Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,3,Mod(351,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.351");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.b (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: | \(21.7984211488\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1827904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 351.6 | ||
Root | \(2.65109i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.351 |
Dual form | 800.3.b.i.351.1 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 5.30219i | 1.76740i | 0.468058 | + | 0.883698i | \(0.344954\pi\) | ||||
−0.468058 | + | 0.883698i | \(0.655046\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.206625i | 0.0295178i | 0.999891 | + | 0.0147589i | \(0.00469807\pi\) | ||||
−0.999891 | + | 0.0147589i | \(0.995302\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.1132 | −2.12369 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 15.0176i | − 1.36524i | −0.730774 | − | 0.682619i | \(-0.760841\pi\) | ||||
0.730774 | − | 0.682619i | \(-0.239159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.6999 | −0.899995 | −0.449998 | − | 0.893030i | \(-0.648575\pi\) | ||||
−0.449998 | + | 0.893030i | \(0.648575\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.1911 | 1.07007 | 0.535033 | − | 0.844831i | \(-0.320299\pi\) | ||||
0.535033 | + | 0.844831i | \(0.320299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 19.3999i | − 1.02105i | −0.859864 | − | 0.510523i | \(-0.829452\pi\) | ||||
0.859864 | − | 0.510523i | \(-0.170548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.09556 | −0.0521696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 27.2242i | − 1.18366i | −0.806062 | − | 0.591831i | \(-0.798405\pi\) | ||||
0.806062 | − | 0.591831i | \(-0.201595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 53.6220i | − 1.98600i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −44.4175 | −1.53164 | −0.765819 | − | 0.643056i | \(-0.777666\pi\) | ||||
−0.765819 | + | 0.643056i | \(0.777666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 20.3822i | − 0.657492i | −0.944418 | − | 0.328746i | \(-0.893374\pi\) | ||||
0.944418 | − | 0.328746i | \(-0.106626\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 79.6262 | 2.41292 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.1089 | 0.489431 | 0.244715 | − | 0.969595i | \(-0.421305\pi\) | ||||
0.244715 | + | 0.969595i | \(0.421305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 62.0352i | − 1.59065i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −32.3043 | −0.787910 | −0.393955 | − | 0.919130i | \(-0.628893\pi\) | ||||
−0.393955 | + | 0.919130i | \(0.628893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.06244i | − 0.0944753i | −0.998884 | − | 0.0472377i | \(-0.984958\pi\) | ||||
0.998884 | − | 0.0472377i | \(-0.0150418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 5.37588i | − 0.114380i | −0.998363 | − | 0.0571902i | \(-0.981786\pi\) | ||||
0.998363 | − | 0.0571902i | \(-0.0182142\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.9573 | 0.999129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 96.4527i | 1.89123i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −79.1703 | −1.49378 | −0.746890 | − | 0.664948i | \(-0.768454\pi\) | ||||
−0.746890 | + | 0.664948i | \(0.768454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 102.862 | 1.80459 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 83.3999i | 1.41356i | 0.707435 | + | 0.706779i | \(0.249852\pi\) | ||||
−0.707435 | + | 0.706779i | \(0.750148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.7486 | −0.602435 | −0.301218 | − | 0.953555i | \(-0.597393\pi\) | ||||
−0.301218 | + | 0.953555i | \(0.597393\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3.94925i | − 0.0626866i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.51518i | 0.0673907i | 0.999432 | + | 0.0336954i | \(0.0107276\pi\) | ||||
−0.999432 | + | 0.0336954i | \(0.989272\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 144.348 | 2.09200 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 41.6530i | − 0.586662i | −0.956011 | − | 0.293331i | \(-0.905236\pi\) | ||||
0.956011 | − | 0.293331i | \(-0.0947638\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41.5910 | 0.569740 | 0.284870 | − | 0.958566i | \(-0.408050\pi\) | ||||
0.284870 | + | 0.958566i | \(0.408050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.10301 | 0.0402988 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 15.5473i | − 0.196801i | −0.995147 | − | 0.0984004i | \(-0.968627\pi\) | ||||
0.995147 | − | 0.0984004i | \(-0.0313726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 112.295 | 1.38636 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 50.9862i | − 0.614291i | −0.951663 | − | 0.307146i | \(-0.900626\pi\) | ||||
0.951663 | − | 0.307146i | \(-0.0993739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 235.510i | − 2.70701i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8885 | −0.122343 | −0.0611713 | − | 0.998127i | \(-0.519484\pi\) | ||||
−0.0611713 | + | 0.998127i | \(0.519484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.41749i | − 0.0265659i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 108.070 | 1.16205 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1559 | 0.125318 | 0.0626592 | − | 0.998035i | \(-0.480042\pi\) | ||||
0.0626592 | + | 0.998035i | \(0.480042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 287.035i | 2.89934i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 127.723 | 1.26459 | 0.632294 | − | 0.774728i | \(-0.282113\pi\) | ||||
0.632294 | + | 0.774728i | \(0.282113\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.77575i | 0.0463665i | 0.999731 | + | 0.0231833i | \(0.00738012\pi\) | ||||
−0.999731 | + | 0.0231833i | \(0.992620\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 107.213i | − 1.00199i | −0.865449 | − | 0.500997i | \(-0.832967\pi\) | ||||
0.865449 | − | 0.500997i | \(-0.167033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −53.6689 | −0.492376 | −0.246188 | − | 0.969222i | \(-0.579178\pi\) | ||||
−0.246188 | + | 0.969222i | \(0.579178\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 96.0170i | 0.865018i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.5063 | 0.181471 | 0.0907356 | − | 0.995875i | \(-0.471078\pi\) | ||||
0.0907356 | + | 0.995875i | \(0.471078\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 223.623 | 1.91131 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.75873i | 0.0315860i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −104.529 | −0.863876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 171.283i | − 1.39255i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 138.477i | 1.09037i | 0.838316 | + | 0.545184i | \(0.183540\pi\) | ||||
−0.838316 | + | 0.545184i | \(0.816460\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.5398 | 0.166975 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 219.105i | − 1.67256i | −0.548304 | − | 0.836279i | \(-0.684726\pi\) | ||||
0.548304 | − | 0.836279i | \(-0.315274\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00849 | 0.0301390 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 59.7821 | 0.436366 | 0.218183 | − | 0.975908i | \(-0.429987\pi\) | ||||
0.218183 | + | 0.975908i | \(0.429987\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 26.6524i | − 0.191744i | −0.995394 | − | 0.0958718i | \(-0.969436\pi\) | ||||
0.995394 | − | 0.0958718i | \(-0.0305639\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 28.5039 | 0.202155 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 175.705i | 1.22871i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 259.581i | 1.76586i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −143.463 | −0.962838 | −0.481419 | − | 0.876490i | \(-0.659879\pi\) | ||||
−0.481419 | + | 0.876490i | \(0.659879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 83.4937i | − 0.552939i | −0.961023 | − | 0.276469i | \(-0.910836\pi\) | ||||
0.961023 | − | 0.276469i | \(-0.0891644\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −347.690 | −2.27249 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −169.673 | −1.08072 | −0.540360 | − | 0.841434i | \(-0.681712\pi\) | ||||
−0.540360 | + | 0.841434i | \(0.681712\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 419.776i | − 2.64010i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.62520 | 0.0349391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 275.478i | 1.69005i | 0.534726 | + | 0.845026i | \(0.320415\pi\) | ||||
−0.534726 | + | 0.845026i | \(0.679585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 132.481i | − 0.793299i | −0.917970 | − | 0.396650i | \(-0.870173\pi\) | ||||
0.917970 | − | 0.396650i | \(-0.129827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −32.1115 | −0.190009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 370.793i | 2.16838i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 272.614 | 1.57580 | 0.787901 | − | 0.615801i | \(-0.211168\pi\) | ||||
0.787901 | + | 0.615801i | \(0.211168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −442.202 | −2.49831 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 157.523i | − 0.880014i | −0.897994 | − | 0.440007i | \(-0.854976\pi\) | ||||
0.897994 | − | 0.440007i | \(-0.145024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −335.063 | −1.85118 | −0.925590 | − | 0.378529i | \(-0.876430\pi\) | ||||
−0.925590 | + | 0.378529i | \(0.876430\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 194.848i | − 1.06474i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 273.187i | − 1.46090i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.0796 | 0.0586223 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 298.575i | − 1.56322i | −0.623766 | − | 0.781611i | \(-0.714398\pi\) | ||||
0.623766 | − | 0.781611i | \(-0.285602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −191.915 | −0.994376 | −0.497188 | − | 0.867643i | \(-0.665634\pi\) | ||||
−0.497188 | + | 0.867643i | \(0.665634\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −59.2472 | −0.300747 | −0.150374 | − | 0.988629i | \(-0.548048\pi\) | ||||
−0.150374 | + | 0.988629i | \(0.548048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 309.100i | − 1.55327i | −0.629953 | − | 0.776633i | \(-0.716926\pi\) | ||||
0.629953 | − | 0.776633i | \(-0.283074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.9403 | −0.119106 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.17775i | − 0.0452106i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 520.342i | 2.51373i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −291.340 | −1.39397 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 205.693i | 0.974850i | 0.873165 | + | 0.487425i | \(0.162064\pi\) | ||||
−0.873165 | + | 0.487425i | \(0.837936\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 220.852 | 1.03686 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.21147 | 0.0194077 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 220.523i | 1.00696i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −212.835 | −0.963054 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 228.723i | − 1.02567i | −0.858488 | − | 0.512833i | \(-0.828596\pi\) | ||||
0.858488 | − | 0.512833i | \(-0.171404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 282.403i | 1.24407i | 0.782991 | + | 0.622033i | \(0.213693\pi\) | ||||
−0.782991 | + | 0.622033i | \(0.786307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −49.2525 | −0.215076 | −0.107538 | − | 0.994201i | \(-0.534297\pi\) | ||||
−0.107538 | + | 0.994201i | \(0.534297\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.4527i | 0.0712240i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 124.273 | 0.533363 | 0.266681 | − | 0.963785i | \(-0.414073\pi\) | ||||
0.266681 | + | 0.963785i | \(0.414073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 82.4345 | 0.347825 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 80.4527i | 0.336622i | 0.985734 | + | 0.168311i | \(0.0538313\pi\) | ||||
−0.985734 | + | 0.168311i | \(0.946169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.20979 | −0.00501988 | −0.00250994 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00250994 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 112.812i | 0.464247i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 226.977i | 0.918936i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 270.338 | 1.08570 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 211.853i | − 0.844034i | −0.906588 | − | 0.422017i | \(-0.861322\pi\) | ||||
0.906588 | − | 0.422017i | \(-0.138678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −408.843 | −1.61598 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 182.646 | 0.710685 | 0.355342 | − | 0.934736i | \(-0.384364\pi\) | ||||
0.355342 | + | 0.934736i | \(0.384364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.74175i | 0.0144469i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 848.960 | 3.25272 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 74.6636i | 0.283892i | 0.989874 | + | 0.141946i | \(0.0453359\pi\) | ||||
−0.989874 | + | 0.141946i | \(0.954664\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 57.7329i | − 0.216228i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 184.089 | 0.684344 | 0.342172 | − | 0.939637i | \(-0.388837\pi\) | ||||
0.342172 | + | 0.939637i | \(0.388837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 234.746i | − 0.866222i | −0.901341 | − | 0.433111i | \(-0.857416\pi\) | ||||
0.901341 | − | 0.433111i | \(-0.142584\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.8180 | 0.0469524 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −452.208 | −1.63252 | −0.816260 | − | 0.577684i | \(-0.803957\pi\) | ||||
−0.816260 | + | 0.577684i | \(0.803957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 389.570i | 1.39631i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −196.110 | −0.697900 | −0.348950 | − | 0.937141i | \(-0.613462\pi\) | ||||
−0.348950 | + | 0.937141i | \(0.613462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 418.449i | 1.47862i | 0.673366 | + | 0.739309i | \(0.264848\pi\) | ||||
−0.673366 | + | 0.739309i | \(0.735152\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 6.67486i | − 0.0232574i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.9170 | 0.145042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 64.4527i | 0.221487i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −286.666 | −0.978383 | −0.489191 | − | 0.872176i | \(-0.662708\pi\) | ||||
−0.489191 | + | 0.872176i | \(0.662708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −805.275 | −2.71136 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 318.522i | 1.06529i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.839400 | 0.00278870 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 677.214i | 2.23503i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 261.715i | 0.852493i | 0.904607 | + | 0.426247i | \(0.140164\pi\) | ||||
−0.904607 | + | 0.426247i | \(0.859836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.3219 | −0.0819480 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 578.904i | 1.86143i | 0.365747 | + | 0.930714i | \(0.380813\pi\) | ||||
−0.365747 | + | 0.930714i | \(0.619187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −99.3124 | −0.317292 | −0.158646 | − | 0.987336i | \(-0.550713\pi\) | ||||
−0.158646 | + | 0.987336i | \(0.550713\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −191.623 | −0.604489 | −0.302245 | − | 0.953230i | \(-0.597736\pi\) | ||||
−0.302245 | + | 0.953230i | \(0.597736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 667.045i | 2.09105i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 568.466 | 1.77092 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 352.905i | − 1.09259i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 284.563i | − 0.870222i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.11079 | 0.00337626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 530.187i | − 1.60177i | −0.598816 | − | 0.800886i | \(-0.704362\pi\) | ||||
0.598816 | − | 0.800886i | \(-0.295638\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −346.120 | −1.03940 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 487.427 | 1.44637 | 0.723186 | − | 0.690653i | \(-0.242677\pi\) | ||||
0.723186 | + | 0.690653i | \(0.242677\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 108.728i | 0.320731i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −306.093 | −0.897633 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.2404i | 0.0590099i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 310.497i | 0.894804i | 0.894333 | + | 0.447402i | \(0.147651\pi\) | ||||
−0.894333 | + | 0.447402i | \(0.852349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 253.004 | 0.724941 | 0.362471 | − | 0.931995i | \(-0.381933\pi\) | ||||
0.362471 | + | 0.931995i | \(0.381933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 627.374i | 1.78739i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 322.639 | 0.913992 | 0.456996 | − | 0.889469i | \(-0.348925\pi\) | ||||
0.456996 | + | 0.889469i | \(0.348925\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.9295 | −0.0558250 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 254.975i | − 0.710236i | −0.934822 | − | 0.355118i | \(-0.884441\pi\) | ||||
0.934822 | − | 0.355118i | \(-0.115559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3550 | −0.0425347 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 554.232i | − 1.52681i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 207.935i | 0.566581i | 0.959034 | + | 0.283291i | \(0.0914261\pi\) | ||||
−0.959034 | + | 0.283291i | \(0.908574\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 617.438 | 1.67327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 16.3585i | − 0.0440931i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −203.826 | −0.546450 | −0.273225 | − | 0.961950i | \(-0.588090\pi\) | ||||
−0.273225 | + | 0.961950i | \(0.588090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 519.682 | 1.37847 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 454.099i | − 1.19815i | −0.800692 | − | 0.599076i | \(-0.795535\pi\) | ||||
0.800692 | − | 0.599076i | \(-0.204465\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −734.229 | −1.92711 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 541.569i | − 1.41402i | −0.707205 | − | 0.707009i | \(-0.750044\pi\) | ||||
0.707205 | − | 0.707009i | \(-0.249956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 77.6462i | 0.200636i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 423.431 | 1.08851 | 0.544256 | − | 0.838919i | \(-0.316812\pi\) | ||||
0.544256 | + | 0.838919i | \(0.316812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 495.240i | − 1.26660i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1161.74 | 2.95607 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7772 | 0.0296654 | 0.0148327 | − | 0.999890i | \(-0.495278\pi\) | ||||
0.0148327 | + | 0.999890i | \(0.495278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.2538i | 0.0532676i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 127.442 | 0.317809 | 0.158905 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158905 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 238.471i | 0.591739i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 271.953i | − 0.668190i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −608.012 | −1.48658 | −0.743290 | − | 0.668969i | \(-0.766736\pi\) | ||||
−0.743290 | + | 0.668969i | \(0.766736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 316.976i | 0.771231i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.2325 | −0.0417251 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 141.316 | 0.338887 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 565.630i | − 1.34995i | −0.737840 | − | 0.674976i | \(-0.764154\pi\) | ||||
0.737840 | − | 0.674976i | \(-0.235846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 711.356 | 1.68968 | 0.844841 | − | 0.535018i | \(-0.179695\pi\) | ||||
0.844841 | + | 0.535018i | \(0.179695\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 102.750i | 0.242908i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 7.59316i | − 0.0177826i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −931.622 | −2.17161 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 309.254i | 0.717526i | 0.933429 | + | 0.358763i | \(0.116801\pi\) | ||||
−0.933429 | + | 0.358763i | \(0.883199\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −187.374 | −0.432735 | −0.216368 | − | 0.976312i | \(-0.569421\pi\) | ||||
−0.216368 | + | 0.976312i | \(0.569421\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −528.147 | −1.20857 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 289.657i | − 0.659811i | −0.944014 | − | 0.329906i | \(-0.892983\pi\) | ||||
0.944014 | − | 0.329906i | \(-0.107017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −935.730 | −2.12184 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 295.516i | − 0.667079i | −0.942736 | − | 0.333539i | \(-0.891757\pi\) | ||||
0.942736 | − | 0.333539i | \(-0.108243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 760.667i | − 1.70172i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 604.409 | 1.34612 | 0.673061 | − | 0.739587i | \(-0.264979\pi\) | ||||
0.673061 | + | 0.739587i | \(0.264979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 485.134i | 1.07569i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 442.699 | 0.977262 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −392.507 | −0.858877 | −0.429438 | − | 0.903096i | \(-0.641288\pi\) | ||||
−0.429438 | + | 0.903096i | \(0.641288\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 975.444i | − 2.12515i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −400.277 | −0.868279 | −0.434139 | − | 0.900846i | \(-0.642947\pi\) | ||||
−0.434139 | + | 0.900846i | \(0.642947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 732.679i | 1.58246i | 0.611518 | + | 0.791230i | \(0.290559\pi\) | ||||
−0.611518 | + | 0.791230i | \(0.709441\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 592.126i | − 1.26794i | −0.773360 | − | 0.633968i | \(-0.781425\pi\) | ||||
0.773360 | − | 0.633968i | \(-0.218575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.932947 | −0.00198923 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 899.639i | − 1.91006i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −61.0082 | −0.128981 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1513.20 | 3.17232 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 309.151i | − 0.645409i | −0.946500 | − | 0.322705i | \(-0.895408\pi\) | ||||
0.946500 | − | 0.322705i | \(-0.104592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −211.873 | −0.440485 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.8259i | 0.0617513i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 570.769i | 1.17201i | 0.810307 | + | 0.586005i | \(0.199300\pi\) | ||||
−0.810307 | + | 0.586005i | \(0.800700\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1460.64 | −2.98699 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 301.659i | − 0.614378i | −0.951649 | − | 0.307189i | \(-0.900612\pi\) | ||||
0.951649 | − | 0.307189i | \(-0.0993883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −808.004 | −1.63895 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.60653 | 0.0173170 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 517.758i | 1.03759i | 0.854898 | + | 0.518795i | \(0.173619\pi\) | ||||
−0.854898 | + | 0.518795i | \(0.826381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 702.439 | 1.40207 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 406.671i | − 0.808491i | −0.914650 | − | 0.404246i | \(-0.867534\pi\) | ||||
0.914650 | − | 0.404246i | \(-0.132466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 170.261i | − 0.335821i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −627.097 | −1.23202 | −0.616009 | − | 0.787739i | \(-0.711252\pi\) | ||||
−0.616009 | + | 0.787739i | \(0.711252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.59372i | 0.0168175i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1040.26 | −2.02780 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −80.7330 | −0.156157 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1445.45i | 2.78507i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −111.743 | −0.214478 | −0.107239 | − | 0.994233i | \(-0.534201\pi\) | ||||
−0.107239 | + | 0.994233i | \(0.534201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 769.813i | 1.47192i | 0.677027 | + | 0.735959i | \(0.263268\pi\) | ||||
−0.677027 | + | 0.735959i | \(0.736732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 370.776i | − 0.703560i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −212.160 | −0.401058 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1594.04i | − 3.00195i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 377.958 | 0.709115 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 835.214 | 1.55533 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 735.222i | − 1.36405i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −225.558 | −0.416927 | −0.208463 | − | 0.978030i | \(-0.566846\pi\) | ||||
−0.208463 | + | 0.978030i | \(0.566846\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1776.57i | − 3.27177i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 882.346i | − 1.61306i | −0.591190 | − | 0.806532i | \(-0.701342\pi\) | ||||
0.591190 | − | 0.806532i | \(-0.298658\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 702.382 | 1.27938 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 861.694i | 1.56387i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.21245 | 0.00580913 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −303.119 | −0.544199 | −0.272100 | − | 0.962269i | \(-0.587718\pi\) | ||||
−0.272100 | + | 0.962269i | \(0.587718\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.5303i | 0.0850273i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1448.49 | 2.58198 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 344.003i | − 0.611017i | −0.952189 | − | 0.305508i | \(-0.901174\pi\) | ||||
0.952189 | − | 0.305508i | \(-0.0988264\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2029i | 0.0409223i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 228.925 | 0.402329 | 0.201165 | − | 0.979557i | \(-0.435527\pi\) | ||||
0.201165 | + | 0.979557i | \(0.435527\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 371.169i | 0.650033i | 0.945708 | + | 0.325017i | \(0.105370\pi\) | ||||
−0.945708 | + | 0.325017i | \(0.894630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1583.10 | 2.76283 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 580.289 | 1.00570 | 0.502850 | − | 0.864374i | \(-0.332285\pi\) | ||||
0.502850 | + | 0.864374i | \(0.332285\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1017.57i | − 1.75746i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5350 | 0.0181325 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1188.95i | 2.03936i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 65.0801i | − 0.110869i | −0.998462 | − | 0.0554345i | \(-0.982346\pi\) | ||||
0.998462 | − | 0.0554345i | \(-0.0176544\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −395.413 | −0.671329 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 314.140i | − 0.531539i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1002.90 | 1.69124 | 0.845619 | − | 0.533787i | \(-0.179232\pi\) | ||||
0.845619 | + | 0.533787i | \(0.179232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1638.91 | 2.74524 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 888.567i | 1.48342i | 0.670722 | + | 0.741709i | \(0.265984\pi\) | ||||
−0.670722 | + | 0.741709i | \(0.734016\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 132.065 | 0.219742 | 0.109871 | − | 0.993946i | \(-0.464956\pi\) | ||||
0.109871 | + | 0.993946i | \(0.464956\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 86.2995i | − 0.143117i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 700.090i | − 1.15336i | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
0.816970 | − | 0.576680i | \(-0.195652\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 48.6621 | 0.0799050 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 62.8975i | 0.102942i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 727.420 | 1.18666 | 0.593328 | − | 0.804961i | \(-0.297814\pi\) | ||||
0.593328 | + | 0.804961i | \(0.297814\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −99.7137 | −0.161611 | −0.0808053 | − | 0.996730i | \(-0.525749\pi\) | ||||
−0.0808053 | + | 0.996730i | \(0.525749\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 721.349i | 1.16535i | 0.812707 | + | 0.582673i | \(0.197993\pi\) | ||||
−0.812707 | + | 0.582673i | \(0.802007\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1459.82 | −2.35075 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.24983i | − 0.00361129i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1544.74i | − 2.46370i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 329.422 | 0.523723 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 796.856i | 1.26285i | 0.775438 | + | 0.631423i | \(0.217529\pi\) | ||||
−0.775438 | + | 0.631423i | \(0.782471\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1090.62 | −1.72295 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −572.797 | −0.899211 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 796.121i | 1.24589i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 205.013 | 0.319833 | 0.159917 | − | 0.987131i | \(-0.448877\pi\) | ||||
0.159917 | + | 0.987131i | \(0.448877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 495.044i | − 0.769897i | −0.922938 | − | 0.384949i | \(-0.874219\pi\) | ||||
0.922938 | − | 0.384949i | \(-0.125781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1121.84i | 1.73391i | 0.498389 | + | 0.866953i | \(0.333925\pi\) | ||||
−0.498389 | + | 0.866953i | \(0.666075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1252.47 | 1.92984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.3300i | 0.0343011i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 622.987 | 0.954038 | 0.477019 | − | 0.878893i | \(-0.341717\pi\) | ||||
0.477019 | + | 0.878893i | \(0.341717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −794.936 | −1.20995 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 264.030i | − 0.400653i | −0.979729 | − | 0.200326i | \(-0.935800\pi\) | ||||
0.979729 | − | 0.200326i | \(-0.0642002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1285.15 | 1.94425 | 0.972124 | − | 0.234469i | \(-0.0753352\pi\) | ||||
0.972124 | + | 0.234469i | \(0.0753352\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1128.49i | − 1.70210i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1209.23i | 1.81294i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1212.73 | 1.81276 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 551.876i | 0.822468i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1244.16 | −1.84868 | −0.924342 | − | 0.381565i | \(-0.875385\pi\) | ||||
−0.924342 | + | 0.381565i | \(0.875385\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 963.335 | 1.42295 | 0.711473 | − | 0.702713i | \(-0.248028\pi\) | ||||
0.711473 | + | 0.702713i | \(0.248028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.51170i | 0.00369912i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1497.35 | −2.19876 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 770.819i | 1.12858i | 0.825577 | + | 0.564289i | \(0.190850\pi\) | ||||
−0.825577 | + | 0.564289i | \(0.809150\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 261.146i | − 0.380125i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 926.287 | 1.34439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 408.765i | 0.591555i | 0.955257 | + | 0.295778i | \(0.0955788\pi\) | ||||
−0.955257 | + | 0.295778i | \(0.904421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −59.3084 | −0.0855821 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −587.652 | −0.843116 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 658.921i | 0.942663i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1335.62 | 1.90530 | 0.952650 | − | 0.304068i | \(-0.0983450\pi\) | ||||
0.952650 | + | 0.304068i | \(0.0983450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 351.311i | − 0.499731i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.3908i | 0.0373279i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −362.956 | −0.511927 | −0.255964 | − | 0.966686i | \(-0.582393\pi\) | ||||
−0.255964 | + | 0.966686i | \(0.582393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 297.158i | 0.417943i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −554.891 | −0.778249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −426.575 | −0.594945 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 648.098i | 0.901388i | 0.892679 | + | 0.450694i | \(0.148823\pi\) | ||||
−0.892679 | + | 0.450694i | \(0.851177\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.986788 | −0.00136864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.41453i | − 0.00887211i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 431.123i | − 0.593017i | −0.955030 | − | 0.296508i | \(-0.904178\pi\) | ||||
0.955030 | − | 0.296508i | \(-0.0958222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 412.506 | 0.565852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 73.9003i | − 0.101095i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1464.87 | −1.99846 | −0.999231 | − | 0.0392126i | \(-0.987515\pi\) | ||||
−0.999231 | + | 0.0392126i | \(0.987515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 67.8073 | 0.0920044 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 99.1951i | − 0.134229i | −0.997745 | − | 0.0671144i | \(-0.978621\pi\) | ||||
0.997745 | − | 0.0671144i | \(-0.0213793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1203.48 | −1.62412 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 602.719i | 0.811196i | 0.914052 | + | 0.405598i | \(0.132937\pi\) | ||||
−0.914052 | + | 0.405598i | \(0.867063\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 974.508i | 1.30456i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.1529 | 0.0295767 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 541.472i | − 0.721001i | −0.932759 | − | 0.360501i | \(-0.882606\pi\) | ||||
0.932759 | − | 0.360501i | \(-0.117394\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1123.28 | 1.49174 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1092.79 | −1.44358 | −0.721789 | − | 0.692113i | \(-0.756680\pi\) | ||||
−0.721789 | + | 0.692113i | \(0.756680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 2167.76i | − 2.85608i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.7706 | −0.0246657 | −0.0123328 | − | 0.999924i | \(-0.503926\pi\) | ||||
−0.0123328 | + | 0.999924i | \(0.503926\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 11.0893i | − 0.0145338i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 975.773i | − 1.27219i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.0830 | −0.0508231 | −0.0254116 | − | 0.999677i | \(-0.508090\pi\) | ||||
−0.0254116 | + | 0.999677i | \(0.508090\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 968.423i | 1.25606i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.2171 | −0.0403843 | −0.0201922 | − | 0.999796i | \(-0.506428\pi\) | ||||
−0.0201922 | + | 0.999796i | \(0.506428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.8395 | −0.0255334 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 626.699i | 0.804492i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −625.529 | −0.800933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2381.75i | 3.04183i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 988.563i | 1.25612i | 0.778167 | + | 0.628058i | \(0.216150\pi\) | ||||
−0.778167 | + | 0.628058i | \(0.783850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −395.880 | −0.501750 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.23710i | 0.00535663i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 429.956 | 0.542189 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 118.920 | 0.149210 | 0.0746048 | − | 0.997213i | \(-0.476230\pi\) | ||||
0.0746048 | + | 0.997213i | \(0.476230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 97.7933i | − 0.122395i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 208.114 | 0.259818 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 624.598i | − 0.777831i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 976.072i | 1.20951i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1214.04 | −1.50067 | −0.750337 | − | 0.661056i | \(-0.770109\pi\) | ||||
−0.750337 | + | 0.661056i | \(0.770109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 706.666i | 0.871351i | 0.900104 | + | 0.435676i | \(0.143491\pi\) | ||||
−0.900104 | + | 0.435676i | \(0.856509\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1244.67 | 1.53096 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −78.8108 | −0.0964636 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 46.2060i | 0.0564176i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 991.775 | 1.20801 | 0.604004 | − | 0.796981i | \(-0.293571\pi\) | ||||
0.604004 | + | 0.796981i | \(0.293571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 523.998i | 0.636693i | 0.947974 | + | 0.318347i | \(0.103128\pi\) | ||||
−0.947974 | + | 0.318347i | \(0.896872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 318.794i | − 0.385483i | −0.981250 | − | 0.192741i | \(-0.938262\pi\) | ||||
0.981250 | − | 0.192741i | \(-0.0617379\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1034.11 | 1.24742 | 0.623711 | − | 0.781655i | \(-0.285624\pi\) | ||||
0.623711 | + | 0.781655i | \(0.285624\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 2397.69i | − 2.88531i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 890.588 | 1.06913 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1092.94 | −1.30578 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 445.284i | 0.530732i | 0.964148 | + | 0.265366i | \(0.0854928\pi\) | ||||
−0.964148 | + | 0.265366i | \(0.914507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1131.91 | 1.34591 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1039.81i | − 1.23346i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 21.5983i | − 0.0254997i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2218.69 | −2.61330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 493.002i | − 0.579321i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1200.49 | −1.40737 | −0.703684 | − | 0.710513i | \(-0.748463\pi\) | ||||
−0.703684 | + | 0.710513i | \(0.748463\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1223.15 | 1.42724 | 0.713622 | − | 0.700531i | \(-0.247054\pi\) | ||||
0.713622 | + | 0.700531i | \(0.247054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 210.033i | − 0.244509i | −0.992499 | − | 0.122254i | \(-0.960988\pi\) | ||||
0.992499 | − | 0.122254i | \(-0.0390124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.3914 | 0.0411050 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1560.47i | − 1.80819i | −0.427333 | − | 0.904095i | \(-0.640547\pi\) | ||||
0.427333 | − | 0.904095i | \(-0.359453\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 222.252i | 0.256346i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −233.483 | −0.268680 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 52.8273i | − 0.0606513i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −232.338 | −0.266137 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1011.66 | 1.15354 | 0.576771 | − | 0.816906i | \(-0.304313\pi\) | ||||
0.576771 | + | 0.816906i | \(0.304313\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1519.96i | − 1.72919i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 266.455 | 0.302446 | 0.151223 | − | 0.988500i | \(-0.451679\pi\) | ||||
0.151223 | + | 0.988500i | \(0.451679\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 469.871i | − 0.532130i | −0.963955 | − | 0.266065i | \(-0.914276\pi\) | ||||
0.963955 | − | 0.266065i | \(-0.0857237\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 764.559i | 0.861961i | 0.902361 | + | 0.430980i | \(0.141832\pi\) | ||||
−0.902361 | + | 0.430980i | \(0.858168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.6127 | −0.0321853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1686.41i | − 1.89271i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −104.291 | −0.116788 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1688.86 | −1.88279 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 905.328i | 1.00704i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1440.20 | −1.59844 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.45065i | 0.00492874i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1333.20i | 1.46990i | 0.678123 | + | 0.734948i | \(0.262794\pi\) | ||||
−0.678123 | + | 0.734948i | \(0.737206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2441.20 | −2.68559 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1496.11i | 1.64227i | 0.570736 | + | 0.821134i | \(0.306658\pi\) | ||||
−0.570736 | + | 0.821134i | \(0.693342\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −765.691 | −0.838654 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.2725 | 0.0493702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 564.228i | − 0.613959i | −0.951716 | − | 0.306980i | \(-0.900682\pi\) | ||||
0.951716 | − | 0.306980i | \(-0.0993183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1387.66 | −1.50669 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 487.337i | 0.527993i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 91.2798i | − 0.0984680i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1449.16 | −1.55991 | −0.779957 | − | 0.625833i | \(-0.784759\pi\) | ||||
−0.779957 | + | 0.625833i | \(0.784759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 949.765i | − 1.02016i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3069.46 | −3.28988 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 258.795 | 0.276196 | 0.138098 | − | 0.990419i | \(-0.455901\pi\) | ||||
0.138098 | + | 0.990419i | \(0.455901\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 526.573i | − 0.560781i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.3444 | 0.0216200 | 0.0108100 | − | 0.999942i | \(-0.496559\pi\) | ||||
0.0108100 | + | 0.999942i | \(0.496559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 879.461i | 0.932620i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 613.539i | − 0.647876i | −0.946078 | − | 0.323938i | \(-0.894993\pi\) | ||||
0.946078 | − | 0.323938i | \(-0.105007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −486.612 | −0.512763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 1016.02i | − 1.06837i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −81.6126 | −0.0856376 | −0.0428188 | − | 0.999083i | \(-0.513634\pi\) | ||||
−0.0428188 | + | 0.999083i | \(0.513634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3536.80 | −3.69571 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.3525i | 0.0128806i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 545.564 | 0.567704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2049.19i | 2.12792i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 127.482i | 0.131833i | 0.997825 | + | 0.0659165i | \(0.0209971\pi\) | ||||
−0.997825 | + | 0.0659165i | \(0.979003\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1871.17 | 1.93103 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1122.62i | − 1.15615i | −0.815983 | − | 0.578076i | \(-0.803804\pi\) | ||||
0.815983 | − | 0.578076i | \(-0.196196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.50703 | 0.00565985 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −424.837 | −0.434838 | −0.217419 | − | 0.976078i | \(-0.569764\pi\) | ||||
−0.217419 | + | 0.976078i | \(0.569764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 163.519i | 0.167027i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1025.78 | 1.04565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 663.324i | 0.674795i | 0.941362 | + | 0.337398i | \(0.109547\pi\) | ||||
−0.941362 | + | 0.337398i | \(0.890453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.88961i | 0.00596719i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −110.597 | −0.111827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1771.36i | 1.78745i | 0.448616 | + | 0.893724i | \(0.351917\pi\) | ||||
−0.448616 | + | 0.893724i | \(0.648083\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2811.15 | 2.83097 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −447.066 | −0.448411 | −0.224205 | − | 0.974542i | \(-0.571979\pi\) | ||||
−0.224205 | + | 0.974542i | \(0.571979\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 971.038i | − 0.972010i |
(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 | 800.3.b.i.351.6 | 6 | ||
4.3 | odd | 2 | inner | 800.3.b.i.351.1 | 6 | ||
5.2 | odd | 4 | 160.3.h.b.159.5 | yes | 6 | ||
5.3 | odd | 4 | 160.3.h.a.159.2 | yes | 6 | ||
5.4 | even | 2 | 800.3.b.h.351.1 | 6 | |||
8.3 | odd | 2 | 1600.3.b.w.1151.6 | 6 | |||
8.5 | even | 2 | 1600.3.b.w.1151.1 | 6 | |||
15.2 | even | 4 | 1440.3.j.b.1279.4 | 6 | |||
15.8 | even | 4 | 1440.3.j.a.1279.3 | 6 | |||
20.3 | even | 4 | 160.3.h.b.159.6 | yes | 6 | ||
20.7 | even | 4 | 160.3.h.a.159.1 | ✓ | 6 | ||
20.19 | odd | 2 | 800.3.b.h.351.6 | 6 | |||
40.3 | even | 4 | 320.3.h.f.319.1 | 6 | |||
40.13 | odd | 4 | 320.3.h.g.319.5 | 6 | |||
40.19 | odd | 2 | 1600.3.b.v.1151.1 | 6 | |||
40.27 | even | 4 | 320.3.h.g.319.6 | 6 | |||
40.29 | even | 2 | 1600.3.b.v.1151.6 | 6 | |||
40.37 | odd | 4 | 320.3.h.f.319.2 | 6 | |||
60.23 | odd | 4 | 1440.3.j.b.1279.3 | 6 | |||
60.47 | odd | 4 | 1440.3.j.a.1279.4 | 6 | |||
80.3 | even | 4 | 1280.3.e.h.639.6 | 6 | |||
80.13 | odd | 4 | 1280.3.e.i.639.1 | 6 | |||
80.27 | even | 4 | 1280.3.e.i.639.6 | 6 | |||
80.37 | odd | 4 | 1280.3.e.h.639.1 | 6 | |||
80.43 | even | 4 | 1280.3.e.f.639.1 | 6 | |||
80.53 | odd | 4 | 1280.3.e.g.639.6 | 6 | |||
80.67 | even | 4 | 1280.3.e.g.639.1 | 6 | |||
80.77 | odd | 4 | 1280.3.e.f.639.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.1 | ✓ | 6 | 20.7 | even | 4 | ||
160.3.h.a.159.2 | yes | 6 | 5.3 | odd | 4 | ||
160.3.h.b.159.5 | yes | 6 | 5.2 | odd | 4 | ||
160.3.h.b.159.6 | yes | 6 | 20.3 | even | 4 | ||
320.3.h.f.319.1 | 6 | 40.3 | even | 4 | |||
320.3.h.f.319.2 | 6 | 40.37 | odd | 4 | |||
320.3.h.g.319.5 | 6 | 40.13 | odd | 4 | |||
320.3.h.g.319.6 | 6 | 40.27 | even | 4 | |||
800.3.b.h.351.1 | 6 | 5.4 | even | 2 | |||
800.3.b.h.351.6 | 6 | 20.19 | odd | 2 | |||
800.3.b.i.351.1 | 6 | 4.3 | odd | 2 | inner | ||
800.3.b.i.351.6 | 6 | 1.1 | even | 1 | trivial | ||
1280.3.e.f.639.1 | 6 | 80.43 | even | 4 | |||
1280.3.e.f.639.6 | 6 | 80.77 | odd | 4 | |||
1280.3.e.g.639.1 | 6 | 80.67 | even | 4 | |||
1280.3.e.g.639.6 | 6 | 80.53 | odd | 4 | |||
1280.3.e.h.639.1 | 6 | 80.37 | odd | 4 | |||
1280.3.e.h.639.6 | 6 | 80.3 | even | 4 | |||
1280.3.e.i.639.1 | 6 | 80.13 | odd | 4 | |||
1280.3.e.i.639.6 | 6 | 80.27 | even | 4 | |||
1440.3.j.a.1279.3 | 6 | 15.8 | even | 4 | |||
1440.3.j.a.1279.4 | 6 | 60.47 | odd | 4 | |||
1440.3.j.b.1279.3 | 6 | 60.23 | odd | 4 | |||
1440.3.j.b.1279.4 | 6 | 15.2 | even | 4 | |||
1600.3.b.v.1151.1 | 6 | 40.19 | odd | 2 | |||
1600.3.b.v.1151.6 | 6 | 40.29 | even | 2 | |||
1600.3.b.w.1151.1 | 6 | 8.5 | even | 2 | |||
1600.3.b.w.1151.6 | 6 | 8.3 | odd | 2 |