LMFDB - Embedded newform 189.2.s.b.89.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(17,189)] 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("189.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10] 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.1
Root			$0.827154 + 1.43267i$ of defining polynomial
Character	$\chi$	$=$	189.89
Dual form			189.2.s.b.17.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.81474 + 1.04774i) q^{2} +(1.19552 - 2.07070i) q^{4} +2.08983 q^{5} +(-0.879217 - 2.49539i) q^{7} +0.819421i q^{8} +(-3.79250 + 2.18960i) q^{10} -3.22878i q^{11} +(2.68740 - 1.55157i) q^{13} +(4.21007 + 3.60729i) q^{14} +(1.53250 + 2.65437i) q^{16} +(0.816304 + 1.41388i) q^{17} +(4.79094 + 2.76605i) q^{19} +(2.49844 - 4.32742i) q^{20} +(3.38292 + 5.85939i) q^{22} -1.16078i q^{23} -0.632608 q^{25} +(-3.25129 + 5.63139i) q^{26} +(-6.21834 - 1.16270i) q^{28} +(7.05749 + 4.07464i) q^{29} +(-5.16886 - 2.98424i) q^{31} +(-6.98146 - 4.03075i) q^{32} +(-2.96276 - 1.71055i) q^{34} +(-1.83741 - 5.21495i) q^{35} +(2.82656 - 4.89575i) q^{37} -11.5924 q^{38} +1.71245i q^{40} +(1.35369 + 2.34465i) q^{41} +(-0.974903 + 1.68858i) q^{43} +(-6.68583 - 3.86007i) q^{44} +(1.21620 + 2.10652i) q^{46} +(-4.06759 - 7.04527i) q^{47} +(-5.45395 + 4.38798i) q^{49} +(1.14802 - 0.662809i) q^{50} -7.41974i q^{52} +(-5.27766 + 3.04706i) q^{53} -6.74759i q^{55} +(2.04477 - 0.720448i) q^{56} -17.0767 q^{58} +(1.98103 - 3.43124i) q^{59} +(-4.15016 + 2.39609i) q^{61} +12.5068 q^{62} +10.7627 q^{64} +(5.61621 - 3.24252i) q^{65} +(0.336981 - 0.583668i) q^{67} +3.90363 q^{68} +(8.79834 + 7.53864i) q^{70} +7.01535i q^{71} +(-2.96276 + 1.71055i) q^{73} +11.8460i q^{74} +(11.4553 - 6.61374i) q^{76} +(-8.05706 + 2.83879i) q^{77} +(7.07973 + 12.2625i) q^{79} +(3.20267 + 5.54718i) q^{80} +(-4.91318 - 2.83662i) q^{82} +(-1.54535 + 2.67662i) q^{83} +(1.70594 + 2.95477i) q^{85} -4.08578i q^{86} +2.64572 q^{88} +(2.45766 - 4.25679i) q^{89} +(-6.23458 - 5.34194i) q^{91} +(-2.40363 - 1.38774i) q^{92} +(14.7632 + 8.52356i) q^{94} +(10.0122 + 5.78057i) q^{95} +(2.07939 + 1.20054i) q^{97} +(5.30004 - 13.6774i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} + 6 q^{13} + 6 q^{14} - 6 q^{16} + 12 q^{17} + 3 q^{19} + 3 q^{20} + 5 q^{22} - 14 q^{25} - 3 q^{26} + 2 q^{28} + 15 q^{29} - 9 q^{31} - 48 q^{32} + 3 q^{34} + 15 q^{35}+ \cdots - 45 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 + 6 * q^13 + 6 * q^14 - 6 * q^16 + 12 * q^17 + 3 * q^19 + 3 * q^20 + 5 * q^22 - 14 * q^25 - 3 * q^26 + 2 * q^28 + 15 * q^29 - 9 * q^31 - 48 * q^32 + 3 * q^34 + 15 * q^35 + 6 * q^37 - 36 * q^38 + 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 - 15 * q^47 - 23 * q^49 - 3 * q^50 + 9 * q^53 + 51 * q^56 - 16 * q^58 + 18 * q^59 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 54 * q^68 + 9 * q^70 + 3 * q^73 + 9 * q^76 - 45 * q^77 + 20 * q^79 + 30 * q^80 + 9 * q^82 + 15 * q^83 + 18 * q^85 + 16 * q^88 - 24 * q^89 - 24 * q^91 - 39 * q^92 - 3 * q^94 + 6 * q^97 - 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.81474	+	1.04774i	−1.28321	+	0.740865i	−0.977435	−	0.211238i	$-0.932251\pi$
$2$	−1.81474	+	1.04774i	−1.28321	+	0.740865i	−0.305780	+	0.952102i	$0.598917\pi$
$3$		0			0
$3$		0			0
$4$	1.19552	−	2.07070i	0.597760	−	1.03535i
$5$	2.08983			0.934601			0.467300	−	0.884099i	$-0.345227\pi$
$5$	2.08983			0.934601			0.467300	+	0.884099i	$0.345227\pi$
$6$		0			0
$7$	−0.879217	−	2.49539i	−0.332313	−	0.943169i
$7$	−0.879217	−	2.49539i	−0.332313	−	0.943169i
$8$			0.819421i			0.289709i
$9$		0			0
$10$	−3.79250	+	2.18960i	−1.19929	+	0.692412i
$11$		−	3.22878i		−	0.973512i	−0.873538	−	0.486756i	$-0.838180\pi$
$11$		−	3.22878i		−	0.973512i	0.873538	−	0.486756i	$-0.161820\pi$
$12$		0			0
$13$	2.68740	−	1.55157i	0.745350	−	0.430328i	−0.0786612	−	0.996901i	$-0.525065\pi$
$13$	2.68740	−	1.55157i	0.745350	−	0.430328i	0.824011	+	0.566573i	$0.191731\pi$
$14$	4.21007	+	3.60729i	1.12519	+	0.964090i
$15$		0			0
$16$	1.53250	+	2.65437i	0.383125	+	0.663593i
$17$	0.816304	+	1.41388i	0.197983	+	0.342916i	0.947874	−	0.318645i	$-0.103228\pi$
$17$	0.816304	+	1.41388i	0.197983	+	0.342916i	−0.749891	+	0.661561i	$0.769894\pi$
$18$		0			0
$19$	4.79094	+	2.76605i	1.09912	+	0.634575i	0.935989	−	0.352030i	$-0.114509\pi$
$19$	4.79094	+	2.76605i	1.09912	+	0.634575i	0.163127	+	0.986605i	$0.447842\pi$
$20$	2.49844	−	4.32742i	0.558667	−	0.967640i
$21$		0			0
$22$	3.38292	+	5.85939i	0.721241	+	1.24923i
$23$		−	1.16078i		−	0.242040i	−0.992650	−	0.121020i	$-0.961384\pi$
$23$		−	1.16078i		−	0.242040i	0.992650	−	0.121020i	$-0.0386165\pi$
$24$		0			0
$25$	−0.632608			−0.126522
$26$	−3.25129	+	5.63139i	−0.637630	+	1.10441i
$27$		0			0
$28$	−6.21834	−	1.16270i	−1.17516	−	0.219729i
$29$	7.05749	+	4.07464i	1.31054	+	0.756643i	0.982186	−	0.187911i	$-0.0601717\pi$
$29$	7.05749	+	4.07464i	1.31054	+	0.756643i	0.328357	+	0.944554i	$0.393505\pi$
$30$		0			0
$31$	−5.16886	−	2.98424i	−0.928355	−	0.535986i	−0.0420638	−	0.999115i	$-0.513393\pi$
$31$	−5.16886	−	2.98424i	−0.928355	−	0.535986i	−0.886291	+	0.463129i	$0.846727\pi$
$32$	−6.98146	−	4.03075i	−1.23416	−	0.712542i
$33$		0			0
$34$	−2.96276	−	1.71055i	−0.508109	−	0.293357i
$35$	−1.83741	−	5.21495i	−0.310580	−	0.881487i
$36$		0			0
$37$	2.82656	−	4.89575i	0.464684	−	0.804857i	−0.534503	−	0.845167i	$-0.679501\pi$
$37$	2.82656	−	4.89575i	0.464684	−	0.804857i	0.999187	+	0.0403097i	$0.0128345\pi$
$38$	−11.5924			−1.88054
$39$		0			0
$40$			1.71245i			0.270762i
$41$	1.35369	+	2.34465i	0.211410	+	0.366173i	0.952156	−	0.305612i	$-0.0988611\pi$
$41$	1.35369	+	2.34465i	0.211410	+	0.366173i	−0.740746	+	0.671785i	$0.765528\pi$
$42$		0			0
$43$	−0.974903	+	1.68858i	−0.148671	+	0.257506i	−0.930737	−	0.365690i	$-0.880833\pi$
$43$	−0.974903	+	1.68858i	−0.148671	+	0.257506i	0.782065	+	0.623196i	$0.214166\pi$
$44$	−6.68583	−	3.86007i	−1.00793	−	0.581927i
$45$		0			0
$46$	1.21620	+	2.10652i	0.179319	+	0.310589i
$47$	−4.06759	−	7.04527i	−0.593319	−	1.02766i	−0.993782	−	0.111346i	$-0.964484\pi$
$47$	−4.06759	−	7.04527i	−0.593319	−	1.02766i	0.400463	−	0.916313i	$-0.368849\pi$
$48$		0			0
$49$	−5.45395	+	4.38798i	−0.779136	+	0.626854i
$50$	1.14802	−	0.662809i	0.162354	−	0.0937353i
$51$		0			0
$52$		−	7.41974i		−	1.02893i
$53$	−5.27766	+	3.04706i	−0.724943	+	0.418546i	−0.816569	−	0.577248i	$-0.804127\pi$
$53$	−5.27766	+	3.04706i	−0.724943	+	0.418546i	0.0916264	+	0.995793i	$0.470793\pi$
$54$		0			0
$55$		−	6.74759i		−	0.909845i
$56$	2.04477	−	0.720448i	0.273245	−	0.0962740i
$57$		0			0
$58$	−17.0767			−2.24228
$59$	1.98103	−	3.43124i	0.257908	−	0.446709i	−0.707773	−	0.706439i	$-0.750300\pi$
$59$	1.98103	−	3.43124i	0.257908	−	0.446709i	0.965681	+	0.259730i	$0.0836336\pi$
$60$		0			0
$61$	−4.15016	+	2.39609i	−0.531373	+	0.306788i	−0.741575	−	0.670869i	$-0.765921\pi$
$61$	−4.15016	+	2.39609i	−0.531373	+	0.306788i	0.210202	+	0.977658i	$0.432588\pi$
$62$	12.5068			1.58837
$63$		0			0
$64$	10.7627			1.34534
$65$	5.61621	−	3.24252i	0.696605	−	0.402185i
$66$		0			0
$67$	0.336981	−	0.583668i	0.0411687	−	0.0713063i	−0.844707	−	0.535229i	$-0.820225\pi$
$67$	0.336981	−	0.583668i	0.0411687	−	0.0713063i	0.885876	+	0.463923i	$0.153559\pi$
$68$	3.90363			0.473385
$69$		0			0
$70$	8.79834	+	7.53864i	1.05160	+	0.901039i
$71$			7.01535i			0.832568i	0.909235	+	0.416284i	$0.136668\pi$
$71$			7.01535i			0.832568i	−0.909235	+	0.416284i	$0.863332\pi$
$72$		0			0
$73$	−2.96276	+	1.71055i	−0.346765	+	0.200205i	−0.663259	−	0.748390i	$-0.730827\pi$
$73$	−2.96276	+	1.71055i	−0.346765	+	0.200205i	0.316495	+	0.948594i	$0.397494\pi$
$74$			11.8460i			1.37707i
$75$		0			0
$76$	11.4553	−	6.61374i	1.31402	−	0.758648i
$77$	−8.05706	+	2.83879i	−0.918187	+	0.323511i
$78$		0			0
$79$	7.07973	+	12.2625i	0.796532	+	1.37963i	0.921862	+	0.387519i	$0.126668\pi$
$79$	7.07973	+	12.2625i	0.796532	+	1.37963i	−0.125330	+	0.992115i	$0.539999\pi$
$80$	3.20267	+	5.54718i	0.358069	+	0.620194i
$81$		0			0
$82$	−4.91318	−	2.83662i	−0.542570	−	0.313253i
$83$	−1.54535	+	2.67662i	−0.169624	+	0.293798i	−0.938288	−	0.345856i	$-0.887589\pi$
$83$	−1.54535	+	2.67662i	−0.169624	+	0.293798i	0.768664	+	0.639653i	$0.220922\pi$
$84$		0			0
$85$	1.70594	+	2.95477i	0.185035	+	0.320490i
$86$		−	4.08578i		−	0.440581i
$87$		0			0
$88$	2.64572			0.282035
$89$	2.45766	−	4.25679i	0.260511	−	0.451219i	−0.705867	−	0.708345i	$-0.749442\pi$
$89$	2.45766	−	4.25679i	0.260511	−	0.451219i	0.966378	+	0.257126i	$0.0827756\pi$
$90$		0			0
$91$	−6.23458	−	5.34194i	−0.653562	−	0.559988i
$92$	−2.40363	−	1.38774i	−0.250596	−	0.144682i
$93$		0			0
$94$	14.7632	+	8.52356i	1.52271	+	0.879138i
$95$	10.0122	+	5.78057i	1.02723	+	0.593074i
$96$		0			0
$97$	2.07939	+	1.20054i	0.211130	+	0.121896i	0.601837	−	0.798619i	$-0.294436\pi$
$97$	2.07939	+	1.20054i	0.211130	+	0.121896i	−0.390706	+	0.920515i	$0.627769\pi$
$98$	5.30004	−	13.6774i	0.535385	−	1.38162i
$99$		0			0
$100$	−0.756296	+	1.30994i	−0.0756296	+	0.130994i
$101$	3.52051			0.350304			0.175152	−	0.984541i	$-0.443958\pi$
$101$	3.52051			0.350304			0.175152	+	0.984541i	$0.443958\pi$
$102$		0			0
$103$		−	15.6846i		−	1.54545i	−0.634743	−	0.772723i	$-0.718894\pi$
$103$		−	15.6846i		−	1.54545i	0.634743	−	0.772723i	$-0.281106\pi$
$104$	1.27139	+	2.20211i	0.124670	+	0.215935i
$105$		0			0
$106$	6.38506	−	11.0592i	0.620172	−	1.07417i
$107$	1.41984	+	0.819746i	0.137261	+	0.0792478i	0.567058	−	0.823678i	$-0.308081\pi$
$107$	1.41984	+	0.819746i	0.137261	+	0.0792478i	−0.429797	+	0.902926i	$0.641415\pi$
$108$		0			0
$109$	2.90672	+	5.03459i	0.278414	+	0.482227i	0.970991	−	0.239117i	$-0.0768581\pi$
$109$	2.90672	+	5.03459i	0.278414	+	0.482227i	−0.692577	+	0.721344i	$0.743525\pi$
$110$	7.06973	+	12.2451i	0.674072	+	1.16753i
$111$		0			0
$112$	5.27629	−	6.15796i	0.498563	−	0.581872i
$113$	−13.9931	+	8.07894i	−1.31636	+	0.760003i	−0.983142	−	0.182845i	$-0.941469\pi$
$113$	−13.9931	+	8.07894i	−1.31636	+	0.760003i	−0.333222	+	0.942848i	$0.608136\pi$
$114$		0			0
$115$		−	2.42584i		−	0.226210i
$116$	16.8748	−	9.74265i	1.56678	−	0.904582i
$117$		0			0
$118$			8.30241i			0.764299i
$119$	2.81047	−	3.28010i	0.257636	−	0.300687i
$120$		0			0
$121$	0.575009			0.0522736
$122$	5.02097	−	8.69658i	0.454577	−	0.787351i
$123$		0			0
$124$	−12.3590	+	7.13545i	−1.10987	+	0.640782i
$125$	−11.7712			−1.05285
$126$		0			0
$127$	−9.59240			−0.851188			−0.425594	−	0.904914i	$-0.639935\pi$
$127$	−9.59240			−0.851188			−0.425594	+	0.904914i	$0.639935\pi$
$128$	−5.56860	+	3.21503i	−0.492199	+	0.284171i
$129$		0			0
$130$	−6.79464	+	11.7687i	−0.595929	+	1.03218i
$131$	−2.46122			−0.215038			−0.107519	−	0.994203i	$-0.534291\pi$
$131$	−2.46122			−0.215038			−0.107519	+	0.994203i	$0.534291\pi$
$132$		0			0
$133$	2.69010	−	14.3872i	0.233261	−	1.24753i
$134$			1.41227i			0.122002i
$135$		0			0
$136$	−1.15856	+	0.668896i	−0.0993459	+	0.0573574i
$137$			17.3864i			1.48542i	0.669611	+	0.742712i	$0.266461\pi$
$137$			17.3864i			1.48542i	−0.669611	+	0.742712i	$0.733539\pi$
$138$		0			0
$139$	−8.61174	+	4.97199i	−0.730438	+	0.421719i	−0.818582	−	0.574389i	$-0.805240\pi$
$139$	−8.61174	+	4.97199i	−0.730438	+	0.421719i	0.0881443	+	0.996108i	$0.471906\pi$
$140$	−12.9953	−	2.42984i	−1.09830	−	0.205359i
$141$		0			0
$142$	−7.35026	−	12.7310i	−0.616820	−	1.06836i
$143$	−5.00967	−	8.67701i	−0.418930	−	0.725608i
$144$		0			0
$145$	14.7490	+	8.51532i	1.22483	+	0.707159i
$146$	3.58442	−	6.20840i	0.296649	−	0.513811i
$147$		0			0
$148$	−6.75843	−	11.7060i	−0.555540	−	0.962223i
$149$			9.25717i			0.758377i	0.925319	+	0.379189i	$0.123797\pi$
$149$			9.25717i			0.758377i	−0.925319	+	0.379189i	$0.876203\pi$
$150$		0			0
$151$	−11.9698			−0.974087			−0.487044	−	0.873378i	$-0.661925\pi$
$151$	−11.9698			−0.974087			−0.487044	+	0.873378i	$0.661925\pi$
$152$	−2.26656	+	3.92579i	−0.183842	+	0.318424i
$153$		0			0
$154$	11.6471	−	13.5934i	0.938554	−	1.09539i
$155$	−10.8020	−	6.23656i	−0.867641	−	0.500933i
$156$		0			0
$157$	15.4598	+	8.92569i	1.23382	+	0.712348i	0.967825	−	0.251626i	$-0.0809651\pi$
$157$	15.4598	+	8.92569i	1.23382	+	0.712348i	0.265998	+	0.963974i	$0.414298\pi$
$158$	−25.6957	−	14.8354i	−2.04424	−	1.18024i
$159$		0			0
$160$	−14.5901	−	8.42358i	−1.15345	−	0.665943i
$161$	−2.89660	+	1.02058i	−0.228284	+	0.0804329i
$162$		0			0
$163$	−8.91768	+	15.4459i	−0.698486	+	1.20981i	0.270505	+	0.962719i	$0.412809\pi$
$163$	−8.91768	+	15.4459i	−0.698486	+	1.20981i	−0.968991	+	0.247095i	$0.920524\pi$
$164$	6.47344			0.505491
$165$		0			0
$166$		−	6.47650i		−	0.502674i
$167$	6.16899	+	10.6850i	0.477371	+	0.826830i	0.999664	−	0.0259359i	$-0.00825657\pi$
$167$	6.16899	+	10.6850i	0.477371	+	0.826830i	−0.522293	+	0.852766i	$0.674923\pi$
$168$		0			0
$169$	−1.68526	+	2.91896i	−0.129635	+	0.224535i
$170$	−6.19166	−	3.57476i	−0.474879	−	0.274171i
$171$		0			0
$172$	2.33103	+	4.03747i	0.177740	+	0.307854i
$173$	−4.53368	−	7.85256i	−0.344689	−	0.597019i	0.640608	−	0.767868i	$-0.278682\pi$
$173$	−4.53368	−	7.85256i	−0.344689	−	0.597019i	−0.985297	+	0.170849i	$0.945349\pi$
$174$		0			0
$175$	0.556199	+	1.57860i	0.0420447	+	0.119331i
$176$	8.57037	−	4.94810i	0.646016	−	0.372977i
$177$		0			0
$178$			10.2999i			0.772014i
$179$	13.0086	−	7.51051i	0.972307	−	0.561362i	0.0723682	−	0.997378i	$-0.476944\pi$
$179$	13.0086	−	7.51051i	0.972307	−	0.561362i	0.899939	+	0.436016i	$0.143611\pi$
$180$		0			0
$181$		−	2.34159i		−	0.174049i	−0.996206	−	0.0870246i	$-0.972264\pi$
$181$		−	2.34159i		−	0.174049i	0.996206	−	0.0870246i	$-0.0277359\pi$
$182$	16.9111	+	3.16201i	1.25354	+	0.234384i
$183$		0			0
$184$	0.951168			0.0701210
$185$	5.90704	−	10.2313i	0.434294	−	0.752220i
$186$		0			0
$187$	4.56510	−	2.63566i	0.333833	−	0.192739i
$188$	−19.4516			−1.41865
$189$		0			0
$190$	−24.2262			−1.75755
$191$	−7.82585	+	4.51825i	−0.566258	+	0.326929i	−0.755654	−	0.654972i	$-0.772681\pi$
$191$	−7.82585	+	4.51825i	−0.566258	+	0.326929i	0.189395	+	0.981901i	$0.439347\pi$
$192$		0			0
$193$	2.74134	−	4.74815i	0.197326	−	0.341779i	−0.750334	−	0.661058i	$-0.770108\pi$
$193$	2.74134	−	4.74815i	0.197326	−	0.341779i	0.947661	+	0.319279i	$0.103441\pi$
$194$	−5.03141			−0.361234
$195$		0			0
$196$	2.56589	+	16.5394i	0.183278	+	1.18139i
$197$		−	2.88946i		−	0.205865i	−0.994688	−	0.102933i	$-0.967177\pi$
$197$		−	2.88946i		−	0.205865i	0.994688	−	0.102933i	$-0.0328226\pi$
$198$		0			0
$199$	4.45419	−	2.57163i	0.315749	−	0.182298i	−0.333747	−	0.942663i	$-0.608313\pi$
$199$	4.45419	−	2.57163i	0.315749	−	0.182298i	0.649496	+	0.760365i	$0.274980\pi$
$200$		−	0.518372i		−	0.0366544i
$201$		0			0
$202$	−6.38881	+	3.68858i	−0.449515	+	0.259528i
$203$	3.96277	−	21.1937i	0.278132	−	1.48751i
$204$		0			0
$205$	2.82897	+	4.89993i	0.197584	+	0.342226i
$206$	16.4334	+	28.4634i	1.14497	+	1.98314i
$207$		0			0
$208$	8.23688	+	4.75557i	0.571125	+	0.329739i
$209$	8.93095	−	15.4689i	0.617767	−	1.07000i
$210$		0			0
$211$	7.93224	+	13.7390i	0.546078	+	0.945835i	0.998538	+	0.0540502i	$0.0172131\pi$
$211$	7.93224	+	13.7390i	0.546078	+	0.945835i	−0.452460	+	0.891785i	$0.649454\pi$
$212$			14.5713i			1.00076i
$213$		0			0
$214$	−3.43552			−0.234848
$215$	−2.03738	+	3.52885i	−0.138948	+	0.240666i
$216$		0			0
$217$	−2.90230	+	15.5221i	−0.197021	+	1.05371i
$218$	−10.5499	−	6.09099i	−0.714529	−	0.412534i
$219$		0			0
$220$	−13.9723	−	8.06689i	−0.942010	−	0.543870i
$221$	4.38747	+	2.53311i	0.295133	+	0.170395i
$222$		0			0
$223$	13.5288	+	7.81085i	0.905955	+	0.523053i	0.879127	−	0.476587i	$-0.158126\pi$
$223$	13.5288	+	7.81085i	0.905955	+	0.523053i	0.0268275	+	0.999640i	$0.491460\pi$
$224$	−3.92008	+	20.9654i	−0.261921	+	1.40081i
$225$		0			0
$226$	16.9293	−	29.3224i	1.12612	−	1.95049i
$227$	−2.08089			−0.138114			−0.0690569	−	0.997613i	$-0.521999\pi$
$227$	−2.08089			−0.138114			−0.0690569	+	0.997613i	$0.521999\pi$
$228$		0			0
$229$			6.43437i			0.425195i	0.977140	+	0.212598i	$0.0681923\pi$
$229$			6.43437i			0.425195i	−0.977140	+	0.212598i	$0.931808\pi$
$230$	2.54165	+	4.40226i	0.167591	+	0.290277i
$231$		0			0
$232$	−3.33885	+	5.78305i	−0.219206	+	0.379676i
$233$	13.5222	+	7.80704i	0.885868	+	0.511456i	0.872589	−	0.488456i	$-0.162440\pi$
$233$	13.5222	+	7.80704i	0.885868	+	0.511456i	0.0132791	+	0.999912i	$0.495773\pi$
$234$		0			0
$235$	−8.50057	−	14.7234i	−0.554516	−	0.960450i
$236$	−4.73672	−	8.20424i	−0.308334	−	0.534050i
$237$		0			0
$238$	−1.66358	+	8.89719i	−0.107834	+	0.576719i
$239$	14.8777	−	8.58964i	0.962358	−	0.555618i	0.0654600	−	0.997855i	$-0.479149\pi$
$239$	14.8777	−	8.58964i	0.962358	−	0.555618i	0.896898	+	0.442238i	$0.145815\pi$
$240$		0			0
$241$		−	11.2184i		−	0.722642i	−0.932441	−	0.361321i	$-0.882326\pi$
$241$		−	11.2184i		−	0.722642i	0.932441	−	0.361321i	$-0.117674\pi$
$242$	−1.04349	+	0.602460i	−0.0670782	+	0.0387276i
$243$		0			0
$244$			11.4583i			0.733544i
$245$	−11.3978	+	9.17014i	−0.728181	+	0.585859i
$246$		0			0
$247$	17.1669			1.09230
$248$	2.44535	−	4.23547i	0.155280	−	0.268953i
$249$		0			0
$250$	21.3617	−	12.3332i	1.35103	−	0.780018i
$251$	−11.3837			−0.718535			−0.359267	−	0.933235i	$-0.616973\pi$
$251$	−11.3837			−0.718535			−0.359267	+	0.933235i	$0.616973\pi$
$252$		0			0
$253$	−3.74790			−0.235629
$254$	17.4077	−	10.0504i	1.09226	−	0.630615i
$255$		0			0
$256$	−4.02567	+	6.97267i	−0.251604	+	0.435792i
$257$	−9.38048			−0.585138			−0.292569	−	0.956244i	$-0.594510\pi$
$257$	−9.38048			−0.585138			−0.292569	+	0.956244i	$0.594510\pi$
$258$		0			0
$259$	−14.7020	−	2.74895i	−0.913537	−	0.170812i
$260$		−	15.5060i		−	0.961641i
$261$		0			0
$262$	4.46647	−	2.57872i	0.275940	−	0.159314i
$263$			8.80306i			0.542820i	0.962464	+	0.271410i	$0.0874899\pi$
$263$			8.80306i			0.542820i	−0.962464	+	0.271410i	$0.912510\pi$
$264$		0			0
$265$	−11.0294	+	6.36784i	−0.677532	+	0.391173i
$266$	10.1922	+	28.9276i	0.624926	+	1.77366i
$267$		0			0
$268$	−0.805735	−	1.39557i	−0.0492181	−	0.0852482i
$269$	−8.16473	−	14.1417i	−0.497812	−	0.862236i	0.502184	−	0.864761i	$-0.332530\pi$
$269$	−8.16473	−	14.1417i	−0.497812	−	0.862236i	−0.999997	+	0.00252412i	$0.999197\pi$
$270$		0			0
$271$	−12.6186	−	7.28538i	−0.766528	−	0.442555i	0.0651065	−	0.997878i	$-0.479261\pi$
$271$	−12.6186	−	7.28538i	−0.766528	−	0.442555i	−0.831635	+	0.555323i	$0.812595\pi$
$272$	−2.50197	+	4.33355i	−0.151704	+	0.262760i
$273$		0			0
$274$	−18.2165	−	31.5519i	−1.10050	−	1.90612i
$275$			2.04255i			0.123170i
$276$		0			0
$277$	28.7137			1.72524			0.862618	−	0.505855i	$-0.168823\pi$
$277$	28.7137			1.72524			0.862618	+	0.505855i	$0.168823\pi$
$278$	10.4187	−	18.0457i	0.624873	−	1.08231i
$279$		0			0
$280$	4.27323	−	1.50562i	0.255375	−	0.0899777i
$281$	4.76893	+	2.75334i	0.284490	+	0.164251i	0.635455	−	0.772138i	$-0.280813\pi$
$281$	4.76893	+	2.75334i	0.284490	+	0.164251i	−0.350964	+	0.936389i	$0.614146\pi$
$282$		0			0
$283$	−26.2257	−	15.1414i	−1.55896	−	0.900065i	−0.997357	−	0.0726567i	$-0.976852\pi$
$283$	−26.2257	−	15.1414i	−1.55896	−	0.900065i	−0.561601	−	0.827408i	$-0.689814\pi$
$284$	14.5267	+	8.38699i	0.862001	+	0.497676i
$285$		0			0
$286$	18.1825	+	10.4977i	1.07515	+	0.620740i
$287$	4.66064	−	5.43943i	0.275109	−	0.321080i
$288$		0			0
$289$	7.16730	−	12.4141i	0.421606	−	0.730242i
$290$	−35.6874			−2.09564
$291$		0			0
$292$			8.17999i			0.478698i
$293$	3.54362	+	6.13773i	0.207021	+	0.358570i	0.950775	−	0.309883i	$-0.100290\pi$
$293$	3.54362	+	6.13773i	0.207021	+	0.358570i	−0.743754	+	0.668453i	$0.766957\pi$
$294$		0			0
$295$	4.14001	−	7.17071i	0.241041	−	0.417495i
$296$	4.01168	+	2.31615i	0.233174	+	0.134623i
$297$		0			0
$298$	−9.69912	−	16.7994i	−0.561855	−	0.973161i
$299$	−1.80103	−	3.11948i	−0.104156	−	0.180404i
$300$		0			0
$301$	5.07082	+	0.948135i	0.292277	+	0.0546496i
$302$	21.7220	−	12.5412i	1.24996	−	0.721667i
$303$		0			0
$304$			16.9559i			0.972487i
$305$	−8.67313	+	5.00743i	−0.496622	+	0.286725i
$306$		0			0
$307$			3.11346i			0.177695i	0.996045	+	0.0888473i	$0.0283183\pi$
$307$			3.11346i			0.177695i	−0.996045	+	0.0888473i	$0.971682\pi$
$308$	−3.75408	+	20.0776i	−0.213909	+	1.14403i
$309$		0			0
$310$	26.1372			1.48449
$311$	−9.72605	+	16.8460i	−0.551514	+	0.955249i	0.446652	+	0.894708i	$0.352616\pi$
$311$	−9.72605	+	16.8460i	−0.551514	+	0.955249i	−0.998166	+	0.0605417i	$0.980717\pi$
$312$		0			0
$313$	−22.1224	+	12.7724i	−1.25043	+	0.721937i	−0.971195	−	0.238285i	$-0.923415\pi$
$313$	−22.1224	+	12.7724i	−1.25043	+	0.721937i	−0.279237	+	0.960222i	$0.590081\pi$
$314$	−37.4073			−2.11101
$315$		0			0
$316$	33.8559			1.90454
$317$	14.0534	−	8.11372i	0.789316	−	0.455712i	−0.0504056	−	0.998729i	$-0.516051\pi$
$317$	14.0534	−	8.11372i	0.789316	−	0.455712i	0.839722	+	0.543017i	$0.182718\pi$
$318$		0			0
$319$	13.1561	−	22.7871i	0.736601	−	1.27583i
$320$	22.4922			1.25735
$321$		0			0
$322$	4.18728	−	4.88697i	0.233348	−	0.272340i
$323$			9.03174i			0.502540i
$324$		0			0
$325$	−1.70007	+	0.981535i	−0.0943029	+	0.0544458i
$326$		−	37.3736i		−	2.06993i
$327$		0			0
$328$	−1.92126	+	1.10924i	−0.106084	+	0.0612474i
$329$	−14.0044	+	16.3446i	−0.772089	+	0.901104i
$330$		0			0
$331$	−11.6558	−	20.1885i	−0.640662	−	1.10966i	−0.985285	−	0.170919i	$-0.945326\pi$
$331$	−11.6558	−	20.1885i	−0.640662	−	1.10966i	0.344623	−	0.938741i	$-0.388007\pi$
$332$	3.69499	+	6.39992i	0.202789	+	0.351241i
$333$		0			0
$334$	−22.3902	−	12.9270i	−1.22514	−	0.707334i
$335$	0.704232	−	1.21977i	0.0384763	−	0.0666430i
$336$		0			0
$337$	5.93515	+	10.2800i	0.323308	+	0.559986i	0.981168	−	0.193154i	$-0.0618717\pi$
$337$	5.93515	+	10.2800i	0.323308	+	0.559986i	−0.657860	+	0.753140i	$0.728538\pi$
$338$		−	7.06286i		−	0.384169i
$339$		0			0
$340$	8.15793			0.442426
$341$	−9.63545	+	16.6891i	−0.521789	+	0.903765i
$342$		0			0
$343$	15.7449	+	9.75176i	0.850147	+	0.526546i
$344$	−1.38366	−	0.798855i	−0.0746019	−	0.0430714i
$345$		0			0
$346$	16.4549	+	9.50024i	0.884621	+	0.510736i
$347$	−18.7979	−	10.8530i	−1.00913	−	0.582619i	−0.0981903	−	0.995168i	$-0.531305\pi$
$347$	−18.7979	−	10.8530i	−1.00913	−	0.582619i	−0.910936	+	0.412549i	$0.864639\pi$
$348$		0			0
$349$	2.20868	+	1.27518i	0.118228	+	0.0682588i	0.557948	−	0.829876i	$-0.311589\pi$
$349$	2.20868	+	1.27518i	0.118228	+	0.0682588i	−0.439720	+	0.898135i	$0.644922\pi$
$350$	−2.66332	−	2.28200i	−0.142361	−	0.121978i
$351$		0			0
$352$	−13.0144	+	22.5416i	−0.693669	+	1.20147i
$353$	25.3747			1.35056			0.675279	−	0.737563i	$-0.264023\pi$
$353$	25.3747			1.35056			0.675279	+	0.737563i	$0.264023\pi$
$354$		0			0
$355$			14.6609i			0.778119i
$356$	−5.87636	−	10.1782i	−0.311446	−	0.539441i
$357$		0			0
$358$	−15.7381	+	27.2592i	−0.831786	+	1.44070i
$359$	9.73735	+	5.62186i	0.513918	+	0.296711i	0.734443	−	0.678671i	$-0.237444\pi$
$359$	9.73735	+	5.62186i	0.513918	+	0.296711i	−0.220525	+	0.975381i	$0.570777\pi$
$360$		0			0
$361$	5.80204	+	10.0494i	0.305371	+	0.528917i
$362$	2.45338	+	4.24938i	0.128947	+	0.223342i
$363$		0			0
$364$	−18.5151	+	6.52356i	−0.970458	+	0.341927i
$365$	−6.19166	+	3.57476i	−0.324086	+	0.187111i
$366$		0			0
$367$		−	3.31180i		−	0.172874i	−0.996257	−	0.0864372i	$-0.972452\pi$
$367$		−	3.31180i		−	0.172874i	0.996257	−	0.0864372i	$-0.0275482\pi$
$368$	3.08114	−	1.77890i	0.160616	−	0.0927315i
$369$		0			0
$370$			24.7562i			1.28701i
$371$	12.2438	+	10.4908i	0.635667	+	0.544656i
$372$		0			0
$373$	−6.64541			−0.344087			−0.172043	−	0.985089i	$-0.555037\pi$
$373$	−6.64541			−0.344087			−0.172043	+	0.985089i	$0.555037\pi$
$374$	−5.52298	+	9.56608i	−0.285586	+	0.494650i
$375$		0			0
$376$	5.77304	−	3.33307i	0.297722	−	0.171890i
$377$	25.2884			1.30242
$378$		0			0
$379$	−3.84940			−0.197730			−0.0988652	−	0.995101i	$-0.531521\pi$
$379$	−3.84940			−0.197730			−0.0988652	+	0.995101i	$0.531521\pi$
$380$	23.9397	−	13.8216i	1.22808	−	0.709033i
$381$		0			0
$382$	9.46792	−	16.3989i	0.484421	−	0.839041i
$383$	34.2223			1.74868			0.874339	−	0.485316i	$-0.161295\pi$
$383$	34.2223			1.74868			0.874339	+	0.485316i	$0.161295\pi$
$384$		0			0
$385$	−16.8379	+	5.93260i	−0.858138	+	0.302353i
$386$			11.4889i			0.584768i
$387$		0			0
$388$	4.97191	−	2.87054i	0.252411	−	0.145729i
$389$		−	13.4796i		−	0.683445i	−0.939801	−	0.341723i	$-0.888990\pi$
$389$		−	13.4796i		−	0.683445i	0.939801	−	0.341723i	$-0.111010\pi$
$390$		0			0
$391$	1.64121	−	0.947550i	0.0829993	−	0.0479197i
$392$	−3.59560	−	4.46908i	−0.181605	−	0.225723i
$393$		0			0
$394$	3.02740	+	5.24361i	0.152518	+	0.264169i
$395$	14.7954	+	25.6265i	0.744440	+	1.28941i
$396$		0			0
$397$	−25.5501	−	14.7513i	−1.28232	−	0.740349i	−0.305049	−	0.952337i	$-0.598673\pi$
$397$	−25.5501	−	14.7513i	−1.28232	−	0.740349i	−0.977272	+	0.211988i	$0.932006\pi$
$398$	−5.38880	+	9.33367i	−0.270116	+	0.467855i
$399$		0			0
$400$	−0.969472	−	1.67918i	−0.0484736	−	0.0839588i
$401$		−	29.0446i		−	1.45042i	−0.688528	−	0.725209i	$-0.741743\pi$
$401$		−	29.0446i		−	1.45042i	0.688528	−	0.725209i	$-0.258257\pi$
$402$		0			0
$403$	−18.5210			−0.922599
$404$	4.20884	−	7.28993i	0.209398	−	0.362687i
$405$		0			0
$406$	15.0141	+	42.6130i	0.745138	+	2.11485i
$407$	−15.8073	−	9.12634i	−0.783538	−	0.452376i
$408$		0			0
$409$	−26.2193	−	15.1377i	−1.29646	−	0.748513i	−0.316671	−	0.948536i	$-0.602565\pi$
$409$	−26.2193	−	15.1377i	−1.29646	−	0.748513i	−0.979791	+	0.200023i	$0.935898\pi$
$410$	−10.2677	−	5.92806i	−0.507086	−	0.292766i
$411$		0			0
$412$	−32.4781	−	18.7512i	−1.60008	−	0.923806i
$413$	−10.3040	−	1.92663i	−0.507029	−	0.0948035i
$414$		0			0
$415$	−3.22952	+	5.59369i	−0.158531	+	0.274583i
$416$	−25.0160			−1.22651
$417$		0			0
$418$			37.4293i			1.83073i
$419$	−18.2902	−	31.6795i	−0.893534	−	1.54765i	−0.835609	−	0.549325i	$-0.814885\pi$
$419$	−18.2902	−	31.6795i	−0.893534	−	1.54765i	−0.0579246	−	0.998321i	$-0.518448\pi$
$420$		0			0
$421$	3.85999	−	6.68570i	0.188124	−	0.325841i	−0.756501	−	0.653993i	$-0.773093\pi$
$421$	3.85999	−	6.68570i	0.188124	−	0.325841i	0.944625	+	0.328152i	$0.106426\pi$
$422$	−28.7899	−	16.6219i	−1.40147	−	0.809140i
$423$		0			0
$424$	−2.49682	−	4.32463i	−0.121256	−	0.210022i
$425$	−0.516400	−	0.894431i	−0.0250491	−	0.0433863i
$426$		0			0
$427$	9.62808	+	8.24958i	0.465935	+	0.399225i
$428$	3.39490	−	1.96005i	0.164099	−	0.0947424i
$429$		0			0
$430$		−	8.53859i		−	0.411767i
$431$	20.0311	−	11.5650i	0.964865	−	0.557065i	0.0671983	−	0.997740i	$-0.478594\pi$
$431$	20.0311	−	11.5650i	0.964865	−	0.557065i	0.897667	+	0.440674i	$0.145261\pi$
$432$		0			0
$433$		−	34.9265i		−	1.67846i	−0.543776	−	0.839230i	$-0.683006\pi$
$433$		−	34.9265i		−	1.67846i	0.543776	−	0.839230i	$-0.316994\pi$
$434$	−10.9962	−	31.2095i	−0.527836	−	1.49810i
$435$		0			0
$436$	13.9002			0.665699
$437$	3.21078	−	5.56123i	0.153592	−	0.266030i
$438$		0			0
$439$	33.6842	−	19.4476i	1.60766	−	0.928184i	0.617770	−	0.786359i	$-0.288036\pi$
$439$	33.6842	−	19.4476i	1.60766	−	0.928184i	0.989892	−	0.141824i	$-0.0452969\pi$
$440$	5.52912			0.263590
$441$		0			0
$442$	−10.6161			−0.504959
$443$	−32.3277	+	18.6644i	−1.53594	+	0.886774i	−0.536867	+	0.843667i	$0.680392\pi$
$443$	−32.3277	+	18.6644i	−1.53594	+	0.886774i	−0.999070	+	0.0431065i	$0.986275\pi$
$444$		0			0
$445$	5.13609	−	8.89596i	0.243474	−	0.421709i
$446$	−32.7350			−1.55005
$447$		0			0
$448$	−9.46276	−	26.8572i	−0.447073	−	1.26888i
$449$		−	23.9224i		−	1.12897i	−0.825445	−	0.564483i	$-0.809076\pi$
$449$		−	23.9224i		−	1.12897i	0.825445	−	0.564483i	$-0.190924\pi$
$450$		0			0
$451$	7.57036	−	4.37075i	0.356474	−	0.205810i
$452$			38.6342i			1.81720i
$453$		0			0
$454$	3.77628	−	2.18024i	0.177230	−	0.102324i
$455$	−13.0292	−	11.1638i	−0.610819	−	0.523365i
$456$		0			0
$457$	−4.99031	−	8.64348i	−0.233437	−	0.404325i	0.725380	−	0.688348i	$-0.241664\pi$
$457$	−4.99031	−	8.64348i	−0.233437	−	0.404325i	−0.958817	+	0.284024i	$0.908331\pi$
$458$	−6.74155	−	11.6767i	−0.315012	−	0.545617i
$459$		0			0
$460$	−5.02319	−	2.90014i	−0.234207	−	0.135220i
$461$	−16.7279	+	28.9735i	−0.779094	+	1.34943i	0.153371	+	0.988169i	$0.450987\pi$
$461$	−16.7279	+	28.9735i	−0.779094	+	1.34943i	−0.932465	+	0.361261i	$0.882346\pi$
$462$		0			0
$463$	11.5353	+	19.9798i	0.536092	+	0.928538i	0.999110	+	0.0421893i	$0.0134333\pi$
$463$	11.5353	+	19.9798i	0.536092	+	0.928538i	−0.463018	+	0.886349i	$0.653233\pi$
$464$			24.9776i			1.15956i
$465$		0			0
$466$	−32.7190			−1.51568
$467$	−20.1395	+	34.8827i	−0.931946	+	1.61418i	−0.151955	+	0.988387i	$0.548557\pi$
$467$	−20.1395	+	34.8827i	−0.931946	+	1.61418i	−0.779991	+	0.625791i	$0.784776\pi$
$468$		0			0
$469$	−1.75276	−	0.327728i	−0.0809349	−	0.0151331i
$470$	30.8527	+	17.8128i	1.42313	+	0.821643i
$471$		0			0
$472$	2.81163	+	1.62329i	0.129416	+	0.0747182i
$473$	5.45205	+	3.14774i	0.250686	+	0.144733i
$474$		0			0
$475$	−3.03078	−	1.74982i	−0.139062	−	0.0802874i
$476$	−3.43214	−	9.74109i	−0.157312	−	0.446482i
$477$		0			0
$478$	−17.9994	+	31.1759i	−0.823275	+	1.42595i
$479$	0.155503			0.00710509			0.00355255	−	0.999994i	$-0.498869\pi$
$479$	0.155503			0.00710509			0.00355255	+	0.999994i	$0.498869\pi$
$480$		0			0
$481$		−	17.5425i		−	0.799867i
$482$	11.7540	+	20.3585i	0.535380	+	0.927305i
$483$		0			0
$484$	0.687435	−	1.19067i	0.0312471	−	0.0541215i
$485$	4.34558	+	2.50892i	0.197323	+	0.113924i
$486$		0			0
$487$	8.25111	+	14.2913i	0.373893	+	0.647602i	0.990161	−	0.139935i	$-0.0446892\pi$
$487$	8.25111	+	14.2913i	0.373893	+	0.647602i	−0.616267	+	0.787537i	$0.711356\pi$
$488$	−1.96341	−	3.40072i	−0.0888793	−	0.153944i
$489$		0			0
$490$	11.0762	−	28.5834i	0.500371	−	1.29127i
$491$	−8.10003	+	4.67655i	−0.365549	+	0.211050i	−0.671512	−	0.740993i	$-0.734355\pi$
$491$	−8.10003	+	4.67655i	−0.365549	+	0.211050i	0.305963	+	0.952043i	$0.401022\pi$
$492$		0			0
$493$			13.3046i			0.599209i
$494$	−31.1534	+	17.9864i	−1.40166	+	0.809248i
$495$		0			0
$496$		−	18.2934i		−	0.821399i
$497$	17.5060	−	6.16801i	0.785253	−	0.276673i
$498$		0			0
$499$	1.99623			0.0893637			0.0446818	−	0.999001i	$-0.485773\pi$
$499$	1.99623			0.0893637			0.0446818	+	0.999001i	$0.485773\pi$
$500$	−14.0727	+	24.3746i	−0.629351	+	1.09007i
$501$		0			0
$502$	20.6585	−	11.9272i	0.922035	−	0.532337i
$503$	15.7008			0.700063			0.350032	−	0.936738i	$-0.386171\pi$
$503$	15.7008			0.700063			0.350032	+	0.936738i	$0.386171\pi$
$504$		0			0
$505$	7.35727			0.327394
$506$	6.80147	−	3.92683i	0.302362	−	0.174569i
$507$		0			0
$508$	−11.4679	+	19.8630i	−0.508807	+	0.881279i
$509$	15.1979			0.673633			0.336817	−	0.941570i	$-0.390650\pi$
$509$	15.1979			0.673633			0.336817	+	0.941570i	$0.390650\pi$
$510$		0			0
$511$	6.87340	+	5.88930i	0.304061	+	0.260527i
$512$		−	29.7316i		−	1.31396i
$513$		0			0
$514$	17.0231	−	9.82831i	0.750858	−	0.433508i
$515$		−	32.7781i		−	1.44437i
$516$		0			0
$517$	−22.7476	+	13.1333i	−1.00044	+	0.577603i
$518$	29.5605	−	10.4152i	1.29881	−	0.457619i
$519$		0			0
$520$	2.65699	+	4.60204i	0.116517	+	0.201813i
$521$	−20.6160	−	35.7080i	−0.903204	−	1.56440i	−0.823310	−	0.567592i	$-0.807875\pi$
$521$	−20.6160	−	35.7080i	−0.903204	−	1.56440i	−0.0798940	−	0.996803i	$-0.525458\pi$
$522$		0			0
$523$	37.0311	+	21.3799i	1.61926	+	0.934878i	0.987113	+	0.160026i	$0.0511577\pi$
$523$	37.0311	+	21.3799i	1.61926	+	0.934878i	0.632143	+	0.774852i	$0.282176\pi$
$524$	−2.94244	+	5.09645i	−0.128541	+	0.222640i
$525$		0			0
$526$	−9.22332	−	15.9753i	−0.402156	−	0.696554i
$527$		−	9.74419i		−	0.424464i
$528$		0			0
$529$	21.6526			0.941417
$530$	13.3437	−	23.1119i	0.579613	−	1.00392i
$531$		0			0
$532$	−26.5756	−	22.7706i	−1.15220	−	0.987231i
$533$	7.27579	+	4.20068i	0.315149	+	0.181952i
$534$		0			0
$535$	2.96723	+	1.71313i	0.128284	+	0.0740650i
$536$	0.478269	+	0.276129i	0.0206581	+	0.0119270i
$537$		0			0
$538$	29.6337	+	17.1090i	1.27760	+	0.737623i
$539$	14.1678	+	17.6096i	0.610251	+	0.758499i
$540$		0			0
$541$	8.04309	−	13.9310i	0.345800	−	0.598942i	−0.639699	−	0.768625i	$-0.720941\pi$
$541$	8.04309	−	13.9310i	0.345800	−	0.598942i	0.985499	+	0.169683i	$0.0542744\pi$
$542$	30.5328			1.31149
$543$		0			0
$544$		−	13.1613i		−	0.564284i
$545$	6.07456	+	10.5214i	0.260206	+	0.450689i
$546$		0			0
$547$	−5.94015	+	10.2886i	−0.253982	+	0.439910i	−0.964619	−	0.263649i	$-0.915074\pi$
$547$	−5.94015	+	10.2886i	−0.253982	+	0.439910i	0.710636	+	0.703560i	$0.248407\pi$
$548$	36.0021	+	20.7858i	1.53794	+	0.887927i
$549$		0			0
$550$	−2.14006	−	3.70669i	−0.0912525	−	0.158054i
$551$	22.5413	+	39.0427i	0.960293	+	1.66328i
$552$		0			0
$553$	24.3750	−	28.4481i	1.03653	−	1.20973i
$554$	−52.1078	+	30.0845i	−2.21385	+	1.27817i
$555$		0			0
$556$			23.7765i			1.00835i
$557$	26.4006	−	15.2424i	1.11863	−	0.645841i	0.177579	−	0.984107i	$-0.443173\pi$
$557$	26.4006	−	15.2424i	1.11863	−	0.645841i	0.941051	+	0.338265i	$0.109840\pi$
$558$		0			0
$559$			6.05052i			0.255910i
$560$	11.0266	−	12.8691i	0.465957	−	0.543818i
$561$		0			0
$562$	−11.5392			−0.486750
$563$	11.2686	−	19.5177i	0.474914	−	0.822575i	−0.524673	−	0.851304i	$-0.675813\pi$
$563$	11.2686	−	19.5177i	0.474914	−	0.822575i	0.999587	+	0.0287288i	$0.00914592\pi$
$564$		0			0
$565$	−29.2433	+	16.8836i	−1.23027	+	0.710300i
$566$	63.4572			2.66730
$567$		0			0
$568$	−5.74852			−0.241202
$569$	−38.5935	+	22.2819i	−1.61792	+	0.934108i	−0.630465	+	0.776218i	$0.717136\pi$
$569$	−38.5935	+	22.2819i	−1.61792	+	0.934108i	−0.987457	+	0.157890i	$0.949531\pi$
$570$		0			0
$571$	−17.6415	+	30.5560i	−0.738274	+	1.27873i	0.214998	+	0.976614i	$0.431025\pi$
$571$	−17.6415	+	30.5560i	−0.738274	+	1.27873i	−0.953272	+	0.302113i	$0.902308\pi$
$572$	−23.9567			−1.00168
$573$		0			0
$574$	−2.75874	+	14.7543i	−0.115147	+	0.615833i
$575$			0.734319i			0.0306232i
$576$		0			0
$577$	3.25158	−	1.87730i	0.135365	−	0.0781531i	−0.430788	−	0.902453i	$-0.641764\pi$
$577$	3.25158	−	1.87730i	0.135365	−	0.0781531i	0.566153	+	0.824300i	$0.308431\pi$
$578$			30.0379i			1.24941i
$579$		0			0
$580$	35.2654	−	20.3605i	1.46432	−	0.845423i
$581$	8.03792	+	1.50292i	0.333469	+	0.0623516i
$582$		0			0
$583$	9.83827	+	17.0404i	0.407460	+	0.705741i
$584$	−1.40166	−	2.42775i	−0.0580011	−	0.100461i
$585$		0			0
$586$	−12.8615	−	7.42559i	−0.531304	−	0.306748i
$587$	15.8021	−	27.3700i	0.652222	−	1.12968i	−0.330361	−	0.943855i	$-0.607171\pi$
$587$	15.8021	−	27.3700i	0.652222	−	1.12968i	0.982583	−	0.185826i	$-0.0594961\pi$
$588$		0			0
$589$	−16.5091	−	28.5946i	−0.680246	−	1.17822i
$590$			17.3506i			0.714314i
$591$		0			0
$592$	17.3269			0.712129
$593$	18.5588	−	32.1448i	0.762120	−	1.32003i	−0.179636	−	0.983733i	$-0.557492\pi$
$593$	18.5588	−	32.1448i	0.762120	−	1.32003i	0.941756	−	0.336297i	$-0.109175\pi$
$594$		0			0
$595$	5.87342	−	6.85486i	0.240787	−	0.281022i
$596$	19.1689	+	11.0671i	0.785187	+	0.453328i
$597$		0			0
$598$	6.53682	+	3.77403i	0.267310	+	0.154332i
$599$	24.5188	+	14.1559i	1.00181	+	0.578396i	0.908784	−	0.417267i	$-0.137012\pi$
$599$	24.5188	+	14.1559i	1.00181	+	0.578396i	0.0930277	+	0.995664i	$0.470345\pi$
$600$		0			0
$601$	20.8341	+	12.0286i	0.849840	+	0.490655i	0.860597	−	0.509287i	$-0.170091\pi$
$601$	20.8341	+	12.0286i	0.849840	+	0.490655i	−0.0107568	+	0.999942i	$0.503424\pi$
$602$	−10.1956	+	3.59229i	−0.415543	+	0.146411i
$603$		0			0
$604$	−14.3101	+	24.7859i	−0.582271	+	1.00852i
$605$	1.20167			0.0488549
$606$		0			0
$607$			9.52047i			0.386424i	0.981157	+	0.193212i	$0.0618905\pi$
$607$			9.52047i			0.386424i	−0.981157	+	0.193212i	$0.938110\pi$
$608$	−22.2985	−	38.6221i	−0.904323	−	1.56633i
$609$		0			0
$610$	10.4930	−	18.1744i	0.424848	−	0.735859i
$611$	−21.8625	−	12.6223i	−0.884461	−	0.510644i
$612$		0			0
$613$	1.23108	+	2.13230i	0.0497230	+	0.0861227i	0.889816	−	0.456320i	$-0.150833\pi$
$613$	1.23108	+	2.13230i	0.0497230	+	0.0861227i	−0.840093	+	0.542443i	$0.817499\pi$
$614$	−3.26210	−	5.65012i	−0.131648	−	0.228020i
$615$		0			0
$616$	−2.32617	−	6.60212i	−0.0937239	−	0.266007i
$617$	−18.7738	+	10.8390i	−0.755804	+	0.436364i	−0.827787	−	0.561042i	$-0.810401\pi$
$617$	−18.7738	+	10.8390i	−0.755804	+	0.436364i	0.0719831	+	0.997406i	$0.477067\pi$
$618$		0			0
$619$			24.1063i			0.968915i	0.874815	+	0.484457i	$0.160983\pi$
$619$			24.1063i			0.968915i	−0.874815	+	0.484457i	$0.839017\pi$
$620$	−25.8281	+	14.9119i	−1.03728	+	0.598875i
$621$		0			0
$622$		−	40.7615i		−	1.63439i
$623$	−12.7832	−	2.39018i	−0.512147	−	0.0957604i
$624$		0			0
$625$	−21.4368			−0.857471
$626$	26.7643	−	46.3571i	1.06972	−	1.85280i
$627$		0			0
$628$	36.9649	−	21.3417i	1.47506	−	0.851627i
$629$	9.22934			0.367998
$630$		0			0
$631$	3.37520			0.134365			0.0671824	−	0.997741i	$-0.478599\pi$
$631$	3.37520			0.134365			0.0671824	+	0.997741i	$0.478599\pi$
$632$	−10.0481	+	5.80128i	−0.399692	+	0.230762i
$633$		0			0
$634$	−17.0021	+	29.4486i	−0.675242	+	1.16955i
$635$	−20.0465			−0.795521
$636$		0			0
$637$	−7.84869	+	20.2544i	−0.310976	+	0.802510i
$638$			55.1368i			2.18289i
$639$		0			0
$640$	−11.6374	+	6.71887i	−0.460010	+	0.265587i
$641$			35.6978i			1.40998i	0.709218	+	0.704989i	$0.249048\pi$
$641$			35.6978i			1.40998i	−0.709218	+	0.704989i	$0.750952\pi$
$642$		0			0
$643$	3.03956	−	1.75489i	0.119868	−	0.0692060i	−0.438867	−	0.898552i	$-0.644620\pi$
$643$	3.03956	−	1.75489i	0.119868	−	0.0692060i	0.558735	+	0.829346i	$0.311287\pi$
$644$	−1.34963	+	7.21813i	−0.0531831	+	0.284434i
$645$		0			0
$646$	−9.46292	−	16.3903i	−0.372314	−	0.644866i
$647$	7.02996	+	12.1762i	0.276376	+	0.478698i	0.970481	−	0.241176i	$-0.0775331\pi$
$647$	7.02996	+	12.1762i	0.276376	+	0.478698i	−0.694105	+	0.719874i	$0.744200\pi$
$648$		0			0
$649$	−11.0787	−	6.39629i	−0.434877	−	0.251076i
$650$	2.05679	−	3.56246i	0.0806739	−	0.139731i
$651$		0			0
$652$	21.3225	+	36.9317i	0.835055	+	1.44636i
$653$		−	11.8558i		−	0.463955i	−0.972721	−	0.231978i	$-0.925480\pi$
$653$		−	11.8558i		−	0.463955i	0.972721	−	0.231978i	$-0.0745196\pi$
$654$		0			0
$655$	−5.14353			−0.200974
$656$	−4.14905	+	7.18637i	−0.161993	+	0.280581i
$657$		0			0
$658$	8.28952	−	44.3341i	0.323159	−	1.72832i
$659$	−5.03144	−	2.90491i	−0.195997	−	0.113159i	0.398790	−	0.917042i	$-0.369430\pi$
$659$	−5.03144	−	2.90491i	−0.195997	−	0.113159i	−0.594787	+	0.803883i	$0.702764\pi$
$660$		0			0
$661$	8.41592	+	4.85893i	0.327341	+	0.188991i	0.654660	−	0.755923i	$-0.272812\pi$
$661$	8.41592	+	4.85893i	0.327341	+	0.188991i	−0.327319	+	0.944914i	$0.606145\pi$
$662$	42.3046	+	24.4246i	1.64422	+	0.949288i
$663$		0			0
$664$	−2.19328	−	1.26629i	−0.0851158	−	0.0491416i
$665$	5.62185	−	30.0668i	0.218006	−	1.16594i
$666$		0			0
$667$	4.72977	−	8.19220i	0.183137	−	0.317203i
$668$	29.5006			1.14141
$669$		0			0
$670$			2.95141i			0.114023i
$671$	7.73645	+	13.3999i	0.298662	+	0.517298i
$672$		0			0
$673$	13.4646	−	23.3214i	0.519023	−	0.898975i	−0.480732	−	0.876867i	$-0.659629\pi$
$673$	13.4646	−	23.3214i	0.519023	−	0.898975i	0.999756	−	0.0221072i	$-0.00703750\pi$
$674$	−21.5415	−	12.4370i	−0.829747	−	0.479055i
$675$		0			0
$676$	4.02953	+	6.97935i	0.154982	+	0.268436i
$677$	−22.7056	−	39.3273i	−0.872648	−	1.51147i	−0.859247	−	0.511560i	$-0.829068\pi$
$677$	−22.7056	−	39.3273i	−0.872648	−	1.51147i	−0.0134007	−	0.999910i	$-0.504266\pi$
$678$		0			0
$679$	1.16757	−	6.24443i	0.0448074	−	0.239639i
$680$	−2.42120	+	1.39788i	−0.0928487	+	0.0536062i
$681$		0			0
$682$		−	40.3818i		−	1.54630i
$683$	−37.6543	+	21.7397i	−1.44080	+	0.831848i	−0.997903	−	0.0647226i	$-0.979384\pi$
$683$	−37.6543	+	21.7397i	−1.44080	+	0.831848i	−0.442900	+	0.896571i	$0.646050\pi$
$684$		0			0
$685$			36.3347i			1.38828i
$686$	−38.7903	−	1.20030i	−1.48102	−	0.0458278i
$687$		0			0
$688$	−5.97616			−0.227839
$689$	−9.45546	+	16.3773i	−0.360224	+	0.623927i
$690$		0			0
$691$	−23.6991	+	13.6827i	−0.901557	+	0.520514i	−0.877705	−	0.479201i	$-0.840926\pi$
$691$	−23.6991	+	13.6827i	−0.901557	+	0.520514i	−0.0238522	+	0.999715i	$0.507593\pi$
$692$	−21.6804			−0.824166
$693$		0			0
$694$	45.4845			1.72657
$695$	−17.9971	+	10.3906i	−0.682668	+	0.394139i
$696$		0			0
$697$	−2.21004	+	3.82790i	−0.0837112	+	0.144992i
$698$	−5.34423			−0.202282
$699$		0			0
$700$	3.93377	+	0.735530i	0.148682	+	0.0278004i
$701$		−	8.26437i		−	0.312141i	−0.987746	−	0.156070i	$-0.950117\pi$
$701$		−	8.26437i		−	0.312141i	0.987746	−	0.156070i	$-0.0498827\pi$
$702$		0			0
$703$	27.0838	−	15.6368i	1.02148	−	0.589754i
$704$		−	34.7504i		−	1.30970i
$705$		0			0
$706$	−46.0484	+	26.5861i	−1.73306	+	1.00058i
$707$	−3.09529	−	8.78505i	−0.116410	−	0.330396i
$708$		0			0
$709$	−21.4086	−	37.0807i	−0.804015	−	1.39260i	−0.916954	−	0.398994i	$-0.869360\pi$
$709$	−21.4086	−	37.0807i	−0.804015	−	1.39260i	0.112938	−	0.993602i	$-0.463974\pi$
$710$	−15.3608	−	26.6057i	−0.576481	−	0.998494i
$711$		0			0
$712$	3.48810	+	2.01385i	0.130722	+	0.0754724i
$713$	−3.46405	+	5.99992i	−0.129730	+	0.224699i
$714$		0			0
$715$	−10.4694	−	18.1335i	−0.391532	−	0.678153i
$716$		−	35.9159i		−	1.34224i
$717$		0			0
$718$	−23.5610			−0.879289
$719$	−11.5725	+	20.0442i	−0.431583	+	0.747523i	−0.997010	−	0.0772751i	$-0.975378\pi$
$719$	−11.5725	+	20.0442i	−0.431583	+	0.747523i	0.565427	+	0.824798i	$0.308711\pi$
$720$		0			0
$721$	−39.1391	+	13.7901i	−1.45762	+	0.513571i
$722$	−21.0584	−	12.1581i	−0.783712	−	0.452477i
$723$		0			0
$724$	−4.84874	−	2.79942i	−0.180202	−	0.104040i
$725$	−4.46462	−	2.57765i	−0.165812	−	0.0957316i
$726$		0			0
$727$	4.76878	+	2.75326i	0.176864	+	0.102113i	0.585819	−	0.810442i	$-0.300773\pi$
$727$	4.76878	+	2.75326i	0.176864	+	0.102113i	−0.408954	+	0.912555i	$0.634106\pi$
$728$	4.37730	−	5.10874i	0.162233	−	0.189343i
$729$		0			0
$730$	7.49084	−	12.9745i	0.277248	−	0.480208i
$731$	−3.18327			−0.117737
$732$		0			0
$733$		−	3.98999i		−	0.147373i	−0.997281	−	0.0736867i	$-0.976524\pi$
$733$		−	3.98999i		−	0.147373i	0.997281	−	0.0736867i	$-0.0234765\pi$
$734$	3.46991	+	6.01005i	0.128077	+	0.221835i
$735$		0			0
$736$	−4.67882	+	8.10395i	−0.172463	+	0.298716i
$737$	−1.88453	−	1.08803i	−0.0694176	−	0.0400783i
$738$		0			0
$739$	0.871657	+	1.50976i	0.0320644	+	0.0555372i	0.881612	−	0.471974i	$-0.156458\pi$
$739$	0.871657	+	1.50976i	0.0320644	+	0.0555372i	−0.849548	+	0.527512i	$0.823125\pi$
$740$	−14.1240	−	24.4635i	−0.519208	−	0.899295i
$741$		0			0
$742$	−33.2110	−	6.20974i	−1.21921	−	0.227967i
$743$	−8.70204	+	5.02413i	−0.319247	+	0.184317i	−0.651057	−	0.759029i	$-0.725674\pi$
$743$	−8.70204	+	5.02413i	−0.319247	+	0.184317i	0.331810	+	0.943346i	$0.392341\pi$
$744$		0			0
$745$			19.3459i			0.708780i
$746$	12.0597	−	6.96267i	0.441537	−	0.254921i
$747$		0			0
$748$		−	12.6040i		−	0.460846i
$749$	0.797238	−	4.26379i	0.0291304	−	0.155796i
$750$		0			0
$751$	−23.3450			−0.851872			−0.425936	−	0.904753i	$-0.640055\pi$
$751$	−23.3450			−0.851872			−0.425936	+	0.904753i	$0.640055\pi$
$752$	12.4672	−	21.5938i	0.454631	−	0.787444i
$753$		0			0
$754$	−45.8919	+	26.4957i	−1.67128	+	0.964916i
$755$	−25.0148			−0.910383
$756$		0			0
$757$	−14.3334			−0.520957			−0.260479	−	0.965480i	$-0.583880\pi$
$757$	−14.3334			−0.520957			−0.260479	+	0.965480i	$0.583880\pi$
$758$	6.98566	−	4.03317i	0.253730	−	0.146491i
$759$		0			0
$760$	−4.73672	+	8.20424i	−0.171819	+	0.297599i
$761$	−22.6355			−0.820537			−0.410268	−	0.911965i	$-0.634565\pi$
$761$	−22.6355			−0.820537			−0.410268	+	0.911965i	$0.634565\pi$
$762$		0			0
$763$	10.0076	−	11.6799i	0.362301	−	0.422841i
$764$			21.6067i			0.781702i
$765$		0			0
$766$	−62.1046	+	35.8561i	−2.24393	+	1.29553i
$767$		−	12.2948i		−	0.443940i
$768$		0			0
$769$	42.6873	−	24.6455i	1.53934	−	0.888741i	0.540468	−	0.841365i	$-0.318247\pi$
$769$	42.6873	−	24.6455i	1.53934	−	0.888741i	0.998877	−	0.0473762i	$-0.0150860\pi$
$770$	24.3406	−	28.4079i	0.877173	−	1.02375i
$771$		0			0
$772$	−6.55467	−	11.3530i	−0.235908	−	0.408604i
$773$	11.0083	+	19.0670i	0.395943	+	0.685793i	0.993221	−	0.116241i	$-0.0370845\pi$
$773$	11.0083	+	19.0670i	0.395943	+	0.685793i	−0.597278	+	0.802034i	$0.703751\pi$
$774$		0			0
$775$	3.26986	+	1.88785i	0.117457	+	0.0678137i
$776$	−0.983745	+	1.70390i	−0.0353144	+	0.0611663i
$777$		0			0
$778$	14.1232	+	24.4621i	0.506340	+	0.877007i
$779$			14.9774i			0.536622i
$780$		0			0
$781$	22.6510			0.810516
$782$	−1.98557	+	3.43911i	−0.0710040	+	0.122982i
$783$		0			0
$784$	−20.0055	−	7.75223i	−0.714483	−	0.276865i
$785$	32.3083	+	18.6532i	1.15313	+	0.665761i
$786$		0			0
$787$	9.40107	+	5.42771i	0.335112	+	0.193477i	0.658108	−	0.752923i	$-0.271357\pi$
$787$	9.40107	+	5.42771i	0.335112	+	0.193477i	−0.322996	+	0.946400i	$0.604690\pi$
$788$	−5.98320	−	3.45440i	−0.213143	−	0.123058i
$789$		0			0
$790$	−53.6998	−	31.0036i	−1.91055	−	1.10306i
$791$	32.4631	+	27.8152i	1.15426	+	0.988995i
$792$		0			0
$793$	−7.43542	+	12.8785i	−0.264039	+	0.457330i
$794$	61.8223			2.19399
$795$		0			0
$796$		−	12.2977i		−	0.435882i
$797$	−1.98299	−	3.43465i	−0.0702412	−	0.121661i	0.828766	−	0.559596i	$-0.189044\pi$
$797$	−1.98299	−	3.43465i	−0.0702412	−	0.121661i	−0.899007	+	0.437934i	$0.855710\pi$
$798$		0			0
$799$	6.64078	−	11.5022i	0.234934	−	0.406917i
$800$	4.41653	+	2.54988i	0.156148	+	0.0901520i
$801$		0			0
$802$	30.4312	+	52.7084i	1.07456	+	1.86120i
$803$	5.52298	+	9.56608i	0.194902	+	0.337580i
$804$		0			0
$805$	−6.05341	+	2.13284i	−0.213355	+	0.0751726i
$806$	33.6109	−	19.4053i	1.18389	−	0.683521i
$807$		0			0
$808$			2.88478i			0.101486i
$809$	−36.0199	+	20.7961i	−1.26639	+	0.731152i	−0.974303	−	0.225240i	$-0.927683\pi$
$809$	−36.0199	+	20.7961i	−1.26639	+	0.731152i	−0.292088	+	0.956391i	$0.594350\pi$
$810$		0			0
$811$		−	13.3293i		−	0.468056i	−0.972230	−	0.234028i	$-0.924809\pi$
$811$		−	13.3293i		−	0.468056i	0.972230	−	0.234028i	$-0.0751907\pi$
$812$	−39.1483	−	33.5432i	−1.37384	−	1.17714i
$813$		0			0
$814$	38.2482			1.34060
$815$	−18.6364	+	32.2792i	−0.652806	+	1.13069i
$816$		0			0
$817$	−9.34139	+	5.39326i	−0.326814	+	0.188686i
$818$	63.4417			2.21819
$819$		0			0
$820$	13.5284			0.472432
$821$	33.4332	−	19.3027i	1.16683	−	0.673668i	0.213897	−	0.976856i	$-0.431384\pi$
$821$	33.4332	−	19.3027i	1.16683	−	0.673668i	0.952931	+	0.303188i	$0.0980510\pi$
$822$		0			0
$823$	5.34881	−	9.26442i	0.186448	−	0.322937i	−0.757616	−	0.652701i	$-0.773636\pi$
$823$	5.34881	−	9.26442i	0.186448	−	0.322937i	0.944063	+	0.329764i	$0.106969\pi$
$824$	12.8523			0.447729
$825$		0			0
$826$	20.7178	−	7.29962i	0.720863	−	0.253986i
$827$			11.7079i			0.407125i	0.979062	+	0.203562i	$0.0652520\pi$
$827$			11.7079i			0.407125i	−0.979062	+	0.203562i	$0.934748\pi$
$828$		0			0
$829$	−15.0948	+	8.71498i	−0.524263	+	0.302684i	−0.738677	−	0.674059i	$-0.764549\pi$
$829$	−15.0948	+	8.71498i	−0.524263	+	0.302684i	0.214414	+	0.976743i	$0.431216\pi$
$830$		−	13.5348i		−	0.469799i
$831$		0			0
$832$	28.9237	−	16.6991i	1.00275	−	0.578937i
$833$	−10.6562	−	4.12931i	−0.369214	−	0.143072i
$834$		0			0
$835$	12.8921	+	22.3298i	0.446151	+	0.772756i
$836$	−21.3543	−	36.9867i	−0.738553	−	1.27921i
$837$		0			0
$838$	66.3838	+	38.3267i	2.29319	+	1.32397i
$839$	−0.704502	+	1.22023i	−0.0243221	+	0.0421271i	−0.877930	−	0.478789i	$-0.841076\pi$
$839$	−0.704502	+	1.22023i	−0.0243221	+	0.0421271i	0.853608	+	0.520916i	$0.174409\pi$
$840$		0			0
$841$	18.7055	+	32.3988i	0.645016	+	1.11720i
$842$			16.1771i			0.557498i
$843$		0			0
$844$	37.9326			1.30570
$845$	−3.52191	+	6.10012i	−0.121157	+	0.209851i
$846$		0			0
$847$	−0.505558	−	1.43487i	−0.0173712	−	0.0493028i
$848$	−16.1761	−	9.33925i	−0.555488	−	0.320711i
$849$		0			0
$850$	1.87426	+	1.08211i	0.0642867	+	0.0371160i
$851$	−5.68290	−	3.28102i	−0.194807	−	0.112472i
$852$		0			0
$853$	−28.0716	−	16.2071i	−0.961153	−	0.554922i	−0.0646255	−	0.997910i	$-0.520585\pi$
$853$	−28.0716	−	16.2071i	−0.961153	−	0.554922i	−0.896528	+	0.442987i	$0.853919\pi$
$854$	−26.1159	−	4.88311i	−0.893667	−	0.167097i
$855$		0			0
$856$	−0.671716	+	1.16345i	−0.0229588	+	0.0397658i
$857$	−44.4539			−1.51852			−0.759258	−	0.650789i	$-0.774438\pi$
$857$	−44.4539			−1.51852			−0.759258	+	0.650789i	$0.774438\pi$
$858$		0			0
$859$			15.6494i			0.533952i	0.963703	+	0.266976i	$0.0860245\pi$
$859$			15.6494i			0.533952i	−0.963703	+	0.266976i	$0.913976\pi$
$860$	4.87147	+	8.43763i	0.166116	+	0.287721i
$861$		0			0
$862$	−24.2342	+	41.9748i	−0.825420	+	1.42967i
$863$	15.6911	+	9.05927i	0.534132	+	0.308381i	0.742697	−	0.669627i	$-0.233546\pi$
$863$	15.6911	+	9.05927i	0.534132	+	0.308381i	−0.208565	+	0.978008i	$0.566879\pi$
$864$		0			0
$865$	−9.47462	−	16.4105i	−0.322147	−	0.557975i
$866$	36.5939	+	63.3825i	1.24351	+	2.15383i
$867$		0			0
$868$	28.6719	+	24.5668i	0.973189	+	0.833853i
$869$	39.5927	−	22.8589i	1.34309	−	0.775434i
$870$		0			0
$871$		−	2.09140i		−	0.0708643i
$872$	−4.12545	+	2.38183i	−0.139705	+	0.0806589i
$873$		0			0
$874$			13.4562i			0.455164i
$875$	10.3494	+	29.3737i	0.349875	+	0.993014i
$876$		0			0
$877$	−2.77853			−0.0938243			−0.0469121	−	0.998899i	$-0.514938\pi$
$877$	−2.77853			−0.0938243			−0.0469121	+	0.998899i	$0.514938\pi$
$878$	−40.7521	+	70.5847i	−1.37532	+	2.38212i
$879$		0			0
$880$	17.9106	−	10.3407i	0.603767	−	0.348585i
$881$	1.96106			0.0660696			0.0330348	−	0.999454i	$-0.489483\pi$
$881$	1.96106			0.0660696			0.0330348	+	0.999454i	$0.489483\pi$
$882$		0			0
$883$	−36.9657			−1.24400			−0.621998	−	0.783019i	$-0.713679\pi$
$883$	−36.9657			−1.24400			−0.621998	+	0.783019i	$0.713679\pi$
$884$	10.4906	−	6.05676i	0.352838	−	0.203711i
$885$		0			0
$886$	39.1110	−	67.7422i	1.31396	−	2.27584i
$887$	22.5168			0.756040			0.378020	−	0.925797i	$-0.376605\pi$
$887$	22.5168			0.756040			0.378020	+	0.925797i	$0.376605\pi$
$888$		0			0
$889$	8.43380	+	23.9368i	0.282861	+	0.802814i
$890$			21.5251i			0.721525i
$891$		0			0
$892$	32.3479	−	18.6761i	1.08309	−	0.625321i
$893$		−	45.0046i		−	1.50602i
$894$		0			0
$895$	27.1857	−	15.6957i	0.908719	−	0.524649i
$896$	12.9188	+	11.0691i	0.431586	+	0.369793i
$897$		0			0
$898$	25.0644	+	43.4129i	0.836411	+	1.44871i
$899$	−24.3195	−	42.1225i	−0.811099	−	1.40487i
$900$		0			0
$901$	−8.61635	−	4.97465i	−0.287052	−	0.165730i
$902$	−9.15882	+	15.8635i	−0.304955	+	0.528198i
$903$		0			0
$904$	−6.62005	−	11.4663i	−0.220180	−	0.381362i
$905$		−	4.89353i		−	0.162666i
$906$		0			0
$907$	−19.1196			−0.634857			−0.317428	−	0.948282i	$-0.602819\pi$
$907$	−19.1196			−0.634857			−0.317428	+	0.948282i	$0.602819\pi$
$908$	−2.48775	+	4.30891i	−0.0825589	+	0.142996i
$909$		0			0
$910$	35.3414	+	6.60808i	1.17155	+	0.219056i
$911$	−4.92610	−	2.84408i	−0.163209	−	0.0942287i	0.416171	−	0.909286i	$-0.363372\pi$
$911$	−4.92610	−	2.84408i	−0.163209	−	0.0942287i	−0.579380	+	0.815058i	$0.696705\pi$
$912$		0			0
$913$	8.64222	+	4.98959i	0.286016	+	0.165131i
$914$	18.1122	+	10.4571i	0.599100	+	0.345890i
$915$		0			0
$916$	13.3237	+	7.69242i	0.440226	+	0.254165i
$917$	2.16395	+	6.14170i	0.0714598	+	0.202817i
$918$		0			0
$919$	−10.9255	+	18.9235i	−0.360399	+	0.624230i	−0.988027	−	0.154284i	$-0.950693\pi$
$919$	−10.9255	+	18.9235i	−0.360399	+	0.624230i	0.627627	+	0.778514i	$0.284026\pi$
$920$	1.98778			0.0655352
$921$		0			0
$922$		−	70.1058i		−	2.30881i
$923$	10.8848	+	18.8530i	0.358278	+	0.620555i
$924$		0			0
$925$	−1.78811	+	3.09709i	−0.0587926	+	0.101832i
$926$	−41.8672	−	24.1720i	−1.37584	−	0.794343i
$927$		0			0
$928$	−32.8477	−	56.8940i	−1.07828	−	1.86764i
$929$	−8.08806	−	14.0089i	−0.265361	−	0.459618i	0.702297	−	0.711884i	$-0.252158\pi$
$929$	−8.08806	−	14.0089i	−0.265361	−	0.459618i	−0.967658	+	0.252266i	$0.918824\pi$
$930$		0			0
$931$	−38.2669	+	5.93663i	−1.25415	+	0.194565i
$932$	32.3321	−	18.6669i	1.05907	−	0.611456i
$933$		0			0
$934$		−	84.4040i		−	2.76178i
$935$	9.54029	−	5.50809i	0.312001	−	0.180134i
$936$		0			0
$937$			14.0440i			0.458799i	0.973332	+	0.229400i	$0.0736762\pi$
$937$			14.0440i			0.458799i	−0.973332	+	0.229400i	$0.926324\pi$
$938$	3.52417	−	1.24169i	0.115068	−	0.0405428i
$939$		0			0
$940$	−40.6505			−1.32587
$941$	−21.5934	+	37.4009i	−0.703924	+	1.21923i	0.263154	+	0.964754i	$0.415237\pi$
$941$	−21.5934	+	37.4009i	−0.703924	+	1.21923i	−0.967078	+	0.254479i	$0.918096\pi$
$942$		0			0
$943$	2.72163	−	1.57133i	0.0886284	−	0.0511696i
$944$	12.1437			0.395244
$945$		0			0
$946$	−13.1921			−0.428911
$947$	−16.6235	+	9.59758i	−0.540191	+	0.311879i	−0.745156	−	0.666890i	$-0.767625\pi$
$947$	−16.6235	+	9.59758i	−0.540191	+	0.311879i	0.204965	+	0.978769i	$0.434292\pi$
$948$		0			0
$949$	−5.30807	+	9.19386i	−0.172307	+	0.298445i
$950$	7.33344			0.237928
$951$		0			0
$952$	2.68779	+	2.30296i	0.0871116	+	0.0746394i
$953$		−	5.62718i		−	0.182282i	−0.995838	−	0.0911411i	$-0.970949\pi$
$953$		−	5.62718i		−	0.182282i	0.995838	−	0.0911411i	$-0.0290514\pi$
$954$		0			0
$955$	−16.3547	+	9.44239i	−0.529225	+	0.305548i
$956$		−	41.0764i		−	1.32850i
$957$		0			0
$958$	−0.282197	+	0.162926i	−0.00911736	+	0.00526391i
$959$	43.3860	−	15.2864i	1.40101	−	0.493625i
$960$		0			0
$961$	2.31141	+	4.00348i	0.0745616	+	0.129144i
$962$	18.3799	+	31.8350i	0.592593	+	1.02640i
$963$		0			0
$964$	−23.2300	−	13.4119i	−0.748189	−	0.431967i
$965$	5.72894	−	9.92282i	0.184421	−	0.319427i
$966$		0			0
$967$	−7.62091	−	13.1998i	−0.245072	−	0.424477i	0.717080	−	0.696991i	$-0.245478\pi$
$967$	−7.62091	−	13.1998i	−0.245072	−	0.424477i	−0.962152	+	0.272514i	$0.912145\pi$
$968$			0.471174i			0.0151441i
$969$		0			0
$970$	−10.5148			−0.337610
$971$	20.4479	−	35.4168i	0.656205	−	1.13658i	−0.325386	−	0.945581i	$-0.605494\pi$
$971$	20.4479	−	35.4168i	0.656205	−	1.13658i	0.981590	−	0.190998i	$-0.0611725\pi$
$972$		0			0
$973$	19.9786	+	17.1182i	0.640486	+	0.548784i
$974$	−29.9472	−	17.2900i	−0.959571	−	0.554009i
$975$		0			0
$976$	−12.7202	−	7.34404i	−0.407165	−	0.235077i
$977$	−8.98296	−	5.18631i	−0.287390	−	0.165925i	0.349374	−	0.936983i	$-0.386394\pi$
$977$	−8.98296	−	5.18631i	−0.287390	−	0.165925i	−0.636764	+	0.771058i	$0.719728\pi$
$978$		0			0
$979$	−13.7442	−	7.93522i	−0.439267	−	0.253611i
$980$	5.36227	+	34.5646i	0.171291	+	1.10413i
$981$		0			0
$982$	9.79963	−	16.9735i	0.312719	−	0.541645i
$983$	−2.11700			−0.0675219			−0.0337609	−	0.999430i	$-0.510748\pi$
$983$	−2.11700			−0.0675219			−0.0337609	+	0.999430i	$0.510748\pi$
$984$		0			0
$985$		−	6.03847i		−	0.192402i
$986$	−13.9398	−	24.1444i	−0.443932	−	0.768914i
$987$		0			0
$988$	20.5234	−	35.5475i	0.652935	−	1.13092i
$989$	1.96007	+	1.13165i	0.0623267	+	0.0359843i
$990$		0			0
$991$	−17.0581	−	29.5456i	−0.541870	−	0.938546i	−0.998797	−	0.0490418i	$-0.984383\pi$
$991$	−17.0581	−	29.5456i	−0.541870	−	0.938546i	0.456927	−	0.889504i	$-0.348950\pi$
$992$	24.0575	+	41.6688i	0.763825	+	1.32298i
$993$		0			0
$994$	−25.3064	+	29.5351i	−0.802671	+	0.936797i
$995$	9.30850	−	5.37427i	0.295099	−	0.170376i
$996$		0			0
$997$		−	45.8235i		−	1.45125i	−0.688093	−	0.725623i	$-0.741552\pi$
$997$		−	45.8235i		−	1.45125i	0.688093	−	0.725623i	$-0.258448\pi$
$998$	−3.62264	+	2.09153i	−0.114673	+	0.0662064i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.s.b.89.1		10
3.2	odd	2		63.2.s.b.47.5	yes	10
4.3	odd	2		3024.2.df.b.1601.5		10
7.2	even	3		1323.2.o.d.440.5		10
7.3	odd	6		189.2.i.b.143.1		10
7.4	even	3		1323.2.i.b.521.1		10
7.5	odd	6		1323.2.o.c.440.5		10
7.6	odd	2		1323.2.s.b.656.1		10
9.2	odd	6		567.2.p.c.404.1		10
9.4	even	3		63.2.i.b.5.1	✓	10
9.5	odd	6		189.2.i.b.152.5		10
9.7	even	3		567.2.p.d.404.5		10
12.11	even	2		1008.2.df.b.929.3		10
21.2	odd	6		441.2.o.c.146.1		10
21.5	even	6		441.2.o.d.146.1		10
21.11	odd	6		441.2.i.b.227.5		10
21.17	even	6		63.2.i.b.38.5	yes	10
21.20	even	2		441.2.s.b.362.5		10
28.3	even	6		3024.2.ca.b.2033.5		10
36.23	even	6		3024.2.ca.b.2609.5		10
36.31	odd	6		1008.2.ca.b.257.5		10
63.4	even	3		441.2.s.b.374.5		10
63.5	even	6		1323.2.o.d.881.5		10
63.13	odd	6		441.2.i.b.68.1		10
63.23	odd	6		1323.2.o.c.881.5		10
63.31	odd	6		63.2.s.b.59.5	yes	10
63.32	odd	6		1323.2.s.b.962.1		10
63.38	even	6		567.2.p.d.80.5		10
63.40	odd	6		441.2.o.c.293.1		10
63.41	even	6		1323.2.i.b.1097.5		10
63.52	odd	6		567.2.p.c.80.1		10
63.58	even	3		441.2.o.d.293.1		10
63.59	even	6	inner	189.2.s.b.17.1		10
84.59	odd	6		1008.2.ca.b.353.5		10
252.31	even	6		1008.2.df.b.689.3		10
252.59	odd	6		3024.2.df.b.17.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.1	✓	10	9.4	even	3
63.2.i.b.38.5	yes	10	21.17	even	6
63.2.s.b.47.5	yes	10	3.2	odd	2
63.2.s.b.59.5	yes	10	63.31	odd	6
189.2.i.b.143.1		10	7.3	odd	6
189.2.i.b.152.5		10	9.5	odd	6
189.2.s.b.17.1		10	63.59	even	6	inner
189.2.s.b.89.1		10	1.1	even	1	trivial
441.2.i.b.68.1		10	63.13	odd	6
441.2.i.b.227.5		10	21.11	odd	6
441.2.o.c.146.1		10	21.2	odd	6
441.2.o.c.293.1		10	63.40	odd	6
441.2.o.d.146.1		10	21.5	even	6
441.2.o.d.293.1		10	63.58	even	3
441.2.s.b.362.5		10	21.20	even	2
441.2.s.b.374.5		10	63.4	even	3
567.2.p.c.80.1		10	63.52	odd	6
567.2.p.c.404.1		10	9.2	odd	6
567.2.p.d.80.5		10	63.38	even	6
567.2.p.d.404.5		10	9.7	even	3
1008.2.ca.b.257.5		10	36.31	odd	6
1008.2.ca.b.353.5		10	84.59	odd	6
1008.2.df.b.689.3		10	252.31	even	6
1008.2.df.b.929.3		10	12.11	even	2
1323.2.i.b.521.1		10	7.4	even	3
1323.2.i.b.1097.5		10	63.41	even	6
1323.2.o.c.440.5		10	7.5	odd	6
1323.2.o.c.881.5		10	63.23	odd	6
1323.2.o.d.440.5		10	7.2	even	3
1323.2.o.d.881.5		10	63.5	even	6
1323.2.s.b.656.1		10	7.6	odd	2
1323.2.s.b.962.1		10	63.32	odd	6
3024.2.ca.b.2033.5		10	28.3	even	6
3024.2.ca.b.2609.5		10	36.23	even	6
3024.2.df.b.17.5		10	252.59	odd	6
3024.2.df.b.1601.5		10	4.3	odd	2

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.81474 + 1.04774i) q^{2} +(1.19552 - 2.07070i) q^{4} +2.08983 q^{5} +(-0.879217 - 2.49539i) q^{7} +0.819421i q^{8} +(-3.79250 + 2.18960i) q^{10} -3.22878i q^{11} +(2.68740 - 1.55157i) q^{13} +(4.21007 + 3.60729i) q^{14} +(1.53250 + 2.65437i) q^{16} +(0.816304 + 1.41388i) q^{17} +(4.79094 + 2.76605i) q^{19} +(2.49844 - 4.32742i) q^{20} +(3.38292 + 5.85939i) q^{22} -1.16078i q^{23} -0.632608 q^{25} +(-3.25129 + 5.63139i) q^{26} +(-6.21834 - 1.16270i) q^{28} +(7.05749 + 4.07464i) q^{29} +(-5.16886 - 2.98424i) q^{31} +(-6.98146 - 4.03075i) q^{32} +(-2.96276 - 1.71055i) q^{34} +(-1.83741 - 5.21495i) q^{35} +(2.82656 - 4.89575i) q^{37} -11.5924 q^{38} +1.71245i q^{40} +(1.35369 + 2.34465i) q^{41} +(-0.974903 + 1.68858i) q^{43} +(-6.68583 - 3.86007i) q^{44} +(1.21620 + 2.10652i) q^{46} +(-4.06759 - 7.04527i) q^{47} +(-5.45395 + 4.38798i) q^{49} +(1.14802 - 0.662809i) q^{50} -7.41974i q^{52} +(-5.27766 + 3.04706i) q^{53} -6.74759i q^{55} +(2.04477 - 0.720448i) q^{56} -17.0767 q^{58} +(1.98103 - 3.43124i) q^{59} +(-4.15016 + 2.39609i) q^{61} +12.5068 q^{62} +10.7627 q^{64} +(5.61621 - 3.24252i) q^{65} +(0.336981 - 0.583668i) q^{67} +3.90363 q^{68} +(8.79834 + 7.53864i) q^{70} +7.01535i q^{71} +(-2.96276 + 1.71055i) q^{73} +11.8460i q^{74} +(11.4553 - 6.61374i) q^{76} +(-8.05706 + 2.83879i) q^{77} +(7.07973 + 12.2625i) q^{79} +(3.20267 + 5.54718i) q^{80} +(-4.91318 - 2.83662i) q^{82} +(-1.54535 + 2.67662i) q^{83} +(1.70594 + 2.95477i) q^{85} -4.08578i q^{86} +2.64572 q^{88} +(2.45766 - 4.25679i) q^{89} +(-6.23458 - 5.34194i) q^{91} +(-2.40363 - 1.38774i) q^{92} +(14.7632 + 8.52356i) q^{94} +(10.0122 + 5.78057i) q^{95} +(2.07939 + 1.20054i) q^{97} +(5.30004 - 13.6774i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} + 6 q^{13} + 6 q^{14} - 6 q^{16} + 12 q^{17} + 3 q^{19} + 3 q^{20} + 5 q^{22} - 14 q^{25} - 3 q^{26} + 2 q^{28} + 15 q^{29} - 9 q^{31} - 48 q^{32} + 3 q^{34} + 15 q^{35}+ \cdots - 45 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 + 6 * q^13 + 6 * q^14 - 6 * q^16 + 12 * q^17 + 3 * q^19 + 3 * q^20 + 5 * q^22 - 14 * q^25 - 3 * q^26 + 2 * q^28 + 15 * q^29 - 9 * q^31 - 48 * q^32 + 3 * q^34 + 15 * q^35 + 6 * q^37 - 36 * q^38 + 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 - 15 * q^47 - 23 * q^49 - 3 * q^50 + 9 * q^53 + 51 * q^56 - 16 * q^58 + 18 * q^59 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 54 * q^68 + 9 * q^70 + 3 * q^73 + 9 * q^76 - 45 * q^77 + 20 * q^79 + 30 * q^80 + 9 * q^82 + 15 * q^83 + 18 * q^85 + 16 * q^88 - 24 * q^89 - 24 * q^91 - 39 * q^92 - 3 * q^94 + 6 * q^97 - 45 * q^98

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