Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - x^{10} - 861 x^{8} - 2158 x^{7} + 8654 x^{6} + 118244 x^{5} + 707300 x^{4} + 1646096 x^{3} + 1391904 x^{2} + 174720 x + 43264 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.7 | ||
Root | \(-0.0488747 + 0.182403i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.f.673.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 17.1345i | − 1.53256i | −0.642507 | − | 0.766280i | \(-0.722106\pi\) | ||||
0.642507 | − | 0.766280i | \(-0.277894\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.98040i | − 0.0816931i | −0.999165 | − | 0.0408465i | \(-0.986995\pi\) | ||||
0.999165 | − | 0.0408465i | \(-0.0130055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 39.8701i | 0.850615i | 0.905049 | + | 0.425307i | \(0.139834\pi\) | ||||
−0.905049 | + | 0.425307i | \(0.860166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 51.4036 | 0.884824 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 132.530 | 1.89077 | 0.945387 | − | 0.325949i | \(-0.105684\pi\) | ||||
0.945387 | + | 0.325949i | \(0.105684\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 83.2004i | − 1.00460i | −0.864692 | − | 0.502302i | \(-0.832486\pi\) | ||||
0.864692 | − | 0.502302i | \(-0.167514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 21.0000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −80.0478 | −0.725701 | −0.362850 | − | 0.931847i | \(-0.618196\pi\) | ||||
−0.362850 | + | 0.931847i | \(0.618196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −168.592 | −1.34874 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 139.743i | 0.894817i | 0.894330 | + | 0.447408i | \(0.147653\pi\) | ||||
−0.894330 | + | 0.447408i | \(0.852347\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 204.541 | 1.18505 | 0.592525 | − | 0.805552i | \(-0.298131\pi\) | ||||
0.592525 | + | 0.805552i | \(0.298131\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.94119 | 0.0471655 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 119.942i | 0.579253i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 377.916i | 1.67916i | 0.543234 | + | 0.839582i | \(0.317200\pi\) | ||||
−0.543234 | + | 0.839582i | \(0.682800\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −119.610 | −0.491103 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 45.3733 | 0.172832 | 0.0864161 | − | 0.996259i | \(-0.472459\pi\) | ||||
0.0864161 | + | 0.996259i | \(0.472459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 540.789i | − 1.91790i | −0.283582 | − | 0.958948i | \(-0.591523\pi\) | ||||
0.283582 | − | 0.958948i | \(-0.408477\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 154.211i | 0.510853i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 362.473 | 1.12494 | 0.562470 | − | 0.826818i | \(-0.309851\pi\) | ||||
0.562470 | + | 0.826818i | \(0.309851\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 397.589i | 1.09164i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 668.494i | 1.73254i | 0.499575 | + | 0.866270i | \(0.333489\pi\) | ||||
−0.499575 | + | 0.866270i | \(0.666511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −51.0677 | −0.125200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 249.601 | 0.580009 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 757.392i | − 1.67125i | −0.549297 | − | 0.835627i | \(-0.685105\pi\) | ||||
0.549297 | − | 0.835627i | \(-0.314895\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 690.035i | − 1.44836i | −0.689611 | − | 0.724180i | \(-0.742218\pi\) | ||||
0.689611 | − | 0.724180i | \(-0.257782\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 683.157 | 1.30362 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 370.530i | − 0.675634i | −0.941212 | − | 0.337817i | \(-0.890311\pi\) | ||||
0.941212 | − | 0.337817i | \(-0.109689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 240.143i | − 0.418984i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −652.184 | −1.09014 | −0.545070 | − | 0.838390i | \(-0.683497\pi\) | ||||
−0.545070 | + | 0.838390i | \(0.683497\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 229.804 | 0.368445 | 0.184223 | − | 0.982885i | \(-0.441023\pi\) | ||||
0.184223 | + | 0.982885i | \(0.441023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 505.777i | − 0.778695i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.8628i | 0.0308771i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 43.3308 | 0.0617101 | 0.0308550 | − | 0.999524i | \(-0.490177\pi\) | ||||
0.0308550 | + | 0.999524i | \(0.490177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 802.404i | − 1.06115i | −0.847639 | − | 0.530574i | \(-0.821976\pi\) | ||||
0.847639 | − | 0.530574i | \(-0.178024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2270.84i | − 2.89773i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −419.230 | −0.516623 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −868.188 | −1.03402 | −0.517010 | − | 0.855980i | \(-0.672955\pi\) | ||||
−0.517010 | + | 0.855980i | \(0.672955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 279.091i | − 0.321502i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 613.622i | 0.684189i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1425.60 | −1.53962 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1181.82 | −1.23707 | −0.618537 | − | 0.785756i | \(-0.712274\pi\) | ||||
−0.618537 | + | 0.785756i | \(0.712274\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 26.8236i | 0.0272310i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 215.909i | − 0.212710i | −0.994328 | − | 0.106355i | \(-0.966082\pi\) | ||||
0.994328 | − | 0.106355i | \(-0.0339180\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1204.93 | 1.15267 | 0.576334 | − | 0.817214i | \(-0.304483\pi\) | ||||
0.576334 | + | 0.817214i | \(0.304483\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −359.825 | −0.334432 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 327.101i | 0.295533i | 0.989022 | + | 0.147767i | \(0.0472085\pi\) | ||||
−0.989022 | + | 0.147767i | \(0.952792\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 668.438i | − 0.587383i | −0.955900 | − | 0.293692i | \(-0.905116\pi\) | ||||
0.955900 | − | 0.293692i | \(-0.0948839\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1133.75 | −0.969465 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −725.333 | −0.603837 | −0.301919 | − | 0.953334i | \(-0.597627\pi\) | ||||
−0.301919 | + | 0.953334i | \(0.597627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1371.58i | 1.11218i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 358.831i | − 0.283538i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −927.708 | −0.714646 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1322.12 | 0.993326 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 136.120i | 0.0997847i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 746.937i | 0.534465i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −672.231 | −0.469692 | −0.234846 | − | 0.972033i | \(-0.575459\pi\) | ||||
−0.234846 | + | 0.972033i | \(0.575459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1622.37 | 1.10730 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2082.36i | 1.38883i | 0.719575 | + | 0.694414i | \(0.244336\pi\) | ||||
−0.719575 | + | 0.694414i | \(0.755664\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 582.403i | 0.379705i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −462.633 | −0.294941 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1221.50 | 0.761749 | 0.380875 | − | 0.924627i | \(-0.375623\pi\) | ||||
0.380875 | + | 0.924627i | \(0.375623\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2590.38i | − 1.58067i | −0.612674 | − | 0.790336i | \(-0.709906\pi\) | ||||
0.612674 | − | 0.790336i | \(-0.290094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1087.42i | 0.649484i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 118.829 | 0.0694893 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2394.44 | 1.37136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3406.10i | − 1.87274i | −0.351015 | − | 0.936370i | \(-0.614163\pi\) | ||||
0.351015 | − | 0.936370i | \(-0.385837\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1795.43 | −0.967619 | −0.483809 | − | 0.875173i | \(-0.660747\pi\) | ||||
−0.483809 | + | 0.875173i | \(0.660747\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1192.77 | −0.630258 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3504.71i | − 1.81616i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2968.25i | − 1.50887i | −0.656377 | − | 0.754433i | \(-0.727912\pi\) | ||||
0.656377 | − | 0.754433i | \(-0.272088\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2005.48 | −1.00028 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 560.335 | 0.274289 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1529.60i | − 0.735016i | −0.930020 | − | 0.367508i | \(-0.880211\pi\) | ||||
0.930020 | − | 0.367508i | \(-0.119789\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 153.203i | − 0.0722840i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −252.934 | −0.117201 | −0.0586007 | − | 0.998282i | \(-0.518664\pi\) | ||||
−0.0586007 | + | 0.998282i | \(0.518664\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 607.371 | 0.276455 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 748.804i | 0.334868i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1196.52i | − 0.525838i | −0.964818 | − | 0.262919i | \(-0.915315\pi\) | ||||
0.964818 | − | 0.262919i | \(-0.0846853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1180.15 | 0.509776 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2272.17 | 0.964899 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3863.73i | − 1.61335i | −0.590998 | − | 0.806673i | \(-0.701266\pi\) | ||||
0.590998 | − | 0.806673i | \(-0.298734\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1166.62i | − 0.479085i | −0.970886 | − | 0.239542i | \(-0.923003\pi\) | ||||
0.970886 | − | 0.239542i | \(-0.0769974\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2070.11 | 0.836211 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6475.42 | 2.57342 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 394.991i | − 0.154463i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1734.96 | 0.657263 | 0.328631 | − | 0.944458i | \(-0.393413\pi\) | ||||
0.328631 | + | 0.944458i | \(0.393413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −308.801 | −0.115171 | −0.0575854 | − | 0.998341i | \(-0.518340\pi\) | ||||
−0.0575854 | + | 0.998341i | \(0.518340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2049.47i | 0.752644i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1297.96i | 0.469420i | 0.972065 | + | 0.234710i | \(0.0754140\pi\) | ||||
−0.972065 | + | 0.234710i | \(0.924586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1750.53 | 0.623576 | 0.311788 | − | 0.950152i | \(-0.399072\pi\) | ||||
0.311788 | + | 0.950152i | \(0.399072\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1111.59 | 0.390078 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 978.203i | − 0.338209i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 777.450i | − 0.264876i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 720.430 | 0.241900 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −247.970 | −0.0820692 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1022.70i | 0.333676i | 0.985984 | + | 0.166838i | \(0.0533557\pi\) | ||||
−0.985984 | + | 0.166838i | \(0.946644\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1956.55i | − 0.629393i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9266.17 | −2.93929 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1431.78 | −0.447907 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 689.411i | 0.212722i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5283.98i | 1.60832i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 255.416 | 0.0766992 | 0.0383496 | − | 0.999264i | \(-0.487790\pi\) | ||||
0.0383496 | + | 0.999264i | \(0.487790\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1517.33 | 0.449580 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1041.15i | 0.304422i | 0.988348 | + | 0.152211i | \(0.0486393\pi\) | ||||
−0.988348 | + | 0.152211i | \(0.951361\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2592.03i | 0.747975i | 0.927434 | + | 0.373988i | \(0.122010\pi\) | ||||
−0.927434 | + | 0.373988i | \(0.877990\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −62.5884 | −0.0178269 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1830.07 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 6210.82i | − 1.72404i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 129.992i | 0.0356283i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 135.227 | 0.0365989 | 0.0182994 | − | 0.999833i | \(-0.494175\pi\) | ||||
0.0182994 | + | 0.999833i | \(0.494175\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −312.681 | −0.0835748 | −0.0417874 | − | 0.999127i | \(-0.513305\pi\) | ||||
−0.0417874 | + | 0.999127i | \(0.513305\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 839.592i | − 0.218937i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3317.21 | 0.854531 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2407.21 | 0.612654 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4385.72i | − 1.10289i | −0.834213 | − | 0.551443i | \(-0.814078\pi\) | ||||
0.834213 | − | 0.551443i | \(-0.185922\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 238.574i | 0.0592847i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6812.51 | 1.67300 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6255.49 | 1.51831 | 0.759157 | − | 0.650908i | \(-0.225612\pi\) | ||||
0.759157 | + | 0.650908i | \(0.225612\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2645.41i | − 0.634664i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1257.69i | − 0.298272i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5952.39 | 1.39559 | 0.697795 | − | 0.716298i | \(-0.254165\pi\) | ||||
0.697795 | + | 0.716298i | \(0.254165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11454.3 | 2.65522 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2604.56i | − 0.596991i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 2997.81i | − 0.679479i | −0.940520 | − | 0.339739i | \(-0.889661\pi\) | ||||
0.940520 | − | 0.339739i | \(-0.110339\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 681.179 | 0.152689 | 0.0763444 | − | 0.997082i | \(-0.475675\pi\) | ||||
0.0763444 | + | 0.997082i | \(0.475675\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 837.273 | 0.185619 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 502.473i | 0.110183i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1466.94i | − 0.318194i | −0.987263 | − | 0.159097i | \(-0.949142\pi\) | ||||
0.987263 | − | 0.159097i | \(-0.0508583\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1840.86 | −0.395017 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6558.87 | −1.39242 | −0.696209 | − | 0.717840i | \(-0.745131\pi\) | ||||
−0.696209 | + | 0.717840i | \(0.745131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8554.70i | 1.79690i | 0.439071 | + | 0.898452i | \(0.355308\pi\) | ||||
−0.439071 | + | 0.898452i | \(0.644692\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 4276.80i | − 0.888898i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −317.613 | −0.0653244 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12651.1 | 2.57503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 3545.47i | − 0.714225i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1262.01i | − 0.251629i | −0.992054 | − | 0.125815i | \(-0.959846\pi\) | ||||
0.992054 | − | 0.125815i | \(-0.0401544\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12977.6 | −2.56130 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −80.4707 | −0.0157218 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3191.52i | − 0.617292i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3785.52i | 0.724896i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 647.726 | 0.122808 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11823.4 | −2.21970 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 234.049i | − 0.0435111i | −0.999763 | − | 0.0217555i | \(-0.993074\pi\) | ||||
0.999763 | − | 0.0217555i | \(-0.00692555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3614.78i | 0.665493i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −182.019 | −0.0331876 | −0.0165938 | − | 0.999862i | \(-0.505282\pi\) | ||||
−0.0165938 | + | 0.999862i | \(0.505282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3515.22 | 0.634799 | 0.317399 | − | 0.948292i | \(-0.397190\pi\) | ||||
0.317399 | + | 0.948292i | \(0.397190\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1079.48i | − 0.193084i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3339.39i | 0.591667i | 0.955239 | + | 0.295834i | \(0.0955974\pi\) | ||||
−0.955239 | + | 0.295834i | \(0.904403\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 416.491 | 0.0731003 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −981.304 | −0.170626 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 11026.5i | − 1.89948i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 6721.81i | − 1.14726i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2005.32 | 0.339126 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2537.31 | −0.425187 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1594.18i | − 0.264725i | −0.991201 | − | 0.132363i | \(-0.957744\pi\) | ||||
0.991201 | − | 0.132363i | \(-0.0422563\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3401.25i | − 0.559721i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6348.87 | −1.03545 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12224.7 | −1.97603 | −0.988017 | − | 0.154342i | \(-0.950674\pi\) | ||||
−0.988017 | + | 0.154342i | \(0.950674\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 2176.00i | − 0.348626i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 609.612i | − 0.0968104i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4114.75 | −0.642117 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3116.35i | 0.482117i | 0.970511 | + | 0.241058i | \(0.0774945\pi\) | ||||
−0.970511 | + | 0.241058i | \(0.922505\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7826.76i | 1.20045i | 0.799831 | + | 0.600225i | \(0.204922\pi\) | ||||
−0.799831 | + | 0.600225i | \(0.795078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1076.49 | 0.163701 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4326.14 | 0.652287 | 0.326143 | − | 0.945320i | \(-0.394251\pi\) | ||||
0.326143 | + | 0.945320i | \(0.394251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11174.9i | 1.67071i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2783.12i | − 0.412601i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3871.77 | −0.569204 | −0.284602 | − | 0.958646i | \(-0.591861\pi\) | ||||
−0.284602 | + | 0.958646i | \(0.591861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −63.3136 | −0.00923073 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3966.35i | 0.573497i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 3937.58i | − 0.564664i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8206.26 | 1.16720 | 0.583601 | − | 0.812041i | \(-0.301643\pi\) | ||||
0.583601 | + | 0.812041i | \(0.301643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −408.360 | −0.0576107 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 4679.46i | − 0.654839i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2149.21i | 0.298343i | 0.988811 | + | 0.149172i | \(0.0476607\pi\) | ||||
−0.988811 | + | 0.149172i | \(0.952339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2240.81 | −0.308573 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5571.59 | −0.761144 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 658.658i | 0.0892690i | 0.999003 | + | 0.0446345i | \(0.0142123\pi\) | ||||
−0.999003 | + | 0.0446345i | \(0.985788\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2016.69i | − 0.271177i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3084.93 | −0.411573 | −0.205786 | − | 0.978597i | \(-0.565975\pi\) | ||||
−0.205786 | + | 0.978597i | \(0.565975\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 357.474 | 0.0473210 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4867.10i | 0.639299i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 4413.01i | − 0.575189i | −0.957752 | − | 0.287595i | \(-0.907144\pi\) | ||||
0.957752 | − | 0.287595i | \(-0.0928556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10608.7 | −1.37214 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6247.08 | −0.801840 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 742.454i | − 0.0945744i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3900.51i | − 0.493101i | −0.969130 | − | 0.246551i | \(-0.920703\pi\) | ||||
0.969130 | − | 0.246551i | \(-0.0792972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1747.21 | −0.219223 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8593.07 | −1.07012 | −0.535059 | − | 0.844814i | \(-0.679711\pi\) | ||||
−0.535059 | + | 0.844814i | \(0.679711\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8155.06i | 1.00802i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1387.90i | − 0.170284i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1126.34 | 0.137176 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11212.2 | 1.35552 | 0.677758 | − | 0.735285i | \(-0.262952\pi\) | ||||
0.677758 | + | 0.735285i | \(0.262952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3664.49i | 0.439796i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5301.74i | 0.631675i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13748.8 | −1.62627 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7771.15 | 0.912601 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 7948.88i | − 0.926798i | −0.886150 | − | 0.463399i | \(-0.846630\pi\) | ||||
0.886150 | − | 0.463399i | \(-0.153370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 11113.8i | − 1.28658i | −0.765622 | − | 0.643291i | \(-0.777568\pi\) | ||||
0.765622 | − | 0.643291i | \(-0.222432\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3262.26 | −0.374980 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22343.5 | −2.55016 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4830.25i | 0.547429i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 356.487i | 0.0401197i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3571.39 | −0.399137 | −0.199568 | − | 0.979884i | \(-0.563954\pi\) | ||||
−0.199568 | + | 0.979884i | \(0.563954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13245.8 | −1.47010 | −0.735050 | − | 0.678013i | \(-0.762841\pi\) | ||||
−0.735050 | + | 0.678013i | \(0.762841\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7183.31i | 0.791755i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6660.01i | 0.729043i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7028.36 | −0.764112 | −0.382056 | − | 0.924139i | \(-0.624784\pi\) | ||||
−0.382056 | + | 0.924139i | \(0.624784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 133.981i | 0.0143694i | 0.999974 | + | 0.00718469i | \(0.00228698\pi\) | ||||
−0.999974 | + | 0.00718469i | \(0.997713\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14876.0i | 1.58470i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10218.3 | 1.08123 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2783.94 | 0.292611 | 0.146306 | − | 0.989239i | \(-0.453262\pi\) | ||||
0.146306 | + | 0.989239i | \(0.453262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 135.230i | − 0.0141192i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 5386.30i | − 0.558655i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4782.10 | −0.492721 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19117.6 | 1.95686 | 0.978428 | − | 0.206590i | \(-0.0662367\pi\) | ||||
0.978428 | + | 0.206590i | \(0.0662367\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3578.30i | − 0.363880i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 6684.09i | − 0.675291i | −0.941273 | − | 0.337645i | \(-0.890370\pi\) | ||||
0.941273 | − | 0.337645i | \(-0.109630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12556.5 | 1.26037 | 0.630185 | − | 0.776445i | \(-0.282979\pi\) | ||||
0.630185 | + | 0.776445i | \(0.282979\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10514.1 | 1.04856 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 5380.24i | − 0.533122i | −0.963818 | − | 0.266561i | \(-0.914113\pi\) | ||||
0.963818 | − | 0.266561i | \(-0.0858873\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2593.71i | 0.255366i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8904.75 | 0.871145 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1611.77 | −0.156679 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14027.0i | 1.35495i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 6016.44i | − 0.577514i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9401.83 | 0.896828 | 0.448414 | − | 0.893826i | \(-0.351989\pi\) | ||||
0.448414 | + | 0.893826i | \(0.351989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15067.6 | −1.42832 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1681.00i | 0.158361i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20250.0i | 1.89589i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6836.64 | 0.636135 | 0.318067 | − | 0.948068i | \(-0.396966\pi\) | ||||
0.318067 | + | 0.948068i | \(0.396966\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4588.80 | 0.424362 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 44.2581i | − 0.00406790i | −0.999998 | − | 0.00203395i | \(-0.999353\pi\) | ||||
0.999998 | − | 0.00203395i | \(-0.000647427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18520.1i | 1.69190i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 459.610 | 0.0417332 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4565.29 | 0.412034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 7884.29i | − 0.707313i | −0.935375 | − | 0.353657i | \(-0.884938\pi\) | ||||
0.935375 | − | 0.353657i | \(-0.115062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 758.803i | − 0.0676663i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14818.8 | −1.31360 | −0.656798 | − | 0.754066i | \(-0.728090\pi\) | ||||
−0.656798 | + | 0.754066i | \(0.728090\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3699.50 | −0.325991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1822.11i | 0.159611i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 5035.72i | − 0.438515i | −0.975667 | − | 0.219258i | \(-0.929637\pi\) | ||||
0.975667 | − | 0.219258i | \(-0.0703635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1608.63 | −0.139259 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2246.41 | −0.193336 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 20645.8i | − 1.76653i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1080.31i | − 0.0918998i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3589.57 | 0.303593 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13373.1 | −1.12454 | −0.562269 | − | 0.826954i | \(-0.690071\pi\) | ||||
−0.562269 | + | 0.826954i | \(0.690071\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7349.16i | 0.614448i | 0.951637 | + | 0.307224i | \(0.0994000\pi\) | ||||
−0.951637 | + | 0.307224i | \(0.900600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3540.44i | 0.294319i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27107.7 | 2.24066 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5759.35 | −0.473358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6816.52i | 0.557085i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1809.04i | 0.147014i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5604.73 | 0.452923 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11591.2 | 0.931465 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 146.039i | − 0.0116704i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 8183.14i | − 0.650315i | −0.945660 | − | 0.325158i | \(-0.894583\pi\) | ||||
0.945660 | − | 0.325158i | \(-0.105417\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3499.87 | 0.276600 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11453.4 | −0.900200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 11819.9i | − 0.923916i | −0.886902 | − | 0.461958i | \(-0.847147\pi\) | ||||
0.886902 | − | 0.461958i | \(-0.152853\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6210.32i | 0.482787i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11626.7 | 0.898937 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −303.316 | −0.0233242 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19426.3i | 1.48576i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22731.0i | 1.72916i | 0.502491 | + | 0.864582i | \(0.332417\pi\) | ||||
−0.502491 | + | 0.864582i | \(0.667583\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21561.3 | 1.63139 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1184.97 | 0.0891794 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7860.21i | − 0.588399i | −0.955744 | − | 0.294199i | \(-0.904947\pi\) | ||||
0.955744 | − | 0.294199i | \(-0.0950530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12428.3i | 0.925417i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11633.8 | −0.857146 | −0.428573 | − | 0.903507i | \(-0.640983\pi\) | ||||
−0.428573 | + | 0.903507i | \(0.640983\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8319.09i | 0.609707i | 0.952399 | + | 0.304854i | \(0.0986076\pi\) | ||||
−0.952399 | + | 0.304854i | \(0.901392\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5204.87i | 0.379471i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13495.5 | 0.978782 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12339.9 | −0.890324 | −0.445162 | − | 0.895450i | \(-0.646854\pi\) | ||||
−0.445162 | + | 0.895450i | \(0.646854\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 926.402i | − 0.0664939i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5616.83i | 0.401076i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1992.38 | 0.141537 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6148.41 | −0.434539 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22785.2i | 1.60212i | 0.598584 | + | 0.801060i | \(0.295730\pi\) | ||||
−0.598584 | + | 0.801060i | \(0.704270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 17017.9i | − 1.19051i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3893.87 | −0.271020 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6786.01 | 0.469929 | 0.234965 | − | 0.972004i | \(-0.424503\pi\) | ||||
0.234965 | + | 0.972004i | \(0.424503\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15895.8i | 1.09524i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5251.59i | 0.360022i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10498.4 | −0.716114 | −0.358057 | − | 0.933700i | \(-0.616561\pi\) | ||||
−0.358057 | + | 0.933700i | \(0.616561\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11360.3 | 0.771045 | 0.385522 | − | 0.922698i | \(-0.374021\pi\) | ||||
0.385522 | + | 0.922698i | \(0.374021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3334.77i | 0.225211i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 22653.9i | − 1.52233i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5460.38 | 0.365124 | 0.182562 | − | 0.983194i | \(-0.441561\pi\) | ||||
0.182562 | + | 0.983194i | \(0.441561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2934.61 | 0.195265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14451.9i | 0.956890i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 17628.3i | − 1.16150i | −0.814082 | − | 0.580750i | \(-0.802759\pi\) | ||||
0.814082 | − | 0.580750i | \(-0.197241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2332.35 | 0.152926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17543.6 | −1.14470 | −0.572351 | − | 0.820009i | \(-0.693968\pi\) | ||||
−0.572351 | + | 0.820009i | \(0.693968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27868.2i | 1.80956i | 0.425880 | + | 0.904779i | \(0.359964\pi\) | ||||
−0.425880 | + | 0.904779i | \(0.640036\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2161.29i | 0.139661i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6077.31 | 0.390823 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8275.64 | −0.529641 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 743.911i | − 0.0473827i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50085.1i | 3.17492i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21948.0 | 1.38469 | 0.692343 | − | 0.721569i | \(-0.256579\pi\) | ||||
0.692343 | + | 0.721569i | \(0.256579\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3068.11 | −0.192648 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11518.4i | 0.719830i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1953.64i | 0.121516i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5869.65 | 0.363380 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5186.49 | 0.319585 | 0.159793 | − | 0.987151i | \(-0.448917\pi\) | ||||
0.159793 | + | 0.987151i | \(0.448917\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 21931.1i | − 1.34507i | −0.740066 | − | 0.672534i | \(-0.765206\pi\) | ||||
0.740066 | − | 0.672534i | \(-0.234794\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 27798.5i | − 1.69700i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19475.1 | −1.18338 | −0.591690 | − | 0.806166i | \(-0.701539\pi\) | ||||
−0.591690 | + | 0.806166i | \(0.701539\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2257.33 | −0.136530 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 4295.35i | − 0.258599i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29761.6i | 1.78355i | 0.452477 | + | 0.891776i | \(0.350540\pi\) | ||||
−0.452477 | + | 0.891776i | \(0.649460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35680.3 | 2.12846 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2068.23 | −0.122815 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12257.3i | 0.724547i | 0.932072 | + | 0.362274i | \(0.117999\pi\) | ||||
−0.932072 | + | 0.362274i | \(0.882001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9737.88i | 0.573010i | 0.958079 | + | 0.286505i | \(0.0924935\pi\) | ||||
−0.958079 | + | 0.286505i | \(0.907506\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15851.9 | −0.928564 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9979.21 | 0.581921 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 11186.1i | − 0.649369i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 766.248i | 0.0442823i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2056.58 | −0.118321 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33809.6 | 1.93650 | 0.968250 | − | 0.249984i | \(-0.0804252\pi\) | ||||
0.968250 | + | 0.249984i | \(0.0804252\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4552.00i | 0.259565i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29402.3i | 1.66916i | 0.550887 | + | 0.834580i | \(0.314289\pi\) | ||||
−0.550887 | + | 0.834580i | \(0.685711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8272.77 | 0.467570 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3123.46 | −0.175758 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5540.58i | 0.310402i | 0.987883 | + | 0.155201i | \(0.0496025\pi\) | ||||
−0.987883 | + | 0.155201i | \(0.950398\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 20929.8i | − 1.16743i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7776.10 | −0.431844 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26652.9 | −1.47372 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33967.2i | 1.87000i | 0.354642 | + | 0.935002i | \(0.384603\pi\) | ||||
−0.354642 | + | 0.935002i | \(0.615397\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 187.765i | − 0.0102924i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −44385.0 | −2.42247 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6013.31 | 0.326787 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 5490.22i | − 0.297080i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 11444.0i | − 0.616597i | −0.951290 | − | 0.308299i | \(-0.900240\pi\) | ||||
0.951290 | − | 0.308299i | \(-0.0997596\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31442.8 | 1.68690 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18632.4 | 0.995374 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1511.36i | 0.0803968i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 30373.3i | − 1.60888i | −0.594036 | − | 0.804438i | \(-0.702466\pi\) | ||||
0.594036 | − | 0.804438i | \(-0.297534\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −389.977 | −0.0205700 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16373.0 | −0.859992 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2036.08i | − 0.106497i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 405.682i | 0.0211304i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36362.7 | −1.88609 | −0.943046 | − | 0.332663i | \(-0.892053\pi\) | ||||
−0.943046 | + | 0.332663i | \(0.892053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8434.48 | −0.435668 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 938.042i | − 0.0482519i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 23559.7i | − 1.20688i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34240.1 | −1.74676 | −0.873379 | − | 0.487041i | \(-0.838076\pi\) | ||||
−0.873379 | + | 0.487041i | \(0.838076\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 71670.6i | − 3.62631i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 30023.1i | − 1.51286i | −0.654074 | − | 0.756431i | \(-0.726941\pi\) | ||||
0.654074 | − | 0.756431i | \(-0.273059\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2518.78 | 0.126403 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1104.33 | −0.0551946 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32000.0i | 1.59288i | 0.604717 | + | 0.796440i | \(0.293286\pi\) | ||||
−0.604717 | + | 0.796440i | \(0.706714\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9951.64i | 0.493364i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8412.86 | −0.415394 | −0.207697 | − | 0.978193i | \(-0.566597\pi\) | ||||
−0.207697 | + | 0.978193i | \(0.566597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −58361.9 | −2.87009 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7221.64i | 0.353716i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2289.71i | − 0.111701i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3889.62 | 0.188994 | 0.0944969 | − | 0.995525i | \(-0.469876\pi\) | ||||
0.0944969 | + | 0.995525i | \(0.469876\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13157.2 | 0.636751 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30763.9i | 1.48293i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17814.2i | 0.855309i | 0.903942 | + | 0.427654i | \(0.140660\pi\) | ||||
−0.903942 | + | 0.427654i | \(0.859340\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −715.723 | −0.0342281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9356.95 | 0.445715 | 0.222857 | − | 0.974851i | \(-0.428462\pi\) | ||||
0.222857 | + | 0.974851i | \(0.428462\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4679.07i | 0.222010i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20437.5i | 0.965909i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30197.3 | 1.42159 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32968.7 | 1.54601 | 0.773005 | − | 0.634400i | \(-0.218753\pi\) | ||||
0.773005 | + | 0.634400i | \(0.218753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18766.5i | 0.876598i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 11914.1i | − 0.554359i | −0.960818 | − | 0.277180i | \(-0.910600\pi\) | ||||
0.960818 | − | 0.277180i | \(-0.0893997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34484.0 | −1.59832 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7936.24 | 0.366423 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 3775.08i | − 0.173628i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1943.77i | 0.0890569i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3773.07 | 0.172208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50859.6 | −2.31243 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 29231.8i | − 1.32402i | −0.749496 | − | 0.662009i | \(-0.769704\pi\) | ||||
0.749496 | − | 0.662009i | \(-0.230296\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17857.2i | 0.805744i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5077.33 | 0.228229 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27511.8 | 1.23200 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34363.0i | 1.53299i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13241.6i | 0.588507i | 0.955727 | + | 0.294254i | \(0.0950710\pi\) | ||||
−0.955727 | + | 0.294254i | \(0.904929\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48038.5 | 2.12701 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7813.69 | 0.344673 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 684.906i | − 0.0300994i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 9601.08i | − 0.420365i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8993.44 | 0.392297 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10389.0 | −0.451491 | −0.225746 | − | 0.974186i | \(-0.572482\pi\) | ||||
−0.225746 | + | 0.974186i | \(0.572482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10637.7i | 0.460593i | 0.973120 | + | 0.230297i | \(0.0739697\pi\) | ||||
−0.973120 | + | 0.230297i | \(0.926030\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2043.54i | 0.0881549i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26209.0 | −1.12646 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44993.9 | −1.92673 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2511.82i | 0.107167i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 4915.12i | − 0.208939i | −0.994528 | − | 0.104470i | \(-0.966686\pi\) | ||||
0.994528 | − | 0.104470i | \(-0.0333145\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22017.8 | 0.932555 | 0.466278 | − | 0.884638i | \(-0.345595\pi\) | ||||
0.466278 | + | 0.884638i | \(0.345595\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1507.42 | −0.0636140 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4114.43i | 0.173002i | 0.996252 | + | 0.0865010i | \(0.0275686\pi\) | ||||
−0.996252 | + | 0.0865010i | \(0.972431\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3132.86i | 0.131253i | 0.997844 | + | 0.0656264i | \(0.0209046\pi\) | ||||
−0.997844 | + | 0.0656264i | \(0.979095\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4400.82 | 0.183710 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6493.96 | 0.270111 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4333.91i | 0.179618i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 5522.59i | − 0.228063i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11892.0 | 0.489341 | 0.244670 | − | 0.969606i | \(-0.421320\pi\) | ||||
0.244670 | + | 0.969606i | \(0.421320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4860.80 | 0.199303 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 19676.6i | − 0.803912i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 10407.0i | − 0.423684i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9254.82 | −0.375442 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25664.1 | −1.03744 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 30251.4i | − 1.21857i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 28626.0i | − 1.14905i | −0.818488 | − | 0.574524i | \(-0.805187\pi\) | ||||
0.818488 | − | 0.574524i | \(-0.194813\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12830.4 | 0.513206 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41513.8 | −1.65471 | −0.827353 | − | 0.561683i | \(-0.810154\pi\) | ||||
−0.827353 | + | 0.561683i | \(0.810154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23085.1i | 0.916944i | 0.888709 | + | 0.458472i | \(0.151603\pi\) | ||||
−0.888709 | + | 0.458472i | \(0.848397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 952.839i | − 0.0377151i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12260.9 | −0.483622 | −0.241811 | − | 0.970323i | \(-0.577741\pi\) | ||||
−0.241811 | + | 0.970323i | \(0.577741\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20501.9 | −0.805879 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37953.4i | 1.48669i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 129.143i | − 0.00504129i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14773.1 | 0.574704 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10636.4 | 0.412358 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5228.56i | − 0.202009i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15969.9i | 0.614896i | 0.951565 | + | 0.307448i | \(0.0994750\pi\) | ||||
−0.951565 | + | 0.307448i | \(0.900525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3786.03 | 0.145278 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42590.6 | 1.62873 | 0.814367 | − | 0.580350i | \(-0.197084\pi\) | ||||
0.814367 | + | 0.580350i | \(0.197084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3087.03i | 0.117652i | 0.998268 | + | 0.0588261i | \(0.0187357\pi\) | ||||
−0.998268 | + | 0.0588261i | \(0.981264\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 38932.7i | − 1.47877i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43586.1 | −1.64992 | −0.824960 | − | 0.565191i | \(-0.808803\pi\) | ||||
−0.824960 | + | 0.565191i | \(0.808803\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4705.61 | 0.177527 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 241.412i | − 0.00907701i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 30158.0i | − 1.13012i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −66203.3 | −2.47255 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9574.55 | 0.356394 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28583.2i | 1.06040i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 88595.3i | 3.27584i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11356.6 | −0.418519 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19989.5 | −0.734226 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 38325.2i | − 1.40305i | −0.712645 | − | 0.701525i | \(-0.752503\pi\) | ||||
0.712645 | − | 0.701525i | \(-0.247497\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1943.18i | 0.0709033i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40999.9 | 1.49109 | 0.745547 | − | 0.666454i | \(-0.232189\pi\) | ||||
0.745547 | + | 0.666454i | \(0.232189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2391.48 | −0.0866884 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 35470.3i | − 1.28154i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 14576.5i | − 0.524928i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51974.3 | −1.86559 | −0.932793 | − | 0.360414i | \(-0.882636\pi\) | ||||
−0.932793 | + | 0.360414i | \(0.882636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 702.148 | 0.0251211 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 26002.7i | − 0.927289i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 63713.8i | − 2.26475i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10844.3 | −0.384223 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1073.91 | 0.0379266 | 0.0189633 | − | 0.999820i | \(-0.493963\pi\) | ||||
0.0189633 | + | 0.999820i | \(0.493963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4076.82i | − 0.143515i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 546.057i | − 0.0191609i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6767.99 | −0.236724 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5315.51 | 0.185326 | 0.0926629 | − | 0.995698i | \(-0.470462\pi\) | ||||
0.0926629 | + | 0.995698i | \(0.470462\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10545.7i | 0.366501i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24770.6i | 0.858127i | 0.903274 | + | 0.429064i | \(0.141156\pi\) | ||||
−0.903274 | + | 0.429064i | \(0.858844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3632.03 | −0.125424 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3238.43 | 0.111477 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1529.99i | 0.0525005i | 0.999655 | + | 0.0262502i | \(0.00835667\pi\) | ||||
−0.999655 | + | 0.0262502i | \(0.991643\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9162.31i | 0.313405i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10018.2 | −0.341599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29634.5 | 1.00730 | 0.503649 | − | 0.863909i | \(-0.331991\pi\) | ||||
0.503649 | + | 0.863909i | \(0.331991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 29727.7i | − 1.00729i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1249.47i | 0.0422045i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8550.49 | −0.287914 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12045.8 | 0.404344 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 2943.91i | − 0.0985112i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5291.16i | 0.176506i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25369.8 | 0.843680 | 0.421840 | − | 0.906670i | \(-0.361384\pi\) | ||||
0.421840 | + | 0.906670i | \(0.361384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33079.6 | 1.09667 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 42309.9i | − 1.39834i | −0.714954 | − | 0.699171i | \(-0.753553\pi\) | ||||
0.714954 | − | 0.699171i | \(-0.246447\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18132.7i | 0.597438i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20165.4 | 0.662370 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37869.9 | 1.24009 | 0.620044 | − | 0.784567i | \(-0.287115\pi\) | ||||
0.620044 | + | 0.784567i | \(0.287115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2587.54i | 0.0844722i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6015.95i | 0.195794i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20941.4 | 0.679477 | 0.339739 | − | 0.940520i | \(-0.389661\pi\) | ||||
0.339739 | + | 0.940520i | \(0.389661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22239.9 | 0.719414 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 7611.94i | − 0.245482i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43289.0i | 1.39182i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21465.4 | −0.688065 | −0.344033 | − | 0.938958i | \(-0.611793\pi\) | ||||
−0.344033 | + | 0.938958i | \(0.611793\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4782.54 | 0.152839 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 29994.5i | − 0.955668i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8105.46i | 0.257475i | 0.991679 | + | 0.128737i | \(0.0410925\pi\) | ||||
−0.991679 | + | 0.128737i | \(0.958908\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10203.7 | 0.323155 |
(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 | 1344.4.c.f.673.7 | yes | 12 | |
4.3 | odd | 2 | 1344.4.c.g.673.1 | yes | 12 | ||
8.3 | odd | 2 | 1344.4.c.g.673.12 | yes | 12 | ||
8.5 | even | 2 | inner | 1344.4.c.f.673.6 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.f.673.6 | ✓ | 12 | 8.5 | even | 2 | inner | |
1344.4.c.f.673.7 | yes | 12 | 1.1 | even | 1 | trivial | |
1344.4.c.g.673.1 | yes | 12 | 4.3 | odd | 2 | ||
1344.4.c.g.673.12 | yes | 12 | 8.3 | odd | 2 |