Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(97,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.f (of order \(2\), degree \(1\), 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: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.97 |
Dual form | 2352.3.f.b.97.1 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.46410i | 0.692820i | 0.938083 | + | 0.346410i | \(0.112599\pi\) | ||||
−0.938083 | + | 0.346410i | \(0.887401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.0000 | −0.909091 | −0.454545 | − | 0.890724i | \(-0.650198\pi\) | ||||
−0.454545 | + | 0.890724i | \(0.650198\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 12.1244i | − 0.932643i | −0.884615 | − | 0.466321i | \(-0.845579\pi\) | ||||
0.884615 | − | 0.466321i | \(-0.154421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.00000 | −0.400000 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.92820i | − 0.407541i | −0.979019 | − | 0.203771i | \(-0.934680\pi\) | ||||
0.979019 | − | 0.203771i | \(-0.0653197\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.9090i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −40.0000 | −1.73913 | −0.869565 | − | 0.493818i | \(-0.835601\pi\) | ||||
−0.869565 | + | 0.493818i | \(0.835601\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.0000 | 0.520000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.0000 | 0.551724 | 0.275862 | − | 0.961197i | \(-0.411037\pi\) | ||||
0.275862 | + | 0.961197i | \(0.411037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 5.19615i | − 0.167618i | −0.996482 | − | 0.0838089i | \(-0.973291\pi\) | ||||
0.996482 | − | 0.0838089i | \(-0.0267085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 17.3205i | − 0.524864i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.135135 | 0.0675676 | − | 0.997715i | \(-0.478476\pi\) | ||||
0.0675676 | + | 0.997715i | \(0.478476\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 21.0000 | 0.538462 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 24.2487i | − 0.591432i | −0.955276 | − | 0.295716i | \(-0.904442\pi\) | ||||
0.955276 | − | 0.295716i | \(-0.0955582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.0000 | 0.441860 | 0.220930 | − | 0.975290i | \(-0.429091\pi\) | ||||
0.220930 | + | 0.975290i | \(0.429091\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 10.3923i | − 0.230940i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 51.9615i | − 1.10556i | −0.833326 | − | 0.552782i | \(-0.813566\pi\) | ||||
0.833326 | − | 0.552782i | \(-0.186434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0000 | 0.235294 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −32.0000 | −0.603774 | −0.301887 | − | 0.953344i | \(-0.597616\pi\) | ||||
−0.301887 | + | 0.953344i | \(0.597616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 34.6410i | − 0.629837i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −57.0000 | −1.00000 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 41.5692i | − 0.704563i | −0.935894 | − | 0.352282i | \(-0.885406\pi\) | ||||
0.935894 | − | 0.352282i | \(-0.114594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 20.7846i | − 0.340731i | −0.985381 | − | 0.170366i | \(-0.945505\pi\) | ||||
0.985381 | − | 0.170366i | \(-0.0544949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 42.0000 | 0.646154 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −59.0000 | −0.880597 | −0.440299 | − | 0.897851i | \(-0.645127\pi\) | ||||
−0.440299 | + | 0.897851i | \(0.645127\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 69.2820i | − 1.00409i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 26.0000 | 0.366197 | 0.183099 | − | 0.983095i | \(-0.441387\pi\) | ||||
0.183099 | + | 0.983095i | \(0.441387\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 19.0526i | − 0.260994i | −0.991449 | − | 0.130497i | \(-0.958343\pi\) | ||||
0.991449 | − | 0.130497i | \(-0.0416573\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.5167i | 0.300222i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −47.0000 | −0.594937 | −0.297468 | − | 0.954732i | \(-0.596142\pi\) | ||||
−0.297468 | + | 0.954732i | \(0.596142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 24.2487i | − 0.292153i | −0.989273 | − | 0.146077i | \(-0.953335\pi\) | ||||
0.989273 | − | 0.146077i | \(-0.0466646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.0000 | 0.282353 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 27.7128i | 0.318538i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 117.779i | − 1.32336i | −0.749784 | − | 0.661682i | \(-0.769843\pi\) | ||||
0.749784 | − | 0.661682i | \(-0.230157\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.00000 | 0.0967742 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −114.000 | −1.20000 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 48.4974i | 0.499973i | 0.968249 | + | 0.249987i | \(0.0804263\pi\) | ||||
−0.968249 | + | 0.249987i | \(0.919574\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 30.0000 | 0.303030 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 128.172i | − 1.26903i | −0.772912 | − | 0.634514i | \(-0.781200\pi\) | ||||
0.772912 | − | 0.634514i | \(-0.218800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.66025i | 0.0840801i | 0.999116 | + | 0.0420401i | \(0.0133857\pi\) | ||||
−0.999116 | + | 0.0420401i | \(0.986614\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 212.000 | 1.98131 | 0.990654 | − | 0.136397i | \(-0.0435524\pi\) | ||||
0.990654 | + | 0.136397i | \(0.0435524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0000 | 0.155963 | 0.0779817 | − | 0.996955i | \(-0.475152\pi\) | ||||
0.0779817 | + | 0.996955i | \(0.475152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.66025i | 0.0780203i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 142.000 | 1.25664 | 0.628319 | − | 0.777956i | \(-0.283743\pi\) | ||||
0.628319 | + | 0.777956i | \(0.283743\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 138.564i | − 1.20490i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 36.3731i | 0.310881i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −0.173554 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 42.0000 | 0.341463 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 131.636i | 1.05309i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 145.000 | 1.14173 | 0.570866 | − | 0.821043i | \(-0.306608\pi\) | ||||
0.570866 | + | 0.821043i | \(0.306608\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 32.9090i | 0.255108i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 148.956i | − 1.13707i | −0.822659 | − | 0.568536i | \(-0.807510\pi\) | ||||
0.822659 | − | 0.568536i | \(-0.192490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.0000 | 0.133333 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −116.000 | −0.846715 | −0.423358 | − | 0.905963i | \(-0.639149\pi\) | ||||
−0.423358 | + | 0.905963i | \(0.639149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 84.8705i | 0.610579i | 0.952260 | + | 0.305290i | \(0.0987532\pi\) | ||||
−0.952260 | + | 0.305290i | \(0.901247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 90.0000 | 0.638298 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 121.244i | 0.847857i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 55.4256i | 0.382246i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 124.000 | 0.832215 | 0.416107 | − | 0.909315i | \(-0.363394\pi\) | ||||
0.416107 | + | 0.909315i | \(0.363394\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 46.0000 | 0.304636 | 0.152318 | − | 0.988332i | \(-0.451326\pi\) | ||||
0.152318 | + | 0.988332i | \(0.451326\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.7846i | 0.135847i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.0000 | 0.116129 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 187.061i | 1.19147i | 0.803179 | + | 0.595737i | \(0.203140\pi\) | ||||
−0.803179 | + | 0.595737i | \(0.796860\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 55.4256i | − 0.348589i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 58.0000 | 0.355828 | 0.177914 | − | 0.984046i | \(-0.443065\pi\) | ||||
0.177914 | + | 0.984046i | \(0.443065\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 60.0000 | 0.363636 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 266.736i | − 1.59722i | −0.601849 | − | 0.798610i | \(-0.705569\pi\) | ||||
0.601849 | − | 0.798610i | \(-0.294431\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.0000 | 0.130178 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 98.7269i | − 0.577350i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 124.708i | 0.720854i | 0.932788 | + | 0.360427i | \(0.117369\pi\) | ||||
−0.932788 | + | 0.360427i | \(0.882631\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 72.0000 | 0.406780 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0000 | −0.0558659 | −0.0279330 | − | 0.999610i | \(-0.508892\pi\) | ||||
−0.0279330 | + | 0.999610i | \(0.508892\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 327.358i | − 1.80861i | −0.426892 | − | 0.904303i | \(-0.640391\pi\) | ||||
0.426892 | − | 0.904303i | \(-0.359609\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 36.0000 | 0.196721 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.3205i | 0.0936244i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 69.2820i | 0.370492i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.00000 | 0.0104712 | 0.00523560 | − | 0.999986i | \(-0.498333\pi\) | ||||
0.00523560 | + | 0.999986i | \(0.498333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −235.000 | −1.21762 | −0.608808 | − | 0.793317i | \(-0.708352\pi\) | ||||
−0.608808 | + | 0.793317i | \(0.708352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 72.7461i | 0.373057i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 100.000 | 0.507614 | 0.253807 | − | 0.967255i | \(-0.418317\pi\) | ||||
0.253807 | + | 0.967255i | \(0.418317\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 200.918i | 1.00964i | 0.863225 | + | 0.504819i | \(0.168441\pi\) | ||||
−0.863225 | + | 0.504819i | \(0.831559\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 102.191i | − 0.508413i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 84.0000 | 0.409756 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 120.000 | 0.579710 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 329.090i | − 1.57459i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.00000 | −0.00947867 | −0.00473934 | − | 0.999989i | \(-0.501509\pi\) | ||||
−0.00473934 | + | 0.999989i | \(0.501509\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 45.0333i | 0.211424i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 65.8179i | 0.306130i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 33.0000 | 0.150685 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −84.0000 | −0.380090 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 339.482i | − 1.52234i | −0.648552 | − | 0.761170i | \(-0.724625\pi\) | ||||
0.648552 | − | 0.761170i | \(-0.275375\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −39.0000 | −0.173333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 162.813i | − 0.717237i | −0.933484 | − | 0.358618i | \(-0.883248\pi\) | ||||
0.933484 | − | 0.358618i | \(-0.116752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 8.66025i | − 0.0378177i | −0.999821 | − | 0.0189089i | \(-0.993981\pi\) | ||||
0.999821 | − | 0.0189089i | \(-0.00601923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −170.000 | −0.729614 | −0.364807 | − | 0.931083i | \(-0.618865\pi\) | ||||
−0.364807 | + | 0.931083i | \(0.618865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 180.000 | 0.765957 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 81.4064i | − 0.343487i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −142.000 | −0.594142 | −0.297071 | − | 0.954855i | \(-0.596010\pi\) | ||||
−0.297071 | + | 0.954855i | \(0.596010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 152.420i | − 0.632450i | −0.948684 | − | 0.316225i | \(-0.897585\pi\) | ||||
0.948684 | − | 0.316225i | \(-0.102415\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 399.000 | 1.61538 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 42.0000 | 0.168675 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 290.985i | − 1.15930i | −0.814865 | − | 0.579650i | \(-0.803189\pi\) | ||||
0.814865 | − | 0.579650i | \(-0.196811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 400.000 | 1.58103 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 41.5692i | 0.163017i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 439.941i | 1.71183i | 0.517115 | + | 0.855916i | \(0.327006\pi\) | ||||
−0.517115 | + | 0.855916i | \(0.672994\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −48.0000 | −0.183908 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −136.000 | −0.517110 | −0.258555 | − | 0.965997i | \(-0.583246\pi\) | ||||
−0.258555 | + | 0.965997i | \(0.583246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 110.851i | − 0.418307i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 204.000 | 0.764045 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 225.167i | − 0.837051i | −0.908205 | − | 0.418525i | \(-0.862547\pi\) | ||||
0.908205 | − | 0.418525i | \(-0.137453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 367.195i | − 1.35496i | −0.735540 | − | 0.677481i | \(-0.763072\pi\) | ||||
0.735540 | − | 0.677481i | \(-0.236928\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −130.000 | −0.472727 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 395.000 | 1.42599 | 0.712996 | − | 0.701168i | \(-0.247338\pi\) | ||||
0.712996 | + | 0.701168i | \(0.247338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.5885i | 0.0558726i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 100.000 | 0.355872 | 0.177936 | − | 0.984042i | \(-0.443058\pi\) | ||||
0.177936 | + | 0.984042i | \(0.443058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 358.535i | 1.26691i | 0.773781 | + | 0.633453i | \(0.218363\pi\) | ||||
−0.773781 | + | 0.633453i | \(0.781637\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 197.454i | − 0.692820i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 241.000 | 0.833910 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −84.0000 | −0.288660 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 242.487i | − 0.827601i | −0.910368 | − | 0.413801i | \(-0.864201\pi\) | ||||
0.910368 | − | 0.413801i | \(-0.135799\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 144.000 | 0.488136 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 51.9615i | 0.174955i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 484.974i | 1.62199i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 222.000 | 0.732673 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 72.0000 | 0.236066 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 181.865i | 0.592395i | 0.955127 | + | 0.296198i | \(0.0957187\pi\) | ||||
−0.955127 | + | 0.296198i | \(0.904281\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0000 | −0.0485437 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 550.792i | − 1.77104i | −0.464605 | − | 0.885518i | \(-0.653804\pi\) | ||||
0.464605 | − | 0.885518i | \(-0.346196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 202.650i | − 0.647444i | −0.946152 | − | 0.323722i | \(-0.895066\pi\) | ||||
0.946152 | − | 0.323722i | \(-0.104934\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 292.000 | 0.921136 | 0.460568 | − | 0.887625i | \(-0.347646\pi\) | ||||
0.460568 | + | 0.887625i | \(0.347646\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −160.000 | −0.501567 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 367.195i | 1.14391i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 228.000 | 0.705882 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 157.617i | − 0.484974i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.4449i | 0.0900455i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | −0.0151057 | −0.00755287 | − | 0.999971i | \(-0.502404\pi\) | ||||
−0.00755287 | + | 0.999971i | \(0.502404\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.0000 | −0.0450450 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 204.382i | − 0.610096i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −439.000 | −1.30267 | −0.651335 | − | 0.758790i | \(-0.725791\pi\) | ||||
−0.651335 | + | 0.758790i | \(0.725791\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 245.951i | 0.725520i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51.9615i | 0.152380i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 240.000 | 0.695652 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −220.000 | −0.634006 | −0.317003 | − | 0.948425i | \(-0.602676\pi\) | ||||
−0.317003 | + | 0.948425i | \(0.602676\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 339.482i | 0.972728i | 0.873756 | + | 0.486364i | \(0.161677\pi\) | ||||
−0.873756 | + | 0.486364i | \(0.838323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −63.0000 | −0.179487 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 308.305i | 0.873385i | 0.899611 | + | 0.436693i | \(0.143850\pi\) | ||||
−0.899611 | + | 0.436693i | \(0.856150\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 90.0666i | 0.253709i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −292.000 | −0.813370 | −0.406685 | − | 0.913568i | \(-0.633315\pi\) | ||||
−0.406685 | + | 0.913568i | \(0.633315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −722.000 | −2.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 36.3731i | − 0.100201i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 66.0000 | 0.180822 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 538.668i | − 1.46776i | −0.679279 | − | 0.733880i | \(-0.737708\pi\) | ||||
0.679279 | − | 0.733880i | \(-0.262292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 72.7461i | 0.197144i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −205.000 | −0.549598 | −0.274799 | − | 0.961502i | \(-0.588611\pi\) | ||||
−0.274799 | + | 0.961502i | \(0.588611\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −228.000 | −0.608000 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 193.990i | − 0.514562i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 523.000 | 1.37995 | 0.689974 | − | 0.723835i | \(-0.257622\pi\) | ||||
0.689974 | + | 0.723835i | \(0.257622\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 251.147i | 0.659179i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 76.2102i | − 0.198982i | −0.995038 | − | 0.0994912i | \(-0.968278\pi\) | ||||
0.995038 | − | 0.0994912i | \(-0.0317215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −57.0000 | −0.147287 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −74.0000 | −0.190231 | −0.0951157 | − | 0.995466i | \(-0.530322\pi\) | ||||
−0.0951157 | + | 0.995466i | \(0.530322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 277.128i | 0.708768i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 258.000 | 0.656489 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 162.813i | − 0.412184i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 323.894i | − 0.815853i | −0.913015 | − | 0.407926i | \(-0.866252\pi\) | ||||
0.913015 | − | 0.407926i | \(-0.133748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −128.000 | −0.319202 | −0.159601 | − | 0.987182i | \(-0.551021\pi\) | ||||
−0.159601 | + | 0.987182i | \(0.551021\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −63.0000 | −0.156328 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.1769i | 0.0769800i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −50.0000 | −0.122850 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 296.181i | 0.724158i | 0.932147 | + | 0.362079i | \(0.117933\pi\) | ||||
−0.932147 | + | 0.362079i | \(0.882067\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 200.918i | − 0.488851i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 84.0000 | 0.202410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −147.000 | −0.352518 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 412.228i | − 0.983838i | −0.870641 | − | 0.491919i | \(-0.836296\pi\) | ||||
0.870641 | − | 0.491919i | \(-0.163704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 107.000 | 0.254157 | 0.127078 | − | 0.991893i | \(-0.459440\pi\) | ||||
0.127078 | + | 0.991893i | \(0.459440\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 155.885i | 0.368521i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 90.0666i | − 0.211922i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −210.000 | −0.489510 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −262.000 | −0.607889 | −0.303944 | − | 0.952690i | \(-0.598304\pi\) | ||||
−0.303944 | + | 0.952690i | \(0.598304\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.3731i | 0.0840025i | 0.999118 | + | 0.0420012i | \(0.0133733\pi\) | ||||
−0.999118 | + | 0.0420012i | \(0.986627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −96.0000 | −0.220690 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1316.36i | − 3.01226i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 311.769i | 0.710180i | 0.934832 | + | 0.355090i | \(0.115550\pi\) | ||||
−0.934832 | + | 0.355090i | \(0.884450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 212.000 | 0.478555 | 0.239278 | − | 0.970951i | \(-0.423089\pi\) | ||||
0.239278 | + | 0.970951i | \(0.423089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 408.000 | 0.916854 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 214.774i | 0.480479i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −782.000 | −1.74165 | −0.870824 | − | 0.491595i | \(-0.836414\pi\) | ||||
−0.870824 | + | 0.491595i | \(0.836414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 242.487i | 0.537665i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 79.6743i | 0.175882i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 677.000 | 1.48140 | 0.740700 | − | 0.671836i | \(-0.234494\pi\) | ||||
0.740700 | + | 0.671836i | \(0.234494\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −36.0000 | −0.0784314 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 484.974i | − 1.05200i | −0.850483 | − | 0.526002i | \(-0.823690\pi\) | ||||
0.850483 | − | 0.526002i | \(-0.176310\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −443.000 | −0.956803 | −0.478402 | − | 0.878141i | \(-0.658784\pi\) | ||||
−0.478402 | + | 0.878141i | \(0.658784\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.1769i | 0.0670471i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 45.0333i | 0.0964311i | 0.998837 | + | 0.0482155i | \(0.0153534\pi\) | ||||
−0.998837 | + | 0.0482155i | \(0.984647\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −324.000 | −0.687898 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −190.000 | −0.401691 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 427.817i | 0.900666i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 96.0000 | 0.201258 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 55.4256i | 0.115711i | 0.998325 | + | 0.0578556i | \(0.0184263\pi\) | ||||
−0.998325 | + | 0.0578556i | \(0.981574\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 60.6218i | − 0.126033i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −168.000 | −0.346392 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 67.0000 | 0.137577 | 0.0687885 | − | 0.997631i | \(-0.478087\pi\) | ||||
0.0687885 | + | 0.997631i | \(0.478087\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 100.459i | 0.205438i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 68.0000 | 0.138493 | 0.0692464 | − | 0.997600i | \(-0.477941\pi\) | ||||
0.0692464 | + | 0.997600i | \(0.477941\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 110.851i | − 0.224850i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 103.923i | 0.209946i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −509.000 | −1.02004 | −0.510020 | − | 0.860163i | \(-0.670362\pi\) | ||||
−0.510020 | + | 0.860163i | \(0.670362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 462.000 | 0.922156 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 654.715i | 1.30162i | 0.759240 | + | 0.650810i | \(0.225571\pi\) | ||||
−0.759240 | + | 0.650810i | \(0.774429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 444.000 | 0.879208 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.1051i | 0.0751580i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 869.490i | − 1.70823i | −0.520083 | − | 0.854115i | \(-0.674099\pi\) | ||||
0.520083 | − | 0.854115i | \(-0.325901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 171.000 | 0.333333 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −30.0000 | −0.0582524 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 519.615i | 1.00506i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −216.000 | −0.416185 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 429.549i | 0.824469i | 0.911078 | + | 0.412235i | \(0.135252\pi\) | ||||
−0.911078 | + | 0.412235i | \(0.864748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 985.537i | − 1.88439i | −0.335063 | − | 0.942196i | \(-0.608757\pi\) | ||||
0.335063 | − | 0.942196i | \(-0.391243\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.0000 | −0.0683112 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1071.00 | 2.02457 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 124.708i | 0.234854i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −294.000 | −0.551595 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 734.390i | 1.37269i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 17.3205i | − 0.0322542i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −121.000 | −0.223660 | −0.111830 | − | 0.993727i | \(-0.535671\pi\) | ||||
−0.111830 | + | 0.993727i | \(0.535671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 567.000 | 1.04420 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 58.8897i | 0.108055i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −926.000 | −1.69287 | −0.846435 | − | 0.532492i | \(-0.821256\pi\) | ||||
−0.846435 | + | 0.532492i | \(0.821256\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 62.3538i | 0.113577i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 526.543i | 0.955614i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.0000 | −0.0540541 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −662.000 | −1.18851 | −0.594255 | − | 0.804277i | \(-0.702553\pi\) | ||||
−0.594255 | + | 0.804277i | \(0.702553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 230.363i | − 0.412098i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −120.000 | −0.213904 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 322.161i | 0.572223i | 0.958196 | + | 0.286111i | \(0.0923627\pi\) | ||||
−0.958196 | + | 0.286111i | \(0.907637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 491.902i | 0.870624i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −758.000 | −1.33216 | −0.666081 | − | 0.745880i | \(-0.732029\pi\) | ||||
−0.666081 | + | 0.745880i | \(0.732029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 865.000 | 1.51489 | 0.757443 | − | 0.652901i | \(-0.226448\pi\) | ||||
0.757443 | + | 0.652901i | \(0.226448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.46410i | 0.00604555i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −520.000 | −0.904348 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1072.14i | 1.85813i | 0.369920 | + | 0.929064i | \(0.379385\pi\) | ||||
−0.369920 | + | 0.929064i | \(0.620615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 407.032i | − 0.702991i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 320.000 | 0.548885 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −126.000 | −0.215385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 339.482i | 0.578334i | 0.957279 | + | 0.289167i | \(0.0933783\pi\) | ||||
−0.957279 | + | 0.289167i | \(0.906622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 171.000 | 0.290323 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 173.205i | 0.293071i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 245.951i | 0.414758i | 0.978261 | + | 0.207379i | \(0.0664933\pi\) | ||||
−0.978261 | + | 0.207379i | \(0.933507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −348.000 | −0.582915 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 284.000 | 0.474124 | 0.237062 | − | 0.971495i | \(-0.423816\pi\) | ||||
0.237062 | + | 0.971495i | \(0.423816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 594.093i | 0.988508i | 0.869317 | + | 0.494254i | \(0.164559\pi\) | ||||
−0.869317 | + | 0.494254i | \(0.835441\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 177.000 | 0.293532 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 72.7461i | − 0.120242i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.66025i | 0.0142673i | 0.999975 | + | 0.00713365i | \(0.00227073\pi\) | ||||
−0.999975 | + | 0.00713365i | \(0.997729\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −630.000 | −1.03110 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 878.000 | 1.43230 | 0.716150 | − | 0.697946i | \(-0.245903\pi\) | ||||
0.716150 | + | 0.697946i | \(0.245903\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 145.492i | 0.236573i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −194.000 | −0.314425 | −0.157212 | − | 0.987565i | \(-0.550251\pi\) | ||||
−0.157212 | + | 0.987565i | \(0.550251\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 611.414i | − 0.987745i | −0.869534 | − | 0.493872i | \(-0.835581\pi\) | ||||
0.869534 | − | 0.493872i | \(-0.164419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 207.846i | 0.334696i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −131.000 | −0.209600 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 570.000 | 0.909091 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 34.6410i | − 0.0550732i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 250.000 | 0.396197 | 0.198098 | − | 0.980182i | \(-0.436523\pi\) | ||||
0.198098 | + | 0.980182i | \(0.436523\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 3.46410i | − 0.00547251i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 502.295i | 0.791015i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −78.0000 | −0.122066 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1124.00 | −1.75351 | −0.876755 | − | 0.480937i | \(-0.840297\pi\) | ||||
−0.876755 | + | 0.480937i | \(0.840297\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 569.845i | − 0.886228i | −0.896465 | − | 0.443114i | \(-0.853874\pi\) | ||||
0.896465 | − | 0.443114i | \(-0.146126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −114.000 | −0.176744 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1084.26i | − 1.67583i | −0.545799 | − | 0.837916i | \(-0.683774\pi\) | ||||
0.545799 | − | 0.837916i | \(-0.316226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 415.692i | 0.640512i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1010.00 | −1.54671 | −0.773354 | − | 0.633975i | \(-0.781422\pi\) | ||||
−0.773354 | + | 0.633975i | \(0.781422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 516.000 | 0.787786 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 57.1577i | 0.0869980i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 908.000 | 1.37785 | 0.688923 | − | 0.724835i | \(-0.258084\pi\) | ||||
0.688923 | + | 0.724835i | \(0.258084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 722.265i | − 1.09269i | −0.837562 | − | 0.546343i | \(-0.816020\pi\) | ||||
0.837562 | − | 0.546343i | \(-0.183980\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 145.492i | − 0.219445i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −640.000 | −0.959520 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 588.000 | 0.878924 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 207.846i | 0.309756i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1027.00 | −1.52600 | −0.763001 | − | 0.646397i | \(-0.776275\pi\) | ||||
−0.763001 | + | 0.646397i | \(0.776275\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 67.5500i | − 0.100074i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 561.184i | 0.828928i | 0.910066 | + | 0.414464i | \(0.136031\pi\) | ||||
−0.910066 | + | 0.414464i | \(0.863969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 282.000 | 0.414097 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −976.000 | −1.42899 | −0.714495 | − | 0.699641i | \(-0.753343\pi\) | ||||
−0.714495 | + | 0.699641i | \(0.753343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 401.836i | − 0.586622i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.0000 | 0.0218341 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 387.979i | 0.563105i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 566.381i | 0.819654i | 0.912163 | + | 0.409827i | \(0.134411\pi\) | ||||
−0.912163 | + | 0.409827i | \(0.865589\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −294.000 | −0.423022 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −168.000 | −0.241033 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 294.449i | − 0.421243i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 352.000 | 0.502140 | 0.251070 | − | 0.967969i | \(-0.419218\pi\) | ||||
0.251070 | + | 0.967969i | \(0.419218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 164.545i | 0.234061i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 311.769i | 0.442226i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1150.00 | −1.62200 | −0.811001 | − | 0.585044i | \(-0.801077\pi\) | ||||
−0.811001 | + | 0.585044i | \(0.801077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 141.000 | 0.198312 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 207.846i | 0.291509i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −420.000 | −0.587413 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 245.951i | − 0.343028i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 973.413i | − 1.35384i | −0.736056 | − | 0.676921i | \(-0.763314\pi\) | ||||
0.736056 | − | 0.676921i | \(-0.236686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 264.000 | 0.365145 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 208.000 | 0.286897 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 206.114i | 0.283513i | 0.989902 | + | 0.141757i | \(0.0452750\pi\) | ||||
−0.989902 | + | 0.141757i | \(0.954725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 131.636i | − 0.180076i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1245.34i | − 1.69897i | −0.527613 | − | 0.849485i | \(-0.676913\pi\) | ||||
0.527613 | − | 0.849485i | \(-0.323087\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 590.000 | 0.800543 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −311.000 | −0.420839 | −0.210419 | − | 0.977611i | \(-0.567483\pi\) | ||||
−0.210419 | + | 0.977611i | \(0.567483\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 691.088i | 0.932643i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −394.000 | −0.530283 | −0.265141 | − | 0.964210i | \(-0.585419\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 429.549i | 0.576575i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 72.7461i | 0.0973844i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 79.0000 | 0.105193 | 0.0525965 | − | 0.998616i | \(-0.483250\pi\) | ||||
0.0525965 | + | 0.998616i | \(0.483250\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 504.000 | 0.669323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 159.349i | 0.211058i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −250.000 | −0.330251 | −0.165125 | − | 0.986273i | \(-0.552803\pi\) | ||||
−0.165125 | + | 0.986273i | \(0.552803\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 692.820i | 0.912807i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 949.164i | 1.24726i | 0.781720 | + | 0.623629i | \(0.214343\pi\) | ||||
−0.781720 | + | 0.623629i | \(0.785657\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −72.0000 | −0.0941176 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −504.000 | −0.657106 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 860.829i | 1.11941i | 0.828691 | + | 0.559707i | \(0.189086\pi\) | ||||
−0.828691 | + | 0.559707i | \(0.810914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −762.000 | −0.988327 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 225.167i | − 0.291289i | −0.989337 | − | 0.145645i | \(-0.953474\pi\) | ||||
0.989337 | − | 0.145645i | \(-0.0465256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 67.5500i | − 0.0871613i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 798.000 | 1.02439 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −260.000 | −0.332907 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 83.1384i | − 0.106179i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −648.000 | −0.825478 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 249.415i | 0.316919i | 0.987365 | + | 0.158460i | \(0.0506527\pi\) | ||||
−0.987365 | + | 0.158460i | \(0.949347\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 235.559i | − 0.298554i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −252.000 | −0.317781 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 192.000 | 0.241509 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1357.93i | 1.70380i | 0.523705 | + | 0.851900i | \(0.324549\pi\) | ||||
−0.523705 | + | 0.851900i | \(0.675451\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −360.000 | −0.450563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 353.338i | 0.441122i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 190.526i | 0.237267i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 390.000 | 0.483271 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1418.00 | −1.75278 | −0.876391 | − | 0.481601i | \(-0.840055\pi\) | ||||
−0.876391 | + | 0.481601i | \(0.840055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 872.954i | 1.07639i | 0.842820 | + | 0.538196i | \(0.180894\pi\) | ||||
−0.842820 | + | 0.538196i | \(0.819106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 636.000 | 0.782288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 200.918i | 0.246525i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 625.270i | 0.765325i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 250.000 | 0.304507 | 0.152253 | − | 0.988341i | \(-0.451347\pi\) | ||||
0.152253 | + | 0.988341i | \(0.451347\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −206.000 | −0.250304 | −0.125152 | − | 0.992138i | \(-0.539942\pi\) | ||||
−0.125152 | + | 0.992138i | \(0.539942\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 225.167i | − 0.272929i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1234.00 | −1.49214 | −0.746070 | − | 0.665867i | \(-0.768062\pi\) | ||||
−0.746070 | + | 0.665867i | \(0.768062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 344.678i | 0.415776i | 0.978153 | + | 0.207888i | \(0.0666589\pi\) | ||||
−0.978153 | + | 0.207888i | \(0.933341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 684.160i | 0.823297i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 924.000 | 1.10659 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.0000 | −0.0322581 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 484.974i | 0.578038i | 0.957323 | + | 0.289019i | \(0.0933291\pi\) | ||||
−0.957323 | + | 0.289019i | \(0.906671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −585.000 | −0.695600 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 173.205i | 0.205463i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 76.2102i | 0.0901896i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −621.000 | −0.731449 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −200.000 | −0.235018 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 278.860i | − 0.326917i | −0.986550 | − | 0.163458i | \(-0.947735\pi\) | ||||
0.986550 | − | 0.163458i | \(-0.0522650\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 342.000 | 0.400000 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 637.395i | − 0.743751i | −0.928283 | − | 0.371876i | \(-0.878715\pi\) | ||||
0.928283 | − | 0.371876i | \(-0.121285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 609.682i | − 0.709758i | −0.934912 | − | 0.354879i | \(-0.884522\pi\) | ||||
0.934912 | − | 0.354879i | \(-0.115478\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −670.000 | −0.776362 | −0.388181 | − | 0.921583i | \(-0.626896\pi\) | ||||
−0.388181 | + | 0.921583i | \(0.626896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −432.000 | −0.499422 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 417.424i | 0.481458i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 470.000 | 0.540852 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 715.337i | 0.821282i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 145.492i | − 0.166658i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −394.000 | −0.449259 | −0.224629 | − | 0.974444i | \(-0.572117\pi\) | ||||
−0.224629 | + | 0.974444i | \(0.572117\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 420.000 | 0.477816 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1163.94i | − 1.32116i | −0.750758 | − | 0.660578i | \(-0.770311\pi\) | ||||
0.750758 | − | 0.660578i | \(-0.229689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −737.000 | −0.834655 | −0.417327 | − | 0.908756i | \(-0.637033\pi\) | ||||
−0.417327 | + | 0.908756i | \(0.637033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 249.415i | 0.281825i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 730.925i | − 0.824042i | −0.911174 | − | 0.412021i | \(-0.864823\pi\) | ||||
0.911174 | − | 0.412021i | \(-0.135177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −90.0000 | −0.101010 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1710.00 | 1.91489 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 34.6410i | − 0.0387050i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −840.000 | −0.936455 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 83.1384i | − 0.0924788i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 221.703i | 0.246063i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1134.00 | 1.25304 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 235.000 | 0.259096 | 0.129548 | − | 0.991573i | \(-0.458647\pi\) | ||||
0.129548 | + | 0.991573i | \(0.458647\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 384.515i | 0.423009i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 740.000 | 0.812294 | 0.406147 | − | 0.913808i | \(-0.366872\pi\) | ||||
0.406147 | + | 0.913808i | \(0.366872\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 242.487i | 0.265594i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 124.708i | 0.136293i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1517.00 | −1.65071 | −0.825354 | − | 0.564616i | \(-0.809024\pi\) | ||||
−0.825354 | + | 0.564616i | \(0.809024\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −315.000 | −0.342020 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 315.233i | − 0.341531i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 65.0000 | 0.0702703 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 25.9808i | − 0.0280267i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1111.98i | − 1.19696i | −0.801137 | − | 0.598480i | \(-0.795771\pi\) | ||||
0.801137 | − | 0.598480i | \(-0.204229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 954.000 | 1.02251 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −240.000 | −0.256684 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 836.581i | 0.892829i | 0.894826 | + | 0.446414i | \(0.147299\pi\) | ||||
−0.894826 | + | 0.446414i | \(0.852701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 351.000 | 0.373802 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 394.908i | − 0.419668i | −0.977737 | − | 0.209834i | \(-0.932708\pi\) | ||||
0.977737 | − | 0.209834i | \(-0.0672924\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 969.948i | 1.02858i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 338.000 | 0.356917 | 0.178458 | − | 0.983947i | \(-0.442889\pi\) | ||||
0.178458 | + | 0.983947i | \(0.442889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −231.000 | −0.243414 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 505.759i | 0.531818i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1244.00 | −1.30535 | −0.652676 | − | 0.757637i | \(-0.726354\pi\) | ||||
−0.652676 | + | 0.757637i | \(0.726354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.92820i | 0.00725466i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 277.128i | − 0.289580i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 934.000 | 0.971904 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −636.000 | −0.660436 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 814.064i | − 0.843590i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1741.00 | 1.80041 | 0.900207 | − | 0.435463i | \(-0.143415\pi\) | ||||
0.900207 | + | 0.435463i | \(0.143415\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 394.908i | 0.407541i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1281.72i | 1.32000i | 0.751267 | + | 0.659999i | \(0.229443\pi\) | ||||
−0.751267 | + | 0.659999i | \(0.770557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 273.000 | 0.280000 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 262.000 | 0.268168 | 0.134084 | − | 0.990970i | \(-0.457191\pi\) | ||||
0.134084 | + | 0.990970i | \(0.457191\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1177.79i | 1.20306i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.0000 | −0.0519878 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1108.51i | − 1.12768i | −0.825883 | − | 0.563842i | \(-0.809323\pi\) | ||||
0.825883 | − | 0.563842i | \(-0.190677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 346.410i | 0.351685i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −760.000 | −0.768453 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 67.0000 | 0.0676085 | 0.0338042 | − | 0.999428i | \(-0.489238\pi\) | ||||
0.0338042 | + | 0.999428i | \(0.489238\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 8.66025i | − 0.00872130i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −696.000 | −0.699497 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 989.001i | − 0.991977i | −0.868329 | − | 0.495988i | \(-0.834806\pi\) | ||||
0.868329 | − | 0.495988i | \(-0.165194\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 25.9808i | − 0.0260068i |
(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 | 2352.3.f.b.97.2 | 2 | ||
4.3 | odd | 2 | 147.3.d.a.97.1 | 2 | |||
7.4 | even | 3 | 336.3.bh.c.145.1 | 2 | |||
7.5 | odd | 6 | 336.3.bh.c.241.1 | 2 | |||
7.6 | odd | 2 | inner | 2352.3.f.b.97.1 | 2 | ||
12.11 | even | 2 | 441.3.d.d.244.1 | 2 | |||
21.5 | even | 6 | 1008.3.cg.f.577.1 | 2 | |||
21.11 | odd | 6 | 1008.3.cg.f.145.1 | 2 | |||
28.3 | even | 6 | 147.3.f.e.19.1 | 2 | |||
28.11 | odd | 6 | 21.3.f.c.19.1 | yes | 2 | ||
28.19 | even | 6 | 21.3.f.c.10.1 | ✓ | 2 | ||
28.23 | odd | 6 | 147.3.f.e.31.1 | 2 | |||
28.27 | even | 2 | 147.3.d.a.97.2 | 2 | |||
84.11 | even | 6 | 63.3.m.a.19.1 | 2 | |||
84.23 | even | 6 | 441.3.m.b.325.1 | 2 | |||
84.47 | odd | 6 | 63.3.m.a.10.1 | 2 | |||
84.59 | odd | 6 | 441.3.m.b.19.1 | 2 | |||
84.83 | odd | 2 | 441.3.d.d.244.2 | 2 | |||
140.19 | even | 6 | 525.3.o.b.451.1 | 2 | |||
140.39 | odd | 6 | 525.3.o.b.376.1 | 2 | |||
140.47 | odd | 12 | 525.3.s.d.199.1 | 4 | |||
140.67 | even | 12 | 525.3.s.d.124.2 | 4 | |||
140.103 | odd | 12 | 525.3.s.d.199.2 | 4 | |||
140.123 | even | 12 | 525.3.s.d.124.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.c.10.1 | ✓ | 2 | 28.19 | even | 6 | ||
21.3.f.c.19.1 | yes | 2 | 28.11 | odd | 6 | ||
63.3.m.a.10.1 | 2 | 84.47 | odd | 6 | |||
63.3.m.a.19.1 | 2 | 84.11 | even | 6 | |||
147.3.d.a.97.1 | 2 | 4.3 | odd | 2 | |||
147.3.d.a.97.2 | 2 | 28.27 | even | 2 | |||
147.3.f.e.19.1 | 2 | 28.3 | even | 6 | |||
147.3.f.e.31.1 | 2 | 28.23 | odd | 6 | |||
336.3.bh.c.145.1 | 2 | 7.4 | even | 3 | |||
336.3.bh.c.241.1 | 2 | 7.5 | odd | 6 | |||
441.3.d.d.244.1 | 2 | 12.11 | even | 2 | |||
441.3.d.d.244.2 | 2 | 84.83 | odd | 2 | |||
441.3.m.b.19.1 | 2 | 84.59 | odd | 6 | |||
441.3.m.b.325.1 | 2 | 84.23 | even | 6 | |||
525.3.o.b.376.1 | 2 | 140.39 | odd | 6 | |||
525.3.o.b.451.1 | 2 | 140.19 | even | 6 | |||
525.3.s.d.124.1 | 4 | 140.123 | even | 12 | |||
525.3.s.d.124.2 | 4 | 140.67 | even | 12 | |||
525.3.s.d.199.1 | 4 | 140.47 | odd | 12 | |||
525.3.s.d.199.2 | 4 | 140.103 | odd | 12 | |||
1008.3.cg.f.145.1 | 2 | 21.11 | odd | 6 | |||
1008.3.cg.f.577.1 | 2 | 21.5 | even | 6 | |||
2352.3.f.b.97.1 | 2 | 7.6 | odd | 2 | inner | ||
2352.3.f.b.97.2 | 2 | 1.1 | even | 1 | trivial |