LMFDB - Embedded newform 990.2.z.b.161.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(161,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.7
Character	$\chi$	$=$	990.161
Dual form			990.2.z.b.701.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(1.89200 - 0.614747i) q^{7} +(-0.309017 + 0.951057i) q^{8} +1.00000i q^{10} +(3.28401 - 0.463949i) q^{11} +(-1.89539 + 2.60879i) q^{13} +(1.89200 + 0.614747i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(5.26884 - 3.82804i) q^{17} +(-1.96673 - 0.639030i) q^{19} +(-0.587785 + 0.809017i) q^{20} +(2.92953 + 1.55495i) q^{22} +3.58100i q^{23} +(-0.309017 + 0.951057i) q^{25} +(-3.06681 + 0.996467i) q^{26} +(1.16932 + 1.60943i) q^{28} +(0.406430 + 1.25086i) q^{29} +(0.993242 + 0.721632i) q^{31} -1.00000 q^{32} +6.51264 q^{34} +(1.60943 + 1.16932i) q^{35} +(-1.08996 - 3.35456i) q^{37} +(-1.21551 - 1.67300i) q^{38} +(-0.951057 + 0.309017i) q^{40} +(-1.32496 + 4.07780i) q^{41} +8.18374i q^{43} +(1.45606 + 2.97992i) q^{44} +(-2.10486 + 2.89709i) q^{46} +(2.18505 + 0.709965i) q^{47} +(-2.46138 + 1.78829i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-3.06681 - 0.996467i) q^{52} +(7.75090 - 10.6682i) q^{53} +(2.30564 + 2.38412i) q^{55} +1.98936i q^{56} +(-0.406430 + 1.25086i) q^{58} +(5.67571 - 1.84415i) q^{59} +(1.18547 + 1.63166i) q^{61} +(0.379385 + 1.16763i) q^{62} +(-0.809017 - 0.587785i) q^{64} -3.22464 q^{65} -7.59383 q^{67} +(5.26884 + 3.82804i) q^{68} +(0.614747 + 1.89200i) q^{70} +(-2.68699 - 3.69833i) q^{71} +(-8.96545 + 2.91305i) q^{73} +(1.08996 - 3.35456i) q^{74} -2.06794i q^{76} +(5.92814 - 2.89663i) q^{77} +(-2.40983 + 3.31685i) q^{79} +(-0.951057 - 0.309017i) q^{80} +(-3.46878 + 2.52022i) q^{82} +(1.91200 - 1.38915i) q^{83} +(6.19389 + 2.01252i) q^{85} +(-4.81028 + 6.62079i) q^{86} +(-0.573574 + 3.26665i) q^{88} +11.4586i q^{89} +(-1.98234 + 6.10101i) q^{91} +(-3.40574 + 1.10659i) q^{92} +(1.35043 + 1.85871i) q^{94} +(-0.639030 - 1.96673i) q^{95} +(-0.221400 - 0.160857i) q^{97} -3.04243 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{2} - 8 q^{4} + 8 q^{8} - 8 q^{16} - 4 q^{17} + 8 q^{25} + 8 q^{29} + 32 q^{31} - 32 q^{32} + 24 q^{34} + 16 q^{37} - 32 q^{41} - 20 q^{46} + 20 q^{47} + 16 q^{49} - 8 q^{50} + 40 q^{53} + 8 q^{55}+ \cdots - 16 q^{98}+O(q^{100}) $ 32 * q + 8 * q^2 - 8 * q^4 + 8 * q^8 - 8 * q^16 - 4 * q^17 + 8 * q^25 + 8 * q^29 + 32 * q^31 - 32 * q^32 + 24 * q^34 + 16 * q^37 - 32 * q^41 - 20 * q^46 + 20 * q^47 + 16 * q^49 - 8 * q^50 + 40 * q^53 + 8 * q^55 - 8 * q^58 - 40 * q^59 + 28 * q^62 - 8 * q^64 - 8 * q^65 - 4 * q^68 + 40 * q^71 + 40 * q^73 - 16 * q^74 + 28 * q^77 + 20 * q^79 - 8 * q^82 + 24 * q^83 - 24 * q^91 + 20 * q^94 - 16 * q^95 + 48 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.587785	+	0.809017i	0.262866	+	0.361803i
$5$	0.587785	+	0.809017i	0.262866	+	0.361803i
$6$		0			0
$7$	1.89200	−	0.614747i	0.715108	−	0.232353i	0.0712071	−	0.997462i	$-0.477315\pi$
$7$	1.89200	−	0.614747i	0.715108	−	0.232353i	0.643901	+	0.765109i	$0.277315\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$		0			0
$10$			1.00000i			0.316228i
$11$	3.28401	−	0.463949i	0.990168	−	0.139886i
$11$	3.28401	−	0.463949i	0.990168	−	0.139886i
$12$		0			0
$13$	−1.89539	+	2.60879i	−0.525688	+	0.723547i	−0.986466	−	0.163969i	$-0.947570\pi$
$13$	−1.89539	+	2.60879i	−0.525688	+	0.723547i	0.460778	+	0.887515i	$0.347570\pi$
$14$	1.89200	+	0.614747i	0.505658	+	0.164298i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	5.26884	−	3.82804i	1.27788	−	0.928435i	0.278394	−	0.960467i	$-0.410198\pi$
$17$	5.26884	−	3.82804i	1.27788	−	0.928435i	0.999487	+	0.0320317i	$0.0101977\pi$
$18$		0			0
$19$	−1.96673	−	0.639030i	−0.451199	−	0.146603i	0.0745977	−	0.997214i	$-0.476233\pi$
$19$	−1.96673	−	0.639030i	−0.451199	−	0.146603i	−0.525797	+	0.850610i	$0.676233\pi$
$20$	−0.587785	+	0.809017i	−0.131433	+	0.180902i
$21$		0			0
$22$	2.92953	+	1.55495i	0.624577	+	0.331517i
$23$			3.58100i			0.746691i	0.927692	+	0.373346i	$0.121789\pi$
$23$			3.58100i			0.746691i	−0.927692	+	0.373346i	$0.878211\pi$
$24$		0			0
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	−3.06681	+	0.996467i	−0.601451	+	0.195423i
$27$		0			0
$28$	1.16932	+	1.60943i	0.220981	+	0.304154i
$29$	0.406430	+	1.25086i	0.0754721	+	0.232279i	0.981675	−	0.190565i	$-0.0610319\pi$
$29$	0.406430	+	1.25086i	0.0754721	+	0.232279i	−0.906203	+	0.422844i	$0.861032\pi$
$30$		0			0
$31$	0.993242	+	0.721632i	0.178391	+	0.129609i	0.673398	−	0.739280i	$-0.264834\pi$
$31$	0.993242	+	0.721632i	0.178391	+	0.129609i	−0.495006	+	0.868889i	$0.664834\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	6.51264			1.11691
$35$	1.60943	+	1.16932i	0.272043	+	0.197651i
$36$		0			0
$37$	−1.08996	−	3.35456i	−0.179189	−	0.551486i	0.820611	−	0.571487i	$-0.193633\pi$
$37$	−1.08996	−	3.35456i	−0.179189	−	0.551486i	−0.999800	+	0.0200005i	$0.993633\pi$
$38$	−1.21551	−	1.67300i	−0.197181	−	0.271397i
$39$		0			0
$40$	−0.951057	+	0.309017i	−0.150375	+	0.0488599i
$41$	−1.32496	+	4.07780i	−0.206924	+	0.636845i	0.792705	+	0.609605i	$0.208672\pi$
$41$	−1.32496	+	4.07780i	−0.206924	+	0.636845i	−0.999629	+	0.0272402i	$0.991328\pi$
$42$		0			0
$43$			8.18374i			1.24801i	0.781421	+	0.624004i	$0.214495\pi$
$43$			8.18374i			1.24801i	−0.781421	+	0.624004i	$0.785505\pi$
$44$	1.45606	+	2.97992i	0.219509	+	0.449239i
$45$		0			0
$46$	−2.10486	+	2.89709i	−0.310345	+	0.427153i
$47$	2.18505	+	0.709965i	0.318722	+	0.103559i	0.464009	−	0.885831i	$-0.346411\pi$
$47$	2.18505	+	0.709965i	0.318722	+	0.103559i	−0.145287	+	0.989390i	$0.546411\pi$
$48$		0			0
$49$	−2.46138	+	1.78829i	−0.351625	+	0.255471i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$		0			0
$52$	−3.06681	−	0.996467i	−0.425290	−	0.138185i
$53$	7.75090	−	10.6682i	1.06467	−	1.46539i	0.189307	−	0.981918i	$-0.439376\pi$
$53$	7.75090	−	10.6682i	1.06467	−	1.46539i	0.875360	−	0.483471i	$-0.160624\pi$
$54$		0			0
$55$	2.30564	+	2.38412i	0.310892	+	0.321475i
$56$			1.98936i			0.265840i
$57$		0			0
$58$	−0.406430	+	1.25086i	−0.0533669	+	0.164246i
$59$	5.67571	−	1.84415i	0.738914	−	0.240088i	0.0847100	−	0.996406i	$-0.473004\pi$
$59$	5.67571	−	1.84415i	0.738914	−	0.240088i	0.654204	+	0.756318i	$0.273004\pi$
$60$		0			0
$61$	1.18547	+	1.63166i	0.151784	+	0.208912i	0.878137	−	0.478409i	$-0.158786\pi$
$61$	1.18547	+	1.63166i	0.151784	+	0.208912i	−0.726353	+	0.687321i	$0.758786\pi$
$62$	0.379385	+	1.16763i	0.0481819	+	0.148289i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−3.22464			−0.399967
$66$		0			0
$67$	−7.59383			−0.927734			−0.463867	−	0.885905i	$-0.653539\pi$
$67$	−7.59383			−0.927734			−0.463867	+	0.885905i	$0.653539\pi$
$68$	5.26884	+	3.82804i	0.638941	+	0.464218i
$69$		0			0
$70$	0.614747	+	1.89200i	0.0734764	+	0.226137i
$71$	−2.68699	−	3.69833i	−0.318888	−	0.438911i	0.619240	−	0.785202i	$-0.287441\pi$
$71$	−2.68699	−	3.69833i	−0.318888	−	0.438911i	−0.938127	+	0.346291i	$0.887441\pi$
$72$		0			0
$73$	−8.96545	+	2.91305i	−1.04933	+	0.340947i	−0.782404	−	0.622771i	$-0.786007\pi$
$73$	−8.96545	+	2.91305i	−1.04933	+	0.340947i	−0.266922	+	0.963718i	$0.586007\pi$
$74$	1.08996	−	3.35456i	0.126706	−	0.389960i
$75$		0			0
$76$		−	2.06794i		−	0.237209i
$77$	5.92814	−	2.89663i	0.675574	−	0.330102i
$78$		0			0
$79$	−2.40983	+	3.31685i	−0.271127	+	0.373175i	−0.922770	−	0.385351i	$-0.874080\pi$
$79$	−2.40983	+	3.31685i	−0.271127	+	0.373175i	0.651643	+	0.758526i	$0.274080\pi$
$80$	−0.951057	−	0.309017i	−0.106331	−	0.0345492i
$81$		0			0
$82$	−3.46878	+	2.52022i	−0.383063	+	0.278311i
$83$	1.91200	−	1.38915i	0.209869	−	0.152479i	−0.477885	−	0.878422i	$-0.658597\pi$
$83$	1.91200	−	1.38915i	0.209869	−	0.152479i	0.687754	+	0.725943i	$0.258597\pi$
$84$		0			0
$85$	6.19389	+	2.01252i	0.671822	+	0.218288i
$86$	−4.81028	+	6.62079i	−0.518706	+	0.713938i
$87$		0			0
$88$	−0.573574	+	3.26665i	−0.0611432	+	0.348226i
$89$			11.4586i			1.21461i	0.794468	+	0.607306i	$0.207750\pi$
$89$			11.4586i			1.21461i	−0.794468	+	0.607306i	$0.792250\pi$
$90$		0			0
$91$	−1.98234	+	6.10101i	−0.207805	+	0.639559i
$92$	−3.40574	+	1.10659i	−0.355073	+	0.115370i
$93$		0			0
$94$	1.35043	+	1.85871i	0.139287	+	0.191711i
$95$	−0.639030	−	1.96673i	−0.0655630	−	0.201782i
$96$		0			0
$97$	−0.221400	−	0.160857i	−0.0224798	−	0.0163325i	0.576489	−	0.817105i	$-0.304423\pi$
$97$	−0.221400	−	0.160857i	−0.0224798	−	0.0163325i	−0.598968	+	0.800773i	$0.704423\pi$
$98$	−3.04243			−0.307332
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−14.7990	−	10.7521i	−1.47255	−	1.06987i	−0.979864	−	0.199665i	$-0.936015\pi$
$101$	−14.7990	−	10.7521i	−1.47255	−	1.06987i	−0.492688	−	0.870206i	$-0.663985\pi$
$102$		0			0
$103$	−0.426688	−	1.31321i	−0.0420428	−	0.129394i	0.927832	−	0.372998i	$-0.121670\pi$
$103$	−0.426688	−	1.31321i	−0.0420428	−	0.129394i	−0.969875	+	0.243604i	$0.921670\pi$
$104$	−1.89539	−	2.60879i	−0.185859	−	0.255812i
$105$		0			0
$106$	12.5412	−	4.07489i	1.21811	−	0.395788i
$107$	4.72453	−	14.5406i	0.456737	−	1.40569i	−0.412346	−	0.911027i	$-0.635291\pi$
$107$	4.72453	−	14.5406i	0.456737	−	1.40569i	0.869084	−	0.494665i	$-0.164709\pi$
$108$		0			0
$109$		−	19.7457i		−	1.89130i	−0.325188	−	0.945649i	$-0.605428\pi$
$109$		−	19.7457i		−	1.89130i	0.325188	−	0.945649i	$-0.394572\pi$
$110$	0.463949	+	3.28401i	0.0442358	+	0.313118i
$111$		0			0
$112$	−1.16932	+	1.60943i	−0.110490	+	0.152077i
$113$	10.9477	+	3.55711i	1.02987	+	0.334625i	0.774738	−	0.632282i	$-0.217882\pi$
$113$	10.9477	+	3.55711i	1.02987	+	0.334625i	0.255130	+	0.966907i	$0.417882\pi$
$114$		0			0
$115$	−2.89709	+	2.10486i	−0.270155	+	0.196279i
$116$	−1.06405	+	0.773076i	−0.0987943	+	0.0717783i
$117$		0			0
$118$	5.67571	+	1.84415i	0.522491	+	0.169768i
$119$	7.61536	−	10.4816i	0.698099	−	0.960851i
$120$		0			0
$121$	10.5695	−	3.04723i	0.960864	−	0.277021i
$122$			2.01684i			0.182596i
$123$		0			0
$124$	−0.379385	+	1.16763i	−0.0340697	+	0.104856i
$125$	−0.951057	+	0.309017i	−0.0850651	+	0.0276393i
$126$		0			0
$127$	−3.61822	−	4.98005i	−0.321065	−	0.441908i	0.617727	−	0.786393i	$-0.288054\pi$
$127$	−3.61822	−	4.98005i	−0.321065	−	0.441908i	−0.938792	+	0.344484i	$0.888054\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	−2.60879	−	1.89539i	−0.228806	−	0.166237i
$131$	−15.9580			−1.39425			−0.697126	−	0.716948i	$-0.745538\pi$
$131$	−15.9580			−1.39425			−0.697126	+	0.716948i	$0.745538\pi$
$132$		0			0
$133$	−4.11389			−0.356720
$134$	−6.14354	−	4.46354i	−0.530721	−	0.385591i
$135$		0			0
$136$	2.01252	+	6.19389i	0.172572	+	0.531122i
$137$	0.610519	+	0.840308i	0.0521602	+	0.0717923i	0.834300	−	0.551310i	$-0.185872\pi$
$137$	0.610519	+	0.840308i	0.0521602	+	0.0717923i	−0.782140	+	0.623103i	$0.785872\pi$
$138$		0			0
$139$	−5.85148	+	1.90126i	−0.496316	+	0.161263i	−0.546470	−	0.837479i	$-0.684029\pi$
$139$	−5.85148	+	1.90126i	−0.496316	+	0.161263i	0.0501541	+	0.998741i	$0.484029\pi$
$140$	−0.614747	+	1.89200i	−0.0519556	+	0.159903i
$141$		0			0
$142$		−	4.57139i		−	0.383622i
$143$	−5.01416	+	9.44665i	−0.419305	+	0.789969i
$144$		0			0
$145$	−0.773076	+	1.06405i	−0.0642004	+	0.0883643i
$146$	−8.96545	−	2.91305i	−0.741986	−	0.241086i
$147$		0			0
$148$	2.85356	−	2.07323i	0.234561	−	0.170419i
$149$	9.75875	−	7.09015i	0.799468	−	0.580848i	−0.111290	−	0.993788i	$-0.535498\pi$
$149$	9.75875	−	7.09015i	0.799468	−	0.580848i	0.910758	+	0.412940i	$0.135498\pi$
$150$		0			0
$151$	4.66255	+	1.51496i	0.379433	+	0.123285i	0.492523	−	0.870299i	$-0.336075\pi$
$151$	4.66255	+	1.51496i	0.379433	+	0.123285i	−0.113090	+	0.993585i	$0.536075\pi$
$152$	1.21551	−	1.67300i	0.0985906	−	0.135698i
$153$		0			0
$154$	6.49856	+	1.14105i	0.523669	+	0.0919483i
$155$			1.22771i			0.0986124i
$156$		0			0
$157$	5.37853	−	16.5534i	0.429253	−	1.32111i	−0.469609	−	0.882874i	$-0.655605\pi$
$157$	5.37853	−	16.5534i	0.429253	−	1.32111i	0.898862	−	0.438231i	$-0.144395\pi$
$158$	−3.89919	+	1.26692i	−0.310203	+	0.100791i
$159$		0			0
$160$	−0.587785	−	0.809017i	−0.0464685	−	0.0639584i
$161$	2.20141	+	6.77525i	0.173496	+	0.533965i
$162$		0			0
$163$	−11.2253	−	8.15565i	−0.879232	−	0.638800i	0.0538159	−	0.998551i	$-0.482862\pi$
$163$	−11.2253	−	8.15565i	−0.879232	−	0.638800i	−0.933048	+	0.359751i	$0.882862\pi$
$164$	−4.28765			−0.334809
$165$		0			0
$166$	2.36336			0.183432
$167$	−12.2139	−	8.87389i	−0.945137	−	0.686683i	0.00451436	−	0.999990i	$-0.498563\pi$
$167$	−12.2139	−	8.87389i	−0.945137	−	0.686683i	−0.949652	+	0.313307i	$0.898563\pi$
$168$		0			0
$169$	0.803977	+	2.47439i	0.0618444	+	0.190337i
$170$	3.82804	+	5.26884i	0.293597	+	0.404102i
$171$		0			0
$172$	−7.78320	+	2.52892i	−0.593464	+	0.192828i
$173$	2.68224	−	8.25508i	0.203927	−	0.627622i	−0.795829	−	0.605521i	$-0.792965\pi$
$173$	2.68224	−	8.25508i	0.203927	−	0.627622i	0.999756	−	0.0221006i	$-0.00703540\pi$
$174$		0			0
$175$			1.98936i			0.150382i
$176$	−2.38412	+	2.30564i	−0.179710	+	0.173794i
$177$		0			0
$178$	−6.73521	+	9.27022i	−0.504825	+	0.694833i
$179$	−7.87244	−	2.55791i	−0.588414	−	0.191187i	−0.000347497	−	1.00000i	$-0.500111\pi$
$179$	−7.87244	−	2.55791i	−0.588414	−	0.191187i	−0.588066	+	0.808813i	$0.700111\pi$
$180$		0			0
$181$	7.53720	−	5.47610i	0.560236	−	0.407035i	−0.271309	−	0.962492i	$-0.587457\pi$
$181$	7.53720	−	5.47610i	0.560236	−	0.407035i	0.831545	+	0.555457i	$0.187457\pi$
$182$	−5.18983	+	3.77063i	−0.384695	+	0.279498i
$183$		0			0
$184$	−3.40574	−	1.10659i	−0.251074	−	0.0815790i
$185$	2.07323	−	2.85356i	0.152427	−	0.209798i
$186$		0			0
$187$	15.5269	−	15.0158i	1.13544	−	1.09806i
$188$			2.29749i			0.167562i
$189$		0			0
$190$	0.639030	−	1.96673i	0.0463601	−	0.142682i
$191$	−22.8697	+	7.43081i	−1.65479	+	0.537675i	−0.979771	−	0.200123i	$-0.935866\pi$
$191$	−22.8697	+	7.43081i	−1.65479	+	0.537675i	−0.675022	+	0.737798i	$0.735866\pi$
$192$		0			0
$193$	−2.35589	−	3.24260i	−0.169580	−	0.233407i	0.715765	−	0.698341i	$-0.246078\pi$
$193$	−2.35589	−	3.24260i	−0.169580	−	0.233407i	−0.885345	+	0.464934i	$0.846078\pi$
$194$	−0.0845673	−	0.260271i	−0.00607158	−	0.0186864i
$195$		0			0
$196$	−2.46138	−	1.78829i	−0.175813	−	0.127735i
$197$	22.8884			1.63073			0.815365	−	0.578948i	$-0.196536\pi$
$197$	22.8884			1.63073			0.815365	+	0.578948i	$0.196536\pi$
$198$		0			0
$199$	−16.4034			−1.16281			−0.581404	−	0.813615i	$-0.697497\pi$
$199$	−16.4034			−1.16281			−0.581404	+	0.813615i	$0.697497\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$		0			0
$202$	−5.65270	−	17.3972i	−0.397723	−	1.22406i
$203$	1.53793	+	2.11678i	0.107941	+	0.148569i
$204$		0			0
$205$	−4.07780	+	1.32496i	−0.284806	+	0.0925390i
$206$	0.426688	−	1.31321i	0.0297288	−	0.0914957i
$207$		0			0
$208$		−	3.22464i		−	0.223588i
$209$	−6.75525	−	1.18612i	−0.467270	−	0.0820456i
$210$		0			0
$211$	−13.9526	+	19.2041i	−0.960534	+	1.32206i	−0.0138480	+	0.999904i	$0.504408\pi$
$211$	−13.9526	+	19.2041i	−0.960534	+	1.32206i	−0.946686	+	0.322158i	$0.895592\pi$
$212$	12.5412	+	4.07489i	0.861334	+	0.279864i
$213$		0			0
$214$	12.3690	−	8.98658i	0.845525	−	0.614310i
$215$	−6.62079	+	4.81028i	−0.451534	+	0.328059i
$216$		0			0
$217$	2.32283	+	0.754734i	0.157684	+	0.0512347i
$218$	11.6063	−	15.9746i	0.786075	−	1.08194i
$219$		0			0
$220$	−1.55495	+	2.92953i	−0.104835	+	0.197509i
$221$			21.0009i			1.41267i
$222$		0			0
$223$	8.64819	−	26.6164i	0.579126	−	1.78237i	−0.0425547	−	0.999094i	$-0.513550\pi$
$223$	8.64819	−	26.6164i	0.579126	−	1.78237i	0.621680	−	0.783271i	$-0.286450\pi$
$224$	−1.89200	+	0.614747i	−0.126414	+	0.0410745i
$225$		0			0
$226$	6.76602	+	9.31263i	0.450069	+	0.619467i
$227$	−6.30941	−	19.4184i	−0.418770	−	1.28884i	−0.908835	−	0.417156i	$-0.863027\pi$
$227$	−6.30941	−	19.4184i	−0.418770	−	1.28884i	0.490065	−	0.871686i	$-0.336973\pi$
$228$		0			0
$229$	−1.24761	−	0.906440i	−0.0824443	−	0.0598993i	0.545800	−	0.837916i	$-0.316226\pi$
$229$	−1.24761	−	0.906440i	−0.0824443	−	0.0598993i	−0.628244	+	0.778016i	$0.716226\pi$
$230$	−3.58100			−0.236124
$231$		0			0
$232$	−1.31523			−0.0863494
$233$	10.4496	+	7.59211i	0.684579	+	0.497376i	0.874874	−	0.484351i	$-0.160944\pi$
$233$	10.4496	+	7.59211i	0.684579	+	0.497376i	−0.190295	+	0.981727i	$0.560944\pi$
$234$		0			0
$235$	0.709965	+	2.18505i	0.0463130	+	0.142537i
$236$	3.50778	+	4.82805i	0.228337	+	0.314279i
$237$		0			0
$238$	12.3219	−	4.00363i	0.798711	−	0.259517i
$239$	−0.700590	+	2.15619i	−0.0453174	+	0.139473i	−0.971155	−	0.238449i	$-0.923361\pi$
$239$	−0.700590	+	2.15619i	−0.0453174	+	0.139473i	0.925838	+	0.377921i	$0.123361\pi$
$240$		0			0
$241$		−	25.7528i		−	1.65889i	−0.558591	−	0.829443i	$-0.688658\pi$
$241$		−	25.7528i		−	1.65889i	0.558591	−	0.829443i	$-0.311342\pi$
$242$	10.3420	+	3.74734i	0.664811	+	0.240888i
$243$		0			0
$244$	−1.18547	+	1.63166i	−0.0758918	+	0.104456i
$245$	−2.89352	−	0.940162i	−0.184860	−	0.0600647i
$246$		0			0
$247$	5.39482	−	3.91957i	0.343264	−	0.249396i
$248$	−0.993242	+	0.721632i	−0.0630709	+	0.0458237i
$249$		0			0
$250$	−0.951057	−	0.309017i	−0.0601501	−	0.0195440i
$251$	−13.6275	+	18.7567i	−0.860162	+	1.18391i	0.121369	+	0.992607i	$0.461272\pi$
$251$	−13.6275	+	18.7567i	−0.860162	+	1.18391i	−0.981531	+	0.191304i	$0.938728\pi$
$252$		0			0
$253$	1.66140	+	11.7601i	0.104452	+	0.739349i
$254$		−	6.15568i		−	0.386242i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−9.79799	+	3.18356i	−0.611182	+	0.198585i	−0.598221	−	0.801331i	$-0.704126\pi$
$257$	−9.79799	+	3.18356i	−0.611182	+	0.198585i	−0.0129608	+	0.999916i	$0.504126\pi$
$258$		0			0
$259$	−4.12442	−	5.67677i	−0.256279	−	0.352737i
$260$	−0.996467	−	3.06681i	−0.0617983	−	0.190196i
$261$		0			0
$262$	−12.9103	−	9.37985i	−0.797598	−	0.579489i
$263$	−21.8652			−1.34827			−0.674133	−	0.738610i	$-0.735482\pi$
$263$	−21.8652			−1.34827			−0.674133	+	0.738610i	$0.735482\pi$
$264$		0			0
$265$	13.1866			0.810047
$266$	−3.32821	−	2.41809i	−0.204066	−	0.148262i
$267$		0			0
$268$	−2.34662	−	7.22216i	−0.143343	−	0.441164i
$269$	9.87617	+	13.5934i	0.602161	+	0.828803i	0.995904	−	0.0904173i	$-0.0288201\pi$
$269$	9.87617	+	13.5934i	0.602161	+	0.828803i	−0.393743	+	0.919220i	$0.628820\pi$
$270$		0			0
$271$	−1.30254	+	0.423220i	−0.0791234	+	0.0257088i	−0.348311	−	0.937379i	$-0.613245\pi$
$271$	−1.30254	+	0.423220i	−0.0791234	+	0.0257088i	0.269188	+	0.963088i	$0.413245\pi$
$272$	−2.01252	+	6.19389i	−0.122027	+	0.375560i
$273$		0			0
$274$			1.03868i			0.0627488i
$275$	−0.573574	+	3.26665i	−0.0345878	+	0.196987i
$276$		0			0
$277$	1.51875	−	2.09038i	0.0912530	−	0.125599i	−0.760949	−	0.648811i	$-0.775266\pi$
$277$	1.51875	−	2.09038i	0.0912530	−	0.125599i	0.852202	+	0.523212i	$0.175266\pi$
$278$	−5.85148	−	1.90126i	−0.350948	−	0.114030i
$279$		0			0
$280$	−1.60943	+	1.16932i	−0.0961818	+	0.0698802i
$281$	−13.1771	+	9.57371i	−0.786079	+	0.571120i	−0.906797	−	0.421567i	$-0.861480\pi$
$281$	−13.1771	+	9.57371i	−0.786079	+	0.571120i	0.120718	+	0.992687i	$0.461480\pi$
$282$		0			0
$283$	13.4479	+	4.36949i	0.799396	+	0.259739i	0.680100	−	0.733119i	$-0.261936\pi$
$283$	13.4479	+	4.36949i	0.799396	+	0.259739i	0.119296	+	0.992859i	$0.461936\pi$
$284$	2.68699	−	3.69833i	0.159444	−	0.219456i
$285$		0			0
$286$	−9.60914	+	4.69526i	−0.568200	+	0.277636i
$287$			8.52970i			0.503492i
$288$		0			0
$289$	7.85352	−	24.1707i	0.461972	−	1.42180i
$290$	−1.25086	+	0.406430i	−0.0734532	+	0.0238664i
$291$		0			0
$292$	−5.54095	−	7.62647i	−0.324260	−	0.446305i
$293$	3.91654	+	12.0539i	0.228807	+	0.704194i	0.997883	+	0.0650371i	$0.0207166\pi$
$293$	3.91654	+	12.0539i	0.228807	+	0.704194i	−0.769076	+	0.639157i	$0.779283\pi$
$294$		0			0
$295$	4.82805	+	3.50778i	0.281100	+	0.204231i
$296$	3.52719			0.205014
$297$		0			0
$298$	12.0625			0.698761
$299$	−9.34207	−	6.78741i	−0.540266	−	0.392526i
$300$		0			0
$301$	5.03093	+	15.4836i	0.289978	+	0.892461i
$302$	2.88162	+	3.96620i	0.165818	+	0.228229i
$303$		0			0
$304$	1.96673	−	0.639030i	0.112800	−	0.0366509i
$305$	−0.623237	+	1.91813i	−0.0356865	+	0.109832i
$306$		0			0
$307$			5.84773i			0.333748i	0.985978	+	0.166874i	$0.0533672\pi$
$307$			5.84773i			0.333748i	−0.985978	+	0.166874i	$0.946633\pi$
$308$	4.58675	+	4.74289i	0.261355	+	0.270251i
$309$		0			0
$310$	−0.721632	+	0.993242i	−0.0409860	+	0.0564123i
$311$	17.4807	+	5.67981i	0.991237	+	0.322072i	0.759359	−	0.650672i	$-0.225513\pi$
$311$	17.4807	+	5.67981i	0.991237	+	0.322072i	0.231878	+	0.972745i	$0.425513\pi$
$312$		0			0
$313$	9.26715	−	6.73298i	0.523810	−	0.380570i	−0.294227	−	0.955736i	$-0.595062\pi$
$313$	9.26715	−	6.73298i	0.523810	−	0.380570i	0.818037	+	0.575165i	$0.195062\pi$
$314$	14.0812	−	10.2306i	0.794646	−	0.577344i
$315$		0			0
$316$	−3.89919	−	1.26692i	−0.219347	−	0.0712700i
$317$	13.0834	−	18.0078i	0.734837	−	1.01142i	−0.264062	−	0.964506i	$-0.585062\pi$
$317$	13.0834	−	18.0078i	0.734837	−	1.01142i	0.998899	−	0.0469108i	$-0.0149377\pi$
$318$		0			0
$319$	1.91506	+	3.91929i	0.107223	+	0.219438i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	−2.20141	+	6.77525i	−0.122680	+	0.377570i
$323$	−12.8086	+	4.16177i	−0.712691	+	0.231567i
$324$		0			0
$325$	−1.89539	−	2.60879i	−0.105138	−	0.144709i
$326$	−4.28768	−	13.1961i	−0.237473	−	0.730865i
$327$		0			0
$328$	−3.46878	−	2.52022i	−0.191531	−	0.139156i
$329$	4.57055			0.251983
$330$		0			0
$331$	17.9026			0.984018			0.492009	−	0.870590i	$-0.336263\pi$
$331$	17.9026			0.984018			0.492009	+	0.870590i	$0.336263\pi$
$332$	1.91200	+	1.38915i	0.104934	+	0.0762394i
$333$		0			0
$334$	−4.66528	−	14.3583i	−0.255273	−	0.785649i
$335$	−4.46354	−	6.14354i	−0.243869	−	0.335657i
$336$		0			0
$337$	18.0053	−	5.85029i	0.980814	−	0.318686i	0.225640	−	0.974211i	$-0.427553\pi$
$337$	18.0053	−	5.85029i	0.980814	−	0.318686i	0.755174	+	0.655525i	$0.227553\pi$
$338$	−0.803977	+	2.47439i	−0.0437306	+	0.134589i
$339$		0			0
$340$			6.51264i			0.353198i
$341$	3.59662	+	1.90904i	0.194768	+	0.103380i
$342$		0			0
$343$	−11.7428	+	16.1626i	−0.634052	+	0.872697i
$344$	−7.78320	−	2.52892i	−0.419642	−	0.136350i
$345$		0			0
$346$	7.02219	−	5.10192i	0.377515	−	0.274281i
$347$	26.3730	−	19.1611i	1.41577	−	1.02862i	0.423324	−	0.905978i	$-0.360863\pi$
$347$	26.3730	−	19.1611i	1.41577	−	1.02862i	0.992451	−	0.122642i	$-0.0391367\pi$
$348$		0			0
$349$	−27.7215	−	9.00727i	−1.48390	−	0.482148i	−0.548624	−	0.836069i	$-0.684848\pi$
$349$	−27.7215	−	9.00727i	−1.48390	−	0.482148i	−0.935275	+	0.353921i	$0.884848\pi$
$350$	−1.16932	+	1.60943i	−0.0625027	+	0.0860276i
$351$		0			0
$352$	−3.28401	+	0.463949i	−0.175039	+	0.0247286i
$353$			8.70013i			0.463061i	0.972828	+	0.231531i	$0.0743734\pi$
$353$			8.70013i			0.463061i	−0.972828	+	0.231531i	$0.925627\pi$
$354$		0			0
$355$	1.41264	−	4.34765i	0.0749750	−	0.230749i
$356$	−10.8978	+	3.54091i	−0.577582	+	0.187668i
$357$		0			0
$358$	−4.86544	−	6.69670i	−0.257146	−	0.353931i
$359$	−0.819179	−	2.52117i	−0.0432346	−	0.133062i	0.927109	−	0.374791i	$-0.122286\pi$
$359$	−0.819179	−	2.52117i	−0.0432346	−	0.133062i	−0.970344	+	0.241729i	$0.922286\pi$
$360$		0			0
$361$	−11.9117	−	8.65432i	−0.626929	−	0.455491i
$362$	9.31649			0.489664
$363$		0			0
$364$	−6.41498			−0.336236
$365$	−7.62647	−	5.54095i	−0.399187	−	0.290027i
$366$		0			0
$367$	10.6218	+	32.6904i	0.554451	+	1.70642i	0.697389	+	0.716693i	$0.254345\pi$
$367$	10.6218	+	32.6904i	0.554451	+	1.70642i	−0.142938	+	0.989732i	$0.545655\pi$
$368$	−2.10486	−	2.89709i	−0.109723	−	0.151021i
$369$		0			0
$370$	3.35456	−	1.08996i	0.174395	−	0.0566645i
$371$	8.10644	−	24.9490i	0.420865	−	1.29529i
$372$		0			0
$373$			0.680689i			0.0352447i	0.999845	+	0.0176224i	$0.00560967\pi$
$373$			0.680689i			0.0352447i	−0.999845	+	0.0176224i	$0.994390\pi$
$374$	21.3876	−	3.02154i	1.10593	−	0.156240i
$375$		0			0
$376$	−1.35043	+	1.85871i	−0.0696433	+	0.0958557i
$377$	−4.03358	−	1.31059i	−0.207740	−	0.0674987i
$378$		0			0
$379$	3.47279	−	2.52313i	0.178385	−	0.129604i	−0.495010	−	0.868888i	$-0.664835\pi$
$379$	3.47279	−	2.52313i	0.178385	−	0.129604i	0.673395	+	0.739283i	$0.264835\pi$
$380$	1.67300	−	1.21551i	0.0858231	−	0.0623542i
$381$		0			0
$382$	−22.8697	−	7.43081i	−1.17012	−	0.380193i
$383$	−1.79016	+	2.46395i	−0.0914731	+	0.125902i	−0.852301	−	0.523052i	$-0.824793\pi$
$383$	−1.79016	+	2.46395i	−0.0914731	+	0.125902i	0.760828	+	0.648954i	$0.224793\pi$
$384$		0			0
$385$	5.82790	+	3.09337i	0.297017	+	0.157653i
$386$		−	4.00807i		−	0.204006i
$387$		0			0
$388$	0.0845673	−	0.260271i	0.00429325	−	0.0132133i
$389$	−9.09639	+	2.95560i	−0.461205	+	0.149855i	−0.530398	−	0.847749i	$-0.677958\pi$
$389$	−9.09639	+	2.95560i	−0.461205	+	0.149855i	0.0691930	+	0.997603i	$0.477958\pi$
$390$		0			0
$391$	13.7082	+	18.8677i	0.693254	+	0.954183i
$392$	−0.940162	−	2.89352i	−0.0474854	−	0.146145i
$393$		0			0
$394$	18.5171	+	13.4534i	0.932877	+	0.677775i
$395$	−4.09985			−0.206286
$396$		0			0
$397$	−12.4217			−0.623428			−0.311714	−	0.950176i	$-0.600903\pi$
$397$	−12.4217			−0.623428			−0.311714	+	0.950176i	$0.600903\pi$
$398$	−13.2707	−	9.64170i	−0.665198	−	0.483295i
$399$		0			0
$400$	−0.309017	−	0.951057i	−0.0154508	−	0.0475528i
$401$	20.0553	+	27.6038i	1.00152	+	1.37847i	0.924390	+	0.381448i	$0.124574\pi$
$401$	20.0553	+	27.6038i	1.00152	+	1.37847i	0.0771259	+	0.997021i	$0.475426\pi$
$402$		0			0
$403$	−3.76517	+	1.22338i	−0.187556	+	0.0609408i
$404$	5.65270	−	17.3972i	0.281232	−	0.865544i
$405$		0			0
$406$			2.61648i			0.129854i
$407$	−5.13580	−	10.5107i	−0.254572	−	0.520998i
$408$		0			0
$409$	−12.0795	+	16.6259i	−0.597291	+	0.822100i	−0.995457	−	0.0952133i	$-0.969647\pi$
$409$	−12.0795	+	16.6259i	−0.597291	+	0.822100i	0.398166	+	0.917313i	$0.369647\pi$
$410$	−4.07780	−	1.32496i	−0.201388	−	0.0654350i
$411$		0			0
$412$	1.11708	−	0.811609i	0.0550347	−	0.0399851i
$413$	9.60475	−	6.97826i	0.472619	−	0.343378i
$414$		0			0
$415$	2.24769	+	0.730318i	0.110335	+	0.0358499i
$416$	1.89539	−	2.60879i	0.0929293	−	0.127906i
$417$		0			0
$418$	−4.76793	−	4.93023i	−0.233207	−	0.241145i
$419$			35.5918i			1.73877i	0.494131	+	0.869387i	$0.335486\pi$
$419$			35.5918i			1.73877i	−0.494131	+	0.869387i	$0.664514\pi$
$420$		0			0
$421$	−9.04539	+	27.8389i	−0.440845	+	1.35678i	0.446131	+	0.894968i	$0.352802\pi$
$421$	−9.04539	+	27.8389i	−0.440845	+	1.35678i	−0.886976	+	0.461815i	$0.847198\pi$
$422$	−22.5757	+	7.33530i	−1.09897	+	0.357077i
$423$		0			0
$424$	7.75090	+	10.6682i	0.376417	+	0.518093i
$425$	2.01252	+	6.19389i	0.0976214	+	0.300448i
$426$		0			0
$427$	3.24596	+	2.35833i	0.157083	+	0.114127i
$428$	15.2889			0.739016
$429$		0			0
$430$	−8.18374			−0.394655
$431$	−6.89142	−	5.00691i	−0.331948	−	0.241174i	0.409309	−	0.912396i	$-0.365770\pi$
$431$	−6.89142	−	5.00691i	−0.331948	−	0.241174i	−0.741257	+	0.671222i	$0.765770\pi$
$432$		0			0
$433$	5.58836	+	17.1992i	0.268559	+	0.826540i	0.990852	+	0.134953i	$0.0430883\pi$
$433$	5.58836	+	17.1992i	0.268559	+	0.826540i	−0.722293	+	0.691587i	$0.756912\pi$
$434$	1.43559	+	1.97592i	0.0689105	+	0.0948472i
$435$		0			0
$436$	18.7793	−	6.10177i	0.899366	−	0.292222i
$437$	2.28837	−	7.04287i	0.109467	−	0.336906i
$438$		0			0
$439$			23.1252i			1.10370i	0.833942	+	0.551852i	$0.186079\pi$
$439$			23.1252i			1.10370i	−0.833942	+	0.551852i	$0.813921\pi$
$440$	−2.97992	+	1.45606i	−0.142062	+	0.0694149i
$441$		0			0
$442$	−12.3440	+	16.9901i	−0.587145	+	0.808136i
$443$	−23.3716	−	7.59390i	−1.11042	−	0.360797i	−0.304316	−	0.952571i	$-0.598428\pi$
$443$	−23.3716	−	7.59390i	−1.11042	−	0.360797i	−0.806104	+	0.591774i	$0.798428\pi$
$444$		0			0
$445$	−9.27022	+	6.73521i	−0.439451	+	0.319280i
$446$	22.6413	−	16.4498i	1.07209	−	0.778922i
$447$		0			0
$448$	−1.89200	−	0.614747i	−0.0893885	−	0.0290441i
$449$	12.2986	−	16.9276i	0.580407	−	0.798862i	−0.413333	−	0.910580i	$-0.635635\pi$
$449$	12.2986	−	16.9276i	0.580407	−	0.798862i	0.993740	+	0.111718i	$0.0356354\pi$
$450$		0			0
$451$	−2.45929	+	14.0063i	−0.115803	+	0.659529i
$452$			11.5110i			0.541434i
$453$		0			0
$454$	6.30941	−	19.4184i	0.296115	−	0.911349i
$455$	−6.10101	+	1.98234i	−0.286020	+	0.0929334i
$456$		0			0
$457$	−1.50614	−	2.07302i	−0.0704541	−	0.0969718i	0.772336	−	0.635215i	$-0.219088\pi$
$457$	−1.50614	−	2.07302i	−0.0704541	−	0.0969718i	−0.842790	+	0.538243i	$0.819088\pi$
$458$	−0.476544	−	1.46665i	−0.0222674	−	0.0685321i
$459$		0			0
$460$	−2.89709	−	2.10486i	−0.135078	−	0.0981397i
$461$	−21.9616			−1.02285			−0.511427	−	0.859327i	$-0.670883\pi$
$461$	−21.9616			−1.02285			−0.511427	+	0.859327i	$0.670883\pi$
$462$		0			0
$463$	−17.3737			−0.807423			−0.403712	−	0.914886i	$-0.632280\pi$
$463$	−17.3737			−0.807423			−0.403712	+	0.914886i	$0.632280\pi$
$464$	−1.06405	−	0.773076i	−0.0493971	−	0.0358891i
$465$		0			0
$466$	3.99141	+	12.2843i	0.184898	+	0.569059i
$467$	19.7056	+	27.1224i	0.911866	+	1.25508i	0.966525	+	0.256571i	$0.0825926\pi$
$467$	19.7056	+	27.1224i	0.911866	+	1.25508i	−0.0546596	+	0.998505i	$0.517407\pi$
$468$		0			0
$469$	−14.3675	+	4.66829i	−0.663430	+	0.215562i
$470$	−0.709965	+	2.18505i	−0.0327482	+	0.100789i
$471$		0			0
$472$			5.96779i			0.274690i
$473$	3.79684	+	26.8755i	0.174579	+	1.23574i
$474$		0			0
$475$	1.21551	−	1.67300i	0.0557713	−	0.0767626i
$476$	12.3219	+	4.00363i	0.564774	+	0.183506i
$477$		0			0
$478$	−1.83417	+	1.33260i	−0.0838929	+	0.0609518i
$479$	−4.84360	+	3.51908i	−0.221310	+	0.160791i	−0.692916	−	0.721018i	$-0.743674\pi$
$479$	−4.84360	+	3.51908i	−0.221310	+	0.160791i	0.471606	+	0.881809i	$0.343674\pi$
$480$		0			0
$481$	10.8172	+	3.51473i	0.493224	+	0.160258i
$482$	15.1371	−	20.8345i	0.689478	−	0.948985i
$483$		0			0
$484$	6.16425	+	9.11055i	0.280193	+	0.414116i
$485$		−	0.273666i		−	0.0124265i
$486$		0			0
$487$	−3.46306	+	10.6582i	−0.156926	+	0.482969i	−0.998351	−	0.0574053i	$-0.981717\pi$
$487$	−3.46306	+	10.6582i	−0.156926	+	0.482969i	0.841425	+	0.540374i	$0.181717\pi$
$488$	−1.91813	+	0.623237i	−0.0868295	+	0.0282126i
$489$		0			0
$490$	−1.78829	−	2.46138i	−0.0807869	−	0.111194i
$491$	−4.81643	−	14.8235i	−0.217363	−	0.668973i	−0.998977	−	0.0452118i	$-0.985604\pi$
$491$	−4.81643	−	14.8235i	−0.217363	−	0.668973i	0.781615	−	0.623761i	$-0.214396\pi$
$492$		0			0
$493$	6.92976	+	5.03477i	0.312101	+	0.226754i
$494$	6.66836			0.300024
$495$		0			0
$496$	−1.22771			−0.0551260
$497$	−7.35733	−	5.34541i	−0.330021	−	0.239774i
$498$		0			0
$499$	12.1829	+	37.4951i	0.545381	+	1.67851i	0.720082	+	0.693889i	$0.244104\pi$
$499$	12.1829	+	37.4951i	0.545381	+	1.67851i	−0.174700	+	0.984622i	$0.555896\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$		0			0
$502$	−22.0498	+	7.16442i	−0.984131	+	0.319764i
$503$	9.40543	−	28.9469i	0.419367	−	1.29068i	−0.488918	−	0.872330i	$-0.662608\pi$
$503$	9.40543	−	28.9469i	0.419367	−	1.29068i	0.908286	−	0.418351i	$-0.137392\pi$
$504$		0			0
$505$		−	18.2925i		−	0.814007i
$506$	−5.56829	+	10.4906i	−0.247541	+	0.466366i
$507$		0			0
$508$	3.61822	−	4.98005i	0.160533	−	0.220954i
$509$	8.13145	+	2.64207i	0.360420	+	0.117108i	0.483629	−	0.875273i	$-0.339318\pi$
$509$	8.13145	+	2.64207i	0.360420	+	0.117108i	−0.123209	+	0.992381i	$0.539318\pi$
$510$		0			0
$511$	−15.1718	+	11.0230i	−0.671162	+	0.487628i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$		0			0
$514$	−9.79799	−	3.18356i	−0.432171	−	0.140421i
$515$	0.811609	−	1.11708i	0.0357637	−	0.0492246i
$516$		0			0
$517$	7.50511	+	1.31778i	0.330074	+	0.0579561i
$518$		−	7.01687i		−	0.308304i
$519$		0			0
$520$	0.996467	−	3.06681i	0.0436980	−	0.134489i
$521$	4.48525	−	1.45734i	0.196502	−	0.0638474i	−0.209112	−	0.977892i	$-0.567057\pi$
$521$	4.48525	−	1.45734i	0.196502	−	0.0638474i	0.405615	+	0.914044i	$0.367057\pi$
$522$		0			0
$523$	−20.7298	−	28.5322i	−0.906452	−	1.24762i	−0.968364	−	0.249543i	$-0.919720\pi$
$523$	−20.7298	−	28.5322i	−0.906452	−	1.24762i	0.0619116	−	0.998082i	$-0.480280\pi$
$524$	−4.93128	−	15.1769i	−0.215424	−	0.663007i
$525$		0			0
$526$	−17.6893	−	12.8520i	−0.771291	−	0.560375i
$527$	7.99567			0.348297
$528$		0			0
$529$	10.1764			0.442452
$530$	10.6682	+	7.75090i	0.463397	+	0.336677i
$531$		0			0
$532$	−1.27126	−	3.91254i	−0.0551162	−	0.169630i
$533$	−8.12678	−	11.1856i	−0.352010	−	0.484500i
$534$		0			0
$535$	14.5406	−	4.72453i	0.628645	−	0.204259i
$536$	2.34662	−	7.22216i	0.101359	−	0.311950i
$537$		0			0
$538$			16.8023i			0.724400i
$539$	−7.25352	+	7.01474i	−0.312431	+	0.302146i
$540$		0			0
$541$	1.40151	−	1.92902i	0.0602558	−	0.0829350i	−0.777826	−	0.628480i	$-0.783677\pi$
$541$	1.40151	−	1.92902i	0.0602558	−	0.0829350i	0.838081	+	0.545545i	$0.183677\pi$
$542$	−1.30254	−	0.423220i	−0.0559487	−	0.0181788i
$543$		0			0
$544$	−5.26884	+	3.82804i	−0.225900	+	0.164126i
$545$	15.9746	−	11.6063i	0.684278	−	0.497157i
$546$		0			0
$547$	13.9478	+	4.53192i	0.596365	+	0.193771i	0.591619	−	0.806218i	$-0.298489\pi$
$547$	13.9478	+	4.53192i	0.596365	+	0.193771i	0.00474659	+	0.999989i	$0.498489\pi$
$548$	−0.610519	+	0.840308i	−0.0260801	+	0.0358962i
$549$		0			0
$550$	−2.38412	+	2.30564i	−0.101659	+	0.0983127i
$551$		−	2.71983i		−	0.115869i
$552$		0			0
$553$	−2.52037	+	7.75691i	−0.107177	+	0.329858i
$554$	2.45739	−	0.798456i	0.104405	−	0.0339231i
$555$		0			0
$556$	−3.61641	−	4.97756i	−0.153370	−	0.211096i
$557$	8.92390	+	27.4649i	0.378118	+	1.16373i	0.941351	+	0.337429i	$0.109557\pi$
$557$	8.92390	+	27.4649i	0.378118	+	1.16373i	−0.563233	+	0.826298i	$0.690443\pi$
$558$		0			0
$559$	−21.3496	−	15.5114i	−0.902993	−	0.656063i
$560$	−1.98936			−0.0840660
$561$		0			0
$562$	−16.2878			−0.687058
$563$	−26.6587	−	19.3687i	−1.12353	−	0.816292i	−0.138789	−	0.990322i	$-0.544321\pi$
$563$	−26.6587	−	19.3687i	−1.12353	−	0.816292i	−0.984740	+	0.174030i	$0.944321\pi$
$564$		0			0
$565$	3.55711	+	10.9477i	0.149649	+	0.460571i
$566$	8.31127	+	11.4395i	0.349349	+	0.480837i
$567$		0			0
$568$	4.34765	−	1.41264i	0.182423	−	0.0592729i
$569$	−4.25580	+	13.0980i	−0.178412	+	0.549097i	−0.999773	−	0.0213127i	$-0.993215\pi$
$569$	−4.25580	+	13.0980i	−0.178412	+	0.549097i	0.821361	+	0.570409i	$0.193215\pi$
$570$		0			0
$571$		−	3.76789i		−	0.157681i	−0.996887	−	0.0788407i	$-0.974878\pi$
$571$		−	3.76789i		−	0.157681i	0.996887	−	0.0788407i	$-0.0251218\pi$
$572$	−10.5338	−	1.84957i	−0.440439	−	0.0773343i
$573$		0			0
$574$	−5.01363	+	6.90067i	−0.209265	+	0.288029i
$575$	−3.40574	−	1.10659i	−0.142029	−	0.0461480i
$576$		0			0
$577$	26.7658	−	19.4465i	1.11428	−	0.809569i	0.130945	−	0.991390i	$-0.458199\pi$
$577$	26.7658	−	19.4465i	1.11428	−	0.809569i	0.983332	+	0.181820i	$0.0581989\pi$
$578$	20.5608	−	14.9383i	0.855216	−	0.621351i
$579$		0			0
$580$	−1.25086	−	0.406430i	−0.0519392	−	0.0168761i
$581$	2.76352	−	3.80366i	0.114650	−	0.157802i
$582$		0			0
$583$	20.5046	−	38.6305i	0.849212	−	1.59991i
$584$		−	9.42683i		−	0.390085i
$585$		0			0
$586$	−3.91654	+	12.0539i	−0.161791	+	0.497940i
$587$	2.79609	−	0.908506i	0.115407	−	0.0374980i	−0.250744	−	0.968053i	$-0.580675\pi$
$587$	2.79609	−	0.908506i	0.115407	−	0.0374980i	0.366151	+	0.930555i	$0.380675\pi$
$588$		0			0
$589$	−1.49229	−	2.05397i	−0.0614889	−	0.0846322i
$590$	1.84415	+	5.67571i	0.0759224	+	0.233665i
$591$		0			0
$592$	2.85356	+	2.07323i	0.117281	+	0.0852093i
$593$	−16.7157			−0.686433			−0.343217	−	0.939256i	$-0.611517\pi$
$593$	−16.7157			−0.686433			−0.343217	+	0.939256i	$0.611517\pi$
$594$		0			0
$595$	12.9560			0.531145
$596$	9.75875	+	7.09015i	0.399734	+	0.290424i
$597$		0			0
$598$	−3.56835	−	10.9823i	−0.145921	−	0.449098i
$599$	18.3703	+	25.2846i	0.750592	+	1.03310i	0.997939	+	0.0641738i	$0.0204412\pi$
$599$	18.3703	+	25.2846i	0.750592	+	1.03310i	−0.247347	+	0.968927i	$0.579559\pi$
$600$		0			0
$601$	−29.2088	+	9.49051i	−1.19145	+	0.387126i	−0.836609	−	0.547800i	$-0.815465\pi$
$601$	−29.2088	+	9.49051i	−1.19145	+	0.387126i	−0.354842	+	0.934926i	$0.615465\pi$
$602$	−5.03093	+	15.4836i	−0.205046	+	0.631065i
$603$		0			0
$604$			4.90250i			0.199480i
$605$	8.67786	+	6.75979i	0.352805	+	0.274825i
$606$		0			0
$607$	−11.8324	+	16.2859i	−0.480263	+	0.661025i	−0.978555	−	0.205984i	$-0.933961\pi$
$607$	−11.8324	+	16.2859i	−0.480263	+	0.661025i	0.498293	+	0.867009i	$0.333961\pi$
$608$	1.96673	+	0.639030i	0.0797615	+	0.0259161i
$609$		0			0
$610$	−1.63166	+	1.18547i	−0.0660638	+	0.0479982i
$611$	−5.99367	+	4.35465i	−0.242478	+	0.176170i
$612$		0			0
$613$	32.0589	+	10.4166i	1.29485	+	0.420722i	0.873786	−	0.486310i	$-0.161657\pi$
$613$	32.0589	+	10.4166i	1.29485	+	0.420722i	0.421062	+	0.907032i	$0.361657\pi$
$614$	−3.43721	+	4.73091i	−0.138714	+	0.190924i
$615$		0			0
$616$	0.922964	+	6.53310i	0.0371873	+	0.263226i
$617$			9.36425i			0.376991i	0.982074	+	0.188495i	$0.0603610\pi$
$617$			9.36425i			0.376991i	−0.982074	+	0.188495i	$0.939639\pi$
$618$		0			0
$619$	−6.51637	+	20.0553i	−0.261915	+	0.806091i	0.730473	+	0.682941i	$0.239300\pi$
$619$	−6.51637	+	20.0553i	−0.261915	+	0.806091i	−0.992388	+	0.123150i	$0.960700\pi$
$620$	−1.16763	+	0.379385i	−0.0468930	+	0.0152365i
$621$		0			0
$622$	10.8036	+	14.8699i	0.433187	+	0.596230i
$623$	7.04416	+	21.6797i	0.282218	+	0.868579i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	11.4548			0.457827
$627$		0			0
$628$	17.4053			0.694546
$629$	−18.5842	−	13.5022i	−0.741001	−	0.538369i
$630$		0			0
$631$	12.6162	+	38.8287i	0.502244	+	1.54575i	0.805355	+	0.592793i	$0.201975\pi$
$631$	12.6162	+	38.8287i	0.502244	+	1.54575i	−0.303111	+	0.952955i	$0.598025\pi$
$632$	−2.40983	−	3.31685i	−0.0958580	−	0.131937i
$633$		0			0
$634$	21.1694	−	6.87835i	0.840744	−	0.273174i
$635$	1.90221	−	5.85440i	0.0754869	−	0.232325i
$636$		0			0
$637$		−	9.81072i		−	0.388715i
$638$	−0.754385	+	4.29641i	−0.0298664	+	0.170097i
$639$		0			0
$640$	0.587785	−	0.809017i	0.0232343	−	0.0319792i
$641$	31.2238	+	10.1452i	1.23327	+	0.400713i	0.851897	−	0.523709i	$-0.175452\pi$
$641$	31.2238	+	10.1452i	1.23327	+	0.400713i	0.381371	+	0.924422i	$0.375452\pi$
$642$		0			0
$643$	−18.2934	+	13.2910i	−0.721423	+	0.524144i	−0.886838	−	0.462080i	$-0.847103\pi$
$643$	−18.2934	+	13.2910i	−0.721423	+	0.524144i	0.165416	+	0.986224i	$0.447103\pi$
$644$	−5.76338	+	4.18734i	−0.227109	+	0.165004i
$645$		0			0
$646$	−12.8086	−	4.16177i	−0.503948	−	0.163743i
$647$	0.851111	−	1.17145i	0.0334606	−	0.0460546i	−0.791959	−	0.610574i	$-0.790939\pi$
$647$	0.851111	−	1.17145i	0.0334606	−	0.0460546i	0.825420	+	0.564520i	$0.190939\pi$
$648$		0			0
$649$	17.7835	−	8.68946i	0.698064	−	0.341091i
$650$		−	3.22464i		−	0.126481i
$651$		0			0
$652$	4.28768	−	13.1961i	0.167918	−	0.516800i
$653$	33.8810	−	11.0086i	1.32587	−	0.430800i	0.441361	−	0.897330i	$-0.354496\pi$
$653$	33.8810	−	11.0086i	1.32587	−	0.430800i	0.884506	+	0.466529i	$0.154496\pi$
$654$		0			0
$655$	−9.37985	−	12.9103i	−0.366501	−	0.504445i
$656$	−1.32496	−	4.07780i	−0.0517309	−	0.159211i
$657$		0			0
$658$	3.69766	+	2.68650i	0.144150	+	0.104731i
$659$	−5.47349			−0.213217			−0.106608	−	0.994301i	$-0.533999\pi$
$659$	−5.47349			−0.213217			−0.106608	+	0.994301i	$0.533999\pi$
$660$		0			0
$661$	−8.75458			−0.340514			−0.170257	−	0.985400i	$-0.554460\pi$
$661$	−8.75458			−0.340514			−0.170257	+	0.985400i	$0.554460\pi$
$662$	14.4835	+	10.5229i	0.562919	+	0.408985i
$663$		0			0
$664$	0.730318	+	2.24769i	0.0283418	+	0.0872272i
$665$	−2.41809	−	3.32821i	−0.0937693	−	0.129062i
$666$		0			0
$667$	−4.47934	+	1.45543i	−0.173441	+	0.0563544i
$668$	4.66528	−	14.3583i	0.180505	−	0.555538i
$669$		0			0
$670$		−	7.59383i		−	0.293375i
$671$	4.65010	+	4.80839i	0.179515	+	0.185626i
$672$		0			0
$673$	−1.46458	+	2.01582i	−0.0564554	+	0.0777042i	−0.836311	−	0.548255i	$-0.815292\pi$
$673$	−1.46458	+	2.01582i	−0.0564554	+	0.0777042i	0.779856	+	0.625959i	$0.215292\pi$
$674$	18.0053	+	5.85029i	0.693540	+	0.225345i
$675$		0			0
$676$	−2.10484	+	1.52925i	−0.0809553	+	0.0588175i
$677$	8.44272	−	6.13400i	0.324480	−	0.235749i	−0.413605	−	0.910457i	$-0.635730\pi$
$677$	8.44272	−	6.13400i	0.324480	−	0.235749i	0.738085	+	0.674708i	$0.235730\pi$
$678$		0			0
$679$	−0.517775	−	0.168235i	−0.0198704	−	0.00645628i
$680$	−3.82804	+	5.26884i	−0.146798	+	0.202051i
$681$		0			0
$682$	1.78762	+	3.65848i	0.0684516	+	0.140091i
$683$			20.0565i			0.767440i	0.923449	+	0.383720i	$0.125357\pi$
$683$			20.0565i			0.767440i	−0.923449	+	0.383720i	$0.874643\pi$
$684$		0			0
$685$	−0.320969	+	0.987841i	−0.0122636	+	0.0377435i
$686$	−19.0003	+	6.17356i	−0.725433	+	0.235708i
$687$		0			0
$688$	−4.81028	−	6.62079i	−0.183390	−	0.252415i
$689$	13.1400	+	40.4408i	0.500595	+	1.54067i
$690$		0			0
$691$	−33.7078	−	24.4902i	−1.28231	−	0.931650i	−0.282686	−	0.959212i	$-0.591226\pi$
$691$	−33.7078	−	24.4902i	−1.28231	−	0.931650i	−0.999620	+	0.0275621i	$0.991226\pi$
$692$	8.67990			0.329960
$693$		0			0
$694$	32.5988			1.23743
$695$	−4.97756	−	3.61641i	−0.188810	−	0.137178i
$696$		0			0
$697$	8.62897	+	26.5572i	0.326846	+	1.00593i
$698$	−17.1329	−	23.5813i	−0.648488	−	0.892567i
$699$		0			0
$700$	−1.89200	+	0.614747i	−0.0715108	+	0.0232353i
$701$	7.01549	−	21.5914i	0.264971	−	0.815498i	−0.726729	−	0.686924i	$-0.758960\pi$
$701$	7.01549	−	21.5914i	0.264971	−	0.815498i	0.991700	−	0.128573i	$-0.0410397\pi$
$702$		0			0
$703$			7.29404i			0.275100i
$704$	−2.92953	−	1.55495i	−0.110411	−	0.0586045i
$705$		0			0
$706$	−5.11381	+	7.03856i	−0.192461	+	0.264900i
$707$	−34.6094	−	11.2453i	−1.30162	−	0.422922i
$708$		0			0
$709$	−1.10372	+	0.801898i	−0.0414510	+	0.0301159i	−0.608318	−	0.793694i	$-0.708155\pi$
$709$	−1.10372	+	0.801898i	−0.0414510	+	0.0301159i	0.566867	+	0.823809i	$0.308155\pi$
$710$	3.69833	−	2.68699i	0.138796	−	0.100841i
$711$		0			0
$712$	−10.8978	−	3.54091i	−0.408412	−	0.132701i
$713$	−2.58417	+	3.55680i	−0.0967779	+	0.133203i
$714$		0			0
$715$	−10.5898	+	1.49607i	−0.396034	+	0.0559497i
$716$		−	8.27757i		−	0.309347i
$717$		0			0
$718$	0.819179	−	2.52117i	0.0305715	−	0.0940894i
$719$	−9.20512	+	2.99093i	−0.343293	+	0.111543i	−0.475589	−	0.879668i	$-0.657765\pi$
$719$	−9.20512	+	2.99093i	−0.343293	+	0.111543i	0.132296	+	0.991210i	$0.457765\pi$
$720$		0			0
$721$	−1.61459	−	2.22229i	−0.0601303	−	0.0827623i
$722$	−4.54985	−	14.0030i	−0.169328	−	0.521137i
$723$		0			0
$724$	7.53720	+	5.47610i	0.280118	+	0.203518i
$725$	−1.31523			−0.0488466
$726$		0			0
$727$	−15.7751			−0.585066			−0.292533	−	0.956256i	$-0.594498\pi$
$727$	−15.7751			−0.585066			−0.292533	+	0.956256i	$0.594498\pi$
$728$	−5.18983	−	3.77063i	−0.192348	−	0.139749i
$729$		0			0
$730$	−2.91305	−	8.96545i	−0.107817	−	0.331826i
$731$	31.3277	+	43.1188i	1.15870	+	1.59481i
$732$		0			0
$733$	17.6980	−	5.75043i	0.653691	−	0.212397i	0.0366502	−	0.999328i	$-0.488331\pi$
$733$	17.6980	−	5.75043i	0.653691	−	0.212397i	0.617041	+	0.786931i	$0.288331\pi$
$734$	−10.6218	+	32.6904i	−0.392056	+	1.20662i
$735$		0			0
$736$		−	3.58100i		−	0.131998i
$737$	−24.9383	+	3.52315i	−0.918613	+	0.129777i
$738$		0			0
$739$	26.8912	−	37.0126i	0.989210	−	1.36153i	0.0574924	−	0.998346i	$-0.481689\pi$
$739$	26.8912	−	37.0126i	0.989210	−	1.36153i	0.931717	−	0.363184i	$-0.118311\pi$
$740$	3.35456	+	1.08996i	0.123316	+	0.0400678i
$741$		0			0
$742$	21.2229	−	15.4194i	0.779118	−	0.566062i
$743$	19.3109	−	14.0302i	0.708447	−	0.514717i	−0.174226	−	0.984706i	$-0.555742\pi$
$743$	19.3109	−	14.0302i	0.708447	−	0.514717i	0.882672	+	0.469989i	$0.155742\pi$
$744$		0			0
$745$	11.4721	+	3.72751i	0.420305	+	0.136565i
$746$	−0.400099	+	0.550689i	−0.0146487	+	0.0201622i
$747$		0			0
$748$	19.0790	+	10.1269i	0.697596	+	0.370274i
$749$		−	30.4152i		−	1.11135i
$750$		0			0
$751$	3.31859	−	10.2136i	0.121097	−	0.372698i	−0.872073	−	0.489376i	$-0.837225\pi$
$751$	3.31859	−	10.2136i	0.121097	−	0.372698i	0.993170	+	0.116678i	$0.0372246\pi$
$752$	−2.18505	+	0.709965i	−0.0796804	+	0.0258897i
$753$		0			0
$754$	−2.49289	−	3.43116i	−0.0907856	−	0.124956i
$755$	1.51496	+	4.66255i	0.0551349	+	0.169688i
$756$		0			0
$757$	28.1869	+	20.4790i	1.02447	+	0.744321i	0.967194	−	0.254037i	$-0.0817587\pi$
$757$	28.1869	+	20.4790i	1.02447	+	0.744321i	0.0572755	+	0.998358i	$0.481759\pi$
$758$	4.29261			0.155914
$759$		0			0
$760$	2.06794			0.0750122
$761$	−8.03206	−	5.83563i	−0.291162	−	0.211541i	0.432609	−	0.901581i	$-0.357593\pi$
$761$	−8.03206	−	5.83563i	−0.291162	−	0.211541i	−0.723771	+	0.690040i	$0.757593\pi$
$762$		0			0
$763$	−12.1386	−	37.3589i	−0.439448	−	1.35248i
$764$	−14.1342	−	19.4541i	−0.511359	−	0.703825i
$765$		0			0
$766$	−2.89655	+	0.941145i	−0.104656	+	0.0340049i
$767$	−5.94671	+	18.3021i	−0.214723	+	0.660850i
$768$		0			0
$769$			18.4116i			0.663941i	0.943290	+	0.331970i	$0.107713\pi$
$769$			18.4116i			0.663941i	−0.943290	+	0.331970i	$0.892287\pi$
$770$	2.89663	+	5.92814i	0.104387	+	0.213635i
$771$		0			0
$772$	2.35589	−	3.24260i	0.0847902	−	0.116704i
$773$	15.7733	+	5.12504i	0.567325	+	0.184335i	0.578614	−	0.815601i	$-0.303594\pi$
$773$	15.7733	+	5.12504i	0.567325	+	0.184335i	−0.0112897	+	0.999936i	$0.503594\pi$
$774$		0			0
$775$	−0.993242	+	0.721632i	−0.0356783	+	0.0259218i
$776$	0.221400	−	0.160857i	0.00794780	−	0.00577441i
$777$		0			0
$778$	−9.09639	−	2.95560i	−0.326121	−	0.105963i
$779$	5.21167	−	7.17324i	0.186727	−	0.257008i
$780$		0			0
$781$	−10.5400	−	10.8987i	−0.377150	−	0.389988i
$782$			23.3218i			0.833986i
$783$		0			0
$784$	0.940162	−	2.89352i	0.0335772	−	0.103340i
$785$	16.5534	−	5.37853i	0.590816	−	0.191968i
$786$		0			0
$787$	14.1151	+	19.4277i	0.503148	+	0.692524i	0.982745	−	0.184965i	$-0.0592171\pi$
$787$	14.1151	+	19.4277i	0.503148	+	0.692524i	−0.479597	+	0.877489i	$0.659217\pi$
$788$	7.07290	+	21.7681i	0.251962	+	0.775458i
$789$		0			0
$790$	−3.31685	−	2.40983i	−0.118008	−	0.0857380i
$791$	22.8997			0.814218
$792$		0			0
$793$	−6.50357			−0.230948
$794$	−10.0494	−	7.30130i	−0.356639	−	0.259113i
$795$		0			0
$796$	−5.06894	−	15.6006i	−0.179664	−	0.552948i
$797$	−26.6640	−	36.6999i	−0.944488	−	1.29998i	−0.953933	−	0.300021i	$-0.903006\pi$
$797$	−26.6640	−	36.6999i	−0.944488	−	1.29998i	0.00944466	−	0.999955i	$-0.496994\pi$
$798$		0			0
$799$	14.2304	−	4.62375i	0.503436	−	0.163576i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$		0			0
$802$			34.1202i			1.20483i
$803$	−28.0912	+	13.7260i	−0.991315	+	0.484380i
$804$		0			0
$805$	−4.18734	+	5.76338i	−0.147584	+	0.203132i
$806$	−3.76517	−	1.22338i	−0.132622	−	0.0430916i
$807$		0			0
$808$	14.7990	−	10.7521i	0.520626	−	0.378257i
$809$	8.48073	−	6.16161i	0.298167	−	0.216631i	−0.428636	−	0.903477i	$-0.641006\pi$
$809$	8.48073	−	6.16161i	0.298167	−	0.216631i	0.726802	+	0.686847i	$0.241006\pi$
$810$		0			0
$811$	22.4272	+	7.28702i	0.787524	+	0.255882i	0.675049	−	0.737773i	$-0.264122\pi$
$811$	22.4272	+	7.28702i	0.787524	+	0.255882i	0.112475	+	0.993655i	$0.464122\pi$
$812$	−1.53793	+	2.11678i	−0.0539707	+	0.0742843i
$813$		0			0
$814$	2.02311	−	11.5221i	0.0709099	−	0.403850i
$815$		−	13.8752i		−	0.486028i
$816$		0			0
$817$	5.22965	−	16.0952i	0.182962	−	0.563100i
$818$	−19.5450	+	6.35054i	−0.683374	+	0.222042i
$819$		0			0
$820$	−2.52022	−	3.46878i	−0.0880098	−	0.121135i
$821$	−16.2627	−	50.0514i	−0.567572	−	1.74681i	−0.660184	−	0.751104i	$-0.729522\pi$
$821$	−16.2627	−	50.0514i	−0.567572	−	1.74681i	0.0926120	−	0.995702i	$-0.470478\pi$
$822$		0			0
$823$	−17.3398	−	12.5981i	−0.604427	−	0.439142i	0.243020	−	0.970021i	$-0.421862\pi$
$823$	−17.3398	−	12.5981i	−0.604427	−	0.439142i	−0.847448	+	0.530879i	$0.821862\pi$
$824$	1.38079			0.0481021
$825$		0			0
$826$	11.8721			0.413084
$827$	−24.6615	−	17.9176i	−0.857564	−	0.623057i	0.0696570	−	0.997571i	$-0.477810\pi$
$827$	−24.6615	−	17.9176i	−0.857564	−	0.623057i	−0.927221	+	0.374514i	$0.877810\pi$
$828$		0			0
$829$	−0.920986	−	2.83450i	−0.0319872	−	0.0984464i	0.933788	−	0.357826i	$-0.116482\pi$
$829$	−0.920986	−	2.83450i	−0.0319872	−	0.0984464i	−0.965775	+	0.259380i	$0.916482\pi$
$830$	1.38915	+	1.91200i	0.0482180	+	0.0663664i
$831$		0			0
$832$	3.06681	−	0.996467i	0.106323	−	0.0345463i
$833$	−6.12294	+	18.8445i	−0.212147	+	0.652922i
$834$		0			0
$835$		−	15.0972i		−	0.522459i
$836$	−0.959421	−	6.79116i	−0.0331823	−	0.234877i
$837$		0			0
$838$	−20.9204	+	28.7944i	−0.722682	+	0.994686i
$839$	−2.21611	−	0.720058i	−0.0765087	−	0.0248592i	0.270513	−	0.962716i	$-0.412807\pi$
$839$	−2.21611	−	0.720058i	−0.0765087	−	0.0248592i	−0.347021	+	0.937857i	$0.612807\pi$
$840$		0			0
$841$	22.0620	−	16.0290i	0.760759	−	0.552724i
$842$	−23.6811	+	17.2054i	−0.816106	+	0.592936i
$843$		0			0
$844$	−22.5757	−	7.33530i	−0.777088	−	0.252491i
$845$	−1.52925	+	2.10484i	−0.0526080	+	0.0724086i
$846$		0			0
$847$	18.1242	−	12.2629i	0.622755	−	0.421359i
$848$			13.1866i			0.452830i
$849$		0			0
$850$	−2.01252	+	6.19389i	−0.0690288	+	0.212449i
$851$	12.0127	−	3.90316i	0.411790	−	0.133799i
$852$		0			0
$853$	−28.8442	−	39.7006i	−0.987605	−	1.35932i	−0.932630	−	0.360834i	$-0.882492\pi$
$853$	−28.8442	−	39.7006i	−0.987605	−	1.35932i	−0.0549754	−	0.998488i	$-0.517508\pi$
$854$	1.23985	+	3.81585i	0.0424267	+	0.130576i
$855$		0			0
$856$	12.3690	+	8.98658i	0.422763	+	0.307155i
$857$	−16.9993			−0.580685			−0.290342	−	0.956923i	$-0.593769\pi$
$857$	−16.9993			−0.580685			−0.290342	+	0.956923i	$0.593769\pi$
$858$		0			0
$859$	−22.5470			−0.769292			−0.384646	−	0.923064i	$-0.625677\pi$
$859$	−22.5470			−0.769292			−0.384646	+	0.923064i	$0.625677\pi$
$860$	−6.62079	−	4.81028i	−0.225767	−	0.164029i
$861$		0			0
$862$	−2.63229	−	8.10135i	−0.0896561	−	0.275933i
$863$	−16.0841	−	22.1379i	−0.547510	−	0.753583i	0.442162	−	0.896935i	$-0.354212\pi$
$863$	−16.0841	−	22.1379i	−0.547510	−	0.753583i	−0.989672	+	0.143353i	$0.954212\pi$
$864$		0			0
$865$	8.25508	−	2.68224i	0.280681	−	0.0911988i
$866$	−5.58836	+	17.1992i	−0.189900	+	0.584452i
$867$		0			0
$868$			2.44237i			0.0828995i
$869$	−6.37508	+	12.0106i	−0.216260	+	0.407433i
$870$		0			0
$871$	14.3933	−	19.8107i	0.487698	−	0.671259i
$872$	18.7793	+	6.10177i	0.635948	+	0.206632i
$873$		0			0
$874$	5.99102	−	4.35273i	0.202649	−	0.147233i
$875$	−1.60943	+	1.16932i	−0.0544087	+	0.0395302i
$876$		0			0
$877$	−41.4783	−	13.4771i	−1.40062	−	0.455090i	−0.491230	−	0.871030i	$-0.663453\pi$
$877$	−41.4783	−	13.4771i	−1.40062	−	0.455090i	−0.909392	+	0.415940i	$0.863453\pi$
$878$	−13.5926	+	18.7087i	−0.458729	+	0.631387i
$879$		0			0
$880$	−3.26665	−	0.573574i	−0.110119	−	0.0193352i
$881$		−	28.1586i		−	0.948688i	−0.880340	−	0.474344i	$-0.842685\pi$
$881$		−	28.1586i		−	0.948688i	0.880340	−	0.474344i	$-0.157315\pi$
$882$		0			0
$883$	−11.7034	+	36.0194i	−0.393852	+	1.21215i	0.536001	+	0.844218i	$0.319934\pi$
$883$	−11.7034	+	36.0194i	−0.393852	+	1.21215i	−0.929852	+	0.367933i	$0.880066\pi$
$884$	−19.9730	+	6.48964i	−0.671766	+	0.218270i
$885$		0			0
$886$	−14.4445	−	19.8811i	−0.485271	−	0.667918i
$887$	6.01979	+	18.5270i	0.202125	+	0.622076i	0.999819	+	0.0190144i	$0.00605285\pi$
$887$	6.01979	+	18.5270i	0.202125	+	0.622076i	−0.797694	+	0.603062i	$0.793947\pi$
$888$		0			0
$889$	−9.90714	−	7.19796i	−0.332275	−	0.241412i
$890$	−11.4586			−0.384094
$891$		0			0
$892$	27.9861			0.937045
$893$	−3.84371	−	2.79262i	−0.128625	−	0.0934514i
$894$		0			0
$895$	−2.55791	−	7.87244i	−0.0855015	−	0.263147i
$896$	−1.16932	−	1.60943i	−0.0390642	−	0.0537673i
$897$		0			0
$898$	19.8996	−	6.46576i	0.664057	−	0.215765i
$899$	−0.498980	+	1.53570i	−0.0166419	+	0.0512185i
$900$		0			0
$901$		−	85.8797i		−	2.86107i
$902$	−10.2223	+	9.88577i	−0.340365	+	0.329160i
$903$		0			0
$904$	−6.76602	+	9.31263i	−0.225035	+	0.309733i
$905$	8.86051	+	2.87895i	0.294533	+	0.0956997i
$906$		0			0
$907$	13.9380	−	10.1265i	0.462803	−	0.336246i	−0.331827	−	0.943340i	$-0.607665\pi$
$907$	13.9380	−	10.1265i	0.462803	−	0.336246i	0.794630	+	0.607094i	$0.207665\pi$
$908$	16.5182	−	12.0012i	0.548177	−	0.398274i
$909$		0			0
$910$	−6.10101	−	1.98234i	−0.202246	−	0.0657138i
$911$	33.8450	−	46.5836i	1.12133	−	1.54338i	0.317768	−	0.948168i	$-0.397067\pi$
$911$	33.8450	−	46.5836i	1.12133	−	1.54338i	0.803566	−	0.595216i	$-0.202933\pi$
$912$		0			0
$913$	5.63453	−	5.44905i	0.186476	−	0.180337i
$914$		−	2.56239i		−	0.0847564i
$915$		0			0
$916$	0.476544	−	1.46665i	0.0157455	−	0.0484595i
$917$	−30.1924	+	9.81011i	−0.997042	+	0.323958i
$918$		0			0
$919$	−26.9226	−	37.0558i	−0.888096	−	1.22236i	−0.974112	−	0.226065i	$-0.927414\pi$
$919$	−26.9226	−	37.0558i	−0.888096	−	1.22236i	0.0860164	−	0.996294i	$-0.472586\pi$
$920$	−1.10659	−	3.40574i	−0.0364832	−	0.112284i
$921$		0			0
$922$	−17.7673	−	12.9087i	−0.585135	−	0.425126i
$923$	14.7411			0.485208
$924$		0			0
$925$	3.52719			0.115973
$926$	−14.0556	−	10.2120i	−0.461896	−	0.335587i
$927$		0			0
$928$	−0.406430	−	1.25086i	−0.0133417	−	0.0410616i
$929$	18.2777	+	25.1571i	0.599671	+	0.825376i	0.995678	−	0.0928711i	$-0.0296045\pi$
$929$	18.2777	+	25.1571i	0.599671	+	0.825376i	−0.396007	+	0.918247i	$0.629604\pi$
$930$		0			0
$931$	5.98364	−	1.94420i	0.196106	−	0.0637186i
$932$	−3.99141	+	12.2843i	−0.130743	+	0.402385i
$933$		0			0
$934$			33.5252i			1.09698i
$935$	21.2745	+	3.73549i	0.695752	+	0.122163i
$936$		0			0
$937$	6.39198	−	8.79780i	0.208817	−	0.287412i	−0.691743	−	0.722144i	$-0.743157\pi$
$937$	6.39198	−	8.79780i	0.208817	−	0.287412i	0.900560	+	0.434732i	$0.143157\pi$
$938$	−14.3675	−	4.66829i	−0.469116	−	0.152425i
$939$		0			0
$940$	−1.85871	+	1.35043i	−0.0606245	+	0.0440463i
$941$	−4.10103	+	2.97957i	−0.133690	+	0.0971313i	−0.652620	−	0.757685i	$-0.726330\pi$
$941$	−4.10103	+	2.97957i	−0.133690	+	0.0971313i	0.518931	+	0.854816i	$0.326330\pi$
$942$		0			0
$943$	−14.6026	−	4.74468i	−0.475527	−	0.154508i
$944$	−3.50778	+	4.82805i	−0.114169	+	0.157140i
$945$		0			0
$946$	−12.7253	+	23.9745i	−0.413736	+	0.779478i
$947$			12.1398i			0.394490i	0.980354	+	0.197245i	$0.0631994\pi$
$947$			12.1398i			0.394490i	−0.980354	+	0.197245i	$0.936801\pi$
$948$		0			0
$949$	9.39353	−	28.9103i	0.304927	−	0.938468i
$950$	1.96673	−	0.639030i	0.0638092	−	0.0207329i
$951$		0			0
$952$	7.61536	+	10.4816i	0.246815	+	0.339712i
$953$	2.43202	+	7.48500i	0.0787810	+	0.242463i	0.982689	−	0.185265i	$-0.0593142\pi$
$953$	2.43202	+	7.48500i	0.0787810	+	0.242463i	−0.903908	+	0.427728i	$0.859314\pi$
$954$		0			0
$955$	−19.4541	−	14.1342i	−0.629520	−	0.457373i
$956$	−2.26716			−0.0733251
$957$		0			0
$958$	−5.98702			−0.193432
$959$	1.67168	+	1.21455i	0.0539813	+	0.0392197i
$960$		0			0
$961$	−9.11375	−	28.0492i	−0.293992	−	0.904814i
$962$	6.68542	+	9.20169i	0.215547	+	0.296674i
$963$		0			0
$964$	24.4924	−	7.95807i	0.788847	−	0.256312i
$965$	1.23856	−	3.81191i	0.0398708	−	0.122710i
$966$		0			0
$967$			39.4912i			1.26995i	0.772532	+	0.634976i	$0.218990\pi$
$967$			39.4912i			1.26995i	−0.772532	+	0.634976i	$0.781010\pi$
$968$	−0.368066	+	10.9938i	−0.0118301	+	0.353355i
$969$		0			0
$970$	0.160857	−	0.221400i	0.00516479	−	0.00710873i
$971$	40.3007	+	13.0945i	1.29331	+	0.420222i	0.873249	−	0.487274i	$-0.162009\pi$
$971$	40.3007	+	13.0945i	1.29331	+	0.420222i	0.420061	+	0.907496i	$0.362009\pi$
$972$		0			0
$973$	−9.90219	+	7.19436i	−0.317450	+	0.230641i
$974$	−9.06640	+	6.58712i	−0.290506	+	0.211065i
$975$		0			0
$976$	−1.91813	−	0.623237i	−0.0613977	−	0.0199493i
$977$	1.68434	−	2.31830i	0.0538869	−	0.0741690i	−0.781223	−	0.624252i	$-0.785404\pi$
$977$	1.68434	−	2.31830i	0.0538869	−	0.0741690i	0.835110	+	0.550083i	$0.185404\pi$
$978$		0			0
$979$	5.31622	+	37.6303i	0.169907	+	1.20267i
$980$		−	3.04243i		−	0.0971868i
$981$		0			0
$982$	4.81643	−	14.8235i	0.153699	−	0.473035i
$983$	−24.8399	+	8.07099i	−0.792271	+	0.257425i	−0.677071	−	0.735918i	$-0.736751\pi$
$983$	−24.8399	+	8.07099i	−0.792271	+	0.257425i	−0.115200	+	0.993342i	$0.536751\pi$
$984$		0			0
$985$	13.4534	+	18.5171i	0.428663	+	0.590003i
$986$	2.64693	+	8.14642i	0.0842955	+	0.259435i
$987$		0			0
$988$	5.39482	+	3.91957i	0.171632	+	0.124698i
$989$	−29.3060			−0.931877
$990$		0			0
$991$	45.7753			1.45410			0.727050	−	0.686584i	$-0.240891\pi$
$991$	45.7753			1.45410			0.727050	+	0.686584i	$0.240891\pi$
$992$	−0.993242	−	0.721632i	−0.0315355	−	0.0229118i
$993$		0			0
$994$	−2.81025	−	8.64906i	−0.0891357	−	0.274331i
$995$	−9.64170	−	13.2707i	−0.305662	−	0.420708i
$996$		0			0
$997$	−54.8625	+	17.8259i	−1.73751	+	0.564552i	−0.994501	−	0.104728i	$-0.966603\pi$
$997$	−54.8625	+	17.8259i	−1.73751	+	0.564552i	−0.743010	+	0.669280i	$0.766603\pi$
$998$	−12.1829	+	37.4951i	−0.385643	+	1.18689i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.z.b.161.7	yes	32
3.2	odd	2		990.2.z.a.161.3	✓	32
11.8	odd	10		990.2.z.a.701.3	yes	32
33.8	even	10	inner	990.2.z.b.701.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.z.a.161.3	✓	32	3.2	odd	2
990.2.z.a.701.3	yes	32	11.8	odd	10
990.2.z.b.161.7	yes	32	1.1	even	1	trivial
990.2.z.b.701.7	yes	32	33.8	even	10	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(1.89200 - 0.614747i) q^{7} +(-0.309017 + 0.951057i) q^{8} +1.00000i q^{10} +(3.28401 - 0.463949i) q^{11} +(-1.89539 + 2.60879i) q^{13} +(1.89200 + 0.614747i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(5.26884 - 3.82804i) q^{17} +(-1.96673 - 0.639030i) q^{19} +(-0.587785 + 0.809017i) q^{20} +(2.92953 + 1.55495i) q^{22} +3.58100i q^{23} +(-0.309017 + 0.951057i) q^{25} +(-3.06681 + 0.996467i) q^{26} +(1.16932 + 1.60943i) q^{28} +(0.406430 + 1.25086i) q^{29} +(0.993242 + 0.721632i) q^{31} -1.00000 q^{32} +6.51264 q^{34} +(1.60943 + 1.16932i) q^{35} +(-1.08996 - 3.35456i) q^{37} +(-1.21551 - 1.67300i) q^{38} +(-0.951057 + 0.309017i) q^{40} +(-1.32496 + 4.07780i) q^{41} +8.18374i q^{43} +(1.45606 + 2.97992i) q^{44} +(-2.10486 + 2.89709i) q^{46} +(2.18505 + 0.709965i) q^{47} +(-2.46138 + 1.78829i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-3.06681 - 0.996467i) q^{52} +(7.75090 - 10.6682i) q^{53} +(2.30564 + 2.38412i) q^{55} +1.98936i q^{56} +(-0.406430 + 1.25086i) q^{58} +(5.67571 - 1.84415i) q^{59} +(1.18547 + 1.63166i) q^{61} +(0.379385 + 1.16763i) q^{62} +(-0.809017 - 0.587785i) q^{64} -3.22464 q^{65} -7.59383 q^{67} +(5.26884 + 3.82804i) q^{68} +(0.614747 + 1.89200i) q^{70} +(-2.68699 - 3.69833i) q^{71} +(-8.96545 + 2.91305i) q^{73} +(1.08996 - 3.35456i) q^{74} -2.06794i q^{76} +(5.92814 - 2.89663i) q^{77} +(-2.40983 + 3.31685i) q^{79} +(-0.951057 - 0.309017i) q^{80} +(-3.46878 + 2.52022i) q^{82} +(1.91200 - 1.38915i) q^{83} +(6.19389 + 2.01252i) q^{85} +(-4.81028 + 6.62079i) q^{86} +(-0.573574 + 3.26665i) q^{88} +11.4586i q^{89} +(-1.98234 + 6.10101i) q^{91} +(-3.40574 + 1.10659i) q^{92} +(1.35043 + 1.85871i) q^{94} +(-0.639030 - 1.96673i) q^{95} +(-0.221400 - 0.160857i) q^{97} -3.04243 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 8 q^{4} + 8 q^{8} - 8 q^{16} - 4 q^{17} + 8 q^{25} + 8 q^{29} + 32 q^{31} - 32 q^{32} + 24 q^{34} + 16 q^{37} - 32 q^{41} - 20 q^{46} + 20 q^{47} + 16 q^{49} - 8 q^{50} + 40 q^{53} + 8 q^{55}+ \cdots - 16 q^{98}+O(q^{100}) \) 32 * q + 8 * q^2 - 8 * q^4 + 8 * q^8 - 8 * q^16 - 4 * q^17 + 8 * q^25 + 8 * q^29 + 32 * q^31 - 32 * q^32 + 24 * q^34 + 16 * q^37 - 32 * q^41 - 20 * q^46 + 20 * q^47 + 16 * q^49 - 8 * q^50 + 40 * q^53 + 8 * q^55 - 8 * q^58 - 40 * q^59 + 28 * q^62 - 8 * q^64 - 8 * q^65 - 4 * q^68 + 40 * q^71 + 40 * q^73 - 16 * q^74 + 28 * q^77 + 20 * q^79 - 8 * q^82 + 24 * q^83 - 24 * q^91 + 20 * q^94 - 16 * q^95 + 48 * q^97 - 16 * q^98

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