Properties

Label 2646.2.e.b.1549.1
Level $2646$
Weight $2$
Character 2646.1549
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2646,2,Mod(1549,2646)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.1549");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1549.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1549
Dual form 2646.2.e.b.2125.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{13} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} +(1.50000 - 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(1.00000 - 1.73205i) q^{26} +(3.00000 + 5.19615i) q^{29} -4.00000 q^{31} -1.00000 q^{32} +(1.50000 + 2.59808i) q^{34} +(2.00000 - 3.46410i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(4.50000 - 7.79423i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +6.00000 q^{47} +(-2.50000 + 4.33013i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-3.00000 - 5.19615i) q^{58} -3.00000 q^{59} +8.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +5.00000 q^{67} +(-1.50000 - 2.59808i) q^{68} +12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(0.500000 - 0.866025i) q^{76} -4.00000 q^{79} +(-4.50000 + 7.79423i) q^{82} +(6.00000 + 10.3923i) q^{83} +(-0.500000 - 0.866025i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-3.00000 - 5.19615i) q^{92} -6.00000 q^{94} +(-2.50000 - 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 3 q^{11} - 2 q^{13} + 2 q^{16} - 3 q^{17} + q^{19} + 3 q^{22} - 6 q^{23} + 5 q^{25} + 2 q^{26} + 6 q^{29} - 8 q^{31} - 2 q^{32} + 3 q^{34} + 4 q^{37} - q^{38} + 9 q^{41} + q^{43} - 3 q^{44} + 6 q^{46} + 12 q^{47} - 5 q^{50} - 2 q^{52} + 12 q^{53} - 6 q^{58} - 6 q^{59} + 16 q^{61} + 8 q^{62} + 2 q^{64} + 10 q^{67} - 3 q^{68} + 24 q^{71} - 11 q^{73} - 4 q^{74} + q^{76} - 8 q^{79} - 9 q^{82} + 12 q^{83} - q^{86} + 3 q^{88} + 6 q^{89} - 6 q^{92} - 12 q^{94} - 5 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 1.50000 + 2.59808i 0.257248 + 0.445566i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) −0.500000 + 0.866025i −0.0811107 + 0.140488i
\(39\) 0 0
\(40\) 0 0
\(41\) 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i \(-0.585274\pi\)
0.967486 0.252924i \(-0.0813924\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.50000 + 4.33013i −0.353553 + 0.612372i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 5.00000 0.610847 0.305424 0.952217i \(-0.401202\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) 0.500000 0.866025i 0.0573539 0.0993399i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −4.50000 + 7.79423i −0.496942 + 0.860729i
\(83\) 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.500000 0.866025i −0.0539164 0.0933859i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.00000 5.19615i −0.312772 0.541736i
\(93\) 0 0
\(94\) −6.00000 −0.618853
\(95\) 0 0
\(96\) 0 0
\(97\) −2.50000 4.33013i −0.253837 0.439658i 0.710742 0.703452i \(-0.248359\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) 1.00000 1.73205i 0.0980581 0.169842i
\(105\) 0 0
\(106\) −6.00000 10.3923i −0.582772 1.00939i
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 0 0
\(118\) 3.00000 0.276172
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −8.00000 −0.724286
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.00000 −0.431934
\(135\) 0 0
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 0 0
\(139\) 9.50000 16.4545i 0.805779 1.39565i −0.109984 0.993933i \(-0.535080\pi\)
0.915764 0.401718i \(-0.131587\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 0 0
\(146\) 5.50000 + 9.52628i 0.455183 + 0.788400i
\(147\) 0 0
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) −0.500000 + 0.866025i −0.0405554 + 0.0702439i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 4.00000 0.318223
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 4.50000 7.79423i 0.351391 0.608627i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) 0 0
\(186\) 0 0
\(187\) 9.00000 0.658145
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 0 0
\(193\) 5.00000 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) 2.50000 + 4.33013i 0.179490 + 0.310885i
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) −2.50000 + 4.33013i −0.176777 + 0.306186i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 0 0
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 1.50000 + 2.59808i 0.103757 + 0.179713i
\(210\) 0 0
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 0 0
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −8.00000 13.8564i −0.541828 0.938474i
\(219\) 0 0
\(220\) 0 0
\(221\) 6.00000 0.403604
\(222\) 0 0
\(223\) −13.0000 22.5167i −0.870544 1.50783i −0.861435 0.507869i \(-0.830434\pi\)
−0.00910984 0.999959i \(-0.502900\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.00000 + 5.19615i −0.199557 + 0.345643i
\(227\) 10.5000 18.1865i 0.696909 1.20708i −0.272623 0.962121i \(-0.587891\pi\)
0.969533 0.244962i \(-0.0787754\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.00000 −0.195283
\(237\) 0 0
\(238\) 0 0
\(239\) 3.00000 5.19615i 0.194054 0.336111i −0.752536 0.658551i \(-0.771170\pi\)
0.946590 + 0.322440i \(0.104503\pi\)
\(240\) 0 0
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) 1.00000 + 1.73205i 0.0636285 + 0.110208i
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) 0 0
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) −2.00000 −0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −10.5000 18.1865i −0.654972 1.13444i −0.981901 0.189396i \(-0.939347\pi\)
0.326929 0.945049i \(-0.393986\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 5.00000 0.305424
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) 0 0
\(271\) −10.0000 + 17.3205i −0.607457 + 1.05215i 0.384201 + 0.923249i \(0.374477\pi\)
−0.991658 + 0.128897i \(0.958856\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) 0 0
\(274\) 1.50000 2.59808i 0.0906183 0.156956i
\(275\) 7.50000 + 12.9904i 0.452267 + 0.783349i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −9.50000 + 16.4545i −0.569772 + 0.986874i
\(279\) 0 0
\(280\) 0 0
\(281\) 3.00000 + 5.19615i 0.178965 + 0.309976i 0.941526 0.336939i \(-0.109392\pi\)
−0.762561 + 0.646916i \(0.776058\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) 3.00000 + 5.19615i 0.177394 + 0.307255i
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) −5.50000 9.52628i −0.321863 0.557483i
\(293\) 15.0000 25.9808i 0.876309 1.51781i 0.0209480 0.999781i \(-0.493332\pi\)
0.855361 0.518032i \(-0.173335\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) 0 0
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 12.0000 0.693978
\(300\) 0 0
\(301\) 0 0
\(302\) −5.00000 + 8.66025i −0.287718 + 0.498342i
\(303\) 0 0
\(304\) 0.500000 0.866025i 0.0286770 0.0496700i
\(305\) 0 0
\(306\) 0 0
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 0 0
\(313\) 29.0000 1.63918 0.819588 0.572953i \(-0.194202\pi\)
0.819588 + 0.572953i \(0.194202\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) 0 0
\(325\) 5.00000 + 8.66025i 0.277350 + 0.480384i
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) 0 0
\(328\) −4.50000 + 7.79423i −0.248471 + 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 6.00000 + 10.3923i 0.329293 + 0.570352i
\(333\) 0 0
\(334\) 6.00000 10.3923i 0.328305 0.568642i
\(335\) 0 0
\(336\) 0 0
\(337\) 0.500000 0.866025i 0.0272367 0.0471754i −0.852086 0.523402i \(-0.824663\pi\)
0.879322 + 0.476227i \(0.157996\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 0 0
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 0 0
\(343\) 0 0
\(344\) −0.500000 0.866025i −0.0269582 0.0466930i
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) −33.0000 −1.77153 −0.885766 0.464131i \(-0.846367\pi\)
−0.885766 + 0.464131i \(0.846367\pi\)
\(348\) 0 0
\(349\) 8.00000 + 13.8564i 0.428230 + 0.741716i 0.996716 0.0809766i \(-0.0258039\pi\)
−0.568486 + 0.822693i \(0.692471\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −10.5000 + 18.1865i −0.558859 + 0.967972i 0.438733 + 0.898617i \(0.355427\pi\)
−0.997592 + 0.0693543i \(0.977906\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.00000 5.19615i 0.159000 0.275396i
\(357\) 0 0
\(358\) −6.00000 10.3923i −0.317110 0.549250i
\(359\) −9.00000 + 15.5885i −0.475002 + 0.822727i −0.999590 0.0286287i \(-0.990886\pi\)
0.524588 + 0.851356i \(0.324219\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −14.0000 −0.735824
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 14.0000 24.2487i 0.730794 1.26577i −0.225750 0.974185i \(-0.572483\pi\)
0.956544 0.291587i \(-0.0941834\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 17.0000 + 29.4449i 0.880227 + 1.52460i 0.851089 + 0.525022i \(0.175943\pi\)
0.0291379 + 0.999575i \(0.490724\pi\)
\(374\) −9.00000 −0.465379
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −18.0000 −0.920960
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) −2.50000 4.33013i −0.126918 0.219829i
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) 0 0
\(391\) −9.00000 + 15.5885i −0.455150 + 0.788342i
\(392\) 0 0
\(393\) 0 0
\(394\) −12.0000 −0.604551
\(395\) 0 0
\(396\) 0 0
\(397\) −10.0000 + 17.3205i −0.501886 + 0.869291i 0.498112 + 0.867113i \(0.334027\pi\)
−0.999998 + 0.00217869i \(0.999307\pi\)
\(398\) −5.00000 8.66025i −0.250627 0.434099i
\(399\) 0 0
\(400\) 2.50000 4.33013i 0.125000 0.216506i
\(401\) −13.5000 23.3827i −0.674158 1.16768i −0.976714 0.214544i \(-0.931173\pi\)
0.302556 0.953131i \(-0.402160\pi\)
\(402\) 0 0
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 + 10.3923i 0.297409 + 0.515127i
\(408\) 0 0
\(409\) 17.0000 0.840596 0.420298 0.907386i \(-0.361926\pi\)
0.420298 + 0.907386i \(0.361926\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −7.00000 12.1244i −0.344865 0.597324i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) 0 0
\(418\) −1.50000 2.59808i −0.0733674 0.127076i
\(419\) −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i \(-0.928027\pi\)
0.681426 + 0.731887i \(0.261360\pi\)
\(420\) 0 0
\(421\) −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i \(-0.328710\pi\)
−0.999895 + 0.0145228i \(0.995377\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 0 0
\(424\) −6.00000 10.3923i −0.291386 0.504695i
\(425\) −15.0000 −0.727607
\(426\) 0 0
\(427\) 0 0
\(428\) 1.50000 2.59808i 0.0725052 0.125583i
\(429\) 0 0
\(430\) 0 0
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) 0 0
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 8.00000 + 13.8564i 0.383131 + 0.663602i
\(437\) −6.00000 −0.287019
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −3.00000 −0.142534 −0.0712672 0.997457i \(-0.522704\pi\)
−0.0712672 + 0.997457i \(0.522704\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 13.0000 + 22.5167i 0.615568 + 1.06619i
\(447\) 0 0
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 13.5000 + 23.3827i 0.635690 + 1.10105i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 0 0
\(454\) −10.5000 + 18.1865i −0.492789 + 0.853536i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i \(-0.920465\pi\)
0.270326 0.962769i \(-0.412869\pi\)
\(462\) 0 0
\(463\) −10.0000 + 17.3205i −0.464739 + 0.804952i −0.999190 0.0402476i \(-0.987185\pi\)
0.534450 + 0.845200i \(0.320519\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) 0 0
\(466\) −1.50000 + 2.59808i −0.0694862 + 0.120354i
\(467\) −7.50000 + 12.9904i −0.347059 + 0.601123i −0.985726 0.168360i \(-0.946153\pi\)
0.638667 + 0.769483i \(0.279486\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 3.00000 0.138086
\(473\) −3.00000 −0.137940
\(474\) 0 0
\(475\) −2.50000 4.33013i −0.114708 0.198680i
\(476\) 0 0
\(477\) 0 0
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) −21.0000 + 36.3731i −0.959514 + 1.66193i −0.235833 + 0.971794i \(0.575782\pi\)
−0.723681 + 0.690134i \(0.757551\pi\)
\(480\) 0 0
\(481\) 4.00000 + 6.92820i 0.182384 + 0.315899i
\(482\) −3.50000 + 6.06218i −0.159421 + 0.276125i
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) 0 0
\(487\) −13.0000 22.5167i −0.589086 1.02033i −0.994352 0.106129i \(-0.966154\pi\)
0.405266 0.914199i \(-0.367179\pi\)
\(488\) −8.00000 −0.362143
\(489\) 0 0
\(490\) 0 0
\(491\) −7.50000 + 12.9904i −0.338470 + 0.586248i −0.984145 0.177365i \(-0.943243\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) −1.00000 1.73205i −0.0449921 0.0779287i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 6.50000 + 11.2583i 0.290980 + 0.503992i 0.974042 0.226369i \(-0.0726854\pi\)
−0.683062 + 0.730361i \(0.739352\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 21.0000 0.937276
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −18.0000 −0.800198
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 10.5000 + 18.1865i 0.463135 + 0.802174i
\(515\) 0 0
\(516\) 0 0
\(517\) −9.00000 + 15.5885i −0.395820 + 0.685580i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.50000 2.59808i −0.0657162 0.113824i 0.831295 0.555831i \(-0.187600\pi\)
−0.897011 + 0.442007i \(0.854267\pi\)
\(522\) 0 0
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −9.00000 + 15.5885i −0.392419 + 0.679689i
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9.00000 + 15.5885i 0.389833 + 0.675211i
\(534\) 0 0
\(535\) 0 0
\(536\) −5.00000 −0.215967
\(537\) 0 0
\(538\) 12.0000 + 20.7846i 0.517357 + 0.896088i
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 3.46410i 0.0859867 0.148933i −0.819825 0.572615i \(-0.805929\pi\)
0.905811 + 0.423681i \(0.139262\pi\)
\(542\) 10.0000 17.3205i 0.429537 0.743980i
\(543\) 0 0
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.500000 + 0.866025i 0.0213785 + 0.0370286i 0.876517 0.481371i \(-0.159861\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) −1.50000 + 2.59808i −0.0640768 + 0.110984i
\(549\) 0 0
\(550\) −7.50000 12.9904i −0.319801 0.553912i
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 0 0
\(554\) −5.00000 + 8.66025i −0.212430 + 0.367939i
\(555\) 0 0
\(556\) 9.50000 16.4545i 0.402890 0.697826i
\(557\) −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) 0 0
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) 39.0000 1.64365 0.821827 0.569737i \(-0.192955\pi\)
0.821827 + 0.569737i \(0.192955\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −45.0000 −1.88650 −0.943249 0.332086i \(-0.892248\pi\)
−0.943249 + 0.332086i \(0.892248\pi\)
\(570\) 0 0
\(571\) −37.0000 −1.54840 −0.774201 0.632940i \(-0.781848\pi\)
−0.774201 + 0.632940i \(0.781848\pi\)
\(572\) −3.00000 5.19615i −0.125436 0.217262i
\(573\) 0 0
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) 0 0
\(577\) −5.50000 9.52628i −0.228968 0.396584i 0.728535 0.685009i \(-0.240202\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −36.0000 −1.49097
\(584\) 5.50000 + 9.52628i 0.227592 + 0.394200i
\(585\) 0 0
\(586\) −15.0000 + 25.9808i −0.619644 + 1.07326i
\(587\) −4.50000 7.79423i −0.185735 0.321702i 0.758089 0.652151i \(-0.226133\pi\)
−0.943824 + 0.330449i \(0.892800\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 0 0
\(591\) 0 0
\(592\) 2.00000 3.46410i 0.0821995 0.142374i
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) −12.0000 −0.490716
\(599\) −12.0000 −0.490307 −0.245153 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) 0 0
\(601\) 18.5000 + 32.0429i 0.754631 + 1.30706i 0.945558 + 0.325455i \(0.105517\pi\)
−0.190927 + 0.981604i \(0.561149\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.00000 8.66025i 0.203447 0.352381i
\(605\) 0 0
\(606\) 0 0
\(607\) 14.0000 + 24.2487i 0.568242 + 0.984225i 0.996740 + 0.0806818i \(0.0257098\pi\)
−0.428497 + 0.903543i \(0.640957\pi\)
\(608\) −0.500000 + 0.866025i −0.0202777 + 0.0351220i
\(609\) 0 0
\(610\) 0 0
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) 0 0
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) 7.00000 0.282497
\(615\) 0 0
\(616\) 0 0
\(617\) 13.5000 23.3827i 0.543490 0.941351i −0.455211 0.890384i \(-0.650436\pi\)
0.998700 0.0509678i \(-0.0162306\pi\)
\(618\) 0 0
\(619\) −17.5000 + 30.3109i −0.703384 + 1.21830i 0.263887 + 0.964554i \(0.414995\pi\)
−0.967271 + 0.253744i \(0.918338\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −29.0000 −1.15907
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 4.00000 0.159111
\(633\) 0 0
\(634\) −18.0000 −0.714871
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 0 0
\(641\) −1.50000 + 2.59808i −0.0592464 + 0.102618i −0.894127 0.447813i \(-0.852203\pi\)
0.834881 + 0.550431i \(0.185536\pi\)
\(642\) 0 0
\(643\) −11.5000 + 19.9186i −0.453516 + 0.785512i −0.998602 0.0528680i \(-0.983164\pi\)
0.545086 + 0.838380i \(0.316497\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3.00000 0.118033
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) 0 0
\(649\) 4.50000 7.79423i 0.176640 0.305950i
\(650\) −5.00000 8.66025i −0.196116 0.339683i
\(651\) 0 0
\(652\) 2.00000 3.46410i 0.0783260 0.135665i
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.50000 7.79423i 0.175695 0.304314i
\(657\) 0 0
\(658\) 0 0
\(659\) −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 0 0
\(661\) −4.00000 −0.155582 −0.0777910 0.996970i \(-0.524787\pi\)
−0.0777910 + 0.996970i \(0.524787\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) −6.00000 10.3923i −0.232845 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) 18.0000 31.1769i 0.696963 1.20717i
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0000 + 20.7846i −0.463255 + 0.802381i
\(672\) 0 0
\(673\) 11.0000 + 19.0526i 0.424019 + 0.734422i 0.996328 0.0856156i \(-0.0272857\pi\)
−0.572309 + 0.820038i \(0.693952\pi\)
\(674\) −0.500000 + 0.866025i −0.0192593 + 0.0333581i
\(675\) 0 0
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −36.0000 −1.38359 −0.691796 0.722093i \(-0.743180\pi\)
−0.691796 + 0.722093i \(0.743180\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) −24.0000 −0.914327
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) 0 0
\(696\) 0 0
\(697\) −27.0000 −1.02270
\(698\) −8.00000 13.8564i −0.302804 0.524473i
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 10.5000 18.1865i 0.395173 0.684459i
\(707\) 0 0
\(708\) 0 0
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 12.0000 + 20.7846i 0.449404 + 0.778390i
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) 9.00000 15.5885i 0.335877 0.581756i
\(719\) −18.0000 + 31.1769i −0.671287 + 1.16270i 0.306253 + 0.951950i \(0.400925\pi\)
−0.977539 + 0.210752i \(0.932409\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −9.00000 15.5885i −0.334945 0.580142i
\(723\) 0 0
\(724\) 14.0000 0.520306
\(725\) 30.0000 1.11417
\(726\) 0 0
\(727\) −13.0000 22.5167i −0.482143 0.835097i 0.517647 0.855595i \(-0.326808\pi\)
−0.999790 + 0.0204978i \(0.993475\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 0 0
\(733\) −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) −14.0000 + 24.2487i −0.516749 + 0.895036i
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) −7.50000 + 12.9904i −0.276266 + 0.478507i
\(738\) 0 0
\(739\) −23.5000 40.7032i −0.864461 1.49729i −0.867581 0.497296i \(-0.834326\pi\)
0.00311943 0.999995i \(-0.499007\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i \(-0.798229\pi\)
0.915794 + 0.401648i \(0.131563\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −17.0000 29.4449i −0.622414 1.07805i
\(747\) 0 0
\(748\) 9.00000 0.329073
\(749\) 0 0
\(750\) 0 0
\(751\) −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i \(-0.213294\pi\)
−0.929731 + 0.368238i \(0.879961\pi\)
\(752\) 6.00000 0.218797
\(753\) 0 0
\(754\) 12.0000 0.437014
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −23.0000 −0.835398
\(759\) 0 0
\(760\) 0 0
\(761\) 21.0000 + 36.3731i 0.761249 + 1.31852i 0.942207 + 0.335032i \(0.108747\pi\)
−0.180957 + 0.983491i \(0.557920\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 0 0
\(767\) 3.00000 5.19615i 0.108324 0.187622i
\(768\) 0 0
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.00000 0.179954
\(773\) 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i \(-0.0617373\pi\)
−0.657542 + 0.753418i \(0.728404\pi\)
\(774\) 0 0
\(775\) −10.0000 + 17.3205i −0.359211 + 0.622171i
\(776\) 2.50000 + 4.33013i 0.0897448 + 0.155443i
\(777\) 0 0
\(778\) −9.00000 + 15.5885i −0.322666 + 0.558873i
\(779\) −4.50000 7.79423i −0.161229 0.279257i
\(780\) 0 0
\(781\) −18.0000 + 31.1769i −0.644091 + 1.11560i
\(782\) 9.00000 15.5885i 0.321839 0.557442i
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 12.0000 0.427482
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −8.00000 + 13.8564i −0.284088 + 0.492055i
\(794\) 10.0000 17.3205i 0.354887 0.614682i
\(795\) 0 0
\(796\) 5.00000 + 8.66025i 0.177220 + 0.306955i
\(797\) −6.00000 + 10.3923i −0.212531 + 0.368114i −0.952506 0.304520i \(-0.901504\pi\)
0.739975 + 0.672634i \(0.234837\pi\)
\(798\) 0 0
\(799\) −9.00000 15.5885i −0.318397 0.551480i
\(800\) −2.50000 + 4.33013i −0.0883883 + 0.153093i
\(801\) 0 0
\(802\) 13.5000 + 23.3827i 0.476702 + 0.825671i
\(803\) 33.0000 1.16454
\(804\) 0 0
\(805\) 0 0
\(806\) −4.00000 + 6.92820i −0.140894 + 0.244036i
\(807\) 0 0
\(808\) 0 0
\(809\) 16.5000 + 28.5788i 0.580109 + 1.00478i 0.995466 + 0.0951198i \(0.0303234\pi\)
−0.415357 + 0.909659i \(0.636343\pi\)
\(810\) 0 0
\(811\) −7.00000 −0.245803 −0.122902 0.992419i \(-0.539220\pi\)
−0.122902 + 0.992419i \(0.539220\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −6.00000 10.3923i −0.210300 0.364250i
\(815\) 0 0
\(816\) 0 0
\(817\) 1.00000 0.0349856
\(818\) −17.0000 −0.594391
\(819\) 0 0
\(820\) 0 0
\(821\) 18.0000 0.628204 0.314102 0.949389i \(-0.398297\pi\)
0.314102 + 0.949389i \(0.398297\pi\)
\(822\) 0 0
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 7.00000 + 12.1244i 0.243857 + 0.422372i
\(825\) 0 0
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) 5.00000 + 8.66025i 0.173657 + 0.300783i 0.939696 0.342012i \(-0.111108\pi\)
−0.766039 + 0.642795i \(0.777775\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 + 1.73205i −0.0346688 + 0.0600481i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 1.50000 + 2.59808i 0.0518786 + 0.0898563i
\(837\) 0 0
\(838\) 6.00000 10.3923i 0.207267 0.358996i
\(839\) 6.00000 + 10.3923i 0.207143 + 0.358782i 0.950813 0.309764i \(-0.100250\pi\)
−0.743670 + 0.668546i \(0.766917\pi\)
\(840\) 0 0
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) 10.0000 + 17.3205i 0.344623 + 0.596904i
\(843\) 0 0
\(844\) −10.0000 + 17.3205i −0.344214 + 0.596196i
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 6.00000 + 10.3923i 0.206041 + 0.356873i
\(849\) 0 0
\(850\) 15.0000 0.514496
\(851\) −24.0000 −0.822709
\(852\) 0 0
\(853\) −13.0000 22.5167i −0.445112 0.770956i 0.552948 0.833215i \(-0.313503\pi\)
−0.998060 + 0.0622597i \(0.980169\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.50000 + 2.59808i −0.0512689 + 0.0888004i
\(857\) −21.0000 + 36.3731i −0.717346 + 1.24248i 0.244701 + 0.969599i \(0.421310\pi\)
−0.962048 + 0.272882i \(0.912023\pi\)
\(858\) 0 0
\(859\) −17.5000 30.3109i −0.597092 1.03419i −0.993248 0.116011i \(-0.962989\pi\)
0.396156 0.918183i \(-0.370344\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 15.0000 + 25.9808i 0.510902 + 0.884908i
\(863\) 12.0000 20.7846i 0.408485 0.707516i −0.586235 0.810141i \(-0.699391\pi\)
0.994720 + 0.102624i \(0.0327240\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 7.00000 0.237870
\(867\) 0 0
\(868\) 0 0
\(869\) 6.00000 10.3923i 0.203536 0.352535i
\(870\) 0 0
\(871\) −5.00000 + 8.66025i −0.169419 + 0.293442i
\(872\) −8.00000 13.8564i −0.270914 0.469237i
\(873\) 0 0
\(874\) 6.00000 0.202953
\(875\) 0 0
\(876\) 0 0
\(877\) −4.00000 6.92820i −0.135070 0.233949i 0.790554 0.612392i \(-0.209793\pi\)
−0.925624 + 0.378444i \(0.876459\pi\)
\(878\) −8.00000 −0.269987
\(879\) 0 0
\(880\) 0 0
\(881\) 42.0000 1.41502 0.707508 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) 0 0
\(883\) −19.0000 −0.639401 −0.319700 0.947519i \(-0.603582\pi\)
−0.319700 + 0.947519i \(0.603582\pi\)
\(884\) 6.00000 0.201802
\(885\) 0 0
\(886\) 3.00000 0.100787
\(887\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −13.0000 22.5167i −0.435272 0.753914i
\(893\) 3.00000 5.19615i 0.100391 0.173883i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 9.00000 0.300334
\(899\) −12.0000 20.7846i −0.400222 0.693206i
\(900\) 0 0
\(901\) 18.0000 31.1769i 0.599667 1.03865i
\(902\) −13.5000 23.3827i −0.449501 0.778558i
\(903\) 0 0
\(904\) −3.00000 + 5.19615i −0.0997785 + 0.172821i
\(905\) 0 0
\(906\) 0 0
\(907\) 15.5000 26.8468i 0.514669 0.891433i −0.485186 0.874411i \(-0.661248\pi\)
0.999855 0.0170220i \(-0.00541854\pi\)
\(908\) 10.5000 18.1865i 0.348455 0.603541i
\(909\) 0 0
\(910\) 0 0
\(911\) 24.0000 + 41.5692i 0.795155 + 1.37725i 0.922740 + 0.385422i \(0.125944\pi\)
−0.127585 + 0.991828i \(0.540723\pi\)
\(912\) 0 0
\(913\) −36.0000 −1.19143
\(914\) −17.0000 −0.562310
\(915\) 0 0
\(916\) −7.00000 12.1244i −0.231287 0.400600i
\(917\) 0 0
\(918\) 0 0
\(919\) −19.0000 + 32.9090i −0.626752 + 1.08557i 0.361447 + 0.932393i \(0.382283\pi\)
−0.988199 + 0.153174i \(0.951051\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 15.0000 + 25.9808i 0.493999 + 0.855631i
\(923\) −12.0000 + 20.7846i −0.394985 + 0.684134i
\(924\) 0 0
\(925\) −10.0000 17.3205i −0.328798 0.569495i
\(926\) 10.0000 17.3205i 0.328620 0.569187i
\(927\) 0 0
\(928\) −3.00000 5.19615i −0.0984798 0.170572i
\(929\) 6.00000 0.196854 0.0984268 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.50000 2.59808i 0.0491341 0.0851028i
\(933\) 0 0
\(934\) 7.50000 12.9904i 0.245407 0.425058i
\(935\) 0 0
\(936\) 0 0
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 60.0000 1.95594 0.977972 0.208736i \(-0.0669349\pi\)
0.977972 + 0.208736i \(0.0669349\pi\)
\(942\) 0 0
\(943\) −54.0000 −1.75848
\(944\) −3.00000 −0.0976417
\(945\) 0 0
\(946\) 3.00000 0.0975384
\(947\) −3.00000 −0.0974869 −0.0487435 0.998811i \(-0.515522\pi\)
−0.0487435 + 0.998811i \(0.515522\pi\)
\(948\) 0 0
\(949\) 22.0000 0.714150
\(950\) 2.50000 + 4.33013i 0.0811107 + 0.140488i
\(951\) 0 0
\(952\) 0 0
\(953\) −9.00000 −0.291539 −0.145769 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 3.00000 5.19615i 0.0970269 0.168056i
\(957\) 0 0
\(958\) 21.0000 36.3731i 0.678479 1.17516i
\(959\) 0 0
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −4.00000 6.92820i −0.128965 0.223374i
\(963\) 0 0
\(964\) 3.50000 6.06218i 0.112727 0.195250i
\(965\) 0 0
\(966\) 0 0
\(967\) 11.0000 19.0526i 0.353736 0.612689i −0.633165 0.774017i \(-0.718244\pi\)
0.986901 + 0.161328i \(0.0515777\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) 0 0
\(970\) 0 0
\(971\) −18.0000 + 31.1769i −0.577647 + 1.00051i 0.418101 + 0.908401i \(0.362696\pi\)
−0.995748 + 0.0921142i \(0.970638\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 13.0000 + 22.5167i 0.416547 + 0.721480i
\(975\) 0 0
\(976\) 8.00000 0.256074
\(977\) 51.0000 1.63163 0.815817 0.578310i \(-0.196287\pi\)
0.815817 + 0.578310i \(0.196287\pi\)
\(978\) 0 0
\(979\) 9.00000 + 15.5885i 0.287641 + 0.498209i
\(980\) 0 0
\(981\) 0 0
\(982\) 7.50000 12.9904i 0.239335 0.414540i
\(983\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −9.00000 + 15.5885i −0.286618 + 0.496438i
\(987\) 0 0
\(988\) 1.00000 + 1.73205i 0.0318142 + 0.0551039i
\(989\) 3.00000 5.19615i 0.0953945 0.165228i
\(990\) 0 0
\(991\) 8.00000 + 13.8564i 0.254128 + 0.440163i 0.964658 0.263504i \(-0.0848781\pi\)
−0.710530 + 0.703667i \(0.751545\pi\)
\(992\) 4.00000 0.127000
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 14.0000 24.2487i 0.443384 0.767964i −0.554554 0.832148i \(-0.687111\pi\)
0.997938 + 0.0641836i \(0.0204443\pi\)
\(998\) −6.50000 11.2583i −0.205754 0.356376i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 2646.2.e.b.1549.1 2
3.2 odd 2 882.2.e.i.373.1 2
7.2 even 3 54.2.c.a.37.1 2
7.3 odd 6 2646.2.h.i.361.1 2
7.4 even 3 2646.2.h.h.361.1 2
7.5 odd 6 2646.2.f.g.1765.1 2
7.6 odd 2 2646.2.e.c.1549.1 2
9.2 odd 6 882.2.h.c.79.1 2
9.7 even 3 2646.2.h.h.667.1 2
21.2 odd 6 18.2.c.a.13.1 yes 2
21.5 even 6 882.2.f.d.589.1 2
21.11 odd 6 882.2.h.c.67.1 2
21.17 even 6 882.2.h.b.67.1 2
21.20 even 2 882.2.e.g.373.1 2
28.23 odd 6 432.2.i.b.145.1 2
35.2 odd 12 1350.2.j.a.199.1 4
35.9 even 6 1350.2.e.c.901.1 2
35.23 odd 12 1350.2.j.a.199.2 4
56.37 even 6 1728.2.i.e.577.1 2
56.51 odd 6 1728.2.i.f.577.1 2
63.2 odd 6 18.2.c.a.7.1 2
63.5 even 6 7938.2.a.x.1.1 1
63.11 odd 6 882.2.e.i.655.1 2
63.16 even 3 54.2.c.a.19.1 2
63.20 even 6 882.2.h.b.79.1 2
63.23 odd 6 162.2.a.c.1.1 1
63.25 even 3 inner 2646.2.e.b.2125.1 2
63.34 odd 6 2646.2.h.i.667.1 2
63.38 even 6 882.2.e.g.655.1 2
63.40 odd 6 7938.2.a.i.1.1 1
63.47 even 6 882.2.f.d.295.1 2
63.52 odd 6 2646.2.e.c.2125.1 2
63.58 even 3 162.2.a.b.1.1 1
63.61 odd 6 2646.2.f.g.883.1 2
84.23 even 6 144.2.i.c.49.1 2
105.2 even 12 450.2.j.e.49.2 4
105.23 even 12 450.2.j.e.49.1 4
105.44 odd 6 450.2.e.i.301.1 2
168.107 even 6 576.2.i.a.193.1 2
168.149 odd 6 576.2.i.g.193.1 2
252.23 even 6 1296.2.a.g.1.1 1
252.79 odd 6 432.2.i.b.289.1 2
252.191 even 6 144.2.i.c.97.1 2
252.247 odd 6 1296.2.a.f.1.1 1
315.2 even 12 450.2.j.e.349.1 4
315.23 even 12 4050.2.c.c.649.1 2
315.58 odd 12 4050.2.c.r.649.2 2
315.79 even 6 1350.2.e.c.451.1 2
315.128 even 12 450.2.j.e.349.2 4
315.142 odd 12 1350.2.j.a.1099.2 4
315.149 odd 6 4050.2.a.c.1.1 1
315.184 even 6 4050.2.a.v.1.1 1
315.212 even 12 4050.2.c.c.649.2 2
315.247 odd 12 4050.2.c.r.649.1 2
315.254 odd 6 450.2.e.i.151.1 2
315.268 odd 12 1350.2.j.a.1099.1 4
504.149 odd 6 5184.2.a.r.1.1 1
504.205 even 6 1728.2.i.e.1153.1 2
504.275 even 6 5184.2.a.o.1.1 1
504.317 odd 6 576.2.i.g.385.1 2
504.331 odd 6 1728.2.i.f.1153.1 2
504.373 even 6 5184.2.a.q.1.1 1
504.443 even 6 576.2.i.a.385.1 2
504.499 odd 6 5184.2.a.p.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.2.c.a.7.1 2 63.2 odd 6
18.2.c.a.13.1 yes 2 21.2 odd 6
54.2.c.a.19.1 2 63.16 even 3
54.2.c.a.37.1 2 7.2 even 3
144.2.i.c.49.1 2 84.23 even 6
144.2.i.c.97.1 2 252.191 even 6
162.2.a.b.1.1 1 63.58 even 3
162.2.a.c.1.1 1 63.23 odd 6
432.2.i.b.145.1 2 28.23 odd 6
432.2.i.b.289.1 2 252.79 odd 6
450.2.e.i.151.1 2 315.254 odd 6
450.2.e.i.301.1 2 105.44 odd 6
450.2.j.e.49.1 4 105.23 even 12
450.2.j.e.49.2 4 105.2 even 12
450.2.j.e.349.1 4 315.2 even 12
450.2.j.e.349.2 4 315.128 even 12
576.2.i.a.193.1 2 168.107 even 6
576.2.i.a.385.1 2 504.443 even 6
576.2.i.g.193.1 2 168.149 odd 6
576.2.i.g.385.1 2 504.317 odd 6
882.2.e.g.373.1 2 21.20 even 2
882.2.e.g.655.1 2 63.38 even 6
882.2.e.i.373.1 2 3.2 odd 2
882.2.e.i.655.1 2 63.11 odd 6
882.2.f.d.295.1 2 63.47 even 6
882.2.f.d.589.1 2 21.5 even 6
882.2.h.b.67.1 2 21.17 even 6
882.2.h.b.79.1 2 63.20 even 6
882.2.h.c.67.1 2 21.11 odd 6
882.2.h.c.79.1 2 9.2 odd 6
1296.2.a.f.1.1 1 252.247 odd 6
1296.2.a.g.1.1 1 252.23 even 6
1350.2.e.c.451.1 2 315.79 even 6
1350.2.e.c.901.1 2 35.9 even 6
1350.2.j.a.199.1 4 35.2 odd 12
1350.2.j.a.199.2 4 35.23 odd 12
1350.2.j.a.1099.1 4 315.268 odd 12
1350.2.j.a.1099.2 4 315.142 odd 12
1728.2.i.e.577.1 2 56.37 even 6
1728.2.i.e.1153.1 2 504.205 even 6
1728.2.i.f.577.1 2 56.51 odd 6
1728.2.i.f.1153.1 2 504.331 odd 6
2646.2.e.b.1549.1 2 1.1 even 1 trivial
2646.2.e.b.2125.1 2 63.25 even 3 inner
2646.2.e.c.1549.1 2 7.6 odd 2
2646.2.e.c.2125.1 2 63.52 odd 6
2646.2.f.g.883.1 2 63.61 odd 6
2646.2.f.g.1765.1 2 7.5 odd 6
2646.2.h.h.361.1 2 7.4 even 3
2646.2.h.h.667.1 2 9.7 even 3
2646.2.h.i.361.1 2 7.3 odd 6
2646.2.h.i.667.1 2 63.34 odd 6
4050.2.a.c.1.1 1 315.149 odd 6
4050.2.a.v.1.1 1 315.184 even 6
4050.2.c.c.649.1 2 315.23 even 12
4050.2.c.c.649.2 2 315.212 even 12
4050.2.c.r.649.1 2 315.247 odd 12
4050.2.c.r.649.2 2 315.58 odd 12
5184.2.a.o.1.1 1 504.275 even 6
5184.2.a.p.1.1 1 504.499 odd 6
5184.2.a.q.1.1 1 504.373 even 6
5184.2.a.r.1.1 1 504.149 odd 6
7938.2.a.i.1.1 1 63.40 odd 6
7938.2.a.x.1.1 1 63.5 even 6