Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,3,Mod(1023,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, 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("1792.1023");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.d (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: | \(48.8284633734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 48x^{12} + 180x^{10} + 1056x^{8} + 2880x^{6} + 12288x^{4} + 20480x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{38} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1023.11 | ||
Root | \(1.69931 + 1.05468i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1023 |
Dual form | 1792.3.d.j.1023.5 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 3.44128i | 1.14709i | 0.819173 | + | 0.573546i | \(0.194433\pi\) | ||||
−0.819173 | + | 0.573546i | \(0.805567\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.88287 | −0.976573 | −0.488287 | − | 0.872683i | \(-0.662378\pi\) | ||||
−0.488287 | + | 0.872683i | \(0.662378\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.84239 | −0.315821 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 21.4776i | − 1.95251i | −0.216632 | − | 0.976253i | \(-0.569507\pi\) | ||||
0.216632 | − | 0.976253i | \(-0.430493\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0760 | 1.00585 | 0.502924 | − | 0.864331i | \(-0.332258\pi\) | ||||
0.502924 | + | 0.864331i | \(0.332258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 16.8033i | − 1.12022i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.234889 | −0.0138170 | −0.00690851 | − | 0.999976i | \(-0.502199\pi\) | ||||
−0.00690851 | + | 0.999976i | \(0.502199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.55872i | − 0.239933i | −0.992778 | − | 0.119966i | \(-0.961721\pi\) | ||||
0.992778 | − | 0.119966i | \(-0.0382787\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.10476 | 0.433560 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10.9523i | 0.476187i | 0.971242 | + | 0.238094i | \(0.0765225\pi\) | ||||
−0.971242 | + | 0.238094i | \(0.923478\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.15761 | −0.0463043 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 21.1900i | 0.784816i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −34.6435 | −1.19460 | −0.597302 | − | 0.802016i | \(-0.703761\pi\) | ||||
−0.597302 | + | 0.802016i | \(0.703761\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.1079i | 1.10025i | 0.835081 | + | 0.550127i | \(0.185421\pi\) | ||||
−0.835081 | + | 0.550127i | \(0.814579\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 73.9103 | 2.23971 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.9189i | 0.369110i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −54.2370 | −1.46586 | −0.732932 | − | 0.680302i | \(-0.761849\pi\) | ||||
−0.732932 | + | 0.680302i | \(0.761849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 44.9982i | 1.15380i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 37.8300 | 0.922682 | 0.461341 | − | 0.887223i | \(-0.347368\pi\) | ||||
0.461341 | + | 0.887223i | \(0.347368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.84714i | − 0.112724i | −0.998410 | − | 0.0563621i | \(-0.982050\pi\) | ||||
0.998410 | − | 0.0563621i | \(-0.0179501\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.8790 | 0.308423 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.3368i | 1.53908i | 0.638598 | + | 0.769541i | \(0.279515\pi\) | ||||
−0.638598 | + | 0.769541i | \(0.720485\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 0.808319i | − 0.0158494i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 21.6707 | 0.408881 | 0.204440 | − | 0.978879i | \(-0.434463\pi\) | ||||
0.204440 | + | 0.978879i | \(0.434463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 104.872i | 1.90677i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.6878 | 0.275225 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34.9007i | 0.591537i | 0.955260 | + | 0.295768i | \(0.0955757\pi\) | ||||
−0.955260 | + | 0.295768i | \(0.904424\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −63.6012 | −1.04264 | −0.521321 | − | 0.853360i | \(-0.674561\pi\) | ||||
−0.521321 | + | 0.853360i | \(0.674561\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.52026i | 0.119369i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −63.8485 | −0.982284 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 18.4344i | − 0.275140i | −0.990492 | − | 0.137570i | \(-0.956071\pi\) | ||||
0.990492 | − | 0.137570i | \(-0.0439292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −37.6899 | −0.546231 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 47.5244i | − 0.669358i | −0.942332 | − | 0.334679i | \(-0.891372\pi\) | ||||
0.942332 | − | 0.334679i | \(-0.108628\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55.9103 | −0.765894 | −0.382947 | − | 0.923770i | \(-0.625091\pi\) | ||||
−0.382947 | + | 0.923770i | \(0.625091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3.98365i | − 0.0531153i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −56.8243 | −0.737978 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 95.0135i | 1.20270i | 0.798985 | + | 0.601351i | \(0.205371\pi\) | ||||
−0.798985 | + | 0.601351i | \(0.794629\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −98.5023 | −1.21608 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 71.5156i | − 0.861634i | −0.902439 | − | 0.430817i | \(-0.858225\pi\) | ||||
0.902439 | − | 0.430817i | \(-0.141775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.14693 | 0.0134933 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 119.218i | − 1.37032i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 159.756 | 1.79501 | 0.897504 | − | 0.441006i | \(-0.145378\pi\) | ||||
0.897504 | + | 0.441006i | \(0.145378\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 34.5959i | − 0.380175i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −117.375 | −1.26209 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 22.2596i | 0.234312i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −90.4794 | −0.932777 | −0.466389 | − | 0.884580i | \(-0.654445\pi\) | ||||
−0.466389 | + | 0.884580i | \(0.654445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 61.0477i | 0.616643i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −181.147 | −1.79353 | −0.896767 | − | 0.442503i | \(-0.854091\pi\) | ||||
−0.896767 | + | 0.442503i | \(0.854091\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 39.3003i | 0.381556i | 0.981633 | + | 0.190778i | \(0.0611010\pi\) | ||||
−0.981633 | + | 0.190778i | \(0.938899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −44.4574 | −0.423403 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 38.4498i | 0.359344i | 0.983727 | + | 0.179672i | \(0.0575037\pi\) | ||||
−0.983727 | + | 0.179672i | \(0.942496\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27.8786 | −0.255767 | −0.127883 | − | 0.991789i | \(-0.540818\pi\) | ||||
−0.127883 | + | 0.991789i | \(0.540818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 186.644i | − 1.68148i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 82.4419 | 0.729574 | 0.364787 | − | 0.931091i | \(-0.381142\pi\) | ||||
0.364787 | + | 0.931091i | \(0.381142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 53.4786i | − 0.465032i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −37.1672 | −0.317668 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.621458i | 0.00522234i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −340.286 | −2.81228 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 130.183i | 1.05840i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 127.724 | 1.02179 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 25.1408i | − 0.197959i | −0.995089 | − | 0.0989796i | \(-0.968442\pi\) | ||||
0.995089 | − | 0.0989796i | \(-0.0315579\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.6804 | 0.129305 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 126.398i | 0.964872i | 0.875931 | + | 0.482436i | \(0.160248\pi\) | ||||
−0.875931 | + | 0.482436i | \(0.839752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0612 | −0.0906861 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 103.468i | − 0.766431i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −34.9456 | −0.255078 | −0.127539 | − | 0.991834i | \(-0.540708\pi\) | ||||
−0.127539 | + | 0.991834i | \(0.540708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 119.148i | − 0.857177i | −0.903500 | − | 0.428589i | \(-0.859011\pi\) | ||||
0.903500 | − | 0.428589i | \(-0.140989\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −248.931 | −1.76547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 280.841i | − 1.96392i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 169.160 | 1.16662 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 24.0889i | − 0.163870i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 121.932 | 0.818334 | 0.409167 | − | 0.912460i | \(-0.365819\pi\) | ||||
0.409167 | + | 0.912460i | \(0.365819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 220.404i | 1.45963i | 0.683645 | + | 0.729815i | \(0.260394\pi\) | ||||
−0.683645 | + | 0.729815i | \(0.739606\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.667647 | 0.00436371 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 166.544i | − 1.07448i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.77014 | −0.0431219 | −0.0215610 | − | 0.999768i | \(-0.506864\pi\) | ||||
−0.0215610 | + | 0.999768i | \(0.506864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 74.5748i | 0.469024i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.9771 | 0.179982 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 207.243i | 1.27143i | 0.771924 | + | 0.635715i | \(0.219294\pi\) | ||||
−0.771924 | + | 0.635715i | \(0.780706\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −360.894 | −2.18724 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 165.529i | − 0.991193i | −0.868553 | − | 0.495596i | \(-0.834950\pi\) | ||||
0.868553 | − | 0.495596i | \(-0.165050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.98237 | 0.0117300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9577i | 0.0757759i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −88.8530 | −0.513601 | −0.256800 | − | 0.966464i | \(-0.582668\pi\) | ||||
−0.256800 | + | 0.966464i | \(0.582668\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.06274i | 0.0175014i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −120.103 | −0.678548 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 80.3791i | − 0.449045i | −0.974469 | − | 0.224523i | \(-0.927918\pi\) | ||||
0.974469 | − | 0.224523i | \(-0.0720823\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −276.353 | −1.52681 | −0.763406 | − | 0.645919i | \(-0.776474\pi\) | ||||
−0.763406 | + | 0.645919i | \(0.776474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 218.869i | − 1.19601i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 264.832 | 1.43152 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.04485i | 0.0269778i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 56.0636 | 0.296633 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 203.015i | 1.06290i | 0.847088 | + | 0.531452i | \(0.178353\pi\) | ||||
−0.847088 | + | 0.531452i | \(0.821647\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 87.3328 | 0.452502 | 0.226251 | − | 0.974069i | \(-0.427353\pi\) | ||||
0.226251 | + | 0.974069i | \(0.427353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 219.720i | − 1.12677i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.6639 | −0.109969 | −0.0549845 | − | 0.998487i | \(-0.517511\pi\) | ||||
−0.0549845 | + | 0.998487i | \(0.517511\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 181.933i | 0.914235i | 0.889406 | + | 0.457118i | \(0.151118\pi\) | ||||
−0.889406 | + | 0.457118i | \(0.848882\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 63.4378 | 0.315611 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 91.6582i | 0.451518i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −184.719 | −0.901067 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 31.1307i | − 0.150390i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −97.9103 | −0.468470 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.4204i | 0.101519i | 0.998711 | + | 0.0507594i | \(0.0161641\pi\) | ||||
−0.998711 | + | 0.0507594i | \(0.983836\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 163.545 | 0.767815 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.6680i | 0.110084i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 90.2410 | 0.415857 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 192.403i | − 0.878552i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.07142 | −0.0138978 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 195.958i | − 0.878735i | −0.898307 | − | 0.439367i | \(-0.855203\pi\) | ||||
0.898307 | − | 0.439367i | \(-0.144797\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.29038 | 0.0146239 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.2652i | 0.120111i | 0.998195 | + | 0.0600554i | \(0.0191277\pi\) | ||||
−0.998195 | + | 0.0600554i | \(0.980872\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −176.347 | −0.770076 | −0.385038 | − | 0.922901i | \(-0.625812\pi\) | ||||
−0.385038 | + | 0.922901i | \(0.625812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 195.548i | − 0.846529i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −71.8366 | −0.308312 | −0.154156 | − | 0.988047i | \(-0.549266\pi\) | ||||
−0.154156 | + | 0.988047i | \(0.549266\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 353.211i | − 1.50303i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −326.968 | −1.37961 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 71.0926i | 0.297459i | 0.988878 | + | 0.148729i | \(0.0475183\pi\) | ||||
−0.988878 | + | 0.148729i | \(0.952482\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 56.1113 | 0.232827 | 0.116413 | − | 0.993201i | \(-0.462860\pi\) | ||||
0.116413 | + | 0.993201i | \(0.462860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 148.264i | − 0.610138i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 34.1801 | 0.139510 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 59.6100i | − 0.241336i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 246.105 | 0.988374 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 368.953i | 1.46993i | 0.678104 | + | 0.734966i | \(0.262802\pi\) | ||||
−0.678104 | + | 0.734966i | \(0.737198\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 235.229 | 0.929759 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.94691i | 0.0154781i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.7428 | 0.0923845 | 0.0461923 | − | 0.998933i | \(-0.485291\pi\) | ||||
0.0461923 | + | 0.998933i | \(0.485291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 143.498i | 0.554044i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 98.4705 | 0.377282 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 73.9707i | − 0.281257i | −0.990062 | − | 0.140629i | \(-0.955088\pi\) | ||||
0.990062 | − | 0.140629i | \(-0.0449124\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −105.815 | −0.399302 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 549.764i | 2.05904i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −335.593 | −1.24756 | −0.623779 | − | 0.781601i | \(-0.714403\pi\) | ||||
−0.623779 | + | 0.781601i | \(0.714403\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 187.276i | − 0.691054i | −0.938409 | − | 0.345527i | \(-0.887700\pi\) | ||||
0.938409 | − | 0.345527i | \(-0.112300\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 119.054 | 0.436096 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.8626i | 0.0904095i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 132.592 | 0.478670 | 0.239335 | − | 0.970937i | \(-0.423071\pi\) | ||||
0.239335 | + | 0.970937i | \(0.423071\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 96.9480i | − 0.347484i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −331.520 | −1.17979 | −0.589894 | − | 0.807481i | \(-0.700830\pi\) | ||||
−0.589894 | + | 0.807481i | \(0.700830\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 66.7158i | − 0.235745i | −0.993029 | − | 0.117873i | \(-0.962393\pi\) | ||||
0.993029 | − | 0.117873i | \(-0.0376074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −76.6016 | −0.268778 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 100.089i | − 0.348741i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.945 | −0.999809 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 311.365i | − 1.06998i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −289.215 | −0.987082 | −0.493541 | − | 0.869723i | \(-0.664298\pi\) | ||||
−0.493541 | + | 0.869723i | \(0.664298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 170.415i | − 0.577679i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 455.111 | 1.53236 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 143.213i | 0.478972i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.8243 | −0.0426058 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 623.377i | − 2.05735i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 310.556 | 1.01822 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.693177i | − 0.00225790i | −0.999999 | − | 0.00112895i | \(-0.999641\pi\) | ||||
0.999999 | − | 0.00112895i | \(-0.000359357\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −135.243 | −0.437680 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 62.1583i | − 0.199866i | −0.994994 | − | 0.0999330i | \(-0.968137\pi\) | ||||
0.994994 | − | 0.0999330i | \(-0.0318628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −213.594 | −0.682408 | −0.341204 | − | 0.939989i | \(-0.610835\pi\) | ||||
−0.341204 | + | 0.939989i | \(0.610835\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 36.7204i | − 0.116573i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.4577 | 0.0739990 | 0.0369995 | − | 0.999315i | \(-0.488220\pi\) | ||||
0.0369995 | + | 0.999315i | \(0.488220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 744.059i | 2.33247i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −132.317 | −0.412201 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.07079i | 0.00331515i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.1369 | −0.0465751 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 95.9380i | − 0.293388i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 191.385 | 0.581718 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 507.406i | 1.53295i | 0.642275 | + | 0.766474i | \(0.277991\pi\) | ||||
−0.642275 | + | 0.766474i | \(0.722009\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 154.163 | 0.462951 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 90.0126i | 0.268694i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −342.726 | −1.01699 | −0.508495 | − | 0.861065i | \(-0.669798\pi\) | ||||
−0.508495 | + | 0.861065i | \(0.669798\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 283.705i | 0.836889i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 732.555 | 2.14825 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 184.035 | 0.533434 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 136.745i | 0.394079i | 0.980396 | + | 0.197039i | \(0.0631327\pi\) | ||||
−0.980396 | + | 0.197039i | \(0.936867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 82.0565 | 0.235119 | 0.117559 | − | 0.993066i | \(-0.462493\pi\) | ||||
0.117559 | + | 0.993066i | \(0.462493\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 277.081i | 0.789406i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 507.367 | 1.43730 | 0.718651 | − | 0.695371i | \(-0.244760\pi\) | ||||
0.718651 | + | 0.695371i | \(0.244760\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 232.055i | 0.653677i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.13861 | −0.00599051 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 560.809i | 1.56214i | 0.624442 | + | 0.781071i | \(0.285326\pi\) | ||||
−0.624442 | + | 0.781071i | \(0.714674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 340.218 | 0.942432 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1171.02i | − 3.22595i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 273.003 | 0.747952 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 26.9431i | − 0.0734145i | −0.999326 | − | 0.0367072i | \(-0.988313\pi\) | ||||
0.999326 | − | 0.0367072i | \(-0.0116869\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −107.528 | −0.291403 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 57.3352i | − 0.154542i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −538.034 | −1.44245 | −0.721225 | − | 0.692701i | \(-0.756421\pi\) | ||||
−0.721225 | + | 0.692701i | \(0.756421\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 439.534i | 1.17209i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −453.000 | −1.20159 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 182.132i | − 0.480560i | −0.970704 | − | 0.240280i | \(-0.922761\pi\) | ||||
0.970704 | − | 0.240280i | \(-0.0772393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 86.5166 | 0.227078 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 333.271i | 0.870160i | 0.900392 | + | 0.435080i | \(0.143280\pi\) | ||||
−0.900392 | + | 0.435080i | \(0.856720\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 277.466 | 0.720690 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.7775i | 0.0356007i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 109.639 | 0.281847 | 0.140924 | − | 0.990020i | \(-0.454993\pi\) | ||||
0.140924 | + | 0.990020i | \(0.454993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 2.57258i | − 0.00657948i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −434.971 | −1.10680 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 463.938i | − 1.17453i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 310.938 | 0.783219 | 0.391610 | − | 0.920131i | \(-0.371918\pi\) | ||||
0.391610 | + | 0.920131i | \(0.371918\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 41.5061i | − 0.104025i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −423.903 | −1.05711 | −0.528557 | − | 0.848898i | \(-0.677267\pi\) | ||||
−0.528557 | + | 0.848898i | \(0.677267\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 445.995i | 1.10669i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 480.974 | 1.18759 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1164.88i | 2.86211i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −444.543 | −1.08690 | −0.543451 | − | 0.839441i | \(-0.682883\pi\) | ||||
−0.543451 | + | 0.839441i | \(0.682883\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 120.258i | − 0.292598i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 92.3385 | 0.223580 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 349.201i | 0.841449i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 410.020 | 0.983261 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 457.129i | − 1.09100i | −0.838111 | − | 0.545500i | \(-0.816340\pi\) | ||||
0.838111 | − | 0.545500i | \(-0.183660\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4812 | 0.0605255 | 0.0302628 | − | 0.999542i | \(-0.490366\pi\) | ||||
0.0302628 | + | 0.999542i | \(0.490366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 205.610i | − 0.486075i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.271910 | 0.000639787 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 168.273i | 0.394082i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 966.453 | 2.25280 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 124.595i | 0.289084i | 0.989499 | + | 0.144542i | \(0.0461709\pi\) | ||||
−0.989499 | + | 0.144542i | \(0.953829\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −272.271 | −0.628802 | −0.314401 | − | 0.949290i | \(-0.601804\pi\) | ||||
−0.314401 | + | 0.949290i | \(0.601804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 582.126i | 1.33822i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 49.9285 | 0.114253 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 255.069i | 0.581023i | 0.956871 | + | 0.290512i | \(0.0938255\pi\) | ||||
−0.956871 | + | 0.290512i | \(0.906174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.8967 | 0.0451173 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 131.274i | 0.296330i | 0.988963 | + | 0.148165i | \(0.0473366\pi\) | ||||
−0.988963 | + | 0.148165i | \(0.952663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −780.066 | −1.75296 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 419.601i | 0.938704i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −642.824 | −1.43168 | −0.715839 | − | 0.698265i | \(-0.753956\pi\) | ||||
−0.715839 | + | 0.698265i | \(0.753956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 812.496i | − 1.80154i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −758.472 | −1.67433 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 168.927i | 0.371269i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −693.088 | −1.51660 | −0.758302 | − | 0.651903i | \(-0.773971\pi\) | ||||
−0.758302 | + | 0.651903i | \(0.773971\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 4.97731i | − 0.0108438i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 258.699 | 0.561170 | 0.280585 | − | 0.959829i | \(-0.409472\pi\) | ||||
0.280585 | + | 0.959829i | \(0.409472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 637.226i | − 1.37630i | −0.725569 | − | 0.688150i | \(-0.758423\pi\) | ||||
0.725569 | − | 0.688150i | \(-0.241577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 573.125 | 1.23253 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 199.483i | 0.427159i | 0.976926 | + | 0.213580i | \(0.0685123\pi\) | ||||
−0.976926 | + | 0.213580i | \(0.931488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −48.7727 | −0.103993 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 23.2979i | − 0.0494648i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −104.105 | −0.220095 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.27721i | 0.0111099i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −61.5966 | −0.129133 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 674.160i | 1.40743i | 0.710481 | + | 0.703716i | \(0.248477\pi\) | ||||
−0.710481 | + | 0.703716i | \(0.751523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −709.204 | −1.47444 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 99.7182i | 0.206456i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 441.799 | 0.910926 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 401.718i | − 0.824883i | −0.910984 | − | 0.412442i | \(-0.864676\pi\) | ||||
0.910984 | − | 0.412442i | \(-0.135324\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −713.181 | −1.45845 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 428.880i | 0.873482i | 0.899587 | + | 0.436741i | \(0.143867\pi\) | ||||
−0.899587 | + | 0.436741i | \(0.856133\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.13739 | 0.0165059 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 298.088i | − 0.602198i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −125.738 | −0.252993 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 182.619i | − 0.365970i | −0.983116 | − | 0.182985i | \(-0.941424\pi\) | ||||
0.983116 | − | 0.182985i | \(-0.0585760\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 569.632 | 1.13699 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 380.158i | − 0.755781i | −0.925850 | − | 0.377891i | \(-0.876650\pi\) | ||||
0.925850 | − | 0.377891i | \(-0.123350\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 884.516 | 1.75152 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.82188i | 0.0134554i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 289.538 | 0.568836 | 0.284418 | − | 0.958700i | \(-0.408200\pi\) | ||||
0.284418 | + | 0.958700i | \(0.408200\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 147.925i | 0.289481i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 96.5995 | 0.188303 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 191.898i | − 0.372617i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1553.62 | 3.00507 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 305.768i | − 0.589148i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 738.899 | 1.41823 | 0.709116 | − | 0.705092i | \(-0.249094\pi\) | ||||
0.709116 | + | 0.705092i | \(0.249094\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 647.126i | 1.23734i | 0.785653 | + | 0.618668i | \(0.212327\pi\) | ||||
−0.785653 | + | 0.618668i | \(0.787673\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.5397 | −0.0200757 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 8.01157i | − 0.0152022i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 409.047 | 0.773246 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 99.2014i | − 0.186820i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 494.666 | 0.928078 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 187.745i | − 0.350926i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 276.607 | 0.515097 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 150.343i | 0.278930i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −178.722 | −0.330355 | −0.165178 | − | 0.986264i | \(-0.552820\pi\) | ||||
−0.165178 | + | 0.986264i | \(0.552820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 951.008i | − 1.75140i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 136.127 | 0.249775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 452.236i | − 0.826758i | −0.910559 | − | 0.413379i | \(-0.864349\pi\) | ||||
0.910559 | − | 0.413379i | \(-0.135651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 180.780 | 0.329289 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 157.930i | 0.286625i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 251.382 | 0.454579 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 911.360i | 1.64209i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 854.108 | 1.53341 | 0.766704 | − | 0.642001i | \(-0.221895\pi\) | ||||
0.766704 | + | 0.642001i | \(0.221895\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 63.3814i | − 0.113383i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.3607 | −0.0309460 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 249.654i | − 0.443436i | −0.975111 | − | 0.221718i | \(-0.928834\pi\) | ||||
0.975111 | − | 0.221718i | \(-0.0711664\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −402.553 | −0.712483 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 260.613i | 0.459634i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −104.353 | −0.183396 | −0.0916982 | − | 0.995787i | \(-0.529229\pi\) | ||||
−0.0916982 | + | 0.995787i | \(0.529229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 649.705i | − 1.13784i | −0.822394 | − | 0.568919i | \(-0.807362\pi\) | ||||
0.822394 | − | 0.568919i | \(-0.192638\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −698.630 | −1.21925 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 12.6785i | − 0.0220495i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −346.022 | −0.599692 | −0.299846 | − | 0.953988i | \(-0.596935\pi\) | ||||
−0.299846 | + | 0.953988i | \(0.596935\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 300.537i | 0.519061i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −189.213 | −0.325667 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 465.434i | − 0.798342i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 181.482 | 0.310226 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1153.54i | − 1.96514i | −0.185885 | − | 0.982572i | \(-0.559515\pi\) | ||||
0.185885 | − | 0.982572i | \(-0.440485\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 155.488 | 0.263987 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 74.5515i | − 0.126145i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 880.135 | 1.48421 | 0.742104 | − | 0.670285i | \(-0.233828\pi\) | ||||
0.742104 | + | 0.670285i | \(0.233828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.03450i | − 0.00510000i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −626.081 | −1.04871 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 554.939i | − 0.926442i | −0.886243 | − | 0.463221i | \(-0.846694\pi\) | ||||
0.886243 | − | 0.463221i | \(-0.153306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 666.057 | 1.10825 | 0.554124 | − | 0.832434i | \(-0.313054\pi\) | ||||
0.554124 | + | 0.832434i | \(0.313054\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 52.3977i | 0.0868950i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1661.57 | 2.74640 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 192.927i | 0.317836i | 0.987292 | + | 0.158918i | \(0.0508006\pi\) | ||||
−0.987292 | + | 0.158918i | \(0.949199\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −315.421 | −0.517933 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 945.878i | 1.54808i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 608.234 | 0.992226 | 0.496113 | − | 0.868258i | \(-0.334760\pi\) | ||||
0.496113 | + | 0.868258i | \(0.334760\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 635.668i | − 1.03361i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.884056 | −0.00143283 | −0.000716415 | − | 1.00000i | \(-0.500228\pi\) | ||||
−0.000716415 | 1.00000i | \(0.500228\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 358.525i | 0.579200i | 0.957148 | + | 0.289600i | \(0.0935222\pi\) | ||||
−0.957148 | + | 0.289600i | \(0.906478\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −232.080 | −0.373719 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 422.674i | − 0.678449i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −594.720 | −0.951552 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 336.937i | − 0.537379i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.7397 | 0.0202539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 390.515i | − 0.618883i | −0.950918 | − | 0.309442i | \(-0.899858\pi\) | ||||
0.950918 | − | 0.309442i | \(-0.100142\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −73.7137 | −0.116451 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 122.759i | 0.193322i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −91.5322 | −0.143693 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 135.083i | 0.211397i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −431.936 | −0.673848 | −0.336924 | − | 0.941532i | \(-0.609386\pi\) | ||||
−0.336924 | + | 0.941532i | \(0.609386\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 49.9370i | − 0.0776625i | −0.999246 | − | 0.0388313i | \(-0.987637\pi\) | ||||
0.999246 | − | 0.0388313i | \(-0.0123635\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −81.4480 | −0.126276 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 224.141i | − 0.346431i | −0.984884 | − | 0.173216i | \(-0.944584\pi\) | ||||
0.984884 | − | 0.173216i | \(-0.0554157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 749.582 | 1.15498 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 310.544i | 0.477027i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −80.7637 | −0.123681 | −0.0618405 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618405 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 617.186i | − 0.942268i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 158.919 | 0.241886 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 940.466i | 1.42711i | 0.700599 | + | 0.713555i | \(0.252916\pi\) | ||||
−0.700599 | + | 0.713555i | \(0.747084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 119.930 | 0.181437 | 0.0907184 | − | 0.995877i | \(-0.471084\pi\) | ||||
0.0907184 | + | 0.995877i | \(0.471084\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 10.5696i | − 0.0159421i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 58.8935 | 0.0885616 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 379.426i | − 0.568855i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 674.346 | 1.00799 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1366.00i | 2.03577i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1085.06 | 1.61227 | 0.806136 | − | 0.591731i | \(-0.201555\pi\) | ||||
0.806136 | + | 0.591731i | \(0.201555\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 24.5298i | − 0.0363404i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 949.901 | 1.40310 | 0.701552 | − | 0.712618i | \(-0.252491\pi\) | ||||
0.701552 | + | 0.712618i | \(0.252491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 239.386i | 0.352557i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −93.8270 | −0.137778 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 893.785i | − 1.30862i | −0.756228 | − | 0.654308i | \(-0.772960\pi\) | ||||
0.756228 | − | 0.654308i | \(-0.227040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 170.635 | 0.249102 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 606.861i | − 0.883349i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 283.366 | 0.411272 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1208.56i | − 1.74901i | −0.485019 | − | 0.874504i | \(-0.661187\pi\) | ||||
0.485019 | − | 0.874504i | \(-0.338813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 161.517 | 0.233069 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 581.782i | 0.837096i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.88585 | −0.0127487 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 247.210i | − 0.353662i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −219.477 | −0.313091 | −0.156546 | − | 0.987671i | \(-0.550036\pi\) | ||||
−0.156546 | + | 0.987671i | \(0.550036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 247.251i | 0.351709i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1215.50 | 1.72411 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 479.270i | 0.677892i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1265.13 | 1.78439 | 0.892195 | − | 0.451651i | \(-0.149165\pi\) | ||||
0.892195 | + | 0.451651i | \(0.149165\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 270.066i | − 0.379839i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −373.560 | −0.523927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1371.31i | 1.91792i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −244.650 | −0.341213 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1163.47i | − 1.61818i | −0.587687 | − | 0.809089i | \(-0.699961\pi\) | ||||
0.587687 | − | 0.809089i | \(-0.300039\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 103.979 | 0.144215 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 193.094i | 0.267074i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.1036 | 0.0553153 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1303.68i | 1.79324i | 0.442803 | + | 0.896619i | \(0.353984\pi\) | ||||
−0.442803 | + | 0.896619i | \(0.646016\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −376.305 | −0.516193 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.13854i | 0.00155751i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1256.12 | 1.71367 | 0.856836 | − | 0.515589i | \(-0.172427\pi\) | ||||
0.856836 | + | 0.515589i | \(0.172427\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 117.623i | 0.160031i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −395.925 | −0.537212 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 687.168i | − 0.929862i | −0.885347 | − | 0.464931i | \(-0.846079\pi\) | ||||
0.885347 | − | 0.464931i | \(-0.153921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 205.134 | 0.276835 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 362.628i | − 0.488059i | −0.969768 | − | 0.244030i | \(-0.921531\pi\) | ||||
0.969768 | − | 0.244030i | \(-0.0784694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −595.376 | −0.799163 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 203.275i | 0.272122i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 101.729 | 0.135819 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 261.366i | − 0.348024i | −0.984744 | − | 0.174012i | \(-0.944327\pi\) | ||||
0.984744 | − | 0.174012i | \(-0.0556732\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1269.67 | −1.68615 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1076.20i | − 1.42544i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1395.34 | −1.84325 | −0.921625 | − | 0.388081i | \(-0.873138\pi\) | ||||
−0.921625 | + | 0.388081i | \(0.873138\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 809.488i | 1.06652i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 319.500 | 0.419843 | 0.209921 | − | 0.977718i | \(-0.432679\pi\) | ||||
0.209921 | + | 0.977718i | \(0.432679\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 73.7598i | 0.0966708i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.26003 | −0.00426148 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 456.362i | 0.594996i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 634.936 | 0.825664 | 0.412832 | − | 0.910807i | \(-0.364540\pi\) | ||||
0.412832 | + | 0.910807i | \(0.364540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 81.7056i | 0.105974i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 96.1663 | 0.124407 | 0.0622033 | − | 0.998063i | \(-0.480187\pi\) | ||||
0.0622033 | + | 0.998063i | \(0.480187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 39.4836i | − 0.0509465i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −493.815 | −0.635540 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 172.456i | − 0.221382i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1020.71 | −1.30693 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 734.098i | − 0.937545i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.0577 | 0.0421117 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1319.25i | 1.67630i | 0.545442 | + | 0.838148i | \(0.316362\pi\) | ||||
−0.545442 | + | 0.838148i | \(0.683638\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 254.554 | 0.322628 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 218.121i | − 0.275753i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −831.651 | −1.04874 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 364.139i | − 0.458036i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 818.575 | 1.02707 | 0.513535 | − | 0.858068i | \(-0.328336\pi\) | ||||
0.513535 | + | 0.858068i | \(0.328336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 16.9911i | − 0.0212655i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −454.088 | −0.566902 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1200.82i | 1.49541i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −141.491 | −0.175765 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1154.87i | − 1.43106i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1232.72 | −1.52376 | −0.761881 | − | 0.647717i | \(-0.775724\pi\) | ||||
−0.761881 | + | 0.647717i | \(0.775724\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1009.05i | − 1.24421i | −0.782935 | − | 0.622103i | \(-0.786278\pi\) | ||||
0.782935 | − | 0.622103i | \(-0.213722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 644.468 | 0.792703 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1011.94i | − 1.24164i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.0968 | −0.0270462 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 98.3351i | 0.120067i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −939.093 | −1.14384 | −0.571920 | − | 0.820309i | \(-0.693801\pi\) | ||||
−0.571920 | + | 0.820309i | \(0.693801\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 911.100i | − 1.10705i | −0.832833 | − | 0.553524i | \(-0.813283\pi\) | ||||
0.832833 | − | 0.553524i | \(-0.186717\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −85.5591 | −0.103708 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 65.6564i | − 0.0793910i | −0.999212 | − | 0.0396955i | \(-0.987361\pi\) | ||||
0.999212 | − | 0.0396955i | \(-0.0126388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1515.94 | −1.82864 | −0.914318 | − | 0.404997i | \(-0.867272\pi\) | ||||
−0.914318 | + | 0.404997i | \(0.867272\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 456.285i | 0.549079i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.64422 | 0.00197386 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 808.257i | 0.967972i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −722.747 | −0.863497 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 869.972i | 1.03692i | 0.855103 | + | 0.518458i | \(0.173494\pi\) | ||||
−0.855103 | + | 0.518458i | \(0.826506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 359.174 | 0.427080 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1140.85i | − 1.35333i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.67964 | −0.0114552 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 900.313i | 1.06294i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 229.588 | 0.270421 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 594.020i | − 0.698026i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1643.91 | −1.92721 | −0.963607 | − | 0.267322i | \(-0.913861\pi\) | ||||
−0.963607 | + | 0.267322i | \(0.913861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 63.2706i | − 0.0740007i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −286.059 | −0.333791 | −0.166895 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166895 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 719.782i | 0.837930i | 0.908002 | + | 0.418965i | \(0.137607\pi\) | ||||
−0.908002 | + | 0.418965i | \(0.862393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 344.433 | 0.400038 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1120.47i | − 1.29835i | −0.760641 | − | 0.649173i | \(-0.775115\pi\) | ||||
0.760641 | − | 0.649173i | \(-0.224885\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 433.857 | 0.501569 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 994.339i | − 1.14687i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2040.66 | 2.34828 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 241.048i | − 0.276749i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 257.178 | 0.294591 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 337.926i | − 0.386201i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −145.400 | −0.165792 | −0.0828960 | − | 0.996558i | \(-0.526417\pi\) | ||||
−0.0828960 | + | 0.996558i | \(0.526417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 995.269i | − 1.13227i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 476.080 | 0.540386 | 0.270193 | − | 0.962806i | \(-0.412913\pi\) | ||||
0.270193 | + | 0.962806i | \(0.412913\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1101.22i | 1.24714i | 0.781769 | + | 0.623568i | \(0.214318\pi\) | ||||
−0.781769 | + | 0.623568i | \(0.785682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 586.447 | 0.662652 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1491.49i | − 1.68150i | −0.541427 | − | 0.840748i | \(-0.682116\pi\) | ||||
0.541427 | − | 0.840748i | \(-0.317884\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −66.5164 | −0.0748216 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2115.59i | 2.37440i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 329.764 | 0.369276 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 392.481i | 0.438526i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −492.834 | −0.549425 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1181.62i | − 1.31437i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.09021 | −0.00564951 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 44.1321i | − 0.0488728i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1349.40 | 1.49104 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1155.46i | 1.27394i | 0.770889 | + | 0.636969i | \(0.219812\pi\) | ||||
−0.770889 | + | 0.636969i | \(0.780188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 514.891 | 0.566436 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 944.690i | 1.03698i | 0.855083 | + | 0.518491i | \(0.173506\pi\) | ||||
−0.855083 | + | 0.518491i | \(0.826494\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1535.98 | −1.68235 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1068.71i | 1.16799i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 334.418 | 0.364687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 149.150i | 0.162296i | 0.996702 | + | 0.0811478i | \(0.0258586\pi\) | ||||
−0.996702 | + | 0.0811478i | \(0.974141\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.38541 | 0.00259003 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 621.430i | − 0.673272i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62.7851 | 0.0678758 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 111.707i | − 0.120503i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −58.8399 | −0.0633368 | −0.0316684 | − | 0.999498i | \(-0.510082\pi\) | ||||
−0.0316684 | + | 0.999498i | \(0.510082\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.9111i | 0.0342761i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 213.904 | 0.229265 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 24.6333i | − 0.0263458i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1700.18 | 1.81449 | 0.907246 | − | 0.420601i | \(-0.138181\pi\) | ||||
0.907246 | + | 0.420601i | \(0.138181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 735.036i | − 0.782786i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.6116 | 0.0601611 | 0.0300805 | − | 0.999547i | \(-0.490424\pi\) | ||||
0.0300805 | + | 0.999547i | \(0.490424\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 414.325i | 0.439369i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −273.751 | −0.289684 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 242.533i | − 0.256107i | −0.991767 | − | 0.128053i | \(-0.959127\pi\) | ||||
0.991767 | − | 0.128053i | \(-0.0408729\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −731.084 | −0.770373 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 80.7244i | 0.0848837i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 364.070 | 0.382025 | 0.191013 | − | 0.981588i | \(-0.438823\pi\) | ||||
0.191013 | + | 0.981588i | \(0.438823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 991.294i | − 1.03800i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2560.51 | −2.67556 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 92.4575i | 0.0964103i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −202.348 | −0.210560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 109.290i | − 0.113489i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −426.435 | −0.441901 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1221.99i | 1.26369i | 0.775093 | + | 0.631847i | \(0.217703\pi\) | ||||
−0.775093 | + | 0.631847i | \(0.782297\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.68490 | −0.00380279 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1088.53i | − 1.12104i | −0.828140 | − | 0.560521i | \(-0.810601\pi\) | ||||
0.828140 | − | 0.560521i | \(-0.189399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −315.235 | −0.323982 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 52.0903i | − 0.0534259i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1061.51 | −1.08650 | −0.543252 | − | 0.839570i | \(-0.682807\pi\) | ||||
−0.543252 | + | 0.839570i | \(0.682807\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3431.17i | − 3.50477i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 79.2419 | 0.0807766 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1322.61i | 1.34549i | 0.739877 | + | 0.672743i | \(0.234884\pi\) | ||||
−0.739877 | + | 0.672743i | \(0.765116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 105.782 | 0.107393 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 658.610i | 0.667285i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 53.0874 | 0.0536778 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 675.806i | 0.681944i | 0.940073 | + | 0.340972i | \(0.110756\pi\) | ||||
−0.940073 | + | 0.340972i | \(0.889244\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1746.12 | −1.75843 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 888.354i | − 0.892818i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −409.220 | −0.410452 | −0.205226 | − | 0.978715i | \(-0.565793\pi\) | ||||
−0.205226 | + | 0.978715i | \(0.565793\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 1149.28i | − 1.15043i |
(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 | 1792.3.d.j.1023.11 | 16 | ||
4.3 | odd | 2 | inner | 1792.3.d.j.1023.5 | 16 | ||
8.3 | odd | 2 | inner | 1792.3.d.j.1023.12 | 16 | ||
8.5 | even | 2 | inner | 1792.3.d.j.1023.6 | 16 | ||
16.3 | odd | 4 | 224.3.g.b.15.6 | 8 | |||
16.5 | even | 4 | 224.3.g.b.15.5 | 8 | |||
16.11 | odd | 4 | 56.3.g.b.43.4 | yes | 8 | ||
16.13 | even | 4 | 56.3.g.b.43.3 | ✓ | 8 | ||
48.5 | odd | 4 | 2016.3.g.b.1135.6 | 8 | |||
48.11 | even | 4 | 504.3.g.b.379.5 | 8 | |||
48.29 | odd | 4 | 504.3.g.b.379.6 | 8 | |||
48.35 | even | 4 | 2016.3.g.b.1135.3 | 8 | |||
112.11 | odd | 12 | 392.3.k.o.275.3 | 16 | |||
112.13 | odd | 4 | 392.3.g.m.99.3 | 8 | |||
112.27 | even | 4 | 392.3.g.m.99.4 | 8 | |||
112.45 | odd | 12 | 392.3.k.n.275.8 | 16 | |||
112.59 | even | 12 | 392.3.k.n.275.3 | 16 | |||
112.61 | odd | 12 | 392.3.k.n.67.3 | 16 | |||
112.69 | odd | 4 | 1568.3.g.m.687.4 | 8 | |||
112.75 | even | 12 | 392.3.k.n.67.8 | 16 | |||
112.83 | even | 4 | 1568.3.g.m.687.3 | 8 | |||
112.93 | even | 12 | 392.3.k.o.67.3 | 16 | |||
112.107 | odd | 12 | 392.3.k.o.67.8 | 16 | |||
112.109 | even | 12 | 392.3.k.o.275.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.3 | ✓ | 8 | 16.13 | even | 4 | ||
56.3.g.b.43.4 | yes | 8 | 16.11 | odd | 4 | ||
224.3.g.b.15.5 | 8 | 16.5 | even | 4 | |||
224.3.g.b.15.6 | 8 | 16.3 | odd | 4 | |||
392.3.g.m.99.3 | 8 | 112.13 | odd | 4 | |||
392.3.g.m.99.4 | 8 | 112.27 | even | 4 | |||
392.3.k.n.67.3 | 16 | 112.61 | odd | 12 | |||
392.3.k.n.67.8 | 16 | 112.75 | even | 12 | |||
392.3.k.n.275.3 | 16 | 112.59 | even | 12 | |||
392.3.k.n.275.8 | 16 | 112.45 | odd | 12 | |||
392.3.k.o.67.3 | 16 | 112.93 | even | 12 | |||
392.3.k.o.67.8 | 16 | 112.107 | odd | 12 | |||
392.3.k.o.275.3 | 16 | 112.11 | odd | 12 | |||
392.3.k.o.275.8 | 16 | 112.109 | even | 12 | |||
504.3.g.b.379.5 | 8 | 48.11 | even | 4 | |||
504.3.g.b.379.6 | 8 | 48.29 | odd | 4 | |||
1568.3.g.m.687.3 | 8 | 112.83 | even | 4 | |||
1568.3.g.m.687.4 | 8 | 112.69 | odd | 4 | |||
1792.3.d.j.1023.5 | 16 | 4.3 | odd | 2 | inner | ||
1792.3.d.j.1023.6 | 16 | 8.5 | even | 2 | inner | ||
1792.3.d.j.1023.11 | 16 | 1.1 | even | 1 | trivial | ||
1792.3.d.j.1023.12 | 16 | 8.3 | odd | 2 | inner | ||
2016.3.g.b.1135.3 | 8 | 48.35 | even | 4 | |||
2016.3.g.b.1135.6 | 8 | 48.5 | odd | 4 |