LMFDB - Embedded newform 702.2.bb.a.197.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] 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("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.9
Character	$\chi$	$=$	702.197
Dual form			702.2.bb.a.449.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.763001 + 2.84756i) q^{5} +(-0.504962 + 1.88454i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.55305 + 1.47400i) q^{10} +(0.566782 - 0.566782i) q^{11} +(2.11327 - 2.92131i) q^{13} +(-1.68964 + 0.975511i) q^{14} -1.00000 q^{16} +(-4.02058 + 6.96385i) q^{17} +(-1.18319 - 4.41574i) q^{19} +(-2.84756 - 0.763001i) q^{20} +0.801550 q^{22} +(-3.49688 + 6.05678i) q^{23} +(-3.19629 - 1.84538i) q^{25} +(3.55999 - 0.571370i) q^{26} +(-1.88454 - 0.504962i) q^{28} -7.87674i q^{29} +(-2.31031 - 0.619046i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.76717 + 2.08121i) q^{34} +(-4.98106 - 2.87582i) q^{35} +(-2.09658 + 7.82455i) q^{37} +(2.28576 - 3.95904i) q^{38} +(-1.47400 - 2.55305i) q^{40} +(5.00455 - 1.34097i) q^{41} +(2.02114 - 1.16691i) q^{43} +(0.566782 + 0.566782i) q^{44} +(-6.75546 + 1.81012i) q^{46} +(1.37959 + 5.14869i) q^{47} +(2.76566 + 1.59676i) q^{49} +(-0.955238 - 3.56500i) q^{50} +(2.92131 + 2.11327i) q^{52} +8.27924i q^{53} +(1.18149 + 2.04640i) q^{55} +(-0.975511 - 1.68964i) q^{56} +(5.56970 - 5.56970i) q^{58} +(6.24226 - 6.24226i) q^{59} +(2.46959 + 4.27745i) q^{61} +(-1.19590 - 2.07137i) q^{62} -1.00000i q^{64} +(6.70618 + 8.24664i) q^{65} +(0.200953 + 0.749969i) q^{67} +(-6.96385 - 4.02058i) q^{68} +(-1.48863 - 5.55565i) q^{70} +(-2.57304 + 0.689443i) q^{71} +(5.68293 + 5.68293i) q^{73} +(-7.01530 + 4.05028i) q^{74} +(4.41574 - 1.18319i) q^{76} +(0.781921 + 1.35433i) q^{77} +(0.554497 - 0.960416i) q^{79} +(0.763001 - 2.84756i) q^{80} +(4.48696 + 2.59055i) q^{82} +(-2.29264 + 0.614312i) q^{83} +(-16.7623 - 16.7623i) q^{85} +(2.25429 + 0.604036i) q^{86} +0.801550i q^{88} +(-2.84070 - 0.761164i) q^{89} +(4.43822 + 5.45771i) q^{91} +(-6.05678 - 3.49688i) q^{92} +(-2.66516 + 4.61619i) q^{94} +13.4769 q^{95} +(-3.54866 - 0.950861i) q^{97} +(0.826542 + 3.08469i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−0.763001	+	2.84756i	−0.341224	+	1.27347i	0.555737	+	0.831358i	$0.312436\pi$
$5$	−0.763001	+	2.84756i	−0.341224	+	1.27347i	−0.896962	+	0.442109i	$0.854231\pi$
$6$		0			0
$7$	−0.504962	+	1.88454i	−0.190858	+	0.712290i	0.802443	+	0.596729i	$0.203533\pi$
$7$	−0.504962	+	1.88454i	−0.190858	+	0.712290i	−0.993300	+	0.115561i	$0.963133\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.55305	+	1.47400i	−0.807345	+	0.466121i
$11$	0.566782	−	0.566782i	0.170891	−	0.170891i	−0.616480	−	0.787371i	$-0.711442\pi$
$11$	0.566782	−	0.566782i	0.170891	−	0.170891i	0.787371	+	0.616480i	$0.211442\pi$
$12$		0			0
$13$	2.11327	−	2.92131i	0.586117	−	0.810226i
$13$	2.11327	−	2.92131i	0.586117	−	0.810226i
$14$	−1.68964	+	0.975511i	−0.451574	+	0.260716i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.02058	+	6.96385i	−0.975135	+	1.68898i	−0.295645	+	0.955298i	$0.595535\pi$
$17$	−4.02058	+	6.96385i	−0.975135	+	1.68898i	−0.679490	+	0.733685i	$0.737799\pi$
$18$		0			0
$19$	−1.18319	−	4.41574i	−0.271443	−	1.01304i	−0.958188	−	0.286141i	$-0.907627\pi$
$19$	−1.18319	−	4.41574i	−0.271443	−	1.01304i	0.686744	−	0.726899i	$-0.259039\pi$
$20$	−2.84756	−	0.763001i	−0.636733	−	0.170612i
$21$		0			0
$22$	0.801550			0.170891
$23$	−3.49688	+	6.05678i	−0.729150	+	1.26293i	0.228093	+	0.973639i	$0.426751\pi$
$23$	−3.49688	+	6.05678i	−0.729150	+	1.26293i	−0.957243	+	0.289286i	$0.906582\pi$
$24$		0			0
$25$	−3.19629	−	1.84538i	−0.639258	−	0.369076i
$26$	3.55999	−	0.571370i	0.698172	−	0.112055i
$27$		0			0
$28$	−1.88454	−	0.504962i	−0.356145	−	0.0954288i
$29$		−	7.87674i		−	1.46267i	−0.682016	−	0.731337i	$-0.738897\pi$
$29$		−	7.87674i		−	1.46267i	0.682016	−	0.731337i	$-0.261103\pi$
$30$		0			0
$31$	−2.31031	−	0.619046i	−0.414944	−	0.111184i	0.0453062	−	0.998973i	$-0.485574\pi$
$31$	−2.31031	−	0.619046i	−0.414944	−	0.111184i	−0.460250	+	0.887789i	$0.652240\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	−7.76717	+	2.08121i	−1.33206	+	0.356924i
$35$	−4.98106	−	2.87582i	−0.841953	−	0.486102i
$36$		0			0
$37$	−2.09658	+	7.82455i	−0.344676	+	1.28635i	0.548314	+	0.836272i	$0.315270\pi$
$37$	−2.09658	+	7.82455i	−0.344676	+	1.28635i	−0.892990	+	0.450076i	$0.851397\pi$
$38$	2.28576	−	3.95904i	0.370798	−	0.642242i
$39$		0			0
$40$	−1.47400	−	2.55305i	−0.233061	−	0.403673i
$41$	5.00455	−	1.34097i	0.781580	−	0.209424i	0.154099	−	0.988055i	$-0.450753\pi$
$41$	5.00455	−	1.34097i	0.781580	−	0.209424i	0.627481	+	0.778632i	$0.284086\pi$
$42$		0			0
$43$	2.02114	−	1.16691i	0.308222	−	0.177952i	−0.337909	−	0.941179i	$-0.609720\pi$
$43$	2.02114	−	1.16691i	0.308222	−	0.177952i	0.646130	+	0.763227i	$0.276386\pi$
$44$	0.566782	+	0.566782i	0.0854456	+	0.0854456i
$45$		0			0
$46$	−6.75546	+	1.81012i	−0.996038	+	0.266887i
$47$	1.37959	+	5.14869i	0.201233	+	0.751013i	0.990565	+	0.137046i	$0.0437608\pi$
$47$	1.37959	+	5.14869i	0.201233	+	0.751013i	−0.789331	+	0.613968i	$0.789573\pi$
$48$		0			0
$49$	2.76566	+	1.59676i	0.395095	+	0.228108i
$50$	−0.955238	−	3.56500i	−0.135091	−	0.504167i
$51$		0			0
$52$	2.92131	+	2.11327i	0.405113	+	0.293058i
$53$			8.27924i			1.13724i	0.822600	+	0.568620i	$0.192523\pi$
$53$			8.27924i			1.13724i	−0.822600	+	0.568620i	$0.807477\pi$
$54$		0			0
$55$	1.18149	+	2.04640i	0.159312	+	0.275936i
$56$	−0.975511	−	1.68964i	−0.130358	−	0.225787i
$57$		0			0
$58$	5.56970	−	5.56970i	0.731337	−	0.731337i
$59$	6.24226	−	6.24226i	0.812673	−	0.812673i	−0.172361	−	0.985034i	$-0.555139\pi$
$59$	6.24226	−	6.24226i	0.812673	−	0.812673i	0.985034	+	0.172361i	$0.0551395\pi$
$60$		0			0
$61$	2.46959	+	4.27745i	0.316198	+	0.547671i	0.979691	−	0.200511i	$-0.0642603\pi$
$61$	2.46959	+	4.27745i	0.316198	+	0.547671i	−0.663493	+	0.748182i	$0.730927\pi$
$62$	−1.19590	−	2.07137i	−0.151880	−	0.263064i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	6.70618	+	8.24664i	0.831799	+	1.02287i
$66$		0			0
$67$	0.200953	+	0.749969i	0.0245504	+	0.0916232i	0.977114	−	0.212716i	$-0.0682310\pi$
$67$	0.200953	+	0.749969i	0.0245504	+	0.0916232i	−0.952564	+	0.304339i	$0.901564\pi$
$68$	−6.96385	−	4.02058i	−0.844491	−	0.487567i
$69$		0			0
$70$	−1.48863	−	5.55565i	−0.177926	−	0.664027i
$71$	−2.57304	+	0.689443i	−0.305363	+	0.0818218i	−0.408247	−	0.912872i	$-0.633860\pi$
$71$	−2.57304	+	0.689443i	−0.305363	+	0.0818218i	0.102884	+	0.994693i	$0.467193\pi$
$72$		0			0
$73$	5.68293	+	5.68293i	0.665137	+	0.665137i	0.956586	−	0.291449i	$-0.0941375\pi$
$73$	5.68293	+	5.68293i	0.665137	+	0.665137i	−0.291449	+	0.956586i	$0.594137\pi$
$74$	−7.01530	+	4.05028i	−0.815512	+	0.470836i
$75$		0			0
$76$	4.41574	−	1.18319i	0.506520	−	0.135722i
$77$	0.781921	+	1.35433i	0.0891082	+	0.154340i
$78$		0			0
$79$	0.554497	−	0.960416i	0.0623857	−	0.108055i	−0.833146	−	0.553054i	$-0.813462\pi$
$79$	0.554497	−	0.960416i	0.0623857	−	0.108055i	0.895531	+	0.444998i	$0.146796\pi$
$80$	0.763001	−	2.84756i	0.0853061	−	0.318367i
$81$		0			0
$82$	4.48696	+	2.59055i	0.495502	+	0.286078i
$83$	−2.29264	+	0.614312i	−0.251650	+	0.0674295i	−0.382439	−	0.923981i	$-0.624916\pi$
$83$	−2.29264	+	0.614312i	−0.251650	+	0.0674295i	0.130789	+	0.991410i	$0.458249\pi$
$84$		0			0
$85$	−16.7623	−	16.7623i	−1.81812	−	1.81812i
$86$	2.25429	+	0.604036i	0.243087	+	0.0651349i
$87$		0			0
$88$			0.801550i			0.0854456i
$89$	−2.84070	−	0.761164i	−0.301114	−	0.0806832i	0.105099	−	0.994462i	$-0.466484\pi$
$89$	−2.84070	−	0.761164i	−0.301114	−	0.0806832i	−0.406213	+	0.913779i	$0.633151\pi$
$90$		0			0
$91$	4.43822	+	5.45771i	0.465252	+	0.572123i
$92$	−6.05678	−	3.49688i	−0.631463	−	0.364575i
$93$		0			0
$94$	−2.66516	+	4.61619i	−0.274890	+	0.476123i
$95$	13.4769			1.38270
$96$		0			0
$97$	−3.54866	−	0.950861i	−0.360312	−	0.0965453i	0.0741216	−	0.997249i	$-0.476385\pi$
$97$	−3.54866	−	0.950861i	−0.360312	−	0.0965453i	−0.434433	+	0.900704i	$0.643051\pi$
$98$	0.826542	+	3.08469i	0.0834933	+	0.311601i
$99$		0			0
$100$	1.84538	−	3.19629i	0.184538	−	0.319629i
$101$	13.6438			1.35761			0.678804	−	0.734319i	$-0.262498\pi$
$101$	13.6438			1.35761			0.678804	+	0.734319i	$0.262498\pi$
$102$		0			0
$103$	11.6669	−	6.73592i	1.14958	−	0.663710i	0.200794	−	0.979633i	$-0.435648\pi$
$103$	11.6669	−	6.73592i	1.14958	−	0.663710i	0.948785	+	0.315924i	$0.102314\pi$
$104$	0.571370	+	3.55999i	0.0560274	+	0.349086i
$105$		0			0
$106$	−5.85430	+	5.85430i	−0.568620	+	0.568620i
$107$	16.0522	−	9.26775i	1.55183	−	0.895947i	0.553833	−	0.832628i	$-0.313165\pi$
$107$	16.0522	−	9.26775i	1.55183	−	0.895947i	0.997993	−	0.0633192i	$-0.0201686\pi$
$108$		0			0
$109$	4.23071	−	4.23071i	0.405229	−	0.405229i	−0.474842	−	0.880071i	$-0.657495\pi$
$109$	4.23071	−	4.23071i	0.405229	−	0.405229i	0.880071	+	0.474842i	$0.157495\pi$
$110$	−0.611584	+	2.28246i	−0.0583122	+	0.217624i
$111$		0			0
$112$	0.504962	−	1.88454i	0.0477144	−	0.178073i
$113$		−	5.97917i		−	0.562473i	−0.959639	−	0.281236i	$-0.909256\pi$
$113$		−	5.97917i		−	0.562473i	0.959639	−	0.281236i	$-0.0907445\pi$
$114$		0			0
$115$	−14.5789	−	14.5789i	−1.35949	−	1.35949i
$116$	7.87674			0.731337
$117$		0			0
$118$	8.82789			0.812673
$119$	−11.0934	−	11.0934i	−1.01693	−	1.01693i
$120$		0			0
$121$			10.3575i			0.941592i
$122$	−1.27835	+	4.77087i	−0.115737	+	0.431935i
$123$		0			0
$124$	0.619046	−	2.31031i	0.0555920	−	0.207472i
$125$	−2.72919	+	2.72919i	−0.244106	+	0.244106i
$126$		0			0
$127$	1.93815	−	1.11899i	0.171983	−	0.0992946i	−0.411537	−	0.911393i	$-0.635008\pi$
$127$	1.93815	−	1.11899i	0.171983	−	0.0992946i	0.583521	+	0.812098i	$0.301675\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−1.08927	+	10.5732i	−0.0955352	+	0.927334i
$131$	−7.37842	+	4.25993i	−0.644656	+	0.372192i	−0.786406	−	0.617710i	$-0.788060\pi$
$131$	−7.37842	+	4.25993i	−0.644656	+	0.372192i	0.141750	+	0.989903i	$0.454727\pi$
$132$		0			0
$133$	8.91912			0.773386
$134$	−0.388212	+	0.672403i	−0.0335364	+	0.0580868i
$135$		0			0
$136$	−2.08121	−	7.76717i	−0.178462	−	0.666029i
$137$	−11.2268	−	3.00821i	−0.959170	−	0.257009i	−0.254921	−	0.966962i	$-0.582049\pi$
$137$	−11.2268	−	3.00821i	−0.959170	−	0.257009i	−0.704249	+	0.709953i	$0.748716\pi$
$138$		0			0
$139$	22.8286			1.93629			0.968147	−	0.250381i	$-0.0805558\pi$
$139$	22.8286			1.93629			0.968147	+	0.250381i	$0.0805558\pi$
$140$	2.87582	−	4.98106i	0.243051	−	0.420976i
$141$		0			0
$142$	−2.30692	−	1.33190i	−0.193593	−	0.111771i
$143$	−0.457981	−	2.85351i	−0.0382983	−	0.238623i
$144$		0			0
$145$	22.4295	+	6.00996i	1.86267	+	0.499100i
$146$			8.03688i			0.665137i
$147$		0			0
$148$	−7.82455	−	2.09658i	−0.643174	−	0.172338i
$149$	5.50303	+	5.50303i	0.450826	+	0.450826i	0.895629	−	0.444803i	$-0.146726\pi$
$149$	5.50303	+	5.50303i	0.450826	+	0.450826i	−0.444803	+	0.895629i	$0.646726\pi$
$150$		0			0
$151$	−7.67704	+	2.05706i	−0.624748	+	0.167401i	−0.557285	−	0.830321i	$-0.688157\pi$
$151$	−7.67704	+	2.05706i	−0.624748	+	0.167401i	−0.0674629	+	0.997722i	$0.521490\pi$
$152$	3.95904	+	2.28576i	0.321121	+	0.185399i
$153$		0			0
$154$	−0.404752	+	1.51056i	−0.0326159	+	0.121724i
$155$	3.52554	−	6.10641i	0.283178	−	0.490479i
$156$		0			0
$157$	1.97021	+	3.41251i	0.157240	+	0.272348i	0.933872	−	0.357606i	$-0.116407\pi$
$157$	1.97021	+	3.41251i	0.157240	+	0.272348i	−0.776632	+	0.629954i	$0.783074\pi$
$158$	1.07121	−	0.287029i	0.0852205	−	0.0228348i
$159$		0			0
$160$	2.55305	−	1.47400i	0.201836	−	0.116530i
$161$	−9.64846	−	9.64846i	−0.760405	−	0.760405i
$162$		0			0
$163$	−19.9290	+	5.33996i	−1.56096	+	0.418258i	−0.932967	−	0.359962i	$-0.882790\pi$
$163$	−19.9290	+	5.33996i	−1.56096	+	0.418258i	−0.627992	+	0.778220i	$0.716123\pi$
$164$	1.34097	+	5.00455i	0.104712	+	0.390790i
$165$		0			0
$166$	−2.05553	−	1.18676i	−0.159540	−	0.0921103i
$167$	−1.46059	−	5.45101i	−0.113024	−	0.421811i	0.886107	−	0.463480i	$-0.153399\pi$
$167$	−1.46059	−	5.45101i	−0.113024	−	0.421811i	−0.999131	+	0.0416684i	$0.986733\pi$
$168$		0			0
$169$	−4.06814	−	12.3471i	−0.312934	−	0.949775i
$170$		−	23.7054i		−	1.81812i
$171$		0			0
$172$	1.16691	+	2.02114i	0.0889759	+	0.154111i
$173$	8.21647	+	14.2313i	0.624687	+	1.08199i	0.988601	+	0.150557i	$0.0481066\pi$
$173$	8.21647	+	14.2313i	0.624687	+	1.08199i	−0.363915	+	0.931432i	$0.618560\pi$
$174$		0			0
$175$	5.09170	−	5.09170i	0.384896	−	0.384896i
$176$	−0.566782	+	0.566782i	−0.0427228	+	0.0427228i
$177$		0			0
$178$	−1.47046	−	2.54690i	−0.110215	−	0.190898i
$179$	−3.02863	−	5.24575i	−0.226371	−	0.392085i	0.730359	−	0.683063i	$-0.239353\pi$
$179$	−3.02863	−	5.24575i	−0.226371	−	0.392085i	−0.956730	+	0.290978i	$0.906019\pi$
$180$		0			0
$181$			12.2487i			0.910436i	0.890380	+	0.455218i	$0.150439\pi$
$181$			12.2487i			0.910436i	−0.890380	+	0.455218i	$0.849561\pi$
$182$	−0.720889	+	6.99748i	−0.0534358	+	0.518687i
$183$		0			0
$184$	−1.81012	−	6.75546i	−0.133444	−	0.498019i
$185$	−20.6812	−	11.9403i	−1.52051	−	0.877867i
$186$		0			0
$187$	1.66819	+	6.22578i	0.121990	+	0.455274i
$188$	−5.14869	+	1.37959i	−0.375507	+	0.100617i
$189$		0			0
$190$	9.52957	+	9.52957i	0.691348	+	0.691348i
$191$	0.364345	−	0.210355i	0.0263631	−	0.0152207i	−0.486761	−	0.873535i	$-0.661822\pi$
$191$	0.364345	−	0.210355i	0.0263631	−	0.0152207i	0.513124	+	0.858315i	$0.328488\pi$
$192$		0			0
$193$	13.1262	−	3.51716i	0.944847	−	0.253171i	0.246673	−	0.969099i	$-0.420663\pi$
$193$	13.1262	−	3.51716i	0.944847	−	0.253171i	0.698174	+	0.715928i	$0.253996\pi$
$194$	−1.83692	−	3.18164i	−0.131883	−	0.228429i
$195$		0			0
$196$	−1.59676	+	2.76566i	−0.114054	+	0.197547i
$197$	0.239457	−	0.893667i	0.0170606	−	0.0636712i	−0.956871	−	0.290514i	$-0.906174\pi$
$197$	0.239457	−	0.893667i	0.0170606	−	0.0636712i	0.973931	+	0.226843i	$0.0728404\pi$
$198$		0			0
$199$	11.1074	+	6.41286i	0.787382	+	0.454595i	0.839040	−	0.544070i	$-0.183117\pi$
$199$	11.1074	+	6.41286i	0.787382	+	0.454595i	−0.0516579	+	0.998665i	$0.516451\pi$
$200$	3.56500	−	0.955238i	0.252083	−	0.0675455i
$201$		0			0
$202$	9.64762	+	9.64762i	0.678804	+	0.678804i
$203$	14.8441	+	3.97745i	1.04185	+	0.279162i
$204$		0			0
$205$			15.2739i			1.06678i
$206$	13.0128	+	3.48677i	0.906644	+	0.242935i
$207$		0			0
$208$	−2.11327	+	2.92131i	−0.146529	+	0.202557i
$209$	−3.17337	−	1.83215i	−0.219507	−	0.126732i
$210$		0			0
$211$	−3.42303	+	5.92886i	−0.235651	+	0.408159i	−0.959462	−	0.281839i	$-0.909056\pi$
$211$	−3.42303	+	5.92886i	−0.235651	+	0.408159i	0.723811	+	0.689999i	$0.242389\pi$
$212$	−8.27924			−0.568620
$213$		0			0
$214$	17.9039	+	4.79734i	1.22389	+	0.327939i
$215$	1.78070	+	6.64568i	0.121443	+	0.453231i
$216$		0			0
$217$	2.33324	−	4.04129i	0.158390	−	0.274340i
$218$	5.98313			0.405229
$219$		0			0
$220$	−2.04640	+	1.18149i	−0.137968	+	0.0796560i
$221$	11.8470	+	26.4619i	0.796916	+	1.78002i
$222$		0			0
$223$	12.5100	−	12.5100i	0.837733	−	0.837733i	−0.150827	−	0.988560i	$-0.548194\pi$
$223$	12.5100	−	12.5100i	0.837733	−	0.837733i	0.988560	+	0.150827i	$0.0481937\pi$
$224$	1.68964	−	0.975511i	0.112893	−	0.0651791i
$225$		0			0
$226$	4.22791	−	4.22791i	0.281236	−	0.281236i
$227$	5.01242	−	18.7066i	0.332686	−	1.24160i	−0.573669	−	0.819087i	$-0.694481\pi$
$227$	5.01242	−	18.7066i	0.332686	−	1.24160i	0.906356	−	0.422515i	$-0.138853\pi$
$228$		0			0
$229$	−6.72179	+	25.0861i	−0.444188	+	1.65773i	0.273882	+	0.961763i	$0.411692\pi$
$229$	−6.72179	+	25.0861i	−0.444188	+	1.65773i	−0.718070	+	0.695971i	$0.754974\pi$
$230$		−	20.6177i		−	1.35949i
$231$		0			0
$232$	5.56970	+	5.56970i	0.365669	+	0.365669i
$233$	−11.9090			−0.780184			−0.390092	−	0.920776i	$-0.627557\pi$
$233$	−11.9090			−0.780184			−0.390092	+	0.920776i	$0.627557\pi$
$234$		0			0
$235$	−15.7138			−1.02506
$236$	6.24226	+	6.24226i	0.406337	+	0.406337i
$237$		0			0
$238$		−	15.6885i		−	1.01693i
$239$	−2.40211	+	8.96480i	−0.155380	+	0.579885i	0.843693	+	0.536826i	$0.180377\pi$
$239$	−2.40211	+	8.96480i	−0.155380	+	0.579885i	−0.999073	+	0.0430587i	$0.986290\pi$
$240$		0			0
$241$	−2.53446	+	9.45875i	−0.163259	+	0.609292i	0.834997	+	0.550255i	$0.185470\pi$
$241$	−2.53446	+	9.45875i	−0.163259	+	0.609292i	−0.998256	+	0.0590365i	$0.981197\pi$
$242$	−7.32387	+	7.32387i	−0.470796	+	0.470796i
$243$		0			0
$244$	−4.27745	+	2.46959i	−0.273836	+	0.158099i
$245$	−6.65706	+	6.65706i	−0.425304	+	0.425304i
$246$		0			0
$247$	−15.4002	−	5.87519i	−0.979890	−	0.373829i
$248$	2.07137	−	1.19590i	0.131532	−	0.0759400i
$249$		0			0
$250$	−3.85966			−0.244106
$251$	7.05445	−	12.2187i	0.445273	−	0.771235i	−0.552798	−	0.833315i	$-0.686440\pi$
$251$	7.05445	−	12.2187i	0.445273	−	0.771235i	0.998071	+	0.0620799i	$0.0197734\pi$
$252$		0			0
$253$	1.45090	+	5.41484i	0.0912174	+	0.340428i
$254$	2.16173	+	0.579234i	0.135639	+	0.0363444i
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.55988	−	4.43384i	0.159681	−	0.276575i	−0.775073	−	0.631872i	$-0.782287\pi$
$257$	2.55988	−	4.43384i	0.159681	−	0.276575i	0.934754	+	0.355297i	$0.115620\pi$
$258$		0			0
$259$	−13.6870	−	7.90220i	−0.850469	−	0.491019i
$260$	−8.24664	+	6.70618i	−0.511435	+	0.415900i
$261$		0			0
$262$	−8.22956	−	2.20510i	−0.508424	−	0.136232i
$263$		−	14.4227i		−	0.889343i	−0.895694	−	0.444671i	$-0.853320\pi$
$263$		−	14.4227i		−	0.889343i	0.895694	−	0.444671i	$-0.146680\pi$
$264$		0			0
$265$	−23.5756	−	6.31706i	−1.44824	−	0.388054i
$266$	6.30677	+	6.30677i	0.386693	+	0.386693i
$267$		0			0
$268$	−0.749969	+	0.200953i	−0.0458116	+	0.0122752i
$269$	−10.3656	−	5.98459i	−0.632002	−	0.364887i	0.149525	−	0.988758i	$-0.452226\pi$
$269$	−10.3656	−	5.98459i	−0.632002	−	0.364887i	−0.781527	+	0.623871i	$0.785559\pi$
$270$		0			0
$271$	6.16812	−	23.0197i	0.374687	−	1.39835i	−0.479115	−	0.877752i	$-0.659042\pi$
$271$	6.16812	−	23.0197i	0.374687	−	1.39835i	0.853802	−	0.520598i	$-0.174291\pi$
$272$	4.02058	−	6.96385i	0.243784	−	0.422246i
$273$		0			0
$274$	−5.81141	−	10.0657i	−0.351080	−	0.608089i
$275$	−2.85752	+	0.765671i	−0.172315	+	0.0461717i
$276$		0			0
$277$	−8.17883	+	4.72205i	−0.491419	+	0.283721i	−0.725163	−	0.688577i	$-0.758235\pi$
$277$	−8.17883	+	4.72205i	−0.491419	+	0.283721i	0.233744	+	0.972298i	$0.424902\pi$
$278$	16.1422	+	16.1422i	0.968147	+	0.968147i
$279$		0			0
$280$	5.55565	−	1.48863i	0.332014	−	0.0889628i
$281$	−5.04768	−	18.8382i	−0.301119	−	1.12379i	−0.936235	−	0.351376i	$-0.885714\pi$
$281$	−5.04768	−	18.8382i	−0.301119	−	1.12379i	0.635115	−	0.772417i	$-0.280953\pi$
$282$		0			0
$283$	17.9472	+	10.3618i	1.06685	+	0.615946i	0.927319	−	0.374272i	$-0.122107\pi$
$283$	17.9472	+	10.3618i	1.06685	+	0.615946i	0.139530	+	0.990218i	$0.455441\pi$
$284$	−0.689443	−	2.57304i	−0.0409109	−	0.152682i
$285$		0			0
$286$	1.69390	−	2.34158i	0.100162	−	0.138461i
$287$			10.1084i			0.596682i
$288$		0			0
$289$	−23.8302	−	41.2751i	−1.40178	−	2.42795i
$290$	11.6104	+	20.1097i	0.681783	+	1.18088i
$291$		0			0
$292$	−5.68293	+	5.68293i	−0.332568	+	0.332568i
$293$	−13.6517	+	13.6517i	−0.797542	+	0.797542i	−0.982707	−	0.185165i	$-0.940718\pi$
$293$	−13.6517	+	13.6517i	−0.797542	+	0.797542i	0.185165	+	0.982707i	$0.440718\pi$
$294$		0			0
$295$	13.0123	+	22.5380i	0.757608	+	1.31222i
$296$	−4.05028	−	7.01530i	−0.235418	−	0.407756i
$297$		0			0
$298$			7.78247i			0.450826i
$299$	10.3039	+	23.0151i	0.595888	+	1.33100i
$300$		0			0
$301$	1.17849	+	4.39818i	0.0679269	+	0.253507i
$302$	−6.88304	−	3.97393i	−0.396075	−	0.228674i
$303$		0			0
$304$	1.18319	+	4.41574i	0.0678608	+	0.253260i
$305$	−14.0646	+	3.76859i	−0.805335	+	0.215789i
$306$		0			0
$307$	−15.5762	−	15.5762i	−0.888978	−	0.888978i	0.105447	−	0.994425i	$-0.466373\pi$
$307$	−15.5762	−	15.5762i	−0.888978	−	0.888978i	−0.994425	+	0.105447i	$0.966373\pi$
$308$	−1.35433	+	0.781921i	−0.0771700	+	0.0445541i
$309$		0			0
$310$	6.81082	−	1.82495i	0.386828	−	0.103650i
$311$	−4.85889	−	8.41584i	−0.275522	−	0.477218i	0.694745	−	0.719257i	$-0.255517\pi$
$311$	−4.85889	−	8.41584i	−0.275522	−	0.477218i	−0.970267	+	0.242038i	$0.922184\pi$
$312$		0			0
$313$	2.74916	−	4.76168i	0.155392	−	0.269146i	−0.777810	−	0.628500i	$-0.783669\pi$
$313$	2.74916	−	4.76168i	0.155392	−	0.269146i	0.933202	+	0.359353i	$0.117003\pi$
$314$	−1.01986	+	3.80616i	−0.0575539	+	0.214794i
$315$		0			0
$316$	0.960416	+	0.554497i	0.0540276	+	0.0311929i
$317$	−1.01082	+	0.270848i	−0.0567731	+	0.0152123i	−0.287094	−	0.957902i	$-0.592689\pi$
$317$	−1.01082	+	0.270848i	−0.0567731	+	0.0152123i	0.230321	+	0.973115i	$0.426022\pi$
$318$		0			0
$319$	−4.46439	−	4.46439i	−0.249958	−	0.249958i
$320$	2.84756	+	0.763001i	0.159183	+	0.0426530i
$321$		0			0
$322$		−	13.6450i		−	0.760405i
$323$	35.5077	+	9.51426i	1.97570	+	0.529388i
$324$		0			0
$325$	−12.1456	+	5.43757i	−0.673715	+	0.301622i
$326$	−17.8678	−	10.3160i	−0.989609	−	0.571351i
$327$		0			0
$328$	−2.59055	+	4.48696i	−0.143039	+	0.247751i
$329$	−10.3996			−0.573346
$330$		0			0
$331$	11.9246	+	3.19520i	0.655438	+	0.175624i	0.571186	−	0.820821i	$-0.306483\pi$
$331$	11.9246	+	3.19520i	0.655438	+	0.175624i	0.0842515	+	0.996445i	$0.473150\pi$
$332$	−0.614312	−	2.29264i	−0.0337147	−	0.125825i
$333$		0			0
$334$	2.82165	−	4.88724i	0.154394	−	0.267418i
$335$	−2.28891			−0.125056
$336$		0			0
$337$	−18.3428	+	10.5902i	−0.999195	+	0.576886i	−0.908010	−	0.418948i	$-0.862399\pi$
$337$	−18.3428	+	10.5902i	−0.999195	+	0.576886i	−0.0911852	+	0.995834i	$0.529066\pi$
$338$	5.85409	−	11.6073i	0.318420	−	0.631354i
$339$		0			0
$340$	16.7623	−	16.7623i	0.909062	−	0.909062i
$341$	−1.66031	+	0.958578i	−0.0899106	+	0.0519099i
$342$		0			0
$343$	−14.0628	+	14.0628i	−0.759319	+	0.759319i
$344$	−0.604036	+	2.25429i	−0.0325674	+	0.121543i
$345$		0			0
$346$	−4.25316	+	15.8730i	−0.228651	+	0.853338i
$347$		−	2.51714i		−	0.135127i	−0.997715	−	0.0675636i	$-0.978477\pi$
$347$		−	2.51714i		−	0.135127i	0.997715	−	0.0675636i	$-0.0215226\pi$
$348$		0			0
$349$	−12.5807	−	12.5807i	−0.673429	−	0.673429i	0.285076	−	0.958505i	$-0.407981\pi$
$349$	−12.5807	−	12.5807i	−0.673429	−	0.673429i	−0.958505	+	0.285076i	$0.907981\pi$
$350$	7.20075			0.384896
$351$		0			0
$352$	−0.801550			−0.0427228
$353$	2.20712	+	2.20712i	0.117473	+	0.117473i	0.763400	−	0.645927i	$-0.223529\pi$
$353$	2.20712	+	2.20712i	0.117473	+	0.117473i	−0.645927	+	0.763400i	$0.723529\pi$
$354$		0			0
$355$		−	7.85291i		−	0.416789i
$356$	0.761164	−	2.84070i	0.0403416	−	0.150557i
$357$		0			0
$358$	1.56774	−	5.85087i	0.0828574	−	0.309228i
$359$	14.3618	−	14.3618i	0.757986	−	0.757986i	−0.217970	−	0.975956i	$-0.569943\pi$
$359$	14.3618	−	14.3618i	0.757986	−	0.757986i	0.975956	+	0.217970i	$0.0699434\pi$
$360$		0			0
$361$	−1.64433	+	0.949354i	−0.0865436	+	0.0499660i
$362$	−8.66111	+	8.66111i	−0.455218	+	0.455218i
$363$		0			0
$364$	−5.45771	+	4.43822i	−0.286062	+	0.232626i
$365$	−20.5186	+	11.8464i	−1.07399	+	0.620069i
$366$		0			0
$367$	23.2205			1.21210			0.606049	−	0.795427i	$-0.292753\pi$
$367$	23.2205			1.21210			0.606049	+	0.795427i	$0.292753\pi$
$368$	3.49688	−	6.05678i	0.182288	−	0.315731i
$369$		0			0
$370$	−6.18074	−	23.0668i	−0.321321	−	1.19919i
$371$	−15.6026	−	4.18070i	−0.810045	−	0.217051i
$372$		0			0
$373$	25.3140			1.31071			0.655355	−	0.755321i	$-0.272519\pi$
$373$	25.3140			1.31071			0.655355	+	0.755321i	$0.272519\pi$
$374$	−3.22270	+	5.58188i	−0.166642	+	0.288632i
$375$		0			0
$376$	−4.61619	−	2.66516i	−0.238062	−	0.137445i
$377$	−23.0104	−	16.6457i	−1.18510	−	0.857298i
$378$		0			0
$379$	−22.2862	−	5.97156i	−1.14476	−	0.306738i	−0.363898	−	0.931439i	$-0.618554\pi$
$379$	−22.2862	−	5.97156i	−1.14476	−	0.306738i	−0.780865	+	0.624700i	$0.785221\pi$
$380$			13.4769i			0.691348i
$381$		0			0
$382$	0.406374	+	0.108888i	0.0207919	+	0.00557117i
$383$	−16.8662	−	16.8662i	−0.861821	−	0.861821i	0.129729	−	0.991550i	$-0.458589\pi$
$383$	−16.8662	−	16.8662i	−0.861821	−	0.861821i	−0.991550	+	0.129729i	$0.958589\pi$
$384$		0			0
$385$	−4.45313	+	1.19321i	−0.226953	+	0.0608118i
$386$	11.7687	+	6.79464i	0.599009	+	0.345838i
$387$		0			0
$388$	0.950861	−	3.54866i	0.0482726	−	0.180156i
$389$	−12.4984	+	21.6479i	−0.633694	+	1.09759i	0.353096	+	0.935587i	$0.385129\pi$
$389$	−12.4984	+	21.6479i	−0.633694	+	1.09759i	−0.986790	+	0.162004i	$0.948204\pi$
$390$		0			0
$391$	−28.1190	−	48.7035i	−1.42204	−	2.46304i
$392$	−3.08469	+	0.826542i	−0.155801	+	0.0417467i
$393$		0			0
$394$	0.801240	−	0.462596i	0.0403659	−	0.0233053i
$395$	2.31176	+	2.31176i	0.116317	+	0.116317i
$396$		0			0
$397$	20.3908	−	5.46370i	1.02338	−	0.274215i	0.292173	−	0.956366i	$-0.405622\pi$
$397$	20.3908	−	5.46370i	1.02338	−	0.274215i	0.731212	+	0.682150i	$0.238955\pi$
$398$	3.31954	+	12.3887i	0.166393	+	0.620989i
$399$		0			0
$400$	3.19629	+	1.84538i	0.159814	+	0.0922689i
$401$	−4.57548	−	17.0759i	−0.228488	−	0.852730i	−0.980977	−	0.194125i	$-0.937813\pi$
$401$	−4.57548	−	17.0759i	−0.228488	−	0.852730i	0.752488	−	0.658606i	$-0.228853\pi$
$402$		0			0
$403$	−6.69075	+	5.44093i	−0.333290	+	0.271032i
$404$			13.6438i			0.678804i
$405$		0			0
$406$	7.68385	+	13.3088i	0.381343	+	0.660506i
$407$	3.24651	+	5.62312i	0.160923	+	0.278727i
$408$		0			0
$409$	−14.7908	+	14.7908i	−0.731359	+	0.731359i	−0.970889	−	0.239530i	$-0.923007\pi$
$409$	−14.7908	+	14.7908i	−0.731359	+	0.731359i	0.239530	+	0.970889i	$0.423007\pi$
$410$	−10.8003	+	10.8003i	−0.533388	+	0.533388i
$411$		0			0
$412$	6.73592	+	11.6669i	0.331855	+	0.574789i
$413$	8.61171	+	14.9159i	0.423754	+	0.733964i
$414$		0			0
$415$		−	6.99715i		−	0.343477i
$416$	−3.55999	+	0.571370i	−0.174543	+	0.0280137i
$417$		0			0
$418$	−0.948390	−	3.53944i	−0.0463872	−	0.173120i
$419$	15.5017	+	8.94990i	0.757306	+	0.437231i	0.828328	−	0.560244i	$-0.189293\pi$
$419$	15.5017	+	8.94990i	0.757306	+	0.437231i	−0.0710214	+	0.997475i	$0.522626\pi$
$420$		0			0
$421$	−0.247286	−	0.922884i	−0.0120520	−	0.0449786i	0.959638	−	0.281238i	$-0.0907451\pi$
$421$	−0.247286	−	0.922884i	−0.0120520	−	0.0449786i	−0.971690	+	0.236260i	$0.924078\pi$
$422$	−6.61278	+	1.77189i	−0.321905	+	0.0862542i
$423$		0			0
$424$	−5.85430	−	5.85430i	−0.284310	−	0.284310i
$425$	25.7019	−	14.8390i	1.24672	−	0.719797i
$426$		0			0
$427$	−9.30808	+	2.49409i	−0.450450	+	0.120698i
$428$	9.26775	+	16.0522i	0.447974	+	0.775913i
$429$		0			0
$430$	−3.44006	+	5.95835i	−0.165894	+	0.287337i
$431$	−10.1624	+	37.9267i	−0.489507	+	1.82687i	0.0693375	+	0.997593i	$0.477911\pi$
$431$	−10.1624	+	37.9267i	−0.489507	+	1.82687i	−0.558845	+	0.829272i	$0.688755\pi$
$432$		0			0
$433$	9.53436	+	5.50467i	0.458192	+	0.264537i	0.711284	−	0.702905i	$-0.248114\pi$
$433$	9.53436	+	5.50467i	0.458192	+	0.264537i	−0.253092	+	0.967442i	$0.581447\pi$
$434$	4.50747	−	1.20777i	0.216365	−	0.0579749i
$435$		0			0
$436$	4.23071	+	4.23071i	0.202614	+	0.202614i
$437$	30.8826	+	8.27498i	1.47732	+	0.395846i
$438$		0			0
$439$		−	4.26304i		−	0.203464i	−0.994812	−	0.101732i	$-0.967562\pi$
$439$		−	4.26304i		−	0.203464i	0.994812	−	0.101732i	$-0.0324384\pi$
$440$	−2.28246	−	0.611584i	−0.108812	−	0.0291561i
$441$		0			0
$442$	−10.3343	+	27.0885i	−0.491553	+	1.28847i
$443$	−24.9846	−	14.4249i	−1.18705	−	0.685346i	−0.229419	−	0.973328i	$-0.573683\pi$
$443$	−24.9846	−	14.4249i	−1.18705	−	0.685346i	−0.957636	+	0.287981i	$0.907016\pi$
$444$		0			0
$445$	4.33492	−	7.50829i	0.205495	−	0.355927i
$446$	17.6918			0.837733
$447$		0			0
$448$	1.88454	+	0.504962i	0.0890363	+	0.0238572i
$449$	6.56424	+	24.4981i	0.309786	+	1.15614i	0.928747	+	0.370714i	$0.120887\pi$
$449$	6.56424	+	24.4981i	0.309786	+	1.15614i	−0.618961	+	0.785421i	$0.712446\pi$
$450$		0			0
$451$	2.07645	−	3.59652i	0.0977764	−	0.169354i
$452$	5.97917			0.281236
$453$		0			0
$454$	16.7719	−	9.68326i	0.787144	−	0.454458i
$455$	−18.9275	+	8.47384i	−0.887335	+	0.397260i
$456$		0			0
$457$	−20.3409	+	20.3409i	−0.951506	+	0.951506i	−0.998877	−	0.0473712i	$-0.984916\pi$
$457$	−20.3409	+	20.3409i	−0.951506	+	0.951506i	0.0473712	+	0.998877i	$0.484916\pi$
$458$	−22.4916	+	12.9855i	−1.05096	+	0.606773i
$459$		0			0
$460$	14.5789	−	14.5789i	0.679745	−	0.679745i
$461$	9.57678	−	35.7410i	0.446035	−	1.66462i	−0.267155	−	0.963654i	$-0.586083\pi$
$461$	9.57678	−	35.7410i	0.446035	−	1.66462i	0.713190	−	0.700971i	$-0.247250\pi$
$462$		0			0
$463$	0.644720	−	2.40613i	0.0299627	−	0.111822i	−0.949325	−	0.314296i	$-0.898231\pi$
$463$	0.644720	−	2.40613i	0.0299627	−	0.111822i	0.979288	+	0.202474i	$0.0648981\pi$
$464$			7.87674i			0.365669i
$465$		0			0
$466$	−8.42093	−	8.42093i	−0.390092	−	0.390092i
$467$	−31.2741			−1.44719			−0.723596	−	0.690223i	$-0.757512\pi$
$467$	−31.2741			−1.44719			−0.723596	+	0.690223i	$0.757512\pi$
$468$		0			0
$469$	−1.51482			−0.0699480
$470$	−11.1113	−	11.1113i	−0.512528	−	0.512528i
$471$		0			0
$472$			8.82789i			0.406337i
$473$	0.484165	−	1.80693i	0.0222619	−	0.0830827i
$474$		0			0
$475$	−4.36688	+	16.2974i	−0.200366	+	0.747777i
$476$	11.0934	−	11.0934i	0.508467	−	0.508467i
$477$		0			0
$478$	−8.03762	+	4.64052i	−0.367632	+	0.212253i
$479$	3.91612	−	3.91612i	0.178932	−	0.178932i	−0.611958	−	0.790890i	$-0.709618\pi$
$479$	3.91612	−	3.91612i	0.178932	−	0.178932i	0.790890	+	0.611958i	$0.209618\pi$
$480$		0			0
$481$	18.4273	+	22.6602i	0.840213	+	1.03322i
$482$	−8.48048	+	4.89621i	−0.386275	+	0.223016i
$483$		0			0
$484$	−10.3575			−0.470796
$485$	5.41526	−	9.37951i	0.245894	−	0.425902i
$486$		0			0
$487$	−0.759319	−	2.83382i	−0.0344080	−	0.128412i	0.946586	−	0.322453i	$-0.104507\pi$
$487$	−0.759319	−	2.83382i	−0.0344080	−	0.128412i	−0.980994	+	0.194040i	$0.937841\pi$
$488$	−4.77087	−	1.27835i	−0.215967	−	0.0578683i
$489$		0			0
$490$	−9.41450			−0.425304
$491$	17.8494	−	30.9160i	0.805531	−	1.39522i	−0.110400	−	0.993887i	$-0.535213\pi$
$491$	17.8494	−	30.9160i	0.805531	−	1.39522i	0.915932	−	0.401334i	$-0.131453\pi$
$492$		0			0
$493$	54.8525	+	31.6691i	2.47043	+	1.42630i
$494$	−6.73518	−	15.0440i	−0.303030	−	0.676860i
$495$		0			0
$496$	2.31031	+	0.619046i	0.103736	+	0.0277960i
$497$		−	5.19714i		−	0.233124i
$498$		0			0
$499$	−17.6124	−	4.71922i	−0.788438	−	0.211261i	−0.157936	−	0.987449i	$-0.550484\pi$
$499$	−17.6124	−	4.71922i	−0.788438	−	0.211261i	−0.630502	+	0.776188i	$0.717151\pi$
$500$	−2.72919	−	2.72919i	−0.122053	−	0.122053i
$501$		0			0
$502$	13.6281	−	3.65165i	0.608254	−	0.162981i
$503$	20.2816	+	11.7096i	0.904310	+	0.522104i	0.878596	−	0.477565i	$-0.158481\pi$
$503$	20.2816	+	11.7096i	0.904310	+	0.522104i	0.0257142	+	0.999669i	$0.491814\pi$
$504$		0			0
$505$	−10.4102	+	38.8515i	−0.463249	+	1.72887i
$506$	−2.80293	+	4.85481i	−0.124605	+	0.215823i
$507$		0			0
$508$	1.11899	+	1.93815i	0.0496473	+	0.0859917i
$509$	−3.19606	+	0.856383i	−0.141663	+	0.0379585i	−0.328954	−	0.944346i	$-0.606696\pi$
$509$	−3.19606	+	0.856383i	−0.141663	+	0.0379585i	0.187291	+	0.982305i	$0.440029\pi$
$510$		0			0
$511$	−13.5794	+	7.84007i	−0.600717	+	0.346824i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	4.94531	−	1.32509i	0.218128	−	0.0584473i
$515$	10.2790	+	38.3618i	0.452948	+	1.69042i
$516$		0			0
$517$	3.70011	+	2.13626i	0.162731	+	0.0939525i
$518$	−4.09048	−	15.2659i	−0.179725	−	0.670744i
$519$		0			0
$520$	−10.5732	−	1.08927i	−0.463667	−	0.0477676i
$521$		−	7.00178i		−	0.306754i	−0.988168	−	0.153377i	$-0.950985\pi$
$521$		−	7.00178i		−	0.306754i	0.988168	−	0.153377i	$-0.0490148\pi$
$522$		0			0
$523$	−21.4957	−	37.2316i	−0.939940	−	1.62802i	−0.765580	−	0.643341i	$-0.777548\pi$
$523$	−21.4957	−	37.2316i	−0.939940	−	1.62802i	−0.174360	−	0.984682i	$-0.555786\pi$
$524$	−4.25993	−	7.37842i	−0.186096	−	0.322328i
$525$		0			0
$526$	10.1984	−	10.1984i	0.444671	−	0.444671i
$527$	13.5997	−	13.5997i	0.592414	−	0.592414i
$528$		0			0
$529$	−12.9564	−	22.4411i	−0.563320	−	0.975698i
$530$	−12.2036	−	21.1373i	−0.530092	−	0.918146i
$531$		0			0
$532$			8.91912i			0.386693i
$533$	6.65861	−	17.4537i	0.288417	−	0.756003i
$534$		0			0
$535$	14.1426	+	52.7809i	0.611438	+	2.28192i
$536$	−0.672403	−	0.388212i	−0.0290434	−	0.0167682i
$537$		0			0
$538$	−3.09785	−	11.5613i	−0.133558	−	0.498445i
$539$	2.47254	−	0.662515i	0.106500	−	0.0285365i
$540$		0			0
$541$	8.12664	+	8.12664i	0.349391	+	0.349391i	0.859883	−	0.510491i	$-0.170536\pi$
$541$	8.12664	+	8.12664i	0.349391	+	0.349391i	−0.510491	+	0.859883i	$0.670536\pi$
$542$	20.6389	−	11.9159i	0.886518	−	0.511832i
$543$		0			0
$544$	7.76717	−	2.08121i	0.333015	−	0.0892310i
$545$	8.81916	+	15.2752i	0.377771	+	0.654319i
$546$		0			0
$547$	2.01972	−	3.49826i	0.0863570	−	0.149575i	−0.819612	−	0.572919i	$-0.805811\pi$
$547$	2.01972	−	3.49826i	0.0863570	−	0.149575i	0.905969	+	0.423345i	$0.139144\pi$
$548$	3.00821	−	11.2268i	0.128504	−	0.479585i
$549$		0			0
$550$	−2.56199	−	1.47916i	−0.109243	−	0.0630717i
$551$	−34.7816	+	9.31971i	−1.48175	+	0.397033i
$552$		0			0
$553$	1.52995	+	1.52995i	0.0650599	+	0.0650599i
$554$	−9.12230	−	2.44431i	−0.387570	−	0.103849i
$555$		0			0
$556$			22.8286i			0.968147i
$557$	−22.2275	−	5.95584i	−0.941810	−	0.252357i	−0.244926	−	0.969542i	$-0.578764\pi$
$557$	−22.2275	−	5.95584i	−0.941810	−	0.252357i	−0.696883	+	0.717185i	$0.745430\pi$
$558$		0			0
$559$	0.862329	−	8.37039i	0.0364726	−	0.354030i
$560$	4.98106	+	2.87582i	0.210488	+	0.121525i
$561$		0			0
$562$	9.75137	−	16.8899i	0.411337	−	0.712456i
$563$	−4.88910			−0.206051			−0.103025	−	0.994679i	$-0.532852\pi$
$563$	−4.88910			−0.206051			−0.103025	+	0.994679i	$0.532852\pi$
$564$		0			0
$565$	17.0260	+	4.56211i	0.716290	+	0.191929i
$566$	5.36367	+	20.0175i	0.225452	+	0.841397i
$567$		0			0
$568$	1.33190	−	2.30692i	0.0558853	−	0.0967963i
$569$	21.3664			0.895725			0.447863	−	0.894102i	$-0.352185\pi$
$569$	21.3664			0.895725			0.447863	+	0.894102i	$0.352185\pi$
$570$		0			0
$571$	−21.5820	+	12.4604i	−0.903179	+	0.521451i	−0.878230	−	0.478238i	$-0.841276\pi$
$571$	−21.5820	+	12.4604i	−0.903179	+	0.521451i	−0.0249486	+	0.999689i	$0.507942\pi$
$572$	2.85351	−	0.457981i	0.119311	−	0.0191492i
$573$		0			0
$574$	−7.14774	+	7.14774i	−0.298341	+	0.298341i
$575$	22.3541	−	12.9061i	0.932230	−	0.538223i
$576$		0			0
$577$	−4.11164	+	4.11164i	−0.171170	+	0.171170i	−0.787493	−	0.616323i	$-0.788621\pi$
$577$	−4.11164	+	4.11164i	−0.171170	+	0.171170i	0.616323	+	0.787493i	$0.288621\pi$
$578$	12.3354	−	46.0364i	0.513085	−	1.91486i
$579$		0			0
$580$	−6.00996	+	22.4295i	−0.249550	+	0.931333i
$581$		−	4.63079i		−	0.192117i
$582$		0			0
$583$	4.69252	+	4.69252i	0.194344	+	0.194344i
$584$	−8.03688			−0.332568
$585$		0			0
$586$	−19.3065			−0.797542
$587$	12.7350	+	12.7350i	0.525630	+	0.525630i	0.919266	−	0.393636i	$-0.128783\pi$
$587$	12.7350	+	12.7350i	0.525630	+	0.525630i	−0.393636	+	0.919266i	$0.628783\pi$
$588$		0			0
$589$			10.9342i			0.450535i
$590$	−6.73569	+	25.1379i	−0.277304	+	1.03491i
$591$		0			0
$592$	2.09658	−	7.82455i	0.0861690	−	0.321587i
$593$	8.08152	−	8.08152i	0.331868	−	0.331868i	−0.521427	−	0.853296i	$-0.674600\pi$
$593$	8.08152	−	8.08152i	0.331868	−	0.331868i	0.853296	+	0.521427i	$0.174600\pi$
$594$		0			0
$595$	40.0535	−	23.1249i	1.64203	−	0.948029i
$596$	−5.50303	+	5.50303i	−0.225413	+	0.225413i
$597$		0			0
$598$	−8.98821	+	23.5601i	−0.367555	+	0.963443i
$599$	0.103217	−	0.0595921i	0.00421731	−	0.00243487i	−0.497890	−	0.867240i	$-0.665892\pi$
$599$	0.103217	−	0.0595921i	0.00421731	−	0.00243487i	0.502107	+	0.864805i	$0.332558\pi$
$600$		0			0
$601$	27.0871			1.10490			0.552452	−	0.833545i	$-0.313692\pi$
$601$	27.0871			1.10490			0.552452	+	0.833545i	$0.313692\pi$
$602$	−2.27666	+	3.94330i	−0.0927899	+	0.160717i
$603$		0			0
$604$	−2.05706	−	7.67704i	−0.0837004	−	0.312374i
$605$	−29.4936	−	7.90279i	−1.19909	−	0.321294i
$606$		0			0
$607$	−18.4983			−0.750823			−0.375412	−	0.926858i	$-0.622499\pi$
$607$	−18.4983			−0.750823			−0.375412	+	0.926858i	$0.622499\pi$
$608$	−2.28576	+	3.95904i	−0.0926996	+	0.160560i
$609$		0			0
$610$	−12.6100	−	7.28036i	−0.510562	−	0.294773i
$611$	17.9564	+	6.85039i	0.726437	+	0.277137i
$612$		0			0
$613$	−21.0392	−	5.63743i	−0.849764	−	0.227694i	−0.192447	−	0.981307i	$-0.561642\pi$
$613$	−21.0392	−	5.63743i	−0.849764	−	0.227694i	−0.657317	+	0.753614i	$0.728309\pi$
$614$		−	22.0280i		−	0.888978i
$615$		0			0
$616$	−1.51056	−	0.404752i	−0.0608620	−	0.0163079i
$617$	1.85763	+	1.85763i	0.0747856	+	0.0747856i	0.743510	−	0.668725i	$-0.233159\pi$
$617$	1.85763	+	1.85763i	0.0747856	+	0.0747856i	−0.668725	+	0.743510i	$0.733159\pi$
$618$		0			0
$619$	13.7714	−	3.69004i	0.553520	−	0.148315i	0.0287923	−	0.999585i	$-0.490834\pi$
$619$	13.7714	−	3.69004i	0.553520	−	0.148315i	0.524728	+	0.851270i	$0.324167\pi$
$620$	6.10641	+	3.52554i	0.245239	+	0.141589i
$621$		0			0
$622$	2.51514	−	9.38665i	0.100848	−	0.376370i
$623$	2.86889	−	4.96907i	0.114940	−	0.199081i
$624$		0			0
$625$	−14.9160	−	25.8354i	−0.596642	−	1.03341i
$626$	5.31097	−	1.42307i	0.212269	−	0.0568773i
$627$		0			0
$628$	−3.41251	+	1.97021i	−0.136174	+	0.0786201i
$629$	−46.0595	−	46.0595i	−1.83651	−	1.83651i
$630$		0			0
$631$	34.0030	−	9.11109i	1.35364	−	0.362707i	0.492163	−	0.870503i	$-0.336206\pi$
$631$	34.0030	−	9.11109i	1.35364	−	0.362707i	0.861477	+	0.507797i	$0.169540\pi$
$632$	0.287029	+	1.07121i	0.0114174	+	0.0426103i
$633$		0			0
$634$	−0.906274	−	0.523237i	−0.0359927	−	0.0207804i
$635$	1.70759	+	6.37280i	0.0677635	+	0.252897i
$636$		0			0
$637$	10.5092	−	4.70498i	0.416391	−	0.186418i
$638$		−	6.31360i		−	0.249958i
$639$		0			0
$640$	1.47400	+	2.55305i	0.0582651	+	0.100918i
$641$	−2.90958	−	5.03954i	−0.114922	−	0.199050i	0.802827	−	0.596212i	$-0.203328\pi$
$641$	−2.90958	−	5.03954i	−0.114922	−	0.199050i	−0.917748	+	0.397162i	$0.869995\pi$
$642$		0			0
$643$	−4.20333	+	4.20333i	−0.165763	+	0.165763i	−0.785114	−	0.619351i	$-0.787396\pi$
$643$	−4.20333	+	4.20333i	−0.165763	+	0.165763i	0.619351	+	0.785114i	$0.287396\pi$
$644$	9.64846	−	9.64846i	0.380203	−	0.380203i
$645$		0			0
$646$	18.3801	+	31.8353i	0.723157	+	1.25254i
$647$	−2.47586	−	4.28832i	−0.0973362	−	0.168591i	0.813245	−	0.581921i	$-0.197699\pi$
$647$	−2.47586	−	4.28832i	−0.0973362	−	0.168591i	−0.910581	+	0.413330i	$0.864366\pi$
$648$		0			0
$649$		−	7.07600i		−	0.277757i
$650$	−12.4332	−	4.74327i	−0.487668	−	0.186046i
$651$		0			0
$652$	−5.33996	−	19.9290i	−0.209129	−	0.780480i
$653$	17.7446	+	10.2448i	0.694400	+	0.400912i	0.805258	−	0.592924i	$-0.202027\pi$
$653$	17.7446	+	10.2448i	0.694400	+	0.400912i	−0.110859	+	0.993836i	$0.535360\pi$
$654$		0			0
$655$	−6.50067	−	24.2608i	−0.254002	−	0.947949i
$656$	−5.00455	+	1.34097i	−0.195395	+	0.0523559i
$657$		0			0
$658$	−7.35360	−	7.35360i	−0.286673	−	0.286673i
$659$	4.16393	−	2.40405i	0.162204	−	0.0936484i	−0.416701	−	0.909044i	$-0.636814\pi$
$659$	4.16393	−	2.40405i	0.162204	−	0.0936484i	0.578905	+	0.815395i	$0.303480\pi$
$660$		0			0
$661$	39.4745	−	10.5772i	1.53538	−	0.411404i	0.610611	−	0.791931i	$-0.290924\pi$
$661$	39.4745	−	10.5772i	1.53538	−	0.411404i	0.924770	+	0.380527i	$0.124257\pi$
$662$	6.17265	+	10.6913i	0.239907	+	0.415531i
$663$		0			0
$664$	1.18676	−	2.05553i	0.0460552	−	0.0797699i
$665$	−6.80530	+	25.3977i	−0.263898	+	0.984881i
$666$		0			0
$667$	47.7077	+	27.5440i	1.84725	+	1.06651i
$668$	5.45101	−	1.46059i	0.210906	−	0.0565120i
$669$		0			0
$670$	−1.61850	−	1.61850i	−0.0625282	−	0.0625282i
$671$	3.82410	+	1.02466i	0.147628	+	0.0395567i
$672$		0			0
$673$		−	26.1416i		−	1.00768i	−0.863796	−	0.503842i	$-0.831919\pi$
$673$		−	26.1416i		−	1.00768i	0.863796	−	0.503842i	$-0.168081\pi$
$674$	−20.4587	−	5.48190i	−0.788040	−	0.211155i
$675$		0			0
$676$	12.3471	−	4.06814i	0.474887	−	0.156467i
$677$	34.5645	+	19.9558i	1.32842	+	0.766964i	0.985055	−	0.172238i	$-0.0551000\pi$
$677$	34.5645	+	19.9558i	1.32842	+	0.766964i	0.343365	+	0.939202i	$0.388433\pi$
$678$		0			0
$679$	3.58388	−	6.20745i	0.137537	−	0.238220i
$680$	23.7054			0.909062
$681$		0			0
$682$	−1.85183	−	0.496197i	−0.0709103	−	0.0190003i
$683$	−9.69531	−	36.1834i	−0.370981	−	1.38452i	−0.859129	−	0.511759i	$-0.828994\pi$
$683$	−9.69531	−	36.1834i	−0.370981	−	1.38452i	0.488148	−	0.872761i	$-0.337673\pi$
$684$		0			0
$685$	17.1321	−	29.6737i	0.654584	−	1.13377i
$686$	−19.8878			−0.759319
$687$		0			0
$688$	−2.02114	+	1.16691i	−0.0770554	+	0.0444880i
$689$	24.1862	+	17.4963i	0.921422	+	0.666556i
$690$		0			0
$691$	32.8832	−	32.8832i	1.25094	−	1.25094i	0.295637	−	0.955300i	$-0.404468\pi$
$691$	32.8832	−	32.8832i	1.25094	−	1.25094i	0.955300	−	0.295637i	$-0.0955319\pi$
$692$	−14.2313	+	8.21647i	−0.540994	+	0.312343i
$693$		0			0
$694$	1.77989	−	1.77989i	0.0675636	−	0.0675636i
$695$	−17.4182	+	65.0057i	−0.660711	+	2.46581i
$696$		0			0
$697$	−10.7829	+	40.2424i	−0.408433	+	1.52429i
$698$		−	17.7918i		−	0.673429i
$699$		0			0
$700$	5.09170	+	5.09170i	0.192448	+	0.192448i
$701$	27.1053			1.02375			0.511876	−	0.859059i	$-0.328951\pi$
$701$	27.1053			1.02375			0.511876	+	0.859059i	$0.328951\pi$
$702$		0			0
$703$	37.0318			1.39668
$704$	−0.566782	−	0.566782i	−0.0213614	−	0.0213614i
$705$		0			0
$706$			3.12134i			0.117473i
$707$	−6.88960	+	25.7123i	−0.259110	+	0.967012i
$708$		0			0
$709$	11.7626	−	43.8986i	0.441753	−	1.64865i	−0.282615	−	0.959233i	$-0.591202\pi$
$709$	11.7626	−	43.8986i	0.441753	−	1.64865i	0.724369	−	0.689413i	$-0.242131\pi$
$710$	5.55285	−	5.55285i	0.208395	−	0.208395i
$711$		0			0
$712$	2.54690	−	1.47046i	0.0954492	−	0.0551076i
$713$	11.8283	−	11.8283i	0.442974	−	0.442974i
$714$		0			0
$715$	8.47498	+	0.873104i	0.316946	+	0.0326522i
$716$	5.24575	−	3.02863i	0.196043	−	0.113185i
$717$		0			0
$718$	20.3106			0.757986
$719$	−10.2199	+	17.7014i	−0.381138	+	0.660150i	−0.991225	−	0.132184i	$-0.957801\pi$
$719$	−10.2199	+	17.7014i	−0.381138	+	0.660150i	0.610087	+	0.792334i	$0.291134\pi$
$720$		0			0
$721$	6.80276	+	25.3882i	0.253348	+	0.945508i
$722$	−1.83401	−	0.491422i	−0.0682548	−	0.0182888i
$723$		0			0
$724$	−12.2487			−0.455218
$725$	−14.5356	+	25.1763i	−0.539837	+	0.935026i
$726$		0			0
$727$	−25.7087	−	14.8430i	−0.953485	−	0.550495i	−0.0593229	−	0.998239i	$-0.518894\pi$
$727$	−25.7087	−	14.8430i	−0.953485	−	0.550495i	−0.894162	+	0.447744i	$0.852227\pi$
$728$	−6.99748	−	0.720889i	−0.259344	−	0.0267179i
$729$		0			0
$730$	−22.8855	−	6.13215i	−0.847030	−	0.226961i
$731$			18.7666i			0.694108i
$732$		0			0
$733$	1.64769	+	0.441496i	0.0608587	+	0.0163070i	0.289120	−	0.957293i	$-0.406637\pi$
$733$	1.64769	+	0.441496i	0.0608587	+	0.0163070i	−0.228261	+	0.973600i	$0.573304\pi$
$734$	16.4194	+	16.4194i	0.606049	+	0.606049i
$735$		0			0
$736$	6.75546	−	1.81012i	0.249009	−	0.0667219i
$737$	0.538965	+	0.311172i	0.0198530	+	0.0114622i
$738$		0			0
$739$	−12.2243	+	45.6218i	−0.449679	+	1.67822i	0.253600	+	0.967309i	$0.418385\pi$
$739$	−12.2243	+	45.6218i	−0.449679	+	1.67822i	−0.703279	+	0.710914i	$0.748281\pi$
$740$	11.9403	−	20.6812i	0.438933	−	0.760255i
$741$		0			0
$742$	−8.07649	−	13.9889i	−0.296497	−	0.513548i
$743$	31.1963	−	8.35903i	1.14448	−	0.306663i	0.363730	−	0.931504i	$-0.381503\pi$
$743$	31.1963	−	8.35903i	1.14448	−	0.306663i	0.780752	+	0.624842i	$0.214836\pi$
$744$		0			0
$745$	−19.8690	+	11.4714i	−0.727945	+	0.420279i
$746$	17.8997	+	17.8997i	0.655355	+	0.655355i
$747$		0			0
$748$	−6.22578	+	1.66819i	−0.227637	+	0.0609952i
$749$	9.35972	+	34.9309i	0.341997	+	1.27635i
$750$		0			0
$751$	31.9440	+	18.4429i	1.16565	+	0.672991i	0.952653	−	0.304061i	$-0.0983427\pi$
$751$	31.9440	+	18.4429i	1.16565	+	0.672991i	0.213002	+	0.977052i	$0.431676\pi$
$752$	−1.37959	−	5.14869i	−0.0503084	−	0.187753i
$753$		0			0
$754$	−4.50053	−	28.0411i	−0.163900	−	1.02120i
$755$		−	23.4303i		−	0.852717i
$756$		0			0
$757$	−6.73813	−	11.6708i	−0.244902	−	0.424182i	0.717202	−	0.696865i	$-0.245422\pi$
$757$	−6.73813	−	11.6708i	−0.244902	−	0.424182i	−0.962104	+	0.272683i	$0.912089\pi$
$758$	−11.5362	−	19.9812i	−0.419012	−	0.725751i
$759$		0			0
$760$	−9.52957	+	9.52957i	−0.345674	+	0.345674i
$761$	28.9718	−	28.9718i	1.05023	−	1.05023i	0.0515555	−	0.998670i	$-0.483582\pi$
$761$	28.9718	−	28.9718i	1.05023	−	1.05023i	0.998670	−	0.0515555i	$-0.0164179\pi$
$762$		0			0
$763$	5.83661	+	10.1093i	0.211299	+	0.365981i
$764$	0.210355	+	0.364345i	0.00761037	+	0.0131815i
$765$		0			0
$766$		−	23.8524i		−	0.861821i
$767$	−5.04399	−	31.4272i	−0.182128	−	1.13477i
$768$		0			0
$769$	−5.66777	−	21.1524i	−0.204385	−	0.762775i	−0.989636	−	0.143598i	$-0.954133\pi$
$769$	−5.66777	−	21.1524i	−0.204385	−	0.762775i	0.785251	−	0.619177i	$-0.212534\pi$
$770$	−3.99257	−	2.30511i	−0.143882	−	0.0830704i
$771$		0			0
$772$	3.51716	+	13.1262i	0.126586	+	0.472424i
$773$	34.2518	−	9.17773i	1.23195	−	0.330100i	0.416611	−	0.909085i	$-0.363218\pi$
$773$	34.2518	−	9.17773i	1.23195	−	0.330100i	0.815338	+	0.578985i	$0.196551\pi$
$774$		0			0
$775$	6.24205	+	6.24205i	0.224221	+	0.224221i
$776$	3.18164	−	1.83692i	0.114214	−	0.0659416i
$777$		0			0
$778$	−24.1451	+	6.46965i	−0.865643	+	0.231948i
$779$	−11.8427	−	20.5122i	−0.424309	−	0.734925i
$780$		0			0
$781$	−1.06759	+	1.84911i	−0.0382012	+	0.0661665i
$782$	14.5555	−	54.3217i	0.520502	−	1.94254i
$783$		0			0
$784$	−2.76566	−	1.59676i	−0.0987736	−	0.0570270i
$785$	−11.2206	+	3.00655i	−0.400480	+	0.107308i
$786$		0			0
$787$	−3.75885	−	3.75885i	−0.133989	−	0.133989i	0.636932	−	0.770920i	$-0.280203\pi$
$787$	−3.75885	−	3.75885i	−0.133989	−	0.133989i	−0.770920	+	0.636932i	$0.780203\pi$
$788$	0.893667	+	0.239457i	0.0318356	+	0.00853032i
$789$		0			0
$790$			3.26932i			0.116317i
$791$	11.2680	+	3.01925i	0.400644	+	0.107352i
$792$		0			0
$793$	17.7147	+	1.82499i	0.629067	+	0.0648073i
$794$	18.2819	+	10.5551i	0.648800	+	0.374585i
$795$		0			0
$796$	−6.41286	+	11.1074i	−0.227298	+	0.393691i
$797$	5.11254			0.181096			0.0905478	−	0.995892i	$-0.471138\pi$
$797$	5.11254			0.181096			0.0905478	+	0.995892i	$0.471138\pi$
$798$		0			0
$799$	−41.4015	−	11.0935i	−1.46468	−	0.392459i
$800$	0.955238	+	3.56500i	0.0337728	+	0.126042i
$801$		0			0
$802$	8.83914	−	15.3098i	0.312121	−	0.540609i
$803$	6.44196			0.227332
$804$		0			0
$805$	34.8363	−	20.1128i	1.22782	−	0.708882i
$806$	−8.57839	−	0.883757i	−0.302161	−	0.0311290i
$807$		0			0
$808$	−9.64762	+	9.64762i	−0.339402	+	0.339402i
$809$	−12.6443	+	7.30018i	−0.444549	+	0.256661i	−0.705525	−	0.708685i	$-0.749289\pi$
$809$	−12.6443	+	7.30018i	−0.444549	+	0.256661i	0.260976	+	0.965345i	$0.415956\pi$
$810$		0			0
$811$	−20.1306	+	20.1306i	−0.706880	+	0.706880i	−0.965878	−	0.258998i	$-0.916608\pi$
$811$	−20.1306	+	20.1306i	−0.706880	+	0.706880i	0.258998	+	0.965878i	$0.416608\pi$
$812$	−3.97745	+	14.8441i	−0.139581	+	0.520924i
$813$		0			0
$814$	−1.68052	+	6.27177i	−0.0589021	+	0.219825i
$815$		−	60.8234i		−	2.13055i
$816$		0			0
$817$	−7.54417	−	7.54417i	−0.263937	−	0.263937i
$818$	−20.9174			−0.731359
$819$		0			0
$820$	−15.2739			−0.533388
$821$	−3.57165	−	3.57165i	−0.124651	−	0.124651i	0.642029	−	0.766680i	$-0.278093\pi$
$821$	−3.57165	−	3.57165i	−0.124651	−	0.124651i	−0.766680	+	0.642029i	$0.778093\pi$
$822$		0			0
$823$		−	44.2701i		−	1.54316i	−0.636133	−	0.771579i	$-0.719467\pi$
$823$		−	44.2701i		−	1.54316i	0.636133	−	0.771579i	$-0.280533\pi$
$824$	−3.48677	+	13.0128i	−0.121467	+	0.453322i
$825$		0			0
$826$	−4.45775	+	16.6365i	−0.155105	+	0.578859i
$827$	−14.3305	+	14.3305i	−0.498320	+	0.498320i	−0.910915	−	0.412595i	$-0.864623\pi$
$827$	−14.3305	+	14.3305i	−0.498320	+	0.498320i	0.412595	+	0.910915i	$0.364623\pi$
$828$		0			0
$829$	18.5330	−	10.7000i	0.643677	−	0.371627i	−0.142352	−	0.989816i	$-0.545467\pi$
$829$	18.5330	−	10.7000i	0.643677	−	0.371627i	0.786030	+	0.618189i	$0.212133\pi$
$830$	4.94773	−	4.94773i	0.171738	−	0.171738i
$831$		0			0
$832$	−2.92131	−	2.11327i	−0.101278	−	0.0732646i
$833$	−22.2391	+	12.8398i	−0.770541	+	0.444872i
$834$		0			0
$835$	16.6365			0.575729
$836$	1.83215	−	3.17337i	0.0633662	−	0.109753i
$837$		0			0
$838$	4.63281	+	17.2899i	0.160038	+	0.597269i
$839$	−47.0116	−	12.5967i	−1.62302	−	0.434887i	−0.671132	−	0.741337i	$-0.734192\pi$
$839$	−47.0116	−	12.5967i	−1.62302	−	0.434887i	−0.951886	+	0.306451i	$0.900858\pi$
$840$		0			0
$841$	−33.0430			−1.13942
$842$	0.477720	−	0.827435i	0.0164633	−	0.0285153i
$843$		0			0
$844$	−5.92886	−	3.42303i	−0.204080	−	0.117825i
$845$	38.2630	−	2.16344i	1.31629	−	0.0744246i
$846$		0			0
$847$	−19.5192	−	5.23015i	−0.670687	−	0.179710i
$848$		−	8.27924i		−	0.284310i
$849$		0			0
$850$	28.6667	+	7.68123i	0.983261	+	0.263464i
$851$	−40.0600	−	40.0600i	−1.37324	−	1.37324i
$852$		0			0
$853$	1.60592	−	0.430304i	0.0549855	−	0.0147333i	−0.231221	−	0.972901i	$-0.574272\pi$
$853$	1.60592	−	0.430304i	0.0549855	−	0.0147333i	0.286207	+	0.958168i	$0.407606\pi$
$854$	−8.34540	−	4.81822i	−0.285574	−	0.164876i
$855$		0			0
$856$	−4.79734	+	17.9039i	−0.163970	+	0.611943i
$857$	6.29501	−	10.9033i	0.215033	−	0.372449i	−0.738249	−	0.674528i	$-0.764347\pi$
$857$	6.29501	−	10.9033i	0.215033	−	0.372449i	0.953283	+	0.302079i	$0.0976806\pi$
$858$		0			0
$859$	11.6155	+	20.1186i	0.396315	+	0.686438i	0.993268	−	0.115838i	$-0.0369554\pi$
$859$	11.6155	+	20.1186i	0.396315	+	0.686438i	−0.596953	+	0.802276i	$0.703622\pi$
$860$	−6.64568	+	1.78070i	−0.226616	+	0.0607215i
$861$		0			0
$862$	−34.0042	+	19.6323i	−1.15819	+	0.668679i
$863$	21.8752	+	21.8752i	0.744642	+	0.744642i	0.973467	−	0.228826i	$-0.0734885\pi$
$863$	21.8752	+	21.8752i	0.744642	+	0.744642i	−0.228826	+	0.973467i	$0.573489\pi$
$864$		0			0
$865$	−46.7937	+	12.5383i	−1.59103	+	0.426316i
$866$	2.84942	+	10.6342i	0.0968274	+	0.361365i
$867$		0			0
$868$	4.04129	+	2.33324i	0.137170	+	0.0791952i
$869$	−0.230068	−	0.858625i	−0.00780452	−	0.0291269i
$870$		0			0
$871$	2.61556	+	0.997842i	0.0886250	+	0.0338106i
$872$			5.98313i			0.202614i
$873$		0			0
$874$	15.9860	+	27.6886i	0.540735	+	0.936581i
$875$	−3.76514	−	6.52142i	−0.127285	−	0.220464i
$876$		0			0
$877$	18.9208	−	18.9208i	0.638911	−	0.638911i	−0.311376	−	0.950287i	$-0.600790\pi$
$877$	18.9208	−	18.9208i	0.638911	−	0.638911i	0.950287	+	0.311376i	$0.100790\pi$
$878$	3.01442	−	3.01442i	0.101732	−	0.101732i
$879$		0			0
$880$	−1.18149	−	2.04640i	−0.0398280	−	0.0689841i
$881$	11.3559	+	19.6690i	0.382589	+	0.662664i	0.991432	−	0.130627i	$-0.0416990\pi$
$881$	11.3559	+	19.6690i	0.382589	+	0.662664i	−0.608842	+	0.793291i	$0.708366\pi$
$882$		0			0
$883$			11.3387i			0.381577i	0.981631	+	0.190789i	$0.0611045\pi$
$883$			11.3387i			0.381577i	−0.981631	+	0.190789i	$0.938895\pi$
$884$	−26.4619	+	11.8470i	−0.890011	+	0.398458i
$885$		0			0
$886$	−7.46686	−	27.8667i	−0.250854	−	0.936201i
$887$	−15.5009	−	8.94943i	−0.520468	−	0.300492i	0.216658	−	0.976248i	$-0.430484\pi$
$887$	−15.5009	−	8.94943i	−0.520468	−	0.300492i	−0.737126	+	0.675755i	$0.763818\pi$
$888$		0			0
$889$	1.13010	+	4.21758i	0.0379023	+	0.141453i
$890$	8.37441	−	2.24392i	0.280711	−	0.0752163i
$891$		0			0
$892$	12.5100	+	12.5100i	0.418866	+	0.418866i
$893$	21.1030	−	12.1838i	0.706183	−	0.407715i
$894$		0			0
$895$	17.2484	−	4.62170i	0.576551	−	0.154486i
$896$	0.975511	+	1.68964i	0.0325895	+	0.0564467i
$897$		0			0
$898$	−12.6811	+	21.9644i	−0.423175	+	0.732961i
$899$	−4.87606	+	18.1977i	−0.162626	+	0.606928i
$900$		0			0
$901$	−57.6554	−	33.2874i	−1.92078	−	1.10896i
$902$	4.01140	−	1.07485i	0.133565	−	0.0357886i
$903$		0			0
$904$	4.22791	+	4.22791i	0.140618	+	0.140618i
$905$	−34.8788	−	9.34574i	−1.15941	−	0.310663i
$906$		0			0
$907$			49.0395i			1.62833i	0.580634	+	0.814165i	$0.302805\pi$
$907$			49.0395i			1.62833i	−0.580634	+	0.814165i	$0.697195\pi$
$908$	18.7066	+	5.01242i	0.620801	+	0.166343i
$909$		0			0
$910$	−19.3757	−	7.39185i	−0.642298	−	0.245038i
$911$	49.7924	+	28.7477i	1.64970	+	0.952453i	0.977191	+	0.212362i	$0.0681155\pi$
$911$	49.7924	+	28.7477i	1.64970	+	0.952453i	0.672506	+	0.740092i	$0.265218\pi$
$912$		0			0
$913$	−0.951247	+	1.64761i	−0.0314817	+	0.0545279i
$914$	−28.7663			−0.951506
$915$		0			0
$916$	−25.0861	−	6.72179i	−0.828867	−	0.222094i
$917$	−4.30221	−	16.0561i	−0.142071	−	0.530218i
$918$		0			0
$919$	−18.6828	+	32.3595i	−0.616288	+	1.06744i	0.373869	+	0.927482i	$0.378031\pi$
$919$	−18.6828	+	32.3595i	−0.616288	+	1.06744i	−0.990157	+	0.139961i	$0.955302\pi$
$920$	20.6177			0.679745
$921$		0			0
$922$	32.0445	−	18.5009i	1.05533	−	0.609295i
$923$	−3.42345	+	8.97363i	−0.112684	+	0.295371i
$924$		0			0
$925$	21.1405	−	21.1405i	0.695096	−	0.695096i
$926$	2.15728	−	1.24550i	0.0708925	−	0.0409298i
$927$		0			0
$928$	−5.56970	+	5.56970i	−0.182834	+	0.182834i
$929$	−4.88234	+	18.2212i	−0.160185	+	0.597817i	0.838421	+	0.545023i	$0.183479\pi$
$929$	−4.88234	+	18.2212i	−0.160185	+	0.597817i	−0.998605	+	0.0527935i	$0.983187\pi$
$930$		0			0
$931$	3.77854	−	14.1017i	0.123837	−	0.462165i
$932$		−	11.9090i		−	0.390092i
$933$		0			0
$934$	−22.1141	−	22.1141i	−0.723596	−	0.723596i
$935$	−19.0011			−0.621402
$936$		0			0
$937$	38.9992			1.27405			0.637025	−	0.770843i	$-0.280165\pi$
$937$	38.9992			1.27405			0.637025	+	0.770843i	$0.280165\pi$
$938$	−1.07114	−	1.07114i	−0.0349740	−	0.0349740i
$939$		0			0
$940$		−	15.7138i		−	0.512528i
$941$	14.1514	−	52.8136i	0.461321	−	1.72167i	−0.207485	−	0.978238i	$-0.566528\pi$
$941$	14.1514	−	52.8136i	0.461321	−	1.72167i	0.668806	−	0.743437i	$-0.266805\pi$
$942$		0			0
$943$	−9.37840	+	35.0007i	−0.305403	+	1.13978i
$944$	−6.24226	+	6.24226i	−0.203168	+	0.203168i
$945$		0			0
$946$	1.62005	−	0.935336i	0.0526723	−	0.0304104i
$947$	1.12052	−	1.12052i	0.0364120	−	0.0364120i	−0.688666	−	0.725078i	$-0.741804\pi$
$947$	1.12052	−	1.12052i	0.0364120	−	0.0364120i	0.725078	+	0.688666i	$0.241804\pi$
$948$		0			0
$949$	28.6112	−	4.59203i	0.928760	−	0.149064i
$950$	−14.6119	+	8.43617i	−0.474072	+	0.273705i
$951$		0			0
$952$	15.6885			0.508467
$953$	10.7911	−	18.6908i	0.349559	−	0.605454i	−0.636612	−	0.771184i	$-0.719665\pi$
$953$	10.7911	−	18.6908i	0.349559	−	0.605454i	0.986171	+	0.165730i	$0.0529981\pi$
$954$		0			0
$955$	0.321002	+	1.19799i	0.0103874	+	0.0387662i
$956$	−8.96480	−	2.40211i	−0.289942	−	0.0776898i
$957$		0			0
$958$	5.53822			0.178932
$959$	11.3382	−	19.6383i	0.366130	−	0.634155i
$960$		0			0
$961$	−21.8925	−	12.6396i	−0.706209	−	0.407730i
$962$	−2.99310	+	29.0532i	−0.0965015	+	0.936714i
$963$		0			0
$964$	−9.45875	−	2.53446i	−0.304646	−	0.0816296i
$965$			40.0613i			1.28962i
$966$		0			0
$967$	−46.7947	−	12.5386i	−1.50482	−	0.403215i	−0.590107	−	0.807325i	$-0.700915\pi$
$967$	−46.7947	−	12.5386i	−1.50482	−	0.403215i	−0.914710	+	0.404110i	$0.867581\pi$
$968$	−7.32387	−	7.32387i	−0.235398	−	0.235398i
$969$		0			0
$970$	10.4615	−	2.80315i	0.335898	−	0.0900036i
$971$	1.30561	+	0.753792i	0.0418989	+	0.0241903i	0.520803	−	0.853677i	$-0.325633\pi$
$971$	1.30561	+	0.753792i	0.0418989	+	0.0241903i	−0.478904	+	0.877867i	$0.658966\pi$
$972$		0			0
$973$	−11.5276	+	43.0214i	−0.369557	+	1.37920i
$974$	1.46689	−	2.54073i	0.0470022	−	0.0814102i
$975$		0			0
$976$	−2.46959	−	4.27745i	−0.0790495	−	0.136918i
$977$	−30.4352	+	8.15508i	−0.973708	+	0.260904i	−0.710393	−	0.703806i	$-0.751483\pi$
$977$	−30.4352	+	8.15508i	−0.973708	+	0.260904i	−0.263315	+	0.964710i	$0.584816\pi$
$978$		0			0
$979$	−2.04147	+	1.17864i	−0.0652457	+	0.0376696i
$980$	−6.65706	−	6.65706i	−0.212652	−	0.212652i
$981$		0			0
$982$	34.4824	−	9.23952i	1.10038	−	0.294845i
$983$	3.72607	+	13.9059i	0.118843	+	0.443529i	0.999546	−	0.0301410i	$-0.00959563\pi$
$983$	3.72607	+	13.9059i	0.118843	+	0.443529i	−0.880702	+	0.473670i	$0.842929\pi$
$984$		0			0
$985$	2.36206	+	1.36374i	0.0752616	+	0.0434523i
$986$	16.3931	+	61.1800i	0.522064	+	1.94837i
$987$		0			0
$988$	5.87519	−	15.4002i	0.186915	−	0.489945i
$989$			16.3222i			0.519014i
$990$		0			0
$991$	9.55307	+	16.5464i	0.303463	+	0.525614i	0.976918	−	0.213615i	$-0.0685236\pi$
$991$	9.55307	+	16.5464i	0.303463	+	0.525614i	−0.673455	+	0.739229i	$0.735190\pi$
$992$	1.19590	+	2.07137i	0.0379700	+	0.0657660i
$993$		0			0
$994$	3.67493	−	3.67493i	0.116562	−	0.116562i
$995$	−26.7359	+	26.7359i	−0.847586	+	0.847586i
$996$		0			0
$997$	−2.47501	−	4.28685i	−0.0783845	−	0.135766i	0.824169	−	0.566345i	$-0.191643\pi$
$997$	−2.47501	−	4.28685i	−0.0783845	−	0.135766i	−0.902553	+	0.430579i	$0.858310\pi$
$998$	−9.11683	−	15.7908i	−0.288588	−	0.499850i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.197.9		56
3.2	odd	2		234.2.y.a.119.1	yes	56
9.4	even	3		234.2.z.a.41.6	yes	56
9.5	odd	6		702.2.bc.a.665.9		56
13.7	odd	12		702.2.bc.a.683.9		56
39.20	even	12		234.2.z.a.137.6	yes	56
117.59	even	12	inner	702.2.bb.a.449.9		56
117.85	odd	12		234.2.y.a.59.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.1	✓	56	117.85	odd	12
234.2.y.a.119.1	yes	56	3.2	odd	2
234.2.z.a.41.6	yes	56	9.4	even	3
234.2.z.a.137.6	yes	56	39.20	even	12
702.2.bb.a.197.9		56	1.1	even	1	trivial
702.2.bb.a.449.9		56	117.59	even	12	inner
702.2.bc.a.665.9		56	9.5	odd	6
702.2.bc.a.683.9		56	13.7	odd	12

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.763001 + 2.84756i) q^{5} +(-0.504962 + 1.88454i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.55305 + 1.47400i) q^{10} +(0.566782 - 0.566782i) q^{11} +(2.11327 - 2.92131i) q^{13} +(-1.68964 + 0.975511i) q^{14} -1.00000 q^{16} +(-4.02058 + 6.96385i) q^{17} +(-1.18319 - 4.41574i) q^{19} +(-2.84756 - 0.763001i) q^{20} +0.801550 q^{22} +(-3.49688 + 6.05678i) q^{23} +(-3.19629 - 1.84538i) q^{25} +(3.55999 - 0.571370i) q^{26} +(-1.88454 - 0.504962i) q^{28} -7.87674i q^{29} +(-2.31031 - 0.619046i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.76717 + 2.08121i) q^{34} +(-4.98106 - 2.87582i) q^{35} +(-2.09658 + 7.82455i) q^{37} +(2.28576 - 3.95904i) q^{38} +(-1.47400 - 2.55305i) q^{40} +(5.00455 - 1.34097i) q^{41} +(2.02114 - 1.16691i) q^{43} +(0.566782 + 0.566782i) q^{44} +(-6.75546 + 1.81012i) q^{46} +(1.37959 + 5.14869i) q^{47} +(2.76566 + 1.59676i) q^{49} +(-0.955238 - 3.56500i) q^{50} +(2.92131 + 2.11327i) q^{52} +8.27924i q^{53} +(1.18149 + 2.04640i) q^{55} +(-0.975511 - 1.68964i) q^{56} +(5.56970 - 5.56970i) q^{58} +(6.24226 - 6.24226i) q^{59} +(2.46959 + 4.27745i) q^{61} +(-1.19590 - 2.07137i) q^{62} -1.00000i q^{64} +(6.70618 + 8.24664i) q^{65} +(0.200953 + 0.749969i) q^{67} +(-6.96385 - 4.02058i) q^{68} +(-1.48863 - 5.55565i) q^{70} +(-2.57304 + 0.689443i) q^{71} +(5.68293 + 5.68293i) q^{73} +(-7.01530 + 4.05028i) q^{74} +(4.41574 - 1.18319i) q^{76} +(0.781921 + 1.35433i) q^{77} +(0.554497 - 0.960416i) q^{79} +(0.763001 - 2.84756i) q^{80} +(4.48696 + 2.59055i) q^{82} +(-2.29264 + 0.614312i) q^{83} +(-16.7623 - 16.7623i) q^{85} +(2.25429 + 0.604036i) q^{86} +0.801550i q^{88} +(-2.84070 - 0.761164i) q^{89} +(4.43822 + 5.45771i) q^{91} +(-6.05678 - 3.49688i) q^{92} +(-2.66516 + 4.61619i) q^{94} +13.4769 q^{95} +(-3.54866 - 0.950861i) q^{97} +(0.826542 + 3.08469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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