LMFDB - Embedded newform 936.2.w.k.307.11

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			307.11
Character	$\chi$	$=$	936.307
Dual form			936.2.w.k.811.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.280631 - 1.38609i) q^{2} +(-1.84249 + 0.777959i) q^{4} +(1.86097 - 1.86097i) q^{5} +(-1.43671 - 1.43671i) q^{7} +(1.59538 + 2.33554i) q^{8} +(-3.10171 - 2.05722i) q^{10} +(-1.79579 + 1.79579i) q^{11} +(1.73435 - 3.16102i) q^{13} +(-1.58823 + 2.39460i) q^{14} +(2.78956 - 2.86677i) q^{16} -0.690579i q^{17} +(-4.78545 - 4.78545i) q^{19} +(-1.98106 + 4.87658i) q^{20} +(2.99308 + 1.98517i) q^{22} -2.64723 q^{23} -1.92640i q^{25} +(-4.86817 - 1.51689i) q^{26} +(3.76484 + 1.52943i) q^{28} -1.62313i q^{29} +(0.151569 - 0.151569i) q^{31} +(-4.75644 - 3.06208i) q^{32} +(-0.957205 + 0.193798i) q^{34} -5.34736 q^{35} +(2.07147 + 2.07147i) q^{37} +(-5.29012 + 7.97600i) q^{38} +(7.31532 + 1.37741i) q^{40} +(-4.35600 - 4.35600i) q^{41} -4.88935i q^{43} +(1.91168 - 4.70577i) q^{44} +(0.742893 + 3.66929i) q^{46} +(-0.307890 - 0.307890i) q^{47} -2.87170i q^{49} +(-2.67016 + 0.540607i) q^{50} +(-0.736393 + 7.17340i) q^{52} +8.52080i q^{53} +6.68380i q^{55} +(1.06340 - 5.64761i) q^{56} +(-2.24980 + 0.455500i) q^{58} +(-4.50238 + 4.50238i) q^{59} -7.02830i q^{61} +(-0.252623 - 0.167553i) q^{62} +(-2.90951 + 7.45216i) q^{64} +(-2.65497 - 9.11012i) q^{65} +(-6.08794 - 6.08794i) q^{67} +(0.537242 + 1.27239i) q^{68} +(1.50063 + 7.41192i) q^{70} +(-4.50930 + 4.50930i) q^{71} +(-5.83515 + 5.83515i) q^{73} +(2.28992 - 3.45256i) q^{74} +(12.5400 + 5.09427i) q^{76} +5.16007 q^{77} -8.26392i q^{79} +(-0.143686 - 10.5262i) q^{80} +(-4.81539 + 7.26024i) q^{82} +(8.80676 + 8.80676i) q^{83} +(-1.28515 - 1.28515i) q^{85} +(-6.77709 + 1.37210i) q^{86} +(-7.05910 - 1.32917i) q^{88} +(-7.46873 + 7.46873i) q^{89} +(-7.03325 + 2.04970i) q^{91} +(4.87749 - 2.05943i) q^{92} +(-0.340360 + 0.513166i) q^{94} -17.8111 q^{95} +(-13.8363 - 13.8363i) q^{97} +(-3.98044 + 0.805889i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.280631	−	1.38609i	−0.198436	−	0.980114i
$2$	−0.280631	−	1.38609i	−0.198436	−	0.980114i
$3$		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	0.381388	−	0.924415i	$-0.375446\pi$
$7$	−1.43671	−	1.43671i	−0.543027	−	0.543027i	−0.924415	+	0.381388i	$0.875446\pi$
$8$	1.59538	+	2.33554i	0.564053	+	0.825739i
$9$		0			0
$10$	−3.10171	−	2.05722i	−0.980848	−	0.650551i
$11$	−1.79579	+	1.79579i	−0.541450	+	0.541450i	−0.923954	−	0.382504i	$-0.875062\pi$
$11$	−1.79579	+	1.79579i	−0.541450	+	0.541450i	0.382504	+	0.923954i	$0.375062\pi$
$12$		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	$-0.973312\pi$
$17$		−	0.690579i		−	0.167490i	0.996487	−	0.0837450i	$-0.0266881\pi$
$18$		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	$-0.532907\pi$
$20$	−1.98106	+	4.87658i	−0.442979	+	1.09044i
$21$		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
$26$	−4.86817	−	1.51689i	−0.954726	−	0.297487i
$27$		0			0
$28$	3.76484	+	1.52943i	0.711488	+	0.289035i
$29$		−	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	−0.693364	−	0.720587i	$-0.743872\pi$
$31$	0.151569	−	0.151569i	0.0272226	−	0.0272226i	0.720587	+	0.693364i	$0.243872\pi$
$32$	−4.75644	−	3.06208i	−0.840827	−	0.541304i
$33$		0			0
$34$	−0.957205	+	0.193798i	−0.164159	+	0.0332360i
$35$	−5.34736			−0.903868
$36$		0			0
$37$	2.07147	+	2.07147i	0.340547	+	0.340547i	0.856573	−	0.516026i	$-0.172589\pi$
$37$	2.07147	+	2.07147i	0.340547	+	0.340547i	−0.516026	+	0.856573i	$0.672589\pi$
$38$	−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	0.279773	−	0.960066i	$-0.409741\pi$
$41$	−4.35600	−	4.35600i	−0.680294	−	0.680294i	−0.960066	+	0.279773i	$0.909741\pi$
$42$		0			0
$43$		−	4.88935i		−	0.745620i	−0.927908	−	0.372810i	$-0.878394\pi$
$43$		−	4.88935i		−	0.745620i	0.927908	−	0.372810i	$-0.121606\pi$
$44$	1.91168	−	4.70577i	0.288196	−	0.709422i
$45$		0			0
$46$	0.742893	+	3.66929i	0.109534	+	0.541008i
$47$	−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
$50$	−2.67016	+	0.540607i	−0.377618	+	0.0764534i
$51$		0			0
$52$	−0.736393	+	7.17340i	−0.102119	+	0.994772i
$53$			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
$58$	−2.24980	+	0.455500i	−0.295413	+	0.0598100i
$59$	−4.50238	+	4.50238i	−0.586160	+	0.586160i	−0.936589	−	0.350429i	$-0.886036\pi$
$59$	−4.50238	+	4.50238i	−0.586160	+	0.586160i	0.350429	+	0.936589i	$0.386036\pi$
$60$		0			0
$61$		−	7.02830i		−	0.899882i	−0.893058	−	0.449941i	$-0.851445\pi$
$61$		−	7.02830i		−	0.899882i	0.893058	−	0.449941i	$-0.148555\pi$
$62$	−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
$70$	1.50063	+	7.41192i	0.179360	+	0.885894i
$71$	−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
$76$	12.5400	+	5.09427i	1.43844	+	0.584352i
$77$	5.16007			0.588044
$78$		0			0
$79$		−	8.26392i		−	0.929764i	−0.885373	−	0.464882i	$-0.846097\pi$
$79$		−	8.26392i		−	0.929764i	0.885373	−	0.464882i	$-0.153903\pi$
$80$	−0.143686	−	10.5262i	−0.0160646	−	1.17687i
$81$		0			0
$82$	−4.81539	+	7.26024i	−0.531770	+	0.801760i
$83$	8.80676	+	8.80676i	0.966668	+	0.966668i	0.999462	−	0.0327944i	$-0.0104407\pi$
$83$	8.80676	+	8.80676i	0.966668	+	0.966668i	−0.0327944	+	0.999462i	$0.510441\pi$
$84$		0			0
$85$	−1.28515	−	1.28515i	−0.139394	−	0.139394i
$86$	−6.77709	+	1.37210i	−0.730792	+	0.147958i
$87$		0			0
$88$	−7.05910	−	1.32917i	−0.752503	−	0.141690i
$89$	−7.46873	+	7.46873i	−0.791684	+	0.791684i	−0.981768	−	0.190084i	$-0.939124\pi$
$89$	−7.46873	+	7.46873i	−0.791684	+	0.791684i	0.190084	+	0.981768i	$0.439124\pi$
$90$		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	$-0.713385\pi$
$98$	−3.98044	+	0.805889i	−0.402085	+	0.0814071i
$99$		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	$-0.348504\pi$
$103$	9.29992			0.916348			0.458174	+	0.888862i	$0.348504\pi$
$104$	10.1496	−	0.992371i	0.995254	−	0.0973100i
$105$		0			0
$106$	11.8106	−	2.39120i	1.14715	−	0.232254i
$107$	−11.2640			−1.08893			−0.544467	−	0.838782i	$-0.683268\pi$
$107$	−11.2640			−1.08893			−0.544467	+	0.838782i	$0.683268\pi$
$108$		0			0
$109$	3.99325	−	3.99325i	0.382484	−	0.382484i	−0.489512	−	0.871996i	$-0.662825\pi$
$109$	3.99325	−	3.99325i	0.382484	−	0.382484i	0.871996	+	0.489512i	$0.162825\pi$
$110$	9.26435	−	1.87568i	0.883322	−	0.178839i
$111$		0			0
$112$	−8.12653	+	0.110929i	−0.767885	+	0.0104818i
$113$	−2.60824			−0.245363			−0.122681	−	0.992446i	$-0.539149\pi$
$113$	−2.60824			−0.245363			−0.122681	+	0.992446i	$0.539149\pi$
$114$		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
$122$	−9.74186	+	1.97236i	−0.881987	+	0.178569i
$123$		0			0
$124$	−0.161350	+	0.397179i	−0.0144897	+	0.0356678i
$125$	5.71987	+	5.71987i	0.511601	+	0.511601i
$126$		0			0
$127$	12.3867			1.09915			0.549573	−	0.835446i	$-0.314790\pi$
$127$	12.3867			1.09915			0.549573	+	0.835446i	$0.314790\pi$
$128$	11.1459	+	1.94154i	0.985165	+	0.171609i
$129$		0			0
$130$	−11.8824	+	6.23661i	−1.04215	+	0.546987i
$131$	21.8937			1.91286			0.956430	−	0.291961i	$-0.0943077\pi$
$131$	21.8937			1.91286			0.956430	+	0.291961i	$0.0943077\pi$
$132$		0			0
$133$			13.7506i			1.19233i
$134$	−6.72997	+	10.1469i	−0.581381	+	0.876559i
$135$		0			0
$136$	1.61288	−	1.10174i	0.138303	−	0.0944732i
$137$	14.3005	−	14.3005i	1.22177	−	1.22177i	0.254773	−	0.967001i	$-0.417999\pi$
$137$	14.3005	−	14.3005i	1.22177	−	1.22177i	0.967001	−	0.254773i	$-0.0820007\pi$
$138$		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
$148$	−5.42818	−	2.20514i	−0.446193	−	0.181262i
$149$	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	0.387090	−	0.922042i	$-0.373480\pi$
$151$	−6.57360	−	6.57360i	−0.534952	−	0.534952i	−0.922042	+	0.387090i	$0.873480\pi$
$152$	3.54199	−	18.8112i	0.287294	−	1.52579i
$153$		0			0
$154$	−1.44807	−	7.15232i	−0.116689	−	0.576350i
$155$		−	0.564130i		−	0.0453120i
$156$		0			0
$157$			10.1738i			0.811955i	0.913883	+	0.405978i	$0.133069\pi$
$157$			10.1738i			0.811955i	−0.913883	+	0.405978i	$0.866931\pi$
$158$	−11.4545	+	2.31911i	−0.911275	+	0.184499i
$159$		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	$0.359473\pi$
$164$	11.4147	+	4.63711i	0.891338	+	0.362098i
$165$		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
$176$	0.138653	+	10.1576i	0.0104514	+	0.765655i
$177$		0			0
$178$	12.4483	+	8.25638i	0.933039	+	0.618842i
$179$		−	4.28017i		−	0.319915i	−0.987124	−	0.159957i	$-0.948864\pi$
$179$		−	4.28017i		−	0.319915i	0.987124	−	0.159957i	$-0.0511357\pi$
$180$		0			0
$181$	16.9272			1.25819			0.629095	−	0.777329i	$-0.283426\pi$
$181$	16.9272			1.25819			0.629095	+	0.777329i	$0.283426\pi$
$182$	4.81482	+	9.17350i	0.356898	+	0.679985i
$183$		0			0
$184$	−4.22334	−	6.18271i	−0.311348	−	0.455795i
$185$	7.70986			0.566840
$186$		0			0
$187$	1.24013	+	1.24013i	0.0906875	+	0.0906875i
$188$	0.806811	+	0.327759i	0.0588427	+	0.0239043i
$189$		0			0
$190$	4.99835	+	24.6878i	0.362618	+	1.79104i
$191$		−	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	$-0.546159\pi$
$199$	−4.07700			−0.289011			−0.144505	+	0.989504i	$0.546159\pi$
$200$	4.49919	−	3.07334i	0.318141	−	0.217318i
$201$		0			0
$202$	−4.92147	−	24.3081i	−0.346274	−	1.71031i
$203$	−2.33197	+	2.33197i	−0.163672	+	0.163672i
$204$		0			0
$205$	−16.2128			−1.13235
$206$	−2.60984	−	12.8905i	−0.181836	−	0.898126i
$207$		0			0
$208$	−4.22382	−	13.7898i	−0.292869	−	0.956153i
$209$	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
$214$	3.16103	+	15.6129i	0.216084	+	1.06728i
$215$	−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	$-0.460774\pi$
$223$	16.6555	−	16.6555i	1.11534	−	1.11534i	0.992417	−	0.122920i	$-0.0392259\pi$
$224$	2.43431	+	11.2330i	0.162649	+	0.750534i
$225$		0			0
$226$	0.731953	+	3.61526i	0.0486888	+	0.240483i
$227$	17.8604	+	17.8604i	1.18543	+	1.18543i	0.978316	+	0.207118i	$0.0664084\pi$
$227$	17.8604	+	17.8604i	1.18543	+	1.18543i	0.207118	+	0.978316i	$0.433592\pi$
$228$		0			0
$229$	−17.7135	−	17.7135i	−1.17054	−	1.17054i	−0.982080	−	0.188462i	$-0.939650\pi$
$229$	−17.7135	−	17.7135i	−1.17054	−	1.17054i	−0.188462	−	0.982080i	$-0.560350\pi$
$230$	8.21094	+	5.44594i	0.541413	+	0.359094i
$231$		0			0
$232$	3.79088	−	2.58951i	0.248884	−	0.170010i
$233$		−	12.8071i		−	0.839018i	−0.907751	−	0.419509i	$-0.862202\pi$
$233$		−	12.8071i		−	0.839018i	0.907751	−	0.419509i	$-0.137798\pi$
$234$		0			0
$235$	−1.14595			−0.0747533
$236$	4.79294	−	11.7983i	0.311994	−	0.768002i
$237$		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	$0.252159\pi$
$242$	6.30712	−	1.27695i	0.405437	−	0.0820857i
$243$		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	$0.136985\pi$
$251$			13.2191i			0.834382i	−0.908819	+	0.417191i	$0.863015\pi$
$252$		0			0
$253$	4.75385	−	4.75385i	0.298872	−	0.298872i
$254$	−3.47610	−	17.1692i	−0.218110	−	1.07729i
$255$		0			0
$256$	−0.436727	−	15.9940i	−0.0272955	−	0.999627i
$257$		−	15.5812i		−	0.971928i	−0.873979	−	0.485964i	$-0.838469\pi$
$257$		−	15.5812i		−	0.971928i	0.873979	−	0.485964i	$-0.161531\pi$
$258$		0			0
$259$		−	5.95221i		−	0.369852i
$260$	11.9791	+	14.7199i	0.742910	+	0.912888i
$261$		0			0
$262$	−6.14404	−	30.3466i	−0.379580	−	1.87482i
$263$			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
$266$	19.0596	−	3.85885i	1.16862	−	0.236601i
$267$		0			0
$268$	15.9532	+	6.48082i	0.974494	+	0.395879i
$269$		−	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	0.347965	−	0.937508i	$-0.386873\pi$
$271$	−9.70510	−	9.70510i	−0.589543	−	0.589543i	−0.937508	+	0.347965i	$0.886873\pi$
$272$	−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	$-0.596023\pi$
$277$	−9.88979			−0.594220			−0.297110	+	0.954843i	$0.596023\pi$
$278$	−4.26908	−	21.0858i	−0.256042	−	1.26464i
$279$		0			0
$280$	−8.53108	−	12.4890i	−0.509829	−	0.746359i
$281$	−0.916519	+	0.916519i	−0.0546749	+	0.0546749i	−0.733916	−	0.679241i	$-0.762309\pi$
$281$	−0.916519	+	0.916519i	−0.0546749	+	0.0546749i	0.679241	+	0.733916i	$0.262309\pi$
$282$		0			0
$283$		−	0.356000i		−	0.0211620i	−0.999944	−	0.0105810i	$-0.996632\pi$
$283$		−	0.356000i		−	0.0211620i	0.999944	−	0.0105810i	$-0.00336810\pi$
$284$	4.80030	−	11.8164i	0.284846	−	0.701175i
$285$		0			0
$286$	11.4662	−	6.01817i	0.678011	−	0.355862i
$287$			12.5167i			0.738836i
$288$		0			0
$289$	16.5231			0.971947
$290$	−3.33914	+	5.03448i	−0.196081	+	0.295635i
$291$		0			0
$292$	6.21171	−	15.2907i	0.363513	−	0.894822i
$293$	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
$304$	−27.0680	+	0.369486i	−1.55246	+	0.0211915i
$305$	−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
$310$	−0.781935	+	0.158312i	−0.0444109	+	0.00899153i
$311$	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	$0.519742\pi$
$314$	14.1018	−	2.85507i	0.795808	−	0.161121i
$315$		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
$320$	8.45373	+	19.2827i	0.472578	+	1.07794i
$321$		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	$0.570180\pi$
$332$	−23.0777	−	9.37509i	−1.26655	−	0.514525i
$333$		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	$0.865492\pi$
$338$	−13.2380	+	12.7575i	−0.720055	+	0.693917i
$339$		0			0
$340$	3.36766	+	1.36808i	0.182637	+	0.0741945i
$341$			0.544371i			0.0294794i
$342$		0			0
$343$	−14.1828	+	14.1828i	−0.765800	+	0.765800i
$344$	11.4193	−	7.80039i	0.615687	−	0.420569i
$345$		0			0
$346$	0.731983	+	3.61541i	0.0393517	+	0.194366i
$347$	−17.4406			−0.936262			−0.468131	−	0.883659i	$-0.655073\pi$
$347$	−17.4406			−0.936262			−0.468131	+	0.883659i	$0.655073\pi$
$348$		0			0
$349$	20.1757	+	20.1757i	1.07998	+	1.07998i	0.996511	+	0.0834674i	$0.0265995\pi$
$349$	20.1757	+	20.1757i	1.07998	+	1.07998i	0.0834674	+	0.996511i	$0.473401\pi$
$350$	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	0.870676	−	0.491858i	$-0.163682\pi$
$353$	7.11735	+	7.11735i	0.378818	+	0.378818i	−0.491858	+	0.870676i	$0.663682\pi$
$354$		0			0
$355$			16.7833i			0.890767i
$356$	7.95071	−	19.5715i	0.421387	−	1.03728i
$357$		0			0
$358$	−5.93270	+	1.20115i	−0.313553	+	0.0634826i
$359$	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
$362$	−4.75029	−	23.4626i	−0.249670	−	1.23317i
$363$		0			0
$364$	11.3641	−	9.24815i	0.595642	−	0.484735i
$365$			21.7180i			1.13677i
$366$		0			0
$367$			19.9759i			1.04273i	0.853333	+	0.521366i	$0.174577\pi$
$367$			19.9759i			1.04273i	−0.853333	+	0.521366i	$0.825423\pi$
$368$	−7.38459	+	7.58898i	−0.384948	+	0.395603i
$369$		0			0
$370$	−2.16362	−	10.6866i	−0.112482	−	0.555568i
$371$	12.2420	−	12.2420i	0.635571	−	0.635571i
$372$		0			0
$373$		−	13.4282i		−	0.695284i	−0.937627	−	0.347642i	$-0.886983\pi$
$373$		−	13.4282i		−	0.695284i	0.937627	−	0.347642i	$-0.113017\pi$
$374$	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
$382$	−21.9374	+	4.44148i	−1.12241	+	0.227246i
$383$	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
$388$	36.2575	+	14.7292i	1.84069	+	0.747764i
$389$	−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
$392$	6.70699	−	4.58147i	0.338754	−	0.231399i
$393$		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	0.815211	−	0.579163i	$-0.196621\pi$
$397$	4.70323	+	4.70323i	0.236048	+	0.236048i	−0.579163	+	0.815211i	$0.696621\pi$
$398$	1.14413	+	5.65109i	0.0573501	+	0.283263i
$399$		0			0
$400$	−5.52254	−	5.37381i	−0.276127	−	0.268690i
$401$	−17.0366	+	17.0366i	−0.850768	+	0.850768i	−0.990228	−	0.139460i	$-0.955463\pi$
$401$	−17.0366	+	17.0366i	−0.850768	+	0.850768i	0.139460	+	0.990228i	$0.455463\pi$
$402$		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	$0.548004\pi$
$410$	4.54980	+	22.4724i	0.224699	+	1.10983i
$411$		0			0
$412$	−17.1350	+	7.23496i	−0.844183	+	0.356441i
$413$	12.9373			0.636602
$414$		0			0
$415$	32.7782			1.60902
$416$	−17.9286	+	9.72444i	−0.879023	+	0.476780i
$417$		0			0
$418$	−4.82328	−	23.8231i	−0.235914	−	1.16523i
$419$	−16.4707			−0.804647			−0.402323	−	0.915498i	$-0.631797\pi$
$419$	−16.4707			−0.804647			−0.402323	+	0.915498i	$0.631797\pi$
$420$		0			0
$421$	25.3822	−	25.3822i	1.23705	−	1.23705i	0.275851	−	0.961201i	$-0.411040\pi$
$421$	25.3822	−	25.3822i	1.23705	−	1.23705i	0.961201	−	0.275851i	$-0.0889595\pi$
$422$	−4.35626	−	21.5164i	−0.212059	−	1.04740i
$423$		0			0
$424$	−19.9007	+	13.5939i	−0.966463	+	0.660180i
$425$	−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	$0.590073\pi$
$434$	0.122221	+	0.603674i	0.00586680	+	0.0289773i
$435$		0			0
$436$	−4.25095	+	10.4641i	−0.203584	+	0.501141i
$437$	12.6682	+	12.6682i	0.606000	+	0.606000i
$438$		0			0
$439$	13.1837			0.629224			0.314612	−	0.949220i	$-0.398126\pi$
$439$	13.1837			0.629224			0.314612	+	0.949220i	$0.398126\pi$
$440$	−15.6103	+	10.6632i	−0.744192	+	0.508349i
$441$		0			0
$442$	−1.04753	+	3.36185i	−0.0498261	+	0.159907i
$443$	−17.6794			−0.839972			−0.419986	−	0.907531i	$-0.637965\pi$
$443$	−17.6794			−0.839972			−0.419986	+	0.907531i	$0.637965\pi$
$444$		0			0
$445$			27.7981i			1.31776i
$446$	−27.7601	−	18.4120i	−1.31448	−	0.871834i
$447$		0			0
$448$	14.8868	−	6.52649i	0.703334	−	0.308348i
$449$	−21.5059	+	21.5059i	−1.01492	+	1.01492i	−0.0150379	+	0.999887i	$0.504787\pi$
$449$	−21.5059	+	21.5059i	−1.01492	+	1.01492i	−0.999887	+	0.0150379i	$0.995213\pi$
$450$		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
$460$	5.24432	−	12.9094i	0.244518	−	0.601904i
$461$	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	0.0111288	−	0.999938i	$-0.496458\pi$
$463$	−21.2766	−	21.2766i	−0.988809	−	0.988809i	−0.999938	+	0.0111288i	$0.996458\pi$
$464$	−4.65313	−	4.52781i	−0.216016	−	0.210198i
$465$		0			0
$466$	−17.7517	+	3.59405i	−0.822333	+	0.166491i
$467$		−	23.4639i		−	1.08578i	−0.839803	−	0.542891i	$-0.817330\pi$
$467$		−	23.4639i		−	1.08578i	0.839803	−	0.542891i	$-0.182670\pi$
$468$		0			0
$469$			17.4933i			0.807764i
$470$	0.321588	+	1.58838i	0.0148337	+	0.0732667i
$471$		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
$476$	1.05619	−	2.59992i	0.0484105	−	0.119167i
$477$		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	$0.543520\pi$
$487$	−24.8699	+	24.8699i	−1.12696	+	1.12696i	−0.990668	+	0.136296i	$0.956480\pi$
$488$	16.4149	−	11.2128i	0.743068	−	0.507581i
$489$		0			0
$490$	−5.90774	+	8.90721i	−0.266884	+	0.402387i
$491$		−	5.71016i		−	0.257696i	−0.991664	−	0.128848i	$-0.958872\pi$
$491$		−	5.71016i		−	0.257696i	0.991664	−	0.128848i	$-0.0411279\pi$
$492$		0			0
$493$	−1.12090			−0.0504827
$494$	16.0373	+	30.5554i	0.721554	+	1.37475i
$495$		0			0
$496$	−0.0117027	−	0.857324i	−0.000525467	−	0.0384950i
$497$	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	$0.505558\pi$
$500$	−14.9886	−	6.08899i	−0.670313	−	0.272308i
$501$		0			0
$502$	18.3229	−	3.70969i	0.817789	−	0.165571i
$503$		−	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
$512$	−22.0466	+	5.09376i	−0.974332	+	0.225115i
$513$		0			0
$514$	−21.5969	+	4.37256i	−0.952600	+	0.192865i
$515$	17.3069	−	17.3069i	0.762631	−	0.762631i
$516$		0			0
$517$	1.10581			0.0486334
$518$	−8.25030	+	1.67037i	−0.362497	+	0.0733920i
$519$		0			0
$520$	17.0414	−	20.7349i	0.747314	−	0.909286i
$521$	−24.1479			−1.05794			−0.528969	−	0.848641i	$-0.677421\pi$
$521$	−24.1479			−1.05794			−0.528969	+	0.848641i	$0.677421\pi$
$522$		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
$526$	21.7225	−	4.39798i	0.947145	−	0.191761i
$527$	−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
$538$	−10.7677	+	2.18006i	−0.464230	+	0.0939889i
$539$	5.15697	+	5.15697i	0.222126	+	0.222126i
$540$		0			0
$541$	−19.7610	−	19.7610i	−0.849593	−	0.849593i	0.140489	−	0.990082i	$-0.455132\pi$
$541$	−19.7610	−	19.7610i	−0.849593	−	0.849593i	−0.990082	+	0.140489i	$0.955132\pi$
$542$	−10.7286	+	16.1757i	−0.460833	+	0.694806i
$543$		0			0
$544$	−2.11461	+	3.28470i	−0.0906630	+	0.140830i
$545$		−	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	$0.494120\pi$
$548$	−15.2234	+	37.4738i	−0.650309	+	1.60080i
$549$		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
$554$	2.77538	+	13.7081i	0.117915	+	0.582403i
$555$		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	$0.302666\pi$
$563$			38.6244i			1.62782i	−0.580989	+	0.813911i	$0.697334\pi$
$564$		0			0
$565$	−4.85385	+	4.85385i	−0.204203	+	0.204203i
$566$	−0.493448	+	0.0999045i	−0.0207412	+	0.00419930i
$567$		0			0
$568$	−17.7257	−	3.33760i	−0.743755	−	0.140043i
$569$			40.1183i			1.68185i	0.541154	+	0.840924i	$0.317988\pi$
$569$			40.1183i			1.68185i	−0.541154	+	0.840924i	$0.682012\pi$
$570$		0			0
$571$			3.97707i			0.166435i	0.996531	+	0.0832175i	$0.0265196\pi$
$571$			3.97707i			0.166435i	−0.996531	+	0.0832175i	$0.973480\pi$
$572$	−11.5595	−	14.2043i	−0.483327	−	0.593912i
$573$		0			0
$574$	17.3492	−	3.51256i	0.724143	−	0.146612i
$575$			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	$0.880114\pi$
$578$	−4.63689	−	22.9025i	−0.192869	−	0.952619i
$579$		0			0
$580$	7.91530	+	3.21552i	0.328665	+	0.133517i
$581$		−	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	0.466383	−	0.884583i	$-0.345557\pi$
$587$	−10.1322	−	10.1322i	−0.418201	−	0.418201i	−0.884583	+	0.466383i	$0.845557\pi$
$588$		0			0
$589$	−1.45065			−0.0597730
$590$	23.2275	−	4.70269i	0.956261	−	0.193607i
$591$		0			0
$592$	11.7169	−	0.159939i	0.481561	−	0.00657344i
$593$	−13.3652	+	13.3652i	−0.548841	+	0.548841i	−0.926106	−	0.377264i	$-0.876865\pi$
$593$	−13.3652	+	13.3652i	−0.548841	+	0.548841i	0.377264	+	0.926106i	$0.376865\pi$
$594$		0			0
$595$			3.69277i			0.151389i
$596$	−15.2873	+	37.6311i	−0.626191	+	1.54143i
$597$		0			0
$598$	12.8871	+	4.01556i	0.526994	+	0.164208i
$599$		−	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
$604$	17.2258	+	6.99781i	0.700908	+	0.284737i
$605$	8.46796	+	8.46796i	0.344271	+	0.344271i
$606$		0			0
$607$		−	22.8716i		−	0.928330i	−0.885749	−	0.464165i	$-0.846354\pi$
$607$		−	22.8716i		−	0.928330i	0.885749	−	0.464165i	$-0.153646\pi$
$608$	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	$0.627398\pi$
$613$	−32.4490	+	32.4490i	−1.31060	+	1.31060i	−0.920971	+	0.389632i	$0.872602\pi$
$614$	−10.6081	−	7.03584i	−0.428107	−	0.283943i
$615$		0			0
$616$	8.23228	+	12.0515i	0.331688	+	0.485571i
$617$	−33.0596	−	33.0596i	−1.33093	−	1.33093i	−0.904538	−	0.426393i	$-0.859784\pi$
$617$	−33.0596	−	33.0596i	−1.33093	−	1.33093i	−0.426393	−	0.904538i	$-0.640216\pi$
$618$		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
$622$	−2.00803	−	9.91804i	−0.0805146	−	0.397677i
$623$	21.4609			0.859811
$624$		0			0
$625$	30.9210			1.23684
$626$	0.615455	+	3.03985i	0.0245985	+	0.121497i
$627$		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	0.729217	−	0.684283i	$-0.239885\pi$
$631$	1.12873	+	1.12873i	0.0449339	+	0.0449339i	−0.684283	+	0.729217i	$0.739885\pi$
$632$	19.3007	−	13.1841i	0.767742	−	0.524436i
$633$		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	$-0.791667\pi$
$641$		−	30.8252i		−	1.21752i	0.793353	−	0.608762i	$-0.208333\pi$
$642$		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	$0.657276\pi$
$644$	−9.96638	−	4.04875i	−0.392730	−	0.159543i
$645$		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
$650$	−2.92214	+	9.37804i	−0.114616	+	0.367837i
$651$		0			0
$652$	6.48082	−	15.9532i	0.253808	−	0.624774i
$653$			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
$656$	−24.6390	+	0.336329i	−0.961991	+	0.0131314i
$657$		0			0
$658$	1.22627	−	0.248274i	0.0478051	−	0.00967873i
$659$	7.81311			0.304356			0.152178	−	0.988353i	$-0.451371\pi$
$659$	7.81311			0.304356			0.152178	+	0.988353i	$0.451371\pi$
$660$		0			0
$661$	11.5710	+	11.5710i	0.450060	+	0.450060i	0.895374	−	0.445314i	$-0.146908\pi$
$661$	11.5710	+	11.5710i	0.450060	+	0.450060i	−0.445314	+	0.895374i	$0.646908\pi$
$662$	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
$668$	42.3771	+	17.2153i	1.63962	+	0.666080i
$669$		0			0
$670$	6.35879	+	31.4073i	0.245662	+	1.21337i
$671$	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	$0.979273\pi$
$674$	20.8705	−	4.22548i	0.803901	−	0.162759i
$675$		0			0
$676$	21.3981	+	14.7690i	0.823003	+	0.568037i
$677$		−	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
$682$	0.754548	−	0.152767i	0.0288931	−	0.00584977i
$683$	14.2243	−	14.2243i	0.544279	−	0.544279i	−0.380501	−	0.924780i	$-0.624249\pi$
$683$	14.2243	−	14.2243i	0.544279	−	0.544279i	0.924780	+	0.380501i	$0.124249\pi$
$684$		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
$694$	4.89438	+	24.1743i	0.185788	+	0.917644i
$695$	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
$700$	2.94629	−	7.25259i	0.111359	−	0.274122i
$701$	−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
$704$	−8.15764	−	18.6074i	−0.307453	−	0.701291i
$705$		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	0.794672	−	0.607039i	$-0.207643\pi$
$709$	4.99613	+	4.99613i	0.187634	+	0.187634i	−0.607039	+	0.794672i	$0.707643\pi$
$710$	23.2632	−	4.70992i	0.873053	−	0.176760i
$711$		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
$722$	37.1486	−	7.52118i	1.38253	−	0.279909i
$723$		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	$-0.477939\pi$
$727$	3.73446			0.138503			0.0692516	+	0.997599i	$0.477939\pi$
$728$	−16.0079	−	13.1564i	−0.593292	−	0.487608i
$729$		0			0
$730$	30.1032	−	6.09475i	1.11417	−	0.225577i
$731$	−3.37649			−0.124884
$732$		0			0
$733$	−3.60035	+	3.60035i	−0.132982	+	0.132982i	−0.770465	−	0.637483i	$-0.779976\pi$
$733$	−3.60035	+	3.60035i	−0.132982	+	0.132982i	0.637483	+	0.770465i	$0.279976\pi$
$734$	27.6884	−	5.60585i	1.02200	−	0.206916i
$735$		0			0
$736$	12.5914	+	8.10601i	0.464124	+	0.298791i
$737$	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
$746$	−18.6126	+	3.76836i	−0.681457	+	0.137969i
$747$		0			0
$748$	−3.24971	−	1.32016i	−0.118821	−	0.0482699i
$749$	16.1832	+	16.1832i	0.591320	+	0.591320i
$750$		0			0
$751$	51.2313			1.86946			0.934728	−	0.355365i	$-0.115643\pi$
$751$	51.2313			1.86946			0.934728	+	0.355365i	$0.115643\pi$
$752$	−1.74153	+	0.0237723i	−0.0635069	+	0.000866887i
$753$		0			0
$754$	−2.46211	+	7.90165i	−0.0896648	+	0.287761i
$755$	−24.4665			−0.890427
$756$		0			0
$757$			17.2708i			0.627717i	0.949470	+	0.313859i	$0.101622\pi$
$757$			17.2708i			0.627717i	−0.949470	+	0.313859i	$0.898378\pi$
$758$	−16.0935	+	24.2645i	−0.584543	+	0.881326i
$759$		0			0
$760$	−28.4155	−	41.5986i	−1.03074	−	1.50894i
$761$	−18.4462	+	18.4462i	−0.668674	+	0.668674i	−0.957409	−	0.288735i	$-0.906765\pi$
$761$	−18.4462	+	18.4462i	−0.668674	+	0.668674i	0.288735	+	0.957409i	$0.406765\pi$
$762$		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
$772$	−7.99863	+	19.6894i	−0.287877	+	0.708637i
$773$	−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
$778$	4.51789	+	22.3147i	0.161974	+	0.800022i
$779$			41.6908i			1.49373i
$780$		0			0
$781$		−	16.1955i		−	0.579520i
$782$	2.53394	−	0.513026i	0.0906134	−	0.0183458i
$783$		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	$0.215452\pi$
$788$	−1.98106	+	4.87658i	−0.0705724	+	0.173721i
$789$		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
$800$	−5.89878	+	9.16280i	−0.208554	+	0.323954i
$801$		0			0
$802$	28.3953	+	18.8333i	1.00267	+	0.665026i
$803$		−	20.9574i		−	0.739570i
$804$		0			0
$805$	14.1557			0.498921
$806$	−0.967777	+	0.507949i	−0.0340885	+	0.0178917i
$807$		0			0
$808$	27.9785	+	40.9588i	0.984281	+	1.44093i
$809$	40.0149			1.40685			0.703425	−	0.710769i	$-0.251653\pi$
$809$	40.0149			1.40685			0.703425	+	0.710769i	$0.251653\pi$
$810$		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	$0.681710\pi$
$812$	2.48246	−	6.11082i	0.0871173	−	0.214448i
$813$		0			0
$814$	2.08784	+	10.3123i	0.0731789	+	0.361445i
$815$			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	$-0.536254\pi$
$823$	−6.52071			−0.227298			−0.113649	+	0.993521i	$0.536254\pi$
$824$	14.8369	+	21.7204i	0.516869	+	0.756664i
$825$		0			0
$826$	−3.63060	−	17.9322i	−0.126325	−	0.623942i
$827$	24.9705	−	24.9705i	0.868308	−	0.868308i	−0.123977	−	0.992285i	$-0.539565\pi$
$827$	24.9705	−	24.9705i	0.868308	−	0.868308i	0.992285	+	0.123977i	$0.0395649\pi$
$828$		0			0
$829$	25.7131			0.893052			0.446526	−	0.894771i	$-0.352661\pi$
$829$	25.7131			0.893052			0.446526	+	0.894771i	$0.352661\pi$
$830$	−9.19857	−	45.4335i	−0.319287	−	1.57702i
$831$		0			0
$832$	18.5103	+	22.1217i	0.641728	+	0.766932i
$833$	−1.98314			−0.0687117
$834$		0			0
$835$	−60.1900			−2.08296
$836$	−31.6674	+	13.3710i	−1.09524	+	0.462446i
$837$		0			0
$838$	4.62219	+	22.8299i	0.159671	+	0.788646i
$839$	−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
$850$	0.373332	+	1.84396i	0.0128052	+	0.0632473i
$851$	−5.48364	−	5.48364i	−0.187977	−	0.187977i
$852$		0			0
$853$	−19.1134	−	19.1134i	−0.654432	−	0.654432i	0.299625	−	0.954057i	$-0.403138\pi$
$853$	−19.1134	−	19.1134i	−0.654432	−	0.654432i	−0.954057	+	0.299625i	$0.903138\pi$
$854$	16.8300	+	11.1626i	0.575910	+	0.381975i
$855$		0			0
$856$	−17.9704	−	26.3076i	−0.614216	−	0.899175i
$857$			19.3319i			0.660365i	0.943917	+	0.330182i	$0.107110\pi$
$857$			19.3319i			0.660365i	−0.943917	+	0.330182i	$0.892890\pi$
$858$		0			0
$859$	−18.2400			−0.622341			−0.311170	−	0.950354i	$-0.600721\pi$
$859$	−18.2400			−0.622341			−0.311170	+	0.950354i	$0.600721\pi$
$860$	23.8433	+	9.68611i	0.813050	+	0.330294i
$861$		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
$866$	55.3912	−	11.2146i	1.88227	−	0.381088i
$867$		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	−0.818409	−	0.574636i	$-0.805144\pi$
$877$	−7.21914	+	7.21914i	−0.243773	+	0.243773i	0.574636	+	0.818409i	$0.305144\pi$
$878$	−3.69975	−	18.2738i	−0.124861	−	0.616711i
$879$		0			0
$880$	19.1609	+	18.6449i	0.645914	+	0.628518i
$881$			46.5683i			1.56893i	0.620175	+	0.784463i	$0.287061\pi$
$881$			46.5683i			1.56893i	−0.620175	+	0.784463i	$0.712939\pi$
$882$		0			0
$883$			17.2990i			0.582156i	0.956699	+	0.291078i	$0.0940139\pi$
$883$			17.2990i			0.582156i	−0.956699	+	0.291078i	$0.905986\pi$
$884$	4.95380	+	0.508538i	0.166614	+	0.0171040i
$885$		0			0
$886$	4.96137	+	24.5052i	0.166681	+	0.823268i
$887$			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
$890$	38.5307	−	7.80101i	1.29155	−	0.261491i
$891$		0			0
$892$	−17.7304	+	43.6450i	−0.593657	+	1.46134i
$893$			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
$902$	−4.39045	−	21.6853i	−0.146186	−	0.722040i
$903$		0			0
$904$	−4.16114	−	6.09165i	−0.138397	−	0.202605i
$905$	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	$-0.211415\pi$
$908$	−46.8022	−	19.0130i	−1.55319	−	0.630967i
$909$		0			0
$910$	26.0318	+	8.11137i	0.862946	+	0.268889i
$911$			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
$916$	46.4174	+	18.8566i	1.53368	+	0.623041i
$917$	−31.4550	−	31.4550i	−1.03873	−	1.03873i
$918$		0			0
$919$			7.88215i			0.260008i	0.991513	+	0.130004i	$0.0414991\pi$
$919$			7.88215i			0.260008i	−0.991513	+	0.130004i	$0.958501\pi$
$920$	−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
$928$	−4.97014	+	7.72030i	−0.163153	+	0.253431i
$929$	−8.30941	−	8.30941i	−0.272623	−	0.272623i	0.557532	−	0.830155i	$-0.311748\pi$
$929$	−8.30941	−	8.30941i	−0.272623	−	0.272623i	−0.830155	+	0.557532i	$0.811748\pi$
$930$		0			0
$931$	−13.7424	+	13.7424i	−0.450388	+	0.450388i
$932$	9.96337	+	23.5969i	0.326361	+	0.772942i
$933$		0			0
$934$	−32.5231	+	6.58471i	−1.06419	+	0.215458i
$935$	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	$0.587125\pi$
$938$	24.2472	−	4.90915i	0.791701	−	0.160289i
$939$		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
$944$	0.347631	+	25.4669i	0.0113144	+	0.828878i
$945$		0			0
$946$	9.70620	−	14.6342i	0.315576	−	0.475799i
$947$	42.7738	−	42.7738i	1.38996	−	1.38996i	0.564594	−	0.825369i	$-0.309033\pi$
$947$	42.7738	−	42.7738i	1.38996	−	1.38996i	0.825369	−	0.564594i	$-0.190967\pi$
$948$		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	$0.156429\pi$
$953$			29.1352i			0.943782i	−0.881657	+	0.471891i	$0.843571\pi$
$954$		0			0
$955$	−29.4531	−	29.4531i	−0.953081	−	0.953081i
$956$	6.60156	−	16.2504i	0.213510	−	0.525575i
$957$		0			0
$958$	−1.61895	+	2.44092i	−0.0523059	+	0.0788625i
$959$	−41.0915			−1.32691
$960$		0			0
$961$			30.9541i			0.998518i
$962$	−6.94205	−	13.2264i	−0.223821	−	0.426437i
$963$		0			0
$964$	0.158491	−	0.390140i	0.00510464	−	0.0125656i
$965$		−	27.9657i		−	0.900247i
$966$		0			0
$967$	10.2496	−	10.2496i	0.329605	−	0.329605i	−0.522831	−	0.852436i	$-0.675124\pi$
$967$	10.2496	−	10.2496i	0.329605	−	0.329605i	0.852436	+	0.522831i	$0.175124\pi$
$968$	−10.6274	+	7.25946i	−0.341578	+	0.233328i
$969$		0			0
$970$	14.4519	+	71.3808i	0.464023	+	2.29190i
$971$	35.4423			1.13740			0.568699	−	0.822546i	$-0.307447\pi$
$971$	35.4423			1.13740			0.568699	+	0.822546i	$0.307447\pi$
$972$		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	0.0534239	−	0.998572i	$-0.482987\pi$
$977$	−29.5425	−	29.5425i	−0.945148	−	0.945148i	−0.998572	+	0.0534239i	$0.982987\pi$
$978$		0			0
$979$		−	26.8245i		−	0.857315i
$980$	14.0041	+	5.68902i	0.447344	+	0.181729i
$981$		0			0
$982$	−7.91480	+	1.60245i	−0.252571	+	0.0511362i
$983$	−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
$986$	0.314558	+	1.55367i	0.0100176	+	0.0494788i
$987$		0			0
$988$	37.8519	−	30.8040i	1.20423	−	0.980005i
$989$			12.9432i			0.411571i
$990$		0			0
$991$		−	39.2069i		−	1.24545i	−0.782442	−	0.622724i	$-0.786026\pi$
$991$		−	39.2069i		−	1.24545i	0.782442	−	0.622724i	$-0.213974\pi$
$992$	−1.18504	+	0.256813i	−0.0376252	+	0.00815381i
$993$		0			0
$994$	−3.63618	−	17.9598i	−0.115333	−	0.569650i
$995$	−7.58716	+	7.58716i	−0.240529	+	0.240529i
$996$		0			0
$997$		−	9.56104i		−	0.302801i	−0.988472	−	0.151401i	$-0.951622\pi$
$997$		−	9.56104i		−	0.302801i	0.988472	−	0.151401i	$-0.0483784\pi$
$998$	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.307.11	yes	48
3.2	odd	2	inner	936.2.w.k.307.14	yes	48
8.3	odd	2	inner	936.2.w.k.307.2	✓	48
13.5	odd	4	inner	936.2.w.k.811.2	yes	48
24.11	even	2	inner	936.2.w.k.307.23	yes	48
39.5	even	4	inner	936.2.w.k.811.23	yes	48
104.83	even	4	inner	936.2.w.k.811.11	yes	48
312.83	odd	4	inner	936.2.w.k.811.14	yes	48

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

\(f(q)\)	\(=\)	\(q+(-0.280631 - 1.38609i) q^{2} +(-1.84249 + 0.777959i) q^{4} +(1.86097 - 1.86097i) q^{5} +(-1.43671 - 1.43671i) q^{7} +(1.59538 + 2.33554i) q^{8} +(-3.10171 - 2.05722i) q^{10} +(-1.79579 + 1.79579i) q^{11} +(1.73435 - 3.16102i) q^{13} +(-1.58823 + 2.39460i) q^{14} +(2.78956 - 2.86677i) q^{16} -0.690579i q^{17} +(-4.78545 - 4.78545i) q^{19} +(-1.98106 + 4.87658i) q^{20} +(2.99308 + 1.98517i) q^{22} -2.64723 q^{23} -1.92640i q^{25} +(-4.86817 - 1.51689i) q^{26} +(3.76484 + 1.52943i) q^{28} -1.62313i q^{29} +(0.151569 - 0.151569i) q^{31} +(-4.75644 - 3.06208i) q^{32} +(-0.957205 + 0.193798i) q^{34} -5.34736 q^{35} +(2.07147 + 2.07147i) q^{37} +(-5.29012 + 7.97600i) q^{38} +(7.31532 + 1.37741i) q^{40} +(-4.35600 - 4.35600i) q^{41} -4.88935i q^{43} +(1.91168 - 4.70577i) q^{44} +(0.742893 + 3.66929i) q^{46} +(-0.307890 - 0.307890i) q^{47} -2.87170i q^{49} +(-2.67016 + 0.540607i) q^{50} +(-0.736393 + 7.17340i) q^{52} +8.52080i q^{53} +6.68380i q^{55} +(1.06340 - 5.64761i) q^{56} +(-2.24980 + 0.455500i) q^{58} +(-4.50238 + 4.50238i) q^{59} -7.02830i q^{61} +(-0.252623 - 0.167553i) q^{62} +(-2.90951 + 7.45216i) q^{64} +(-2.65497 - 9.11012i) q^{65} +(-6.08794 - 6.08794i) q^{67} +(0.537242 + 1.27239i) q^{68} +(1.50063 + 7.41192i) q^{70} +(-4.50930 + 4.50930i) q^{71} +(-5.83515 + 5.83515i) q^{73} +(2.28992 - 3.45256i) q^{74} +(12.5400 + 5.09427i) q^{76} +5.16007 q^{77} -8.26392i q^{79} +(-0.143686 - 10.5262i) q^{80} +(-4.81539 + 7.26024i) q^{82} +(8.80676 + 8.80676i) q^{83} +(-1.28515 - 1.28515i) q^{85} +(-6.77709 + 1.37210i) q^{86} +(-7.05910 - 1.32917i) q^{88} +(-7.46873 + 7.46873i) q^{89} +(-7.03325 + 2.04970i) q^{91} +(4.87749 - 2.05943i) q^{92} +(-0.340360 + 0.513166i) q^{94} -17.8111 q^{95} +(-13.8363 - 13.8363i) q^{97} +(-3.98044 + 0.805889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 40 q^{16} - 8 q^{19} - 32 q^{22} + 24 q^{28} + 8 q^{34} + 16 q^{40} - 8 q^{46} + 24 q^{52} - 24 q^{58} + 40 q^{67} - 24 q^{70} + 56 q^{76} + 104 q^{91} - 64 q^{94} - 32 q^{97}+O(q^{100}) \) 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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