LMFDB - Embedded newform 216.2.t.a.157.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] 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("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			157.4
Character	$\chi$	$=$	216.157
Dual form			216.2.t.a.205.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35161 + 0.416109i) q^{2} +(-0.195652 - 1.72096i) q^{3} +(1.65371 - 1.12483i) q^{4} +(-1.34802 - 3.70366i) q^{5} +(0.980554 + 2.24466i) q^{6} +(0.00177522 + 0.0100678i) q^{7} +(-1.76712 + 2.20846i) q^{8} +(-2.92344 + 0.673422i) q^{9} +(3.36313 + 4.44499i) q^{10} +(-0.343808 + 0.944604i) q^{11} +(-2.25935 - 2.62590i) q^{12} +(-2.57400 + 3.06757i) q^{13} +(-0.00658870 - 0.0128690i) q^{14} +(-6.11013 + 3.04453i) q^{15} +(1.46950 - 3.72029i) q^{16} +(-0.948987 + 1.64369i) q^{17} +(3.67114 - 2.12667i) q^{18} +(3.76245 - 2.17225i) q^{19} +(-6.39524 - 4.60847i) q^{20} +(0.0169790 - 0.00502488i) q^{21} +(0.0716366 - 1.41980i) q^{22} +(1.19728 - 6.79010i) q^{23} +(4.14642 + 2.60905i) q^{24} +(-8.06972 + 6.77130i) q^{25} +(2.20260 - 5.21723i) q^{26} +(1.73091 + 4.89938i) q^{27} +(0.0142603 + 0.0146523i) q^{28} +(-3.82827 - 4.56236i) q^{29} +(6.99166 - 6.65750i) q^{30} +(1.38501 - 7.85480i) q^{31} +(-0.438140 + 5.63986i) q^{32} +(1.69290 + 0.406867i) q^{33} +(0.598707 - 2.61652i) q^{34} +(0.0348946 - 0.0201464i) q^{35} +(-4.07703 + 4.40203i) q^{36} +(-6.65823 - 3.84413i) q^{37} +(-4.18148 + 4.50163i) q^{38} +(5.78279 + 3.82958i) q^{39} +(10.5615 + 3.56775i) q^{40} +(4.44753 + 3.73192i) q^{41} +(-0.0208581 + 0.0138568i) q^{42} +(1.42511 - 3.91546i) q^{43} +(0.493966 + 1.94882i) q^{44} +(6.43499 + 9.91964i) q^{45} +(1.20716 + 9.67577i) q^{46} +(1.37530 + 7.79973i) q^{47} +(-6.69000 - 1.80107i) q^{48} +(6.57775 - 2.39411i) q^{49} +(8.08953 - 12.5100i) q^{50} +(3.01441 + 1.31158i) q^{51} +(-0.806130 + 7.96819i) q^{52} -2.25567i q^{53} +(-4.37820 - 5.90181i) q^{54} +3.96195 q^{55} +(-0.0253713 - 0.0138704i) q^{56} +(-4.47450 - 6.05004i) q^{57} +(7.07277 + 4.57356i) q^{58} +(-2.24610 - 6.17111i) q^{59} +(-6.67977 + 11.9076i) q^{60} +(0.106836 - 0.0188381i) q^{61} +(1.39645 + 11.1930i) q^{62} +(-0.0119696 - 0.0282371i) q^{63} +(-1.75460 - 7.80522i) q^{64} +(14.8311 + 5.39806i) q^{65} +(-2.45744 + 0.154503i) q^{66} +(-2.47342 + 2.94771i) q^{67} +(0.279537 + 3.78564i) q^{68} +(-11.9198 - 0.731973i) q^{69} +(-0.0387808 + 0.0417500i) q^{70} +(0.442665 - 0.766718i) q^{71} +(3.67883 - 7.64632i) q^{72} +(-7.26116 - 12.5767i) q^{73} +(10.5989 + 2.42523i) q^{74} +(13.2320 + 12.5629i) q^{75} +(3.77857 - 7.82441i) q^{76} +(-0.0101204 - 0.00178450i) q^{77} +(-9.40961 - 2.76984i) q^{78} +(2.46319 - 2.06686i) q^{79} +(-15.7596 - 0.427473i) q^{80} +(8.09301 - 3.93742i) q^{81} +(-7.56422 - 3.19345i) q^{82} +(9.76904 + 11.6423i) q^{83} +(0.0224261 - 0.0274082i) q^{84} +(7.36694 + 1.29899i) q^{85} +(-0.296940 + 5.88518i) q^{86} +(-7.10265 + 7.48096i) q^{87} +(-1.47857 - 2.42851i) q^{88} +(-1.45362 - 2.51775i) q^{89} +(-12.8253 - 10.7298i) q^{90} +(-0.0354530 - 0.0204688i) q^{91} +(-5.65779 - 12.5756i) q^{92} +(-13.7888 - 0.846748i) q^{93} +(-5.10441 - 9.96993i) q^{94} +(-13.1172 - 11.0066i) q^{95} +(9.79173 - 0.349428i) q^{96} +(-12.0217 - 4.37554i) q^{97} +(-7.89435 + 5.97296i) q^{98} +(0.368984 - 2.99302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.35161	+	0.416109i	−0.955734	+	0.294233i
$2$	−1.35161	+	0.416109i	−0.955734	+	0.294233i
$3$	−0.195652	−	1.72096i	−0.112960	−	0.993600i
$3$	−0.195652	−	1.72096i	−0.112960	−	0.993600i
$4$	1.65371	−	1.12483i	0.826854	−	0.562417i
$5$	−1.34802	−	3.70366i	−0.602854	−	1.65633i	−0.745462	−	0.666548i	$-0.767771\pi$
$5$	−1.34802	−	3.70366i	−0.602854	−	1.65633i	0.142608	−	0.989779i	$-0.454451\pi$
$6$	0.980554	+	2.24466i	0.400310	+	0.916380i
$7$	0.00177522	+	0.0100678i	0.000670970	+	0.00380526i	0.985141	−	0.171745i	$-0.0549406\pi$
$7$	0.00177522	+	0.0100678i	0.000670970	+	0.00380526i	−0.984470	+	0.175550i	$0.943829\pi$
$8$	−1.76712	+	2.20846i	−0.624770	+	0.780809i
$9$	−2.92344	+	0.673422i	−0.974480	+	0.224474i
$10$	3.36313	+	4.44499i	1.06351	+	1.40563i
$11$	−0.343808	+	0.944604i	−0.103662	+	0.284809i	−0.980671	−	0.195666i	$-0.937313\pi$
$11$	−0.343808	+	0.944604i	−0.103662	+	0.284809i	0.877009	+	0.480474i	$0.159535\pi$
$12$	−2.25935	−	2.62590i	−0.652219	−	0.758031i
$13$	−2.57400	+	3.06757i	−0.713899	+	0.850792i	−0.994023	−	0.109172i	$-0.965180\pi$
$13$	−2.57400	+	3.06757i	−0.713899	+	0.850792i	0.280124	+	0.959964i	$0.409624\pi$
$14$	−0.00658870	−	0.0128690i	−0.00176090	−	0.00343939i
$15$	−6.11013	+	3.04453i	−1.57763	+	0.786094i
$16$	1.46950	−	3.72029i	0.367374	−	0.930073i
$17$	−0.948987	+	1.64369i	−0.230163	+	0.398654i	−0.957856	−	0.287249i	$-0.907259\pi$
$17$	−0.948987	+	1.64369i	−0.230163	+	0.398654i	0.727693	+	0.685903i	$0.240593\pi$
$18$	3.67114	−	2.12667i	0.865296	−	0.501262i
$19$	3.76245	−	2.17225i	0.863166	−	0.498349i	−0.00190536	−	0.999998i	$-0.500606\pi$
$19$	3.76245	−	2.17225i	0.863166	−	0.498349i	0.865071	+	0.501649i	$0.167273\pi$
$20$	−6.39524	−	4.60847i	−1.43002	−	1.03049i
$21$	0.0169790	−	0.00502488i	0.00370511	−	0.00109652i
$22$	0.0716366	−	1.41980i	0.0152730	−	0.302702i
$23$	1.19728	−	6.79010i	0.249650	−	1.41583i	−0.559792	−	0.828633i	$-0.689119\pi$
$23$	1.19728	−	6.79010i	0.249650	−	1.41583i	0.809442	−	0.587200i	$-0.199770\pi$
$24$	4.14642	+	2.60905i	0.846385	+	0.532571i
$25$	−8.06972	+	6.77130i	−1.61394	+	1.35426i
$26$	2.20260	−	5.21723i	0.431966	−	1.02318i
$27$	1.73091	+	4.89938i	0.333115	+	0.942886i
$28$	0.0142603	+	0.0146523i	0.00269494	+	0.00276903i
$29$	−3.82827	−	4.56236i	−0.710892	−	0.847208i	0.282820	−	0.959173i	$-0.408730\pi$
$29$	−3.82827	−	4.56236i	−0.710892	−	0.847208i	−0.993712	+	0.111965i	$0.964286\pi$
$30$	6.99166	−	6.65750i	1.27650	−	1.21549i
$31$	1.38501	−	7.85480i	0.248756	−	1.41076i	−0.562850	−	0.826559i	$-0.690295\pi$
$31$	1.38501	−	7.85480i	0.248756	−	1.41076i	0.811606	−	0.584205i	$-0.198594\pi$
$32$	−0.438140	+	5.63986i	−0.0774530	+	0.996996i
$33$	1.69290	+	0.406867i	0.294696	+	0.0708264i
$34$	0.598707	−	2.61652i	0.102677	−	0.448729i
$35$	0.0348946	−	0.0201464i	0.00589826	−	0.00340536i
$36$	−4.07703	+	4.40203i	−0.679504	+	0.733672i
$37$	−6.65823	−	3.84413i	−1.09461	−	0.631971i	−0.159807	−	0.987148i	$-0.551087\pi$
$37$	−6.65823	−	3.84413i	−1.09461	−	0.631971i	−0.934799	+	0.355177i	$0.884421\pi$
$38$	−4.18148	+	4.50163i	−0.678326	+	0.730261i
$39$	5.78279	+	3.82958i	0.925988	+	0.613224i
$40$	10.5615	+	3.56775i	1.66992	+	0.564110i
$41$	4.44753	+	3.73192i	0.694588	+	0.582828i	0.920228	−	0.391382i	$-0.128003\pi$
$41$	4.44753	+	3.73192i	0.694588	+	0.582828i	−0.225641	+	0.974211i	$0.572447\pi$
$42$	−0.0208581	+	0.0138568i	−0.00321847	+	0.00213815i
$43$	1.42511	−	3.91546i	0.217327	−	0.597102i	−0.782341	−	0.622850i	$-0.785975\pi$
$43$	1.42511	−	3.91546i	0.217327	−	0.597102i	0.999668	+	0.0257481i	$0.00819679\pi$
$44$	0.493966	+	1.94882i	0.0744681	+	0.293796i
$45$	6.43499	+	9.91964i	0.959272	+	1.47873i
$46$	1.20716	+	9.67577i	0.177987	+	1.42661i
$47$	1.37530	+	7.79973i	0.200608	+	1.13771i	0.904202	+	0.427105i	$0.140466\pi$
$47$	1.37530	+	7.79973i	0.200608	+	1.13771i	−0.703594	+	0.710602i	$0.748422\pi$
$48$	−6.69000	−	1.80107i	−0.965619	−	0.259961i
$49$	6.57775	−	2.39411i	0.939679	−	0.342015i
$50$	8.08953	−	12.5100i	1.14403	−	1.76919i
$51$	3.01441	+	1.31158i	0.422102	+	0.183658i
$52$	−0.806130	+	7.96819i	−0.111790	+	1.10499i
$53$		−	2.25567i		−	0.309840i	−0.987927	−	0.154920i	$-0.950488\pi$
$53$		−	2.25567i		−	0.309840i	0.987927	−	0.154920i	$-0.0495120\pi$
$54$	−4.37820	−	5.90181i	−0.595797	−	0.803135i
$55$	3.96195			0.534230
$56$	−0.0253713	−	0.0138704i	−0.00339038	−	0.00185351i
$57$	−4.47450	−	6.05004i	−0.592663	−	0.801348i
$58$	7.07277	+	4.57356i	0.928701	+	0.600537i
$59$	−2.24610	−	6.17111i	−0.292417	−	0.803410i	−0.995712	−	0.0925111i	$-0.970511\pi$
$59$	−2.24610	−	6.17111i	−0.292417	−	0.803410i	0.703294	−	0.710899i	$-0.251712\pi$
$60$	−6.67977	+	11.9076i	−0.862354	+	1.53727i
$61$	0.106836	−	0.0188381i	0.0136789	−	0.00241197i	−0.166805	−	0.985990i	$-0.553345\pi$
$61$	0.106836	−	0.0188381i	0.0136789	−	0.00241197i	0.180483	+	0.983578i	$0.442234\pi$
$62$	1.39645	+	11.1930i	0.177349	+	1.42151i
$63$	−0.0119696	−	0.0282371i	−0.00150803	−	0.00355754i
$64$	−1.75460	−	7.80522i	−0.219325	−	0.975652i
$65$	14.8311	+	5.39806i	1.83957	+	0.669547i
$66$	−2.45744	+	0.154503i	−0.302490	+	0.0190180i
$67$	−2.47342	+	2.94771i	−0.302177	+	0.360120i	−0.895670	−	0.444718i	$-0.853304\pi$
$67$	−2.47342	+	2.94771i	−0.302177	+	0.360120i	0.593494	+	0.804839i	$0.297748\pi$
$68$	0.279537	+	3.78564i	0.0338988	+	0.459076i
$69$	−11.9198	−	0.731973i	−1.43497	−	0.0881192i
$70$	−0.0387808	+	0.0417500i	−0.00463520	+	0.00499009i
$71$	0.442665	−	0.766718i	0.0525346	−	0.0909926i	−0.838562	−	0.544806i	$-0.816603\pi$
$71$	0.442665	−	0.766718i	0.0525346	−	0.0909926i	0.891097	+	0.453813i	$0.149937\pi$
$72$	3.67883	−	7.64632i	0.433555	−	0.901127i
$73$	−7.26116	−	12.5767i	−0.849854	−	1.47199i	−0.881338	−	0.472486i	$-0.843357\pi$
$73$	−7.26116	−	12.5767i	−0.849854	−	1.47199i	0.0314838	−	0.999504i	$-0.489977\pi$
$74$	10.5989	+	2.42523i	1.23210	+	0.281927i
$75$	13.2320	+	12.5629i	1.52790	+	1.45064i
$76$	3.77857	−	7.82441i	0.433432	−	0.897521i
$77$	−0.0101204	−	0.00178450i	−0.00115333	−	0.000203362i
$78$	−9.40961	−	2.76984i	−1.06543	−	0.313623i
$79$	2.46319	−	2.06686i	0.277131	−	0.232540i	−0.493619	−	0.869678i	$-0.664326\pi$
$79$	2.46319	−	2.06686i	0.277131	−	0.232540i	0.770750	+	0.637138i	$0.219882\pi$
$80$	−15.7596	−	0.427473i	−1.76198	−	0.0477930i
$81$	8.09301	−	3.93742i	0.899223	−	0.437491i
$82$	−7.56422	−	3.19345i	−0.835328	−	0.352658i
$83$	9.76904	+	11.6423i	1.07229	+	1.27791i	0.958712	+	0.284378i	$0.0917872\pi$
$83$	9.76904	+	11.6423i	1.07229	+	1.27791i	0.113579	+	0.993529i	$0.463768\pi$
$84$	0.0224261	−	0.0274082i	0.00244689	−	0.00299048i
$85$	7.36694	+	1.29899i	0.799057	+	0.140895i
$86$	−0.296940	+	5.88518i	−0.0320198	+	0.634616i
$87$	−7.10265	+	7.48096i	−0.761483	+	0.802043i
$88$	−1.47857	−	2.42851i	−0.157616	−	0.258880i
$89$	−1.45362	−	2.51775i	−0.154084	−	0.266881i	0.778641	−	0.627469i	$-0.215909\pi$
$89$	−1.45362	−	2.51775i	−0.154084	−	0.266881i	−0.932725	+	0.360588i	$0.882576\pi$
$90$	−12.8253	−	10.7298i	−1.35190	−	1.13103i
$91$	−0.0354530	−	0.0204688i	−0.00371649	−	0.00214572i
$92$	−5.65779	−	12.5756i	−0.589865	−	1.31109i
$93$	−13.7888	−	0.846748i	−1.42983	−	0.0878037i
$94$	−5.10441	−	9.96993i	−0.526480	−	1.02832i
$95$	−13.1172	−	11.0066i	−1.34579	−	1.12925i
$96$	9.79173	−	0.349428i	0.999364	−	0.0356634i
$97$	−12.0217	−	4.37554i	−1.22062	−	0.444269i	−0.350244	−	0.936658i	$-0.613901\pi$
$97$	−12.0217	−	4.37554i	−1.22062	−	0.444269i	−0.870375	+	0.492389i	$0.836124\pi$
$98$	−7.89435	+	5.97296i	−0.797450	+	0.603360i
$99$	0.368984	−	2.99302i	0.0370843	−	0.300810i
$100$	−5.72836	+	20.2748i	−0.572836	+	2.02748i
$101$	8.25225	−	1.45509i	0.821129	−	0.144787i	0.252727	−	0.967538i	$-0.418673\pi$
$101$	8.25225	−	1.45509i	0.821129	−	0.144787i	0.568403	+	0.822751i	$0.307562\pi$
$102$	−4.62007	−	0.518425i	−0.457455	−	0.0513317i
$103$	6.53199	−	2.37745i	0.643617	−	0.234257i	0.000469418	−	1.00000i	$-0.499851\pi$
$103$	6.53199	−	2.37745i	0.643617	−	0.234257i	0.643147	+	0.765743i	$0.277628\pi$
$104$	−2.22606	−	11.1053i	−0.218283	−	1.08897i
$105$	−0.0414985	−	0.0561107i	−0.00404984	−	0.00547584i
$106$	0.938605	+	3.04879i	0.0911653	+	0.296125i
$107$		−	14.2756i		−	1.38007i	−0.723776	−	0.690035i	$-0.757595\pi$
$107$		−	14.2756i		−	1.38007i	0.723776	−	0.690035i	$-0.242405\pi$
$108$	8.37342	+	6.15515i	0.805732	+	0.592280i
$109$			4.88426i			0.467827i	0.972257	+	0.233914i	$0.0751533\pi$
$109$			4.88426i			0.467827i	−0.972257	+	0.233914i	$0.924847\pi$
$110$	−5.35502	+	1.64860i	−0.510581	+	0.157188i
$111$	−5.31292	+	12.2107i	−0.504280	+	1.15899i
$112$	0.0400638	+	0.00819021i	0.00378567	+	0.000773902i
$113$	4.20463	−	1.53036i	0.395538	−	0.143964i	−0.136591	−	0.990628i	$-0.543614\pi$
$113$	4.20463	−	1.53036i	0.395538	−	0.143964i	0.532129	+	0.846663i	$0.321392\pi$
$114$	8.56527	+	6.31543i	0.802211	+	0.591494i
$115$	−26.7622	+	4.71889i	−2.49559	+	0.440039i
$116$	−11.4627	−	3.23863i	−1.06429	−	0.300699i
$117$	5.45916	−	10.7013i	0.504700	−	0.989331i
$118$	5.60371	+	7.40632i	0.515863	+	0.681807i
$119$	−0.0182330	−	0.00663627i	−0.00167142	−	0.000608346i
$120$	4.07358	−	18.8740i	0.371865	−	1.72295i
$121$	7.65242	+	6.42114i	0.695674	+	0.583740i
$122$	−0.136562	+	0.0699171i	−0.0123638	+	0.00633000i
$123$	5.55233	−	8.38420i	0.500637	−	0.755978i
$124$	−6.54495	−	14.5475i	−0.587754	−	1.30640i
$125$	18.8902	+	10.9063i	1.68959	+	0.975485i
$126$	0.0279280	+	0.0331849i	0.00248802	+	0.00295634i
$127$	−0.733337	−	1.27018i	−0.0650731	−	0.112710i	0.831653	−	0.555295i	$-0.187395\pi$
$127$	−0.733337	−	1.27018i	−0.0650731	−	0.112710i	−0.896726	+	0.442585i	$0.854061\pi$
$128$	5.61935	+	9.81951i	0.496685	+	0.867931i
$129$	−7.01720	−	1.68650i	−0.617830	−	0.148488i
$130$	−22.2920	−	1.12475i	−1.95514	−	0.0986474i
$131$	11.2373	+	1.98143i	0.981805	+	0.173119i	0.641439	−	0.767174i	$-0.278338\pi$
$131$	11.2373	+	1.98143i	0.981805	+	0.173119i	0.340366	+	0.940293i	$0.389449\pi$
$132$	3.25721	−	1.23139i	0.283504	−	0.107179i
$133$	0.0285489	+	0.0340233i	0.00247551	+	0.00295019i
$134$	2.11654	−	5.01337i	0.182841	−	0.433089i
$135$	15.8123	−	13.0152i	1.36091	−	1.12017i
$136$	−1.95306	−	5.00040i	−0.167474	−	0.428781i
$137$	3.27137	−	2.74501i	0.279492	−	0.234522i	−0.492255	−	0.870451i	$-0.663827\pi$
$137$	3.27137	−	2.74501i	0.279492	−	0.234522i	0.771748	+	0.635929i	$0.219383\pi$
$138$	16.4155	−	3.97058i	1.39738	−	0.337998i
$139$	−1.04893	−	0.184955i	−0.0889693	−	0.0156877i	0.128986	−	0.991646i	$-0.458828\pi$
$139$	−1.04893	−	0.184955i	−0.0889693	−	0.0156877i	−0.217956	+	0.975959i	$0.569939\pi$
$140$	0.0350441	−	0.0725669i	0.00296176	−	0.00613302i
$141$	13.1540	−	3.89288i	1.10776	−	0.327840i
$142$	−0.279273	+	1.22050i	−0.0234360	+	0.102422i
$143$	−2.01268	−	3.48606i	−0.168309	−	0.291519i
$144$	−1.79065	+	11.8656i	−0.149221	+	0.988804i
$145$	−11.7368	+	20.3288i	−0.974690	+	1.68821i
$146$	15.0475	+	13.9774i	1.24534	+	1.15678i
$147$	−5.40712	−	10.8517i	−0.445972	−	0.895030i
$148$	−15.3348	+	1.13234i	−1.26051	+	0.0930777i
$149$	−1.34236	+	1.59976i	−0.109970	+	0.131058i	−0.818222	−	0.574903i	$-0.805040\pi$
$149$	−1.34236	+	1.59976i	−0.109970	+	0.131058i	0.708251	+	0.705960i	$0.249484\pi$
$150$	−23.1121	−	11.4742i	−1.88709	−	0.936862i
$151$	9.89970	+	3.60320i	0.805626	+	0.293224i	0.711816	−	0.702366i	$-0.247873\pi$
$151$	9.89970	+	3.60320i	0.805626	+	0.293224i	0.0938105	+	0.995590i	$0.470095\pi$
$152$	−1.85136	+	12.1479i	−0.150165	+	0.985321i
$153$	1.66741	−	5.44431i	0.134802	−	0.440146i
$154$	0.0144214	−	0.00179923i	0.00116211	−	0.000144986i
$155$	−30.9586	+	5.45883i	−2.48665	+	0.438464i
$156$	13.8707	−	0.171675i	1.11054	−	0.0137450i
$157$	7.61747	+	20.9288i	0.607940	+	1.67030i	0.734720	+	0.678371i	$0.237314\pi$
$157$	7.61747	+	20.9288i	0.607940	+	1.67030i	−0.126779	+	0.991931i	$0.540464\pi$
$158$	−2.46924	+	3.81855i	−0.196442	+	0.303788i
$159$	−3.88193	+	0.441328i	−0.307857	+	0.0349996i
$160$	21.4788	−	5.97993i	1.69804	−	0.472755i
$161$	0.0704866			0.00555512
$162$	−9.30021	+	8.68943i	−0.730693	+	0.682706i
$163$			8.64571i			0.677184i	0.940933	+	0.338592i	$0.109951\pi$
$163$			8.64571i			0.677184i	−0.940933	+	0.338592i	$0.890049\pi$
$164$	11.5527	+	1.16877i	0.902115	+	0.0912656i
$165$	−0.775166	−	6.81838i	−0.0603466	−	0.530810i
$166$	−18.0484	−	11.6709i	−1.40083	−	0.905835i
$167$	−7.93163	+	2.88688i	−0.613768	+	0.223393i	−0.630151	−	0.776473i	$-0.717007\pi$
$167$	−7.93163	+	2.88688i	−0.613768	+	0.223393i	0.0163833	+	0.999866i	$0.494785\pi$
$168$	−0.0189066	+	0.0463769i	−0.00145867	+	0.00357806i
$169$	−0.527105	−	2.98936i	−0.0405465	−	0.229951i
$170$	−10.4978	+	1.30972i	−0.805142	+	0.100451i
$171$	−9.53646	+	8.88417i	−0.729271	+	0.679389i
$172$	−2.04753	−	8.07804i	−0.156123	−	0.615945i
$173$	−4.65008	+	12.7760i	−0.353539	+	0.971340i	0.627685	+	0.778467i	$0.284003\pi$
$173$	−4.65008	+	12.7760i	−0.353539	+	0.971340i	−0.981224	+	0.192872i	$0.938220\pi$
$174$	6.48713	−	13.0668i	0.491788	−	0.990593i
$175$	−0.0824974	−	0.0692236i	−0.00623622	−	0.00523281i
$176$	3.00898	+	2.66716i	0.226810	+	0.201044i
$177$	−10.1808	+	5.07285i	−0.765236	+	0.381299i
$178$	3.01239	+	2.79815i	0.225788	+	0.209731i
$179$	0.257187	+	0.148487i	0.0192231	+	0.0110985i	0.509581	−	0.860423i	$-0.329801\pi$
$179$	0.257187	+	0.148487i	0.0192231	+	0.0110985i	−0.490358	+	0.871521i	$0.663134\pi$
$180$	21.7995	+	9.16589i	1.62484	+	0.683185i
$181$	1.63626	−	0.944694i	0.121622	−	0.0702186i	−0.437955	−	0.898997i	$-0.644297\pi$
$181$	1.63626	−	0.944694i	0.121622	−	0.0702186i	0.559577	+	0.828778i	$0.310964\pi$
$182$	0.0564360	+	0.0129136i	0.00418332	+	0.000957218i
$183$	−0.0533224	−	0.180175i	−0.00394170	−	0.0133189i
$184$	12.8799	+	14.6430i	0.949521	+	1.07950i
$185$	−5.26192	+	29.8418i	−0.386864	+	2.19401i
$186$	18.9895	−	4.59317i	1.39238	−	0.336788i
$187$	−1.22637	−	1.46153i	−0.0896811	−	0.106878i
$188$	11.0477	+	11.3515i	0.805740	+	0.827892i
$189$	−0.0462531	+	0.0261239i	−0.00336442	+	0.00190024i
$190$	22.3092	+	9.41849i	1.61848	+	0.683289i
$191$	10.6897	−	8.96976i	0.773483	−	0.649029i	−0.168116	−	0.985767i	$-0.553768\pi$
$191$	10.6897	−	8.96976i	0.773483	−	0.649029i	0.941598	+	0.336738i	$0.109324\pi$
$192$	−13.0892	+	4.54671i	−0.944632	+	0.328131i
$193$	1.65530	−	9.38768i	0.119151	−	0.675740i	−0.865460	−	0.500979i	$-0.832974\pi$
$193$	1.65530	−	9.38768i	0.119151	−	0.675740i	0.984611	−	0.174761i	$-0.0559153\pi$
$194$	18.0694	+	0.911699i	1.29731	+	0.0654562i
$195$	6.38814	−	26.5799i	0.457465	−	1.90342i
$196$	8.18470	−	11.3580i	0.584622	−	0.811288i
$197$	7.61046	−	4.39390i	0.542223	−	0.313052i	−0.203757	−	0.979022i	$-0.565315\pi$
$197$	7.61046	−	4.39390i	0.542223	−	0.313052i	0.745979	+	0.665969i	$0.231982\pi$
$198$	0.746699	+	4.19894i	0.0530656	+	0.298406i
$199$	4.70991	−	8.15780i	0.333876	−	0.578291i	−0.649392	−	0.760454i	$-0.724977\pi$
$199$	4.70991	−	8.15780i	0.333876	−	0.578291i	0.983268	+	0.182163i	$0.0583098\pi$
$200$	−0.694014	−	29.7873i	−0.0490742	−	2.10628i
$201$	5.55684	+	3.67995i	0.391949	+	0.259563i
$202$	−10.5484	+	5.40055i	−0.742180	+	0.379982i
$203$	0.0391368	−	0.0466414i	0.00274686	−	0.00327358i
$204$	6.46026	−	1.22174i	0.452309	−	0.0855391i
$205$	7.82640	−	21.5029i	0.546619	−	1.50182i
$206$	−7.83944	+	5.93141i	−0.546200	+	0.413261i
$207$	1.07243	+	20.6567i	0.0745393	+	1.43574i
$208$	7.62979	+	14.0838i	0.529031	+	0.976537i
$209$	0.758358	+	4.30086i	0.0524567	+	0.297497i
$210$	0.0794379	+	0.0585720i	0.00548174	+	0.00404185i
$211$	−4.12560	−	11.3350i	−0.284018	−	0.780333i	−0.996873	−	0.0790214i	$-0.974820\pi$
$211$	−4.12560	−	11.3350i	−0.284018	−	0.780333i	0.712855	−	0.701311i	$-0.247402\pi$
$212$	−2.53726	−	3.73022i	−0.174260	−	0.256193i
$213$	−1.40610	−	0.611800i	−0.0963445	−	0.0419198i
$214$	5.94018	+	19.2950i	0.406062	+	1.31898i
$215$	−16.4226			−1.12001
$216$	−13.8788	−	4.83512i	−0.944334	−	0.328988i
$217$	0.0815391			0.00553524
$218$	−2.03238	−	6.60162i	−0.137650	−	0.447118i
$219$	−20.2234	+	14.9569i	−1.36657	+	1.01069i
$220$	6.55191	−	4.45654i	0.441730	−	0.300460i
$221$	−2.59946	−	7.14195i	−0.174858	−	0.480420i
$222$	2.10002	−	18.7149i	0.140944	−	1.25606i
$223$	0.616341	+	3.49544i	0.0412732	+	0.234072i	0.998465	−	0.0553815i	$-0.0176375\pi$
$223$	0.616341	+	3.49544i	0.0412732	+	0.234072i	−0.957192	+	0.289454i	$0.906526\pi$
$224$	−0.0575587	+	0.00560090i	−0.00384580	+	0.000374226i
$225$	19.0314	−	25.2298i	1.26876	−	1.68199i
$226$	−5.04623	+	3.81803i	−0.335670	+	0.253972i
$227$	−3.72066	+	10.2224i	−0.246949	+	0.678486i	0.752846	+	0.658197i	$0.228681\pi$
$227$	−3.72066	+	10.2224i	−0.246949	+	0.678486i	−0.999794	+	0.0202886i	$0.993542\pi$
$228$	−14.2048	−	4.97192i	−0.940737	−	0.329274i
$229$	−5.05083	+	6.01935i	−0.333769	+	0.397770i	−0.906661	−	0.421861i	$-0.861377\pi$
$229$	−5.05083	+	6.01935i	−0.333769	+	0.397770i	0.572892	+	0.819631i	$0.305821\pi$
$230$	34.2085	−	17.5141i	2.25564	−	1.15484i
$231$	−0.00109098	+	0.0177660i	−7.17811e−5	+	0.00116892i
$232$	16.8408	−	0.392373i	1.10565	−	0.0257606i
$233$	12.0985	−	20.9553i	0.792602	−	1.37283i	−0.131749	−	0.991283i	$-0.542059\pi$
$233$	12.0985	−	20.9553i	0.792602	−	1.37283i	0.924351	−	0.381544i	$-0.124608\pi$
$234$	−2.92578	+	16.7355i	−0.191264	+	1.09404i
$235$	27.0336	−	15.6079i	1.76348	−	1.01814i
$236$	−10.6559	−	7.67872i	−0.693638	−	0.499842i
$237$	−4.03893	−	3.83468i	−0.262357	−	0.249089i
$238$	0.0274053	+	0.00138275i	0.00177642	+	8.96303e-5i
$239$	−5.23764	+	29.7041i	−0.338795	+	1.92140i	0.0471684	+	0.998887i	$0.484980\pi$
$239$	−5.23764	+	29.7041i	−0.338795	+	1.92140i	−0.385963	+	0.922514i	$0.626131\pi$
$240$	2.34774	+	27.2054i	0.151546	+	1.75610i
$241$	−1.91756	+	1.60903i	−0.123521	+	0.103647i	−0.702456	−	0.711727i	$-0.747913\pi$
$241$	−1.91756	+	1.60903i	−0.123521	+	0.103647i	0.578935	+	0.815374i	$0.303469\pi$
$242$	−13.0150	−	5.49465i	−0.836635	−	0.353209i
$243$	−8.35958	−	13.1574i	−0.536267	−	0.844048i
$244$	0.155486	−	0.151325i	0.00995396	−	0.00968762i
$245$	−17.7339	−	21.1344i	−1.13298	−	1.35023i
$246$	−4.01586	+	13.6426i	−0.256042	+	0.869818i
$247$	−3.02101	+	17.1330i	−0.192222	+	1.09015i
$248$	14.8995	+	16.9391i	0.946122	+	1.07563i
$249$	18.1246	−	19.0900i	1.14860	−	1.20978i
$250$	−30.0704	−	6.88065i	−1.90182	−	0.435170i
$251$	−14.5027	+	8.37314i	−0.915402	+	0.528508i	−0.882165	−	0.470940i	$-0.843915\pi$
$251$	−14.5027	+	8.37314i	−0.915402	+	0.528508i	−0.0332368	+	0.999448i	$0.510582\pi$
$252$	−0.0515563	−	0.0332320i	−0.00324774	−	0.00209342i
$253$	6.00232	+	3.46544i	0.377363	+	0.217870i
$254$	1.51972	+	1.41164i	0.0953556	+	0.0885741i
$255$	0.794157	−	12.9324i	0.0497320	−	0.809858i
$256$	−11.6812	−	10.9339i	−0.730073	−	0.683369i
$257$	−20.4870	−	17.1907i	−1.27795	−	1.07232i	−0.993524	−	0.113626i	$-0.963753\pi$
$257$	−20.4870	−	17.1907i	−1.27795	−	1.07232i	−0.284423	−	0.958699i	$-0.591802\pi$
$258$	10.1863	−	0.640428i	0.634171	−	0.0398713i
$259$	0.0268820	−	0.0738578i	0.00167037	−	0.00458930i
$260$	30.5982	−	7.75567i	1.89762	−	0.480986i
$261$	14.2641	+	10.7597i	0.882927	+	0.666011i
$262$	−16.0129	+	1.99780i	−0.989281	+	0.123424i
$263$	−0.762315	−	4.32330i	−0.0470064	−	0.266586i	0.952242	−	0.305343i	$-0.0987713\pi$
$263$	−0.762315	−	4.32330i	−0.0470064	−	0.266586i	−0.999249	+	0.0387571i	$0.987660\pi$
$264$	−3.89010	+	3.01972i	−0.239419	+	0.185851i
$265$	−8.35424	+	3.04070i	−0.513197	+	0.186788i
$266$	−0.0527445	−	0.0341068i	−0.00323397	−	0.00209122i
$267$	−4.04855	+	2.99424i	−0.247767	+	0.183244i
$268$	−0.774631	+	7.65684i	−0.0473181	+	0.467716i
$269$			0.741050i			0.0451826i	0.999745	+	0.0225913i	$0.00719165\pi$
$269$			0.741050i			0.0451826i	−0.999745	+	0.0225913i	$0.992808\pi$
$270$	−15.9564	+	24.1711i	−0.971076	+	1.47101i
$271$	−14.1450			−0.859245			−0.429622	−	0.903009i	$-0.641353\pi$
$271$	−14.1450			−0.859245			−0.429622	+	0.903009i	$0.641353\pi$
$272$	4.72049	+	5.94591i	0.286222	+	0.360524i
$273$	−0.0282897	+	0.0650182i	−0.00171217	+	0.00393508i
$274$	−3.27940	+	5.07143i	−0.198116	+	0.306376i
$275$	−3.62176	−	9.95071i	−0.218400	−	0.600050i
$276$	−20.5352	+	12.1973i	−1.23607	+	0.734191i
$277$	−8.42697	+	1.48590i	−0.506327	+	0.0892792i	−0.420976	−	0.907072i	$-0.638312\pi$
$277$	−8.42697	+	1.48590i	−0.506327	+	0.0892792i	−0.0853514	+	0.996351i	$0.527201\pi$
$278$	1.49471	−	0.186482i	0.0896468	−	0.0111845i
$279$	1.24059	+	23.8958i	0.0742724	+	1.43060i
$280$	−0.0171703	+	0.112664i	−0.00102612	+	0.00673298i
$281$	−17.6483	−	6.42344i	−1.05281	−	0.383191i	−0.243086	−	0.970005i	$-0.578160\pi$
$281$	−17.6483	−	6.42344i	−1.05281	−	0.383191i	−0.809722	+	0.586814i	$0.800382\pi$
$282$	−16.1592	+	10.7351i	−0.962266	+	0.639269i
$283$	16.5234	−	19.6918i	0.982214	−	1.17056i	−0.00313343	−	0.999995i	$-0.500997\pi$
$283$	16.5234	−	19.6918i	0.982214	−	1.17056i	0.985347	−	0.170562i	$-0.0545582\pi$
$284$	−0.130393	−	1.76585i	−0.00773738	−	0.104784i
$285$	−16.3756	+	24.7276i	−0.970005	+	1.46474i
$286$	4.17094	+	3.87431i	0.246633	+	0.229093i
$287$	−0.0296768	+	0.0514017i	−0.00175177	+	0.00303415i
$288$	−2.51713	−	16.7829i	−0.148323	−	0.988939i
$289$	6.69885	+	11.6027i	0.394050	+	0.682514i
$290$	7.40465	−	32.3604i	0.434816	−	1.90027i
$291$	−5.17808	+	21.5450i	−0.303544	+	1.26299i
$292$	−26.1545	−	12.6306i	−1.53058	−	0.739148i
$293$	−14.3663	−	2.53317i	−0.839288	−	0.147989i	−0.262550	−	0.964918i	$-0.584564\pi$
$293$	−14.3663	−	2.53317i	−0.839288	−	0.147989i	−0.576738	+	0.816929i	$0.695675\pi$
$294$	11.8238	+	12.4173i	0.689578	+	0.724191i
$295$	−19.8279	+	16.6376i	−1.15442	+	0.968678i
$296$	20.2555	−	7.91142i	1.17733	−	0.459842i
$297$	−5.22308	−	0.0494167i	−0.303074	−	0.00286745i
$298$	1.14868	−	2.72083i	0.0665410	−	0.157613i
$299$	17.7473	+	21.1504i	1.02635	+	1.22316i
$300$	36.0131	+	5.89149i	2.07921	+	0.340145i
$301$	0.0419499	+	0.00739689i	0.00241795	+	0.000426350i
$302$	−14.8799	−	0.750771i	−0.856241	−	0.0432020i
$303$	−4.11874	−	13.9171i	−0.236615	−	0.799518i
$304$	−2.55251	−	17.1895i	−0.146397	−	0.985888i
$305$	−0.213787	−	0.370290i	−0.0122414	−	0.0212028i
$306$	0.0117374	+	8.05241i	0.000670985	+	0.460326i
$307$	8.07578	+	4.66255i	0.460909	+	0.266106i	0.712426	−	0.701747i	$-0.247596\pi$
$307$	8.07578	+	4.66255i	0.460909	+	0.266106i	−0.251517	+	0.967853i	$0.580930\pi$
$308$	−0.0187434	+	0.00843273i	−0.00106801	+	0.000480499i
$309$	−5.36951	−	10.7762i	−0.305461	−	0.613035i
$310$	39.5725	−	20.2603i	2.24757	−	1.15071i
$311$	−6.15253	−	5.16259i	−0.348878	−	0.292743i	0.451461	−	0.892291i	$-0.350903\pi$
$311$	−6.15253	−	5.16259i	−0.348878	−	0.292743i	−0.800339	+	0.599547i	$0.795347\pi$
$312$	−18.6764	+	6.00375i	−1.05734	+	0.339896i
$313$	31.0694	+	11.3083i	1.75615	+	0.639185i	0.999886	−	0.0150840i	$-0.00480156\pi$
$313$	31.0694	+	11.3083i	1.75615	+	0.639185i	0.756261	+	0.654269i	$0.227024\pi$
$314$	−19.0045	−	25.1179i	−1.07249	−	1.41749i
$315$	−0.0884452	+	0.0823956i	−0.00498332	+	0.00464247i
$316$	1.74852	−	6.18867i	0.0983619	−	0.348140i
$317$	25.6721	−	4.52669i	1.44189	−	0.254244i	0.602650	−	0.798006i	$-0.294112\pi$
$317$	25.6721	−	4.52669i	1.44189	−	0.254244i	0.839240	+	0.543762i	$0.183000\pi$
$318$	5.06322	−	2.21181i	0.283932	−	0.124032i
$319$	5.62581	−	2.04763i	0.314985	−	0.114645i
$320$	−26.5426	+	17.0200i	−1.48378	+	0.951449i
$321$	−24.5677	+	2.79305i	−1.37124	+	0.155893i
$322$	−0.0952705	+	0.0293301i	−0.00530922	+	0.00163450i
$323$			8.24576i			0.458806i
$324$	8.95452	−	15.6146i	0.497473	−	0.867479i
$325$		−	42.1838i		−	2.33993i
$326$	−3.59755	−	11.6856i	−0.199250	−	0.647207i
$327$	8.40564	−	0.955617i	0.464833	−	0.0528457i
$328$	−16.1011	+	3.22746i	−0.889035	+	0.178207i
$329$	−0.0760844	+	0.0276925i	−0.00419467	+	0.00152674i
$330$	3.88491	+	8.89325i	0.213857	+	0.489557i
$331$	2.73256	−	0.481823i	0.150195	−	0.0264834i	−0.0980451	−	0.995182i	$-0.531259\pi$
$331$	2.73256	−	0.481823i	0.150195	−	0.0264834i	0.248240	+	0.968699i	$0.420148\pi$
$332$	29.2508	+	8.26439i	1.60535	+	0.453567i
$333$	22.0537	+	6.75429i	1.20853	+	0.370133i
$334$	9.51922	−	7.20235i	0.520869	−	0.394095i
$335$	14.2516	+	5.18714i	0.778645	+	0.283404i
$336$	0.00625648	−	0.0705508i	0.000341319	−	0.00384886i
$337$	−10.0326	−	8.41837i	−0.546512	−	0.458578i	0.327246	−	0.944939i	$-0.393879\pi$
$337$	−10.0326	−	8.41837i	−0.546512	−	0.458578i	−0.873758	+	0.486361i	$0.838324\pi$
$338$	1.95634	+	3.82112i	0.106411	+	0.207841i
$339$	−3.45634	−	6.93660i	−0.187723	−	0.376744i
$340$	13.6439	−	6.13844i	0.739945	−	0.332904i
$341$	6.94350	+	4.00883i	0.376012	+	0.217090i
$342$	9.19281	−	15.9762i	0.497090	−	0.863891i
$343$	0.0715611	+	0.123947i	0.00386393	+	0.00669253i
$344$	6.12880	+	10.0664i	0.330443	+	0.542743i
$345$	13.3571	+	45.1335i	0.719124	+	2.42991i
$346$	0.968901	−	19.2031i	0.0520885	−	1.03236i
$347$	14.2864	+	2.51907i	0.766932	+	0.135231i	0.543409	−	0.839468i	$-0.317133\pi$
$347$	14.2864	+	2.51907i	0.766932	+	0.135231i	0.223523	+	0.974699i	$0.428244\pi$
$348$	−3.33086	+	20.3606i	−0.178553	+	1.09144i
$349$	15.0245	+	17.9055i	0.804242	+	0.958459i	0.999753	−	0.0222430i	$-0.00708074\pi$
$349$	15.0245	+	17.9055i	0.804242	+	0.958459i	−0.195510	+	0.980702i	$0.562636\pi$
$350$	0.140309	+	0.0592355i	0.00749983	+	0.00316627i
$351$	−19.4846	−	7.30130i	−1.04001	−	0.389714i
$352$	−5.17680	−	2.35290i	−0.275924	−	0.125410i
$353$	−26.1780	+	21.9660i	−1.39332	+	1.16913i	−0.429340	+	0.903143i	$0.641254\pi$
$353$	−26.1780	+	21.9660i	−1.39332	+	1.16913i	−0.963976	+	0.265988i	$0.914302\pi$
$354$	11.6496	−	11.0928i	0.619171	−	0.589578i
$355$	−3.43638	−	0.605927i	−0.182384	−	0.0321593i
$356$	−5.23592	−	2.52854i	−0.277503	−	0.134012i
$357$	−0.00785346	+	0.0326768i	−0.000415649	+	0.00172944i
$358$	−0.409404	−	0.0936791i	−0.0216377	−	0.00495110i
$359$	−13.5391	−	23.4504i	−0.714565	−	1.23766i	−0.963127	−	0.269047i	$-0.913291\pi$
$359$	−13.5391	−	23.4504i	−0.714565	−	1.23766i	0.248562	−	0.968616i	$-0.420042\pi$
$360$	−33.2785	−	3.31774i	−1.75393	−	0.174860i
$361$	−0.0626343	+	0.108486i	−0.00329654	+	0.00570978i
$362$	−1.81849	+	1.95772i	−0.0955777	+	0.102896i
$363$	9.55334	−	14.4259i	0.501420	−	0.757161i
$364$	−0.0816530	+	0.00602936i	−0.00427978	+	0.000316024i
$365$	−36.7916	+	43.8465i	−1.92576	+	2.29503i
$366$	0.147044	+	0.221339i	0.00768609	+	0.0115696i
$367$	4.30354	+	1.56636i	0.224643	+	0.0817633i	0.451890	−	0.892074i	$-0.350750\pi$
$367$	4.30354	+	1.56636i	0.224643	+	0.0817633i	−0.227247	+	0.973837i	$0.572972\pi$
$368$	−23.5018	−	14.4322i	−1.22511	−	0.752332i
$369$	−15.5152	−	7.91498i	−0.807691	−	0.412038i
$370$	−5.30537	−	42.5241i	−0.275813	−	2.21072i
$371$	0.0227096	−	0.00400432i	0.00117902	−	0.000207894i
$372$	−23.7551	+	14.1099i	−1.23165	+	0.731563i
$373$	5.86591	+	16.1165i	0.303725	+	0.834479i	0.993845	+	0.110783i	$0.0353359\pi$
$373$	5.86591	+	16.1165i	0.303725	+	0.834479i	−0.690119	+	0.723696i	$0.742442\pi$
$374$	2.26573	+	1.46512i	0.117158	+	0.0757595i
$375$	15.0734	−	34.6432i	0.778385	−	1.78897i
$376$	−19.6557	−	10.7457i	−1.01367	−	0.554168i
$377$	23.8493			1.22830
$378$	0.0516458	−	0.0545557i	0.00265638	−	0.00280604i
$379$			0.380673i			0.0195538i	0.999952	+	0.00977692i	$0.00311214\pi$
$379$			0.380673i			0.0195538i	−0.999952	+	0.00977692i	$0.996888\pi$
$380$	−34.0725	−	3.44707i	−1.74788	−	0.176831i
$381$	−2.04245	+	1.51056i	−0.104638	+	0.0773884i
$382$	−10.7160	+	16.5717i	−0.548278	+	0.847883i
$383$	34.6697	−	12.6187i	1.77154	−	0.644788i	0.771578	−	0.636135i	$-0.219468\pi$
$383$	34.6697	−	12.6187i	1.77154	−	0.644788i	0.999963	−	0.00865253i	$-0.00275422\pi$
$384$	15.7996	−	11.5919i	0.806270	−	0.591548i
$385$	0.00703334	+	0.0398880i	0.000358452	+	0.00203288i
$386$	1.66897	+	13.3773i	0.0849483	+	0.680885i
$387$	−1.52947	+	12.4063i	−0.0777473	+	0.630649i
$388$	−24.8021	+	6.28656i	−1.25914	+	0.319152i
$389$	2.44660	−	6.72197i	0.124047	−	0.340817i	−0.862088	−	0.506758i	$-0.830844\pi$
$389$	2.44660	−	6.72197i	0.124047	−	0.340817i	0.986136	+	0.165941i	$0.0530660\pi$
$390$	2.42583	+	38.5838i	0.122836	+	1.95377i
$391$	10.0246	+	8.41167i	0.506968	+	0.425397i
$392$	−6.33636	+	18.7574i	−0.320035	+	0.947390i
$393$	1.21138	−	19.7266i	0.0611060	−	0.995077i
$394$	−8.45804	+	9.10562i	−0.426110	+	0.458735i
$395$	−10.9754	−	6.33665i	−0.552233	−	0.318832i
$396$	−2.75646	−	5.36463i	−0.138517	−	0.269583i
$397$	−22.6986	+	13.1051i	−1.13921	+	0.657724i	−0.946235	−	0.323479i	$-0.895147\pi$
$397$	−22.6986	+	13.1051i	−1.13921	+	0.657724i	−0.192976	+	0.981203i	$0.561814\pi$
$398$	−2.97143	+	12.9860i	−0.148945	+	0.650930i
$399$	0.0529672	−	0.0557885i	0.00265168	−	0.00279292i
$400$	13.3328	+	39.9721i	0.666640	+	1.99861i
$401$	3.00071	−	17.0179i	0.149848	−	0.849832i	−0.813497	−	0.581569i	$-0.802439\pi$
$401$	3.00071	−	17.0179i	0.149848	−	0.849832i	0.963346	−	0.268263i	$-0.0864497\pi$
$402$	−9.04194	−	2.66161i	−0.450971	−	0.132749i
$403$	20.5302	+	24.4669i	1.02268	+	1.21878i
$404$	12.0101	−	11.6887i	0.597523	−	0.581535i
$405$	−25.4924	−	24.6660i	−1.26673	−	1.22566i
$406$	−0.0334898	+	0.0793262i	−0.00166207	+	0.00393689i
$407$	5.92033	−	4.96775i	0.293460	−	0.246242i
$408$	−8.22339	+	4.33949i	−0.407118	+	0.214837i
$409$	−4.27076	+	24.2207i	−0.211176	+	1.19764i	0.676245	+	0.736677i	$0.263606\pi$
$409$	−4.27076	+	24.2207i	−0.211176	+	1.19764i	−0.887421	+	0.460960i	$0.847505\pi$
$410$	−1.63073	+	32.3201i	−0.0805359	+	1.59618i
$411$	−5.36412	−	5.09285i	−0.264592	−	0.251212i
$412$	8.12777	−	11.2790i	0.400426	−	0.555677i
$413$	0.0581420	−	0.0335683i	0.00286098	−	0.00165179i
$414$	−10.0450	−	27.4736i	−0.493682	−	1.35025i
$415$	29.9502	−	51.8753i	1.47020	−	2.54646i
$416$	−16.1729	−	15.8610i	−0.792942	−	0.777651i
$417$	−0.113075	+	1.84136i	−0.00553731	+	0.0901720i
$418$	−2.81463	−	5.49754i	−0.137668	−	0.268893i
$419$	8.86909	−	10.5698i	0.433283	−	0.516367i	−0.504583	−	0.863363i	$-0.668354\pi$
$419$	8.86909	−	10.5698i	0.433283	−	0.516367i	0.937867	+	0.346996i	$0.112798\pi$
$420$	−0.131742	−	0.0461117i	−0.00642833	−	0.00225002i
$421$	12.5029	−	34.3515i	0.609355	−	1.67419i	−0.122281	−	0.992496i	$-0.539021\pi$
$421$	12.5029	−	34.3515i	0.609355	−	1.67419i	0.731637	−	0.681695i	$-0.238757\pi$
$422$	10.2928	+	13.6038i	0.501045	+	0.662223i
$423$	−9.27312	−	21.8759i	−0.450875	−	1.06364i
$424$	4.98156	+	3.98604i	0.241926	+	0.193579i
$425$	−3.47188	−	19.6900i	−0.168411	−	0.955106i
$426$	2.15508	+	0.241825i	0.104414	+	0.0117164i
$427$	0.000379315		0.00104216i	1.83563e−5		5.04336e-5i
$428$	−16.0576	−	23.6076i	−0.776175	−	1.14112i
$429$	−5.60561	+	4.14581i	−0.270641	+	0.200162i
$430$	22.1970	−	6.83359i	1.07043	−	0.329545i
$431$	7.44743			0.358730			0.179365	−	0.983783i	$-0.442596\pi$
$431$	7.44743			0.358730			0.179365	+	0.983783i	$0.442596\pi$
$432$	20.7707	+	0.760109i	0.999331	+	0.0365707i
$433$	20.9407			1.00634			0.503172	−	0.864186i	$-0.332166\pi$
$433$	20.9407			1.00634			0.503172	+	0.864186i	$0.332166\pi$
$434$	−0.110209	+	0.0339291i	−0.00529021	+	0.00162865i
$435$	37.2815	+	16.2213i	1.78751	+	0.777751i
$436$	5.49398	+	8.07713i	0.263114	+	0.386824i
$437$	−10.2451	−	28.1482i	−0.490090	−	1.34651i
$438$	21.1105	−	28.6310i	1.00870	−	1.36804i
$439$	4.88555	+	27.7073i	0.233174	+	1.32240i	0.846424	+	0.532509i	$0.178751\pi$
$439$	4.88555	+	27.7073i	0.233174	+	1.32240i	−0.613250	+	0.789889i	$0.710138\pi$
$440$	−7.00123	+	8.74982i	−0.333771	+	0.417131i
$441$	−17.6174	+	11.4286i	−0.838925	+	0.544220i
$442$	6.48529	+	8.57149i	0.308474	+	0.407704i
$443$	5.98423	−	16.4415i	0.284319	−	0.781161i	−0.712515	−	0.701657i	$-0.752444\pi$
$443$	5.98423	−	16.4415i	0.284319	−	0.781161i	0.996835	−	0.0795043i	$-0.0253338\pi$
$444$	4.94900	+	26.1691i	0.234869	+	1.24193i
$445$	−7.36537	+	8.77771i	−0.349152	+	0.416103i
$446$	−2.28754	−	4.46801i	−0.108318	−	0.211567i
$447$	3.01577	+	1.99716i	0.142641	+	0.0944624i
$448$	0.0754664	−	0.0315209i	0.00356545	−	0.00148922i
$449$	−2.99357	+	5.18501i	−0.141275	+	0.244696i	−0.927977	−	0.372637i	$-0.878454\pi$
$449$	−2.99357	+	5.18501i	−0.141275	+	0.244696i	0.786702	+	0.617333i	$0.211787\pi$
$450$	−15.2247	+	42.0200i	−0.717700	+	1.98084i
$451$	−5.05428	+	2.91809i	−0.237997	+	0.137408i
$452$	5.23182	−	7.26028i	0.246084	−	0.341495i
$453$	4.26407	−	17.7420i	0.200344	−	0.833593i
$454$	0.775245	−	15.3649i	0.0363841	−	0.721112i
$455$	−0.0280181	+	0.158899i	−0.00131351	+	0.00744928i
$456$	21.2683	+	0.809361i	0.995977	+	0.0379018i
$457$	18.6279	−	15.6306i	0.871375	−	0.731170i	−0.0930125	−	0.995665i	$-0.529650\pi$
$457$	18.6279	−	15.6306i	0.871375	−	0.731170i	0.964387	+	0.264495i	$0.0852052\pi$
$458$	4.32206	−	10.2375i	0.201957	−	0.478368i
$459$	−9.69570	−	1.80436i	−0.452556	−	0.0842201i
$460$	−38.9488	+	37.9067i	−1.81600	+	1.76741i
$461$	10.3010	+	12.2762i	0.479764	+	0.571761i	0.950584	−	0.310469i	$-0.100486\pi$
$461$	10.3010	+	12.2762i	0.479764	+	0.571761i	−0.470819	+	0.882230i	$0.656042\pi$
$462$	−0.00591800	−	0.0244667i	−0.000275330	−	0.00113829i
$463$	0.124840	−	0.708003i	0.00580181	−	0.0329037i	−0.981769	−	0.190076i	$-0.939127\pi$
$463$	0.124840	−	0.708003i	0.00580181	−	0.0329037i	0.987571	+	0.157172i	$0.0502377\pi$
$464$	−22.5989	+	7.53793i	−1.04913	+	0.349940i
$465$	15.4516	+	52.2106i	0.716550	+	2.42121i
$466$	−7.63285	+	33.3577i	−0.353585	+	1.54527i
$467$	16.8793	−	9.74528i	0.781082	−	0.450958i	−0.0557318	−	0.998446i	$-0.517749\pi$
$467$	16.8793	−	9.74528i	0.781082	−	0.450958i	0.836814	+	0.547488i	$0.184416\pi$
$468$	−3.00928	−	23.8374i	−0.139104	−	1.10188i
$469$	−0.0340678	−	0.0196690i	−0.00157310	−	0.000908231i
$470$	−30.0444	+	32.3447i	−1.38584	+	1.49195i
$471$	34.5274	−	17.2042i	1.59094	−	0.792726i
$472$	17.5978	+	5.94464i	0.810003	+	0.273624i
$473$	3.20859	+	2.69233i	0.147531	+	0.123794i
$474$	7.05471	+	3.50237i	0.324034	+	0.160869i
$475$	−15.6530	+	43.0062i	−0.718207	+	1.97326i
$476$	−0.0376168	+	0.00953466i	−0.00172416	+	0.000437020i
$477$	1.51902	+	6.59432i	0.0695511	+	0.301933i
$478$	−5.28089	−	42.3279i	−0.241542	−	1.93603i
$479$	1.69552	+	9.61575i	0.0774701	+	0.439355i	0.998729	+	0.0504046i	$0.0160511\pi$
$479$	1.69552	+	9.61575i	0.0774701	+	0.439355i	−0.921259	+	0.388950i	$0.872838\pi$
$480$	−14.4936	−	35.7942i	−0.661541	−	1.63377i
$481$	28.9304	−	10.5298i	1.31911	−	0.480118i
$482$	1.92227	−	2.97269i	0.0875571	−	0.135403i
$483$	−0.0137909	−	0.121305i	−0.000627507	−	0.00551957i
$484$	19.8776	+	2.01098i	0.903526	+	0.0914084i
$485$			50.4227i			2.28958i
$486$	16.7738	+	14.3052i	0.760876	+	0.648898i
$487$	−40.7197			−1.84519			−0.922594	−	0.385773i	$-0.873935\pi$
$487$	−40.7197			−1.84519			−0.922594	+	0.385773i	$0.873935\pi$
$488$	−0.147189	+	0.269232i	−0.00666291	+	0.0121876i
$489$	14.8790	−	1.69155i	0.672850	−	0.0764947i
$490$	32.7636	+	21.1863i	1.48011	+	0.957101i
$491$	−4.27622	−	11.7488i	−0.192983	−	0.530217i	0.805029	−	0.593235i	$-0.202150\pi$
$491$	−4.27622	−	11.7488i	−0.192983	−	0.530217i	−0.998012	+	0.0630180i	$0.979927\pi$
$492$	−0.248904	−	20.1105i	−0.0112215	−	0.906650i
$493$	11.1321	−	1.96289i	0.501365	−	0.0884041i
$494$	−3.04595	−	24.4142i	−0.137044	−	1.09845i
$495$	−11.5825	+	2.66807i	−0.520596	+	0.119921i
$496$	−27.1869	−	16.6953i	−1.22073	−	0.749639i
$497$	0.00850497	+	0.00309555i	0.000381500	+	0.000138855i
$498$	−16.5539	+	33.3441i	−0.741800	+	1.49419i
$499$	−2.94192	+	3.50604i	−0.131698	+	0.156952i	−0.827863	−	0.560930i	$-0.810444\pi$
$499$	−2.94192	+	3.50604i	−0.131698	+	0.156952i	0.696165	+	0.717882i	$0.254888\pi$
$500$	43.5066	−	3.21258i	1.94567	−	0.143671i
$501$	6.52006	+	13.0852i	0.291295	+	0.584605i
$502$	16.1179	−	17.3519i	0.719376	−	0.774454i
$503$	−9.68900	+	16.7818i	−0.432011	+	0.748265i	−0.997046	−	0.0768015i	$-0.975529\pi$
$503$	−9.68900	+	16.7818i	−0.432011	+	0.748265i	0.565035	+	0.825067i	$0.308863\pi$
$504$	0.0835122	+	0.0234638i	0.00371993	+	0.00104516i
$505$	−16.5134	−	28.6020i	−0.734836	−	1.27277i
$506$	−9.55480	−	2.18631i	−0.424763	−	0.0971934i
$507$	−5.04145	+	1.49200i	−0.223899	+	0.0662622i
$508$	−2.64146	−	1.27562i	−0.117196	−	0.0565964i
$509$	−2.30682	−	0.406755i	−0.102248	−	0.0180291i	0.122290	−	0.992494i	$-0.460976\pi$
$509$	−2.30682	−	0.406755i	−0.102248	−	0.0180291i	−0.224538	+	0.974465i	$0.572087\pi$
$510$	4.30789	+	17.8100i	0.190757	+	0.788641i
$511$	0.113729	−	0.0954301i	0.00503108	−	0.00422158i
$512$	20.3381	+	9.91776i	0.898825	+	0.438307i
$513$	17.1552	+	14.6737i	0.757420	+	0.647860i
$514$	34.8437	+	14.7103i	1.53689	+	0.648842i
$515$	−17.6105	−	20.9874i	−0.776014	−	0.924817i
$516$	−13.5014	+	5.10421i	−0.594367	+	0.224700i
$517$	−7.84049	−	1.38249i	−0.344824	−	0.0608018i
$518$	−0.00560121	+	0.111013i	−0.000246103	+	0.00487762i
$519$	22.8968	+	5.50296i	1.00506	+	0.241553i
$520$	−38.1296	+	23.2148i	−1.67209	+	1.01804i
$521$	−3.33988	−	5.78485i	−0.146323	−	0.253439i	0.783543	−	0.621338i	$-0.213411\pi$
$521$	−3.33988	−	5.78485i	−0.146323	−	0.253439i	−0.929866	+	0.367899i	$0.880077\pi$
$522$	−23.7568	−	8.60756i	−1.03981	−	0.376743i
$523$	25.4719	+	14.7062i	1.11381	+	0.643057i	0.939813	−	0.341690i	$-0.110999\pi$
$523$	25.4719	+	14.7062i	1.11381	+	0.643057i	0.173994	+	0.984747i	$0.444333\pi$
$524$	20.8119	−	9.36336i	0.909174	−	0.409040i
$525$	−0.102990	+	0.155519i	−0.00449487	+	0.00678740i
$526$	2.82932	+	5.52622i	0.123364	+	0.240955i
$527$	11.5965	+	9.73065i	0.505153	+	0.423874i
$528$	4.00137	−	5.70018i	0.174137	−	0.248069i
$529$	−23.0590	−	8.39280i	−1.00257	−	0.364904i
$530$	10.0264	−	7.58611i	0.435520	−	0.329520i
$531$	10.7221	+	16.5283i	0.465299	+	0.717267i
$532$	0.0854822	+	0.0241517i	0.00370612	+	0.00104711i
$533$	−22.8959	+	4.03716i	−0.991731	+	0.174869i
$534$	4.22614	−	5.73169i	0.182883	−	0.248034i
$535$	−52.8718	+	19.2438i	−2.28585	+	0.831980i
$536$	−2.13908	−	10.6714i	−0.0923941	−	0.460935i
$537$	0.205222	−	0.471662i	0.00885598	−	0.0203537i
$538$	−0.308357	−	1.00161i	−0.0132942	−	0.0431826i
$539$			7.03648i			0.303083i
$540$	11.5090	−	39.3096i	0.495270	−	1.69161i
$541$		−	1.09392i		−	0.0470312i	−0.999723	−	0.0235156i	$-0.992514\pi$
$541$		−	1.09392i		−	0.0470312i	0.999723	−	0.0235156i	$-0.00748594\pi$
$542$	19.1185	−	5.88584i	0.821209	−	0.252818i
$543$	−1.94592	−	2.63111i	−0.0835076	−	0.112912i
$544$	−8.85442	−	6.07232i	−0.379630	−	0.260349i
$545$	18.0896	−	6.58409i	0.774875	−	0.282031i
$546$	0.0111820	−	0.0996510i	0.000478544	−	0.00426467i
$547$	−11.4033	+	2.01070i	−0.487568	+	0.0859714i	−0.412028	−	0.911171i	$-0.635179\pi$
$547$	−11.4033	+	2.01070i	−0.487568	+	0.0859714i	−0.0755403	+	0.997143i	$0.524068\pi$
$548$	2.32221	−	8.21919i	0.0992001	−	0.351107i
$549$	−0.299643	+	0.127018i	−0.0127884	+	0.00542098i
$550$	9.03579	+	11.9424i	0.385287	+	0.509228i
$551$	−24.3143	−	8.84968i	−1.03582	−	0.377009i
$552$	22.6802	−	25.0309i	0.965331	−	1.06538i
$553$	0.0251814	+	0.0211297i	0.00107082	+	0.000898528i
$554$	10.7717	−	5.51490i	0.457645	−	0.234305i
$555$	52.3862	+	3.21695i	2.22367	+	0.136552i
$556$	−1.94267	+	0.874014i	−0.0823876	+	0.0370665i
$557$	−11.9979	−	6.92697i	−0.508366	−	0.293505i	0.223796	−	0.974636i	$-0.428155\pi$
$557$	−11.9979	−	6.92697i	−0.508366	−	0.293505i	−0.732162	+	0.681131i	$0.761488\pi$
$558$	−11.6200	−	31.7815i	−0.491915	−	1.34542i
$559$	8.34273	+	14.4500i	0.352860	+	0.611171i
$560$	−0.0236731	−	0.159423i	−0.00100037	−	0.00673686i
$561$	−2.27530	+	2.39649i	−0.0960633	+	0.101180i
$562$	26.5264	+	1.33840i	1.11895	+	0.0564572i
$563$	29.5384	+	5.20841i	1.24489	+	0.219508i	0.757012	−	0.653401i	$-0.226659\pi$
$563$	29.5384	+	5.20841i	1.24489	+	0.219508i	0.487882	+	0.872910i	$0.337770\pi$
$564$	17.3740	−	21.2337i	0.731576	−	0.894101i
$565$	−11.3359	−	13.5096i	−0.476903	−	0.568351i
$566$	−14.1393	+	33.4912i	−0.594318	+	1.40774i
$567$	0.0540079	+	0.0744888i	0.00226812	+	0.00312823i
$568$	0.911026	+	2.33249i	0.0382258	+	0.0978690i
$569$	−13.1491	+	11.0334i	−0.551241	+	0.462546i	−0.875361	−	0.483470i	$-0.839376\pi$
$569$	−13.1491	+	11.0334i	−0.551241	+	0.462546i	0.324120	+	0.946016i	$0.394932\pi$
$570$	11.8440	−	40.2362i	0.496092	−	1.68531i
$571$	−16.7116	−	2.94670i	−0.699357	−	0.123316i	−0.187346	−	0.982294i	$-0.559988\pi$
$571$	−16.7116	−	2.94670i	−0.699357	−	0.123316i	−0.512012	+	0.858978i	$0.671100\pi$
$572$	−7.24963	−	3.50100i	−0.303122	−	0.146384i
$573$	−17.5281	−	16.6417i	−0.732248	−	0.695218i
$574$	0.0187228	−	0.0818239i	0.000781475	−	0.00341526i
$575$	36.3161	+	62.9013i	1.51449	+	2.62317i
$576$	10.3857	+	21.6365i	0.432736	+	0.901521i
$577$	−4.49809	+	7.79092i	−0.187258	+	0.324340i	−0.944335	−	0.328985i	$-0.893293\pi$
$577$	−4.49809	+	7.79092i	−0.187258	+	0.324340i	0.757077	+	0.653326i	$0.226627\pi$
$578$	−13.8822	−	12.8950i	−0.577425	−	0.536359i
$579$	−16.4797	−	1.01199i	−0.684874	−	0.0420570i
$580$	3.45724	+	46.8198i	0.143554	+	1.94409i
$581$	−0.0998698	+	0.119020i	−0.00414330	+	0.00493779i
$582$	−1.96632	−	31.2751i	−0.0815065	−	1.29640i
$583$	2.13072	+	0.775517i	0.0882453	+	0.0321186i
$584$	40.6064	+	6.18850i	1.68031	+	0.256082i
$585$	−46.9929	−	5.79335i	−1.94292	−	0.239526i
$586$	20.4717	−	2.55408i	0.845679	−	0.105508i
$587$	29.2734	−	5.16169i	1.20824	−	0.213046i	0.466984	−	0.884266i	$-0.345340\pi$
$587$	29.2734	−	5.16169i	1.20824	−	0.213046i	0.741258	+	0.671220i	$0.234229\pi$
$588$	−21.1481	−	11.8634i	−0.872134	−	0.489237i
$589$	−11.8516	−	32.5619i	−0.488336	−	1.34169i
$590$	19.8766	−	30.7381i	0.818306	−	1.26547i
$591$	−9.05075	−	12.2376i	−0.372298	−	0.503390i
$592$	−24.0855	+	19.1216i	−0.989909	+	0.785895i
$593$	−21.5451			−0.884750			−0.442375	−	0.896830i	$-0.645864\pi$
$593$	−21.5451			−0.884750			−0.442375	+	0.896830i	$0.645864\pi$
$594$	7.08013	−	2.10657i	0.290501	−	0.0864338i
$595$			0.0764747i			0.00313516i
$596$	−0.420403	+	4.15547i	−0.0172204	+	0.170215i
$597$	−14.9608	−	6.50949i	−0.612304	−	0.266416i
$598$	−32.7884	−	21.2024i	−1.34082	−	0.867029i
$599$	−10.2586	+	3.73384i	−0.419156	+	0.152560i	−0.542983	−	0.839743i	$-0.682705\pi$
$599$	−10.2586	+	3.73384i	−0.419156	+	0.152560i	0.123827	+	0.992304i	$0.460483\pi$
$600$	−51.1272	+	7.02234i	−2.08726	+	0.286686i
$601$	−2.62710	−	14.8990i	−0.107162	−	0.607744i	−0.990335	−	0.138697i	$-0.955709\pi$
$601$	−2.62710	−	14.8990i	−0.107162	−	0.607744i	0.883173	−	0.469047i	$-0.155403\pi$
$602$	−0.0597778	+	0.00745798i	−0.00243636	+	0.000303964i
$603$	5.24585	−	10.2831i	0.213628	−	0.418761i
$604$	20.4242	−	5.17689i	0.831049	−	0.210645i
$605$	13.4661	−	36.9978i	0.547475	−	1.50417i
$606$	11.3580	+	17.0967i	0.461386	+	0.694507i
$607$	−18.8283	−	15.7988i	−0.764216	−	0.641253i	0.175005	−	0.984568i	$-0.444006\pi$
$607$	−18.8283	−	15.7988i	−0.764216	−	0.641253i	−0.939221	+	0.343314i	$0.888450\pi$
$608$	10.6027	+	22.1715i	0.429997	+	0.899171i
$609$	−0.0879254	−	0.0582275i	−0.00356292	−	0.00235950i
$610$	0.443038	+	0.411530i	0.0179381	+	0.0166624i
$611$	−27.4663	−	15.8577i	−1.11117	−	0.641532i
$612$	−3.36654	−	10.8789i	−0.136084	−	0.439751i
$613$	−15.6018	+	9.00768i	−0.630149	+	0.363817i	−0.780810	−	0.624769i	$-0.785193\pi$
$613$	−15.6018	+	9.00768i	−0.630149	+	0.363817i	0.150661	+	0.988586i	$0.451860\pi$
$614$	−12.8554	−	2.94156i	−0.518804	−	0.118712i
$615$	−38.5369	−	9.26187i	−1.55396	−	0.373475i
$616$	0.0218249	−	0.0191971i	0.000879351	−	0.000773472i
$617$	−4.06887	+	23.0757i	−0.163807	+	0.928994i	0.786480	+	0.617616i	$0.211902\pi$
$617$	−4.06887	+	23.0757i	−0.163807	+	0.928994i	−0.950286	+	0.311378i	$0.899210\pi$
$618$	11.7416	+	12.3309i	0.472315	+	0.496022i
$619$	−21.6871	−	25.8457i	−0.871679	−	1.03883i	−0.998897	−	0.0469514i	$-0.985049\pi$
$619$	−21.6871	−	25.8457i	−0.871679	−	1.03883i	0.127219	−	0.991875i	$-0.459395\pi$
$620$	−45.0561	+	43.8506i	−1.80950	+	1.76108i
$621$	35.3397	−	5.88716i	1.41813	−	0.236244i
$622$	10.4640	+	4.41769i	0.419569	+	0.177133i
$623$	0.0227676	−	0.0191043i	0.000912166	−	0.000765398i
$624$	22.7450	−	15.8861i	0.910527	−	0.635954i
$625$	5.78239	−	32.7936i	0.231296	−	1.31174i
$626$	−46.6993	−	2.35623i	−1.86648	−	0.0941741i
$627$	7.25326	−	2.14658i	0.289667	−	0.0857263i
$628$	36.1385	+	26.0418i	1.44208	+	1.03918i
$629$	12.6372	−	7.29606i	0.503876	−	0.290913i
$630$	0.0852581	−	0.148170i	0.00339676	−	0.00590322i
$631$	−3.55095	+	6.15043i	−0.141361	+	0.244845i	−0.928009	−	0.372557i	$-0.878481\pi$
$631$	−3.55095	+	6.15043i	−0.141361	+	0.244845i	0.786648	+	0.617401i	$0.211815\pi$
$632$	0.211840	+	9.09226i	0.00842655	+	0.361671i
$633$	−18.6999	+	9.31773i	−0.743256	+	0.370346i
$634$	−32.8151	+	16.8007i	−1.30326	+	0.667241i
$635$	−3.71575	+	4.42826i	−0.147455	+	0.175730i
$636$	−5.92316	+	5.09636i	−0.234869	+	0.202084i
$637$	−9.58703	+	26.3402i	−0.379852	+	1.04363i
$638$	−6.75187	+	5.10854i	−0.267309	+	0.202249i
$639$	−0.777779	+	2.53955i	−0.0307685	+	0.100463i
$640$	28.7931	−	34.0491i	1.13815	−	1.34591i
$641$	−0.826096	−	4.68502i	−0.0326288	−	0.185047i	0.964137	−	0.265404i	$-0.0855052\pi$
$641$	−0.826096	−	4.68502i	−0.0326288	−	0.185047i	−0.996766	+	0.0803565i	$0.974394\pi$
$642$	32.0438	−	13.9980i	1.26467	−	0.552455i
$643$	−5.88956	−	16.1814i	−0.232262	−	0.638134i	0.767735	−	0.640768i	$-0.221384\pi$
$643$	−5.88956	−	16.1814i	−0.232262	−	0.638134i	−0.999997	+	0.00263392i	$0.999162\pi$
$644$	0.116564	−	0.0792858i	0.00459327	−	0.00312430i
$645$	3.21313	+	28.2628i	0.126517	+	1.11284i
$646$	−3.43113	−	11.1451i	−0.134996	−	0.438497i
$647$	38.9704			1.53208			0.766042	−	0.642791i	$-0.222224\pi$
$647$	38.9704			1.53208			0.766042	+	0.642791i	$0.222224\pi$
$648$	−5.60565	+	24.8310i	−0.220211	+	0.975452i
$649$	6.60148			0.259131
$650$	17.5530	+	57.0161i	0.688486	+	2.23635i
$651$	−0.0159533	−	0.140326i	−0.000625260	−	0.00549981i
$652$	9.72499	+	14.2975i	0.380860	+	0.559932i
$653$	7.50821	+	20.6286i	0.293819	+	0.807261i	0.995499	+	0.0947692i	$0.0302113\pi$
$653$	7.50821	+	20.6286i	0.293819	+	0.807261i	−0.701680	+	0.712492i	$0.747566\pi$
$654$	−10.9635	+	4.78928i	−0.428707	+	0.187276i
$655$	−7.80953	−	44.2901i	−0.305144	−	1.73056i
$656$	20.4195	−	11.0621i	0.797246	−	0.431902i
$657$	29.6970	+	31.8774i	1.15859	+	1.24366i
$658$	0.0913135	−	0.0690889i	0.00355977	−	0.00269336i
$659$	−10.8064	+	29.6905i	−0.420960	+	1.15658i	0.530199	+	0.847873i	$0.322117\pi$
$659$	−10.8064	+	29.6905i	−0.420960	+	1.15658i	−0.951158	+	0.308703i	$0.900105\pi$
$660$	−8.95145	−	10.4037i	−0.348435	−	0.404962i
$661$	−0.564964	+	0.673298i	−0.0219746	+	0.0261883i	−0.776920	−	0.629600i	$-0.783219\pi$
$661$	−0.564964	+	0.673298i	−0.0219746	+	0.0261883i	0.754945	+	0.655788i	$0.227663\pi$
$662$	−3.49286	+	1.78828i	−0.135754	+	0.0695034i
$663$	−11.7825	+	5.87092i	−0.457593	+	0.228008i
$664$	−42.9746	+	1.00126i	−1.66774	+	0.0388566i
$665$	0.0875262	−	0.151600i	0.00339412	−	0.00587879i
$666$	−32.6185	+	0.0475457i	−1.26394	+	0.00184236i
$667$	−35.5624	+	20.5319i	−1.37698	+	0.795000i
$668$	−9.86933	+	13.6958i	−0.381856	+	0.529907i
$669$	5.89494	−	1.74459i	0.227912	−	0.0674498i
$670$	−21.4210	−	1.08081i	−0.827564	−	0.0417552i
$671$	−0.0189365	+	0.107394i	−0.000731036	+	0.00414591i
$672$	0.0209004	+	0.0979606i	0.000806252	+	0.00377891i
$673$	2.60760	−	2.18804i	0.100516	−	0.0843426i	−0.591145	−	0.806565i	$-0.701324\pi$
$673$	2.60760	−	2.18804i	0.100516	−	0.0843426i	0.691661	+	0.722223i	$0.256879\pi$
$674$	17.0632	+	7.20371i	0.657249	+	0.277477i
$675$	−47.1432	−	27.8161i	−1.81454	−	1.07064i
$676$	−4.23421	−	4.35062i	−0.162854	−	0.167331i
$677$	−12.0910	−	14.4095i	−0.464695	−	0.553802i	0.481900	−	0.876226i	$-0.339947\pi$
$677$	−12.0910	−	14.4095i	−0.464695	−	0.553802i	−0.946595	+	0.322424i	$0.895502\pi$
$678$	7.55801	+	7.93737i	0.290264	+	0.304833i
$679$	0.0227108	−	0.128799i	0.000871561	−	0.00494287i
$680$	−15.8870	+	13.9741i	−0.609239	+	0.535884i
$681$	18.3204	+	4.40308i	0.702038	+	0.168726i
$682$	−11.0530	−	2.52913i	−0.423242	−	0.0968455i
$683$	19.4488	−	11.2288i	0.744188	−	0.429657i	−0.0794021	−	0.996843i	$-0.525301\pi$
$683$	19.4488	−	11.2288i	0.744188	−	0.429657i	0.823590	+	0.567186i	$0.191968\pi$
$684$	−5.77730	+	25.4188i	−0.220900	+	0.971910i
$685$	−14.5765	−	8.41573i	−0.556938	−	0.321548i
$686$	−0.148298	−	0.137752i	−0.00566206	−	0.00525938i
$687$	11.3473	+	7.51461i	0.432926	+	0.286700i
$688$	−12.4725	−	11.0556i	−0.475508	−	0.421490i
$689$	6.91944	+	5.80610i	0.263610	+	0.221195i
$690$	−36.8341	−	55.4449i	−1.40225	−	2.11075i
$691$	14.6665	−	40.2960i	0.557941	−	1.53293i	−0.264677	−	0.964337i	$-0.585265\pi$
$691$	14.6665	−	40.2960i	0.557941	−	1.53293i	0.822618	−	0.568594i	$-0.192512\pi$
$692$	6.68100	+	26.3583i	0.253973	+	1.00199i
$693$	0.0307881	−	0.00159842i	0.00116954	−	6.07191e-5i
$694$	−20.3578	+	2.53987i	−0.772773	+	0.0964123i
$695$	0.728974	+	4.13422i	0.0276515	+	0.156820i
$696$	−3.97020	−	28.9056i	−0.150490	−	1.09567i
$697$	−10.3548	+	3.76883i	−0.392215	+	0.142755i
$698$	−27.7579	−	17.9494i	−1.05065	−	0.679396i
$699$	−38.4304	−	16.7212i	−1.45357	−	0.632455i
$700$	−0.214292	−	0.0216796i	−0.00809946	−	0.000819410i
$701$		−	30.9274i		−	1.16811i	−0.811714	−	0.584055i	$-0.801465\pi$
$701$		−	30.9274i		−	1.16811i	0.811714	−	0.584055i	$-0.198535\pi$
$702$	29.3737	+	1.76082i	1.10864	+	0.0664577i
$703$	−33.4017			−1.25977
$704$	7.97608	+	1.02609i	0.300610	+	0.0386723i
$705$	−32.1498	−	43.4702i	−1.21083	−	1.63718i
$706$	26.2423	−	40.5824i	0.987642	−	1.52734i
$707$	0.0292991	+	0.0804987i	0.00110191	+	0.00302746i
$708$	−11.1300	+	19.8407i	−0.418289	+	0.745660i
$709$	−10.5402	+	1.85852i	−0.395845	+	0.0697982i	−0.368028	−	0.929815i	$-0.619967\pi$
$709$	−10.5402	+	1.85852i	−0.395845	+	0.0697982i	−0.0278175	+	0.999613i	$0.508856\pi$
$710$	4.89679	−	0.610931i	0.183773	−	0.0229278i
$711$	−5.80913	+	7.70112i	−0.217859	+	0.288815i
$712$	8.12907	+	1.23889i	0.304650	+	0.0464292i
$713$	−51.6766	−	18.8088i	−1.93531	−	0.704394i
$714$	−0.00298226	−	0.0474342i	−0.000111608	−	0.00177518i
$715$	−10.1981	+	12.1536i	−0.381386	+	0.454518i
$716$	0.592336	−	0.0437388i	0.0221366	−	0.00163460i
$717$	52.1445	+	3.20211i	1.94737	+	0.119585i
$718$	28.0575	+	26.0621i	1.04710	+	0.972628i
$719$	7.98318	−	13.8273i	0.297723	−	0.515671i	−0.677892	−	0.735161i	$-0.737106\pi$
$719$	7.98318	−	13.8273i	0.297723	−	0.515671i	0.975615	+	0.219491i	$0.0704397\pi$
$720$	46.3602	−	9.36318i	1.72774	−	0.348945i
$721$	0.0355314	+	0.0615422i	0.00132326	+	0.00229195i
$722$	0.0395154	−	0.172693i	0.00147061	−	0.00642698i
$723$	3.14426	+	2.98525i	0.116936	+	0.111023i
$724$	1.64327	−	3.40277i	0.0610716	−	0.126463i
$725$	61.7861	+	10.8946i	2.29468	+	0.404614i
$726$	−6.90968	+	23.4734i	−0.256442	+	0.871179i
$727$	18.0652	−	15.1585i	0.670002	−	0.562198i	−0.243064	−	0.970010i	$-0.578153\pi$
$727$	18.0652	−	15.1585i	0.670002	−	0.562198i	0.913066	+	0.407812i	$0.133708\pi$
$728$	0.107854	−	0.0421259i	0.00399735	−	0.00156129i
$729$	−21.0079	+	16.9608i	−0.778069	+	0.628178i
$730$	31.4830	−	74.5728i	1.16524	−	2.76006i
$731$	5.08341	+	6.05817i	0.188017	+	0.224069i
$732$	−0.290847	−	0.237978i	−0.0107500	−	0.00879593i
$733$	−5.12011	−	0.902813i	−0.189115	−	0.0333462i	0.0782882	−	0.996931i	$-0.475055\pi$
$733$	−5.12011	−	0.902813i	−0.189115	−	0.0333462i	−0.267404	+	0.963585i	$0.586166\pi$
$734$	−6.46849	−	0.326371i	−0.238756	−	0.0120466i
$735$	−32.9020	+	34.6544i	−1.21361	+	1.27825i
$736$	37.7706	+	9.72749i	1.39224	+	0.358560i
$737$	−1.93404	−	3.34985i	−0.0712412	−	0.123393i
$738$	24.2641	+	4.24195i	0.893173	+	0.156148i
$739$	−10.5638	−	6.09903i	−0.388596	−	0.224356i	0.292955	−	0.956126i	$-0.405361\pi$
$739$	−10.5638	−	6.09903i	−0.388596	−	0.224356i	−0.681552	+	0.731770i	$0.738695\pi$
$740$	24.8654	+	55.2684i	0.914071	+	2.03171i
$741$	30.0763	+	1.84694i	1.10488	+	0.0678489i
$742$	−0.0290283	+	0.0148619i	−0.00106566	+	0.000545599i
$743$	−11.5486	−	9.69040i	−0.423676	−	0.355506i	0.405883	−	0.913925i	$-0.366964\pi$
$743$	−11.5486	−	9.69040i	−0.423676	−	0.355506i	−0.829559	+	0.558419i	$0.811408\pi$
$744$	26.2365	−	28.9558i	0.961876	−	1.06157i
$745$	7.73451	+	2.81513i	0.283371	+	0.103138i
$746$	−14.6346	−	19.3423i	−0.535812	−	0.708173i
$747$	−36.3994	−	27.4568i	−1.33178	−	1.00459i
$748$	−3.67204	−	1.03748i	−0.134263	−	0.0379341i
$749$	0.143723	−	0.0253422i	0.00525153	−	0.000925986i
$750$	−5.95801	+	53.0963i	−0.217556	+	1.93880i
$751$	−1.35242	+	0.492239i	−0.0493504	+	0.0179621i	−0.366577	−	0.930388i	$-0.619471\pi$
$751$	−1.35242	+	0.492239i	−0.0493504	+	0.0179621i	0.317227	+	0.948350i	$0.397248\pi$
$752$	31.0383	+	6.34513i	1.13185	+	0.231383i
$753$	17.2474	+	23.3204i	0.628529	+	0.849843i
$754$	−32.2350	+	9.92391i	−1.17393	+	0.361408i
$755$		−	41.5223i		−	1.51115i
$756$	−0.0471040	+	0.0952284i	−0.00171316	+	0.00346342i
$757$			15.3476i			0.557818i	0.960318	+	0.278909i	$0.0899727\pi$
$757$			15.3476i			0.557818i	−0.960318	+	0.278909i	$0.910027\pi$
$758$	−0.158401	−	0.514521i	−0.00575339	−	0.0186883i
$759$	4.78953	−	11.0078i	0.173849	−	0.399558i
$760$	47.4872	−	9.51878i	1.72254	−	0.345283i
$761$	−3.86991	+	1.40853i	−0.140284	+	0.0510593i	−0.411208	−	0.911541i	$-0.634893\pi$
$761$	−3.86991	+	1.40853i	−0.140284	+	0.0510593i	0.270924	+	0.962601i	$0.412671\pi$
$762$	2.13204	−	2.89157i	0.0772358	−	0.104751i
$763$	−0.0491736	+	0.00867063i	−0.00178020	+	0.000313898i
$764$	7.58821	−	26.8576i	0.274532	−	0.971672i
$765$	−22.4116	+	1.16354i	−0.810292	+	0.0420679i
$766$	−41.6092	+	31.4820i	−1.50340	+	1.13749i
$767$	24.7118	+	8.99435i	0.892291	+	0.324767i
$768$	−16.5314	+	22.2421i	−0.596526	+	0.802594i
$769$	36.4911	+	30.6197i	1.31590	+	1.10417i	0.987156	+	0.159757i	$0.0510710\pi$
$769$	36.4911	+	30.6197i	1.31590	+	1.10417i	0.328748	+	0.944418i	$0.393373\pi$
$770$	−0.0261041	−	0.0509865i	−0.000940727	−	0.00183743i
$771$	−25.5762	+	38.6209i	−0.921104	+	1.39090i
$772$	−7.82220	−	17.3864i	−0.281527	−	0.625751i
$773$	−4.04314	−	2.33431i	−0.145422	−	0.0839592i	0.425524	−	0.904947i	$-0.360090\pi$
$773$	−4.04314	−	2.33431i	−0.145422	−	0.0839592i	−0.570945	+	0.820988i	$0.693423\pi$
$774$	−3.09513	−	17.4049i	−0.111252	−	0.625608i
$775$	42.0105	+	72.7644i	1.50906	+	2.61377i
$776$	30.9070	−	18.8174i	1.10950	−	0.675504i
$777$	−0.132366	−	0.0318126i	−0.00474861	−	0.00114127i
$778$	−0.509779	+	10.1035i	−0.0182765	+	0.362229i
$779$	24.8403	+	4.38001i	0.889996	+	0.156930i
$780$	−19.3338	−	51.1409i	−0.692262	−	1.83114i
$781$	0.572053	+	0.681746i	0.0204697	+	0.0243948i
$782$	−17.0496	−	7.19797i	−0.609692	−	0.257399i
$783$	15.7263	−	26.6532i	0.562013	−	0.952508i
$784$	0.759198	−	27.9893i	0.0271142	−	0.999617i
$785$	67.2447	−	56.4250i	2.40007	−	2.01390i
$786$	6.57110	+	27.1668i	0.234384	+	0.969008i
$787$	16.1106	+	2.84073i	0.574279	+	0.101261i	0.453243	−	0.891387i	$-0.350267\pi$
$787$	16.1106	+	2.84073i	0.574279	+	0.101261i	0.121037	+	0.992648i	$0.461378\pi$
$788$	7.64306	−	15.8267i	0.272273	−	0.563804i
$789$	−7.29111	+	2.15778i	−0.259570	+	0.0768191i
$790$	17.4712	+	3.99773i	0.621598	+	0.142233i
$791$	0.0228715	+	0.0396145i	0.000813215	+	0.00140853i
$792$	5.95793	+	6.10390i	0.211706	+	0.216893i
$793$	−0.217209	+	0.376216i	−0.00771330	+	0.0133598i
$794$	25.2266	−	27.1580i	0.895258	−	0.963803i
$795$	6.86746	+	13.7824i	0.243564	+	0.488813i
$796$	−1.38736	−	18.7885i	−0.0491738	−	0.665940i
$797$	6.71611	−	8.00395i	0.237897	−	0.283514i	−0.633866	−	0.773443i	$-0.718533\pi$
$797$	6.71611	−	8.00395i	0.237897	−	0.283514i	0.871762	+	0.489929i	$0.162977\pi$
$798$	−0.0483771	+	0.0974444i	−0.00171253	+	0.00344950i
$799$	−14.1255	−	5.14126i	−0.499725	−	0.181885i
$800$	−34.6535	−	48.4789i	−1.22519	−	1.71399i
$801$	5.94509	+	6.38159i	0.210059	+	0.225482i
$802$	3.02549	+	24.2502i	0.106834	+	0.856303i
$803$	14.3764	−	2.53495i	0.507333	−	0.0894566i
$804$	13.3287	−	0.164967i	0.470068	−	0.00581794i
$805$	−0.0950175	−	0.261058i	−0.00334893	−	0.00920110i
$806$	−37.9297	−	24.5270i	−1.33602	−	0.863925i
$807$	1.27532	−	0.144988i	0.0448934	−	0.00510383i
$808$	−11.3692	+	20.7961i	−0.399966	+	0.731604i
$809$	5.87774			0.206650			0.103325	−	0.994648i	$-0.467052\pi$
$809$	5.87774			0.206650			0.103325	+	0.994648i	$0.467052\pi$
$810$	44.7196	+	22.7313i	1.57129	+	0.798695i
$811$			40.3341i			1.41632i	0.706052	+	0.708160i	$0.250475\pi$
$811$			40.3341i			1.41632i	−0.706052	+	0.708160i	$0.749525\pi$
$812$	0.0122569	−	0.121154i	0.000430134	−	0.00425166i
$813$	2.76750	+	24.3430i	0.0970603	+	0.853745i
$814$	−5.93487	+	9.17797i	−0.208017	+	0.321688i
$815$	32.0208	−	11.6546i	1.12164	−	0.408243i
$816$	9.30913	−	9.28713i	0.325885	−	0.325115i
$817$	−3.14346	−	17.8274i	−0.109976	−	0.623703i
$818$	−4.30603	−	34.5141i	−0.150557	−	1.20676i
$819$	0.117429	+	0.0359645i	0.00410330	+	0.00125670i
$820$	−11.2446	−	44.3628i	−0.392678	−	1.54922i
$821$	8.31903	−	22.8563i	0.290336	−	0.797692i	−0.705681	−	0.708530i	$-0.749359\pi$
$821$	8.31903	−	22.8563i	0.290336	−	0.797692i	0.996017	−	0.0891622i	$-0.0284190\pi$
$822$	9.36938	+	4.65150i	0.326795	+	0.162240i
$823$	−22.0384	−	18.4924i	−0.768211	−	0.644605i	0.172039	−	0.985090i	$-0.444964\pi$
$823$	−22.0384	−	18.4924i	−0.768211	−	0.644605i	−0.940250	+	0.340485i	$0.889409\pi$
$824$	−6.29229	+	18.6269i	−0.219202	+	0.648898i
$825$	−16.4162	+	8.17981i	−0.571539	+	0.284784i
$826$	−0.0646173	+	0.0695647i	−0.00224833	+	0.00242047i
$827$	−12.6598	−	7.30915i	−0.440225	−	0.254164i	0.263468	−	0.964668i	$-0.415134\pi$
$827$	−12.6598	−	7.30915i	−0.440225	−	0.254164i	−0.703693	+	0.710504i	$0.748467\pi$
$828$	25.0089	+	32.9539i	0.869119	+	1.14523i
$829$	−38.2098	+	22.0604i	−1.32708	+	0.766191i	−0.984847	−	0.173424i	$-0.944517\pi$
$829$	−38.2098	+	22.0604i	−1.32708	+	0.766191i	−0.342234	+	0.939615i	$0.611184\pi$
$830$	−18.8953	+	82.5778i	−0.655865	+	2.86632i
$831$	4.20594	+	14.2118i	0.145903	+	0.493002i
$832$	28.4594	+	14.7083i	0.986652	+	0.509917i
$833$	−2.30702	+	13.0838i	−0.0799336	+	0.453326i
$834$	−0.613374	−	2.53586i	−0.0212394	−	0.0878096i
$835$	21.3840	+	25.4845i	0.740025	+	0.881927i
$836$	6.09186	+	6.25934i	0.210691	+	0.216484i
$837$	40.8810	−	6.81028i	1.41305	−	0.235398i
$838$	−7.58939	+	17.9767i	−0.262171	+	0.620995i
$839$	−28.2388	+	23.6951i	−0.974911	+	0.818047i	−0.983314	−	0.181917i	$-0.941770\pi$
$839$	−28.2388	+	23.6951i	−0.974911	+	0.818047i	0.00840301	+	0.999965i	$0.497325\pi$
$840$	0.197251	+	0.00750636i	0.00680580	+	0.000258994i
$841$	−1.12364	+	6.37246i	−0.0387461	+	0.219740i
$842$	−2.60514	+	51.6325i	−0.0897791	+	1.77937i
$843$	−7.60159	+	31.6288i	−0.261813	+	1.08935i
$844$	−19.5725	−	14.1041i	−0.673714	−	0.485484i
$845$	−10.3610	+	5.98194i	−0.356430	+	0.205785i
$846$	21.6364	+	25.7091i	0.743875	+	0.883896i
$847$	−0.0510619	+	0.0884417i	−0.00175451	+	0.00303889i
$848$	−8.39176	−	3.31470i	−0.288174	−	0.113827i
$849$	−37.1218	−	24.5834i	−1.27402	−	0.843701i
$850$	12.8858	+	25.1686i	0.441980	+	0.863275i
$851$	−34.0738	+	40.6075i	−1.16803	+	1.39201i
$852$	−3.01346	+	0.569894i	−0.103239	+	0.0195243i
$853$	−12.7574	+	35.0506i	−0.436804	+	1.20011i	0.504756	+	0.863262i	$0.331583\pi$
$853$	−12.7574	+	35.0506i	−0.436804	+	1.20011i	−0.941560	+	0.336846i	$0.890640\pi$
$854$	−0.000946338	−	0.00125076i	−3.23830e−5	−	4.28001e-5i
$855$	45.7593	+	23.3438i	1.56494	+	0.798340i
$856$	31.5270	+	25.2266i	1.07757	+	0.862226i
$857$	−2.38265	−	13.5127i	−0.0813899	−	0.461585i	−0.998077	−	0.0619803i	$-0.980258\pi$
$857$	−2.38265	−	13.5127i	−0.0813899	−	0.461585i	0.916687	−	0.399605i	$-0.130853\pi$
$858$	5.85150	−	7.93607i	0.199767	−	0.270933i
$859$	−10.4655	−	28.7538i	−0.357079	−	0.981067i	−0.980038	−	0.198812i	$-0.936292\pi$
$859$	−10.4655	−	28.7538i	−0.357079	−	0.981067i	0.622958	−	0.782255i	$-0.285931\pi$
$860$	−27.1582	+	18.4727i	−0.926087	+	0.629915i
$861$	0.0942669	+	0.0410158i	0.00321261	+	0.00139782i
$862$	−10.0660	+	3.09894i	−0.342850	+	0.105550i
$863$	−7.80840			−0.265801			−0.132900	−	0.991129i	$-0.542429\pi$
$863$	−7.80840			−0.265801			−0.132900	+	0.991129i	$0.542429\pi$
$864$	−28.3902	+	7.61550i	−0.965855	+	0.259085i
$865$	53.5863			1.82199
$866$	−28.3037	+	8.71360i	−0.961797	+	0.296100i
$867$	18.6573	−	13.7986i	0.633634	−	0.468625i
$868$	0.134842	−	0.0917180i	0.00457683	−	0.00311311i
$869$	1.10550	+	3.03735i	0.0375016	+	0.103035i
$870$	−57.1399	−	6.41175i	−1.93722	−	0.217379i
$871$	−2.67573	−	15.1748i	−0.0906636	−	0.514179i
$872$	−10.7867	−	8.63105i	−0.365283	−	0.292284i
$873$	38.0913	+	4.69596i	1.28920	+	0.158934i
$874$	25.5601	+	33.7824i	0.864584	+	1.14271i
$875$	−0.0762675	+	0.209543i	−0.00257831	+	0.00708385i
$876$	−16.6196	+	47.4822i	−0.561523	+	1.60428i
$877$	22.5373	−	26.8589i	0.761029	−	0.906959i	−0.236883	−	0.971538i	$-0.576126\pi$
$877$	22.5373	−	26.8589i	0.761029	−	0.906959i	0.997913	+	0.0645787i	$0.0205703\pi$
$878$	−18.1326	−	35.4166i	−0.611946	−	1.19525i
$879$	−1.54869	+	25.2195i	−0.0522359	+	0.850633i
$880$	5.82207	−	14.7396i	0.196262	−	0.496873i
$881$	−17.3596	+	30.0677i	−0.584859	+	1.01301i	0.410034	+	0.912070i	$0.365517\pi$
$881$	−17.3596	+	30.0677i	−0.584859	+	1.01301i	−0.994893	+	0.100936i	$0.967816\pi$
$882$	19.0564	−	22.7778i	0.641661	−	0.766969i
$883$	48.4749	−	27.9870i	1.63131	−	0.941837i	0.647620	−	0.761963i	$-0.275764\pi$
$883$	48.4749	−	27.9870i	1.63131	−	0.941837i	0.983690	−	0.179874i	$-0.0575690\pi$
$884$	−12.3323	−	8.88674i	−0.414779	−	0.298893i
$885$	32.5121	+	30.8679i	1.09288	+	1.03761i
$886$	−1.24689	+	24.7127i	−0.0418901	+	0.830238i
$887$	5.13500	−	29.1221i	0.172417	−	0.977823i	−0.768667	−	0.639649i	$-0.779080\pi$
$887$	5.13500	−	29.1221i	0.172417	−	0.977823i	0.941084	−	0.338174i	$-0.109809\pi$
$888$	−17.5783	−	33.3111i	−0.589889	−	1.11785i
$889$	0.0114860	−	0.00963792i	0.000385229	−	0.000323245i
$890$	6.30264	−	14.9289i	0.211265	−	0.500416i
$891$	0.936863	+	8.99840i	0.0313861	+	0.301458i
$892$	4.95104	+	5.08716i	0.165773	+	0.170331i
$893$	22.1175	+	26.3586i	0.740134	+	0.882057i
$894$	−4.90719	−	1.44449i	−0.164121	−	0.0483111i
$895$	0.203252	−	1.15270i	0.00679396	−	0.0385305i
$896$	−0.0888851	+	0.0740062i	−0.00296944	+	0.00247237i
$897$	32.9269	−	34.6807i	1.09940	−	1.15795i
$898$	1.88861	−	8.25377i	0.0630239	−	0.275432i
$899$	−41.1386	+	23.7514i	−1.37205	+	0.792154i
$900$	3.09300	−	63.1299i	0.103100	−	2.10433i
$901$	3.70763	+	2.14060i	0.123519	+	0.0713138i
$902$	5.61718	−	6.04726i	0.187032	−	0.201352i
$903$	0.00452220	−	0.0736415i	0.000150489	−	0.00245063i
$904$	−4.05033	+	11.9901i	−0.134712	+	0.398784i
$905$	−5.70454	−	4.78668i	−0.189625	−	0.159115i
$906$	1.61923	+	25.7546i	0.0537954	+	0.855640i
$907$	−11.8324	+	32.5093i	−0.392889	+	1.07945i	0.572787	+	0.819704i	$0.305862\pi$
$907$	−11.8324	+	32.5093i	−0.392889	+	1.07945i	−0.965676	+	0.259749i	$0.916360\pi$
$908$	5.34565	+	21.0900i	0.177402	+	0.699897i
$909$	−23.1451	+	9.81113i	−0.767673	+	0.325414i
$910$	−0.0282495	−	0.226428i	−0.000936461	−	0.00750600i
$911$	−2.10465	−	11.9361i	−0.0697303	−	0.395460i	−0.999619	−	0.0276180i	$-0.991208\pi$
$911$	−2.10465	−	11.9361i	−0.0697303	−	0.395460i	0.929888	−	0.367842i	$-0.119903\pi$
$912$	−29.0832	+	7.75596i	−0.963041	+	0.256826i
$913$	−14.3560	+	5.22516i	−0.475115	+	0.172928i
$914$	−18.6736	+	28.8778i	−0.617668	+	0.955191i
$915$	−0.595428	+	0.440368i	−0.0196843	+	0.0145581i
$916$	−1.58183	+	15.6356i	−0.0522651	+	0.516615i
$917$			0.116652i			0.00385218i
$918$	13.8556	−	1.59567i	0.457304	−	0.0526651i
$919$	11.2018			0.369514			0.184757	−	0.982784i	$-0.440850\pi$
$919$	11.2018			0.369514			0.184757	+	0.982784i	$0.440850\pi$
$920$	36.8704	−	67.4421i	1.21558	−	2.22350i
$921$	6.44404	−	14.8104i	0.212338	−	0.488018i
$922$	−19.0312	−	12.3064i	−0.626758	−	0.405288i
$923$	1.21254	+	3.33144i	0.0399114	+	0.109656i
$924$	0.0181796	+	0.0306069i	0.000598066	+	0.00100689i
$925$	79.7598	−	14.0638i	2.62249	−	0.462415i
$926$	0.125871	+	1.00889i	0.00413637	+	0.0331542i
$927$	−17.4949	+	11.3491i	−0.574607	+	0.372754i
$928$	27.4084	−	19.5920i	0.899724	−	0.643138i
$929$	33.5582	+	12.2142i	1.10101	+	0.400734i	0.827687	−	0.561189i	$-0.189656\pi$
$929$	33.5582	+	12.2142i	1.10101	+	0.400734i	0.273320	+	0.961923i	$0.411878\pi$
$930$	−42.6098	−	64.1389i	−1.39723	−	2.10320i
$931$	19.5479	−	23.2962i	0.640656	−	0.763504i
$932$	−3.56378	−	48.2628i	−0.116736	−	1.58090i
$933$	−7.68087	+	11.5984i	−0.251460	+	0.379713i
$934$	−18.7592	+	20.1955i	−0.613819	+	0.660816i
$935$	−3.75984	+	6.51224i	−0.122960	+	0.212973i
$936$	13.9863	+	30.9667i	0.457157	+	1.01218i
$937$	−13.9023	−	24.0795i	−0.454169	−	0.786643i	0.544471	−	0.838779i	$-0.316730\pi$
$937$	−13.9023	−	24.0795i	−0.454169	−	0.786643i	−0.998640	+	0.0521363i	$0.983397\pi$
$938$	0.0542308	+	0.0124090i	0.00177070	+	0.000405168i
$939$	13.3825	−	55.6819i	0.436720	−	1.81711i
$940$	27.1494	−	56.2192i	0.885516	−	1.83367i
$941$	−17.4040	−	3.06880i	−0.567355	−	0.100040i	−0.117390	−	0.993086i	$-0.537453\pi$
$941$	−17.4040	−	3.06880i	−0.567355	−	0.100040i	−0.449965	+	0.893046i	$0.648564\pi$
$942$	−39.5088	+	37.6205i	−1.28727	+	1.22574i
$943$	30.6650	−	25.7310i	0.998591	−	0.837917i
$944$	−26.2590	−	0.712264i	−0.854657	−	0.0231822i
$945$	0.159104	+	0.136090i	0.00517567	+	0.00442701i
$946$	−5.45708	−	2.30386i	−0.177425	−	0.0749050i
$947$	−31.1472	−	37.1197i	−1.01215	−	1.20623i	−0.978383	−	0.206800i	$-0.933695\pi$
$947$	−31.1472	−	37.1197i	−1.01215	−	1.20623i	−0.0337637	−	0.999430i	$-0.510749\pi$
$948$	−10.9926	−	1.79831i	−0.357023	−	0.0584065i
$949$	57.2701	+	10.0983i	1.85907	+	0.327804i
$950$	3.26149	−	64.6409i	0.105817	−	2.09723i
$951$	−12.8131	−	43.2951i	−0.415493	−	1.40394i
$952$	0.0468758	−	0.0285398i	0.00151925	−	0.000924981i
$953$	6.84000	+	11.8472i	0.221569	+	0.383770i	0.955285	−	0.295688i	$-0.0955487\pi$
$953$	6.84000	+	11.8472i	0.221569	+	0.383770i	−0.733715	+	0.679457i	$0.762215\pi$
$954$	−4.79708	−	8.28089i	−0.155311	−	0.268104i
$955$	−47.6310	−	27.4998i	−1.54130	−	0.889871i
$956$	24.7507	+	55.0134i	0.800495	+	1.77926i
$957$	−4.62460	−	9.28120i	−0.149492	−	0.300018i
$958$	−6.29288	−	12.2912i	−0.203314	−	0.397112i
$959$	0.0334435	+	0.0280625i	0.00107995	+	0.000906184i
$960$	34.4840	+	42.3489i	1.11297	+	1.36681i
$961$	−30.6492	−	11.1554i	−0.988684	−	0.359852i
$962$	−34.7212	+	26.2704i	−1.11946	+	0.846993i
$963$	9.61347	+	41.7337i	0.309790	+	1.34485i
$964$	−1.36120	+	4.81780i	−0.0438413	+	0.155171i
$965$	−37.0002	+	6.52413i	−1.19108	+	0.210019i
$966$	0.0691160	+	0.158219i	0.00222377	+	0.00509060i
$967$	28.0120	−	10.1955i	0.900806	−	0.327867i	0.150230	−	0.988651i	$-0.451999\pi$
$967$	28.0120	−	10.1955i	0.900806	−	0.327867i	0.750576	+	0.660785i	$0.229776\pi$
$968$	−27.7035	+	5.55316i	−0.890426	+	0.178485i
$969$	14.1907	−	1.61330i	0.455870	−	0.0518268i
$970$	−20.9813	−	68.1518i	−0.673669	−	2.18822i
$971$			31.5563i			1.01269i	0.862331	+	0.506345i	$0.169004\pi$
$971$			31.5563i			1.01269i	−0.862331	+	0.506345i	$0.830996\pi$
$972$	−28.6242	−	12.3554i	−0.918122	−	0.396299i
$973$		−	0.0108888i		−	0.000349078i
$974$	55.0373	−	16.9438i	1.76351	−	0.542916i
$975$	−72.5968	+	8.25336i	−2.32496	+	0.264319i
$976$	0.0869119	−	0.425144i	0.00278198	−	0.0136085i
$977$	26.2819	−	9.56585i	0.840834	−	0.306039i	0.114536	−	0.993419i	$-0.463462\pi$
$977$	26.2819	−	9.56585i	0.840834	−	0.306039i	0.726297	+	0.687381i	$0.241240\pi$
$978$	−19.4067	+	8.47759i	−0.620558	+	0.271083i
$979$	2.87804	−	0.507477i	0.0919827	−	0.0162190i
$980$	−53.0994	−	15.0025i	−1.69620	−	0.479237i
$981$	−3.28917	−	14.2788i	−0.105015	−	0.455888i
$982$	10.6686	+	14.1005i	0.340448	+	0.449964i
$983$	23.5384	+	8.56727i	0.750758	+	0.273253i	0.688925	−	0.724833i	$-0.258083\pi$
$983$	23.5384	+	8.56727i	0.750758	+	0.273253i	0.0618331	+	0.998087i	$0.480305\pi$
$984$	8.70456	+	27.0780i	0.277491	+	0.863214i
$985$	−26.5326	−	22.2635i	−0.845398	−	0.709373i
$986$	−14.2295	+	7.28523i	−0.453160	+	0.232009i
$987$	0.0625439	+	0.125521i	0.00199079	+	0.00399536i
$988$	14.2759	+	31.7311i	0.454177	+	1.00950i
$989$	−24.8801	−	14.3645i	−0.791141	−	0.456766i
$990$	14.5449	−	8.42578i	0.462267	−	0.267789i
$991$	11.3147	+	19.5976i	0.359422	+	0.622537i	0.987864	−	0.155319i	$-0.0496405\pi$
$991$	11.3147	+	19.5976i	0.359422	+	0.622537i	−0.628442	+	0.777856i	$0.716307\pi$
$992$	43.6932	+	11.2528i	1.38726	+	0.357277i
$993$	−1.36383	−	4.60836i	−0.0432799	−	0.146242i
$994$	−0.0127835		0.000644997i	−0.000405468		2.04581e-5i
$995$	−36.5628	−	6.44700i	−1.15912	−	0.204384i
$996$	8.49973	−	51.9565i	0.269324	−	1.64631i
$997$	6.16806	+	7.35081i	0.195344	+	0.232802i	0.854821	−	0.518922i	$-0.173667\pi$
$997$	6.16806	+	7.35081i	0.195344	+	0.232802i	−0.659477	+	0.751725i	$0.729222\pi$
$998$	2.51744	−	5.96297i	0.0796881	−	0.188754i
$999$	7.30904	−	39.2751i	0.231248	−	1.24261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.157.4	✓	204
3.2	odd	2		648.2.t.a.37.31		204
4.3	odd	2		864.2.bf.a.49.19		204
8.3	odd	2		864.2.bf.a.49.16		204
8.5	even	2	inner	216.2.t.a.157.13	yes	204
24.5	odd	2		648.2.t.a.37.22		204
27.11	odd	18		648.2.t.a.613.22		204
27.16	even	9	inner	216.2.t.a.205.13	yes	204
108.43	odd	18		864.2.bf.a.529.16		204
216.43	odd	18		864.2.bf.a.529.19		204
216.173	odd	18		648.2.t.a.613.31		204
216.205	even	18	inner	216.2.t.a.205.4	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.4	✓	204	1.1	even	1	trivial
216.2.t.a.157.13	yes	204	8.5	even	2	inner
216.2.t.a.205.4	yes	204	216.205	even	18	inner
216.2.t.a.205.13	yes	204	27.16	even	9	inner
648.2.t.a.37.22		204	24.5	odd	2
648.2.t.a.37.31		204	3.2	odd	2
648.2.t.a.613.22		204	27.11	odd	18
648.2.t.a.613.31		204	216.173	odd	18
864.2.bf.a.49.16		204	8.3	odd	2
864.2.bf.a.49.19		204	4.3	odd	2
864.2.bf.a.529.16		204	108.43	odd	18
864.2.bf.a.529.19		204	216.43	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35161 + 0.416109i) q^{2} +(-0.195652 - 1.72096i) q^{3} +(1.65371 - 1.12483i) q^{4} +(-1.34802 - 3.70366i) q^{5} +(0.980554 + 2.24466i) q^{6} +(0.00177522 + 0.0100678i) q^{7} +(-1.76712 + 2.20846i) q^{8} +(-2.92344 + 0.673422i) q^{9} +(3.36313 + 4.44499i) q^{10} +(-0.343808 + 0.944604i) q^{11} +(-2.25935 - 2.62590i) q^{12} +(-2.57400 + 3.06757i) q^{13} +(-0.00658870 - 0.0128690i) q^{14} +(-6.11013 + 3.04453i) q^{15} +(1.46950 - 3.72029i) q^{16} +(-0.948987 + 1.64369i) q^{17} +(3.67114 - 2.12667i) q^{18} +(3.76245 - 2.17225i) q^{19} +(-6.39524 - 4.60847i) q^{20} +(0.0169790 - 0.00502488i) q^{21} +(0.0716366 - 1.41980i) q^{22} +(1.19728 - 6.79010i) q^{23} +(4.14642 + 2.60905i) q^{24} +(-8.06972 + 6.77130i) q^{25} +(2.20260 - 5.21723i) q^{26} +(1.73091 + 4.89938i) q^{27} +(0.0142603 + 0.0146523i) q^{28} +(-3.82827 - 4.56236i) q^{29} +(6.99166 - 6.65750i) q^{30} +(1.38501 - 7.85480i) q^{31} +(-0.438140 + 5.63986i) q^{32} +(1.69290 + 0.406867i) q^{33} +(0.598707 - 2.61652i) q^{34} +(0.0348946 - 0.0201464i) q^{35} +(-4.07703 + 4.40203i) q^{36} +(-6.65823 - 3.84413i) q^{37} +(-4.18148 + 4.50163i) q^{38} +(5.78279 + 3.82958i) q^{39} +(10.5615 + 3.56775i) q^{40} +(4.44753 + 3.73192i) q^{41} +(-0.0208581 + 0.0138568i) q^{42} +(1.42511 - 3.91546i) q^{43} +(0.493966 + 1.94882i) q^{44} +(6.43499 + 9.91964i) q^{45} +(1.20716 + 9.67577i) q^{46} +(1.37530 + 7.79973i) q^{47} +(-6.69000 - 1.80107i) q^{48} +(6.57775 - 2.39411i) q^{49} +(8.08953 - 12.5100i) q^{50} +(3.01441 + 1.31158i) q^{51} +(-0.806130 + 7.96819i) q^{52} -2.25567i q^{53} +(-4.37820 - 5.90181i) q^{54} +3.96195 q^{55} +(-0.0253713 - 0.0138704i) q^{56} +(-4.47450 - 6.05004i) q^{57} +(7.07277 + 4.57356i) q^{58} +(-2.24610 - 6.17111i) q^{59} +(-6.67977 + 11.9076i) q^{60} +(0.106836 - 0.0188381i) q^{61} +(1.39645 + 11.1930i) q^{62} +(-0.0119696 - 0.0282371i) q^{63} +(-1.75460 - 7.80522i) q^{64} +(14.8311 + 5.39806i) q^{65} +(-2.45744 + 0.154503i) q^{66} +(-2.47342 + 2.94771i) q^{67} +(0.279537 + 3.78564i) q^{68} +(-11.9198 - 0.731973i) q^{69} +(-0.0387808 + 0.0417500i) q^{70} +(0.442665 - 0.766718i) q^{71} +(3.67883 - 7.64632i) q^{72} +(-7.26116 - 12.5767i) q^{73} +(10.5989 + 2.42523i) q^{74} +(13.2320 + 12.5629i) q^{75} +(3.77857 - 7.82441i) q^{76} +(-0.0101204 - 0.00178450i) q^{77} +(-9.40961 - 2.76984i) q^{78} +(2.46319 - 2.06686i) q^{79} +(-15.7596 - 0.427473i) q^{80} +(8.09301 - 3.93742i) q^{81} +(-7.56422 - 3.19345i) q^{82} +(9.76904 + 11.6423i) q^{83} +(0.0224261 - 0.0274082i) q^{84} +(7.36694 + 1.29899i) q^{85} +(-0.296940 + 5.88518i) q^{86} +(-7.10265 + 7.48096i) q^{87} +(-1.47857 - 2.42851i) q^{88} +(-1.45362 - 2.51775i) q^{89} +(-12.8253 - 10.7298i) q^{90} +(-0.0354530 - 0.0204688i) q^{91} +(-5.65779 - 12.5756i) q^{92} +(-13.7888 - 0.846748i) q^{93} +(-5.10441 - 9.96993i) q^{94} +(-13.1172 - 11.0066i) q^{95} +(9.79173 - 0.349428i) q^{96} +(-12.0217 - 4.37554i) q^{97} +(-7.89435 + 5.97296i) q^{98} +(0.368984 - 2.99302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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