Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,4,Mod(287,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.287");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.l (of order \(4\), degree \(2\), 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: | \(67.9702003266\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 287.5 | ||
Character | \(\chi\) | \(=\) | 1152.287 |
Dual form | 1152.4.l.b.863.5 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(5\) | −9.40057 | + | 9.40057i | −0.840813 | + | 0.840813i | −0.988965 | − | 0.148152i | \(-0.952668\pi\) |
0.148152 | + | 0.988965i | \(0.452668\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.57327 | −0.192938 | −0.0964691 | − | 0.995336i | \(-0.530755\pi\) | ||||
−0.0964691 | + | 0.995336i | \(0.530755\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.36191 | − | 3.36191i | −0.0921504 | − | 0.0921504i | 0.659529 | − | 0.751679i | \(-0.270756\pi\) |
−0.751679 | + | 0.659529i | \(0.770756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26.9332 | + | 26.9332i | −0.574611 | + | 0.574611i | −0.933413 | − | 0.358803i | \(-0.883185\pi\) |
0.358803 | + | 0.933413i | \(0.383185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 12.7764i | − | 0.182278i | −0.995838 | − | 0.0911390i | \(-0.970949\pi\) | ||
0.995838 | − | 0.0911390i | \(-0.0290507\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 50.0373 | + | 50.0373i | 0.604176 | + | 0.604176i | 0.941418 | − | 0.337242i | \(-0.109494\pi\) |
−0.337242 | + | 0.941418i | \(0.609494\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 208.377i | 1.88912i | 0.328344 | + | 0.944558i | \(0.393509\pi\) | ||||
−0.328344 | + | 0.944558i | \(0.606491\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 51.7415i | − | 0.413932i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −134.170 | − | 134.170i | −0.859129 | − | 0.859129i | 0.132107 | − | 0.991235i | \(-0.457826\pi\) |
−0.991235 | + | 0.132107i | \(0.957826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 80.1170i | − | 0.464175i | −0.972695 | − | 0.232088i | \(-0.925444\pi\) | ||
0.972695 | − | 0.232088i | \(-0.0745556\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 33.5907 | − | 33.5907i | 0.162225 | − | 0.162225i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 308.445 | + | 308.445i | 1.37049 | + | 1.37049i | 0.859714 | + | 0.510775i | \(0.170642\pi\) |
0.510775 | + | 0.859714i | \(0.329358\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −172.761 | −0.658068 | −0.329034 | − | 0.944318i | \(-0.606723\pi\) | ||||
−0.329034 | + | 0.944318i | \(0.606723\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 87.0630 | − | 87.0630i | 0.308767 | − | 0.308767i | −0.535664 | − | 0.844431i | \(-0.679939\pi\) |
0.844431 | + | 0.535664i | \(0.179939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −525.793 | −1.63180 | −0.815902 | − | 0.578191i | \(-0.803759\pi\) | ||||
−0.815902 | + | 0.578191i | \(0.803759\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −330.232 | −0.962775 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −127.310 | + | 127.310i | −0.329951 | + | 0.329951i | −0.852568 | − | 0.522617i | \(-0.824956\pi\) |
0.522617 | + | 0.852568i | \(0.324956\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 63.2078 | 0.154962 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 172.640 | + | 172.640i | 0.380945 | + | 0.380945i | 0.871443 | − | 0.490498i | \(-0.163185\pi\) |
−0.490498 | + | 0.871443i | \(0.663185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 332.465 | − | 332.465i | 0.697832 | − | 0.697832i | −0.266111 | − | 0.963943i | \(-0.585739\pi\) |
0.963943 | + | 0.266111i | \(0.0857386\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 506.376i | − | 0.966280i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −556.127 | − | 556.127i | −1.01406 | − | 1.01406i | −0.999900 | − | 0.0141558i | \(-0.995494\pi\) |
−0.0141558 | − | 0.999900i | \(-0.504506\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 450.409i | 0.752868i | 0.926443 | + | 0.376434i | \(0.122850\pi\) | ||||
−0.926443 | + | 0.376434i | \(0.877150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 797.249i | − | 1.27823i | −0.769111 | − | 0.639116i | \(-0.779300\pi\) | ||
0.769111 | − | 0.639116i | \(-0.220700\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0130 | + | 12.0130i | 0.0177793 | + | 0.0177793i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 70.1603i | 0.0999197i | 0.998751 | + | 0.0499598i | \(0.0159093\pi\) | ||||
−0.998751 | + | 0.0499598i | \(0.984091\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 636.357 | − | 636.357i | 0.841558 | − | 0.841558i | −0.147504 | − | 0.989062i | \(-0.547124\pi\) |
0.989062 | + | 0.147504i | \(0.0471238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 120.105 | + | 120.105i | 0.153262 | + | 0.153262i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 925.357 | 1.10211 | 0.551054 | − | 0.834470i | \(-0.314226\pi\) | ||||
0.551054 | + | 0.834470i | \(0.314226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96.2396 | − | 96.2396i | 0.110864 | − | 0.110864i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −940.759 | −1.01600 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1263.11 | 1.32216 | 0.661081 | − | 0.750315i | \(-0.270098\pi\) | ||||
0.661081 | + | 0.750315i | \(0.270098\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −643.591 | + | 643.591i | −0.634057 | + | 0.634057i | −0.949083 | − | 0.315026i | \(-0.897987\pi\) |
0.315026 | + | 0.949083i | \(0.397987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −977.275 | −0.934891 | −0.467445 | − | 0.884022i | \(-0.654826\pi\) | ||||
−0.467445 | + | 0.884022i | \(0.654826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −982.491 | − | 982.491i | −0.887672 | − | 0.887672i | 0.106627 | − | 0.994299i | \(-0.465995\pi\) |
−0.994299 | + | 0.106627i | \(0.965995\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 849.380 | − | 849.380i | 0.746384 | − | 0.746384i | −0.227414 | − | 0.973798i | \(-0.573027\pi\) |
0.973798 | + | 0.227414i | \(0.0730271\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1760.93i | − | 1.46597i | −0.680247 | − | 0.732983i | \(-0.738127\pi\) | ||
0.680247 | − | 0.732983i | \(-0.261873\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1958.87 | − | 1958.87i | −1.58839 | − | 1.58839i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 45.6534i | 0.0351684i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1308.40i | − | 0.983017i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −688.672 | − | 688.672i | −0.492773 | − | 0.492773i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1625.59i | − | 1.13581i | −0.823094 | − | 0.567905i | \(-0.807754\pi\) | ||
0.823094 | − | 0.567905i | \(-0.192246\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1291.78 | + | 1291.78i | −0.861550 | + | 0.861550i | −0.991518 | − | 0.129969i | \(-0.958512\pi\) |
0.129969 | + | 0.991518i | \(0.458512\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −178.797 | − | 178.797i | −0.116569 | − | 0.116569i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1257.75 | 0.784357 | 0.392179 | − | 0.919889i | \(-0.371722\pi\) | ||||
0.392179 | + | 0.919889i | \(0.371722\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −90.6450 | + | 90.6450i | −0.0553123 | + | 0.0553123i | −0.734222 | − | 0.678910i | \(-0.762453\pi\) |
0.678910 | + | 0.734222i | \(0.262453\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 181.094 | 0.105901 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2522.55 | 1.44473 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 27.0087 | − | 27.0087i | 0.0148499 | − | 0.0148499i | −0.699643 | − | 0.714493i | \(-0.746658\pi\) |
0.714493 | + | 0.699643i | \(0.246658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1808.06 | 0.974422 | 0.487211 | − | 0.873284i | \(-0.338014\pi\) | ||||
0.487211 | + | 0.873284i | \(0.338014\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 753.145 | + | 753.145i | 0.390284 | + | 0.390284i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1223.22 | − | 1223.22i | 0.621809 | − | 0.621809i | −0.324185 | − | 0.945994i | \(-0.605090\pi\) |
0.945994 | + | 0.324185i | \(0.105090\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 744.587i | − | 0.364483i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2395.40 | − | 2395.40i | −1.15106 | − | 1.15106i | −0.986341 | − | 0.164715i | \(-0.947330\pi\) |
−0.164715 | − | 0.986341i | \(-0.552670\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 895.247i | 0.414828i | 0.978253 | + | 0.207414i | \(0.0665047\pi\) | ||||
−0.978253 | + | 0.207414i | \(0.933495\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 746.201i | 0.339645i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2272.33 | − | 2272.33i | −0.998624 | − | 0.998624i | 0.00137536 | − | 0.999999i | \(-0.499562\pi\) |
−0.999999 | + | 0.00137536i | \(0.999562\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 184.886i | 0.0798633i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2206.38 | + | 2206.38i | −0.921301 | + | 0.921301i | −0.997121 | − | 0.0758204i | \(-0.975842\pi\) |
0.0758204 | + | 0.997121i | \(0.475842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 986.710 | + | 986.710i | 0.405202 | + | 0.405202i | 0.880062 | − | 0.474860i | \(-0.157501\pi\) |
−0.474860 | + | 0.880062i | \(0.657501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5799.13 | −2.30465 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −42.9530 | + | 42.9530i | −0.0167970 | + | 0.0167970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3104.61 | −1.17613 | −0.588067 | − | 0.808812i | \(-0.700111\pi\) | ||||
−0.588067 | + | 0.808812i | \(0.700111\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −441.815 | −0.164780 | −0.0823900 | − | 0.996600i | \(-0.526255\pi\) | ||||
−0.0823900 | + | 0.996600i | \(0.526255\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1039.58 | − | 1039.58i | 0.375976 | − | 0.375976i | −0.493672 | − | 0.869648i | \(-0.664346\pi\) |
0.869648 | + | 0.493672i | \(0.164346\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4338.31 | −1.54540 | −0.772700 | − | 0.634772i | \(-0.781094\pi\) | ||||
−0.772700 | + | 0.634772i | \(0.781094\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 479.425 | + | 479.425i | 0.165759 | + | 0.165759i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1624.05 | − | 1624.05i | 0.553312 | − | 0.553312i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 336.442i | − | 0.111350i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3907.28 | + | 3907.28i | 1.27483 | + | 1.27483i | 0.943525 | + | 0.331301i | \(0.107488\pi\) |
0.331301 | + | 0.943525i | \(0.392512\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1636.88i | 0.519231i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 286.279i | 0.0895571i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 344.109 | + | 344.109i | 0.104739 | + | 0.104739i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6191.70i | − | 1.85931i | −0.368427 | − | 0.929657i | \(-0.620104\pi\) | ||
0.368427 | − | 0.929657i | \(-0.379896\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2584.86 | + | 2584.86i | −0.755785 | + | 0.755785i | −0.975552 | − | 0.219767i | \(-0.929470\pi\) |
0.219767 | + | 0.975552i | \(0.429470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −727.799 | − | 727.799i | −0.210019 | − | 0.210019i | 0.594257 | − | 0.804275i | \(-0.297446\pi\) |
−0.804275 | + | 0.594257i | \(0.797446\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4374.36 | −1.22993 | −0.614965 | − | 0.788554i | \(-0.710830\pi\) | ||||
−0.614965 | + | 0.788554i | \(0.710830\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4942.75 | − | 4942.75i | 1.37204 | − | 1.37204i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 918.623 | 0.248622 | 0.124311 | − | 0.992243i | \(-0.460328\pi\) | ||||
0.124311 | + | 0.992243i | \(0.460328\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3401.67 | 0.909215 | 0.454608 | − | 0.890692i | \(-0.349779\pi\) | ||||
0.454608 | + | 0.890692i | \(0.349779\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3104.37 | − | 3104.37i | 0.809513 | − | 0.809513i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2695.33 | −0.694332 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −310.888 | − | 310.888i | −0.0781796 | − | 0.0781796i | 0.666936 | − | 0.745115i | \(-0.267606\pi\) |
−0.745115 | + | 0.666936i | \(0.767606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 700.546 | − | 700.546i | 0.174083 | − | 0.174083i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 558.847i | 0.135642i | 0.997698 | + | 0.0678208i | \(0.0216046\pi\) | ||||
−0.997698 | + | 0.0678208i | \(0.978395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1102.16 | − | 1102.16i | −0.264420 | − | 0.264420i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1037.09i | 0.243155i | 0.992582 | + | 0.121577i | \(0.0387953\pi\) | ||||
−0.992582 | + | 0.121577i | \(0.961205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2393.58i | − | 0.554855i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1664.16 | − | 1664.16i | −0.377196 | − | 0.377196i | 0.492894 | − | 0.870090i | \(-0.335939\pi\) |
−0.870090 | + | 0.492894i | \(0.835939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3882.80i | − | 0.870344i | −0.900347 | − | 0.435172i | \(-0.856688\pi\) | ||
0.900347 | − | 0.435172i | \(-0.143312\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −173.950 | + | 173.950i | −0.0381440 | + | 0.0381440i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −519.147 | − | 519.147i | −0.112608 | − | 0.112608i | 0.648557 | − | 0.761166i | \(-0.275373\pi\) |
−0.761166 | + | 0.648557i | \(0.775373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1938.11 | 0.411452 | 0.205726 | − | 0.978610i | \(-0.434044\pi\) | ||||
0.205726 | + | 0.978610i | \(0.434044\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5546.76 | + | 5546.76i | −1.16509 | + | 1.16509i | −0.181745 | + | 0.983346i | \(0.558175\pi\) |
−0.983346 | + | 0.181745i | \(0.941825\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 617.322 | 0.126966 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4749.76 | 0.966775 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3176.54 | − | 3176.54i | 0.633363 | − | 0.633363i | −0.315547 | − | 0.948910i | \(-0.602188\pi\) |
0.948910 | + | 0.315547i | \(0.102188\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3245.82 | −0.640607 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5612.28 | − | 5612.28i | −1.08551 | − | 1.08551i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −311.099 | + | 311.099i | −0.0595730 | + | 0.0595730i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6250.72i | 1.17349i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2494.33 | + | 2494.33i | 0.463710 | + | 0.463710i | 0.899869 | − | 0.436159i | \(-0.143662\pi\) |
−0.436159 | + | 0.899869i | \(0.643662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8539.18i | − | 1.55695i | −0.627674 | − | 0.778476i | \(-0.715993\pi\) | ||
0.627674 | − | 0.778476i | \(-0.284007\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 256.378i | 0.0462982i | 0.999732 | + | 0.0231491i | \(0.00736925\pi\) | ||||
−0.999732 | + | 0.0231491i | \(0.992631\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −46.2282 | − | 46.2282i | −0.00819065 | − | 0.00819065i | 0.703000 | − | 0.711190i | \(-0.251844\pi\) |
−0.711190 | + | 0.703000i | \(0.751844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 902.134i | 0.158338i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 639.295 | − | 639.295i | 0.110128 | − | 0.110128i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1393.57 | + | 1393.57i | 0.237850 | + | 0.237850i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1878.80 | 0.314837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2514.21 | + | 2514.21i | −0.417503 | + | 0.417503i | −0.884342 | − | 0.466839i | \(-0.845393\pi\) |
0.466839 | + | 0.884342i | \(0.345393\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10455.8 | 1.70526 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9524.70 | −1.53959 | −0.769797 | − | 0.638288i | \(-0.779643\pi\) | ||||
−0.769797 | + | 0.638288i | \(0.779643\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −269.346 | + | 269.346i | −0.0427739 | + | 0.0427739i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2405.64 | 0.378694 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6076.54 | + | 6076.54i | 0.940074 | + | 0.940074i | 0.998303 | − | 0.0582292i | \(-0.0185454\pi\) |
−0.0582292 | + | 0.998303i | \(0.518545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2783.60 | − | 2783.60i | 0.426942 | − | 0.426942i | −0.460643 | − | 0.887585i | \(-0.652381\pi\) |
0.887585 | + | 0.460643i | \(0.152381\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2070.44i | 0.312177i | 0.987743 | + | 0.156088i | \(0.0498885\pi\) | ||||
−0.987743 | + | 0.156088i | \(0.950112\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4234.10 | − | 4234.10i | −0.633021 | − | 0.633021i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 792.325i | − | 0.116483i | −0.998303 | − | 0.0582414i | \(-0.981451\pi\) | ||
0.998303 | − | 0.0582414i | \(-0.0185493\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1851.53i | − | 0.269942i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7494.59 | + | 7494.59i | 1.07475 | + | 1.07475i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4380.56i | 0.623061i | 0.950236 | + | 0.311530i | \(0.100842\pi\) | ||||
−0.950236 | + | 0.311530i | \(0.899158\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 454.914 | − | 454.914i | 0.0636602 | − | 0.0636602i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6602.76 | − | 6602.76i | −0.916563 | − | 0.916563i | 0.0802143 | − | 0.996778i | \(-0.474440\pi\) |
−0.996778 | + | 0.0802143i | \(0.974440\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7227.26 | 0.987329 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3757.17 | − | 3757.17i | 0.509216 | − | 0.509216i | −0.405070 | − | 0.914286i | \(-0.632753\pi\) |
0.914286 | + | 0.405070i | \(0.132753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8220.76 | −1.09677 | −0.548383 | − | 0.836227i | \(-0.684756\pi\) | ||||
−0.548383 | + | 0.836227i | \(0.684756\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −225.858 | −0.0298982 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1269.20 | + | 1269.20i | −0.165427 | + | 0.165427i | −0.784966 | − | 0.619539i | \(-0.787320\pi\) |
0.619539 | + | 0.784966i | \(0.287320\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2662.31 | 0.344344 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −659.547 | − | 659.547i | −0.0840137 | − | 0.0840137i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5888.81 | + | 5888.81i | −0.744460 | + | 0.744460i | −0.973433 | − | 0.228973i | \(-0.926463\pi\) |
0.228973 | + | 0.973433i | \(0.426463\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7300.97i | − | 0.909210i | −0.890693 | − | 0.454605i | \(-0.849780\pi\) | ||
0.890693 | − | 0.454605i | \(-0.150220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2157.81 | + | 2157.81i | 0.266720 | + | 0.266720i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2073.93i | − | 0.252582i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10278.9i | 1.24268i | 0.783540 | + | 0.621341i | \(0.213412\pi\) | ||||
−0.783540 | + | 0.621341i | \(0.786588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −616.887 | − | 616.887i | −0.0734988 | − | 0.0734988i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11964.2i | 1.41519i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5762.20 | − | 5762.20i | 0.671842 | − | 0.671842i | −0.286298 | − | 0.958141i | \(-0.592425\pi\) |
0.958141 | + | 0.286298i | \(0.0924248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 100.297 | + | 100.297i | 0.0116109 | + | 0.0116109i | 0.712888 | − | 0.701278i | \(-0.247387\pi\) |
−0.701278 | + | 0.712888i | \(0.747387\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −661.069 | −0.0754507 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1187.98 | + | 1187.98i | −0.134638 | + | 0.134638i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4634.34 | 0.517932 | 0.258966 | − | 0.965886i | \(-0.416618\pi\) | ||||
0.258966 | + | 0.965886i | \(0.416618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8964.00 | 0.994878 | 0.497439 | − | 0.867499i | \(-0.334274\pi\) | ||||
0.497439 | + | 0.867499i | \(0.334274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10426.6 | + | 10426.6i | −1.14136 | + | 1.14136i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16072.0 | 1.74732 | 0.873662 | − | 0.486533i | \(-0.161739\pi\) | ||||
0.873662 | + | 0.486533i | \(0.161739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −834.705 | − | 834.705i | −0.0895215 | − | 0.0895215i | 0.660928 | − | 0.750449i | \(-0.270163\pi\) |
−0.750449 | + | 0.660928i | \(0.770163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8698.88 | + | 8698.88i | −0.926666 | + | 0.926666i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3827.41i | − | 0.402286i | −0.979562 | − | 0.201143i | \(-0.935534\pi\) | ||
0.979562 | − | 0.201143i | \(-0.0644657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 580.808 | + | 580.808i | 0.0606412 | + | 0.0606412i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1809.42i | 0.186432i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11649.3i | 1.19241i | 0.802834 | + | 0.596203i | \(0.203325\pi\) | ||||
−0.802834 | + | 0.596203i | \(0.796675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3254.45 | + | 3254.45i | 0.328796 | + | 0.328796i | 0.852128 | − | 0.523333i | \(-0.175311\pi\) |
−0.523333 | + | 0.852128i | \(0.675311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13371.1i | 1.34213i | 0.741397 | + | 0.671067i | \(0.234164\pi\) | ||||
−0.741397 | + | 0.671067i | \(0.765836\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2009.07 | − | 2009.07i | 0.199076 | − | 0.199076i | −0.600528 | − | 0.799604i | \(-0.705043\pi\) |
0.799604 | + | 0.600528i | \(0.205043\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1987.19 | + | 1987.19i | 0.195650 | + | 0.195650i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −585.396 | −0.0569060 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2589.01 | − | 2589.01i | 0.250088 | − | 0.250088i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3070.02 | −0.292845 | −0.146422 | − | 0.989222i | \(-0.546776\pi\) | ||||
−0.146422 | + | 0.989222i | \(0.546776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16614.9 | −1.57500 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11874.0 | + | 11874.0i | −1.11169 | + | 1.11169i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −113.794 | −0.0105883 | −0.00529416 | − | 0.999986i | \(-0.501685\pi\) | ||||
−0.00529416 | + | 0.999986i | \(0.501685\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8646.06 | + | 8646.06i | 0.794686 | + | 0.794686i | 0.982252 | − | 0.187566i | \(-0.0600597\pi\) |
−0.187566 | + | 0.982252i | \(0.560060\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1714.20 | + | 1714.20i | −0.156600 | + | 0.156600i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1609.43i | − | 0.145257i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8311.88 | + | 8311.88i | 0.745673 | + | 0.745673i | 0.973663 | − | 0.227991i | \(-0.0732155\pi\) |
−0.227991 | + | 0.973663i | \(0.573216\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19595.5i | 1.73702i | 0.495675 | + | 0.868508i | \(0.334921\pi\) | ||||
−0.495675 | + | 0.868508i | \(0.665079\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 12100.3i | − | 1.06625i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 964.944 | + | 964.944i | 0.0840283 | + | 0.0840283i | 0.747872 | − | 0.663843i | \(-0.231076\pi\) |
−0.663843 | + | 0.747872i | \(0.731076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2848.78i | 0.246620i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9186.94 | − | 9186.94i | 0.786068 | − | 0.786068i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1767.67 | + | 1767.67i | 0.150371 | + | 0.150371i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11558.6 | 0.971962 | 0.485981 | − | 0.873969i | \(-0.338462\pi\) | ||||
0.485981 | + | 0.873969i | \(0.338462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −174.386 | + | 174.386i | −0.0145801 | + | 0.0145801i | −0.714359 | − | 0.699779i | \(-0.753282\pi\) |
0.699779 | + | 0.714359i | \(0.253282\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1023.60 | −0.0846089 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31254.1 | −2.56876 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4653.02 | − | 4653.02i | 0.378133 | − | 0.378133i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18471.9 | 1.49273 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1110.21 | + | 1110.21i | 0.0887201 | + | 0.0887201i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17450.8 | + | 17450.8i | −1.38682 | + | 1.38682i | −0.554899 | + | 0.831918i | \(0.687243\pi\) |
−0.831918 | + | 0.554899i | \(0.812757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15969.3i | 1.25514i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8294.19 | + | 8294.19i | 0.648325 | + | 0.648325i | 0.952588 | − | 0.304263i | \(-0.0984101\pi\) |
−0.304263 | + | 0.952588i | \(0.598410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13427.0i | − | 1.03813i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 250.701i | − | 0.0192783i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8685.44 | − | 8685.44i | −0.660707 | − | 0.660707i | 0.294840 | − | 0.955547i | \(-0.404734\pi\) |
−0.955547 | + | 0.294840i | \(0.904734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4689.78i | 0.354842i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6079.67 | − | 6079.67i | 0.455111 | − | 0.455111i | −0.441936 | − | 0.897047i | \(-0.645708\pi\) |
0.897047 | + | 0.441936i | \(0.145708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16553.7 | + | 16553.7i | 1.23260 | + | 1.23260i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8341.99 | 0.614612 | 0.307306 | − | 0.951611i | \(-0.400572\pi\) | ||||
0.307306 | + | 0.951611i | \(0.400572\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7249.79 | + | 7249.79i | −0.531338 | + | 0.531338i | −0.920970 | − | 0.389632i | \(-0.872602\pi\) |
0.389632 | + | 0.920970i | \(0.372602\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10781.8 | 0.781966 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7557.93 | −0.545305 | −0.272652 | − | 0.962113i | \(-0.587901\pi\) | ||||
−0.272652 | + | 0.962113i | \(0.587901\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2273.87 | + | 2273.87i | −0.162369 | + | 0.162369i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 856.012 | 0.0608103 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16053.1 | − | 16053.1i | −1.12876 | − | 1.12876i | −0.990379 | − | 0.138378i | \(-0.955811\pi\) |
−0.138378 | − | 0.990379i | \(-0.544189\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4008.84 | − | 4008.84i | 0.280444 | − | 0.280444i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17978.4i | 1.24500i | 0.782621 | + | 0.622499i | \(0.213882\pi\) | ||||
−0.782621 | + | 0.622499i | \(0.786118\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −429.168 | − | 429.168i | −0.0295700 | − | 0.0295700i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12555.7i | 0.856446i | 0.903673 | + | 0.428223i | \(0.140860\pi\) | ||||
−0.903673 | + | 0.428223i | \(0.859140\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1874.61i | − | 0.127233i | −0.997974 | − | 0.0636164i | \(-0.979737\pi\) | ||
0.997974 | − | 0.0636164i | \(-0.0202634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12299.7 | + | 12299.7i | 0.826533 | + | 0.826533i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10180.2i | 0.680731i | 0.940293 | + | 0.340365i | \(0.110551\pi\) | ||||
−0.940293 | + | 0.340365i | \(0.889449\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14161.3 | − | 14161.3i | 0.937651 | − | 0.937651i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4822.54 | − | 4822.54i | −0.317750 | − | 0.317750i | 0.530152 | − | 0.847902i | \(-0.322135\pi\) |
−0.847902 | + | 0.530152i | \(0.822135\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2024.64 | −0.132105 | −0.0660526 | − | 0.997816i | \(-0.521041\pi\) | ||||
−0.0660526 | + | 0.997816i | \(0.521041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17426.4 | + | 17426.4i | −1.13154 | + | 1.13154i | −0.141624 | + | 0.989921i | \(0.545232\pi\) |
−0.989921 | + | 0.141624i | \(0.954768\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3306.55 | −0.212639 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19415.5 | 1.24259 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3940.81 | − | 3940.81i | 0.249810 | − | 0.249810i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18780.7 | −1.18486 | −0.592432 | − | 0.805620i | \(-0.701832\pi\) | ||||
−0.592432 | + | 0.805620i | \(0.701832\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15281.5 | + | 15281.5i | 0.955003 | + | 0.955003i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8894.21 | − | 8894.21i | 0.553221 | − | 0.553221i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12312.7i | − | 0.758690i | −0.925255 | − | 0.379345i | \(-0.876149\pi\) | ||
0.925255 | − | 0.379345i | \(-0.123851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1553.86 | + | 1553.86i | 0.0953008 | + | 0.0953008i | 0.753150 | − | 0.657849i | \(-0.228534\pi\) |
−0.657849 | + | 0.753150i | \(0.728534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 23625.3i | − | 1.43556i | −0.696269 | − | 0.717781i | \(-0.745158\pi\) | ||
0.696269 | − | 0.717781i | \(-0.254842\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1160.80i | − | 0.0702084i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10161.7 | + | 10161.7i | 0.608971 | + | 0.608971i | 0.942677 | − | 0.333706i | \(-0.108299\pi\) |
−0.333706 | + | 0.942677i | \(0.608299\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 24286.9i | − | 1.44880i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 957.830 | − | 957.830i | 0.0566187 | − | 0.0566187i | −0.678230 | − | 0.734849i | \(-0.737253\pi\) |
0.734849 | + | 0.678230i | \(0.237253\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2569.18 | − | 2569.18i | −0.151179 | − | 0.151179i | 0.627465 | − | 0.778644i | \(-0.284092\pi\) |
−0.778644 | + | 0.627465i | \(0.784092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3361.58 | 0.196025 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27958.0 | − | 27958.0i | 1.62299 | − | 1.62299i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2235.43 | −0.128611 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15018.0 | −0.860183 | −0.430091 | − | 0.902785i | \(-0.641519\pi\) | ||||
−0.430091 | + | 0.902785i | \(0.641519\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18508.2 | − | 18508.2i | 1.05071 | − | 1.05071i | 0.0520645 | − | 0.998644i | \(-0.483420\pi\) |
0.998644 | − | 0.0520645i | \(-0.0165801\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4513.44 | −0.255096 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5041.00 | − | 5041.00i | −0.282414 | − | 0.282414i | 0.551657 | − | 0.834071i | \(-0.313996\pi\) |
−0.834071 | + | 0.551657i | \(0.813996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11823.6 | + | 11823.6i | −0.659498 | + | 0.659498i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 6857.76i | − | 0.379187i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8172.76 | + | 8172.76i | 0.449937 | + | 0.449937i | 0.895333 | − | 0.445396i | \(-0.146937\pi\) |
−0.445396 | + | 0.895333i | \(0.646937\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1704.23i | − | 0.0930146i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2207.26i | 0.119951i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10848.0 | + | 10848.0i | 0.584486 | + | 0.584486i | 0.936133 | − | 0.351647i | \(-0.114378\pi\) |
−0.351647 | + | 0.936133i | \(0.614378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30867.6i | 1.65603i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2299.72 | − | 2299.72i | 0.122334 | − | 0.122334i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9117.64 | − | 9117.64i | −0.482962 | − | 0.482962i | 0.423114 | − | 0.906076i | \(-0.360937\pi\) |
−0.906076 | + | 0.423114i | \(0.860937\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16694.6 | 0.876881 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1702.39 | + | 1702.39i | −0.0890430 | + | 0.0890430i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6812.47 | 0.353355 | 0.176678 | − | 0.984269i | \(-0.443465\pi\) | ||||
0.176678 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3492.06 | 0.180376 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6942.16 | + | 6942.16i | −0.355621 | + | 0.355621i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18664.2 | −0.952153 | −0.476076 | − | 0.879404i | \(-0.657941\pi\) | ||||
−0.476076 | + | 0.879404i | \(0.657941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1112.35 | − | 1112.35i | −0.0562814 | − | 0.0562814i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14517.0 | − | 14517.0i | 0.731510 | − | 0.731510i | −0.239408 | − | 0.970919i | \(-0.576953\pi\) |
0.970919 | + | 0.239408i | \(0.0769535\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3739.30i | 0.186891i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5245.53 | + | 5245.53i | 0.261110 | + | 0.261110i | 0.825505 | − | 0.564395i | \(-0.190891\pi\) |
−0.564395 | + | 0.825505i | \(0.690891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 10157.8i | − | 0.501552i | −0.968045 | − | 0.250776i | \(-0.919314\pi\) | ||
0.968045 | − | 0.250776i | \(-0.0806858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 507.794i | 0.0249720i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3510.70 | + | 3510.70i | 0.171266 | + | 0.171266i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 35581.6i | − | 1.72888i | −0.502734 | − | 0.864441i | \(-0.667672\pi\) | ||
0.502734 | − | 0.864441i | \(-0.332328\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16996.8 | + | 16996.8i | −0.819307 | + | 0.819307i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17559.8 | − | 17559.8i | −0.843094 | − | 0.843094i | 0.146166 | − | 0.989260i | \(-0.453307\pi\) |
−0.989260 | + | 0.146166i | \(0.953307\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38591.1 | −1.83828 | −0.919138 | − | 0.393936i | \(-0.871113\pi\) | ||||
−0.919138 | + | 0.393936i | \(0.871113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3035.06 | + | 3035.06i | −0.144006 | + | 0.144006i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9299.48 | −0.437790 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21740.3 | 1.01948 | 0.509738 | − | 0.860330i | \(-0.329742\pi\) | ||||
0.509738 | + | 0.860330i | \(0.329742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2913.88 | − | 2913.88i | 0.135582 | − | 0.135582i | −0.636058 | − | 0.771641i | \(-0.719436\pi\) |
0.771641 | + | 0.636058i | \(0.219436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4145.37 | −0.192137 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8644.51 | − | 8644.51i | −0.397589 | − | 0.397589i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1514.23 | − | 1514.23i | 0.0693771 | − | 0.0693771i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22998.0i | 1.04565i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15745.4 | − | 15745.4i | −0.713168 | − | 0.713168i | 0.254028 | − | 0.967197i | \(-0.418244\pi\) |
−0.967197 | + | 0.254028i | \(0.918244\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6292.26i | 0.282841i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17908.7i | 0.801963i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26542.1 | − | 26542.1i | −1.17964 | − | 1.17964i | −0.979837 | − | 0.199799i | \(-0.935971\pi\) |
−0.199799 | − | 0.979837i | \(-0.564029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6717.72i | 0.297442i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2680.28 | + | 2680.28i | −0.117790 | + | 0.117790i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6999.55 | + | 6999.55i | 0.306462 | + | 0.306462i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36199.3 | −1.57318 | −0.786588 | − | 0.617479i | \(-0.788154\pi\) | ||||
−0.786588 | + | 0.617479i | \(0.788154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20813.2 | + | 20813.2i | −0.901170 | + | 0.901170i | −0.995537 | − | 0.0943671i | \(-0.969917\pi\) |
0.0943671 | + | 0.995537i | \(0.469917\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45036.2 | 1.93565 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8712.80 | 0.373099 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4975.98 | − | 4975.98i | 0.211526 | − | 0.211526i | −0.593389 | − | 0.804916i | \(-0.702211\pi\) |
0.804916 | + | 0.593389i | \(0.202211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26415.2 | 1.11880 | 0.559401 | − | 0.828897i | \(-0.311031\pi\) | ||||
0.559401 | + | 0.828897i | \(0.311031\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11809.1 | + | 11809.1i | 0.496546 | + | 0.496546i | 0.910361 | − | 0.413815i | \(-0.135804\pi\) |
−0.413815 | + | 0.910361i | \(0.635804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5975.62 | + | 5975.62i | −0.250352 | + | 0.250352i | −0.821115 | − | 0.570763i | \(-0.806648\pi\) |
0.570763 | + | 0.821115i | \(0.306648\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4219.16i | 0.175493i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8415.84 | − | 8415.84i | −0.348793 | − | 0.348793i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 34562.9i | − | 1.42222i | −0.703079 | − | 0.711111i | \(-0.748192\pi\) | ||
0.703079 | − | 0.711111i | \(-0.251808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11614.1i | 0.476204i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7014.72 | − | 7014.72i | −0.285578 | − | 0.285578i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4675.24i | 0.189661i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −64273.0 | + | 64273.0i | −2.58901 | + | 2.58901i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16216.8 | − | 16216.8i | −0.650941 | − | 0.650941i | 0.302279 | − | 0.953220i | \(-0.402253\pi\) |
−0.953220 | + | 0.302279i | \(0.902253\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41556.4 | 1.65640 | 0.828202 | − | 0.560430i | \(-0.189364\pi\) | ||||
0.828202 | + | 0.560430i | \(0.189364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19887.3 | − | 19887.3i | 0.789927 | − | 0.789927i | −0.191555 | − | 0.981482i | \(-0.561353\pi\) |
0.981482 | + | 0.191555i | \(0.0613529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2405.75 | −0.0948929 | −0.0474464 | − | 0.998874i | \(-0.515108\pi\) | ||||
−0.0474464 | + | 0.998874i | \(0.515108\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42722.4 | 1.67931 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 235.873 | − | 235.873i | 0.00920763 | − | 0.00920763i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29956.6 | 1.16537 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2460.81 | + | 2460.81i | 0.0950748 | + | 0.0950748i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10981.7 | − | 10981.7i | 0.422835 | − | 0.422835i | −0.463344 | − | 0.886179i | \(-0.653351\pi\) |
0.886179 | + | 0.463344i | \(0.153351\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 34086.6i | − | 1.30352i | −0.758423 | − | 0.651762i | \(-0.774030\pi\) | ||
0.758423 | − | 0.651762i | \(-0.225970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1641.73 | + | 1641.73i | 0.0625691 | + | 0.0625691i | 0.737699 | − | 0.675130i | \(-0.235912\pi\) |
−0.675130 | + | 0.737699i | \(0.735912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44633.8i | 1.68958i | 0.535098 | + | 0.844790i | \(0.320275\pi\) | ||||
−0.535098 | + | 0.844790i | \(0.679725\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5808.67i | 0.219141i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26309.3 | − | 26309.3i | −0.985897 | − | 0.985897i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 41482.5i | − | 1.54928i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10749.3 | + | 10749.3i | −0.398786 | + | 0.398786i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1626.56 | + | 1626.56i | 0.0601428 | + | 0.0601428i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18551.3 | −0.681398 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9652.37 | + | 9652.37i | −0.353364 | + | 0.353364i | −0.861360 | − | 0.507995i | \(-0.830387\pi\) |
0.507995 | + | 0.861360i | \(0.330387\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26739.3 | −0.972463 | −0.486232 | − | 0.873830i | \(-0.661629\pi\) | ||||
−0.486232 | + | 0.873830i | \(0.661629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4278.75 | −0.155100 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4615.86 | − | 4615.86i | 0.166226 | − | 0.166226i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18146.3 | −0.651351 | −0.325676 | − | 0.945482i | \(-0.605592\pi\) | ||||
−0.325676 | + | 0.945482i | \(0.605592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12131.0 | − | 12131.0i | −0.432606 | − | 0.432606i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15959.4 | − | 15959.4i | 0.567290 | − | 0.567290i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 34344.9i | − | 1.21294i | −0.795107 | − | 0.606469i | \(-0.792585\pi\) | ||
0.795107 | − | 0.606469i | \(-0.207415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16523.9 | − | 16523.9i | −0.581686 | − | 0.581686i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 807.566i | − | 0.0282462i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39419.7i | − | 1.37437i | −0.726482 | − | 0.687185i | \(-0.758846\pi\) | ||
0.726482 | − | 0.687185i | \(-0.241154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13204.3 | − | 13204.3i | −0.457435 | − | 0.457435i | 0.440378 | − | 0.897813i | \(-0.354845\pi\) |
−0.897813 | + | 0.440378i | \(0.854845\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 35999.5i | − | 1.24317i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23749.6 | + | 23749.6i | −0.814952 | + | 0.814952i | −0.985372 | − | 0.170420i | \(-0.945488\pi\) |
0.170420 | + | 0.985372i | \(0.445488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21472.5 | + | 21472.5i | 0.734485 | + | 0.734485i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51211.8 | −1.74073 | −0.870363 | − | 0.492410i | \(-0.836116\pi\) | ||||
−0.870363 | + | 0.492410i | \(0.836116\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29185.1 | − | 29185.1i | 0.988909 | − | 0.988909i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4494.28 | −0.151332 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23372.3 | 0.784541 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4153.32 | − | 4153.32i | 0.138549 | − | 0.138549i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46964.2 | −1.56181 | −0.780903 | − | 0.624653i | \(-0.785241\pi\) | ||||
−0.780903 | + | 0.624653i | \(0.785241\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11140.6 | + | 11140.6i | 0.368198 | + | 0.368198i | 0.866820 | − | 0.498622i | \(-0.166160\pi\) |
−0.498622 | + | 0.866820i | \(0.666160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 323.899 | − | 323.899i | 0.0106719 | − | 0.0106719i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32688.3i | 1.07041i | 0.844722 | + | 0.535205i | \(0.179766\pi\) | ||||
−0.844722 | + | 0.535205i | \(0.820234\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3110.97 | − | 3110.97i | −0.101560 | − | 0.101560i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10414.9i | 0.337929i | 0.985622 | + | 0.168965i | \(0.0540423\pi\) | ||||
−0.985622 | + | 0.168965i | \(0.945958\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19545.4i | 0.632251i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18142.0 | + | 18142.0i | 0.583297 | + | 0.583297i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27162.5i | 0.870682i | 0.900266 | + | 0.435341i | \(0.143372\pi\) | ||||
−0.900266 | + | 0.435341i | \(0.856628\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40782.6 | − | 40782.6i | 1.29939 | − | 1.29939i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4529.97 | − | 4529.97i | −0.143897 | − | 0.143897i | 0.631488 | − | 0.775386i | \(-0.282444\pi\) |
−0.775386 | + | 0.631488i | \(0.782444\pi\) | |||||||
\(998\) | 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 | 1152.4.l.b.287.5 | 48 | ||
3.2 | odd | 2 | inner | 1152.4.l.b.287.20 | 48 | ||
4.3 | odd | 2 | 1152.4.l.a.287.5 | 48 | |||
8.3 | odd | 2 | 576.4.l.a.143.20 | 48 | |||
8.5 | even | 2 | 144.4.l.a.107.23 | yes | 48 | ||
12.11 | even | 2 | 1152.4.l.a.287.20 | 48 | |||
16.3 | odd | 4 | inner | 1152.4.l.b.863.20 | 48 | ||
16.5 | even | 4 | 576.4.l.a.431.5 | 48 | |||
16.11 | odd | 4 | 144.4.l.a.35.2 | ✓ | 48 | ||
16.13 | even | 4 | 1152.4.l.a.863.20 | 48 | |||
24.5 | odd | 2 | 144.4.l.a.107.2 | yes | 48 | ||
24.11 | even | 2 | 576.4.l.a.143.5 | 48 | |||
48.5 | odd | 4 | 576.4.l.a.431.20 | 48 | |||
48.11 | even | 4 | 144.4.l.a.35.23 | yes | 48 | ||
48.29 | odd | 4 | 1152.4.l.a.863.5 | 48 | |||
48.35 | even | 4 | inner | 1152.4.l.b.863.5 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.4.l.a.35.2 | ✓ | 48 | 16.11 | odd | 4 | ||
144.4.l.a.35.23 | yes | 48 | 48.11 | even | 4 | ||
144.4.l.a.107.2 | yes | 48 | 24.5 | odd | 2 | ||
144.4.l.a.107.23 | yes | 48 | 8.5 | even | 2 | ||
576.4.l.a.143.5 | 48 | 24.11 | even | 2 | |||
576.4.l.a.143.20 | 48 | 8.3 | odd | 2 | |||
576.4.l.a.431.5 | 48 | 16.5 | even | 4 | |||
576.4.l.a.431.20 | 48 | 48.5 | odd | 4 | |||
1152.4.l.a.287.5 | 48 | 4.3 | odd | 2 | |||
1152.4.l.a.287.20 | 48 | 12.11 | even | 2 | |||
1152.4.l.a.863.5 | 48 | 48.29 | odd | 4 | |||
1152.4.l.a.863.20 | 48 | 16.13 | even | 4 | |||
1152.4.l.b.287.5 | 48 | 1.1 | even | 1 | trivial | ||
1152.4.l.b.287.20 | 48 | 3.2 | odd | 2 | inner | ||
1152.4.l.b.863.5 | 48 | 48.35 | even | 4 | inner | ||
1152.4.l.b.863.20 | 48 | 16.3 | odd | 4 | inner |