Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,48,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 48, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 48);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 48 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(125.916896390\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 832803191366x^{2} + 3710135215485780x + 13175318942671469337000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{11}\cdot 5^{3}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-124721.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.54692e6 | 0.130396 | 0.0651980 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651980 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.38345e14 | −0.982997 | ||||||||
\(5\) | −4.23962e16 | −1.59049 | −0.795246 | − | 0.606286i | \(-0.792659\pi\) | ||||
−0.795246 | + | 0.606286i | \(0.792659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.90714e19 | −0.539579 | −0.269790 | − | 0.962919i | \(-0.586954\pi\) | ||||
−0.269790 | + | 0.962919i | \(0.586954\pi\) | |||||||
\(8\) | −4.31719e20 | −0.258575 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.55837e22 | −0.207394 | ||||||||
\(11\) | −2.66558e24 | −0.897561 | −0.448781 | − | 0.893642i | \(-0.648142\pi\) | ||||
−0.448781 | + | 0.893642i | \(0.648142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.26259e26 | 1.50293 | 0.751463 | − | 0.659776i | \(-0.229349\pi\) | ||||
0.751463 | + | 0.659776i | \(0.229349\pi\) | |||||||
\(14\) | −6.04405e25 | −0.0703589 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.88024e28 | 0.949280 | ||||||||
\(17\) | −8.41583e28 | −1.02223 | −0.511114 | − | 0.859513i | \(-0.670767\pi\) | ||||
−0.511114 | + | 0.859513i | \(0.670767\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.16735e29 | 0.281830 | 0.140915 | − | 0.990022i | \(-0.454996\pi\) | ||||
0.140915 | + | 0.990022i | \(0.454996\pi\) | |||||||
\(20\) | 5.86528e30 | 1.56345 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.12345e30 | −0.117038 | ||||||||
\(23\) | −2.26985e31 | −0.226669 | −0.113335 | − | 0.993557i | \(-0.536153\pi\) | ||||
−0.113335 | + | 0.993557i | \(0.536153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.08689e33 | 1.52967 | ||||||||
\(26\) | 3.50006e32 | 0.195975 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.40532e33 | 0.530405 | ||||||||
\(29\) | 3.39685e34 | 1.46125 | 0.730624 | − | 0.682780i | \(-0.239229\pi\) | ||||
0.730624 | + | 0.682780i | \(0.239229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.81646e35 | 1.63015 | 0.815074 | − | 0.579357i | \(-0.196696\pi\) | ||||
0.815074 | + | 0.579357i | \(0.196696\pi\) | |||||||
\(32\) | 8.98449e34 | 0.382357 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.30186e35 | −0.133294 | ||||||||
\(35\) | 1.65648e36 | 0.858197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.13789e36 | −1.00191 | −0.500956 | − | 0.865473i | \(-0.667018\pi\) | ||||
−0.500956 | + | 0.865473i | \(0.667018\pi\) | |||||||
\(38\) | 4.89965e35 | 0.0367494 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.83032e37 | 0.411261 | ||||||||
\(41\) | 2.78383e37 | 0.350124 | 0.175062 | − | 0.984557i | \(-0.443987\pi\) | ||||
0.175062 | + | 0.984557i | \(0.443987\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.92777e37 | −0.202368 | −0.101184 | − | 0.994868i | \(-0.532263\pi\) | ||||
−0.101184 | + | 0.994868i | \(0.532263\pi\) | |||||||
\(44\) | 3.68769e38 | 0.882300 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.51128e37 | −0.0295567 | ||||||||
\(47\) | −1.86825e39 | −0.948716 | −0.474358 | − | 0.880332i | \(-0.657320\pi\) | ||||
−0.474358 | + | 0.880332i | \(0.657320\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.71676e39 | −0.708854 | ||||||||
\(50\) | 1.68134e39 | 0.199462 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.13017e40 | −1.47737 | ||||||||
\(53\) | 2.48904e40 | 0.750843 | 0.375421 | − | 0.926854i | \(-0.377498\pi\) | ||||
0.375421 | + | 0.926854i | \(0.377498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.13011e41 | 1.42756 | ||||||||
\(56\) | 1.68679e40 | 0.139522 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.25467e40 | 0.190541 | ||||||||
\(59\) | −3.69239e40 | −0.0895953 | −0.0447976 | − | 0.998996i | \(-0.514264\pi\) | ||||
−0.0447976 | + | 0.998996i | \(0.514264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.52589e41 | 0.390857 | 0.195429 | − | 0.980718i | \(-0.437390\pi\) | ||||
0.195429 | + | 0.980718i | \(0.437390\pi\) | |||||||
\(62\) | 2.80993e41 | 0.212565 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.50722e42 | −0.899422 | ||||||||
\(65\) | −9.59253e42 | −2.39039 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.26183e42 | −0.154257 | −0.0771283 | − | 0.997021i | \(-0.524575\pi\) | ||||
−0.0771283 | + | 0.997021i | \(0.524575\pi\) | |||||||
\(68\) | 1.16428e43 | 1.00485 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.56245e42 | 0.111905 | ||||||||
\(71\) | 3.26023e43 | 1.02018 | 0.510090 | − | 0.860121i | \(-0.329612\pi\) | ||||
0.510090 | + | 0.860121i | \(0.329612\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.59179e43 | 0.585092 | 0.292546 | − | 0.956251i | \(-0.405498\pi\) | ||||
0.292546 | + | 0.956251i | \(0.405498\pi\) | |||||||
\(74\) | −1.10418e43 | −0.130645 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.38186e43 | −0.277038 | ||||||||
\(77\) | 1.04148e44 | 0.484305 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.82596e44 | −1.48297 | −0.741483 | − | 0.670972i | \(-0.765877\pi\) | ||||
−0.741483 | + | 0.670972i | \(0.765877\pi\) | |||||||
\(80\) | −7.97151e44 | −1.50982 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.30637e43 | 0.0456547 | ||||||||
\(83\) | 3.51619e44 | 0.280373 | 0.140187 | − | 0.990125i | \(-0.455230\pi\) | ||||
0.140187 | + | 0.990125i | \(0.455230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.56799e45 | 1.62584 | ||||||||
\(86\) | −7.62288e43 | −0.0263879 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.15078e45 | 0.232087 | ||||||||
\(89\) | 2.92401e45 | 0.452182 | 0.226091 | − | 0.974106i | \(-0.427405\pi\) | ||||
0.226091 | + | 0.974106i | \(0.427405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.84027e45 | −0.810947 | ||||||||
\(92\) | 3.14021e45 | 0.222815 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.89005e45 | −0.123709 | ||||||||
\(95\) | −1.34284e46 | −0.448248 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.17182e46 | 0.444311 | 0.222156 | − | 0.975011i | \(-0.428691\pi\) | ||||
0.222156 | + | 0.975011i | \(0.428691\pi\) | |||||||
\(98\) | −5.74955e45 | −0.0924317 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.50366e47 | −1.50366 | ||||||||
\(101\) | 5.11557e46 | 0.404894 | 0.202447 | − | 0.979293i | \(-0.435111\pi\) | ||||
0.202447 | + | 0.979293i | \(0.435111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.19569e47 | 1.59547 | 0.797736 | − | 0.603006i | \(-0.206031\pi\) | ||||
0.797736 | + | 0.603006i | \(0.206031\pi\) | |||||||
\(104\) | −9.76803e46 | −0.388618 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.85036e46 | 0.0979068 | ||||||||
\(107\) | −2.00584e47 | −0.409051 | −0.204526 | − | 0.978861i | \(-0.565565\pi\) | ||||
−0.204526 | + | 0.978861i | \(0.565565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.86410e47 | −0.773888 | −0.386944 | − | 0.922103i | \(-0.626469\pi\) | ||||
−0.386944 | + | 0.922103i | \(0.626469\pi\) | |||||||
\(110\) | 1.74819e47 | 0.186149 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.34637e47 | −0.512212 | ||||||||
\(113\) | −3.11593e47 | −0.176297 | −0.0881484 | − | 0.996107i | \(-0.528095\pi\) | ||||
−0.0881484 | + | 0.996107i | \(0.528095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.62329e47 | 0.360516 | ||||||||
\(116\) | −4.69936e48 | −1.43640 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.71184e46 | −0.0116829 | ||||||||
\(119\) | 3.28818e48 | 0.551572 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.71442e48 | −0.194384 | ||||||||
\(122\) | 5.45429e47 | 0.0509662 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.51298e49 | −1.60243 | ||||||||
\(125\) | −1.59559e49 | −0.842432 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.66165e49 | 0.967749 | 0.483875 | − | 0.875137i | \(-0.339229\pi\) | ||||
0.483875 | + | 0.875137i | \(0.339229\pi\) | |||||||
\(128\) | −1.65230e49 | −0.499638 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.48389e49 | −0.311697 | ||||||||
\(131\) | −6.34924e49 | −1.11390 | −0.556950 | − | 0.830546i | \(-0.688028\pi\) | ||||
−0.556950 | + | 0.830546i | \(0.688028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.23753e49 | −0.152069 | ||||||||
\(134\) | −1.95196e48 | −0.0201144 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.63327e49 | 0.264322 | ||||||||
\(137\) | −1.99734e50 | −1.22326 | −0.611631 | − | 0.791143i | \(-0.709486\pi\) | ||||
−0.611631 | + | 0.791143i | \(0.709486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.16608e50 | −1.37935 | −0.689674 | − | 0.724120i | \(-0.742246\pi\) | ||||
−0.689674 | + | 0.724120i | \(0.742246\pi\) | |||||||
\(140\) | −2.29165e50 | −0.843605 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.04332e49 | 0.133027 | ||||||||
\(143\) | −6.03113e50 | −1.34897 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.44014e51 | −2.32410 | ||||||||
\(146\) | 5.55623e49 | 0.0762936 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.87488e50 | 0.984876 | ||||||||
\(149\) | −1.00267e50 | −0.0853651 | −0.0426826 | − | 0.999089i | \(-0.513590\pi\) | ||||
−0.0426826 | + | 0.999089i | \(0.513590\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.40479e49 | −0.0149664 | −0.00748321 | − | 0.999972i | \(-0.502382\pi\) | ||||
−0.00748321 | + | 0.999972i | \(0.502382\pi\) | |||||||
\(152\) | −1.36740e50 | −0.0728740 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.61109e50 | 0.0631514 | ||||||||
\(155\) | −7.70111e51 | −2.59274 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.42274e51 | −0.354391 | −0.177196 | − | 0.984176i | \(-0.556702\pi\) | ||||
−0.177196 | + | 0.984176i | \(0.556702\pi\) | |||||||
\(158\) | −9.01232e50 | −0.193373 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.80908e51 | −0.608136 | ||||||||
\(161\) | 8.86862e50 | 0.122306 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.79256e51 | −0.494492 | −0.247246 | − | 0.968953i | \(-0.579525\pi\) | ||||
−0.247246 | + | 0.968953i | \(0.579525\pi\) | |||||||
\(164\) | −3.85127e51 | −0.344170 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.43927e50 | 0.0365596 | ||||||||
\(167\) | 9.89736e51 | 0.577673 | 0.288837 | − | 0.957378i | \(-0.406732\pi\) | ||||
0.288837 | + | 0.957378i | \(0.406732\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.85292e52 | 1.25878 | ||||||||
\(170\) | 5.51941e51 | 0.212004 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.81729e51 | 0.198927 | ||||||||
\(173\) | 7.43991e52 | 1.89446 | 0.947228 | − | 0.320562i | \(-0.103872\pi\) | ||||
0.947228 | + | 0.320562i | \(0.103872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.24665e52 | −0.825377 | ||||||||
\(176\) | −5.01194e52 | −0.852037 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.52321e51 | 0.0589627 | ||||||||
\(179\) | −3.60632e52 | −0.412115 | −0.206057 | − | 0.978540i | \(-0.566063\pi\) | ||||
−0.206057 | + | 0.978540i | \(0.566063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.19557e52 | 0.545299 | 0.272650 | − | 0.962113i | \(-0.412100\pi\) | ||||
0.272650 | + | 0.962113i | \(0.412100\pi\) | |||||||
\(182\) | −1.36752e52 | −0.105744 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.79935e51 | 0.0586109 | ||||||||
\(185\) | 3.02619e53 | 1.59353 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.24331e53 | 0.917511 | ||||||||
\(188\) | 2.58463e53 | 0.932585 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.07727e52 | −0.0584497 | ||||||||
\(191\) | 3.09862e53 | 0.770699 | 0.385349 | − | 0.922771i | \(-0.374081\pi\) | ||||
0.385349 | + | 0.922771i | \(0.374081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.75475e53 | 0.925829 | 0.462914 | − | 0.886403i | \(-0.346804\pi\) | ||||
0.462914 | + | 0.886403i | \(0.346804\pi\) | |||||||
\(194\) | 3.35963e52 | 0.0579364 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.14194e53 | 0.696802 | ||||||||
\(197\) | 7.61644e53 | 0.915790 | 0.457895 | − | 0.889006i | \(-0.348604\pi\) | ||||
0.457895 | + | 0.889006i | \(0.348604\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.90631e54 | −1.80778 | −0.903890 | − | 0.427765i | \(-0.859301\pi\) | ||||
−0.903890 | + | 0.427765i | \(0.859301\pi\) | |||||||
\(200\) | −4.69232e53 | −0.395533 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.91339e52 | 0.0527965 | ||||||||
\(203\) | −1.32720e54 | −0.788459 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.18024e54 | −0.556869 | ||||||||
\(206\) | 4.94348e53 | 0.208043 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.25422e54 | 1.42670 | ||||||||
\(209\) | −8.44284e53 | −0.252959 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.25520e54 | 0.300660 | 0.150330 | − | 0.988636i | \(-0.451966\pi\) | ||||
0.150330 | + | 0.988636i | \(0.451966\pi\) | |||||||
\(212\) | −3.44345e54 | −0.738076 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.10288e53 | −0.0533386 | ||||||||
\(215\) | 2.08918e54 | 0.321864 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.09718e54 | −0.879594 | ||||||||
\(218\) | −9.07131e53 | −0.100912 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.56344e55 | −1.40329 | ||||||||
\(221\) | −1.90416e55 | −1.53633 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.43141e54 | −0.0934545 | −0.0467272 | − | 0.998908i | \(-0.514879\pi\) | ||||
−0.0467272 | + | 0.998908i | \(0.514879\pi\) | |||||||
\(224\) | −3.51037e54 | −0.206312 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.82011e53 | −0.0229884 | ||||||||
\(227\) | −3.38487e55 | −1.45524 | −0.727619 | − | 0.685982i | \(-0.759373\pi\) | ||||
−0.727619 | + | 0.685982i | \(0.759373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.65218e54 | −0.162750 | −0.0813752 | − | 0.996684i | \(-0.525931\pi\) | ||||
−0.0813752 | + | 0.996684i | \(0.525931\pi\) | |||||||
\(230\) | 1.48865e54 | 0.0470098 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.46649e55 | −0.377842 | ||||||||
\(233\) | 6.87236e55 | 1.60045 | 0.800225 | − | 0.599700i | \(-0.204713\pi\) | ||||
0.800225 | + | 0.599700i | \(0.204713\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.92068e55 | 1.50893 | ||||||||
\(236\) | 5.10822e54 | 0.0880719 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.08657e54 | 0.0719228 | ||||||||
\(239\) | −1.09219e56 | −1.39942 | −0.699710 | − | 0.714427i | \(-0.746687\pi\) | ||||
−0.699710 | + | 0.714427i | \(0.746687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.82622e55 | −0.508401 | −0.254201 | − | 0.967152i | \(-0.581812\pi\) | ||||
−0.254201 | + | 0.967152i | \(0.581812\pi\) | |||||||
\(242\) | −2.65207e54 | −0.0253468 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.87788e55 | −0.384211 | ||||||||
\(245\) | 1.57577e56 | 1.12743 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.16642e55 | 0.423569 | ||||||||
\(248\) | −7.84201e55 | −0.421515 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.46825e55 | −0.109850 | ||||||||
\(251\) | 4.06217e56 | 1.64599 | 0.822993 | − | 0.568052i | \(-0.192303\pi\) | ||||
0.822993 | + | 0.568052i | \(0.192303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.05047e55 | 0.203450 | ||||||||
\(254\) | 4.11736e55 | 0.126191 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.27300e56 | 0.834271 | ||||||||
\(257\) | −1.93698e56 | −0.450501 | −0.225251 | − | 0.974301i | \(-0.572320\pi\) | ||||
−0.225251 | + | 0.974301i | \(0.572320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.78887e56 | 0.540611 | ||||||||
\(260\) | 1.32707e57 | 2.34975 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.82178e55 | −0.145248 | ||||||||
\(263\) | −8.33659e56 | −1.12727 | −0.563636 | − | 0.826023i | \(-0.690598\pi\) | ||||
−0.563636 | + | 0.826023i | \(0.690598\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05526e57 | −1.19421 | ||||||||
\(266\) | −1.91436e55 | −0.0198292 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.74568e56 | 0.151634 | ||||||||
\(269\) | 1.88490e57 | 1.50006 | 0.750032 | − | 0.661402i | \(-0.230038\pi\) | ||||
0.750032 | + | 0.661402i | \(0.230038\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.56612e57 | 1.71593 | 0.857963 | − | 0.513712i | \(-0.171730\pi\) | ||||
0.857963 | + | 0.513712i | \(0.171730\pi\) | |||||||
\(272\) | −1.58238e57 | −0.970380 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.08974e56 | −0.159508 | ||||||||
\(275\) | −2.89721e57 | −1.37297 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.36679e56 | −0.334414 | −0.167207 | − | 0.985922i | \(-0.553475\pi\) | ||||
−0.167207 | + | 0.985922i | \(0.553475\pi\) | |||||||
\(278\) | −4.89768e56 | −0.179861 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.15133e56 | −0.221908 | ||||||||
\(281\) | 3.96974e57 | 1.13283 | 0.566414 | − | 0.824121i | \(-0.308330\pi\) | ||||
0.566414 | + | 0.824121i | \(0.308330\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.45361e57 | −1.07580 | −0.537900 | − | 0.843009i | \(-0.680782\pi\) | ||||
−0.537900 | + | 0.843009i | \(0.680782\pi\) | |||||||
\(284\) | −4.51034e57 | −1.00283 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.32969e56 | −0.175900 | ||||||||
\(287\) | −1.08768e57 | −0.188919 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.04657e56 | 0.0449481 | ||||||||
\(290\) | −2.22778e57 | −0.303054 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.96905e57 | −0.575144 | ||||||||
\(293\) | −1.05167e58 | −1.12328 | −0.561641 | − | 0.827381i | \(-0.689830\pi\) | ||||
−0.561641 | + | 0.827381i | \(0.689830\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.56543e57 | 0.142501 | ||||||||
\(296\) | 3.08156e57 | 0.259069 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.55105e56 | −0.0111313 | ||||||||
\(299\) | −5.13574e57 | −0.340667 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.92535e57 | 0.109193 | ||||||||
\(302\) | −3.72002e55 | −0.00195156 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.95539e57 | 0.267535 | ||||||||
\(305\) | −1.49484e58 | −0.621656 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.43218e57 | 0.193741 | 0.0968707 | − | 0.995297i | \(-0.469117\pi\) | ||||
0.0968707 | + | 0.995297i | \(0.469117\pi\) | |||||||
\(308\) | −1.44083e58 | −0.476071 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.19130e58 | −0.338082 | ||||||||
\(311\) | 4.80030e58 | 1.26299 | 0.631493 | − | 0.775381i | \(-0.282442\pi\) | ||||
0.631493 | + | 0.775381i | \(0.282442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.50321e58 | −0.566507 | −0.283253 | − | 0.959045i | \(-0.591414\pi\) | ||||
−0.283253 | + | 0.959045i | \(0.591414\pi\) | |||||||
\(314\) | −2.20087e57 | −0.0462111 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.05990e58 | 1.45775 | ||||||||
\(317\) | 6.65301e58 | 1.11719 | 0.558593 | − | 0.829442i | \(-0.311341\pi\) | ||||
0.558593 | + | 0.829442i | \(0.311341\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.05460e58 | −1.31156 | ||||||||
\(320\) | 1.06297e59 | 1.43052 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.37191e57 | 0.0159482 | ||||||||
\(323\) | −2.66559e58 | −0.288094 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.45920e59 | 2.29898 | ||||||||
\(326\) | −7.41372e57 | −0.0644797 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.20183e58 | −0.0905331 | ||||||||
\(329\) | 7.29953e58 | 0.511907 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.52984e58 | −0.0930438 | −0.0465219 | − | 0.998917i | \(-0.514814\pi\) | ||||
−0.0465219 | + | 0.998917i | \(0.514814\pi\) | |||||||
\(332\) | −4.86445e58 | −0.275606 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.53105e58 | 0.0753262 | ||||||||
\(335\) | 5.34969e58 | 0.245344 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.19696e59 | −0.477284 | −0.238642 | − | 0.971108i | \(-0.576702\pi\) | ||||
−0.238642 | + | 0.971108i | \(0.576702\pi\) | |||||||
\(338\) | 4.41324e58 | 0.164140 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.93612e59 | −1.59820 | ||||||||
\(341\) | −4.84194e59 | −1.46316 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.50084e59 | 0.922062 | ||||||||
\(344\) | 2.12741e58 | 0.0523272 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.15090e59 | 0.247029 | ||||||||
\(347\) | 6.60768e59 | 1.32528 | 0.662638 | − | 0.748940i | \(-0.269437\pi\) | ||||
0.662638 | + | 0.748940i | \(0.269437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.13810e59 | 1.25079 | 0.625396 | − | 0.780308i | \(-0.284937\pi\) | ||||
0.625396 | + | 0.780308i | \(0.284937\pi\) | |||||||
\(350\) | −6.56924e58 | −0.107626 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.39489e59 | −0.343189 | ||||||||
\(353\) | −4.98386e58 | −0.0668129 | −0.0334064 | − | 0.999442i | \(-0.510636\pi\) | ||||
−0.0334064 | + | 0.999442i | \(0.510636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.38221e60 | −1.62259 | ||||||||
\(356\) | −4.04520e59 | −0.444493 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.57870e58 | −0.0537381 | ||||||||
\(359\) | −2.08989e60 | −1.88540 | −0.942700 | − | 0.333641i | \(-0.891723\pi\) | ||||
−0.942700 | + | 0.333641i | \(0.891723\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.16273e60 | −0.920572 | ||||||||
\(362\) | 9.58408e58 | 0.0711048 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.22300e60 | 0.797159 | ||||||||
\(365\) | −1.52278e60 | −0.930585 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.22059e59 | −0.0656021 | −0.0328011 | − | 0.999462i | \(-0.510443\pi\) | ||||
−0.0328011 | + | 0.999462i | \(0.510443\pi\) | |||||||
\(368\) | −4.26786e59 | −0.215173 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.68129e59 | 0.207790 | ||||||||
\(371\) | −9.72503e59 | −0.405139 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.41910e60 | −0.888172 | −0.444086 | − | 0.895984i | \(-0.646472\pi\) | ||||
−0.444086 | + | 0.895984i | \(0.646472\pi\) | |||||||
\(374\) | 3.47023e59 | 0.119640 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.06560e59 | 0.245314 | ||||||||
\(377\) | 7.68569e60 | 2.19615 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.29795e60 | 1.58920 | 0.794598 | − | 0.607135i | \(-0.207681\pi\) | ||||
0.794598 | + | 0.607135i | \(0.207681\pi\) | |||||||
\(380\) | 1.85774e60 | 0.440626 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.79333e59 | 0.100496 | ||||||||
\(383\) | −3.88964e60 | −0.766898 | −0.383449 | − | 0.923562i | \(-0.625264\pi\) | ||||
−0.383449 | + | 0.923562i | \(0.625264\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.41548e60 | −0.770284 | ||||||||
\(386\) | 7.35523e59 | 0.120724 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.00459e60 | −0.436757 | ||||||||
\(389\) | −5.15774e60 | −0.705739 | −0.352869 | − | 0.935673i | \(-0.614794\pi\) | ||||
−0.352869 | + | 0.935673i | \(0.614794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.91027e60 | 0.231707 | ||||||||
\(392\) | 1.60460e60 | 0.183292 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.17821e60 | 0.119415 | ||||||||
\(395\) | 2.46999e61 | 2.35865 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.92619e61 | −1.63351 | −0.816754 | − | 0.576986i | \(-0.804229\pi\) | ||||
−0.816754 | + | 0.576986i | \(0.804229\pi\) | |||||||
\(398\) | −2.94891e60 | −0.235727 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.04362e61 | 1.45208 | ||||||||
\(401\) | −5.06490e58 | −0.00339374 | −0.00169687 | − | 0.999999i | \(-0.500540\pi\) | ||||
−0.00169687 | + | 0.999999i | \(0.500540\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.10992e61 | 2.44999 | ||||||||
\(404\) | −7.07710e60 | −0.398010 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.05308e60 | −0.102812 | ||||||||
\(407\) | 1.90266e61 | 0.899277 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.50217e61 | 0.632733 | 0.316367 | − | 0.948637i | \(-0.397537\pi\) | ||||
0.316367 | + | 0.948637i | \(0.397537\pi\) | |||||||
\(410\) | −1.82574e60 | −0.0726135 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.42106e61 | −1.56834 | ||||||||
\(413\) | 1.44267e60 | 0.0483437 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.49073e61 | −0.445932 | ||||||||
\(416\) | 2.03282e61 | 0.574654 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.30604e60 | −0.0329849 | ||||||||
\(419\) | −6.95944e61 | −1.66167 | −0.830835 | − | 0.556518i | \(-0.812137\pi\) | ||||
−0.830835 | + | 0.556518i | \(0.812137\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.78966e61 | −0.809042 | −0.404521 | − | 0.914529i | \(-0.632562\pi\) | ||||
−0.404521 | + | 0.914529i | \(0.632562\pi\) | |||||||
\(422\) | 1.94170e60 | 0.0392049 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.07457e61 | −0.194149 | ||||||||
\(425\) | −9.14712e61 | −1.56367 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.37762e61 | −0.210898 | ||||||||
\(428\) | 2.77497e61 | 0.402096 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.23181e60 | 0.0419698 | ||||||||
\(431\) | −4.06747e60 | −0.0500160 | −0.0250080 | − | 0.999687i | \(-0.507961\pi\) | ||||
−0.0250080 | + | 0.999687i | \(0.507961\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.59125e61 | −0.285788 | −0.142894 | − | 0.989738i | \(-0.545641\pi\) | ||||
−0.142894 | + | 0.989738i | \(0.545641\pi\) | |||||||
\(434\) | −1.09788e61 | −0.114695 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.11265e61 | 0.760730 | ||||||||
\(437\) | −7.18941e60 | −0.0638821 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.51058e61 | 0.280196 | 0.140098 | − | 0.990138i | \(-0.455258\pi\) | ||||
0.140098 | + | 0.990138i | \(0.455258\pi\) | |||||||
\(440\) | −4.87888e61 | −0.369132 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.94559e61 | −0.200331 | ||||||||
\(443\) | 4.43894e61 | 0.286281 | 0.143140 | − | 0.989702i | \(-0.454280\pi\) | ||||
0.143140 | + | 0.989702i | \(0.454280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.23967e62 | −0.719192 | ||||||||
\(446\) | −2.21428e60 | −0.0121861 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.79607e61 | 0.485309 | ||||||||
\(449\) | −3.43198e62 | −1.61345 | −0.806725 | − | 0.590927i | \(-0.798762\pi\) | ||||
−0.806725 | + | 0.590927i | \(0.798762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.42052e61 | −0.314257 | ||||||||
\(452\) | 4.31072e61 | 0.173299 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.23613e61 | −0.189757 | ||||||||
\(455\) | 3.74794e62 | 1.28981 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.64466e60 | −0.0299403 | −0.0149701 | − | 0.999888i | \(-0.504765\pi\) | ||||
−0.0149701 | + | 0.999888i | \(0.504765\pi\) | |||||||
\(458\) | −7.19656e60 | −0.0212220 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.33133e62 | −0.354386 | ||||||||
\(461\) | 6.32143e61 | 0.159898 | 0.0799491 | − | 0.996799i | \(-0.474524\pi\) | ||||
0.0799491 | + | 0.996799i | \(0.474524\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.86213e62 | 1.56785 | 0.783927 | − | 0.620853i | \(-0.213214\pi\) | ||||
0.783927 | + | 0.620853i | \(0.213214\pi\) | |||||||
\(464\) | 6.38691e62 | 1.38713 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.06310e62 | 0.208692 | ||||||||
\(467\) | 2.91371e62 | 0.543876 | 0.271938 | − | 0.962315i | \(-0.412335\pi\) | ||||
0.271938 | + | 0.962315i | \(0.412335\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.93016e61 | 0.0832337 | ||||||||
\(470\) | 1.22527e62 | 0.196758 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.59407e61 | 0.0231671 | ||||||||
\(473\) | 1.31354e62 | 0.181637 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.44258e62 | 0.431106 | ||||||||
\(476\) | −4.54902e62 | −0.542194 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.68954e62 | −0.182479 | ||||||||
\(479\) | 9.39830e62 | 0.966417 | 0.483209 | − | 0.875505i | \(-0.339471\pi\) | ||||
0.483209 | + | 0.875505i | \(0.339471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.61501e63 | −1.50580 | ||||||||
\(482\) | −7.46579e61 | −0.0662934 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.37180e62 | 0.191079 | ||||||||
\(485\) | −9.20767e62 | −0.706674 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.39350e63 | 1.66764 | 0.833820 | − | 0.552037i | \(-0.186149\pi\) | ||||
0.833820 | + | 0.552037i | \(0.186149\pi\) | |||||||
\(488\) | −1.52219e62 | −0.101066 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.43759e62 | 0.147012 | ||||||||
\(491\) | −1.23586e63 | −0.710481 | −0.355241 | − | 0.934775i | \(-0.615601\pi\) | ||||
−0.355241 | + | 0.934775i | \(0.615601\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.85874e63 | −1.49373 | ||||||||
\(494\) | 1.10859e62 | 0.0552317 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.41539e63 | 1.54747 | ||||||||
\(497\) | −1.27382e63 | −0.550468 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.94657e63 | −1.15865 | −0.579327 | − | 0.815095i | \(-0.696684\pi\) | ||||
−0.579327 | + | 0.815095i | \(0.696684\pi\) | |||||||
\(500\) | 2.20741e63 | 0.828108 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.28387e62 | 0.214630 | ||||||||
\(503\) | 1.27808e63 | 0.416591 | 0.208296 | − | 0.978066i | \(-0.433208\pi\) | ||||
0.208296 | + | 0.978066i | \(0.433208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.16880e63 | −0.643981 | ||||||||
\(506\) | 9.35961e61 | 0.0265290 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.68224e63 | −0.951294 | ||||||||
\(509\) | −7.25177e63 | −1.78886 | −0.894429 | − | 0.447209i | \(-0.852418\pi\) | ||||
−0.894429 | + | 0.447209i | \(0.852418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.40336e63 | −0.315704 | ||||||||
\(512\) | 2.83172e63 | 0.608423 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.99635e62 | −0.0587435 | ||||||||
\(515\) | −1.35485e64 | −2.53759 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.97998e63 | 0.851531 | ||||||||
\(518\) | 4.31418e62 | 0.0704934 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.14127e63 | 0.618095 | ||||||||
\(521\) | 9.84138e63 | 1.40401 | 0.702004 | − | 0.712173i | \(-0.252289\pi\) | ||||
0.702004 | + | 0.712173i | \(0.252289\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.91409e62 | 0.0640698 | 0.0320349 | − | 0.999487i | \(-0.489801\pi\) | ||||
0.0320349 | + | 0.999487i | \(0.489801\pi\) | |||||||
\(524\) | 8.78382e63 | 1.09496 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.28961e63 | −0.146992 | ||||||||
\(527\) | −1.52871e64 | −1.66638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.51264e63 | −0.948621 | ||||||||
\(530\) | −1.63240e63 | −0.155720 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.71205e63 | 0.149484 | ||||||||
\(533\) | 6.29866e63 | 0.526210 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.50400e63 | 0.650593 | ||||||||
\(536\) | 5.44756e62 | 0.0398869 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.91580e63 | 0.195602 | ||||||||
\(539\) | 9.90734e63 | 0.636240 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.71742e61 | 0.00395428 | 0.00197714 | − | 0.999998i | \(-0.499371\pi\) | ||||
0.00197714 | + | 0.999998i | \(0.499371\pi\) | |||||||
\(542\) | 3.96959e63 | 0.223750 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.56119e63 | −0.390856 | ||||||||
\(545\) | 2.48615e64 | 1.23086 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.01645e62 | 0.0182449 | 0.00912243 | − | 0.999958i | \(-0.497096\pi\) | ||||
0.00912243 | + | 0.999958i | \(0.497096\pi\) | |||||||
\(548\) | 2.76322e64 | 1.20246 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.48176e63 | −0.179030 | ||||||||
\(551\) | 1.07590e64 | 0.411823 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.27629e64 | 0.800177 | ||||||||
\(554\) | −1.29428e63 | −0.0436062 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.38010e64 | 1.35589 | ||||||||
\(557\) | −6.03614e64 | −1.79127 | −0.895637 | − | 0.444785i | \(-0.853280\pi\) | ||||
−0.895637 | + | 0.444785i | \(0.853280\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.11495e64 | −0.304144 | ||||||||
\(560\) | 3.11458e64 | 0.814669 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.14089e63 | 0.147716 | ||||||||
\(563\) | 3.47404e63 | 0.0801470 | 0.0400735 | − | 0.999197i | \(-0.487241\pi\) | ||||
0.0400735 | + | 0.999197i | \(0.487241\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.32104e64 | 0.280399 | ||||||||
\(566\) | −6.88940e63 | −0.140280 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.40750e64 | −0.263793 | ||||||||
\(569\) | −9.25178e64 | −1.66375 | −0.831873 | − | 0.554966i | \(-0.812731\pi\) | ||||
−0.831873 | + | 0.554966i | \(0.812731\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.04188e65 | −1.72532 | −0.862658 | − | 0.505787i | \(-0.831202\pi\) | ||||
−0.862658 | + | 0.505787i | \(0.831202\pi\) | |||||||
\(572\) | 8.34373e64 | 1.32603 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.68256e63 | −0.0246343 | ||||||||
\(575\) | −2.46708e64 | −0.346728 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.68105e64 | −1.12445 | −0.562225 | − | 0.826984i | \(-0.690055\pi\) | ||||
−0.562225 | + | 0.826984i | \(0.690055\pi\) | |||||||
\(578\) | 4.71281e62 | 0.00586105 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.99235e65 | 2.28459 | ||||||||
\(581\) | −1.37382e64 | −0.151284 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.63474e64 | −0.673928 | ||||||||
\(584\) | −1.55064e64 | −0.151290 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.62685e64 | −0.146471 | ||||||||
\(587\) | −5.04453e64 | −0.436340 | −0.218170 | − | 0.975911i | \(-0.570009\pi\) | ||||
−0.218170 | + | 0.975911i | \(0.570009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.75338e64 | 0.459424 | ||||||||
\(590\) | 2.42160e63 | 0.0185815 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.34210e65 | −0.951094 | ||||||||
\(593\) | −1.82757e65 | −1.24477 | −0.622385 | − | 0.782712i | \(-0.713836\pi\) | ||||
−0.622385 | + | 0.782712i | \(0.713836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.39406e65 | −0.877272 | ||||||||
\(596\) | 1.38714e64 | 0.0839137 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.94459e63 | −0.0444216 | ||||||||
\(599\) | −6.30818e64 | −0.339136 | −0.169568 | − | 0.985519i | \(-0.554237\pi\) | ||||
−0.169568 | + | 0.985519i | \(0.554237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.16613e65 | 0.579693 | 0.289847 | − | 0.957073i | \(-0.406396\pi\) | ||||
0.289847 | + | 0.957073i | \(0.406396\pi\) | |||||||
\(602\) | 2.97837e63 | 0.0142384 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.32689e63 | 0.0147119 | ||||||||
\(605\) | 7.26847e64 | 0.309166 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.69736e64 | −0.342337 | −0.171168 | − | 0.985242i | \(-0.554754\pi\) | ||||
−0.171168 | + | 0.985242i | \(0.554754\pi\) | |||||||
\(608\) | 2.84570e64 | 0.107760 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.31241e64 | −0.0810614 | ||||||||
\(611\) | −4.22709e65 | −1.42585 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.95467e65 | 1.23535 | 0.617674 | − | 0.786435i | \(-0.288075\pi\) | ||||
0.617674 | + | 0.786435i | \(0.288075\pi\) | |||||||
\(614\) | 8.40317e63 | 0.0252631 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.49627e64 | −0.125229 | ||||||||
\(617\) | 4.10300e65 | 1.10002 | 0.550009 | − | 0.835159i | \(-0.314624\pi\) | ||||
0.550009 | + | 0.835159i | \(0.314624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.39273e65 | 0.346047 | 0.173024 | − | 0.984918i | \(-0.444646\pi\) | ||||
0.173024 | + | 0.984918i | \(0.444646\pi\) | |||||||
\(620\) | 1.06541e66 | 2.54865 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.42569e64 | 0.164688 | ||||||||
\(623\) | −1.14245e65 | −0.243988 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.58171e64 | −0.189785 | ||||||||
\(626\) | −3.87227e64 | −0.0738702 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.96828e65 | 0.348365 | ||||||||
\(629\) | 6.00713e65 | 1.02418 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.54026e65 | 0.243728 | 0.121864 | − | 0.992547i | \(-0.461113\pi\) | ||||
0.121864 | + | 0.992547i | \(0.461113\pi\) | |||||||
\(632\) | 2.51518e65 | 0.383457 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.02917e65 | 0.145677 | ||||||||
\(635\) | −1.12844e66 | −1.53920 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.40952e65 | −1.06536 | ||||||||
\(638\) | −1.40068e65 | −0.171022 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.00513e65 | 0.794670 | ||||||||
\(641\) | 1.65837e65 | 0.181350 | 0.0906752 | − | 0.995881i | \(-0.471097\pi\) | ||||
0.0906752 | + | 0.995881i | \(0.471097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.22213e66 | −1.24211 | −0.621053 | − | 0.783768i | \(-0.713295\pi\) | ||||
−0.621053 | + | 0.783768i | \(0.713295\pi\) | |||||||
\(644\) | −1.22692e65 | −0.120226 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.12346e64 | −0.0375663 | ||||||||
\(647\) | 9.62351e65 | 0.845440 | 0.422720 | − | 0.906260i | \(-0.361075\pi\) | ||||
0.422720 | + | 0.906260i | \(0.361075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.84237e64 | 0.0804173 | ||||||||
\(650\) | 3.80419e65 | 0.299777 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.63024e65 | 0.486084 | ||||||||
\(653\) | −3.91841e65 | −0.277109 | −0.138554 | − | 0.990355i | \(-0.544246\pi\) | ||||
−0.138554 | + | 0.990355i | \(0.544246\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.69183e66 | 1.77165 | ||||||||
\(656\) | 5.23427e65 | 0.332365 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.12918e65 | 0.0667506 | ||||||||
\(659\) | −2.16961e66 | −1.23758 | −0.618792 | − | 0.785555i | \(-0.712378\pi\) | ||||
−0.618792 | + | 0.785555i | \(0.712378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.87453e65 | −0.524544 | −0.262272 | − | 0.964994i | \(-0.584472\pi\) | ||||
−0.262272 | + | 0.964994i | \(0.584472\pi\) | |||||||
\(662\) | −2.36654e64 | −0.0121325 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.51800e65 | −0.0724975 | ||||||||
\(665\) | 5.24665e65 | 0.241865 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.71034e65 | −0.331220 | ||||||||
\(668\) | −1.36925e66 | −0.567851 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.27556e64 | 0.0319919 | ||||||||
\(671\) | −9.39857e65 | −0.350818 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.18176e66 | −1.80353 | −0.901765 | − | 0.432227i | \(-0.857728\pi\) | ||||
−0.901765 | + | 0.432227i | \(0.857728\pi\) | |||||||
\(674\) | −1.85161e65 | −0.0622359 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.94685e66 | −1.23738 | ||||||||
\(677\) | −5.62905e66 | −1.70452 | −0.852259 | − | 0.523120i | \(-0.824768\pi\) | ||||
−0.852259 | + | 0.523120i | \(0.824768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.48559e65 | −0.239741 | ||||||||
\(680\) | −1.54037e66 | −0.420402 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.49010e65 | −0.190790 | ||||||||
\(683\) | 2.17309e66 | 0.534800 | 0.267400 | − | 0.963586i | \(-0.413835\pi\) | ||||
0.267400 | + | 0.963586i | \(0.413835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.46798e66 | 1.94559 | ||||||||
\(686\) | 5.41553e65 | 0.120233 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.26539e65 | −0.192104 | ||||||||
\(689\) | 5.63168e66 | 1.12846 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.80507e66 | 0.712244 | 0.356122 | − | 0.934439i | \(-0.384099\pi\) | ||||
0.356122 | + | 0.934439i | \(0.384099\pi\) | |||||||
\(692\) | −1.02927e67 | −1.86224 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.02216e66 | 0.172811 | ||||||||
\(695\) | 1.34230e67 | 2.19384 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.34282e66 | −0.357906 | ||||||||
\(698\) | 1.10421e66 | 0.163098 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.87500e66 | 0.811343 | ||||||||
\(701\) | −4.48575e66 | −0.599048 | −0.299524 | − | 0.954089i | \(-0.596828\pi\) | ||||
−0.299524 | + | 0.954089i | \(0.596828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.26082e66 | −0.282368 | ||||||||
\(704\) | 6.68321e66 | 0.807286 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.70965e64 | −0.00871212 | ||||||||
\(707\) | −1.99872e66 | −0.218472 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.23589e67 | −1.26414 | −0.632068 | − | 0.774913i | \(-0.717794\pi\) | ||||
−0.632068 | + | 0.774913i | \(0.717794\pi\) | |||||||
\(710\) | −2.13818e66 | −0.211579 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.26235e66 | −0.116923 | ||||||||
\(713\) | −4.12310e66 | −0.369504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.55697e67 | 2.14552 | ||||||||
\(716\) | 4.98915e66 | 0.405108 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.23290e66 | −0.245848 | ||||||||
\(719\) | 5.05205e66 | 0.371825 | 0.185913 | − | 0.982566i | \(-0.440476\pi\) | ||||
0.185913 | + | 0.982566i | \(0.440476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.24860e67 | −0.860884 | ||||||||
\(722\) | −1.79865e66 | −0.120039 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.57124e66 | −0.536028 | ||||||||
\(725\) | 3.69202e67 | 2.23522 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.10795e67 | 1.19619 | 0.598097 | − | 0.801424i | \(-0.295924\pi\) | ||||
0.598097 | + | 0.801424i | \(0.295924\pi\) | |||||||
\(728\) | 3.81651e66 | 0.209690 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.35563e66 | −0.121344 | ||||||||
\(731\) | 4.14712e66 | 0.206866 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.34941e67 | 1.09905 | 0.549523 | − | 0.835478i | \(-0.314809\pi\) | ||||
0.549523 | + | 0.835478i | \(0.314809\pi\) | |||||||
\(734\) | −1.88816e65 | −0.00855425 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.03934e66 | −0.0866685 | ||||||||
\(737\) | 3.36352e66 | 0.138455 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.69448e66 | −0.335814 | −0.167907 | − | 0.985803i | \(-0.553701\pi\) | ||||
−0.167907 | + | 0.985803i | \(0.553701\pi\) | |||||||
\(740\) | −4.18657e67 | −1.56644 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.50439e66 | −0.0528285 | ||||||||
\(743\) | −1.83903e67 | −0.625679 | −0.312840 | − | 0.949806i | \(-0.601280\pi\) | ||||
−0.312840 | + | 0.949806i | \(0.601280\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.25094e66 | 0.135773 | ||||||||
\(746\) | −3.74217e66 | −0.115814 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.10350e67 | −0.901911 | ||||||||
\(749\) | 7.83710e66 | 0.220715 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.92872e67 | −0.774709 | −0.387355 | − | 0.921931i | \(-0.626611\pi\) | ||||
−0.387355 | + | 0.921931i | \(0.626611\pi\) | |||||||
\(752\) | −3.51277e67 | −0.900597 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.18892e67 | 0.286369 | ||||||||
\(755\) | 1.01954e66 | 0.0238040 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.60671e67 | −0.791330 | −0.395665 | − | 0.918395i | \(-0.629486\pi\) | ||||
−0.395665 | + | 0.918395i | \(0.629486\pi\) | |||||||
\(758\) | 9.74245e66 | 0.207225 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.79727e66 | 0.115906 | ||||||||
\(761\) | −6.36047e67 | −1.23296 | −0.616481 | − | 0.787370i | \(-0.711442\pi\) | ||||
−0.616481 | + | 0.787370i | \(0.711442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.29118e67 | 0.417574 | ||||||||
\(764\) | −4.28678e67 | −0.757595 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.01697e66 | −0.100000 | ||||||||
\(767\) | −8.35437e66 | −0.134655 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.58030e67 | −0.239591 | −0.119795 | − | 0.992799i | \(-0.538224\pi\) | ||||
−0.119795 | + | 0.992799i | \(0.538224\pi\) | |||||||
\(770\) | −6.83041e66 | −0.100442 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.57793e67 | −0.910087 | ||||||||
\(773\) | 1.20430e68 | 1.61628 | 0.808142 | − | 0.588988i | \(-0.200474\pi\) | ||||
0.808142 | + | 0.588988i | \(0.200474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.97430e68 | 2.49358 | ||||||||
\(776\) | −9.37613e66 | −0.114888 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.97864e66 | −0.0920255 | ||||||||
\(779\) | 8.81736e66 | 0.0986752 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.69040e67 | −0.915674 | ||||||||
\(782\) | 2.95503e66 | 0.0302137 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.98842e67 | −0.672901 | ||||||||
\(785\) | 6.03186e67 | 0.563656 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.72836e68 | −1.52134 | −0.760671 | − | 0.649137i | \(-0.775130\pi\) | ||||
−0.760671 | + | 0.649137i | \(0.775130\pi\) | |||||||
\(788\) | −1.05369e68 | −0.900219 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.82088e67 | 0.307558 | ||||||||
\(791\) | 1.21744e67 | 0.0951261 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.97766e67 | 0.587429 | ||||||||
\(794\) | −2.97966e67 | −0.213003 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.63727e68 | 1.77704 | ||||||||
\(797\) | 5.17743e67 | 0.338722 | 0.169361 | − | 0.985554i | \(-0.445830\pi\) | ||||
0.169361 | + | 0.985554i | \(0.445830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.57229e68 | 0.969803 | ||||||||
\(800\) | 9.76519e67 | 0.584879 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.83502e64 | −0.000442530 0 | ||||||||
\(803\) | −9.57423e67 | −0.525156 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.75995e67 | −0.194527 | ||||||||
\(806\) | 6.35773e67 | 0.319469 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.20848e67 | −0.104695 | ||||||||
\(809\) | 1.34819e68 | 0.620812 | 0.310406 | − | 0.950604i | \(-0.399535\pi\) | ||||
0.310406 | + | 0.950604i | \(0.399535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.29768e68 | −0.563869 | −0.281934 | − | 0.959434i | \(-0.590976\pi\) | ||||
−0.281934 | + | 0.959434i | \(0.590976\pi\) | |||||||
\(812\) | 1.83611e68 | 0.775053 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.94328e67 | 0.117262 | ||||||||
\(815\) | 2.03186e68 | 0.786485 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.56080e67 | −0.0570332 | ||||||||
\(818\) | 2.32374e67 | 0.0825059 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.63279e68 | 0.547401 | ||||||||
\(821\) | 3.05518e68 | 0.995342 | 0.497671 | − | 0.867366i | \(-0.334189\pi\) | ||||
0.497671 | + | 0.867366i | \(0.334189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.54128e68 | −1.08959 | −0.544796 | − | 0.838568i | \(-0.683393\pi\) | ||||
−0.544796 | + | 0.838568i | \(0.683393\pi\) | |||||||
\(824\) | −1.37964e68 | −0.412549 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.23170e66 | 0.00630383 | ||||||||
\(827\) | −5.88899e68 | −1.61682 | −0.808410 | − | 0.588620i | \(-0.799672\pi\) | ||||
−0.808410 | + | 0.588620i | \(0.799672\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.14204e68 | 1.85264 | 0.926319 | − | 0.376740i | \(-0.122955\pi\) | ||||
0.926319 | + | 0.376740i | \(0.122955\pi\) | |||||||
\(830\) | −2.30604e67 | −0.0581477 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.67282e68 | −1.35176 | ||||||||
\(833\) | 3.12797e68 | 0.724610 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.19610e68 | −0.918785 | ||||||||
\(836\) | 1.16802e68 | 0.248658 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.07657e68 | −0.216675 | ||||||||
\(839\) | −4.08251e68 | −0.798953 | −0.399477 | − | 0.916743i | \(-0.630808\pi\) | ||||
−0.399477 | + | 0.916743i | \(0.630808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.13474e68 | 1.13525 | ||||||||
\(842\) | −5.86231e67 | −0.105496 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.73650e68 | −0.295548 | ||||||||
\(845\) | −1.20953e69 | −2.00209 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.69846e67 | 0.104885 | ||||||||
\(848\) | 4.68000e68 | 0.712760 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.41499e68 | −0.203896 | ||||||||
\(851\) | 1.62019e68 | 0.227102 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.69695e68 | 0.888331 | 0.444166 | − | 0.895945i | \(-0.353500\pi\) | ||||
0.444166 | + | 0.895945i | \(0.353500\pi\) | |||||||
\(854\) | −2.13107e67 | −0.0275003 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.65958e67 | 0.105770 | ||||||||
\(857\) | −1.01115e69 | −1.20162 | −0.600809 | − | 0.799393i | \(-0.705155\pi\) | ||||
−0.600809 | + | 0.799393i | \(0.705155\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.13647e68 | −0.465361 | −0.232681 | − | 0.972553i | \(-0.574750\pi\) | ||||
−0.232681 | + | 0.972553i | \(0.574750\pi\) | |||||||
\(860\) | −2.89027e68 | −0.316392 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.29207e66 | −0.00652188 | ||||||||
\(863\) | −6.85332e68 | −0.691270 | −0.345635 | − | 0.938369i | \(-0.612336\pi\) | ||||
−0.345635 | + | 0.938369i | \(0.612336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.15424e69 | −3.01312 | ||||||||
\(866\) | −4.00847e67 | −0.0372656 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.81856e68 | 0.864638 | ||||||||
\(869\) | 1.55296e69 | 1.33105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.85501e68 | −0.231836 | ||||||||
\(872\) | 2.53164e68 | 0.200108 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.11215e67 | −0.00832997 | ||||||||
\(875\) | 6.23418e68 | 0.454559 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.43840e68 | 0.444925 | 0.222463 | − | 0.974941i | \(-0.428590\pi\) | ||||
0.222463 | + | 0.974941i | \(0.428590\pi\) | |||||||
\(878\) | 5.43059e67 | 0.0365364 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.12487e69 | 1.35516 | ||||||||
\(881\) | −8.86127e68 | −0.550253 | −0.275126 | − | 0.961408i | \(-0.588720\pi\) | ||||
−0.275126 | + | 0.961408i | \(0.588720\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.16643e68 | 0.245294 | 0.122647 | − | 0.992450i | \(-0.460862\pi\) | ||||
0.122647 | + | 0.992450i | \(0.460862\pi\) | |||||||
\(884\) | 2.63430e69 | 1.51021 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.86670e67 | 0.0373298 | ||||||||
\(887\) | −2.94393e69 | −1.55856 | −0.779278 | − | 0.626679i | \(-0.784414\pi\) | ||||
−0.779278 | + | 0.626679i | \(0.784414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.03994e69 | −0.522177 | ||||||||
\(890\) | −1.91767e68 | −0.0937797 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.98028e68 | 0.0918654 | ||||||||
\(893\) | −5.91742e68 | −0.267376 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.52894e69 | 0.655466 | ||||||||
\(896\) | 6.45578e68 | 0.269594 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.30901e68 | −0.210387 | ||||||||
\(899\) | 6.17026e69 | 2.38205 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.09473e69 | −0.767532 | ||||||||
\(902\) | −1.14790e68 | −0.0409779 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.34521e68 | 0.0455859 | ||||||||
\(905\) | −2.62669e69 | −0.867295 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.36233e69 | 1.05407 | 0.527034 | − | 0.849844i | \(-0.323304\pi\) | ||||
0.527034 | + | 0.849844i | \(0.323304\pi\) | |||||||
\(908\) | 4.68278e69 | 1.43049 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.79777e68 | 0.168185 | ||||||||
\(911\) | −4.29823e69 | −1.21509 | −0.607544 | − | 0.794286i | \(-0.707845\pi\) | ||||
−0.607544 | + | 0.794286i | \(0.707845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.37269e68 | −0.251652 | ||||||||
\(914\) | −1.49195e67 | −0.00390409 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.43603e68 | 0.159983 | ||||||||
\(917\) | 2.48074e69 | 0.601037 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.89124e69 | 1.35610 | 0.678050 | − | 0.735015i | \(-0.262825\pi\) | ||||
0.678050 | + | 0.735015i | \(0.262825\pi\) | |||||||
\(920\) | −4.15455e68 | −0.0932202 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.77877e67 | 0.0208501 | ||||||||
\(923\) | 7.37656e69 | 1.53325 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.75813e69 | −1.53259 | ||||||||
\(926\) | 1.06152e69 | 0.204442 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.05190e69 | 0.558718 | ||||||||
\(929\) | 3.81127e69 | 0.680301 | 0.340150 | − | 0.940371i | \(-0.389522\pi\) | ||||
0.340150 | + | 0.940371i | \(0.389522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.17723e69 | −0.199776 | ||||||||
\(932\) | −9.50754e69 | −1.57324 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.50729e68 | 0.0709192 | ||||||||
\(935\) | −9.51078e69 | −1.45930 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.18868e69 | −0.465298 | −0.232649 | − | 0.972561i | \(-0.574739\pi\) | ||||
−0.232649 | + | 0.972561i | \(0.574739\pi\) | |||||||
\(938\) | 7.62658e67 | 0.0108533 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.09578e70 | −1.48327 | ||||||||
\(941\) | −7.20176e69 | −0.950785 | −0.475393 | − | 0.879774i | \(-0.657694\pi\) | ||||
−0.475393 | + | 0.879774i | \(0.657694\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.31886e68 | −0.0793623 | ||||||||
\(944\) | −6.94259e68 | −0.0850510 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.03194e68 | 0.0236848 | ||||||||
\(947\) | −7.19607e69 | −0.818222 | −0.409111 | − | 0.912485i | \(-0.634161\pi\) | ||||
−0.409111 | + | 0.912485i | \(0.634161\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.12676e69 | 0.879350 | ||||||||
\(950\) | 5.32540e68 | 0.0562144 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.41957e69 | −0.142623 | ||||||||
\(953\) | −1.03533e70 | −1.01483 | −0.507417 | − | 0.861700i | \(-0.669400\pi\) | ||||
−0.507417 | + | 0.861700i | \(0.669400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.31370e70 | −1.22579 | ||||||||
\(956\) | 1.51099e70 | 1.37563 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.45384e69 | 0.126017 | ||||||||
\(959\) | 7.80391e69 | 0.660047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.05789e70 | 1.65738 | ||||||||
\(962\) | −2.49830e69 | −0.196350 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.67681e69 | 0.499757 | ||||||||
\(965\) | −2.01583e70 | −1.47252 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.88655e70 | −1.31264 | −0.656321 | − | 0.754482i | \(-0.727888\pi\) | ||||
−0.656321 | + | 0.754482i | \(0.727888\pi\) | |||||||
\(968\) | 7.40145e68 | 0.0502627 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.42436e69 | −0.0921474 | ||||||||
\(971\) | 1.54065e70 | 0.972862 | 0.486431 | − | 0.873719i | \(-0.338299\pi\) | ||||
0.486431 | + | 0.873719i | \(0.338299\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.23703e70 | 0.744268 | ||||||||
\(974\) | 3.70256e69 | 0.217453 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.62954e69 | 0.371033 | ||||||||
\(977\) | 1.28077e70 | 0.699760 | 0.349880 | − | 0.936795i | \(-0.386222\pi\) | ||||
0.349880 | + | 0.936795i | \(0.386222\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.79418e69 | −0.405861 | ||||||||
\(980\) | −2.17999e70 | −1.10826 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.91177e69 | −0.0926438 | ||||||||
\(983\) | −1.22658e70 | −0.580349 | −0.290174 | − | 0.956974i | \(-0.593713\pi\) | ||||
−0.290174 | + | 0.956974i | \(0.593713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.22908e70 | −1.45656 | ||||||||
\(986\) | −4.42225e69 | −0.194776 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.91435e69 | −0.416367 | ||||||||
\(989\) | 1.11853e69 | 0.0458705 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.78865e70 | 1.09059 | 0.545296 | − | 0.838244i | \(-0.316417\pi\) | ||||
0.545296 | + | 0.838244i | \(0.316417\pi\) | |||||||
\(992\) | 1.63200e70 | 0.623298 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.97050e69 | −0.0717787 | ||||||||
\(995\) | 8.08202e70 | 2.87526 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.05189e70 | 0.696336 | 0.348168 | − | 0.937432i | \(-0.386804\pi\) | ||||
0.348168 | + | 0.937432i | \(0.386804\pi\) | |||||||
\(998\) | −4.55812e69 | −0.151084 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9.48.a.c.1.3 | 4 | ||
3.2 | odd | 2 | 1.48.a.a.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 16.48.a.d.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.48.a.a.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
9.48.a.c.1.3 | 4 | 1.1 | even | 1 | trivial | ||
16.48.a.d.1.1 | 4 | 12.11 | even | 2 |