LMFDB - Embedded newform 936.2.w.k.307.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(307,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.23
Character	$\chi$	$=$	936.307
Dual form			936.2.w.k.811.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38609 + 0.280631i) q^{2} +(1.84249 + 0.777959i) q^{4} +(1.86097 - 1.86097i) q^{5} +(1.43671 + 1.43671i) q^{7} +(2.33554 + 1.59538i) q^{8} +(3.10171 - 2.05722i) q^{10} +(1.79579 - 1.79579i) q^{11} +(-1.73435 + 3.16102i) q^{13} +(1.58823 + 2.39460i) q^{14} +(2.78956 + 2.86677i) q^{16} +0.690579i q^{17} +(-4.78545 - 4.78545i) q^{19} +(4.87658 - 1.98106i) q^{20} +(2.99308 - 1.98517i) q^{22} -2.64723 q^{23} -1.92640i q^{25} +(-3.29105 + 3.89474i) q^{26} +(1.52943 + 3.76484i) q^{28} -1.62313i q^{29} +(-0.151569 + 0.151569i) q^{31} +(3.06208 + 4.75644i) q^{32} +(-0.193798 + 0.957205i) q^{34} +5.34736 q^{35} +(-2.07147 - 2.07147i) q^{37} +(-5.29012 - 7.97600i) q^{38} +(7.31532 - 1.37741i) q^{40} +(4.35600 + 4.35600i) q^{41} -4.88935i q^{43} +(4.70577 - 1.91168i) q^{44} +(-3.66929 - 0.742893i) q^{46} +(-0.307890 - 0.307890i) q^{47} -2.87170i q^{49} +(0.540607 - 2.67016i) q^{50} +(-5.65468 + 4.47489i) q^{52} +8.52080i q^{53} -6.68380i q^{55} +(1.06340 + 5.64761i) q^{56} +(0.455500 - 2.24980i) q^{58} +(4.50238 - 4.50238i) q^{59} +7.02830i q^{61} +(-0.252623 + 0.167553i) q^{62} +(2.90951 + 7.45216i) q^{64} +(2.65497 + 9.11012i) q^{65} +(-6.08794 - 6.08794i) q^{67} +(-0.537242 + 1.27239i) q^{68} +(7.41192 + 1.50063i) q^{70} +(-4.50930 + 4.50930i) q^{71} +(-5.83515 + 5.83515i) q^{73} +(-2.28992 - 3.45256i) q^{74} +(-5.09427 - 12.5400i) q^{76} +5.16007 q^{77} +8.26392i q^{79} +(10.5262 + 0.143686i) q^{80} +(4.81539 + 7.26024i) q^{82} +(-8.80676 - 8.80676i) q^{83} +(1.28515 + 1.28515i) q^{85} +(1.37210 - 6.77709i) q^{86} +(7.05910 - 1.32917i) q^{88} +(7.46873 - 7.46873i) q^{89} +(-7.03325 + 2.04970i) q^{91} +(-4.87749 - 2.05943i) q^{92} +(-0.340360 - 0.513166i) q^{94} -17.8111 q^{95} +(-13.8363 - 13.8363i) q^{97} +(0.805889 - 3.98044i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 40 q^{16} - 8 q^{19} - 32 q^{22} + 24 q^{28} + 8 q^{34} + 16 q^{40} - 8 q^{46} + 24 q^{52} - 24 q^{58} + 40 q^{67} - 24 q^{70} + 56 q^{76} + 104 q^{91} - 64 q^{94} - 32 q^{97}+O(q^{100}) $ 48 * q - 40 * q^16 - 8 * q^19 - 32 * q^22 + 24 * q^28 + 8 * q^34 + 16 * q^40 - 8 * q^46 + 24 * q^52 - 24 * q^58 + 40 * q^67 - 24 * q^70 + 56 * q^76 + 104 * q^91 - 64 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.38609	+	0.280631i	0.980114	+	0.198436i
$2$	1.38609	+	0.280631i	0.980114	+	0.198436i
$3$		0			0
$3$		0			0
$4$	1.84249	+	0.777959i	0.921246	+	0.388980i
$5$	1.86097	−	1.86097i	0.832250	−	0.832250i	−0.155574	−	0.987824i	$-0.549723\pi$
$5$	1.86097	−	1.86097i	0.832250	−	0.832250i	0.987824	+	0.155574i	$0.0497228\pi$
$6$		0			0
$7$	1.43671	+	1.43671i	0.543027	+	0.543027i	0.924415	−	0.381388i	$-0.124554\pi$
$7$	1.43671	+	1.43671i	0.543027	+	0.543027i	−0.381388	+	0.924415i	$0.624554\pi$
$8$	2.33554	+	1.59538i	0.825739	+	0.564053i
$9$		0			0
$10$	3.10171	−	2.05722i	0.980848	−	0.650551i
$11$	1.79579	−	1.79579i	0.541450	−	0.541450i	−0.382504	−	0.923954i	$-0.624938\pi$
$11$	1.79579	−	1.79579i	0.541450	−	0.541450i	0.923954	+	0.382504i	$0.124938\pi$
$12$		0			0
$13$	−1.73435	+	3.16102i	−0.481023	+	0.876708i
$13$	−1.73435	+	3.16102i	−0.481023	+	0.876708i
$14$	1.58823	+	2.39460i	0.424472	+	0.639984i
$15$		0			0
$16$	2.78956	+	2.86677i	0.697390	+	0.716692i
$17$			0.690579i			0.167490i	0.996487	+	0.0837450i	$0.0266881\pi$
$17$			0.690579i			0.167490i	−0.996487	+	0.0837450i	$0.973312\pi$
$18$		0			0
$19$	−4.78545	−	4.78545i	−1.09786	−	1.09786i	−0.994661	−	0.103195i	$-0.967093\pi$
$19$	−4.78545	−	4.78545i	−1.09786	−	1.09786i	−0.103195	−	0.994661i	$-0.532907\pi$
$20$	4.87658	−	1.98106i	1.09044	−	0.442979i
$21$		0			0
$22$	2.99308	−	1.98517i	0.638126	−	0.423240i
$23$	−2.64723			−0.551985			−0.275992	−	0.961160i	$-0.589006\pi$
$23$	−2.64723			−0.551985			−0.275992	+	0.961160i	$0.589006\pi$
$24$		0			0
$25$		−	1.92640i		−	0.385280i
$26$	−3.29105	+	3.89474i	−0.645428	+	0.763821i
$27$		0			0
$28$	1.52943	+	3.76484i	0.289035	+	0.711488i
$29$		−	1.62313i		−	0.301407i	−0.988579	−	0.150704i	$-0.951846\pi$
$29$		−	1.62313i		−	0.301407i	0.988579	−	0.150704i	$-0.0481539\pi$
$30$		0			0
$31$	−0.151569	+	0.151569i	−0.0272226	+	0.0272226i	−0.720587	−	0.693364i	$-0.756128\pi$
$31$	−0.151569	+	0.151569i	−0.0272226	+	0.0272226i	0.693364	+	0.720587i	$0.256128\pi$
$32$	3.06208	+	4.75644i	0.541304	+	0.840827i
$33$		0			0
$34$	−0.193798	+	0.957205i	−0.0332360	+	0.164159i
$35$	5.34736			0.903868
$36$		0			0
$37$	−2.07147	−	2.07147i	−0.340547	−	0.340547i	0.516026	−	0.856573i	$-0.327411\pi$
$37$	−2.07147	−	2.07147i	−0.340547	−	0.340547i	−0.856573	+	0.516026i	$0.827411\pi$
$38$	−5.29012	−	7.97600i	−0.858170	−	1.29388i
$39$		0			0
$40$	7.31532	−	1.37741i	1.15665	−	0.217788i
$41$	4.35600	+	4.35600i	0.680294	+	0.680294i	0.960066	−	0.279773i	$-0.0902591\pi$
$41$	4.35600	+	4.35600i	0.680294	+	0.680294i	−0.279773	+	0.960066i	$0.590259\pi$
$42$		0			0
$43$		−	4.88935i		−	0.745620i	−0.927908	−	0.372810i	$-0.878394\pi$
$43$		−	4.88935i		−	0.745620i	0.927908	−	0.372810i	$-0.121606\pi$
$44$	4.70577	−	1.91168i	0.709422	−	0.288196i
$45$		0			0
$46$	−3.66929	−	0.742893i	−0.541008	−	0.109534i
$47$	−0.307890	−	0.307890i	−0.0449103	−	0.0449103i	0.684295	−	0.729205i	$-0.260110\pi$
$47$	−0.307890	−	0.307890i	−0.0449103	−	0.0449103i	−0.729205	+	0.684295i	$0.760110\pi$
$48$		0			0
$49$		−	2.87170i		−	0.410243i
$50$	0.540607	−	2.67016i	0.0764534	−	0.377618i
$51$		0			0
$52$	−5.65468	+	4.47489i	−0.784162	+	0.620556i
$53$			8.52080i			1.17042i	0.810881	+	0.585211i	$0.198988\pi$
$53$			8.52080i			1.17042i	−0.810881	+	0.585211i	$0.801012\pi$
$54$		0			0
$55$		−	6.68380i		−	0.901244i
$56$	1.06340	+	5.64761i	0.142103	+	0.754694i
$57$		0			0
$58$	0.455500	−	2.24980i	0.0598100	−	0.295413i
$59$	4.50238	−	4.50238i	0.586160	−	0.586160i	−0.350429	−	0.936589i	$-0.613964\pi$
$59$	4.50238	−	4.50238i	0.586160	−	0.586160i	0.936589	+	0.350429i	$0.113964\pi$
$60$		0			0
$61$			7.02830i			0.899882i	0.893058	+	0.449941i	$0.148555\pi$
$61$			7.02830i			0.899882i	−0.893058	+	0.449941i	$0.851445\pi$
$62$	−0.252623	+	0.167553i	−0.0320832	+	0.0212793i
$63$		0			0
$64$	2.90951	+	7.45216i	0.363689	+	0.931520i
$65$	2.65497	+	9.11012i	0.329309	+	1.12997i
$66$		0			0
$67$	−6.08794	−	6.08794i	−0.743761	−	0.743761i	0.229539	−	0.973299i	$-0.426278\pi$
$67$	−6.08794	−	6.08794i	−0.743761	−	0.743761i	−0.973299	+	0.229539i	$0.926278\pi$
$68$	−0.537242	+	1.27239i	−0.0651502	+	0.154300i
$69$		0			0
$70$	7.41192	+	1.50063i	0.885894	+	0.179360i
$71$	−4.50930	+	4.50930i	−0.535156	+	0.535156i	−0.922102	−	0.386946i	$-0.873530\pi$
$71$	−4.50930	+	4.50930i	−0.535156	+	0.535156i	0.386946	+	0.922102i	$0.373530\pi$
$72$		0			0
$73$	−5.83515	+	5.83515i	−0.682953	+	0.682953i	−0.960664	−	0.277712i	$-0.910424\pi$
$73$	−5.83515	+	5.83515i	−0.682953	+	0.682953i	0.277712	+	0.960664i	$0.410424\pi$
$74$	−2.28992	−	3.45256i	−0.266198	−	0.401351i
$75$		0			0
$76$	−5.09427	−	12.5400i	−0.584352	−	1.43844i
$77$	5.16007			0.588044
$78$		0			0
$79$			8.26392i			0.929764i	0.885373	+	0.464882i	$0.153903\pi$
$79$			8.26392i			0.929764i	−0.885373	+	0.464882i	$0.846097\pi$
$80$	10.5262	+	0.143686i	1.17687	+	0.0160646i
$81$		0			0
$82$	4.81539	+	7.26024i	0.531770	+	0.801760i
$83$	−8.80676	−	8.80676i	−0.966668	−	0.966668i	0.0327944	−	0.999462i	$-0.489559\pi$
$83$	−8.80676	−	8.80676i	−0.966668	−	0.966668i	−0.999462	+	0.0327944i	$0.989559\pi$
$84$		0			0
$85$	1.28515	+	1.28515i	0.139394	+	0.139394i
$86$	1.37210	−	6.77709i	0.147958	−	0.730792i
$87$		0			0
$88$	7.05910	−	1.32917i	0.752503	−	0.141690i
$89$	7.46873	−	7.46873i	0.791684	−	0.791684i	−0.190084	−	0.981768i	$-0.560876\pi$
$89$	7.46873	−	7.46873i	0.791684	−	0.791684i	0.981768	+	0.190084i	$0.0608760\pi$
$90$		0			0
$91$	−7.03325	+	2.04970i	−0.737285	+	0.214867i
$92$	−4.87749	−	2.05943i	−0.508514	−	0.214711i
$93$		0			0
$94$	−0.340360	−	0.513166i	−0.0351054	−	0.0529291i
$95$	−17.8111			−1.82738
$96$		0			0
$97$	−13.8363	−	13.8363i	−1.40487	−	1.40487i	−0.783592	−	0.621276i	$-0.786615\pi$
$97$	−13.8363	−	13.8363i	−1.40487	−	1.40487i	−0.621276	−	0.783592i	$-0.713385\pi$
$98$	0.805889	−	3.98044i	0.0814071	−	0.402085i
$99$		0			0
$100$	1.49866	−	3.54938i	0.149866	−	0.354938i
$101$	17.5372			1.74502			0.872508	−	0.488601i	$-0.162492\pi$
$101$	17.5372			1.74502			0.872508	+	0.488601i	$0.162492\pi$
$102$		0			0
$103$	−9.29992			−0.916348			−0.458174	−	0.888862i	$-0.651496\pi$
$103$	−9.29992			−0.916348			−0.458174	+	0.888862i	$0.651496\pi$
$104$	−9.09368	+	4.61573i	−0.891709	+	0.452609i
$105$		0			0
$106$	−2.39120	+	11.8106i	−0.232254	+	1.14715i
$107$	11.2640			1.08893			0.544467	−	0.838782i	$-0.316732\pi$
$107$	11.2640			1.08893			0.544467	+	0.838782i	$0.316732\pi$
$108$		0			0
$109$	−3.99325	+	3.99325i	−0.382484	+	0.382484i	−0.871996	−	0.489512i	$-0.837175\pi$
$109$	−3.99325	+	3.99325i	−0.382484	+	0.382484i	0.489512	+	0.871996i	$0.337175\pi$
$110$	1.87568	−	9.26435i	0.178839	−	0.883322i
$111$		0			0
$112$	−0.110929	+	8.12653i	−0.0104818	+	0.767885i
$113$	2.60824			0.245363			0.122681	−	0.992446i	$-0.460851\pi$
$113$	2.60824			0.245363			0.122681	+	0.992446i	$0.460851\pi$
$114$		0			0
$115$	−4.92640	+	4.92640i	−0.459389	+	0.459389i
$116$	1.26273	−	2.99060i	0.117241	−	0.277670i
$117$		0			0
$118$	7.50422	−	4.97720i	0.690819	−	0.458188i
$119$	−0.992165	+	0.992165i	−0.0909516	+	0.0909516i
$120$		0			0
$121$			4.55030i			0.413663i
$122$	−1.97236	+	9.74186i	−0.178569	+	0.881987i
$123$		0			0
$124$	−0.397179	+	0.161350i	−0.0356678	+	0.0144897i
$125$	5.71987	+	5.71987i	0.511601	+	0.511601i
$126$		0			0
$127$	−12.3867			−1.09915			−0.549573	−	0.835446i	$-0.685210\pi$
$127$	−12.3867			−1.09915			−0.549573	+	0.835446i	$0.685210\pi$
$128$	1.94154	+	11.1459i	0.171609	+	0.985165i
$129$		0			0
$130$	1.12345	+	13.3725i	0.0985328	+	1.17285i
$131$	−21.8937			−1.91286			−0.956430	−	0.291961i	$-0.905692\pi$
$131$	−21.8937			−1.91286			−0.956430	+	0.291961i	$0.905692\pi$
$132$		0			0
$133$		−	13.7506i		−	1.19233i
$134$	−6.72997	−	10.1469i	−0.581381	−	0.876559i
$135$		0			0
$136$	−1.10174	+	1.61288i	−0.0944732	+	0.138303i
$137$	−14.3005	+	14.3005i	−1.22177	+	1.22177i	−0.254773	+	0.967001i	$0.582001\pi$
$137$	−14.3005	+	14.3005i	−1.22177	+	1.22177i	−0.967001	+	0.254773i	$0.917999\pi$
$138$		0			0
$139$	15.2124			1.29030			0.645151	−	0.764055i	$-0.276794\pi$
$139$	15.2124			1.29030			0.645151	+	0.764055i	$0.276794\pi$
$140$	9.85247	+	4.16003i	0.832685	+	0.351586i
$141$		0			0
$142$	−7.51575	+	4.98485i	−0.630708	+	0.418319i
$143$	2.56198	+	8.79104i	0.214244	+	0.735144i
$144$		0			0
$145$	−3.02059	−	3.02059i	−0.250846	−	0.250846i
$146$	−9.72557	+	6.45052i	−0.804894	+	0.533849i
$147$		0			0
$148$	−2.20514	−	5.42818i	−0.181262	−	0.446193i
$149$	14.3605	−	14.3605i	1.17646	−	1.17646i	0.195821	−	0.980640i	$-0.437263\pi$
$149$	14.3605	−	14.3605i	1.17646	−	1.17646i	0.980640	−	0.195821i	$-0.0627372\pi$
$150$		0			0
$151$	6.57360	+	6.57360i	0.534952	+	0.534952i	0.922042	−	0.387090i	$-0.126520\pi$
$151$	6.57360	+	6.57360i	0.534952	+	0.534952i	−0.387090	+	0.922042i	$0.626520\pi$
$152$	−3.54199	−	18.8112i	−0.287294	−	1.52579i
$153$		0			0
$154$	7.15232	+	1.44807i	0.576350	+	0.116689i
$155$			0.564130i			0.0453120i
$156$		0			0
$157$		−	10.1738i		−	0.811955i	−0.913883	−	0.405978i	$-0.866931\pi$
$157$		−	10.1738i		−	0.811955i	0.913883	−	0.405978i	$-0.133069\pi$
$158$	−2.31911	+	11.4545i	−0.184499	+	0.911275i
$159$		0			0
$160$	14.5500	+	3.15315i	1.15028	+	0.249278i
$161$	−3.80331	−	3.80331i	−0.299743	−	0.299743i
$162$		0			0
$163$	−6.08794	+	6.08794i	−0.476844	+	0.476844i	−0.904121	−	0.427277i	$-0.859473\pi$
$163$	−6.08794	+	6.08794i	−0.476844	+	0.476844i	0.427277	+	0.904121i	$0.359473\pi$
$164$	4.63711	+	11.4147i	0.362098	+	0.891338i
$165$		0			0
$166$	−9.73552	−	14.6784i	−0.755623	−	1.13927i
$167$	−16.1717	−	16.1717i	−1.25140	−	1.25140i	−0.955091	−	0.296311i	$-0.904243\pi$
$167$	−16.1717	−	16.1717i	−1.25140	−	1.25140i	−0.296311	−	0.955091i	$-0.595757\pi$
$168$		0			0
$169$	−6.98403	−	10.9646i	−0.537233	−	0.843434i
$170$	1.42068	+	2.14198i	0.108961	+	0.164282i
$171$		0			0
$172$	3.80372	−	9.00860i	0.290031	−	0.686899i
$173$	−2.60835			−0.198309			−0.0991546	−	0.995072i	$-0.531614\pi$
$173$	−2.60835			−0.198309			−0.0991546	+	0.995072i	$0.531614\pi$
$174$		0			0
$175$	2.76769	−	2.76769i	0.209217	−	0.209217i
$176$	10.1576	+	0.138653i	0.765655	+	0.0104514i
$177$		0			0
$178$	12.4483	−	8.25638i	0.933039	−	0.618842i
$179$			4.28017i			0.319915i	0.987124	+	0.159957i	$0.0511357\pi$
$179$			4.28017i			0.319915i	−0.987124	+	0.159957i	$0.948864\pi$
$180$		0			0
$181$	−16.9272			−1.25819			−0.629095	−	0.777329i	$-0.716574\pi$
$181$	−16.9272			−1.25819			−0.629095	+	0.777329i	$0.716574\pi$
$182$	−10.3239	+	0.867330i	−0.765260	+	0.0642907i
$183$		0			0
$184$	−6.18271	−	4.22334i	−0.455795	−	0.311348i
$185$	−7.70986			−0.566840
$186$		0			0
$187$	1.24013	+	1.24013i	0.0906875	+	0.0906875i
$188$	−0.327759	−	0.806811i	−0.0239043	−	0.0588427i
$189$		0			0
$190$	−24.6878	−	4.99835i	−1.79104	−	0.362618i
$191$		−	15.8268i		−	1.14519i	−0.819840	−	0.572593i	$-0.805938\pi$
$191$		−	15.8268i		−	1.14519i	0.819840	−	0.572593i	$-0.194062\pi$
$192$		0			0
$193$	7.51374	−	7.51374i	0.540851	−	0.540851i	−0.382927	−	0.923778i	$-0.625084\pi$
$193$	7.51374	−	7.51374i	0.540851	−	0.540851i	0.923778	+	0.382927i	$0.125084\pi$
$194$	−15.2955	−	23.0613i	−1.09815	−	1.65571i
$195$		0			0
$196$	2.23407	−	5.29109i	0.159576	−	0.377935i
$197$	1.86097	−	1.86097i	0.132588	−	0.132588i	−0.637698	−	0.770286i	$-0.720113\pi$
$197$	1.86097	−	1.86097i	0.132588	−	0.132588i	0.770286	+	0.637698i	$0.220113\pi$
$198$		0			0
$199$	4.07700			0.289011			0.144505	−	0.989504i	$-0.453841\pi$
$199$	4.07700			0.289011			0.144505	+	0.989504i	$0.453841\pi$
$200$	3.07334	−	4.49919i	0.217318	−	0.318141i
$201$		0			0
$202$	24.3081	+	4.92147i	1.71031	+	0.346274i
$203$	2.33197	−	2.33197i	0.163672	−	0.163672i
$204$		0			0
$205$	16.2128			1.13235
$206$	−12.8905	−	2.60984i	−0.898126	−	0.181836i
$207$		0			0
$208$	−13.9000	+	3.84584i	−0.963790	+	0.266661i
$209$	−17.1873			−1.18887
$210$		0			0
$211$	15.5231			1.06865			0.534327	−	0.845278i	$-0.320565\pi$
$211$	15.5231			1.06865			0.534327	+	0.845278i	$0.320565\pi$
$212$	−6.62884	+	15.6995i	−0.455270	+	1.07825i
$213$		0			0
$214$	15.6129	+	3.16103i	1.06728	+	0.216084i
$215$	−9.09893	−	9.09893i	−0.620542	−	0.620542i
$216$		0			0
$217$	−0.435523			−0.0295652
$218$	−6.65564	+	4.41438i	−0.450777	+	0.298980i
$219$		0			0
$220$	5.19973	−	12.3149i	0.350566	−	0.830268i
$221$	−2.18293	−	1.19771i	−0.146840	−	0.0805666i
$222$		0			0
$223$	−16.6555	+	16.6555i	−1.11534	+	1.11534i	−0.122920	+	0.992417i	$0.539226\pi$
$223$	−16.6555	+	16.6555i	−1.11534	+	1.11534i	−0.992417	+	0.122920i	$0.960774\pi$
$224$	−2.43431	+	11.2330i	−0.162649	+	0.750534i
$225$		0			0
$226$	3.61526	+	0.731953i	0.240483	+	0.0486888i
$227$	−17.8604	−	17.8604i	−1.18543	−	1.18543i	−0.978316	−	0.207118i	$-0.933592\pi$
$227$	−17.8604	−	17.8604i	−1.18543	−	1.18543i	−0.207118	−	0.978316i	$-0.566408\pi$
$228$		0			0
$229$	17.7135	+	17.7135i	1.17054	+	1.17054i	0.982080	+	0.188462i	$0.0603503\pi$
$229$	17.7135	+	17.7135i	1.17054	+	1.17054i	0.188462	+	0.982080i	$0.439650\pi$
$230$	−8.21094	+	5.44594i	−0.541413	+	0.359094i
$231$		0			0
$232$	2.58951	−	3.79088i	0.170010	−	0.248884i
$233$			12.8071i			0.839018i	0.907751	+	0.419509i	$0.137798\pi$
$233$			12.8071i			0.839018i	−0.907751	+	0.419509i	$0.862202\pi$
$234$		0			0
$235$	−1.14595			−0.0747533
$236$	11.7983	−	4.79294i	0.768002	−	0.311994i
$237$		0			0
$238$	−1.65366	+	1.09680i	−0.107191	+	0.0710949i
$239$	−6.20137	+	6.20137i	−0.401133	+	0.401133i	−0.878632	−	0.477499i	$-0.841543\pi$
$239$	−6.20137	+	6.20137i	−0.401133	+	0.401133i	0.477499	+	0.878632i	$0.341543\pi$
$240$		0			0
$241$	−0.148883	+	0.148883i	−0.00959039	+	0.00959039i	−0.711886	−	0.702295i	$-0.752159\pi$
$241$	−0.148883	+	0.148883i	−0.00959039	+	0.00959039i	0.702295	+	0.711886i	$0.252159\pi$
$242$	−1.27695	+	6.30712i	−0.0820857	+	0.405437i
$243$		0			0
$244$	−5.46773	+	12.9496i	−0.350036	+	0.829013i
$245$	−5.34415	−	5.34415i	−0.341425	−	0.341425i
$246$		0			0
$247$	23.4265	−	6.82721i	1.49059	−	0.434405i
$248$	−0.595806	+	0.112185i	−0.0378337	+	0.00712377i
$249$		0			0
$250$	6.32308	+	9.53343i	0.399907	+	0.602947i
$251$		−	13.2191i		−	0.834382i	−0.908819	−	0.417191i	$-0.863015\pi$
$251$		−	13.2191i		−	0.834382i	0.908819	−	0.417191i	$-0.136985\pi$
$252$		0			0
$253$	−4.75385	+	4.75385i	−0.298872	+	0.298872i
$254$	−17.1692	−	3.47610i	−1.07729	−	0.218110i
$255$		0			0
$256$	−0.436727	+	15.9940i	−0.0272955	+	0.999627i
$257$			15.5812i			0.971928i	0.873979	+	0.485964i	$0.161531\pi$
$257$			15.5812i			0.971928i	−0.873979	+	0.485964i	$0.838469\pi$
$258$		0			0
$259$		−	5.95221i		−	0.369852i
$260$	−2.19554	+	18.8508i	−0.136162	+	1.16908i
$261$		0			0
$262$	−30.3466	−	6.14404i	−1.87482	−	0.379580i
$263$			15.6718i			0.966363i	0.875520	+	0.483181i	$0.160519\pi$
$263$			15.6718i			0.966363i	−0.875520	+	0.483181i	$0.839481\pi$
$264$		0			0
$265$	15.8569	+	15.8569i	0.974083	+	0.974083i
$266$	3.85885	−	19.0596i	0.236601	−	1.16862i
$267$		0			0
$268$	−6.48082	−	15.9532i	−0.395879	−	0.974494i
$269$		−	7.76842i		−	0.473649i	−0.971552	−	0.236824i	$-0.923893\pi$
$269$		−	7.76842i		−	0.473649i	0.971552	−	0.236824i	$-0.0761066\pi$
$270$		0			0
$271$	9.70510	+	9.70510i	0.589543	+	0.589543i	0.937508	−	0.347965i	$-0.113127\pi$
$271$	9.70510	+	9.70510i	0.589543	+	0.589543i	−0.347965	+	0.937508i	$0.613127\pi$
$272$	−1.97973	+	1.92641i	−0.120039	+	0.116806i
$273$		0			0
$274$	−23.8349	+	15.8086i	−1.43992	+	0.955034i
$275$	−3.45940	−	3.45940i	−0.208610	−	0.208610i
$276$		0			0
$277$	9.88979			0.594220			0.297110	−	0.954843i	$-0.403977\pi$
$277$	9.88979			0.594220			0.297110	+	0.954843i	$0.403977\pi$
$278$	21.0858	+	4.26908i	1.26464	+	0.256042i
$279$		0			0
$280$	12.4890	+	8.53108i	0.746359	+	0.509829i
$281$	0.916519	−	0.916519i	0.0546749	−	0.0546749i	−0.679241	−	0.733916i	$-0.737691\pi$
$281$	0.916519	−	0.916519i	0.0546749	−	0.0546749i	0.733916	+	0.679241i	$0.237691\pi$
$282$		0			0
$283$		−	0.356000i		−	0.0211620i	−0.999944	−	0.0105810i	$-0.996632\pi$
$283$		−	0.356000i		−	0.0211620i	0.999944	−	0.0105810i	$-0.00336810\pi$
$284$	−11.8164	+	4.80030i	−0.701175	+	0.284846i
$285$		0			0
$286$	1.08410	+	12.9041i	0.0641041	+	0.763038i
$287$			12.5167i			0.738836i
$288$		0			0
$289$	16.5231			0.971947
$290$	−3.33914	−	5.03448i	−0.196081	−	0.295635i
$291$		0			0
$292$	−15.2907	+	6.21171i	−0.894822	+	0.363513i
$293$	15.6762	+	15.6762i	0.915814	+	0.915814i	0.996722	−	0.0809073i	$-0.0257818\pi$
$293$	15.6762	+	15.6762i	0.915814	+	0.915814i	−0.0809073	+	0.996722i	$0.525782\pi$
$294$		0			0
$295$		−	16.7576i		−	0.975664i
$296$	−1.53322	−	8.14278i	−0.0891163	−	0.473289i
$297$		0			0
$298$	23.9350	−	15.8750i	1.38652	−	0.919613i
$299$	4.59123	−	8.36792i	0.265517	−	0.483929i
$300$		0			0
$301$	7.02461	−	7.02461i	0.404892	−	0.404892i
$302$	7.26684	+	10.9564i	0.418160	+	0.630467i
$303$		0			0
$304$	0.369486	−	27.0680i	0.0211915	−	1.55246i
$305$	13.0794	+	13.0794i	0.748927	+	0.748927i
$306$		0			0
$307$	6.36463	−	6.36463i	0.363249	−	0.363249i	−0.501759	−	0.865008i	$-0.667314\pi$
$307$	6.36463	−	6.36463i	0.363249	−	0.363249i	0.865008	+	0.501759i	$0.167314\pi$
$308$	9.50738	+	4.01432i	0.541733	+	0.228737i
$309$		0			0
$310$	−0.158312	+	0.781935i	−0.00899153	+	0.0444109i
$311$	7.15541			0.405746			0.202873	−	0.979205i	$-0.434972\pi$
$311$	7.15541			0.405746			0.202873	+	0.979205i	$0.434972\pi$
$312$		0			0
$313$	−2.19311			−0.123962			−0.0619810	−	0.998077i	$-0.519742\pi$
$313$	−2.19311			−0.123962			−0.0619810	+	0.998077i	$0.519742\pi$
$314$	2.85507	−	14.1018i	0.161121	−	0.795808i
$315$		0			0
$316$	−6.42900	+	15.2262i	−0.361659	+	0.856542i
$317$	9.33835	−	9.33835i	0.524494	−	0.524494i	−0.394431	−	0.918925i	$-0.629058\pi$
$317$	9.33835	−	9.33835i	0.524494	−	0.524494i	0.918925	+	0.394431i	$0.129058\pi$
$318$		0			0
$319$	−2.91479	−	2.91479i	−0.163197	−	0.163197i
$320$	19.2827	+	8.45373i	1.07794	+	0.472578i
$321$		0			0
$322$	−4.20440	−	6.33905i	−0.234302	−	0.353261i
$323$	3.30473	−	3.30473i	0.183880	−	0.183880i
$324$		0			0
$325$	6.08938	+	3.34106i	0.337778	+	0.185329i
$326$	−10.1469	+	6.72997i	−0.561985	+	0.372739i
$327$		0			0
$328$	3.22414	+	17.1231i	0.178023	+	0.945466i
$329$		−	0.884699i		−	0.0487751i
$330$		0			0
$331$	13.7742	+	13.7742i	0.757099	+	0.757099i	0.975793	−	0.218694i	$-0.0701798\pi$
$331$	13.7742	+	13.7742i	0.757099	+	0.757099i	−0.218694	+	0.975793i	$0.570180\pi$
$332$	−9.37509	−	23.0777i	−0.514525	−	1.26655i
$333$		0			0
$334$	−17.8771	−	26.9537i	−0.978194	−	1.47484i
$335$	−22.6589			−1.23799
$336$		0			0
$337$			15.0571i			0.820211i	0.912038	+	0.410106i	$0.134508\pi$
$337$			15.0571i			0.820211i	−0.912038	+	0.410106i	$0.865492\pi$
$338$	−6.60348	−	17.1579i	−0.359182	−	0.933267i
$339$		0			0
$340$	1.36808	+	3.36766i	0.0741945	+	0.182637i
$341$			0.544371i			0.0294794i
$342$		0			0
$343$	14.1828	−	14.1828i	0.765800	−	0.765800i
$344$	7.80039	−	11.4193i	0.420569	−	0.615687i
$345$		0			0
$346$	−3.61541	−	0.731983i	−0.194366	−	0.0393517i
$347$	17.4406			0.936262			0.468131	−	0.883659i	$-0.344927\pi$
$347$	17.4406			0.936262			0.468131	+	0.883659i	$0.344927\pi$
$348$		0			0
$349$	−20.1757	−	20.1757i	−1.07998	−	1.07998i	−0.996511	−	0.0834674i	$-0.973401\pi$
$349$	−20.1757	−	20.1757i	−1.07998	−	1.07998i	−0.0834674	−	0.996511i	$-0.526599\pi$
$350$	4.61296	−	3.05957i	0.246573	−	0.163541i
$351$		0			0
$352$	14.0404	+	3.04271i	0.748355	+	0.162177i
$353$	−7.11735	−	7.11735i	−0.378818	−	0.378818i	0.491858	−	0.870676i	$-0.336318\pi$
$353$	−7.11735	−	7.11735i	−0.378818	−	0.378818i	−0.870676	+	0.491858i	$0.836318\pi$
$354$		0			0
$355$			16.7833i			0.890767i
$356$	19.5715	−	7.95071i	1.03728	−	0.421387i
$357$		0			0
$358$	−1.20115	+	5.93270i	−0.0634826	+	0.313553i
$359$	20.7087	+	20.7087i	1.09296	+	1.09296i	0.995211	+	0.0977514i	$0.0311650\pi$
$359$	20.7087	+	20.7087i	1.09296	+	1.09296i	0.0977514	+	0.995211i	$0.468835\pi$
$360$		0			0
$361$			26.8010i			1.41058i
$362$	−23.4626	−	4.75029i	−1.23317	−	0.249670i
$363$		0			0
$364$	−14.5533	−	1.69501i	−0.762800	−	0.0888429i
$365$			21.7180i			1.13677i
$366$		0			0
$367$		−	19.9759i		−	1.04273i	−0.853333	−	0.521366i	$-0.825423\pi$
$367$		−	19.9759i		−	1.04273i	0.853333	−	0.521366i	$-0.174577\pi$
$368$	−7.38459	−	7.58898i	−0.384948	−	0.395603i
$369$		0			0
$370$	−10.6866	−	2.16362i	−0.555568	−	0.112482i
$371$	−12.2420	+	12.2420i	−0.635571	+	0.635571i
$372$		0			0
$373$			13.4282i			0.695284i	0.937627	+	0.347642i	$0.113017\pi$
$373$			13.4282i			0.695284i	−0.937627	+	0.347642i	$0.886983\pi$
$374$	1.37092	+	2.06696i	0.0708884	+	0.106880i
$375$		0			0
$376$	−0.227888	−	1.21029i	−0.0117524	−	0.0624160i
$377$	5.13073	+	2.81508i	0.264246	+	0.144984i
$378$		0			0
$379$	−14.5582	−	14.5582i	−0.747806	−	0.747806i	0.226261	−	0.974067i	$-0.427350\pi$
$379$	−14.5582	−	14.5582i	−0.747806	−	0.747806i	−0.974067	+	0.226261i	$0.927350\pi$
$380$	−32.8169	−	13.8563i	−1.68347	−	0.710815i
$381$		0			0
$382$	4.44148	−	21.9374i	0.227246	−	1.12241i
$383$	16.8510	−	16.8510i	0.861048	−	0.861048i	−0.130412	−	0.991460i	$-0.541630\pi$
$383$	16.8510	−	16.8510i	0.861048	−	0.861048i	0.991460	+	0.130412i	$0.0416300\pi$
$384$		0			0
$385$	9.60271	−	9.60271i	0.489400	−	0.489400i
$386$	12.5233	−	8.30614i	0.637420	−	0.422771i
$387$		0			0
$388$	−14.7292	−	36.2575i	−0.747764	−	1.84069i
$389$	−16.0991			−0.816254			−0.408127	−	0.912925i	$-0.633818\pi$
$389$	−16.0991			−0.816254			−0.408127	+	0.912925i	$0.633818\pi$
$390$		0			0
$391$		−	1.82812i		−	0.0924519i
$392$	4.58147	−	6.70699i	0.231399	−	0.338754i
$393$		0			0
$394$	3.10171	−	2.05722i	0.156262	−	0.103641i
$395$	15.3789	+	15.3789i	0.773796	+	0.773796i
$396$		0			0
$397$	−4.70323	−	4.70323i	−0.236048	−	0.236048i	0.579163	−	0.815211i	$-0.303379\pi$
$397$	−4.70323	−	4.70323i	−0.236048	−	0.236048i	−0.815211	+	0.579163i	$0.803379\pi$
$398$	5.65109	+	1.14413i	0.283263	+	0.0573501i
$399$		0			0
$400$	5.52254	−	5.37381i	0.276127	−	0.268690i
$401$	17.0366	−	17.0366i	0.850768	−	0.850768i	−0.139460	−	0.990228i	$-0.544537\pi$
$401$	17.0366	−	17.0366i	0.850768	−	0.850768i	0.990228	+	0.139460i	$0.0445366\pi$
$402$		0			0
$403$	−0.216238	−	0.741986i	−0.0107716	−	0.0369610i
$404$	32.3121	+	13.6432i	1.60759	+	0.678775i
$405$		0			0
$406$	3.88674	−	2.57790i	0.192896	−	0.127939i
$407$	−7.43982			−0.368778
$408$		0			0
$409$	16.9559	+	16.9559i	0.838413	+	0.838413i	0.988650	−	0.150237i	$-0.0480037\pi$
$409$	16.9559	+	16.9559i	0.838413	+	0.838413i	−0.150237	+	0.988650i	$0.548004\pi$
$410$	22.4724	+	4.54980i	1.10983	+	0.224699i
$411$		0			0
$412$	−17.1350	−	7.23496i	−0.844183	−	0.356441i
$413$	12.9373			0.636602
$414$		0			0
$415$	−32.7782			−1.60902
$416$	−20.3459	+	1.42992i	−0.997539	+	0.0701078i
$417$		0			0
$418$	−23.8231	−	4.82328i	−1.16523	−	0.235914i
$419$	16.4707			0.804647			0.402323	−	0.915498i	$-0.368203\pi$
$419$	16.4707			0.804647			0.402323	+	0.915498i	$0.368203\pi$
$420$		0			0
$421$	−25.3822	+	25.3822i	−1.23705	+	1.23705i	−0.275851	+	0.961201i	$0.588960\pi$
$421$	−25.3822	+	25.3822i	−1.23705	+	1.23705i	−0.961201	+	0.275851i	$0.911040\pi$
$422$	21.5164	+	4.35626i	1.04740	+	0.212059i
$423$		0			0
$424$	−13.5939	+	19.9007i	−0.660180	+	0.966463i
$425$	1.33033			0.0645306
$426$		0			0
$427$	−10.0977	+	10.0977i	−0.488660	+	0.488660i
$428$	20.7539	+	8.76295i	1.00318	+	0.423573i
$429$		0			0
$430$	−10.0585	−	15.1654i	−0.485064	−	0.731340i
$431$	8.12815	−	8.12815i	0.391519	−	0.391519i	−0.483710	−	0.875229i	$-0.660711\pi$
$431$	8.12815	−	8.12815i	0.391519	−	0.391519i	0.875229	+	0.483710i	$0.160711\pi$
$432$		0			0
$433$			39.9622i			1.92046i	0.279212	+	0.960229i	$0.409927\pi$
$433$			39.9622i			1.92046i	−0.279212	+	0.960229i	$0.590073\pi$
$434$	−0.603674	−	0.122221i	−0.0289773	−	0.00586680i
$435$		0			0
$436$	−10.4641	+	4.25095i	−0.501141	+	0.203584i
$437$	12.6682	+	12.6682i	0.606000	+	0.606000i
$438$		0			0
$439$	−13.1837			−0.629224			−0.314612	−	0.949220i	$-0.601874\pi$
$439$	−13.1837			−0.629224			−0.314612	+	0.949220i	$0.601874\pi$
$440$	10.6632	−	15.6103i	0.508349	−	0.744192i
$441$		0			0
$442$	−2.68963	−	2.27273i	−0.127932	−	0.108103i
$443$	17.6794			0.839972			0.419986	−	0.907531i	$-0.362035\pi$
$443$	17.6794			0.839972			0.419986	+	0.907531i	$0.362035\pi$
$444$		0			0
$445$		−	27.7981i		−	1.31776i
$446$	−27.7601	+	18.4120i	−1.31448	+	0.871834i
$447$		0			0
$448$	−6.52649	+	14.8868i	−0.308348	+	0.703334i
$449$	21.5059	−	21.5059i	1.01492	−	1.01492i	0.0150379	−	0.999887i	$-0.495213\pi$
$449$	21.5059	−	21.5059i	1.01492	−	1.01492i	0.999887	−	0.0150379i	$-0.00478689\pi$
$450$		0			0
$451$	15.6449			0.736690
$452$	4.80566	+	2.02911i	0.226039	+	0.0954411i
$453$		0			0
$454$	−19.7439	−	29.7682i	−0.926628	−	1.39709i
$455$	−9.27421	+	16.9031i	−0.434782	+	0.792428i
$456$		0			0
$457$	2.81456	+	2.81456i	0.131660	+	0.131660i	0.769866	−	0.638206i	$-0.220323\pi$
$457$	2.81456	+	2.81456i	0.131660	+	0.131660i	−0.638206	+	0.769866i	$0.720323\pi$
$458$	19.5816	+	29.5235i	0.914987	+	1.37954i
$459$		0			0
$460$	−12.9094	+	5.24432i	−0.601904	+	0.244518i
$461$	4.19670	−	4.19670i	0.195460	−	0.195460i	−0.602591	−	0.798050i	$-0.705865\pi$
$461$	4.19670	−	4.19670i	0.195460	−	0.195460i	0.798050	+	0.602591i	$0.205865\pi$
$462$		0			0
$463$	21.2766	+	21.2766i	0.988809	+	0.988809i	0.999938	−	0.0111288i	$-0.00354247\pi$
$463$	21.2766	+	21.2766i	0.988809	+	0.988809i	−0.0111288	+	0.999938i	$0.503542\pi$
$464$	4.65313	−	4.52781i	0.216016	−	0.210198i
$465$		0			0
$466$	−3.59405	+	17.7517i	−0.166491	+	0.822333i
$467$			23.4639i			1.08578i	0.839803	+	0.542891i	$0.182670\pi$
$467$			23.4639i			1.08578i	−0.839803	+	0.542891i	$0.817330\pi$
$468$		0			0
$469$		−	17.4933i		−	0.807764i
$470$	−1.58838	−	0.321588i	−0.0732667	−	0.0148337i
$471$		0			0
$472$	17.6985	−	3.33248i	0.814640	−	0.153390i
$473$	−8.78024	−	8.78024i	−0.403716	−	0.403716i
$474$		0			0
$475$	−9.21868	+	9.21868i	−0.422982	+	0.422982i
$476$	−2.59992	+	1.05619i	−0.119167	+	0.0484105i
$477$		0			0
$478$	−10.3360	+	6.85536i	−0.472756	+	0.313557i
$479$	−1.46450	−	1.46450i	−0.0669149	−	0.0669149i	0.672857	−	0.739772i	$-0.265067\pi$
$479$	−1.46450	−	1.46450i	−0.0669149	−	0.0669149i	−0.739772	+	0.672857i	$0.765067\pi$
$480$		0			0
$481$	10.1406	−	2.95528i	0.462371	−	0.134749i
$482$	−0.248146	+	0.164584i	−0.0113027	+	0.00749659i
$483$		0			0
$484$	−3.53995	+	8.38389i	−0.160907	+	0.381086i
$485$	−51.4980			−2.33840
$486$		0			0
$487$	24.8699	−	24.8699i	1.12696	−	1.12696i	0.136296	−	0.990668i	$-0.456480\pi$
$487$	24.8699	−	24.8699i	1.12696	−	1.12696i	0.990668	−	0.136296i	$-0.0435198\pi$
$488$	−11.2128	+	16.4149i	−0.507581	+	0.743068i
$489$		0			0
$490$	−5.90774	−	8.90721i	−0.266884	−	0.402387i
$491$			5.71016i			0.257696i	0.991664	+	0.128848i	$0.0411279\pi$
$491$			5.71016i			0.257696i	−0.991664	+	0.128848i	$0.958872\pi$
$492$		0			0
$493$	1.12090			0.0504827
$494$	34.3872	−	2.88892i	1.54715	−	0.129979i
$495$		0			0
$496$	−0.857324	−	0.0117027i	−0.0384950	−	0.000525467i
$497$	−12.9572			−0.581208
$498$		0			0
$499$	21.9449	+	21.9449i	0.982387	+	0.982387i	0.999848	−	0.0174602i	$-0.00555803\pi$
$499$	21.9449	+	21.9449i	0.982387	+	0.982387i	−0.0174602	+	0.999848i	$0.505558\pi$
$500$	6.08899	+	14.9886i	0.272308	+	0.670313i
$501$		0			0
$502$	3.70969	−	18.3229i	0.165571	−	0.817789i
$503$		−	34.1145i		−	1.52109i	−0.649284	−	0.760546i	$-0.724931\pi$
$503$		−	34.1145i		−	1.52109i	0.649284	−	0.760546i	$-0.275069\pi$
$504$		0			0
$505$	32.6361	−	32.6361i	1.45229	−	1.45229i
$506$	−7.92335	+	5.25519i	−0.352236	+	0.233622i
$507$		0			0
$508$	−22.8225	−	9.63639i	−1.01258	−	0.427546i
$509$	7.58084	−	7.58084i	0.336015	−	0.336015i	−0.518850	−	0.854865i	$-0.673640\pi$
$509$	7.58084	−	7.58084i	0.336015	−	0.336015i	0.854865	+	0.518850i	$0.173640\pi$
$510$		0			0
$511$	−16.7669			−0.741723
$512$	−5.09376	+	22.0466i	−0.225115	+	0.974332i
$513$		0			0
$514$	−4.37256	+	21.5969i	−0.192865	+	0.952600i
$515$	−17.3069	+	17.3069i	−0.762631	+	0.762631i
$516$		0			0
$517$	−1.10581			−0.0486334
$518$	1.67037	−	8.25030i	0.0733920	−	0.362497i
$519$		0			0
$520$	−8.33333	+	25.5128i	−0.365441	+	1.11881i
$521$	24.1479			1.05794			0.528969	−	0.848641i	$-0.322579\pi$
$521$	24.1479			1.05794			0.528969	+	0.848641i	$0.322579\pi$
$522$		0			0
$523$	−18.7933			−0.821774			−0.410887	−	0.911686i	$-0.634781\pi$
$523$	−18.7933			−0.821774			−0.410887	+	0.911686i	$0.634781\pi$
$524$	−40.3390	−	17.0324i	−1.76222	−	0.744064i
$525$		0			0
$526$	−4.39798	+	21.7225i	−0.191761	+	0.947145i
$527$	−0.104670	−	0.104670i	−0.00455951	−	0.00455951i
$528$		0			0
$529$	−15.9922			−0.695313
$530$	17.5292	+	26.4291i	0.761419	+	1.14801i
$531$		0			0
$532$	10.6974	−	25.3354i	0.463793	−	1.09843i
$533$	−21.3242	+	6.21454i	−0.923656	+	0.269182i
$534$		0			0
$535$	20.9620	−	20.9620i	0.906265	−	0.906265i
$536$	−4.50605	−	23.9312i	−0.194632	−	1.03367i
$537$		0			0
$538$	2.18006	−	10.7677i	0.0939889	−	0.464230i
$539$	−5.15697	−	5.15697i	−0.222126	−	0.222126i
$540$		0			0
$541$	19.7610	+	19.7610i	0.849593	+	0.849593i	0.990082	−	0.140489i	$-0.0448675\pi$
$541$	19.7610	+	19.7610i	0.849593	+	0.849593i	−0.140489	+	0.990082i	$0.544868\pi$
$542$	10.7286	+	16.1757i	0.460833	+	0.694806i
$543$		0			0
$544$	−3.28470	+	2.11461i	−0.140830	+	0.0906630i
$545$			14.8626i			0.636645i
$546$		0			0
$547$	0.864037			0.0369435			0.0184718	−	0.999829i	$-0.494120\pi$
$547$	0.864037			0.0369435			0.0184718	+	0.999829i	$0.494120\pi$
$548$	−37.4738	+	15.2234i	−1.60080	+	0.650309i
$549$		0			0
$550$	−3.82423	−	5.76586i	−0.163066	−	0.245857i
$551$	−7.76739	+	7.76739i	−0.330902	+	0.330902i
$552$		0			0
$553$	−11.8729	+	11.8729i	−0.504887	+	0.504887i
$554$	13.7081	+	2.77538i	0.582403	+	0.117915i
$555$		0			0
$556$	28.0288	+	11.8347i	1.18869	+	0.501901i
$557$	−10.9293	−	10.9293i	−0.463089	−	0.463089i	0.436578	−	0.899666i	$-0.356190\pi$
$557$	−10.9293	−	10.9293i	−0.463089	−	0.463089i	−0.899666	+	0.436578i	$0.856190\pi$
$558$		0			0
$559$	15.4553	+	8.47987i	0.653691	+	0.358660i
$560$	14.9168	+	15.3296i	0.630348	+	0.647795i
$561$		0			0
$562$	1.52758	−	1.01317i	0.0644371	−	0.0427382i
$563$		−	38.6244i		−	1.62782i	−0.580989	−	0.813911i	$-0.697334\pi$
$563$		−	38.6244i		−	1.62782i	0.580989	−	0.813911i	$-0.302666\pi$
$564$		0			0
$565$	4.85385	−	4.85385i	0.204203	−	0.204203i
$566$	0.0999045	−	0.493448i	0.00419930	−	0.0207412i
$567$		0			0
$568$	−17.7257	+	3.33760i	−0.743755	+	0.140043i
$569$		−	40.1183i		−	1.68185i	−0.541154	−	0.840924i	$-0.682012\pi$
$569$		−	40.1183i		−	1.68185i	0.541154	−	0.840924i	$-0.317988\pi$
$570$		0			0
$571$			3.97707i			0.166435i	0.996531	+	0.0832175i	$0.0265196\pi$
$571$			3.97707i			0.166435i	−0.996531	+	0.0832175i	$0.973480\pi$
$572$	−2.11864	+	18.1905i	−0.0885849	+	0.760585i
$573$		0			0
$574$	−3.51256	+	17.3492i	−0.146612	+	0.724143i
$575$			5.09962i			0.212669i
$576$		0			0
$577$	−13.5025	−	13.5025i	−0.562117	−	0.562117i	0.367791	−	0.929908i	$-0.380114\pi$
$577$	−13.5025	−	13.5025i	−0.562117	−	0.562117i	−0.929908	+	0.367791i	$0.880114\pi$
$578$	22.9025	+	4.63689i	0.952619	+	0.192869i
$579$		0			0
$580$	−3.21552	−	7.91530i	−0.133517	−	0.328665i
$581$		−	25.3056i		−	1.04985i
$582$		0			0
$583$	15.3015	+	15.3015i	0.633725	+	0.633725i
$584$	−22.9375	+	4.31894i	−0.949162	+	0.178719i
$585$		0			0
$586$	17.3294	+	26.1279i	0.715872	+	1.07933i
$587$	10.1322	+	10.1322i	0.418201	+	0.418201i	0.884583	−	0.466383i	$-0.154443\pi$
$587$	10.1322	+	10.1322i	0.418201	+	0.418201i	−0.466383	+	0.884583i	$0.654443\pi$
$588$		0			0
$589$	1.45065			0.0597730
$590$	4.70269	−	23.2275i	0.193607	−	0.956261i
$591$		0			0
$592$	0.159939	−	11.7169i	0.00657344	−	0.481561i
$593$	13.3652	−	13.3652i	0.548841	−	0.548841i	−0.377264	−	0.926106i	$-0.623135\pi$
$593$	13.3652	−	13.3652i	0.548841	−	0.548841i	0.926106	+	0.377264i	$0.123135\pi$
$594$		0			0
$595$			3.69277i			0.151389i
$596$	37.6311	−	15.2873i	1.54143	−	0.626191i
$597$		0			0
$598$	8.71215	−	10.3103i	0.356266	−	0.421618i
$599$		−	5.46359i		−	0.223236i	−0.993751	−	0.111618i	$-0.964397\pi$
$599$		−	5.46359i		−	0.223236i	0.993751	−	0.111618i	$-0.0356033\pi$
$600$		0			0
$601$	−36.5697			−1.49171			−0.745855	−	0.666108i	$-0.767959\pi$
$601$	−36.5697			−1.49171			−0.745855	+	0.666108i	$0.767959\pi$
$602$	11.7081	−	7.76542i	0.477185	−	0.316495i
$603$		0			0
$604$	6.99781	+	17.2258i	0.284737	+	0.700908i
$605$	8.46796	+	8.46796i	0.344271	+	0.344271i
$606$		0			0
$607$			22.8716i			0.928330i	0.885749	+	0.464165i	$0.153646\pi$
$607$			22.8716i			0.928330i	−0.885749	+	0.464165i	$0.846354\pi$
$608$	8.10827	−	37.4151i	0.328834	−	1.51738i
$609$		0			0
$610$	14.4588	+	21.7998i	0.585420	+	0.882648i
$611$	1.50723	−	0.439254i	0.0609762	−	0.0177703i
$612$		0			0
$613$	32.4490	−	32.4490i	1.31060	−	1.31060i	0.389632	−	0.920971i	$-0.372602\pi$
$613$	32.4490	−	32.4490i	1.31060	−	1.31060i	0.920971	−	0.389632i	$-0.127398\pi$
$614$	10.6081	−	7.03584i	0.428107	−	0.283943i
$615$		0			0
$616$	12.0515	+	8.23228i	0.485571	+	0.331688i
$617$	33.0596	+	33.0596i	1.33093	+	1.33093i	0.904538	+	0.426393i	$0.140216\pi$
$617$	33.0596	+	33.0596i	1.33093	+	1.33093i	0.426393	+	0.904538i	$0.359784\pi$
$618$		0			0
$619$	26.1845	−	26.1845i	1.05244	−	1.05244i	0.0538980	−	0.998546i	$-0.482835\pi$
$619$	26.1845	−	26.1845i	1.05244	−	1.05244i	0.998546	−	0.0538980i	$-0.0171646\pi$
$620$	−0.438870	+	1.03941i	−0.0176255	+	0.0417435i
$621$		0			0
$622$	9.91804	+	2.00803i	0.397677	+	0.0805146i
$623$	21.4609			0.859811
$624$		0			0
$625$	30.9210			1.23684
$626$	−3.03985	−	0.615455i	−0.121497	−	0.0245985i
$627$		0			0
$628$	7.91478	−	18.7451i	0.315834	−	0.748011i
$629$	1.43051	−	1.43051i	0.0570382	−	0.0570382i
$630$		0			0
$631$	−1.12873	−	1.12873i	−0.0449339	−	0.0449339i	0.684283	−	0.729217i	$-0.260115\pi$
$631$	−1.12873	−	1.12873i	−0.0449339	−	0.0449339i	−0.729217	+	0.684283i	$0.760115\pi$
$632$	−13.1841	+	19.3007i	−0.524436	+	0.767742i
$633$		0			0
$634$	15.5644	−	10.3232i	0.618142	−	0.409985i
$635$	−23.0513	+	23.0513i	−0.914764	+	0.914764i
$636$		0			0
$637$	9.07750	+	4.98055i	0.359664	+	0.197337i
$638$	−3.22218	−	4.85814i	−0.127567	−	0.192336i
$639$		0			0
$640$	24.3552	+	17.1290i	0.962726	+	0.677082i
$641$			30.8252i			1.21752i	0.793353	+	0.608762i	$0.208333\pi$
$641$			30.8252i			1.21752i	−0.793353	+	0.608762i	$0.791667\pi$
$642$		0			0
$643$	10.2992	+	10.2992i	0.406161	+	0.406161i	0.880397	−	0.474237i	$-0.157276\pi$
$643$	10.2992	+	10.2992i	0.406161	+	0.406161i	−0.474237	+	0.880397i	$0.657276\pi$
$644$	−4.04875	−	9.96638i	−0.159543	−	0.392730i
$645$		0			0
$646$	5.50806	−	3.65324i	0.216712	−	0.143735i
$647$	49.1102			1.93072			0.965360	−	0.260922i	$-0.0840264\pi$
$647$	49.1102			1.93072			0.965360	+	0.260922i	$0.0840264\pi$
$648$		0			0
$649$		−	16.1706i		−	0.634753i
$650$	7.50283	+	6.33988i	0.294285	+	0.248670i
$651$		0			0
$652$	−15.9532	+	6.48082i	−0.624774	+	0.253808i
$653$			5.00990i			0.196052i	0.995184	+	0.0980262i	$0.0312529\pi$
$653$			5.00990i			0.196052i	−0.995184	+	0.0980262i	$0.968747\pi$
$654$		0			0
$655$	−40.7434	+	40.7434i	−1.59198	+	1.59198i
$656$	−0.336329	+	24.6390i	−0.0131314	+	0.961991i
$657$		0			0
$658$	0.248274	−	1.22627i	0.00967873	−	0.0478051i
$659$	−7.81311			−0.304356			−0.152178	−	0.988353i	$-0.548629\pi$
$659$	−7.81311			−0.304356			−0.152178	+	0.988353i	$0.548629\pi$
$660$		0			0
$661$	−11.5710	−	11.5710i	−0.450060	−	0.450060i	0.445314	−	0.895374i	$-0.353092\pi$
$661$	−11.5710	−	11.5710i	−0.450060	−	0.450060i	−0.895374	+	0.445314i	$0.853092\pi$
$662$	15.2268	+	22.9578i	0.591808	+	0.892279i
$663$		0			0
$664$	−6.51841	−	34.6187i	−0.252963	−	1.34347i
$665$	−25.5895	−	25.5895i	−0.992318	−	0.992318i
$666$		0			0
$667$			4.29678i			0.166372i
$668$	−17.2153	−	42.3771i	−0.666080	−	1.63962i
$669$		0			0
$670$	−31.4073	−	6.35879i	−1.21337	−	0.245662i
$671$	12.6213	+	12.6213i	0.487241	+	0.487241i
$672$		0			0
$673$			3.37609i			0.130139i	0.997881	+	0.0650693i	$0.0207269\pi$
$673$			3.37609i			0.130139i	−0.997881	+	0.0650693i	$0.979273\pi$
$674$	−4.22548	+	20.8705i	−0.162759	+	0.803901i
$675$		0			0
$676$	−4.33799	−	25.6356i	−0.166846	−	0.985983i
$677$		−	8.56189i		−	0.329060i	−0.986372	−	0.164530i	$-0.947389\pi$
$677$		−	8.56189i		−	0.329060i	0.986372	−	0.164530i	$-0.0526108\pi$
$678$		0			0
$679$		−	39.7577i		−	1.52576i
$680$	0.951213	+	5.05181i	0.0364773	+	0.193728i
$681$		0			0
$682$	−0.152767	+	0.754548i	−0.00584977	+	0.0288931i
$683$	−14.2243	+	14.2243i	−0.544279	+	0.544279i	−0.924780	−	0.380501i	$-0.875751\pi$
$683$	−14.2243	+	14.2243i	−0.544279	+	0.544279i	0.380501	+	0.924780i	$0.375751\pi$
$684$		0			0
$685$			53.2255i			2.03364i
$686$	23.6388	−	15.6785i	0.902534	−	0.598609i
$687$		0			0
$688$	14.0167	−	13.6391i	0.534380	−	0.519987i
$689$	−26.9344	−	14.7781i	−1.02612	−	0.563000i
$690$		0			0
$691$	−10.0702	−	10.0702i	−0.383090	−	0.383090i	0.489124	−	0.872214i	$-0.337316\pi$
$691$	−10.0702	−	10.0702i	−0.383090	−	0.383090i	−0.872214	+	0.489124i	$0.837316\pi$
$692$	−4.80587	−	2.02919i	−0.182692	−	0.0771382i
$693$		0			0
$694$	24.1743	+	4.89438i	0.917644	+	0.185788i
$695$	28.3099	−	28.3099i	1.07385	−	1.07385i
$696$		0			0
$697$	−3.00817	+	3.00817i	−0.113942	+	0.113942i
$698$	−22.3034	−	33.6272i	−0.844195	−	1.27281i
$699$		0			0
$700$	7.25259	−	2.94629i	0.274122	−	0.111359i
$701$	−44.3514			−1.67513			−0.837565	−	0.546337i	$-0.816022\pi$
$701$	−44.3514			−1.67513			−0.837565	+	0.546337i	$0.816022\pi$
$702$		0			0
$703$			19.8258i			0.747743i
$704$	18.6074	+	8.15764i	0.701291	+	0.307453i
$705$		0			0
$706$	−7.86794	−	11.8626i	−0.296114	−	0.446456i
$707$	25.1959	+	25.1959i	0.947590	+	0.947590i
$708$		0			0
$709$	−4.99613	−	4.99613i	−0.187634	−	0.187634i	0.607039	−	0.794672i	$-0.292357\pi$
$709$	−4.99613	−	4.99613i	−0.187634	−	0.187634i	−0.794672	+	0.607039i	$0.792357\pi$
$710$	−4.70992	+	23.2632i	−0.176760	+	0.873053i
$711$		0			0
$712$	29.3590	−	5.52805i	1.10028	−	0.207173i
$713$	0.401237	−	0.401237i	0.0150265	−	0.0150265i
$714$		0			0
$715$	21.1276	+	11.5921i	0.790128	+	0.433519i
$716$	−3.32980	+	7.88617i	−0.124440	+	0.294720i
$717$		0			0
$718$	22.8926	+	34.5156i	0.854344	+	1.28811i
$719$	20.9602			0.781683			0.390842	−	0.920458i	$-0.372184\pi$
$719$	20.9602			0.781683			0.390842	+	0.920458i	$0.372184\pi$
$720$		0			0
$721$	−13.3613	−	13.3613i	−0.497602	−	0.497602i
$722$	−7.52118	+	37.1486i	−0.279909	+	1.38253i
$723$		0			0
$724$	−31.1882	−	13.1687i	−1.15910	−	0.489410i
$725$	−3.12679			−0.116126
$726$		0			0
$727$	−3.73446			−0.138503			−0.0692516	−	0.997599i	$-0.522061\pi$
$727$	−3.73446			−0.138503			−0.0692516	+	0.997599i	$0.522061\pi$
$728$	−19.6965	−	6.43355i	−0.730001	−	0.238443i
$729$		0			0
$730$	−6.09475	+	30.1032i	−0.225577	+	1.11417i
$731$	3.37649			0.124884
$732$		0			0
$733$	3.60035	−	3.60035i	0.132982	−	0.132982i	−0.637483	−	0.770465i	$-0.720024\pi$
$733$	3.60035	−	3.60035i	0.132982	−	0.132982i	0.770465	+	0.637483i	$0.220024\pi$
$734$	5.60585	−	27.6884i	0.206916	−	1.02200i
$735$		0			0
$736$	−8.10601	−	12.5914i	−0.298791	−	0.464124i
$737$	−21.8653			−0.805419
$738$		0			0
$739$	27.7960	−	27.7960i	1.02249	−	1.02249i	0.0227511	−	0.999741i	$-0.492757\pi$
$739$	27.7960	−	27.7960i	1.02249	−	1.02249i	0.999741	−	0.0227511i	$-0.00724252\pi$
$740$	−14.2054	−	5.99796i	−0.522200	−	0.220489i
$741$		0			0
$742$	−20.4039	+	13.5330i	−0.749052	+	0.496811i
$743$	0.361398	−	0.361398i	0.0132584	−	0.0132584i	−0.700447	−	0.713705i	$-0.747016\pi$
$743$	0.361398	−	0.361398i	0.0132584	−	0.0132584i	0.713705	+	0.700447i	$0.247016\pi$
$744$		0			0
$745$		−	53.4490i		−	1.95822i
$746$	−3.76836	+	18.6126i	−0.137969	+	0.681457i
$747$		0			0
$748$	1.32016	+	3.24971i	0.0482699	+	0.118821i
$749$	16.1832	+	16.1832i	0.591320	+	0.591320i
$750$		0			0
$751$	−51.2313			−1.86946			−0.934728	−	0.355365i	$-0.884357\pi$
$751$	−51.2313			−1.86946			−0.934728	+	0.355365i	$0.884357\pi$
$752$	0.0237723	−	1.74153i	0.000866887	−	0.0635069i
$753$		0			0
$754$	6.32166	+	5.34179i	0.230221	+	0.194537i
$755$	24.4665			0.890427
$756$		0			0
$757$		−	17.2708i		−	0.627717i	−0.949470	−	0.313859i	$-0.898378\pi$
$757$		−	17.2708i		−	0.627717i	0.949470	−	0.313859i	$-0.101622\pi$
$758$	−16.0935	−	24.2645i	−0.584543	−	0.881326i
$759$		0			0
$760$	−41.5986	−	28.4155i	−1.50894	−	1.03074i
$761$	18.4462	−	18.4462i	0.668674	−	0.668674i	−0.288735	−	0.957409i	$-0.593235\pi$
$761$	18.4462	−	18.4462i	0.668674	−	0.668674i	0.957409	+	0.288735i	$0.0932347\pi$
$762$		0			0
$763$	−11.4743			−0.415399
$764$	12.3126	−	29.1607i	0.445454	−	1.05500i
$765$		0			0
$766$	28.0860	−	18.6281i	1.01479	−	0.673062i
$767$	6.42337	+	22.0408i	0.231935	+	0.795848i
$768$		0			0
$769$	−5.58213	−	5.58213i	−0.201297	−	0.201297i	0.599259	−	0.800555i	$-0.295462\pi$
$769$	−5.58213	−	5.58213i	−0.201297	−	0.201297i	−0.800555	+	0.599259i	$0.795462\pi$
$770$	16.0050	−	10.6154i	0.576782	−	0.382553i
$771$		0			0
$772$	19.6894	−	7.99863i	0.708637	−	0.287877i
$773$	−24.5063	+	24.5063i	−0.881430	+	0.881430i	−0.993680	−	0.112250i	$-0.964194\pi$
$773$	−24.5063	+	24.5063i	−0.881430	+	0.881430i	0.112250	+	0.993680i	$0.464194\pi$
$774$		0			0
$775$	0.291983	+	0.291983i	0.0104883	+	0.0104883i
$776$	−10.2411	−	54.3896i	−0.367634	−	1.95247i
$777$		0			0
$778$	−22.3147	−	4.51789i	−0.800022	−	0.161974i
$779$		−	41.6908i		−	1.49373i
$780$		0			0
$781$			16.1955i			0.579520i
$782$	0.513026	−	2.53394i	0.0183458	−	0.0906134i
$783$		0			0
$784$	8.23251	−	8.01079i	0.294018	−	0.286100i
$785$	−18.9331	−	18.9331i	−0.675750	−	0.675750i
$786$		0			0
$787$	4.29751	−	4.29751i	0.153190	−	0.153190i	−0.626351	−	0.779541i	$-0.715452\pi$
$787$	4.29751	−	4.29751i	0.153190	−	0.153190i	0.779541	+	0.626351i	$0.215452\pi$
$788$	4.87658	−	1.98106i	0.173721	−	0.0705724i
$789$		0			0
$790$	17.0007	+	25.6323i	0.604859	+	0.911957i
$791$	3.74730	+	3.74730i	0.133239	+	0.133239i
$792$		0			0
$793$	−22.2166	−	12.1896i	−0.788934	−	0.432864i
$794$	−5.19922	−	7.83897i	−0.184514	−	0.278194i
$795$		0			0
$796$	7.51184	+	3.17174i	0.266250	+	0.112419i
$797$	−42.5322			−1.50657			−0.753284	−	0.657696i	$-0.771531\pi$
$797$	−42.5322			−1.50657			−0.753284	+	0.657696i	$0.771531\pi$
$798$		0			0
$799$	0.212622	−	0.212622i	0.00752204	−	0.00752204i
$800$	9.16280	−	5.89878i	0.323954	−	0.208554i
$801$		0			0
$802$	28.3953	−	18.8333i	1.00267	−	0.665026i
$803$			20.9574i			0.739570i
$804$		0			0
$805$	−14.1557			−0.498921
$806$	−0.0915007	−	1.08914i	−0.00322297	−	0.0383634i
$807$		0			0
$808$	40.9588	+	27.9785i	1.44093	+	0.984281i
$809$	−40.0149			−1.40685			−0.703425	−	0.710769i	$-0.748347\pi$
$809$	−40.0149			−1.40685			−0.703425	+	0.710769i	$0.748347\pi$
$810$		0			0
$811$	8.57419	+	8.57419i	0.301081	+	0.301081i	0.841437	−	0.540356i	$-0.181710\pi$
$811$	8.57419	+	8.57419i	0.301081	+	0.301081i	−0.540356	+	0.841437i	$0.681710\pi$
$812$	6.11082	−	2.48246i	0.214448	−	0.0871173i
$813$		0			0
$814$	−10.3123	−	2.08784i	−0.361445	−	0.0731789i
$815$			22.6589i			0.793708i
$816$		0			0
$817$	−23.3977	+	23.3977i	−0.818583	+	0.818583i
$818$	18.7440	+	28.2607i	0.655369	+	0.988112i
$819$		0			0
$820$	29.8719	+	12.6129i	1.04317	+	0.440461i
$821$	−8.87942	+	8.87942i	−0.309894	+	0.309894i	−0.844868	−	0.534974i	$-0.820321\pi$
$821$	−8.87942	+	8.87942i	−0.309894	+	0.309894i	0.534974	+	0.844868i	$0.320321\pi$
$822$		0			0
$823$	6.52071			0.227298			0.113649	−	0.993521i	$-0.463746\pi$
$823$	6.52071			0.227298			0.113649	+	0.993521i	$0.463746\pi$
$824$	−21.7204	−	14.8369i	−0.756664	−	0.516869i
$825$		0			0
$826$	17.9322	+	3.63060i	0.623942	+	0.126325i
$827$	−24.9705	+	24.9705i	−0.868308	+	0.868308i	−0.992285	−	0.123977i	$-0.960435\pi$
$827$	−24.9705	+	24.9705i	−0.868308	+	0.868308i	0.123977	+	0.992285i	$0.460435\pi$
$828$		0			0
$829$	−25.7131			−0.893052			−0.446526	−	0.894771i	$-0.647339\pi$
$829$	−25.7131			−0.893052			−0.446526	+	0.894771i	$0.647339\pi$
$830$	−45.4335	−	9.19857i	−1.57702	−	0.319287i
$831$		0			0
$832$	−28.6025	−	3.72768i	−0.991614	−	0.129234i
$833$	1.98314			0.0687117
$834$		0			0
$835$	−60.1900			−2.08296
$836$	−31.6674	−	13.3710i	−1.09524	−	0.462446i
$837$		0			0
$838$	22.8299	+	4.62219i	0.788646	+	0.159671i
$839$	−10.9775	−	10.9775i	−0.378984	−	0.378984i	0.491751	−	0.870736i	$-0.336357\pi$
$839$	−10.9775	−	10.9775i	−0.378984	−	0.378984i	−0.870736	+	0.491751i	$0.836357\pi$
$840$		0			0
$841$	26.3655			0.909154
$842$	−42.3050	+	28.0590i	−1.45793	+	0.966976i
$843$		0			0
$844$	28.6012	+	12.0763i	0.984494	+	0.415685i
$845$	−33.4019	−	7.40778i	−1.14906	−	0.254835i
$846$		0			0
$847$	−6.53748	+	6.53748i	−0.224630	+	0.224630i
$848$	−24.4272	+	23.7693i	−0.838832	+	0.816240i
$849$		0			0
$850$	1.84396	+	0.373332i	0.0632473	+	0.0128052i
$851$	5.48364	+	5.48364i	0.187977	+	0.187977i
$852$		0			0
$853$	19.1134	+	19.1134i	0.654432	+	0.654432i	0.954057	−	0.299625i	$-0.0968616\pi$
$853$	19.1134	+	19.1134i	0.654432	+	0.654432i	−0.299625	+	0.954057i	$0.596862\pi$
$854$	−16.8300	+	11.1626i	−0.575910	+	0.381975i
$855$		0			0
$856$	26.3076	+	17.9704i	0.899175	+	0.614216i
$857$		−	19.3319i		−	0.660365i	−0.943917	−	0.330182i	$-0.892890\pi$
$857$		−	19.3319i		−	0.660365i	0.943917	−	0.330182i	$-0.107110\pi$
$858$		0			0
$859$	−18.2400			−0.622341			−0.311170	−	0.950354i	$-0.600721\pi$
$859$	−18.2400			−0.622341			−0.311170	+	0.950354i	$0.600721\pi$
$860$	−9.68611	−	23.8433i	−0.330294	−	0.813050i
$861$		0			0
$862$	13.5474	−	8.98533i	0.461425	−	0.306042i
$863$	26.8308	−	26.8308i	0.913333	−	0.913333i	−0.0832003	−	0.996533i	$-0.526514\pi$
$863$	26.8308	−	26.8308i	0.913333	−	0.913333i	0.996533	+	0.0832003i	$0.0265141\pi$
$864$		0			0
$865$	−4.85405	+	4.85405i	−0.165043	+	0.165043i
$866$	−11.2146	+	55.3912i	−0.381088	+	1.88227i
$867$		0			0
$868$	−0.802447	−	0.338819i	−0.0272368	−	0.0115003i
$869$	14.8402	+	14.8402i	0.503421	+	0.503421i
$870$		0			0
$871$	29.8027	−	8.68543i	1.00983	−	0.294295i
$872$	−15.6972	+	2.95564i	−0.531573	+	0.100091i
$873$		0			0
$874$	14.0041	+	21.1143i	0.473697	+	0.714201i
$875$			16.4356i			0.555626i
$876$		0			0
$877$	7.21914	−	7.21914i	0.243773	−	0.243773i	−0.574636	−	0.818409i	$-0.694856\pi$
$877$	7.21914	−	7.21914i	0.243773	−	0.243773i	0.818409	+	0.574636i	$0.194856\pi$
$878$	−18.2738	−	3.69975i	−0.616711	−	0.124861i
$879$		0			0
$880$	19.1609	−	18.6449i	0.645914	−	0.628518i
$881$		−	46.5683i		−	1.56893i	−0.620175	−	0.784463i	$-0.712939\pi$
$881$		−	46.5683i		−	1.56893i	0.620175	−	0.784463i	$-0.287061\pi$
$882$		0			0
$883$			17.2990i			0.582156i	0.956699	+	0.291078i	$0.0940139\pi$
$883$			17.2990i			0.582156i	−0.956699	+	0.291078i	$0.905986\pi$
$884$	−3.09027	−	3.90500i	−0.103937	−	0.131339i
$885$		0			0
$886$	24.5052	+	4.96137i	0.823268	+	0.166681i
$887$			52.8158i			1.77338i	0.462363	+	0.886691i	$0.347002\pi$
$887$			52.8158i			1.77338i	−0.462363	+	0.886691i	$0.652998\pi$
$888$		0			0
$889$	−17.7962	−	17.7962i	−0.596866	−	0.596866i
$890$	7.80101	−	38.5307i	0.261491	−	1.29155i
$891$		0			0
$892$	−43.6450	+	17.7304i	−1.46134	+	0.593657i
$893$			2.94678i			0.0986102i
$894$		0			0
$895$	7.96525	+	7.96525i	0.266249	+	0.266249i
$896$	−13.2240	+	18.8029i	−0.441783	+	0.628160i
$897$		0			0
$898$	35.8443	−	23.7739i	1.19614	−	0.793344i
$899$	0.246016	+	0.246016i	0.00820509	+	0.00820509i
$900$		0			0
$901$	−5.88429			−0.196034
$902$	21.6853	+	4.39045i	0.722040	+	0.146186i
$903$		0			0
$904$	6.09165	+	4.16114i	0.202605	+	0.138397i
$905$	−31.5010	+	31.5010i	−1.04713	+	1.04713i
$906$		0			0
$907$		−	37.1283i		−	1.23283i	−0.787423	−	0.616413i	$-0.788585\pi$
$907$		−	37.1283i		−	1.23283i	0.787423	−	0.616413i	$-0.211415\pi$
$908$	−19.0130	−	46.8022i	−0.630967	−	1.55319i
$909$		0			0
$910$	−17.5984	+	20.8266i	−0.583382	+	0.690394i
$911$			15.7211i			0.520864i	0.965492	+	0.260432i	$0.0838650\pi$
$911$			15.7211i			0.520864i	−0.965492	+	0.260432i	$0.916135\pi$
$912$		0			0
$913$	−31.6301			−1.04680
$914$	3.11139	+	4.69109i	0.102915	+	0.155168i
$915$		0			0
$916$	18.8566	+	46.4174i	0.623041	+	1.53368i
$917$	−31.4550	−	31.4550i	−1.03873	−	1.03873i
$918$		0			0
$919$		−	7.88215i		−	0.260008i	−0.991513	−	0.130004i	$-0.958501\pi$
$919$		−	7.88215i		−	0.260008i	0.991513	−	0.130004i	$-0.0414991\pi$
$920$	−19.3653	+	3.64632i	−0.638455	+	0.120216i
$921$		0			0
$922$	6.99473	−	4.63928i	0.230359	−	0.152787i
$923$	−6.43325	−	22.0747i	−0.211753	−	0.726598i
$924$		0			0
$925$	−3.99047	+	3.99047i	−0.131206	+	0.131206i
$926$	23.5205	+	35.4622i	0.772930	+	1.16536i
$927$		0			0
$928$	7.72030	−	4.97014i	0.253431	−	0.163153i
$929$	8.30941	+	8.30941i	0.272623	+	0.272623i	0.830155	−	0.557532i	$-0.188252\pi$
$929$	8.30941	+	8.30941i	0.272623	+	0.272623i	−0.557532	+	0.830155i	$0.688252\pi$
$930$		0			0
$931$	−13.7424	+	13.7424i	−0.450388	+	0.450388i
$932$	−9.96337	+	23.5969i	−0.326361	+	0.772942i
$933$		0			0
$934$	−6.58471	+	32.5231i	−0.215458	+	1.06419i
$935$	4.61569			0.150949
$936$		0			0
$937$	−16.5484			−0.540614			−0.270307	−	0.962774i	$-0.587125\pi$
$937$	−16.5484			−0.540614			−0.270307	+	0.962774i	$0.587125\pi$
$938$	4.90915	−	24.2472i	0.160289	−	0.791701i
$939$		0			0
$940$	−2.11140	−	0.891499i	−0.0688662	−	0.0290775i
$941$	25.9580	−	25.9580i	0.846207	−	0.846207i	−0.143450	−	0.989658i	$-0.545820\pi$
$941$	25.9580	−	25.9580i	0.846207	−	0.846207i	0.989658	+	0.143450i	$0.0458197\pi$
$942$		0			0
$943$	−11.5313	−	11.5313i	−0.375512	−	0.375512i
$944$	25.4669	+	0.347631i	0.828878	+	0.0113144i
$945$		0			0
$946$	−9.70620	−	14.6342i	−0.315576	−	0.475799i
$947$	−42.7738	+	42.7738i	−1.38996	+	1.38996i	−0.564594	+	0.825369i	$0.690967\pi$
$947$	−42.7738	+	42.7738i	−1.38996	+	1.38996i	−0.825369	+	0.564594i	$0.809033\pi$
$948$		0			0
$949$	−8.32478	−	28.5652i	−0.270234	−	0.927266i
$950$	−15.3650	+	10.1909i	−0.498506	+	0.330636i
$951$		0			0
$952$	−3.90012	+	0.734360i	−0.126404	+	0.0238008i
$953$		−	29.1352i		−	0.943782i	−0.881657	−	0.471891i	$-0.843571\pi$
$953$		−	29.1352i		−	0.943782i	0.881657	−	0.471891i	$-0.156429\pi$
$954$		0			0
$955$	−29.4531	−	29.4531i	−0.953081	−	0.953081i
$956$	−16.2504	+	6.60156i	−0.525575	+	0.213510i
$957$		0			0
$958$	−1.61895	−	2.44092i	−0.0523059	−	0.0788625i
$959$	−41.0915			−1.32691
$960$		0			0
$961$			30.9541i			0.998518i
$962$	14.8851	−	1.25052i	0.479915	−	0.0403185i
$963$		0			0
$964$	−0.390140	+	0.158491i	−0.0125656	+	0.00510464i
$965$		−	27.9657i		−	0.900247i
$966$		0			0
$967$	−10.2496	+	10.2496i	−0.329605	+	0.329605i	−0.852436	−	0.522831i	$-0.824876\pi$
$967$	−10.2496	+	10.2496i	−0.329605	+	0.329605i	0.522831	+	0.852436i	$0.324876\pi$
$968$	−7.25946	+	10.6274i	−0.233328	+	0.341578i
$969$		0			0
$970$	−71.3808	−	14.4519i	−2.29190	−	0.464023i
$971$	−35.4423			−1.13740			−0.568699	−	0.822546i	$-0.692553\pi$
$971$	−35.4423			−1.13740			−0.568699	+	0.822546i	$0.692553\pi$
$972$		0			0
$973$	21.8559	+	21.8559i	0.700669	+	0.700669i
$974$	41.4512	−	27.4927i	1.32818	−	0.880923i
$975$		0			0
$976$	−20.1485	+	19.6059i	−0.644938	+	0.627568i
$977$	29.5425	+	29.5425i	0.945148	+	0.945148i	0.998572	−	0.0534239i	$-0.0170135\pi$
$977$	29.5425	+	29.5425i	0.945148	+	0.945148i	−0.0534239	+	0.998572i	$0.517013\pi$
$978$		0			0
$979$		−	26.8245i		−	0.857315i
$980$	−5.68902	−	14.0041i	−0.181729	−	0.447344i
$981$		0			0
$982$	−1.60245	+	7.91480i	−0.0511362	+	0.252571i
$983$	−3.65881	−	3.65881i	−0.116698	−	0.116698i	0.646346	−	0.763044i	$-0.276296\pi$
$983$	−3.65881	−	3.65881i	−0.116698	−	0.116698i	−0.763044	+	0.646346i	$0.776296\pi$
$984$		0			0
$985$		−	6.92640i		−	0.220693i
$986$	1.55367	+	0.314558i	0.0494788	+	0.0100176i
$987$		0			0
$988$	48.4745	+	5.64580i	1.54218	+	0.179617i
$989$			12.9432i			0.411571i
$990$		0			0
$991$			39.2069i			1.24545i	0.782442	+	0.622724i	$0.213974\pi$
$991$			39.2069i			1.24545i	−0.782442	+	0.622724i	$0.786026\pi$
$992$	−1.18504	−	0.256813i	−0.0376252	−	0.00815381i
$993$		0			0
$994$	−17.9598	−	3.63618i	−0.569650	−	0.115333i
$995$	7.58716	−	7.58716i	0.240529	−	0.240529i
$996$		0			0
$997$			9.56104i			0.302801i	0.988472	+	0.151401i	$0.0483784\pi$
$997$			9.56104i			0.302801i	−0.988472	+	0.151401i	$0.951622\pi$
$998$	24.2592	+	36.5760i	0.767910	+	1.15779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.w.k.307.23	yes	48
3.2	odd	2	inner	936.2.w.k.307.2	✓	48
8.3	odd	2	inner	936.2.w.k.307.14	yes	48
13.5	odd	4	inner	936.2.w.k.811.14	yes	48
24.11	even	2	inner	936.2.w.k.307.11	yes	48
39.5	even	4	inner	936.2.w.k.811.11	yes	48
104.83	even	4	inner	936.2.w.k.811.23	yes	48
312.83	odd	4	inner	936.2.w.k.811.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.w.k.307.2	✓	48	3.2	odd	2	inner
936.2.w.k.307.11	yes	48	24.11	even	2	inner
936.2.w.k.307.14	yes	48	8.3	odd	2	inner
936.2.w.k.307.23	yes	48	1.1	even	1	trivial
936.2.w.k.811.2	yes	48	312.83	odd	4	inner
936.2.w.k.811.11	yes	48	39.5	even	4	inner
936.2.w.k.811.14	yes	48	13.5	odd	4	inner
936.2.w.k.811.23	yes	48	104.83	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38609 + 0.280631i) q^{2} +(1.84249 + 0.777959i) q^{4} +(1.86097 - 1.86097i) q^{5} +(1.43671 + 1.43671i) q^{7} +(2.33554 + 1.59538i) q^{8} +(3.10171 - 2.05722i) q^{10} +(1.79579 - 1.79579i) q^{11} +(-1.73435 + 3.16102i) q^{13} +(1.58823 + 2.39460i) q^{14} +(2.78956 + 2.86677i) q^{16} +0.690579i q^{17} +(-4.78545 - 4.78545i) q^{19} +(4.87658 - 1.98106i) q^{20} +(2.99308 - 1.98517i) q^{22} -2.64723 q^{23} -1.92640i q^{25} +(-3.29105 + 3.89474i) q^{26} +(1.52943 + 3.76484i) q^{28} -1.62313i q^{29} +(-0.151569 + 0.151569i) q^{31} +(3.06208 + 4.75644i) q^{32} +(-0.193798 + 0.957205i) q^{34} +5.34736 q^{35} +(-2.07147 - 2.07147i) q^{37} +(-5.29012 - 7.97600i) q^{38} +(7.31532 - 1.37741i) q^{40} +(4.35600 + 4.35600i) q^{41} -4.88935i q^{43} +(4.70577 - 1.91168i) q^{44} +(-3.66929 - 0.742893i) q^{46} +(-0.307890 - 0.307890i) q^{47} -2.87170i q^{49} +(0.540607 - 2.67016i) q^{50} +(-5.65468 + 4.47489i) q^{52} +8.52080i q^{53} -6.68380i q^{55} +(1.06340 + 5.64761i) q^{56} +(0.455500 - 2.24980i) q^{58} +(4.50238 - 4.50238i) q^{59} +7.02830i q^{61} +(-0.252623 + 0.167553i) q^{62} +(2.90951 + 7.45216i) q^{64} +(2.65497 + 9.11012i) q^{65} +(-6.08794 - 6.08794i) q^{67} +(-0.537242 + 1.27239i) q^{68} +(7.41192 + 1.50063i) q^{70} +(-4.50930 + 4.50930i) q^{71} +(-5.83515 + 5.83515i) q^{73} +(-2.28992 - 3.45256i) q^{74} +(-5.09427 - 12.5400i) q^{76} +5.16007 q^{77} +8.26392i q^{79} +(10.5262 + 0.143686i) q^{80} +(4.81539 + 7.26024i) q^{82} +(-8.80676 - 8.80676i) q^{83} +(1.28515 + 1.28515i) q^{85} +(1.37210 - 6.77709i) q^{86} +(7.05910 - 1.32917i) q^{88} +(7.46873 - 7.46873i) q^{89} +(-7.03325 + 2.04970i) q^{91} +(-4.87749 - 2.05943i) q^{92} +(-0.340360 - 0.513166i) q^{94} -17.8111 q^{95} +(-13.8363 - 13.8363i) q^{97} +(0.805889 - 3.98044i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 40 q^{16} - 8 q^{19} - 32 q^{22} + 24 q^{28} + 8 q^{34} + 16 q^{40} - 8 q^{46} + 24 q^{52} - 24 q^{58} + 40 q^{67} - 24 q^{70} + 56 q^{76} + 104 q^{91} - 64 q^{94} - 32 q^{97}+O(q^{100}) \) 48 * q - 40 * q^16 - 8 * q^19 - 32 * q^22 + 24 * q^28 + 8 * q^34 + 16 * q^40 - 8 * q^46 + 24 * q^52 - 24 * q^58 + 40 * q^67 - 24 * q^70 + 56 * q^76 + 104 * q^91 - 64 * q^94 - 32 * q^97

Introduction

L-functions

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