Properties

Label 216.2.f.a.107.5
Level $216$
Weight $2$
Character 216.107
Analytic conductor $1.725$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [216,2,Mod(107,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.f (of order \(2\), degree \(1\), 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: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.23123460096.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 2x^{6} + 6x^{4} + 8x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.5
Root \(-0.563016 - 1.29731i\) of defining polynomial
Character \(\chi\) \(=\) 216.107
Dual form 216.2.f.a.107.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.563016 - 1.29731i) q^{2} +(-1.36603 - 1.46081i) q^{4} -3.07638 q^{5} -3.99102i q^{7} +(-2.66422 + 0.949697i) q^{8} +O(q^{10})\) \(q+(0.563016 - 1.29731i) q^{2} +(-1.36603 - 1.46081i) q^{4} -3.07638 q^{5} -3.99102i q^{7} +(-2.66422 + 0.949697i) q^{8} +(-1.73205 + 3.99102i) q^{10} +1.89939i q^{11} -1.06939i q^{13} +(-5.17758 - 2.24701i) q^{14} +(-0.267949 + 3.99102i) q^{16} -7.08863i q^{17} +3.73205 q^{19} +(4.20241 + 4.49401i) q^{20} +(2.46410 + 1.06939i) q^{22} +0.824313 q^{23} +4.46410 q^{25} +(-1.38733 - 0.602084i) q^{26} +(-5.83013 + 5.45183i) q^{28} +4.50413 q^{29} +5.84325i q^{31} +(5.02672 + 2.59462i) q^{32} +(-9.19615 - 3.99102i) q^{34} +12.2779i q^{35} -6.91264i q^{37} +(2.10121 - 4.84163i) q^{38} +(8.19615 - 2.92163i) q^{40} -3.79879i q^{41} +2.00000 q^{43} +(2.77466 - 2.59462i) q^{44} +(0.464102 - 1.06939i) q^{46} +6.97707 q^{47} -8.92820 q^{49} +(2.51336 - 5.79132i) q^{50} +(-1.56218 + 1.46081i) q^{52} -10.6569 q^{53} -5.84325i q^{55} +(3.79025 + 10.6329i) q^{56} +(2.53590 - 5.84325i) q^{58} +1.89939i q^{59} +1.06939i q^{61} +(7.58051 + 3.28985i) q^{62} +(6.19615 - 5.06040i) q^{64} +3.28985i q^{65} -9.19615 q^{67} +(-10.3552 + 9.68325i) q^{68} +(15.9282 + 6.91264i) q^{70} +10.6569 q^{71} +5.92820 q^{73} +(-8.96784 - 3.89193i) q^{74} +(-5.09808 - 5.45183i) q^{76} +7.58051 q^{77} +6.12979i q^{79} +(0.824313 - 12.2779i) q^{80} +(-4.92820 - 2.13878i) q^{82} -10.3785i q^{83} +21.8073i q^{85} +(1.12603 - 2.59462i) q^{86} +(-1.80385 - 5.06040i) q^{88} -13.6683i q^{89} -4.26795 q^{91} +(-1.12603 - 1.20417i) q^{92} +(3.92820 - 9.05142i) q^{94} -11.4812 q^{95} -11.3923 q^{97} +(-5.02672 + 11.5826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{4} - 16 q^{16} + 16 q^{19} - 8 q^{22} + 8 q^{25} - 12 q^{28} - 32 q^{34} + 24 q^{40} + 16 q^{43} - 24 q^{46} - 16 q^{49} + 36 q^{52} + 48 q^{58} + 8 q^{64} - 32 q^{67} + 72 q^{70} - 8 q^{73} - 20 q^{76} + 16 q^{82} - 56 q^{88} - 48 q^{91} - 24 q^{94} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.563016 1.29731i 0.398113 0.917337i
\(3\) 0 0
\(4\) −1.36603 1.46081i −0.683013 0.730406i
\(5\) −3.07638 −1.37580 −0.687899 0.725806i \(-0.741467\pi\)
−0.687899 + 0.725806i \(0.741467\pi\)
\(6\) 0 0
\(7\) 3.99102i 1.50846i −0.656609 0.754231i \(-0.728010\pi\)
0.656609 0.754231i \(-0.271990\pi\)
\(8\) −2.66422 + 0.949697i −0.941945 + 0.335768i
\(9\) 0 0
\(10\) −1.73205 + 3.99102i −0.547723 + 1.26207i
\(11\) 1.89939i 0.572689i 0.958127 + 0.286344i \(0.0924401\pi\)
−0.958127 + 0.286344i \(0.907560\pi\)
\(12\) 0 0
\(13\) 1.06939i 0.296595i −0.988943 0.148298i \(-0.952621\pi\)
0.988943 0.148298i \(-0.0473794\pi\)
\(14\) −5.17758 2.24701i −1.38377 0.600538i
\(15\) 0 0
\(16\) −0.267949 + 3.99102i −0.0669873 + 0.997754i
\(17\) 7.08863i 1.71925i −0.510929 0.859623i \(-0.670698\pi\)
0.510929 0.859623i \(-0.329302\pi\)
\(18\) 0 0
\(19\) 3.73205 0.856191 0.428096 0.903733i \(-0.359185\pi\)
0.428096 + 0.903733i \(0.359185\pi\)
\(20\) 4.20241 + 4.49401i 0.939688 + 1.00489i
\(21\) 0 0
\(22\) 2.46410 + 1.06939i 0.525348 + 0.227995i
\(23\) 0.824313 0.171881 0.0859406 0.996300i \(-0.472610\pi\)
0.0859406 + 0.996300i \(0.472610\pi\)
\(24\) 0 0
\(25\) 4.46410 0.892820
\(26\) −1.38733 0.602084i −0.272078 0.118078i
\(27\) 0 0
\(28\) −5.83013 + 5.45183i −1.10179 + 1.03030i
\(29\) 4.50413 0.836396 0.418198 0.908356i \(-0.362662\pi\)
0.418198 + 0.908356i \(0.362662\pi\)
\(30\) 0 0
\(31\) 5.84325i 1.04948i 0.851263 + 0.524740i \(0.175837\pi\)
−0.851263 + 0.524740i \(0.824163\pi\)
\(32\) 5.02672 + 2.59462i 0.888608 + 0.458668i
\(33\) 0 0
\(34\) −9.19615 3.99102i −1.57713 0.684453i
\(35\) 12.2779i 2.07534i
\(36\) 0 0
\(37\) 6.91264i 1.13643i −0.822880 0.568216i \(-0.807634\pi\)
0.822880 0.568216i \(-0.192366\pi\)
\(38\) 2.10121 4.84163i 0.340861 0.785415i
\(39\) 0 0
\(40\) 8.19615 2.92163i 1.29593 0.461950i
\(41\) 3.79879i 0.593271i −0.954991 0.296635i \(-0.904135\pi\)
0.954991 0.296635i \(-0.0958646\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 2.77466 2.59462i 0.418296 0.391154i
\(45\) 0 0
\(46\) 0.464102 1.06939i 0.0684280 0.157673i
\(47\) 6.97707 1.01771 0.508855 0.860852i \(-0.330069\pi\)
0.508855 + 0.860852i \(0.330069\pi\)
\(48\) 0 0
\(49\) −8.92820 −1.27546
\(50\) 2.51336 5.79132i 0.355443 0.819017i
\(51\) 0 0
\(52\) −1.56218 + 1.46081i −0.216635 + 0.202578i
\(53\) −10.6569 −1.46384 −0.731918 0.681393i \(-0.761375\pi\)
−0.731918 + 0.681393i \(0.761375\pi\)
\(54\) 0 0
\(55\) 5.84325i 0.787904i
\(56\) 3.79025 + 10.6329i 0.506494 + 1.42089i
\(57\) 0 0
\(58\) 2.53590 5.84325i 0.332980 0.767257i
\(59\) 1.89939i 0.247280i 0.992327 + 0.123640i \(0.0394568\pi\)
−0.992327 + 0.123640i \(0.960543\pi\)
\(60\) 0 0
\(61\) 1.06939i 0.136921i 0.997654 + 0.0684606i \(0.0218088\pi\)
−0.997654 + 0.0684606i \(0.978191\pi\)
\(62\) 7.58051 + 3.28985i 0.962725 + 0.417811i
\(63\) 0 0
\(64\) 6.19615 5.06040i 0.774519 0.632551i
\(65\) 3.28985i 0.408055i
\(66\) 0 0
\(67\) −9.19615 −1.12349 −0.561744 0.827311i \(-0.689870\pi\)
−0.561744 + 0.827311i \(0.689870\pi\)
\(68\) −10.3552 + 9.68325i −1.25575 + 1.17427i
\(69\) 0 0
\(70\) 15.9282 + 6.91264i 1.90378 + 0.826219i
\(71\) 10.6569 1.26474 0.632370 0.774667i \(-0.282082\pi\)
0.632370 + 0.774667i \(0.282082\pi\)
\(72\) 0 0
\(73\) 5.92820 0.693844 0.346922 0.937894i \(-0.387227\pi\)
0.346922 + 0.937894i \(0.387227\pi\)
\(74\) −8.96784 3.89193i −1.04249 0.452428i
\(75\) 0 0
\(76\) −5.09808 5.45183i −0.584789 0.625368i
\(77\) 7.58051 0.863879
\(78\) 0 0
\(79\) 6.12979i 0.689656i 0.938666 + 0.344828i \(0.112063\pi\)
−0.938666 + 0.344828i \(0.887937\pi\)
\(80\) 0.824313 12.2779i 0.0921610 1.37271i
\(81\) 0 0
\(82\) −4.92820 2.13878i −0.544229 0.236189i
\(83\) 10.3785i 1.13919i −0.821927 0.569593i \(-0.807101\pi\)
0.821927 0.569593i \(-0.192899\pi\)
\(84\) 0 0
\(85\) 21.8073i 2.36534i
\(86\) 1.12603 2.59462i 0.121423 0.279785i
\(87\) 0 0
\(88\) −1.80385 5.06040i −0.192291 0.539441i
\(89\) 13.6683i 1.44884i −0.689359 0.724420i \(-0.742108\pi\)
0.689359 0.724420i \(-0.257892\pi\)
\(90\) 0 0
\(91\) −4.26795 −0.447403
\(92\) −1.12603 1.20417i −0.117397 0.125543i
\(93\) 0 0
\(94\) 3.92820 9.05142i 0.405163 0.933583i
\(95\) −11.4812 −1.17795
\(96\) 0 0
\(97\) −11.3923 −1.15671 −0.578357 0.815784i \(-0.696306\pi\)
−0.578357 + 0.815784i \(0.696306\pi\)
\(98\) −5.02672 + 11.5826i −0.507776 + 1.17002i
\(99\) 0 0
\(100\) −6.09808 6.52122i −0.609808 0.652122i
\(101\) −6.15276 −0.612222 −0.306111 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(102\) 0 0
\(103\) 3.99102i 0.393246i 0.980479 + 0.196623i \(0.0629976\pi\)
−0.980479 + 0.196623i \(0.937002\pi\)
\(104\) 1.01560 + 2.84909i 0.0995873 + 0.279376i
\(105\) 0 0
\(106\) −6.00000 + 13.8253i −0.582772 + 1.34283i
\(107\) 8.47908i 0.819704i 0.912152 + 0.409852i \(0.134420\pi\)
−0.912152 + 0.409852i \(0.865580\pi\)
\(108\) 0 0
\(109\) 10.1208i 0.969398i 0.874681 + 0.484699i \(0.161071\pi\)
−0.874681 + 0.484699i \(0.838929\pi\)
\(110\) −7.58051 3.28985i −0.722773 0.313674i
\(111\) 0 0
\(112\) 15.9282 + 1.06939i 1.50507 + 0.101048i
\(113\) 10.8874i 1.02420i 0.858925 + 0.512101i \(0.171133\pi\)
−0.858925 + 0.512101i \(0.828867\pi\)
\(114\) 0 0
\(115\) −2.53590 −0.236474
\(116\) −6.15276 6.57969i −0.571269 0.610909i
\(117\) 0 0
\(118\) 2.46410 + 1.06939i 0.226839 + 0.0984453i
\(119\) −28.2908 −2.59342
\(120\) 0 0
\(121\) 7.39230 0.672028
\(122\) 1.38733 + 0.602084i 0.125603 + 0.0545101i
\(123\) 0 0
\(124\) 8.53590 7.98203i 0.766546 0.716808i
\(125\) 1.64863 0.147458
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −3.07638 10.8874i −0.271916 0.962321i
\(129\) 0 0
\(130\) 4.26795 + 1.85224i 0.374324 + 0.162452i
\(131\) 10.3785i 0.906772i −0.891314 0.453386i \(-0.850216\pi\)
0.891314 0.453386i \(-0.149784\pi\)
\(132\) 0 0
\(133\) 14.8947i 1.29153i
\(134\) −5.17758 + 11.9303i −0.447275 + 1.03062i
\(135\) 0 0
\(136\) 6.73205 + 18.8857i 0.577269 + 1.61943i
\(137\) 17.4671i 1.49232i 0.665769 + 0.746158i \(0.268104\pi\)
−0.665769 + 0.746158i \(0.731896\pi\)
\(138\) 0 0
\(139\) −3.19615 −0.271094 −0.135547 0.990771i \(-0.543279\pi\)
−0.135547 + 0.990771i \(0.543279\pi\)
\(140\) 17.9357 16.7719i 1.51584 1.41748i
\(141\) 0 0
\(142\) 6.00000 13.8253i 0.503509 1.16019i
\(143\) 2.03119 0.169857
\(144\) 0 0
\(145\) −13.8564 −1.15071
\(146\) 3.33767 7.69072i 0.276228 0.636488i
\(147\) 0 0
\(148\) −10.0981 + 9.44284i −0.830057 + 0.776197i
\(149\) 6.15276 0.504053 0.252027 0.967720i \(-0.418903\pi\)
0.252027 + 0.967720i \(0.418903\pi\)
\(150\) 0 0
\(151\) 9.83427i 0.800301i 0.916449 + 0.400151i \(0.131042\pi\)
−0.916449 + 0.400151i \(0.868958\pi\)
\(152\) −9.94301 + 3.54432i −0.806485 + 0.287482i
\(153\) 0 0
\(154\) 4.26795 9.83427i 0.343921 0.792468i
\(155\) 17.9761i 1.44387i
\(156\) 0 0
\(157\) 21.8073i 1.74041i −0.492687 0.870207i \(-0.663985\pi\)
0.492687 0.870207i \(-0.336015\pi\)
\(158\) 7.95224 + 3.45117i 0.632646 + 0.274561i
\(159\) 0 0
\(160\) −15.4641 7.98203i −1.22254 0.631035i
\(161\) 3.28985i 0.259276i
\(162\) 0 0
\(163\) 8.80385 0.689571 0.344785 0.938682i \(-0.387952\pi\)
0.344785 + 0.938682i \(0.387952\pi\)
\(164\) −5.54932 + 5.18924i −0.433329 + 0.405212i
\(165\) 0 0
\(166\) −13.4641 5.84325i −1.04502 0.453524i
\(167\) 22.1381 1.71310 0.856548 0.516067i \(-0.172604\pi\)
0.856548 + 0.516067i \(0.172604\pi\)
\(168\) 0 0
\(169\) 11.8564 0.912031
\(170\) 28.2908 + 12.2779i 2.16981 + 0.941670i
\(171\) 0 0
\(172\) −2.73205 2.92163i −0.208317 0.222772i
\(173\) 1.64863 0.125343 0.0626714 0.998034i \(-0.480038\pi\)
0.0626714 + 0.998034i \(0.480038\pi\)
\(174\) 0 0
\(175\) 17.8163i 1.34679i
\(176\) −7.58051 0.508941i −0.571402 0.0383629i
\(177\) 0 0
\(178\) −17.7321 7.69549i −1.32907 0.576801i
\(179\) 3.79879i 0.283935i −0.989871 0.141967i \(-0.954657\pi\)
0.989871 0.141967i \(-0.0453428\pi\)
\(180\) 0 0
\(181\) 3.20817i 0.238461i −0.992867 0.119231i \(-0.961957\pi\)
0.992867 0.119231i \(-0.0380428\pi\)
\(182\) −2.40292 + 5.53685i −0.178117 + 0.410419i
\(183\) 0 0
\(184\) −2.19615 + 0.782847i −0.161903 + 0.0577123i
\(185\) 21.2659i 1.56350i
\(186\) 0 0
\(187\) 13.4641 0.984593
\(188\) −9.53085 10.1922i −0.695109 0.743342i
\(189\) 0 0
\(190\) −6.46410 + 14.8947i −0.468955 + 1.08057i
\(191\) 6.97707 0.504843 0.252421 0.967617i \(-0.418773\pi\)
0.252421 + 0.967617i \(0.418773\pi\)
\(192\) 0 0
\(193\) −5.39230 −0.388147 −0.194073 0.980987i \(-0.562170\pi\)
−0.194073 + 0.980987i \(0.562170\pi\)
\(194\) −6.41405 + 14.7793i −0.460502 + 1.06110i
\(195\) 0 0
\(196\) 12.1962 + 13.0424i 0.871154 + 0.931603i
\(197\) 17.0305 1.21337 0.606687 0.794941i \(-0.292498\pi\)
0.606687 + 0.794941i \(0.292498\pi\)
\(198\) 0 0
\(199\) 15.6775i 1.11135i 0.831400 + 0.555675i \(0.187540\pi\)
−0.831400 + 0.555675i \(0.812460\pi\)
\(200\) −11.8934 + 4.23954i −0.840987 + 0.299781i
\(201\) 0 0
\(202\) −3.46410 + 7.98203i −0.243733 + 0.561614i
\(203\) 17.9761i 1.26167i
\(204\) 0 0
\(205\) 11.6865i 0.816221i
\(206\) 5.17758 + 2.24701i 0.360739 + 0.156556i
\(207\) 0 0
\(208\) 4.26795 + 0.286542i 0.295929 + 0.0198681i
\(209\) 7.08863i 0.490331i
\(210\) 0 0
\(211\) 21.0526 1.44932 0.724659 0.689108i \(-0.241997\pi\)
0.724659 + 0.689108i \(0.241997\pi\)
\(212\) 14.5576 + 15.5677i 0.999818 + 1.06920i
\(213\) 0 0
\(214\) 11.0000 + 4.77386i 0.751945 + 0.326335i
\(215\) −6.15276 −0.419614
\(216\) 0 0
\(217\) 23.3205 1.58310
\(218\) 13.1298 + 5.69818i 0.889264 + 0.385929i
\(219\) 0 0
\(220\) −8.53590 + 7.98203i −0.575490 + 0.538148i
\(221\) −7.58051 −0.509920
\(222\) 0 0
\(223\) 26.0849i 1.74677i −0.487029 0.873386i \(-0.661919\pi\)
0.487029 0.873386i \(-0.338081\pi\)
\(224\) 10.3552 20.0617i 0.691884 1.34043i
\(225\) 0 0
\(226\) 14.1244 + 6.12979i 0.939538 + 0.407748i
\(227\) 3.79879i 0.252134i −0.992022 0.126067i \(-0.959765\pi\)
0.992022 0.126067i \(-0.0402355\pi\)
\(228\) 0 0
\(229\) 11.6865i 0.772266i −0.922443 0.386133i \(-0.873811\pi\)
0.922443 0.386133i \(-0.126189\pi\)
\(230\) −1.42775 + 3.28985i −0.0941432 + 0.216926i
\(231\) 0 0
\(232\) −12.0000 + 4.27756i −0.787839 + 0.280835i
\(233\) 14.1773i 0.928784i 0.885630 + 0.464392i \(0.153727\pi\)
−0.885630 + 0.464392i \(0.846273\pi\)
\(234\) 0 0
\(235\) −21.4641 −1.40016
\(236\) 2.77466 2.59462i 0.180615 0.168895i
\(237\) 0 0
\(238\) −15.9282 + 36.7020i −1.03247 + 2.37904i
\(239\) −12.3055 −0.795977 −0.397989 0.917390i \(-0.630292\pi\)
−0.397989 + 0.917390i \(0.630292\pi\)
\(240\) 0 0
\(241\) −5.39230 −0.347349 −0.173674 0.984803i \(-0.555564\pi\)
−0.173674 + 0.984803i \(0.555564\pi\)
\(242\) 4.16199 9.59011i 0.267543 0.616476i
\(243\) 0 0
\(244\) 1.56218 1.46081i 0.100008 0.0935190i
\(245\) 27.4665 1.75477
\(246\) 0 0
\(247\) 3.99102i 0.253942i
\(248\) −5.54932 15.5677i −0.352382 0.988551i
\(249\) 0 0
\(250\) 0.928203 2.13878i 0.0587047 0.135268i
\(251\) 14.1773i 0.894861i 0.894319 + 0.447431i \(0.147661\pi\)
−0.894319 + 0.447431i \(0.852339\pi\)
\(252\) 0 0
\(253\) 1.56569i 0.0984344i
\(254\) 0 0
\(255\) 0 0
\(256\) −15.8564 2.13878i −0.991025 0.133674i
\(257\) 3.79879i 0.236962i −0.992956 0.118481i \(-0.962198\pi\)
0.992956 0.118481i \(-0.0378024\pi\)
\(258\) 0 0
\(259\) −27.5885 −1.71426
\(260\) 4.80585 4.49401i 0.298046 0.278707i
\(261\) 0 0
\(262\) −13.4641 5.84325i −0.831815 0.360997i
\(263\) −3.29725 −0.203317 −0.101659 0.994819i \(-0.532415\pi\)
−0.101659 + 0.994819i \(0.532415\pi\)
\(264\) 0 0
\(265\) 32.7846 2.01394
\(266\) −19.3230 8.38594i −1.18477 0.514175i
\(267\) 0 0
\(268\) 12.5622 + 13.4339i 0.767357 + 0.820604i
\(269\) −19.8860 −1.21247 −0.606236 0.795285i \(-0.707321\pi\)
−0.606236 + 0.795285i \(0.707321\pi\)
\(270\) 0 0
\(271\) 11.9730i 0.727311i −0.931534 0.363655i \(-0.881529\pi\)
0.931534 0.363655i \(-0.118471\pi\)
\(272\) 28.2908 + 1.89939i 1.71538 + 0.115168i
\(273\) 0 0
\(274\) 22.6603 + 9.83427i 1.36896 + 0.594110i
\(275\) 8.47908i 0.511308i
\(276\) 0 0
\(277\) 21.8073i 1.31027i 0.755510 + 0.655137i \(0.227389\pi\)
−0.755510 + 0.655137i \(0.772611\pi\)
\(278\) −1.79949 + 4.14640i −0.107926 + 0.248685i
\(279\) 0 0
\(280\) −11.6603 32.7110i −0.696833 1.95485i
\(281\) 10.3785i 0.619128i −0.950879 0.309564i \(-0.899817\pi\)
0.950879 0.309564i \(-0.100183\pi\)
\(282\) 0 0
\(283\) 27.8564 1.65589 0.827946 0.560808i \(-0.189509\pi\)
0.827946 + 0.560808i \(0.189509\pi\)
\(284\) −14.5576 15.5677i −0.863833 0.923774i
\(285\) 0 0
\(286\) 1.14359 2.63508i 0.0676221 0.155816i
\(287\) −15.1610 −0.894926
\(288\) 0 0
\(289\) −33.2487 −1.95581
\(290\) −7.80138 + 17.9761i −0.458113 + 1.05559i
\(291\) 0 0
\(292\) −8.09808 8.66000i −0.473904 0.506788i
\(293\) 7.58051 0.442858 0.221429 0.975176i \(-0.428928\pi\)
0.221429 + 0.975176i \(0.428928\pi\)
\(294\) 0 0
\(295\) 5.84325i 0.340207i
\(296\) 6.56491 + 18.4168i 0.381578 + 1.07046i
\(297\) 0 0
\(298\) 3.46410 7.98203i 0.200670 0.462387i
\(299\) 0.881512i 0.0509791i
\(300\) 0 0
\(301\) 7.98203i 0.460077i
\(302\) 12.7581 + 5.53685i 0.734146 + 0.318610i
\(303\) 0 0
\(304\) −1.00000 + 14.8947i −0.0573539 + 0.854268i
\(305\) 3.28985i 0.188376i
\(306\) 0 0
\(307\) 20.9282 1.19444 0.597218 0.802079i \(-0.296273\pi\)
0.597218 + 0.802079i \(0.296273\pi\)
\(308\) −10.3552 11.0737i −0.590040 0.630983i
\(309\) 0 0
\(310\) −23.3205 10.1208i −1.32452 0.574823i
\(311\) −20.4895 −1.16185 −0.580925 0.813957i \(-0.697309\pi\)
−0.580925 + 0.813957i \(0.697309\pi\)
\(312\) 0 0
\(313\) 9.39230 0.530884 0.265442 0.964127i \(-0.414482\pi\)
0.265442 + 0.964127i \(0.414482\pi\)
\(314\) −28.2908 12.2779i −1.59654 0.692880i
\(315\) 0 0
\(316\) 8.95448 8.37345i 0.503729 0.471044i
\(317\) −16.8096 −0.944124 −0.472062 0.881565i \(-0.656490\pi\)
−0.472062 + 0.881565i \(0.656490\pi\)
\(318\) 0 0
\(319\) 8.55511i 0.478994i
\(320\) −19.0617 + 15.5677i −1.06558 + 0.870262i
\(321\) 0 0
\(322\) −4.26795 1.85224i −0.237844 0.103221i
\(323\) 26.4551i 1.47200i
\(324\) 0 0
\(325\) 4.77386i 0.264806i
\(326\) 4.95671 11.4213i 0.274527 0.632568i
\(327\) 0 0
\(328\) 3.60770 + 10.1208i 0.199202 + 0.558828i
\(329\) 27.8456i 1.53518i
\(330\) 0 0
\(331\) 1.87564 0.103095 0.0515474 0.998671i \(-0.483585\pi\)
0.0515474 + 0.998671i \(0.483585\pi\)
\(332\) −15.1610 + 14.1773i −0.832069 + 0.778079i
\(333\) 0 0
\(334\) 12.4641 28.7200i 0.682005 1.57149i
\(335\) 28.2908 1.54569
\(336\) 0 0
\(337\) −11.3923 −0.620578 −0.310289 0.950642i \(-0.600426\pi\)
−0.310289 + 0.950642i \(0.600426\pi\)
\(338\) 6.67535 15.3814i 0.363091 0.836640i
\(339\) 0 0
\(340\) 31.8564 29.7893i 1.72766 1.61555i
\(341\) −11.0986 −0.601025
\(342\) 0 0
\(343\) 7.69549i 0.415517i
\(344\) −5.32844 + 1.89939i −0.287290 + 0.102408i
\(345\) 0 0
\(346\) 0.928203 2.13878i 0.0499005 0.114981i
\(347\) 7.59757i 0.407859i 0.978986 + 0.203930i \(0.0653714\pi\)
−0.978986 + 0.203930i \(0.934629\pi\)
\(348\) 0 0
\(349\) 2.63508i 0.141053i −0.997510 0.0705264i \(-0.977532\pi\)
0.997510 0.0705264i \(-0.0224679\pi\)
\(350\) −23.1133 10.0309i −1.23546 0.536172i
\(351\) 0 0
\(352\) −4.92820 + 9.54773i −0.262674 + 0.508895i
\(353\) 7.59757i 0.404378i 0.979347 + 0.202189i \(0.0648055\pi\)
−0.979347 + 0.202189i \(0.935194\pi\)
\(354\) 0 0
\(355\) −32.7846 −1.74003
\(356\) −19.9669 + 18.6713i −1.05824 + 0.989576i
\(357\) 0 0
\(358\) −4.92820 2.13878i −0.260464 0.113038i
\(359\) 23.7867 1.25541 0.627707 0.778449i \(-0.283993\pi\)
0.627707 + 0.778449i \(0.283993\pi\)
\(360\) 0 0
\(361\) −5.07180 −0.266937
\(362\) −4.16199 1.80625i −0.218749 0.0949344i
\(363\) 0 0
\(364\) 5.83013 + 6.23468i 0.305582 + 0.326786i
\(365\) −18.2374 −0.954589
\(366\) 0 0
\(367\) 37.4848i 1.95669i 0.206975 + 0.978346i \(0.433638\pi\)
−0.206975 + 0.978346i \(0.566362\pi\)
\(368\) −0.220874 + 3.28985i −0.0115139 + 0.171495i
\(369\) 0 0
\(370\) 27.5885 + 11.9730i 1.43426 + 0.622449i
\(371\) 42.5318i 2.20814i
\(372\) 0 0
\(373\) 18.5991i 0.963027i −0.876439 0.481514i \(-0.840087\pi\)
0.876439 0.481514i \(-0.159913\pi\)
\(374\) 7.58051 17.4671i 0.391979 0.903203i
\(375\) 0 0
\(376\) −18.5885 + 6.62610i −0.958626 + 0.341715i
\(377\) 4.81667i 0.248071i
\(378\) 0 0
\(379\) −26.2679 −1.34929 −0.674647 0.738141i \(-0.735704\pi\)
−0.674647 + 0.738141i \(0.735704\pi\)
\(380\) 15.6836 + 16.7719i 0.804552 + 0.860380i
\(381\) 0 0
\(382\) 3.92820 9.05142i 0.200984 0.463111i
\(383\) −1.64863 −0.0842409 −0.0421204 0.999113i \(-0.513411\pi\)
−0.0421204 + 0.999113i \(0.513411\pi\)
\(384\) 0 0
\(385\) −23.3205 −1.18852
\(386\) −3.03596 + 6.99549i −0.154526 + 0.356061i
\(387\) 0 0
\(388\) 15.5622 + 16.6420i 0.790050 + 0.844871i
\(389\) −15.3819 −0.779893 −0.389946 0.920838i \(-0.627506\pi\)
−0.389946 + 0.920838i \(0.627506\pi\)
\(390\) 0 0
\(391\) 5.84325i 0.295506i
\(392\) 23.7867 8.47908i 1.20141 0.428258i
\(393\) 0 0
\(394\) 9.58846 22.0939i 0.483059 1.11307i
\(395\) 18.8576i 0.948827i
\(396\) 0 0
\(397\) 10.1208i 0.507949i 0.967211 + 0.253974i \(0.0817379\pi\)
−0.967211 + 0.253974i \(0.918262\pi\)
\(398\) 20.3386 + 8.82670i 1.01948 + 0.442442i
\(399\) 0 0
\(400\) −1.19615 + 17.8163i −0.0598076 + 0.890815i
\(401\) 15.1951i 0.758809i −0.925231 0.379405i \(-0.876129\pi\)
0.925231 0.379405i \(-0.123871\pi\)
\(402\) 0 0
\(403\) 6.24871 0.311270
\(404\) 8.40482 + 8.98803i 0.418155 + 0.447171i
\(405\) 0 0
\(406\) −23.3205 10.1208i −1.15738 0.502287i
\(407\) 13.1298 0.650821
\(408\) 0 0
\(409\) −8.60770 −0.425623 −0.212812 0.977093i \(-0.568262\pi\)
−0.212812 + 0.977093i \(0.568262\pi\)
\(410\) 15.1610 + 6.57969i 0.748749 + 0.324948i
\(411\) 0 0
\(412\) 5.83013 5.45183i 0.287230 0.268592i
\(413\) 7.58051 0.373012
\(414\) 0 0
\(415\) 31.9281i 1.56729i
\(416\) 2.77466 5.37552i 0.136039 0.263557i
\(417\) 0 0
\(418\) 9.19615 + 3.99102i 0.449799 + 0.195207i
\(419\) 26.4551i 1.29242i 0.763160 + 0.646209i \(0.223647\pi\)
−0.763160 + 0.646209i \(0.776353\pi\)
\(420\) 0 0
\(421\) 4.77386i 0.232664i 0.993210 + 0.116332i \(0.0371136\pi\)
−0.993210 + 0.116332i \(0.962886\pi\)
\(422\) 11.8529 27.3117i 0.576992 1.32951i
\(423\) 0 0
\(424\) 28.3923 10.1208i 1.37885 0.491510i
\(425\) 31.6444i 1.53498i
\(426\) 0 0
\(427\) 4.26795 0.206541
\(428\) 12.3864 11.5826i 0.598717 0.559868i
\(429\) 0 0
\(430\) −3.46410 + 7.98203i −0.167054 + 0.384928i
\(431\) −0.382565 −0.0184275 −0.00921375 0.999958i \(-0.502933\pi\)
−0.00921375 + 0.999958i \(0.502933\pi\)
\(432\) 0 0
\(433\) 4.53590 0.217981 0.108991 0.994043i \(-0.465238\pi\)
0.108991 + 0.994043i \(0.465238\pi\)
\(434\) 13.1298 30.2539i 0.630252 1.45223i
\(435\) 0 0
\(436\) 14.7846 13.8253i 0.708054 0.662111i
\(437\) 3.07638 0.147163
\(438\) 0 0
\(439\) 14.3984i 0.687197i 0.939117 + 0.343598i \(0.111646\pi\)
−0.939117 + 0.343598i \(0.888354\pi\)
\(440\) 5.54932 + 15.5677i 0.264553 + 0.742162i
\(441\) 0 0
\(442\) −4.26795 + 9.83427i −0.203006 + 0.467768i
\(443\) 27.3366i 1.29880i 0.760446 + 0.649402i \(0.224981\pi\)
−0.760446 + 0.649402i \(0.775019\pi\)
\(444\) 0 0
\(445\) 42.0489i 1.99331i
\(446\) −33.8402 14.6862i −1.60238 0.695412i
\(447\) 0 0
\(448\) −20.1962 24.7289i −0.954179 1.16833i
\(449\) 24.0468i 1.13484i 0.823429 + 0.567419i \(0.192058\pi\)
−0.823429 + 0.567419i \(0.807942\pi\)
\(450\) 0 0
\(451\) 7.21539 0.339759
\(452\) 15.9045 14.8725i 0.748084 0.699543i
\(453\) 0 0
\(454\) −4.92820 2.13878i −0.231292 0.100378i
\(455\) 13.1298 0.615536
\(456\) 0 0
\(457\) 6.39230 0.299019 0.149510 0.988760i \(-0.452230\pi\)
0.149510 + 0.988760i \(0.452230\pi\)
\(458\) −15.1610 6.57969i −0.708428 0.307449i
\(459\) 0 0
\(460\) 3.46410 + 3.70447i 0.161515 + 0.172722i
\(461\) 5.93188 0.276275 0.138138 0.990413i \(-0.455888\pi\)
0.138138 + 0.990413i \(0.455888\pi\)
\(462\) 0 0
\(463\) 2.42532i 0.112714i −0.998411 0.0563571i \(-0.982051\pi\)
0.998411 0.0563571i \(-0.0179485\pi\)
\(464\) −1.20688 + 17.9761i −0.0560279 + 0.834517i
\(465\) 0 0
\(466\) 18.3923 + 7.98203i 0.852007 + 0.369760i
\(467\) 19.8754i 0.919726i 0.887990 + 0.459863i \(0.152101\pi\)
−0.887990 + 0.459863i \(0.847899\pi\)
\(468\) 0 0
\(469\) 36.7020i 1.69474i
\(470\) −12.0846 + 27.8456i −0.557423 + 1.28442i
\(471\) 0 0
\(472\) −1.80385 5.06040i −0.0830288 0.232924i
\(473\) 3.79879i 0.174668i
\(474\) 0 0
\(475\) 16.6603 0.764425
\(476\) 38.6460 + 41.3276i 1.77134 + 1.89425i
\(477\) 0 0
\(478\) −6.92820 + 15.9641i −0.316889 + 0.730179i
\(479\) −6.15276 −0.281127 −0.140563 0.990072i \(-0.544891\pi\)
−0.140563 + 0.990072i \(0.544891\pi\)
\(480\) 0 0
\(481\) −7.39230 −0.337060
\(482\) −3.03596 + 6.99549i −0.138284 + 0.318636i
\(483\) 0 0
\(484\) −10.0981 10.7988i −0.459003 0.490853i
\(485\) 35.0470 1.59140
\(486\) 0 0
\(487\) 33.2073i 1.50477i −0.658726 0.752383i \(-0.728904\pi\)
0.658726 0.752383i \(-0.271096\pi\)
\(488\) −1.01560 2.84909i −0.0459738 0.128972i
\(489\) 0 0
\(490\) 15.4641 35.6326i 0.698597 1.60972i
\(491\) 33.0348i 1.49084i 0.666595 + 0.745420i \(0.267751\pi\)
−0.666595 + 0.745420i \(0.732249\pi\)
\(492\) 0 0
\(493\) 31.9281i 1.43797i
\(494\) −5.17758 2.24701i −0.232950 0.101098i
\(495\) 0 0
\(496\) −23.3205 1.56569i −1.04712 0.0703018i
\(497\) 42.5318i 1.90781i
\(498\) 0 0
\(499\) −5.60770 −0.251035 −0.125517 0.992091i \(-0.540059\pi\)
−0.125517 + 0.992091i \(0.540059\pi\)
\(500\) −2.25207 2.40833i −0.100715 0.107704i
\(501\) 0 0
\(502\) 18.3923 + 7.98203i 0.820889 + 0.356255i
\(503\) −29.4977 −1.31524 −0.657619 0.753351i \(-0.728436\pi\)
−0.657619 + 0.753351i \(0.728436\pi\)
\(504\) 0 0
\(505\) 18.9282 0.842294
\(506\) 2.03119 + 0.881512i 0.0902975 + 0.0391880i
\(507\) 0 0
\(508\) 0 0
\(509\) −0.220874 −0.00979007 −0.00489503 0.999988i \(-0.501558\pi\)
−0.00489503 + 0.999988i \(0.501558\pi\)
\(510\) 0 0
\(511\) 23.6595i 1.04664i
\(512\) −11.7021 + 19.3665i −0.517163 + 0.855887i
\(513\) 0 0
\(514\) −4.92820 2.13878i −0.217374 0.0943375i
\(515\) 12.2779i 0.541028i
\(516\) 0 0
\(517\) 13.2522i 0.582831i
\(518\) −15.5327 + 35.7908i −0.682470 + 1.57256i
\(519\) 0 0
\(520\) −3.12436 8.76488i −0.137012 0.384365i
\(521\) 7.08863i 0.310559i −0.987871 0.155279i \(-0.950372\pi\)
0.987871 0.155279i \(-0.0496278\pi\)
\(522\) 0 0
\(523\) −37.5885 −1.64363 −0.821814 0.569756i \(-0.807038\pi\)
−0.821814 + 0.569756i \(0.807038\pi\)
\(524\) −15.1610 + 14.1773i −0.662312 + 0.619337i
\(525\) 0 0
\(526\) −1.85641 + 4.27756i −0.0809432 + 0.186510i
\(527\) 41.4207 1.80431
\(528\) 0 0
\(529\) −22.3205 −0.970457
\(530\) 18.4583 42.5318i 0.801776 1.84746i
\(531\) 0 0
\(532\) −21.7583 + 20.3465i −0.943343 + 0.882133i
\(533\) −4.06238 −0.175961
\(534\) 0 0
\(535\) 26.0849i 1.12775i
\(536\) 24.5006 8.73356i 1.05826 0.377232i
\(537\) 0 0
\(538\) −11.1962 + 25.7983i −0.482700 + 1.11224i
\(539\) 16.9582i 0.730440i
\(540\) 0 0
\(541\) 34.5632i 1.48599i −0.669298 0.742994i \(-0.733405\pi\)
0.669298 0.742994i \(-0.266595\pi\)
\(542\) −15.5327 6.74102i −0.667189 0.289552i
\(543\) 0 0
\(544\) 18.3923 35.6326i 0.788564 1.52773i
\(545\) 31.1354i 1.33370i
\(546\) 0 0
\(547\) −31.5885 −1.35062 −0.675312 0.737532i \(-0.735991\pi\)
−0.675312 + 0.737532i \(0.735991\pi\)
\(548\) 25.5162 23.8605i 1.09000 1.01927i
\(549\) 0 0
\(550\) 11.0000 + 4.77386i 0.469042 + 0.203558i
\(551\) 16.8096 0.716115
\(552\) 0 0
\(553\) 24.4641 1.04032
\(554\) 28.2908 + 12.2779i 1.20196 + 0.521637i
\(555\) 0 0
\(556\) 4.36603 + 4.66898i 0.185161 + 0.198009i
\(557\) 14.9401 0.633034 0.316517 0.948587i \(-0.397487\pi\)
0.316517 + 0.948587i \(0.397487\pi\)
\(558\) 0 0
\(559\) 2.13878i 0.0904607i
\(560\) −49.0012 3.28985i −2.07068 0.139021i
\(561\) 0 0
\(562\) −13.4641 5.84325i −0.567949 0.246483i
\(563\) 34.9342i 1.47230i −0.676817 0.736151i \(-0.736641\pi\)
0.676817 0.736151i \(-0.263359\pi\)
\(564\) 0 0
\(565\) 33.4938i 1.40910i
\(566\) 15.6836 36.1384i 0.659231 1.51901i
\(567\) 0 0
\(568\) −28.3923 + 10.1208i −1.19131 + 0.424660i
\(569\) 6.07075i 0.254499i 0.991871 + 0.127250i \(0.0406149\pi\)
−0.991871 + 0.127250i \(0.959385\pi\)
\(570\) 0 0
\(571\) −3.19615 −0.133755 −0.0668774 0.997761i \(-0.521304\pi\)
−0.0668774 + 0.997761i \(0.521304\pi\)
\(572\) −2.77466 2.96719i −0.116014 0.124064i
\(573\) 0 0
\(574\) −8.53590 + 19.6685i −0.356282 + 0.820949i
\(575\) 3.67982 0.153459
\(576\) 0 0
\(577\) 11.9282 0.496578 0.248289 0.968686i \(-0.420132\pi\)
0.248289 + 0.968686i \(0.420132\pi\)
\(578\) −18.7196 + 43.1339i −0.778631 + 1.79413i
\(579\) 0 0
\(580\) 18.9282 + 20.2416i 0.785951 + 0.840487i
\(581\) −41.4207 −1.71842
\(582\) 0 0
\(583\) 20.2416i 0.838322i
\(584\) −15.7940 + 5.62999i −0.653562 + 0.232971i
\(585\) 0 0
\(586\) 4.26795 9.83427i 0.176307 0.406250i
\(587\) 33.0348i 1.36349i 0.731588 + 0.681747i \(0.238779\pi\)
−0.731588 + 0.681747i \(0.761221\pi\)
\(588\) 0 0
\(589\) 21.8073i 0.898555i
\(590\) −7.58051 3.28985i −0.312085 0.135441i
\(591\) 0 0
\(592\) 27.5885 + 1.85224i 1.13388 + 0.0761265i
\(593\) 38.7330i 1.59057i 0.606233 + 0.795287i \(0.292680\pi\)
−0.606233 + 0.795287i \(0.707320\pi\)
\(594\) 0 0
\(595\) 87.0333 3.56802
\(596\) −8.40482 8.98803i −0.344275 0.368164i
\(597\) 0 0
\(598\) −1.14359 0.496305i −0.0467650 0.0202954i
\(599\) 22.5207 0.920169 0.460084 0.887875i \(-0.347819\pi\)
0.460084 + 0.887875i \(0.347819\pi\)
\(600\) 0 0
\(601\) 30.3923 1.23973 0.619864 0.784709i \(-0.287188\pi\)
0.619864 + 0.784709i \(0.287188\pi\)
\(602\) −10.3552 4.49401i −0.422045 0.183162i
\(603\) 0 0
\(604\) 14.3660 13.4339i 0.584545 0.546616i
\(605\) −22.7415 −0.924574
\(606\) 0 0
\(607\) 35.3461i 1.43465i 0.696738 + 0.717326i \(0.254634\pi\)
−0.696738 + 0.717326i \(0.745366\pi\)
\(608\) 18.7600 + 9.68325i 0.760818 + 0.392708i
\(609\) 0 0
\(610\) −4.26795 1.85224i −0.172804 0.0749949i
\(611\) 7.46120i 0.301848i
\(612\) 0 0
\(613\) 6.91264i 0.279199i 0.990208 + 0.139599i \(0.0445815\pi\)
−0.990208 + 0.139599i \(0.955418\pi\)
\(614\) 11.7829 27.1504i 0.475520 1.09570i
\(615\) 0 0
\(616\) −20.1962 + 7.19918i −0.813726 + 0.290063i
\(617\) 28.8635i 1.16200i 0.813904 + 0.581000i \(0.197338\pi\)
−0.813904 + 0.581000i \(0.802662\pi\)
\(618\) 0 0
\(619\) 37.1962 1.49504 0.747520 0.664240i \(-0.231245\pi\)
0.747520 + 0.664240i \(0.231245\pi\)
\(620\) −26.2597 + 24.5557i −1.05461 + 0.986182i
\(621\) 0 0
\(622\) −11.5359 + 26.5812i −0.462547 + 1.06581i
\(623\) −54.5505 −2.18552
\(624\) 0 0
\(625\) −27.3923 −1.09569
\(626\) 5.28802 12.1847i 0.211352 0.487000i
\(627\) 0 0
\(628\) −31.8564 + 29.7893i −1.27121 + 1.18872i
\(629\) −49.0012 −1.95380
\(630\) 0 0
\(631\) 22.0939i 0.879542i −0.898110 0.439771i \(-0.855060\pi\)
0.898110 0.439771i \(-0.144940\pi\)
\(632\) −5.82145 16.3311i −0.231565 0.649617i
\(633\) 0 0
\(634\) −9.46410 + 21.8073i −0.375867 + 0.866079i
\(635\) 0 0
\(636\) 0 0
\(637\) 9.54773i 0.378295i
\(638\) 11.0986 + 4.81667i 0.439399 + 0.190694i
\(639\) 0 0
\(640\) 9.46410 + 33.4938i 0.374101 + 1.32396i
\(641\) 34.9342i 1.37982i −0.723896 0.689909i \(-0.757650\pi\)
0.723896 0.689909i \(-0.242350\pi\)
\(642\) 0 0
\(643\) −18.7846 −0.740793 −0.370396 0.928874i \(-0.620778\pi\)
−0.370396 + 0.928874i \(0.620778\pi\)
\(644\) −4.80585 + 4.49401i −0.189377 + 0.177089i
\(645\) 0 0
\(646\) −34.3205 14.8947i −1.35032 0.586023i
\(647\) −39.7720 −1.56360 −0.781800 0.623529i \(-0.785698\pi\)
−0.781800 + 0.623529i \(0.785698\pi\)
\(648\) 0 0
\(649\) −3.60770 −0.141614
\(650\) −6.19318 2.68776i −0.242916 0.105423i
\(651\) 0 0
\(652\) −12.0263 12.8608i −0.470985 0.503667i
\(653\) 32.4124 1.26840 0.634198 0.773171i \(-0.281331\pi\)
0.634198 + 0.773171i \(0.281331\pi\)
\(654\) 0 0
\(655\) 31.9281i 1.24753i
\(656\) 15.1610 + 1.01788i 0.591938 + 0.0397416i
\(657\) 0 0
\(658\) −36.1244 15.6775i −1.40827 0.611173i
\(659\) 21.7748i 0.848227i −0.905609 0.424114i \(-0.860586\pi\)
0.905609 0.424114i \(-0.139414\pi\)
\(660\) 0 0
\(661\) 45.2571i 1.76030i −0.474698 0.880149i \(-0.657443\pi\)
0.474698 0.880149i \(-0.342557\pi\)
\(662\) 1.05602 2.43329i 0.0410433 0.0945726i
\(663\) 0 0
\(664\) 9.85641 + 27.6506i 0.382503 + 1.07305i
\(665\) 45.8216i 1.77689i
\(666\) 0 0
\(667\) 3.71281 0.143761
\(668\) −30.2412 32.3396i −1.17007 1.25126i
\(669\) 0 0
\(670\) 15.9282 36.7020i 0.615360 1.41792i
\(671\) −2.03119 −0.0784133
\(672\) 0 0
\(673\) 35.2487 1.35874 0.679369 0.733797i \(-0.262254\pi\)
0.679369 + 0.733797i \(0.262254\pi\)
\(674\) −6.41405 + 14.7793i −0.247060 + 0.569279i
\(675\) 0 0
\(676\) −16.1962 17.3200i −0.622929 0.666154i
\(677\) −44.4970 −1.71016 −0.855080 0.518496i \(-0.826492\pi\)
−0.855080 + 0.518496i \(0.826492\pi\)
\(678\) 0 0
\(679\) 45.4669i 1.74486i
\(680\) −20.7103 58.0995i −0.794205 2.22801i
\(681\) 0 0
\(682\) −6.24871 + 14.3984i −0.239276 + 0.551342i
\(683\) 39.7509i 1.52103i −0.649323 0.760513i \(-0.724948\pi\)
0.649323 0.760513i \(-0.275052\pi\)
\(684\) 0 0
\(685\) 53.7354i 2.05313i
\(686\) 9.98343 + 4.33269i 0.381169 + 0.165423i
\(687\) 0 0
\(688\) −0.535898 + 7.98203i −0.0204309 + 0.304312i
\(689\) 11.3964i 0.434167i
\(690\) 0 0
\(691\) 3.85641 0.146705 0.0733523 0.997306i \(-0.476630\pi\)
0.0733523 + 0.997306i \(0.476630\pi\)
\(692\) −2.25207 2.40833i −0.0856107 0.0915511i
\(693\) 0 0
\(694\) 9.85641 + 4.27756i 0.374144 + 0.162374i
\(695\) 9.83257 0.372971
\(696\) 0 0
\(697\) −26.9282 −1.01998
\(698\) −3.41852 1.48360i −0.129393 0.0561549i
\(699\) 0 0
\(700\) −26.0263 + 24.3375i −0.983701 + 0.919872i
\(701\) 51.8567 1.95860 0.979300 0.202415i \(-0.0648790\pi\)
0.979300 + 0.202415i \(0.0648790\pi\)
\(702\) 0 0
\(703\) 25.7983i 0.973002i
\(704\) 9.61170 + 11.7689i 0.362255 + 0.443558i
\(705\) 0 0
\(706\) 9.85641 + 4.27756i 0.370951 + 0.160988i
\(707\) 24.5557i 0.923514i
\(708\) 0 0
\(709\) 35.1363i 1.31957i 0.751454 + 0.659786i \(0.229353\pi\)
−0.751454 + 0.659786i \(0.770647\pi\)
\(710\) −18.4583 + 42.5318i −0.692726 + 1.59619i
\(711\) 0 0
\(712\) 12.9808 + 36.4154i 0.486475 + 1.36473i
\(713\) 4.81667i 0.180386i
\(714\) 0 0
\(715\) −6.24871 −0.233689
\(716\) −5.54932 + 5.18924i −0.207388 + 0.193931i
\(717\) 0 0
\(718\) 13.3923 30.8587i 0.499796 1.15164i
\(719\) 7.80138 0.290942 0.145471 0.989362i \(-0.453530\pi\)
0.145471 + 0.989362i \(0.453530\pi\)
\(720\) 0 0
\(721\) 15.9282 0.593197
\(722\) −2.85550 + 6.57969i −0.106271 + 0.244871i
\(723\) 0 0
\(724\) −4.68653 + 4.38244i −0.174174 + 0.162872i
\(725\) 20.1069 0.746751
\(726\) 0 0
\(727\) 26.0849i 0.967434i −0.875224 0.483717i \(-0.839286\pi\)
0.875224 0.483717i \(-0.160714\pi\)
\(728\) 11.3708 4.05326i 0.421428 0.150224i
\(729\) 0 0
\(730\) −10.2679 + 23.6595i −0.380034 + 0.875679i
\(731\) 14.1773i 0.524365i
\(732\) 0 0
\(733\) 13.2522i 0.489481i 0.969589 + 0.244741i \(0.0787028\pi\)
−0.969589 + 0.244741i \(0.921297\pi\)
\(734\) 48.6294 + 21.1046i 1.79495 + 0.778984i
\(735\) 0 0
\(736\) 4.14359 + 2.13878i 0.152735 + 0.0788364i
\(737\) 17.4671i 0.643409i
\(738\) 0 0
\(739\) −20.6410 −0.759292 −0.379646 0.925132i \(-0.623954\pi\)
−0.379646 + 0.925132i \(0.623954\pi\)
\(740\) 31.0655 29.0498i 1.14199 1.06789i
\(741\) 0 0
\(742\) 55.1769 + 23.9461i 2.02561 + 0.879089i
\(743\) −51.6950 −1.89651 −0.948253 0.317517i \(-0.897151\pi\)
−0.948253 + 0.317517i \(0.897151\pi\)
\(744\) 0 0
\(745\) −18.9282 −0.693476
\(746\) −24.1289 10.4716i −0.883420 0.383393i
\(747\) 0 0
\(748\) −18.3923 19.6685i −0.672489 0.719153i
\(749\) 33.8402 1.23649
\(750\) 0 0
\(751\) 19.9551i 0.728171i −0.931366 0.364086i \(-0.881382\pi\)
0.931366 0.364086i \(-0.118618\pi\)
\(752\) −1.86950 + 27.8456i −0.0681737 + 1.01542i
\(753\) 0 0
\(754\) −6.24871 2.71186i −0.227565 0.0987602i
\(755\) 30.2539i 1.10105i
\(756\) 0 0
\(757\) 52.0930i 1.89335i −0.322189 0.946675i \(-0.604419\pi\)
0.322189 0.946675i \(-0.395581\pi\)
\(758\) −14.7893 + 34.0777i −0.537171 + 1.23776i
\(759\) 0 0
\(760\) 30.5885 10.9037i 1.10956 0.395517i
\(761\) 43.0407i 1.56023i −0.625639 0.780113i \(-0.715162\pi\)
0.625639 0.780113i \(-0.284838\pi\)
\(762\) 0 0
\(763\) 40.3923 1.46230
\(764\) −9.53085 10.1922i −0.344814 0.368741i
\(765\) 0 0
\(766\) −0.928203 + 2.13878i −0.0335373 + 0.0772772i
\(767\) 2.03119 0.0733421
\(768\) 0 0
\(769\) 4.07180 0.146833 0.0734164 0.997301i \(-0.476610\pi\)
0.0734164 + 0.997301i \(0.476610\pi\)
\(770\) −13.1298 + 30.2539i −0.473166 + 1.09028i
\(771\) 0 0
\(772\) 7.36603 + 7.87715i 0.265109 + 0.283505i
\(773\) 44.7179 1.60839 0.804196 0.594364i \(-0.202596\pi\)
0.804196 + 0.594364i \(0.202596\pi\)
\(774\) 0 0
\(775\) 26.0849i 0.936996i
\(776\) 30.3516 10.8192i 1.08956 0.388388i
\(777\) 0 0
\(778\) −8.66025 + 19.9551i −0.310485 + 0.715424i
\(779\) 14.1773i 0.507953i
\(780\) 0 0
\(781\) 20.2416i 0.724302i
\(782\) −7.58051 3.28985i −0.271078 0.117645i
\(783\) 0 0
\(784\) 2.39230 35.6326i 0.0854395 1.27259i
\(785\) 67.0875i 2.39446i
\(786\) 0 0
\(787\) 7.44486 0.265381 0.132690 0.991158i \(-0.457638\pi\)
0.132690 + 0.991158i \(0.457638\pi\)
\(788\) −23.2641 24.8784i −0.828750 0.886256i
\(789\) 0 0
\(790\) −24.4641 10.6171i −0.870394 0.377740i
\(791\) 43.4519 1.54497
\(792\) 0 0
\(793\) 1.14359 0.0406102
\(794\) 13.1298 + 5.69818i 0.465960 + 0.202221i
\(795\) 0 0
\(796\) 22.9019 21.4159i 0.811737 0.759066i
\(797\) 27.4665 0.972914 0.486457 0.873704i \(-0.338289\pi\)
0.486457 + 0.873704i \(0.338289\pi\)
\(798\) 0 0
\(799\) 49.4579i 1.74969i
\(800\) 22.4398 + 11.5826i 0.793367 + 0.409508i
\(801\) 0 0
\(802\) −19.7128 8.55511i −0.696084 0.302092i
\(803\) 11.2600i 0.397356i
\(804\) 0 0
\(805\) 10.1208i 0.356712i
\(806\) 3.51813 8.10651i 0.123921 0.285540i
\(807\) 0 0
\(808\) 16.3923 5.84325i 0.576679 0.205565i
\(809\) 14.1773i 0.498446i 0.968446 + 0.249223i \(0.0801752\pi\)
−0.968446 + 0.249223i \(0.919825\pi\)
\(810\) 0 0
\(811\) −27.0718 −0.950619 −0.475310 0.879819i \(-0.657664\pi\)
−0.475310 + 0.879819i \(0.657664\pi\)
\(812\) −26.2597 + 24.5557i −0.921533 + 0.861738i
\(813\) 0 0
\(814\) 7.39230 17.0335i 0.259100 0.597022i
\(815\) −27.0840 −0.948710
\(816\) 0 0
\(817\) 7.46410 0.261136
\(818\) −4.84627 + 11.1668i −0.169446 + 0.390440i
\(819\) 0 0
\(820\) 17.0718 15.9641i 0.596173 0.557489i
\(821\) 10.8778 0.379636 0.189818 0.981819i \(-0.439210\pi\)
0.189818 + 0.981819i \(0.439210\pi\)
\(822\) 0 0
\(823\) 24.2326i 0.844697i 0.906434 + 0.422348i \(0.138794\pi\)
−0.906434 + 0.422348i \(0.861206\pi\)
\(824\) −3.79025 10.6329i −0.132040 0.370416i
\(825\) 0 0
\(826\) 4.26795 9.83427i 0.148501 0.342178i
\(827\) 40.6324i 1.41293i −0.707749 0.706464i \(-0.750289\pi\)
0.707749 0.706464i \(-0.249711\pi\)
\(828\) 0 0
\(829\) 34.5632i 1.20043i 0.799839 + 0.600215i \(0.204918\pi\)
−0.799839 + 0.600215i \(0.795082\pi\)
\(830\) 41.4207 + 17.9761i 1.43773 + 0.623958i
\(831\) 0 0
\(832\) −5.41154 6.62610i −0.187611 0.229719i
\(833\) 63.2888i 2.19283i
\(834\) 0 0
\(835\) −68.1051 −2.35687
\(836\) 10.3552 9.68325i 0.358141 0.334902i
\(837\) 0 0
\(838\) 34.3205 + 14.8947i 1.18558 + 0.514528i
\(839\) 25.0528 0.864918 0.432459 0.901654i \(-0.357646\pi\)
0.432459 + 0.901654i \(0.357646\pi\)
\(840\) 0 0
\(841\) −8.71281 −0.300442
\(842\) 6.19318 + 2.68776i 0.213431 + 0.0926264i
\(843\) 0 0
\(844\) −28.7583 30.7539i −0.989903 1.05859i
\(845\) −36.4748 −1.25477
\(846\) 0 0
\(847\) 29.5028i 1.01373i
\(848\) 2.85550 42.5318i 0.0980584 1.46055i
\(849\) 0 0
\(850\) −41.0526 17.8163i −1.40809 0.611094i
\(851\) 5.69818i 0.195331i
\(852\) 0 0
\(853\) 14.8947i 0.509984i 0.966943 + 0.254992i \(0.0820728\pi\)
−0.966943 + 0.254992i \(0.917927\pi\)
\(854\) 2.40292 5.53685i 0.0822264 0.189467i
\(855\) 0 0
\(856\) −8.05256 22.5902i −0.275231 0.772116i
\(857\) 1.01788i 0.0347702i 0.999849 + 0.0173851i \(0.00553413\pi\)
−0.999849 + 0.0173851i \(0.994466\pi\)
\(858\) 0 0
\(859\) 11.5885 0.395393 0.197697 0.980263i \(-0.436654\pi\)
0.197697 + 0.980263i \(0.436654\pi\)
\(860\) 8.40482 + 8.98803i 0.286602 + 0.306489i
\(861\) 0 0
\(862\) −0.215390 + 0.496305i −0.00733622 + 0.0169042i
\(863\) 15.9853 0.544147 0.272073 0.962276i \(-0.412291\pi\)
0.272073 + 0.962276i \(0.412291\pi\)
\(864\) 0 0
\(865\) −5.07180 −0.172446
\(866\) 2.55378 5.88447i 0.0867811 0.199962i
\(867\) 0 0
\(868\) −31.8564 34.0669i −1.08128 1.15631i
\(869\) −11.6429 −0.394958
\(870\) 0 0
\(871\) 9.83427i 0.333221i
\(872\) −9.61170 26.9641i −0.325493 0.913119i
\(873\) 0 0
\(874\) 1.73205 3.99102i 0.0585875 0.134998i
\(875\) 6.57969i 0.222434i
\(876\) 0 0
\(877\) 19.1722i 0.647400i 0.946160 + 0.323700i \(0.104927\pi\)
−0.946160 + 0.323700i \(0.895073\pi\)
\(878\) 18.6791 + 8.10651i 0.630391 + 0.273582i
\(879\) 0 0
\(880\) 23.3205 + 1.56569i 0.786134 + 0.0527796i
\(881\) 6.07075i 0.204529i 0.994757 + 0.102264i \(0.0326088\pi\)
−0.994757 + 0.102264i \(0.967391\pi\)
\(882\) 0 0
\(883\) 44.1244 1.48490 0.742451 0.669900i \(-0.233663\pi\)
0.742451 + 0.669900i \(0.233663\pi\)
\(884\) 10.3552 + 11.0737i 0.348282 + 0.372449i
\(885\) 0 0
\(886\) 35.4641 + 15.3910i 1.19144 + 0.517070i
\(887\) −25.8179 −0.866880 −0.433440 0.901182i \(-0.642700\pi\)
−0.433440 + 0.901182i \(0.642700\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 54.5505 + 23.6742i 1.82854 + 0.793562i
\(891\) 0 0
\(892\) −38.1051 + 35.6326i −1.27585 + 1.19307i
\(893\) 26.0388 0.871354
\(894\) 0 0
\(895\) 11.6865i 0.390637i
\(896\) −43.4519 + 12.2779i −1.45162 + 0.410175i
\(897\) 0 0
\(898\) 31.1962 + 13.5387i 1.04103 + 0.451794i
\(899\) 26.3188i 0.877780i
\(900\) 0 0
\(901\) 75.5427i 2.51669i
\(902\) 4.06238 9.36060i 0.135263 0.311674i
\(903\) 0 0
\(904\) −10.3397 29.0065i −0.343895 0.964742i
\(905\) 9.86954i 0.328075i
\(906\) 0 0
\(907\) −46.3731 −1.53979 −0.769896 0.638169i \(-0.779692\pi\)
−0.769896 + 0.638169i \(0.779692\pi\)
\(908\) −5.54932 + 5.18924i −0.184161 + 0.172211i
\(909\) 0 0
\(910\) 7.39230 17.0335i 0.245053 0.564653i
\(911\) −0.441748 −0.0146358 −0.00731788 0.999973i \(-0.502329\pi\)
−0.00731788 + 0.999973i \(0.502329\pi\)
\(912\) 0 0
\(913\) 19.7128 0.652399
\(914\) 3.59897 8.29280i 0.119043 0.274301i
\(915\) 0 0
\(916\) −17.0718 + 15.9641i −0.564068 + 0.527467i
\(917\) −41.4207 −1.36783
\(918\) 0 0
\(919\) 58.0130i 1.91367i 0.290628 + 0.956836i \(0.406136\pi\)
−0.290628 + 0.956836i \(0.593864\pi\)
\(920\) 6.75620 2.40833i 0.222745 0.0794004i
\(921\) 0 0
\(922\) 3.33975 7.69549i 0.109989 0.253437i
\(923\) 11.3964i 0.375116i
\(924\) 0 0
\(925\) 30.8587i 1.01463i
\(926\) −3.14639 1.36549i −0.103397 0.0448729i
\(927\) 0 0
\(928\) 22.6410 + 11.6865i 0.743228 + 0.383628i
\(929\) 20.7570i 0.681014i 0.940242 + 0.340507i \(0.110599\pi\)
−0.940242 + 0.340507i \(0.889401\pi\)
\(930\) 0 0
\(931\) −33.3205 −1.09204
\(932\) 20.7103 19.3665i 0.678390 0.634371i
\(933\) 0 0
\(934\) 25.7846 + 11.1902i 0.843698 + 0.366154i
\(935\) −41.4207 −1.35460
\(936\) 0 0
\(937\) −23.3923 −0.764193 −0.382097 0.924122i \(-0.624798\pi\)
−0.382097 + 0.924122i \(0.624798\pi\)
\(938\) 47.6138 + 20.6638i 1.55465 + 0.674697i
\(939\) 0 0
\(940\) 29.3205 + 31.3550i 0.956330 + 1.02269i
\(941\) −18.6791 −0.608923 −0.304461 0.952525i \(-0.598476\pi\)
−0.304461 + 0.952525i \(0.598476\pi\)
\(942\) 0 0
\(943\) 3.13139i 0.101972i
\(944\) −7.58051 0.508941i −0.246725 0.0165646i
\(945\) 0 0
\(946\) 4.92820 + 2.13878i 0.160230 + 0.0695377i
\(947\) 29.2360i 0.950044i −0.879974 0.475022i \(-0.842440\pi\)
0.879974 0.475022i \(-0.157560\pi\)
\(948\) 0 0
\(949\) 6.33956i 0.205791i
\(950\) 9.37999 21.6135i 0.304327 0.701235i
\(951\) 0 0
\(952\) 75.3731 26.8677i 2.44286 0.870788i
\(953\) 15.7041i 0.508705i 0.967112 + 0.254353i \(0.0818624\pi\)
−0.967112 + 0.254353i \(0.918138\pi\)
\(954\) 0 0
\(955\) −21.4641 −0.694562
\(956\) 16.8096 + 17.9761i 0.543663 + 0.581387i
\(957\) 0 0
\(958\) −3.46410 + 7.98203i −0.111920 + 0.257888i
\(959\) 69.7115 2.25110
\(960\) 0 0
\(961\) −3.14359 −0.101406
\(962\) −4.16199 + 9.59011i −0.134188 + 0.309198i
\(963\) 0 0
\(964\) 7.36603 + 7.87715i 0.237244 + 0.253706i
\(965\) 16.5888 0.534011
\(966\) 0 0
\(967\) 9.83427i 0.316249i −0.987419 0.158124i \(-0.949455\pi\)
0.987419 0.158124i \(-0.0505447\pi\)
\(968\) −19.6947 + 7.02045i −0.633013 + 0.225646i
\(969\) 0 0
\(970\) 19.7321 45.4669i 0.633558 1.45985i
\(971\) 55.8275i 1.79159i 0.444466 + 0.895796i \(0.353393\pi\)
−0.444466 + 0.895796i \(0.646607\pi\)
\(972\) 0 0
\(973\) 12.7559i 0.408935i
\(974\) −43.0801 18.6962i −1.38038 0.599066i
\(975\) 0 0
\(976\) −4.26795 0.286542i −0.136614 0.00917199i
\(977\) 23.5379i 0.753043i −0.926408 0.376521i \(-0.877120\pi\)
0.926408 0.376521i \(-0.122880\pi\)
\(978\) 0 0
\(979\) 25.9615 0.829734
\(980\) −37.5200 40.1235i −1.19853 1.28170i
\(981\) 0 0
\(982\) 42.8564 + 18.5991i 1.36760 + 0.593523i
\(983\) 55.3156 1.76429 0.882147 0.470974i \(-0.156097\pi\)
0.882147 + 0.470974i \(0.156097\pi\)
\(984\) 0 0
\(985\) −52.3923 −1.66936
\(986\) −41.4207 17.9761i −1.31910 0.572474i
\(987\) 0 0
\(988\) −5.83013 + 5.45183i −0.185481 + 0.173446i
\(989\) 1.64863 0.0524233
\(990\) 0 0
\(991\) 25.7983i 0.819511i 0.912195 + 0.409755i \(0.134386\pi\)
−0.912195 + 0.409755i \(0.865614\pi\)
\(992\) −15.1610 + 29.3724i −0.481363 + 0.932575i
\(993\) 0 0
\(994\) −55.1769 23.9461i −1.75011 0.759524i
\(995\) 48.2300i 1.52899i
\(996\) 0 0
\(997\) 1.56569i 0.0495860i 0.999693 + 0.0247930i \(0.00789267\pi\)
−0.999693 + 0.0247930i \(0.992107\pi\)
\(998\) −3.15722 + 7.27492i −0.0999402 + 0.230284i
\(999\) 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 216.2.f.a.107.5 yes 8
3.2 odd 2 inner 216.2.f.a.107.4 yes 8
4.3 odd 2 864.2.f.a.431.2 8
8.3 odd 2 inner 216.2.f.a.107.3 8
8.5 even 2 864.2.f.a.431.7 8
9.2 odd 6 648.2.l.f.539.8 16
9.4 even 3 648.2.l.f.107.6 16
9.5 odd 6 648.2.l.f.107.3 16
9.7 even 3 648.2.l.f.539.1 16
12.11 even 2 864.2.f.a.431.8 8
24.5 odd 2 864.2.f.a.431.1 8
24.11 even 2 inner 216.2.f.a.107.6 yes 8
36.7 odd 6 2592.2.p.f.2159.8 16
36.11 even 6 2592.2.p.f.2159.2 16
36.23 even 6 2592.2.p.f.431.1 16
36.31 odd 6 2592.2.p.f.431.7 16
72.5 odd 6 2592.2.p.f.431.8 16
72.11 even 6 648.2.l.f.539.6 16
72.13 even 6 2592.2.p.f.431.2 16
72.29 odd 6 2592.2.p.f.2159.7 16
72.43 odd 6 648.2.l.f.539.3 16
72.59 even 6 648.2.l.f.107.1 16
72.61 even 6 2592.2.p.f.2159.1 16
72.67 odd 6 648.2.l.f.107.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.f.a.107.3 8 8.3 odd 2 inner
216.2.f.a.107.4 yes 8 3.2 odd 2 inner
216.2.f.a.107.5 yes 8 1.1 even 1 trivial
216.2.f.a.107.6 yes 8 24.11 even 2 inner
648.2.l.f.107.1 16 72.59 even 6
648.2.l.f.107.3 16 9.5 odd 6
648.2.l.f.107.6 16 9.4 even 3
648.2.l.f.107.8 16 72.67 odd 6
648.2.l.f.539.1 16 9.7 even 3
648.2.l.f.539.3 16 72.43 odd 6
648.2.l.f.539.6 16 72.11 even 6
648.2.l.f.539.8 16 9.2 odd 6
864.2.f.a.431.1 8 24.5 odd 2
864.2.f.a.431.2 8 4.3 odd 2
864.2.f.a.431.7 8 8.5 even 2
864.2.f.a.431.8 8 12.11 even 2
2592.2.p.f.431.1 16 36.23 even 6
2592.2.p.f.431.2 16 72.13 even 6
2592.2.p.f.431.7 16 36.31 odd 6
2592.2.p.f.431.8 16 72.5 odd 6
2592.2.p.f.2159.1 16 72.61 even 6
2592.2.p.f.2159.2 16 36.11 even 6
2592.2.p.f.2159.7 16 72.29 odd 6
2592.2.p.f.2159.8 16 36.7 odd 6