Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,7,Mod(161,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.h (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(132.511152165\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 964 x^{14} - 6608 x^{13} + 404616 x^{12} - 2342156 x^{11} + 95125730 x^{10} + \cdots + 39\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{36} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.10 | ||
Root | \(-2.36747 - 7.23051i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.161 |
Dual form | 576.7.h.a.161.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.3796 | 0.115037 | 0.0575186 | − | 0.998344i | \(-0.481681\pi\) | ||||
0.0575186 | + | 0.998344i | \(0.481681\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −532.635 | −1.55287 | −0.776436 | − | 0.630196i | \(-0.782975\pi\) | ||||
−0.776436 | + | 0.630196i | \(0.782975\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1840.27 | 1.38262 | 0.691312 | − | 0.722557i | \(-0.257033\pi\) | ||||
0.691312 | + | 0.722557i | \(0.257033\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1004.26i | 0.457106i | 0.973531 | + | 0.228553i | \(0.0733995\pi\) | ||||
−0.973531 | + | 0.228553i | \(0.926601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3718.73i | − 0.756916i | −0.925618 | − | 0.378458i | \(-0.876454\pi\) | ||||
0.925618 | − | 0.378458i | \(-0.123546\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7863.61i | − 1.14647i | −0.819392 | − | 0.573233i | \(-0.805689\pi\) | ||||
0.819392 | − | 0.573233i | \(-0.194311\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19532.8i | 1.60539i | 0.596391 | + | 0.802694i | \(0.296601\pi\) | ||||
−0.596391 | + | 0.802694i | \(0.703399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15418.2 | −0.986766 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42502.3 | 1.74268 | 0.871341 | − | 0.490679i | \(-0.163251\pi\) | ||||
0.871341 | + | 0.490679i | \(0.163251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −39103.0 | −1.31258 | −0.656289 | − | 0.754510i | \(-0.727875\pi\) | ||||
−0.656289 | + | 0.754510i | \(0.727875\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7659.11 | −0.178638 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 61799.6i | 1.22006i | 0.792379 | + | 0.610029i | \(0.208842\pi\) | ||||
−0.792379 | + | 0.610029i | \(0.791158\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13324.3i | 0.193327i | 0.995317 | + | 0.0966634i | \(0.0308170\pi\) | ||||
−0.995317 | + | 0.0966634i | \(0.969183\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 57908.9i | 0.728350i | 0.931331 | + | 0.364175i | \(0.118649\pi\) | ||||
−0.931331 | + | 0.364175i | \(0.881351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 51926.1i | 0.500141i | 0.968228 | + | 0.250070i | \(0.0804538\pi\) | ||||
−0.968228 | + | 0.250070i | \(0.919546\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 166051. | 1.41141 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 52999.4 | 0.355995 | 0.177997 | − | 0.984031i | \(-0.443038\pi\) | ||||
0.177997 | + | 0.984031i | \(0.443038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26462.5 | 0.159053 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −95850.6 | −0.466701 | −0.233351 | − | 0.972393i | \(-0.574969\pi\) | ||||
−0.233351 | + | 0.972393i | \(0.574969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 248790.i | − 1.09608i | −0.836451 | − | 0.548042i | \(-0.815373\pi\) | ||||
0.836451 | − | 0.548042i | \(-0.184627\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14440.9i | 0.0525842i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 170554.i | − 0.567072i | −0.958962 | − | 0.283536i | \(-0.908493\pi\) | ||||
0.958962 | − | 0.283536i | \(-0.0915075\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 477668.i | − 1.33460i | −0.744790 | − | 0.667299i | \(-0.767450\pi\) | ||||
0.744790 | − | 0.667299i | \(-0.232550\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −481200. | −1.23696 | −0.618482 | − | 0.785799i | \(-0.712252\pi\) | ||||
−0.618482 | + | 0.785799i | \(0.712252\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −980194. | −2.14704 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 358403. | 0.726927 | 0.363463 | − | 0.931609i | \(-0.381594\pi\) | ||||
0.363463 | + | 0.931609i | \(0.381594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 85889.4 | 0.150212 | 0.0751061 | − | 0.997176i | \(-0.476070\pi\) | ||||
0.0751061 | + | 0.997176i | \(0.476070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 53474.0i | − 0.0870735i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.09316e6i | − 1.55065i | −0.631561 | − | 0.775326i | \(-0.717586\pi\) | ||||
0.631561 | − | 0.775326i | \(-0.282414\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 534906.i | − 0.709828i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 113076.i | − 0.131886i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01923e6 | 1.11675 | 0.558377 | − | 0.829588i | \(-0.311424\pi\) | ||||
0.558377 | + | 0.829588i | \(0.311424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.56917e6 | 1.52302 | 0.761512 | − | 0.648150i | \(-0.224457\pi\) | ||||
0.761512 | + | 0.648150i | \(0.224457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 129905. | 0.118881 | 0.0594407 | − | 0.998232i | \(-0.481068\pi\) | ||||
0.0594407 | + | 0.998232i | \(0.481068\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −891258. | −0.727532 | −0.363766 | − | 0.931490i | \(-0.618509\pi\) | ||||
−0.363766 | + | 0.931490i | \(0.618509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 26047.2i | 0.0201132i | 0.999949 | + | 0.0100566i | \(0.00320117\pi\) | ||||
−0.999949 | + | 0.0100566i | \(0.996799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 905823.i | 0.627781i | 0.949459 | + | 0.313890i | \(0.101632\pi\) | ||||
−0.949459 | + | 0.313890i | \(0.898368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 280874.i | 0.184679i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.98073e6i | 1.17539i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.61504e6 | 0.911648 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −446391. | −0.228552 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.11555e6 | −1.03279 | −0.516395 | − | 0.856350i | \(-0.672726\pi\) | ||||
−0.516395 | + | 0.856350i | \(0.672726\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.08682e6 | −1.81791 | −0.908953 | − | 0.416898i | \(-0.863117\pi\) | ||||
−0.908953 | + | 0.416898i | \(0.863117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.18844e6i | 1.78032i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2.90000e6i | − 1.12781i | −0.825839 | − | 0.563906i | \(-0.809298\pi\) | ||||
0.825839 | − | 0.563906i | \(-0.190702\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1.47985e6i | − 0.551029i | −0.961297 | − | 0.275515i | \(-0.911152\pi\) | ||||
0.961297 | − | 0.275515i | \(-0.0888482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.84812e6i | 0.632006i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 611167. | 0.200473 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.02979e6 | 1.21822 | 0.609108 | − | 0.793087i | \(-0.291528\pi\) | ||||
0.609108 | + | 0.793087i | \(0.291528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.21957e6 | −0.354222 | −0.177111 | − | 0.984191i | \(-0.556675\pi\) | ||||
−0.177111 | + | 0.984191i | \(0.556675\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −562287. | −0.150995 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 6.97067e6i | − 1.80126i | −0.434591 | − | 0.900628i | \(-0.643107\pi\) | ||||
0.434591 | − | 0.900628i | \(-0.356893\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 1.04038e7i | − 2.49296i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.97866e6i | − 1.61142i | −0.592309 | − | 0.805711i | \(-0.701784\pi\) | ||||
0.592309 | − | 0.805711i | \(-0.298216\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3.99941e6i | − 0.858710i | −0.903136 | − | 0.429355i | \(-0.858741\pi\) | ||||
0.903136 | − | 0.429355i | \(-0.141259\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.81827e6 | 0.791054 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.10654e6 | −1.56566 | −0.782830 | − | 0.622236i | \(-0.786224\pi\) | ||||
−0.782830 | + | 0.622236i | \(0.786224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.21229e6 | 1.53232 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.38256e6 | −0.589775 | −0.294887 | − | 0.955532i | \(-0.595282\pi\) | ||||
−0.294887 | + | 0.955532i | \(0.595282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.56556e6i | 0.264019i | 0.991248 | + | 0.132009i | \(0.0421429\pi\) | ||||
−0.991248 | + | 0.132009i | \(0.957857\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 888657.i | 0.140352i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.84347e6i | − 1.04653i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 9.46841e6i | − 1.35887i | −0.733737 | − | 0.679434i | \(-0.762226\pi\) | ||||
0.733737 | − | 0.679434i | \(-0.237774\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.71838e6 | 0.517228 | 0.258614 | − | 0.965981i | \(-0.416734\pi\) | ||||
0.258614 | + | 0.965981i | \(0.416734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.13905e6 | −0.410582 | −0.205291 | − | 0.978701i | \(-0.565814\pi\) | ||||
−0.205291 | + | 0.978701i | \(0.565814\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.62533e6 | −0.333139 | −0.166569 | − | 0.986030i | \(-0.553269\pi\) | ||||
−0.166569 | + | 0.986030i | \(0.553269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.26382e7 | −2.70616 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 191598.i | 0.0222398i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 1.44712e7i | − 1.58513i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.03189e6i | − 0.216298i | −0.994135 | − | 0.108149i | \(-0.965508\pi\) | ||||
0.994135 | − | 0.108149i | \(-0.0344924\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 832710.i | 0.0837873i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.08276e7 | 2.03826 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.73458e6 | 0.345991 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.62230e6 | −0.326641 | −0.163320 | − | 0.986573i | \(-0.552220\pi\) | ||||
−0.163320 | + | 0.986573i | \(0.552220\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.59003e7 | −1.35934 | −0.679671 | − | 0.733517i | \(-0.737877\pi\) | ||||
−0.679671 | + | 0.733517i | \(0.737877\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.56301e7i | − 1.30154i | −0.759277 | − | 0.650768i | \(-0.774447\pi\) | ||||
0.759277 | − | 0.650768i | \(-0.225553\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1.79932e7i | − 1.42246i | −0.702957 | − | 0.711232i | \(-0.748137\pi\) | ||||
0.702957 | − | 0.711232i | \(-0.251863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 746679.i | 0.0575348i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.01345e7i | 1.47485i | 0.675429 | + | 0.737425i | \(0.263958\pi\) | ||||
−0.675429 | + | 0.737425i | \(0.736042\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.32181e6 | 0.665962 | 0.332981 | − | 0.942934i | \(-0.391946\pi\) | ||||
0.332981 | + | 0.942934i | \(0.391946\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.38776e6 | 0.162365 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.89713e6 | 0.524057 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.90202e6 | 0.120280 | 0.0601401 | − | 0.998190i | \(-0.480845\pi\) | ||||
0.0601401 | + | 0.998190i | \(0.480845\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.59456e7i | 2.21965i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1.16315e7i | − 0.685231i | −0.939476 | − | 0.342616i | \(-0.888687\pi\) | ||||
0.939476 | − | 0.342616i | \(-0.111313\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 3.29167e7i | − 1.89460i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.05144e7i | 0.577984i | 0.957332 | + | 0.288992i | \(0.0933200\pi\) | ||||
−0.957332 | + | 0.288992i | \(0.906680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 762113. | 0.0409526 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.14970e7 | 1.61813 | 0.809064 | − | 0.587721i | \(-0.199975\pi\) | ||||
0.809064 | + | 0.587721i | \(0.199975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.21890e7 | −1.61733 | −0.808667 | − | 0.588266i | \(-0.799811\pi\) | ||||
−0.808667 | + | 0.588266i | \(0.799811\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.83737e7 | −1.36433 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.02479e7i | 0.482167i | 0.970504 | + | 0.241083i | \(0.0775027\pi\) | ||||
−0.970504 | + | 0.241083i | \(0.922497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 3.73088e7i | − 1.68148i | −0.541438 | − | 0.840741i | \(-0.682120\pi\) | ||||
0.541438 | − | 0.840741i | \(-0.317880\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.95134e7i | − 1.74335i | −0.490082 | − | 0.871676i | \(-0.663033\pi\) | ||||
0.490082 | − | 0.871676i | \(-0.336967\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 7.09698e6i | − 0.300212i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.03086e7 | 0.427078 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.50715e7 | −0.996731 | −0.498365 | − | 0.866967i | \(-0.666066\pi\) | ||||
−0.498365 | + | 0.866967i | \(0.666066\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.37830e6 | −0.0536880 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.96160e7 | −0.733833 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3.08443e7i | − 1.13103i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 3.57752e6i | − 0.126090i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.64086e6i | 0.298636i | 0.988789 | + | 0.149318i | \(0.0477078\pi\) | ||||
−0.988789 | + | 0.149318i | \(0.952292\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 2.01336e7i | − 0.669329i | −0.942337 | − | 0.334665i | \(-0.891377\pi\) | ||||
0.942337 | − | 0.334665i | \(-0.108623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.42830e6 | 0.0465786 | 0.0232893 | − | 0.999729i | \(-0.492586\pi\) | ||||
0.0232893 | + | 0.999729i | \(0.492586\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.13641e7 | 0.356745 | 0.178373 | − | 0.983963i | \(-0.442917\pi\) | ||||
0.178373 | + | 0.983963i | \(0.442917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.82157e7 | 2.40947 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.92426e7 | −0.867779 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.54839e7i | − 0.451057i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 2.76577e7i | − 0.776655i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.32471e7i | 1.19254i | 0.802784 | + | 0.596271i | \(0.203351\pi\) | ||||
−0.802784 | + | 0.596271i | \(0.796649\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 2.45251e6i | − 0.0652343i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.62511e7 | 1.73103 | 0.865513 | − | 0.500886i | \(-0.166993\pi\) | ||||
0.865513 | + | 0.500886i | \(0.166993\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.19601e7 | −1.81480 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.57807e7 | −0.638871 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.91544e7 | 0.458437 | 0.229219 | − | 0.973375i | \(-0.426383\pi\) | ||||
0.229219 | + | 0.973375i | \(0.426383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.86099e6i | 0.161403i | 0.996738 | + | 0.0807013i | \(0.0257160\pi\) | ||||
−0.996738 | + | 0.0807013i | \(0.974284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.57294e7i | 0.584932i | 0.956276 | + | 0.292466i | \(0.0944758\pi\) | ||||
−0.956276 | + | 0.292466i | \(0.905524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6.86869e6i | − 0.153528i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 3.37299e7i | − 0.729007i | −0.931202 | − | 0.364503i | \(-0.881239\pi\) | ||||
0.931202 | − | 0.364503i | \(-0.118761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.47905e7 | −0.314385 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.91949e6 | −0.142297 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.34156e7 | −1.28291 | −0.641457 | − | 0.767159i | \(-0.721670\pi\) | ||||
−0.641457 | + | 0.767159i | \(0.721670\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.82293e7 | −0.552814 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6.59689e7i | − 1.27120i | −0.772020 | − | 0.635598i | \(-0.780753\pi\) | ||||
0.772020 | − | 0.635598i | \(-0.219247\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.26834e7i | 0.796591i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 4.89537e7i | − 0.899225i | −0.893224 | − | 0.449612i | \(-0.851562\pi\) | ||||
0.893224 | − | 0.449612i | \(-0.148438\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 5.14530e7i | − 0.915830i | −0.888996 | − | 0.457915i | \(-0.848596\pi\) | ||||
0.888996 | − | 0.457915i | \(-0.151404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.40948e7 | −0.246989 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.56825e7 | 0.606187 | 0.303094 | − | 0.952961i | \(-0.401981\pi\) | ||||
0.303094 | + | 0.952961i | \(0.401981\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.26370e7 | 1.21514 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.15371e6 | 0.0836236 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.15422e7i | 1.14338i | 0.820469 | + | 0.571691i | \(0.193712\pi\) | ||||
−0.820469 | + | 0.571691i | \(0.806288\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 5.88082e7i | − 0.912021i | −0.889974 | − | 0.456011i | \(-0.849278\pi\) | ||||
0.889974 | − | 0.456011i | \(-0.150722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3.92697e7i | − 0.599987i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.13728e8i | 1.68688i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.97534e7 | −1.16568 | −0.582840 | − | 0.812587i | \(-0.698058\pi\) | ||||
−0.582840 | + | 0.812587i | \(0.698058\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.10534e7 | 0.724727 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.23506e6 | 0.0172800 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.32343e8 | 1.79912 | 0.899558 | − | 0.436802i | \(-0.143889\pi\) | ||||
0.899558 | + | 0.436802i | \(0.143889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.98882e7i | 0.802592i | 0.915948 | + | 0.401296i | \(0.131440\pi\) | ||||
−0.915948 | + | 0.401296i | \(0.868560\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.73362e7i | 0.746899i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.32514e8i | 1.70208i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.68795e7i | 1.21004i | 0.796210 | + | 0.605021i | \(0.206835\pi\) | ||||
−0.796210 | + | 0.605021i | \(0.793165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.29433e8 | −1.59434 | −0.797171 | − | 0.603754i | \(-0.793671\pi\) | ||||
−0.797171 | + | 0.603754i | \(0.793671\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.53598e8 | 1.84052 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.05824e7 | −1.07066 | −0.535328 | − | 0.844644i | \(-0.679812\pi\) | ||||
−0.535328 | + | 0.844644i | \(0.679812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.24978e8 | 1.43755 | 0.718773 | − | 0.695245i | \(-0.244704\pi\) | ||||
0.718773 | + | 0.695245i | \(0.244704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.57193e7i | − 0.178383i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.62993e7i | 0.511488i | 0.966745 | + | 0.255744i | \(0.0823205\pi\) | ||||
−0.966745 | + | 0.255744i | \(0.917680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.45203e7i | 0.267298i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 7.69176e6i | − 0.0816566i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.10415e8 | 1.15686 | 0.578430 | − | 0.815732i | \(-0.303666\pi\) | ||||
0.578430 | + | 0.815732i | \(0.303666\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.38554e8 | −1.41421 | −0.707107 | − | 0.707106i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707106i | \(0.750000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.36448e7 | −0.943498 | −0.471749 | − | 0.881733i | \(-0.656377\pi\) | ||||
−0.471749 | + | 0.881733i | \(0.656377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.08817e8 | −1.06843 | −0.534214 | − | 0.845350i | \(-0.679392\pi\) | ||||
−0.534214 | + | 0.845350i | \(0.679392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.08432e7i | 0.880590i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.06568e8i | 1.00703i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.21243e8i | 1.13129i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 1.14845e8i | − 1.04497i | −0.852647 | − | 0.522487i | \(-0.825004\pi\) | ||||
0.852647 | − | 0.522487i | \(-0.174996\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.20631e7 | −0.557697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.46562e7 | 0.128468 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.88400e7 | 0.422852 | 0.211426 | − | 0.977394i | \(-0.432189\pi\) | ||||
0.211426 | + | 0.977394i | \(0.432189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.74342e8 | 1.47285 | 0.736425 | − | 0.676519i | \(-0.236513\pi\) | ||||
0.736425 | + | 0.676519i | \(0.236513\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.58054e8i | − 1.31906i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.54423e8i | 2.07246i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.75384e7i | 0.141152i | 0.997506 | + | 0.0705762i | \(0.0224838\pi\) | ||||
−0.997506 | + | 0.0705762i | \(0.977516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.19431e6i | 0.0172423i | 0.999963 | + | 0.00862114i | \(0.00274423\pi\) | ||||
−0.999963 | + | 0.00862114i | \(0.997256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.25642e7 | 0.175204 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.55819e8 | −1.18159 | −0.590794 | − | 0.806823i | \(-0.701185\pi\) | ||||
−0.590794 | + | 0.806823i | \(0.701185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.56304e8 | 1.92085 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.86799e6 | 0.0136758 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.55582e7i | 0.691506i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.84025e8i | 1.30126i | 0.759394 | + | 0.650631i | \(0.225495\pi\) | ||||
−0.759394 | + | 0.650631i | \(0.774505\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.66067e8i | 1.16086i | 0.814311 | + | 0.580428i | \(0.197115\pi\) | ||||
−0.814311 | + | 0.580428i | \(0.802885\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.45413e8i | 0.993511i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.33493e8 | −1.57727 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.33811e7 | −0.0883709 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.28160e7 | −0.0836932 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.05579e8 | 1.95145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 2.97979e8i | − 1.88189i | −0.338563 | − | 0.940944i | \(-0.609941\pi\) | ||||
0.338563 | − | 0.940944i | \(-0.390059\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 374549.i | 0.00231376i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.85340e7i | 0.418740i | 0.977836 | + | 0.209370i | \(0.0671413\pi\) | ||||
−0.977836 | + | 0.209370i | \(0.932859\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 3.34221e8i | − 1.99793i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.90898e8 | −1.12882 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.92323e6 | −0.0516365 | −0.0258182 | − | 0.999667i | \(-0.508219\pi\) | ||||
−0.0258182 | + | 0.999667i | \(0.508219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.81558e7 | −0.332933 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.27610e8 | 0.715088 | 0.357544 | − | 0.933896i | \(-0.383614\pi\) | ||||
0.357544 | + | 0.933896i | \(0.383614\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.30254e7i | 0.0722181i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 9.40278e7i | − 0.510410i | −0.966887 | − | 0.255205i | \(-0.917857\pi\) | ||||
0.966887 | − | 0.255205i | \(-0.0821430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.09226e7i | 0.273528i | 0.990604 | + | 0.136764i | \(0.0436703\pi\) | ||||
−0.990604 | + | 0.136764i | \(0.956330\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 3.01160e8i | − 1.58414i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.59555e7 | −0.291283 | −0.145641 | − | 0.989337i | \(-0.546525\pi\) | ||||
−0.145641 | + | 0.989337i | \(0.546525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.57477e7 | −0.233260 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.75333e7 | 0.492206 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.98205e8 | 1.47435 | 0.737175 | − | 0.675702i | \(-0.236160\pi\) | ||||
0.737175 | + | 0.675702i | \(0.236160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.07491e8i | 1.50483i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.66078e7i | 0.175554i | 0.996140 | + | 0.0877769i | \(0.0279763\pi\) | ||||
−0.996140 | + | 0.0877769i | \(0.972024\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.84821e7i | 0.135214i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.08514e8i | 0.970186i | 0.874463 | + | 0.485093i | \(0.161214\pi\) | ||||
−0.874463 | + | 0.485093i | \(0.838786\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.59296e8 | −1.19446 | −0.597232 | − | 0.802069i | \(-0.703733\pi\) | ||||
−0.597232 | + | 0.802069i | \(0.703733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.32237e7 | 0.104873 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.21946e8 | −1.43952 | −0.719759 | − | 0.694224i | \(-0.755748\pi\) | ||||
−0.719759 | + | 0.694224i | \(0.755748\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.21475e7 | −0.228618 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.19987e8i | − 0.520899i | −0.965487 | − | 0.260450i | \(-0.916129\pi\) | ||||
0.965487 | − | 0.260450i | \(-0.0838708\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.56694e8i | 1.51859i | 0.650748 | + | 0.759294i | \(0.274456\pi\) | ||||
−0.650748 | + | 0.759294i | \(0.725544\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5.20499e7i | − 0.219456i | −0.993962 | − | 0.109728i | \(-0.965002\pi\) | ||||
0.993962 | − | 0.109728i | \(-0.0349980\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.82256e8i | 2.40796i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.34491e8 | 0.960474 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.29816e8 | 0.923482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.25904e8 | 0.501131 | 0.250565 | − | 0.968100i | \(-0.419384\pi\) | ||||
0.250565 | + | 0.968100i | \(0.419384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.04209e7 | −0.118809 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.66759e8i | 0.645166i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.04089e8i | 1.15459i | 0.816537 | + | 0.577294i | \(0.195891\pi\) | ||||
−0.816537 | + | 0.577294i | \(0.804109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.05787e8i | − 0.397921i | −0.980007 | − | 0.198961i | \(-0.936243\pi\) | ||||
0.980007 | − | 0.198961i | \(-0.0637566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.17062e8i | 1.17066i | 0.810795 | + | 0.585330i | \(0.199035\pi\) | ||||
−0.810795 | + | 0.585330i | \(0.800965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.76391e8 | −0.645272 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.23336e8 | 1.16122 | 0.580610 | − | 0.814182i | \(-0.302814\pi\) | ||||
0.580610 | + | 0.814182i | \(0.302814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.87670e7 | −0.209127 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.55905e8 | −0.544757 | −0.272379 | − | 0.962190i | \(-0.587810\pi\) | ||||
−0.272379 | + | 0.962190i | \(0.587810\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.52039e7i | − 0.225771i | −0.993608 | − | 0.112886i | \(-0.963991\pi\) | ||||
0.993608 | − | 0.112886i | \(-0.0360094\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.02283e7i | 0.204803i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.30186e8i | 2.79768i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 4.57842e8i | − 1.51547i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.26382e8 | 1.07073 | 0.535365 | − | 0.844621i | \(-0.320174\pi\) | ||||
0.535365 | + | 0.844621i | \(0.320174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.44774e8 | 0.466580 | 0.233290 | − | 0.972407i | \(-0.425051\pi\) | ||||
0.233290 | + | 0.972407i | \(0.425051\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.42878e8 | −1.73418 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.29560e8 | 1.66208 | 0.831042 | − | 0.556210i | \(-0.187745\pi\) | ||||
0.831042 | + | 0.556210i | \(0.187745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 4.17010e7i | − 0.129740i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.32253e7i | 0.162727i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.84591e8i | − 0.862555i | −0.902219 | − | 0.431277i | \(-0.858063\pi\) | ||||
0.902219 | − | 0.431277i | \(-0.141937\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 2.12798e7i | − 0.0633888i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.95494e7 | 0.146332 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.68763e8 | −0.780216 | −0.390108 | − | 0.920769i | \(-0.627562\pi\) | ||||
−0.390108 | + | 0.920769i | \(0.627562\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.85968e8 | 1.39876 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.35797e8 | −2.36506 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.60170e7i | 0.101057i | 0.998723 | + | 0.0505287i | \(0.0160906\pi\) | ||||
−0.998723 | + | 0.0505287i | \(0.983909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 7.63789e8i | − 2.10720i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.65753e7i | 0.0727042i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.01849e8i | 0.274012i | 0.990570 | + | 0.137006i | \(0.0437479\pi\) | ||||
−0.990570 | + | 0.137006i | \(0.956252\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.91919e7 | −0.184608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.55309e8 | −1.71962 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.74848e7 | 0.0455049 | 0.0227524 | − | 0.999741i | \(-0.492757\pi\) | ||||
0.0227524 | + | 0.999741i | \(0.492757\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.15347e8 | 0.551299 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.93038e8i | 1.50581i | 0.658128 | + | 0.752906i | \(0.271348\pi\) | ||||
−0.658128 | + | 0.752906i | \(0.728652\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 3.13866e8i | − 0.784047i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 6.40859e8i | − 1.58792i | −0.607969 | − | 0.793961i | \(-0.708015\pi\) | ||||
0.607969 | − | 0.793961i | \(-0.291985\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 3.54358e8i | − 0.863925i | −0.901892 | − | 0.431963i | \(-0.857821\pi\) | ||||
0.901892 | − | 0.431963i | \(-0.142179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.79470e7 | 0.140140 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.74715e8 | 1.12976 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.91251e8 | 0.451527 | 0.225763 | − | 0.974182i | \(-0.427512\pi\) | ||||
0.225763 | + | 0.974182i | \(0.427512\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.75370e7 | −0.0407487 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 5.16142e8i | − 1.18982i | −0.803792 | − | 0.594910i | \(-0.797188\pi\) | ||||
0.803792 | − | 0.594910i | \(-0.202812\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.06817e8i | 0.469281i | 0.972082 | + | 0.234640i | \(0.0753912\pi\) | ||||
−0.972082 | + | 0.234640i | \(0.924609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.38736e7i | − 0.0312332i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 9.62592e7i | − 0.213332i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.45353e8 | −0.759423 | −0.379711 | − | 0.925105i | \(-0.623977\pi\) | ||||
−0.379711 | + | 0.925105i | \(0.623977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.05512e8 | −1.31094 | −0.655472 | − | 0.755219i | \(-0.727530\pi\) | ||||
−0.655472 | + | 0.755219i | \(0.727530\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.02899e8 | 1.29521 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.04777e8 | 0.221643 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 8.79038e8i | − 1.84525i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1.00236e8i | − 0.207211i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 7.52622e8i | − 1.54402i | −0.635611 | − | 0.772009i | \(-0.719252\pi\) | ||||
0.635611 | − | 0.772009i | \(-0.280748\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 4.82473e8i | − 0.974863i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.49851e8 | 0.501027 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.45541e8 | 0.880062 | 0.440031 | − | 0.897983i | \(-0.354967\pi\) | ||||
0.440031 | + | 0.897983i | \(0.354967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.93099e8 | 0.378565 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.85539e8 | −1.71026 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.49603e8i | − 0.286783i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 5.08582e8i | − 0.960540i | −0.877121 | − | 0.480270i | \(-0.840539\pi\) | ||||
0.877121 | − | 0.480270i | \(-0.159461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 4.00397e8i | − 0.750633i | −0.926897 | − | 0.375317i | \(-0.877534\pi\) | ||||
0.926897 | − | 0.375317i | \(-0.122466\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1.00351e8i | − 0.185373i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.55373e8 | 0.835028 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.91805e8 | −1.61154 | −0.805769 | − | 0.592230i | \(-0.798248\pi\) | ||||
−0.805769 | + | 0.592230i | \(0.798248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.37666e8 | −0.785134 | −0.392567 | − | 0.919723i | \(-0.628413\pi\) | ||||
−0.392567 | + | 0.919723i | \(0.628413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.07859e8 | −0.367497 | −0.183748 | − | 0.982973i | \(-0.558823\pi\) | ||||
−0.183748 | + | 0.982973i | \(0.558823\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.17032e8i | 0.556467i | 0.960513 | + | 0.278234i | \(0.0897490\pi\) | ||||
−0.960513 | + | 0.278234i | \(0.910251\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 6.17499e8i | − 1.06832i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 5.75101e7i | − 0.0987836i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.78582e8i | 0.641024i | 0.947245 | + | 0.320512i | \(0.103855\pi\) | ||||
−0.947245 | + | 0.320512i | \(0.896145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.21162e9 | 2.03694 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.49053e7 | 0.0910006 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.60227e8 | −1.41567 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.20712e9 | −1.95867 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.37740e8i | 0.866413i | 0.901295 | + | 0.433206i | \(0.142618\pi\) | ||||
−0.901295 | + | 0.433206i | \(0.857382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 3.49442e8i | − 0.555179i | −0.960700 | − | 0.277589i | \(-0.910465\pi\) | ||||
0.960700 | − | 0.277589i | \(-0.0895355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.75469e8i | 1.38121i | 0.723230 | + | 0.690607i | \(0.242657\pi\) | ||||
−0.723230 | + | 0.690607i | \(0.757343\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.65174e8i | 0.879325i | 0.898163 | + | 0.439663i | \(0.144902\pi\) | ||||
−0.898163 | + | 0.439663i | \(0.855098\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.16569e8 | −0.180109 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.59559e8 | 1.00507 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.71281e8 | 0.259212 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.37763e8 | 0.354912 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.08310e9i | 1.60573i | 0.596164 | + | 0.802863i | \(0.296691\pi\) | ||||
−0.596164 | + | 0.802863i | \(0.703309\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 9.68321e8i | − 1.41609i | −0.706166 | − | 0.708047i | \(-0.749577\pi\) | ||||
0.706166 | − | 0.708047i | \(-0.250423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.60909e8i | − 0.233721i | −0.993148 | − | 0.116860i | \(-0.962717\pi\) | ||||
0.993148 | − | 0.116860i | \(-0.0372830\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.06540e9i | 1.52666i | 0.646011 | + | 0.763328i | \(0.276436\pi\) | ||||
−0.646011 | + | 0.763328i | \(0.723564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.12682e9 | 1.60379 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.08327e8 | 0.573395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.86400e7 | −0.0678460 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.66197e9 | −2.28740 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.97090e8i | − 0.269458i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.25122e7i | 0.0303720i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 5.33348e8i | − 0.714807i | −0.933950 | − | 0.357404i | \(-0.883662\pi\) | ||||
0.933950 | − | 0.357404i | \(-0.116338\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.01975e9i | − 1.34878i | −0.738377 | − | 0.674388i | \(-0.764407\pi\) | ||||
0.738377 | − | 0.674388i | \(-0.235593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.58060e8 | 0.207687 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.17678e9 | 2.82298 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.70464e8 | −0.219627 | −0.109814 | − | 0.993952i | \(-0.535025\pi\) | ||||
−0.109814 | + | 0.993952i | \(0.535025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.79704e8 | 0.610054 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 9.52841e8i | − 1.20391i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1.76995e8i | − 0.220756i | −0.993890 | − | 0.110378i | \(-0.964794\pi\) | ||||
0.993890 | − | 0.110378i | \(-0.0352062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.30576e9i | − 1.61814i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 9.84067e7i | − 0.120390i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.47406e8 | −1.15164 | −0.575821 | − | 0.817576i | \(-0.695318\pi\) | ||||
−0.575821 | + | 0.817576i | \(0.695318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.18896e9 | −1.42691 | −0.713457 | − | 0.700699i | \(-0.752871\pi\) | ||||
−0.713457 | + | 0.700699i | \(0.752871\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.60260e8 | −0.310365 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.32630e8 | −1.09814 | −0.549072 | − | 0.835775i | \(-0.685019\pi\) | ||||
−0.549072 | + | 0.835775i | \(0.685019\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.83251e8i | − 0.565424i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.90222e8i | 0.219777i | 0.993944 | + | 0.109888i | \(0.0350494\pi\) | ||||
−0.993944 | + | 0.109888i | \(0.964951\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.36152e8i | − 0.156320i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.54464e9i | 1.75135i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.41540e8 | 0.722859 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.34691e7 | 0.0595005 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.01606e8 | 0.333549 | 0.166775 | − | 0.985995i | \(-0.446665\pi\) | ||||
0.166775 | + | 0.985995i | \(0.446665\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.86164e8 | 0.312577 | 0.156289 | − | 0.987711i | \(-0.450047\pi\) | ||||
0.156289 | + | 0.987711i | \(0.450047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.88223e8i | 0.855678i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1.63284e9i | − 1.75090i | −0.483313 | − | 0.875448i | \(-0.660567\pi\) | ||||
0.483313 | − | 0.875448i | \(-0.339433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 2.01171e9i | − 2.14397i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.09869e9i | − 1.15668i | −0.815794 | − | 0.578342i | \(-0.803700\pi\) | ||||
0.815794 | − | 0.578342i | \(-0.196300\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.51385e7 | −0.0472322 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.13112e9 | −1.16928 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.53484e6 | 0.00260453 | 0.00130227 | − | 0.999999i | \(-0.499585\pi\) | ||||
0.00130227 | + | 0.999999i | \(0.499585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.77514e7 | −0.0383233 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.83353e9i | 1.85013i | 0.379810 | + | 0.925065i | \(0.375989\pi\) | ||||
−0.379810 | + | 0.925065i | \(0.624011\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 576.7.h.a.161.10 | yes | 16 | |
3.2 | odd | 2 | inner | 576.7.h.a.161.6 | yes | 16 | |
4.3 | odd | 2 | inner | 576.7.h.a.161.12 | yes | 16 | |
8.3 | odd | 2 | inner | 576.7.h.a.161.7 | yes | 16 | |
8.5 | even | 2 | inner | 576.7.h.a.161.5 | ✓ | 16 | |
12.11 | even | 2 | inner | 576.7.h.a.161.8 | yes | 16 | |
24.5 | odd | 2 | inner | 576.7.h.a.161.9 | yes | 16 | |
24.11 | even | 2 | inner | 576.7.h.a.161.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.7.h.a.161.5 | ✓ | 16 | 8.5 | even | 2 | inner | |
576.7.h.a.161.6 | yes | 16 | 3.2 | odd | 2 | inner | |
576.7.h.a.161.7 | yes | 16 | 8.3 | odd | 2 | inner | |
576.7.h.a.161.8 | yes | 16 | 12.11 | even | 2 | inner | |
576.7.h.a.161.9 | yes | 16 | 24.5 | odd | 2 | inner | |
576.7.h.a.161.10 | yes | 16 | 1.1 | even | 1 | trivial | |
576.7.h.a.161.11 | yes | 16 | 24.11 | even | 2 | inner | |
576.7.h.a.161.12 | yes | 16 | 4.3 | odd | 2 | inner |