Properties

Label 576.2.y.a.47.4
Level $576$
Weight $2$
Character 576.47
Analytic conductor $4.599$
Analytic rank $0$
Dimension $88$
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] = [576,2,Mod(47,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.y (of order \(12\), degree \(4\), 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: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 47.4
Character \(\chi\) \(=\) 576.47
Dual form 576.2.y.a.527.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38573 + 1.03912i) q^{3} +(0.310357 - 1.15827i) q^{5} +(-0.356047 + 0.616691i) q^{7} +(0.840471 - 2.87986i) q^{9} +O(q^{10})\) \(q+(-1.38573 + 1.03912i) q^{3} +(0.310357 - 1.15827i) q^{5} +(-0.356047 + 0.616691i) q^{7} +(0.840471 - 2.87986i) q^{9} +(0.611314 + 2.28146i) q^{11} +(-1.31401 + 4.90394i) q^{13} +(0.773508 + 1.92754i) q^{15} -0.863180i q^{17} +(0.539682 - 0.539682i) q^{19} +(-0.147431 - 1.22454i) q^{21} +(0.689728 - 0.398215i) q^{23} +(3.08486 + 1.78104i) q^{25} +(1.82785 + 4.86405i) q^{27} +(2.22809 + 8.31534i) q^{29} +(-4.18508 + 2.41626i) q^{31} +(-3.21781 - 2.52625i) q^{33} +(0.603793 + 0.603793i) q^{35} +(-6.95600 + 6.95600i) q^{37} +(-3.27492 - 8.16093i) q^{39} +(3.17027 + 5.49108i) q^{41} +(-12.0362 + 3.22509i) q^{43} +(-3.07481 - 1.86728i) q^{45} +(1.31575 - 2.27895i) q^{47} +(3.24646 + 5.62304i) q^{49} +(0.896946 + 1.19613i) q^{51} +(-8.87081 - 8.87081i) q^{53} +2.83227 q^{55} +(-0.187058 + 1.30864i) q^{57} +(12.7025 + 3.40363i) q^{59} +(0.548319 - 0.146922i) q^{61} +(1.47674 + 1.54368i) q^{63} +(5.27228 + 3.04395i) q^{65} +(6.89625 + 1.84784i) q^{67} +(-0.541982 + 1.26852i) q^{69} -3.03550i q^{71} -11.6817i q^{73} +(-6.12548 + 0.737491i) q^{75} +(-1.62461 - 0.435313i) q^{77} +(-0.841919 - 0.486082i) q^{79} +(-7.58722 - 4.84088i) q^{81} +(11.1696 - 2.99289i) q^{83} +(-0.999796 - 0.267894i) q^{85} +(-11.7281 - 9.20754i) q^{87} +4.35531 q^{89} +(-2.55637 - 2.55637i) q^{91} +(3.28860 - 7.69706i) q^{93} +(-0.457603 - 0.792591i) q^{95} +(-2.89654 + 5.01695i) q^{97} +(7.08407 + 0.156998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 0
\(3\) −1.38573 + 1.03912i −0.800049 + 0.599935i
\(4\) 0 0
\(5\) 0.310357 1.15827i 0.138796 0.517994i −0.861157 0.508339i \(-0.830260\pi\)
0.999953 0.00965542i \(-0.00307346\pi\)
\(6\) 0 0
\(7\) −0.356047 + 0.616691i −0.134573 + 0.233087i −0.925434 0.378908i \(-0.876300\pi\)
0.790861 + 0.611996i \(0.209633\pi\)
\(8\) 0 0
\(9\) 0.840471 2.87986i 0.280157 0.959954i
\(10\) 0 0
\(11\) 0.611314 + 2.28146i 0.184318 + 0.687885i 0.994775 + 0.102087i \(0.0325521\pi\)
−0.810457 + 0.585798i \(0.800781\pi\)
\(12\) 0 0
\(13\) −1.31401 + 4.90394i −0.364440 + 1.36011i 0.503738 + 0.863857i \(0.331958\pi\)
−0.868178 + 0.496253i \(0.834709\pi\)
\(14\) 0 0
\(15\) 0.773508 + 1.92754i 0.199719 + 0.497689i
\(16\) 0 0
\(17\) 0.863180i 0.209352i −0.994506 0.104676i \(-0.966619\pi\)
0.994506 0.104676i \(-0.0333806\pi\)
\(18\) 0 0
\(19\) 0.539682 0.539682i 0.123811 0.123811i −0.642486 0.766297i \(-0.722097\pi\)
0.766297 + 0.642486i \(0.222097\pi\)
\(20\) 0 0
\(21\) −0.147431 1.22454i −0.0321721 0.267216i
\(22\) 0 0
\(23\) 0.689728 0.398215i 0.143818 0.0830335i −0.426364 0.904552i \(-0.640206\pi\)
0.570182 + 0.821518i \(0.306872\pi\)
\(24\) 0 0
\(25\) 3.08486 + 1.78104i 0.616972 + 0.356209i
\(26\) 0 0
\(27\) 1.82785 + 4.86405i 0.351770 + 0.936086i
\(28\) 0 0
\(29\) 2.22809 + 8.31534i 0.413746 + 1.54412i 0.787335 + 0.616526i \(0.211460\pi\)
−0.373589 + 0.927594i \(0.621873\pi\)
\(30\) 0 0
\(31\) −4.18508 + 2.41626i −0.751663 + 0.433973i −0.826295 0.563238i \(-0.809555\pi\)
0.0746314 + 0.997211i \(0.476222\pi\)
\(32\) 0 0
\(33\) −3.21781 2.52625i −0.560150 0.439763i
\(34\) 0 0
\(35\) 0.603793 + 0.603793i 0.102060 + 0.102060i
\(36\) 0 0
\(37\) −6.95600 + 6.95600i −1.14356 + 1.14356i −0.155765 + 0.987794i \(0.549784\pi\)
−0.987794 + 0.155765i \(0.950216\pi\)
\(38\) 0 0
\(39\) −3.27492 8.16093i −0.524407 1.30679i
\(40\) 0 0
\(41\) 3.17027 + 5.49108i 0.495114 + 0.857562i 0.999984 0.00563304i \(-0.00179306\pi\)
−0.504870 + 0.863195i \(0.668460\pi\)
\(42\) 0 0
\(43\) −12.0362 + 3.22509i −1.83550 + 0.491822i −0.998468 0.0553283i \(-0.982379\pi\)
−0.837035 + 0.547150i \(0.815713\pi\)
\(44\) 0 0
\(45\) −3.07481 1.86728i −0.458366 0.278358i
\(46\) 0 0
\(47\) 1.31575 2.27895i 0.191923 0.332420i −0.753965 0.656915i \(-0.771861\pi\)
0.945887 + 0.324495i \(0.105194\pi\)
\(48\) 0 0
\(49\) 3.24646 + 5.62304i 0.463780 + 0.803291i
\(50\) 0 0
\(51\) 0.896946 + 1.19613i 0.125597 + 0.167492i
\(52\) 0 0
\(53\) −8.87081 8.87081i −1.21850 1.21850i −0.968157 0.250342i \(-0.919457\pi\)
−0.250342 0.968157i \(-0.580543\pi\)
\(54\) 0 0
\(55\) 2.83227 0.381903
\(56\) 0 0
\(57\) −0.187058 + 1.30864i −0.0247765 + 0.173334i
\(58\) 0 0
\(59\) 12.7025 + 3.40363i 1.65373 + 0.443115i 0.960654 0.277749i \(-0.0895885\pi\)
0.693076 + 0.720865i \(0.256255\pi\)
\(60\) 0 0
\(61\) 0.548319 0.146922i 0.0702051 0.0188114i −0.223546 0.974693i \(-0.571763\pi\)
0.293751 + 0.955882i \(0.405096\pi\)
\(62\) 0 0
\(63\) 1.47674 + 1.54368i 0.186052 + 0.194485i
\(64\) 0 0
\(65\) 5.27228 + 3.04395i 0.653946 + 0.377556i
\(66\) 0 0
\(67\) 6.89625 + 1.84784i 0.842511 + 0.225750i 0.654164 0.756352i \(-0.273020\pi\)
0.188347 + 0.982103i \(0.439687\pi\)
\(68\) 0 0
\(69\) −0.541982 + 1.26852i −0.0652470 + 0.152712i
\(70\) 0 0
\(71\) 3.03550i 0.360248i −0.983644 0.180124i \(-0.942350\pi\)
0.983644 0.180124i \(-0.0576499\pi\)
\(72\) 0 0
\(73\) 11.6817i 1.36724i −0.729839 0.683619i \(-0.760405\pi\)
0.729839 0.683619i \(-0.239595\pi\)
\(74\) 0 0
\(75\) −6.12548 + 0.737491i −0.707310 + 0.0851581i
\(76\) 0 0
\(77\) −1.62461 0.435313i −0.185142 0.0496085i
\(78\) 0 0
\(79\) −0.841919 0.486082i −0.0947233 0.0546885i 0.451890 0.892074i \(-0.350750\pi\)
−0.546613 + 0.837385i \(0.684083\pi\)
\(80\) 0 0
\(81\) −7.58722 4.84088i −0.843024 0.537876i
\(82\) 0 0
\(83\) 11.1696 2.99289i 1.22602 0.328512i 0.412994 0.910734i \(-0.364483\pi\)
0.813030 + 0.582221i \(0.197816\pi\)
\(84\) 0 0
\(85\) −0.999796 0.267894i −0.108443 0.0290572i
\(86\) 0 0
\(87\) −11.7281 9.20754i −1.25739 0.987152i
\(88\) 0 0
\(89\) 4.35531 0.461662 0.230831 0.972994i \(-0.425856\pi\)
0.230831 + 0.972994i \(0.425856\pi\)
\(90\) 0 0
\(91\) −2.55637 2.55637i −0.267981 0.267981i
\(92\) 0 0
\(93\) 3.28860 7.69706i 0.341012 0.798148i
\(94\) 0 0
\(95\) −0.457603 0.792591i −0.0469490 0.0813181i
\(96\) 0 0
\(97\) −2.89654 + 5.01695i −0.294099 + 0.509395i −0.974775 0.223190i \(-0.928353\pi\)
0.680676 + 0.732585i \(0.261686\pi\)
\(98\) 0 0
\(99\) 7.08407 + 0.156998i 0.711976 + 0.0157789i
\(100\) 0 0
\(101\) 9.01216 2.41480i 0.896744 0.240282i 0.219127 0.975696i \(-0.429679\pi\)
0.677617 + 0.735415i \(0.263013\pi\)
\(102\) 0 0
\(103\) 2.02100 + 3.50047i 0.199135 + 0.344911i 0.948248 0.317530i \(-0.102854\pi\)
−0.749113 + 0.662442i \(0.769520\pi\)
\(104\) 0 0
\(105\) −1.46410 0.209280i −0.142882 0.0204236i
\(106\) 0 0
\(107\) 7.91703 7.91703i 0.765368 0.765368i −0.211919 0.977287i \(-0.567971\pi\)
0.977287 + 0.211919i \(0.0679712\pi\)
\(108\) 0 0
\(109\) −8.25467 8.25467i −0.790654 0.790654i 0.190946 0.981600i \(-0.438844\pi\)
−0.981600 + 0.190946i \(0.938844\pi\)
\(110\) 0 0
\(111\) 2.41101 16.8672i 0.228843 1.60096i
\(112\) 0 0
\(113\) −6.70455 + 3.87087i −0.630711 + 0.364141i −0.781027 0.624497i \(-0.785304\pi\)
0.150316 + 0.988638i \(0.451971\pi\)
\(114\) 0 0
\(115\) −0.247178 0.922480i −0.0230494 0.0860217i
\(116\) 0 0
\(117\) 13.0183 + 7.90579i 1.20354 + 0.730890i
\(118\) 0 0
\(119\) 0.532316 + 0.307333i 0.0487973 + 0.0281731i
\(120\) 0 0
\(121\) 4.69494 2.71063i 0.426813 0.246421i
\(122\) 0 0
\(123\) −10.0990 4.31484i −0.910596 0.389056i
\(124\) 0 0
\(125\) 7.25990 7.25990i 0.649345 0.649345i
\(126\) 0 0
\(127\) 7.21656i 0.640366i 0.947356 + 0.320183i \(0.103744\pi\)
−0.947356 + 0.320183i \(0.896256\pi\)
\(128\) 0 0
\(129\) 13.3276 16.9761i 1.17343 1.49466i
\(130\) 0 0
\(131\) −1.56297 + 5.83309i −0.136558 + 0.509640i 0.863429 + 0.504470i \(0.168312\pi\)
−0.999987 + 0.00516943i \(0.998355\pi\)
\(132\) 0 0
\(133\) 0.140665 + 0.524969i 0.0121972 + 0.0455206i
\(134\) 0 0
\(135\) 6.20117 0.607551i 0.533711 0.0522897i
\(136\) 0 0
\(137\) 2.72483 4.71954i 0.232798 0.403217i −0.725833 0.687871i \(-0.758545\pi\)
0.958630 + 0.284654i \(0.0918787\pi\)
\(138\) 0 0
\(139\) 3.85291 14.3793i 0.326800 1.21963i −0.585691 0.810534i \(-0.699177\pi\)
0.912490 0.409098i \(-0.134157\pi\)
\(140\) 0 0
\(141\) 0.544825 + 4.52523i 0.0458825 + 0.381093i
\(142\) 0 0
\(143\) −11.9914 −1.00277
\(144\) 0 0
\(145\) 10.3229 0.857271
\(146\) 0 0
\(147\) −10.3417 4.41853i −0.852969 0.364434i
\(148\) 0 0
\(149\) 2.98723 11.1485i 0.244724 0.913321i −0.728798 0.684728i \(-0.759921\pi\)
0.973522 0.228593i \(-0.0734125\pi\)
\(150\) 0 0
\(151\) −4.79677 + 8.30825i −0.390355 + 0.676116i −0.992496 0.122274i \(-0.960981\pi\)
0.602141 + 0.798390i \(0.294315\pi\)
\(152\) 0 0
\(153\) −2.48584 0.725479i −0.200968 0.0586515i
\(154\) 0 0
\(155\) 1.49981 + 5.59736i 0.120467 + 0.449591i
\(156\) 0 0
\(157\) −2.82669 + 10.5494i −0.225595 + 0.841931i 0.756571 + 0.653912i \(0.226873\pi\)
−0.982165 + 0.188019i \(0.939793\pi\)
\(158\) 0 0
\(159\) 21.5103 + 3.07470i 1.70588 + 0.243840i
\(160\) 0 0
\(161\) 0.567132i 0.0446963i
\(162\) 0 0
\(163\) −10.4644 + 10.4644i −0.819633 + 0.819633i −0.986055 0.166422i \(-0.946779\pi\)
0.166422 + 0.986055i \(0.446779\pi\)
\(164\) 0 0
\(165\) −3.92475 + 2.94306i −0.305541 + 0.229117i
\(166\) 0 0
\(167\) −11.5061 + 6.64303i −0.890367 + 0.514053i −0.874062 0.485814i \(-0.838523\pi\)
−0.0163043 + 0.999867i \(0.505190\pi\)
\(168\) 0 0
\(169\) −11.0637 6.38764i −0.851056 0.491357i
\(170\) 0 0
\(171\) −1.10062 2.00780i −0.0841667 0.153540i
\(172\) 0 0
\(173\) −1.95118 7.28191i −0.148346 0.553633i −0.999584 0.0288536i \(-0.990814\pi\)
0.851238 0.524780i \(-0.175852\pi\)
\(174\) 0 0
\(175\) −2.19671 + 1.26827i −0.166056 + 0.0958723i
\(176\) 0 0
\(177\) −21.1390 + 8.48292i −1.58890 + 0.637615i
\(178\) 0 0
\(179\) −15.1045 15.1045i −1.12896 1.12896i −0.990346 0.138617i \(-0.955734\pi\)
−0.138617 0.990346i \(-0.544266\pi\)
\(180\) 0 0
\(181\) −3.08895 + 3.08895i −0.229600 + 0.229600i −0.812525 0.582926i \(-0.801908\pi\)
0.582926 + 0.812525i \(0.301908\pi\)
\(182\) 0 0
\(183\) −0.607151 + 0.773361i −0.0448819 + 0.0571685i
\(184\) 0 0
\(185\) 5.89808 + 10.2158i 0.433635 + 0.751078i
\(186\) 0 0
\(187\) 1.96931 0.527675i 0.144010 0.0385874i
\(188\) 0 0
\(189\) −3.65042 0.604609i −0.265529 0.0439788i
\(190\) 0 0
\(191\) −2.50481 + 4.33846i −0.181242 + 0.313920i −0.942304 0.334759i \(-0.891345\pi\)
0.761062 + 0.648679i \(0.224678\pi\)
\(192\) 0 0
\(193\) −2.87512 4.97985i −0.206956 0.358457i 0.743799 0.668404i \(-0.233022\pi\)
−0.950754 + 0.309946i \(0.899689\pi\)
\(194\) 0 0
\(195\) −10.4690 + 1.26043i −0.749697 + 0.0902615i
\(196\) 0 0
\(197\) −0.515447 0.515447i −0.0367240 0.0367240i 0.688506 0.725230i \(-0.258267\pi\)
−0.725230 + 0.688506i \(0.758267\pi\)
\(198\) 0 0
\(199\) 21.6583 1.53532 0.767659 0.640858i \(-0.221421\pi\)
0.767659 + 0.640858i \(0.221421\pi\)
\(200\) 0 0
\(201\) −11.4764 + 4.60541i −0.809486 + 0.324840i
\(202\) 0 0
\(203\) −5.92130 1.58661i −0.415594 0.111358i
\(204\) 0 0
\(205\) 7.34407 1.96784i 0.512932 0.137440i
\(206\) 0 0
\(207\) −0.567107 2.32101i −0.0394166 0.161321i
\(208\) 0 0
\(209\) 1.56118 + 0.901345i 0.107989 + 0.0623473i
\(210\) 0 0
\(211\) −2.24771 0.602272i −0.154739 0.0414621i 0.180618 0.983553i \(-0.442190\pi\)
−0.335357 + 0.942091i \(0.608857\pi\)
\(212\) 0 0
\(213\) 3.15424 + 4.20637i 0.216125 + 0.288216i
\(214\) 0 0
\(215\) 14.9421i 1.01904i
\(216\) 0 0
\(217\) 3.44121i 0.233604i
\(218\) 0 0
\(219\) 12.1386 + 16.1876i 0.820253 + 1.09386i
\(220\) 0 0
\(221\) 4.23299 + 1.13423i 0.284742 + 0.0762963i
\(222\) 0 0
\(223\) 16.3604 + 9.44569i 1.09557 + 0.632530i 0.935055 0.354502i \(-0.115350\pi\)
0.160520 + 0.987033i \(0.448683\pi\)
\(224\) 0 0
\(225\) 7.72190 7.38706i 0.514793 0.492470i
\(226\) 0 0
\(227\) −7.88169 + 2.11189i −0.523126 + 0.140171i −0.510712 0.859752i \(-0.670618\pi\)
−0.0124139 + 0.999923i \(0.503952\pi\)
\(228\) 0 0
\(229\) −7.31287 1.95948i −0.483248 0.129486i 0.00896646 0.999960i \(-0.497146\pi\)
−0.492215 + 0.870474i \(0.663813\pi\)
\(230\) 0 0
\(231\) 2.70361 1.08494i 0.177884 0.0713836i
\(232\) 0 0
\(233\) 6.77947 0.444138 0.222069 0.975031i \(-0.428719\pi\)
0.222069 + 0.975031i \(0.428719\pi\)
\(234\) 0 0
\(235\) −2.23129 2.23129i −0.145553 0.145553i
\(236\) 0 0
\(237\) 1.67177 0.201276i 0.108593 0.0130743i
\(238\) 0 0
\(239\) −9.48431 16.4273i −0.613489 1.06259i −0.990648 0.136445i \(-0.956432\pi\)
0.377159 0.926149i \(-0.376901\pi\)
\(240\) 0 0
\(241\) 0.0512556 0.0887774i 0.00330167 0.00571865i −0.864370 0.502857i \(-0.832282\pi\)
0.867672 + 0.497138i \(0.165616\pi\)
\(242\) 0 0
\(243\) 15.5440 1.17587i 0.997151 0.0754319i
\(244\) 0 0
\(245\) 7.52056 2.01513i 0.480471 0.128742i
\(246\) 0 0
\(247\) 1.93742 + 3.35571i 0.123275 + 0.213519i
\(248\) 0 0
\(249\) −12.3681 + 15.7539i −0.783794 + 0.998360i
\(250\) 0 0
\(251\) 6.59142 6.59142i 0.416047 0.416047i −0.467792 0.883839i \(-0.654950\pi\)
0.883839 + 0.467792i \(0.154950\pi\)
\(252\) 0 0
\(253\) 1.33015 + 1.33015i 0.0836258 + 0.0836258i
\(254\) 0 0
\(255\) 1.66382 0.667677i 0.104192 0.0418115i
\(256\) 0 0
\(257\) −14.3072 + 8.26024i −0.892456 + 0.515260i −0.874745 0.484583i \(-0.838971\pi\)
−0.0177109 + 0.999843i \(0.505638\pi\)
\(258\) 0 0
\(259\) −1.81304 6.76637i −0.112657 0.420442i
\(260\) 0 0
\(261\) 25.8197 + 0.572217i 1.59820 + 0.0354194i
\(262\) 0 0
\(263\) 22.2913 + 12.8699i 1.37454 + 0.793593i 0.991496 0.130136i \(-0.0415415\pi\)
0.383047 + 0.923729i \(0.374875\pi\)
\(264\) 0 0
\(265\) −13.0279 + 7.52167i −0.800298 + 0.462052i
\(266\) 0 0
\(267\) −6.03526 + 4.52567i −0.369352 + 0.276967i
\(268\) 0 0
\(269\) −4.62506 + 4.62506i −0.281995 + 0.281995i −0.833904 0.551909i \(-0.813899\pi\)
0.551909 + 0.833904i \(0.313899\pi\)
\(270\) 0 0
\(271\) 6.13012i 0.372378i −0.982514 0.186189i \(-0.940386\pi\)
0.982514 0.186189i \(-0.0596137\pi\)
\(272\) 0 0
\(273\) 6.19880 + 0.886060i 0.375168 + 0.0536268i
\(274\) 0 0
\(275\) −2.17756 + 8.12675i −0.131312 + 0.490062i
\(276\) 0 0
\(277\) −0.185077 0.690716i −0.0111202 0.0415011i 0.960143 0.279510i \(-0.0901720\pi\)
−0.971263 + 0.238009i \(0.923505\pi\)
\(278\) 0 0
\(279\) 3.44105 + 14.0833i 0.206010 + 0.843143i
\(280\) 0 0
\(281\) −5.17559 + 8.96438i −0.308750 + 0.534770i −0.978089 0.208187i \(-0.933244\pi\)
0.669339 + 0.742957i \(0.266577\pi\)
\(282\) 0 0
\(283\) 6.79689 25.3663i 0.404033 1.50787i −0.401799 0.915728i \(-0.631615\pi\)
0.805832 0.592144i \(-0.201718\pi\)
\(284\) 0 0
\(285\) 1.45771 + 0.622811i 0.0863471 + 0.0368921i
\(286\) 0 0
\(287\) −4.51507 −0.266516
\(288\) 0 0
\(289\) 16.2549 0.956172
\(290\) 0 0
\(291\) −1.19939 9.96197i −0.0703097 0.583981i
\(292\) 0 0
\(293\) −5.21478 + 19.4618i −0.304651 + 1.13697i 0.628595 + 0.777733i \(0.283630\pi\)
−0.933246 + 0.359239i \(0.883036\pi\)
\(294\) 0 0
\(295\) 7.88465 13.6566i 0.459062 0.795119i
\(296\) 0 0
\(297\) −9.97972 + 7.14362i −0.579082 + 0.414515i
\(298\) 0 0
\(299\) 1.04651 + 3.90564i 0.0605215 + 0.225869i
\(300\) 0 0
\(301\) 2.29657 8.57090i 0.132372 0.494018i
\(302\) 0 0
\(303\) −9.97913 + 12.7109i −0.573286 + 0.730225i
\(304\) 0 0
\(305\) 0.680700i 0.0389768i
\(306\) 0 0
\(307\) 5.92691 5.92691i 0.338267 0.338267i −0.517448 0.855715i \(-0.673118\pi\)
0.855715 + 0.517448i \(0.173118\pi\)
\(308\) 0 0
\(309\) −6.43794 2.75064i −0.366242 0.156478i
\(310\) 0 0
\(311\) −22.5904 + 13.0426i −1.28098 + 0.739576i −0.977028 0.213110i \(-0.931641\pi\)
−0.303956 + 0.952686i \(0.598308\pi\)
\(312\) 0 0
\(313\) 0.538716 + 0.311028i 0.0304500 + 0.0175803i 0.515148 0.857101i \(-0.327737\pi\)
−0.484698 + 0.874682i \(0.661070\pi\)
\(314\) 0 0
\(315\) 2.24631 1.23137i 0.126565 0.0693798i
\(316\) 0 0
\(317\) −3.67189 13.7037i −0.206234 0.769675i −0.989070 0.147447i \(-0.952894\pi\)
0.782836 0.622228i \(-0.213772\pi\)
\(318\) 0 0
\(319\) −17.6090 + 10.1666i −0.985916 + 0.569219i
\(320\) 0 0
\(321\) −2.74411 + 19.1976i −0.153161 + 1.07150i
\(322\) 0 0
\(323\) −0.465843 0.465843i −0.0259202 0.0259202i
\(324\) 0 0
\(325\) −12.7877 + 12.7877i −0.709333 + 0.709333i
\(326\) 0 0
\(327\) 20.0163 + 2.86114i 1.10690 + 0.158221i
\(328\) 0 0
\(329\) 0.936941 + 1.62283i 0.0516552 + 0.0894694i
\(330\) 0 0
\(331\) −10.3567 + 2.77508i −0.569257 + 0.152532i −0.531956 0.846772i \(-0.678543\pi\)
−0.0373014 + 0.999304i \(0.511876\pi\)
\(332\) 0 0
\(333\) 14.1860 + 25.8786i 0.777388 + 1.41814i
\(334\) 0 0
\(335\) 4.28061 7.41423i 0.233874 0.405082i
\(336\) 0 0
\(337\) −5.91237 10.2405i −0.322067 0.557837i 0.658847 0.752277i \(-0.271044\pi\)
−0.980914 + 0.194440i \(0.937711\pi\)
\(338\) 0 0
\(339\) 5.26838 12.3308i 0.286139 0.669716i
\(340\) 0 0
\(341\) −8.07099 8.07099i −0.437069 0.437069i
\(342\) 0 0
\(343\) −9.60823 −0.518795
\(344\) 0 0
\(345\) 1.30108 + 1.02146i 0.0700481 + 0.0549934i
\(346\) 0 0
\(347\) 0.332138 + 0.0889961i 0.0178301 + 0.00477756i 0.267723 0.963496i \(-0.413729\pi\)
−0.249893 + 0.968273i \(0.580395\pi\)
\(348\) 0 0
\(349\) 23.9142 6.40780i 1.28010 0.343001i 0.446207 0.894930i \(-0.352774\pi\)
0.833892 + 0.551928i \(0.186108\pi\)
\(350\) 0 0
\(351\) −26.2548 + 2.57228i −1.40138 + 0.137298i
\(352\) 0 0
\(353\) −5.76381 3.32774i −0.306776 0.177117i 0.338707 0.940892i \(-0.390011\pi\)
−0.645483 + 0.763775i \(0.723344\pi\)
\(354\) 0 0
\(355\) −3.51593 0.942090i −0.186606 0.0500010i
\(356\) 0 0
\(357\) −1.05700 + 0.127260i −0.0559423 + 0.00673530i
\(358\) 0 0
\(359\) 25.7733i 1.36026i −0.733091 0.680130i \(-0.761923\pi\)
0.733091 0.680130i \(-0.238077\pi\)
\(360\) 0 0
\(361\) 18.4175i 0.969341i
\(362\) 0 0
\(363\) −3.68924 + 8.63478i −0.193635 + 0.453208i
\(364\) 0 0
\(365\) −13.5305 3.62550i −0.708221 0.189767i
\(366\) 0 0
\(367\) 10.6689 + 6.15969i 0.556912 + 0.321533i 0.751905 0.659271i \(-0.229135\pi\)
−0.194993 + 0.980805i \(0.562468\pi\)
\(368\) 0 0
\(369\) 18.4781 4.51486i 0.961930 0.235034i
\(370\) 0 0
\(371\) 8.62898 2.31213i 0.447994 0.120040i
\(372\) 0 0
\(373\) 26.8045 + 7.18223i 1.38788 + 0.371882i 0.873978 0.485966i \(-0.161532\pi\)
0.513904 + 0.857848i \(0.328199\pi\)
\(374\) 0 0
\(375\) −2.51634 + 17.6041i −0.129943 + 0.909073i
\(376\) 0 0
\(377\) −43.7057 −2.25096
\(378\) 0 0
\(379\) 20.2758 + 20.2758i 1.04150 + 1.04150i 0.999101 + 0.0423953i \(0.0134989\pi\)
0.0423953 + 0.999101i \(0.486501\pi\)
\(380\) 0 0
\(381\) −7.49885 10.0002i −0.384178 0.512324i
\(382\) 0 0
\(383\) 12.9618 + 22.4505i 0.662317 + 1.14717i 0.980005 + 0.198971i \(0.0637599\pi\)
−0.317689 + 0.948195i \(0.602907\pi\)
\(384\) 0 0
\(385\) −1.00842 + 1.74663i −0.0513938 + 0.0890167i
\(386\) 0 0
\(387\) −0.828267 + 37.3732i −0.0421032 + 1.89979i
\(388\) 0 0
\(389\) 6.90667 1.85064i 0.350182 0.0938310i −0.0794404 0.996840i \(-0.525313\pi\)
0.429622 + 0.903009i \(0.358647\pi\)
\(390\) 0 0
\(391\) −0.343731 0.595360i −0.0173832 0.0301086i
\(392\) 0 0
\(393\) −3.89541 9.70718i −0.196498 0.489662i
\(394\) 0 0
\(395\) −0.824310 + 0.824310i −0.0414756 + 0.0414756i
\(396\) 0 0
\(397\) −14.8178 14.8178i −0.743683 0.743683i 0.229602 0.973285i \(-0.426258\pi\)
−0.973285 + 0.229602i \(0.926258\pi\)
\(398\) 0 0
\(399\) −0.740427 0.581296i −0.0370677 0.0291012i
\(400\) 0 0
\(401\) −4.39082 + 2.53504i −0.219267 + 0.126594i −0.605611 0.795761i \(-0.707071\pi\)
0.386344 + 0.922355i \(0.373738\pi\)
\(402\) 0 0
\(403\) −6.34997 23.6984i −0.316314 1.18050i
\(404\) 0 0
\(405\) −7.96180 + 7.28564i −0.395625 + 0.362026i
\(406\) 0 0
\(407\) −20.1221 11.6175i −0.997416 0.575858i
\(408\) 0 0
\(409\) 20.8923 12.0622i 1.03306 0.596436i 0.115199 0.993342i \(-0.463250\pi\)
0.917859 + 0.396906i \(0.129916\pi\)
\(410\) 0 0
\(411\) 1.12829 + 9.37140i 0.0556545 + 0.462257i
\(412\) 0 0
\(413\) −6.62169 + 6.62169i −0.325832 + 0.325832i
\(414\) 0 0
\(415\) 13.8663i 0.680670i
\(416\) 0 0
\(417\) 9.60265 + 23.9293i 0.470244 + 1.17182i
\(418\) 0 0
\(419\) −5.15499 + 19.2387i −0.251838 + 0.939871i 0.717985 + 0.696059i \(0.245065\pi\)
−0.969822 + 0.243812i \(0.921602\pi\)
\(420\) 0 0
\(421\) −8.46180 31.5799i −0.412403 1.53911i −0.789981 0.613131i \(-0.789910\pi\)
0.377578 0.925978i \(-0.376757\pi\)
\(422\) 0 0
\(423\) −5.45722 5.70459i −0.265339 0.277367i
\(424\) 0 0
\(425\) 1.53736 2.66279i 0.0745731 0.129164i
\(426\) 0 0
\(427\) −0.104622 + 0.390455i −0.00506302 + 0.0188954i
\(428\) 0 0
\(429\) 16.6168 12.4605i 0.802267 0.601597i
\(430\) 0 0
\(431\) 11.5413 0.555923 0.277962 0.960592i \(-0.410341\pi\)
0.277962 + 0.960592i \(0.410341\pi\)
\(432\) 0 0
\(433\) 24.2215 1.16401 0.582006 0.813184i \(-0.302268\pi\)
0.582006 + 0.813184i \(0.302268\pi\)
\(434\) 0 0
\(435\) −14.3047 + 10.7267i −0.685859 + 0.514307i
\(436\) 0 0
\(437\) 0.157324 0.587143i 0.00752585 0.0280868i
\(438\) 0 0
\(439\) 4.47756 7.75537i 0.213702 0.370143i −0.739168 0.673521i \(-0.764781\pi\)
0.952870 + 0.303378i \(0.0981144\pi\)
\(440\) 0 0
\(441\) 18.9221 4.62336i 0.901054 0.220160i
\(442\) 0 0
\(443\) −5.29309 19.7541i −0.251482 0.938545i −0.970014 0.243051i \(-0.921852\pi\)
0.718531 0.695495i \(-0.244815\pi\)
\(444\) 0 0
\(445\) 1.35170 5.04462i 0.0640768 0.239138i
\(446\) 0 0
\(447\) 7.44512 + 18.5529i 0.352142 + 0.877520i
\(448\) 0 0
\(449\) 2.34595i 0.110712i 0.998467 + 0.0553561i \(0.0176294\pi\)
−0.998467 + 0.0553561i \(0.982371\pi\)
\(450\) 0 0
\(451\) −10.5896 + 10.5896i −0.498646 + 0.498646i
\(452\) 0 0
\(453\) −1.98624 16.4974i −0.0933215 0.775113i
\(454\) 0 0
\(455\) −3.75436 + 2.16758i −0.176007 + 0.101618i
\(456\) 0 0
\(457\) 24.1000 + 13.9141i 1.12735 + 0.650876i 0.943267 0.332034i \(-0.107735\pi\)
0.184084 + 0.982911i \(0.441068\pi\)
\(458\) 0 0
\(459\) 4.19855 1.57777i 0.195972 0.0736438i
\(460\) 0 0
\(461\) 5.15168 + 19.2263i 0.239937 + 0.895459i 0.975861 + 0.218394i \(0.0700817\pi\)
−0.735923 + 0.677065i \(0.763252\pi\)
\(462\) 0 0
\(463\) −21.3818 + 12.3448i −0.993699 + 0.573712i −0.906378 0.422468i \(-0.861164\pi\)
−0.0873209 + 0.996180i \(0.527831\pi\)
\(464\) 0 0
\(465\) −7.89463 6.19793i −0.366105 0.287422i
\(466\) 0 0
\(467\) 14.0708 + 14.0708i 0.651120 + 0.651120i 0.953263 0.302143i \(-0.0977019\pi\)
−0.302143 + 0.953263i \(0.597702\pi\)
\(468\) 0 0
\(469\) −3.59494 + 3.59494i −0.165999 + 0.165999i
\(470\) 0 0
\(471\) −7.04500 17.5558i −0.324616 0.808928i
\(472\) 0 0
\(473\) −14.7158 25.4885i −0.676633 1.17196i
\(474\) 0 0
\(475\) 2.62604 0.703645i 0.120491 0.0322855i
\(476\) 0 0
\(477\) −33.0024 + 18.0911i −1.51108 + 0.828332i
\(478\) 0 0
\(479\) 12.8097 22.1870i 0.585288 1.01375i −0.409551 0.912287i \(-0.634315\pi\)
0.994839 0.101462i \(-0.0323520\pi\)
\(480\) 0 0
\(481\) −24.9716 43.2521i −1.13861 1.97212i
\(482\) 0 0
\(483\) −0.589317 0.785890i −0.0268148 0.0357592i
\(484\) 0 0
\(485\) 4.91202 + 4.91202i 0.223043 + 0.223043i
\(486\) 0 0
\(487\) −24.8039 −1.12397 −0.561986 0.827147i \(-0.689962\pi\)
−0.561986 + 0.827147i \(0.689962\pi\)
\(488\) 0 0
\(489\) 3.62704 25.3745i 0.164020 1.14747i
\(490\) 0 0
\(491\) −36.3890 9.75039i −1.64221 0.440029i −0.684793 0.728737i \(-0.740108\pi\)
−0.957417 + 0.288708i \(0.906774\pi\)
\(492\) 0 0
\(493\) 7.17764 1.92324i 0.323265 0.0866185i
\(494\) 0 0
\(495\) 2.38044 8.15654i 0.106993 0.366609i
\(496\) 0 0
\(497\) 1.87197 + 1.08078i 0.0839692 + 0.0484796i
\(498\) 0 0
\(499\) 20.1205 + 5.39127i 0.900717 + 0.241346i 0.679324 0.733838i \(-0.262273\pi\)
0.221393 + 0.975185i \(0.428940\pi\)
\(500\) 0 0
\(501\) 9.04137 21.1616i 0.403939 0.945430i
\(502\) 0 0
\(503\) 4.55397i 0.203051i −0.994833 0.101526i \(-0.967628\pi\)
0.994833 0.101526i \(-0.0323724\pi\)
\(504\) 0 0
\(505\) 11.1880i 0.497858i
\(506\) 0 0
\(507\) 21.9688 2.64498i 0.975668 0.117468i
\(508\) 0 0
\(509\) −7.44927 1.99603i −0.330183 0.0884723i 0.0899191 0.995949i \(-0.471339\pi\)
−0.420102 + 0.907477i \(0.638006\pi\)
\(510\) 0 0
\(511\) 7.20399 + 4.15923i 0.318686 + 0.183993i
\(512\) 0 0
\(513\) 3.61149 + 1.63858i 0.159451 + 0.0723451i
\(514\) 0 0
\(515\) 4.68172 1.25446i 0.206301 0.0552782i
\(516\) 0 0
\(517\) 6.00367 + 1.60868i 0.264041 + 0.0707496i
\(518\) 0 0
\(519\) 10.2706 + 8.06322i 0.450828 + 0.353936i
\(520\) 0 0
\(521\) 41.5553 1.82057 0.910286 0.413980i \(-0.135862\pi\)
0.910286 + 0.413980i \(0.135862\pi\)
\(522\) 0 0
\(523\) −7.94661 7.94661i −0.347481 0.347481i 0.511689 0.859171i \(-0.329020\pi\)
−0.859171 + 0.511689i \(0.829020\pi\)
\(524\) 0 0
\(525\) 1.72615 4.04011i 0.0753356 0.176325i
\(526\) 0 0
\(527\) 2.08567 + 3.61248i 0.0908531 + 0.157362i
\(528\) 0 0
\(529\) −11.1829 + 19.3693i −0.486211 + 0.842142i
\(530\) 0 0
\(531\) 20.4781 33.7209i 0.888675 1.46336i
\(532\) 0 0
\(533\) −31.0937 + 8.33153i −1.34682 + 0.360879i
\(534\) 0 0
\(535\) −6.71295 11.6272i −0.290226 0.502686i
\(536\) 0 0
\(537\) 36.6260 + 5.23535i 1.58053 + 0.225922i
\(538\) 0 0
\(539\) −10.8441 + 10.8441i −0.467089 + 0.467089i
\(540\) 0 0
\(541\) 23.7454 + 23.7454i 1.02090 + 1.02090i 0.999777 + 0.0211185i \(0.00672274\pi\)
0.0211185 + 0.999777i \(0.493277\pi\)
\(542\) 0 0
\(543\) 1.07066 7.49021i 0.0459462 0.321436i
\(544\) 0 0
\(545\) −12.1230 + 6.99924i −0.519294 + 0.299814i
\(546\) 0 0
\(547\) 0.183171 + 0.683605i 0.00783185 + 0.0292288i 0.969731 0.244175i \(-0.0785171\pi\)
−0.961899 + 0.273404i \(0.911850\pi\)
\(548\) 0 0
\(549\) 0.0377324 1.70257i 0.00161038 0.0726638i
\(550\) 0 0
\(551\) 5.69010 + 3.28518i 0.242406 + 0.139953i
\(552\) 0 0
\(553\) 0.599525 0.346136i 0.0254944 0.0147192i
\(554\) 0 0
\(555\) −18.7885 8.02746i −0.797527 0.340747i
\(556\) 0 0
\(557\) −11.0432 + 11.0432i −0.467916 + 0.467916i −0.901239 0.433322i \(-0.857341\pi\)
0.433322 + 0.901239i \(0.357341\pi\)
\(558\) 0 0
\(559\) 63.2626i 2.67572i
\(560\) 0 0
\(561\) −2.18061 + 2.77755i −0.0920652 + 0.117268i
\(562\) 0 0
\(563\) 11.6019 43.2988i 0.488961 1.82483i −0.0725616 0.997364i \(-0.523117\pi\)
0.561522 0.827462i \(-0.310216\pi\)
\(564\) 0 0
\(565\) 2.40271 + 8.96703i 0.101083 + 0.377246i
\(566\) 0 0
\(567\) 5.68674 2.95539i 0.238820 0.124115i
\(568\) 0 0
\(569\) 12.4715 21.6013i 0.522833 0.905574i −0.476814 0.879004i \(-0.658208\pi\)
0.999647 0.0265695i \(-0.00845831\pi\)
\(570\) 0 0
\(571\) −9.27714 + 34.6227i −0.388236 + 1.44892i 0.444766 + 0.895647i \(0.353287\pi\)
−0.833002 + 0.553270i \(0.813380\pi\)
\(572\) 0 0
\(573\) −1.03719 8.61470i −0.0433291 0.359884i
\(574\) 0 0
\(575\) 2.83695 0.118309
\(576\) 0 0
\(577\) −20.2125 −0.841457 −0.420729 0.907187i \(-0.638226\pi\)
−0.420729 + 0.907187i \(0.638226\pi\)
\(578\) 0 0
\(579\) 9.15877 + 3.91312i 0.380626 + 0.162624i
\(580\) 0 0
\(581\) −2.13122 + 7.95381i −0.0884178 + 0.329980i
\(582\) 0 0
\(583\) 14.8155 25.6612i 0.613596 1.06278i
\(584\) 0 0
\(585\) 13.1974 12.6251i 0.545644 0.521983i
\(586\) 0 0
\(587\) −0.425823 1.58919i −0.0175756 0.0655930i 0.956581 0.291466i \(-0.0941431\pi\)
−0.974157 + 0.225873i \(0.927476\pi\)
\(588\) 0 0
\(589\) −0.954602 + 3.56262i −0.0393337 + 0.146795i
\(590\) 0 0
\(591\) 1.24988 + 0.178658i 0.0514131 + 0.00734902i
\(592\) 0 0
\(593\) 35.7642i 1.46866i −0.678793 0.734329i \(-0.737497\pi\)
0.678793 0.734329i \(-0.262503\pi\)
\(594\) 0 0
\(595\) 0.521182 0.521182i 0.0213664 0.0213664i
\(596\) 0 0
\(597\) −30.0125 + 22.5055i −1.22833 + 0.921090i
\(598\) 0 0
\(599\) 24.2410 13.9955i 0.990460 0.571842i 0.0850481 0.996377i \(-0.472896\pi\)
0.905412 + 0.424535i \(0.139562\pi\)
\(600\) 0 0
\(601\) −9.43704 5.44848i −0.384945 0.222248i 0.295023 0.955490i \(-0.404673\pi\)
−0.679968 + 0.733242i \(0.738006\pi\)
\(602\) 0 0
\(603\) 11.1176 18.3072i 0.452745 0.745527i
\(604\) 0 0
\(605\) −1.68253 6.27927i −0.0684044 0.255289i
\(606\) 0 0
\(607\) 36.6954 21.1861i 1.48942 0.859916i 0.489492 0.872008i \(-0.337182\pi\)
0.999927 + 0.0120914i \(0.00384892\pi\)
\(608\) 0 0
\(609\) 9.85397 3.95432i 0.399303 0.160237i
\(610\) 0 0
\(611\) 9.44695 + 9.44695i 0.382183 + 0.382183i
\(612\) 0 0
\(613\) 11.5060 11.5060i 0.464722 0.464722i −0.435477 0.900200i \(-0.643420\pi\)
0.900200 + 0.435477i \(0.143420\pi\)
\(614\) 0 0
\(615\) −8.13205 + 10.3582i −0.327916 + 0.417684i
\(616\) 0 0
\(617\) −0.520100 0.900840i −0.0209384 0.0362665i 0.855366 0.518024i \(-0.173332\pi\)
−0.876305 + 0.481757i \(0.839999\pi\)
\(618\) 0 0
\(619\) 17.6575 4.73131i 0.709714 0.190167i 0.114136 0.993465i \(-0.463590\pi\)
0.595578 + 0.803298i \(0.296923\pi\)
\(620\) 0 0
\(621\) 3.19765 + 2.62699i 0.128317 + 0.105418i
\(622\) 0 0
\(623\) −1.55069 + 2.68588i −0.0621272 + 0.107608i
\(624\) 0 0
\(625\) 2.74947 + 4.76221i 0.109979 + 0.190489i
\(626\) 0 0
\(627\) −3.09996 + 0.373227i −0.123801 + 0.0149052i
\(628\) 0 0
\(629\) 6.00428 + 6.00428i 0.239406 + 0.239406i
\(630\) 0 0
\(631\) −18.9729 −0.755301 −0.377650 0.925948i \(-0.623268\pi\)
−0.377650 + 0.925948i \(0.623268\pi\)
\(632\) 0 0
\(633\) 3.74054 1.50105i 0.148673 0.0596614i
\(634\) 0 0
\(635\) 8.35872 + 2.23971i 0.331706 + 0.0888803i
\(636\) 0 0
\(637\) −31.8409 + 8.53175i −1.26158 + 0.338040i
\(638\) 0 0
\(639\) −8.74183 2.55125i −0.345821 0.100926i
\(640\) 0 0
\(641\) 6.62975 + 3.82769i 0.261859 + 0.151185i 0.625182 0.780479i \(-0.285025\pi\)
−0.363323 + 0.931663i \(0.618358\pi\)
\(642\) 0 0
\(643\) 18.3287 + 4.91116i 0.722813 + 0.193677i 0.601427 0.798928i \(-0.294599\pi\)
0.121387 + 0.992605i \(0.461266\pi\)
\(644\) 0 0
\(645\) −15.5266 20.7056i −0.611359 0.815284i
\(646\) 0 0
\(647\) 1.59451i 0.0626865i −0.999509 0.0313432i \(-0.990022\pi\)
0.999509 0.0313432i \(-0.00997849\pi\)
\(648\) 0 0
\(649\) 31.0610i 1.21925i
\(650\) 0 0
\(651\) 3.57582 + 4.76857i 0.140147 + 0.186895i
\(652\) 0 0
\(653\) −1.34296 0.359845i −0.0525540 0.0140818i 0.232446 0.972609i \(-0.425327\pi\)
−0.285000 + 0.958527i \(0.591994\pi\)
\(654\) 0 0
\(655\) 6.27121 + 3.62069i 0.245037 + 0.141472i
\(656\) 0 0
\(657\) −33.6417 9.81813i −1.31249 0.383042i
\(658\) 0 0
\(659\) −28.0586 + 7.51827i −1.09301 + 0.292870i −0.759914 0.650024i \(-0.774759\pi\)
−0.333093 + 0.942894i \(0.608092\pi\)
\(660\) 0 0
\(661\) −0.302749 0.0811214i −0.0117756 0.00315526i 0.252926 0.967486i \(-0.418607\pi\)
−0.264702 + 0.964330i \(0.585274\pi\)
\(662\) 0 0
\(663\) −7.04435 + 2.82684i −0.273580 + 0.109786i
\(664\) 0 0
\(665\) 0.651712 0.0252723
\(666\) 0 0
\(667\) 4.84807 + 4.84807i 0.187718 + 0.187718i
\(668\) 0 0
\(669\) −32.4862 + 3.91125i −1.25599 + 0.151218i
\(670\) 0 0
\(671\) 0.670391 + 1.16115i 0.0258802 + 0.0448257i
\(672\) 0 0
\(673\) −14.6918 + 25.4470i −0.566329 + 0.980911i 0.430595 + 0.902545i \(0.358304\pi\)
−0.996925 + 0.0783659i \(0.975030\pi\)
\(674\) 0 0
\(675\) −3.02442 + 18.2604i −0.116410 + 0.702843i
\(676\) 0 0
\(677\) −7.06366 + 1.89270i −0.271478 + 0.0727424i −0.391990 0.919969i \(-0.628213\pi\)
0.120511 + 0.992712i \(0.461547\pi\)
\(678\) 0 0
\(679\) −2.06261 3.57254i −0.0791556 0.137102i
\(680\) 0 0
\(681\) 8.72736 11.1165i 0.334433 0.425985i
\(682\) 0 0
\(683\) −20.6264 + 20.6264i −0.789247 + 0.789247i −0.981371 0.192123i \(-0.938463\pi\)
0.192123 + 0.981371i \(0.438463\pi\)
\(684\) 0 0
\(685\) −4.62083 4.62083i −0.176553 0.176553i
\(686\) 0 0
\(687\) 12.1698 4.88363i 0.464305 0.186322i
\(688\) 0 0
\(689\) 55.1583 31.8456i 2.10136 1.21322i
\(690\) 0 0
\(691\) 0.467582 + 1.74504i 0.0177876 + 0.0663844i 0.974249 0.225474i \(-0.0723931\pi\)
−0.956462 + 0.291858i \(0.905726\pi\)
\(692\) 0 0
\(693\) −2.61908 + 4.31279i −0.0994907 + 0.163829i
\(694\) 0 0
\(695\) −15.4593 8.92542i −0.586404 0.338560i
\(696\) 0 0
\(697\) 4.73979 2.73652i 0.179532 0.103653i
\(698\) 0 0
\(699\) −9.39449 + 7.04467i −0.355332 + 0.266454i
\(700\) 0 0
\(701\) 31.2193 31.2193i 1.17914 1.17914i 0.199174 0.979964i \(-0.436174\pi\)
0.979964 0.199174i \(-0.0638260\pi\)
\(702\) 0 0
\(703\) 7.50805i 0.283171i
\(704\) 0 0
\(705\) 5.41053 + 0.773384i 0.203772 + 0.0291273i
\(706\) 0 0
\(707\) −1.71957 + 6.41751i −0.0646709 + 0.241355i
\(708\) 0 0
\(709\) −5.00387 18.6747i −0.187924 0.701344i −0.993986 0.109511i \(-0.965071\pi\)
0.806061 0.591832i \(-0.201595\pi\)
\(710\) 0 0
\(711\) −2.10746 + 2.01607i −0.0790359 + 0.0756087i
\(712\) 0 0
\(713\) −1.92438 + 3.33312i −0.0720686 + 0.124826i
\(714\) 0 0
\(715\) −3.72162 + 13.8893i −0.139181 + 0.519430i
\(716\) 0 0
\(717\) 30.2125 + 12.9084i 1.12831 + 0.482074i
\(718\) 0 0
\(719\) −5.23889 −0.195378 −0.0976889 0.995217i \(-0.531145\pi\)
−0.0976889 + 0.995217i \(0.531145\pi\)
\(720\) 0 0
\(721\) −2.87828 −0.107193
\(722\) 0 0
\(723\) 0.0212238 + 0.176282i 0.000789323 + 0.00655599i
\(724\) 0 0
\(725\) −7.93665 + 29.6200i −0.294760 + 1.10006i
\(726\) 0 0
\(727\) −20.0812 + 34.7817i −0.744772 + 1.28998i 0.205530 + 0.978651i \(0.434108\pi\)
−0.950301 + 0.311332i \(0.899225\pi\)
\(728\) 0 0
\(729\) −20.3179 + 17.7815i −0.752516 + 0.658574i
\(730\) 0 0
\(731\) 2.78383 + 10.3894i 0.102964 + 0.384266i
\(732\) 0 0
\(733\) −12.3274 + 46.0065i −0.455324 + 1.69929i 0.231811 + 0.972761i \(0.425535\pi\)
−0.687135 + 0.726530i \(0.741132\pi\)
\(734\) 0 0
\(735\) −8.32747 + 10.6072i −0.307164 + 0.391251i
\(736\) 0 0
\(737\) 16.8631i 0.621161i
\(738\) 0 0
\(739\) −9.18363 + 9.18363i −0.337825 + 0.337825i −0.855548 0.517723i \(-0.826780\pi\)
0.517723 + 0.855548i \(0.326780\pi\)
\(740\) 0 0
\(741\) −6.17172 2.63689i −0.226724 0.0968686i
\(742\) 0 0
\(743\) 42.0760 24.2926i 1.54362 0.891208i 0.545011 0.838429i \(-0.316525\pi\)
0.998606 0.0527792i \(-0.0168079\pi\)
\(744\) 0 0
\(745\) −11.9859 6.92004i −0.439128 0.253531i
\(746\) 0 0
\(747\) 0.768633 34.6824i 0.0281228 1.26896i
\(748\) 0 0
\(749\) 2.06353 + 7.70120i 0.0753998 + 0.281396i
\(750\) 0 0
\(751\) −25.5639 + 14.7593i −0.932839 + 0.538575i −0.887708 0.460406i \(-0.847704\pi\)
−0.0451310 + 0.998981i \(0.514371\pi\)
\(752\) 0 0
\(753\) −2.28464 + 15.9832i −0.0832571 + 0.582459i
\(754\) 0 0
\(755\) 8.13448 + 8.13448i 0.296044 + 0.296044i
\(756\) 0 0
\(757\) 30.3982 30.3982i 1.10484 1.10484i 0.111022 0.993818i \(-0.464588\pi\)
0.993818 0.111022i \(-0.0354123\pi\)
\(758\) 0 0
\(759\) −3.22540 0.461041i −0.117075 0.0167347i
\(760\) 0 0
\(761\) −2.97086 5.14568i −0.107694 0.186531i 0.807142 0.590357i \(-0.201013\pi\)
−0.914836 + 0.403827i \(0.867680\pi\)
\(762\) 0 0
\(763\) 8.02963 2.15153i 0.290692 0.0778907i
\(764\) 0 0
\(765\) −1.61180 + 2.65412i −0.0582747 + 0.0959598i
\(766\) 0 0
\(767\) −33.3825 + 57.8201i −1.20537 + 2.08776i
\(768\) 0 0
\(769\) −6.00863 10.4073i −0.216677 0.375295i 0.737113 0.675769i \(-0.236188\pi\)
−0.953790 + 0.300474i \(0.902855\pi\)
\(770\) 0 0
\(771\) 11.2424 26.3132i 0.404887 0.947648i
\(772\) 0 0
\(773\) 22.2746 + 22.2746i 0.801163 + 0.801163i 0.983277 0.182114i \(-0.0582940\pi\)
−0.182114 + 0.983277i \(0.558294\pi\)
\(774\) 0 0
\(775\) −17.2139 −0.618340
\(776\) 0 0
\(777\) 9.54343 + 7.49236i 0.342368 + 0.268787i
\(778\) 0 0
\(779\) 4.67437 + 1.25249i 0.167477 + 0.0448753i
\(780\) 0 0
\(781\) 6.92536 1.85565i 0.247809 0.0664002i
\(782\) 0 0
\(783\) −36.3736 + 26.0367i −1.29989 + 0.930477i
\(784\) 0 0
\(785\) 11.3417 + 6.54815i 0.404803 + 0.233713i
\(786\) 0 0
\(787\) 5.98650 + 1.60408i 0.213396 + 0.0571792i 0.363933 0.931425i \(-0.381434\pi\)
−0.150537 + 0.988604i \(0.548100\pi\)
\(788\) 0 0
\(789\) −44.2630 + 5.32914i −1.57581 + 0.189723i
\(790\) 0 0
\(791\) 5.51285i 0.196014i
\(792\) 0 0
\(793\) 2.88198i 0.102342i
\(794\) 0 0
\(795\) 10.2372 23.9605i 0.363077 0.849791i
\(796\) 0 0
\(797\) 33.1217 + 8.87494i 1.17323 + 0.314367i 0.792239 0.610211i \(-0.208915\pi\)
0.380993 + 0.924578i \(0.375582\pi\)
\(798\) 0 0
\(799\) −1.96715 1.13573i −0.0695927 0.0401794i
\(800\) 0 0
\(801\) 3.66051 12.5427i 0.129338 0.443174i
\(802\) 0 0
\(803\) 26.6513 7.14118i 0.940503 0.252007i
\(804\) 0 0
\(805\) 0.656892 + 0.176014i 0.0231524 + 0.00620367i
\(806\) 0 0
\(807\) 1.60309 11.2150i 0.0564313 0.394788i
\(808\) 0 0
\(809\) −12.8401 −0.451432 −0.225716 0.974193i \(-0.572472\pi\)
−0.225716 + 0.974193i \(0.572472\pi\)
\(810\) 0 0
\(811\) 37.1183 + 37.1183i 1.30340 + 1.30340i 0.926086 + 0.377314i \(0.123152\pi\)
0.377314 + 0.926086i \(0.376848\pi\)
\(812\) 0 0
\(813\) 6.36991 + 8.49466i 0.223402 + 0.297921i
\(814\) 0 0
\(815\) 8.87287 + 15.3683i 0.310803 + 0.538327i
\(816\) 0 0
\(817\) −4.75519 + 8.23624i −0.166363 + 0.288149i
\(818\) 0 0
\(819\) −9.51055 + 5.21344i −0.332326 + 0.182172i
\(820\) 0 0
\(821\) 27.1312 7.26977i 0.946884 0.253717i 0.247844 0.968800i \(-0.420278\pi\)
0.699040 + 0.715083i \(0.253611\pi\)
\(822\) 0 0
\(823\) −9.61847 16.6597i −0.335279 0.580720i 0.648260 0.761419i \(-0.275497\pi\)
−0.983538 + 0.180700i \(0.942164\pi\)
\(824\) 0 0
\(825\) −5.42715 13.5242i −0.188949 0.470852i
\(826\) 0 0
\(827\) −28.7848 + 28.7848i −1.00095 + 1.00095i −0.000945916 1.00000i \(0.500301\pi\)
−1.00000 0.000945916i \(0.999699\pi\)
\(828\) 0 0
\(829\) −23.5696 23.5696i −0.818606 0.818606i 0.167300 0.985906i \(-0.446495\pi\)
−0.985906 + 0.167300i \(0.946495\pi\)
\(830\) 0 0
\(831\) 0.974201 + 0.764827i 0.0337946 + 0.0265315i
\(832\) 0 0
\(833\) 4.85369 2.80228i 0.168171 0.0970933i
\(834\) 0 0
\(835\) 4.12343 + 15.3889i 0.142697 + 0.532553i
\(836\) 0 0
\(837\) −19.4025 15.9399i −0.670649 0.550963i
\(838\) 0 0
\(839\) −5.76796 3.33013i −0.199132 0.114969i 0.397119 0.917767i \(-0.370010\pi\)
−0.596251 + 0.802798i \(0.703344\pi\)
\(840\) 0 0
\(841\) −39.0658 + 22.5546i −1.34710 + 0.777747i
\(842\) 0 0
\(843\) −2.14310 17.8002i −0.0738121 0.613072i
\(844\) 0 0
\(845\) −10.8323 + 10.8323i −0.372643 + 0.372643i
\(846\) 0 0
\(847\) 3.86044i 0.132646i
\(848\) 0 0
\(849\) 16.9400 + 42.2135i 0.581378 + 1.44877i
\(850\) 0 0
\(851\) −2.02777 + 7.56773i −0.0695109 + 0.259418i
\(852\) 0 0
\(853\) −2.94440 10.9887i −0.100814 0.376245i 0.897022 0.441985i \(-0.145726\pi\)
−0.997837 + 0.0657407i \(0.979059\pi\)
\(854\) 0 0
\(855\) −2.66716 + 0.651683i −0.0912148 + 0.0222871i
\(856\) 0 0
\(857\) −15.7885 + 27.3465i −0.539326 + 0.934140i 0.459615 + 0.888118i \(0.347987\pi\)
−0.998940 + 0.0460211i \(0.985346\pi\)
\(858\) 0 0
\(859\) −7.30262 + 27.2537i −0.249162 + 0.929886i 0.722084 + 0.691806i \(0.243185\pi\)
−0.971246 + 0.238080i \(0.923482\pi\)
\(860\) 0 0
\(861\) 6.25664 4.69168i 0.213226 0.159892i
\(862\) 0 0
\(863\) 29.1288 0.991557 0.495779 0.868449i \(-0.334883\pi\)
0.495779 + 0.868449i \(0.334883\pi\)
\(864\) 0 0
\(865\) −9.03998 −0.307369
\(866\) 0 0
\(867\) −22.5249 + 16.8908i −0.764984 + 0.573640i
\(868\) 0 0
\(869\) 0.594298 2.21795i 0.0201602 0.0752388i
\(870\) 0 0
\(871\) −18.1235 + 31.3907i −0.614090 + 1.06363i
\(872\) 0 0
\(873\) 12.0137 + 12.5582i 0.406601 + 0.425032i
\(874\) 0 0
\(875\) 1.89225 + 7.06198i 0.0639698 + 0.238739i
\(876\) 0 0
\(877\) 8.63165 32.2138i 0.291470 1.08778i −0.652510 0.757780i \(-0.726284\pi\)
0.943980 0.330001i \(-0.107049\pi\)
\(878\) 0 0
\(879\) −12.9969 32.3875i −0.438373 1.09240i
\(880\) 0 0
\(881\) 10.4223i 0.351136i −0.984467 0.175568i \(-0.943824\pi\)
0.984467 0.175568i \(-0.0561763\pi\)
\(882\) 0 0
\(883\) −7.73247 + 7.73247i −0.260218 + 0.260218i −0.825143 0.564924i \(-0.808905\pi\)
0.564924 + 0.825143i \(0.308905\pi\)
\(884\) 0 0
\(885\) 3.26486 + 27.1174i 0.109747 + 0.911542i
\(886\) 0 0
\(887\) 22.0565 12.7343i 0.740584 0.427577i −0.0816974 0.996657i \(-0.526034\pi\)
0.822282 + 0.569081i \(0.192701\pi\)
\(888\) 0 0
\(889\) −4.45039 2.56943i −0.149261 0.0861761i
\(890\) 0 0
\(891\) 6.40609 20.2692i 0.214612 0.679044i
\(892\) 0 0
\(893\) −0.519821 1.94000i −0.0173951 0.0649196i
\(894\) 0 0
\(895\) −22.1829 + 12.8073i −0.741492 + 0.428100i
\(896\) 0 0
\(897\) −5.50860 4.32470i −0.183927 0.144398i
\(898\) 0 0
\(899\) −29.4168 29.4168i −0.981104 0.981104i
\(900\) 0 0
\(901\) −7.65711 + 7.65711i −0.255095 + 0.255095i
\(902\) 0 0
\(903\) 5.72376 + 14.2633i 0.190475 + 0.474654i
\(904\) 0 0
\(905\) 2.61915 + 4.53651i 0.0870637 + 0.150799i
\(906\) 0 0
\(907\) −35.2550 + 9.44656i −1.17062 + 0.313668i −0.791202 0.611555i \(-0.790544\pi\)
−0.379423 + 0.925223i \(0.623877\pi\)
\(908\) 0 0
\(909\) 0.620169 27.9834i 0.0205697 0.928150i
\(910\) 0 0
\(911\) 4.86150 8.42037i 0.161069 0.278979i −0.774183 0.632961i \(-0.781839\pi\)
0.935252 + 0.353982i \(0.115173\pi\)
\(912\) 0 0
\(913\) 13.6563 + 23.6534i 0.451957 + 0.782813i
\(914\) 0 0
\(915\) 0.707327 + 0.943263i 0.0233835 + 0.0311833i
\(916\) 0 0
\(917\) −3.04073 3.04073i −0.100414 0.100414i
\(918\) 0 0
\(919\) 26.5741 0.876599 0.438300 0.898829i \(-0.355581\pi\)
0.438300 + 0.898829i \(0.355581\pi\)
\(920\) 0 0
\(921\) −2.05432 + 14.3718i −0.0676921 + 0.473568i
\(922\) 0 0
\(923\) 14.8859 + 3.98867i 0.489976 + 0.131289i
\(924\) 0 0
\(925\) −33.8472 + 9.06934i −1.11289 + 0.298198i
\(926\) 0 0
\(927\) 11.7795 2.87815i 0.386888 0.0945308i
\(928\) 0 0
\(929\) 20.9365 + 12.0877i 0.686904 + 0.396584i 0.802451 0.596718i \(-0.203529\pi\)
−0.115547 + 0.993302i \(0.536862\pi\)
\(930\) 0 0
\(931\) 4.78670 + 1.28259i 0.156878 + 0.0420353i
\(932\) 0 0
\(933\) 17.7513 41.5475i 0.581153 1.36020i
\(934\) 0 0
\(935\) 2.44476i 0.0799521i
\(936\) 0 0
\(937\) 1.33551i 0.0436291i 0.999762 + 0.0218146i \(0.00694434\pi\)
−0.999762 + 0.0218146i \(0.993056\pi\)
\(938\) 0 0
\(939\) −1.06971 + 0.128790i −0.0349086 + 0.00420289i
\(940\) 0 0
\(941\) 21.3261 + 5.71431i 0.695211 + 0.186281i 0.589085 0.808071i \(-0.299488\pi\)
0.106126 + 0.994353i \(0.466155\pi\)
\(942\) 0 0
\(943\) 4.37325 + 2.52490i 0.142413 + 0.0822220i
\(944\) 0 0
\(945\) −1.83323 + 4.04052i −0.0596351 + 0.131438i
\(946\) 0 0
\(947\) −23.4634 + 6.28700i −0.762458 + 0.204300i −0.619037 0.785362i \(-0.712477\pi\)
−0.143421 + 0.989662i \(0.545810\pi\)
\(948\) 0 0
\(949\) 57.2863 + 15.3498i 1.85959 + 0.498277i
\(950\) 0 0
\(951\) 19.3279 + 15.1740i 0.626752 + 0.492051i
\(952\) 0 0
\(953\) −15.2157 −0.492885 −0.246442 0.969157i \(-0.579262\pi\)
−0.246442 + 0.969157i \(0.579262\pi\)
\(954\) 0 0
\(955\) 4.24772 + 4.24772i 0.137453 + 0.137453i
\(956\) 0 0
\(957\) 13.8370 32.3859i 0.447287 1.04689i
\(958\) 0 0
\(959\) 1.94033 + 3.36075i 0.0626566 + 0.108524i
\(960\) 0 0
\(961\) −3.82339 + 6.62230i −0.123335 + 0.213623i
\(962\) 0 0
\(963\) −16.1459 29.4540i −0.520295 0.949142i
\(964\) 0 0
\(965\) −6.66032 + 1.78463i −0.214403 + 0.0574492i
\(966\) 0 0
\(967\) 16.3260 + 28.2775i 0.525010 + 0.909344i 0.999576 + 0.0291241i \(0.00927179\pi\)
−0.474566 + 0.880220i \(0.657395\pi\)
\(968\) 0 0
\(969\) 1.12960 + 0.161465i 0.0362878 + 0.00518701i
\(970\) 0 0
\(971\) 23.6028 23.6028i 0.757449 0.757449i −0.218408 0.975858i \(-0.570086\pi\)
0.975858 + 0.218408i \(0.0700864\pi\)
\(972\) 0 0
\(973\) 7.49574 + 7.49574i 0.240303 + 0.240303i
\(974\) 0 0
\(975\) 4.43232 31.0081i 0.141948 0.993054i
\(976\) 0 0
\(977\) 30.2605 17.4709i 0.968119 0.558944i 0.0694570 0.997585i \(-0.477873\pi\)
0.898662 + 0.438641i \(0.144540\pi\)
\(978\) 0 0
\(979\) 2.66246 + 9.93644i 0.0850926 + 0.317570i
\(980\) 0 0
\(981\) −30.7101 + 16.8345i −0.980499 + 0.537484i
\(982\) 0 0
\(983\) 28.8301 + 16.6450i 0.919536 + 0.530895i 0.883487 0.468455i \(-0.155189\pi\)
0.0360492 + 0.999350i \(0.488523\pi\)
\(984\) 0 0
\(985\) −0.756999 + 0.437053i −0.0241200 + 0.0139257i
\(986\) 0 0
\(987\) −2.98465 1.27520i −0.0950025 0.0405902i
\(988\) 0 0
\(989\) −7.01742 + 7.01742i −0.223141 + 0.223141i
\(990\) 0 0
\(991\) 10.4637i 0.332390i 0.986093 + 0.166195i \(0.0531482\pi\)
−0.986093 + 0.166195i \(0.946852\pi\)
\(992\) 0 0
\(993\) 11.4680 14.6074i 0.363925 0.463550i
\(994\) 0 0
\(995\) 6.72182 25.0862i 0.213096 0.795286i
\(996\) 0 0
\(997\) 7.47474 + 27.8961i 0.236727 + 0.883479i 0.977363 + 0.211571i \(0.0678580\pi\)
−0.740635 + 0.671907i \(0.765475\pi\)
\(998\) 0 0
\(999\) −46.5488 21.1198i −1.47274 0.668200i
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 576.2.y.a.47.4 88
3.2 odd 2 1728.2.z.a.1007.8 88
4.3 odd 2 144.2.u.a.83.7 yes 88
9.4 even 3 1728.2.z.a.1583.8 88
9.5 odd 6 inner 576.2.y.a.239.8 88
12.11 even 2 432.2.v.a.35.16 88
16.5 even 4 144.2.u.a.11.1 88
16.11 odd 4 inner 576.2.y.a.335.8 88
36.23 even 6 144.2.u.a.131.1 yes 88
36.31 odd 6 432.2.v.a.179.22 88
48.5 odd 4 432.2.v.a.251.22 88
48.11 even 4 1728.2.z.a.143.8 88
144.5 odd 12 144.2.u.a.59.7 yes 88
144.59 even 12 inner 576.2.y.a.527.4 88
144.85 even 12 432.2.v.a.395.16 88
144.139 odd 12 1728.2.z.a.719.8 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.1 88 16.5 even 4
144.2.u.a.59.7 yes 88 144.5 odd 12
144.2.u.a.83.7 yes 88 4.3 odd 2
144.2.u.a.131.1 yes 88 36.23 even 6
432.2.v.a.35.16 88 12.11 even 2
432.2.v.a.179.22 88 36.31 odd 6
432.2.v.a.251.22 88 48.5 odd 4
432.2.v.a.395.16 88 144.85 even 12
576.2.y.a.47.4 88 1.1 even 1 trivial
576.2.y.a.239.8 88 9.5 odd 6 inner
576.2.y.a.335.8 88 16.11 odd 4 inner
576.2.y.a.527.4 88 144.59 even 12 inner
1728.2.z.a.143.8 88 48.11 even 4
1728.2.z.a.719.8 88 144.139 odd 12
1728.2.z.a.1007.8 88 3.2 odd 2
1728.2.z.a.1583.8 88 9.4 even 3