Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,4,Mod(287,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.287");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.l (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(67.9702003266\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 287.16 | ||
Character | \(\chi\) | \(=\) | 1152.287 |
Dual form | 1152.4.l.b.863.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.62348 | − | 3.62348i | 0.324094 | − | 0.324094i | −0.526241 | − | 0.850335i | \(-0.676399\pi\) |
0.850335 | + | 0.526241i | \(0.176399\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −33.7361 | −1.82158 | −0.910790 | − | 0.412869i | \(-0.864527\pi\) | ||||
−0.910790 | + | 0.412869i | \(0.864527\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.1694 | + | 44.1694i | 1.21069 | + | 1.21069i | 0.970800 | + | 0.239889i | \(0.0771111\pi\) |
0.239889 | + | 0.970800i | \(0.422889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.1143 | + | 42.1143i | −0.898493 | + | 0.898493i | −0.995303 | − | 0.0968099i | \(-0.969136\pi\) |
0.0968099 | + | 0.995303i | \(0.469136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 17.6392i | − | 0.251654i | −0.992052 | − | 0.125827i | \(-0.959842\pi\) | ||
0.992052 | − | 0.125827i | \(-0.0401585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −99.2533 | − | 99.2533i | −1.19844 | − | 1.19844i | −0.974635 | − | 0.223801i | \(-0.928153\pi\) |
−0.223801 | − | 0.974635i | \(-0.571847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 83.8215i | − | 0.759913i | −0.925004 | − | 0.379956i | \(-0.875939\pi\) | ||
0.925004 | − | 0.379956i | \(-0.124061\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 98.7408i | 0.789926i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 89.7300 | + | 89.7300i | 0.574567 | + | 0.574567i | 0.933401 | − | 0.358834i | \(-0.116826\pi\) |
−0.358834 | + | 0.933401i | \(0.616826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 46.2516i | − | 0.267969i | −0.990983 | − | 0.133984i | \(-0.957223\pi\) | ||
0.990983 | − | 0.133984i | \(-0.0427772\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −122.242 | + | 122.242i | −0.590363 | + | 0.590363i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.47930 | + | 7.47930i | 0.0332321 | + | 0.0332321i | 0.723528 | − | 0.690295i | \(-0.242519\pi\) |
−0.690295 | + | 0.723528i | \(0.742519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 299.247 | 1.13986 | 0.569932 | − | 0.821692i | \(-0.306969\pi\) | ||||
0.569932 | + | 0.821692i | \(0.306969\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 56.3439 | − | 56.3439i | 0.199823 | − | 0.199823i | −0.600101 | − | 0.799924i | \(-0.704873\pi\) |
0.799924 | + | 0.600101i | \(0.204873\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −280.235 | −0.869711 | −0.434855 | − | 0.900500i | \(-0.643201\pi\) | ||||
−0.434855 | + | 0.900500i | \(0.643201\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 795.127 | 2.31816 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.15996 | + | 8.15996i | −0.0211482 | + | 0.0211482i | −0.717602 | − | 0.696454i | \(-0.754760\pi\) |
0.696454 | + | 0.717602i | \(0.254760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 320.094 | 0.784754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 193.284 | + | 193.284i | 0.426499 | + | 0.426499i | 0.887434 | − | 0.460935i | \(-0.152486\pi\) |
−0.460935 | + | 0.887434i | \(0.652486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −127.057 | + | 127.057i | −0.266688 | + | 0.266688i | −0.827764 | − | 0.561076i | \(-0.810388\pi\) |
0.561076 | + | 0.827764i | \(0.310388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 305.201i | 0.582392i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 110.221 | + | 110.221i | 0.200980 | + | 0.200980i | 0.800420 | − | 0.599440i | \(-0.204610\pi\) |
−0.599440 | + | 0.800420i | \(0.704610\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1070.35i | − | 1.78911i | −0.446955 | − | 0.894556i | \(-0.647492\pi\) | ||
0.446955 | − | 0.894556i | \(-0.352508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1015.84i | − | 1.62870i | −0.580373 | − | 0.814351i | \(-0.697093\pi\) | ||
0.580373 | − | 0.814351i | \(-0.302907\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1490.11 | − | 1490.11i | −2.20537 | − | 2.20537i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 161.531i | − | 0.230047i | −0.993363 | − | 0.115023i | \(-0.963306\pi\) | ||
0.993363 | − | 0.115023i | \(-0.0366943\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 64.4215 | − | 64.4215i | 0.0851950 | − | 0.0851950i | −0.663225 | − | 0.748420i | \(-0.730813\pi\) |
0.748420 | + | 0.663225i | \(0.230813\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −63.9151 | − | 63.9151i | −0.0815596 | − | 0.0815596i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −177.502 | −0.211406 | −0.105703 | − | 0.994398i | \(-0.533709\pi\) | ||||
−0.105703 | + | 0.994398i | \(0.533709\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1420.77 | − | 1420.77i | 1.63668 | − | 1.63668i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −719.285 | −0.776811 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 559.412 | 0.585564 | 0.292782 | − | 0.956179i | \(-0.405419\pi\) | ||||
0.292782 | + | 0.956179i | \(0.405419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 850.608 | − | 850.608i | 0.838006 | − | 0.838006i | −0.150590 | − | 0.988596i | \(-0.548117\pi\) |
0.988596 | + | 0.150590i | \(0.0481173\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −757.707 | −0.724845 | −0.362423 | − | 0.932014i | \(-0.618050\pi\) | ||||
−0.362423 | + | 0.932014i | \(0.618050\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −364.469 | − | 364.469i | −0.329295 | − | 0.329295i | 0.523024 | − | 0.852318i | \(-0.324804\pi\) |
−0.852318 | + | 0.523024i | \(0.824804\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 206.900 | − | 206.900i | 0.181812 | − | 0.181812i | −0.610333 | − | 0.792145i | \(-0.708964\pi\) |
0.792145 | + | 0.610333i | \(0.208964\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1379.24i | − | 1.14821i | −0.818781 | − | 0.574105i | \(-0.805350\pi\) | ||
0.818781 | − | 0.574105i | \(-0.194650\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −303.726 | − | 303.726i | −0.246283 | − | 0.246283i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 595.077i | 0.458409i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2570.88i | 1.93154i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 810.720 | + | 810.720i | 0.580104 | + | 0.580104i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1260.84i | − | 0.880958i | −0.897763 | − | 0.440479i | \(-0.854809\pi\) | ||
0.897763 | − | 0.440479i | \(-0.145191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1015.28 | + | 1015.28i | −0.677138 | + | 0.677138i | −0.959352 | − | 0.282214i | \(-0.908931\pi\) |
0.282214 | + | 0.959352i | \(0.408931\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3348.43 | + | 3348.43i | 2.18305 | + | 2.18305i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1875.46 | 1.16957 | 0.584785 | − | 0.811189i | \(-0.301179\pi\) | ||||
0.584785 | + | 0.811189i | \(0.301179\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1048.87 | − | 1048.87i | 0.640031 | − | 0.640031i | −0.310532 | − | 0.950563i | \(-0.600507\pi\) |
0.950563 | + | 0.310532i | \(0.100507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3720.33 | −2.17559 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 650.270 | 0.372427 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1943.41 | − | 1943.41i | 1.06852 | − | 1.06852i | 0.0710521 | − | 0.997473i | \(-0.477364\pi\) |
0.997473 | − | 0.0710521i | \(-0.0226357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1790.47 | −0.964945 | −0.482472 | − | 0.875911i | \(-0.660261\pi\) | ||||
−0.482472 | + | 0.875911i | \(0.660261\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −167.592 | − | 167.592i | −0.0868470 | − | 0.0868470i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 872.163 | − | 872.163i | 0.443351 | − | 0.443351i | −0.449785 | − | 0.893137i | \(-0.648500\pi\) |
0.893137 | + | 0.449785i | \(0.148500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2827.82i | 1.38424i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −541.663 | − | 541.663i | −0.260284 | − | 0.260284i | 0.564885 | − | 0.825169i | \(-0.308920\pi\) |
−0.825169 | + | 0.564885i | \(0.808920\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 271.228i | 0.125678i | 0.998024 | + | 0.0628390i | \(0.0200155\pi\) | ||||
−0.998024 | + | 0.0628390i | \(0.979985\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1350.23i | − | 0.614579i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1396.64 | − | 1396.64i | −0.613783 | − | 0.613783i | 0.330147 | − | 0.943930i | \(-0.392902\pi\) |
−0.943930 | + | 0.330147i | \(0.892902\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3331.13i | − | 1.43891i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −675.124 | + | 675.124i | −0.281906 | + | 0.281906i | −0.833869 | − | 0.551963i | \(-0.813879\pi\) |
0.551963 | + | 0.833869i | \(0.313879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1306.81 | − | 1306.81i | −0.536655 | − | 0.536655i | 0.385890 | − | 0.922545i | \(-0.373894\pi\) |
−0.922545 | + | 0.385890i | \(0.873894\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 54.2021 | 0.0215407 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 779.111 | − | 779.111i | 0.304675 | − | 0.304675i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1942.70 | 0.735961 | 0.367980 | − | 0.929834i | \(-0.380049\pi\) | ||||
0.367980 | + | 0.929834i | \(0.380049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4145.80 | 1.54623 | 0.773113 | − | 0.634269i | \(-0.218699\pi\) | ||||
0.773113 | + | 0.634269i | \(0.218699\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1926.84 | + | 1926.84i | −0.696860 | + | 0.696860i | −0.963732 | − | 0.266872i | \(-0.914010\pi\) |
0.266872 | + | 0.963732i | \(0.414010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3804.49 | 1.35524 | 0.677622 | − | 0.735411i | \(-0.263011\pi\) | ||||
0.677622 | + | 0.735411i | \(0.263011\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3027.15 | − | 3027.15i | −1.04662 | − | 1.04662i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1084.31 | − | 1084.31i | 0.369423 | − | 0.369423i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8767.93i | − | 2.90187i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2274.25 | − | 2274.25i | −0.742019 | − | 0.742019i | 0.230947 | − | 0.972966i | \(-0.425818\pi\) |
−0.972966 | + | 0.230947i | \(0.925818\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 408.322i | − | 0.129523i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1560.35i | 0.488126i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 742.861 | + | 742.861i | 0.226110 | + | 0.226110i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2370.49i | − | 0.711836i | −0.934517 | − | 0.355918i | \(-0.884168\pi\) | ||
0.934517 | − | 0.355918i | \(-0.115832\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3494.40 | − | 3494.40i | 1.02172 | − | 1.02172i | 0.0219659 | − | 0.999759i | \(-0.493007\pi\) |
0.999759 | − | 0.0219659i | \(-0.00699253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2251.16 | + | 2251.16i | 0.649611 | + | 0.649611i | 0.952899 | − | 0.303288i | \(-0.0980844\pi\) |
−0.303288 | + | 0.952899i | \(0.598084\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3104.86 | −0.872989 | −0.436494 | − | 0.899707i | \(-0.643780\pi\) | ||||
−0.436494 | + | 0.899707i | \(0.643780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1015.42 | + | 1015.42i | −0.281868 | + | 0.281868i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5602.27 | 1.51624 | 0.758119 | − | 0.652117i | \(-0.226119\pi\) | ||||
0.758119 | + | 0.652117i | \(0.226119\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −278.260 | −0.0743748 | −0.0371874 | − | 0.999308i | \(-0.511840\pi\) | ||||
−0.0371874 | + | 0.999308i | \(0.511840\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2881.13 | − | 2881.13i | 0.751300 | − | 0.751300i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8359.97 | 2.15357 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4432.83 | − | 4432.83i | −1.11473 | − | 1.11473i | −0.992502 | − | 0.122231i | \(-0.960995\pi\) |
−0.122231 | − | 0.992502i | \(-0.539005\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3702.35 | − | 3702.35i | 0.920019 | − | 0.920019i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3828.87i | − | 0.929332i | −0.885486 | − | 0.464666i | \(-0.846174\pi\) | ||
0.885486 | − | 0.464666i | \(-0.153826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −252.323 | − | 252.323i | −0.0605350 | − | 0.0605350i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2299.83i | − | 0.539216i | −0.962970 | − | 0.269608i | \(-0.913106\pi\) | ||
0.962970 | − | 0.269608i | \(-0.0868941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 59.1349i | 0.0137080i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3350.78 | + | 3350.78i | 0.759481 | + | 0.759481i | 0.976228 | − | 0.216747i | \(-0.0695446\pi\) |
−0.216747 | + | 0.976228i | \(0.569545\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3778.66i | − | 0.847000i | −0.905896 | − | 0.423500i | \(-0.860801\pi\) | ||
0.905896 | − | 0.423500i | \(-0.139199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4361.32 | + | 4361.32i | −0.956356 | + | 0.956356i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 161.818 | + | 161.818i | 0.0351000 | + | 0.0351000i | 0.724439 | − | 0.689339i | \(-0.242099\pi\) |
−0.689339 | + | 0.724439i | \(0.742099\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4259.63 | −0.904299 | −0.452149 | − | 0.891942i | \(-0.649343\pi\) | ||||
−0.452149 | + | 0.891942i | \(0.649343\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 769.856 | − | 769.856i | 0.161707 | − | 0.161707i | −0.621615 | − | 0.783323i | \(-0.713523\pi\) |
0.783323 | + | 0.621615i | \(0.213523\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10095.4 | −2.07636 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4601.86 | 0.936670 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4375.88 | + | 4375.88i | −0.872497 | + | 0.872497i | −0.992744 | − | 0.120247i | \(-0.961631\pi\) |
0.120247 | + | 0.992744i | \(0.461631\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1400.72 | 0.276451 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3530.09 | + | 3530.09i | 0.682776 | + | 0.682776i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1900.83 | + | 1900.83i | −0.363993 | + | 0.363993i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 920.776i | 0.172864i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1892.89 | + | 1892.89i | 0.351899 | + | 0.351899i | 0.860816 | − | 0.508917i | \(-0.169954\pi\) |
−0.508917 | + | 0.860816i | \(0.669954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4969.36i | 0.906067i | 0.891494 | + | 0.453033i | \(0.149658\pi\) | ||||
−0.891494 | + | 0.453033i | \(0.850342\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 431.319i | 0.0778901i | 0.999241 | + | 0.0389450i | \(0.0123997\pi\) | ||||
−0.999241 | + | 0.0389450i | \(0.987600\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4151.14 | + | 4151.14i | 0.735493 | + | 0.735493i | 0.971702 | − | 0.236209i | \(-0.0759051\pi\) |
−0.236209 | + | 0.971702i | \(0.575905\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7926.65i | 1.39125i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1750.74 | + | 1750.74i | −0.301591 | + | 0.301591i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4158.40 | − | 4158.40i | −0.709743 | − | 0.709743i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9454.03 | 1.58425 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3350.31 | + | 3350.31i | −0.556343 | + | 0.556343i | −0.928264 | − | 0.371921i | \(-0.878699\pi\) |
0.371921 | + | 0.928264i | \(0.378699\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 798.770 | 0.130273 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9901.48 | −1.60050 | −0.800249 | − | 0.599668i | \(-0.795299\pi\) | ||||
−0.800249 | + | 0.599668i | \(0.795299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2042.90 | − | 2042.90i | 0.324427 | − | 0.324427i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15253.0 | −2.40113 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1244.90 | + | 1244.90i | 0.192593 | + | 0.192593i | 0.796816 | − | 0.604222i | \(-0.206516\pi\) |
−0.604222 | + | 0.796816i | \(0.706516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −84.2939 | + | 84.2939i | −0.0129288 | + | 0.0129288i | −0.713542 | − | 0.700613i | \(-0.752910\pi\) |
0.700613 | + | 0.713542i | \(0.252910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 366.806i | 0.0553063i | 0.999618 | + | 0.0276531i | \(0.00880339\pi\) | ||||
−0.999618 | + | 0.0276531i | \(0.991197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3878.39 | − | 3878.39i | −0.579840 | − | 0.579840i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6841.31i | 1.00577i | 0.864354 | + | 0.502884i | \(0.167728\pi\) | ||||
−0.864354 | + | 0.502884i | \(0.832272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12843.5i | 1.87250i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3680.88 | − | 3680.88i | −0.527852 | − | 0.527852i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1916.32i | − | 0.272564i | −0.990670 | − | 0.136282i | \(-0.956485\pi\) | ||
0.990670 | − | 0.136282i | \(-0.0435153\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 275.286 | − | 275.286i | 0.0385232 | − | 0.0385232i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7158.65 | + | 7158.65i | 0.993728 | + | 0.993728i | 0.999980 | − | 0.00625218i | \(-0.00199014\pi\) |
−0.00625218 | + | 0.999980i | \(0.501990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7557.84 | −1.03249 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5108.00 | + | 5108.00i | −0.692297 | + | 0.692297i | −0.962737 | − | 0.270440i | \(-0.912831\pi\) |
0.270440 | + | 0.962737i | \(0.412831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10334.0 | 1.37870 | 0.689349 | − | 0.724429i | \(-0.257897\pi\) | ||||
0.689349 | + | 0.724429i | \(0.257897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10798.7 | −1.42949 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4119.25 | − | 4119.25i | 0.536900 | − | 0.536900i | −0.385717 | − | 0.922617i | \(-0.626046\pi\) |
0.922617 | + | 0.385717i | \(0.126046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1478.54 | −0.191235 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −585.306 | − | 585.306i | −0.0745568 | − | 0.0745568i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6024.12 | + | 6024.12i | −0.761566 | + | 0.761566i | −0.976605 | − | 0.215039i | \(-0.931012\pi\) |
0.215039 | + | 0.976605i | \(0.431012\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11848.6i | 1.47554i | 0.675050 | + | 0.737772i | \(0.264122\pi\) | ||||
−0.675050 | + | 0.737772i | \(0.735878\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1947.85 | + | 1947.85i | 0.240768 | + | 0.240768i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 660.713i | 0.0804676i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12692.3i | − | 1.53446i | −0.641374 | − | 0.767228i | \(-0.721635\pi\) | ||
0.641374 | − | 0.767228i | \(-0.278365\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6520.66 | − | 6520.66i | −0.776903 | − | 0.776903i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 466.860i | − | 0.0552223i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9974.97 | − | 9974.97i | 1.16303 | − | 1.16303i | 0.179220 | − | 0.983809i | \(-0.442643\pi\) |
0.983809 | − | 0.179220i | \(-0.0573574\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6979.64 | − | 6979.64i | −0.807997 | − | 0.807997i | 0.176333 | − | 0.984331i | \(-0.443576\pi\) |
−0.984331 | + | 0.176333i | \(0.943576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1741.70 | 0.198788 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4286.41 | − | 4286.41i | 0.485794 | − | 0.485794i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6433.80 | 0.719038 | 0.359519 | − | 0.933138i | \(-0.382941\pi\) | ||||
0.359519 | + | 0.933138i | \(0.382941\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2276.81 | 0.252694 | 0.126347 | − | 0.991986i | \(-0.459675\pi\) | ||||
0.126347 | + | 0.991986i | \(0.459675\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8319.57 | + | 8319.57i | −0.910707 | + | 0.910707i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8874.90 | 0.964866 | 0.482433 | − | 0.875933i | \(-0.339753\pi\) | ||||
0.482433 | + | 0.875933i | \(0.339753\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 801.170 | + | 801.170i | 0.0859249 | + | 0.0859249i | 0.748763 | − | 0.662838i | \(-0.230648\pi\) |
−0.662838 | + | 0.748763i | \(0.730648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −643.173 | + | 643.173i | −0.0685154 | + | 0.0685154i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 453.819i | − | 0.0476995i | −0.999716 | − | 0.0238497i | \(-0.992408\pi\) | ||
0.999716 | − | 0.0238497i | \(-0.00759232\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13217.6 | + | 13217.6i | 1.38002 | + | 1.38002i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 10296.3i | − | 1.06087i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17430.4i | − | 1.78416i | −0.451876 | − | 0.892081i | \(-0.649245\pi\) | ||
0.451876 | − | 0.892081i | \(-0.350755\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2812.24 | + | 2812.24i | 0.284119 | + | 0.284119i | 0.834749 | − | 0.550630i | \(-0.185613\pi\) |
−0.550630 | + | 0.834749i | \(0.685613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8580.37i | 0.861260i | 0.902528 | + | 0.430630i | \(0.141709\pi\) | ||||
−0.902528 | + | 0.430630i | \(0.858291\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4028.61 | − | 4028.61i | 0.399190 | − | 0.399190i | −0.478757 | − | 0.877947i | \(-0.658913\pi\) |
0.877947 | + | 0.478757i | \(0.158913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3718.45 | − | 3718.45i | −0.366102 | − | 0.366102i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4977.36 | 0.483846 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9800.35 | − | 9800.35i | 0.946676 | − | 0.946676i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7073.65 | −0.674746 | −0.337373 | − | 0.941371i | \(-0.609538\pi\) | ||||
−0.337373 | + | 0.941371i | \(0.609538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −629.971 | −0.0597177 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2027.02 | − | 2027.02i | 0.189778 | − | 0.189778i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16066.6 | −1.49497 | −0.747483 | − | 0.664281i | \(-0.768738\pi\) | ||||
−0.747483 | + | 0.664281i | \(0.768738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4947.42 | + | 4947.42i | 0.454733 | + | 0.454733i | 0.896922 | − | 0.442189i | \(-0.145798\pi\) |
−0.442189 | + | 0.896922i | \(0.645798\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1582.76 | − | 1582.76i | 0.144592 | − | 0.144592i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36109.4i | 3.25901i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10229.8 | + | 10229.8i | 0.917733 | + | 0.917733i | 0.996864 | − | 0.0791313i | \(-0.0252146\pi\) |
−0.0791313 | + | 0.996864i | \(0.525215\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 6091.42i | − | 0.539966i | −0.962865 | − | 0.269983i | \(-0.912982\pi\) | ||
0.962865 | − | 0.269983i | \(-0.0870181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6164.32i | − | 0.543185i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10933.5 | − | 10933.5i | −0.952097 | − | 0.952097i | 0.0468068 | − | 0.998904i | \(-0.485096\pi\) |
−0.998904 | + | 0.0468068i | \(0.985096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34270.6i | 2.96681i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2745.53 | + | 2745.53i | −0.234918 | + | 0.234918i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12377.8 | − | 12377.8i | −1.05295 | − | 1.05295i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8966.41 | −0.753984 | −0.376992 | − | 0.926217i | \(-0.623042\pi\) | ||||
−0.376992 | + | 0.926217i | \(0.623042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14085.5 | + | 14085.5i | −1.17766 | + | 1.17766i | −0.197318 | + | 0.980340i | \(0.563223\pi\) |
−0.980340 | + | 0.197318i | \(0.936777\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −815.838 | −0.0674354 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5140.95 | 0.422532 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12602.6 | + | 12602.6i | −1.02416 | + | 1.02416i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2641.29 | −0.213445 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35120.3 | + | 35120.3i | 2.80657 | + | 2.80657i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3398.59 | + | 3398.59i | −0.270087 | + | 0.270087i | −0.829135 | − | 0.559048i | \(-0.811167\pi\) |
0.559048 | + | 0.829135i | \(0.311167\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1499.40i | − | 0.117848i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15912.7 | − | 15912.7i | −1.24383 | − | 1.24383i | −0.958397 | − | 0.285438i | \(-0.907861\pi\) |
−0.285438 | − | 0.958397i | \(-0.592139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 17812.0i | − | 1.37716i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5449.45i | 0.419049i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12309.2 | + | 12309.2i | 0.936371 | + | 0.936371i | 0.998093 | − | 0.0617225i | \(-0.0196594\pi\) |
−0.0617225 | + | 0.998093i | \(0.519659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4745.77i | 0.359078i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13010.7 | + | 13010.7i | −0.973955 | + | 0.973955i | −0.999669 | − | 0.0257144i | \(-0.991814\pi\) |
0.0257144 | + | 0.999669i | \(0.491814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4997.64 | − | 4997.64i | −0.372128 | − | 0.372128i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20663.0 | 1.52238 | 0.761192 | − | 0.648527i | \(-0.224615\pi\) | ||||
0.761192 | + | 0.648527i | \(0.224615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6847.53 | + | 6847.53i | −0.501857 | + | 0.501857i | −0.912015 | − | 0.410158i | \(-0.865474\pi\) |
0.410158 | + | 0.912015i | \(0.365474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8276.60 | 0.600275 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12587.4 | −0.908178 | −0.454089 | − | 0.890956i | \(-0.650035\pi\) | ||||
−0.454089 | + | 0.890956i | \(0.650035\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2173.33 | + | 2173.33i | −0.155189 | + | 0.155189i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −720.841 | −0.0512079 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10285.9 | − | 10285.9i | −0.723241 | − | 0.723241i | 0.246023 | − | 0.969264i | \(-0.420876\pi\) |
−0.969264 | + | 0.246023i | \(0.920876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4590.62 | + | 4590.62i | −0.321143 | + | 0.321143i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 19189.3i | − | 1.32886i | −0.747353 | − | 0.664428i | \(-0.768675\pi\) | ||
0.747353 | − | 0.664428i | \(-0.231325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2156.25 | + | 2156.25i | 0.148567 | + | 0.148567i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25709.1i | 1.75366i | 0.480796 | + | 0.876832i | \(0.340348\pi\) | ||||
−0.480796 | + | 0.876832i | \(0.659652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6062.56i | 0.411476i | 0.978607 | + | 0.205738i | \(0.0659595\pi\) | ||||
−0.978607 | + | 0.205738i | \(0.934041\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9315.52 | + | 9315.52i | 0.625999 | + | 0.625999i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21062.9i | − | 1.40843i | −0.709989 | − | 0.704213i | \(-0.751300\pi\) | ||
0.709989 | − | 0.704213i | \(-0.248700\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11801.9 | − | 11801.9i | 0.781429 | − | 0.781429i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5955.84 | − | 5955.84i | −0.392421 | − | 0.392421i | 0.483128 | − | 0.875550i | \(-0.339500\pi\) |
−0.875550 | + | 0.483128i | \(0.839500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28289.5 | −1.84586 | −0.922929 | − | 0.384970i | \(-0.874212\pi\) | ||||
−0.922929 | + | 0.384970i | \(0.874212\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9943.57 | + | 9943.57i | −0.645664 | + | 0.645664i | −0.951942 | − | 0.306278i | \(-0.900916\pi\) |
0.306278 | + | 0.951942i | \(0.400916\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5988.22 | 0.385093 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6467.35 | −0.413910 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 131.928 | − | 131.928i | 0.00836301 | − | 0.00836301i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9728.67 | 0.613775 | 0.306888 | − | 0.951746i | \(-0.400712\pi\) | ||||
0.306888 | + | 0.951746i | \(0.400712\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4568.64 | − | 4568.64i | −0.285513 | − | 0.285513i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33486.2 | + | 33486.2i | −2.08285 | + | 2.08285i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 445.753i | 0.0274667i | 0.999906 | + | 0.0137334i | \(0.00437160\pi\) | ||||
−0.999906 | + | 0.0137334i | \(0.995628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −879.050 | − | 879.050i | −0.0539134 | − | 0.0539134i | 0.679636 | − | 0.733549i | \(-0.262138\pi\) |
−0.733549 | + | 0.679636i | \(0.762138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 4067.41i | − | 0.247150i | −0.992335 | − | 0.123575i | \(-0.960564\pi\) | ||
0.992335 | − | 0.123575i | \(-0.0394360\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17074.5i | 1.03272i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −595.450 | − | 595.450i | −0.0356842 | − | 0.0356842i | 0.689040 | − | 0.724724i | \(-0.258033\pi\) |
−0.724724 | + | 0.689040i | \(0.758033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7357.66i | 0.438912i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9075.08 | − | 9075.08i | 0.536441 | − | 0.536441i | −0.386041 | − | 0.922482i | \(-0.626158\pi\) |
0.922482 | + | 0.386041i | \(0.126158\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1351.64 | − | 1351.64i | −0.0795353 | − | 0.0795353i | 0.666220 | − | 0.745755i | \(-0.267911\pi\) |
−0.745755 | + | 0.666220i | \(0.767911\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24265.9 | 1.41502 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7521.31 | − | 7521.31i | 0.436621 | − | 0.436621i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11224.1 | −0.645753 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10501.3 | −0.601482 | −0.300741 | − | 0.953706i | \(-0.597234\pi\) | ||||
−0.300741 | + | 0.953706i | \(0.597234\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10590.4 | − | 10590.4i | 0.601215 | − | 0.601215i | −0.339420 | − | 0.940635i | \(-0.610231\pi\) |
0.940635 | + | 0.339420i | \(0.110231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18872.4 | −1.06665 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2888.12 | + | 2888.12i | 0.161802 | + | 0.161802i | 0.783365 | − | 0.621563i | \(-0.213502\pi\) |
−0.621563 | + | 0.783365i | \(0.713502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6795.68 | − | 6795.68i | 0.379050 | − | 0.379050i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 687.302i | − | 0.0380031i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12657.6 | − | 12657.6i | −0.696844 | − | 0.696844i | 0.266885 | − | 0.963728i | \(-0.414006\pi\) |
−0.963728 | + | 0.266885i | \(0.914006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7601.14i | − | 0.414860i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5278.46i | − | 0.286852i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18873.8 | − | 18873.8i | −1.01691 | − | 1.01691i | −0.999855 | − | 0.0170555i | \(-0.994571\pi\) |
−0.0170555 | − | 0.999855i | \(-0.505429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1484.69i | − | 0.0796531i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28696.2 | + | 28696.2i | −1.52650 | + | 1.52650i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21572.6 | + | 21572.6i | 1.14270 | + | 1.14270i | 0.987954 | + | 0.154747i | \(0.0494561\pi\) |
0.154747 | + | 0.987954i | \(0.450544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3876.88 | −0.203633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13480.5 | + | 13480.5i | −0.705096 | + | 0.705096i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29101.6 | 1.50947 | 0.754733 | − | 0.656032i | \(-0.227766\pi\) | ||||
0.754733 | + | 0.656032i | \(0.227766\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25562.1 | 1.32036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8860.02 | + | 8860.02i | −0.453866 | + | 0.453866i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23683.7 | 1.20822 | 0.604112 | − | 0.796899i | \(-0.293528\pi\) | ||||
0.604112 | + | 0.796899i | \(0.293528\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −993.859 | − | 993.859i | −0.0502862 | − | 0.0502862i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1650.17 | − | 1650.17i | 0.0831521 | − | 0.0831521i | −0.664307 | − | 0.747460i | \(-0.731273\pi\) |
0.747460 | + | 0.664307i | \(0.231273\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9736.83i | 0.486650i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9966.72 | + | 9966.72i | 0.496119 | + | 0.496119i | 0.910227 | − | 0.414109i | \(-0.135907\pi\) |
−0.414109 | + | 0.910227i | \(0.635907\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13180.6i | 0.650806i | 0.945576 | + | 0.325403i | \(0.105500\pi\) | ||||
−0.945576 | + | 0.325403i | \(0.894500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 14083.8i | − | 0.692605i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12295.8 | + | 12295.8i | 0.599837 | + | 0.599837i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18926.8i | 0.919641i | 0.888012 | + | 0.459821i | \(0.152086\pi\) | ||||
−0.888012 | + | 0.459821i | \(0.847914\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6487.74 | + | 6487.74i | −0.312733 | + | 0.312733i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23156.4 | − | 23156.4i | −1.11180 | − | 1.11180i | −0.992907 | − | 0.118896i | \(-0.962065\pi\) |
−0.118896 | − | 0.992907i | \(-0.537935\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6699.86 | −0.319146 | −0.159573 | − | 0.987186i | \(-0.551012\pi\) | ||||
−0.159573 | + | 0.987186i | \(0.551012\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6980.02 | + | 6980.02i | −0.331184 | + | 0.331184i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16280.1 | −0.766413 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13009.6 | −0.610064 | −0.305032 | − | 0.952342i | \(-0.598667\pi\) | ||||
−0.305032 | + | 0.952342i | \(0.598667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 991.579 | − | 991.579i | 0.0461379 | − | 0.0461379i | −0.683661 | − | 0.729799i | \(-0.739613\pi\) |
0.729799 | + | 0.683661i | \(0.239613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4566.92 | 0.211675 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29701.2 | − | 29701.2i | −1.36605 | − | 1.36605i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47276.7 | − | 47276.7i | 2.16606 | − | 2.16606i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6320.53i | − | 0.287375i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19796.5 | + | 19796.5i | 0.896659 | + | 0.896659i | 0.995139 | − | 0.0984801i | \(-0.0313981\pi\) |
−0.0984801 | + | 0.995139i | \(0.531398\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46530.2i | 2.09156i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10701.8i | − | 0.479235i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13170.1 | + | 13170.1i | 0.585331 | + | 0.585331i | 0.936363 | − | 0.351032i | \(-0.114169\pi\) |
−0.351032 | + | 0.936363i | \(0.614169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4943.10i | 0.218866i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44869.1 | − | 44869.1i | 1.97185 | − | 1.97185i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10246.5 | + | 10246.5i | 0.448624 | + | 0.448624i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19658.9 | −0.854352 | −0.427176 | − | 0.904169i | \(-0.640491\pi\) | ||||
−0.427176 | + | 0.904169i | \(0.640491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26123.4 | − | 26123.4i | 1.13109 | − | 1.13109i | 0.141099 | − | 0.989996i | \(-0.454936\pi\) |
0.989996 | − | 0.141099i | \(-0.0450636\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3925.41 | −0.168713 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11184.6 | −0.478949 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8922.97 | + | 8922.97i | −0.379310 | + | 0.379310i | −0.870853 | − | 0.491543i | \(-0.836433\pi\) |
0.491543 | + | 0.870853i | \(0.336433\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19943.0 | 0.844677 | 0.422339 | − | 0.906438i | \(-0.361209\pi\) | ||||
0.422339 | + | 0.906438i | \(0.361209\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18332.6 | − | 18332.6i | −0.770843 | − | 0.770843i | 0.207411 | − | 0.978254i | \(-0.433496\pi\) |
−0.978254 | + | 0.207411i | \(0.933496\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26778.5 | − | 26778.5i | 1.12190 | − | 1.12190i | 0.130446 | − | 0.991455i | \(-0.458359\pi\) |
0.991455 | − | 0.130446i | \(-0.0416408\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 14025.4i | − | 0.583374i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 982.788 | + | 982.788i | 0.0407315 | + | 0.0407315i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 28064.1i | − | 1.15480i | −0.816461 | − | 0.577401i | \(-0.804067\pi\) | ||
0.816461 | − | 0.577401i | \(-0.195933\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 8286.04i | − | 0.339745i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4892.53 | − | 4892.53i | −0.199181 | − | 0.199181i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 86731.5i | − | 3.51845i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 626.926 | − | 626.926i | 0.0252535 | − | 0.0252535i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25918.5 | + | 25918.5i | 1.04037 | + | 1.04037i | 0.999150 | + | 0.0412172i | \(0.0131236\pi\) |
0.0412172 | + | 0.999150i | \(0.486876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23507.5 | −0.936992 | −0.468496 | − | 0.883466i | \(-0.655204\pi\) | ||||
−0.468496 | + | 0.883466i | \(0.655204\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11981.1 | − | 11981.1i | 0.475890 | − | 0.475890i | −0.427925 | − | 0.903814i | \(-0.640755\pi\) |
0.903814 | + | 0.427925i | \(0.140755\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8191.53 | −0.323109 | −0.161554 | − | 0.986864i | \(-0.551651\pi\) | ||||
−0.161554 | + | 0.986864i | \(0.551651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10121.4 | −0.397846 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7134.75 | − | 7134.75i | 0.278515 | − | 0.278515i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9283.80 | −0.361159 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27350.6 | − | 27350.6i | −1.05671 | − | 1.05671i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7896.06 | − | 7896.06i | 0.304026 | − | 0.304026i | −0.538561 | − | 0.842587i | \(-0.681032\pi\) |
0.842587 | + | 0.538561i | \(0.181032\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 43097.6i | − | 1.64812i | −0.566501 | − | 0.824061i | \(-0.691703\pi\) | ||
0.566501 | − | 0.824061i | \(-0.308297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21106.8 | + | 21106.8i | 0.804418 | + | 0.804418i | 0.983783 | − | 0.179364i | \(-0.0574041\pi\) |
−0.179364 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 5713.71i | − | 0.216288i | −0.994135 | − | 0.108144i | \(-0.965509\pi\) | ||
0.994135 | − | 0.108144i | \(-0.0344908\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42536.0i | 1.60474i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27814.2 | + | 27814.2i | 1.04229 | + | 1.04229i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4892.59i | 0.182728i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4150.15 | − | 4150.15i | 0.153966 | − | 0.153966i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 143.935 | + | 143.935i | 0.00532204 | + | 0.00532204i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9470.40 | −0.347853 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2440.45 | − | 2440.45i | 0.0893426 | − | 0.0893426i | −0.661023 | − | 0.750366i | \(-0.729877\pi\) |
0.750366 | + | 0.661023i | \(0.229877\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41215.3 | 1.49893 | 0.749463 | − | 0.662046i | \(-0.230312\pi\) | ||||
0.749463 | + | 0.662046i | \(0.230312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5690.92 | 0.206289 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34251.5 | − | 34251.5i | 1.23346 | − | 1.23346i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4600.68 | 0.165139 | 0.0825694 | − | 0.996585i | \(-0.473687\pi\) | ||||
0.0825694 | + | 0.996585i | \(0.473687\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45077.0 | + | 45077.0i | 1.60751 | + | 1.60751i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −738.512 | + | 738.512i | −0.0262509 | + | 0.0262509i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 22590.7i | − | 0.797821i | −0.916990 | − | 0.398911i | \(-0.869388\pi\) | ||
0.916990 | − | 0.398911i | \(-0.130612\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −78919.1 | − | 78919.1i | −2.77816 | − | 2.77816i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5646.19i | − | 0.197487i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37208.7i | 1.29728i | 0.761094 | + | 0.648642i | \(0.224663\pi\) | ||||
−0.761094 | + | 0.648642i | \(0.775337\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29322.0 | − | 29322.0i | −1.01580 | − | 1.01580i | −0.999873 | − | 0.0159300i | \(-0.994929\pi\) |
−0.0159300 | − | 0.999873i | \(-0.505071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 25083.3i | − | 0.866198i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24343.1 | + | 24343.1i | −0.835315 | + | 0.835315i | −0.988238 | − | 0.152923i | \(-0.951131\pi\) |
0.152923 | + | 0.988238i | \(0.451131\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42781.4 | + | 42781.4i | 1.46338 | + | 1.46338i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12372.3 | 0.420542 | 0.210271 | − | 0.977643i | \(-0.432565\pi\) | ||||
0.210271 | + | 0.977643i | \(0.432565\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7039.32 | − | 7039.32i | 0.238520 | − | 0.238520i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −63270.7 | −2.13046 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27651.8 | 0.928193 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15022.2 | − | 15022.2i | 0.501122 | − | 0.501122i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18615.7 | −0.619069 | −0.309534 | − | 0.950888i | \(-0.600173\pi\) | ||||
−0.309534 | + | 0.950888i | \(0.600173\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23920.0 | − | 23920.0i | −0.790555 | − | 0.790555i | 0.191029 | − | 0.981584i | \(-0.438817\pi\) |
−0.981584 | + | 0.191029i | \(0.938817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35384.9 | + | 35384.9i | −1.16587 | + | 1.16587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3892.45i | 0.127462i | 0.997967 | + | 0.0637311i | \(0.0203000\pi\) | ||||
−0.997967 | + | 0.0637311i | \(0.979700\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7840.14 | − | 7840.14i | −0.255947 | − | 0.255947i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1771.35i | 0.0574742i | 0.999587 | + | 0.0287371i | \(0.00914857\pi\) | ||||
−0.999587 | + | 0.0287371i | \(0.990851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13963.7i | 0.451696i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4722.84 | − | 4722.84i | −0.151848 | − | 0.151848i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2828.01i | − | 0.0906504i | −0.998972 | − | 0.0453252i | \(-0.985568\pi\) | ||
0.998972 | − | 0.0453252i | \(-0.0144324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13785.5 | − | 13785.5i | 0.439226 | − | 0.439226i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14851.0 | + | 14851.0i | 0.471750 | + | 0.471750i | 0.902480 | − | 0.430731i | \(-0.141744\pi\) |
−0.430731 | + | 0.902480i | \(0.641744\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.4.l.b.287.16 | 48 | ||
3.2 | odd | 2 | inner | 1152.4.l.b.287.9 | 48 | ||
4.3 | odd | 2 | 1152.4.l.a.287.16 | 48 | |||
8.3 | odd | 2 | 576.4.l.a.143.9 | 48 | |||
8.5 | even | 2 | 144.4.l.a.107.20 | yes | 48 | ||
12.11 | even | 2 | 1152.4.l.a.287.9 | 48 | |||
16.3 | odd | 4 | inner | 1152.4.l.b.863.9 | 48 | ||
16.5 | even | 4 | 576.4.l.a.431.16 | 48 | |||
16.11 | odd | 4 | 144.4.l.a.35.5 | ✓ | 48 | ||
16.13 | even | 4 | 1152.4.l.a.863.9 | 48 | |||
24.5 | odd | 2 | 144.4.l.a.107.5 | yes | 48 | ||
24.11 | even | 2 | 576.4.l.a.143.16 | 48 | |||
48.5 | odd | 4 | 576.4.l.a.431.9 | 48 | |||
48.11 | even | 4 | 144.4.l.a.35.20 | yes | 48 | ||
48.29 | odd | 4 | 1152.4.l.a.863.16 | 48 | |||
48.35 | even | 4 | inner | 1152.4.l.b.863.16 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.4.l.a.35.5 | ✓ | 48 | 16.11 | odd | 4 | ||
144.4.l.a.35.20 | yes | 48 | 48.11 | even | 4 | ||
144.4.l.a.107.5 | yes | 48 | 24.5 | odd | 2 | ||
144.4.l.a.107.20 | yes | 48 | 8.5 | even | 2 | ||
576.4.l.a.143.9 | 48 | 8.3 | odd | 2 | |||
576.4.l.a.143.16 | 48 | 24.11 | even | 2 | |||
576.4.l.a.431.9 | 48 | 48.5 | odd | 4 | |||
576.4.l.a.431.16 | 48 | 16.5 | even | 4 | |||
1152.4.l.a.287.9 | 48 | 12.11 | even | 2 | |||
1152.4.l.a.287.16 | 48 | 4.3 | odd | 2 | |||
1152.4.l.a.863.9 | 48 | 16.13 | even | 4 | |||
1152.4.l.a.863.16 | 48 | 48.29 | odd | 4 | |||
1152.4.l.b.287.9 | 48 | 3.2 | odd | 2 | inner | ||
1152.4.l.b.287.16 | 48 | 1.1 | even | 1 | trivial | ||
1152.4.l.b.863.9 | 48 | 16.3 | odd | 4 | inner | ||
1152.4.l.b.863.16 | 48 | 48.35 | even | 4 | inner |