LMFDB - Embedded newform 819.2.gh.d.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(19,819)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("819.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.gh (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	819.19
Dual form			819.2.gh.d.388.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.39126 - 0.640737i) q^{2} +(3.57554 + 2.06434i) q^{4} +(1.06950 - 0.286571i) q^{5} +(0.327682 - 2.62538i) q^{7} +(-3.72630 - 3.72630i) q^{8} +O(q^{10})$	\(q+(-2.39126 - 0.640737i) q^{2} +(3.57554 + 2.06434i) q^{4} +(1.06950 - 0.286571i) q^{5} +(0.327682 - 2.62538i) q^{7} +(-3.72630 - 3.72630i) q^{8} -2.74106 q^{10} +(-1.52947 - 1.52947i) q^{11} +(-3.47248 + 0.970511i) q^{13} +(-2.46575 + 6.06801i) q^{14} +(2.39431 + 4.14706i) q^{16} +(-1.59647 + 2.76517i) q^{17} +(-2.51496 - 2.51496i) q^{19} +(4.41561 + 1.18316i) q^{20} +(2.67738 + 4.63735i) q^{22} +(-0.620322 + 0.358143i) q^{23} +(-3.26843 + 1.88703i) q^{25} +(8.92545 - 0.0958025i) q^{26} +(6.59131 - 8.71070i) q^{28} +(-1.58131 + 2.73892i) q^{29} +(-0.625845 + 2.33568i) q^{31} +(-0.340399 - 1.27039i) q^{32} +(5.58933 - 5.58933i) q^{34} +(-0.401902 - 2.90174i) q^{35} +(0.726571 - 2.71160i) q^{37} +(4.40250 + 7.62535i) q^{38} +(-5.05312 - 2.91742i) q^{40} +(-4.01046 + 1.07460i) q^{41} +(7.32559 - 4.22943i) q^{43} +(-2.31134 - 8.62603i) q^{44} +(1.71283 - 0.458951i) q^{46} +(-2.85863 - 10.6686i) q^{47} +(-6.78525 - 1.72058i) q^{49} +(9.02475 - 2.41817i) q^{50} +(-14.4194 - 3.69827i) q^{52} +(-4.54930 - 7.87963i) q^{53} +(-2.07407 - 1.19746i) q^{55} +(-11.0040 + 8.56192i) q^{56} +(5.53626 - 5.53626i) q^{58} +(2.10905 + 7.87107i) q^{59} +13.1295i q^{61} +(2.99312 - 5.18423i) q^{62} -6.32129i q^{64} +(-3.43569 + 2.03307i) q^{65} +(-8.40090 + 8.40090i) q^{67} +(-11.4165 + 6.59131i) q^{68} +(-0.898198 + 7.19634i) q^{70} +(14.8017 + 3.96611i) q^{71} +(-4.86210 - 1.30280i) q^{73} +(-3.47484 + 6.01860i) q^{74} +(-3.80061 - 14.1841i) q^{76} +(-4.51663 + 3.51426i) q^{77} +(-8.54505 + 14.8005i) q^{79} +(3.74913 + 3.74913i) q^{80} +10.2786 q^{82} +(-3.63623 - 3.63623i) q^{83} +(-0.915005 + 3.41484i) q^{85} +(-20.2274 + 5.41991i) q^{86} +11.3985i q^{88} +(5.24668 + 1.40584i) q^{89} +(1.41009 + 9.43460i) q^{91} -2.95732 q^{92} +27.3430i q^{94} +(-3.41045 - 1.96903i) q^{95} +(3.61174 - 13.4792i) q^{97} +(15.1229 + 8.46192i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^7	$ 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) $ 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.39126	−	0.640737i	−1.69088	−	0.453069i	−0.720261	−	0.693703i	$-0.755978\pi$
$2$	−2.39126	−	0.640737i	−1.69088	−	0.453069i	−0.970616	+	0.240634i	$0.922645\pi$
$3$		0			0
$3$		0			0
$4$	3.57554	+	2.06434i	1.78777	+	1.03217i
$5$	1.06950	−	0.286571i	0.478294	−	0.128158i	−0.0116143	−	0.999933i	$-0.503697\pi$
$5$	1.06950	−	0.286571i	0.478294	−	0.128158i	0.489908	+	0.871774i	$0.337030\pi$
$6$		0			0
$7$	0.327682	−	2.62538i	0.123852	−	0.992301i
$7$	0.327682	−	2.62538i	0.123852	−	0.992301i
$8$	−3.72630	−	3.72630i	−1.31745	−	1.31745i
$9$		0			0
$10$	−2.74106			−0.866801
$11$	−1.52947	−	1.52947i	−0.461153	−	0.461153i	0.437880	−	0.899033i	$-0.355729\pi$
$11$	−1.52947	−	1.52947i	−0.461153	−	0.461153i	−0.899033	+	0.437880i	$0.855729\pi$
$12$		0			0
$13$	−3.47248	+	0.970511i	−0.963092	+	0.269171i
$13$	−3.47248	+	0.970511i	−0.963092	+	0.269171i
$14$	−2.46575	+	6.06801i	−0.659000	+	1.62175i
$15$		0			0
$16$	2.39431	+	4.14706i	0.598577	+	1.03677i
$17$	−1.59647	+	2.76517i	−0.387201	+	0.670652i	−0.992072	−	0.125671i	$-0.959891\pi$
$17$	−1.59647	+	2.76517i	−0.387201	+	0.670652i	0.604871	+	0.796324i	$0.293225\pi$
$18$		0			0
$19$	−2.51496	−	2.51496i	−0.576971	−	0.576971i	0.357097	−	0.934067i	$-0.383767\pi$
$19$	−2.51496	−	2.51496i	−0.576971	−	0.576971i	−0.934067	+	0.357097i	$0.883767\pi$
$20$	4.41561	+	1.18316i	0.987360	+	0.264562i
$21$		0			0
$22$	2.67738	+	4.63735i	0.570819	+	0.988687i
$23$	−0.620322	+	0.358143i	−0.129346	+	0.0746781i	−0.563277	−	0.826268i	$-0.690460\pi$
$23$	−0.620322	+	0.358143i	−0.129346	+	0.0746781i	0.433931	+	0.900946i	$0.357126\pi$
$24$		0			0
$25$	−3.26843	+	1.88703i	−0.653685	+	0.377405i
$26$	8.92545	−	0.0958025i	1.75042	−	0.0187884i
$27$		0			0
$28$	6.59131	−	8.71070i	1.24564	−	1.64617i
$29$	−1.58131	+	2.73892i	−0.293643	+	0.508604i	−0.974668	−	0.223656i	$-0.928201\pi$
$29$	−1.58131	+	2.73892i	−0.293643	+	0.508604i	0.681026	+	0.732260i	$0.261534\pi$
$30$		0			0
$31$	−0.625845	+	2.33568i	−0.112405	+	0.419501i	−0.999080	−	0.0428926i	$-0.986343\pi$
$31$	−0.625845	+	2.33568i	−0.112405	+	0.419501i	0.886675	+	0.462394i	$0.153009\pi$
$32$	−0.340399	−	1.27039i	−0.0601747	−	0.224575i
$33$		0			0
$34$	5.58933	−	5.58933i	0.958562	−	0.958562i
$35$	−0.401902	−	2.90174i	−0.0679339	−	0.490484i
$36$		0			0
$37$	0.726571	−	2.71160i	0.119448	−	0.445784i	−0.880134	−	0.474726i	$-0.842547\pi$
$37$	0.726571	−	2.71160i	0.119448	−	0.445784i	0.999581	+	0.0289419i	$0.00921379\pi$
$38$	4.40250	+	7.62535i	0.714179	+	1.23699i
$39$		0			0
$40$	−5.05312	−	2.91742i	−0.798968	−	0.461284i
$41$	−4.01046	+	1.07460i	−0.626329	+	0.167824i	−0.558003	−	0.829839i	$-0.688432\pi$
$41$	−4.01046	+	1.07460i	−0.626329	+	0.167824i	−0.0683255	+	0.997663i	$0.521766\pi$
$42$		0			0
$43$	7.32559	−	4.22943i	1.11714	−	0.644983i	0.176473	−	0.984306i	$-0.443531\pi$
$43$	7.32559	−	4.22943i	1.11714	−	0.644983i	0.940670	+	0.339323i	$0.110198\pi$
$44$	−2.31134	−	8.62603i	−0.348447	−	1.30042i
$45$		0			0
$46$	1.71283	−	0.458951i	0.252543	−	0.0676687i
$47$	−2.85863	−	10.6686i	−0.416975	−	1.55617i	−0.780847	−	0.624722i	$-0.785212\pi$
$47$	−2.85863	−	10.6686i	−0.416975	−	1.55617i	0.363872	−	0.931449i	$-0.381454\pi$
$48$		0			0
$49$	−6.78525	−	1.72058i	−0.969321	−	0.245797i
$50$	9.02475	−	2.41817i	1.27629	−	0.341981i
$51$		0			0
$52$	−14.4194	−	3.69827i	−1.99962	−	0.512858i
$53$	−4.54930	−	7.87963i	−0.624895	−	1.08235i	−0.988561	−	0.150820i	$-0.951808\pi$
$53$	−4.54930	−	7.87963i	−0.624895	−	1.08235i	0.363666	−	0.931529i	$-0.381525\pi$
$54$		0			0
$55$	−2.07407	−	1.19746i	−0.279667	−	0.161466i
$56$	−11.0040	+	8.56192i	−1.47047	+	1.14413i
$57$		0			0
$58$	5.53626	−	5.53626i	0.726946	−	0.726946i
$59$	2.10905	+	7.87107i	0.274575	+	1.02473i	0.956126	+	0.292956i	$0.0946389\pi$
$59$	2.10905	+	7.87107i	0.274575	+	1.02473i	−0.681551	+	0.731770i	$0.738694\pi$
$60$		0			0
$61$			13.1295i			1.68106i	0.541768	+	0.840528i	$0.317755\pi$
$61$			13.1295i			1.68106i	−0.541768	+	0.840528i	$0.682245\pi$
$62$	2.99312	−	5.18423i	0.380126	−	0.658398i
$63$		0			0
$64$		−	6.32129i		−	0.790162i
$65$	−3.43569	+	2.03307i	−0.426144	+	0.252171i
$66$		0			0
$67$	−8.40090	+	8.40090i	−1.02633	+	1.02633i	−0.0266890	+	0.999644i	$0.508496\pi$
$67$	−8.40090	+	8.40090i	−1.02633	+	1.02633i	−0.999644	+	0.0266890i	$0.991504\pi$
$68$	−11.4165	+	6.59131i	−1.38445	+	0.799314i
$69$		0			0
$70$	−0.898198	+	7.19634i	−0.107355	+	0.860127i
$71$	14.8017	+	3.96611i	1.75664	+	0.470691i	0.986024	−	0.166605i	$-0.0532804\pi$
$71$	14.8017	+	3.96611i	1.75664	+	0.470691i	0.770619	+	0.637296i	$0.219947\pi$
$72$		0			0
$73$	−4.86210	−	1.30280i	−0.569066	−	0.152481i	−0.0371977	−	0.999308i	$-0.511843\pi$
$73$	−4.86210	−	1.30280i	−0.569066	−	0.152481i	−0.531868	+	0.846827i	$0.678510\pi$
$74$	−3.47484	+	6.01860i	−0.403942	+	0.699648i
$75$		0			0
$76$	−3.80061	−	14.1841i	−0.435959	−	1.62702i
$77$	−4.51663	+	3.51426i	−0.514717	+	0.400487i
$78$		0			0
$79$	−8.54505	+	14.8005i	−0.961393	+	1.66518i	−0.242385	+	0.970180i	$0.577930\pi$
$79$	−8.54505	+	14.8005i	−0.961393	+	1.66518i	−0.719008	+	0.695001i	$0.755404\pi$
$80$	3.74913	+	3.74913i	0.419166	+	0.419166i
$81$		0			0
$82$	10.2786			1.13508
$83$	−3.63623	−	3.63623i	−0.399128	−	0.399128i	0.478797	−	0.877926i	$-0.341073\pi$
$83$	−3.63623	−	3.63623i	−0.399128	−	0.399128i	−0.877926	+	0.478797i	$0.841073\pi$
$84$		0			0
$85$	−0.915005	+	3.41484i	−0.0992462	+	0.370392i
$86$	−20.2274	+	5.41991i	−2.18117	+	0.584443i
$87$		0			0
$88$			11.3985i			1.21509i
$89$	5.24668	+	1.40584i	0.556146	+	0.149019i	0.525935	−	0.850525i	$-0.323715\pi$
$89$	5.24668	+	1.40584i	0.556146	+	0.149019i	0.0302111	+	0.999544i	$0.490382\pi$
$90$		0			0
$91$	1.41009	+	9.43460i	0.147818	+	0.989015i
$92$	−2.95732			−0.308321
$93$		0			0
$94$			27.3430i			2.82021i
$95$	−3.41045	−	1.96903i	−0.349905	−	0.202018i
$96$		0			0
$97$	3.61174	−	13.4792i	0.366717	−	1.36861i	−0.498361	−	0.866969i	$-0.666065\pi$
$97$	3.61174	−	13.4792i	0.366717	−	1.36861i	0.865078	−	0.501637i	$-0.167269\pi$
$98$	15.1229	+	8.46192i	1.52764	+	0.854783i
$99$		0			0
$100$	−15.5818			−1.55818
$101$	−18.9217			−1.88278			−0.941390	−	0.337320i	$-0.890480\pi$
$101$	−18.9217			−1.88278			−0.941390	+	0.337320i	$0.890480\pi$
$102$		0			0
$103$	−4.50207	+	7.79781i	−0.443602	+	0.768341i	−0.997954	−	0.0639412i	$-0.979633\pi$
$103$	−4.50207	+	7.79781i	−0.443602	+	0.768341i	0.554352	+	0.832283i	$0.312966\pi$
$104$	16.5559	+	9.32308i	1.62344	+	0.914204i
$105$		0			0
$106$	5.82981	+	21.7572i	0.566241	+	2.11324i
$107$	−6.49988	−	11.2581i	−0.628367	−	1.08836i	−0.987879	−	0.155223i	$-0.950390\pi$
$107$	−6.49988	−	11.2581i	−0.628367	−	1.08836i	0.359512	−	0.933140i	$-0.382943\pi$
$108$		0			0
$109$	−0.626065	−	0.167754i	−0.0599662	−	0.0160679i	0.228711	−	0.973494i	$-0.426549\pi$
$109$	−0.626065	−	0.167754i	−0.0599662	−	0.0160679i	−0.288677	+	0.957426i	$0.593216\pi$
$110$	4.19238	+	4.19238i	0.399728	+	0.399728i
$111$		0			0
$112$	11.6722	−	4.92705i	1.10292	−	0.465562i
$113$	2.55967	+	4.43348i	0.240794	+	0.417067i	0.960941	−	0.276755i	$-0.0892590\pi$
$113$	2.55967	+	4.43348i	0.240794	+	0.417067i	−0.720147	+	0.693822i	$0.755926\pi$
$114$		0			0
$115$	−0.560800	+	0.560800i	−0.0522948	+	0.0522948i
$116$	−11.3081	+	6.52873i	−1.04993	+	0.606178i
$117$		0			0
$118$		−	20.1731i		−	1.85709i
$119$	6.73649	+	5.09744i	0.617533	+	0.467282i
$120$		0			0
$121$		−	6.32144i		−	0.574676i
$122$	8.41253	−	31.3960i	0.761635	−	2.84246i
$123$		0			0
$124$	−7.05937	+	7.05937i	−0.633950	+	0.633950i
$125$	−6.86944	+	6.86944i	−0.614421	+	0.614421i
$126$		0			0
$127$	−11.5953	−	6.69453i	−1.02891	−	0.594044i	−0.112240	−	0.993681i	$-0.535803\pi$
$127$	−11.5953	−	6.69453i	−1.02891	−	0.594044i	−0.916673	+	0.399638i	$0.869136\pi$
$128$	−4.73108	+	17.6566i	−0.418173	+	1.56064i
$129$		0			0
$130$	9.51829	−	2.66023i	0.834809	−	0.233318i
$131$	−2.22446	−	1.28429i	−0.194352	−	0.112209i	0.399666	−	0.916661i	$-0.369126\pi$
$131$	−2.22446	−	1.28429i	−0.194352	−	0.112209i	−0.594018	+	0.804452i	$0.702459\pi$
$132$		0			0
$133$	−7.42683	+	5.77862i	−0.643988	+	0.501069i
$134$	25.4715	−	14.7060i	2.20040	−	1.27040i
$135$		0			0
$136$	16.2528	−	4.35492i	1.39367	−	0.373431i
$137$	−14.8475	+	3.97837i	−1.26851	+	0.339895i	−0.829458	−	0.558569i	$-0.811351\pi$
$137$	−14.8475	+	3.97837i	−1.26851	+	0.339895i	−0.439047	+	0.898464i	$0.644684\pi$
$138$		0			0
$139$	2.84843	−	1.64454i	0.241601	−	0.139488i	−0.374312	−	0.927303i	$-0.622121\pi$
$139$	2.84843	−	1.64454i	0.241601	−	0.139488i	0.615912	+	0.787815i	$0.288788\pi$
$140$	4.55316	−	11.2050i	0.384812	−	0.946991i
$141$		0			0
$142$	−32.8536	−	18.9680i	−2.75701	−	1.59176i
$143$	6.79543	+	3.82669i	0.568262	+	0.320004i
$144$		0			0
$145$	−0.906317	+	3.38242i	−0.0752655	+	0.280895i
$146$	10.7918	+	6.23065i	0.893136	+	0.515652i
$147$		0			0
$148$	8.19554	−	8.19554i	0.673669	−	0.673669i
$149$	2.78449	−	2.78449i	0.228114	−	0.228114i	−0.583790	−	0.811904i	$-0.698431\pi$
$149$	2.78449	−	2.78449i	0.228114	−	0.228114i	0.811904	+	0.583790i	$0.198431\pi$
$150$		0			0
$151$	2.01661	−	7.52610i	0.164110	−	0.612465i	−0.834043	−	0.551700i	$-0.813979\pi$
$151$	2.01661	−	7.52610i	0.164110	−	0.612465i	0.998152	−	0.0607650i	$-0.0193540\pi$
$152$			18.7430i			1.52026i
$153$		0			0
$154$	13.0522	−	5.50956i	1.05177	−	0.443973i
$155$			2.67736i			0.215050i
$156$		0			0
$157$	9.33603	−	5.39016i	0.745096	−	0.430181i	−0.0788232	−	0.996889i	$-0.525116\pi$
$157$	9.33603	−	5.39016i	0.745096	−	0.430181i	0.823919	+	0.566707i	$0.191783\pi$
$158$	29.9166	−	29.9166i	2.38004	−	2.38004i
$159$		0			0
$160$	−0.728112	−	1.26113i	−0.0575623	−	0.0997009i
$161$	0.736994	+	1.74594i	0.0580833	+	0.137599i
$162$		0			0
$163$	3.25130	+	3.25130i	0.254662	+	0.254662i	0.822879	−	0.568217i	$-0.192367\pi$
$163$	3.25130	+	3.25130i	0.254662	+	0.254662i	−0.568217	+	0.822879i	$0.692367\pi$
$164$	−16.5579	−	4.43667i	−1.29295	−	0.346446i
$165$		0			0
$166$	6.36532	+	11.0251i	0.494044	+	0.855710i
$167$	−2.67718	−	9.99136i	−0.207166	−	0.773154i	−0.988778	−	0.149390i	$-0.952269\pi$
$167$	−2.67718	−	9.99136i	−0.207166	−	0.773154i	0.781612	−	0.623765i	$-0.214398\pi$
$168$		0			0
$169$	11.1162	−	6.74016i	0.855093	−	0.518474i
$170$	4.37603	−	7.57951i	0.335626	−	0.581322i
$171$		0			0
$172$	34.9239			2.66292
$173$	−7.92507			−0.602532			−0.301266	−	0.953540i	$-0.597409\pi$
$173$	−7.92507			−0.602532			−0.301266	+	0.953540i	$0.597409\pi$
$174$		0			0
$175$	3.88316	+	9.19921i	0.293539	+	0.695395i
$176$	2.68079	−	10.0048i	0.202072	−	0.754143i
$177$		0			0
$178$	−11.6454	−	6.72347i	−0.872860	−	0.503946i
$179$			0.776613i			0.0580468i	0.999579	+	0.0290234i	$0.00923973\pi$
$179$			0.776613i			0.0580468i	−0.999579	+	0.0290234i	$0.990760\pi$
$180$		0			0
$181$	10.5598			0.784905			0.392452	−	0.919772i	$-0.371627\pi$
$181$	10.5598			0.784905			0.392452	+	0.919772i	$0.371627\pi$
$182$	2.67319	−	23.4641i	0.198150	−	1.73927i
$183$		0			0
$184$	3.64606	+	0.976958i	0.268791	+	0.0720223i
$185$		−	3.10826i		−	0.228524i
$186$		0			0
$187$	6.67101	−	1.78749i	0.487832	−	0.130714i
$188$	11.8024	−	44.0471i	0.860777	−	3.21246i
$189$		0			0
$190$	6.89366	+	6.89366i	0.500119	+	0.500119i
$191$	5.45039			0.394376			0.197188	−	0.980366i	$-0.436819\pi$
$191$	5.45039			0.394376			0.197188	+	0.980366i	$0.436819\pi$
$192$		0			0
$193$	−10.1470	−	10.1470i	−0.730394	−	0.730394i	0.240303	−	0.970698i	$-0.422753\pi$
$193$	−10.1470	−	10.1470i	−0.730394	−	0.730394i	−0.970698	+	0.240303i	$0.922753\pi$
$194$	−17.2732	+	29.9181i	−1.24015	+	2.14800i
$195$		0			0
$196$	−20.7091	−	20.1591i	−1.47922	−	1.43993i
$197$	−5.97264	−	22.2902i	−0.425533	−	1.58811i	−0.762757	−	0.646686i	$-0.776155\pi$
$197$	−5.97264	−	22.2902i	−0.425533	−	1.58811i	0.337224	−	0.941424i	$-0.390512\pi$
$198$		0			0
$199$	−4.48268	+	7.76424i	−0.317769	+	0.550392i	−0.980022	−	0.198888i	$-0.936267\pi$
$199$	−4.48268	+	7.76424i	−0.317769	+	0.550392i	0.662253	+	0.749280i	$0.269600\pi$
$200$	19.2108	+	5.14751i	1.35841	+	0.363984i
$201$		0			0
$202$	45.2468	+	12.1238i	3.18355	+	0.853030i
$203$	6.67253	+	5.04905i	0.468320	+	0.354374i
$204$		0			0
$205$	−3.98123	+	2.29856i	−0.278061	+	0.160539i
$206$	15.7620	−	15.7620i	1.09819	−	1.09819i
$207$		0			0
$208$	−12.3390	−	12.0769i	−0.855552	−	0.837381i
$209$			7.69311i			0.532144i
$210$		0			0
$211$	1.93953	−	3.35936i	0.133523	−	0.231268i	−0.791509	−	0.611157i	$-0.790704\pi$
$211$	1.93953	−	3.35936i	0.133523	−	0.231268i	0.925032	+	0.379889i	$0.124038\pi$
$212$		−	37.5652i		−	2.57999i
$213$		0			0
$214$	8.32942	+	31.0858i	0.569388	+	2.12498i
$215$	6.62267	−	6.62267i	0.451662	−	0.451662i
$216$		0			0
$217$	5.92698	+	2.40844i	0.402350	+	0.163496i
$218$	1.38960	+	0.802286i	0.0941156	+	0.0543377i
$219$		0			0
$220$	−4.94394	−	8.56315i	−0.333320	−	0.577328i
$221$	2.86008	−	11.1514i	0.192390	−	0.750124i
$222$		0			0
$223$	19.2784	−	5.16562i	1.29097	−	0.345916i	0.452944	−	0.891539i	$-0.350374\pi$
$223$	19.2784	−	5.16562i	1.29097	−	0.345916i	0.838031	+	0.545623i	$0.183707\pi$
$224$	−3.44679	+	0.477394i	−0.230299	+	0.0318972i
$225$		0			0
$226$	−3.28015	−	12.2417i	−0.218192	−	0.814305i
$227$	−9.28427	+	2.48771i	−0.616219	+	0.165115i	−0.553408	−	0.832910i	$-0.686673\pi$
$227$	−9.28427	+	2.48771i	−0.616219	+	0.165115i	−0.0628104	+	0.998025i	$0.520006\pi$
$228$		0			0
$229$	−6.89824	−	25.7446i	−0.455848	−	1.70125i	−0.685582	−	0.727996i	$-0.740452\pi$
$229$	−6.89824	−	25.7446i	−0.455848	−	1.70125i	0.229733	−	0.973254i	$-0.426215\pi$
$230$	1.70034	−	0.981694i	0.112117	−	0.0647310i
$231$		0			0
$232$	16.0985	−	4.31357i	1.05692	−	0.283200i
$233$	−1.53044	−	0.883603i	−0.100263	−	0.0578867i	0.449030	−	0.893517i	$-0.351770\pi$
$233$	−1.53044	−	0.883603i	−0.100263	−	0.0578867i	−0.549293	+	0.835630i	$0.685103\pi$
$234$		0			0
$235$	−6.11460	−	10.5908i	−0.398873	−	0.690868i
$236$	−8.70757	+	32.4971i	−0.566815	+	2.11538i
$237$		0			0
$238$	−12.8426	−	16.5056i	−0.832461	−	1.06990i
$239$	−21.4837	+	21.4837i	−1.38967	+	1.38967i	−0.563654	+	0.826011i	$0.690605\pi$
$239$	−21.4837	+	21.4837i	−1.38967	+	1.38967i	−0.826011	+	0.563654i	$0.809395\pi$
$240$		0			0
$241$	−2.48199	−	9.26292i	−0.159879	−	0.596677i	−0.998638	−	0.0521742i	$-0.983385\pi$
$241$	−2.48199	−	9.26292i	−0.159879	−	0.596677i	0.838759	−	0.544503i	$-0.183282\pi$
$242$	−4.05038	+	15.1162i	−0.260368	+	0.971707i
$243$		0			0
$244$	−27.1037	+	46.9449i	−1.73513	+	3.00534i
$245$	−7.74987	+	0.104297i	−0.495121	+	0.00666329i
$246$		0			0
$247$	11.1739	+	6.29234i	0.710980	+	0.400372i
$248$	11.0355	−	6.37138i	0.700758	−	0.404583i
$249$		0			0
$250$	20.8281	−	12.0251i	1.31729	−	0.760535i
$251$	7.01379	+	12.1482i	0.442706	+	0.766790i	0.997889	−	0.0649385i	$-0.0206851\pi$
$251$	7.01379	+	12.1482i	0.442706	+	0.766790i	−0.555183	+	0.831728i	$0.687352\pi$
$252$		0			0
$253$	1.49654	+	0.400995i	0.0940864	+	0.0252104i
$254$	23.4379	+	23.4379i	1.47062	+	1.47062i
$255$		0			0
$256$	16.3052	−	28.2415i	1.01908	−	1.76509i
$257$	3.92232	+	6.79366i	0.244668	+	0.423777i	0.962038	−	0.272915i	$-0.0879878\pi$
$257$	3.92232	+	6.79366i	0.244668	+	0.423777i	−0.717370	+	0.696692i	$0.754654\pi$
$258$		0			0
$259$	−6.88090	−	2.79607i	−0.427558	−	0.173739i
$260$	−16.4814	+	0.176905i	−1.02213	+	0.0109712i
$261$		0			0
$262$	4.49637	+	4.49637i	0.277787	+	0.277787i
$263$	30.1387			1.85843			0.929217	−	0.369535i	$-0.120483\pi$
$263$	30.1387			1.85843			0.929217	+	0.369535i	$0.120483\pi$
$264$		0			0
$265$	−7.12354	−	7.12354i	−0.437595	−	0.437595i
$266$	21.4621	−	9.05954i	1.31592	−	0.555476i
$267$		0			0
$268$	−47.3800	+	12.6954i	−2.89420	+	0.775497i
$269$	1.57674	+	0.910328i	0.0961352	+	0.0555037i	0.547297	−	0.836939i	$-0.315657\pi$
$269$	1.57674	+	0.910328i	0.0961352	+	0.0555037i	−0.451162	+	0.892442i	$0.648990\pi$
$270$		0			0
$271$	−4.75330	−	1.27364i	−0.288742	−	0.0773682i	0.111541	−	0.993760i	$-0.464421\pi$
$271$	−4.75330	−	1.27364i	−0.288742	−	0.0773682i	−0.400283	+	0.916392i	$0.631088\pi$
$272$	−15.2898			−0.927079
$273$		0			0
$274$	38.0533			2.29888
$275$	7.88512	+	2.11281i	0.475490	+	0.127407i
$276$		0			0
$277$	−4.09191	−	2.36247i	−0.245859	−	0.141947i	0.372008	−	0.928230i	$-0.378670\pi$
$277$	−4.09191	−	2.36247i	−0.245859	−	0.141947i	−0.617867	+	0.786283i	$0.712003\pi$
$278$	−7.86506	+	2.10744i	−0.471715	+	0.126396i
$279$		0			0
$280$	−9.31515	+	12.3104i	−0.556687	+	0.735685i
$281$	12.5689	+	12.5689i	0.749799	+	0.749799i	0.974441	−	0.224642i	$-0.0721213\pi$
$281$	12.5689	+	12.5689i	0.749799	+	0.749799i	−0.224642	+	0.974441i	$0.572121\pi$
$282$		0			0
$283$	−16.8354			−1.00076			−0.500379	−	0.865806i	$-0.666806\pi$
$283$	−16.8354			−1.00076			−0.500379	+	0.865806i	$0.666806\pi$
$284$	44.7368	+	44.7368i	2.65464	+	2.65464i
$285$		0			0
$286$	−13.7977	−	13.5047i	−0.815878	−	0.798549i
$287$	1.50708	+	10.8811i	0.0889599	+	0.642292i
$288$		0			0
$289$	3.40256	+	5.89340i	0.200150	+	0.346671i
$290$	4.33448	−	7.50754i	0.254530	−	0.440858i
$291$		0			0
$292$	−14.6952	−	14.6952i	−0.859972	−	0.859972i
$293$	−2.69125	−	0.721119i	−0.157225	−	0.0421282i	0.179348	−	0.983786i	$-0.442601\pi$
$293$	−2.69125	−	0.721119i	−0.157225	−	0.0421282i	−0.336573	+	0.941657i	$0.609268\pi$
$294$		0			0
$295$	4.51124	+	7.81370i	0.262655	+	0.454931i
$296$	−12.8117	+	7.39681i	−0.744662	+	0.429931i
$297$		0			0
$298$	−8.44256	+	4.87432i	−0.489065	+	0.282362i
$299$	1.80647	−	1.84568i	0.104471	−	0.106738i
$300$		0			0
$301$	−8.70341	−	20.6184i	−0.501656	−	1.18842i
$302$	−9.64449	+	16.7047i	−0.554978	+	0.961250i
$303$		0			0
$304$	4.40810	−	16.4513i	0.252822	−	0.943545i
$305$	3.76252	+	14.0419i	0.215442	+	0.804039i
$306$		0			0
$307$	−11.1210	+	11.1210i	−0.634708	+	0.634708i	−0.949245	−	0.314537i	$-0.898151\pi$
$307$	−11.1210	+	11.1210i	−0.634708	+	0.634708i	0.314537	+	0.949245i	$0.398151\pi$
$308$	−23.4040	+	3.24154i	−1.33357	+	0.184704i
$309$		0			0
$310$	1.71548	−	6.40226i	0.0974327	−	0.363624i
$311$	−12.9496	−	22.4293i	−0.734304	−	1.27185i	−0.955028	−	0.296515i	$-0.904176\pi$
$311$	−12.9496	−	22.4293i	−0.734304	−	1.27185i	0.220725	−	0.975336i	$-0.429158\pi$
$312$		0			0
$313$	6.50589	+	3.75618i	0.367734	+	0.212312i	0.672468	−	0.740126i	$-0.265234\pi$
$313$	6.50589	+	3.75618i	0.367734	+	0.212312i	−0.304734	+	0.952438i	$0.598567\pi$
$314$	−25.7786	+	6.90734i	−1.45477	+	0.389804i
$315$		0			0
$316$	−61.1063	+	35.2797i	−3.43750	+	1.98464i
$317$	1.89185	+	7.06048i	0.106257	+	0.396556i	0.998485	−	0.0550295i	$-0.0175253\pi$
$317$	1.89185	+	7.06048i	0.106257	+	0.396556i	−0.892228	+	0.451585i	$0.850859\pi$
$318$		0			0
$319$	6.60767	−	1.77052i	0.369958	−	0.0991300i
$320$	−1.81150	−	6.76061i	−0.101266	−	0.377929i
$321$		0			0
$322$	−0.643658	−	4.64722i	−0.0358696	−	0.258979i
$323$	10.9693	−	2.93923i	0.610351	−	0.163543i
$324$		0			0
$325$	9.51816	−	9.72470i	0.527972	−	0.539429i
$326$	−5.69149	−	9.85795i	−0.315223	−	0.545981i
$327$		0			0
$328$	18.9485	+	10.9399i	1.04625	+	0.604055i
$329$	−28.9458	+	4.00910i	−1.59583	+	0.221029i
$330$		0			0
$331$	23.2409	−	23.2409i	1.27744	−	1.27744i	0.335339	−	0.942098i	$-0.391149\pi$
$331$	23.2409	−	23.2409i	1.27744	−	1.27744i	0.942098	−	0.335339i	$-0.108851\pi$
$332$	−5.49508	−	20.5079i	−0.301581	−	1.12552i
$333$		0			0
$334$			25.6073i			1.40117i
$335$	−6.57728	+	11.3922i	−0.359355	+	0.622422i
$336$		0			0
$337$		−	6.18416i		−	0.336873i	−0.985713	−	0.168436i	$-0.946128\pi$
$337$		−	6.18416i		−	0.336873i	0.985713	−	0.168436i	$-0.0538718\pi$
$338$	−30.9004	+	8.99492i	−1.68076	+	0.489259i
$339$		0			0
$340$	−10.3210	+	10.3210i	−0.559736	+	0.559736i
$341$	4.52957	−	2.61515i	0.245290	−	0.141618i
$342$		0			0
$343$	−6.74059	+	17.2501i	−0.363958	+	0.931416i
$344$	−43.0575	−	11.5372i	−2.32151	−	0.622045i
$345$		0			0
$346$	18.9509	+	5.07788i	1.01881	+	0.272989i
$347$	12.5904	−	21.8072i	0.675889	−	1.17067i	−0.300319	−	0.953839i	$-0.597093\pi$
$347$	12.5904	−	21.8072i	0.675889	−	1.17067i	0.976208	−	0.216835i	$-0.0695734\pi$
$348$		0			0
$349$	−4.81860	−	17.9833i	−0.257934	−	0.962622i	−0.966435	−	0.256912i	$-0.917295\pi$
$349$	−4.81860	−	17.9833i	−0.257934	−	0.962622i	0.708501	−	0.705710i	$-0.249372\pi$
$350$	−3.39138	−	24.4858i	−0.181277	−	1.30882i
$351$		0			0
$352$	−1.42239	+	2.46365i	−0.0758137	+	0.131313i
$353$	14.5922	+	14.5922i	0.776665	+	0.776665i	0.979262	−	0.202597i	$-0.0649382\pi$
$353$	14.5922	+	14.5922i	0.776665	+	0.776665i	−0.202597	+	0.979262i	$0.564938\pi$
$354$		0			0
$355$	16.9670			0.900514
$356$	15.8576	+	15.8576i	0.840449	+	0.840449i
$357$		0			0
$358$	0.497605	−	1.85709i	0.0262992	−	0.0981500i
$359$	8.98361	−	2.40715i	0.474137	−	0.127045i	−0.0138345	−	0.999904i	$-0.504404\pi$
$359$	8.98361	−	2.40715i	0.474137	−	0.127045i	0.487971	+	0.872860i	$0.337737\pi$
$360$		0			0
$361$		−	6.34997i		−	0.334209i
$362$	−25.2513	−	6.76606i	−1.32718	−	0.355616i
$363$		0			0
$364$	−14.4344	+	36.6447i	−0.756566	+	1.92070i
$365$	−5.57335			−0.291722
$366$		0			0
$367$			34.0704i			1.77846i	0.457460	+	0.889230i	$0.348759\pi$
$367$			34.0704i			1.77846i	−0.457460	+	0.889230i	$0.651241\pi$
$368$	−2.97049	−	1.71501i	−0.154847	−	0.0894011i
$369$		0			0
$370$	−1.99158	+	7.43267i	−0.103537	+	0.386406i
$371$	−22.1777	+	9.36164i	−1.15141	+	0.486032i
$372$		0			0
$373$	22.0202			1.14016			0.570082	−	0.821588i	$-0.306912\pi$
$373$	22.0202			1.14016			0.570082	+	0.821588i	$0.306912\pi$
$374$	−17.0974			−0.884087
$375$		0			0
$376$	−29.1022	+	50.4064i	−1.50083	+	2.59951i
$377$	2.83293	−	11.0455i	0.145903	−	0.568873i
$378$		0			0
$379$	−0.321459	−	1.19970i	−0.0165123	−	0.0616246i	0.957178	−	0.289500i	$-0.0934889\pi$
$379$	−0.321459	−	1.19970i	−0.0165123	−	0.0616246i	−0.973690	+	0.227875i	$0.926822\pi$
$380$	−8.12947	−	14.0807i	−0.417033	−	0.722323i
$381$		0			0
$382$	−13.0333	−	3.49226i	−0.666842	−	0.178680i
$383$	10.3254	+	10.3254i	0.527603	+	0.527603i	0.919857	−	0.392254i	$-0.128305\pi$
$383$	10.3254	+	10.3254i	0.527603	+	0.527603i	−0.392254	+	0.919857i	$0.628305\pi$
$384$		0			0
$385$	−3.82343	+	5.05283i	−0.194860	+	0.257516i
$386$	17.7625	+	30.7656i	0.904088	+	1.56593i
$387$		0			0
$388$	40.7396	−	40.7396i	2.06824	−	2.06824i
$389$	−14.0217	+	8.09545i	−0.710930	+	0.410456i	−0.811405	−	0.584484i	$-0.801297\pi$
$389$	−14.0217	+	8.09545i	−0.710930	+	0.410456i	0.100475	+	0.994940i	$0.467964\pi$
$390$		0			0
$391$		−	2.28706i		−	0.115662i
$392$	18.8725	+	31.6953i	0.953204	+	1.60085i
$393$		0			0
$394$			57.1286i			2.87810i
$395$	−4.89752	+	18.2778i	−0.246421	+	0.919656i
$396$		0			0
$397$	−21.7086	+	21.7086i	−1.08952	+	1.08952i	−0.0939469	+	0.995577i	$0.529948\pi$
$397$	−21.7086	+	21.7086i	−1.08952	+	1.08952i	−0.995577	+	0.0939469i	$0.970052\pi$
$398$	15.6941	−	15.6941i	0.786674	−	0.786674i
$399$		0			0
$400$	−15.6512	−	9.03624i	−0.782562	−	0.451812i
$401$	−1.25827	+	4.69592i	−0.0628349	+	0.234503i	−0.990200	−	0.139654i	$-0.955401\pi$
$401$	−1.25827	+	4.69592i	−0.0628349	+	0.234503i	0.927366	+	0.374157i	$0.122068\pi$
$402$		0			0
$403$	−0.0935758	−	8.71800i	−0.00466134	−	0.434275i
$404$	−67.6553	−	39.0608i	−3.36598	−	1.94335i
$405$		0			0
$406$	−12.7207	−	16.3489i	−0.631315	−	0.811383i
$407$	−5.25858	+	3.03604i	−0.260658	+	0.150491i
$408$		0			0
$409$	−7.01765	+	1.88037i	−0.347000	+	0.0929784i	−0.428110	−	0.903727i	$-0.640820\pi$
$409$	−7.01765	+	1.88037i	−0.347000	+	0.0929784i	0.0811095	+	0.996705i	$0.474154\pi$
$410$	10.9929	−	2.94555i	0.542902	−	0.145470i
$411$		0			0
$412$	−32.1947	+	18.5876i	−1.58612	+	0.915745i
$413$	21.3557	−	2.95784i	1.05084	−	0.145546i
$414$		0			0
$415$	−4.93098	−	2.84690i	−0.242052	−	0.139749i
$416$	2.41496	+	4.08103i	0.118403	+	0.200089i
$417$		0			0
$418$	4.92926	−	18.3962i	0.241098	−	0.899790i
$419$	3.79902	+	2.19337i	0.185594	+	0.107153i	0.589918	−	0.807463i	$-0.299160\pi$
$419$	3.79902	+	2.19337i	0.185594	+	0.107153i	−0.404324	+	0.914616i	$0.632493\pi$
$420$		0			0
$421$	2.39860	−	2.39860i	0.116901	−	0.116901i	−0.646236	−	0.763137i	$-0.723658\pi$
$421$	2.39860	−	2.39860i	0.116901	−	0.116901i	0.763137	+	0.646236i	$0.223658\pi$
$422$	−6.79039	+	6.79039i	−0.330551	+	0.330551i
$423$		0			0
$424$	−12.4098	+	46.3139i	−0.602672	+	2.24920i
$425$		−	12.0503i		−	0.584527i
$426$		0			0
$427$	34.4699	+	4.30230i	1.66811	+	0.208203i
$428$		−	53.6718i		−	2.59432i
$429$		0			0
$430$	−20.0799	+	11.5931i	−0.968340	+	0.559071i
$431$	19.8131	−	19.8131i	0.954365	−	0.954365i	−0.0446380	−	0.999003i	$-0.514213\pi$
$431$	19.8131	−	19.8131i	0.954365	−	0.954365i	0.999003	+	0.0446380i	$0.0142134\pi$
$432$		0			0
$433$	0.984147	+	1.70459i	0.0472951	+	0.0819175i	0.888704	−	0.458482i	$-0.151607\pi$
$433$	0.984147	+	1.70459i	0.0472951	+	0.0819175i	−0.841409	+	0.540399i	$0.818273\pi$
$434$	−12.6298	−	9.55685i	−0.606249	−	0.458744i
$435$		0			0
$436$	−1.89222	−	1.89222i	−0.0906209	−	0.0906209i
$437$	2.46080	+	0.659370i	0.117716	+	0.0315419i
$438$		0			0
$439$	−4.86693	−	8.42976i	−0.232286	−	0.402331i	0.726195	−	0.687489i	$-0.241287\pi$
$439$	−4.86693	−	8.42976i	−0.232286	−	0.402331i	−0.958480	+	0.285158i	$0.907954\pi$
$440$	3.26649	+	12.1907i	0.155724	+	0.581169i
$441$		0			0
$442$	−13.9843	+	24.8333i	−0.665166	+	1.18120i
$443$	14.0996	−	24.4213i	0.669894	−	1.16029i	−0.308040	−	0.951373i	$-0.599673\pi$
$443$	14.0996	−	24.4213i	0.669894	−	1.16029i	0.977933	−	0.208916i	$-0.0669937\pi$
$444$		0			0
$445$	6.01418			0.285099
$446$	−49.4094			−2.33960
$447$		0			0
$448$	−16.5958	−	2.07138i	−0.784078	−	0.0978634i
$449$	6.46808	−	24.1392i	0.305247	−	1.13920i	−0.627485	−	0.778629i	$-0.715916\pi$
$449$	6.46808	−	24.1392i	0.305247	−	1.13920i	0.932732	−	0.360570i	$-0.117418\pi$
$450$		0			0
$451$	7.77745	+	4.49031i	0.366226	+	0.211441i
$452$			21.1361i			0.994159i
$453$		0			0
$454$	23.7951			1.11676
$455$	4.21177	+	9.68618i	0.197451	+	0.454095i
$456$		0			0
$457$	18.3479	+	4.91632i	0.858281	+	0.229976i	0.661013	−	0.750374i	$-0.270127\pi$
$457$	18.3479	+	4.91632i	0.858281	+	0.229976i	0.197267	+	0.980350i	$0.436793\pi$
$458$			65.9820i			3.08313i
$459$		0			0
$460$	−3.16284	+	0.847481i	−0.147468	+	0.0395140i
$461$	4.98997	−	18.6228i	0.232406	−	0.867350i	−0.746895	−	0.664942i	$-0.768456\pi$
$461$	4.98997	−	18.6228i	0.232406	−	0.867350i	0.979301	−	0.202409i	$-0.0648770\pi$
$462$		0			0
$463$	−9.73196	−	9.73196i	−0.452283	−	0.452283i	0.443829	−	0.896112i	$-0.353620\pi$
$463$	−9.73196	−	9.73196i	−0.452283	−	0.452283i	−0.896112	+	0.443829i	$0.853620\pi$
$464$	−15.1446			−0.703071
$465$		0			0
$466$	3.09354	+	3.09354i	0.143305	+	0.143305i
$467$	15.2510	−	26.4155i	0.705733	−	1.22237i	−0.260693	−	0.965422i	$-0.583951\pi$
$467$	15.2510	−	26.4155i	0.705733	−	1.22237i	0.966426	−	0.256944i	$-0.0827155\pi$
$468$		0			0
$469$	19.3027	+	24.8084i	0.891317	+	1.14554i
$470$	7.83570	+	29.2432i	0.361434	+	1.34889i
$471$		0			0
$472$	21.4710	−	37.1889i	0.988285	−	1.71176i
$473$	−17.6731	−	4.73549i	−0.812609	−	0.217738i
$474$		0			0
$475$	12.9657	+	3.47416i	0.594909	+	0.159405i
$476$	13.5637	+	32.1325i	0.621692	+	1.47279i
$477$		0			0
$478$	65.1385	−	37.6078i	2.97937	−	1.72014i
$479$	−7.15853	+	7.15853i	−0.327082	+	0.327082i	−0.851476	−	0.524394i	$-0.824292\pi$
$479$	−7.15853	+	7.15853i	−0.327082	+	0.327082i	0.524394	+	0.851476i	$0.324292\pi$
$480$		0			0
$481$	0.108636	+	10.1211i	0.00495339	+	0.461483i
$482$			23.7404i			1.08134i
$483$		0			0
$484$	13.0496	−	22.6025i	0.593163	−	1.02739i
$485$		−	15.4510i		−	0.701594i
$486$		0			0
$487$	−6.33502	−	23.6426i	−0.287067	−	1.07135i	−0.947316	−	0.320301i	$-0.896216\pi$
$487$	−6.33502	−	23.6426i	−0.287067	−	1.07135i	0.660249	−	0.751047i	$-0.270451\pi$
$488$	48.9244	−	48.9244i	2.21470	−	2.21470i
$489$		0			0
$490$	18.5988	+	4.71623i	0.840208	+	0.213057i
$491$	−3.99686	−	2.30759i	−0.180376	−	0.104140i	0.407093	−	0.913387i	$-0.366542\pi$
$491$	−3.99686	−	2.30759i	−0.180376	−	0.104140i	−0.587469	+	0.809247i	$0.699876\pi$
$492$		0			0
$493$	−5.04905	−	8.74520i	−0.227398	−	0.393864i
$494$	−22.6881	−	22.2062i	−1.02078	−	0.999104i
$495$		0			0
$496$	−11.1847	+	2.99693i	−0.502207	+	0.134566i
$497$	15.2628	−	37.5606i	0.684631	−	1.68482i
$498$		0			0
$499$	3.12405	+	11.6591i	0.139852	+	0.521934i	0.999931	+	0.0117728i	$0.00374750\pi$
$499$	3.12405	+	11.6591i	0.139852	+	0.521934i	−0.860079	+	0.510161i	$0.829586\pi$
$500$	−38.7428	+	10.3811i	−1.73263	+	0.464257i
$501$		0			0
$502$	−8.98798	−	33.5436i	−0.401153	−	1.49712i
$503$	−26.0380	+	15.0331i	−1.16098	+	0.670291i	−0.951538	−	0.307531i	$-0.900497\pi$
$503$	−26.0380	+	15.0331i	−1.16098	+	0.670291i	−0.209440	+	0.977822i	$0.567164\pi$
$504$		0			0
$505$	−20.2367	+	5.42241i	−0.900522	+	0.241294i
$506$	−3.32168	−	1.91777i	−0.147666	−	0.0852553i
$507$		0			0
$508$	−27.6396	−	47.8731i	−1.22631	−	2.12403i
$509$	−5.60832	+	20.9305i	−0.248584	+	0.927730i	0.722963	+	0.690886i	$0.242779\pi$
$509$	−5.60832	+	20.9305i	−0.248584	+	0.927730i	−0.971548	+	0.236843i	$0.923887\pi$
$510$		0			0
$511$	−5.01356	+	12.3380i	−0.221787	+	0.545799i
$512$	−31.2343	+	31.2343i	−1.38037	+	1.38037i
$513$		0			0
$514$	−5.02635	−	18.7586i	−0.221703	−	0.827406i
$515$	−2.58032	+	9.62990i	−0.113703	+	0.424344i
$516$		0			0
$517$	−11.9451	+	20.6895i	−0.525344	+	0.909922i
$518$	14.6625	+	11.0950i	0.644232	+	0.487485i
$519$		0			0
$520$	20.3782	+	5.22657i	0.893645	+	0.229200i
$521$	10.6562	−	6.15238i	0.466858	−	0.269541i	−0.248065	−	0.968743i	$-0.579795\pi$
$521$	10.6562	−	6.15238i	0.466858	−	0.269541i	0.714924	+	0.699203i	$0.246461\pi$
$522$		0			0
$523$	3.57584	−	2.06451i	0.156360	−	0.0902747i	−0.419778	−	0.907627i	$-0.637892\pi$
$523$	3.57584	−	2.06451i	0.156360	−	0.0902747i	0.576139	+	0.817352i	$0.304559\pi$
$524$	−5.30242	−	9.18407i	−0.231638	−	0.401208i
$525$		0			0
$526$	−72.0696	−	19.3110i	−3.14238	−	0.841999i
$527$	−5.45942	−	5.45942i	−0.237816	−	0.237816i
$528$		0			0
$529$	−11.2435	+	19.4743i	−0.488846	+	0.846707i
$530$	12.4699	+	21.5986i	0.541659	+	0.938181i
$531$		0			0
$532$	−38.4839	+	5.33017i	−1.66849	+	0.231092i
$533$	12.8833	−	7.62372i	0.558039	−	0.330220i
$534$		0			0
$535$	−10.1779	−	10.1779i	−0.440027	−	0.440027i
$536$	62.6085			2.70428
$537$		0			0
$538$	−3.18711	−	3.18711i	−0.137406	−	0.137406i
$539$	7.74626	+	13.0094i	0.333655	+	0.560356i
$540$		0			0
$541$	−10.1891	+	2.73015i	−0.438062	+	0.117378i	−0.471108	−	0.882075i	$-0.656146\pi$
$541$	−10.1891	+	2.73015i	−0.438062	+	0.117378i	0.0330459	+	0.999454i	$0.489479\pi$
$542$	10.5503	+	6.09122i	0.453175	+	0.261640i
$543$		0			0
$544$	4.05628	+	1.08688i	0.173911	+	0.0465994i
$545$	−0.717648			−0.0307407
$546$		0			0
$547$	33.3666			1.42665			0.713327	−	0.700831i	$-0.247187\pi$
$547$	33.3666			1.42665			0.713327	+	0.700831i	$0.247187\pi$
$548$	−61.3004	−	16.4254i	−2.61862	−	0.701658i
$549$		0			0
$550$	−17.5016	−	10.1046i	−0.746272	−	0.430860i
$551$	10.8652	−	2.91132i	0.462873	−	0.124026i
$552$		0			0
$553$	36.0568	+	27.2839i	1.53329	+	1.16023i
$554$	8.27111	+	8.27111i	0.351406	+	0.351406i
$555$		0			0
$556$	13.5796			0.575902
$557$	−7.06829	−	7.06829i	−0.299493	−	0.299493i	0.541322	−	0.840815i	$-0.317924\pi$
$557$	−7.06829	−	7.06829i	−0.299493	−	0.299493i	−0.840815	+	0.541322i	$0.817924\pi$
$558$		0			0
$559$	−21.3333	+	21.7962i	−0.902300	+	0.921881i
$560$	11.0714	−	8.61438i	0.467853	−	0.364024i
$561$		0			0
$562$	−22.0022	−	38.1090i	−0.928108	−	1.60753i
$563$	−1.69542	+	2.93656i	−0.0714535	+	0.123761i	−0.899539	−	0.436841i	$-0.856097\pi$
$563$	−1.69542	+	2.93656i	−0.0714535	+	0.123761i	0.828085	+	0.560603i	$0.189430\pi$
$564$		0			0
$565$	4.00807	+	4.00807i	0.168621	+	0.168621i
$566$	40.2578	+	10.7870i	1.69216	+	0.453413i
$567$		0			0
$568$	−40.3768	−	69.9347i	−1.69417	−	2.93439i
$569$	0.943027	−	0.544457i	0.0395337	−	0.0228248i	−0.480103	−	0.877212i	$-0.659401\pi$
$569$	0.943027	−	0.544457i	0.0395337	−	0.0228248i	0.519637	+	0.854387i	$0.326067\pi$
$570$		0			0
$571$	29.1820	−	16.8482i	1.22123	−	0.705076i	0.256048	−	0.966664i	$-0.417579\pi$
$571$	29.1820	−	16.8482i	1.22123	−	0.705076i	0.965180	+	0.261588i	$0.0842462\pi$
$572$	16.3977	+	27.7105i	0.685623	+	1.15864i
$573$		0			0
$574$	3.36811	−	26.9852i	0.140582	−	1.12634i
$575$	1.35165	−	2.34113i	0.0563678	−	0.0976319i
$576$		0			0
$577$	1.97749	−	7.38008i	0.0823239	−	0.307237i	−0.912470	−	0.409143i	$-0.865828\pi$
$577$	1.97749	−	7.38008i	0.0823239	−	0.307237i	0.994794	+	0.101907i	$0.0324943\pi$
$578$	−4.36029	−	16.2728i	−0.181364	−	0.676859i
$579$		0			0
$580$	−10.2230	+	10.2230i	−0.424488	+	0.424488i
$581$	−10.7380	+	8.35497i	−0.445488	+	0.346622i
$582$		0			0
$583$	−5.09363	+	19.0097i	−0.210957	+	0.787301i
$584$	13.2630	+	22.9723i	0.548828	+	0.950599i
$585$		0			0
$586$	5.97344	+	3.44877i	0.246761	+	0.142467i
$587$	−7.85719	+	2.10533i	−0.324301	+	0.0868961i	−0.417297	−	0.908770i	$-0.637022\pi$
$587$	−7.85719	+	2.10533i	−0.324301	+	0.0868961i	0.0929958	+	0.995667i	$0.470356\pi$
$588$		0			0
$589$	7.44812	−	4.30017i	0.306894	−	0.177186i
$590$	−5.78103	−	21.5751i	−0.238001	−	0.888233i
$591$		0			0
$592$	12.9848	−	3.47927i	0.533672	−	0.142997i
$593$	0.989650	+	3.69342i	0.0406400	+	0.151671i	0.983264	−	0.182185i	$-0.0583169\pi$
$593$	0.989650	+	3.69342i	0.0406400	+	0.151671i	−0.942624	+	0.333855i	$0.891650\pi$
$594$		0			0
$595$	8.66543	+	3.52122i	0.355248	+	0.144356i
$596$	15.7042	−	4.20792i	0.643268	−	0.172363i
$597$		0			0
$598$	−5.50234	+	3.25602i	−0.225008	+	0.133148i
$599$	14.5091	+	25.1304i	0.592824	+	1.02680i	0.993850	+	0.110734i	$0.0353203\pi$
$599$	14.5091	+	25.1304i	0.592824	+	1.02680i	−0.401026	+	0.916067i	$0.631346\pi$
$600$		0			0
$601$	−18.8192	−	10.8653i	−0.767653	−	0.443205i	0.0643839	−	0.997925i	$-0.479492\pi$
$601$	−18.8192	−	10.8653i	−0.767653	−	0.443205i	−0.832037	+	0.554721i	$0.812825\pi$
$602$	7.60117	+	54.8805i	0.309800	+	2.23676i
$603$		0			0
$604$	22.7469	−	22.7469i	0.925557	−	0.925557i
$605$	−1.81154	−	6.76076i	−0.0736496	−	0.274864i
$606$		0			0
$607$			41.5379i			1.68597i	0.537936	+	0.842985i	$0.319204\pi$
$607$			41.5379i			1.68597i	−0.537936	+	0.842985i	$0.680796\pi$
$608$	−2.33888	+	4.05106i	−0.0948542	+	0.164292i
$609$		0			0
$610$		−	35.9887i		−	1.45714i
$611$	20.2805	+	34.2720i	0.820462	+	1.38650i
$612$		0			0
$613$	4.78251	−	4.78251i	0.193164	−	0.193164i	−0.603898	−	0.797062i	$-0.706387\pi$
$613$	4.78251	−	4.78251i	0.193164	−	0.193164i	0.797062	+	0.603898i	$0.206387\pi$
$614$	33.7188	−	19.4676i	1.36078	−	0.785647i
$615$		0			0
$616$	29.9255	+	3.73510i	1.20573	+	0.150492i
$617$	−36.0435	−	9.65782i	−1.45106	−	0.388809i	−0.554665	−	0.832074i	$-0.687154\pi$
$617$	−36.0435	−	9.65782i	−1.45106	−	0.388809i	−0.896391	+	0.443264i	$0.853820\pi$
$618$		0			0
$619$	−19.8305	−	5.31356i	−0.797054	−	0.213570i	−0.162764	−	0.986665i	$-0.552041\pi$
$619$	−19.8305	−	5.31356i	−0.797054	−	0.213570i	−0.634290	+	0.773095i	$0.718707\pi$
$620$	−5.52697	+	9.57299i	−0.221968	+	0.384461i
$621$		0			0
$622$	16.5945	+	61.9317i	0.665381	+	2.48323i
$623$	5.41011	−	13.3139i	0.216752	−	0.533408i
$624$		0			0
$625$	4.05687	−	7.02671i	0.162275	−	0.281068i
$626$	−13.1506	−	13.1506i	−0.525602	−	0.525602i
$627$		0			0
$628$	44.5084			1.77608
$629$	6.33808	+	6.33808i	0.252716	+	0.252716i
$630$		0			0
$631$	11.1735	−	41.7002i	0.444812	−	1.66006i	−0.271622	−	0.962404i	$-0.587560\pi$
$631$	11.1735	−	41.7002i	0.444812	−	1.66006i	0.716433	−	0.697656i	$-0.245773\pi$
$632$	86.9924	−	23.3095i	3.46037	−	0.927204i
$633$		0			0
$634$		−	18.0956i		−	0.718669i
$635$	−14.3196	−	3.83692i	−0.568255	−	0.152263i
$636$		0			0
$637$	25.2315	−	0.610476i	0.999707	−	0.0241880i
$638$	−16.9351			−0.670467
$639$		0			0
$640$			20.2395i			0.800037i
$641$	−22.8765	−	13.2078i	−0.903567	−	0.521675i	−0.0252115	−	0.999682i	$-0.508026\pi$
$641$	−22.8765	−	13.2078i	−0.903567	−	0.521675i	−0.878356	+	0.478007i	$0.841359\pi$
$642$		0			0
$643$	2.34913	−	8.76709i	0.0926408	−	0.345740i	−0.904010	−	0.427510i	$-0.859391\pi$
$643$	2.34913	−	8.76709i	0.0926408	−	0.345740i	0.996651	+	0.0817702i	$0.0260574\pi$
$644$	−0.969060	+	7.76408i	−0.0381863	+	0.305948i
$645$		0			0
$646$	−28.1138			−1.10612
$647$	9.91733			0.389891			0.194945	−	0.980814i	$-0.437547\pi$
$647$	9.91733			0.389891			0.194945	+	0.980814i	$0.437547\pi$
$648$		0			0
$649$	8.81285	−	15.2643i	0.345935	−	0.599176i
$650$	−28.9914	+	17.1557i	−1.13714	+	0.672901i
$651$		0			0
$652$	4.91337	+	18.3370i	0.192423	+	0.718131i
$653$	−21.8886	−	37.9122i	−0.856567	−	1.48362i	−0.875183	−	0.483792i	$-0.839259\pi$
$653$	−21.8886	−	37.9122i	−0.856567	−	1.48362i	0.0186158	−	0.999827i	$-0.494074\pi$
$654$		0			0
$655$	−2.74709	−	0.736081i	−0.107338	−	0.0287611i
$656$	−14.0587	−	14.0587i	−0.548900	−	0.548900i
$657$		0			0
$658$	71.7857	+	8.95981i	2.79850	+	0.349290i
$659$	−2.58887	−	4.48406i	−0.100848	−	0.174674i	0.811186	−	0.584788i	$-0.198822\pi$
$659$	−2.58887	−	4.48406i	−0.100848	−	0.174674i	−0.912034	+	0.410114i	$0.865489\pi$
$660$		0			0
$661$	−22.6178	+	22.6178i	−0.879730	+	0.879730i	−0.993506	−	0.113776i	$-0.963705\pi$
$661$	−22.6178	+	22.6178i	−0.879730	+	0.879730i	0.113776	+	0.993506i	$0.463705\pi$
$662$	−70.4664	+	40.6838i	−2.73876	+	1.58122i
$663$		0			0
$664$			27.0994i			1.05166i
$665$	−6.28699	+	8.30853i	−0.243799	+	0.322191i
$666$		0			0
$667$		−	2.26535i		−	0.0877146i
$668$	11.0532	−	41.2511i	0.427661	−	1.59605i
$669$		0			0
$670$	23.0274	−	23.0274i	0.889626	−	0.889626i
$671$	20.0811	−	20.0811i	0.775224	−	0.775224i
$672$		0			0
$673$	30.4851	+	17.6006i	1.17511	+	0.678452i	0.954879	−	0.296995i	$-0.0959846\pi$
$673$	30.4851	+	17.6006i	1.17511	+	0.678452i	0.220234	+	0.975447i	$0.429318\pi$
$674$	−3.96242	+	14.7880i	−0.152627	+	0.569611i
$675$		0			0
$676$	53.6604	−	1.15208i	2.06386	−	0.0443106i
$677$	33.9514	+	19.6018i	1.30486	+	0.753360i	0.981233	−	0.192825i	$-0.0617651\pi$
$677$	33.9514	+	19.6018i	1.30486	+	0.753360i	0.323625	+	0.946185i	$0.395098\pi$
$678$		0			0
$679$	−34.2046	−	13.8991i	−1.31265	−	0.533399i
$680$	16.1343	−	9.31515i	0.618723	−	0.357220i
$681$		0			0
$682$	−12.5070	+	3.35124i	−0.478918	+	0.128326i
$683$	10.6441	−	2.85209i	0.407286	−	0.109132i	−0.0493586	−	0.998781i	$-0.515718\pi$
$683$	10.6441	−	2.85209i	0.407286	−	0.109132i	0.456645	+	0.889649i	$0.349051\pi$
$684$		0			0
$685$	−14.7393	+	8.50971i	−0.563158	+	0.325139i
$686$	27.1713	−	36.9305i	1.03740	−	1.41001i
$687$		0			0
$688$	35.0794	+	20.2531i	1.33739	+	0.772143i
$689$	23.4446	+	22.9467i	0.893169	+	0.874199i
$690$		0			0
$691$	1.35724	−	5.06530i	0.0516320	−	0.192693i	−0.935293	−	0.353875i	$-0.884864\pi$
$691$	1.35724	−	5.06530i	0.0516320	−	0.192693i	0.986925	+	0.161182i	$0.0515305\pi$
$692$	−28.3364	−	16.3600i	−1.07719	−	0.621915i
$693$		0			0
$694$	−44.0797	+	44.0797i	−1.67324	+	1.67324i
$695$	2.57511	−	2.57511i	0.0976795	−	0.0976795i
$696$		0			0
$697$	3.43114	−	12.8052i	0.129964	−	0.485031i
$698$			46.0901i			1.74454i
$699$		0			0
$700$	−5.10590	+	40.9083i	−0.192985	+	1.54619i
$701$		−	51.3651i		−	1.94003i	−0.243039	−	0.970017i	$-0.578144\pi$
$701$		−	51.3651i		−	1.94003i	0.243039	−	0.970017i	$-0.421856\pi$
$702$		0			0
$703$	−8.64685	+	4.99226i	−0.326122	+	0.188287i
$704$	−9.66824	+	9.66824i	−0.364385	+	0.364385i
$705$		0			0
$706$	−25.5440	−	44.2436i	−0.961362	−	1.66513i
$707$	−6.20031	+	49.6767i	−0.233187	+	1.86828i
$708$		0			0
$709$	−20.8652	−	20.8652i	−0.783609	−	0.783609i	0.196829	−	0.980438i	$-0.436936\pi$
$709$	−20.8652	−	20.8652i	−0.783609	−	0.783609i	−0.980438	+	0.196829i	$0.936936\pi$
$710$	−40.5725	−	10.8714i	−1.52266	−	0.407995i
$711$		0			0
$712$	−14.3121	−	24.7893i	−0.536369	−	0.929018i
$713$	−0.448284	−	1.67302i	−0.0167884	−	0.0626551i
$714$		0			0
$715$	8.36430	+	2.14526i	0.312807	+	0.0802282i
$716$	−1.60319	+	2.77681i	−0.0599141	+	0.103774i
$717$		0			0
$718$	−23.0245			−0.859267
$719$	42.9826			1.60298			0.801491	−	0.598007i	$-0.204041\pi$
$719$	42.9826			1.60298			0.801491	+	0.598007i	$0.204041\pi$
$720$		0			0
$721$	18.9970	+	14.3749i	0.707485	+	0.535348i
$722$	−4.06866	+	15.1844i	−0.151420	+	0.565107i
$723$		0			0
$724$	37.7570	+	21.7990i	1.40323	+	0.810155i
$725$		−	11.9359i		−	0.443289i
$726$		0			0
$727$	3.84403			0.142567			0.0712836	−	0.997456i	$-0.477290\pi$
$727$	3.84403			0.142567			0.0712836	+	0.997456i	$0.477290\pi$
$728$	29.9017	−	40.4106i	1.10823	−	1.49772i
$729$		0			0
$730$	13.3273	+	3.57105i	0.493267	+	0.132170i
$731$			27.0087i			0.998952i
$732$		0			0
$733$	13.8365	−	3.70749i	0.511064	−	0.136939i	0.00593416	−	0.999982i	$-0.498111\pi$
$733$	13.8365	−	3.70749i	0.511064	−	0.136939i	0.505130	+	0.863043i	$0.331444\pi$
$734$	21.8302	−	81.4713i	0.805766	−	3.00716i
$735$		0			0
$736$	0.666138	+	0.666138i	0.0245542	+	0.0245542i
$737$	25.6979			0.946593
$738$		0			0
$739$	−5.58487	−	5.58487i	−0.205443	−	0.205443i	0.596885	−	0.802327i	$-0.296405\pi$
$739$	−5.58487	−	5.58487i	−0.205443	−	0.205443i	−0.802327	+	0.596885i	$0.796405\pi$
$740$	6.41650	−	11.1137i	0.235875	−	0.408548i
$741$		0			0
$742$	59.0311	−	8.17604i	2.16710	−	0.300152i
$743$	−11.2562	−	42.0089i	−0.412952	−	1.54116i	−0.788903	−	0.614517i	$-0.789351\pi$
$743$	−11.2562	−	42.0089i	−0.412952	−	1.54116i	0.375952	−	0.926639i	$-0.377316\pi$
$744$		0			0
$745$	2.18005	−	3.77596i	0.0798708	−	0.138340i
$746$	−52.6561	−	14.1092i	−1.92788	−	0.516573i
$747$		0			0
$748$	27.5424	+	7.37997i	1.00705	+	0.269838i
$749$	−31.6867	+	13.3756i	−1.15781	+	0.488733i
$750$		0			0
$751$	2.13841	−	1.23461i	0.0780318	−	0.0450517i	−0.460476	−	0.887672i	$-0.652321\pi$
$751$	2.13841	−	1.23461i	0.0780318	−	0.0450517i	0.538508	+	0.842620i	$0.318988\pi$
$752$	37.3988	−	37.3988i	1.36379	−	1.36379i
$753$		0			0
$754$	−13.8515	+	24.5975i	−0.504443	+	0.895790i
$755$		−	8.62704i		−	0.313970i
$756$		0			0
$757$	1.03968	−	1.80079i	0.0377880	−	0.0654507i	−0.846513	−	0.532368i	$-0.821302\pi$
$757$	1.03968	−	1.80079i	0.0377880	−	0.0654507i	0.884301	+	0.466918i	$0.154636\pi$
$758$			3.07477i			0.111681i
$759$		0			0
$760$	5.37119	+	20.0456i	0.194834	+	0.727129i
$761$	−15.8414	+	15.8414i	−0.574249	+	0.574249i	−0.933313	−	0.359064i	$-0.883096\pi$
$761$	−15.8414	+	15.8414i	−0.574249	+	0.574249i	0.359064	+	0.933313i	$0.383096\pi$
$762$		0			0
$763$	−0.645568	+	1.58869i	−0.0233711	+	0.0575144i
$764$	19.4881	+	11.2514i	0.705054	+	0.407063i
$765$		0			0
$766$	−18.0749	−	31.3066i	−0.653071	−	1.13115i
$767$	−14.9626	−	25.2853i	−0.540268	−	0.912998i
$768$		0			0
$769$	−48.4921	+	12.9934i	−1.74867	+	0.468555i	−0.984342	−	0.176271i	$-0.943597\pi$
$769$	−48.4921	+	12.9934i	−1.74867	+	0.468555i	−0.764330	+	0.644826i	$0.776930\pi$
$770$	12.3804	−	9.63282i	0.446157	−	0.347143i
$771$		0			0
$772$	−15.3341	−	57.2276i	−0.551886	−	2.05967i
$773$	−26.9533	+	7.22211i	−0.969443	+	0.259761i	−0.708592	−	0.705618i	$-0.750669\pi$
$773$	−26.9533	+	7.22211i	−0.969443	+	0.259761i	−0.260850	+	0.965379i	$0.584003\pi$
$774$		0			0
$775$	−2.36197	−	8.81499i	−0.0848445	−	0.316644i
$776$	−63.6860	+	36.7692i	−2.28620	+	1.31994i
$777$		0			0
$778$	38.7167	−	10.3741i	1.38806	−	0.371930i
$779$	12.7887	+	7.38357i	0.458203	+	0.264544i
$780$		0			0
$781$	−16.5728	−	28.7049i	−0.593020	−	1.02714i
$782$	−1.46540	+	5.46897i	−0.0524028	+	0.195570i
$783$		0			0
$784$	−9.11061	−	32.2585i	−0.325379	−	1.15209i
$785$	8.44019	−	8.44019i	0.301243	−	0.301243i
$786$		0			0
$787$	2.90188	+	10.8300i	0.103441	+	0.386047i	0.998164	−	0.0605752i	$-0.0192935\pi$
$787$	2.90188	+	10.8300i	0.103441	+	0.386047i	−0.894723	+	0.446622i	$0.852627\pi$
$788$	24.6591	−	92.0290i	0.878444	−	3.27840i
$789$		0			0
$790$	23.4225	−	40.5690i	0.833336	−	1.44338i
$791$	12.4783	−	5.26734i	0.443678	−	0.187285i
$792$		0			0
$793$	−12.7423	−	45.5918i	−0.452492	−	1.61901i
$794$	65.8205	−	38.0015i	2.33588	−	1.34862i
$795$		0			0
$796$	−32.0560	+	18.5076i	−1.13620	+	0.655983i
$797$	5.68925	+	9.85408i	0.201524	+	0.349049i	0.949020	−	0.315217i	$-0.102077\pi$
$797$	5.68925	+	9.85408i	0.201524	+	0.349049i	−0.747496	+	0.664266i	$0.768744\pi$
$798$		0			0
$799$	34.0641	+	9.12746i	1.20510	+	0.322906i
$800$	3.50983	+	3.50983i	0.124091	+	0.124091i
$801$		0			0
$802$	6.01770	−	10.4230i	0.212492	−	0.368047i
$803$	5.44385	+	9.42903i	0.192109	+	0.332743i
$804$		0			0
$805$	1.28855	+	1.65608i	0.0454154	+	0.0583690i
$806$	−5.36218	+	20.9070i	−0.188875	+	0.736417i
$807$		0			0
$808$	70.5080	+	70.5080i	2.48046	+	2.48046i
$809$	14.6689			0.515730			0.257865	−	0.966181i	$-0.416981\pi$
$809$	14.6689			0.515730			0.257865	+	0.966181i	$0.416981\pi$
$810$		0			0
$811$	3.00038	+	3.00038i	0.105358	+	0.105358i	0.757821	−	0.652463i	$-0.226264\pi$
$811$	3.00038	+	3.00038i	0.105358	+	0.105358i	−0.652463	+	0.757821i	$0.726264\pi$
$812$	13.4349	+	31.8274i	0.471474	+	1.11692i
$813$		0			0
$814$	14.5199	−	3.89061i	0.508924	−	0.136366i
$815$	4.40899	+	2.54553i	0.154440	+	0.0891661i
$816$		0			0
$817$	−29.0604	−	7.78671i	−1.01669	−	0.272423i
$818$	17.9859			0.628861
$819$		0			0
$820$	−18.9800			−0.662812
$821$	−0.618781	−	0.165802i	−0.0215956	−	0.00578653i	0.248005	−	0.968759i	$-0.420225\pi$
$821$	−0.618781	−	0.165802i	−0.0215956	−	0.00578653i	−0.269601	+	0.962972i	$0.586892\pi$
$822$		0			0
$823$	−40.5425	−	23.4072i	−1.41322	−	0.815925i	−0.417532	−	0.908662i	$-0.637105\pi$
$823$	−40.5425	−	23.4072i	−1.41322	−	0.815925i	−0.995691	+	0.0927374i	$0.970438\pi$
$824$	45.8331	−	12.2809i	1.59667	−	0.427827i
$825$		0			0
$826$	−52.9622	−	6.61038i	−1.84279	−	0.230005i
$827$	−3.71960	−	3.71960i	−0.129343	−	0.129343i	0.639472	−	0.768815i	$-0.279153\pi$
$827$	−3.71960	−	3.71960i	−0.129343	−	0.129343i	−0.768815	+	0.639472i	$0.779153\pi$
$828$		0			0
$829$	−34.9744			−1.21471			−0.607356	−	0.794430i	$-0.707770\pi$
$829$	−34.9744			−1.21471			−0.607356	+	0.794430i	$0.707770\pi$
$830$	9.96715	+	9.96715i	0.345965	+	0.345965i
$831$		0			0
$832$	6.13489	+	21.9506i	0.212689	+	0.760999i
$833$	15.5902	−	16.0155i	0.540167	−	0.554904i
$834$		0			0
$835$	−5.72646	−	9.91853i	−0.198172	−	0.343245i
$836$	−15.8812	+	27.5070i	−0.549262	+	0.951350i
$837$		0			0
$838$	−7.67908	−	7.67908i	−0.265270	−	0.265270i
$839$	13.1988	+	3.53660i	0.455673	+	0.122097i	0.479352	−	0.877622i	$-0.340872\pi$
$839$	13.1988	+	3.53660i	0.455673	+	0.122097i	−0.0236798	+	0.999720i	$0.507538\pi$
$840$		0			0
$841$	9.49889	+	16.4526i	0.327548	+	0.567330i
$842$	−7.27256	+	4.19882i	−0.250629	+	0.144701i
$843$		0			0
$844$	13.8697	−	8.00769i	0.477416	−	0.275636i
$845$	9.95723	−	10.3942i	0.342539	−	0.357570i
$846$		0			0
$847$	−16.5962	−	2.07142i	−0.570251	−	0.0711749i
$848$	21.7849	−	37.7325i	0.748095	−	1.29574i
$849$		0			0
$850$	−7.72109	+	28.8155i	−0.264831	+	0.988364i
$851$	0.520433	+	1.94228i	0.0178402	+	0.0665806i
$852$		0			0
$853$	−15.3692	+	15.3692i	−0.526232	+	0.526232i	−0.919447	−	0.393215i	$-0.871363\pi$
$853$	−15.3692	+	15.3692i	−0.526232	+	0.526232i	0.393215	+	0.919447i	$0.371363\pi$
$854$	−79.6698	−	32.3740i	−2.72625	−	1.10782i
$855$		0			0
$856$	−17.7306	+	66.1717i	−0.606021	+	2.26170i
$857$	15.8211	+	27.4030i	0.540439	+	0.936068i	0.998879	+	0.0473423i	$0.0150751\pi$
$857$	15.8211	+	27.4030i	0.540439	+	0.936068i	−0.458440	+	0.888725i	$0.651592\pi$
$858$		0			0
$859$	−10.4333	−	6.02368i	−0.355980	−	0.205525i	0.311336	−	0.950300i	$-0.399224\pi$
$859$	−10.4333	−	6.02368i	−0.355980	−	0.205525i	−0.667316	+	0.744775i	$0.732557\pi$
$860$	37.3510	−	10.0082i	1.27366	−	0.341276i
$861$		0			0
$862$	−60.0734	+	34.6834i	−2.04611	+	1.18132i
$863$	7.52533	+	28.0849i	0.256165	+	0.956021i	0.967439	+	0.253106i	$0.0814521\pi$
$863$	7.52533	+	28.0849i	0.256165	+	0.956021i	−0.711273	+	0.702915i	$0.751881\pi$
$864$		0			0
$865$	−8.47584	+	2.27109i	−0.288187	+	0.0772195i
$866$	−1.26116	−	4.70671i	−0.0428559	−	0.159940i
$867$		0			0
$868$	16.2203	+	20.8468i	0.550553	+	0.707586i
$869$	35.7063	−	9.56747i	1.21125	−	0.324554i
$870$		0			0
$871$	21.0188	−	37.3251i	0.712194	−	1.26471i
$872$	1.70781	+	2.95801i	0.0578336	+	0.100171i
$873$		0			0
$874$	−5.46194	−	3.15345i	−0.184753	−	0.106667i
$875$	15.7839	+	20.2859i	0.533593	+	0.685788i
$876$		0			0
$877$	−10.3979	+	10.3979i	−0.351110	+	0.351110i	−0.860523	−	0.509412i	$-0.829863\pi$
$877$	−10.3979	+	10.3979i	−0.351110	+	0.351110i	0.509412	+	0.860523i	$0.329863\pi$
$878$	6.23684	+	23.2762i	0.210483	+	0.785533i
$879$		0			0
$880$		−	11.4684i		−	0.386599i
$881$	−21.1447	+	36.6236i	−0.712382	+	1.23388i	0.251578	+	0.967837i	$0.419050\pi$
$881$	−21.1447	+	36.6236i	−0.712382	+	1.23388i	−0.963961	+	0.266045i	$0.914283\pi$
$882$		0			0
$883$		−	18.1723i		−	0.611547i	−0.952104	−	0.305773i	$-0.901085\pi$
$883$		−	18.1723i		−	0.611547i	0.952104	−	0.305773i	$-0.0989150\pi$
$884$	33.2466	−	33.9680i	1.11820	−	1.14247i
$885$		0			0
$886$	−49.3635	+	49.3635i	−1.65840	+	1.65840i
$887$	−37.9692	+	21.9215i	−1.27488	+	0.736053i	−0.975903	−	0.218206i	$-0.929979\pi$
$887$	−37.9692	+	21.9215i	−1.27488	+	0.736053i	−0.298979	+	0.954260i	$0.596646\pi$
$888$		0			0
$889$	−21.3753	+	28.2483i	−0.716903	+	0.947418i
$890$	−14.3815	−	3.85350i	−0.482068	−	0.129170i
$891$		0			0
$892$	79.5941	+	21.3272i	2.66501	+	0.714087i
$893$	−19.6417	+	34.0204i	−0.657283	+	1.13845i
$894$		0			0
$895$	0.222555	+	0.830586i	0.00743919	+	0.0277634i
$896$	44.8051	+	18.2067i	1.49683	+	0.608242i
$897$		0			0
$898$	−30.9337	+	53.5788i	−1.03227	+	1.78795i
$899$	−5.40758	−	5.40758i	−0.180353	−	0.180353i
$900$		0			0
$901$	29.0513			0.967840
$902$	−15.7208	−	15.7208i	−0.523446	−	0.523446i
$903$		0			0
$904$	6.98238	−	26.0586i	0.232230	−	0.866696i
$905$	11.2937	−	3.02614i	0.375415	−	0.100592i
$906$		0			0
$907$			21.0681i			0.699555i	0.936833	+	0.349778i	$0.113743\pi$
$907$			21.0681i			0.699555i	−0.936833	+	0.349778i	$0.886257\pi$
$908$	−38.3317	−	10.2710i	−1.27208	−	0.340854i
$909$		0			0
$910$	−3.86515	−	25.8608i	−0.128129	−	0.857278i
$911$	50.4372			1.67106			0.835530	−	0.549445i	$-0.185161\pi$
$911$	50.4372			1.67106			0.835530	+	0.549445i	$0.185161\pi$
$912$		0			0
$913$			11.1230i			0.368118i
$914$	−40.7247	−	23.5124i	−1.34705	−	0.777721i
$915$		0			0
$916$	28.4806	−	106.291i	0.941025	−	3.51195i
$917$	−4.10067	+	5.41921i	−0.135416	+	0.178958i
$918$		0			0
$919$	16.0192			0.528423			0.264212	−	0.964465i	$-0.414888\pi$
$919$	16.0192			0.528423			0.264212	+	0.964465i	$0.414888\pi$
$920$	4.17942			0.137791
$921$		0			0
$922$	−23.8646	+	41.3347i	−0.785940	+	1.36129i
$923$	−55.2479	+	0.593010i	−1.81851	+	0.0195192i
$924$		0			0
$925$	2.74212	+	10.2337i	0.0901602	+	0.336483i
$926$	17.0360	+	29.5073i	0.559839	+	0.969670i
$927$		0			0
$928$	4.01776	+	1.07656i	0.131890	+	0.0353397i
$929$	−14.3914	−	14.3914i	−0.472166	−	0.472166i	0.430449	−	0.902615i	$-0.358355\pi$
$929$	−14.3914	−	14.3914i	−0.472166	−	0.472166i	−0.902615	+	0.430449i	$0.858355\pi$
$930$		0			0
$931$	12.7374	+	21.3918i	0.417452	+	0.701088i
$932$	−3.64811	−	6.31871i	−0.119498	−	0.206976i
$933$		0			0
$934$	−53.3946	+	53.3946i	−1.74712	+	1.74712i
$935$	6.62238	−	3.82343i	0.216575	−	0.125040i
$936$		0			0
$937$			51.5507i			1.68409i	0.539410	+	0.842043i	$0.318647\pi$
$937$			51.5507i			1.68409i	−0.539410	+	0.842043i	$0.681353\pi$
$938$	−30.2622	−	71.6913i	−0.988097	−	2.34080i
$939$		0			0
$940$		−	50.4904i		−	1.64682i
$941$	3.60461	−	13.4526i	0.117507	−	0.438542i	−0.881955	−	0.471333i	$-0.843773\pi$
$941$	3.60461	−	13.4526i	0.117507	−	0.438542i	0.999462	+	0.0327912i	$0.0104396\pi$
$942$		0			0
$943$	2.10292	−	2.10292i	0.0684804	−	0.0684804i
$944$	−27.5921	+	27.5921i	−0.898047	+	0.898047i
$945$		0			0
$946$	39.2268	+	22.6476i	1.27537	+	0.736336i
$947$	−1.46661	+	5.47346i	−0.0476584	+	0.177864i	−0.985652	−	0.168788i	$-0.946015\pi$
$947$	−1.46661	+	5.47346i	−0.0476584	+	0.177864i	0.937994	+	0.346652i	$0.112681\pi$
$948$		0			0
$949$	18.1479	−	0.194793i	0.589106	−	0.00632325i
$950$	−28.7785	−	16.6153i	−0.933697	−	0.539070i
$951$		0			0
$952$	−6.10758	−	44.0968i	−0.197948	−	1.42919i
$953$	−28.3739	+	16.3817i	−0.919121	+	0.530654i	−0.883354	−	0.468706i	$-0.844720\pi$
$953$	−28.3739	+	16.3817i	−0.919121	+	0.530654i	−0.0357662	+	0.999360i	$0.511387\pi$
$954$		0			0
$955$	5.82917	−	1.56192i	0.188628	−	0.0505426i
$956$	−121.165	+	32.4662i	−3.91877	+	1.05003i
$957$		0			0
$958$	21.7046	−	12.5312i	0.701245	−	0.404864i
$959$	5.57948	+	40.2839i	0.180171	+	1.30084i
$960$		0			0
$961$	21.7830	+	12.5764i	0.702679	+	0.405692i
$962$	6.22519	−	24.2718i	0.200708	−	0.782556i
$963$		0			0
$964$	10.2473	−	38.2436i	0.330045	−	1.23174i
$965$	−13.7600	−	7.94432i	−0.442949	−	0.255737i
$966$		0			0
$967$	−29.4635	+	29.4635i	−0.947483	+	0.947483i	−0.998688	−	0.0512055i	$-0.983694\pi$
$967$	−29.4635	+	29.4635i	−0.947483	+	0.947483i	0.0512055	+	0.998688i	$0.483694\pi$
$968$	−23.5556	+	23.5556i	−0.757105	+	0.757105i
$969$		0			0
$970$	−9.90002	+	36.9474i	−0.317870	+	1.18631i
$971$			18.5931i			0.596681i	0.954460	+	0.298340i	$0.0964330\pi$
$971$			18.5931i			0.596681i	−0.954460	+	0.298340i	$0.903567\pi$
$972$		0			0
$973$	−3.38417	−	8.01710i	−0.108491	−	0.257016i
$974$			60.5947i			1.94158i
$975$		0			0
$976$	−54.4487	+	31.4360i	−1.74286	+	1.00624i
$977$	6.71191	−	6.71191i	0.214733	−	0.214733i	−0.591542	−	0.806274i	$-0.701480\pi$
$977$	6.71191	−	6.71191i	0.214733	−	0.214733i	0.806274	+	0.591542i	$0.201480\pi$
$978$		0			0
$979$	−5.87444	−	10.1748i	−0.187748	−	0.325189i
$980$	−27.9253	−	15.6254i	−0.892040	−	0.499136i
$981$		0			0
$982$	8.07898	+	8.07898i	0.257811	+	0.257811i
$983$	−41.4077	−	11.0952i	−1.32070	−	0.353881i	−0.471461	−	0.881887i	$-0.656273\pi$
$983$	−41.4077	−	11.0952i	−1.32070	−	0.353881i	−0.849241	+	0.528006i	$0.822940\pi$
$984$		0			0
$985$	−12.7754	−	22.1277i	−0.407059	−	0.705047i
$986$	6.47022	+	24.1472i	0.206054	+	0.769003i
$987$		0			0
$988$	26.9633	+	45.5653i	0.857817	+	1.44962i
$989$	−3.02949	+	5.24723i	−0.0963321	+	0.166852i
$990$		0			0
$991$	16.4509			0.522580			0.261290	−	0.965260i	$-0.415852\pi$
$991$	16.4509			0.522580			0.261290	+	0.965260i	$0.415852\pi$
$992$	3.18026			0.100973
$993$		0			0
$994$	−60.5638	+	80.0377i	−1.92097	+	2.53864i
$995$	−2.56921	+	9.58844i	−0.0814496	+	0.303974i
$996$		0			0
$997$	−12.7995	−	7.38978i	−0.405364	−	0.234037i	0.283432	−	0.958992i	$-0.408527\pi$
$997$	−12.7995	−	7.38978i	−0.405364	−	0.234037i	−0.688796	+	0.724956i	$0.741860\pi$
$998$		−	29.8817i		−	0.945889i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.19.1		40
3.2	odd	2		273.2.cg.b.19.10	yes	40
7.3	odd	6		819.2.et.d.136.10		40
13.11	odd	12		819.2.et.d.271.10		40
21.17	even	6		273.2.bt.b.136.1	✓	40
39.11	even	12		273.2.bt.b.271.1	yes	40
91.24	even	12	inner	819.2.gh.d.388.1		40
273.206	odd	12		273.2.cg.b.115.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.1	✓	40	21.17	even	6
273.2.bt.b.271.1	yes	40	39.11	even	12
273.2.cg.b.19.10	yes	40	3.2	odd	2
273.2.cg.b.115.10	yes	40	273.206	odd	12
819.2.et.d.136.10		40	7.3	odd	6
819.2.et.d.271.10		40	13.11	odd	12
819.2.gh.d.19.1		40	1.1	even	1	trivial
819.2.gh.d.388.1		40	91.24	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.gh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.39126 - 0.640737i) q^{2} +(3.57554 + 2.06434i) q^{4} +(1.06950 - 0.286571i) q^{5} +(0.327682 - 2.62538i) q^{7} +(-3.72630 - 3.72630i) q^{8} +O(q^{10})\)	\(q+(-2.39126 - 0.640737i) q^{2} +(3.57554 + 2.06434i) q^{4} +(1.06950 - 0.286571i) q^{5} +(0.327682 - 2.62538i) q^{7} +(-3.72630 - 3.72630i) q^{8} -2.74106 q^{10} +(-1.52947 - 1.52947i) q^{11} +(-3.47248 + 0.970511i) q^{13} +(-2.46575 + 6.06801i) q^{14} +(2.39431 + 4.14706i) q^{16} +(-1.59647 + 2.76517i) q^{17} +(-2.51496 - 2.51496i) q^{19} +(4.41561 + 1.18316i) q^{20} +(2.67738 + 4.63735i) q^{22} +(-0.620322 + 0.358143i) q^{23} +(-3.26843 + 1.88703i) q^{25} +(8.92545 - 0.0958025i) q^{26} +(6.59131 - 8.71070i) q^{28} +(-1.58131 + 2.73892i) q^{29} +(-0.625845 + 2.33568i) q^{31} +(-0.340399 - 1.27039i) q^{32} +(5.58933 - 5.58933i) q^{34} +(-0.401902 - 2.90174i) q^{35} +(0.726571 - 2.71160i) q^{37} +(4.40250 + 7.62535i) q^{38} +(-5.05312 - 2.91742i) q^{40} +(-4.01046 + 1.07460i) q^{41} +(7.32559 - 4.22943i) q^{43} +(-2.31134 - 8.62603i) q^{44} +(1.71283 - 0.458951i) q^{46} +(-2.85863 - 10.6686i) q^{47} +(-6.78525 - 1.72058i) q^{49} +(9.02475 - 2.41817i) q^{50} +(-14.4194 - 3.69827i) q^{52} +(-4.54930 - 7.87963i) q^{53} +(-2.07407 - 1.19746i) q^{55} +(-11.0040 + 8.56192i) q^{56} +(5.53626 - 5.53626i) q^{58} +(2.10905 + 7.87107i) q^{59} +13.1295i q^{61} +(2.99312 - 5.18423i) q^{62} -6.32129i q^{64} +(-3.43569 + 2.03307i) q^{65} +(-8.40090 + 8.40090i) q^{67} +(-11.4165 + 6.59131i) q^{68} +(-0.898198 + 7.19634i) q^{70} +(14.8017 + 3.96611i) q^{71} +(-4.86210 - 1.30280i) q^{73} +(-3.47484 + 6.01860i) q^{74} +(-3.80061 - 14.1841i) q^{76} +(-4.51663 + 3.51426i) q^{77} +(-8.54505 + 14.8005i) q^{79} +(3.74913 + 3.74913i) q^{80} +10.2786 q^{82} +(-3.63623 - 3.63623i) q^{83} +(-0.915005 + 3.41484i) q^{85} +(-20.2274 + 5.41991i) q^{86} +11.3985i q^{88} +(5.24668 + 1.40584i) q^{89} +(1.41009 + 9.43460i) q^{91} -2.95732 q^{92} +27.3430i q^{94} +(-3.41045 - 1.96903i) q^{95} +(3.61174 - 13.4792i) q^{97} +(15.1229 + 8.46192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^7	\( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

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