LMFDB - Embedded newform 990.2.z.a.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.a.701.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(-0.756962 + 0.245952i) q^{7} +(0.309017 - 0.951057i) q^{8} -1.00000i q^{10} +(-2.85682 - 1.68481i) q^{11} +(-1.56843 + 2.15876i) q^{13} +(0.756962 + 0.245952i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(4.29120 - 3.11774i) q^{17} +(7.97920 + 2.59260i) q^{19} +(-0.587785 + 0.809017i) q^{20} +(1.32091 + 3.04224i) q^{22} -1.65090i q^{23} +(-0.309017 + 0.951057i) q^{25} +(2.53777 - 0.824571i) q^{26} +(-0.467828 - 0.643910i) q^{28} +(0.0872476 + 0.268521i) q^{29} +(5.39925 + 3.92279i) q^{31} +1.00000 q^{32} -5.30422 q^{34} +(-0.643910 - 0.467828i) q^{35} +(2.08813 + 6.42660i) q^{37} +(-4.93142 - 6.78751i) q^{38} +(0.951057 - 0.309017i) q^{40} +(-1.88718 + 5.80815i) q^{41} +1.23422i q^{43} +(0.719545 - 3.23763i) q^{44} +(-0.970374 + 1.33560i) q^{46} +(2.13242 + 0.692866i) q^{47} +(-5.15062 + 3.74214i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-2.53777 - 0.824571i) q^{52} +(-4.30050 + 5.91913i) q^{53} +(-0.316156 - 3.30152i) q^{55} +0.795917i q^{56} +(0.0872476 - 0.268521i) q^{58} +(9.85184 - 3.20106i) q^{59} +(8.32796 + 11.4625i) q^{61} +(-2.06233 - 6.34720i) q^{62} +(-0.809017 - 0.587785i) q^{64} -2.66837 q^{65} -9.51970 q^{67} +(4.29120 + 3.11774i) q^{68} +(0.245952 + 0.756962i) q^{70} +(5.83827 + 8.03570i) q^{71} +(11.7675 - 3.82350i) q^{73} +(2.08813 - 6.42660i) q^{74} +8.38982i q^{76} +(2.57688 + 0.572697i) q^{77} +(5.46381 - 7.52029i) q^{79} +(-0.951057 - 0.309017i) q^{80} +(4.94071 - 3.58963i) q^{82} +(2.80102 - 2.03506i) q^{83} +(5.04461 + 1.63909i) q^{85} +(0.725455 - 0.998503i) q^{86} +(-2.48516 + 2.19636i) q^{88} +0.594975i q^{89} +(0.656290 - 2.01985i) q^{91} +(1.57010 - 0.510156i) q^{92} +(-1.31791 - 1.81395i) q^{94} +(2.59260 + 7.97920i) q^{95} +(-2.68136 - 1.94812i) q^{97} +6.36652 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−0.756962	+	0.245952i	−0.286105	+	0.0929610i	−0.448554	−	0.893756i	$-0.648061\pi$
$7$	−0.756962	+	0.245952i	−0.286105	+	0.0929610i	0.162449	+	0.986717i	$0.448061\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	−2.85682	−	1.68481i	−0.861363	−	0.507990i
$11$	−2.85682	−	1.68481i	−0.861363	−	0.507990i
$12$		0			0
$13$	−1.56843	+	2.15876i	−0.435003	+	0.598731i	−0.969093	−	0.246697i	$-0.920655\pi$
$13$	−1.56843	+	2.15876i	−0.435003	+	0.598731i	0.534089	+	0.845428i	$0.320655\pi$
$14$	0.756962	+	0.245952i	0.202307	+	0.0657334i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.29120	−	3.11774i	1.04077	−	0.756163i	0.0703337	−	0.997524i	$-0.477594\pi$
$17$	4.29120	−	3.11774i	1.04077	−	0.756163i	0.970436	+	0.241360i	$0.0775936\pi$
$18$		0			0
$19$	7.97920	+	2.59260i	1.83055	+	0.594783i	0.999240	+	0.0389789i	$0.0124105\pi$
$19$	7.97920	+	2.59260i	1.83055	+	0.594783i	0.831313	+	0.555804i	$0.187589\pi$
$20$	−0.587785	+	0.809017i	−0.131433	+	0.180902i
$21$		0			0
$22$	1.32091	+	3.04224i	0.281619	+	0.648607i
$23$		−	1.65090i		−	0.344236i	−0.985076	−	0.172118i	$-0.944939\pi$
$23$		−	1.65090i		−	0.344236i	0.985076	−	0.172118i	$-0.0550611\pi$
$24$		0			0
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	2.53777	−	0.824571i	0.497697	−	0.161712i
$27$		0			0
$28$	−0.467828	−	0.643910i	−0.0884112	−	0.121688i
$29$	0.0872476	+	0.268521i	0.0162015	+	0.0498630i	0.958830	−	0.283979i	$-0.0916547\pi$
$29$	0.0872476	+	0.268521i	0.0162015	+	0.0498630i	−0.942629	+	0.333842i	$0.891655\pi$
$30$		0			0
$31$	5.39925	+	3.92279i	0.969735	+	0.704554i	0.955391	−	0.295344i	$-0.0954341\pi$
$31$	5.39925	+	3.92279i	0.969735	+	0.704554i	0.0143437	+	0.999897i	$0.495434\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−5.30422			−0.909666
$35$	−0.643910	−	0.467828i	−0.108841	−	0.0790774i
$36$		0			0
$37$	2.08813	+	6.42660i	0.343286	+	1.05653i	0.962495	+	0.271300i	$0.0874535\pi$
$37$	2.08813	+	6.42660i	0.343286	+	1.05653i	−0.619209	+	0.785226i	$0.712547\pi$
$38$	−4.93142	−	6.78751i	−0.799981	−	1.10108i
$39$		0			0
$40$	0.951057	−	0.309017i	0.150375	−	0.0488599i
$41$	−1.88718	+	5.80815i	−0.294728	+	0.907080i	0.688584	+	0.725156i	$0.258233\pi$
$41$	−1.88718	+	5.80815i	−0.294728	+	0.907080i	−0.983313	+	0.181924i	$0.941767\pi$
$42$		0			0
$43$			1.23422i			0.188216i	0.995562	+	0.0941082i	$0.0300000\pi$
$43$			1.23422i			0.188216i	−0.995562	+	0.0941082i	$0.970000\pi$
$44$	0.719545	−	3.23763i	0.108475	−	0.488091i
$45$		0			0
$46$	−0.970374	+	1.33560i	−0.143074	+	0.196924i
$47$	2.13242	+	0.692866i	0.311046	+	0.101065i	0.460380	−	0.887722i	$-0.347713\pi$
$47$	2.13242	+	0.692866i	0.311046	+	0.101065i	−0.149335	+	0.988787i	$0.547713\pi$
$48$		0			0
$49$	−5.15062	+	3.74214i	−0.735803	+	0.534592i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$		0			0
$52$	−2.53777	−	0.824571i	−0.351925	−	0.114347i
$53$	−4.30050	+	5.91913i	−0.590719	+	0.813055i	−0.994819	−	0.101660i	$-0.967585\pi$
$53$	−4.30050	+	5.91913i	−0.590719	+	0.813055i	0.404100	+	0.914715i	$0.367585\pi$
$54$		0			0
$55$	−0.316156	−	3.30152i	−0.0426304	−	0.445177i
$56$			0.795917i			0.106359i
$57$		0			0
$58$	0.0872476	−	0.268521i	0.0114562	−	0.0352585i
$59$	9.85184	−	3.20106i	1.28260	−	0.416742i	0.413105	−	0.910683i	$-0.364444\pi$
$59$	9.85184	−	3.20106i	1.28260	−	0.416742i	0.869495	+	0.493942i	$0.164444\pi$
$60$		0			0
$61$	8.32796	+	11.4625i	1.06629	+	1.46762i	0.873780	+	0.486321i	$0.161662\pi$
$61$	8.32796	+	11.4625i	1.06629	+	1.46762i	0.192506	+	0.981296i	$0.438338\pi$
$62$	−2.06233	−	6.34720i	−0.261916	−	0.806096i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−2.66837			−0.330970
$66$		0			0
$67$	−9.51970			−1.16302			−0.581509	−	0.813540i	$-0.697537\pi$
$67$	−9.51970			−1.16302			−0.581509	+	0.813540i	$0.697537\pi$
$68$	4.29120	+	3.11774i	0.520385	+	0.378082i
$69$		0			0
$70$	0.245952	+	0.756962i	0.0293969	+	0.0904742i
$71$	5.83827	+	8.03570i	0.692876	+	0.953662i	0.999998	+	0.00199153i	$0.000633924\pi$
$71$	5.83827	+	8.03570i	0.692876	+	0.953662i	−0.307122	+	0.951670i	$0.599366\pi$
$72$		0			0
$73$	11.7675	−	3.82350i	1.37728	−	0.447507i	0.475509	−	0.879711i	$-0.342264\pi$
$73$	11.7675	−	3.82350i	1.37728	−	0.447507i	0.901776	+	0.432204i	$0.142264\pi$
$74$	2.08813	−	6.42660i	0.242740	−	0.747077i
$75$		0			0
$76$			8.38982i			0.962379i
$77$	2.57688	+	0.572697i	0.293663	+	0.0652649i
$78$		0			0
$79$	5.46381	−	7.52029i	0.614726	−	0.846098i	−0.382229	−	0.924067i	$-0.624844\pi$
$79$	5.46381	−	7.52029i	0.614726	−	0.846098i	0.996956	+	0.0779693i	$0.0248436\pi$
$80$	−0.951057	−	0.309017i	−0.106331	−	0.0345492i
$81$		0			0
$82$	4.94071	−	3.58963i	0.545610	−	0.396409i
$83$	2.80102	−	2.03506i	0.307452	−	0.223377i	−0.423350	−	0.905966i	$-0.639146\pi$
$83$	2.80102	−	2.03506i	0.307452	−	0.223377i	0.730803	+	0.682589i	$0.239146\pi$
$84$		0			0
$85$	5.04461	+	1.63909i	0.547165	+	0.177785i
$86$	0.725455	−	0.998503i	0.0782278	−	0.107671i
$87$		0			0
$88$	−2.48516	+	2.19636i	−0.264918	+	0.234133i
$89$			0.594975i			0.0630672i	0.999503	+	0.0315336i	$0.0100391\pi$
$89$			0.594975i			0.0630672i	−0.999503	+	0.0315336i	$0.989961\pi$
$90$		0			0
$91$	0.656290	−	2.01985i	0.0687979	−	0.211738i
$92$	1.57010	−	0.510156i	0.163694	−	0.0531874i
$93$		0			0
$94$	−1.31791	−	1.81395i	−0.135932	−	0.187094i
$95$	2.59260	+	7.97920i	0.265995	+	0.818648i
$96$		0			0
$97$	−2.68136	−	1.94812i	−0.272251	−	0.197802i	0.443280	−	0.896383i	$-0.353815\pi$
$97$	−2.68136	−	1.94812i	−0.272251	−	0.197802i	−0.715530	+	0.698582i	$0.753815\pi$
$98$	6.36652			0.643115
$99$		0			0
$100$	−1.00000			−0.100000
$101$	11.0262	+	8.01103i	1.09715	+	0.797127i	0.980593	−	0.196057i	$-0.0628137\pi$
$101$	11.0262	+	8.01103i	1.09715	+	0.797127i	0.116559	+	0.993184i	$0.462814\pi$
$102$		0			0
$103$	−6.10046	−	18.7753i	−0.601096	−	1.84998i	−0.521677	−	0.853143i	$-0.674693\pi$
$103$	−6.10046	−	18.7753i	−0.601096	−	1.84998i	−0.0794194	−	0.996841i	$-0.525307\pi$
$104$	1.56843	+	2.15876i	0.153797	+	0.211683i
$105$		0			0
$106$	6.95835	−	2.26091i	0.675855	−	0.219599i
$107$	1.71040	−	5.26408i	0.165351	−	0.508898i	−0.833711	−	0.552201i	$-0.813788\pi$
$107$	1.71040	−	5.26408i	0.165351	−	0.508898i	0.999062	+	0.0433030i	$0.0137881\pi$
$108$		0			0
$109$		−	10.6696i		−	1.02196i	−0.859592	−	0.510981i	$-0.829282\pi$
$109$		−	10.6696i		−	1.02196i	0.859592	−	0.510981i	$-0.170718\pi$
$110$	−1.68481	+	2.85682i	−0.160640	+	0.272387i
$111$		0			0
$112$	0.467828	−	0.643910i	0.0442056	−	0.0608438i
$113$	−16.0761	−	5.22345i	−1.51231	−	0.491381i	−0.568733	−	0.822522i	$-0.692566\pi$
$113$	−16.0761	−	5.22345i	−1.51231	−	0.491381i	−0.943581	+	0.331142i	$0.892566\pi$
$114$		0			0
$115$	1.33560	−	0.970374i	0.124546	−	0.0904878i
$116$	−0.228417	+	0.165955i	−0.0212080	+	0.0154085i
$117$		0			0
$118$	−9.85184	−	3.20106i	−0.906935	−	0.294681i
$119$	−2.48146	+	3.41544i	−0.227475	+	0.313093i
$120$		0			0
$121$	5.32283	+	9.62640i	0.483893	+	0.875127i
$122$		−	14.1684i		−	1.28274i
$123$		0			0
$124$	−2.06233	+	6.34720i	−0.185203	+	0.569996i
$125$	−0.951057	+	0.309017i	−0.0850651	+	0.0276393i
$126$		0			0
$127$	0.650566	+	0.895428i	0.0577284	+	0.0794564i	0.836905	−	0.547348i	$-0.184363\pi$
$127$	0.650566	+	0.895428i	0.0577284	+	0.0794564i	−0.779177	+	0.626804i	$0.784363\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	2.15876	+	1.56843i	0.189335	+	0.137560i
$131$	−1.21327			−0.106004			−0.0530019	−	0.998594i	$-0.516879\pi$
$131$	−1.21327			−0.106004			−0.0530019	+	0.998594i	$0.516879\pi$
$132$		0			0
$133$	−6.67760			−0.579021
$134$	7.70160	+	5.59554i	0.665317	+	0.483381i
$135$		0			0
$136$	−1.63909	−	5.04461i	−0.140551	−	0.432572i
$137$	−5.47420	−	7.53459i	−0.467693	−	0.643724i	0.508389	−	0.861127i	$-0.330241\pi$
$137$	−5.47420	−	7.53459i	−0.467693	−	0.643724i	−0.976082	+	0.217404i	$0.930241\pi$
$138$		0			0
$139$	2.63783	−	0.857082i	0.223738	−	0.0726968i	−0.195003	−	0.980803i	$-0.562472\pi$
$139$	2.63783	−	0.857082i	0.223738	−	0.0726968i	0.418741	+	0.908106i	$0.362472\pi$
$140$	0.245952	−	0.756962i	0.0207867	−	0.0639749i
$141$		0			0
$142$		−	9.93267i		−	0.833531i
$143$	8.11781	−	3.52467i	0.678845	−	0.294748i
$144$		0			0
$145$	−0.165955	+	0.228417i	−0.0137818	+	0.0189690i
$146$	−11.7675	−	3.82350i	−0.973887	−	0.316435i
$147$		0			0
$148$	−5.46679	+	3.97186i	−0.449367	+	0.326485i
$149$	−4.68800	+	3.40603i	−0.384056	+	0.279033i	−0.763015	−	0.646380i	$-0.776282\pi$
$149$	−4.68800	+	3.40603i	−0.384056	+	0.279033i	0.378960	+	0.925413i	$0.376282\pi$
$150$		0			0
$151$	3.89611	+	1.26592i	0.317061	+	0.103019i	0.463224	−	0.886241i	$-0.346692\pi$
$151$	3.89611	+	1.26592i	0.317061	+	0.103019i	−0.146163	+	0.989261i	$0.546692\pi$
$152$	4.93142	−	6.78751i	0.399991	−	0.550540i
$153$		0			0
$154$	−1.74812	−	1.97798i	−0.140868	−	0.159390i
$155$			6.67385i			0.536056i
$156$		0			0
$157$	0.0964332	−	0.296791i	0.00769621	−	0.0236865i	−0.947135	−	0.320836i	$-0.896036\pi$
$157$	0.0964332	−	0.296791i	0.00769621	−	0.0236865i	0.954831	+	0.297150i	$0.0960361\pi$
$158$	−8.84063	+	2.87249i	−0.703322	+	0.228523i
$159$		0			0
$160$	0.587785	+	0.809017i	0.0464685	+	0.0639584i
$161$	0.406041	+	1.24967i	0.0320005	+	0.0984875i
$162$		0			0
$163$	6.80226	+	4.94213i	0.532794	+	0.387097i	0.821402	−	0.570350i	$-0.193192\pi$
$163$	6.80226	+	4.94213i	0.532794	+	0.387097i	−0.288608	+	0.957447i	$0.593192\pi$
$164$	−6.10705			−0.476880
$165$		0			0
$166$	−3.46225			−0.268723
$167$	20.0318	+	14.5539i	1.55010	+	1.12622i	0.943577	+	0.331154i	$0.107438\pi$
$167$	20.0318	+	14.5539i	1.55010	+	1.12622i	0.606527	+	0.795063i	$0.292562\pi$
$168$		0			0
$169$	1.81696	+	5.59203i	0.139766	+	0.430156i
$170$	−3.11774	−	4.29120i	−0.239120	−	0.329120i
$171$		0			0
$172$	−1.17381	+	0.381394i	−0.0895022	+	0.0290810i
$173$	−4.46070	+	13.7286i	−0.339141	+	1.04377i	0.625505	+	0.780220i	$0.284893\pi$
$173$	−4.46070	+	13.7286i	−0.339141	+	1.04377i	−0.964646	+	0.263549i	$0.915107\pi$
$174$		0			0
$175$		−	0.795917i		−	0.0601656i
$176$	3.30152	−	0.316156i	0.248862	−	0.0238311i
$177$		0			0
$178$	0.349717	−	0.481345i	0.0262124	−	0.0360783i
$179$	−1.95739	−	0.635994i	−0.146302	−	0.0475364i	0.234951	−	0.972007i	$-0.424507\pi$
$179$	−1.95739	−	0.635994i	−0.146302	−	0.0475364i	−0.381253	+	0.924471i	$0.624507\pi$
$180$		0			0
$181$	9.49391	−	6.89773i	0.705677	−	0.512704i	−0.176099	−	0.984372i	$-0.556348\pi$
$181$	9.49391	−	6.89773i	0.705677	−	0.512704i	0.881776	+	0.471668i	$0.156348\pi$
$182$	−1.71819	+	1.24834i	−0.127361	+	0.0925329i
$183$		0			0
$184$	−1.57010	−	0.510156i	−0.115749	−	0.0376092i
$185$	−3.97186	+	5.46679i	−0.292017	+	0.401926i
$186$		0			0
$187$	−17.5120	+	1.67696i	−1.28060	+	0.122631i
$188$			2.24216i			0.163526i
$189$		0			0
$190$	2.59260	−	7.97920i	0.188087	−	0.578872i
$191$	−17.3703	+	5.64395i	−1.25687	+	0.408382i	−0.860378	−	0.509657i	$-0.829772\pi$
$191$	−17.3703	+	5.64395i	−1.25687	+	0.408382i	−0.396492	+	0.918038i	$0.629772\pi$
$192$		0			0
$193$	−7.52512	−	10.3574i	−0.541670	−	0.745545i	0.447183	−	0.894443i	$-0.352427\pi$
$193$	−7.52512	−	10.3574i	−0.541670	−	0.745545i	−0.988853	+	0.148898i	$0.952427\pi$
$194$	1.02419	+	3.15212i	0.0735324	+	0.226309i
$195$		0			0
$196$	−5.15062	−	3.74214i	−0.367901	−	0.267296i
$197$	−8.42064			−0.599946			−0.299973	−	0.953948i	$-0.596978\pi$
$197$	−8.42064			−0.599946			−0.299973	+	0.953948i	$0.596978\pi$
$198$		0			0
$199$	−17.9161			−1.27004			−0.635019	−	0.772496i	$-0.719008\pi$
$199$	−17.9161			−1.27004			−0.635019	+	0.772496i	$0.719008\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$		0			0
$202$	−4.21165	−	12.9621i	−0.296330	−	0.912011i
$203$	−0.132086	−	0.181801i	−0.00927064	−	0.0127599i
$204$		0			0
$205$	−5.80815	+	1.88718i	−0.405659	+	0.131807i
$206$	−6.10046	+	18.7753i	−0.425039	+	1.30814i
$207$		0			0
$208$		−	2.66837i		−	0.185018i
$209$	−18.4271	−	20.8500i	−1.27463	−	1.44223i
$210$		0			0
$211$	9.82460	−	13.5224i	0.676353	−	0.930920i	−0.323530	−	0.946218i	$-0.604870\pi$
$211$	9.82460	−	13.5224i	0.676353	−	0.930920i	0.999883	+	0.0152979i	$0.00486965\pi$
$212$	−6.95835	−	2.26091i	−0.477902	−	0.155280i
$213$		0			0
$214$	−4.47790	+	3.25338i	−0.306103	+	0.222397i
$215$	−0.998503	+	0.725455i	−0.0680973	+	0.0494756i
$216$		0			0
$217$	−5.05185	−	1.64144i	−0.342942	−	0.111428i
$218$	−6.27143	+	8.63188i	−0.424755	+	0.584625i
$219$		0			0
$220$	3.04224	−	1.32091i	0.205108	−	0.0890556i
$221$			14.1536i			0.952074i
$222$		0			0
$223$	3.67652	−	11.3152i	0.246198	−	0.757719i	−0.749239	−	0.662300i	$-0.769581\pi$
$223$	3.67652	−	11.3152i	0.246198	−	0.757719i	0.995437	−	0.0954199i	$-0.0304194\pi$
$224$	−0.756962	+	0.245952i	−0.0505766	+	0.0164333i
$225$		0			0
$226$	9.93559	+	13.6752i	0.660905	+	0.909658i
$227$	−5.53094	−	17.0225i	−0.367101	−	1.12982i	−0.948655	−	0.316313i	$-0.897555\pi$
$227$	−5.53094	−	17.0225i	−0.367101	−	1.12982i	0.581554	−	0.813508i	$-0.302445\pi$
$228$		0			0
$229$	−10.1538	−	7.37718i	−0.670983	−	0.487498i	0.199371	−	0.979924i	$-0.436110\pi$
$229$	−10.1538	−	7.37718i	−0.670983	−	0.487498i	−0.870354	+	0.492426i	$0.836110\pi$
$230$	−1.65090			−0.108857
$231$		0			0
$232$	0.282339			0.0185365
$233$	−1.32229	−	0.960702i	−0.0866263	−	0.0629377i	0.543629	−	0.839326i	$-0.317050\pi$
$233$	−1.32229	−	0.960702i	−0.0866263	−	0.0629377i	−0.630255	+	0.776388i	$0.717050\pi$
$234$		0			0
$235$	0.692866	+	2.13242i	0.0451976	+	0.139104i
$236$	6.08877	+	8.38047i	0.396345	+	0.545522i
$237$		0			0
$238$	4.01509	−	1.30458i	0.260260	−	0.0845635i
$239$	7.89453	−	24.2969i	0.510655	−	1.57163i	−0.280396	−	0.959884i	$-0.590466\pi$
$239$	7.89453	−	24.2969i	0.510655	−	1.57163i	0.791051	−	0.611750i	$-0.209534\pi$
$240$		0			0
$241$		−	2.71641i		−	0.174979i	−0.996165	−	0.0874897i	$-0.972116\pi$
$241$		−	2.71641i		−	0.174979i	0.996165	−	0.0874897i	$-0.0278845\pi$
$242$	1.35200	−	10.9166i	0.0869097	−	0.701745i
$243$		0			0
$244$	−8.32796	+	11.4625i	−0.533143	+	0.733809i
$245$	−6.05492	−	1.96736i	−0.386834	−	0.125690i
$246$		0			0
$247$	−18.1116	+	13.1588i	−1.15241	+	0.837276i
$248$	5.39925	−	3.92279i	0.342853	−	0.249097i
$249$		0			0
$250$	0.951057	+	0.309017i	0.0601501	+	0.0195440i
$251$	−13.1287	+	18.0701i	−0.828676	+	1.14058i	0.159492	+	0.987199i	$0.449015\pi$
$251$	−13.1287	+	18.0701i	−0.828676	+	1.14058i	−0.988168	+	0.153376i	$0.950985\pi$
$252$		0			0
$253$	−2.78145	+	4.71632i	−0.174868	+	0.296512i
$254$		−	1.10681i		−	0.0694474i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	25.4719	−	8.27631i	1.58889	−	0.516262i	0.624564	−	0.780974i	$-0.285277\pi$
$257$	25.4719	−	8.27631i	1.58889	−	0.516262i	0.964328	+	0.264711i	$0.0852767\pi$
$258$		0			0
$259$	−3.16127	−	4.35111i	−0.196432	−	0.270365i
$260$	−0.824571	−	2.53777i	−0.0511377	−	0.157386i
$261$		0			0
$262$	0.981556	+	0.713142i	0.0606407	+	0.0440581i
$263$	−21.1316			−1.30303			−0.651515	−	0.758636i	$-0.725866\pi$
$263$	−21.1316			−1.30303			−0.651515	+	0.758636i	$0.725866\pi$
$264$		0			0
$265$	−7.31645			−0.449446
$266$	5.40229	+	3.92500i	0.331236	+	0.240657i
$267$		0			0
$268$	−2.94175	−	9.05378i	−0.179696	−	0.553047i
$269$	−5.64037	−	7.76331i	−0.343900	−	0.473337i	0.601676	−	0.798740i	$-0.294500\pi$
$269$	−5.64037	−	7.76331i	−0.343900	−	0.473337i	−0.945575	+	0.325403i	$0.894500\pi$
$270$		0			0
$271$	−8.85526	+	2.87725i	−0.537919	+	0.174780i	−0.565362	−	0.824843i	$-0.691263\pi$
$271$	−8.85526	+	2.87725i	−0.537919	+	0.174780i	0.0274431	+	0.999623i	$0.491263\pi$
$272$	−1.63909	+	5.04461i	−0.0993846	+	0.305874i
$273$		0			0
$274$			9.31327i			0.562635i
$275$	2.48516	−	2.19636i	0.149861	−	0.132446i
$276$		0			0
$277$	−2.67156	+	3.67709i	−0.160519	+	0.220935i	−0.881699	−	0.471812i	$-0.843600\pi$
$277$	−2.67156	+	3.67709i	−0.160519	+	0.220935i	0.721180	+	0.692747i	$0.243600\pi$
$278$	−2.63783	−	0.857082i	−0.158206	−	0.0514044i
$279$		0			0
$280$	−0.643910	+	0.467828i	−0.0384810	+	0.0279581i
$281$	−24.3965	+	17.7251i	−1.45537	+	1.05739i	−0.470834	+	0.882222i	$0.656047\pi$
$281$	−24.3965	+	17.7251i	−1.45537	+	1.05739i	−0.984538	+	0.175169i	$0.943953\pi$
$282$		0			0
$283$	14.9973	+	4.87291i	0.891496	+	0.289665i	0.718723	−	0.695297i	$-0.244727\pi$
$283$	14.9973	+	4.87291i	0.891496	+	0.289665i	0.172773	+	0.984962i	$0.444727\pi$
$284$	−5.83827	+	8.03570i	−0.346438	+	0.476831i
$285$		0			0
$286$	−8.63919	−	1.92001i	−0.510846	−	0.113533i
$287$		−	4.86070i		−	0.286918i
$288$		0			0
$289$	3.44082	−	10.5897i	0.202401	−	0.622926i
$290$	0.268521	−	0.0872476i	0.0157681	−	0.00512336i
$291$		0			0
$292$	7.27273	+	10.0101i	0.425604	+	0.585794i
$293$	1.72886	+	5.32089i	0.101001	+	0.310849i	0.988771	−	0.149438i	$-0.0477464\pi$
$293$	1.72886	+	5.32089i	0.101001	+	0.310849i	−0.887770	+	0.460287i	$0.847746\pi$
$294$		0			0
$295$	8.38047	+	6.08877i	0.487930	+	0.354502i
$296$	6.75732			0.392762
$297$		0			0
$298$	5.79469			0.335677
$299$	3.56388	+	2.58931i	0.206105	+	0.149744i
$300$		0			0
$301$	−0.303558	−	0.934256i	−0.0174968	−	0.0538496i
$302$	−2.40793	−	3.31423i	−0.138561	−	0.190713i
$303$		0			0
$304$	−7.97920	+	2.59260i	−0.457638	+	0.148696i
$305$	−4.37827	+	13.4749i	−0.250699	+	0.771572i
$306$		0			0
$307$		−	28.4225i		−	1.62216i	−0.584938	−	0.811078i	$-0.698881\pi$
$307$		−	28.4225i		−	1.62216i	0.584938	−	0.811078i	$-0.301119\pi$
$308$	0.251633	+	2.62774i	0.0143381	+	0.149729i
$309$		0			0
$310$	3.92279	−	5.39925i	0.222799	−	0.306657i
$311$	14.5344	+	4.72252i	0.824171	+	0.267790i	0.690588	−	0.723248i	$-0.257352\pi$
$311$	14.5344	+	4.72252i	0.824171	+	0.267790i	0.133583	+	0.991038i	$0.457352\pi$
$312$		0			0
$313$	−15.8787	+	11.5366i	−0.897519	+	0.652086i	−0.937828	−	0.347102i	$-0.887166\pi$
$313$	−15.8787	+	11.5366i	−0.897519	+	0.652086i	0.0403086	+	0.999187i	$0.487166\pi$
$314$	−0.252465	+	0.183427i	−0.0142475	+	0.0103514i
$315$		0			0
$316$	8.84063	+	2.87249i	0.497324	+	0.161590i
$317$	−14.8957	+	20.5022i	−0.836628	+	1.15152i	0.150025	+	0.988682i	$0.452065\pi$
$317$	−14.8957	+	20.5022i	−0.836628	+	1.15152i	−0.986653	+	0.162838i	$0.947935\pi$
$318$		0			0
$319$	0.203156	−	0.914111i	0.0113745	−	0.0511804i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	0.406041	−	1.24967i	0.0226278	−	0.0696412i
$323$	42.3234	−	13.7517i	2.35494	−	0.765165i
$324$		0			0
$325$	−1.56843	−	2.15876i	−0.0870007	−	0.119746i
$326$	−2.59823	−	7.99653i	−0.143903	−	0.442887i
$327$		0			0
$328$	4.94071	+	3.58963i	0.272805	+	0.198204i
$329$	−1.78457			−0.0983867
$330$		0			0
$331$	−22.2481			−1.22286			−0.611432	−	0.791297i	$-0.709406\pi$
$331$	−22.2481			−1.22286			−0.611432	+	0.791297i	$0.709406\pi$
$332$	2.80102	+	2.03506i	0.153726	+	0.111689i
$333$		0			0
$334$	−7.65145	−	23.5487i	−0.418669	−	1.28853i
$335$	−5.59554	−	7.70160i	−0.305717	−	0.420784i
$336$		0			0
$337$	−19.9218	+	6.47299i	−1.08521	+	0.352606i	−0.796394	−	0.604778i	$-0.793262\pi$
$337$	−19.9218	+	6.47299i	−1.08521	+	0.352606i	−0.288817	+	0.957384i	$0.593262\pi$
$338$	1.81696	−	5.59203i	0.0988297	−	0.304167i
$339$		0			0
$340$			5.30422i			0.287662i
$341$	−8.81554	−	20.3034i	−0.477388	−	1.09949i
$342$		0			0
$343$	6.25323	−	8.60683i	0.337643	−	0.464725i
$344$	1.17381	+	0.381394i	0.0632876	+	0.0205634i
$345$		0			0
$346$	11.6783	−	8.48476i	0.627828	−	0.456144i
$347$	2.15904	−	1.56863i	0.115903	−	0.0842086i	−0.528324	−	0.849043i	$-0.677179\pi$
$347$	2.15904	−	1.56863i	0.115903	−	0.0842086i	0.644227	+	0.764834i	$0.277179\pi$
$348$		0			0
$349$	29.7938	+	9.68058i	1.59482	+	0.518190i	0.965820	−	0.259213i	$-0.0834632\pi$
$349$	29.7938	+	9.68058i	1.59482	+	0.518190i	0.629003	+	0.777403i	$0.283463\pi$
$350$	−0.467828	+	0.643910i	−0.0250065	+	0.0344184i
$351$		0			0
$352$	−2.85682	−	1.68481i	−0.152269	−	0.0898007i
$353$		−	18.8861i		−	1.00520i	−0.864518	−	0.502602i	$-0.832376\pi$
$353$		−	18.8861i		−	1.00520i	0.864518	−	0.502602i	$-0.167624\pi$
$354$		0			0
$355$	−3.06936	+	9.44653i	−0.162905	+	0.501370i
$356$	−0.565855	+	0.183857i	−0.0299902	+	0.00974442i
$357$		0			0
$358$	1.20973	+	1.66505i	0.0639364	+	0.0880008i
$359$	−2.91047	−	8.95750i	−0.153609	−	0.472759i	0.844409	−	0.535700i	$-0.179952\pi$
$359$	−2.91047	−	8.95750i	−0.153609	−	0.472759i	−0.998017	+	0.0629410i	$0.979952\pi$
$360$		0			0
$361$	41.5747	+	30.2058i	2.18814	+	1.58978i
$362$	−11.7351			−0.616784
$363$		0			0
$364$	2.12380			0.111317
$365$	10.0101	+	7.27273i	0.523950	+	0.380672i
$366$		0			0
$367$	−1.31882	−	4.05891i	−0.0688418	−	0.211873i	0.910717	−	0.413031i	$-0.135530\pi$
$367$	−1.31882	−	4.05891i	−0.0688418	−	0.211873i	−0.979559	+	0.201157i	$0.935530\pi$
$368$	0.970374	+	1.33560i	0.0505842	+	0.0696232i
$369$		0			0
$370$	6.42660	−	2.08813i	0.334103	−	0.108557i
$371$	1.79949	−	5.53827i	0.0934250	−	0.287533i
$372$		0			0
$373$		−	16.9282i		−	0.876509i	−0.898851	−	0.438254i	$-0.855597\pi$
$373$		−	16.9282i		−	0.876509i	0.898851	−	0.438254i	$-0.144403\pi$
$374$	15.1532	+	8.93660i	0.783553	+	0.462101i
$375$		0			0
$376$	1.31791	−	1.81395i	0.0679660	−	0.0935471i
$377$	−0.716512	−	0.232809i	−0.0369022	−	0.0119903i
$378$		0			0
$379$	9.11473	−	6.62224i	0.468192	−	0.340162i	−0.328544	−	0.944489i	$-0.606558\pi$
$379$	9.11473	−	6.62224i	0.468192	−	0.340162i	0.796736	+	0.604327i	$0.206558\pi$
$380$	−6.78751	+	4.93142i	−0.348192	+	0.252976i
$381$		0			0
$382$	17.3703	+	5.64395i	0.888741	+	0.288769i
$383$	9.61756	−	13.2374i	0.491434	−	0.676401i	−0.489217	−	0.872162i	$-0.662718\pi$
$383$	9.61756	−	13.2374i	0.491434	−	0.676401i	0.980652	+	0.195761i	$0.0627175\pi$
$384$		0			0
$385$	1.05133	+	2.42137i	0.0535809	+	0.123404i
$386$			12.8025i			0.651630i
$387$		0			0
$388$	1.02419	−	3.15212i	0.0519952	−	0.160025i
$389$	1.49827	−	0.486817i	0.0759653	−	0.0246826i	−0.270788	−	0.962639i	$-0.587284\pi$
$389$	1.49827	−	0.486817i	0.0759653	−	0.0246826i	0.346753	+	0.937956i	$0.387284\pi$
$390$		0			0
$391$	−5.14707	−	7.08434i	−0.260299	−	0.358270i
$392$	1.96736	+	6.05492i	0.0993668	+	0.305820i
$393$		0			0
$394$	6.81244	+	4.94953i	0.343206	+	0.249354i
$395$	9.29558			0.467712
$396$		0			0
$397$	−21.1992			−1.06396			−0.531979	−	0.846758i	$-0.678551\pi$
$397$	−21.1992			−1.06396			−0.531979	+	0.846758i	$0.678551\pi$
$398$	14.4944	+	10.5308i	0.726540	+	0.527862i
$399$		0			0
$400$	−0.309017	−	0.951057i	−0.0154508	−	0.0475528i
$401$	−11.7573	−	16.1825i	−0.587131	−	0.808117i	0.407323	−	0.913284i	$-0.366462\pi$
$401$	−11.7573	−	16.1825i	−0.587131	−	0.808117i	−0.994455	+	0.105167i	$0.966462\pi$
$402$		0			0
$403$	−16.9367	+	5.50306i	−0.843676	+	0.274127i
$404$	−4.21165	+	12.9621i	−0.209537	+	0.644889i
$405$		0			0
$406$			0.224719i			0.0111526i
$407$	4.86220	−	21.8777i	0.241010	−	1.08444i
$408$		0			0
$409$	−2.14096	+	2.94678i	−0.105864	+	0.145709i	−0.858662	−	0.512543i	$-0.828704\pi$
$409$	−2.14096	+	2.94678i	−0.105864	+	0.145709i	0.752798	+	0.658252i	$0.228704\pi$
$410$	5.80815	+	1.88718i	0.286844	+	0.0932013i
$411$		0			0
$412$	15.9712	−	11.6038i	0.786845	−	0.571677i
$413$	−6.67016	+	4.84615i	−0.328217	+	0.238464i
$414$		0			0
$415$	3.29280	+	1.06990i	0.161637	+	0.0525191i
$416$	−1.56843	+	2.15876i	−0.0768985	+	0.105842i
$417$		0			0
$418$	2.65249	+	27.6992i	0.129737	+	1.35481i
$419$		−	10.5299i		−	0.514420i	−0.966356	−	0.257210i	$-0.917197\pi$
$419$		−	10.5299i		−	0.514420i	0.966356	−	0.257210i	$-0.0828032\pi$
$420$		0			0
$421$	0.659475	−	2.02965i	0.0321408	−	0.0989193i	−0.933699	−	0.358059i	$-0.883439\pi$
$421$	0.659475	−	2.02965i	0.0321408	−	0.0989193i	0.965840	+	0.259139i	$0.0834388\pi$
$422$	−15.8965	+	5.16510i	−0.773831	+	0.251433i
$423$		0			0
$424$	4.30050	+	5.91913i	0.208851	+	0.287458i
$425$	1.63909	+	5.04461i	0.0795077	+	0.244700i
$426$		0			0
$427$	−9.12316	−	6.62836i	−0.441501	−	0.320769i
$428$	5.53498			0.267544
$429$		0			0
$430$	1.23422			0.0595193
$431$	10.6178	+	7.71425i	0.511440	+	0.371583i	0.813369	−	0.581748i	$-0.197631\pi$
$431$	10.6178	+	7.71425i	0.511440	+	0.371583i	−0.301930	+	0.953330i	$0.597631\pi$
$432$		0			0
$433$	7.84190	+	24.1349i	0.376857	+	1.15985i	0.942217	+	0.335003i	$0.108737\pi$
$433$	7.84190	+	24.1349i	0.376857	+	1.15985i	−0.565359	+	0.824845i	$0.691263\pi$
$434$	3.12221	+	4.29736i	0.149871	+	0.206280i
$435$		0			0
$436$	10.1474	−	3.29709i	0.485972	−	0.157902i
$437$	4.28012	−	13.1728i	0.204746	−	0.630143i
$438$		0			0
$439$			4.32343i			0.206346i	0.994663	+	0.103173i	$0.0328995\pi$
$439$			4.32343i			0.206346i	−0.994663	+	0.103173i	$0.967100\pi$
$440$	−3.23763	−	0.719545i	−0.154348	−	0.0343029i
$441$		0			0
$442$	8.31928	−	11.4505i	0.395708	−	0.544645i
$443$	−2.10108	−	0.682681i	−0.0998251	−	0.0324352i	0.258679	−	0.965963i	$-0.416713\pi$
$443$	−2.10108	−	0.682681i	−0.0998251	−	0.0324352i	−0.358504	+	0.933528i	$0.616713\pi$
$444$		0			0
$445$	−0.481345	+	0.349717i	−0.0228179	+	0.0165782i
$446$	−9.62525	+	6.99316i	−0.455769	+	0.331136i
$447$		0			0
$448$	0.756962	+	0.245952i	0.0357631	+	0.0116201i
$449$	5.27979	−	7.26701i	0.249169	−	0.342951i	−0.666051	−	0.745906i	$-0.732017\pi$
$449$	5.27979	−	7.26701i	0.249169	−	0.342951i	0.915220	+	0.402955i	$0.132017\pi$
$450$		0			0
$451$	15.1770	−	13.4133i	0.714655	−	0.631607i
$452$		−	16.9034i		−	0.795070i
$453$		0			0
$454$	−5.53094	+	17.0225i	−0.259580	+	0.798904i
$455$	2.01985	−	0.656290i	0.0946921	−	0.0307673i
$456$		0			0
$457$	13.9828	+	19.2457i	0.654087	+	0.900274i	0.999268	−	0.0382622i	$-0.0121822\pi$
$457$	13.9828	+	19.2457i	0.654087	+	0.900274i	−0.345180	+	0.938536i	$0.612182\pi$
$458$	3.87841	+	11.9365i	0.181226	+	0.557758i
$459$		0			0
$460$	1.33560	+	0.970374i	0.0622729	+	0.0452439i
$461$	15.6097			0.727018			0.363509	−	0.931591i	$-0.381579\pi$
$461$	15.6097			0.727018			0.363509	+	0.931591i	$0.381579\pi$
$462$		0			0
$463$	2.15079			0.0999556			0.0499778	−	0.998750i	$-0.484085\pi$
$463$	2.15079			0.0999556			0.0499778	+	0.998750i	$0.484085\pi$
$464$	−0.228417	−	0.165955i	−0.0106040	−	0.00770426i
$465$		0			0
$466$	0.505071	+	1.55445i	0.0233970	+	0.0720085i
$467$	7.46324	+	10.2723i	0.345358	+	0.475344i	0.945997	−	0.324176i	$-0.105087\pi$
$467$	7.46324	+	10.2723i	0.345358	+	0.475344i	−0.600639	+	0.799520i	$0.705087\pi$
$468$		0			0
$469$	7.20605	−	2.34139i	0.332745	−	0.108115i
$470$	0.692866	−	2.13242i	0.0319595	−	0.0983612i
$471$		0			0
$472$		−	10.3588i		−	0.476804i
$473$	2.07942	−	3.52594i	0.0956120	−	0.162123i
$474$		0			0
$475$	−4.93142	+	6.78751i	−0.226269	+	0.311432i
$476$	−4.01509	−	1.30458i	−0.184031	−	0.0597954i
$477$		0			0
$478$	−20.6682	+	15.0163i	−0.945339	+	0.686829i
$479$	−5.61819	+	4.08185i	−0.256702	+	0.186505i	−0.708692	−	0.705518i	$-0.750714\pi$
$479$	−5.61819	+	4.08185i	−0.256702	+	0.186505i	0.451990	+	0.892023i	$0.350714\pi$
$480$		0			0
$481$	−17.1485	−	5.57189i	−0.781906	−	0.254057i
$482$	−1.59667	+	2.19762i	−0.0727262	+	0.100099i
$483$		0			0
$484$	−7.51040	+	8.03703i	−0.341382	+	0.365320i
$485$		−	3.31434i		−	0.150496i
$486$		0			0
$487$	−6.54467	+	20.1424i	−0.296567	+	0.912740i	0.686123	+	0.727485i	$0.259311\pi$
$487$	−6.54467	+	20.1424i	−0.296567	+	0.912740i	−0.982690	+	0.185255i	$0.940689\pi$
$488$	13.4749	−	4.37827i	0.609981	−	0.198195i
$489$		0			0
$490$	3.74214	+	5.15062i	0.169053	+	0.232681i
$491$	5.13344	+	15.7991i	0.231669	+	0.713003i	0.997546	+	0.0700161i	$0.0223051\pi$
$491$	5.13344	+	15.7991i	0.231669	+	0.713003i	−0.765877	+	0.642987i	$0.777695\pi$
$492$		0			0
$493$	1.21157	+	0.880261i	0.0545666	+	0.0396449i
$494$	22.3871			1.00725
$495$		0			0
$496$	−6.67385			−0.299665
$497$	−6.39574	−	4.64678i	−0.286888	−	0.208437i
$498$		0			0
$499$	−12.9860	−	39.9667i	−0.581332	−	1.78916i	−0.613526	−	0.789674i	$-0.710250\pi$
$499$	−12.9860	−	39.9667i	−0.581332	−	1.78916i	0.0321945	−	0.999482i	$-0.489750\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$		0			0
$502$	21.2427	−	6.90217i	0.948108	−	0.308059i
$503$	3.62478	−	11.1559i	0.161621	−	0.497418i	−0.837151	−	0.546973i	$-0.815780\pi$
$503$	3.62478	−	11.1559i	0.161621	−	0.497418i	0.998771	+	0.0495547i	$0.0157802\pi$
$504$		0			0
$505$			13.6292i			0.606490i
$506$	5.02242	−	2.18068i	0.223274	−	0.0969433i
$507$		0			0
$508$	−0.650566	+	0.895428i	−0.0288642	+	0.0397282i
$509$	−5.74740	−	1.86745i	−0.254749	−	0.0827730i	0.178858	−	0.983875i	$-0.442760\pi$
$509$	−5.74740	−	1.86745i	−0.254749	−	0.0827730i	−0.433608	+	0.901102i	$0.642760\pi$
$510$		0			0
$511$	−7.96717	+	5.78849i	−0.352447	+	0.256068i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	−25.4719	−	8.27631i	−1.12352	−	0.365052i
$515$	11.6038	−	15.9712i	0.511323	−	0.703776i
$516$		0			0
$517$	−4.92459	−	5.57212i	−0.216583	−	0.245061i
$518$			5.37827i			0.236307i
$519$		0			0
$520$	−0.824571	+	2.53777i	−0.0361598	+	0.111289i
$521$	28.2903	−	9.19208i	1.23942	−	0.402712i	0.385302	−	0.922791i	$-0.374097\pi$
$521$	28.2903	−	9.19208i	1.23942	−	0.402712i	0.854119	+	0.520078i	$0.174097\pi$
$522$		0			0
$523$	18.6570	+	25.6791i	0.815813	+	1.12287i	0.990400	+	0.138229i	$0.0441410\pi$
$523$	18.6570	+	25.6791i	0.815813	+	1.12287i	−0.174587	+	0.984642i	$0.555859\pi$
$524$	−0.374921	−	1.15389i	−0.0163785	−	0.0504078i
$525$		0			0
$526$	17.0958	+	12.4208i	0.745413	+	0.541574i
$527$	35.3995			1.54203
$528$		0			0
$529$	20.2745			0.881502
$530$	5.91913	+	4.30050i	0.257111	+	0.186802i
$531$		0			0
$532$	−2.06349	−	6.35078i	−0.0894637	−	0.275341i
$533$	−9.57846	−	13.1836i	−0.414889	−	0.571046i
$534$		0			0
$535$	5.26408	−	1.71040i	0.227586	−	0.0739472i
$536$	−2.94175	+	9.05378i	−0.127064	+	0.391064i
$537$		0			0
$538$			9.59598i			0.413712i
$539$	21.0192	−	2.01281i	0.905361	−	0.0866978i
$540$		0			0
$541$	4.15677	−	5.72131i	0.178714	−	0.245978i	−0.710257	−	0.703943i	$-0.751421\pi$
$541$	4.15677	−	5.72131i	0.178714	−	0.245978i	0.888971	+	0.457964i	$0.151421\pi$
$542$	8.85526	+	2.87725i	0.380366	+	0.123588i
$543$		0			0
$544$	4.29120	−	3.11774i	0.183984	−	0.133672i
$545$	8.63188	−	6.27143i	0.369749	−	0.268639i
$546$		0			0
$547$	13.8905	+	4.51329i	0.593914	+	0.192974i	0.590524	−	0.807020i	$-0.298921\pi$
$547$	13.8905	+	4.51329i	0.593914	+	0.192974i	0.00338990	+	0.999994i	$0.498921\pi$
$548$	5.47420	−	7.53459i	0.233846	−	0.321862i
$549$		0			0
$550$	−3.30152	+	0.316156i	−0.140777	+	0.0134809i
$551$			2.36878i			0.100913i
$552$		0			0
$553$	−2.28627	+	7.03640i	−0.0972219	+	0.299218i
$554$	4.32268	−	1.40452i	0.183653	−	0.0596725i
$555$		0			0
$556$	1.63027	+	2.24387i	0.0691387	+	0.0951613i
$557$	4.06437	+	12.5088i	0.172213	+	0.530016i	0.999495	−	0.0317698i	$-0.0101144\pi$
$557$	4.06437	+	12.5088i	0.172213	+	0.530016i	−0.827282	+	0.561786i	$0.810114\pi$
$558$		0			0
$559$	−2.66437	−	1.93578i	−0.112691	−	0.0818748i
$560$	0.795917			0.0336336
$561$		0			0
$562$	30.1557			1.27204
$563$	24.6828	+	17.9331i	1.04025	+	0.755789i	0.970335	−	0.241764i	$-0.0777259\pi$
$563$	24.6828	+	17.9331i	1.04025	+	0.755789i	0.0699190	+	0.997553i	$0.477726\pi$
$564$		0			0
$565$	−5.22345	−	16.0761i	−0.219752	−	0.676327i
$566$	−9.26883	−	12.7575i	−0.389598	−	0.536236i
$567$		0			0
$568$	9.44653	−	3.06936i	0.396367	−	0.128788i
$569$	−3.61169	+	11.1156i	−0.151410	+	0.465992i	−0.997779	−	0.0666041i	$-0.978784\pi$
$569$	−3.61169	+	11.1156i	−0.151410	+	0.465992i	0.846369	+	0.532596i	$0.178784\pi$
$570$		0			0
$571$		−	12.8664i		−	0.538441i	−0.963079	−	0.269221i	$-0.913234\pi$
$571$		−	12.8664i		−	0.538441i	0.963079	−	0.269221i	$-0.0867661\pi$
$572$	5.86070	+	6.63131i	0.245048	+	0.277269i
$573$		0			0
$574$	−2.85705	+	3.93239i	−0.119251	+	0.164135i
$575$	1.57010	+	0.510156i	0.0654776	+	0.0212750i
$576$		0			0
$577$	−29.8443	+	21.6832i	−1.24244	+	0.902683i	−0.997758	−	0.0669218i	$-0.978682\pi$
$577$	−29.8443	+	21.6832i	−1.24244	+	0.902683i	−0.244678	+	0.969604i	$0.578682\pi$
$578$	−9.00818	+	6.54482i	−0.374691	+	0.272229i
$579$		0			0
$580$	−0.268521	−	0.0872476i	−0.0111497	−	0.00362276i
$581$	−1.61974	+	2.22938i	−0.0671981	+	0.0924903i
$582$		0			0
$583$	22.2584	−	9.66435i	0.921847	−	0.400257i
$584$		−	12.3731i		−	0.512003i
$585$		0			0
$586$	1.72886	−	5.32089i	0.0714186	−	0.219804i
$587$	6.13283	−	1.99268i	0.253129	−	0.0822466i	−0.179704	−	0.983721i	$-0.557514\pi$
$587$	6.13283	−	1.99268i	0.253129	−	0.0822466i	0.432833	+	0.901474i	$0.357514\pi$
$588$		0			0
$589$	32.9115	+	45.2988i	1.35609	+	1.86650i
$590$	−3.20106	−	9.85184i	−0.131785	−	0.405594i
$591$		0			0
$592$	−5.46679	−	3.97186i	−0.224684	−	0.163242i
$593$	−35.3094			−1.44998			−0.724992	−	0.688757i	$-0.758157\pi$
$593$	−35.3094			−1.44998			−0.724992	+	0.688757i	$0.758157\pi$
$594$		0			0
$595$	−4.22171			−0.173073
$596$	−4.68800	−	3.40603i	−0.192028	−	0.139516i
$597$		0			0
$598$	−1.36128	−	4.18960i	−0.0556670	−	0.171325i
$599$	−14.3414	−	19.7393i	−0.585975	−	0.806526i	0.408359	−	0.912821i	$-0.366101\pi$
$599$	−14.3414	−	19.7393i	−0.585975	−	0.806526i	−0.994335	+	0.106295i	$0.966101\pi$
$600$		0			0
$601$	−18.1414	+	5.89450i	−0.740004	+	0.240442i	−0.654674	−	0.755911i	$-0.727194\pi$
$601$	−18.1414	+	5.89450i	−0.740004	+	0.240442i	−0.0853293	+	0.996353i	$0.527194\pi$
$602$	−0.303558	+	0.934256i	−0.0123721	+	0.0380774i
$603$		0			0
$604$			4.09662i			0.166689i
$605$	−4.65924	+	9.96451i	−0.189425	+	0.405115i
$606$		0			0
$607$	1.92389	−	2.64801i	0.0780884	−	0.107479i	−0.768186	−	0.640227i	$-0.778840\pi$
$607$	1.92389	−	2.64801i	0.0780884	−	0.107479i	0.846274	+	0.532747i	$0.178840\pi$
$608$	7.97920	+	2.59260i	0.323599	+	0.105144i
$609$		0			0
$610$	11.4625	−	8.32796i	0.464101	−	0.337189i
$611$	−4.84027	+	3.51667i	−0.195817	+	0.142269i
$612$		0			0
$613$	34.3620	+	11.1649i	1.38787	+	0.450946i	0.905248	−	0.424884i	$-0.139685\pi$
$613$	34.3620	+	11.1649i	1.38787	+	0.450946i	0.482620	+	0.875830i	$0.339685\pi$
$614$	−16.7063	+	22.9943i	−0.674212	+	0.927973i
$615$		0			0
$616$	1.34097	−	2.27379i	0.0540292	−	0.0916136i
$617$		−	18.8061i		−	0.757103i	−0.925580	−	0.378552i	$-0.876422\pi$
$617$		−	18.8061i		−	0.757103i	0.925580	−	0.378552i	$-0.123578\pi$
$618$		0			0
$619$	−8.95166	+	27.5504i	−0.359798	+	1.10734i	0.593378	+	0.804924i	$0.297794\pi$
$619$	−8.95166	+	27.5504i	−0.359798	+	1.10734i	−0.953175	+	0.302419i	$0.902206\pi$
$620$	−6.34720	+	2.06233i	−0.254910	+	0.0828252i
$621$		0			0
$622$	−8.98277	−	12.3637i	−0.360176	−	0.495740i
$623$	−0.146335	−	0.450373i	−0.00586279	−	0.0180438i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	19.6272			0.784460
$627$		0			0
$628$	0.312064			0.0124527
$629$	28.9970	+	21.0676i	1.15619	+	0.840020i
$630$		0			0
$631$	−0.900444	−	2.77128i	−0.0358461	−	0.110323i	0.931532	−	0.363658i	$-0.118472\pi$
$631$	−0.900444	−	2.77128i	−0.0358461	−	0.110323i	−0.967379	+	0.253335i	$0.918472\pi$
$632$	−5.46381	−	7.52029i	−0.217339	−	0.299141i
$633$		0			0
$634$	24.1018	−	7.83115i	0.957205	−	0.311015i
$635$	−0.342023	+	1.05264i	−0.0135728	+	0.0417727i
$636$		0			0
$637$		−	16.9882i		−	0.673097i
$638$	−0.701657	+	0.620119i	−0.0277789	+	0.0245507i
$639$		0			0
$640$	−0.587785	+	0.809017i	−0.0232343	+	0.0319792i
$641$	−43.7396	−	14.2119i	−1.72761	−	0.561335i	−0.734510	−	0.678598i	$-0.762588\pi$
$641$	−43.7396	−	14.2119i	−1.72761	−	0.561335i	−0.993101	+	0.117263i	$0.962588\pi$
$642$		0			0
$643$	−16.1488	+	11.7328i	−0.636845	+	0.462695i	−0.858765	−	0.512370i	$-0.828768\pi$
$643$	−16.1488	+	11.7328i	−0.636845	+	0.462695i	0.221920	+	0.975065i	$0.428768\pi$
$644$	−1.06303	+	0.772337i	−0.0418893	+	0.0304343i
$645$		0			0
$646$	−42.3234	−	13.7517i	−1.66519	−	0.541054i
$647$	−17.6010	+	24.2257i	−0.691966	+	0.952410i	0.308033	+	0.951376i	$0.400329\pi$
$647$	−17.6010	+	24.2257i	−0.691966	+	0.952410i	−0.999999	+	0.00103445i	$0.999671\pi$
$648$		0			0
$649$	−33.5381	−	7.45364i	−1.31648	−	0.292581i
$650$			2.66837i			0.104662i
$651$		0			0
$652$	−2.59823	+	7.99653i	−0.101755	+	0.313168i
$653$	25.8777	−	8.40816i	1.01267	−	0.329037i	0.244753	−	0.969585i	$-0.421293\pi$
$653$	25.8777	−	8.40816i	1.01267	−	0.329037i	0.767918	+	0.640549i	$0.221293\pi$
$654$		0			0
$655$	−0.713142	−	0.981556i	−0.0278648	−	0.0383526i
$656$	−1.88718	−	5.80815i	−0.0736821	−	0.226770i
$657$		0			0
$658$	1.44375	+	1.04895i	0.0562832	+	0.0408922i
$659$	−13.6818			−0.532968			−0.266484	−	0.963839i	$-0.585862\pi$
$659$	−13.6818			−0.532968			−0.266484	+	0.963839i	$0.585862\pi$
$660$		0			0
$661$	−20.0009			−0.777947			−0.388973	−	0.921249i	$-0.627170\pi$
$661$	−20.0009			−0.777947			−0.388973	+	0.921249i	$0.627170\pi$
$662$	17.9991	+	13.0771i	0.699554	+	0.508256i
$663$		0			0
$664$	−1.06990	−	3.29280i	−0.0415200	−	0.127785i
$665$	−3.92500	−	5.40229i	−0.152205	−	0.209492i
$666$		0			0
$667$	0.443300	−	0.144037i	0.0171647	−	0.00557713i
$668$	−7.65145	+	23.5487i	−0.296044	+	0.911128i
$669$		0			0
$670$			9.51970i			0.367778i
$671$	−4.47941	−	46.7772i	−0.172926	−	1.80581i
$672$		0			0
$673$	28.1261	−	38.7123i	1.08418	−	1.49225i	0.229350	−	0.973344i	$-0.426340\pi$
$673$	28.1261	−	38.7123i	1.08418	−	1.49225i	0.854832	−	0.518904i	$-0.173660\pi$
$674$	19.9218	+	6.47299i	0.767360	+	0.249330i
$675$		0			0
$676$	−4.75687	+	3.45607i	−0.182956	+	0.132926i
$677$	−28.5118	+	20.7150i	−1.09580	+	0.796143i	−0.980369	−	0.197172i	$-0.936824\pi$
$677$	−28.5118	+	20.7150i	−1.09580	+	0.796143i	−0.115429	+	0.993316i	$0.536824\pi$
$678$		0			0
$679$	2.50883	+	0.815168i	0.0962800	+	0.0312833i
$680$	3.11774	−	4.29120i	0.119560	−	0.164560i
$681$		0			0
$682$	−4.80213	+	21.6075i	−0.183883	+	0.827392i
$683$		−	11.3841i		−	0.435601i	−0.975993	−	0.217800i	$-0.930112\pi$
$683$		−	11.3841i		−	0.435601i	0.975993	−	0.217800i	$-0.0698882\pi$
$684$		0			0
$685$	2.87796	−	8.85745i	0.109961	−	0.338426i
$686$	−10.1179	+	3.28752i	−0.386305	+	0.125518i
$687$		0			0
$688$	−0.725455	−	0.998503i	−0.0276577	−	0.0380676i
$689$	−6.03293	−	18.5675i	−0.229836	−	0.707364i
$690$		0			0
$691$	−5.57808	−	4.05271i	−0.212200	−	0.154172i	0.476608	−	0.879116i	$-0.341866\pi$
$691$	−5.57808	−	4.05271i	−0.212200	−	0.154172i	−0.688809	+	0.724943i	$0.741866\pi$
$692$	−14.4351			−0.548742
$693$		0			0
$694$	−2.66872			−0.101303
$695$	2.24387	+	1.63027i	0.0851149	+	0.0618396i
$696$		0			0
$697$	10.0100	+	30.8077i	0.379157	+	1.16692i
$698$	−18.4136	−	25.3441i	−0.696963	−	0.959288i
$699$		0			0
$700$	0.756962	−	0.245952i	0.0286105	−	0.00929610i
$701$	4.24417	−	13.0622i	0.160300	−	0.493353i	−0.838359	−	0.545118i	$-0.816485\pi$
$701$	4.24417	−	13.0622i	0.160300	−	0.493353i	0.998659	+	0.0517650i	$0.0164847\pi$
$702$		0			0
$703$			56.6928i			2.13821i
$704$	1.32091	+	3.04224i	0.0497836	+	0.114659i
$705$		0			0
$706$	−11.1009	+	15.2791i	−0.417790	+	0.575038i
$707$	−10.3168	−	3.35212i	−0.388002	−	0.126069i
$708$		0			0
$709$	8.35306	−	6.06886i	0.313706	−	0.227921i	−0.419779	−	0.907626i	$-0.637892\pi$
$709$	8.35306	−	6.06886i	0.313706	−	0.227921i	0.733485	+	0.679706i	$0.237892\pi$
$710$	8.03570	−	5.83827i	0.301574	−	0.219107i
$711$		0			0
$712$	0.565855	+	0.183857i	0.0212063	+	0.00689034i
$713$	6.47612	−	8.91362i	0.242533	−	0.333818i
$714$		0			0
$715$	7.62304	+	4.49569i	0.285086	+	0.168129i
$716$		−	2.05812i		−	0.0769156i
$717$		0			0
$718$	−2.91047	+	8.95750i	−0.108618	+	0.334291i
$719$	9.01798	−	2.93012i	0.336314	−	0.109275i	−0.135991	−	0.990710i	$-0.543422\pi$
$719$	9.01798	−	2.93012i	0.336314	−	0.109275i	0.472305	+	0.881435i	$0.343422\pi$
$720$		0			0
$721$	9.23563	+	12.7118i	0.343953	+	0.473411i
$722$	−15.8801	−	48.8740i	−0.590997	−	1.81890i
$723$		0			0
$724$	9.49391	+	6.89773i	0.352838	+	0.256352i
$725$	−0.282339			−0.0104858
$726$		0			0
$727$	30.1669			1.11883			0.559413	−	0.828889i	$-0.311026\pi$
$727$	30.1669			1.11883			0.559413	+	0.828889i	$0.311026\pi$
$728$	−1.71819	−	1.24834i	−0.0636803	−	0.0462665i
$729$		0			0
$730$	−3.82350	−	11.7675i	−0.141514	−	0.435536i
$731$	3.84797	+	5.29628i	0.142322	+	0.195890i
$732$		0			0
$733$	−35.1232	+	11.4122i	−1.29730	+	0.421520i	−0.874643	−	0.484768i	$-0.838904\pi$
$733$	−35.1232	+	11.4122i	−1.29730	+	0.421520i	−0.422662	+	0.906287i	$0.638904\pi$
$734$	−1.31882	+	4.05891i	−0.0486785	+	0.149817i
$735$		0			0
$736$		−	1.65090i		−	0.0608529i
$737$	27.1961	+	16.0389i	1.00178	+	0.590800i
$738$		0			0
$739$	14.2581	−	19.6246i	0.524493	−	0.721903i	−0.461785	−	0.886992i	$-0.652791\pi$
$739$	14.2581	−	19.6246i	0.524493	−	0.721903i	0.986279	+	0.165088i	$0.0527910\pi$
$740$	−6.42660	−	2.08813i	−0.236246	−	0.0767611i
$741$		0			0
$742$	−4.71113	+	3.42284i	−0.172951	+	0.125656i
$743$	−1.20779	+	0.877512i	−0.0443096	+	0.0321928i	−0.609720	−	0.792617i	$-0.708718\pi$
$743$	−1.20779	+	0.877512i	−0.0443096	+	0.0321928i	0.565410	+	0.824810i	$0.308718\pi$
$744$		0			0
$745$	−5.51107	−	1.79066i	−0.201910	−	0.0656046i
$746$	−9.95014	+	13.6952i	−0.364301	+	0.501417i
$747$		0			0
$748$	−7.00638	−	16.1367i	−0.256179	−	0.590016i
$749$			4.40539i			0.160969i
$750$		0			0
$751$	8.73522	−	26.8842i	0.318753	−	0.981020i	−0.655429	−	0.755256i	$-0.727512\pi$
$751$	8.73522	−	26.8842i	0.318753	−	0.981020i	0.974182	−	0.225763i	$-0.0724876\pi$
$752$	−2.13242	+	0.692866i	−0.0777614	+	0.0252662i
$753$		0			0
$754$	0.442829	+	0.609501i	0.0161269	+	0.0221967i
$755$	1.26592	+	3.89611i	0.0460717	+	0.141794i
$756$		0			0
$757$	23.1578	+	16.8251i	0.841685	+	0.611520i	0.922841	−	0.385181i	$-0.125861\pi$
$757$	23.1578	+	16.8251i	0.841685	+	0.611520i	−0.0811557	+	0.996701i	$0.525861\pi$
$758$	−11.2664			−0.409215
$759$		0			0
$760$	8.38982			0.304331
$761$	−42.5349	−	30.9034i	−1.54189	−	1.12025i	−0.949137	−	0.314865i	$-0.898041\pi$
$761$	−42.5349	−	30.9034i	−1.54189	−	1.12025i	−0.592753	−	0.805384i	$-0.701959\pi$
$762$		0			0
$763$	2.62421	+	8.07648i	0.0950026	+	0.292388i
$764$	−10.7354	−	14.7760i	−0.388394	−	0.534579i
$765$		0			0
$766$	−15.5615	+	5.05625i	−0.562261	+	0.182690i
$767$	−8.54160	+	26.2883i	−0.308419	+	0.949216i
$768$		0			0
$769$		−	35.7351i		−	1.28864i	−0.764756	−	0.644320i	$-0.777141\pi$
$769$		−	35.7351i		−	1.28864i	0.764756	−	0.644320i	$-0.222859\pi$
$770$	0.572697	−	2.57688i	0.0206386	−	0.0928645i
$771$		0			0
$772$	7.52512	−	10.3574i	0.270835	−	0.372772i
$773$	12.1513	+	3.94821i	0.437054	+	0.142007i	0.519276	−	0.854607i	$-0.326202\pi$
$773$	12.1513	+	3.94821i	0.437054	+	0.142007i	−0.0822222	+	0.996614i	$0.526202\pi$
$774$		0			0
$775$	−5.39925	+	3.92279i	−0.193947	+	0.140911i
$776$	−2.68136	+	1.94812i	−0.0962551	+	0.0699334i
$777$		0			0
$778$	−1.49827	−	0.486817i	−0.0537156	−	0.0174532i
$779$	−30.1164	+	41.4517i	−1.07903	+	1.48516i
$780$		0			0
$781$	−3.14027	−	32.7929i	−0.112368	−	1.17342i
$782$			8.75672i			0.313140i
$783$		0			0
$784$	1.96736	−	6.05492i	0.0702629	−	0.216247i
$785$	0.296791	−	0.0964332i	0.0105929	−	0.00344185i
$786$		0			0
$787$	−24.4315	−	33.6270i	−0.870888	−	1.19867i	−0.978862	−	0.204521i	$-0.934436\pi$
$787$	−24.4315	−	33.6270i	−0.870888	−	1.19867i	0.107974	−	0.994154i	$-0.465564\pi$
$788$	−2.60212	−	8.00851i	−0.0926968	−	0.285291i
$789$		0			0
$790$	−7.52029	−	5.46381i	−0.267560	−	0.194394i
$791$	13.4537			0.478359
$792$		0			0
$793$	−37.8064			−1.34255
$794$	17.1505	+	12.4606i	0.608649	+	0.442209i
$795$		0			0
$796$	−5.53638	−	17.0392i	−0.196232	−	0.603939i
$797$	18.3221	+	25.2182i	0.649002	+	0.893275i	0.999055	−	0.0434548i	$-0.0138364\pi$
$797$	18.3221	+	25.2182i	0.649002	+	0.893275i	−0.350053	+	0.936730i	$0.613836\pi$
$798$		0			0
$799$	11.3108	−	3.67511i	0.400148	−	0.130016i
$800$	−0.309017	+	0.951057i	−0.0109254	+	0.0336249i
$801$		0			0
$802$			20.0027i			0.706320i
$803$	−40.0596	−	8.90300i	−1.41367	−	0.314180i
$804$		0			0
$805$	−0.772337	+	1.06303i	−0.0272213	+	0.0374669i
$806$	16.9367	+	5.50306i	0.596569	+	0.193837i
$807$		0			0
$808$	11.0262	−	8.01103i	0.387902	−	0.281827i
$809$	−14.0877	+	10.2353i	−0.495298	+	0.359855i	−0.807218	−	0.590253i	$-0.799028\pi$
$809$	−14.0877	+	10.2353i	−0.495298	+	0.359855i	0.311920	+	0.950108i	$0.399028\pi$
$810$		0			0
$811$	−27.8930	−	9.06300i	−0.979457	−	0.318245i	−0.224829	−	0.974398i	$-0.572182\pi$
$811$	−27.8930	−	9.06300i	−0.979457	−	0.318245i	−0.754628	+	0.656153i	$0.772182\pi$
$812$	0.132086	−	0.181801i	0.00463532	−	0.00637997i
$813$		0			0
$814$	−16.7930	+	14.8415i	−0.588594	+	0.520195i
$815$			8.40805i			0.294521i
$816$		0			0
$817$	−3.19983	+	9.84807i	−0.111948	+	0.344540i
$818$	3.46415	−	1.12557i	0.121121	−	0.0393546i
$819$		0			0
$820$	−3.58963	−	4.94071i	−0.125355	−	0.172537i
$821$	5.82290	+	17.9210i	0.203221	+	0.625449i	0.999782	+	0.0208909i	$0.00665026\pi$
$821$	5.82290	+	17.9210i	0.203221	+	0.625449i	−0.796561	+	0.604558i	$0.793350\pi$
$822$		0			0
$823$	5.43261	+	3.94702i	0.189369	+	0.137585i	0.678430	−	0.734665i	$-0.262661\pi$
$823$	5.43261	+	3.94702i	0.189369	+	0.137585i	−0.489061	+	0.872249i	$0.662661\pi$
$824$	−19.7415			−0.687728
$825$		0			0
$826$	8.24477			0.286872
$827$	−35.5333	−	25.8165i	−1.23561	−	0.897726i	−0.238316	−	0.971188i	$-0.576595\pi$
$827$	−35.5333	−	25.8165i	−1.23561	−	0.897726i	−0.997298	+	0.0734612i	$0.976595\pi$
$828$		0			0
$829$	−2.61430	−	8.04598i	−0.0907983	−	0.279449i	0.895338	−	0.445388i	$-0.146934\pi$
$829$	−2.61430	−	8.04598i	−0.0907983	−	0.279449i	−0.986136	+	0.165940i	$0.946934\pi$
$830$	−2.03506	−	2.80102i	−0.0706380	−	0.0972249i
$831$		0			0
$832$	2.53777	−	0.824571i	0.0879813	−	0.0285869i
$833$	−10.4353	+	32.1166i	−0.361562	+	1.11277i
$834$		0			0
$835$			24.7606i			0.856876i
$836$	14.1353	−	23.9682i	0.488878	−	0.828958i
$837$		0			0
$838$	−6.18933	+	8.51888i	−0.213807	+	0.294280i
$839$	26.1770	+	8.50542i	0.903730	+	0.293640i	0.723776	−	0.690035i	$-0.242405\pi$
$839$	26.1770	+	8.50542i	0.903730	+	0.293640i	0.179954	+	0.983675i	$0.442405\pi$
$840$		0			0
$841$	23.3970	−	16.9989i	0.806793	−	0.586170i
$842$	−1.72653	+	1.25440i	−0.0595001	+	0.0432293i
$843$		0			0
$844$	15.8965	+	5.16510i	0.547181	+	0.177790i
$845$	−3.45607	+	4.75687i	−0.118892	+	0.163641i
$846$		0			0
$847$	−6.39681	−	5.97766i	−0.219797	−	0.205395i
$848$		−	7.31645i		−	0.251248i
$849$		0			0
$850$	1.63909	−	5.04461i	0.0562204	−	0.173029i
$851$	10.6097	−	3.44729i	0.363694	−	0.118171i
$852$		0			0
$853$	−28.1351	−	38.7246i	−0.963327	−	1.32591i	−0.945347	−	0.326067i	$-0.894276\pi$
$853$	−28.1351	−	38.7246i	−0.963327	−	1.32591i	−0.0179801	−	0.999838i	$-0.505724\pi$
$854$	3.48474	+	10.7249i	0.119245	+	0.366999i
$855$		0			0
$856$	−4.47790	−	3.25338i	−0.153051	−	0.111198i
$857$	−45.7485			−1.56274			−0.781370	−	0.624069i	$-0.785479\pi$
$857$	−45.7485			−1.56274			−0.781370	+	0.624069i	$0.785479\pi$
$858$		0			0
$859$	30.8386			1.05220			0.526100	−	0.850422i	$-0.323654\pi$
$859$	30.8386			1.05220			0.526100	+	0.850422i	$0.323654\pi$
$860$	−0.998503	−	0.725455i	−0.0340487	−	0.0247378i
$861$		0			0
$862$	−4.05562	−	12.4819i	−0.138135	−	0.425136i
$863$	−2.30109	−	3.16718i	−0.0783299	−	0.107812i	0.768054	−	0.640385i	$-0.221225\pi$
$863$	−2.30109	−	3.16718i	−0.0783299	−	0.107812i	−0.846384	+	0.532573i	$0.821225\pi$
$864$		0			0
$865$	−13.7286	+	4.46070i	−0.466788	+	0.151669i
$866$	7.84190	−	24.1349i	0.266478	−	0.820136i
$867$		0			0
$868$		−	5.31182i		−	0.180295i
$869$	−28.2794	+	12.2786i	−0.959312	+	0.416523i
$870$		0			0
$871$	14.9310	−	20.5507i	0.505916	−	0.696334i
$872$	−10.1474	−	3.29709i	−0.343634	−	0.111653i
$873$		0			0
$874$	−11.2055	+	8.14126i	−0.379031	+	0.275382i
$875$	0.643910	−	0.467828i	0.0217681	−	0.0158155i
$876$		0			0
$877$	22.9963	+	7.47196i	0.776531	+	0.252310i	0.670358	−	0.742038i	$-0.266140\pi$
$877$	22.9963	+	7.47196i	0.776531	+	0.252310i	0.106173	+	0.994348i	$0.466140\pi$
$878$	2.54125	−	3.49773i	0.0857630	−	0.118043i
$879$		0			0
$880$	2.19636	+	2.48516i	0.0740393	+	0.0837746i
$881$		−	12.2977i		−	0.414320i	−0.978307	−	0.207160i	$-0.933578\pi$
$881$		−	12.2977i		−	0.414320i	0.978307	−	0.207160i	$-0.0664221\pi$
$882$		0			0
$883$	2.63652	−	8.11437i	0.0887259	−	0.273070i	−0.896842	−	0.442351i	$-0.854144\pi$
$883$	2.63652	−	8.11437i	0.0887259	−	0.273070i	0.985568	+	0.169281i	$0.0541445\pi$
$884$	−13.4609	+	4.37370i	−0.452738	+	0.147104i
$885$		0			0
$886$	1.29854	+	1.78728i	0.0436252	+	0.0600449i
$887$	15.3510	+	47.2454i	0.515435	+	1.58635i	0.782489	+	0.622665i	$0.213950\pi$
$887$	15.3510	+	47.2454i	0.515435	+	1.58635i	−0.267053	+	0.963682i	$0.586050\pi$
$888$		0			0
$889$	−0.712686	−	0.517796i	−0.0239027	−	0.0173663i
$890$	0.594975			0.0199436
$891$		0			0
$892$	11.8975			0.398357
$893$	15.2187	+	11.0570i	0.509274	+	0.370009i
$894$		0			0
$895$	−0.635994	−	1.95739i	−0.0212589	−	0.0654283i
$896$	−0.467828	−	0.643910i	−0.0156290	−	0.0215115i
$897$		0			0
$898$	−8.54288	+	2.77575i	−0.285080	+	0.0926280i
$899$	−0.582277	+	1.79207i	−0.0194200	+	0.0597687i
$900$		0			0
$901$			38.8080i			1.29288i
$902$	−20.1626	+	1.93078i	−0.671340	+	0.0642878i
$903$		0			0
$904$	−9.93559	+	13.6752i	−0.330453	+	0.454829i
$905$	11.1608	+	3.62635i	0.370996	+	0.120544i
$906$		0			0
$907$	−30.3543	+	22.0537i	−1.00790	+	0.732282i	−0.963767	−	0.266744i	$-0.914052\pi$
$907$	−30.3543	+	22.0537i	−1.00790	+	0.732282i	−0.0441320	+	0.999026i	$0.514052\pi$
$908$	14.4802	−	10.5205i	0.480542	−	0.349134i
$909$		0			0
$910$	−2.01985	−	0.656290i	−0.0669575	−	0.0217558i
$911$	21.3296	−	29.3577i	0.706682	−	0.972664i	−0.293180	−	0.956057i	$-0.594714\pi$
$911$	21.3296	−	29.3577i	0.706682	−	0.972664i	0.999862	−	0.0166072i	$-0.00528647\pi$
$912$		0			0
$913$	−11.4307	+	1.09461i	−0.378301	+	0.0362263i
$914$		−	23.7889i		−	0.786869i
$915$		0			0
$916$	3.87841	−	11.9365i	0.128146	−	0.394394i
$917$	0.918399	−	0.298406i	0.0303282	−	0.00985423i
$918$		0			0
$919$	−30.1012	−	41.4307i	−0.992947	−	1.36667i	−0.929554	−	0.368685i	$-0.879808\pi$
$919$	−30.1012	−	41.4307i	−0.992947	−	1.36667i	−0.0633921	−	0.997989i	$-0.520192\pi$
$920$	−0.510156	−	1.57010i	−0.0168193	−	0.0517646i
$921$		0			0
$922$	−12.6285	−	9.17517i	−0.415899	−	0.302168i
$923$	−26.5040			−0.872390
$924$		0			0
$925$	−6.75732			−0.222179
$926$	−1.74002	−	1.26420i	−0.0571807	−	0.0415442i
$927$		0			0
$928$	0.0872476	+	0.268521i	0.00286404	+	0.00881462i
$929$	6.37078	+	8.76863i	0.209019	+	0.287689i	0.900636	−	0.434575i	$-0.143101\pi$
$929$	6.37078	+	8.76863i	0.209019	+	0.287689i	−0.691617	+	0.722264i	$0.743101\pi$
$930$		0			0
$931$	−50.7997	+	16.5058i	−1.66489	+	0.540956i
$932$	0.505071	−	1.55445i	0.0165442	−	0.0509177i
$933$		0			0
$934$		−	12.6972i		−	0.415466i
$935$	−11.6500	−	13.1818i	−0.380995	−	0.431091i
$936$		0			0
$937$	12.2529	−	16.8647i	0.400284	−	0.550944i	−0.560531	−	0.828134i	$-0.689403\pi$
$937$	12.2529	−	16.8647i	0.400284	−	0.550944i	0.960815	+	0.277189i	$0.0894029\pi$
$938$	−7.20605	−	2.34139i	−0.235286	−	0.0764490i
$939$		0			0
$940$	−1.81395	+	1.31791i	−0.0591644	+	0.0429854i
$941$	28.2873	−	20.5519i	0.922140	−	0.669974i	−0.0219157	−	0.999760i	$-0.506977\pi$
$941$	28.2873	−	20.5519i	0.922140	−	0.669974i	0.944056	+	0.329786i	$0.106977\pi$
$942$		0			0
$943$	9.58866	+	3.11555i	0.312250	+	0.101456i
$944$	−6.08877	+	8.38047i	−0.198173	+	0.272761i
$945$		0			0
$946$	−3.75478	+	1.63029i	−0.122078	+	0.0530052i
$947$			47.0886i			1.53017i	0.643927	+	0.765087i	$0.277304\pi$
$947$			47.0886i			1.53017i	−0.643927	+	0.765087i	$0.722696\pi$
$948$		0			0
$949$	−10.2025	+	31.4001i	−0.331187	+	1.01929i
$950$	7.97920	−	2.59260i	0.258879	−	0.0841150i
$951$		0			0
$952$	2.48146	+	3.41544i	0.0804246	+	0.110695i
$953$	6.40188	+	19.7030i	0.207377	+	0.638242i	0.999607	+	0.0280192i	$0.00891995\pi$
$953$	6.40188	+	19.7030i	0.207377	+	0.638242i	−0.792230	+	0.610222i	$0.791080\pi$
$954$		0			0
$955$	−14.7760	−	10.7354i	−0.478142	−	0.347390i
$956$	25.5472			0.826257
$957$		0			0
$958$	6.94446			0.224365
$959$	5.99691	+	4.35701i	0.193650	+	0.140695i
$960$		0			0
$961$	4.18416	+	12.8775i	0.134973	+	0.415404i
$962$	10.5984	+	14.5874i	0.341705	+	0.470317i
$963$		0			0
$964$	2.58346	−	0.839417i	0.0832077	−	0.0270358i
$965$	3.95619	−	12.1759i	0.127354	−	0.391956i
$966$		0			0
$967$		−	54.7792i		−	1.76158i	−0.473506	−	0.880791i	$-0.657012\pi$
$967$		−	54.7792i		−	1.76158i	0.473506	−	0.880791i	$-0.342988\pi$
$968$	10.8001	−	2.08759i	0.347128	−	0.0670976i
$969$		0			0
$970$	−1.94812	+	2.68136i	−0.0625504	+	0.0860932i
$971$	−32.9598	−	10.7093i	−1.05773	−	0.343678i	−0.272033	−	0.962288i	$-0.587696\pi$
$971$	−32.9598	−	10.7093i	−1.05773	−	0.343678i	−0.785698	+	0.618610i	$0.787696\pi$
$972$		0			0
$973$	−1.78593	+	1.29756i	−0.0572544	+	0.0415978i
$974$	17.1342	−	12.4487i	0.549014	−	0.398882i
$975$		0			0
$976$	−13.4749	−	4.37827i	−0.431322	−	0.140145i
$977$	−29.1696	+	40.1486i	−0.933220	+	1.28447i	0.0253707	+	0.999678i	$0.491923\pi$
$977$	−29.1696	+	40.1486i	−0.933220	+	1.28447i	−0.958590	+	0.284789i	$0.908077\pi$
$978$		0			0
$979$	1.00242	−	1.69974i	0.0320375	−	0.0543238i
$980$		−	6.36652i		−	0.203371i
$981$		0			0
$982$	5.13344	−	15.7991i	0.163815	−	0.504169i
$983$	20.9001	−	6.79084i	0.666608	−	0.216594i	0.0438853	−	0.999037i	$-0.486026\pi$
$983$	20.9001	−	6.79084i	0.666608	−	0.216594i	0.622723	+	0.782442i	$0.286026\pi$
$984$		0			0
$985$	−4.94953	−	6.81244i	−0.157705	−	0.217062i
$986$	−0.462780	−	1.42429i	−0.0147379	−	0.0453587i
$987$		0			0
$988$	−18.1116	−	13.1588i	−0.576206	−	0.418638i
$989$	2.03757			0.0647909
$990$		0			0
$991$	−54.4994			−1.73123			−0.865616	−	0.500709i	$-0.833073\pi$
$991$	−54.4994			−1.73123			−0.865616	+	0.500709i	$0.833073\pi$
$992$	5.39925	+	3.92279i	0.171427	+	0.124549i
$993$		0			0
$994$	2.44296	+	7.51865i	0.0774859	+	0.238477i
$995$	−10.5308	−	14.4944i	−0.333849	−	0.459504i
$996$		0			0
$997$	58.1173	−	18.8834i	1.84059	−	0.598045i	0.842340	−	0.538946i	$-0.181177\pi$
$997$	58.1173	−	18.8834i	1.84059	−	0.598045i	0.998252	−	0.0590988i	$-0.0188227\pi$
$998$	−12.9860	+	39.9667i	−0.411064	+	1.26512i
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(-0.756962 + 0.245952i) q^{7} +(0.309017 - 0.951057i) q^{8} -1.00000i q^{10} +(-2.85682 - 1.68481i) q^{11} +(-1.56843 + 2.15876i) q^{13} +(0.756962 + 0.245952i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(4.29120 - 3.11774i) q^{17} +(7.97920 + 2.59260i) q^{19} +(-0.587785 + 0.809017i) q^{20} +(1.32091 + 3.04224i) q^{22} -1.65090i q^{23} +(-0.309017 + 0.951057i) q^{25} +(2.53777 - 0.824571i) q^{26} +(-0.467828 - 0.643910i) q^{28} +(0.0872476 + 0.268521i) q^{29} +(5.39925 + 3.92279i) q^{31} +1.00000 q^{32} -5.30422 q^{34} +(-0.643910 - 0.467828i) q^{35} +(2.08813 + 6.42660i) q^{37} +(-4.93142 - 6.78751i) q^{38} +(0.951057 - 0.309017i) q^{40} +(-1.88718 + 5.80815i) q^{41} +1.23422i q^{43} +(0.719545 - 3.23763i) q^{44} +(-0.970374 + 1.33560i) q^{46} +(2.13242 + 0.692866i) q^{47} +(-5.15062 + 3.74214i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-2.53777 - 0.824571i) q^{52} +(-4.30050 + 5.91913i) q^{53} +(-0.316156 - 3.30152i) q^{55} +0.795917i q^{56} +(0.0872476 - 0.268521i) q^{58} +(9.85184 - 3.20106i) q^{59} +(8.32796 + 11.4625i) q^{61} +(-2.06233 - 6.34720i) q^{62} +(-0.809017 - 0.587785i) q^{64} -2.66837 q^{65} -9.51970 q^{67} +(4.29120 + 3.11774i) q^{68} +(0.245952 + 0.756962i) q^{70} +(5.83827 + 8.03570i) q^{71} +(11.7675 - 3.82350i) q^{73} +(2.08813 - 6.42660i) q^{74} +8.38982i q^{76} +(2.57688 + 0.572697i) q^{77} +(5.46381 - 7.52029i) q^{79} +(-0.951057 - 0.309017i) q^{80} +(4.94071 - 3.58963i) q^{82} +(2.80102 - 2.03506i) q^{83} +(5.04461 + 1.63909i) q^{85} +(0.725455 - 0.998503i) q^{86} +(-2.48516 + 2.19636i) q^{88} +0.594975i q^{89} +(0.656290 - 2.01985i) q^{91} +(1.57010 - 0.510156i) q^{92} +(-1.31791 - 1.81395i) q^{94} +(2.59260 + 7.97920i) q^{95} +(-2.68136 - 1.94812i) q^{97} +6.36652 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) \) 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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