LMFDB - Embedded newform 416.2.bk.a.271.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(15,416)] 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("416.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bk (of order $12$, degree $4$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.4
Character	$\chi$	$=$	416.271
Dual form			416.2.bk.a.175.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05427 - 1.82605i) q^{3} +(2.29020 - 2.29020i) q^{5} +(1.21025 - 0.324286i) q^{7} +(-0.722984 + 1.25224i) q^{9} +(3.76618 + 1.00915i) q^{11} +(-3.23415 - 1.59382i) q^{13} +(-6.59652 - 1.76753i) q^{15} +(3.99899 + 2.30882i) q^{17} +(-2.52138 + 0.675601i) q^{19} +(-1.86810 - 1.86810i) q^{21} +(-1.62930 - 2.82203i) q^{23} -5.49003i q^{25} -3.27675 q^{27} +(-7.35890 + 4.24866i) q^{29} +(2.29122 - 2.29122i) q^{31} +(-2.12783 - 7.94117i) q^{33} +(2.02904 - 3.51440i) q^{35} +(1.94326 - 7.25236i) q^{37} +(0.499278 + 7.58606i) q^{39} +(-0.391230 + 1.46009i) q^{41} +(9.48630 + 5.47692i) q^{43} +(1.21211 + 4.52367i) q^{45} +(-3.31585 - 3.31585i) q^{47} +(-4.70263 + 2.71507i) q^{49} -9.73651i q^{51} +2.94222i q^{53} +(10.9365 - 6.31416i) q^{55} +(3.89190 + 3.89190i) q^{57} +(-0.115929 - 0.432654i) q^{59} +(9.70024 + 5.60044i) q^{61} +(-0.468907 + 1.74998i) q^{63} +(-11.0570 + 3.75669i) q^{65} +(-2.48521 + 9.27491i) q^{67} +(-3.43545 + 5.95037i) q^{69} +(-0.740035 - 2.76185i) q^{71} +(0.0928135 - 0.0928135i) q^{73} +(-10.0251 + 5.78799i) q^{75} +4.88528 q^{77} +9.86517i q^{79} +(5.62354 + 9.74026i) q^{81} +(7.31249 + 7.31249i) q^{83} +(14.4462 - 3.87084i) q^{85} +(15.5166 + 8.95850i) q^{87} +(0.299076 + 0.0801373i) q^{89} +(-4.43099 - 0.880132i) q^{91} +(-6.59946 - 1.76832i) q^{93} +(-4.22719 + 7.32172i) q^{95} +(10.4399 - 2.79736i) q^{97} +(-3.98659 + 3.98659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{3} - 20 q^{9} + 8 q^{11} - 12 q^{17} + 8 q^{19} - 8 q^{27} + 4 q^{33} + 4 q^{35} + 12 q^{43} - 60 q^{49} + 36 q^{57} + 64 q^{59} - 16 q^{65} + 8 q^{67} - 12 q^{73} - 24 q^{75} - 8 q^{81} + 48 q^{83}+ \cdots - 168 q^{99}+O(q^{100}) $ 48 * q + 4 * q^3 - 20 * q^9 + 8 * q^11 - 12 * q^17 + 8 * q^19 - 8 * q^27 + 4 * q^33 + 4 * q^35 + 12 * q^43 - 60 * q^49 + 36 * q^57 + 64 * q^59 - 16 * q^65 + 8 * q^67 - 12 * q^73 - 24 * q^75 - 8 * q^81 + 48 * q^83 + 12 * q^89 - 104 * q^91 + 4 * q^97 - 168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.05427	−	1.82605i	−0.608685	−	1.05427i	−0.991457	−	0.130431i	$-0.958364\pi$
$3$	−1.05427	−	1.82605i	−0.608685	−	1.05427i	0.382773	−	0.923843i	$-0.374969\pi$
$4$		0			0
$5$	2.29020	−	2.29020i	1.02421	−	1.02421i	0.0245086	−	0.999700i	$-0.492198\pi$
$5$	2.29020	−	2.29020i	1.02421	−	1.02421i	0.999700	−	0.0245086i	$-0.00780212\pi$
$6$		0			0
$7$	1.21025	−	0.324286i	0.457432	−	0.122569i	−0.0227429	−	0.999741i	$-0.507240\pi$
$7$	1.21025	−	0.324286i	0.457432	−	0.122569i	0.480175	+	0.877173i	$0.340573\pi$
$8$		0			0
$9$	−0.722984	+	1.25224i	−0.240995	+	0.417415i
$10$		0			0
$11$	3.76618	+	1.00915i	1.13555	+	0.304269i	0.777159	−	0.629304i	$-0.216660\pi$
$11$	3.76618	+	1.00915i	1.13555	+	0.304269i	0.358387	+	0.933573i	$0.383327\pi$
$12$		0			0
$13$	−3.23415	−	1.59382i	−0.896992	−	0.442046i
$13$	−3.23415	−	1.59382i	−0.896992	−	0.442046i
$14$		0			0
$15$	−6.59652	−	1.76753i	−1.70322	−	0.456375i
$16$		0			0
$17$	3.99899	+	2.30882i	0.969899	+	0.559971i	0.899205	−	0.437527i	$-0.144146\pi$
$17$	3.99899	+	2.30882i	0.969899	+	0.559971i	0.0706933	+	0.997498i	$0.477479\pi$
$18$		0			0
$19$	−2.52138	+	0.675601i	−0.578444	+	0.154993i	−0.536166	−	0.844112i	$-0.680128\pi$
$19$	−2.52138	+	0.675601i	−0.578444	+	0.154993i	−0.0422773	+	0.999106i	$0.513461\pi$
$20$		0			0
$21$	−1.86810	−	1.86810i	−0.407653	−	0.407653i
$22$		0			0
$23$	−1.62930	−	2.82203i	−0.339732	−	0.588433i	0.644650	−	0.764478i	$-0.277003\pi$
$23$	−1.62930	−	2.82203i	−0.339732	−	0.588433i	−0.984382	+	0.176044i	$0.943670\pi$
$24$		0			0
$25$		−	5.49003i		−	1.09801i
$26$		0			0
$27$	−3.27675			−0.630611
$28$		0			0
$29$	−7.35890	+	4.24866i	−1.36651	+	0.788957i	−0.990481	−	0.137650i	$-0.956045\pi$
$29$	−7.35890	+	4.24866i	−1.36651	+	0.788957i	−0.376032	+	0.926607i	$0.622712\pi$
$30$		0			0
$31$	2.29122	−	2.29122i	0.411515	−	0.411515i	−0.470751	−	0.882266i	$-0.656017\pi$
$31$	2.29122	−	2.29122i	0.411515	−	0.411515i	0.882266	+	0.470751i	$0.156017\pi$
$32$		0			0
$33$	−2.12783	−	7.94117i	−0.370408	−	1.38238i
$34$		0			0
$35$	2.02904	−	3.51440i	0.342970	−	0.594041i
$36$		0			0
$37$	1.94326	−	7.25236i	0.319471	−	1.19228i	−0.600284	−	0.799787i	$-0.704946\pi$
$37$	1.94326	−	7.25236i	0.319471	−	1.19228i	0.919755	−	0.392494i	$-0.128388\pi$
$38$		0			0
$39$	0.499278	+	7.58606i	0.0799485	+	1.21474i
$40$		0			0
$41$	−0.391230	+	1.46009i	−0.0610999	+	0.228028i	−0.989723	−	0.142996i	$-0.954326\pi$
$41$	−0.391230	+	1.46009i	−0.0610999	+	0.228028i	0.928623	+	0.371024i	$0.120993\pi$
$42$		0			0
$43$	9.48630	+	5.47692i	1.44665	+	0.835222i	0.998280	−	0.0586272i	$-0.0186723\pi$
$43$	9.48630	+	5.47692i	1.44665	+	0.835222i	0.448367	+	0.893849i	$0.352006\pi$
$44$		0			0
$45$	1.21211	+	4.52367i	0.180691	+	0.674349i
$46$		0			0
$47$	−3.31585	−	3.31585i	−0.483667	−	0.483667i	0.422634	−	0.906301i	$-0.361106\pi$
$47$	−3.31585	−	3.31585i	−0.483667	−	0.483667i	−0.906301	+	0.422634i	$0.861106\pi$
$48$		0			0
$49$	−4.70263	+	2.71507i	−0.671805	+	0.387867i
$50$		0			0
$51$		−	9.73651i		−	1.36338i
$52$		0			0
$53$			2.94222i			0.404144i	0.979371	+	0.202072i	$0.0647676\pi$
$53$			2.94222i			0.404144i	−0.979371	+	0.202072i	$0.935232\pi$
$54$		0			0
$55$	10.9365	−	6.31416i	1.47467	−	0.851402i
$56$		0			0
$57$	3.89190	+	3.89190i	0.515495	+	0.515495i
$58$		0			0
$59$	−0.115929	−	0.432654i	−0.0150927	−	0.0563267i	0.957969	−	0.286872i	$-0.0926156\pi$
$59$	−0.115929	−	0.432654i	−0.0150927	−	0.0563267i	−0.973062	+	0.230546i	$0.925949\pi$
$60$		0			0
$61$	9.70024	+	5.60044i	1.24199	+	0.717063i	0.969499	−	0.245096i	$-0.0788194\pi$
$61$	9.70024	+	5.60044i	1.24199	+	0.717063i	0.272490	+	0.962159i	$0.412153\pi$
$62$		0			0
$63$	−0.468907	+	1.74998i	−0.0590767	+	0.220477i
$64$		0			0
$65$	−11.0570	+	3.75669i	−1.37145	+	0.465960i
$66$		0			0
$67$	−2.48521	+	9.27491i	−0.303616	+	1.13311i	0.630514	+	0.776178i	$0.282844\pi$
$67$	−2.48521	+	9.27491i	−0.303616	+	1.13311i	−0.934130	+	0.356933i	$0.883822\pi$
$68$		0			0
$69$	−3.43545	+	5.95037i	−0.413580	+	0.716341i
$70$		0			0
$71$	−0.740035	−	2.76185i	−0.0878259	−	0.327771i	0.908008	−	0.418952i	$-0.137602\pi$
$71$	−0.740035	−	2.76185i	−0.0878259	−	0.327771i	−0.995834	+	0.0911811i	$0.970936\pi$
$72$		0			0
$73$	0.0928135	−	0.0928135i	0.0108630	−	0.0108630i	−0.701654	−	0.712517i	$-0.747555\pi$
$73$	0.0928135	−	0.0928135i	0.0108630	−	0.0108630i	0.712517	+	0.701654i	$0.247555\pi$
$74$		0			0
$75$	−10.0251	+	5.78799i	−1.15760	+	0.668339i
$76$		0			0
$77$	4.88528			0.556729
$78$		0			0
$79$			9.86517i			1.10992i	0.831877	+	0.554959i	$0.187266\pi$
$79$			9.86517i			1.10992i	−0.831877	+	0.554959i	$0.812734\pi$
$80$		0			0
$81$	5.62354	+	9.74026i	0.624838	+	1.08225i
$82$		0			0
$83$	7.31249	+	7.31249i	0.802650	+	0.802650i	0.983509	−	0.180859i	$-0.0578878\pi$
$83$	7.31249	+	7.31249i	0.802650	+	0.802650i	−0.180859	+	0.983509i	$0.557888\pi$
$84$		0			0
$85$	14.4462	−	3.87084i	1.56691	−	0.419851i
$86$		0			0
$87$	15.5166	+	8.95850i	1.66355	+	0.960452i
$88$		0			0
$89$	0.299076	+	0.0801373i	0.0317020	+	0.00849454i	0.274635	−	0.961548i	$-0.411443\pi$
$89$	0.299076	+	0.0801373i	0.0317020	+	0.00849454i	−0.242933	+	0.970043i	$0.578110\pi$
$90$		0			0
$91$	−4.43099	−	0.880132i	−0.464494	−	0.0922629i
$92$		0			0
$93$	−6.59946	−	1.76832i	−0.684332	−	0.183366i
$94$		0			0
$95$	−4.22719	+	7.32172i	−0.433701	+	0.751192i
$96$		0			0
$97$	10.4399	−	2.79736i	1.06001	−	0.284029i	0.313628	−	0.949546i	$-0.398456\pi$
$97$	10.4399	−	2.79736i	1.06001	−	0.284029i	0.746382	+	0.665517i	$0.231789\pi$
$98$		0			0
$99$	−3.98659	+	3.98659i	−0.400667	+	0.400667i
$100$		0			0
$101$	−1.29598	−	2.24470i	−0.128955	−	0.223356i	0.794317	−	0.607503i	$-0.207829\pi$
$101$	−1.29598	−	2.24470i	−0.128955	−	0.223356i	−0.923272	+	0.384147i	$0.874496\pi$
$102$		0			0
$103$	6.17989			0.608923			0.304461	−	0.952525i	$-0.401524\pi$
$103$	6.17989			0.608923			0.304461	+	0.952525i	$0.401524\pi$
$104$		0			0
$105$	−8.55664			−0.835042
$106$		0			0
$107$	−8.60555	−	14.9053i	−0.831930	−	1.44095i	−0.896505	−	0.443033i	$-0.853903\pi$
$107$	−8.60555	−	14.9053i	−0.831930	−	1.44095i	0.0645752	−	0.997913i	$-0.479431\pi$
$108$		0			0
$109$	−2.35705	+	2.35705i	−0.225764	+	0.225764i	−0.810920	−	0.585156i	$-0.801033\pi$
$109$	−2.35705	+	2.35705i	−0.225764	+	0.225764i	0.585156	+	0.810920i	$0.301033\pi$
$110$		0			0
$111$	−15.2919	+	4.09746i	−1.45145	+	0.388914i
$112$		0			0
$113$	3.88399	−	6.72727i	0.365375	−	0.632849i	−0.623461	−	0.781854i	$-0.714274\pi$
$113$	3.88399	−	6.72727i	0.365375	−	0.632849i	0.988836	+	0.149006i	$0.0476073\pi$
$114$		0			0
$115$	−10.1944	−	2.73159i	−0.950635	−	0.254722i
$116$		0			0
$117$	4.33409	−	2.89764i	0.400687	−	0.267887i
$118$		0			0
$119$	5.58851	+	1.49744i	0.512297	+	0.137270i
$120$		0			0
$121$	3.63947	+	2.10125i	0.330861	+	0.191023i
$122$		0			0
$123$	3.07867	−	0.824927i	0.277594	−	0.0743811i
$124$		0			0
$125$	−1.12226	−	1.12226i	−0.100378	−	0.100378i
$126$		0			0
$127$	−3.89299	−	6.74286i	−0.345447	−	0.598332i	0.639988	−	0.768385i	$-0.278939\pi$
$127$	−3.89299	−	6.74286i	−0.345447	−	0.598332i	−0.985435	+	0.170053i	$0.945606\pi$
$128$		0			0
$129$		−	23.0967i		−	2.03355i
$130$		0			0
$131$	6.90178			0.603011			0.301505	−	0.953464i	$-0.402511\pi$
$131$	6.90178			0.603011			0.301505	+	0.953464i	$0.402511\pi$
$132$		0			0
$133$	−2.83241	+	1.63529i	−0.245601	+	0.141798i
$134$		0			0
$135$	−7.50441	+	7.50441i	−0.645877	+	0.645877i
$136$		0			0
$137$	0.462635	+	1.72658i	0.0395256	+	0.147512i	0.982869	−	0.184308i	$-0.0590043\pi$
$137$	0.462635	+	1.72658i	0.0395256	+	0.147512i	−0.943343	+	0.331819i	$0.892338\pi$
$138$		0			0
$139$	3.70296	−	6.41371i	0.314081	−	0.544004i	−0.665161	−	0.746700i	$-0.731637\pi$
$139$	3.70296	−	6.41371i	0.314081	−	0.544004i	0.979242	+	0.202696i	$0.0649703\pi$
$140$		0			0
$141$	−2.55912	+	9.55075i	−0.215516	+	0.804318i
$142$		0			0
$143$	−10.5720	−	9.26634i	−0.884076	−	0.774891i
$144$		0			0
$145$	−7.12306	+	26.5836i	−0.591538	+	2.20765i
$146$		0			0
$147$	9.91572	+	5.72484i	0.817835	+	0.472177i
$148$		0			0
$149$	5.80875	+	21.6786i	0.475872	+	1.77598i	0.618053	+	0.786136i	$0.287922\pi$
$149$	5.80875	+	21.6786i	0.475872	+	1.77598i	−0.142182	+	0.989841i	$0.545412\pi$
$150$		0			0
$151$	7.33817	+	7.33817i	0.597172	+	0.597172i	0.939559	−	0.342387i	$-0.111236\pi$
$151$	7.33817	+	7.33817i	0.597172	+	0.597172i	−0.342387	+	0.939559i	$0.611236\pi$
$152$		0			0
$153$	−5.78242	+	3.33848i	−0.467481	+	0.269900i
$154$		0			0
$155$		−	10.4947i		−	0.842954i
$156$		0			0
$157$		−	12.2573i		−	0.978235i	−0.872218	−	0.489118i	$-0.837319\pi$
$157$		−	12.2573i		−	0.978235i	0.872218	−	0.489118i	$-0.162681\pi$
$158$		0			0
$159$	5.37265	−	3.10190i	0.426079	−	0.245997i
$160$		0			0
$161$	−2.88700	−	2.88700i	−0.227528	−	0.227528i
$162$		0			0
$163$	−1.40055	−	5.22694i	−0.109700	−	0.409405i	0.889136	−	0.457643i	$-0.151306\pi$
$163$	−1.40055	−	5.22694i	−0.109700	−	0.409405i	−0.998836	+	0.0482377i	$0.984640\pi$
$164$		0			0
$165$	−23.0600	−	13.3137i	−1.79522	−	1.03647i
$166$		0			0
$167$	0.577213	−	2.15419i	0.0446661	−	0.166696i	−0.939990	−	0.341202i	$-0.889166\pi$
$167$	0.577213	−	2.15419i	0.0446661	−	0.166696i	0.984656	+	0.174506i	$0.0558327\pi$
$168$		0			0
$169$	7.91948	+	10.3093i	0.609191	+	0.793024i
$170$		0			0
$171$	0.976897	−	3.64583i	0.0747052	−	0.278804i
$172$		0			0
$173$	7.82068	−	13.5458i	0.594596	−	1.02987i	−0.399008	−	0.916947i	$-0.630646\pi$
$173$	7.82068	−	13.5458i	0.594596	−	1.02987i	0.993604	−	0.112922i	$-0.0360211\pi$
$174$		0			0
$175$	−1.78034	−	6.64431i	−0.134581	−	0.502263i
$176$		0			0
$177$	−0.667828	+	0.667828i	−0.0501971	+	0.0501971i
$178$		0			0
$179$	−9.96811	+	5.75509i	−0.745052	+	0.430156i	−0.823903	−	0.566731i	$-0.808208\pi$
$179$	−9.96811	+	5.75509i	−0.745052	+	0.430156i	0.0788516	+	0.996886i	$0.474875\pi$
$180$		0			0
$181$	7.79567			0.579447			0.289724	−	0.957110i	$-0.406437\pi$
$181$	7.79567			0.579447			0.289724	+	0.957110i	$0.406437\pi$
$182$		0			0
$183$		−	23.6176i		−	1.74586i
$184$		0			0
$185$	−12.1589	−	21.0598i	−0.893939	−	1.54835i
$186$		0			0
$187$	12.7310	+	12.7310i	0.930983	+	0.930983i
$188$		0			0
$189$	−3.96569	+	1.06260i	−0.288461	+	0.0772930i
$190$		0			0
$191$	−17.2652	−	9.96807i	−1.24927	−	0.721265i	−0.278304	−	0.960493i	$-0.589772\pi$
$191$	−17.2652	−	9.96807i	−1.24927	−	0.721265i	−0.970963	+	0.239229i	$0.923105\pi$
$192$		0			0
$193$	1.92417	+	0.515579i	0.138504	+	0.0371122i	0.327405	−	0.944884i	$-0.393826\pi$
$193$	1.92417	+	0.515579i	0.138504	+	0.0371122i	−0.188901	+	0.981996i	$0.560492\pi$
$194$		0			0
$195$	18.5170	+	16.2301i	1.32603	+	1.16226i
$196$		0			0
$197$	−12.2994	−	3.29561i	−0.876294	−	0.234802i	−0.207486	−	0.978238i	$-0.566528\pi$
$197$	−12.2994	−	3.29561i	−0.876294	−	0.234802i	−0.668807	+	0.743436i	$0.733195\pi$
$198$		0			0
$199$	−4.99633	+	8.65390i	−0.354180	+	0.613458i	−0.986977	−	0.160859i	$-0.948573\pi$
$199$	−4.99633	+	8.65390i	−0.354180	+	0.613458i	0.632797	+	0.774318i	$0.281907\pi$
$200$		0			0
$201$	19.5566	−	5.24017i	1.37942	−	0.369613i
$202$		0			0
$203$	−7.52833	+	7.52833i	−0.528385	+	0.528385i
$204$		0			0
$205$	2.44790	+	4.23989i	0.170969	+	0.296127i
$206$		0			0
$207$	4.71183			0.327495
$208$		0			0
$209$	−10.1777			−0.704009
$210$		0			0
$211$	1.69925	+	2.94319i	0.116981	+	0.202617i	0.918570	−	0.395258i	$-0.129345\pi$
$211$	1.69925	+	2.94319i	0.116981	+	0.202617i	−0.801589	+	0.597876i	$0.796012\pi$
$212$		0			0
$213$	−4.26308	+	4.26308i	−0.292102	+	0.292102i
$214$		0			0
$215$	34.2688	−	9.18228i	2.33711	−	0.626227i
$216$		0			0
$217$	2.02994	−	3.51596i	0.137801	−	0.238679i
$218$		0			0
$219$	−0.267333	−	0.0716317i	−0.0180647	−	0.00484042i
$220$		0			0
$221$	−9.25351	−	13.8408i	−0.622459	−	0.931030i
$222$		0			0
$223$	16.7653	+	4.49225i	1.12269	+	0.300823i	0.771971	−	0.635658i	$-0.219271\pi$
$223$	16.7653	+	4.49225i	1.12269	+	0.300823i	0.350717	+	0.936481i	$0.385938\pi$
$224$		0			0
$225$	6.87486	+	3.96920i	0.458324	+	0.264613i
$226$		0			0
$227$	7.61599	−	2.04070i	0.505491	−	0.135446i	0.00294381	−	0.999996i	$-0.499063\pi$
$227$	7.61599	−	2.04070i	0.505491	−	0.135446i	0.502547	+	0.864550i	$0.332396\pi$
$228$		0			0
$229$	4.45287	+	4.45287i	0.294254	+	0.294254i	0.838758	−	0.544504i	$-0.183282\pi$
$229$	4.45287	+	4.45287i	0.294254	+	0.294254i	−0.544504	+	0.838758i	$0.683282\pi$
$230$		0			0
$231$	−5.15042	−	8.92078i	−0.338873	−	0.586944i
$232$		0			0
$233$			5.68518i			0.372449i	0.982507	+	0.186224i	$0.0596251\pi$
$233$			5.68518i			0.372449i	−0.982507	+	0.186224i	$0.940375\pi$
$234$		0			0
$235$	−15.1879			−0.990752
$236$		0			0
$237$	18.0143	−	10.4006i	1.17016	−	0.675591i
$238$		0			0
$239$	−16.8128	+	16.8128i	−1.08753	+	1.08753i	−0.0917504	+	0.995782i	$0.529246\pi$
$239$	−16.8128	+	16.8128i	−1.08753	+	1.08753i	−0.995782	+	0.0917504i	$0.970754\pi$
$240$		0			0
$241$	−5.03466	−	18.7896i	−0.324311	−	1.21035i	−0.915002	−	0.403448i	$-0.867812\pi$
$241$	−5.03466	−	18.7896i	−0.324311	−	1.21035i	0.590691	−	0.806898i	$-0.298855\pi$
$242$		0			0
$243$	6.94237	−	12.0245i	0.445353	−	0.771375i
$244$		0			0
$245$	−4.55192	+	16.9880i	−0.290812	+	1.08532i
$246$		0			0
$247$	9.23130	+	1.83362i	0.587374	+	0.116671i
$248$		0			0
$249$	5.64364	−	21.0624i	0.357651	−	1.33477i
$250$		0			0
$251$	−2.07027	−	1.19527i	−0.130674	−	0.0754449i	0.433238	−	0.901280i	$-0.357371\pi$
$251$	−2.07027	−	1.19527i	−0.130674	−	0.0754449i	−0.563912	+	0.825835i	$0.690704\pi$
$252$		0			0
$253$	−3.28840	−	12.2725i	−0.206740	−	0.771563i
$254$		0			0
$255$	−22.2986	−	22.2986i	−1.39639	−	1.39639i
$256$		0			0
$257$	5.65573	−	3.26534i	0.352795	−	0.203686i	−0.313121	−	0.949713i	$-0.601374\pi$
$257$	5.65573	−	3.26534i	0.352795	−	0.203686i	0.665915	+	0.746027i	$0.268041\pi$
$258$		0			0
$259$		−	9.40735i		−	0.584544i
$260$		0			0
$261$		−	12.2869i		−	0.760537i
$262$		0			0
$263$	−20.7443	+	11.9767i	−1.27915	+	0.738515i	−0.976691	−	0.214649i	$-0.931139\pi$
$263$	−20.7443	+	11.9767i	−1.27915	+	0.738515i	−0.302454	+	0.953164i	$0.597806\pi$
$264$		0			0
$265$	6.73826	+	6.73826i	0.413928	+	0.413928i
$266$		0			0
$267$	−0.168973	−	0.630617i	−0.0103410	−	0.0385931i
$268$		0			0
$269$	−9.95910	−	5.74989i	−0.607217	−	0.350577i	0.164659	−	0.986351i	$-0.447348\pi$
$269$	−9.95910	−	5.74989i	−0.607217	−	0.350577i	−0.771875	+	0.635774i	$0.780681\pi$
$270$		0			0
$271$	3.39502	−	12.6704i	0.206233	−	0.769672i	−0.782837	−	0.622227i	$-0.786228\pi$
$271$	3.39502	−	12.6704i	0.206233	−	0.769672i	0.989070	−	0.147446i	$-0.0471051\pi$
$272$		0			0
$273$	3.06430	+	9.01913i	0.185460	+	0.545862i
$274$		0			0
$275$	5.54023	−	20.6764i	0.334089	−	1.24684i
$276$		0			0
$277$	−5.80918	+	10.0618i	−0.349040	+	0.604554i	−0.986079	−	0.166277i	$-0.946825\pi$
$277$	−5.80918	+	10.0618i	−0.349040	+	0.604554i	0.637040	+	0.770831i	$0.280159\pi$
$278$		0			0
$279$	1.21265	+	4.52568i	0.0725996	+	0.270946i
$280$		0			0
$281$	−21.2569	+	21.2569i	−1.26808	+	1.26808i	−0.320998	+	0.947080i	$0.604018\pi$
$281$	−21.2569	+	21.2569i	−1.26808	+	1.26808i	−0.947080	+	0.320998i	$0.895982\pi$
$282$		0			0
$283$	13.0633	−	7.54209i	0.776532	−	0.448331i	−0.0586678	−	0.998278i	$-0.518685\pi$
$283$	13.0633	−	7.54209i	0.776532	−	0.448331i	0.835200	+	0.549947i	$0.185352\pi$
$284$		0			0
$285$	17.8265			1.05595
$286$		0			0
$287$			1.89395i			0.111796i
$288$		0			0
$289$	2.16131	+	3.74349i	0.127136	+	0.220205i
$290$		0			0
$291$	−16.1146	−	16.1146i	−0.944656	−	0.944656i
$292$		0			0
$293$	−19.0818	+	5.11294i	−1.11477	+	0.298701i	−0.768765	−	0.639532i	$-0.779128\pi$
$293$	−19.0818	+	5.11294i	−1.11477	+	0.298701i	−0.346004	+	0.938233i	$0.612462\pi$
$294$		0			0
$295$	−1.25636	−	0.725362i	−0.0731484	−	0.0422322i
$296$		0			0
$297$	−12.3408	−	3.30672i	−0.716088	−	0.191875i
$298$		0			0
$299$	0.771596	+	11.7237i	0.0446226	+	0.677997i
$300$		0			0
$301$	13.2569	+	3.55217i	0.764115	+	0.204744i
$302$		0			0
$303$	−2.73263	+	4.73306i	−0.156986	+	0.271907i
$304$		0			0
$305$	35.0416	−	9.38937i	2.00648	−	0.537634i
$306$		0			0
$307$	−16.7842	+	16.7842i	−0.957925	+	0.957925i	−0.999150	−	0.0412249i	$-0.986874\pi$
$307$	−16.7842	+	16.7842i	−0.957925	+	0.957925i	0.0412249	+	0.999150i	$0.486874\pi$
$308$		0			0
$309$	−6.51530	−	11.2848i	−0.370642	−	0.641971i
$310$		0			0
$311$	−2.69726			−0.152947			−0.0764737	−	0.997072i	$-0.524366\pi$
$311$	−2.69726			−0.152947			−0.0764737	+	0.997072i	$0.524366\pi$
$312$		0			0
$313$	−1.31716			−0.0744504			−0.0372252	−	0.999307i	$-0.511852\pi$
$313$	−1.31716			−0.0744504			−0.0372252	+	0.999307i	$0.511852\pi$
$314$		0			0
$315$	2.93392	+	5.08170i	0.165308	+	0.286322i
$316$		0			0
$317$	−1.39773	+	1.39773i	−0.0785043	+	0.0785043i	−0.745269	−	0.666764i	$-0.767679\pi$
$317$	−1.39773	+	1.39773i	−0.0785043	+	0.0785043i	0.666764	+	0.745269i	$0.267679\pi$
$318$		0			0
$319$	−32.0025	+	8.57503i	−1.79179	+	0.480110i
$320$		0			0
$321$	−18.1452	+	31.4284i	−1.01277	+	1.75416i
$322$		0			0
$323$	−11.6428	−	3.11968i	−0.647823	−	0.173584i
$324$		0			0
$325$	−8.75011	+	17.7556i	−0.485369	+	0.984902i
$326$		0			0
$327$	6.78906	+	1.81912i	0.375436	+	0.100598i
$328$		0			0
$329$	−5.08830	−	2.93773i	−0.280527	−	0.161962i
$330$		0			0
$331$	21.5728	−	5.78041i	1.18575	−	0.317720i	0.388543	−	0.921430i	$-0.372978\pi$
$331$	21.5728	−	5.78041i	1.18575	−	0.317720i	0.797204	+	0.603710i	$0.206312\pi$
$332$		0			0
$333$	7.67678	+	7.67678i	0.420685	+	0.420685i
$334$		0			0
$335$	15.5498	+	26.9330i	0.849575	+	1.47151i
$336$		0			0
$337$		−	5.34167i		−	0.290980i	−0.989360	−	0.145490i	$-0.953524\pi$
$337$		−	5.34167i		−	0.290980i	0.989360	−	0.145490i	$-0.0464758\pi$
$338$		0			0
$339$	−16.3792			−0.889594
$340$		0			0
$341$	10.9413	−	6.31698i	0.592506	−	0.342083i
$342$		0			0
$343$	−11.0127	+	11.0127i	−0.594628	+	0.594628i
$344$		0			0
$345$	5.75968	+	21.4954i	0.310091	+	1.15727i
$346$		0			0
$347$	−10.3411	+	17.9114i	−0.555141	+	0.961532i	0.442752	+	0.896644i	$0.354002\pi$
$347$	−10.3411	+	17.9114i	−0.555141	+	0.961532i	−0.997893	+	0.0648876i	$0.979331\pi$
$348$		0			0
$349$	2.22015	−	8.28571i	0.118842	−	0.443524i	−0.880704	−	0.473668i	$-0.842930\pi$
$349$	2.22015	−	8.28571i	0.118842	−	0.443524i	0.999546	+	0.0301437i	$0.00959651\pi$
$350$		0			0
$351$	10.5975	+	5.22255i	0.565653	+	0.278759i
$352$		0			0
$353$	0.901606	−	3.36484i	0.0479877	−	0.179092i	−0.937772	−	0.347251i	$-0.887115\pi$
$353$	0.901606	−	3.36484i	0.0479877	−	0.179092i	0.985760	+	0.168158i	$0.0537820\pi$
$354$		0			0
$355$	−8.02001	−	4.63035i	−0.425658	−	0.245754i
$356$		0			0
$357$	−3.15741	−	11.7836i	−0.167108	−	0.623655i
$358$		0			0
$359$	6.93846	+	6.93846i	0.366198	+	0.366198i	0.866089	−	0.499891i	$-0.166626\pi$
$359$	6.93846	+	6.93846i	0.366198	+	0.366198i	−0.499891	+	0.866089i	$0.666626\pi$
$360$		0			0
$361$	−10.5536	+	6.09311i	−0.555451	+	0.320690i
$362$		0			0
$363$		−	8.86117i		−	0.465091i
$364$		0			0
$365$		−	0.425123i		−	0.0222519i
$366$		0			0
$367$	22.4992	−	12.9899i	1.17445	−	0.678069i	0.219725	−	0.975562i	$-0.429484\pi$
$367$	22.4992	−	12.9899i	1.17445	−	0.678069i	0.954724	+	0.297493i	$0.0961506\pi$
$368$		0			0
$369$	−1.54554	−	1.54554i	−0.0804575	−	0.0804575i
$370$		0			0
$371$	0.954119	+	3.56082i	0.0495354	+	0.184869i
$372$		0			0
$373$	26.2714	+	15.1678i	1.36028	+	0.785360i	0.989661	−	0.143424i	$-0.0458111\pi$
$373$	26.2714	+	15.1678i	1.36028	+	0.785360i	0.370622	+	0.928784i	$0.379144\pi$
$374$		0			0
$375$	−0.866136	+	3.23246i	−0.0447271	+	0.166924i
$376$		0			0
$377$	30.5714	−	2.01206i	1.57451	−	0.103627i
$378$		0			0
$379$	−2.16766	+	8.08981i	−0.111345	+	0.415545i	−0.998988	−	0.0449877i	$-0.985675\pi$
$379$	−2.16766	+	8.08981i	−0.111345	+	0.415545i	0.887642	+	0.460533i	$0.152342\pi$
$380$		0			0
$381$	−8.20856	+	14.2176i	−0.420537	+	0.728392i
$382$		0			0
$383$	7.70643	+	28.7608i	0.393780	+	1.46961i	0.823848	+	0.566811i	$0.191823\pi$
$383$	7.70643	+	28.7608i	0.393780	+	1.46961i	−0.430067	+	0.902797i	$0.641510\pi$
$384$		0			0
$385$	11.1883	−	11.1883i	0.570206	−	0.570206i
$386$		0			0
$387$	−13.7169	+	7.91945i	−0.697269	+	0.402568i
$388$		0			0
$389$	−3.84623			−0.195011			−0.0975057	−	0.995235i	$-0.531086\pi$
$389$	−3.84623			−0.195011			−0.0975057	+	0.995235i	$0.531086\pi$
$390$		0			0
$391$		−	15.0470i		−	0.760961i
$392$		0			0
$393$	−7.27636	−	12.6030i	−0.367044	−	0.635738i
$394$		0			0
$395$	22.5932	+	22.5932i	1.13679	+	1.13679i
$396$		0			0
$397$	9.31163	−	2.49504i	0.467337	−	0.125223i	−0.0174631	−	0.999848i	$-0.505559\pi$
$397$	9.31163	−	2.49504i	0.467337	−	0.125223i	0.484800	+	0.874625i	$0.338892\pi$
$398$		0			0
$399$	5.97227	+	3.44809i	0.298987	+	0.172621i
$400$		0			0
$401$	−1.97323	−	0.528724i	−0.0985382	−	0.0264032i	0.209213	−	0.977870i	$-0.432910\pi$
$401$	−1.97323	−	0.528724i	−0.0985382	−	0.0264032i	−0.307751	+	0.951467i	$0.599576\pi$
$402$		0			0
$403$	−11.0619	+	3.75836i	−0.551035	+	0.187217i
$404$		0			0
$405$	35.1862	+	9.42810i	1.74841	+	0.468486i
$406$		0			0
$407$	14.6374	−	25.3527i	0.725548	−	1.25669i
$408$		0			0
$409$	−29.2634	+	7.84111i	−1.44698	+	0.387718i	−0.894973	−	0.446120i	$-0.852805\pi$
$409$	−29.2634	+	7.84111i	−1.44698	+	0.387718i	−0.552010	+	0.833838i	$0.686139\pi$
$410$		0			0
$411$	2.66508	−	2.66508i	0.131459	−	0.131459i
$412$		0			0
$413$	−0.280607	−	0.486026i	−0.0138078	−	0.0239158i
$414$		0			0
$415$	33.4941			1.64416
$416$		0			0
$417$	−15.6157			−0.764705
$418$		0			0
$419$	−6.89015	−	11.9341i	−0.336606	−	0.583018i	0.647186	−	0.762332i	$-0.275946\pi$
$419$	−6.89015	−	11.9341i	−0.336606	−	0.583018i	−0.983792	+	0.179314i	$0.942612\pi$
$420$		0			0
$421$	−4.93256	+	4.93256i	−0.240398	+	0.240398i	−0.817015	−	0.576617i	$-0.804373\pi$
$421$	−4.93256	+	4.93256i	−0.240398	+	0.240398i	0.576617	+	0.817015i	$0.304373\pi$
$422$		0			0
$423$	6.54957	−	1.75495i	0.318451	−	0.0853287i
$424$		0			0
$425$	12.6755	−	21.9546i	0.614851	−	1.06495i
$426$		0			0
$427$	13.5559	+	3.63229i	0.656015	+	0.175779i
$428$		0			0
$429$	−5.77506	+	29.0743i	−0.278823	+	1.40372i
$430$		0			0
$431$	−8.44752	−	2.26351i	−0.406903	−	0.109029i	0.0495614	−	0.998771i	$-0.484218\pi$
$431$	−8.44752	−	2.26351i	−0.406903	−	0.109029i	−0.456464	+	0.889742i	$0.650884\pi$
$432$		0			0
$433$	−27.8926	−	16.1038i	−1.34043	−	0.773899i	−0.353561	−	0.935411i	$-0.615029\pi$
$433$	−27.8926	−	16.1038i	−1.34043	−	0.773899i	−0.986871	+	0.161513i	$0.948363\pi$
$434$		0			0
$435$	56.0528	−	15.0193i	2.68753	−	0.720120i
$436$		0			0
$437$	6.01464	+	6.01464i	0.287719	+	0.287719i
$438$		0			0
$439$	5.69401	+	9.86231i	0.271760	+	0.470702i	0.969313	−	0.245831i	$-0.0790609\pi$
$439$	5.69401	+	9.86231i	0.271760	+	0.470702i	−0.697552	+	0.716534i	$0.745728\pi$
$440$		0			0
$441$		−	7.85180i		−	0.373895i
$442$		0			0
$443$	−27.4615			−1.30474			−0.652368	−	0.757902i	$-0.726224\pi$
$443$	−27.4615			−1.30474			−0.652368	+	0.757902i	$0.726224\pi$
$444$		0			0
$445$	0.868475	−	0.501414i	0.0411697	−	0.0237693i
$446$		0			0
$447$	33.4622	−	33.4622i	1.58271	−	1.58271i
$448$		0			0
$449$	2.24637	+	8.38356i	0.106013	+	0.395645i	0.998458	−	0.0555107i	$-0.0176787\pi$
$449$	2.24637	+	8.38356i	0.106013	+	0.395645i	−0.892445	+	0.451155i	$0.851012\pi$
$450$		0			0
$451$	−2.94689	+	5.10416i	−0.138763	+	0.240345i
$452$		0			0
$453$	5.66346	−	21.1363i	0.266093	−	0.993071i
$454$		0			0
$455$	−12.1635	+	8.13217i	−0.570235	+	0.381242i
$456$		0			0
$457$	4.80284	−	17.9244i	0.224667	−	0.838470i	−0.757870	−	0.652405i	$-0.773760\pi$
$457$	4.80284	−	17.9244i	0.224667	−	0.838470i	0.982538	−	0.186064i	$-0.0595733\pi$
$458$		0			0
$459$	−13.1037	−	7.56543i	−0.611628	−	0.353124i
$460$		0			0
$461$	10.0386	+	37.4647i	0.467546	+	1.74491i	0.648308	+	0.761379i	$0.275477\pi$
$461$	10.0386	+	37.4647i	0.467546	+	1.74491i	−0.180762	+	0.983527i	$0.557856\pi$
$462$		0			0
$463$	−9.92788	−	9.92788i	−0.461388	−	0.461388i	0.437722	−	0.899110i	$-0.355785\pi$
$463$	−9.92788	−	9.92788i	−0.461388	−	0.461388i	−0.899110	+	0.437722i	$0.855785\pi$
$464$		0			0
$465$	−19.1639	+	11.0643i	−0.888704	+	0.513094i
$466$		0			0
$467$			35.4639i			1.64107i	0.571593	+	0.820537i	$0.306326\pi$
$467$			35.4639i			1.64107i	−0.571593	+	0.820537i	$0.693674\pi$
$468$		0			0
$469$			12.0309i			0.555535i
$470$		0			0
$471$	−22.3824	+	12.9225i	−1.03133	+	0.595437i
$472$		0			0
$473$	30.2001	+	30.2001i	1.38860	+	1.38860i
$474$		0			0
$475$	3.70907	+	13.8424i	0.170184	+	0.635134i
$476$		0			0
$477$	−3.68437	−	2.12717i	−0.168696	−	0.0973966i
$478$		0			0
$479$	−1.42073	+	5.30222i	−0.0649146	+	0.242265i	−0.990758	−	0.135644i	$-0.956690\pi$
$479$	−1.42073	+	5.30222i	−0.0649146	+	0.242265i	0.925843	+	0.377908i	$0.123356\pi$
$480$		0			0
$481$	−17.8438	+	20.3580i	−0.813606	+	0.928246i
$482$		0			0
$483$	−2.22814	+	8.31552i	−0.101384	+	0.378369i
$484$		0			0
$485$	17.5029	−	30.3159i	0.794766	−	1.37658i
$486$		0			0
$487$	4.62678	+	17.2674i	0.209659	+	0.782459i	0.987979	+	0.154590i	$0.0494058\pi$
$487$	4.62678	+	17.2674i	0.209659	+	0.782459i	−0.778319	+	0.627869i	$0.783928\pi$
$488$		0			0
$489$	−8.06811	+	8.06811i	−0.364852	+	0.364852i
$490$		0			0
$491$	8.57769	−	4.95233i	0.387106	−	0.223496i	−0.293800	−	0.955867i	$-0.594920\pi$
$491$	8.57769	−	4.95233i	0.387106	−	0.223496i	0.680905	+	0.732371i	$0.261586\pi$
$492$		0			0
$493$	−39.2376			−1.76717
$494$		0			0
$495$			18.2602i			0.820733i
$496$		0			0
$497$	−1.79126	−	3.10255i	−0.0803488	−	0.139168i
$498$		0			0
$499$	−3.67656	−	3.67656i	−0.164586	−	0.164586i	0.620009	−	0.784595i	$-0.287129\pi$
$499$	−3.67656	−	3.67656i	−0.164586	−	0.164586i	−0.784595	+	0.620009i	$0.787129\pi$
$500$		0			0
$501$	−4.54220	+	1.21708i	−0.202931	+	0.0543751i
$502$		0			0
$503$	−1.93976	−	1.11992i	−0.0864895	−	0.0499347i	0.456131	−	0.889912i	$-0.349235\pi$
$503$	−1.93976	−	1.11992i	−0.0864895	−	0.0499347i	−0.542621	+	0.839978i	$0.682568\pi$
$504$		0			0
$505$	−8.10887	−	2.17276i	−0.360840	−	0.0966868i
$506$		0			0
$507$	10.4761	−	25.3302i	0.465258	−	1.12496i
$508$		0			0
$509$	−32.3428	−	8.66622i	−1.43357	−	0.384123i	−0.543292	−	0.839544i	$-0.682822\pi$
$509$	−32.3428	−	8.66622i	−1.43357	−	0.384123i	−0.890276	+	0.455420i	$0.849489\pi$
$510$		0			0
$511$	0.0822295	−	0.142426i	0.00363762	−	0.00630054i
$512$		0			0
$513$	8.26192	−	2.21377i	0.364773	−	0.0977405i
$514$		0			0
$515$	14.1532	−	14.1532i	0.623664	−	0.623664i
$516$		0			0
$517$	−9.14193	−	15.8343i	−0.402062	−	0.696391i
$518$		0			0
$519$	−32.9805			−1.44769
$520$		0			0
$521$	−3.39964			−0.148941			−0.0744704	−	0.997223i	$-0.523727\pi$
$521$	−3.39964			−0.148941			−0.0744704	+	0.997223i	$0.523727\pi$
$522$		0			0
$523$	−6.71270	−	11.6267i	−0.293526	−	0.508402i	0.681115	−	0.732176i	$-0.261495\pi$
$523$	−6.71270	−	11.6267i	−0.293526	−	0.508402i	−0.974641	+	0.223775i	$0.928162\pi$
$524$		0			0
$525$	−10.2559	+	10.2559i	−0.447605	+	0.447605i
$526$		0			0
$527$	14.4526	−	3.87256i	0.629565	−	0.168691i
$528$		0			0
$529$	6.19078	−	10.7227i	0.269164	−	0.466206i
$530$		0			0
$531$	0.625604	+	0.167630i	0.0271489	+	0.00727452i
$532$		0			0
$533$	3.59242	−	4.09860i	0.155605	−	0.177530i
$534$		0			0
$535$	−53.8444	−	14.4276i	−2.32790	−	0.623758i
$536$		0			0
$537$	21.0182	+	12.1349i	0.907003	+	0.523659i
$538$		0			0
$539$	−20.4509	+	5.47979i	−0.880881	+	0.236031i
$540$		0			0
$541$	−18.5776	−	18.5776i	−0.798712	−	0.798712i	0.184180	−	0.982892i	$-0.441037\pi$
$541$	−18.5776	−	18.5776i	−0.798712	−	0.798712i	−0.982892	+	0.184180i	$0.941037\pi$
$542$		0			0
$543$	−8.21876	−	14.2353i	−0.352701	−	0.610896i
$544$		0			0
$545$			10.7962i			0.462459i
$546$		0			0
$547$	20.0481			0.857194			0.428597	−	0.903496i	$-0.359008\pi$
$547$	20.0481			0.857194			0.428597	+	0.903496i	$0.359008\pi$
$548$		0			0
$549$	−14.0262	+	8.09805i	−0.598625	+	0.345617i
$550$		0			0
$551$	15.6842	−	15.6842i	0.668167	−	0.668167i
$552$		0			0
$553$	3.19914	+	11.9393i	0.136041	+	0.507712i
$554$		0			0
$555$	−25.6376	+	44.4056i	−1.08825	+	1.88491i
$556$		0			0
$557$	10.3278	−	38.5437i	0.437601	−	1.63315i	−0.297164	−	0.954827i	$-0.596041\pi$
$557$	10.3278	−	38.5437i	0.437601	−	1.63315i	0.734765	−	0.678322i	$-0.237293\pi$
$558$		0			0
$559$	−21.9509	−	32.8326i	−0.928425	−	1.38867i
$560$		0			0
$561$	9.82556	−	36.6695i	0.414835	−	1.54819i
$562$		0			0
$563$	−14.7019	−	8.48814i	−0.619611	−	0.357732i	0.157107	−	0.987582i	$-0.449783\pi$
$563$	−14.7019	−	8.48814i	−0.619611	−	0.357732i	−0.776717	+	0.629849i	$0.783117\pi$
$564$		0			0
$565$	−6.51168	−	24.3019i	−0.273948	−	1.02239i
$566$		0			0
$567$	9.96452	+	9.96452i	0.418471	+	0.418471i
$568$		0			0
$569$	16.8884	−	9.75054i	0.708000	−	0.408764i	−0.102320	−	0.994752i	$-0.532627\pi$
$569$	16.8884	−	9.75054i	0.708000	−	0.408764i	0.810320	+	0.585988i	$0.199293\pi$
$570$		0			0
$571$		−	41.0843i		−	1.71933i	−0.510861	−	0.859663i	$-0.670673\pi$
$571$		−	41.0843i		−	1.71933i	0.510861	−	0.859663i	$-0.329327\pi$
$572$		0			0
$573$			42.0363i			1.75609i
$574$		0			0
$575$	−15.4930	+	8.94489i	−0.646103	+	0.373028i
$576$		0			0
$577$	9.64086	+	9.64086i	0.401354	+	0.401354i	0.878710	−	0.477356i	$-0.158405\pi$
$577$	9.64086	+	9.64086i	0.401354	+	0.401354i	−0.477356	+	0.878710i	$0.658405\pi$
$578$		0			0
$579$	−1.08712	−	4.05719i	−0.0451792	−	0.168611i
$580$		0			0
$581$	11.2213	+	6.47861i	0.465537	+	0.268778i
$582$		0			0
$583$	−2.96912	+	11.0809i	−0.122969	+	0.458925i
$584$		0			0
$585$	3.28975	−	16.5621i	0.136014	−	0.684759i
$586$		0			0
$587$	5.31077	−	19.8201i	0.219199	−	0.818062i	−0.765447	−	0.643499i	$-0.777482\pi$
$587$	5.31077	−	19.8201i	0.219199	−	0.818062i	0.984646	−	0.174563i	$-0.0558513\pi$
$588$		0			0
$589$	−4.22908	+	7.32498i	−0.174256	+	0.301820i
$590$		0			0
$591$	6.94894	+	25.9338i	0.285841	+	1.06677i
$592$		0			0
$593$	2.37364	−	2.37364i	0.0974736	−	0.0974736i	−0.656688	−	0.754162i	$-0.728043\pi$
$593$	2.37364	−	2.37364i	0.0974736	−	0.0974736i	0.754162	+	0.656688i	$0.228043\pi$
$594$		0			0
$595$	16.2282	−	9.36936i	0.665292	−	0.384107i
$596$		0			0
$597$	21.0700			0.862337
$598$		0			0
$599$		−	24.3394i		−	0.994482i	−0.867613	−	0.497241i	$-0.834347\pi$
$599$		−	24.3394i		−	0.994482i	0.867613	−	0.497241i	$-0.165653\pi$
$600$		0			0
$601$	−10.6546	−	18.4543i	−0.434609	−	0.752765i	0.562654	−	0.826692i	$-0.309780\pi$
$601$	−10.6546	−	18.4543i	−0.434609	−	0.752765i	−0.997264	+	0.0739270i	$0.976447\pi$
$602$		0			0
$603$	−9.81770	−	9.81770i	−0.399808	−	0.399808i
$604$		0			0
$605$	13.1474	−	3.52284i	0.534518	−	0.143224i
$606$		0			0
$607$	6.84369	+	3.95121i	0.277777	+	0.160375i	0.632417	−	0.774628i	$-0.282063\pi$
$607$	6.84369	+	3.95121i	0.277777	+	0.160375i	−0.354640	+	0.935003i	$0.615396\pi$
$608$		0			0
$609$	21.6841	+	5.81023i	0.878683	+	0.235442i
$610$		0			0
$611$	5.43911	+	16.0089i	0.220043	+	0.647649i
$612$		0			0
$613$	−6.78166	−	1.81714i	−0.273909	−	0.0733936i	0.119250	−	0.992864i	$-0.461951\pi$
$613$	−6.78166	−	1.81714i	−0.273909	−	0.0733936i	−0.393159	+	0.919471i	$0.628618\pi$
$614$		0			0
$615$	5.16152	−	8.94001i	0.208132	−	0.360496i
$616$		0			0
$617$	−40.4764	+	10.8456i	−1.62952	+	0.436628i	−0.953778	−	0.300512i	$-0.902842\pi$
$617$	−40.4764	+	10.8456i	−1.62952	+	0.436628i	−0.675740	+	0.737140i	$0.736176\pi$
$618$		0			0
$619$	26.0395	−	26.0395i	1.04662	−	1.04662i	0.0477560	−	0.998859i	$-0.484793\pi$
$619$	26.0395	−	26.0395i	1.04662	−	1.04662i	0.998859	−	0.0477560i	$-0.0152070\pi$
$620$		0			0
$621$	5.33880	+	9.24707i	0.214239	+	0.371072i
$622$		0			0
$623$	0.387945			0.0155427
$624$		0			0
$625$	22.3097			0.892390
$626$		0			0
$627$	10.7301	+	18.5851i	0.428520	+	0.742218i
$628$		0			0
$629$	24.5155	−	24.5155i	0.977497	−	0.977497i
$630$		0			0
$631$	−14.7339	+	3.94794i	−0.586549	+	0.157165i	−0.539875	−	0.841745i	$-0.681529\pi$
$631$	−14.7339	+	3.94794i	−0.586549	+	0.157165i	−0.0466732	+	0.998910i	$0.514862\pi$
$632$		0			0
$633$	3.58295	−	6.20585i	0.142409	−	0.246660i
$634$		0			0
$635$	−24.3582	−	6.52677i	−0.966627	−	0.259007i
$636$		0			0
$637$	19.5363	−	1.28579i	0.774058	−	0.0509448i
$638$		0			0
$639$	3.99354	+	1.07007i	0.157982	+	0.0423312i
$640$		0			0
$641$	−7.34895	−	4.24292i	−0.290266	−	0.167585i	0.347796	−	0.937570i	$-0.386930\pi$
$641$	−7.34895	−	4.24292i	−0.290266	−	0.167585i	−0.638062	+	0.769985i	$0.720264\pi$
$642$		0			0
$643$	−14.0735	+	3.77097i	−0.555003	+	0.148713i	−0.525410	−	0.850849i	$-0.676088\pi$
$643$	−14.0735	+	3.77097i	−0.555003	+	0.148713i	−0.0295934	+	0.999562i	$0.509421\pi$
$644$		0			0
$645$	−52.8960	−	52.8960i	−2.08278	−	2.08278i
$646$		0			0
$647$	−18.7622	−	32.4970i	−0.737617	−	1.27759i	−0.953566	−	0.301185i	$-0.902618\pi$
$647$	−18.7622	−	32.4970i	−0.737617	−	1.27759i	0.215949	−	0.976405i	$-0.430715\pi$
$648$		0			0
$649$		−	1.74644i		−	0.0685539i
$650$		0			0
$651$	−8.56045			−0.335510
$652$		0			0
$653$	7.35887	−	4.24865i	0.287975	−	0.166262i	−0.349053	−	0.937103i	$-0.613497\pi$
$653$	7.35887	−	4.24865i	0.287975	−	0.166262i	0.637028	+	0.770840i	$0.280163\pi$
$654$		0			0
$655$	15.8064	−	15.8064i	0.617609	−	0.617609i
$656$		0			0
$657$	0.0491226	+	0.183328i	0.00191645	+	0.00715230i
$658$		0			0
$659$	19.3603	−	33.5330i	0.754170	−	1.30626i	−0.191615	−	0.981470i	$-0.561373\pi$
$659$	19.3603	−	33.5330i	0.754170	−	1.30626i	0.945786	−	0.324791i	$-0.105294\pi$
$660$		0			0
$661$	−5.01953	+	18.7331i	−0.195237	+	0.728635i	0.796968	+	0.604021i	$0.206436\pi$
$661$	−5.01953	+	18.7331i	−0.195237	+	0.728635i	−0.992205	+	0.124614i	$0.960231\pi$
$662$		0			0
$663$	−15.5182	+	31.4894i	−0.602678	+	1.22295i
$664$		0			0
$665$	−2.74164	+	10.2319i	−0.106316	+	0.396777i
$666$		0			0
$667$	23.9797	+	13.8447i	0.928497	+	0.536068i
$668$		0			0
$669$	−9.47212	−	35.3504i	−0.366213	−	1.36673i
$670$		0			0
$671$	30.8812	+	30.8812i	1.19216	+	1.19216i
$672$		0			0
$673$	29.8245	−	17.2192i	1.14965	−	0.663750i	0.200848	−	0.979622i	$-0.435630\pi$
$673$	29.8245	−	17.2192i	1.14965	−	0.663750i	0.948802	+	0.315872i	$0.102297\pi$
$674$		0			0
$675$			17.9894i			0.692414i
$676$		0			0
$677$		−	25.5730i		−	0.982851i	−0.870920	−	0.491425i	$-0.836476\pi$
$677$		−	25.5730i		−	0.982851i	0.870920	−	0.491425i	$-0.163524\pi$
$678$		0			0
$679$	11.7277	−	6.77101i	0.450069	−	0.259848i
$680$		0			0
$681$	−11.7558	−	11.7558i	−0.450482	−	0.450482i
$682$		0			0
$683$	−6.43982	−	24.0338i	−0.246413	−	0.919626i	−0.972668	−	0.232201i	$-0.925407\pi$
$683$	−6.43982	−	24.0338i	−0.246413	−	0.919626i	0.726255	−	0.687426i	$-0.241259\pi$
$684$		0			0
$685$	5.01373	+	2.89468i	0.191565	+	0.110600i
$686$		0			0
$687$	3.43664	−	12.8257i	0.131116	−	0.489332i
$688$		0			0
$689$	4.68936	−	9.51557i	0.178650	−	0.362514i
$690$		0			0
$691$	−11.2681	+	42.0530i	−0.428658	+	1.59977i	0.327146	+	0.944974i	$0.393913\pi$
$691$	−11.2681	+	42.0530i	−0.428658	+	1.59977i	−0.755803	+	0.654799i	$0.772753\pi$
$692$		0			0
$693$	−3.53198	+	6.11756i	−0.134169	+	0.232387i
$694$		0			0
$695$	−6.20817	−	23.1692i	−0.235489	−	0.878858i
$696$		0			0
$697$	−4.93561	+	4.93561i	−0.186950	+	0.186950i
$698$		0			0
$699$	10.3815	−	5.99373i	0.392663	−	0.226704i
$700$		0			0
$701$	−10.1949			−0.385056			−0.192528	−	0.981292i	$-0.561669\pi$
$701$	−10.1949			−0.385056			−0.192528	+	0.981292i	$0.561669\pi$
$702$		0			0
$703$			19.5988i			0.739183i
$704$		0			0
$705$	16.0122	+	27.7340i	0.603056	+	1.04452i
$706$		0			0
$707$	−2.29639	−	2.29639i	−0.0863645	−	0.0863645i
$708$		0			0
$709$	−16.4497	+	4.40767i	−0.617780	+	0.165534i	−0.554118	−	0.832438i	$-0.686944\pi$
$709$	−16.4497	+	4.40767i	−0.617780	+	0.165534i	−0.0636615	+	0.997972i	$0.520278\pi$
$710$		0			0
$711$	−12.3536	−	7.13236i	−0.463297	−	0.267484i
$712$		0			0
$713$	−10.1990	−	2.73280i	−0.381954	−	0.102344i
$714$		0			0
$715$	−45.4338	+	2.99024i	−1.69913	+	0.111828i
$716$		0			0
$717$	48.4265	+	12.9758i	1.80852	+	0.484592i
$718$		0			0
$719$	15.8375	−	27.4313i	0.590639	−	1.02302i	−0.403508	−	0.914976i	$-0.632209\pi$
$719$	15.8375	−	27.4313i	0.590639	−	1.02302i	0.994147	−	0.108040i	$-0.0344575\pi$
$720$		0			0
$721$	7.47922	−	2.00405i	0.278541	−	0.0746348i
$722$		0			0
$723$	−29.0030	+	29.0030i	−1.07863	+	1.07863i
$724$		0			0
$725$	23.3253	+	40.4005i	0.866278	+	1.50044i
$726$		0			0
$727$	−51.1295			−1.89629			−0.948144	−	0.317841i	$-0.897042\pi$
$727$	−51.1295			−1.89629			−0.948144	+	0.317841i	$0.897042\pi$
$728$		0			0
$729$	4.46461			0.165356
$730$		0			0
$731$	25.2904	+	43.8043i	0.935401	+	1.62016i
$732$		0			0
$733$	−11.7589	+	11.7589i	−0.434323	+	0.434323i	−0.890096	−	0.455773i	$-0.849363\pi$
$733$	−11.7589	+	11.7589i	−0.434323	+	0.434323i	0.455773	+	0.890096i	$0.349363\pi$
$734$		0			0
$735$	35.8200	−	9.59794i	1.32124	−	0.354025i
$736$		0			0
$737$	−18.7195	+	32.4231i	−0.689541	+	1.19432i
$738$		0			0
$739$	31.0502	+	8.31988i	1.14220	+	0.306052i	0.779835	−	0.625985i	$-0.215303\pi$
$739$	31.0502	+	8.31988i	1.14220	+	0.306052i	0.362365	+	0.932036i	$0.381969\pi$
$740$		0			0
$741$	−6.38402	−	18.7900i	−0.234523	−	0.690268i
$742$		0			0
$743$	21.3536	+	5.72168i	0.783388	+	0.209908i	0.628278	−	0.777989i	$-0.283760\pi$
$743$	21.3536	+	5.72168i	0.783388	+	0.209908i	0.155110	+	0.987897i	$0.450427\pi$
$744$		0			0
$745$	62.9514	+	36.3450i	2.30636	+	1.33158i
$746$		0			0
$747$	−14.4438	+	3.87022i	−0.528472	+	0.141604i
$748$		0			0
$749$	−15.2484	−	15.2484i	−0.557166	−	0.557166i
$750$		0			0
$751$	12.7994	+	22.1693i	0.467058	+	0.808969i	0.999292	−	0.0376290i	$-0.0119805\pi$
$751$	12.7994	+	22.1693i	0.467058	+	0.808969i	−0.532234	+	0.846598i	$0.678647\pi$
$752$		0			0
$753$			5.04058i			0.183689i
$754$		0			0
$755$	33.6117			1.22326
$756$		0			0
$757$	2.23415	−	1.28989i	0.0812015	−	0.0468817i	−0.458849	−	0.888514i	$-0.651738\pi$
$757$	2.23415	−	1.28989i	0.0812015	−	0.0468817i	0.540051	+	0.841632i	$0.318405\pi$
$758$		0			0
$759$	−18.9433	+	18.9433i	−0.687599	+	0.687599i
$760$		0			0
$761$	0.542840	+	2.02591i	0.0196779	+	0.0734390i	0.975067	−	0.221912i	$-0.0712299\pi$
$761$	0.542840	+	2.02591i	0.0196779	+	0.0734390i	−0.955389	+	0.295351i	$0.904563\pi$
$762$		0			0
$763$	−2.08826	+	3.61697i	−0.0756001	+	0.130943i
$764$		0			0
$765$	−5.59710	+	20.8887i	−0.202364	+	0.755232i
$766$		0			0
$767$	−0.314639	+	1.58404i	−0.0113610	+	0.0571963i
$768$		0			0
$769$	−9.36439	+	34.9484i	−0.337688	+	1.26027i	0.563237	+	0.826296i	$0.309556\pi$
$769$	−9.36439	+	34.9484i	−0.337688	+	1.26027i	−0.900925	+	0.433975i	$0.857111\pi$
$770$		0			0
$771$	−11.9254	−	6.88511i	−0.429482	−	0.247961i
$772$		0			0
$773$	−0.0318054	−	0.118699i	−0.00114396	−	0.00426932i	0.965351	−	0.260953i	$-0.0840368\pi$
$773$	−0.0318054	−	0.118699i	−0.00114396	−	0.00426932i	−0.966495	+	0.256684i	$0.917370\pi$
$774$		0			0
$775$	−12.5789	−	12.5789i	−0.451846	−	0.451846i
$776$		0			0
$777$	−17.1783	+	9.91792i	−0.616269	+	0.355803i
$778$		0			0
$779$		−	3.94575i		−	0.141371i
$780$		0			0
$781$		−	11.1484i		−	0.398922i
$782$		0			0
$783$	24.1133	−	13.9218i	0.861738	−	0.497524i
$784$		0			0
$785$	−28.0716	−	28.0716i	−1.00192	−	1.00192i
$786$		0			0
$787$	−12.5110	−	46.6918i	−0.445970	−	1.66438i	−0.713364	−	0.700794i	$-0.752829\pi$
$787$	−12.5110	−	46.6918i	−0.445970	−	1.66438i	0.267394	−	0.963587i	$-0.413837\pi$
$788$		0			0
$789$	43.7402	+	25.2534i	1.55719	+	0.899046i
$790$		0			0
$791$	2.51905	−	9.40121i	0.0895670	−	0.334269i
$792$		0			0
$793$	−22.4460	−	33.5731i	−0.797080	−	1.19222i
$794$		0			0
$795$	5.20046	−	19.4084i	0.184441	−	0.688345i
$796$		0			0
$797$	−25.2414	+	43.7194i	−0.894097	+	1.54862i	−0.0591787	+	0.998247i	$0.518848\pi$
$797$	−25.2414	+	43.7194i	−0.894097	+	1.54862i	−0.834918	+	0.550374i	$0.814485\pi$
$798$		0			0
$799$	−5.60437	−	20.9158i	−0.198268	−	0.739948i
$800$		0			0
$801$	−0.316579	+	0.316579i	−0.0111858	+	0.0111858i
$802$		0			0
$803$	0.443215	−	0.255890i	0.0156407	−	0.00903017i
$804$		0			0
$805$	−13.2236			−0.466071
$806$		0			0
$807$			24.2478i			0.853563i
$808$		0			0
$809$	−14.2698	−	24.7160i	−0.501700	−	0.868970i	−0.999998	−	0.00196414i	$-0.999375\pi$
$809$	−14.2698	−	24.7160i	−0.501700	−	0.868970i	0.498298	−	0.867006i	$-0.333959\pi$
$810$		0			0
$811$	−2.06103	−	2.06103i	−0.0723725	−	0.0723725i	0.669994	−	0.742367i	$-0.266297\pi$
$811$	−2.06103	−	2.06103i	−0.0723725	−	0.0723725i	−0.742367	+	0.669994i	$0.766297\pi$
$812$		0			0
$813$	−26.7161	+	7.15857i	−0.936976	+	0.251062i
$814$		0			0
$815$	−15.1783	−	8.76318i	−0.531672	−	0.306961i
$816$		0			0
$817$	−27.6187	−	7.40042i	−0.966258	−	0.258908i
$818$		0			0
$819$	4.30567	−	4.91236i	0.150452	−	0.171652i
$820$		0			0
$821$	−19.2311	−	5.15295i	−0.671169	−	0.179839i	−0.0928874	−	0.995677i	$-0.529610\pi$
$821$	−19.2311	−	5.15295i	−0.671169	−	0.179839i	−0.578281	+	0.815838i	$0.696276\pi$
$822$		0			0
$823$	−24.7340	+	42.8406i	−0.862174	+	1.49333i	0.00765139	+	0.999971i	$0.497564\pi$
$823$	−24.7340	+	42.8406i	−0.862174	+	1.49333i	−0.869826	+	0.493359i	$0.835769\pi$
$824$		0			0
$825$	−43.5972	+	11.6818i	−1.51786	+	0.406709i
$826$		0			0
$827$	29.4872	−	29.4872i	1.02537	−	1.02537i	0.0256999	−	0.999670i	$-0.491819\pi$
$827$	29.4872	−	29.4872i	1.02537	−	1.02537i	0.999670	−	0.0256999i	$-0.00818142\pi$
$828$		0			0
$829$	−20.6361	−	35.7427i	−0.716720	−	1.24140i	−0.962292	−	0.272017i	$-0.912309\pi$
$829$	−20.6361	−	35.7427i	−0.716720	−	1.24140i	0.245573	−	0.969378i	$-0.421024\pi$
$830$		0			0
$831$	24.4978			0.849821
$832$		0			0
$833$	−25.0744			−0.868776
$834$		0			0
$835$	−3.61159	−	6.25545i	−0.124984	−	0.216479i
$836$		0			0
$837$	−7.50775	+	7.50775i	−0.259506	+	0.259506i
$838$		0			0
$839$	4.33187	−	1.16072i	0.149553	−	0.0400726i	−0.183266	−	0.983063i	$-0.558667\pi$
$839$	4.33187	−	1.16072i	0.149553	−	0.0400726i	0.332819	+	0.942991i	$0.392000\pi$
$840$		0			0
$841$	21.6022	−	37.4162i	0.744905	−	1.29021i
$842$		0			0
$843$	61.2267	+	16.4056i	2.10876	+	0.565041i
$844$		0			0
$845$	41.7476	+	5.47318i	1.43616	+	0.188283i
$846$		0			0
$847$	5.08608	+	1.36281i	0.174760	+	0.0468268i
$848$		0			0
$849$	−27.5446	−	15.9029i	−0.945327	−	0.545785i
$850$		0			0
$851$	−23.6325	+	6.33231i	−0.810112	+	0.217069i
$852$		0			0
$853$	37.6495	+	37.6495i	1.28909	+	1.28909i	0.935338	+	0.353757i	$0.115096\pi$
$853$	37.6495	+	37.6495i	1.28909	+	1.28909i	0.353757	+	0.935338i	$0.384904\pi$
$854$		0			0
$855$	−6.11239	−	10.5870i	−0.209039	−	0.362067i
$856$		0			0
$857$			26.5260i			0.906111i	0.891482	+	0.453056i	$0.149666\pi$
$857$			26.5260i			0.906111i	−0.891482	+	0.453056i	$0.850334\pi$
$858$		0			0
$859$	12.7866			0.436275			0.218137	−	0.975918i	$-0.430002\pi$
$859$	12.7866			0.436275			0.218137	+	0.975918i	$0.430002\pi$
$860$		0			0
$861$	3.45845	−	1.99674i	0.117864	−	0.0680486i
$862$		0			0
$863$	−0.543555	+	0.543555i	−0.0185028	+	0.0185028i	−0.716298	−	0.697795i	$-0.754165\pi$
$863$	−0.543555	+	0.543555i	−0.0185028	+	0.0185028i	0.697795	+	0.716298i	$0.254165\pi$
$864$		0			0
$865$	−13.1117	−	48.9335i	−0.445811	−	1.66379i
$866$		0			0
$867$	4.55721	−	7.89332i	0.154771	−	0.268071i
$868$		0			0
$869$	−9.95539	+	37.1540i	−0.337714	+	1.26036i
$870$		0			0
$871$	22.8201	−	26.0355i	0.773229	−	0.882180i
$872$		0			0
$873$	−4.04489	+	15.0957i	−0.136899	+	0.510914i
$874$		0			0
$875$	−1.72214	−	0.994280i	−0.0582191	−	0.0336128i
$876$		0			0
$877$	−0.0541703	−	0.202166i	−0.00182920	−	0.00682667i	0.965005	−	0.262231i	$-0.0844582\pi$
$877$	−0.0541703	−	0.202166i	−0.00182920	−	0.00682667i	−0.966834	+	0.255404i	$0.917791\pi$
$878$		0			0
$879$	29.4539	+	29.4539i	0.993456	+	0.993456i
$880$		0			0
$881$	23.2483	−	13.4224i	0.783257	−	0.452213i	−0.0543265	−	0.998523i	$-0.517301\pi$
$881$	23.2483	−	13.4224i	0.783257	−	0.452213i	0.837583	+	0.546310i	$0.183968\pi$
$882$		0			0
$883$			13.3689i			0.449900i	0.974370	+	0.224950i	$0.0722219\pi$
$883$			13.3689i			0.449900i	−0.974370	+	0.224950i	$0.927778\pi$
$884$		0			0
$885$			3.05892i			0.102824i
$886$		0			0
$887$	−15.7025	+	9.06585i	−0.527239	+	0.304402i	−0.739891	−	0.672726i	$-0.765123\pi$
$887$	−15.7025	+	9.06585i	−0.527239	+	0.304402i	0.212652	+	0.977128i	$0.431790\pi$
$888$		0			0
$889$	−6.89811	−	6.89811i	−0.231355	−	0.231355i
$890$		0			0
$891$	11.3499	+	42.3586i	0.380237	+	1.41906i
$892$		0			0
$893$	10.6007	+	6.12033i	0.354739	+	0.204809i
$894$		0			0
$895$	−9.64865	+	36.0093i	−0.322519	+	1.20366i
$896$		0			0
$897$	20.5946	−	13.7689i	0.687633	−	0.459731i
$898$		0			0
$899$	−7.12623	+	26.5955i	−0.237673	+	0.887008i
$900$		0			0
$901$	−6.79305	+	11.7659i	−0.226309	+	0.391979i
$902$		0			0
$903$	−7.48992	−	27.9528i	−0.249249	−	0.930210i
$904$		0			0
$905$	17.8536	−	17.8536i	0.593475	−	0.593475i
$906$		0			0
$907$	−45.5299	+	26.2867i	−1.51180	+	0.872835i	−0.511890	+	0.859051i	$0.671054\pi$
$907$	−45.5299	+	26.2867i	−1.51180	+	0.872835i	−0.999905	+	0.0137843i	$0.995612\pi$
$908$		0			0
$909$	3.74789			0.124310
$910$		0			0
$911$			35.3565i			1.17141i	0.810523	+	0.585706i	$0.199183\pi$
$911$			35.3565i			1.17141i	−0.810523	+	0.585706i	$0.800817\pi$
$912$		0			0
$913$	20.1608	+	34.9195i	0.667225	+	1.15567i
$914$		0			0
$915$	−54.0889	−	54.0889i	−1.78813	−	1.78813i
$916$		0			0
$917$	8.35288	−	2.23815i	0.275836	−	0.0739101i
$918$		0			0
$919$	−8.61424	−	4.97343i	−0.284158	−	0.164058i	0.351147	−	0.936321i	$-0.385792\pi$
$919$	−8.61424	−	4.97343i	−0.284158	−	0.164058i	−0.635304	+	0.772262i	$0.719125\pi$
$920$		0			0
$921$	48.3440	+	12.9537i	1.59299	+	0.426840i
$922$		0			0
$923$	−2.00850	+	10.1117i	−0.0661106	+	0.332831i
$924$		0			0
$925$	−39.8156	−	10.6686i	−1.30913	−	0.350780i
$926$		0			0
$927$	−4.46796	+	7.73874i	−0.146747	+	0.254174i
$928$		0			0
$929$	0.422561	−	0.113225i	0.0138638	−	0.00371478i	−0.251880	−	0.967758i	$-0.581049\pi$
$929$	0.422561	−	0.113225i	0.0138638	−	0.00371478i	0.265744	+	0.964044i	$0.414382\pi$
$930$		0			0
$931$	10.0228	−	10.0228i	0.328484	−	0.328484i
$932$		0			0
$933$	2.84365	+	4.92534i	0.0930968	+	0.161248i
$934$		0			0
$935$	58.3131			1.90704
$936$		0			0
$937$	51.7178			1.68955			0.844773	−	0.535125i	$-0.179736\pi$
$937$	51.7178			1.68955			0.844773	+	0.535125i	$0.179736\pi$
$938$		0			0
$939$	1.38865	+	2.40521i	0.0453168	+	0.0784910i
$940$		0			0
$941$	13.5346	−	13.5346i	0.441216	−	0.441216i	−0.451204	−	0.892421i	$-0.649005\pi$
$941$	13.5346	−	13.5346i	0.441216	−	0.441216i	0.892421	+	0.451204i	$0.149005\pi$
$942$		0			0
$943$	4.75784	−	1.27486i	0.154937	−	0.0415152i
$944$		0			0
$945$	−6.64864	+	11.5158i	−0.216280	+	0.374609i
$946$		0			0
$947$	−42.1120	−	11.2839i	−1.36846	−	0.366676i	−0.501541	−	0.865134i	$-0.667233\pi$
$947$	−42.1120	−	11.2839i	−1.36846	−	0.366676i	−0.866914	+	0.498457i	$0.833900\pi$
$948$		0			0
$949$	−0.448101	+	0.152245i	−0.0145460	+	0.00494208i
$950$		0			0
$951$	4.02592	+	1.07874i	0.130549	+	0.0349806i
$952$		0			0
$953$	−7.41906	−	4.28340i	−0.240327	−	0.138753i	0.375000	−	0.927025i	$-0.377643\pi$
$953$	−7.41906	−	4.28340i	−0.240327	−	0.138753i	−0.615327	+	0.788272i	$0.710976\pi$
$954$		0			0
$955$	−62.3696	+	16.7119i	−2.01823	+	0.540784i
$956$		0			0
$957$	49.3978	+	49.3978i	1.59680	+	1.59680i
$958$		0			0
$959$	1.11981	+	1.93957i	0.0361605	+	0.0626319i
$960$		0			0
$961$			20.5006i			0.661311i
$962$		0			0
$963$	24.8867			0.801963
$964$		0			0
$965$	5.58750	−	3.22595i	0.179868	−	0.103847i
$966$		0			0
$967$	−8.23209	+	8.23209i	−0.264726	+	0.264726i	−0.826971	−	0.562245i	$-0.809938\pi$
$967$	−8.23209	+	8.23209i	−0.264726	+	0.264726i	0.562245	+	0.826971i	$0.309938\pi$
$968$		0			0
$969$	6.57800	+	24.5494i	0.211316	+	0.788641i
$970$		0			0
$971$	−5.46039	+	9.45767i	−0.175232	+	0.303511i	−0.940242	−	0.340508i	$-0.889401\pi$
$971$	−5.46039	+	9.45767i	−0.175232	+	0.303511i	0.765009	+	0.644019i	$0.222734\pi$
$972$		0			0
$973$	2.40163	−	8.96302i	0.0769929	−	0.287341i
$974$		0			0
$975$	41.6477	−	2.74105i	1.33379	−	0.0877839i
$976$		0			0
$977$	−13.2470	+	49.4385i	−0.423810	+	1.58168i	0.342699	+	0.939445i	$0.388659\pi$
$977$	−13.2470	+	49.4385i	−0.423810	+	1.58168i	−0.766509	+	0.642234i	$0.778008\pi$
$978$		0			0
$979$	1.04551	+	0.603623i	0.0334145	+	0.0192919i
$980$		0			0
$981$	−1.24749	−	4.65570i	−0.0398294	−	0.148645i
$982$		0			0
$983$	2.46458	+	2.46458i	0.0786077	+	0.0786077i	0.745317	−	0.666710i	$-0.232298\pi$
$983$	2.46458	+	2.46458i	0.0786077	+	0.0786077i	−0.666710	+	0.745317i	$0.732298\pi$
$984$		0			0
$985$	−35.7156	+	20.6204i	−1.13799	+	0.657021i
$986$		0			0
$987$			12.3887i			0.394336i
$988$		0			0
$989$		−	35.6941i		−	1.13501i
$990$		0			0
$991$	−27.6587	+	15.9687i	−0.878607	+	0.507264i	−0.870199	−	0.492701i	$-0.836010\pi$
$991$	−27.6587	+	15.9687i	−0.878607	+	0.507264i	−0.00840818	+	0.999965i	$0.502676\pi$
$992$		0			0
$993$	−33.2989	−	33.2989i	−1.05671	−	1.05671i
$994$		0			0
$995$	8.37656	+	31.2617i	0.265555	+	0.991064i
$996$		0			0
$997$	−45.7679	−	26.4241i	−1.44948	−	0.836860i	−0.451033	−	0.892507i	$-0.648944\pi$
$997$	−45.7679	−	26.4241i	−1.44948	−	0.836860i	−0.998450	+	0.0556477i	$0.982278\pi$
$998$		0			0
$999$	−6.36759	+	23.7642i	−0.201462	+	0.751865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bk.a.271.4		48
4.3	odd	2		104.2.u.a.11.7	yes	48
8.3	odd	2	inner	416.2.bk.a.271.3		48
8.5	even	2		104.2.u.a.11.4	✓	48
12.11	even	2		936.2.ed.d.739.6		48
13.6	odd	12	inner	416.2.bk.a.175.3		48
24.5	odd	2		936.2.ed.d.739.9		48
52.19	even	12		104.2.u.a.19.4	yes	48
104.19	even	12	inner	416.2.bk.a.175.4		48
104.45	odd	12		104.2.u.a.19.7	yes	48
156.71	odd	12		936.2.ed.d.19.9		48
312.149	even	12		936.2.ed.d.19.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.u.a.11.4	✓	48	8.5	even	2
104.2.u.a.11.7	yes	48	4.3	odd	2
104.2.u.a.19.4	yes	48	52.19	even	12
104.2.u.a.19.7	yes	48	104.45	odd	12
416.2.bk.a.175.3		48	13.6	odd	12	inner
416.2.bk.a.175.4		48	104.19	even	12	inner
416.2.bk.a.271.3		48	8.3	odd	2	inner
416.2.bk.a.271.4		48	1.1	even	1	trivial
936.2.ed.d.19.6		48	312.149	even	12
936.2.ed.d.19.9		48	156.71	odd	12
936.2.ed.d.739.6		48	12.11	even	2
936.2.ed.d.739.9		48	24.5	odd	2

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bk (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.05427 - 1.82605i) q^{3} +(2.29020 - 2.29020i) q^{5} +(1.21025 - 0.324286i) q^{7} +(-0.722984 + 1.25224i) q^{9} +(3.76618 + 1.00915i) q^{11} +(-3.23415 - 1.59382i) q^{13} +(-6.59652 - 1.76753i) q^{15} +(3.99899 + 2.30882i) q^{17} +(-2.52138 + 0.675601i) q^{19} +(-1.86810 - 1.86810i) q^{21} +(-1.62930 - 2.82203i) q^{23} -5.49003i q^{25} -3.27675 q^{27} +(-7.35890 + 4.24866i) q^{29} +(2.29122 - 2.29122i) q^{31} +(-2.12783 - 7.94117i) q^{33} +(2.02904 - 3.51440i) q^{35} +(1.94326 - 7.25236i) q^{37} +(0.499278 + 7.58606i) q^{39} +(-0.391230 + 1.46009i) q^{41} +(9.48630 + 5.47692i) q^{43} +(1.21211 + 4.52367i) q^{45} +(-3.31585 - 3.31585i) q^{47} +(-4.70263 + 2.71507i) q^{49} -9.73651i q^{51} +2.94222i q^{53} +(10.9365 - 6.31416i) q^{55} +(3.89190 + 3.89190i) q^{57} +(-0.115929 - 0.432654i) q^{59} +(9.70024 + 5.60044i) q^{61} +(-0.468907 + 1.74998i) q^{63} +(-11.0570 + 3.75669i) q^{65} +(-2.48521 + 9.27491i) q^{67} +(-3.43545 + 5.95037i) q^{69} +(-0.740035 - 2.76185i) q^{71} +(0.0928135 - 0.0928135i) q^{73} +(-10.0251 + 5.78799i) q^{75} +4.88528 q^{77} +9.86517i q^{79} +(5.62354 + 9.74026i) q^{81} +(7.31249 + 7.31249i) q^{83} +(14.4462 - 3.87084i) q^{85} +(15.5166 + 8.95850i) q^{87} +(0.299076 + 0.0801373i) q^{89} +(-4.43099 - 0.880132i) q^{91} +(-6.59946 - 1.76832i) q^{93} +(-4.22719 + 7.32172i) q^{95} +(10.4399 - 2.79736i) q^{97} +(-3.98659 + 3.98659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{3} - 20 q^{9} + 8 q^{11} - 12 q^{17} + 8 q^{19} - 8 q^{27} + 4 q^{33} + 4 q^{35} + 12 q^{43} - 60 q^{49} + 36 q^{57} + 64 q^{59} - 16 q^{65} + 8 q^{67} - 12 q^{73} - 24 q^{75} - 8 q^{81} + 48 q^{83}+ \cdots - 168 q^{99}+O(q^{100}) \) 48 * q + 4 * q^3 - 20 * q^9 + 8 * q^11 - 12 * q^17 + 8 * q^19 - 8 * q^27 + 4 * q^33 + 4 * q^35 + 12 * q^43 - 60 * q^49 + 36 * q^57 + 64 * q^59 - 16 * q^65 + 8 * q^67 - 12 * q^73 - 24 * q^75 - 8 * q^81 + 48 * q^83 + 12 * q^89 - 104 * q^91 + 4 * q^97 - 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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