Properties

Label 112.2.i.b.81.1
Level $112$
Weight $2$
Character 112.81
Analytic conductor $0.894$
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] = [112,2,Mod(65,112)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(112, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("112.65");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.894324502638\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 112.81
Dual form 112.2.i.b.65.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +2.00000 q^{13} -3.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 - 2.59808i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +5.00000 q^{27} -6.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(1.50000 + 2.59808i) q^{33} +(-7.50000 - 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(1.00000 - 1.73205i) q^{39} +6.00000 q^{41} +4.00000 q^{43} +(3.00000 - 5.19615i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(1.50000 + 2.59808i) q^{51} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{55} -1.00000 q^{57} +(4.50000 - 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} +(5.00000 + 1.73205i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(-3.50000 + 6.06218i) q^{67} +3.00000 q^{69} +(0.500000 - 0.866025i) q^{73} +(2.00000 + 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(-6.50000 - 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} +9.00000 q^{85} +(-3.00000 + 5.19615i) q^{87} +(-7.50000 - 12.9904i) q^{89} +(4.00000 - 3.46410i) q^{91} +(3.50000 + 6.06218i) q^{93} +(-1.50000 + 2.59808i) q^{95} -10.0000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} - 3 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} - 3 q^{5} + 4 q^{7} + 2 q^{9} - 3 q^{11} + 4 q^{13} - 6 q^{15} - 3 q^{17} - q^{19} - q^{21} + 3 q^{23} - 4 q^{25} + 10 q^{27} - 12 q^{29} - 7 q^{31} + 3 q^{33} - 15 q^{35} + q^{37} + 2 q^{39} + 12 q^{41} + 8 q^{43} + 6 q^{45} - 9 q^{47} + 2 q^{49} + 3 q^{51} - 3 q^{53} + 18 q^{55} - 2 q^{57} + 9 q^{59} + q^{61} + 10 q^{63} - 6 q^{65} - 7 q^{67} + 6 q^{69} + q^{73} + 4 q^{75} + 3 q^{77} - 13 q^{79} - q^{81} - 24 q^{83} + 18 q^{85} - 6 q^{87} - 15 q^{89} + 8 q^{91} + 7 q^{93} - 3 q^{95} - 20 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) −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
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 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
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −3.00000 −0.774597
\(16\) 0 0
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) −0.500000 2.59808i −0.109109 0.566947i
\(22\) 0 0
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 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 0
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 0 0
\(35\) −7.50000 2.59808i −1.26773 0.439155i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 1.00000 1.73205i 0.160128 0.277350i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 3.00000 5.19615i 0.447214 0.774597i
\(46\) 0 0
\(47\) −4.50000 7.79423i −0.656392 1.13691i −0.981543 0.191243i \(-0.938748\pi\)
0.325150 0.945662i \(-0.394585\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) 0 0
\(53\) −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
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) 5.00000 + 1.73205i 0.629941 + 0.218218i
\(64\) 0 0
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0 0
\(67\) −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) 0 0
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0.500000 0.866025i 0.0585206 0.101361i −0.835281 0.549823i \(-0.814695\pi\)
0.893801 + 0.448463i \(0.148028\pi\)
\(74\) 0 0
\(75\) 2.00000 + 3.46410i 0.230940 + 0.400000i
\(76\) 0 0
\(77\) 1.50000 + 7.79423i 0.170941 + 0.888235i
\(78\) 0 0
\(79\) −6.50000 11.2583i −0.731307 1.26666i −0.956325 0.292306i \(-0.905577\pi\)
0.225018 0.974355i \(-0.427756\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 9.00000 0.976187
\(86\) 0 0
\(87\) −3.00000 + 5.19615i −0.321634 + 0.557086i
\(88\) 0 0
\(89\) −7.50000 12.9904i −0.794998 1.37698i −0.922840 0.385183i \(-0.874138\pi\)
0.127842 0.991795i \(-0.459195\pi\)
\(90\) 0 0
\(91\) 4.00000 3.46410i 0.419314 0.363137i
\(92\) 0 0
\(93\) 3.50000 + 6.06218i 0.362933 + 0.628619i
\(94\) 0 0
\(95\) −1.50000 + 2.59808i −0.153897 + 0.266557i
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) −7.50000 + 12.9904i −0.746278 + 1.29259i 0.203317 + 0.979113i \(0.434828\pi\)
−0.949595 + 0.313478i \(0.898506\pi\)
\(102\) 0 0
\(103\) 5.50000 + 9.52628i 0.541931 + 0.938652i 0.998793 + 0.0491146i \(0.0156400\pi\)
−0.456862 + 0.889538i \(0.651027\pi\)
\(104\) 0 0
\(105\) −6.00000 + 5.19615i −0.585540 + 0.507093i
\(106\) 0 0
\(107\) 7.50000 + 12.9904i 0.725052 + 1.25583i 0.958952 + 0.283567i \(0.0915178\pi\)
−0.233900 + 0.972261i \(0.575149\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 0 0
\(111\) 1.00000 0.0949158
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) 0 0
\(117\) 2.00000 + 3.46410i 0.184900 + 0.320256i
\(118\) 0 0
\(119\) 1.50000 + 7.79423i 0.137505 + 0.714496i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 0 0
\(131\) 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) 0 0
\(133\) −2.50000 0.866025i −0.216777 0.0750939i
\(134\) 0 0
\(135\) −7.50000 12.9904i −0.645497 1.11803i
\(136\) 0 0
\(137\) 10.5000 18.1865i 0.897076 1.55378i 0.0658609 0.997829i \(-0.479021\pi\)
0.831215 0.555952i \(-0.187646\pi\)
\(138\) 0 0
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) −9.00000 −0.757937
\(142\) 0 0
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) 0 0
\(145\) 9.00000 + 15.5885i 0.747409 + 1.29455i
\(146\) 0 0
\(147\) −5.50000 4.33013i −0.453632 0.357143i
\(148\) 0 0
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 0 0
\(151\) 8.50000 14.7224i 0.691720 1.19809i −0.279554 0.960130i \(-0.590186\pi\)
0.971274 0.237964i \(-0.0764802\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 21.0000 1.68676
\(156\) 0 0
\(157\) 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) 0 0
\(159\) 1.50000 + 2.59808i 0.118958 + 0.206041i
\(160\) 0 0
\(161\) 7.50000 + 2.59808i 0.591083 + 0.204757i
\(162\) 0 0
\(163\) 5.50000 + 9.52628i 0.430793 + 0.746156i 0.996942 0.0781474i \(-0.0249005\pi\)
−0.566149 + 0.824303i \(0.691567\pi\)
\(164\) 0 0
\(165\) 4.50000 7.79423i 0.350325 0.606780i
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 1.00000 1.73205i 0.0764719 0.132453i
\(172\) 0 0
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) 0 0
\(175\) 2.00000 + 10.3923i 0.151186 + 0.785584i
\(176\) 0 0
\(177\) −4.50000 7.79423i −0.338241 0.585850i
\(178\) 0 0
\(179\) 10.5000 18.1865i 0.784807 1.35933i −0.144308 0.989533i \(-0.546095\pi\)
0.929114 0.369792i \(-0.120571\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 1.00000 0.0739221
\(184\) 0 0
\(185\) 1.50000 2.59808i 0.110282 0.191014i
\(186\) 0 0
\(187\) −4.50000 7.79423i −0.329073 0.569970i
\(188\) 0 0
\(189\) 10.0000 8.66025i 0.727393 0.629941i
\(190\) 0 0
\(191\) −4.50000 7.79423i −0.325609 0.563971i 0.656027 0.754738i \(-0.272236\pi\)
−0.981635 + 0.190767i \(0.938902\pi\)
\(192\) 0 0
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) 0 0
\(195\) −6.00000 −0.429669
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −3.50000 + 6.06218i −0.248108 + 0.429736i −0.963001 0.269498i \(-0.913142\pi\)
0.714893 + 0.699234i \(0.246476\pi\)
\(200\) 0 0
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) 0 0
\(203\) −12.0000 + 10.3923i −0.842235 + 0.729397i
\(204\) 0 0
\(205\) −9.00000 15.5885i −0.628587 1.08875i
\(206\) 0 0
\(207\) −3.00000 + 5.19615i −0.208514 + 0.361158i
\(208\) 0 0
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.00000 10.3923i −0.409197 0.708749i
\(216\) 0 0
\(217\) 3.50000 + 18.1865i 0.237595 + 1.23458i
\(218\) 0 0
\(219\) −0.500000 0.866025i −0.0337869 0.0585206i
\(220\) 0 0
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) −8.00000 −0.533333
\(226\) 0 0
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 0 0
\(229\) −5.50000 9.52628i −0.363450 0.629514i 0.625076 0.780564i \(-0.285068\pi\)
−0.988526 + 0.151050i \(0.951735\pi\)
\(230\) 0 0
\(231\) 7.50000 + 2.59808i 0.493464 + 0.170941i
\(232\) 0 0
\(233\) 10.5000 + 18.1865i 0.687878 + 1.19144i 0.972523 + 0.232806i \(0.0747909\pi\)
−0.284645 + 0.958633i \(0.591876\pi\)
\(234\) 0 0
\(235\) −13.5000 + 23.3827i −0.880643 + 1.52532i
\(236\) 0 0
\(237\) −13.0000 −0.844441
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 0 0
\(245\) −19.5000 + 7.79423i −1.24581 + 0.497955i
\(246\) 0 0
\(247\) −1.00000 1.73205i −0.0636285 0.110208i
\(248\) 0 0
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) 0 0
\(255\) 4.50000 7.79423i 0.281801 0.488094i
\(256\) 0 0
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 0 0
\(259\) 2.50000 + 0.866025i 0.155342 + 0.0538122i
\(260\) 0 0
\(261\) −6.00000 10.3923i −0.371391 0.643268i
\(262\) 0 0
\(263\) −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i \(-0.862817\pi\)
0.816066 + 0.577959i \(0.196151\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) −15.0000 −0.917985
\(268\) 0 0
\(269\) −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i \(-0.862486\pi\)
0.816668 + 0.577108i \(0.195819\pi\)
\(270\) 0 0
\(271\) 5.50000 + 9.52628i 0.334101 + 0.578680i 0.983312 0.181928i \(-0.0582339\pi\)
−0.649211 + 0.760609i \(0.724901\pi\)
\(272\) 0 0
\(273\) −1.00000 5.19615i −0.0605228 0.314485i
\(274\) 0 0
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0 0
\(277\) 6.50000 11.2583i 0.390547 0.676448i −0.601975 0.798515i \(-0.705619\pi\)
0.992522 + 0.122068i \(0.0389525\pi\)
\(278\) 0 0
\(279\) −14.0000 −0.838158
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) 14.5000 25.1147i 0.861936 1.49292i −0.00812260 0.999967i \(-0.502586\pi\)
0.870058 0.492949i \(-0.164081\pi\)
\(284\) 0 0
\(285\) 1.50000 + 2.59808i 0.0888523 + 0.153897i
\(286\) 0 0
\(287\) 12.0000 10.3923i 0.708338 0.613438i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) −5.00000 + 8.66025i −0.293105 + 0.507673i
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −27.0000 −1.57200
\(296\) 0 0
\(297\) −7.50000 + 12.9904i −0.435194 + 0.753778i
\(298\) 0 0
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) 8.00000 6.92820i 0.461112 0.399335i
\(302\) 0 0
\(303\) 7.50000 + 12.9904i 0.430864 + 0.746278i
\(304\) 0 0
\(305\) 1.50000 2.59808i 0.0858898 0.148765i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) −13.5000 + 23.3827i −0.765515 + 1.32591i 0.174459 + 0.984664i \(0.444182\pi\)
−0.939974 + 0.341246i \(0.889151\pi\)
\(312\) 0 0
\(313\) −11.5000 19.9186i −0.650018 1.12586i −0.983118 0.182973i \(-0.941428\pi\)
0.333099 0.942892i \(-0.391906\pi\)
\(314\) 0 0
\(315\) −3.00000 15.5885i −0.169031 0.878310i
\(316\) 0 0
\(317\) 4.50000 + 7.79423i 0.252745 + 0.437767i 0.964281 0.264883i \(-0.0853332\pi\)
−0.711535 + 0.702650i \(0.752000\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) 0 0
\(321\) 15.0000 0.837218
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) −4.00000 + 6.92820i −0.221880 + 0.384308i
\(326\) 0 0
\(327\) −0.500000 0.866025i −0.0276501 0.0478913i
\(328\) 0 0
\(329\) −22.5000 7.79423i −1.24047 0.429710i
\(330\) 0 0
\(331\) −6.50000 11.2583i −0.357272 0.618814i 0.630232 0.776407i \(-0.282960\pi\)
−0.987504 + 0.157593i \(0.949627\pi\)
\(332\) 0 0
\(333\) −1.00000 + 1.73205i −0.0547997 + 0.0949158i
\(334\) 0 0
\(335\) 21.0000 1.14735
\(336\) 0 0
\(337\) −34.0000 −1.85210 −0.926049 0.377403i \(-0.876817\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) 0 0
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 0 0
\(341\) −10.5000 18.1865i −0.568607 0.984856i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) −4.50000 7.79423i −0.242272 0.419627i
\(346\) 0 0
\(347\) 4.50000 7.79423i 0.241573 0.418416i −0.719590 0.694399i \(-0.755670\pi\)
0.961162 + 0.275983i \(0.0890035\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) 10.0000 0.533761
\(352\) 0 0
\(353\) 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i \(-0.644573\pi\)
0.997592 0.0693543i \(-0.0220939\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 7.50000 + 2.59808i 0.396942 + 0.137505i
\(358\) 0 0
\(359\) 7.50000 + 12.9904i 0.395835 + 0.685606i 0.993207 0.116358i \(-0.0371219\pi\)
−0.597372 + 0.801964i \(0.703789\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) −3.00000 −0.157027
\(366\) 0 0
\(367\) 2.50000 4.33013i 0.130499 0.226031i −0.793370 0.608740i \(-0.791675\pi\)
0.923869 + 0.382709i \(0.125009\pi\)
\(368\) 0 0
\(369\) 6.00000 + 10.3923i 0.312348 + 0.541002i
\(370\) 0 0
\(371\) 1.50000 + 7.79423i 0.0778761 + 0.404656i
\(372\) 0 0
\(373\) 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) 0 0
\(375\) −1.50000 + 2.59808i −0.0774597 + 0.134164i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 0 0
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 0 0
\(383\) −16.5000 28.5788i −0.843111 1.46031i −0.887252 0.461285i \(-0.847389\pi\)
0.0441413 0.999025i \(-0.485945\pi\)
\(384\) 0 0
\(385\) 18.0000 15.5885i 0.917365 0.794461i
\(386\) 0 0
\(387\) 4.00000 + 6.92820i 0.203331 + 0.352180i
\(388\) 0 0
\(389\) −7.50000 + 12.9904i −0.380265 + 0.658638i −0.991100 0.133120i \(-0.957501\pi\)
0.610835 + 0.791758i \(0.290834\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) 3.00000 0.151330
\(394\) 0 0
\(395\) −19.5000 + 33.7750i −0.981151 + 1.69940i
\(396\) 0 0
\(397\) 18.5000 + 32.0429i 0.928488 + 1.60819i 0.785853 + 0.618414i \(0.212224\pi\)
0.142636 + 0.989775i \(0.454442\pi\)
\(398\) 0 0
\(399\) −2.00000 + 1.73205i −0.100125 + 0.0867110i
\(400\) 0 0
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) −7.00000 + 12.1244i −0.348695 + 0.603957i
\(404\) 0 0
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) 0 0
\(411\) −10.5000 18.1865i −0.517927 0.897076i
\(412\) 0 0
\(413\) −4.50000 23.3827i −0.221431 1.15059i
\(414\) 0 0
\(415\) 18.0000 + 31.1769i 0.883585 + 1.53041i
\(416\) 0 0
\(417\) −10.0000 + 17.3205i −0.489702 + 0.848189i
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 9.00000 15.5885i 0.437595 0.757937i
\(424\) 0 0
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) 0 0
\(427\) 2.50000 + 0.866025i 0.120983 + 0.0419099i
\(428\) 0 0
\(429\) 3.00000 + 5.19615i 0.144841 + 0.250873i
\(430\) 0 0
\(431\) −7.50000 + 12.9904i −0.361262 + 0.625725i −0.988169 0.153370i \(-0.950987\pi\)
0.626907 + 0.779094i \(0.284321\pi\)
\(432\) 0 0
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) 0 0
\(435\) 18.0000 0.863034
\(436\) 0 0
\(437\) 1.50000 2.59808i 0.0717547 0.124283i
\(438\) 0 0
\(439\) −0.500000 0.866025i −0.0238637 0.0413331i 0.853847 0.520524i \(-0.174263\pi\)
−0.877711 + 0.479191i \(0.840930\pi\)
\(440\) 0 0
\(441\) 13.0000 5.19615i 0.619048 0.247436i
\(442\) 0 0
\(443\) −4.50000 7.79423i −0.213801 0.370315i 0.739100 0.673596i \(-0.235251\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(444\) 0 0
\(445\) −22.5000 + 38.9711i −1.06660 + 1.84741i
\(446\) 0 0
\(447\) −3.00000 −0.141895
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −9.00000 + 15.5885i −0.423793 + 0.734032i
\(452\) 0 0
\(453\) −8.50000 14.7224i −0.399365 0.691720i
\(454\) 0 0
\(455\) −15.0000 5.19615i −0.703211 0.243599i
\(456\) 0 0
\(457\) −11.5000 19.9186i −0.537947 0.931752i −0.999014 0.0443868i \(-0.985867\pi\)
0.461067 0.887365i \(-0.347467\pi\)
\(458\) 0 0
\(459\) −7.50000 + 12.9904i −0.350070 + 0.606339i
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) 10.5000 18.1865i 0.486926 0.843380i
\(466\) 0 0
\(467\) −10.5000 18.1865i −0.485882 0.841572i 0.513986 0.857798i \(-0.328168\pi\)
−0.999868 + 0.0162260i \(0.994835\pi\)
\(468\) 0 0
\(469\) 3.50000 + 18.1865i 0.161615 + 0.839776i
\(470\) 0 0
\(471\) −6.50000 11.2583i −0.299504 0.518756i
\(472\) 0 0
\(473\) −6.00000 + 10.3923i −0.275880 + 0.477839i
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i \(-0.855166\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(480\) 0 0
\(481\) 1.00000 + 1.73205i 0.0455961 + 0.0789747i
\(482\) 0 0
\(483\) 6.00000 5.19615i 0.273009 0.236433i
\(484\) 0 0
\(485\) 15.0000 + 25.9808i 0.681115 + 1.17973i
\(486\) 0 0
\(487\) −9.50000 + 16.4545i −0.430486 + 0.745624i −0.996915 0.0784867i \(-0.974991\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) 0 0
\(489\) 11.0000 0.497437
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) 0 0
\(495\) 9.00000 + 15.5885i 0.404520 + 0.700649i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 5.50000 + 9.52628i 0.246214 + 0.426455i 0.962472 0.271380i \(-0.0874801\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 0 0
\(501\) 6.00000 10.3923i 0.268060 0.464294i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 45.0000 2.00247
\(506\) 0 0
\(507\) −4.50000 + 7.79423i −0.199852 + 0.346154i
\(508\) 0 0
\(509\) −1.50000 2.59808i −0.0664863 0.115158i 0.830866 0.556473i \(-0.187846\pi\)
−0.897352 + 0.441315i \(0.854512\pi\)
\(510\) 0 0
\(511\) −0.500000 2.59808i −0.0221187 0.114932i
\(512\) 0 0
\(513\) −2.50000 4.33013i −0.110378 0.191180i
\(514\) 0 0
\(515\) 16.5000 28.5788i 0.727077 1.25933i
\(516\) 0 0
\(517\) 27.0000 1.18746
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) 0 0
\(521\) −19.5000 + 33.7750i −0.854311 + 1.47971i 0.0229727 + 0.999736i \(0.492687\pi\)
−0.877283 + 0.479973i \(0.840646\pi\)
\(522\) 0 0
\(523\) −0.500000 0.866025i −0.0218635 0.0378686i 0.854887 0.518815i \(-0.173627\pi\)
−0.876750 + 0.480946i \(0.840293\pi\)
\(524\) 0 0
\(525\) 10.0000 + 3.46410i 0.436436 + 0.151186i
\(526\) 0 0
\(527\) −10.5000 18.1865i −0.457387 0.792218i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 22.5000 38.9711i 0.972760 1.68487i
\(536\) 0 0
\(537\) −10.5000 18.1865i −0.453108 0.784807i
\(538\) 0 0
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) 0 0
\(541\) −17.5000 30.3109i −0.752384 1.30317i −0.946664 0.322221i \(-0.895571\pi\)
0.194281 0.980946i \(-0.437763\pi\)
\(542\) 0 0
\(543\) −5.00000 + 8.66025i −0.214571 + 0.371647i
\(544\) 0 0
\(545\) −3.00000 −0.128506
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 3.00000 + 5.19615i 0.127804 + 0.221364i
\(552\) 0 0
\(553\) −32.5000 11.2583i −1.38204 0.478753i
\(554\) 0 0
\(555\) −1.50000 2.59808i −0.0636715 0.110282i
\(556\) 0 0
\(557\) 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i \(-0.586905\pi\)
0.968769 0.247964i \(-0.0797613\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) 4.50000 7.79423i 0.189652 0.328488i −0.755482 0.655169i \(-0.772597\pi\)
0.945134 + 0.326682i \(0.105931\pi\)
\(564\) 0 0
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 0 0
\(567\) 0.500000 + 2.59808i 0.0209980 + 0.109109i
\(568\) 0 0
\(569\) 4.50000 + 7.79423i 0.188650 + 0.326751i 0.944800 0.327647i \(-0.106256\pi\)
−0.756151 + 0.654398i \(0.772922\pi\)
\(570\) 0 0
\(571\) 14.5000 25.1147i 0.606806 1.05102i −0.384957 0.922934i \(-0.625784\pi\)
0.991763 0.128085i \(-0.0408829\pi\)
\(572\) 0 0
\(573\) −9.00000 −0.375980
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) 0.500000 0.866025i 0.0208153 0.0360531i −0.855430 0.517918i \(-0.826707\pi\)
0.876245 + 0.481865i \(0.160040\pi\)
\(578\) 0 0
\(579\) 5.50000 + 9.52628i 0.228572 + 0.395899i
\(580\) 0 0
\(581\) −24.0000 + 20.7846i −0.995688 + 0.862291i
\(582\) 0 0
\(583\) −4.50000 7.79423i −0.186371 0.322804i
\(584\) 0 0
\(585\) 6.00000 10.3923i 0.248069 0.429669i
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 7.00000 0.288430
\(590\) 0 0
\(591\) 9.00000 15.5885i 0.370211 0.641223i
\(592\) 0 0
\(593\) 10.5000 + 18.1865i 0.431183 + 0.746831i 0.996976 0.0777165i \(-0.0247629\pi\)
−0.565792 + 0.824548i \(0.691430\pi\)
\(594\) 0 0
\(595\) 18.0000 15.5885i 0.737928 0.639064i
\(596\) 0 0
\(597\) 3.50000 + 6.06218i 0.143245 + 0.248108i
\(598\) 0 0
\(599\) −13.5000 + 23.3827i −0.551595 + 0.955391i 0.446565 + 0.894751i \(0.352647\pi\)
−0.998160 + 0.0606393i \(0.980686\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) 0 0
\(607\) 23.5000 + 40.7032i 0.953836 + 1.65209i 0.737011 + 0.675881i \(0.236237\pi\)
0.216825 + 0.976210i \(0.430430\pi\)
\(608\) 0 0
\(609\) 3.00000 + 15.5885i 0.121566 + 0.631676i
\(610\) 0 0
\(611\) −9.00000 15.5885i −0.364101 0.630641i
\(612\) 0 0
\(613\) 12.5000 21.6506i 0.504870 0.874461i −0.495114 0.868828i \(-0.664874\pi\)
0.999984 0.00563283i \(-0.00179300\pi\)
\(614\) 0 0
\(615\) −18.0000 −0.725830
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) −15.5000 + 26.8468i −0.622998 + 1.07906i 0.365927 + 0.930644i \(0.380752\pi\)
−0.988924 + 0.148420i \(0.952581\pi\)
\(620\) 0 0
\(621\) 7.50000 + 12.9904i 0.300965 + 0.521286i
\(622\) 0 0
\(623\) −37.5000 12.9904i −1.50241 0.520449i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) 1.50000 2.59808i 0.0599042 0.103757i
\(628\) 0 0
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 2.00000 3.46410i 0.0794929 0.137686i
\(634\) 0 0
\(635\) 12.0000 + 20.7846i 0.476205 + 0.824812i
\(636\) 0 0
\(637\) 2.00000 13.8564i 0.0792429 0.549011i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.50000 + 12.9904i −0.296232 + 0.513089i −0.975271 0.221013i \(-0.929064\pi\)
0.679039 + 0.734103i \(0.262397\pi\)
\(642\) 0 0
\(643\) −20.0000 −0.788723 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) −12.0000 −0.472500
\(646\) 0 0
\(647\) 10.5000 18.1865i 0.412798 0.714986i −0.582397 0.812905i \(-0.697885\pi\)
0.995194 + 0.0979182i \(0.0312184\pi\)
\(648\) 0 0
\(649\) 13.5000 + 23.3827i 0.529921 + 0.917851i
\(650\) 0 0
\(651\) 17.5000 + 6.06218i 0.685879 + 0.237595i
\(652\) 0 0
\(653\) −19.5000 33.7750i −0.763094 1.32172i −0.941248 0.337715i \(-0.890346\pi\)
0.178154 0.984003i \(-0.442987\pi\)
\(654\) 0 0
\(655\) 4.50000 7.79423i 0.175830 0.304546i
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −5.50000 + 9.52628i −0.213925 + 0.370529i −0.952940 0.303160i \(-0.901958\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 0 0
\(663\) 3.00000 + 5.19615i 0.116510 + 0.201802i
\(664\) 0 0
\(665\) 1.50000 + 7.79423i 0.0581675 + 0.302247i
\(666\) 0 0
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 0 0
\(669\) −4.00000 + 6.92820i −0.154649 + 0.267860i
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 0 0
\(675\) −10.0000 + 17.3205i −0.384900 + 0.666667i
\(676\) 0 0
\(677\) −13.5000 23.3827i −0.518847 0.898670i −0.999760 0.0219013i \(-0.993028\pi\)
0.480913 0.876768i \(-0.340305\pi\)
\(678\) 0 0
\(679\) −20.0000 + 17.3205i −0.767530 + 0.664700i
\(680\) 0 0
\(681\) 1.50000 + 2.59808i 0.0574801 + 0.0995585i
\(682\) 0 0
\(683\) 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i \(-0.701728\pi\)
0.993940 + 0.109926i \(0.0350613\pi\)
\(684\) 0 0
\(685\) −63.0000 −2.40711
\(686\) 0 0
\(687\) −11.0000 −0.419676
\(688\) 0 0
\(689\) −3.00000 + 5.19615i −0.114291 + 0.197958i
\(690\) 0 0
\(691\) −6.50000 11.2583i −0.247272 0.428287i 0.715496 0.698617i \(-0.246201\pi\)
−0.962768 + 0.270330i \(0.912867\pi\)
\(692\) 0 0
\(693\) −12.0000 + 10.3923i −0.455842 + 0.394771i
\(694\) 0 0
\(695\) 30.0000 + 51.9615i 1.13796 + 1.97101i
\(696\) 0 0
\(697\) −9.00000 + 15.5885i −0.340899 + 0.590455i
\(698\) 0 0
\(699\) 21.0000 0.794293
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 0.500000 0.866025i 0.0188579 0.0326628i
\(704\) 0 0
\(705\) 13.5000 + 23.3827i 0.508439 + 0.880643i
\(706\) 0 0
\(707\) 7.50000 + 38.9711i 0.282067 + 1.46566i
\(708\) 0 0
\(709\) 0.500000 + 0.866025i 0.0187779 + 0.0325243i 0.875262 0.483650i \(-0.160689\pi\)
−0.856484 + 0.516174i \(0.827356\pi\)
\(710\) 0 0
\(711\) 13.0000 22.5167i 0.487538 0.844441i
\(712\) 0 0
\(713\) −21.0000 −0.786456
\(714\) 0 0
\(715\) 18.0000 0.673162
\(716\) 0 0
\(717\) 6.00000 10.3923i 0.224074 0.388108i
\(718\) 0 0
\(719\) −10.5000 18.1865i −0.391584 0.678243i 0.601075 0.799193i \(-0.294739\pi\)
−0.992659 + 0.120950i \(0.961406\pi\)
\(720\) 0 0
\(721\) 27.5000 + 9.52628i 1.02415 + 0.354777i
\(722\) 0 0
\(723\) −0.500000 0.866025i −0.0185952 0.0322078i
\(724\) 0 0
\(725\) 12.0000 20.7846i 0.445669 0.771921i
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −6.00000 + 10.3923i −0.221918 + 0.384373i
\(732\) 0 0
\(733\) 12.5000 + 21.6506i 0.461698 + 0.799684i 0.999046 0.0436764i \(-0.0139070\pi\)
−0.537348 + 0.843361i \(0.680574\pi\)
\(734\) 0 0
\(735\) −3.00000 + 20.7846i −0.110657 + 0.766652i
\(736\) 0 0
\(737\) −10.5000 18.1865i −0.386772 0.669910i
\(738\) 0 0
\(739\) −9.50000 + 16.4545i −0.349463 + 0.605288i −0.986154 0.165831i \(-0.946969\pi\)
0.636691 + 0.771119i \(0.280303\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 0 0
\(745\) −4.50000 + 7.79423i −0.164867 + 0.285558i
\(746\) 0 0
\(747\) −12.0000 20.7846i −0.439057 0.760469i
\(748\) 0 0
\(749\) 37.5000 + 12.9904i 1.37022 + 0.474658i
\(750\) 0 0
\(751\) −12.5000 21.6506i −0.456131 0.790043i 0.542621 0.839978i \(-0.317432\pi\)
−0.998752 + 0.0499348i \(0.984099\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −51.0000 −1.85608
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) −4.50000 + 7.79423i −0.163340 + 0.282913i
\(760\) 0 0
\(761\) −1.50000 2.59808i −0.0543750 0.0941802i 0.837557 0.546350i \(-0.183983\pi\)
−0.891932 + 0.452170i \(0.850650\pi\)
\(762\) 0 0
\(763\) −0.500000 2.59808i −0.0181012 0.0940567i
\(764\) 0 0
\(765\) 9.00000 + 15.5885i 0.325396 + 0.563602i
\(766\) 0 0
\(767\) 9.00000 15.5885i 0.324971 0.562867i
\(768\) 0 0
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) 0 0
\(773\) 16.5000 28.5788i 0.593464 1.02791i −0.400298 0.916385i \(-0.631093\pi\)
0.993762 0.111524i \(-0.0355733\pi\)
\(774\) 0 0
\(775\) −14.0000 24.2487i −0.502895 0.871039i
\(776\) 0 0
\(777\) 2.00000 1.73205i 0.0717496 0.0621370i
\(778\) 0 0
\(779\) −3.00000 5.19615i −0.107486 0.186171i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −30.0000 −1.07211
\(784\) 0 0
\(785\) −39.0000 −1.39197
\(786\) 0 0
\(787\) −15.5000 + 26.8468i −0.552515 + 0.956985i 0.445577 + 0.895244i \(0.352999\pi\)
−0.998092 + 0.0617409i \(0.980335\pi\)
\(788\) 0 0
\(789\) 1.50000 + 2.59808i 0.0534014 + 0.0924940i
\(790\) 0 0
\(791\) 12.0000 10.3923i 0.426671 0.369508i
\(792\) 0 0
\(793\) 1.00000 + 1.73205i 0.0355110 + 0.0615069i
\(794\) 0 0
\(795\) 4.50000 7.79423i 0.159599 0.276433i
\(796\) 0 0
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) 27.0000 0.955191
\(800\) 0 0
\(801\) 15.0000 25.9808i 0.529999 0.917985i
\(802\) 0 0
\(803\) 1.50000 + 2.59808i 0.0529339 + 0.0916841i
\(804\) 0 0
\(805\) −4.50000 23.3827i −0.158604 0.824131i
\(806\) 0 0
\(807\) 1.50000 + 2.59808i 0.0528025 + 0.0914566i
\(808\) 0 0
\(809\) 16.5000 28.5788i 0.580109 1.00478i −0.415357 0.909659i \(-0.636343\pi\)
0.995466 0.0951198i \(-0.0303234\pi\)
\(810\) 0 0
\(811\) 52.0000 1.82597 0.912983 0.407997i \(-0.133772\pi\)
0.912983 + 0.407997i \(0.133772\pi\)
\(812\) 0 0
\(813\) 11.0000 0.385787
\(814\) 0 0
\(815\) 16.5000 28.5788i 0.577970 1.00107i
\(816\) 0 0
\(817\) −2.00000 3.46410i −0.0699711 0.121194i
\(818\) 0 0
\(819\) 10.0000 + 3.46410i 0.349428 + 0.121046i
\(820\) 0 0
\(821\) −13.5000 23.3827i −0.471153 0.816061i 0.528302 0.849056i \(-0.322829\pi\)
−0.999456 + 0.0329950i \(0.989495\pi\)
\(822\) 0 0
\(823\) 2.50000 4.33013i 0.0871445 0.150939i −0.819159 0.573567i \(-0.805559\pi\)
0.906303 + 0.422628i \(0.138892\pi\)
\(824\) 0 0
\(825\) −12.0000 −0.417786
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) 0.500000 0.866025i 0.0173657 0.0300783i −0.857212 0.514964i \(-0.827805\pi\)
0.874578 + 0.484885i \(0.161139\pi\)
\(830\) 0 0
\(831\) −6.50000 11.2583i −0.225483 0.390547i
\(832\) 0 0
\(833\) 16.5000 + 12.9904i 0.571691 + 0.450090i
\(834\) 0 0
\(835\) −18.0000 31.1769i −0.622916 1.07892i
\(836\) 0 0
\(837\) −17.5000 + 30.3109i −0.604888 + 1.04770i
\(838\) 0 0
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 15.0000 25.9808i 0.516627 0.894825i
\(844\) 0 0
\(845\) 13.5000 + 23.3827i 0.464414 + 0.804389i
\(846\) 0 0
\(847\) 5.00000 + 1.73205i 0.171802 + 0.0595140i
\(848\) 0 0
\(849\) −14.5000 25.1147i −0.497639 0.861936i
\(850\) 0 0
\(851\) −1.50000 + 2.59808i −0.0514193 + 0.0890609i
\(852\) 0 0
\(853\) −22.0000 −0.753266 −0.376633 0.926363i \(-0.622918\pi\)
−0.376633 + 0.926363i \(0.622918\pi\)
\(854\) 0 0
\(855\) −6.00000 −0.205196
\(856\) 0 0
\(857\) −7.50000 + 12.9904i −0.256195 + 0.443743i −0.965219 0.261441i \(-0.915802\pi\)
0.709024 + 0.705184i \(0.249136\pi\)
\(858\) 0 0
\(859\) 11.5000 + 19.9186i 0.392375 + 0.679613i 0.992762 0.120096i \(-0.0383202\pi\)
−0.600387 + 0.799709i \(0.704987\pi\)
\(860\) 0 0
\(861\) −3.00000 15.5885i −0.102240 0.531253i
\(862\) 0 0
\(863\) 25.5000 + 44.1673i 0.868030 + 1.50347i 0.864007 + 0.503480i \(0.167947\pi\)
0.00402340 + 0.999992i \(0.498719\pi\)
\(864\) 0 0
\(865\) 13.5000 23.3827i 0.459014 0.795035i
\(866\) 0 0
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) 39.0000 1.32298
\(870\) 0 0
\(871\) −7.00000 + 12.1244i −0.237186 + 0.410818i
\(872\) 0 0
\(873\) −10.0000 17.3205i −0.338449 0.586210i
\(874\) 0 0
\(875\) −6.00000 + 5.19615i −0.202837 + 0.175662i
\(876\) 0 0
\(877\) 6.50000 + 11.2583i 0.219489 + 0.380167i 0.954652 0.297724i \(-0.0962275\pi\)
−0.735163 + 0.677891i \(0.762894\pi\)
\(878\) 0 0
\(879\) 3.00000 5.19615i 0.101187 0.175262i
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) −44.0000 −1.48072 −0.740359 0.672212i \(-0.765344\pi\)
−0.740359 + 0.672212i \(0.765344\pi\)
\(884\) 0 0
\(885\) −13.5000 + 23.3827i −0.453798 + 0.786000i
\(886\) 0 0
\(887\) 19.5000 + 33.7750i 0.654746 + 1.13405i 0.981957 + 0.189102i \(0.0605577\pi\)
−0.327212 + 0.944951i \(0.606109\pi\)
\(888\) 0 0
\(889\) −16.0000 + 13.8564i −0.536623 + 0.464729i
\(890\) 0 0
\(891\) −1.50000 2.59808i −0.0502519 0.0870388i
\(892\) 0 0
\(893\) −4.50000 + 7.79423i −0.150587 + 0.260824i
\(894\) 0 0
\(895\) −63.0000 −2.10586
\(896\) 0 0
\(897\) 6.00000 0.200334
\(898\) 0 0
\(899\) 21.0000 36.3731i 0.700389 1.21311i
\(900\) 0 0
\(901\) −4.50000 7.79423i −0.149917 0.259663i
\(902\) 0 0
\(903\) −2.00000 10.3923i −0.0665558 0.345834i
\(904\) 0 0
\(905\) 15.0000 + 25.9808i 0.498617 + 0.863630i
\(906\) 0 0
\(907\) 20.5000 35.5070i 0.680691 1.17899i −0.294079 0.955781i \(-0.595013\pi\)
0.974770 0.223211i \(-0.0716538\pi\)
\(908\) 0 0
\(909\) −30.0000 −0.995037
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 0 0
\(913\) 18.0000 31.1769i 0.595713 1.03181i
\(914\) 0 0
\(915\) −1.50000 2.59808i −0.0495885 0.0858898i
\(916\) 0 0
\(917\) 7.50000 + 2.59808i 0.247672 + 0.0857960i
\(918\) 0 0
\(919\) −0.500000 0.866025i −0.0164935 0.0285675i 0.857661 0.514216i \(-0.171917\pi\)
−0.874154 + 0.485648i \(0.838584\pi\)
\(920\) 0 0
\(921\) 14.0000 24.2487i 0.461316 0.799022i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −4.00000 −0.131519
\(926\) 0 0
\(927\) −11.0000 + 19.0526i −0.361287 + 0.625768i
\(928\) 0 0
\(929\) 4.50000 + 7.79423i 0.147640 + 0.255720i 0.930355 0.366660i \(-0.119499\pi\)
−0.782715 + 0.622381i \(0.786166\pi\)
\(930\) 0 0
\(931\) −6.50000 + 2.59808i −0.213029 + 0.0851485i
\(932\) 0 0
\(933\) 13.5000 + 23.3827i 0.441970 + 0.765515i
\(934\) 0 0
\(935\) −13.5000 + 23.3827i −0.441497 + 0.764696i
\(936\) 0 0
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 0 0
\(939\) −23.0000 −0.750577
\(940\) 0 0
\(941\) −13.5000 + 23.3827i −0.440087 + 0.762254i −0.997695 0.0678506i \(-0.978386\pi\)
0.557608 + 0.830104i \(0.311719\pi\)
\(942\) 0 0
\(943\) 9.00000 + 15.5885i 0.293080 + 0.507630i
\(944\) 0 0
\(945\) −37.5000 12.9904i −1.21988 0.422577i
\(946\) 0 0
\(947\) −22.5000 38.9711i −0.731152 1.26639i −0.956391 0.292089i \(-0.905650\pi\)
0.225240 0.974303i \(-0.427684\pi\)
\(948\) 0 0
\(949\) 1.00000 1.73205i 0.0324614 0.0562247i
\(950\) 0 0
\(951\) 9.00000 0.291845
\(952\) 0 0
\(953\) −18.0000 −0.583077 −0.291539 0.956559i \(-0.594167\pi\)
−0.291539 + 0.956559i \(0.594167\pi\)
\(954\) 0 0
\(955\) −13.5000 + 23.3827i −0.436850 + 0.756646i
\(956\) 0 0
\(957\) −9.00000 15.5885i −0.290929 0.503903i
\(958\) 0 0
\(959\) −10.5000 54.5596i −0.339063 1.76182i
\(960\) 0 0
\(961\) −9.00000 15.5885i −0.290323 0.502853i
\(962\) 0 0
\(963\) −15.0000 + 25.9808i −0.483368 + 0.837218i
\(964\) 0 0
\(965\) 33.0000 1.06231
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) 0 0
\(969\) 1.50000 2.59808i 0.0481869 0.0834622i
\(970\) 0 0
\(971\) 25.5000 + 44.1673i 0.818334 + 1.41740i 0.906909 + 0.421326i \(0.138435\pi\)
−0.0885751 + 0.996070i \(0.528231\pi\)
\(972\) 0 0
\(973\) −40.0000 + 34.6410i −1.28234 + 1.11054i
\(974\) 0 0
\(975\) 4.00000 + 6.92820i 0.128103 + 0.221880i
\(976\) 0 0
\(977\) −13.5000 + 23.3827i −0.431903 + 0.748078i −0.997037 0.0769208i \(-0.975491\pi\)
0.565134 + 0.824999i \(0.308824\pi\)
\(978\) 0 0
\(979\) 45.0000 1.43821
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 0 0
\(983\) 16.5000 28.5788i 0.526268 0.911523i −0.473263 0.880921i \(-0.656924\pi\)
0.999532 0.0306024i \(-0.00974257\pi\)
\(984\) 0 0
\(985\) −27.0000 46.7654i −0.860292 1.49007i
\(986\) 0 0
\(987\) −18.0000 + 15.5885i −0.572946 + 0.496186i
\(988\) 0 0
\(989\) 6.00000 + 10.3923i 0.190789 + 0.330456i
\(990\) 0 0
\(991\) −9.50000 + 16.4545i −0.301777 + 0.522694i −0.976539 0.215342i \(-0.930913\pi\)
0.674761 + 0.738036i \(0.264247\pi\)
\(992\) 0 0
\(993\) −13.0000 −0.412543
\(994\) 0 0
\(995\) 21.0000 0.665745
\(996\) 0 0
\(997\) −29.5000 + 51.0955i −0.934274 + 1.61821i −0.158352 + 0.987383i \(0.550618\pi\)
−0.775923 + 0.630828i \(0.782715\pi\)
\(998\) 0 0
\(999\) 2.50000 + 4.33013i 0.0790965 + 0.136999i
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 112.2.i.b.81.1 2
3.2 odd 2 1008.2.s.p.865.1 2
4.3 odd 2 28.2.e.a.25.1 yes 2
7.2 even 3 inner 112.2.i.b.65.1 2
7.3 odd 6 784.2.a.g.1.1 1
7.4 even 3 784.2.a.d.1.1 1
7.5 odd 6 784.2.i.d.177.1 2
7.6 odd 2 784.2.i.d.753.1 2
8.3 odd 2 448.2.i.e.193.1 2
8.5 even 2 448.2.i.c.193.1 2
12.11 even 2 252.2.k.c.109.1 2
20.3 even 4 700.2.r.b.249.1 4
20.7 even 4 700.2.r.b.249.2 4
20.19 odd 2 700.2.i.c.501.1 2
21.2 odd 6 1008.2.s.p.289.1 2
21.11 odd 6 7056.2.a.f.1.1 1
21.17 even 6 7056.2.a.bw.1.1 1
28.3 even 6 196.2.a.a.1.1 1
28.11 odd 6 196.2.a.b.1.1 1
28.19 even 6 196.2.e.a.177.1 2
28.23 odd 6 28.2.e.a.9.1 2
28.27 even 2 196.2.e.a.165.1 2
36.7 odd 6 2268.2.l.h.109.1 2
36.11 even 6 2268.2.l.a.109.1 2
36.23 even 6 2268.2.i.h.865.1 2
36.31 odd 6 2268.2.i.a.865.1 2
56.3 even 6 3136.2.a.v.1.1 1
56.11 odd 6 3136.2.a.h.1.1 1
56.37 even 6 448.2.i.c.65.1 2
56.45 odd 6 3136.2.a.k.1.1 1
56.51 odd 6 448.2.i.e.65.1 2
56.53 even 6 3136.2.a.s.1.1 1
84.11 even 6 1764.2.a.a.1.1 1
84.23 even 6 252.2.k.c.37.1 2
84.47 odd 6 1764.2.k.b.1549.1 2
84.59 odd 6 1764.2.a.j.1.1 1
84.83 odd 2 1764.2.k.b.361.1 2
140.3 odd 12 4900.2.e.h.2549.1 2
140.23 even 12 700.2.r.b.149.2 4
140.39 odd 6 4900.2.a.g.1.1 1
140.59 even 6 4900.2.a.n.1.1 1
140.67 even 12 4900.2.e.i.2549.1 2
140.79 odd 6 700.2.i.c.401.1 2
140.87 odd 12 4900.2.e.h.2549.2 2
140.107 even 12 700.2.r.b.149.1 4
140.123 even 12 4900.2.e.i.2549.2 2
252.23 even 6 2268.2.l.a.541.1 2
252.79 odd 6 2268.2.i.a.2053.1 2
252.191 even 6 2268.2.i.h.2053.1 2
252.247 odd 6 2268.2.l.h.541.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.2.e.a.9.1 2 28.23 odd 6
28.2.e.a.25.1 yes 2 4.3 odd 2
112.2.i.b.65.1 2 7.2 even 3 inner
112.2.i.b.81.1 2 1.1 even 1 trivial
196.2.a.a.1.1 1 28.3 even 6
196.2.a.b.1.1 1 28.11 odd 6
196.2.e.a.165.1 2 28.27 even 2
196.2.e.a.177.1 2 28.19 even 6
252.2.k.c.37.1 2 84.23 even 6
252.2.k.c.109.1 2 12.11 even 2
448.2.i.c.65.1 2 56.37 even 6
448.2.i.c.193.1 2 8.5 even 2
448.2.i.e.65.1 2 56.51 odd 6
448.2.i.e.193.1 2 8.3 odd 2
700.2.i.c.401.1 2 140.79 odd 6
700.2.i.c.501.1 2 20.19 odd 2
700.2.r.b.149.1 4 140.107 even 12
700.2.r.b.149.2 4 140.23 even 12
700.2.r.b.249.1 4 20.3 even 4
700.2.r.b.249.2 4 20.7 even 4
784.2.a.d.1.1 1 7.4 even 3
784.2.a.g.1.1 1 7.3 odd 6
784.2.i.d.177.1 2 7.5 odd 6
784.2.i.d.753.1 2 7.6 odd 2
1008.2.s.p.289.1 2 21.2 odd 6
1008.2.s.p.865.1 2 3.2 odd 2
1764.2.a.a.1.1 1 84.11 even 6
1764.2.a.j.1.1 1 84.59 odd 6
1764.2.k.b.361.1 2 84.83 odd 2
1764.2.k.b.1549.1 2 84.47 odd 6
2268.2.i.a.865.1 2 36.31 odd 6
2268.2.i.a.2053.1 2 252.79 odd 6
2268.2.i.h.865.1 2 36.23 even 6
2268.2.i.h.2053.1 2 252.191 even 6
2268.2.l.a.109.1 2 36.11 even 6
2268.2.l.a.541.1 2 252.23 even 6
2268.2.l.h.109.1 2 36.7 odd 6
2268.2.l.h.541.1 2 252.247 odd 6
3136.2.a.h.1.1 1 56.11 odd 6
3136.2.a.k.1.1 1 56.45 odd 6
3136.2.a.s.1.1 1 56.53 even 6
3136.2.a.v.1.1 1 56.3 even 6
4900.2.a.g.1.1 1 140.39 odd 6
4900.2.a.n.1.1 1 140.59 even 6
4900.2.e.h.2549.1 2 140.3 odd 12
4900.2.e.h.2549.2 2 140.87 odd 12
4900.2.e.i.2549.1 2 140.67 even 12
4900.2.e.i.2549.2 2 140.123 even 12
7056.2.a.f.1.1 1 21.11 odd 6
7056.2.a.bw.1.1 1 21.17 even 6