LMFDB - Embedded newform 432.2.v.a.35.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(35,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, 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("432.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (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:	$3.44953736732$
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			35.16
Character	$\chi$	$=$	432.35
Dual form			432.2.v.a.395.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.845208 + 1.13385i) q^{2} +(-0.571246 + 1.91668i) q^{4} +(-0.310357 + 1.15827i) q^{5} +(0.356047 - 0.616691i) q^{7} +(-2.65606 + 0.972288i) q^{8} +O(q^{10})$	\(q+(0.845208 + 1.13385i) q^{2} +(-0.571246 + 1.91668i) q^{4} +(-0.310357 + 1.15827i) q^{5} +(0.356047 - 0.616691i) q^{7} +(-2.65606 + 0.972288i) q^{8} +(-1.57562 + 0.627079i) q^{10} +(0.611314 + 2.28146i) q^{11} +(-1.31401 + 4.90394i) q^{13} +(1.00017 - 0.117528i) q^{14} +(-3.34736 - 2.18980i) q^{16} +0.863180i q^{17} +(-0.539682 + 0.539682i) q^{19} +(-2.04275 - 1.25651i) q^{20} +(-2.07015 + 2.62145i) q^{22} +(0.689728 - 0.398215i) q^{23} +(3.08486 + 1.78104i) q^{25} +(-6.67096 + 2.65496i) q^{26} +(0.978612 + 1.03471i) q^{28} +(-2.22809 - 8.31534i) q^{29} +(4.18508 - 2.41626i) q^{31} +(-0.346304 - 5.64624i) q^{32} +(-0.978720 + 0.729567i) q^{34} +(0.603793 + 0.603793i) q^{35} +(-6.95600 + 6.95600i) q^{37} +(-1.06806 - 0.155776i) q^{38} +(-0.301843 - 3.37819i) q^{40} +(-3.17027 - 5.49108i) q^{41} +(12.0362 - 3.22509i) q^{43} +(-4.72204 - 0.131577i) q^{44} +(1.03448 + 0.445476i) q^{46} +(1.31575 - 2.27895i) q^{47} +(3.24646 + 5.62304i) q^{49} +(0.587906 + 5.00313i) q^{50} +(-8.64869 - 5.31990i) q^{52} +(8.87081 + 8.87081i) q^{53} -2.83227 q^{55} +(-0.346081 + 1.98415i) q^{56} +(7.54518 - 9.55452i) q^{58} +(12.7025 + 3.40363i) q^{59} +(0.548319 - 0.146922i) q^{61} +(6.27695 + 2.70303i) q^{62} +(6.10931 - 5.16491i) q^{64} +(-5.27228 - 3.04395i) q^{65} +(-6.89625 - 1.84784i) q^{67} +(-1.65444 - 0.493089i) q^{68} +(-0.174282 + 1.19494i) q^{70} -3.03550i q^{71} -11.6817i q^{73} +(-13.7663 - 2.00781i) q^{74} +(-0.726108 - 1.34269i) q^{76} +(1.62461 + 0.435313i) q^{77} +(0.841919 + 0.486082i) q^{79} +(3.57525 - 3.19752i) q^{80} +(3.54653 - 8.23573i) q^{82} +(11.1696 - 2.99289i) q^{83} +(-0.999796 - 0.267894i) q^{85} +(13.8299 + 10.9214i) q^{86} +(-3.84192 - 5.46531i) q^{88} -4.35531 q^{89} +(2.55637 + 2.55637i) q^{91} +(0.369247 + 1.54947i) q^{92} +(3.69609 - 0.434318i) q^{94} +(-0.457603 - 0.792591i) q^{95} +(-2.89654 + 5.01695i) q^{97} +(-3.63176 + 8.43365i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.845208	+	1.13385i	0.597652	+	0.801755i
$2$	0.845208	+	1.13385i	0.597652	+	0.801755i
$3$		0			0
$3$		0			0
$4$	−0.571246	+	1.91668i	−0.285623	+	0.958342i
$5$	−0.310357	+	1.15827i	−0.138796	+	0.517994i	0.861157	+	0.508339i	$0.169740\pi$
$5$	−0.310357	+	1.15827i	−0.138796	+	0.517994i	−0.999953	+	0.00965542i	$0.996927\pi$
$6$		0			0
$7$	0.356047	−	0.616691i	0.134573	−	0.233087i	−0.790861	−	0.611996i	$-0.790367\pi$
$7$	0.356047	−	0.616691i	0.134573	−	0.233087i	0.925434	+	0.378908i	$0.123700\pi$
$8$	−2.65606	+	0.972288i	−0.939059	+	0.343756i
$9$		0			0
$10$	−1.57562	+	0.627079i	−0.498256	+	0.198300i
$11$	0.611314	+	2.28146i	0.184318	+	0.687885i	0.994775	+	0.102087i	$0.0325521\pi$
$11$	0.611314	+	2.28146i	0.184318	+	0.687885i	−0.810457	+	0.585798i	$0.800781\pi$
$12$		0			0
$13$	−1.31401	+	4.90394i	−0.364440	+	1.36011i	0.503738	+	0.863857i	$0.331958\pi$
$13$	−1.31401	+	4.90394i	−0.364440	+	1.36011i	−0.868178	+	0.496253i	$0.834709\pi$
$14$	1.00017	−	0.117528i	0.267307	−	0.0314106i
$15$		0			0
$16$	−3.34736	−	2.18980i	−0.836839	−	0.547449i
$17$			0.863180i			0.209352i	0.994506	+	0.104676i	$0.0333806\pi$
$17$			0.863180i			0.209352i	−0.994506	+	0.104676i	$0.966619\pi$
$18$		0			0
$19$	−0.539682	+	0.539682i	−0.123811	+	0.123811i	−0.766297	−	0.642486i	$-0.777903\pi$
$19$	−0.539682	+	0.539682i	−0.123811	+	0.123811i	0.642486	+	0.766297i	$0.277903\pi$
$20$	−2.04275	−	1.25651i	−0.456772	−	0.280965i
$21$		0			0
$22$	−2.07015	+	2.62145i	−0.441357	+	0.558894i
$23$	0.689728	−	0.398215i	0.143818	−	0.0830335i	−0.426364	−	0.904552i	$-0.640206\pi$
$23$	0.689728	−	0.398215i	0.143818	−	0.0830335i	0.570182	+	0.821518i	$0.306872\pi$
$24$		0			0
$25$	3.08486	+	1.78104i	0.616972	+	0.356209i
$26$	−6.67096	+	2.65496i	−1.30828	+	0.520681i
$27$		0			0
$28$	0.978612	+	1.03471i	0.184940	+	0.195542i
$29$	−2.22809	−	8.31534i	−0.413746	−	1.54412i	−0.787335	−	0.616526i	$-0.788540\pi$
$29$	−2.22809	−	8.31534i	−0.413746	−	1.54412i	0.373589	−	0.927594i	$-0.378127\pi$
$30$		0			0
$31$	4.18508	−	2.41626i	0.751663	−	0.433973i	−0.0746314	−	0.997211i	$-0.523778\pi$
$31$	4.18508	−	2.41626i	0.751663	−	0.433973i	0.826295	+	0.563238i	$0.190445\pi$
$32$	−0.346304	−	5.64624i	−0.0612184	−	0.998124i
$33$		0			0
$34$	−0.978720	+	0.729567i	−0.167849	+	0.125120i
$35$	0.603793	+	0.603793i	0.102060	+	0.102060i
$36$		0			0
$37$	−6.95600	+	6.95600i	−1.14356	+	1.14356i	−0.155765	+	0.987794i	$0.549784\pi$
$37$	−6.95600	+	6.95600i	−1.14356	+	1.14356i	−0.987794	+	0.155765i	$0.950216\pi$
$38$	−1.06806	−	0.155776i	−0.173263	−	0.0252703i
$39$		0			0
$40$	−0.301843	−	3.37819i	−0.0477256	−	0.534139i
$41$	−3.17027	−	5.49108i	−0.495114	−	0.857562i	0.504870	−	0.863195i	$-0.331540\pi$
$41$	−3.17027	−	5.49108i	−0.495114	−	0.857562i	−0.999984	+	0.00563304i	$0.998207\pi$
$42$		0			0
$43$	12.0362	−	3.22509i	1.83550	−	0.491822i	0.837035	−	0.547150i	$-0.184287\pi$
$43$	12.0362	−	3.22509i	1.83550	−	0.491822i	0.998468	+	0.0553283i	$0.0176206\pi$
$44$	−4.72204	−	0.131577i	−0.711875	−	0.0198359i
$45$		0			0
$46$	1.03448	+	0.445476i	0.152526	+	0.0656818i
$47$	1.31575	−	2.27895i	0.191923	−	0.332420i	−0.753965	−	0.656915i	$-0.771861\pi$
$47$	1.31575	−	2.27895i	0.191923	−	0.332420i	0.945887	+	0.324495i	$0.105194\pi$
$48$		0			0
$49$	3.24646	+	5.62304i	0.463780	+	0.803291i
$50$	0.587906	+	5.00313i	0.0831424	+	0.707550i
$51$		0			0
$52$	−8.64869	−	5.31990i	−1.19936	−	0.737737i
$53$	8.87081	+	8.87081i	1.21850	+	1.21850i	0.968157	+	0.250342i	$0.0805431\pi$
$53$	8.87081	+	8.87081i	1.21850	+	1.21850i	0.250342	+	0.968157i	$0.419457\pi$
$54$		0			0
$55$	−2.83227			−0.381903
$56$	−0.346081	+	1.98415i	−0.0462470	+	0.265143i
$57$		0			0
$58$	7.54518	−	9.55452i	0.990730	−	1.25457i
$59$	12.7025	+	3.40363i	1.65373	+	0.443115i	0.960654	−	0.277749i	$-0.0895885\pi$
$59$	12.7025	+	3.40363i	1.65373	+	0.443115i	0.693076	+	0.720865i	$0.256255\pi$
$60$		0			0
$61$	0.548319	−	0.146922i	0.0702051	−	0.0188114i	−0.223546	−	0.974693i	$-0.571763\pi$
$61$	0.548319	−	0.146922i	0.0702051	−	0.0188114i	0.293751	+	0.955882i	$0.405096\pi$
$62$	6.27695	+	2.70303i	0.797173	+	0.343285i
$63$		0			0
$64$	6.10931	−	5.16491i	0.763664	−	0.645614i
$65$	−5.27228	−	3.04395i	−0.653946	−	0.377556i
$66$		0			0
$67$	−6.89625	−	1.84784i	−0.842511	−	0.225750i	−0.188347	−	0.982103i	$-0.560313\pi$
$67$	−6.89625	−	1.84784i	−0.842511	−	0.225750i	−0.654164	+	0.756352i	$0.726980\pi$
$68$	−1.65444	−	0.493089i	−0.200631	−	0.0597958i
$69$		0			0
$70$	−0.174282	+	1.19494i	−0.0208307	+	0.142823i
$71$		−	3.03550i		−	0.360248i	−0.983644	−	0.180124i	$-0.942350\pi$
$71$		−	3.03550i		−	0.360248i	0.983644	−	0.180124i	$-0.0576499\pi$
$72$		0			0
$73$		−	11.6817i		−	1.36724i	−0.729839	−	0.683619i	$-0.760405\pi$
$73$		−	11.6817i		−	1.36724i	0.729839	−	0.683619i	$-0.239595\pi$
$74$	−13.7663	−	2.00781i	−1.60031	−	0.233404i
$75$		0			0
$76$	−0.726108	−	1.34269i	−0.0832903	−	0.154017i
$77$	1.62461	+	0.435313i	0.185142	+	0.0496085i
$78$		0			0
$79$	0.841919	+	0.486082i	0.0947233	+	0.0546885i	0.546613	−	0.837385i	$-0.315917\pi$
$79$	0.841919	+	0.486082i	0.0947233	+	0.0546885i	−0.451890	+	0.892074i	$0.649250\pi$
$80$	3.57525	−	3.19752i	0.399725	−	0.357494i
$81$		0			0
$82$	3.54653	−	8.23573i	0.391649	−	0.909484i
$83$	11.1696	−	2.99289i	1.22602	−	0.328512i	0.412994	−	0.910734i	$-0.364483\pi$
$83$	11.1696	−	2.99289i	1.22602	−	0.328512i	0.813030	+	0.582221i	$0.197816\pi$
$84$		0			0
$85$	−0.999796	−	0.267894i	−0.108443	−	0.0290572i
$86$	13.8299	+	10.9214i	1.49131	+	1.17769i
$87$		0			0
$88$	−3.84192	−	5.46531i	−0.409550	−	0.582604i
$89$	−4.35531			−0.461662			−0.230831	−	0.972994i	$-0.574144\pi$
$89$	−4.35531			−0.461662			−0.230831	+	0.972994i	$0.574144\pi$
$90$		0			0
$91$	2.55637	+	2.55637i	0.267981	+	0.267981i
$92$	0.369247	+	1.54947i	0.0384967	+	0.161543i
$93$		0			0
$94$	3.69609	−	0.434318i	0.381222	−	0.0447965i
$95$	−0.457603	−	0.792591i	−0.0469490	−	0.0813181i
$96$		0			0
$97$	−2.89654	+	5.01695i	−0.294099	+	0.509395i	−0.974775	−	0.223190i	$-0.928353\pi$
$97$	−2.89654	+	5.01695i	−0.294099	+	0.509395i	0.680676	+	0.732585i	$0.261686\pi$
$98$	−3.63176	+	8.43365i	−0.366863	+	0.851927i
$99$		0			0
$100$	−5.17591	+	4.89529i	−0.517591	+	0.489529i
$101$	−9.01216	+	2.41480i	−0.896744	+	0.240282i	−0.677617	−	0.735415i	$-0.736987\pi$
$101$	−9.01216	+	2.41480i	−0.896744	+	0.240282i	−0.219127	+	0.975696i	$0.570321\pi$
$102$		0			0
$103$	−2.02100	−	3.50047i	−0.199135	−	0.344911i	0.749113	−	0.662442i	$-0.230480\pi$
$103$	−2.02100	−	3.50047i	−0.199135	−	0.344911i	−0.948248	+	0.317530i	$0.897146\pi$
$104$	−1.27796	−	14.3028i	−0.125314	−	1.40250i
$105$		0			0
$106$	−2.56052	+	17.5559i	−0.248699	+	1.70518i
$107$	7.91703	−	7.91703i	0.765368	−	0.765368i	−0.211919	−	0.977287i	$-0.567971\pi$
$107$	7.91703	−	7.91703i	0.765368	−	0.765368i	0.977287	+	0.211919i	$0.0679712\pi$
$108$		0			0
$109$	−8.25467	−	8.25467i	−0.790654	−	0.790654i	0.190946	−	0.981600i	$-0.438844\pi$
$109$	−8.25467	−	8.25467i	−0.790654	−	0.790654i	−0.981600	+	0.190946i	$0.938844\pi$
$110$	−2.39386	−	3.21138i	−0.228245	−	0.306193i
$111$		0			0
$112$	−2.54224	+	1.28461i	−0.240219	+	0.121385i
$113$	6.70455	−	3.87087i	0.630711	−	0.364141i	−0.150316	−	0.988638i	$-0.548029\pi$
$113$	6.70455	−	3.87087i	0.630711	−	0.364141i	0.781027	+	0.624497i	$0.214696\pi$
$114$		0			0
$115$	0.247178	+	0.922480i	0.0230494	+	0.0860217i
$116$	17.2107	+	0.479565i	1.59797	+	0.0445265i
$117$		0			0
$118$	6.87707	+	17.2796i	0.633085	+	1.59072i
$119$	0.532316	+	0.307333i	0.0487973	+	0.0281731i
$120$		0			0
$121$	4.69494	−	2.71063i	0.426813	−	0.246421i
$122$	0.630032	+	0.497534i	0.0570404	+	0.0450446i
$123$		0			0
$124$	2.24049	+	9.40176i	0.201202	+	0.844303i
$125$	−7.25990	+	7.25990i	−0.649345	+	0.649345i
$126$		0			0
$127$		−	7.21656i		−	0.640366i	−0.947356	−	0.320183i	$-0.896256\pi$
$127$		−	7.21656i		−	0.640366i	0.947356	−	0.320183i	$-0.103744\pi$
$128$	11.0199	+	2.56164i	0.974030	+	0.226419i
$129$		0			0
$130$	−1.00478	−	8.55076i	−0.0881249	−	0.749951i
$131$	−1.56297	+	5.83309i	−0.136558	+	0.509640i	0.863429	+	0.504470i	$0.168312\pi$
$131$	−1.56297	+	5.83309i	−0.136558	+	0.509640i	−0.999987	+	0.00516943i	$0.998355\pi$
$132$		0			0
$133$	0.140665	+	0.524969i	0.0121972	+	0.0455206i
$134$	−3.73358	−	9.38115i	−0.322532	−	0.810408i
$135$		0			0
$136$	−0.839260	−	2.29266i	−0.0719659	−	0.196594i
$137$	−2.72483	+	4.71954i	−0.232798	+	0.403217i	−0.958630	−	0.284654i	$-0.908121\pi$
$137$	−2.72483	+	4.71954i	−0.232798	+	0.403217i	0.725833	+	0.687871i	$0.241455\pi$
$138$		0			0
$139$	−3.85291	+	14.3793i	−0.326800	+	1.21963i	0.585691	+	0.810534i	$0.300823\pi$
$139$	−3.85291	+	14.3793i	−0.326800	+	1.21963i	−0.912490	+	0.409098i	$0.865843\pi$
$140$	−1.50219	+	0.812366i	−0.126959	+	0.0686575i
$141$		0			0
$142$	3.44181	−	2.56563i	0.288831	−	0.215303i
$143$	−11.9914			−1.00277
$144$		0			0
$145$	10.3229			0.857271
$146$	13.2453	−	9.87346i	1.09619	−	0.817133i
$147$		0			0
$148$	−9.35886	−	17.3060i	−0.769294	−	1.42255i
$149$	−2.98723	+	11.1485i	−0.244724	+	0.913321i	0.728798	+	0.684728i	$0.240079\pi$
$149$	−2.98723	+	11.1485i	−0.244724	+	0.913321i	−0.973522	+	0.228593i	$0.926588\pi$
$150$		0			0
$151$	4.79677	−	8.30825i	0.390355	−	0.676116i	−0.602141	−	0.798390i	$-0.705685\pi$
$151$	4.79677	−	8.30825i	0.390355	−	0.676116i	0.992496	+	0.122274i	$0.0390188\pi$
$152$	0.908701	−	1.95815i	0.0737054	−	0.158827i
$153$		0			0
$154$	0.879553	+	2.21000i	0.0708764	+	0.178087i
$155$	1.49981	+	5.59736i	0.120467	+	0.449591i
$156$		0			0
$157$	−2.82669	+	10.5494i	−0.225595	+	0.841931i	0.756571	+	0.653912i	$0.226873\pi$
$157$	−2.82669	+	10.5494i	−0.225595	+	0.841931i	−0.982165	+	0.188019i	$0.939793\pi$
$158$	0.160451	+	1.36545i	0.0127648	+	0.108630i
$159$		0			0
$160$	6.64735	+	1.35124i	0.525519	+	0.106825i
$161$		−	0.567132i		−	0.0446963i
$162$		0			0
$163$	10.4644	−	10.4644i	0.819633	−	0.819633i	−0.166422	−	0.986055i	$-0.553221\pi$
$163$	10.4644	−	10.4644i	0.819633	−	0.819633i	0.986055	+	0.166422i	$0.0532214\pi$
$164$	12.3357	−	2.93966i	0.963254	−	0.229549i
$165$		0			0
$166$	12.8341	+	10.1351i	0.996123	+	0.786636i
$167$	−11.5061	+	6.64303i	−0.890367	+	0.514053i	−0.874062	−	0.485814i	$-0.838523\pi$
$167$	−11.5061	+	6.64303i	−0.890367	+	0.514053i	−0.0163043	+	0.999867i	$0.505190\pi$
$168$		0			0
$169$	−11.0637	−	6.38764i	−0.851056	−	0.491357i
$170$	−0.541283	−	1.36005i	−0.0415145	−	0.104311i
$171$		0			0
$172$	−0.694155	+	24.9119i	−0.0529288	+	1.89952i
$173$	1.95118	+	7.28191i	0.148346	+	0.553633i	0.999584	+	0.0288536i	$0.00918567\pi$
$173$	1.95118	+	7.28191i	0.148346	+	0.553633i	−0.851238	+	0.524780i	$0.824148\pi$
$174$		0			0
$175$	2.19671	−	1.26827i	0.166056	−	0.0958723i
$176$	2.94964	−	8.97550i	0.222337	−	0.676554i
$177$		0			0
$178$	−3.68114	−	4.93828i	−0.275913	−	0.370140i
$179$	−15.1045	−	15.1045i	−1.12896	−	1.12896i	−0.990346	−	0.138617i	$-0.955734\pi$
$179$	−15.1045	−	15.1045i	−1.12896	−	1.12896i	−0.138617	−	0.990346i	$-0.544266\pi$
$180$		0			0
$181$	−3.08895	+	3.08895i	−0.229600	+	0.229600i	−0.812525	−	0.582926i	$-0.801908\pi$
$181$	−3.08895	+	3.08895i	−0.229600	+	0.229600i	0.582926	+	0.812525i	$0.301908\pi$
$182$	−0.737884	+	5.05922i	−0.0546956	+	0.375014i
$183$		0			0
$184$	−1.44478	+	1.72830i	−0.106511	+	0.127412i
$185$	−5.89808	−	10.2158i	−0.433635	−	0.751078i
$186$		0			0
$187$	−1.96931	+	0.527675i	−0.144010	+	0.0385874i
$188$	3.61641	+	3.82373i	0.263754	+	0.278874i
$189$		0			0
$190$	0.511912	−	1.18876i	0.0371380	−	0.0862416i
$191$	−2.50481	+	4.33846i	−0.181242	+	0.313920i	−0.942304	−	0.334759i	$-0.891345\pi$
$191$	−2.50481	+	4.33846i	−0.181242	+	0.313920i	0.761062	+	0.648679i	$0.224678\pi$
$192$		0			0
$193$	−2.87512	−	4.97985i	−0.206956	−	0.358457i	0.743799	−	0.668404i	$-0.233022\pi$
$193$	−2.87512	−	4.97985i	−0.206956	−	0.358457i	−0.950754	+	0.309946i	$0.899689\pi$
$194$	−8.13667	+	0.956120i	−0.584179	+	0.0686454i
$195$		0			0
$196$	−12.6321	+	3.01030i	−0.902294	+	0.215022i
$197$	0.515447	+	0.515447i	0.0367240	+	0.0367240i	0.725230	−	0.688506i	$-0.241733\pi$
$197$	0.515447	+	0.515447i	0.0367240	+	0.0367240i	−0.688506	+	0.725230i	$0.741733\pi$
$198$		0			0
$199$	−21.6583			−1.53532			−0.767659	−	0.640858i	$-0.778579\pi$
$199$	−21.6583			−1.53532			−0.767659	+	0.640858i	$0.778579\pi$
$200$	−9.92526	−	1.73119i	−0.701822	−	0.122414i
$201$		0			0
$202$	−10.3552	−	8.17746i	−0.728588	−	0.575364i
$203$	−5.92130	−	1.58661i	−0.415594	−	0.111358i
$204$		0			0
$205$	7.34407	−	1.96784i	0.512932	−	0.137440i
$206$	2.26085	−	5.25014i	0.157521	−	0.365794i
$207$		0			0
$208$	15.1371	−	13.5378i	1.04957	−	0.938680i
$209$	−1.56118	−	0.901345i	−0.107989	−	0.0623473i
$210$		0			0
$211$	2.24771	+	0.602272i	0.154739	+	0.0414621i	0.335357	−	0.942091i	$-0.391143\pi$
$211$	2.24771	+	0.602272i	0.154739	+	0.0414621i	−0.180618	+	0.983553i	$0.557810\pi$
$212$	−22.0700	+	11.9351i	−1.51577	+	0.819708i
$213$		0			0
$214$	15.6683	+	2.28521i	1.07106	+	0.156214i
$215$			14.9421i			1.01904i
$216$		0			0
$217$		−	3.44121i		−	0.233604i
$218$	2.38267	−	16.3365i	0.161375	−	1.10645i
$219$		0			0
$220$	1.61792	−	5.42856i	0.109080	−	0.365994i
$221$	−4.23299	−	1.13423i	−0.284742	−	0.0762963i
$222$		0			0
$223$	−16.3604	−	9.44569i	−1.09557	−	0.632530i	−0.160520	−	0.987033i	$-0.551317\pi$
$223$	−16.3604	−	9.44569i	−1.09557	−	0.632530i	−0.935055	+	0.354502i	$0.884650\pi$
$224$	−3.60529	−	1.79676i	−0.240889	−	0.120051i
$225$		0			0
$226$	10.0557	+	4.33028i	0.668898	+	0.288046i
$227$	−7.88169	+	2.11189i	−0.523126	+	0.140171i	−0.510712	−	0.859752i	$-0.670618\pi$
$227$	−7.88169	+	2.11189i	−0.523126	+	0.140171i	−0.0124139	+	0.999923i	$0.503952\pi$
$228$		0			0
$229$	−7.31287	−	1.95948i	−0.483248	−	0.129486i	0.00896646	−	0.999960i	$-0.497146\pi$
$229$	−7.31287	−	1.95948i	−0.483248	−	0.129486i	−0.492215	+	0.870474i	$0.663813\pi$
$230$	−0.837040	+	1.05995i	−0.0551928	+	0.0698911i
$231$		0			0
$232$	14.0028	+	19.9197i	0.919332	+	1.30779i
$233$	−6.77947			−0.444138			−0.222069	−	0.975031i	$-0.571281\pi$
$233$	−6.77947			−0.444138			−0.222069	+	0.975031i	$0.571281\pi$
$234$		0			0
$235$	2.23129	+	2.23129i	0.145553	+	0.145553i
$236$	−13.7800	+	22.4024i	−0.896999	+	1.45827i
$237$		0			0
$238$	0.101448	+	0.863328i	0.00657587	+	0.0559613i
$239$	−9.48431	−	16.4273i	−0.613489	−	1.06259i	−0.990648	−	0.136445i	$-0.956432\pi$
$239$	−9.48431	−	16.4273i	−0.613489	−	1.06259i	0.377159	−	0.926149i	$-0.376901\pi$
$240$		0			0
$241$	0.0512556	−	0.0887774i	0.00330167	−	0.00571865i	−0.864370	−	0.502857i	$-0.832282\pi$
$241$	0.0512556	−	0.0887774i	0.00330167	−	0.00571865i	0.867672	+	0.497138i	$0.165616\pi$
$242$	7.04166	+	3.03233i	0.452655	+	0.194926i
$243$		0			0
$244$	−0.0316228	+	1.13488i	−0.00202444	+	0.0726535i
$245$	−7.52056	+	2.01513i	−0.480471	+	0.128742i
$246$		0			0
$247$	−1.93742	−	3.35571i	−0.123275	−	0.213519i
$248$	−8.76653	+	10.4868i	−0.556675	+	0.665915i
$249$		0			0
$250$	−14.3678	−	2.09553i	−0.908699	−	0.132533i
$251$	6.59142	−	6.59142i	0.416047	−	0.416047i	−0.467792	−	0.883839i	$-0.654950\pi$
$251$	6.59142	−	6.59142i	0.416047	−	0.416047i	0.883839	+	0.467792i	$0.154950\pi$
$252$		0			0
$253$	1.33015	+	1.33015i	0.0836258	+	0.0836258i
$254$	8.18252	−	6.09950i	0.513417	−	0.382716i
$255$		0			0
$256$	6.40958	+	14.6601i	0.400599	+	0.916254i
$257$	14.3072	−	8.26024i	0.892456	−	0.515260i	0.0177109	−	0.999843i	$-0.494362\pi$
$257$	14.3072	−	8.26024i	0.892456	−	0.515260i	0.874745	+	0.484583i	$0.161029\pi$
$258$		0			0
$259$	1.81304	+	6.76637i	0.112657	+	0.420442i
$260$	8.84606	−	8.36645i	0.548609	−	0.518865i
$261$		0			0
$262$	−7.93491	+	3.15800i	−0.490220	+	0.195102i
$263$	22.2913	+	12.8699i	1.37454	+	0.793593i	0.991496	−	0.130136i	$-0.0415415\pi$
$263$	22.2913	+	12.8699i	1.37454	+	0.793593i	0.383047	+	0.923729i	$0.374875\pi$
$264$		0			0
$265$	−13.0279	+	7.52167i	−0.800298	+	0.462052i
$266$	−0.476346	+	0.603201i	−0.0292067	+	0.0369847i
$267$		0			0
$268$	7.48119	−	12.1624i	0.456987	−	0.742934i
$269$	4.62506	−	4.62506i	0.281995	−	0.281995i	−0.551909	−	0.833904i	$-0.686101\pi$
$269$	4.62506	−	4.62506i	0.281995	−	0.281995i	0.833904	+	0.551909i	$0.186101\pi$
$270$		0			0
$271$			6.13012i			0.372378i	0.982514	+	0.186189i	$0.0596137\pi$
$271$			6.13012i			0.372378i	−0.982514	+	0.186189i	$0.940386\pi$
$272$	1.89019	−	2.88937i	0.114610	−	0.175194i
$273$		0			0
$274$	−7.65431	+	0.899439i	−0.462414	+	0.0543371i
$275$	−2.17756	+	8.12675i	−0.131312	+	0.490062i
$276$		0			0
$277$	−0.185077	−	0.690716i	−0.0111202	−	0.0415011i	0.960143	−	0.279510i	$-0.0901720\pi$
$277$	−0.185077	−	0.690716i	−0.0111202	−	0.0415011i	−0.971263	+	0.238009i	$0.923505\pi$
$278$	−19.5605	+	7.78483i	−1.17316	+	0.466903i
$279$		0			0
$280$	−2.19077	−	1.01665i	−0.130924	−	0.0607565i
$281$	5.17559	−	8.96438i	0.308750	−	0.534770i	−0.669339	−	0.742957i	$-0.733423\pi$
$281$	5.17559	−	8.96438i	0.308750	−	0.534770i	0.978089	+	0.208187i	$0.0667561\pi$
$282$		0			0
$283$	−6.79689	+	25.3663i	−0.404033	+	1.50787i	0.401799	+	0.915728i	$0.368385\pi$
$283$	−6.79689	+	25.3663i	−0.404033	+	1.50787i	−0.805832	+	0.592144i	$0.798282\pi$
$284$	5.81810	+	1.73402i	0.345241	+	0.102895i
$285$		0			0
$286$	−10.1352	−	13.5965i	−0.599309	−	0.803978i
$287$	−4.51507			−0.266516
$288$		0			0
$289$	16.2549			0.956172
$290$	8.72501	+	11.7047i	0.512350	+	0.687322i
$291$		0			0
$292$	22.3901	+	6.67312i	1.31028	+	0.390515i
$293$	5.21478	−	19.4618i	0.304651	−	1.13697i	−0.628595	−	0.777733i	$-0.716370\pi$
$293$	5.21478	−	19.4618i	0.304651	−	1.13697i	0.933246	−	0.359239i	$-0.116964\pi$
$294$		0			0
$295$	−7.88465	+	13.6566i	−0.459062	+	0.795119i
$296$	11.7123	−	25.2388i	0.680765	−	1.46697i
$297$		0			0
$298$	−15.1656	+	6.03573i	−0.878520	+	0.349640i
$299$	1.04651	+	3.90564i	0.0605215	+	0.225869i
$300$		0			0
$301$	2.29657	−	8.57090i	0.132372	−	0.494018i
$302$	13.4746	−	1.58337i	0.775376	−	0.0911125i
$303$		0			0
$304$	2.98830	−	0.624713i	0.171391	−	0.0358297i
$305$			0.680700i			0.0389768i
$306$		0			0
$307$	−5.92691	+	5.92691i	−0.338267	+	0.338267i	−0.855715	−	0.517448i	$-0.826882\pi$
$307$	−5.92691	+	5.92691i	−0.338267	+	0.338267i	0.517448	+	0.855715i	$0.326882\pi$
$308$	−1.76241	+	2.86519i	−0.100423	+	0.163260i
$309$		0			0
$310$	−5.07893	+	6.43150i	−0.288464	+	0.365284i
$311$	−22.5904	+	13.0426i	−1.28098	+	0.739576i	−0.977028	−	0.213110i	$-0.931641\pi$
$311$	−22.5904	+	13.0426i	−1.28098	+	0.739576i	−0.303956	+	0.952686i	$0.598308\pi$
$312$		0			0
$313$	0.538716	+	0.311028i	0.0304500	+	0.0175803i	0.515148	−	0.857101i	$-0.327737\pi$
$313$	0.538716	+	0.311028i	0.0304500	+	0.0175803i	−0.484698	+	0.874682i	$0.661070\pi$
$314$	−14.3506	+	5.71135i	−0.809850	+	0.322310i
$315$		0			0
$316$	−1.41261	+	1.33602i	−0.0794655	+	0.0751570i
$317$	3.67189	+	13.7037i	0.206234	+	0.769675i	0.989070	+	0.147447i	$0.0471056\pi$
$317$	3.67189	+	13.7037i	0.206234	+	0.769675i	−0.782836	+	0.622228i	$0.786228\pi$
$318$		0			0
$319$	17.6090	−	10.1666i	0.985916	−	0.569219i
$320$	4.08629	+	8.67920i	0.228430	+	0.485182i
$321$		0			0
$322$	0.643045	−	0.479345i	0.0358355	−	0.0267128i
$323$	−0.465843	−	0.465843i	−0.0259202	−	0.0259202i
$324$		0			0
$325$	−12.7877	+	12.7877i	−0.709333	+	0.709333i
$326$	20.7096	+	3.02049i	1.14700	+	0.167289i
$327$		0			0
$328$	13.7593	+	11.5022i	0.759733	+	0.635103i
$329$	−0.936941	−	1.62283i	−0.0516552	−	0.0894694i
$330$		0			0
$331$	10.3567	−	2.77508i	0.569257	−	0.152532i	0.0373014	−	0.999304i	$-0.488124\pi$
$331$	10.3567	−	2.77508i	0.569257	−	0.152532i	0.531956	+	0.846772i	$0.321457\pi$
$332$	−0.644177	+	23.1183i	−0.0353538	+	1.26878i
$333$		0			0
$334$	−17.2573	−	7.43145i	−0.944275	−	0.406631i
$335$	4.28061	−	7.41423i	0.233874	−	0.405082i
$336$		0			0
$337$	−5.91237	−	10.2405i	−0.322067	−	0.557837i	0.658847	−	0.752277i	$-0.271044\pi$
$337$	−5.91237	−	10.2405i	−0.322067	−	0.557837i	−0.980914	+	0.194440i	$0.937711\pi$
$338$	−2.10850	−	17.9435i	−0.114687	−	0.975999i
$339$		0			0
$340$	1.08460	−	1.76326i	0.0588206	−	0.0956261i
$341$	8.07099	+	8.07099i	0.437069	+	0.437069i
$342$		0			0
$343$	9.60823			0.518795
$344$	−28.8332	+	20.2687i	−1.55458	+	1.09281i
$345$		0			0
$346$	−6.60746	+	8.36708i	−0.355219	+	0.449817i
$347$	0.332138	+	0.0889961i	0.0178301	+	0.00477756i	0.267723	−	0.963496i	$-0.413729\pi$
$347$	0.332138	+	0.0889961i	0.0178301	+	0.00477756i	−0.249893	+	0.968273i	$0.580395\pi$
$348$		0			0
$349$	23.9142	−	6.40780i	1.28010	−	0.343001i	0.446207	−	0.894930i	$-0.352774\pi$
$349$	23.9142	−	6.40780i	1.28010	−	0.343001i	0.833892	+	0.551928i	$0.186108\pi$
$350$	3.29471	+	1.41879i	0.176110	+	0.0758377i
$351$		0			0
$352$	12.6700	−	4.24171i	0.675311	−	0.226084i
$353$	5.76381	+	3.32774i	0.306776	+	0.177117i	0.645483	−	0.763775i	$-0.276656\pi$
$353$	5.76381	+	3.32774i	0.306776	+	0.177117i	−0.338707	+	0.940892i	$0.609989\pi$
$354$		0			0
$355$	3.51593	+	0.942090i	0.186606	+	0.0500010i
$356$	2.48795	−	8.34775i	0.131861	−	0.442430i
$357$		0			0
$358$	4.35984	−	29.8927i	0.230425	−	1.57988i
$359$		−	25.7733i		−	1.36026i	−0.733091	−	0.680130i	$-0.761923\pi$
$359$		−	25.7733i		−	1.36026i	0.733091	−	0.680130i	$-0.238077\pi$
$360$		0			0
$361$			18.4175i			0.969341i
$362$	−6.11321	−	0.891609i	−0.321303	−	0.0468619i
$363$		0			0
$364$	−6.36007	+	3.43944i	−0.333358	+	0.180276i
$365$	13.5305	+	3.62550i	0.708221	+	0.189767i
$366$		0			0
$367$	−10.6689	−	6.15969i	−0.556912	−	0.321533i	0.194993	−	0.980805i	$-0.437532\pi$
$367$	−10.6689	−	6.15969i	−0.556912	−	0.321533i	−0.751905	+	0.659271i	$0.770865\pi$
$368$	−3.18077	−	0.177398i	−0.165809	−	0.00924753i
$369$		0			0
$370$	6.59808	−	15.3220i	0.343018	−	0.796553i
$371$	8.62898	−	2.31213i	0.447994	−	0.120040i
$372$		0			0
$373$	26.8045	+	7.18223i	1.38788	+	0.371882i	0.873978	−	0.485966i	$-0.161532\pi$
$373$	26.8045	+	7.18223i	1.38788	+	0.371882i	0.513904	+	0.857848i	$0.328199\pi$
$374$	−2.26278	−	1.78691i	−0.117006	−	0.0923990i
$375$		0			0
$376$	−1.27892	+	7.33233i	−0.0659555	+	0.378136i
$377$	43.7057			2.25096
$378$		0			0
$379$	−20.2758	−	20.2758i	−1.04150	−	1.04150i	−0.999101	−	0.0423953i	$-0.986501\pi$
$379$	−20.2758	−	20.2758i	−1.04150	−	1.04150i	−0.0423953	−	0.999101i	$-0.513499\pi$
$380$	1.78055	−	0.424315i	0.0913403	−	0.0217669i
$381$		0			0
$382$	−7.03626	+	0.826813i	−0.360006	+	0.0423035i
$383$	12.9618	+	22.4505i	0.662317	+	1.14717i	0.980005	+	0.198971i	$0.0637599\pi$
$383$	12.9618	+	22.4505i	0.662317	+	1.14717i	−0.317689	+	0.948195i	$0.602907\pi$
$384$		0			0
$385$	−1.00842	+	1.74663i	−0.0513938	+	0.0890167i
$386$	3.21635	−	7.46897i	0.163708	−	0.380161i
$387$		0			0
$388$	−7.96128	−	8.41767i	−0.404173	−	0.427342i
$389$	−6.90667	+	1.85064i	−0.350182	+	0.0938310i	−0.429622	−	0.903009i	$-0.641353\pi$
$389$	−6.90667	+	1.85064i	−0.350182	+	0.0938310i	0.0794404	+	0.996840i	$0.474687\pi$
$390$		0			0
$391$	0.343731	+	0.595360i	0.0173832	+	0.0301086i
$392$	−14.0900	−	11.7786i	−0.711653	−	0.594911i
$393$		0			0
$394$	−0.148781	+	1.02010i	−0.00749548	+	0.0513919i
$395$	−0.824310	+	0.824310i	−0.0414756	+	0.0414756i
$396$		0			0
$397$	−14.8178	−	14.8178i	−0.743683	−	0.743683i	0.229602	−	0.973285i	$-0.426258\pi$
$397$	−14.8178	−	14.8178i	−0.743683	−	0.743683i	−0.973285	+	0.229602i	$0.926258\pi$
$398$	−18.3058	−	24.5574i	−0.917587	−	1.23095i
$399$		0			0
$400$	−6.42600	−	12.7170i	−0.321300	−	0.635850i
$401$	4.39082	−	2.53504i	0.219267	−	0.126594i	−0.386344	−	0.922355i	$-0.626262\pi$
$401$	4.39082	−	2.53504i	0.219267	−	0.126594i	0.605611	+	0.795761i	$0.292929\pi$
$402$		0			0
$403$	6.34997	+	23.6984i	0.316314	+	1.18050i
$404$	0.519752	−	18.6529i	0.0258586	−	0.928017i
$405$		0			0
$406$	−3.20575	−	8.05490i	−0.159099	−	0.399758i
$407$	−20.1221	−	11.6175i	−0.997416	−	0.575858i
$408$		0			0
$409$	20.8923	−	12.0622i	1.03306	−	0.596436i	0.115199	−	0.993342i	$-0.463250\pi$
$409$	20.8923	−	12.0622i	1.03306	−	0.596436i	0.917859	+	0.396906i	$0.129916\pi$
$410$	8.43850	+	6.66386i	0.416748	+	0.329105i
$411$		0			0
$412$	7.86378	−	1.87398i	0.387421	−	0.0923245i
$413$	6.62169	−	6.62169i	0.325832	−	0.325832i
$414$		0			0
$415$			13.8663i			0.680670i
$416$	28.1439	+	5.72095i	1.37987	+	0.280493i
$417$		0			0
$418$	−0.297525	−	2.53197i	−0.0145524	−	0.123843i
$419$	−5.15499	+	19.2387i	−0.251838	+	0.939871i	0.717985	+	0.696059i	$0.245065\pi$
$419$	−5.15499	+	19.2387i	−0.251838	+	0.939871i	−0.969822	+	0.243812i	$0.921602\pi$
$420$		0			0
$421$	−8.46180	−	31.5799i	−0.412403	−	1.53911i	−0.789981	−	0.613131i	$-0.789910\pi$
$421$	−8.46180	−	31.5799i	−0.412403	−	1.53911i	0.377578	−	0.925978i	$-0.376757\pi$
$422$	1.21689	+	3.05762i	0.0592375	+	0.148843i
$423$		0			0
$424$	−32.1864	−	14.9364i	−1.56311	−	0.725377i
$425$	−1.53736	+	2.66279i	−0.0745731	+	0.129164i
$426$		0			0
$427$	0.104622	−	0.390455i	0.00506302	−	0.0188954i
$428$	10.6519	+	19.6970i	0.514878	+	0.952092i
$429$		0			0
$430$	−16.9421	+	12.6292i	−0.817023	+	0.609033i
$431$	11.5413			0.555923			0.277962	−	0.960592i	$-0.410341\pi$
$431$	11.5413			0.555923			0.277962	+	0.960592i	$0.410341\pi$
$432$		0			0
$433$	24.2215			1.16401			0.582006	−	0.813184i	$-0.302268\pi$
$433$	24.2215			1.16401			0.582006	+	0.813184i	$0.302268\pi$
$434$	3.90182	−	2.90854i	0.187293	−	0.139614i
$435$		0			0
$436$	20.5370	−	11.1061i	0.983546	−	0.531888i
$437$	−0.157324	+	0.587143i	−0.00752585	+	0.0280868i
$438$		0			0
$439$	−4.47756	+	7.75537i	−0.213702	+	0.370143i	−0.952870	−	0.303378i	$-0.901886\pi$
$439$	−4.47756	+	7.75537i	−0.213702	+	0.370143i	0.739168	+	0.673521i	$0.235219\pi$
$440$	7.52267	−	2.75378i	0.358629	−	0.131281i
$441$		0			0
$442$	−2.29171	−	5.75825i	−0.109006	−	0.273892i
$443$	−5.29309	−	19.7541i	−0.251482	−	0.938545i	−0.970014	−	0.243051i	$-0.921852\pi$
$443$	−5.29309	−	19.7541i	−0.251482	−	0.938545i	0.718531	−	0.695495i	$-0.244815\pi$
$444$		0			0
$445$	1.35170	−	5.04462i	0.0640768	−	0.239138i
$446$	−3.11793	−	26.5339i	−0.147638	−	1.25642i
$447$		0			0
$448$	−1.00995	−	5.60651i	−0.0477158	−	0.264883i
$449$		−	2.34595i		−	0.110712i	−0.998467	−	0.0553561i	$-0.982371\pi$
$449$		−	2.34595i		−	0.110712i	0.998467	−	0.0553561i	$-0.0176294\pi$
$450$		0			0
$451$	10.5896	−	10.5896i	0.498646	−	0.498646i
$452$	3.58929	+	15.0617i	0.168826	+	0.708444i
$453$		0			0
$454$	−9.05624	−	7.15169i	−0.425031	−	0.335645i
$455$	−3.75436	+	2.16758i	−0.176007	+	0.101618i
$456$		0			0
$457$	24.1000	+	13.9141i	1.12735	+	0.650876i	0.943267	−	0.332034i	$-0.107735\pi$
$457$	24.1000	+	13.9141i	1.12735	+	0.650876i	0.184084	+	0.982911i	$0.441068\pi$
$458$	−3.95914	−	9.94789i	−0.184998	−	0.464834i
$459$		0			0
$460$	−1.90930	−	0.0532015i	−0.0890216	−	0.00248053i
$461$	−5.15168	−	19.2263i	−0.239937	−	0.895459i	−0.975861	−	0.218394i	$-0.929918\pi$
$461$	−5.15168	−	19.2263i	−0.239937	−	0.895459i	0.735923	−	0.677065i	$-0.236748\pi$
$462$		0			0
$463$	21.3818	−	12.3448i	0.993699	−	0.573712i	0.0873209	−	0.996180i	$-0.472169\pi$
$463$	21.3818	−	12.3448i	0.993699	−	0.573712i	0.906378	+	0.422468i	$0.138836\pi$
$464$	−10.7507	+	32.7135i	−0.499089	+	1.51868i
$465$		0			0
$466$	−5.73007	−	7.68693i	−0.265440	−	0.356090i
$467$	14.0708	+	14.0708i	0.651120	+	0.651120i	0.953263	−	0.302143i	$-0.0977019\pi$
$467$	14.0708	+	14.0708i	0.651120	+	0.651120i	−0.302143	+	0.953263i	$0.597702\pi$
$468$		0			0
$469$	−3.59494	+	3.59494i	−0.165999	+	0.165999i
$470$	−0.644050	+	4.41586i	−0.0297078	+	0.203688i
$471$		0			0
$472$	−37.0480	+	3.31026i	−1.70527	+	0.152367i
$473$	14.7158	+	25.4885i	0.676633	+	1.17196i
$474$		0			0
$475$	−2.62604	+	0.703645i	−0.120491	+	0.0322855i
$476$	−0.893143	+	0.844719i	−0.0409371	+	0.0387176i
$477$		0			0
$478$	10.6099	−	24.6383i	0.485287	−	1.12693i
$479$	12.8097	−	22.1870i	0.585288	−	1.01375i	−0.409551	−	0.912287i	$-0.634315\pi$
$479$	12.8097	−	22.1870i	0.585288	−	1.01375i	0.994839	−	0.101462i	$-0.0323520\pi$
$480$		0			0
$481$	−24.9716	−	43.2521i	−1.13861	−	1.97212i
$482$	0.143982	−	0.0169190i	0.00655821	−	0.000770639i
$483$		0			0
$484$	2.51345	+	10.5472i	0.114248	+	0.479416i
$485$	−4.91202	−	4.91202i	−0.223043	−	0.223043i
$486$		0			0
$487$	24.8039			1.12397			0.561986	−	0.827147i	$-0.310038\pi$
$487$	24.8039			1.12397			0.561986	+	0.827147i	$0.310038\pi$
$488$	−1.31352	+	0.923357i	−0.0594602	+	0.0417984i
$489$		0			0
$490$	−8.64129	−	6.82400i	−0.390374	−	0.308277i
$491$	−36.3890	−	9.75039i	−1.64221	−	0.440029i	−0.684793	−	0.728737i	$-0.740108\pi$
$491$	−36.3890	−	9.75039i	−1.64221	−	0.440029i	−0.957417	+	0.288708i	$0.906774\pi$
$492$		0			0
$493$	7.17764	−	1.92324i	0.323265	−	0.0866185i
$494$	2.16736	−	5.03303i	0.0975142	−	0.226447i
$495$		0			0
$496$	−19.3001	−	1.07641i	−0.866599	−	0.0483320i
$497$	−1.87197	−	1.08078i	−0.0839692	−	0.0484796i
$498$		0			0
$499$	−20.1205	−	5.39127i	−0.900717	−	0.241346i	−0.221393	−	0.975185i	$-0.571060\pi$
$499$	−20.1205	−	5.39127i	−0.900717	−	0.241346i	−0.679324	+	0.733838i	$0.737727\pi$
$500$	−9.76775	−	18.0621i	−0.436827	−	0.807763i
$501$		0			0
$502$	13.0448	+	1.90258i	0.582219	+	0.0849164i
$503$		−	4.55397i		−	0.203051i	−0.994833	−	0.101526i	$-0.967628\pi$
$503$		−	4.55397i		−	0.203051i	0.994833	−	0.101526i	$-0.0323724\pi$
$504$		0			0
$505$		−	11.1880i		−	0.497858i
$506$	−0.383941	+	2.63245i	−0.0170683	+	0.117027i
$507$		0			0
$508$	13.8319	+	4.12243i	0.613690	+	0.182903i
$509$	7.44927	+	1.99603i	0.330183	+	0.0884723i	0.420102	−	0.907477i	$-0.361994\pi$
$509$	7.44927	+	1.99603i	0.330183	+	0.0884723i	−0.0899191	+	0.995949i	$0.528661\pi$
$510$		0			0
$511$	−7.20399	−	4.15923i	−0.318686	−	0.183993i
$512$	−11.2049	+	19.6583i	−0.495192	+	0.868783i
$513$		0			0
$514$	21.4584	+	9.24059i	0.946491	+	0.407585i
$515$	4.68172	−	1.25446i	0.206301	−	0.0552782i
$516$		0			0
$517$	6.00367	+	1.60868i	0.264041	+	0.0707496i
$518$	−6.13967	+	7.77471i	−0.269761	+	0.341601i
$519$		0			0
$520$	16.9631	+	2.95875i	0.743880	+	0.129750i
$521$	−41.5553			−1.82057			−0.910286	−	0.413980i	$-0.864138\pi$
$521$	−41.5553			−1.82057			−0.910286	+	0.413980i	$0.864138\pi$
$522$		0			0
$523$	7.94661	+	7.94661i	0.347481	+	0.347481i	0.859171	−	0.511689i	$-0.170980\pi$
$523$	7.94661	+	7.94661i	0.347481	+	0.347481i	−0.511689	+	0.859171i	$0.670980\pi$
$524$	−10.2874	−	6.32786i	−0.449405	−	0.276434i
$525$		0			0
$526$	4.24823	+	36.1529i	0.185232	+	1.57634i
$527$	2.08567	+	3.61248i	0.0908531	+	0.157362i
$528$		0			0
$529$	−11.1829	+	19.3693i	−0.486211	+	0.842142i
$530$	−19.5398	−	8.41436i	−0.848753	−	0.365497i
$531$		0			0
$532$	−1.08655	−	0.0302762i	−0.0471081	−	0.00131264i
$533$	31.0937	−	8.33153i	1.34682	−	0.360879i
$534$		0			0
$535$	6.71295	+	11.6272i	0.290226	+	0.502686i
$536$	20.1135	−	1.79715i	0.868771	−	0.0776252i
$537$		0			0
$538$	9.15328	+	1.33500i	0.394626	+	0.0575560i
$539$	−10.8441	+	10.8441i	−0.467089	+	0.467089i
$540$		0			0
$541$	23.7454	+	23.7454i	1.02090	+	1.02090i	0.999777	+	0.0211185i	$0.00672274\pi$
$541$	23.7454	+	23.7454i	1.02090	+	1.02090i	0.0211185	+	0.999777i	$0.493277\pi$
$542$	−6.95065	+	5.18122i	−0.298556	+	0.222553i
$543$		0			0
$544$	4.87373	−	0.298923i	0.208959	−	0.0128162i
$545$	12.1230	−	6.99924i	0.519294	−	0.299814i
$546$		0			0
$547$	−0.183171	−	0.683605i	−0.00783185	−	0.0292288i	0.961899	−	0.273404i	$-0.0881495\pi$
$547$	−0.183171	−	0.683605i	−0.00783185	−	0.0292288i	−0.969731	+	0.244175i	$0.921483\pi$
$548$	−7.48932	−	7.91865i	−0.319928	−	0.338268i
$549$		0			0
$550$	−11.0550	+	4.39977i	−0.471388	+	0.187607i
$551$	5.69010	+	3.28518i	0.242406	+	0.139953i
$552$		0			0
$553$	0.599525	−	0.346136i	0.0254944	−	0.0147192i
$554$	0.626742	−	0.793649i	0.0266277	−	0.0337189i
$555$		0			0
$556$	−25.3595	−	15.5989i	−1.07548	−	0.661541i
$557$	11.0432	−	11.0432i	0.467916	−	0.467916i	−0.433322	−	0.901239i	$-0.642659\pi$
$557$	11.0432	−	11.0432i	0.467916	−	0.467916i	0.901239	+	0.433322i	$0.142659\pi$
$558$		0			0
$559$			63.2626i			2.67572i
$560$	−0.698926	−	3.34329i	−0.0295350	−	0.141280i
$561$		0			0
$562$	14.5387	−	1.70841i	0.613280	−	0.0720650i
$563$	11.6019	−	43.2988i	0.488961	−	1.82483i	−0.0725616	−	0.997364i	$-0.523117\pi$
$563$	11.6019	−	43.2988i	0.488961	−	1.82483i	0.561522	−	0.827462i	$-0.310216\pi$
$564$		0			0
$565$	2.40271	+	8.96703i	0.101083	+	0.377246i
$566$	−34.5065	+	13.7332i	−1.45042	+	0.577248i
$567$		0			0
$568$	2.95138	+	8.06248i	0.123837	+	0.338294i
$569$	−12.4715	+	21.6013i	−0.522833	+	0.905574i	0.476814	+	0.879004i	$0.341792\pi$
$569$	−12.4715	+	21.6013i	−0.522833	+	0.905574i	−0.999647	+	0.0265695i	$0.991542\pi$
$570$		0			0
$571$	9.27714	−	34.6227i	0.388236	−	1.44892i	−0.444766	−	0.895647i	$-0.646713\pi$
$571$	9.27714	−	34.6227i	0.388236	−	1.44892i	0.833002	−	0.553270i	$-0.186620\pi$
$572$	6.85005	−	22.9837i	0.286415	−	0.960998i
$573$		0			0
$574$	−3.81617	−	5.11942i	−0.159284	−	0.213681i
$575$	2.83695			0.118309
$576$		0			0
$577$	−20.2125			−0.841457			−0.420729	−	0.907187i	$-0.638226\pi$
$577$	−20.2125			−0.841457			−0.420729	+	0.907187i	$0.638226\pi$
$578$	13.7388	+	18.4307i	0.571458	+	0.766616i
$579$		0			0
$580$	−5.89693	+	19.7858i	−0.244856	+	0.821559i
$581$	2.13122	−	7.95381i	0.0884178	−	0.329980i
$582$		0			0
$583$	−14.8155	+	25.6612i	−0.613596	+	1.06278i
$584$	11.3580	+	31.0273i	0.469996	+	1.28392i
$585$		0			0
$586$	26.4744	−	10.5365i	1.09365	−	0.435259i
$587$	−0.425823	−	1.58919i	−0.0175756	−	0.0655930i	0.956581	−	0.291466i	$-0.0941431\pi$
$587$	−0.425823	−	1.58919i	−0.0175756	−	0.0655930i	−0.974157	+	0.225873i	$0.927476\pi$
$588$		0			0
$589$	−0.954602	+	3.56262i	−0.0393337	+	0.146795i
$590$	−22.1488	+	2.60265i	−0.911851	+	0.107149i
$591$		0			0
$592$	38.5164	−	8.05198i	1.58302	−	0.330934i
$593$			35.7642i			1.46866i	0.678793	+	0.734329i	$0.262503\pi$
$593$			35.7642i			1.46866i	−0.678793	+	0.734329i	$0.737497\pi$
$594$		0			0
$595$	−0.521182	+	0.521182i	−0.0213664	+	0.0213664i
$596$	−19.6617	−	12.0941i	−0.805375	−	0.495395i
$597$		0			0
$598$	−3.54390	+	4.48768i	−0.144921	+	0.183515i
$599$	24.2410	−	13.9955i	0.990460	−	0.571842i	0.0850481	−	0.996377i	$-0.472896\pi$
$599$	24.2410	−	13.9955i	0.990460	−	0.571842i	0.905412	+	0.424535i	$0.139562\pi$
$600$		0			0
$601$	−9.43704	−	5.44848i	−0.384945	−	0.222248i	0.295023	−	0.955490i	$-0.404673\pi$
$601$	−9.43704	−	5.44848i	−0.384945	−	0.222248i	−0.679968	+	0.733242i	$0.738006\pi$
$602$	11.6592	−	4.64023i	0.475194	−	0.189122i
$603$		0			0
$604$	13.1841	+	13.9399i	0.536455	+	0.567208i
$605$	1.68253	+	6.27927i	0.0684044	+	0.255289i
$606$		0			0
$607$	−36.6954	+	21.1861i	−1.48942	+	0.859916i	−0.999927	−	0.0120914i	$-0.996151\pi$
$607$	−36.6954	+	21.1861i	−1.48942	+	0.859916i	−0.489492	+	0.872008i	$0.662818\pi$
$608$	3.23407	+	2.86028i	0.131159	+	0.116000i
$609$		0			0
$610$	−0.771814	+	0.575333i	−0.0312498	+	0.0232946i
$611$	9.44695	+	9.44695i	0.382183	+	0.382183i
$612$		0			0
$613$	11.5060	−	11.5060i	0.464722	−	0.464722i	−0.435477	−	0.900200i	$-0.643420\pi$
$613$	11.5060	−	11.5060i	0.464722	−	0.464722i	0.900200	+	0.435477i	$0.143420\pi$
$614$	−11.7297	−	1.71077i	−0.473373	−	0.0690412i
$615$		0			0
$616$	−4.73831	+	0.423371i	−0.190912	+	0.0170581i
$617$	0.520100	+	0.900840i	0.0209384	+	0.0362665i	0.876305	−	0.481757i	$-0.160001\pi$
$617$	0.520100	+	0.900840i	0.0209384	+	0.0362665i	−0.855366	+	0.518024i	$0.826668\pi$
$618$		0			0
$619$	−17.6575	+	4.73131i	−0.709714	+	0.190167i	−0.595578	−	0.803298i	$-0.703077\pi$
$619$	−17.6575	+	4.73131i	−0.709714	+	0.190167i	−0.114136	+	0.993465i	$0.536410\pi$
$620$	−11.5851	−	0.322812i	−0.465270	−	0.0129645i
$621$		0			0
$622$	−33.8820	−	14.5905i	−1.35854	−	0.585026i
$623$	−1.55069	+	2.68588i	−0.0621272	+	0.107608i
$624$		0			0
$625$	2.74947	+	4.76221i	0.109979	+	0.190489i
$626$	0.102667	+	0.873708i	0.00410341	+	0.0349204i
$627$		0			0
$628$	−18.6051	−	11.4442i	−0.742423	−	0.456672i
$629$	−6.00428	−	6.00428i	−0.239406	−	0.239406i
$630$		0			0
$631$	18.9729			0.755301			0.377650	−	0.925948i	$-0.376732\pi$
$631$	18.9729			0.755301			0.377650	+	0.925948i	$0.376732\pi$
$632$	−2.70880	−	0.472476i	−0.107750	−	0.0187941i
$633$		0			0
$634$	−12.4344	+	15.7458i	−0.493835	+	0.625347i
$635$	8.35872	+	2.23971i	0.331706	+	0.0888803i
$636$		0			0
$637$	−31.8409	+	8.53175i	−1.26158	+	0.338040i
$638$	26.4107	+	11.3732i	1.04561	+	0.450268i
$639$		0			0
$640$	−6.38718	+	11.9690i	−0.252475	+	0.473116i
$641$	−6.62975	−	3.82769i	−0.261859	−	0.151185i	0.363323	−	0.931663i	$-0.381642\pi$
$641$	−6.62975	−	3.82769i	−0.261859	−	0.151185i	−0.625182	+	0.780479i	$0.714975\pi$
$642$		0			0
$643$	−18.3287	−	4.91116i	−0.722813	−	0.193677i	−0.121387	−	0.992605i	$-0.538734\pi$
$643$	−18.3287	−	4.91116i	−0.722813	−	0.193677i	−0.601427	+	0.798928i	$0.705401\pi$
$644$	1.08701	+	0.323972i	0.0428343	+	0.0127663i
$645$		0			0
$646$	0.134463	−	0.921931i	0.00529038	−	0.0362729i
$647$		−	1.59451i		−	0.0626865i	−0.999509	−	0.0313432i	$-0.990022\pi$
$647$		−	1.59451i		−	0.0626865i	0.999509	−	0.0313432i	$-0.00997849\pi$
$648$		0			0
$649$			31.0610i			1.21925i
$650$	−25.3076	−	3.69110i	−0.992645	−	0.144777i
$651$		0			0
$652$	14.0792	+	26.0346i	0.551382	+	1.01959i
$653$	1.34296	+	0.359845i	0.0525540	+	0.0140818i	0.285000	−	0.958527i	$-0.408006\pi$
$653$	1.34296	+	0.359845i	0.0525540	+	0.0140818i	−0.232446	+	0.972609i	$0.574673\pi$
$654$		0			0
$655$	−6.27121	−	3.62069i	−0.245037	−	0.141472i
$656$	−1.41231	+	25.3228i	−0.0551413	+	0.988691i
$657$		0			0
$658$	1.04814	−	2.43398i	0.0408607	−	0.0948865i
$659$	−28.0586	+	7.51827i	−1.09301	+	0.292870i	−0.759914	−	0.650024i	$-0.774759\pi$
$659$	−28.0586	+	7.51827i	−1.09301	+	0.292870i	−0.333093	+	0.942894i	$0.608092\pi$
$660$		0			0
$661$	−0.302749	−	0.0811214i	−0.0117756	−	0.00315526i	0.252926	−	0.967486i	$-0.418607\pi$
$661$	−0.302749	−	0.0811214i	−0.0117756	−	0.00315526i	−0.264702	+	0.964330i	$0.585274\pi$
$662$	11.9001	+	9.39749i	0.462511	+	0.365244i
$663$		0			0
$664$	−26.7572	+	18.8094i	−1.03838	+	0.729945i
$665$	−0.651712			−0.0252723
$666$		0			0
$667$	−4.84807	−	4.84807i	−0.187718	−	0.187718i
$668$	−6.15980	−	25.8483i	−0.238330	−	1.00010i
$669$		0			0
$670$	12.0246	−	1.41299i	0.464553	−	0.0545884i
$671$	0.670391	+	1.16115i	0.0258802	+	0.0448257i
$672$		0			0
$673$	−14.6918	+	25.4470i	−0.566329	+	0.980911i	0.430595	+	0.902545i	$0.358304\pi$
$673$	−14.6918	+	25.4470i	−0.566329	+	0.980911i	−0.996925	+	0.0783659i	$0.975030\pi$
$674$	6.61407	−	15.3591i	0.254764	−	0.591612i
$675$		0			0
$676$	18.5632	−	17.5567i	0.713969	−	0.675259i
$677$	7.06366	−	1.89270i	0.271478	−	0.0727424i	−0.120511	−	0.992712i	$-0.538453\pi$
$677$	7.06366	−	1.89270i	0.271478	−	0.0727424i	0.391990	+	0.919969i	$0.371787\pi$
$678$		0			0
$679$	2.06261	+	3.57254i	0.0791556	+	0.137102i
$680$	2.91599	−	0.260545i	0.111823	−	0.00999145i
$681$		0			0
$682$	−2.32965	+	15.9730i	−0.0892069	+	0.611637i
$683$	−20.6264	+	20.6264i	−0.789247	+	0.789247i	−0.981371	−	0.192123i	$-0.938463\pi$
$683$	−20.6264	+	20.6264i	−0.789247	+	0.789247i	0.192123	+	0.981371i	$0.438463\pi$
$684$		0			0
$685$	−4.62083	−	4.62083i	−0.176553	−	0.176553i
$686$	8.12095	+	10.8943i	0.310059	+	0.415947i
$687$		0			0
$688$	−47.3517	−	15.5613i	−1.80527	−	0.593269i
$689$	−55.1583	+	31.8456i	−2.10136	+	1.21322i
$690$		0			0
$691$	−0.467582	−	1.74504i	−0.0177876	−	0.0663844i	0.956462	−	0.291858i	$-0.0942736\pi$
$691$	−0.467582	−	1.74504i	−0.0177876	−	0.0663844i	−0.974249	+	0.225474i	$0.927607\pi$
$692$	−15.0717	−	0.419964i	−0.572941	−	0.0159647i
$693$		0			0
$694$	0.179817	+	0.451816i	0.00682577	+	0.0171507i
$695$	−15.4593	−	8.92542i	−0.586404	−	0.338560i
$696$		0			0
$697$	4.73979	−	2.73652i	0.179532	−	0.103653i
$698$	27.4780	+	21.6993i	1.04006	+	0.821330i
$699$		0			0
$700$	1.17601	+	4.93489i	0.0444491	+	0.186521i
$701$	−31.2193	+	31.2193i	−1.17914	+	1.17914i	−0.199174	+	0.979964i	$0.563826\pi$
$701$	−31.2193	+	31.2193i	−1.17914	+	1.17914i	−0.979964	+	0.199174i	$0.936174\pi$
$702$		0			0
$703$		−	7.50805i		−	0.283171i
$704$	15.5182	+	10.7807i	0.584865	+	0.406315i
$705$		0			0
$706$	1.09845	+	9.34794i	0.0413408	+	0.351814i
$707$	−1.71957	+	6.41751i	−0.0646709	+	0.241355i
$708$		0			0
$709$	−5.00387	−	18.6747i	−0.187924	−	0.701344i	−0.993986	−	0.109511i	$-0.965071\pi$
$709$	−5.00387	−	18.6747i	−0.187924	−	0.701344i	0.806061	−	0.591832i	$-0.201595\pi$
$710$	1.90350	+	4.78281i	0.0714371	+	0.179496i
$711$		0			0
$712$	11.5680	−	4.23461i	0.433528	−	0.158699i
$713$	1.92438	−	3.33312i	0.0720686	−	0.124826i
$714$		0			0
$715$	3.72162	−	13.8893i	0.139181	−	0.519430i
$716$	37.5789	−	20.3222i	1.40439	−	0.759475i
$717$		0			0
$718$	29.2231	−	21.7838i	1.09060	−	0.812963i
$719$	−5.23889			−0.195378			−0.0976889	−	0.995217i	$-0.531145\pi$
$719$	−5.23889			−0.195378			−0.0976889	+	0.995217i	$0.531145\pi$
$720$		0			0
$721$	−2.87828			−0.107193
$722$	−20.8827	+	15.5666i	−0.777175	+	0.579329i
$723$		0			0
$724$	−4.15598	−	7.68508i	−0.154456	−	0.285614i
$725$	7.93665	−	29.6200i	0.294760	−	1.10006i
$726$		0			0
$727$	20.0812	−	34.7817i	0.744772	−	1.28998i	−0.205530	−	0.978651i	$-0.565892\pi$
$727$	20.0812	−	34.7817i	0.744772	−	1.28998i	0.950301	−	0.311332i	$-0.100775\pi$
$728$	−9.27540	−	4.30435i	−0.343769	−	0.159530i
$729$		0			0
$730$	7.32534	+	18.4060i	0.271123	+	0.681235i
$731$	2.78383	+	10.3894i	0.102964	+	0.384266i
$732$		0			0
$733$	−12.3274	+	46.0065i	−0.455324	+	1.69929i	0.231811	+	0.972761i	$0.425535\pi$
$733$	−12.3274	+	46.0065i	−0.455324	+	1.69929i	−0.687135	+	0.726530i	$0.741132\pi$
$734$	−2.03325	−	17.3032i	−0.0750488	−	0.638672i
$735$		0			0
$736$	−2.48727	−	3.75647i	−0.0916821	−	0.138465i
$737$		−	16.8631i		−	0.621161i
$738$		0			0
$739$	9.18363	−	9.18363i	0.337825	−	0.337825i	−0.517723	−	0.855548i	$-0.673220\pi$
$739$	9.18363	−	9.18363i	0.337825	−	0.337825i	0.855548	+	0.517723i	$0.173220\pi$
$740$	22.9497	−	5.46903i	0.843646	−	0.201046i
$741$		0			0
$742$	9.91489	+	7.82976i	0.363987	+	0.287440i
$743$	42.0760	−	24.2926i	1.54362	−	0.891208i	0.545011	−	0.838429i	$-0.316525\pi$
$743$	42.0760	−	24.2926i	1.54362	−	0.891208i	0.998606	−	0.0527792i	$-0.0168079\pi$
$744$		0			0
$745$	−11.9859	−	6.92004i	−0.439128	−	0.253531i
$746$	14.5117	+	36.4628i	0.531313	+	1.33500i
$747$		0			0
$748$	0.113575	−	4.07597i	0.00415270	−	0.149032i
$749$	−2.06353	−	7.70120i	−0.0753998	−	0.281396i
$750$		0			0
$751$	25.5639	−	14.7593i	0.932839	−	0.538575i	0.0451310	−	0.998981i	$-0.485629\pi$
$751$	25.5639	−	14.7593i	0.932839	−	0.538575i	0.887708	+	0.460406i	$0.152296\pi$
$752$	−9.39475	+	4.74723i	−0.342591	+	0.173114i
$753$		0			0
$754$	36.9404	+	49.5559i	1.34529	+	1.80472i
$755$	8.13448	+	8.13448i	0.296044	+	0.296044i
$756$		0			0
$757$	30.3982	−	30.3982i	1.10484	−	1.10484i	0.111022	−	0.993818i	$-0.464588\pi$
$757$	30.3982	−	30.3982i	1.10484	−	1.10484i	0.993818	−	0.111022i	$-0.0354123\pi$
$758$	5.85250	−	40.1270i	0.212572	−	1.45748i
$759$		0			0
$760$	1.98605	+	1.66025i	0.0720415	+	0.0602235i
$761$	2.97086	+	5.14568i	0.107694	+	0.186531i	0.914836	−	0.403827i	$-0.132320\pi$
$761$	2.97086	+	5.14568i	0.107694	+	0.186531i	−0.807142	+	0.590357i	$0.798987\pi$
$762$		0			0
$763$	−8.02963	+	2.15153i	−0.290692	+	0.0778907i
$764$	−6.88459	−	7.27926i	−0.249076	−	0.263354i
$765$		0			0
$766$	−14.5001	+	33.6721i	−0.523911	+	1.21662i
$767$	−33.3825	+	57.8201i	−1.20537	+	2.08776i
$768$		0			0
$769$	−6.00863	−	10.4073i	−0.216677	−	0.375295i	0.737113	−	0.675769i	$-0.236188\pi$
$769$	−6.00863	−	10.4073i	−0.216677	−	0.375295i	−0.953790	+	0.300474i	$0.902855\pi$
$770$	−2.83275	+	0.332870i	−0.102085	+	0.0119958i
$771$		0			0
$772$	11.1872	−	2.66597i	0.402636	−	0.0959504i
$773$	−22.2746	−	22.2746i	−0.801163	−	0.801163i	0.182114	−	0.983277i	$-0.441706\pi$
$773$	−22.2746	−	22.2746i	−0.801163	−	0.801163i	−0.983277	+	0.182114i	$0.941706\pi$
$774$		0			0
$775$	17.2139			0.618340
$776$	2.81546	−	16.1416i	0.101069	−	0.579450i
$777$		0			0
$778$	−7.93592	−	6.26697i	−0.284517	−	0.224682i
$779$	4.67437	+	1.25249i	0.167477	+	0.0448753i
$780$		0			0
$781$	6.92536	−	1.85565i	0.247809	−	0.0664002i
$782$	−0.384526	+	0.892943i	−0.0137506	+	0.0319316i
$783$		0			0
$784$	1.44625	−	25.9314i	0.0516517	−	0.926121i
$785$	−11.3417	−	6.54815i	−0.404803	−	0.233713i
$786$		0			0
$787$	−5.98650	−	1.60408i	−0.213396	−	0.0571792i	0.150537	−	0.988604i	$-0.451900\pi$
$787$	−5.98650	−	1.60408i	−0.213396	−	0.0571792i	−0.363933	+	0.931425i	$0.618566\pi$
$788$	−1.28240	+	0.693501i	−0.0456834	+	0.0247050i
$789$		0			0
$790$	−1.63136	−	0.237933i	−0.0580412	−	0.00846528i
$791$		−	5.51285i		−	0.196014i
$792$		0			0
$793$			2.88198i			0.102342i
$794$	4.27708	−	29.3253i	0.151788	−	1.04072i
$795$		0			0
$796$	12.3722	−	41.5122i	0.438522	−	1.47136i
$797$	−33.1217	−	8.87494i	−1.17323	−	0.314367i	−0.380993	−	0.924578i	$-0.624418\pi$
$797$	−33.1217	−	8.87494i	−1.17323	−	0.314367i	−0.792239	+	0.610211i	$0.791085\pi$
$798$		0			0
$799$	1.96715	+	1.13573i	0.0695927	+	0.0401794i
$800$	8.98791	−	18.0347i	0.317771	−	0.637621i
$801$		0			0
$802$	6.58552	+	2.83591i	0.232543	+	0.100139i
$803$	26.6513	−	7.14118i	0.940503	−	0.252007i
$804$		0			0
$805$	0.656892	+	0.176014i	0.0231524	+	0.00620367i
$806$	−21.5035	+	27.2300i	−0.757427	+	0.959136i
$807$		0			0
$808$	21.5890	−	15.1763i	0.759497	−	0.533900i
$809$	12.8401			0.451432			0.225716	−	0.974193i	$-0.427528\pi$
$809$	12.8401			0.451432			0.225716	+	0.974193i	$0.427528\pi$
$810$		0			0
$811$	−37.1183	−	37.1183i	−1.30340	−	1.30340i	−0.926086	−	0.377314i	$-0.876848\pi$
$811$	−37.1183	−	37.1183i	−1.30340	−	1.30340i	−0.377314	−	0.926086i	$-0.623152\pi$
$812$	6.42355	−	10.4429i	0.225422	−	0.366475i
$813$		0			0
$814$	−3.83483	−	32.6347i	−0.134411	−	1.14385i
$815$	8.87287	+	15.3683i	0.310803	+	0.538327i
$816$		0			0
$817$	−4.75519	+	8.23624i	−0.166363	+	0.288149i
$818$	31.3351	+	13.4938i	1.09561	+	0.471798i
$819$		0			0
$820$	−0.423549	+	15.2004i	−0.0147910	+	0.530820i
$821$	−27.1312	+	7.26977i	−0.946884	+	0.253717i	−0.699040	−	0.715083i	$-0.746389\pi$
$821$	−27.1312	+	7.26977i	−0.946884	+	0.253717i	−0.247844	+	0.968800i	$0.579722\pi$
$822$		0			0
$823$	9.61847	+	16.6597i	0.335279	+	0.580720i	0.983538	−	0.180700i	$-0.0578362\pi$
$823$	9.61847	+	16.6597i	0.335279	+	0.580720i	−0.648260	+	0.761419i	$0.724503\pi$
$824$	8.77135	+	7.33247i	0.305565	+	0.255439i
$825$		0			0
$826$	13.1047	+	1.91132i	0.455972	+	0.0665032i
$827$	−28.7848	+	28.7848i	−1.00095	+	1.00095i	−0.000945916		1.00000i	$0.500301\pi$
$827$	−28.7848	+	28.7848i	−1.00095	+	1.00095i	−1.00000		0.000945916i	$0.999699\pi$
$828$		0			0
$829$	−23.5696	−	23.5696i	−0.818606	−	0.818606i	0.167300	−	0.985906i	$-0.446495\pi$
$829$	−23.5696	−	23.5696i	−0.818606	−	0.818606i	−0.985906	+	0.167300i	$0.946495\pi$
$830$	−15.7223	+	11.7199i	−0.545730	+	0.406804i
$831$		0			0
$832$	17.3007	+	36.7465i	0.599795	+	1.27395i
$833$	−4.85369	+	2.80228i	−0.168171	+	0.0970933i
$834$		0			0
$835$	−4.12343	−	15.3889i	−0.142697	−	0.532553i
$836$	2.61941	−	2.47739i	0.0905941	−	0.0856823i
$837$		0			0
$838$	−26.1709	+	10.4157i	−0.904058	+	0.359804i
$839$	−5.76796	−	3.33013i	−0.199132	−	0.114969i	0.397119	−	0.917767i	$-0.370010\pi$
$839$	−5.76796	−	3.33013i	−0.199132	−	0.114969i	−0.596251	+	0.802798i	$0.703344\pi$
$840$		0			0
$841$	−39.0658	+	22.5546i	−1.34710	+	0.777747i
$842$	28.6550	−	36.2860i	0.987515	−	1.25050i
$843$		0			0
$844$	−2.43836	+	3.96410i	−0.0839319	+	0.136450i
$845$	10.8323	−	10.8323i	0.372643	−	0.372643i
$846$		0			0
$847$		−	3.86044i		−	0.132646i
$848$	−10.2685	−	49.1190i	−0.352621	−	1.68675i
$849$		0			0
$850$	−4.31861	+	0.507469i	−0.148127	+	0.0174060i
$851$	−2.02777	+	7.56773i	−0.0695109	+	0.259418i
$852$		0			0
$853$	−2.94440	−	10.9887i	−0.100814	−	0.376245i	0.897022	−	0.441985i	$-0.145726\pi$
$853$	−2.94440	−	10.9887i	−0.100814	−	0.376245i	−0.997837	+	0.0657407i	$0.979059\pi$
$854$	0.531146	−	0.211390i	0.0181754	−	0.00723360i
$855$		0			0
$856$	−13.3305	+	28.7258i	−0.455627	+	0.981826i
$857$	15.7885	−	27.3465i	0.539326	−	0.934140i	−0.459615	−	0.888118i	$-0.652013\pi$
$857$	15.7885	−	27.3465i	0.539326	−	0.934140i	0.998940	−	0.0460211i	$-0.0146542\pi$
$858$		0			0
$859$	7.30262	−	27.2537i	0.249162	−	0.929886i	−0.722084	−	0.691806i	$-0.756815\pi$
$859$	7.30262	−	27.2537i	0.249162	−	0.929886i	0.971246	−	0.238080i	$-0.0765180\pi$
$860$	−28.6393	−	8.53561i	−0.976591	−	0.291062i
$861$		0			0
$862$	9.75477	+	13.0861i	0.332249	+	0.445714i
$863$	29.1288			0.991557			0.495779	−	0.868449i	$-0.334883\pi$
$863$	29.1288			0.991557			0.495779	+	0.868449i	$0.334883\pi$
$864$		0			0
$865$	−9.03998			−0.307369
$866$	20.4722	+	27.4637i	0.695675	+	0.933253i
$867$		0			0
$868$	6.59570	+	1.96578i	0.223873	+	0.0667228i
$869$	−0.594298	+	2.21795i	−0.0201602	+	0.0752388i
$870$		0			0
$871$	18.1235	−	31.3907i	0.614090	−	1.06363i
$872$	29.9508	+	13.8990i	1.01426	+	0.470679i
$873$		0			0
$874$	−0.798705	+	0.317875i	−0.0270166	+	0.0107523i
$875$	1.89225	+	7.06198i	0.0639698	+	0.238739i
$876$		0			0
$877$	8.63165	−	32.2138i	0.291470	−	1.08778i	−0.652510	−	0.757780i	$-0.726284\pi$
$877$	8.63165	−	32.2138i	0.291470	−	1.08778i	0.943980	−	0.330001i	$-0.107049\pi$
$878$	−12.5779	+	1.47800i	−0.424484	+	0.0498801i
$879$		0			0
$880$	9.48061	+	6.20209i	0.319591	+	0.209072i
$881$			10.4223i			0.351136i	0.984467	+	0.175568i	$0.0561763\pi$
$881$			10.4223i			0.351136i	−0.984467	+	0.175568i	$0.943824\pi$
$882$		0			0
$883$	7.73247	−	7.73247i	0.260218	−	0.260218i	−0.564924	−	0.825143i	$-0.691095\pi$
$883$	7.73247	−	7.73247i	0.260218	−	0.260218i	0.825143	+	0.564924i	$0.191095\pi$
$884$	4.59203	−	7.46538i	0.154447	−	0.251088i
$885$		0			0
$886$	17.9245	−	22.6979i	0.602185	−	0.762551i
$887$	22.0565	−	12.7343i	0.740584	−	0.427577i	−0.0816974	−	0.996657i	$-0.526034\pi$
$887$	22.0565	−	12.7343i	0.740584	−	0.427577i	0.822282	+	0.569081i	$0.192701\pi$
$888$		0			0
$889$	−4.45039	−	2.56943i	−0.149261	−	0.0861761i
$890$	6.86233	−	2.73112i	0.230026	−	0.0915474i
$891$		0			0
$892$	27.4502	−	25.9619i	0.919102	−	0.869270i
$893$	0.519821	+	1.94000i	0.0173951	+	0.0649196i
$894$		0			0
$895$	22.1829	−	12.8073i	0.741492	−	0.428100i
$896$	5.50334	−	5.88381i	0.183854	−	0.196564i
$897$		0			0
$898$	2.65996	−	1.98282i	0.0887641	−	0.0661674i
$899$	−29.4168	−	29.4168i	−0.981104	−	0.981104i
$900$		0			0
$901$	−7.65711	+	7.65711i	−0.255095	+	0.255095i
$902$	20.9575	+	3.05664i	0.697808	+	0.101775i
$903$		0			0
$904$	−14.0441	+	16.8000i	−0.467099	+	0.558760i
$905$	−2.61915	−	4.53651i	−0.0870637	−	0.150799i
$906$		0			0
$907$	35.2550	−	9.44656i	1.17062	−	0.313668i	0.379423	−	0.925223i	$-0.376123\pi$
$907$	35.2550	−	9.44656i	1.17062	−	0.313668i	0.791202	+	0.611555i	$0.209456\pi$
$908$	0.454555	−	16.3131i	0.0150849	−	0.541370i
$909$		0			0
$910$	−5.63093	−	2.42483i	−0.186663	−	0.0803824i
$911$	4.86150	−	8.42037i	0.161069	−	0.278979i	−0.774183	−	0.632961i	$-0.781839\pi$
$911$	4.86150	−	8.42037i	0.161069	−	0.278979i	0.935252	+	0.353982i	$0.115173\pi$
$912$		0			0
$913$	13.6563	+	23.6534i	0.451957	+	0.782813i
$914$	4.59293	+	39.0862i	0.151920	+	1.29286i
$915$		0			0
$916$	7.93315	−	12.8971i	0.262119	−	0.426133i
$917$	3.04073	+	3.04073i	0.100414	+	0.100414i
$918$		0			0
$919$	−26.5741			−0.876599			−0.438300	−	0.898829i	$-0.644419\pi$
$919$	−26.5741			−0.876599			−0.438300	+	0.898829i	$0.644419\pi$
$920$	−1.55343	−	2.20983i	−0.0512152	−	0.0728561i
$921$		0			0
$922$	17.4456	−	22.0915i	0.574540	−	0.727544i
$923$	14.8859	+	3.98867i	0.489976	+	0.131289i
$924$		0			0
$925$	−33.8472	+	9.06934i	−1.11289	+	0.298198i
$926$	32.0693	+	13.8099i	1.05386	+	0.453823i
$927$		0			0
$928$	−46.1789	+	15.4600i	−1.51590	+	0.507498i
$929$	−20.9365	−	12.0877i	−0.686904	−	0.396584i	0.115547	−	0.993302i	$-0.463138\pi$
$929$	−20.9365	−	12.0877i	−0.686904	−	0.396584i	−0.802451	+	0.596718i	$0.796471\pi$
$930$		0			0
$931$	−4.78670	−	1.28259i	−0.156878	−	0.0420353i
$932$	3.87275	−	12.9941i	0.126856	−	0.425636i
$933$		0			0
$934$	−4.06147	+	27.8470i	−0.132895	+	0.911182i
$935$		−	2.44476i		−	0.0799521i
$936$		0			0
$937$			1.33551i			0.0436291i	0.999762	+	0.0218146i	$0.00694434\pi$
$937$			1.33551i			0.0436291i	−0.999762	+	0.0218146i	$0.993056\pi$
$938$	−7.11460	−	1.03766i	−0.232300	−	0.0338808i
$939$		0			0
$940$	−5.55129	+	3.00206i	−0.181063	+	0.0979164i
$941$	−21.3261	−	5.71431i	−0.695211	−	0.186281i	−0.106126	−	0.994353i	$-0.533845\pi$
$941$	−21.3261	−	5.71431i	−0.695211	−	0.186281i	−0.589085	+	0.808071i	$0.700512\pi$
$942$		0			0
$943$	−4.37325	−	2.52490i	−0.142413	−	0.0822220i
$944$	−35.0666	−	39.2091i	−1.14132	−	1.27615i
$945$		0			0
$946$	−16.4623	+	38.2287i	−0.535236	+	1.24292i
$947$	−23.4634	+	6.28700i	−0.762458	+	0.204300i	−0.619037	−	0.785362i	$-0.712477\pi$
$947$	−23.4634	+	6.28700i	−0.762458	+	0.204300i	−0.143421	+	0.989662i	$0.545810\pi$
$948$		0			0
$949$	57.2863	+	15.3498i	1.85959	+	0.498277i
$950$	−3.01738	−	2.38282i	−0.0978967	−	0.0773088i
$951$		0			0
$952$	−1.71268	−	0.298730i	−0.0555082	−	0.00968190i
$953$	15.2157			0.492885			0.246442	−	0.969157i	$-0.420738\pi$
$953$	15.2157			0.492885			0.246442	+	0.969157i	$0.420738\pi$
$954$		0			0
$955$	−4.24772	−	4.24772i	−0.137453	−	0.137453i
$956$	36.9038	−	8.79439i	1.19355	−	0.284431i
$957$		0			0
$958$	35.9836	−	4.22835i	1.16258	−	0.136612i
$959$	1.94033	+	3.36075i	0.0626566	+	0.108524i
$960$		0			0
$961$	−3.82339	+	6.62230i	−0.123335	+	0.213623i
$962$	27.9353	−	64.8711i	0.900670	−	2.09153i
$963$		0			0
$964$	0.140879	+	0.148955i	0.00453739	+	0.00479751i
$965$	6.66032	−	1.78463i	0.214403	−	0.0574492i
$966$		0			0
$967$	−16.3260	−	28.2775i	−0.525010	−	0.909344i	−0.999576	−	0.0291241i	$-0.990728\pi$
$967$	−16.3260	−	28.2775i	−0.525010	−	0.909344i	0.474566	−	0.880220i	$-0.342605\pi$
$968$	−9.83454	+	11.7644i	−0.316094	+	0.378123i
$969$		0			0
$970$	1.41783	−	9.72120i	0.0455238	−	0.312129i
$971$	23.6028	−	23.6028i	0.757449	−	0.757449i	−0.218408	−	0.975858i	$-0.570086\pi$
$971$	23.6028	−	23.6028i	0.757449	−	0.757449i	0.975858	+	0.218408i	$0.0700864\pi$
$972$		0			0
$973$	7.49574	+	7.49574i	0.240303	+	0.240303i
$974$	20.9644	+	28.1240i	0.671744	+	0.901150i
$975$		0			0
$976$	−2.15715	−	0.708909i	−0.0690486	−	0.0226916i
$977$	−30.2605	+	17.4709i	−0.968119	+	0.558944i	−0.898662	−	0.438641i	$-0.855460\pi$
$977$	−30.2605	+	17.4709i	−0.968119	+	0.558944i	−0.0694570	+	0.997585i	$0.522127\pi$
$978$		0			0
$979$	−2.66246	−	9.93644i	−0.0850926	−	0.317570i
$980$	0.433728	−	15.5657i	0.0138549	−	0.497227i
$981$		0			0
$982$	−19.7007	−	49.5008i	−0.628676	−	1.57964i
$983$	28.8301	+	16.6450i	0.919536	+	0.530895i	0.883487	−	0.468455i	$-0.155189\pi$
$983$	28.8301	+	16.6450i	0.919536	+	0.530895i	0.0360492	+	0.999350i	$0.488523\pi$
$984$		0			0
$985$	−0.756999	+	0.437053i	−0.0241200	+	0.0139257i
$986$	8.24728	+	6.51285i	0.262647	+	0.207411i
$987$		0			0
$988$	7.53859	−	1.79649i	0.239834	−	0.0571539i
$989$	7.01742	−	7.01742i	0.223141	−	0.223141i
$990$		0			0
$991$		−	10.4637i		−	0.332390i	−0.986093	−	0.166195i	$-0.946852\pi$
$991$		−	10.4637i		−	0.332390i	0.986093	−	0.166195i	$-0.0531482\pi$
$992$	−15.0921	−	22.7932i	−0.479175	−	0.723686i
$993$		0			0
$994$	−0.356755	−	3.03602i	−0.0113156	−	0.0962967i
$995$	6.72182	−	25.0862i	0.213096	−	0.795286i
$996$		0			0
$997$	7.47474	+	27.8961i	0.236727	+	0.883479i	0.977363	+	0.211571i	$0.0678580\pi$
$997$	7.47474	+	27.8961i	0.236727	+	0.883479i	−0.740635	+	0.671907i	$0.765475\pi$
$998$	−10.8931	−	27.3704i	−0.344815	−	0.866396i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.35.16		88
3.2	odd	2		144.2.u.a.83.7	yes	88
4.3	odd	2		1728.2.z.a.1007.8		88
9.4	even	3		144.2.u.a.131.1	yes	88
9.5	odd	6	inner	432.2.v.a.179.22		88
12.11	even	2		576.2.y.a.47.4		88
16.5	even	4		1728.2.z.a.143.8		88
16.11	odd	4	inner	432.2.v.a.251.22		88
36.23	even	6		1728.2.z.a.1583.8		88
36.31	odd	6		576.2.y.a.239.8		88
48.5	odd	4		576.2.y.a.335.8		88
48.11	even	4		144.2.u.a.11.1	✓	88
144.5	odd	12		1728.2.z.a.719.8		88
144.59	even	12	inner	432.2.v.a.395.16		88
144.85	even	12		576.2.y.a.527.4		88
144.139	odd	12		144.2.u.a.59.7	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.1	✓	88	48.11	even	4
144.2.u.a.59.7	yes	88	144.139	odd	12
144.2.u.a.83.7	yes	88	3.2	odd	2
144.2.u.a.131.1	yes	88	9.4	even	3
432.2.v.a.35.16		88	1.1	even	1	trivial
432.2.v.a.179.22		88	9.5	odd	6	inner
432.2.v.a.251.22		88	16.11	odd	4	inner
432.2.v.a.395.16		88	144.59	even	12	inner
576.2.y.a.47.4		88	12.11	even	2
576.2.y.a.239.8		88	36.31	odd	6
576.2.y.a.335.8		88	48.5	odd	4
576.2.y.a.527.4		88	144.85	even	12
1728.2.z.a.143.8		88	16.5	even	4
1728.2.z.a.719.8		88	144.5	odd	12
1728.2.z.a.1007.8		88	4.3	odd	2
1728.2.z.a.1583.8		88	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.845208 + 1.13385i) q^{2} +(-0.571246 + 1.91668i) q^{4} +(-0.310357 + 1.15827i) q^{5} +(0.356047 - 0.616691i) q^{7} +(-2.65606 + 0.972288i) q^{8} +O(q^{10})\)	\(q+(0.845208 + 1.13385i) q^{2} +(-0.571246 + 1.91668i) q^{4} +(-0.310357 + 1.15827i) q^{5} +(0.356047 - 0.616691i) q^{7} +(-2.65606 + 0.972288i) q^{8} +(-1.57562 + 0.627079i) q^{10} +(0.611314 + 2.28146i) q^{11} +(-1.31401 + 4.90394i) q^{13} +(1.00017 - 0.117528i) q^{14} +(-3.34736 - 2.18980i) q^{16} +0.863180i q^{17} +(-0.539682 + 0.539682i) q^{19} +(-2.04275 - 1.25651i) q^{20} +(-2.07015 + 2.62145i) q^{22} +(0.689728 - 0.398215i) q^{23} +(3.08486 + 1.78104i) q^{25} +(-6.67096 + 2.65496i) q^{26} +(0.978612 + 1.03471i) q^{28} +(-2.22809 - 8.31534i) q^{29} +(4.18508 - 2.41626i) q^{31} +(-0.346304 - 5.64624i) q^{32} +(-0.978720 + 0.729567i) q^{34} +(0.603793 + 0.603793i) q^{35} +(-6.95600 + 6.95600i) q^{37} +(-1.06806 - 0.155776i) q^{38} +(-0.301843 - 3.37819i) q^{40} +(-3.17027 - 5.49108i) q^{41} +(12.0362 - 3.22509i) q^{43} +(-4.72204 - 0.131577i) q^{44} +(1.03448 + 0.445476i) q^{46} +(1.31575 - 2.27895i) q^{47} +(3.24646 + 5.62304i) q^{49} +(0.587906 + 5.00313i) q^{50} +(-8.64869 - 5.31990i) q^{52} +(8.87081 + 8.87081i) q^{53} -2.83227 q^{55} +(-0.346081 + 1.98415i) q^{56} +(7.54518 - 9.55452i) q^{58} +(12.7025 + 3.40363i) q^{59} +(0.548319 - 0.146922i) q^{61} +(6.27695 + 2.70303i) q^{62} +(6.10931 - 5.16491i) q^{64} +(-5.27228 - 3.04395i) q^{65} +(-6.89625 - 1.84784i) q^{67} +(-1.65444 - 0.493089i) q^{68} +(-0.174282 + 1.19494i) q^{70} -3.03550i q^{71} -11.6817i q^{73} +(-13.7663 - 2.00781i) q^{74} +(-0.726108 - 1.34269i) q^{76} +(1.62461 + 0.435313i) q^{77} +(0.841919 + 0.486082i) q^{79} +(3.57525 - 3.19752i) q^{80} +(3.54653 - 8.23573i) q^{82} +(11.1696 - 2.99289i) q^{83} +(-0.999796 - 0.267894i) q^{85} +(13.8299 + 10.9214i) q^{86} +(-3.84192 - 5.46531i) q^{88} -4.35531 q^{89} +(2.55637 + 2.55637i) q^{91} +(0.369247 + 1.54947i) q^{92} +(3.69609 - 0.434318i) q^{94} +(-0.457603 - 0.792591i) q^{95} +(-2.89654 + 5.01695i) q^{97} +(-3.63176 + 8.43365i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

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