LMFDB - Embedded newform 936.2.q.g.625.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(313,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.313"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [22,0,0,0,-3,0,-4] 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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.10
Character	$\chi$	$=$	936.625
Dual form			936.2.q.g.313.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41854 - 0.993855i) q^{3} +(-0.804884 + 1.39410i) q^{5} +(-1.44881 - 2.50941i) q^{7} +(1.02450 - 2.81964i) q^{9} +(-2.83578 - 4.91172i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(0.243775 + 2.77752i) q^{15} +4.32766 q^{17} -8.25781 q^{19} +(-4.54918 - 2.11979i) q^{21} +(-0.834069 + 1.44465i) q^{23} +(1.20432 + 2.08595i) q^{25} +(-1.34902 - 5.01798i) q^{27} +(-2.99925 - 5.19486i) q^{29} +(-2.15875 + 3.73906i) q^{31} +(-8.90421 - 4.14911i) q^{33} +4.66449 q^{35} +1.37003 q^{37} +(0.151435 + 1.72542i) q^{39} +(3.62998 - 6.28730i) q^{41} +(-3.95061 - 6.84266i) q^{43} +(3.10626 + 3.69775i) q^{45} +(-1.90852 - 3.30565i) q^{47} +(-0.698094 + 1.20913i) q^{49} +(6.13896 - 4.30107i) q^{51} +7.26904 q^{53} +9.12991 q^{55} +(-11.7140 + 8.20707i) q^{57} +(5.93765 - 10.2843i) q^{59} +(-0.141636 - 0.245321i) q^{61} +(-8.55995 + 1.51423i) q^{63} +(-0.804884 - 1.39410i) q^{65} +(-1.31735 + 2.28172i) q^{67} +(0.252614 + 2.87824i) q^{69} +4.10735 q^{71} +7.43820 q^{73} +(3.78151 + 1.76208i) q^{75} +(-8.21702 + 14.2323i) q^{77} +(1.54994 + 2.68458i) q^{79} +(-6.90079 - 5.77747i) q^{81} +(4.06719 + 7.04459i) q^{83} +(-3.48327 + 6.03320i) q^{85} +(-9.41749 - 4.38828i) q^{87} -15.7980 q^{89} +2.89762 q^{91} +(0.653819 + 7.44949i) q^{93} +(6.64658 - 11.5122i) q^{95} +(-0.917545 - 1.58924i) q^{97} +(-16.7546 + 2.96383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) $ 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Character values

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

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.41854	−	0.993855i	0.818994	−	0.573803i
$3$	1.41854	−	0.993855i	0.818994	−	0.573803i
$4$		0			0
$5$	−0.804884	+	1.39410i	−0.359955	+	0.623461i	−0.987953	−	0.154755i	$-0.950541\pi$
$5$	−0.804884	+	1.39410i	−0.359955	+	0.623461i	0.627998	+	0.778215i	$0.283875\pi$
$6$		0			0
$7$	−1.44881	−	2.50941i	−0.547598	−	0.948468i	−0.998438	−	0.0558633i	$-0.982209\pi$
$7$	−1.44881	−	2.50941i	−0.547598	−	0.948468i	0.450840	−	0.892605i	$-0.351124\pi$
$8$		0			0
$9$	1.02450	−	2.81964i	0.341501	−	0.939881i
$10$		0			0
$11$	−2.83578	−	4.91172i	−0.855021	−	1.48094i	−0.876626	−	0.481173i	$-0.840211\pi$
$11$	−2.83578	−	4.91172i	−0.855021	−	1.48094i	0.0216049	−	0.999767i	$-0.493122\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$		0			0
$15$	0.243775	+	2.77752i	0.0629424	+	0.717153i
$16$		0			0
$17$	4.32766			1.04961			0.524806	−	0.851222i	$-0.324138\pi$
$17$	4.32766			1.04961			0.524806	+	0.851222i	$0.324138\pi$
$18$		0			0
$19$	−8.25781			−1.89447			−0.947236	−	0.320538i	$-0.896136\pi$
$19$	−8.25781			−1.89447			−0.947236	+	0.320538i	$0.896136\pi$
$20$		0			0
$21$	−4.54918	−	2.11979i	−0.992713	−	0.462576i
$22$		0			0
$23$	−0.834069	+	1.44465i	−0.173915	+	0.301230i	−0.939785	−	0.341765i	$-0.888975\pi$
$23$	−0.834069	+	1.44465i	−0.173915	+	0.301230i	0.765870	+	0.642996i	$0.222309\pi$
$24$		0			0
$25$	1.20432	+	2.08595i	0.240865	+	0.417190i
$26$		0			0
$27$	−1.34902	−	5.01798i	−0.259619	−	0.965711i
$28$		0			0
$29$	−2.99925	−	5.19486i	−0.556947	−	0.964661i	−0.997749	−	0.0670564i	$-0.978639\pi$
$29$	−2.99925	−	5.19486i	−0.556947	−	0.964661i	0.440802	−	0.897604i	$-0.354694\pi$
$30$		0			0
$31$	−2.15875	+	3.73906i	−0.387723	+	0.671555i	−0.992143	−	0.125110i	$-0.960072\pi$
$31$	−2.15875	+	3.73906i	−0.387723	+	0.671555i	0.604420	+	0.796666i	$0.293405\pi$
$32$		0			0
$33$	−8.90421	−	4.14911i	−1.55002	−	0.722267i
$34$		0			0
$35$	4.66449			0.788443
$36$		0			0
$37$	1.37003			0.225231			0.112616	−	0.993639i	$-0.464077\pi$
$37$	1.37003			0.225231			0.112616	+	0.993639i	$0.464077\pi$
$38$		0			0
$39$	0.151435	+	1.72542i	0.0242490	+	0.276288i
$40$		0			0
$41$	3.62998	−	6.28730i	0.566907	−	0.981911i	−0.429963	−	0.902847i	$-0.641473\pi$
$41$	3.62998	−	6.28730i	0.566907	−	0.981911i	0.996869	−	0.0790648i	$-0.0251934\pi$
$42$		0			0
$43$	−3.95061	−	6.84266i	−0.602463	−	1.04350i	−0.992447	−	0.122674i	$-0.960853\pi$
$43$	−3.95061	−	6.84266i	−0.602463	−	1.04350i	0.389984	−	0.920821i	$-0.372480\pi$
$44$		0			0
$45$	3.10626	+	3.69775i	0.463054	+	0.551227i
$46$		0			0
$47$	−1.90852	−	3.30565i	−0.278386	−	0.482179i	0.692598	−	0.721324i	$-0.256466\pi$
$47$	−1.90852	−	3.30565i	−0.278386	−	0.482179i	−0.970984	+	0.239145i	$0.923133\pi$
$48$		0			0
$49$	−0.698094	+	1.20913i	−0.0997277	+	0.172733i
$50$		0			0
$51$	6.13896	−	4.30107i	0.859626	−	0.602271i
$52$		0			0
$53$	7.26904			0.998480			0.499240	−	0.866464i	$-0.333613\pi$
$53$	7.26904			0.998480			0.499240	+	0.866464i	$0.333613\pi$
$54$		0			0
$55$	9.12991			1.23108
$56$		0			0
$57$	−11.7140	+	8.20707i	−1.55156	+	1.08705i
$58$		0			0
$59$	5.93765	−	10.2843i	0.773016	−	1.33890i	−0.162886	−	0.986645i	$-0.552080\pi$
$59$	5.93765	−	10.2843i	0.773016	−	1.33890i	0.935903	−	0.352259i	$-0.114586\pi$
$60$		0			0
$61$	−0.141636	−	0.245321i	−0.0181347	−	0.0314102i	0.856816	−	0.515623i	$-0.172439\pi$
$61$	−0.141636	−	0.245321i	−0.0181347	−	0.0314102i	−0.874950	+	0.484213i	$0.839106\pi$
$62$		0			0
$63$	−8.55995	+	1.51423i	−1.07845	+	0.190775i
$64$		0			0
$65$	−0.804884	−	1.39410i	−0.0998336	−	0.172917i
$66$		0			0
$67$	−1.31735	+	2.28172i	−0.160940	+	0.278756i	−0.935206	−	0.354104i	$-0.884786\pi$
$67$	−1.31735	+	2.28172i	−0.160940	+	0.278756i	0.774266	+	0.632860i	$0.218119\pi$
$68$		0			0
$69$	0.252614	+	2.87824i	0.0304112	+	0.346499i
$70$		0			0
$71$	4.10735			0.487452			0.243726	−	0.969844i	$-0.421630\pi$
$71$	4.10735			0.487452			0.243726	+	0.969844i	$0.421630\pi$
$72$		0			0
$73$	7.43820			0.870575			0.435288	−	0.900291i	$-0.356647\pi$
$73$	7.43820			0.870575			0.435288	+	0.900291i	$0.356647\pi$
$74$		0			0
$75$	3.78151	+	1.76208i	0.436651	+	0.203467i
$76$		0			0
$77$	−8.21702	+	14.2323i	−0.936416	+	1.62192i
$78$		0			0
$79$	1.54994	+	2.68458i	0.174382	+	0.302039i	0.939947	−	0.341320i	$-0.110874\pi$
$79$	1.54994	+	2.68458i	0.174382	+	0.302039i	−0.765565	+	0.643358i	$0.777541\pi$
$80$		0			0
$81$	−6.90079	−	5.77747i	−0.766754	−	0.641941i
$82$		0			0
$83$	4.06719	+	7.04459i	0.446433	+	0.773244i	0.998151	−	0.0607867i	$-0.0193609\pi$
$83$	4.06719	+	7.04459i	0.446433	+	0.773244i	−0.551718	+	0.834031i	$0.686028\pi$
$84$		0			0
$85$	−3.48327	+	6.03320i	−0.377814	+	0.654392i
$86$		0			0
$87$	−9.41749	−	4.38828i	−1.00966	−	0.470473i
$88$		0			0
$89$	−15.7980			−1.67459			−0.837293	−	0.546755i	$-0.815863\pi$
$89$	−15.7980			−1.67459			−0.837293	+	0.546755i	$0.815863\pi$
$90$		0			0
$91$	2.89762			0.303753
$92$		0			0
$93$	0.653819	+	7.44949i	0.0677979	+	0.772476i
$94$		0			0
$95$	6.64658	−	11.5122i	0.681925	−	1.18113i
$96$		0			0
$97$	−0.917545	−	1.58924i	−0.0931626	−	0.161362i	0.815678	−	0.578507i	$-0.196364\pi$
$97$	−0.917545	−	1.58924i	−0.0931626	−	0.161362i	−0.908840	+	0.417144i	$0.863031\pi$
$98$		0			0
$99$	−16.7546	+	2.96383i	−1.68390	+	0.297876i
$100$		0			0
$101$	0.774536	+	1.34154i	0.0770692	+	0.133488i	0.901984	−	0.431769i	$-0.142110\pi$
$101$	0.774536	+	1.34154i	0.0770692	+	0.133488i	−0.824915	+	0.565257i	$0.808777\pi$
$102$		0			0
$103$	−8.18778	+	14.1817i	−0.806766	+	1.39736i	0.108326	+	0.994115i	$0.465451\pi$
$103$	−8.18778	+	14.1817i	−0.806766	+	1.39736i	−0.915092	+	0.403245i	$0.867882\pi$
$104$		0			0
$105$	6.61676	−	4.63583i	0.645730	−	0.452411i
$106$		0			0
$107$	9.74315			0.941906			0.470953	−	0.882158i	$-0.343910\pi$
$107$	9.74315			0.941906			0.470953	+	0.882158i	$0.343910\pi$
$108$		0			0
$109$	17.5510			1.68108			0.840538	−	0.541752i	$-0.182239\pi$
$109$	17.5510			1.68108			0.840538	+	0.541752i	$0.182239\pi$
$110$		0			0
$111$	1.94344	−	1.36161i	0.184463	−	0.129238i
$112$		0			0
$113$	−3.41327	+	5.91196i	−0.321094	+	0.556151i	−0.980714	−	0.195448i	$-0.937384\pi$
$113$	−3.41327	+	5.91196i	−0.321094	+	0.556151i	0.659620	+	0.751599i	$0.270717\pi$
$114$		0			0
$115$	−1.34266	−	2.32555i	−0.125204	−	0.216859i
$116$		0			0
$117$	1.92963	+	2.29707i	0.178395	+	0.212364i
$118$		0			0
$119$	−6.26996	−	10.8599i	−0.574766	−	0.995524i
$120$		0			0
$121$	−10.5833	+	18.3309i	−0.962121	+	1.66644i
$122$		0			0
$123$	−1.09941	−	12.5264i	−0.0991304	−	1.12947i
$124$		0			0
$125$	−11.9262			−1.06671
$126$		0			0
$127$	17.5901			1.56086			0.780432	−	0.625240i	$-0.214999\pi$
$127$	17.5901			1.56086			0.780432	+	0.625240i	$0.214999\pi$
$128$		0			0
$129$	−12.4047	−	5.78024i	−1.09217	−	0.508922i
$130$		0			0
$131$	7.07583	−	12.2557i	0.618219	−	1.07079i	−0.371592	−	0.928396i	$-0.621188\pi$
$131$	7.07583	−	12.2557i	0.618219	−	1.07079i	0.989811	−	0.142390i	$-0.0454787\pi$
$132$		0			0
$133$	11.9640	+	20.7222i	1.03741	+	1.79685i
$134$		0			0
$135$	8.08138	+	2.15822i	0.695534	+	0.185750i
$136$		0			0
$137$	3.59328	+	6.22374i	0.306994	+	0.531730i	0.977703	−	0.209991i	$-0.0673434\pi$
$137$	3.59328	+	6.22374i	0.306994	+	0.531730i	−0.670709	+	0.741721i	$0.734010\pi$
$138$		0			0
$139$	5.98564	−	10.3674i	0.507696	−	0.879355i	−0.492265	−	0.870446i	$-0.663831\pi$
$139$	5.98564	−	10.3674i	0.507696	−	0.879355i	0.999960	−	0.00890898i	$-0.00283585\pi$
$140$		0			0
$141$	−5.99265	−	2.79240i	−0.504672	−	0.235163i
$142$		0			0
$143$	5.67157			0.474280
$144$		0			0
$145$	9.65620			0.801904
$146$		0			0
$147$	0.211431	+	2.40901i	0.0174386	+	0.198692i
$148$		0			0
$149$	5.98534	−	10.3669i	0.490338	−	0.849291i	−0.509600	−	0.860412i	$-0.670207\pi$
$149$	5.98534	−	10.3669i	0.490338	−	0.849291i	0.999938	+	0.0111205i	$0.00353984\pi$
$150$		0			0
$151$	11.2826	+	19.5421i	0.918169	+	1.59032i	0.802194	+	0.597063i	$0.203666\pi$
$151$	11.2826	+	19.5421i	0.918169	+	1.59032i	0.115975	+	0.993252i	$0.463001\pi$
$152$		0			0
$153$	4.43370	−	12.2025i	0.358444	−	0.986512i
$154$		0			0
$155$	−3.47509	−	6.01902i	−0.279126	−	0.483460i
$156$		0			0
$157$	−5.00929	+	8.67634i	−0.399785	+	0.692447i	−0.993699	−	0.112081i	$-0.964248\pi$
$157$	−5.00929	+	8.67634i	−0.399785	+	0.692447i	0.593914	+	0.804528i	$0.297582\pi$
$158$		0			0
$159$	10.3114	−	7.22438i	0.817749	−	0.572930i
$160$		0			0
$161$	4.83363			0.380943
$162$		0			0
$163$	−16.8597			−1.32055			−0.660276	−	0.751023i	$-0.729561\pi$
$163$	−16.8597			−1.32055			−0.660276	+	0.751023i	$0.729561\pi$
$164$		0			0
$165$	12.9511	−	9.07381i	1.00824	−	0.706395i
$166$		0			0
$167$	7.76568	−	13.4506i	0.600927	−	1.04084i	−0.391754	−	0.920070i	$-0.628132\pi$
$167$	7.76568	−	13.4506i	0.600927	−	1.04084i	0.992681	−	0.120766i	$-0.0385350\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$	−8.46015	+	23.2841i	−0.646964	+	1.78058i
$172$		0			0
$173$	−5.99609	−	10.3855i	−0.455874	−	0.789597i	0.542864	−	0.839821i	$-0.317340\pi$
$173$	−5.99609	−	10.3855i	−0.455874	−	0.789597i	−0.998738	+	0.0502237i	$0.984007\pi$
$174$		0			0
$175$	3.48967	−	6.04428i	0.263794	−	0.456905i
$176$		0			0
$177$	−1.79833	−	20.4899i	−0.135171	−	1.54011i
$178$		0			0
$179$	−0.296088			−0.0221307			−0.0110653	−	0.999939i	$-0.503522\pi$
$179$	−0.296088			−0.0221307			−0.0110653	+	0.999939i	$0.503522\pi$
$180$		0			0
$181$	−22.7246			−1.68910			−0.844552	−	0.535473i	$-0.820133\pi$
$181$	−22.7246			−1.68910			−0.844552	+	0.535473i	$0.820133\pi$
$182$		0			0
$183$	−0.444730	−	0.207232i	−0.0328754	−	0.0153190i
$184$		0			0
$185$	−1.10271	+	1.90995i	−0.0810731	+	0.140423i
$186$		0			0
$187$	−12.2723	−	21.2563i	−0.897441	−	1.55441i
$188$		0			0
$189$	−10.6377	+	10.6553i	−0.773779	+	0.775062i
$190$		0			0
$191$	3.21533	+	5.56911i	0.232653	+	0.402967i	0.958588	−	0.284797i	$-0.0919260\pi$
$191$	3.21533	+	5.56911i	0.232653	+	0.402967i	−0.725935	+	0.687763i	$0.758593\pi$
$192$		0			0
$193$	3.76630	−	6.52342i	0.271104	−	0.469566i	−0.698041	−	0.716058i	$-0.745945\pi$
$193$	3.76630	−	6.52342i	0.271104	−	0.469566i	0.969145	+	0.246492i	$0.0792779\pi$
$194$		0			0
$195$	−2.52729	−	1.17765i	−0.180983	−	0.0843330i
$196$		0			0
$197$	14.1456			1.00783			0.503916	−	0.863753i	$-0.331892\pi$
$197$	14.1456			1.00783			0.503916	+	0.863753i	$0.331892\pi$
$198$		0			0
$199$	0.643592			0.0456230			0.0228115	−	0.999740i	$-0.492738\pi$
$199$	0.643592			0.0456230			0.0228115	+	0.999740i	$0.492738\pi$
$200$		0			0
$201$	0.398985	+	4.54595i	0.0281422	+	0.320647i
$202$		0			0
$203$	−8.69069	+	15.0527i	−0.609967	+	1.05649i
$204$		0			0
$205$	5.84342	+	10.1211i	0.408122	+	0.706888i
$206$		0			0
$207$	3.21889	+	3.83183i	0.223729	+	0.266330i
$208$		0			0
$209$	23.4174	+	40.5601i	1.61981	+	2.80560i
$210$		0			0
$211$	−10.3451	+	17.9183i	−0.712187	+	1.23354i	0.251848	+	0.967767i	$0.418962\pi$
$211$	−10.3451	+	17.9183i	−0.712187	+	1.23354i	−0.964035	+	0.265777i	$0.914372\pi$
$212$		0			0
$213$	5.82643	−	4.08211i	0.399220	−	0.279701i
$214$		0			0
$215$	12.7191			0.867438
$216$		0			0
$217$	12.5105			0.849265
$218$		0			0
$219$	10.5514	−	7.39249i	0.712996	−	0.499538i
$220$		0			0
$221$	−2.16383	+	3.74787i	−0.145555	+	0.252109i
$222$		0			0
$223$	−1.66319	−	2.88073i	−0.111375	−	0.192908i	0.804950	−	0.593343i	$-0.202192\pi$
$223$	−1.66319	−	2.88073i	−0.111375	−	0.192908i	−0.916325	+	0.400435i	$0.868859\pi$
$224$		0			0
$225$	7.11547	−	1.25870i	0.474364	−	0.0839135i
$226$		0			0
$227$	4.35549	+	7.54393i	0.289084	+	0.500708i	0.973591	−	0.228298i	$-0.0733160\pi$
$227$	4.35549	+	7.54393i	0.289084	+	0.500708i	−0.684507	+	0.729006i	$0.739983\pi$
$228$		0			0
$229$	9.82878	−	17.0240i	0.649504	−	1.12497i	−0.333737	−	0.942666i	$-0.608310\pi$
$229$	9.82878	−	17.0240i	0.649504	−	1.12497i	0.983241	−	0.182308i	$-0.0583569\pi$
$230$		0			0
$231$	2.48868	+	28.3556i	0.163743	+	1.86566i
$232$		0			0
$233$	3.31654			0.217274			0.108637	−	0.994081i	$-0.465351\pi$
$233$	3.31654			0.217274			0.108637	+	0.994081i	$0.465351\pi$
$234$		0			0
$235$	6.14455			0.400826
$236$		0			0
$237$	4.86673	+	2.26776i	0.316128	+	0.147307i
$238$		0			0
$239$	−7.52273	+	13.0297i	−0.486605	+	0.842824i	−0.999881	−	0.0153991i	$-0.995098\pi$
$239$	−7.52273	+	13.0297i	−0.486605	+	0.842824i	0.513277	+	0.858223i	$0.328431\pi$
$240$		0			0
$241$	0.101896	+	0.176490i	0.00656372	+	0.0113687i	0.869289	−	0.494305i	$-0.164577\pi$
$241$	0.101896	+	0.176490i	0.00656372	+	0.0113687i	−0.862725	+	0.505674i	$0.831244\pi$
$242$		0			0
$243$	−15.5310	−	1.33717i	−0.996314	−	0.0857797i
$244$		0			0
$245$	−1.12377	−	1.94643i	−0.0717950	−	0.124353i
$246$		0			0
$247$	4.12890	−	7.15147i	0.262716	−	0.455037i
$248$		0			0
$249$	12.7708	+	5.95082i	0.809315	+	0.377118i
$250$		0			0
$251$	18.6719			1.17856			0.589280	−	0.807929i	$-0.299411\pi$
$251$	18.6719			1.17856			0.589280	+	0.807929i	$0.299411\pi$
$252$		0			0
$253$	9.46096			0.594805
$254$		0			0
$255$	1.05498	+	12.0202i	0.0660652	+	0.752733i
$256$		0			0
$257$	13.0755	−	22.6475i	0.815629	−	1.41271i	−0.0932465	−	0.995643i	$-0.529724\pi$
$257$	13.0755	−	22.6475i	0.815629	−	1.41271i	0.908875	−	0.417068i	$-0.136942\pi$
$258$		0			0
$259$	−1.98491	−	3.43796i	−0.123336	−	0.213624i
$260$		0			0
$261$	−17.7204	+	3.13468i	−1.09686	+	0.194032i
$262$		0			0
$263$	14.2962	+	24.7618i	0.881544	+	1.52688i	0.849624	+	0.527389i	$0.176829\pi$
$263$	14.2962	+	24.7618i	0.881544	+	1.52688i	0.0319205	+	0.999490i	$0.489838\pi$
$264$		0			0
$265$	−5.85074	+	10.1338i	−0.359408	+	0.622513i
$266$		0			0
$267$	−22.4101	+	15.7009i	−1.37147	+	0.960882i
$268$		0			0
$269$	−4.59176			−0.279964			−0.139982	−	0.990154i	$-0.544705\pi$
$269$	−4.59176			−0.279964			−0.139982	+	0.990154i	$0.544705\pi$
$270$		0			0
$271$	−31.1500			−1.89223			−0.946115	−	0.323830i	$-0.895029\pi$
$271$	−31.1500			−1.89223			−0.946115	+	0.323830i	$0.895029\pi$
$272$		0			0
$273$	4.11038	−	2.87981i	0.248772	−	0.174294i
$274$		0			0
$275$	6.83040	−	11.8306i	0.411889	−	0.713412i
$276$		0			0
$277$	−2.85590	−	4.94657i	−0.171595	−	0.297210i	0.767383	−	0.641189i	$-0.221559\pi$
$277$	−2.85590	−	4.94657i	−0.171595	−	0.297210i	−0.938977	+	0.343979i	$0.888225\pi$
$278$		0			0
$279$	8.33118	+	9.91758i	0.498775	+	0.593750i
$280$		0			0
$281$	−5.70085	−	9.87416i	−0.340084	−	0.589043i	0.644364	−	0.764719i	$-0.277122\pi$
$281$	−5.70085	−	9.87416i	−0.340084	−	0.589043i	−0.984448	+	0.175676i	$0.943789\pi$
$282$		0			0
$283$	5.02801	−	8.70877i	0.298884	−	0.517682i	−0.676997	−	0.735986i	$-0.736719\pi$
$283$	5.02801	−	8.70877i	0.298884	−	0.517682i	0.975881	+	0.218304i	$0.0700523\pi$
$284$		0			0
$285$	−2.01305	−	22.9363i	−0.119243	−	1.35863i
$286$		0			0
$287$	−21.0366			−1.24175
$288$		0			0
$289$	1.72868			0.101687
$290$		0			0
$291$	−2.88104	−	1.34248i	−0.168890	−	0.0786978i
$292$		0			0
$293$	−8.78165	+	15.2103i	−0.513029	+	0.888593i	0.486857	+	0.873482i	$0.338143\pi$
$293$	−8.78165	+	15.2103i	−0.513029	+	0.888593i	−0.999886	+	0.0151108i	$0.995190\pi$
$294$		0			0
$295$	9.55824	+	16.5554i	0.556502	+	0.963890i
$296$		0			0
$297$	−20.8214	+	20.8559i	−1.20818	+	1.21018i
$298$		0			0
$299$	−0.834069	−	1.44465i	−0.0482355	−	0.0835463i
$300$		0			0
$301$	−11.4474	+	19.8274i	−0.659815	+	1.14283i
$302$		0			0
$303$	2.43200	+	1.13324i	0.139715	+	0.0651031i
$304$		0			0
$305$	0.456003			0.0261107
$306$		0			0
$307$	15.8280			0.903352			0.451676	−	0.892182i	$-0.350826\pi$
$307$	15.8280			0.903352			0.451676	+	0.892182i	$0.350826\pi$
$308$		0			0
$309$	2.47983	+	28.2547i	0.141073	+	1.60735i
$310$		0			0
$311$	6.10724	−	10.5781i	0.346310	−	0.599827i	−0.639281	−	0.768973i	$-0.720768\pi$
$311$	6.10724	−	10.5781i	0.346310	−	0.599827i	0.985591	+	0.169147i	$0.0541012\pi$
$312$		0			0
$313$	−8.50666	−	14.7340i	−0.480825	−	0.832813i	0.518933	−	0.854815i	$-0.326329\pi$
$313$	−8.50666	−	14.7340i	−0.480825	−	0.832813i	−0.999758	+	0.0220019i	$0.992996\pi$
$314$		0			0
$315$	4.77879	−	13.1522i	0.269254	−	0.741043i
$316$		0			0
$317$	−14.2906	−	24.7521i	−0.802641	−	1.39022i	−0.917872	−	0.396877i	$-0.870094\pi$
$317$	−14.2906	−	24.7521i	−0.802641	−	1.39022i	0.115231	−	0.993339i	$-0.463239\pi$
$318$		0			0
$319$	−17.0105	+	29.4630i	−0.952403	+	1.64961i
$320$		0			0
$321$	13.8210	−	9.68328i	0.771415	−	0.540468i
$322$		0			0
$323$	−35.7370			−1.98846
$324$		0			0
$325$	−2.40865			−0.133608
$326$		0			0
$327$	24.8967	−	17.4431i	1.37679	−	0.964606i
$328$		0			0
$329$	−5.53016	+	9.57851i	−0.304887	+	0.528081i
$330$		0			0
$331$	9.80110	+	16.9760i	0.538717	+	0.933085i	0.998973	+	0.0452993i	$0.0144242\pi$
$331$	9.80110	+	16.9760i	0.538717	+	0.933085i	−0.460256	+	0.887786i	$0.652243\pi$
$332$		0			0
$333$	1.40360	−	3.86299i	0.0769166	−	0.211690i
$334$		0			0
$335$	−2.12063	−	3.67303i	−0.115862	−	0.200679i
$336$		0			0
$337$	1.20439	−	2.08606i	0.0656072	−	0.113635i	−0.831356	−	0.555740i	$-0.812435\pi$
$337$	1.20439	−	2.08606i	0.0656072	−	0.113635i	0.896963	+	0.442105i	$0.145768\pi$
$338$		0			0
$339$	1.03378	+	11.7787i	0.0561471	+	0.639729i
$340$		0			0
$341$	24.4870			1.32604
$342$		0			0
$343$	−16.2377			−0.876754
$344$		0			0
$345$	−4.21588	−	1.96448i	−0.226975	−	0.105764i
$346$		0			0
$347$	2.82819	−	4.89856i	0.151825	−	0.262969i	−0.780073	−	0.625688i	$-0.784818\pi$
$347$	2.82819	−	4.89856i	0.151825	−	0.262969i	0.931898	+	0.362719i	$0.118152\pi$
$348$		0			0
$349$	1.09257	+	1.89239i	0.0584839	+	0.101297i	0.893785	−	0.448496i	$-0.148040\pi$
$349$	1.09257	+	1.89239i	0.0584839	+	0.101297i	−0.835301	+	0.549793i	$0.814707\pi$
$350$		0			0
$351$	5.02021	+	1.34070i	0.267959	+	0.0715615i
$352$		0			0
$353$	−1.68642	−	2.92096i	−0.0897589	−	0.155467i	0.817650	−	0.575715i	$-0.195276\pi$
$353$	−1.68642	−	2.92096i	−0.0897589	−	0.155467i	−0.907409	+	0.420248i	$0.861943\pi$
$354$		0			0
$355$	−3.30594	+	5.72605i	−0.175461	+	0.303907i
$356$		0			0
$357$	−19.6873	−	9.17374i	−1.04196	−	0.485526i
$358$		0			0
$359$	22.6756			1.19677			0.598387	−	0.801207i	$-0.295809\pi$
$359$	22.6756			1.19677			0.598387	+	0.801207i	$0.295809\pi$
$360$		0			0
$361$	49.1914			2.58902
$362$		0			0
$363$	3.20537	+	36.5213i	0.168238	+	1.91687i
$364$		0			0
$365$	−5.98689	+	10.3696i	−0.313368	+	0.542769i
$366$		0			0
$367$	−12.8781	−	22.3054i	−0.672229	−	1.16433i	−0.977271	−	0.211996i	$-0.932004\pi$
$367$	−12.8781	−	22.3054i	−0.672229	−	1.16433i	0.305042	−	0.952339i	$-0.401330\pi$
$368$		0			0
$369$	−14.0090	−	16.6766i	−0.729281	−	0.868149i
$370$		0			0
$371$	−10.5315	−	18.2410i	−0.546766	−	0.947026i
$372$		0			0
$373$	−2.77948	+	4.81421i	−0.143916	+	0.249270i	−0.928968	−	0.370160i	$-0.879303\pi$
$373$	−2.77948	+	4.81421i	−0.143916	+	0.249270i	0.785052	+	0.619430i	$0.212636\pi$
$374$		0			0
$375$	−16.9178	+	11.8529i	−0.873630	+	0.612082i
$376$		0			0
$377$	5.99850			0.308939
$378$		0			0
$379$	12.2525			0.629371			0.314685	−	0.949196i	$-0.398101\pi$
$379$	12.2525			0.629371			0.314685	+	0.949196i	$0.398101\pi$
$380$		0			0
$381$	24.9522	−	17.4820i	1.27834	−	0.895628i
$382$		0			0
$383$	9.33013	−	16.1603i	0.476747	−	0.825750i	−0.522898	−	0.852395i	$-0.675149\pi$
$383$	9.33013	−	16.1603i	0.476747	−	0.825750i	0.999645	+	0.0266451i	$0.00848240\pi$
$384$		0			0
$385$	−13.2275	−	22.9107i	−0.674135	−	1.16764i
$386$		0			0
$387$	−23.3413	+	4.12900i	−1.18650	+	0.209889i
$388$		0			0
$389$	−12.8764	−	22.3026i	−0.652861	−	1.13079i	−0.982425	−	0.186656i	$-0.940235\pi$
$389$	−12.8764	−	22.3026i	−0.652861	−	1.13079i	0.329564	−	0.944133i	$-0.393098\pi$
$390$		0			0
$391$	−3.60957	+	6.25196i	−0.182544	+	0.316175i
$392$		0			0
$393$	−2.14306	−	24.4175i	−0.108103	−	1.23170i
$394$		0			0
$395$	−4.99009			−0.251079
$396$		0			0
$397$	17.9208			0.899419			0.449710	−	0.893175i	$-0.351527\pi$
$397$	17.9208			0.899419			0.449710	+	0.893175i	$0.351527\pi$
$398$		0			0
$399$	37.5663	+	17.5048i	1.88067	+	0.876337i
$400$		0			0
$401$	−10.2566	+	17.7650i	−0.512191	+	0.887141i	0.487709	+	0.873006i	$0.337833\pi$
$401$	−10.2566	+	17.7650i	−0.512191	+	0.887141i	−0.999900	+	0.0141345i	$0.995501\pi$
$402$		0			0
$403$	−2.15875	−	3.73906i	−0.107535	−	0.186256i
$404$		0			0
$405$	13.6087	−	4.97020i	0.676222	−	0.246971i
$406$		0			0
$407$	−3.88510	−	6.72919i	−0.192577	−	0.333554i
$408$		0			0
$409$	11.6278	−	20.1399i	0.574957	−	0.995854i	−0.421090	−	0.907019i	$-0.638352\pi$
$409$	11.6278	−	20.1399i	0.574957	−	0.995854i	0.996046	−	0.0888353i	$-0.0283145\pi$
$410$		0			0
$411$	11.2827	+	5.25742i	0.556535	+	0.259329i
$412$		0			0
$413$	−34.4101			−1.69321
$414$		0			0
$415$	−13.0945			−0.642783
$416$		0			0
$417$	−1.81287	−	20.6555i	−0.0887766	−	1.01150i
$418$		0			0
$419$	3.01143	−	5.21594i	0.147118	−	0.254816i	−0.783043	−	0.621967i	$-0.786334\pi$
$419$	3.01143	−	5.21594i	0.147118	−	0.254816i	0.930161	+	0.367152i	$0.119667\pi$
$420$		0			0
$421$	−13.9110	−	24.0945i	−0.677978	−	1.17429i	−0.975589	−	0.219605i	$-0.929523\pi$
$421$	−13.9110	−	24.0945i	−0.677978	−	1.17429i	0.297610	−	0.954687i	$-0.403810\pi$
$422$		0			0
$423$	−11.2760	+	1.99469i	−0.548260	+	0.0969854i
$424$		0			0
$425$	5.21191	+	9.02729i	0.252815	+	0.437888i
$426$		0			0
$427$	−0.410408	+	0.710847i	−0.0198610	+	0.0344003i
$428$		0			0
$429$	8.04534	−	5.63672i	0.388432	−	0.272143i
$430$		0			0
$431$	−30.8395			−1.48549			−0.742743	−	0.669576i	$-0.766476\pi$
$431$	−30.8395			−1.48549			−0.742743	+	0.669576i	$0.766476\pi$
$432$		0			0
$433$	23.2262			1.11618			0.558091	−	0.829780i	$-0.311534\pi$
$433$	23.2262			1.11618			0.558091	+	0.829780i	$0.311534\pi$
$434$		0			0
$435$	13.6977	−	9.59687i	0.656754	−	0.460135i
$436$		0			0
$437$	6.88759	−	11.9297i	0.329478	−	0.570673i
$438$		0			0
$439$	−9.12719	−	15.8088i	−0.435617	−	0.754511i	0.561729	−	0.827321i	$-0.310136\pi$
$439$	−9.12719	−	15.8088i	−0.435617	−	0.754511i	−0.997346	+	0.0728108i	$0.976803\pi$
$440$		0			0
$441$	2.69413	+	3.20714i	0.128292	+	0.152721i
$442$		0			0
$443$	0.452515	+	0.783779i	0.0214996	+	0.0372385i	0.876575	−	0.481265i	$-0.159823\pi$
$443$	0.452515	+	0.783779i	0.0214996	+	0.0372385i	−0.855075	+	0.518504i	$0.826489\pi$
$444$		0			0
$445$	12.7156	−	22.0240i	0.602776	−	1.04404i
$446$		0			0
$447$	−1.81278	−	20.6544i	−0.0857415	−	0.976921i
$448$		0			0
$449$	−6.11406			−0.288540			−0.144270	−	0.989538i	$-0.546083\pi$
$449$	−6.11406			−0.288540			−0.144270	+	0.989538i	$0.546083\pi$
$450$		0			0
$451$	−41.1753			−1.93887
$452$		0			0
$453$	35.4269	+	16.5079i	1.66450	+	0.775610i
$454$		0			0
$455$	−2.33225	+	4.03957i	−0.109337	+	0.189378i
$456$		0			0
$457$	−8.68386	−	15.0409i	−0.406214	−	0.703583i	0.588248	−	0.808681i	$-0.299818\pi$
$457$	−8.68386	−	15.0409i	−0.406214	−	0.703583i	−0.994462	+	0.105097i	$0.966485\pi$
$458$		0			0
$459$	−5.83812	−	21.7161i	−0.272500	−	1.01362i
$460$		0			0
$461$	−6.49976	−	11.2579i	−0.302724	−	0.524333i	0.674028	−	0.738706i	$-0.264563\pi$
$461$	−6.49976	−	11.2579i	−0.302724	−	0.524333i	−0.976752	+	0.214373i	$0.931229\pi$
$462$		0			0
$463$	1.93117	−	3.34488i	0.0897489	−	0.155450i	−0.817656	−	0.575707i	$-0.804727\pi$
$463$	1.93117	−	3.34488i	0.0897489	−	0.155450i	0.907405	+	0.420257i	$0.138060\pi$
$464$		0			0
$465$	−10.9116	−	5.08449i	−0.506013	−	0.235787i
$466$		0			0
$467$	−30.3460			−1.40425			−0.702123	−	0.712056i	$-0.747764\pi$
$467$	−30.3460			−1.40425			−0.702123	+	0.712056i	$0.747764\pi$
$468$		0			0
$469$	7.63435			0.352521
$470$		0			0
$471$	1.51716	+	17.2862i	0.0699071	+	0.796508i
$472$		0			0
$473$	−22.4062	+	38.8086i	−1.03024	+	1.78442i
$474$		0			0
$475$	−9.94507	−	17.2254i	−0.456311	−	0.790354i
$476$		0			0
$477$	7.44716	−	20.4961i	0.340982	−	0.938453i
$478$		0			0
$479$	20.5870	+	35.6578i	0.940645	+	1.62924i	0.764245	+	0.644926i	$0.223112\pi$
$479$	20.5870	+	35.6578i	0.940645	+	1.62924i	0.176400	+	0.984319i	$0.443555\pi$
$480$		0			0
$481$	−0.685013	+	1.18648i	−0.0312339	+	0.0540987i
$482$		0			0
$483$	6.85669	−	4.80393i	0.311990	−	0.218586i
$484$		0			0
$485$	2.95407			0.134137
$486$		0			0
$487$	40.0582			1.81521			0.907605	−	0.419824i	$-0.137908\pi$
$487$	40.0582			1.81521			0.907605	+	0.419824i	$0.137908\pi$
$488$		0			0
$489$	−23.9161	+	16.7561i	−1.08152	+	0.757736i
$490$		0			0
$491$	8.04240	−	13.9298i	0.362948	−	0.628645i	−0.625496	−	0.780227i	$-0.715104\pi$
$491$	8.04240	−	13.9298i	0.362948	−	0.628645i	0.988445	+	0.151582i	$0.0484368\pi$
$492$		0			0
$493$	−12.9798	−	22.4816i	−0.584579	−	1.01252i
$494$		0			0
$495$	9.35362	−	25.7431i	0.420414	−	1.15707i
$496$		0			0
$497$	−5.95076	−	10.3070i	−0.266928	−	0.462333i
$498$		0			0
$499$	10.9793	−	19.0166i	0.491499	−	0.851301i	−0.508453	−	0.861090i	$-0.669783\pi$
$499$	10.9793	−	19.0166i	0.491499	−	0.851301i	0.999952	+	0.00978866i	$0.00311588\pi$
$500$		0			0
$501$	−2.35199	−	26.7981i	−0.105079	−	1.19725i
$502$		0			0
$503$	−11.7924			−0.525797			−0.262899	−	0.964823i	$-0.584678\pi$
$503$	−11.7924			−0.525797			−0.262899	+	0.964823i	$0.584678\pi$
$504$		0			0
$505$	−2.49365			−0.110966
$506$		0			0
$507$	−1.56997	−	0.731563i	−0.0697250	−	0.0324898i
$508$		0			0
$509$	−13.0155	+	22.5435i	−0.576902	+	0.999224i	0.418930	+	0.908018i	$0.362405\pi$
$509$	−13.0155	+	22.5435i	−0.576902	+	0.999224i	−0.995832	+	0.0912052i	$0.970928\pi$
$510$		0			0
$511$	−10.7765	−	18.6655i	−0.476726	−	0.825713i
$512$		0			0
$513$	11.1400	+	41.4375i	0.491842	+	1.82951i
$514$		0			0
$515$	−13.1804	−	22.8292i	−0.580799	−	1.00597i
$516$		0			0
$517$	−10.8243	+	18.7482i	−0.476052	+	0.824546i
$518$		0			0
$519$	−18.8274	−	8.77303i	−0.826431	−	0.385093i
$520$		0			0
$521$	14.3702			0.629571			0.314786	−	0.949163i	$-0.398067\pi$
$521$	14.3702			0.629571			0.314786	+	0.949163i	$0.398067\pi$
$522$		0			0
$523$	−24.6825			−1.07929			−0.539644	−	0.841893i	$-0.681441\pi$
$523$	−24.6825			−1.07929			−0.539644	+	0.841893i	$0.681441\pi$
$524$		0			0
$525$	−1.05691	−	12.0423i	−0.0461275	−	0.525568i
$526$		0			0
$527$	−9.34234	+	16.1814i	−0.406959	+	0.704873i
$528$		0			0
$529$	10.1087	+	17.5087i	0.439507	+	0.761248i
$530$		0			0
$531$	−22.9150	−	27.2784i	−0.994425	−	1.18378i
$532$		0			0
$533$	3.62998	+	6.28730i	0.157232	+	0.272333i
$534$		0			0
$535$	−7.84211	+	13.5829i	−0.339044	+	0.587241i
$536$		0			0
$537$	−0.420013	+	0.294269i	−0.0181249	+	0.0126986i
$538$		0			0
$539$	7.91857			0.341077
$540$		0			0
$541$	−20.9800			−0.902000			−0.451000	−	0.892524i	$-0.648933\pi$
$541$	−20.9800			−0.902000			−0.451000	+	0.892524i	$0.648933\pi$
$542$		0			0
$543$	−32.2357	+	22.5849i	−1.38337	+	0.969212i
$544$		0			0
$545$	−14.1265	+	24.4678i	−0.605112	+	1.04809i
$546$		0			0
$547$	−12.6478	−	21.9066i	−0.540780	−	0.936659i	−0.998859	−	0.0477474i	$-0.984796\pi$
$547$	−12.6478	−	21.9066i	−0.540780	−	0.936659i	0.458079	−	0.888911i	$-0.348538\pi$
$548$		0			0
$549$	−0.836826	+	0.148032i	−0.0357148	+	0.00631784i
$550$		0			0
$551$	24.7673	+	42.8981i	1.05512	+	1.82752i
$552$		0			0
$553$	4.49114	−	7.77888i	0.190983	−	0.330792i
$554$		0			0
$555$	0.333978	+	3.80528i	0.0141766	+	0.161525i
$556$		0			0
$557$	7.04885			0.298670			0.149335	−	0.988787i	$-0.452287\pi$
$557$	7.04885			0.298670			0.149335	+	0.988787i	$0.452287\pi$
$558$		0			0
$559$	7.90122			0.334186
$560$		0			0
$561$	−38.5344	−	17.9559i	−1.62692	−	0.758100i
$562$		0			0
$563$	6.98261	−	12.0942i	0.294282	−	0.509711i	−0.680536	−	0.732715i	$-0.738253\pi$
$563$	6.98261	−	12.0942i	0.294282	−	0.509711i	0.974818	+	0.223004i	$0.0715862\pi$
$564$		0			0
$565$	−5.49458	−	9.51689i	−0.231159	−	0.400379i
$566$		0			0
$567$	−4.50011	+	25.6874i	−0.188987	+	1.07877i
$568$		0			0
$569$	−9.62667	−	16.6739i	−0.403571	−	0.699006i	0.590583	−	0.806977i	$-0.298898\pi$
$569$	−9.62667	−	16.6739i	−0.403571	−	0.699006i	−0.994154	+	0.107971i	$0.965565\pi$
$570$		0			0
$571$	−12.1751	+	21.0880i	−0.509514	+	0.882504i	0.490425	+	0.871483i	$0.336841\pi$
$571$	−12.1751	+	21.0880i	−0.509514	+	0.882504i	−0.999939	+	0.0110210i	$0.996492\pi$
$572$		0			0
$573$	10.0960	+	4.70443i	0.421765	+	0.196530i
$574$		0			0
$575$	−4.01796			−0.167560
$576$		0			0
$577$	−14.3504			−0.597414			−0.298707	−	0.954345i	$-0.596555\pi$
$577$	−14.3504			−0.597414			−0.298707	+	0.954345i	$0.596555\pi$
$578$		0			0
$579$	−1.14070	−	12.9969i	−0.0474058	−	0.540132i
$580$		0			0
$581$	11.7852	−	20.4125i	0.488931	−	0.846854i
$582$		0			0
$583$	−20.6134	−	35.7035i	−0.853721	−	1.47869i
$584$		0			0
$585$	−4.75547	+	0.841227i	−0.196615	+	0.0347805i
$586$		0			0
$587$	−1.38679	−	2.40198i	−0.0572388	−	0.0991405i	0.835986	−	0.548751i	$-0.184896\pi$
$587$	−1.38679	−	2.40198i	−0.0572388	−	0.0991405i	−0.893225	+	0.449610i	$0.851563\pi$
$588$		0			0
$589$	17.8265	−	30.8765i	0.734530	−	1.27224i
$590$		0			0
$591$	20.0661	−	14.0587i	0.825407	−	0.578296i
$592$		0			0
$593$	5.07967			0.208597			0.104299	−	0.994546i	$-0.466740\pi$
$593$	5.07967			0.208597			0.104299	+	0.994546i	$0.466740\pi$
$594$		0			0
$595$	20.1864			0.827560
$596$		0			0
$597$	0.912960	−	0.639637i	0.0373650	−	0.0261786i
$598$		0			0
$599$	2.95659	−	5.12097i	0.120803	−	0.209237i	−0.799281	−	0.600957i	$-0.794786\pi$
$599$	2.95659	−	5.12097i	0.120803	−	0.209237i	0.920085	+	0.391720i	$0.128120\pi$
$600$		0			0
$601$	−14.0561	−	24.3460i	−0.573362	−	0.993092i	−0.996217	−	0.0868952i	$-0.972305\pi$
$601$	−14.0561	−	24.3460i	−0.573362	−	0.993092i	0.422855	−	0.906197i	$-0.361028\pi$
$602$		0			0
$603$	5.08400	+	6.05208i	0.207036	+	0.246460i
$604$		0			0
$605$	−17.0367	−	29.5085i	−0.692641	−	1.19969i
$606$		0			0
$607$	11.9330	−	20.6685i	0.484344	−	0.838909i	−0.515494	−	0.856893i	$-0.672392\pi$
$607$	11.9330	−	20.6685i	0.484344	−	0.838909i	0.999838	+	0.0179843i	$0.00572489\pi$
$608$		0			0
$609$	2.63214	+	29.9901i	0.106660	+	1.21526i
$610$		0			0
$611$	3.81704			0.154421
$612$		0			0
$613$	−7.62213			−0.307855			−0.153927	−	0.988082i	$-0.549192\pi$
$613$	−7.62213			−0.307855			−0.153927	+	0.988082i	$0.549192\pi$
$614$		0			0
$615$	18.3480	+	8.54965i	0.739864	+	0.344755i
$616$		0			0
$617$	−6.54893	+	11.3431i	−0.263650	+	0.456655i	−0.967209	−	0.253982i	$-0.918260\pi$
$617$	−6.54893	+	11.3431i	−0.263650	+	0.456655i	0.703559	+	0.710637i	$0.251593\pi$
$618$		0			0
$619$	17.4754	+	30.2683i	0.702396	+	1.21659i	0.967623	+	0.252400i	$0.0812198\pi$
$619$	17.4754	+	30.2683i	0.702396	+	1.21659i	−0.265227	+	0.964186i	$0.585447\pi$
$620$		0			0
$621$	8.37441	+	2.23648i	0.336053	+	0.0897468i
$622$		0			0
$623$	22.8883	+	39.6437i	0.917000	+	1.58829i
$624$		0			0
$625$	3.57760	−	6.19658i	0.143104	−	0.247863i
$626$		0			0
$627$	73.5293	+	34.2625i	2.93648	+	1.36831i
$628$		0			0
$629$	5.92902			0.236405
$630$		0			0
$631$	34.0914			1.35716			0.678579	−	0.734527i	$-0.262596\pi$
$631$	34.0914			1.35716			0.678579	+	0.734527i	$0.262596\pi$
$632$		0			0
$633$	3.13322	+	35.6993i	0.124534	+	1.41892i
$634$		0			0
$635$	−14.1580	+	24.5223i	−0.561841	+	0.973138i
$636$		0			0
$637$	−0.698094	−	1.20913i	−0.0276595	−	0.0479077i
$638$		0			0
$639$	4.20799	−	11.5813i	0.166465	−	0.458147i
$640$		0			0
$641$	17.6408	+	30.5547i	0.696769	+	1.20684i	0.969581	+	0.244771i	$0.0787129\pi$
$641$	17.6408	+	30.5547i	0.696769	+	1.20684i	−0.272812	+	0.962067i	$0.587954\pi$
$642$		0			0
$643$	−9.67066	+	16.7501i	−0.381374	+	0.660559i	−0.991259	−	0.131931i	$-0.957882\pi$
$643$	−9.67066	+	16.7501i	−0.381374	+	0.660559i	0.609885	+	0.792490i	$0.291216\pi$
$644$		0			0
$645$	18.0426	−	12.6410i	0.710426	−	0.497738i
$646$		0			0
$647$	−19.9094			−0.782718			−0.391359	−	0.920238i	$-0.627995\pi$
$647$	−19.9094			−0.782718			−0.391359	+	0.920238i	$0.627995\pi$
$648$		0			0
$649$	−67.3516			−2.64378
$650$		0			0
$651$	17.7466	−	12.4336i	0.695543	−	0.487311i
$652$		0			0
$653$	7.34363	−	12.7195i	0.287378	−	0.497754i	−0.685805	−	0.727785i	$-0.740550\pi$
$653$	7.34363	−	12.7195i	0.287378	−	0.497754i	0.973183	+	0.230032i	$0.0738830\pi$
$654$		0			0
$655$	11.3905	+	19.7288i	0.445062	+	0.770870i
$656$		0			0
$657$	7.62046	−	20.9731i	0.297302	−	0.818238i
$658$		0			0
$659$	19.6127	+	33.9702i	0.764003	+	1.32329i	0.940772	+	0.339040i	$0.110102\pi$
$659$	19.6127	+	33.9702i	0.764003	+	1.32329i	−0.176769	+	0.984252i	$0.556564\pi$
$660$		0			0
$661$	−10.9667	+	18.9950i	−0.426557	+	0.738818i	−0.996564	−	0.0828214i	$-0.973607\pi$
$661$	−10.9667	+	18.9950i	−0.426557	+	0.738818i	0.570008	+	0.821639i	$0.306940\pi$
$662$		0			0
$663$	0.655359	+	7.46703i	0.0254520	+	0.289995i
$664$		0			0
$665$	−38.5185			−1.49368
$666$		0			0
$667$	10.0063			0.387447
$668$		0			0
$669$	−5.22232	−	2.43345i	−0.201907	−	0.0940827i
$670$		0			0
$671$	−0.803300	+	1.39136i	−0.0310110	+	0.0537127i
$672$		0			0
$673$	1.14213	+	1.97823i	0.0440260	+	0.0762553i	0.887199	−	0.461388i	$-0.152648\pi$
$673$	1.14213	+	1.97823i	0.0440260	+	0.0762553i	−0.843173	+	0.537643i	$0.819315\pi$
$674$		0			0
$675$	8.84259	−	8.85726i	0.340352	−	0.340916i
$676$		0			0
$677$	9.40122	+	16.2834i	0.361318	+	0.625821i	0.988178	−	0.153311i	$-0.0489935\pi$
$677$	9.40122	+	16.2834i	0.361318	+	0.625821i	−0.626860	+	0.779132i	$0.715660\pi$
$678$		0			0
$679$	−2.65870	+	4.60500i	−0.102031	+	0.176724i
$680$		0			0
$681$	13.6760	+	6.37263i	0.524066	+	0.244200i
$682$		0			0
$683$	−43.1705			−1.65187			−0.825936	−	0.563763i	$-0.809353\pi$
$683$	−43.1705			−1.65187			−0.825936	+	0.563763i	$0.809353\pi$
$684$		0			0
$685$	−11.5687			−0.442017
$686$		0			0
$687$	−2.97684	−	33.9175i	−0.113574	−	1.29403i
$688$		0			0
$689$	−3.63452	+	6.29518i	−0.138464	+	0.239827i
$690$		0			0
$691$	−1.55075	−	2.68598i	−0.0589933	−	0.102179i	0.835020	−	0.550219i	$-0.185456\pi$
$691$	−1.55075	−	2.68598i	−0.0589933	−	0.102179i	−0.894014	+	0.448039i	$0.852122\pi$
$692$		0			0
$693$	31.7116	+	37.7501i	1.20463	+	1.43401i
$694$		0			0
$695$	9.63550	+	16.6892i	0.365495	+	0.633056i
$696$		0			0
$697$	15.7093	−	27.2093i	0.595033	−	1.03063i
$698$		0			0
$699$	4.70464	−	3.29616i	0.177946	−	0.124672i
$700$		0			0
$701$	−11.3838			−0.429960			−0.214980	−	0.976618i	$-0.568969\pi$
$701$	−11.3838			−0.429960			−0.214980	+	0.976618i	$0.568969\pi$
$702$		0			0
$703$	−11.3134			−0.426694
$704$		0			0
$705$	8.71627	−	6.10679i	0.328274	−	0.229995i
$706$		0			0
$707$	2.24431	−	3.88726i	0.0844059	−	0.146195i
$708$		0			0
$709$	13.7715	+	23.8529i	0.517200	+	0.895816i	0.999800	+	0.0199757i	$0.00635888\pi$
$709$	13.7715	+	23.8529i	0.517200	+	0.895816i	−0.482601	+	0.875840i	$0.660308\pi$
$710$		0			0
$711$	9.15747	−	1.61993i	0.343432	−	0.0607520i
$712$		0			0
$713$	−3.60109	−	6.23728i	−0.134862	−	0.233588i
$714$		0			0
$715$	−4.56495	+	7.90673i	−0.170720	+	0.295695i
$716$		0			0
$717$	2.27841	+	25.9597i	0.0850886	+	0.969483i
$718$		0			0
$719$	−9.38378			−0.349956			−0.174978	−	0.984572i	$-0.555985\pi$
$719$	−9.38378			−0.349956			−0.174978	+	0.984572i	$0.555985\pi$
$720$		0			0
$721$	47.4501			1.76714
$722$		0			0
$723$	0.319949	+	0.149087i	0.0118990	+	0.00554461i
$724$		0			0
$725$	7.22414	−	12.5126i	0.268298	−	0.464705i
$726$		0			0
$727$	−19.1669	−	33.1980i	−0.710859	−	1.23124i	−0.964535	−	0.263955i	$-0.914973\pi$
$727$	−19.1669	−	33.1980i	−0.710859	−	1.23124i	0.253676	−	0.967289i	$-0.418360\pi$
$728$		0			0
$729$	−23.3603	+	13.5387i	−0.865196	+	0.501435i
$730$		0			0
$731$	−17.0969	−	29.6127i	−0.632352	−	1.09527i
$732$		0			0
$733$	−18.9625	+	32.8440i	−0.700395	+	1.21312i	0.267933	+	0.963437i	$0.413659\pi$
$733$	−18.9625	+	32.8440i	−0.700395	+	1.21312i	−0.968328	+	0.249682i	$0.919674\pi$
$734$		0			0
$735$	−3.52858	−	1.64422i	−0.130154	−	0.0606478i
$736$		0			0
$737$	14.9429			0.550427
$738$		0			0
$739$	29.4326			1.08269			0.541347	−	0.840799i	$-0.317914\pi$
$739$	29.4326			1.08269			0.541347	+	0.840799i	$0.317914\pi$
$740$		0			0
$741$	−1.25052	−	14.2482i	−0.0459390	−	0.523420i
$742$		0			0
$743$	−8.78556	+	15.2170i	−0.322311	+	0.558259i	−0.980964	−	0.194188i	$-0.937793\pi$
$743$	−8.78556	+	15.2170i	−0.322311	+	0.558259i	0.658654	+	0.752446i	$0.271126\pi$
$744$		0			0
$745$	9.63502	+	16.6883i	0.353000	+	0.611413i
$746$		0			0
$747$	24.0301	−	4.25084i	0.879215	−	0.155530i
$748$		0			0
$749$	−14.1160	−	24.4496i	−0.515786	−	0.893368i
$750$		0			0
$751$	12.9846	−	22.4901i	0.473816	−	0.820674i	−0.525735	−	0.850649i	$-0.676209\pi$
$751$	12.9846	−	22.4901i	0.473816	−	0.820674i	0.999551	+	0.0299751i	$0.00954280\pi$
$752$		0			0
$753$	26.4868	−	18.5572i	0.965233	−	0.676261i
$754$		0			0
$755$	−36.3249			−1.32200
$756$		0			0
$757$	6.14605			0.223382			0.111691	−	0.993743i	$-0.464373\pi$
$757$	6.14605			0.223382			0.111691	+	0.993743i	$0.464373\pi$
$758$		0			0
$759$	13.4207	−	9.40283i	0.487142	−	0.341301i
$760$		0			0
$761$	−14.9298	+	25.8592i	−0.541205	+	0.937394i	0.457630	+	0.889142i	$0.348698\pi$
$761$	−14.9298	+	25.8592i	−0.541205	+	0.937394i	−0.998835	+	0.0482516i	$0.984635\pi$
$762$		0			0
$763$	−25.4280	−	44.0426i	−0.920555	−	1.59445i
$764$		0			0
$765$	13.4429	+	16.0026i	0.486027	+	0.578575i
$766$		0			0
$767$	5.93765	+	10.2843i	0.214396	+	0.371345i
$768$		0			0
$769$	−9.44482	+	16.3589i	−0.340589	+	0.589917i	−0.984542	−	0.175147i	$-0.943960\pi$
$769$	−9.44482	+	16.3589i	−0.340589	+	0.589917i	0.643953	+	0.765065i	$0.277293\pi$
$770$		0			0
$771$	−3.96018	−	45.1215i	−0.142622	−	1.62501i
$772$		0			0
$773$	27.3117			0.982334			0.491167	−	0.871066i	$-0.336571\pi$
$773$	27.3117			0.982334			0.491167	+	0.871066i	$0.336571\pi$
$774$		0			0
$775$	−10.3993			−0.373555
$776$		0			0
$777$	−6.23250	−	2.90417i	−0.223590	−	0.104186i
$778$		0			0
$779$	−29.9756	+	51.9193i	−1.07399	+	1.86020i
$780$		0			0
$781$	−11.6475	−	20.1741i	−0.416782	−	0.721887i
$782$		0			0
$783$	−22.0216	+	22.0582i	−0.786989	+	0.788295i
$784$		0			0
$785$	−8.06379	−	13.9669i	−0.287809	−	0.498500i
$786$		0			0
$787$	22.3982	−	38.7949i	0.798411	−	1.38289i	−0.122240	−	0.992501i	$-0.539008\pi$
$787$	22.3982	−	38.7949i	0.798411	−	1.38289i	0.920651	−	0.390388i	$-0.127659\pi$
$788$		0			0
$789$	44.8894	+	20.9172i	1.59811	+	0.744672i
$790$		0			0
$791$	19.7807			0.703322
$792$		0			0
$793$	0.283273			0.0100593
$794$		0			0
$795$	1.77201	+	20.1899i	0.0628467	+	0.716063i
$796$		0			0
$797$	−4.14872	+	7.18579i	−0.146955	+	0.254534i	−0.930101	−	0.367305i	$-0.880281\pi$
$797$	−4.14872	+	7.18579i	−0.146955	+	0.254534i	0.783146	+	0.621838i	$0.213614\pi$
$798$		0			0
$799$	−8.25943	−	14.3057i	−0.292198	−	0.506101i
$800$		0			0
$801$	−16.1851	+	44.5448i	−0.571872	+	1.57391i
$802$		0			0
$803$	−21.0931	−	36.5344i	−0.744360	−	1.28927i
$804$		0			0
$805$	−3.89051	+	6.73856i	−0.137122	+	0.237503i
$806$		0			0
$807$	−6.51359	+	4.56354i	−0.229289	+	0.160644i
$808$		0			0
$809$	30.1958			1.06163			0.530813	−	0.847489i	$-0.321886\pi$
$809$	30.1958			1.06163			0.530813	+	0.847489i	$0.321886\pi$
$810$		0			0
$811$	−9.96847			−0.350040			−0.175020	−	0.984565i	$-0.555999\pi$
$811$	−9.96847			−0.350040			−0.175020	+	0.984565i	$0.555999\pi$
$812$		0			0
$813$	−44.1875	+	30.9586i	−1.54972	+	1.08577i
$814$		0			0
$815$	13.5701	−	23.5041i	0.475340	−	0.823312i
$816$		0			0
$817$	32.6234	+	56.5054i	1.14135	+	1.97687i
$818$		0			0
$819$	2.96862	−	8.17025i	0.103732	−	0.285492i
$820$		0			0
$821$	−15.7467	−	27.2741i	−0.549564	−	0.951873i	−0.998304	−	0.0582104i	$-0.981461\pi$
$821$	−15.7467	−	27.2741i	−0.549564	−	0.951873i	0.448740	−	0.893662i	$-0.351873\pi$
$822$		0			0
$823$	−6.06383	+	10.5029i	−0.211372	+	0.366107i	−0.952144	−	0.305649i	$-0.901126\pi$
$823$	−6.06383	+	10.5029i	−0.211372	+	0.366107i	0.740772	+	0.671756i	$0.234460\pi$
$824$		0			0
$825$	−2.06872	−	23.5706i	−0.0720236	−	0.820622i
$826$		0			0
$827$	51.5625			1.79301			0.896503	−	0.443038i	$-0.146099\pi$
$827$	51.5625			1.79301			0.896503	+	0.443038i	$0.146099\pi$
$828$		0			0
$829$	−48.4620			−1.68316			−0.841578	−	0.540135i	$-0.818373\pi$
$829$	−48.4620			−1.68316			−0.841578	+	0.540135i	$0.818373\pi$
$830$		0			0
$831$	−8.96738	−	4.17854i	−0.311075	−	0.144952i
$832$		0			0
$833$	−3.02112	+	5.23273i	−0.104676	+	0.181303i
$834$		0			0
$835$	12.5010	+	21.6523i	0.432613	+	0.749308i
$836$		0			0
$837$	21.6747	+	5.78848i	0.749189	+	0.200079i
$838$		0			0
$839$	−5.01668	−	8.68915i	−0.173195	−	0.299983i	0.766340	−	0.642435i	$-0.222076\pi$
$839$	−5.01668	−	8.68915i	−0.173195	−	0.299983i	−0.939535	+	0.342452i	$0.888742\pi$
$840$		0			0
$841$	−3.49103	+	6.04664i	−0.120380	+	0.208505i
$842$		0			0
$843$	−17.9004	−	8.34106i	−0.616521	−	0.287281i
$844$		0			0
$845$	1.60977			0.0553777
$846$		0			0
$847$	61.3329			2.10742
$848$		0			0
$849$	−1.52283	−	17.3508i	−0.0522634	−	0.595479i
$850$		0			0
$851$	−1.14270	+	1.97921i	−0.0391712	+	0.0678464i
$852$		0			0
$853$	20.8972	+	36.1950i	0.715507	+	1.23929i	0.962764	+	0.270344i	$0.0871376\pi$
$853$	20.8972	+	36.1950i	0.715507	+	1.23929i	−0.247257	+	0.968950i	$0.579529\pi$
$854$		0			0
$855$	−25.6509	−	30.5353i	−0.877243	−	1.04428i
$856$		0			0
$857$	8.27930	+	14.3402i	0.282815	+	0.489851i	0.972077	−	0.234662i	$-0.0753983\pi$
$857$	8.27930	+	14.3402i	0.282815	+	0.489851i	−0.689262	+	0.724513i	$0.742065\pi$
$858$		0			0
$859$	−13.7568	+	23.8274i	−0.469375	+	0.812981i	−0.999387	−	0.0350088i	$-0.988854\pi$
$859$	−13.7568	+	23.8274i	−0.469375	+	0.812981i	0.530012	+	0.847990i	$0.322187\pi$
$860$		0			0
$861$	−29.8412	+	20.9073i	−1.01698	+	0.712519i
$862$		0			0
$863$	−17.4729			−0.594783			−0.297391	−	0.954756i	$-0.596117\pi$
$863$	−17.4729			−0.594783			−0.297391	+	0.954756i	$0.596117\pi$
$864$		0			0
$865$	19.3046			0.656377
$866$		0			0
$867$	2.45220	−	1.71806i	0.0832811	−	0.0583483i
$868$		0			0
$869$	8.79060	−	15.2258i	0.298201	−	0.516499i
$870$		0			0
$871$	−1.31735	−	2.28172i	−0.0446367	−	0.0773130i
$872$		0			0
$873$	−5.42111	+	0.958976i	−0.183477	+	0.0324564i
$874$		0			0
$875$	17.2788	+	29.9277i	0.584130	+	1.01174i
$876$		0			0
$877$	−11.8206	+	20.4739i	−0.399153	+	0.691353i	−0.993622	−	0.112766i	$-0.964029\pi$
$877$	−11.8206	+	20.4739i	−0.399153	+	0.691353i	0.594469	+	0.804119i	$0.297362\pi$
$878$		0			0
$879$	2.65969	+	30.3040i	0.0897093	+	1.02213i
$880$		0			0
$881$	39.2429			1.32213			0.661064	−	0.750330i	$-0.270105\pi$
$881$	39.2429			1.32213			0.661064	+	0.750330i	$0.270105\pi$
$882$		0			0
$883$	10.6796			0.359397			0.179699	−	0.983722i	$-0.442488\pi$
$883$	10.6796			0.359397			0.179699	+	0.983722i	$0.442488\pi$
$884$		0			0
$885$	30.0124	+	13.9849i	1.00885	+	0.470097i
$886$		0			0
$887$	4.98368	−	8.63200i	0.167336	−	0.289834i	−0.770147	−	0.637867i	$-0.779817\pi$
$887$	4.98368	−	8.63200i	0.167336	−	0.289834i	0.937482	+	0.348033i	$0.113150\pi$
$888$		0			0
$889$	−25.4846	−	44.1407i	−0.854727	−	1.48043i
$890$		0			0
$891$	−8.80816	+	50.2784i	−0.295085	+	1.68439i
$892$		0			0
$893$	15.7602	+	27.2974i	0.527394	+	0.913474i
$894$		0			0
$895$	0.238317	−	0.412777i	0.00796605	−	0.0137976i
$896$		0			0
$897$	−2.61893	−	1.22035i	−0.0874436	−	0.0407462i
$898$		0			0
$899$	25.8985			0.863764
$900$		0			0
$901$	31.4580			1.04802
$902$		0			0
$903$	3.46706	+	39.5030i	0.115376	+	1.31458i
$904$		0			0
$905$	18.2906	−	31.6803i	0.608002	−	1.05309i
$906$		0			0
$907$	−8.23145	−	14.2573i	−0.273321	−	0.473405i	0.696389	−	0.717664i	$-0.254789\pi$
$907$	−8.23145	−	14.2573i	−0.273321	−	0.473405i	−0.969710	+	0.244259i	$0.921455\pi$
$908$		0			0
$909$	4.57617	−	0.809509i	0.151782	−	0.0268497i
$910$		0			0
$911$	−10.1543	−	17.5878i	−0.336428	−	0.582711i	0.647330	−	0.762210i	$-0.275886\pi$
$911$	−10.1543	−	17.5878i	−0.336428	−	0.582711i	−0.983758	+	0.179499i	$0.942552\pi$
$912$		0			0
$913$	23.0674	−	39.9538i	0.763418	−	1.32228i
$914$		0			0
$915$	0.646858	−	0.453201i	0.0213845	−	0.0149824i
$916$		0			0
$917$	−41.0061			−1.35414
$918$		0			0
$919$	−11.8028			−0.389340			−0.194670	−	0.980869i	$-0.562364\pi$
$919$	−11.8028			−0.389340			−0.194670	+	0.980869i	$0.562364\pi$
$920$		0			0
$921$	22.4526	−	15.7307i	0.739839	−	0.518346i
$922$		0			0
$923$	−2.05367	+	3.55707i	−0.0675975	+	0.117082i
$924$		0			0
$925$	1.64996	+	2.85781i	0.0542502	+	0.0939641i
$926$		0			0
$927$	31.5988	+	37.6158i	1.03784	+	1.23546i
$928$		0			0
$929$	17.9408	+	31.0745i	0.588620	+	1.01952i	0.994413	+	0.105555i	$0.0336619\pi$
$929$	17.9408	+	31.0745i	0.588620	+	1.01952i	−0.405793	+	0.913965i	$0.633005\pi$
$930$		0			0
$931$	5.76473	−	9.98480i	0.188931	−	0.327239i
$932$		0			0
$933$	−1.84970	−	21.0751i	−0.0605564	−	0.689968i
$934$		0			0
$935$	39.5112			1.29215
$936$		0			0
$937$	0.492587			0.0160921			0.00804606	−	0.999968i	$-0.497439\pi$
$937$	0.492587			0.0160921			0.00804606	+	0.999968i	$0.497439\pi$
$938$		0			0
$939$	−26.7105	−	12.4463i	−0.871663	−	0.406170i
$940$		0			0
$941$	−12.8095	+	22.1867i	−0.417577	+	0.723264i	−0.995695	−	0.0926887i	$-0.970454\pi$
$941$	−12.8095	+	22.1867i	−0.417577	+	0.723264i	0.578118	+	0.815953i	$0.303787\pi$
$942$		0			0
$943$	6.05530	+	10.4881i	0.197188	+	0.341539i
$944$		0			0
$945$	−6.29250	−	23.4063i	−0.204695	−	0.761408i
$946$		0			0
$947$	−12.6845	−	21.9702i	−0.412190	−	0.713934i	0.582939	−	0.812516i	$-0.301903\pi$
$947$	−12.6845	−	21.9702i	−0.412190	−	0.713934i	−0.995129	+	0.0985817i	$0.968569\pi$
$948$		0			0
$949$	−3.71910	+	6.44167i	−0.120727	+	0.209105i
$950$		0			0
$951$	−44.8718	−	20.9090i	−1.45507	−	0.678020i
$952$		0			0
$953$	−13.3452			−0.432293			−0.216146	−	0.976361i	$-0.569349\pi$
$953$	−13.3452			−0.432293			−0.216146	+	0.976361i	$0.569349\pi$
$954$		0			0
$955$	−10.3519			−0.334979
$956$		0			0
$957$	5.15195	+	58.7003i	0.166539	+	1.89751i
$958$		0			0
$959$	10.4119	−	18.0340i	0.336219	−	0.582349i
$960$		0			0
$961$	6.17961	+	10.7034i	0.199342	+	0.345271i
$962$		0			0
$963$	9.98188	−	27.4722i	0.321662	−	0.885280i
$964$		0			0
$965$	6.06287	+	10.5012i	0.195171	+	0.338045i
$966$		0			0
$967$	−3.43388	+	5.94766i	−0.110426	+	0.191264i	−0.915942	−	0.401310i	$-0.868555\pi$
$967$	−3.43388	+	5.94766i	−0.110426	+	0.191264i	0.805516	+	0.592574i	$0.201888\pi$
$968$		0			0
$969$	−50.6944	+	35.5174i	−1.62854	+	1.14098i
$970$		0			0
$971$	35.4548			1.13780			0.568899	−	0.822407i	$-0.307370\pi$
$971$	35.4548			1.13780			0.568899	+	0.822407i	$0.307370\pi$
$972$		0			0
$973$	−34.6882			−1.11205
$974$		0			0
$975$	−3.41676	+	2.39385i	−0.109424	+	0.0766644i
$976$		0			0
$977$	21.7385	−	37.6521i	0.695475	−	1.20460i	−0.274545	−	0.961574i	$-0.588527\pi$
$977$	21.7385	−	37.6521i	0.695475	−	1.20460i	0.970020	−	0.243024i	$-0.0781395\pi$
$978$		0			0
$979$	44.7997	+	77.5954i	1.43181	+	2.47996i
$980$		0			0
$981$	17.9810	−	49.4875i	0.574089	−	1.58001i
$982$		0			0
$983$	−16.1529	−	27.9776i	−0.515197	−	0.892347i	−0.999844	−	0.0176376i	$-0.994385\pi$
$983$	−16.1529	−	27.9776i	−0.515197	−	0.892347i	0.484648	−	0.874710i	$-0.338948\pi$
$984$		0			0
$985$	−11.3856	+	19.7204i	−0.362774	+	0.628343i
$986$		0			0
$987$	1.67492	+	19.0837i	0.0533132	+	0.607440i
$988$		0			0
$989$	13.1803			0.419110
$990$		0			0
$991$	23.2443			0.738380			0.369190	−	0.929354i	$-0.379635\pi$
$991$	23.2443			0.738380			0.369190	+	0.929354i	$0.379635\pi$
$992$		0			0
$993$	30.7749	+	14.3402i	0.976613	+	0.455074i
$994$		0			0
$995$	−0.518017	+	0.897231i	−0.0164222	+	0.0284441i
$996$		0			0
$997$	−27.8090	−	48.1666i	−0.880720	−	1.52545i	−0.850542	−	0.525908i	$-0.823726\pi$
$997$	−27.8090	−	48.1666i	−0.880720	−	1.52545i	−0.0301788	−	0.999545i	$-0.509608\pi$
$998$		0			0
$999$	−1.84820	−	6.87477i	−0.0584744	−	0.217508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.g.625.10	yes	22
3.2	odd	2		2808.2.q.g.1873.7		22
9.2	odd	6		2808.2.q.g.937.7		22
9.4	even	3		8424.2.a.bf.1.7		11
9.5	odd	6		8424.2.a.be.1.5		11
9.7	even	3	inner	936.2.q.g.313.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.g.313.10	✓	22	9.7	even	3	inner
936.2.q.g.625.10	yes	22	1.1	even	1	trivial
2808.2.q.g.937.7		22	9.2	odd	6
2808.2.q.g.1873.7		22	3.2	odd	2
8424.2.a.be.1.5		11	9.5	odd	6
8424.2.a.bf.1.7		11	9.4	even	3

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.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41854 - 0.993855i) q^{3} +(-0.804884 + 1.39410i) q^{5} +(-1.44881 - 2.50941i) q^{7} +(1.02450 - 2.81964i) q^{9} +(-2.83578 - 4.91172i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(0.243775 + 2.77752i) q^{15} +4.32766 q^{17} -8.25781 q^{19} +(-4.54918 - 2.11979i) q^{21} +(-0.834069 + 1.44465i) q^{23} +(1.20432 + 2.08595i) q^{25} +(-1.34902 - 5.01798i) q^{27} +(-2.99925 - 5.19486i) q^{29} +(-2.15875 + 3.73906i) q^{31} +(-8.90421 - 4.14911i) q^{33} +4.66449 q^{35} +1.37003 q^{37} +(0.151435 + 1.72542i) q^{39} +(3.62998 - 6.28730i) q^{41} +(-3.95061 - 6.84266i) q^{43} +(3.10626 + 3.69775i) q^{45} +(-1.90852 - 3.30565i) q^{47} +(-0.698094 + 1.20913i) q^{49} +(6.13896 - 4.30107i) q^{51} +7.26904 q^{53} +9.12991 q^{55} +(-11.7140 + 8.20707i) q^{57} +(5.93765 - 10.2843i) q^{59} +(-0.141636 - 0.245321i) q^{61} +(-8.55995 + 1.51423i) q^{63} +(-0.804884 - 1.39410i) q^{65} +(-1.31735 + 2.28172i) q^{67} +(0.252614 + 2.87824i) q^{69} +4.10735 q^{71} +7.43820 q^{73} +(3.78151 + 1.76208i) q^{75} +(-8.21702 + 14.2323i) q^{77} +(1.54994 + 2.68458i) q^{79} +(-6.90079 - 5.77747i) q^{81} +(4.06719 + 7.04459i) q^{83} +(-3.48327 + 6.03320i) q^{85} +(-9.41749 - 4.38828i) q^{87} -15.7980 q^{89} +2.89762 q^{91} +(0.653819 + 7.44949i) q^{93} +(6.64658 - 11.5122i) q^{95} +(-0.917545 - 1.58924i) q^{97} +(-16.7546 + 2.96383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) \) 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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