Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(193,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.bg (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: | \(26.1581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.193 |
Dual form | 960.3.bg.i.577.2 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.67423 | + | 1.77526i | 0.934847 | + | 0.355051i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.44949 | − | 3.44949i | 0.492784 | − | 0.492784i | −0.416398 | − | 0.909182i | \(-0.636708\pi\) |
0.909182 | + | 0.416398i | \(0.136708\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.3485 | −1.03168 | −0.515840 | − | 0.856685i | \(-0.672520\pi\) | ||||
−0.515840 | + | 0.856685i | \(0.672520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.55051 | + | 5.55051i | 0.426962 | + | 0.426962i | 0.887592 | − | 0.460630i | \(-0.152376\pi\) |
−0.460630 | + | 0.887592i | \(0.652376\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.55051 | + | 7.89898i | 0.236701 | + | 0.526599i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.3485 | + | 17.3485i | −1.02050 | + | 1.02050i | −0.0207127 | + | 0.999785i | \(0.506594\pi\) |
−0.999785 | + | 0.0207127i | \(0.993406\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.69694i | 0.457734i | 0.973458 | + | 0.228867i | \(0.0735020\pi\) | ||||
−0.973458 | + | 0.228867i | \(0.926498\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.44949 | 0.402357 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.5505 | + | 11.5505i | 0.502196 | + | 0.502196i | 0.912120 | − | 0.409924i | \(-0.134445\pi\) |
−0.409924 | + | 0.912120i | \(0.634445\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.6969 | + | 16.5959i | 0.747878 | + | 0.663837i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 35.1464i | 1.21195i | 0.795485 | + | 0.605973i | \(0.207216\pi\) | ||||
−0.795485 | + | 0.605973i | \(0.792784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6969 | 0.345063 | 0.172531 | − | 0.985004i | \(-0.444805\pi\) | ||||
0.172531 | + | 0.985004i | \(0.444805\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.8990 | − | 13.8990i | −0.421181 | − | 0.421181i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 22.2474 | − | 10.0000i | 0.635641 | − | 0.285714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.04541 | − | 6.04541i | 0.163389 | − | 0.163389i | −0.620677 | − | 0.784066i | \(-0.713142\pi\) |
0.784066 | + | 0.620677i | \(0.213142\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.5959i | 0.348613i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.696938 | 0.0169985 | 0.00849925 | − | 0.999964i | \(-0.497295\pi\) | ||||
0.00849925 | + | 0.999964i | \(0.497295\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.4949 | + | 26.4949i | 0.616160 | + | 0.616160i | 0.944544 | − | 0.328384i | \(-0.106504\pi\) |
−0.328384 | + | 0.944544i | \(0.606504\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.32577 | + | 14.0227i | −0.118350 | + | 0.311616i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 44.2474 | − | 44.2474i | 0.941435 | − | 0.941435i | −0.0569424 | − | 0.998377i | \(-0.518135\pi\) |
0.998377 | + | 0.0569424i | \(0.0181351\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.2020i | 0.514327i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −42.4949 | −0.833233 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.696938 | + | 0.696938i | 0.0131498 | + | 0.0131498i | 0.713651 | − | 0.700501i | \(-0.247040\pi\) |
−0.700501 | + | 0.713651i | \(0.747040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −53.0454 | − | 20.1464i | −0.964462 | − | 0.366299i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.6515 | + | 10.6515i | −0.186869 | + | 0.186869i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 39.9342i | − | 0.676851i | −0.940993 | − | 0.338425i | \(-0.890106\pi\) | ||
0.940993 | − | 0.338425i | \(-0.109894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.90918 | −0.0968719 | −0.0484359 | − | 0.998826i | \(-0.515424\pi\) | ||||
−0.0484359 | + | 0.998826i | \(0.515424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.3485 | + | 10.3485i | 0.164261 | + | 0.164261i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.0908 | + | 35.7980i | 0.247551 | + | 0.550738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 45.1010 | − | 45.1010i | 0.673150 | − | 0.673150i | −0.285291 | − | 0.958441i | \(-0.592090\pi\) |
0.958441 | + | 0.285291i | \(0.0920903\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 28.2929i | 0.410041i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −68.0000 | −0.957746 | −0.478873 | − | 0.877884i | \(-0.658955\pi\) | ||||
−0.478873 | + | 0.877884i | \(0.658955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 77.7878 | + | 77.7878i | 1.06559 | + | 1.06559i | 0.997693 | + | 0.0678931i | \(0.0216277\pi\) |
0.0678931 | + | 0.997693i | \(0.478372\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.57321 | + | 43.2247i | 0.0343095 | + | 0.576330i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −39.1464 | + | 39.1464i | −0.508395 | + | 0.508395i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24.4949i | 0.310062i | 0.987910 | + | 0.155031i | \(0.0495477\pi\) | ||||
−0.987910 | + | 0.155031i | \(0.950452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.1464 | − | 13.1464i | −0.158391 | − | 0.158391i | 0.623463 | − | 0.781853i | \(-0.285725\pi\) |
−0.781853 | + | 0.623463i | \(0.785725\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −111.889 | + | 50.2929i | −1.31634 | + | 0.591681i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −43.0454 | + | 43.0454i | −0.494775 | + | 0.494775i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 82.1816i | − | 0.923389i | −0.887039 | − | 0.461695i | \(-0.847242\pi\) | ||
0.887039 | − | 0.461695i | \(-0.152758\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 38.2929 | 0.420801 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.1010 | + | 13.1010i | 0.140871 | + | 0.140871i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.4393 | + | 40.6515i | −0.162519 | + | 0.427911i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −24.5959 | + | 24.5959i | −0.253566 | + | 0.253566i | −0.822431 | − | 0.568865i | \(-0.807383\pi\) |
0.568865 | + | 0.822431i | \(0.307383\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 34.0454i | − | 0.343893i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 105.621 | 1.04575 | 0.522876 | − | 0.852409i | \(-0.324859\pi\) | ||||
0.522876 | + | 0.852409i | \(0.324859\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −89.2474 | − | 89.2474i | −0.866480 | − | 0.866480i | 0.125601 | − | 0.992081i | \(-0.459914\pi\) |
−0.992081 | + | 0.125601i | \(0.959914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 39.4949 | + | 15.0000i | 0.376142 | + | 0.142857i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −68.7423 | + | 68.7423i | −0.642452 | + | 0.642452i | −0.951158 | − | 0.308706i | \(-0.900104\pi\) |
0.308706 | + | 0.951158i | \(0.400104\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 68.6969i | 0.630247i | 0.949051 | + | 0.315124i | \(0.102046\pi\) | ||||
−0.949051 | + | 0.315124i | \(0.897954\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.8082 | 0.133407 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 97.6413 | + | 97.6413i | 0.864083 | + | 0.864083i | 0.991809 | − | 0.127727i | \(-0.0407681\pi\) |
−0.127727 | + | 0.991809i | \(0.540768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33.4847 | + | 74.4949i | 0.291171 | + | 0.647782i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.6515 | + | 16.6515i | −0.142321 | + | 0.142321i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 119.687i | 1.00577i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.78775 | 0.0643616 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.853572 | + | 0.853572i | 0.00693961 | + | 0.00693961i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 57.9319 | + | 110.765i | 0.463455 | + | 0.886120i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 164.621 | − | 164.621i | 1.29623 | − | 1.29623i | 0.365362 | − | 0.930865i | \(-0.380945\pi\) |
0.930865 | − | 0.365362i | \(-0.119055\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 64.8990i | 0.503093i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −106.136 | −0.810200 | −0.405100 | − | 0.914272i | \(-0.632763\pi\) | ||||
−0.405100 | + | 0.914272i | \(0.632763\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.0000 | + | 30.0000i | 0.225564 | + | 0.225564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −23.6969 | + | 10.6515i | −0.175533 | + | 0.0789002i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −166.631 | + | 166.631i | −1.21629 | + | 1.21629i | −0.247363 | + | 0.968923i | \(0.579564\pi\) |
−0.968923 | + | 0.247363i | \(0.920436\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 191.171i | − | 1.37533i | −0.726026 | − | 0.687667i | \(-0.758635\pi\) | ||
0.726026 | − | 0.687667i | \(-0.241365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 108.384 | 0.768679 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −62.9898 | − | 62.9898i | −0.440488 | − | 0.440488i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −62.3939 | + | 164.283i | −0.430303 | + | 1.13298i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −30.8661 | + | 30.8661i | −0.209973 | + | 0.209973i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 84.8536i | 0.569487i | 0.958604 | + | 0.284744i | \(0.0919084\pi\) | ||||
−0.958604 | + | 0.284744i | \(0.908092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 148.969 | 0.986552 | 0.493276 | − | 0.869873i | \(-0.335799\pi\) | ||||
0.493276 | + | 0.869873i | \(0.335799\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −52.0454 | − | 52.0454i | −0.340166 | − | 0.340166i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 50.0000 | + | 18.9898i | 0.322581 | + | 0.122515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8536 | + | 16.8536i | −0.107348 | + | 0.107348i | −0.758741 | − | 0.651393i | \(-0.774185\pi\) |
0.651393 | + | 0.758741i | \(0.274185\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.70714i | 0.0107368i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 79.6867 | 0.494949 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −130.606 | − | 130.606i | −0.801265 | − | 0.801265i | 0.182029 | − | 0.983293i | \(-0.441734\pi\) |
−0.983293 | + | 0.182029i | \(0.941734\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −40.2929 | − | 89.6413i | −0.244199 | − | 0.543281i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −45.0352 | + | 45.0352i | −0.269672 | + | 0.269672i | −0.828968 | − | 0.559296i | \(-0.811071\pi\) |
0.559296 | + | 0.828968i | \(0.311071\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 107.384i | − | 0.635406i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −26.0908 | −0.152578 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −146.631 | − | 146.631i | −0.847579 | − | 0.847579i | 0.142252 | − | 0.989831i | \(-0.454566\pi\) |
−0.989831 | + | 0.142252i | \(0.954566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 121.742 | − | 7.24745i | 0.695671 | − | 0.0414140i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 48.9092 | − | 48.9092i | 0.276323 | − | 0.276323i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 183.712i | 1.02632i | 0.858292 | + | 0.513161i | \(0.171526\pi\) | ||||
−0.858292 | + | 0.513161i | \(0.828474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 286.272 | 1.58162 | 0.790808 | − | 0.612064i | \(-0.209661\pi\) | ||||
0.790808 | + | 0.612064i | \(0.209661\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.23724 | − | 7.23724i | −0.0395478 | − | 0.0395478i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 38.9898 | − | 17.5255i | 0.210756 | − | 0.0947325i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 196.879 | − | 196.879i | 1.05283 | − | 1.05283i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.3485i | 0.134119i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 48.0908 | 0.251784 | 0.125892 | − | 0.992044i | \(-0.459821\pi\) | ||||
0.125892 | + | 0.992044i | \(0.459821\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −255.565 | − | 255.565i | −1.32417 | − | 1.32417i | −0.910364 | − | 0.413809i | \(-0.864198\pi\) |
−0.413809 | − | 0.910364i | \(-0.635802\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.1362 | + | 63.5505i | −0.123776 | + | 0.325900i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 96.6969 | − | 96.6969i | 0.490847 | − | 0.490847i | −0.417726 | − | 0.908573i | \(-0.637173\pi\) |
0.908573 | + | 0.417726i | \(0.137173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 192.606i | − | 0.967870i | −0.875104 | − | 0.483935i | \(-0.839207\pi\) | ||
0.875104 | − | 0.483935i | \(-0.160793\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 110.474 | 0.549624 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 121.237 | + | 121.237i | 0.597228 | + | 0.597228i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.25765 | + | 1.23724i | 0.0158910 | + | 0.00603533i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −34.6515 | + | 34.6515i | −0.167399 | + | 0.167399i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 98.6969i | − | 0.472234i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −147.212 | −0.697688 | −0.348844 | − | 0.937181i | \(-0.613426\pi\) | ||||
−0.348844 | + | 0.937181i | \(0.613426\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −83.2827 | − | 83.2827i | −0.390998 | − | 0.390998i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 76.8082 | + | 170.879i | 0.357247 | + | 0.794784i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 36.8990 | − | 36.8990i | 0.170041 | − | 0.170041i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 190.540i | 0.870047i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −192.586 | −0.871429 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 167.429 | + | 167.429i | 0.750803 | + | 0.750803i | 0.974629 | − | 0.223826i | \(-0.0718548\pi\) |
−0.223826 | + | 0.974629i | \(0.571855\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −49.7878 | + | 56.0908i | −0.221279 | + | 0.249293i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −253.171 | + | 253.171i | −1.11529 | + | 1.11529i | −0.122870 | + | 0.992423i | \(0.539210\pi\) |
−0.992423 | + | 0.122870i | \(0.960790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 224.202i | − | 0.979048i | −0.871990 | − | 0.489524i | \(-0.837171\pi\) | ||
0.871990 | − | 0.489524i | \(-0.162829\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −95.8888 | −0.415103 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −205.712 | − | 205.712i | −0.882883 | − | 0.882883i | 0.110944 | − | 0.993827i | \(-0.464613\pi\) |
−0.993827 | + | 0.110944i | \(0.964613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 285.373 | − | 128.272i | 1.21436 | − | 0.545840i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.0000 | + | 30.0000i | −0.126582 | + | 0.126582i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 345.798i | 1.44685i | 0.690401 | + | 0.723427i | \(0.257434\pi\) | ||||
−0.690401 | + | 0.723427i | \(0.742566\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 101.576 | 0.421475 | 0.210738 | − | 0.977543i | \(-0.432413\pi\) | ||||
0.210738 | + | 0.977543i | \(0.432413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −44.7401 | + | 117.800i | −0.182612 | + | 0.480817i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −48.2724 | + | 48.2724i | −0.195435 | + | 0.195435i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 32.2020i | − | 0.129325i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 331.258 | 1.31975 | 0.659876 | − | 0.751375i | \(-0.270609\pi\) | ||||
0.659876 | + | 0.751375i | \(0.270609\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −131.081 | − | 131.081i | −0.518105 | − | 0.518105i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −198.631 | − | 75.4393i | −0.778946 | − | 0.295840i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 33.2372 | − | 33.2372i | 0.129328 | − | 0.129328i | −0.639480 | − | 0.768808i | \(-0.720850\pi\) |
0.768808 | + | 0.639480i | \(0.220850\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 41.7071i | − | 0.161031i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −105.439 | −0.403982 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −278.157 | − | 278.157i | −1.05763 | − | 1.05763i | −0.998235 | − | 0.0593952i | \(-0.981083\pi\) |
−0.0593952 | − | 0.998235i | \(-0.518917\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.02041 | + | 4.49490i | 0.00762419 | + | 0.0169619i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 100.652 | − | 100.652i | 0.376972 | − | 0.376972i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 488.499i | − | 1.81598i | −0.418988 | − | 0.907992i | \(-0.637615\pi\) | ||
0.418988 | − | 0.907992i | \(-0.362385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 131.576 | 0.485518 | 0.242759 | − | 0.970087i | \(-0.421947\pi\) | ||||
0.242759 | + | 0.970087i | \(0.421947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 46.8990 | + | 46.8990i | 0.171791 | + | 0.171791i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −212.182 | − | 188.338i | −0.771570 | − | 0.684866i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −101.510 | + | 101.510i | −0.366461 | + | 0.366461i | −0.866185 | − | 0.499724i | \(-0.833435\pi\) |
0.499724 | + | 0.866185i | \(0.333435\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 32.0908i | 0.115021i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 343.303 | 1.22172 | 0.610860 | − | 0.791739i | \(-0.290824\pi\) | ||||
0.610860 | + | 0.791739i | \(0.290824\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.19184 | − | 1.19184i | −0.00421143 | − | 0.00421143i | 0.704998 | − | 0.709209i | \(-0.250948\pi\) |
−0.709209 | + | 0.704998i | \(0.750948\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −68.6969 | + | 30.8786i | −0.241042 | + | 0.108346i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.40408 | − | 2.40408i | 0.00837659 | − | 0.00837659i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 312.939i | − | 1.08283i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −60.2474 | −0.207036 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −96.5653 | − | 96.5653i | −0.329574 | − | 0.329574i | 0.522850 | − | 0.852425i | \(-0.324869\pi\) |
−0.852425 | + | 0.522850i | \(0.824869\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 70.8934 | − | 186.662i | 0.240316 | − | 0.632752i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 41.6969 | − | 41.6969i | 0.140394 | − | 0.140394i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 128.222i | 0.428838i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 182.788 | 0.607268 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 129.359 | + | 129.359i | 0.426926 | + | 0.426926i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.6209 | − | 10.4903i | −0.0905604 | − | 0.0343945i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 124.969 | − | 124.969i | 0.407066 | − | 0.407066i | −0.473648 | − | 0.880714i | \(-0.657063\pi\) |
0.880714 | + | 0.473648i | \(0.157063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 218.611i | − | 0.707478i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −586.302 | −1.88522 | −0.942608 | − | 0.333902i | \(-0.891635\pi\) | ||||
−0.942608 | + | 0.333902i | \(0.891635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −102.373 | − | 102.373i | −0.327072 | − | 0.327072i | 0.524400 | − | 0.851472i | \(-0.324290\pi\) |
−0.851472 | + | 0.524400i | \(0.824290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 30.0000 | + | 66.7423i | 0.0952381 | + | 0.211880i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 108.783 | − | 108.783i | 0.343165 | − | 0.343165i | −0.514391 | − | 0.857556i | \(-0.671982\pi\) |
0.857556 | + | 0.514391i | \(0.171982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 398.858i | − | 1.25034i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −168.384 | −0.524560 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −150.879 | − | 150.879i | −0.467116 | − | 0.467116i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.6617 | + | 195.893i | 0.0358823 | + | 0.602749i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −84.1362 | + | 84.1362i | −0.257297 | + | 0.257297i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 305.262i | − | 0.927849i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 245.423 | 0.741461 | 0.370730 | − | 0.928741i | \(-0.379107\pi\) | ||||
0.370730 | + | 0.928741i | \(0.379107\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.1362 | + | 18.1362i | 0.0544631 | + | 0.0544631i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 290.879 | − | 130.747i | 0.868294 | − | 0.390289i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 213.808 | − | 213.808i | 0.634446 | − | 0.634446i | −0.314734 | − | 0.949180i | \(-0.601915\pi\) |
0.949180 | + | 0.314734i | \(0.101915\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 239.171i | 0.705520i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −121.394 | −0.355994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 255.959 | + | 255.959i | 0.746237 | + | 0.746237i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −50.2270 | + | 132.247i | −0.145586 | + | 0.383326i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 160.050 | − | 160.050i | 0.461239 | − | 0.461239i | −0.437822 | − | 0.899062i | \(-0.644250\pi\) |
0.899062 | + | 0.437822i | \(0.144250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 298.009i | − | 0.853894i | −0.904277 | − | 0.426947i | \(-0.859589\pi\) | ||
0.904277 | − | 0.426947i | \(-0.140411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −40.7878 | −0.116204 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.5199 | − | 22.5199i | −0.0637957 | − | 0.0637957i | 0.674489 | − | 0.738285i | \(-0.264364\pi\) |
−0.738285 | + | 0.674489i | \(0.764364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −317.848 | − | 120.717i | −0.895346 | − | 0.340049i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −146.586 | + | 146.586i | −0.410604 | + | 0.410604i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 48.2724i | − | 0.134464i | −0.997737 | − | 0.0672318i | \(-0.978583\pi\) | ||
0.997737 | − | 0.0672318i | \(-0.0214167\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 285.363 | 0.790480 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.53801 | + | 9.53801i | 0.0262755 | + | 0.0262755i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 225.505 | + | 501.691i | 0.617822 | + | 1.37450i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 146.510 | − | 146.510i | 0.399209 | − | 0.399209i | −0.478745 | − | 0.877954i | \(-0.658908\pi\) |
0.877954 | + | 0.478745i | \(0.158908\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.09082i | 0.00566617i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.80816 | 0.0129600 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −86.2066 | − | 86.2066i | −0.231117 | − | 0.231117i | 0.582042 | − | 0.813159i | \(-0.302254\pi\) |
−0.813159 | + | 0.582042i | \(0.802254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −64.7071 | + | 206.611i | −0.172552 | + | 0.550962i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −195.081 | + | 195.081i | −0.517455 | + | 0.517455i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 210.000i | − | 0.554090i | −0.960857 | − | 0.277045i | \(-0.910645\pi\) | ||
0.960857 | − | 0.277045i | \(-0.0893551\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 403.237 | 1.05837 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.6311 | − | 10.6311i | −0.0277575 | − | 0.0277575i | 0.693092 | − | 0.720849i | \(-0.256248\pi\) |
−0.720849 | + | 0.693092i | \(0.756248\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −252.474 | + | 113.485i | −0.655778 | + | 0.294765i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −79.4847 | + | 79.4847i | −0.205387 | + | 0.205387i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 535.337i | − | 1.37619i | −0.725621 | − | 0.688094i | \(-0.758448\pi\) | ||
0.725621 | − | 0.688094i | \(-0.241552\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −400.767 | −1.02498 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −129.990 | − | 129.990i | −0.330763 | − | 0.330763i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −43.4847 | + | 114.495i | −0.110088 | + | 0.289860i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −118.742 | + | 118.742i | −0.299099 | + | 0.299099i | −0.840661 | − | 0.541562i | \(-0.817833\pi\) |
0.541562 | + | 0.840661i | \(0.317833\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 73.4847i | 0.184172i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 420.302 | 1.04813 | 0.524067 | − | 0.851677i | \(-0.324414\pi\) | ||||
0.524067 | + | 0.851677i | \(0.324414\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 59.3735 | + | 59.3735i | 0.147329 | + | 0.147329i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −42.0681 | − | 15.9773i | −0.103872 | − | 0.0394501i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −68.6061 | + | 68.6061i | −0.168565 | + | 0.168565i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 515.110i | 1.25944i | 0.776823 | + | 0.629719i | \(0.216830\pi\) | ||||
−0.776823 | + | 0.629719i | \(0.783170\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −408.161 | −0.993093 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −137.753 | − | 137.753i | −0.333541 | − | 0.333541i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.1112 | − | 84.7878i | −0.0918343 | − | 0.204308i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 234.136 | − | 234.136i | 0.561478 | − | 0.561478i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 88.6015i | − | 0.211460i | −0.994395 | − | 0.105730i | \(-0.966282\pi\) | ||
0.994395 | − | 0.105730i | \(-0.0337178\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 257.151 | 0.610810 | 0.305405 | − | 0.952223i | \(-0.401208\pi\) | ||||
0.305405 | + | 0.952223i | \(0.401208\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 132.742 | + | 132.742i | 0.313812 | + | 0.313812i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −612.277 | + | 36.4495i | −1.44065 | + | 0.0857635i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.3837 | + | 20.3837i | −0.0477369 | + | 0.0477369i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 154.293i | − | 0.359657i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 804.636 | 1.86690 | 0.933452 | − | 0.358702i | \(-0.116781\pi\) | ||||
0.933452 | + | 0.358702i | \(0.116781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −344.848 | − | 344.848i | −0.796416 | − | 0.796416i | 0.186113 | − | 0.982528i | \(-0.440411\pi\) |
−0.982528 | + | 0.186113i | \(0.940411\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −277.621 | + | 124.788i | −0.638209 | + | 0.286868i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −100.454 | + | 100.454i | −0.229872 | + | 0.229872i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 432.929i | − | 0.986170i | −0.869981 | − | 0.493085i | \(-0.835869\pi\) | ||
0.869981 | − | 0.493085i | \(-0.164131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −75.6061 | −0.171442 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −245.131 | − | 245.131i | −0.553342 | − | 0.553342i | 0.374062 | − | 0.927404i | \(-0.377965\pi\) |
−0.927404 | + | 0.374062i | \(0.877965\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 145.893 | − | 384.136i | 0.327850 | − | 0.863227i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −103.924 | + | 103.924i | −0.232492 | + | 0.232492i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 386.091i | − | 0.859890i | −0.902855 | − | 0.429945i | \(-0.858533\pi\) | ||
0.902855 | − | 0.429945i | \(-0.141467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.90918 | −0.0175370 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 182.449 | + | 182.449i | 0.402758 | + | 0.402758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 178.990 | + | 67.9796i | 0.393384 | + | 0.149406i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −223.747 | + | 223.747i | −0.489599 | + | 0.489599i | −0.908180 | − | 0.418580i | \(-0.862528\pi\) |
0.418580 | + | 0.908180i | \(0.362528\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 127.485i | − | 0.277744i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 722.620 | 1.56751 | 0.783753 | − | 0.621073i | \(-0.213303\pi\) | ||||
0.783753 | + | 0.621073i | \(0.213303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −129.702 | − | 129.702i | −0.280133 | − | 0.280133i | 0.553029 | − | 0.833162i | \(-0.313472\pi\) |
−0.833162 | + | 0.553029i | \(0.813472\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.9796 | + | 84.4949i | 0.0816765 | + | 0.181709i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −415.258 | + | 415.258i | −0.889203 | + | 0.889203i | −0.994446 | − | 0.105244i | \(-0.966438\pi\) |
0.105244 | + | 0.994446i | \(0.466438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 311.151i | − | 0.663435i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −41.2827 | −0.0876489 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −300.677 | − | 300.677i | −0.635680 | − | 0.635680i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −144.334 | + | 162.606i | −0.303860 | + | 0.342329i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.09082 | + | 2.09082i | −0.00438326 | + | 0.00438326i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 304.949i | − | 0.636637i | −0.947984 | − | 0.318318i | \(-0.896882\pi\) | ||
0.947984 | − | 0.318318i | \(-0.103118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 67.1102 | 0.139522 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 97.5959 | + | 97.5959i | 0.202062 | + | 0.202062i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −158.631 | + | 71.3031i | −0.327074 | + | 0.147017i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −429.318 | + | 429.318i | −0.881556 | + | 0.881556i | −0.993693 | − | 0.112137i | \(-0.964231\pi\) |
0.112137 | + | 0.993693i | \(0.464231\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 319.918i | − | 0.654230i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 414.318 | 0.843825 | 0.421912 | − | 0.906637i | \(-0.361359\pi\) | ||||
0.421912 | + | 0.906637i | \(0.361359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −609.737 | − | 609.737i | −1.23679 | − | 1.23679i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 60.4393 | − | 159.136i | 0.122100 | − | 0.321487i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −234.565 | + | 234.565i | −0.471962 | + | 0.471962i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 367.585i | 0.736643i | 0.929699 | + | 0.368321i | \(0.120067\pi\) | ||||
−0.929699 | + | 0.368321i | \(0.879933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −110.313 | −0.220186 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.59133 | − | 9.59133i | −0.0190683 | − | 0.0190683i | 0.697508 | − | 0.716577i | \(-0.254292\pi\) |
−0.716577 | + | 0.697508i | \(0.754292\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 493.697 | + | 187.504i | 0.977618 | + | 0.371295i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 131.518 | − | 131.518i | 0.259404 | − | 0.259404i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 777.489i | 1.52748i | 0.645522 | + | 0.763742i | \(0.276640\pi\) | ||||
−0.645522 | + | 0.763742i | \(0.723360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 536.656 | 1.05021 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −31.9546 | − | 31.9546i | −0.0622897 | − | 0.0622897i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −258.727 | − | 575.601i | −0.502382 | − | 1.11767i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −502.141 | + | 502.141i | −0.971259 | + | 0.971259i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 359.171i | − | 0.692045i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 321.605 | 0.617284 | 0.308642 | − | 0.951178i | \(-0.400125\pi\) | ||||
0.308642 | + | 0.951178i | \(0.400125\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 582.454 | + | 582.454i | 1.11368 | + | 1.11368i | 0.992649 | + | 0.121030i | \(0.0386198\pi\) |
0.121030 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 157.980 | + | 140.227i | 0.300914 | + | 0.267099i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −185.576 | + | 185.576i | −0.352136 | + | 0.352136i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 262.171i | − | 0.495598i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 119.803 | 0.225617 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.86836 | + | 3.86836i | 0.00725772 | + | 0.00725772i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −443.353 | + | 199.283i | −0.828697 | + | 0.372491i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −225.000 | + | 225.000i | −0.418994 | + | 0.418994i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 286.005i | − | 0.530621i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −460.697 | −0.851566 | −0.425783 | − | 0.904825i | \(-0.640001\pi\) | ||||
−0.425783 | + | 0.904825i | \(0.640001\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 350.611 | + | 350.611i | 0.645692 | + | 0.645692i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −121.955 | + | 321.106i | −0.223770 | + | 0.589185i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 661.778 | − | 661.778i | 1.20983 | − | 1.20983i | 0.238750 | − | 0.971081i | \(-0.423262\pi\) |
0.971081 | − | 0.238750i | \(-0.0767376\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 17.7276i | − | 0.0322906i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −305.666 | −0.554748 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 84.4949 | + | 84.4949i | 0.152794 | + | 0.152794i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 69.2168 | + | 26.2883i | 0.124715 | + | 0.0473663i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −125.909 | + | 125.909i | −0.226049 | + | 0.226049i | −0.811040 | − | 0.584991i | \(-0.801098\pi\) |
0.584991 | + | 0.811040i | \(0.301098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 294.120i | 0.526155i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 482.252 | 0.859629 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 200.009 | + | 200.009i | 0.355256 | + | 0.355256i | 0.862061 | − | 0.506805i | \(-0.169174\pi\) |
−0.506805 | + | 0.862061i | \(0.669174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 283.060 | + | 629.737i | 0.500992 | + | 1.11458i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −31.0454 | + | 31.0454i | −0.0547538 | + | 0.0547538i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 599.839i | 1.05420i | 0.849804 | + | 0.527099i | \(0.176720\pi\) | ||||
−0.849804 | + | 0.527099i | \(0.823280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 247.970 | 0.434274 | 0.217137 | − | 0.976141i | \(-0.430328\pi\) | ||||
0.217137 | + | 0.976141i | \(0.430328\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 58.8990 | + | 58.8990i | 0.102791 | + | 0.102791i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.2679 | + | 407.650i | 0.0422050 | + | 0.708957i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −292.121 | + | 292.121i | −0.506276 | + | 0.506276i | −0.913381 | − | 0.407105i | \(-0.866538\pi\) |
0.407105 | + | 0.913381i | \(0.366538\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 626.005i | − | 1.08118i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −90.6969 | −0.156105 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.90918 | − | 7.90918i | −0.0135664 | − | 0.0135664i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −107.394 | + | 48.2724i | −0.183579 | + | 0.0825170i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −611.217 | + | 611.217i | −1.04126 | + | 1.04126i | −0.0421437 | + | 0.999112i | \(0.513419\pi\) |
−0.999112 | + | 0.0421437i | \(0.986581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 93.0306i | 0.157947i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 236.858 | 0.400775 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 524.742 | + | 524.742i | 0.884894 | + | 0.884894i | 0.994027 | − | 0.109133i | \(-0.0348074\pi\) |
−0.109133 | + | 0.994027i | \(0.534807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −212.474 | + | 559.444i | −0.357100 | + | 0.940242i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 235.893 | − | 235.893i | 0.395131 | − | 0.395131i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 368.858i | 0.615790i | 0.951420 | + | 0.307895i | \(0.0996245\pi\) | ||||
−0.951420 | + | 0.307895i | \(0.900375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 932.484 | 1.55155 | 0.775777 | − | 0.631007i | \(-0.217358\pi\) | ||||
0.775777 | + | 0.631007i | \(0.217358\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 135.303 | + | 135.303i | 0.224383 | + | 0.224383i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.4018 | + | 13.8252i | 0.0601682 | + | 0.0228517i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 513.611 | − | 513.611i | 0.846146 | − | 0.846146i | −0.143504 | − | 0.989650i | \(-0.545837\pi\) |
0.989650 | + | 0.143504i | \(0.0458369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 296.969i | 0.487634i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 491.192 | 0.803915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 615.287 | + | 615.287i | 1.00373 | + | 1.00373i | 0.999993 | + | 0.00373821i | \(0.00118991\pi\) |
0.00373821 | + | 0.999993i | \(0.498810\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.47449 | + | 5.50510i | 0.00402356 | + | 0.00895139i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 546.752 | − | 546.752i | 0.886145 | − | 0.886145i | −0.108005 | − | 0.994150i | \(-0.534446\pi\) |
0.994150 | + | 0.108005i | \(0.0344463\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 152.869i | 0.246962i | 0.992347 | + | 0.123481i | \(0.0394058\pi\) | ||||
−0.992347 | + | 0.123481i | \(0.960594\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −84.8786 | −0.136680 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −283.485 | − | 283.485i | −0.455032 | − | 0.455032i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 74.1510 | + | 620.586i | 0.118642 | + | 0.992937i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 120.879 | − | 120.879i | 0.192789 | − | 0.192789i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 209.757i | 0.333477i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.4847 | −0.0657444 | −0.0328722 | − | 0.999460i | \(-0.510465\pi\) | ||||
−0.0328722 | + | 0.999460i | \(0.510465\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −180.297 | − | 180.297i | −0.284830 | − | 0.284830i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1061.72 | − | 477.233i | 1.67200 | − | 0.751547i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −139.884 | + | 139.884i | −0.219598 | + | 0.219598i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 204.000i | − | 0.319249i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.2122 | 0.0736541 | 0.0368270 | − | 0.999322i | \(-0.488275\pi\) | ||||
0.0368270 | + | 0.999322i | \(0.488275\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −460.372 | − | 460.372i | −0.715976 | − | 0.715976i | 0.251803 | − | 0.967779i | \(-0.418977\pi\) |
−0.967779 | + | 0.251803i | \(0.918977\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −115.212 | + | 303.353i | −0.178624 | + | 0.470315i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −281.287 | + | 281.287i | −0.434756 | + | 0.434756i | −0.890243 | − | 0.455487i | \(-0.849465\pi\) |
0.455487 | + | 0.890243i | \(0.349465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 453.192i | 0.698293i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 90.3837 | 0.138838 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −89.8230 | − | 89.8230i | −0.137554 | − | 0.137554i | 0.634977 | − | 0.772531i | \(-0.281010\pi\) |
−0.772531 | + | 0.634977i | \(0.781010\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −496.106 | − | 188.419i | −0.757413 | − | 0.287662i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −233.363 | + | 233.363i | −0.355195 | + | 0.355195i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1081.24i | 1.64072i | 0.571844 | + | 0.820362i | \(0.306228\pi\) | ||||
−0.571844 | + | 0.820362i | \(0.693772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 632.393 | 0.956721 | 0.478361 | − | 0.878163i | \(-0.341231\pi\) | ||||
0.478361 | + | 0.878163i | \(0.341231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −235.868 | − | 235.868i | −0.355759 | − | 0.355759i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 86.9694 | + | 193.485i | 0.130781 | + | 0.290954i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −405.959 | + | 405.959i | −0.608634 | + | 0.608634i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 410.116i | 0.613028i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 67.0602 | 0.0999407 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 233.293 | + | 233.293i | 0.346646 | + | 0.346646i | 0.858859 | − | 0.512213i | \(-0.171174\pi\) |
−0.512213 | + | 0.858859i | \(0.671174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −129.674 | + | 7.71964i | −0.192110 | + | 0.0114365i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.3883 | − | 48.3883i | 0.0714745 | − | 0.0714745i | −0.670466 | − | 0.741940i | \(-0.733906\pi\) |
0.741940 | + | 0.670466i | \(0.233906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 169.687i | 0.249907i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −620.141 | −0.910633 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −213.410 | − | 213.410i | −0.312459 | − | 0.312459i | 0.533402 | − | 0.845862i | \(-0.320913\pi\) |
−0.845862 | + | 0.533402i | \(0.820913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1074.69 | + | 483.060i | −1.56888 | + | 0.705197i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 274.590 | − | 274.590i | 0.399695 | − | 0.399695i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.73673i | 0.0112289i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −151.121 | −0.218700 | −0.109350 | − | 0.994003i | \(-0.534877\pi\) | ||||
−0.109350 | + | 0.994003i | \(0.534877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −117.439 | − | 117.439i | −0.169465 | − | 0.169465i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 339.378 | − | 893.580i | 0.488314 | − | 1.28573i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0908 | + | 12.0908i | −0.0173469 | + | 0.0173469i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 503.889i | − | 0.720871i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 745.680 | 1.06374 | 0.531869 | − | 0.846827i | \(-0.321490\pi\) | ||||
0.531869 | + | 0.846827i | \(0.321490\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.5765 | + | 52.5765i | 0.0747888 | + | 0.0747888i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 506.611 | + | 192.409i | 0.718597 | + | 0.272920i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 364.338 | − | 364.338i | 0.515330 | − | 0.515330i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 719.049i | 1.01417i | 0.861895 | + | 0.507087i | \(0.169278\pi\) | ||||
−0.861895 | + | 0.507087i | \(0.830722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −73.4847 | −0.103354 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 123.555 | + | 123.555i | 0.173289 | + | 0.173289i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −182.606 | − | 406.252i | −0.255393 | − | 0.568185i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −423.514 | + | 423.514i | −0.590675 | + | 0.590675i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 605.271i | 0.841824i | 0.907101 | + | 0.420912i | \(0.138290\pi\) | ||||
−0.907101 | + | 0.420912i | \(0.861710\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −615.716 | −0.853975 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 124.404 | + | 124.404i | 0.172067 | + | 0.172067i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −583.287 | + | 657.131i | −0.804534 | + | 0.906387i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −246.126 | + | 246.126i | −0.338550 | + | 0.338550i | −0.855821 | − | 0.517271i | \(-0.826948\pi\) |
0.517271 | + | 0.855821i | \(0.326948\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −919.292 | −1.25758 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 270.763 | + | 270.763i | 0.369390 | + | 0.369390i | 0.867255 | − | 0.497865i | \(-0.165882\pi\) |
−0.497865 | + | 0.867255i | \(0.665882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −199.070 | + | 89.4801i | −0.270844 | + | 0.121742i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −511.828 | + | 511.828i | −0.694474 | + | 0.694474i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 515.666i | − | 0.697789i | −0.937162 | − | 0.348895i | \(-0.886557\pi\) | ||
0.937162 | − | 0.348895i | \(-0.113443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −118.243 | −0.159572 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 420.702 | + | 420.702i | 0.566220 | + | 0.566220i | 0.931067 | − | 0.364847i | \(-0.118879\pi\) |
−0.364847 | + | 0.931067i | \(0.618879\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −150.637 | + | 396.626i | −0.202197 | + | 0.532383i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.4393 | − | 39.4393i | 0.0527969 | − | 0.0527969i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 474.252i | 0.633180i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −859.787 | −1.14486 | −0.572428 | − | 0.819955i | \(-0.693998\pi\) | ||||
−0.572428 | + | 0.819955i | \(0.693998\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 405.706 | + | 405.706i | 0.538786 | + | 0.538786i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 696.318 | + | 264.459i | 0.922275 | + | 0.350276i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 956.075 | − | 956.075i | 1.26298 | − | 1.26298i | 0.313337 | − | 0.949642i | \(-0.398553\pi\) |
0.949642 | − | 0.313337i | \(-0.101447\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 321.081i | − | 0.423031i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −322.758 | −0.424124 | −0.212062 | − | 0.977256i | \(-0.568018\pi\) | ||||
−0.212062 | + | 0.977256i | \(0.568018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 236.969 | + | 236.969i | 0.310576 | + | 0.310576i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −150.879 | − | 335.666i | −0.197227 | − | 0.438780i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 221.655 | − | 221.655i | 0.288990 | − | 0.288990i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 692.402i | − | 0.900393i | −0.892930 | − | 0.450196i | \(-0.851354\pi\) | ||
0.892930 | − | 0.450196i | \(-0.148646\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 81.4143 | 0.105596 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −375.226 | − | 375.226i | −0.485415 | − | 0.485415i | 0.421441 | − | 0.906856i | \(-0.361525\pi\) |
−0.906856 | + | 0.421441i | \(0.861525\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 200.000 | + | 177.526i | 0.258065 | + | 0.229065i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 51.0806 | − | 51.0806i | 0.0657408 | − | 0.0657408i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.06123i | 0.00778078i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 771.696 | 0.988087 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −129.136 | − | 129.136i | −0.164925 | − | 0.164925i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −108.697 | + | 48.8582i | −0.138467 | + | 0.0622397i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −910.990 | + | 910.990i | −1.15755 | + | 1.15755i | −0.172546 | + | 0.985001i | \(0.555199\pi\) |
−0.985001 | + | 0.172546i | \(0.944801\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 681.342i | − | 0.863551i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 673.626 | 0.851613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.7990 | − | 32.7990i | −0.0413606 | − | 0.0413606i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.03062 | + | 7.97959i | −0.00381209 | + | 0.0100372i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.21683 | − | 7.21683i | 0.00905500 | − | 0.00905500i | −0.702565 | − | 0.711620i | \(-0.747962\pi\) |
0.711620 | + | 0.702565i | \(0.247962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1535.25i | 1.92147i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 246.545 | 0.307796 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −882.772 | − | 882.772i | −1.09934 | − | 1.09934i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 372.474 | + | 141.464i | 0.462701 | + | 0.175732i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 598.287 | − | 598.287i | 0.741372 | − | 0.741372i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 150.000i | 0.185414i | 0.995693 | + | 0.0927070i | \(0.0295520\pi\) | ||||
−0.995693 | + | 0.0927070i | \(0.970448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1336.85 | −1.64839 | −0.824197 | − | 0.566304i | \(-0.808373\pi\) | ||||
−0.824197 | + | 0.566304i | \(0.808373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 161.146 | + | 161.146i | 0.198212 | + | 0.198212i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −378.624 | − | 842.343i | −0.464570 | − | 1.03355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −230.424 | + | 230.424i | −0.282037 | + | 0.282037i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 114.879i | 0.140267i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.8934 | 0.0412830 | 0.0206415 | − | 0.999787i | \(-0.493429\pi\) | ||||
0.0206415 | + | 0.999787i | \(0.493429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 481.631 | + | 481.631i | 0.585214 | + | 0.585214i | 0.936331 | − | 0.351117i | \(-0.114198\pi\) |
−0.351117 | + | 0.936331i | \(0.614198\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.2020 | − | 490.535i | −0.0353964 | − | 0.594587i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −350.756 | + | 350.756i | −0.424131 | + | 0.424131i | −0.886623 | − | 0.462492i | \(-0.846955\pi\) |
0.462492 | + | 0.886623i | \(0.346955\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 697.423i | − | 0.841283i | −0.907227 | − | 0.420641i | \(-0.861805\pi\) | ||
0.907227 | − | 0.420641i | \(-0.138195\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −248.647 | −0.299214 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −437.217 | − | 437.217i | −0.524870 | − | 0.524870i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −290.454 | + | 130.556i | −0.347849 | + | 0.156355i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −39.3031 | + | 39.3031i | −0.0469571 | + | 0.0469571i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 72.3724i | − | 0.0862604i | −0.999069 | − | 0.0431302i | \(-0.986267\pi\) | ||
0.999069 | − | 0.0431302i | \(-0.0137330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −394.271 | −0.468813 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 420.459 | + | 420.459i | 0.498765 | + | 0.498765i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 190.633 | − | 501.936i | 0.225602 | − | 0.594008i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.8638 | − | 26.8638i | 0.0317164 | − | 0.0317164i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 2.91939i | − | 0.00343862i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 139.655 | 0.164107 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 74.5699 | + | 74.5699i | 0.0874207 | + | 0.0874207i | 0.749465 | − | 0.662044i | \(-0.230311\pi\) |
−0.662044 | + | 0.749465i | \(0.730311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −121.955 | − | 46.3179i | −0.142637 | − | 0.0541729i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −293.176 | + | 293.176i | −0.342096 | + | 0.342096i | −0.857155 | − | 0.515059i | \(-0.827770\pi\) |
0.515059 | + | 0.857155i | \(0.327770\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 786.867i | − | 0.916027i | −0.888945 | − | 0.458014i | \(-0.848561\pi\) | ||
0.888945 | − | 0.458014i | \(-0.151439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.88877 | 0.00683946 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1072.68 | − | 1072.68i | −1.24297 | − | 1.24297i | −0.958764 | − | 0.284204i | \(-0.908271\pi\) |
−0.284204 | − | 0.958764i | \(-0.591729\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −425.081 | − | 945.696i | −0.491423 | − | 1.09329i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 383.270 | − | 383.270i | 0.442065 | − | 0.442065i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 277.980i | − | 0.319884i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 500.667 | 0.574819 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −73.7878 | − | 73.7878i | −0.0845221 | − | 0.0845221i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 581.918 | + | 182.247i | 0.665050 | + | 0.208283i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −239.460 | + | 239.460i | −0.273044 | + | 0.273044i | −0.830324 | − | 0.557280i | \(-0.811845\pi\) |
0.557280 | + | 0.830324i | \(0.311845\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 236.536i | − | 0.269096i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 62.8490 | 0.0713382 | 0.0356691 | − | 0.999364i | \(-0.488644\pi\) | ||||
0.0356691 | + | 0.999364i | \(0.488644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 158.061 | + | 158.061i | 0.179005 | + | 0.179005i | 0.790922 | − | 0.611917i | \(-0.209601\pi\) |
−0.611917 | + | 0.790922i | \(0.709601\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 315.439 | − | 141.787i | 0.356429 | − | 0.160211i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.2066 | − | 30.2066i | 0.0340548 | − | 0.0340548i | −0.689874 | − | 0.723929i | \(-0.742334\pi\) |
0.723929 | + | 0.689874i | \(0.242334\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1135.72i | − | 1.27752i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 102.136 | 0.114631 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 384.817 | + | 384.817i | 0.430926 | + | 0.430926i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −326.135 | + | 858.712i | −0.364397 | + | 0.959454i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −157.040 | + | 157.040i | −0.175072 | + | 0.175072i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 375.959i | 0.418197i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.1816 | −0.0268387 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 223.868 | + | 223.868i | 0.247916 | + | 0.247916i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1338.10 | + | 508.207i | 1.47857 | + | 0.561554i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −571.342 | + | 571.342i | −0.629925 | + | 0.629925i | −0.948049 | − | 0.318124i | \(-0.896947\pi\) |
0.318124 | + | 0.948049i | \(0.396947\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 316.863i | 0.348584i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 173.362 | 0.190299 | 0.0951494 | − | 0.995463i | \(-0.469667\pi\) | ||||
0.0951494 | + | 0.995463i | \(0.469667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 149.192 | + | 149.192i | 0.163408 | + | 0.163408i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.9806 | − | 46.6765i | −0.0229296 | − | 0.0510126i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −366.116 | + | 366.116i | −0.399254 | + | 0.399254i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1147.42i | − | 1.24856i | −0.781202 | − | 0.624278i | \(-0.785393\pi\) | ||
0.781202 | − | 0.624278i | \(-0.214607\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 306.111 | 0.332368 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −377.435 | − | 377.435i | −0.408922 | − | 0.408922i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 213.360 | − | 12.7015i | 0.230659 | − | 0.0137314i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 267.742 | − | 267.742i | 0.288827 | − | 0.288827i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 220.293i | 0.237129i | 0.992946 | + | 0.118565i | \(0.0378292\pi\) | ||||
−0.992946 | + | 0.118565i | \(0.962171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −219.181 | −0.235425 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −718.070 | − | 718.070i | −0.769636 | − | 0.769636i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1269.77 | − | 570.747i | 1.35804 | − | 0.610425i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −396.090 | + | 396.090i | −0.422721 | + | 0.422721i | −0.886140 | − | 0.463418i | \(-0.846623\pi\) |
0.463418 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 250.763i | − | 0.267053i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −185.771 | −0.197419 | −0.0987093 | − | 0.995116i | \(-0.531471\pi\) | ||||
−0.0987093 | + | 0.995116i | \(0.531471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.04999 | + | 8.04999i | 0.00853658 | + | 0.00853658i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −45.0000 | + | 118.485i | −0.0476190 | + | 0.125381i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 845.190 | − | 845.190i | 0.892492 | − | 0.892492i | −0.102265 | − | 0.994757i | \(-0.532609\pi\) |
0.994757 | + | 0.102265i | \(0.0326091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 863.523i | 0.909930i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 266.463 | 0.280193 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −630.499 | − | 630.499i | −0.661594 | − | 0.661594i | 0.294161 | − | 0.955756i | \(-0.404960\pi\) |
−0.955756 | + | 0.294161i | \(0.904960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 224.788 | + | 85.3735i | 0.235380 | + | 0.0893963i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 488.499 | − | 488.499i | 0.510449 | − | 0.510449i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1149.58i | 1.19873i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −846.576 | −0.880932 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −206.227 | − | 206.227i | −0.214151 | − | 0.214151i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −740.879 | − | 1648.27i | −0.767750 | − | 1.70805i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −381.690 | + | 381.690i | −0.394716 | + | 0.394716i | −0.876364 | − | 0.481649i | \(-0.840038\pi\) |
0.481649 | + | 0.876364i | \(0.340038\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 369.576i | − | 0.381399i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1000.44 | 1.03032 | 0.515159 | − | 0.857095i | \(-0.327733\pi\) | ||||
0.515159 | + | 0.857095i | \(0.327733\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −659.444 | − | 659.444i | −0.677743 | − | 0.677743i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −225.637 | + | 254.202i | −0.231422 | + | 0.260720i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 593.662 | − | 593.662i | 0.607637 | − | 0.607637i | −0.334691 | − | 0.942328i | \(-0.608632\pi\) |
0.942328 | + | 0.334691i | \(0.108632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 932.636i | 0.952641i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −206.091 | −0.210082 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1217.34 | − | 1217.34i | −1.23839 | − | 1.23839i | −0.960659 | − | 0.277731i | \(-0.910418\pi\) |
−0.277731 | − | 0.960659i | \(-0.589582\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 623.646 | − | 280.322i | 0.633143 | − | 0.284591i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 373.868 | − | 373.868i | 0.378793 | − | 0.378793i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 612.059i | 0.618867i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −544.061 | −0.549002 | −0.274501 | − | 0.961587i | \(-0.588513\pi\) | ||||
−0.274501 | + | 0.961587i | \(0.588513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 300.581 | + | 300.581i | 0.302700 | + | 0.302700i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 341.925 | − | 900.286i | 0.343643 | − | 0.904810i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 316.733 | − | 316.733i | 0.317686 | − | 0.317686i | −0.530192 | − | 0.847878i | \(-0.677880\pi\) |
0.847878 | + | 0.530192i | \(0.177880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.4245i | 0.0444690i |
(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 | 960.3.bg.i.193.2 | 4 | ||
4.3 | odd | 2 | 960.3.bg.h.193.1 | 4 | |||
5.2 | odd | 4 | inner | 960.3.bg.i.577.2 | 4 | ||
8.3 | odd | 2 | 240.3.bg.a.193.2 | 4 | |||
8.5 | even | 2 | 15.3.f.a.13.2 | yes | 4 | ||
20.7 | even | 4 | 960.3.bg.h.577.1 | 4 | |||
24.5 | odd | 2 | 45.3.g.b.28.1 | 4 | |||
24.11 | even | 2 | 720.3.bh.k.433.2 | 4 | |||
40.3 | even | 4 | 1200.3.bg.k.1057.1 | 4 | |||
40.13 | odd | 4 | 75.3.f.c.7.1 | 4 | |||
40.19 | odd | 2 | 1200.3.bg.k.193.1 | 4 | |||
40.27 | even | 4 | 240.3.bg.a.97.2 | 4 | |||
40.29 | even | 2 | 75.3.f.c.43.1 | 4 | |||
40.37 | odd | 4 | 15.3.f.a.7.2 | ✓ | 4 | ||
72.5 | odd | 6 | 405.3.l.f.298.1 | 8 | |||
72.13 | even | 6 | 405.3.l.h.298.2 | 8 | |||
72.29 | odd | 6 | 405.3.l.f.28.2 | 8 | |||
72.61 | even | 6 | 405.3.l.h.28.1 | 8 | |||
120.29 | odd | 2 | 225.3.g.a.118.2 | 4 | |||
120.53 | even | 4 | 225.3.g.a.82.2 | 4 | |||
120.77 | even | 4 | 45.3.g.b.37.1 | 4 | |||
120.107 | odd | 4 | 720.3.bh.k.577.2 | 4 | |||
360.77 | even | 12 | 405.3.l.f.217.2 | 8 | |||
360.157 | odd | 12 | 405.3.l.h.217.1 | 8 | |||
360.277 | odd | 12 | 405.3.l.h.352.2 | 8 | |||
360.317 | even | 12 | 405.3.l.f.352.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.f.a.7.2 | ✓ | 4 | 40.37 | odd | 4 | ||
15.3.f.a.13.2 | yes | 4 | 8.5 | even | 2 | ||
45.3.g.b.28.1 | 4 | 24.5 | odd | 2 | |||
45.3.g.b.37.1 | 4 | 120.77 | even | 4 | |||
75.3.f.c.7.1 | 4 | 40.13 | odd | 4 | |||
75.3.f.c.43.1 | 4 | 40.29 | even | 2 | |||
225.3.g.a.82.2 | 4 | 120.53 | even | 4 | |||
225.3.g.a.118.2 | 4 | 120.29 | odd | 2 | |||
240.3.bg.a.97.2 | 4 | 40.27 | even | 4 | |||
240.3.bg.a.193.2 | 4 | 8.3 | odd | 2 | |||
405.3.l.f.28.2 | 8 | 72.29 | odd | 6 | |||
405.3.l.f.217.2 | 8 | 360.77 | even | 12 | |||
405.3.l.f.298.1 | 8 | 72.5 | odd | 6 | |||
405.3.l.f.352.1 | 8 | 360.317 | even | 12 | |||
405.3.l.h.28.1 | 8 | 72.61 | even | 6 | |||
405.3.l.h.217.1 | 8 | 360.157 | odd | 12 | |||
405.3.l.h.298.2 | 8 | 72.13 | even | 6 | |||
405.3.l.h.352.2 | 8 | 360.277 | odd | 12 | |||
720.3.bh.k.433.2 | 4 | 24.11 | even | 2 | |||
720.3.bh.k.577.2 | 4 | 120.107 | odd | 4 | |||
960.3.bg.h.193.1 | 4 | 4.3 | odd | 2 | |||
960.3.bg.h.577.1 | 4 | 20.7 | even | 4 | |||
960.3.bg.i.193.2 | 4 | 1.1 | even | 1 | trivial | ||
960.3.bg.i.577.2 | 4 | 5.2 | odd | 4 | inner | ||
1200.3.bg.k.193.1 | 4 | 40.19 | odd | 2 | |||
1200.3.bg.k.1057.1 | 4 | 40.3 | even | 4 |