Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (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: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 80 x^{18} - 152 x^{17} + 4326 x^{16} - 10096 x^{15} + 70116 x^{14} - 93436 x^{13} + 597327 x^{12} - 837564 x^{11} + 2838686 x^{10} - 2898276 x^{9} + \cdots + 36100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{37} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.16 | ||
Root | \(0.855886 - 1.48244i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.r.721.15 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 3.78754 | 0.757507 | 0.378754 | − | 0.925498i | \(-0.376353\pi\) | ||||
0.378754 | + | 0.925498i | \(0.376353\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.363991 | −0.0519988 | −0.0259994 | − | 0.999662i | \(-0.508277\pi\) | ||||
−0.0259994 | + | 0.999662i | \(0.508277\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.03560 | −0.730509 | −0.365255 | − | 0.930908i | \(-0.619018\pi\) | ||||
−0.365255 | + | 0.930908i | \(0.619018\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.0897i | 1.31459i | 0.753632 | + | 0.657296i | \(0.228300\pi\) | ||||
−0.753632 | + | 0.657296i | \(0.771700\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −31.1440 | −1.83200 | −0.916000 | − | 0.401179i | \(-0.868600\pi\) | ||||
−0.916000 | + | 0.401179i | \(0.868600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.3197 | − | 15.2599i | 0.595775 | − | 0.803152i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.4232 | 1.49666 | 0.748330 | − | 0.663327i | \(-0.230856\pi\) | ||||
0.748330 | + | 0.663327i | \(0.230856\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.6546 | −0.426183 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.21270i | − | 0.179748i | −0.995953 | − | 0.0898741i | \(-0.971354\pi\) | ||
0.995953 | − | 0.0898741i | \(-0.0286465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.14913i | 0.133843i | 0.997758 | + | 0.0669215i | \(0.0213177\pi\) | ||||
−0.997758 | + | 0.0669215i | \(0.978682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.37863 | −0.0393894 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 37.7395i | 1.01999i | 0.860178 | + | 0.509994i | \(0.170352\pi\) | ||||
−0.860178 | + | 0.509994i | \(0.829648\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 36.6108i | − | 0.892947i | −0.894797 | − | 0.446473i | \(-0.852680\pi\) | ||
0.894797 | − | 0.446473i | \(-0.147320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −53.5899 | −1.24628 | −0.623138 | − | 0.782112i | \(-0.714142\pi\) | ||||
−0.623138 | + | 0.782112i | \(0.714142\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23.4910 | 0.499809 | 0.249905 | − | 0.968270i | \(-0.419601\pi\) | ||||
0.249905 | + | 0.968270i | \(0.419601\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.8675 | −0.997296 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 79.9131i | − | 1.50779i | −0.656992 | − | 0.753897i | \(-0.728172\pi\) | ||
0.656992 | − | 0.753897i | \(-0.271828\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −30.4351 | −0.553366 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 31.2858i | − | 0.530268i | −0.964212 | − | 0.265134i | \(-0.914584\pi\) | ||
0.964212 | − | 0.265134i | \(-0.0854161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 59.5399 | 0.976064 | 0.488032 | − | 0.872826i | \(-0.337715\pi\) | ||||
0.488032 | + | 0.872826i | \(0.337715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 64.7279i | 0.995813i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 108.865i | − | 1.62485i | −0.583068 | − | 0.812423i | \(-0.698148\pi\) | ||
0.583068 | − | 0.812423i | \(-0.301852\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 100.436i | − | 1.41459i | −0.706916 | − | 0.707297i | \(-0.749914\pi\) | ||
0.706916 | − | 0.707297i | \(-0.250086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −132.046 | −1.80885 | −0.904427 | − | 0.426628i | \(-0.859701\pi\) | ||||
−0.904427 | + | 0.426628i | \(0.859701\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.92489 | 0.0379856 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.6681i | − | 0.185673i | −0.995681 | − | 0.0928364i | \(-0.970407\pi\) | ||
0.995681 | − | 0.0928364i | \(-0.0295933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 69.7261 | 0.840074 | 0.420037 | − | 0.907507i | \(-0.362017\pi\) | ||||
0.420037 | + | 0.907507i | \(0.362017\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −117.959 | −1.38775 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 150.974i | − | 1.69634i | −0.529723 | − | 0.848171i | \(-0.677704\pi\) | ||
0.529723 | − | 0.848171i | \(-0.322296\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.22051i | − | 0.0683572i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 42.8738 | − | 57.7973i | 0.451304 | − | 0.608393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 51.4768i | − | 0.530689i | −0.964154 | − | 0.265345i | \(-0.914514\pi\) | ||
0.964154 | − | 0.265345i | \(-0.0854857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 91.1672 | 0.902646 | 0.451323 | − | 0.892361i | \(-0.350952\pi\) | ||||
0.451323 | + | 0.892361i | \(0.350952\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 60.0393i | − | 0.582906i | −0.956585 | − | 0.291453i | \(-0.905861\pi\) | ||
0.956585 | − | 0.291453i | \(-0.0941386\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 31.8715i | 0.297864i | 0.988847 | + | 0.148932i | \(0.0475836\pi\) | ||||
−0.988847 | + | 0.148932i | \(0.952416\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 119.535i | 1.09665i | 0.836266 | + | 0.548324i | \(0.184734\pi\) | ||||
−0.836266 | + | 0.548324i | \(0.815266\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 126.867i | 1.12272i | 0.827573 | + | 0.561358i | \(0.189721\pi\) | ||||
−0.827573 | + | 0.561358i | \(0.810279\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 130.379 | 1.13373 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.3361 | 0.0952617 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −56.4291 | −0.466356 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −135.043 | −1.08034 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 212.297i | 1.67163i | 0.549012 | + | 0.835814i | \(0.315004\pi\) | ||||
−0.549012 | + | 0.835814i | \(0.684996\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −254.455 | −1.94241 | −0.971203 | − | 0.238254i | \(-0.923425\pi\) | ||||
−0.971203 | + | 0.238254i | \(0.923425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.12028 | + | 5.55446i | −0.0309796 | + | 0.0417629i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.84460 | 0.0572599 | 0.0286299 | − | 0.999590i | \(-0.490886\pi\) | ||||
0.0286299 | + | 0.999590i | \(0.490886\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 123.658 | 0.889625 | 0.444813 | − | 0.895624i | \(-0.353270\pi\) | ||||
0.444813 | + | 0.895624i | \(0.353270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 137.326i | − | 0.960322i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 19.7433i | − | 0.136161i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.13822 | −0.0210619 | −0.0105309 | − | 0.999945i | \(-0.503352\pi\) | ||||
−0.0105309 | + | 0.999945i | \(0.503352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.31415i | − | 0.0616831i | −0.999524 | − | 0.0308415i | \(-0.990181\pi\) | ||
0.999524 | − | 0.0308415i | \(-0.00981873\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.7150i | 0.101387i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −162.867 | −1.03737 | −0.518684 | − | 0.854966i | \(-0.673578\pi\) | ||||
−0.518684 | + | 0.854966i | \(0.673578\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.5297 | −0.0778245 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −67.5305 | −0.414297 | −0.207149 | − | 0.978309i | \(-0.566418\pi\) | ||||
−0.207149 | + | 0.978309i | \(0.566418\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 41.7421i | − | 0.249953i | −0.992160 | − | 0.124976i | \(-0.960114\pi\) | ||
0.992160 | − | 0.124976i | \(-0.0398855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −123.058 | −0.728154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 106.215i | 0.613957i | 0.951716 | + | 0.306978i | \(0.0993179\pi\) | ||||
−0.951716 | + | 0.306978i | \(0.900682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.87817 | 0.0221610 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 292.085i | − | 1.63176i | −0.578220 | − | 0.815881i | \(-0.696252\pi\) | ||
0.578220 | − | 0.815881i | \(-0.303748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 55.2420i | − | 0.305204i | −0.988288 | − | 0.152602i | \(-0.951235\pi\) | ||
0.988288 | − | 0.152602i | \(-0.0487653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 142.940i | 0.772647i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 250.261 | 1.33829 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 183.468 | 0.960563 | 0.480282 | − | 0.877114i | \(-0.340534\pi\) | ||||
0.480282 | + | 0.877114i | \(0.340534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 122.921i | 0.636896i | 0.947940 | + | 0.318448i | \(0.103162\pi\) | ||||
−0.947940 | + | 0.318448i | \(0.896838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −270.998 | −1.37563 | −0.687813 | − | 0.725888i | \(-0.741429\pi\) | ||||
−0.687813 | + | 0.725888i | \(0.741429\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −170.801 | −0.858295 | −0.429148 | − | 0.903234i | \(-0.641186\pi\) | ||||
−0.429148 | + | 0.903234i | \(0.641186\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.89738i | 0.00934669i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 138.665i | − | 0.676413i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −90.9608 | + | 122.622i | −0.435219 | + | 0.586710i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 150.250i | − | 0.712083i | −0.934470 | − | 0.356042i | \(-0.884126\pi\) | ||
0.934470 | − | 0.356042i | \(-0.115874\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −202.973 | −0.944063 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.51025i | − | 0.00695967i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 532.242i | − | 2.40833i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 394.139i | − | 1.76744i | −0.468015 | − | 0.883721i | \(-0.655031\pi\) | ||
0.468015 | − | 0.883721i | \(-0.344969\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 187.168i | − | 0.824528i | −0.911064 | − | 0.412264i | \(-0.864738\pi\) | ||
0.911064 | − | 0.412264i | \(-0.135262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 386.050 | 1.68581 | 0.842905 | − | 0.538062i | \(-0.180844\pi\) | ||||
0.842905 | + | 0.538062i | \(0.180844\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.9836 | −0.124393 | −0.0621965 | − | 0.998064i | \(-0.519811\pi\) | ||||
−0.0621965 | + | 0.998064i | \(0.519811\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 88.9731 | 0.378609 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3544 | 0.0977174 | 0.0488587 | − | 0.998806i | \(-0.484442\pi\) | ||||
0.0488587 | + | 0.998806i | \(0.484442\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 152.708i | 0.633643i | 0.948485 | + | 0.316821i | \(0.102616\pi\) | ||||
−0.948485 | + | 0.316821i | \(0.897384\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −185.087 | −0.755459 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 260.787 | + | 193.451i | 1.05582 | + | 0.783201i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −122.289 | −0.487208 | −0.243604 | − | 0.969875i | \(-0.578330\pi\) | ||||
−0.243604 | + | 0.969875i | \(0.578330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −276.611 | −1.09332 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 184.338i | − | 0.717268i | −0.933478 | − | 0.358634i | \(-0.883243\pi\) | ||
0.933478 | − | 0.358634i | \(-0.116757\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 13.7369i | − | 0.0530381i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −130.697 | −0.496945 | −0.248473 | − | 0.968639i | \(-0.579929\pi\) | ||||
−0.248473 | + | 0.968639i | \(0.579929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 302.674i | − | 1.14217i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 91.2275i | 0.339136i | 0.985519 | + | 0.169568i | \(0.0542372\pi\) | ||||
−0.985519 | + | 0.169568i | \(0.945763\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −211.416 | −0.780134 | −0.390067 | − | 0.920786i | \(-0.627548\pi\) | ||||
−0.390067 | + | 0.920786i | \(0.627548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 85.6160 | 0.311331 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −205.340 | −0.741298 | −0.370649 | − | 0.928773i | \(-0.620865\pi\) | ||||
−0.370649 | + | 0.928773i | \(0.620865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 488.604i | − | 1.73881i | −0.494104 | − | 0.869403i | \(-0.664504\pi\) | ||
0.494104 | − | 0.869403i | \(-0.335496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −216.924 | −0.766515 | −0.383258 | − | 0.923641i | \(-0.625198\pi\) | ||||
−0.383258 | + | 0.923641i | \(0.625198\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.3260i | 0.0464321i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 680.948 | 2.35622 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 153.381i | − | 0.523485i | −0.965138 | − | 0.261743i | \(-0.915703\pi\) | ||
0.965138 | − | 0.261743i | \(-0.0842972\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 118.496i | − | 0.401681i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 588.282i | 1.96750i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.5062 | 0.0648048 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 225.510 | 0.739376 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 165.972i | − | 0.540624i | −0.962773 | − | 0.270312i | \(-0.912873\pi\) | ||
0.962773 | − | 0.270312i | \(-0.0871269\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −183.105 | −0.588762 | −0.294381 | − | 0.955688i | \(-0.595114\pi\) | ||||
−0.294381 | + | 0.955688i | \(0.595114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 243.119 | 0.776738 | 0.388369 | − | 0.921504i | \(-0.373039\pi\) | ||||
0.388369 | + | 0.921504i | \(0.373039\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 381.617i | 1.20384i | 0.798556 | + | 0.601920i | \(0.205597\pi\) | ||||
−0.798556 | + | 0.601920i | \(0.794403\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 41.8872i | 0.131308i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −352.541 | + | 475.253i | −1.09146 | + | 1.47137i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 182.084i | − | 0.560257i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.55053 | −0.0259895 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 116.607i | − | 0.352287i | −0.984365 | − | 0.176143i | \(-0.943638\pi\) | ||
0.984365 | − | 0.176143i | \(-0.0563622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 412.329i | − | 1.23083i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 274.008i | − | 0.813081i | −0.913633 | − | 0.406541i | \(-0.866735\pi\) | ||
0.913633 | − | 0.406541i | \(-0.133265\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 33.3408i | − | 0.0977735i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 35.6229 | 0.103857 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −531.768 | −1.53247 | −0.766236 | − | 0.642560i | \(-0.777872\pi\) | ||||
−0.766236 | + | 0.642560i | \(0.777872\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 190.284 | 0.545227 | 0.272614 | − | 0.962124i | \(-0.412112\pi\) | ||||
0.272614 | + | 0.962124i | \(0.412112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −534.492 | −1.51414 | −0.757071 | − | 0.653333i | \(-0.773370\pi\) | ||||
−0.757071 | + | 0.653333i | \(0.773370\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 380.406i | − | 1.07157i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 234.606 | 0.653500 | 0.326750 | − | 0.945111i | \(-0.394046\pi\) | ||||
0.326750 | + | 0.945111i | \(0.394046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −104.728 | − | 345.475i | −0.290105 | − | 0.956995i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −500.130 | −1.37022 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −386.010 | −1.05180 | −0.525899 | − | 0.850547i | \(-0.676271\pi\) | ||||
−0.525899 | + | 0.850547i | \(0.676271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.0877i | 0.0784035i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 196.177i | 0.525944i | 0.964804 | + | 0.262972i | \(0.0847026\pi\) | ||||
−0.964804 | + | 0.262972i | \(0.915297\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 89.0835 | 0.236296 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 208.596i | − | 0.550384i | −0.961389 | − | 0.275192i | \(-0.911259\pi\) | ||
0.961389 | − | 0.275192i | \(-0.0887415\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 481.127i | 1.25621i | 0.778130 | + | 0.628104i | \(0.216169\pi\) | ||||
−0.778130 | + | 0.628104i | \(0.783831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.0781 | 0.0287744 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −361.111 | −0.928306 | −0.464153 | − | 0.885755i | \(-0.653641\pi\) | ||||
−0.464153 | + | 0.885755i | \(0.653641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1072.08 | −2.74188 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 55.5561i | − | 0.140648i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 317.576 | 0.799941 | 0.399970 | − | 0.916528i | \(-0.369020\pi\) | ||||
0.399970 | + | 0.916528i | \(0.369020\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 115.524i | − | 0.288089i | −0.989571 | − | 0.144045i | \(-0.953989\pi\) | ||
0.989571 | − | 0.144045i | \(-0.0460109\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −70.9074 | −0.175949 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 303.260i | − | 0.745110i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 363.245i | 0.888130i | 0.895995 | + | 0.444065i | \(0.146464\pi\) | ||||
−0.895995 | + | 0.444065i | \(0.853536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3878i | 0.0275733i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 264.090 | 0.636362 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −104.376 | −0.249108 | −0.124554 | − | 0.992213i | \(-0.539750\pi\) | ||||
−0.124554 | + | 0.992213i | \(0.539750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 720.332i | − | 1.71100i | −0.517800 | − | 0.855502i | \(-0.673249\pi\) | ||
0.517800 | − | 0.855502i | \(-0.326751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 331.826 | 0.780767 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.6720 | −0.0507541 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 515.127i | − | 1.19519i | −0.801798 | − | 0.597595i | \(-0.796123\pi\) | ||
0.801798 | − | 0.597595i | \(-0.203877\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.37332i | − | 0.0101000i | −0.999987 | − | 0.00505002i | \(-0.998393\pi\) | ||
0.999987 | − | 0.00505002i | \(-0.00160748\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 389.661 | − | 525.294i | 0.891672 | − | 1.20204i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 492.579i | 1.12205i | 0.827800 | + | 0.561024i | \(0.189592\pi\) | ||||
−0.827800 | + | 0.561024i | \(0.810408\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −314.485 | −0.709898 | −0.354949 | − | 0.934886i | \(-0.615502\pi\) | ||||
−0.354949 | + | 0.934886i | \(0.615502\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 571.821i | − | 1.28499i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 169.326i | 0.377118i | 0.982062 | + | 0.188559i | \(0.0603817\pi\) | ||||
−0.982062 | + | 0.188559i | \(0.939618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 294.190i | 0.652306i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 23.5604i | − | 0.0517811i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −489.329 | −1.07074 | −0.535371 | − | 0.844617i | \(-0.679828\pi\) | ||||
−0.535371 | + | 0.844617i | \(0.679828\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 225.978 | 0.490191 | 0.245096 | − | 0.969499i | \(-0.421181\pi\) | ||||
0.245096 | + | 0.969499i | \(0.421181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −198.625 | −0.428995 | −0.214498 | − | 0.976725i | \(-0.568811\pi\) | ||||
−0.214498 | + | 0.976725i | \(0.568811\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 125.888 | 0.269568 | 0.134784 | − | 0.990875i | \(-0.456966\pi\) | ||||
0.134784 | + | 0.990875i | \(0.456966\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.6258i | 0.0844900i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 430.627 | 0.910416 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −120.607 | + | 162.588i | −0.253909 | + | 0.342290i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 576.515 | 1.20358 | 0.601790 | − | 0.798654i | \(-0.294454\pi\) | ||||
0.601790 | + | 0.798654i | \(0.294454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −644.957 | −1.34087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 194.970i | − | 0.402001i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 546.813i | 1.12282i | 0.827538 | + | 0.561410i | \(0.189741\pi\) | ||||
−0.827538 | + | 0.561410i | \(0.810259\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −520.490 | −1.06006 | −0.530030 | − | 0.847979i | \(-0.677819\pi\) | ||||
−0.530030 | + | 0.847979i | \(0.677819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 162.344i | 0.329299i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36.5579i | 0.0735572i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 796.126 | 1.59544 | 0.797722 | − | 0.603026i | \(-0.206038\pi\) | ||||
0.797722 | + | 0.603026i | \(0.206038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 285.969 | 0.568528 | 0.284264 | − | 0.958746i | \(-0.408251\pi\) | ||||
0.284264 | + | 0.958746i | \(0.408251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 345.299 | 0.683761 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 430.356i | − | 0.845493i | −0.906248 | − | 0.422746i | \(-0.861066\pi\) | ||
0.906248 | − | 0.422746i | \(-0.138934\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.0637 | 0.0940582 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 227.401i | − | 0.441555i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −188.765 | −0.365115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 467.790i | 0.897869i | 0.893565 | + | 0.448934i | \(0.148196\pi\) | ||||
−0.893565 | + | 0.448934i | \(0.851804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 637.179i | 1.21831i | 0.793049 | + | 0.609157i | \(0.208492\pi\) | ||||
−0.793049 | + | 0.609157i | \(0.791508\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 129.220i | − | 0.245200i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 655.956 | 1.23999 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 625.668 | 1.17386 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 120.714i | 0.225634i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 392.680 | 0.728534 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 390.249 | 0.721348 | 0.360674 | − | 0.932692i | \(-0.382547\pi\) | ||||
0.360674 | + | 0.932692i | \(0.382547\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 452.742i | 0.830719i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 438.152i | 0.801009i | 0.916295 | + | 0.400504i | \(0.131165\pi\) | ||||
−0.916295 | + | 0.400504i | \(0.868835\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −79.5452 | − | 59.0063i | −0.144365 | − | 0.107090i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.33908i | 0.00965475i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 708.962 | 1.27282 | 0.636411 | − | 0.771350i | \(-0.280418\pi\) | ||||
0.636411 | + | 0.771350i | \(0.280418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 915.835i | − | 1.63835i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 752.460i | − | 1.33652i | −0.743929 | − | 0.668259i | \(-0.767040\pi\) | ||
0.743929 | − | 0.668259i | \(-0.232960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 480.513i | 0.850465i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 481.551i | 0.846311i | 0.906057 | + | 0.423155i | \(0.139078\pi\) | ||||
−0.906057 | + | 0.423155i | \(0.860922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 686.556 | 1.20237 | 0.601187 | − | 0.799108i | \(-0.294695\pi\) | ||||
0.601187 | + | 0.799108i | \(0.294695\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −366.764 | −0.637851 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 780.175 | 1.35212 | 0.676062 | − | 0.736845i | \(-0.263685\pi\) | ||||
0.676062 | + | 0.736845i | \(0.263685\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.3797 | −0.0436828 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 642.150i | 1.10146i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 162.138 | 0.276215 | 0.138108 | − | 0.990417i | \(-0.455898\pi\) | ||||
0.138108 | + | 0.990417i | \(0.455898\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 63.3152 | + | 46.9670i | 0.107496 | + | 0.0797402i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −265.476 | −0.447683 | −0.223841 | − | 0.974626i | \(-0.571860\pi\) | ||||
−0.223841 | + | 0.974626i | \(0.571860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 42.9360 | 0.0721614 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 73.4493i | 0.122620i | 0.998119 | + | 0.0613099i | \(0.0195278\pi\) | ||||
−0.998119 | + | 0.0613099i | \(0.980472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1056.53i | 1.75795i | 0.476869 | + | 0.878974i | \(0.341771\pi\) | ||||
−0.476869 | + | 0.878974i | \(0.658229\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −213.727 | −0.353268 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 743.206i | 1.22439i | 0.790706 | + | 0.612196i | \(0.209714\pi\) | ||||
−0.790706 | + | 0.612196i | \(0.790286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 401.455i | 0.657045i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1037.93 | −1.69319 | −0.846597 | − | 0.532235i | \(-0.821352\pi\) | ||||
−0.846597 | + | 0.532235i | \(0.821352\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 709.227 | 1.14948 | 0.574738 | − | 0.818337i | \(-0.305104\pi\) | ||||
0.574738 | + | 0.818337i | \(0.305104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −551.078 | −0.890272 | −0.445136 | − | 0.895463i | \(-0.646845\pi\) | ||||
−0.445136 | + | 0.895463i | \(0.646845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 54.9534i | 0.0882077i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −245.116 | −0.392185 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1175.36i | − | 1.86862i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −63.8795 | −0.101235 | −0.0506177 | − | 0.998718i | \(-0.516119\pi\) | ||||
−0.0506177 | + | 0.998718i | \(0.516119\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 804.082i | 1.26627i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 835.131i | − | 1.31104i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 579.947i | 0.904753i | 0.891827 | + | 0.452377i | \(0.149424\pi\) | ||||
−0.891827 | + | 0.452377i | \(0.850576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −948.558 | −1.47521 | −0.737603 | − | 0.675234i | \(-0.764043\pi\) | ||||
−0.737603 | + | 0.675234i | \(0.764043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 244.438 | 0.377803 | 0.188901 | − | 0.981996i | \(-0.439507\pi\) | ||||
0.188901 | + | 0.981996i | \(0.439507\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 251.400i | 0.387365i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −247.358 | −0.378803 | −0.189401 | − | 0.981900i | \(-0.560655\pi\) | ||||
−0.189401 | + | 0.981900i | \(0.560655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −963.758 | −1.47139 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 179.151i | − | 0.271853i | −0.990719 | − | 0.135926i | \(-0.956599\pi\) | ||
0.990719 | − | 0.135926i | \(-0.0434011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 779.968i | − | 1.17998i | −0.807410 | − | 0.589991i | \(-0.799131\pi\) | ||
0.807410 | − | 0.589991i | \(-0.200869\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.6057 | + | 21.0377i | −0.0234672 | + | 0.0316357i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 179.438i | − | 0.269022i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −478.439 | −0.713024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 485.801i | − | 0.721843i | −0.932596 | − | 0.360922i | \(-0.882462\pi\) | ||
0.932596 | − | 0.360922i | \(-0.117538\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 270.632i | 0.399751i | 0.979821 | + | 0.199876i | \(0.0640538\pi\) | ||||
−0.979821 | + | 0.199876i | \(0.935946\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.7371i | 0.0275952i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 418.415i | 0.612614i | 0.951933 | + | 0.306307i | \(0.0990934\pi\) | ||||
−0.951933 | + | 0.306307i | \(0.900907\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.7117 | 0.0433748 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1365.69 | 1.98214 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −639.926 | −0.926086 | −0.463043 | − | 0.886336i | \(-0.653242\pi\) | ||||
−0.463043 | + | 0.886336i | \(0.653242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 468.359 | 0.673898 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1140.21i | 1.63588i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1137.14 | −1.62217 | −0.811085 | − | 0.584928i | \(-0.801123\pi\) | ||||
−0.811085 | + | 0.584928i | \(0.801123\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 575.901 | + | 427.201i | 0.819204 | + | 0.607683i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.1841 | −0.0469365 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1297.36 | −1.82984 | −0.914921 | − | 0.403634i | \(-0.867747\pi\) | ||||
−0.914921 | + | 0.403634i | \(0.867747\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 142.826i | 0.200317i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 520.128i | − | 0.727451i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 232.620 | 0.323532 | 0.161766 | − | 0.986829i | \(-0.448281\pi\) | ||||
0.161766 | + | 0.986829i | \(0.448281\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.8538i | 0.0303104i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 55.5391i | 0.0766057i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1275.80 | 1.75489 | 0.877445 | − | 0.479678i | \(-0.159247\pi\) | ||||
0.877445 | + | 0.479678i | \(0.159247\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1669.00 | 2.28318 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 543.697 | 0.741742 | 0.370871 | − | 0.928684i | \(-0.379059\pi\) | ||||
0.370871 | + | 0.928684i | \(0.379059\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 874.794i | 1.18697i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 829.948 | 1.12307 | 0.561535 | − | 0.827453i | \(-0.310211\pi\) | ||||
0.561535 | + | 0.827453i | \(0.310211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 988.314i | 1.33017i | 0.746769 | + | 0.665084i | \(0.231604\pi\) | ||||
−0.746769 | + | 0.665084i | \(0.768396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.8861 | −0.0159545 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 11.6009i | − | 0.0154886i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 271.579i | − | 0.361624i | −0.983518 | − | 0.180812i | \(-0.942127\pi\) | ||
0.983518 | − | 0.180812i | \(-0.0578725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 35.2777i | − | 0.0467254i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −621.388 | −0.820856 | −0.410428 | − | 0.911893i | \(-0.634621\pi\) | ||||
−0.410428 | + | 0.911893i | \(0.634621\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 639.560 | 0.840420 | 0.420210 | − | 0.907427i | \(-0.361956\pi\) | ||||
0.420210 | + | 0.907427i | \(0.361956\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 43.5096i | − | 0.0570244i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 534.665 | 0.697086 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 839.975 | 1.09229 | 0.546147 | − | 0.837689i | \(-0.316094\pi\) | ||||
0.546147 | + | 0.837689i | \(0.316094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 811.652i | − | 1.05000i | −0.851101 | − | 0.525001i | \(-0.824065\pi\) | ||
0.851101 | − | 0.525001i | \(-0.175935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 44.2072i | − | 0.0570416i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −558.677 | − | 414.424i | −0.717171 | − | 0.531995i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 807.066i | 1.03337i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −616.864 | −0.785814 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 463.393i | − | 0.588810i | −0.955681 | − | 0.294405i | \(-0.904879\pi\) | ||
0.955681 | − | 0.294405i | \(-0.0951215\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 46.1785i | − | 0.0583799i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1017.52i | 1.28313i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 191.296i | − | 0.240021i | −0.992773 | − | 0.120010i | \(-0.961707\pi\) | ||
0.992773 | − | 0.120010i | \(-0.0382928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −731.604 | −0.915650 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1061.07 | 1.32139 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −47.4568 | −0.0589526 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 65.3407 | 0.0807672 | 0.0403836 | − | 0.999184i | \(-0.487142\pi\) | ||||
0.0403836 | + | 0.999184i | \(0.487142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 469.404i | 0.578796i | 0.957209 | + | 0.289398i | \(0.0934551\pi\) | ||||
−0.957209 | + | 0.289398i | \(0.906545\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −255.774 | −0.313833 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −606.622 | + | 817.775i | −0.742500 | + | 1.00095i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −854.605 | −1.04093 | −0.520466 | − | 0.853883i | \(-0.674242\pi\) | ||||
−0.520466 | + | 0.853883i | \(0.674242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.7419 | 0.0300630 | 0.0150315 | − | 0.999887i | \(-0.495215\pi\) | ||||
0.0150315 | + | 0.999887i | \(0.495215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1516.75i | − | 1.83404i | −0.398841 | − | 0.917020i | \(-0.630587\pi\) | ||
0.398841 | − | 0.917020i | \(-0.369413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 922.491i | 1.11278i | 0.830923 | + | 0.556388i | \(0.187813\pi\) | ||||
−0.830923 | + | 0.556388i | \(0.812187\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1521.93 | 1.82705 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 158.100i | − | 0.189341i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1051.69i | 1.25351i | 0.779218 | + | 0.626753i | \(0.215617\pi\) | ||||
−0.779218 | + | 0.626753i | \(0.784383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 813.828 | 0.967691 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −466.087 | −0.551582 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.5397 | 0.0242499 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1299.11i | 1.52657i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 937.436 | 1.09899 | 0.549494 | − | 0.835498i | \(-0.314821\pi\) | ||||
0.549494 | + | 0.835498i | \(0.314821\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1508.90i | 1.76067i | 0.474348 | + | 0.880337i | \(0.342684\pi\) | ||||
−0.474348 | + | 0.880337i | \(0.657316\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1441.65 | −1.67829 | −0.839144 | − | 0.543909i | \(-0.816944\pi\) | ||||
−0.839144 | + | 0.543909i | \(0.816944\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1143.05i | 1.32450i | 0.749281 | + | 0.662252i | \(0.230399\pi\) | ||||
−0.749281 | + | 0.662252i | \(0.769601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 402.291i | 0.465077i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 117.867i | 0.135636i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1860.47 | 2.13601 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 49.1545 | 0.0561765 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 809.431i | − | 0.922954i | −0.887152 | − | 0.461477i | \(-0.847320\pi\) | ||
0.887152 | − | 0.461477i | \(-0.152680\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 356.009 | 0.404096 | 0.202048 | − | 0.979376i | \(-0.435240\pi\) | ||||
0.202048 | + | 0.979376i | \(0.435240\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 584.439 | 0.661879 | 0.330940 | − | 0.943652i | \(-0.392634\pi\) | ||||
0.330940 | + | 0.943652i | \(0.392634\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1056.68i | 1.19129i | 0.803247 | + | 0.595646i | \(0.203104\pi\) | ||||
−0.803247 | + | 0.595646i | \(0.796896\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 77.2742i | − | 0.0869226i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 265.912 | − | 358.470i | 0.297774 | − | 0.401422i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1106.28i | − | 1.23607i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.6282 | 0.0240580 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2488.81i | 2.76228i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 209.231i | − | 0.231194i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1768.14i | − | 1.94944i | −0.223426 | − | 0.974721i | \(-0.571724\pi\) | ||
0.223426 | − | 0.974721i | \(-0.428276\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 277.297i | 0.304388i | 0.988351 | + | 0.152194i | \(0.0486338\pi\) | ||||
−0.988351 | + | 0.152194i | \(0.951366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −560.291 | −0.613682 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 92.6195 | 0.101003 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1438.17 | 1.56493 | 0.782463 | − | 0.622697i | \(-0.213963\pi\) | ||||
0.782463 | + | 0.622697i | \(0.213963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1716.43 | 1.85962 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 402.099i | − | 0.434701i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −501.787 | −0.540136 | −0.270068 | − | 0.962841i | \(-0.587046\pi\) | ||||
−0.270068 | + | 0.962841i | \(0.587046\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −553.167 | + | 745.712i | −0.594164 | + | 0.800980i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 947.871 | 1.01377 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −516.414 | −0.551136 | −0.275568 | − | 0.961282i | \(-0.588866\pi\) | ||||
−0.275568 | + | 0.961282i | \(0.588866\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 14.8505i | − | 0.0157816i | −0.999969 | − | 0.00789079i | \(-0.997488\pi\) | ||
0.999969 | − | 0.00789079i | \(-0.00251174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1260.26i | − | 1.33644i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −121.697 | −0.128508 | −0.0642541 | − | 0.997934i | \(-0.520467\pi\) | ||||
−0.0642541 | + | 0.997934i | \(0.520467\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2256.63i | − | 2.37791i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 294.229i | 0.308740i | 0.988013 | + | 0.154370i | \(0.0493347\pi\) | ||||
−0.988013 | + | 0.154370i | \(0.950665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 694.890 | 0.727633 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.85537 | −0.00297744 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 943.785 | 0.982086 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 465.567i | 0.482453i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1443.55 | 1.49282 | 0.746408 | − | 0.665489i | \(-0.231777\pi\) | ||||
0.746408 | + | 0.665489i | \(0.231777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 595.844i | − | 0.613639i | −0.951768 | − | 0.306820i | \(-0.900735\pi\) | ||
0.951768 | − | 0.306820i | \(-0.0992649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.0104 | −0.0462594 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1755.69i | 1.79702i | 0.438956 | + | 0.898509i | \(0.355349\pi\) | ||||
−0.438956 | + | 0.898509i | \(0.644651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1213.17i | 1.23919i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1591.20i | − | 1.61872i | −0.587312 | − | 0.809361i | \(-0.699814\pi\) | ||
0.587312 | − | 0.809361i | \(-0.300186\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1026.42 | −1.04205 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1844.73 | −1.86525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 781.379i | 0.788475i | 0.919009 | + | 0.394237i | \(0.128991\pi\) | ||||
−0.919009 | + | 0.394237i | \(0.871009\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −646.914 | −0.650165 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −907.423 | −0.910154 | −0.455077 | − | 0.890452i | \(-0.650388\pi\) | ||||
−0.455077 | + | 0.890452i | \(0.650388\pi\) | |||||||
\(998\) | 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 | 2736.3.o.r.721.16 | 20 | ||
3.2 | odd | 2 | 912.3.o.e.721.13 | 20 | |||
4.3 | odd | 2 | 1368.3.o.c.721.16 | 20 | |||
12.11 | even | 2 | 456.3.o.a.265.3 | ✓ | 20 | ||
19.18 | odd | 2 | inner | 2736.3.o.r.721.15 | 20 | ||
57.56 | even | 2 | 912.3.o.e.721.3 | 20 | |||
76.75 | even | 2 | 1368.3.o.c.721.15 | 20 | |||
228.227 | odd | 2 | 456.3.o.a.265.13 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.3.o.a.265.3 | ✓ | 20 | 12.11 | even | 2 | ||
456.3.o.a.265.13 | yes | 20 | 228.227 | odd | 2 | ||
912.3.o.e.721.3 | 20 | 57.56 | even | 2 | |||
912.3.o.e.721.13 | 20 | 3.2 | odd | 2 | |||
1368.3.o.c.721.15 | 20 | 76.75 | even | 2 | |||
1368.3.o.c.721.16 | 20 | 4.3 | odd | 2 | |||
2736.3.o.r.721.15 | 20 | 19.18 | odd | 2 | inner | ||
2736.3.o.r.721.16 | 20 | 1.1 | even | 1 | trivial |