Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-14.0604\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −14.0604 | −1.24278 | −0.621388 | − | 0.783503i | \(-0.713431\pi\) | ||||
−0.621388 | + | 0.783503i | \(0.713431\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 69.6949 | 0.544491 | ||||||||
\(5\) | −153.219 | −0.548173 | −0.274087 | − | 0.961705i | \(-0.588375\pi\) | ||||
−0.274087 | + | 0.961705i | \(0.588375\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −215.221 | −0.237160 | −0.118580 | − | 0.992944i | \(-0.537834\pi\) | ||||
−0.118580 | + | 0.992944i | \(0.537834\pi\) | |||||||
\(8\) | 819.793 | 0.566095 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2154.32 | 0.681256 | ||||||||
\(11\) | −7869.22 | −1.78261 | −0.891307 | − | 0.453401i | \(-0.850211\pi\) | ||||
−0.891307 | + | 0.453401i | \(0.850211\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14239.1 | −1.79754 | −0.898772 | − | 0.438416i | \(-0.855540\pi\) | ||||
−0.898772 | + | 0.438416i | \(0.855540\pi\) | |||||||
\(14\) | 3026.10 | 0.294737 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −20447.6 | −1.24802 | ||||||||
\(17\) | 14439.7 | 0.712830 | 0.356415 | − | 0.934328i | \(-0.383999\pi\) | ||||
0.356415 | + | 0.934328i | \(0.383999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 52274.2 | 1.74844 | 0.874218 | − | 0.485533i | \(-0.161375\pi\) | ||||
0.874218 | + | 0.485533i | \(0.161375\pi\) | |||||||
\(20\) | −10678.6 | −0.298475 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 110644. | 2.21539 | ||||||||
\(23\) | 20917.2 | 0.358473 | 0.179237 | − | 0.983806i | \(-0.442637\pi\) | ||||
0.179237 | + | 0.983806i | \(0.442637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −54648.9 | −0.699506 | ||||||||
\(26\) | 200207. | 2.23394 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −14999.8 | −0.129132 | ||||||||
\(29\) | 136874. | 1.04214 | 0.521070 | − | 0.853514i | \(-0.325533\pi\) | ||||
0.521070 | + | 0.853514i | \(0.325533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9325.59 | 0.0562225 | 0.0281113 | − | 0.999605i | \(-0.491051\pi\) | ||||
0.0281113 | + | 0.999605i | \(0.491051\pi\) | |||||||
\(32\) | 182567. | 0.984914 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −203028. | −0.885888 | ||||||||
\(35\) | 32976.0 | 0.130005 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −525467. | −1.70545 | −0.852726 | − | 0.522358i | \(-0.825052\pi\) | ||||
−0.852726 | + | 0.522358i | \(0.825052\pi\) | |||||||
\(38\) | −734996. | −2.17291 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −125608. | −0.310318 | ||||||||
\(41\) | −197767. | −0.448136 | −0.224068 | − | 0.974574i | \(-0.571934\pi\) | ||||
−0.224068 | + | 0.974574i | \(0.571934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 410661. | 0.787669 | 0.393835 | − | 0.919181i | \(-0.371148\pi\) | ||||
0.393835 | + | 0.919181i | \(0.371148\pi\) | |||||||
\(44\) | −548444. | −0.970617 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −294105. | −0.445502 | ||||||||
\(47\) | 946517. | 1.32980 | 0.664899 | − | 0.746933i | \(-0.268475\pi\) | ||||
0.664899 | + | 0.746933i | \(0.268475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −777223. | −0.943755 | ||||||||
\(50\) | 768386. | 0.869329 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −992389. | −0.978747 | ||||||||
\(53\) | 1.55829e6 | 1.43775 | 0.718873 | − | 0.695141i | \(-0.244658\pi\) | ||||
0.718873 | + | 0.695141i | \(0.244658\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.20571e6 | 0.977181 | ||||||||
\(56\) | −176437. | −0.134255 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.92450e6 | −1.29515 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −659307. | −0.371906 | −0.185953 | − | 0.982559i | \(-0.559537\pi\) | ||||
−0.185953 | + | 0.982559i | \(0.559537\pi\) | |||||||
\(62\) | −131121. | −0.0698720 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 50317.0 | 0.0239930 | ||||||||
\(65\) | 2.18169e6 | 0.985365 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.30296e6 | −0.935457 | −0.467729 | − | 0.883872i | \(-0.654928\pi\) | ||||
−0.467729 | + | 0.883872i | \(0.654928\pi\) | |||||||
\(68\) | 1.00637e6 | 0.388130 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −463656. | −0.161567 | ||||||||
\(71\) | 1.68822e6 | 0.559788 | 0.279894 | − | 0.960031i | \(-0.409701\pi\) | ||||
0.279894 | + | 0.960031i | \(0.409701\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.53442e6 | 0.762514 | 0.381257 | − | 0.924469i | \(-0.375491\pi\) | ||||
0.381257 | + | 0.924469i | \(0.375491\pi\) | |||||||
\(74\) | 7.38828e6 | 2.11949 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.64324e6 | 0.952008 | ||||||||
\(77\) | 1.69362e6 | 0.422765 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.26627e6 | −0.288957 | −0.144478 | − | 0.989508i | \(-0.546150\pi\) | ||||
−0.144478 | + | 0.989508i | \(0.546150\pi\) | |||||||
\(80\) | 3.13296e6 | 0.684131 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.78068e6 | 0.556932 | ||||||||
\(83\) | −2.22258e6 | −0.426662 | −0.213331 | − | 0.976980i | \(-0.568431\pi\) | ||||
−0.213331 | + | 0.976980i | \(0.568431\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.21243e6 | −0.390754 | ||||||||
\(86\) | −5.77406e6 | −0.978896 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.45113e6 | −1.00913 | ||||||||
\(89\) | 1.04798e7 | 1.57575 | 0.787876 | − | 0.615834i | \(-0.211181\pi\) | ||||
0.787876 | + | 0.615834i | \(0.211181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.06455e6 | 0.426306 | ||||||||
\(92\) | 1.45782e6 | 0.195186 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.33084e7 | −1.65264 | ||||||||
\(95\) | −8.00940e6 | −0.958446 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.41316e6 | 0.602212 | 0.301106 | − | 0.953591i | \(-0.402644\pi\) | ||||
0.301106 | + | 0.953591i | \(0.402644\pi\) | |||||||
\(98\) | 1.09281e7 | 1.17288 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.80875e6 | −0.380875 | ||||||||
\(101\) | 8.00726e6 | 0.773320 | 0.386660 | − | 0.922222i | \(-0.373629\pi\) | ||||
0.386660 | + | 0.922222i | \(0.373629\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.41569e6 | 0.217826 | 0.108913 | − | 0.994051i | \(-0.465263\pi\) | ||||
0.108913 | + | 0.994051i | \(0.465263\pi\) | |||||||
\(104\) | −1.16731e7 | −1.01758 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.19102e7 | −1.78680 | ||||||||
\(107\) | −1.50841e7 | −1.19035 | −0.595175 | − | 0.803596i | \(-0.702917\pi\) | ||||
−0.595175 | + | 0.803596i | \(0.702917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.30931e7 | 0.968386 | 0.484193 | − | 0.874961i | \(-0.339113\pi\) | ||||
0.484193 | + | 0.874961i | \(0.339113\pi\) | |||||||
\(110\) | −1.69528e7 | −1.21442 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.40075e6 | 0.295981 | ||||||||
\(113\) | 8.64628e6 | 0.563709 | 0.281854 | − | 0.959457i | \(-0.409050\pi\) | ||||
0.281854 | + | 0.959457i | \(0.409050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.20492e6 | −0.196505 | ||||||||
\(116\) | 9.53938e6 | 0.567437 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.88771e6 | 0.161796 | ||||||||
\(119\) | −3.10772e6 | −0.169055 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.24374e7 | 2.17771 | ||||||||
\(122\) | 9.27012e6 | 0.462196 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 649946. | 0.0306127 | ||||||||
\(125\) | 2.03435e7 | 0.931624 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.77631e7 | 1.20269 | 0.601347 | − | 0.798988i | \(-0.294631\pi\) | ||||
0.601347 | + | 0.798988i | \(0.294631\pi\) | |||||||
\(128\) | −2.40761e7 | −1.01473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.06755e7 | −1.22459 | ||||||||
\(131\) | −2.08878e7 | −0.811788 | −0.405894 | − | 0.913920i | \(-0.633040\pi\) | ||||
−0.405894 | + | 0.913920i | \(0.633040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.12505e7 | −0.414660 | ||||||||
\(134\) | 3.23805e7 | 1.16256 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.18375e7 | 0.403530 | ||||||||
\(137\) | 1.47003e7 | 0.488432 | 0.244216 | − | 0.969721i | \(-0.421469\pi\) | ||||
0.244216 | + | 0.969721i | \(0.421469\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.38613e7 | −1.06943 | −0.534715 | − | 0.845033i | \(-0.679581\pi\) | ||||
−0.534715 | + | 0.845033i | \(0.679581\pi\) | |||||||
\(140\) | 2.29826e6 | 0.0707865 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.37370e7 | −0.695691 | ||||||||
\(143\) | 1.12050e8 | 3.20433 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.09716e7 | −0.571274 | ||||||||
\(146\) | −3.56349e7 | −0.947634 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.66224e7 | −0.928604 | ||||||||
\(149\) | 3.52382e7 | 0.872694 | 0.436347 | − | 0.899778i | \(-0.356272\pi\) | ||||
0.436347 | + | 0.899778i | \(0.356272\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.31481e7 | 1.01986 | 0.509932 | − | 0.860215i | \(-0.329671\pi\) | ||||
0.509932 | + | 0.860215i | \(0.329671\pi\) | |||||||
\(152\) | 4.28541e7 | 0.989781 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.38130e7 | −0.525402 | ||||||||
\(155\) | −1.42886e6 | −0.0308197 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00495e6 | 0.144463 | 0.0722314 | − | 0.997388i | \(-0.476988\pi\) | ||||
0.0722314 | + | 0.997388i | \(0.476988\pi\) | |||||||
\(158\) | 1.78043e7 | 0.359108 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.79728e7 | −0.539904 | ||||||||
\(161\) | −4.50183e6 | −0.0850156 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.15447e7 | 0.932240 | 0.466120 | − | 0.884722i | \(-0.345652\pi\) | ||||
0.466120 | + | 0.884722i | \(0.345652\pi\) | |||||||
\(164\) | −1.37833e7 | −0.244006 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.12503e7 | 0.530245 | ||||||||
\(167\) | 8.79382e6 | 0.146107 | 0.0730533 | − | 0.997328i | \(-0.476726\pi\) | ||||
0.0730533 | + | 0.997328i | \(0.476726\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.40002e8 | 2.23116 | ||||||||
\(170\) | 3.11077e7 | 0.485620 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.86210e7 | 0.428879 | ||||||||
\(173\) | −5.52334e7 | −0.811037 | −0.405518 | − | 0.914087i | \(-0.632909\pi\) | ||||
−0.405518 | + | 0.914087i | \(0.632909\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.17616e7 | 0.165895 | ||||||||
\(176\) | 1.60906e8 | 2.22474 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.47350e8 | −1.95831 | ||||||||
\(179\) | −1.14162e8 | −1.48776 | −0.743882 | − | 0.668311i | \(-0.767018\pi\) | ||||
−0.743882 | + | 0.668311i | \(0.767018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.45147e6 | 0.0934044 | 0.0467022 | − | 0.998909i | \(-0.485129\pi\) | ||||
0.0467022 | + | 0.998909i | \(0.485129\pi\) | |||||||
\(182\) | −4.30888e7 | −0.529803 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.71478e7 | 0.202930 | ||||||||
\(185\) | 8.05116e7 | 0.934883 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.13629e8 | −1.27070 | ||||||||
\(188\) | 6.59674e7 | 0.724063 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.12615e8 | 1.19113 | ||||||||
\(191\) | 2.65020e7 | 0.275208 | 0.137604 | − | 0.990487i | \(-0.456060\pi\) | ||||
0.137604 | + | 0.990487i | \(0.456060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.95433e7 | −0.796440 | −0.398220 | − | 0.917290i | \(-0.630372\pi\) | ||||
−0.398220 | + | 0.917290i | \(0.630372\pi\) | |||||||
\(194\) | −7.61112e7 | −0.748415 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.41685e7 | −0.513866 | ||||||||
\(197\) | −6.69673e7 | −0.624067 | −0.312033 | − | 0.950071i | \(-0.601010\pi\) | ||||
−0.312033 | + | 0.950071i | \(0.601010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.47720e7 | −0.492689 | −0.246345 | − | 0.969182i | \(-0.579229\pi\) | ||||
−0.246345 | + | 0.969182i | \(0.579229\pi\) | |||||||
\(200\) | −4.48008e7 | −0.395987 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.12585e8 | −0.961063 | ||||||||
\(203\) | −2.94581e7 | −0.247154 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.03016e7 | 0.245656 | ||||||||
\(206\) | −3.39655e7 | −0.270709 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.91154e8 | 2.24337 | ||||||||
\(209\) | −4.11357e8 | −3.11679 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.45829e7 | −0.473292 | −0.236646 | − | 0.971596i | \(-0.576048\pi\) | ||||
−0.236646 | + | 0.971596i | \(0.576048\pi\) | |||||||
\(212\) | 1.08605e8 | 0.782840 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.12088e8 | 1.47934 | ||||||||
\(215\) | −6.29211e7 | −0.431779 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00706e6 | −0.0133337 | ||||||||
\(218\) | −1.84094e8 | −1.20349 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.40321e7 | 0.532066 | ||||||||
\(221\) | −2.05607e8 | −1.28134 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.02022e8 | −1.21992 | −0.609961 | − | 0.792431i | \(-0.708815\pi\) | ||||
−0.609961 | + | 0.792431i | \(0.708815\pi\) | |||||||
\(224\) | −3.92924e7 | −0.233583 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.21570e8 | −0.700564 | ||||||||
\(227\) | 2.76130e8 | 1.56683 | 0.783416 | − | 0.621497i | \(-0.213475\pi\) | ||||
0.783416 | + | 0.621497i | \(0.213475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.40164e8 | −0.771280 | −0.385640 | − | 0.922649i | \(-0.626019\pi\) | ||||
−0.385640 | + | 0.922649i | \(0.626019\pi\) | |||||||
\(230\) | 4.50624e7 | 0.244212 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.12208e8 | 0.589951 | ||||||||
\(233\) | −8.67302e7 | −0.449185 | −0.224592 | − | 0.974453i | \(-0.572105\pi\) | ||||
−0.224592 | + | 0.974453i | \(0.572105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.45024e8 | −0.728960 | ||||||||
\(236\) | −1.43139e7 | −0.0708867 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.36958e7 | 0.210097 | ||||||||
\(239\) | −2.22648e8 | −1.05494 | −0.527469 | − | 0.849574i | \(-0.676859\pi\) | ||||
−0.527469 | + | 0.849574i | \(0.676859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.27798e8 | 1.96870 | 0.984350 | − | 0.176226i | \(-0.0563888\pi\) | ||||
0.984350 | + | 0.176226i | \(0.0563888\pi\) | |||||||
\(242\) | −5.96687e8 | −2.70641 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.59503e7 | −0.202500 | ||||||||
\(245\) | 1.19085e8 | 0.517341 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.44335e8 | −3.14289 | ||||||||
\(248\) | 7.64505e6 | 0.0318273 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.86038e8 | −1.15780 | ||||||||
\(251\) | −4.79689e7 | −0.191471 | −0.0957353 | − | 0.995407i | \(-0.530520\pi\) | ||||
−0.0957353 | + | 0.995407i | \(0.530520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.64602e8 | −0.639019 | ||||||||
\(254\) | −3.90360e8 | −1.49468 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.32079e8 | 1.23709 | ||||||||
\(257\) | −1.81282e8 | −0.666175 | −0.333087 | − | 0.942896i | \(-0.608090\pi\) | ||||
−0.333087 | + | 0.942896i | \(0.608090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.13092e8 | 0.404466 | ||||||||
\(260\) | 1.52053e8 | 0.536523 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.93691e8 | 1.00887 | ||||||||
\(263\) | 2.00422e8 | 0.679359 | 0.339680 | − | 0.940541i | \(-0.389681\pi\) | ||||
0.339680 | + | 0.940541i | \(0.389681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.38759e8 | −0.788134 | ||||||||
\(266\) | 1.58187e8 | 0.515329 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.60504e8 | −0.509348 | ||||||||
\(269\) | −2.62947e8 | −0.823637 | −0.411819 | − | 0.911266i | \(-0.635106\pi\) | ||||
−0.411819 | + | 0.911266i | \(0.635106\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.69328e8 | 1.12725 | 0.563625 | − | 0.826031i | \(-0.309406\pi\) | ||||
0.563625 | + | 0.826031i | \(0.309406\pi\) | |||||||
\(272\) | −2.95256e8 | −0.889627 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.06692e8 | −0.607011 | ||||||||
\(275\) | 4.30044e8 | 1.24695 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.94313e8 | −0.832014 | −0.416007 | − | 0.909361i | \(-0.636571\pi\) | ||||
−0.416007 | + | 0.909361i | \(0.636571\pi\) | |||||||
\(278\) | 4.76104e8 | 1.32906 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.70335e7 | 0.0735951 | ||||||||
\(281\) | −4.33874e8 | −1.16652 | −0.583258 | − | 0.812287i | \(-0.698223\pi\) | ||||
−0.583258 | + | 0.812287i | \(0.698223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.12492e7 | −0.213092 | −0.106546 | − | 0.994308i | \(-0.533979\pi\) | ||||
−0.106546 | + | 0.994308i | \(0.533979\pi\) | |||||||
\(284\) | 1.17660e8 | 0.304800 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.57547e9 | −3.98226 | ||||||||
\(287\) | 4.25636e7 | 0.106280 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.01835e8 | −0.491873 | ||||||||
\(290\) | 2.94869e8 | 0.709965 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.76636e8 | 0.415182 | ||||||||
\(293\) | 6.42476e8 | 1.49218 | 0.746089 | − | 0.665847i | \(-0.231929\pi\) | ||||
0.746089 | + | 0.665847i | \(0.231929\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.14680e7 | 0.0713661 | ||||||||
\(296\) | −4.30775e8 | −0.965448 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.95463e8 | −1.08456 | ||||||||
\(299\) | −2.97842e8 | −0.644372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.83829e7 | −0.186804 | ||||||||
\(302\) | −6.06679e8 | −1.26746 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.06888e9 | −2.18208 | ||||||||
\(305\) | 1.01018e8 | 0.203869 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.93624e8 | −1.36817 | −0.684084 | − | 0.729403i | \(-0.739798\pi\) | ||||
−0.684084 | + | 0.729403i | \(0.739798\pi\) | |||||||
\(308\) | 1.18037e8 | 0.230192 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.00903e7 | 0.0383019 | ||||||||
\(311\) | 1.86724e8 | 0.351997 | 0.175999 | − | 0.984390i | \(-0.443685\pi\) | ||||
0.175999 | + | 0.984390i | \(0.443685\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50446e8 | 0.830304 | 0.415152 | − | 0.909752i | \(-0.363728\pi\) | ||||
0.415152 | + | 0.909752i | \(0.363728\pi\) | |||||||
\(314\) | −9.84924e7 | −0.179535 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.82527e7 | −0.157334 | ||||||||
\(317\) | 3.97194e8 | 0.700318 | 0.350159 | − | 0.936690i | \(-0.386128\pi\) | ||||
0.350159 | + | 0.936690i | \(0.386128\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.07709e9 | −1.85773 | ||||||||
\(320\) | −7.70953e6 | −0.0131523 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.32976e7 | 0.105655 | ||||||||
\(323\) | 7.54822e8 | 1.24634 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.78149e8 | 1.25739 | ||||||||
\(326\) | −7.24740e8 | −1.15856 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.62128e8 | −0.253687 | ||||||||
\(329\) | −2.03710e8 | −0.315375 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.65695e8 | −1.16053 | −0.580267 | − | 0.814426i | \(-0.697052\pi\) | ||||
−0.580267 | + | 0.814426i | \(0.697052\pi\) | |||||||
\(332\) | −1.54902e8 | −0.232314 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.23645e8 | −0.181578 | ||||||||
\(335\) | 3.52857e8 | 0.512793 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.34277e8 | 0.191116 | 0.0955581 | − | 0.995424i | \(-0.469536\pi\) | ||||
0.0955581 | + | 0.995424i | \(0.469536\pi\) | |||||||
\(338\) | −1.96849e9 | −2.77284 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.54195e8 | −0.212762 | ||||||||
\(341\) | −7.33851e7 | −0.100223 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.44519e8 | 0.460981 | ||||||||
\(344\) | 3.36657e8 | 0.445896 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.76604e8 | 1.00794 | ||||||||
\(347\) | −1.31108e9 | −1.68451 | −0.842257 | − | 0.539076i | \(-0.818773\pi\) | ||||
−0.842257 | + | 0.539076i | \(0.818773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.04850e9 | −1.32032 | −0.660160 | − | 0.751125i | \(-0.729511\pi\) | ||||
−0.660160 | + | 0.751125i | \(0.729511\pi\) | |||||||
\(350\) | −1.65373e8 | −0.206170 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.43666e9 | −1.75572 | ||||||||
\(353\) | 1.06498e9 | 1.28863 | 0.644317 | − | 0.764758i | \(-0.277142\pi\) | ||||
0.644317 | + | 0.764758i | \(0.277142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.58667e8 | −0.306861 | ||||||||
\(356\) | 7.30388e8 | 0.857983 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.60516e9 | 1.84896 | ||||||||
\(359\) | 8.86207e8 | 1.01089 | 0.505446 | − | 0.862858i | \(-0.331328\pi\) | ||||
0.505446 | + | 0.862858i | \(0.331328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.83872e9 | 2.05703 | ||||||||
\(362\) | −1.04771e8 | −0.116081 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.13583e8 | 0.232120 | ||||||||
\(365\) | −3.88321e8 | −0.417990 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.92035e8 | −1.04760 | −0.523801 | − | 0.851841i | \(-0.675486\pi\) | ||||
−0.523801 | + | 0.851841i | \(0.675486\pi\) | |||||||
\(368\) | −4.27707e8 | −0.447382 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.13203e9 | −1.16185 | ||||||||
\(371\) | −3.35377e8 | −0.340976 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.84405e8 | 0.982184 | 0.491092 | − | 0.871108i | \(-0.336598\pi\) | ||||
0.491092 | + | 0.871108i | \(0.336598\pi\) | |||||||
\(374\) | 1.59767e9 | 1.57920 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.75948e8 | 0.752792 | ||||||||
\(377\) | −1.94895e9 | −1.87329 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.03216e9 | −0.973888 | −0.486944 | − | 0.873433i | \(-0.661888\pi\) | ||||
−0.486944 | + | 0.873433i | \(0.661888\pi\) | |||||||
\(380\) | −5.58214e8 | −0.521865 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.72629e8 | −0.342022 | ||||||||
\(383\) | −1.11996e9 | −1.01861 | −0.509303 | − | 0.860587i | \(-0.670097\pi\) | ||||
−0.509303 | + | 0.860587i | \(0.670097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.59495e8 | −0.231748 | ||||||||
\(386\) | 1.11841e9 | 0.989796 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.77269e8 | 0.327899 | ||||||||
\(389\) | 2.19361e9 | 1.88945 | 0.944725 | − | 0.327865i | \(-0.106329\pi\) | ||||
0.944725 | + | 0.327865i | \(0.106329\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.02038e8 | 0.255531 | ||||||||
\(392\) | −6.37162e8 | −0.534255 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.41587e8 | 0.775575 | ||||||||
\(395\) | 1.94017e8 | 0.158398 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.87970e9 | −1.50772 | −0.753862 | − | 0.657033i | \(-0.771811\pi\) | ||||
−0.753862 | + | 0.657033i | \(0.771811\pi\) | |||||||
\(398\) | 7.70117e8 | 0.612302 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.11744e9 | 0.872998 | ||||||||
\(401\) | −1.82808e9 | −1.41576 | −0.707881 | − | 0.706332i | \(-0.750349\pi\) | ||||
−0.707881 | + | 0.706332i | \(0.750349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.32788e8 | −0.101062 | ||||||||
\(404\) | 5.58065e8 | 0.421066 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.14192e8 | 0.307157 | ||||||||
\(407\) | 4.13502e9 | 3.04016 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.05110e9 | −1.48237 | −0.741183 | − | 0.671303i | \(-0.765735\pi\) | ||||
−0.741183 | + | 0.671303i | \(0.765735\pi\) | |||||||
\(410\) | −4.26053e8 | −0.305295 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.68361e8 | 0.118604 | ||||||||
\(413\) | 4.42019e7 | 0.0308756 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.40541e8 | 0.233884 | ||||||||
\(416\) | −2.59959e9 | −1.77043 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.78385e9 | 3.87347 | ||||||||
\(419\) | 1.07209e8 | 0.0712005 | 0.0356002 | − | 0.999366i | \(-0.488666\pi\) | ||||
0.0356002 | + | 0.999366i | \(0.488666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.81280e9 | −1.83718 | −0.918589 | − | 0.395213i | \(-0.870671\pi\) | ||||
−0.918589 | + | 0.395213i | \(0.870671\pi\) | |||||||
\(422\) | 9.08061e8 | 0.588195 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.27747e9 | 0.813901 | ||||||||
\(425\) | −7.89113e8 | −0.498629 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.41897e8 | 0.0882013 | ||||||||
\(428\) | −1.05128e9 | −0.648135 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.84696e8 | 0.536604 | ||||||||
\(431\) | −1.62988e9 | −0.980583 | −0.490292 | − | 0.871558i | \(-0.663110\pi\) | ||||
−0.490292 | + | 0.871558i | \(0.663110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.30649e8 | −0.491711 | −0.245856 | − | 0.969306i | \(-0.579069\pi\) | ||||
−0.245856 | + | 0.969306i | \(0.579069\pi\) | |||||||
\(434\) | 2.82201e7 | 0.0165709 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.12520e8 | 0.527278 | ||||||||
\(437\) | 1.09343e9 | 0.626768 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.22387e9 | 1.25454 | 0.627270 | − | 0.778802i | \(-0.284172\pi\) | ||||
0.627270 | + | 0.778802i | \(0.284172\pi\) | |||||||
\(440\) | 9.88436e8 | 0.553177 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.89092e9 | 1.59242 | ||||||||
\(443\) | −1.30013e9 | −0.710516 | −0.355258 | − | 0.934768i | \(-0.615607\pi\) | ||||
−0.355258 | + | 0.934768i | \(0.615607\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.60570e9 | −0.863785 | ||||||||
\(446\) | 2.84052e9 | 1.51609 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.08293e7 | −0.00569019 | ||||||||
\(449\) | −1.41883e9 | −0.739720 | −0.369860 | − | 0.929088i | \(-0.620594\pi\) | ||||
−0.369860 | + | 0.929088i | \(0.620594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.55627e9 | 0.798852 | ||||||||
\(452\) | 6.02602e8 | 0.306935 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.88249e9 | −1.94722 | ||||||||
\(455\) | −4.69547e8 | −0.233689 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.30832e9 | −1.13133 | −0.565664 | − | 0.824636i | \(-0.691380\pi\) | ||||
−0.565664 | + | 0.824636i | \(0.691380\pi\) | |||||||
\(458\) | 1.97076e9 | 0.958528 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.23366e8 | −0.106995 | ||||||||
\(461\) | 2.65874e8 | 0.126393 | 0.0631965 | − | 0.998001i | \(-0.479871\pi\) | ||||
0.0631965 | + | 0.998001i | \(0.479871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.76799e9 | −0.827840 | −0.413920 | − | 0.910313i | \(-0.635841\pi\) | ||||
−0.413920 | + | 0.910313i | \(0.635841\pi\) | |||||||
\(464\) | −2.79873e9 | −1.30061 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.21946e9 | 0.558236 | ||||||||
\(467\) | −3.74007e9 | −1.69930 | −0.849652 | − | 0.527344i | \(-0.823188\pi\) | ||||
−0.849652 | + | 0.527344i | \(0.823188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.95645e8 | 0.221853 | ||||||||
\(470\) | 2.03910e9 | 0.905933 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.68368e8 | −0.0736993 | ||||||||
\(473\) | −3.23158e9 | −1.40411 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.85673e9 | −1.22304 | ||||||||
\(476\) | −2.16592e8 | −0.0920490 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.13052e9 | 1.31105 | ||||||||
\(479\) | 4.49040e8 | 0.186686 | 0.0933428 | − | 0.995634i | \(-0.470245\pi\) | ||||
0.0933428 | + | 0.995634i | \(0.470245\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.48216e9 | 3.06563 | ||||||||
\(482\) | −6.01502e9 | −2.44665 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.95767e9 | 1.18574 | ||||||||
\(485\) | −8.29399e8 | −0.330117 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.09706e9 | −1.21506 | −0.607531 | − | 0.794296i | \(-0.707840\pi\) | ||||
−0.607531 | + | 0.794296i | \(0.707840\pi\) | |||||||
\(488\) | −5.40495e8 | −0.210534 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.67439e9 | −0.642939 | ||||||||
\(491\) | 2.15480e9 | 0.821527 | 0.410763 | − | 0.911742i | \(-0.365262\pi\) | ||||
0.410763 | + | 0.911742i | \(0.365262\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.97641e9 | 0.742869 | ||||||||
\(494\) | 1.04657e10 | 3.90591 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.90686e8 | −0.0701669 | ||||||||
\(497\) | −3.63340e8 | −0.132759 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.11219e9 | 1.84185 | 0.920926 | − | 0.389738i | \(-0.127434\pi\) | ||||
0.920926 | + | 0.389738i | \(0.127434\pi\) | |||||||
\(500\) | 1.41784e9 | 0.507261 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.74462e8 | 0.237955 | ||||||||
\(503\) | 3.11720e9 | 1.09214 | 0.546069 | − | 0.837740i | \(-0.316124\pi\) | ||||
0.546069 | + | 0.837740i | \(0.316124\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.22687e9 | −0.423913 | ||||||||
\(506\) | 2.31437e9 | 0.794158 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.93495e9 | 0.654856 | ||||||||
\(509\) | 3.33182e9 | 1.11988 | 0.559938 | − | 0.828535i | \(-0.310825\pi\) | ||||
0.559938 | + | 0.828535i | \(0.310825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.45460e8 | −0.180838 | ||||||||
\(512\) | −1.58742e9 | −0.522695 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.54889e9 | 0.827905 | ||||||||
\(515\) | −3.70129e8 | −0.119406 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.44834e9 | −2.37052 | ||||||||
\(518\) | −1.59011e9 | −0.502660 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.78854e9 | 0.557811 | ||||||||
\(521\) | 1.20322e8 | 0.0372745 | 0.0186373 | − | 0.999826i | \(-0.494067\pi\) | ||||
0.0186373 | + | 0.999826i | \(0.494067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.56158e9 | 0.477318 | 0.238659 | − | 0.971103i | \(-0.423292\pi\) | ||||
0.238659 | + | 0.971103i | \(0.423292\pi\) | |||||||
\(524\) | −1.45577e9 | −0.442012 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.81801e9 | −0.844291 | ||||||||
\(527\) | 1.34658e8 | 0.0400771 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.96729e9 | −0.871497 | ||||||||
\(530\) | 3.35705e9 | 0.979473 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.84103e8 | −0.225779 | ||||||||
\(533\) | 2.81601e9 | 0.805543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.31116e9 | 0.652518 | ||||||||
\(536\) | −1.88795e9 | −0.529558 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.69715e9 | 1.02360 | ||||||||
\(539\) | 6.11614e9 | 1.68235 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.94601e9 | 0.799914 | 0.399957 | − | 0.916534i | \(-0.369025\pi\) | ||||
0.399957 | + | 0.916534i | \(0.369025\pi\) | |||||||
\(542\) | −5.19290e9 | −1.40092 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.63621e9 | 0.702077 | ||||||||
\(545\) | −2.00611e9 | −0.530843 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.07000e9 | 1.32450 | 0.662251 | − | 0.749282i | \(-0.269601\pi\) | ||||
0.662251 | + | 0.749282i | \(0.269601\pi\) | |||||||
\(548\) | 1.02453e9 | 0.265947 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.04659e9 | −1.54968 | ||||||||
\(551\) | 7.15495e9 | 1.82212 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.72529e8 | 0.0685290 | ||||||||
\(554\) | 4.13816e9 | 1.03401 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.35996e9 | −0.582295 | ||||||||
\(557\) | −7.03628e9 | −1.72524 | −0.862621 | − | 0.505851i | \(-0.831179\pi\) | ||||
−0.862621 | + | 0.505851i | \(0.831179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.84742e9 | −1.41587 | ||||||||
\(560\) | −6.74279e8 | −0.162249 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.10044e9 | 1.44972 | ||||||||
\(563\) | 4.94078e9 | 1.16685 | 0.583426 | − | 0.812166i | \(-0.301712\pi\) | ||||
0.583426 | + | 0.812166i | \(0.301712\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.32478e9 | −0.309010 | ||||||||
\(566\) | 1.14240e9 | 0.264825 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.38399e9 | 0.316893 | ||||||||
\(569\) | −2.66776e9 | −0.607090 | −0.303545 | − | 0.952817i | \(-0.598170\pi\) | ||||
−0.303545 | + | 0.952817i | \(0.598170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.77696e9 | 1.52338 | 0.761690 | − | 0.647941i | \(-0.224370\pi\) | ||||
0.761690 | + | 0.647941i | \(0.224370\pi\) | |||||||
\(572\) | 7.80933e9 | 1.74473 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.98461e8 | −0.132082 | ||||||||
\(575\) | −1.14310e9 | −0.250754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.53458e9 | −1.19941 | −0.599707 | − | 0.800219i | \(-0.704716\pi\) | ||||
−0.599707 | + | 0.800219i | \(0.704716\pi\) | |||||||
\(578\) | 2.83787e9 | 0.611288 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.46162e9 | −0.311053 | ||||||||
\(581\) | 4.78346e8 | 0.101187 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.22625e10 | −2.56294 | ||||||||
\(584\) | 2.07770e9 | 0.431655 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.03347e9 | −1.85444 | ||||||||
\(587\) | −5.22919e9 | −1.06709 | −0.533545 | − | 0.845771i | \(-0.679141\pi\) | ||||
−0.533545 | + | 0.845771i | \(0.679141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.87488e8 | 0.0983015 | ||||||||
\(590\) | −4.42452e8 | −0.0886920 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.07445e10 | 2.12844 | ||||||||
\(593\) | −8.33930e8 | −0.164224 | −0.0821122 | − | 0.996623i | \(-0.526167\pi\) | ||||
−0.0821122 | + | 0.996623i | \(0.526167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.76162e8 | 0.0926714 | ||||||||
\(596\) | 2.45592e9 | 0.475174 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.18777e9 | 0.800809 | ||||||||
\(599\) | −3.80759e9 | −0.723863 | −0.361931 | − | 0.932205i | \(-0.617883\pi\) | ||||
−0.361931 | + | 0.932205i | \(0.617883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.81584e9 | 1.65654 | 0.828272 | − | 0.560326i | \(-0.189324\pi\) | ||||
0.828272 | + | 0.560326i | \(0.189324\pi\) | |||||||
\(602\) | 1.24270e9 | 0.232155 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.00720e9 | 0.555307 | ||||||||
\(605\) | −6.50222e9 | −1.19376 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.12869e9 | 0.567809 | 0.283904 | − | 0.958853i | \(-0.408370\pi\) | ||||
0.283904 | + | 0.958853i | \(0.408370\pi\) | |||||||
\(608\) | 9.54357e9 | 1.72206 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.42036e9 | −0.253363 | ||||||||
\(611\) | −1.34775e10 | −2.39037 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.07990e9 | 1.06607 | 0.533034 | − | 0.846094i | \(-0.321052\pi\) | ||||
0.533034 | + | 0.846094i | \(0.321052\pi\) | |||||||
\(614\) | 9.75263e9 | 1.70033 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.38842e9 | 0.239325 | ||||||||
\(617\) | 1.45081e9 | 0.248664 | 0.124332 | − | 0.992241i | \(-0.460321\pi\) | ||||
0.124332 | + | 0.992241i | \(0.460321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.93245e9 | −0.666416 | −0.333208 | − | 0.942853i | \(-0.608131\pi\) | ||||
−0.333208 | + | 0.942853i | \(0.608131\pi\) | |||||||
\(620\) | −9.95841e7 | −0.0167810 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.62542e9 | −0.437454 | ||||||||
\(623\) | −2.25547e9 | −0.373706 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.15244e9 | 0.188815 | ||||||||
\(626\) | −6.33345e9 | −1.03188 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.88209e8 | 0.0786588 | ||||||||
\(629\) | −7.58757e9 | −1.21570 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.82173e9 | 1.55627 | 0.778135 | − | 0.628097i | \(-0.216166\pi\) | ||||
0.778135 | + | 0.628097i | \(0.216166\pi\) | |||||||
\(632\) | −1.03808e9 | −0.163577 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.58470e9 | −0.870338 | ||||||||
\(635\) | −4.25383e9 | −0.659284 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.10669e10 | 1.69644 | ||||||||
\(638\) | 1.51443e10 | 2.30875 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.68892e9 | 0.556249 | ||||||||
\(641\) | 7.96630e9 | 1.19469 | 0.597343 | − | 0.801986i | \(-0.296223\pi\) | ||||
0.597343 | + | 0.801986i | \(0.296223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.54836e9 | 1.11973 | 0.559866 | − | 0.828583i | \(-0.310852\pi\) | ||||
0.559866 | + | 0.828583i | \(0.310852\pi\) | |||||||
\(644\) | −3.13755e8 | −0.0462903 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.06131e10 | −1.54892 | ||||||||
\(647\) | −1.12209e10 | −1.62878 | −0.814388 | − | 0.580321i | \(-0.802927\pi\) | ||||
−0.814388 | + | 0.580321i | \(0.802927\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.61617e9 | 0.232076 | ||||||||
\(650\) | −1.09411e10 | −1.56266 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.59240e9 | 0.507596 | ||||||||
\(653\) | 6.06010e9 | 0.851694 | 0.425847 | − | 0.904795i | \(-0.359976\pi\) | ||||
0.425847 | + | 0.904795i | \(0.359976\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.20041e9 | 0.445001 | ||||||||
\(656\) | 4.04385e9 | 0.559282 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.86425e9 | 0.391941 | ||||||||
\(659\) | 1.39437e10 | 1.89792 | 0.948960 | − | 0.315398i | \(-0.102138\pi\) | ||||
0.948960 | + | 0.315398i | \(0.102138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.46218e9 | −1.13966 | −0.569832 | − | 0.821761i | \(-0.692992\pi\) | ||||
−0.569832 | + | 0.821761i | \(0.692992\pi\) | |||||||
\(662\) | 1.07660e10 | 1.44228 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.82205e9 | −0.241531 | ||||||||
\(665\) | 1.72379e9 | 0.227305 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.86302e9 | 0.373580 | ||||||||
\(668\) | 6.12884e8 | 0.0795538 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.96131e9 | −0.637286 | ||||||||
\(671\) | 5.18823e9 | 0.662965 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.59986e9 | 0.328773 | 0.164387 | − | 0.986396i | \(-0.447436\pi\) | ||||
0.164387 | + | 0.986396i | \(0.447436\pi\) | |||||||
\(674\) | −1.88799e9 | −0.237514 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.75744e9 | 1.21485 | ||||||||
\(677\) | −2.24286e8 | −0.0277807 | −0.0138903 | − | 0.999904i | \(-0.504422\pi\) | ||||
−0.0138903 | + | 0.999904i | \(0.504422\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.16503e9 | −0.142821 | ||||||||
\(680\) | −1.81374e9 | −0.221204 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.03182e9 | 0.124555 | ||||||||
\(683\) | 1.29921e9 | 0.156029 | 0.0780146 | − | 0.996952i | \(-0.475142\pi\) | ||||
0.0780146 | + | 0.996952i | \(0.475142\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.25236e9 | −0.267745 | ||||||||
\(686\) | −4.84407e9 | −0.572896 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.39702e9 | −0.983027 | ||||||||
\(689\) | −2.21886e10 | −2.58441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.09890e10 | −1.26703 | −0.633514 | − | 0.773732i | \(-0.718388\pi\) | ||||
−0.633514 | + | 0.773732i | \(0.718388\pi\) | |||||||
\(692\) | −3.84949e9 | −0.441602 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.84342e10 | 2.09347 | ||||||||
\(695\) | 5.18820e9 | 0.586232 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.85568e9 | −0.319445 | ||||||||
\(698\) | 1.47423e10 | 1.64086 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.19724e8 | 0.0903284 | ||||||||
\(701\) | −1.12676e10 | −1.23543 | −0.617715 | − | 0.786402i | \(-0.711941\pi\) | ||||
−0.617715 | + | 0.786402i | \(0.711941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.74684e10 | −2.98188 | ||||||||
\(704\) | −3.95956e8 | −0.0427703 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.49740e10 | −1.60148 | ||||||||
\(707\) | −1.72333e9 | −0.183401 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.10979e9 | −0.854571 | −0.427285 | − | 0.904117i | \(-0.640530\pi\) | ||||
−0.427285 | + | 0.904117i | \(0.640530\pi\) | |||||||
\(710\) | 3.63696e9 | 0.381359 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.59127e9 | 0.892026 | ||||||||
\(713\) | 1.95065e8 | 0.0201543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.71682e10 | −1.75653 | ||||||||
\(716\) | −7.95647e9 | −0.810075 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.24604e10 | −1.25631 | ||||||||
\(719\) | −1.37914e10 | −1.38375 | −0.691873 | − | 0.722019i | \(-0.743214\pi\) | ||||
−0.691873 | + | 0.722019i | \(0.743214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.19907e8 | −0.0516597 | ||||||||
\(722\) | −2.58532e10 | −2.55643 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.19330e8 | 0.0508579 | ||||||||
\(725\) | −7.47999e9 | −0.728984 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.25616e9 | −0.796907 | −0.398454 | − | 0.917189i | \(-0.630453\pi\) | ||||
−0.398454 | + | 0.917189i | \(0.630453\pi\) | |||||||
\(728\) | 2.51230e9 | 0.241330 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.45994e9 | 0.519467 | ||||||||
\(731\) | 5.92981e9 | 0.561474 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.14387e10 | 1.07279 | 0.536395 | − | 0.843967i | \(-0.319786\pi\) | ||||
0.536395 | + | 0.843967i | \(0.319786\pi\) | |||||||
\(734\) | 1.39484e10 | 1.30193 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.81881e9 | 0.353065 | ||||||||
\(737\) | 1.81225e10 | 1.66756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.48024e10 | 1.34920 | 0.674598 | − | 0.738185i | \(-0.264317\pi\) | ||||
0.674598 | + | 0.738185i | \(0.264317\pi\) | |||||||
\(740\) | 5.61125e9 | 0.509036 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.71553e9 | 0.423757 | ||||||||
\(743\) | −1.21140e10 | −1.08349 | −0.541746 | − | 0.840542i | \(-0.682236\pi\) | ||||
−0.541746 | + | 0.840542i | \(0.682236\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.39917e9 | −0.478387 | ||||||||
\(746\) | −1.38411e10 | −1.22063 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.91935e9 | −0.691885 | ||||||||
\(749\) | 3.24641e9 | 0.282304 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.71223e9 | −0.319812 | −0.159906 | − | 0.987132i | \(-0.551119\pi\) | ||||
−0.159906 | + | 0.987132i | \(0.551119\pi\) | |||||||
\(752\) | −1.93540e10 | −1.65962 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.74030e10 | 2.32808 | ||||||||
\(755\) | −6.61111e9 | −0.559062 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.68089e9 | 0.224617 | 0.112309 | − | 0.993673i | \(-0.464175\pi\) | ||||
0.112309 | + | 0.993673i | \(0.464175\pi\) | |||||||
\(758\) | 1.45126e10 | 1.21032 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.56606e9 | −0.542572 | ||||||||
\(761\) | 8.48234e9 | 0.697701 | 0.348850 | − | 0.937178i | \(-0.386572\pi\) | ||||
0.348850 | + | 0.937178i | \(0.386572\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.81791e9 | −0.229663 | ||||||||
\(764\) | 1.84705e9 | 0.149849 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.57471e10 | 1.26590 | ||||||||
\(767\) | 2.92440e9 | 0.234020 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.34767e9 | 0.344758 | 0.172379 | − | 0.985031i | \(-0.444855\pi\) | ||||
0.172379 | + | 0.985031i | \(0.444855\pi\) | |||||||
\(770\) | 3.64861e9 | 0.288011 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.54376e9 | −0.433655 | ||||||||
\(773\) | 1.06536e10 | 0.829601 | 0.414800 | − | 0.909912i | \(-0.363851\pi\) | ||||
0.414800 | + | 0.909912i | \(0.363851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.09633e8 | −0.0393280 | ||||||||
\(776\) | 4.43767e9 | 0.340910 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.08430e10 | −2.34816 | ||||||||
\(779\) | −1.03381e10 | −0.783537 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.32849e10 | −0.997886 | ||||||||
\(782\) | −4.24678e9 | −0.317567 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.58923e10 | 1.17783 | ||||||||
\(785\) | −1.07329e9 | −0.0791907 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.49085e9 | 0.182153 | 0.0910763 | − | 0.995844i | \(-0.470969\pi\) | ||||
0.0910763 | + | 0.995844i | \(0.470969\pi\) | |||||||
\(788\) | −4.66728e9 | −0.339799 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.72796e9 | −0.196853 | ||||||||
\(791\) | −1.86086e9 | −0.133689 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.38791e9 | 0.668517 | ||||||||
\(794\) | 2.64293e10 | 1.87376 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.81733e9 | −0.268265 | ||||||||
\(797\) | −6.71594e9 | −0.469897 | −0.234949 | − | 0.972008i | \(-0.575492\pi\) | ||||
−0.234949 | + | 0.972008i | \(0.575492\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36674e10 | 0.947920 | ||||||||
\(800\) | −9.97712e9 | −0.688954 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.57036e10 | 1.75947 | ||||||||
\(803\) | −1.99439e10 | −1.35927 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.89766e8 | 0.0466033 | ||||||||
\(806\) | 1.86705e9 | 0.125598 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.56430e9 | 0.437773 | ||||||||
\(809\) | 5.26318e9 | 0.349485 | 0.174743 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174743 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.05418e10 | 0.693971 | 0.346985 | − | 0.937870i | \(-0.387205\pi\) | ||||
0.346985 | + | 0.937870i | \(0.387205\pi\) | |||||||
\(812\) | −2.05308e9 | −0.134573 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.81400e10 | −3.77824 | ||||||||
\(815\) | −7.89763e9 | −0.511029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.14670e10 | 1.37719 | ||||||||
\(818\) | 2.88393e10 | 1.84225 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.11187e9 | 0.133757 | ||||||||
\(821\) | −2.59089e10 | −1.63399 | −0.816994 | − | 0.576646i | \(-0.804361\pi\) | ||||
−0.816994 | + | 0.576646i | \(0.804361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.31491e9 | −0.519946 | −0.259973 | − | 0.965616i | \(-0.583714\pi\) | ||||
−0.259973 | + | 0.965616i | \(0.583714\pi\) | |||||||
\(824\) | 1.98036e9 | 0.123310 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.21497e8 | −0.0383715 | ||||||||
\(827\) | 6.36168e9 | 0.391113 | 0.195557 | − | 0.980692i | \(-0.437349\pi\) | ||||
0.195557 | + | 0.980692i | \(0.437349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.31191e10 | −1.40938 | −0.704692 | − | 0.709513i | \(-0.748915\pi\) | ||||
−0.704692 | + | 0.709513i | \(0.748915\pi\) | |||||||
\(830\) | −4.78815e9 | −0.290666 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.16467e8 | −0.0431285 | ||||||||
\(833\) | −1.12228e10 | −0.672737 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.34738e9 | −0.0800918 | ||||||||
\(836\) | −2.86695e10 | −1.69706 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.50740e9 | −0.0884862 | ||||||||
\(839\) | −1.96736e10 | −1.15005 | −0.575026 | − | 0.818135i | \(-0.695008\pi\) | ||||
−0.575026 | + | 0.818135i | \(0.695008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.48448e9 | 0.0860574 | ||||||||
\(842\) | 3.95491e10 | 2.28320 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.50110e9 | −0.257703 | ||||||||
\(845\) | −2.14510e10 | −1.22306 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.13343e9 | −0.516466 | ||||||||
\(848\) | −3.18632e10 | −1.79434 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.10952e10 | 0.619684 | ||||||||
\(851\) | −1.09913e10 | −0.611359 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.05583e10 | −1.13413 | −0.567067 | − | 0.823671i | \(-0.691922\pi\) | ||||
−0.567067 | + | 0.823671i | \(0.691922\pi\) | |||||||
\(854\) | −1.99513e9 | −0.109614 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.23658e10 | −0.673852 | ||||||||
\(857\) | 1.22990e10 | 0.667476 | 0.333738 | − | 0.942666i | \(-0.391690\pi\) | ||||
0.333738 | + | 0.942666i | \(0.391690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.11395e9 | 0.329114 | 0.164557 | − | 0.986368i | \(-0.447381\pi\) | ||||
0.164557 | + | 0.986368i | \(0.447381\pi\) | |||||||
\(860\) | −4.38528e9 | −0.235100 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.29167e10 | 1.21864 | ||||||||
\(863\) | 5.85317e9 | 0.309994 | 0.154997 | − | 0.987915i | \(-0.450463\pi\) | ||||
0.154997 | + | 0.987915i | \(0.450463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.46281e9 | 0.444589 | ||||||||
\(866\) | 1.16793e10 | 0.611087 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.39882e8 | −0.00726011 | ||||||||
\(869\) | 9.96458e9 | 0.515098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.27919e10 | 1.68153 | ||||||||
\(872\) | 1.07336e10 | 0.548199 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.53741e10 | −0.778932 | ||||||||
\(875\) | −4.37835e9 | −0.220944 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.35250e9 | −0.267953 | −0.133976 | − | 0.990985i | \(-0.542775\pi\) | ||||
−0.133976 | + | 0.990985i | \(0.542775\pi\) | |||||||
\(878\) | −3.12686e10 | −1.55911 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.46539e10 | −1.21954 | ||||||||
\(881\) | 9.28115e9 | 0.457284 | 0.228642 | − | 0.973511i | \(-0.426571\pi\) | ||||
0.228642 | + | 0.973511i | \(0.426571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.19702e10 | −0.585114 | −0.292557 | − | 0.956248i | \(-0.594506\pi\) | ||||
−0.292557 | + | 0.956248i | \(0.594506\pi\) | |||||||
\(884\) | −1.43298e10 | −0.697680 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.82804e10 | 0.883012 | ||||||||
\(887\) | −2.48052e10 | −1.19347 | −0.596734 | − | 0.802439i | \(-0.703535\pi\) | ||||
−0.596734 | + | 0.802439i | \(0.703535\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.97521e9 | −0.285231 | ||||||||
\(890\) | 2.25769e10 | 1.07349 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.40799e10 | −0.664237 | ||||||||
\(893\) | 4.94784e10 | 2.32507 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.74917e10 | 0.815552 | ||||||||
\(896\) | 5.18169e9 | 0.240654 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.99493e10 | 0.919306 | ||||||||
\(899\) | 1.27643e9 | 0.0585918 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.25012e10 | 1.02487 | ||||||||
\(902\) | −2.18818e10 | −0.992794 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.08816e9 | 0.319113 | ||||||||
\(905\) | −1.14171e9 | −0.0512018 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.90452e9 | 0.440766 | 0.220383 | − | 0.975413i | \(-0.429269\pi\) | ||||
0.220383 | + | 0.975413i | \(0.429269\pi\) | |||||||
\(908\) | 1.92448e10 | 0.853127 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.60202e9 | 0.290424 | ||||||||
\(911\) | 8.15910e8 | 0.0357543 | 0.0178771 | − | 0.999840i | \(-0.494309\pi\) | ||||
0.0178771 | + | 0.999840i | \(0.494309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.74899e10 | 0.760573 | ||||||||
\(914\) | 3.24559e10 | 1.40599 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.76871e9 | −0.419955 | ||||||||
\(917\) | 4.49549e9 | 0.192524 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.65375e9 | −0.155287 | −0.0776434 | − | 0.996981i | \(-0.524740\pi\) | ||||
−0.0776434 | + | 0.996981i | \(0.524740\pi\) | |||||||
\(920\) | −2.62737e9 | −0.111241 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.73830e9 | −0.157078 | ||||||||
\(923\) | −2.40386e10 | −1.00624 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.87162e10 | 1.19297 | ||||||||
\(926\) | 2.48587e10 | 1.02882 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.49886e10 | 1.02642 | ||||||||
\(929\) | −3.46180e10 | −1.41660 | −0.708299 | − | 0.705913i | \(-0.750537\pi\) | ||||
−0.708299 | + | 0.705913i | \(0.750537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.06287e10 | −1.65010 | ||||||||
\(932\) | −6.04465e9 | −0.244577 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.25869e10 | 2.11185 | ||||||||
\(935\) | 1.74101e10 | 0.696564 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.64978e10 | −0.655143 | −0.327572 | − | 0.944826i | \(-0.606230\pi\) | ||||
−0.327572 | + | 0.944826i | \(0.606230\pi\) | |||||||
\(938\) | −6.96897e9 | −0.275714 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.01075e10 | −0.396912 | ||||||||
\(941\) | 2.07806e10 | 0.813009 | 0.406504 | − | 0.913649i | \(-0.366748\pi\) | ||||
0.406504 | + | 0.913649i | \(0.366748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.13673e9 | −0.160645 | ||||||||
\(944\) | 4.19950e9 | 0.162478 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.54373e10 | 1.74499 | ||||||||
\(947\) | 3.39662e10 | 1.29964 | 0.649818 | − | 0.760090i | \(-0.274845\pi\) | ||||
0.649818 | + | 0.760090i | \(0.274845\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.60877e10 | −1.37065 | ||||||||
\(950\) | 4.01668e10 | 1.51997 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.54769e9 | −0.0957012 | ||||||||
\(953\) | −1.25066e9 | −0.0468074 | −0.0234037 | − | 0.999726i | \(-0.507450\pi\) | ||||
−0.0234037 | + | 0.999726i | \(0.507450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.06061e9 | −0.150862 | ||||||||
\(956\) | −1.55174e10 | −0.574404 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.31369e9 | −0.232008 | ||||||||
\(959\) | −3.16381e9 | −0.115837 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.74256e10 | −0.996839 | ||||||||
\(962\) | −1.05202e11 | −3.80989 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.98154e10 | 1.07194 | ||||||||
\(965\) | 1.21876e10 | 0.436587 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.99659e10 | 0.710063 | 0.355032 | − | 0.934854i | \(-0.384470\pi\) | ||||
0.355032 | + | 0.934854i | \(0.384470\pi\) | |||||||
\(968\) | 3.47899e10 | 1.23279 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.16617e10 | 0.410261 | ||||||||
\(971\) | 5.02413e10 | 1.76114 | 0.880569 | − | 0.473919i | \(-0.157161\pi\) | ||||
0.880569 | + | 0.473919i | \(0.157161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.28767e9 | 0.253626 | ||||||||
\(974\) | 4.35459e10 | 1.51005 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.34812e10 | 0.464146 | ||||||||
\(977\) | 5.76202e10 | 1.97671 | 0.988357 | − | 0.152155i | \(-0.0486213\pi\) | ||||
0.988357 | + | 0.152155i | \(0.0486213\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.24678e10 | −2.80896 | ||||||||
\(980\) | 8.29964e9 | 0.281688 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.02974e10 | −1.02097 | ||||||||
\(983\) | −1.60520e10 | −0.539003 | −0.269502 | − | 0.963000i | \(-0.586859\pi\) | ||||
−0.269502 | + | 0.963000i | \(0.586859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.02607e10 | 0.342096 | ||||||||
\(986\) | −2.77891e10 | −0.923220 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.18764e10 | −1.71128 | ||||||||
\(989\) | 8.58989e9 | 0.282358 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.99460e9 | −0.293578 | −0.146789 | − | 0.989168i | \(-0.546894\pi\) | ||||
−0.146789 | + | 0.989168i | \(0.546894\pi\) | |||||||
\(992\) | 1.70255e9 | 0.0553744 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.10870e9 | 0.164990 | ||||||||
\(995\) | 8.39212e9 | 0.270079 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.62638e9 | 0.0519744 | 0.0259872 | − | 0.999662i | \(-0.491727\pi\) | ||||
0.0259872 | + | 0.999662i | \(0.491727\pi\) | |||||||
\(998\) | −7.18794e10 | −2.28901 | ||||||||
\(999\) | 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 | 531.8.a.b.1.4 | 16 | ||
3.2 | odd | 2 | 177.8.a.a.1.13 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.13 | ✓ | 16 | 3.2 | odd | 2 | ||
531.8.a.b.1.4 | 16 | 1.1 | even | 1 | trivial |