Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,34,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(6.89828288810\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 589050 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(767.996\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −171359. | −1.84890 | −0.924449 | − | 0.381305i | \(-0.875475\pi\) | ||||
−0.924449 | + | 0.381305i | \(0.875475\pi\) | |||||||
\(3\) | 5.34420e7 | 0.716774 | 0.358387 | − | 0.933573i | \(-0.383327\pi\) | ||||
0.358387 | + | 0.933573i | \(0.383327\pi\) | |||||||
\(4\) | 2.07741e10 | 2.41843 | ||||||||
\(5\) | −2.01492e11 | −0.590545 | −0.295273 | − | 0.955413i | \(-0.595411\pi\) | ||||
−0.295273 | + | 0.955413i | \(0.595411\pi\) | |||||||
\(6\) | −9.15779e12 | −1.32524 | ||||||||
\(7\) | 5.50153e13 | 0.625699 | 0.312850 | − | 0.949803i | \(-0.398716\pi\) | ||||
0.312850 | + | 0.949803i | \(0.398716\pi\) | |||||||
\(8\) | −2.08788e15 | −2.62253 | ||||||||
\(9\) | −2.70301e15 | −0.486236 | ||||||||
\(10\) | 3.45276e16 | 1.09186 | ||||||||
\(11\) | −8.18909e16 | −0.537349 | −0.268674 | − | 0.963231i | \(-0.586586\pi\) | ||||
−0.268674 | + | 0.963231i | \(0.586586\pi\) | |||||||
\(12\) | 1.11021e18 | 1.73346 | ||||||||
\(13\) | −1.90399e18 | −0.793597 | −0.396798 | − | 0.917906i | \(-0.629879\pi\) | ||||
−0.396798 | + | 0.917906i | \(0.629879\pi\) | |||||||
\(14\) | −9.42739e18 | −1.15685 | ||||||||
\(15\) | −1.07682e19 | −0.423287 | ||||||||
\(16\) | 1.79329e20 | 2.43036 | ||||||||
\(17\) | −3.33893e20 | −1.66418 | −0.832090 | − | 0.554640i | \(-0.812856\pi\) | ||||
−0.832090 | + | 0.554640i | \(0.812856\pi\) | |||||||
\(18\) | 4.63187e20 | 0.899000 | ||||||||
\(19\) | −1.40494e20 | −0.111743 | −0.0558717 | − | 0.998438i | \(-0.517794\pi\) | ||||
−0.0558717 | + | 0.998438i | \(0.517794\pi\) | |||||||
\(20\) | −4.18583e21 | −1.42819 | ||||||||
\(21\) | 2.94013e21 | 0.448485 | ||||||||
\(22\) | 1.40328e22 | 0.993503 | ||||||||
\(23\) | 3.12767e22 | 1.06344 | 0.531718 | − | 0.846922i | \(-0.321547\pi\) | ||||
0.531718 | + | 0.846922i | \(0.321547\pi\) | |||||||
\(24\) | −1.11580e23 | −1.87976 | ||||||||
\(25\) | −7.58162e22 | −0.651256 | ||||||||
\(26\) | 3.26267e23 | 1.46728 | ||||||||
\(27\) | −4.41542e23 | −1.06529 | ||||||||
\(28\) | 1.14289e24 | 1.51321 | ||||||||
\(29\) | −1.50979e24 | −1.12034 | −0.560168 | − | 0.828379i | \(-0.689264\pi\) | ||||
−0.560168 | + | 0.828379i | \(0.689264\pi\) | |||||||
\(30\) | 1.84522e24 | 0.782616 | ||||||||
\(31\) | 5.18762e23 | 0.128086 | 0.0640428 | − | 0.997947i | \(-0.479601\pi\) | ||||
0.0640428 | + | 0.997947i | \(0.479601\pi\) | |||||||
\(32\) | −1.27950e25 | −1.87096 | ||||||||
\(33\) | −4.37641e24 | −0.385157 | ||||||||
\(34\) | 5.72158e25 | 3.07690 | ||||||||
\(35\) | −1.10852e25 | −0.369504 | ||||||||
\(36\) | −5.61527e25 | −1.17592 | ||||||||
\(37\) | −3.01507e25 | −0.401762 | −0.200881 | − | 0.979616i | \(-0.564380\pi\) | ||||
−0.200881 | + | 0.979616i | \(0.564380\pi\) | |||||||
\(38\) | 2.40749e25 | 0.206602 | ||||||||
\(39\) | −1.01753e26 | −0.568829 | ||||||||
\(40\) | 4.20691e26 | 1.54872 | ||||||||
\(41\) | −2.18887e26 | −0.536149 | −0.268075 | − | 0.963398i | \(-0.586387\pi\) | ||||
−0.268075 | + | 0.963398i | \(0.586387\pi\) | |||||||
\(42\) | −5.03818e26 | −0.829203 | ||||||||
\(43\) | 1.76701e27 | 1.97246 | 0.986232 | − | 0.165369i | \(-0.0528817\pi\) | ||||
0.986232 | + | 0.165369i | \(0.0528817\pi\) | |||||||
\(44\) | −1.70121e27 | −1.29954 | ||||||||
\(45\) | 5.44636e26 | 0.287144 | ||||||||
\(46\) | −5.35955e27 | −1.96618 | ||||||||
\(47\) | 3.25654e27 | 0.837802 | 0.418901 | − | 0.908032i | \(-0.362415\pi\) | ||||
0.418901 | + | 0.908032i | \(0.362415\pi\) | |||||||
\(48\) | 9.58369e27 | 1.74202 | ||||||||
\(49\) | −4.70431e27 | −0.608500 | ||||||||
\(50\) | 1.29918e28 | 1.20411 | ||||||||
\(51\) | −1.78439e28 | −1.19284 | ||||||||
\(52\) | −3.95538e28 | −1.91926 | ||||||||
\(53\) | 9.17652e27 | 0.325182 | 0.162591 | − | 0.986694i | \(-0.448015\pi\) | ||||
0.162591 | + | 0.986694i | \(0.448015\pi\) | |||||||
\(54\) | 7.56623e28 | 1.96962 | ||||||||
\(55\) | 1.65004e28 | 0.317329 | ||||||||
\(56\) | −1.14865e29 | −1.64091 | ||||||||
\(57\) | −7.50826e27 | −0.0800948 | ||||||||
\(58\) | 2.58716e29 | 2.07139 | ||||||||
\(59\) | −1.18267e29 | −0.714174 | −0.357087 | − | 0.934071i | \(-0.616230\pi\) | ||||
−0.357087 | + | 0.934071i | \(0.616230\pi\) | |||||||
\(60\) | −2.23699e29 | −1.02369 | ||||||||
\(61\) | −9.92930e27 | −0.0345920 | −0.0172960 | − | 0.999850i | \(-0.505506\pi\) | ||||
−0.0172960 | + | 0.999850i | \(0.505506\pi\) | |||||||
\(62\) | −8.88948e28 | −0.236817 | ||||||||
\(63\) | −1.48707e29 | −0.304237 | ||||||||
\(64\) | 6.52116e29 | 1.02886 | ||||||||
\(65\) | 3.83640e29 | 0.468655 | ||||||||
\(66\) | 7.49940e29 | 0.712117 | ||||||||
\(67\) | 1.11293e30 | 0.824583 | 0.412291 | − | 0.911052i | \(-0.364729\pi\) | ||||
0.412291 | + | 0.911052i | \(0.364729\pi\) | |||||||
\(68\) | −6.93634e30 | −4.02470 | ||||||||
\(69\) | 1.67149e30 | 0.762242 | ||||||||
\(70\) | 1.89955e30 | 0.683175 | ||||||||
\(71\) | 7.58425e29 | 0.215849 | 0.107924 | − | 0.994159i | \(-0.465580\pi\) | ||||
0.107924 | + | 0.994159i | \(0.465580\pi\) | |||||||
\(72\) | 5.64355e30 | 1.27517 | ||||||||
\(73\) | −6.06835e30 | −1.09205 | −0.546026 | − | 0.837768i | \(-0.683860\pi\) | ||||
−0.546026 | + | 0.837768i | \(0.683860\pi\) | |||||||
\(74\) | 5.16661e30 | 0.742818 | ||||||||
\(75\) | −4.05177e30 | −0.466803 | ||||||||
\(76\) | −2.91863e30 | −0.270243 | ||||||||
\(77\) | −4.50525e30 | −0.336219 | ||||||||
\(78\) | 1.74364e31 | 1.05171 | ||||||||
\(79\) | −5.57890e30 | −0.272711 | −0.136355 | − | 0.990660i | \(-0.543539\pi\) | ||||
−0.136355 | + | 0.990660i | \(0.543539\pi\) | |||||||
\(80\) | −3.61334e31 | −1.43524 | ||||||||
\(81\) | −8.57067e30 | −0.277339 | ||||||||
\(82\) | 3.75083e31 | 0.991286 | ||||||||
\(83\) | 4.13746e31 | 0.895252 | 0.447626 | − | 0.894221i | \(-0.352270\pi\) | ||||
0.447626 | + | 0.894221i | \(0.352270\pi\) | |||||||
\(84\) | 6.10785e31 | 1.08463 | ||||||||
\(85\) | 6.72769e31 | 0.982775 | ||||||||
\(86\) | −3.02793e32 | −3.64688 | ||||||||
\(87\) | −8.06860e31 | −0.803028 | ||||||||
\(88\) | 1.70978e32 | 1.40921 | ||||||||
\(89\) | 6.21572e31 | 0.425164 | 0.212582 | − | 0.977143i | \(-0.431813\pi\) | ||||
0.212582 | + | 0.977143i | \(0.431813\pi\) | |||||||
\(90\) | −9.33286e31 | −0.530900 | ||||||||
\(91\) | −1.04749e32 | −0.496553 | ||||||||
\(92\) | 6.49745e32 | 2.57184 | ||||||||
\(93\) | 2.77237e31 | 0.0918084 | ||||||||
\(94\) | −5.58039e32 | −1.54901 | ||||||||
\(95\) | 2.83084e31 | 0.0659896 | ||||||||
\(96\) | −6.83789e32 | −1.34106 | ||||||||
\(97\) | 4.04003e32 | 0.667808 | 0.333904 | − | 0.942607i | \(-0.391634\pi\) | ||||
0.333904 | + | 0.942607i | \(0.391634\pi\) | |||||||
\(98\) | 8.06129e32 | 1.12506 | ||||||||
\(99\) | 2.21352e32 | 0.261278 | ||||||||
\(100\) | −1.57501e33 | −1.57501 | ||||||||
\(101\) | −1.20576e33 | −1.02319 | −0.511596 | − | 0.859226i | \(-0.670946\pi\) | ||||
−0.511596 | + | 0.859226i | \(0.670946\pi\) | |||||||
\(102\) | 3.05773e33 | 2.20544 | ||||||||
\(103\) | −1.69378e33 | −1.04002 | −0.520011 | − | 0.854159i | \(-0.674072\pi\) | ||||
−0.520011 | + | 0.854159i | \(0.674072\pi\) | |||||||
\(104\) | 3.97530e33 | 2.08123 | ||||||||
\(105\) | −5.92413e32 | −0.264851 | ||||||||
\(106\) | −1.57248e33 | −0.601228 | ||||||||
\(107\) | 7.07121e32 | 0.231559 | 0.115780 | − | 0.993275i | \(-0.463063\pi\) | ||||
0.115780 | + | 0.993275i | \(0.463063\pi\) | |||||||
\(108\) | −9.17264e33 | −2.57634 | ||||||||
\(109\) | 4.42814e33 | 1.06828 | 0.534139 | − | 0.845397i | \(-0.320636\pi\) | ||||
0.534139 | + | 0.845397i | \(0.320636\pi\) | |||||||
\(110\) | −2.82750e33 | −0.586709 | ||||||||
\(111\) | −1.61131e33 | −0.287973 | ||||||||
\(112\) | 9.86582e33 | 1.52067 | ||||||||
\(113\) | 1.36496e34 | 1.81687 | 0.908437 | − | 0.418023i | \(-0.137277\pi\) | ||||
0.908437 | + | 0.418023i | \(0.137277\pi\) | |||||||
\(114\) | 1.28661e33 | 0.148087 | ||||||||
\(115\) | −6.30200e33 | −0.628007 | ||||||||
\(116\) | −3.13645e34 | −2.70945 | ||||||||
\(117\) | 5.14652e33 | 0.385875 | ||||||||
\(118\) | 2.02661e34 | 1.32043 | ||||||||
\(119\) | −1.83692e34 | −1.04128 | ||||||||
\(120\) | 2.24826e34 | 1.11008 | ||||||||
\(121\) | −1.65190e34 | −0.711256 | ||||||||
\(122\) | 1.70148e33 | 0.0639572 | ||||||||
\(123\) | −1.16977e34 | −0.384298 | ||||||||
\(124\) | 1.07768e34 | 0.309766 | ||||||||
\(125\) | 3.87332e34 | 0.975142 | ||||||||
\(126\) | 2.54823e34 | 0.562504 | ||||||||
\(127\) | −7.12185e34 | −1.37985 | −0.689925 | − | 0.723881i | \(-0.742356\pi\) | ||||
−0.689925 | + | 0.723881i | \(0.742356\pi\) | |||||||
\(128\) | −1.83832e33 | −0.0312936 | ||||||||
\(129\) | 9.44324e34 | 1.41381 | ||||||||
\(130\) | −6.57403e34 | −0.866496 | ||||||||
\(131\) | −2.95217e34 | −0.342898 | −0.171449 | − | 0.985193i | \(-0.554845\pi\) | ||||
−0.171449 | + | 0.985193i | \(0.554845\pi\) | |||||||
\(132\) | −9.09161e34 | −0.931475 | ||||||||
\(133\) | −7.72929e33 | −0.0699178 | ||||||||
\(134\) | −1.90711e35 | −1.52457 | ||||||||
\(135\) | 8.89673e34 | 0.629105 | ||||||||
\(136\) | 6.97128e35 | 4.36436 | ||||||||
\(137\) | 8.90834e34 | 0.494205 | 0.247103 | − | 0.968989i | \(-0.420521\pi\) | ||||
0.247103 | + | 0.968989i | \(0.420521\pi\) | |||||||
\(138\) | −2.86425e35 | −1.40931 | ||||||||
\(139\) | −3.61707e35 | −1.57984 | −0.789920 | − | 0.613210i | \(-0.789878\pi\) | ||||
−0.789920 | + | 0.613210i | \(0.789878\pi\) | |||||||
\(140\) | −2.30284e35 | −0.893618 | ||||||||
\(141\) | 1.74036e35 | 0.600515 | ||||||||
\(142\) | −1.29963e35 | −0.399083 | ||||||||
\(143\) | 1.55920e35 | 0.426438 | ||||||||
\(144\) | −4.84728e35 | −1.18173 | ||||||||
\(145\) | 3.04210e35 | 0.661610 | ||||||||
\(146\) | 1.03987e36 | 2.01909 | ||||||||
\(147\) | −2.51408e35 | −0.436157 | ||||||||
\(148\) | −6.26354e35 | −0.971632 | ||||||||
\(149\) | 1.73500e35 | 0.240839 | 0.120419 | − | 0.992723i | \(-0.461576\pi\) | ||||
0.120419 | + | 0.992723i | \(0.461576\pi\) | |||||||
\(150\) | 6.94309e35 | 0.863072 | ||||||||
\(151\) | −1.35744e36 | −1.51217 | −0.756085 | − | 0.654473i | \(-0.772891\pi\) | ||||
−0.756085 | + | 0.654473i | \(0.772891\pi\) | |||||||
\(152\) | 2.93333e35 | 0.293050 | ||||||||
\(153\) | 9.02518e35 | 0.809184 | ||||||||
\(154\) | 7.72017e35 | 0.621634 | ||||||||
\(155\) | −1.04527e35 | −0.0756404 | ||||||||
\(156\) | −2.11383e36 | −1.37567 | ||||||||
\(157\) | −2.78049e36 | −1.62846 | −0.814229 | − | 0.580543i | \(-0.802840\pi\) | ||||
−0.814229 | + | 0.580543i | \(0.802840\pi\) | |||||||
\(158\) | 9.55998e35 | 0.504214 | ||||||||
\(159\) | 4.90411e35 | 0.233082 | ||||||||
\(160\) | 2.57809e36 | 1.10489 | ||||||||
\(161\) | 1.72069e36 | 0.665390 | ||||||||
\(162\) | 1.46866e36 | 0.512773 | ||||||||
\(163\) | 2.81381e36 | 0.887565 | 0.443782 | − | 0.896135i | \(-0.353636\pi\) | ||||
0.443782 | + | 0.896135i | \(0.353636\pi\) | |||||||
\(164\) | −4.54718e36 | −1.29664 | ||||||||
\(165\) | 8.81813e35 | 0.227453 | ||||||||
\(166\) | −7.08993e36 | −1.65523 | ||||||||
\(167\) | 6.77893e36 | 1.43331 | 0.716653 | − | 0.697430i | \(-0.245673\pi\) | ||||
0.716653 | + | 0.697430i | \(0.245673\pi\) | |||||||
\(168\) | −6.13862e36 | −1.17616 | ||||||||
\(169\) | −2.13094e36 | −0.370204 | ||||||||
\(170\) | −1.15285e37 | −1.81705 | ||||||||
\(171\) | 3.79756e35 | 0.0543336 | ||||||||
\(172\) | 3.67080e37 | 4.77026 | ||||||||
\(173\) | −1.42570e37 | −1.68370 | −0.841852 | − | 0.539708i | \(-0.818535\pi\) | ||||
−0.841852 | + | 0.539708i | \(0.818535\pi\) | |||||||
\(174\) | 1.38263e37 | 1.48472 | ||||||||
\(175\) | −4.17105e36 | −0.407490 | ||||||||
\(176\) | −1.46854e37 | −1.30595 | ||||||||
\(177\) | −6.32040e36 | −0.511901 | ||||||||
\(178\) | −1.06512e37 | −0.786085 | ||||||||
\(179\) | 7.37934e36 | 0.496527 | 0.248263 | − | 0.968693i | \(-0.420140\pi\) | ||||
0.248263 | + | 0.968693i | \(0.420140\pi\) | |||||||
\(180\) | 1.13143e37 | 0.694437 | ||||||||
\(181\) | 2.39313e36 | 0.134051 | 0.0670254 | − | 0.997751i | \(-0.478649\pi\) | ||||
0.0670254 | + | 0.997751i | \(0.478649\pi\) | |||||||
\(182\) | 1.79497e37 | 0.918076 | ||||||||
\(183\) | −5.30642e35 | −0.0247947 | ||||||||
\(184\) | −6.53018e37 | −2.78889 | ||||||||
\(185\) | 6.07513e36 | 0.237259 | ||||||||
\(186\) | −4.75072e36 | −0.169744 | ||||||||
\(187\) | 2.73428e37 | 0.894245 | ||||||||
\(188\) | 6.76517e37 | 2.02616 | ||||||||
\(189\) | −2.42915e37 | −0.666554 | ||||||||
\(190\) | −4.85091e36 | −0.122008 | ||||||||
\(191\) | −6.98026e35 | −0.0160998 | −0.00804991 | − | 0.999968i | \(-0.502562\pi\) | ||||
−0.00804991 | + | 0.999968i | \(0.502562\pi\) | |||||||
\(192\) | 3.48504e37 | 0.737458 | ||||||||
\(193\) | 6.67098e36 | 0.129567 | 0.0647835 | − | 0.997899i | \(-0.479364\pi\) | ||||
0.0647835 | + | 0.997899i | \(0.479364\pi\) | |||||||
\(194\) | −6.92298e37 | −1.23471 | ||||||||
\(195\) | 2.05025e37 | 0.335920 | ||||||||
\(196\) | −9.77280e37 | −1.47161 | ||||||||
\(197\) | −8.89563e37 | −1.23164 | −0.615821 | − | 0.787886i | \(-0.711175\pi\) | ||||
−0.615821 | + | 0.787886i | \(0.711175\pi\) | |||||||
\(198\) | −3.79308e37 | −0.483077 | ||||||||
\(199\) | 1.05106e38 | 1.23183 | 0.615916 | − | 0.787812i | \(-0.288786\pi\) | ||||
0.615916 | + | 0.787812i | \(0.288786\pi\) | |||||||
\(200\) | 1.58295e38 | 1.70794 | ||||||||
\(201\) | 5.94773e37 | 0.591039 | ||||||||
\(202\) | 2.06618e38 | 1.89178 | ||||||||
\(203\) | −8.30613e37 | −0.700994 | ||||||||
\(204\) | −3.70692e38 | −2.88480 | ||||||||
\(205\) | 4.41040e37 | 0.316621 | ||||||||
\(206\) | 2.90245e38 | 1.92290 | ||||||||
\(207\) | −8.45412e37 | −0.517080 | ||||||||
\(208\) | −3.41441e38 | −1.92873 | ||||||||
\(209\) | 1.15051e37 | 0.0600452 | ||||||||
\(210\) | 1.01516e38 | 0.489682 | ||||||||
\(211\) | −5.59870e37 | −0.249705 | −0.124852 | − | 0.992175i | \(-0.539846\pi\) | ||||
−0.124852 | + | 0.992175i | \(0.539846\pi\) | |||||||
\(212\) | 1.90634e38 | 0.786428 | ||||||||
\(213\) | 4.05318e37 | 0.154715 | ||||||||
\(214\) | −1.21172e38 | −0.428129 | ||||||||
\(215\) | −3.56038e38 | −1.16483 | ||||||||
\(216\) | 9.21884e38 | 2.79376 | ||||||||
\(217\) | 2.85398e37 | 0.0801431 | ||||||||
\(218\) | −7.58804e38 | −1.97514 | ||||||||
\(219\) | −3.24305e38 | −0.782755 | ||||||||
\(220\) | 3.42781e38 | 0.767436 | ||||||||
\(221\) | 6.35730e38 | 1.32069 | ||||||||
\(222\) | 2.76114e38 | 0.532432 | ||||||||
\(223\) | 4.65676e38 | 0.833784 | 0.416892 | − | 0.908956i | \(-0.363119\pi\) | ||||
0.416892 | + | 0.908956i | \(0.363119\pi\) | |||||||
\(224\) | −7.03919e38 | −1.17066 | ||||||||
\(225\) | 2.04932e38 | 0.316664 | ||||||||
\(226\) | −2.33898e39 | −3.35921 | ||||||||
\(227\) | −2.61802e38 | −0.349580 | −0.174790 | − | 0.984606i | \(-0.555925\pi\) | ||||
−0.174790 | + | 0.984606i | \(0.555925\pi\) | |||||||
\(228\) | −1.55977e38 | −0.193703 | ||||||||
\(229\) | 9.20963e38 | 1.06404 | 0.532018 | − | 0.846733i | \(-0.321434\pi\) | ||||
0.532018 | + | 0.846733i | \(0.321434\pi\) | |||||||
\(230\) | 1.07991e39 | 1.16112 | ||||||||
\(231\) | −2.40770e38 | −0.240993 | ||||||||
\(232\) | 3.15225e39 | 2.93811 | ||||||||
\(233\) | 7.13755e37 | 0.0619693 | 0.0309847 | − | 0.999520i | \(-0.490136\pi\) | ||||
0.0309847 | + | 0.999520i | \(0.490136\pi\) | |||||||
\(234\) | −8.81904e38 | −0.713444 | ||||||||
\(235\) | −6.56167e38 | −0.494760 | ||||||||
\(236\) | −2.45688e39 | −1.72718 | ||||||||
\(237\) | −2.98148e38 | −0.195472 | ||||||||
\(238\) | 3.14774e39 | 1.92522 | ||||||||
\(239\) | −1.83178e39 | −1.04546 | −0.522731 | − | 0.852498i | \(-0.675087\pi\) | ||||
−0.522731 | + | 0.852498i | \(0.675087\pi\) | |||||||
\(240\) | −1.93104e39 | −1.02874 | ||||||||
\(241\) | −3.05313e39 | −1.51867 | −0.759336 | − | 0.650698i | \(-0.774476\pi\) | ||||
−0.759336 | + | 0.650698i | \(0.774476\pi\) | |||||||
\(242\) | 2.83069e39 | 1.31504 | ||||||||
\(243\) | 1.99652e39 | 0.866505 | ||||||||
\(244\) | −2.06272e38 | −0.0836583 | ||||||||
\(245\) | 9.47883e38 | 0.359347 | ||||||||
\(246\) | 2.00452e39 | 0.710527 | ||||||||
\(247\) | 2.67499e38 | 0.0886793 | ||||||||
\(248\) | −1.08311e39 | −0.335908 | ||||||||
\(249\) | 2.21114e39 | 0.641693 | ||||||||
\(250\) | −6.63729e39 | −1.80294 | ||||||||
\(251\) | 3.03407e39 | 0.771631 | 0.385815 | − | 0.922576i | \(-0.373920\pi\) | ||||
0.385815 | + | 0.922576i | \(0.373920\pi\) | |||||||
\(252\) | −3.08926e39 | −0.735775 | ||||||||
\(253\) | −2.56127e39 | −0.571435 | ||||||||
\(254\) | 1.22040e40 | 2.55120 | ||||||||
\(255\) | 3.59541e39 | 0.704427 | ||||||||
\(256\) | −5.28662e39 | −0.970999 | ||||||||
\(257\) | −2.91186e39 | −0.501503 | −0.250752 | − | 0.968051i | \(-0.580678\pi\) | ||||
−0.250752 | + | 0.968051i | \(0.580678\pi\) | |||||||
\(258\) | −1.61819e40 | −2.61399 | ||||||||
\(259\) | −1.65875e39 | −0.251382 | ||||||||
\(260\) | 7.96978e39 | 1.13341 | ||||||||
\(261\) | 4.08097e39 | 0.544748 | ||||||||
\(262\) | 5.05883e39 | 0.633984 | ||||||||
\(263\) | −5.62907e39 | −0.662471 | −0.331236 | − | 0.943548i | \(-0.607466\pi\) | ||||
−0.331236 | + | 0.943548i | \(0.607466\pi\) | |||||||
\(264\) | 9.13740e39 | 1.01009 | ||||||||
\(265\) | −1.84900e39 | −0.192035 | ||||||||
\(266\) | 1.32449e39 | 0.129271 | ||||||||
\(267\) | 3.32180e39 | 0.304746 | ||||||||
\(268\) | 2.31202e40 | 1.99419 | ||||||||
\(269\) | −9.77080e39 | −0.792533 | −0.396266 | − | 0.918136i | \(-0.629694\pi\) | ||||
−0.396266 | + | 0.918136i | \(0.629694\pi\) | |||||||
\(270\) | −1.52454e40 | −1.16315 | ||||||||
\(271\) | 2.38779e40 | 1.71397 | 0.856985 | − | 0.515342i | \(-0.172335\pi\) | ||||
0.856985 | + | 0.515342i | \(0.172335\pi\) | |||||||
\(272\) | −5.98767e40 | −4.04456 | ||||||||
\(273\) | −5.59798e39 | −0.355916 | ||||||||
\(274\) | −1.52653e40 | −0.913736 | ||||||||
\(275\) | 6.20865e39 | 0.349952 | ||||||||
\(276\) | 3.47237e40 | 1.84343 | ||||||||
\(277\) | −1.39835e40 | −0.699358 | −0.349679 | − | 0.936870i | \(-0.613709\pi\) | ||||
−0.349679 | + | 0.936870i | \(0.613709\pi\) | |||||||
\(278\) | 6.19820e40 | 2.92096 | ||||||||
\(279\) | −1.40222e39 | −0.0622798 | ||||||||
\(280\) | 2.31444e40 | 0.969033 | ||||||||
\(281\) | −2.89927e40 | −1.14455 | −0.572274 | − | 0.820062i | \(-0.693939\pi\) | ||||
−0.572274 | + | 0.820062i | \(0.693939\pi\) | |||||||
\(282\) | −2.98227e40 | −1.11029 | ||||||||
\(283\) | −1.50945e40 | −0.530081 | −0.265040 | − | 0.964237i | \(-0.585385\pi\) | ||||
−0.265040 | + | 0.964237i | \(0.585385\pi\) | |||||||
\(284\) | 1.57556e40 | 0.522015 | ||||||||
\(285\) | 1.51286e39 | 0.0472996 | ||||||||
\(286\) | −2.67183e40 | −0.788441 | ||||||||
\(287\) | −1.20421e40 | −0.335468 | ||||||||
\(288\) | 3.45850e40 | 0.909728 | ||||||||
\(289\) | 7.12303e40 | 1.76950 | ||||||||
\(290\) | −5.21293e40 | −1.22325 | ||||||||
\(291\) | 2.15907e40 | 0.478667 | ||||||||
\(292\) | −1.26065e41 | −2.64105 | ||||||||
\(293\) | −1.40305e40 | −0.277816 | −0.138908 | − | 0.990305i | \(-0.544359\pi\) | ||||
−0.138908 | + | 0.990305i | \(0.544359\pi\) | |||||||
\(294\) | 4.30811e40 | 0.806410 | ||||||||
\(295\) | 2.38298e40 | 0.421752 | ||||||||
\(296\) | 6.29509e40 | 1.05363 | ||||||||
\(297\) | 3.61582e40 | 0.572435 | ||||||||
\(298\) | −2.97309e40 | −0.445286 | ||||||||
\(299\) | −5.95505e40 | −0.843939 | ||||||||
\(300\) | −8.41719e40 | −1.12893 | ||||||||
\(301\) | 9.72124e40 | 1.23417 | ||||||||
\(302\) | 2.32610e41 | 2.79585 | ||||||||
\(303\) | −6.44381e40 | −0.733398 | ||||||||
\(304\) | −2.51945e40 | −0.271577 | ||||||||
\(305\) | 2.00068e39 | 0.0204282 | ||||||||
\(306\) | −1.54655e41 | −1.49610 | ||||||||
\(307\) | −2.92194e40 | −0.267848 | −0.133924 | − | 0.990992i | \(-0.542758\pi\) | ||||
−0.133924 | + | 0.990992i | \(0.542758\pi\) | |||||||
\(308\) | −9.35926e40 | −0.813120 | ||||||||
\(309\) | −9.05190e40 | −0.745461 | ||||||||
\(310\) | 1.79116e40 | 0.139851 | ||||||||
\(311\) | −2.24927e41 | −1.66531 | −0.832653 | − | 0.553794i | \(-0.813179\pi\) | ||||
−0.832653 | + | 0.553794i | \(0.813179\pi\) | |||||||
\(312\) | 2.12448e41 | 1.49177 | ||||||||
\(313\) | 1.17836e41 | 0.784868 | 0.392434 | − | 0.919780i | \(-0.371633\pi\) | ||||
0.392434 | + | 0.919780i | \(0.371633\pi\) | |||||||
\(314\) | 4.76463e41 | 3.01086 | ||||||||
\(315\) | 2.99633e40 | 0.179666 | ||||||||
\(316\) | −1.15897e41 | −0.659530 | ||||||||
\(317\) | −9.02704e40 | −0.487604 | −0.243802 | − | 0.969825i | \(-0.578395\pi\) | ||||
−0.243802 | + | 0.969825i | \(0.578395\pi\) | |||||||
\(318\) | −8.40366e40 | −0.430944 | ||||||||
\(319\) | 1.23638e41 | 0.602012 | ||||||||
\(320\) | −1.31396e41 | −0.607588 | ||||||||
\(321\) | 3.77900e40 | 0.165975 | ||||||||
\(322\) | −2.94857e41 | −1.23024 | ||||||||
\(323\) | 4.69099e40 | 0.185961 | ||||||||
\(324\) | −1.78048e41 | −0.670725 | ||||||||
\(325\) | 1.44353e41 | 0.516835 | ||||||||
\(326\) | −4.82174e41 | −1.64102 | ||||||||
\(327\) | 2.36649e41 | 0.765714 | ||||||||
\(328\) | 4.57008e41 | 1.40607 | ||||||||
\(329\) | 1.79159e41 | 0.524212 | ||||||||
\(330\) | −1.51107e41 | −0.420537 | ||||||||
\(331\) | −2.91394e41 | −0.771469 | −0.385734 | − | 0.922610i | \(-0.626052\pi\) | ||||
−0.385734 | + | 0.922610i | \(0.626052\pi\) | |||||||
\(332\) | 8.59521e41 | 2.16510 | ||||||||
\(333\) | 8.14977e40 | 0.195351 | ||||||||
\(334\) | −1.16163e42 | −2.65004 | ||||||||
\(335\) | −2.24247e41 | −0.486954 | ||||||||
\(336\) | 5.27249e41 | 1.08998 | ||||||||
\(337\) | −5.69474e41 | −1.12094 | −0.560468 | − | 0.828176i | \(-0.689379\pi\) | ||||
−0.560468 | + | 0.828176i | \(0.689379\pi\) | |||||||
\(338\) | 3.65157e41 | 0.684470 | ||||||||
\(339\) | 7.29460e41 | 1.30229 | ||||||||
\(340\) | 1.39762e42 | 2.37677 | ||||||||
\(341\) | −4.24819e40 | −0.0688266 | ||||||||
\(342\) | −6.50748e40 | −0.100457 | ||||||||
\(343\) | −6.84132e41 | −1.00644 | ||||||||
\(344\) | −3.68929e42 | −5.17284 | ||||||||
\(345\) | −3.36792e41 | −0.450139 | ||||||||
\(346\) | 2.44306e42 | 3.11300 | ||||||||
\(347\) | 4.85020e41 | 0.589283 | 0.294641 | − | 0.955608i | \(-0.404800\pi\) | ||||
0.294641 | + | 0.955608i | \(0.404800\pi\) | |||||||
\(348\) | −1.67618e42 | −1.94206 | ||||||||
\(349\) | 5.38533e41 | 0.595104 | 0.297552 | − | 0.954706i | \(-0.403830\pi\) | ||||
0.297552 | + | 0.954706i | \(0.403830\pi\) | |||||||
\(350\) | 7.14748e41 | 0.753408 | ||||||||
\(351\) | 8.40692e41 | 0.845414 | ||||||||
\(352\) | 1.04779e42 | 1.00536 | ||||||||
\(353\) | −9.77578e41 | −0.895094 | −0.447547 | − | 0.894260i | \(-0.647702\pi\) | ||||
−0.447547 | + | 0.894260i | \(0.647702\pi\) | |||||||
\(354\) | 1.08306e42 | 0.946453 | ||||||||
\(355\) | −1.52817e41 | −0.127469 | ||||||||
\(356\) | 1.29126e42 | 1.02823 | ||||||||
\(357\) | −9.81689e41 | −0.746360 | ||||||||
\(358\) | −1.26452e42 | −0.918027 | ||||||||
\(359\) | 1.18143e42 | 0.819124 | 0.409562 | − | 0.912282i | \(-0.365682\pi\) | ||||
0.409562 | + | 0.912282i | \(0.365682\pi\) | |||||||
\(360\) | −1.13713e42 | −0.753043 | ||||||||
\(361\) | −1.56103e42 | −0.987513 | ||||||||
\(362\) | −4.10085e41 | −0.247846 | ||||||||
\(363\) | −8.82811e41 | −0.509810 | ||||||||
\(364\) | −2.17606e42 | −1.20088 | ||||||||
\(365\) | 1.22273e42 | 0.644907 | ||||||||
\(366\) | 9.09304e40 | 0.0458428 | ||||||||
\(367\) | 7.16875e41 | 0.345504 | 0.172752 | − | 0.984965i | \(-0.444734\pi\) | ||||
0.172752 | + | 0.984965i | \(0.444734\pi\) | |||||||
\(368\) | 5.60881e42 | 2.58453 | ||||||||
\(369\) | 5.91654e41 | 0.260695 | ||||||||
\(370\) | −1.04103e42 | −0.438668 | ||||||||
\(371\) | 5.04849e41 | 0.203466 | ||||||||
\(372\) | 5.75935e41 | 0.222032 | ||||||||
\(373\) | −6.80691e41 | −0.251047 | −0.125523 | − | 0.992091i | \(-0.540061\pi\) | ||||
−0.125523 | + | 0.992091i | \(0.540061\pi\) | |||||||
\(374\) | −4.68545e42 | −1.65337 | ||||||||
\(375\) | 2.06998e42 | 0.698956 | ||||||||
\(376\) | −6.79925e42 | −2.19716 | ||||||||
\(377\) | 2.87462e42 | 0.889096 | ||||||||
\(378\) | 4.16258e42 | 1.23239 | ||||||||
\(379\) | 5.14200e42 | 1.45742 | 0.728711 | − | 0.684821i | \(-0.240120\pi\) | ||||
0.728711 | + | 0.684821i | \(0.240120\pi\) | |||||||
\(380\) | 5.88082e41 | 0.159591 | ||||||||
\(381\) | −3.80606e42 | −0.989040 | ||||||||
\(382\) | 1.19613e41 | 0.0297669 | ||||||||
\(383\) | −6.82496e42 | −1.62675 | −0.813375 | − | 0.581740i | \(-0.802372\pi\) | ||||
−0.813375 | + | 0.581740i | \(0.802372\pi\) | |||||||
\(384\) | −9.82434e40 | −0.0224305 | ||||||||
\(385\) | 9.07773e41 | 0.198552 | ||||||||
\(386\) | −1.14314e42 | −0.239556 | ||||||||
\(387\) | −4.77624e42 | −0.959082 | ||||||||
\(388\) | 8.39281e42 | 1.61504 | ||||||||
\(389\) | 3.03602e42 | 0.559933 | 0.279966 | − | 0.960010i | \(-0.409677\pi\) | ||||
0.279966 | + | 0.960010i | \(0.409677\pi\) | |||||||
\(390\) | −3.51329e42 | −0.621081 | ||||||||
\(391\) | −1.04431e43 | −1.76975 | ||||||||
\(392\) | 9.82202e42 | 1.59581 | ||||||||
\(393\) | −1.57770e42 | −0.245781 | ||||||||
\(394\) | 1.52435e43 | 2.27718 | ||||||||
\(395\) | 1.12411e42 | 0.161048 | ||||||||
\(396\) | 4.59839e42 | 0.631882 | ||||||||
\(397\) | 8.54761e42 | 1.12668 | 0.563341 | − | 0.826225i | \(-0.309516\pi\) | ||||
0.563341 | + | 0.826225i | \(0.309516\pi\) | |||||||
\(398\) | −1.80109e43 | −2.27753 | ||||||||
\(399\) | −4.13069e41 | −0.0501152 | ||||||||
\(400\) | −1.35960e43 | −1.58279 | ||||||||
\(401\) | 4.64638e42 | 0.519078 | 0.259539 | − | 0.965733i | \(-0.416429\pi\) | ||||
0.259539 | + | 0.965733i | \(0.416429\pi\) | |||||||
\(402\) | −1.01920e43 | −1.09277 | ||||||||
\(403\) | −9.87719e41 | −0.101648 | ||||||||
\(404\) | −2.50486e43 | −2.47452 | ||||||||
\(405\) | 1.72692e42 | 0.163782 | ||||||||
\(406\) | 1.42333e43 | 1.29607 | ||||||||
\(407\) | 2.46907e42 | 0.215886 | ||||||||
\(408\) | 3.72559e43 | 3.12826 | ||||||||
\(409\) | 1.73477e43 | 1.39897 | 0.699483 | − | 0.714649i | \(-0.253414\pi\) | ||||
0.699483 | + | 0.714649i | \(0.253414\pi\) | |||||||
\(410\) | −7.55763e42 | −0.585399 | ||||||||
\(411\) | 4.76080e42 | 0.354233 | ||||||||
\(412\) | −3.51868e43 | −2.51522 | ||||||||
\(413\) | −6.50647e42 | −0.446858 | ||||||||
\(414\) | 1.44869e43 | 0.956028 | ||||||||
\(415\) | −8.33667e42 | −0.528687 | ||||||||
\(416\) | 2.43615e43 | 1.48479 | ||||||||
\(417\) | −1.93304e43 | −1.13239 | ||||||||
\(418\) | −1.97151e42 | −0.111017 | ||||||||
\(419\) | 1.59552e43 | 0.863717 | 0.431858 | − | 0.901941i | \(-0.357858\pi\) | ||||
0.431858 | + | 0.901941i | \(0.357858\pi\) | |||||||
\(420\) | −1.23069e43 | −0.640522 | ||||||||
\(421\) | −2.07154e43 | −1.03667 | −0.518333 | − | 0.855179i | \(-0.673447\pi\) | ||||
−0.518333 | + | 0.855179i | \(0.673447\pi\) | |||||||
\(422\) | 9.59390e42 | 0.461679 | ||||||||
\(423\) | −8.80247e42 | −0.407369 | ||||||||
\(424\) | −1.91594e43 | −0.852797 | ||||||||
\(425\) | 2.53145e43 | 1.08381 | ||||||||
\(426\) | −6.94550e42 | −0.286052 | ||||||||
\(427\) | −5.46263e41 | −0.0216442 | ||||||||
\(428\) | 1.46898e43 | 0.560008 | ||||||||
\(429\) | 8.33266e42 | 0.305660 | ||||||||
\(430\) | 6.10105e43 | 2.15365 | ||||||||
\(431\) | −2.15255e43 | −0.731272 | −0.365636 | − | 0.930758i | \(-0.619149\pi\) | ||||
−0.365636 | + | 0.930758i | \(0.619149\pi\) | |||||||
\(432\) | −7.91812e43 | −2.58905 | ||||||||
\(433\) | −2.62411e43 | −0.825908 | −0.412954 | − | 0.910752i | \(-0.635503\pi\) | ||||
−0.412954 | + | 0.910752i | \(0.635503\pi\) | |||||||
\(434\) | −4.89057e42 | −0.148176 | ||||||||
\(435\) | 1.62576e43 | 0.474225 | ||||||||
\(436\) | 9.19908e43 | 2.58355 | ||||||||
\(437\) | −4.39417e42 | −0.118832 | ||||||||
\(438\) | 5.55727e43 | 1.44723 | ||||||||
\(439\) | 1.50091e43 | 0.376434 | 0.188217 | − | 0.982127i | \(-0.439729\pi\) | ||||
0.188217 | + | 0.982127i | \(0.439729\pi\) | |||||||
\(440\) | −3.44507e43 | −0.832203 | ||||||||
\(441\) | 1.27158e43 | 0.295875 | ||||||||
\(442\) | −1.08938e44 | −2.44182 | ||||||||
\(443\) | 1.03686e43 | 0.223902 | 0.111951 | − | 0.993714i | \(-0.464290\pi\) | ||||
0.111951 | + | 0.993714i | \(0.464290\pi\) | |||||||
\(444\) | −3.34736e43 | −0.696440 | ||||||||
\(445\) | −1.25242e43 | −0.251079 | ||||||||
\(446\) | −7.97979e43 | −1.54158 | ||||||||
\(447\) | 9.27219e42 | 0.172627 | ||||||||
\(448\) | 3.58764e43 | 0.643756 | ||||||||
\(449\) | −3.05007e42 | −0.0527528 | −0.0263764 | − | 0.999652i | \(-0.508397\pi\) | ||||
−0.0263764 | + | 0.999652i | \(0.508397\pi\) | |||||||
\(450\) | −3.51171e43 | −0.585479 | ||||||||
\(451\) | 1.79248e43 | 0.288099 | ||||||||
\(452\) | 2.83558e44 | 4.39397 | ||||||||
\(453\) | −7.25443e43 | −1.08388 | ||||||||
\(454\) | 4.48623e43 | 0.646338 | ||||||||
\(455\) | 2.11061e43 | 0.293237 | ||||||||
\(456\) | 1.56763e43 | 0.210051 | ||||||||
\(457\) | −8.15124e43 | −1.05343 | −0.526716 | − | 0.850042i | \(-0.676577\pi\) | ||||
−0.526716 | + | 0.850042i | \(0.676577\pi\) | |||||||
\(458\) | −1.57816e44 | −1.96730 | ||||||||
\(459\) | 1.47428e44 | 1.77284 | ||||||||
\(460\) | −1.30919e44 | −1.51879 | ||||||||
\(461\) | 9.49311e43 | 1.06253 | 0.531267 | − | 0.847204i | \(-0.321716\pi\) | ||||
0.531267 | + | 0.847204i | \(0.321716\pi\) | |||||||
\(462\) | 4.12581e43 | 0.445571 | ||||||||
\(463\) | −6.84730e43 | −0.713564 | −0.356782 | − | 0.934188i | \(-0.616126\pi\) | ||||
−0.356782 | + | 0.934188i | \(0.616126\pi\) | |||||||
\(464\) | −2.70748e44 | −2.72282 | ||||||||
\(465\) | −5.58611e42 | −0.0542170 | ||||||||
\(466\) | −1.22309e43 | −0.114575 | ||||||||
\(467\) | 1.13867e44 | 1.02961 | 0.514803 | − | 0.857308i | \(-0.327865\pi\) | ||||
0.514803 | + | 0.857308i | \(0.327865\pi\) | |||||||
\(468\) | 1.06914e44 | 0.933210 | ||||||||
\(469\) | 6.12282e43 | 0.515941 | ||||||||
\(470\) | 1.12440e44 | 0.914762 | ||||||||
\(471\) | −1.48595e44 | −1.16724 | ||||||||
\(472\) | 2.46926e44 | 1.87294 | ||||||||
\(473\) | −1.44702e44 | −1.05990 | ||||||||
\(474\) | 5.10904e43 | 0.361407 | ||||||||
\(475\) | 1.06517e43 | 0.0727736 | ||||||||
\(476\) | −3.81605e44 | −2.51825 | ||||||||
\(477\) | −2.48042e43 | −0.158115 | ||||||||
\(478\) | 3.13893e44 | 1.93295 | ||||||||
\(479\) | −2.43710e44 | −1.44990 | −0.724948 | − | 0.688804i | \(-0.758136\pi\) | ||||
−0.724948 | + | 0.688804i | \(0.758136\pi\) | |||||||
\(480\) | 1.37778e44 | 0.791954 | ||||||||
\(481\) | 5.74067e43 | 0.318837 | ||||||||
\(482\) | 5.23183e44 | 2.80787 | ||||||||
\(483\) | 9.19573e43 | 0.476934 | ||||||||
\(484\) | −3.43169e44 | −1.72012 | ||||||||
\(485\) | −8.14036e43 | −0.394371 | ||||||||
\(486\) | −3.42123e44 | −1.60208 | ||||||||
\(487\) | −1.55812e44 | −0.705300 | −0.352650 | − | 0.935755i | \(-0.614719\pi\) | ||||
−0.352650 | + | 0.935755i | \(0.614719\pi\) | |||||||
\(488\) | 2.07311e43 | 0.0907185 | ||||||||
\(489\) | 1.50376e44 | 0.636183 | ||||||||
\(490\) | −1.62429e44 | −0.664397 | ||||||||
\(491\) | −2.64492e43 | −0.104609 | −0.0523044 | − | 0.998631i | \(-0.516657\pi\) | ||||
−0.0523044 | + | 0.998631i | \(0.516657\pi\) | |||||||
\(492\) | −2.43010e44 | −0.929396 | ||||||||
\(493\) | 5.04108e44 | 1.86444 | ||||||||
\(494\) | −4.58384e43 | −0.163959 | ||||||||
\(495\) | −4.46007e43 | −0.154297 | ||||||||
\(496\) | 9.30290e43 | 0.311294 | ||||||||
\(497\) | 4.17250e43 | 0.135057 | ||||||||
\(498\) | −3.78900e44 | −1.18643 | ||||||||
\(499\) | 3.31565e44 | 1.00441 | 0.502203 | − | 0.864750i | \(-0.332523\pi\) | ||||
0.502203 | + | 0.864750i | \(0.332523\pi\) | |||||||
\(500\) | 8.04647e44 | 2.35831 | ||||||||
\(501\) | 3.62279e44 | 1.02736 | ||||||||
\(502\) | −5.19917e44 | −1.42667 | ||||||||
\(503\) | −4.39485e44 | −1.16700 | −0.583502 | − | 0.812112i | \(-0.698318\pi\) | ||||
−0.583502 | + | 0.812112i | \(0.698318\pi\) | |||||||
\(504\) | 3.10482e44 | 0.797870 | ||||||||
\(505\) | 2.42951e44 | 0.604242 | ||||||||
\(506\) | 4.38898e44 | 1.05653 | ||||||||
\(507\) | −1.13882e44 | −0.265352 | ||||||||
\(508\) | −1.47950e45 | −3.33706 | ||||||||
\(509\) | −7.37330e44 | −1.60997 | −0.804986 | − | 0.593294i | \(-0.797827\pi\) | ||||
−0.804986 | + | 0.593294i | \(0.797827\pi\) | |||||||
\(510\) | −6.16108e44 | −1.30241 | ||||||||
\(511\) | −3.33852e44 | −0.683296 | ||||||||
\(512\) | 9.21704e44 | 1.82657 | ||||||||
\(513\) | 6.20338e43 | 0.119040 | ||||||||
\(514\) | 4.98975e44 | 0.927229 | ||||||||
\(515\) | 3.41284e44 | 0.614181 | ||||||||
\(516\) | 1.96175e45 | 3.41919 | ||||||||
\(517\) | −2.66681e44 | −0.450192 | ||||||||
\(518\) | 2.84242e44 | 0.464780 | ||||||||
\(519\) | −7.61920e44 | −1.20684 | ||||||||
\(520\) | −8.00992e44 | −1.22906 | ||||||||
\(521\) | 1.67201e43 | 0.0248552 | 0.0124276 | − | 0.999923i | \(-0.496044\pi\) | ||||
0.0124276 | + | 0.999923i | \(0.496044\pi\) | |||||||
\(522\) | −6.99313e44 | −1.00718 | ||||||||
\(523\) | 1.06261e45 | 1.48284 | 0.741420 | − | 0.671041i | \(-0.234153\pi\) | ||||
0.741420 | + | 0.671041i | \(0.234153\pi\) | |||||||
\(524\) | −6.13288e44 | −0.829275 | ||||||||
\(525\) | −2.22909e44 | −0.292078 | ||||||||
\(526\) | 9.64595e44 | 1.22484 | ||||||||
\(527\) | −1.73211e44 | −0.213158 | ||||||||
\(528\) | −7.84817e44 | −0.936071 | ||||||||
\(529\) | 1.13224e44 | 0.130894 | ||||||||
\(530\) | 3.16843e44 | 0.355052 | ||||||||
\(531\) | 3.19676e44 | 0.347257 | ||||||||
\(532\) | −1.60569e44 | −0.169091 | ||||||||
\(533\) | 4.16759e44 | 0.425486 | ||||||||
\(534\) | −5.69223e44 | −0.563445 | ||||||||
\(535\) | −1.42480e44 | −0.136746 | ||||||||
\(536\) | −2.32366e45 | −2.16249 | ||||||||
\(537\) | 3.94367e44 | 0.355897 | ||||||||
\(538\) | 1.67432e45 | 1.46531 | ||||||||
\(539\) | 3.85240e44 | 0.326977 | ||||||||
\(540\) | 1.84822e45 | 1.52144 | ||||||||
\(541\) | −1.73107e45 | −1.38217 | −0.691084 | − | 0.722774i | \(-0.742867\pi\) | ||||
−0.691084 | + | 0.722774i | \(0.742867\pi\) | |||||||
\(542\) | −4.09171e45 | −3.16896 | ||||||||
\(543\) | 1.27894e44 | 0.0960841 | ||||||||
\(544\) | 4.27216e45 | 3.11362 | ||||||||
\(545\) | −8.92237e44 | −0.630867 | ||||||||
\(546\) | 9.59267e44 | 0.658053 | ||||||||
\(547\) | 1.88809e45 | 1.25670 | 0.628350 | − | 0.777931i | \(-0.283731\pi\) | ||||
0.628350 | + | 0.777931i | \(0.283731\pi\) | |||||||
\(548\) | 1.85063e45 | 1.19520 | ||||||||
\(549\) | 2.68390e43 | 0.0168199 | ||||||||
\(550\) | −1.06391e45 | −0.647025 | ||||||||
\(551\) | 2.12115e44 | 0.125190 | ||||||||
\(552\) | −3.48986e45 | −1.99900 | ||||||||
\(553\) | −3.06925e44 | −0.170635 | ||||||||
\(554\) | 2.39620e45 | 1.29304 | ||||||||
\(555\) | 3.24667e44 | 0.170061 | ||||||||
\(556\) | −7.51415e45 | −3.82073 | ||||||||
\(557\) | 1.82254e45 | 0.899636 | 0.449818 | − | 0.893120i | \(-0.351489\pi\) | ||||
0.449818 | + | 0.893120i | \(0.351489\pi\) | |||||||
\(558\) | 2.40284e44 | 0.115149 | ||||||||
\(559\) | −3.36437e45 | −1.56534 | ||||||||
\(560\) | −1.98789e45 | −0.898027 | ||||||||
\(561\) | 1.46125e45 | 0.640972 | ||||||||
\(562\) | 4.96817e45 | 2.11615 | ||||||||
\(563\) | 3.54966e45 | 1.46824 | 0.734122 | − | 0.679018i | \(-0.237594\pi\) | ||||
0.734122 | + | 0.679018i | \(0.237594\pi\) | |||||||
\(564\) | 3.61544e45 | 1.45230 | ||||||||
\(565\) | −2.75028e45 | −1.07295 | ||||||||
\(566\) | 2.58658e45 | 0.980066 | ||||||||
\(567\) | −4.71517e44 | −0.173531 | ||||||||
\(568\) | −1.58350e45 | −0.566070 | ||||||||
\(569\) | −3.23817e45 | −1.12447 | −0.562234 | − | 0.826978i | \(-0.690058\pi\) | ||||
−0.562234 | + | 0.826978i | \(0.690058\pi\) | |||||||
\(570\) | −2.59242e44 | −0.0874522 | ||||||||
\(571\) | 1.75221e45 | 0.574237 | 0.287118 | − | 0.957895i | \(-0.407303\pi\) | ||||
0.287118 | + | 0.957895i | \(0.407303\pi\) | |||||||
\(572\) | 3.23909e45 | 1.03131 | ||||||||
\(573\) | −3.73039e43 | −0.0115399 | ||||||||
\(574\) | 2.06353e45 | 0.620247 | ||||||||
\(575\) | −2.37128e45 | −0.692569 | ||||||||
\(576\) | −1.76268e45 | −0.500267 | ||||||||
\(577\) | −2.22828e45 | −0.614566 | −0.307283 | − | 0.951618i | \(-0.599420\pi\) | ||||
−0.307283 | + | 0.951618i | \(0.599420\pi\) | |||||||
\(578\) | −1.22060e46 | −3.27162 | ||||||||
\(579\) | 3.56511e44 | 0.0928702 | ||||||||
\(580\) | 6.31970e45 | 1.60005 | ||||||||
\(581\) | 2.27624e45 | 0.560159 | ||||||||
\(582\) | −3.69978e45 | −0.885006 | ||||||||
\(583\) | −7.51473e44 | −0.174736 | ||||||||
\(584\) | 1.26700e46 | 2.86394 | ||||||||
\(585\) | −1.03698e45 | −0.227877 | ||||||||
\(586\) | 2.40426e45 | 0.513654 | ||||||||
\(587\) | 1.91072e45 | 0.396889 | 0.198444 | − | 0.980112i | \(-0.436411\pi\) | ||||
0.198444 | + | 0.980112i | \(0.436411\pi\) | |||||||
\(588\) | −5.22278e45 | −1.05481 | ||||||||
\(589\) | −7.28827e43 | −0.0143127 | ||||||||
\(590\) | −4.08346e45 | −0.779777 | ||||||||
\(591\) | −4.75400e45 | −0.882808 | ||||||||
\(592\) | −5.40689e45 | −0.976426 | ||||||||
\(593\) | 8.87275e45 | 1.55832 | 0.779158 | − | 0.626827i | \(-0.215647\pi\) | ||||
0.779158 | + | 0.626827i | \(0.215647\pi\) | |||||||
\(594\) | −6.19606e45 | −1.05837 | ||||||||
\(595\) | 3.70126e45 | 0.614921 | ||||||||
\(596\) | 3.60431e45 | 0.582451 | ||||||||
\(597\) | 5.61707e45 | 0.882945 | ||||||||
\(598\) | 1.02045e46 | 1.56036 | ||||||||
\(599\) | −1.96939e45 | −0.292947 | −0.146474 | − | 0.989215i | \(-0.546792\pi\) | ||||
−0.146474 | + | 0.989215i | \(0.546792\pi\) | |||||||
\(600\) | 8.45959e45 | 1.22420 | ||||||||
\(601\) | 6.49113e45 | 0.913885 | 0.456942 | − | 0.889496i | \(-0.348945\pi\) | ||||
0.456942 | + | 0.889496i | \(0.348945\pi\) | |||||||
\(602\) | −1.66583e46 | −2.28185 | ||||||||
\(603\) | −3.00827e45 | −0.400941 | ||||||||
\(604\) | −2.81996e46 | −3.65707 | ||||||||
\(605\) | 3.32846e45 | 0.420029 | ||||||||
\(606\) | 1.10421e46 | 1.35598 | ||||||||
\(607\) | −1.08656e46 | −1.29849 | −0.649247 | − | 0.760577i | \(-0.724916\pi\) | ||||
−0.649247 | + | 0.760577i | \(0.724916\pi\) | |||||||
\(608\) | 1.79761e45 | 0.209068 | ||||||||
\(609\) | −4.43896e45 | −0.502454 | ||||||||
\(610\) | −3.42835e44 | −0.0377696 | ||||||||
\(611\) | −6.20043e45 | −0.664877 | ||||||||
\(612\) | 1.87490e46 | 1.95695 | ||||||||
\(613\) | 8.70542e45 | 0.884488 | 0.442244 | − | 0.896895i | \(-0.354182\pi\) | ||||
0.442244 | + | 0.896895i | \(0.354182\pi\) | |||||||
\(614\) | 5.00703e45 | 0.495224 | ||||||||
\(615\) | 2.35701e45 | 0.226945 | ||||||||
\(616\) | 9.40640e45 | 0.881742 | ||||||||
\(617\) | −1.12685e46 | −1.02840 | −0.514199 | − | 0.857671i | \(-0.671911\pi\) | ||||
−0.514199 | + | 0.857671i | \(0.671911\pi\) | |||||||
\(618\) | 1.55113e46 | 1.37828 | ||||||||
\(619\) | −1.07685e46 | −0.931663 | −0.465831 | − | 0.884874i | \(-0.654245\pi\) | ||||
−0.465831 | + | 0.884874i | \(0.654245\pi\) | |||||||
\(620\) | −2.17145e45 | −0.182931 | ||||||||
\(621\) | −1.38099e46 | −1.13287 | ||||||||
\(622\) | 3.85433e46 | 3.07898 | ||||||||
\(623\) | 3.41959e45 | 0.266025 | ||||||||
\(624\) | −1.82473e46 | −1.38246 | ||||||||
\(625\) | 1.02173e45 | 0.0753905 | ||||||||
\(626\) | −2.01923e46 | −1.45114 | ||||||||
\(627\) | 6.14858e44 | 0.0430388 | ||||||||
\(628\) | −5.77622e46 | −3.93831 | ||||||||
\(629\) | 1.00671e46 | 0.668605 | ||||||||
\(630\) | −5.13450e45 | −0.332184 | ||||||||
\(631\) | 2.47581e46 | 1.56039 | 0.780196 | − | 0.625535i | \(-0.215119\pi\) | ||||
0.780196 | + | 0.625535i | \(0.215119\pi\) | |||||||
\(632\) | 1.16481e46 | 0.715190 | ||||||||
\(633\) | −2.99206e45 | −0.178982 | ||||||||
\(634\) | 1.54687e46 | 0.901531 | ||||||||
\(635\) | 1.43500e46 | 0.814864 | ||||||||
\(636\) | 1.01879e46 | 0.563691 | ||||||||
\(637\) | 8.95698e45 | 0.482904 | ||||||||
\(638\) | −2.11865e46 | −1.11306 | ||||||||
\(639\) | −2.05003e45 | −0.104953 | ||||||||
\(640\) | 3.70407e44 | 0.0184803 | ||||||||
\(641\) | −6.66844e45 | −0.324240 | −0.162120 | − | 0.986771i | \(-0.551833\pi\) | ||||
−0.162120 | + | 0.986771i | \(0.551833\pi\) | |||||||
\(642\) | −6.47567e45 | −0.306872 | ||||||||
\(643\) | −8.88748e42 | −0.000410485 0 | −0.000205243 | − | 1.00000i | \(-0.500065\pi\) | ||||
−0.000205243 | 1.00000i | \(0.500065\pi\) | ||||||||
\(644\) | 3.57459e46 | 1.60920 | ||||||||
\(645\) | −1.90274e46 | −0.834919 | ||||||||
\(646\) | −8.03845e45 | −0.343824 | ||||||||
\(647\) | −1.36920e46 | −0.570884 | −0.285442 | − | 0.958396i | \(-0.592140\pi\) | ||||
−0.285442 | + | 0.958396i | \(0.592140\pi\) | |||||||
\(648\) | 1.78945e46 | 0.727330 | ||||||||
\(649\) | 9.68495e45 | 0.383760 | ||||||||
\(650\) | −2.47363e46 | −0.955575 | ||||||||
\(651\) | 1.52523e45 | 0.0574444 | ||||||||
\(652\) | 5.84545e46 | 2.14651 | ||||||||
\(653\) | −1.32140e46 | −0.473115 | −0.236557 | − | 0.971618i | \(-0.576019\pi\) | ||||
−0.236557 | + | 0.971618i | \(0.576019\pi\) | |||||||
\(654\) | −4.05520e46 | −1.41573 | ||||||||
\(655\) | 5.94840e45 | 0.202497 | ||||||||
\(656\) | −3.92527e46 | −1.30304 | ||||||||
\(657\) | 1.64028e46 | 0.530995 | ||||||||
\(658\) | −3.07007e46 | −0.969215 | ||||||||
\(659\) | 3.14029e46 | 0.966852 | 0.483426 | − | 0.875385i | \(-0.339392\pi\) | ||||
0.483426 | + | 0.875385i | \(0.339392\pi\) | |||||||
\(660\) | 1.83189e46 | 0.550078 | ||||||||
\(661\) | −5.62366e46 | −1.64701 | −0.823503 | − | 0.567313i | \(-0.807983\pi\) | ||||
−0.823503 | + | 0.567313i | \(0.807983\pi\) | |||||||
\(662\) | 4.99331e46 | 1.42637 | ||||||||
\(663\) | 3.39747e46 | 0.946635 | ||||||||
\(664\) | −8.63851e46 | −2.34782 | ||||||||
\(665\) | 1.55739e45 | 0.0412896 | ||||||||
\(666\) | −1.39654e46 | −0.361184 | ||||||||
\(667\) | −4.72211e46 | −1.19141 | ||||||||
\(668\) | 1.40826e47 | 3.46635 | ||||||||
\(669\) | 2.48866e46 | 0.597634 | ||||||||
\(670\) | 3.84269e46 | 0.900328 | ||||||||
\(671\) | 8.13119e44 | 0.0185880 | ||||||||
\(672\) | −3.76188e46 | −0.839097 | ||||||||
\(673\) | 1.86687e45 | 0.0406317 | 0.0203159 | − | 0.999794i | \(-0.493533\pi\) | ||||
0.0203159 | + | 0.999794i | \(0.493533\pi\) | |||||||
\(674\) | 9.75848e46 | 2.07250 | ||||||||
\(675\) | 3.34760e46 | 0.693779 | ||||||||
\(676\) | −4.42685e46 | −0.895311 | ||||||||
\(677\) | −3.19535e46 | −0.630674 | −0.315337 | − | 0.948980i | \(-0.602118\pi\) | ||||
−0.315337 | + | 0.948980i | \(0.602118\pi\) | |||||||
\(678\) | −1.25000e47 | −2.40780 | ||||||||
\(679\) | 2.22264e46 | 0.417847 | ||||||||
\(680\) | −1.40466e47 | −2.57735 | ||||||||
\(681\) | −1.39912e46 | −0.250570 | ||||||||
\(682\) | 7.27967e45 | 0.127253 | ||||||||
\(683\) | −9.67204e46 | −1.65035 | −0.825176 | − | 0.564876i | \(-0.808924\pi\) | ||||
−0.825176 | + | 0.564876i | \(0.808924\pi\) | |||||||
\(684\) | 7.88910e45 | 0.131402 | ||||||||
\(685\) | −1.79496e46 | −0.291851 | ||||||||
\(686\) | 1.17232e47 | 1.86080 | ||||||||
\(687\) | 4.92181e46 | 0.762673 | ||||||||
\(688\) | 3.16875e47 | 4.79379 | ||||||||
\(689\) | −1.74720e46 | −0.258063 | ||||||||
\(690\) | 5.77124e46 | 0.832261 | ||||||||
\(691\) | −4.21417e46 | −0.593368 | −0.296684 | − | 0.954976i | \(-0.595881\pi\) | ||||
−0.296684 | + | 0.954976i | \(0.595881\pi\) | |||||||
\(692\) | −2.96176e47 | −4.07192 | ||||||||
\(693\) | 1.21777e46 | 0.163481 | ||||||||
\(694\) | −8.31128e46 | −1.08952 | ||||||||
\(695\) | 7.28813e46 | 0.932968 | ||||||||
\(696\) | 1.68462e47 | 2.10596 | ||||||||
\(697\) | 7.30848e46 | 0.892249 | ||||||||
\(698\) | −9.22827e46 | −1.10029 | ||||||||
\(699\) | 3.81445e45 | 0.0444180 | ||||||||
\(700\) | −8.66499e46 | −0.985485 | ||||||||
\(701\) | 1.07382e47 | 1.19284 | 0.596422 | − | 0.802671i | \(-0.296589\pi\) | ||||
0.596422 | + | 0.802671i | \(0.296589\pi\) | |||||||
\(702\) | −1.44061e47 | −1.56309 | ||||||||
\(703\) | 4.23598e45 | 0.0448943 | ||||||||
\(704\) | −5.34024e46 | −0.552856 | ||||||||
\(705\) | −3.50669e46 | −0.354631 | ||||||||
\(706\) | 1.67517e47 | 1.65494 | ||||||||
\(707\) | −6.63351e46 | −0.640211 | ||||||||
\(708\) | −1.31301e47 | −1.23799 | ||||||||
\(709\) | 9.99645e46 | 0.920837 | 0.460419 | − | 0.887702i | \(-0.347699\pi\) | ||||
0.460419 | + | 0.887702i | \(0.347699\pi\) | |||||||
\(710\) | 2.61866e46 | 0.235677 | ||||||||
\(711\) | 1.50798e46 | 0.132602 | ||||||||
\(712\) | −1.29776e47 | −1.11500 | ||||||||
\(713\) | 1.62251e46 | 0.136211 | ||||||||
\(714\) | 1.68222e47 | 1.37994 | ||||||||
\(715\) | −3.14166e46 | −0.251831 | ||||||||
\(716\) | 1.53299e47 | 1.20081 | ||||||||
\(717\) | −9.78940e46 | −0.749359 | ||||||||
\(718\) | −2.02449e47 | −1.51448 | ||||||||
\(719\) | −7.93598e46 | −0.580195 | −0.290097 | − | 0.956997i | \(-0.593688\pi\) | ||||
−0.290097 | + | 0.956997i | \(0.593688\pi\) | |||||||
\(720\) | 9.76690e46 | 0.697863 | ||||||||
\(721\) | −9.31838e46 | −0.650741 | ||||||||
\(722\) | 2.67498e47 | 1.82581 | ||||||||
\(723\) | −1.63165e47 | −1.08854 | ||||||||
\(724\) | 4.97151e46 | 0.324192 | ||||||||
\(725\) | 1.14466e47 | 0.729626 | ||||||||
\(726\) | 1.51278e47 | 0.942587 | ||||||||
\(727\) | 1.33485e47 | 0.813046 | 0.406523 | − | 0.913641i | \(-0.366741\pi\) | ||||
0.406523 | + | 0.913641i | \(0.366741\pi\) | |||||||
\(728\) | 2.18702e47 | 1.30222 | ||||||||
\(729\) | 1.54343e47 | 0.898427 | ||||||||
\(730\) | −2.09526e47 | −1.19237 | ||||||||
\(731\) | −5.89992e47 | −3.28254 | ||||||||
\(732\) | −1.10236e46 | −0.0599641 | ||||||||
\(733\) | 8.41792e46 | 0.447702 | 0.223851 | − | 0.974623i | \(-0.428137\pi\) | ||||
0.223851 | + | 0.974623i | \(0.428137\pi\) | |||||||
\(734\) | −1.22843e47 | −0.638802 | ||||||||
\(735\) | 5.06568e46 | 0.257571 | ||||||||
\(736\) | −4.00184e47 | −1.98965 | ||||||||
\(737\) | −9.11389e46 | −0.443088 | ||||||||
\(738\) | −1.01385e47 | −0.481998 | ||||||||
\(739\) | 2.39720e47 | 1.11448 | 0.557239 | − | 0.830352i | \(-0.311861\pi\) | ||||
0.557239 | + | 0.830352i | \(0.311861\pi\) | |||||||
\(740\) | 1.26206e47 | 0.573793 | ||||||||
\(741\) | 1.42957e46 | 0.0635630 | ||||||||
\(742\) | −8.65106e46 | −0.376188 | ||||||||
\(743\) | 4.51636e47 | 1.92076 | 0.960380 | − | 0.278695i | \(-0.0899020\pi\) | ||||
0.960380 | + | 0.278695i | \(0.0899020\pi\) | |||||||
\(744\) | −5.78836e46 | −0.240770 | ||||||||
\(745\) | −3.49589e46 | −0.142226 | ||||||||
\(746\) | 1.16643e47 | 0.464160 | ||||||||
\(747\) | −1.11836e47 | −0.435304 | ||||||||
\(748\) | 5.68023e47 | 2.16267 | ||||||||
\(749\) | 3.89025e46 | 0.144886 | ||||||||
\(750\) | −3.54710e47 | −1.29230 | ||||||||
\(751\) | −2.31769e46 | −0.0826030 | −0.0413015 | − | 0.999147i | \(-0.513150\pi\) | ||||
−0.0413015 | + | 0.999147i | \(0.513150\pi\) | |||||||
\(752\) | 5.83991e47 | 2.03616 | ||||||||
\(753\) | 1.62147e47 | 0.553085 | ||||||||
\(754\) | −4.92594e47 | −1.64385 | ||||||||
\(755\) | 2.73514e47 | 0.893006 | ||||||||
\(756\) | −5.04635e47 | −1.61201 | ||||||||
\(757\) | −6.14297e46 | −0.191998 | −0.0959989 | − | 0.995381i | \(-0.530605\pi\) | ||||
−0.0959989 | + | 0.995381i | \(0.530605\pi\) | |||||||
\(758\) | −8.81131e47 | −2.69463 | ||||||||
\(759\) | −1.36880e47 | −0.409590 | ||||||||
\(760\) | −5.91044e46 | −0.173059 | ||||||||
\(761\) | −4.18126e47 | −1.19801 | −0.599004 | − | 0.800746i | \(-0.704437\pi\) | ||||
−0.599004 | + | 0.800746i | \(0.704437\pi\) | |||||||
\(762\) | 6.52205e47 | 1.82863 | ||||||||
\(763\) | 2.43616e47 | 0.668421 | ||||||||
\(764\) | −1.45009e46 | −0.0389362 | ||||||||
\(765\) | −1.81850e47 | −0.477860 | ||||||||
\(766\) | 1.16952e48 | 3.00769 | ||||||||
\(767\) | 2.25179e47 | 0.566766 | ||||||||
\(768\) | −2.82528e47 | −0.695987 | ||||||||
\(769\) | −2.07493e47 | −0.500286 | −0.250143 | − | 0.968209i | \(-0.580478\pi\) | ||||
−0.250143 | + | 0.968209i | \(0.580478\pi\) | |||||||
\(770\) | −1.55555e47 | −0.367103 | ||||||||
\(771\) | −1.55616e47 | −0.359464 | ||||||||
\(772\) | 1.38584e47 | 0.313348 | ||||||||
\(773\) | −3.82656e47 | −0.846930 | −0.423465 | − | 0.905912i | \(-0.639186\pi\) | ||||
−0.423465 | + | 0.905912i | \(0.639186\pi\) | |||||||
\(774\) | 8.18455e47 | 1.77324 | ||||||||
\(775\) | −3.93306e46 | −0.0834165 | ||||||||
\(776\) | −8.43509e47 | −1.75134 | ||||||||
\(777\) | −8.86469e46 | −0.180184 | ||||||||
\(778\) | −5.20250e47 | −1.03526 | ||||||||
\(779\) | 3.07522e46 | 0.0599112 | ||||||||
\(780\) | 4.25921e47 | 0.812397 | ||||||||
\(781\) | −6.21081e46 | −0.115986 | ||||||||
\(782\) | 1.78952e48 | 3.27209 | ||||||||
\(783\) | 6.66634e47 | 1.19349 | ||||||||
\(784\) | −8.43619e47 | −1.47887 | ||||||||
\(785\) | 5.60247e47 | 0.961679 | ||||||||
\(786\) | 2.70354e47 | 0.454423 | ||||||||
\(787\) | −6.26036e47 | −1.03043 | −0.515213 | − | 0.857062i | \(-0.672287\pi\) | ||||
−0.515213 | + | 0.857062i | \(0.672287\pi\) | |||||||
\(788\) | −1.84799e48 | −2.97863 | ||||||||
\(789\) | −3.00829e47 | −0.474842 | ||||||||
\(790\) | −1.92626e47 | −0.297761 | ||||||||
\(791\) | 7.50935e47 | 1.13682 | ||||||||
\(792\) | −4.62156e47 | −0.685208 | ||||||||
\(793\) | 1.89053e46 | 0.0274521 | ||||||||
\(794\) | −1.46471e48 | −2.08312 | ||||||||
\(795\) | −9.88141e46 | −0.137645 | ||||||||
\(796\) | 2.18348e48 | 2.97910 | ||||||||
\(797\) | 1.56391e47 | 0.209002 | 0.104501 | − | 0.994525i | \(-0.466675\pi\) | ||||
0.104501 | + | 0.994525i | \(0.466675\pi\) | |||||||
\(798\) | 7.07833e46 | 0.0926580 | ||||||||
\(799\) | −1.08734e48 | −1.39425 | ||||||||
\(800\) | 9.70066e47 | 1.21847 | ||||||||
\(801\) | −1.68012e47 | −0.206730 | ||||||||
\(802\) | −7.96201e47 | −0.959722 | ||||||||
\(803\) | 4.96943e47 | 0.586813 | ||||||||
\(804\) | 1.23559e48 | 1.42938 | ||||||||
\(805\) | −3.46706e47 | −0.392943 | ||||||||
\(806\) | 1.69255e47 | 0.187937 | ||||||||
\(807\) | −5.22171e47 | −0.568067 | ||||||||
\(808\) | 2.51747e48 | 2.68335 | ||||||||
\(809\) | 4.01144e47 | 0.418938 | 0.209469 | − | 0.977815i | \(-0.432826\pi\) | ||||
0.209469 | + | 0.977815i | \(0.432826\pi\) | |||||||
\(810\) | −2.95925e47 | −0.302816 | ||||||||
\(811\) | 2.34209e47 | 0.234833 | 0.117417 | − | 0.993083i | \(-0.462539\pi\) | ||||
0.117417 | + | 0.993083i | \(0.462539\pi\) | |||||||
\(812\) | −1.72553e48 | −1.69530 | ||||||||
\(813\) | 1.27608e48 | 1.22853 | ||||||||
\(814\) | −4.23098e47 | −0.399152 | ||||||||
\(815\) | −5.66962e47 | −0.524147 | ||||||||
\(816\) | −3.19993e48 | −2.89903 | ||||||||
\(817\) | −2.48253e47 | −0.220410 | ||||||||
\(818\) | −2.97269e48 | −2.58655 | ||||||||
\(819\) | 2.83137e47 | 0.241442 | ||||||||
\(820\) | 9.16221e47 | 0.765723 | ||||||||
\(821\) | 4.03504e47 | 0.330510 | 0.165255 | − | 0.986251i | \(-0.447155\pi\) | ||||
0.165255 | + | 0.986251i | \(0.447155\pi\) | |||||||
\(822\) | −8.15807e47 | −0.654942 | ||||||||
\(823\) | 1.82505e48 | 1.43608 | 0.718039 | − | 0.696002i | \(-0.245040\pi\) | ||||
0.718039 | + | 0.696002i | \(0.245040\pi\) | |||||||
\(824\) | 3.53640e48 | 2.72749 | ||||||||
\(825\) | 3.31803e47 | 0.250836 | ||||||||
\(826\) | 1.11494e48 | 0.826195 | ||||||||
\(827\) | 7.52706e47 | 0.546744 | 0.273372 | − | 0.961908i | \(-0.411861\pi\) | ||||
0.273372 | + | 0.961908i | \(0.411861\pi\) | |||||||
\(828\) | −1.75627e48 | −1.25052 | ||||||||
\(829\) | −2.19354e48 | −1.53107 | −0.765537 | − | 0.643392i | \(-0.777526\pi\) | ||||
−0.765537 | + | 0.643392i | \(0.777526\pi\) | |||||||
\(830\) | 1.42857e48 | 0.977489 | ||||||||
\(831\) | −7.47306e47 | −0.501281 | ||||||||
\(832\) | −1.24162e48 | −0.816499 | ||||||||
\(833\) | 1.57074e48 | 1.01265 | ||||||||
\(834\) | 3.31244e48 | 2.09367 | ||||||||
\(835\) | −1.36590e48 | −0.846433 | ||||||||
\(836\) | 2.39009e47 | 0.145215 | ||||||||
\(837\) | −2.29055e47 | −0.136449 | ||||||||
\(838\) | −2.73408e48 | −1.59693 | ||||||||
\(839\) | −2.86394e48 | −1.64018 | −0.820091 | − | 0.572233i | \(-0.806077\pi\) | ||||
−0.820091 | + | 0.572233i | \(0.806077\pi\) | |||||||
\(840\) | 1.23688e48 | 0.694578 | ||||||||
\(841\) | 4.63381e47 | 0.255155 | ||||||||
\(842\) | 3.54978e48 | 1.91669 | ||||||||
\(843\) | −1.54943e48 | −0.820382 | ||||||||
\(844\) | −1.16308e48 | −0.603892 | ||||||||
\(845\) | 4.29368e47 | 0.218622 | ||||||||
\(846\) | 1.50839e48 | 0.753185 | ||||||||
\(847\) | −9.08800e47 | −0.445033 | ||||||||
\(848\) | 1.64561e48 | 0.790308 | ||||||||
\(849\) | −8.06680e47 | −0.379948 | ||||||||
\(850\) | −4.33788e48 | −2.00385 | ||||||||
\(851\) | −9.43013e47 | −0.427248 | ||||||||
\(852\) | 8.42012e47 | 0.374166 | ||||||||
\(853\) | 4.28657e48 | 1.86832 | 0.934158 | − | 0.356859i | \(-0.116152\pi\) | ||||
0.934158 | + | 0.356859i | \(0.116152\pi\) | |||||||
\(854\) | 9.36073e46 | 0.0400180 | ||||||||
\(855\) | −7.65179e46 | −0.0320865 | ||||||||
\(856\) | −1.47638e48 | −0.607270 | ||||||||
\(857\) | −8.64522e47 | −0.348813 | −0.174406 | − | 0.984674i | \(-0.555801\pi\) | ||||
−0.174406 | + | 0.984674i | \(0.555801\pi\) | |||||||
\(858\) | −1.42788e48 | −0.565134 | ||||||||
\(859\) | 2.35883e48 | 0.915817 | 0.457909 | − | 0.888999i | \(-0.348599\pi\) | ||||
0.457909 | + | 0.888999i | \(0.348599\pi\) | |||||||
\(860\) | −7.39639e48 | −2.81705 | ||||||||
\(861\) | −6.43555e47 | −0.240455 | ||||||||
\(862\) | 3.68860e48 | 1.35205 | ||||||||
\(863\) | −6.27316e46 | −0.0225584 | −0.0112792 | − | 0.999936i | \(-0.503590\pi\) | ||||
−0.0112792 | + | 0.999936i | \(0.503590\pi\) | |||||||
\(864\) | 5.64951e48 | 1.99312 | ||||||||
\(865\) | 2.87267e48 | 0.994304 | ||||||||
\(866\) | 4.49666e48 | 1.52702 | ||||||||
\(867\) | 3.80669e48 | 1.26833 | ||||||||
\(868\) | 5.92890e47 | 0.193820 | ||||||||
\(869\) | 4.56861e47 | 0.146541 | ||||||||
\(870\) | −2.78590e48 | −0.876793 | ||||||||
\(871\) | −2.11901e48 | −0.654386 | ||||||||
\(872\) | −9.24541e48 | −2.80159 | ||||||||
\(873\) | −1.09203e48 | −0.324712 | ||||||||
\(874\) | 7.52982e47 | 0.219708 | ||||||||
\(875\) | 2.13092e48 | 0.610145 | ||||||||
\(876\) | −6.73715e48 | −1.89303 | ||||||||
\(877\) | −2.00783e48 | −0.553647 | −0.276823 | − | 0.960921i | \(-0.589282\pi\) | ||||
−0.276823 | + | 0.960921i | \(0.589282\pi\) | |||||||
\(878\) | −2.57194e48 | −0.695988 | ||||||||
\(879\) | −7.49818e47 | −0.199131 | ||||||||
\(880\) | 2.95899e48 | 0.771223 | ||||||||
\(881\) | −4.20296e48 | −1.07511 | −0.537555 | − | 0.843229i | \(-0.680652\pi\) | ||||
−0.537555 | + | 0.843229i | \(0.680652\pi\) | |||||||
\(882\) | −2.17898e48 | −0.547042 | ||||||||
\(883\) | 7.94997e48 | 1.95891 | 0.979453 | − | 0.201672i | \(-0.0646376\pi\) | ||||
0.979453 | + | 0.201672i | \(0.0646376\pi\) | |||||||
\(884\) | 1.32067e49 | 3.19399 | ||||||||
\(885\) | 1.27351e48 | 0.302301 | ||||||||
\(886\) | −1.77675e48 | −0.413971 | ||||||||
\(887\) | −7.43922e48 | −1.70133 | −0.850664 | − | 0.525710i | \(-0.823800\pi\) | ||||
−0.850664 | + | 0.525710i | \(0.823800\pi\) | |||||||
\(888\) | 3.36422e48 | 0.755216 | ||||||||
\(889\) | −3.91811e48 | −0.863371 | ||||||||
\(890\) | 2.14614e48 | 0.464219 | ||||||||
\(891\) | 7.01859e47 | 0.149028 | ||||||||
\(892\) | 9.67400e48 | 2.01644 | ||||||||
\(893\) | −4.57523e47 | −0.0936189 | ||||||||
\(894\) | −1.58888e48 | −0.319170 | ||||||||
\(895\) | −1.48688e48 | −0.293222 | ||||||||
\(896\) | −1.01136e47 | −0.0195804 | ||||||||
\(897\) | −3.18250e48 | −0.604913 | ||||||||
\(898\) | 5.22659e47 | 0.0975345 | ||||||||
\(899\) | −7.83220e47 | −0.143499 | ||||||||
\(900\) | 4.25728e48 | 0.765828 | ||||||||
\(901\) | −3.06398e48 | −0.541161 | ||||||||
\(902\) | −3.07159e48 | −0.532666 | ||||||||
\(903\) | 5.19523e48 | 0.884620 | ||||||||
\(904\) | −2.84986e49 | −4.76480 | ||||||||
\(905\) | −4.82197e47 | −0.0791631 | ||||||||
\(906\) | 1.24311e49 | 2.00399 | ||||||||
\(907\) | 8.96944e48 | 1.41986 | 0.709929 | − | 0.704273i | \(-0.248727\pi\) | ||||
0.709929 | + | 0.704273i | \(0.248727\pi\) | |||||||
\(908\) | −5.43871e48 | −0.845433 | ||||||||
\(909\) | 3.25918e48 | 0.497513 | ||||||||
\(910\) | −3.61672e48 | −0.542166 | ||||||||
\(911\) | 2.25421e48 | 0.331850 | 0.165925 | − | 0.986138i | \(-0.446939\pi\) | ||||
0.165925 | + | 0.986138i | \(0.446939\pi\) | |||||||
\(912\) | −1.34645e48 | −0.194659 | ||||||||
\(913\) | −3.38820e48 | −0.481063 | ||||||||
\(914\) | 1.39679e49 | 1.94769 | ||||||||
\(915\) | 1.06920e47 | 0.0146424 | ||||||||
\(916\) | 1.91322e49 | 2.57329 | ||||||||
\(917\) | −1.62415e48 | −0.214551 | ||||||||
\(918\) | −2.52632e49 | −3.27781 | ||||||||
\(919\) | −7.04277e48 | −0.897507 | −0.448754 | − | 0.893656i | \(-0.648132\pi\) | ||||
−0.448754 | + | 0.893656i | \(0.648132\pi\) | |||||||
\(920\) | 1.31578e49 | 1.64696 | ||||||||
\(921\) | −1.56155e48 | −0.191987 | ||||||||
\(922\) | −1.62673e49 | −1.96452 | ||||||||
\(923\) | −1.44404e48 | −0.171297 | ||||||||
\(924\) | −5.00178e48 | −0.582823 | ||||||||
\(925\) | 2.28591e48 | 0.261650 | ||||||||
\(926\) | 1.17335e49 | 1.31931 | ||||||||
\(927\) | 4.57831e48 | 0.505696 | ||||||||
\(928\) | 1.93177e49 | 2.09611 | ||||||||
\(929\) | 1.56732e49 | 1.67070 | 0.835348 | − | 0.549721i | \(-0.185266\pi\) | ||||
0.835348 | + | 0.549721i | \(0.185266\pi\) | |||||||
\(930\) | 9.57233e47 | 0.100242 | ||||||||
\(931\) | 6.60926e47 | 0.0679959 | ||||||||
\(932\) | 1.48276e48 | 0.149868 | ||||||||
\(933\) | −1.20205e49 | −1.19365 | ||||||||
\(934\) | −1.95123e49 | −1.90364 | ||||||||
\(935\) | −5.50937e48 | −0.528093 | ||||||||
\(936\) | −1.07453e49 | −1.01197 | ||||||||
\(937\) | 4.17295e48 | 0.386136 | 0.193068 | − | 0.981185i | \(-0.438156\pi\) | ||||
0.193068 | + | 0.981185i | \(0.438156\pi\) | |||||||
\(938\) | −1.04920e49 | −0.953922 | ||||||||
\(939\) | 6.29740e48 | 0.562573 | ||||||||
\(940\) | −1.36313e49 | −1.19654 | ||||||||
\(941\) | −5.21719e48 | −0.449995 | −0.224998 | − | 0.974359i | \(-0.572237\pi\) | ||||
−0.224998 | + | 0.974359i | \(0.572237\pi\) | |||||||
\(942\) | 2.54631e49 | 2.15810 | ||||||||
\(943\) | −6.84604e48 | −0.570160 | ||||||||
\(944\) | −2.12086e49 | −1.73570 | ||||||||
\(945\) | 4.89456e48 | 0.393630 | ||||||||
\(946\) | 2.47960e49 | 1.95965 | ||||||||
\(947\) | −1.05918e49 | −0.822616 | −0.411308 | − | 0.911496i | \(-0.634928\pi\) | ||||
−0.411308 | + | 0.911496i | \(0.634928\pi\) | |||||||
\(948\) | −6.19376e48 | −0.472734 | ||||||||
\(949\) | 1.15541e49 | 0.866650 | ||||||||
\(950\) | −1.82527e48 | −0.134551 | ||||||||
\(951\) | −4.82423e48 | −0.349502 | ||||||||
\(952\) | 3.83527e49 | 2.73078 | ||||||||
\(953\) | 1.49599e49 | 1.04688 | 0.523438 | − | 0.852064i | \(-0.324649\pi\) | ||||
0.523438 | + | 0.852064i | \(0.324649\pi\) | |||||||
\(954\) | 4.25044e48 | 0.292338 | ||||||||
\(955\) | 1.40647e47 | 0.00950767 | ||||||||
\(956\) | −3.80536e49 | −2.52837 | ||||||||
\(957\) | 6.60745e48 | 0.431506 | ||||||||
\(958\) | 4.17619e49 | 2.68071 | ||||||||
\(959\) | 4.90095e48 | 0.309224 | ||||||||
\(960\) | −7.02209e48 | −0.435503 | ||||||||
\(961\) | −1.61344e49 | −0.983594 | ||||||||
\(962\) | −9.83718e48 | −0.589498 | ||||||||
\(963\) | −1.91136e48 | −0.112592 | ||||||||
\(964\) | −6.34261e49 | −3.67280 | ||||||||
\(965\) | −1.34415e48 | −0.0765152 | ||||||||
\(966\) | −1.57578e49 | −0.881803 | ||||||||
\(967\) | −2.39619e49 | −1.31821 | −0.659106 | − | 0.752050i | \(-0.729065\pi\) | ||||
−0.659106 | + | 0.752050i | \(0.729065\pi\) | |||||||
\(968\) | 3.44897e49 | 1.86529 | ||||||||
\(969\) | 2.50696e48 | 0.133292 | ||||||||
\(970\) | 1.39493e49 | 0.729151 | ||||||||
\(971\) | −1.35152e47 | −0.00694552 | −0.00347276 | − | 0.999994i | \(-0.501105\pi\) | ||||
−0.00347276 | + | 0.999994i | \(0.501105\pi\) | |||||||
\(972\) | 4.14760e49 | 2.09558 | ||||||||
\(973\) | −1.98994e49 | −0.988505 | ||||||||
\(974\) | 2.66999e49 | 1.30403 | ||||||||
\(975\) | 7.71454e48 | 0.370454 | ||||||||
\(976\) | −1.78061e48 | −0.0840711 | ||||||||
\(977\) | 1.84460e48 | 0.0856333 | 0.0428166 | − | 0.999083i | \(-0.486367\pi\) | ||||
0.0428166 | + | 0.999083i | \(0.486367\pi\) | |||||||
\(978\) | −2.57683e49 | −1.17624 | ||||||||
\(979\) | −5.09011e48 | −0.228461 | ||||||||
\(980\) | 1.96914e49 | 0.869055 | ||||||||
\(981\) | −1.19693e49 | −0.519435 | ||||||||
\(982\) | 4.53233e48 | 0.193411 | ||||||||
\(983\) | −6.69809e48 | −0.281072 | −0.140536 | − | 0.990076i | \(-0.544883\pi\) | ||||
−0.140536 | + | 0.990076i | \(0.544883\pi\) | |||||||
\(984\) | 2.44234e49 | 1.00783 | ||||||||
\(985\) | 1.79240e49 | 0.727340 | ||||||||
\(986\) | −8.63836e49 | −3.44717 | ||||||||
\(987\) | 9.57464e48 | 0.375742 | ||||||||
\(988\) | 5.55705e48 | 0.214464 | ||||||||
\(989\) | 5.52661e49 | 2.09759 | ||||||||
\(990\) | 7.64276e48 | 0.285279 | ||||||||
\(991\) | 1.17168e49 | 0.430123 | 0.215062 | − | 0.976600i | \(-0.431005\pi\) | ||||
0.215062 | + | 0.976600i | \(0.431005\pi\) | |||||||
\(992\) | −6.63755e48 | −0.239643 | ||||||||
\(993\) | −1.55727e49 | −0.552969 | ||||||||
\(994\) | −7.14997e48 | −0.249706 | ||||||||
\(995\) | −2.11780e49 | −0.727453 | ||||||||
\(996\) | 4.59345e49 | 1.55189 | ||||||||
\(997\) | 2.44007e49 | 0.810834 | 0.405417 | − | 0.914132i | \(-0.367126\pi\) | ||||
0.405417 | + | 0.914132i | \(0.367126\pi\) | |||||||
\(998\) | −5.68168e49 | −1.85705 | ||||||||
\(999\) | 1.33128e49 | 0.427995 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1.34.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 9.34.a.b.1.2 | 2 | |||
4.3 | odd | 2 | 16.34.a.b.1.1 | 2 | |||
5.2 | odd | 4 | 25.34.b.a.24.1 | 4 | |||
5.3 | odd | 4 | 25.34.b.a.24.4 | 4 | |||
5.4 | even | 2 | 25.34.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.34.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.34.a.b.1.2 | 2 | 3.2 | odd | 2 | |||
16.34.a.b.1.1 | 2 | 4.3 | odd | 2 | |||
25.34.a.a.1.2 | 2 | 5.4 | even | 2 | |||
25.34.b.a.24.1 | 4 | 5.2 | odd | 4 | |||
25.34.b.a.24.4 | 4 | 5.3 | odd | 4 |