LMFDB - Embedded newform 891.2.k.a.404.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(161,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 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("891.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			404.10
Character	$\chi$	$=$	891.404
Dual form			891.2.k.a.161.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.299321 + 0.217469i) q^{2} +(-0.575734 + 1.77193i) q^{4} +(-1.39685 + 1.92260i) q^{5} +(-1.49987 - 0.487337i) q^{7} +(-0.441671 - 1.35932i) q^{8} -0.879247i q^{10} +(1.13773 + 3.11538i) q^{11} +(-3.60270 - 4.95870i) q^{13} +(0.554923 - 0.180306i) q^{14} +(-2.58677 - 1.87940i) q^{16} +(-0.887473 - 0.644787i) q^{17} +(-0.534855 + 0.173785i) q^{19} +(-2.60249 - 3.58202i) q^{20} +(-1.01805 - 0.685076i) q^{22} +5.56398i q^{23} +(-0.200115 - 0.615892i) q^{25} +(2.15673 + 0.700764i) q^{26} +(1.72705 - 2.37708i) q^{28} +(0.229389 - 0.705986i) q^{29} +(5.11890 - 3.71910i) q^{31} +4.04154 q^{32} +0.405861 q^{34} +(3.03205 - 2.20291i) q^{35} +(1.32443 - 4.07617i) q^{37} +(0.122300 - 0.168332i) q^{38} +(3.23039 + 1.04962i) q^{40} +(-3.75539 - 11.5579i) q^{41} -8.49248i q^{43} +(-6.17525 + 0.222344i) q^{44} +(-1.20999 - 1.66541i) q^{46} +(-0.731927 + 0.237817i) q^{47} +(-3.65101 - 2.65261i) q^{49} +(0.193836 + 0.140830i) q^{50} +(10.8606 - 3.52884i) q^{52} +(2.66042 + 3.66175i) q^{53} +(-7.57886 - 2.16432i) q^{55} +2.25405i q^{56} +(0.0848695 + 0.261201i) q^{58} +(0.0106843 + 0.00347154i) q^{59} +(-3.36853 + 4.63638i) q^{61} +(-0.723404 + 2.22641i) q^{62} +(3.96382 - 2.87988i) q^{64} +14.5660 q^{65} +1.47666 q^{67} +(1.65346 - 1.20131i) q^{68} +(-0.428490 + 1.31876i) q^{70} +(-4.89992 + 6.74417i) q^{71} +(-14.9894 - 4.87035i) q^{73} +(0.490013 + 1.50811i) q^{74} -1.04778i q^{76} +(-0.188206 - 5.22712i) q^{77} +(1.86989 + 2.57368i) q^{79} +(7.22666 - 2.34809i) q^{80} +(3.63756 + 2.64284i) q^{82} +(-8.40013 - 6.10305i) q^{83} +(2.47934 - 0.805585i) q^{85} +(1.84685 + 2.54198i) q^{86} +(3.73231 - 2.92252i) q^{88} +9.01115i q^{89} +(2.98703 + 9.19313i) q^{91} +(-9.85896 - 3.20337i) q^{92} +(0.167363 - 0.230355i) q^{94} +(0.412994 - 1.27106i) q^{95} +(-4.48177 + 3.25619i) q^{97} +1.66968 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

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 $

$2$	−0.299321	+	0.217469i	−0.211652	+	0.153774i	−0.688561	−	0.725179i	$-0.741757\pi$
$2$	−0.299321	+	0.217469i	−0.211652	+	0.153774i	0.476909	+	0.878953i	$0.341757\pi$
$3$		0			0
$3$		0			0
$4$	−0.575734	+	1.77193i	−0.287867	+	0.885963i
$5$	−1.39685	+	1.92260i	−0.624691	+	0.859813i	−0.997684	−	0.0680209i	$-0.978332\pi$
$5$	−1.39685	+	1.92260i	−0.624691	+	0.859813i	0.372993	+	0.927834i	$0.378332\pi$
$6$		0			0
$7$	−1.49987	−	0.487337i	−0.566898	−	0.184196i	0.0115248	−	0.999934i	$-0.496331\pi$
$7$	−1.49987	−	0.487337i	−0.566898	−	0.184196i	−0.578422	+	0.815737i	$0.696331\pi$
$8$	−0.441671	−	1.35932i	−0.156154	−	0.480594i
$9$		0			0
$10$		−	0.879247i		−	0.278042i
$11$	1.13773	+	3.11538i	0.343038	+	0.939321i
$11$	1.13773	+	3.11538i	0.343038	+	0.939321i
$12$		0			0
$13$	−3.60270	−	4.95870i	−0.999210	−	1.37529i	−0.925809	−	0.377992i	$-0.876615\pi$
$13$	−3.60270	−	4.95870i	−0.999210	−	1.37529i	−0.0734014	−	0.997302i	$-0.523385\pi$
$14$	0.554923	−	0.180306i	0.148310	−	0.0481887i
$15$		0			0
$16$	−2.58677	−	1.87940i	−0.646692	−	0.469849i
$17$	−0.887473	−	0.644787i	−0.215244	−	0.156384i	0.474939	−	0.880019i	$-0.342470\pi$
$17$	−0.887473	−	0.644787i	−0.215244	−	0.156384i	−0.690183	+	0.723635i	$0.742470\pi$
$18$		0			0
$19$	−0.534855	+	0.173785i	−0.122704	+	0.0398690i	−0.369725	−	0.929141i	$-0.620548\pi$
$19$	−0.534855	+	0.173785i	−0.122704	+	0.0398690i	0.247021	+	0.969010i	$0.420548\pi$
$20$	−2.60249	−	3.58202i	−0.581935	−	0.800965i
$21$		0			0
$22$	−1.01805	−	0.685076i	−0.217048	−	0.146059i
$23$			5.56398i			1.16017i	0.814556	+	0.580085i	$0.196980\pi$
$23$			5.56398i			1.16017i	−0.814556	+	0.580085i	$0.803020\pi$
$24$		0			0
$25$	−0.200115	−	0.615892i	−0.0400231	−	0.123178i
$26$	2.15673	+	0.700764i	0.422969	+	0.137431i
$27$		0			0
$28$	1.72705	−	2.37708i	0.326382	−	0.449227i
$29$	0.229389	−	0.705986i	0.0425964	−	0.131098i	−0.927497	−	0.373831i	$-0.878044\pi$
$29$	0.229389	−	0.705986i	0.0425964	−	0.131098i	0.970093	+	0.242733i	$0.0780439\pi$
$30$		0			0
$31$	5.11890	−	3.71910i	0.919382	−	0.667970i	−0.0239881	−	0.999712i	$-0.507636\pi$
$31$	5.11890	−	3.71910i	0.919382	−	0.667970i	0.943370	+	0.331742i	$0.107636\pi$
$32$	4.04154			0.714451
$33$		0			0
$34$	0.405861			0.0696045
$35$	3.03205	−	2.20291i	0.512510	−	0.372360i
$36$		0			0
$37$	1.32443	−	4.07617i	0.217735	−	0.670118i	−0.781214	−	0.624264i	$-0.785399\pi$
$37$	1.32443	−	4.07617i	0.217735	−	0.670118i	0.998948	−	0.0458543i	$-0.0146010\pi$
$38$	0.122300	−	0.168332i	0.0198397	−	0.0273070i
$39$		0			0
$40$	3.23039	+	1.04962i	0.510769	+	0.165959i
$41$	−3.75539	−	11.5579i	−0.586494	−	1.80504i	−0.593186	−	0.805066i	$-0.702130\pi$
$41$	−3.75539	−	11.5579i	−0.586494	−	1.80504i	0.00669163	−	0.999978i	$-0.497870\pi$
$42$		0			0
$43$		−	8.49248i		−	1.29509i	−0.762027	−	0.647546i	$-0.775795\pi$
$43$		−	8.49248i		−	1.29509i	0.762027	−	0.647546i	$-0.224205\pi$
$44$	−6.17525	+	0.222344i	−0.930954	+	0.0335197i
$45$		0			0
$46$	−1.20999	−	1.66541i	−0.178404	−	0.245552i
$47$	−0.731927	+	0.237817i	−0.106763	+	0.0346892i	−0.361911	−	0.932213i	$-0.617876\pi$
$47$	−0.731927	+	0.237817i	−0.106763	+	0.0346892i	0.255149	+	0.966902i	$0.417876\pi$
$48$		0			0
$49$	−3.65101	−	2.65261i	−0.521572	−	0.378944i
$50$	0.193836	+	0.140830i	0.0274126	+	0.0199164i
$51$		0			0
$52$	10.8606	−	3.52884i	1.50610	−	0.489362i
$53$	2.66042	+	3.66175i	0.365437	+	0.502981i	0.951653	−	0.307174i	$-0.0993833\pi$
$53$	2.66042	+	3.66175i	0.365437	+	0.502981i	−0.586217	+	0.810154i	$0.699383\pi$
$54$		0			0
$55$	−7.57886	−	2.16432i	−1.02193	−	0.291837i
$56$			2.25405i			0.301211i
$57$		0			0
$58$	0.0848695	+	0.261201i	0.0111439	+	0.0342974i
$59$	0.0106843	+	0.00347154i	0.00139098	+	0.000451956i	0.309712	−	0.950830i	$-0.399767\pi$
$59$	0.0106843	+	0.00347154i	0.00139098	+	0.000451956i	−0.308321	+	0.951282i	$0.599767\pi$
$60$		0			0
$61$	−3.36853	+	4.63638i	−0.431296	+	0.593628i	−0.968250	−	0.249983i	$-0.919575\pi$
$61$	−3.36853	+	4.63638i	−0.431296	+	0.593628i	0.536954	+	0.843611i	$0.319575\pi$
$62$	−0.723404	+	2.22641i	−0.0918724	+	0.282754i
$63$		0			0
$64$	3.96382	−	2.87988i	0.495477	−	0.359985i
$65$	14.5660			1.80669
$66$		0			0
$67$	1.47666			0.180403			0.0902017	−	0.995924i	$-0.471249\pi$
$67$	1.47666			0.180403			0.0902017	+	0.995924i	$0.471249\pi$
$68$	1.65346	−	1.20131i	0.200512	−	0.145680i
$69$		0			0
$70$	−0.428490	+	1.31876i	−0.0512143	+	0.157622i
$71$	−4.89992	+	6.74417i	−0.581514	+	0.800385i	−0.993860	−	0.110642i	$-0.964709\pi$
$71$	−4.89992	+	6.74417i	−0.581514	+	0.800385i	0.412346	+	0.911027i	$0.364709\pi$
$72$		0			0
$73$	−14.9894	−	4.87035i	−1.75438	−	0.570031i	−0.757783	−	0.652507i	$-0.773717\pi$
$73$	−14.9894	−	4.87035i	−1.75438	−	0.570031i	−0.996593	+	0.0824752i	$0.973717\pi$
$74$	0.490013	+	1.50811i	0.0569629	+	0.175314i
$75$		0			0
$76$		−	1.04778i		−	0.120188i
$77$	−0.188206	−	5.22712i	−0.0214481	−	0.595685i
$78$		0			0
$79$	1.86989	+	2.57368i	0.210379	+	0.289562i	0.901146	−	0.433515i	$-0.142727\pi$
$79$	1.86989	+	2.57368i	0.210379	+	0.289562i	−0.690767	+	0.723077i	$0.742727\pi$
$80$	7.22666	−	2.34809i	0.807965	−	0.262524i
$81$		0			0
$82$	3.63756	+	2.64284i	0.401701	+	0.291853i
$83$	−8.40013	−	6.10305i	−0.922034	−	0.669897i	0.0219956	−	0.999758i	$-0.492998\pi$
$83$	−8.40013	−	6.10305i	−0.922034	−	0.669897i	−0.944029	+	0.329861i	$0.892998\pi$
$84$		0			0
$85$	2.47934	−	0.805585i	0.268922	−	0.0873779i
$86$	1.84685	+	2.54198i	0.199151	+	0.274108i
$87$		0			0
$88$	3.73231	−	2.92252i	0.397865	−	0.311541i
$89$			9.01115i			0.955180i	0.878583	+	0.477590i	$0.158489\pi$
$89$			9.01115i			0.955180i	−0.878583	+	0.477590i	$0.841511\pi$
$90$		0			0
$91$	2.98703	+	9.19313i	0.313126	+	0.963702i
$92$	−9.85896	−	3.20337i	−1.02787	−	0.333974i
$93$		0			0
$94$	0.167363	−	0.230355i	0.0172622	−	0.0237593i
$95$	0.412994	−	1.27106i	0.0423723	−	0.130408i
$96$		0			0
$97$	−4.48177	+	3.25619i	−0.455054	+	0.330616i	−0.791588	−	0.611055i	$-0.790745\pi$
$97$	−4.48177	+	3.25619i	−0.455054	+	0.330616i	0.336534	+	0.941671i	$0.390745\pi$
$98$	1.66968			0.168664
$99$		0			0
$100$	1.20653			0.120653
$101$	−7.87579	+	5.72209i	−0.783670	+	0.569370i	−0.906078	−	0.423110i	$-0.860938\pi$
$101$	−7.87579	+	5.72209i	−0.783670	+	0.569370i	0.122408	+	0.992480i	$0.460938\pi$
$102$		0			0
$103$	0.584954	−	1.80030i	0.0576372	−	0.177389i	−0.918093	−	0.396365i	$-0.870272\pi$
$103$	0.584954	−	1.80030i	0.0576372	−	0.177389i	0.975730	+	0.218976i	$0.0702715\pi$
$104$	−5.14927	+	7.08736i	−0.504927	+	0.694973i
$105$		0			0
$106$	−1.59264	−	0.517480i	−0.154691	−	0.0502621i
$107$	−3.79203	−	11.6707i	−0.366590	−	1.12825i	−0.948980	−	0.315337i	$-0.897882\pi$
$107$	−3.79203	−	11.6707i	−0.366590	−	1.12825i	0.582390	−	0.812910i	$-0.302118\pi$
$108$		0			0
$109$			8.79322i			0.842238i	0.907005	+	0.421119i	$0.138362\pi$
$109$			8.79322i			0.842238i	−0.907005	+	0.421119i	$0.861638\pi$
$110$	2.73919	−	1.00034i	0.261171	−	0.0953791i
$111$		0			0
$112$	2.96392	+	4.07948i	0.280064	+	0.385475i
$113$	0.0441193	−	0.0143352i	0.00415039	−	0.00134854i	−0.306941	−	0.951729i	$-0.599305\pi$
$113$	0.0441193	−	0.0143352i	0.00415039	−	0.00134854i	0.311091	+	0.950380i	$0.399305\pi$
$114$		0			0
$115$	−10.6973	−	7.77205i	−0.997529	−	0.724747i
$116$	1.11889	+	0.812920i	0.103886	+	0.0754777i
$117$		0			0
$118$	−0.00395298	+	0.00128440i	−0.000363902	+	0.000118239i
$119$	1.01687	+	1.39960i	0.0932159	+	0.128301i
$120$		0			0
$121$	−8.41115	+	7.08891i	−0.764650	+	0.644446i
$122$		−	2.12032i		−	0.191965i
$123$		0			0
$124$	3.64285	+	11.2115i	0.327137	+	1.00683i
$125$	−9.83712	−	3.19627i	−0.879859	−	0.285883i
$126$		0			0
$127$	3.88014	−	5.34055i	0.344307	−	0.473898i	−0.601386	−	0.798958i	$-0.705385\pi$
$127$	3.88014	−	5.34055i	0.344307	−	0.473898i	0.945693	+	0.325061i	$0.105385\pi$
$128$	−3.05798	+	9.41149i	−0.270290	+	0.831866i
$129$		0			0
$130$	−4.35992	+	3.16767i	−0.382390	+	0.277823i
$131$	−7.88337			−0.688773			−0.344387	−	0.938828i	$-0.611913\pi$
$131$	−7.88337			−0.688773			−0.344387	+	0.938828i	$0.611913\pi$
$132$		0			0
$133$	0.886904			0.0769044
$134$	−0.441997	+	0.321129i	−0.0381827	+	0.0277414i
$135$		0			0
$136$	−0.484503	+	1.49115i	−0.0415458	+	0.127865i
$137$	10.3791	−	14.2857i	0.886749	−	1.22051i	−0.0877559	−	0.996142i	$-0.527970\pi$
$137$	10.3791	−	14.2857i	0.886749	−	1.22051i	0.974505	−	0.224364i	$-0.0720304\pi$
$138$		0			0
$139$	−13.3927	−	4.35156i	−1.13596	−	0.369094i	−0.320119	−	0.947377i	$-0.603723\pi$
$139$	−13.3927	−	4.35156i	−1.13596	−	0.369094i	−0.815836	+	0.578283i	$0.803723\pi$
$140$	2.15775	+	6.64086i	0.182363	+	0.561255i
$141$		0			0
$142$		−	3.08425i		−	0.258825i
$143$	11.3493	−	16.8654i	0.949077	−	1.41036i
$144$		0			0
$145$	1.03691	+	1.42718i	0.0861105	+	0.118521i
$146$	5.54579	−	1.80194i	0.458973	−	0.149129i
$147$		0			0
$148$	6.46016	+	4.69358i	0.531022	+	0.385810i
$149$	11.5245	+	8.37303i	0.944123	+	0.685946i	0.949410	−	0.314040i	$-0.101683\pi$
$149$	11.5245	+	8.37303i	0.944123	+	0.685946i	−0.00528647	+	0.999986i	$0.501683\pi$
$150$		0			0
$151$	−2.45014	+	0.796099i	−0.199390	+	0.0647856i	−0.407009	−	0.913424i	$-0.633428\pi$
$151$	−2.45014	+	0.796099i	−0.199390	+	0.0647856i	0.207620	+	0.978210i	$0.433428\pi$
$152$	0.472460	+	0.650285i	0.0383216	+	0.0527451i
$153$		0			0
$154$	1.19307	+	1.52366i	0.0961405	+	0.122780i
$155$			15.0366i			1.20777i
$156$		0			0
$157$	1.75945	+	5.41504i	0.140420	+	0.432167i	0.996394	−	0.0848519i	$-0.0270417\pi$
$157$	1.75945	+	5.41504i	0.140420	+	0.432167i	−0.855974	+	0.517019i	$0.827042\pi$
$158$	−1.11939	−	0.363713i	−0.0890542	−	0.0289355i
$159$		0			0
$160$	−5.64543	+	7.77027i	−0.446311	+	0.614294i
$161$	2.71153	−	8.34524i	0.213699	−	0.657697i
$162$		0			0
$163$	6.92500	−	5.03131i	0.542408	−	0.394083i	−0.282570	−	0.959247i	$-0.591187\pi$
$163$	6.92500	−	5.03131i	0.542408	−	0.394083i	0.824979	+	0.565164i	$0.191187\pi$
$164$	22.6419			1.76803
$165$		0			0
$166$	3.84156			0.298163
$167$	−2.46778	+	1.79294i	−0.190962	+	0.138742i	−0.679158	−	0.733992i	$-0.737655\pi$
$167$	−2.46778	+	1.79294i	−0.190962	+	0.138742i	0.488196	+	0.872734i	$0.337655\pi$
$168$		0			0
$169$	−7.59197	+	23.3657i	−0.583998	+	1.79736i
$170$	−0.566927	+	0.780308i	−0.0434813	+	0.0598469i
$171$		0			0
$172$	15.0481	+	4.88941i	1.14740	+	0.372814i
$173$	−3.51506	−	10.8183i	−0.267245	−	0.822497i	−0.991168	−	0.132615i	$-0.957663\pi$
$173$	−3.51506	−	10.8183i	−0.267245	−	0.822497i	0.723922	−	0.689882i	$-0.242337\pi$
$174$		0			0
$175$			1.02128i			0.0772016i
$176$	2.91199	−	10.1970i	0.219500	−	0.768628i
$177$		0			0
$178$	−1.95965	−	2.69722i	−0.146882	−	0.202166i
$179$	−10.1952	+	3.31261i	−0.762023	+	0.247596i	−0.664147	−	0.747602i	$-0.731205\pi$
$179$	−10.1952	+	3.31261i	−0.762023	+	0.247596i	−0.0978766	+	0.995199i	$0.531205\pi$
$180$		0			0
$181$	14.3857	+	10.4518i	1.06928	+	0.776879i	0.975783	−	0.218741i	$-0.0701949\pi$
$181$	14.3857	+	10.4518i	1.06928	+	0.776879i	0.0934987	+	0.995619i	$0.470195\pi$
$182$	−2.89330	−	2.10211i	−0.214466	−	0.155819i
$183$		0			0
$184$	7.56325	−	2.45745i	0.557570	−	0.181166i
$185$	5.98682	+	8.24015i	0.440160	+	0.605828i
$186$		0			0
$187$	0.999050	−	3.49840i	0.0730578	−	0.255829i
$188$		−	1.43384i		−	0.104574i
$189$		0			0
$190$	0.152800	+	0.470269i	0.0110853	+	0.0341169i
$191$	−19.4453	−	6.31817i	−1.40701	−	0.457167i	−0.495562	−	0.868572i	$-0.665038\pi$
$191$	−19.4453	−	6.31817i	−1.40701	−	0.457167i	−0.911452	+	0.411406i	$0.865038\pi$
$192$		0			0
$193$	−8.98083	+	12.3610i	−0.646454	+	0.889768i	−0.998939	−	0.0460498i	$-0.985337\pi$
$193$	−8.98083	+	12.3610i	−0.646454	+	0.889768i	0.352485	+	0.935817i	$0.385337\pi$
$194$	0.633364	−	1.94929i	0.0454729	−	0.139951i
$195$		0			0
$196$	6.80224	−	4.94212i	0.485874	−	0.353008i
$197$	13.1024			0.933507			0.466754	−	0.884387i	$-0.345424\pi$
$197$	13.1024			0.933507			0.466754	+	0.884387i	$0.345424\pi$
$198$		0			0
$199$	−4.72311			−0.334812			−0.167406	−	0.985888i	$-0.553539\pi$
$199$	−4.72311			−0.334812			−0.167406	+	0.985888i	$0.553539\pi$
$200$	−0.748812	+	0.544044i	−0.0529490	+	0.0384697i
$201$		0			0
$202$	1.11301	−	3.42548i	0.0783109	−	0.241016i
$203$	−0.688107	+	0.947098i	−0.0482956	+	0.0664732i
$204$		0			0
$205$	27.4670	+	8.92456i	1.91838	+	0.623319i
$206$	0.216422	+	0.666078i	0.0150788	+	0.0464078i
$207$		0			0
$208$			19.5979i			1.35887i
$209$	−1.14992	−	1.46855i	−0.0795420	−	0.101582i
$210$		0			0
$211$	11.4835	+	15.8056i	0.790554	+	1.08810i	0.994039	+	0.109026i	$0.0347732\pi$
$211$	11.4835	+	15.8056i	0.790554	+	1.08810i	−0.203485	+	0.979078i	$0.565227\pi$
$212$	−8.02005	+	2.60587i	−0.550820	+	0.178972i
$213$		0			0
$214$	3.67305	+	2.66863i	0.251085	+	0.182424i
$215$	16.3277	+	11.8627i	1.11354	+	0.809032i
$216$		0			0
$217$	−9.49015	+	3.08354i	−0.644233	+	0.209324i
$218$	−1.91226	−	2.63199i	−0.129514	−	0.178261i
$219$		0			0
$220$	8.19842	−	12.1831i	0.552738	−	0.821386i
$221$			6.72368i			0.452284i
$222$		0			0
$223$	−5.07706	−	15.6256i	−0.339985	−	1.04637i	−0.964214	−	0.265125i	$-0.914587\pi$
$223$	−5.07706	−	15.6256i	−0.339985	−	1.04637i	0.624229	−	0.781242i	$-0.285413\pi$
$224$	−6.06179	−	1.96959i	−0.405020	−	0.131599i
$225$		0			0
$226$	−0.0100884	+	0.0138854i	−0.000671067	+	0.000923645i
$227$	−8.39445	+	25.8355i	−0.557159	+	1.71476i	0.133012	+	0.991114i	$0.457535\pi$
$227$	−8.39445	+	25.8355i	−0.557159	+	1.71476i	−0.690171	+	0.723646i	$0.742465\pi$
$228$		0			0
$229$	3.50738	−	2.54826i	0.231774	−	0.168394i	−0.465837	−	0.884871i	$-0.654247\pi$
$229$	3.50738	−	2.54826i	0.231774	−	0.168394i	0.697611	+	0.716477i	$0.254247\pi$
$230$	4.89211			0.322576
$231$		0			0
$232$	−1.06098			−0.0696567
$233$	−9.48697	+	6.89268i	−0.621512	+	0.451555i	−0.853449	−	0.521176i	$-0.825494\pi$
$233$	−9.48697	+	6.89268i	−0.621512	+	0.451555i	0.231937	+	0.972731i	$0.425494\pi$
$234$		0			0
$235$	0.565165	−	1.73940i	0.0368673	−	0.113466i
$236$	−0.0123026	+	0.0169331i	−0.000800832	+	0.00110225i
$237$		0			0
$238$	−0.608738	−	0.197791i	−0.0394586	−	0.0128209i
$239$	−5.54433	−	17.0637i	−0.358633	−	1.10376i	−0.953873	−	0.300210i	$-0.902943\pi$
$239$	−5.54433	−	17.0637i	−0.358633	−	1.10376i	0.595240	−	0.803548i	$-0.297057\pi$
$240$		0			0
$241$		−	2.67184i		−	0.172108i	−0.996290	−	0.0860541i	$-0.972574\pi$
$241$		−	2.67184i		−	0.172108i	0.996290	−	0.0860541i	$-0.0274258\pi$
$242$	0.976011	−	3.95102i	0.0627404	−	0.253982i
$243$		0			0
$244$	−6.27595	−	8.63811i	−0.401777	−	0.552998i
$245$	10.1998	−	3.31412i	0.651643	−	0.211732i
$246$		0			0
$247$	2.78867	+	2.02609i	0.177439	+	0.128917i
$248$	−7.31634	−	5.31563i	−0.464588	−	0.337543i
$249$		0			0
$250$	3.63955	−	1.18256i	0.230185	−	0.0747917i
$251$	−7.98861	−	10.9954i	−0.504237	−	0.694022i	0.478697	−	0.877980i	$-0.341109\pi$
$251$	−7.98861	−	10.9954i	−0.504237	−	0.694022i	−0.982934	+	0.183958i	$0.941109\pi$
$252$		0			0
$253$	−17.3339	+	6.33030i	−1.08977	+	0.397982i
$254$			2.44235i			0.153247i
$255$		0			0
$256$	1.89669	+	5.83743i	0.118543	+	0.364839i
$257$	−4.52222	−	1.46936i	−0.282088	−	0.0916561i	0.164556	−	0.986368i	$-0.447381\pi$
$257$	−4.52222	−	1.46936i	−0.282088	−	0.0916561i	−0.446644	+	0.894712i	$0.647381\pi$
$258$		0			0
$259$	−3.97294	+	5.46828i	−0.246866	+	0.339783i
$260$	−8.38616	+	25.8099i	−0.520088	+	1.60066i
$261$		0			0
$262$	2.35966	−	1.71439i	0.145780	−	0.105915i
$263$	−18.5223			−1.14213			−0.571067	−	0.820903i	$-0.693471\pi$
$263$	−18.5223			−1.14213			−0.571067	+	0.820903i	$0.693471\pi$
$264$		0			0
$265$	−10.7563			−0.660754
$266$	−0.265469	+	0.192875i	−0.0162770	+	0.0118259i
$267$		0			0
$268$	−0.850166	+	2.61654i	−0.0519322	+	0.159831i
$269$	−12.6954	+	17.4737i	−0.774049	+	1.06539i	0.221864	+	0.975078i	$0.428786\pi$
$269$	−12.6954	+	17.4737i	−0.774049	+	1.06539i	−0.995914	+	0.0903100i	$0.971214\pi$
$270$		0			0
$271$	−0.869236	−	0.282432i	−0.0528023	−	0.0171565i	0.282497	−	0.959268i	$-0.408837\pi$
$271$	−0.869236	−	0.282432i	−0.0528023	−	0.0171565i	−0.335299	+	0.942112i	$0.608837\pi$
$272$	1.08388	+	3.33583i	0.0657197	+	0.202264i
$273$		0			0
$274$			6.53314i			0.394681i
$275$	1.69106	−	1.32415i	0.101975	−	0.0798494i
$276$		0			0
$277$	8.70688	+	11.9840i	0.523145	+	0.720048i	0.986067	−	0.166352i	$-0.0531986\pi$
$277$	8.70688	+	11.9840i	0.523145	+	0.720048i	−0.462921	+	0.886400i	$0.653199\pi$
$278$	4.95505	−	1.60999i	0.297184	−	0.0965610i
$279$		0			0
$280$	−4.33365	−	3.14858i	−0.258985	−	0.188164i
$281$	−1.48662	−	1.08010i	−0.0886846	−	0.0644331i	0.542559	−	0.840017i	$-0.317455\pi$
$281$	−1.48662	−	1.08010i	−0.0886846	−	0.0644331i	−0.631244	+	0.775584i	$0.717455\pi$
$282$		0			0
$283$	−11.4793	+	3.72985i	−0.682373	+	0.221716i	−0.629634	−	0.776892i	$-0.716795\pi$
$283$	−11.4793	+	3.72985i	−0.682373	+	0.221716i	−0.0527388	+	0.998608i	$0.516795\pi$
$284$	−9.12912	−	12.5652i	−0.541713	−	0.745605i
$285$		0			0
$286$	0.270630	+	7.51630i	0.0160027	+	0.444448i
$287$			19.1655i			1.13130i
$288$		0			0
$289$	−4.88143	−	15.0235i	−0.287143	−	0.883735i
$290$	−0.620736	−	0.201689i	−0.0364509	−	0.0118436i
$291$		0			0
$292$	17.2598	−	23.7561i	1.01005	−	1.39022i
$293$	−5.27855	+	16.2457i	−0.308376	+	0.949085i	0.670019	+	0.742344i	$0.266286\pi$
$293$	−5.27855	+	16.2457i	−0.308376	+	0.949085i	−0.978396	+	0.206741i	$0.933714\pi$
$294$		0			0
$295$	−0.0215987	+	0.0156924i	−0.00125753	+	0.000913647i
$296$	−6.12580			−0.356055
$297$		0			0
$298$	−5.27040			−0.305306
$299$	27.5901	−	20.0454i	1.59557	−	1.15925i
$300$		0			0
$301$	−4.13870	+	12.7376i	−0.238551	+	0.734184i
$302$	0.560251	−	0.771119i	0.0322388	−	0.0443729i
$303$		0			0
$304$	1.71016	+	0.555663i	0.0980842	+	0.0318695i
$305$	−4.20858	−	12.9527i	−0.240983	−	0.741668i
$306$		0			0
$307$		−	16.6906i		−	0.952585i	−0.879287	−	0.476293i	$-0.841980\pi$
$307$		−	16.6906i		−	0.952585i	0.879287	−	0.476293i	$-0.158020\pi$
$308$	9.37043	+	2.67594i	0.533930	+	0.152476i
$309$		0			0
$310$	−3.27001	−	4.50078i	−0.185724	−	0.255627i
$311$	28.0994	−	9.13006i	1.59337	−	0.517718i	0.627915	−	0.778282i	$-0.283908\pi$
$311$	28.0994	−	9.13006i	1.59337	−	0.517718i	0.965457	+	0.260564i	$0.0839083\pi$
$312$		0			0
$313$	−13.0604	−	9.48891i	−0.738215	−	0.536345i	0.153936	−	0.988081i	$-0.450805\pi$
$313$	−13.0604	−	9.48891i	−0.738215	−	0.536345i	−0.892152	+	0.451736i	$0.850805\pi$
$314$	−1.70424	−	1.23821i	−0.0961761	−	0.0698760i
$315$		0			0
$316$	−5.63693	+	1.83155i	−0.317102	+	0.103033i
$317$	4.92818	+	6.78306i	0.276794	+	0.380974i	0.924669	−	0.380773i	$-0.124342\pi$
$317$	4.92818	+	6.78306i	0.276794	+	0.380974i	−0.647875	+	0.761747i	$0.724342\pi$
$318$		0			0
$319$	2.46039	−	0.0885883i	0.137756	−	0.00495999i
$320$			11.6436i			0.650898i
$321$		0			0
$322$	1.00322	+	3.08758i	0.0559070	+	0.172064i
$323$	0.586723	+	0.190638i	0.0326462	+	0.0106074i
$324$		0			0
$325$	−2.33306	+	3.21119i	−0.129415	+	0.178125i
$326$	−0.978643	+	3.01195i	−0.0542020	+	0.166817i
$327$		0			0
$328$	−14.0523	+	10.2096i	−0.775909	+	0.563731i
$329$	1.21369			0.0669130
$330$		0			0
$331$	−1.00708			−0.0553542			−0.0276771	−	0.999617i	$-0.508811\pi$
$331$	−1.00708			−0.0553542			−0.0276771	+	0.999617i	$0.508811\pi$
$332$	15.6504	−	11.3707i	0.858927	−	0.624047i
$333$		0			0
$334$	0.348746	−	1.07333i	0.0190826	−	0.0587301i
$335$	−2.06268	+	2.83904i	−0.112696	+	0.155113i
$336$		0			0
$337$	21.1314	+	6.86601i	1.15110	+	0.374015i	0.821558	−	0.570125i	$-0.193105\pi$
$337$	21.1314	+	6.86601i	1.15110	+	0.374015i	0.329543	+	0.944141i	$0.393105\pi$
$338$	−2.80889	−	8.64486i	−0.152783	−	0.470218i
$339$		0			0
$340$			4.85700i			0.263408i
$341$	17.4103	+	11.7160i	0.942822	+	0.634456i
$342$		0			0
$343$	10.6721	+	14.6889i	0.576240	+	0.793126i
$344$	−11.5440	+	3.75089i	−0.622413	+	0.202234i
$345$		0			0
$346$	3.40477	+	2.47371i	0.183042	+	0.132988i
$347$	9.70317	+	7.04977i	0.520894	+	0.378451i	0.816940	−	0.576722i	$-0.195668\pi$
$347$	9.70317	+	7.04977i	0.520894	+	0.378451i	−0.296047	+	0.955173i	$0.595668\pi$
$348$		0			0
$349$	−9.66986	+	3.14193i	−0.517616	+	0.168183i	−0.556163	−	0.831073i	$-0.687727\pi$
$349$	−9.66986	+	3.14193i	−0.517616	+	0.168183i	0.0385474	+	0.999257i	$0.487727\pi$
$350$	−0.222097	−	0.305691i	−0.0118716	−	0.0163399i
$351$		0			0
$352$	4.59818	+	12.5909i	0.245084	+	0.671099i
$353$		−	4.61511i		−	0.245638i	−0.992429	−	0.122819i	$-0.960807\pi$
$353$		−	4.61511i		−	0.245638i	0.992429	−	0.122819i	$-0.0391934\pi$
$354$		0			0
$355$	−6.12188	−	18.8412i	−0.324915	−	0.999987i
$356$	−15.9671	−	5.18802i	−0.846254	−	0.274965i
$357$		0			0
$358$	2.33124	−	3.20867i	0.123210	−	0.169584i
$359$	2.51158	−	7.72985i	0.132556	−	0.407966i	−0.862646	−	0.505809i	$-0.831194\pi$
$359$	2.51158	−	7.72985i	0.132556	−	0.407966i	0.995202	+	0.0978426i	$0.0311942\pi$
$360$		0			0
$361$	−15.1155	+	10.9820i	−0.795550	+	0.578001i
$362$	−6.57890			−0.345779
$363$		0			0
$364$	−18.0093			−0.943943
$365$	30.3017	−	22.0155i	1.58606	−	1.15234i
$366$		0			0
$367$	11.7284	−	36.0963i	0.612217	−	1.88421i	0.175928	−	0.984403i	$-0.443707\pi$
$367$	11.7284	−	36.0963i	0.612217	−	1.88421i	0.436289	−	0.899807i	$-0.356293\pi$
$368$	10.4569	−	14.3927i	0.545105	−	0.750272i
$369$		0			0
$370$	−3.58396	−	1.16450i	−0.186321	−	0.0605394i
$371$	−2.20578	−	6.78868i	−0.114518	−	0.352451i
$372$		0			0
$373$		−	6.48359i		−	0.335707i	−0.985812	−	0.167854i	$-0.946316\pi$
$373$		−	6.48359i		−	0.335707i	0.985812	−	0.167854i	$-0.0536836\pi$
$374$	0.461759	+	1.26441i	0.0238770	+	0.0653810i
$375$		0			0
$376$	0.646542	+	0.889889i	0.0333429	+	0.0458925i
$377$	−4.32719	+	1.40599i	−0.222862	+	0.0724121i
$378$		0			0
$379$	−10.0492	−	7.30119i	−0.516194	−	0.375037i	0.298974	−	0.954261i	$-0.403356\pi$
$379$	−10.0492	−	7.30119i	−0.516194	−	0.375037i	−0.815168	+	0.579224i	$0.803356\pi$
$380$	2.01446	+	1.46359i	0.103339	+	0.0750805i
$381$		0			0
$382$	7.19440	−	2.33760i	0.368098	−	0.119602i
$383$	−8.38804	−	11.5452i	−0.428609	−	0.589930i	0.539024	−	0.842290i	$-0.318793\pi$
$383$	−8.38804	−	11.5452i	−0.428609	−	0.589930i	−0.967633	+	0.252361i	$0.918793\pi$
$384$		0			0
$385$	10.3126	+	6.93966i	0.525577	+	0.353678i
$386$		−	5.65297i		−	0.287729i
$387$		0			0
$388$	−3.18943	−	9.81606i	−0.161919	−	0.498335i
$389$	−10.2422	−	3.32789i	−0.519300	−	0.168731i	0.0376278	−	0.999292i	$-0.488020\pi$
$389$	−10.2422	−	3.32789i	−0.519300	−	0.168731i	−0.556927	+	0.830561i	$0.688020\pi$
$390$		0			0
$391$	3.58758	−	4.93788i	0.181432	−	0.249719i
$392$	−1.99322	+	6.13449i	−0.100673	+	0.309838i
$393$		0			0
$394$	−3.92182	+	2.84937i	−0.197578	+	0.143549i
$395$	−7.56012			−0.380391
$396$		0			0
$397$	13.8356			0.694387			0.347193	−	0.937794i	$-0.387135\pi$
$397$	13.8356			0.694387			0.347193	+	0.937794i	$0.387135\pi$
$398$	1.41373	−	1.02713i	0.0708637	−	0.0514855i
$399$		0			0
$400$	−0.639853	+	1.96927i	−0.0319927	+	0.0984633i
$401$	−21.0754	+	29.0078i	−1.05245	+	1.44858i	−0.165792	+	0.986161i	$0.553018\pi$
$401$	−21.0754	+	29.0078i	−1.05245	+	1.44858i	−0.886662	+	0.462418i	$0.846982\pi$
$402$		0			0
$403$	−36.8838	−	11.9843i	−1.83731	−	0.596979i
$404$	−5.60477	−	17.2497i	−0.278848	−	0.858206i
$405$		0			0
$406$		−	0.433128i		−	0.0214958i
$407$	14.2056	−	0.511484i	0.704148	−	0.0253533i
$408$		0			0
$409$	−9.23715	−	12.7138i	−0.456748	−	0.628659i	0.517083	−	0.855935i	$-0.327018\pi$
$409$	−9.23715	−	12.7138i	−0.456748	−	0.628659i	−0.973830	+	0.227276i	$0.927018\pi$
$410$	−10.1623	+	3.30192i	−0.501878	+	0.163070i
$411$		0			0
$412$	2.85323	+	2.07299i	0.140568	+	0.102129i
$413$	−0.0143332	−	0.0104137i	−0.000705293	−	0.000512425i
$414$		0			0
$415$	23.4675	−	7.62504i	1.15197	−	0.374298i
$416$	−14.5605	−	20.0408i	−0.713886	−	0.982580i
$417$		0			0
$418$	0.663562	+	0.189495i	0.0324559	+	0.00926853i
$419$			15.2101i			0.743062i	0.928421	+	0.371531i	$0.121167\pi$
$419$			15.2101i			0.743062i	−0.928421	+	0.371531i	$0.878833\pi$
$420$		0			0
$421$	−3.75191	−	11.5472i	−0.182857	−	0.562776i	0.817048	−	0.576570i	$-0.195609\pi$
$421$	−3.75191	−	11.5472i	−0.182857	−	0.562776i	−0.999905	+	0.0137940i	$0.995609\pi$
$422$	−6.87448	−	2.23365i	−0.334644	−	0.108733i
$423$		0			0
$424$	3.80248	−	5.23367i	0.184665	−	0.254169i
$425$	−0.219522	+	0.675619i	−0.0106484	+	0.0327723i
$426$		0			0
$427$	7.31184	−	5.31236i	0.353845	−	0.257083i
$428$	22.8628			1.10511
$429$		0			0
$430$	−7.46699			−0.360090
$431$	20.7468	−	15.0734i	0.999336	−	0.726060i	0.0373906	−	0.999301i	$-0.488095\pi$
$431$	20.7468	−	15.0734i	0.999336	−	0.726060i	0.961946	+	0.273240i	$0.0880954\pi$
$432$		0			0
$433$	−0.399073	+	1.22822i	−0.0191782	+	0.0590245i	−0.960188	−	0.279356i	$-0.909879\pi$
$433$	−0.399073	+	1.22822i	−0.0191782	+	0.0590245i	0.941009	+	0.338380i	$0.109879\pi$
$434$	2.17002	−	2.98678i	0.104165	−	0.143370i
$435$		0			0
$436$	−15.5809	−	5.06256i	−0.746192	−	0.242452i
$437$	−0.966935	−	2.97592i	−0.0462548	−	0.142357i
$438$		0			0
$439$			8.98876i			0.429010i	0.976723	+	0.214505i	$0.0688138\pi$
$439$			8.98876i			0.429010i	−0.976723	+	0.214505i	$0.931186\pi$
$440$	0.405354	+	11.2581i	0.0193245	+	0.536707i
$441$		0			0
$442$	−1.46220	−	2.01254i	−0.0695495	−	0.0957267i
$443$	−13.6420	+	4.43255i	−0.648151	+	0.210597i	−0.614599	−	0.788840i	$-0.710682\pi$
$443$	−13.6420	+	4.43255i	−0.648151	+	0.210597i	−0.0335523	+	0.999437i	$0.510682\pi$
$444$		0			0
$445$	−17.3248	−	12.5872i	−0.821276	−	0.596692i
$446$	4.91776	+	3.57296i	0.232863	+	0.169185i
$447$		0			0
$448$	−7.34869	+	2.38773i	−0.347193	+	0.112810i
$449$	−8.37515	−	11.5274i	−0.395248	−	0.544012i	0.564296	−	0.825573i	$-0.309148\pi$
$449$	−8.37515	−	11.5274i	−0.395248	−	0.544012i	−0.959543	+	0.281561i	$0.909148\pi$
$450$		0			0
$451$	31.7346	−	24.8492i	1.49433	−	1.17011i
$452$			0.0864294i			0.00406530i
$453$		0			0
$454$	−3.10579	−	9.55863i	−0.145762	−	0.448609i
$455$	−21.8472	−	7.09857i	−1.02421	−	0.332786i
$456$		0			0
$457$	15.2683	−	21.0150i	0.714220	−	0.983039i	−0.285476	−	0.958386i	$-0.592152\pi$
$457$	15.2683	−	21.0150i	0.714220	−	0.983039i	0.999696	−	0.0246533i	$-0.00784819\pi$
$458$	−0.495664	+	1.52550i	−0.0231608	+	0.0712817i
$459$		0			0
$460$	19.9303	−	14.4802i	0.929255	−	0.675143i
$461$	11.6547			0.542812			0.271406	−	0.962465i	$-0.412511\pi$
$461$	11.6547			0.542812			0.271406	+	0.962465i	$0.412511\pi$
$462$		0			0
$463$	18.6647			0.867423			0.433712	−	0.901052i	$-0.357204\pi$
$463$	18.6647			0.867423			0.433712	+	0.901052i	$0.357204\pi$
$464$	−1.92020	+	1.39511i	−0.0891432	+	0.0647664i
$465$		0			0
$466$	1.34070	−	4.12625i	0.0621067	−	0.191145i
$467$	1.77499	−	2.44307i	0.0821369	−	0.113052i	−0.765971	−	0.642875i	$-0.777742\pi$
$467$	1.77499	−	2.44307i	0.0821369	−	0.113052i	0.848108	+	0.529823i	$0.177742\pi$
$468$		0			0
$469$	−2.21481	−	0.719634i	−0.102270	−	0.0332296i
$470$	0.209100	+	0.643544i	0.00964508	+	0.0296845i
$471$		0			0
$472$		−	0.0160567i		−	0.000739070i
$473$	26.4573	−	9.66214i	1.21651	−	0.444266i
$474$		0			0
$475$	0.214065	+	0.294636i	0.00982199	+	0.0135188i
$476$	−3.06542	+	0.996017i	−0.140503	+	0.0456523i
$477$		0			0
$478$	5.37036	+	3.90180i	0.245635	+	0.178464i
$479$	31.2962	+	22.7380i	1.42996	+	1.03893i	0.990025	+	0.140895i	$0.0449979\pi$
$479$	31.2962	+	22.7380i	1.42996	+	1.03893i	0.439933	+	0.898031i	$0.355002\pi$
$480$		0			0
$481$	−24.9840	+	8.11780i	−1.13917	+	0.370140i
$482$	0.581043	+	0.799737i	0.0264658	+	0.0364270i
$483$		0			0
$484$	−7.71845	−	18.9853i	−0.350838	−	0.862966i
$485$		−	13.1651i		−	0.597795i
$486$		0			0
$487$	−3.79422	−	11.6774i	−0.171933	−	0.529154i	0.827548	−	0.561396i	$-0.189735\pi$
$487$	−3.79422	−	11.6774i	−0.171933	−	0.529154i	−0.999480	+	0.0322416i	$0.989735\pi$
$488$	7.79013	+	2.53117i	0.352643	+	0.114581i
$489$		0			0
$490$	−2.33230	+	3.21014i	−0.105363	+	0.145019i
$491$	−11.2694	+	34.6836i	−0.508580	+	1.56525i	0.286087	+	0.958204i	$0.407645\pi$
$491$	−11.2694	+	34.6836i	−0.508580	+	1.56525i	−0.794667	+	0.607045i	$0.792355\pi$
$492$		0			0
$493$	−0.658787	+	0.478637i	−0.0296703	+	0.0215567i
$494$	−1.27532			−0.0573793
$495$		0			0
$496$	−20.2311			−0.908403
$497$	10.6359	−	7.72746i	0.477087	−	0.346624i
$498$		0			0
$499$	7.50331	−	23.0928i	0.335894	−	1.03378i	−0.630386	−	0.776282i	$-0.717103\pi$
$499$	7.50331	−	23.0928i	0.335894	−	1.03378i	0.966280	−	0.257494i	$-0.0828968\pi$
$500$	11.3271	−	15.5905i	0.506564	−	0.697226i
$501$		0			0
$502$	4.78232	+	1.55387i	0.213445	+	0.0693526i
$503$	6.87821	+	21.1689i	0.306684	+	0.943876i	0.979043	+	0.203652i	$0.0652810\pi$
$503$	6.87821	+	21.1689i	0.306684	+	0.943876i	−0.672359	+	0.740225i	$0.734719\pi$
$504$		0			0
$505$		−	23.1349i		−	1.02949i
$506$	3.81175	−	5.66438i	0.169453	−	0.251812i
$507$		0			0
$508$	7.22914	+	9.95006i	0.320741	+	0.441463i
$509$	−26.9514	+	8.75705i	−1.19460	+	0.388150i	−0.837772	−	0.546020i	$-0.816142\pi$
$509$	−26.9514	+	8.75705i	−1.19460	+	0.388150i	−0.356830	+	0.934170i	$0.616142\pi$
$510$		0			0
$511$	20.1086	+	14.6098i	0.889554	+	0.646299i
$512$	−17.8490	−	12.9680i	−0.788820	−	0.573111i
$513$		0			0
$514$	1.67314	−	0.543635i	0.0737989	−	0.0239787i
$515$	2.64417	+	3.63939i	0.116516	+	0.160371i
$516$		0			0
$517$	−1.57363	−	2.00966i	−0.0692080	−	0.0883846i
$518$		−	2.50076i		−	0.109877i
$519$		0			0
$520$	−6.43340	−	19.8000i	−0.282123	−	0.868286i
$521$	−14.9548	−	4.85911i	−0.655182	−	0.212882i	−0.0374843	−	0.999297i	$-0.511934\pi$
$521$	−14.9548	−	4.85911i	−0.655182	−	0.212882i	−0.617698	+	0.786416i	$0.711934\pi$
$522$		0			0
$523$	8.59617	−	11.8316i	0.375884	−	0.517360i	−0.578604	−	0.815609i	$-0.696402\pi$
$523$	8.59617	−	11.8316i	0.375884	−	0.517360i	0.954488	+	0.298248i	$0.0964023\pi$
$524$	4.53872	−	13.9688i	0.198275	−	0.610228i
$525$		0			0
$526$	5.54412	−	4.02804i	0.241735	−	0.175631i
$527$	−6.94091			−0.302351
$528$		0			0
$529$	−7.95782			−0.345992
$530$	3.21959	−	2.33917i	0.139850	−	0.101607i
$531$		0			0
$532$	−0.510621	+	1.57153i	−0.0221382	+	0.0681345i
$533$	−43.7826	+	60.2616i	−1.89644	+	2.61022i
$534$		0			0
$535$	27.7350	+	9.01164i	1.19909	+	0.389607i
$536$	−0.652201	−	2.00727i	−0.0281708	−	0.0867007i
$537$		0			0
$538$		−	7.99108i		−	0.344520i
$539$	4.11003	−	14.3922i	0.177031	−	0.619916i
$540$		0			0
$541$	10.4934	+	14.4429i	0.451146	+	0.620950i	0.972643	−	0.232303i	$-0.0746262\pi$
$541$	10.4934	+	14.4429i	0.451146	+	0.620950i	−0.521497	+	0.853253i	$0.674626\pi$
$542$	0.321601	−	0.104494i	0.0138139	−	0.00448842i
$543$		0			0
$544$	−3.58676	−	2.60593i	−0.153781	−	0.111728i
$545$	−16.9059	−	12.2828i	−0.724167	−	0.526138i
$546$		0			0
$547$	4.29253	−	1.39473i	0.183535	−	0.0596342i	−0.215807	−	0.976436i	$-0.569238\pi$
$547$	4.29253	−	1.39473i	0.183535	−	0.0596342i	0.399343	+	0.916802i	$0.369238\pi$
$548$	19.3375	+	26.6158i	0.826058	+	1.13697i
$549$		0			0
$550$	−0.218206	+	0.764100i	−0.00930435	+	0.0325813i
$551$			0.417464i			0.0177846i
$552$		0			0
$553$	−1.55034	−	4.77146i	−0.0659272	−	0.202903i
$554$	−5.21230	−	1.69358i	−0.221449	−	0.0719533i
$555$		0			0
$556$	15.4213	−	21.2256i	0.654008	−	0.900165i
$557$	−8.48770	+	26.1225i	−0.359635	+	1.10684i	0.593637	+	0.804733i	$0.297691\pi$
$557$	−8.48770	+	26.1225i	−0.359635	+	1.10684i	−0.953273	+	0.302111i	$0.902309\pi$
$558$		0			0
$559$	−42.1116	+	30.5959i	−1.78113	+	1.29407i
$560$	−11.9834			−0.506390
$561$		0			0
$562$	0.679865			0.0286784
$563$	8.46897	−	6.15307i	0.356925	−	0.259321i	−0.394844	−	0.918748i	$-0.629201\pi$
$563$	8.46897	−	6.15307i	0.356925	−	0.259321i	0.751768	+	0.659427i	$0.229201\pi$
$564$		0			0
$565$	−0.0340672	+	0.104848i	−0.00143322	+	0.00441099i
$566$	2.62486	−	3.61281i	0.110331	−	0.151858i
$567$		0			0
$568$	11.3317	+	3.68188i	0.475466	+	0.154488i
$569$	−11.4567	−	35.2600i	−0.480288	−	1.47818i	−0.838690	−	0.544608i	$-0.816678\pi$
$569$	−11.4567	−	35.2600i	−0.480288	−	1.47818i	0.358402	−	0.933567i	$-0.383322\pi$
$570$		0			0
$571$		−	6.14821i		−	0.257295i	−0.991690	−	0.128647i	$-0.958936\pi$
$571$		−	6.14821i		−	0.257295i	0.991690	−	0.128647i	$-0.0410635\pi$
$572$	23.3501	+	29.8201i	0.976318	+	1.24684i
$573$		0			0
$574$	−4.16791	−	5.73664i	−0.173965	−	0.239443i
$575$	3.42681	−	1.11344i	0.142908	−	0.0464335i
$576$		0			0
$577$	−8.59300	−	6.24318i	−0.357731	−	0.259907i	0.394374	−	0.918950i	$-0.370961\pi$
$577$	−8.59300	−	6.24318i	−0.357731	−	0.259907i	−0.752105	+	0.659043i	$0.770961\pi$
$578$	4.72826	+	3.43529i	0.196670	+	0.142889i
$579$		0			0
$580$	−3.12584	+	1.01565i	−0.129794	+	0.0421725i
$581$	9.62486	+	13.2475i	0.399306	+	0.549598i
$582$		0			0
$583$	−8.38091	+	12.4543i	−0.347102	+	0.515804i
$584$			22.5266i			0.932155i
$585$		0			0
$586$	−1.95296	−	6.01061i	−0.0806762	−	0.248296i
$587$	−5.97470	−	1.94130i	−0.246602	−	0.0801259i	0.183108	−	0.983093i	$-0.441384\pi$
$587$	−5.97470	−	1.94130i	−0.246602	−	0.0801259i	−0.429710	+	0.902967i	$0.641384\pi$
$588$		0			0
$589$	−2.09155	+	2.87877i	−0.0861806	+	0.118617i
$590$	0.00305234	−	0.00939413i	0.000125663	−	0.000386750i
$591$		0			0
$592$	−11.0867	+	8.05498i	−0.455662	+	0.331058i
$593$	13.2967			0.546030			0.273015	−	0.962010i	$-0.411979\pi$
$593$	13.2967			0.546030			0.273015	+	0.962010i	$0.411979\pi$
$594$		0			0
$595$	−4.11127			−0.168546
$596$	−21.4714	+	15.5999i	−0.879505	+	0.638997i
$597$		0			0
$598$	−3.89903	+	12.0000i	−0.159443	+	0.490716i
$599$	20.5665	−	28.3074i	0.840325	−	1.15661i	−0.145587	−	0.989345i	$-0.546507\pi$
$599$	20.5665	−	28.3074i	0.840325	−	1.15661i	0.985912	−	0.167263i	$-0.0534928\pi$
$600$		0			0
$601$	−5.01758	−	1.63031i	−0.204671	−	0.0665017i	0.204887	−	0.978786i	$-0.434317\pi$
$601$	−5.01758	−	1.63031i	−0.204671	−	0.0665017i	−0.409558	+	0.912284i	$0.634317\pi$
$602$	−1.53124	−	4.71268i	−0.0624087	−	0.192074i
$603$		0			0
$604$		−	4.79981i		−	0.195301i
$605$	−1.88002	−	26.0734i	−0.0764338	−	1.06004i
$606$		0			0
$607$	−12.2253	−	16.8267i	−0.496211	−	0.682976i	0.485307	−	0.874344i	$-0.338708\pi$
$607$	−12.2253	−	16.8267i	−0.496211	−	0.682976i	−0.981518	+	0.191367i	$0.938708\pi$
$608$	−2.16164	+	0.702359i	−0.0876660	+	0.0284844i
$609$		0			0
$610$	4.07653	+	2.96177i	0.165054	+	0.119919i
$611$	3.81618	+	2.77262i	0.154386	+	0.112168i
$612$		0			0
$613$	−25.6016	+	8.31845i	−1.03404	+	0.335979i	−0.776385	−	0.630259i	$-0.782949\pi$
$613$	−25.6016	+	8.31845i	−1.03404	+	0.335979i	−0.257652	+	0.966238i	$0.582949\pi$
$614$	3.62970	+	4.99586i	0.146483	+	0.201616i
$615$		0			0
$616$	−7.02223	+	2.56450i	−0.282934	+	0.103327i
$617$		−	33.5621i		−	1.35116i	−0.737287	−	0.675580i	$-0.763893\pi$
$617$		−	33.5621i		−	1.35116i	0.737287	−	0.675580i	$-0.236107\pi$
$618$		0			0
$619$	11.5298	+	35.4851i	0.463422	+	1.42627i	0.860956	+	0.508680i	$0.169866\pi$
$619$	11.5298	+	35.4851i	0.463422	+	1.42627i	−0.397534	+	0.917588i	$0.630134\pi$
$620$	−26.6438	−	8.65710i	−1.07004	−	0.347678i
$621$		0			0
$622$	−6.42524	+	8.84358i	−0.257629	+	0.354595i
$623$	4.39147	−	13.5156i	0.175940	−	0.541489i
$624$		0			0
$625$	22.5057	−	16.3513i	0.900228	−	0.654054i
$626$	5.97279			0.238721
$627$		0			0
$628$	−10.6080			−0.423306
$629$	−3.80365	+	2.76352i	−0.151662	+	0.110189i
$630$		0			0
$631$	−5.33541	+	16.4207i	−0.212399	+	0.653698i	0.786929	+	0.617044i	$0.211670\pi$
$631$	−5.33541	+	16.4207i	−0.212399	+	0.653698i	−0.999328	+	0.0366537i	$0.988330\pi$
$632$	2.67259	−	3.67851i	0.106310	−	0.146323i
$633$		0			0
$634$	−2.95021	−	0.958583i	−0.117168	−	0.0380702i
$635$	4.84778	+	14.9199i	0.192378	+	0.592079i
$636$		0			0
$637$			27.6608i			1.09596i
$638$	−0.717182	+	0.561577i	−0.0283935	+	0.0222330i
$639$		0			0
$640$	−13.8230	−	19.0257i	−0.546402	−	0.752058i
$641$	8.97340	−	2.91563i	0.354428	−	0.115161i	−0.126391	−	0.991980i	$-0.540339\pi$
$641$	8.97340	−	2.91563i	0.354428	−	0.115161i	0.480819	+	0.876820i	$0.340339\pi$
$642$		0			0
$643$	−6.60864	−	4.80146i	−0.260619	−	0.189351i	0.449801	−	0.893129i	$-0.351495\pi$
$643$	−6.60864	−	4.80146i	−0.260619	−	0.189351i	−0.710420	+	0.703778i	$0.751495\pi$
$644$	13.2260	+	9.60928i	0.521179	+	0.378659i
$645$		0			0
$646$	−0.217076	+	0.0705324i	−0.00854076	+	0.00277506i
$647$	12.6621	+	17.4279i	0.497799	+	0.685162i	0.981803	−	0.189904i	$-0.0608178\pi$
$647$	12.6621	+	17.4279i	0.497799	+	0.685162i	−0.484003	+	0.875066i	$0.660818\pi$
$648$		0			0
$649$	0.00134068	+	0.0372353i	5.26264e−5	+	0.00146161i
$650$		−	1.46855i		−	0.0576011i
$651$		0			0
$652$	4.92815	+	15.1673i	0.193001	+	0.593997i
$653$	−43.4797	−	14.1274i	−1.70149	−	0.552848i	−0.712610	−	0.701560i	$-0.752487\pi$
$653$	−43.4797	−	14.1274i	−1.70149	−	0.552848i	−0.988880	+	0.148713i	$0.952487\pi$
$654$		0			0
$655$	11.0119	−	15.1566i	0.430270	−	0.592216i
$656$	−12.0076	+	36.9555i	−0.468817	+	1.44287i
$657$		0			0
$658$	−0.363284	+	0.263941i	−0.0141623	+	0.0102895i
$659$	−5.75272			−0.224094			−0.112047	−	0.993703i	$-0.535741\pi$
$659$	−5.75272			−0.224094			−0.112047	+	0.993703i	$0.535741\pi$
$660$		0			0
$661$	29.9259			1.16398			0.581991	−	0.813195i	$-0.302274\pi$
$661$	29.9259			1.16398			0.581991	+	0.813195i	$0.302274\pi$
$662$	0.301440	−	0.219009i	0.0117158	−	0.00851204i
$663$		0			0
$664$	−4.58593	+	14.1140i	−0.177969	+	0.547731i
$665$	−1.23887	+	1.70516i	−0.0480415	+	0.0661234i
$666$		0			0
$667$	3.92809	+	1.27631i	0.152096	+	0.0494190i
$668$	−1.75618	−	5.40498i	−0.0679488	−	0.209125i
$669$		0			0
$670$		−	1.29835i		−	0.0501598i
$671$	−18.2766	−	5.21929i	−0.705559	−	0.201489i
$672$		0			0
$673$	−0.761268	−	1.04780i	−0.0293447	−	0.0403895i	0.794093	−	0.607797i	$-0.207947\pi$
$673$	−0.761268	−	1.04780i	−0.0293447	−	0.0403895i	−0.823437	+	0.567407i	$0.807947\pi$
$674$	−7.81821	+	2.54029i	−0.301146	+	0.0978484i
$675$		0			0
$676$	−37.0313	−	26.9048i	−1.42428	−	1.03480i
$677$	16.9486	+	12.3139i	0.651389	+	0.473262i	0.863744	−	0.503931i	$-0.168113\pi$
$677$	16.9486	+	12.3139i	0.651389	+	0.473262i	−0.212355	+	0.977193i	$0.568113\pi$
$678$		0			0
$679$	8.30893	−	2.69974i	0.318868	−	0.103606i
$680$	−2.19010	−	3.01442i	−0.0839866	−	0.115598i
$681$		0			0
$682$	−7.75914	+	0.279373i	−0.297113	+	0.0106978i
$683$		−	12.7750i		−	0.488822i	−0.969672	−	0.244411i	$-0.921405\pi$
$683$		−	12.7750i		−	0.488822i	0.969672	−	0.244411i	$-0.0785945\pi$
$684$		0			0
$685$	12.9675	+	39.9099i	0.495463	+	1.52488i
$686$	−6.38877	−	2.07584i	−0.243924	−	0.0792559i
$687$		0			0
$688$	−15.9608	+	21.9681i	−0.608498	+	0.837526i
$689$	8.57282	−	26.3844i	0.326598	−	1.00517i
$690$		0			0
$691$	23.3392	−	16.9569i	0.887866	−	0.645073i	−0.0474545	−	0.998873i	$-0.515111\pi$
$691$	23.3392	−	16.9569i	0.887866	−	0.645073i	0.935321	+	0.353801i	$0.115111\pi$
$692$	21.1929			0.805633
$693$		0			0
$694$	−4.43747			−0.168444
$695$	27.0739	−	19.6704i	1.02697	−	0.746139i
$696$		0			0
$697$	−4.11958	+	12.6788i	−0.156040	+	0.480242i
$698$	2.21112	−	3.04334i	0.0836920	−	0.115192i
$699$		0			0
$700$	−1.80964	−	0.587986i	−0.0683978	−	0.0222238i
$701$	−1.64023	−	5.04812i	−0.0619507	−	0.190665i	0.915291	−	0.402793i	$-0.131961\pi$
$701$	−1.64023	−	5.04812i	−0.0619507	−	0.190665i	−0.977242	+	0.212128i	$0.931961\pi$
$702$		0			0
$703$			2.41032i			0.0909071i
$704$	13.4817	+	9.07227i	0.508110	+	0.341924i
$705$		0			0
$706$	1.00365	+	1.38140i	0.0377727	+	0.0519896i
$707$	14.6012	−	4.74423i	0.549136	−	0.178425i
$708$		0			0
$709$	23.3574	+	16.9701i	0.877204	+	0.637326i	0.932510	−	0.361143i	$-0.117613\pi$
$709$	23.3574	+	16.9701i	0.877204	+	0.637326i	−0.0553060	+	0.998469i	$0.517613\pi$
$710$	5.92979	+	4.30824i	0.222541	+	0.161685i
$711$		0			0
$712$	12.2491	−	3.97997i	0.459054	−	0.149156i
$713$	20.6930	+	28.4814i	0.774958	+	1.06664i
$714$		0			0
$715$	16.5722	+	45.3787i	0.619765	+	1.69707i
$716$		−	19.9723i		−	0.746400i
$717$		0			0
$718$	0.929237	+	2.85990i	0.0346788	+	0.106730i
$719$	−35.5978	−	11.5664i	−1.32757	−	0.431355i	−0.442484	−	0.896776i	$-0.645903\pi$
$719$	−35.5978	−	11.5664i	−1.32757	−	0.431355i	−0.885089	+	0.465422i	$0.845903\pi$
$720$		0			0
$721$	−1.75471	+	2.41515i	−0.0653488	+	0.0899449i
$722$	2.13612	−	6.57430i	0.0794981	−	0.244670i
$723$		0			0
$724$	−26.8022	+	19.4730i	−0.996097	+	0.723707i
$725$	−0.480715			−0.0178533
$726$		0			0
$727$	43.7941			1.62423			0.812116	−	0.583496i	$-0.198316\pi$
$727$	43.7941			1.62423			0.812116	+	0.583496i	$0.198316\pi$
$728$	11.1772	−	8.12069i	0.414253	−	0.300973i
$729$		0			0
$730$	−4.28224	+	13.1794i	−0.158493	+	0.487791i
$731$	−5.47584	+	7.53685i	−0.202531	+	0.278760i
$732$		0			0
$733$	−5.05270	−	1.64172i	−0.186626	−	0.0606384i	0.214213	−	0.976787i	$-0.431281\pi$
$733$	−5.05270	−	1.64172i	−0.186626	−	0.0606384i	−0.400839	+	0.916149i	$0.631281\pi$
$734$	4.33928	+	13.3549i	0.160166	+	0.492940i
$735$		0			0
$736$			22.4870i			0.828883i
$737$	1.68004	+	4.60037i	0.0618852	+	0.169457i
$738$		0			0
$739$	3.62411	+	4.98816i	0.133315	+	0.183492i	0.870455	−	0.492247i	$-0.163824\pi$
$739$	3.62411	+	4.98816i	0.133315	+	0.183492i	−0.737140	+	0.675740i	$0.763824\pi$
$740$	−18.0478	+	5.86407i	−0.663449	+	0.215568i
$741$		0			0
$742$	2.13656	+	1.55230i	0.0784357	+	0.0569869i
$743$	−5.40513	−	3.92705i	−0.198295	−	0.144070i	0.484207	−	0.874953i	$-0.339108\pi$
$743$	−5.40513	−	3.92705i	−0.198295	−	0.144070i	−0.682502	+	0.730884i	$0.739108\pi$
$744$		0			0
$745$	−32.1960	+	10.4611i	−1.17957	+	0.383266i
$746$	1.40998	+	1.94067i	0.0516231	+	0.0710531i
$747$		0			0
$748$	5.62373	+	3.78439i	0.205624	+	0.138371i
$749$			19.3525i			0.707125i
$750$		0			0
$751$	−8.75807	−	26.9546i	−0.319587	−	0.983586i	−0.973825	−	0.227298i	$-0.927011\pi$
$751$	−8.75807	−	26.9546i	−0.319587	−	0.983586i	0.654239	−	0.756288i	$-0.272989\pi$
$752$	2.34028	+	0.760403i	0.0853412	+	0.0277290i
$753$		0			0
$754$	0.989459	−	1.36187i	0.0360340	−	0.0495965i
$755$	1.89190	−	5.82267i	0.0688533	−	0.211909i
$756$		0			0
$757$	10.7918	−	7.84073i	0.392236	−	0.284976i	−0.374135	−	0.927374i	$-0.622060\pi$
$757$	10.7918	−	7.84073i	0.392236	−	0.284976i	0.766371	+	0.642398i	$0.222060\pi$
$758$	4.59573			0.166924
$759$		0			0
$760$	−1.91020			−0.0692901
$761$	−0.449868	+	0.326848i	−0.0163077	+	0.0118482i	−0.595909	−	0.803052i	$-0.703208\pi$
$761$	−0.449868	+	0.326848i	−0.0163077	+	0.0118482i	0.579602	+	0.814900i	$0.303208\pi$
$762$		0			0
$763$	4.28526	−	13.1887i	0.155137	−	0.477463i
$764$	22.3907	−	30.8181i	0.810066	−	1.11496i
$765$		0			0
$766$	5.02143	+	1.63156i	0.181432	+	0.0589507i
$767$	−0.0212780	−	0.0654871i	−0.000768305	−	0.00236460i
$768$		0			0
$769$			32.6962i			1.17906i	0.807748	+	0.589528i	$0.200686\pi$
$769$			32.6962i			1.17906i	−0.807748	+	0.589528i	$0.799314\pi$
$770$	−4.59593	+	0.165480i	−0.165626	+	0.00596347i
$771$		0			0
$772$	−16.7323	−	23.0300i	−0.602209	−	0.828869i
$773$	1.30242	−	0.423182i	0.0468448	−	0.0152208i	−0.285501	−	0.958378i	$-0.592160\pi$
$773$	1.30242	−	0.423182i	0.0468448	−	0.0152208i	0.332346	+	0.943158i	$0.392160\pi$
$774$		0			0
$775$	−3.31493	−	2.40844i	−0.119076	−	0.0865138i
$776$	6.40569	+	4.65401i	0.229951	+	0.167069i
$777$		0			0
$778$	3.78942	−	1.23126i	0.135857	−	0.0441427i
$779$	4.01718	+	5.52918i	0.143930	+	0.198103i
$780$		0			0
$781$	−26.5854	−	7.59208i	−0.951301	−	0.271666i
$782$			2.25820i			0.0807530i
$783$		0			0
$784$	4.45900	+	13.7234i	0.159250	+	0.490121i
$785$	−12.8686	−	4.18128i	−0.459302	−	0.149236i
$786$		0			0
$787$	5.09353	−	7.01064i	0.181565	−	0.249902i	−0.708527	−	0.705684i	$-0.750640\pi$
$787$	5.09353	−	7.01064i	0.181565	−	0.249902i	0.890092	+	0.455781i	$0.150640\pi$
$788$	−7.54349	+	23.2165i	−0.268726	+	0.827053i
$789$		0			0
$790$	2.26290	−	1.64409i	0.0805104	−	0.0584943i
$791$	−0.0731593			−0.00260125
$792$		0			0
$793$	35.1262			1.24737
$794$	−4.14127	+	3.00881i	−0.146968	+	0.106779i
$795$		0			0
$796$	2.71926	−	8.36901i	0.0963815	−	0.296632i
$797$	−7.92940	+	10.9139i	−0.280874	+	0.386590i	−0.926023	−	0.377467i	$-0.876795\pi$
$797$	−7.92940	+	10.9139i	−0.280874	+	0.386590i	0.645149	+	0.764057i	$0.276795\pi$
$798$		0			0
$799$	0.802907	+	0.260880i	0.0284048	+	0.00922928i
$800$	−0.808775	−	2.48915i	−0.0285945	−	0.0880049i
$801$		0			0
$802$		−	13.2659i		−	0.468435i
$803$	−1.88089	−	52.2388i	−0.0663753	−	1.84347i
$804$		0			0
$805$	12.2570	+	16.8703i	0.432001	+	0.594598i
$806$	13.6463	−	4.43395i	0.480670	−	0.156179i
$807$		0			0
$808$	11.2567	+	8.17847i	0.396009	+	0.287717i
$809$	35.6994	+	25.9371i	1.25512	+	0.911900i	0.998508	−	0.0546139i	$-0.0173928\pi$
$809$	35.6994	+	25.9371i	1.25512	+	0.911900i	0.256615	+	0.966514i	$0.417393\pi$
$810$		0			0
$811$	39.0505	−	12.6883i	1.37125	−	0.445546i	0.471466	−	0.881884i	$-0.343725\pi$
$811$	39.0505	−	12.6883i	1.37125	−	0.445546i	0.899782	+	0.436339i	$0.143725\pi$
$812$	−1.28202	−	1.76455i	−0.0449901	−	0.0619236i
$813$		0			0
$814$	−4.14081	+	3.24239i	−0.145135	+	0.113646i
$815$			20.3420i			0.712550i
$816$		0			0
$817$	1.47586	+	4.54224i	0.0516340	+	0.158913i
$818$	5.52974	+	1.79672i	0.193343	+	0.0628209i
$819$		0			0
$820$	−31.6274	+	43.5313i	−1.10447	+	1.52018i
$821$	−4.85689	+	14.9480i	−0.169507	+	0.521688i	−0.999340	−	0.0363233i	$-0.988435\pi$
$821$	−4.85689	+	14.9480i	−0.169507	+	0.521688i	0.829833	+	0.558011i	$0.188435\pi$
$822$		0			0
$823$	4.59885	−	3.34126i	0.160306	−	0.116469i	−0.504740	−	0.863271i	$-0.668412\pi$
$823$	4.59885	−	3.34126i	0.160306	−	0.116469i	0.665046	+	0.746802i	$0.268412\pi$
$824$	−2.70555			−0.0942525
$825$		0			0
$826$	0.00655490			0.000228074
$827$	−11.5227	+	8.37170i	−0.400682	+	0.291113i	−0.769819	−	0.638263i	$-0.779653\pi$
$827$	−11.5227	+	8.37170i	−0.400682	+	0.291113i	0.369137	+	0.929375i	$0.379653\pi$
$828$		0			0
$829$	−1.17567	+	3.61833i	−0.0408326	+	0.125670i	−0.969395	−	0.245507i	$-0.921046\pi$
$829$	−1.17567	+	3.61833i	−0.0408326	+	0.125670i	0.928562	+	0.371177i	$0.121046\pi$
$830$	−5.36609	+	7.38579i	−0.186260	+	0.256364i
$831$		0			0
$832$	−28.5609	−	9.28001i	−0.990172	−	0.321726i
$833$	1.52980	+	4.70824i	0.0530044	+	0.163131i
$834$		0			0
$835$		−	7.24902i		−	0.250863i
$836$	3.26422	−	1.19209i	0.112895	−	0.0412292i
$837$		0			0
$838$	−3.30773	−	4.55270i	−0.114264	−	0.157270i
$839$	3.70686	−	1.20443i	0.127975	−	0.0415816i	−0.244329	−	0.969692i	$-0.578568\pi$
$839$	3.70686	−	1.20443i	0.127975	−	0.0415816i	0.372304	+	0.928111i	$0.378568\pi$
$840$		0			0
$841$	23.0157	+	16.7219i	0.793645	+	0.576617i
$842$	3.63419	+	2.64039i	0.125242	+	0.0909939i
$843$		0			0
$844$	−34.6178	+	11.2480i	−1.19159	+	0.387173i
$845$	−34.3180	−	47.2347i	−1.18058	−	1.62492i
$846$		0			0
$847$	16.0703	−	6.53338i	0.552183	−	0.224489i
$848$		−	14.4721i		−	0.496974i
$849$		0			0
$850$	−0.0812189	−	0.249966i	−0.00278579	−	0.00857377i
$851$	22.6797	+	7.36908i	0.777450	+	0.252609i
$852$		0			0
$853$	−18.6366	+	25.6510i	−0.638104	+	0.878275i	−0.998513	−	0.0545195i	$-0.982637\pi$
$853$	−18.6366	+	25.6510i	−0.638104	+	0.878275i	0.360409	+	0.932795i	$0.382637\pi$
$854$	−1.03331	+	3.18020i	−0.0353592	+	0.108824i
$855$		0			0
$856$	−14.1894	+	10.3092i	−0.484984	+	0.352362i
$857$	−39.5636			−1.35147			−0.675733	−	0.737147i	$-0.736173\pi$
$857$	−39.5636			−1.35147			−0.675733	+	0.737147i	$0.736173\pi$
$858$		0			0
$859$	−38.3183			−1.30740			−0.653701	−	0.756753i	$-0.726785\pi$
$859$	−38.3183			−1.30740			−0.653701	+	0.756753i	$0.726785\pi$
$860$	−30.4203	+	22.1016i	−1.03732	+	0.753659i
$861$		0			0
$862$	−2.93194	+	9.02357i	−0.0998621	+	0.307344i
$863$	−27.4819	+	37.8256i	−0.935495	+	1.28760i	0.0221825	+	0.999754i	$0.492939\pi$
$863$	−27.4819	+	37.8256i	−0.935495	+	1.28760i	−0.957677	+	0.287844i	$0.907061\pi$
$864$		0			0
$865$	25.7092	+	8.35343i	0.874139	+	0.284025i
$866$	−0.147649	−	0.454418i	−0.00501733	−	0.0154417i
$867$		0			0
$868$		−	18.5911i		−	0.631024i
$869$	−5.89056	+	8.75356i	−0.199824	+	0.296944i
$870$		0			0
$871$	−5.31999	−	7.32233i	−0.180261	−	0.248108i
$872$	11.9528	−	3.88371i	0.404774	−	0.131519i
$873$		0			0
$874$	0.936595	+	0.680476i	0.0316808	+	0.0230174i
$875$	13.1967	+	9.58799i	0.446131	+	0.324133i
$876$		0			0
$877$	29.9762	−	9.73986i	1.01222	−	0.328892i	0.244484	−	0.969653i	$-0.421381\pi$
$877$	29.9762	−	9.73986i	1.01222	−	0.328892i	0.767740	+	0.640762i	$0.221381\pi$
$878$	−1.95478	−	2.69052i	−0.0659706	−	0.0908008i
$879$		0			0
$880$	15.5372	+	19.8423i	0.523757	+	0.668884i
$881$		−	42.0051i		−	1.41519i	−0.706619	−	0.707595i	$-0.749780\pi$
$881$		−	42.0051i		−	1.41519i	0.706619	−	0.707595i	$-0.250220\pi$
$882$		0			0
$883$	0.787007	+	2.42216i	0.0264849	+	0.0815122i	0.963425	−	0.267977i	$-0.0863551\pi$
$883$	0.787007	+	2.42216i	0.0264849	+	0.0815122i	−0.936940	+	0.349489i	$0.886355\pi$
$884$	−11.9139	−	3.87105i	−0.400707	−	0.130198i
$885$		0			0
$886$	3.11939	−	4.29347i	0.104798	−	0.144242i
$887$	−4.30244	+	13.2415i	−0.144462	+	0.444607i	−0.996941	−	0.0781530i	$-0.975098\pi$
$887$	−4.30244	+	13.2415i	−0.144462	+	0.444607i	0.852480	+	0.522760i	$0.175098\pi$
$888$		0			0
$889$	−8.42236	+	6.11920i	−0.282477	+	0.205231i
$890$	7.92302			0.265580
$891$		0			0
$892$	30.6104			1.02491
$893$	0.350145	−	0.254396i	0.0117172	−	0.00851302i
$894$		0			0
$895$	7.87231	−	24.2285i	0.263142	−	0.809869i
$896$	9.17314	−	12.6257i	0.306453	−	0.421797i
$897$		0			0
$898$	5.01372	+	1.62905i	0.167310	+	0.0543623i
$899$	−1.45141	−	4.46699i	−0.0484074	−	0.148983i
$900$		0			0
$901$		−	4.96511i		−	0.165412i
$902$	−4.09489	+	14.3392i	−0.136345	+	0.477443i
$903$		0			0
$904$	−0.0389725	−	0.0536410i	−0.00129620	−	0.00178407i
$905$	−40.1894	+	13.0583i	−1.33594	+	0.434074i
$906$		0			0
$907$	26.9528	+	19.5824i	0.894953	+	0.650222i	0.937165	−	0.348887i	$-0.113440\pi$
$907$	26.9528	+	19.5824i	0.894953	+	0.650222i	−0.0422115	+	0.999109i	$0.513440\pi$
$908$	−40.9456	−	29.7487i	−1.35883	−	0.987246i
$909$		0			0
$910$	8.08303	−	2.62634i	0.267950	−	0.0870622i
$911$	3.87278	+	5.33042i	0.128311	+	0.176605i	0.868339	−	0.495971i	$-0.165188\pi$
$911$	3.87278	+	5.33042i	0.128311	+	0.176605i	−0.740028	+	0.672576i	$0.765188\pi$
$912$		0			0
$913$	9.45623	−	33.1132i	0.312956	−	1.09589i
$914$			9.61060i			0.317890i
$915$		0			0
$916$	2.49601	+	7.68194i	0.0824706	+	0.253819i
$917$	11.8240	+	3.84186i	0.390464	+	0.126869i
$918$		0			0
$919$	−19.1361	+	26.3386i	−0.631241	+	0.868829i	−0.998111	−	0.0614433i	$-0.980430\pi$
$919$	−19.1361	+	26.3386i	−0.631241	+	0.868829i	0.366869	+	0.930273i	$0.380430\pi$
$920$	−5.84004	+	17.9738i	−0.192540	+	0.592579i
$921$		0			0
$922$	−3.48848	+	2.53453i	−0.114887	+	0.0834703i
$923$	51.0952			1.68182
$924$		0			0
$925$	−2.77552			−0.0912585
$926$	−5.58674	+	4.05901i	−0.183592	+	0.133387i
$927$		0			0
$928$	0.927084	−	2.85327i	0.0304330	−	0.0936633i
$929$	−8.24635	+	11.3501i	−0.270554	+	0.372386i	−0.922577	−	0.385814i	$-0.873921\pi$
$929$	−8.24635	+	11.3501i	−0.270554	+	0.372386i	0.652023	+	0.758199i	$0.273921\pi$
$930$		0			0
$931$	2.41374	+	0.784272i	0.0791072	+	0.0257035i
$932$	−6.75136	−	20.7786i	−0.221148	−	0.680624i
$933$		0			0
$934$			1.11727i			0.0365581i
$935$	5.33051	+	6.80753i	0.174326	+	0.222630i
$936$		0			0
$937$	31.0358	+	42.7172i	1.01390	+	1.39551i	0.916396	+	0.400273i	$0.131085\pi$
$937$	31.0358	+	42.7172i	1.01390	+	1.39551i	0.0975008	+	0.995235i	$0.468915\pi$
$938$	0.819436	−	0.266251i	0.0267555	−	0.00869340i
$939$		0			0
$940$	2.75670	+	2.00286i	0.0899137	+	0.0653262i
$941$	1.79920	+	1.30719i	0.0586522	+	0.0426133i	0.616725	−	0.787179i	$-0.288459\pi$
$941$	1.79920	+	1.30719i	0.0586522	+	0.0426133i	−0.558073	+	0.829792i	$0.688459\pi$
$942$		0			0
$943$	64.3080	−	20.8949i	2.09416	−	0.680432i
$944$	−0.0211134	−	0.0290601i	−0.000687183	−	0.000945826i
$945$		0			0
$946$	−5.81800	+	8.64573i	−0.189159	+	0.281097i
$947$		−	21.9181i		−	0.712241i	−0.934440	−	0.356121i	$-0.884099\pi$
$947$		−	21.9181i		−	0.712241i	0.934440	−	0.356121i	$-0.115901\pi$
$948$		0			0
$949$	29.8518	+	91.8743i	0.969029	+	2.98237i
$950$	−0.128148	−	0.0416380i	−0.00415768	−	0.00135091i
$951$		0			0
$952$	1.45338	−	2.00041i	0.0471044	−	0.0648337i
$953$	6.64425	−	20.4489i	0.215228	−	0.662404i	−0.783909	−	0.620876i	$-0.786777\pi$
$953$	6.64425	−	20.4489i	0.215228	−	0.662404i	0.999137	−	0.0415288i	$-0.0132228\pi$
$954$		0			0
$955$	39.3095	−	28.5601i	1.27203	−	0.924182i
$956$	33.4277			1.08113
$957$		0			0
$958$	−14.3124			−0.462413
$959$	−22.5293	+	16.3685i	−0.727509	+	0.528566i
$960$		0			0
$961$	2.79193	−	8.59267i	0.0900622	−	0.277183i
$962$	5.71286	−	7.86308i	0.184190	−	0.253516i
$963$		0			0
$964$	4.73430	+	1.53827i	0.152482	+	0.0495443i
$965$	−11.2205	−	34.5331i	−0.361200	−	1.11166i
$966$		0			0
$967$			15.7910i			0.507803i	0.967230	+	0.253901i	$0.0817139\pi$
$967$			15.7910i			0.507803i	−0.967230	+	0.253901i	$0.918286\pi$
$968$	13.3511	+	8.30251i	0.429120	+	0.266853i
$969$		0			0
$970$	2.86300	+	3.94058i	0.0919253	+	0.126524i
$971$	7.29530	−	2.37039i	0.234117	−	0.0760693i	−0.189609	−	0.981860i	$-0.560722\pi$
$971$	7.29530	−	2.37039i	0.234117	−	0.0760693i	0.423726	+	0.905790i	$0.360722\pi$
$972$		0			0
$973$	17.9667	+	13.0535i	0.575984	+	0.418477i
$974$	3.67517	+	2.67017i	0.117760	+	0.0855577i
$975$		0			0
$976$	17.4272	−	5.66245i	0.557832	−	0.181250i
$977$	4.39314	+	6.04664i	0.140549	+	0.193449i	0.873489	−	0.486845i	$-0.161852\pi$
$977$	4.39314	+	6.04664i	0.140549	+	0.193449i	−0.732940	+	0.680294i	$0.761852\pi$
$978$		0			0
$979$	−28.0731	+	10.2522i	−0.897221	+	0.327663i
$980$			19.9814i			0.638282i
$981$		0			0
$982$	−4.16946	−	12.8323i	−0.133053	−	0.409494i
$983$	47.5184	+	15.4397i	1.51560	+	0.492449i	0.944523	−	0.328446i	$-0.106525\pi$
$983$	47.5184	+	15.4397i	1.51560	+	0.492449i	0.571079	+	0.820895i	$0.306525\pi$
$984$		0			0
$985$	−18.3021	+	25.1907i	−0.583153	+	0.802642i
$986$	0.0930998	−	0.286532i	0.00296490	−	0.00912503i
$987$		0			0
$988$	−5.19561	+	3.77483i	−0.165294	+	0.120093i
$989$	47.2520			1.50252
$990$		0			0
$991$	−32.0166			−1.01704			−0.508520	−	0.861050i	$-0.669807\pi$
$991$	−32.0166			−1.01704			−0.508520	+	0.861050i	$0.669807\pi$
$992$	20.6883	−	15.0309i	0.656853	−	0.477232i
$993$		0			0
$994$	−1.50307	+	4.62598i	−0.0476745	+	0.146727i
$995$	6.59748	−	9.08066i	0.209154	−	0.287876i
$996$		0			0
$997$	−18.0018	−	5.84914i	−0.570123	−	0.185244i	0.00974795	−	0.999952i	$-0.496897\pi$
$997$	−18.0018	−	5.84914i	−0.570123	−	0.185244i	−0.579871	+	0.814708i	$0.696897\pi$
$998$	2.77608	+	8.54390i	0.0878753	+	0.270452i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.404.10		80
3.2	odd	2	inner	891.2.k.a.404.11		80
9.2	odd	6		297.2.t.a.206.5		80
9.4	even	3		297.2.t.a.8.5		80
9.5	odd	6		99.2.p.a.74.6	yes	80
9.7	even	3		99.2.p.a.41.6	yes	80
11.7	odd	10	inner	891.2.k.a.161.11		80
33.29	even	10	inner	891.2.k.a.161.10		80
99.7	odd	30		99.2.p.a.95.6	yes	80
99.29	even	30		297.2.t.a.260.5		80
99.40	odd	30		297.2.t.a.62.5		80
99.95	even	30		99.2.p.a.29.6	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.6	✓	80	99.95	even	30
99.2.p.a.41.6	yes	80	9.7	even	3
99.2.p.a.74.6	yes	80	9.5	odd	6
99.2.p.a.95.6	yes	80	99.7	odd	30
297.2.t.a.8.5		80	9.4	even	3
297.2.t.a.62.5		80	99.40	odd	30
297.2.t.a.206.5		80	9.2	odd	6
297.2.t.a.260.5		80	99.29	even	30
891.2.k.a.161.10		80	33.29	even	10	inner
891.2.k.a.161.11		80	11.7	odd	10	inner
891.2.k.a.404.10		80	1.1	even	1	trivial
891.2.k.a.404.11		80	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.299321 + 0.217469i) q^{2} +(-0.575734 + 1.77193i) q^{4} +(-1.39685 + 1.92260i) q^{5} +(-1.49987 - 0.487337i) q^{7} +(-0.441671 - 1.35932i) q^{8} -0.879247i q^{10} +(1.13773 + 3.11538i) q^{11} +(-3.60270 - 4.95870i) q^{13} +(0.554923 - 0.180306i) q^{14} +(-2.58677 - 1.87940i) q^{16} +(-0.887473 - 0.644787i) q^{17} +(-0.534855 + 0.173785i) q^{19} +(-2.60249 - 3.58202i) q^{20} +(-1.01805 - 0.685076i) q^{22} +5.56398i q^{23} +(-0.200115 - 0.615892i) q^{25} +(2.15673 + 0.700764i) q^{26} +(1.72705 - 2.37708i) q^{28} +(0.229389 - 0.705986i) q^{29} +(5.11890 - 3.71910i) q^{31} +4.04154 q^{32} +0.405861 q^{34} +(3.03205 - 2.20291i) q^{35} +(1.32443 - 4.07617i) q^{37} +(0.122300 - 0.168332i) q^{38} +(3.23039 + 1.04962i) q^{40} +(-3.75539 - 11.5579i) q^{41} -8.49248i q^{43} +(-6.17525 + 0.222344i) q^{44} +(-1.20999 - 1.66541i) q^{46} +(-0.731927 + 0.237817i) q^{47} +(-3.65101 - 2.65261i) q^{49} +(0.193836 + 0.140830i) q^{50} +(10.8606 - 3.52884i) q^{52} +(2.66042 + 3.66175i) q^{53} +(-7.57886 - 2.16432i) q^{55} +2.25405i q^{56} +(0.0848695 + 0.261201i) q^{58} +(0.0106843 + 0.00347154i) q^{59} +(-3.36853 + 4.63638i) q^{61} +(-0.723404 + 2.22641i) q^{62} +(3.96382 - 2.87988i) q^{64} +14.5660 q^{65} +1.47666 q^{67} +(1.65346 - 1.20131i) q^{68} +(-0.428490 + 1.31876i) q^{70} +(-4.89992 + 6.74417i) q^{71} +(-14.9894 - 4.87035i) q^{73} +(0.490013 + 1.50811i) q^{74} -1.04778i q^{76} +(-0.188206 - 5.22712i) q^{77} +(1.86989 + 2.57368i) q^{79} +(7.22666 - 2.34809i) q^{80} +(3.63756 + 2.64284i) q^{82} +(-8.40013 - 6.10305i) q^{83} +(2.47934 - 0.805585i) q^{85} +(1.84685 + 2.54198i) q^{86} +(3.73231 - 2.92252i) q^{88} +9.01115i q^{89} +(2.98703 + 9.19313i) q^{91} +(-9.85896 - 3.20337i) q^{92} +(0.167363 - 0.230355i) q^{94} +(0.412994 - 1.27106i) q^{95} +(-4.48177 + 3.25619i) q^{97} +1.66968 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more