Properties

Label 1323.2.g.h.667.3
Level $1323$
Weight $2$
Character 1323.667
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
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] = [1323,2,Mod(361,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.3
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.h.361.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.863305 - 1.49529i) q^{2} +(-0.490592 + 0.849731i) q^{4} -3.51231 q^{5} -1.75910 q^{8} +O(q^{10})\) \(q+(-0.863305 - 1.49529i) q^{2} +(-0.490592 + 0.849731i) q^{4} -3.51231 q^{5} -1.75910 q^{8} +(3.03220 + 5.25192i) q^{10} +6.09064 q^{11} +(0.560139 + 0.970190i) q^{13} +(2.49982 + 4.32982i) q^{16} +(0.601978 + 1.04266i) q^{17} +(1.10269 - 1.90991i) q^{19} +(1.72311 - 2.98452i) q^{20} +(-5.25808 - 9.10727i) q^{22} +1.27339 q^{23} +7.33633 q^{25} +(0.967143 - 1.67514i) q^{26} +(3.10262 - 5.37390i) q^{29} +(0.0942019 - 0.163162i) q^{31} +(2.55712 - 4.42907i) q^{32} +(1.03938 - 1.80026i) q^{34} +(-1.78835 + 3.09752i) q^{37} -3.80782 q^{38} +6.17850 q^{40} +(-1.68320 - 2.91538i) q^{41} +(-1.90276 + 3.29567i) q^{43} +(-2.98802 + 5.17540i) q^{44} +(-1.09932 - 1.90408i) q^{46} +(-2.86035 - 4.95427i) q^{47} +(-6.33349 - 10.9699i) q^{50} -1.09920 q^{52} +(-4.16913 - 7.22115i) q^{53} -21.3922 q^{55} -10.7140 q^{58} +(-5.63427 + 9.75883i) q^{59} +(-6.00109 - 10.3942i) q^{61} -0.325300 q^{62} +1.16898 q^{64} +(-1.96738 - 3.40761i) q^{65} +(3.95652 - 6.85289i) q^{67} -1.18130 q^{68} +12.2052 q^{71} +(2.65737 + 4.60269i) q^{73} +6.17557 q^{74} +(1.08194 + 1.87397i) q^{76} +(-4.60855 - 7.98225i) q^{79} +(-8.78016 - 15.2077i) q^{80} +(-2.90623 + 5.03373i) q^{82} +(-0.624950 + 1.08245i) q^{83} +(-2.11433 - 3.66213i) q^{85} +6.57064 q^{86} -10.7140 q^{88} +(2.77066 - 4.79892i) q^{89} +(-0.624715 + 1.08204i) q^{92} +(-4.93871 + 8.55409i) q^{94} +(-3.87298 + 6.70820i) q^{95} +(8.24277 - 14.2769i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} + 40 q^{11} - 12 q^{16} + 64 q^{23} + 24 q^{25} - 16 q^{29} - 48 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} + 136 q^{74} + 12 q^{79} + 12 q^{85} + 152 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.863305 1.49529i −0.610449 1.05733i −0.991165 0.132637i \(-0.957656\pi\)
0.380716 0.924692i \(-0.375678\pi\)
\(3\) 0 0
\(4\) −0.490592 + 0.849731i −0.245296 + 0.424865i
\(5\) −3.51231 −1.57075 −0.785377 0.619018i \(-0.787531\pi\)
−0.785377 + 0.619018i \(0.787531\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.75910 −0.621935
\(9\) 0 0
\(10\) 3.03220 + 5.25192i 0.958865 + 1.66080i
\(11\) 6.09064 1.83640 0.918199 0.396120i \(-0.129644\pi\)
0.918199 + 0.396120i \(0.129644\pi\)
\(12\) 0 0
\(13\) 0.560139 + 0.970190i 0.155355 + 0.269082i 0.933188 0.359388i \(-0.117015\pi\)
−0.777833 + 0.628471i \(0.783681\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.49982 + 4.32982i 0.624956 + 1.08246i
\(17\) 0.601978 + 1.04266i 0.146001 + 0.252881i 0.929746 0.368202i \(-0.120026\pi\)
−0.783745 + 0.621083i \(0.786693\pi\)
\(18\) 0 0
\(19\) 1.10269 1.90991i 0.252974 0.438163i −0.711370 0.702818i \(-0.751925\pi\)
0.964343 + 0.264655i \(0.0852581\pi\)
\(20\) 1.72311 2.98452i 0.385300 0.667359i
\(21\) 0 0
\(22\) −5.25808 9.10727i −1.12103 1.94168i
\(23\) 1.27339 0.265520 0.132760 0.991148i \(-0.457616\pi\)
0.132760 + 0.991148i \(0.457616\pi\)
\(24\) 0 0
\(25\) 7.33633 1.46727
\(26\) 0.967143 1.67514i 0.189672 0.328522i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.10262 5.37390i 0.576142 0.997907i −0.419774 0.907628i \(-0.637891\pi\)
0.995917 0.0902789i \(-0.0287758\pi\)
\(30\) 0 0
\(31\) 0.0942019 0.163162i 0.0169192 0.0293048i −0.857442 0.514581i \(-0.827948\pi\)
0.874361 + 0.485276i \(0.161281\pi\)
\(32\) 2.55712 4.42907i 0.452040 0.782956i
\(33\) 0 0
\(34\) 1.03938 1.80026i 0.178252 0.308742i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.78835 + 3.09752i −0.294003 + 0.509228i −0.974753 0.223288i \(-0.928321\pi\)
0.680749 + 0.732516i \(0.261654\pi\)
\(38\) −3.80782 −0.617710
\(39\) 0 0
\(40\) 6.17850 0.976907
\(41\) −1.68320 2.91538i −0.262871 0.455307i 0.704132 0.710069i \(-0.251336\pi\)
−0.967004 + 0.254762i \(0.918003\pi\)
\(42\) 0 0
\(43\) −1.90276 + 3.29567i −0.290168 + 0.502585i −0.973849 0.227195i \(-0.927044\pi\)
0.683681 + 0.729781i \(0.260378\pi\)
\(44\) −2.98802 + 5.17540i −0.450461 + 0.780221i
\(45\) 0 0
\(46\) −1.09932 1.90408i −0.162086 0.280742i
\(47\) −2.86035 4.95427i −0.417225 0.722654i 0.578434 0.815729i \(-0.303664\pi\)
−0.995659 + 0.0930746i \(0.970331\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −6.33349 10.9699i −0.895691 1.55138i
\(51\) 0 0
\(52\) −1.09920 −0.152432
\(53\) −4.16913 7.22115i −0.572675 0.991901i −0.996290 0.0860593i \(-0.972573\pi\)
0.423615 0.905842i \(-0.360761\pi\)
\(54\) 0 0
\(55\) −21.3922 −2.88453
\(56\) 0 0
\(57\) 0 0
\(58\) −10.7140 −1.40682
\(59\) −5.63427 + 9.75883i −0.733519 + 1.27049i 0.221851 + 0.975081i \(0.428790\pi\)
−0.955370 + 0.295411i \(0.904543\pi\)
\(60\) 0 0
\(61\) −6.00109 10.3942i −0.768361 1.33084i −0.938451 0.345411i \(-0.887739\pi\)
0.170091 0.985428i \(-0.445594\pi\)
\(62\) −0.325300 −0.0413131
\(63\) 0 0
\(64\) 1.16898 0.146123
\(65\) −1.96738 3.40761i −0.244024 0.422662i
\(66\) 0 0
\(67\) 3.95652 6.85289i 0.483366 0.837214i −0.516452 0.856316i \(-0.672748\pi\)
0.999818 + 0.0191025i \(0.00608088\pi\)
\(68\) −1.18130 −0.143254
\(69\) 0 0
\(70\) 0 0
\(71\) 12.2052 1.44850 0.724248 0.689540i \(-0.242187\pi\)
0.724248 + 0.689540i \(0.242187\pi\)
\(72\) 0 0
\(73\) 2.65737 + 4.60269i 0.311021 + 0.538704i 0.978584 0.205849i \(-0.0659957\pi\)
−0.667563 + 0.744554i \(0.732662\pi\)
\(74\) 6.17557 0.717896
\(75\) 0 0
\(76\) 1.08194 + 1.87397i 0.124107 + 0.214959i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.60855 7.98225i −0.518503 0.898073i −0.999769 0.0214988i \(-0.993156\pi\)
0.481266 0.876575i \(-0.340177\pi\)
\(80\) −8.78016 15.2077i −0.981651 1.70027i
\(81\) 0 0
\(82\) −2.90623 + 5.03373i −0.320939 + 0.555883i
\(83\) −0.624950 + 1.08245i −0.0685972 + 0.118814i −0.898284 0.439415i \(-0.855186\pi\)
0.829687 + 0.558229i \(0.188519\pi\)
\(84\) 0 0
\(85\) −2.11433 3.66213i −0.229332 0.397214i
\(86\) 6.57064 0.708531
\(87\) 0 0
\(88\) −10.7140 −1.14212
\(89\) 2.77066 4.79892i 0.293689 0.508684i −0.680990 0.732293i \(-0.738450\pi\)
0.974679 + 0.223608i \(0.0717837\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.624715 + 1.08204i −0.0651310 + 0.112810i
\(93\) 0 0
\(94\) −4.93871 + 8.55409i −0.509389 + 0.882287i
\(95\) −3.87298 + 6.70820i −0.397359 + 0.688246i
\(96\) 0 0
\(97\) 8.24277 14.2769i 0.836926 1.44960i −0.0555261 0.998457i \(-0.517684\pi\)
0.892452 0.451142i \(-0.148983\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.59915 + 6.23391i −0.359915 + 0.623391i
\(101\) 12.9638 1.28995 0.644975 0.764203i \(-0.276868\pi\)
0.644975 + 0.764203i \(0.276868\pi\)
\(102\) 0 0
\(103\) 2.70182 0.266218 0.133109 0.991101i \(-0.457504\pi\)
0.133109 + 0.991101i \(0.457504\pi\)
\(104\) −0.985340 1.70666i −0.0966205 0.167352i
\(105\) 0 0
\(106\) −7.19847 + 12.4681i −0.699177 + 1.21101i
\(107\) −0.0892402 + 0.154569i −0.00862718 + 0.0149427i −0.870307 0.492510i \(-0.836079\pi\)
0.861680 + 0.507453i \(0.169413\pi\)
\(108\) 0 0
\(109\) −4.67927 8.10473i −0.448192 0.776292i 0.550076 0.835115i \(-0.314599\pi\)
−0.998268 + 0.0588226i \(0.981265\pi\)
\(110\) 18.4680 + 31.9876i 1.76086 + 3.04989i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.21019 7.29226i −0.396061 0.685998i 0.597175 0.802111i \(-0.296290\pi\)
−0.993236 + 0.116113i \(0.962957\pi\)
\(114\) 0 0
\(115\) −4.47254 −0.417067
\(116\) 3.04424 + 5.27278i 0.282651 + 0.489565i
\(117\) 0 0
\(118\) 19.4564 1.79110
\(119\) 0 0
\(120\) 0 0
\(121\) 26.0959 2.37235
\(122\) −10.3615 + 17.9467i −0.938090 + 1.62482i
\(123\) 0 0
\(124\) 0.0924294 + 0.160092i 0.00830040 + 0.0143767i
\(125\) −8.20593 −0.733960
\(126\) 0 0
\(127\) −9.92438 −0.880647 −0.440323 0.897839i \(-0.645136\pi\)
−0.440323 + 0.897839i \(0.645136\pi\)
\(128\) −6.12343 10.6061i −0.541240 0.937455i
\(129\) 0 0
\(130\) −3.39691 + 5.88361i −0.297928 + 0.516027i
\(131\) 15.2467 1.33211 0.666055 0.745902i \(-0.267981\pi\)
0.666055 + 0.745902i \(0.267981\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −13.6627 −1.18028
\(135\) 0 0
\(136\) −1.05894 1.83413i −0.0908032 0.157276i
\(137\) −6.14700 −0.525174 −0.262587 0.964908i \(-0.584576\pi\)
−0.262587 + 0.964908i \(0.584576\pi\)
\(138\) 0 0
\(139\) 0.438687 + 0.759829i 0.0372090 + 0.0644478i 0.884030 0.467430i \(-0.154820\pi\)
−0.846821 + 0.531878i \(0.821487\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.5368 18.2504i −0.884233 1.53154i
\(143\) 3.41161 + 5.90908i 0.285293 + 0.494142i
\(144\) 0 0
\(145\) −10.8974 + 18.8748i −0.904977 + 1.56747i
\(146\) 4.58824 7.94706i 0.379725 0.657703i
\(147\) 0 0
\(148\) −1.75470 3.03923i −0.144236 0.249823i
\(149\) −5.77553 −0.473150 −0.236575 0.971613i \(-0.576025\pi\)
−0.236575 + 0.971613i \(0.576025\pi\)
\(150\) 0 0
\(151\) −2.02643 −0.164908 −0.0824541 0.996595i \(-0.526276\pi\)
−0.0824541 + 0.996595i \(0.526276\pi\)
\(152\) −1.93973 + 3.35972i −0.157333 + 0.272509i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.330866 + 0.573077i −0.0265758 + 0.0460307i
\(156\) 0 0
\(157\) 1.52378 2.63927i 0.121611 0.210636i −0.798792 0.601607i \(-0.794527\pi\)
0.920403 + 0.390971i \(0.127861\pi\)
\(158\) −7.95718 + 13.7822i −0.633039 + 1.09646i
\(159\) 0 0
\(160\) −8.98141 + 15.5563i −0.710043 + 1.22983i
\(161\) 0 0
\(162\) 0 0
\(163\) 2.69445 4.66693i 0.211046 0.365542i −0.740996 0.671509i \(-0.765646\pi\)
0.952042 + 0.305967i \(0.0989797\pi\)
\(164\) 3.30306 0.257925
\(165\) 0 0
\(166\) 2.15809 0.167500
\(167\) 8.30480 + 14.3843i 0.642645 + 1.11309i 0.984840 + 0.173464i \(0.0554961\pi\)
−0.342196 + 0.939629i \(0.611171\pi\)
\(168\) 0 0
\(169\) 5.87249 10.1714i 0.451730 0.782419i
\(170\) −3.65063 + 6.32308i −0.279991 + 0.484958i
\(171\) 0 0
\(172\) −1.86696 3.23366i −0.142354 0.246564i
\(173\) −8.82516 15.2856i −0.670965 1.16214i −0.977631 0.210328i \(-0.932547\pi\)
0.306666 0.951817i \(-0.400786\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 15.2255 + 26.3714i 1.14767 + 1.98782i
\(177\) 0 0
\(178\) −9.56769 −0.717128
\(179\) 1.31422 + 2.27630i 0.0982294 + 0.170138i 0.910952 0.412513i \(-0.135349\pi\)
−0.812722 + 0.582651i \(0.802015\pi\)
\(180\) 0 0
\(181\) 3.97391 0.295378 0.147689 0.989034i \(-0.452816\pi\)
0.147689 + 0.989034i \(0.452816\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.24002 −0.165136
\(185\) 6.28125 10.8794i 0.461806 0.799872i
\(186\) 0 0
\(187\) 3.66643 + 6.35045i 0.268116 + 0.464391i
\(188\) 5.61306 0.409374
\(189\) 0 0
\(190\) 13.3743 0.970270
\(191\) −9.10295 15.7668i −0.658666 1.14084i −0.980961 0.194204i \(-0.937787\pi\)
0.322295 0.946639i \(-0.395546\pi\)
\(192\) 0 0
\(193\) 0.101193 0.175271i 0.00728401 0.0126163i −0.862360 0.506295i \(-0.831015\pi\)
0.869644 + 0.493679i \(0.164348\pi\)
\(194\) −28.4641 −2.04360
\(195\) 0 0
\(196\) 0 0
\(197\) 1.63136 0.116229 0.0581147 0.998310i \(-0.481491\pi\)
0.0581147 + 0.998310i \(0.481491\pi\)
\(198\) 0 0
\(199\) −3.14605 5.44912i −0.223018 0.386278i 0.732705 0.680546i \(-0.238257\pi\)
−0.955723 + 0.294268i \(0.904924\pi\)
\(200\) −12.9053 −0.912544
\(201\) 0 0
\(202\) −11.1918 19.3847i −0.787449 1.36390i
\(203\) 0 0
\(204\) 0 0
\(205\) 5.91192 + 10.2397i 0.412906 + 0.715174i
\(206\) −2.33249 4.04000i −0.162512 0.281480i
\(207\) 0 0
\(208\) −2.80050 + 4.85061i −0.194180 + 0.336329i
\(209\) 6.71607 11.6326i 0.464560 0.804642i
\(210\) 0 0
\(211\) 8.14368 + 14.1053i 0.560634 + 0.971046i 0.997441 + 0.0714912i \(0.0227758\pi\)
−0.436807 + 0.899555i \(0.643891\pi\)
\(212\) 8.18138 0.561899
\(213\) 0 0
\(214\) 0.308166 0.0210658
\(215\) 6.68308 11.5754i 0.455782 0.789438i
\(216\) 0 0
\(217\) 0 0
\(218\) −8.07927 + 13.9937i −0.547197 + 0.947773i
\(219\) 0 0
\(220\) 10.4949 18.1776i 0.707563 1.22554i
\(221\) −0.674383 + 1.16807i −0.0453639 + 0.0785726i
\(222\) 0 0
\(223\) −9.98472 + 17.2940i −0.668626 + 1.15809i 0.309662 + 0.950847i \(0.399784\pi\)
−0.978288 + 0.207248i \(0.933549\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.26936 + 12.5909i −0.483551 + 0.837534i
\(227\) −3.61283 −0.239792 −0.119896 0.992786i \(-0.538256\pi\)
−0.119896 + 0.992786i \(0.538256\pi\)
\(228\) 0 0
\(229\) 13.7147 0.906290 0.453145 0.891437i \(-0.350302\pi\)
0.453145 + 0.891437i \(0.350302\pi\)
\(230\) 3.86117 + 6.68774i 0.254598 + 0.440976i
\(231\) 0 0
\(232\) −5.45781 + 9.45321i −0.358323 + 0.620634i
\(233\) −12.6271 + 21.8707i −0.827227 + 1.43280i 0.0729776 + 0.997334i \(0.476750\pi\)
−0.900205 + 0.435466i \(0.856583\pi\)
\(234\) 0 0
\(235\) 10.0464 + 17.4009i 0.655357 + 1.13511i
\(236\) −5.52825 9.57521i −0.359859 0.623293i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.49495 + 7.78549i 0.290754 + 0.503601i 0.973988 0.226598i \(-0.0727604\pi\)
−0.683234 + 0.730200i \(0.739427\pi\)
\(240\) 0 0
\(241\) 9.25724 0.596311 0.298156 0.954517i \(-0.403629\pi\)
0.298156 + 0.954517i \(0.403629\pi\)
\(242\) −22.5287 39.0209i −1.44820 2.50836i
\(243\) 0 0
\(244\) 11.7763 0.753903
\(245\) 0 0
\(246\) 0 0
\(247\) 2.47063 0.157203
\(248\) −0.165710 + 0.287019i −0.0105226 + 0.0182257i
\(249\) 0 0
\(250\) 7.08422 + 12.2702i 0.448045 + 0.776037i
\(251\) −20.6517 −1.30353 −0.651763 0.758422i \(-0.725970\pi\)
−0.651763 + 0.758422i \(0.725970\pi\)
\(252\) 0 0
\(253\) 7.75576 0.487600
\(254\) 8.56777 + 14.8398i 0.537590 + 0.931133i
\(255\) 0 0
\(256\) −9.40380 + 16.2879i −0.587738 + 1.01799i
\(257\) 2.44579 0.152564 0.0762819 0.997086i \(-0.475695\pi\)
0.0762819 + 0.997086i \(0.475695\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.86073 0.239432
\(261\) 0 0
\(262\) −13.1626 22.7982i −0.813186 1.40848i
\(263\) 24.5628 1.51460 0.757302 0.653065i \(-0.226517\pi\)
0.757302 + 0.653065i \(0.226517\pi\)
\(264\) 0 0
\(265\) 14.6433 + 25.3629i 0.899531 + 1.55803i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.88207 + 6.72395i 0.237135 + 0.410730i
\(269\) −14.7851 25.6086i −0.901466 1.56139i −0.825592 0.564268i \(-0.809158\pi\)
−0.0758746 0.997117i \(-0.524175\pi\)
\(270\) 0 0
\(271\) 12.3958 21.4701i 0.752989 1.30421i −0.193380 0.981124i \(-0.561945\pi\)
0.946368 0.323090i \(-0.104722\pi\)
\(272\) −3.00968 + 5.21291i −0.182488 + 0.316079i
\(273\) 0 0
\(274\) 5.30674 + 9.19154i 0.320592 + 0.555281i
\(275\) 44.6830 2.69448
\(276\) 0 0
\(277\) 1.87850 0.112868 0.0564340 0.998406i \(-0.482027\pi\)
0.0564340 + 0.998406i \(0.482027\pi\)
\(278\) 0.757442 1.31193i 0.0454284 0.0786842i
\(279\) 0 0
\(280\) 0 0
\(281\) −6.03965 + 10.4610i −0.360295 + 0.624049i −0.988009 0.154395i \(-0.950657\pi\)
0.627714 + 0.778444i \(0.283991\pi\)
\(282\) 0 0
\(283\) 13.9859 24.2244i 0.831378 1.43999i −0.0655680 0.997848i \(-0.520886\pi\)
0.896946 0.442140i \(-0.145781\pi\)
\(284\) −5.98779 + 10.3712i −0.355310 + 0.615415i
\(285\) 0 0
\(286\) 5.89052 10.2027i 0.348314 0.603297i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.77524 13.4671i 0.457367 0.792183i
\(290\) 37.6310 2.20977
\(291\) 0 0
\(292\) −5.21473 −0.305169
\(293\) 4.41163 + 7.64117i 0.257730 + 0.446402i 0.965634 0.259908i \(-0.0836921\pi\)
−0.707903 + 0.706309i \(0.750359\pi\)
\(294\) 0 0
\(295\) 19.7893 34.2761i 1.15218 1.99563i
\(296\) 3.14589 5.44883i 0.182851 0.316707i
\(297\) 0 0
\(298\) 4.98604 + 8.63608i 0.288834 + 0.500275i
\(299\) 0.713276 + 1.23543i 0.0412498 + 0.0714467i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.74942 + 3.03009i 0.100668 + 0.174362i
\(303\) 0 0
\(304\) 11.0261 0.632389
\(305\) 21.0777 + 36.5076i 1.20691 + 2.09042i
\(306\) 0 0
\(307\) 1.05532 0.0602304 0.0301152 0.999546i \(-0.490413\pi\)
0.0301152 + 0.999546i \(0.490413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1.14255 0.0648927
\(311\) 1.53608 2.66056i 0.0871029 0.150867i −0.819182 0.573533i \(-0.805572\pi\)
0.906285 + 0.422666i \(0.138906\pi\)
\(312\) 0 0
\(313\) −14.0810 24.3891i −0.795907 1.37855i −0.922262 0.386566i \(-0.873661\pi\)
0.126355 0.991985i \(-0.459672\pi\)
\(314\) −5.26196 −0.296949
\(315\) 0 0
\(316\) 9.04368 0.508747
\(317\) 6.42324 + 11.1254i 0.360765 + 0.624863i 0.988087 0.153897i \(-0.0491823\pi\)
−0.627322 + 0.778760i \(0.715849\pi\)
\(318\) 0 0
\(319\) 18.8969 32.7305i 1.05803 1.83255i
\(320\) −4.10582 −0.229523
\(321\) 0 0
\(322\) 0 0
\(323\) 2.65517 0.147738
\(324\) 0 0
\(325\) 4.10937 + 7.11763i 0.227947 + 0.394815i
\(326\) −9.30454 −0.515331
\(327\) 0 0
\(328\) 2.96091 + 5.12845i 0.163489 + 0.283171i
\(329\) 0 0
\(330\) 0 0
\(331\) 10.7780 + 18.6681i 0.592413 + 1.02609i 0.993906 + 0.110228i \(0.0351581\pi\)
−0.401493 + 0.915862i \(0.631509\pi\)
\(332\) −0.613191 1.06208i −0.0336532 0.0582891i
\(333\) 0 0
\(334\) 14.3392 24.8361i 0.784604 1.35897i
\(335\) −13.8965 + 24.0695i −0.759248 + 1.31506i
\(336\) 0 0
\(337\) 6.30340 + 10.9178i 0.343368 + 0.594731i 0.985056 0.172235i \(-0.0550989\pi\)
−0.641688 + 0.766966i \(0.721766\pi\)
\(338\) −20.2790 −1.10303
\(339\) 0 0
\(340\) 4.14910 0.225017
\(341\) 0.573750 0.993764i 0.0310703 0.0538153i
\(342\) 0 0
\(343\) 0 0
\(344\) 3.34714 5.79741i 0.180466 0.312575i
\(345\) 0 0
\(346\) −15.2376 + 26.3923i −0.819179 + 1.41886i
\(347\) 11.5683 20.0369i 0.621020 1.07564i −0.368276 0.929716i \(-0.620052\pi\)
0.989296 0.145922i \(-0.0466147\pi\)
\(348\) 0 0
\(349\) 8.24346 14.2781i 0.441262 0.764289i −0.556521 0.830833i \(-0.687864\pi\)
0.997783 + 0.0665448i \(0.0211975\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 15.5745 26.9759i 0.830124 1.43782i
\(353\) 24.4875 1.30334 0.651669 0.758503i \(-0.274069\pi\)
0.651669 + 0.758503i \(0.274069\pi\)
\(354\) 0 0
\(355\) −42.8686 −2.27523
\(356\) 2.71852 + 4.70862i 0.144081 + 0.249556i
\(357\) 0 0
\(358\) 2.26915 3.93028i 0.119928 0.207722i
\(359\) 10.2389 17.7342i 0.540386 0.935977i −0.458495 0.888697i \(-0.651611\pi\)
0.998882 0.0472797i \(-0.0150552\pi\)
\(360\) 0 0
\(361\) 7.06816 + 12.2424i 0.372009 + 0.644338i
\(362\) −3.43070 5.94214i −0.180313 0.312312i
\(363\) 0 0
\(364\) 0 0
\(365\) −9.33349 16.1661i −0.488537 0.846172i
\(366\) 0 0
\(367\) 22.2539 1.16164 0.580821 0.814031i \(-0.302732\pi\)
0.580821 + 0.814031i \(0.302732\pi\)
\(368\) 3.18325 + 5.51355i 0.165938 + 0.287414i
\(369\) 0 0
\(370\) −21.6905 −1.12764
\(371\) 0 0
\(372\) 0 0
\(373\) −32.5369 −1.68469 −0.842347 0.538935i \(-0.818827\pi\)
−0.842347 + 0.538935i \(0.818827\pi\)
\(374\) 6.33050 10.9647i 0.327342 0.566974i
\(375\) 0 0
\(376\) 5.03163 + 8.71504i 0.259487 + 0.449444i
\(377\) 6.95160 0.358026
\(378\) 0 0
\(379\) 1.54440 0.0793306 0.0396653 0.999213i \(-0.487371\pi\)
0.0396653 + 0.999213i \(0.487371\pi\)
\(380\) −3.80011 6.58198i −0.194941 0.337648i
\(381\) 0 0
\(382\) −15.7173 + 27.2231i −0.804165 + 1.39285i
\(383\) −31.6294 −1.61619 −0.808093 0.589055i \(-0.799500\pi\)
−0.808093 + 0.589055i \(0.799500\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.349441 −0.0177861
\(387\) 0 0
\(388\) 8.08767 + 14.0083i 0.410589 + 0.711162i
\(389\) 5.24626 0.265996 0.132998 0.991116i \(-0.457540\pi\)
0.132998 + 0.991116i \(0.457540\pi\)
\(390\) 0 0
\(391\) 0.766552 + 1.32771i 0.0387662 + 0.0671451i
\(392\) 0 0
\(393\) 0 0
\(394\) −1.40836 2.43935i −0.0709521 0.122893i
\(395\) 16.1867 + 28.0362i 0.814440 + 1.41065i
\(396\) 0 0
\(397\) −0.0138175 + 0.0239325i −0.000693478 + 0.00120114i −0.866372 0.499399i \(-0.833554\pi\)
0.865678 + 0.500600i \(0.166887\pi\)
\(398\) −5.43201 + 9.40851i −0.272282 + 0.471606i
\(399\) 0 0
\(400\) 18.3395 + 31.7650i 0.916977 + 1.58825i
\(401\) −12.1377 −0.606127 −0.303064 0.952970i \(-0.598009\pi\)
−0.303064 + 0.952970i \(0.598009\pi\)
\(402\) 0 0
\(403\) 0.211065 0.0105139
\(404\) −6.35996 + 11.0158i −0.316420 + 0.548055i
\(405\) 0 0
\(406\) 0 0
\(407\) −10.8922 + 18.8659i −0.539907 + 0.935146i
\(408\) 0 0
\(409\) −15.6726 + 27.1458i −0.774963 + 1.34227i 0.159853 + 0.987141i \(0.448898\pi\)
−0.934816 + 0.355134i \(0.884435\pi\)
\(410\) 10.2076 17.6800i 0.504116 0.873155i
\(411\) 0 0
\(412\) −1.32549 + 2.29582i −0.0653022 + 0.113107i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.19502 3.80189i 0.107749 0.186627i
\(416\) 5.72938 0.280906
\(417\) 0 0
\(418\) −23.1921 −1.13436
\(419\) −7.44319 12.8920i −0.363623 0.629814i 0.624931 0.780680i \(-0.285127\pi\)
−0.988554 + 0.150866i \(0.951794\pi\)
\(420\) 0 0
\(421\) −4.54213 + 7.86721i −0.221370 + 0.383424i −0.955224 0.295883i \(-0.904386\pi\)
0.733854 + 0.679307i \(0.237720\pi\)
\(422\) 14.0610 24.3543i 0.684477 1.18555i
\(423\) 0 0
\(424\) 7.33392 + 12.7027i 0.356166 + 0.616898i
\(425\) 4.41631 + 7.64927i 0.214223 + 0.371044i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.0875611 0.151660i −0.00423243 0.00733078i
\(429\) 0 0
\(430\) −23.0781 −1.11293
\(431\) −8.31776 14.4068i −0.400652 0.693950i 0.593152 0.805090i \(-0.297883\pi\)
−0.993805 + 0.111140i \(0.964550\pi\)
\(432\) 0 0
\(433\) 19.7423 0.948756 0.474378 0.880321i \(-0.342673\pi\)
0.474378 + 0.880321i \(0.342673\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9.18244 0.439759
\(437\) 1.40415 2.43206i 0.0671696 0.116341i
\(438\) 0 0
\(439\) 3.36757 + 5.83280i 0.160725 + 0.278384i 0.935129 0.354307i \(-0.115283\pi\)
−0.774404 + 0.632692i \(0.781950\pi\)
\(440\) 37.6310 1.79399
\(441\) 0 0
\(442\) 2.32879 0.110769
\(443\) 14.3202 + 24.8033i 0.680372 + 1.17844i 0.974867 + 0.222786i \(0.0715150\pi\)
−0.294496 + 0.955653i \(0.595152\pi\)
\(444\) 0 0
\(445\) −9.73141 + 16.8553i −0.461313 + 0.799017i
\(446\) 34.4794 1.63265
\(447\) 0 0
\(448\) 0 0
\(449\) 6.66872 0.314716 0.157358 0.987542i \(-0.449702\pi\)
0.157358 + 0.987542i \(0.449702\pi\)
\(450\) 0 0
\(451\) −10.2518 17.7566i −0.482736 0.836124i
\(452\) 8.26194 0.388609
\(453\) 0 0
\(454\) 3.11898 + 5.40223i 0.146381 + 0.253539i
\(455\) 0 0
\(456\) 0 0
\(457\) 14.3287 + 24.8180i 0.670266 + 1.16093i 0.977829 + 0.209407i \(0.0671533\pi\)
−0.307563 + 0.951528i \(0.599513\pi\)
\(458\) −11.8399 20.5074i −0.553244 0.958246i
\(459\) 0 0
\(460\) 2.19419 3.80045i 0.102305 0.177197i
\(461\) 10.0087 17.3355i 0.466150 0.807395i −0.533103 0.846050i \(-0.678974\pi\)
0.999253 + 0.0386554i \(0.0123075\pi\)
\(462\) 0 0
\(463\) −4.95789 8.58731i −0.230413 0.399086i 0.727517 0.686090i \(-0.240674\pi\)
−0.957930 + 0.287003i \(0.907341\pi\)
\(464\) 31.0240 1.44025
\(465\) 0 0
\(466\) 43.6041 2.01992
\(467\) −8.04035 + 13.9263i −0.372063 + 0.644432i −0.989883 0.141888i \(-0.954683\pi\)
0.617820 + 0.786320i \(0.288016\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 17.3463 30.0446i 0.800124 1.38586i
\(471\) 0 0
\(472\) 9.91123 17.1667i 0.456201 0.790164i
\(473\) −11.5890 + 20.0728i −0.532863 + 0.922946i
\(474\) 0 0
\(475\) 8.08967 14.0117i 0.371180 0.642902i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.76103 13.4425i 0.354981 0.614846i
\(479\) −8.20255 −0.374784 −0.187392 0.982285i \(-0.560003\pi\)
−0.187392 + 0.982285i \(0.560003\pi\)
\(480\) 0 0
\(481\) −4.00690 −0.182699
\(482\) −7.99183 13.8423i −0.364018 0.630497i
\(483\) 0 0
\(484\) −12.8024 + 22.1745i −0.581929 + 1.00793i
\(485\) −28.9512 + 50.1449i −1.31460 + 2.27696i
\(486\) 0 0
\(487\) −1.36840 2.37014i −0.0620081 0.107401i 0.833355 0.552738i \(-0.186417\pi\)
−0.895363 + 0.445337i \(0.853084\pi\)
\(488\) 10.5565 + 18.2844i 0.477871 + 0.827696i
\(489\) 0 0
\(490\) 0 0
\(491\) −9.85482 17.0690i −0.444742 0.770315i 0.553293 0.832987i \(-0.313371\pi\)
−0.998034 + 0.0626719i \(0.980038\pi\)
\(492\) 0 0
\(493\) 7.47084 0.336470
\(494\) −2.13291 3.69431i −0.0959642 0.166215i
\(495\) 0 0
\(496\) 0.941952 0.0422949
\(497\) 0 0
\(498\) 0 0
\(499\) −33.0960 −1.48158 −0.740789 0.671737i \(-0.765548\pi\)
−0.740789 + 0.671737i \(0.765548\pi\)
\(500\) 4.02576 6.97283i 0.180038 0.311834i
\(501\) 0 0
\(502\) 17.8288 + 30.8803i 0.795737 + 1.37826i
\(503\) 12.1860 0.543346 0.271673 0.962390i \(-0.412423\pi\)
0.271673 + 0.962390i \(0.412423\pi\)
\(504\) 0 0
\(505\) −45.5331 −2.02619
\(506\) −6.69559 11.5971i −0.297655 0.515554i
\(507\) 0 0
\(508\) 4.86882 8.43305i 0.216019 0.374156i
\(509\) 13.6393 0.604551 0.302276 0.953221i \(-0.402254\pi\)
0.302276 + 0.953221i \(0.402254\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 7.97968 0.352656
\(513\) 0 0
\(514\) −2.11146 3.65715i −0.0931325 0.161310i
\(515\) −9.48962 −0.418163
\(516\) 0 0
\(517\) −17.4214 30.1747i −0.766190 1.32708i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.46082 + 5.99432i 0.151767 + 0.262868i
\(521\) 17.7745 + 30.7863i 0.778714 + 1.34877i 0.932683 + 0.360697i \(0.117461\pi\)
−0.153969 + 0.988076i \(0.549206\pi\)
\(522\) 0 0
\(523\) 13.3593 23.1391i 0.584163 1.01180i −0.410816 0.911718i \(-0.634756\pi\)
0.994979 0.100082i \(-0.0319105\pi\)
\(524\) −7.47991 + 12.9556i −0.326761 + 0.565967i
\(525\) 0 0
\(526\) −21.2052 36.7284i −0.924589 1.60143i
\(527\) 0.226830 0.00988086
\(528\) 0 0
\(529\) −21.3785 −0.929499
\(530\) 25.2833 43.7919i 1.09824 1.90220i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.88565 3.26604i 0.0816766 0.141468i
\(534\) 0 0
\(535\) 0.313440 0.542893i 0.0135512 0.0234713i
\(536\) −6.95990 + 12.0549i −0.300622 + 0.520693i
\(537\) 0 0
\(538\) −25.5282 + 44.2161i −1.10060 + 1.90629i
\(539\) 0 0
\(540\) 0 0
\(541\) −18.7927 + 32.5500i −0.807963 + 1.39943i 0.106309 + 0.994333i \(0.466097\pi\)
−0.914272 + 0.405100i \(0.867237\pi\)
\(542\) −42.8053 −1.83864
\(543\) 0 0
\(544\) 6.15733 0.263993
\(545\) 16.4350 + 28.4663i 0.704000 + 1.21936i
\(546\) 0 0
\(547\) −9.13381 + 15.8202i −0.390533 + 0.676424i −0.992520 0.122082i \(-0.961043\pi\)
0.601986 + 0.798506i \(0.294376\pi\)
\(548\) 3.01567 5.22329i 0.128823 0.223128i
\(549\) 0 0
\(550\) −38.5750 66.8139i −1.64485 2.84896i
\(551\) −6.84243 11.8514i −0.291498 0.504889i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.62172 2.80890i −0.0689002 0.119339i
\(555\) 0 0
\(556\) −0.860866 −0.0365089
\(557\) −1.94636 3.37119i −0.0824698 0.142842i 0.821840 0.569718i \(-0.192947\pi\)
−0.904310 + 0.426876i \(0.859614\pi\)
\(558\) 0 0
\(559\) −4.26324 −0.180316
\(560\) 0 0
\(561\) 0 0
\(562\) 20.8562 0.879767
\(563\) 1.66428 2.88261i 0.0701409 0.121488i −0.828822 0.559512i \(-0.810988\pi\)
0.898963 + 0.438025i \(0.144322\pi\)
\(564\) 0 0
\(565\) 14.7875 + 25.6127i 0.622115 + 1.07753i
\(566\) −48.2965 −2.03006
\(567\) 0 0
\(568\) −21.4702 −0.900870
\(569\) −18.3122 31.7177i −0.767688 1.32967i −0.938814 0.344425i \(-0.888074\pi\)
0.171126 0.985249i \(-0.445259\pi\)
\(570\) 0 0
\(571\) 11.2912 19.5569i 0.472522 0.818432i −0.526984 0.849875i \(-0.676677\pi\)
0.999506 + 0.0314435i \(0.0100104\pi\)
\(572\) −6.69483 −0.279925
\(573\) 0 0
\(574\) 0 0
\(575\) 9.34201 0.389589
\(576\) 0 0
\(577\) −11.2725 19.5245i −0.469279 0.812815i 0.530104 0.847932i \(-0.322153\pi\)
−0.999383 + 0.0351177i \(0.988819\pi\)
\(578\) −26.8496 −1.11680
\(579\) 0 0
\(580\) −10.6923 18.5197i −0.443975 0.768987i
\(581\) 0 0
\(582\) 0 0
\(583\) −25.3927 43.9814i −1.05166 1.82152i
\(584\) −4.67457 8.09659i −0.193435 0.335039i
\(585\) 0 0
\(586\) 7.61717 13.1933i 0.314662 0.545011i
\(587\) 12.1198 20.9921i 0.500237 0.866436i −0.499763 0.866162i \(-0.666579\pi\)
1.00000 0.000273884i \(-8.71801e-5\pi\)
\(588\) 0 0
\(589\) −0.207750 0.359834i −0.00856020 0.0148267i
\(590\) −68.3368 −2.81338
\(591\) 0 0
\(592\) −17.8822 −0.734956
\(593\) −22.8663 + 39.6056i −0.939007 + 1.62641i −0.171680 + 0.985153i \(0.554919\pi\)
−0.767328 + 0.641255i \(0.778414\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.83343 4.90764i 0.116062 0.201025i
\(597\) 0 0
\(598\) 1.23155 2.13311i 0.0503618 0.0872292i
\(599\) −15.0834 + 26.1252i −0.616290 + 1.06745i 0.373866 + 0.927483i \(0.378032\pi\)
−0.990157 + 0.139963i \(0.955302\pi\)
\(600\) 0 0
\(601\) 7.36933 12.7641i 0.300601 0.520657i −0.675671 0.737203i \(-0.736146\pi\)
0.976272 + 0.216547i \(0.0694794\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.994149 1.72192i 0.0404513 0.0700638i
\(605\) −91.6569 −3.72638
\(606\) 0 0
\(607\) −6.07836 −0.246713 −0.123356 0.992362i \(-0.539366\pi\)
−0.123356 + 0.992362i \(0.539366\pi\)
\(608\) −5.63941 9.76774i −0.228708 0.396134i
\(609\) 0 0
\(610\) 36.3930 63.0345i 1.47351 2.55219i
\(611\) 3.20439 5.55016i 0.129636 0.224535i
\(612\) 0 0
\(613\) −5.88668 10.1960i −0.237761 0.411814i 0.722311 0.691569i \(-0.243080\pi\)
−0.960071 + 0.279755i \(0.909747\pi\)
\(614\) −0.911065 1.57801i −0.0367676 0.0636833i
\(615\) 0 0
\(616\) 0 0
\(617\) 16.0319 + 27.7680i 0.645418 + 1.11790i 0.984205 + 0.177034i \(0.0566503\pi\)
−0.338786 + 0.940863i \(0.610016\pi\)
\(618\) 0 0
\(619\) −12.5518 −0.504498 −0.252249 0.967662i \(-0.581170\pi\)
−0.252249 + 0.967662i \(0.581170\pi\)
\(620\) −0.324641 0.562294i −0.0130379 0.0225823i
\(621\) 0 0
\(622\) −5.30441 −0.212688
\(623\) 0 0
\(624\) 0 0
\(625\) −7.85989 −0.314396
\(626\) −24.3125 + 42.1104i −0.971721 + 1.68307i
\(627\) 0 0
\(628\) 1.49511 + 2.58961i 0.0596614 + 0.103337i
\(629\) −4.30619 −0.171699
\(630\) 0 0
\(631\) 33.4642 1.33219 0.666095 0.745867i \(-0.267964\pi\)
0.666095 + 0.745867i \(0.267964\pi\)
\(632\) 8.10690 + 14.0416i 0.322475 + 0.558543i
\(633\) 0 0
\(634\) 11.0904 19.2092i 0.440457 0.762894i
\(635\) 34.8575 1.38328
\(636\) 0 0
\(637\) 0 0
\(638\) −65.2553 −2.58348
\(639\) 0 0
\(640\) 21.5074 + 37.2519i 0.850155 + 1.47251i
\(641\) 18.9837 0.749809 0.374905 0.927063i \(-0.377675\pi\)
0.374905 + 0.927063i \(0.377675\pi\)
\(642\) 0 0
\(643\) 4.81347 + 8.33718i 0.189825 + 0.328786i 0.945192 0.326516i \(-0.105875\pi\)
−0.755367 + 0.655302i \(0.772541\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.29222 3.97025i −0.0901864 0.156207i
\(647\) −3.90607 6.76551i −0.153564 0.265980i 0.778972 0.627059i \(-0.215742\pi\)
−0.932535 + 0.361079i \(0.882408\pi\)
\(648\) 0 0
\(649\) −34.3163 + 59.4375i −1.34703 + 2.33313i
\(650\) 7.09528 12.2894i 0.278300 0.482029i
\(651\) 0 0
\(652\) 2.64376 + 4.57912i 0.103537 + 0.179332i
\(653\) −31.7429 −1.24219 −0.621097 0.783734i \(-0.713313\pi\)
−0.621097 + 0.783734i \(0.713313\pi\)
\(654\) 0 0
\(655\) −53.5512 −2.09242
\(656\) 8.41540 14.5759i 0.328566 0.569093i
\(657\) 0 0
\(658\) 0 0
\(659\) −3.10685 + 5.38122i −0.121026 + 0.209623i −0.920172 0.391513i \(-0.871952\pi\)
0.799147 + 0.601136i \(0.205285\pi\)
\(660\) 0 0
\(661\) −13.7631 + 23.8384i −0.535324 + 0.927208i 0.463824 + 0.885927i \(0.346477\pi\)
−0.999148 + 0.0412802i \(0.986856\pi\)
\(662\) 18.6094 32.2325i 0.723276 1.25275i
\(663\) 0 0
\(664\) 1.09935 1.90413i 0.0426630 0.0738945i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.95084 6.84306i 0.152977 0.264964i
\(668\) −16.2971 −0.630553
\(669\) 0 0
\(670\) 47.9878 1.85393
\(671\) −36.5505 63.3073i −1.41102 2.44395i
\(672\) 0 0
\(673\) −8.10894 + 14.0451i −0.312577 + 0.541399i −0.978919 0.204247i \(-0.934526\pi\)
0.666343 + 0.745646i \(0.267859\pi\)
\(674\) 10.8835 18.8508i 0.419217 0.726106i
\(675\) 0 0
\(676\) 5.76199 + 9.98006i 0.221615 + 0.383849i
\(677\) −10.2545 17.7613i −0.394112 0.682623i 0.598875 0.800842i \(-0.295615\pi\)
−0.992987 + 0.118220i \(0.962281\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3.71932 + 6.44205i 0.142629 + 0.247041i
\(681\) 0 0
\(682\) −1.98128 −0.0758673
\(683\) −0.0561542 0.0972618i −0.00214868 0.00372162i 0.864949 0.501860i \(-0.167351\pi\)
−0.867098 + 0.498138i \(0.834017\pi\)
\(684\) 0 0
\(685\) 21.5902 0.824918
\(686\) 0 0
\(687\) 0 0
\(688\) −19.0262 −0.725368
\(689\) 4.67059 8.08970i 0.177935 0.308193i
\(690\) 0 0
\(691\) −9.43351 16.3393i −0.358868 0.621577i 0.628904 0.777483i \(-0.283504\pi\)
−0.987772 + 0.155906i \(0.950170\pi\)
\(692\) 17.3182 0.658340
\(693\) 0 0
\(694\) −39.9480 −1.51640
\(695\) −1.54081 2.66876i −0.0584461 0.101232i
\(696\) 0 0
\(697\) 2.02650 3.51000i 0.0767590 0.132951i
\(698\) −28.4665 −1.07747
\(699\) 0 0
\(700\) 0 0
\(701\) 3.16006 0.119354 0.0596770 0.998218i \(-0.480993\pi\)
0.0596770 + 0.998218i \(0.480993\pi\)
\(702\) 0 0
\(703\) 3.94398 + 6.83118i 0.148750 + 0.257643i
\(704\) 7.11984 0.268339
\(705\) 0 0
\(706\) −21.1402 36.6159i −0.795622 1.37806i
\(707\) 0 0
\(708\) 0 0
\(709\) 10.7606 + 18.6378i 0.404121 + 0.699959i 0.994219 0.107373i \(-0.0342440\pi\)
−0.590097 + 0.807332i \(0.700911\pi\)
\(710\) 37.0087 + 64.1009i 1.38891 + 2.40567i
\(711\) 0 0
\(712\) −4.87385 + 8.44176i −0.182655 + 0.316368i
\(713\) 0.119956 0.207769i 0.00449237 0.00778102i
\(714\) 0 0
\(715\) −11.9826 20.7545i −0.448125 0.776175i
\(716\) −2.57898 −0.0963812
\(717\) 0 0
\(718\) −35.3570 −1.31951
\(719\) −9.41508 + 16.3074i −0.351123 + 0.608163i −0.986447 0.164083i \(-0.947533\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 12.2040 21.1379i 0.454185 0.786671i
\(723\) 0 0
\(724\) −1.94957 + 3.37675i −0.0724551 + 0.125496i
\(725\) 22.7618 39.4247i 0.845354 1.46420i
\(726\) 0 0
\(727\) −19.5426 + 33.8489i −0.724797 + 1.25538i 0.234261 + 0.972174i \(0.424733\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −16.1153 + 27.9125i −0.596454 + 1.03309i
\(731\) −4.58167 −0.169459
\(732\) 0 0
\(733\) 18.5985 0.686951 0.343475 0.939162i \(-0.388396\pi\)
0.343475 + 0.939162i \(0.388396\pi\)
\(734\) −19.2119 33.2759i −0.709123 1.22824i
\(735\) 0 0
\(736\) 3.25621 5.63993i 0.120026 0.207890i
\(737\) 24.0977 41.7385i 0.887651 1.53746i
\(738\) 0 0
\(739\) −2.75068 4.76432i −0.101185 0.175258i 0.810988 0.585063i \(-0.198930\pi\)
−0.912173 + 0.409805i \(0.865597\pi\)
\(740\) 6.16306 + 10.6747i 0.226559 + 0.392411i
\(741\) 0 0
\(742\) 0 0
\(743\) −10.2326 17.7234i −0.375399 0.650210i 0.614988 0.788537i \(-0.289161\pi\)
−0.990387 + 0.138327i \(0.955828\pi\)
\(744\) 0 0
\(745\) 20.2855 0.743201
\(746\) 28.0892 + 48.6520i 1.02842 + 1.78128i
\(747\) 0 0
\(748\) −7.19489 −0.263071
\(749\) 0 0
\(750\) 0 0
\(751\) 38.0460 1.38832 0.694159 0.719822i \(-0.255777\pi\)
0.694159 + 0.719822i \(0.255777\pi\)
\(752\) 14.3007 24.7696i 0.521494 0.903254i
\(753\) 0 0
\(754\) −6.00135 10.3946i −0.218556 0.378551i
\(755\) 7.11744 0.259030
\(756\) 0 0
\(757\) −51.0780 −1.85646 −0.928230 0.372006i \(-0.878670\pi\)
−0.928230 + 0.372006i \(0.878670\pi\)
\(758\) −1.33329 2.30933i −0.0484273 0.0838786i
\(759\) 0 0
\(760\) 6.81295 11.8004i 0.247132 0.428045i
\(761\) 40.0749 1.45271 0.726357 0.687317i \(-0.241212\pi\)
0.726357 + 0.687317i \(0.241212\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 17.8633 0.646273
\(765\) 0 0
\(766\) 27.3058 + 47.2951i 0.986599 + 1.70884i
\(767\) −12.6239 −0.455822
\(768\) 0 0
\(769\) 22.4828 + 38.9414i 0.810751 + 1.40426i 0.912339 + 0.409436i \(0.134274\pi\)
−0.101587 + 0.994827i \(0.532392\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.0992886 + 0.171973i 0.00357348 + 0.00618944i
\(773\) −12.1781 21.0930i −0.438014 0.758663i 0.559522 0.828816i \(-0.310985\pi\)
−0.997536 + 0.0701524i \(0.977651\pi\)
\(774\) 0 0
\(775\) 0.691096 1.19701i 0.0248249 0.0429980i
\(776\) −14.4998 + 25.1145i −0.520514 + 0.901556i
\(777\) 0 0
\(778\) −4.52913 7.84468i −0.162377 0.281245i
\(779\) −7.42416 −0.265998
\(780\) 0 0
\(781\) 74.3377 2.66001
\(782\) 1.32354 2.29243i 0.0473296 0.0819773i
\(783\) 0 0
\(784\) 0 0
\(785\) −5.35200 + 9.26993i −0.191021 + 0.330858i
\(786\) 0 0
\(787\) −20.7617 + 35.9603i −0.740073 + 1.28184i 0.212388 + 0.977185i \(0.431876\pi\)
−0.952461 + 0.304659i \(0.901457\pi\)
\(788\) −0.800331 + 1.38621i −0.0285106 + 0.0493818i
\(789\) 0 0
\(790\) 27.9481 48.4075i 0.994349 1.72226i
\(791\) 0 0
\(792\) 0 0
\(793\) 6.72289 11.6444i 0.238737 0.413504i
\(794\) 0.0477147 0.00169333
\(795\) 0 0
\(796\) 6.17372 0.218822
\(797\) 17.3018 + 29.9676i 0.612861 + 1.06151i 0.990756 + 0.135657i \(0.0433146\pi\)
−0.377895 + 0.925848i \(0.623352\pi\)
\(798\) 0 0
\(799\) 3.44373 5.96472i 0.121831 0.211017i
\(800\) 18.7599 32.4931i 0.663263 1.14880i
\(801\) 0 0
\(802\) 10.4785 + 18.1494i 0.370010 + 0.640876i
\(803\) 16.1851 + 28.0333i 0.571158 + 0.989275i
\(804\) 0 0
\(805\) 0 0
\(806\) −0.182213 0.315603i −0.00641819 0.0111166i
\(807\) 0 0
\(808\) −22.8047 −0.802266
\(809\) −5.62597 9.74446i −0.197799 0.342597i 0.750016 0.661420i \(-0.230046\pi\)
−0.947814 + 0.318823i \(0.896713\pi\)
\(810\) 0 0
\(811\) −29.6803 −1.04222 −0.521108 0.853491i \(-0.674481\pi\)
−0.521108 + 0.853491i \(0.674481\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 37.6132 1.31834
\(815\) −9.46376 + 16.3917i −0.331501 + 0.574177i
\(816\) 0 0
\(817\) 4.19629 + 7.26819i 0.146810 + 0.254282i
\(818\) 54.1211 1.89230
\(819\) 0 0
\(820\) −11.6014 −0.405137
\(821\) 17.3215 + 30.0018i 0.604526 + 1.04707i 0.992126 + 0.125242i \(0.0399709\pi\)
−0.387600 + 0.921828i \(0.626696\pi\)
\(822\) 0 0
\(823\) −18.1935 + 31.5121i −0.634186 + 1.09844i 0.352501 + 0.935811i \(0.385331\pi\)
−0.986687 + 0.162631i \(0.948002\pi\)
\(824\) −4.75276 −0.165570
\(825\) 0 0
\(826\) 0 0
\(827\) 24.3576 0.846997 0.423498 0.905897i \(-0.360802\pi\)
0.423498 + 0.905897i \(0.360802\pi\)
\(828\) 0 0
\(829\) −19.5851 33.9224i −0.680219 1.17817i −0.974914 0.222583i \(-0.928551\pi\)
0.294694 0.955592i \(-0.404782\pi\)
\(830\) −7.57989 −0.263102
\(831\) 0 0
\(832\) 0.654792 + 1.13413i 0.0227008 + 0.0393190i
\(833\) 0 0
\(834\) 0 0
\(835\) −29.1690 50.5223i −1.00944 1.74839i
\(836\) 6.58970 + 11.4137i 0.227910 + 0.394751i
\(837\) 0 0
\(838\) −12.8515 + 22.2594i −0.443947 + 0.768939i
\(839\) 17.1739 29.7460i 0.592907 1.02695i −0.400931 0.916108i \(-0.631313\pi\)
0.993839 0.110838i \(-0.0353534\pi\)
\(840\) 0 0
\(841\) −4.75250 8.23157i −0.163879 0.283847i
\(842\) 15.6850 0.540541
\(843\) 0 0
\(844\) −15.9809 −0.550085
\(845\) −20.6260 + 35.7253i −0.709556 + 1.22899i
\(846\) 0 0
\(847\) 0 0
\(848\) 20.8442 36.1032i 0.715793 1.23979i
\(849\) 0 0
\(850\) 7.62525 13.2073i 0.261544 0.453007i
\(851\) −2.27727 + 3.94434i −0.0780637 + 0.135210i
\(852\) 0 0
\(853\) −16.3371 + 28.2967i −0.559373 + 0.968862i 0.438176 + 0.898889i \(0.355625\pi\)
−0.997549 + 0.0699730i \(0.977709\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.156982 0.271901i 0.00536555 0.00929340i
\(857\) 57.6679 1.96990 0.984950 0.172841i \(-0.0552945\pi\)
0.984950 + 0.172841i \(0.0552945\pi\)
\(858\) 0 0
\(859\) 29.9768 1.02279 0.511397 0.859344i \(-0.329128\pi\)
0.511397 + 0.859344i \(0.329128\pi\)
\(860\) 6.55733 + 11.3576i 0.223603 + 0.387292i
\(861\) 0 0
\(862\) −14.3615 + 24.8749i −0.489156 + 0.847243i
\(863\) −11.5888 + 20.0724i −0.394487 + 0.683272i −0.993036 0.117815i \(-0.962411\pi\)
0.598548 + 0.801087i \(0.295744\pi\)
\(864\) 0 0
\(865\) 30.9967 + 53.6879i 1.05392 + 1.82544i
\(866\) −17.0437 29.5205i −0.579167 1.00315i
\(867\) 0 0
\(868\) 0 0
\(869\) −28.0690 48.6170i −0.952177 1.64922i
\(870\) 0 0
\(871\) 8.86480 0.300372
\(872\) 8.23129 + 14.2570i 0.278747 + 0.482803i
\(873\) 0 0
\(874\) −4.84884 −0.164014
\(875\) 0 0
\(876\) 0 0
\(877\) −0.739956 −0.0249865 −0.0124933 0.999922i \(-0.503977\pi\)
−0.0124933 + 0.999922i \(0.503977\pi\)
\(878\) 5.81448 10.0710i 0.196229 0.339879i
\(879\) 0 0
\(880\) −53.4768 92.6245i −1.80270 3.12237i
\(881\) 18.0285 0.607395 0.303697 0.952769i \(-0.401779\pi\)
0.303697 + 0.952769i \(0.401779\pi\)
\(882\) 0 0
\(883\) 43.0928 1.45019 0.725095 0.688649i \(-0.241796\pi\)
0.725095 + 0.688649i \(0.241796\pi\)
\(884\) −0.661694 1.14609i −0.0222552 0.0385471i
\(885\) 0 0
\(886\) 24.7254 42.8256i 0.830664 1.43875i
\(887\) 30.9527 1.03929 0.519645 0.854382i \(-0.326064\pi\)
0.519645 + 0.854382i \(0.326064\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 33.6047 1.12643
\(891\) 0 0
\(892\) −9.79685 16.9686i −0.328023 0.568152i
\(893\) −12.6163 −0.422187
\(894\) 0 0
\(895\) −4.61595 7.99506i −0.154294 0.267245i
\(896\) 0 0
\(897\) 0 0
\(898\) −5.75714 9.97165i −0.192118 0.332758i
\(899\) −0.584545 1.01246i −0.0194957 0.0337675i
\(900\) 0 0
\(901\) 5.01945 8.69395i 0.167222 0.289637i
\(902\) −17.7008 + 30.6587i −0.589372 + 1.02082i
\(903\) 0 0
\(904\) 7.40614 + 12.8278i 0.246324 + 0.426646i
\(905\) −13.9576 −0.463966
\(906\) 0 0
\(907\) −42.8083 −1.42143 −0.710714 0.703481i \(-0.751628\pi\)
−0.710714 + 0.703481i \(0.751628\pi\)
\(908\) 1.77243 3.06993i 0.0588200 0.101879i
\(909\) 0 0
\(910\) 0 0
\(911\) −3.04869 + 5.28049i −0.101008 + 0.174950i −0.912100 0.409968i \(-0.865540\pi\)
0.811092 + 0.584918i \(0.198873\pi\)
\(912\) 0 0
\(913\) −3.80635 + 6.59278i −0.125972 + 0.218189i
\(914\) 24.7400 42.8509i 0.818327 1.41738i
\(915\) 0 0
\(916\) −6.72830 + 11.6538i −0.222309 + 0.385051i
\(917\) 0 0
\(918\) 0 0
\(919\) −12.4307 + 21.5305i −0.410050 + 0.710227i −0.994895 0.100918i \(-0.967822\pi\)
0.584845 + 0.811145i \(0.301155\pi\)
\(920\) 7.86764 0.259388
\(921\) 0 0
\(922\) −34.5621 −1.13824
\(923\) 6.83664 + 11.8414i 0.225031 + 0.389764i
\(924\) 0 0
\(925\) −13.1199 + 22.7244i −0.431381 + 0.747174i
\(926\) −8.56034 + 14.8269i −0.281310 + 0.487244i
\(927\) 0 0
\(928\) −15.8676 27.4834i −0.520878 0.902188i
\(929\) −20.9201 36.2347i −0.686366 1.18882i −0.973005 0.230783i \(-0.925871\pi\)
0.286639 0.958039i \(-0.407462\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −12.3895 21.4592i −0.405831 0.702920i
\(933\) 0 0
\(934\) 27.7651 0.908502
\(935\) −12.8776 22.3047i −0.421144 0.729443i
\(936\) 0 0
\(937\) −29.2537 −0.955676 −0.477838 0.878448i \(-0.658579\pi\)
−0.477838 + 0.878448i \(0.658579\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −19.7148 −0.643026
\(941\) −1.67869 + 2.90757i −0.0547236 + 0.0947841i −0.892090 0.451859i \(-0.850761\pi\)
0.837366 + 0.546643i \(0.184094\pi\)
\(942\) 0 0
\(943\) −2.14337 3.71242i −0.0697976 0.120893i
\(944\) −56.3387 −1.83367
\(945\) 0 0
\(946\) 40.0194 1.30114
\(947\) 2.63300 + 4.56050i 0.0855612 + 0.148196i 0.905630 0.424068i \(-0.139398\pi\)
−0.820069 + 0.572265i \(0.806065\pi\)
\(948\) 0 0
\(949\) −2.97699 + 5.15630i −0.0966372 + 0.167381i
\(950\) −27.9354 −0.906345
\(951\) 0 0
\(952\) 0 0
\(953\) −56.2520 −1.82218 −0.911090 0.412208i \(-0.864758\pi\)
−0.911090 + 0.412208i \(0.864758\pi\)
\(954\) 0 0
\(955\) 31.9724 + 55.3778i 1.03460 + 1.79198i
\(956\) −8.82075 −0.285284
\(957\) 0 0
\(958\) 7.08131 + 12.2652i 0.228787 + 0.396270i
\(959\) 0 0
\(960\) 0 0
\(961\) 15.4823 + 26.8160i 0.499427 + 0.865034i
\(962\) 3.45918 + 5.99148i 0.111528 + 0.193173i
\(963\) 0 0
\(964\) −4.54153 + 7.86616i −0.146273 + 0.253352i
\(965\) −0.355420 + 0.615606i −0.0114414 + 0.0198171i
\(966\) 0 0
\(967\) −6.88641 11.9276i −0.221452 0.383566i 0.733797 0.679369i \(-0.237746\pi\)
−0.955249 + 0.295803i \(0.904413\pi\)
\(968\) −45.9052 −1.47545
\(969\) 0 0
\(970\) 99.9748 3.21000
\(971\) 25.6627 44.4491i 0.823555 1.42644i −0.0794635 0.996838i \(-0.525321\pi\)
0.903019 0.429602i \(-0.141346\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −2.36269 + 4.09230i −0.0757055 + 0.131126i
\(975\) 0 0
\(976\) 30.0033 51.9673i 0.960383 1.66343i
\(977\) 8.84252 15.3157i 0.282897 0.489992i −0.689200 0.724571i \(-0.742038\pi\)
0.972097 + 0.234579i \(0.0753711\pi\)
\(978\) 0 0
\(979\) 16.8751 29.2285i 0.539329 0.934146i
\(980\) 0 0
\(981\) 0 0
\(982\) −17.0154 + 29.4716i −0.542984 + 0.940476i
\(983\) −16.0041 −0.510453 −0.255226 0.966881i \(-0.582150\pi\)
−0.255226 + 0.966881i \(0.582150\pi\)
\(984\) 0 0
\(985\) −5.72984 −0.182568
\(986\) −6.44961 11.1711i −0.205397 0.355759i
\(987\) 0 0
\(988\) −1.21207 + 2.09937i −0.0385612 + 0.0667899i
\(989\) −2.42295 + 4.19667i −0.0770454 + 0.133446i
\(990\) 0 0
\(991\) 5.43319 + 9.41055i 0.172591 + 0.298936i 0.939325 0.343029i \(-0.111453\pi\)
−0.766734 + 0.641965i \(0.778120\pi\)
\(992\) −0.481771 0.834453i −0.0152963 0.0264939i
\(993\) 0 0
\(994\) 0 0
\(995\) 11.0499 + 19.1390i 0.350306 + 0.606748i
\(996\) 0 0
\(997\) −41.0375 −1.29967 −0.649835 0.760075i \(-0.725162\pi\)
−0.649835 + 0.760075i \(0.725162\pi\)
\(998\) 28.5719 + 49.4880i 0.904428 + 1.56652i
\(999\) 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 1323.2.g.h.667.3 24
3.2 odd 2 441.2.g.h.79.10 24
7.2 even 3 1323.2.f.h.883.4 24
7.3 odd 6 1323.2.h.h.802.10 24
7.4 even 3 1323.2.h.h.802.9 24
7.5 odd 6 1323.2.f.h.883.3 24
7.6 odd 2 inner 1323.2.g.h.667.4 24
9.4 even 3 1323.2.h.h.226.9 24
9.5 odd 6 441.2.h.h.373.3 24
21.2 odd 6 441.2.f.h.295.10 yes 24
21.5 even 6 441.2.f.h.295.9 yes 24
21.11 odd 6 441.2.h.h.214.3 24
21.17 even 6 441.2.h.h.214.4 24
21.20 even 2 441.2.g.h.79.9 24
63.2 odd 6 3969.2.a.bh.1.4 12
63.4 even 3 inner 1323.2.g.h.361.3 24
63.5 even 6 441.2.f.h.148.9 24
63.13 odd 6 1323.2.h.h.226.10 24
63.16 even 3 3969.2.a.bi.1.9 12
63.23 odd 6 441.2.f.h.148.10 yes 24
63.31 odd 6 inner 1323.2.g.h.361.4 24
63.32 odd 6 441.2.g.h.67.10 24
63.40 odd 6 1323.2.f.h.442.3 24
63.41 even 6 441.2.h.h.373.4 24
63.47 even 6 3969.2.a.bh.1.3 12
63.58 even 3 1323.2.f.h.442.4 24
63.59 even 6 441.2.g.h.67.9 24
63.61 odd 6 3969.2.a.bi.1.10 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.f.h.148.9 24 63.5 even 6
441.2.f.h.148.10 yes 24 63.23 odd 6
441.2.f.h.295.9 yes 24 21.5 even 6
441.2.f.h.295.10 yes 24 21.2 odd 6
441.2.g.h.67.9 24 63.59 even 6
441.2.g.h.67.10 24 63.32 odd 6
441.2.g.h.79.9 24 21.20 even 2
441.2.g.h.79.10 24 3.2 odd 2
441.2.h.h.214.3 24 21.11 odd 6
441.2.h.h.214.4 24 21.17 even 6
441.2.h.h.373.3 24 9.5 odd 6
441.2.h.h.373.4 24 63.41 even 6
1323.2.f.h.442.3 24 63.40 odd 6
1323.2.f.h.442.4 24 63.58 even 3
1323.2.f.h.883.3 24 7.5 odd 6
1323.2.f.h.883.4 24 7.2 even 3
1323.2.g.h.361.3 24 63.4 even 3 inner
1323.2.g.h.361.4 24 63.31 odd 6 inner
1323.2.g.h.667.3 24 1.1 even 1 trivial
1323.2.g.h.667.4 24 7.6 odd 2 inner
1323.2.h.h.226.9 24 9.4 even 3
1323.2.h.h.226.10 24 63.13 odd 6
1323.2.h.h.802.9 24 7.4 even 3
1323.2.h.h.802.10 24 7.3 odd 6
3969.2.a.bh.1.3 12 63.47 even 6
3969.2.a.bh.1.4 12 63.2 odd 6
3969.2.a.bi.1.9 12 63.16 even 3
3969.2.a.bi.1.10 12 63.61 odd 6