LMFDB - Embedded newform 171.2.u.c.118.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(28,171)] 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("171.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			118.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	171.118
Dual form			171.2.u.c.100.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.826352 + 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(1.93969 - 1.62760i) q^{5} +(0.939693 - 1.62760i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(2.09240 - 0.761570i) q^{10} +(1.70574 + 2.95442i) q^{11} +(-0.918748 + 5.21048i) q^{13} +(1.26604 - 1.06234i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(1.55303 + 0.565258i) q^{17} +(-2.52094 - 3.55596i) q^{19} -3.10607 q^{20} +(0.520945 + 2.95442i) q^{22} +(-1.34730 - 1.13052i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-2.32635 + 4.02936i) q^{26} +(-2.16637 + 0.788496i) q^{28} +(-3.25877 + 1.18610i) q^{29} +(-0.971782 + 1.68317i) q^{31} +(-0.979055 + 5.55250i) q^{32} +(1.11334 + 0.934204i) q^{34} +(-0.826352 - 4.68647i) q^{35} -0.837496 q^{37} +(-1.01367 - 3.69669i) q^{38} +(-6.75150 - 2.45734i) q^{40} +(0.779715 + 4.42198i) q^{41} +(3.67752 - 3.08580i) q^{43} +(0.726682 - 4.12122i) q^{44} +(-0.773318 - 1.33943i) q^{46} +(0.673648 - 0.245188i) q^{47} +(1.73396 + 3.00330i) q^{49} +(0.620615 - 1.07494i) q^{50} +(4.97178 - 4.17182i) q^{52} +(4.67752 + 3.92490i) q^{53} +(8.11721 + 2.95442i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(-10.1099 - 3.67972i) q^{59} +(3.36231 + 2.82131i) q^{61} +(-1.30928 + 1.09861i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(6.69846 + 11.6021i) q^{65} +(-13.3550 + 4.86084i) q^{67} +(-1.01367 - 1.75573i) q^{68} +(0.726682 - 4.12122i) q^{70} +(10.5398 - 8.84397i) q^{71} +(-1.30541 - 7.40333i) q^{73} +(-0.692066 - 0.251892i) q^{74} +(-0.434945 + 5.32926i) q^{76} +6.41147 q^{77} +(-1.20914 - 6.85738i) q^{79} +(-0.0812519 - 0.0681784i) q^{80} +(-0.685670 + 3.88863i) q^{82} +(1.25624 - 2.17588i) q^{83} +(3.93242 - 1.43128i) q^{85} +(3.96703 - 1.44388i) q^{86} +(4.84002 - 8.38316i) q^{88} +(0.396459 - 2.24843i) q^{89} +(7.61721 + 6.39160i) q^{91} +(0.374638 + 2.12467i) q^{92} +0.630415 q^{94} +(-10.6775 - 2.79439i) q^{95} +(1.71301 + 0.623485i) q^{97} +(0.529563 + 3.00330i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8} + 9 q^{10} - 3 q^{13} + 3 q^{14} - 18 q^{16} - 3 q^{17} - 12 q^{19} + 6 q^{20} - 6 q^{23} - 15 q^{26} + 6 q^{28} + 3 q^{29} + 9 q^{31} - 9 q^{32} - 6 q^{35} + 15 q^{38}+ \cdots + 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8 + 9 * q^10 - 3 * q^13 + 3 * q^14 - 18 * q^16 - 3 * q^17 - 12 * q^19 + 6 * q^20 - 6 * q^23 - 15 * q^26 + 6 * q^28 + 3 * q^29 + 9 * q^31 - 9 * q^32 - 6 * q^35 + 15 * q^38 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 18 * q^46 + 3 * q^47 + 15 * q^49 + 15 * q^50 + 15 * q^52 + 3 * q^53 + 18 * q^55 + 6 * q^56 + 36 * q^58 - 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^64 + 12 * q^65 - 30 * q^67 + 15 * q^68 - 9 * q^70 + 6 * q^71 - 12 * q^73 - 15 * q^74 + 36 * q^76 + 18 * q^77 - 39 * q^79 - 3 * q^80 - 54 * q^82 - 24 * q^86 + 9 * q^88 + 12 * q^89 + 15 * q^91 - 42 * q^92 + 18 * q^94 - 39 * q^95 + 18 * q^97 + 9 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.826352	+	0.300767i	0.584319	+	0.212675i	0.617229	−	0.786784i	$-0.288255\pi$
$2$	0.826352	+	0.300767i	0.584319	+	0.212675i	−0.0329100	+	0.999458i	$0.510477\pi$
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.788496i	−0.469846	−	0.394248i
$5$	1.93969	−	1.62760i	0.867457	−	0.727883i	−0.0961041	−	0.995371i	$-0.530638\pi$
$5$	1.93969	−	1.62760i	0.867457	−	0.727883i	0.963561	+	0.267489i	$0.0861937\pi$
$6$		0			0
$7$	0.939693	−	1.62760i	0.355170	−	0.615173i	−0.631977	−	0.774987i	$-0.717756\pi$
$7$	0.939693	−	1.62760i	0.355170	−	0.615173i	0.987147	+	0.159814i	$0.0510895\pi$
$8$	−1.41875	−	2.45734i	−0.501603	−	0.868802i
$9$		0			0
$10$	2.09240	−	0.761570i	0.661674	−	0.240830i
$11$	1.70574	+	2.95442i	0.514299	+	0.890792i	0.999862	+	0.0165906i	$0.00528120\pi$
$11$	1.70574	+	2.95442i	0.514299	+	0.890792i	−0.485563	+	0.874202i	$0.661385\pi$
$12$		0			0
$13$	−0.918748	+	5.21048i	−0.254815	+	1.44513i	0.541733	+	0.840551i	$0.317769\pi$
$13$	−0.918748	+	5.21048i	−0.254815	+	1.44513i	−0.796547	+	0.604576i	$0.793343\pi$
$14$	1.26604	−	1.06234i	0.338365	−	0.283922i
$15$		0			0
$16$	−0.00727396	−	0.0412527i	−0.00181849	−	0.0103132i
$17$	1.55303	+	0.565258i	0.376666	+	0.137095i	0.523414	−	0.852079i	$-0.324658\pi$
$17$	1.55303	+	0.565258i	0.376666	+	0.137095i	−0.146748	+	0.989174i	$0.546881\pi$
$18$		0			0
$19$	−2.52094	−	3.55596i	−0.578344	−	0.815793i
$19$	−2.52094	−	3.55596i	−0.578344	−	0.815793i
$20$	−3.10607			−0.694538
$21$		0			0
$22$	0.520945	+	2.95442i	0.111066	+	0.629885i
$23$	−1.34730	−	1.13052i	−0.280931	−	0.235729i	0.491424	−	0.870921i	$-0.336477\pi$
$23$	−1.34730	−	1.13052i	−0.280931	−	0.235729i	−0.772354	+	0.635192i	$0.780921\pi$
$24$		0			0
$25$	0.245100	−	1.39003i	0.0490200	−	0.278006i
$26$	−2.32635	+	4.02936i	−0.456235	+	0.790222i
$27$		0			0
$28$	−2.16637	+	0.788496i	−0.409406	+	0.149012i
$29$	−3.25877	+	1.18610i	−0.605138	+	0.220252i	−0.626375	−	0.779522i	$-0.715462\pi$
$29$	−3.25877	+	1.18610i	−0.605138	+	0.220252i	0.0212363	+	0.999774i	$0.493240\pi$
$30$		0			0
$31$	−0.971782	+	1.68317i	−0.174537	+	0.302307i	−0.940001	−	0.341172i	$-0.889176\pi$
$31$	−0.971782	+	1.68317i	−0.174537	+	0.302307i	0.765464	+	0.643479i	$0.222510\pi$
$32$	−0.979055	+	5.55250i	−0.173074	+	0.981553i
$33$		0			0
$34$	1.11334	+	0.934204i	0.190936	+	0.160215i
$35$	−0.826352	−	4.68647i	−0.139679	−	0.792159i
$36$		0			0
$37$	−0.837496			−0.137684			−0.0688418	−	0.997628i	$-0.521930\pi$
$37$	−0.837496			−0.137684			−0.0688418	+	0.997628i	$0.521930\pi$
$38$	−1.01367	−	3.69669i	−0.164439	−	0.599682i
$39$		0			0
$40$	−6.75150	−	2.45734i	−1.06751	−	0.388540i
$41$	0.779715	+	4.42198i	0.121771	+	0.690598i	0.983173	+	0.182675i	$0.0584755\pi$
$41$	0.779715	+	4.42198i	0.121771	+	0.690598i	−0.861402	+	0.507923i	$0.830413\pi$
$42$		0			0
$43$	3.67752	−	3.08580i	0.560816	−	0.470581i	−0.317768	−	0.948169i	$-0.602933\pi$
$43$	3.67752	−	3.08580i	0.560816	−	0.470581i	0.878584	+	0.477588i	$0.158489\pi$
$44$	0.726682	−	4.12122i	0.109551	−	0.621297i
$45$		0			0
$46$	−0.773318	−	1.33943i	−0.114020	−	0.197488i
$47$	0.673648	−	0.245188i	0.0982617	−	0.0357643i	−0.292422	−	0.956290i	$-0.594461\pi$
$47$	0.673648	−	0.245188i	0.0982617	−	0.0357643i	0.390683	+	0.920525i	$0.372239\pi$
$48$		0			0
$49$	1.73396	+	3.00330i	0.247708	+	0.429043i
$50$	0.620615	−	1.07494i	0.0877682	−	0.152019i
$51$		0			0
$52$	4.97178	−	4.17182i	0.689462	−	0.578527i
$53$	4.67752	+	3.92490i	0.642507	+	0.539127i	0.904787	−	0.425865i	$-0.140030\pi$
$53$	4.67752	+	3.92490i	0.642507	+	0.539127i	−0.262280	+	0.964992i	$0.584474\pi$
$54$		0			0
$55$	8.11721	+	2.95442i	1.09452	+	0.398374i
$56$	−5.33275			−0.712618
$57$		0			0
$58$	−3.04963			−0.400436
$59$	−10.1099	−	3.67972i	−1.31620	−	0.479058i	−0.413962	−	0.910294i	$-0.635856\pi$
$59$	−10.1099	−	3.67972i	−1.31620	−	0.479058i	−0.902239	+	0.431236i	$0.858078\pi$
$60$		0			0
$61$	3.36231	+	2.82131i	0.430500	+	0.361232i	0.832140	−	0.554565i	$-0.187115\pi$
$61$	3.36231	+	2.82131i	0.430500	+	0.361232i	−0.401640	+	0.915797i	$0.631560\pi$
$62$	−1.30928	+	1.09861i	−0.166278	+	0.139524i
$63$		0			0
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	6.69846	+	11.6021i	0.830842	+	1.43906i
$66$		0			0
$67$	−13.3550	+	4.86084i	−1.63158	+	0.593846i	−0.985537	−	0.169458i	$-0.945798\pi$
$67$	−13.3550	+	4.86084i	−1.63158	+	0.593846i	−0.646040	+	0.763304i	$0.723576\pi$
$68$	−1.01367	−	1.75573i	−0.122926	−	0.212913i
$69$		0			0
$70$	0.726682	−	4.12122i	0.0868551	−	0.492580i
$71$	10.5398	−	8.84397i	1.25085	−	1.04959i	0.254252	−	0.967138i	$-0.418171\pi$
$71$	10.5398	−	8.84397i	1.25085	−	1.04959i	0.996595	−	0.0824479i	$-0.0262738\pi$
$72$		0			0
$73$	−1.30541	−	7.40333i	−0.152786	−	0.866495i	−0.960782	−	0.277306i	$-0.910559\pi$
$73$	−1.30541	−	7.40333i	−0.152786	−	0.866495i	0.807995	−	0.589189i	$-0.200553\pi$
$74$	−0.692066	−	0.251892i	−0.0804511	−	0.0292818i
$75$		0			0
$76$	−0.434945	+	5.32926i	−0.0498916	+	0.611308i
$77$	6.41147			0.730655
$78$		0			0
$79$	−1.20914	−	6.85738i	−0.136039	−	0.771515i	−0.974131	−	0.225986i	$-0.927440\pi$
$79$	−1.20914	−	6.85738i	−0.136039	−	0.771515i	0.838092	−	0.545529i	$-0.183671\pi$
$80$	−0.0812519	−	0.0681784i	−0.00908424	−	0.00762258i
$81$		0			0
$82$	−0.685670	+	3.88863i	−0.0757196	+	0.429427i
$83$	1.25624	−	2.17588i	0.137891	−	0.238834i	−0.788807	−	0.614641i	$-0.789301\pi$
$83$	1.25624	−	2.17588i	0.137891	−	0.238834i	0.926698	+	0.375807i	$0.122634\pi$
$84$		0			0
$85$	3.93242	−	1.43128i	0.426531	−	0.155244i
$86$	3.96703	−	1.44388i	0.427776	−	0.155698i
$87$		0			0
$88$	4.84002	−	8.38316i	0.515948	−	0.893648i
$89$	0.396459	−	2.24843i	0.0420246	−	0.238333i	−0.956559	−	0.291539i	$-0.905833\pi$
$89$	0.396459	−	2.24843i	0.0420246	−	0.238333i	0.998584	+	0.0532055i	$0.0169438\pi$
$90$		0			0
$91$	7.61721	+	6.39160i	0.798501	+	0.670022i
$92$	0.374638	+	2.12467i	0.0390587	+	0.221513i
$93$		0			0
$94$	0.630415			0.0650223
$95$	−10.6775	−	2.79439i	−1.09549	−	0.286698i
$96$		0			0
$97$	1.71301	+	0.623485i	0.173930	+	0.0633053i	0.427517	−	0.904007i	$-0.359388\pi$
$97$	1.71301	+	0.623485i	0.173930	+	0.0633053i	−0.253587	+	0.967312i	$0.581611\pi$
$98$	0.529563	+	3.00330i	0.0534939	+	0.303379i
$99$		0			0
$100$	−1.32635	+	1.11294i	−0.132635	+	0.111294i
$101$	1.37551	−	7.80093i	0.136869	−	0.776222i	−0.836671	−	0.547705i	$-0.815501\pi$
$101$	1.37551	−	7.80093i	0.136869	−	0.776222i	0.973540	−	0.228516i	$-0.0733874\pi$
$102$		0			0
$103$	0.00727396	+	0.0125989i	0.000716725	+	0.00124140i	0.866384	−	0.499379i	$-0.166439\pi$
$103$	0.00727396	+	0.0125989i	0.000716725	+	0.00124140i	−0.865667	+	0.500621i	$0.833105\pi$
$104$	14.1074	−	5.13468i	1.38335	−	0.503497i
$105$		0			0
$106$	2.68479	+	4.65020i	0.260770	+	0.451667i
$107$	−1.77719	+	3.07818i	−0.171807	+	0.297579i	−0.939052	−	0.343776i	$-0.888294\pi$
$107$	−1.77719	+	3.07818i	−0.171807	+	0.297579i	0.767244	+	0.641355i	$0.221627\pi$
$108$		0			0
$109$	5.64543	−	4.73708i	0.540734	−	0.453730i	−0.331055	−	0.943612i	$-0.607404\pi$
$109$	5.64543	−	4.73708i	0.540734	−	0.453730i	0.871789	+	0.489882i	$0.162960\pi$
$110$	5.81908	+	4.88279i	0.554827	+	0.465555i
$111$		0			0
$112$	−0.0739780	−	0.0269258i	−0.00699026	−	0.00254425i
$113$	−7.37733			−0.694000			−0.347000	−	0.937865i	$-0.612800\pi$
$113$	−7.37733			−0.694000			−0.347000	+	0.937865i	$0.612800\pi$
$114$		0			0
$115$	−4.45336			−0.415278
$116$	3.99747	+	1.45496i	0.371156	+	0.135090i
$117$		0			0
$118$	−7.24763	−	6.08148i	−0.667198	−	0.559846i
$119$	2.37939	−	1.99654i	0.218118	−	0.183023i
$120$		0			0
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$	1.92989	+	3.34267i	0.174724	+	0.302631i
$123$		0			0
$124$	2.24035	−	0.815422i	0.201190	−	0.0732270i
$125$	4.54323	+	7.86911i	0.406359	+	0.703835i
$126$		0			0
$127$	−0.0175410	+	0.0994798i	−0.00155651	+	0.00882740i	−0.985576	−	0.169233i	$-0.945871\pi$
$127$	−0.0175410	+	0.0994798i	−0.00155651	+	0.00882740i	0.984020	+	0.178060i	$0.0569822\pi$
$128$	5.24170	−	4.39831i	0.463305	−	0.388759i
$129$		0			0
$130$	2.04576	+	11.6021i	0.179425	+	1.01757i
$131$	−2.85369	−	1.03866i	−0.249328	−	0.0907481i	0.214333	−	0.976761i	$-0.431242\pi$
$131$	−2.85369	−	1.03866i	−0.249328	−	0.0907481i	−0.463661	+	0.886013i	$0.653464\pi$
$132$		0			0
$133$	−8.15657	+	0.761570i	−0.707265	+	0.0660365i
$134$	−12.4979			−1.07966
$135$		0			0
$136$	−0.814330	−	4.61830i	−0.0698282	−	0.396016i
$137$	−14.9684	−	12.5600i	−1.27883	−	1.07307i	−0.993404	−	0.114671i	$-0.963419\pi$
$137$	−14.9684	−	12.5600i	−1.27883	−	1.07307i	−0.285431	−	0.958399i	$-0.592137\pi$
$138$		0			0
$139$	2.67365	−	15.1630i	0.226776	−	1.28611i	−0.632485	−	0.774573i	$-0.717965\pi$
$139$	2.67365	−	15.1630i	0.226776	−	1.28611i	0.859261	−	0.511537i	$-0.170924\pi$
$140$	−2.91875	+	5.05542i	−0.246679	+	0.427261i
$141$		0			0
$142$	11.3696	−	4.13819i	0.954114	−	0.347269i
$143$	−16.9611	+	6.17334i	−1.41836	+	0.516240i
$144$		0			0
$145$	−4.39053	+	7.60462i	−0.364614	+	0.631529i
$146$	1.14796	−	6.51038i	0.0950055	−	0.538803i
$147$		0			0
$148$	0.786989	+	0.660362i	0.0646901	+	0.0542814i
$149$	0.654048	+	3.70929i	0.0535817	+	0.303877i	0.999807	−	0.0196306i	$-0.00624903\pi$
$149$	0.654048	+	3.70929i	0.0535817	+	0.303877i	−0.946226	+	0.323507i	$0.895138\pi$
$150$		0			0
$151$	−14.5963			−1.18783			−0.593914	−	0.804529i	$-0.702418\pi$
$151$	−14.5963			−1.18783			−0.593914	+	0.804529i	$0.702418\pi$
$152$	−5.16163	+	11.2398i	−0.418663	+	0.911671i
$153$		0			0
$154$	5.29813	+	1.92836i	0.426936	+	0.155392i
$155$	0.854570	+	4.84651i	0.0686407	+	0.389281i
$156$		0			0
$157$	−7.94743	+	6.66869i	−0.634274	+	0.532219i	−0.902254	−	0.431205i	$-0.858088\pi$
$157$	−7.94743	+	6.66869i	−0.634274	+	0.532219i	0.267980	+	0.963425i	$0.413644\pi$
$158$	1.06330	−	6.03028i	0.0845916	−	0.479743i
$159$		0			0
$160$	7.13816	+	12.3636i	0.564321	+	0.977432i
$161$	−3.10607	+	1.13052i	−0.244792	+	0.0890971i
$162$		0			0
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	0.902905	−	0.429841i	$-0.141430\pi$
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	−0.823706	+	0.567018i	$0.808097\pi$
$164$	2.75402	−	4.77011i	0.215053	−	0.372483i
$165$		0			0
$166$	1.69253	−	1.42020i	0.131366	−	0.110229i
$167$	17.8157	+	14.9491i	1.37862	+	1.15680i	0.969720	+	0.244218i	$0.0785312\pi$
$167$	17.8157	+	14.9491i	1.37862	+	1.15680i	0.408898	+	0.912580i	$0.365913\pi$
$168$		0			0
$169$	−14.0890	−	5.12797i	−1.08377	−	0.394460i
$170$	3.68004			0.282247
$171$		0			0
$172$	−5.88888			−0.449023
$173$	0.842549	+	0.306663i	0.0640578	+	0.0233151i	0.373850	−	0.927489i	$-0.378037\pi$
$173$	0.842549	+	0.306663i	0.0640578	+	0.0233151i	−0.309793	+	0.950804i	$0.600260\pi$
$174$		0			0
$175$	−2.03209	−	1.70513i	−0.153611	−	0.128895i
$176$	0.109470	−	0.0918566i	0.00825164	−	0.00692395i
$177$		0			0
$178$	1.00387	−	1.73875i	0.0752433	−	0.130325i
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	−0.921755	−	0.387773i	$-0.873245\pi$
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	0.125056	−	0.992150i	$-0.460089\pi$
$180$		0			0
$181$	15.1284	−	5.50627i	1.12448	−	0.409278i	0.288196	−	0.957571i	$-0.406945\pi$
$181$	15.1284	−	5.50627i	1.12448	−	0.409278i	0.836286	+	0.548294i	$0.184722\pi$
$182$	4.37211	+	7.57272i	0.324082	+	0.561327i
$183$		0			0
$184$	−0.866592	+	4.91469i	−0.0638860	+	0.362316i
$185$	−1.62449	+	1.36310i	−0.119435	+	0.100217i
$186$		0			0
$187$	0.979055	+	5.55250i	0.0715956	+	0.406039i
$188$	−0.826352	−	0.300767i	−0.0602679	−	0.0219357i
$189$		0			0
$190$	−7.98293	−	5.52060i	−0.579142	−	0.400506i
$191$	−18.9486			−1.37107			−0.685537	−	0.728038i	$-0.740432\pi$
$191$	−18.9486			−1.37107			−0.685537	+	0.728038i	$0.740432\pi$
$192$		0			0
$193$	2.24035	+	12.7057i	0.161264	+	0.914574i	0.952833	+	0.303494i	$0.0981534\pi$
$193$	2.24035	+	12.7057i	0.161264	+	0.914574i	−0.791569	+	0.611080i	$0.790736\pi$
$194$	1.22803	+	1.03044i	0.0881671	+	0.0739810i
$195$		0			0
$196$	0.738703	−	4.18939i	0.0527645	−	0.299242i
$197$	−11.6001	+	20.0920i	−0.826476	+	1.43150i	0.0743108	+	0.997235i	$0.476324\pi$
$197$	−11.6001	+	20.0920i	−0.826476	+	1.43150i	−0.900786	+	0.434263i	$0.857009\pi$
$198$		0			0
$199$	−8.66550	+	3.15398i	−0.614281	+	0.223580i	−0.630375	−	0.776291i	$-0.717099\pi$
$199$	−8.66550	+	3.15398i	−0.614281	+	0.223580i	0.0160945	+	0.999870i	$0.494877\pi$
$200$	−3.76352	+	1.36981i	−0.266121	+	0.0968601i
$201$		0			0
$202$	3.48293	−	6.03260i	0.245058	−	0.424453i
$203$	−1.13176	+	6.41852i	−0.0794339	+	0.450492i
$204$		0			0
$205$	8.70961	+	7.30823i	0.608305	+	0.510429i
$206$	0.00222152	+	0.0125989i	0.000154781	+	0.000877805i
$207$		0			0
$208$	0.221629			0.0153672
$209$	6.20574	−	13.5135i	0.429260	−	0.934746i
$210$		0			0
$211$	−13.7417	−	5.00157i	−0.946017	−	0.344322i	−0.177478	−	0.984125i	$-0.556794\pi$
$211$	−13.7417	−	5.00157i	−0.946017	−	0.344322i	−0.768539	+	0.639803i	$0.779016\pi$
$212$	−1.30066	−	7.37641i	−0.0893297	−	0.506614i
$213$		0			0
$214$	−2.39440	+	2.00914i	−0.163678	+	0.137342i
$215$	2.11081	−	11.9710i	0.143956	−	0.816417i
$216$		0			0
$217$	1.82635	+	3.16333i	0.123981	+	0.214741i
$218$	6.08987	−	2.21653i	0.412458	−	0.150122i
$219$		0			0
$220$	−5.29813	−	9.17664i	−0.357200	−	0.618689i
$221$	−4.37211	+	7.57272i	−0.294100	+	0.509396i
$222$		0			0
$223$	−2.30928	+	1.93771i	−0.154641	+	0.129759i	−0.716825	−	0.697253i	$-0.754405\pi$
$223$	−2.30928	+	1.93771i	−0.154641	+	0.129759i	0.562185	+	0.827012i	$0.309961\pi$
$224$	8.11721	+	6.81115i	0.542354	+	0.455089i
$225$		0			0
$226$	−6.09627	−	2.21886i	−0.405518	−	0.147596i
$227$	13.7219			0.910757			0.455378	−	0.890298i	$-0.349504\pi$
$227$	13.7219			0.910757			0.455378	+	0.890298i	$0.349504\pi$
$228$		0			0
$229$	9.41416			0.622105			0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416			0.622105			0.311053	+	0.950393i	$0.399318\pi$
$230$	−3.68004	−	1.33943i	−0.242655	−	0.0883192i
$231$		0			0
$232$	7.53802	+	6.32515i	0.494895	+	0.415266i
$233$	18.5273	−	15.5463i	1.21377	−	1.01847i	0.214640	−	0.976693i	$-0.431142\pi$
$233$	18.5273	−	15.5463i	1.21377	−	1.01847i	0.999127	−	0.0417777i	$-0.0133021\pi$
$234$		0			0
$235$	0.907604	−	1.57202i	0.0592055	−	0.102547i
$236$	6.59879	+	11.4294i	0.429545	+	0.743993i
$237$		0			0
$238$	2.56670	−	0.934204i	0.166375	−	0.0605554i
$239$	−11.6630	−	20.2009i	−0.754415	−	1.30668i	−0.945665	−	0.325143i	$-0.894587\pi$
$239$	−11.6630	−	20.2009i	−0.754415	−	1.30668i	0.191250	−	0.981541i	$-0.438746\pi$
$240$		0			0
$241$	0.0516892	−	0.293144i	0.00332960	−	0.0188831i	−0.983098	−	0.183082i	$-0.941393\pi$
$241$	0.0516892	−	0.293144i	0.00332960	−	0.0188831i	0.986427	+	0.164199i	$0.0525038\pi$
$242$	−0.429892	+	0.360723i	−0.0276345	+	0.0231881i
$243$		0			0
$244$	−0.934945	−	5.30234i	−0.0598537	−	0.339447i
$245$	8.25150	+	3.00330i	0.527169	+	0.191874i
$246$		0			0
$247$	20.8444	−	9.86830i	1.32629	−	0.627905i
$248$	5.51485			0.350193
$249$		0			0
$250$	1.38754	+	7.86911i	0.0877555	+	0.497686i
$251$	12.4081	+	10.4116i	0.783190	+	0.657175i	0.944050	−	0.329802i	$-0.106982\pi$
$251$	12.4081	+	10.4116i	0.783190	+	0.657175i	−0.160859	+	0.986977i	$0.551427\pi$
$252$		0			0
$253$	1.04189	−	5.90885i	0.0655030	−	0.371486i
$254$	−0.0444153	+	0.0769295i	−0.00278686	+	0.00482699i
$255$		0			0
$256$	15.1300	−	5.50687i	0.945625	−	0.344179i
$257$	14.4290	−	5.25173i	0.900057	−	0.327594i	0.149782	−	0.988719i	$-0.452143\pi$
$257$	14.4290	−	5.25173i	0.900057	−	0.327594i	0.750276	+	0.661125i	$0.229921\pi$
$258$		0			0
$259$	−0.786989	+	1.36310i	−0.0489011	+	0.0846992i
$260$	2.85369	−	16.1841i	0.176979	−	1.00370i
$261$		0			0
$262$	−2.04576	−	1.71660i	−0.126387	−	0.106052i
$263$	−1.67453	−	9.49671i	−0.103256	−	0.585592i	−0.991903	−	0.127000i	$-0.959465\pi$
$263$	−1.67453	−	9.49671i	−0.103256	−	0.585592i	0.888647	−	0.458592i	$-0.151646\pi$
$264$		0			0
$265$	15.4611			0.949768
$266$	−6.96926	−	1.82391i	−0.427312	−	0.111831i
$267$		0			0
$268$	16.3824	+	5.96270i	1.00071	+	0.364230i
$269$	3.17412	+	18.0013i	0.193529	+	1.09756i	0.914498	+	0.404591i	$0.132586\pi$
$269$	3.17412	+	18.0013i	0.193529	+	1.09756i	−0.720969	+	0.692968i	$0.756303\pi$
$270$		0			0
$271$	14.5273	−	12.1899i	0.882473	−	0.740483i	−0.0842129	−	0.996448i	$-0.526838\pi$
$271$	14.5273	−	12.1899i	0.882473	−	0.740483i	0.966686	+	0.255965i	$0.0823932\pi$
$272$	0.0120217	−	0.0681784i	0.000728923	−	0.00413393i
$273$		0			0
$274$	−8.59152	−	14.8809i	−0.519033	−	0.898991i
$275$	4.52481	−	1.64690i	0.272857	−	0.0993117i
$276$		0			0
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	0.581775	−	0.813350i	$-0.302358\pi$
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	−0.995269	+	0.0971571i	$0.969025\pi$
$278$	6.76991	−	11.7258i	0.406033	−	0.703269i
$279$		0			0
$280$	−10.3439	+	8.67956i	−0.618166	+	0.518703i
$281$	−10.0437	−	8.42767i	−0.599157	−	0.502752i	0.292018	−	0.956413i	$-0.405673\pi$
$281$	−10.0437	−	8.42767i	−0.599157	−	0.502752i	−0.891175	+	0.453661i	$0.850118\pi$
$282$		0			0
$283$	16.3293	+	5.94340i	0.970679	+	0.353298i	0.778209	−	0.628005i	$-0.216128\pi$
$283$	16.3293	+	5.94340i	0.970679	+	0.353298i	0.192469	+	0.981303i	$0.438350\pi$
$284$	−16.8776			−1.00150
$285$		0			0
$286$	−15.8726			−0.938565
$287$	7.92989	+	2.88624i	0.468087	+	0.170370i
$288$		0			0
$289$	−10.9304	−	9.17166i	−0.642962	−	0.539509i
$290$	−5.91534	+	4.96356i	−0.347361	+	0.291470i
$291$		0			0
$292$	−4.61081	+	7.98617i	−0.269828	+	0.467355i
$293$	7.80200	+	13.5135i	0.455798	+	0.789465i	0.998734	−	0.0503091i	$-0.0160206\pi$
$293$	7.80200	+	13.5135i	0.455798	+	0.789465i	−0.542936	+	0.839774i	$0.682687\pi$
$294$		0			0
$295$	−25.5993	+	9.31737i	−1.49045	+	0.542478i
$296$	1.18820	+	2.05802i	0.0690625	+	0.119620i
$297$		0			0
$298$	−0.575160	+	3.26189i	−0.0333181	+	0.188956i
$299$	7.12836	−	5.98140i	0.412243	−	0.345913i
$300$		0			0
$301$	−1.56670	−	8.88522i	−0.0903033	−	0.512136i
$302$	−12.0617	−	4.39008i	−0.694070	−	0.252621i
$303$		0			0
$304$	−0.128356	+	0.129862i	−0.00736170	+	0.00744807i
$305$	11.1138			0.636375
$306$		0			0
$307$	3.73695	+	21.1933i	0.213279	+	1.20956i	0.883868	+	0.467736i	$0.154930\pi$
$307$	3.73695	+	21.1933i	0.213279	+	1.20956i	−0.670589	+	0.741829i	$0.733959\pi$
$308$	−6.02481	−	5.05542i	−0.343296	−	0.288059i
$309$		0			0
$310$	−0.751497	+	4.26195i	−0.0426821	+	0.242062i
$311$	7.24763	−	12.5533i	0.410975	−	0.711830i	−0.584021	−	0.811738i	$-0.698522\pi$
$311$	7.24763	−	12.5533i	0.410975	−	0.711830i	0.994997	+	0.0999083i	$0.0318550\pi$
$312$		0			0
$313$	−18.3414	+	6.67571i	−1.03672	+	0.377334i	−0.803634	−	0.595124i	$-0.797103\pi$
$313$	−18.3414	+	6.67571i	−1.03672	+	0.377334i	−0.233081	+	0.972457i	$0.574881\pi$
$314$	−8.57310	+	3.12035i	−0.483808	+	0.176092i
$315$		0			0
$316$	−4.27079	+	7.39723i	−0.240251	+	0.416127i
$317$	−4.92246	+	27.9166i	−0.276473	+	1.56795i	0.457772	+	0.889070i	$0.348648\pi$
$317$	−4.92246	+	27.9166i	−0.276473	+	1.56795i	−0.734245	+	0.678885i	$0.762464\pi$
$318$		0			0
$319$	−9.06283	−	7.60462i	−0.507421	−	0.425777i
$320$	2.21688	+	12.5726i	0.123927	+	0.702827i
$321$		0			0
$322$	−2.90673			−0.161986
$323$	−1.90508	−	6.94751i	−0.106001	−	0.386570i
$324$		0			0
$325$	7.01754	+	2.55418i	0.389263	+	0.141680i
$326$	0.308811	+	1.75135i	0.0171035	+	0.0969985i
$327$		0			0
$328$	9.76011	−	8.18971i	0.538912	−	0.452201i
$329$	0.233956	−	1.32683i	0.0128984	−	0.0731504i
$330$		0			0
$331$	0.855037	+	1.48097i	0.0469971	+	0.0814014i	0.888567	−	0.458747i	$-0.151702\pi$
$331$	0.855037	+	1.48097i	0.0469971	+	0.0814014i	−0.841570	+	0.540148i	$0.818368\pi$
$332$	−2.89615	+	1.05411i	−0.158947	+	0.0578520i
$333$		0			0
$334$	10.2258	+	17.7116i	0.559531	+	0.969136i
$335$	−17.9932	+	31.1651i	−0.983073	+	1.70273i
$336$		0			0
$337$	19.4873	−	16.3518i	1.06154	−	0.890737i	0.0672796	−	0.997734i	$-0.478568\pi$
$337$	19.4873	−	16.3518i	1.06154	−	0.890737i	0.994259	+	0.106997i	$0.0341236\pi$
$338$	−10.1001	−	8.47502i	−0.549375	−	0.460980i
$339$		0			0
$340$	−4.82383	−	1.75573i	−0.261609	−	0.0952178i
$341$	−6.63041			−0.359057
$342$		0			0
$343$	19.6732			1.06225
$344$	−12.8004	−	4.65895i	−0.690149	−	0.251194i
$345$		0			0
$346$	0.604007	+	0.506822i	0.0324716	+	0.0272469i
$347$	−5.90033	+	4.95096i	−0.316746	+	0.265782i	−0.787274	−	0.616604i	$-0.788508\pi$
$347$	−5.90033	+	4.95096i	−0.316746	+	0.265782i	0.470527	+	0.882385i	$0.344064\pi$
$348$		0			0
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	0.382315	+	0.924032i	$0.375127\pi$
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	−0.991393	+	0.130921i	$0.958206\pi$
$350$	−1.16637	−	2.02022i	−0.0623453	−	0.107985i
$351$		0			0
$352$	−18.0744	+	6.57856i	−0.963371	+	0.350638i
$353$	−5.72281	−	9.91220i	−0.304595	−	0.527573i	0.672576	−	0.740028i	$-0.265188\pi$
$353$	−5.72281	−	9.91220i	−0.304595	−	0.527573i	−0.977171	+	0.212454i	$0.931854\pi$
$354$		0			0
$355$	6.04963	−	34.3092i	0.321081	−	1.82094i
$356$	−2.14543	+	1.80023i	−0.113708	+	0.0954120i
$357$		0			0
$358$	−3.25537	−	18.4621i	−0.172051	−	0.975752i
$359$	9.75789	+	3.55158i	0.515002	+	0.187445i	0.586429	−	0.810000i	$-0.300533\pi$
$359$	9.75789	+	3.55158i	0.515002	+	0.187445i	−0.0714274	+	0.997446i	$0.522755\pi$
$360$		0			0
$361$	−6.28968	+	17.9287i	−0.331036	+	0.943618i
$362$	14.1575			0.744099
$363$		0			0
$364$	−2.11809	−	12.0123i	−0.111018	−	0.629614i
$365$	−14.5817	−	12.2355i	−0.763242	−	0.640436i
$366$		0			0
$367$	−5.64930	+	32.0388i	−0.294891	+	1.67241i	0.372754	+	0.927930i	$0.378414\pi$
$367$	−5.64930	+	32.0388i	−0.294891	+	1.67241i	−0.667645	+	0.744480i	$0.732697\pi$
$368$	−0.0368366	+	0.0638029i	−0.00192024	+	0.00332596i
$369$		0			0
$370$	−1.75237	+	0.637812i	−0.0911016	+	0.0331583i
$371$	10.7836	−	3.92490i	0.559856	−	0.203771i
$372$		0			0
$373$	−15.2429	+	26.4014i	−0.789246	+	1.36701i	0.137183	+	0.990546i	$0.456195\pi$
$373$	−15.2429	+	26.4014i	−0.789246	+	1.36701i	−0.926429	+	0.376469i	$0.877138\pi$
$374$	−0.860967	+	4.88279i	−0.0445195	+	0.252483i
$375$		0			0
$376$	−1.55825	−	1.30753i	−0.0803605	−	0.0674305i
$377$	−3.18614	−	18.0695i	−0.164094	−	0.930626i
$378$		0			0
$379$	17.8598			0.917396			0.458698	−	0.888592i	$-0.348316\pi$
$379$	17.8598			0.917396			0.458698	+	0.888592i	$0.348316\pi$
$380$	7.83022	+	11.0450i	0.401682	+	0.566599i
$381$		0			0
$382$	−15.6582	−	5.69913i	−0.801144	−	0.291593i
$383$	4.07310	+	23.0997i	0.208126	+	1.18034i	0.892445	+	0.451157i	$0.148988\pi$
$383$	4.07310	+	23.0997i	0.208126	+	1.18034i	−0.684319	+	0.729183i	$0.739900\pi$
$384$		0			0
$385$	12.4363	−	10.4353i	0.633812	−	0.531831i
$386$	−1.97013	+	11.1732i	−0.100277	+	0.568700i
$387$		0			0
$388$	−1.11809	−	1.93659i	−0.0567623	−	0.0983153i
$389$	3.67365	−	1.33710i	0.186261	−	0.0677936i	−0.247206	−	0.968963i	$-0.579512\pi$
$389$	3.67365	−	1.33710i	0.186261	−	0.0677936i	0.433467	+	0.901169i	$0.357290\pi$
$390$		0			0
$391$	−1.45336	−	2.51730i	−0.0734997	−	0.127305i
$392$	4.92009	−	8.52185i	0.248502	−	0.430418i
$393$		0			0
$394$	−15.6288	+	13.1141i	−0.787369	+	0.660681i
$395$	−13.5064	−	11.3332i	−0.679581	−	0.570236i
$396$		0			0
$397$	−8.41875	−	3.06417i	−0.422525	−	0.153786i	0.122002	−	0.992530i	$-0.461069\pi$
$397$	−8.41875	−	3.06417i	−0.422525	−	0.153786i	−0.544527	+	0.838743i	$0.683291\pi$
$398$	−8.10936			−0.406486
$399$		0			0
$400$	−0.0591253			−0.00295627
$401$	−1.90508	−	0.693392i	−0.0951350	−	0.0346263i	0.294014	−	0.955801i	$-0.405009\pi$
$401$	−1.90508	−	0.693392i	−0.0951350	−	0.0346263i	−0.389149	+	0.921175i	$0.627231\pi$
$402$		0			0
$403$	−7.87733	−	6.60986i	−0.392398	−	0.329261i
$404$	−7.44356	+	6.24589i	−0.370331	+	0.310745i
$405$		0			0
$406$	−2.86571	+	4.96356i	−0.142223	+	0.246338i
$407$	−1.42855	−	2.47432i	−0.0708105	−	0.122647i
$408$		0			0
$409$	30.2656	−	11.0158i	1.49654	−	0.544696i	0.541377	−	0.840780i	$-0.317903\pi$
$409$	30.2656	−	11.0158i	1.49654	−	0.544696i	0.955162	+	0.296084i	$0.0956808\pi$
$410$	4.99912	+	8.65873i	0.246889	+	0.427624i
$411$		0			0
$412$	0.00309887	−	0.0175745i	0.000152670	−	0.000865836i
$413$	−15.4893	+	12.9971i	−0.762180	+	0.639545i
$414$		0			0
$415$	−1.10472	−	6.26519i	−0.0542287	−	0.307546i
$416$	−28.0317	−	10.2027i	−1.37437	−	0.500228i
$417$		0			0
$418$	9.19253	−	9.30039i	0.449622	−	0.454897i
$419$	23.2499			1.13583			0.567916	−	0.823086i	$-0.307750\pi$
$419$	23.2499			1.13583			0.567916	+	0.823086i	$0.307750\pi$
$420$		0			0
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	0.999862	−	0.0166178i	$-0.00528986\pi$
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	−0.945246	+	0.326357i	$0.894179\pi$
$422$	−9.85117	−	8.26611i	−0.479547	−	0.402388i
$423$		0			0
$424$	3.00862	−	17.0627i	0.146111	−	0.828639i
$425$	1.16637	−	2.02022i	0.0565775	−	0.0979950i
$426$		0			0
$427$	7.75150	−	2.82131i	0.375121	−	0.136533i
$428$	4.09714	−	1.49124i	0.198043	−	0.0720817i
$429$		0			0
$430$	5.34477	−	9.25741i	0.257748	−	0.446432i
$431$	2.43061	−	13.7847i	0.117078	−	0.663984i	−0.868622	−	0.495475i	$-0.834994\pi$
$431$	2.43061	−	13.7847i	0.117078	−	0.663984i	0.985700	−	0.168508i	$-0.0538950\pi$
$432$		0			0
$433$	−21.9800	−	18.4434i	−1.05629	−	0.886333i	−0.0625499	−	0.998042i	$-0.519923\pi$
$433$	−21.9800	−	18.4434i	−1.05629	−	0.886333i	−0.993741	+	0.111709i	$0.964368\pi$
$434$	0.557781	+	3.16333i	0.0267744	+	0.151845i
$435$		0			0
$436$	−9.04013			−0.432944
$437$	−0.623608	+	7.64090i	−0.0298312	+	0.365514i
$438$		0			0
$439$	12.5376	+	4.56332i	0.598387	+	0.217795i	0.623414	−	0.781892i	$-0.285745\pi$
$439$	12.5376	+	4.56332i	0.598387	+	0.217795i	−0.0250271	+	0.999687i	$0.507967\pi$
$440$	−4.25624	−	24.1384i	−0.202908	−	1.15075i
$441$		0			0
$442$	−5.89053	+	4.94274i	−0.280184	+	0.235102i
$443$	−5.88372	+	33.3682i	−0.279544	+	1.58537i	0.444603	+	0.895728i	$0.353345\pi$
$443$	−5.88372	+	33.3682i	−0.279544	+	1.58537i	−0.724147	+	0.689646i	$0.757766\pi$
$444$		0			0
$445$	−2.89053	−	5.00654i	−0.137024	−	0.237333i
$446$	−2.49108	+	0.906678i	−0.117956	+	0.0429324i
$447$		0			0
$448$	4.73783	+	8.20616i	0.223841	+	0.387704i
$449$	9.42009	−	16.3161i	0.444562	−	0.770003i	−0.553460	−	0.832876i	$-0.686693\pi$
$449$	9.42009	−	16.3161i	0.444562	−	0.770003i	0.998022	+	0.0628725i	$0.0200261\pi$
$450$		0			0
$451$	−11.7344	+	9.84635i	−0.552552	+	0.463646i
$452$	6.93242	+	5.81699i	0.326074	+	0.273608i
$453$		0			0
$454$	11.3391	+	4.12711i	0.532172	+	0.193695i
$455$	25.1780			1.18036
$456$		0			0
$457$	14.2790			0.667943			0.333972	−	0.942583i	$-0.391611\pi$
$457$	14.2790			0.667943			0.333972	+	0.942583i	$0.391611\pi$
$458$	7.77941	+	2.83147i	0.363508	+	0.132306i
$459$		0			0
$460$	4.18479	+	3.51146i	0.195117	+	0.163723i
$461$	10.6695	−	8.95280i	0.496930	−	0.416973i	−0.359572	−	0.933117i	$-0.617077\pi$
$461$	10.6695	−	8.95280i	0.496930	−	0.416973i	0.856502	+	0.516144i	$0.172633\pi$
$462$		0			0
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	−0.844816	−	0.535056i	$-0.820290\pi$
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	0.885781	+	0.464104i	$0.153624\pi$
$464$	0.0726338	+	0.125805i	0.00337194	+	0.00584037i
$465$		0			0
$466$	19.9859	−	7.27428i	0.925830	−	0.336974i
$467$	11.0209	+	19.0888i	0.509988	+	0.883326i	0.999933	+	0.0115724i	$0.00368368\pi$
$467$	11.0209	+	19.0888i	0.509988	+	0.883326i	−0.489945	+	0.871754i	$0.662983\pi$
$468$		0			0
$469$	−4.63816	+	26.3043i	−0.214170	+	1.21462i
$470$	1.22281	−	1.02606i	0.0564041	−	0.0473286i
$471$		0			0
$472$	5.30113	+	30.0642i	0.244004	+	1.38382i
$473$	15.3897	+	5.60138i	0.707617	+	0.257552i
$474$		0			0
$475$	−5.56077	+	2.63263i	−0.255146	+	0.120793i
$476$	−3.81016			−0.174638
$477$		0			0
$478$	−3.56196	−	20.2009i	−0.162920	−	0.923966i
$479$	19.5012	+	16.3634i	0.891032	+	0.747664i	0.968417	−	0.249337i	$-0.0802126\pi$
$479$	19.5012	+	16.3634i	0.891032	+	0.747664i	−0.0773851	+	0.997001i	$0.524657\pi$
$480$		0			0
$481$	0.769448	−	4.36376i	0.0350838	−	0.198970i
$482$	0.130882	−	0.226694i	0.00596150	−	0.0103256i
$483$		0			0
$484$	0.735604	−	0.267738i	0.0334366	−	0.0121699i
$485$	4.33750	−	1.57872i	0.196956	−	0.0716860i
$486$		0			0
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	−0.489903	−	0.871777i	$-0.662968\pi$
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	0.999932	−	0.0116199i	$-0.00369881\pi$
$488$	2.16267	−	12.2651i	0.0978993	−	0.555214i
$489$		0			0
$490$	5.91534	+	4.96356i	0.267228	+	0.224231i
$491$	−2.71482	−	15.3965i	−0.122518	−	0.694835i	−0.982751	−	0.184934i	$-0.940793\pi$
$491$	−2.71482	−	15.3965i	−0.122518	−	0.694835i	0.860233	−	0.509902i	$-0.170318\pi$
$492$		0			0
$493$	−5.73143			−0.258131
$494$	20.1928	−	1.88538i	0.908519	−	0.0848274i
$495$		0			0
$496$	0.0765042	+	0.0278452i	0.00343514	+	0.00125029i
$497$	−4.49020	−	25.4652i	−0.201413	−	1.14227i
$498$		0			0
$499$	−21.9217	+	18.3945i	−0.981352	+	0.823452i	−0.984293	−	0.176544i	$-0.943508\pi$
$499$	−21.9217	+	18.3945i	−0.981352	+	0.823452i	0.00294090	+	0.999996i	$0.499064\pi$
$500$	1.93552	−	10.9769i	0.0865590	−	0.490900i
$501$		0			0
$502$	7.12196	+	12.3356i	0.317869	+	0.550565i
$503$	−23.5351	+	8.56607i	−1.04938	+	0.381942i	−0.808428	−	0.588595i	$-0.799681\pi$
$503$	−23.5351	+	8.56607i	−1.04938	+	0.381942i	−0.240950	+	0.970538i	$0.577459\pi$
$504$		0			0
$505$	−10.0287	−	17.3702i	−0.446271	−	0.772963i
$506$	2.63816	−	4.56942i	0.117280	−	0.203135i
$507$		0			0
$508$	0.0949225	−	0.0796494i	0.00421150	−	0.00353387i
$509$	−25.6787	−	21.5470i	−1.13819	−	0.955053i	−0.138810	−	0.990319i	$-0.544328\pi$
$509$	−25.6787	−	21.5470i	−1.13819	−	0.955053i	−0.999378	+	0.0352655i	$0.988772\pi$
$510$		0			0
$511$	−13.2763	−	4.83218i	−0.587309	−	0.213763i
$512$	0.473897			0.0209435
$513$		0			0
$514$	13.5030			0.595591
$515$	0.0346151	+	0.0125989i	0.00152532	+	0.000555172i
$516$		0			0
$517$	1.87346	+	1.57202i	0.0823945	+	0.0691372i
$518$	−1.06031	+	0.889704i	−0.0465872	+	0.0390913i
$519$		0			0
$520$	19.0069	−	32.9209i	0.833506	−	1.44367i
$521$	−13.7392	−	23.7969i	−0.601924	−	1.04256i	−0.992530	−	0.122005i	$-0.961068\pi$
$521$	−13.7392	−	23.7969i	−0.601924	−	1.04256i	0.390606	−	0.920558i	$-0.372266\pi$
$522$		0			0
$523$	9.73277	−	3.54244i	0.425584	−	0.154900i	−0.120343	−	0.992732i	$-0.538400\pi$
$523$	9.73277	−	3.54244i	0.425584	−	0.154900i	0.545928	+	0.837832i	$0.316177\pi$
$524$	1.86262	+	3.22615i	0.0813687	+	0.140935i
$525$		0			0
$526$	1.47255	−	8.35126i	0.0642064	−	0.364132i
$527$	−2.46064	+	2.06472i	−0.107187	+	0.0899406i
$528$		0			0
$529$	−3.45677	−	19.6043i	−0.150294	−	0.852361i
$530$	12.7763	+	4.65020i	0.554968	+	0.201992i
$531$		0			0
$532$	8.26517	+	5.71578i	0.358340	+	0.247811i
$533$	−23.7570			−1.02903
$534$		0			0
$535$	1.56283	+	8.86327i	0.0675672	+	0.383193i
$536$	30.8922	+	25.9216i	1.33434	+	1.11964i
$537$		0			0
$538$	−2.79127	+	15.8301i	−0.120340	+	0.682483i
$539$	−5.91534	+	10.2457i	−0.254792	+	0.441313i
$540$		0			0
$541$	−2.37211	+	0.863378i	−0.101985	+	0.0371195i	−0.392509	−	0.919748i	$-0.628393\pi$
$541$	−2.37211	+	0.863378i	−0.101985	+	0.0371195i	0.290524	+	0.956868i	$0.406170\pi$
$542$	15.6710	−	5.70378i	0.673128	−	0.244998i
$543$		0			0
$544$	−4.65910	+	8.06980i	−0.199757	+	0.345990i
$545$	3.24035	−	18.3770i	0.138801	−	0.787182i
$546$		0			0
$547$	5.87939	+	4.93339i	0.251384	+	0.210937i	0.759768	−	0.650194i	$-0.225312\pi$
$547$	5.87939	+	4.93339i	0.251384	+	0.210937i	−0.508384	+	0.861131i	$0.669757\pi$
$548$	4.16220	+	23.6050i	0.177800	+	1.00836i
$549$		0			0
$550$	4.23442			0.180556
$551$	12.4329	+	8.59797i	0.529659	+	0.366286i
$552$		0			0
$553$	−12.2973	−	4.47584i	−0.522933	−	0.190332i
$554$	−2.10179	−	11.9198i	−0.0892963	−	0.506425i
$555$		0			0
$556$	−14.4684	+	12.1404i	−0.613596	+	0.514868i
$557$	−0.565360	+	3.20631i	−0.0239551	+	0.135856i	−0.994440	−	0.105307i	$-0.966418\pi$
$557$	−0.565360	+	3.20631i	−0.0239551	+	0.135856i	0.970485	+	0.241163i	$0.0775287\pi$
$558$		0			0
$559$	12.6998	+	21.9967i	0.537145	+	0.930362i
$560$	−0.187319	+	0.0681784i	−0.00791566	+	0.00288107i
$561$		0			0
$562$	−5.76486	−	9.98503i	−0.243176	−	0.421193i
$563$	2.62954	−	4.55449i	0.110822	−	0.191949i	−0.805280	−	0.592895i	$-0.797985\pi$
$563$	2.62954	−	4.55449i	0.110822	−	0.191949i	0.916102	+	0.400946i	$0.131318\pi$
$564$		0			0
$565$	−14.3097	+	12.0073i	−0.602015	+	0.505151i
$566$	11.7062	+	9.82267i	0.492048	+	0.412878i
$567$		0			0
$568$	−36.6860	−	13.3526i	−1.53931	−	0.560264i
$569$	29.9564			1.25584			0.627918	−	0.778280i	$-0.283907\pi$
$569$	29.9564			1.25584			0.627918	+	0.778280i	$0.283907\pi$
$570$		0			0
$571$	−16.7101			−0.699295			−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101			−0.699295			−0.349647	+	0.936881i	$0.613699\pi$
$572$	20.8059	+	7.57272i	0.869937	+	0.316631i
$573$		0			0
$574$	5.68479	+	4.77011i	0.237279	+	0.199100i
$575$	−1.90167	+	1.59569i	−0.0793053	+	0.0665450i
$576$		0			0
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	−0.687796	−	0.725904i	$-0.741421\pi$
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	0.972549	+	0.232696i	$0.0747548\pi$
$578$	−6.27379	−	10.8665i	−0.260955	−	0.451987i
$579$		0			0
$580$	10.1220	−	3.68409i	0.420291	−	0.152974i
$581$	−2.36097	−	4.08931i	−0.0979494	−	0.169653i
$582$		0			0
$583$	−3.61721	+	20.5142i	−0.149810	+	0.849612i
$584$	−16.3405	+	13.7113i	−0.676174	+	0.567378i
$585$		0			0
$586$	2.38279	+	13.5135i	0.0984321	+	0.558236i
$587$	−22.5872	−	8.22108i	−0.932275	−	0.339320i	−0.169164	−	0.985588i	$-0.554107\pi$
$587$	−22.5872	−	8.22108i	−0.932275	−	0.339320i	−0.763111	+	0.646268i	$0.776329\pi$
$588$		0			0
$589$	8.43511	−	0.787576i	0.347563	−	0.0324515i
$590$	−23.9564			−0.986268
$591$		0			0
$592$	0.00609191	+	0.0345490i	0.000250376	+	0.00141995i
$593$	3.24897	+	2.72621i	0.133419	+	0.111952i	0.707055	−	0.707158i	$-0.250023\pi$
$593$	3.24897	+	2.72621i	0.133419	+	0.111952i	−0.573636	+	0.819110i	$0.694468\pi$
$594$		0			0
$595$	1.36571	−	7.74535i	0.0559888	−	0.317529i
$596$	2.31016	−	4.00131i	0.0946276	−	0.163900i
$597$		0			0
$598$	7.68954	−	2.79876i	0.314449	−	0.114450i
$599$	−24.6894	+	8.98622i	−1.00878	+	0.367167i	−0.792965	−	0.609267i	$-0.791464\pi$
$599$	−24.6894	+	8.98622i	−1.00878	+	0.367167i	−0.215818	+	0.976434i	$0.569242\pi$
$600$		0			0
$601$	21.1197	−	36.5805i	0.861492	−	1.49215i	−0.00899659	−	0.999960i	$-0.502864\pi$
$601$	21.1197	−	36.5805i	0.861492	−	1.49215i	0.870489	−	0.492188i	$-0.163803\pi$
$602$	1.37774	−	7.81353i	0.0561523	−	0.318456i
$603$		0			0
$604$	13.7160	+	11.5091i	0.558096	+	0.468298i
$605$	0.280592	+	1.59132i	0.0114077	+	0.0646963i
$606$		0			0
$607$	−22.0969			−0.896885			−0.448443	−	0.893812i	$-0.648021\pi$
$607$	−22.0969			−0.896885			−0.448443	+	0.893812i	$0.648021\pi$
$608$	22.2126	−	10.5161i	0.900840	−	0.426483i
$609$		0			0
$610$	9.18392	+	3.34267i	0.371846	+	0.135341i
$611$	0.658633	+	3.73530i	0.0266455	+	0.151114i
$612$		0			0
$613$	5.49794	−	4.61332i	0.222060	−	0.186330i	−0.524970	−	0.851121i	$-0.675924\pi$
$613$	5.49794	−	4.61332i	0.222060	−	0.186330i	0.747030	+	0.664790i	$0.231479\pi$
$614$	−3.28622	+	18.6371i	−0.132621	+	0.752131i
$615$		0			0
$616$	−9.09627	−	15.7552i	−0.366499	−	0.634795i
$617$	−46.3953	+	16.8865i	−1.86781	+	0.679826i	−0.895995	+	0.444065i	$0.853536\pi$
$617$	−46.3953	+	16.8865i	−1.86781	+	0.679826i	−0.971811	+	0.235761i	$0.924242\pi$
$618$		0			0
$619$	−13.2490	−	22.9479i	−0.532521	−	0.922354i	−0.999279	−	0.0379684i	$-0.987911\pi$
$619$	−13.2490	−	22.9479i	−0.532521	−	0.922354i	0.466758	−	0.884385i	$-0.345422\pi$
$620$	3.01842	−	5.22805i	0.121223	−	0.209964i
$621$		0			0
$622$	9.76470	−	8.19356i	0.391529	−	0.328532i
$623$	−3.28699	−	2.75811i	−0.131690	−	0.110501i
$624$		0			0
$625$	28.2520	+	10.2829i	1.13008	+	0.411315i
$626$	−17.1643			−0.686022
$627$		0			0
$628$	12.7264			0.507838
$629$	−1.30066	−	0.473401i	−0.0518607	−	0.0188757i
$630$		0			0
$631$	25.5253	+	21.4183i	1.01615	+	0.852647i	0.989138	−	0.146988i	$-0.0469579\pi$
$631$	25.5253	+	21.4183i	1.01615	+	0.852647i	0.0270071	+	0.999635i	$0.491402\pi$
$632$	−15.1355	+	12.7002i	−0.602057	+	0.505185i
$633$		0			0
$634$	−12.4641	+	21.5884i	−0.495013	+	0.857387i
$635$	0.127889	+	0.221510i	0.00507511	+	0.00879035i
$636$		0			0
$637$	−17.2417	+	6.27546i	−0.683141	+	0.248643i
$638$	−5.20187	−	9.00990i	−0.205944	−	0.356705i
$639$		0			0
$640$	3.00862	−	17.0627i	0.118926	−	0.674463i
$641$	0.104256	−	0.0874810i	0.00411786	−	0.00345529i	−0.640726	−	0.767769i	$-0.721367\pi$
$641$	0.104256	−	0.0874810i	0.00411786	−	0.00345529i	0.644844	+	0.764314i	$0.276922\pi$
$642$		0			0
$643$	8.36602	+	47.4461i	0.329924	+	1.87109i	0.472536	+	0.881311i	$0.343339\pi$
$643$	8.36602	+	47.4461i	0.329924	+	1.87109i	−0.142613	+	0.989779i	$0.545550\pi$
$644$	3.81016	+	1.38678i	0.150141	+	0.0546469i
$645$		0			0
$646$	0.515319	−	6.31407i	0.0202750	−	0.248424i
$647$	36.9718			1.45351			0.726756	−	0.686895i	$-0.241027\pi$
$647$	36.9718			1.45351			0.726756	+	0.686895i	$0.241027\pi$
$648$		0			0
$649$	−6.37346	−	36.1457i	−0.250180	−	1.41884i
$650$	5.03074	+	4.22130i	0.197322	+	0.165573i
$651$		0			0
$652$	0.430770	−	2.44302i	0.0168702	−	0.0956759i
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$		0			0
$655$	−7.22580	+	2.62998i	−0.282336	+	0.102762i
$656$	0.176747	−	0.0643307i	0.00690081	−	0.00251169i
$657$		0			0
$658$	0.592396	−	1.02606i	0.0230940	−	0.0400000i
$659$	−3.27760	+	18.5882i	−0.127677	+	0.724093i	0.852005	+	0.523534i	$0.175387\pi$
$659$	−3.27760	+	18.5882i	−0.127677	+	0.724093i	−0.979682	+	0.200559i	$0.935724\pi$
$660$		0			0
$661$	−23.4500	−	19.6769i	−0.912098	−	0.765341i	0.0604192	−	0.998173i	$-0.480756\pi$
$661$	−23.4500	−	19.6769i	−0.912098	−	0.765341i	−0.972517	+	0.232832i	$0.925201\pi$
$662$	0.261135	+	1.48097i	0.0101493	+	0.0575594i
$663$		0			0
$664$	−7.12918			−0.276666
$665$	−14.5817	+	14.7528i	−0.565455	+	0.572090i
$666$		0			0
$667$	5.73143	+	2.08607i	0.221922	+	0.0807729i
$668$	−4.95394	−	28.0952i	−0.191674	−	1.08703i
$669$		0			0
$670$	−24.2422	+	20.3416i	−0.936556	+	0.785864i
$671$	−2.60014	+	14.7461i	−0.100377	+	0.569267i
$672$		0			0
$673$	−5.95471	−	10.3139i	−0.229537	−	0.397570i	0.728134	−	0.685435i	$-0.240388\pi$
$673$	−5.95471	−	10.3139i	−0.229537	−	0.397570i	−0.957671	+	0.287865i	$0.907055\pi$
$674$	21.0214	−	7.65117i	0.809715	−	0.294712i
$675$		0			0
$676$	9.19594	+	15.9278i	0.353690	+	0.612609i
$677$	2.89053	−	5.00654i	0.111092	−	0.192417i	−0.805119	−	0.593114i	$-0.797898\pi$
$677$	2.89053	−	5.00654i	0.111092	−	0.192417i	0.916211	+	0.400696i	$0.131232\pi$
$678$		0			0
$679$	2.62449	−	2.20220i	0.100718	−	0.0845129i
$680$	−9.09627	−	7.63267i	−0.348826	−	0.292700i
$681$		0			0
$682$	−5.47906	−	1.99421i	−0.209804	−	0.0763624i
$683$	−21.0496			−0.805442			−0.402721	−	0.915323i	$-0.631935\pi$
$683$	−21.0496			−0.805442			−0.402721	+	0.915323i	$0.631935\pi$
$684$		0			0
$685$	−49.4766			−1.89040
$686$	16.2570	+	5.91707i	0.620696	+	0.225915i
$687$		0			0
$688$	−0.154048	−	0.129261i	−0.00587302	−	0.00492805i
$689$	−24.7481	+	20.7661i	−0.942827	+	0.791126i
$690$		0			0
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	−0.361744	−	0.932278i	$-0.617818\pi$
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	0.988248	−	0.152860i	$-0.0488483\pi$
$692$	−0.549935	−	0.952515i	−0.0209054	−	0.0362092i
$693$		0			0
$694$	−6.36484	+	2.31661i	−0.241606	+	0.0879374i
$695$	−19.4932	−	33.7632i	−0.739419	−	1.28071i
$696$		0			0
$697$	−1.28864	+	7.30823i	−0.0488106	+	0.276819i
$698$	−15.3302	+	12.8636i	−0.580257	+	0.486894i
$699$		0			0
$700$	0.565055	+	3.20459i	0.0213571	+	0.121122i
$701$	20.0694	+	7.30466i	0.758010	+	0.275893i	0.691973	−	0.721924i	$-0.256742\pi$
$701$	20.0694	+	7.30466i	0.758010	+	0.275893i	0.0660380	+	0.997817i	$0.478964\pi$
$702$		0			0
$703$	2.11128	+	2.97810i	0.0796285	+	0.112321i
$704$	−17.2003			−0.648260
$705$		0			0
$706$	−1.74779	−	9.91220i	−0.0657789	−	0.373051i
$707$	−11.4042	−	9.56926i	−0.428899	−	0.359889i
$708$		0			0
$709$	−2.73854	+	15.5310i	−0.102848	+	0.583280i	0.889210	+	0.457499i	$0.151255\pi$
$709$	−2.73854	+	15.5310i	−0.102848	+	0.583280i	−0.992058	+	0.125781i	$0.959856\pi$
$710$	15.3182	−	26.5319i	0.574882	−	0.995725i
$711$		0			0
$712$	−6.08765	+	2.21572i	−0.228144	+	0.0830377i
$713$	3.21213	−	1.16912i	0.120295	−	0.0437839i
$714$		0			0
$715$	−22.8516	+	39.5802i	−0.854603	+	1.48022i
$716$	−4.54101	+	25.7534i	−0.169706	+	0.962448i
$717$		0			0
$718$	6.99525	+	5.86971i	0.261060	+	0.219056i
$719$	6.13470	+	34.7916i	0.228786	+	1.29751i	0.855314	+	0.518109i	$0.173364\pi$
$719$	6.13470	+	34.7916i	0.228786	+	1.29751i	−0.626529	+	0.779398i	$0.715525\pi$
$720$		0			0
$721$	0.0273411			0.00101824
$722$	−10.5899	+	12.9237i	−0.394114	+	0.480971i
$723$		0			0
$724$	−18.5577	−	6.75444i	−0.689691	−	0.251027i
$725$	0.849985	+	4.82050i	0.0315676	+	0.179029i
$726$		0			0
$727$	30.9647	−	25.9825i	1.14842	−	0.963637i	0.148737	−	0.988877i	$-0.452479\pi$
$727$	30.9647	−	25.9825i	1.14842	−	0.963637i	0.999681	+	0.0252396i	$0.00803487\pi$
$728$	4.89945	−	27.7862i	0.181586	−	1.02982i
$729$		0			0
$730$	−8.36959	−	14.4965i	−0.309772	−	0.536541i
$731$	7.45558	−	2.71361i	0.275755	−	0.100367i
$732$		0			0
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	0.977918	+	0.208988i	$0.0670170\pi$
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	−0.307970	+	0.951396i	$0.599650\pi$
$734$	−14.3045	+	24.7762i	−0.527990	+	0.914505i
$735$		0			0
$736$	7.59627	−	6.37402i	0.280002	−	0.234950i
$737$	−37.1411	−	31.1651i	−1.36811	−	1.14798i
$738$		0			0
$739$	19.4290	+	7.07158i	0.714708	+	0.260132i	0.673677	−	0.739026i	$-0.264714\pi$
$739$	19.4290	+	7.07158i	0.714708	+	0.260132i	0.0410304	+	0.999158i	$0.486936\pi$
$740$	2.60132			0.0956264
$741$		0			0
$742$	10.0915			0.370471
$743$	6.29978	+	2.29293i	0.231117	+	0.0841196i	0.454982	−	0.890500i	$-0.349646\pi$
$743$	6.29978	+	2.29293i	0.231117	+	0.0841196i	−0.223866	+	0.974620i	$0.571868\pi$
$744$		0			0
$745$	7.30587	+	6.13036i	0.267667	+	0.224599i
$746$	−20.5367	+	17.2323i	−0.751901	+	0.630920i
$747$		0			0
$748$	3.45811	−	5.98962i	0.126441	−	0.219002i
$749$	3.34002	+	5.78509i	0.122042	+	0.211383i
$750$		0			0
$751$	−10.0617	+	3.66214i	−0.367155	+	0.133633i	−0.519007	−	0.854770i	$-0.673698\pi$
$751$	−10.0617	+	3.66214i	−0.367155	+	0.133633i	0.151853	+	0.988403i	$0.451476\pi$
$752$	−0.0150147	−	0.0260063i	−0.000547531	−	0.000948352i
$753$		0			0
$754$	2.80184	−	15.8900i	0.102037	−	0.578681i
$755$	−28.3123	+	23.7568i	−1.03039	+	0.864599i
$756$		0			0
$757$	−0.705432	−	4.00071i	−0.0256394	−	0.145408i	0.969301	−	0.245878i	$-0.0790764\pi$
$757$	−0.705432	−	4.00071i	−0.0256394	−	0.145408i	−0.994940	+	0.100470i	$0.967965\pi$
$758$	14.7585	+	5.37164i	0.536052	+	0.195107i
$759$		0			0
$760$	8.28194	+	30.2029i	0.300417	+	1.09557i
$761$	11.0077			0.399030			0.199515	−	0.979895i	$-0.436063\pi$
$761$	11.0077			0.399030			0.199515	+	0.979895i	$0.436063\pi$
$762$		0			0
$763$	−2.40508	−	13.6399i	−0.0870697	−	0.493797i
$764$	17.8059	+	14.9409i	0.644194	+	0.540543i
$765$		0			0
$766$	−3.58182	+	20.3135i	−0.129417	+	0.733958i
$767$	28.4616	−	49.2969i	1.02769	−	1.78001i
$768$		0			0
$769$	−20.0599	+	7.30121i	−0.723378	+	0.263288i	−0.677359	−	0.735652i	$-0.736876\pi$
$769$	−20.0599	+	7.30121i	−0.723378	+	0.263288i	−0.0460191	+	0.998941i	$0.514654\pi$
$770$	13.4153	−	4.88279i	0.483455	−	0.175963i
$771$		0			0
$772$	7.91312	−	13.7059i	0.284800	−	0.493287i
$773$	−3.11128	+	17.6450i	−0.111905	+	0.634645i	0.876331	+	0.481709i	$0.159984\pi$
$773$	−3.11128	+	17.6450i	−0.111905	+	0.634645i	−0.988236	+	0.152936i	$0.951127\pi$
$774$		0			0
$775$	2.10148	+	1.76335i	0.0754874	+	0.0633415i
$776$	−0.898214	−	5.09403i	−0.0322440	−	0.182865i
$777$		0			0
$778$	3.43788			0.123254
$779$	13.7588	−	13.9202i	0.492959	−	0.498743i
$780$		0			0
$781$	44.1070	+	16.0536i	1.57827	+	0.574444i
$782$	−0.443868	−	2.51730i	−0.0158727	−	0.0900184i
$783$		0			0
$784$	0.111281	−	0.0933762i	0.00397434	−	0.00333486i
$785$	−4.56165	+	25.8704i	−0.162812	+	0.923355i
$786$		0			0
$787$	−24.4158	−	42.2894i	−0.870330	−	1.50746i	−0.861656	−	0.507493i	$-0.830572\pi$
$787$	−24.4158	−	42.2894i	−0.870330	−	1.50746i	−0.00867371	−	0.999962i	$-0.502761\pi$
$788$	26.7430	−	9.73367i	0.952681	−	0.346748i
$789$		0			0
$790$	−7.75237	−	13.4275i	−0.275817	−	0.477729i
$791$	−6.93242	+	12.0073i	−0.246488	+	0.426930i
$792$		0			0
$793$	−17.7895	+	14.9272i	−0.631724	+	0.530080i
$794$	−6.03524	−	5.06417i	−0.214183	−	0.179721i
$795$		0			0
$796$	10.6298	+	3.86893i	0.376763	+	0.137131i
$797$	28.5262			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$798$		0			0
$799$	1.18479			0.0419149
$800$	7.47818	+	2.72183i	0.264394	+	0.0962314i
$801$		0			0
$802$	−1.36571	−	1.14597i	−0.0482251	−	0.0404656i
$803$	19.6459	−	16.4849i	0.693289	−	0.581738i
$804$		0			0
$805$	−4.18479	+	7.24827i	−0.147495	+	0.255468i
$806$	−4.52141	−	7.83131i	−0.159260	−	0.275846i
$807$		0			0
$808$	−21.1211	+	7.68745i	−0.743037	+	0.270443i
$809$	−7.41834	−	12.8489i	−0.260815	−	0.451745i	0.705644	−	0.708567i	$-0.250658\pi$
$809$	−7.41834	−	12.8489i	−0.260815	−	0.451745i	−0.966459	+	0.256822i	$0.917325\pi$
$810$		0			0
$811$	−1.45471	+	8.25006i	−0.0510817	+	0.289699i	−0.999638	−	0.0269103i	$-0.991433\pi$
$811$	−1.45471	+	8.25006i	−0.0510817	+	0.289699i	0.948556	+	0.316609i	$0.102544\pi$
$812$	6.12449	−	5.13905i	0.214927	−	0.180345i
$813$		0			0
$814$	−0.436289	−	2.47432i	−0.0152919	−	0.0867248i
$815$	4.81180	+	1.75135i	0.168550	+	0.0613472i
$816$		0			0
$817$	−20.2438	−	5.29796i	−0.708241	−	0.185352i
$818$	28.3233			0.990299
$819$		0			0
$820$	−2.42185	−	13.7350i	−0.0845746	−	0.479646i
$821$	−4.80999	−	4.03606i	−0.167870	−	0.140860i	0.554983	−	0.831862i	$-0.312725\pi$
$821$	−4.80999	−	4.03606i	−0.167870	−	0.140860i	−0.722852	+	0.691002i	$0.757169\pi$
$822$		0			0
$823$	1.91472	−	10.8589i	0.0667428	−	0.378517i	−0.933080	−	0.359670i	$-0.882889\pi$
$823$	1.91472	−	10.8589i	0.0667428	−	0.378517i	0.999822	−	0.0188472i	$-0.00599961\pi$
$824$	0.0206398	−	0.0357492i	0.000719023	−	0.00124538i
$825$		0			0
$826$	−16.7087	+	6.08148i	−0.581371	+	0.211602i
$827$	31.8892	−	11.6067i	1.10890	−	0.403606i	0.278309	−	0.960492i	$-0.410226\pi$
$827$	31.8892	−	11.6067i	1.10890	−	0.403606i	0.830589	+	0.556886i	$0.188004\pi$
$828$		0			0
$829$	10.1834	−	17.6382i	0.353686	−	0.612602i	−0.633206	−	0.773983i	$-0.718262\pi$
$829$	10.1834	−	17.6382i	0.353686	−	0.612602i	0.986892	+	0.161381i	$0.0515949\pi$
$830$	0.971477	−	5.50952i	0.0337205	−	0.191238i
$831$		0			0
$832$	−20.4349	−	17.1470i	−0.708454	−	0.594464i
$833$	0.995252	+	5.64436i	0.0344834	+	0.195565i
$834$		0			0
$835$	58.8881			2.03791
$836$	−16.4868	+	7.80531i	−0.570208	+	0.269952i
$837$		0			0
$838$	19.2126	+	6.99281i	0.663688	+	0.241563i
$839$	−2.74526	−	15.5692i	−0.0947770	−	0.537507i	−0.994815	−	0.101697i	$-0.967573\pi$
$839$	−2.74526	−	15.5692i	−0.0947770	−	0.537507i	0.900038	−	0.435810i	$-0.143538\pi$
$840$		0			0
$841$	−13.0025	+	10.9104i	−0.448363	+	0.376221i
$842$	−0.985452	+	5.58878i	−0.0339609	+	0.192602i
$843$		0			0
$844$	8.96926	+	15.5352i	0.308734	+	0.534744i
$845$	−35.6746	+	12.9845i	−1.22724	+	0.446680i
$846$		0			0
$847$	0.599670	+	1.03866i	0.0206049	+	0.0356888i
$848$	0.127889	−	0.221510i	0.00439172	−	0.00760668i
$849$		0			0
$850$	1.57145	−	1.31860i	0.0539003	−	0.0452278i
$851$	1.12836	+	0.946803i	0.0386795	+	0.0324560i
$852$		0			0
$853$	49.4741	+	18.0071i	1.69396	+	0.616551i	0.995115	−	0.0987227i	$-0.0314757\pi$
$853$	49.4741	+	18.0071i	1.69396	+	0.616551i	0.698845	+	0.715274i	$0.253698\pi$
$854$	7.25402			0.248228
$855$		0			0
$856$	10.0855			0.344716
$857$	−21.6386	−	7.87581i	−0.739161	−	0.269033i	−0.0551238	−	0.998480i	$-0.517555\pi$
$857$	−21.6386	−	7.87581i	−0.739161	−	0.269033i	−0.684038	+	0.729447i	$0.739778\pi$
$858$		0			0
$859$	6.82501	+	5.72686i	0.232866	+	0.195398i	0.751753	−	0.659445i	$-0.229209\pi$
$859$	6.82501	+	5.72686i	0.232866	+	0.195398i	−0.518886	+	0.854843i	$0.673653\pi$
$860$	−11.4226	+	9.58471i	−0.389508	+	0.326836i
$861$		0			0
$862$	6.15451	−	10.6599i	0.209624	−	0.363079i
$863$	14.8849	+	25.7814i	0.506688	+	0.877609i	0.999970	+	0.00773998i	$0.00246374\pi$
$863$	14.8849	+	25.7814i	0.506688	+	0.877609i	−0.493282	+	0.869869i	$0.664203\pi$
$864$		0			0
$865$	2.13341	−	0.776497i	0.0725380	−	0.0264017i
$866$	−12.6160	−	21.8516i	−0.428710	−	0.742548i
$867$		0			0
$868$	0.778066	−	4.41263i	0.0264093	−	0.149775i
$869$	18.1971	−	15.2692i	0.617295	−	0.517972i
$870$		0			0
$871$	−13.0574	−	74.0520i	−0.442432	−	2.50916i
$872$	−19.6501	−	7.15204i	−0.665435	−	0.242199i
$873$		0			0
$874$	−2.81345	+	6.12651i	−0.0951665	+	0.207232i
$875$	17.0770			0.577307
$876$		0			0
$877$	−4.34642	−	24.6498i	−0.146768	−	0.832363i	−0.965930	−	0.258802i	$-0.916672\pi$
$877$	−4.34642	−	24.6498i	−0.146768	−	0.832363i	0.819162	−	0.573562i	$-0.194439\pi$
$878$	8.98798	+	7.54181i	0.303330	+	0.254524i
$879$		0			0
$880$	0.0628336	−	0.356347i	0.00211812	−	0.0120125i
$881$	10.1980	−	17.6634i	0.343579	−	0.595097i	−0.641515	−	0.767110i	$-0.721694\pi$
$881$	10.1980	−	17.6634i	0.343579	−	0.595097i	0.985095	+	0.172014i	$0.0550273\pi$
$882$		0			0
$883$	9.98710	−	3.63501i	0.336093	−	0.122328i	−0.168460	−	0.985708i	$-0.553880\pi$
$883$	9.98710	−	3.63501i	0.336093	−	0.122328i	0.504553	+	0.863381i	$0.331657\pi$
$884$	10.0795	−	3.66864i	0.339010	−	0.123390i
$885$		0			0
$886$	−14.8981	+	25.8043i	−0.500512	+	0.866912i
$887$	9.78312	−	55.4828i	0.328485	−	1.86293i	−0.155474	−	0.987840i	$-0.549690\pi$
$887$	9.78312	−	55.4828i	0.328485	−	1.86293i	0.483959	−	0.875091i	$-0.339198\pi$
$888$		0			0
$889$	0.145430	+	0.122030i	0.00487756	+	0.00409275i
$890$	−0.882789	−	5.00654i	−0.0295911	−	0.167820i
$891$		0			0
$892$	3.69789			0.123815
$893$	−2.57011	−	1.77736i	−0.0860054	−	0.0594771i
$894$		0			0
$895$	−50.7242	−	18.4621i	−1.69552	−	0.617120i
$896$	−2.23308	−	12.6644i	−0.0746019	−	0.423088i
$897$		0			0
$898$	12.6917	−	10.6496i	0.423526	−	0.355381i
$899$	1.17041	−	6.63771i	0.0390353	−	0.221380i
$900$		0			0
$901$	5.04576	+	8.73951i	0.168099	+	0.291155i
$902$	−12.6582	+	4.60722i	−0.421473	+	0.153404i
$903$		0			0
$904$	10.4666	+	18.1286i	0.348113	+	0.602949i
$905$	20.3824	−	35.3033i	0.677533	−	1.17352i
$906$		0			0
$907$	−4.53777	+	3.80764i	−0.150674	+	0.126431i	−0.715009	−	0.699116i	$-0.753577\pi$
$907$	−4.53777	+	3.80764i	−0.150674	+	0.126431i	0.564334	+	0.825546i	$0.309133\pi$
$908$	−12.8944	−	10.8197i	−0.427916	−	0.359064i
$909$		0			0
$910$	20.8059	+	7.57272i	0.689708	+	0.251033i
$911$	34.0591			1.12843			0.564215	−	0.825628i	$-0.309179\pi$
$911$	34.0591			1.12843			0.564215	+	0.825628i	$0.309179\pi$
$912$		0			0
$913$	8.57129			0.283668
$914$	11.7995	+	4.29466i	0.390292	+	0.142055i
$915$		0			0
$916$	−8.84642	−	7.42303i	−0.292294	−	0.245264i
$917$	−4.37211	+	3.66864i	−0.144380	+	0.121149i
$918$		0			0
$919$	3.13697	−	5.43340i	0.103479	−	0.179231i	−0.809637	−	0.586931i	$-0.800336\pi$
$919$	3.13697	−	5.43340i	0.103479	−	0.179231i	0.913116	+	0.407700i	$0.133669\pi$
$920$	6.31820	+	10.9434i	0.208305	+	0.360795i
$921$		0			0
$922$	11.5095	−	4.18911i	0.379045	−	0.137961i
$923$	36.3979	+	63.0429i	1.19805	+	2.07508i
$924$		0			0
$925$	−0.205270	+	1.16415i	−0.00674924	+	0.0382769i
$926$	1.18757	−	0.996487i	0.0390259	−	0.0327466i
$927$		0			0
$928$	−3.39528	−	19.2556i	−0.111455	−	0.632095i
$929$	26.6152	+	9.68712i	0.873215	+	0.317824i	0.739468	−	0.673191i	$-0.235077\pi$
$929$	26.6152	+	9.68712i	0.873215	+	0.317824i	0.133747	+	0.991016i	$0.457299\pi$
$930$		0			0
$931$	6.30840	−	13.7370i	0.206749	−	0.450213i
$932$	−29.6682			−0.971814
$933$		0			0
$934$	3.36588	+	19.0888i	0.110135	+	0.624606i
$935$	10.9363	+	9.17664i	0.357655	+	0.300108i
$936$		0			0
$937$	−3.48545	+	19.7670i	−0.113865	+	0.645759i	0.873441	+	0.486930i	$0.161883\pi$
$937$	−3.48545	+	19.7670i	−0.113865	+	0.645759i	−0.987306	+	0.158830i	$0.949228\pi$
$938$	−11.7442	+	20.3416i	−0.383462	+	0.664176i
$939$		0			0
$940$	−2.09240	+	0.761570i	−0.0682464	+	0.0248397i
$941$	5.06980	−	1.84526i	0.165271	−	0.0601537i	−0.258060	−	0.966129i	$-0.583083\pi$
$941$	5.06980	−	1.84526i	0.165271	−	0.0601537i	0.423331	+	0.905975i	$0.360861\pi$
$942$		0			0
$943$	3.94862	−	6.83920i	0.128585	−	0.222715i
$944$	−0.0782589	+	0.443828i	−0.00254711	+	0.0144454i
$945$		0			0
$946$	11.0326	+	9.25741i	0.358699	+	0.300984i
$947$	−1.15358	−	6.54228i	−0.0374863	−	0.212596i	0.960311	−	0.278931i	$-0.0899802\pi$
$947$	−1.15358	−	6.54228i	−0.0374863	−	0.212596i	−0.997797	+	0.0663359i	$0.978869\pi$
$948$		0			0
$949$	39.7743			1.29113
$950$	−5.38696	+	0.502975i	−0.174776	+	0.0163187i
$951$		0			0
$952$	−8.28194	−	3.01438i	−0.268419	−	0.0976966i
$953$	2.57414	+	14.5987i	0.0833846	+	0.472897i	0.997693	+	0.0678799i	$0.0216235\pi$
$953$	2.57414	+	14.5987i	0.0833846	+	0.472897i	−0.914309	+	0.405018i	$0.867265\pi$
$954$		0			0
$955$	−36.7545	+	30.8407i	−1.18935	+	0.997981i
$956$	−4.96868	+	28.1788i	−0.160699	+	0.911368i
$957$		0			0
$958$	11.1932	+	19.3873i	0.361637	+	0.626374i
$959$	−34.5082	+	12.5600i	−1.11433	+	0.405582i
$960$		0			0
$961$	13.6113	+	23.5754i	0.439074	+	0.760498i
$962$	1.94831	−	3.37457i	0.0628161	−	0.108801i
$963$		0			0
$964$	−0.279715	+	0.234709i	−0.00900901	+	0.00755946i
$965$	25.0253	+	20.9987i	0.805592	+	0.675972i
$966$		0			0
$967$	−19.9418	−	7.25822i	−0.641285	−	0.233409i	0.000850519	−	1.00000i	$-0.499729\pi$
$967$	−19.9418	−	7.25822i	−0.641285	−	0.233409i	−0.642136	+	0.766591i	$0.721951\pi$
$968$	1.81076			0.0582002
$969$		0			0
$970$	4.05913			0.130331
$971$	−35.3387	−	12.8622i	−1.13407	−	0.412769i	−0.294304	−	0.955712i	$-0.595088\pi$
$971$	−35.3387	−	12.8622i	−1.13407	−	0.412769i	−0.839770	+	0.542943i	$0.817310\pi$
$972$		0			0
$973$	−22.1668	−	18.6002i	−0.710636	−	0.596295i
$974$	15.1643	−	12.7244i	0.485896	−	0.407715i
$975$		0			0
$976$	0.0919294	−	0.159226i	0.00294259	−	0.00509671i
$977$	−23.0107	−	39.8558i	−0.736179	−	1.27510i	−0.954204	−	0.299156i	$-0.903295\pi$
$977$	−23.0107	−	39.8558i	−0.736179	−	1.27510i	0.218026	−	0.975943i	$-0.430038\pi$
$978$		0			0
$979$	7.31908	−	2.66393i	0.233919	−	0.0851395i
$980$	−5.38578	−	9.32845i	−0.172042	−	0.297986i
$981$		0			0
$982$	2.38737	−	13.5395i	0.0761842	−	0.432062i
$983$	−46.4195	+	38.9506i	−1.48055	+	1.24233i	−0.574961	+	0.818181i	$0.694983\pi$
$983$	−46.4195	+	38.9506i	−1.48055	+	1.24233i	−0.905592	+	0.424150i	$0.860573\pi$
$984$		0			0
$985$	10.2010	+	57.8527i	0.325031	+	1.84334i
$986$	−4.73618	−	1.72383i	−0.150831	−	0.0548979i
$987$		0			0
$988$	−27.3684	−	7.16252i	−0.870705	−	0.227870i
$989$	−8.44326			−0.268480
$990$		0			0
$991$	7.27554	+	41.2616i	0.231115	+	1.31072i	0.850643	+	0.525744i	$0.176213\pi$
$991$	7.27554	+	41.2616i	0.231115	+	1.31072i	−0.619528	+	0.784975i	$0.712676\pi$
$992$	−8.39440	−	7.04374i	−0.266522	−	0.223639i
$993$		0			0
$994$	3.94862	−	22.3937i	0.125242	−	0.710285i
$995$	−11.6750	+	20.2217i	−0.370122	+	0.641070i
$996$		0			0
$997$	−31.6819	+	11.5313i	−1.00337	+	0.365198i	−0.790885	−	0.611965i	$-0.790379\pi$
$997$	−31.6819	+	11.5313i	−1.00337	+	0.365198i	−0.212490	+	0.977163i	$0.568157\pi$
$998$	−23.6475	+	8.60700i	−0.748550	+	0.272450i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.u.c.118.1		6
3.2	odd	2		19.2.e.a.4.1	✓	6
12.11	even	2		304.2.u.b.289.1		6
15.2	even	4		475.2.u.a.99.2		12
15.8	even	4		475.2.u.a.99.1		12
15.14	odd	2		475.2.l.a.251.1		6
19.5	even	9	inner	171.2.u.c.100.1		6
19.9	even	9		3249.2.a.z.1.1		3
19.10	odd	18		3249.2.a.s.1.3		3
21.2	odd	6		931.2.x.a.802.1		6
21.5	even	6		931.2.x.b.802.1		6
21.11	odd	6		931.2.v.b.422.1		6
21.17	even	6		931.2.v.a.422.1		6
21.20	even	2		931.2.w.a.99.1		6
57.2	even	18		361.2.e.b.54.1		6
57.5	odd	18		19.2.e.a.5.1	yes	6
57.8	even	6		361.2.e.a.28.1		6
57.11	odd	6		361.2.e.g.28.1		6
57.14	even	18		361.2.e.h.62.1		6
57.17	odd	18		361.2.e.f.54.1		6
57.23	odd	18		361.2.c.i.292.1		6
57.26	odd	6		361.2.e.f.234.1		6
57.29	even	18		361.2.a.h.1.1		3
57.32	even	18		361.2.c.h.68.3		6
57.35	odd	18		361.2.e.g.245.1		6
57.41	even	18		361.2.e.a.245.1		6
57.44	odd	18		361.2.c.i.68.1		6
57.47	odd	18		361.2.a.g.1.3		3
57.50	even	6		361.2.e.b.234.1		6
57.53	even	18		361.2.c.h.292.3		6
57.56	even	2		361.2.e.h.99.1		6
228.47	even	18		5776.2.a.br.1.1		3
228.119	even	18		304.2.u.b.81.1		6
228.143	odd	18		5776.2.a.bi.1.3		3
285.29	even	18		9025.2.a.x.1.3		3
285.62	even	36		475.2.u.a.24.1		12
285.104	odd	18		9025.2.a.bd.1.1		3
285.119	odd	18		475.2.l.a.176.1		6
285.233	even	36		475.2.u.a.24.2		12
399.5	even	18		931.2.v.a.214.1		6
399.62	even	18		931.2.w.a.442.1		6
399.233	odd	18		931.2.v.b.214.1		6
399.290	even	18		931.2.x.b.765.1		6
399.347	odd	18		931.2.x.a.765.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	3.2	odd	2
19.2.e.a.5.1	yes	6	57.5	odd	18
171.2.u.c.100.1		6	19.5	even	9	inner
171.2.u.c.118.1		6	1.1	even	1	trivial
304.2.u.b.81.1		6	228.119	even	18
304.2.u.b.289.1		6	12.11	even	2
361.2.a.g.1.3		3	57.47	odd	18
361.2.a.h.1.1		3	57.29	even	18
361.2.c.h.68.3		6	57.32	even	18
361.2.c.h.292.3		6	57.53	even	18
361.2.c.i.68.1		6	57.44	odd	18
361.2.c.i.292.1		6	57.23	odd	18
361.2.e.a.28.1		6	57.8	even	6
361.2.e.a.245.1		6	57.41	even	18
361.2.e.b.54.1		6	57.2	even	18
361.2.e.b.234.1		6	57.50	even	6
361.2.e.f.54.1		6	57.17	odd	18
361.2.e.f.234.1		6	57.26	odd	6
361.2.e.g.28.1		6	57.11	odd	6
361.2.e.g.245.1		6	57.35	odd	18
361.2.e.h.62.1		6	57.14	even	18
361.2.e.h.99.1		6	57.56	even	2
475.2.l.a.176.1		6	285.119	odd	18
475.2.l.a.251.1		6	15.14	odd	2
475.2.u.a.24.1		12	285.62	even	36
475.2.u.a.24.2		12	285.233	even	36
475.2.u.a.99.1		12	15.8	even	4
475.2.u.a.99.2		12	15.2	even	4
931.2.v.a.214.1		6	399.5	even	18
931.2.v.a.422.1		6	21.17	even	6
931.2.v.b.214.1		6	399.233	odd	18
931.2.v.b.422.1		6	21.11	odd	6
931.2.w.a.99.1		6	21.20	even	2
931.2.w.a.442.1		6	399.62	even	18
931.2.x.a.765.1		6	399.347	odd	18
931.2.x.a.802.1		6	21.2	odd	6
931.2.x.b.765.1		6	399.290	even	18
931.2.x.b.802.1		6	21.5	even	6
3249.2.a.s.1.3		3	19.10	odd	18
3249.2.a.z.1.1		3	19.9	even	9
5776.2.a.bi.1.3		3	228.143	odd	18
5776.2.a.br.1.1		3	228.47	even	18
9025.2.a.x.1.3		3	285.29	even	18
9025.2.a.bd.1.1		3	285.104	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.826352 + 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(1.93969 - 1.62760i) q^{5} +(0.939693 - 1.62760i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(2.09240 - 0.761570i) q^{10} +(1.70574 + 2.95442i) q^{11} +(-0.918748 + 5.21048i) q^{13} +(1.26604 - 1.06234i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(1.55303 + 0.565258i) q^{17} +(-2.52094 - 3.55596i) q^{19} -3.10607 q^{20} +(0.520945 + 2.95442i) q^{22} +(-1.34730 - 1.13052i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-2.32635 + 4.02936i) q^{26} +(-2.16637 + 0.788496i) q^{28} +(-3.25877 + 1.18610i) q^{29} +(-0.971782 + 1.68317i) q^{31} +(-0.979055 + 5.55250i) q^{32} +(1.11334 + 0.934204i) q^{34} +(-0.826352 - 4.68647i) q^{35} -0.837496 q^{37} +(-1.01367 - 3.69669i) q^{38} +(-6.75150 - 2.45734i) q^{40} +(0.779715 + 4.42198i) q^{41} +(3.67752 - 3.08580i) q^{43} +(0.726682 - 4.12122i) q^{44} +(-0.773318 - 1.33943i) q^{46} +(0.673648 - 0.245188i) q^{47} +(1.73396 + 3.00330i) q^{49} +(0.620615 - 1.07494i) q^{50} +(4.97178 - 4.17182i) q^{52} +(4.67752 + 3.92490i) q^{53} +(8.11721 + 2.95442i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(-10.1099 - 3.67972i) q^{59} +(3.36231 + 2.82131i) q^{61} +(-1.30928 + 1.09861i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(6.69846 + 11.6021i) q^{65} +(-13.3550 + 4.86084i) q^{67} +(-1.01367 - 1.75573i) q^{68} +(0.726682 - 4.12122i) q^{70} +(10.5398 - 8.84397i) q^{71} +(-1.30541 - 7.40333i) q^{73} +(-0.692066 - 0.251892i) q^{74} +(-0.434945 + 5.32926i) q^{76} +6.41147 q^{77} +(-1.20914 - 6.85738i) q^{79} +(-0.0812519 - 0.0681784i) q^{80} +(-0.685670 + 3.88863i) q^{82} +(1.25624 - 2.17588i) q^{83} +(3.93242 - 1.43128i) q^{85} +(3.96703 - 1.44388i) q^{86} +(4.84002 - 8.38316i) q^{88} +(0.396459 - 2.24843i) q^{89} +(7.61721 + 6.39160i) q^{91} +(0.374638 + 2.12467i) q^{92} +0.630415 q^{94} +(-10.6775 - 2.79439i) q^{95} +(1.71301 + 0.623485i) q^{97} +(0.529563 + 3.00330i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8} + 9 q^{10} - 3 q^{13} + 3 q^{14} - 18 q^{16} - 3 q^{17} - 12 q^{19} + 6 q^{20} - 6 q^{23} - 15 q^{26} + 6 q^{28} + 3 q^{29} + 9 q^{31} - 9 q^{32} - 6 q^{35} + 15 q^{38}+ \cdots + 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8 + 9 * q^10 - 3 * q^13 + 3 * q^14 - 18 * q^16 - 3 * q^17 - 12 * q^19 + 6 * q^20 - 6 * q^23 - 15 * q^26 + 6 * q^28 + 3 * q^29 + 9 * q^31 - 9 * q^32 - 6 * q^35 + 15 * q^38 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 18 * q^46 + 3 * q^47 + 15 * q^49 + 15 * q^50 + 15 * q^52 + 3 * q^53 + 18 * q^55 + 6 * q^56 + 36 * q^58 - 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^64 + 12 * q^65 - 30 * q^67 + 15 * q^68 - 9 * q^70 + 6 * q^71 - 12 * q^73 - 15 * q^74 + 36 * q^76 + 18 * q^77 - 39 * q^79 - 3 * q^80 - 54 * q^82 - 24 * q^86 + 9 * q^88 + 12 * q^89 + 15 * q^91 - 42 * q^92 + 18 * q^94 - 39 * q^95 + 18 * q^97 + 9 * q^98

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