152503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.82159e128 | −0.0154796 | ||||||||
\(638\) | −7.93615e129 | −0.298847 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00732e131 | −3.27942 | ||||||||
\(641\) | −5.07224e130 | −1.53568 | −0.767841 | − | 0.640640i | \(-0.778669\pi\) | ||||
−0.767841 | + | 0.640640i | \(0.778669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.10656e130 | 1.33757 | 0.668787 | − | 0.743454i | \(-0.266814\pi\) | ||||
0.668787 | + | 0.743454i | \(0.266814\pi\) | |||||||
\(644\) | −7.27955e130 | −1.77383 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.90343e129 | −0.124535 | ||||||||
\(647\) | 1.41954e130 | 0.278675 | 0.139337 | − | 0.990245i | \(-0.455503\pi\) | ||||
0.139337 | + | 0.990245i | \(0.455503\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.05490e130 | 0.179404 | ||||||||
\(650\) | −1.74077e129 | −0.0275594 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.84466e130 | −0.664890 | ||||||||
\(653\) | 1.15140e131 | 1.47150 | 0.735752 | − | 0.677251i | \(-0.236829\pi\) | ||||
0.735752 | + | 0.677251i | \(0.236829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.61485e129 | 0.0400747 | ||||||||
\(656\) | −1.17483e130 | −0.121324 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.25408e131 | −2.91692 | ||||||||
\(659\) | −1.96031e131 | −1.63740 | −0.818698 | − | 0.574224i | \(-0.805304\pi\) | ||||
−0.818698 | + | 0.574224i | \(0.805304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.17070e131 | −1.57482 | −0.787410 | − | 0.616429i | \(-0.788579\pi\) | ||||
−0.787410 | + | 0.616429i | \(0.788579\pi\) | |||||||
\(662\) | −2.12432e130 | −0.143656 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.05212e131 | 1.79385 | ||||||||
\(665\) | −9.78126e130 | −0.536029 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.20153e131 | 0.572642 | ||||||||
\(668\) | −4.50492e130 | −0.200254 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.33509e131 | 0.516454 | ||||||||
\(671\) | 6.69067e130 | 0.241475 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.57783e131 | 0.810127 | 0.405063 | − | 0.914289i | \(-0.367249\pi\) | ||||
0.405063 | + | 0.914289i | \(0.367249\pi\) | |||||||
\(674\) | −2.90599e131 | −0.852332 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.13589e131 | −1.82359 | ||||||||
\(677\) | −3.80729e131 | −0.908328 | −0.454164 | − | 0.890918i | \(-0.650062\pi\) | ||||
−0.454164 | + | 0.890918i | \(0.650062\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.94309e131 | −0.612152 | ||||||||
\(680\) | 5.56675e131 | 1.08128 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.82701e129 | −0.0115680 | ||||||||
\(683\) | −6.39876e131 | −1.01282 | −0.506411 | − | 0.862292i | \(-0.669028\pi\) | ||||
−0.506411 | + | 0.862292i | \(0.669028\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.10746e132 | 1.53009 | ||||||||
\(686\) | 2.49390e132 | 3.21964 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.07229e130 | −0.102295 | ||||||||
\(689\) | −1.12658e130 | −0.0118732 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.56983e131 | 0.144585 | 0.0722925 | − | 0.997383i | \(-0.476968\pi\) | ||||
0.0722925 | + | 0.997383i | \(0.476968\pi\) | |||||||
\(692\) | −8.30297e131 | −0.714990 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.13327e132 | −1.60631 | ||||||||
\(695\) | 4.83968e132 | 3.40819 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.70867e131 | −0.105277 | ||||||||
\(698\) | −1.51266e132 | −0.871894 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.40680e133 | 7.09862 | ||||||||
\(701\) | 1.73944e132 | 0.821335 | 0.410668 | − | 0.911785i | \(-0.365296\pi\) | ||||
0.410668 | + | 0.911785i | \(0.365296\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.91369e131 | −0.120509 | ||||||||
\(704\) | −6.25908e131 | −0.242316 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.70024e132 | −2.27338 | ||||||||
\(707\) | −4.57425e132 | −1.45317 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.69886e132 | 1.58759 | 0.793794 | − | 0.608186i | \(-0.208103\pi\) | ||||
0.793794 | + | 0.608186i | \(0.208103\pi\) | |||||||
\(710\) | 1.65847e133 | 4.32708 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.96545e132 | 0.449928 | ||||||||
\(713\) | 1.03361e131 | 0.0221662 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.21209e130 | −0.00228193 | ||||||||
\(716\) | 6.32594e132 | 1.11601 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.22546e132 | 0.964683 | ||||||||
\(719\) | 5.60725e131 | 0.0814435 | 0.0407218 | − | 0.999171i | \(-0.487034\pi\) | ||||
0.0407218 | + | 0.999171i | \(0.487034\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.22572e132 | −0.539399 | ||||||||
\(722\) | −1.36345e133 | −1.63177 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.06956e133 | −2.17789 | ||||||||
\(725\) | −2.32200e133 | −2.29163 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.95282e132 | −0.343207 | −0.171604 | − | 0.985166i | \(-0.554895\pi\) | ||||
−0.171604 | + | 0.985166i | \(0.554895\pi\) | |||||||
\(728\) | −2.21246e131 | −0.0180205 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.43021e133 | −3.17623 | ||||||||
\(731\) | −1.31947e132 | −0.0887652 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.21179e133 | −0.717950 | −0.358975 | − | 0.933347i | \(-0.616874\pi\) | ||||
−0.358975 | + | 0.933347i | \(0.616874\pi\) | |||||||
\(734\) | −2.99480e132 | −0.166533 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.10159e132 | 0.298968 | ||||||||
\(737\) | 6.40405e131 | 0.0294589 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.87595e133 | 1.16631 | 0.583157 | − | 0.812360i | \(-0.301817\pi\) | ||||
0.583157 | + | 0.812360i | \(0.301817\pi\) | |||||||
\(740\) | 6.08315e133 | 2.31661 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.40967e134 | 4.73519 | ||||||||
\(743\) | 9.00234e132 | 0.284037 | 0.142019 | − | 0.989864i | \(-0.454641\pi\) | ||||
0.142019 | + | 0.989864i | \(0.454641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.55412e133 | −2.10338 | ||||||||
\(746\) | 7.34366e133 | 1.92113 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.91200e132 | 0.136556 | ||||||||
\(749\) | 5.43518e133 | 1.17980 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.48940e133 | −1.43612 | −0.718059 | − | 0.695982i | \(-0.754969\pi\) | ||||
−0.718059 | + | 0.695982i | \(0.754969\pi\) | |||||||
\(752\) | −2.75106e133 | −0.495873 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.08525e131 | 0.0128803 | ||||||||
\(755\) | −1.96948e134 | −2.94998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.10318e134 | 1.46113 | 0.730565 | − | 0.682843i | \(-0.239257\pi\) | ||||
0.730565 | + | 0.682843i | \(0.239257\pi\) | |||||||
\(758\) | −1.11419e134 | −1.38784 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.83012e133 | −0.422066 | ||||||||
\(761\) | 1.06465e134 | 1.10362 | 0.551811 | − | 0.833969i | \(-0.313937\pi\) | ||||
0.551811 | + | 0.833969i | \(0.313937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.01349e134 | 0.929881 | ||||||||
\(764\) | −2.90503e134 | −2.50790 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.00433e134 | −2.29673 | ||||||||
\(767\) | −1.07472e132 | −0.00773231 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.64666e134 | 1.68703 | 0.843515 | − | 0.537105i | \(-0.180482\pi\) | ||||
0.843515 | + | 0.537105i | \(0.180482\pi\) | |||||||
\(770\) | 1.51667e134 | 0.910065 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.08273e134 | −1.63957 | ||||||||
\(773\) | 1.28102e134 | 0.641518 | 0.320759 | − | 0.947161i | \(-0.396062\pi\) | ||||
0.320759 | + | 0.947161i | \(0.396062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.99748e133 | −0.0887062 | ||||||||
\(776\) | −1.15245e134 | −0.482005 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.27167e134 | 2.32719 | ||||||||
\(779\) | 1.17563e133 | 0.0410939 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.95523e133 | 0.246820 | ||||||||
\(782\) | −1.38588e134 | −0.405146 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.04271e134 | 1.04948 | ||||||||
\(785\) | −8.59326e134 | −2.10242 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.01831e133 | 0.0438696 | 0.0219348 | − | 0.999759i | \(-0.493017\pi\) | ||||
0.0219348 | + | 0.999759i | \(0.493017\pi\) | |||||||
\(788\) | −5.60951e134 | −1.14936 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.80488e135 | −3.28692 | ||||||||
\(791\) | 1.75014e135 | 3.00515 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.81636e132 | −0.0104076 | ||||||||
\(794\) | −1.16024e134 | −0.167069 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.11545e135 | −1.42887 | ||||||||
\(797\) | −1.38083e134 | −0.166850 | −0.0834252 | − | 0.996514i | \(-0.526586\pi\) | ||||
−0.0834252 | + | 0.996514i | \(0.526586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00113e134 | −0.430287 | ||||||||
\(800\) | −1.17916e135 | −1.19643 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.32924e134 | 0.662141 | ||||||||
\(803\) | −2.12505e134 | −0.181174 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.29623e135 | −1.74384 | ||||||||
\(806\) | 6.95527e131 | 0.000498579 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.79118e135 | −1.14422 | ||||||||
\(809\) | −6.20202e134 | −0.374047 | −0.187024 | − | 0.982355i | \(-0.559884\pi\) | ||||
−0.187024 | + | 0.982355i | \(0.559884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.84479e135 | 0.991922 | 0.495961 | − | 0.868345i | \(-0.334816\pi\) | ||||
0.495961 | + | 0.868345i | \(0.334816\pi\) | |||||||
\(812\) | −6.53408e135 | −3.31764 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.51794e134 | 0.204600 | ||||||||
\(815\) | −1.52818e135 | −0.653650 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.07846e133 | 0.0346487 | ||||||||
\(818\) | 2.00600e135 | 0.723272 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.45445e135 | −0.789970 | ||||||||
\(821\) | 2.15187e135 | 0.654425 | 0.327213 | − | 0.944951i | \(-0.393891\pi\) | ||||
0.327213 | + | 0.944951i | \(0.393891\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.23448e135 | −1.42161 | −0.710806 | − | 0.703388i | \(-0.751670\pi\) | ||||
−0.710806 | + | 0.703388i | \(0.751670\pi\) | |||||||
\(824\) | −1.65470e135 | −0.424720 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.34478e136 | 3.08375 | ||||||||
\(827\) | 4.54736e135 | 0.985719 | 0.492860 | − | 0.870109i | \(-0.335952\pi\) | ||||
0.492860 | + | 0.870109i | \(0.335952\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.79485e135 | 1.89763 | 0.948816 | − | 0.315828i | \(-0.102282\pi\) | ||||
0.948816 | + | 0.315828i | \(0.102282\pi\) | |||||||
\(830\) | 2.13158e136 | 3.90454 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.37666e133 | 0.0104438 | ||||||||
\(833\) | 5.87971e135 | 0.910675 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.42101e135 | −0.196869 | ||||||||
\(836\) | −4.06767e134 | −0.0533033 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.59692e136 | 3.04517 | ||||||||
\(839\) | −7.42245e135 | −0.823409 | −0.411705 | − | 0.911317i | \(-0.635066\pi\) | ||||
−0.411705 | + | 0.911317i | \(0.635066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.15226e134 | 0.0710280 | ||||||||
\(842\) | 2.01924e136 | 1.89747 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.49133e136 | −1.25502 | ||||||||
\(845\) | −2.25092e136 | −1.79276 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.39077e136 | −1.70592 | ||||||||
\(848\) | 1.19176e136 | 0.804976 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.67826e136 | 1.62134 | ||||||||
\(851\) | −6.84013e135 | −0.392049 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.84936e135 | 0.146426 | 0.0732128 | − | 0.997316i | \(-0.476675\pi\) | ||||
0.0732128 | + | 0.997316i | \(0.476675\pi\) | |||||||
\(854\) | 8.52923e136 | 4.15068 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.12830e136 | 0.928971 | ||||||||
\(857\) | −1.21549e136 | −0.502507 | −0.251254 | − | 0.967921i | \(-0.580843\pi\) | ||||
−0.251254 | + | 0.967921i | \(0.580843\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.04217e135 | −0.261231 | −0.130615 | − | 0.991433i | \(-0.541695\pi\) | ||||
−0.130615 | + | 0.991433i | \(0.541695\pi\) | |||||||
\(860\) | −1.89538e136 | −0.666069 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.41769e136 | −0.762629 | ||||||||
\(863\) | −2.08063e136 | −0.621859 | −0.310930 | − | 0.950433i | \(-0.600640\pi\) | ||||
−0.310930 | + | 0.950433i | \(0.600640\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.61906e136 | −0.702903 | ||||||||
\(866\) | −1.12691e137 | −2.86621 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.62089e135 | −0.128422 | ||||||||
\(869\) | −8.65754e135 | −0.187489 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.52436e133 | −0.00126968 | ||||||||
\(872\) | 3.96859e136 | 0.732183 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.53535e135 | 0.158145 | ||||||||
\(875\) | 2.43355e137 | 3.82707 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.05763e136 | 0.432418 | 0.216209 | − | 0.976347i | \(-0.430631\pi\) | ||||
0.216209 | + | 0.976347i | \(0.430631\pi\) | |||||||
\(878\) | −2.06612e137 | −2.77115 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.28222e136 | 0.154710 | ||||||||
\(881\) | 7.50481e136 | 0.858935 | 0.429467 | − | 0.903082i | \(-0.358701\pi\) | ||||
0.429467 | + | 0.903082i | \(0.358701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.64375e136 | −0.581293 | −0.290647 | − | 0.956830i | \(-0.593870\pi\) | ||||
−0.290647 | + | 0.956830i | \(0.593870\pi\) | |||||||
\(884\) | −6.02307e134 | −0.00588555 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.66318e136 | −0.322248 | ||||||||
\(887\) | −1.61696e136 | −0.134974 | −0.0674872 | − | 0.997720i | \(-0.521498\pi\) | ||||
−0.0674872 | + | 0.997720i | \(0.521498\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.98903e136 | 0.149523 | ||||||||
\(890\) | 1.37266e137 | 0.979324 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.49352e137 | −2.88816 | ||||||||
\(893\) | 2.75293e136 | 0.167958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.99543e137 | 1.09715 | ||||||||
\(896\) | −6.15959e137 | −3.21536 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.20156e137 | −0.565452 | ||||||||
\(899\) | 9.27759e135 | 0.0414581 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.73330e137 | 0.698507 | ||||||||
\(902\) | −1.82291e136 | −0.0697689 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.85316e137 | 2.36624 | ||||||||
\(905\) | −6.52815e137 | −2.14107 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.22741e137 | −1.54721 | −0.773603 | − | 0.633671i | \(-0.781547\pi\) | ||||
−0.773603 | + | 0.633671i | \(0.781547\pi\) | |||||||
\(908\) | 7.64306e137 | 2.14919 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.54516e136 | −0.0392238 | ||||||||
\(911\) | −2.17562e137 | −0.524781 | −0.262391 | − | 0.964962i | \(-0.584511\pi\) | ||||
−0.262391 | + | 0.964962i | \(0.584511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.02246e137 | 0.222718 | ||||||||
\(914\) | 7.90224e137 | 1.63588 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.06538e138 | 1.99235 | ||||||||
\(917\) | 2.21043e136 | 0.0392918 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.13720e137 | −0.343301 | −0.171650 | − | 0.985158i | \(-0.554910\pi\) | ||||
−0.171650 | + | 0.985158i | \(0.554910\pi\) | |||||||
\(920\) | −8.99153e137 | −1.37309 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.06821e138 | −2.85500 | ||||||||
\(923\) | −8.10468e135 | −0.0106379 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.32188e138 | 1.56893 | ||||||||
\(926\) | 1.28751e138 | 1.45325 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.47675e137 | 0.559168 | ||||||||
\(929\) | −1.80381e138 | −1.75171 | −0.875853 | − | 0.482578i | \(-0.839700\pi\) | ||||
−0.875853 | + | 0.482578i | \(0.839700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.04546e137 | −0.355474 | ||||||||
\(932\) | −3.84861e138 | −3.21710 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.75048e138 | 2.08104 | ||||||||
\(935\) | 1.86486e137 | 0.134247 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.75823e138 | −1.14600 | −0.573001 | − | 0.819555i | \(-0.694221\pi\) | ||||
−0.573001 | + | 0.819555i | \(0.694221\pi\) | |||||||
\(938\) | 8.16386e137 | 0.506365 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.74751e138 | −3.22875 | ||||||||
\(941\) | 2.47445e138 | 1.32301 | 0.661503 | − | 0.749943i | \(-0.269919\pi\) | ||||
0.661503 | + | 0.749943i | \(0.269919\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.75988e137 | 0.133689 | ||||||||
\(944\) | 1.13690e138 | 0.524233 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.40769e137 | −0.0588262 | ||||||||
\(947\) | −5.09791e137 | −0.202823 | −0.101412 | − | 0.994845i | \(-0.532336\pi\) | ||||
−0.101412 | + | 0.994845i | \(0.532336\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.16497e136 | 0.00780861 | ||||||||
\(950\) | −1.84274e138 | −0.632874 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.40398e138 | 1.06015 | ||||||||
\(953\) | −4.08950e138 | −1.21297 | −0.606485 | − | 0.795095i | \(-0.707421\pi\) | ||||
−0.606485 | + | 0.795095i | \(0.707421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.16351e138 | −2.46550 | ||||||||
\(956\) | 1.48190e138 | 0.379775 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.67736e138 | 1.08769 | ||||||||
\(959\) | 6.77196e138 | 1.50020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.96524e138 | −0.998395 | ||||||||
\(962\) | −4.60281e136 | −0.00881825 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.04930e138 | 1.22621 | ||||||||
\(965\) | −9.72403e138 | −1.61186 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.90772e138 | −1.34102 | −0.670511 | − | 0.741900i | \(-0.733925\pi\) | ||||
−0.670511 | + | 0.741900i | \(0.733925\pi\) | |||||||
\(968\) | −9.36174e138 | −1.34324 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.04862e138 | −1.04915 | ||||||||
\(971\) | 9.30395e138 | 1.15604 | 0.578021 | − | 0.816022i | \(-0.303825\pi\) | ||||
0.578021 | + | 0.816022i | \(0.303825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.95939e139 | 3.34161 | ||||||||
\(974\) | 3.59563e138 | 0.387065 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.21076e138 | 0.705610 | ||||||||
\(977\) | −1.24550e139 | −1.16210 | −0.581052 | − | 0.813867i | \(-0.697359\pi\) | ||||
−0.581052 | + | 0.813867i | \(0.697359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.58426e137 | 0.0558614 | ||||||||
\(980\) | 8.44603e139 | 6.83345 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.31750e137 | 0.0317723 | ||||||||
\(983\) | 4.90628e138 | 0.344361 | 0.172181 | − | 0.985065i | \(-0.444919\pi\) | ||||
0.172181 | + | 0.985065i | \(0.444919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.76944e139 | −1.12993 | ||||||||
\(986\) | −1.24396e139 | −0.757755 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.14409e136 | 0.00229737 | ||||||||
\(989\) | 2.13124e138 | 0.112721 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.86403e138 | −0.234192 | −0.117096 | − | 0.993121i | \(-0.537358\pi\) | ||||
−0.117096 | + | 0.993121i | \(0.537358\pi\) | |||||||
\(992\) | 4.71133e137 | 0.0216447 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.01413e140 | 4.24255 | ||||||||
\(995\) | −3.51852e139 | −1.40471 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15939e139 | 0.421602 | 0.210801 | − | 0.977529i | \(-0.432393\pi\) | ||||
0.210801 | + | 0.977529i | \(0.432393\pi\) | |||||||
\(998\) | 7.09332e139 | 2.46195 | ||||||||
\(999\) | 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 | 9.94.a.b.1.7 | 7 | ||
3.2 | odd | 2 | 1.94.a.a.1.1 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.94.a.a.1.1 | ✓ | 7 | 3.2 | odd | 2 | ||
9.94.a.b.1.7 | 7 | 1.1 | even | 1 | trivial |