Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(589,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.j (of order \(3\), degree \(2\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} + 16x^{8} - 39x^{6} + 144x^{4} - 162x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 589.6 | ||
Root | \(0.965975 + 1.43767i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.589 |
Dual form | 1764.2.j.f.1177.6 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.72805 | + | 0.117725i | 0.997687 | + | 0.0679684i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.95014 | + | 3.37774i | −0.872128 | + | 1.51057i | −0.0123362 | + | 0.999924i | \(0.503927\pi\) |
−0.859791 | + | 0.510645i | \(0.829407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.97228 | + | 0.406867i | 0.990761 | + | 0.135622i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.13378 | + | 3.69582i | 0.643360 | + | 1.11433i | 0.984678 | + | 0.174384i | \(0.0557935\pi\) |
−0.341318 | + | 0.939948i | \(0.610873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.71221 | − | 4.69768i | 0.752231 | − | 1.30290i | −0.194508 | − | 0.980901i | \(-0.562311\pi\) |
0.946739 | − | 0.322001i | \(-0.104355\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.76757 | + | 5.60730i | −0.972782 | + | 1.44780i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.98023 | 1.20788 | 0.603942 | − | 0.797028i | \(-0.293596\pi\) | ||||
0.603942 | + | 0.797028i | \(0.293596\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.444182 | −0.101902 | −0.0509512 | − | 0.998701i | \(-0.516225\pi\) | ||||
−0.0509512 | + | 0.998701i | \(0.516225\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.10607 | + | 7.11191i | −0.856174 | + | 1.48294i | 0.0193779 | + | 0.999812i | \(0.493831\pi\) |
−0.875552 | + | 0.483124i | \(0.839502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.10607 | − | 8.84396i | −1.02121 | − | 1.76879i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.08834 | + | 1.05300i | 0.979251 | + | 0.202649i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.33850 | + | 2.31835i | 0.248553 | + | 0.430506i | 0.963125 | − | 0.269056i | \(-0.0867117\pi\) |
−0.714572 | + | 0.699562i | \(0.753378\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.425996 | + | 0.737847i | −0.0765112 | + | 0.132521i | −0.901742 | − | 0.432274i | \(-0.857711\pi\) |
0.825231 | + | 0.564795i | \(0.191045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.25219 | + | 6.63775i | 0.566133 | + | 1.15548i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.80270 | −1.61155 | −0.805777 | − | 0.592219i | \(-0.798252\pi\) | ||||
−0.805777 | + | 0.592219i | \(0.798252\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.23985 | − | 7.79851i | 0.839047 | − | 1.24876i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.69402 | − | 4.66618i | 0.420735 | − | 0.728735i | −0.575276 | − | 0.817959i | \(-0.695105\pi\) |
0.996012 | + | 0.0892242i | \(0.0284388\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.31078 | + | 7.46649i | 0.657388 | + | 1.13863i | 0.981289 | + | 0.192538i | \(0.0616720\pi\) |
−0.323902 | + | 0.946091i | \(0.604995\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.17065 | + | 9.24614i | −1.06894 | + | 1.37833i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.74623 | − | 3.02456i | −0.254714 | − | 0.441178i | 0.710104 | − | 0.704097i | \(-0.248648\pi\) |
−0.964818 | + | 0.262919i | \(0.915315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.60607 | + | 0.586296i | 1.20509 | + | 0.0820979i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.67700 | −0.779795 | −0.389898 | − | 0.920858i | \(-0.627490\pi\) | ||||
−0.389898 | + | 0.920858i | \(0.627490\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.6447 | −2.24437 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.767567 | − | 0.0522912i | −0.101667 | − | 0.00692614i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.947789 | − | 1.64162i | 0.123392 | − | 0.213721i | −0.797711 | − | 0.603039i | \(-0.793956\pi\) |
0.921103 | + | 0.389319i | \(0.127290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.62832 | + | 9.74853i | 0.720632 | + | 1.24817i | 0.960747 | + | 0.277427i | \(0.0894817\pi\) |
−0.240114 | + | 0.970745i | \(0.577185\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.5783 | + | 18.3222i | 1.31208 | + | 2.27259i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.29529 | + | 2.24350i | −0.158244 | + | 0.274087i | −0.934236 | − | 0.356656i | \(-0.883917\pi\) |
0.775991 | + | 0.630744i | \(0.217250\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.93272 | + | 11.8063i | −0.954987 | + | 1.42131i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.141862 | 0.0168359 | 0.00841794 | − | 0.999965i | \(-0.497320\pi\) | ||||
0.00841794 | + | 0.999965i | \(0.497320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.3319 | −1.20926 | −0.604629 | − | 0.796507i | \(-0.706678\pi\) | ||||
−0.604629 | + | 0.796507i | \(0.706678\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.78236 | − | 15.8839i | −0.898630 | − | 1.83411i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.204714 | + | 0.354576i | 0.0230322 | + | 0.0398929i | 0.877312 | − | 0.479921i | \(-0.159335\pi\) |
−0.854280 | + | 0.519814i | \(0.826001\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.66892 | + | 2.41865i | 0.963213 | + | 0.268739i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.08231 | + | 3.60666i | 0.228563 | + | 0.395882i | 0.957382 | − | 0.288823i | \(-0.0932641\pi\) |
−0.728820 | + | 0.684706i | \(0.759931\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.71213 | + | 16.8219i | −1.05343 | + | 1.82459i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.04006 | + | 4.16378i | 0.218717 | + | 0.446404i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.41251 | 0.255725 | 0.127863 | − | 0.991792i | \(-0.459188\pi\) | ||||
0.127863 | + | 0.991792i | \(0.459188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.823004 | + | 1.22488i | −0.0853415 | + | 0.127014i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.866216 | − | 1.50033i | 0.0888719 | − | 0.153931i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.80448 | + | 6.58955i | 0.386286 | + | 0.669067i | 0.991947 | − | 0.126656i | \(-0.0404244\pi\) |
−0.605661 | + | 0.795723i | \(0.707091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.83850 | + | 11.8532i | 0.486287 | + | 1.19129i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.56185 | − | 4.43726i | −0.254914 | − | 0.441524i | 0.709958 | − | 0.704244i | \(-0.248714\pi\) |
−0.964872 | + | 0.262720i | \(0.915380\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.48031 | − | 11.2242i | 0.638524 | − | 1.10596i | −0.347233 | − | 0.937779i | \(-0.612879\pi\) |
0.985757 | − | 0.168177i | \(-0.0537880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.5351 | −1.11514 | −0.557572 | − | 0.830129i | \(-0.688267\pi\) | ||||
−0.557572 | + | 0.830129i | \(0.688267\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.409429 | −0.0392162 | −0.0196081 | − | 0.999808i | \(-0.506242\pi\) | ||||
−0.0196081 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.9395 | − | 1.15402i | −1.60783 | − | 0.109535i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.94456 | + | 12.0283i | −0.653290 | + | 1.13153i | 0.329030 | + | 0.944319i | \(0.393278\pi\) |
−0.982320 | + | 0.187211i | \(0.940055\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.0148 | − | 27.7384i | −1.49339 | − | 2.58662i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.97277 | − | 12.8593i | 0.921983 | − | 1.18884i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.60607 | + | 6.24589i | −0.327824 | + | 0.567808i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.20471 | − | 7.74622i | 0.469293 | − | 0.698453i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.3287 | 1.81826 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6216 | 1.03125 | 0.515623 | − | 0.856815i | \(-0.327560\pi\) | ||||
0.515623 | + | 0.856815i | \(0.327560\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.57023 | + | 13.4099i | 0.578477 | + | 1.18068i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.02775 | + | 3.51216i | −0.177165 | + | 0.306859i | −0.940908 | − | 0.338661i | \(-0.890026\pi\) |
0.763743 | + | 0.645520i | \(0.223359\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.4797 | + | 15.1336i | −1.16015 | + | 1.30249i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.57835 | − | 7.92993i | −0.391155 | − | 0.677500i | 0.601448 | − | 0.798912i | \(-0.294591\pi\) |
−0.992602 | + | 0.121413i | \(0.961258\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.23869 | − | 9.07369i | 0.444340 | − | 0.769620i | −0.553666 | − | 0.832739i | \(-0.686771\pi\) |
0.998006 | + | 0.0631191i | \(0.0201048\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.66150 | − | 5.43215i | −0.224139 | − | 0.457470i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.1490 | 1.93582 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4410 | −0.867079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.13378 | − | 14.0881i | 0.666346 | − | 1.15414i | −0.312573 | − | 0.949894i | \(-0.601191\pi\) |
0.978919 | − | 0.204251i | \(-0.0654757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.60607 | + | 6.24589i | 0.293457 | + | 0.508283i | 0.974625 | − | 0.223844i | \(-0.0718608\pi\) |
−0.681167 | + | 0.732128i | \(0.738527\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.8027 | + | 2.02629i | 1.19672 | + | 0.163816i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.66150 | − | 2.87781i | −0.133455 | − | 0.231151i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.593529 | + | 1.02802i | −0.0473688 | + | 0.0820451i | −0.888738 | − | 0.458416i | \(-0.848417\pi\) |
0.841369 | + | 0.540461i | \(0.181750\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.81011 | − | 0.668322i | −0.777992 | − | 0.0530014i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0148 | 1.64601 | 0.823004 | − | 0.568035i | \(-0.192296\pi\) | ||||
0.823004 | + | 0.568035i | \(0.192296\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −28.7628 | − | 1.95949i | −2.23918 | − | 0.152546i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.0322 | − | 17.3763i | 0.776315 | − | 1.34462i | −0.157738 | − | 0.987481i | \(-0.550420\pi\) |
0.934053 | − | 0.357136i | \(-0.116247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.21213 | − | 14.2238i | −0.631702 | − | 1.09414i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.32024 | − | 0.180723i | −0.100961 | − | 0.0138202i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.03009 | − | 5.24828i | −0.230374 | − | 0.399019i | 0.727544 | − | 0.686061i | \(-0.240662\pi\) |
−0.957918 | + | 0.287042i | \(0.907328\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.83108 | − | 2.72521i | 0.137633 | − | 0.204840i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.83369 | 0.660261 | 0.330131 | − | 0.943935i | \(-0.392907\pi\) | ||||
0.330131 | + | 0.943935i | \(0.392907\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.1809 | −1.79735 | −0.898676 | − | 0.438614i | \(-0.855470\pi\) | ||||
−0.898676 | + | 0.438614i | \(0.855470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.57835 | + | 17.5085i | 0.634130 | + | 1.29427i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.1166 | − | 33.1109i | 1.40548 | − | 2.43436i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.6267 | + | 18.4060i | 0.777104 | + | 1.34598i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1135 | − | 17.5171i | −0.731786 | − | 1.26749i | −0.956119 | − | 0.292978i | \(-0.905354\pi\) |
0.224333 | − | 0.974512i | \(-0.427980\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.19664 | − | 10.7329i | 0.446044 | − | 0.772570i | −0.552081 | − | 0.833791i | \(-0.686166\pi\) |
0.998124 | + | 0.0612205i | \(0.0194993\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.1229 | + | 32.9070i | 1.15458 | + | 2.35652i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.3933 | 1.02548 | 0.512739 | − | 0.858544i | \(-0.328631\pi\) | ||||
0.512739 | + | 0.858544i | \(0.328631\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5138 | 0.745301 | 0.372650 | − | 0.927972i | \(-0.378449\pi\) | ||||
0.372650 | + | 0.927972i | \(0.378449\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.50243 | + | 3.72438i | −0.176508 | + | 0.262698i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.5074 | + | 18.1994i | 0.733870 | + | 1.27110i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.0980 | + | 19.4680i | −1.04938 | + | 1.35312i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.947789 | − | 1.64162i | −0.0655599 | − | 0.113553i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7121 | − | 20.2860i | 0.806296 | − | 1.39655i | −0.109116 | − | 0.994029i | \(-0.534802\pi\) |
0.915412 | − | 0.402517i | \(-0.131865\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.245143 | + | 0.0167006i | 0.0167969 | + | 0.00114431i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.6264 | −2.29330 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.8540 | − | 1.21632i | −1.20646 | − | 0.0821912i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.5074 | − | 23.3955i | 0.908607 | − | 1.57375i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6727 | − | 21.9497i | −0.848625 | − | 1.46986i | −0.882436 | − | 0.470433i | \(-0.844098\pi\) |
0.0338111 | − | 0.999428i | \(-0.489236\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.5783 | − | 28.3642i | −0.771890 | − | 1.89095i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.01267 | + | 15.6104i | 0.598192 | + | 1.03610i | 0.993088 | + | 0.117373i | \(0.0374474\pi\) |
−0.394896 | + | 0.918726i | \(0.629219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.71221 | − | 4.69768i | 0.179228 | − | 0.310431i | −0.762389 | − | 0.647120i | \(-0.775973\pi\) |
0.941616 | + | 0.336688i | \(0.109307\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.84331 | −0.186271 | −0.0931356 | − | 0.995653i | \(-0.529689\pi\) | ||||
−0.0931356 | + | 0.995653i | \(0.529689\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.6216 | 0.888573 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.312014 | + | 0.636823i | 0.0202675 | + | 0.0413661i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.09057 | + | 10.5492i | −0.393966 | + | 0.682370i | −0.992969 | − | 0.118378i | \(-0.962231\pi\) |
0.599002 | + | 0.800747i | \(0.295564\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.31237 | − | 16.1295i | −0.599863 | − | 1.03899i | −0.992841 | − | 0.119445i | \(-0.961888\pi\) |
0.392978 | − | 0.919548i | \(-0.371445\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.6956 | + | 5.20008i | 0.942720 | + | 0.333585i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.20471 | + | 2.08663i | −0.0766541 | + | 0.132769i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.17373 | + | 6.47761i | 0.201127 | + | 0.410502i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.14015 | 0.450682 | 0.225341 | − | 0.974280i | \(-0.427650\pi\) | ||||
0.225341 | + | 0.974280i | \(0.427650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.0458 | −2.20331 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.7634 | + | 27.9257i | −1.17501 | + | 1.74877i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.672148 | − | 1.16419i | 0.0419274 | − | 0.0726204i | −0.844300 | − | 0.535871i | \(-0.819984\pi\) |
0.886228 | + | 0.463250i | \(0.153317\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.03513 | + | 7.43537i | 0.187870 | + | 0.460238i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.1493 | + | 21.0432i | 0.749157 | + | 1.29758i | 0.948227 | + | 0.317592i | \(0.102874\pi\) |
−0.199071 | + | 0.979985i | \(0.563792\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0709 | − | 19.1754i | 0.680081 | − | 1.17794i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.16892 | + | 0.284011i | 0.255134 | + | 0.0173812i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.39979 | 0.329231 | 0.164615 | − | 0.986358i | \(-0.447362\pi\) | ||||
0.164615 | + | 0.986358i | \(0.447362\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.5718 | 0.824427 | 0.412213 | − | 0.911087i | \(-0.364756\pi\) | ||||
0.412213 | + | 0.911087i | \(0.364756\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.7905 | − | 37.7422i | 1.31402 | − | 2.27594i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5074 | + | 25.1276i | 0.871666 | + | 1.50977i | 0.860272 | + | 0.509835i | \(0.170294\pi\) |
0.0113940 | + | 0.999935i | \(0.496373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.56639 | + | 2.01977i | −0.0937771 | + | 0.120920i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.885857 | + | 1.53435i | 0.0528458 | + | 0.0915316i | 0.891238 | − | 0.453536i | \(-0.149837\pi\) |
−0.838392 | + | 0.545067i | \(0.816504\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.1268 | + | 21.0043i | −0.720864 | + | 1.24857i | 0.239789 | + | 0.970825i | \(0.422922\pi\) |
−0.960654 | + | 0.277749i | \(0.910412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.67349 | − | 2.49066i | 0.0991288 | − | 0.147534i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.80270 | 0.458982 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.79856 | + | 11.8349i | 0.339917 | + | 0.693775i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.52491 | + | 13.0335i | −0.439610 | + | 0.761426i | −0.997659 | − | 0.0683813i | \(-0.978217\pi\) |
0.558050 | + | 0.829808i | \(0.311550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.69664 | + | 6.40276i | 0.215226 | + | 0.372783i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.96573 | + | 21.0525i | 0.404193 | + | 1.22159i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.2730 | + | 38.5780i | 1.28808 | + | 2.23102i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.90462 | − | 7.96938i | −0.224315 | − | 0.457829i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −43.9040 | −2.51393 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.01912 | −0.229383 | −0.114692 | − | 0.993401i | \(-0.536588\pi\) | ||||
−0.114692 | + | 0.993401i | \(0.536588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.5196 | − | 18.6331i | 0.712217 | − | 1.06000i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.798442 | + | 1.38294i | −0.0452755 | + | 0.0784195i | −0.887775 | − | 0.460278i | \(-0.847750\pi\) |
0.842500 | + | 0.538697i | \(0.181083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.43556 | + | 4.21851i | 0.137666 | + | 0.238444i | 0.926613 | − | 0.376017i | \(-0.122707\pi\) |
−0.788947 | + | 0.614461i | \(0.789373\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.18922 | + | 7.25594i | 0.235290 | + | 0.407534i | 0.959357 | − | 0.282195i | \(-0.0910627\pi\) |
−0.724067 | + | 0.689730i | \(0.757729\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.71213 | + | 9.89370i | −0.319818 | + | 0.553941i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.9332 | − | 1.35797i | −1.11256 | − | 0.0757945i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.21213 | −0.123086 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −55.3948 | −3.07275 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.707512 | − | 0.0481999i | −0.0391255 | − | 0.00266546i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9168 | − | 22.3726i | −0.709974 | − | 1.22971i | −0.964866 | − | 0.262742i | \(-0.915373\pi\) |
0.254892 | − | 0.966969i | \(-0.417960\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −29.1364 | − | 3.98840i | −1.59666 | − | 0.218563i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.05197 | − | 8.75026i | −0.276018 | − | 0.478078i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.81820 | − | 17.0056i | 0.534831 | − | 0.926355i | −0.464340 | − | 0.885657i | \(-0.653709\pi\) |
0.999171 | − | 0.0406980i | \(-0.0129582\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.4166 | + | 19.9680i | −0.728687 | + | 1.08451i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.63594 | −0.196897 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.4088 | − | 49.8186i | −1.31412 | − | 2.68214i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2047 | − | 19.4071i | 0.601501 | − | 1.04183i | −0.391093 | − | 0.920351i | \(-0.627903\pi\) |
0.992594 | − | 0.121479i | \(-0.0387636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.38804 | − | 9.33236i | −0.288415 | − | 0.499550i | 0.685016 | − | 0.728528i | \(-0.259795\pi\) |
−0.973432 | + | 0.228978i | \(0.926462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.7473 | − | 21.0474i | 1.00066 | − | 1.12343i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.70106 | + | 9.87453i | 0.303437 | + | 0.525568i | 0.976912 | − | 0.213642i | \(-0.0685325\pi\) |
−0.673475 | + | 0.739210i | \(0.735199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.276650 | + | 0.479171i | −0.0146830 | + | 0.0254318i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.7634 | −0.990296 | −0.495148 | − | 0.868809i | \(-0.664886\pi\) | ||||
−0.495148 | + | 0.868809i | \(0.664886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8027 | −0.989616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.96674 | + | 10.3687i | −0.365659 | + | 0.544213i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.1486 | − | 34.8984i | 1.05463 | − | 1.82667i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.833806 | − | 1.44420i | −0.0435243 | − | 0.0753864i | 0.843443 | − | 0.537219i | \(-0.180525\pi\) |
−0.886967 | + | 0.461833i | \(0.847192\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.90590 | − | 12.7731i | 0.515681 | − | 0.664941i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5229 | − | 21.6903i | 0.648412 | − | 1.12308i | −0.335090 | − | 0.942186i | \(-0.608767\pi\) |
0.983502 | − | 0.180896i | \(-0.0578998\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 35.1290 | + | 2.39319i | 1.81405 | + | 0.123584i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.5211 | 0.747876 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.21213 | 0.267729 | 0.133865 | − | 0.991000i | \(-0.457261\pi\) | ||||
0.133865 | + | 0.991000i | \(0.457261\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.0826 | + | 1.36814i | 1.02886 | + | 0.0700921i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.2385 | + | 19.4656i | −0.574258 | + | 0.994644i | 0.421864 | + | 0.906659i | \(0.361376\pi\) |
−0.996122 | + | 0.0879849i | \(0.971957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.77498 | + | 23.9464i | 0.496890 | + | 1.21727i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.20471 | + | 9.01483i | 0.263889 | + | 0.457070i | 0.967272 | − | 0.253741i | \(-0.0816612\pi\) |
−0.703383 | + | 0.710811i | \(0.748328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.4492 | + | 35.4190i | −1.03416 | + | 1.79121i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.91751 | + | 5.83046i | −0.197612 | + | 0.294108i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.59688 | −0.0803480 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.62872 | 0.131932 | 0.0659659 | − | 0.997822i | \(-0.478987\pi\) | ||||
0.0659659 | + | 0.997822i | \(0.478987\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.59865 | − | 9.69714i | 0.279583 | − | 0.484252i | −0.691698 | − | 0.722187i | \(-0.743137\pi\) |
0.971281 | + | 0.237935i | \(0.0764704\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.31078 | + | 4.00239i | 0.115108 | + | 0.199373i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −25.0751 | + | 24.5646i | −1.24599 | + | 1.22063i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.9168 | − | 36.2290i | −1.03681 | − | 1.79581i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8654 | − | 27.4797i | 0.784495 | − | 1.35879i | −0.144805 | − | 0.989460i | \(-0.546256\pi\) |
0.929300 | − | 0.369325i | \(-0.120411\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.97804 | − | 14.2423i | −0.344202 | − | 0.702519i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.2431 | −0.797343 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.1209 | − | 15.0630i | 0.495623 | − | 0.737639i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.0449 | − | 32.9867i | 0.930403 | − | 1.61151i | 0.147770 | − | 0.989022i | \(-0.452791\pi\) |
0.782633 | − | 0.622483i | \(-0.213876\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.614143 | − | 1.06373i | −0.0299315 | − | 0.0518429i | 0.850672 | − | 0.525697i | \(-0.176196\pi\) |
−0.880603 | + | 0.473855i | \(0.842862\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.95970 | − | 9.70033i | −0.192527 | − | 0.471646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.4294 | − | 44.0450i | −1.23351 | − | 2.13650i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 40.0026 | + | 2.72521i | 1.93134 | + | 0.131575i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.32300 | −0.449073 | −0.224537 | − | 0.974466i | \(-0.572087\pi\) | ||||
−0.224537 | + | 0.974466i | \(0.572087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3849 | −0.739350 | −0.369675 | − | 0.929161i | \(-0.620531\pi\) | ||||
−0.369675 | + | 0.929161i | \(0.620531\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0426 | − | 1.22917i | −0.865074 | − | 0.0589340i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.82384 | − | 3.15899i | 0.0872462 | − | 0.151115i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.54467 | + | 4.40750i | 0.121451 | + | 0.210359i | 0.920340 | − | 0.391119i | \(-0.127912\pi\) |
−0.798889 | + | 0.601478i | \(0.794579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.3933 | + | 30.1260i | 0.826379 | + | 1.43133i | 0.900861 | + | 0.434109i | \(0.142937\pi\) |
−0.0744812 | + | 0.997222i | \(0.523730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.70471 | + | 8.14880i | −0.223025 | + | 0.386290i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.7141 | − | 23.3874i | 0.743250 | − | 1.10618i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.8337 | −1.12478 | −0.562391 | − | 0.826872i | \(-0.690118\pi\) | ||||
−0.562391 | + | 0.826872i | \(0.690118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.9938 | 1.08274 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.49615 | + | 11.2177i | 0.258232 | + | 0.527054i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.41685 | − | 14.5784i | −0.393723 | − | 0.681949i | 0.599214 | − | 0.800589i | \(-0.295480\pi\) |
−0.992937 | + | 0.118640i | \(0.962147\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.3411 | + | 5.24416i | 1.18282 | + | 0.244777i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.13780 | + | 10.6310i | 0.285866 | + | 0.495134i | 0.972819 | − | 0.231568i | \(-0.0743855\pi\) |
−0.686953 | + | 0.726702i | \(0.741052\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.10607 | − | 10.5760i | 0.283773 | − | 0.491509i | −0.688538 | − | 0.725200i | \(-0.741747\pi\) |
0.972311 | + | 0.233691i | \(0.0750805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.53236 | − | 5.16858i | −0.117435 | − | 0.239687i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.7582 | 1.56214 | 0.781071 | − | 0.624443i | \(-0.214674\pi\) | ||||
0.781071 | + | 0.624443i | \(0.214674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.14667 | + | 1.70660i | −0.0528357 | + | 0.0786358i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.3965 | + | 31.8637i | −0.845874 | + | 1.46510i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.26802 | + | 3.92833i | 0.104064 | + | 0.180244i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.8736 | − | 2.30978i | −0.772591 | − | 0.105758i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.9593 | − | 20.7141i | −0.546434 | − | 0.946451i | −0.998515 | − | 0.0544741i | \(-0.982652\pi\) |
0.452082 | − | 0.891977i | \(-0.350682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.5870 | + | 46.0500i | −1.21226 | + | 2.09970i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.6770 | −1.34756 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.3933 | −0.470964 | −0.235482 | − | 0.971879i | \(-0.575667\pi\) | ||||
−0.235482 | + | 0.971879i | \(0.575667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.3146 | + | 2.47396i | 1.64220 | + | 0.111877i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.68922 | + | 4.65787i | −0.121363 | + | 0.210207i | −0.920305 | − | 0.391201i | \(-0.872060\pi\) |
0.798943 | + | 0.601407i | \(0.205393\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.66603 | + | 11.5459i | 0.300223 | + | 0.520001i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −49.4727 | − | 6.77217i | −2.22363 | − | 0.304386i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.62156 | − | 16.6650i | 0.430720 | − | 0.746029i | −0.566215 | − | 0.824257i | \(-0.691593\pi\) |
0.996935 | + | 0.0782282i | \(0.0249263\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.3817 | − | 28.8460i | 0.865911 | − | 1.28874i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.3334 | 0.995798 | 0.497899 | − | 0.867235i | \(-0.334105\pi\) | ||||
0.497899 | + | 0.867235i | \(0.334105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.9838 | 0.889269 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.5164 | − | 25.5462i | −0.555875 | − | 1.13455i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.1131 | − | 34.8369i | 0.891497 | − | 1.54412i | 0.0534152 | − | 0.998572i | \(-0.482989\pi\) |
0.838081 | − | 0.545545i | \(-0.183677\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.26015 | − | 0.467722i | −0.0997881 | − | 0.0206504i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.2750 | + | 43.7776i | 1.11375 | + | 1.92907i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.45216 | − | 12.9075i | 0.327746 | − | 0.567672i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.61829 | − | 9.42598i | −0.202720 | − | 0.413755i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.6993 | 1.60783 | 0.803914 | − | 0.594746i | \(-0.202747\pi\) | ||||
0.803914 | + | 0.594746i | \(0.202747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3455 | 1.23946 | 0.619731 | − | 0.784814i | \(-0.287242\pi\) | ||||
0.619731 | + | 0.784814i | \(0.287242\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.12156 | + | 3.67465i | −0.0924166 | + | 0.160070i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2195 | − | 38.4854i | −0.966067 | − | 1.67328i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.48502 | − | 4.49373i | 0.151237 | − | 0.195011i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.6135 | − | 25.3113i | −0.632980 | − | 1.09635i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.4951 | − | 38.9626i | 0.972547 | − | 1.68450i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.2650 | + | 1.03994i | 0.658734 | + | 0.0448769i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.6054 | −1.05787 | −0.528934 | − | 0.848663i | \(-0.677408\pi\) | ||||
−0.528934 | + | 0.848663i | \(0.677408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −41.7857 | − | 2.84669i | −1.79319 | − | 0.122163i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.798442 | − | 1.38294i | 0.0342015 | − | 0.0592388i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.106065 | − | 0.183711i | −0.00453503 | − | 0.00785491i | 0.863749 | − | 0.503922i | \(-0.168110\pi\) |
−0.868284 | + | 0.496067i | \(0.834777\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.7626 | + | 31.2654i | 0.544694 | + | 1.33437i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.594537 | − | 1.02977i | −0.0253281 | − | 0.0438696i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36.9323 | − | 54.9667i | 1.56769 | − | 2.33321i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.8175 | 0.797325 | 0.398662 | − | 0.917098i | \(-0.369475\pi\) | ||||
0.398662 | + | 0.917098i | \(0.369475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.7669 | 1.97803 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.1966 | + | 33.0575i | 0.683823 | + | 1.39569i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.43907 | − | 11.1528i | 0.271375 | − | 0.470035i | −0.697839 | − | 0.716254i | \(-0.745855\pi\) |
0.969214 | + | 0.246220i | \(0.0791885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.0857 | − | 46.9138i | −1.13950 | − | 1.97368i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5000 | + | 23.3827i | 0.565949 | + | 0.980253i | 0.996961 | + | 0.0779066i | \(0.0248236\pi\) |
−0.431011 | + | 0.902347i | \(0.641843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.42492 | − | 9.39624i | 0.227026 | − | 0.393221i | −0.729899 | − | 0.683555i | \(-0.760433\pi\) |
0.956925 | + | 0.290334i | \(0.0937664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.4144 | − | 31.4609i | −0.643944 | − | 1.31430i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 83.8634 | 3.49734 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.2171 | −0.883279 | −0.441640 | − | 0.897192i | \(-0.645603\pi\) | ||||
−0.441640 | + | 0.897192i | \(0.645603\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.9716 | − | 17.8174i | 0.497523 | − | 0.740467i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.1135 | − | 20.9812i | −0.501689 | − | 0.868951i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.9871 | + | 58.7628i | 0.991745 | + | 2.42954i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.92684 | + | 13.7297i | 0.327176 | + | 0.566685i | 0.981950 | − | 0.189139i | \(-0.0605698\pi\) |
−0.654775 | + | 0.755824i | \(0.727236\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.189220 | − | 0.327739i | 0.00779668 | − | 0.0135042i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.8722 | + | 1.69444i | 1.02311 | + | 0.0697001i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.5160 | −1.00675 | −0.503375 | − | 0.864068i | \(-0.667908\pi\) | ||||
−0.503375 | + | 0.864068i | \(0.667908\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.1683 | + | 1.23773i | 0.743577 | + | 0.0506569i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.21213 | + | 3.83152i | −0.0903852 | + | 0.156552i | −0.907673 | − | 0.419678i | \(-0.862143\pi\) |
0.817288 | + | 0.576229i | \(0.195476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.47075 | − | 7.74357i | −0.182366 | − | 0.315867i | 0.760320 | − | 0.649549i | \(-0.225042\pi\) |
−0.942686 | + | 0.333682i | \(0.891709\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.76276 | + | 6.14131i | −0.193955 | + | 0.250093i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.0646 | − | 24.3607i | −0.571809 | − | 0.990402i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.9127 | − | 32.7578i | 0.767643 | − | 1.32960i | −0.171195 | − | 0.985237i | \(-0.554763\pi\) |
0.938838 | − | 0.344359i | \(-0.111904\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.9446 | −0.766415 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.6674 | −0.753968 | −0.376984 | − | 0.926220i | \(-0.623039\pi\) | ||||
−0.376984 | + | 0.926220i | \(0.623039\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0148 | + | 32.6863i | 0.645778 | + | 1.31804i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.9365 | + | 25.8708i | −0.601320 | + | 1.04152i | 0.391301 | + | 0.920263i | \(0.372025\pi\) |
−0.992621 | + | 0.121255i | \(0.961308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.90789 | − | 3.30456i | −0.0766846 | − | 0.132822i | 0.825133 | − | 0.564938i | \(-0.191100\pi\) |
−0.901818 | + | 0.432117i | \(0.857767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.3819 | + | 31.8642i | −1.13893 | + | 1.27866i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.1135 | + | 24.4453i | −0.564539 | + | 0.977811i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.44456 | − | 2.94837i | −0.0576903 | − | 0.117747i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −48.8197 | −1.94657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0458 | 0.798012 | 0.399006 | − | 0.916948i | \(-0.369355\pi\) | ||||
0.399006 | + | 0.916948i | \(0.369355\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.6273 | − | 33.6763i | 0.899353 | − | 1.33851i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.6636 | + | 39.2546i | −0.899379 | + | 1.55777i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.421653 | + | 0.0577188i | 0.0166803 | + | 0.00228332i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.75207 | + | 8.23083i | 0.187696 | + | 0.325098i | 0.944482 | − | 0.328564i | \(-0.106565\pi\) |
−0.756786 | + | 0.653663i | \(0.773231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0611 | + | 26.0866i | −0.593952 | + | 1.02876i | 0.399741 | + | 0.916628i | \(0.369100\pi\) |
−0.993694 | + | 0.112128i | \(0.964233\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −58.1080 | − | 3.95866i | −2.28800 | − | 0.155872i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.2535 | −0.835560 | −0.417780 | − | 0.908548i | \(-0.637192\pi\) | ||||
−0.417780 | + | 0.908548i | \(0.637192\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.08951 | 0.317541 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.225016 | − | 0.389739i | 0.00880556 | − | 0.0152517i | −0.861589 | − | 0.507606i | \(-0.830530\pi\) |
0.870395 | + | 0.492355i | \(0.163864\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.90877 | − | 13.6984i | −0.309021 | − | 0.535240i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.7093 | − | 4.20371i | −1.19808 | − | 0.164002i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.68441 | + | 15.0418i | 0.338297 | + | 0.585947i | 0.984112 | − | 0.177546i | \(-0.0568159\pi\) |
−0.645816 | + | 0.763493i | \(0.723483\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0048 | + | 29.4532i | −0.661411 | + | 1.14560i | 0.318835 | + | 0.947810i | \(0.396709\pi\) |
−0.980245 | + | 0.197786i | \(0.936625\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.0957 | − | 38.8384i | 1.01347 | − | 1.50836i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.9838 | −0.851218 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.3149 | − | 39.4220i | −0.746758 | − | 1.52414i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0192 | + | 41.6025i | −0.927252 | + | 1.60605i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.5825 | − | 18.3294i | −0.407925 | − | 0.706547i | 0.586732 | − | 0.809781i | \(-0.300414\pi\) |
−0.994657 | + | 0.103234i | \(0.967081\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.6687 | − | 50.3778i | −0.641580 | − | 1.93904i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.85745 | + | 15.3416i | 0.340420 | + | 0.589624i | 0.984511 | − | 0.175325i | \(-0.0560976\pi\) |
−0.644091 | + | 0.764949i | \(0.722764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.7366 | + | 28.0365i | 0.526387 | + | 1.07436i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.5351 | −1.24492 | −0.622461 | − | 0.782651i | \(-0.713867\pi\) | ||||
−0.622461 | + | 0.782651i | \(0.713867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.7136 | 1.36455 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.23985 | − | 7.79851i | 0.199913 | − | 0.297532i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.3972 | + | 26.6687i | −0.586586 | + | 1.01600i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.6910 | − | 27.1776i | −0.596914 | − | 1.03389i | −0.993274 | − | 0.115791i | \(-0.963060\pi\) |
0.396359 | − | 0.918095i | \(-0.370273\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.4323 | + | 35.3899i | 0.775043 | + | 1.34241i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4168 | − | 23.2387i | 0.508199 | − | 0.880227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.91336 | − | 0.334727i | −0.185840 | − | 0.0126605i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.7163 | −0.442518 | −0.221259 | − | 0.975215i | \(-0.571017\pi\) | ||||
−0.221259 | + | 0.975215i | \(0.571017\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.35419 | 0.164221 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.5387 | + | 1.60359i | 0.886518 | + | 0.0603948i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.59057 | − | 6.21905i | −0.134847 | − | 0.233561i | 0.790692 | − | 0.612214i | \(-0.209721\pi\) |
−0.925539 | + | 0.378653i | \(0.876388\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.464204 | + | 1.13719i | 0.0174090 | + | 0.0426480i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.49834 | − | 6.05930i | −0.131014 | − | 0.226922i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45.1438 | + | 78.1914i | −1.68828 | + | 2.92419i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.7667 | + | 17.5124i | −0.439435 | + | 0.654014i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.6472 | 0.583542 | 0.291771 | − | 0.956488i | \(-0.405755\pi\) | ||||
0.291771 | + | 0.956488i | \(0.405755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.1934 | − | 28.9688i | −0.527857 | − | 1.07736i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.6689 | − | 23.6753i | 0.507651 | − | 0.879277i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.5678 | − | 39.0886i | −0.836995 | − | 1.44972i | −0.892396 | − | 0.451253i | \(-0.850977\pi\) |
0.0554015 | − | 0.998464i | \(-0.482356\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.7824 | + | 10.7160i | 0.917867 | + | 0.396889i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.4687 | + | 37.1848i | 0.794048 | + | 1.37533i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.6167 | + | 35.7092i | −0.761495 | + | 1.31895i | 0.180585 | + | 0.983559i | \(0.442201\pi\) |
−0.942080 | + | 0.335388i | \(0.891133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.0554 | −0.407232 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.2418 | 1.22282 | 0.611410 | − | 0.791314i | \(-0.290603\pi\) | ||||
0.611410 | + | 0.791314i | \(0.290603\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.32745 | + | 3.46396i | −0.0855010 | + | 0.127252i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.3263 | + | 28.2779i | −0.598953 | + | 1.03742i | 0.394023 | + | 0.919101i | \(0.371083\pi\) |
−0.992976 | + | 0.118316i | \(0.962250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.7240 | + | 54.9475i | 1.16228 | + | 2.01312i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.72177 | + | 11.5672i | 0.172760 | + | 0.423223i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0384 | + | 34.7075i | −0.731212 | + | 1.26650i | 0.225154 | + | 0.974323i | \(0.427712\pi\) |
−0.956366 | + | 0.292173i | \(0.905622\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.3385 | + | 0.840571i | 0.449640 | + | 0.0306321i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.1293 | −1.02373 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8337 | 0.793559 | 0.396779 | − | 0.917914i | \(-0.370128\pi\) | ||||
0.396779 | + | 0.917914i | \(0.370128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −60.5608 | − | 4.12576i | −2.19822 | − | 0.149756i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.56067 | + | 7.89932i | −0.165324 | + | 0.286350i | −0.936770 | − | 0.349945i | \(-0.886200\pi\) |
0.771446 | + | 0.636295i | \(0.219534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −35.7115 | + | 46.0479i | −1.29115 | + | 1.66487i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.14120 | − | 8.90482i | −0.185638 | − | 0.321534i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.3654 | + | 24.8815i | −0.518028 | + | 0.897250i | 0.481753 | + | 0.876307i | \(0.340000\pi\) |
−0.999781 | + | 0.0209433i | \(0.993333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.29856 | − | 1.93265i | 0.0467664 | − | 0.0696028i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.4566 | −1.41916 | −0.709578 | − | 0.704626i | \(-0.751115\pi\) | ||||
−0.709578 | + | 0.704626i | \(0.751115\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.70066 | 0.312537 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.19664 | + | 2.07264i | −0.0428740 | + | 0.0742599i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.302702 | + | 0.524295i | 0.0108315 | + | 0.0187608i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.36952 | + | 13.2060i | 0.156154 | + | 0.471943i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.31493 | − | 4.00957i | −0.0826232 | − | 0.143108i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.51534 | + | 9.55286i | −0.196601 | + | 0.340523i | −0.947424 | − | 0.319981i | \(-0.896324\pi\) |
0.750823 | + | 0.660503i | \(0.229657\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.5172 | + | 37.7938i | 0.659230 | + | 1.34550i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61.0607 | 2.16833 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.3885 | − | 31.8326i | 0.758571 | − | 1.12899i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.15757 | + | 2.00497i | −0.0410032 | + | 0.0710196i | −0.885799 | − | 0.464070i | \(-0.846389\pi\) |
0.844796 | + | 0.535089i | \(0.179722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.69664 | − | 15.0630i | −0.307665 | − | 0.532891i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.17065 | + | 0.981569i | 0.253362 | + | 0.0346820i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.0460 | − | 38.1849i | −0.777988 | − | 1.34751i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.33108 | + | 0.635688i | 0.328470 | + | 0.0223773i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.40943 | −0.260502 | −0.130251 | − | 0.991481i | \(-0.541578\pi\) | ||||
−0.130251 | + | 0.991481i | \(0.541578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.8879 | 0.452555 | 0.226277 | − | 0.974063i | \(-0.427344\pi\) | ||||
0.226277 | + | 0.974063i | \(0.427344\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.4526 | + | 1.59773i | 0.822520 | + | 0.0560349i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.9818 | + | 70.9826i | −1.43553 | + | 2.48641i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.91477 | − | 3.31648i | −0.0669894 | − | 0.116029i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.9371 | + | 22.4078i | 0.451510 | + | 0.782037i | 0.998480 | − | 0.0551144i | \(-0.0175524\pi\) |
−0.546970 | + | 0.837152i | \(0.684219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.0310 | + | 38.1588i | −0.767952 | + | 1.33013i | 0.170720 | + | 0.985320i | \(0.445391\pi\) |
−0.938672 | + | 0.344812i | \(0.887943\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.0981 | − | 62.6550i | 1.46567 | − | 2.18137i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.81753 | −0.237069 | −0.118534 | − | 0.992950i | \(-0.537820\pi\) | ||||
−0.118534 | + | 0.992950i | \(0.537820\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.55517 | 0.297133 | 0.148567 | − | 0.988902i | \(-0.452534\pi\) | ||||
0.148567 | + | 0.988902i | \(0.452534\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.1113 | + | 45.1295i | 0.767034 | + | 1.56552i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.1283 | + | 67.7722i | 1.35409 | + | 2.34535i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.94456 | + | 3.30584i | −0.101779 | + | 0.114267i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0971 | − | 31.3451i | −0.624781 | − | 1.08215i | −0.988583 | − | 0.150676i | \(-0.951855\pi\) |
0.363803 | − | 0.931476i | \(-0.381478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.9168 | − | 18.9085i | 0.376443 | − | 0.652018i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.35017 | + | 2.75571i | 0.0465023 | + | 0.0949117i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 64.0591 | 2.20370 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.4284 | + | 34.8687i | −0.804061 | + | 1.19669i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.2505 | − | 69.7160i | 1.37977 | − | 2.38983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.97889 | + | 6.89164i | 0.136235 | + | 0.235965i | 0.926068 | − | 0.377356i | \(-0.123167\pi\) |
−0.789834 | + | 0.613321i | \(0.789833\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.18507 | − | 4.10697i | 0.108927 | − | 0.140455i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.7899 | − | 39.4733i | −0.778489 | − | 1.34838i | −0.932813 | − | 0.360362i | \(-0.882653\pi\) |
0.154324 | − | 0.988020i | \(-0.450680\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4518 | − | 18.1030i | 0.356609 | − | 0.617666i | −0.630783 | − | 0.775960i | \(-0.717266\pi\) |
0.987392 | + | 0.158294i | \(0.0505994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.77171 | −0.264552 | −0.132276 | − | 0.991213i | \(-0.542229\pi\) | ||||
−0.132276 | + | 0.991213i | \(0.542229\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.6364 | 0.803661 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.4834 | + | 0.918570i | 0.457921 | + | 0.0311963i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.873633 | + | 1.51318i | −0.0296360 | + | 0.0513310i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.02616 | + | 12.1697i | 0.238072 | + | 0.412354i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.62691 | + | 21.1339i | 0.291977 | + | 0.715274i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.6886 | − | 34.1016i | 0.664835 | − | 1.15153i | −0.314495 | − | 0.949259i | \(-0.601835\pi\) |
0.979330 | − | 0.202269i | \(-0.0648317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.5377 | + | 21.6366i | −0.490346 | + | 0.729786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.7967 | −0.902805 | −0.451402 | − | 0.892320i | \(-0.649076\pi\) | ||||
−0.451402 | + | 0.892320i | \(0.649076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.0755 | −1.44961 | −0.724803 | − | 0.688956i | \(-0.758069\pi\) | ||||
−0.724803 | + | 0.688956i | \(0.758069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.63419 | + | 11.4994i | 0.189391 | + | 0.386550i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.6253 | − | 32.2600i | 0.625377 | − | 1.08318i | −0.363091 | − | 0.931754i | \(-0.618279\pi\) |
0.988468 | − | 0.151431i | \(-0.0483881\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.55871 | + | 37.1996i | 0.320229 | + | 1.24624i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.775645 | + | 1.34346i | 0.0259560 | + | 0.0449571i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.2269 | + | 29.8379i | −0.575832 | + | 0.997370i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.9472 | + | 69.2866i | 1.13346 | + | 2.31341i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.28078 | −0.0760683 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.2728 | −0.941902 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 47.1560 | − | 81.6766i | 1.56752 | − | 2.71502i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.89327 | + | 8.47540i | 0.162478 | + | 0.281421i | 0.935757 | − | 0.352646i | \(-0.114718\pi\) |
−0.773279 | + | 0.634067i | \(0.781385\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.80917 | − | 14.2311i | −0.192678 | − | 0.472016i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2979 | + | 24.7647i | 0.473710 | + | 0.820490i | 0.999547 | − | 0.0300951i | \(-0.00958102\pi\) |
−0.525837 | + | 0.850586i | \(0.676248\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.88638 | + | 15.3917i | −0.294096 | + | 0.509390i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −75.8680 | − | 5.16858i | −2.50812 | − | 0.170868i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.2270 | −0.568265 | −0.284133 | − | 0.958785i | \(-0.591706\pi\) | ||||
−0.284133 | + | 0.958785i | \(0.591706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.94523 | − | 0.473150i | −0.228853 | − | 0.0155908i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.384758 | − | 0.666420i | 0.0126645 | − | 0.0219355i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.0532 | + | 86.6948i | 1.64574 | + | 2.85051i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.8281 | − | 30.7249i | 0.782617 | − | 1.00914i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.4299 | + | 23.2612i | 0.440620 | + | 0.763176i | 0.997736 | − | 0.0672589i | \(-0.0214254\pi\) |
−0.557116 | + | 0.830435i | \(0.688092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.54255 | + | 2.29579i | −0.0505009 | + | 0.0751608i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −82.8943 | −2.71093 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.5653 | 1.68456 | 0.842282 | − | 0.539037i | \(-0.181212\pi\) | ||||
0.842282 | + | 0.539037i | \(0.181212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.71213 | + | 7.57650i | 0.121141 | + | 0.247250i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.9002 | − | 36.2002i | 0.681328 | − | 1.18009i | −0.293248 | − | 0.956036i | \(-0.594736\pi\) |
0.974576 | − | 0.224058i | \(-0.0719305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.1237 | + | 38.3193i | 0.720445 | + | 1.24785i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.75207 | − | 8.23083i | −0.154422 | − | 0.267466i | 0.778427 | − | 0.627736i | \(-0.216018\pi\) |
−0.932848 | + | 0.360269i | \(0.882685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0222 | + | 48.5360i | −0.909641 | + | 1.57554i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.38496 | + | 13.0318i | 0.207046 | + | 0.422584i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.4539 | −1.89351 | −0.946754 | − | 0.321957i | \(-0.895659\pi\) | ||||
−0.946754 | + | 0.321957i | \(0.895659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 78.8907 | 2.55284 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.0356 | + | 16.4243i | −0.356729 | + | 0.530922i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1371 | + | 26.2181i | 0.488292 | + | 0.845747i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.2857 | − | 4.69327i | −1.10484 | − | 0.151238i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.1686 | + | 41.8612i | 0.778014 | + | 1.34756i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.09799 | + | 8.82997i | −0.163940 | + | 0.283953i | −0.936278 | − | 0.351259i | \(-0.885754\pi\) |
0.772338 | + | 0.635212i | \(0.219087\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.82266 | − | 0.260422i | −0.122802 | − | 0.00836597i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.8475 | −1.24668 | −0.623338 | − | 0.781953i | \(-0.714224\pi\) | ||||
−0.623338 | + | 0.781953i | \(0.714224\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −95.7248 | − | 6.52134i | −3.06565 | − | 0.208850i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0661 | − | 36.4876i | 0.673965 | − | 1.16734i | −0.302805 | − | 0.953052i | \(-0.597923\pi\) |
0.976770 | − | 0.214289i | \(-0.0687435\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.14776 | + | 8.91619i | 0.164523 | + | 0.284963i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.21694 | − | 0.166583i | −0.0388538 | − | 0.00531859i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.0284 | + | 29.4941i | 0.543123 | + | 0.940716i | 0.998722 | + | 0.0505312i | \(0.0160914\pi\) |
−0.455600 | + | 0.890185i | \(0.650575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.0688 | + | 48.6167i | −0.894348 | + | 1.54906i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −70.8014 | −2.25135 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.1960 | 1.30863 | 0.654317 | − | 0.756221i | \(-0.272956\pi\) | ||||
0.654317 | + | 0.756221i | \(0.272956\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.6871 | − | 40.1816i | −0.624751 | − | 1.27512i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.5033 | + | 35.5127i | −0.649997 | + | 1.12583i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.7199 | + | 27.2277i | 0.497856 | + | 0.862311i | 0.999997 | − | 0.00247444i | \(-0.000787640\pi\) |
−0.502141 | + | 0.864786i | \(0.667454\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.8795 | − | 10.3222i | −1.57812 | − | 0.326580i |
(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 | 1764.2.j.f.589.6 | yes | 12 | |
3.2 | odd | 2 | 5292.2.j.f.1765.6 | 12 | |||
7.2 | even | 3 | 1764.2.l.h.949.3 | 12 | |||
7.3 | odd | 6 | 1764.2.i.h.373.5 | 12 | |||
7.4 | even | 3 | 1764.2.i.h.373.2 | 12 | |||
7.5 | odd | 6 | 1764.2.l.h.949.4 | 12 | |||
7.6 | odd | 2 | inner | 1764.2.j.f.589.1 | ✓ | 12 | |
9.2 | odd | 6 | 5292.2.j.f.3529.6 | 12 | |||
9.7 | even | 3 | inner | 1764.2.j.f.1177.6 | yes | 12 | |
21.2 | odd | 6 | 5292.2.l.h.361.1 | 12 | |||
21.5 | even | 6 | 5292.2.l.h.361.6 | 12 | |||
21.11 | odd | 6 | 5292.2.i.h.1549.6 | 12 | |||
21.17 | even | 6 | 5292.2.i.h.1549.1 | 12 | |||
21.20 | even | 2 | 5292.2.j.f.1765.1 | 12 | |||
63.2 | odd | 6 | 5292.2.i.h.2125.6 | 12 | |||
63.11 | odd | 6 | 5292.2.l.h.3313.1 | 12 | |||
63.16 | even | 3 | 1764.2.i.h.1537.2 | 12 | |||
63.20 | even | 6 | 5292.2.j.f.3529.1 | 12 | |||
63.25 | even | 3 | 1764.2.l.h.961.3 | 12 | |||
63.34 | odd | 6 | inner | 1764.2.j.f.1177.1 | yes | 12 | |
63.38 | even | 6 | 5292.2.l.h.3313.6 | 12 | |||
63.47 | even | 6 | 5292.2.i.h.2125.1 | 12 | |||
63.52 | odd | 6 | 1764.2.l.h.961.4 | 12 | |||
63.61 | odd | 6 | 1764.2.i.h.1537.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.i.h.373.2 | 12 | 7.4 | even | 3 | |||
1764.2.i.h.373.5 | 12 | 7.3 | odd | 6 | |||
1764.2.i.h.1537.2 | 12 | 63.16 | even | 3 | |||
1764.2.i.h.1537.5 | 12 | 63.61 | odd | 6 | |||
1764.2.j.f.589.1 | ✓ | 12 | 7.6 | odd | 2 | inner | |
1764.2.j.f.589.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1764.2.j.f.1177.1 | yes | 12 | 63.34 | odd | 6 | inner | |
1764.2.j.f.1177.6 | yes | 12 | 9.7 | even | 3 | inner | |
1764.2.l.h.949.3 | 12 | 7.2 | even | 3 | |||
1764.2.l.h.949.4 | 12 | 7.5 | odd | 6 | |||
1764.2.l.h.961.3 | 12 | 63.25 | even | 3 | |||
1764.2.l.h.961.4 | 12 | 63.52 | odd | 6 | |||
5292.2.i.h.1549.1 | 12 | 21.17 | even | 6 | |||
5292.2.i.h.1549.6 | 12 | 21.11 | odd | 6 | |||
5292.2.i.h.2125.1 | 12 | 63.47 | even | 6 | |||
5292.2.i.h.2125.6 | 12 | 63.2 | odd | 6 | |||
5292.2.j.f.1765.1 | 12 | 21.20 | even | 2 | |||
5292.2.j.f.1765.6 | 12 | 3.2 | odd | 2 | |||
5292.2.j.f.3529.1 | 12 | 63.20 | even | 6 | |||
5292.2.j.f.3529.6 | 12 | 9.2 | odd | 6 | |||
5292.2.l.h.361.1 | 12 | 21.2 | odd | 6 | |||
5292.2.l.h.361.6 | 12 | 21.5 | even | 6 | |||
5292.2.l.h.3313.1 | 12 | 63.11 | odd | 6 | |||
5292.2.l.h.3313.6 | 12 | 63.38 | even | 6 |