Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,32,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 32, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 32);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 32 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(152.192832048\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} - 15839611600 x^{8} - 45590087880320 x^{7} + \cdots - 25\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{39}\cdot 3^{11}\cdot 5^{24} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(53026.3\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 50468.3 | 1.08907 | 0.544533 | − | 0.838740i | \(-0.316707\pi\) | ||||
0.544533 | + | 0.838740i | \(0.316707\pi\) | |||||||
\(3\) | 3.54185e7 | 1.42512 | 0.712558 | − | 0.701613i | \(-0.247536\pi\) | ||||
0.712558 | + | 0.701613i | \(0.247536\pi\) | |||||||
\(4\) | 3.99569e8 | 0.186064 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.78751e12 | 1.55205 | ||||||||
\(7\) | 7.37897e12 | 0.587457 | 0.293729 | − | 0.955889i | \(-0.405104\pi\) | ||||
0.293729 | + | 0.955889i | \(0.405104\pi\) | |||||||
\(8\) | −8.82143e13 | −0.886430 | ||||||||
\(9\) | 6.36795e14 | 1.03096 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56911e16 | −1.85437 | −0.927183 | − | 0.374609i | \(-0.877777\pi\) | ||||
−0.927183 | + | 0.374609i | \(0.877777\pi\) | |||||||
\(12\) | 1.41521e16 | 0.265163 | ||||||||
\(13\) | 1.59954e17 | 0.866708 | 0.433354 | − | 0.901224i | \(-0.357330\pi\) | ||||
0.433354 | + | 0.901224i | \(0.357330\pi\) | |||||||
\(14\) | 3.72404e17 | 0.639780 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.31010e18 | −1.15144 | ||||||||
\(17\) | −5.12967e18 | −0.434642 | −0.217321 | − | 0.976100i | \(-0.569732\pi\) | ||||
−0.217321 | + | 0.976100i | \(0.569732\pi\) | |||||||
\(18\) | 3.21380e19 | 1.12278 | ||||||||
\(19\) | 6.46616e19 | 0.977160 | 0.488580 | − | 0.872519i | \(-0.337515\pi\) | ||||
0.488580 | + | 0.872519i | \(0.337515\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.61352e20 | 0.837195 | ||||||||
\(22\) | −1.29658e21 | −2.01953 | ||||||||
\(23\) | −1.49288e21 | −1.16747 | −0.583734 | − | 0.811945i | \(-0.698409\pi\) | ||||
−0.583734 | + | 0.811945i | \(0.698409\pi\) | |||||||
\(24\) | −3.12442e21 | −1.26327 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.07260e21 | 0.943901 | ||||||||
\(27\) | 6.77267e20 | 0.0441186 | ||||||||
\(28\) | 2.94841e21 | 0.109304 | ||||||||
\(29\) | −5.23737e22 | −1.12705 | −0.563527 | − | 0.826098i | \(-0.690556\pi\) | ||||
−0.563527 | + | 0.826098i | \(0.690556\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.77195e22 | 0.212168 | 0.106084 | − | 0.994357i | \(-0.466169\pi\) | ||||
0.106084 | + | 0.994357i | \(0.466169\pi\) | |||||||
\(32\) | −7.85529e22 | −0.367568 | ||||||||
\(33\) | −9.09938e23 | −2.64269 | ||||||||
\(34\) | −2.58886e23 | −0.473353 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.54443e23 | 0.191824 | ||||||||
\(37\) | −6.74592e23 | −0.332594 | −0.166297 | − | 0.986076i | \(-0.553181\pi\) | ||||
−0.166297 | + | 0.986076i | \(0.553181\pi\) | |||||||
\(38\) | 3.26336e24 | 1.06419 | ||||||||
\(39\) | 5.66532e24 | 1.23516 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.66926e24 | −0.669773 | −0.334887 | − | 0.942258i | \(-0.608698\pi\) | ||||
−0.334887 | + | 0.942258i | \(0.608698\pi\) | |||||||
\(42\) | 1.31900e25 | 0.911761 | ||||||||
\(43\) | 2.14950e25 | 1.03175 | 0.515876 | − | 0.856663i | \(-0.327466\pi\) | ||||
0.515876 | + | 0.856663i | \(0.327466\pi\) | |||||||
\(44\) | −1.02653e25 | −0.345030 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.53434e25 | −1.27145 | ||||||||
\(47\) | −1.75727e25 | −0.212482 | −0.106241 | − | 0.994340i | \(-0.533882\pi\) | ||||
−0.106241 | + | 0.994340i | \(0.533882\pi\) | |||||||
\(48\) | −1.88076e26 | −1.64094 | ||||||||
\(49\) | −1.03326e26 | −0.654894 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.81685e26 | −0.619415 | ||||||||
\(52\) | 6.39125e25 | 0.161263 | ||||||||
\(53\) | −3.62828e26 | −0.681436 | −0.340718 | − | 0.940166i | \(-0.610670\pi\) | ||||
−0.340718 | + | 0.940166i | \(0.610670\pi\) | |||||||
\(54\) | 3.41806e25 | 0.0480481 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.50931e26 | −0.520740 | ||||||||
\(57\) | 2.29022e27 | 1.39257 | ||||||||
\(58\) | −2.64322e27 | −1.22744 | ||||||||
\(59\) | −4.99188e27 | −1.77852 | −0.889258 | − | 0.457407i | \(-0.848778\pi\) | ||||
−0.889258 | + | 0.457407i | \(0.848778\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.77843e27 | −1.65302 | −0.826512 | − | 0.562918i | \(-0.809679\pi\) | ||||
−0.826512 | + | 0.562918i | \(0.809679\pi\) | |||||||
\(62\) | 1.39896e27 | 0.231064 | ||||||||
\(63\) | 4.69890e27 | 0.605644 | ||||||||
\(64\) | 7.43891e27 | 0.751138 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.59231e28 | −2.87806 | ||||||||
\(67\) | 2.47542e28 | 1.22883 | 0.614413 | − | 0.788985i | \(-0.289393\pi\) | ||||
0.614413 | + | 0.788985i | \(0.289393\pi\) | |||||||
\(68\) | −2.04966e27 | −0.0808710 | ||||||||
\(69\) | −5.28757e28 | −1.66378 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.55888e28 | 1.72947 | 0.864734 | − | 0.502229i | \(-0.167487\pi\) | ||||
0.864734 | + | 0.502229i | \(0.167487\pi\) | |||||||
\(72\) | −5.61745e28 | −0.913872 | ||||||||
\(73\) | −7.99777e28 | −1.05067 | −0.525333 | − | 0.850897i | \(-0.676059\pi\) | ||||
−0.525333 | + | 0.850897i | \(0.676059\pi\) | |||||||
\(74\) | −3.40455e28 | −0.362217 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.58368e28 | 0.181814 | ||||||||
\(77\) | −1.89574e29 | −1.08936 | ||||||||
\(78\) | 2.85919e29 | 1.34517 | ||||||||
\(79\) | −1.78848e29 | −0.690661 | −0.345330 | − | 0.938481i | \(-0.612233\pi\) | ||||
−0.345330 | + | 0.938481i | \(0.612233\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.69344e29 | −0.968084 | ||||||||
\(82\) | −3.36586e29 | −0.729427 | ||||||||
\(83\) | 8.73583e29 | 1.56889 | 0.784447 | − | 0.620196i | \(-0.212947\pi\) | ||||
0.784447 | + | 0.620196i | \(0.212947\pi\) | |||||||
\(84\) | 1.04428e29 | 0.155772 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.08481e30 | 1.12365 | ||||||||
\(87\) | −1.85500e30 | −1.60618 | ||||||||
\(88\) | 2.26632e30 | 1.64377 | ||||||||
\(89\) | −2.53778e30 | −1.54493 | −0.772464 | − | 0.635058i | \(-0.780976\pi\) | ||||
−0.772464 | + | 0.635058i | \(0.780976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18029e30 | 0.509154 | ||||||||
\(92\) | −5.96510e29 | −0.217223 | ||||||||
\(93\) | 9.81782e29 | 0.302364 | ||||||||
\(94\) | −8.86867e29 | −0.231407 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.78223e30 | −0.523827 | ||||||||
\(97\) | −2.82605e30 | −0.453125 | −0.226563 | − | 0.973997i | \(-0.572749\pi\) | ||||
−0.226563 | + | 0.973997i | \(0.572749\pi\) | |||||||
\(98\) | −5.21470e30 | −0.713222 | ||||||||
\(99\) | −1.63599e31 | −1.91177 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.71242e31 | −1.46767 | −0.733834 | − | 0.679328i | \(-0.762271\pi\) | ||||
−0.733834 | + | 0.679328i | \(0.762271\pi\) | |||||||
\(102\) | −9.16935e30 | −0.674583 | ||||||||
\(103\) | 1.58163e30 | 0.100029 | 0.0500146 | − | 0.998748i | \(-0.484073\pi\) | ||||
0.0500146 | + | 0.998748i | \(0.484073\pi\) | |||||||
\(104\) | −1.41102e31 | −0.768276 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.83113e31 | −0.742128 | ||||||||
\(107\) | 5.00191e31 | 1.75262 | 0.876310 | − | 0.481748i | \(-0.159998\pi\) | ||||
0.876310 | + | 0.481748i | \(0.159998\pi\) | |||||||
\(108\) | 2.70615e29 | 0.00820887 | ||||||||
\(109\) | −5.02620e30 | −0.132169 | −0.0660844 | − | 0.997814i | \(-0.521051\pi\) | ||||
−0.0660844 | + | 0.997814i | \(0.521051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.38930e31 | −0.473986 | ||||||||
\(112\) | −3.91831e31 | −0.676424 | ||||||||
\(113\) | 4.36896e31 | 0.657146 | 0.328573 | − | 0.944479i | \(-0.393432\pi\) | ||||
0.328573 | + | 0.944479i | \(0.393432\pi\) | |||||||
\(114\) | 1.15583e32 | 1.51660 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.09269e31 | −0.209704 | ||||||||
\(117\) | 1.01858e32 | 0.893539 | ||||||||
\(118\) | −2.51932e32 | −1.93692 | ||||||||
\(119\) | −3.78517e31 | −0.255333 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.68087e32 | 2.43867 | ||||||||
\(122\) | −3.92564e32 | −1.80025 | ||||||||
\(123\) | −2.36215e32 | −0.954505 | ||||||||
\(124\) | 1.10758e31 | 0.0394767 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.37145e32 | 0.659586 | ||||||||
\(127\) | 7.87167e32 | 1.93691 | 0.968454 | − | 0.249191i | \(-0.0801646\pi\) | ||||
0.968454 | + | 0.249191i | \(0.0801646\pi\) | |||||||
\(128\) | 5.44121e32 | 1.18561 | ||||||||
\(129\) | 7.61319e32 | 1.47037 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.96406e32 | 0.755322 | 0.377661 | − | 0.925944i | \(-0.376728\pi\) | ||||
0.377661 | + | 0.925944i | \(0.376728\pi\) | |||||||
\(132\) | −3.63583e32 | −0.491708 | ||||||||
\(133\) | 4.77136e32 | 0.574040 | ||||||||
\(134\) | 1.24931e33 | 1.33827 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.52511e32 | 0.385279 | ||||||||
\(137\) | −1.28980e33 | −0.980291 | −0.490146 | − | 0.871640i | \(-0.663056\pi\) | ||||
−0.490146 | + | 0.871640i | \(0.663056\pi\) | |||||||
\(138\) | −2.66855e33 | −1.81196 | ||||||||
\(139\) | −1.17433e33 | −0.712952 | −0.356476 | − | 0.934304i | \(-0.616022\pi\) | ||||
−0.356476 | + | 0.934304i | \(0.616022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.22400e32 | −0.302812 | ||||||||
\(142\) | 4.31953e33 | 1.88350 | ||||||||
\(143\) | −4.10938e33 | −1.60719 | ||||||||
\(144\) | −3.38145e33 | −1.18709 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.03634e33 | −1.14424 | ||||||||
\(147\) | −3.65965e33 | −0.933300 | ||||||||
\(148\) | −2.69546e32 | −0.0618837 | ||||||||
\(149\) | −6.31685e33 | −1.30651 | −0.653256 | − | 0.757137i | \(-0.726597\pi\) | ||||
−0.653256 | + | 0.757137i | \(0.726597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.39621e33 | 0.571283 | 0.285642 | − | 0.958336i | \(-0.407793\pi\) | ||||
0.285642 | + | 0.958336i | \(0.407793\pi\) | |||||||
\(152\) | −5.70408e33 | −0.866184 | ||||||||
\(153\) | −3.26655e33 | −0.448097 | ||||||||
\(154\) | −9.56746e33 | −1.18639 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.26368e33 | 0.229818 | ||||||||
\(157\) | −1.12435e33 | −0.103385 | −0.0516925 | − | 0.998663i | \(-0.516462\pi\) | ||||
−0.0516925 | + | 0.998663i | \(0.516462\pi\) | |||||||
\(158\) | −9.02617e33 | −0.752175 | ||||||||
\(159\) | −1.28508e34 | −0.971126 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.10160e34 | −0.685837 | ||||||||
\(162\) | −1.86402e34 | −1.05431 | ||||||||
\(163\) | 1.80084e34 | 0.925907 | 0.462954 | − | 0.886383i | \(-0.346790\pi\) | ||||
0.462954 | + | 0.886383i | \(0.346790\pi\) | |||||||
\(164\) | −2.66483e33 | −0.124620 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.40883e34 | 1.70863 | ||||||||
\(167\) | −1.75097e34 | −0.618262 | −0.309131 | − | 0.951019i | \(-0.600038\pi\) | ||||
−0.309131 | + | 0.951019i | \(0.600038\pi\) | |||||||
\(168\) | −2.30550e34 | −0.742115 | ||||||||
\(169\) | −8.47473e33 | −0.248818 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.11762e34 | 1.00741 | ||||||||
\(172\) | 8.58871e33 | 0.191972 | ||||||||
\(173\) | −2.82466e34 | −0.577101 | −0.288550 | − | 0.957465i | \(-0.593173\pi\) | ||||
−0.288550 | + | 0.957465i | \(0.593173\pi\) | |||||||
\(174\) | −9.36187e34 | −1.74924 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.36422e35 | 2.13520 | ||||||||
\(177\) | −1.76805e35 | −2.53459 | ||||||||
\(178\) | −1.28077e35 | −1.68253 | ||||||||
\(179\) | −1.63675e34 | −0.197134 | −0.0985668 | − | 0.995130i | \(-0.531426\pi\) | ||||
−0.0985668 | + | 0.995130i | \(0.531426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.55817e33 | 0.0462139 | 0.0231069 | − | 0.999733i | \(-0.492644\pi\) | ||||
0.0231069 | + | 0.999733i | \(0.492644\pi\) | |||||||
\(182\) | 5.95675e34 | 0.554502 | ||||||||
\(183\) | −2.75500e35 | −2.35575 | ||||||||
\(184\) | 1.31694e35 | 1.03488 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.95489e34 | 0.329294 | ||||||||
\(187\) | 1.31787e35 | 0.805984 | ||||||||
\(188\) | −7.02152e33 | −0.0395352 | ||||||||
\(189\) | 4.99754e33 | 0.0259178 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.84946e35 | −0.814755 | −0.407377 | − | 0.913260i | \(-0.633557\pi\) | ||||
−0.407377 | + | 0.913260i | \(0.633557\pi\) | |||||||
\(192\) | 2.63475e35 | 1.07046 | ||||||||
\(193\) | −3.01732e35 | −1.13105 | −0.565527 | − | 0.824730i | \(-0.691327\pi\) | ||||
−0.565527 | + | 0.824730i | \(0.691327\pi\) | |||||||
\(194\) | −1.42626e35 | −0.493483 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.12859e34 | −0.121852 | ||||||||
\(197\) | 3.75808e35 | 1.02504 | 0.512519 | − | 0.858676i | \(-0.328712\pi\) | ||||
0.512519 | + | 0.858676i | \(0.328712\pi\) | |||||||
\(198\) | −8.25659e35 | −2.08205 | ||||||||
\(199\) | −2.95593e35 | −0.689401 | −0.344700 | − | 0.938713i | \(-0.612020\pi\) | ||||
−0.344700 | + | 0.938713i | \(0.612020\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.76758e35 | 1.75122 | ||||||||
\(202\) | −8.64228e35 | −1.59839 | ||||||||
\(203\) | −3.86464e35 | −0.662096 | ||||||||
\(204\) | −7.25957e34 | −0.115251 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.98220e34 | 0.108938 | ||||||||
\(207\) | −9.50662e35 | −1.20361 | ||||||||
\(208\) | −8.49370e35 | −0.997965 | ||||||||
\(209\) | −1.66123e36 | −1.81201 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.80125e35 | 0.828259 | 0.414129 | − | 0.910218i | \(-0.364086\pi\) | ||||
0.414129 | + | 0.910218i | \(0.364086\pi\) | |||||||
\(212\) | −1.44975e35 | −0.126790 | ||||||||
\(213\) | 3.03143e36 | 2.46470 | ||||||||
\(214\) | 2.52438e36 | 1.90872 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.97447e34 | −0.0391081 | ||||||||
\(217\) | 2.04541e35 | 0.124639 | ||||||||
\(218\) | −2.53664e35 | −0.143940 | ||||||||
\(219\) | −2.83269e36 | −1.49732 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.20510e35 | −0.376707 | ||||||||
\(222\) | −1.20584e36 | −0.516201 | ||||||||
\(223\) | 1.84633e36 | 0.737196 | 0.368598 | − | 0.929589i | \(-0.379838\pi\) | ||||
0.368598 | + | 0.929589i | \(0.379838\pi\) | |||||||
\(224\) | −5.79640e35 | −0.215931 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.20494e36 | 0.715675 | ||||||||
\(227\) | −3.93136e36 | −1.19163 | −0.595816 | − | 0.803121i | \(-0.703171\pi\) | ||||
−0.595816 | + | 0.803121i | \(0.703171\pi\) | |||||||
\(228\) | 9.15099e35 | 0.259106 | ||||||||
\(229\) | 1.69716e35 | 0.0449028 | 0.0224514 | − | 0.999748i | \(-0.492853\pi\) | ||||
0.0224514 | + | 0.999748i | \(0.492853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.71441e36 | −1.55247 | ||||||||
\(232\) | 4.62012e36 | 0.999054 | ||||||||
\(233\) | 7.56158e36 | 1.52966 | 0.764831 | − | 0.644231i | \(-0.222822\pi\) | ||||
0.764831 | + | 0.644231i | \(0.222822\pi\) | |||||||
\(234\) | 5.14059e36 | 0.973122 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.99460e36 | −0.330917 | ||||||||
\(237\) | −6.33453e36 | −0.984272 | ||||||||
\(238\) | −1.91031e36 | −0.278075 | ||||||||
\(239\) | −9.22168e36 | −1.25789 | −0.628945 | − | 0.777450i | \(-0.716513\pi\) | ||||
−0.628945 | + | 0.777450i | \(0.716513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.75610e36 | −0.570147 | −0.285073 | − | 0.958506i | \(-0.592018\pi\) | ||||
−0.285073 | + | 0.958506i | \(0.592018\pi\) | |||||||
\(242\) | 2.36236e37 | 2.65587 | ||||||||
\(243\) | −1.34999e37 | −1.42375 | ||||||||
\(244\) | −3.10802e36 | −0.307568 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.19214e37 | −1.03952 | ||||||||
\(247\) | 1.03429e37 | 0.846912 | ||||||||
\(248\) | −2.44526e36 | −0.188072 | ||||||||
\(249\) | 3.09410e37 | 2.23586 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.37631e36 | −0.407030 | −0.203515 | − | 0.979072i | \(-0.565237\pi\) | ||||
−0.203515 | + | 0.979072i | \(0.565237\pi\) | |||||||
\(252\) | 1.87753e36 | 0.112688 | ||||||||
\(253\) | 3.83538e37 | 2.16491 | ||||||||
\(254\) | 3.97270e37 | 2.10942 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.14859e37 | 0.540065 | ||||||||
\(257\) | 1.08857e37 | 0.481831 | 0.240915 | − | 0.970546i | \(-0.422552\pi\) | ||||
0.240915 | + | 0.970546i | \(0.422552\pi\) | |||||||
\(258\) | 3.84225e37 | 1.60133 | ||||||||
\(259\) | −4.97780e36 | −0.195385 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.33514e37 | −1.16194 | ||||||||
\(262\) | 2.50528e37 | 0.822596 | ||||||||
\(263\) | −6.84363e36 | −0.211823 | −0.105911 | − | 0.994376i | \(-0.533776\pi\) | ||||
−0.105911 | + | 0.994376i | \(0.533776\pi\) | |||||||
\(264\) | 8.02696e37 | 2.34256 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.40803e37 | 0.625167 | ||||||||
\(267\) | −8.98842e37 | −2.20170 | ||||||||
\(268\) | 9.89102e36 | 0.228640 | ||||||||
\(269\) | −3.81449e37 | −0.832293 | −0.416147 | − | 0.909297i | \(-0.636620\pi\) | ||||
−0.416147 | + | 0.909297i | \(0.636620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.16564e37 | 1.78295 | 0.891474 | − | 0.453072i | \(-0.149672\pi\) | ||||
0.891474 | + | 0.453072i | \(0.149672\pi\) | |||||||
\(272\) | 2.72391e37 | 0.500465 | ||||||||
\(273\) | 4.18042e37 | 0.725603 | ||||||||
\(274\) | −6.50943e37 | −1.06760 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.11275e37 | −0.309568 | ||||||||
\(277\) | 5.62673e37 | 0.779507 | 0.389753 | − | 0.920919i | \(-0.372560\pi\) | ||||
0.389753 | + | 0.920919i | \(0.372560\pi\) | |||||||
\(278\) | −5.92664e37 | −0.776451 | ||||||||
\(279\) | 1.76516e37 | 0.218736 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.25587e37 | −0.472107 | −0.236053 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236053 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(282\) | −3.14115e37 | −0.329782 | ||||||||
\(283\) | 1.21210e38 | 1.20461 | 0.602306 | − | 0.798266i | \(-0.294249\pi\) | ||||
0.602306 | + | 0.798266i | \(0.294249\pi\) | |||||||
\(284\) | 3.41986e37 | 0.321791 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.07394e38 | −1.75034 | ||||||||
\(287\) | −4.92123e37 | −0.393463 | ||||||||
\(288\) | −5.00221e37 | −0.378947 | ||||||||
\(289\) | −1.12975e38 | −0.811087 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00094e38 | −0.645756 | ||||||||
\(292\) | −3.19566e37 | −0.195491 | ||||||||
\(293\) | 2.43751e38 | 1.41416 | 0.707080 | − | 0.707134i | \(-0.250012\pi\) | ||||
0.707080 | + | 0.707134i | \(0.250012\pi\) | |||||||
\(294\) | −1.84697e38 | −1.01643 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.95087e37 | 0.294821 | ||||||||
\(297\) | −1.73997e37 | −0.0818120 | ||||||||
\(298\) | −3.18801e38 | −1.42288 | ||||||||
\(299\) | −2.38792e38 | −1.01185 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.58611e38 | 0.606111 | ||||||||
\(302\) | 1.71401e38 | 0.622165 | ||||||||
\(303\) | −6.06512e38 | −2.09160 | ||||||||
\(304\) | −3.43360e38 | −1.12515 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.64857e38 | −0.488007 | ||||||||
\(307\) | −2.30206e38 | −0.647845 | −0.323922 | − | 0.946084i | \(-0.605002\pi\) | ||||
−0.323922 | + | 0.946084i | \(0.605002\pi\) | |||||||
\(308\) | −7.57477e37 | −0.202690 | ||||||||
\(309\) | 5.60188e37 | 0.142553 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.45531e38 | 1.48638 | 0.743192 | − | 0.669078i | \(-0.233311\pi\) | ||||
0.743192 | + | 0.669078i | \(0.233311\pi\) | |||||||
\(312\) | −4.99763e38 | −1.09488 | ||||||||
\(313\) | −2.25998e38 | −0.471159 | −0.235580 | − | 0.971855i | \(-0.575699\pi\) | ||||
−0.235580 | + | 0.971855i | \(0.575699\pi\) | |||||||
\(314\) | −5.67441e37 | −0.112593 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.14622e37 | −0.128507 | ||||||||
\(317\) | 3.33447e38 | 0.570964 | 0.285482 | − | 0.958384i | \(-0.407846\pi\) | ||||
0.285482 | + | 0.958384i | \(0.407846\pi\) | |||||||
\(318\) | −6.48560e38 | −1.05762 | ||||||||
\(319\) | 1.34554e39 | 2.08997 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.77160e39 | 2.49769 | ||||||||
\(322\) | −5.55957e38 | −0.746922 | ||||||||
\(323\) | −3.31693e38 | −0.424714 | ||||||||
\(324\) | −1.47578e38 | −0.180125 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.08854e38 | 1.00837 | ||||||||
\(327\) | −1.78020e38 | −0.188356 | ||||||||
\(328\) | 5.88324e38 | 0.593707 | ||||||||
\(329\) | −1.29669e38 | −0.124824 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.21055e38 | 0.456614 | 0.228307 | − | 0.973589i | \(-0.426681\pi\) | ||||
0.228307 | + | 0.973589i | \(0.426681\pi\) | |||||||
\(332\) | 3.49056e38 | 0.291914 | ||||||||
\(333\) | −4.29577e38 | −0.342891 | ||||||||
\(334\) | −8.83684e38 | −0.673328 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.38780e39 | −0.963984 | ||||||||
\(337\) | 1.07632e39 | 0.713968 | 0.356984 | − | 0.934110i | \(-0.383805\pi\) | ||||
0.356984 | + | 0.934110i | \(0.383805\pi\) | |||||||
\(338\) | −4.27705e38 | −0.270979 | ||||||||
\(339\) | 1.54742e39 | 0.936510 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.12143e38 | −0.393436 | ||||||||
\(342\) | 2.07810e39 | 1.09714 | ||||||||
\(343\) | −1.92666e39 | −0.972180 | ||||||||
\(344\) | −1.89616e39 | −0.914576 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.42556e39 | −0.628500 | ||||||||
\(347\) | −4.50521e39 | −1.89937 | −0.949683 | − | 0.313213i | \(-0.898595\pi\) | ||||
−0.949683 | + | 0.313213i | \(0.898595\pi\) | |||||||
\(348\) | −7.41199e38 | −0.298852 | ||||||||
\(349\) | 1.00452e39 | 0.387405 | 0.193703 | − | 0.981060i | \(-0.437950\pi\) | ||||
0.193703 | + | 0.981060i | \(0.437950\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.08331e38 | 0.0382379 | ||||||||
\(352\) | 2.01811e39 | 0.681605 | ||||||||
\(353\) | −2.32272e39 | −0.750738 | −0.375369 | − | 0.926876i | \(-0.622484\pi\) | ||||
−0.375369 | + | 0.926876i | \(0.622484\pi\) | |||||||
\(354\) | −8.92304e39 | −2.76034 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.01402e39 | −0.287455 | ||||||||
\(357\) | −1.34065e39 | −0.363880 | ||||||||
\(358\) | −8.26041e38 | −0.214691 | ||||||||
\(359\) | 7.12748e39 | 1.77408 | 0.887038 | − | 0.461696i | \(-0.152759\pi\) | ||||
0.887038 | + | 0.461696i | \(0.152759\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.97739e38 | −0.0451576 | ||||||||
\(362\) | 2.30043e38 | 0.0503299 | ||||||||
\(363\) | 1.65789e40 | 3.47539 | ||||||||
\(364\) | 4.71609e38 | 0.0947350 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.39040e40 | −2.56557 | ||||||||
\(367\) | 5.20594e39 | 0.920821 | 0.460411 | − | 0.887706i | \(-0.347702\pi\) | ||||
0.460411 | + | 0.887706i | \(0.347702\pi\) | |||||||
\(368\) | 7.92736e39 | 1.34427 | ||||||||
\(369\) | −4.24695e39 | −0.690508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.67730e39 | −0.400315 | ||||||||
\(372\) | 3.92289e38 | 0.0562589 | ||||||||
\(373\) | 8.13982e39 | 1.11977 | 0.559884 | − | 0.828571i | \(-0.310846\pi\) | ||||
0.559884 | + | 0.828571i | \(0.310846\pi\) | |||||||
\(374\) | 6.65105e39 | 0.877770 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.55017e39 | 0.188351 | ||||||||
\(377\) | −8.37738e39 | −0.976826 | ||||||||
\(378\) | 2.52217e38 | 0.0282262 | ||||||||
\(379\) | −5.97264e38 | −0.0641592 | −0.0320796 | − | 0.999485i | \(-0.510213\pi\) | ||||
−0.0320796 | + | 0.999485i | \(0.510213\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.78803e40 | 2.76032 | ||||||||
\(382\) | −9.33390e39 | −0.887322 | ||||||||
\(383\) | −2.19654e39 | −0.200520 | −0.100260 | − | 0.994961i | \(-0.531968\pi\) | ||||
−0.100260 | + | 0.994961i | \(0.531968\pi\) | |||||||
\(384\) | 1.92719e40 | 1.68963 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.52279e40 | −1.23179 | ||||||||
\(387\) | 1.36879e40 | 1.06369 | ||||||||
\(388\) | −1.12920e39 | −0.0843101 | ||||||||
\(389\) | −7.52607e39 | −0.539945 | −0.269973 | − | 0.962868i | \(-0.587015\pi\) | ||||
−0.269973 | + | 0.962868i | \(0.587015\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.65800e39 | 0.507430 | ||||||||
\(392\) | 9.11485e39 | 0.580518 | ||||||||
\(393\) | 1.75820e40 | 1.07642 | ||||||||
\(394\) | 1.89664e40 | 1.11633 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.53692e39 | −0.355712 | ||||||||
\(397\) | −9.21070e39 | −0.481992 | −0.240996 | − | 0.970526i | \(-0.577474\pi\) | ||||
−0.240996 | + | 0.970526i | \(0.577474\pi\) | |||||||
\(398\) | −1.49181e40 | −0.750803 | ||||||||
\(399\) | 1.68994e40 | 0.818074 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.82642e39 | 0.171417 | 0.0857087 | − | 0.996320i | \(-0.472685\pi\) | ||||
0.0857087 | + | 0.996320i | \(0.472685\pi\) | |||||||
\(402\) | 4.42485e40 | 1.90719 | ||||||||
\(403\) | 4.43384e39 | 0.183887 | ||||||||
\(404\) | −6.84228e39 | −0.273080 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.95042e40 | −0.721066 | ||||||||
\(407\) | 1.73310e40 | 0.616751 | ||||||||
\(408\) | 1.60272e40 | 0.549068 | ||||||||
\(409\) | 3.63528e40 | 1.19902 | 0.599510 | − | 0.800367i | \(-0.295362\pi\) | ||||
0.599510 | + | 0.800367i | \(0.295362\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.56829e40 | −1.39703 | ||||||||
\(412\) | 6.31968e38 | 0.0186118 | ||||||||
\(413\) | −3.68349e40 | −1.04480 | ||||||||
\(414\) | −4.79783e40 | −1.31081 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.25648e40 | −0.318574 | ||||||||
\(417\) | −4.15929e40 | −1.01604 | ||||||||
\(418\) | −8.38393e40 | −1.97340 | ||||||||
\(419\) | 9.79817e38 | 0.0222243 | 0.0111121 | − | 0.999938i | \(-0.496463\pi\) | ||||
0.0111121 | + | 0.999938i | \(0.496463\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.79926e40 | −1.22180 | −0.610900 | − | 0.791708i | \(-0.709192\pi\) | ||||
−0.610900 | + | 0.791708i | \(0.709192\pi\) | |||||||
\(422\) | 4.44184e40 | 0.902028 | ||||||||
\(423\) | −1.11902e40 | −0.219060 | ||||||||
\(424\) | 3.20067e40 | 0.604045 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.52991e41 | 2.68421 | ||||||||
\(427\) | −5.73968e40 | −0.971082 | ||||||||
\(428\) | 1.99861e40 | 0.326099 | ||||||||
\(429\) | −1.45548e41 | −2.29044 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.23157e41 | 1.80327 | 0.901633 | − | 0.432502i | \(-0.142369\pi\) | ||||
0.901633 | + | 0.432502i | \(0.142369\pi\) | |||||||
\(432\) | −3.59636e39 | −0.0508001 | ||||||||
\(433\) | 1.08651e41 | 1.48072 | 0.740360 | − | 0.672211i | \(-0.234655\pi\) | ||||
0.740360 | + | 0.672211i | \(0.234655\pi\) | |||||||
\(434\) | 1.03229e40 | 0.135740 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00831e39 | −0.0245918 | ||||||||
\(437\) | −9.65323e40 | −1.14080 | ||||||||
\(438\) | −1.42961e41 | −1.63068 | ||||||||
\(439\) | −1.31452e41 | −1.44732 | −0.723662 | − | 0.690154i | \(-0.757543\pi\) | ||||
−0.723662 | + | 0.690154i | \(0.757543\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.57976e40 | −0.675168 | ||||||||
\(442\) | −4.14098e40 | −0.410259 | ||||||||
\(443\) | −7.34404e40 | −0.702550 | −0.351275 | − | 0.936272i | \(-0.614252\pi\) | ||||
−0.351275 | + | 0.936272i | \(0.614252\pi\) | |||||||
\(444\) | −9.54691e39 | −0.0881915 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.31810e40 | 0.802855 | ||||||||
\(447\) | −2.23733e41 | −1.86193 | ||||||||
\(448\) | 5.48915e40 | 0.441262 | ||||||||
\(449\) | 8.88276e39 | 0.0689810 | 0.0344905 | − | 0.999405i | \(-0.489019\pi\) | ||||
0.0344905 | + | 0.999405i | \(0.489019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.71340e41 | 1.24200 | ||||||||
\(452\) | 1.74570e40 | 0.122271 | ||||||||
\(453\) | 1.20289e41 | 0.814146 | ||||||||
\(454\) | −1.98409e41 | −1.29776 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.02030e41 | −1.23441 | ||||||||
\(457\) | 1.73624e41 | 1.02544 | 0.512719 | − | 0.858556i | \(-0.328638\pi\) | ||||
0.512719 | + | 0.858556i | \(0.328638\pi\) | |||||||
\(458\) | 8.56530e39 | 0.0489021 | ||||||||
\(459\) | −3.47416e39 | −0.0191758 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.69460e41 | −0.874384 | −0.437192 | − | 0.899368i | \(-0.644027\pi\) | ||||
−0.437192 | + | 0.899368i | \(0.644027\pi\) | |||||||
\(462\) | −3.38865e41 | −1.69074 | ||||||||
\(463\) | −1.59616e41 | −0.770141 | −0.385070 | − | 0.922887i | \(-0.625823\pi\) | ||||
−0.385070 | + | 0.922887i | \(0.625823\pi\) | |||||||
\(464\) | 2.78110e41 | 1.29774 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.81620e41 | 1.66590 | ||||||||
\(467\) | 3.56199e41 | 1.50411 | 0.752057 | − | 0.659098i | \(-0.229062\pi\) | ||||
0.752057 | + | 0.659098i | \(0.229062\pi\) | |||||||
\(468\) | 4.06992e40 | 0.166255 | ||||||||
\(469\) | 1.82661e41 | 0.721883 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.98228e40 | −0.147336 | ||||||||
\(472\) | 4.40355e41 | 1.57653 | ||||||||
\(473\) | −5.52228e41 | −1.91325 | ||||||||
\(474\) | −3.19693e41 | −1.07194 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.51244e40 | −0.0475083 | ||||||||
\(477\) | −2.31047e41 | −0.702532 | ||||||||
\(478\) | −4.65403e41 | −1.36992 | ||||||||
\(479\) | −2.77088e41 | −0.789619 | −0.394809 | − | 0.918763i | \(-0.629189\pi\) | ||||
−0.394809 | + | 0.918763i | \(0.629189\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.07904e41 | −0.288262 | ||||||||
\(482\) | −2.40032e41 | −0.620927 | ||||||||
\(483\) | −3.90168e41 | −0.977398 | ||||||||
\(484\) | 1.87033e41 | 0.453748 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.81319e41 | −1.55056 | ||||||||
\(487\) | 8.87356e41 | 1.95614 | 0.978068 | − | 0.208285i | \(-0.0667882\pi\) | ||||
0.978068 | + | 0.208285i | \(0.0667882\pi\) | |||||||
\(488\) | 6.86169e41 | 1.46529 | ||||||||
\(489\) | 6.37830e41 | 1.31953 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.02124e41 | 0.198319 | 0.0991596 | − | 0.995072i | \(-0.468385\pi\) | ||||
0.0991596 | + | 0.995072i | \(0.468385\pi\) | |||||||
\(492\) | −9.43841e40 | −0.177599 | ||||||||
\(493\) | 2.68660e41 | 0.489864 | ||||||||
\(494\) | 5.21988e41 | 0.922343 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.47193e41 | −0.244299 | ||||||||
\(497\) | 6.31558e41 | 1.01599 | ||||||||
\(498\) | 1.56154e42 | 2.43499 | ||||||||
\(499\) | 1.15532e42 | 1.74640 | 0.873202 | − | 0.487359i | \(-0.162040\pi\) | ||||
0.873202 | + | 0.487359i | \(0.162040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.20166e41 | −0.881096 | ||||||||
\(502\) | −3.21802e41 | −0.443282 | ||||||||
\(503\) | 8.98250e41 | 1.19976 | 0.599878 | − | 0.800091i | \(-0.295216\pi\) | ||||
0.599878 | + | 0.800091i | \(0.295216\pi\) | |||||||
\(504\) | −4.14510e41 | −0.536861 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.93565e42 | 2.35773 | ||||||||
\(507\) | −3.00162e41 | −0.354595 | ||||||||
\(508\) | 3.14527e41 | 0.360388 | ||||||||
\(509\) | −2.04179e41 | −0.226927 | −0.113463 | − | 0.993542i | \(-0.536194\pi\) | ||||
−0.113463 | + | 0.993542i | \(0.536194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.90153e41 | −0.617221 | ||||||||
\(512\) | −5.88815e41 | −0.597440 | ||||||||
\(513\) | 4.37932e40 | 0.0431110 | ||||||||
\(514\) | 5.49385e41 | 0.524745 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.04199e41 | 0.273582 | ||||||||
\(517\) | 4.51462e41 | 0.394020 | ||||||||
\(518\) | −2.51221e41 | −0.212787 | ||||||||
\(519\) | −1.00045e42 | −0.822436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.50719e41 | −0.349077 | −0.174538 | − | 0.984650i | \(-0.555843\pi\) | ||||
−0.174538 | + | 0.984650i | \(0.555843\pi\) | |||||||
\(522\) | −1.68319e42 | −1.26543 | ||||||||
\(523\) | −3.50199e41 | −0.255587 | −0.127794 | − | 0.991801i | \(-0.540790\pi\) | ||||
−0.127794 | + | 0.991801i | \(0.540790\pi\) | |||||||
\(524\) | 1.98349e41 | 0.140538 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.45387e41 | −0.230689 | ||||||||
\(527\) | −1.42192e41 | −0.0922168 | ||||||||
\(528\) | 4.83186e42 | 3.04291 | ||||||||
\(529\) | 5.93533e41 | 0.362979 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.17880e42 | −1.83357 | ||||||||
\(532\) | 1.90649e41 | 0.106808 | ||||||||
\(533\) | −1.06677e42 | −0.580498 | ||||||||
\(534\) | −4.53631e42 | −2.39780 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.18368e42 | −1.08927 | ||||||||
\(537\) | −5.79712e41 | −0.280938 | ||||||||
\(538\) | −1.92511e42 | −0.906422 | ||||||||
\(539\) | 2.65456e42 | 1.21441 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.03013e42 | 0.444974 | 0.222487 | − | 0.974936i | \(-0.428583\pi\) | ||||
0.222487 | + | 0.974936i | \(0.428583\pi\) | |||||||
\(542\) | 4.62574e42 | 1.94175 | ||||||||
\(543\) | 1.61443e41 | 0.0658601 | ||||||||
\(544\) | 4.02951e41 | 0.159760 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.10979e42 | 0.790230 | ||||||||
\(547\) | −2.42722e42 | −0.883701 | −0.441851 | − | 0.897089i | \(-0.645678\pi\) | ||||
−0.441851 | + | 0.897089i | \(0.645678\pi\) | |||||||
\(548\) | −5.15366e41 | −0.182397 | ||||||||
\(549\) | −4.95327e42 | −1.70420 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.38657e42 | −1.10131 | ||||||||
\(552\) | 4.66439e42 | 1.47482 | ||||||||
\(553\) | −1.31972e42 | −0.405734 | ||||||||
\(554\) | 2.83972e42 | 0.848934 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.69225e41 | −0.132654 | ||||||||
\(557\) | −8.00704e41 | −0.220149 | −0.110074 | − | 0.993923i | \(-0.535109\pi\) | ||||
−0.110074 | + | 0.993923i | \(0.535109\pi\) | |||||||
\(558\) | 8.90849e41 | 0.238218 | ||||||||
\(559\) | 3.43820e42 | 0.894228 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.66768e42 | 1.14862 | ||||||||
\(562\) | −2.14787e42 | −0.514155 | ||||||||
\(563\) | −5.81315e42 | −1.35373 | −0.676864 | − | 0.736108i | \(-0.736661\pi\) | ||||
−0.676864 | + | 0.736108i | \(0.736661\pi\) | |||||||
\(564\) | −2.48691e41 | −0.0563423 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.11724e42 | 1.31190 | ||||||||
\(567\) | −2.72538e42 | −0.568708 | ||||||||
\(568\) | −7.55016e42 | −1.53305 | ||||||||
\(569\) | 3.55543e42 | 0.702510 | 0.351255 | − | 0.936280i | \(-0.385755\pi\) | ||||
0.351255 | + | 0.936280i | \(0.385755\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.36185e42 | −0.254840 | −0.127420 | − | 0.991849i | \(-0.540670\pi\) | ||||
−0.127420 | + | 0.991849i | \(0.540670\pi\) | |||||||
\(572\) | −1.64198e42 | −0.299040 | ||||||||
\(573\) | −6.55049e42 | −1.16112 | ||||||||
\(574\) | −2.48366e42 | −0.428507 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.73707e42 | 0.774392 | ||||||||
\(577\) | 3.39833e42 | 0.540805 | 0.270403 | − | 0.962747i | \(-0.412843\pi\) | ||||
0.270403 | + | 0.962747i | \(0.412843\pi\) | |||||||
\(578\) | −5.70168e42 | −0.883327 | ||||||||
\(579\) | −1.06869e43 | −1.61188 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.44614e42 | 0.921658 | ||||||||
\(582\) | −5.05160e42 | −0.703271 | ||||||||
\(583\) | 9.32144e42 | 1.26363 | ||||||||
\(584\) | 7.05518e42 | 0.931342 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.23017e43 | 1.54011 | ||||||||
\(587\) | −6.84778e42 | −0.834948 | −0.417474 | − | 0.908689i | \(-0.637084\pi\) | ||||
−0.417474 | + | 0.908689i | \(0.637084\pi\) | |||||||
\(588\) | −1.46228e42 | −0.173653 | ||||||||
\(589\) | 1.79239e42 | 0.207322 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.33106e43 | 1.46080 | ||||||||
\(592\) | 3.58215e42 | 0.382964 | ||||||||
\(593\) | 5.19197e42 | 0.540735 | 0.270367 | − | 0.962757i | \(-0.412855\pi\) | ||||
0.270367 | + | 0.962757i | \(0.412855\pi\) | |||||||
\(594\) | −8.78135e41 | −0.0890987 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.52402e42 | −0.243094 | ||||||||
\(597\) | −1.04695e43 | −0.982477 | ||||||||
\(598\) | −1.20515e43 | −1.10197 | ||||||||
\(599\) | 3.82744e42 | 0.341030 | 0.170515 | − | 0.985355i | \(-0.445457\pi\) | ||||
0.170515 | + | 0.985355i | \(0.445457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.00425e43 | −1.69589 | −0.847944 | − | 0.530086i | \(-0.822159\pi\) | ||||
−0.847944 | + | 0.530086i | \(0.822159\pi\) | |||||||
\(602\) | 8.00482e42 | 0.660094 | ||||||||
\(603\) | 1.57634e43 | 1.26687 | ||||||||
\(604\) | 1.35702e42 | 0.106295 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.06096e43 | −2.27789 | ||||||||
\(607\) | 5.42746e42 | 0.393706 | 0.196853 | − | 0.980433i | \(-0.436928\pi\) | ||||
0.196853 | + | 0.980433i | \(0.436928\pi\) | |||||||
\(608\) | −5.07936e42 | −0.359173 | ||||||||
\(609\) | −1.36880e43 | −0.943564 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.81083e42 | −0.184160 | ||||||||
\(612\) | −1.30521e42 | −0.0833746 | ||||||||
\(613\) | −9.70689e42 | −0.604565 | −0.302282 | − | 0.953218i | \(-0.597749\pi\) | ||||
−0.302282 | + | 0.953218i | \(0.597749\pi\) | |||||||
\(614\) | −1.16181e43 | −0.705545 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.67231e43 | 0.965642 | ||||||||
\(617\) | −2.73058e42 | −0.153757 | −0.0768786 | − | 0.997040i | \(-0.524495\pi\) | ||||
−0.0768786 | + | 0.997040i | \(0.524495\pi\) | |||||||
\(618\) | 2.82717e42 | 0.155250 | ||||||||
\(619\) | −2.73719e43 | −1.46588 | −0.732942 | − | 0.680291i | \(-0.761853\pi\) | ||||
−0.732942 | + | 0.680291i | \(0.761853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.01108e42 | −0.0515070 | ||||||||
\(622\) | 3.25789e43 | 1.61877 | ||||||||
\(623\) | −1.87262e43 | −0.907580 | ||||||||
\(624\) | −3.00834e43 | −1.42222 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.14058e43 | −0.513123 | ||||||||
\(627\) | −5.88381e43 | −2.58233 | ||||||||
\(628\) | −4.49256e41 | −0.0192362 | ||||||||
\(629\) | 3.46044e42 | 0.144559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.09278e43 | −0.832280 | −0.416140 | − | 0.909301i | \(-0.636617\pi\) | ||||
−0.416140 | + | 0.909301i | \(0.636617\pi\) | |||||||
\(632\) | 1.57770e43 | 0.612222 | ||||||||
\(633\) | 3.11727e43 | 1.18037 | ||||||||
\(634\) | 1.68285e43 | 0.621817 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.13479e42 | −0.180691 | ||||||||
\(637\) | −1.65274e43 | −0.567601 | ||||||||
\(638\) | 6.79070e43 | 2.27611 | ||||||||
\(639\) | 5.45026e43 | 1.78301 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.79186e41 | −0.0274019 | −0.0137010 | − | 0.999906i | \(-0.504361\pi\) | ||||
−0.0137010 | + | 0.999906i | \(0.504361\pi\) | |||||||
\(642\) | 8.94098e43 | 2.72015 | ||||||||
\(643\) | 4.86507e42 | 0.144484 | 0.0722418 | − | 0.997387i | \(-0.476985\pi\) | ||||
0.0722418 | + | 0.997387i | \(0.476985\pi\) | |||||||
\(644\) | −4.40163e42 | −0.127609 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.67400e43 | −0.462542 | ||||||||
\(647\) | −3.20540e43 | −0.864701 | −0.432351 | − | 0.901706i | \(-0.642316\pi\) | ||||
−0.432351 | + | 0.901706i | \(0.642316\pi\) | |||||||
\(648\) | 3.25814e43 | 0.858138 | ||||||||
\(649\) | 1.28247e44 | 3.29802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.24454e42 | 0.177626 | ||||||||
\(652\) | 7.19560e42 | 0.172278 | ||||||||
\(653\) | 2.55276e43 | 0.596838 | 0.298419 | − | 0.954435i | \(-0.403541\pi\) | ||||
0.298419 | + | 0.954435i | \(0.403541\pi\) | |||||||
\(654\) | −8.98439e42 | −0.205132 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.54144e43 | 0.771206 | ||||||||
\(657\) | −5.09294e43 | −1.08319 | ||||||||
\(658\) | −6.54417e42 | −0.135942 | ||||||||
\(659\) | 4.03603e43 | 0.818900 | 0.409450 | − | 0.912333i | \(-0.365721\pi\) | ||||
0.409450 | + | 0.912333i | \(0.365721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.96661e43 | −0.574299 | −0.287149 | − | 0.957886i | \(-0.592708\pi\) | ||||
−0.287149 | + | 0.957886i | \(0.592708\pi\) | |||||||
\(662\) | 2.62968e43 | 0.497283 | ||||||||
\(663\) | −2.90612e43 | −0.536852 | ||||||||
\(664\) | −7.70625e43 | −1.39071 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.16800e43 | −0.373430 | ||||||||
\(667\) | 7.81879e43 | 1.31580 | ||||||||
\(668\) | −6.99632e42 | −0.115036 | ||||||||
\(669\) | 6.53940e43 | 1.05059 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.99836e44 | 3.06531 | ||||||||
\(672\) | −2.05300e43 | −0.307726 | ||||||||
\(673\) | −9.75824e42 | −0.142935 | −0.0714674 | − | 0.997443i | \(-0.522768\pi\) | ||||
−0.0714674 | + | 0.997443i | \(0.522768\pi\) | |||||||
\(674\) | 5.43202e43 | 0.777558 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.38624e42 | −0.0462960 | ||||||||
\(677\) | 5.75918e43 | 0.769549 | 0.384775 | − | 0.923011i | \(-0.374279\pi\) | ||||
0.384775 | + | 0.923011i | \(0.374279\pi\) | |||||||
\(678\) | 7.80956e43 | 1.01992 | ||||||||
\(679\) | −2.08534e43 | −0.266192 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.39243e44 | −1.69821 | ||||||||
\(682\) | −3.59407e43 | −0.428478 | ||||||||
\(683\) | 1.28137e42 | 0.0149332 | 0.00746659 | − | 0.999972i | \(-0.497623\pi\) | ||||
0.00746659 | + | 0.999972i | \(0.497623\pi\) | |||||||
\(684\) | 1.64527e43 | 0.187443 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.72354e43 | −1.05877 | ||||||||
\(687\) | 6.01110e42 | 0.0639918 | ||||||||
\(688\) | −1.14140e44 | −1.18801 | ||||||||
\(689\) | −5.80357e43 | −0.590606 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.04701e44 | −1.01869 | −0.509344 | − | 0.860563i | \(-0.670112\pi\) | ||||
−0.509344 | + | 0.860563i | \(0.670112\pi\) | |||||||
\(692\) | −1.12865e43 | −0.107377 | ||||||||
\(693\) | −1.20720e44 | −1.12308 | ||||||||
\(694\) | −2.27371e44 | −2.06853 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.63637e44 | 1.42377 | ||||||||
\(697\) | 3.42111e43 | 0.291111 | ||||||||
\(698\) | 5.06966e43 | 0.421910 | ||||||||
\(699\) | 2.67820e44 | 2.17995 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.97574e43 | −0.231721 | −0.115861 | − | 0.993265i | \(-0.536963\pi\) | ||||
−0.115861 | + | 0.993265i | \(0.536963\pi\) | |||||||
\(702\) | 5.46731e42 | 0.0416436 | ||||||||
\(703\) | −4.36202e43 | −0.324998 | ||||||||
\(704\) | −1.91114e44 | −1.39289 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.17224e44 | −0.817603 | ||||||||
\(707\) | −1.26359e44 | −0.862193 | ||||||||
\(708\) | −7.06456e43 | −0.471596 | ||||||||
\(709\) | −1.24196e44 | −0.811132 | −0.405566 | − | 0.914066i | \(-0.632926\pi\) | ||||
−0.405566 | + | 0.914066i | \(0.632926\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.13890e44 | −0.712042 | ||||||||
\(712\) | 2.23868e44 | 1.36947 | ||||||||
\(713\) | −4.13820e43 | −0.247699 | ||||||||
\(714\) | −6.76604e43 | −0.396289 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.53994e42 | −0.0366794 | ||||||||
\(717\) | −3.26618e44 | −1.79264 | ||||||||
\(718\) | 3.59712e44 | 1.93209 | ||||||||
\(719\) | −2.70426e44 | −1.42151 | −0.710755 | − | 0.703439i | \(-0.751647\pi\) | ||||
−0.710755 | + | 0.703439i | \(0.751647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.16708e43 | 0.0587629 | ||||||||
\(722\) | −9.97956e42 | −0.0491796 | ||||||||
\(723\) | −1.68454e44 | −0.812526 | ||||||||
\(724\) | 1.82130e42 | 0.00859872 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.36711e44 | 3.78493 | ||||||||
\(727\) | −2.23994e44 | −0.991867 | −0.495934 | − | 0.868360i | \(-0.665174\pi\) | ||||
−0.495934 | + | 0.868360i | \(0.665174\pi\) | |||||||
\(728\) | −1.04119e44 | −0.451329 | ||||||||
\(729\) | −2.50013e44 | −1.06093 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.10262e44 | −0.448443 | ||||||||
\(732\) | −1.10081e44 | −0.438320 | ||||||||
\(733\) | −3.60937e44 | −1.40708 | −0.703541 | − | 0.710655i | \(-0.748399\pi\) | ||||
−0.703541 | + | 0.710655i | \(0.748399\pi\) | |||||||
\(734\) | 2.62735e44 | 1.00283 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.17270e44 | 0.429124 | ||||||||
\(737\) | −6.35963e44 | −2.27869 | ||||||||
\(738\) | −2.14337e44 | −0.752008 | ||||||||
\(739\) | −1.34591e44 | −0.462409 | −0.231205 | − | 0.972905i | \(-0.574267\pi\) | ||||
−0.231205 | + | 0.972905i | \(0.574267\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.66329e44 | 1.20695 | ||||||||
\(742\) | −1.35119e44 | −0.435969 | ||||||||
\(743\) | 2.29970e44 | 0.726682 | 0.363341 | − | 0.931656i | \(-0.381636\pi\) | ||||
0.363341 | + | 0.931656i | \(0.381636\pi\) | |||||||
\(744\) | −8.66073e43 | −0.268024 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.10803e44 | 1.21950 | ||||||||
\(747\) | 5.56293e44 | 1.61746 | ||||||||
\(748\) | 5.26578e43 | 0.149964 | ||||||||
\(749\) | 3.69090e44 | 1.02959 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.82476e44 | −1.82671 | −0.913353 | − | 0.407169i | \(-0.866516\pi\) | ||||
−0.913353 | + | 0.407169i | \(0.866516\pi\) | |||||||
\(752\) | 9.33130e43 | 0.244661 | ||||||||
\(753\) | −2.25839e44 | −0.580065 | ||||||||
\(754\) | −4.22792e44 | −1.06383 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.99686e42 | 0.00482236 | ||||||||
\(757\) | 5.83963e44 | 1.38165 | 0.690827 | − | 0.723020i | \(-0.257247\pi\) | ||||
0.690827 | + | 0.723020i | \(0.257247\pi\) | |||||||
\(758\) | −3.01429e43 | −0.0698736 | ||||||||
\(759\) | 1.35843e45 | 3.08525 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.47927e44 | −0.976664 | −0.488332 | − | 0.872658i | \(-0.662394\pi\) | ||||
−0.488332 | + | 0.872658i | \(0.662394\pi\) | |||||||
\(762\) | 1.40707e45 | 3.00617 | ||||||||
\(763\) | −3.70882e43 | −0.0776435 | ||||||||
\(764\) | −7.38985e43 | −0.151596 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.10856e44 | −0.218380 | ||||||||
\(767\) | −7.98469e44 | −1.54145 | ||||||||
\(768\) | 4.06814e44 | 0.769656 | ||||||||
\(769\) | −5.08233e44 | −0.942334 | −0.471167 | − | 0.882044i | \(-0.656167\pi\) | ||||
−0.471167 | + | 0.882044i | \(0.656167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.85556e44 | 0.686665 | ||||||||
\(772\) | −1.20563e44 | −0.210448 | ||||||||
\(773\) | −2.24846e44 | −0.384682 | −0.192341 | − | 0.981328i | \(-0.561608\pi\) | ||||
−0.192341 | + | 0.981328i | \(0.561608\pi\) | |||||||
\(774\) | 6.90805e44 | 1.15843 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.49298e44 | 0.401664 | ||||||||
\(777\) | −1.76306e44 | −0.278446 | ||||||||
\(778\) | −3.79828e44 | −0.588036 | ||||||||
\(779\) | −4.31245e44 | −0.654476 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.19887e45 | −3.20707 | ||||||||
\(782\) | 3.86487e44 | 0.552624 | ||||||||
\(783\) | −3.54710e43 | −0.0497240 | ||||||||
\(784\) | 5.48672e44 | 0.754074 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.87332e44 | 1.17229 | ||||||||
\(787\) | −1.36341e45 | −1.76612 | −0.883059 | − | 0.469263i | \(-0.844520\pi\) | ||||
−0.883059 | + | 0.469263i | \(0.844520\pi\) | |||||||
\(788\) | 1.50161e44 | 0.190722 | ||||||||
\(789\) | −2.42391e44 | −0.301872 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.22384e44 | 0.386045 | ||||||||
\(792\) | 1.44318e45 | 1.69465 | ||||||||
\(793\) | −1.24419e45 | −1.43269 | ||||||||
\(794\) | −4.64849e44 | −0.524921 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.18110e44 | −0.128272 | ||||||||
\(797\) | 9.47512e44 | 1.00921 | 0.504604 | − | 0.863351i | \(-0.331638\pi\) | ||||
0.504604 | + | 0.863351i | \(0.331638\pi\) | |||||||
\(798\) | 8.52887e44 | 0.890936 | ||||||||
\(799\) | 9.01423e43 | 0.0923536 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.61604e45 | −1.59276 | ||||||||
\(802\) | 1.93113e44 | 0.186685 | ||||||||
\(803\) | 2.05471e45 | 1.94832 | ||||||||
\(804\) | 3.50325e44 | 0.325839 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.23768e44 | 0.200265 | ||||||||
\(807\) | −1.35104e45 | −1.18612 | ||||||||
\(808\) | 1.51060e45 | 1.30099 | ||||||||
\(809\) | 5.00741e44 | 0.423069 | 0.211535 | − | 0.977371i | \(-0.432154\pi\) | ||||
0.211535 | + | 0.977371i | \(0.432154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.64497e44 | −0.377711 | −0.188856 | − | 0.982005i | \(-0.560478\pi\) | ||||
−0.188856 | + | 0.982005i | \(0.560478\pi\) | |||||||
\(812\) | −1.54419e44 | −0.123192 | ||||||||
\(813\) | 3.24633e45 | 2.54091 | ||||||||
\(814\) | 8.74666e44 | 0.671682 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.64766e44 | 0.713222 | ||||||||
\(817\) | 1.38990e45 | 1.00819 | ||||||||
\(818\) | 1.83466e45 | 1.30581 | ||||||||
\(819\) | 7.51606e44 | 0.524916 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.53797e44 | 0.574164 | 0.287082 | − | 0.957906i | \(-0.407315\pi\) | ||||
0.287082 | + | 0.957906i | \(0.407315\pi\) | |||||||
\(822\) | −2.30554e45 | −1.52146 | ||||||||
\(823\) | −1.45427e45 | −0.941779 | −0.470890 | − | 0.882192i | \(-0.656067\pi\) | ||||
−0.470890 | + | 0.882192i | \(0.656067\pi\) | |||||||
\(824\) | −1.39522e44 | −0.0886688 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.85900e45 | −1.13786 | ||||||||
\(827\) | −2.09313e45 | −1.25736 | −0.628681 | − | 0.777663i | \(-0.716405\pi\) | ||||
−0.628681 | + | 0.777663i | \(0.716405\pi\) | |||||||
\(828\) | −3.79855e44 | −0.223948 | ||||||||
\(829\) | −2.58269e45 | −1.49444 | −0.747219 | − | 0.664578i | \(-0.768611\pi\) | ||||
−0.747219 | + | 0.664578i | \(0.768611\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.99290e45 | 1.11089 | ||||||||
\(832\) | 1.18988e45 | 0.651017 | ||||||||
\(833\) | 5.30029e44 | 0.284644 | ||||||||
\(834\) | −2.09913e45 | −1.10653 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.63774e44 | −0.337150 | ||||||||
\(837\) | 1.87735e43 | 0.00936054 | ||||||||
\(838\) | 4.94497e43 | 0.0242037 | ||||||||
\(839\) | 1.29282e45 | 0.621192 | 0.310596 | − | 0.950542i | \(-0.399471\pi\) | ||||
0.310596 | + | 0.950542i | \(0.399471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.83585e44 | 0.270250 | ||||||||
\(842\) | −2.92679e45 | −1.33062 | ||||||||
\(843\) | −1.50736e45 | −0.672807 | ||||||||
\(844\) | 3.51670e44 | 0.154109 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.64752e44 | −0.238571 | ||||||||
\(847\) | 3.45400e45 | 1.43262 | ||||||||
\(848\) | 1.92665e45 | 0.784635 | ||||||||
\(849\) | 4.29306e45 | 1.71671 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.00709e45 | 0.388293 | ||||||||
\(852\) | 1.21126e45 | 0.458590 | ||||||||
\(853\) | −4.80470e45 | −1.78631 | −0.893154 | − | 0.449752i | \(-0.851512\pi\) | ||||
−0.893154 | + | 0.449752i | \(0.851512\pi\) | |||||||
\(854\) | −2.89672e45 | −1.05757 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.41241e45 | −1.55357 | ||||||||
\(857\) | 4.21760e44 | 0.145835 | 0.0729176 | − | 0.997338i | \(-0.476769\pi\) | ||||
0.0729176 | + | 0.997338i | \(0.476769\pi\) | |||||||
\(858\) | −7.34557e45 | −2.49444 | ||||||||
\(859\) | −4.58182e45 | −1.52807 | −0.764037 | − | 0.645172i | \(-0.776786\pi\) | ||||
−0.764037 | + | 0.645172i | \(0.776786\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.74302e45 | −0.560731 | ||||||||
\(862\) | 6.21550e45 | 1.96387 | ||||||||
\(863\) | −1.31315e45 | −0.407518 | −0.203759 | − | 0.979021i | \(-0.565316\pi\) | ||||
−0.203759 | + | 0.979021i | \(0.565316\pi\) | |||||||
\(864\) | −5.32013e43 | −0.0162166 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.48345e45 | 1.61260 | ||||||||
\(867\) | −4.00142e45 | −1.15589 | ||||||||
\(868\) | 8.17283e43 | 0.0231909 | ||||||||
\(869\) | 4.59480e45 | 1.28074 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.95954e45 | 1.06503 | ||||||||
\(872\) | 4.43383e44 | 0.117158 | ||||||||
\(873\) | −1.79962e45 | −0.467153 | ||||||||
\(874\) | −4.87183e45 | −1.24241 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.13185e45 | −0.278597 | ||||||||
\(877\) | 2.11951e45 | 0.512557 | 0.256279 | − | 0.966603i | \(-0.417504\pi\) | ||||
0.256279 | + | 0.966603i | \(0.417504\pi\) | |||||||
\(878\) | −6.63415e45 | −1.57623 | ||||||||
\(879\) | 8.63329e45 | 2.01534 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.35738e45 | −0.531255 | −0.265627 | − | 0.964076i | \(-0.585579\pi\) | ||||
−0.265627 | + | 0.964076i | \(0.585579\pi\) | |||||||
\(882\) | −3.32069e45 | −0.735302 | ||||||||
\(883\) | 3.51964e45 | 0.765786 | 0.382893 | − | 0.923793i | \(-0.374928\pi\) | ||||
0.382893 | + | 0.923793i | \(0.374928\pi\) | |||||||
\(884\) | −3.27850e44 | −0.0700915 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.70641e45 | −0.765123 | ||||||||
\(887\) | −1.81896e45 | −0.368983 | −0.184492 | − | 0.982834i | \(-0.559064\pi\) | ||||
−0.184492 | + | 0.982834i | \(0.559064\pi\) | |||||||
\(888\) | 2.10771e45 | 0.420155 | ||||||||
\(889\) | 5.80848e45 | 1.13785 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.48883e45 | 1.79518 | ||||||||
\(892\) | 7.37734e44 | 0.137165 | ||||||||
\(893\) | −1.13628e45 | −0.207629 | ||||||||
\(894\) | −1.12914e46 | −2.02777 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.01505e45 | 0.696493 | ||||||||
\(897\) | −8.45767e45 | −1.44201 | ||||||||
\(898\) | 4.48298e44 | 0.0751249 | ||||||||
\(899\) | −1.45177e45 | −0.239124 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.86119e45 | 0.296180 | ||||||||
\(902\) | 8.64726e45 | 1.35262 | ||||||||
\(903\) | 5.61775e45 | 0.863778 | ||||||||
\(904\) | −3.85405e45 | −0.582514 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.07076e45 | 0.886658 | ||||||||
\(907\) | −3.55045e45 | −0.509765 | −0.254883 | − | 0.966972i | \(-0.582037\pi\) | ||||
−0.254883 | + | 0.966972i | \(0.582037\pi\) | |||||||
\(908\) | −1.57085e45 | −0.221719 | ||||||||
\(909\) | −1.09046e46 | −1.51310 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.17856e46 | 1.58059 | 0.790293 | − | 0.612729i | \(-0.209928\pi\) | ||||
0.790293 | + | 0.612729i | \(0.209928\pi\) | |||||||
\(912\) | −1.21613e46 | −1.60346 | ||||||||
\(913\) | −2.24433e46 | −2.90930 | ||||||||
\(914\) | 8.76254e45 | 1.11677 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.78134e43 | 0.00835479 | ||||||||
\(917\) | 3.66297e45 | 0.443720 | ||||||||
\(918\) | −1.75335e44 | −0.0208837 | ||||||||
\(919\) | −3.13788e45 | −0.367491 | −0.183745 | − | 0.982974i | \(-0.558822\pi\) | ||||
−0.183745 | + | 0.982974i | \(0.558822\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.15353e45 | −0.923255 | ||||||||
\(922\) | −8.55235e45 | −0.952261 | ||||||||
\(923\) | 1.36903e46 | 1.49894 | ||||||||
\(924\) | −2.68287e45 | −0.288858 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.05554e45 | −0.838734 | ||||||||
\(927\) | 1.00717e45 | 0.103126 | ||||||||
\(928\) | 4.11411e45 | 0.414269 | ||||||||
\(929\) | −1.03965e46 | −1.02954 | −0.514772 | − | 0.857327i | \(-0.672123\pi\) | ||||
−0.514772 | + | 0.857327i | \(0.672123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.68124e45 | −0.639936 | ||||||||
\(932\) | 3.02137e45 | 0.284615 | ||||||||
\(933\) | 2.28637e46 | 2.11827 | ||||||||
\(934\) | 1.79768e46 | 1.63808 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.98532e45 | −0.792060 | ||||||||
\(937\) | 1.31609e45 | 0.114110 | 0.0570550 | − | 0.998371i | \(-0.481829\pi\) | ||||
0.0570550 | + | 0.998371i | \(0.481829\pi\) | |||||||
\(938\) | 9.21859e45 | 0.786178 | ||||||||
\(939\) | −8.00451e45 | −0.671457 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.70374e45 | −0.381772 | −0.190886 | − | 0.981612i | \(-0.561136\pi\) | ||||
−0.190886 | + | 0.981612i | \(0.561136\pi\) | |||||||
\(942\) | −2.00979e45 | −0.160458 | ||||||||
\(943\) | 9.95643e45 | 0.781938 | ||||||||
\(944\) | 2.65074e46 | 2.04786 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.78700e46 | −2.08365 | ||||||||
\(947\) | −7.16058e43 | −0.00526652 | −0.00263326 | − | 0.999997i | \(-0.500838\pi\) | ||||
−0.00263326 | + | 0.999997i | \(0.500838\pi\) | |||||||
\(948\) | −2.53108e45 | −0.183137 | ||||||||
\(949\) | −1.27927e46 | −0.910620 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.18102e46 | 0.813691 | ||||||||
\(952\) | 3.33906e45 | 0.226335 | ||||||||
\(953\) | −1.01545e46 | −0.677202 | −0.338601 | − | 0.940930i | \(-0.609954\pi\) | ||||
−0.338601 | + | 0.940930i | \(0.609954\pi\) | |||||||
\(954\) | −1.16606e46 | −0.765103 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.68470e45 | −0.234048 | ||||||||
\(957\) | 4.76569e46 | 2.97845 | ||||||||
\(958\) | −1.39842e46 | −0.859946 | ||||||||
\(959\) | −9.51744e45 | −0.575879 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.63008e46 | −0.954985 | ||||||||
\(962\) | −5.44571e45 | −0.313936 | ||||||||
\(963\) | 3.18520e46 | 1.80688 | ||||||||
\(964\) | −1.90039e45 | −0.106084 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.96911e46 | −1.06445 | ||||||||
\(967\) | 1.15264e46 | 0.613172 | 0.306586 | − | 0.951843i | \(-0.400813\pi\) | ||||
0.306586 | + | 0.951843i | \(0.400813\pi\) | |||||||
\(968\) | −4.12920e46 | −2.16171 | ||||||||
\(969\) | −1.17481e46 | −0.605268 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.72203e45 | 0.485131 | 0.242565 | − | 0.970135i | \(-0.422011\pi\) | ||||
0.242565 | + | 0.970135i | \(0.422011\pi\) | |||||||
\(972\) | −5.39415e45 | −0.264908 | ||||||||
\(973\) | −8.66534e45 | −0.418829 | ||||||||
\(974\) | 4.47834e46 | 2.13036 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.13042e46 | 1.90337 | ||||||||
\(977\) | −1.50140e46 | −0.680973 | −0.340486 | − | 0.940249i | \(-0.610592\pi\) | ||||
−0.340486 | + | 0.940249i | \(0.610592\pi\) | |||||||
\(978\) | 3.21902e46 | 1.43705 | ||||||||
\(979\) | 6.51982e46 | 2.86486 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.20066e45 | −0.136260 | ||||||||
\(982\) | 5.15403e45 | 0.215983 | ||||||||
\(983\) | −2.48076e45 | −0.102331 | −0.0511653 | − | 0.998690i | \(-0.516294\pi\) | ||||
−0.0511653 | + | 0.998690i | \(0.516294\pi\) | |||||||
\(984\) | 2.08376e46 | 0.846102 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.35588e46 | 0.533494 | ||||||||
\(987\) | −4.59267e45 | −0.177889 | ||||||||
\(988\) | 4.13269e45 | 0.157580 | ||||||||
\(989\) | −3.20895e46 | −1.20454 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.22619e45 | −0.0809879 | −0.0404939 | − | 0.999180i | \(-0.512893\pi\) | ||||
−0.0404939 | + | 0.999180i | \(0.512893\pi\) | |||||||
\(992\) | −2.17745e45 | −0.0779860 | ||||||||
\(993\) | 1.84550e46 | 0.650728 | ||||||||
\(994\) | 3.18737e46 | 1.10648 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.23630e46 | 0.416012 | ||||||||
\(997\) | 4.15949e46 | 1.37805 | 0.689025 | − | 0.724738i | \(-0.258039\pi\) | ||||
0.689025 | + | 0.724738i | \(0.258039\pi\) | |||||||
\(998\) | 5.83072e46 | 1.90195 | ||||||||
\(999\) | −4.56879e44 | −0.0146736 |
(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 | 25.32.a.d.1.8 | ✓ | 10 | |
5.2 | odd | 4 | 25.32.b.d.24.16 | 20 | |||
5.3 | odd | 4 | 25.32.b.d.24.5 | 20 | |||
5.4 | even | 2 | 25.32.a.e.1.3 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.32.a.d.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial | |
25.32.a.e.1.3 | yes | 10 | 5.4 | even | 2 | ||
25.32.b.d.24.5 | 20 | 5.3 | odd | 4 | |||
25.32.b.d.24.16 | 20 | 5.2 | odd | 4 |