Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,5,Mod(161,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.161");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.e (of order \(2\), degree \(1\), not 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: | \(133.967472157\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{20} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(4.23522 + 4.06612i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.161 |
Dual form | 1296.5.e.g.161.6 |
$q$-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 \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 12.2819i | − 0.491275i | −0.969362 | − | 0.245638i | \(-0.921003\pi\) | ||||
0.969362 | − | 0.245638i | \(-0.0789974\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.2840 | 0.291511 | 0.145756 | − | 0.989321i | \(-0.453439\pi\) | ||||
0.145756 | + | 0.989321i | \(0.453439\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 104.171i | − 0.860916i | −0.902611 | − | 0.430458i | \(-0.858352\pi\) | ||||
0.902611 | − | 0.430458i | \(-0.141648\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 75.2346 | 0.445175 | 0.222588 | − | 0.974913i | \(-0.428550\pi\) | ||||
0.222588 | + | 0.974913i | \(0.428550\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 341.998i | − 1.18338i | −0.806164 | − | 0.591692i | \(-0.798460\pi\) | ||||
0.806164 | − | 0.591692i | \(-0.201540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 706.329 | 1.95659 | 0.978295 | − | 0.207218i | \(-0.0664411\pi\) | ||||
0.978295 | + | 0.207218i | \(0.0664411\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 596.312i | − 1.12724i | −0.826033 | − | 0.563622i | \(-0.809407\pi\) | ||||
0.826033 | − | 0.563622i | \(-0.190593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 474.155 | 0.758648 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1302.39i | 1.54862i | 0.632807 | + | 0.774309i | \(0.281903\pi\) | ||||
−0.632807 | + | 0.774309i | \(0.718097\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1029.02 | −1.07078 | −0.535391 | − | 0.844605i | \(-0.679836\pi\) | ||||
−0.535391 | + | 0.844605i | \(0.679836\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 175.435i | − 0.143212i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 563.132 | 0.411346 | 0.205673 | − | 0.978621i | \(-0.434062\pi\) | ||||
0.205673 | + | 0.978621i | \(0.434062\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 99.1448i | − 0.0589797i | −0.999565 | − | 0.0294898i | \(-0.990612\pi\) | ||||
0.999565 | − | 0.0294898i | \(-0.00938826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 896.514 | 0.484864 | 0.242432 | − | 0.970168i | \(-0.422055\pi\) | ||||
0.242432 | + | 0.970168i | \(0.422055\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 430.570i | − 0.194916i | −0.995240 | − | 0.0974581i | \(-0.968929\pi\) | ||||
0.995240 | − | 0.0974581i | \(-0.0310712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2196.97 | −0.915021 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5271.47i | 1.87664i | 0.345773 | + | 0.938318i | \(0.387617\pi\) | ||||
−0.345773 | + | 0.938318i | \(0.612383\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1279.41 | −0.422947 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5639.26i | − 1.62001i | −0.586423 | − | 0.810005i | \(-0.699464\pi\) | ||||
0.586423 | − | 0.810005i | \(-0.300536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1131.25 | 0.304018 | 0.152009 | − | 0.988379i | \(-0.451426\pi\) | ||||
0.152009 | + | 0.988379i | \(0.451426\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 924.023i | − 0.218704i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1352.82 | 0.301364 | 0.150682 | − | 0.988582i | \(-0.451853\pi\) | ||||
0.150682 | + | 0.988582i | \(0.451853\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 5681.42i | − 1.12704i | −0.826101 | − | 0.563522i | \(-0.809446\pi\) | ||||
0.826101 | − | 0.563522i | \(-0.190554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4236.54 | 0.794996 | 0.397498 | − | 0.917603i | \(-0.369878\pi\) | ||||
0.397498 | + | 0.917603i | \(0.369878\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1487.98i | − 0.250967i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6135.42 | 0.983083 | 0.491542 | − | 0.870854i | \(-0.336434\pi\) | ||||
0.491542 | + | 0.870854i | \(0.336434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7509.88i | − 1.09013i | −0.838395 | − | 0.545063i | \(-0.816506\pi\) | ||||
0.838395 | − | 0.545063i | \(-0.183494\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4200.38 | −0.581367 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8721.70i | 1.10109i | 0.834807 | + | 0.550543i | \(0.185579\pi\) | ||||
−0.834807 | + | 0.550543i | \(0.814421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1074.65 | 0.129774 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 8675.05i | − 0.961224i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5441.31 | 0.578309 | 0.289154 | − | 0.957282i | \(-0.406626\pi\) | ||||
0.289154 | + | 0.957282i | \(0.406626\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7482.63i | 0.733519i | 0.930316 | + | 0.366759i | \(0.119533\pi\) | ||||
−0.930316 | + | 0.366759i | \(0.880467\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13576.5 | −1.27972 | −0.639860 | − | 0.768492i | \(-0.721008\pi\) | ||||
−0.639860 | + | 0.768492i | \(0.721008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16741.7i | 1.46229i | 0.682224 | + | 0.731143i | \(0.261013\pi\) | ||||
−0.682224 | + | 0.731143i | \(0.738987\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12068.7 | −1.01579 | −0.507897 | − | 0.861418i | \(-0.669577\pi\) | ||||
−0.507897 | + | 0.861418i | \(0.669577\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 704.601i | − 0.0551806i | −0.999619 | − | 0.0275903i | \(-0.991217\pi\) | ||||
0.999619 | − | 0.0275903i | \(-0.00878337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7323.84 | −0.553787 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 4885.11i | − 0.344970i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3789.45 | 0.258824 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 13499.7i | − 0.863981i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16050.0 | 0.995105 | 0.497552 | − | 0.867434i | \(-0.334232\pi\) | ||||
0.497552 | + | 0.867434i | \(0.334232\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 15504.3i | − 0.903463i | −0.892154 | − | 0.451732i | \(-0.850806\pi\) | ||||
0.892154 | − | 0.451732i | \(-0.149194\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10089.2 | 0.570368 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 890.615i | − 0.0474514i | −0.999719 | − | 0.0237257i | \(-0.992447\pi\) | ||||
0.999719 | − | 0.0237257i | \(-0.00755283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9358.18 | −0.484353 | −0.242176 | − | 0.970232i | \(-0.577861\pi\) | ||||
−0.242176 | + | 0.970232i | \(0.577861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 7837.25i | − 0.383258i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15995.8 | 0.760798 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 40669.4i | − 1.83187i | −0.401323 | − | 0.915937i | \(-0.631450\pi\) | ||||
0.401323 | − | 0.915937i | \(-0.368550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24974.5 | 1.09532 | 0.547661 | − | 0.836700i | \(-0.315518\pi\) | ||||
0.547661 | + | 0.836700i | \(0.315518\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12638.3i | 0.526049i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −32918.4 | −1.33549 | −0.667743 | − | 0.744392i | \(-0.732739\pi\) | ||||
−0.667743 | + | 0.744392i | \(0.732739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 8517.75i | − 0.328604i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13796.3 | −0.519262 | −0.259631 | − | 0.965708i | \(-0.583601\pi\) | ||||
−0.259631 | + | 0.965708i | \(0.583601\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11332.4i | 0.406339i | 0.979144 | + | 0.203170i | \(0.0651243\pi\) | ||||
−0.979144 | + | 0.203170i | \(0.934876\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22900.8 | −0.801819 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 39170.4i | − 1.30878i | −0.756158 | − | 0.654389i | \(-0.772926\pi\) | ||||
0.756158 | − | 0.654389i | \(-0.227074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6772.86 | 0.221155 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 24097.3i | − 0.752078i | −0.926604 | − | 0.376039i | \(-0.877286\pi\) | ||||
0.926604 | − | 0.376039i | \(-0.122714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10277.1 | 0.313699 | 0.156850 | − | 0.987623i | \(-0.449866\pi\) | ||||
0.156850 | + | 0.987623i | \(0.449866\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 6916.33i | − 0.202084i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −35626.2 | −1.01879 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 35030.4i | 0.960237i | 0.877204 | + | 0.480119i | \(0.159406\pi\) | ||||
−0.877204 | + | 0.480119i | \(0.840594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5240.55 | 0.140690 | 0.0703448 | − | 0.997523i | \(-0.477590\pi\) | ||||
0.0703448 | + | 0.997523i | \(0.477590\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 42421.5i | − 1.09308i | −0.837431 | − | 0.546542i | \(-0.815944\pi\) | ||||
0.837431 | − | 0.546542i | \(-0.184056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −31270.0 | −0.789627 | −0.394814 | − | 0.918761i | \(-0.629191\pi\) | ||||
−0.394814 | + | 0.918761i | \(0.629191\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18603.4i | 0.451440i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1217.69 | −0.0289753 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 73578.8i | − 1.68446i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 31124.4 | 0.699096 | 0.349548 | − | 0.936918i | \(-0.386335\pi\) | ||||
0.349548 | + | 0.936918i | \(0.386335\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 11010.9i | − 0.238202i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14698.6 | −0.312145 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 25730.1i | − 0.526813i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16027.9 | −0.322305 | −0.161153 | − | 0.986930i | \(-0.551521\pi\) | ||||
−0.161153 | + | 0.986930i | \(0.551521\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 67528.9i | − 1.31050i | −0.755411 | − | 0.655251i | \(-0.772563\pi\) | ||||
0.755411 | − | 0.655251i | \(-0.227437\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 78065.8 | 1.48864 | 0.744321 | − | 0.667823i | \(-0.232773\pi\) | ||||
0.744321 | + | 0.667823i | \(0.232773\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 61204.9i | − 1.12739i | −0.825983 | − | 0.563696i | \(-0.809379\pi\) | ||||
0.825983 | − | 0.563696i | \(-0.190621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5288.21 | −0.0957576 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 43154.9i | 0.755500i | 0.925908 | + | 0.377750i | \(0.123302\pi\) | ||||
−0.925908 | + | 0.377750i | \(0.876698\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −56207.6 | −0.967745 | −0.483873 | − | 0.875138i | \(-0.660770\pi\) | ||||
−0.483873 | + | 0.875138i | \(0.660770\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26982.9i | 0.449527i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 53140.4 | 0.871025 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 15739.4i | − 0.249828i | −0.992168 | − | 0.124914i | \(-0.960135\pi\) | ||||
0.992168 | − | 0.124914i | \(-0.0398655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −62118.3 | −0.970462 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 58760.1i | 0.889643i | 0.895619 | + | 0.444822i | \(0.146733\pi\) | ||||
−0.895619 | + | 0.444822i | \(0.853267\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8043.81 | 0.119912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 94338.8i | − 1.36389i | −0.731404 | − | 0.681944i | \(-0.761135\pi\) | ||||
0.731404 | − | 0.681944i | \(-0.238865\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 64743.6 | 0.921945 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 79782.6i | − 1.10256i | −0.834319 | − | 0.551282i | \(-0.814139\pi\) | ||||
0.834319 | − | 0.551282i | \(-0.185861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 76677.1 | 1.04406 | 0.522032 | − | 0.852926i | \(-0.325174\pi\) | ||||
0.522032 | + | 0.852926i | \(0.325174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 49393.1i | − 0.653132i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 113156. | 1.47475 | 0.737374 | − | 0.675485i | \(-0.236066\pi\) | ||||
0.737374 | + | 0.675485i | \(0.236066\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 96549.7i | − 1.22275i | −0.791341 | − | 0.611376i | \(-0.790616\pi\) | ||||
0.791341 | − | 0.611376i | \(-0.209384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30537.1 | −0.381289 | −0.190645 | − | 0.981659i | \(-0.561058\pi\) | ||||
−0.190645 | + | 0.981659i | \(0.561058\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1416.19i | − 0.0171932i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33441.6 | −0.400397 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 4054.67i | − 0.0472303i | −0.999721 | − | 0.0236151i | \(-0.992482\pi\) | ||||
0.999721 | − | 0.0236151i | \(-0.00751763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −69260.7 | −0.795872 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 44863.3i | − 0.501821i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12805.8 | 0.141343 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 13893.9i | − 0.149357i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −44297.5 | −0.470005 | −0.235002 | − | 0.971995i | \(-0.575510\pi\) | ||||
−0.235002 | + | 0.971995i | \(0.575510\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 95089.7i | − 0.983134i | −0.870840 | − | 0.491567i | \(-0.836424\pi\) | ||||
0.870840 | − | 0.491567i | \(-0.163576\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −170572. | −1.74108 | −0.870541 | − | 0.492097i | \(-0.836231\pi\) | ||||
−0.870541 | + | 0.492097i | \(0.836231\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 121998.i | 1.21405i | 0.794684 | + | 0.607024i | \(0.207637\pi\) | ||||
−0.794684 | + | 0.607024i | \(0.792363\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 135671. | 1.33323 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 241563.i | − 2.31540i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 35672.9 | 0.337731 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 6150.28i | − 0.0568203i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 95214.2 | 0.869052 | 0.434526 | − | 0.900659i | \(-0.356916\pi\) | ||||
0.434526 | + | 0.900659i | \(0.356916\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 16615.2i | − 0.148053i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8409.77 | 0.0740499 | 0.0370249 | − | 0.999314i | \(-0.488212\pi\) | ||||
0.0370249 | + | 0.999314i | \(0.488212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 107194.i | 0.921852i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −65677.6 | −0.558250 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6032.75i | 0.0501022i | 0.999686 | + | 0.0250511i | \(0.00797484\pi\) | ||||
−0.999686 | + | 0.0250511i | \(0.992025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 139600. | 1.14613 | 0.573065 | − | 0.819510i | \(-0.305754\pi\) | ||||
0.573065 | + | 0.819510i | \(0.305754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 85395.3i | − 0.685306i | −0.939462 | − | 0.342653i | \(-0.888674\pi\) | ||||
0.939462 | − | 0.342653i | \(-0.111326\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −69778.6 | −0.553689 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 90712.4i | − 0.703846i | −0.936029 | − | 0.351923i | \(-0.885528\pi\) | ||||
0.936029 | − | 0.351923i | \(-0.114472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 368579. | 2.82824 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 52032.6i | − 0.390562i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25541.3 | 0.189632 | 0.0948160 | − | 0.995495i | \(-0.469774\pi\) | ||||
0.0948160 | + | 0.995495i | \(0.469774\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 75297.9i | 0.547060i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −234528. | −1.68569 | −0.842844 | − | 0.538158i | \(-0.819120\pi\) | ||||
−0.842844 | + | 0.538158i | \(0.819120\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 97984.7i | 0.689407i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 107483. | 0.748278 | 0.374139 | − | 0.927373i | \(-0.377938\pi\) | ||||
0.374139 | + | 0.927373i | \(0.377938\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 164427.i | − 1.12093i | −0.828180 | − | 0.560463i | \(-0.810623\pi\) | ||||
0.828180 | − | 0.560463i | \(-0.189377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18275.2 | −0.123294 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 182900.i | 1.20869i | 0.796724 | + | 0.604343i | \(0.206565\pi\) | ||||
−0.796724 | + | 0.604343i | \(0.793435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −203937. | −1.33396 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 75354.6i | − 0.482965i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −277717. | −1.76206 | −0.881031 | − | 0.473059i | \(-0.843150\pi\) | ||||
−0.881031 | + | 0.473059i | \(0.843150\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 168062.i | 1.04515i | 0.852593 | + | 0.522576i | \(0.175029\pi\) | ||||
−0.852593 | + | 0.522576i | \(0.824971\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −77418.0 | −0.476685 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 58661.9i | − 0.354134i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −88381.1 | −0.528339 | −0.264170 | − | 0.964476i | \(-0.585098\pi\) | ||||
−0.264170 | + | 0.964476i | \(0.585098\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 80551.4i | − 0.472251i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −92235.5 | −0.535552 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 151429.i | − 0.862542i | −0.902222 | − | 0.431271i | \(-0.858065\pi\) | ||||
0.902222 | − | 0.431271i | \(-0.141935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −132220. | −0.745992 | −0.372996 | − | 0.927833i | \(-0.621669\pi\) | ||||
−0.372996 | + | 0.927833i | \(0.621669\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 162160.i | − 0.897772i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16158.9 | 0.0886247 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 231482.i | 1.24613i | 0.782170 | + | 0.623065i | \(0.214113\pi\) | ||||
−0.782170 | + | 0.623065i | \(0.785887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −218090. | −1.16321 | −0.581607 | − | 0.813470i | \(-0.697576\pi\) | ||||
−0.581607 | + | 0.813470i | \(0.697576\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 421192.i | − 2.20555i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −89557.0 | −0.464698 | −0.232349 | − | 0.972633i | \(-0.574641\pi\) | ||||
−0.232349 | + | 0.972633i | \(0.574641\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 264286.i | − 1.34669i | −0.739330 | − | 0.673343i | \(-0.764858\pi\) | ||||
0.739330 | − | 0.673343i | \(-0.235142\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 107119. | 0.540936 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 33967.2i | − 0.168487i | −0.996445 | − | 0.0842435i | \(-0.973153\pi\) | ||||
0.996445 | − | 0.0842435i | \(-0.0268474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10328.0 | −0.0507765 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 13198.8i | − 0.0637546i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 83273.7 | 0.398727 | 0.199363 | − | 0.979926i | \(-0.436113\pi\) | ||||
0.199363 | + | 0.979926i | \(0.436113\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 57510.4i | − 0.270610i | −0.990804 | − | 0.135305i | \(-0.956799\pi\) | ||||
0.990804 | − | 0.135305i | \(-0.0432015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −81793.9 | −0.381557 | −0.190778 | − | 0.981633i | \(-0.561101\pi\) | ||||
−0.190778 | + | 0.981633i | \(0.561101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 161762.i | 0.741726i | 0.928688 | + | 0.370863i | \(0.120938\pi\) | ||||
−0.928688 | + | 0.370863i | \(0.879062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19323.8 | 0.0878511 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 93390.6i | − 0.417427i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 334910. | 1.48436 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 128459.i | − 0.559878i | −0.960018 | − | 0.279939i | \(-0.909686\pi\) | ||||
0.960018 | − | 0.279939i | \(-0.0903142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42367.0 | 0.183121 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 66829.5i | − 0.284109i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 255021. | 1.07527 | 0.537636 | − | 0.843177i | \(-0.319318\pi\) | ||||
0.537636 | + | 0.843177i | \(0.319318\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 174548.i | − 0.724023i | −0.932174 | − | 0.362012i | \(-0.882090\pi\) | ||||
0.932174 | − | 0.362012i | \(-0.117910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 445414. | 1.83261 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 81153.7i | − 0.328546i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −209729. | −0.842282 | −0.421141 | − | 0.906995i | \(-0.638370\pi\) | ||||
−0.421141 | + | 0.906995i | \(0.638370\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 288148.i | 1.13888i | 0.822031 | + | 0.569442i | \(0.192841\pi\) | ||||
−0.822031 | + | 0.569442i | \(0.807159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 91900.8 | 0.360360 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 84680.9i | − 0.326851i | −0.986556 | − | 0.163426i | \(-0.947746\pi\) | ||||
0.986556 | − | 0.163426i | \(-0.0522544\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 60514.9 | 0.231750 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 166746.i | 0.628695i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44852.8 | −0.167806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 80148.3i | 0.295270i | 0.989042 | + | 0.147635i | \(0.0471660\pi\) | ||||
−0.989042 | + | 0.147635i | \(0.952834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −127783. | −0.467163 | −0.233581 | − | 0.972337i | \(-0.575045\pi\) | ||||
−0.233581 | + | 0.972337i | \(0.575045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 351923.i | 1.26715i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −75747.1 | −0.270679 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7459.12i | − 0.0262563i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 205620. | 0.718385 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 228860.i | 0.787756i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1167.97 | 0.00399060 | 0.00199530 | − | 0.999998i | \(-0.499365\pi\) | ||||
0.00199530 | + | 0.999998i | \(0.499365\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 148226.i | 0.499035i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −277805. | −0.928465 | −0.464232 | − | 0.885713i | \(-0.653670\pi\) | ||||
−0.464232 | + | 0.885713i | \(0.653670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 919914.i | 3.03001i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 87638.7 | 0.286580 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 127126.i | 0.409755i | 0.978788 | + | 0.204877i | \(0.0656795\pi\) | ||||
−0.978788 | + | 0.204877i | \(0.934320\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 67448.9 | 0.215850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 123792.i | 0.390550i | 0.980749 | + | 0.195275i | \(0.0625599\pi\) | ||||
−0.980749 | + | 0.195275i | \(0.937440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8653.83 | −0.0271089 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 61812.5i | 0.190920i | 0.995433 | + | 0.0954601i | \(0.0304322\pi\) | ||||
−0.995433 | + | 0.0954601i | \(0.969568\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 204135. | 0.626101 | 0.313050 | − | 0.949737i | \(-0.398649\pi\) | ||||
0.313050 | + | 0.949737i | \(0.398649\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 282745.i | − 0.855182i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 555504. | 1.66854 | 0.834269 | − | 0.551358i | \(-0.185890\pi\) | ||||
0.834269 | + | 0.551358i | \(0.185890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 107272.i | − 0.317784i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 549133. | 1.61563 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7016.77i | − 0.0203639i | −0.999948 | − | 0.0101820i | \(-0.996759\pi\) | ||||
0.999948 | − | 0.0101820i | \(-0.00324107\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −726827. | −2.09508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 77064.9i | 0.219153i | 0.993978 | + | 0.109576i | \(0.0349494\pi\) | ||||
−0.993978 | + | 0.109576i | \(0.965051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −59998.4 | −0.169475 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 546962.i | 1.52442i | 0.647333 | + | 0.762208i | \(0.275884\pi\) | ||||
−0.647333 | + | 0.762208i | \(0.724116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −539976. | −1.49495 | −0.747473 | − | 0.664292i | \(-0.768733\pi\) | ||||
−0.747473 | + | 0.664292i | \(0.768733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 46541.6i | − 0.127154i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −499326. | −1.35521 | −0.677606 | − | 0.735425i | \(-0.736982\pi\) | ||||
−0.677606 | + | 0.735425i | \(0.736982\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 32393.8i | − 0.0867719i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 80551.4 | 0.214364 | 0.107182 | − | 0.994239i | \(-0.465817\pi\) | ||||
0.107182 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 444845.i | − 1.16853i | −0.811564 | − | 0.584263i | \(-0.801383\pi\) | ||||
0.811564 | − | 0.584263i | \(-0.198617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −560941. | −1.46398 | −0.731992 | − | 0.681314i | \(-0.761409\pi\) | ||||
−0.731992 | + | 0.681314i | \(0.761409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 124581.i | 0.320979i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 130545. | 0.334196 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 192590.i | − 0.486780i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −621772. | −1.56161 | −0.780805 | − | 0.624775i | \(-0.785191\pi\) | ||||
−0.780805 | + | 0.624775i | \(0.785191\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 197125.i | − 0.488871i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −165288. | −0.407345 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 322644.i | − 0.785248i | −0.919699 | − | 0.392624i | \(-0.871567\pi\) | ||||
0.919699 | − | 0.392624i | \(-0.128433\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 489813. | 1.18470 | 0.592350 | − | 0.805681i | \(-0.298200\pi\) | ||||
0.592350 | + | 0.805681i | \(0.298200\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26885.7i | 0.0642263i | 0.999484 | + | 0.0321132i | \(0.0102237\pi\) | ||||
−0.999484 | + | 0.0321132i | \(0.989776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −587446. | −1.39469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 714229.i | 1.67498i | 0.546449 | + | 0.837492i | \(0.315979\pi\) | ||||
−0.546449 | + | 0.837492i | \(0.684021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −190422. | −0.443849 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 234697.i | − 0.540428i | −0.962800 | − | 0.270214i | \(-0.912906\pi\) | ||||
0.962800 | − | 0.270214i | \(-0.0870944\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 626562. | 1.43404 | 0.717020 | − | 0.697053i | \(-0.245506\pi\) | ||||
0.717020 | + | 0.697053i | \(0.245506\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 123915.i | − 0.280208i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 776630. | 1.74567 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 117843.i | − 0.261734i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 641998. | 1.41744 | 0.708718 | − | 0.705491i | \(-0.249274\pi\) | ||||
0.708718 | + | 0.705491i | \(0.249274\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 656946.i | 1.43335i | 0.697407 | + | 0.716675i | \(0.254337\pi\) | ||||
−0.697407 | + | 0.716675i | \(0.745663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 77723.9 | 0.168583 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 76710.6i | − 0.164442i | −0.996614 | − | 0.0822212i | \(-0.973799\pi\) | ||||
0.996614 | − | 0.0822212i | \(-0.0262014\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10938.4 | −0.0233117 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 396597.i | 0.835432i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 570869. | 1.19559 | 0.597793 | − | 0.801651i | \(-0.296045\pi\) | ||||
0.597793 | + | 0.801651i | \(0.296045\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 114936.i | 0.237951i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33907.3 | −0.0697956 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4271.71i | 0.00869292i | 0.999991 | + | 0.00434646i | \(0.00138353\pi\) | ||||
−0.999991 | + | 0.00434646i | \(0.998616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 397757. | 0.804835 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 106882.i | 0.213829i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 148443. | 0.295303 | 0.147652 | − | 0.989039i | \(-0.452829\pi\) | ||||
0.147652 | + | 0.989039i | \(0.452829\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 613618.i | 1.20703i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −96256.2 | −0.188285 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 549881.i | 1.06368i | 0.846845 | + | 0.531840i | \(0.178499\pi\) | ||||
−0.846845 | + | 0.531840i | \(0.821501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −193928. | −0.373052 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 617534.i | 1.17486i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −644007. | −1.21849 | −0.609244 | − | 0.792982i | \(-0.708527\pi\) | ||||
−0.609244 | + | 0.792982i | \(0.708527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 306606.i | − 0.573780i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 832831. | 1.55006 | 0.775031 | − | 0.631924i | \(-0.217734\pi\) | ||||
0.775031 | + | 0.631924i | \(0.217734\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 140925.i | − 0.259449i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −472487. | −0.865170 | −0.432585 | − | 0.901593i | \(-0.642398\pi\) | ||||
−0.432585 | + | 0.901593i | \(0.642398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 978422.i | 1.77235i | 0.463354 | + | 0.886173i | \(0.346646\pi\) | ||||
−0.463354 | + | 0.886173i | \(0.653354\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −499497. | −0.899954 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 239139.i | 0.426273i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 166281. | 0.294824 | 0.147412 | − | 0.989075i | \(-0.452906\pi\) | ||||
0.147412 | + | 0.989075i | \(0.452906\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 306733.i | − 0.538105i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −238453. | −0.416114 | −0.208057 | − | 0.978117i | \(-0.566714\pi\) | ||||
−0.208057 | + | 0.978117i | \(0.566714\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 598335.i | 1.03318i | 0.856233 | + | 0.516589i | \(0.172799\pi\) | ||||
−0.856233 | + | 0.516589i | \(0.827201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −172389. | −0.296116 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 424267.i | − 0.721189i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 667323. | 1.12845 | 0.564227 | − | 0.825620i | \(-0.309174\pi\) | ||||
0.564227 | + | 0.825620i | \(0.309174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 848153.i | 1.41943i | 0.704487 | + | 0.709717i | \(0.251177\pi\) | ||||
−0.704487 | + | 0.709717i | \(0.748823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −487916. | −0.812347 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 70028.8i | − 0.115399i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −591838. | −0.970289 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 404300.i | 0.656091i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 967733. | 1.56245 | 0.781225 | − | 0.624250i | \(-0.214595\pi\) | ||||
0.781225 | + | 0.624250i | \(0.214595\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 10064.6i | − 0.0160858i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 85109.3 | 0.135341 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 674146.i | 1.06130i | 0.847592 | + | 0.530649i | \(0.178052\pi\) | ||||
−0.847592 | + | 0.530649i | \(0.821948\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −147254. | −0.230661 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 441323.i | − 0.684425i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −104614. | −0.161435 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 570317.i | 0.871403i | 0.900091 | + | 0.435702i | \(0.143500\pi\) | ||||
−0.900091 | + | 0.435702i | \(0.856500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 111731. | 0.169876 | 0.0849379 | − | 0.996386i | \(-0.472931\pi\) | ||||
0.0849379 | + | 0.996386i | \(0.472931\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 169444.i | 0.255100i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 633234. | 0.948680 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.04162e6i | − 1.54534i | −0.634811 | − | 0.772668i | \(-0.718922\pi\) | ||||
0.634811 | − | 0.772668i | \(-0.281078\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 108973. | 0.160886 | 0.0804432 | − | 0.996759i | \(-0.474366\pi\) | ||||
0.0804432 | + | 0.996759i | \(0.474366\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 550908.i | − 0.805505i | −0.915309 | − | 0.402753i | \(-0.868053\pi\) | ||||
0.915309 | − | 0.402753i | \(-0.131947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −57256.0 | −0.0833128 | −0.0416564 | − | 0.999132i | \(-0.513263\pi\) | ||||
−0.0416564 | + | 0.999132i | \(0.513263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 751358.i | 1.08282i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 139183. | 0.199624 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 951705.i | 1.35201i | 0.736899 | + | 0.676003i | \(0.236289\pi\) | ||||
−0.736899 | + | 0.676003i | \(0.763711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −988934. | −1.39822 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 281264.i | 0.393914i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 54128.7 | 0.0754502 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 335803.i | − 0.463687i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.02287e6 | −1.40579 | −0.702896 | − | 0.711293i | \(-0.748110\pi\) | ||||
−0.702896 | + | 0.711293i | \(0.748110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 661433.i | 0.900584i | 0.892881 | + | 0.450292i | \(0.148680\pi\) | ||||
−0.892881 | + | 0.450292i | \(0.851320\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −102749. | −0.139249 | −0.0696246 | − | 0.997573i | \(-0.522180\pi\) | ||||
−0.0696246 | + | 0.997573i | \(0.522180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 168806.i | 0.226655i | 0.993558 | + | 0.113328i | \(0.0361509\pi\) | ||||
−0.993558 | + | 0.113328i | \(0.963849\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −481087. | −0.642971 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 639132.i | − 0.846352i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 101779. | 0.134160 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 192830.i | − 0.251860i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −190156. | −0.247235 | −0.123618 | − | 0.992330i | \(-0.539450\pi\) | ||||
−0.123618 | + | 0.992330i | \(0.539450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 171490.i | 0.220946i | 0.993879 | + | 0.110473i | \(0.0352366\pi\) | ||||
−0.993879 | + | 0.110473i | \(0.964763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −869284. | −1.11491 | −0.557456 | − | 0.830207i | \(-0.688222\pi\) | ||||
−0.557456 | + | 0.830207i | \(0.688222\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 144353.i | 0.183476i | 0.995783 | + | 0.0917378i | \(0.0292422\pi\) | ||||
−0.995783 | + | 0.0917378i | \(0.970758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 229260. | 0.290084 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 304124.i | − 0.381371i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −295961. | −0.369477 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.34018e6i | − 1.65823i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.80283e6 | 2.22078 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 126222.i | − 0.154113i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −107697. | −0.130915 | −0.0654574 | − | 0.997855i | \(-0.520851\pi\) | ||||
−0.0654574 | + | 0.997855i | \(0.520851\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 712977.i | 0.859091i | 0.903045 | + | 0.429545i | \(0.141326\pi\) | ||||
−0.903045 | + | 0.429545i | \(0.858674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −782310. | −0.938507 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 221465.i | − 0.263370i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −239512. | −0.283594 | −0.141797 | − | 0.989896i | \(-0.545288\pi\) | ||||
−0.141797 | + | 0.989896i | \(0.545288\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 427440.i | − 0.501732i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 267012. | 0.312067 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.28407e6i | 1.48785i | 0.668266 | + | 0.743923i | \(0.267037\pi\) | ||||
−0.668266 | + | 0.743923i | \(0.732963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.55178e6 | −1.79032 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 437557.i | 0.500508i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −471000. | −0.536466 | −0.268233 | − | 0.963354i | \(-0.586440\pi\) | ||||
−0.268233 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 721460.i | − 0.814766i | −0.913257 | − | 0.407383i | \(-0.866441\pi\) | ||||
0.913257 | − | 0.407383i | \(-0.133559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −59121.2 | −0.0664845 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 605552.i | 0.675229i | 0.941284 | + | 0.337615i | \(0.109620\pi\) | ||||
−0.941284 | + | 0.337615i | \(0.890380\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 318734. | 0.353913 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 527043.i | 0.580310i | 0.956980 | + | 0.290155i | \(0.0937069\pi\) | ||||
−0.956980 | + | 0.290155i | \(0.906293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 430240. | 0.471741 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 12721.6i | − 0.0138326i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 135363. | 0.146573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 64363.8i | − 0.0691174i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.24031e6 | 1.32641 | 0.663203 | − | 0.748439i | \(-0.269196\pi\) | ||||
0.663203 | + | 0.748439i | \(0.269196\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.27298e6i | 1.35015i | 0.737748 | + | 0.675076i | \(0.235889\pi\) | ||||
−0.737748 | + | 0.675076i | \(0.764111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −133673. | −0.141194 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1.38469e6i | − 1.45065i | −0.688406 | − | 0.725325i | \(-0.741689\pi\) | ||||
0.688406 | − | 0.725325i | \(-0.258311\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 908546. | 0.947942 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 169030.i | 0.174927i | 0.996168 | + | 0.0874633i | \(0.0278761\pi\) | ||||
−0.996168 | + | 0.0874633i | \(0.972124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −521016. | −0.537006 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 534602.i | − 0.546560i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.57481e6 | 1.60354 | 0.801772 | − | 0.597630i | \(-0.203891\pi\) | ||||
0.801772 | + | 0.597630i | \(0.203891\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 384055.i | 0.387924i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 570747. | 0.574187 | 0.287094 | − | 0.957903i | \(-0.407311\pi\) | ||||
0.287094 | + | 0.957903i | \(0.407311\pi\) | |||||||
\(998\) | 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 | 1296.5.e.g.161.3 | 8 | ||
3.2 | odd | 2 | inner | 1296.5.e.g.161.6 | 8 | ||
4.3 | odd | 2 | 324.5.c.a.161.3 | 8 | |||
9.2 | odd | 6 | 432.5.q.c.17.2 | 8 | |||
9.4 | even | 3 | 432.5.q.c.305.2 | 8 | |||
9.5 | odd | 6 | 144.5.q.c.65.1 | 8 | |||
9.7 | even | 3 | 144.5.q.c.113.1 | 8 | |||
12.11 | even | 2 | 324.5.c.a.161.6 | 8 | |||
36.7 | odd | 6 | 36.5.g.a.5.4 | ✓ | 8 | ||
36.11 | even | 6 | 108.5.g.a.17.2 | 8 | |||
36.23 | even | 6 | 36.5.g.a.29.4 | yes | 8 | ||
36.31 | odd | 6 | 108.5.g.a.89.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.g.a.5.4 | ✓ | 8 | 36.7 | odd | 6 | ||
36.5.g.a.29.4 | yes | 8 | 36.23 | even | 6 | ||
108.5.g.a.17.2 | 8 | 36.11 | even | 6 | |||
108.5.g.a.89.2 | 8 | 36.31 | odd | 6 | |||
144.5.q.c.65.1 | 8 | 9.5 | odd | 6 | |||
144.5.q.c.113.1 | 8 | 9.7 | even | 3 | |||
324.5.c.a.161.3 | 8 | 4.3 | odd | 2 | |||
324.5.c.a.161.6 | 8 | 12.11 | even | 2 | |||
432.5.q.c.17.2 | 8 | 9.2 | odd | 6 | |||
432.5.q.c.305.2 | 8 | 9.4 | even | 3 | |||
1296.5.e.g.161.3 | 8 | 1.1 | even | 1 | trivial | ||
1296.5.e.g.161.6 | 8 | 3.2 | odd | 2 | inner |