Properties

Label 252.2.e.a.71.4
Level $252$
Weight $2$
Character 252.71
Analytic conductor $2.012$
Analytic rank $0$
Dimension $12$
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] = [252,2,Mod(71,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.e (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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.653473922154496.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 71.4
Root \(-1.16947 + 0.795191i\) of defining polynomial
Character \(\chi\) \(=\) 252.71
Dual form 252.2.e.a.71.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.16947 + 0.795191i) q^{2} +(0.735342 - 1.85991i) q^{4} +0.665647i q^{5} -1.00000i q^{7} +(0.619022 + 2.75986i) q^{8} +O(q^{10})\) \(q+(-1.16947 + 0.795191i) q^{2} +(0.735342 - 1.85991i) q^{4} +0.665647i q^{5} -1.00000i q^{7} +(0.619022 + 2.75986i) q^{8} +(-0.529317 - 0.778457i) q^{10} +2.07986 q^{11} +5.55691 q^{13} +(0.795191 + 1.16947i) q^{14} +(-2.91855 - 2.73534i) q^{16} -2.16278i q^{17} +4.49828i q^{19} +(1.23804 + 0.489478i) q^{20} +(-2.43234 + 1.65389i) q^{22} +4.28167 q^{23} +4.55691 q^{25} +(-6.49867 + 4.41881i) q^{26} +(-1.85991 - 0.735342i) q^{28} +1.41421i q^{29} +6.61555i q^{31} +(5.58828 + 0.878111i) q^{32} +(1.71982 + 2.52932i) q^{34} +0.665647 q^{35} -5.43965 q^{37} +(-3.57699 - 5.26063i) q^{38} +(-1.83709 + 0.412050i) q^{40} -5.69588i q^{41} -2.11727i q^{43} +(1.52941 - 3.86836i) q^{44} +(-5.00730 + 3.40475i) q^{46} -10.5213 q^{47} -1.00000 q^{49} +(-5.32920 + 3.62362i) q^{50} +(4.08623 - 10.3354i) q^{52} -10.6042i q^{53} +1.38445i q^{55} +(2.75986 - 0.619022i) q^{56} +(-1.12457 - 1.65389i) q^{58} +13.5155 q^{59} -0.615547 q^{61} +(-5.26063 - 7.73671i) q^{62} +(-7.23362 + 3.41683i) q^{64} +3.69894i q^{65} -14.0552i q^{67} +(-4.02258 - 1.59038i) q^{68} +(-0.778457 + 0.529317i) q^{70} -15.5954 q^{71} -11.9379 q^{73} +(6.36153 - 4.32556i) q^{74} +(8.36641 + 3.30777i) q^{76} -2.07986i q^{77} -0.824101i q^{79} +(1.82077 - 1.94272i) q^{80} +(4.52932 + 6.66119i) q^{82} -6.36153 q^{83} +1.43965 q^{85} +(1.68363 + 2.47609i) q^{86} +(1.28748 + 5.74012i) q^{88} +12.6840i q^{89} -5.55691i q^{91} +(3.14849 - 7.96353i) q^{92} +(12.3043 - 8.36641i) q^{94} -2.99427 q^{95} +0.824101 q^{97} +(1.16947 - 0.795191i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 8 q^{4} - 8 q^{10} - 20 q^{16} + 20 q^{22} - 12 q^{25} - 4 q^{28} - 16 q^{34} + 8 q^{37} + 8 q^{40} - 36 q^{46} - 12 q^{49} - 16 q^{52} + 4 q^{58} + 56 q^{61} - 16 q^{64} + 24 q^{70} + 72 q^{76} + 56 q^{82} - 56 q^{85} + 28 q^{88} - 24 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16947 + 0.795191i −0.826943 + 0.562285i
\(3\) 0 0
\(4\) 0.735342 1.85991i 0.367671 0.929956i
\(5\) 0.665647i 0.297686i 0.988861 + 0.148843i \(0.0475550\pi\)
−0.988861 + 0.148843i \(0.952445\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0.619022 + 2.75986i 0.218857 + 0.975757i
\(9\) 0 0
\(10\) −0.529317 0.778457i −0.167385 0.246170i
\(11\) 2.07986 0.627102 0.313551 0.949571i \(-0.398481\pi\)
0.313551 + 0.949571i \(0.398481\pi\)
\(12\) 0 0
\(13\) 5.55691 1.54121 0.770605 0.637313i \(-0.219954\pi\)
0.770605 + 0.637313i \(0.219954\pi\)
\(14\) 0.795191 + 1.16947i 0.212524 + 0.312555i
\(15\) 0 0
\(16\) −2.91855 2.73534i −0.729636 0.683835i
\(17\) 2.16278i 0.524551i −0.964993 0.262276i \(-0.915527\pi\)
0.964993 0.262276i \(-0.0844730\pi\)
\(18\) 0 0
\(19\) 4.49828i 1.03198i 0.856596 + 0.515988i \(0.172575\pi\)
−0.856596 + 0.515988i \(0.827425\pi\)
\(20\) 1.23804 + 0.489478i 0.276835 + 0.109451i
\(21\) 0 0
\(22\) −2.43234 + 1.65389i −0.518577 + 0.352610i
\(23\) 4.28167 0.892790 0.446395 0.894836i \(-0.352708\pi\)
0.446395 + 0.894836i \(0.352708\pi\)
\(24\) 0 0
\(25\) 4.55691 0.911383
\(26\) −6.49867 + 4.41881i −1.27449 + 0.866600i
\(27\) 0 0
\(28\) −1.85991 0.735342i −0.351490 0.138967i
\(29\) 1.41421i 0.262613i 0.991342 + 0.131306i \(0.0419172\pi\)
−0.991342 + 0.131306i \(0.958083\pi\)
\(30\) 0 0
\(31\) 6.61555i 1.18819i 0.804396 + 0.594094i \(0.202489\pi\)
−0.804396 + 0.594094i \(0.797511\pi\)
\(32\) 5.58828 + 0.878111i 0.987878 + 0.155230i
\(33\) 0 0
\(34\) 1.71982 + 2.52932i 0.294947 + 0.433774i
\(35\) 0.665647 0.112515
\(36\) 0 0
\(37\) −5.43965 −0.894273 −0.447136 0.894466i \(-0.647556\pi\)
−0.447136 + 0.894466i \(0.647556\pi\)
\(38\) −3.57699 5.26063i −0.580265 0.853386i
\(39\) 0 0
\(40\) −1.83709 + 0.412050i −0.290469 + 0.0651509i
\(41\) 5.69588i 0.889548i −0.895643 0.444774i \(-0.853284\pi\)
0.895643 0.444774i \(-0.146716\pi\)
\(42\) 0 0
\(43\) 2.11727i 0.322880i −0.986883 0.161440i \(-0.948386\pi\)
0.986883 0.161440i \(-0.0516138\pi\)
\(44\) 1.52941 3.86836i 0.230567 0.583177i
\(45\) 0 0
\(46\) −5.00730 + 3.40475i −0.738287 + 0.502002i
\(47\) −10.5213 −1.53468 −0.767341 0.641239i \(-0.778421\pi\)
−0.767341 + 0.641239i \(0.778421\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) −5.32920 + 3.62362i −0.753662 + 0.512457i
\(51\) 0 0
\(52\) 4.08623 10.3354i 0.566658 1.43326i
\(53\) 10.6042i 1.45659i −0.685261 0.728297i \(-0.740312\pi\)
0.685261 0.728297i \(-0.259688\pi\)
\(54\) 0 0
\(55\) 1.38445i 0.186680i
\(56\) 2.75986 0.619022i 0.368801 0.0827203i
\(57\) 0 0
\(58\) −1.12457 1.65389i −0.147663 0.217166i
\(59\) 13.5155 1.75957 0.879785 0.475371i \(-0.157686\pi\)
0.879785 + 0.475371i \(0.157686\pi\)
\(60\) 0 0
\(61\) −0.615547 −0.0788128 −0.0394064 0.999223i \(-0.512547\pi\)
−0.0394064 + 0.999223i \(0.512547\pi\)
\(62\) −5.26063 7.73671i −0.668100 0.982564i
\(63\) 0 0
\(64\) −7.23362 + 3.41683i −0.904203 + 0.427103i
\(65\) 3.69894i 0.458797i
\(66\) 0 0
\(67\) 14.0552i 1.71712i −0.512717 0.858558i \(-0.671361\pi\)
0.512717 0.858558i \(-0.328639\pi\)
\(68\) −4.02258 1.59038i −0.487810 0.192862i
\(69\) 0 0
\(70\) −0.778457 + 0.529317i −0.0930434 + 0.0632654i
\(71\) −15.5954 −1.85083 −0.925415 0.378954i \(-0.876284\pi\)
−0.925415 + 0.378954i \(0.876284\pi\)
\(72\) 0 0
\(73\) −11.9379 −1.39723 −0.698614 0.715498i \(-0.746200\pi\)
−0.698614 + 0.715498i \(0.746200\pi\)
\(74\) 6.36153 4.32556i 0.739513 0.502836i
\(75\) 0 0
\(76\) 8.36641 + 3.30777i 0.959693 + 0.379428i
\(77\) 2.07986i 0.237022i
\(78\) 0 0
\(79\) 0.824101i 0.0927186i −0.998925 0.0463593i \(-0.985238\pi\)
0.998925 0.0463593i \(-0.0147619\pi\)
\(80\) 1.82077 1.94272i 0.203568 0.217203i
\(81\) 0 0
\(82\) 4.52932 + 6.66119i 0.500179 + 0.735605i
\(83\) −6.36153 −0.698269 −0.349134 0.937073i \(-0.613524\pi\)
−0.349134 + 0.937073i \(0.613524\pi\)
\(84\) 0 0
\(85\) 1.43965 0.156152
\(86\) 1.68363 + 2.47609i 0.181551 + 0.267004i
\(87\) 0 0
\(88\) 1.28748 + 5.74012i 0.137246 + 0.611899i
\(89\) 12.6840i 1.34450i 0.740322 + 0.672252i \(0.234673\pi\)
−0.740322 + 0.672252i \(0.765327\pi\)
\(90\) 0 0
\(91\) 5.55691i 0.582523i
\(92\) 3.14849 7.96353i 0.328253 0.830255i
\(93\) 0 0
\(94\) 12.3043 8.36641i 1.26910 0.862929i
\(95\) −2.99427 −0.307205
\(96\) 0 0
\(97\) 0.824101 0.0836747 0.0418374 0.999124i \(-0.486679\pi\)
0.0418374 + 0.999124i \(0.486679\pi\)
\(98\) 1.16947 0.795191i 0.118135 0.0803264i
\(99\) 0 0
\(100\) 3.35089 8.47546i 0.335089 0.847546i
\(101\) 17.8801i 1.77914i 0.456802 + 0.889569i \(0.348995\pi\)
−0.456802 + 0.889569i \(0.651005\pi\)
\(102\) 0 0
\(103\) 12.4983i 1.23149i 0.787945 + 0.615746i \(0.211145\pi\)
−0.787945 + 0.615746i \(0.788855\pi\)
\(104\) 3.43985 + 15.3363i 0.337305 + 1.50385i
\(105\) 0 0
\(106\) 8.43234 + 12.4013i 0.819022 + 1.20452i
\(107\) 13.3936 1.29481 0.647403 0.762148i \(-0.275855\pi\)
0.647403 + 0.762148i \(0.275855\pi\)
\(108\) 0 0
\(109\) −6.11727 −0.585928 −0.292964 0.956123i \(-0.594642\pi\)
−0.292964 + 0.956123i \(0.594642\pi\)
\(110\) −1.10090 1.61908i −0.104967 0.154373i
\(111\) 0 0
\(112\) −2.73534 + 2.91855i −0.258465 + 0.275777i
\(113\) 3.61602i 0.340167i −0.985430 0.170083i \(-0.945596\pi\)
0.985430 0.170083i \(-0.0544037\pi\)
\(114\) 0 0
\(115\) 2.85008i 0.265771i
\(116\) 2.63031 + 1.03993i 0.244218 + 0.0965551i
\(117\) 0 0
\(118\) −15.8061 + 10.7474i −1.45507 + 0.989380i
\(119\) −2.16278 −0.198262
\(120\) 0 0
\(121\) −6.67418 −0.606744
\(122\) 0.719867 0.489478i 0.0651737 0.0443152i
\(123\) 0 0
\(124\) 12.3043 + 4.86469i 1.10496 + 0.436862i
\(125\) 6.36153i 0.568993i
\(126\) 0 0
\(127\) 8.17246i 0.725189i −0.931947 0.362594i \(-0.881891\pi\)
0.931947 0.362594i \(-0.118109\pi\)
\(128\) 5.74251 9.74801i 0.507571 0.861610i
\(129\) 0 0
\(130\) −2.94137 4.32582i −0.257975 0.379399i
\(131\) 2.99427 0.261610 0.130805 0.991408i \(-0.458244\pi\)
0.130805 + 0.991408i \(0.458244\pi\)
\(132\) 0 0
\(133\) 4.49828 0.390050
\(134\) 11.1766 + 16.4372i 0.965508 + 1.41996i
\(135\) 0 0
\(136\) 5.96896 1.33881i 0.511834 0.114802i
\(137\) 10.7700i 0.920144i 0.887882 + 0.460072i \(0.152176\pi\)
−0.887882 + 0.460072i \(0.847824\pi\)
\(138\) 0 0
\(139\) 16.0000i 1.35710i −0.734553 0.678551i \(-0.762608\pi\)
0.734553 0.678551i \(-0.237392\pi\)
\(140\) 0.489478 1.23804i 0.0413684 0.104634i
\(141\) 0 0
\(142\) 18.2384 12.4013i 1.53053 1.04069i
\(143\) 11.5576 0.966496
\(144\) 0 0
\(145\) −0.941367 −0.0781763
\(146\) 13.9611 9.49294i 1.15543 0.785641i
\(147\) 0 0
\(148\) −4.00000 + 10.1173i −0.328798 + 0.831634i
\(149\) 2.57967i 0.211335i 0.994402 + 0.105667i \(0.0336979\pi\)
−0.994402 + 0.105667i \(0.966302\pi\)
\(150\) 0 0
\(151\) 5.23109i 0.425700i −0.977085 0.212850i \(-0.931725\pi\)
0.977085 0.212850i \(-0.0682746\pi\)
\(152\) −12.4146 + 2.78454i −1.00696 + 0.225856i
\(153\) 0 0
\(154\) 1.65389 + 2.43234i 0.133274 + 0.196004i
\(155\) −4.40362 −0.353707
\(156\) 0 0
\(157\) −5.61211 −0.447895 −0.223948 0.974601i \(-0.571894\pi\)
−0.223948 + 0.974601i \(0.571894\pi\)
\(158\) 0.655318 + 0.963765i 0.0521343 + 0.0766730i
\(159\) 0 0
\(160\) −0.584512 + 3.71982i −0.0462097 + 0.294078i
\(161\) 4.28167i 0.337443i
\(162\) 0 0
\(163\) 8.17246i 0.640117i 0.947398 + 0.320058i \(0.103703\pi\)
−0.947398 + 0.320058i \(0.896297\pi\)
\(164\) −10.5938 4.18842i −0.827240 0.327061i
\(165\) 0 0
\(166\) 7.43965 5.05863i 0.577429 0.392626i
\(167\) −16.5098 −1.27757 −0.638783 0.769387i \(-0.720562\pi\)
−0.638783 + 0.769387i \(0.720562\pi\)
\(168\) 0 0
\(169\) 17.8793 1.37533
\(170\) −1.68363 + 1.14480i −0.129129 + 0.0878018i
\(171\) 0 0
\(172\) −3.93793 1.55691i −0.300264 0.118714i
\(173\) 4.19875i 0.319225i −0.987180 0.159613i \(-0.948976\pi\)
0.987180 0.159613i \(-0.0510245\pi\)
\(174\) 0 0
\(175\) 4.55691i 0.344470i
\(176\) −6.07017 5.68913i −0.457556 0.428834i
\(177\) 0 0
\(178\) −10.0862 14.8337i −0.755995 1.11183i
\(179\) 2.07986 0.155456 0.0777280 0.996975i \(-0.475233\pi\)
0.0777280 + 0.996975i \(0.475233\pi\)
\(180\) 0 0
\(181\) −11.4396 −0.850302 −0.425151 0.905122i \(-0.639779\pi\)
−0.425151 + 0.905122i \(0.639779\pi\)
\(182\) 4.41881 + 6.49867i 0.327544 + 0.481713i
\(183\) 0 0
\(184\) 2.65045 + 11.8168i 0.195394 + 0.871146i
\(185\) 3.62088i 0.266213i
\(186\) 0 0
\(187\) 4.49828i 0.328947i
\(188\) −7.73671 + 19.5686i −0.564258 + 1.42719i
\(189\) 0 0
\(190\) 3.50172 2.38101i 0.254041 0.172737i
\(191\) −8.44139 −0.610798 −0.305399 0.952225i \(-0.598790\pi\)
−0.305399 + 0.952225i \(0.598790\pi\)
\(192\) 0 0
\(193\) 9.67418 0.696363 0.348181 0.937427i \(-0.386799\pi\)
0.348181 + 0.937427i \(0.386799\pi\)
\(194\) −0.963765 + 0.655318i −0.0691943 + 0.0470491i
\(195\) 0 0
\(196\) −0.735342 + 1.85991i −0.0525244 + 0.132851i
\(197\) 13.4326i 0.957033i −0.878079 0.478516i \(-0.841175\pi\)
0.878079 0.478516i \(-0.158825\pi\)
\(198\) 0 0
\(199\) 27.1138i 1.92205i 0.276464 + 0.961024i \(0.410837\pi\)
−0.276464 + 0.961024i \(0.589163\pi\)
\(200\) 2.82083 + 12.5764i 0.199463 + 0.889288i
\(201\) 0 0
\(202\) −14.2181 20.9103i −1.00038 1.47125i
\(203\) 1.41421 0.0992583
\(204\) 0 0
\(205\) 3.79145 0.264806
\(206\) −9.93852 14.6164i −0.692450 1.01837i
\(207\) 0 0
\(208\) −16.2181 15.2001i −1.12452 1.05393i
\(209\) 9.35580i 0.647154i
\(210\) 0 0
\(211\) 11.1138i 0.765108i −0.923933 0.382554i \(-0.875045\pi\)
0.923933 0.382554i \(-0.124955\pi\)
\(212\) −19.7228 7.79769i −1.35457 0.535547i
\(213\) 0 0
\(214\) −15.6634 + 10.6504i −1.07073 + 0.728050i
\(215\) 1.40935 0.0961170
\(216\) 0 0
\(217\) 6.61555 0.449093
\(218\) 7.15399 4.86440i 0.484529 0.329459i
\(219\) 0 0
\(220\) 2.57496 + 1.01805i 0.173604 + 0.0686366i
\(221\) 12.0184i 0.808444i
\(222\) 0 0
\(223\) 6.87930i 0.460672i 0.973111 + 0.230336i \(0.0739825\pi\)
−0.973111 + 0.230336i \(0.926018\pi\)
\(224\) 0.878111 5.58828i 0.0586713 0.373383i
\(225\) 0 0
\(226\) 2.87543 + 4.22885i 0.191271 + 0.281299i
\(227\) 5.19608 0.344876 0.172438 0.985020i \(-0.444836\pi\)
0.172438 + 0.985020i \(0.444836\pi\)
\(228\) 0 0
\(229\) 5.55691 0.367211 0.183606 0.983000i \(-0.441223\pi\)
0.183606 + 0.983000i \(0.441223\pi\)
\(230\) −2.26636 3.33310i −0.149439 0.219778i
\(231\) 0 0
\(232\) −3.90303 + 0.875430i −0.256246 + 0.0574748i
\(233\) 24.1197i 1.58013i −0.613021 0.790067i \(-0.710046\pi\)
0.613021 0.790067i \(-0.289954\pi\)
\(234\) 0 0
\(235\) 7.00344i 0.456854i
\(236\) 9.93852 25.1377i 0.646943 1.63632i
\(237\) 0 0
\(238\) 2.52932 1.71982i 0.163951 0.111480i
\(239\) 8.44139 0.546028 0.273014 0.962010i \(-0.411979\pi\)
0.273014 + 0.962010i \(0.411979\pi\)
\(240\) 0 0
\(241\) −25.8207 −1.66326 −0.831628 0.555334i \(-0.812591\pi\)
−0.831628 + 0.555334i \(0.812591\pi\)
\(242\) 7.80528 5.30725i 0.501743 0.341163i
\(243\) 0 0
\(244\) −0.452638 + 1.14486i −0.0289772 + 0.0732924i
\(245\) 0.665647i 0.0425266i
\(246\) 0 0
\(247\) 24.9966i 1.59049i
\(248\) −18.2580 + 4.09517i −1.15938 + 0.260044i
\(249\) 0 0
\(250\) −5.05863 7.43965i −0.319936 0.470525i
\(251\) 19.8770 1.25463 0.627314 0.778766i \(-0.284154\pi\)
0.627314 + 0.778766i \(0.284154\pi\)
\(252\) 0 0
\(253\) 8.90528 0.559870
\(254\) 6.49867 + 9.55749i 0.407763 + 0.599690i
\(255\) 0 0
\(256\) 1.03581 + 15.9664i 0.0647382 + 0.997902i
\(257\) 21.3352i 1.33085i −0.746465 0.665425i \(-0.768250\pi\)
0.746465 0.665425i \(-0.231750\pi\)
\(258\) 0 0
\(259\) 5.43965i 0.338003i
\(260\) 6.87971 + 2.71999i 0.426661 + 0.168686i
\(261\) 0 0
\(262\) −3.50172 + 2.38101i −0.216337 + 0.147100i
\(263\) −19.7551 −1.21815 −0.609076 0.793112i \(-0.708459\pi\)
−0.609076 + 0.793112i \(0.708459\pi\)
\(264\) 0 0
\(265\) 7.05863 0.433608
\(266\) −5.26063 + 3.57699i −0.322550 + 0.219320i
\(267\) 0 0
\(268\) −26.1414 10.3354i −1.59684 0.631333i
\(269\) 2.62356i 0.159961i 0.996796 + 0.0799806i \(0.0254858\pi\)
−0.996796 + 0.0799806i \(0.974514\pi\)
\(270\) 0 0
\(271\) 0.732814i 0.0445153i 0.999752 + 0.0222576i \(0.00708541\pi\)
−0.999752 + 0.0222576i \(0.992915\pi\)
\(272\) −5.91594 + 6.31217i −0.358707 + 0.382732i
\(273\) 0 0
\(274\) −8.56422 12.5953i −0.517383 0.760907i
\(275\) 9.47775 0.571530
\(276\) 0 0
\(277\) 11.4396 0.687342 0.343671 0.939090i \(-0.388330\pi\)
0.343671 + 0.939090i \(0.388330\pi\)
\(278\) 12.7231 + 18.7116i 0.763078 + 1.12225i
\(279\) 0 0
\(280\) 0.412050 + 1.83709i 0.0246247 + 0.109787i
\(281\) 0.875377i 0.0522206i 0.999659 + 0.0261103i \(0.00831212\pi\)
−0.999659 + 0.0261103i \(0.991688\pi\)
\(282\) 0 0
\(283\) 22.4914i 1.33698i 0.743723 + 0.668488i \(0.233058\pi\)
−0.743723 + 0.668488i \(0.766942\pi\)
\(284\) −11.4679 + 29.0060i −0.680497 + 1.72119i
\(285\) 0 0
\(286\) −13.5163 + 9.19051i −0.799237 + 0.543446i
\(287\) −5.69588 −0.336217
\(288\) 0 0
\(289\) 12.3224 0.724846
\(290\) 1.10090 0.748567i 0.0646473 0.0439573i
\(291\) 0 0
\(292\) −8.77846 + 22.2035i −0.513720 + 1.29936i
\(293\) 24.2416i 1.41621i −0.706106 0.708106i \(-0.749550\pi\)
0.706106 0.708106i \(-0.250450\pi\)
\(294\) 0 0
\(295\) 8.99656i 0.523800i
\(296\) −3.36726 15.0127i −0.195718 0.872593i
\(297\) 0 0
\(298\) −2.05133 3.01686i −0.118830 0.174762i
\(299\) 23.7929 1.37598
\(300\) 0 0
\(301\) −2.11727 −0.122037
\(302\) 4.15972 + 6.11763i 0.239365 + 0.352030i
\(303\) 0 0
\(304\) 12.3043 13.1284i 0.705702 0.752967i
\(305\) 0.409737i 0.0234615i
\(306\) 0 0
\(307\) 7.61211i 0.434446i −0.976122 0.217223i \(-0.930300\pi\)
0.976122 0.217223i \(-0.0696999\pi\)
\(308\) −3.86836 1.52941i −0.220420 0.0871461i
\(309\) 0 0
\(310\) 5.14992 3.50172i 0.292496 0.198884i
\(311\) −13.5155 −0.766395 −0.383197 0.923666i \(-0.625177\pi\)
−0.383197 + 0.923666i \(0.625177\pi\)
\(312\) 0 0
\(313\) −7.64820 −0.432302 −0.216151 0.976360i \(-0.569350\pi\)
−0.216151 + 0.976360i \(0.569350\pi\)
\(314\) 6.56322 4.46270i 0.370384 0.251845i
\(315\) 0 0
\(316\) −1.53275 0.605995i −0.0862242 0.0340899i
\(317\) 29.7765i 1.67242i 0.548411 + 0.836209i \(0.315233\pi\)
−0.548411 + 0.836209i \(0.684767\pi\)
\(318\) 0 0
\(319\) 2.94137i 0.164685i
\(320\) −2.27440 4.81504i −0.127143 0.269169i
\(321\) 0 0
\(322\) 3.40475 + 5.00730i 0.189739 + 0.279046i
\(323\) 9.72879 0.541325
\(324\) 0 0
\(325\) 25.3224 1.40463
\(326\) −6.49867 9.55749i −0.359928 0.529340i
\(327\) 0 0
\(328\) 15.7198 3.52588i 0.867982 0.194684i
\(329\) 10.5213i 0.580055i
\(330\) 0 0
\(331\) 11.1138i 0.610871i −0.952213 0.305436i \(-0.901198\pi\)
0.952213 0.305436i \(-0.0988021\pi\)
\(332\) −4.67790 + 11.8319i −0.256733 + 0.649359i
\(333\) 0 0
\(334\) 19.3078 13.1284i 1.05647 0.718356i
\(335\) 9.35580 0.511162
\(336\) 0 0
\(337\) −5.88273 −0.320453 −0.160226 0.987080i \(-0.551222\pi\)
−0.160226 + 0.987080i \(0.551222\pi\)
\(338\) −20.9094 + 14.2175i −1.13732 + 0.773328i
\(339\) 0 0
\(340\) 1.05863 2.67762i 0.0574124 0.145214i
\(341\) 13.7594i 0.745114i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 5.84335 1.31064i 0.315052 0.0706647i
\(345\) 0 0
\(346\) 3.33881 + 4.91033i 0.179495 + 0.263981i
\(347\) −10.6432 −0.571357 −0.285678 0.958326i \(-0.592219\pi\)
−0.285678 + 0.958326i \(0.592219\pi\)
\(348\) 0 0
\(349\) 2.49828 0.133730 0.0668650 0.997762i \(-0.478700\pi\)
0.0668650 + 0.997762i \(0.478700\pi\)
\(350\) 3.62362 + 5.32920i 0.193691 + 0.284857i
\(351\) 0 0
\(352\) 11.6229 + 1.82635i 0.619500 + 0.0973447i
\(353\) 0.126811i 0.00674945i −0.999994 0.00337472i \(-0.998926\pi\)
0.999994 0.00337472i \(-0.00107421\pi\)
\(354\) 0 0
\(355\) 10.3810i 0.550967i
\(356\) 23.5912 + 9.32710i 1.25033 + 0.494335i
\(357\) 0 0
\(358\) −2.43234 + 1.65389i −0.128553 + 0.0874106i
\(359\) −19.7551 −1.04263 −0.521317 0.853363i \(-0.674559\pi\)
−0.521317 + 0.853363i \(0.674559\pi\)
\(360\) 0 0
\(361\) −1.23453 −0.0649754
\(362\) 13.3784 9.09671i 0.703152 0.478112i
\(363\) 0 0
\(364\) −10.3354 4.08623i −0.541721 0.214177i
\(365\) 7.94645i 0.415936i
\(366\) 0 0
\(367\) 28.7620i 1.50137i −0.660663 0.750683i \(-0.729725\pi\)
0.660663 0.750683i \(-0.270275\pi\)
\(368\) −12.4962 11.7118i −0.651412 0.610521i
\(369\) 0 0
\(370\) 2.87930 + 4.23453i 0.149687 + 0.220143i
\(371\) −10.6042 −0.550541
\(372\) 0 0
\(373\) −0.879296 −0.0455282 −0.0227641 0.999741i \(-0.507247\pi\)
−0.0227641 + 0.999741i \(0.507247\pi\)
\(374\) 3.57699 + 5.26063i 0.184962 + 0.272020i
\(375\) 0 0
\(376\) −6.51289 29.0371i −0.335877 1.49748i
\(377\) 7.85866i 0.404742i
\(378\) 0 0
\(379\) 22.8793i 1.17523i −0.809140 0.587615i \(-0.800067\pi\)
0.809140 0.587615i \(-0.199933\pi\)
\(380\) −2.20181 + 5.56907i −0.112950 + 0.285687i
\(381\) 0 0
\(382\) 9.87199 6.71252i 0.505095 0.343442i
\(383\) 32.3562 1.65333 0.826663 0.562698i \(-0.190237\pi\)
0.826663 + 0.562698i \(0.190237\pi\)
\(384\) 0 0
\(385\) 1.38445 0.0705582
\(386\) −11.3137 + 7.69282i −0.575853 + 0.391554i
\(387\) 0 0
\(388\) 0.605995 1.53275i 0.0307648 0.0778138i
\(389\) 16.3391i 0.828424i 0.910180 + 0.414212i \(0.135943\pi\)
−0.910180 + 0.414212i \(0.864057\pi\)
\(390\) 0 0
\(391\) 9.26031i 0.468314i
\(392\) −0.619022 2.75986i −0.0312653 0.139394i
\(393\) 0 0
\(394\) 10.6815 + 15.7091i 0.538125 + 0.791412i
\(395\) 0.548560 0.0276010
\(396\) 0 0
\(397\) −4.85008 −0.243419 −0.121709 0.992566i \(-0.538838\pi\)
−0.121709 + 0.992566i \(0.538838\pi\)
\(398\) −21.5607 31.7089i −1.08074 1.58943i
\(399\) 0 0
\(400\) −13.2996 12.4647i −0.664978 0.623236i
\(401\) 20.8305i 1.04022i 0.854098 + 0.520112i \(0.174110\pi\)
−0.854098 + 0.520112i \(0.825890\pi\)
\(402\) 0 0
\(403\) 36.7620i 1.83125i
\(404\) 33.2554 + 13.1480i 1.65452 + 0.654137i
\(405\) 0 0
\(406\) −1.65389 + 1.12457i −0.0820810 + 0.0558115i
\(407\) −11.3137 −0.560800
\(408\) 0 0
\(409\) 12.9345 0.639569 0.319785 0.947490i \(-0.396389\pi\)
0.319785 + 0.947490i \(0.396389\pi\)
\(410\) −4.43400 + 3.01493i −0.218980 + 0.148897i
\(411\) 0 0
\(412\) 23.2457 + 9.19051i 1.14523 + 0.452784i
\(413\) 13.5155i 0.665055i
\(414\) 0 0
\(415\) 4.23453i 0.207865i
\(416\) 31.0536 + 4.87959i 1.52253 + 0.239241i
\(417\) 0 0
\(418\) −7.43965 10.9414i −0.363885 0.535160i
\(419\) −14.5519 −0.710906 −0.355453 0.934694i \(-0.615673\pi\)
−0.355453 + 0.934694i \(0.615673\pi\)
\(420\) 0 0
\(421\) −29.9018 −1.45733 −0.728663 0.684872i \(-0.759858\pi\)
−0.728663 + 0.684872i \(0.759858\pi\)
\(422\) 8.83762 + 12.9973i 0.430209 + 0.632701i
\(423\) 0 0
\(424\) 29.2660 6.56422i 1.42128 0.318787i
\(425\) 9.85560i 0.478067i
\(426\) 0 0
\(427\) 0.615547i 0.0297884i
\(428\) 9.84885 24.9109i 0.476062 1.20411i
\(429\) 0 0
\(430\) −1.64820 + 1.12070i −0.0794833 + 0.0540452i
\(431\) 5.86658 0.282583 0.141292 0.989968i \(-0.454874\pi\)
0.141292 + 0.989968i \(0.454874\pi\)
\(432\) 0 0
\(433\) 26.1104 1.25479 0.627393 0.778703i \(-0.284122\pi\)
0.627393 + 0.778703i \(0.284122\pi\)
\(434\) −7.73671 + 5.26063i −0.371374 + 0.252518i
\(435\) 0 0
\(436\) −4.49828 + 11.3776i −0.215429 + 0.544887i
\(437\) 19.2602i 0.921338i
\(438\) 0 0
\(439\) 25.9931i 1.24058i −0.784371 0.620292i \(-0.787014\pi\)
0.784371 0.620292i \(-0.212986\pi\)
\(440\) −3.82089 + 0.857007i −0.182154 + 0.0408562i
\(441\) 0 0
\(442\) 9.55691 + 14.0552i 0.454576 + 0.668537i
\(443\) −9.23385 −0.438713 −0.219357 0.975645i \(-0.570396\pi\)
−0.219357 + 0.975645i \(0.570396\pi\)
\(444\) 0 0
\(445\) −8.44309 −0.400241
\(446\) −5.47036 8.04516i −0.259029 0.380949i
\(447\) 0 0
\(448\) 3.41683 + 7.23362i 0.161430 + 0.341757i
\(449\) 33.4755i 1.57981i 0.613232 + 0.789903i \(0.289869\pi\)
−0.613232 + 0.789903i \(0.710131\pi\)
\(450\) 0 0
\(451\) 11.8466i 0.557837i
\(452\) −6.72548 2.65901i −0.316340 0.125069i
\(453\) 0 0
\(454\) −6.07668 + 4.13187i −0.285193 + 0.193918i
\(455\) 3.69894 0.173409
\(456\) 0 0
\(457\) −30.2277 −1.41399 −0.706995 0.707218i \(-0.749950\pi\)
−0.706995 + 0.707218i \(0.749950\pi\)
\(458\) −6.49867 + 4.41881i −0.303663 + 0.206477i
\(459\) 0 0
\(460\) 5.30090 + 2.09578i 0.247156 + 0.0977164i
\(461\) 10.4822i 0.488206i −0.969749 0.244103i \(-0.921507\pi\)
0.969749 0.244103i \(-0.0784935\pi\)
\(462\) 0 0
\(463\) 9.82066i 0.456405i −0.973614 0.228202i \(-0.926715\pi\)
0.973614 0.228202i \(-0.0732848\pi\)
\(464\) 3.86836 4.12745i 0.179584 0.191612i
\(465\) 0 0
\(466\) 19.1798 + 28.2074i 0.888485 + 1.30668i
\(467\) −21.4620 −0.993141 −0.496571 0.867996i \(-0.665408\pi\)
−0.496571 + 0.867996i \(0.665408\pi\)
\(468\) 0 0
\(469\) −14.0552 −0.649009
\(470\) 5.56907 + 8.19034i 0.256882 + 0.377792i
\(471\) 0 0
\(472\) 8.36641 + 37.3009i 0.385095 + 1.71691i
\(473\) 4.40362i 0.202479i
\(474\) 0 0
\(475\) 20.4983i 0.940526i
\(476\) −1.59038 + 4.02258i −0.0728951 + 0.184375i
\(477\) 0 0
\(478\) −9.87199 + 6.71252i −0.451534 + 0.307024i
\(479\) −8.56334 −0.391269 −0.195634 0.980677i \(-0.562677\pi\)
−0.195634 + 0.980677i \(0.562677\pi\)
\(480\) 0 0
\(481\) −30.2277 −1.37826
\(482\) 30.1966 20.5324i 1.37542 0.935224i
\(483\) 0 0
\(484\) −4.90780 + 12.4134i −0.223082 + 0.564245i
\(485\) 0.548560i 0.0249088i
\(486\) 0 0
\(487\) 9.46563i 0.428929i 0.976732 + 0.214464i \(0.0688005\pi\)
−0.976732 + 0.214464i \(0.931199\pi\)
\(488\) −0.381038 1.69882i −0.0172488 0.0769021i
\(489\) 0 0
\(490\) 0.529317 + 0.778457i 0.0239121 + 0.0351671i
\(491\) 19.6260 0.885709 0.442854 0.896593i \(-0.353966\pi\)
0.442854 + 0.896593i \(0.353966\pi\)
\(492\) 0 0
\(493\) 3.05863 0.137754
\(494\) −19.8770 29.2328i −0.894311 1.31525i
\(495\) 0 0
\(496\) 18.0958 19.3078i 0.812525 0.866945i
\(497\) 15.5954i 0.699548i
\(498\) 0 0
\(499\) 2.11727i 0.0947819i −0.998876 0.0473909i \(-0.984909\pi\)
0.998876 0.0473909i \(-0.0150907\pi\)
\(500\) 11.8319 + 4.67790i 0.529138 + 0.209202i
\(501\) 0 0
\(502\) −23.2457 + 15.8061i −1.03751 + 0.705459i
\(503\) 4.03062 0.179717 0.0898583 0.995955i \(-0.471359\pi\)
0.0898583 + 0.995955i \(0.471359\pi\)
\(504\) 0 0
\(505\) −11.9018 −0.529625
\(506\) −10.4145 + 7.08140i −0.462981 + 0.314807i
\(507\) 0 0
\(508\) −15.2001 6.00955i −0.674394 0.266631i
\(509\) 13.6423i 0.604686i 0.953199 + 0.302343i \(0.0977687\pi\)
−0.953199 + 0.302343i \(0.902231\pi\)
\(510\) 0 0
\(511\) 11.9379i 0.528103i
\(512\) −13.9077 17.8487i −0.614640 0.788807i
\(513\) 0 0
\(514\) 16.9655 + 24.9509i 0.748317 + 1.10054i
\(515\) −8.31944 −0.366598
\(516\) 0 0
\(517\) −21.8827 −0.962402
\(518\) −4.32556 6.36153i −0.190054 0.279510i
\(519\) 0 0
\(520\) −10.2086 + 2.28973i −0.447675 + 0.100411i
\(521\) 24.4585i 1.07155i −0.844362 0.535774i \(-0.820020\pi\)
0.844362 0.535774i \(-0.179980\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) 2.20181 5.56907i 0.0961865 0.243286i
\(525\) 0 0
\(526\) 23.1031 15.7091i 1.00734 0.684949i
\(527\) 14.3080 0.623265
\(528\) 0 0
\(529\) −4.66730 −0.202926
\(530\) −8.25489 + 5.61296i −0.358570 + 0.243812i
\(531\) 0 0
\(532\) 3.30777 8.36641i 0.143410 0.362730i
\(533\) 31.6515i 1.37098i
\(534\) 0 0
\(535\) 8.91539i 0.385446i
\(536\) 38.7903 8.70048i 1.67549 0.375803i
\(537\) 0 0
\(538\) −2.08623 3.06819i −0.0899438 0.132279i
\(539\) −2.07986 −0.0895859
\(540\) 0 0
\(541\) 7.20512 0.309772 0.154886 0.987932i \(-0.450499\pi\)
0.154886 + 0.987932i \(0.450499\pi\)
\(542\) −0.582727 0.857007i −0.0250303 0.0368116i
\(543\) 0 0
\(544\) 1.89916 12.0862i 0.0814259 0.518193i
\(545\) 4.07194i 0.174423i
\(546\) 0 0
\(547\) 39.0518i 1.66973i 0.550453 + 0.834866i \(0.314455\pi\)
−0.550453 + 0.834866i \(0.685545\pi\)
\(548\) 20.0313 + 7.91964i 0.855694 + 0.338310i
\(549\) 0 0
\(550\) −11.0840 + 7.53662i −0.472623 + 0.321363i
\(551\) −6.36153 −0.271010
\(552\) 0 0
\(553\) −0.824101 −0.0350443
\(554\) −13.3784 + 9.09671i −0.568393 + 0.386482i
\(555\) 0 0
\(556\) −29.7586 11.7655i −1.26205 0.498967i
\(557\) 3.99874i 0.169432i −0.996405 0.0847161i \(-0.973002\pi\)
0.996405 0.0847161i \(-0.0269983\pi\)
\(558\) 0 0
\(559\) 11.7655i 0.497626i
\(560\) −1.94272 1.82077i −0.0820949 0.0769416i
\(561\) 0 0
\(562\) −0.696092 1.02373i −0.0293629 0.0431835i
\(563\) −39.1372 −1.64944 −0.824718 0.565544i \(-0.808666\pi\)
−0.824718 + 0.565544i \(0.808666\pi\)
\(564\) 0 0
\(565\) 2.40699 0.101263
\(566\) −17.8850 26.3031i −0.751761 1.10560i
\(567\) 0 0
\(568\) −9.65389 43.0410i −0.405068 1.80596i
\(569\) 32.7708i 1.37382i −0.726741 0.686912i \(-0.758966\pi\)
0.726741 0.686912i \(-0.241034\pi\)
\(570\) 0 0
\(571\) 18.8172i 0.787476i −0.919223 0.393738i \(-0.871182\pi\)
0.919223 0.393738i \(-0.128818\pi\)
\(572\) 8.49879 21.4961i 0.355352 0.898798i
\(573\) 0 0
\(574\) 6.66119 4.52932i 0.278033 0.189050i
\(575\) 19.5112 0.813673
\(576\) 0 0
\(577\) −5.00344 −0.208296 −0.104148 0.994562i \(-0.533212\pi\)
−0.104148 + 0.994562i \(0.533212\pi\)
\(578\) −14.4107 + 9.79865i −0.599407 + 0.407570i
\(579\) 0 0
\(580\) −0.692226 + 1.75086i −0.0287431 + 0.0727005i
\(581\) 6.36153i 0.263921i
\(582\) 0 0
\(583\) 22.0552i 0.913433i
\(584\) −7.38984 32.9470i −0.305794 1.36336i
\(585\) 0 0
\(586\) 19.2767 + 28.3500i 0.796315 + 1.17113i
\(587\) 24.8292 1.02481 0.512406 0.858743i \(-0.328754\pi\)
0.512406 + 0.858743i \(0.328754\pi\)
\(588\) 0 0
\(589\) −29.7586 −1.22618
\(590\) −7.15399 10.5213i −0.294525 0.433153i
\(591\) 0 0
\(592\) 15.8759 + 14.8793i 0.652494 + 0.611535i
\(593\) 16.1391i 0.662752i −0.943499 0.331376i \(-0.892487\pi\)
0.943499 0.331376i \(-0.107513\pi\)
\(594\) 0 0
\(595\) 1.43965i 0.0590198i
\(596\) 4.79795 + 1.89694i 0.196532 + 0.0777016i
\(597\) 0 0
\(598\) −27.8252 + 18.9199i −1.13786 + 0.773692i
\(599\) −7.03204 −0.287321 −0.143661 0.989627i \(-0.545887\pi\)
−0.143661 + 0.989627i \(0.545887\pi\)
\(600\) 0 0
\(601\) −2.99656 −0.122232 −0.0611162 0.998131i \(-0.519466\pi\)
−0.0611162 + 0.998131i \(0.519466\pi\)
\(602\) 2.47609 1.68363i 0.100918 0.0686197i
\(603\) 0 0
\(604\) −9.72938 3.84664i −0.395883 0.156518i
\(605\) 4.44265i 0.180619i
\(606\) 0 0
\(607\) 9.46563i 0.384198i −0.981376 0.192099i \(-0.938471\pi\)
0.981376 0.192099i \(-0.0615295\pi\)
\(608\) −3.94999 + 25.1377i −0.160193 + 1.01947i
\(609\) 0 0
\(610\) 0.325819 + 0.479177i 0.0131920 + 0.0194013i
\(611\) −58.4657 −2.36527
\(612\) 0 0
\(613\) 11.2311 0.453620 0.226810 0.973939i \(-0.427170\pi\)
0.226810 + 0.973939i \(0.427170\pi\)
\(614\) 6.05308 + 8.90217i 0.244283 + 0.359262i
\(615\) 0 0
\(616\) 5.74012 1.28748i 0.231276 0.0518740i
\(617\) 37.6352i 1.51514i 0.652756 + 0.757568i \(0.273613\pi\)
−0.652756 + 0.757568i \(0.726387\pi\)
\(618\) 0 0
\(619\) 43.3346i 1.74177i −0.491491 0.870883i \(-0.663548\pi\)
0.491491 0.870883i \(-0.336452\pi\)
\(620\) −3.23816 + 8.19034i −0.130048 + 0.328932i
\(621\) 0 0
\(622\) 15.8061 10.7474i 0.633765 0.430932i
\(623\) 12.6840 0.508175
\(624\) 0 0
\(625\) 18.5500 0.742002
\(626\) 8.94438 6.08178i 0.357489 0.243077i
\(627\) 0 0
\(628\) −4.12682 + 10.4380i −0.164678 + 0.416523i
\(629\) 11.7648i 0.469092i
\(630\) 0 0
\(631\) 18.2897i 0.728103i 0.931379 + 0.364051i \(0.118607\pi\)
−0.931379 + 0.364051i \(0.881393\pi\)
\(632\) 2.27440 0.510137i 0.0904708 0.0202921i
\(633\) 0 0
\(634\) −23.6780 34.8229i −0.940375 1.38299i
\(635\) 5.43997 0.215879
\(636\) 0 0
\(637\) −5.55691 −0.220173
\(638\) −2.33895 3.43985i −0.0925999 0.136185i
\(639\) 0 0
\(640\) 6.48873 + 3.82248i 0.256490 + 0.151097i
\(641\) 14.2251i 0.561856i 0.959729 + 0.280928i \(0.0906422\pi\)
−0.959729 + 0.280928i \(0.909358\pi\)
\(642\) 0 0
\(643\) 38.4914i 1.51795i 0.651118 + 0.758976i \(0.274300\pi\)
−0.651118 + 0.758976i \(0.725700\pi\)
\(644\) −7.96353 3.14849i −0.313807 0.124068i
\(645\) 0 0
\(646\) −11.3776 + 7.73625i −0.447645 + 0.304379i
\(647\) −0.792458 −0.0311547 −0.0155774 0.999879i \(-0.504959\pi\)
−0.0155774 + 0.999879i \(0.504959\pi\)
\(648\) 0 0
\(649\) 28.1104 1.10343
\(650\) −29.6139 + 20.1361i −1.16155 + 0.789804i
\(651\) 0 0
\(652\) 15.2001 + 6.00955i 0.595280 + 0.235352i
\(653\) 7.85380i 0.307343i 0.988122 + 0.153672i \(0.0491098\pi\)
−0.988122 + 0.153672i \(0.950890\pi\)
\(654\) 0 0
\(655\) 1.99312i 0.0778778i
\(656\) −15.5802 + 16.6237i −0.608304 + 0.649046i
\(657\) 0 0
\(658\) −8.36641 12.3043i −0.326156 0.479673i
\(659\) −13.3936 −0.521739 −0.260870 0.965374i \(-0.584009\pi\)
−0.260870 + 0.965374i \(0.584009\pi\)
\(660\) 0 0
\(661\) 35.2603 1.37147 0.685734 0.727853i \(-0.259482\pi\)
0.685734 + 0.727853i \(0.259482\pi\)
\(662\) 8.83762 + 12.9973i 0.343484 + 0.505156i
\(663\) 0 0
\(664\) −3.93793 17.5569i −0.152821 0.681340i
\(665\) 2.99427i 0.116113i
\(666\) 0 0
\(667\) 6.05520i 0.234458i
\(668\) −12.1403 + 30.7067i −0.469724 + 1.18808i
\(669\) 0 0
\(670\) −10.9414 + 7.43965i −0.422702 + 0.287419i
\(671\) −1.28025 −0.0494236
\(672\) 0 0
\(673\) 40.1364 1.54714 0.773572 0.633709i \(-0.218468\pi\)
0.773572 + 0.633709i \(0.218468\pi\)
\(674\) 6.87971 4.67790i 0.264996 0.180186i
\(675\) 0 0
\(676\) 13.1474 33.2539i 0.505669 1.27900i
\(677\) 20.2478i 0.778184i −0.921199 0.389092i \(-0.872789\pi\)
0.921199 0.389092i \(-0.127211\pi\)
\(678\) 0 0
\(679\) 0.824101i 0.0316261i
\(680\) 0.891174 + 3.97322i 0.0341750 + 0.152366i
\(681\) 0 0
\(682\) −10.9414 16.0913i −0.418967 0.616167i
\(683\) 40.6685 1.55614 0.778068 0.628179i \(-0.216200\pi\)
0.778068 + 0.628179i \(0.216200\pi\)
\(684\) 0 0
\(685\) −7.16902 −0.273914
\(686\) −0.795191 1.16947i −0.0303605 0.0446507i
\(687\) 0 0
\(688\) −5.79145 + 6.17934i −0.220797 + 0.235585i
\(689\) 58.9265i 2.24492i
\(690\) 0 0
\(691\) 35.1138i 1.33579i 0.744254 + 0.667896i \(0.232805\pi\)
−0.744254 + 0.667896i \(0.767195\pi\)
\(692\) −7.80931 3.08752i −0.296865 0.117370i
\(693\) 0 0
\(694\) 12.4470 8.46338i 0.472480 0.321265i
\(695\) 10.6504 0.403991
\(696\) 0 0
\(697\) −12.3189 −0.466613
\(698\) −2.92168 + 1.98661i −0.110587 + 0.0751943i
\(699\) 0 0
\(700\) −8.47546 3.35089i −0.320342 0.126652i
\(701\) 6.73939i 0.254543i 0.991868 + 0.127272i \(0.0406220\pi\)
−0.991868 + 0.127272i \(0.959378\pi\)
\(702\) 0 0
\(703\) 24.4691i 0.922868i
\(704\) −15.0449 + 7.10652i −0.567027 + 0.267837i
\(705\) 0 0
\(706\) 0.100839 + 0.148302i 0.00379512 + 0.00558141i
\(707\) 17.8801 0.672451
\(708\) 0 0
\(709\) 24.1104 0.905485 0.452742 0.891641i \(-0.350446\pi\)
0.452742 + 0.891641i \(0.350446\pi\)
\(710\) 8.25489 + 12.1403i 0.309801 + 0.455619i
\(711\) 0 0
\(712\) −35.0061 + 7.85170i −1.31191 + 0.294255i
\(713\) 28.3256i 1.06080i
\(714\) 0 0
\(715\) 7.69328i 0.287713i
\(716\) 1.52941 3.86836i 0.0571567 0.144567i
\(717\) 0 0
\(718\) 23.1031 15.7091i 0.862200 0.586258i
\(719\) −17.1267 −0.638717 −0.319359 0.947634i \(-0.603467\pi\)
−0.319359 + 0.947634i \(0.603467\pi\)
\(720\) 0 0
\(721\) 12.4983 0.465460
\(722\) 1.44375 0.981690i 0.0537310 0.0365347i
\(723\) 0 0
\(724\) −8.41205 + 21.2767i −0.312631 + 0.790744i
\(725\) 6.44445i 0.239341i
\(726\) 0 0
\(727\) 2.72594i 0.101099i 0.998722 + 0.0505497i \(0.0160973\pi\)
−0.998722 + 0.0505497i \(0.983903\pi\)
\(728\) 15.3363 3.43985i 0.568401 0.127489i
\(729\) 0 0
\(730\) 6.31894 + 9.29317i 0.233875 + 0.343955i
\(731\) −4.57918 −0.169367
\(732\) 0 0
\(733\) 46.5535 1.71949 0.859746 0.510722i \(-0.170622\pi\)
0.859746 + 0.510722i \(0.170622\pi\)
\(734\) 22.8713 + 33.6365i 0.844196 + 1.24154i
\(735\) 0 0
\(736\) 23.9272 + 3.75978i 0.881968 + 0.138587i
\(737\) 29.2328i 1.07681i
\(738\) 0 0
\(739\) 18.2897i 0.672799i 0.941719 + 0.336399i \(0.109209\pi\)
−0.941719 + 0.336399i \(0.890791\pi\)
\(740\) −6.73453 2.66259i −0.247566 0.0978787i
\(741\) 0 0
\(742\) 12.4013 8.43234i 0.455266 0.309561i
\(743\) 37.3012 1.36845 0.684225 0.729271i \(-0.260141\pi\)
0.684225 + 0.729271i \(0.260141\pi\)
\(744\) 0 0
\(745\) −1.71715 −0.0629114
\(746\) 1.02831 0.699208i 0.0376493 0.0255998i
\(747\) 0 0
\(748\) −8.36641 3.30777i −0.305906 0.120944i
\(749\) 13.3936i 0.489390i
\(750\) 0 0
\(751\) 12.2345i 0.446444i −0.974768 0.223222i \(-0.928342\pi\)
0.974768 0.223222i \(-0.0716576\pi\)
\(752\) 30.7067 + 28.7792i 1.11976 + 1.04947i
\(753\) 0 0
\(754\) −6.24914 9.19051i −0.227580 0.334699i
\(755\) 3.48206 0.126725
\(756\) 0 0
\(757\) 3.87586 0.140870 0.0704352 0.997516i \(-0.477561\pi\)
0.0704352 + 0.997516i \(0.477561\pi\)
\(758\) 18.1934 + 26.7568i 0.660815 + 0.971849i
\(759\) 0 0
\(760\) −1.85352 8.26375i −0.0672342 0.299758i
\(761\) 33.0219i 1.19704i 0.801107 + 0.598521i \(0.204245\pi\)
−0.801107 + 0.598521i \(0.795755\pi\)
\(762\) 0 0
\(763\) 6.11727i 0.221460i
\(764\) −6.20731 + 15.7002i −0.224572 + 0.568015i
\(765\) 0 0
\(766\) −37.8398 + 25.7294i −1.36721 + 0.929640i
\(767\) 75.1046 2.71187
\(768\) 0 0
\(769\) −23.3415 −0.841715 −0.420858 0.907127i \(-0.638271\pi\)
−0.420858 + 0.907127i \(0.638271\pi\)
\(770\) −1.61908 + 1.10090i −0.0583477 + 0.0396738i
\(771\) 0 0
\(772\) 7.11383 17.9931i 0.256032 0.647587i
\(773\) 31.7783i 1.14299i 0.820606 + 0.571494i \(0.193636\pi\)
−0.820606 + 0.571494i \(0.806364\pi\)
\(774\) 0 0
\(775\) 30.1465i 1.08289i
\(776\) 0.510137 + 2.27440i 0.0183128 + 0.0816462i
\(777\) 0 0
\(778\) −12.9927 19.1081i −0.465811 0.685060i
\(779\) 25.6217 0.917992
\(780\) 0 0
\(781\) −32.4362 −1.16066
\(782\) 7.36372 + 10.8297i 0.263326 + 0.387269i
\(783\) 0 0
\(784\) 2.91855 + 2.73534i 0.104234 + 0.0976908i
\(785\) 3.73568i 0.133332i
\(786\) 0 0
\(787\) 1.64820i 0.0587520i 0.999568 + 0.0293760i \(0.00935202\pi\)
−0.999568 + 0.0293760i \(0.990648\pi\)
\(788\) −24.9834 9.87755i −0.889999 0.351873i
\(789\) 0 0
\(790\) −0.641527 + 0.436210i −0.0228245 + 0.0155197i
\(791\) −3.61602 −0.128571
\(792\) 0 0
\(793\) −3.42054 −0.121467
\(794\) 5.67205 3.85674i 0.201293 0.136871i
\(795\) 0 0
\(796\) 50.4293 + 19.9379i 1.78742 + 0.706681i
\(797\) 20.8376i 0.738107i −0.929408 0.369053i \(-0.879682\pi\)
0.929408 0.369053i \(-0.120318\pi\)
\(798\) 0 0
\(799\) 22.7552i 0.805019i
\(800\) 25.4653 + 4.00148i 0.900335 + 0.141474i
\(801\) 0 0
\(802\) −16.5642 24.3607i −0.584903 0.860207i
\(803\) −24.8292 −0.876204
\(804\) 0 0
\(805\) 2.85008 0.100452
\(806\) −29.2328 42.9923i −1.02968 1.51434i
\(807\) 0 0
\(808\) −49.3465 + 11.0682i −1.73601 + 0.389377i
\(809\) 27.0262i 0.950190i 0.879935 + 0.475095i \(0.157586\pi\)
−0.879935 + 0.475095i \(0.842414\pi\)
\(810\) 0 0
\(811\) 8.65164i 0.303800i −0.988396 0.151900i \(-0.951461\pi\)
0.988396 0.151900i \(-0.0485392\pi\)
\(812\) 1.03993 2.63031i 0.0364944 0.0923059i
\(813\) 0 0
\(814\) 13.2311 8.99656i 0.463750 0.315329i
\(815\) −5.43997 −0.190554
\(816\) 0 0
\(817\) 9.52406 0.333205
\(818\) −15.1266 + 10.2854i −0.528888 + 0.359620i
\(819\) 0 0
\(820\) 2.78801 7.05176i 0.0973615 0.246258i
\(821\) 19.2456i 0.671675i −0.941920 0.335837i \(-0.890981\pi\)
0.941920 0.335837i \(-0.109019\pi\)
\(822\) 0 0
\(823\) 21.4036i 0.746081i 0.927815 + 0.373041i \(0.121685\pi\)
−0.927815 + 0.373041i \(0.878315\pi\)
\(824\) −34.4935 + 7.73671i −1.20164 + 0.269521i
\(825\) 0 0
\(826\) 10.7474 + 15.8061i 0.373951 + 0.549963i
\(827\) −37.4303 −1.30158 −0.650790 0.759258i \(-0.725562\pi\)
−0.650790 + 0.759258i \(0.725562\pi\)
\(828\) 0 0
\(829\) 49.0157 1.70238 0.851192 0.524854i \(-0.175880\pi\)
0.851192 + 0.524854i \(0.175880\pi\)
\(830\) 3.36726 + 4.95218i 0.116879 + 0.171893i
\(831\) 0 0
\(832\) −40.1966 + 18.9870i −1.39357 + 0.658256i
\(833\) 2.16278i 0.0749359i
\(834\) 0 0
\(835\) 10.9897i 0.380314i
\(836\) 17.4010 + 6.87971i 0.601825 + 0.237940i
\(837\) 0 0
\(838\) 17.0180 11.5715i 0.587879 0.399732i
\(839\) 15.9612 0.551043 0.275521 0.961295i \(-0.411150\pi\)
0.275521 + 0.961295i \(0.411150\pi\)
\(840\) 0 0
\(841\) 27.0000 0.931034
\(842\) 34.9694 23.7777i 1.20513 0.819433i
\(843\) 0 0
\(844\) −20.6707 8.17246i −0.711516 0.281308i
\(845\) 11.9013i 0.409417i
\(846\) 0 0
\(847\) 6.67418i 0.229328i
\(848\) −29.0060 + 30.9488i −0.996071 + 1.06278i
\(849\) 0 0
\(850\) 7.83709 + 11.5259i 0.268810 + 0.395334i
\(851\) −23.2908 −0.798398
\(852\) 0 0
\(853\) 5.50172 0.188375 0.0941876 0.995554i \(-0.469975\pi\)
0.0941876 + 0.995554i \(0.469975\pi\)
\(854\) −0.489478 0.719867i −0.0167496 0.0246333i
\(855\) 0 0
\(856\) 8.29092 + 36.9643i 0.283378 + 1.26342i
\(857\) 38.6007i 1.31857i −0.751892 0.659287i \(-0.770858\pi\)
0.751892 0.659287i \(-0.229142\pi\)
\(858\) 0 0
\(859\) 6.14648i 0.209715i 0.994487 + 0.104858i \(0.0334387\pi\)
−0.994487 + 0.104858i \(0.966561\pi\)
\(860\) 1.03636 2.62127i 0.0353394 0.0893846i
\(861\) 0 0
\(862\) −6.86082 + 4.66506i −0.233681 + 0.158892i
\(863\) 41.9631 1.42844 0.714220 0.699922i \(-0.246782\pi\)
0.714220 + 0.699922i \(0.246782\pi\)
\(864\) 0 0
\(865\) 2.79488 0.0950289
\(866\) −30.5354 + 20.7628i −1.03764 + 0.705547i
\(867\) 0 0
\(868\) 4.86469 12.3043i 0.165118 0.417636i
\(869\) 1.71401i 0.0581439i
\(870\) 0 0
\(871\) 78.1035i 2.64644i
\(872\) −3.78672 16.8828i −0.128235 0.571723i
\(873\) 0 0
\(874\) −15.3155 22.5243i −0.518055 0.761894i
\(875\) 6.36153 0.215059
\(876\) 0 0
\(877\) 45.8759 1.54912 0.774559 0.632502i \(-0.217972\pi\)
0.774559 + 0.632502i \(0.217972\pi\)
\(878\) 20.6695 + 30.3983i 0.697562 + 1.02589i
\(879\) 0 0
\(880\) 3.78695 4.04059i 0.127658 0.136208i
\(881\) 39.3323i 1.32514i 0.749000 + 0.662570i \(0.230534\pi\)
−0.749000 + 0.662570i \(0.769466\pi\)
\(882\) 0 0
\(883\) 34.1173i 1.14814i 0.818807 + 0.574069i \(0.194636\pi\)
−0.818807 + 0.574069i \(0.805364\pi\)
\(884\) −22.3531 8.83762i −0.751817 0.297241i
\(885\) 0 0
\(886\) 10.7988 7.34268i 0.362791 0.246682i
\(887\) −35.9674 −1.20767 −0.603833 0.797111i \(-0.706361\pi\)
−0.603833 + 0.797111i \(0.706361\pi\)
\(888\) 0 0
\(889\) −8.17246 −0.274096
\(890\) 9.87397 6.71387i 0.330976 0.225049i
\(891\) 0 0
\(892\) 12.7949 + 5.05863i 0.428404 + 0.169376i
\(893\) 47.3275i 1.58376i
\(894\) 0 0
\(895\) 1.38445i 0.0462771i
\(896\) −9.74801 5.74251i −0.325658 0.191844i
\(897\) 0 0
\(898\) −26.6194 39.1487i −0.888301 1.30641i
\(899\) −9.35580 −0.312033
\(900\) 0 0
\(901\) −22.9345 −0.764059
\(902\) 9.42035 + 13.8543i 0.313663 + 0.461299i
\(903\) 0 0
\(904\) 9.97971 2.23840i 0.331920 0.0744480i
\(905\) 7.61477i 0.253123i
\(906\) 0 0
\(907\) 24.3449i 0.808360i 0.914679 + 0.404180i \(0.132443\pi\)
−0.914679 + 0.404180i \(0.867557\pi\)
\(908\) 3.82089 9.66424i 0.126801 0.320719i
\(909\) 0 0
\(910\) −4.32582 + 2.94137i −0.143400 + 0.0975054i
\(911\) 17.4242 0.577289 0.288645 0.957436i \(-0.406795\pi\)
0.288645 + 0.957436i \(0.406795\pi\)
\(912\) 0 0
\(913\) −13.2311 −0.437885
\(914\) 35.3505 24.0368i 1.16929 0.795066i
\(915\) 0 0
\(916\) 4.08623 10.3354i 0.135013 0.341490i
\(917\) 2.99427i 0.0988794i
\(918\) 0 0
\(919\) 7.22422i 0.238305i −0.992876 0.119152i \(-0.961982\pi\)
0.992876 0.119152i \(-0.0380177\pi\)
\(920\) −7.86581 + 1.76426i −0.259328 + 0.0581660i
\(921\) 0 0
\(922\) 8.33537 + 12.2587i 0.274511 + 0.403719i
\(923\) −86.6622 −2.85252
\(924\) 0 0
\(925\) −24.7880 −0.815025
\(926\) 7.80931 + 11.4850i 0.256630 + 0.377421i
\(927\) 0 0
\(928\) −1.24184 + 7.90303i −0.0407653 + 0.259430i
\(929\) 36.7208i 1.20477i −0.798206 0.602385i \(-0.794217\pi\)
0.798206 0.602385i \(-0.205783\pi\)
\(930\) 0 0
\(931\) 4.49828i 0.147425i
\(932\) −44.8605 17.7362i −1.46945 0.580969i
\(933\) 0 0
\(934\) 25.0992 17.0664i 0.821272 0.558429i
\(935\) 2.99427 0.0979230
\(936\) 0 0
\(937\) −20.6448 −0.674435 −0.337218 0.941427i \(-0.609486\pi\)
−0.337218 + 0.941427i \(0.609486\pi\)
\(938\) 16.4372 11.1766i 0.536693 0.364928i
\(939\) 0 0
\(940\) −13.0258 5.14992i −0.424854 0.167972i
\(941\) 39.9687i 1.30294i 0.758674 + 0.651471i \(0.225848\pi\)
−0.758674 + 0.651471i \(0.774152\pi\)
\(942\) 0 0
\(943\) 24.3879i 0.794179i
\(944\) −39.4456 36.9696i −1.28385 1.20326i
\(945\) 0 0
\(946\) 3.50172 + 5.14992i 0.113851 + 0.167438i
\(947\) −16.1439 −0.524607 −0.262304 0.964985i \(-0.584482\pi\)
−0.262304 + 0.964985i \(0.584482\pi\)
\(948\) 0 0
\(949\) −66.3380 −2.15342
\(950\) −16.3001 23.9722i −0.528844 0.777761i
\(951\) 0 0
\(952\) −1.33881 5.96896i −0.0433911 0.193455i
\(953\) 23.2394i 0.752800i −0.926457 0.376400i \(-0.877162\pi\)
0.926457 0.376400i \(-0.122838\pi\)
\(954\) 0 0
\(955\) 5.61899i 0.181826i
\(956\) 6.20731 15.7002i 0.200759 0.507782i
\(957\) 0 0
\(958\) 10.0146 6.80949i 0.323557 0.220005i
\(959\) 10.7700 0.347782
\(960\) 0 0
\(961\) −12.7655 −0.411789
\(962\) 35.3505 24.0368i 1.13975 0.774977i
\(963\) 0 0
\(964\) −18.9870 + 48.0242i −0.611530 + 1.54675i
\(965\) 6.43959i 0.207298i
\(966\) 0 0
\(967\) 16.0483i 0.516079i −0.966134 0.258040i \(-0.916924\pi\)
0.966134 0.258040i \(-0.0830765\pi\)
\(968\) −4.13147 18.4198i −0.132790 0.592034i
\(969\) 0 0
\(970\) −0.436210 0.641527i −0.0140059 0.0205982i
\(971\) −28.8134 −0.924665 −0.462333 0.886707i \(-0.652987\pi\)
−0.462333 + 0.886707i \(0.652987\pi\)
\(972\) 0 0
\(973\) −16.0000 −0.512936
\(974\) −7.52698 11.0698i −0.241180 0.354700i
\(975\) 0 0
\(976\) 1.79650 + 1.68373i 0.0575047 + 0.0538950i
\(977\) 35.3043i 1.12948i 0.825267 + 0.564742i \(0.191024\pi\)
−0.825267 + 0.564742i \(0.808976\pi\)
\(978\) 0 0
\(979\) 26.3810i 0.843141i
\(980\) −1.23804 0.489478i −0.0395479 0.0156358i
\(981\) 0 0
\(982\) −22.9521 + 15.6064i −0.732431 + 0.498021i
\(983\) 10.2774 0.327797 0.163898 0.986477i \(-0.447593\pi\)
0.163898 + 0.986477i \(0.447593\pi\)
\(984\) 0 0
\(985\) 8.94137 0.284896
\(986\) −3.57699 + 2.43220i −0.113915 + 0.0774570i
\(987\) 0 0
\(988\) 46.4914 + 18.3810i 1.47909 + 0.584778i
\(989\) 9.06543i 0.288264i
\(990\) 0 0
\(991\) 57.2173i 1.81757i −0.417266 0.908784i \(-0.637012\pi\)
0.417266 0.908784i \(-0.362988\pi\)
\(992\) −5.80919 + 36.9696i −0.184442 + 1.17378i
\(993\) 0 0
\(994\) −12.4013 18.2384i −0.393346 0.578487i
\(995\) −18.0482 −0.572168
\(996\) 0 0
\(997\) 5.73625 0.181669 0.0908345 0.995866i \(-0.471047\pi\)
0.0908345 + 0.995866i \(0.471047\pi\)
\(998\) 1.68363 + 2.47609i 0.0532944 + 0.0783792i
\(999\) 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 252.2.e.a.71.4 yes 12
3.2 odd 2 inner 252.2.e.a.71.9 yes 12
4.3 odd 2 inner 252.2.e.a.71.10 yes 12
7.6 odd 2 1764.2.e.g.1079.4 12
8.3 odd 2 4032.2.h.h.575.6 12
8.5 even 2 4032.2.h.h.575.5 12
12.11 even 2 inner 252.2.e.a.71.3 12
21.20 even 2 1764.2.e.g.1079.9 12
24.5 odd 2 4032.2.h.h.575.7 12
24.11 even 2 4032.2.h.h.575.8 12
28.27 even 2 1764.2.e.g.1079.10 12
84.83 odd 2 1764.2.e.g.1079.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.e.a.71.3 12 12.11 even 2 inner
252.2.e.a.71.4 yes 12 1.1 even 1 trivial
252.2.e.a.71.9 yes 12 3.2 odd 2 inner
252.2.e.a.71.10 yes 12 4.3 odd 2 inner
1764.2.e.g.1079.3 12 84.83 odd 2
1764.2.e.g.1079.4 12 7.6 odd 2
1764.2.e.g.1079.9 12 21.20 even 2
1764.2.e.g.1079.10 12 28.27 even 2
4032.2.h.h.575.5 12 8.5 even 2
4032.2.h.h.575.6 12 8.3 odd 2
4032.2.h.h.575.7 12 24.5 odd 2
4032.2.h.h.575.8 12 24.11 even 2