LMFDB - Embedded newform 819.2.o.h.757.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(568,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.568"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-1,0,-5,14,0,4,12,0,11,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.59066497296.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.3
Root			$-0.115680 - 0.200364i$ of defining polynomial
Character	$\chi$	$=$	819.757
Dual form			819.2.o.h.568.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.115680 + 0.200364i) q^{2} +(0.973236 - 1.68569i) q^{4} +2.23136 q^{5} +(0.500000 - 0.866025i) q^{7} +0.913059 q^{8} +(0.258125 + 0.447085i) q^{10} +(1.66113 + 2.87716i) q^{11} +(3.40300 - 1.19146i) q^{13} +0.231361 q^{14} +(-1.84085 - 3.18844i) q^{16} +(-0.687890 + 1.19146i) q^{17} +(-1.61766 + 2.80186i) q^{19} +(2.17164 - 3.76139i) q^{20} +(-0.384320 + 0.665661i) q^{22} +(0.419251 + 0.726164i) q^{23} -0.0210289 q^{25} +(0.632387 + 0.544012i) q^{26} +(-0.973236 - 1.68569i) q^{28} +(-0.303571 - 0.525800i) q^{29} +1.71511 q^{31} +(1.33896 - 2.31915i) q^{32} -0.318302 q^{34} +(1.11568 - 1.93242i) q^{35} +(-0.776807 - 1.34547i) q^{37} -0.748524 q^{38} +2.03736 q^{40} +(-4.58892 - 7.94824i) q^{41} +(-0.615680 + 1.06639i) q^{43} +6.46667 q^{44} +(-0.0969983 + 0.168006i) q^{46} +1.62817 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-0.00243263 - 0.00421343i) q^{50} +(1.30348 - 6.89599i) q^{52} -8.39607 q^{53} +(3.70657 + 6.41997i) q^{55} +(0.456530 - 0.790732i) q^{56} +(0.0702344 - 0.121650i) q^{58} +(4.41117 - 7.64037i) q^{59} +(-2.73334 + 4.73428i) q^{61} +(0.198405 + 0.343647i) q^{62} -6.74383 q^{64} +(7.59332 - 2.65858i) q^{65} +(5.09287 + 8.82111i) q^{67} +(1.33896 + 2.31915i) q^{68} +0.516249 q^{70} +(-2.60714 + 4.51570i) q^{71} -3.96355 q^{73} +(0.179723 - 0.311289i) q^{74} +(3.14872 + 5.45375i) q^{76} +3.32225 q^{77} +6.45051 q^{79} +(-4.10760 - 7.11457i) q^{80} +(1.06170 - 1.83891i) q^{82} +4.64055 q^{83} +(-1.53493 + 2.65858i) q^{85} -0.284889 q^{86} +(1.51671 + 2.62701i) q^{88} +(4.56413 + 7.90530i) q^{89} +(0.669665 - 3.54282i) q^{91} +1.63212 q^{92} +(0.188347 + 0.326227i) q^{94} +(-3.60957 + 6.25197i) q^{95} +(7.67944 - 13.3012i) q^{97} +(0.115680 - 0.200364i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 5 q^{4} + 14 q^{5} + 4 q^{7} + 12 q^{8} + 11 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 19 q^{16} - 4 q^{17} - q^{19} - 2 q^{20} - 5 q^{22} - 2 q^{23} + 10 q^{25} - 12 q^{26} + 5 q^{28} + q^{29}+ \cdots - q^{98}+O(q^{100}) $ 8 * q - q^2 - 5 * q^4 + 14 * q^5 + 4 * q^7 + 12 * q^8 + 11 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 19 * q^16 - 4 * q^17 - q^19 - 2 * q^20 - 5 * q^22 - 2 * q^23 + 10 * q^25 - 12 * q^26 + 5 * q^28 + q^29 - 8 * q^31 - 33 * q^32 + 6 * q^34 + 7 * q^35 + 10 * q^37 + 46 * q^38 - 34 * q^40 - 22 * q^41 - 3 * q^43 + 24 * q^44 - 24 * q^46 - 4 * q^47 - 4 * q^49 + 43 * q^50 + 65 * q^52 - 4 * q^53 + 3 * q^55 + 6 * q^56 + 11 * q^58 - 8 * q^59 - 8 * q^61 - 5 * q^62 + 28 * q^64 - 7 * q^65 + 6 * q^67 - 33 * q^68 + 22 * q^70 - 14 * q^71 - 16 * q^73 + 20 * q^74 - 32 * q^76 - 2 * q^77 - 52 * q^79 + 7 * q^80 + 14 * q^82 - 5 * q^85 - 24 * q^86 - 3 * q^88 - q^89 - 4 * q^91 - 24 * q^92 - 33 * q^94 + 21 * q^95 - 3 * q^97 - q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.115680	+	0.200364i	0.0817984	+	0.141679i	0.904022	−	0.427485i	$-0.140600\pi$
$2$	0.115680	+	0.200364i	0.0817984	+	0.141679i	−0.822224	+	0.569164i	$0.807267\pi$
$3$		0			0
$3$		0			0
$4$	0.973236	−	1.68569i	0.486618	−	0.842847i
$5$	2.23136			0.997895			0.498947	−	0.866632i	$-0.333720\pi$
$5$	2.23136			0.997895			0.498947	+	0.866632i	$0.333720\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	0.913059			0.322815
$9$		0			0
$10$	0.258125	+	0.447085i	0.0816262	+	0.141381i
$11$	1.66113	+	2.87716i	0.500848	+	0.867495i	1.00000		0.000980003i	$0.000311945\pi$
$11$	1.66113	+	2.87716i	0.500848	+	0.867495i	−0.499151	+	0.866515i	$0.666355\pi$
$12$		0			0
$13$	3.40300	−	1.19146i	0.943823	−	0.330452i
$13$	3.40300	−	1.19146i	0.943823	−	0.330452i
$14$	0.231361			0.0618338
$15$		0			0
$16$	−1.84085	−	3.18844i	−0.460212	−	0.797111i
$17$	−0.687890	+	1.19146i	−0.166838	+	0.288972i	−0.937306	−	0.348506i	$-0.886689\pi$
$17$	−0.687890	+	1.19146i	−0.166838	+	0.288972i	0.770469	+	0.637478i	$0.220022\pi$
$18$		0			0
$19$	−1.61766	+	2.80186i	−0.371116	+	0.642791i	−0.989737	−	0.142898i	$-0.954358\pi$
$19$	−1.61766	+	2.80186i	−0.371116	+	0.642791i	0.618622	+	0.785689i	$0.287691\pi$
$20$	2.17164	−	3.76139i	0.485594	−	0.841073i
$21$		0			0
$22$	−0.384320	+	0.665661i	−0.0819372	+	0.141919i
$23$	0.419251	+	0.726164i	0.0874199	+	0.151416i	0.906420	−	0.422378i	$-0.138804\pi$
$23$	0.419251	+	0.726164i	0.0874199	+	0.151416i	−0.819000	+	0.573794i	$0.805471\pi$
$24$		0			0
$25$	−0.0210289			−0.00420577
$26$	0.632387	+	0.544012i	0.124021	+	0.106689i
$27$		0			0
$28$	−0.973236	−	1.68569i	−0.183924	−	0.318566i
$29$	−0.303571	−	0.525800i	−0.0563717	−	0.0976386i	0.836462	−	0.548024i	$-0.184620\pi$
$29$	−0.303571	−	0.525800i	−0.0563717	−	0.0976386i	−0.892834	+	0.450386i	$0.851287\pi$
$30$		0			0
$31$	1.71511			0.308043			0.154022	−	0.988067i	$-0.450777\pi$
$31$	1.71511			0.308043			0.154022	+	0.988067i	$0.450777\pi$
$32$	1.33896	−	2.31915i	0.236697	−	0.409971i
$33$		0			0
$34$	−0.318302			−0.0545883
$35$	1.11568	−	1.93242i	0.188584	−	0.326638i
$36$		0			0
$37$	−0.776807	−	1.34547i	−0.127706	−	0.221194i	0.795081	−	0.606503i	$-0.207428\pi$
$37$	−0.776807	−	1.34547i	−0.127706	−	0.221194i	−0.922788	+	0.385309i	$0.874095\pi$
$38$	−0.748524			−0.121427
$39$		0			0
$40$	2.03736			0.322136
$41$	−4.58892	−	7.94824i	−0.716668	−	1.24131i	−0.962313	−	0.271946i	$-0.912333\pi$
$41$	−4.58892	−	7.94824i	−0.716668	−	1.24131i	0.245644	−	0.969360i	$-0.421001\pi$
$42$		0			0
$43$	−0.615680	+	1.06639i	−0.0938904	+	0.162623i	−0.909145	−	0.416480i	$-0.863264\pi$
$43$	−0.615680	+	1.06639i	−0.0938904	+	0.162623i	0.815255	+	0.579103i	$0.196597\pi$
$44$	6.46667			0.974888
$45$		0			0
$46$	−0.0969983	+	0.168006i	−0.0143016	+	0.0247711i
$47$	1.62817			0.237493			0.118747	−	0.992925i	$-0.462112\pi$
$47$	1.62817			0.237493			0.118747	+	0.992925i	$0.462112\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.00243263	−	0.00421343i	−0.000344025	−	0.000595870i
$51$		0			0
$52$	1.30348	−	6.89599i	0.180761	−	0.956302i
$53$	−8.39607			−1.15329			−0.576644	−	0.816995i	$-0.695638\pi$
$53$	−8.39607			−1.15329			−0.576644	+	0.816995i	$0.695638\pi$
$54$		0			0
$55$	3.70657	+	6.41997i	0.499794	+	0.865669i
$56$	0.456530	−	0.790732i	0.0610063	−	0.105666i
$57$		0			0
$58$	0.0702344	−	0.121650i	0.00922223	−	0.0159734i
$59$	4.41117	−	7.64037i	0.574285	−	0.994691i	−0.421834	−	0.906673i	$-0.638613\pi$
$59$	4.41117	−	7.64037i	0.574285	−	0.994691i	0.996119	−	0.0880181i	$-0.0280533\pi$
$60$		0			0
$61$	−2.73334	+	4.73428i	−0.349968	+	0.606162i	−0.986243	−	0.165300i	$-0.947141\pi$
$61$	−2.73334	+	4.73428i	−0.349968	+	0.606162i	0.636276	+	0.771462i	$0.280474\pi$
$62$	0.198405	+	0.343647i	0.0251974	+	0.0436432i
$63$		0			0
$64$	−6.74383			−0.842979
$65$	7.59332	−	2.65858i	0.941836	−	0.329756i
$66$		0			0
$67$	5.09287	+	8.82111i	0.622193	+	1.07767i	0.989077	+	0.147403i	$0.0470913\pi$
$67$	5.09287	+	8.82111i	0.622193	+	1.07767i	−0.366884	+	0.930267i	$0.619575\pi$
$68$	1.33896	+	2.31915i	0.162373	+	0.281238i
$69$		0			0
$70$	0.516249			0.0617036
$71$	−2.60714	+	4.51570i	−0.309411	+	0.535915i	−0.978234	−	0.207507i	$-0.933465\pi$
$71$	−2.60714	+	4.51570i	−0.309411	+	0.535915i	0.668823	+	0.743422i	$0.266798\pi$
$72$		0			0
$73$	−3.96355			−0.463898			−0.231949	−	0.972728i	$-0.574510\pi$
$73$	−3.96355			−0.463898			−0.231949	+	0.972728i	$0.574510\pi$
$74$	0.179723	−	0.311289i	0.0208923	−	0.0361866i
$75$		0			0
$76$	3.14872	+	5.45375i	0.361183	+	0.625588i
$77$	3.32225			0.378606
$78$		0			0
$79$	6.45051			0.725739			0.362869	−	0.931840i	$-0.381797\pi$
$79$	6.45051			0.725739			0.362869	+	0.931840i	$0.381797\pi$
$80$	−4.10760	−	7.11457i	−0.459243	−	0.795433i
$81$		0			0
$82$	1.06170	−	1.83891i	0.117245	−	0.203074i
$83$	4.64055			0.509367			0.254684	−	0.967024i	$-0.418029\pi$
$83$	4.64055			0.509367			0.254684	+	0.967024i	$0.418029\pi$
$84$		0			0
$85$	−1.53493	+	2.65858i	−0.166487	+	0.288363i
$86$	−0.284889			−0.0307203
$87$		0			0
$88$	1.51671	+	2.62701i	0.161681	+	0.280041i
$89$	4.56413	+	7.90530i	0.483797	+	0.837960i	0.999827	−	0.0186101i	$-0.00592411\pi$
$89$	4.56413	+	7.90530i	0.483797	+	0.837960i	−0.516030	+	0.856570i	$0.672591\pi$
$90$		0			0
$91$	0.669665	−	3.54282i	0.0702000	−	0.371388i
$92$	1.63212			0.170160
$93$		0			0
$94$	0.188347	+	0.326227i	0.0194266	+	0.0336478i
$95$	−3.60957	+	6.25197i	−0.370334	+	0.641438i
$96$		0			0
$97$	7.67944	−	13.3012i	0.779729	−	1.35053i	−0.152369	−	0.988324i	$-0.548690\pi$
$97$	7.67944	−	13.3012i	0.779729	−	1.35053i	0.932098	−	0.362206i	$-0.117976\pi$
$98$	0.115680	−	0.200364i	0.0116855	−	0.0202399i
$99$		0			0
$100$	−0.0204660	+	0.0354482i	−0.00204660	+	0.00354482i
$101$	−3.97521	−	6.88527i	−0.395548	−	0.685110i	0.597623	−	0.801777i	$-0.296112\pi$
$101$	−3.97521	−	6.88527i	−0.395548	−	0.685110i	−0.993171	+	0.116668i	$0.962779\pi$
$102$		0			0
$103$	0.694825			0.0684631			0.0342316	−	0.999414i	$-0.489102\pi$
$103$	0.694825			0.0684631			0.0342316	+	0.999414i	$0.489102\pi$
$104$	3.10714	−	1.08787i	0.304680	−	0.106675i
$105$		0			0
$106$	−0.971261	−	1.68227i	−0.0943372	−	0.163397i
$107$	4.47324	+	7.74787i	0.432444	+	0.749015i	0.997083	−	0.0763228i	$-0.0243180\pi$
$107$	4.47324	+	7.74787i	0.432444	+	0.749015i	−0.564639	+	0.825338i	$0.690985\pi$
$108$		0			0
$109$	−2.27268			−0.217683			−0.108841	−	0.994059i	$-0.534714\pi$
$109$	−2.27268			−0.217683			−0.108841	+	0.994059i	$0.534714\pi$
$110$	−0.857556	+	1.48533i	−0.0817647	+	0.141621i
$111$		0			0
$112$	−3.68170			−0.347888
$113$	−4.75239	+	8.23138i	−0.447067	+	0.774343i	−0.998194	−	0.0600786i	$-0.980865\pi$
$113$	−4.75239	+	8.23138i	−0.447067	+	0.774343i	0.551126	+	0.834422i	$0.314198\pi$
$114$		0			0
$115$	0.935501	+	1.62033i	0.0872359	+	0.151097i
$116$	−1.18178			−0.109726
$117$		0			0
$118$	2.04114			0.187902
$119$	0.687890	+	1.19146i	0.0630588	+	0.109221i
$120$		0			0
$121$	−0.0186821	+	0.0323584i	−0.00169837	+	0.00294167i
$122$	−1.26477			−0.114507
$123$		0			0
$124$	1.66921	−	2.89115i	0.149899	−	0.259633i
$125$	−11.2037			−1.00209
$126$		0			0
$127$	−9.21672	−	15.9638i	−0.817851	−	1.41656i	−0.907262	−	0.420565i	$-0.861832\pi$
$127$	−9.21672	−	15.9638i	−0.817851	−	1.41656i	0.0894111	−	0.995995i	$-0.471502\pi$
$128$	−3.45805	−	5.98951i	−0.305651	−	0.529403i
$129$		0			0
$130$	1.41108	+	1.21389i	0.123760	+	0.106465i
$131$	1.74835			0.152754			0.0763771	−	0.997079i	$-0.475665\pi$
$131$	1.74835			0.152754			0.0763771	+	0.997079i	$0.475665\pi$
$132$		0			0
$133$	1.61766	+	2.80186i	0.140269	+	0.242952i
$134$	−1.17829	+	2.04086i	−0.101789	+	0.176303i
$135$		0			0
$136$	−0.628085	+	1.08787i	−0.0538578	+	0.0932845i
$137$	−9.00160	+	15.5912i	−0.769059	+	1.33205i	0.169015	+	0.985614i	$0.445941\pi$
$137$	−9.00160	+	15.5912i	−0.769059	+	1.33205i	−0.938074	+	0.346436i	$0.887392\pi$
$138$		0			0
$139$	−6.95896	+	12.0533i	−0.590251	+	1.02235i	0.403947	+	0.914782i	$0.367638\pi$
$139$	−6.95896	+	12.0533i	−0.590251	+	1.02235i	−0.994198	+	0.107563i	$0.965695\pi$
$140$	−2.17164	−	3.76139i	−0.183537	−	0.317896i
$141$		0			0
$142$	−1.20638			−0.101237
$143$	9.08083	+	7.81180i	0.759378	+	0.653255i
$144$		0			0
$145$	−0.677376	−	1.17325i	−0.0562530	−	0.0974331i
$146$	−0.458505	−	0.794154i	−0.0379462	−	0.0657247i
$147$		0			0
$148$	−3.02407			−0.248577
$149$	−7.96515	+	13.7961i	−0.652531	+	1.13022i	0.329976	+	0.943989i	$0.392959\pi$
$149$	−7.96515	+	13.7961i	−0.652531	+	1.13022i	−0.982507	+	0.186227i	$0.940374\pi$
$150$		0			0
$151$	−13.9497			−1.13521			−0.567604	−	0.823301i	$-0.692130\pi$
$151$	−13.9497			−1.13521			−0.567604	+	0.823301i	$0.692130\pi$
$152$	−1.47702	+	2.55827i	−0.119802	+	0.207503i
$153$		0			0
$154$	0.384320	+	0.665661i	0.0309694	+	0.0536405i
$155$	3.82703			0.307395
$156$		0			0
$157$	−12.9747			−1.03549			−0.517745	−	0.855535i	$-0.673229\pi$
$157$	−12.9747			−1.03549			−0.517745	+	0.855535i	$0.673229\pi$
$158$	0.746198	+	1.29245i	0.0593643	+	0.102822i
$159$		0			0
$160$	2.98770	−	5.17485i	0.236199	−	0.409108i
$161$	0.838502			0.0660832
$162$		0			0
$163$	−9.20423	+	15.9422i	−0.720931	+	1.24869i	0.239697	+	0.970848i	$0.422952\pi$
$163$	−9.20423	+	15.9422i	−0.720931	+	1.24869i	−0.960627	+	0.277841i	$0.910381\pi$
$164$	−17.8644			−1.39498
$165$		0			0
$166$	0.536821	+	0.929802i	0.0416654	+	0.0721666i
$167$	−9.24967	−	16.0209i	−0.715761	−	1.23973i	−0.962665	−	0.270695i	$-0.912747\pi$
$167$	−9.24967	−	16.0209i	−0.715761	−	1.23973i	0.246904	−	0.969040i	$-0.420587\pi$
$168$		0			0
$169$	10.1608	−	8.10909i	0.781603	−	0.623776i
$170$	−0.710246			−0.0544734
$171$		0			0
$172$	1.19840	+	2.07570i	0.0913775	+	0.158270i
$173$	−8.59906	+	14.8940i	−0.653774	+	1.13237i	0.328425	+	0.944530i	$0.393482\pi$
$173$	−8.59906	+	14.8940i	−0.653774	+	1.13237i	−0.982200	+	0.187840i	$0.939851\pi$
$174$		0			0
$175$	−0.0105144	+	0.0182115i	−0.000794816	+	0.00137666i
$176$	6.11577	−	10.5928i	0.460993	−	0.798464i
$177$		0			0
$178$	−1.05596	+	1.82898i	−0.0791476	+	0.137088i
$179$	7.24431	+	12.5475i	0.541465	+	0.937845i	0.998820	+	0.0485608i	$0.0154635\pi$
$179$	7.24431	+	12.5475i	0.541465	+	0.937845i	−0.457355	+	0.889284i	$0.651203\pi$
$180$		0			0
$181$	6.85484			0.509516			0.254758	−	0.967005i	$-0.418004\pi$
$181$	6.85484			0.509516			0.254758	+	0.967005i	$0.418004\pi$
$182$	0.787321	−	0.275657i	0.0583601	−	0.0204331i
$183$		0			0
$184$	0.382801	+	0.663031i	0.0282205	+	0.0488793i
$185$	−1.73334	−	3.00223i	−0.127437	−	0.220728i
$186$		0			0
$187$	−4.57069			−0.334242
$188$	1.58459	−	2.74460i	0.115568	−	0.200170i
$189$		0			0
$190$	−1.67023			−0.121171
$191$	−1.42581	+	2.46958i	−0.103168	+	0.178693i	−0.912988	−	0.407986i	$-0.866231\pi$
$191$	−1.42581	+	2.46958i	−0.103168	+	0.178693i	0.809820	+	0.586678i	$0.199565\pi$
$192$		0			0
$193$	5.02525	+	8.70398i	0.361725	+	0.626526i	0.988245	−	0.152879i	$-0.0488546\pi$
$193$	5.02525	+	8.70398i	0.361725	+	0.626526i	−0.626520	+	0.779406i	$0.715521\pi$
$194$	3.55344			0.255122
$195$		0			0
$196$	−1.94647			−0.139034
$197$	−12.7085	−	22.0119i	−0.905447	−	1.56828i	−0.820317	−	0.571910i	$-0.806203\pi$
$197$	−12.7085	−	22.0119i	−0.905447	−	1.56828i	−0.0851299	−	0.996370i	$-0.527131\pi$
$198$		0			0
$199$	6.22328	−	10.7790i	0.441157	−	0.764106i	−0.556619	−	0.830768i	$-0.687902\pi$
$199$	6.22328	−	10.7790i	0.441157	−	0.764106i	0.997776	+	0.0666623i	$0.0212350\pi$
$200$	−0.0192006			−0.00135769
$201$		0			0
$202$	0.919708	−	1.59298i	0.0647104	−	0.112082i
$203$	−0.607142			−0.0426130
$204$		0			0
$205$	−10.2395	−	17.7354i	−0.715160	−	1.23869i
$206$	0.0803776	+	0.139218i	0.00560017	+	0.00969979i
$207$		0			0
$208$	−10.0633	−	8.65698i	−0.697766	−	0.600254i
$209$	−10.7485			−0.743491
$210$		0			0
$211$	12.1961	+	21.1243i	0.839617	+	1.45426i	0.890215	+	0.455540i	$0.150554\pi$
$211$	12.1961	+	21.1243i	0.839617	+	1.45426i	−0.0505979	+	0.998719i	$0.516113\pi$
$212$	−8.17136	+	14.1532i	−0.561211	+	0.972046i
$213$		0			0
$214$	−1.03493	+	1.79255i	−0.0707465	+	0.122536i
$215$	−1.37381	+	2.37950i	−0.0936927	+	0.162281i
$216$		0			0
$217$	0.857556	−	1.48533i	0.0582147	−	0.100831i
$218$	−0.262904	−	0.455363i	−0.0178061	−	0.0308411i
$219$		0			0
$220$	14.4295			0.972835
$221$	−0.921313	+	4.87414i	−0.0619742	+	0.327870i
$222$		0			0
$223$	−11.3247	−	19.6149i	−0.758357	−	1.31351i	−0.943688	−	0.330837i	$-0.892669\pi$
$223$	−11.3247	−	19.6149i	−0.758357	−	1.31351i	0.185331	−	0.982676i	$-0.440664\pi$
$224$	−1.33896	−	2.31915i	−0.0894630	−	0.154954i
$225$		0			0
$226$	−2.19903			−0.146278
$227$	0.642530	−	1.11289i	0.0426462	−	0.0738654i	−0.843914	−	0.536478i	$-0.819754\pi$
$227$	0.642530	−	1.11289i	0.0426462	−	0.0738654i	0.886561	+	0.462612i	$0.153088\pi$
$228$		0			0
$229$	−4.64451			−0.306918			−0.153459	−	0.988155i	$-0.549041\pi$
$229$	−4.64451			−0.306918			−0.153459	+	0.988155i	$0.549041\pi$
$230$	−0.216438	+	0.374882i	−0.0142715	+	0.0247190i
$231$		0			0
$232$	−0.277178	−	0.480086i	−0.0181976	−	0.0315192i
$233$	−11.8877			−0.778790			−0.389395	−	0.921071i	$-0.627316\pi$
$233$	−11.8877			−0.778790			−0.389395	+	0.921071i	$0.627316\pi$
$234$		0			0
$235$	3.63304			0.236993
$236$	−8.58622	−	14.8718i	−0.558915	−	0.968070i
$237$		0			0
$238$	−0.159151	+	0.275657i	−0.0103162	+	0.0178682i
$239$	4.17783			0.270242			0.135121	−	0.990829i	$-0.456858\pi$
$239$	4.17783			0.270242			0.135121	+	0.990829i	$0.456858\pi$
$240$		0			0
$241$	−2.01671	+	3.49304i	−0.129907	+	0.225006i	−0.923641	−	0.383260i	$-0.874801\pi$
$241$	−2.01671	+	3.49304i	−0.129907	+	0.225006i	0.793733	+	0.608266i	$0.208135\pi$
$242$	−0.00864462			−0.000555697
$243$		0			0
$244$	5.32036	+	9.21514i	0.340601	+	0.589939i
$245$	−1.11568	−	1.93242i	−0.0712782	−	0.123457i
$246$		0			0
$247$	−2.16658	+	11.4621i	−0.137856	+	0.729317i
$248$	1.56600			0.0994410
$249$		0			0
$250$	−1.29605	−	2.24483i	−0.0819695	−	0.141975i
$251$	13.9343	−	24.1348i	0.879523	−	1.52338i	0.0276571	−	0.999617i	$-0.491195\pi$
$251$	13.9343	−	24.1348i	0.879523	−	1.52338i	0.851866	−	0.523760i	$-0.175471\pi$
$252$		0			0
$253$	−1.39286	+	2.41250i	−0.0875683	+	0.151673i
$254$	2.13239	−	3.69340i	0.133798	−	0.231745i
$255$		0			0
$256$	−5.94377	+	10.2949i	−0.371486	+	0.643432i
$257$	−3.57032	−	6.18398i	−0.222710	−	0.385746i	0.732920	−	0.680315i	$-0.238157\pi$
$257$	−3.57032	−	6.18398i	−0.222710	−	0.385746i	−0.955630	+	0.294569i	$0.904824\pi$
$258$		0			0
$259$	−1.55361			−0.0965369
$260$	2.90855	−	15.3874i	0.180380	−	0.954289i
$261$		0			0
$262$	0.202250	+	0.350308i	0.0124951	+	0.0216421i
$263$	10.6596	+	18.4630i	0.657300	+	1.13848i	0.981312	+	0.192423i	$0.0616347\pi$
$263$	10.6596	+	18.4630i	0.657300	+	1.13848i	−0.324012	+	0.946053i	$0.605032\pi$
$264$		0			0
$265$	−18.7347			−1.15086
$266$	−0.374262	+	0.648241i	−0.0229475	+	0.0397462i
$267$		0			0
$268$	19.8263			1.21108
$269$	1.39438	−	2.41513i	0.0850167	−	0.147253i	−0.820382	−	0.571816i	$-0.806239\pi$
$269$	1.39438	−	2.41513i	0.0850167	−	0.147253i	0.905398	+	0.424563i	$0.139572\pi$
$270$		0			0
$271$	7.73737	+	13.4015i	0.470012	+	0.814085i	0.999412	−	0.0342877i	$-0.0109163\pi$
$271$	7.73737	+	13.4015i	0.470012	+	0.814085i	−0.529400	+	0.848372i	$0.677583\pi$
$272$	5.06521			0.307123
$273$		0			0
$274$	−4.16524			−0.251631
$275$	−0.0349316	−	0.0605033i	−0.00210645	−	0.00364849i
$276$		0			0
$277$	−2.76477	+	4.78873i	−0.166119	+	0.287727i	−0.937052	−	0.349189i	$-0.886457\pi$
$277$	−2.76477	+	4.78873i	−0.166119	+	0.287727i	0.770933	+	0.636916i	$0.219790\pi$
$278$	−3.22006			−0.193127
$279$		0			0
$280$	1.01868	−	1.76441i	0.0608779	−	0.105444i
$281$	31.4871			1.87836			0.939182	−	0.343419i	$-0.111585\pi$
$281$	31.4871			1.87836			0.939182	+	0.343419i	$0.111585\pi$
$282$		0			0
$283$	3.67559	+	6.36631i	0.218491	+	0.378438i	0.954347	−	0.298700i	$-0.0965531\pi$
$283$	3.67559	+	6.36631i	0.218491	+	0.378438i	−0.735856	+	0.677138i	$0.763220\pi$
$284$	5.07473	+	8.78969i	0.301130	+	0.521572i
$285$		0			0
$286$	−0.514731	+	2.72315i	−0.0304367	+	0.161023i
$287$	−9.17783			−0.541750
$288$		0			0
$289$	7.55361	+	13.0832i	0.444330	+	0.769603i
$290$	0.156718	−	0.271444i	0.00920281	−	0.0159397i
$291$		0			0
$292$	−3.85747	+	6.68133i	−0.225741	+	0.390995i
$293$	−6.76675	+	11.7204i	−0.395318	+	0.684710i	−0.993142	−	0.116917i	$-0.962699\pi$
$293$	−6.76675	+	11.7204i	−0.395318	+	0.684710i	0.597824	+	0.801627i	$0.296032\pi$
$294$		0			0
$295$	9.84291	−	17.0484i	0.573076	−	0.992597i
$296$	−0.709271	−	1.22849i	−0.0412255	−	0.0714047i
$297$		0			0
$298$	−3.68565			−0.213504
$299$	2.29191	+	1.97162i	0.132545	+	0.114022i
$300$		0			0
$301$	0.615680	+	1.06639i	0.0354872	+	0.0614657i
$302$	−1.61370	−	2.79502i	−0.0928583	−	0.160835i
$303$		0			0
$304$	11.9114			0.683168
$305$	−6.09906	+	10.5639i	−0.349231	+	0.604886i
$306$		0			0
$307$	−3.30609			−0.188688			−0.0943442	−	0.995540i	$-0.530075\pi$
$307$	−3.30609			−0.188688			−0.0943442	+	0.995540i	$0.530075\pi$
$308$	3.23334	−	5.60030i	0.184236	−	0.319107i
$309$		0			0
$310$	0.442713	+	0.766801i	0.0251444	+	0.0435514i
$311$	34.3063			1.94533			0.972665	−	0.232214i	$-0.0745969\pi$
$311$	34.3063			1.94533			0.972665	+	0.232214i	$0.0745969\pi$
$312$		0			0
$313$	7.21428			0.407775			0.203888	−	0.978994i	$-0.434642\pi$
$313$	7.21428			0.407775			0.203888	+	0.978994i	$0.434642\pi$
$314$	−1.50091	−	2.59966i	−0.0847015	−	0.146707i
$315$		0			0
$316$	6.27787	−	10.8736i	0.353158	−	0.611687i
$317$	8.04040			0.451594			0.225797	−	0.974174i	$-0.427501\pi$
$317$	8.04040			0.451594			0.225797	+	0.974174i	$0.427501\pi$
$318$		0			0
$319$	1.00854	−	1.74684i	0.0564673	−	0.0978043i
$320$	−15.0479			−0.841204
$321$		0			0
$322$	0.0969983	+	0.168006i	0.00540550	+	0.00936261i
$323$	−2.22554	−	3.85475i	−0.123832	−	0.214484i
$324$		0			0
$325$	−0.0715613	+	0.0250551i	−0.00396950	+	0.00138981i
$326$	−4.25899			−0.235884
$327$		0			0
$328$	−4.18995	−	7.25721i	−0.231351	−	0.400712i
$329$	0.814085	−	1.41004i	0.0448820	−	0.0777379i
$330$		0			0
$331$	−0.446843	+	0.773955i	−0.0245607	+	0.0425404i	−0.878045	−	0.478579i	$-0.841152\pi$
$331$	−0.446843	+	0.773955i	−0.0245607	+	0.0425404i	0.853484	+	0.521119i	$0.174485\pi$
$332$	4.51636	−	7.82256i	0.247867	−	0.429319i
$333$		0			0
$334$	2.14001	−	3.70661i	0.117096	−	0.202817i
$335$	11.3640	+	19.6831i	0.620883	+	1.07540i
$336$		0			0
$337$	15.0717			0.821007			0.410504	−	0.911859i	$-0.365353\pi$
$337$	15.0717			0.821007			0.410504	+	0.911859i	$0.365353\pi$
$338$	2.80018	+	1.09781i	0.152310	+	0.0597129i
$339$		0			0
$340$	2.98770	+	5.17485i	0.162031	+	0.280646i
$341$	2.84902	+	4.93464i	0.154283	+	0.267226i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−0.562153	+	0.973677i	−0.0303092	+	0.0524971i
$345$		0			0
$346$	−3.97897			−0.213911
$347$	−8.20818	+	14.2170i	−0.440638	+	0.763207i	−0.997737	−	0.0672387i	$-0.978581\pi$
$347$	−8.20818	+	14.2170i	−0.440638	+	0.763207i	0.557099	+	0.830446i	$0.311914\pi$
$348$		0			0
$349$	−17.1861	−	29.7672i	−0.919950	−	1.59340i	−0.799488	−	0.600682i	$-0.794896\pi$
$349$	−17.1861	−	29.7672i	−0.919950	−	1.59340i	−0.120462	−	0.992718i	$-0.538438\pi$
$350$	−0.00486525			−0.000260059
$351$		0			0
$352$	8.89672			0.474197
$353$	−11.9581	−	20.7121i	−0.636467	−	1.10239i	−0.986202	−	0.165545i	$-0.947062\pi$
$353$	−11.9581	−	20.7121i	−0.636467	−	1.10239i	0.349735	−	0.936849i	$-0.386272\pi$
$354$		0			0
$355$	−5.81747	+	10.0762i	−0.308759	+	0.534787i
$356$	17.7679			0.941697
$357$		0			0
$358$	−1.67605	+	2.90300i	−0.0885819	+	0.153428i
$359$	6.17875			0.326102			0.163051	−	0.986618i	$-0.447867\pi$
$359$	6.17875			0.326102			0.163051	+	0.986618i	$0.447867\pi$
$360$		0			0
$361$	4.26638	+	7.38958i	0.224546	+	0.388925i
$362$	0.792970	+	1.37347i	0.0416776	+	0.0721877i
$363$		0			0
$364$	−5.32036	−	4.57685i	−0.278863	−	0.239892i
$365$	−8.84411			−0.462922
$366$		0			0
$367$	−9.92798	−	17.1958i	−0.518236	−	0.897612i	−0.999776	−	0.0211872i	$-0.993255\pi$
$367$	−9.92798	−	17.1958i	−0.518236	−	0.897612i	0.481539	−	0.876425i	$-0.340078\pi$
$368$	1.54356	−	2.67352i	0.0804634	−	0.139367i
$369$		0			0
$370$	0.401026	−	0.694598i	0.0208484	−	0.0361104i
$371$	−4.19803	+	7.27121i	−0.217951	+	0.377502i
$372$		0			0
$373$	−15.0975	+	26.1497i	−0.781721	+	1.35398i	0.149217	+	0.988804i	$0.452325\pi$
$373$	−15.0975	+	26.1497i	−0.781721	+	1.35398i	−0.930938	+	0.365176i	$0.881009\pi$
$374$	−0.528739	−	0.915804i	−0.0273405	−	0.0473551i
$375$		0			0
$376$	1.48662			0.0766664
$377$	−1.65952	−	1.42761i	−0.0854697	−	0.0735254i
$378$		0			0
$379$	2.16121	+	3.74333i	0.111014	+	0.192282i	0.916179	−	0.400768i	$-0.131257\pi$
$379$	2.16121	+	3.74333i	0.111014	+	0.192282i	−0.805165	+	0.593050i	$0.797923\pi$
$380$	7.02594	+	12.1693i	0.360423	+	0.624271i
$381$		0			0
$382$	−0.659755			−0.0337560
$383$	−8.67407	+	15.0239i	−0.443224	+	0.767687i	−0.997927	−	0.0643617i	$-0.979499\pi$
$383$	−8.67407	+	15.0239i	−0.443224	+	0.767687i	0.554702	+	0.832049i	$0.312832\pi$
$384$		0			0
$385$	7.41314			0.377809
$386$	−1.16264	+	2.01376i	−0.0591771	+	0.102498i
$387$		0			0
$388$	−14.9478	−	25.8904i	−0.758860	−	1.31438i
$389$	25.3474			1.28516			0.642582	−	0.766217i	$-0.277863\pi$
$389$	25.3474			1.28516			0.642582	+	0.766217i	$0.277863\pi$
$390$		0			0
$391$	−1.15360			−0.0583398
$392$	−0.456530	−	0.790732i	−0.0230582	−	0.0399380i
$393$		0			0
$394$	2.94026	−	5.09268i	0.148128	−	0.256566i
$395$	14.3934			0.724211
$396$		0			0
$397$	13.5375	−	23.4476i	0.679425	−	1.17680i	−0.295729	−	0.955272i	$-0.595563\pi$
$397$	13.5375	−	23.4476i	0.679425	−	1.17680i	0.975154	−	0.221527i	$-0.0711041\pi$
$398$	2.87965			0.144344
$399$		0			0
$400$	0.0387110	+	0.0670494i	0.00193555	+	0.00335247i
$401$	−14.6429	−	25.3622i	−0.731232	−	1.26653i	−0.956357	−	0.292201i	$-0.905613\pi$
$401$	−14.6429	−	25.3622i	−0.731232	−	1.26653i	0.225125	−	0.974330i	$-0.427721\pi$
$402$		0			0
$403$	5.83653	−	2.04349i	0.290738	−	0.101793i
$404$	−15.4753			−0.769924
$405$		0			0
$406$	−0.0702344	−	0.121650i	−0.00348567	−	0.00603736i
$407$	2.58075	−	4.46999i	0.127923	−	0.221569i
$408$		0			0
$409$	−11.6856	+	20.2401i	−0.577817	+	1.00081i	0.417912	+	0.908487i	$0.362762\pi$
$409$	−11.6856	+	20.2401i	−0.577817	+	1.00081i	−0.995729	+	0.0923213i	$0.970571\pi$
$410$	2.36903	−	4.10327i	0.116998	−	0.202646i
$411$		0			0
$412$	0.676229	−	1.17126i	0.0333154	−	0.0577040i
$413$	−4.41117	−	7.64037i	−0.217059	−	0.375958i
$414$		0			0
$415$	10.3548			0.508295
$416$	1.79331	−	9.48738i	0.0879242	−	0.465157i
$417$		0			0
$418$	−1.24339	−	2.15362i	−0.0608164	−	0.105337i
$419$	7.30320	+	12.6495i	0.356785	+	0.617969i	0.987422	−	0.158109i	$-0.0505397\pi$
$419$	7.30320	+	12.6495i	0.356785	+	0.617969i	−0.630637	+	0.776078i	$0.717206\pi$
$420$		0			0
$421$	10.2728			0.500668			0.250334	−	0.968160i	$-0.419460\pi$
$421$	10.2728			0.500668			0.250334	+	0.968160i	$0.419460\pi$
$422$	−2.82171	+	4.88734i	−0.137359	+	0.237912i
$423$		0			0
$424$	−7.66611			−0.372299
$425$	0.0144656	−	0.0250551i	0.000701682	−	0.00121535i
$426$		0			0
$427$	2.73334	+	4.73428i	0.132275	+	0.229108i
$428$	17.4141			0.841740
$429$		0			0
$430$	−0.635689			−0.0306557
$431$	−6.25087	−	10.8268i	−0.301094	−	0.521510i	0.675290	−	0.737552i	$-0.264018\pi$
$431$	−6.25087	−	10.8268i	−0.301094	−	0.521510i	−0.976384	+	0.216042i	$0.930685\pi$
$432$		0			0
$433$	5.47361	−	9.48057i	0.263045	−	0.455607i	−0.704005	−	0.710195i	$-0.748607\pi$
$433$	5.47361	−	9.48057i	0.263045	−	0.455607i	0.967050	+	0.254588i	$0.0819400\pi$
$434$	0.396810			0.0190475
$435$		0			0
$436$	−2.21185	+	3.83104i	−0.105928	+	0.183473i
$437$	−2.71282			−0.129772
$438$		0			0
$439$	8.95896	+	15.5174i	0.427588	+	0.740604i	0.996658	−	0.0816849i	$-0.0260301\pi$
$439$	8.95896	+	15.5174i	0.427588	+	0.740604i	−0.569070	+	0.822289i	$0.692697\pi$
$440$	3.38432	+	5.86181i	0.161341	+	0.279451i
$441$		0			0
$442$	−1.08318	+	0.379244i	−0.0515217	+	0.0180388i
$443$	−27.7194			−1.31699			−0.658494	−	0.752586i	$-0.728806\pi$
$443$	−27.7194			−1.31699			−0.658494	+	0.752586i	$0.728806\pi$
$444$		0			0
$445$	10.1842	+	17.6396i	0.482778	+	0.836196i
$446$	2.62009	−	4.53813i	0.124065	−	0.214887i
$447$		0			0
$448$	−3.37192	+	5.84033i	−0.159308	+	0.275930i
$449$	−0.0829898	+	0.143743i	−0.00391653	+	0.00678363i	−0.867977	−	0.496604i	$-0.834580\pi$
$449$	−0.0829898	+	0.143743i	−0.00391653	+	0.00678363i	0.864060	+	0.503388i	$0.167913\pi$
$450$		0			0
$451$	15.2455	−	26.4061i	0.717884	−	1.24341i
$452$	9.25039	+	16.0222i	0.435102	+	0.753619i
$453$		0			0
$454$	0.297313			0.0139536
$455$	1.49426	−	7.90530i	0.0700522	−	0.370606i
$456$		0			0
$457$	−15.8677	−	27.4837i	−0.742260	−	1.28563i	−0.951464	−	0.307760i	$-0.900421\pi$
$457$	−15.8677	−	27.4837i	−0.742260	−	1.28563i	0.209205	−	0.977872i	$-0.432913\pi$
$458$	−0.537278	−	0.930593i	−0.0251054	−	0.0434838i
$459$		0			0
$460$	3.64185			0.169802
$461$	14.5328	−	25.1715i	0.676859	−	1.17235i	−0.299063	−	0.954233i	$-0.596674\pi$
$461$	14.5328	−	25.1715i	0.676859	−	1.17235i	0.975922	−	0.218121i	$-0.0699926\pi$
$462$		0			0
$463$	6.31904			0.293671			0.146835	−	0.989161i	$-0.453091\pi$
$463$	6.31904			0.293671			0.146835	+	0.989161i	$0.453091\pi$
$464$	−1.11766	+	1.93584i	−0.0518859	+	0.0898690i
$465$		0			0
$466$	−1.37518	−	2.38188i	−0.0637038	−	0.110338i
$467$	34.6409			1.60299			0.801495	−	0.598002i	$-0.204038\pi$
$467$	34.6409			1.60299			0.801495	+	0.598002i	$0.204038\pi$
$468$		0			0
$469$	10.1857			0.470334
$470$	0.420271	+	0.727931i	0.0193857	+	0.0335769i
$471$		0			0
$472$	4.02766	−	6.97611i	0.185388	−	0.321101i
$473$	−4.09089			−0.188099
$474$		0			0
$475$	0.0340175	−	0.0589200i	0.00156083	−	0.00270343i
$476$	2.67792			0.122742
$477$		0			0
$478$	0.483293	+	0.837089i	0.0221053	+	0.0382876i
$479$	−3.57115	−	6.18541i	−0.163170	−	0.282619i	0.772834	−	0.634608i	$-0.218839\pi$
$479$	−3.57115	−	6.18541i	−0.163170	−	0.282619i	−0.936004	+	0.351990i	$0.885505\pi$
$480$		0			0
$481$	−4.24655	−	3.65310i	−0.193626	−	0.166567i
$482$	−0.933174			−0.0425049
$483$		0			0
$484$	0.0363642	+	0.0629847i	0.00165292	+	0.00286294i
$485$	17.1356	−	29.6797i	0.778087	−	1.34769i
$486$		0			0
$487$	9.25013	−	16.0217i	0.419163	−	0.726012i	−0.576692	−	0.816962i	$-0.695657\pi$
$487$	9.25013	−	16.0217i	0.419163	−	0.726012i	0.995856	+	0.0909493i	$0.0289901\pi$
$488$	−2.49570	+	4.32267i	−0.112975	+	0.195678i
$489$		0			0
$490$	0.258125	−	0.447085i	0.0116609	−	0.0201972i
$491$	−7.63904	−	13.2312i	−0.344745	−	0.597116i	0.640563	−	0.767906i	$-0.278701\pi$
$491$	−7.63904	−	13.2312i	−0.344745	−	0.597116i	−0.985307	+	0.170790i	$0.945368\pi$
$492$		0			0
$493$	0.835294			0.0376197
$494$	−2.54723	+	0.891838i	−0.114605	+	0.0401257i
$495$		0			0
$496$	−3.15726	−	5.46854i	−0.141765	−	0.245545i
$497$	2.60714	+	4.51570i	0.116946	+	0.202557i
$498$		0			0
$499$	12.4783			0.558606			0.279303	−	0.960203i	$-0.409897\pi$
$499$	12.4783			0.558606			0.279303	+	0.960203i	$0.409897\pi$
$500$	−10.9039	+	18.8861i	−0.487636	+	0.844610i
$501$		0			0
$502$	6.44768			0.287774
$503$	−1.29004	+	2.23441i	−0.0575200	+	0.0996276i	−0.893352	−	0.449358i	$-0.851653\pi$
$503$	−1.29004	+	2.23441i	−0.0575200	+	0.0996276i	0.835832	+	0.548986i	$0.184986\pi$
$504$		0			0
$505$	−8.87013	−	15.3635i	−0.394716	−	0.683668i
$506$	−0.644506			−0.0286518
$507$		0			0
$508$	−35.8802			−1.59192
$509$	17.8404	+	30.9005i	0.790761	+	1.36964i	0.925496	+	0.378757i	$0.123648\pi$
$509$	17.8404	+	30.9005i	0.790761	+	1.36964i	−0.134735	+	0.990882i	$0.543018\pi$
$510$		0			0
$511$	−1.98177	+	3.43253i	−0.0876686	+	0.151846i
$512$	−16.5825			−0.732850
$513$		0			0
$514$	0.826032	−	1.43073i	0.0364347	−	0.0631068i
$515$	1.55040			0.0683190
$516$		0			0
$517$	2.70460	+	4.68450i	0.118948	+	0.206024i
$518$	−0.179723	−	0.311289i	−0.00789656	−	0.0136772i
$519$		0			0
$520$	6.93315	−	2.42744i	0.304039	−	0.106450i
$521$	20.9637			0.918437			0.459219	−	0.888323i	$-0.348129\pi$
$521$	20.9637			0.918437			0.459219	+	0.888323i	$0.348129\pi$
$522$		0			0
$523$	11.4131	+	19.7681i	0.499062	+	0.864401i	0.999999	−	0.00108279i	$-0.000344663\pi$
$523$	11.4131	+	19.7681i	0.499062	+	0.864401i	−0.500937	+	0.865484i	$0.667011\pi$
$524$	1.70156	−	2.94719i	0.0743330	−	0.128749i
$525$		0			0
$526$	−2.46622	+	4.27161i	−0.107532	+	0.186251i
$527$	−1.17981	+	2.04349i	−0.0513933	+	0.0890158i
$528$		0			0
$529$	11.1485	−	19.3097i	0.484716	−	0.839552i
$530$	−2.16723	−	3.75376i	−0.0941386	−	0.163053i
$531$		0			0
$532$	6.29744			0.273029
$533$	−25.0861	−	21.5803i	−1.08660	−	0.934749i
$534$		0			0
$535$	9.98140	+	17.2883i	0.431534	+	0.747438i
$536$	4.65009	+	8.05419i	0.200853	+	0.347888i
$537$		0			0
$538$	0.645208			0.0278169
$539$	1.66113	−	2.87716i	0.0715498	−	0.123928i
$540$		0			0
$541$	30.2191			1.29922			0.649611	−	0.760266i	$-0.274932\pi$
$541$	30.2191			1.29922			0.649611	+	0.760266i	$0.274932\pi$
$542$	−1.79013	+	3.10059i	−0.0768925	+	0.133182i
$543$		0			0
$544$	1.84211	+	3.19064i	0.0789800	+	0.136797i
$545$	−5.07116			−0.217225
$546$		0			0
$547$	−16.8223			−0.719271			−0.359636	−	0.933093i	$-0.617099\pi$
$547$	−16.8223			−0.719271			−0.359636	+	0.933093i	$0.617099\pi$
$548$	17.5214	+	30.3479i	0.748476	+	1.29640i
$549$		0			0
$550$	0.00808180	−	0.0139981i	0.000344609	−	0.000596881i
$551$	1.96429			0.0836817
$552$		0			0
$553$	3.22525	−	5.58630i	0.137152	−	0.237554i
$554$	−1.27932			−0.0543531
$555$		0			0
$556$	13.5454	+	23.4614i	0.574454	+	0.994984i
$557$	−5.24591	−	9.08619i	−0.222276	−	0.384994i	0.733222	−	0.679989i	$-0.238015\pi$
$557$	−5.24591	−	9.08619i	−0.222276	−	0.384994i	−0.955499	+	0.294995i	$0.904682\pi$
$558$		0			0
$559$	−0.824600	+	4.36249i	−0.0348768	+	0.184513i
$560$	−8.21520			−0.347155
$561$		0			0
$562$	3.64244	+	6.30890i	0.153647	+	0.266125i
$563$	15.4737	−	26.8012i	0.652138	−	1.12954i	−0.330465	−	0.943818i	$-0.607205\pi$
$563$	15.4737	−	26.8012i	0.652138	−	1.12954i	0.982603	−	0.185718i	$-0.0594612\pi$
$564$		0			0
$565$	−10.6043	+	18.3672i	−0.446126	+	0.772713i
$566$	−0.850388	+	1.47292i	−0.0357445	+	0.0619112i
$567$		0			0
$568$	−2.38047	+	4.12310i	−0.0998825	+	0.173002i
$569$	−18.4545	−	31.9641i	−0.773651	−	1.34000i	−0.935549	−	0.353196i	$-0.885095\pi$
$569$	−18.4545	−	31.9641i	−0.773651	−	1.34000i	0.161898	−	0.986807i	$-0.448238\pi$
$570$		0			0
$571$	−1.77093			−0.0741113			−0.0370556	−	0.999313i	$-0.511798\pi$
$571$	−1.77093			−0.0741113			−0.0370556	+	0.999313i	$0.511798\pi$
$572$	22.0061	−	7.70479i	0.920121	−	0.322153i
$573$		0			0
$574$	−1.06170	−	1.83891i	−0.0443143	−	0.0767546i
$575$	−0.00881638	−	0.0152704i	−0.000367668	−	0.000636820i
$576$		0			0
$577$	−9.83999			−0.409644			−0.204822	−	0.978799i	$-0.565662\pi$
$577$	−9.83999			−0.409644			−0.204822	+	0.978799i	$0.565662\pi$
$578$	−1.74761	+	3.02695i	−0.0726910	+	0.125905i
$579$		0			0
$580$	−2.63699			−0.109495
$581$	2.32028	−	4.01884i	0.0962613	−	0.166730i
$582$		0			0
$583$	−13.9469	−	24.1568i	−0.577623	−	1.00047i
$584$	−3.61896			−0.149753
$585$		0			0
$586$	−3.13112			−0.129345
$587$	−7.56917	−	13.1102i	−0.312413	−	0.541116i	0.666471	−	0.745531i	$-0.267804\pi$
$587$	−7.56917	−	13.1102i	−0.312413	−	0.541116i	−0.978884	+	0.204415i	$0.934471\pi$
$588$		0			0
$589$	−2.77446	+	4.80551i	−0.114320	+	0.198007i
$590$	4.55453			0.187507
$591$		0			0
$592$	−2.85997	+	4.95361i	−0.117544	+	0.203592i
$593$	−9.17148			−0.376628			−0.188314	−	0.982109i	$-0.560302\pi$
$593$	−9.17148			−0.376628			−0.188314	+	0.982109i	$0.560302\pi$
$594$		0			0
$595$	1.53493	+	2.65858i	0.0629261	+	0.108991i
$596$	15.5040	+	26.8536i	0.635067	+	1.09997i
$597$		0			0
$598$	−0.129913	+	0.687294i	−0.00531253	+	0.0281056i
$599$	18.5811			0.759202			0.379601	−	0.925150i	$-0.376061\pi$
$599$	18.5811			0.759202			0.379601	+	0.925150i	$0.376061\pi$
$600$		0			0
$601$	6.70179	+	11.6078i	0.273372	+	0.473494i	0.969723	−	0.244207i	$-0.0785277\pi$
$601$	6.70179	+	11.6078i	0.273372	+	0.473494i	−0.696351	+	0.717701i	$0.745194\pi$
$602$	−0.142444	+	0.246721i	−0.00580560	+	0.0100556i
$603$		0			0
$604$	−13.5763	+	23.5149i	−0.552413	+	0.956808i
$605$	−0.0416865	+	0.0722032i	−0.00169480	+	0.00293548i
$606$		0			0
$607$	−6.31812	+	10.9433i	−0.256445	+	0.444175i	−0.965287	−	0.261192i	$-0.915884\pi$
$607$	−6.31812	+	10.9433i	−0.256445	+	0.444175i	0.708842	+	0.705367i	$0.249218\pi$
$608$	4.33195	+	7.50316i	0.175684	+	0.304293i
$609$		0			0
$610$	−2.82217			−0.114266
$611$	5.54067	−	1.93990i	0.224151	−	0.0784800i
$612$		0			0
$613$	−12.8540	−	22.2637i	−0.519167	−	0.899223i	−0.999752	−	0.0222753i	$-0.992909\pi$
$613$	−12.8540	−	22.2637i	−0.519167	−	0.899223i	0.480585	−	0.876948i	$-0.340424\pi$
$614$	−0.382450	−	0.662422i	−0.0154344	−	0.0267332i
$615$		0			0
$616$	3.03341			0.122220
$617$	−3.29810	+	5.71248i	−0.132777	+	0.229976i	−0.924746	−	0.380585i	$-0.875723\pi$
$617$	−3.29810	+	5.71248i	−0.132777	+	0.229976i	0.791969	+	0.610561i	$0.209056\pi$
$618$		0			0
$619$	−21.0124			−0.844559			−0.422280	−	0.906466i	$-0.638770\pi$
$619$	−21.0124			−0.844559			−0.422280	+	0.906466i	$0.638770\pi$
$620$	3.72461	−	6.45121i	0.149584	−	0.259087i
$621$		0			0
$622$	3.96856	+	6.87375i	0.159125	+	0.275612i
$623$	9.12826			0.365716
$624$		0			0
$625$	−24.8944			−0.995777
$626$	0.834551	+	1.44549i	0.0333554	+	0.0577732i
$627$		0			0
$628$	−12.6274	+	21.8713i	−0.503888	+	0.872760i
$629$	2.13743			0.0852250
$630$		0			0
$631$	−13.0105	+	22.5349i	−0.517940	+	0.897099i	0.481842	+	0.876258i	$0.339968\pi$
$631$	−13.0105	+	22.5349i	−0.517940	+	0.897099i	−0.999783	+	0.0208412i	$0.993366\pi$
$632$	5.88970			0.234280
$633$		0			0
$634$	0.930117	+	1.61101i	0.0369397	+	0.0639814i
$635$	−20.5658	−	35.6210i	−0.816130	−	1.41358i
$636$		0			0
$637$	−2.73334	−	2.35136i	−0.108299	−	0.0931641i
$638$	0.466673			0.0184758
$639$		0			0
$640$	−7.71615	−	13.3648i	−0.305008	−	0.528289i
$641$	9.26694	−	16.0508i	0.366022	−	0.633969i	−0.622917	−	0.782288i	$-0.714053\pi$
$641$	9.26694	−	16.0508i	0.366022	−	0.633969i	0.988940	+	0.148319i	$0.0473861\pi$
$642$		0			0
$643$	7.22328	−	12.5111i	0.284858	−	0.493389i	−0.687716	−	0.725979i	$-0.741387\pi$
$643$	7.22328	−	12.5111i	0.284858	−	0.493389i	0.972575	+	0.232590i	$0.0747201\pi$
$644$	0.816061	−	1.41346i	0.0321573	−	0.0556981i
$645$		0			0
$646$	0.514903	−	0.891838i	0.0202586	−	0.0350889i
$647$	14.6438	+	25.3637i	0.575706	+	0.997152i	0.995965	+	0.0897473i	$0.0286059\pi$
$647$	14.6438	+	25.3637i	0.575706	+	0.997152i	−0.420259	+	0.907404i	$0.638061\pi$
$648$		0			0
$649$	29.3100			1.15052
$650$	−0.0132984	−	0.0114399i	−0.000521605	−	0.000448711i
$651$		0			0
$652$	17.9158	+	31.0310i	0.701636	+	1.21527i
$653$	−15.4807	−	26.8134i	−0.605808	−	1.04929i	−0.991923	−	0.126840i	$-0.959516\pi$
$653$	−15.4807	−	26.8134i	−0.605808	−	1.04929i	0.386115	−	0.922451i	$-0.373817\pi$
$654$		0			0
$655$	3.90121			0.152433
$656$	−16.8950	+	29.2630i	−0.659639	+	1.14253i
$657$		0			0
$658$	0.376695			0.0146851
$659$	−18.5414	+	32.1146i	−0.722270	+	1.25101i	0.237817	+	0.971310i	$0.423568\pi$
$659$	−18.5414	+	32.1146i	−0.722270	+	1.25101i	−0.960088	+	0.279699i	$0.909765\pi$
$660$		0			0
$661$	10.2009	+	17.6685i	0.396770	+	0.687226i	0.993325	−	0.115346i	$-0.0367977\pi$
$661$	10.2009	+	17.6685i	0.396770	+	0.687226i	−0.596555	+	0.802572i	$0.703464\pi$
$662$	−0.206764			−0.00803611
$663$		0			0
$664$	4.23710			0.164431
$665$	3.60957	+	6.25197i	0.139973	+	0.242441i
$666$		0			0
$667$	0.254545	−	0.440885i	0.00985601	−	0.0170711i
$668$	−36.0085			−1.39321
$669$		0			0
$670$	−2.62919	+	4.55389i	−0.101574	+	0.175932i
$671$	−18.1617			−0.701123
$672$		0			0
$673$	−7.25551	−	12.5669i	−0.279679	−	0.484419i	0.691626	−	0.722256i	$-0.256895\pi$
$673$	−7.25551	−	12.5669i	−0.279679	−	0.484419i	−0.971305	+	0.237837i	$0.923562\pi$
$674$	1.74350	+	3.01983i	0.0671571	+	0.116319i
$675$		0			0
$676$	−3.78055	−	25.0201i	−0.145406	−	0.962313i
$677$	3.51476			0.135083			0.0675417	−	0.997716i	$-0.478484\pi$
$677$	3.51476			0.135083			0.0675417	+	0.997716i	$0.478484\pi$
$678$		0			0
$679$	−7.67944	−	13.3012i	−0.294710	−	0.510452i
$680$	−1.40148	+	2.42744i	−0.0537444	+	0.0930881i
$681$		0			0
$682$	−0.659151	+	1.14168i	−0.0252402	+	0.0437173i
$683$	−13.5376	+	23.4479i	−0.518003	+	0.897208i	0.481778	+	0.876293i	$0.339991\pi$
$683$	−13.5376	+	23.4479i	−0.518003	+	0.897208i	−0.999781	+	0.0209144i	$0.993342\pi$
$684$		0			0
$685$	−20.0858	+	34.7897i	−0.767440	+	1.32925i
$686$	−0.115680	−	0.200364i	−0.00441670	−	0.00764995i
$687$		0			0
$688$	4.53350			0.172838
$689$	−28.5718	+	10.0036i	−1.08850	+	0.381106i
$690$		0			0
$691$	−14.8702	−	25.7560i	−0.565690	−	0.979803i	−0.996985	−	0.0775926i	$-0.975277\pi$
$691$	−14.8702	−	25.7560i	−0.565690	−	0.979803i	0.431295	−	0.902211i	$-0.358057\pi$
$692$	16.7378	+	28.9908i	0.636277	+	1.10206i
$693$		0			0
$694$	−3.79810			−0.144174
$695$	−15.5280	+	26.8952i	−0.589009	+	1.02019i
$696$		0			0
$697$	12.6267			0.478270
$698$	3.97619	−	6.88696i	0.150501	−	0.260675i
$699$		0			0
$700$	0.0204660	+	0.0354482i	0.000773544	+	0.00133982i
$701$	−18.2888			−0.690760			−0.345380	−	0.938463i	$-0.612250\pi$
$701$	−18.2888			−0.690760			−0.345380	+	0.938463i	$0.612250\pi$
$702$		0			0
$703$	5.02642			0.189575
$704$	−11.2024	−	19.4030i	−0.422205	−	0.731280i
$705$		0			0
$706$	2.76664	−	4.79197i	0.104124	−	0.180348i
$707$	−7.95042			−0.299006
$708$		0			0
$709$	14.3402	−	24.8379i	0.538557	−	0.932808i	−0.460425	−	0.887699i	$-0.652303\pi$
$709$	14.3402	−	24.8379i	0.538557	−	0.932808i	0.998982	−	0.0451098i	$-0.0143638\pi$
$710$	−2.69187			−0.101024
$711$		0			0
$712$	4.16732	+	7.21801i	0.156177	+	0.270506i
$713$	0.719062	+	1.24545i	0.0269291	+	0.0466426i
$714$		0			0
$715$	20.2626	+	17.4309i	0.757779	+	0.651880i
$716$	28.2017			1.05395
$717$		0			0
$718$	0.714760	+	1.23800i	0.0266746	+	0.0462018i
$719$	12.7381	−	22.0631i	0.475052	−	0.822813i	−0.524540	−	0.851386i	$-0.675763\pi$
$719$	12.7381	−	22.0631i	0.475052	−	0.822813i	0.999592	+	0.0285723i	$0.00909607\pi$
$720$		0			0
$721$	0.347412	−	0.601736i	0.0129383	−	0.0224098i
$722$	−0.987073	+	1.70966i	−0.0367350	+	0.0636270i
$723$		0			0
$724$	6.67138	−	11.5552i	0.247940	−	0.429444i
$725$	0.00638375	+	0.0110570i	0.000237086	+	0.000410646i
$726$		0			0
$727$	−9.02572			−0.334746			−0.167373	−	0.985894i	$-0.553528\pi$
$727$	−9.02572			−0.334746			−0.167373	+	0.985894i	$0.553528\pi$
$728$	0.611444	−	3.23480i	0.0226616	−	0.119890i
$729$		0			0
$730$	−1.02309	−	1.77204i	−0.0378663	−	0.0655863i
$731$	−0.847041	−	1.46712i	−0.0313290	−	0.0542633i
$732$		0			0
$733$	−7.57069			−0.279630			−0.139815	−	0.990178i	$-0.544651\pi$
$733$	−7.57069			−0.279630			−0.139815	+	0.990178i	$0.544651\pi$
$734$	2.29695	−	3.97843i	0.0847818	−	0.146846i
$735$		0			0
$736$	2.24544			0.0827681
$737$	−16.9198	+	29.3059i	−0.623249	+	1.07950i
$738$		0			0
$739$	3.18648	+	5.51914i	0.117216	+	0.203025i	0.918664	−	0.395041i	$-0.129270\pi$
$739$	3.18648	+	5.51914i	0.117216	+	0.203025i	−0.801447	+	0.598066i	$0.795936\pi$
$740$	−6.74778			−0.248053
$741$		0			0
$742$	−1.94252			−0.0713122
$743$	−11.4148	−	19.7711i	−0.418770	−	0.725330i	0.577046	−	0.816711i	$-0.304205\pi$
$743$	−11.4148	−	19.7711i	−0.418770	−	0.725330i	−0.995816	+	0.0913811i	$0.970872\pi$
$744$		0			0
$745$	−17.7731	+	30.7840i	−0.651157	+	1.12784i
$746$	−6.98596			−0.255774
$747$		0			0
$748$	−4.44836	+	7.70479i	−0.162648	+	0.281715i
$749$	8.94647			0.326897
$750$		0			0
$751$	−19.6848	−	34.0950i	−0.718307	−	1.24414i	−0.961670	−	0.274209i	$-0.911584\pi$
$751$	−19.6848	−	34.0950i	−0.718307	−	1.24414i	0.243363	−	0.969935i	$-0.421749\pi$
$752$	−2.99722	−	5.19133i	−0.109297	−	0.189308i
$753$		0			0
$754$	0.0940671	−	0.497655i	0.00342572	−	0.0181235i
$755$	−31.1268			−1.13282
$756$		0			0
$757$	−4.36357	−	7.55792i	−0.158597	−	0.274697i	0.775766	−	0.631020i	$-0.217364\pi$
$757$	−4.36357	−	7.55792i	−0.158597	−	0.274697i	−0.934363	+	0.356323i	$0.884030\pi$
$758$	−0.500020	+	0.866060i	−0.0181615	+	0.0314567i
$759$		0			0
$760$	−3.29575	+	5.70841i	−0.119550	+	0.207066i
$761$	−11.4195	+	19.7792i	−0.413958	+	0.716996i	−0.995318	−	0.0966503i	$-0.969187\pi$
$761$	−11.4195	+	19.7792i	−0.413958	+	0.716996i	0.581361	+	0.813646i	$0.302520\pi$
$762$		0			0
$763$	−1.13634	+	1.96820i	−0.0411382	+	0.0712535i
$764$	2.77531	+	4.80697i	0.100407	+	0.173910i
$765$		0			0
$766$	−4.01368			−0.145020
$767$	5.90801	−	31.2559i	0.213326	−	1.12859i
$768$		0			0
$769$	−17.4174	−	30.1679i	−0.628089	−	1.08788i	−0.987935	−	0.154871i	$-0.950504\pi$
$769$	−17.4174	−	30.1679i	−0.628089	−	1.08788i	0.359846	−	0.933012i	$-0.382829\pi$
$770$	0.857556	+	1.48533i	0.0309042	+	0.0535276i
$771$		0			0
$772$	19.5630			0.704088
$773$	−16.6372	+	28.8164i	−0.598397	+	1.03645i	0.394661	+	0.918827i	$0.370862\pi$
$773$	−16.6372	+	28.8164i	−0.598397	+	1.03645i	−0.993058	+	0.117627i	$0.962471\pi$
$774$		0			0
$775$	−0.0360668			−0.00129556
$776$	7.01178	−	12.1448i	0.251708	−	0.435971i
$777$		0			0
$778$	2.93220	+	5.07872i	0.105124	+	0.182081i
$779$	29.6932			1.06387
$780$		0			0
$781$	−17.3232			−0.619872
$782$	−0.133448	−	0.231139i	−0.00477210	−	0.00826553i
$783$		0			0
$784$	−1.84085	+	3.18844i	−0.0657446	+	0.113873i
$785$	−28.9512			−1.03331
$786$		0			0
$787$	13.9079	−	24.0891i	0.495762	−	0.858685i	−0.504226	−	0.863572i	$-0.668222\pi$
$787$	13.9079	−	24.0891i	0.495762	−	0.858685i	0.999988	+	0.00488682i	$0.00155553\pi$
$788$	−49.4737			−1.76243
$789$		0			0
$790$	1.66504	+	2.88393i	0.0592393	+	0.102606i
$791$	4.75239	+	8.23138i	0.168976	+	0.292674i
$792$		0			0
$793$	−3.66084	+	19.3674i	−0.130000	+	0.687757i
$794$	6.26407			0.222304
$795$		0			0
$796$	−12.1134	−	20.9811i	−0.429349	−	0.743655i
$797$	17.9343	−	31.0630i	0.635264	−	1.10031i	−0.351195	−	0.936302i	$-0.614225\pi$
$797$	17.9343	−	31.0630i	0.635264	−	1.10031i	0.986459	−	0.164007i	$-0.0524421\pi$
$798$		0			0
$799$	−1.12000	+	1.93990i	−0.0396228	+	0.0686288i
$800$	−0.0281568	+	0.0487690i	−0.000995493	+	0.00172424i
$801$		0			0
$802$	3.38779	−	5.86783i	0.119627	−	0.207200i
$803$	−6.58396	−	11.4037i	−0.232343	−	0.402430i
$804$		0			0
$805$	1.87100			0.0659441
$806$	1.08461	+	0.933040i	0.0382039	+	0.0328649i
$807$		0			0
$808$	−3.62960	−	6.28666i	−0.127689	−	0.221164i
$809$	−8.91223	−	15.4364i	−0.313337	−	0.542716i	0.665745	−	0.746179i	$-0.268114\pi$
$809$	−8.91223	−	15.4364i	−0.313337	−	0.542716i	−0.979083	+	0.203463i	$0.934780\pi$
$810$		0			0
$811$	25.2152			0.885425			0.442713	−	0.896664i	$-0.354016\pi$
$811$	25.2152			0.885425			0.442713	+	0.896664i	$0.354016\pi$
$812$	−0.590892	+	1.02346i	−0.0207362	+	0.0359162i
$813$		0			0
$814$	1.19417			0.0418556
$815$	−20.5379	+	35.5728i	−0.719413	+	1.24606i
$816$		0			0
$817$	−1.99192	−	3.45010i	−0.0696884	−	0.120704i
$818$	−5.40719			−0.189058
$819$		0			0
$820$	−39.8619			−1.39204
$821$	−5.22797	−	9.05511i	−0.182457	−	0.316026i	0.760259	−	0.649620i	$-0.225072\pi$
$821$	−5.22797	−	9.05511i	−0.182457	−	0.316026i	−0.942717	+	0.333594i	$0.891739\pi$
$822$		0			0
$823$	16.6203	−	28.7871i	0.579346	−	1.00346i	−0.416209	−	0.909269i	$-0.636641\pi$
$823$	16.6203	−	28.7871i	0.579346	−	1.00346i	0.995554	−	0.0941873i	$-0.0300253\pi$
$824$	0.634416			0.0221009
$825$		0			0
$826$	1.02057	−	1.76768i	0.0355102	−	0.0615055i
$827$	37.9927			1.32113			0.660567	−	0.750767i	$-0.270316\pi$
$827$	37.9927			1.32113			0.660567	+	0.750767i	$0.270316\pi$
$828$		0			0
$829$	−8.34721	−	14.4578i	−0.289911	−	0.502140i	0.683877	−	0.729597i	$-0.260292\pi$
$829$	−8.34721	−	14.4578i	−0.289911	−	0.502140i	−0.973788	+	0.227457i	$0.926959\pi$
$830$	1.19784	+	2.07472i	0.0415777	+	0.0720147i
$831$		0			0
$832$	−22.9493	+	8.03501i	−0.795623	+	0.278564i
$833$	1.37578			0.0476680
$834$		0			0
$835$	−20.6394	−	35.7484i	−0.714254	−	1.23712i
$836$	−10.4609	+	18.1187i	−0.361796	+	0.626649i
$837$		0			0
$838$	−1.68967	+	2.92660i	−0.0583688	+	0.101098i
$839$	−23.3206	+	40.3924i	−0.805115	+	1.39450i	0.111098	+	0.993809i	$0.464563\pi$
$839$	−23.3206	+	40.3924i	−0.805115	+	1.39450i	−0.916213	+	0.400691i	$0.868770\pi$
$840$		0			0
$841$	14.3157	−	24.7955i	0.493644	−	0.855017i
$842$	1.18837	+	2.05831i	0.0409538	+	0.0709341i
$843$		0			0
$844$	47.4789			1.63429
$845$	22.6725	−	18.0943i	0.779958	−	0.622463i
$846$		0			0
$847$	0.0186821	+	0.0323584i	0.000641925	+	0.00111185i
$848$	15.4559	+	26.7704i	0.530758	+	0.919299i
$849$		0			0
$850$	0.00669352			0.000229586
$851$	0.651354	−	1.12818i	0.0223281	−	0.0386735i
$852$		0			0
$853$	39.5640			1.35464			0.677322	−	0.735686i	$-0.263140\pi$
$853$	39.5640			1.35464			0.677322	+	0.735686i	$0.263140\pi$
$854$	−0.632387	+	1.09533i	−0.0216398	+	0.0374813i
$855$		0			0
$856$	4.08433	+	7.07426i	0.139599	+	0.241793i
$857$	19.5613			0.668201			0.334101	−	0.942537i	$-0.391567\pi$
$857$	19.5613			0.668201			0.334101	+	0.942537i	$0.391567\pi$
$858$		0			0
$859$	−10.1632			−0.346762			−0.173381	−	0.984855i	$-0.555469\pi$
$859$	−10.1632			−0.346762			−0.173381	+	0.984855i	$0.555469\pi$
$860$	2.67407	+	4.63163i	0.0911851	+	0.157937i
$861$		0			0
$862$	1.44621	−	2.50490i	0.0492580	−	0.0853174i
$863$	−26.8903			−0.915356			−0.457678	−	0.889118i	$-0.651319\pi$
$863$	−26.8903			−0.915356			−0.457678	+	0.889118i	$0.651319\pi$
$864$		0			0
$865$	−19.1876	+	33.2339i	−0.652398	+	1.12999i
$866$	2.53276			0.0860666
$867$		0			0
$868$	−1.66921	−	2.89115i	−0.0566566	−	0.0981321i
$869$	10.7151	+	18.5591i	0.363485	+	0.629575i
$870$		0			0
$871$	27.8410	+	23.9503i	0.943358	+	0.811524i
$872$	−2.07509			−0.0702713
$873$		0			0
$874$	−0.313820	−	0.543552i	−0.0106151	−	0.0183859i
$875$	−5.60186	+	9.70271i	−0.189378	+	0.328012i
$876$		0			0
$877$	0.850801	−	1.47363i	0.0287295	−	0.0497610i	−0.851303	−	0.524674i	$-0.824187\pi$
$877$	0.850801	−	1.47363i	0.0287295	−	0.0497610i	0.880033	+	0.474913i	$0.157521\pi$
$878$	−2.07275	+	3.59011i	−0.0699520	+	0.121160i
$879$		0			0
$880$	13.6465	−	23.6364i	0.460023	−	0.796783i
$881$	−5.65448	−	9.79384i	−0.190504	−	0.329963i	0.754913	−	0.655825i	$-0.227679\pi$
$881$	−5.65448	−	9.79384i	−0.190504	−	0.329963i	−0.945417	+	0.325862i	$0.894346\pi$
$882$		0			0
$883$	−46.9068			−1.57854			−0.789270	−	0.614047i	$-0.789541\pi$
$883$	−46.9068			−1.57854			−0.789270	+	0.614047i	$0.789541\pi$
$884$	7.31965	+	6.29674i	0.246187	+	0.211782i
$885$		0			0
$886$	−3.20659	−	5.55398i	−0.107728	−	0.186590i
$887$	−1.22346	−	2.11909i	−0.0410797	−	0.0711522i	0.844755	−	0.535154i	$-0.179746\pi$
$887$	−1.22346	−	2.11909i	−0.0410797	−	0.0711522i	−0.885834	+	0.464002i	$0.846413\pi$
$888$		0			0
$889$	−18.4334			−0.618237
$890$	−2.35623	+	4.08111i	−0.0789810	+	0.136799i
$891$		0			0
$892$	−44.0864			−1.47612
$893$	−2.63382	+	4.56191i	−0.0881374	+	0.152658i
$894$		0			0
$895$	16.1647	+	27.9980i	0.540325	+	0.935871i
$896$	−6.91610			−0.231051
$897$		0			0
$898$	−0.0384012			−0.00128146
$899$	−0.520658	−	0.901806i	−0.0173649	−	0.0300769i
$900$		0			0
$901$	5.77557	−	10.0036i	0.192412	−	0.333268i
$902$	7.05444			0.234887
$903$		0			0
$904$	−4.33921	+	7.51574i	−0.144320	+	0.249970i
$905$	15.2956			0.508443
$906$		0			0
$907$	20.7083	+	35.8678i	0.687607	+	1.19097i	0.972610	+	0.232443i	$0.0746719\pi$
$907$	20.7083	+	35.8678i	0.687607	+	1.19097i	−0.285003	+	0.958526i	$0.591995\pi$
$908$	−1.25067	−	2.16622i	−0.0415048	−	0.0718885i
$909$		0			0
$910$	1.75680	−	0.615091i	0.0582373	−	0.0203901i
$911$	11.9951			0.397416			0.198708	−	0.980059i	$-0.436325\pi$
$911$	11.9951			0.397416			0.198708	+	0.980059i	$0.436325\pi$
$912$		0			0
$913$	7.70855	+	13.3516i	0.255116	+	0.441873i
$914$	3.67116	−	6.35864i	0.121431	−	0.210325i
$915$		0			0
$916$	−4.52020	+	7.82922i	−0.149352	+	0.258685i
$917$	0.874176	−	1.51412i	0.0288678	−	0.0500006i
$918$		0			0
$919$	−22.4708	+	38.9206i	−0.741243	+	1.28387i	0.210686	+	0.977554i	$0.432430\pi$
$919$	−22.4708	+	38.9206i	−0.741243	+	1.28387i	−0.951930	+	0.306317i	$0.900903\pi$
$920$	0.854167	+	1.47946i	0.0281611	+	0.0487764i
$921$		0			0
$922$	6.72463			0.221464
$923$	−3.49182	+	18.4732i	−0.114935	+	0.608054i
$924$		0			0
$925$	0.0163354	+	0.0282937i	0.000537103	+	0.000930290i
$926$	0.730990	+	1.26611i	0.0240218	+	0.0416070i
$927$		0			0
$928$	−1.62588			−0.0533720
$929$	14.1298	−	24.4735i	0.463582	−	0.802948i	−0.535554	−	0.844501i	$-0.679897\pi$
$929$	14.1298	−	24.4735i	0.463582	−	0.802948i	0.999136	+	0.0415530i	$0.0132305\pi$
$930$		0			0
$931$	3.23531			0.106033
$932$	−11.5696	+	20.0391i	−0.378973	+	0.656401i
$933$		0			0
$934$	4.00727	+	6.94080i	0.131122	+	0.227110i
$935$	−10.1989			−0.333538
$936$		0			0
$937$	32.4601			1.06042			0.530212	−	0.847865i	$-0.322112\pi$
$937$	32.4601			1.06042			0.530212	+	0.847865i	$0.322112\pi$
$938$	1.17829	+	2.04086i	0.0384725	+	0.0666364i
$939$		0			0
$940$	3.53580	−	6.12419i	0.115325	−	0.199749i
$941$	12.6051			0.410913			0.205457	−	0.978666i	$-0.434132\pi$
$941$	12.6051			0.410913			0.205457	+	0.978666i	$0.434132\pi$
$942$		0			0
$943$	3.84782	−	6.66462i	0.125302	−	0.217030i
$944$	−32.4812			−1.05717
$945$		0			0
$946$	−0.473236	−	0.819669i	−0.0153862	−	0.0266497i
$947$	−6.64010	−	11.5010i	−0.215774	−	0.373732i	0.737738	−	0.675088i	$-0.235894\pi$
$947$	−6.64010	−	11.5010i	−0.215774	−	0.373732i	−0.953512	+	0.301356i	$0.902561\pi$
$948$		0			0
$949$	−13.4880	+	4.72242i	−0.437838	+	0.153296i
$950$	0.0157406			0.000510693
$951$		0			0
$952$	0.628085	+	1.08787i	0.0203563	+	0.0352582i
$953$	−29.2159	+	50.6035i	−0.946397	+	1.63921i	−0.193467	+	0.981107i	$0.561973\pi$
$953$	−29.2159	+	50.6035i	−0.946397	+	1.63921i	−0.752930	+	0.658101i	$0.771360\pi$
$954$		0			0
$955$	−3.18151	+	5.51053i	−0.102951	+	0.178317i
$956$	4.06602	−	7.04255i	0.131504	−	0.227772i
$957$		0			0
$958$	0.826224	−	1.43106i	0.0266941	−	0.0462355i
$959$	9.00160	+	15.5912i	0.290677	+	0.503467i
$960$		0			0
$961$	−28.0584			−0.905109
$962$	0.240708	−	1.27345i	0.00776074	−	0.0410576i
$963$		0			0
$964$	3.92546	+	6.79910i	0.126431	+	0.218984i
$965$	11.2131	+	19.4217i	0.360964	+	0.625207i
$966$		0			0
$967$	33.2182			1.06823			0.534113	−	0.845413i	$-0.320646\pi$
$967$	33.2182			1.06823			0.534113	+	0.845413i	$0.320646\pi$
$968$	−0.0170579	+	0.0295451i	−0.000548261	+	0.000949616i
$969$		0			0
$970$	7.92901			0.254585
$971$	8.38890	−	14.5300i	0.269213	−	0.466290i	−0.699446	−	0.714685i	$-0.746570\pi$
$971$	8.38890	−	14.5300i	0.269213	−	0.466290i	0.968659	+	0.248395i	$0.0799032\pi$
$972$		0			0
$973$	6.95896	+	12.0533i	0.223094	+	0.386410i
$974$	4.28023			0.137148
$975$		0			0
$976$	20.1266			0.644238
$977$	−25.0211	−	43.3378i	−0.800496	−	1.38650i	−0.919290	−	0.393581i	$-0.871236\pi$
$977$	−25.0211	−	43.3378i	−0.800496	−	1.38650i	0.118793	−	0.992919i	$-0.462097\pi$
$978$		0			0
$979$	−15.1632	+	26.2634i	−0.484618	+	0.839382i
$980$	−4.34328			−0.138741
$981$		0			0
$982$	1.76737	−	3.06118i	0.0563992	−	0.0976862i
$983$	−16.6741			−0.531822			−0.265911	−	0.963998i	$-0.585673\pi$
$983$	−16.6741			−0.531822			−0.265911	+	0.963998i	$0.585673\pi$
$984$		0			0
$985$	−28.3574	−	49.1164i	−0.903540	−	1.56498i
$986$	0.0966271	+	0.167363i	0.00307723	+	0.00532993i
$987$		0			0
$988$	17.2130	+	14.8075i	0.547620	+	0.471090i
$989$	−1.03250			−0.0328316
$990$		0			0
$991$	−10.1642	−	17.6050i	−0.322878	−	0.559241i	0.658203	−	0.752841i	$-0.271317\pi$
$991$	−10.1642	−	17.6050i	−0.322878	−	0.559241i	−0.981081	+	0.193600i	$0.937984\pi$
$992$	2.29646	−	3.97759i	0.0729128	−	0.126289i
$993$		0			0
$994$	−0.603190	+	1.04476i	−0.0191320	+	0.0331377i
$995$	13.8864	−	24.0519i	0.440228	−	0.762497i
$996$		0			0
$997$	−3.13823	+	5.43557i	−0.0993887	+	0.172146i	−0.911432	−	0.411451i	$-0.865022\pi$
$997$	−3.13823	+	5.43557i	−0.0993887	+	0.172146i	0.812043	+	0.583597i	$0.198355\pi$
$998$	1.44350	+	2.50021i	0.0456931	+	0.0791427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.h.757.3		8
3.2	odd	2		91.2.f.c.29.2	yes	8
12.11	even	2		1456.2.s.q.1121.1		8
13.9	even	3	inner	819.2.o.h.568.3		8
21.2	odd	6		637.2.g.k.263.2		8
21.5	even	6		637.2.g.j.263.2		8
21.11	odd	6		637.2.h.h.471.3		8
21.17	even	6		637.2.h.i.471.3		8
21.20	even	2		637.2.f.i.393.2		8
39.2	even	12		1183.2.c.g.337.4		8
39.11	even	12		1183.2.c.g.337.5		8
39.23	odd	6		1183.2.a.l.1.2		4
39.29	odd	6		1183.2.a.k.1.3		4
39.35	odd	6		91.2.f.c.22.2	✓	8
156.35	even	6		1456.2.s.q.113.1		8
273.62	even	6		8281.2.a.bt.1.2		4
273.74	odd	6		637.2.g.k.373.2		8
273.146	even	6		8281.2.a.bp.1.3		4
273.152	even	6		637.2.h.i.165.3		8
273.191	odd	6		637.2.h.h.165.3		8
273.230	even	6		637.2.f.i.295.2		8
273.269	even	6		637.2.g.j.373.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.2	✓	8	39.35	odd	6
91.2.f.c.29.2	yes	8	3.2	odd	2
637.2.f.i.295.2		8	273.230	even	6
637.2.f.i.393.2		8	21.20	even	2
637.2.g.j.263.2		8	21.5	even	6
637.2.g.j.373.2		8	273.269	even	6
637.2.g.k.263.2		8	21.2	odd	6
637.2.g.k.373.2		8	273.74	odd	6
637.2.h.h.165.3		8	273.191	odd	6
637.2.h.h.471.3		8	21.11	odd	6
637.2.h.i.165.3		8	273.152	even	6
637.2.h.i.471.3		8	21.17	even	6
819.2.o.h.568.3		8	13.9	even	3	inner
819.2.o.h.757.3		8	1.1	even	1	trivial
1183.2.a.k.1.3		4	39.29	odd	6
1183.2.a.l.1.2		4	39.23	odd	6
1183.2.c.g.337.4		8	39.2	even	12
1183.2.c.g.337.5		8	39.11	even	12
1456.2.s.q.113.1		8	156.35	even	6
1456.2.s.q.1121.1		8	12.11	even	2
8281.2.a.bp.1.3		4	273.146	even	6
8281.2.a.bt.1.2		4	273.62	even	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.115680 + 0.200364i) q^{2} +(0.973236 - 1.68569i) q^{4} +2.23136 q^{5} +(0.500000 - 0.866025i) q^{7} +0.913059 q^{8} +(0.258125 + 0.447085i) q^{10} +(1.66113 + 2.87716i) q^{11} +(3.40300 - 1.19146i) q^{13} +0.231361 q^{14} +(-1.84085 - 3.18844i) q^{16} +(-0.687890 + 1.19146i) q^{17} +(-1.61766 + 2.80186i) q^{19} +(2.17164 - 3.76139i) q^{20} +(-0.384320 + 0.665661i) q^{22} +(0.419251 + 0.726164i) q^{23} -0.0210289 q^{25} +(0.632387 + 0.544012i) q^{26} +(-0.973236 - 1.68569i) q^{28} +(-0.303571 - 0.525800i) q^{29} +1.71511 q^{31} +(1.33896 - 2.31915i) q^{32} -0.318302 q^{34} +(1.11568 - 1.93242i) q^{35} +(-0.776807 - 1.34547i) q^{37} -0.748524 q^{38} +2.03736 q^{40} +(-4.58892 - 7.94824i) q^{41} +(-0.615680 + 1.06639i) q^{43} +6.46667 q^{44} +(-0.0969983 + 0.168006i) q^{46} +1.62817 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-0.00243263 - 0.00421343i) q^{50} +(1.30348 - 6.89599i) q^{52} -8.39607 q^{53} +(3.70657 + 6.41997i) q^{55} +(0.456530 - 0.790732i) q^{56} +(0.0702344 - 0.121650i) q^{58} +(4.41117 - 7.64037i) q^{59} +(-2.73334 + 4.73428i) q^{61} +(0.198405 + 0.343647i) q^{62} -6.74383 q^{64} +(7.59332 - 2.65858i) q^{65} +(5.09287 + 8.82111i) q^{67} +(1.33896 + 2.31915i) q^{68} +0.516249 q^{70} +(-2.60714 + 4.51570i) q^{71} -3.96355 q^{73} +(0.179723 - 0.311289i) q^{74} +(3.14872 + 5.45375i) q^{76} +3.32225 q^{77} +6.45051 q^{79} +(-4.10760 - 7.11457i) q^{80} +(1.06170 - 1.83891i) q^{82} +4.64055 q^{83} +(-1.53493 + 2.65858i) q^{85} -0.284889 q^{86} +(1.51671 + 2.62701i) q^{88} +(4.56413 + 7.90530i) q^{89} +(0.669665 - 3.54282i) q^{91} +1.63212 q^{92} +(0.188347 + 0.326227i) q^{94} +(-3.60957 + 6.25197i) q^{95} +(7.67944 - 13.3012i) q^{97} +(0.115680 - 0.200364i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 5 q^{4} + 14 q^{5} + 4 q^{7} + 12 q^{8} + 11 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 19 q^{16} - 4 q^{17} - q^{19} - 2 q^{20} - 5 q^{22} - 2 q^{23} + 10 q^{25} - 12 q^{26} + 5 q^{28} + q^{29}+ \cdots - q^{98}+O(q^{100}) \) 8 * q - q^2 - 5 * q^4 + 14 * q^5 + 4 * q^7 + 12 * q^8 + 11 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 19 * q^16 - 4 * q^17 - q^19 - 2 * q^20 - 5 * q^22 - 2 * q^23 + 10 * q^25 - 12 * q^26 + 5 * q^28 + q^29 - 8 * q^31 - 33 * q^32 + 6 * q^34 + 7 * q^35 + 10 * q^37 + 46 * q^38 - 34 * q^40 - 22 * q^41 - 3 * q^43 + 24 * q^44 - 24 * q^46 - 4 * q^47 - 4 * q^49 + 43 * q^50 + 65 * q^52 - 4 * q^53 + 3 * q^55 + 6 * q^56 + 11 * q^58 - 8 * q^59 - 8 * q^61 - 5 * q^62 + 28 * q^64 - 7 * q^65 + 6 * q^67 - 33 * q^68 + 22 * q^70 - 14 * q^71 - 16 * q^73 + 20 * q^74 - 32 * q^76 - 2 * q^77 - 52 * q^79 + 7 * q^80 + 14 * q^82 - 5 * q^85 - 24 * q^86 - 3 * q^88 - q^89 - 4 * q^91 - 24 * q^92 - 33 * q^94 + 21 * q^95 - 3 * q^97 - q^98

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