Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [208,4,Mod(81,208)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(208, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("208.81");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 208.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.2723972812\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 81.2 | ||
Root | \(1.28078 + 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 208.81 |
Dual form | 208.4.i.e.113.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.34233 | + | 7.52113i | 0.835682 | + | 1.44744i | 0.893474 | + | 0.449114i | \(0.148260\pi\) |
−0.0577926 | + | 0.998329i | \(0.518406\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.80776 | 0.251134 | 0.125567 | − | 0.992085i | \(-0.459925\pi\) | ||||
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.78078 | − | 8.28055i | 0.258138 | − | 0.447108i | −0.707605 | − | 0.706608i | \(-0.750225\pi\) |
0.965743 | + | 0.259500i | \(0.0835579\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.2116 | + | 41.9358i | −0.896728 | + | 1.55318i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.7116 | + | 34.1416i | 0.540299 | + | 0.935825i | 0.998887 | + | 0.0471757i | \(0.0150221\pi\) |
−0.458588 | + | 0.888649i | \(0.651645\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.5270 | + | 23.5492i | 0.864628 | + | 0.502413i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.1922 | + | 21.1176i | 0.209868 | + | 0.363502i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00758 | + | 1.74518i | −0.0143749 | + | 0.0248981i | −0.873123 | − | 0.487499i | \(-0.837909\pi\) |
0.858748 | + | 0.512397i | \(0.171242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −30.0961 | + | 52.1280i | −0.363396 | + | 0.629420i | −0.988517 | − | 0.151107i | \(-0.951716\pi\) |
0.625121 | + | 0.780528i | \(0.285049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 83.0388 | 0.862884 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.23438 | + | 3.87006i | 0.0202565 | + | 0.0350853i | 0.875976 | − | 0.482355i | \(-0.160218\pi\) |
−0.855719 | + | 0.517440i | \(0.826885\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −117.116 | −0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −186.054 | −1.32615 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −70.3466 | − | 121.844i | −0.450449 | − | 0.780201i | 0.547964 | − | 0.836502i | \(-0.315403\pi\) |
−0.998414 | + | 0.0563003i | \(0.982070\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −136.155 | −0.788845 | −0.394423 | − | 0.918929i | \(-0.629055\pi\) | ||||
−0.394423 | + | 0.918929i | \(0.629055\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −171.189 | + | 296.508i | −0.903035 | + | 1.56410i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.4233 | − | 23.2498i | 0.0648272 | − | 0.112284i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 92.8542 | + | 160.828i | 0.412571 | + | 0.714594i | 0.995170 | − | 0.0981657i | \(-0.0312975\pi\) |
−0.582599 | + | 0.812760i | \(0.697964\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.13494 | + | 407.067i | −0.00465989 | + | 1.67136i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −155.116 | − | 268.668i | −0.590853 | − | 1.02339i | −0.994118 | − | 0.108304i | \(-0.965458\pi\) |
0.403265 | − | 0.915083i | \(-0.367875\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 213.735 | − | 370.200i | 0.758008 | − | 1.31291i | −0.185857 | − | 0.982577i | \(-0.559506\pi\) |
0.943865 | − | 0.330331i | \(-0.107160\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −67.9806 | + | 117.746i | −0.225199 | + | 0.390056i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 258.617 | 0.802622 | 0.401311 | − | 0.915942i | \(-0.368555\pi\) | ||||
0.401311 | + | 0.915942i | \(0.368555\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 125.788 | + | 217.872i | 0.366730 | + | 0.635195i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.5009 | −0.0480514 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 612.656 | 1.58783 | 0.793913 | − | 0.608031i | \(-0.208040\pi\) | ||||
0.793913 | + | 0.608031i | \(0.208040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 55.3457 | + | 95.8615i | 0.135687 | + | 0.235017i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −522.749 | −1.21473 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −258.943 | + | 448.502i | −0.571381 | + | 0.989661i | 0.425044 | + | 0.905173i | \(0.360259\pi\) |
−0.996425 | + | 0.0844878i | \(0.973075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 80.6553 | − | 139.699i | 0.169293 | − | 0.293223i | −0.768879 | − | 0.639395i | \(-0.779185\pi\) |
0.938171 | + | 0.346171i | \(0.112518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 231.501 | + | 400.971i | 0.462958 | + | 0.801867i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 113.790 | + | 66.1205i | 0.217138 | + | 0.126173i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24.9493 | − | 43.2135i | −0.0454933 | − | 0.0787966i | 0.842382 | − | 0.538881i | \(-0.181153\pi\) |
−0.887875 | + | 0.460084i | \(0.847819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19.4048 | + | 33.6101i | −0.0338560 | + | 0.0586403i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 139.982 | − | 242.455i | 0.233982 | − | 0.405269i | −0.724994 | − | 0.688755i | \(-0.758158\pi\) |
0.958976 | + | 0.283486i | \(0.0914909\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 467.732 | 0.749916 | 0.374958 | − | 0.927042i | \(-0.377657\pi\) | ||||
0.374958 | + | 0.927042i | \(0.377657\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −508.558 | − | 880.849i | −0.782977 | − | 1.35616i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 376.948 | 0.557886 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −37.5379 | −0.0534600 | −0.0267300 | − | 0.999643i | \(-0.508509\pi\) | ||||
−0.0267300 | + | 0.999643i | \(0.508509\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −154.193 | − | 267.070i | −0.211513 | − | 0.366352i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.1553 | 0.100712 | 0.0503562 | − | 0.998731i | \(-0.483964\pi\) | ||||
0.0503562 | + | 0.998731i | \(0.483964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82904 | + | 4.90004i | −0.00361003 | + | 0.00625275i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 610.936 | − | 1058.17i | 0.752865 | − | 1.30400i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −101.403 | − | 175.635i | −0.120772 | − | 0.209183i | 0.799300 | − | 0.600932i | \(-0.205204\pi\) |
−0.920072 | + | 0.391749i | \(0.871870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 388.750 | − | 223.002i | 0.447826 | − | 0.256890i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −591.231 | − | 1024.04i | −0.659224 | − | 1.14181i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −84.5028 | + | 146.363i | −0.0912611 | + | 0.158069i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 587.184 | − | 1017.03i | 0.614634 | − | 1.06458i | −0.375814 | − | 0.926695i | \(-0.622637\pi\) |
0.990449 | − | 0.137883i | \(-0.0440297\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1909.01 | −1.93800 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −485.348 | − | 840.648i | −0.478158 | − | 0.828194i | 0.521528 | − | 0.853234i | \(-0.325362\pi\) |
−0.999686 | + | 0.0250397i | \(0.992029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1899.70 | 1.81731 | 0.908654 | − | 0.417550i | \(-0.137111\pi\) | ||||
0.908654 | + | 0.417550i | \(0.137111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 233.153 | 0.216699 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −953.247 | − | 1651.07i | −0.861251 | − | 1.49173i | −0.870722 | − | 0.491775i | \(-0.836348\pi\) |
0.00947163 | − | 0.999955i | \(-0.496985\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −896.004 | −0.787354 | −0.393677 | − | 0.919249i | \(-0.628797\pi\) | ||||
−0.393677 | + | 0.919249i | \(0.628797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −806.407 | + | 1396.74i | −0.689556 | + | 1.19435i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 167.441 | − | 290.017i | 0.139394 | − | 0.241438i | −0.787873 | − | 0.615837i | \(-0.788818\pi\) |
0.927267 | + | 0.374400i | \(0.122151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.27361 | + | 10.8662i | 0.00508710 | + | 0.00881112i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1968.78 | + | 1129.37i | −1.55567 | + | 0.892394i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.63401 | + | 16.6866i | 0.00742141 | + | 0.0128543i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −111.598 | + | 193.293i | −0.0838452 | + | 0.145224i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1347.13 | − | 2333.29i | 0.987530 | − | 1.71045i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −679.806 | −0.486430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 310.447 | + | 537.709i | 0.216911 | + | 0.375701i | 0.953862 | − | 0.300245i | \(-0.0970686\pi\) |
−0.736951 | + | 0.675946i | \(0.763735\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3712.44 | 2.53381 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1331.70 | 0.888180 | 0.444090 | − | 0.895982i | \(-0.353527\pi\) | ||||
0.444090 | + | 0.895982i | \(0.353527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 287.766 | + | 498.425i | 0.187612 | + | 0.324954i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −522.396 | −0.333042 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −311.008 | + | 538.681i | −0.193950 | + | 0.335932i | −0.946556 | − | 0.322540i | \(-0.895463\pi\) |
0.752606 | + | 0.658471i | \(0.228797\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 165.290 | − | 286.291i | 0.100861 | − | 0.174697i | −0.811178 | − | 0.584799i | \(-0.801173\pi\) |
0.912040 | + | 0.410102i | \(0.134507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1123.00 | + | 1945.10i | 0.670736 | + | 1.16175i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.15196 | + | 1847.85i | −0.00301279 | + | 1.08059i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −197.517 | − | 342.109i | −0.113123 | − | 0.195935i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1092.43 | + | 1892.14i | −0.612939 | + | 1.06164i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 905.269 | − | 1567.97i | 0.497735 | − | 0.862102i | −0.502262 | − | 0.864716i | \(-0.667499\pi\) |
0.999997 | + | 0.00261337i | \(0.000831864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 423.239 | 0.228097 | 0.114049 | − | 0.993475i | \(-0.463618\pi\) | ||||
0.114049 | + | 0.993475i | \(0.463618\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −48.7902 | − | 84.5071i | −0.0257808 | − | 0.0446536i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −382.292 | −0.198106 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1322.17 | 0.672105 | 0.336052 | − | 0.941843i | \(-0.390908\pi\) | ||||
0.336052 | + | 0.941843i | \(0.390908\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2660.35 | + | 4607.87i | 1.32692 | + | 2.29829i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 42.7283 | 0.0209159 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1803.20 | + | 3123.23i | −0.866486 | + | 1.50080i | −0.000922205 | 1.00000i | \(0.500294\pi\) | |
−0.865564 | + | 0.500798i | \(0.833040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −480.658 | + | 832.524i | −0.226783 | + | 0.392800i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1707.72 | − | 2957.85i | −0.791300 | − | 1.37057i | −0.925162 | − | 0.379571i | \(-0.876071\pi\) |
0.133863 | − | 0.991000i | \(-0.457262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1087.87 | + | 1908.75i | 0.495163 | + | 0.868800i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1457.35 | − | 2524.21i | −0.651734 | − | 1.12884i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1171.11 | + | 2028.43i | −0.514671 | + | 0.891436i | 0.485184 | + | 0.874412i | \(0.338753\pi\) |
−0.999855 | + | 0.0170243i | \(0.994581\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −559.908 | + | 969.788i | −0.241857 | + | 0.418909i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4497.66 | −1.90997 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −333.446 | − | 577.545i | −0.139234 | − | 0.241160i | 0.787973 | − | 0.615710i | \(-0.211131\pi\) |
−0.927207 | + | 0.374550i | \(0.877797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −701.037 | −0.287888 | −0.143944 | − | 0.989586i | \(-0.545978\pi\) | ||||
−0.143944 | + | 0.989586i | \(0.545978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1400.93 | 0.565899 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 260.713 | + | 451.567i | 0.103611 | + | 0.179459i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −79.4440 | −0.0310670 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −889.482 | + | 1540.63i | −0.342330 | + | 0.592933i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 650.440 | − | 1126.59i | 0.246409 | − | 0.426793i | −0.716118 | − | 0.697980i | \(-0.754083\pi\) |
0.962527 | + | 0.271186i | \(0.0874159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 259.667 | + | 449.756i | 0.0968457 | + | 0.167742i | 0.910377 | − | 0.413779i | \(-0.135791\pi\) |
−0.813532 | + | 0.581521i | \(0.802458\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.18664 | + | 1142.95i | −0.00117026 | + | 0.419735i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1560.52 | − | 2702.91i | −0.564379 | − | 0.977534i | −0.997107 | − | 0.0760091i | \(-0.975782\pi\) |
0.432728 | − | 0.901525i | \(-0.357551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 618.529 | − | 1071.32i | 0.220333 | − | 0.381629i | −0.734576 | − | 0.678527i | \(-0.762619\pi\) |
0.954909 | + | 0.296898i | \(0.0959521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 216.677 | − | 375.295i | 0.0760358 | − | 0.131698i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1345.25 | −0.465112 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −435.528 | − | 754.356i | −0.148383 | − | 0.257007i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −216.392 | −0.0726584 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2372.98 | −0.785369 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1265.83 | − | 2192.49i | −0.413003 | − | 0.715342i | 0.582214 | − | 0.813036i | \(-0.302187\pi\) |
−0.995217 | + | 0.0976940i | \(0.968853\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2431.38 | 0.782139 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 600.118 | − | 1039.44i | 0.190362 | − | 0.329716i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −650.928 | + | 1127.44i | −0.203631 | + | 0.352699i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2031.05 | + | 3517.88i | 0.626691 | + | 1.08546i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −81.9315 | + | 46.9991i | −0.0249381 | + | 0.0143054i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −597.766 | − | 1035.36i | −0.179504 | − | 0.310910i | 0.762207 | − | 0.647333i | \(-0.224116\pi\) |
−0.941711 | + | 0.336424i | \(0.890783\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2835.58 | − | 4911.37i | 0.840173 | − | 1.45522i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −434.596 | + | 752.742i | −0.127071 | + | 0.220094i | −0.922541 | − | 0.385900i | \(-0.873891\pi\) |
0.795469 | + | 0.605994i | \(0.207224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4684.64 | 1.35183 | 0.675916 | − | 0.736978i | \(-0.263748\pi\) | ||||
0.675916 | + | 0.736978i | \(0.263748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1636.83 | + | 2835.08i | 0.466215 | + | 0.807508i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4868.99 | −1.36900 | −0.684502 | − | 0.729011i | \(-0.739980\pi\) | ||||
−0.684502 | + | 0.729011i | \(0.739980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 726.137 | 0.201566 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −163.002 | − | 282.328i | −0.0446756 | − | 0.0773803i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4807.53 | −1.30114 | −0.650572 | − | 0.759444i | \(-0.725471\pi\) | ||||
−0.650572 | + | 0.759444i | \(0.725471\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2937.98 | + | 5088.73i | −0.785278 | + | 1.36014i | 0.143555 | + | 0.989642i | \(0.454147\pi\) |
−0.928833 | + | 0.370499i | \(0.879187\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1172.61 | + | 2031.03i | −0.309561 | + | 0.536175i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 353.184 | + | 611.733i | 0.0920984 | + | 0.159519i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2447.28 | + | 1403.85i | −0.630431 | + | 0.361640i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 330.691 | + | 572.774i | 0.0841635 | + | 0.145775i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2903.13 | − | 5028.38i | 0.730057 | − | 1.26450i | −0.226802 | − | 0.973941i | \(-0.572827\pi\) |
0.956858 | − | 0.290554i | \(-0.0938397\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −88.0866 | + | 152.570i | −0.0218891 | + | 0.0379131i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −49.1385 | −0.0120673 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 597.930 | + | 1035.65i | 0.145128 | + | 0.251369i | 0.929421 | − | 0.369022i | \(-0.120307\pi\) |
−0.784293 | + | 0.620391i | \(0.786974\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1775.66 | 0.426001 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6812.83 | 1.61572 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 117.092 | + | 202.810i | 0.0274533 | + | 0.0475505i | 0.879426 | − | 0.476036i | \(-0.157927\pi\) |
−0.851972 | + | 0.523587i | \(0.824594\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1720.19 | 0.398757 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 880.650 | − | 1525.33i | 0.201854 | − | 0.349621i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1334.13 | − | 2310.79i | 0.302393 | − | 0.523760i | −0.674285 | − | 0.738471i | \(-0.735548\pi\) |
0.976677 | + | 0.214712i | \(0.0688813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2850.64 | + | 4937.45i | 0.638982 | + | 1.10675i | 0.985657 | + | 0.168763i | \(0.0539774\pi\) |
−0.346675 | + | 0.937985i | \(0.612689\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3365.31 | + | 1955.50i | 0.746073 | + | 0.433524i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2308.56 | − | 3998.54i | −0.506223 | − | 0.876804i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3576.24 | − | 6194.24i | 0.775725 | − | 1.34359i | −0.158662 | − | 0.987333i | \(-0.550718\pi\) |
0.934386 | − | 0.356261i | \(-0.115949\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3296.54 | − | 5709.78i | 0.707380 | − | 1.22522i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6132.87 | −1.30198 | −0.650990 | − | 0.759086i | \(-0.725646\pi\) | ||||
−0.650990 | + | 0.759086i | \(0.725646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1688.58 | + | 2924.70i | 0.354683 | + | 0.614330i | 0.987064 | − | 0.160328i | \(-0.0512553\pi\) |
−0.632380 | + | 0.774658i | \(0.717922\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1467.76 | −0.305061 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2966.29 | −0.610086 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2454.47 | + | 4251.27i | 0.499587 | + | 0.865310i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10199.0 | 2.05455 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2352.38 | − | 4074.45i | 0.469037 | − | 0.812395i | −0.530337 | − | 0.847787i | \(-0.677935\pi\) |
0.999374 | + | 0.0353917i | \(0.0112679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −727.050 | + | 1259.29i | −0.143493 | + | 0.248537i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3667.43 | − | 6352.18i | −0.716518 | − | 1.24105i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.583991 | + | 209.460i | −0.000112953 | + | 0.0405129i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2043.64 | − | 3539.69i | −0.391341 | − | 0.677822i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4215.09 | − | 7300.74i | 0.799176 | − | 1.38421i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 226.461 | − | 392.242i | 0.0425151 | − | 0.0736384i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5130.49 | −0.953787 | −0.476894 | − | 0.878961i | \(-0.658237\pi\) | ||||
−0.476894 | + | 0.878961i | \(0.658237\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8249.11 | + | 14287.9i | 1.51869 | + | 2.63045i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7948.94 | −1.44933 | −0.724667 | − | 0.689099i | \(-0.758006\pi\) | ||||
−0.724667 | + | 0.689099i | \(0.758006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8521.87 | −1.53893 | −0.769465 | − | 0.638689i | \(-0.779477\pi\) | ||||
−0.769465 | + | 0.638689i | \(0.779477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 650.000 | + | 1125.83i | 0.116265 | + | 0.201376i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6662.46 | −1.18044 | −0.590222 | − | 0.807241i | \(-0.700960\pi\) | ||||
−0.590222 | + | 0.807241i | \(0.700960\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2773.29 | − | 4803.49i | 0.486754 | − | 0.843083i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8278.62 | − | 14339.0i | 1.43946 | − | 2.49322i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −60.6483 | − | 105.046i | −0.0104476 | − | 0.0180957i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4746.38 | − | 2758.00i | −0.810097 | − | 0.470726i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3890.74 | − | 6738.96i | −0.657977 | − | 1.13965i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1236.39 | − | 2141.49i | 0.207187 | − | 0.358858i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1955.89 | + | 3387.69i | −0.324789 | + | 0.562551i | −0.981470 | − | 0.191618i | \(-0.938627\pi\) |
0.656681 | + | 0.754169i | \(0.271960\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8992.61 | −1.47986 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −70.0519 | − | 121.333i | −0.0114249 | − | 0.0197885i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −627.211 | −0.101384 | −0.0506919 | − | 0.998714i | \(-0.516143\pi\) | ||||
−0.0506919 | + | 0.998714i | \(0.516143\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2908.34 | 0.465957 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2683.84 | − | 4648.56i | −0.426212 | − | 0.738221i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5685.08 | 0.894943 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −54.4841 | + | 94.3693i | −0.00850240 | + | 0.0147266i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1911.51 | + | 3310.83i | −0.295721 | + | 0.512204i | −0.975152 | − | 0.221535i | \(-0.928893\pi\) |
0.679431 | + | 0.733739i | \(0.262227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1705.33 | − | 2953.72i | −0.261560 | − | 0.453035i | 0.705097 | − | 0.709111i | \(-0.250904\pi\) |
−0.966657 | + | 0.256076i | \(0.917570\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7540.21 | − | 4381.42i | −1.14663 | − | 0.666275i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2793.82 | + | 4839.03i | 0.421246 | + | 0.729620i | 0.996062 | − | 0.0886632i | \(-0.0282595\pi\) |
−0.574815 | + | 0.818283i | \(0.694926\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 393.035 | − | 680.757i | 0.0587609 | − | 0.101777i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −83.6680 | + | 144.917i | −0.0124039 | + | 0.0214841i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2230.14 | −0.327861 | −0.163931 | − | 0.986472i | \(-0.552417\pi\) | ||||
−0.163931 | + | 0.986472i | \(0.552417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1617.95 | + | 2802.37i | 0.235887 | + | 0.408568i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1938.38 | −0.280272 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1313.28 | 0.188330 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4349.57 | − | 7533.68i | −0.618653 | − | 1.07154i | −0.989732 | − | 0.142938i | \(-0.954345\pi\) |
0.371078 | − | 0.928602i | \(-0.378988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15022.4 | 2.11934 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2928.97 | − | 5073.13i | 0.409878 | − | 0.709929i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5482.09 | + | 9495.26i | −0.760997 | + | 1.31809i | 0.181340 | + | 0.983420i | \(0.441956\pi\) |
−0.942337 | + | 0.334665i | \(0.891377\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2951.94 | − | 5112.91i | −0.406500 | − | 0.704079i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.3862 | − | 6594.57i | 0.00251177 | − | 0.900895i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6955.06 | + | 12046.5i | 0.942631 | + | 1.63269i | 0.760426 | + | 0.649425i | \(0.224990\pi\) |
0.182206 | + | 0.983260i | \(0.441676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2696.12 | + | 4669.82i | −0.362537 | + | 0.627932i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −247.377 | + | 428.469i | −0.0330035 | + | 0.0571638i | −0.882055 | − | 0.471146i | \(-0.843841\pi\) |
0.849052 | + | 0.528310i | \(0.177174\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1058.38 | 0.140104 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10349.8 | + | 17926.3i | 1.35945 | + | 2.35464i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4140.47 | −0.539666 | −0.269833 | − | 0.962907i | \(-0.586968\pi\) | ||||
−0.269833 | + | 0.962907i | \(0.586968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00524 | −0.00116474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5782.70 | + | 10015.9i | 0.742236 | + | 1.28559i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −105.398 | −0.0134256 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 940.896 | − | 1629.68i | 0.118948 | − | 0.206023i | −0.800403 | − | 0.599462i | \(-0.795381\pi\) |
0.919351 | + | 0.393439i | \(0.128715\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2499.15 | + | 4328.65i | −0.313568 | + | 0.543116i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −210.883 | − | 365.259i | −0.0262618 | − | 0.0454867i | 0.852596 | − | 0.522571i | \(-0.175027\pi\) |
−0.878858 | + | 0.477084i | \(0.841694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5517.96 | − | 3206.34i | −0.682058 | − | 0.396326i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −432.938 | − | 749.871i | −0.0531182 | − | 0.0920034i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3660.62 | + | 6340.37i | −0.445823 | + | 0.772188i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1275.11 | + | 2208.55i | −0.154157 | + | 0.267007i | −0.932752 | − | 0.360520i | \(-0.882599\pi\) |
0.778595 | + | 0.627527i | \(0.215933\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5401.99 | −0.648322 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2475.89 | + | 4288.37i | 0.294990 | + | 0.510937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 213.826 | 0.0252923 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2870.98 | 0.337152 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6192.41 | + | 10725.6i | 0.722002 | + | 1.25054i | 0.960196 | + | 0.279327i | \(0.0901112\pi\) |
−0.238194 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10463.0 | 1.21124 | 0.605622 | − | 0.795752i | \(-0.292924\pi\) | ||||
0.605622 | + | 0.795752i | \(0.292924\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6261.55 | + | 10845.3i | −0.719733 | + | 1.24661i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 118.004 | − | 204.389i | 0.0134683 | − | 0.0233278i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −771.190 | − | 1335.74i | −0.0874016 | − | 0.151384i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13920.3 | + | 7985.22i | −1.56661 | + | 0.898671i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1981.19 | − | 3431.53i | −0.221417 | − | 0.383506i | 0.733821 | − | 0.679342i | \(-0.237735\pi\) |
−0.955238 | + | 0.295837i | \(0.904402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4197.07 | − | 7269.54i | 0.465816 | − | 0.806817i | −0.533422 | − | 0.845849i | \(-0.679094\pi\) |
0.999238 | + | 0.0390321i | \(0.0124275\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1715.36 | − | 2971.10i | 0.189070 | − | 0.327479i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −268.984 | −0.0294446 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5087.26 | + | 8811.39i | 0.553079 | + | 0.957960i | 0.998050 | + | 0.0624156i | \(0.0198804\pi\) |
−0.444972 | + | 0.895545i | \(0.646786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12182.2 | −1.31543 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5880.74 | 0.630705 | 0.315353 | − | 0.948975i | \(-0.397877\pi\) | ||||
0.315353 | + | 0.948975i | \(0.397877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −284.716 | − | 493.142i | −0.0303299 | − | 0.0525330i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15723.9 | 1.66379 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5332.43 | + | 9236.05i | −0.560475 | + | 0.970771i | 0.436980 | + | 0.899471i | \(0.356048\pi\) |
−0.997455 | + | 0.0712996i | \(0.977285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6115.16 | − | 10591.8i | 0.638474 | − | 1.10587i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1837.84 | + | 3183.23i | 0.190617 | + | 0.330158i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1091.52 | − | 626.138i | 0.112464 | − | 0.0645138i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7414.43 | + | 12842.2i | 0.758933 | + | 1.31451i | 0.943395 | + | 0.331671i | \(0.107612\pi\) |
−0.184462 | + | 0.982840i | \(0.559054\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 187.464 | − | 324.697i | 0.0190633 | − | 0.0330186i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4855.85 | − | 8410.58i | 0.490585 | − | 0.849717i | −0.509357 | − | 0.860555i | \(-0.670117\pi\) |
0.999941 | + | 0.0108381i | \(0.00344995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11353.5 | −1.13962 | −0.569809 | − | 0.821777i | \(-0.692983\pi\) | ||||
−0.569809 | + | 0.821777i | \(0.692983\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1660.04 | − | 2875.27i | −0.165554 | − | 0.286747i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6451.31 | −0.639252 | −0.319626 | − | 0.947544i | \(-0.603557\pi\) | ||||
−0.319626 | + | 0.947544i | \(0.603557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −477.109 | −0.0469741 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5741.29 | + | 9944.20i | 0.561666 | + | 0.972833i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16852.3 | 1.63820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3524.75 | − | 6105.05i | 0.340477 | − | 0.589724i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14833.4 | + | 25692.2i | −1.42385 | + | 2.46618i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4783.23 | − | 8284.79i | −0.456266 | − | 0.790275i | 0.542494 | − | 0.840059i | \(-0.317480\pi\) |
−0.998760 | + | 0.0497842i | \(0.984147\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.2689 | + | 8704.52i | −0.00230056 | + | 0.825139i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 185.540 | + | 321.365i | 0.0174790 | + | 0.0302746i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1648.67 | − | 2855.59i | 0.154356 | − | 0.267352i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2458.56 | − | 4258.35i | 0.228764 | − | 0.396230i | −0.728678 | − | 0.684856i | \(-0.759865\pi\) |
0.957442 | + | 0.288626i | \(0.0931984\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31320.3 | −2.89643 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1475.41 | + | 2555.49i | 0.135610 | + | 0.234883i | 0.925830 | − | 0.377940i | \(-0.123367\pi\) |
−0.790220 | + | 0.612823i | \(0.790034\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 283.519 | 0.0259007 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5360.04 | −0.486699 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1338.44 | − | 2318.25i | −0.120799 | − | 0.209231i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13430.1 | −1.20484 | −0.602418 | − | 0.798180i | \(-0.705796\pi\) | ||||
−0.602418 | + | 0.798180i | \(0.705796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14830.9 | − | 25687.9i | 1.32255 | − | 2.29072i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 660.143 | − | 1143.40i | 0.0585175 | − | 0.101355i | −0.835283 | − | 0.549821i | \(-0.814696\pi\) |
0.893800 | + | 0.448466i | \(0.148029\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1362.74 | − | 2360.34i | −0.120082 | − | 0.207988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9632.09 | + | 16470.5i | −0.843740 | + | 1.44276i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10458.2 | − | 18114.2i | −0.910713 | − | 1.57740i | −0.813060 | − | 0.582180i | \(-0.802200\pi\) |
−0.0976524 | − | 0.995221i | \(-0.531133\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2236.12 | − | 3873.08i | 0.193582 | − | 0.335293i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5599.50 | − | 9698.62i | 0.481918 | − | 0.834707i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5333.90 | 0.456388 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5097.77 | + | 8829.60i | 0.433655 | + | 0.751113i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20341.4 | −1.72040 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10104.2 | −0.849661 | −0.424831 | − | 0.905273i | \(-0.639666\pi\) | ||||
−0.424831 | + | 0.905273i | \(0.639666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3565.61 | + | 6175.82i | 0.298113 | + | 0.516347i | 0.975704 | − | 0.219092i | \(-0.0703093\pi\) |
−0.677591 | + | 0.735439i | \(0.736976\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9725.21 | −0.808463 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 137.187 | − | 237.615i | 0.0113396 | − | 0.0196407i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6073.52 | − | 10519.6i | 0.499179 | − | 0.864604i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12538.9 | − | 21717.9i | −1.02475 | − | 1.77491i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.5420 | − | 14541.1i | 0.00329469 | − | 1.18170i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2676.49 | − | 4635.82i | −0.216289 | − | 0.374624i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2895.86 | − | 5015.78i | 0.232711 | − | 0.403067i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4958.99 | + | 8589.22i | −0.396287 | + | 0.686390i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16831.7 | 1.33762 | 0.668809 | − | 0.743435i | \(-0.266805\pi\) | ||||
0.668809 | + | 0.743435i | \(0.266805\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3044.13 | − | 5272.59i | −0.240582 | − | 0.416701i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2515.77 | −0.197731 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9560.55 | 0.747312 | 0.373656 | − | 0.927567i | \(-0.378104\pi\) | ||||
0.373656 | + | 0.927567i | \(0.378104\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3905.59 | + | 6764.69i | 0.303619 | + | 0.525883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8468.64 | 0.654766 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −179.460 | + | 310.834i | −0.0138000 | + | 0.0239024i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2264.20 | + | 3921.71i | −0.173171 | + | 0.299941i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11414.0 | + | 19769.5i | 0.868267 | + | 1.50388i | 0.863766 | + | 0.503893i | \(0.168099\pi\) |
0.00450060 | + | 0.999990i | \(0.498567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17380.0 | − | 9969.82i | 1.31502 | − | 0.754344i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −344.972 | − | 597.509i | −0.0259621 | − | 0.0449677i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10814.9 | − | 18731.9i | 0.809578 | − | 1.40223i | −0.103579 | − | 0.994621i | \(-0.533029\pi\) |
0.913157 | − | 0.407609i | \(-0.133637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 470.136 | − | 814.299i | 0.0350066 | − | 0.0606333i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2948.65 | −0.218398 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5294.93 | + | 9171.09i | 0.390114 | + | 0.675698i | 0.992464 | − | 0.122534i | \(-0.0391022\pi\) |
−0.602350 | + | 0.798232i | \(0.705769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1757.27 | 0.128791 | 0.0643954 | − | 0.997924i | \(-0.479488\pi\) | ||||
0.0643954 | + | 0.997924i | \(0.479488\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11297.7 | 0.823679 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −261.683 | − | 453.247i | −0.0189790 | − | 0.0328726i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13580.6 | −0.979840 | −0.489920 | − | 0.871767i | \(-0.662974\pi\) | ||||
−0.489920 | + | 0.871767i | \(0.662974\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2255.12 | + | 3905.98i | −0.161864 | + | 0.280357i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 364.081 | − | 630.607i | 0.0259977 | − | 0.0450293i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12076.5 | + | 20917.0i | 0.857900 | + | 1.48593i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5527.86 | + | 3171.00i | −0.390682 | + | 0.224110i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −478.663 | − | 829.068i | −0.0336568 | − | 0.0582952i | 0.848706 | − | 0.528864i | \(-0.177382\pi\) |
−0.882363 | + | 0.470569i | \(0.844049\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4097.75 | − | 7097.50i | 0.286663 | − | 0.496515i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13552.6 | − | 23473.8i | 0.943283 | − | 1.63381i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6729.49 | 0.466015 | 0.233007 | − | 0.972475i | \(-0.425143\pi\) | ||||
0.233007 | + | 0.972475i | \(0.425143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.0500 | + | 46.8520i | 0.00186377 | + | 0.00322814i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10743.4 | 0.736514 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2281.52 | −0.155626 | −0.0778132 | − | 0.996968i | \(-0.524794\pi\) | ||||
−0.0778132 | + | 0.996968i | \(0.524794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3200.71 | − | 5543.79i | −0.217237 | − | 0.376266i | 0.736725 | − | 0.676192i | \(-0.236371\pi\) |
−0.953962 | + | 0.299926i | \(0.903038\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2416.26 | 0.163180 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −313.341 | + | 542.722i | −0.0210564 | + | 0.0364707i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1389.62 | − | 2406.89i | 0.0929207 | − | 0.160943i | −0.815818 | − | 0.578308i | \(-0.803713\pi\) |
0.908739 | + | 0.417365i | \(0.137046\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5841.50 | − | 10117.8i | −0.388685 | − | 0.673223i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10481.0 | + | 6090.22i | 0.693969 | + | 0.403247i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11310.4 | − | 19590.2i | −0.745226 | − | 1.29077i | −0.950089 | − | 0.311979i | \(-0.899008\pi\) |
0.204863 | − | 0.978791i | \(-0.434325\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3782.41 | − | 6551.33i | 0.248002 | − | 0.429553i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10987.0 | + | 19030.1i | −0.716889 | + | 1.24169i | 0.245337 | + | 0.969438i | \(0.421101\pi\) |
−0.962226 | + | 0.272250i | \(0.912232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7145.19 | −0.463957 | −0.231979 | − | 0.972721i | \(-0.574520\pi\) | ||||
−0.231979 | + | 0.972721i | \(0.574520\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −415.715 | − | 720.040i | −0.0268632 | − | 0.0465285i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1939.14 | −0.124703 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12730.8 | 0.814773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10304.2 | − | 17847.5i | −0.656319 | − | 1.13678i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −374.231 | −0.0237227 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9441.62 | + | 16353.4i | −0.595666 | + | 1.03172i | 0.397787 | + | 0.917478i | \(0.369778\pi\) |
−0.993453 | + | 0.114245i | \(0.963555\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10993.3 | − | 19041.0i | 0.690278 | − | 1.19560i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 871.661 | + | 1509.76i | 0.0544737 | + | 0.0943512i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.8768 | + | 11791.9i | −0.00204494 | + | 0.733457i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6778.37 | + | 11740.5i | 0.419637 | + | 0.726833i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1815.54 | − | 3144.61i | 0.111871 | − | 0.193767i | −0.804653 | − | 0.593745i | \(-0.797649\pi\) |
0.916525 | + | 0.399978i | \(0.130982\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5385.98 | + | 9328.78i | −0.330330 | + | 0.572148i | −0.982576 | − | 0.185859i | \(-0.940493\pi\) |
0.652247 | + | 0.758007i | \(0.273827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10423.6 | 0.636327 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7574.14 | + | 13118.8i | 0.460232 | + | 0.797146i | 0.998972 | − | 0.0453265i | \(-0.0144328\pi\) |
−0.538740 | + | 0.842472i | \(0.681099\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20416.7 | −1.23487 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11306.2 | −0.680682 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3679.45 | − | 6372.99i | −0.220502 | − | 0.381921i | 0.734458 | − | 0.678654i | \(-0.237436\pi\) |
−0.954961 | + | 0.296733i | \(0.904103\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3739.11 | 0.223052 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11324.6 | + | 19614.7i | −0.672471 | + | 1.16475i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14166.6 | − | 24537.3i | 0.837411 | − | 1.45044i | −0.0546414 | − | 0.998506i | \(-0.517402\pi\) |
0.892052 | − | 0.451932i | \(-0.149265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −554.842 | − | 961.014i | −0.0326488 | − | 0.0565493i | 0.849239 | − | 0.528008i | \(-0.177061\pi\) |
−0.881888 | + | 0.471459i | \(0.843728\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −709.260 | − | 412.132i | −0.0415466 | − | 0.0241416i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 807.978 | + | 1399.46i | 0.0471159 | + | 0.0816071i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 314.362 | − | 544.491i | 0.0182491 | − | 0.0316083i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5191.39 | − | 8991.75i | 0.300016 | − | 0.519643i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6359.39 | 0.365874 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10489.5 | − | 18168.4i | −0.600806 | − | 1.04063i | −0.992699 | − | 0.120616i | \(-0.961513\pi\) |
0.391893 | − | 0.920011i | \(-0.371820\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21790.0 | 1.24251 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30941.9 | 1.75656 | 0.878282 | − | 0.478142i | \(-0.158690\pi\) | ||||
0.878282 | + | 0.478142i | \(0.158690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5614.39 | − | 9724.41i | −0.317320 | − | 0.549615i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7548.64 | −0.424764 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2713.11 | − | 4699.24i | 0.151997 | − | 0.263267i | −0.779964 | − | 0.625824i | \(-0.784763\pi\) |
0.931962 | + | 0.362557i | \(0.118096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −873.236 | + | 1512.49i | −0.0487075 | + | 0.0843638i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20342.2 | + | 35233.8i | 1.12970 | + | 1.95670i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24829.1 | + | 14427.5i | 1.37288 | + | 0.797744i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16896.3 | − | 29265.3i | −0.930199 | − | 1.61115i | −0.782979 | − | 0.622048i | \(-0.786301\pi\) |
−0.147219 | − | 0.989104i | \(-0.547032\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9126.53 | + | 15807.6i | −0.500272 | + | 0.866496i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 464.096 | − | 803.838i | 0.0253297 | − | 0.0438724i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 625.164 | 0.0339738 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21142.8 | − | 36620.3i | −1.14405 | − | 1.98156i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6905.96 | 0.372089 | 0.186045 | − | 0.982541i | \(-0.440433\pi\) | ||||
0.186045 | + | 0.982541i | \(0.440433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11178.2 | −0.599707 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3153.12 | + | 5461.37i | 0.168445 | + | 0.291755i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9281.37 | −0.493723 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1003.56 | − | 1738.22i | 0.0531589 | − | 0.0920739i | −0.838221 | − | 0.545330i | \(-0.816404\pi\) |
0.891380 | + | 0.453256i | \(0.149738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 908.854 | − | 1574.18i | 0.0479391 | − | 0.0830329i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −304.222 | − | 526.929i | −0.0159793 | − | 0.0276769i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.4655 | + | 5188.32i | −0.000756613 | + | 0.271374i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20875.9 | − | 36158.1i | −1.08734 | − | 1.88333i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6393.72 | + | 11074.3i | −0.331635 | + | 0.574409i | −0.982833 | − | 0.184499i | \(-0.940934\pi\) |
0.651198 | + | 0.758908i | \(0.274267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9082.03 | − | 15730.5i | 0.469116 | − | 0.812532i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −51030.7 | −2.62497 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8238.74 | + | 14269.9i | 0.422040 | + | 0.730995i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6090.70 | 0.310717 | 0.155359 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155359 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28693.9 | −1.45780 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 430.710 | + | 746.011i | 0.0217926 | + | 0.0377459i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38846.5 | −1.95747 | −0.978737 | − | 0.205117i | \(-0.934243\pi\) | ||||
−0.978737 | + | 0.205117i | \(0.934243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3067.28 | + | 5312.69i | −0.153930 | + | 0.266614i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 983.585 | − | 1703.62i | 0.0491599 | − | 0.0851474i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7228.77 | + | 12520.6i | 0.359830 | + | 0.623245i | 0.987932 | − | 0.154887i | \(-0.0495012\pi\) |
−0.628102 | + | 0.778131i | \(0.716168\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21185.4 | − | 12310.3i | −1.05029 | − | 0.610297i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −638.901 | − | 1106.61i | −0.0315464 | − | 0.0546400i | 0.849821 | − | 0.527071i | \(-0.176710\pi\) |
−0.881368 | + | 0.472431i | \(0.843377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2541.78 | − | 4402.49i | 0.124998 | − | 0.216503i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1843.84 | + | 3193.63i | −0.0903116 | + | 0.156424i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18229.0 | −0.889285 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6503.93 | − | 11265.1i | −0.316021 | − | 0.547364i | 0.663633 | − | 0.748058i | \(-0.269014\pi\) |
−0.979654 | + | 0.200694i | \(0.935680\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 50425.5 | 2.44038 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1188.35 | 0.0572829 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5361.61 | + | 9286.57i | 0.257425 | + | 0.445874i | 0.965551 | − | 0.260212i | \(-0.0837926\pi\) |
−0.708126 | + | 0.706086i | \(0.750459\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1530.00 | −0.0731694 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6810.90 | + | 11796.8i | −0.324435 | + | 0.561938i | −0.981398 | − | 0.191985i | \(-0.938508\pi\) |
0.656963 | + | 0.753923i | \(0.271841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4283.59 | + | 7419.40i | −0.203246 | + | 0.352032i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −136.991 | − | 237.276i | −0.00647443 | − | 0.0112140i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21056.0 | + | 12078.5i | −0.991250 | + | 0.568619i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4247.57 | + | 7357.01i | 0.199183 | + | 0.344994i | 0.948264 | − | 0.317484i | \(-0.102838\pi\) |
−0.749081 | + | 0.662478i | \(0.769505\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5192.82 | + | 8994.22i | −0.242561 | + | 0.420128i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17131.3 | + | 29672.2i | −0.797113 | + | 1.38064i | 0.124375 | + | 0.992235i | \(0.460307\pi\) |
−0.921489 | + | 0.388405i | \(0.873026\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15946.0 | 0.739094 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7710.50 | + | 13355.0i | 0.356001 | + | 0.616612i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18673.5 | 0.858854 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11037.1 | 0.505681 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13088.3 | + | 22669.5i | 0.597364 | + | 1.03467i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3712.33 | 0.168788 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6321.29 | + | 10948.8i | −0.286315 | + | 0.495912i | −0.972927 | − | 0.231112i | \(-0.925764\pi\) |
0.686612 | + | 0.727024i | \(0.259097\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1016.91 | + | 1761.33i | −0.0458844 | + | 0.0794741i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1601.00 | − | 2773.01i | −0.0719658 | − | 0.124648i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6558.51 | − | 3762.22i | 0.293694 | − | 0.168474i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7469.65 | + | 12937.8i | 0.333234 | + | 0.577178i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9542.18 | + | 16527.5i | −0.424092 | + | 0.734549i | −0.996335 | − | 0.0855350i | \(-0.972740\pi\) |
0.572243 | + | 0.820084i | \(0.306073\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −260.577 | + | 451.333i | −0.0115376 | + | 0.0199837i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9820.53 | 0.433198 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9219.77 | + | 15969.1i | 0.405179 | + | 0.701790i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 119.971 | 0.00525269 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23173.0 | 1.01082 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5805.02 | − | 10054.6i | −0.252279 | − | 0.436960i | 0.711874 | − | 0.702307i | \(-0.247847\pi\) |
−0.964153 | + | 0.265347i | \(0.914513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9613.36 | −0.416240 | −0.208120 | − | 0.978103i | \(-0.566734\pi\) | ||||
−0.208120 | + | 0.978103i | \(0.566734\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24756.8 | + | 42880.1i | −1.06797 | + | 1.84978i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5062.95 | + | 8769.29i | −0.217604 | + | 0.376901i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12865.2 | + | 22283.2i | 0.550914 | + | 0.954211i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −60.5065 | + | 21701.8i | −0.00258153 | + | 0.925913i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13240.7 | + | 22933.6i | 0.562856 | + | 0.974895i | 0.997246 | + | 0.0741699i | \(0.0236307\pi\) |
−0.434390 | + | 0.900725i | \(0.643036\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6907.25 | − | 11963.7i | 0.292553 | − | 0.506718i | −0.681859 | − | 0.731483i | \(-0.738828\pi\) |
0.974413 | + | 0.224766i | \(0.0721617\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20049.0 | − | 34726.0i | 0.846082 | − | 1.46546i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44401.0 | 1.86696 | 0.933479 | − | 0.358633i | \(-0.116757\pi\) | ||||
0.933479 | + | 0.358633i | \(0.116757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12168.7 | − | 21076.8i | −0.509815 | − | 0.883025i | −0.999935 | − | 0.0113707i | \(-0.996381\pi\) |
0.490120 | − | 0.871655i | \(-0.336953\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 62116.9 | 2.59303 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −506.966 | −0.0210868 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4794.86 | − | 8304.95i | −0.198722 | − | 0.344197i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25332.2 | 1.04613 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12340.0 | + | 21373.6i | −0.507778 | + | 0.879497i | 0.492181 | + | 0.870493i | \(0.336200\pi\) |
−0.999959 | + | 0.00900472i | \(0.997134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2297.22 | − | 3978.90i | 0.0941907 | − | 0.163143i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26631.0 | − | 46126.2i | −1.08804 | − | 1.88454i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3054.49 | + | 5359.33i | 0.124352 | + | 0.218185i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1067.05 | + | 1848.18i | 0.0432872 | + | 0.0749757i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14664.7 | + | 25400.0i | −0.592805 | + | 1.02677i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −414.943 | + | 718.702i | −0.0167145 | + | 0.0289504i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10151.7 | −0.407490 | −0.203745 | − | 0.979024i | \(-0.565311\pi\) | ||||
−0.203745 | + | 0.979024i | \(0.565311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4091.90 | − | 7087.39i | −0.163673 | − | 0.283489i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2028.92 | 0.0808713 | 0.0404357 | − | 0.999182i | \(-0.487125\pi\) | ||||
0.0404357 | + | 0.999182i | \(0.487125\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6655.76 | −0.264367 | −0.132184 | − | 0.991225i | \(-0.542199\pi\) | ||||
−0.132184 | + | 0.991225i | \(0.542199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12880.6 | − | 22309.9i | −0.509837 | − | 0.883064i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45690.8 | −1.80224 | −0.901121 | − | 0.433568i | \(-0.857254\pi\) | ||||
−0.901121 | + | 0.433568i | \(0.857254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3288.21 | + | 5695.35i | −0.129251 | + | 0.223870i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21316.2 | + | 36920.8i | −0.834991 | + | 1.44625i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −739.934 | − | 1281.60i | −0.0288844 | − | 0.0500292i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.52092 | − | 2338.85i | 0.000253677 | − | 0.0909861i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28433.4 | + | 49248.1i | 1.10232 | + | 1.90927i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3250.00 | + | 5629.17i | −0.125566 | + | 0.217486i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15223.8 | + | 26368.3i | −0.586168 | + | 1.01527i | 0.408560 | + | 0.912731i | \(0.366031\pi\) |
−0.994729 | + | 0.102542i | \(0.967302\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 40859.3 | 1.56786 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16271.0 | − | 28182.2i | −0.622230 | − | 1.07773i | −0.989070 | − | 0.147450i | \(-0.952894\pi\) |
0.366840 | − | 0.930284i | \(-0.380440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27641.9 | −1.05348 | −0.526741 | − | 0.850026i | \(-0.676586\pi\) | ||||
−0.526741 | + | 0.850026i | \(0.676586\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12628.4 | −0.479658 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20050.0 | + | 34727.5i | 0.758976 | + | 1.31458i | 0.943373 | + | 0.331733i | \(0.107633\pi\) |
−0.184397 | + | 0.982852i | \(0.559033\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5936.70 | 0.223971 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6078.80 | − | 10528.8i | 0.228561 | − | 0.395879i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7783.38 | + | 13481.2i | −0.291670 | + | 0.505186i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −936.236 | − | 1621.61i | −0.0349664 | − | 0.0605636i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1577.91 | + | 905.150i | −0.0587345 | + | 0.0336924i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9578.06 | + | 16589.7i | 0.355335 | + | 0.615458i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −617.299 | + | 1069.19i | −0.0228249 | + | 0.0395338i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17748.3 | − | 30741.0i | 0.654072 | − | 1.13289i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1968.35 | −0.0722984 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18412.4 | − | 31891.3i | −0.674062 | − | 1.16751i | −0.976742 | − | 0.214418i | \(-0.931215\pi\) |
0.302679 | − | 0.953092i | \(-0.402119\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 47004.3 | 1.71511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34520.5 | −1.25545 | −0.627725 | − | 0.778435i | \(-0.716014\pi\) | ||||
−0.627725 | + | 0.778435i | \(0.716014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1501.15 | + | 2600.06i | 0.0544148 | + | 0.0942491i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3933.47 | 0.142117 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6366.58 | − | 11027.2i | 0.229273 | − | 0.397112i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11761.4 | − | 20371.3i | 0.422168 | − | 0.731216i | −0.573983 | − | 0.818867i | \(-0.694603\pi\) |
0.996151 | + | 0.0876506i | \(0.0279359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22278.3 | − | 38587.1i | −0.797062 | − | 1.38055i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11382.6 | − | 6529.53i | 0.405920 | − | 0.232852i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10874.8 | − | 18835.6i | −0.386551 | − | 0.669526i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45994.8 | + | 79665.3i | −1.62963 | + | 2.82260i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12281.6 | − | 21272.3i | 0.433741 | − | 0.751262i | −0.563451 | − | 0.826150i | \(-0.690527\pi\) |
0.997192 | + | 0.0748880i | \(0.0238599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15143.0 | −0.533073 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34516.9 | − | 59785.0i | −1.21118 | − | 2.09783i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −223.060 | −0.00780197 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12115.6 | −0.422411 | −0.211206 | − | 0.977442i | \(-0.567739\pi\) | ||||
−0.211206 | + | 0.977442i | \(0.567739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37004.8 | − | 64094.2i | −1.28605 | − | 2.22751i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14898.3 | 0.516123 | 0.258062 | − | 0.966128i | \(-0.416916\pi\) | ||||
0.258062 | + | 0.966128i | \(0.416916\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 693.174 | − | 1200.61i | 0.0239373 | − | 0.0414606i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2497.46 | + | 4325.72i | −0.0859707 | + | 0.148906i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3717.16 | + | 6438.31i | 0.127552 | + | 0.220926i | 0.922727 | − | 0.385453i | \(-0.125955\pi\) |
−0.795176 | + | 0.606379i | \(0.792621\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18955.8 | + | 11014.7i | 0.648399 | + | 0.376767i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28930.6 | − | 50109.2i | −0.986476 | − | 1.70863i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11764.3 | − | 20376.3i | 0.399877 | − | 0.692607i | −0.593833 | − | 0.804588i | \(-0.702386\pi\) |
0.993710 | + | 0.111981i | \(0.0357195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1826.28 | − | 3163.21i | 0.0618818 | − | 0.107182i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 48170.2 | 1.62709 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2973.72 | + | 5150.63i | 0.100132 | + | 0.173433i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11252.7 | −0.377723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 92318.7 | 3.08923 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 729.083 | + | 1262.81i | 0.0243213 | + | 0.0421256i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23558.0 | −0.783427 | −0.391713 | − | 0.920087i | \(-0.628118\pi\) | ||||
−0.391713 | + | 0.920087i | \(0.628118\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 526.710 | − | 912.289i | 0.0174617 | − | 0.0302445i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −131.169 | + | 227.191i | −0.00433513 | + | 0.00750866i | −0.868185 | − | 0.496241i | \(-0.834713\pi\) |
0.863850 | + | 0.503750i | \(0.168047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1580.43 | − | 2737.39i | −0.0520722 | − | 0.0901918i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 132.920 | − | 47674.3i | 0.00436600 | − | 1.56595i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16572.2 | − | 28703.9i | −0.542673 | − | 0.939936i | −0.998749 | − | 0.0499960i | \(-0.984079\pi\) |
0.456077 | − | 0.889940i | \(-0.349254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3997.64 | − | 6924.11i | 0.130506 | − | 0.226042i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21693.7 | − | 37574.6i | 0.706042 | − | 1.22290i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4866.80 | 0.157911 | 0.0789557 | − | 0.996878i | \(-0.474841\pi\) | ||||
0.0789557 | + | 0.996878i | \(0.474841\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4381.58 | − | 7589.12i | −0.141735 | − | 0.245492i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21475.3 | 0.692569 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1910.26 | 0.0614184 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6266.97 | + | 10854.7i | 0.200885 | + | 0.347943i | 0.948814 | − | 0.315836i | \(-0.102285\pi\) |
−0.747929 | + | 0.663779i | \(0.768952\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33972.4 | −1.08568 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1736.68 | − | 3008.02i | 0.0553332 | − | 0.0958399i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1780.46 | − | 3083.84i | 0.0565574 | − | 0.0979602i | −0.836361 | − | 0.548180i | \(-0.815321\pi\) |
0.892918 | + | 0.450220i | \(0.148654\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17275.9 | − | 29922.7i | −0.547132 | − | 0.947660i |
(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 | 208.4.i.e.81.2 | 4 | ||
4.3 | odd | 2 | 13.4.c.b.3.2 | ✓ | 4 | ||
12.11 | even | 2 | 117.4.g.d.55.1 | 4 | |||
13.9 | even | 3 | inner | 208.4.i.e.113.2 | 4 | ||
52.3 | odd | 6 | 169.4.a.f.1.1 | 2 | |||
52.7 | even | 12 | 169.4.e.g.147.4 | 8 | |||
52.11 | even | 12 | 169.4.b.e.168.1 | 4 | |||
52.15 | even | 12 | 169.4.b.e.168.4 | 4 | |||
52.19 | even | 12 | 169.4.e.g.147.1 | 8 | |||
52.23 | odd | 6 | 169.4.a.j.1.2 | 2 | |||
52.31 | even | 4 | 169.4.e.g.23.4 | 8 | |||
52.35 | odd | 6 | 13.4.c.b.9.2 | yes | 4 | ||
52.43 | odd | 6 | 169.4.c.f.22.1 | 4 | |||
52.47 | even | 4 | 169.4.e.g.23.1 | 8 | |||
52.51 | odd | 2 | 169.4.c.f.146.1 | 4 | |||
156.23 | even | 6 | 1521.4.a.l.1.1 | 2 | |||
156.35 | even | 6 | 117.4.g.d.100.1 | 4 | |||
156.107 | even | 6 | 1521.4.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.c.b.3.2 | ✓ | 4 | 4.3 | odd | 2 | ||
13.4.c.b.9.2 | yes | 4 | 52.35 | odd | 6 | ||
117.4.g.d.55.1 | 4 | 12.11 | even | 2 | |||
117.4.g.d.100.1 | 4 | 156.35 | even | 6 | |||
169.4.a.f.1.1 | 2 | 52.3 | odd | 6 | |||
169.4.a.j.1.2 | 2 | 52.23 | odd | 6 | |||
169.4.b.e.168.1 | 4 | 52.11 | even | 12 | |||
169.4.b.e.168.4 | 4 | 52.15 | even | 12 | |||
169.4.c.f.22.1 | 4 | 52.43 | odd | 6 | |||
169.4.c.f.146.1 | 4 | 52.51 | odd | 2 | |||
169.4.e.g.23.1 | 8 | 52.47 | even | 4 | |||
169.4.e.g.23.4 | 8 | 52.31 | even | 4 | |||
169.4.e.g.147.1 | 8 | 52.19 | even | 12 | |||
169.4.e.g.147.4 | 8 | 52.7 | even | 12 | |||
208.4.i.e.81.2 | 4 | 1.1 | even | 1 | trivial | ||
208.4.i.e.113.2 | 4 | 13.9 | even | 3 | inner | ||
1521.4.a.l.1.1 | 2 | 156.23 | even | 6 | |||
1521.4.a.t.1.2 | 2 | 156.107 | even | 6 |