Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.a (trivial) |
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: | yes |
Analytic conductor: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.438447 | −0.155014 | −0.0775072 | − | 0.996992i | \(-0.524696\pi\) | ||||
−0.0775072 | + | 0.996992i | \(0.524696\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.80776 | −0.975971 | ||||||||
\(5\) | −17.8078 | −1.59277 | −0.796387 | − | 0.604787i | \(-0.793258\pi\) | ||||
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.43845 | −0.293649 | −0.146824 | − | 0.989163i | \(-0.546905\pi\) | ||||
−0.146824 | + | 0.989163i | \(0.546905\pi\) | |||||||
\(8\) | 6.93087 | 0.306304 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.80776 | 0.246903 | ||||||||
\(11\) | −22.4233 | −0.614625 | −0.307313 | − | 0.951609i | \(-0.599430\pi\) | ||||
−0.307313 | + | 0.951609i | \(0.599430\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.38447 | 0.0455198 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 59.4233 | 0.928489 | ||||||||
\(17\) | −67.9848 | −0.969926 | −0.484963 | − | 0.874535i | \(-0.661167\pi\) | ||||
−0.484963 | + | 0.874535i | \(0.661167\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 80.8078 | 0.975714 | 0.487857 | − | 0.872923i | \(-0.337779\pi\) | ||||
0.487857 | + | 0.872923i | \(0.337779\pi\) | |||||||
\(20\) | 139.039 | 1.55450 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.83143 | 0.0952758 | ||||||||
\(23\) | −140.531 | −1.27403 | −0.637017 | − | 0.770850i | \(-0.719832\pi\) | ||||
−0.637017 | + | 0.770850i | \(0.719832\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 192.116 | 1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 42.4621 | 0.286592 | ||||||||
\(29\) | 106.693 | 0.683187 | 0.341594 | − | 0.939848i | \(-0.389033\pi\) | ||||
0.341594 | + | 0.939848i | \(0.389033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 276.155 | 1.59997 | 0.799983 | − | 0.600023i | \(-0.204842\pi\) | ||||
0.799983 | + | 0.600023i | \(0.204842\pi\) | |||||||
\(32\) | −81.5009 | −0.450233 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 29.8078 | 0.150353 | ||||||||
\(35\) | 96.8466 | 0.467716 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.29168 | 0.0190688 | 0.00953442 | − | 0.999955i | \(-0.496965\pi\) | ||||
0.00953442 | + | 0.999955i | \(0.496965\pi\) | |||||||
\(38\) | −35.4299 | −0.151250 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −123.423 | −0.487873 | ||||||||
\(41\) | 227.769 | 0.867598 | 0.433799 | − | 0.901010i | \(-0.357173\pi\) | ||||
0.433799 | + | 0.901010i | \(0.357173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.5294 | 0.0976323 | 0.0488162 | − | 0.998808i | \(-0.484455\pi\) | ||||
0.0488162 | + | 0.998808i | \(0.484455\pi\) | |||||||
\(44\) | 175.076 | 0.599856 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 61.6155 | 0.197494 | ||||||||
\(47\) | 318.617 | 0.988832 | 0.494416 | − | 0.869225i | \(-0.335382\pi\) | ||||
0.494416 | + | 0.869225i | \(0.335382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −313.423 | −0.913771 | ||||||||
\(50\) | −84.2329 | −0.238247 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 67.6562 | 0.175345 | 0.0876726 | − | 0.996149i | \(-0.472057\pi\) | ||||
0.0876726 | + | 0.996149i | \(0.472057\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 399.309 | 0.978960 | ||||||||
\(56\) | −37.6932 | −0.0899457 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −46.7793 | −0.105904 | ||||||||
\(59\) | −291.115 | −0.642371 | −0.321186 | − | 0.947016i | \(-0.604081\pi\) | ||||
−0.321186 | + | 0.947016i | \(0.604081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 663.311 | 1.39227 | 0.696133 | − | 0.717913i | \(-0.254902\pi\) | ||||
0.696133 | + | 0.717913i | \(0.254902\pi\) | |||||||
\(62\) | −121.080 | −0.248018 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −439.652 | −0.858696 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 425.101 | 0.775140 | 0.387570 | − | 0.921840i | \(-0.373315\pi\) | ||||
0.387570 | + | 0.921840i | \(0.373315\pi\) | |||||||
\(68\) | 530.810 | 0.946619 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −42.4621 | −0.0725028 | ||||||||
\(71\) | −152.963 | −0.255681 | −0.127841 | − | 0.991795i | \(-0.540805\pi\) | ||||
−0.127841 | + | 0.991795i | \(0.540805\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −117.268 | −0.188016 | −0.0940081 | − | 0.995571i | \(-0.529968\pi\) | ||||
−0.0940081 | + | 0.995571i | \(0.529968\pi\) | |||||||
\(74\) | −1.88167 | −0.00295595 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −630.928 | −0.952268 | ||||||||
\(77\) | 121.948 | 0.180484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 202.462 | 0.288339 | 0.144169 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144169 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(80\) | −1058.20 | −1.47887 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −99.8647 | −0.134490 | ||||||||
\(83\) | 336.155 | 0.444552 | 0.222276 | − | 0.974984i | \(-0.428651\pi\) | ||||
0.222276 | + | 0.974984i | \(0.428651\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1210.66 | 1.54487 | ||||||||
\(86\) | −12.0702 | −0.0151344 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −155.413 | −0.188262 | ||||||||
\(89\) | 718.194 | 0.855376 | 0.427688 | − | 0.903927i | \(-0.359328\pi\) | ||||
0.427688 | + | 0.903927i | \(0.359328\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1097.23 | 1.24342 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −139.697 | −0.153283 | ||||||||
\(95\) | −1439.01 | −1.55409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −759.368 | −0.794868 | −0.397434 | − | 0.917631i | \(-0.630099\pi\) | ||||
−0.397434 | + | 0.917631i | \(0.630099\pi\) | |||||||
\(98\) | 137.420 | 0.141648 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1500.00 | −1.50000 | ||||||||
\(101\) | 348.697 | 0.343531 | 0.171766 | − | 0.985138i | \(-0.445053\pi\) | ||||
0.171766 | + | 0.985138i | \(0.445053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −580.303 | −0.555136 | −0.277568 | − | 0.960706i | \(-0.589528\pi\) | ||||
−0.277568 | + | 0.960706i | \(0.589528\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.6637 | −0.0271810 | ||||||||
\(107\) | −571.493 | −0.516340 | −0.258170 | − | 0.966100i | \(-0.583119\pi\) | ||||
−0.258170 | + | 0.966100i | \(0.583119\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −176.004 | −0.154661 | −0.0773307 | − | 0.997005i | \(-0.524640\pi\) | ||||
−0.0773307 | + | 0.997005i | \(0.524640\pi\) | |||||||
\(110\) | −175.076 | −0.151753 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −323.170 | −0.272649 | ||||||||
\(113\) | −1264.88 | −1.05301 | −0.526505 | − | 0.850172i | \(-0.676498\pi\) | ||||
−0.526505 | + | 0.850172i | \(0.676498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2502.55 | 2.02925 | ||||||||
\(116\) | −833.035 | −0.666770 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 127.638 | 0.0995768 | ||||||||
\(119\) | 369.732 | 0.284817 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −828.196 | −0.622236 | ||||||||
\(122\) | −290.827 | −0.215821 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2156.16 | −1.56152 | ||||||||
\(125\) | −1195.19 | −0.855211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2604.11 | 1.81950 | 0.909752 | − | 0.415151i | \(-0.136271\pi\) | ||||
0.909752 | + | 0.415151i | \(0.136271\pi\) | |||||||
\(128\) | 844.772 | 0.583344 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2131.70 | −1.42174 | −0.710870 | − | 0.703324i | \(-0.751698\pi\) | ||||
−0.710870 | + | 0.703324i | \(0.751698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −439.469 | −0.286517 | ||||||||
\(134\) | −186.384 | −0.120158 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −471.194 | −0.297092 | ||||||||
\(137\) | 687.985 | 0.429040 | 0.214520 | − | 0.976720i | \(-0.431181\pi\) | ||||
0.214520 | + | 0.976720i | \(0.431181\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −679.580 | −0.414685 | −0.207343 | − | 0.978268i | \(-0.566482\pi\) | ||||
−0.207343 | + | 0.978268i | \(0.566482\pi\) | |||||||
\(140\) | −756.155 | −0.456477 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 67.0662 | 0.0396343 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1899.97 | −1.08816 | ||||||||
\(146\) | 51.4158 | 0.0291452 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −33.5084 | −0.0186106 | ||||||||
\(149\) | −1975.46 | −1.08615 | −0.543074 | − | 0.839685i | \(-0.682740\pi\) | ||||
−0.543074 | + | 0.839685i | \(0.682740\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1803.24 | −0.971824 | −0.485912 | − | 0.874008i | \(-0.661513\pi\) | ||||
−0.485912 | + | 0.874008i | \(0.661513\pi\) | |||||||
\(152\) | 560.068 | 0.298865 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −53.4677 | −0.0279776 | ||||||||
\(155\) | −4917.71 | −2.54839 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −397.168 | −0.201894 | −0.100947 | − | 0.994892i | \(-0.532187\pi\) | ||||
−0.100947 | + | 0.994892i | \(0.532187\pi\) | |||||||
\(158\) | −88.7689 | −0.0446967 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1451.35 | 0.717120 | ||||||||
\(161\) | 764.272 | 0.374118 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −941.393 | −0.452365 | −0.226183 | − | 0.974085i | \(-0.572625\pi\) | ||||
−0.226183 | + | 0.974085i | \(0.572625\pi\) | |||||||
\(164\) | −1778.37 | −0.846750 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −147.386 | −0.0689120 | ||||||||
\(167\) | 3680.43 | 1.70539 | 0.852696 | − | 0.522408i | \(-0.174966\pi\) | ||||
0.852696 | + | 0.522408i | \(0.174966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −530.810 | −0.239478 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −214.943 | −0.0952863 | ||||||||
\(173\) | −1422.77 | −0.625269 | −0.312634 | − | 0.949874i | \(-0.601211\pi\) | ||||
−0.312634 | + | 0.949874i | \(0.601211\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1044.82 | −0.451318 | ||||||||
\(176\) | −1332.47 | −0.570673 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −314.890 | −0.132596 | ||||||||
\(179\) | −1167.89 | −0.487666 | −0.243833 | − | 0.969817i | \(-0.578405\pi\) | ||||
−0.243833 | + | 0.969817i | \(0.578405\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1133.96 | −0.465673 | −0.232836 | − | 0.972516i | \(-0.574801\pi\) | ||||
−0.232836 | + | 0.972516i | \(0.574801\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −974.004 | −0.390242 | ||||||||
\(185\) | −76.4252 | −0.0303724 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1524.44 | 0.596141 | ||||||||
\(188\) | −2487.69 | −0.965071 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 630.928 | 0.240907 | ||||||||
\(191\) | −2682.12 | −1.01608 | −0.508040 | − | 0.861333i | \(-0.669630\pi\) | ||||
−0.508040 | + | 0.861333i | \(0.669630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1970.67 | 0.734983 | 0.367491 | − | 0.930027i | \(-0.380217\pi\) | ||||
0.367491 | + | 0.930027i | \(0.380217\pi\) | |||||||
\(194\) | 332.943 | 0.123216 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2447.14 | 0.891813 | ||||||||
\(197\) | −4016.05 | −1.45244 | −0.726222 | − | 0.687460i | \(-0.758726\pi\) | ||||
−0.726222 | + | 0.687460i | \(0.758726\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4226.06 | −1.50541 | −0.752707 | − | 0.658356i | \(-0.771252\pi\) | ||||
−0.752707 | + | 0.658356i | \(0.771252\pi\) | |||||||
\(200\) | 1331.53 | 0.470768 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −152.885 | −0.0532523 | ||||||||
\(203\) | −580.245 | −0.200617 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4056.06 | −1.38189 | ||||||||
\(206\) | 254.432 | 0.0860541 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1811.98 | −0.599699 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1364.67 | 0.445249 | 0.222625 | − | 0.974904i | \(-0.428538\pi\) | ||||
0.222625 | + | 0.974904i | \(0.428538\pi\) | |||||||
\(212\) | −528.244 | −0.171132 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 250.570 | 0.0800401 | ||||||||
\(215\) | −490.237 | −0.155506 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1501.86 | −0.469828 | ||||||||
\(218\) | 77.1683 | 0.0239748 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3117.71 | −0.955436 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1059.47 | 0.318149 | 0.159075 | − | 0.987267i | \(-0.449149\pi\) | ||||
0.159075 | + | 0.987267i | \(0.449149\pi\) | |||||||
\(224\) | 443.239 | 0.132210 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 554.584 | 0.163232 | ||||||||
\(227\) | 3464.19 | 1.01289 | 0.506446 | − | 0.862272i | \(-0.330959\pi\) | ||||
0.506446 | + | 0.862272i | \(0.330959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2324.64 | 0.670815 | 0.335407 | − | 0.942073i | \(-0.391126\pi\) | ||||
0.335407 | + | 0.942073i | \(0.391126\pi\) | |||||||
\(230\) | −1097.23 | −0.314563 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 739.476 | 0.209263 | ||||||||
\(233\) | 3731.01 | 1.04904 | 0.524521 | − | 0.851398i | \(-0.324245\pi\) | ||||
0.524521 | + | 0.851398i | \(0.324245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5673.86 | −1.57499 | ||||||||
\(236\) | 2272.95 | 0.626935 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −162.108 | −0.0441508 | ||||||||
\(239\) | 6044.47 | 1.63592 | 0.817958 | − | 0.575278i | \(-0.195106\pi\) | ||||
0.817958 | + | 0.575278i | \(0.195106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5173.96 | 1.38292 | 0.691461 | − | 0.722414i | \(-0.256967\pi\) | ||||
0.691461 | + | 0.722414i | \(0.256967\pi\) | |||||||
\(242\) | 363.120 | 0.0964556 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5178.97 | −1.35881 | ||||||||
\(245\) | 5581.37 | 1.45543 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1914.00 | 0.490076 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 524.029 | 0.132570 | ||||||||
\(251\) | −5620.73 | −1.41346 | −0.706728 | − | 0.707486i | \(-0.749829\pi\) | ||||
−0.706728 | + | 0.707486i | \(0.749829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3151.17 | 0.783054 | ||||||||
\(254\) | −1141.76 | −0.282050 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3146.83 | 0.768270 | ||||||||
\(257\) | 1674.14 | 0.406342 | 0.203171 | − | 0.979143i | \(-0.434875\pi\) | ||||
0.203171 | + | 0.979143i | \(0.434875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.3401 | −0.00559954 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 934.640 | 0.220390 | ||||||||
\(263\) | 6309.18 | 1.47924 | 0.739622 | − | 0.673023i | \(-0.235004\pi\) | ||||
0.739622 | + | 0.673023i | \(0.235004\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1204.81 | −0.279285 | ||||||||
\(266\) | 192.684 | 0.0444143 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3319.09 | −0.756514 | ||||||||
\(269\) | 2482.73 | 0.562731 | 0.281366 | − | 0.959601i | \(-0.409213\pi\) | ||||
0.281366 | + | 0.959601i | \(0.409213\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2835.72 | −0.635638 | −0.317819 | − | 0.948151i | \(-0.602950\pi\) | ||||
−0.317819 | + | 0.948151i | \(0.602950\pi\) | |||||||
\(272\) | −4039.88 | −0.900566 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −301.645 | −0.0665075 | ||||||||
\(275\) | −4307.88 | −0.944637 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3837.51 | −0.832396 | −0.416198 | − | 0.909274i | \(-0.636638\pi\) | ||||
−0.416198 | + | 0.909274i | \(0.636638\pi\) | |||||||
\(278\) | 297.960 | 0.0642822 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 671.231 | 0.143263 | ||||||||
\(281\) | −9122.13 | −1.93659 | −0.968293 | − | 0.249819i | \(-0.919629\pi\) | ||||
−0.968293 | + | 0.249819i | \(0.919629\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2127.85 | 0.446952 | 0.223476 | − | 0.974709i | \(-0.428260\pi\) | ||||
0.223476 | + | 0.974709i | \(0.428260\pi\) | |||||||
\(284\) | 1194.30 | 0.249537 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1238.71 | −0.254769 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −291.061 | −0.0592430 | ||||||||
\(290\) | 833.035 | 0.168681 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 915.601 | 0.183498 | ||||||||
\(293\) | 8274.77 | 1.64989 | 0.824944 | − | 0.565215i | \(-0.191207\pi\) | ||||
0.824944 | + | 0.565215i | \(0.191207\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5184.10 | 1.02315 | ||||||||
\(296\) | 29.7450 | 0.00584086 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 866.136 | 0.168369 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −149.717 | −0.0286696 | ||||||||
\(302\) | 790.625 | 0.150647 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4801.86 | 0.905940 | ||||||||
\(305\) | −11812.1 | −2.21757 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3610.49 | 0.671211 | 0.335605 | − | 0.942003i | \(-0.391059\pi\) | ||||
0.335605 | + | 0.942003i | \(0.391059\pi\) | |||||||
\(308\) | −952.140 | −0.176147 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2156.16 | 0.395037 | ||||||||
\(311\) | −3331.06 | −0.607354 | −0.303677 | − | 0.952775i | \(-0.598214\pi\) | ||||
−0.303677 | + | 0.952775i | \(0.598214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −358.125 | −0.0646724 | −0.0323362 | − | 0.999477i | \(-0.510295\pi\) | ||||
−0.0323362 | + | 0.999477i | \(0.510295\pi\) | |||||||
\(314\) | 174.137 | 0.0312966 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1580.78 | −0.281410 | ||||||||
\(317\) | 3047.46 | 0.539944 | 0.269972 | − | 0.962868i | \(-0.412986\pi\) | ||||
0.269972 | + | 0.962868i | \(0.412986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2392.41 | −0.419904 | ||||||||
\(320\) | 7829.23 | 1.36771 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −335.093 | −0.0579938 | ||||||||
\(323\) | −5493.70 | −0.946371 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 412.751 | 0.0701232 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1578.64 | 0.265749 | ||||||||
\(329\) | −1732.78 | −0.290369 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7694.77 | −1.27777 | −0.638887 | − | 0.769301i | \(-0.720605\pi\) | ||||
−0.638887 | + | 0.769301i | \(0.720605\pi\) | |||||||
\(332\) | −2624.62 | −0.433870 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1613.68 | −0.264360 | ||||||||
\(335\) | −7570.10 | −1.23462 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4712.21 | 0.761693 | 0.380846 | − | 0.924638i | \(-0.375633\pi\) | ||||
0.380846 | + | 0.924638i | \(0.375633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9452.53 | −1.50775 | ||||||||
\(341\) | −6192.31 | −0.983380 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3569.92 | 0.561976 | ||||||||
\(344\) | 190.803 | 0.0299052 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 623.811 | 0.0969257 | ||||||||
\(347\) | 5261.98 | 0.814058 | 0.407029 | − | 0.913415i | \(-0.366565\pi\) | ||||
0.407029 | + | 0.913415i | \(0.366565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −50.3345 | −0.00772018 | −0.00386009 | − | 0.999993i | \(-0.501229\pi\) | ||||
−0.00386009 | + | 0.999993i | \(0.501229\pi\) | |||||||
\(350\) | 458.096 | 0.0699608 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1827.52 | 0.276725 | ||||||||
\(353\) | 9057.64 | 1.36569 | 0.682846 | − | 0.730562i | \(-0.260742\pi\) | ||||
0.682846 | + | 0.730562i | \(0.260742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2723.93 | 0.407243 | ||||||||
\(356\) | −5607.49 | −0.834821 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 512.059 | 0.0755953 | ||||||||
\(359\) | 7177.86 | 1.05525 | 0.527623 | − | 0.849479i | \(-0.323083\pi\) | ||||
0.527623 | + | 0.849479i | \(0.323083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −329.105 | −0.0479815 | ||||||||
\(362\) | 497.183 | 0.0721861 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2088.28 | 0.299467 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4004.14 | 0.569522 | 0.284761 | − | 0.958599i | \(-0.408086\pi\) | ||||
0.284761 | + | 0.958599i | \(0.408086\pi\) | |||||||
\(368\) | −8350.83 | −1.18293 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 33.5084 | 0.00470816 | ||||||||
\(371\) | −367.945 | −0.0514899 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10014.2 | −1.39012 | −0.695060 | − | 0.718952i | \(-0.744622\pi\) | ||||
−0.695060 | + | 0.718952i | \(0.744622\pi\) | |||||||
\(374\) | −668.388 | −0.0924105 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2208.30 | 0.302883 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8169.12 | 1.10717 | 0.553587 | − | 0.832791i | \(-0.313258\pi\) | ||||
0.553587 | + | 0.832791i | \(0.313258\pi\) | |||||||
\(380\) | 11235.4 | 1.51675 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1175.97 | 0.157507 | ||||||||
\(383\) | −7310.25 | −0.975290 | −0.487645 | − | 0.873042i | \(-0.662144\pi\) | ||||
−0.487645 | + | 0.873042i | \(0.662144\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2171.62 | −0.287470 | ||||||||
\(386\) | −864.033 | −0.113933 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5928.97 | 0.775767 | ||||||||
\(389\) | −8785.47 | −1.14509 | −0.572546 | − | 0.819872i | \(-0.694044\pi\) | ||||
−0.572546 | + | 0.819872i | \(0.694044\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9553.99 | 1.23572 | ||||||||
\(392\) | −2172.30 | −0.279892 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1760.82 | 0.225150 | ||||||||
\(395\) | −3605.40 | −0.459259 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11266.8 | −1.42434 | −0.712171 | − | 0.702006i | \(-0.752288\pi\) | ||||
−0.712171 | + | 0.702006i | \(0.752288\pi\) | |||||||
\(398\) | 1852.90 | 0.233361 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11416.2 | 1.42702 | ||||||||
\(401\) | 1576.23 | 0.196293 | 0.0981464 | − | 0.995172i | \(-0.468709\pi\) | ||||
0.0981464 | + | 0.995172i | \(0.468709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2722.54 | −0.335276 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 254.407 | 0.0310985 | ||||||||
\(407\) | −96.2335 | −0.0117202 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6755.78 | −0.816753 | −0.408377 | − | 0.912814i | \(-0.633905\pi\) | ||||
−0.408377 | + | 0.912814i | \(0.633905\pi\) | |||||||
\(410\) | 1778.37 | 0.214213 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4530.87 | 0.541796 | ||||||||
\(413\) | 1583.21 | 0.188631 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5986.17 | −0.708072 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 794.456 | 0.0929620 | ||||||||
\(419\) | −10756.2 | −1.25411 | −0.627057 | − | 0.778973i | \(-0.715741\pi\) | ||||
−0.627057 | + | 0.778973i | \(0.715741\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7886.03 | −0.912925 | −0.456463 | − | 0.889743i | \(-0.650884\pi\) | ||||
−0.456463 | + | 0.889743i | \(0.650884\pi\) | |||||||
\(422\) | −598.335 | −0.0690201 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 468.916 | 0.0537089 | ||||||||
\(425\) | −13061.0 | −1.49071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3607.38 | −0.408837 | ||||||||
\(428\) | 4462.08 | 0.503932 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 214.943 | 0.0241057 | ||||||||
\(431\) | −14084.6 | −1.57409 | −0.787044 | − | 0.616897i | \(-0.788390\pi\) | ||||
−0.787044 | + | 0.616897i | \(0.788390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1864.14 | 0.206894 | 0.103447 | − | 0.994635i | \(-0.467013\pi\) | ||||
0.103447 | + | 0.994635i | \(0.467013\pi\) | |||||||
\(434\) | 658.485 | 0.0728301 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1374.20 | 0.150945 | ||||||||
\(437\) | −11356.0 | −1.24309 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6154.49 | 0.669106 | 0.334553 | − | 0.942377i | \(-0.391415\pi\) | ||||
0.334553 | + | 0.942377i | \(0.391415\pi\) | |||||||
\(440\) | 2767.56 | 0.299859 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14539.3 | 1.55933 | 0.779663 | − | 0.626200i | \(-0.215391\pi\) | ||||
0.779663 | + | 0.626200i | \(0.215391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12789.4 | −1.36242 | ||||||||
\(446\) | −464.521 | −0.0493177 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2391.03 | 0.252155 | ||||||||
\(449\) | −7043.87 | −0.740358 | −0.370179 | − | 0.928960i | \(-0.620704\pi\) | ||||
−0.370179 | + | 0.928960i | \(0.620704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5107.33 | −0.533248 | ||||||||
\(452\) | 9875.90 | 1.02771 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1518.87 | −0.157013 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14098.9 | −1.44314 | −0.721572 | − | 0.692340i | \(-0.756580\pi\) | ||||
−0.721572 | + | 0.692340i | \(0.756580\pi\) | |||||||
\(458\) | −1019.23 | −0.103986 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −19539.3 | −1.98049 | ||||||||
\(461\) | 14449.7 | 1.45985 | 0.729924 | − | 0.683529i | \(-0.239556\pi\) | ||||
0.729924 | + | 0.683529i | \(0.239556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15806.5 | −1.58659 | −0.793293 | − | 0.608840i | \(-0.791635\pi\) | ||||
−0.793293 | + | 0.608840i | \(0.791635\pi\) | |||||||
\(464\) | 6340.06 | 0.634332 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1635.85 | −0.162617 | ||||||||
\(467\) | 15071.3 | 1.49340 | 0.746699 | − | 0.665162i | \(-0.231638\pi\) | ||||
0.746699 | + | 0.665162i | \(0.231638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2311.89 | −0.227619 | ||||||||
\(470\) | 2487.69 | 0.244146 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2017.68 | −0.196761 | ||||||||
\(473\) | −617.299 | −0.0600073 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15524.5 | 1.49961 | ||||||||
\(476\) | −2886.78 | −0.277973 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2650.18 | −0.253591 | ||||||||
\(479\) | −392.545 | −0.0374443 | −0.0187222 | − | 0.999825i | \(-0.505960\pi\) | ||||
−0.0187222 | + | 0.999825i | \(0.505960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2268.51 | −0.214373 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6466.36 | 0.607284 | ||||||||
\(485\) | 13522.7 | 1.26605 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9497.89 | −0.883758 | −0.441879 | − | 0.897075i | \(-0.645688\pi\) | ||||
−0.441879 | + | 0.897075i | \(0.645688\pi\) | |||||||
\(488\) | 4597.32 | 0.426457 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2447.14 | −0.225613 | ||||||||
\(491\) | 1893.82 | 0.174067 | 0.0870337 | − | 0.996205i | \(-0.472261\pi\) | ||||
0.0870337 | + | 0.996205i | \(0.472261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7253.52 | −0.662641 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16410.1 | 1.48555 | ||||||||
\(497\) | 831.881 | 0.0750804 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13370.1 | 1.19945 | 0.599727 | − | 0.800205i | \(-0.295276\pi\) | ||||
0.599727 | + | 0.800205i | \(0.295276\pi\) | |||||||
\(500\) | 9331.79 | 0.834661 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2464.39 | 0.219106 | ||||||||
\(503\) | −5554.71 | −0.492391 | −0.246195 | − | 0.969220i | \(-0.579180\pi\) | ||||
−0.246195 | + | 0.969220i | \(0.579180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6209.51 | −0.547168 | ||||||||
\(506\) | −1381.62 | −0.121385 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20332.3 | −1.77578 | ||||||||
\(509\) | 2197.55 | 0.191365 | 0.0956824 | − | 0.995412i | \(-0.469497\pi\) | ||||
0.0956824 | + | 0.995412i | \(0.469497\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 637.756 | 0.0552107 | ||||||||
\(512\) | −8137.89 | −0.702437 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −734.022 | −0.0629890 | ||||||||
\(515\) | 10333.9 | 0.884206 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7144.45 | −0.607761 | ||||||||
\(518\) | 10.2334 | 0.000868010 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17005.2 | −1.42997 | −0.714983 | − | 0.699142i | \(-0.753565\pi\) | ||||
−0.714983 | + | 0.699142i | \(0.753565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14486.2 | −1.21116 | −0.605581 | − | 0.795783i | \(-0.707059\pi\) | ||||
−0.605581 | + | 0.795783i | \(0.707059\pi\) | |||||||
\(524\) | 16643.8 | 1.38758 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2766.24 | −0.229304 | ||||||||
\(527\) | −18774.4 | −1.55185 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7582.03 | 0.623163 | ||||||||
\(530\) | 528.244 | 0.0432933 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3431.27 | 0.279632 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10177.0 | 0.822413 | ||||||||
\(536\) | 2946.32 | 0.237429 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1088.55 | −0.0872315 | ||||||||
\(539\) | 7027.98 | 0.561626 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15266.7 | 1.21325 | 0.606623 | − | 0.794990i | \(-0.292524\pi\) | ||||
0.606623 | + | 0.794990i | \(0.292524\pi\) | |||||||
\(542\) | 1243.31 | 0.0985330 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5540.83 | 0.436693 | ||||||||
\(545\) | 3134.23 | 0.246341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15260.5 | 1.19286 | 0.596430 | − | 0.802665i | \(-0.296586\pi\) | ||||
0.596430 | + | 0.802665i | \(0.296586\pi\) | |||||||
\(548\) | −5371.62 | −0.418731 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1888.78 | 0.146432 | ||||||||
\(551\) | 8621.64 | 0.666595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1101.08 | −0.0846703 | ||||||||
\(554\) | 1682.55 | 0.129033 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5306.00 | 0.404721 | ||||||||
\(557\) | −10442.1 | −0.794337 | −0.397169 | − | 0.917746i | \(-0.630007\pi\) | ||||
−0.397169 | + | 0.917746i | \(0.630007\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5754.94 | 0.434269 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3999.57 | 0.300199 | ||||||||
\(563\) | −7145.26 | −0.534879 | −0.267440 | − | 0.963575i | \(-0.586178\pi\) | ||||
−0.267440 | + | 0.963575i | \(0.586178\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22524.7 | 1.67721 | ||||||||
\(566\) | −932.950 | −0.0692841 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1060.17 | −0.0783162 | ||||||||
\(569\) | −4438.86 | −0.327042 | −0.163521 | − | 0.986540i | \(-0.552285\pi\) | ||||
−0.163521 | + | 0.986540i | \(0.552285\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10117.3 | 0.741497 | 0.370748 | − | 0.928733i | \(-0.379101\pi\) | ||||
0.370748 | + | 0.928733i | \(0.379101\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 543.109 | 0.0394929 | ||||||||
\(575\) | −26998.4 | −1.95810 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3105.60 | −0.224069 | −0.112035 | − | 0.993704i | \(-0.535737\pi\) | ||||
−0.112035 | + | 0.993704i | \(0.535737\pi\) | |||||||
\(578\) | 127.615 | 0.00918352 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14834.5 | 1.06202 | ||||||||
\(581\) | −1828.16 | −0.130542 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1517.08 | −0.107772 | ||||||||
\(584\) | −812.769 | −0.0575901 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3628.05 | −0.255757 | ||||||||
\(587\) | 19662.3 | 1.38254 | 0.691270 | − | 0.722597i | \(-0.257052\pi\) | ||||
0.691270 | + | 0.722597i | \(0.257052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22315.5 | 1.56111 | ||||||||
\(590\) | −2272.95 | −0.158603 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 255.026 | 0.0177052 | ||||||||
\(593\) | 6395.51 | 0.442888 | 0.221444 | − | 0.975173i | \(-0.428923\pi\) | ||||
0.221444 | + | 0.975173i | \(0.428923\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6584.10 | −0.453650 | ||||||||
\(596\) | 15423.9 | 1.06005 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8878.48 | −0.605618 | −0.302809 | − | 0.953051i | \(-0.597924\pi\) | ||||
−0.302809 | + | 0.953051i | \(0.597924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19100.6 | 1.29639 | 0.648194 | − | 0.761475i | \(-0.275525\pi\) | ||||
0.648194 | + | 0.761475i | \(0.275525\pi\) | |||||||
\(602\) | 65.6430 | 0.00444420 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14079.3 | 0.948472 | ||||||||
\(605\) | 14748.3 | 0.991082 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16595.8 | 1.10972 | 0.554861 | − | 0.831943i | \(-0.312771\pi\) | ||||
0.554861 | + | 0.831943i | \(0.312771\pi\) | |||||||
\(608\) | −6585.91 | −0.439299 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5178.97 | 0.343755 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16469.2 | −1.08513 | −0.542564 | − | 0.840015i | \(-0.682546\pi\) | ||||
−0.542564 | + | 0.840015i | \(0.682546\pi\) | |||||||
\(614\) | −1583.01 | −0.104047 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 845.205 | 0.0552829 | ||||||||
\(617\) | 10116.0 | 0.660055 | 0.330027 | − | 0.943971i | \(-0.392942\pi\) | ||||
0.330027 | + | 0.943971i | \(0.392942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18854.8 | −1.22430 | −0.612148 | − | 0.790743i | \(-0.709694\pi\) | ||||
−0.612148 | + | 0.790743i | \(0.709694\pi\) | |||||||
\(620\) | 38396.3 | 2.48715 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1460.49 | 0.0941487 | ||||||||
\(623\) | −3905.86 | −0.251180 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2730.82 | −0.174773 | ||||||||
\(626\) | 157.019 | 0.0100252 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3100.99 | 0.197043 | ||||||||
\(629\) | −291.769 | −0.0184954 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18946.2 | −1.19531 | −0.597653 | − | 0.801755i | \(-0.703900\pi\) | ||||
−0.597653 | + | 0.801755i | \(0.703900\pi\) | |||||||
\(632\) | 1403.24 | 0.0883194 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1336.15 | −0.0836991 | ||||||||
\(635\) | −46373.3 | −2.89806 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1048.95 | 0.0650912 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15043.5 | −0.929135 | ||||||||
\(641\) | 23586.9 | 1.45340 | 0.726698 | − | 0.686957i | \(-0.241054\pi\) | ||||
0.726698 | + | 0.686957i | \(0.241054\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27153.0 | 1.66534 | 0.832669 | − | 0.553772i | \(-0.186812\pi\) | ||||
0.832669 | + | 0.553772i | \(0.186812\pi\) | |||||||
\(644\) | −5967.25 | −0.365128 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2408.70 | 0.146701 | ||||||||
\(647\) | −6856.72 | −0.416639 | −0.208319 | − | 0.978061i | \(-0.566799\pi\) | ||||
−0.208319 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6527.75 | 0.394817 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7350.17 | 0.441495 | ||||||||
\(653\) | 8073.89 | 0.483853 | 0.241926 | − | 0.970295i | \(-0.422221\pi\) | ||||
0.241926 | + | 0.970295i | \(0.422221\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37960.9 | 2.26451 | ||||||||
\(656\) | 13534.8 | 0.805555 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 759.734 | 0.0450114 | ||||||||
\(659\) | −5305.73 | −0.313629 | −0.156815 | − | 0.987628i | \(-0.550123\pi\) | ||||
−0.156815 | + | 0.987628i | \(0.550123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25848.3 | −1.52100 | −0.760502 | − | 0.649336i | \(-0.775047\pi\) | ||||
−0.760502 | + | 0.649336i | \(0.775047\pi\) | |||||||
\(662\) | 3373.75 | 0.198073 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2329.85 | 0.136168 | ||||||||
\(665\) | 7825.96 | 0.456357 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14993.7 | −0.870404 | ||||||||
\(668\) | −28735.9 | −1.66441 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3319.09 | 0.191385 | ||||||||
\(671\) | −14873.6 | −0.855722 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14529.1 | −0.832177 | −0.416089 | − | 0.909324i | \(-0.636599\pi\) | ||||
−0.416089 | + | 0.909324i | \(0.636599\pi\) | |||||||
\(674\) | −2066.06 | −0.118073 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12058.1 | −0.684535 | −0.342267 | − | 0.939603i | \(-0.611195\pi\) | ||||
−0.342267 | + | 0.939603i | \(0.611195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4129.78 | 0.233412 | ||||||||
\(680\) | 8390.91 | 0.473201 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2715.00 | 0.152438 | ||||||||
\(683\) | 30028.8 | 1.68231 | 0.841156 | − | 0.540792i | \(-0.181875\pi\) | ||||
0.841156 | + | 0.540792i | \(0.181875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12251.5 | −0.683364 | ||||||||
\(686\) | −1565.22 | −0.0871144 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1635.89 | 0.0906505 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −449.696 | −0.0247572 | −0.0123786 | − | 0.999923i | \(-0.503940\pi\) | ||||
−0.0123786 | + | 0.999923i | \(0.503940\pi\) | |||||||
\(692\) | 11108.7 | 0.610244 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2307.10 | −0.126191 | ||||||||
\(695\) | 12101.8 | 0.660500 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15484.8 | −0.841506 | ||||||||
\(698\) | 22.0690 | 0.00119674 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8157.67 | 0.440473 | ||||||||
\(701\) | 26986.0 | 1.45399 | 0.726994 | − | 0.686644i | \(-0.240917\pi\) | ||||
0.726994 | + | 0.686644i | \(0.240917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 346.801 | 0.0186057 | ||||||||
\(704\) | 9858.46 | 0.527776 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3971.29 | −0.211702 | ||||||||
\(707\) | −1896.37 | −0.100877 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9098.87 | 0.481968 | 0.240984 | − | 0.970529i | \(-0.422530\pi\) | ||||
0.240984 | + | 0.970529i | \(0.422530\pi\) | |||||||
\(710\) | −1194.30 | −0.0631285 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4977.71 | 0.262005 | ||||||||
\(713\) | −38808.4 | −2.03841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9118.62 | 0.475948 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3147.11 | −0.163578 | ||||||||
\(719\) | 6293.55 | 0.326439 | 0.163220 | − | 0.986590i | \(-0.447812\pi\) | ||||
0.163220 | + | 0.986590i | \(0.447812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3155.95 | 0.163015 | ||||||||
\(722\) | 144.295 | 0.00743783 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8853.72 | 0.454483 | ||||||||
\(725\) | 20497.5 | 1.05001 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18070.7 | 0.921878 | 0.460939 | − | 0.887432i | \(-0.347513\pi\) | ||||
0.460939 | + | 0.887432i | \(0.347513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −915.601 | −0.0464218 | ||||||||
\(731\) | −1871.58 | −0.0946962 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34771.5 | −1.75214 | −0.876068 | − | 0.482188i | \(-0.839842\pi\) | ||||
−0.876068 | + | 0.482188i | \(0.839842\pi\) | |||||||
\(734\) | −1755.61 | −0.0882842 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11453.4 | 0.573613 | ||||||||
\(737\) | −9532.17 | −0.476421 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23631.5 | −1.17632 | −0.588158 | − | 0.808746i | \(-0.700147\pi\) | ||||
−0.588158 | + | 0.808746i | \(0.700147\pi\) | |||||||
\(740\) | 596.710 | 0.0296425 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 161.324 | 0.00798167 | ||||||||
\(743\) | 32502.8 | 1.60486 | 0.802431 | − | 0.596745i | \(-0.203540\pi\) | ||||
0.802431 | + | 0.596745i | \(0.203540\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35178.6 | 1.72999 | ||||||||
\(746\) | 4390.69 | 0.215489 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11902.5 | −0.581816 | ||||||||
\(749\) | 3108.04 | 0.151622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2020.86 | 0.0981920 | 0.0490960 | − | 0.998794i | \(-0.484366\pi\) | ||||
0.0490960 | + | 0.998794i | \(0.484366\pi\) | |||||||
\(752\) | 18933.3 | 0.918120 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32111.6 | 1.54790 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12568.2 | 0.603434 | 0.301717 | − | 0.953398i | \(-0.402440\pi\) | ||||
0.301717 | + | 0.953398i | \(0.402440\pi\) | |||||||
\(758\) | −3581.73 | −0.171628 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9973.56 | −0.476025 | ||||||||
\(761\) | −8704.81 | −0.414651 | −0.207325 | − | 0.978272i | \(-0.566476\pi\) | ||||
−0.207325 | + | 0.978272i | \(0.566476\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 957.187 | 0.0454161 | ||||||||
\(764\) | 20941.4 | 0.991665 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3205.16 | 0.151184 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21915.9 | 1.02771 | 0.513853 | − | 0.857878i | \(-0.328218\pi\) | ||||
0.513853 | + | 0.857878i | \(0.328218\pi\) | |||||||
\(770\) | 952.140 | 0.0445620 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15386.5 | −0.717322 | ||||||||
\(773\) | −23077.5 | −1.07379 | −0.536896 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536896 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 53054.0 | 2.45904 | ||||||||
\(776\) | −5263.08 | −0.243471 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3851.96 | 0.177506 | ||||||||
\(779\) | 18405.5 | 0.846528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3429.94 | 0.157148 | ||||||||
\(782\) | −4188.92 | −0.191554 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18624.6 | −0.848426 | ||||||||
\(785\) | 7072.67 | 0.321572 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16522.4 | 0.748362 | 0.374181 | − | 0.927356i | \(-0.377924\pi\) | ||||
0.374181 | + | 0.927356i | \(0.377924\pi\) | |||||||
\(788\) | 31356.4 | 1.41754 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1580.78 | 0.0711918 | ||||||||
\(791\) | 6879.00 | 0.309215 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 4939.89 | 0.220794 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32996.1 | 1.46924 | ||||||||
\(797\) | 11719.4 | 0.520855 | 0.260427 | − | 0.965493i | \(-0.416137\pi\) | ||||
0.260427 | + | 0.965493i | \(0.416137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21661.2 | −0.959095 | ||||||||
\(800\) | −15657.7 | −0.691978 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −691.096 | −0.0304282 | ||||||||
\(803\) | 2629.53 | 0.115559 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13610.0 | −0.595886 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2416.77 | 0.105225 | ||||||||
\(809\) | 24096.0 | 1.04718 | 0.523592 | − | 0.851969i | \(-0.324592\pi\) | ||||
0.523592 | + | 0.851969i | \(0.324592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16622.6 | −0.719729 | −0.359864 | − | 0.933005i | \(-0.617177\pi\) | ||||
−0.359864 | + | 0.933005i | \(0.617177\pi\) | |||||||
\(812\) | 4530.42 | 0.195796 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 42.1933 | 0.00181680 | ||||||||
\(815\) | 16764.1 | 0.720516 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2224.59 | 0.0952613 | ||||||||
\(818\) | 2962.05 | 0.126609 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 31668.7 | 1.34868 | ||||||||
\(821\) | −38005.5 | −1.61559 | −0.807797 | − | 0.589461i | \(-0.799340\pi\) | ||||
−0.807797 | + | 0.589461i | \(0.799340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15859.5 | −0.671722 | −0.335861 | − | 0.941912i | \(-0.609027\pi\) | ||||
−0.335861 | + | 0.941912i | \(0.609027\pi\) | |||||||
\(824\) | −4022.01 | −0.170040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −694.155 | −0.0292406 | ||||||||
\(827\) | 12201.0 | 0.513023 | 0.256512 | − | 0.966541i | \(-0.417427\pi\) | ||||
0.256512 | + | 0.966541i | \(0.417427\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5431.41 | −0.227552 | −0.113776 | − | 0.993506i | \(-0.536295\pi\) | ||||
−0.113776 | + | 0.993506i | \(0.536295\pi\) | |||||||
\(830\) | 2624.62 | 0.109761 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21308.0 | 0.886290 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −65540.3 | −2.71630 | ||||||||
\(836\) | 14147.5 | 0.585288 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4716.02 | 0.194406 | ||||||||
\(839\) | −7960.90 | −0.327582 | −0.163791 | − | 0.986495i | \(-0.552372\pi\) | ||||
−0.163791 | + | 0.986495i | \(0.552372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13005.6 | −0.533255 | ||||||||
\(842\) | 3457.61 | 0.141517 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10655.0 | −0.434550 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4504.10 | 0.182719 | ||||||||
\(848\) | 4020.35 | 0.162806 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5726.56 | 0.231082 | ||||||||
\(851\) | −603.115 | −0.0242944 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13576.7 | −0.544969 | −0.272485 | − | 0.962160i | \(-0.587845\pi\) | ||||
−0.272485 | + | 0.962160i | \(0.587845\pi\) | |||||||
\(854\) | 1581.65 | 0.0633756 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3960.95 | −0.158157 | ||||||||
\(857\) | 31223.9 | 1.24456 | 0.622281 | − | 0.782794i | \(-0.286206\pi\) | ||||
0.622281 | + | 0.782794i | \(0.286206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11815.8 | −0.469323 | −0.234661 | − | 0.972077i | \(-0.575398\pi\) | ||||
−0.234661 | + | 0.972077i | \(0.575398\pi\) | |||||||
\(860\) | 3827.65 | 0.151770 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6175.36 | 0.244006 | ||||||||
\(863\) | −1790.84 | −0.0706384 | −0.0353192 | − | 0.999376i | \(-0.511245\pi\) | ||||
−0.0353192 | + | 0.999376i | \(0.511245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25336.4 | 0.995912 | ||||||||
\(866\) | −817.328 | −0.0320715 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11726.1 | 0.458538 | ||||||||
\(869\) | −4539.87 | −0.177220 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1219.86 | −0.0473734 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4979.01 | 0.192698 | ||||||||
\(875\) | 6500.00 | 0.251132 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43542.5 | −1.67654 | −0.838270 | − | 0.545255i | \(-0.816433\pi\) | ||||
−0.838270 | + | 0.545255i | \(0.816433\pi\) | |||||||
\(878\) | −2698.42 | −0.103721 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23728.2 | 0.908953 | ||||||||
\(881\) | 1020.04 | 0.0390080 | 0.0195040 | − | 0.999810i | \(-0.493791\pi\) | ||||
0.0195040 | + | 0.999810i | \(0.493791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34781.9 | −1.32560 | −0.662800 | − | 0.748797i | \(-0.730632\pi\) | ||||
−0.662800 | + | 0.748797i | \(0.730632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6374.70 | −0.241718 | ||||||||
\(887\) | −49785.1 | −1.88458 | −0.942288 | − | 0.334802i | \(-0.891330\pi\) | ||||
−0.942288 | + | 0.334802i | \(0.891330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14162.3 | −0.534295 | ||||||||
\(890\) | 5607.49 | 0.211195 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8272.08 | −0.310504 | ||||||||
\(893\) | 25746.8 | 0.964818 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20797.5 | 0.776743 | ||||||||
\(896\) | −4594.25 | −0.171298 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3088.36 | 0.114766 | ||||||||
\(899\) | 29463.9 | 1.09308 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4599.60 | −0.170072 | ||||||||
\(902\) | 2239.29 | 0.0826611 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8766.74 | −0.322541 | ||||||||
\(905\) | 20193.3 | 0.741712 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17389.9 | 0.636627 | 0.318314 | − | 0.947985i | \(-0.396884\pi\) | ||||
0.318314 | + | 0.947985i | \(0.396884\pi\) | |||||||
\(908\) | −27047.6 | −0.988553 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20419.5 | −0.742621 | −0.371311 | − | 0.928509i | \(-0.621091\pi\) | ||||
−0.371311 | + | 0.928509i | \(0.621091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7537.71 | −0.273233 | ||||||||
\(914\) | 6181.60 | 0.223708 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18150.2 | −0.654695 | ||||||||
\(917\) | 11593.2 | 0.417492 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33231.8 | −1.19283 | −0.596417 | − | 0.802674i | \(-0.703410\pi\) | ||||
−0.596417 | + | 0.802674i | \(0.703410\pi\) | |||||||
\(920\) | 17344.8 | 0.621567 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6335.43 | −0.226297 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 824.502 | 0.0293075 | ||||||||
\(926\) | 6930.31 | 0.245944 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8695.59 | −0.307594 | ||||||||
\(929\) | −25222.8 | −0.890780 | −0.445390 | − | 0.895337i | \(-0.646935\pi\) | ||||
−0.445390 | + | 0.895337i | \(0.646935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25327.0 | −0.891579 | ||||||||
\(932\) | −29130.9 | −1.02383 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6607.97 | −0.231498 | ||||||||
\(935\) | −27146.9 | −0.949519 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26979.4 | −0.940639 | −0.470319 | − | 0.882496i | \(-0.655861\pi\) | ||||
−0.470319 | + | 0.882496i | \(0.655861\pi\) | |||||||
\(938\) | 1013.64 | 0.0352842 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 44300.2 | 1.53714 | ||||||||
\(941\) | 7641.67 | 0.264730 | 0.132365 | − | 0.991201i | \(-0.457743\pi\) | ||||
0.132365 | + | 0.991201i | \(0.457743\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32008.7 | −1.10535 | ||||||||
\(944\) | −17299.0 | −0.596434 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 270.653 | 0.00930200 | ||||||||
\(947\) | −2869.32 | −0.0984587 | −0.0492293 | − | 0.998788i | \(-0.515677\pi\) | ||||
−0.0492293 | + | 0.998788i | \(0.515677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6806.67 | −0.232461 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2562.56 | 0.0872407 | ||||||||
\(953\) | −12313.6 | −0.418548 | −0.209274 | − | 0.977857i | \(-0.567110\pi\) | ||||
−0.209274 | + | 0.977857i | \(0.567110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47762.6 | 1.61839 | ||||||||
\(956\) | −47193.8 | −1.59661 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 172.110 | 0.00580442 | ||||||||
\(959\) | −3741.57 | −0.125987 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46470.7 | 1.55989 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −40397.1 | −1.34969 | ||||||||
\(965\) | −35093.2 | −1.17066 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17838.0 | 0.593207 | 0.296603 | − | 0.955001i | \(-0.404146\pi\) | ||||
0.296603 | + | 0.955001i | \(0.404146\pi\) | |||||||
\(968\) | −5740.12 | −0.190593 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5928.97 | −0.196255 | ||||||||
\(971\) | −41525.3 | −1.37241 | −0.686206 | − | 0.727408i | \(-0.740725\pi\) | ||||
−0.686206 | + | 0.727408i | \(0.740725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3695.86 | 0.121772 | ||||||||
\(974\) | 4164.32 | 0.136995 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39416.1 | 1.29270 | ||||||||
\(977\) | −31654.4 | −1.03655 | −0.518277 | − | 0.855213i | \(-0.673426\pi\) | ||||
−0.518277 | + | 0.855213i | \(0.673426\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16104.3 | −0.525735 | ||||||||
\(980\) | −43578.0 | −1.42046 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −830.342 | −0.0269830 | ||||||||
\(983\) | −39913.2 | −1.29505 | −0.647525 | − | 0.762045i | \(-0.724196\pi\) | ||||
−0.647525 | + | 0.762045i | \(0.724196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 71516.8 | 2.31342 | ||||||||
\(986\) | 3180.28 | 0.102719 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3868.74 | −0.124387 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2700.94 | −0.0865773 | −0.0432887 | − | 0.999063i | \(-0.513784\pi\) | ||||
−0.0432887 | + | 0.999063i | \(0.513784\pi\) | |||||||
\(992\) | −22506.9 | −0.720358 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −364.736 | −0.0116386 | ||||||||
\(995\) | 75256.6 | 2.39778 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9729.08 | −0.309050 | −0.154525 | − | 0.987989i | \(-0.549385\pi\) | ||||
−0.154525 | + | 0.987989i | \(0.549385\pi\) | |||||||
\(998\) | −5862.08 | −0.185933 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1521.4.a.l.1.2 | 2 | ||
3.2 | odd | 2 | 169.4.a.j.1.1 | 2 | |||
13.4 | even | 6 | 117.4.g.d.55.2 | 4 | |||
13.10 | even | 6 | 117.4.g.d.100.2 | 4 | |||
13.12 | even | 2 | 1521.4.a.t.1.1 | 2 | |||
39.2 | even | 12 | 169.4.e.g.147.3 | 8 | |||
39.5 | even | 4 | 169.4.b.e.168.2 | 4 | |||
39.8 | even | 4 | 169.4.b.e.168.3 | 4 | |||
39.11 | even | 12 | 169.4.e.g.147.2 | 8 | |||
39.17 | odd | 6 | 13.4.c.b.3.1 | ✓ | 4 | ||
39.20 | even | 12 | 169.4.e.g.23.3 | 8 | |||
39.23 | odd | 6 | 13.4.c.b.9.1 | yes | 4 | ||
39.29 | odd | 6 | 169.4.c.f.22.2 | 4 | |||
39.32 | even | 12 | 169.4.e.g.23.2 | 8 | |||
39.35 | odd | 6 | 169.4.c.f.146.2 | 4 | |||
39.38 | odd | 2 | 169.4.a.f.1.2 | 2 | |||
156.23 | even | 6 | 208.4.i.e.113.1 | 4 | |||
156.95 | even | 6 | 208.4.i.e.81.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.c.b.3.1 | ✓ | 4 | 39.17 | odd | 6 | ||
13.4.c.b.9.1 | yes | 4 | 39.23 | odd | 6 | ||
117.4.g.d.55.2 | 4 | 13.4 | even | 6 | |||
117.4.g.d.100.2 | 4 | 13.10 | even | 6 | |||
169.4.a.f.1.2 | 2 | 39.38 | odd | 2 | |||
169.4.a.j.1.1 | 2 | 3.2 | odd | 2 | |||
169.4.b.e.168.2 | 4 | 39.5 | even | 4 | |||
169.4.b.e.168.3 | 4 | 39.8 | even | 4 | |||
169.4.c.f.22.2 | 4 | 39.29 | odd | 6 | |||
169.4.c.f.146.2 | 4 | 39.35 | odd | 6 | |||
169.4.e.g.23.2 | 8 | 39.32 | even | 12 | |||
169.4.e.g.23.3 | 8 | 39.20 | even | 12 | |||
169.4.e.g.147.2 | 8 | 39.11 | even | 12 | |||
169.4.e.g.147.3 | 8 | 39.2 | even | 12 | |||
208.4.i.e.81.1 | 4 | 156.95 | even | 6 | |||
208.4.i.e.113.1 | 4 | 156.23 | even | 6 | |||
1521.4.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1521.4.a.t.1.1 | 2 | 13.12 | even | 2 |