Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,5,Mod(65,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.q (of order \(6\), 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: | \(14.8852746841\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 113.1 | ||
Root | \(4.23522 - 4.06612i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.113 |
Dual form | 144.5.q.c.65.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −8.37420 | − | 3.29740i | −0.930466 | − | 0.366378i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.6364 | + | 6.14094i | 0.425457 | + | 0.245638i | 0.697409 | − | 0.716673i | \(-0.254336\pi\) |
−0.271952 | + | 0.962311i | \(0.587669\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.14202 | − | 12.3703i | −0.145756 | − | 0.252456i | 0.783899 | − | 0.620888i | \(-0.213228\pi\) |
−0.929655 | + | 0.368432i | \(0.879895\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 59.2543 | + | 55.2261i | 0.731535 | + | 0.681804i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −90.2145 | + | 52.0854i | −0.745575 | + | 0.430458i | −0.824093 | − | 0.566455i | \(-0.808315\pi\) |
0.0785180 | + | 0.996913i | \(0.474981\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.6173 | + | 65.1551i | −0.222588 | + | 0.385533i | −0.955593 | − | 0.294690i | \(-0.904784\pi\) |
0.733005 | + | 0.680223i | \(0.238117\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −68.8224 | − | 86.4980i | −0.305877 | − | 0.384436i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 341.998i | − | 1.18338i | −0.806164 | − | 0.591692i | \(-0.798460\pi\) | ||
0.806164 | − | 0.591692i | \(-0.201540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 706.329 | 1.95659 | 0.978295 | − | 0.207218i | \(-0.0664411\pi\) | ||||
0.978295 | + | 0.207218i | \(0.0664411\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 19.0187 | + | 127.142i | 0.0431264 | + | 0.288303i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 516.421 | + | 298.156i | 0.976222 | + | 0.563622i | 0.901127 | − | 0.433554i | \(-0.142741\pi\) |
0.0750946 | + | 0.997176i | \(0.476074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −237.078 | − | 410.630i | −0.379324 | − | 0.657009i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −314.105 | − | 657.860i | −0.430871 | − | 0.902414i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1127.90 | − | 651.194i | 1.34114 | − | 0.774309i | 0.354168 | − | 0.935182i | \(-0.384764\pi\) |
0.986975 | + | 0.160873i | \(0.0514308\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 514.510 | − | 891.158i | 0.535391 | − | 0.927324i | −0.463754 | − | 0.885964i | \(-0.653498\pi\) |
0.999144 | − | 0.0413597i | \(-0.0131690\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 927.221 | − | 138.700i | 0.851442 | − | 0.127365i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 175.435i | − | 0.143212i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 563.132 | 0.411346 | 0.205673 | − | 0.978621i | \(-0.434062\pi\) | ||||
0.205673 | + | 0.978621i | \(0.434062\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 529.857 | − | 421.582i | 0.348361 | − | 0.277174i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 85.8619 | + | 49.5724i | 0.0510779 | + | 0.0294898i | 0.525321 | − | 0.850904i | \(-0.323945\pi\) |
−0.474244 | + | 0.880394i | \(0.657278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −448.257 | − | 776.404i | −0.242432 | − | 0.419905i | 0.718974 | − | 0.695037i | \(-0.244612\pi\) |
−0.961407 | + | 0.275132i | \(0.911279\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 291.114 | + | 951.286i | 0.143760 | + | 0.469771i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −372.885 | + | 215.285i | −0.168802 | + | 0.0974581i | −0.582021 | − | 0.813174i | \(-0.697738\pi\) |
0.413219 | + | 0.910632i | \(0.364405\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1098.48 | − | 1902.63i | 0.457511 | − | 0.792432i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1127.70 | + | 2863.96i | −0.433565 | + | 1.10110i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5271.47i | 1.87664i | 0.345773 | + | 0.938318i | \(0.387617\pi\) | ||||
−0.345773 | + | 0.938318i | \(0.612383\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1279.41 | −0.422947 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5914.94 | − | 2329.05i | −1.82054 | − | 0.716851i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4883.74 | + | 2819.63i | 1.40297 | + | 0.810005i | 0.994696 | − | 0.102854i | \(-0.0327975\pi\) |
0.408274 | + | 0.912859i | \(0.366131\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −565.626 | − | 979.693i | −0.152009 | − | 0.263287i | 0.779957 | − | 0.625833i | \(-0.215241\pi\) |
−0.931966 | + | 0.362546i | \(0.881908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 259.971 | − | 1127.42i | 0.0655003 | − | 0.284057i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −800.227 | + | 462.012i | −0.189403 | + | 0.109352i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −676.412 | + | 1171.58i | −0.150682 | + | 0.260989i | −0.931478 | − | 0.363797i | \(-0.881480\pi\) |
0.780796 | + | 0.624786i | \(0.214814\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3341.48 | − | 4199.66i | −0.701843 | − | 0.882097i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5681.42i | − | 1.12704i | −0.826101 | − | 0.563522i | \(-0.809446\pi\) | ||
0.826101 | − | 0.563522i | \(-0.190554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4236.54 | 0.794996 | 0.397498 | − | 0.917603i | \(-0.369878\pi\) | ||||
0.397498 | + | 0.917603i | \(0.369878\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 631.322 | + | 4220.44i | 0.112235 | + | 0.750300i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1288.63 | + | 743.990i | 0.217343 | + | 0.125483i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3067.71 | − | 5313.43i | −0.491542 | − | 0.851375i | 0.508411 | − | 0.861115i | \(-0.330233\pi\) |
−0.999953 | + | 0.00973957i | \(0.996900\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 461.150 | + | 6544.77i | 0.0702866 | + | 0.997527i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6503.75 | + | 3754.94i | −0.944077 | + | 0.545063i | −0.891236 | − | 0.453540i | \(-0.850161\pi\) |
−0.0528411 | + | 0.998603i | \(0.516828\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2100.19 | − | 3637.64i | 0.290684 | − | 0.503479i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11592.5 | + | 1734.09i | −1.53158 | + | 0.229104i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8721.70i | 1.10109i | 0.834807 | + | 0.550543i | \(0.185579\pi\) | ||||
−0.834807 | + | 0.550543i | \(0.814421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1074.65 | 0.129774 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7247.12 | + | 5766.19i | −0.837914 | + | 0.666688i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7512.81 | + | 4337.53i | 0.832445 | + | 0.480612i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2720.65 | − | 4712.31i | −0.289154 | − | 0.500830i | 0.684454 | − | 0.729056i | \(-0.260041\pi\) |
−0.973608 | + | 0.228226i | \(0.926707\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8222.08 | − | 1895.92i | −0.838902 | − | 0.193441i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6480.14 | − | 3741.31i | 0.635246 | − | 0.366759i | −0.147535 | − | 0.989057i | \(-0.547134\pi\) |
0.782781 | + | 0.622297i | \(0.213801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6788.27 | − | 11757.6i | 0.639860 | − | 1.10827i | −0.345604 | − | 0.938381i | \(-0.612326\pi\) |
0.985463 | − | 0.169889i | \(-0.0543408\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −578.479 | + | 1469.13i | −0.0524698 | + | 0.133254i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16741.7i | 1.46229i | 0.682224 | + | 0.731143i | \(0.261013\pi\) | ||||
−0.682224 | + | 0.731143i | \(0.738987\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12068.7 | −1.01579 | −0.507897 | − | 0.861418i | \(-0.669577\pi\) | ||||
−0.507897 | + | 0.861418i | \(0.669577\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4715.78 | − | 1856.87i | −0.382743 | − | 0.150708i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 610.202 | + | 352.300i | 0.0477878 | + | 0.0275903i | 0.523704 | − | 0.851901i | \(-0.324550\pi\) |
−0.475916 | + | 0.879491i | \(0.657883\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3661.92 | + | 6342.63i | 0.276894 | + | 0.479594i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5827.25 | + | 1783.26i | −0.425689 | + | 0.130270i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4230.63 | + | 2442.56i | −0.298752 | + | 0.172485i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1894.72 | + | 3281.76i | −0.129412 | + | 0.224148i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −555.565 | − | 698.250i | −0.0367218 | − | 0.0461531i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 13499.7i | − | 0.863981i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16050.0 | 0.995105 | 0.497552 | − | 0.867434i | \(-0.334232\pi\) | ||||
0.497552 | + | 0.867434i | \(0.334232\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1193.68 | + | 7979.84i | 0.0717312 | + | 0.479529i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13427.1 | + | 7752.17i | 0.782422 | + | 0.451732i | 0.837288 | − | 0.546762i | \(-0.184140\pi\) |
−0.0548658 | + | 0.998494i | \(0.517473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5044.62 | − | 8737.53i | −0.285184 | − | 0.493953i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 698.926 | − | 8926.17i | 0.0383498 | − | 0.489776i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −771.295 | + | 445.307i | −0.0410941 | + | 0.0237257i | −0.520406 | − | 0.853919i | \(-0.674219\pi\) |
0.479312 | + | 0.877644i | \(0.340886\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4679.09 | − | 8104.42i | 0.242176 | − | 0.419462i | −0.719158 | − | 0.694847i | \(-0.755472\pi\) |
0.961334 | + | 0.275385i | \(0.0888054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3832.49 | − | 573.290i | 0.192771 | − | 0.0288361i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 7837.25i | − | 0.383258i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15995.8 | 0.760798 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15472.6 | + | 12310.8i | −0.716027 | + | 0.569709i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 35220.7 | + | 20334.7i | 1.58645 | + | 0.915937i | 0.993886 | + | 0.110412i | \(0.0352171\pi\) |
0.592563 | + | 0.805524i | \(0.298116\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12487.2 | − | 21628.5i | −0.547661 | − | 0.948577i | −0.998434 | − | 0.0559386i | \(-0.982185\pi\) |
0.450773 | − | 0.892639i | \(-0.351148\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18887.2 | − | 20264.9i | 0.806836 | − | 0.865686i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10945.1 | − | 6319.16i | 0.455572 | − | 0.263024i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16459.2 | − | 28508.2i | 0.667743 | − | 1.15656i | −0.310791 | − | 0.950478i | \(-0.600594\pi\) |
0.978534 | − | 0.206086i | \(-0.0660727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17382.1 | − | 44144.3i | 0.687557 | − | 1.74615i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 8517.75i | − | 0.328604i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13796.3 | −0.519262 | −0.259631 | − | 0.965708i | \(-0.583601\pi\) | ||||
−0.259631 | + | 0.965708i | \(0.583601\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10714.1 | + | 4218.74i | 0.393538 | + | 0.154958i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9814.14 | − | 5666.20i | −0.351900 | − | 0.203170i | 0.313622 | − | 0.949548i | \(-0.398458\pi\) |
−0.665522 | + | 0.746378i | \(0.731791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11450.4 | + | 19832.6i | 0.400910 | + | 0.694396i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 41853.0 | + | 39007.8i | 1.43131 | + | 1.33401i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −33922.6 | + | 19585.2i | −1.13344 | + | 0.654389i | −0.944797 | − | 0.327657i | \(-0.893741\pi\) |
−0.188639 | + | 0.982047i | \(0.560408\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3386.43 | + | 5865.47i | −0.110577 | + | 0.191525i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −31600.0 | − | 39715.8i | −1.00865 | − | 1.26770i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 24097.3i | − | 0.752078i | −0.926604 | − | 0.376039i | \(-0.877286\pi\) | ||
0.926604 | − | 0.376039i | \(-0.122714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10277.1 | 0.313699 | 0.156850 | − | 0.987623i | \(-0.449866\pi\) | ||||
0.156850 | + | 0.987623i | \(0.449866\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1506.22 | + | 10069.2i | 0.0449767 | + | 0.300673i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5989.72 | + | 3458.16i | 0.175010 | + | 0.101042i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17813.1 | + | 30853.2i | 0.509397 | + | 0.882301i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5894.61 | + | 8584.03i | −0.165018 | + | 0.240308i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 30337.2 | − | 17515.2i | 0.831590 | − | 0.480119i | −0.0228068 | − | 0.999740i | \(-0.507260\pi\) |
0.854397 | + | 0.519621i | \(0.173927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2620.27 | + | 4538.45i | −0.0703448 | + | 0.121841i | −0.899052 | − | 0.437841i | \(-0.855743\pi\) |
0.828708 | + | 0.559682i | \(0.189077\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8224.70 | − | 1230.31i | 0.216297 | − | 0.0323552i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 42421.5i | − | 1.09308i | −0.837431 | − | 0.546542i | \(-0.815944\pi\) | ||
0.837431 | − | 0.546542i | \(-0.184056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −31270.0 | −0.789627 | −0.394814 | − | 0.918761i | \(-0.629191\pi\) | ||||
−0.394814 | + | 0.918761i | \(0.629191\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9527.58 | − | 7580.64i | 0.235825 | − | 0.187635i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16111.0 | − | 9301.69i | −0.390958 | − | 0.225720i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 608.843 | + | 1054.55i | 0.0144876 | + | 0.0250933i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14134.2 | + | 46187.0i | 0.329861 | + | 1.07790i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −63721.1 | + | 36789.4i | −1.45878 | + | 0.842229i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15562.2 | + | 26954.6i | −0.349548 | + | 0.605435i | −0.986169 | − | 0.165742i | \(-0.946998\pi\) |
0.636621 | + | 0.771177i | \(0.280331\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18733.9 | + | 47577.4i | −0.412923 | + | 1.04868i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 11010.9i | − | 0.238202i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14698.6 | −0.312145 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −35477.6 | − | 13969.5i | −0.739717 | − | 0.291269i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22282.9 | + | 12865.0i | 0.456234 | + | 0.263407i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8013.95 | + | 13880.6i | 0.161153 | + | 0.279124i | 0.935282 | − | 0.353903i | \(-0.115146\pi\) |
−0.774130 | + | 0.633027i | \(0.781812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8629.66 | − | 37424.5i | 0.170462 | − | 0.739250i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −58481.7 | + | 33764.5i | −1.13493 | + | 0.655251i | −0.945170 | − | 0.326579i | \(-0.894104\pi\) |
−0.189759 | + | 0.981831i | \(0.560771\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −39032.9 | + | 67607.0i | −0.744321 | + | 1.28920i | 0.206191 | + | 0.978512i | \(0.433893\pi\) |
−0.950512 | + | 0.310689i | \(0.899440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8338.00 | − | 10479.4i | −0.156256 | − | 0.196388i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 61204.9i | − | 1.12739i | −0.825983 | − | 0.563696i | \(-0.809379\pi\) | ||
0.825983 | − | 0.563696i | \(-0.190621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5288.21 | −0.0957576 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8169.11 | + | 54611.2i | 0.145438 | + | 0.972266i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −37373.3 | − | 21577.5i | −0.654282 | − | 0.377750i | 0.135813 | − | 0.990735i | \(-0.456635\pi\) |
−0.790095 | + | 0.612984i | \(0.789969\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28103.8 | + | 48677.2i | 0.483873 | + | 0.838092i | 0.999828 | − | 0.0185233i | \(-0.00589649\pi\) |
−0.515956 | + | 0.856615i | \(0.672563\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17719.0 | − | 56327.8i | 0.300072 | − | 0.953916i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23367.9 | − | 13491.4i | 0.389302 | − | 0.224764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26570.2 | + | 46020.9i | −0.435513 | + | 0.754330i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 66845.2 | − | 9999.16i | 1.07813 | − | 0.161274i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15739.4i | − | 0.249828i | −0.992168 | − | 0.124914i | \(-0.960135\pi\) | ||
0.992168 | − | 0.124914i | \(-0.0398655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −62118.3 | −0.970462 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −29582.1 | + | 23537.1i | −0.454935 | + | 0.361970i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −50887.7 | − | 29380.0i | −0.770454 | − | 0.444822i | 0.0625827 | − | 0.998040i | \(-0.480066\pi\) |
−0.833036 | + | 0.553218i | \(0.813400\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4021.91 | − | 6966.14i | −0.0599560 | − | 0.103847i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 102796. | + | 23703.6i | 1.50902 | + | 0.347962i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −81699.8 | + | 47169.4i | −1.18116 | + | 0.681944i | −0.956283 | − | 0.292443i | \(-0.905532\pi\) |
−0.224879 | + | 0.974387i | \(0.572199\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32371.8 | + | 56069.6i | −0.460973 | + | 0.798428i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28758.9 | − | 73037.2i | 0.403413 | − | 1.02452i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 79782.6i | − | 1.10256i | −0.834319 | − | 0.551282i | \(-0.814139\pi\) | ||
0.834319 | − | 0.551282i | \(-0.185861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 76677.1 | 1.04406 | 0.522032 | − | 0.852926i | \(-0.325174\pi\) | ||||
0.522032 | + | 0.852926i | \(0.325174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8999.37 | − | 3543.57i | −0.120750 | − | 0.0475461i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 42775.7 | + | 24696.6i | 0.565629 | + | 0.326566i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −56577.9 | − | 97995.9i | −0.737374 | − | 1.27717i | −0.953674 | − | 0.300842i | \(-0.902732\pi\) |
0.216300 | − | 0.976327i | \(-0.430601\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 79702.2 | − | 24390.6i | 1.02391 | − | 0.313338i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −83614.5 | + | 48274.8i | −1.05893 | + | 0.611376i | −0.925137 | − | 0.379633i | \(-0.876050\pi\) |
−0.133797 | + | 0.991009i | \(0.542717\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15268.5 | − | 26445.9i | 0.190645 | − | 0.330206i | −0.754819 | − | 0.655933i | \(-0.772275\pi\) |
0.945464 | + | 0.325726i | \(0.105609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −48611.2 | − | 61096.0i | −0.598476 | − | 0.752183i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1416.19i | − | 0.0171932i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33441.6 | −0.400397 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7244.92 | + | 48432.9i | 0.0855555 | + | 0.571945i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3511.45 | + | 2027.34i | 0.0409026 | + | 0.0236151i | 0.520312 | − | 0.853976i | \(-0.325816\pi\) |
−0.479409 | + | 0.877591i | \(0.659149\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34630.4 | + | 59981.5i | 0.397936 | + | 0.689245i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 62601.7 | + | 42988.2i | 0.709697 | + | 0.487345i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38852.8 | + | 22431.7i | −0.434590 | + | 0.250911i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6402.92 | + | 11090.2i | −0.0706717 | + | 0.122407i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −66602.6 | + | 9962.87i | −0.725447 | + | 0.108517i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13893.9i | − | 0.149357i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −44297.5 | −0.470005 | −0.235002 | − | 0.971995i | \(-0.575510\pi\) | ||||
−0.235002 | + | 0.971995i | \(0.575510\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −95615.9 | + | 76077.1i | −1.00141 | + | 0.796777i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 82350.1 | + | 47544.8i | 0.851419 | + | 0.491567i | 0.861129 | − | 0.508386i | \(-0.169758\pi\) |
−0.00971065 | + | 0.999953i | \(0.503091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 85286.0 | + | 147720.i | 0.870541 | + | 1.50782i | 0.861438 | + | 0.507862i | \(0.169564\pi\) |
0.00910220 | + | 0.999959i | \(0.497103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9688.60 | − | 10395.3i | 0.0976427 | − | 0.104765i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 105654. | − | 60999.2i | 1.05140 | − | 0.607024i | 0.128356 | − | 0.991728i | \(-0.459030\pi\) |
0.923040 | + | 0.384704i | \(0.125697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −67835.4 | + | 117494.i | −0.666615 | + | 1.15461i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 55204.1 | − | 140198.i | 0.535749 | − | 1.36061i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 241563.i | − | 2.31540i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 35672.9 | 0.337731 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 101065. | + | 39795.2i | 0.945163 | + | 0.372164i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5326.30 | + | 3075.14i | 0.0492078 | + | 0.0284101i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −47607.1 | − | 82457.9i | −0.434526 | − | 0.752621i | 0.562731 | − | 0.826640i | \(-0.309751\pi\) |
−0.997257 | + | 0.0740192i | \(0.976417\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 33368.0 | + | 31099.6i | 0.300914 | + | 0.280457i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14389.2 | + | 8307.62i | −0.128218 | + | 0.0740265i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4204.88 | + | 7283.07i | −0.0370249 | + | 0.0641291i | −0.883944 | − | 0.467593i | \(-0.845121\pi\) |
0.846919 | + | 0.531722i | \(0.178455\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3948.28 | − | 4962.31i | −0.0343564 | − | 0.0431802i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 107194.i | 0.921852i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −65677.6 | −0.558250 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9751.45 | − | 65189.2i | −0.0819277 | − | 0.547694i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5224.52 | − | 3016.38i | −0.0433897 | − | 0.0250511i | 0.478148 | − | 0.878279i | \(-0.341308\pi\) |
−0.521538 | + | 0.853228i | \(0.674642\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −69799.9 | − | 120897.i | −0.573065 | − | 0.992577i | −0.996249 | − | 0.0865335i | \(-0.972421\pi\) |
0.423184 | − | 0.906044i | \(-0.360912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 54678.7 | + | 4281.38i | 0.443817 | + | 0.0347512i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −73954.5 | + | 42697.7i | −0.593493 | + | 0.342653i | −0.766477 | − | 0.642271i | \(-0.777992\pi\) |
0.172985 | + | 0.984925i | \(0.444659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34889.3 | − | 60430.1i | 0.276844 | − | 0.479508i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 43482.2 | − | 6504.37i | 0.341174 | − | 0.0510351i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 90712.4i | − | 0.703846i | −0.936029 | − | 0.351923i | \(-0.885528\pi\) | ||
0.936029 | − | 0.351923i | \(-0.114472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 368579. | 2.82824 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26688.1 | − | 21234.4i | 0.202537 | − | 0.161149i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 45061.6 | + | 26016.3i | 0.338237 | + | 0.195281i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12770.7 | − | 22119.5i | −0.0948160 | − | 0.164226i | 0.814716 | − | 0.579860i | \(-0.196893\pi\) |
−0.909532 | + | 0.415634i | \(0.863560\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2350.00 | + | 7679.20i | 0.0172590 | + | 0.0563979i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 65209.9 | − | 37649.0i | 0.473768 | − | 0.273530i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 117264. | − | 203107.i | 0.842844 | − | 1.45985i | −0.0446361 | − | 0.999003i | \(-0.514213\pi\) |
0.887480 | − | 0.460846i | \(-0.152454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −44513.9 | + | 113049.i | −0.316543 | + | 0.803905i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 97984.7i | 0.689407i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 107483. | 0.748278 | 0.374139 | − | 0.927373i | \(-0.377938\pi\) | ||||
0.374139 | + | 0.927373i | \(0.377938\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −134406. | − | 52923.4i | −0.925911 | − | 0.364584i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 142398. | + | 82213.7i | 0.970750 | + | 0.560463i | 0.899465 | − | 0.436993i | \(-0.143957\pi\) |
0.0712849 | + | 0.997456i | \(0.477290\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9137.60 | + | 15826.8i | 0.0616468 | + | 0.106775i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16316.6 | − | 70760.8i | 0.108945 | − | 0.472466i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 158396. | − | 91449.9i | 1.04675 | − | 0.604343i | 0.125015 | − | 0.992155i | \(-0.460102\pi\) |
0.921739 | + | 0.387811i | \(0.126769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 101969. | − | 176615.i | 0.666981 | − | 1.15525i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −86879.6 | − | 109193.i | −0.562513 | − | 0.706983i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 75354.6i | − | 0.482965i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −277717. | −1.76206 | −0.881031 | − | 0.473059i | \(-0.843150\pi\) | ||||
−0.881031 | + | 0.473059i | \(0.843150\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13433.5 | + | 89803.9i | 0.0843807 | + | 0.564092i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −145546. | − | 84030.8i | −0.905128 | − | 0.522576i | −0.0262679 | − | 0.999655i | \(-0.508362\pi\) |
−0.878861 | + | 0.477079i | \(0.841696\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38709.0 | + | 67046.0i | 0.238343 | + | 0.412822i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −35286.1 | + | 72444.9i | −0.215126 | + | 0.441670i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −50802.7 | + | 29331.0i | −0.306689 | + | 0.177067i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 44190.6 | − | 76540.3i | 0.264170 | − | 0.457555i | −0.703176 | − | 0.711016i | \(-0.748235\pi\) |
0.967346 | + | 0.253461i | \(0.0815688\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7927.33 | − | 1185.82i | 0.0469292 | − | 0.00701999i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 80551.4i | − | 0.472251i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −92235.5 | −0.535552 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −65907.1 | + | 52439.2i | −0.379018 | + | 0.301567i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 131141. | + | 75714.4i | 0.746983 | + | 0.431271i | 0.824603 | − | 0.565712i | \(-0.191399\pi\) |
−0.0776195 | + | 0.996983i | \(0.524732\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 66110.2 | + | 114506.i | 0.372996 | + | 0.646048i | 0.990025 | − | 0.140893i | \(-0.0449972\pi\) |
−0.617029 | + | 0.786940i | \(0.711664\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −33984.4 | − | 7836.40i | −0.189932 | − | 0.0437962i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −140435. | + | 81080.0i | −0.777494 | + | 0.448886i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8079.43 | + | 13994.0i | −0.0443124 | + | 0.0767512i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25842.5 | + | 65630.7i | −0.140417 | + | 0.356609i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 231482.i | 1.24613i | 0.782170 | + | 0.623065i | \(0.214113\pi\) | ||||
−0.782170 | + | 0.623065i | \(0.785887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −218090. | −1.16321 | −0.581607 | − | 0.813470i | \(-0.697576\pi\) | ||||
−0.581607 | + | 0.813470i | \(0.697576\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −133952. | − | 52744.5i | −0.707897 | − | 0.278739i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 364763. | + | 210596.i | 1.91007 | + | 1.10278i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 44778.5 | + | 77558.6i | 0.232349 | + | 0.402440i | 0.958499 | − | 0.285096i | \(-0.0920256\pi\) |
−0.726150 | + | 0.687536i | \(0.758692\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 170165. | − | 52074.0i | 0.874968 | − | 0.267759i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −228878. | + | 132143.i | −1.16626 | + | 0.673343i | −0.952797 | − | 0.303607i | \(-0.901809\pi\) |
−0.213467 | + | 0.976950i | \(0.568476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −53559.5 | + | 92767.7i | −0.270468 | + | 0.468465i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −227894. | − | 286424.i | −1.14056 | − | 1.43349i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 33967.2i | − | 0.168487i | −0.996445 | − | 0.0842435i | \(-0.973153\pi\) | ||
0.996445 | − | 0.0842435i | \(-0.0268474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10328.0 | −0.0507765 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33252.7 | + | 222297.i | 0.162043 | + | 1.08327i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11430.5 | + | 6599.40i | 0.0552131 | + | 0.0318773i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41636.9 | − | 72117.2i | −0.199363 | − | 0.345308i | 0.748959 | − | 0.662617i | \(-0.230554\pi\) |
−0.948322 | + | 0.317309i | \(0.897221\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −224987. | + | 107423.i | −1.06790 | + | 0.509885i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −49805.5 | + | 28755.2i | −0.234355 | + | 0.135305i | −0.612580 | − | 0.790409i | \(-0.709868\pi\) |
0.378224 | + | 0.925714i | \(0.376535\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40897.0 | − | 70835.6i | 0.190778 | − | 0.330438i | −0.754730 | − | 0.656035i | \(-0.772232\pi\) |
0.945508 | + | 0.325598i | \(0.105566\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −112493. | + | 16827.5i | −0.520260 | + | 0.0778241i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 161762.i | 0.741726i | 0.928688 | + | 0.370863i | \(0.120938\pi\) | ||||
−0.928688 | + | 0.370863i | \(0.879062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19323.8 | 0.0878511 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −231835. | + | 184460.i | −1.04505 | + | 0.831498i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 80878.6 | + | 46695.3i | 0.361503 | + | 0.208714i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −167455. | − | 290040.i | −0.742182 | − | 1.28550i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −291123. | + | 312357.i | −1.27950 | + | 1.37282i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −111249. | + | 64229.4i | −0.484868 | + | 0.279939i | −0.722443 | − | 0.691430i | \(-0.756981\pi\) |
0.237575 | + | 0.971369i | \(0.423648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21183.5 | + | 36690.9i | −0.0915605 | + | 0.158587i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28086.4 | + | 71329.3i | −0.120393 | + | 0.305755i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 66829.5i | − | 0.284109i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 255021. | 1.07527 | 0.537636 | − | 0.843177i | \(-0.319318\pi\) | ||||
0.537636 | + | 0.843177i | \(0.319318\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 115533. | + | 45491.8i | 0.483155 | + | 0.190246i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 151163. | + | 87274.1i | 0.627023 | + | 0.362012i | 0.779598 | − | 0.626280i | \(-0.215423\pi\) |
−0.152575 | + | 0.988292i | \(0.548757\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −222707. | − | 385740.i | −0.916305 | − | 1.58709i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −75810.8 | − | 70657.1i | −0.309400 | − | 0.288367i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −70281.2 | + | 40576.9i | −0.284529 | + | 0.164273i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 104865. | − | 181631.i | 0.421141 | − | 0.729438i | −0.574910 | − | 0.818216i | \(-0.694963\pi\) |
0.996051 | + | 0.0887787i | \(0.0282964\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 63501.8 | + | 79811.0i | 0.252994 | + | 0.317971i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 288148.i | 1.13888i | 0.822031 | + | 0.569442i | \(0.192841\pi\) | ||||
−0.822031 | + | 0.569442i | \(0.807159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 91900.8 | 0.360360 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30491.6 | − | 203839.i | −0.118622 | − | 0.792996i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 73335.8 | + | 42340.5i | 0.283061 | + | 0.163426i | 0.634809 | − | 0.772669i | \(-0.281079\pi\) |
−0.351747 | + | 0.936095i | \(0.614412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30257.4 | − | 52407.4i | −0.115875 | − | 0.200702i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −221861. | − | 464665.i | −0.843037 | − | 1.76565i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 144406. | − | 83372.8i | 0.544466 | − | 0.314347i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22426.4 | − | 38843.7i | 0.0839032 | − | 0.145325i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 348655. | − | 52154.2i | 1.29438 | − | 0.193622i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 80148.3i | 0.295270i | 0.989042 | + | 0.147635i | \(0.0471660\pi\) | ||||
−0.989042 | + | 0.147635i | \(0.952834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −127783. | −0.467163 | −0.233581 | − | 0.972337i | \(-0.575045\pi\) | ||||
−0.233581 | + | 0.972337i | \(0.575045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 47699.4 | − | 37952.2i | 0.173059 | − | 0.137695i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −304774. | − | 175962.i | −1.09738 | − | 0.633573i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37873.6 | + | 65598.9i | 0.135340 | + | 0.234415i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 133666. | + | 436785.i | 0.474057 | + | 1.54910i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6459.79 | + | 3729.56i | −0.0227386 | + | 0.0131281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −102810. | + | 178072.i | −0.359193 | + | 0.622140i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −79458.5 | + | 201796.i | −0.275544 | + | 0.699783i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 228860.i | 0.787756i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1167.97 | 0.00399060 | 0.00199530 | − | 0.999998i | \(-0.499365\pi\) | ||||
0.00199530 | + | 0.999998i | \(0.499365\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −86062.4 | − | 33887.7i | −0.291886 | − | 0.114932i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −128367. | − | 74112.9i | −0.432177 | − | 0.249518i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 138903. | + | 240586.i | 0.464232 | + | 0.804074i | 0.999167 | − | 0.0408196i | \(-0.0129969\pi\) |
−0.534934 | + | 0.844894i | \(0.679664\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20588.9 | − | 89288.4i | 0.0683105 | − | 0.296244i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 796669. | − | 459957.i | 2.62407 | − | 1.51501i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43819.3 | + | 75897.3i | −0.143290 | + | 0.248185i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −38756.1 | − | 48709.8i | −0.125821 | − | 0.158136i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 127126.i | 0.409755i | 0.978788 | + | 0.204877i | \(0.0656795\pi\) | ||||
−0.978788 | + | 0.204877i | \(0.934320\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 67448.9 | 0.215850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −47435.1 | − | 317107.i | −0.150721 | − | 1.00758i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −107207. | − | 61896.1i | −0.338226 | − | 0.195275i | 0.321261 | − | 0.946991i | \(-0.395893\pi\) |
−0.659487 | + | 0.751716i | \(0.729227\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4326.91 | + | 7494.43i | 0.0135544 | + | 0.0234770i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 77667.6 | − | 52447.5i | 0.241587 | − | 0.163139i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 53531.2 | − | 30906.3i | 0.165342 | − | 0.0954601i | −0.415046 | − | 0.909801i | \(-0.636234\pi\) |
0.580388 | + | 0.814340i | \(0.302901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −102067. | + | 176786.i | −0.313050 | + | 0.542219i | −0.979021 | − | 0.203759i | \(-0.934684\pi\) |
0.665971 | + | 0.745978i | \(0.268018\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −311805. | + | 46641.9i | −0.949671 | + | 0.142058i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 282745.i | − | 0.855182i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 555504. | 1.66854 | 0.834269 | − | 0.551358i | \(-0.185890\pi\) | ||||
0.834269 | + | 0.551358i | \(0.185890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36907.8 | − | 29365.8i | 0.110093 | − | 0.0875960i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 92899.9 | + | 53635.8i | 0.275209 | + | 0.158892i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −274567. | − | 475563.i | −0.807813 | − | 1.39917i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −72932.0 | − | 16817.3i | −0.213111 | − | 0.0491410i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6076.70 | + | 3508.38i | −0.0176357 | + | 0.0101820i | −0.508792 | − | 0.860890i | \(-0.669908\pi\) |
0.491156 | + | 0.871071i | \(0.336574\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 363414. | − | 629451.i | 1.04754 | − | 1.81439i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −139881. | + | 355246.i | −0.400482 | + | 1.01708i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 77064.9i | 0.219153i | 0.993978 | + | 0.109576i | \(0.0349494\pi\) | ||||
−0.993978 | + | 0.109576i | \(0.965051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −59998.4 | −0.169475 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 261861. | + | 103110.i | 0.734721 | + | 0.289302i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −473683. | − | 273481.i | −1.32018 | − | 0.762208i | −0.336425 | − | 0.941710i | \(-0.609218\pi\) |
−0.983757 | + | 0.179503i | \(0.942551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 269988. | + | 467633.i | 0.747473 | + | 1.29466i | 0.949030 | + | 0.315184i | \(0.102066\pi\) |
−0.201558 | + | 0.979477i | \(0.564600\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −104782. | + | 32065.6i | −0.288173 | + | 0.0881870i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40306.2 | + | 23270.8i | −0.110119 | + | 0.0635770i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 249663. | − | 432429.i | 0.677606 | − | 1.17365i | −0.298094 | − | 0.954536i | \(-0.596351\pi\) |
0.975700 | − | 0.219111i | \(-0.0703157\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 104245. | + | 131019.i | 0.281075 | + | 0.353263i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 32393.8i | − | 0.0867719i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 80551.4 | 0.214364 | 0.107182 | − | 0.994239i | \(-0.465817\pi\) | ||||
0.107182 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1621.31 | − | 10838.6i | −0.00428662 | − | 0.0286564i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 385247. | + | 222423.i | 1.01197 | + | 0.584263i | 0.911769 | − | 0.410703i | \(-0.134717\pi\) |
0.100205 | + | 0.994967i | \(0.468050\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 280471. | + | 485789.i | 0.731992 | + | 1.26785i | 0.956031 | + | 0.293267i | \(0.0947423\pi\) |
−0.224039 | + | 0.974580i | \(0.571924\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 33934.4 | − | 433385.i | 0.0879947 | − | 1.12380i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 107890. | − | 62290.6i | 0.277976 | − | 0.160489i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −65272.6 | + | 113055.i | −0.167098 | + | 0.289422i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 654923. | − | 97967.8i | 1.66592 | − | 0.249200i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 192590.i | − | 0.486780i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −621772. | −1.56161 | −0.780805 | − | 0.624775i | \(-0.785191\pi\) | ||||
−0.780805 | + | 0.624775i | \(0.785191\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 219201. | − | 174408.i | 0.547060 | − | 0.435270i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 170715. | + | 98562.4i | 0.423374 | + | 0.244435i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 82643.9 | + | 143144.i | 0.203672 | + | 0.352771i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 313763. | − | 336649.i | 0.768423 | − | 0.824471i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −279418. | + | 161322.i | −0.680045 | + | 0.392624i | −0.799872 | − | 0.600171i | \(-0.795099\pi\) |
0.119827 | + | 0.992795i | \(0.461766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −244906. | + | 424190.i | −0.592350 | + | 1.02598i | 0.401565 | + | 0.915830i | \(0.368466\pi\) |
−0.993915 | + | 0.110149i | \(0.964867\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −36307.3 | + | 92207.3i | −0.0872718 | + | 0.221639i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26885.7i | 0.0642263i | 0.999484 | + | 0.0321132i | \(0.0102237\pi\) | ||||
−0.999484 | + | 0.0321132i | \(0.989776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −587446. | −1.39469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 123089. | + | 48467.1i | 0.290440 | + | 0.114363i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −618540. | − | 357114.i | −1.45058 | − | 0.837492i | −0.452065 | − | 0.891985i | \(-0.649313\pi\) |
−0.998514 | + | 0.0544925i | \(0.982646\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 95211.2 | + | 164911.i | 0.221925 | + | 0.384385i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 251033. | + | 233967.i | 0.581568 | + | 0.542032i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −203254. | + | 117349.i | −0.468024 | + | 0.270214i | −0.715412 | − | 0.698703i | \(-0.753761\pi\) |
0.247388 | + | 0.968916i | \(0.420428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −313281. | + | 542619.i | −0.717020 | + | 1.24191i | 0.245155 | + | 0.969484i | \(0.421161\pi\) |
−0.962175 | + | 0.272431i | \(0.912172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −144180. | − | 181210.i | −0.328004 | − | 0.412245i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 123915.i | − | 0.280208i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 776630. | 1.74567 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21340.6 | − | 142664.i | −0.0476821 | − | 0.318758i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 102055. | + | 58921.7i | 0.226668 | + | 0.130867i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −320999. | − | 555987.i | −0.708718 | − | 1.22754i | −0.965333 | − | 0.261022i | \(-0.915940\pi\) |
0.256614 | − | 0.966514i | \(-0.417393\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −195670. | + | 284945.i | −0.429454 | + | 0.625393i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 568932. | − | 328473.i | 1.24132 | − | 0.716675i | 0.271955 | − | 0.962310i | \(-0.412330\pi\) |
0.969362 | + | 0.245635i | \(0.0789964\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38861.9 | + | 67310.9i | −0.0842917 | + | 0.145998i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 601072. | − | 89912.5i | 1.29608 | − | 0.193877i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 76710.6i | − | 0.164442i | −0.996614 | − | 0.0822212i | \(-0.973799\pi\) | ||
0.996614 | − | 0.0822212i | \(-0.0262014\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10938.4 | −0.0233117 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 549796. | − | 437447.i | 1.16490 | − | 0.926856i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −343463. | − | 198299.i | −0.723505 | − | 0.417716i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −285435. | − | 494387.i | −0.597793 | − | 1.03541i | −0.993146 | − | 0.116878i | \(-0.962711\pi\) |
0.395354 | − | 0.918529i | \(-0.370622\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 35269.1 | + | 115251.i | 0.0734393 | + | 0.239981i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 99537.6 | − | 57468.1i | 0.206071 | − | 0.118975i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16953.7 | − | 29364.6i | 0.0348978 | − | 0.0604447i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −201817. | + | 512542.i | −0.413051 | + | 1.04900i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4271.71i | 0.00869292i | 0.999991 | + | 0.00434646i | \(0.00138353\pi\) | ||||
−0.999991 | + | 0.00434646i | \(0.998616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 397757. | 0.804835 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 44284.5 | + | 17437.3i | 0.0890992 | + | 0.0350834i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −92562.7 | − | 53441.1i | −0.185181 | − | 0.106914i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −74221.7 | − | 128556.i | −0.147652 | − | 0.255740i | 0.782707 | − | 0.622390i | \(-0.213838\pi\) |
−0.930359 | + | 0.366650i | \(0.880505\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 111665. | − | 484262.i | 0.220891 | − | 0.957946i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 531408. | − | 306809.i | 1.04532 | − | 0.603516i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48128.1 | − | 83360.3i | 0.0941427 | − | 0.163060i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 241822. | + | 303928.i | 0.470389 | + | 0.591198i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 549881.i | 1.06368i | 0.846845 | + | 0.531840i | \(0.178499\pi\) | ||||
−0.846845 | + | 0.531840i | \(0.821501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −193928. | −0.373052 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −74838.6 | − | 500302.i | −0.143169 | − | 0.957096i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −534800. | − | 308767.i | −1.01746 | − | 0.587429i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 322003. | + | 557726.i | 0.609244 | + | 1.05524i | 0.991365 | + | 0.131130i | \(0.0418605\pi\) |
−0.382121 | + | 0.924112i | \(0.624806\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −334117. | + | 413274.i | −0.628701 | + | 0.777647i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −265528. | + | 153303.i | −0.496908 | + | 0.286890i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −416415. | + | 721253.i | −0.775031 | + | 1.34239i | 0.159747 | + | 0.987158i | \(0.448932\pi\) |
−0.934777 | + | 0.355234i | \(0.884401\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −240174. | + | 35926.8i | −0.444581 | + | 0.0665035i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 140925.i | − | 0.259449i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −472487. | −0.865170 | −0.432585 | − | 0.901593i | \(-0.642398\pi\) | ||||
−0.432585 | + | 0.901593i | \(0.642398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 374253. | − | 297776.i | 0.681599 | − | 0.542316i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −847338. | − | 489211.i | −1.53490 | − | 0.886173i | −0.999126 | − | 0.0418100i | \(-0.986688\pi\) |
−0.535771 | − | 0.844363i | \(-0.679979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 249749. | + | 432577.i | 0.449977 | + | 0.779383i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −592746. | − | 136680.i | −1.06225 | − | 0.244943i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 207101. | − | 119570.i | 0.369163 | − | 0.213136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −83140.6 | + | 144004.i | −0.147412 | + | 0.255325i | −0.930270 | − | 0.366875i | \(-0.880428\pi\) |
0.782858 | + | 0.622200i | \(0.213761\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −51899.1 | + | 131805.i | −0.0915313 | + | 0.232456i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 306733.i | − | 0.538105i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −238453. | −0.416114 | −0.208057 | − | 0.978117i | \(-0.566714\pi\) | ||||
−0.208057 | + | 0.978117i | \(0.566714\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 520191. | + | 204829.i | 0.902982 | + | 0.355556i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −518174. | − | 299168.i | −0.894759 | − | 0.516589i | −0.0192628 | − | 0.999814i | \(-0.506132\pi\) |
−0.875496 | + | 0.483225i | \(0.839465\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 86194.6 | + | 149294.i | 0.148058 | + | 0.256444i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 325338. | − | 99560.3i | 0.555919 | − | 0.170123i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −367426. | + | 212134.i | −0.624568 | + | 0.360594i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −333662. | + | 577919.i | −0.564227 | + | 0.977270i | 0.432894 | + | 0.901445i | \(0.357492\pi\) |
−0.997121 | + | 0.0758248i | \(0.975841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 329266. | + | 413831.i | 0.553909 | + | 0.696169i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 848153.i | 1.41943i | 0.704487 | + | 0.709717i | \(0.251177\pi\) | ||||
−0.704487 | + | 0.709717i | \(0.748823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −487916. | −0.812347 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10710.1 | + | 71597.7i | 0.0177399 | + | 0.118592i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 60646.7 | + | 35014.4i | 0.0999384 | + | 0.0576995i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 295919. | + | 512547.i | 0.485145 | + | 0.840295i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −782673. | − | 537457.i | −1.27661 | − | 0.876639i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 350134. | − | 202150.i | 0.568192 | − | 0.328046i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −483866. | + | 838081.i | −0.781225 | + | 1.35312i | 0.150004 | + | 0.988685i | \(0.452071\pi\) |
−0.931229 | + | 0.364436i | \(0.881262\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 839706. | − | 125609.i | 1.34888 | − | 0.201775i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10064.6i | − | 0.0160858i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 85109.3 | 0.135341 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 455972. | − | 362795.i | 0.721446 | − | 0.574020i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −583828. | − | 337073.i | −0.919111 | − | 0.530649i | −0.0357599 | − | 0.999360i | \(-0.511385\pi\) |
−0.883351 | + | 0.468711i | \(0.844718\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 73627.0 | + | 127526.i | 0.115330 | + | 0.199758i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −481666. | + | 516798.i | −0.750725 | + | 0.805482i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −382197. | + | 220662.i | −0.592729 | + | 0.342212i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 52307.0 | − | 90598.4i | 0.0807176 | − | 0.139807i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −263075. | + | 668115.i | −0.403955 | + | 1.02590i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 570317.i | 0.871403i | 0.900091 | + | 0.435702i | \(0.143500\pi\) | ||||
−0.900091 | + | 0.435702i | \(0.856500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 111731. | 0.169876 | 0.0849379 | − | 0.996386i | \(-0.472931\pi\) | ||||
0.0849379 | + | 0.996386i | \(0.472931\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −642109. | − | 252835.i | −0.971466 | − | 0.382522i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −146743. | − | 84722.1i | −0.220923 | − | 0.127550i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −316617. | − | 548396.i | −0.474340 | − | 0.821581i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 63678.0 | + | 59349.0i | 0.0949339 | + | 0.0884801i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −902069. | + | 520810.i | −1.33830 | + | 0.772668i | −0.986555 | − | 0.163429i | \(-0.947745\pi\) |
−0.351744 | + | 0.936096i | \(0.614411\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54486.5 | + | 94373.5i | −0.0804432 | + | 0.139332i | −0.903440 | − | 0.428714i | \(-0.858967\pi\) |
0.822997 | + | 0.568045i | \(0.192300\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −276778. | − | 347862.i | −0.406652 | − | 0.511093i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 550908.i | − | 0.805505i | −0.915309 | − | 0.402753i | \(-0.868053\pi\) | ||
0.915309 | − | 0.402753i | \(-0.131947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −57256.0 | −0.0833128 | −0.0416564 | − | 0.999132i | \(-0.513263\pi\) | ||||
−0.0416564 | + | 0.999132i | \(0.513263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 150663. | + | 1.00720e6i | 0.218175 | + | 1.45852i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −650695. | − | 375679.i | −0.937751 | − | 0.541411i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −69591.6 | − | 120536.i | −0.0998122 | − | 0.172880i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −747867. | − | 58558.5i | −1.06751 | − | 0.0835871i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 824201. | − | 475853.i | 1.17087 | − | 0.676003i | 0.216986 | − | 0.976175i | \(-0.430377\pi\) |
0.953885 | + | 0.300172i | \(0.0970439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 494467. | − | 856442.i | 0.699110 | − | 1.21089i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 859385. | − | 128553.i | 1.20930 | − | 0.180895i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 281264.i | 0.393914i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 54128.7 | 0.0754502 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −215064. | + | 171117.i | −0.298369 | + | 0.237398i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 290814. | + | 167901.i | 0.401565 | + | 0.231844i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 511433. | + | 885829.i | 0.702896 | + | 1.21745i | 0.967446 | + | 0.253079i | \(0.0814434\pi\) |
−0.264550 | + | 0.964372i | \(0.585223\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 205622. | + | 671921.i | 0.281279 | + | 0.919149i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 572818. | − | 330717.i | 0.779929 | − | 0.450292i | −0.0564763 | − | 0.998404i | \(-0.517987\pi\) |
0.836405 | + | 0.548112i | \(0.184653\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51374.6 | − | 88983.5i | 0.0696246 | − | 0.120593i | −0.829112 | − | 0.559083i | \(-0.811153\pi\) |
0.898736 | + | 0.438490i | \(0.144487\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4669.74 | + | 11859.4i | −0.00629921 | + | 0.0159977i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 168806.i | 0.226655i | 0.993558 | + | 0.113328i | \(0.0361509\pi\) | ||||
−0.993558 | + | 0.113328i | \(0.963849\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −481087. | −0.642971 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 280046. | + | 110270.i | 0.372556 | + | 0.146697i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 553504. | + | 319566.i | 0.732962 | + | 0.423176i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −50889.6 | − | 88143.4i | −0.0670800 | − | 0.116186i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 99032.1 | − | 429476.i | 0.129941 | − | 0.563521i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −166996. | + | 96415.2i | −0.218117 | + | 0.125930i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 95077.8 | − | 164680.i | 0.123618 | − | 0.214112i | −0.797574 | − | 0.603221i | \(-0.793884\pi\) |
0.921192 | + | 0.389109i | \(0.127217\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22720.6 | − | 28556.0i | −0.0294065 | − | 0.0369589i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 171490.i | 0.220946i | 0.993879 | + | 0.110473i | \(0.0352366\pi\) | ||||
−0.993879 | + | 0.110473i | \(0.964763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −869284. | −1.11491 | −0.557456 | − | 0.830207i | \(-0.688222\pi\) | ||||
−0.557456 | + | 0.830207i | \(0.688222\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −92218.4 | − | 616487.i | −0.117742 | − | 0.787114i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −125013. | − | 72176.4i | −0.158894 | − | 0.0917378i | 0.418444 | − | 0.908242i | \(-0.362575\pi\) |
−0.577339 | + | 0.816505i | \(0.695909\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −114630. | − | 198545.i | −0.145042 | − | 0.251220i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −382490. | − | 566415.i | −0.481797 | − | 0.713475i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −263379. | + | 152062.i | −0.330277 | + | 0.190686i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 147980. | − | 256309.i | 0.184739 | − | 0.319977i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 399327. | − | 59734.0i | 0.496299 | − | 0.0742398i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.34018e6i | − | 1.65823i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.80283e6 | 2.22078 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 90188.1 | − | 71758.4i | 0.110605 | − | 0.0880030i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 109312. | + | 63111.1i | 0.133466 | + | 0.0770563i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53848.5 | + | 93268.3i | 0.0654574 | + | 0.113376i | 0.896897 | − | 0.442240i | \(-0.145816\pi\) |
−0.831439 | + | 0.555615i | \(0.812483\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 590595. | + | 136184.i | 0.714763 | + | 0.164816i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 617457. | − | 356489.i | 0.743994 | − | 0.429545i | −0.0795255 | − | 0.996833i | \(-0.525341\pi\) |
0.823520 | + | 0.567287i | \(0.192007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 391155. | − | 677501.i | 0.469253 | − | 0.812771i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −45813.7 | + | 116350.i | −0.0547209 | + | 0.138971i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 221465.i | − | 0.263370i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −239512. | −0.283594 | −0.141797 | − | 0.989896i | \(-0.545288\pi\) | ||||
−0.141797 | + | 0.989896i | \(0.545288\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 370956. | + | 146066.i | 0.437324 | + | 0.172199i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 370174. | + | 213720.i | 0.434512 | + | 0.250866i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −133506. | − | 231239.i | −0.156033 | − | 0.270258i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.05156e6 | − | 321801.i | 1.22370 | − | 0.374479i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.11204e6 | − | 642036.i | 1.28851 | − | 0.743923i | 0.310123 | − | 0.950696i | \(-0.399630\pi\) |
0.978389 | + | 0.206774i | \(0.0662964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 775890. | − | 1.34388e6i | 0.895160 | − | 1.55046i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −532841. | − | 669691.i | −0.612117 | − | 0.769327i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 437557.i | 0.500508i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −471000. | −0.536466 | −0.268233 | − | 0.963354i | \(-0.586440\pi\) | ||||
−0.268233 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −227111. | − | 1.51826e6i | −0.257577 | − | 1.72192i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 624803. | + | 360730.i | 0.705608 | + | 0.407383i | 0.809433 | − | 0.587212i | \(-0.199775\pi\) |
−0.103825 | + | 0.994596i | \(0.533108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29560.6 | + | 51200.5i | 0.0332422 | + | 0.0575772i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −115412. | + | 55105.0i | −0.129237 | + | 0.0617060i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 524423. | − | 302776.i | 0.584766 | − | 0.337615i | −0.178259 | − | 0.983984i | \(-0.557047\pi\) |
0.763025 | + | 0.646369i | \(0.223713\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −159367. | + | 276032.i | −0.176956 | + | 0.306497i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.08590e6 | + | 162437.i | −1.20069 | + | 0.179607i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 527043.i | 0.580310i | 0.956980 | + | 0.290155i | \(0.0937069\pi\) | ||||
−0.956980 | + | 0.290155i | \(0.906293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 430240. | 0.471741 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 955493. | − | 760240.i | 1.04329 | − | 0.830094i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11017.2 | + | 6360.79i | 0.0119794 | + | 0.00691630i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −67681.6 | − | 117228.i | −0.0732865 | − | 0.126936i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −924580. | + | 992019.i | −0.996993 | + | 1.06971i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −55740.7 | + | 32181.9i | −0.0598574 | + | 0.0345587i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −620154. | + | 1.07414e6i | −0.663203 | + | 1.14870i | 0.316566 | + | 0.948571i | \(0.397470\pi\) |
−0.979769 | + | 0.200131i | \(0.935863\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −796529. | + | 2.02290e6i | −0.848309 | + | 2.15440i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.27298e6i | 1.35015i | 0.737748 | + | 0.675076i | \(0.235889\pi\) | ||||
−0.737748 | + | 0.675076i | \(0.764111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −133673. | −0.141194 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −298732. | − | 117628.i | −0.314248 | − | 0.123737i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.19918e6 | + | 692344.i | 1.25630 | + | 0.725325i | 0.972353 | − | 0.233515i | \(-0.0750227\pi\) |
0.283947 | + | 0.958840i | \(0.408356\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −454273. | − | 786824.i | −0.473971 | − | 0.820942i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −715120. | − | 666505.i | −0.743089 | − | 0.692573i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 146384. | − | 84514.9i | 0.151491 | − | 0.0874633i | −0.422338 | − | 0.906438i | \(-0.638791\pi\) |
0.573829 | + | 0.818975i | \(0.305457\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 260508. | − | 451213.i | 0.268503 | − | 0.465061i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34463.5 | − | 43314.8i | −0.0353774 | − | 0.0444633i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 534602.i | − | 0.546560i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.57481e6 | 1.60354 | 0.801772 | − | 0.597630i | \(-0.203891\pi\) | ||||
0.801772 | + | 0.597630i | \(0.203891\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 126775. | + | 847498.i | 0.128568 | + | 0.859489i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −332601. | − | 192027.i | −0.335952 | − | 0.193962i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −285374. | − | 494282.i | −0.287094 | − | 0.497261i | 0.686021 | − | 0.727582i | \(-0.259356\pi\) |
−0.973115 | + | 0.230321i | \(0.926022\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −176883. | − | 370462.i | −0.177237 | − | 0.371204i |
(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 | 144.5.q.c.113.1 | 8 | ||
3.2 | odd | 2 | 432.5.q.c.17.2 | 8 | |||
4.3 | odd | 2 | 36.5.g.a.5.4 | ✓ | 8 | ||
9.2 | odd | 6 | inner | 144.5.q.c.65.1 | 8 | ||
9.4 | even | 3 | 1296.5.e.g.161.3 | 8 | |||
9.5 | odd | 6 | 1296.5.e.g.161.6 | 8 | |||
9.7 | even | 3 | 432.5.q.c.305.2 | 8 | |||
12.11 | even | 2 | 108.5.g.a.17.2 | 8 | |||
36.7 | odd | 6 | 108.5.g.a.89.2 | 8 | |||
36.11 | even | 6 | 36.5.g.a.29.4 | yes | 8 | ||
36.23 | even | 6 | 324.5.c.a.161.6 | 8 | |||
36.31 | odd | 6 | 324.5.c.a.161.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.g.a.5.4 | ✓ | 8 | 4.3 | odd | 2 | ||
36.5.g.a.29.4 | yes | 8 | 36.11 | even | 6 | ||
108.5.g.a.17.2 | 8 | 12.11 | even | 2 | |||
108.5.g.a.89.2 | 8 | 36.7 | odd | 6 | |||
144.5.q.c.65.1 | 8 | 9.2 | odd | 6 | inner | ||
144.5.q.c.113.1 | 8 | 1.1 | even | 1 | trivial | ||
324.5.c.a.161.3 | 8 | 36.31 | odd | 6 | |||
324.5.c.a.161.6 | 8 | 36.23 | even | 6 | |||
432.5.q.c.17.2 | 8 | 3.2 | odd | 2 | |||
432.5.q.c.305.2 | 8 | 9.7 | even | 3 | |||
1296.5.e.g.161.3 | 8 | 9.4 | even | 3 | |||
1296.5.e.g.161.6 | 8 | 9.5 | odd | 6 |