Properties

Label 882.2.g.g.361.1
Level $882$
Weight $2$
Character 882.361
Analytic conductor $7.043$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(361,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.g (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: \(7.04280545828\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.2.g.g.667.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{10} +(-1.50000 + 2.59808i) q^{11} -2.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(1.00000 + 1.73205i) q^{19} +3.00000 q^{20} -3.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} -9.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(0.500000 - 0.866025i) q^{32} -6.00000 q^{34} +(5.00000 + 8.66025i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{40} -4.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-6.00000 - 10.3923i) q^{47} -4.00000 q^{50} +(1.00000 - 1.73205i) q^{52} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(-4.50000 - 7.79423i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-2.00000 - 3.46410i) q^{61} -7.00000 q^{62} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(1.00000 - 1.73205i) q^{73} +(-5.00000 + 8.66025i) q^{74} -2.00000 q^{76} +(-2.50000 - 4.33013i) q^{79} +(-1.50000 + 2.59808i) q^{80} +9.00000 q^{83} +18.0000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +6.00000 q^{92} +(6.00000 - 10.3923i) q^{94} +(3.00000 - 5.19615i) q^{95} +13.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - 3 q^{5} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} - 3 q^{5} - 2 q^{8} + 3 q^{10} - 3 q^{11} - 4 q^{13} - q^{16} - 6 q^{17} + 2 q^{19} + 6 q^{20} - 6 q^{22} - 6 q^{23} - 4 q^{25} - 2 q^{26} - 18 q^{29} - 7 q^{31} + q^{32} - 12 q^{34} + 10 q^{37} - 2 q^{38} + 3 q^{40} - 8 q^{43} - 3 q^{44} + 6 q^{46} - 12 q^{47} - 8 q^{50} + 2 q^{52} - 3 q^{53} + 18 q^{55} - 9 q^{58} + 3 q^{59} - 4 q^{61} - 14 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{67} - 6 q^{68} + 2 q^{73} - 10 q^{74} - 4 q^{76} - 5 q^{79} - 3 q^{80} + 18 q^{83} + 36 q^{85} - 4 q^{86} + 3 q^{88} + 6 q^{89} + 12 q^{92} + 12 q^{94} + 6 q^{95} + 26 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) −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
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) 0 0
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) −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
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) −3.50000 + 6.06218i −0.628619 + 1.08880i 0.359211 + 0.933257i \(0.383046\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 0 0
\(37\) 5.00000 + 8.66025i 0.821995 + 1.42374i 0.904194 + 0.427121i \(0.140472\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −1.00000 + 1.73205i −0.162221 + 0.280976i
\(39\) 0 0
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −1.50000 2.59808i −0.226134 0.391675i
\(45\) 0 0
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) −6.00000 10.3923i −0.875190 1.51587i −0.856560 0.516047i \(-0.827403\pi\)
−0.0186297 0.999826i \(-0.505930\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) 0 0
\(58\) −4.50000 7.79423i −0.590879 1.02343i
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) −7.00000 −0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.00000 + 5.19615i 0.372104 + 0.644503i
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) −5.00000 + 8.66025i −0.581238 + 1.00673i
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 0 0
\(79\) −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) 0 0
\(82\) 0 0
\(83\) 9.00000 0.987878 0.493939 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) 0 0
\(85\) 18.0000 1.95237
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) 6.00000 10.3923i 0.618853 1.07188i
\(95\) 3.00000 5.19615i 0.307794 0.533114i
\(96\) 0 0
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) −8.00000 13.8564i −0.788263 1.36531i −0.927030 0.374987i \(-0.877647\pi\)
0.138767 0.990325i \(-0.455686\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −3.00000 −0.291386
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) 4.50000 + 7.79423i 0.429058 + 0.743151i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −9.00000 + 15.5885i −0.839254 + 1.45363i
\(116\) 4.50000 7.79423i 0.417815 0.723676i
\(117\) 0 0
\(118\) 3.00000 0.276172
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 2.00000 3.46410i 0.181071 0.313625i
\(123\) 0 0
\(124\) −3.50000 6.06218i −0.314309 0.544400i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −3.00000 + 5.19615i −0.263117 + 0.455733i
\(131\) 7.50000 + 12.9904i 0.655278 + 1.13497i 0.981824 + 0.189794i \(0.0607819\pi\)
−0.326546 + 0.945181i \(0.605885\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −2.00000 −0.172774
\(135\) 0 0
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) 0 0
\(145\) 13.5000 + 23.3827i 1.12111 + 1.94183i
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) −10.0000 −0.821995
\(149\) −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
\(151\) −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i \(-0.898548\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(152\) −1.00000 1.73205i −0.0811107 0.140488i
\(153\) 0 0
\(154\) 0 0
\(155\) 21.0000 1.68676
\(156\) 0 0
\(157\) −2.00000 + 3.46410i −0.159617 + 0.276465i −0.934731 0.355357i \(-0.884359\pi\)
0.775113 + 0.631822i \(0.217693\pi\)
\(158\) 2.50000 4.33013i 0.198889 0.344486i
\(159\) 0 0
\(160\) −3.00000 −0.237171
\(161\) 0 0
\(162\) 0 0
\(163\) 5.00000 + 8.66025i 0.391630 + 0.678323i 0.992665 0.120900i \(-0.0385779\pi\)
−0.601035 + 0.799223i \(0.705245\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 4.50000 + 7.79423i 0.349268 + 0.604949i
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 9.00000 + 15.5885i 0.690268 + 1.19558i
\(171\) 0 0
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0 0
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) 15.0000 25.9808i 1.10282 1.91014i
\(186\) 0 0
\(187\) −9.00000 15.5885i −0.658145 1.13994i
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) 6.50000 + 11.2583i 0.466673 + 0.808301i
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 0 0
\(202\) −6.00000 −0.422159
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 13.8564i 0.557386 0.965422i
\(207\) 0 0
\(208\) 1.00000 + 1.73205i 0.0693375 + 0.120096i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) 0 0
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) 6.00000 + 10.3923i 0.409197 + 0.708749i
\(216\) 0 0
\(217\) 0 0
\(218\) 10.0000 0.677285
\(219\) 0 0
\(220\) −4.50000 + 7.79423i −0.303390 + 0.525487i
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) 1.00000 0.0669650 0.0334825 0.999439i \(-0.489340\pi\)
0.0334825 + 0.999439i \(0.489340\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.50000 + 12.9904i −0.497792 + 0.862202i −0.999997 0.00254715i \(-0.999189\pi\)
0.502204 + 0.864749i \(0.332523\pi\)
\(228\) 0 0
\(229\) 10.0000 + 17.3205i 0.660819 + 1.14457i 0.980401 + 0.197013i \(0.0631241\pi\)
−0.319582 + 0.947559i \(0.603543\pi\)
\(230\) −18.0000 −1.18688
\(231\) 0 0
\(232\) 9.00000 0.590879
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 0 0
\(235\) −18.0000 + 31.1769i −1.17419 + 2.03376i
\(236\) 1.50000 + 2.59808i 0.0976417 + 0.169120i
\(237\) 0 0
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) 11.5000 19.9186i 0.740780 1.28307i −0.211360 0.977408i \(-0.567789\pi\)
0.952141 0.305661i \(-0.0988773\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) 0 0
\(244\) 4.00000 0.256074
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 3.46410i −0.127257 0.220416i
\(248\) 3.50000 6.06218i 0.222250 0.384949i
\(249\) 0 0
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) −0.500000 0.866025i −0.0313728 0.0543393i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −6.00000 −0.372104
\(261\) 0 0
\(262\) −7.50000 + 12.9904i −0.463352 + 0.802548i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) 0 0
\(268\) −1.00000 1.73205i −0.0610847 0.105802i
\(269\) 1.50000 2.59808i 0.0914566 0.158408i −0.816668 0.577108i \(-0.804181\pi\)
0.908124 + 0.418701i \(0.137514\pi\)
\(270\) 0 0
\(271\) −9.50000 16.4545i −0.577084 0.999539i −0.995812 0.0914269i \(-0.970857\pi\)
0.418728 0.908112i \(-0.362476\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0 0
\(277\) 2.00000 3.46410i 0.120168 0.208138i −0.799666 0.600446i \(-0.794990\pi\)
0.919834 + 0.392308i \(0.128323\pi\)
\(278\) −1.00000 1.73205i −0.0599760 0.103882i
\(279\) 0 0
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i \(-0.630708\pi\)
0.993626 0.112728i \(-0.0359589\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 6.00000 0.354787
\(287\) 0 0
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) −13.5000 + 23.3827i −0.792747 + 1.37308i
\(291\) 0 0
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) −9.00000 −0.524000
\(296\) −5.00000 8.66025i −0.290619 0.503367i
\(297\) 0 0
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 6.00000 + 10.3923i 0.346989 + 0.601003i
\(300\) 0 0
\(301\) 0 0
\(302\) −5.00000 −0.287718
\(303\) 0 0
\(304\) 1.00000 1.73205i 0.0573539 0.0993399i
\(305\) −6.00000 + 10.3923i −0.343559 + 0.595062i
\(306\) 0 0
\(307\) −26.0000 −1.48390 −0.741949 0.670456i \(-0.766098\pi\)
−0.741949 + 0.670456i \(0.766098\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 10.5000 + 18.1865i 0.596360 + 1.03293i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 0 0
\(313\) 8.50000 + 14.7224i 0.480448 + 0.832161i 0.999748 0.0224310i \(-0.00714060\pi\)
−0.519300 + 0.854592i \(0.673807\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 5.00000 0.281272
\(317\) 10.5000 + 18.1865i 0.589739 + 1.02146i 0.994266 + 0.106932i \(0.0341026\pi\)
−0.404528 + 0.914526i \(0.632564\pi\)
\(318\) 0 0
\(319\) 13.5000 23.3827i 0.755855 1.30918i
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) 0 0
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 4.00000 6.92820i 0.221880 0.384308i
\(326\) −5.00000 + 8.66025i −0.276924 + 0.479647i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) −4.50000 + 7.79423i −0.246970 + 0.427764i
\(333\) 0 0
\(334\) −9.00000 15.5885i −0.492458 0.852962i
\(335\) 6.00000 0.327815
\(336\) 0 0
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 0 0
\(340\) −9.00000 + 15.5885i −0.488094 + 0.845403i
\(341\) −10.5000 18.1865i −0.568607 0.984856i
\(342\) 0 0
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 15.0000 + 25.9808i 0.791670 + 1.37121i 0.924932 + 0.380131i \(0.124121\pi\)
−0.133263 + 0.991081i \(0.542545\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −10.0000 17.3205i −0.525588 0.910346i
\(363\) 0 0
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) −18.5000 + 32.0429i −0.965692 + 1.67263i −0.257948 + 0.966159i \(0.583046\pi\)
−0.707744 + 0.706469i \(0.750287\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) 0 0
\(370\) 30.0000 1.55963
\(371\) 0 0
\(372\) 0 0
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) 9.00000 15.5885i 0.465379 0.806060i
\(375\) 0 0
\(376\) 6.00000 + 10.3923i 0.309426 + 0.535942i
\(377\) 18.0000 0.927047
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 3.00000 + 5.19615i 0.153897 + 0.266557i
\(381\) 0 0
\(382\) −6.00000 + 10.3923i −0.306987 + 0.531717i
\(383\) −15.0000 25.9808i −0.766464 1.32755i −0.939469 0.342634i \(-0.888681\pi\)
0.173005 0.984921i \(-0.444652\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 7.00000 0.356291
\(387\) 0 0
\(388\) −6.50000 + 11.2583i −0.329988 + 0.571555i
\(389\) −15.0000 + 25.9808i −0.760530 + 1.31728i 0.182047 + 0.983290i \(0.441728\pi\)
−0.942578 + 0.333987i \(0.891606\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) 0 0
\(393\) 0 0
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) −7.50000 + 12.9904i −0.377366 + 0.653617i
\(396\) 0 0
\(397\) 4.00000 + 6.92820i 0.200754 + 0.347717i 0.948772 0.315963i \(-0.102327\pi\)
−0.748017 + 0.663679i \(0.768994\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 0 0
\(403\) 7.00000 12.1244i 0.348695 0.603957i
\(404\) −3.00000 5.19615i −0.149256 0.258518i
\(405\) 0 0
\(406\) 0 0
\(407\) −30.0000 −1.48704
\(408\) 0 0
\(409\) 5.50000 9.52628i 0.271957 0.471044i −0.697406 0.716677i \(-0.745662\pi\)
0.969363 + 0.245633i \(0.0789957\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) 0 0
\(415\) −13.5000 23.3827i −0.662689 1.14781i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) −36.0000 −1.75872 −0.879358 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −8.00000 13.8564i −0.389434 0.674519i
\(423\) 0 0
\(424\) 1.50000 2.59808i 0.0728464 0.126174i
\(425\) −12.0000 20.7846i −0.582086 1.00820i
\(426\) 0 0
\(427\) 0 0
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) −6.00000 + 10.3923i −0.289346 + 0.501161i
\(431\) 12.0000 20.7846i 0.578020 1.00116i −0.417687 0.908591i \(-0.637159\pi\)
0.995706 0.0925683i \(-0.0295076\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) 6.00000 10.3923i 0.287019 0.497131i
\(438\) 0 0
\(439\) −9.50000 16.4545i −0.453410 0.785330i 0.545185 0.838316i \(-0.316459\pi\)
−0.998595 + 0.0529862i \(0.983126\pi\)
\(440\) −9.00000 −0.429058
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −7.50000 12.9904i −0.356336 0.617192i 0.631010 0.775775i \(-0.282641\pi\)
−0.987346 + 0.158583i \(0.949307\pi\)
\(444\) 0 0
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) 0.500000 + 0.866025i 0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −15.0000 −0.703985
\(455\) 0 0
\(456\) 0 0
\(457\) 6.50000 + 11.2583i 0.304057 + 0.526642i 0.977051 0.213006i \(-0.0683253\pi\)
−0.672994 + 0.739648i \(0.734992\pi\)
\(458\) −10.0000 + 17.3205i −0.467269 + 0.809334i
\(459\) 0 0
\(460\) −9.00000 15.5885i −0.419627 0.726816i
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 4.50000 + 7.79423i 0.208907 + 0.361838i
\(465\) 0 0
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i \(-0.256221\pi\)
−0.970799 + 0.239892i \(0.922888\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −36.0000 −1.66056
\(471\) 0 0
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) 6.00000 10.3923i 0.275880 0.477839i
\(474\) 0 0
\(475\) −8.00000 −0.367065
\(476\) 0 0
\(477\) 0 0
\(478\) −9.00000 15.5885i −0.411650 0.712999i
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 0 0
\(481\) −10.0000 17.3205i −0.455961 0.789747i
\(482\) 23.0000 1.04762
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −19.5000 33.7750i −0.885449 1.53364i
\(486\) 0 0
\(487\) −5.50000 + 9.52628i −0.249229 + 0.431677i −0.963312 0.268384i \(-0.913510\pi\)
0.714083 + 0.700061i \(0.246844\pi\)
\(488\) 2.00000 + 3.46410i 0.0905357 + 0.156813i
\(489\) 0 0
\(490\) 0 0
\(491\) −9.00000 −0.406164 −0.203082 0.979162i \(-0.565096\pi\)
−0.203082 + 0.979162i \(0.565096\pi\)
\(492\) 0 0
\(493\) 27.0000 46.7654i 1.21602 2.10621i
\(494\) 2.00000 3.46410i 0.0899843 0.155857i
\(495\) 0 0
\(496\) 7.00000 0.314309
\(497\) 0 0
\(498\) 0 0
\(499\) −19.0000 32.9090i −0.850557 1.47321i −0.880707 0.473662i \(-0.842932\pi\)
0.0301498 0.999545i \(-0.490402\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 0 0
\(502\) 4.50000 + 7.79423i 0.200845 + 0.347873i
\(503\) 18.0000 0.802580 0.401290 0.915951i \(-0.368562\pi\)
0.401290 + 0.915951i \(0.368562\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 9.00000 + 15.5885i 0.400099 + 0.692991i
\(507\) 0 0
\(508\) 0.500000 0.866025i 0.0221839 0.0384237i
\(509\) 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −3.00000 + 5.19615i −0.132324 + 0.229192i
\(515\) −24.0000 + 41.5692i −1.05757 + 1.83176i
\(516\) 0 0
\(517\) 36.0000 1.58328
\(518\) 0 0
\(519\) 0 0
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) −12.0000 + 20.7846i −0.525730 + 0.910590i 0.473821 + 0.880621i \(0.342874\pi\)
−0.999551 + 0.0299693i \(0.990459\pi\)
\(522\) 0 0
\(523\) 13.0000 + 22.5167i 0.568450 + 0.984585i 0.996719 + 0.0809336i \(0.0257902\pi\)
−0.428269 + 0.903651i \(0.640876\pi\)
\(524\) −15.0000 −0.655278
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) −21.0000 36.3731i −0.914774 1.58444i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 4.50000 + 7.79423i 0.195468 + 0.338560i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 4.50000 7.79423i 0.194552 0.336974i
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) 0 0
\(538\) 3.00000 0.129339
\(539\) 0 0
\(540\) 0 0
\(541\) 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) 9.50000 16.4545i 0.408060 0.706781i
\(543\) 0 0
\(544\) 3.00000 + 5.19615i 0.128624 + 0.222783i
\(545\) −30.0000 −1.28506
\(546\) 0 0
\(547\) 14.0000 0.598597 0.299298 0.954160i \(-0.403247\pi\)
0.299298 + 0.954160i \(0.403247\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 0 0
\(550\) 6.00000 10.3923i 0.255841 0.443129i
\(551\) −9.00000 15.5885i −0.383413 0.664091i
\(552\) 0 0
\(553\) 0 0
\(554\) 4.00000 0.169944
\(555\) 0 0
\(556\) 1.00000 1.73205i 0.0424094 0.0734553i
\(557\) 7.50000 12.9904i 0.317785 0.550420i −0.662240 0.749291i \(-0.730394\pi\)
0.980026 + 0.198871i \(0.0637276\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) 1.50000 2.59808i 0.0632175 0.109496i −0.832684 0.553748i \(-0.813197\pi\)
0.895902 + 0.444252i \(0.146530\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) 0 0
\(569\) 15.0000 + 25.9808i 0.628833 + 1.08917i 0.987786 + 0.155815i \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) 0 0
\(574\) 0 0
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) −0.500000 + 0.866025i −0.0208153 + 0.0360531i −0.876245 0.481865i \(-0.839960\pi\)
0.855430 + 0.517918i \(0.173293\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) 0 0
\(580\) −27.0000 −1.12111
\(581\) 0 0
\(582\) 0 0
\(583\) −4.50000 7.79423i −0.186371 0.322804i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) 27.0000 1.11441 0.557205 0.830375i \(-0.311874\pi\)
0.557205 + 0.830375i \(0.311874\pi\)
\(588\) 0 0
\(589\) −14.0000 −0.576860
\(590\) −4.50000 7.79423i −0.185262 0.320883i
\(591\) 0 0
\(592\) 5.00000 8.66025i 0.205499 0.355934i
\(593\) −15.0000 25.9808i −0.615976 1.06690i −0.990212 0.139569i \(-0.955428\pi\)
0.374236 0.927333i \(-0.377905\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) −6.00000 + 10.3923i −0.245358 + 0.424973i
\(599\) −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(600\) 0 0
\(601\) −23.0000 −0.938190 −0.469095 0.883148i \(-0.655420\pi\)
−0.469095 + 0.883148i \(0.655420\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2.50000 4.33013i −0.101724 0.176190i
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) 0 0
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) −12.0000 −0.485866
\(611\) 12.0000 + 20.7846i 0.485468 + 0.840855i
\(612\) 0 0
\(613\) −13.0000 + 22.5167i −0.525065 + 0.909439i 0.474509 + 0.880251i \(0.342626\pi\)
−0.999574 + 0.0291886i \(0.990708\pi\)
\(614\) −13.0000 22.5167i −0.524637 0.908698i
\(615\) 0 0
\(616\) 0 0
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 0 0
\(619\) −2.00000 + 3.46410i −0.0803868 + 0.139234i −0.903416 0.428765i \(-0.858949\pi\)
0.823029 + 0.567999i \(0.192282\pi\)
\(620\) −10.5000 + 18.1865i −0.421690 + 0.730389i
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −8.50000 + 14.7224i −0.339728 + 0.588427i
\(627\) 0 0
\(628\) −2.00000 3.46410i −0.0798087 0.138233i
\(629\) −60.0000 −2.39236
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) 2.50000 + 4.33013i 0.0994447 + 0.172243i
\(633\) 0 0
\(634\) −10.5000 + 18.1865i −0.417008 + 0.722280i
\(635\) 1.50000 + 2.59808i 0.0595257 + 0.103102i
\(636\) 0 0
\(637\) 0 0
\(638\) 27.0000 1.06894
\(639\) 0 0
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) −6.00000 + 10.3923i −0.236986 + 0.410471i −0.959848 0.280521i \(-0.909493\pi\)
0.722862 + 0.690992i \(0.242826\pi\)
\(642\) 0 0
\(643\) −38.0000 −1.49857 −0.749287 0.662246i \(-0.769604\pi\)
−0.749287 + 0.662246i \(0.769604\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 6.00000 10.3923i 0.235884 0.408564i −0.723645 0.690172i \(-0.757535\pi\)
0.959529 + 0.281609i \(0.0908680\pi\)
\(648\) 0 0
\(649\) 4.50000 + 7.79423i 0.176640 + 0.305950i
\(650\) 8.00000 0.313786
\(651\) 0 0
\(652\) −10.0000 −0.391630
\(653\) 19.5000 + 33.7750i 0.763094 + 1.32172i 0.941248 + 0.337715i \(0.109654\pi\)
−0.178154 + 0.984003i \(0.557013\pi\)
\(654\) 0 0
\(655\) 22.5000 38.9711i 0.879148 1.52273i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −20.0000 + 34.6410i −0.777910 + 1.34738i 0.155235 + 0.987878i \(0.450387\pi\)
−0.933144 + 0.359502i \(0.882947\pi\)
\(662\) 4.00000 6.92820i 0.155464 0.269272i
\(663\) 0 0
\(664\) −9.00000 −0.349268
\(665\) 0 0
\(666\) 0 0
\(667\) 27.0000 + 46.7654i 1.04544 + 1.81076i
\(668\) 9.00000 15.5885i 0.348220 0.603136i
\(669\) 0 0
\(670\) 3.00000 + 5.19615i 0.115900 + 0.200745i
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) 17.0000 0.655302 0.327651 0.944799i \(-0.393743\pi\)
0.327651 + 0.944799i \(0.393743\pi\)
\(674\) 2.50000 + 4.33013i 0.0962964 + 0.166790i
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) 16.5000 + 28.5788i 0.634147 + 1.09837i 0.986695 + 0.162581i \(0.0519817\pi\)
−0.352549 + 0.935793i \(0.614685\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −18.0000 −0.690268
\(681\) 0 0
\(682\) 10.5000 18.1865i 0.402066 0.696398i
\(683\) 25.5000 44.1673i 0.975730 1.69001i 0.298227 0.954495i \(-0.403605\pi\)
0.677503 0.735520i \(-0.263062\pi\)
\(684\) 0 0
\(685\) −18.0000 −0.687745
\(686\) 0 0
\(687\) 0 0
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) 3.00000 5.19615i 0.114291 0.197958i
\(690\) 0 0
\(691\) 16.0000 + 27.7128i 0.608669 + 1.05425i 0.991460 + 0.130410i \(0.0416295\pi\)
−0.382791 + 0.923835i \(0.625037\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 3.00000 + 5.19615i 0.113796 + 0.197101i
\(696\) 0 0
\(697\) 0 0
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) 0 0
\(700\) 0 0
\(701\) −9.00000 −0.339925 −0.169963 0.985451i \(-0.554365\pi\)
−0.169963 + 0.985451i \(0.554365\pi\)
\(702\) 0 0
\(703\) −10.0000 + 17.3205i −0.377157 + 0.653255i
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) 0 0
\(709\) −7.00000 12.1244i −0.262891 0.455340i 0.704118 0.710083i \(-0.251342\pi\)
−0.967009 + 0.254743i \(0.918009\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) 42.0000 1.57291
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 0 0
\(718\) −15.0000 + 25.9808i −0.559795 + 0.969593i
\(719\) 21.0000 + 36.3731i 0.783168 + 1.35649i 0.930087 + 0.367338i \(0.119731\pi\)
−0.146920 + 0.989148i \(0.546936\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 10.0000 17.3205i 0.371647 0.643712i
\(725\) 18.0000 31.1769i 0.668503 1.15788i
\(726\) 0 0
\(727\) 31.0000 1.14973 0.574863 0.818250i \(-0.305055\pi\)
0.574863 + 0.818250i \(0.305055\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −3.00000 5.19615i −0.111035 0.192318i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 0 0
\(733\) 10.0000 + 17.3205i 0.369358 + 0.639748i 0.989465 0.144770i \(-0.0462441\pi\)
−0.620107 + 0.784517i \(0.712911\pi\)
\(734\) −37.0000 −1.36569
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) −3.00000 5.19615i −0.110506 0.191403i
\(738\) 0 0
\(739\) −13.0000 + 22.5167i −0.478213 + 0.828289i −0.999688 0.0249776i \(-0.992049\pi\)
0.521475 + 0.853266i \(0.325382\pi\)
\(740\) 15.0000 + 25.9808i 0.551411 + 0.955072i
\(741\) 0 0
\(742\) 0 0
\(743\) 54.0000 1.98107 0.990534 0.137268i \(-0.0438322\pi\)
0.990534 + 0.137268i \(0.0438322\pi\)
\(744\) 0 0
\(745\) −9.00000 + 15.5885i −0.329734 + 0.571117i
\(746\) −2.00000 + 3.46410i −0.0732252 + 0.126830i
\(747\) 0 0
\(748\) 18.0000 0.658145
\(749\) 0 0
\(750\) 0 0
\(751\) −11.5000 19.9186i −0.419641 0.726839i 0.576262 0.817265i \(-0.304511\pi\)
−0.995903 + 0.0904254i \(0.971177\pi\)
\(752\) −6.00000 + 10.3923i −0.218797 + 0.378968i
\(753\) 0 0
\(754\) 9.00000 + 15.5885i 0.327761 + 0.567698i
\(755\) 15.0000 0.545906
\(756\) 0 0
\(757\) −28.0000 −1.01768 −0.508839 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) 0 0
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) 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
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 15.0000 25.9808i 0.541972 0.938723i
\(767\) −3.00000 + 5.19615i −0.108324 + 0.187622i
\(768\) 0 0
\(769\) −5.00000 −0.180305 −0.0901523 0.995928i \(-0.528735\pi\)
−0.0901523 + 0.995928i \(0.528735\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i \(-0.867747\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(774\) 0 0
\(775\) −14.0000 24.2487i −0.502895 0.871039i
\(776\) −13.0000 −0.466673
\(777\) 0 0
\(778\) −30.0000 −1.07555
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 18.0000 + 31.1769i 0.643679 + 1.11488i
\(783\) 0 0
\(784\) 0 0
\(785\) 12.0000 0.428298
\(786\) 0 0
\(787\) −8.00000 + 13.8564i −0.285169 + 0.493928i −0.972650 0.232275i \(-0.925383\pi\)
0.687481 + 0.726202i \(0.258716\pi\)
\(788\) −9.00000 + 15.5885i −0.320612 + 0.555316i
\(789\) 0 0
\(790\) −15.0000 −0.533676
\(791\) 0 0
\(792\) 0 0
\(793\) 4.00000 + 6.92820i 0.142044 + 0.246028i
\(794\) −4.00000 + 6.92820i −0.141955 + 0.245873i
\(795\) 0 0
\(796\) 4.00000 + 6.92820i 0.141776 + 0.245564i
\(797\) 27.0000 0.956389 0.478195 0.878254i \(-0.341291\pi\)
0.478195 + 0.878254i \(0.341291\pi\)
\(798\) 0 0
\(799\) 72.0000 2.54718
\(800\) 2.00000 + 3.46410i 0.0707107 + 0.122474i
\(801\) 0 0
\(802\) 12.0000 20.7846i 0.423735 0.733930i
\(803\) 3.00000 + 5.19615i 0.105868 + 0.183368i
\(804\) 0 0
\(805\) 0 0
\(806\) 14.0000 0.493129
\(807\) 0 0
\(808\) 3.00000 5.19615i 0.105540 0.182800i
\(809\) −6.00000 + 10.3923i −0.210949 + 0.365374i −0.952012 0.306062i \(-0.900989\pi\)
0.741063 + 0.671436i \(0.234322\pi\)
\(810\) 0 0
\(811\) −2.00000 −0.0702295 −0.0351147 0.999383i \(-0.511180\pi\)
−0.0351147 + 0.999383i \(0.511180\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −15.0000 25.9808i −0.525750 0.910625i
\(815\) 15.0000 25.9808i 0.525427 0.910066i
\(816\) 0 0
\(817\) −4.00000 6.92820i −0.139942 0.242387i
\(818\) 11.0000 0.384606
\(819\) 0 0
\(820\) 0 0
\(821\) −7.50000 12.9904i −0.261752 0.453367i 0.704956 0.709251i \(-0.250967\pi\)
−0.966708 + 0.255884i \(0.917634\pi\)
\(822\) 0 0
\(823\) 8.00000 13.8564i 0.278862 0.483004i −0.692240 0.721668i \(-0.743376\pi\)
0.971102 + 0.238664i \(0.0767093\pi\)
\(824\) 8.00000 + 13.8564i 0.278693 + 0.482711i
\(825\) 0 0
\(826\) 0 0
\(827\) −9.00000 −0.312961 −0.156480 0.987681i \(-0.550015\pi\)
−0.156480 + 0.987681i \(0.550015\pi\)
\(828\) 0 0
\(829\) 1.00000 1.73205i 0.0347314 0.0601566i −0.848137 0.529777i \(-0.822276\pi\)
0.882869 + 0.469620i \(0.155609\pi\)
\(830\) 13.5000 23.3827i 0.468592 0.811625i
\(831\) 0 0
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) 0 0
\(835\) 27.0000 + 46.7654i 0.934374 + 1.61838i
\(836\) 3.00000 5.19615i 0.103757 0.179713i
\(837\) 0 0
\(838\) −18.0000 31.1769i −0.621800 1.07699i
\(839\) −54.0000 −1.86429 −0.932144 0.362089i \(-0.882064\pi\)
−0.932144 + 0.362089i \(0.882064\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) 4.00000 + 6.92820i 0.137849 + 0.238762i
\(843\) 0 0
\(844\) 8.00000 13.8564i 0.275371 0.476957i
\(845\) 13.5000 + 23.3827i 0.464414 + 0.804389i
\(846\) 0 0
\(847\) 0 0
\(848\) 3.00000 0.103020
\(849\) 0 0
\(850\) 12.0000 20.7846i 0.411597 0.712906i
\(851\) 30.0000 51.9615i 1.02839 1.78122i
\(852\) 0 0
\(853\) 46.0000 1.57501 0.787505 0.616308i \(-0.211372\pi\)
0.787505 + 0.616308i \(0.211372\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.50000 2.59808i −0.0512689 0.0888004i
\(857\) 6.00000 10.3923i 0.204956 0.354994i −0.745163 0.666883i \(-0.767628\pi\)
0.950119 + 0.311888i \(0.100962\pi\)
\(858\) 0 0
\(859\) −8.00000 13.8564i −0.272956 0.472774i 0.696661 0.717400i \(-0.254668\pi\)
−0.969618 + 0.244626i \(0.921335\pi\)
\(860\) −12.0000 −0.409197
\(861\) 0 0
\(862\) 24.0000 0.817443
\(863\) −3.00000 5.19615i −0.102121 0.176879i 0.810437 0.585826i \(-0.199230\pi\)
−0.912558 + 0.408946i \(0.865896\pi\)
\(864\) 0 0
\(865\) 9.00000 15.5885i 0.306009 0.530023i
\(866\) −13.0000 22.5167i −0.441758 0.765147i
\(867\) 0 0
\(868\) 0 0
\(869\) 15.0000 0.508840
\(870\) 0 0
\(871\) 2.00000 3.46410i 0.0677674 0.117377i
\(872\) −5.00000 + 8.66025i −0.169321 + 0.293273i
\(873\) 0 0
\(874\) 12.0000 0.405906
\(875\) 0 0
\(876\) 0 0
\(877\) −28.0000 48.4974i −0.945493 1.63764i −0.754761 0.655999i \(-0.772247\pi\)
−0.190731 0.981642i \(-0.561086\pi\)
\(878\) 9.50000 16.4545i 0.320609 0.555312i
\(879\) 0 0
\(880\) −4.50000 7.79423i −0.151695 0.262743i
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 6.00000 + 10.3923i 0.201802 + 0.349531i
\(885\) 0 0
\(886\) 7.50000 12.9904i 0.251967 0.436420i
\(887\) 3.00000 + 5.19615i 0.100730 + 0.174470i 0.911986 0.410222i \(-0.134549\pi\)
−0.811256 + 0.584692i \(0.801215\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 18.0000 0.603361
\(891\) 0 0
\(892\) −0.500000 + 0.866025i −0.0167412 + 0.0289967i
\(893\) 12.0000 20.7846i 0.401565 0.695530i
\(894\) 0 0
\(895\) 36.0000 1.20335
\(896\) 0 0
\(897\) 0 0
\(898\) −9.00000 15.5885i −0.300334 0.520194i
\(899\) 31.5000 54.5596i 1.05058 1.81966i
\(900\) 0 0
\(901\) −9.00000 15.5885i −0.299833 0.519327i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 30.0000 + 51.9615i 0.997234 + 1.72726i
\(906\) 0 0
\(907\) −25.0000 + 43.3013i −0.830111 + 1.43780i 0.0678380 + 0.997696i \(0.478390\pi\)
−0.897949 + 0.440099i \(0.854943\pi\)
\(908\) −7.50000 12.9904i −0.248896 0.431101i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) −13.5000 + 23.3827i −0.446785 + 0.773854i
\(914\) −6.50000 + 11.2583i −0.215001 + 0.372392i
\(915\) 0 0
\(916\) −20.0000 −0.660819
\(917\) 0 0
\(918\) 0 0
\(919\) 14.0000 + 24.2487i 0.461817 + 0.799891i 0.999052 0.0435419i \(-0.0138642\pi\)
−0.537234 + 0.843433i \(0.680531\pi\)
\(920\) 9.00000 15.5885i 0.296721 0.513936i
\(921\) 0 0
\(922\) 9.00000 + 15.5885i 0.296399 + 0.513378i
\(923\) 0 0
\(924\) 0 0
\(925\) −40.0000 −1.31519
\(926\) −2.00000 3.46410i −0.0657241 0.113837i
\(927\) 0 0
\(928\) −4.50000 + 7.79423i −0.147720 + 0.255858i
\(929\) 12.0000 + 20.7846i 0.393707 + 0.681921i 0.992935 0.118657i \(-0.0378590\pi\)
−0.599228 + 0.800578i \(0.704526\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 6.00000 0.196537
\(933\) 0 0
\(934\) 6.00000 10.3923i 0.196326 0.340047i
\(935\) −27.0000 + 46.7654i −0.882994 + 1.52939i
\(936\) 0 0
\(937\) 37.0000 1.20874 0.604369 0.796705i \(-0.293425\pi\)
0.604369 + 0.796705i \(0.293425\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −18.0000 31.1769i −0.587095 1.01688i
\(941\) −7.50000 + 12.9904i −0.244493 + 0.423474i −0.961989 0.273088i \(-0.911955\pi\)
0.717496 + 0.696563i \(0.245288\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −3.00000 −0.0976417
\(945\) 0 0
\(946\) 12.0000 0.390154
\(947\) 6.00000 + 10.3923i 0.194974 + 0.337705i 0.946892 0.321552i \(-0.104204\pi\)
−0.751918 + 0.659256i \(0.770871\pi\)
\(948\) 0 0
\(949\) −2.00000 + 3.46410i −0.0649227 + 0.112449i
\(950\) −4.00000 6.92820i −0.129777 0.224781i
\(951\) 0 0
\(952\) 0 0
\(953\) 36.0000 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) 0 0
\(955\) 18.0000 31.1769i 0.582466 1.00886i
\(956\) 9.00000 15.5885i 0.291081 0.504167i
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) 0 0
\(960\) 0 0
\(961\) −9.00000 15.5885i −0.290323 0.502853i
\(962\) 10.0000 17.3205i 0.322413 0.558436i
\(963\) 0 0
\(964\) 11.5000 + 19.9186i 0.370390 + 0.641534i
\(965\) −21.0000 −0.676014
\(966\) 0 0
\(967\) 29.0000 0.932577 0.466289 0.884633i \(-0.345591\pi\)
0.466289 + 0.884633i \(0.345591\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) 0 0
\(970\) 19.5000 33.7750i 0.626107 1.08445i
\(971\) −19.5000 33.7750i −0.625785 1.08389i −0.988389 0.151948i \(-0.951445\pi\)
0.362604 0.931943i \(-0.381888\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −11.0000 −0.352463
\(975\) 0 0
\(976\) −2.00000 + 3.46410i −0.0640184 + 0.110883i
\(977\) −6.00000 + 10.3923i −0.191957 + 0.332479i −0.945899 0.324462i \(-0.894817\pi\)
0.753942 + 0.656941i \(0.228150\pi\)
\(978\) 0 0
\(979\) −18.0000 −0.575282
\(980\) 0 0
\(981\) 0 0
\(982\) −4.50000 7.79423i −0.143601 0.248724i
\(983\) −12.0000 + 20.7846i −0.382741 + 0.662926i −0.991453 0.130465i \(-0.958353\pi\)
0.608712 + 0.793391i \(0.291686\pi\)
\(984\) 0 0
\(985\) −27.0000 46.7654i −0.860292 1.49007i
\(986\) 54.0000 1.71971
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) 12.0000 + 20.7846i 0.381578 + 0.660912i
\(990\) 0 0
\(991\) 9.50000 16.4545i 0.301777 0.522694i −0.674761 0.738036i \(-0.735753\pi\)
0.976539 + 0.215342i \(0.0690867\pi\)
\(992\) 3.50000 + 6.06218i 0.111125 + 0.192474i
\(993\) 0 0
\(994\) 0 0
\(995\) −24.0000 −0.760851
\(996\) 0 0
\(997\) −11.0000 + 19.0526i −0.348373 + 0.603401i −0.985961 0.166978i \(-0.946599\pi\)
0.637587 + 0.770378i \(0.279933\pi\)
\(998\) 19.0000 32.9090i 0.601434 1.04172i
\(999\) 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 882.2.g.g.361.1 2
3.2 odd 2 882.2.g.e.361.1 2
7.2 even 3 inner 882.2.g.g.667.1 2
7.3 odd 6 882.2.a.a.1.1 1
7.4 even 3 882.2.a.e.1.1 1
7.5 odd 6 126.2.g.d.37.1 yes 2
7.6 odd 2 126.2.g.d.109.1 yes 2
21.2 odd 6 882.2.g.e.667.1 2
21.5 even 6 126.2.g.a.37.1 2
21.11 odd 6 882.2.a.h.1.1 1
21.17 even 6 882.2.a.j.1.1 1
21.20 even 2 126.2.g.a.109.1 yes 2
28.3 even 6 7056.2.a.e.1.1 1
28.11 odd 6 7056.2.a.bx.1.1 1
28.19 even 6 1008.2.s.o.289.1 2
28.27 even 2 1008.2.s.o.865.1 2
63.5 even 6 1134.2.h.f.541.1 2
63.13 odd 6 1134.2.e.g.865.1 2
63.20 even 6 1134.2.h.f.109.1 2
63.34 odd 6 1134.2.h.j.109.1 2
63.40 odd 6 1134.2.h.j.541.1 2
63.41 even 6 1134.2.e.k.865.1 2
63.47 even 6 1134.2.e.k.919.1 2
63.61 odd 6 1134.2.e.g.919.1 2
84.11 even 6 7056.2.a.h.1.1 1
84.47 odd 6 1008.2.s.b.289.1 2
84.59 odd 6 7056.2.a.by.1.1 1
84.83 odd 2 1008.2.s.b.865.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.g.a.37.1 2 21.5 even 6
126.2.g.a.109.1 yes 2 21.20 even 2
126.2.g.d.37.1 yes 2 7.5 odd 6
126.2.g.d.109.1 yes 2 7.6 odd 2
882.2.a.a.1.1 1 7.3 odd 6
882.2.a.e.1.1 1 7.4 even 3
882.2.a.h.1.1 1 21.11 odd 6
882.2.a.j.1.1 1 21.17 even 6
882.2.g.e.361.1 2 3.2 odd 2
882.2.g.e.667.1 2 21.2 odd 6
882.2.g.g.361.1 2 1.1 even 1 trivial
882.2.g.g.667.1 2 7.2 even 3 inner
1008.2.s.b.289.1 2 84.47 odd 6
1008.2.s.b.865.1 2 84.83 odd 2
1008.2.s.o.289.1 2 28.19 even 6
1008.2.s.o.865.1 2 28.27 even 2
1134.2.e.g.865.1 2 63.13 odd 6
1134.2.e.g.919.1 2 63.61 odd 6
1134.2.e.k.865.1 2 63.41 even 6
1134.2.e.k.919.1 2 63.47 even 6
1134.2.h.f.109.1 2 63.20 even 6
1134.2.h.f.541.1 2 63.5 even 6
1134.2.h.j.109.1 2 63.34 odd 6
1134.2.h.j.541.1 2 63.40 odd 6
7056.2.a.e.1.1 1 28.3 even 6
7056.2.a.h.1.1 1 84.11 even 6
7056.2.a.bx.1.1 1 28.11 odd 6
7056.2.a.by.1.1 1 84.59 odd 6