LMFDB - Embedded newform 864.2.bn.a.35.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(35,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.12
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.908095 + 1.08414i) q^{2} +(-0.350728 - 1.96901i) q^{4} +(-0.210277 - 0.161351i) q^{5} +(-2.90937 + 0.779563i) q^{7} +(2.45318 + 1.40781i) q^{8} +(0.365879 - 0.0814479i) q^{10} +(-0.148813 + 1.13035i) q^{11} +(3.34662 - 0.440591i) q^{13} +(1.79683 - 3.86209i) q^{14} +(-3.75398 + 1.38117i) q^{16} -6.62015 q^{17} +(5.15825 + 2.13662i) q^{19} +(-0.243952 + 0.470627i) q^{20} +(-1.09032 - 1.18780i) q^{22} +(0.367075 - 1.36994i) q^{23} +(-1.27591 - 4.76177i) q^{25} +(-2.56139 + 4.02831i) q^{26} +(2.55536 + 5.45516i) q^{28} +(-3.09172 - 4.02920i) q^{29} +(-2.63335 + 1.52037i) q^{31} +(1.91159 - 5.32408i) q^{32} +(6.01173 - 7.17719i) q^{34} +(0.737557 + 0.305506i) q^{35} +(-2.21656 - 5.35125i) q^{37} +(-7.00058 + 3.65203i) q^{38} +(-0.288696 - 0.691853i) q^{40} +(-7.28329 - 1.95155i) q^{41} +(-7.08839 - 0.933204i) q^{43} +(2.27785 - 0.103430i) q^{44} +(1.15187 + 1.64200i) q^{46} +(-2.30774 - 1.33237i) q^{47} +(1.79453 - 1.03607i) q^{49} +(6.32109 + 2.94087i) q^{50} +(-2.04128 - 6.43500i) q^{52} +(-4.56045 - 11.0099i) q^{53} +(0.213675 - 0.213675i) q^{55} +(-8.23467 - 2.18342i) q^{56} +(7.17580 + 0.307039i) q^{58} +(-3.12133 + 4.06780i) q^{59} +(-9.81382 + 7.53041i) q^{61} +(0.743041 - 4.23557i) q^{62} +(4.03616 + 6.90720i) q^{64} +(-0.774808 - 0.447335i) q^{65} +(-7.30222 + 0.961355i) q^{67} +(2.32187 + 13.0351i) q^{68} +(-1.00098 + 0.522188i) q^{70} +(3.28684 - 3.28684i) q^{71} +(2.26326 + 2.26326i) q^{73} +(7.81437 + 2.45638i) q^{74} +(2.39788 - 10.9060i) q^{76} +(-0.448225 - 3.40460i) q^{77} +(7.66807 - 13.2815i) q^{79} +(1.01223 + 0.315281i) q^{80} +(8.72967 - 6.12392i) q^{82} +(-0.719644 - 0.937859i) q^{83} +(1.39207 + 1.06817i) q^{85} +(7.44866 - 6.83738i) q^{86} +(-1.95637 + 2.56344i) q^{88} +(7.53778 + 7.53778i) q^{89} +(-9.39309 + 3.89075i) q^{91} +(-2.82617 - 0.242297i) q^{92} +(3.54013 - 1.29199i) q^{94} +(-0.739916 - 1.28157i) q^{95} +(-0.177831 + 0.308013i) q^{97} +(-0.506355 + 2.88638i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.908095	+	1.08414i	−0.642120	+	0.766604i
$2$	−0.908095	+	1.08414i	−0.642120	+	0.766604i
$3$		0			0
$3$		0			0
$4$	−0.350728	−	1.96901i	−0.175364	−	0.984504i
$5$	−0.210277	−	0.161351i	−0.0940388	−	0.0721585i	0.560672	−	0.828038i	$-0.310543\pi$
$5$	−0.210277	−	0.161351i	−0.0940388	−	0.0721585i	−0.654711	+	0.755880i	$0.727210\pi$
$6$		0			0
$7$	−2.90937	+	0.779563i	−1.09964	+	0.294647i	−0.762617	−	0.646850i	$-0.776086\pi$
$7$	−2.90937	+	0.779563i	−1.09964	+	0.294647i	−0.337021	+	0.941497i	$0.609419\pi$
$8$	2.45318	+	1.40781i	0.867329	+	0.497735i
$9$		0			0
$10$	0.365879	−	0.0814479i	0.115701	−	0.0257561i
$11$	−0.148813	+	1.13035i	−0.0448688	+	0.340812i	0.954256	+	0.298990i	$0.0966497\pi$
$11$	−0.148813	+	1.13035i	−0.0448688	+	0.340812i	−0.999125	+	0.0418224i	$0.986684\pi$
$12$		0			0
$13$	3.34662	−	0.440591i	0.928186	−	0.122198i	0.348750	−	0.937216i	$-0.386606\pi$
$13$	3.34662	−	0.440591i	0.928186	−	0.122198i	0.579436	+	0.815018i	$0.303273\pi$
$14$	1.79683	−	3.86209i	0.480222	−	1.03219i
$15$		0			0
$16$	−3.75398	+	1.38117i	−0.938495	+	0.345293i
$17$	−6.62015			−1.60562			−0.802812	−	0.596233i	$-0.796664\pi$
$17$	−6.62015			−1.60562			−0.802812	+	0.596233i	$0.796664\pi$
$18$		0			0
$19$	5.15825	+	2.13662i	1.18338	+	0.490174i	0.885595	−	0.464458i	$-0.153751\pi$
$19$	5.15825	+	2.13662i	1.18338	+	0.490174i	0.297789	+	0.954632i	$0.403751\pi$
$20$	−0.243952	+	0.470627i	−0.0545493	+	0.105236i
$21$		0			0
$22$	−1.09032	−	1.18780i	−0.232457	−	0.253239i
$23$	0.367075	−	1.36994i	0.0765404	−	0.285653i	−0.917038	−	0.398800i	$-0.869427\pi$
$23$	0.367075	−	1.36994i	0.0765404	−	0.285653i	0.993578	+	0.113148i	$0.0360933\pi$
$24$		0			0
$25$	−1.27591	−	4.76177i	−0.255183	−	0.952354i
$26$	−2.56139	+	4.02831i	−0.502329	+	0.790017i
$27$		0			0
$28$	2.55536	+	5.45516i	0.482918	+	1.03093i
$29$	−3.09172	−	4.02920i	−0.574117	−	0.748204i	0.412554	−	0.910933i	$-0.364637\pi$
$29$	−3.09172	−	4.02920i	−0.574117	−	0.748204i	−0.986671	+	0.162729i	$0.947970\pi$
$30$		0			0
$31$	−2.63335	+	1.52037i	−0.472964	+	0.273066i	−0.717480	−	0.696579i	$-0.754704\pi$
$31$	−2.63335	+	1.52037i	−0.472964	+	0.273066i	0.244515	+	0.969645i	$0.421371\pi$
$32$	1.91159	−	5.32408i	0.337924	−	0.941173i
$33$		0			0
$34$	6.01173	−	7.17719i	1.03100	−	1.23088i
$35$	0.737557	+	0.305506i	0.124670	+	0.0516400i
$36$		0			0
$37$	−2.21656	−	5.35125i	−0.364401	−	0.879741i	−0.994646	−	0.103344i	$-0.967046\pi$
$37$	−2.21656	−	5.35125i	−0.364401	−	0.879741i	0.630245	−	0.776396i	$-0.282954\pi$
$38$	−7.00058	+	3.65203i	−1.13564	+	0.592437i
$39$		0			0
$40$	−0.288696	−	0.691853i	−0.0456468	−	0.109392i
$41$	−7.28329	−	1.95155i	−1.13746	−	0.304781i	−0.359530	−	0.933134i	$-0.617063\pi$
$41$	−7.28329	−	1.95155i	−1.13746	−	0.304781i	−0.777929	+	0.628353i	$0.783729\pi$
$42$		0			0
$43$	−7.08839	−	0.933204i	−1.08097	−	0.142312i	−0.431060	−	0.902323i	$-0.641860\pi$
$43$	−7.08839	−	0.933204i	−1.08097	−	0.142312i	−0.649910	+	0.760011i	$0.725193\pi$
$44$	2.27785	−	0.103430i	0.343399	−	0.0155926i
$45$		0			0
$46$	1.15187	+	1.64200i	0.169834	+	0.242099i
$47$	−2.30774	−	1.33237i	−0.336618	−	0.194347i	0.322157	−	0.946686i	$-0.395592\pi$
$47$	−2.30774	−	1.33237i	−0.336618	−	0.194347i	−0.658776	+	0.752339i	$0.728925\pi$
$48$		0			0
$49$	1.79453	−	1.03607i	0.256362	−	0.148011i
$50$	6.32109	+	2.94087i	0.893937	+	0.415902i
$51$		0			0
$52$	−2.04128	−	6.43500i	−0.283075	−	0.892373i
$53$	−4.56045	−	11.0099i	−0.626426	−	1.51233i	−0.844034	−	0.536290i	$-0.819826\pi$
$53$	−4.56045	−	11.0099i	−0.626426	−	1.51233i	0.217608	−	0.976036i	$-0.430174\pi$
$54$		0			0
$55$	0.213675	−	0.213675i	0.0288119	−	0.0288119i
$56$	−8.23467	−	2.18342i	−1.10040	−	0.291772i
$57$		0			0
$58$	7.17580	+	0.307039i	0.942228	+	0.0403162i
$59$	−3.12133	+	4.06780i	−0.406363	+	0.529582i	−0.951042	−	0.309062i	$-0.899985\pi$
$59$	−3.12133	+	4.06780i	−0.406363	+	0.529582i	0.544679	+	0.838645i	$0.316652\pi$
$60$		0			0
$61$	−9.81382	+	7.53041i	−1.25653	+	0.964170i	−0.999997	−	0.00236571i	$-0.999247\pi$
$61$	−9.81382	+	7.53041i	−1.25653	+	0.964170i	−0.256533	+	0.966535i	$0.582580\pi$
$62$	0.743041	−	4.23557i	0.0943663	−	0.537918i
$63$		0			0
$64$	4.03616	+	6.90720i	0.504520	+	0.863400i
$65$	−0.774808	−	0.447335i	−0.0961031	−	0.0554851i
$66$		0			0
$67$	−7.30222	+	0.961355i	−0.892108	+	0.117448i	−0.562624	−	0.826713i	$-0.690208\pi$
$67$	−7.30222	+	0.961355i	−0.892108	+	0.117448i	−0.329484	+	0.944161i	$0.606875\pi$
$68$	2.32187	+	13.0351i	0.281568	+	1.58074i
$69$		0			0
$70$	−1.00098	+	0.522188i	−0.119640	+	0.0624134i
$71$	3.28684	−	3.28684i	0.390076	−	0.390076i	−0.484639	−	0.874714i	$-0.661049\pi$
$71$	3.28684	−	3.28684i	0.390076	−	0.390076i	0.874714	+	0.484639i	$0.161049\pi$
$72$		0			0
$73$	2.26326	+	2.26326i	0.264894	+	0.264894i	0.827039	−	0.562145i	$-0.190024\pi$
$73$	2.26326	+	2.26326i	0.264894	+	0.264894i	−0.562145	+	0.827039i	$0.690024\pi$
$74$	7.81437	+	2.45638i	0.908402	+	0.285548i
$75$		0			0
$76$	2.39788	−	10.9060i	0.275055	−	1.25101i
$77$	−0.448225	−	3.40460i	−0.0510799	−	0.387991i
$78$		0			0
$79$	7.66807	−	13.2815i	0.862726	−	1.49428i	−0.00656230	−	0.999978i	$-0.502089\pi$
$79$	7.66807	−	13.2815i	0.862726	−	1.49428i	0.869288	−	0.494306i	$-0.164578\pi$
$80$	1.01223	+	0.315281i	0.113171	+	0.0352495i
$81$		0			0
$82$	8.72967	−	6.12392i	0.964031	−	0.676274i
$83$	−0.719644	−	0.937859i	−0.0789912	−	0.102943i	0.752186	−	0.658951i	$-0.228999\pi$
$83$	−0.719644	−	0.937859i	−0.0789912	−	0.102943i	−0.831177	+	0.556007i	$0.812333\pi$
$84$		0			0
$85$	1.39207	+	1.06817i	0.150991	+	0.115859i
$86$	7.44866	−	6.83738i	0.803209	−	0.737294i
$87$		0			0
$88$	−1.95637	+	2.56344i	−0.208550	+	0.273264i
$89$	7.53778	+	7.53778i	0.799003	+	0.799003i	0.982938	−	0.183935i	$-0.0588836\pi$
$89$	7.53778	+	7.53778i	0.799003	+	0.799003i	−0.183935	+	0.982938i	$0.558884\pi$
$90$		0			0
$91$	−9.39309	+	3.89075i	−0.984663	+	0.407861i
$92$	−2.82617	−	0.242297i	−0.294648	−	0.0252612i
$93$		0			0
$94$	3.54013	−	1.29199i	0.365136	−	0.133259i
$95$	−0.739916	−	1.28157i	−0.0759138	−	0.131487i
$96$		0			0
$97$	−0.177831	+	0.308013i	−0.0180560	+	0.0312740i	−0.874912	−	0.484282i	$-0.839081\pi$
$97$	−0.177831	+	0.308013i	−0.0180560	+	0.0312740i	0.856856	+	0.515555i	$0.172414\pi$
$98$	−0.506355	+	2.88638i	−0.0511496	+	0.291569i
$99$		0			0
$100$	−8.92847	+	4.18237i	−0.892847	+	0.418237i
$101$	1.08747	−	8.26017i	0.108207	−	0.821917i	−0.848158	−	0.529744i	$-0.822288\pi$
$101$	1.08747	−	8.26017i	0.108207	−	0.821917i	0.956365	−	0.292174i	$-0.0943785\pi$
$102$		0			0
$103$	0.0706001	−	0.263483i	0.00695644	−	0.0259618i	−0.962360	−	0.271777i	$-0.912389\pi$
$103$	0.0706001	−	0.263483i	0.00695644	−	0.0259618i	0.969317	+	0.245815i	$0.0790555\pi$
$104$	8.83012	+	3.63055i	0.865865	+	0.356005i
$105$		0			0
$106$	16.0776	+	5.05386i	1.56160	+	0.490874i
$107$	6.64771	−	2.75357i	0.642659	−	0.266198i	−0.0374621	−	0.999298i	$-0.511927\pi$
$107$	6.64771	−	2.75357i	0.642659	−	0.266198i	0.680121	+	0.733100i	$0.261927\pi$
$108$		0			0
$109$	1.54546	−	3.73107i	0.148028	−	0.357372i	−0.832421	−	0.554144i	$-0.813046\pi$
$109$	1.54546	−	3.73107i	0.148028	−	0.357372i	0.980449	+	0.196772i	$0.0630459\pi$
$110$	0.0376168	+	0.425691i	0.00358662	+	0.0405880i
$111$		0			0
$112$	9.84501	−	6.94480i	0.930266	−	0.656222i
$113$	−8.65034	−	14.9828i	−0.813756	−	1.40947i	−0.910218	−	0.414129i	$-0.864086\pi$
$113$	−8.65034	−	14.9828i	−0.813756	−	1.40947i	0.0964624	−	0.995337i	$-0.469247\pi$
$114$		0			0
$115$	−0.298229	+	0.228839i	−0.0278100	+	0.0213394i
$116$	−6.84918	+	7.50076i	−0.635930	+	0.696428i
$117$		0			0
$118$	−1.57561	−	7.07792i	−0.145046	−	0.651575i
$119$	19.2605	−	5.16083i	1.76560	−	0.473092i
$120$		0			0
$121$	9.36965	+	2.51059i	0.851786	+	0.228235i
$122$	0.747847	−	17.4779i	0.0677069	−	1.58237i
$123$		0			0
$124$	3.91721	+	4.65186i	0.351775	+	0.417749i
$125$	−1.00717	+	2.43153i	−0.0900841	+	0.217482i
$126$		0			0
$127$		−	0.469475i		−	0.0416592i	−0.999783	−	0.0208296i	$-0.993369\pi$
$127$		−	0.469475i		−	0.0416592i	0.999783	−	0.0208296i	$-0.00663074\pi$
$128$	−11.1536	−	1.89662i	−0.985848	−	0.167640i
$129$		0			0
$130$	1.18857	−	0.433779i	0.104245	−	0.0380449i
$131$	1.20273	+	9.13565i	0.105083	+	0.798185i	0.960114	+	0.279608i	$0.0902047\pi$
$131$	1.20273	+	9.13565i	0.105083	+	0.798185i	−0.855031	+	0.518577i	$0.826462\pi$
$132$		0			0
$133$	−16.6729	−	2.19503i	−1.44572	−	0.190333i
$134$	5.58886	−	8.78964i	0.482804	−	0.759309i
$135$		0			0
$136$	−16.2404	−	9.31990i	−1.39260	−	0.799175i
$137$	5.48217	+	20.4598i	0.468374	+	1.74799i	0.645455	+	0.763798i	$0.276668\pi$
$137$	5.48217	+	20.4598i	0.468374	+	1.74799i	−0.177081	+	0.984196i	$0.556665\pi$
$138$		0			0
$139$	−4.05034	+	5.27850i	−0.343545	+	0.447717i	−0.932888	−	0.360166i	$-0.882720\pi$
$139$	−4.05034	+	5.27850i	−0.343545	+	0.447717i	0.589343	+	0.807883i	$0.299387\pi$
$140$	0.342862	−	1.55941i	0.0289772	−	0.131794i
$141$		0			0
$142$	0.578638	+	6.54816i	0.0485582	+	0.549509i
$143$			3.84841i			0.321820i
$144$		0			0
$145$			1.34610i			0.111788i
$146$	−4.50894	+	0.398440i	−0.373163	+	0.0329751i
$147$		0			0
$148$	−9.75925	+	6.24126i	−0.802205	+	0.513028i
$149$	−2.47158	+	3.22103i	−0.202480	+	0.263877i	−0.883545	−	0.468346i	$-0.844850\pi$
$149$	−2.47158	+	3.22103i	−0.202480	+	0.263877i	0.681066	+	0.732222i	$0.261517\pi$
$150$		0			0
$151$	4.92505	+	18.3805i	0.400795	+	1.49579i	0.811681	+	0.584101i	$0.198553\pi$
$151$	4.92505	+	18.3805i	0.400795	+	1.49579i	−0.410886	+	0.911687i	$0.634781\pi$
$152$	9.64617	+	12.5033i	0.782407	+	1.01415i
$153$		0			0
$154$	4.09811	+	2.60576i	0.330235	+	0.209979i
$155$	0.799047	+	0.105197i	0.0641810	+	0.00844959i
$156$		0			0
$157$	−2.68887	−	20.4240i	−0.214595	−	1.63001i	−0.671857	−	0.740681i	$-0.734503\pi$
$157$	−2.68887	−	20.4240i	−0.214595	−	1.63001i	0.457262	−	0.889332i	$-0.348830\pi$
$158$	7.43568	+	20.3741i	0.591551	+	1.62088i
$159$		0			0
$160$	−1.26101	+	0.811095i	−0.0996916	+	0.0641227i
$161$			4.27182i			0.336667i
$162$		0			0
$163$	−7.29151	+	17.6033i	−0.571115	+	1.37879i	0.329492	+	0.944159i	$0.393123\pi$
$163$	−7.29151	+	17.6033i	−0.571115	+	1.37879i	−0.900607	+	0.434635i	$0.856877\pi$
$164$	−1.28817	+	15.0253i	−0.100589	+	1.17328i
$165$		0			0
$166$	1.67028	+	0.0714681i	0.129639	+	0.00554700i
$167$	2.33777	+	0.626404i	0.180902	+	0.0484726i	0.348133	−	0.937445i	$-0.386816\pi$
$167$	2.33777	+	0.626404i	0.180902	+	0.0484726i	−0.167231	+	0.985918i	$0.553482\pi$
$168$		0			0
$169$	−1.55128	+	0.415664i	−0.119329	+	0.0319742i
$170$	−2.42218	+	0.539198i	−0.185772	+	0.0413546i
$171$		0			0
$172$	0.648607	+	14.2844i	0.0494559	+	1.08917i
$173$	16.9437	−	13.0014i	1.28821	−	0.988477i	0.288691	−	0.957422i	$-0.406780\pi$
$173$	16.9437	−	13.0014i	1.28821	−	0.988477i	0.999518	−	0.0310548i	$-0.00988664\pi$
$174$		0			0
$175$	7.42420	+	12.8591i	0.561217	+	0.972057i
$176$	−1.00256	−	4.44883i	−0.0755708	−	0.335344i
$177$		0			0
$178$	−15.0170	+	1.32700i	−1.12558	+	0.0994632i
$179$	0.878974	−	2.12203i	0.0656976	−	0.158608i	−0.887621	−	0.460575i	$-0.847643\pi$
$179$	0.878974	−	2.12203i	0.0656976	−	0.158608i	0.953318	+	0.301967i	$0.0976432\pi$
$180$		0			0
$181$	−10.5272	+	4.36050i	−0.782478	+	0.324113i	−0.737915	−	0.674893i	$-0.764190\pi$
$181$	−10.5272	+	4.36050i	−0.782478	+	0.324113i	−0.0445631	+	0.999007i	$0.514190\pi$
$182$	4.31170	−	13.7166i	0.319604	−	1.01674i
$183$		0			0
$184$	2.82911	−	2.84394i	0.208565	−	0.209658i
$185$	−0.397340	+	1.48289i	−0.0292130	+	0.109024i
$186$		0			0
$187$	0.985165	−	7.48307i	0.0720424	−	0.547216i
$188$	−1.81407	+	5.01126i	−0.132304	+	0.365483i
$189$		0			0
$190$	2.06132	+	0.361615i	0.149544	+	0.0262343i
$191$	−4.80107	+	8.31569i	−0.347393	+	0.601703i	−0.985786	−	0.168009i	$-0.946266\pi$
$191$	−4.80107	+	8.31569i	−0.347393	+	0.601703i	0.638392	+	0.769711i	$0.279600\pi$
$192$		0			0
$193$	−13.3346	−	23.0963i	−0.959848	−	1.66251i	−0.722861	−	0.690993i	$-0.757173\pi$
$193$	−13.3346	−	23.0963i	−0.959848	−	1.66251i	−0.236987	−	0.971513i	$-0.576160\pi$
$194$	−0.172442	−	0.472499i	−0.0123806	−	0.0339235i
$195$		0			0
$196$	−2.66943	−	3.17007i	−0.190674	−	0.226434i
$197$	−1.38480	+	0.573602i	−0.0986628	+	0.0408675i	−0.431469	−	0.902128i	$-0.642005\pi$
$197$	−1.38480	+	0.573602i	−0.0986628	+	0.0408675i	0.332806	+	0.942995i	$0.392005\pi$
$198$		0			0
$199$	6.42238	+	6.42238i	0.455271	+	0.455271i	0.897099	−	0.441829i	$-0.145670\pi$
$199$	6.42238	+	6.42238i	0.455271	+	0.455271i	−0.441829	+	0.897099i	$0.645670\pi$
$200$	3.57362	−	13.4777i	0.252693	−	0.953018i
$201$		0			0
$202$	7.96767	+	8.67999i	0.560603	+	0.610722i
$203$	12.1360	+	9.31225i	0.851777	+	0.653592i
$204$		0			0
$205$	1.21662	+	1.58553i	0.0849726	+	0.110738i
$206$	0.221542	+	0.315808i	0.0154355	+	0.0220034i
$207$		0			0
$208$	−11.9546	+	6.27622i	−0.828904	+	0.435178i
$209$	−3.18273	+	5.51266i	−0.220154	+	0.381319i
$210$		0			0
$211$	1.35350	+	10.2808i	0.0931785	+	0.707761i	0.972727	+	0.231952i	$0.0745112\pi$
$211$	1.35350	+	10.2808i	0.0931785	+	0.707761i	−0.879549	+	0.475809i	$0.842155\pi$
$212$	−20.0791	+	12.8410i	−1.37904	+	0.881926i
$213$		0			0
$214$	−3.05149	+	9.70757i	−0.208596	+	0.663596i
$215$	1.33995	+	1.33995i	0.0913840	+	0.0913840i
$216$		0			0
$217$	6.47618	−	6.47618i	0.439632	−	0.439632i
$218$	2.64159	+	5.06366i	0.178911	+	0.342955i
$219$		0			0
$220$	−0.495669	−	0.345786i	−0.0334180	−	0.0233129i
$221$	−22.1552	+	2.91678i	−1.49032	+	0.196204i
$222$		0			0
$223$	−18.1004	−	10.4503i	−1.21209	−	0.699802i	−0.248878	−	0.968535i	$-0.580062\pi$
$223$	−18.1004	−	10.4503i	−1.21209	−	0.699802i	−0.963215	+	0.268733i	$0.913395\pi$
$224$	−1.41105	+	16.9799i	−0.0942799	+	1.13452i
$225$		0			0
$226$	24.0988	+	4.22763i	1.60303	+	0.281218i
$227$	−8.21757	+	6.30556i	−0.545419	+	0.418515i	−0.844375	−	0.535752i	$-0.820028\pi$
$227$	−8.21757	+	6.30556i	−0.545419	+	0.418515i	0.298956	+	0.954267i	$0.403362\pi$
$228$		0			0
$229$	−4.84880	+	6.31907i	−0.320418	+	0.417576i	−0.925596	−	0.378514i	$-0.876435\pi$
$229$	−4.84880	+	6.31907i	−0.320418	+	0.417576i	0.605178	+	0.796090i	$0.293102\pi$
$230$	0.0227261	−	0.531131i	0.00149851	−	0.0350217i
$231$		0			0
$232$	−1.91219	−	14.2369i	−0.125541	−	0.934697i
$233$	1.21008	−	1.21008i	0.0792748	−	0.0792748i	−0.666358	−	0.745632i	$-0.732148\pi$
$233$	1.21008	−	1.21008i	0.0792748	−	0.0792748i	0.745632	+	0.666358i	$0.232148\pi$
$234$		0			0
$235$	0.270284	+	0.652524i	0.0176314	+	0.0425660i
$236$	9.10426	+	4.71924i	0.592637	+	0.307196i
$237$		0			0
$238$	−11.8953	+	25.5676i	−0.771056	+	1.65730i
$239$	−15.6470	+	9.03378i	−1.01212	+	0.584347i	−0.911811	−	0.410610i	$-0.865316\pi$
$239$	−15.6470	+	9.03378i	−1.01212	+	0.584347i	−0.100307	+	0.994957i	$0.531983\pi$
$240$		0			0
$241$	12.1405	+	7.00930i	0.782036	+	0.451509i	0.837151	−	0.546971i	$-0.184219\pi$
$241$	12.1405	+	7.00930i	0.782036	+	0.451509i	−0.0551154	+	0.998480i	$0.517553\pi$
$242$	−11.2304	+	7.87817i	−0.721915	+	0.506428i
$243$		0			0
$244$	18.2694	+	16.6824i	1.16958	+	1.06798i
$245$	−0.544521	−	0.0716876i	−0.0347882	−	0.00457995i
$246$		0			0
$247$	18.2041	+	4.87777i	1.15830	+	0.310365i
$248$	−8.60047	+	0.0224771i	−0.546130	+	0.00142730i
$249$		0			0
$250$	−1.72151	−	3.29997i	−0.108878	−	0.208709i
$251$	−10.1807	−	24.5783i	−0.642597	−	1.55137i	−0.823164	−	0.567804i	$-0.807793\pi$
$251$	−10.1807	−	24.5783i	−0.642597	−	1.55137i	0.180567	−	0.983563i	$-0.442207\pi$
$252$		0			0
$253$	1.49388	+	0.618787i	0.0939196	+	0.0389028i
$254$	0.508977	+	0.426328i	0.0319361	+	0.0267502i
$255$		0			0
$256$	12.1847	−	10.3698i	0.761546	−	0.648111i
$257$	−15.6830	+	9.05459i	−0.978279	+	0.564810i	−0.901750	−	0.432258i	$-0.857717\pi$
$257$	−15.6830	+	9.05459i	−0.978279	+	0.564810i	−0.0765289	+	0.997067i	$0.524384\pi$
$258$		0			0
$259$	10.6204	+	13.8408i	0.659922	+	0.860027i
$260$	−0.609060	+	1.68250i	−0.0377723	+	0.104344i
$261$		0			0
$262$	−10.9965	−	6.99210i	−0.679368	−	0.431974i
$263$	3.68384	+	13.7483i	0.227155	+	0.847755i	0.981530	+	0.191310i	$0.0612737\pi$
$263$	3.68384	+	13.7483i	0.227155	+	0.847755i	−0.754374	+	0.656444i	$0.772060\pi$
$264$		0			0
$265$	−0.817503	+	3.05096i	−0.0502188	+	0.187419i
$266$	17.5203	−	16.0825i	1.07424	−	0.986081i
$267$		0			0
$268$	4.45400	+	14.0409i	0.272072	+	0.857687i
$269$	−9.33715	−	3.86758i	−0.569296	−	0.235810i	0.0794191	−	0.996841i	$-0.474693\pi$
$269$	−9.33715	−	3.86758i	−0.569296	−	0.235810i	−0.648715	+	0.761031i	$0.724693\pi$
$270$		0			0
$271$	−1.06895			−0.0649338			−0.0324669	−	0.999473i	$-0.510336\pi$
$271$	−1.06895			−0.0649338			−0.0324669	+	0.999473i	$0.510336\pi$
$272$	24.8519	−	9.14356i	1.50687	−	0.554410i
$273$		0			0
$274$	−27.1596	−	12.6359i	−1.64077	−	0.763365i
$275$	5.57233	−	0.733611i	0.336024	−	0.0442384i
$276$		0			0
$277$	−2.21942	+	16.8582i	−0.133352	+	1.01291i	0.785654	+	0.618666i	$0.212327\pi$
$277$	−2.21942	+	16.8582i	−0.133352	+	1.01291i	−0.919006	+	0.394244i	$0.871007\pi$
$278$	−2.04456	−	9.18453i	−0.122624	−	0.550851i
$279$		0			0
$280$	1.37926	+	1.78780i	0.0824268	+	0.106841i
$281$	16.6133	−	4.45151i	0.991064	−	0.265555i	0.273367	−	0.961910i	$-0.411863\pi$
$281$	16.6133	−	4.45151i	0.991064	−	0.265555i	0.717698	+	0.696355i	$0.245196\pi$
$282$		0			0
$283$	5.14158	+	3.94527i	0.305635	+	0.234522i	0.750179	−	0.661235i	$-0.229967\pi$
$283$	5.14158	+	3.94527i	0.305635	+	0.234522i	−0.444544	+	0.895757i	$0.646634\pi$
$284$	−7.62459	−	5.31902i	−0.452436	−	0.315626i
$285$		0			0
$286$	−4.17222	−	3.49472i	−0.246709	−	0.206647i
$287$	22.7111			1.34060
$288$		0			0
$289$	26.8264			1.57803
$290$	−1.45936	−	1.22239i	−0.0856968	−	0.0717811i
$291$		0			0
$292$	3.66258	−	5.25016i	0.214336	−	0.307242i
$293$	21.1155	+	16.2025i	1.23358	+	0.946559i	0.999670	−	0.0256991i	$-0.00818119\pi$
$293$	21.1155	+	16.2025i	1.23358	+	0.946559i	0.233910	+	0.972258i	$0.424848\pi$
$294$		0			0
$295$	1.31269	−	0.351734i	0.0764277	−	0.0204787i
$296$	2.09591	−	16.2481i	0.121823	−	0.944400i
$297$		0			0
$298$	−1.24762	−	5.60454i	−0.0722727	−	0.324662i
$299$	0.624876	−	4.74641i	0.0361375	−	0.274492i
$300$		0			0
$301$	21.3502	−	2.81081i	1.23061	−	0.162013i
$302$	−24.3995	−	11.3518i	−1.40404	−	0.653224i
$303$		0			0
$304$	−22.3150	−	0.896399i	−1.27985	−	0.0514120i
$305$	3.27866			0.187736
$306$		0			0
$307$	−5.20812	−	2.15728i	−0.297243	−	0.123122i	0.229078	−	0.973408i	$-0.426429\pi$
$307$	−5.20812	−	2.15728i	−0.297243	−	0.123122i	−0.526321	+	0.850286i	$0.676429\pi$
$308$	−6.54649	+	2.07665i	−0.373021	+	0.118328i
$309$		0			0
$310$	−0.839659	+	0.770752i	−0.0476894	+	0.0437758i
$311$	5.26787	−	19.6599i	0.298713	−	1.11481i	−0.639510	−	0.768783i	$-0.720863\pi$
$311$	5.26787	−	19.6599i	0.298713	−	1.11481i	0.938223	−	0.346030i	$-0.112471\pi$
$312$		0			0
$313$	0.335953	+	1.25379i	0.0189892	+	0.0708686i	0.974770	−	0.223211i	$-0.0716537\pi$
$313$	0.335953	+	1.25379i	0.0189892	+	0.0708686i	−0.955781	+	0.294079i	$0.904987\pi$
$314$	24.5843	+	15.6318i	1.38737	+	0.882155i
$315$		0			0
$316$	−28.8408	−	10.4403i	−1.62242	−	0.587313i
$317$	−14.3516	−	18.7033i	−0.806064	−	1.05048i	−0.997617	−	0.0690007i	$-0.978019\pi$
$317$	−14.3516	−	18.7033i	−0.806064	−	1.05048i	0.191553	−	0.981482i	$-0.438648\pi$
$318$		0			0
$319$	5.01448	−	2.89511i	0.280757	−	0.162095i
$320$	0.265774	−	2.10367i	0.0148572	−	0.117598i
$321$		0			0
$322$	−4.63126	−	3.87922i	−0.258090	−	0.216181i
$323$	−34.1484	−	14.1447i	−1.90007	−	0.787035i
$324$		0			0
$325$	−6.36799	−	15.3737i	−0.353233	−	0.852779i
$326$	−12.4631	−	23.8905i	−0.690265	−	1.32317i
$327$		0			0
$328$	−15.1198	−	15.0410i	−0.834851	−	0.830498i
$329$	7.75273	+	2.07734i	0.427422	+	0.114527i
$330$		0			0
$331$	35.8982	+	4.72609i	1.97314	+	0.259769i	0.999497	+	0.0317045i	$0.0100935\pi$
$331$	35.8982	+	4.72609i	1.97314	+	0.259769i	0.973646	+	0.228065i	$0.0732398\pi$
$332$	−1.59425	+	1.74592i	−0.0874960	+	0.0958197i
$333$		0			0
$334$	−2.80203	+	1.96564i	−0.153320	+	0.107555i
$335$	1.69060	+	0.976071i	0.0923676	+	0.0533285i
$336$		0			0
$337$	0.235650	−	0.136053i	0.0128367	−	0.00741126i	−0.493568	−	0.869707i	$-0.664308\pi$
$337$	0.235650	−	0.136053i	0.0128367	−	0.00741126i	0.506405	+	0.862296i	$0.330974\pi$
$338$	0.958070	−	2.05927i	0.0521121	−	0.112009i
$339$		0			0
$340$	1.61500	−	3.11563i	0.0875856	−	0.168969i
$341$	−1.32667	−	3.20285i	−0.0718429	−	0.173444i
$342$		0			0
$343$	10.4954	−	10.4954i	0.566697	−	0.566697i
$344$	−16.0753	−	12.2684i	−0.866723	−	0.661468i
$345$		0			0
$346$	−1.29117	+	30.1759i	−0.0694138	+	1.62227i
$347$	−12.8514	+	16.7483i	−0.689900	+	0.899095i	−0.998644	−	0.0520501i	$-0.983424\pi$
$347$	−12.8514	+	16.7483i	−0.689900	+	0.899095i	0.308745	+	0.951145i	$0.400091\pi$
$348$		0			0
$349$	18.9817	−	14.5652i	1.01607	−	0.779656i	0.0404601	−	0.999181i	$-0.487118\pi$
$349$	18.9817	−	14.5652i	1.01607	−	0.779656i	0.975607	+	0.219526i	$0.0704510\pi$
$350$	−20.6830	−	3.62839i	−1.10555	−	0.193946i
$351$		0			0
$352$	5.73359	+	2.95305i	0.305601	+	0.157398i
$353$	11.5807	+	6.68611i	0.616378	+	0.355866i	0.775457	−	0.631400i	$-0.217519\pi$
$353$	11.5807	+	6.68611i	0.616378	+	0.355866i	−0.159080	+	0.987266i	$0.550853\pi$
$354$		0			0
$355$	−1.22148	+	0.160811i	−0.0648295	+	0.00853497i
$356$	12.1982	−	17.4857i	0.646506	−	0.926738i
$357$		0			0
$358$	1.50239	+	2.87994i	0.0794038	+	0.152209i
$359$	9.45820	−	9.45820i	0.499185	−	0.499185i	−0.411999	−	0.911184i	$-0.635169\pi$
$359$	9.45820	−	9.45820i	0.499185	−	0.499185i	0.911184	+	0.411999i	$0.135169\pi$
$360$		0			0
$361$	8.60742	+	8.60742i	0.453022	+	0.453022i
$362$	4.83227	−	15.3727i	0.253978	−	0.807971i
$363$		0			0
$364$	10.9553	+	17.1305i	0.574215	+	0.897881i
$365$	−0.110732	−	0.841091i	−0.00579596	−	0.0440247i
$366$		0			0
$367$	17.9630	−	31.1128i	0.937661	−	1.62408i	0.167841	−	0.985814i	$-0.446320\pi$
$367$	17.9630	−	31.1128i	0.937661	−	1.62408i	0.769819	−	0.638262i	$-0.220346\pi$
$368$	0.514131	+	5.64973i	0.0268009	+	0.294512i
$369$		0			0
$370$	−1.24684	−	1.77738i	−0.0648203	−	0.0924015i
$371$	21.8509	+	28.4767i	1.13444	+	1.47844i
$372$		0			0
$373$	−27.3672	−	20.9996i	−1.41702	−	1.08732i	−0.982418	−	0.186693i	$-0.940223\pi$
$373$	−27.3672	−	20.9996i	−1.41702	−	1.08732i	−0.434600	−	0.900623i	$-0.643110\pi$
$374$	7.21809	+	7.86339i	0.373238	+	0.406606i
$375$		0			0
$376$	−3.78557	−	6.51740i	−0.195226	−	0.336109i
$377$	−12.1220	−	12.1220i	−0.624316	−	0.624316i
$378$		0			0
$379$	−27.9266	+	11.5676i	−1.43449	+	0.594187i	−0.958457	−	0.285238i	$-0.907927\pi$
$379$	−27.9266	+	11.5676i	−1.43449	+	0.594187i	−0.476038	+	0.879425i	$0.657927\pi$
$380$	−2.26392	+	1.90638i	−0.116137	+	0.0977954i
$381$		0			0
$382$	−4.65557	−	12.7565i	−0.238200	−	0.652678i
$383$	13.9736	+	24.2030i	0.714017	+	1.23671i	0.963337	+	0.268293i	$0.0864595\pi$
$383$	13.9736	+	24.2030i	0.714017	+	1.23671i	−0.249320	+	0.968421i	$0.580207\pi$
$384$		0			0
$385$	−0.455086	+	0.788232i	−0.0231933	+	0.0401720i
$386$	37.1488	+	6.51696i	1.89082	+	0.331705i
$387$		0			0
$388$	0.668850	+	0.242122i	0.0339557	+	0.0122919i
$389$	−2.97285	+	22.5810i	−0.150729	+	1.14490i	0.734118	+	0.679022i	$0.237596\pi$
$389$	−2.97285	+	22.5810i	−0.150729	+	1.14490i	−0.884847	+	0.465881i	$0.845737\pi$
$390$		0			0
$391$	−2.43009	+	9.06922i	−0.122895	+	0.458650i
$392$	5.86090	−	0.0153173i	0.296020	−	0.000773640i
$393$		0			0
$394$	0.635662	−	2.02220i	0.0320242	−	0.101877i
$395$	−3.75541	+	1.55554i	−0.188955	+	0.0782677i
$396$		0			0
$397$	4.54017	−	10.9609i	0.227864	−	0.550113i	−0.768053	−	0.640387i	$-0.778774\pi$
$397$	4.54017	−	10.9609i	0.227864	−	0.550113i	0.995917	+	0.0902734i	$0.0287741\pi$
$398$	−12.7949	+	1.13064i	−0.641351	+	0.0566739i
$399$		0			0
$400$	11.3666	+	16.1133i	0.568328	+	0.805667i
$401$	11.6633	+	20.2014i	0.582437	+	1.00881i	0.995190	+	0.0979670i	$0.0312340\pi$
$401$	11.6633	+	20.2014i	0.582437	+	1.00881i	−0.412753	+	0.910843i	$0.635433\pi$
$402$		0			0
$403$	−8.14298	+	6.24833i	−0.405631	+	0.311251i
$404$	−16.6457	+	0.755828i	−0.828156	+	0.0376039i
$405$		0			0
$406$	−21.1164	+	4.70070i	−1.04799	+	0.233292i
$407$	6.37862	−	1.70915i	0.316177	−	0.0847193i
$408$		0			0
$409$	0.724424	+	0.194109i	0.0358205	+	0.00959807i	0.276685	−	0.960961i	$-0.410764\pi$
$409$	0.724424	+	0.194109i	0.0358205	+	0.00959807i	−0.240864	+	0.970559i	$0.577431\pi$
$410$	−2.82375	−	0.120823i	−0.139455	−	0.00596703i
$411$		0			0
$412$	−0.543562	−	0.0466013i	−0.0267794	−	0.00229588i
$413$	5.91000	−	14.2680i	0.290812	−	0.702083i
$414$		0			0
$415$			0.313326i			0.0153806i
$416$	4.05161	−	18.6599i	0.198647	−	0.914878i
$417$		0			0
$418$	−3.08628	−	8.45655i	−0.150955	−	0.413624i
$419$	0.139977	+	1.06323i	0.00683834	+	0.0519424i	0.994524	−	0.104510i	$-0.0333275\pi$
$419$	0.139977	+	1.06323i	0.00683834	+	0.0519424i	−0.987685	+	0.156453i	$0.949994\pi$
$420$		0			0
$421$	−19.5063	−	2.56805i	−0.950677	−	0.125159i	−0.360792	−	0.932646i	$-0.617493\pi$
$421$	−19.5063	−	2.56805i	−0.950677	−	0.125159i	−0.589885	+	0.807487i	$0.700827\pi$
$422$	−12.3750	−	7.86858i	−0.602404	−	0.383036i
$423$		0			0
$424$	4.31222	−	33.4295i	0.209420	−	1.62348i
$425$	8.44674	+	31.5237i	0.409727	+	1.52912i
$426$		0			0
$427$	22.6816	−	29.5592i	1.09764	−	1.43047i
$428$	−7.75334	−	12.1236i	−0.374772	−	0.586018i
$429$		0			0
$430$	−2.66950	+	0.235895i	−0.128735	+	0.0113759i
$431$			1.14937i			0.0553631i	0.999617	+	0.0276815i	$0.00881243\pi$
$431$			1.14937i			0.0553631i	−0.999617	+	0.0276815i	$0.991188\pi$
$432$		0			0
$433$			13.4381i			0.645792i	0.946434	+	0.322896i	$0.104656\pi$
$433$			13.4381i			0.645792i	−0.946434	+	0.322896i	$0.895344\pi$
$434$	1.14011	+	12.9021i	0.0547271	+	0.619320i
$435$		0			0
$436$	−7.88854	−	1.73443i	−0.377792	−	0.0830643i
$437$	4.82051	−	6.28221i	0.230596	−	0.300519i
$438$		0			0
$439$	−4.96986	−	18.5478i	−0.237199	−	0.885237i	−0.977145	−	0.212572i	$-0.931816\pi$
$439$	−4.96986	−	18.5478i	−0.237199	−	0.885237i	0.739947	−	0.672665i	$-0.234851\pi$
$440$	0.824995	−	0.223369i	0.0393301	−	0.0106487i
$441$		0			0
$442$	16.9568	−	26.6680i	0.806551	−	1.26847i
$443$	−25.6471	−	3.37651i	−1.21853	−	0.160423i	−0.506294	−	0.862361i	$-0.668985\pi$
$443$	−25.6471	−	3.37651i	−1.21853	−	0.160423i	−0.712238	+	0.701938i	$0.752318\pi$
$444$		0			0
$445$	−0.368792	−	2.80125i	−0.0174824	−	0.132792i
$446$	27.7665	−	10.1336i	1.31478	−	0.479838i
$447$		0			0
$448$	−17.1273	−	16.9492i	−0.809188	−	0.800772i
$449$		−	28.8086i		−	1.35956i	−0.733414	−	0.679782i	$-0.762074\pi$
$449$		−	28.8086i		−	1.35956i	0.733414	−	0.679782i	$-0.237926\pi$
$450$		0			0
$451$	3.28978	−	7.94222i	0.154909	−	0.373985i
$452$	−26.4674	+	22.2875i	−1.24492	+	1.04831i
$453$		0			0
$454$	0.626207	−	14.6351i	0.0293894	−	0.686857i
$455$	2.60293	+	0.697453i	0.122027	+	0.0326971i
$456$		0			0
$457$	−9.52070	+	2.55106i	−0.445360	+	0.119334i	−0.474527	−	0.880241i	$-0.657381\pi$
$457$	−9.52070	+	2.55106i	−0.445360	+	0.119334i	0.0291677	+	0.999575i	$0.490714\pi$
$458$	−2.44761	−	10.9951i	−0.114369	−	0.513767i
$459$		0			0
$460$	0.555183	+	0.506955i	0.0258856	+	0.0236369i
$461$	14.8054	−	11.3606i	0.689555	−	0.529115i	−0.203492	−	0.979077i	$-0.565229\pi$
$461$	14.8054	−	11.3606i	0.689555	−	0.529115i	0.893048	+	0.449962i	$0.148562\pi$
$462$		0			0
$463$	−12.7222	−	22.0354i	−0.591249	−	1.02407i	−0.994065	−	0.108792i	$-0.965302\pi$
$463$	−12.7222	−	22.0354i	−0.591249	−	1.02407i	0.402816	−	0.915281i	$-0.368032\pi$
$464$	17.1713	+	10.8554i	0.797155	+	0.503947i
$465$		0			0
$466$	0.213031	+	2.41076i	0.00986845	+	0.111676i
$467$	0.653601	−	1.57793i	0.0302451	−	0.0730181i	−0.908035	−	0.418894i	$-0.862418\pi$
$467$	0.653601	−	1.57793i	0.0302451	−	0.0730181i	0.938280	+	0.345875i	$0.112418\pi$
$468$		0			0
$469$	20.4954	−	8.48948i	0.946390	−	0.392008i
$470$	−0.952873	−	0.299527i	−0.0439527	−	0.0138162i
$471$		0			0
$472$	−13.3839	+	5.58480i	−0.616042	+	0.257061i
$473$	2.10969	−	7.87347i	0.0970036	−	0.362022i
$474$		0			0
$475$	3.59261	−	27.2886i	0.164840	−	1.25209i
$476$	−16.9169	−	36.1140i	−0.775384	−	1.65528i
$477$		0			0
$478$	4.41503	−	25.1671i	0.201939	−	1.15111i
$479$	3.28151	−	5.68375i	0.149936	−	0.259697i	−0.781267	−	0.624196i	$-0.785426\pi$
$479$	3.28151	−	5.68375i	0.149936	−	0.259697i	0.931204	+	0.364499i	$0.118760\pi$
$480$		0			0
$481$	−9.77571	−	16.9320i	−0.445734	−	0.772034i
$482$	−18.6238	+	6.79688i	−0.848289	+	0.309589i
$483$		0			0
$484$	1.65718	−	19.3294i	0.0753262	−	0.878611i
$485$	0.0870921	−	0.0360747i	0.00395465	−	0.00163807i
$486$		0			0
$487$	−24.6314	−	24.6314i	−1.11616	−	1.11616i	−0.992300	−	0.123856i	$-0.960474\pi$
$487$	−24.6314	−	24.6314i	−1.11616	−	1.11616i	−0.123856	−	0.992300i	$-0.539526\pi$
$488$	−34.6764	+	4.65746i	−1.56973	+	0.210833i
$489$		0			0
$490$	0.572196	−	0.525239i	0.0258492	−	0.0237279i
$491$	−22.0969	−	16.9556i	−0.997221	−	0.765195i	−0.0251026	−	0.999685i	$-0.507991\pi$
$491$	−22.0969	−	16.9556i	−0.997221	−	0.765195i	−0.972118	+	0.234490i	$0.924658\pi$
$492$		0			0
$493$	20.4676	+	26.6739i	0.921816	+	1.20133i
$494$	−21.8192	+	15.3063i	−0.981694	+	0.688665i
$495$		0			0
$496$	7.78567	−	9.34454i	0.349587	−	0.419582i
$497$	−7.00032	+	12.1249i	−0.314007	+	0.543877i
$498$		0			0
$499$	3.06588	+	23.2877i	0.137248	+	1.04250i	0.911987	+	0.410219i	$0.134548\pi$
$499$	3.06588	+	23.2877i	0.137248	+	1.04250i	−0.774740	+	0.632281i	$0.782119\pi$
$500$	5.14094	+	1.13032i	0.229910	+	0.0505496i
$501$		0			0
$502$	35.8913	+	11.2821i	1.60191	+	0.503546i
$503$	20.8337	+	20.8337i	0.928930	+	0.928930i	0.997637	−	0.0687068i	$-0.0218873\pi$
$503$	20.8337	+	20.8337i	0.928930	+	0.928930i	−0.0687068	+	0.997637i	$0.521887\pi$
$504$		0			0
$505$	−1.56146	+	1.56146i	−0.0694840	+	0.0694840i
$506$	−2.02744	+	1.05766i	−0.0901307	+	0.0470189i
$507$		0			0
$508$	−0.924399	+	0.164658i	−0.0410136	+	0.00730551i
$509$	13.0450	−	1.71741i	0.578211	−	0.0761229i	0.164252	−	0.986418i	$-0.447479\pi$
$509$	13.0450	−	1.71741i	0.578211	−	0.0761229i	0.413959	+	0.910296i	$0.364146\pi$
$510$		0			0
$511$	−8.34900	−	4.82030i	−0.369338	−	0.213237i
$512$	0.177406	+	22.6267i	0.00784031	+	0.999969i
$513$		0			0
$514$	4.42520	−	25.2250i	0.195187	−	1.11263i
$515$	−0.0573589	+	0.0440131i	−0.00252754	+	0.00193945i
$516$		0			0
$517$	1.84947	−	2.41027i	0.0813394	−	0.106004i
$518$	−24.6498	−	1.05472i	−1.08305	−	0.0463417i
$519$		0			0
$520$	−1.27098	−	2.18817i	−0.0557361	−	0.0959577i
$521$	−11.1752	+	11.1752i	−0.489592	+	0.489592i	−0.908178	−	0.418585i	$-0.862526\pi$
$521$	−11.1752	+	11.1752i	−0.489592	+	0.489592i	0.418585	+	0.908178i	$0.362526\pi$
$522$		0			0
$523$	4.41161	+	10.6506i	0.192906	+	0.465717i	0.990506	−	0.137470i	$-0.0438971\pi$
$523$	4.41161	+	10.6506i	0.192906	+	0.465717i	−0.797600	+	0.603187i	$0.793897\pi$
$524$	17.5663	−	5.57231i	0.767389	−	0.243427i
$525$		0			0
$526$	−18.2504	−	8.49093i	−0.795753	−	0.370222i
$527$	17.4332	−	10.0651i	0.759403	−	0.438441i
$528$		0			0
$529$	18.1766	+	10.4943i	0.790286	+	0.456272i
$530$	−2.56531	−	3.65685i	−0.111430	−	0.158844i
$531$		0			0
$532$	1.52562	+	33.5989i	0.0661438	+	1.45670i
$533$	−25.2342	−	3.32215i	−1.09302	−	0.143898i
$534$		0			0
$535$	−1.84215	−	0.493604i	−0.0796433	−	0.0213404i
$536$	−19.2670	−	7.92174i	−0.832209	−	0.342167i
$537$		0			0
$538$	12.6720	−	6.61067i	0.546330	−	0.285006i
$539$	0.904073	+	2.18263i	0.0389412	+	0.0940123i
$540$		0			0
$541$	−4.88193	−	2.02216i	−0.209891	−	0.0869396i	0.275261	−	0.961369i	$-0.411236\pi$
$541$	−4.88193	−	2.02216i	−0.209891	−	0.0869396i	−0.485152	+	0.874430i	$0.661236\pi$
$542$	0.970704	−	1.15889i	0.0416953	−	0.0497785i
$543$		0			0
$544$	−12.6550	+	35.2462i	−0.542578	+	1.51117i
$545$	−0.926988	+	0.535197i	−0.0397078	+	0.0229253i
$546$		0			0
$547$	1.55433	+	2.02565i	0.0664585	+	0.0866104i	0.825400	−	0.564549i	$-0.190950\pi$
$547$	1.55433	+	2.02565i	0.0664585	+	0.0866104i	−0.758941	+	0.651159i	$0.774283\pi$
$548$	38.3627	−	17.9702i	1.63877	−	0.767651i
$549$		0			0
$550$	−4.26486	+	6.70738i	−0.181854	+	0.286004i
$551$	−7.33899	−	27.3895i	−0.312651	−	1.16683i
$552$		0			0
$553$	−11.9555	+	44.6185i	−0.508399	+	1.89737i
$554$	−16.2612	−	17.7150i	−0.690873	−	0.752638i
$555$		0			0
$556$	11.8140	+	6.12383i	0.501024	+	0.259708i
$557$	19.4433	+	8.05366i	0.823838	+	0.341245i	0.754460	−	0.656346i	$-0.227899\pi$
$557$	19.4433	+	8.05366i	0.823838	+	0.341245i	0.0693774	+	0.997590i	$0.477899\pi$
$558$		0			0
$559$	−24.1333			−1.02073
$560$	−3.19073	−	0.128172i	−0.134833	−	0.00541627i
$561$		0			0
$562$	−10.2604	+	22.0535i	−0.432807	+	0.930272i
$563$	−18.2863	+	2.40744i	−0.770676	+	0.101461i	−0.505602	−	0.862767i	$-0.668730\pi$
$563$	−18.2863	+	2.40744i	−0.770676	+	0.101461i	−0.265074	+	0.964228i	$0.585396\pi$
$564$		0			0
$565$	−0.598530	+	4.54629i	−0.0251804	+	0.191264i
$566$	−8.94627	+	1.99152i	−0.376040	+	0.0837098i
$567$		0			0
$568$	12.6904	−	3.43596i	0.532478	−	0.144170i
$569$	−0.220973	+	0.0592096i	−0.00926368	+	0.00248220i	−0.263448	−	0.964674i	$-0.584860\pi$
$569$	−0.220973	+	0.0592096i	−0.00926368	+	0.00248220i	0.254184	+	0.967156i	$0.418193\pi$
$570$		0			0
$571$	15.5154	+	11.9054i	0.649299	+	0.498225i	0.880108	−	0.474774i	$-0.157470\pi$
$571$	15.5154	+	11.9054i	0.649299	+	0.498225i	−0.230808	+	0.972999i	$0.574137\pi$
$572$	7.57754	−	1.34974i	0.316833	−	0.0564356i
$573$		0			0
$574$	−20.6239	+	24.6221i	−0.860823	+	1.02771i
$575$	−6.99170			−0.291574
$576$		0			0
$577$	14.9051			0.620507			0.310254	−	0.950654i	$-0.399586\pi$
$577$	14.9051			0.620507			0.310254	+	0.950654i	$0.399586\pi$
$578$	−24.3610	+	29.0837i	−1.01328	+	1.20972i
$579$		0			0
$580$	2.65048	−	0.472115i	0.110055	−	0.0196035i
$581$	2.82483	+	2.16757i	0.117194	+	0.0899259i
$582$		0			0
$583$	13.1237	−	3.51647i	0.543526	−	0.145637i
$584$	2.36594	+	8.73840i	0.0979034	+	0.361598i
$585$		0			0
$586$	−36.7407	+	8.17879i	−1.51774	+	0.337863i
$587$	3.50875	−	26.6516i	0.144822	−	1.10003i	−0.752481	−	0.658614i	$-0.771143\pi$
$587$	3.50875	−	26.6516i	0.144822	−	1.10003i	0.897303	−	0.441416i	$-0.145524\pi$
$588$		0			0
$589$	−16.8320	+	2.21597i	−0.693549	+	0.0913074i
$590$	−0.810717	+	1.74255i	−0.0333767	+	0.0717396i
$591$		0			0
$592$	15.7119	+	17.0271i	0.645756	+	0.699808i
$593$	11.8751			0.487652			0.243826	−	0.969819i	$-0.421597\pi$
$593$	11.8751			0.487652			0.243826	+	0.969819i	$0.421597\pi$
$594$		0			0
$595$	−4.88274	−	2.02250i	−0.200173	−	0.0829143i
$596$	7.20908	+	3.73686i	0.295295	+	0.153068i
$597$		0			0
$598$	4.57833	+	4.98764i	0.187222	+	0.203960i
$599$	10.8060	−	40.3284i	0.441520	−	1.64777i	−0.283445	−	0.958988i	$-0.591477\pi$
$599$	10.8060	−	40.3284i	0.441520	−	1.64777i	0.724965	−	0.688786i	$-0.241856\pi$
$600$		0			0
$601$	2.40892	+	8.99022i	0.0982620	+	0.366719i	0.997494	−	0.0707537i	$-0.0225404\pi$
$601$	2.40892	+	8.99022i	0.0982620	+	0.366719i	−0.899232	+	0.437472i	$0.855874\pi$
$602$	−16.3407	+	25.6992i	−0.665998	+	1.04742i
$603$		0			0
$604$	34.4641	−	16.1440i	1.40232	−	0.656891i
$605$	−1.56514	−	2.03972i	−0.0636318	−	0.0829266i
$606$		0			0
$607$	−35.1470	+	20.2921i	−1.42657	+	0.823632i	−0.996849	−	0.0793280i	$-0.974723\pi$
$607$	−35.1470	+	20.2921i	−1.42657	+	0.823632i	−0.429724	+	0.902960i	$0.641389\pi$
$608$	21.2360	−	23.3786i	0.861233	−	0.948129i
$609$		0			0
$610$	−2.97734	+	3.55453i	−0.120549	+	0.143919i
$611$	−8.31016	−	3.44218i	−0.336193	−	0.139256i
$612$		0			0
$613$	11.7152	+	28.2829i	0.473171	+	1.14234i	0.962754	+	0.270379i	$0.0871489\pi$
$613$	11.7152	+	28.2829i	0.473171	+	1.14234i	−0.489583	+	0.871957i	$0.662851\pi$
$614$	7.06826	−	3.68733i	0.285252	−	0.148809i
$615$		0			0
$616$	3.69345	−	8.98311i	0.148813	−	0.361940i
$617$	19.2947	+	5.17000i	0.776776	+	0.208136i	0.625363	−	0.780334i	$-0.284951\pi$
$617$	19.2947	+	5.17000i	0.776776	+	0.208136i	0.151413	+	0.988471i	$0.451618\pi$
$618$		0			0
$619$	10.3832	+	1.36697i	0.417336	+	0.0549433i	0.336270	−	0.941765i	$-0.390834\pi$
$619$	10.3832	+	1.36697i	0.417336	+	0.0549433i	0.0810655	+	0.996709i	$0.474168\pi$
$620$	−0.0731150	−	1.61023i	−0.00293637	−	0.0646682i
$621$		0			0
$622$	16.5304	+	23.5642i	0.662811	+	0.944839i
$623$	−27.8064	−	16.0540i	−1.11404	−	0.643191i
$624$		0			0
$625$	−20.7423	+	11.9756i	−0.829693	+	0.479023i
$626$	−1.66437	−	0.774342i	−0.0665215	−	0.0309489i
$627$		0			0
$628$	−39.2720	+	12.4577i	−1.56712	+	0.497115i
$629$	14.6740	+	35.4261i	0.585090	+	1.41253i
$630$		0			0
$631$	22.7060	−	22.7060i	0.903913	−	0.903913i	−0.0918593	−	0.995772i	$-0.529281\pi$
$631$	22.7060	−	22.7060i	0.903913	−	0.903913i	0.995772	+	0.0918593i	$0.0292810\pi$
$632$	37.5089	−	21.7867i	1.49202	−	0.866628i
$633$		0			0
$634$	33.3096	+	1.42526i	1.32289	+	0.0566042i
$635$	−0.0757504	+	0.0987198i	−0.00300606	+	0.00391758i
$636$		0			0
$637$	5.54914	−	4.25800i	0.219865	−	0.168708i
$638$	−1.41491	+	8.06545i	−0.0560169	+	0.319314i
$639$		0			0
$640$	2.03932	+	2.19846i	0.0806114	+	0.0869019i
$641$	−27.5561	−	15.9095i	−1.08840	−	0.628389i	−0.155251	−	0.987875i	$-0.549619\pi$
$641$	−27.5561	−	15.9095i	−1.08840	−	0.628389i	−0.933150	+	0.359486i	$0.882952\pi$
$642$		0			0
$643$	−35.6089	+	4.68800i	−1.40428	+	0.184877i	−0.794292	−	0.607536i	$-0.792158\pi$
$643$	−35.6089	+	4.68800i	−1.40428	+	0.184877i	−0.609985	+	0.792413i	$0.708825\pi$
$644$	8.41125	−	1.49825i	0.331450	−	0.0590392i
$645$		0			0
$646$	46.3449	−	24.1770i	1.82342	−	0.951231i
$647$	−24.1345	+	24.1345i	−0.948824	+	0.948824i	−0.998753	−	0.0499284i	$-0.984101\pi$
$647$	−24.1345	+	24.1345i	−0.948824	+	0.948824i	0.0499284	+	0.998753i	$0.484101\pi$
$648$		0			0
$649$	−4.13353	−	4.13353i	−0.162255	−	0.162255i
$650$	22.4500	+	7.05696i	0.880562	+	0.276797i
$651$		0			0
$652$	37.2183	+	8.18309i	1.45758	+	0.320474i
$653$	−0.437870	−	3.32595i	−0.0171352	−	0.130155i	0.980739	−	0.195322i	$-0.0625752\pi$
$653$	−0.437870	−	3.32595i	−0.0171352	−	0.130155i	−0.997874	+	0.0651674i	$0.979242\pi$
$654$		0			0
$655$	1.22114	−	2.11508i	0.0477140	−	0.0826430i
$656$	30.0367	−	2.73337i	1.17274	−	0.106720i
$657$		0			0
$658$	−9.29235	+	6.51864i	−0.362253	+	0.254123i
$659$	19.2238	+	25.0530i	0.748853	+	0.975924i	0.999968	+	0.00796717i	$0.00253606\pi$
$659$	19.2238	+	25.0530i	0.748853	+	0.975924i	−0.251115	+	0.967957i	$0.580797\pi$
$660$		0			0
$661$	0.346580	+	0.265940i	0.0134804	+	0.0103439i	0.615480	−	0.788153i	$-0.288962\pi$
$661$	0.346580	+	0.265940i	0.0134804	+	0.0103439i	−0.601999	+	0.798497i	$0.705629\pi$
$662$	−37.7227	+	34.6270i	−1.46613	+	1.34582i
$663$		0			0
$664$	−0.445091	−	3.31385i	−0.0172729	−	0.128603i
$665$	3.15176	+	3.15176i	0.122220	+	0.122220i
$666$		0			0
$667$	−6.65466	+	2.75645i	−0.257670	+	0.106730i
$668$	0.413473	−	4.82279i	0.0159978	−	0.186599i
$669$		0			0
$670$	−2.59343	+	0.946490i	−0.100193	+	0.0365661i
$671$	−7.05155	−	12.2136i	−0.272222	−	0.471502i
$672$		0			0
$673$	−4.03557	+	6.98981i	−0.155560	+	0.269438i	−0.933263	−	0.359194i	$-0.883051\pi$
$673$	−4.03557	+	6.98981i	−0.155560	+	0.269438i	0.777703	+	0.628632i	$0.216385\pi$
$674$	−0.0664923	+	0.379027i	−0.00256119	+	0.0145996i
$675$		0			0
$676$	1.36252	+	2.90870i	0.0524047	+	0.111873i
$677$	2.64930	−	20.1234i	0.101821	−	0.773405i	−0.862010	−	0.506891i	$-0.830795\pi$
$677$	2.64930	−	20.1234i	0.101821	−	0.773405i	0.963831	−	0.266514i	$-0.0858719\pi$
$678$		0			0
$679$	0.277261	−	1.03475i	0.0106403	−	0.0397102i
$680$	1.91121	+	4.58017i	0.0732915	+	0.175642i
$681$		0			0
$682$	4.67709	+	1.47020i	0.179095	+	0.0562969i
$683$	2.59322	−	1.07415i	0.0992269	−	0.0411011i	−0.332518	−	0.943097i	$-0.607898\pi$
$683$	2.59322	−	1.07415i	0.0992269	−	0.0411011i	0.431745	+	0.901996i	$0.357898\pi$
$684$		0			0
$685$	2.14843	−	5.18677i	0.0820874	−	0.198176i
$686$	1.84768	+	20.9093i	0.0705447	+	0.798319i
$687$		0			0
$688$	27.8986	−	6.28704i	1.06362	−	0.239691i
$689$	−20.1130	−	34.8367i	−0.766243	−	1.32717i
$690$		0			0
$691$	−12.2502	+	9.39991i	−0.466020	+	0.357589i	−0.814923	−	0.579569i	$-0.803221\pi$
$691$	−12.2502	+	9.39991i	−0.466020	+	0.357589i	0.348903	+	0.937159i	$0.386554\pi$
$692$	−31.5425	−	28.8024i	−1.19906	−	1.09490i
$693$		0			0
$694$	−6.48722	−	29.1418i	−0.246251	−	1.10621i
$695$	1.70339	−	0.456421i	0.0646132	−	0.0173130i
$696$		0			0
$697$	48.2165	+	12.9196i	1.82633	+	0.489363i
$698$	−1.44647	+	33.8054i	−0.0547497	+	1.27955i
$699$		0			0
$700$	22.7158	−	19.1284i	0.858576	−	0.722984i
$701$	−3.78858	+	9.14644i	−0.143093	+	0.345456i	−0.979136	−	0.203208i	$-0.934863\pi$
$701$	−3.78858	+	9.14644i	−0.143093	+	0.345456i	0.836043	+	0.548664i	$0.184863\pi$
$702$		0			0
$703$		−	32.3391i		−	1.21969i
$704$	−8.40816	+	3.53438i	−0.316895	+	0.133207i
$705$		0			0
$706$	−17.7651	+	6.48348i	−0.668597	+	0.244009i
$707$	3.27547	+	24.8796i	0.123187	+	0.935695i
$708$		0			0
$709$	−4.54942	−	0.598942i	−0.170857	−	0.0224937i	0.0446123	−	0.999004i	$-0.485795\pi$
$709$	−4.54942	−	0.598942i	−0.170857	−	0.0224937i	−0.215469	+	0.976511i	$0.569128\pi$
$710$	0.934879	−	1.47029i	0.0350854	−	0.0551790i
$711$		0			0
$712$	7.87977	+	29.1033i	0.295307	+	1.09069i
$713$	1.11618	+	4.16563i	0.0418012	+	0.156004i
$714$		0			0
$715$	0.620946	−	0.809232i	0.0232220	−	0.0302636i
$716$	−4.48657	−	0.986451i	−0.167671	−	0.0368654i
$717$		0			0
$718$	1.66509	+	18.8430i	0.0621406	+	0.703214i
$719$			51.3863i			1.91639i	0.286124	+	0.958193i	$0.407633\pi$
$719$			51.3863i			1.91639i	−0.286124	+	0.958193i	$0.592367\pi$
$720$		0			0
$721$			0.821607i			0.0305983i
$722$	−17.1480	+	1.51531i	−0.638183	+	0.0563940i
$723$		0			0
$724$	12.2780	+	19.1987i	0.456309	+	0.713515i
$725$	−15.2414	+	19.8630i	−0.566051	+	0.737692i
$726$		0			0
$727$	5.47760	+	20.4427i	0.203153	+	0.758177i	0.990005	+	0.141035i	$0.0450429\pi$
$727$	5.47760	+	20.4427i	0.203153	+	0.758177i	−0.786852	+	0.617142i	$0.788290\pi$
$728$	−28.5203	−	3.67897i	−1.05703	−	0.136352i
$729$		0			0
$730$	1.01242	+	0.643741i	0.0374712	+	0.0238259i
$731$	46.9262	+	6.17796i	1.73563	+	0.228500i
$732$		0			0
$733$	1.16346	+	8.83733i	0.0429732	+	0.326414i	0.999406	+	0.0344615i	$0.0109716\pi$
$733$	1.16346	+	8.83733i	0.0429732	+	0.326414i	−0.956433	+	0.291953i	$0.905695\pi$
$734$	17.4186	+	47.7278i	0.642933	+	1.76167i
$735$		0			0
$736$	−6.59198	−	4.57310i	−0.242984	−	0.168567i
$737$		−	8.39710i		−	0.309311i
$738$		0			0
$739$	6.91091	−	16.6844i	0.254222	−	0.613746i	−0.744315	−	0.667829i	$-0.767224\pi$
$739$	6.91091	−	16.6844i	0.254222	−	0.613746i	0.998536	+	0.0540833i	$0.0172236\pi$
$740$	3.05918	+	0.262274i	0.112458	+	0.00964137i
$741$		0			0
$742$	−50.7155	−	2.17002i	−1.86182	−	0.0796641i
$743$	−4.49432	−	1.20425i	−0.164880	−	0.0441796i	0.175434	−	0.984491i	$-0.443867\pi$
$743$	−4.49432	−	1.20425i	−0.164880	−	0.0441796i	−0.340315	+	0.940312i	$0.610534\pi$
$744$		0			0
$745$	1.03943	−	0.278515i	0.0380819	−	0.0102040i
$746$	47.6185	−	10.6003i	1.74344	−	0.388105i
$747$		0			0
$748$	−15.0797	+	0.684721i	−0.551370	+	0.0250359i
$749$	−17.1941	+	13.1935i	−0.628258	+	0.482079i
$750$		0			0
$751$	12.6948	+	21.9881i	0.463241	+	0.802357i	0.999120	−	0.0419377i	$-0.0133531\pi$
$751$	12.6948	+	21.9881i	0.463241	+	0.802357i	−0.535879	+	0.844295i	$0.680020\pi$
$752$	10.5034	+	1.81432i	0.383021	+	0.0661616i
$753$		0			0
$754$	24.1500	−	2.13405i	0.879490	−	0.0777175i
$755$	1.93010	−	4.65967i	0.0702435	−	0.169583i
$756$		0			0
$757$	−5.75348	+	2.38317i	−0.209114	+	0.0866178i	−0.484782	−	0.874635i	$-0.661101\pi$
$757$	−5.75348	+	2.38317i	−0.209114	+	0.0866178i	0.275668	+	0.961253i	$0.411101\pi$
$758$	12.8191	−	40.7809i	0.465611	−	1.48123i
$759$		0			0
$760$	−0.0109389	−	4.18559i	−0.000396796	−	0.151827i
$761$	2.20043	−	8.21213i	0.0797657	−	0.297689i	−0.914506	−	0.404572i	$-0.867420\pi$
$761$	2.20043	−	8.21213i	0.0797657	−	0.297689i	0.994272	+	0.106883i	$0.0340870\pi$
$762$		0			0
$763$	−1.58771	+	12.0598i	−0.0574789	+	0.436596i
$764$	18.0575	+	6.53680i	0.653299	+	0.236493i
$765$		0			0
$766$	−38.9288	−	6.82924i	−1.40655	−	0.246750i
$767$	−8.65368	+	14.9886i	−0.312466	+	0.541208i
$768$		0			0
$769$	−6.57551	−	11.3891i	−0.237119	−	0.410702i	0.722767	−	0.691091i	$-0.242870\pi$
$769$	−6.57551	−	11.3891i	−0.237119	−	0.410702i	−0.959886	+	0.280389i	$0.909537\pi$
$770$	−0.441294	−	1.20917i	−0.0159031	−	0.0435754i
$771$		0			0
$772$	−40.7999	+	34.3565i	−1.46842	+	1.23652i
$773$	−29.2765	+	12.1267i	−1.05300	+	0.436168i	−0.840963	−	0.541093i	$-0.818011\pi$
$773$	−29.2765	+	12.1267i	−1.05300	+	0.436168i	−0.212040	+	0.977261i	$0.568011\pi$
$774$		0			0
$775$	10.5996	+	10.5996i	0.380748	+	0.380748i
$776$	−0.869874	+	0.505258i	−0.0312267	+	0.0181377i
$777$		0			0
$778$	−21.7814	−	23.7287i	−0.780901	−	0.850715i
$779$	−33.3993	−	25.6282i	−1.19665	−	0.918226i
$780$		0			0
$781$	3.22614	+	4.20439i	0.115440	+	0.150445i
$782$	−7.62557	−	10.8703i	−0.272690	−	0.388720i
$783$		0			0
$784$	−5.30565	+	6.36796i	−0.189487	+	0.227427i
$785$	−2.73003	+	4.72855i	−0.0974390	+	0.168769i
$786$		0			0
$787$	−0.782593	−	5.94438i	−0.0278964	−	0.211894i	0.971820	−	0.235726i	$-0.0757468\pi$
$787$	−0.782593	−	5.94438i	−0.0278964	−	0.211894i	−0.999716	+	0.0238316i	$0.992413\pi$
$788$	1.61511	+	2.52550i	0.0575360	+	0.0899672i
$789$		0			0
$790$	1.72384	−	5.48397i	0.0613314	−	0.195111i
$791$	36.8471	+	36.8471i	1.31013	+	1.31013i
$792$		0			0
$793$	−29.5253	+	29.5253i	−1.04847	+	1.04847i
$794$	7.76030	+	14.8757i	0.275403	+	0.527921i
$795$		0			0
$796$	10.3932	−	14.8982i	0.368378	−	0.528054i
$797$	41.2386	−	5.42916i	1.46075	−	0.192311i	0.642105	−	0.766617i	$-0.278061\pi$
$797$	41.2386	−	5.42916i	1.46075	−	0.192311i	0.818641	+	0.574306i	$0.194728\pi$
$798$		0			0
$799$	15.2776	+	8.82052i	0.540482	+	0.312048i
$800$	−27.7911	−	2.30947i	−0.982563	−	0.0816522i
$801$		0			0
$802$	−32.4926	−	5.70013i	−1.14735	−	0.201279i
$803$	−2.89507	+	2.22146i	−0.102165	+	0.0783937i
$804$		0			0
$805$	0.689264	−	0.898267i	0.0242934	−	0.0316597i
$806$	0.620523	−	14.5022i	0.0218570	−	0.510819i
$807$		0			0
$808$	14.2965	−	18.7327i	0.502948	−	0.659014i
$809$	27.0808	−	27.0808i	0.952111	−	0.952111i	−0.0467934	−	0.998905i	$-0.514900\pi$
$809$	27.0808	−	27.0808i	0.952111	−	0.952111i	0.998905	+	0.0467934i	$0.0149002\pi$
$810$		0			0
$811$	−20.6708	−	49.9036i	−0.725848	−	1.75235i	−0.655957	−	0.754798i	$-0.727735\pi$
$811$	−20.6708	−	49.9036i	−0.725848	−	1.75235i	−0.0698911	−	0.997555i	$-0.522265\pi$
$812$	14.0795	−	27.1619i	0.494093	−	0.953194i
$813$		0			0
$814$	−3.93944	+	8.46740i	−0.138077	+	0.296782i
$815$	4.37355	−	2.52507i	0.153199	−	0.0884493i
$816$		0			0
$817$	−34.5698	−	19.9589i	−1.20944	−	0.698273i
$818$	−0.868288	+	0.609109i	−0.0303590	+	0.0212970i
$819$		0			0
$820$	2.69522	−	2.95163i	0.0941213	−	0.103075i
$821$	−17.2654	−	2.27303i	−0.602565	−	0.0793292i	−0.176929	−	0.984224i	$-0.556616\pi$
$821$	−17.2654	−	2.27303i	−0.602565	−	0.0793292i	−0.425636	+	0.904894i	$0.639950\pi$
$822$		0			0
$823$	36.6703	+	9.82579i	1.27825	+	0.342505i	0.833185	−	0.552994i	$-0.186515\pi$
$823$	36.6703	+	9.82579i	1.27825	+	0.342505i	0.445063	+	0.895499i	$0.353181\pi$
$824$	0.544128	−	0.546980i	0.0189556	−	0.0190549i
$825$		0			0
$826$	10.1017	+	19.3640i	0.351483	+	0.673759i
$827$	−8.01205	−	19.3428i	−0.278606	−	0.672615i	0.721191	−	0.692736i	$-0.243595\pi$
$827$	−8.01205	−	19.3428i	−0.278606	−	0.672615i	−0.999798	+	0.0201210i	$0.993595\pi$
$828$		0			0
$829$	−19.1561	−	7.93471i	−0.665318	−	0.275584i	0.0243563	−	0.999703i	$-0.492246\pi$
$829$	−19.1561	−	7.93471i	−0.665318	−	0.275584i	−0.689675	+	0.724119i	$0.742246\pi$
$830$	−0.339690	−	0.284530i	−0.0117908	−	0.00987617i
$831$		0			0
$832$	16.5507	+	21.3375i	0.573794	+	0.739744i
$833$	−11.8801	+	6.85897i	−0.411621	+	0.237649i
$834$		0			0
$835$	−0.390509	−	0.508921i	−0.0135141	−	0.0176119i
$836$	11.9707	+	4.33339i	0.414017	+	0.149873i
$837$		0			0
$838$	−1.27981	−	0.813762i	−0.0442103	−	0.0281109i
$839$	−1.23246	−	4.59959i	−0.0425491	−	0.158795i	0.941383	−	0.337341i	$-0.109527\pi$
$839$	−1.23246	−	4.59959i	−0.0425491	−	0.158795i	−0.983932	+	0.178546i	$0.942861\pi$
$840$		0			0
$841$	0.829987	−	3.09755i	0.0286202	−	0.106812i
$842$	20.4977	−	18.8155i	0.706396	−	0.648425i
$843$		0			0
$844$	19.7683	−	6.27081i	0.680453	−	0.215850i
$845$	0.393266	+	0.162896i	0.0135288	+	0.00560380i
$846$		0			0
$847$	−29.2169			−1.00391
$848$	32.3264	+	35.0322i	1.11009	+	1.20301i
$849$		0			0
$850$	−41.8466	−	19.4690i	−1.43533	−	0.667782i
$851$	−8.14455	+	1.07225i	−0.279192	+	0.0367563i
$852$		0			0
$853$	3.52744	−	26.7935i	0.120777	−	0.917394i	−0.818565	−	0.574413i	$-0.805230\pi$
$853$	3.52744	−	26.7935i	0.120777	−	0.917394i	0.939343	−	0.342980i	$-0.111436\pi$
$854$	11.4494	+	51.4326i	0.391789	+	1.75999i
$855$		0			0
$856$	20.1845	+	2.60369i	0.689893	+	0.0889925i
$857$	16.5485	−	4.43416i	0.565286	−	0.151468i	0.0351522	−	0.999382i	$-0.488808\pi$
$857$	16.5485	−	4.43416i	0.565286	−	0.151468i	0.530134	+	0.847914i	$0.322142\pi$
$858$		0			0
$859$	−17.9789	−	13.7957i	−0.613433	−	0.470704i	0.254710	−	0.967017i	$-0.418020\pi$
$859$	−17.9789	−	13.7957i	−0.613433	−	0.470704i	−0.868143	+	0.496314i	$0.834687\pi$
$860$	2.16842	−	3.10833i	0.0739425	−	0.105993i
$861$		0			0
$862$	−1.24608	−	1.04373i	−0.0424416	−	0.0355497i
$863$	−37.9392			−1.29147			−0.645733	−	0.763564i	$-0.723448\pi$
$863$	−37.9392			−1.29147			−0.645733	+	0.763564i	$0.723448\pi$
$864$		0			0
$865$	−5.66067			−0.192469
$866$	−14.5688	−	12.2030i	−0.495067	−	0.414676i
$867$		0			0
$868$	−15.0230	−	10.4803i	−0.509914	−	0.355723i
$869$	13.8716	+	10.6440i	0.470561	+	0.361074i
$870$		0			0
$871$	−24.0142	+	6.43458i	−0.813690	+	0.218028i
$872$	9.04391	−	6.97727i	0.306266	−	0.236280i
$873$		0			0
$874$	2.43333	+	10.9310i	0.0823085	+	0.369745i
$875$	1.03470	−	7.85936i	0.0349794	−	0.265695i
$876$		0			0
$877$	−14.5653	+	1.91756i	−0.491835	+	0.0647513i	−0.372365	−	0.928086i	$-0.621453\pi$
$877$	−14.5653	+	1.91756i	−0.491835	+	0.0647513i	−0.119470	+	0.992838i	$0.538120\pi$
$878$	24.6215	+	11.4551i	0.830936	+	0.386591i
$879$		0			0
$880$	−0.507010	+	1.09725i	−0.0170913	+	0.0369884i
$881$	39.5715			1.33320			0.666598	−	0.745417i	$-0.267750\pi$
$881$	39.5715			1.33320			0.666598	+	0.745417i	$0.267750\pi$
$882$		0			0
$883$	−7.71952	−	3.19753i	−0.259782	−	0.107605i	0.248991	−	0.968506i	$-0.419901\pi$
$883$	−7.71952	−	3.19753i	−0.259782	−	0.107605i	−0.508774	+	0.860900i	$0.669901\pi$
$884$	13.5136	+	42.6007i	0.454511	+	1.43282i
$885$		0			0
$886$	26.9506	−	24.7389i	0.905424	−	0.831121i
$887$	−1.62588	+	6.06787i	−0.0545918	+	0.203739i	−0.987835	−	0.155506i	$-0.950299\pi$
$887$	−1.62588	+	6.06787i	−0.0545918	+	0.203739i	0.933243	+	0.359245i	$0.116966\pi$
$888$		0			0
$889$	0.365985	+	1.36588i	0.0122748	+	0.0458100i
$890$	3.37186	+	2.14398i	0.113025	+	0.0718664i
$891$		0			0
$892$	−14.2283	+	39.3050i	−0.476400	+	1.31603i
$893$	−9.05713	−	11.8035i	−0.303085	−	0.394988i
$894$		0			0
$895$	−0.527220	+	0.304391i	−0.0176230	+	0.0101747i
$896$	33.9285	−	3.17695i	1.13347	−	0.106135i
$897$		0			0
$898$	31.2327	+	26.1610i	1.04225	+	0.873003i
$899$	14.2675	+	5.90977i	0.475846	+	0.197102i
$900$		0			0
$901$	30.1909	+	72.8872i	1.00580	+	2.42823i
$902$	5.62307	+	10.7789i	0.187228	+	0.358897i
$903$		0			0
$904$	−0.127886	−	48.9335i	−0.00425344	−	1.62751i
$905$	2.91719	+	0.781660i	0.0969708	+	0.0259832i
$906$		0			0
$907$	−21.3147	−	2.80614i	−0.707744	−	0.0931762i	−0.231943	−	0.972729i	$-0.574508\pi$
$907$	−21.3147	−	2.80614i	−0.707744	−	0.0931762i	−0.475801	+	0.879553i	$0.657842\pi$
$908$	15.2978	+	13.9689i	0.507676	+	0.463575i
$909$		0			0
$910$	−3.11984	+	2.18859i	−0.103422	+	0.0725511i
$911$	−41.5522	−	23.9902i	−1.37668	−	0.794829i	−0.384926	−	0.922948i	$-0.625773\pi$
$911$	−41.5522	−	23.9902i	−1.37668	−	0.794829i	−0.991759	+	0.128118i	$0.959106\pi$
$912$		0			0
$913$	1.16720	−	0.673882i	0.0386286	−	0.0223022i
$914$	5.87998	−	12.6384i	0.194493	−	0.418041i
$915$		0			0
$916$	14.1429	+	7.33104i	0.467295	+	0.242224i
$917$	−10.6210	−	25.6414i	−0.350736	−	0.846753i
$918$		0			0
$919$	−19.6503	+	19.6503i	−0.648203	+	0.648203i	−0.952558	−	0.304356i	$-0.901559\pi$
$919$	−19.6503	+	19.6503i	−0.648203	+	0.648203i	0.304356	+	0.952558i	$0.401559\pi$
$920$	−1.05377	+	0.141534i	−0.0347418	+	0.00466625i
$921$		0			0
$922$	−1.12822	+	26.3676i	−0.0371560	+	0.868371i
$923$	9.55165	−	12.4479i	0.314396	−	0.409729i
$924$		0			0
$925$	−22.6533	+	17.3825i	−0.744836	+	0.571533i
$926$	35.4425	+	6.21763i	1.16471	+	0.204324i
$927$		0			0
$928$	−27.3619	+	8.75838i	−0.898198	+	0.287508i
$929$	−12.4296	−	7.17623i	−0.407802	−	0.235445i	0.282043	−	0.959402i	$-0.408988\pi$
$929$	−12.4296	−	7.17623i	−0.407802	−	0.235445i	−0.689845	+	0.723957i	$0.742321\pi$
$930$		0			0
$931$	11.4704	−	1.51010i	0.375926	−	0.0494916i
$932$	−2.80706	−	1.95824i	−0.0919482	−	0.0641444i
$933$		0			0
$934$	1.11717	+	2.14151i	0.0365550	+	0.0700724i
$935$	−1.41456	+	1.41456i	−0.0462611	+	0.0462611i
$936$		0			0
$937$	18.7763	+	18.7763i	0.613394	+	0.613394i	0.943829	−	0.330435i	$-0.107195\pi$
$937$	18.7763	+	18.7763i	0.613394	+	0.613394i	−0.330435	+	0.943829i	$0.607195\pi$
$938$	−9.40798	+	29.9292i	−0.307181	+	0.977222i
$939$		0			0
$940$	1.19003	−	0.761050i	0.0388145	−	0.0248227i
$941$	−0.503730	−	3.82621i	−0.0164211	−	0.124731i	0.981271	−	0.192633i	$-0.0617027\pi$
$941$	−0.503730	−	3.82621i	−0.0164211	−	0.124731i	−0.997692	+	0.0679022i	$0.978369\pi$
$942$		0			0
$943$	−5.34702	+	9.26131i	−0.174123	+	0.301590i
$944$	6.09910	−	19.5815i	0.198509	−	0.637325i
$945$		0			0
$946$	6.62016	+	9.43706i	0.215240	+	0.306825i
$947$	−13.1772	−	17.1728i	−0.428200	−	0.558042i	0.528569	−	0.848891i	$-0.322729\pi$
$947$	−13.1772	−	17.1728i	−0.428200	−	0.558042i	−0.956769	+	0.290849i	$0.906062\pi$
$948$		0			0
$949$	8.57144	+	6.57709i	0.278241	+	0.213502i
$950$	26.3223	+	28.6755i	0.854007	+	0.930356i
$951$		0			0
$952$	54.5148	+	14.4546i	1.76684	+	0.468476i
$953$	33.7540	+	33.7540i	1.09340	+	1.09340i	0.995163	+	0.0982373i	$0.0313204\pi$
$953$	33.7540	+	33.7540i	1.09340	+	1.09340i	0.0982373	+	0.995163i	$0.468680\pi$
$954$		0			0
$955$	2.35130	−	0.973941i	0.0760864	−	0.0315160i
$956$	23.2754	+	27.6406i	0.752780	+	0.893961i
$957$		0			0
$958$	3.18207	+	8.71901i	0.102808	+	0.281698i
$959$	−31.8993	−	55.2513i	−1.03008	−	1.78416i
$960$		0			0
$961$	−10.8770	+	18.8395i	−0.350870	+	0.607724i
$962$	27.2340	+	4.77763i	0.878059	+	0.154037i
$963$		0			0
$964$	9.54337	−	26.3630i	0.307371	−	0.849096i
$965$	−0.922644	+	7.00818i	−0.0297010	+	0.225601i
$966$		0			0
$967$	13.4545	−	50.2128i	0.432667	−	1.61474i	−0.313921	−	0.949449i	$-0.601643\pi$
$967$	13.4545	−	50.2128i	0.432667	−	1.61474i	0.746588	−	0.665286i	$-0.231691\pi$
$968$	19.4510	+	19.3496i	0.625178	+	0.621919i
$969$		0			0
$970$	−0.0399777	+	0.127179i	−0.00128361	+	0.00408349i
$971$	−22.5790	+	9.35251i	−0.724593	+	0.300136i	−0.714328	−	0.699811i	$-0.753268\pi$
$971$	−22.5790	+	9.35251i	−0.724593	+	0.300136i	−0.0102652	+	0.999947i	$0.503268\pi$
$972$		0			0
$973$	7.66900	−	18.5146i	0.245857	−	0.593551i
$974$	49.0716	−	4.33629i	1.57236	−	0.138944i
$975$		0			0
$976$	26.4401	−	41.8235i	0.846327	−	1.33874i
$977$	18.3789	+	31.8332i	0.587994	+	1.01844i	0.994495	+	0.104785i	$0.0334155\pi$
$977$	18.3789	+	31.8332i	0.587994	+	1.01844i	−0.406501	+	0.913650i	$0.633251\pi$
$978$		0			0
$979$	−9.64203	+	7.39859i	−0.308161	+	0.236460i
$980$	0.0498252	+	1.09731i	0.00159161	+	0.0350522i
$981$		0			0
$982$	38.4484	−	8.55895i	1.22694	−	0.273127i
$983$	−37.0629	+	9.93099i	−1.18212	+	0.316749i	−0.795769	−	0.605601i	$-0.792933\pi$
$983$	−37.0629	+	9.93099i	−1.18212	+	0.316749i	−0.386356	+	0.922350i	$0.626266\pi$
$984$		0			0
$985$	0.383743	+	0.102824i	0.0122271	+	0.00327623i
$986$	−47.5049	−	2.03265i	−1.51286	−	0.0647327i
$987$		0			0
$988$	3.21969	−	37.5548i	0.102432	−	1.19478i
$989$	−3.88040	+	9.36813i	−0.123390	+	0.297889i
$990$		0			0
$991$			7.63952i			0.242677i	0.992611	+	0.121339i	$0.0387187\pi$
$991$			7.63952i			0.242677i	−0.992611	+	0.121339i	$0.961281\pi$
$992$	3.06068	+	16.9265i	0.0971766	+	0.537417i
$993$		0			0
$994$	−6.78817	−	18.5999i	−0.215308	−	0.589954i
$995$	−0.314220	−	2.38674i	−0.00996145	−	0.0756647i
$996$		0			0
$997$	−52.3776	−	6.89564i	−1.65881	−	0.218387i	−0.757896	−	0.652375i	$-0.773773\pi$
$997$	−52.3776	−	6.89564i	−1.65881	−	0.218387i	−0.900918	+	0.433988i	$0.857106\pi$
$998$	−28.0312	−	17.8236i	−0.887314	−	0.564195i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.12		368
3.2	odd	2		288.2.bf.a.227.35	yes	368
9.4	even	3		288.2.bf.a.131.19	yes	368
9.5	odd	6	inner	864.2.bn.a.611.28		368
32.11	odd	8	inner	864.2.bn.a.683.28		368
96.11	even	8		288.2.bf.a.11.19	✓	368
288.139	odd	24		288.2.bf.a.203.35	yes	368
288.203	even	24	inner	864.2.bn.a.395.12		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.19	✓	368	96.11	even	8
288.2.bf.a.131.19	yes	368	9.4	even	3
288.2.bf.a.203.35	yes	368	288.139	odd	24
288.2.bf.a.227.35	yes	368	3.2	odd	2
864.2.bn.a.35.12		368	1.1	even	1	trivial
864.2.bn.a.395.12		368	288.203	even	24	inner
864.2.bn.a.611.28		368	9.5	odd	6	inner
864.2.bn.a.683.28		368	32.11	odd	8	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.908095 + 1.08414i) q^{2} +(-0.350728 - 1.96901i) q^{4} +(-0.210277 - 0.161351i) q^{5} +(-2.90937 + 0.779563i) q^{7} +(2.45318 + 1.40781i) q^{8} +(0.365879 - 0.0814479i) q^{10} +(-0.148813 + 1.13035i) q^{11} +(3.34662 - 0.440591i) q^{13} +(1.79683 - 3.86209i) q^{14} +(-3.75398 + 1.38117i) q^{16} -6.62015 q^{17} +(5.15825 + 2.13662i) q^{19} +(-0.243952 + 0.470627i) q^{20} +(-1.09032 - 1.18780i) q^{22} +(0.367075 - 1.36994i) q^{23} +(-1.27591 - 4.76177i) q^{25} +(-2.56139 + 4.02831i) q^{26} +(2.55536 + 5.45516i) q^{28} +(-3.09172 - 4.02920i) q^{29} +(-2.63335 + 1.52037i) q^{31} +(1.91159 - 5.32408i) q^{32} +(6.01173 - 7.17719i) q^{34} +(0.737557 + 0.305506i) q^{35} +(-2.21656 - 5.35125i) q^{37} +(-7.00058 + 3.65203i) q^{38} +(-0.288696 - 0.691853i) q^{40} +(-7.28329 - 1.95155i) q^{41} +(-7.08839 - 0.933204i) q^{43} +(2.27785 - 0.103430i) q^{44} +(1.15187 + 1.64200i) q^{46} +(-2.30774 - 1.33237i) q^{47} +(1.79453 - 1.03607i) q^{49} +(6.32109 + 2.94087i) q^{50} +(-2.04128 - 6.43500i) q^{52} +(-4.56045 - 11.0099i) q^{53} +(0.213675 - 0.213675i) q^{55} +(-8.23467 - 2.18342i) q^{56} +(7.17580 + 0.307039i) q^{58} +(-3.12133 + 4.06780i) q^{59} +(-9.81382 + 7.53041i) q^{61} +(0.743041 - 4.23557i) q^{62} +(4.03616 + 6.90720i) q^{64} +(-0.774808 - 0.447335i) q^{65} +(-7.30222 + 0.961355i) q^{67} +(2.32187 + 13.0351i) q^{68} +(-1.00098 + 0.522188i) q^{70} +(3.28684 - 3.28684i) q^{71} +(2.26326 + 2.26326i) q^{73} +(7.81437 + 2.45638i) q^{74} +(2.39788 - 10.9060i) q^{76} +(-0.448225 - 3.40460i) q^{77} +(7.66807 - 13.2815i) q^{79} +(1.01223 + 0.315281i) q^{80} +(8.72967 - 6.12392i) q^{82} +(-0.719644 - 0.937859i) q^{83} +(1.39207 + 1.06817i) q^{85} +(7.44866 - 6.83738i) q^{86} +(-1.95637 + 2.56344i) q^{88} +(7.53778 + 7.53778i) q^{89} +(-9.39309 + 3.89075i) q^{91} +(-2.82617 - 0.242297i) q^{92} +(3.54013 - 1.29199i) q^{94} +(-0.739916 - 1.28157i) q^{95} +(-0.177831 + 0.308013i) q^{97} +(-0.506355 + 2.88638i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

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