LMFDB - Embedded newform 864.2.bn.a.35.23

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)

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")

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);

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			35.23
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0869556 + 1.41154i) q^{2} +(-1.98488 + 0.245482i) q^{4} +(0.0538553 + 0.0413246i) q^{5} +(-2.48836 + 0.666754i) q^{7} +(-0.519104 - 2.78038i) q^{8} +(-0.0536483 + 0.0796122i) q^{10} +(0.0546768 - 0.415312i) q^{11} +(-6.12318 + 0.806132i) q^{13} +(-1.15753 - 3.45444i) q^{14} +(3.87948 - 0.974505i) q^{16} +3.64897 q^{17} +(3.97733 + 1.64746i) q^{19} +(-0.117041 - 0.0688038i) q^{20} +(0.590983 + 0.0410647i) q^{22} +(2.35051 - 8.77221i) q^{23} +(-1.29290 - 4.82518i) q^{25} +(-1.67033 - 8.57300i) q^{26} +(4.77541 - 1.93427i) q^{28} +(-4.46654 - 5.82091i) q^{29} +(-1.77380 + 1.02410i) q^{31} +(1.71289 + 5.39129i) q^{32} +(0.317298 + 5.15065i) q^{34} +(-0.161565 - 0.0669223i) q^{35} +(-3.36655 - 8.12758i) q^{37} +(-1.97960 + 5.75740i) q^{38} +(0.0869418 - 0.171190i) q^{40} +(-5.42911 - 1.45472i) q^{41} +(3.51829 + 0.463192i) q^{43} +(-0.00657510 + 0.837765i) q^{44} +(12.5867 + 2.55503i) q^{46} +(-2.05961 - 1.18912i) q^{47} +(-0.314804 + 0.181752i) q^{49} +(6.69850 - 2.24456i) q^{50} +(11.9559 - 3.10320i) q^{52} +(-0.0730018 - 0.176242i) q^{53} +(0.0201073 - 0.0201073i) q^{55} +(3.14555 + 6.57248i) q^{56} +(7.82805 - 6.81086i) q^{58} +(-3.20000 + 4.17032i) q^{59} +(2.17432 - 1.66842i) q^{61} +(-1.59980 - 2.41473i) q^{62} +(-7.46106 + 2.88662i) q^{64} +(-0.363079 - 0.209624i) q^{65} +(1.57962 - 0.207960i) q^{67} +(-7.24275 + 0.895757i) q^{68} +(0.0804144 - 0.233874i) q^{70} +(7.18803 - 7.18803i) q^{71} +(-6.62149 - 6.62149i) q^{73} +(11.1796 - 5.45876i) q^{74} +(-8.29893 - 2.29365i) q^{76} +(0.140855 + 1.06990i) q^{77} +(-4.97251 + 8.61265i) q^{79} +(0.249202 + 0.107836i) q^{80} +(1.58131 - 7.78988i) q^{82} +(2.61687 + 3.41038i) q^{83} +(0.196516 + 0.150792i) q^{85} +(-0.347877 + 5.00648i) q^{86} +(-1.18311 + 0.0635674i) q^{88} +(2.46723 + 2.46723i) q^{89} +(14.6992 - 6.08860i) q^{91} +(-2.51204 + 17.9888i) q^{92} +(1.49939 - 3.01062i) q^{94} +(0.146119 + 0.253086i) q^{95} +(-7.74713 + 13.4184i) q^{97} +(-0.283924 - 0.428554i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.0869556	+	1.41154i	0.0614869	+	0.998108i
$2$	0.0869556	+	1.41154i	0.0614869	+	0.998108i
$3$		0			0
$3$		0			0
$4$	−1.98488	+	0.245482i	−0.992439	+	0.122741i
$5$	0.0538553	+	0.0413246i	0.0240848	+	0.0184809i	0.620734	−	0.784021i	$-0.286835\pi$
$5$	0.0538553	+	0.0413246i	0.0240848	+	0.0184809i	−0.596649	+	0.802502i	$0.703501\pi$
$6$		0			0
$7$	−2.48836	+	0.666754i	−0.940512	+	0.252009i	−0.696331	−	0.717721i	$-0.745186\pi$
$7$	−2.48836	+	0.666754i	−0.940512	+	0.252009i	−0.244180	+	0.969730i	$0.578519\pi$
$8$	−0.519104	−	2.78038i	−0.183531	−	0.983014i
$9$		0			0
$10$	−0.0536483	+	0.0796122i	−0.0169651	+	0.0251756i
$11$	0.0546768	−	0.415312i	0.0164857	−	0.125221i	−0.981223	−	0.192876i	$-0.938218\pi$
$11$	0.0546768	−	0.415312i	0.0164857	−	0.125221i	0.997709	+	0.0676551i	$0.0215517\pi$
$12$		0			0
$13$	−6.12318	+	0.806132i	−1.69826	+	0.223581i	−0.916512	−	0.400008i	$-0.869007\pi$
$13$	−6.12318	+	0.806132i	−1.69826	+	0.223581i	−0.781752	+	0.623589i	$0.785674\pi$
$14$	−1.15753	−	3.45444i	−0.309362	−	0.923237i
$15$		0			0
$16$	3.87948	−	0.974505i	0.969869	−	0.243626i
$17$	3.64897			0.885004			0.442502	−	0.896767i	$-0.354091\pi$
$17$	3.64897			0.885004			0.442502	+	0.896767i	$0.354091\pi$
$18$		0			0
$19$	3.97733	+	1.64746i	0.912461	+	0.377954i	0.788998	−	0.614395i	$-0.210600\pi$
$19$	3.97733	+	1.64746i	0.912461	+	0.377954i	0.123463	+	0.992349i	$0.460600\pi$
$20$	−0.117041	−	0.0688038i	−0.0261711	−	0.0153850i
$21$		0			0
$22$	0.590983	+	0.0410647i	0.125998	+	0.00875502i
$23$	2.35051	−	8.77221i	0.490114	−	1.82913i	−0.0657198	−	0.997838i	$-0.520934\pi$
$23$	2.35051	−	8.77221i	0.490114	−	1.82913i	0.555834	−	0.831293i	$-0.312399\pi$
$24$		0			0
$25$	−1.29290	−	4.82518i	−0.258581	−	0.965036i
$26$	−1.67033	−	8.57300i	−0.327579	−	1.68130i
$27$		0			0
$28$	4.77541	−	1.93427i	0.902468	−	0.365543i
$29$	−4.46654	−	5.82091i	−0.829416	−	1.08092i	−0.995496	−	0.0948040i	$-0.969778\pi$
$29$	−4.46654	−	5.82091i	−0.829416	−	1.08092i	0.166080	−	0.986112i	$-0.446889\pi$
$30$		0			0
$31$	−1.77380	+	1.02410i	−0.318584	+	0.183935i	−0.650761	−	0.759282i	$-0.725550\pi$
$31$	−1.77380	+	1.02410i	−0.318584	+	0.183935i	0.332177	+	0.943217i	$0.392217\pi$
$32$	1.71289	+	5.39129i	0.302800	+	0.953054i
$33$		0			0
$34$	0.317298	+	5.15065i	0.0544162	+	0.883330i
$35$	−0.161565	−	0.0669223i	−0.0273094	−	0.0113119i
$36$		0			0
$37$	−3.36655	−	8.12758i	−0.553458	−	1.33617i	−0.914866	−	0.403758i	$-0.867704\pi$
$37$	−3.36655	−	8.12758i	−0.553458	−	1.33617i	0.361408	−	0.932408i	$-0.382296\pi$
$38$	−1.97960	+	5.75740i	−0.321134	+	0.933974i
$39$		0			0
$40$	0.0869418	−	0.171190i	0.0137467	−	0.0270676i
$41$	−5.42911	−	1.45472i	−0.847884	−	0.227190i	−0.191383	−	0.981515i	$-0.561297\pi$
$41$	−5.42911	−	1.45472i	−0.847884	−	0.227190i	−0.656501	+	0.754326i	$0.727964\pi$
$42$		0			0
$43$	3.51829	+	0.463192i	0.536534	+	0.0706361i	0.393924	−	0.919143i	$-0.371117\pi$
$43$	3.51829	+	0.463192i	0.536534	+	0.0706361i	0.142610	+	0.989779i	$0.454451\pi$
$44$	−0.00657510	+	0.837765i	−0.000991233	+	0.126298i
$45$		0			0
$46$	12.5867	+	2.55503i	1.85581	+	0.376719i
$47$	−2.05961	−	1.18912i	−0.300425	−	0.173450i	0.342209	−	0.939624i	$-0.388825\pi$
$47$	−2.05961	−	1.18912i	−0.300425	−	0.173450i	−0.642634	+	0.766173i	$0.722158\pi$
$48$		0			0
$49$	−0.314804	+	0.181752i	−0.0449720	+	0.0259646i
$50$	6.69850	−	2.24456i	0.947310	−	0.317428i
$51$		0			0
$52$	11.9559	−	3.10320i	1.65798	−	0.430337i
$53$	−0.0730018	−	0.176242i	−0.0100276	−	0.0242087i	0.918786	−	0.394755i	$-0.129171\pi$
$53$	−0.0730018	−	0.176242i	−0.0100276	−	0.0242087i	−0.928814	+	0.370546i	$0.879171\pi$
$54$		0			0
$55$	0.0201073	−	0.0201073i	0.00271126	−	0.00271126i
$56$	3.14555	+	6.57248i	0.420342	+	0.878284i
$57$		0			0
$58$	7.82805	−	6.81086i	1.02787	−	0.894309i
$59$	−3.20000	+	4.17032i	−0.416604	+	0.542929i	−0.953766	−	0.300550i	$-0.902830\pi$
$59$	−3.20000	+	4.17032i	−0.416604	+	0.542929i	0.537162	+	0.843479i	$0.319496\pi$
$60$		0			0
$61$	2.17432	−	1.66842i	0.278393	−	0.213619i	−0.460121	−	0.887856i	$-0.652194\pi$
$61$	2.17432	−	1.66842i	0.278393	−	0.213619i	0.738515	+	0.674237i	$0.235527\pi$
$62$	−1.59980	−	2.41473i	−0.203175	−	0.306672i
$63$		0			0
$64$	−7.46106	+	2.88662i	−0.932633	+	0.360827i
$65$	−0.363079	−	0.209624i	−0.0450344	−	0.0260006i
$66$		0			0
$67$	1.57962	−	0.207960i	0.192981	−	0.0254064i	−0.0334162	−	0.999442i	$-0.510639\pi$
$67$	1.57962	−	0.207960i	0.192981	−	0.0254064i	0.226397	+	0.974035i	$0.427305\pi$
$68$	−7.24275	+	0.895757i	−0.878313	+	0.108626i
$69$		0			0
$70$	0.0804144	−	0.233874i	0.00961136	−	0.0279533i
$71$	7.18803	−	7.18803i	0.853063	−	0.853063i	−0.137446	−	0.990509i	$-0.543889\pi$
$71$	7.18803	−	7.18803i	0.853063	−	0.853063i	0.990509	+	0.137446i	$0.0438895\pi$
$72$		0			0
$73$	−6.62149	−	6.62149i	−0.774986	−	0.774986i	0.203987	−	0.978974i	$-0.434610\pi$
$73$	−6.62149	−	6.62149i	−0.774986	−	0.774986i	−0.978974	+	0.203987i	$0.934610\pi$
$74$	11.1796	−	5.45876i	1.29961	−	0.634568i
$75$		0			0
$76$	−8.29893	−	2.29365i	−0.951952	−	0.263099i
$77$	0.140855	+	1.06990i	0.0160519	+	0.121927i
$78$		0			0
$79$	−4.97251	+	8.61265i	−0.559452	+	0.968999i	0.438091	+	0.898931i	$0.355655\pi$
$79$	−4.97251	+	8.61265i	−0.559452	+	0.968999i	−0.997542	+	0.0700678i	$0.977678\pi$
$80$	0.249202	+	0.107836i	0.0278616	+	0.0120564i
$81$		0			0
$82$	1.58131	−	7.78988i	0.174626	−	0.860249i
$83$	2.61687	+	3.41038i	0.287239	+	0.374337i	0.914578	−	0.404409i	$-0.132523\pi$
$83$	2.61687	+	3.41038i	0.287239	+	0.374337i	−0.627339	+	0.778746i	$0.715856\pi$
$84$		0			0
$85$	0.196516	+	0.150792i	0.0213152	+	0.0163557i
$86$	−0.347877	+	5.00648i	−0.0375126	+	0.539862i
$87$		0			0
$88$	−1.18311	+	0.0635674i	−0.126120	+	0.00677631i
$89$	2.46723	+	2.46723i	0.261526	+	0.261526i	0.825674	−	0.564148i	$-0.190795\pi$
$89$	2.46723	+	2.46723i	0.261526	+	0.261526i	−0.564148	+	0.825674i	$0.690795\pi$
$90$		0			0
$91$	14.6992	−	6.08860i	1.54089	−	0.638259i
$92$	−2.51204	+	17.9888i	−0.261899	+	1.87546i
$93$		0			0
$94$	1.49939	−	3.01062i	0.154650	−	0.310521i
$95$	0.146119	+	0.253086i	0.0149915	+	0.0259661i
$96$		0			0
$97$	−7.74713	+	13.4184i	−0.786602	+	1.36243i	0.141436	+	0.989947i	$0.454828\pi$
$97$	−7.74713	+	13.4184i	−0.786602	+	1.36243i	−0.928038	+	0.372486i	$0.878505\pi$
$98$	−0.283924	−	0.428554i	−0.0286807	−	0.0432905i
$99$		0			0
$100$	3.75075	+	9.26000i	0.375075	+	0.926000i
$101$	−0.560913	+	4.26055i	−0.0558129	+	0.423941i	0.940614	+	0.339479i	$0.110251\pi$
$101$	−0.560913	+	4.26055i	−0.0558129	+	0.423941i	−0.996427	+	0.0844624i	$0.973083\pi$
$102$		0			0
$103$	0.454001	−	1.69436i	0.0447341	−	0.166950i	−0.939945	−	0.341326i	$-0.889124\pi$
$103$	0.454001	−	1.69436i	0.0447341	−	0.166950i	0.984679	+	0.174376i	$0.0557908\pi$
$104$	5.41992	+	16.6063i	0.531467	+	1.62838i
$105$		0			0
$106$	0.242424	−	0.118370i	0.0235463	−	0.0114971i
$107$	−6.52327	+	2.70203i	−0.630628	+	0.261215i	−0.675020	−	0.737799i	$-0.735865\pi$
$107$	−6.52327	+	2.70203i	−0.630628	+	0.261215i	0.0443917	+	0.999014i	$0.485865\pi$
$108$		0			0
$109$	−2.14998	+	5.19051i	−0.205931	+	0.497161i	−0.992775	−	0.119991i	$-0.961713\pi$
$109$	−2.14998	+	5.19051i	−0.205931	+	0.497161i	0.786844	+	0.617152i	$0.211713\pi$
$110$	0.0301306	+	0.0266337i	0.00287284	+	0.00253942i
$111$		0			0
$112$	−9.00378	+	5.01158i	−0.850777	+	0.473549i
$113$	−6.18560	−	10.7138i	−0.581893	−	1.00787i	−0.995255	−	0.0973009i	$-0.968979\pi$
$113$	−6.18560	−	10.7138i	−0.581893	−	1.00787i	0.413362	−	0.910567i	$-0.364354\pi$
$114$		0			0
$115$	0.489096	−	0.375296i	0.0456084	−	0.0349966i
$116$	10.2945	+	10.4573i	0.955818	+	0.970940i
$117$		0			0
$118$	−6.16482	−	4.15428i	−0.567518	−	0.382433i
$119$	−9.07994	+	2.43296i	−0.832357	+	0.223029i
$120$		0			0
$121$	10.4557	+	2.80159i	0.950517	+	0.254690i
$122$	2.54410	+	2.92406i	0.230332	+	0.264732i
$123$		0			0
$124$	3.26938	−	2.46816i	0.293599	−	0.221647i
$125$	0.259658	−	0.626870i	0.0232245	−	0.0560689i
$126$		0			0
$127$		−	6.09879i		−	0.541180i	−0.962695	−	0.270590i	$-0.912781\pi$
$127$		−	6.09879i		−	0.541180i	0.962695	−	0.270590i	$-0.0872188\pi$
$128$	−4.72335	−	10.2806i	−0.417489	−	0.908682i
$129$		0			0
$130$	0.264320	−	0.530727i	0.0231824	−	0.0465479i
$131$	−1.80518	−	13.7117i	−0.157720	−	1.19800i	−0.868899	−	0.494989i	$-0.835172\pi$
$131$	−1.80518	−	13.7117i	−0.157720	−	1.19800i	0.711180	−	0.703010i	$-0.248161\pi$
$132$		0			0
$133$	−10.9955	−	1.44758i	−0.953428	−	0.125521i
$134$	0.430900	+	2.21160i	0.0372241	+	0.191053i
$135$		0			0
$136$	−1.89419	−	10.1455i	−0.162426	−	0.869972i
$137$	−5.27697	−	19.6939i	−0.450842	−	1.68256i	−0.700033	−	0.714110i	$-0.746831\pi$
$137$	−5.27697	−	19.6939i	−0.450842	−	1.68256i	0.249191	−	0.968454i	$-0.419835\pi$
$138$		0			0
$139$	−13.6376	+	17.7729i	−1.15673	+	1.50747i	−0.330795	+	0.943703i	$0.607317\pi$
$139$	−13.6376	+	17.7729i	−1.15673	+	1.50747i	−0.825931	+	0.563772i	$0.809350\pi$
$140$	0.337115	+	0.0931713i	0.0284914	+	0.00787441i
$141$		0			0
$142$	10.7712	+	9.52114i	0.903901	+	0.798996i
$143$			2.58710i			0.216345i
$144$		0			0
$145$		−	0.498066i		−	0.0413621i
$146$	8.77070	−	9.92225i	0.725869	−	0.821172i
$147$		0			0
$148$	8.67738	+	15.3058i	0.713276	+	1.25813i
$149$	−5.68607	+	7.41022i	−0.465821	+	0.607069i	−0.965902	−	0.258909i	$-0.916637\pi$
$149$	−5.68607	+	7.41022i	−0.465821	+	0.607069i	0.500081	+	0.865979i	$0.333304\pi$
$150$		0			0
$151$	1.19573	+	4.46253i	0.0973071	+	0.363155i	0.997359	−	0.0726273i	$-0.0231384\pi$
$151$	1.19573	+	4.46253i	0.0973071	+	0.363155i	−0.900052	+	0.435782i	$0.856472\pi$
$152$	2.51593	−	11.9137i	0.204069	−	0.966328i
$153$		0			0
$154$	−1.49796	+	0.291856i	−0.120709	+	0.0235185i
$155$	−0.137849	−	0.0181482i	−0.0110723	−	0.00145770i
$156$		0			0
$157$	−0.640445	−	4.86466i	−0.0511131	−	0.388242i	−0.997812	−	0.0661214i	$-0.978938\pi$
$157$	−0.640445	−	4.86466i	−0.0511131	−	0.388242i	0.946699	−	0.322121i	$-0.104396\pi$
$158$	−12.5895	−	6.26997i	−1.00156	−	0.498812i
$159$		0			0
$160$	−0.130545	+	0.361134i	−0.0103205	+	0.0285502i
$161$			23.3956i			1.84383i
$162$		0			0
$163$	−2.68046	+	6.47120i	−0.209950	+	0.506863i	−0.993415	−	0.114572i	$-0.963450\pi$
$163$	−2.68046	+	6.47120i	−0.209950	+	0.506863i	0.783465	+	0.621436i	$0.213450\pi$
$164$	11.1332	+	1.55470i	0.869358	+	0.121402i
$165$		0			0
$166$	−4.58632	+	3.99037i	−0.355968	+	0.309713i
$167$	19.7262	+	5.28563i	1.52646	+	0.409014i	0.921863	−	0.387516i	$-0.126667\pi$
$167$	19.7262	+	5.28563i	1.52646	+	0.409014i	0.604599	+	0.796530i	$0.293333\pi$
$168$		0			0
$169$	24.2864	−	6.50753i	1.86819	−	0.500579i
$170$	−0.195761	+	0.290502i	−0.0150142	+	0.0222805i
$171$		0			0
$172$	−7.09708	−	0.0557006i	−0.541147	−	0.00424713i
$173$	−7.15432	+	5.48970i	−0.543933	+	0.417374i	−0.843841	−	0.536594i	$-0.819711\pi$
$173$	−7.15432	+	5.48970i	−0.543933	+	0.417374i	0.299908	+	0.953968i	$0.403044\pi$
$174$		0			0
$175$	6.43441	+	11.1447i	0.486396	+	0.842462i
$176$	−0.192606	−	1.66448i	−0.0145182	−	0.125465i
$177$		0			0
$178$	−3.26805	+	3.69713i	−0.244951	+	0.277112i
$179$	−3.79147	+	9.15342i	−0.283388	+	0.684159i	−0.999910	−	0.0134054i	$-0.995733\pi$
$179$	−3.79147	+	9.15342i	−0.283388	+	0.684159i	0.716522	+	0.697564i	$0.245733\pi$
$180$		0			0
$181$	−19.1915	+	7.94937i	−1.42649	+	0.590872i	−0.956482	−	0.291790i	$-0.905749\pi$
$181$	−19.1915	+	7.94937i	−1.42649	+	0.590872i	−0.470009	+	0.882662i	$0.655749\pi$
$182$	9.87246	+	20.2190i	0.731796	+	1.49873i
$183$		0			0
$184$	−25.6103	−	1.98162i	−1.88801	−	0.146087i
$185$	0.154563	−	0.576835i	0.0113637	−	0.0424098i
$186$		0			0
$187$	0.199514	−	1.51546i	0.0145899	−	0.110821i
$188$	4.37998	+	1.85465i	0.319443	+	0.135264i
$189$		0			0
$190$	−0.344535	+	0.228260i	−0.0249952	+	0.0165597i
$191$	4.73817	−	8.20675i	0.342842	−	0.593820i	−0.642117	−	0.766606i	$-0.721944\pi$
$191$	4.73817	−	8.20675i	0.342842	−	0.593820i	0.984959	+	0.172787i	$0.0552771\pi$
$192$		0			0
$193$	−8.97329	−	15.5422i	−0.645912	−	1.11875i	−0.984090	−	0.177670i	$-0.943144\pi$
$193$	−8.97329	−	15.5422i	−0.645912	−	1.11875i	0.338178	−	0.941082i	$-0.390189\pi$
$194$	−19.6143	−	9.76855i	−1.40822	−	0.701341i
$195$		0			0
$196$	0.580231	−	0.438035i	0.0414451	−	0.0312882i
$197$	−4.82042	+	1.99668i	−0.343441	+	0.142258i	−0.547735	−	0.836652i	$-0.684510\pi$
$197$	−4.82042	+	1.99668i	−0.343441	+	0.142258i	0.204295	+	0.978909i	$0.434510\pi$
$198$		0			0
$199$	−14.2378	−	14.2378i	−1.00929	−	1.00929i	−0.999956	−	0.00933576i	$-0.997028\pi$
$199$	−14.2378	−	14.2378i	−1.00929	−	1.00929i	−0.00933576	−	0.999956i	$-0.502972\pi$
$200$	−12.7447	+	6.09953i	−0.901186	+	0.431302i
$201$		0			0
$202$	−6.06271	−	0.421270i	−0.426571	−	0.0296405i
$203$	14.9955	+	11.5064i	1.05248	+	0.807594i
$204$		0			0
$205$	−0.232270	−	0.302701i	−0.0162225	−	0.0211415i
$206$	2.43113	+	0.493506i	0.169385	+	0.0343842i
$207$		0			0
$208$	−22.9691	+	9.09444i	−1.59262	+	0.630586i
$209$	0.901678	−	1.56175i	0.0623704	−	0.108029i
$210$		0			0
$211$	0.857445	+	6.51294i	0.0590290	+	0.448369i	0.995281	+	0.0970392i	$0.0309372\pi$
$211$	0.857445	+	6.51294i	0.0590290	+	0.448369i	−0.936252	+	0.351330i	$0.885729\pi$
$212$	0.188164	+	0.331898i	0.0129232	+	0.0227948i
$213$		0			0
$214$	−4.38125	−	8.97289i	−0.299496	−	0.613374i
$215$	0.170337	+	0.170337i	0.0116169	+	0.0116169i
$216$		0			0
$217$	3.73103	−	3.73103i	0.253279	−	0.253279i
$218$	−7.51355	−	2.58343i	−0.508882	−	0.174972i
$219$		0			0
$220$	−0.0349745	+	0.0448464i	−0.00235798	+	0.00302354i
$221$	−22.3433	+	2.94155i	−1.50297	+	0.197870i
$222$		0			0
$223$	2.03938	+	1.17744i	0.136567	+	0.0788471i	0.566727	−	0.823906i	$-0.308209\pi$
$223$	2.03938	+	1.17744i	0.136567	+	0.0788471i	−0.430160	+	0.902753i	$0.641543\pi$
$224$	−7.85696	−	12.2734i	−0.524965	−	0.820050i
$225$		0			0
$226$	14.5850	−	9.66283i	0.970182	−	0.642762i
$227$	12.6258	−	9.68813i	0.838005	−	0.643024i	−0.0979313	−	0.995193i	$-0.531223\pi$
$227$	12.6258	−	9.68813i	0.838005	−	0.643024i	0.935936	+	0.352169i	$0.114556\pi$
$228$		0			0
$229$	9.41277	−	12.2670i	0.622013	−	0.810623i	−0.370999	−	0.928633i	$-0.620985\pi$
$229$	9.41277	−	12.2670i	0.622013	−	0.810623i	0.993012	+	0.118010i	$0.0376514\pi$
$230$	0.572274	+	0.657743i	0.0377347	+	0.0433703i
$231$		0			0
$232$	−13.8658	+	15.4404i	−0.910332	+	1.01371i
$233$	−5.49432	+	5.49432i	−0.359945	+	0.359945i	−0.863793	−	0.503848i	$-0.831917\pi$
$233$	−5.49432	+	5.49432i	−0.359945	+	0.359945i	0.503848	+	0.863793i	$0.331917\pi$
$234$		0			0
$235$	−0.0617812	−	0.149153i	−0.00403016	−	0.00972966i
$236$	5.32786	−	9.06311i	0.346814	−	0.589958i
$237$		0			0
$238$	−4.22377	−	12.6051i	−0.273786	−	0.817069i
$239$	17.3751	−	10.0315i	1.12390	−	0.648883i	0.181506	−	0.983390i	$-0.441903\pi$
$239$	17.3751	−	10.0315i	1.12390	−	0.648883i	0.942393	+	0.334507i	$0.108570\pi$
$240$		0			0
$241$	−9.35807	−	5.40288i	−0.602806	−	0.348030i	0.167339	−	0.985899i	$-0.446483\pi$
$241$	−9.35807	−	5.40288i	−0.602806	−	0.348030i	−0.770145	+	0.637869i	$0.779816\pi$
$242$	−3.04537	+	15.0022i	−0.195764	+	0.964379i
$243$		0			0
$244$	−3.90620	+	3.84536i	−0.250069	+	0.246174i
$245$	−0.0244647	−	0.00322084i	−0.00156299	−	0.000205772i
$246$		0			0
$247$	−25.6819	−	6.88146i	−1.63410	−	0.437857i
$248$	3.76819	+	4.40023i	0.239280	+	0.279415i
$249$		0			0
$250$	0.907429	+	0.312007i	0.0573908	+	0.0197331i
$251$	3.41749	+	8.25055i	0.215710	+	0.520770i	0.994282	−	0.106785i	$-0.0340557\pi$
$251$	3.41749	+	8.25055i	0.215710	+	0.520770i	−0.778572	+	0.627555i	$0.784056\pi$
$252$		0			0
$253$	−3.51468	−	1.45583i	−0.220966	−	0.0915272i
$254$	8.60868	−	0.530325i	0.540157	−	0.0332755i
$255$		0			0
$256$	14.1007	−	7.56114i	0.881293	−	0.472571i
$257$	23.7599	−	13.7178i	1.48210	−	0.855692i	0.482308	−	0.876002i	$-0.339799\pi$
$257$	23.7599	−	13.7178i	1.48210	−	0.855692i	0.999794	+	0.0203099i	$0.00646527\pi$
$258$		0			0
$259$	13.7963	+	17.9797i	0.857260	+	1.11720i
$260$	0.772126	+	0.326948i	0.0478852	+	0.0202764i
$261$		0			0
$262$	19.1976	−	3.74040i	1.18603	−	0.231082i
$263$	−5.87988	−	21.9440i	−0.362569	−	1.35313i	−0.870686	−	0.491838i	$-0.836325\pi$
$263$	−5.87988	−	21.9440i	−0.362569	−	1.35313i	0.508117	−	0.861288i	$-0.330342\pi$
$264$		0			0
$265$	0.00335160	−	0.0125083i	0.000205887	−	0.000768381i
$266$	1.08720	−	15.6464i	0.0666603	−	0.959342i
$267$		0			0
$268$	−3.08429	+	0.800543i	−0.188403	+	0.0489010i
$269$	−26.9125	−	11.1475i	−1.64088	−	0.679677i	−0.644498	−	0.764606i	$-0.722933\pi$
$269$	−26.9125	−	11.1475i	−1.64088	−	0.679677i	−0.996387	+	0.0849297i	$0.972933\pi$
$270$		0			0
$271$	4.68410			0.284539			0.142269	−	0.989828i	$-0.454560\pi$
$271$	4.68410			0.284539			0.142269	+	0.989828i	$0.454560\pi$
$272$	14.1561	−	3.55594i	0.858338	−	0.215610i
$273$		0			0
$274$	27.3398	−	9.16114i	1.65166	−	0.553445i
$275$	−2.07465	+	0.273132i	−0.125106	+	0.0164705i
$276$		0			0
$277$	−1.62376	+	12.3337i	−0.0975625	+	0.741060i	0.870822	+	0.491598i	$0.163587\pi$
$277$	−1.62376	+	12.3337i	−0.0975625	+	0.741060i	−0.968385	+	0.249462i	$0.919746\pi$
$278$	−26.2729	−	17.7045i	−1.57575	−	1.06185i
$279$		0			0
$280$	−0.102201	+	0.483952i	−0.00610767	+	0.0289216i
$281$	−11.7286	+	3.14266i	−0.699668	+	0.187475i	−0.591082	−	0.806612i	$-0.701299\pi$
$281$	−11.7286	+	3.14266i	−0.699668	+	0.187475i	−0.108586	+	0.994087i	$0.534632\pi$
$282$		0			0
$283$	−6.44707	−	4.94701i	−0.383238	−	0.294069i	0.399119	−	0.916899i	$-0.369316\pi$
$283$	−6.44707	−	4.94701i	−0.383238	−	0.294069i	−0.782357	+	0.622830i	$0.785983\pi$
$284$	−12.5028	+	16.0319i	−0.741907	+	0.951318i
$285$		0			0
$286$	−3.65180	+	0.224963i	−0.215935	+	0.0133024i
$287$	14.4795			0.854699
$288$		0			0
$289$	−3.68505			−0.216767
$290$	0.703038	−	0.0433096i	0.0412838	−	0.00254323i
$291$		0			0
$292$	14.7683	+	11.5174i	0.864249	+	0.674004i
$293$	6.46185	+	4.95835i	0.377505	+	0.289670i	0.780034	−	0.625737i	$-0.215202\pi$
$293$	6.46185	+	4.95835i	0.377505	+	0.289670i	−0.402528	+	0.915408i	$0.631869\pi$
$294$		0			0
$295$	−0.344674	+	0.0923551i	−0.0200677	+	0.00537712i
$296$	−20.8502	+	13.5794i	−1.21189	+	0.789285i
$297$		0			0
$298$	−10.9542	−	7.38173i	−0.634562	−	0.427612i
$299$	−7.32101	+	55.6086i	−0.423385	+	3.21593i
$300$		0			0
$301$	−9.06361	+	1.19325i	−0.522418	+	0.0687776i
$302$	−6.19505	+	2.07586i	−0.356485	+	0.119452i
$303$		0			0
$304$	17.0354	+	2.51537i	0.977047	+	0.144266i
$305$	0.186046			0.0106529
$306$		0			0
$307$	30.9448	+	12.8178i	1.76611	+	0.731549i	0.995555	+	0.0941803i	$0.0300230\pi$
$307$	30.9448	+	12.8178i	1.76611	+	0.731549i	0.770559	+	0.637368i	$0.219977\pi$
$308$	−0.542222	−	2.08905i	−0.0308960	−	0.119034i
$309$		0			0
$310$	0.0136301	−	0.196158i	0.000774138	−	0.0111410i
$311$	−4.12235	+	15.3848i	−0.233757	+	0.872393i	0.744948	+	0.667122i	$0.232474\pi$
$311$	−4.12235	+	15.3848i	−0.233757	+	0.872393i	−0.978705	+	0.205270i	$0.934193\pi$
$312$		0			0
$313$	−7.15224	−	26.6925i	−0.404268	−	1.50875i	−0.805401	−	0.592730i	$-0.798050\pi$
$313$	−7.15224	−	26.6925i	−0.404268	−	1.50875i	0.401132	−	0.916020i	$-0.368617\pi$
$314$	6.81096	−	1.32702i	0.384365	−	0.0748882i
$315$		0			0
$316$	7.75558	−	18.3157i	0.436285	−	1.03034i
$317$	0.505667	+	0.658999i	0.0284011	+	0.0370131i	0.807338	−	0.590089i	$-0.200907\pi$
$317$	0.505667	+	0.658999i	0.0284011	+	0.0370131i	−0.778937	+	0.627102i	$0.784241\pi$
$318$		0			0
$319$	−2.66171	+	1.53674i	−0.149027	+	0.0860409i
$320$	−0.521106	−	0.152866i	−0.0291307	−	0.00854548i
$321$		0			0
$322$	−33.0238	+	2.03438i	−1.84034	+	0.113372i
$323$	14.5131	+	6.01153i	0.807532	+	0.334491i
$324$		0			0
$325$	11.8064	+	28.5032i	0.654901	+	1.58107i
$326$	−9.36742	−	3.22086i	−0.518813	−	0.178387i
$327$		0			0
$328$	−1.22642	+	15.8501i	−0.0677178	+	0.875178i
$329$	5.91790	+	1.58570i	0.326264	+	0.0874222i
$330$		0			0
$331$	−14.8891	−	1.96019i	−0.818378	−	0.107742i	−0.290298	−	0.956936i	$-0.593755\pi$
$331$	−14.8891	−	1.96019i	−0.818378	−	0.107742i	−0.528080	+	0.849195i	$0.677088\pi$
$332$	−6.03136	−	6.12678i	−0.331014	−	0.336251i
$333$		0			0
$334$	−5.74556	+	28.3039i	−0.314383	+	1.54872i
$335$	0.0936646	+	0.0540773i	0.00511744	+	0.00295456i
$336$		0			0
$337$	17.1129	−	9.88013i	0.932198	−	0.538205i	0.0446921	−	0.999001i	$-0.485769\pi$
$337$	17.1129	−	9.88013i	0.932198	−	0.538205i	0.887506	+	0.460796i	$0.152436\pi$
$338$	11.2975	+	33.7153i	0.614501	+	1.83387i
$339$		0			0
$340$	−0.427078	−	0.251063i	−0.0231615	−	0.0136158i
$341$	0.328337	+	0.792675i	0.0177804	+	0.0429258i
$342$		0			0
$343$	13.4134	−	13.4134i	0.724256	−	0.724256i
$344$	−0.538508	−	10.0226i	−0.0290344	−	0.540385i
$345$		0			0
$346$	−8.37103	−	9.62123i	−0.450029	−	0.517240i
$347$	7.17492	−	9.35054i	0.385170	−	0.501963i	−0.560022	−	0.828477i	$-0.689207\pi$
$347$	7.17492	−	9.35054i	0.385170	−	0.501963i	0.945192	+	0.326514i	$0.105874\pi$
$348$		0			0
$349$	13.8028	−	10.5912i	0.738846	−	0.566936i	−0.169313	−	0.985562i	$-0.554155\pi$
$349$	13.8028	−	10.5912i	0.738846	−	0.566936i	0.908159	+	0.418626i	$0.137488\pi$
$350$	−15.1717	+	10.0515i	−0.810961	+	0.537276i
$351$		0			0
$352$	2.33272	−	0.416606i	0.124334	−	0.0222052i
$353$	10.1154	+	5.84016i	0.538391	+	0.310840i	0.744427	−	0.667704i	$-0.232723\pi$
$353$	10.1154	+	5.84016i	0.538391	+	0.310840i	−0.206036	+	0.978544i	$0.566056\pi$
$354$		0			0
$355$	0.684157	−	0.0900710i	0.0363113	−	0.00478047i
$356$	−5.50282	−	4.29149i	−0.291649	−	0.227449i
$357$		0			0
$358$	−13.2501	−	4.55586i	−0.700289	−	0.240785i
$359$	−5.22831	+	5.22831i	−0.275939	+	0.275939i	−0.831486	−	0.555546i	$-0.812509\pi$
$359$	−5.22831	+	5.22831i	−0.275939	+	0.275939i	0.555546	+	0.831486i	$0.312509\pi$
$360$		0			0
$361$	−0.330044	−	0.330044i	−0.0173707	−	0.0173707i
$362$	−12.8896	−	26.3982i	−0.677465	−	1.38746i
$363$		0			0
$364$	−27.6814	+	15.6935i	−1.45090	+	0.822564i
$365$	−0.0829717	−	0.630233i	−0.00434294	−	0.0329879i
$366$		0			0
$367$	−0.612755	+	1.06132i	−0.0319855	+	0.0554006i	−0.881575	−	0.472044i	$-0.843516\pi$
$367$	−0.612755	+	1.06132i	−0.0319855	+	0.0554006i	0.849590	+	0.527444i	$0.176850\pi$
$368$	0.570175	−	36.3221i	0.0297224	−	1.89342i
$369$		0			0
$370$	0.827665	+	0.168012i	0.0430282	+	0.00873452i
$371$	0.299165	+	0.389879i	0.0155319	+	0.0202415i
$372$		0			0
$373$	13.3587	+	10.2505i	0.691689	+	0.530752i	0.893719	−	0.448628i	$-0.148087\pi$
$373$	13.3587	+	10.2505i	0.691689	+	0.530752i	−0.202030	+	0.979379i	$0.564754\pi$
$374$	2.15648	+	0.149844i	0.111509	+	0.00774823i
$375$		0			0
$376$	−2.23705	+	6.34378i	−0.115367	+	0.327155i
$377$	32.0419	+	32.0419i	1.65024	+	1.65024i
$378$		0			0
$379$	10.2546	−	4.24759i	0.526742	−	0.218184i	−0.103433	−	0.994636i	$-0.532983\pi$
$379$	10.2546	−	4.24759i	0.526742	−	0.218184i	0.630176	+	0.776453i	$0.282983\pi$
$380$	−0.352157	−	0.466475i	−0.0180653	−	0.0239297i
$381$		0			0
$382$	11.9961	+	5.97448i	0.613776	+	0.305681i
$383$	2.90214	+	5.02665i	0.148292	+	0.256850i	0.930596	−	0.366047i	$-0.119289\pi$
$383$	2.90214	+	5.02665i	0.148292	+	0.256850i	−0.782304	+	0.622897i	$0.785956\pi$
$384$		0			0
$385$	−0.0366275	+	0.0634407i	−0.00186671	+	0.00323324i
$386$	21.1581	−	14.0176i	1.07692	−	0.713478i
$387$		0			0
$388$	12.0831	−	28.5357i	0.613427	−	1.44868i
$389$	0.532383	−	4.04385i	0.0269929	−	0.205031i	−0.972634	−	0.232342i	$-0.925361\pi$
$389$	0.532383	−	4.04385i	0.0269929	−	0.205031i	0.999627	+	0.0273109i	$0.00869441\pi$
$390$		0			0
$391$	8.57692	−	32.0095i	0.433753	−	1.61879i
$392$	0.668757	+	0.780928i	0.0337773	+	0.0394428i
$393$		0			0
$394$	−3.23756	−	6.63058i	−0.163106	−	0.334044i
$395$	−0.623711	+	0.258350i	−0.0313823	+	0.0129990i
$396$		0			0
$397$	−10.8114	+	26.1011i	−0.542610	+	1.30998i	0.380266	+	0.924877i	$0.375833\pi$
$397$	−10.8114	+	26.1011i	−0.542610	+	1.30998i	−0.922875	+	0.385099i	$0.874167\pi$
$398$	18.8592	−	21.3353i	0.945324	−	1.06944i
$399$		0			0
$400$	−9.71794	−	17.4592i	−0.485897	−	0.872961i
$401$	13.2637	+	22.9733i	0.662355	+	1.14723i	0.979995	+	0.199022i	$0.0637764\pi$
$401$	13.2637	+	22.9733i	0.662355	+	1.14723i	−0.317640	+	0.948211i	$0.602890\pi$
$402$		0			0
$403$	10.0357	−	7.70069i	0.499915	−	0.383599i
$404$	0.0674519	−	8.59437i	0.00335586	−	0.427586i
$405$		0			0
$406$	−14.9378	+	22.1672i	−0.741352	+	1.10014i
$407$	−3.55955	+	0.953779i	−0.176440	+	0.0472771i
$408$		0			0
$409$	26.5949	+	7.12609i	1.31503	+	0.352362i	0.847116	−	0.531409i	$-0.178337\pi$
$409$	26.5949	+	7.12609i	1.31503	+	0.352362i	0.467919	+	0.883771i	$0.345004\pi$
$410$	0.407076	−	0.354180i	0.0201041	−	0.0174917i
$411$		0			0
$412$	−0.485203	+	3.47454i	−0.0239042	+	0.171178i
$413$	5.18217	−	12.5109i	0.254998	−	0.615619i
$414$		0			0
$415$			0.291808i			0.0143243i
$416$	−14.8344	−	31.6310i	−0.727318	−	1.55084i
$417$		0			0
$418$	2.28288	+	1.13695i	0.111659	+	0.0556100i
$419$	−0.769500	−	5.84494i	−0.0375926	−	0.285544i	−0.999907	−	0.0136062i	$-0.995669\pi$
$419$	−0.769500	−	5.84494i	−0.0375926	−	0.285544i	0.962315	−	0.271938i	$-0.0876644\pi$
$420$		0			0
$421$	36.3814	+	4.78971i	1.77312	+	0.233436i	0.944991	−	0.327097i	$-0.106070\pi$
$421$	36.3814	+	4.78971i	1.77312	+	0.233436i	0.828132	+	0.560533i	$0.189404\pi$
$422$	−9.11870	+	1.77665i	−0.443892	+	0.0864861i
$423$		0			0
$424$	−0.452125	+	0.294461i	−0.0219571	+	0.0143003i
$425$	−4.71776	−	17.6069i	−0.228845	−	0.854061i
$426$		0			0
$427$	−4.29807	+	5.60136i	−0.207998	+	0.271069i
$428$	12.2846	−	6.96454i	0.593798	−	0.336644i
$429$		0			0
$430$	−0.225626	+	0.255250i	−0.0108806	+	0.0123092i
$431$			5.39534i			0.259884i	0.991522	+	0.129942i	$0.0414792\pi$
$431$			5.39534i			0.259884i	−0.991522	+	0.129942i	$0.958521\pi$
$432$		0			0
$433$			1.07138i			0.0514873i	0.999669	+	0.0257436i	$0.00819536\pi$
$433$			1.07138i			0.0514873i	−0.999669	+	0.0257436i	$0.991805\pi$
$434$	5.59092	+	4.94205i	0.268373	+	0.237226i
$435$		0			0
$436$	2.99327	−	10.8303i	0.143351	−	0.518678i
$437$	23.8006	−	31.0175i	1.13854	−	1.48377i
$438$		0			0
$439$	1.63703	+	6.10948i	0.0781312	+	0.291589i	0.993925	−	0.110059i	$-0.0351040\pi$
$439$	1.63703	+	6.10948i	0.0781312	+	0.291589i	−0.915794	+	0.401649i	$0.868437\pi$
$440$	−0.0663436	−	0.0454681i	−0.00316281	−	0.00216761i
$441$		0			0
$442$	−6.09498	−	31.2826i	−0.289909	−	1.48796i
$443$	−19.9890	−	2.63160i	−0.949706	−	0.125031i	−0.360272	−	0.932847i	$-0.617316\pi$
$443$	−19.9890	−	2.63160i	−0.949706	−	0.125031i	−0.589435	+	0.807816i	$0.700649\pi$
$444$		0			0
$445$	0.0309161	+	0.234831i	0.00146556	+	0.0111321i
$446$	−1.48466	+	2.98105i	−0.0703009	+	0.141157i
$447$		0			0
$448$	16.6411	−	12.1576i	0.786220	−	0.574394i
$449$			2.03680i			0.0961223i	0.998844	+	0.0480612i	$0.0153042\pi$
$449$			2.03680i			0.0961223i	−0.998844	+	0.0480612i	$0.984696\pi$
$450$		0			0
$451$	−0.901011	+	2.17523i	−0.0424269	+	0.102428i
$452$	14.9077	+	19.7471i	0.701200	+	0.928824i
$453$		0			0
$454$	14.7730	+	16.9794i	0.693334	+	0.796882i
$455$	1.04324	+	0.279535i	0.0489078	+	0.0131048i
$456$		0			0
$457$	10.6951	−	2.86574i	0.500295	−	0.134054i	0.000158032	−	1.00000i	$-0.499950\pi$
$457$	10.6951	−	2.86574i	0.500295	−	0.134054i	0.500137	+	0.865946i	$0.333283\pi$
$458$	18.1338	+	12.2198i	0.847335	+	0.570994i
$459$		0			0
$460$	−0.878666	+	0.864981i	−0.0409680	+	0.0403300i
$461$	−22.9338	+	17.5977i	−1.06813	+	0.819607i	−0.984235	−	0.176867i	$-0.943404\pi$
$461$	−22.9338	+	17.5977i	−1.06813	+	0.819607i	−0.0838979	+	0.996474i	$0.526737\pi$
$462$		0			0
$463$	−3.25725	−	5.64172i	−0.151377	−	0.262193i	0.780357	−	0.625334i	$-0.215037\pi$
$463$	−3.25725	−	5.64172i	−0.151377	−	0.262193i	−0.931734	+	0.363142i	$0.881704\pi$
$464$	−23.0004	−	18.2294i	−1.06776	−	0.846280i
$465$		0			0
$466$	−8.23320	−	7.27768i	−0.381396	−	0.337132i
$467$	8.14793	−	19.6708i	0.377041	−	0.910258i	−0.615476	−	0.788156i	$-0.711036\pi$
$467$	8.14793	−	19.6708i	0.377041	−	0.910258i	0.992517	−	0.122103i	$-0.0389638\pi$
$468$		0			0
$469$	−3.79199	+	1.57069i	−0.175098	+	0.0725279i
$470$	0.205163	−	0.100176i	0.00946345	−	0.00462078i
$471$		0			0
$472$	13.2562	+	6.73239i	0.610167	+	0.309883i
$473$	0.384738	−	1.43586i	0.0176903	−	0.0660210i
$474$		0			0
$475$	2.80700	−	21.3213i	0.128794	−	0.978289i
$476$	17.4253	−	7.05810i	0.798688	−	0.323507i
$477$		0			0
$478$	15.6707	+	23.6533i	0.716761	+	1.08187i
$479$	0.238327	−	0.412794i	0.0108894	−	0.0188611i	−0.860529	−	0.509401i	$-0.829867\pi$
$479$	0.238327	−	0.412794i	0.0108894	−	0.0188611i	0.871419	+	0.490540i	$0.163200\pi$
$480$		0			0
$481$	27.1659	+	47.0527i	1.23866	+	2.14542i
$482$	6.81264	−	13.6791i	0.310307	−	0.623065i
$483$		0			0
$484$	−21.4410	−	2.99413i	−0.974591	−	0.136097i
$485$	−0.971735	+	0.402506i	−0.0441242	+	0.0182769i
$486$		0			0
$487$	19.6952	+	19.6952i	0.892476	+	0.892476i	0.994756	−	0.102280i	$-0.0326138\pi$
$487$	19.6952	+	19.6952i	0.892476	+	0.892476i	−0.102280	+	0.994756i	$0.532614\pi$
$488$	−5.76754	−	5.17937i	−0.261084	−	0.234459i
$489$		0			0
$490$	0.00241900	−	0.0348130i	0.000109279	−	0.00157269i
$491$	−24.1906	−	18.5621i	−1.09171	−	0.837697i	−0.104089	−	0.994568i	$-0.533193\pi$
$491$	−24.1906	−	18.5621i	−1.09171	−	0.837697i	−0.987619	+	0.156871i	$0.949859\pi$
$492$		0			0
$493$	−16.2983	−	21.2403i	−0.734037	−	0.956616i
$494$	7.48024	−	36.8494i	0.336552	−	1.65793i
$495$		0			0
$496$	−5.88342	+	5.70157i	−0.264173	+	0.256008i
$497$	−13.0938	+	22.6791i	−0.587336	+	1.01730i
$498$		0			0
$499$	−4.42487	−	33.6102i	−0.198084	−	1.50460i	−0.744804	−	0.667284i	$-0.767457\pi$
$499$	−4.42487	−	33.6102i	−0.198084	−	1.50460i	0.546719	−	0.837316i	$-0.315877\pi$
$500$	−0.361504	+	1.30800i	−0.0161669	+	0.0584956i
$501$		0			0
$502$	−11.3488	+	5.54135i	−0.506521	+	0.247322i
$503$	−24.6072	−	24.6072i	−1.09718	−	1.09718i	−0.994739	−	0.102441i	$-0.967335\pi$
$503$	−24.6072	−	24.6072i	−1.09718	−	1.09718i	−0.102441	−	0.994739i	$-0.532665\pi$
$504$		0			0
$505$	−0.206274	+	0.206274i	−0.00917908	+	0.00917908i
$506$	1.74934	−	5.08770i	0.0777675	−	0.226176i
$507$		0			0
$508$	1.49715	+	12.1054i	0.0664251	+	0.537088i
$509$	18.5649	−	2.44412i	0.822876	−	0.108334i	0.292682	−	0.956210i	$-0.405452\pi$
$509$	18.5649	−	2.44412i	0.822876	−	0.108334i	0.530194	+	0.847876i	$0.322119\pi$
$510$		0			0
$511$	20.8915	+	12.0617i	0.924188	+	0.533580i
$512$	11.8990	+	19.2462i	0.525865	+	0.850568i
$513$		0			0
$514$	21.4292	+	32.3452i	0.945203	+	1.42668i
$515$	0.0944691	−	0.0724887i	0.00416281	−	0.00319423i
$516$		0			0
$517$	−0.606467	+	0.790363i	−0.0266724	+	0.0347601i
$518$	−24.1793	+	21.0374i	−1.06238	+	0.924332i
$519$		0			0
$520$	−0.394359	+	1.11831i	−0.0172938	+	0.0490414i
$521$	26.8438	−	26.8438i	1.17605	−	1.17605i	0.195305	−	0.980743i	$-0.437430\pi$
$521$	26.8438	−	26.8438i	1.17605	−	1.17605i	0.980743	−	0.195305i	$-0.0625697\pi$
$522$		0			0
$523$	−8.96802	−	21.6507i	−0.392144	−	0.946720i	−0.989472	−	0.144723i	$-0.953771\pi$
$523$	−8.96802	−	21.6507i	−0.392144	−	0.946720i	0.597328	−	0.801997i	$-0.296229\pi$
$524$	6.94905	+	26.7730i	0.303571	+	1.16958i
$525$		0			0
$526$	30.4635	−	10.2078i	1.32827	−	0.445083i
$527$	−6.47254	+	3.73692i	−0.281948	+	0.162783i
$528$		0			0
$529$	−51.5081	−	29.7382i	−2.23948	−	1.29297i
$530$	0.0179474	+	0.00364324i	0.000779587	+	0.000158252i
$531$		0			0
$532$	22.1800	+	0.174077i	0.961625	+	0.00754720i
$533$	34.4161	+	4.53096i	1.49073	+	0.196258i
$534$		0			0
$535$	−0.462973	−	0.124053i	−0.0200161	−	0.00536329i
$536$	−1.39819	−	4.28398i	−0.0603928	−	0.185040i
$537$		0			0
$538$	13.3950	−	38.9574i	0.577498	−	1.67957i
$539$	0.0582714	+	0.140680i	0.00250993	+	0.00605950i
$540$		0			0
$541$	−8.00916	−	3.31750i	−0.344341	−	0.142631i	0.203809	−	0.979011i	$-0.434668\pi$
$541$	−8.00916	−	3.31750i	−0.344341	−	0.142631i	−0.548150	+	0.836380i	$0.684668\pi$
$542$	0.407309	+	6.61179i	0.0174954	+	0.284001i
$543$		0			0
$544$	6.25029	+	19.6726i	0.267979	+	0.843457i
$545$	−0.330284	+	0.190689i	−0.0141478	+	0.00816824i
$546$		0			0
$547$	27.7113	+	36.1141i	1.18485	+	1.54413i	0.774984	+	0.631981i	$0.217758\pi$
$547$	27.7113	+	36.1141i	1.18485	+	1.54413i	0.409866	+	0.912146i	$0.365576\pi$
$548$	15.3086	+	37.7946i	0.653953	+	1.61451i
$549$		0			0
$550$	−0.565939	−	2.90469i	−0.0241317	−	0.123856i
$551$	−8.17516	−	30.5101i	−0.348274	−	1.29978i
$552$		0			0
$553$	6.63089	−	24.7468i	0.281974	−	1.05234i
$554$	−17.5507	−	1.21952i	−0.745657	−	0.0518123i
$555$		0			0
$556$	22.7060	−	38.6247i	0.962950	−	1.63805i
$557$	−19.9105	−	8.24722i	−0.843637	−	0.349446i	−0.0813502	−	0.996686i	$-0.525923\pi$
$557$	−19.9105	−	8.24722i	−0.843637	−	0.349446i	−0.762286	+	0.647240i	$0.775923\pi$
$558$		0			0
$559$	−21.9165			−0.926970
$560$	−0.692003	−	0.102178i	−0.0292425	−	0.00431781i
$561$		0			0
$562$	−5.45585	−	16.2821i	−0.230141	−	0.686817i
$563$	6.60330	−	0.869341i	0.278296	−	0.0366384i	0.00991376	−	0.999951i	$-0.496844\pi$
$563$	6.60330	−	0.869341i	0.278296	−	0.0366384i	0.268382	+	0.963312i	$0.413511\pi$
$564$		0			0
$565$	0.109615	−	0.832612i	0.00461156	−	0.0350282i
$566$	6.42228	−	9.53045i	0.269949	−	0.400595i
$567$		0			0
$568$	−23.7168	−	16.2542i	−0.995136	−	0.682009i
$569$	−6.63825	+	1.77871i	−0.278290	+	0.0745676i	−0.395265	−	0.918567i	$-0.629347\pi$
$569$	−6.63825	+	1.77871i	−0.278290	+	0.0745676i	0.116975	+	0.993135i	$0.462680\pi$
$570$		0			0
$571$	27.9199	+	21.4237i	1.16841	+	0.896554i	0.996078	−	0.0884846i	$-0.0282024\pi$
$571$	27.9199	+	21.4237i	1.16841	+	0.896554i	0.172334	+	0.985039i	$0.444869\pi$
$572$	−0.635089	−	5.13509i	−0.0265544	−	0.214709i
$573$		0			0
$574$	1.25908	+	20.4384i	0.0525528	+	0.853081i
$575$	−45.3664			−1.89191
$576$		0			0
$577$	27.6999			1.15316			0.576580	−	0.817041i	$-0.304387\pi$
$577$	27.6999			1.15316			0.576580	+	0.817041i	$0.304387\pi$
$578$	−0.320436	−	5.20158i	−0.0133284	−	0.216357i
$579$		0			0
$580$	0.122266	+	0.988599i	0.00507683	+	0.0410493i
$581$	−8.78561	−	6.74143i	−0.364488	−	0.279682i
$582$		0			0
$583$	−0.0771869	+	0.0206822i	−0.00319675	+	0.000856567i
$584$	−14.9730	+	21.8475i	−0.619588	+	0.904056i
$585$		0			0
$586$	−6.43701	+	9.55231i	−0.265910	+	0.394602i
$587$	−0.902546	+	6.85551i	−0.0372520	+	0.282957i	0.962672	+	0.270669i	$0.0872449\pi$
$587$	−0.902546	+	6.85551i	−0.0372520	+	0.282957i	−0.999924	+	0.0122883i	$0.996088\pi$
$588$		0			0
$589$	−8.74215	+	1.15093i	−0.360214	+	0.0474231i
$590$	−0.160334	−	0.478489i	−0.00660085	−	0.0196991i
$591$		0			0
$592$	−20.9808	−	28.2500i	−0.862307	−	1.16107i
$593$	0.448752			0.0184280			0.00921401	−	0.999958i	$-0.497067\pi$
$593$	0.448752			0.0184280			0.00921401	+	0.999958i	$0.497067\pi$
$594$		0			0
$595$	−0.589545	−	0.244197i	−0.0241690	−	0.0100111i
$596$	9.46706	−	16.1042i	0.387786	−	0.659654i
$597$		0			0
$598$	−79.1302	−	5.49840i	−3.23588	−	0.224846i
$599$	−4.73585	+	17.6744i	−0.193501	+	0.722157i	0.799148	+	0.601134i	$0.205284\pi$
$599$	−4.73585	+	17.6744i	−0.193501	+	0.722157i	−0.992650	+	0.121023i	$0.961382\pi$
$600$		0			0
$601$	1.27794	+	4.76933i	0.0521282	+	0.194545i	0.987080	−	0.160231i	$-0.0512239\pi$
$601$	1.27794	+	4.76933i	0.0521282	+	0.194545i	−0.934951	+	0.354776i	$0.884557\pi$
$602$	−2.47244	−	12.6899i	−0.100769	−	0.517200i
$603$		0			0
$604$	−3.46885	−	8.56404i	−0.141145	−	0.348466i
$605$	0.447320	+	0.582958i	0.0181861	+	0.0237006i
$606$		0			0
$607$	−11.1380	+	6.43050i	−0.452075	+	0.261006i	−0.708706	−	0.705504i	$-0.750721\pi$
$607$	−11.1380	+	6.43050i	−0.452075	+	0.261006i	0.256631	+	0.966509i	$0.417388\pi$
$608$	−2.06921	+	24.2648i	−0.0839177	+	0.984069i
$609$		0			0
$610$	0.0161777	+	0.262610i	0.000655016	+	0.0106328i
$611$	13.5699	+	5.62085i	0.548981	+	0.227395i
$612$		0			0
$613$	1.29501	+	3.12642i	0.0523048	+	0.126275i	0.947872	−	0.318651i	$-0.103230\pi$
$613$	1.29501	+	3.12642i	0.0523048	+	0.126275i	−0.895567	+	0.444926i	$0.853230\pi$
$614$	−15.4019	+	44.7944i	−0.621571	+	1.80775i
$615$		0			0
$616$	2.90162	−	0.947021i	0.116909	−	0.0381566i
$617$	−13.9289	−	3.73222i	−0.560755	−	0.150254i	−0.0327016	−	0.999465i	$-0.510411\pi$
$617$	−13.9289	−	3.73222i	−0.560755	−	0.150254i	−0.528053	+	0.849211i	$0.677078\pi$
$618$		0			0
$619$	4.33694	+	0.570969i	0.174316	+	0.0229492i	0.217179	−	0.976132i	$-0.430314\pi$
$619$	4.33694	+	0.570969i	0.174316	+	0.0229492i	−0.0428626	+	0.999081i	$0.513648\pi$
$620$	0.278069	+	0.00218239i	0.0111675	+	8.76469e-5i
$621$		0			0
$622$	−22.0747	−	4.48105i	−0.885115	−	0.179674i
$623$	−7.78440	−	4.49433i	−0.311875	−	0.180061i
$624$		0			0
$625$	−21.5908	+	12.4654i	−0.863632	+	0.498618i
$626$	37.0556	−	12.4167i	1.48104	−	0.496272i
$627$		0			0
$628$	2.46539	+	9.49854i	0.0983799	+	0.379033i
$629$	−12.2844	−	29.6573i	−0.489813	−	1.18251i
$630$		0			0
$631$	−10.5738	+	10.5738i	−0.420937	+	0.420937i	−0.885526	−	0.464589i	$-0.846202\pi$
$631$	−10.5738	+	10.5738i	−0.420937	+	0.420937i	0.464589	+	0.885526i	$0.346202\pi$
$632$	26.5277	+	9.35464i	1.05522	+	0.372108i
$633$		0			0
$634$	−0.886231	+	0.771072i	−0.0351967	+	0.0306232i
$635$	0.252031	−	0.328453i	0.0100015	−	0.0130342i
$636$		0			0
$637$	1.78109	−	1.36668i	0.0705692	−	0.0541497i
$638$	−2.40062	−	3.62348i	−0.0950413	−	0.143455i
$639$		0			0
$640$	0.170463	−	0.748854i	0.00673815	−	0.0296010i
$641$	25.9177	+	14.9636i	1.02369	+	0.591027i	0.915170	−	0.403067i	$-0.132056\pi$
$641$	25.9177	+	14.9636i	1.02369	+	0.591027i	0.108519	+	0.994094i	$0.465389\pi$
$642$		0			0
$643$	−5.66881	+	0.746313i	−0.223556	+	0.0294317i	−0.241472	−	0.970408i	$-0.577630\pi$
$643$	−5.66881	+	0.746313i	−0.223556	+	0.0294317i	0.0179159	+	0.999839i	$0.494297\pi$
$644$	−5.74321	−	46.4374i	−0.226314	−	1.82989i
$645$		0			0
$646$	−7.22351	+	21.0086i	−0.284205	+	0.826571i
$647$	−5.34200	+	5.34200i	−0.210016	+	0.210016i	−0.804274	−	0.594258i	$-0.797446\pi$
$647$	−5.34200	+	5.34200i	−0.210016	+	0.210016i	0.594258	+	0.804274i	$0.297446\pi$
$648$		0			0
$649$	1.55702	+	1.55702i	0.0611182	+	0.0611182i
$650$	−39.2067	+	19.1437i	−1.53781	+	0.750877i
$651$		0			0
$652$	3.73181	−	13.5025i	0.146149	−	0.528800i
$653$	4.94781	+	37.5823i	0.193623	+	1.47071i	0.761804	+	0.647807i	$0.224314\pi$
$653$	4.94781	+	37.5823i	0.193623	+	1.47071i	−0.568181	+	0.822903i	$0.692353\pi$
$654$		0			0
$655$	0.469413	−	0.813048i	0.0183415	−	0.0317684i
$656$	−22.4797	−	0.352880i	−0.877686	−	0.0137777i
$657$		0			0
$658$	−1.72367	+	8.49122i	−0.0671958	+	0.331022i
$659$	17.2631	+	22.4977i	0.672474	+	0.876386i	0.997597	−	0.0692864i	$-0.0220722\pi$
$659$	17.2631	+	22.4977i	0.672474	+	0.876386i	−0.325123	+	0.945672i	$0.605406\pi$
$660$		0			0
$661$	22.1638	+	17.0069i	0.862074	+	0.661492i	0.942112	−	0.335299i	$-0.108837\pi$
$661$	22.1638	+	17.0069i	0.862074	+	0.661492i	−0.0800379	+	0.996792i	$0.525504\pi$
$662$	1.47219	−	21.1870i	0.0572181	−	0.823454i
$663$		0			0
$664$	8.12372	−	9.04625i	0.315262	−	0.351063i
$665$	−0.532344	−	0.532344i	−0.0206434	−	0.0206434i
$666$		0			0
$667$	−61.5609	+	25.4994i	−2.38365	+	0.987339i
$668$	−40.4517	−	5.64888i	−1.56512	−	0.218562i
$669$		0			0
$670$	−0.0681874	+	0.136913i	−0.00263431	+	0.00528943i
$671$	−0.574028	−	0.994245i	−0.0221601	−	0.0383824i
$672$		0			0
$673$	0.577904	−	1.00096i	0.0222766	−	0.0385841i	−0.854672	−	0.519168i	$-0.826242\pi$
$673$	0.577904	−	1.00096i	0.0222766	−	0.0385841i	0.876949	+	0.480584i	$0.159575\pi$
$674$	15.4342	+	23.2963i	0.594505	+	0.897342i
$675$		0			0
$676$	−46.6081	+	18.8785i	−1.79262	+	0.726097i
$677$	2.34857	−	17.8391i	0.0902628	−	0.685614i	−0.885162	−	0.465283i	$-0.845953\pi$
$677$	2.34857	−	17.8391i	0.0902628	−	0.685614i	0.975425	−	0.220332i	$-0.0707139\pi$
$678$		0			0
$679$	10.3309	−	38.5553i	0.396462	−	1.47962i
$680$	0.317248	−	0.624667i	0.0121659	−	0.0239549i
$681$		0			0
$682$	−1.09034	+	0.532387i	−0.0417513	+	0.0203862i
$683$	−10.9938	+	4.55377i	−0.420665	+	0.174245i	−0.582967	−	0.812496i	$-0.698108\pi$
$683$	−10.9938	+	4.55377i	−0.420665	+	0.174245i	0.162302	+	0.986741i	$0.448108\pi$
$684$		0			0
$685$	0.529651	−	1.27869i	0.0202369	−	0.0488563i
$686$	20.0999	+	17.7672i	0.767418	+	0.678353i
$687$		0			0
$688$	14.1005	−	1.63165i	0.537577	−	0.0622060i
$689$	0.589077	+	1.02031i	0.0224421	+	0.0388708i
$690$		0			0
$691$	−37.8025	+	29.0069i	−1.43807	+	1.10347i	−0.461787	+	0.886991i	$0.652792\pi$
$691$	−37.8025	+	29.0069i	−1.43807	+	1.10347i	−0.976287	+	0.216482i	$0.930542\pi$
$692$	12.8528	−	12.6526i	0.488591	−	0.480981i
$693$		0			0
$694$	13.8225	+	9.31459i	0.524696	+	0.353577i
$695$	−1.46891	+	0.393594i	−0.0557191	+	0.0149299i
$696$		0			0
$697$	−19.8106	−	5.30824i	−0.750381	−	0.201064i
$698$	16.1502	+	18.5622i	0.611293	+	0.702589i
$699$		0			0
$700$	−15.5074	−	20.5414i	−0.586123	−	0.776392i
$701$	−4.28366	+	10.3417i	−0.161792	+	0.390599i	−0.983897	−	0.178736i	$-0.942799\pi$
$701$	−4.28366	+	10.3417i	−0.161792	+	0.390599i	0.822106	+	0.569335i	$0.192799\pi$
$702$		0			0
$703$		−	37.8723i		−	1.42838i
$704$	0.790898	+	3.25650i	0.0298081	+	0.122734i
$705$		0			0
$706$	−7.36401	+	14.7862i	−0.277148	+	0.556485i
$707$	−1.44499	−	10.9758i	−0.0543444	−	0.412787i
$708$		0			0
$709$	−36.2480	−	4.77214i	−1.36132	−	0.179221i	−0.585756	−	0.810487i	$-0.699202\pi$
$709$	−36.2480	−	4.77214i	−1.36132	−	0.179221i	−0.775566	+	0.631266i	$0.782536\pi$
$710$	0.186630	+	0.957881i	0.00700410	+	0.0359486i
$711$		0			0
$712$	5.57910	−	8.14060i	0.209086	−	0.305082i
$713$	4.81432	+	17.9673i	0.180298	+	0.672881i
$714$		0			0
$715$	−0.106911	+	0.139329i	−0.00399825	+	0.00521062i
$716$	5.27860	−	19.0992i	0.197271	−	0.713769i
$717$		0			0
$718$	−7.83458	−	6.92532i	−0.292384	−	0.258451i
$719$			35.9890i			1.34216i	0.741383	+	0.671082i	$0.234170\pi$
$719$			35.9890i			1.34216i	−0.741383	+	0.671082i	$0.765830\pi$
$720$		0			0
$721$			4.51888i			0.168292i
$722$	0.437170	−	0.494569i	0.0162698	−	0.0184059i
$723$		0			0
$724$	36.1413	−	20.4897i	1.34318	−	0.761493i
$725$	−22.3121	+	29.0777i	−0.828652	+	1.07992i
$726$		0			0
$727$	−12.7413	−	47.5511i	−0.472548	−	1.76357i	−0.630565	−	0.776137i	$-0.717177\pi$
$727$	−12.7413	−	47.5511i	−0.472548	−	1.76357i	0.158017	−	0.987436i	$-0.449490\pi$
$728$	−24.5590	−	37.7087i	−0.910219	−	1.39758i
$729$		0			0
$730$	0.882383	−	0.171920i	0.0326585	−	0.00636305i
$731$	12.8381	+	1.69017i	0.474835	+	0.0625132i
$732$		0			0
$733$	1.60005	+	12.1536i	0.0590992	+	0.448903i	0.995254	+	0.0973143i	$0.0310252\pi$
$733$	1.60005	+	12.1536i	0.0590992	+	0.448903i	−0.936154	+	0.351589i	$0.885641\pi$
$734$	−1.55138	−	0.772639i	−0.0572625	−	0.0285186i
$735$		0			0
$736$	51.3197	−	2.35359i	1.89167	−	0.0867546i
$737$		−	0.667403i		−	0.0245841i
$738$		0			0
$739$	15.0548	−	36.3454i	0.553798	−	1.33699i	−0.360807	−	0.932640i	$-0.617499\pi$
$739$	15.0548	−	36.3454i	0.553798	−	1.33699i	0.914606	−	0.404347i	$-0.132501\pi$
$740$	−0.165185	+	1.18289i	−0.00607232	+	0.0434839i
$741$		0			0
$742$	−0.524315	+	0.456185i	−0.0192482	+	0.0167471i
$743$	−47.7455	−	12.7934i	−1.75161	−	0.469344i	−0.766644	−	0.642072i	$-0.778075\pi$
$743$	−47.7455	−	12.7934i	−1.75161	−	0.469344i	−0.984969	+	0.172728i	$0.944742\pi$
$744$		0			0
$745$	−0.612450	+	0.164105i	−0.0224384	+	0.00601236i
$746$	−13.3074	+	19.7477i	−0.487217	+	0.723014i
$747$		0			0
$748$	−0.0239923	+	3.05698i	−0.000877246	+	0.111774i
$749$	14.4307	−	11.0730i	0.527285	−	0.404600i
$750$		0			0
$751$	19.0194	+	32.9426i	0.694028	+	1.20209i	0.970507	+	0.241073i	$0.0774992\pi$
$751$	19.0194	+	32.9426i	0.694028	+	1.20209i	−0.276479	+	0.961020i	$0.589168\pi$
$752$	−9.14901	−	2.60605i	−0.333630	−	0.0950328i
$753$		0			0
$754$	−42.4421	+	48.0145i	−1.54565	+	1.74859i
$755$	−0.120016	+	0.289744i	−0.00436782	+	0.0105449i
$756$		0			0
$757$	−13.4464	+	5.56969i	−0.488718	+	0.202434i	−0.613414	−	0.789761i	$-0.710204\pi$
$757$	−13.4464	+	5.56969i	−0.488718	+	0.202434i	0.124696	+	0.992195i	$0.460204\pi$
$758$	6.88732	+	14.1054i	0.250159	+	0.512330i
$759$		0			0
$760$	0.627825	−	0.537646i	0.0227736	−	0.0195025i
$761$	6.18093	−	23.0675i	0.224058	−	0.836197i	−0.758721	−	0.651415i	$-0.774176\pi$
$761$	6.18093	−	23.0675i	0.224058	−	0.836197i	0.982780	−	0.184782i	$-0.0591578\pi$
$762$		0			0
$763$	1.88913	−	14.3494i	0.0683911	−	0.519482i
$764$	−7.39007	+	17.4525i	−0.267364	+	0.631410i
$765$		0			0
$766$	−6.84295	+	4.53357i	−0.247246	+	0.163805i
$767$	16.2323	−	28.1152i	0.586115	−	1.01518i
$768$		0			0
$769$	−1.73319	−	3.00198i	−0.0625005	−	0.108254i	0.833082	−	0.553149i	$-0.186574\pi$
$769$	−1.73319	−	3.00198i	−0.0625005	−	0.108254i	−0.895583	+	0.444895i	$0.853241\pi$
$770$	−0.0927339	−	0.0461846i	−0.00334190	−	0.00166438i
$771$		0			0
$772$	21.6262	+	28.6466i	0.778345	+	1.03101i
$773$	17.9811	−	7.44800i	0.646734	−	0.267886i	−0.0351102	−	0.999383i	$-0.511178\pi$
$773$	17.9811	−	7.44800i	0.646734	−	0.267886i	0.681844	+	0.731497i	$0.261178\pi$
$774$		0			0
$775$	7.23484	+	7.23484i	0.259883	+	0.259883i
$776$	41.3299	+	14.5744i	1.48366	+	0.523191i
$777$		0			0
$778$	5.75434	+	0.399843i	0.206303	+	0.0143351i
$779$	−19.1967	−	14.7302i	−0.687794	−	0.527763i
$780$		0			0
$781$	−2.59226	−	3.37829i	−0.0927582	−	0.120885i
$782$	45.9284	+	9.32323i	1.64240	+	0.333398i
$783$		0			0
$784$	−1.04416	+	1.01188i	−0.0372913	+	0.0361386i
$785$	0.166539	−	0.288454i	0.00594404	−	0.0102954i
$786$		0			0
$787$	−3.12531	−	23.7391i	−0.111405	−	0.846206i	−0.952333	−	0.305059i	$-0.901324\pi$
$787$	−3.12531	−	23.7391i	−0.111405	−	0.846206i	0.840928	−	0.541147i	$-0.182010\pi$
$788$	9.07779	−	5.14650i	0.323383	−	0.183336i
$789$		0			0
$790$	−0.418905	−	0.857927i	−0.0149040	−	0.0305237i
$791$	22.5355	+	22.5355i	0.801269	+	0.801269i
$792$		0			0
$793$	−11.9688	+	11.9688i	−0.425025	+	0.425025i
$794$	−37.7828	−	12.9911i	−1.34086	−	0.461037i
$795$		0			0
$796$	31.7555	+	24.7652i	1.12554	+	0.877779i
$797$	10.7783	−	1.41899i	0.381788	−	0.0502634i	0.0628102	−	0.998025i	$-0.479994\pi$
$797$	10.7783	−	1.41899i	0.381788	−	0.0502634i	0.318978	+	0.947762i	$0.396660\pi$
$798$		0			0
$799$	−7.51545	−	4.33904i	−0.265877	−	0.153504i
$800$	23.7993	−	15.2354i	0.841433	−	0.538654i
$801$		0			0
$802$	−31.2744	+	20.7198i	−1.10434	+	0.731642i
$803$	−3.11202	+	2.38794i	−0.109821	+	0.0842686i
$804$		0			0
$805$	−0.966815	+	1.25998i	−0.0340758	+	0.0444084i
$806$	11.7425	+	13.4962i	0.413611	+	0.475383i
$807$		0			0
$808$	12.1371	−	0.652118i	0.426983	−	0.0229414i
$809$	11.2197	−	11.2197i	0.394464	−	0.394464i	−0.481811	−	0.876275i	$-0.660021\pi$
$809$	11.2197	−	11.2197i	0.394464	−	0.394464i	0.876275	+	0.481811i	$0.160021\pi$
$810$		0			0
$811$	15.3654	+	37.0955i	0.539554	+	1.30260i	0.925035	+	0.379882i	$0.124036\pi$
$811$	15.3654	+	37.0955i	0.539554	+	1.30260i	−0.385481	+	0.922716i	$0.625964\pi$
$812$	−32.5888	−	19.1577i	−1.14364	−	0.672305i
$813$		0			0
$814$	−1.65582	−	4.94151i	−0.0580364	−	0.173200i
$815$	−0.411777	+	0.237739i	−0.0144239	+	0.00832765i
$816$		0			0
$817$	13.2303	+	7.63851i	0.462869	+	0.267238i
$818$	−7.74617	+	38.1594i	−0.270838	+	1.33421i
$819$		0			0
$820$	0.535336	+	0.543805i	0.0186947	+	0.0189905i
$821$	23.8397	+	3.13855i	0.832011	+	0.109536i	0.534486	−	0.845178i	$-0.320505\pi$
$821$	23.8397	+	3.13855i	0.832011	+	0.109536i	0.297525	+	0.954714i	$0.403839\pi$
$822$		0			0
$823$	−6.36218	−	1.70474i	−0.221772	−	0.0594236i	0.146222	−	0.989252i	$-0.453289\pi$
$823$	−6.36218	−	1.70474i	−0.221772	−	0.0594236i	−0.367994	+	0.929828i	$0.619955\pi$
$824$	−4.94663	−	0.382751i	−0.172324	−	0.0133338i
$825$		0			0
$826$	18.1102	+	6.22694i	0.630134	+	0.216663i
$827$	−12.8972	−	31.1365i	−0.448478	−	1.08272i	−0.972892	−	0.231259i	$-0.925716\pi$
$827$	−12.8972	−	31.1365i	−0.448478	−	1.08272i	0.524414	−	0.851463i	$-0.324284\pi$
$828$		0			0
$829$	21.8417	+	9.04712i	0.758593	+	0.314220i	0.728242	−	0.685320i	$-0.240338\pi$
$829$	21.8417	+	9.04712i	0.758593	+	0.314220i	0.0303508	+	0.999539i	$0.490338\pi$
$830$	−0.411899	+	0.0253744i	−0.0142972	+	0.000880758i
$831$		0			0
$832$	43.3584	−	23.6899i	1.50318	−	0.821298i
$833$	−1.14871	+	0.663208i	−0.0398004	+	0.0229788i
$834$		0			0
$835$	0.843936	+	1.09984i	0.0292056	+	0.0380615i
$836$	−1.40634	+	3.32123i	−0.0486392	+	0.114867i
$837$		0			0
$838$	8.18343	−	1.59443i	0.282692	−	0.0550786i
$839$	−7.67802	−	28.6548i	−0.265075	−	0.989272i	−0.962205	−	0.272328i	$-0.912207\pi$
$839$	−7.67802	−	28.6548i	−0.265075	−	0.989272i	0.697130	−	0.716945i	$-0.254460\pi$
$840$		0			0
$841$	−6.42726	+	23.9869i	−0.221630	+	0.827134i
$842$	−3.59728	+	51.7703i	−0.123970	+	1.78412i
$843$		0			0
$844$	−3.30074	−	12.7169i	−0.113616	−	0.437734i
$845$	1.57687	+	0.653163i	0.0542461	+	0.0224695i
$846$		0			0
$847$	−27.8855			−0.958157
$848$	−0.454957	−	0.612586i	−0.0156233	−	0.0210363i
$849$		0			0
$850$	24.4426	−	8.19031i	0.838374	−	0.280925i
$851$	−79.2099	+	10.4282i	−2.71528	+	0.357474i
$852$		0			0
$853$	−0.702171	+	5.33352i	−0.0240419	+	0.182616i	−0.999252	−	0.0386634i	$-0.987690\pi$
$853$	−0.702171	+	5.33352i	−0.0240419	+	0.182616i	0.975210	+	0.221280i	$0.0710233\pi$
$854$	−8.28027	−	5.57982i	−0.283345	−	0.190938i
$855$		0			0
$856$	10.8989	+	16.7346i	0.372518	+	0.571976i
$857$	25.9152	−	6.94395i	0.885246	−	0.237201i	0.212577	−	0.977144i	$-0.431814\pi$
$857$	25.9152	−	6.94395i	0.885246	−	0.237201i	0.672669	+	0.739943i	$0.265148\pi$
$858$		0			0
$859$	−31.6416	−	24.2794i	−1.07960	−	0.828404i	−0.0936736	−	0.995603i	$-0.529861\pi$
$859$	−31.6416	−	24.2794i	−1.07960	−	0.828404i	−0.985923	+	0.167199i	$0.946528\pi$
$860$	−0.379914	−	0.296284i	−0.0129550	−	0.0101032i
$861$		0			0
$862$	−7.61572	+	0.469155i	−0.259393	+	0.0159795i
$863$	31.8190			1.08313			0.541566	−	0.840658i	$-0.317831\pi$
$863$	31.8190			1.08313			0.541566	+	0.840658i	$0.317831\pi$
$864$		0			0
$865$	−0.612158			−0.0208140
$866$	−1.51229	+	0.0931626i	−0.0513899	+	0.00316580i
$867$		0			0
$868$	−6.48973	+	8.32153i	−0.220276	+	0.282451i
$869$	3.30505	+	2.53606i	0.112116	+	0.0860298i
$870$		0			0
$871$	−9.50462	+	2.54676i	−0.322052	+	0.0862935i
$872$	15.5477	+	3.28335i	0.526510	+	0.111188i
$873$		0			0
$874$	45.8520	+	30.8983i	1.55097	+	1.04515i
$875$	−0.228154	+	1.73301i	−0.00771303	+	0.0585863i
$876$		0			0
$877$	−26.0842	+	3.43405i	−0.880802	+	0.115960i	−0.557343	−	0.830283i	$-0.688179\pi$
$877$	−26.0842	+	3.43405i	−0.880802	+	0.115960i	−0.323459	+	0.946242i	$0.604846\pi$
$878$	−8.48141	+	2.84198i	−0.286234	+	0.0959123i
$879$		0			0
$880$	0.0584110	−	0.0976002i	0.00196903	−	0.00329010i
$881$	28.0517			0.945086			0.472543	−	0.881308i	$-0.343336\pi$
$881$	28.0517			0.945086			0.472543	+	0.881308i	$0.343336\pi$
$882$		0			0
$883$	−19.5098	−	8.08123i	−0.656558	−	0.271955i	0.0294315	−	0.999567i	$-0.490630\pi$
$883$	−19.5098	−	8.08123i	−0.656558	−	0.271955i	−0.685989	+	0.727612i	$0.740630\pi$
$884$	43.6266	−	11.3235i	1.46732	−	0.380850i
$885$		0			0
$886$	1.97645	−	28.4441i	0.0664001	−	0.955597i
$887$	1.38469	−	5.16774i	0.0464934	−	0.173516i	−0.938775	−	0.344531i	$-0.888038\pi$
$887$	1.38469	−	5.16774i	0.0464934	−	0.173516i	0.985268	+	0.171015i	$0.0547047\pi$
$888$		0			0
$889$	4.06640	+	15.1760i	0.136383	+	0.508987i
$890$	−0.328785	+	0.0640592i	−0.0110209	+	0.00214727i
$891$		0			0
$892$	−4.33697	−	1.83644i	−0.145212	−	0.0614885i
$893$	−6.23271	−	8.12263i	−0.208570	−	0.271813i
$894$		0			0
$895$	−0.582453	+	0.336279i	−0.0194693	+	0.0112406i
$896$	18.6080	+	22.4324i	0.621650	+	0.749415i
$897$		0			0
$898$	−2.87501	+	0.177111i	−0.0959404	+	0.00591027i
$899$	13.8840	+	5.75093i	0.463057	+	0.191804i
$900$		0			0
$901$	−0.266381	−	0.643101i	−0.00887444	−	0.0214248i
$902$	−3.14877	−	1.08266i	−0.104843	−	0.0360487i
$903$		0			0
$904$	−26.5774	+	22.7599i	−0.883952	+	0.756983i
$905$	−1.36207	−	0.364965i	−0.0452767	−	0.0121318i
$906$		0			0
$907$	−39.9939	−	5.26530i	−1.32798	−	0.174831i	−0.567057	−	0.823679i	$-0.691918\pi$
$907$	−39.9939	−	5.26530i	−1.32798	−	0.174831i	−0.760919	+	0.648847i	$0.775251\pi$
$908$	−22.6824	+	22.3292i	−0.752743	+	0.741019i
$909$		0			0
$910$	−0.303859	+	1.49688i	−0.0100728	+	0.0496210i
$911$	46.5326	+	26.8656i	1.54169	+	0.890097i	0.998732	+	0.0503391i	$0.0160302\pi$
$911$	46.5326	+	26.8656i	1.54169	+	0.890097i	0.542961	+	0.839758i	$0.317303\pi$
$912$		0			0
$913$	1.55945	−	0.900350i	0.0516103	−	0.0297972i
$914$	4.97510	+	14.8473i	0.164562	+	0.491106i
$915$		0			0
$916$	−15.6719	+	26.6591i	−0.517813	+	0.880841i
$917$	13.6343	+	32.9161i	0.450244	+	1.08699i
$918$		0			0
$919$	−18.7622	+	18.7622i	−0.618909	+	0.618909i	−0.945252	−	0.326343i	$-0.894184\pi$
$919$	−18.7622	+	18.7622i	−0.618909	+	0.618909i	0.326343	+	0.945252i	$0.394184\pi$
$920$	−1.29736	−	1.16506i	−0.0427727	−	0.0384107i
$921$		0			0
$922$	−26.8340	−	30.8417i	−0.883732	−	1.01572i
$923$	−38.2191	+	49.8081i	−1.25800	+	1.63945i
$924$		0			0
$925$	−34.8644	+	26.7524i	−1.14633	+	0.879613i
$926$	7.68026	−	5.08831i	0.252389	−	0.167212i
$927$		0			0
$928$	23.7315	−	34.0510i	0.779025	−	1.11778i
$929$	−38.2126	−	22.0621i	−1.25371	−	0.723832i	−0.281869	−	0.959453i	$-0.590954\pi$
$929$	−38.2126	−	22.0621i	−1.25371	−	0.723832i	−0.971845	+	0.235620i	$0.924288\pi$
$930$		0			0
$931$	−1.55151	+	0.204260i	−0.0508487	+	0.00669435i
$932$	9.55680	−	12.2543i	0.313043	−	0.401403i
$933$		0			0
$934$	28.4747	+	9.79062i	0.931719	+	0.320359i
$935$	0.0733707	−	0.0733707i	0.00239948	−	0.00239948i
$936$		0			0
$937$	−17.0883	−	17.0883i	−0.558251	−	0.558251i	0.370558	−	0.928809i	$-0.379166\pi$
$937$	−17.0883	−	17.0883i	−0.558251	−	0.558251i	−0.928809	+	0.370558i	$0.879166\pi$
$938$	−2.54683	−	5.21596i	−0.0831569	−	0.170307i
$939$		0			0
$940$	0.159242	+	0.280884i	0.00519391	+	0.00916143i
$941$	−1.15593	−	8.78014i	−0.0376822	−	0.286224i	−0.999903	−	0.0139530i	$-0.995558\pi$
$941$	−1.15593	−	8.78014i	−0.0376822	−	0.286224i	0.962220	−	0.272271i	$-0.0877748\pi$
$942$		0			0
$943$	−25.5223	+	44.2059i	−0.831120	+	1.43954i
$944$	−8.35032	+	19.2971i	−0.271780	+	0.628066i
$945$		0			0
$946$	2.06023	+	0.418216i	0.0669838	+	0.0135974i
$947$	−27.0782	−	35.2891i	−0.879925	−	1.14674i	−0.988284	−	0.152628i	$-0.951226\pi$
$947$	−27.0782	−	35.2891i	−0.879925	−	1.14674i	0.108359	−	0.994112i	$-0.465440\pi$
$948$		0			0
$949$	45.8823	+	35.2068i	1.48940	+	1.14286i
$950$	30.3399	+	2.10818i	0.984357	+	0.0683985i
$951$		0			0
$952$	11.4780	+	23.9828i	0.372004	+	0.777286i
$953$	−31.3869	−	31.3869i	−1.01672	−	1.01672i	−0.999858	−	0.0168649i	$-0.994631\pi$
$953$	−31.3869	−	31.3869i	−1.01672	−	1.01672i	−0.0168649	−	0.999858i	$-0.505369\pi$
$954$		0			0
$955$	0.594317	−	0.246174i	0.0192316	−	0.00796601i
$956$	−32.0248	+	24.1766i	−1.03576	+	0.781926i
$957$		0			0
$958$	0.603399	+	0.300513i	0.0194949	+	0.00970912i
$959$	26.2620	+	45.4871i	0.848044	+	1.46886i
$960$		0			0
$961$	−13.4024	+	23.2137i	−0.432336	+	0.748828i
$962$	−64.0545	+	42.4372i	−2.06520	+	1.36823i
$963$		0			0
$964$	19.9009	+	8.42682i	0.640966	+	0.271410i
$965$	0.159016	−	1.20785i	0.00511891	−	0.0388820i
$966$		0			0
$967$	−0.809787	+	3.02217i	−0.0260410	+	0.0971863i	−0.977723	−	0.209898i	$-0.932687\pi$
$967$	−0.809787	+	3.02217i	−0.0260410	+	0.0971863i	0.951682	+	0.307084i	$0.0993534\pi$
$968$	2.36191	−	30.5251i	0.0759148	−	0.981115i
$969$		0			0
$970$	−0.652650	−	1.33664i	−0.0209553	−	0.0429170i
$971$	38.1764	−	15.8132i	1.22514	−	0.507470i	0.326100	−	0.945335i	$-0.394265\pi$
$971$	38.1764	−	15.8132i	1.22514	−	0.507470i	0.899040	+	0.437866i	$0.144265\pi$
$972$		0			0
$973$	22.0851	−	53.3182i	0.708016	−	1.70930i
$974$	−26.0879	+	29.5132i	−0.835911	+	0.945662i
$975$		0			0
$976$	6.80935	−	8.59147i	0.217962	−	0.275006i
$977$	−15.1894	−	26.3088i	−0.485951	−	0.841692i	0.513919	−	0.857839i	$-0.328193\pi$
$977$	−15.1894	−	26.3088i	−0.485951	−	0.841692i	−0.999870	+	0.0161471i	$0.994860\pi$
$978$		0			0
$979$	1.15957	−	0.889770i	0.0370601	−	0.0284372i
$980$	0.0493502		0.000387319i	0.00157643		1.23724e-5i
$981$		0			0
$982$	24.0976	−	35.7601i	0.768986	−	1.14115i
$983$	−35.6589	+	9.55477i	−1.13734	+	0.304750i	−0.777882	−	0.628411i	$-0.783706\pi$
$983$	−35.6589	+	9.55477i	−1.13734	+	0.304750i	−0.359460	+	0.933161i	$0.617039\pi$
$984$		0			0
$985$	−0.342118	−	0.0916701i	−0.0109008	−	0.00292085i
$986$	28.5643	−	24.8526i	0.909672	−	0.791467i
$987$		0			0
$988$	52.6648	+	7.35438i	1.67549	+	0.233974i
$989$	12.3330	−	29.7744i	0.392166	−	0.946772i
$990$		0			0
$991$		−	43.6720i		−	1.38729i	−0.720319	−	0.693643i	$-0.756005\pi$
$991$		−	43.6720i		−	1.38729i	0.720319	−	0.693643i	$-0.243995\pi$
$992$	−8.55957	−	7.80889i	−0.271767	−	0.247933i
$993$		0			0
$994$	−33.1509	−	16.5103i	−1.05148	−	0.523674i
$995$	−0.178410	−	1.35516i	−0.00565596	−	0.0429613i
$996$		0			0
$997$	2.16770	+	0.285384i	0.0686519	+	0.00903819i	0.164774	−	0.986331i	$-0.447311\pi$
$997$	2.16770	+	0.285384i	0.0686519	+	0.00903819i	−0.0961220	+	0.995370i	$0.530644\pi$
$998$	47.0573	−	9.16847i	1.48957	−	0.290223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.23		368
3.2	odd	2		288.2.bf.a.227.24	yes	368
9.4	even	3		288.2.bf.a.131.8	yes	368
9.5	odd	6	inner	864.2.bn.a.611.39		368
32.11	odd	8	inner	864.2.bn.a.683.39		368
96.11	even	8		288.2.bf.a.11.8	✓	368
288.139	odd	24		288.2.bf.a.203.24	yes	368
288.203	even	24	inner	864.2.bn.a.395.23		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.8	✓	368	96.11	even	8
288.2.bf.a.131.8	yes	368	9.4	even	3
288.2.bf.a.203.24	yes	368	288.139	odd	24
288.2.bf.a.227.24	yes	368	3.2	odd	2
864.2.bn.a.35.23		368	1.1	even	1	trivial
864.2.bn.a.395.23		368	288.203	even	24	inner
864.2.bn.a.611.39		368	9.5	odd	6	inner
864.2.bn.a.683.39		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)

\(f(q)\)	\(=\)	\(q+(0.0869556 + 1.41154i) q^{2} +(-1.98488 + 0.245482i) q^{4} +(0.0538553 + 0.0413246i) q^{5} +(-2.48836 + 0.666754i) q^{7} +(-0.519104 - 2.78038i) q^{8} +(-0.0536483 + 0.0796122i) q^{10} +(0.0546768 - 0.415312i) q^{11} +(-6.12318 + 0.806132i) q^{13} +(-1.15753 - 3.45444i) q^{14} +(3.87948 - 0.974505i) q^{16} +3.64897 q^{17} +(3.97733 + 1.64746i) q^{19} +(-0.117041 - 0.0688038i) q^{20} +(0.590983 + 0.0410647i) q^{22} +(2.35051 - 8.77221i) q^{23} +(-1.29290 - 4.82518i) q^{25} +(-1.67033 - 8.57300i) q^{26} +(4.77541 - 1.93427i) q^{28} +(-4.46654 - 5.82091i) q^{29} +(-1.77380 + 1.02410i) q^{31} +(1.71289 + 5.39129i) q^{32} +(0.317298 + 5.15065i) q^{34} +(-0.161565 - 0.0669223i) q^{35} +(-3.36655 - 8.12758i) q^{37} +(-1.97960 + 5.75740i) q^{38} +(0.0869418 - 0.171190i) q^{40} +(-5.42911 - 1.45472i) q^{41} +(3.51829 + 0.463192i) q^{43} +(-0.00657510 + 0.837765i) q^{44} +(12.5867 + 2.55503i) q^{46} +(-2.05961 - 1.18912i) q^{47} +(-0.314804 + 0.181752i) q^{49} +(6.69850 - 2.24456i) q^{50} +(11.9559 - 3.10320i) q^{52} +(-0.0730018 - 0.176242i) q^{53} +(0.0201073 - 0.0201073i) q^{55} +(3.14555 + 6.57248i) q^{56} +(7.82805 - 6.81086i) q^{58} +(-3.20000 + 4.17032i) q^{59} +(2.17432 - 1.66842i) q^{61} +(-1.59980 - 2.41473i) q^{62} +(-7.46106 + 2.88662i) q^{64} +(-0.363079 - 0.209624i) q^{65} +(1.57962 - 0.207960i) q^{67} +(-7.24275 + 0.895757i) q^{68} +(0.0804144 - 0.233874i) q^{70} +(7.18803 - 7.18803i) q^{71} +(-6.62149 - 6.62149i) q^{73} +(11.1796 - 5.45876i) q^{74} +(-8.29893 - 2.29365i) q^{76} +(0.140855 + 1.06990i) q^{77} +(-4.97251 + 8.61265i) q^{79} +(0.249202 + 0.107836i) q^{80} +(1.58131 - 7.78988i) q^{82} +(2.61687 + 3.41038i) q^{83} +(0.196516 + 0.150792i) q^{85} +(-0.347877 + 5.00648i) q^{86} +(-1.18311 + 0.0635674i) q^{88} +(2.46723 + 2.46723i) q^{89} +(14.6992 - 6.08860i) q^{91} +(-2.51204 + 17.9888i) q^{92} +(1.49939 - 3.01062i) q^{94} +(0.146119 + 0.253086i) q^{95} +(-7.74713 + 13.4184i) q^{97} +(-0.283924 - 0.428554i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 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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