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: | \(6\) |
Coefficient field: | 6.0.14024243776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 17x^{4} - 164x^{3} + 299x^{2} + 2466x + 13042 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.1 | ||
Root | \(-3.08965 - 2.87659i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.c.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 | ||||||||
\(5\) | − 13.9325i | − 1.24616i | −0.782159 | − | 0.623079i | \(-0.785881\pi\) | ||||
0.782159 | − | 0.623079i | \(-0.214119\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.5866i | 1.22212i | 0.791583 | + | 0.611062i | \(0.209257\pi\) | ||||
−0.791583 | + | 0.611062i | \(0.790743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 81.2363i | − 1.73315i | −0.499051 | − | 0.866573i | \(-0.666318\pi\) | ||||
0.499051 | − | 0.866573i | \(-0.333682\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −41.7974 | −0.719470 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −136.899 | −1.95311 | −0.976553 | − | 0.215277i | \(-0.930934\pi\) | ||||
−0.976553 | + | 0.215277i | \(0.930934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 114.510i | 1.38265i | 0.722542 | + | 0.691327i | \(0.242974\pi\) | ||||
−0.722542 | + | 0.691327i | \(0.757026\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 21.0000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 67.0337 | 0.607717 | 0.303859 | − | 0.952717i | \(-0.401725\pi\) | ||||
0.303859 | + | 0.952717i | \(0.401725\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −69.1139 | −0.552912 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 222.366i | 1.42388i | 0.702243 | + | 0.711938i | \(0.252182\pi\) | ||||
−0.702243 | + | 0.711938i | \(0.747818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 135.161 | 0.783085 | 0.391542 | − | 0.920160i | \(-0.371942\pi\) | ||||
0.391542 | + | 0.920160i | \(0.371942\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 133.760 | 0.705594 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 97.5273i | − 0.471004i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 298.444i | 1.32605i | 0.748597 | + | 0.663025i | \(0.230728\pi\) | ||||
−0.748597 | + | 0.663025i | \(0.769272\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −243.709 | −1.00063 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 88.8987 | 0.338625 | 0.169313 | − | 0.985562i | \(-0.445845\pi\) | ||||
0.169313 | + | 0.985562i | \(0.445845\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 241.435i | 0.856245i | 0.903721 | + | 0.428123i | \(0.140825\pi\) | ||||
−0.903721 | + | 0.428123i | \(0.859175\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 125.392i | 0.415386i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −377.065 | −1.17022 | −0.585112 | − | 0.810953i | \(-0.698949\pi\) | ||||
−0.585112 | + | 0.810953i | \(0.698949\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 410.696i | 1.12763i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 174.621i | 0.452567i | 0.974062 | + | 0.226283i | \(0.0726576\pi\) | ||||
−0.974062 | + | 0.226283i | \(0.927342\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 621.202 | 1.52296 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 343.531 | 0.798276 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 26.8799i | − 0.0593129i | −0.999560 | − | 0.0296564i | \(-0.990559\pi\) | ||||
0.999560 | − | 0.0296564i | \(-0.00944132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 51.2106i | − 0.107489i | −0.998555 | − | 0.0537446i | \(-0.982884\pi\) | ||||
0.998555 | − | 0.0537446i | \(-0.0171157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1131.82 | −2.15977 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1011.62i | − 1.84461i | −0.386460 | − | 0.922306i | \(-0.626302\pi\) | ||||
0.386460 | − | 0.922306i | \(-0.373698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 201.101i | − 0.350866i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −502.872 | −0.840562 | −0.420281 | − | 0.907394i | \(-0.638069\pi\) | ||||
−0.420281 | + | 0.907394i | \(0.638069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −709.769 | −1.13798 | −0.568988 | − | 0.822346i | \(-0.692665\pi\) | ||||
−0.568988 | + | 0.822346i | \(0.692665\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 207.342i | 0.319224i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 312.106i | 0.461919i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −716.903 | −1.02099 | −0.510493 | − | 0.859882i | \(-0.670537\pi\) | ||||
−0.510493 | + | 0.859882i | \(0.670537\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 882.618i | 1.16723i | 0.812031 | + | 0.583614i | \(0.198362\pi\) | ||||
−0.812031 | + | 0.583614i | \(0.801638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1907.34i | 2.43388i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 667.099 | 0.822075 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1294.29 | 1.54151 | 0.770756 | − | 0.637131i | \(-0.219879\pi\) | ||||
0.770756 | + | 0.637131i | \(0.219879\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 568.654i | − 0.655067i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 405.483i | − 0.452114i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1595.41 | 1.72301 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −386.914 | −0.405002 | −0.202501 | − | 0.979282i | \(-0.564907\pi\) | ||||
−0.202501 | + | 0.979282i | \(0.564907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 401.279i | − 0.407375i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 277.366i | 0.273257i | 0.990622 | + | 0.136629i | \(0.0436267\pi\) | ||||
−0.990622 | + | 0.136629i | \(0.956373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 626.953 | 0.599762 | 0.299881 | − | 0.953977i | \(-0.403053\pi\) | ||||
0.299881 | + | 0.953977i | \(0.403053\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −292.582 | −0.271934 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 14.3217i | − 0.0129396i | −0.999979 | − | 0.00646979i | \(-0.997941\pi\) | ||||
0.999979 | − | 0.00646979i | \(-0.00205941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 467.212i | 0.410558i | 0.978704 | + | 0.205279i | \(0.0658101\pi\) | ||||
−0.978704 | + | 0.205279i | \(0.934190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 895.331 | 0.765595 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1098.35 | 0.914375 | 0.457188 | − | 0.889370i | \(-0.348857\pi\) | ||||
0.457188 | + | 0.889370i | \(0.348857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 933.946i | − 0.757312i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 731.126i | 0.577715i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −958.291 | −0.738205 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −656.964 | −0.493587 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 266.696i | − 0.195505i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 778.631i | − 0.557143i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1213.62 | 0.847961 | 0.423980 | − | 0.905671i | \(-0.360633\pi\) | ||||
0.423980 | + | 0.905671i | \(0.360633\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 724.306 | 0.494353 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1391.85i | 0.928295i | 0.885758 | + | 0.464147i | \(0.153639\pi\) | ||||
−0.885758 | + | 0.464147i | \(0.846361\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 801.571i | 0.522594i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 376.177 | 0.239823 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1455.00 | 0.907363 | 0.453681 | − | 0.891164i | \(-0.350110\pi\) | ||||
0.453681 | + | 0.891164i | \(0.350110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2512.86i | − 1.53337i | −0.642025 | − | 0.766684i | \(-0.721905\pi\) | ||||
0.642025 | − | 0.766684i | \(-0.278095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1131.19i | 0.675629i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3622.05 | 2.11812 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3098.11 | 1.77437 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 147.000i | − 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2790.64i | 1.53435i | 0.641438 | + | 0.767174i | \(0.278338\pi\) | ||||
−0.641438 | + | 0.767174i | \(0.721662\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.1006 | −0.00813819 | −0.00406910 | − | 0.999992i | \(-0.501295\pi\) | ||||
−0.00406910 | + | 0.999992i | \(0.501295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1232.09 | 0.651035 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1883.13i | − 0.975848i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3608.78i | − 1.83447i | −0.398345 | − | 0.917236i | \(-0.630415\pi\) | ||||
0.398345 | − | 0.917236i | \(-0.369585\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 523.863 | 0.261290 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 469.236 | 0.229695 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2469.78i | 1.18680i | 0.804908 | + | 0.593400i | \(0.202215\pi\) | ||||
−0.804908 | + | 0.593400i | \(0.797785\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1863.61i | − 0.879282i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1617.23 | −0.749372 | −0.374686 | − | 0.927152i | \(-0.622250\pi\) | ||||
−0.374686 | + | 0.927152i | \(0.622250\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4402.33 | −2.00379 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1030.59i | − 0.460885i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3969.48i | 1.74448i | 0.489082 | + | 0.872238i | \(0.337332\pi\) | ||||
−0.489082 | + | 0.872238i | \(0.662668\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −483.798 | −0.208981 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −80.6396 | −0.0342443 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2232.89i | 0.932368i | 0.884688 | + | 0.466184i | \(0.154371\pi\) | ||||
−0.884688 | + | 0.466184i | \(0.845629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2565.36i | 1.05349i | 0.850024 | + | 0.526745i | \(0.176588\pi\) | ||||
−0.850024 | + | 0.526745i | \(0.823412\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −153.632 | −0.0620590 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4158.06 | 1.65247 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6103.84i | − 2.38694i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2884.75 | 1.09285 | 0.546423 | − | 0.837510i | \(-0.315989\pi\) | ||||
0.546423 | + | 0.837510i | \(0.315989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2841.50 | −1.05977 | −0.529886 | − | 0.848069i | \(-0.677765\pi\) | ||||
−0.529886 | + | 0.848069i | \(0.677765\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3395.47i | 1.24695i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 512.567i | 0.185375i | 0.995695 | + | 0.0926876i | \(0.0295458\pi\) | ||||
−0.995695 | + | 0.0926876i | \(0.970454\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2817.72 | 1.00373 | 0.501866 | − | 0.864946i | \(-0.332647\pi\) | ||||
0.501866 | + | 0.864946i | \(0.332647\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3034.86 | −1.06499 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1556.56i | 0.538174i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1238.58i | − 0.421981i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −603.303 | −0.202572 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5105.62 | −1.68978 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4903.85i | 1.59998i | 0.600016 | + | 0.799988i | \(0.295161\pi\) | ||||
−0.600016 | + | 0.799988i | \(0.704839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1508.62i | 0.485299i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3363.79 | 1.06702 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 946.127 | 0.295978 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2129.31i | 0.657011i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11121.1i | 3.38502i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5283.25 | 1.58651 | 0.793257 | − | 0.608887i | \(-0.208384\pi\) | ||||
0.793257 | + | 0.608887i | \(0.208384\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 622.025 | 0.184304 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 348.589i | − 0.101924i | −0.998701 | − | 0.0509619i | \(-0.983771\pi\) | ||||
0.998701 | − | 0.0509619i | \(-0.0162287\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4394.50i | − 1.26811i | −0.773289 | − | 0.634054i | \(-0.781390\pi\) | ||||
0.773289 | − | 0.634054i | \(-0.218610\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 936.318 | 0.266689 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3230.16 | −0.908219 | −0.454109 | − | 0.890946i | \(-0.650043\pi\) | ||||
−0.454109 | + | 0.890946i | \(0.650043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5253.44i | 1.45828i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2150.71i | 0.589466i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3610.19 | −0.977087 | −0.488543 | − | 0.872540i | \(-0.662472\pi\) | ||||
−0.488543 | + | 0.872540i | \(0.662472\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4528.15 | −1.21031 | −0.605153 | − | 0.796109i | \(-0.706888\pi\) | ||||
−0.605153 | + | 0.796109i | \(0.706888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 682.691i | − 0.178023i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9302.38 | 2.39634 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2647.85 | 0.673899 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 804.637i | 0.202344i | 0.994869 | + | 0.101172i | \(0.0322592\pi\) | ||||
−0.994869 | + | 0.101172i | \(0.967741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2988.80i | 0.742706i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5722.01 | 1.40520 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1150.13 | −0.279156 | −0.139578 | − | 0.990211i | \(-0.544575\pi\) | ||||
−0.139578 | + | 0.990211i | \(0.544575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2089.11i | 0.501200i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2001.30i | − 0.474625i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 548.868 | 0.128687 | 0.0643434 | − | 0.997928i | \(-0.479505\pi\) | ||||
0.0643434 | + | 0.997928i | \(0.479505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2432.90 | 0.563970 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3882.87i | − 0.889992i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 8040.48i | − 1.82244i | −0.411919 | − | 0.911221i | \(-0.635141\pi\) | ||||
0.411919 | − | 0.911221i | \(-0.364859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3517.37 | 0.788431 | 0.394215 | − | 0.919018i | \(-0.371016\pi\) | ||||
0.394215 | + | 0.919018i | \(0.371016\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1705.96 | −0.378203 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 3081.56i | − 0.675726i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1995.99i | 0.432952i | 0.976288 | + | 0.216476i | \(0.0694563\pi\) | ||||
−0.976288 | + | 0.216476i | \(0.930544\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1216.45 | −0.261028 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4672.94 | −0.992043 | −0.496022 | − | 0.868310i | \(-0.665206\pi\) | ||||
−0.496022 | + | 0.868310i | \(0.665206\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2886.12i | 0.606227i | 0.952954 | + | 0.303114i | \(0.0980261\pi\) | ||||
−0.952954 | + | 0.303114i | \(0.901974\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 4786.23i | − 0.994779i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 622.291 | 0.127988 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13828.2 | 2.81462 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1160.74i | 0.233828i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6019.24i | 1.20016i | 0.799939 | + | 0.600082i | \(0.204865\pi\) | ||||
−0.799939 | + | 0.600082i | \(0.795135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −374.503 | −0.0739133 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1203.84 | −0.235198 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5445.57i | − 1.05326i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1690.05i | 0.323630i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 832.098 | 0.157765 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −713.491 | −0.133949 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5862.19i | − 1.08981i | −0.838497 | − | 0.544907i | \(-0.816565\pi\) | ||||
0.838497 | − | 0.544907i | \(-0.183435\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1880.86i | − 0.346273i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5811.82 | −1.05967 | −0.529836 | − | 0.848100i | \(-0.677747\pi\) | ||||
−0.529836 | + | 0.848100i | \(0.677747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2373.97 | 0.428705 | 0.214352 | − | 0.976756i | \(-0.431236\pi\) | ||||
0.214352 | + | 0.976756i | \(0.431236\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 877.746i | 0.157001i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7220.24i | − 1.27927i | −0.768678 | − | 0.639636i | \(-0.779085\pi\) | ||||
0.768678 | − | 0.639636i | \(-0.220915\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9914.55 | −1.74015 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.9652 | −0.00747067 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 15676.3i | − 2.70047i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5614.56i | 0.958276i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1401.64 | 0.237035 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2639.45 | −0.442303 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4717.39i | 0.783357i | 0.920102 | + | 0.391678i | \(0.128105\pi\) | ||||
−0.920102 | + | 0.391678i | \(0.871895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2685.99i | − 0.442017i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14094.4 | −2.29868 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4639.32 | 0.749911 | 0.374955 | − | 0.927043i | \(-0.377658\pi\) | ||||
0.374955 | + | 0.927043i | \(0.377658\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 3295.06i | − 0.527915i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6026.37i | 0.957027i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2801.84 | −0.437234 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3262.45i | 0.504718i | 0.967634 | + | 0.252359i | \(0.0812065\pi\) | ||||
−0.967634 | + | 0.252359i | \(0.918794\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12732.2i | 1.95283i | 0.215892 | + | 0.976417i | \(0.430734\pi\) | ||||
−0.215892 | + | 0.976417i | \(0.569266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2193.38 | 0.333544 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2903.14 | −0.437729 | −0.218865 | − | 0.975755i | \(-0.570235\pi\) | ||||
−0.218865 | + | 0.975755i | \(0.570235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7006.25i | 1.04747i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2874.87i | 0.426203i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3001.72 | −0.441295 | −0.220648 | − | 0.975354i | \(-0.570817\pi\) | ||||
−0.220648 | + | 0.975354i | \(0.570817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6253.58 | −0.911734 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1970.89i | 0.284973i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9888.85i | 1.41810i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9286.04 | 1.32078 | 0.660391 | − | 0.750922i | \(-0.270390\pi\) | ||||
0.660391 | + | 0.750922i | \(0.270390\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −800.088 | −0.112875 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1222.35i | 0.171054i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2865.96i | 0.397838i | 0.980016 | + | 0.198919i | \(0.0637431\pi\) | ||||
−0.980016 | + | 0.198919i | \(0.936257\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2335.89 | −0.321667 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18064.2 | 2.46778 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3785.48i | 0.513054i | 0.966537 | + | 0.256527i | \(0.0825782\pi\) | ||||
−0.966537 | + | 0.256527i | \(0.917422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3640.85i | − 0.489570i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11670.1 | 1.55696 | 0.778478 | − | 0.627671i | \(-0.215992\pi\) | ||||
0.778478 | + | 0.627671i | \(0.215992\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4348.41 | 0.575625 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2172.92i | − 0.285415i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9918.63i | 1.29279i | 0.763004 | + | 0.646394i | \(0.223724\pi\) | ||||
−0.763004 | + | 0.646394i | \(0.776276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9176.82 | −1.18694 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4175.55 | 0.535951 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9988.23i | 1.27231i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5101.56i | − 0.644937i | −0.946580 | − | 0.322468i | \(-0.895487\pi\) | ||||
0.946580 | − | 0.322468i | \(-0.104513\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2404.71 | 0.301720 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1288.07 | −0.160407 | −0.0802035 | − | 0.996779i | \(-0.525557\pi\) | ||||
−0.0802035 | + | 0.996779i | \(0.525557\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 10980.0i | − 1.35720i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1128.53i | − 0.138462i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13306.6 | −1.62060 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7250.96 | −0.876619 | −0.438309 | − | 0.898824i | \(-0.644423\pi\) | ||||
−0.438309 | + | 0.898824i | \(0.644423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 4364.99i | − 0.523866i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 188.159i | − 0.0224182i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12297.1 | 1.45455 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7538.59 | −0.885291 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3254.76i | 0.379488i | 0.981834 | + | 0.189744i | \(0.0607659\pi\) | ||||
−0.981834 | + | 0.189744i | \(0.939234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 9719.85i | − 1.12522i | −0.826723 | − | 0.562609i | \(-0.809798\pi\) | ||||
0.826723 | − | 0.562609i | \(-0.190202\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3393.58 | 0.390075 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9461.61 | 1.07989 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 358.474i | − 0.0406271i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 10866.1i | − 1.22290i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −940.465 | −0.105106 | −0.0525529 | − | 0.998618i | \(-0.516736\pi\) | ||||
−0.0525529 | + | 0.998618i | \(0.516736\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1346.44 | 0.149436 | 0.0747179 | − | 0.997205i | \(-0.476194\pi\) | ||||
0.0747179 | + | 0.997205i | \(0.476194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 9294.34i | − 1.02444i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7676.04i | 0.840263i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13724.4 | −1.49209 | −0.746047 | − | 0.665894i | \(-0.768050\pi\) | ||||
−0.746047 | + | 0.665894i | \(0.768050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4032.04i | − 0.432433i | −0.976345 | − | 0.216217i | \(-0.930628\pi\) | ||||
0.976345 | − | 0.216217i | \(-0.0693718\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 18032.7i | − 1.92097i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8371.91 | 0.885857 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4730.47 | 0.497204 | 0.248602 | − | 0.968606i | \(-0.420029\pi\) | ||||
0.248602 | + | 0.968606i | \(0.420029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3963.69i | 0.413842i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 45.3017i | 0.00469859i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7922.76 | −0.816318 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3220.47 | −0.329644 | −0.164822 | − | 0.986323i | \(-0.552705\pi\) | ||||
−0.164822 | + | 0.986323i | \(0.552705\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3696.26i | − 0.375875i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 967.010i | 0.0976967i | 0.998806 | + | 0.0488483i | \(0.0155551\pi\) | ||||
−0.998806 | + | 0.0488483i | \(0.984445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9771.32 | 0.980803 | 0.490401 | − | 0.871497i | \(-0.336850\pi\) | ||||
0.490401 | + | 0.871497i | \(0.336850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5649.38 | −0.563406 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12153.9i | 1.20432i | 0.798376 | + | 0.602160i | \(0.205693\pi\) | ||||
−0.798376 | + | 0.602160i | \(0.794307\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 7081.34i | − 0.697198i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10826.3 | −1.05913 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10764.8 | −1.04644 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 7914.25i | − 0.764486i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1571.59i | − 0.150856i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6972.65 | −0.665112 | −0.332556 | − | 0.943084i | \(-0.607911\pi\) | ||||
−0.332556 | + | 0.943084i | \(0.607911\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24244.5 | 2.29824 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1407.71i | − 0.132615i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5390.67i | 0.504697i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7725.74 | −0.718864 | −0.359432 | − | 0.933171i | \(-0.617030\pi\) | ||||
−0.359432 | + | 0.933171i | \(0.617030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7409.35 | 0.685200 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7923.75i | 0.728297i | 0.931341 | + | 0.364149i | \(0.118640\pi\) | ||||
−0.931341 | + | 0.364149i | \(0.881360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 30441.6i | − 2.78098i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5590.82 | −0.507653 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3520.10 | −0.317703 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 370.120i | 0.0332041i | 0.999862 | + | 0.0166021i | \(0.00528484\pi\) | ||||
−0.999862 | + | 0.0166021i | \(0.994715\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4851.70i | 0.432650i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8617.94 | −0.763927 | −0.381963 | − | 0.924177i | \(-0.624752\pi\) | ||||
−0.381963 | + | 0.924177i | \(0.624752\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3864.40 | 0.340522 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13207.0i | 1.15689i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6721.34i | 0.585301i | 0.956219 | + | 0.292650i | \(0.0945372\pi\) | ||||
−0.956219 | + | 0.292650i | \(0.905463\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4968.39 | −0.430114 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3091.78 | −0.266092 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 8735.01i | − 0.747399i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16812.0i | − 1.43016i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11908.5 | 1.00717 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19093.7 | −1.60558 | −0.802792 | − | 0.596260i | \(-0.796653\pi\) | ||||
−0.802792 | + | 0.596260i | \(0.796653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12741.7i | 1.06530i | 0.846334 | + | 0.532652i | \(0.178805\pi\) | ||||
−0.846334 | + | 0.532652i | \(0.821195\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1451.39i | 0.120655i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18503.4 | −1.52945 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7673.48 | −0.630680 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 241.919i | 0.0197710i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7221.80i | − 0.586887i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −199.537 | −0.0161248 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6698.66 | 0.538303 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2184.74i | 0.174589i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7575.99i | 0.602065i | 0.953614 | + | 0.301033i | \(0.0973313\pi\) | ||||
−0.953614 | + | 0.301033i | \(0.902669\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7696.07 | 0.608232 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6509.42 | 0.511620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 22515.9i | − 1.75998i | −0.474989 | − | 0.879992i | \(-0.657548\pi\) | ||||
0.474989 | − | 0.879992i | \(-0.342452\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 460.895i | 0.0358298i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25463.2 | −1.96873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5018.32 | −0.385896 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 12474.2i | − 0.954053i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11313.2i | 0.860605i | 0.902685 | + | 0.430302i | \(0.141593\pi\) | ||||
−0.902685 | + | 0.430302i | \(0.858407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19613.3 | 1.48400 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18311.5 | −1.37810 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 23180.4i | − 1.73523i | −0.497234 | − | 0.867616i | \(-0.665651\pi\) | ||||
0.497234 | − | 0.867616i | \(-0.334349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 15302.8i | − 1.13946i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4268.03 | −0.314455 | −0.157228 | − | 0.987562i | \(-0.550256\pi\) | ||||
−0.157228 | + | 0.987562i | \(0.550256\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7080.94i | 0.518963i | 0.965748 | + | 0.259482i | \(0.0835517\pi\) | ||||
−0.965748 | + | 0.259482i | \(0.916448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 8654.26i | − 0.630954i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4632.96 | −0.336014 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10667.7 | −0.769676 | −0.384838 | − | 0.922984i | \(-0.625743\pi\) | ||||
−0.384838 | + | 0.922984i | \(0.625743\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8524.51i | 0.611859i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6178.33i | 0.441171i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7785.76 | −0.553093 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10186.4 | 0.719925 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13401.8i | 0.942333i | 0.882044 | + | 0.471166i | \(0.156167\pi\) | ||||
−0.882044 | + | 0.471166i | \(0.843833\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15477.3i | 1.08274i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1537.70 | 0.107026 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −207.518 | −0.0143705 | −0.00718526 | − | 0.999974i | \(-0.502287\pi\) | ||||
−0.00718526 | + | 0.999974i | \(0.502287\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13351.4i | 0.919920i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 8453.15i | − 0.579505i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 624.815 | 0.0426198 | 0.0213099 | − | 0.999773i | \(-0.493216\pi\) | ||||
0.0213099 | + | 0.999773i | \(0.493216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15573.3 | −1.05699 | −0.528494 | − | 0.848937i | \(-0.677243\pi\) | ||||
−0.528494 | + | 0.848937i | \(0.677243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9104.58i | 0.614871i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9153.14i | 0.615088i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7372.78 | −0.493002 | −0.246501 | − | 0.969143i | \(-0.579281\pi\) | ||||
−0.246501 | + | 0.969143i | \(0.579281\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4669.69 | 0.310715 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30631.3i | 2.02817i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20963.2i | − 1.38123i | −0.723223 | − | 0.690615i | \(-0.757340\pi\) | ||||
0.723223 | − | 0.690615i | \(-0.242660\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3715.74 | −0.243631 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19585.5 | −1.27793 | −0.638966 | − | 0.769235i | \(-0.720638\pi\) | ||||
−0.638966 | + | 0.769235i | \(0.720638\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 11978.4i | − 0.777792i | −0.921282 | − | 0.388896i | \(-0.872856\pi\) | ||||
0.921282 | − | 0.388896i | \(-0.127144\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1809.91i | 0.116955i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9060.03 | 0.582637 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19487.5 | −1.24720 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15316.9i | 0.975592i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 40856.6i | − 2.58992i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25115.4 | −1.58452 | −0.792258 | − | 0.610187i | \(-0.791094\pi\) | ||||
−0.792258 | + | 0.610187i | \(0.791094\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14711.5 | 0.923747 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 16908.7i | − 1.05669i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3980.58i | − 0.247592i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4525.85 | 0.280187 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10400.7 | −0.640877 | −0.320438 | − | 0.947269i | \(-0.603830\pi\) | ||||
−0.320438 | + | 0.947269i | \(0.603830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27866.0i | 1.70906i | 0.519398 | + | 0.854532i | \(0.326156\pi\) | ||||
−0.519398 | + | 0.854532i | \(0.673844\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 10091.4i | − 0.616043i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20115.3 | −1.22228 | −0.611139 | − | 0.791523i | \(-0.709288\pi\) | ||||
−0.611139 | + | 0.791523i | \(0.709288\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1198.48 | 0.0724877 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2838.38i | − 0.170883i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3473.50i | − 0.208160i | −0.994569 | − | 0.104080i | \(-0.966810\pi\) | ||||
0.994569 | − | 0.104080i | \(-0.0331898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19391.9 | 1.15680 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6387.93 | 0.379325 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1216.52i | − 0.0719102i | −0.999353 | − | 0.0359551i | \(-0.988553\pi\) | ||||
0.999353 | − | 0.0359551i | \(-0.0114473\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 94.5174i | 0.00556173i | 0.999996 | + | 0.00278086i | \(0.000885177\pi\) | ||||
−0.999996 | + | 0.00278086i | \(0.999115\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33363.4 | 1.95434 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11167.9 | 0.651236 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14906.0i | 0.865313i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 15849.8i | − 0.915974i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2283.31 | 0.131365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3226.20 | −0.184786 | −0.0923928 | − | 0.995723i | \(-0.529452\pi\) | ||||
−0.0923928 | + | 0.995723i | \(0.529452\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1866.08i | − 0.106408i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 17261.8i | − 0.979949i | −0.871737 | − | 0.489975i | \(-0.837006\pi\) | ||||
0.871737 | − | 0.489975i | \(-0.162994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2708.40 | −0.153076 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1045.77 | −0.0588457 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8923.41i | 0.499919i | 0.968256 | + | 0.249960i | \(0.0804173\pi\) | ||||
−0.968256 | + | 0.249960i | \(0.919583\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 20271.7i | − 1.13072i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13183.5 | −0.732142 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14185.6 | 0.784364 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 20790.4i | − 1.14458i | −0.820052 | − | 0.572289i | \(-0.806056\pi\) | ||||
0.820052 | − | 0.572289i | \(-0.193944\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2808.96i | − 0.153973i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35010.4 | −1.91082 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12170.1 | −0.661371 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9690.49i | 0.524360i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5947.55i | 0.320450i | 0.987080 | + | 0.160225i | \(0.0512221\pi\) | ||||
−0.987080 | + | 0.160225i | \(0.948778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34174.9 | −1.83347 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15760.3 | 0.841941 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1941.56i | 0.103281i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25595.4i | 1.35579i | 0.735157 | + | 0.677896i | \(0.237108\pi\) | ||||
−0.735157 | + | 0.677896i | \(0.762892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6452.12 | 0.340328 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9060.34 | 0.475894 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 50464.1i | − 2.63951i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10830.6i | 0.564121i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19000.8 | −0.985552 | −0.492776 | − | 0.870156i | \(-0.664018\pi\) | ||||
−0.492776 | + | 0.870156i | \(0.664018\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4388.67 | 0.226689 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13584.5i | 0.698771i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 15368.6i | − 0.787277i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17873.0 | 0.911790 | 0.455895 | − | 0.890033i | \(-0.349319\pi\) | ||||
0.455895 | + | 0.890033i | \(0.349319\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 33052.2i | − 1.67234i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1862.48i | 0.0938503i | 0.998898 | + | 0.0469252i | \(0.0149422\pi\) | ||||
−0.998898 | + | 0.0469252i | \(0.985058\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2048.07 | −0.102781 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45104.7 | 2.25435 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 21671.9i | − 1.07877i | −0.842058 | − | 0.539386i | \(-0.818656\pi\) | ||||
0.842058 | − | 0.539386i | \(-0.181344\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 27907.1i | − 1.38353i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12546.0 | −0.619474 | −0.309737 | − | 0.950822i | \(-0.600241\pi\) | ||||
−0.309737 | + | 0.950822i | \(0.600241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38880.5 | 1.91204 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 7943.56i | − 0.389076i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 100.252i | − 0.00489070i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32680.9 | 1.58794 | 0.793970 | − | 0.607957i | \(-0.208011\pi\) | ||||
0.793970 | + | 0.607957i | \(0.208011\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2413.91 | 0.116823 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 210.388i | 0.0101415i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 15404.1i | − 0.739592i | −0.929113 | − | 0.369796i | \(-0.879428\pi\) | ||||
0.929113 | − | 0.369796i | \(-0.120572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8966.41 | 0.428801 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33194.8 | 1.58122 | 0.790612 | − | 0.612317i | \(-0.209762\pi\) | ||||
0.790612 | + | 0.612317i | \(0.209762\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3270.48i | 0.155176i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 17166.0i | − 0.811293i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2183.62 | −0.102798 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6375.25 | 0.298956 | 0.149478 | − | 0.988765i | \(-0.452241\pi\) | ||||
0.149478 | + | 0.988765i | \(0.452241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3450.39i | 0.161171i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30988.7i | 1.44190i | 0.692988 | + | 0.720949i | \(0.256294\pi\) | ||||
−0.692988 | + | 0.720949i | \(0.743706\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9341.51 | −0.432977 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6267.32 | 0.289368 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10179.8i | 0.468202i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 22421.3i | − 1.02727i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6003.89 | −0.274025 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50279.3 | −2.28604 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 21179.0i | − 0.959274i | −0.877467 | − | 0.479637i | \(-0.840768\pi\) | ||||
0.877467 | − | 0.479637i | \(-0.159232\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1646.60i | − 0.0742974i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7688.47 | 0.345601 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4160.16 | −0.186295 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 7298.71i | − 0.325608i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38721.4i | 1.72093i | 0.509509 | + | 0.860465i | \(0.329827\pi\) | ||||
−0.509509 | + | 0.860465i | \(0.670173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51619.6 | 2.28557 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11648.6 | −0.513837 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 31646.2i | − 1.39075i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6537.62i | − 0.286237i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24121.4 | −1.05219 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8127.66 | 0.353218 | 0.176609 | − | 0.984281i | \(-0.443487\pi\) | ||||
0.176609 | + | 0.984281i | \(0.443487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 4986.26i | − 0.215896i | −0.994157 | − | 0.107948i | \(-0.965572\pi\) | ||||
0.994157 | − | 0.107948i | \(-0.0344280\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 10552.1i | − 0.455201i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34410.2 | 1.47894 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27646.8 | −1.18389 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5117.88i | 0.218356i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12495.4i | 0.531174i | 0.964087 | + | 0.265587i | \(0.0855658\pi\) | ||||
−0.964087 | + | 0.265587i | \(0.914434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12736.1 | 0.539432 | 0.269716 | − | 0.962940i | \(-0.413070\pi\) | ||||
0.269716 | + | 0.962940i | \(0.413070\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9244.67 | −0.390131 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6806.65i | − 0.286204i | −0.989708 | − | 0.143102i | \(-0.954292\pi\) | ||||
0.989708 | − | 0.143102i | \(-0.0457076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3291.88i | 0.137915i | 0.997620 | + | 0.0689577i | \(0.0219674\pi\) | ||||
−0.997620 | + | 0.0689577i | \(0.978033\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5987.98 | 0.249965 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6708.03 | −0.279015 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22532.0i | 0.933837i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3649.35i | 0.150705i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3389.45 | 0.139472 | 0.0697360 | − | 0.997565i | \(-0.477784\pi\) | ||||
0.0697360 | + | 0.997565i | \(0.477784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25057.8 | −1.02742 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14018.8i | 0.572756i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 61335.4i | 2.49704i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4598.75 | −0.186558 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8658.37 | 0.350005 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20005.8i | 0.805863i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42012.1i | 1.68636i | 0.537629 | + | 0.843181i | \(0.319320\pi\) | ||||
−0.537629 | + | 0.843181i | \(0.680680\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14358.7 | −0.574336 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9947.12 | −0.396484 | −0.198242 | − | 0.980153i | \(-0.563523\pi\) | ||||
−0.198242 | + | 0.980153i | \(0.563523\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36287.5i | 1.44134i | 0.693276 | + | 0.720672i | \(0.256167\pi\) | ||||
−0.693276 | + | 0.720672i | \(0.743833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1866.87i | − 0.0738941i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34147.4 | −1.34692 | −0.673459 | − | 0.739225i | \(-0.735192\pi\) | ||||
−0.673459 | + | 0.739225i | \(0.735192\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55304.7 | 2.17389 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 41484.7i | − 1.62502i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 31964.2i | − 1.24777i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −82180.2 | −3.19698 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3482.23 | 0.135001 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5450.42i | − 0.210580i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 10423.3i | − 0.401332i | −0.979660 | − | 0.200666i | \(-0.935689\pi\) | ||||
0.979660 | − | 0.200666i | \(-0.0643107\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18057.7 | 0.692915 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16973.7 | 0.649101 | 0.324551 | − | 0.945868i | \(-0.394787\pi\) | ||||
0.324551 | + | 0.945868i | \(0.394787\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 40684.6i | − 1.55056i | −0.631617 | − | 0.775281i | \(-0.717608\pi\) | ||||
0.631617 | − | 0.775281i | \(-0.282392\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1123.51i | 0.0426738i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22220.1 | −0.841125 | −0.420563 | − | 0.907264i | \(-0.638167\pi\) | ||||
−0.420563 | + | 0.907264i | \(0.638167\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8495.31 | 0.320499 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3611.51i | 0.135792i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 43177.7i | − 1.61802i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31109.6 | 1.16188 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16336.7 | −0.608101 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30055.2i | 1.11501i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 23905.4i | − 0.883911i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5070.14 | 0.186848 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35741.8 | 1.31281 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8719.36i | 0.319208i | 0.987181 | + | 0.159604i | \(0.0510217\pi\) | ||||
−0.987181 | + | 0.159604i | \(0.948978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2496.30i | − 0.0910857i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17835.7 | 0.648652 | 0.324326 | − | 0.945945i | \(-0.394863\pi\) | ||||
0.324326 | + | 0.945945i | \(0.394863\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39352.9 | −1.42650 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2140.47i | 0.0773353i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9742.96i | 0.350862i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17565.7 | 0.630509 | 0.315254 | − | 0.949007i | \(-0.397910\pi\) | ||||
0.315254 | + | 0.949007i | \(0.397910\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17586.6 | −0.629204 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40851.4i | 1.45682i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 20626.6i | − 0.733188i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5642.58 | −0.199921 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21421.2 | 0.756521 | 0.378260 | − | 0.925699i | \(-0.376522\pi\) | ||||
0.378260 | + | 0.925699i | \(0.376522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5611.00i | 0.197522i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17435.5i | 0.611802i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −85041.7 | −2.97450 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20707.3 | −0.721962 | −0.360981 | − | 0.932573i | \(-0.617558\pi\) | ||||
−0.360981 | + | 0.932573i | \(0.617558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 7121.90i | − 0.247513i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56436.2i | 1.95512i | 0.210654 | + | 0.977561i | \(0.432441\pi\) | ||||
−0.210654 | + | 0.977561i | \(0.567559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5959.21 | 0.205788 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2633.24 | 0.0906447 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29599.4i | 1.01568i | 0.861451 | + | 0.507841i | \(0.169556\pi\) | ||||
−0.861451 | + | 0.507841i | \(0.830444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57659.0i | 1.97228i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21660.7 | −0.738588 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25206.5 | −0.856786 | −0.428393 | − | 0.903592i | \(-0.640920\pi\) | ||||
−0.428393 | + | 0.903592i | \(0.640920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 40191.8i | − 1.36186i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29743.7i | 1.00468i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10185.0 | 0.342951 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11522.5 | −0.386778 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 128.896i | 0.00431319i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39589.2i | 1.32064i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31256.7 | 1.03945 | 0.519724 | − | 0.854334i | \(-0.326035\pi\) | ||||
0.519724 | + | 0.854334i | \(0.326035\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −47028.9 | −1.55912 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31271.1i | 1.03351i | 0.856134 | + | 0.516754i | \(0.172860\pi\) | ||||
−0.856134 | + | 0.516754i | \(0.827140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 17590.0i | − 0.579559i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16843.7 | 0.553261 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17413.6 | −0.570224 | −0.285112 | − | 0.958494i | \(-0.592031\pi\) | ||||
−0.285112 | + | 0.958494i | \(0.592031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57708.0i | 1.88392i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 4204.91i | − 0.136853i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18772.3 | −0.609098 | −0.304549 | − | 0.952497i | \(-0.598506\pi\) | ||||
−0.304549 | + | 0.952497i | \(0.598506\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7141.33 | 0.231007 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7918.36i | 0.255364i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16184.3i | 0.520355i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5324.36 | −0.170670 | −0.0853350 | − | 0.996352i | \(-0.527196\pi\) | ||||
−0.0853350 | + | 0.996352i | \(0.527196\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14152.2 | 0.452271 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 39257.8i | − 1.25081i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 48823.0i | − 1.55089i | −0.631413 | − | 0.775447i | \(-0.717525\pi\) | ||||
0.631413 | − | 0.775447i | \(-0.282475\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8057.98 | −0.255198 |
(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.c.673.1 | yes | 6 | |
4.3 | odd | 2 | 1344.4.c.b.673.4 | yes | 6 | ||
8.3 | odd | 2 | 1344.4.c.b.673.3 | ✓ | 6 | ||
8.5 | even | 2 | inner | 1344.4.c.c.673.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.b.673.3 | ✓ | 6 | 8.3 | odd | 2 | ||
1344.4.c.b.673.4 | yes | 6 | 4.3 | odd | 2 | ||
1344.4.c.c.673.1 | yes | 6 | 1.1 | even | 1 | trivial | |
1344.4.c.c.673.6 | yes | 6 | 8.5 | even | 2 | inner |