LMFDB - Embedded newform 729.2.e.r.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			163.1
Root			$-0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.r.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85083 + 0.673648i) q^{2} +(1.43969 - 1.20805i) q^{4} +(-0.642788 - 3.64543i) q^{5} +(-1.79813 - 1.50881i) q^{7} +(0.118782 - 0.205737i) q^{8} +O(q^{10})$	\(q+(-1.85083 + 0.673648i) q^{2} +(1.43969 - 1.20805i) q^{4} +(-0.642788 - 3.64543i) q^{5} +(-1.79813 - 1.50881i) q^{7} +(0.118782 - 0.205737i) q^{8} +(3.64543 + 6.31407i) q^{10} +(0.378297 - 2.14543i) q^{11} +(4.43242 + 1.61327i) q^{13} +(4.34445 + 1.58125i) q^{14} +(-0.733956 + 4.16247i) q^{16} +(-1.46756 - 2.54189i) q^{17} +(3.11334 - 5.39246i) q^{19} +(-5.32926 - 4.47178i) q^{20} +(0.745100 + 4.22567i) q^{22} +(-0.397600 + 0.333626i) q^{23} +(-8.17752 + 2.97637i) q^{25} -9.29044 q^{26} -4.41147 q^{28} +(-3.28212 + 1.19459i) q^{29} +(-3.29813 + 2.76746i) q^{31} +(-1.36310 - 7.73055i) q^{32} +(4.42855 + 3.71599i) q^{34} +(-4.34445 + 7.52481i) q^{35} +(-1.20574 - 2.08840i) q^{37} +(-2.12965 + 12.0778i) q^{38} +(-0.826352 - 0.300767i) q^{40} +(2.34791 + 0.854570i) q^{41} +(0.184793 - 1.04801i) q^{43} +(-2.04715 - 3.54576i) q^{44} +(0.511144 - 0.885328i) q^{46} +(0.181985 + 0.152704i) q^{47} +(-0.258770 - 1.46756i) q^{49} +(13.1302 - 11.0175i) q^{50} +(8.33022 - 3.03195i) q^{52} -4.66717 q^{53} -8.06418 q^{55} +(-0.524005 + 0.190722i) q^{56} +(5.26991 - 4.42198i) q^{58} +(2.31164 + 13.1099i) q^{59} +(-2.81521 - 2.36224i) q^{61} +(4.24000 - 7.34389i) q^{62} +(3.50387 + 6.06888i) q^{64} +(3.03195 - 17.1951i) q^{65} +(-13.4363 - 4.89041i) q^{67} +(-5.18355 - 1.88666i) q^{68} +(2.97178 - 16.8538i) q^{70} +(0.601535 + 1.04189i) q^{71} +(2.34002 - 4.05304i) q^{73} +(3.63846 + 3.05303i) q^{74} +(-2.03209 - 11.5245i) q^{76} +(-3.91728 + 3.28699i) q^{77} +(12.0287 - 4.37808i) q^{79} +15.6458 q^{80} -4.92127 q^{82} +(-10.6222 + 3.86618i) q^{83} +(-8.32295 + 6.98378i) q^{85} +(0.363970 + 2.06418i) q^{86} +(-0.396459 - 0.332669i) q^{88} +(0.349643 - 0.605600i) q^{89} +(-5.53596 - 9.58856i) q^{91} +(-0.169386 + 0.960637i) q^{92} +(-0.439693 - 0.160035i) q^{94} +(-21.6591 - 7.88326i) q^{95} +(-1.23055 + 6.97881i) q^{97} +(1.46756 + 2.54189i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) $ 12 * q + 6 * q^4 + 6 * q^7	$ 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 + 6 * q^7 + 12 * q^10 + 6 * q^13 - 18 * q^16 + 24 * q^19 + 6 * q^22 - 48 * q^25 - 12 * q^28 - 12 * q^31 + 54 * q^34 + 6 * q^37 - 12 * q^40 - 12 * q^43 - 6 * q^46 + 42 * q^49 + 54 * q^52 - 60 * q^55 + 6 * q^58 - 48 * q^61 - 6 * q^64 - 66 * q^67 + 6 * q^70 - 12 * q^73 - 6 * q^76 + 42 * q^79 - 24 * q^82 - 18 * q^85 - 24 * q^88 + 6 * q^94 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	−1.85083	+	0.673648i	−1.30874	+	0.476341i	−0.899832	−	0.436236i	$-0.856311\pi$
$2$	−1.85083	+	0.673648i	−1.30874	+	0.476341i	−0.408904	+	0.912577i	$0.634089\pi$
$3$		0			0
$3$		0			0
$4$	1.43969	−	1.20805i	0.719846	−	0.604023i
$5$	−0.642788	−	3.64543i	−0.287463	−	1.63029i	−0.696351	−	0.717701i	$-0.745194\pi$
$5$	−0.642788	−	3.64543i	−0.287463	−	1.63029i	0.408888	−	0.912585i	$-0.365917\pi$
$6$		0			0
$7$	−1.79813	−	1.50881i	−0.679631	−	0.570278i	0.236268	−	0.971688i	$-0.424076\pi$
$7$	−1.79813	−	1.50881i	−0.679631	−	0.570278i	−0.915898	+	0.401410i	$0.868520\pi$
$8$	0.118782	−	0.205737i	0.0419959	−	0.0727390i
$9$		0			0
$10$	3.64543	+	6.31407i	1.15279	+	1.99668i
$11$	0.378297	−	2.14543i	0.114061	−	0.646871i	−0.873150	−	0.487452i	$-0.837927\pi$
$11$	0.378297	−	2.14543i	0.114061	−	0.646871i	0.987211	−	0.159420i	$-0.0509623\pi$
$12$		0			0
$13$	4.43242	+	1.61327i	1.22933	+	0.447440i	0.873369	−	0.487060i	$-0.161931\pi$
$13$	4.43242	+	1.61327i	1.22933	+	0.447440i	0.355963	+	0.934500i	$0.384153\pi$
$14$	4.34445	+	1.58125i	1.16110	+	0.422607i
$15$		0			0
$16$	−0.733956	+	4.16247i	−0.183489	+	1.04062i
$17$	−1.46756	−	2.54189i	−0.355936	−	0.616499i	0.631342	−	0.775505i	$-0.282504\pi$
$17$	−1.46756	−	2.54189i	−0.355936	−	0.616499i	−0.987278	+	0.159006i	$0.949171\pi$
$18$		0			0
$19$	3.11334	−	5.39246i	0.714249	−	1.23712i	−0.248999	−	0.968504i	$-0.580102\pi$
$19$	3.11334	−	5.39246i	0.714249	−	1.23712i	0.963248	−	0.268612i	$-0.0865651\pi$
$20$	−5.32926	−	4.47178i	−1.19166	−	0.999921i
$21$		0			0
$22$	0.745100	+	4.22567i	0.158856	+	0.900916i
$23$	−0.397600	+	0.333626i	−0.0829053	+	0.0695658i	−0.683298	−	0.730139i	$-0.739455\pi$
$23$	−0.397600	+	0.333626i	−0.0829053	+	0.0695658i	0.600393	+	0.799705i	$0.295011\pi$
$24$		0			0
$25$	−8.17752	+	2.97637i	−1.63550	+	0.595275i
$26$	−9.29044			−1.82201
$27$		0			0
$28$	−4.41147			−0.833690
$29$	−3.28212	+	1.19459i	−0.609474	+	0.221830i	−0.628273	−	0.777993i	$-0.716238\pi$
$29$	−3.28212	+	1.19459i	−0.609474	+	0.221830i	0.0187992	+	0.999823i	$0.494016\pi$
$30$		0			0
$31$	−3.29813	+	2.76746i	−0.592362	+	0.497051i	−0.888980	−	0.457945i	$-0.848586\pi$
$31$	−3.29813	+	2.76746i	−0.592362	+	0.497051i	0.296618	+	0.954996i	$0.404141\pi$
$32$	−1.36310	−	7.73055i	−0.240965	−	1.36658i
$33$		0			0
$34$	4.42855	+	3.71599i	0.759490	+	0.637288i
$35$	−4.34445	+	7.52481i	−0.734347	+	1.27193i
$36$		0			0
$37$	−1.20574	−	2.08840i	−0.198222	−	0.343330i	0.749730	−	0.661744i	$-0.230183\pi$
$37$	−1.20574	−	2.08840i	−0.198222	−	0.343330i	−0.947952	+	0.318413i	$0.896850\pi$
$38$	−2.12965	+	12.0778i	−0.345475	+	1.95929i
$39$		0			0
$40$	−0.826352	−	0.300767i	−0.130658	−	0.0475555i
$41$	2.34791	+	0.854570i	0.366682	+	0.133461i	0.518788	−	0.854903i	$-0.326383\pi$
$41$	2.34791	+	0.854570i	0.366682	+	0.133461i	−0.152106	+	0.988364i	$0.548606\pi$
$42$		0			0
$43$	0.184793	−	1.04801i	0.0281806	−	0.159820i	−0.967470	−	0.252986i	$-0.918587\pi$
$43$	0.184793	−	1.04801i	0.0281806	−	0.159820i	0.995651	+	0.0931655i	$0.0296986\pi$
$44$	−2.04715	−	3.54576i	−0.308619	−	0.534543i
$45$		0			0
$46$	0.511144	−	0.885328i	0.0753641	−	0.130534i
$47$	0.181985	+	0.152704i	0.0265453	+	0.0222741i	0.655964	−	0.754792i	$-0.272262\pi$
$47$	0.181985	+	0.152704i	0.0265453	+	0.0222741i	−0.629418	+	0.777067i	$0.716707\pi$
$48$		0			0
$49$	−0.258770	−	1.46756i	−0.0369672	−	0.209651i
$50$	13.1302	−	11.0175i	1.85689	−	1.55812i
$51$		0			0
$52$	8.33022	−	3.03195i	1.15519	−	0.420456i
$53$	−4.66717			−0.641085			−0.320543	−	0.947234i	$-0.603865\pi$
$53$	−4.66717			−0.641085			−0.320543	+	0.947234i	$0.603865\pi$
$54$		0			0
$55$	−8.06418			−1.08737
$56$	−0.524005	+	0.190722i	−0.0700231	+	0.0254863i
$57$		0			0
$58$	5.26991	−	4.42198i	0.691974	−	0.580635i
$59$	2.31164	+	13.1099i	0.300949	+	1.70677i	0.641984	+	0.766718i	$0.278111\pi$
$59$	2.31164	+	13.1099i	0.300949	+	1.70677i	−0.341035	+	0.940051i	$0.610777\pi$
$60$		0			0
$61$	−2.81521	−	2.36224i	−0.360450	−	0.302454i	0.444520	−	0.895769i	$-0.353374\pi$
$61$	−2.81521	−	2.36224i	−0.360450	−	0.302454i	−0.804970	+	0.593315i	$0.797819\pi$
$62$	4.24000	−	7.34389i	0.538480	−	0.932675i
$63$		0			0
$64$	3.50387	+	6.06888i	0.437984	+	0.758610i
$65$	3.03195	−	17.1951i	0.376067	−	2.13278i
$66$		0			0
$67$	−13.4363	−	4.89041i	−1.64150	−	0.597459i	−0.654203	−	0.756319i	$-0.726996\pi$
$67$	−13.4363	−	4.89041i	−1.64150	−	0.597459i	−0.987301	+	0.158860i	$0.949218\pi$
$68$	−5.18355	−	1.88666i	−0.628598	−	0.228791i
$69$		0			0
$70$	2.97178	−	16.8538i	0.355196	−	2.01442i
$71$	0.601535	+	1.04189i	0.0713891	+	0.123649i	0.899510	−	0.436900i	$-0.143923\pi$
$71$	0.601535	+	1.04189i	0.0713891	+	0.123649i	−0.828121	+	0.560549i	$0.810590\pi$
$72$		0			0
$73$	2.34002	−	4.05304i	0.273879	−	0.474372i	−0.695973	−	0.718068i	$-0.745027\pi$
$73$	2.34002	−	4.05304i	0.273879	−	0.474372i	0.969852	+	0.243696i	$0.0783599\pi$
$74$	3.63846	+	3.05303i	0.422963	+	0.354908i
$75$		0			0
$76$	−2.03209	−	11.5245i	−0.233097	−	1.32196i
$77$	−3.91728	+	3.28699i	−0.446416	+	0.374587i
$78$		0			0
$79$	12.0287	−	4.37808i	1.35333	−	0.492573i	0.439346	−	0.898318i	$-0.355210\pi$
$79$	12.0287	−	4.37808i	1.35333	−	0.492573i	0.913986	+	0.405745i	$0.132988\pi$
$80$	15.6458			1.74925
$81$		0			0
$82$	−4.92127			−0.543464
$83$	−10.6222	+	3.86618i	−1.16594	+	0.424369i	−0.851217	−	0.524814i	$-0.824135\pi$
$83$	−10.6222	+	3.86618i	−1.16594	+	0.424369i	−0.314726	+	0.949183i	$0.601913\pi$
$84$		0			0
$85$	−8.32295	+	6.98378i	−0.902750	+	0.757498i
$86$	0.363970	+	2.06418i	0.0392479	+	0.222586i
$87$		0			0
$88$	−0.396459	−	0.332669i	−0.0422627	−	0.0354626i
$89$	0.349643	−	0.605600i	0.0370621	−	0.0641935i	−0.846899	−	0.531753i	$-0.821533\pi$
$89$	0.349643	−	0.605600i	0.0370621	−	0.0641935i	0.883961	+	0.467560i	$0.154867\pi$
$90$		0			0
$91$	−5.53596	−	9.58856i	−0.580326	−	1.00515i
$92$	−0.169386	+	0.960637i	−0.0176597	+	0.100153i
$93$		0			0
$94$	−0.439693	−	0.160035i	−0.0453508	−	0.0165064i
$95$	−21.6591	−	7.88326i	−2.22217	−	0.808805i
$96$		0			0
$97$	−1.23055	+	6.97881i	−0.124944	+	0.708591i	0.856398	+	0.516317i	$0.172697\pi$
$97$	−1.23055	+	6.97881i	−0.124944	+	0.708591i	−0.981341	+	0.192274i	$0.938414\pi$
$98$	1.46756	+	2.54189i	0.148246	+	0.256770i
$99$		0			0
$100$	−8.17752	+	14.1639i	−0.817752	+	1.41639i
$101$	−3.58288	−	3.00640i	−0.356510	−	0.299148i	0.446888	−	0.894590i	$-0.352532\pi$
$101$	−3.58288	−	3.00640i	−0.356510	−	0.299148i	−0.803398	+	0.595442i	$0.796977\pi$
$102$		0			0
$103$	−2.36571	−	13.4166i	−0.233101	−	1.32198i	−0.846577	−	0.532267i	$-0.821340\pi$
$103$	−2.36571	−	13.4166i	−0.233101	−	1.32198i	0.613476	−	0.789713i	$-0.289771\pi$
$104$	0.858402	−	0.720285i	0.0841733	−	0.0706298i
$105$		0			0
$106$	8.63816	−	3.14403i	0.839012	−	0.305375i
$107$	−11.6340			−1.12470			−0.562350	−	0.826900i	$-0.690102\pi$
$107$	−11.6340			−1.12470			−0.562350	+	0.826900i	$0.690102\pi$
$108$		0			0
$109$	14.6040			1.39881			0.699405	−	0.714725i	$-0.253448\pi$
$109$	14.6040			1.39881			0.699405	+	0.714725i	$0.253448\pi$
$110$	14.9254	−	5.43242i	1.42309	−	0.517961i
$111$		0			0
$112$	7.60014	−	6.37727i	0.718145	−	0.602596i
$113$	−0.815422	−	4.62449i	−0.0767084	−	0.435035i	−0.998840	−	0.0481580i	$-0.984665\pi$
$113$	−0.815422	−	4.62449i	−0.0767084	−	0.435035i	0.922131	−	0.386877i	$-0.126446\pi$
$114$		0			0
$115$	1.47178	+	1.23497i	0.137244	+	0.115162i
$116$	−3.28212	+	5.68479i	−0.304737	+	0.527820i
$117$		0			0
$118$	−13.1099	−	22.7071i	−1.20687	−	2.09036i
$119$	−1.19637	+	6.78493i	−0.109671	+	0.621973i
$120$		0			0
$121$	5.87686	+	2.13900i	0.534260	+	0.194455i
$122$	6.80180	+	2.47565i	0.615806	+	0.224135i
$123$		0			0
$124$	−1.40508	+	7.96859i	−0.126180	+	0.715601i
$125$	6.85240	+	11.8687i	0.612897	+	1.06157i
$126$		0			0
$127$	−3.04576	+	5.27541i	−0.270267	+	0.468117i	−0.968930	−	0.247334i	$-0.920445\pi$
$127$	−3.04576	+	5.27541i	−0.270267	+	0.468117i	0.698663	+	0.715451i	$0.253779\pi$
$128$	1.45323	+	1.21941i	0.128449	+	0.107781i
$129$		0			0
$130$	5.97178	+	33.8677i	0.523760	+	2.97039i
$131$	−7.92734	+	6.65183i	−0.692615	+	0.581173i	−0.919662	−	0.392711i	$-0.871537\pi$
$131$	−7.92734	+	6.65183i	−0.692615	+	0.581173i	0.227047	+	0.973884i	$0.427093\pi$
$132$		0			0
$133$	−13.7344	+	4.99892i	−1.19093	+	0.433461i
$134$	28.1627			2.43289
$135$		0			0
$136$	−0.697281			−0.0597914
$137$	17.9337	−	6.52734i	1.53218	−	0.557668i	0.568027	−	0.823010i	$-0.307707\pi$
$137$	17.9337	−	6.52734i	1.53218	−	0.557668i	0.964154	+	0.265342i	$0.0854847\pi$
$138$		0			0
$139$	−17.8516	+	14.9793i	−1.51416	+	1.27053i	−0.659018	+	0.752128i	$0.729028\pi$
$139$	−17.8516	+	14.9793i	−1.51416	+	1.27053i	−0.855138	+	0.518400i	$0.826528\pi$
$140$	2.83564	+	16.0817i	0.239655	+	1.35915i
$141$		0			0
$142$	−1.81521	−	1.52314i	−0.152329	−	0.127819i
$143$	5.13793	−	8.89915i	0.429655	−	0.744184i
$144$		0			0
$145$	6.46451	+	11.1969i	0.536848	+	0.929848i
$146$	−1.60067	+	9.07785i	−0.132472	+	0.751288i
$147$		0			0
$148$	−4.25877	−	1.55007i	−0.350069	−	0.127415i
$149$	14.5708	+	5.30335i	1.19369	+	0.434467i	0.861017	−	0.508576i	$-0.169828\pi$
$149$	14.5708	+	5.30335i	1.19369	+	0.434467i	0.332671	+	0.943043i	$0.392050\pi$
$150$		0			0
$151$	−1.02481	+	5.81201i	−0.0833983	+	0.472975i	0.914292	+	0.405055i	$0.132748\pi$
$151$	−1.02481	+	5.81201i	−0.0833983	+	0.472975i	−0.997691	+	0.0679204i	$0.978364\pi$
$152$	−0.739620	−	1.28106i	−0.0599911	−	0.103908i
$153$		0			0
$154$	5.03596	−	8.72254i	0.405809	−	0.702882i
$155$	12.2086	+	10.2442i	0.980617	+	0.822836i
$156$		0			0
$157$	−0.210485	−	1.19372i	−0.0167985	−	0.0952691i	0.975256	−	0.221079i	$-0.0709580\pi$
$157$	−0.210485	−	1.19372i	−0.0167985	−	0.0952691i	−0.992054	+	0.125810i	$0.959847\pi$
$158$	−19.3138	+	16.2062i	−1.53652	+	1.28930i
$159$		0			0
$160$	−27.3050	+	9.93821i	−2.15865	+	0.785684i
$161$	1.21832			0.0960168
$162$		0			0
$163$	2.77332			0.217223			0.108612	−	0.994084i	$-0.465360\pi$
$163$	2.77332			0.217223			0.108612	+	0.994084i	$0.465360\pi$
$164$	4.41263	−	1.60607i	0.344569	−	0.125413i
$165$		0			0
$166$	17.0556	−	14.3113i	1.32377	−	1.11077i
$167$	0.664738	+	3.76991i	0.0514389	+	0.291725i	0.999665	−	0.0258705i	$-0.00823577\pi$
$167$	0.664738	+	3.76991i	0.0514389	+	0.291725i	−0.948226	+	0.317595i	$0.897125\pi$
$168$		0			0
$169$	7.08512	+	5.94512i	0.545009	+	0.457317i
$170$	10.6998	−	18.5326i	0.820635	−	1.42138i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	1.22064	−	6.92262i	0.0928039	−	0.526317i	−0.902594	−	0.430492i	$-0.858340\pi$
$173$	1.22064	−	6.92262i	0.0928039	−	0.526317i	0.995398	−	0.0958248i	$-0.0305489\pi$
$174$		0			0
$175$	19.1951	+	6.98643i	1.45101	+	0.528124i
$176$	8.65263	+	3.14930i	0.652217	+	0.237387i
$177$		0			0
$178$	−0.239170	+	1.35640i	−0.0179266	+	0.101667i
$179$	−7.19269	−	12.4581i	−0.537607	−	0.931163i	−0.999032	−	0.0439838i	$-0.985995\pi$
$179$	−7.19269	−	12.4581i	−0.537607	−	0.931163i	0.461425	−	0.887179i	$-0.347338\pi$
$180$		0			0
$181$	−6.60014	+	11.4318i	−0.490584	+	0.849717i	−0.999941	−	0.0108384i	$-0.996550\pi$
$181$	−6.60014	+	11.4318i	−0.490584	+	0.849717i	0.509357	+	0.860555i	$0.329883\pi$
$182$	16.7055	+	14.0175i	1.23829	+	1.03905i
$183$		0			0
$184$	0.0214114	+	0.121430i	0.00157847	+	0.00895193i
$185$	−6.83807	+	5.73783i	−0.502745	+	0.421853i
$186$		0			0
$187$	−6.00862	+	2.18696i	−0.439394	+	0.159926i
$188$	0.446476			0.0325626
$189$		0			0
$190$	45.3979			3.29351
$191$	12.6138	−	4.59105i	0.912703	−	0.332197i	0.157372	−	0.987539i	$-0.449698\pi$
$191$	12.6138	−	4.59105i	0.912703	−	0.332197i	0.755332	+	0.655343i	$0.227476\pi$
$192$		0			0
$193$	11.4945	−	9.64506i	0.827395	−	0.694267i	−0.127296	−	0.991865i	$-0.540630\pi$
$193$	11.4945	−	9.64506i	0.827395	−	0.694267i	0.954691	+	0.297598i	$0.0961855\pi$
$194$	−2.42371	−	13.7456i	−0.174013	−	0.986874i
$195$		0			0
$196$	−2.14543	−	1.80023i	−0.153245	−	0.128588i
$197$	−11.1606	+	19.3307i	−0.795158	+	1.37725i	0.127580	+	0.991828i	$0.459279\pi$
$197$	−11.1606	+	19.3307i	−0.795158	+	1.37725i	−0.922739	+	0.385426i	$0.874054\pi$
$198$		0			0
$199$	4.55051	+	7.88171i	0.322577	+	0.558720i	0.981019	−	0.193912i	$-0.0621176\pi$
$199$	4.55051	+	7.88171i	0.322577	+	0.558720i	−0.658442	+	0.752631i	$0.728784\pi$
$200$	−0.358995	+	2.03596i	−0.0253847	+	0.143964i
$201$		0			0
$202$	8.65657	+	3.15074i	0.609074	+	0.221685i
$203$	7.70410	+	2.80406i	0.540722	+	0.196807i
$204$		0			0
$205$	1.60607	−	9.10846i	0.112173	−	0.636162i
$206$	13.4166	+	23.2383i	0.934781	+	1.61909i
$207$		0			0
$208$	−9.96838	+	17.2657i	−0.691183	+	1.19716i
$209$	−10.3914	−	8.71941i	−0.718787	−	0.603134i
$210$		0			0
$211$	−1.03802	−	5.88690i	−0.0714602	−	0.405271i	−0.999465	−	0.0327028i	$-0.989589\pi$
$211$	−1.03802	−	5.88690i	−0.0714602	−	0.405271i	0.928005	−	0.372568i	$-0.121523\pi$
$212$	−6.71929	+	5.63816i	−0.461483	+	0.387230i
$213$		0			0
$214$	21.5326	−	7.83721i	1.47194	−	0.535741i
$215$	−3.93923			−0.268653
$216$		0			0
$217$	10.1061			0.686045
$218$	−27.0296	+	9.83796i	−1.83067	+	0.666311i
$219$		0			0
$220$	−11.6099	+	9.74189i	−0.782742	+	0.656798i
$221$	−2.40409	−	13.6343i	−0.161717	−	0.917141i
$222$		0			0
$223$	−6.81908	−	5.72189i	−0.456639	−	0.383166i	0.385253	−	0.922811i	$-0.374114\pi$
$223$	−6.81908	−	5.72189i	−0.456639	−	0.383166i	−0.841893	+	0.539645i	$0.818558\pi$
$224$	−9.21291	+	15.9572i	−0.615564	+	1.06619i
$225$		0			0
$226$	4.62449	+	8.00984i	0.307616	+	0.532807i
$227$	1.85256	−	10.5064i	0.122959	−	0.697334i	−0.859540	−	0.511068i	$-0.829250\pi$
$227$	1.85256	−	10.5064i	0.122959	−	0.697334i	0.982499	−	0.186266i	$-0.0596387\pi$
$228$		0			0
$229$	7.77244	+	2.82894i	0.513617	+	0.186941i	0.585809	−	0.810449i	$-0.300777\pi$
$229$	7.77244	+	2.82894i	0.513617	+	0.186941i	−0.0721913	+	0.997391i	$0.522999\pi$
$230$	−3.55596	−	1.29426i	−0.234473	−	0.0853412i
$231$		0			0
$232$	−0.144086	+	0.817150i	−0.00945968	+	0.0536485i
$233$	6.36965	+	11.0326i	0.417290	+	0.722767i	0.995666	−	0.0930034i	$-0.0296467\pi$
$233$	6.36965	+	11.0326i	0.417290	+	0.722767i	−0.578376	+	0.815770i	$0.696313\pi$
$234$		0			0
$235$	0.439693	−	0.761570i	0.0286824	−	0.0496793i
$236$	19.1654	+	16.0817i	1.24756	+	1.04683i
$237$		0			0
$238$	−2.35638	−	13.3637i	−0.152742	−	0.866240i
$239$	−11.5026	+	9.65183i	−0.744041	+	0.624325i	−0.933920	−	0.357483i	$-0.883635\pi$
$239$	−11.5026	+	9.65183i	−0.744041	+	0.624325i	0.189878	+	0.981808i	$0.439191\pi$
$240$		0			0
$241$	−0.747626	+	0.272114i	−0.0481588	+	0.0175284i	−0.365987	−	0.930620i	$-0.619269\pi$
$241$	−0.747626	+	0.272114i	−0.0481588	+	0.0175284i	0.317828	+	0.948148i	$0.397046\pi$
$242$	−12.3180			−0.791832
$243$		0			0
$244$	−6.90673			−0.442158
$245$	−5.18355	+	1.88666i	−0.331165	+	0.120534i
$246$		0			0
$247$	22.4991	−	18.8790i	1.43158	−	1.20124i
$248$	0.177610	+	1.00727i	0.0112782	+	0.0639620i
$249$		0			0
$250$	−20.6780	−	17.3509i	−1.30779	−	1.09737i
$251$	4.15749	−	7.20099i	0.262419	−	0.454522i	−0.704465	−	0.709738i	$-0.748813\pi$
$251$	4.15749	−	7.20099i	0.262419	−	0.454522i	0.966884	+	0.255216i	$0.0821465\pi$
$252$		0			0
$253$	0.565360	+	0.979232i	0.0355439	+	0.0615638i
$254$	2.08342	−	11.8157i	0.130726	−	0.741381i
$255$		0			0
$256$	−16.6814	−	6.07153i	−1.04259	−	0.379471i
$257$	−24.0752	−	8.76264i	−1.50177	−	0.546599i	−0.545250	−	0.838274i	$-0.683565\pi$
$257$	−24.0752	−	8.76264i	−1.50177	−	0.546599i	−0.956517	+	0.291675i	$0.905787\pi$
$258$		0			0
$259$	−0.982926	+	5.57445i	−0.0610760	+	0.346379i
$260$	−16.4073	−	28.4183i	−1.01754	−	1.76243i
$261$		0			0
$262$	10.1912	−	17.6517i	0.629614	−	1.09052i
$263$	−21.4990	−	18.0398i	−1.32569	−	1.11238i	−0.985065	−	0.172183i	$-0.944918\pi$
$263$	−21.4990	−	18.0398i	−1.32569	−	1.11238i	−0.340622	−	0.940200i	$-0.610638\pi$
$264$		0			0
$265$	3.00000	+	17.0138i	0.184289	+	1.04515i
$266$	22.0526	−	18.5043i	1.35213	−	1.13457i
$267$		0			0
$268$	−25.2520	+	9.19096i	−1.54251	+	0.561427i
$269$	30.1710			1.83956			0.919778	−	0.392439i	$-0.128369\pi$
$269$	30.1710			1.83956			0.919778	+	0.392439i	$0.128369\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	11.6577	−	4.24304i	0.706849	−	0.257272i
$273$		0			0
$274$	−28.7952	+	24.1620i	−1.73958	+	1.45968i
$275$	3.29207	+	18.6702i	0.198519	+	1.12586i
$276$		0			0
$277$	16.1800	+	13.5767i	0.972165	+	0.815743i	0.982889	−	0.184199i	$-0.0589692\pi$
$277$	16.1800	+	13.5767i	0.972165	+	0.815743i	−0.0107242	+	0.999942i	$0.503414\pi$
$278$	22.9496	−	39.7499i	1.37643	−	2.38404i
$279$		0			0
$280$	1.03209	+	1.78763i	0.0616791	+	0.106831i
$281$	0.303415	−	1.72075i	0.0181002	−	0.102651i	−0.974419	−	0.224738i	$-0.927847\pi$
$281$	0.303415	−	1.72075i	0.0181002	−	0.102651i	0.992519	+	0.122086i	$0.0389585\pi$
$282$		0			0
$283$	6.84864	+	2.49270i	0.407109	+	0.148176i	0.537454	−	0.843293i	$-0.319386\pi$
$283$	6.84864	+	2.49270i	0.407109	+	0.148176i	−0.130345	+	0.991469i	$0.541608\pi$
$284$	2.12467	+	0.773318i	0.126076	+	0.0458880i
$285$		0			0
$286$	−3.51455	+	19.9320i	−0.207820	+	1.17860i
$287$	−2.93247	−	5.07919i	−0.173098	−	0.299815i
$288$		0			0
$289$	4.19253	−	7.26168i	0.246620	−	0.427158i
$290$	−19.5075	−	16.3687i	−1.14552	−	0.961204i
$291$		0			0
$292$	−1.52734	−	8.66198i	−0.0893809	−	0.506904i
$293$	11.7595	−	9.86736i	0.686995	−	0.576458i	−0.231046	−	0.972943i	$-0.574215\pi$
$293$	11.7595	−	9.86736i	0.686995	−	0.576458i	0.918041	+	0.396485i	$0.129770\pi$
$294$		0			0
$295$	46.3055	−	16.8538i	2.69601	−	0.981267i
$296$	−0.572881			−0.0332980
$297$		0			0
$298$	−30.5408			−1.76918
$299$	−2.30056	+	0.837334i	−0.133045	+	0.0484243i
$300$		0			0
$301$	−1.91353	+	1.60565i	−0.110294	+	0.0925479i
$302$	−2.01849	−	11.4474i	−0.116151	−	0.658726i
$303$		0			0
$304$	20.1609	+	16.9170i	1.15631	+	0.970257i
$305$	−6.80180	+	11.7811i	−0.389470	+	0.674581i
$306$		0			0
$307$	−8.38191	−	14.5179i	−0.478381	−	0.828580i	0.521312	−	0.853366i	$-0.325443\pi$
$307$	−8.38191	−	14.5179i	−0.478381	−	0.828580i	−0.999693	+	0.0247861i	$0.992110\pi$
$308$	−1.66885	+	9.46451i	−0.0950914	+	0.539290i
$309$		0			0
$310$	−29.4971	−	10.7361i	−1.67532	−	0.609767i
$311$	15.0568	+	5.48024i	0.853794	+	0.310756i	0.731586	−	0.681749i	$-0.238780\pi$
$311$	15.0568	+	5.48024i	0.853794	+	0.310756i	0.122208	+	0.992505i	$0.461002\pi$
$312$		0			0
$313$	5.97447	−	33.8829i	0.337697	−	1.91517i	−0.0610920	−	0.998132i	$-0.519458\pi$
$313$	5.97447	−	33.8829i	0.337697	−	1.91517i	0.398789	−	0.917043i	$-0.369431\pi$
$314$	1.19372	+	2.06758i	0.0673654	+	0.116680i
$315$		0			0
$316$	12.0287	−	20.8343i	0.676666	−	1.17202i
$317$	−12.4950	−	10.4846i	−0.701791	−	0.588872i	0.220492	−	0.975389i	$-0.429234\pi$
$317$	−12.4950	−	10.4846i	−0.701791	−	0.588872i	−0.922283	+	0.386516i	$0.873678\pi$
$318$		0			0
$319$	1.32130	+	7.49346i	0.0739786	+	0.419553i
$320$	19.8714	−	16.6741i	1.11085	−	0.932111i
$321$		0			0
$322$	−2.25490	+	0.820717i	−0.125661	+	0.0457367i
$323$	−18.2761			−1.01691
$324$		0			0
$325$	−41.0479			−2.27693
$326$	−5.13295	+	1.86824i	−0.284288	+	0.103472i
$327$		0			0
$328$	0.454707	−	0.381545i	0.0251070	−	0.0210673i
$329$	−0.0968323	−	0.549163i	−0.00533854	−	0.0302763i
$330$		0			0
$331$	−24.1917	−	20.2992i	−1.32969	−	1.11575i	−0.984149	−	0.177343i	$-0.943250\pi$
$331$	−24.1917	−	20.2992i	−1.32969	−	1.11575i	−0.345545	−	0.938402i	$-0.612306\pi$
$332$	−10.6222	+	18.3983i	−0.582972	+	1.00974i
$333$		0			0
$334$	−3.76991	−	6.52968i	−0.206281	−	0.357288i
$335$	−9.19096	+	52.1245i	−0.502156	+	2.84787i
$336$		0			0
$337$	−5.64290	−	2.05385i	−0.307389	−	0.111880i	0.183720	−	0.982979i	$-0.441186\pi$
$337$	−5.64290	−	2.05385i	−0.307389	−	0.111880i	−0.491109	+	0.871098i	$0.663408\pi$
$338$	−17.1183	−	6.23055i	−0.931113	−	0.338897i
$339$		0			0
$340$	−3.54576	+	20.1090i	−0.192296	+	1.09056i
$341$	4.68972	+	8.12284i	0.253963	+	0.439876i
$342$		0			0
$343$	−9.96451	+	17.2590i	−0.538033	+	0.931900i
$344$	−0.193665	−	0.162504i	−0.0104417	−	0.00876162i
$345$		0			0
$346$	2.40420	+	13.6349i	0.129251	+	0.733017i
$347$	17.6423	−	14.8037i	0.947089	−	0.794702i	−0.0317162	−	0.999497i	$-0.510097\pi$
$347$	17.6423	−	14.8037i	0.947089	−	0.794702i	0.978805	+	0.204795i	$0.0656528\pi$
$348$		0			0
$349$	10.8687	−	3.95589i	0.581789	−	0.211754i	−0.0343254	−	0.999411i	$-0.510928\pi$
$349$	10.8687	−	3.95589i	0.581789	−	0.211754i	0.616114	+	0.787657i	$0.288706\pi$
$350$	−40.2332			−2.15056
$351$		0			0
$352$	−17.1010			−0.911487
$353$	2.00589	−	0.730085i	0.106763	−	0.0388585i	−0.288086	−	0.957604i	$-0.593019\pi$
$353$	2.00589	−	0.730085i	0.106763	−	0.0388585i	0.394849	+	0.918746i	$0.370797\pi$
$354$		0			0
$355$	3.41147	−	2.86257i	0.181062	−	0.151929i
$356$	−0.228213	−	1.29426i	−0.0120953	−	0.0685958i
$357$		0			0
$358$	21.7049	+	18.2125i	1.14714	+	0.962563i
$359$	−12.1118	+	20.9782i	−0.639234	+	1.10719i	0.346367	+	0.938099i	$0.387415\pi$
$359$	−12.1118	+	20.9782i	−0.639234	+	1.10719i	−0.985601	+	0.169087i	$0.945918\pi$
$360$		0			0
$361$	−9.88578	−	17.1227i	−0.520304	−	0.901193i
$362$	4.51476	−	25.6045i	0.237290	−	1.34574i
$363$		0			0
$364$	−19.5535	−	7.11689i	−1.02488	−	0.373027i
$365$	−16.2792	−	5.92514i	−0.852092	−	0.310136i
$366$		0			0
$367$	−0.492259	+	2.79174i	−0.0256957	+	0.145728i	−0.994956	−	0.100308i	$-0.968017\pi$
$367$	−0.492259	+	2.79174i	−0.0256957	+	0.145728i	0.969261	+	0.246036i	$0.0791282\pi$
$368$	−1.09689	−	1.89986i	−0.0571792	−	0.0990372i
$369$		0			0
$370$	8.79086	−	15.2262i	0.457015	−	0.791573i
$371$	8.39220	+	7.04189i	0.435701	+	0.365597i
$372$		0			0
$373$	−5.00686	−	28.3953i	−0.259246	−	1.47025i	−0.784935	−	0.619578i	$-0.787304\pi$
$373$	−5.00686	−	28.3953i	−0.259246	−	1.47025i	0.525689	−	0.850677i	$-0.323807\pi$
$374$	9.64771	−	8.09539i	0.498871	−	0.418603i
$375$		0			0
$376$	0.0530334	−	0.0193026i	0.00273499	−	0.000995455i
$377$	−16.4749			−0.848501
$378$		0			0
$379$	32.1985			1.65393			0.826963	−	0.562256i	$-0.190066\pi$
$379$	32.1985			1.65393			0.826963	+	0.562256i	$0.190066\pi$
$380$	−40.7057	+	14.8157i	−2.08816	+	0.760028i
$381$		0			0
$382$	−20.2533	+	16.9945i	−1.03625	+	0.869516i
$383$	0.116735	+	0.662037i	0.00596488	+	0.0338285i	0.987645	−	0.156708i	$-0.0500883\pi$
$383$	0.116735	+	0.662037i	0.00596488	+	0.0338285i	−0.981680	+	0.190537i	$0.938977\pi$
$384$		0			0
$385$	14.5005	+	12.1673i	0.739012	+	0.620105i
$386$	−14.7771	+	25.5947i	−0.752134	+	1.30273i
$387$		0			0
$388$	6.65910	+	11.5339i	0.338065	+	0.585545i
$389$	−0.739620	+	4.19459i	−0.0375002	+	0.212674i	−0.997800	−	0.0662958i	$-0.978882\pi$
$389$	−0.739620	+	4.19459i	−0.0375002	+	0.212674i	0.960300	+	0.278970i	$0.0899930\pi$
$390$		0			0
$391$	1.43154	+	0.521038i	0.0723962	+	0.0263500i
$392$	−0.332669	−	0.121082i	−0.0168023	−	0.00611554i
$393$		0			0
$394$	7.63429	−	43.2962i	0.384610	−	2.18123i
$395$	−23.6919	−	41.0355i	−1.19207	−	2.06472i
$396$		0			0
$397$	4.43242	−	7.67717i	0.222457	−	0.385306i	−0.733097	−	0.680124i	$-0.761926\pi$
$397$	4.43242	−	7.67717i	0.222457	−	0.385306i	0.955553	+	0.294818i	$0.0952591\pi$
$398$	−13.7317	−	11.5223i	−0.688309	−	0.577560i
$399$		0			0
$400$	−6.38713	−	36.2232i	−0.319356	−	1.81116i
$401$	28.4079	−	23.8371i	1.41862	−	1.19037i	0.466552	−	0.884494i	$-0.345496\pi$
$401$	28.4079	−	23.8371i	1.41862	−	1.19037i	0.952072	−	0.305874i	$-0.0989485\pi$
$402$		0			0
$403$	−19.0834	+	6.94578i	−0.950610	+	0.345994i
$404$	−8.79012			−0.437325
$405$		0			0
$406$	−16.1480			−0.801410
$407$	−4.93664	+	1.79679i	−0.244700	+	0.0890635i
$408$		0			0
$409$	−2.59627	+	2.17853i	−0.128377	+	0.107721i	−0.704716	−	0.709490i	$-0.748925\pi$
$409$	−2.59627	+	2.17853i	−0.128377	+	0.107721i	0.576339	+	0.817211i	$0.304481\pi$
$410$	3.16333	+	17.9402i	0.156226	+	0.886001i
$411$		0			0
$412$	−19.6138	−	16.4579i	−0.966303	−	0.810824i
$413$	15.6238	−	27.0612i	0.768798	−	1.33160i
$414$		0			0
$415$	20.9217	+	36.2375i	1.02701	+	1.77883i
$416$	6.42960	−	36.4641i	0.315237	−	1.78780i
$417$		0			0
$418$	25.1065	+	9.13803i	1.22800	+	0.446956i
$419$	19.4106	+	7.06489i	0.948272	+	0.345143i	0.769427	−	0.638735i	$-0.220542\pi$
$419$	19.4106	+	7.06489i	0.948272	+	0.345143i	0.178845	+	0.983877i	$0.442764\pi$
$420$		0			0
$421$	4.78106	−	27.1147i	0.233015	−	1.32149i	−0.613740	−	0.789508i	$-0.710336\pi$
$421$	4.78106	−	27.1147i	0.233015	−	1.32149i	0.846755	−	0.531983i	$-0.178553\pi$
$422$	5.88690	+	10.1964i	0.286570	+	0.496353i
$423$		0			0
$424$	−0.554378	+	0.960210i	−0.0269230	+	0.0466319i
$425$	19.5666	+	16.4183i	0.949120	+	0.796406i
$426$		0			0
$427$	1.49794	+	8.49524i	0.0724904	+	0.411114i
$428$	−16.7494	+	14.0544i	−0.809611	+	0.679344i
$429$		0			0
$430$	7.29086	−	2.65366i	0.351596	−	0.127971i
$431$	−2.58110			−0.124327			−0.0621636	−	0.998066i	$-0.519800\pi$
$431$	−2.58110			−0.124327			−0.0621636	+	0.998066i	$0.519800\pi$
$432$		0			0
$433$	−27.0137			−1.29820			−0.649098	−	0.760704i	$-0.724854\pi$
$433$	−27.0137			−1.29820			−0.649098	+	0.760704i	$0.724854\pi$
$434$	−18.7046	+	6.80793i	−0.897852	+	0.326791i
$435$		0			0
$436$	21.0253	−	17.6423i	1.00693	−	0.844913i
$437$	0.561202	+	3.18273i	0.0268459	+	0.152251i
$438$		0			0
$439$	8.97044	+	7.52709i	0.428136	+	0.359248i	0.831248	−	0.555902i	$-0.187627\pi$
$439$	8.97044	+	7.52709i	0.428136	+	0.359248i	−0.403112	+	0.915151i	$0.632072\pi$
$440$	−0.957882	+	1.65910i	−0.0456652	+	0.0790945i
$441$		0			0
$442$	13.6343	+	23.6153i	0.648517	+	1.12326i
$443$	0.361323	−	2.04916i	0.0171670	−	0.0973587i	−0.975020	−	0.222115i	$-0.928704\pi$
$443$	0.361323	−	2.04916i	0.0171670	−	0.0973587i	0.992187	+	0.124757i	$0.0398150\pi$
$444$		0			0
$445$	−2.43242	−	0.885328i	−0.115308	−	0.0419686i
$446$	16.4755	+	5.99660i	0.780138	+	0.283947i
$447$		0			0
$448$	2.85638	−	16.1993i	0.134951	−	0.765347i
$449$	−5.27541	−	9.13728i	−0.248962	−	0.431215i	0.714276	−	0.699864i	$-0.246756\pi$
$449$	−5.27541	−	9.13728i	−0.248962	−	0.431215i	−0.963238	+	0.268649i	$0.913423\pi$
$450$		0			0
$451$	2.72163	−	4.71400i	0.128157	−	0.221974i
$452$	−6.76055	−	5.67277i	−0.317989	−	0.266825i
$453$		0			0
$454$	3.64883	+	20.6936i	0.171248	+	0.971197i
$455$	−31.3960	+	26.3444i	−1.47187	+	1.23504i
$456$		0			0
$457$	7.43242	−	2.70518i	0.347674	−	0.126543i	−0.162280	−	0.986745i	$-0.551885\pi$
$457$	7.43242	−	2.70518i	0.347674	−	0.126543i	0.509954	+	0.860202i	$0.329663\pi$
$458$	−16.2912			−0.761238
$459$		0			0
$460$	3.61081			0.168355
$461$	36.7352	−	13.3705i	1.71093	−	0.622727i	0.713935	−	0.700212i	$-0.246911\pi$
$461$	36.7352	−	13.3705i	1.71093	−	0.622727i	0.996994	+	0.0774846i	$0.0246889\pi$
$462$		0			0
$463$	18.1498	−	15.2295i	0.843491	−	0.707773i	−0.114855	−	0.993382i	$-0.536640\pi$
$463$	18.1498	−	15.2295i	0.843491	−	0.707773i	0.958346	+	0.285609i	$0.0921959\pi$
$464$	−2.56353	−	14.5385i	−0.119009	−	0.674932i
$465$		0			0
$466$	−19.2212	−	16.1285i	−0.890406	−	0.747139i
$467$	17.3576	−	30.0642i	0.803214	−	1.39121i	−0.114277	−	0.993449i	$-0.536455\pi$
$467$	17.3576	−	30.0642i	0.803214	−	1.39121i	0.917490	−	0.397758i	$-0.130212\pi$
$468$		0			0
$469$	16.7815	+	29.0665i	0.774899	+	1.34216i
$470$	−0.300767	+	1.70574i	−0.0138734	+	0.0786798i
$471$		0			0
$472$	2.97178	+	1.08164i	0.136787	+	0.0497865i
$473$	−2.17853	−	0.792919i	−0.100169	−	0.0364584i
$474$		0			0
$475$	−9.40941	+	53.3634i	−0.431734	+	2.44848i
$476$	6.47410	+	11.2135i	0.296740	+	0.513969i
$477$		0			0
$478$	14.7875	−	25.6126i	0.676362	−	1.17149i
$479$	−4.96529	−	4.16637i	−0.226870	−	0.190366i	0.522266	−	0.852782i	$-0.325087\pi$
$479$	−4.96529	−	4.16637i	−0.226870	−	0.190366i	−0.749136	+	0.662416i	$0.769531\pi$
$480$		0			0
$481$	−1.97519	−	11.2018i	−0.0900607	−	0.510760i
$482$	1.20042	−	1.00727i	0.0546777	−	0.0458801i
$483$		0			0
$484$	11.0449	−	4.02001i	0.502040	−	0.182728i
$485$	26.2317			1.19112
$486$		0			0
$487$	19.9828			0.905505			0.452753	−	0.891636i	$-0.350442\pi$
$487$	19.9828			0.905505			0.452753	+	0.891636i	$0.350442\pi$
$488$	−0.820397	+	0.298600i	−0.0371376	+	0.0135170i
$489$		0			0
$490$	8.32295	−	6.98378i	0.375992	−	0.315495i
$491$	−4.55428	−	25.8286i	−0.205532	−	1.16563i	−0.896600	−	0.442840i	$-0.853971\pi$
$491$	−4.55428	−	25.8286i	−0.205532	−	1.16563i	0.691068	−	0.722789i	$-0.257140\pi$
$492$		0			0
$493$	7.85323	+	6.58964i	0.353692	+	0.296782i
$494$	−28.9243	+	50.0984i	−1.30137	+	2.25403i
$495$		0			0
$496$	−9.09879	−	15.7596i	−0.408548	−	0.707626i
$497$	0.490376	−	2.78106i	0.0219964	−	0.124748i
$498$		0			0
$499$	−5.93629	−	2.16063i	−0.265745	−	0.0967232i	0.205711	−	0.978613i	$-0.434049\pi$
$499$	−5.93629	−	2.16063i	−0.265745	−	0.0967232i	−0.471456	+	0.881890i	$0.656271\pi$
$500$	24.2033	+	8.80928i	1.08240	+	0.393963i
$501$		0			0
$502$	−2.84389	+	16.1285i	−0.126929	+	0.719851i
$503$	10.9131	+	18.9020i	0.486589	+	0.842798i	0.999881	−	0.0154166i	$-0.00490745\pi$
$503$	10.9131	+	18.9020i	0.486589	+	0.842798i	−0.513292	+	0.858214i	$0.671574\pi$
$504$		0			0
$505$	−8.65657	+	14.9936i	−0.385212	+	0.667208i
$506$	−1.70604	−	1.43154i	−0.0758429	−	0.0636398i
$507$		0			0
$508$	1.98798	+	11.2744i	0.0882023	+	0.500220i
$509$	22.2866	−	18.7007i	0.987837	−	0.828893i	0.00258346	−	0.999997i	$-0.499178\pi$
$509$	22.2866	−	18.7007i	0.987837	−	0.828893i	0.985253	+	0.171103i	$0.0547332\pi$
$510$		0			0
$511$	−10.3229	+	3.75725i	−0.456660	+	0.166211i
$512$	31.1704			1.37755
$513$		0			0
$514$	50.4620			2.22579
$515$	−47.3887	+	17.2481i	−2.08820	+	0.760042i
$516$		0			0
$517$	0.396459	−	0.332669i	0.0174363	−	0.0146308i
$518$	−1.93599	−	10.9795i	−0.0850623	−	0.482413i
$519$		0			0
$520$	−3.17752	−	2.66625i	−0.139343	−	0.116923i
$521$	6.84743	−	11.8601i	0.299991	−	0.519600i	−0.676142	−	0.736771i	$-0.736350\pi$
$521$	6.84743	−	11.8601i	0.299991	−	0.519600i	0.976134	+	0.217171i	$0.0696829\pi$
$522$		0			0
$523$	−6.57532	−	11.3888i	−0.287519	−	0.497997i	0.685698	−	0.727886i	$-0.259497\pi$
$523$	−6.57532	−	11.3888i	−0.287519	−	0.497997i	−0.973217	+	0.229889i	$0.926164\pi$
$524$	−3.37722	+	19.1532i	−0.147535	+	0.836710i
$525$		0			0
$526$	51.9436	+	18.9059i	2.26485	+	0.824338i
$527$	11.8748	+	4.32207i	0.517274	+	0.188272i
$528$		0			0
$529$	−3.94713	+	22.3853i	−0.171614	+	0.973273i
$530$	−17.0138	−	29.4688i	−0.739034	−	1.28004i
$531$		0			0
$532$	−13.7344	+	23.7887i	−0.595463	+	1.03137i
$533$	9.02828	+	7.57563i	0.391058	+	0.328137i
$534$		0			0
$535$	7.47818	+	42.4109i	0.323310	+	1.83358i
$536$	−2.60213	+	2.18345i	−0.112395	+	0.0943106i
$537$		0			0
$538$	−55.8414	+	20.3246i	−2.40749	+	0.876256i
$539$	−3.24644			−0.139834
$540$		0			0
$541$	6.26083			0.269174			0.134587	−	0.990902i	$-0.457029\pi$
$541$	6.26083			0.269174			0.134587	+	0.990902i	$0.457029\pi$
$542$	35.1658	−	12.7993i	1.51050	−	0.549778i
$543$		0			0
$544$	−17.6498	+	14.8099i	−0.756728	+	0.634970i
$545$	−9.38728	−	53.2379i	−0.402107	−	2.28046i
$546$		0			0
$547$	−24.0371	−	20.1696i	−1.02775	−	0.862388i	−0.0371720	−	0.999309i	$-0.511835\pi$
$547$	−24.0371	−	20.1696i	−1.02775	−	0.862388i	−0.990582	+	0.136921i	$0.956279\pi$
$548$	17.9337	−	31.0621i	0.766091	−	1.32691i
$549$		0			0
$550$	−18.6702	−	32.3378i	−0.796102	−	1.37889i
$551$	−3.77655	+	21.4179i	−0.160886	+	0.912432i
$552$		0			0
$553$	−28.2349	−	10.2767i	−1.20067	−	0.437008i
$554$	−39.0925	−	14.2285i	−1.66088	−	0.604511i
$555$		0			0
$556$	−7.60519	+	43.1312i	−0.322532	+	1.82917i
$557$	21.7196	+	37.6195i	0.920290	+	1.59399i	0.798966	+	0.601376i	$0.205381\pi$
$557$	21.7196	+	37.6195i	0.920290	+	1.59399i	0.121324	+	0.992613i	$0.461286\pi$
$558$		0			0
$559$	2.50980	−	4.34710i	0.106153	−	0.183863i
$560$	−28.1332	−	23.6065i	−1.18884	−	0.997558i
$561$		0			0
$562$	0.597611	+	3.38922i	0.0252087	+	0.142966i
$563$	−24.5269	+	20.5805i	−1.03369	+	0.867366i	−0.991285	−	0.131734i	$-0.957945\pi$
$563$	−24.5269	+	20.5805i	−1.03369	+	0.867366i	−0.0424018	+	0.999101i	$0.513501\pi$
$564$		0			0
$565$	−16.3341	+	5.94512i	−0.687180	+	0.250113i
$566$	−14.3549			−0.603381
$567$		0			0
$568$	0.285807			0.0119922
$569$	6.36355	−	2.31614i	0.266774	−	0.0970977i	−0.205170	−	0.978726i	$-0.565775\pi$
$569$	6.36355	−	2.31614i	0.266774	−	0.0970977i	0.471944	+	0.881629i	$0.343553\pi$
$570$		0			0
$571$	−16.2041	+	13.5969i	−0.678122	+	0.569012i	−0.915457	−	0.402416i	$-0.868171\pi$
$571$	−16.2041	+	13.5969i	−0.678122	+	0.569012i	0.237335	+	0.971428i	$0.423726\pi$
$572$	−3.35354	−	19.0189i	−0.140219	−	0.795220i
$573$		0			0
$574$	8.84911	+	7.42528i	0.369355	+	0.309925i
$575$	2.25838	−	3.91164i	0.0941811	−	0.163127i
$576$		0			0
$577$	−5.95811	−	10.3198i	−0.248039	−	0.429617i	0.714942	−	0.699183i	$-0.246453\pi$
$577$	−5.95811	−	10.3198i	−0.248039	−	0.429617i	−0.962982	+	0.269567i	$0.913120\pi$
$578$	−2.86786	+	16.2645i	−0.119287	+	0.676512i
$579$		0			0
$580$	22.8332	+	8.31061i	0.948098	+	0.345079i
$581$	24.9336	+	9.07507i	1.03442	+	0.376497i
$582$		0			0
$583$	−1.76558	+	10.0131i	−0.0731228	+	0.414700i
$584$	−0.555907	−	0.962859i	−0.0230036	−	0.0398434i
$585$		0			0
$586$	−15.1177	+	26.1846i	−0.624506	+	1.08168i
$587$	−0.0994798	−	0.0834734i	−0.00410597	−	0.00344532i	0.640732	−	0.767764i	$-0.278631\pi$
$587$	−0.0994798	−	0.0834734i	−0.00410597	−	0.00344532i	−0.644838	+	0.764319i	$0.723075\pi$
$588$		0			0
$589$	4.65523	+	26.4011i	0.191815	+	1.08784i
$590$	−74.3501	+	62.3872i	−3.06095	+	2.56844i
$591$		0			0
$592$	9.57785	−	3.48605i	0.393647	−	0.143276i
$593$	26.2622			1.07846			0.539230	−	0.842158i	$-0.318715\pi$
$593$	26.2622			1.07846			0.539230	+	0.842158i	$0.318715\pi$
$594$		0			0
$595$	25.5030			1.04552
$596$	27.3842	−	9.96703i	1.12170	−	0.408266i
$597$		0			0
$598$	3.69388	−	3.09953i	0.151054	−	0.126749i
$599$	4.79185	+	27.1759i	0.195790	+	1.11038i	0.911290	+	0.411766i	$0.135088\pi$
$599$	4.79185	+	27.1759i	0.195790	+	1.11038i	−0.715500	+	0.698613i	$0.753801\pi$
$600$		0			0
$601$	1.02094	+	0.856674i	0.0416452	+	0.0349445i	0.663373	−	0.748289i	$-0.269124\pi$
$601$	1.02094	+	0.856674i	0.0416452	+	0.0349445i	−0.621728	+	0.783234i	$0.713569\pi$
$602$	2.45999	−	4.26083i	0.100262	−	0.173658i
$603$		0			0
$604$	5.54576	+	9.60554i	0.225654	+	0.390844i
$605$	4.02001	−	22.7986i	0.163437	−	0.926895i
$606$		0			0
$607$	11.8068	+	4.29731i	0.479221	+	0.174422i	0.570325	−	0.821419i	$-0.306817\pi$
$607$	11.8068	+	4.29731i	0.479221	+	0.174422i	−0.0911037	+	0.995841i	$0.529039\pi$
$608$	−45.9305	−	16.7173i	−1.86273	−	0.677978i
$609$		0			0
$610$	4.65270	−	26.3868i	0.188382	−	1.06837i
$611$	0.560282	+	0.970437i	0.0226666	+	0.0392597i
$612$		0			0
$613$	6.99912	−	12.1228i	0.282692	−	0.489637i	−0.689355	−	0.724424i	$-0.742106\pi$
$613$	6.99912	−	12.1228i	0.282692	−	0.489637i	0.972047	+	0.234787i	$0.0754393\pi$
$614$	25.2935	+	21.2237i	1.02076	+	0.856521i
$615$		0			0
$616$	0.210952	+	1.19637i	0.00849948	+	0.0482030i
$617$	18.4209	−	15.4569i	0.741596	−	0.622273i	−0.191670	−	0.981459i	$-0.561390\pi$
$617$	18.4209	−	15.4569i	0.741596	−	0.622273i	0.933266	+	0.359187i	$0.116946\pi$
$618$		0			0
$619$	−6.45723	+	2.35024i	−0.259538	+	0.0944642i	−0.468512	−	0.883457i	$-0.655210\pi$
$619$	−6.45723	+	2.35024i	−0.259538	+	0.0944642i	0.208974	+	0.977921i	$0.432988\pi$
$620$	29.9521			1.20291
$621$		0			0
$622$	−31.5594			−1.26542
$623$	−1.54244	+	0.561403i	−0.0617967	+	0.0224921i
$624$		0			0
$625$	5.53003	−	4.64025i	0.221201	−	0.185610i
$626$	11.7674	+	66.7363i	0.470320	+	2.66732i
$627$		0			0
$628$	−1.74510	−	1.46431i	−0.0696371	−	0.0584324i
$629$	−3.53898	+	6.12970i	−0.141109	+	0.244407i
$630$		0			0
$631$	17.6887	+	30.6377i	0.704175	+	1.21967i	0.966989	+	0.254820i	$0.0820161\pi$
$631$	17.6887	+	30.6377i	0.704175	+	1.21967i	−0.262814	+	0.964847i	$0.584651\pi$
$632$	0.528061	−	2.99479i	0.0210052	−	0.119126i
$633$		0			0
$634$	30.1891	+	10.9879i	1.19896	+	0.436387i
$635$	21.1889	+	7.71213i	0.840856	+	0.306047i
$636$		0			0
$637$	1.22059	−	6.92231i	0.0483615	−	0.274272i
$638$	−7.49346	−	12.9791i	−0.296669	−	0.513846i
$639$		0			0
$640$	3.51114	−	6.08148i	0.138790	−	0.240392i
$641$	−14.6879	−	12.3246i	−0.580136	−	0.486792i	0.304855	−	0.952399i	$-0.401392\pi$
$641$	−14.6879	−	12.3246i	−0.580136	−	0.486792i	−0.884992	+	0.465606i	$0.845836\pi$
$642$		0			0
$643$	3.36468	+	19.0820i	0.132690	+	0.752521i	0.976441	+	0.215786i	$0.0692315\pi$
$643$	3.36468	+	19.0820i	0.132690	+	0.752521i	−0.843751	+	0.536735i	$0.819657\pi$
$644$	1.75400	−	1.47178i	0.0691173	−	0.0579963i
$645$		0			0
$646$	33.8259	−	12.3116i	1.33086	−	0.484395i
$647$	8.77141			0.344840			0.172420	−	0.985024i	$-0.444841\pi$
$647$	8.77141			0.344840			0.172420	+	0.985024i	$0.444841\pi$
$648$		0			0
$649$	29.0009			1.13839
$650$	75.9728	−	27.6518i	2.97990	−	1.08459i
$651$		0			0
$652$	3.99273	−	3.35029i	0.156367	−	0.131208i
$653$	5.69729	+	32.3109i	0.222952	+	1.26442i	0.866562	+	0.499070i	$0.166325\pi$
$653$	5.69729	+	32.3109i	0.222952	+	1.26442i	−0.643609	+	0.765354i	$0.722564\pi$
$654$		0			0
$655$	29.3444	+	24.6228i	1.14658	+	0.962094i
$656$	−5.28039	+	9.14590i	−0.206164	+	0.357087i
$657$		0			0
$658$	0.549163	+	0.951178i	0.0214086	+	0.0370808i
$659$	3.23882	−	18.3682i	0.126166	−	0.715525i	−0.854442	−	0.519547i	$-0.826101\pi$
$659$	3.23882	−	18.3682i	0.126166	−	0.715525i	0.980608	−	0.195978i	$-0.0627882\pi$
$660$		0			0
$661$	−34.2117	−	12.4520i	−1.33068	−	0.484329i	−0.423816	−	0.905748i	$-0.639310\pi$
$661$	−34.2117	−	12.4520i	−1.33068	−	0.484329i	−0.906866	+	0.421420i	$0.861532\pi$
$662$	58.4492	+	21.2738i	2.27169	+	0.826829i
$663$		0			0
$664$	−0.466319	+	2.64462i	−0.0180967	+	0.102631i
$665$	27.0515	+	46.8546i	1.04901	+	1.81694i
$666$		0			0
$667$	0.906422	−	1.56997i	0.0350968	−	0.0607894i
$668$	5.51125	+	4.62449i	0.213237	+	0.178927i
$669$		0			0
$670$	−18.1027	−	102.665i	−0.699367	−	3.96631i
$671$	−6.13300	+	5.14620i	−0.236762	+	0.198667i
$672$		0			0
$673$	−37.0146	+	13.4722i	−1.42681	+	0.519316i	−0.936015	−	0.351960i	$-0.885515\pi$
$673$	−37.0146	+	13.4722i	−1.42681	+	0.519316i	−0.490793	+	0.871276i	$0.663293\pi$
$674$	11.8276			0.455584
$675$		0			0
$676$	17.3824			0.668553
$677$	−29.7651	+	10.8336i	−1.14397	+	0.416370i	−0.843345	−	0.537373i	$-0.819417\pi$
$677$	−29.7651	+	10.8336i	−1.14397	+	0.416370i	−0.300623	+	0.953743i	$0.597194\pi$
$678$		0			0
$679$	12.7424	−	10.6922i	0.489009	−	0.410327i
$680$	0.448204	+	2.54189i	0.0171878	+	0.0974770i
$681$		0			0
$682$	−14.1518	−	11.8748i	−0.541901	−	0.454709i
$683$	14.5328	−	25.1716i	0.556083	−	0.963164i	−0.441735	−	0.897145i	$-0.645637\pi$
$683$	14.5328	−	25.1716i	0.556083	−	0.963164i	0.997818	−	0.0660187i	$-0.0210297\pi$
$684$		0			0
$685$	−35.3225	−	61.1804i	−1.34960	−	2.33758i
$686$	6.81612	−	38.6562i	0.260241	−	1.47590i
$687$		0			0
$688$	4.22668	+	1.53839i	0.161141	+	0.0586504i
$689$	−20.6869	−	7.52940i	−0.788107	−	0.286847i
$690$		0			0
$691$	0.930303	−	5.27601i	0.0353904	−	0.200709i	−0.961986	−	0.273099i	$-0.911951\pi$
$691$	0.930303	−	5.27601i	0.0353904	−	0.200709i	0.997376	+	0.0723898i	$0.0230626\pi$
$692$	−6.60549	−	11.4410i	−0.251103	−	0.434923i
$693$		0			0
$694$	−22.6805	+	39.2838i	−0.860940	+	1.49119i
$695$	66.0808	+	55.4484i	2.50659	+	2.10328i
$696$		0			0
$697$	−1.27348	−	7.22227i	−0.0482365	−	0.273563i
$698$	−17.4513	+	14.6434i	−0.660541	+	0.554260i
$699$		0			0
$700$	36.0749	−	13.1302i	1.36350	−	0.496275i
$701$	−25.6536			−0.968922			−0.484461	−	0.874813i	$-0.660984\pi$
$701$	−25.6536			−0.968922			−0.484461	+	0.874813i	$0.660984\pi$
$702$		0			0
$703$	−15.0155			−0.566320
$704$	14.3459	−	5.22147i	0.540680	−	0.196791i
$705$		0			0
$706$	−3.22075	+	2.70253i	−0.121215	+	0.101711i
$707$	1.90641	+	10.8118i	0.0716980	+	0.406620i
$708$		0			0
$709$	−3.59311	−	3.01498i	−0.134942	−	0.113230i	0.572818	−	0.819682i	$-0.305850\pi$
$709$	−3.59311	−	3.01498i	−0.134942	−	0.113230i	−0.707761	+	0.706452i	$0.750294\pi$
$710$	−4.38571	+	7.59627i	−0.164593	+	0.285083i
$711$		0			0
$712$	−0.0830629	−	0.143869i	−0.00311291	−	0.00539173i
$713$	0.388040	−	2.20068i	0.0145322	−	0.0824163i
$714$		0			0
$715$	−35.7438	−	13.0097i	−1.33674	−	0.486535i
$716$	−25.4052	−	9.24675i	−0.949438	−	0.345567i
$717$		0			0
$718$	8.28493	−	46.9862i	0.309191	−	1.75351i
$719$	−19.5335	−	33.8330i	−0.728476	−	1.26176i	−0.957527	−	0.288343i	$-0.906896\pi$
$719$	−19.5335	−	33.8330i	−0.728476	−	1.26176i	0.229052	−	0.973414i	$-0.426438\pi$
$720$		0			0
$721$	−15.9893	+	27.6943i	−0.595473	+	1.03139i
$722$	29.8316	+	25.0317i	1.11022	+	0.931583i
$723$		0			0
$724$	4.30793	+	24.4315i	0.160103	+	0.907990i
$725$	23.2840	−	19.5376i	0.864747	−	0.725609i
$726$		0			0
$727$	10.1725	−	3.70247i	0.377276	−	0.137317i	−0.146420	−	0.989223i	$-0.546775\pi$
$727$	10.1725	−	3.70247i	0.377276	−	0.137317i	0.523696	+	0.851905i	$0.324553\pi$
$728$	−2.63030			−0.0974853
$729$		0			0
$730$	34.1215			1.26290
$731$	−2.93512	+	1.06830i	−0.108559	+	0.0395124i
$732$		0			0
$733$	−2.61406	+	2.19345i	−0.0965524	+	0.0810171i	−0.689786	−	0.724013i	$-0.742295\pi$
$733$	−2.61406	+	2.19345i	−0.0965524	+	0.0810171i	0.593234	+	0.805030i	$0.297851\pi$
$734$	−0.969561	−	5.49866i	−0.0357872	−	0.202959i
$735$		0			0
$736$	3.12108	+	2.61890i	0.115045	+	0.0965339i
$737$	−15.5749	+	26.9766i	−0.573710	+	0.993695i
$738$		0			0
$739$	−13.1505	−	22.7773i	−0.483748	−	0.837877i	0.516077	−	0.856542i	$-0.327392\pi$
$739$	−13.1505	−	22.7773i	−0.483748	−	0.837877i	−0.999826	+	0.0186653i	$0.994058\pi$
$740$	−2.91317	+	16.5214i	−0.107090	+	0.607339i
$741$		0			0
$742$	−20.2763	−	7.37997i	−0.744367	−	0.270927i
$743$	−27.1984	−	9.89940i	−0.997811	−	0.363174i	−0.209071	−	0.977900i	$-0.567044\pi$
$743$	−27.1984	−	9.89940i	−0.997811	−	0.363174i	−0.788740	+	0.614727i	$0.789266\pi$
$744$		0			0
$745$	9.96703	−	56.5259i	0.365164	−	2.07095i
$746$	28.3953	+	49.1822i	1.03963	+	1.80069i
$747$		0			0
$748$	−6.00862	+	10.4072i	−0.219697	+	0.380526i
$749$	20.9194	+	17.5535i	0.764380	+	0.641391i
$750$		0			0
$751$	−3.37716	−	19.1528i	−0.123234	−	0.698897i	−0.982341	−	0.187100i	$-0.940091\pi$
$751$	−3.37716	−	19.1528i	−0.123234	−	0.698897i	0.859106	−	0.511797i	$-0.171020\pi$
$752$	−0.769193	+	0.645430i	−0.0280496	+	0.0235364i
$753$		0			0
$754$	30.4923	−	11.0983i	1.11046	−	0.404176i
$755$	21.8460			0.795058
$756$		0			0
$757$	6.59627			0.239745			0.119873	−	0.992789i	$-0.461751\pi$
$757$	6.59627			0.239745			0.119873	+	0.992789i	$0.461751\pi$
$758$	−59.5941	+	21.6905i	−2.16455	+	0.787833i
$759$		0			0
$760$	−4.19459	+	3.51968i	−0.152154	+	0.127672i
$761$	1.79373	+	10.1728i	0.0650228	+	0.368763i	0.999905	+	0.0138038i	$0.00439402\pi$
$761$	1.79373	+	10.1728i	0.0650228	+	0.368763i	−0.934882	+	0.354959i	$0.884495\pi$
$762$		0			0
$763$	−26.2600	−	22.0347i	−0.950674	−	0.797710i
$764$	12.6138	−	21.8478i	0.456352	−	0.790424i
$765$		0			0
$766$	−0.662037	−	1.14668i	−0.0239204	−	0.0414313i
$767$	−10.9037	+	61.8380i	−0.393710	+	2.23284i
$768$		0			0
$769$	−42.1536	−	15.3427i	−1.52010	−	0.553271i	−0.558926	−	0.829217i	$-0.688786\pi$
$769$	−42.1536	−	15.3427i	−1.52010	−	0.553271i	−0.961173	+	0.275947i	$0.911009\pi$
$770$	−35.0344	−	12.7515i	−1.26255	−	0.459532i
$771$		0			0
$772$	4.89693	−	27.7718i	0.176244	−	0.999531i
$773$	−21.4677	−	37.1832i	−0.772141	−	1.33739i	−0.936388	−	0.350968i	$-0.885853\pi$
$773$	−21.4677	−	37.1832i	−0.772141	−	1.33739i	0.164247	−	0.986419i	$-0.447481\pi$
$774$		0			0
$775$	18.7335	−	32.4475i	0.672929	−	1.16555i
$776$	1.28963	+	1.08213i	0.0462951	+	0.0388462i
$777$		0			0
$778$	−1.45677	−	8.26173i	−0.0522276	−	0.296198i
$779$	11.9181	−	10.0005i	0.427010	−	0.358304i
$780$		0			0
$781$	2.46286	−	0.896407i	0.0881280	−	0.0320760i
$782$	−3.00054			−0.107299
$783$		0			0
$784$	6.29860			0.224950
$785$	−4.21632	+	1.53462i	−0.150487	+	0.0547728i
$786$		0			0
$787$	0.365715	−	0.306871i	0.0130363	−	0.0109388i	−0.636246	−	0.771486i	$-0.719514\pi$
$787$	0.365715	−	0.306871i	0.0130363	−	0.0109388i	0.649283	+	0.760547i	$0.275069\pi$
$788$	7.28455	+	41.3127i	0.259501	+	1.47171i
$789$		0			0
$790$	71.4932	+	59.9900i	2.54362	+	2.13435i
$791$	−5.51125	+	9.54576i	−0.195957	+	0.339408i
$792$		0			0
$793$	−8.66725	−	15.0121i	−0.307783	−	0.533096i
$794$	−3.03195	+	17.1951i	−0.107600	+	0.610230i
$795$		0			0
$796$	16.0728	+	5.85002i	0.569685	+	0.207348i
$797$	−10.7773	−	3.92262i	−0.381752	−	0.138946i	0.144014	−	0.989576i	$-0.453999\pi$
$797$	−10.7773	−	3.92262i	−0.381752	−	0.138946i	−0.525766	+	0.850629i	$0.676221\pi$
$798$		0			0
$799$	0.121082	−	0.686688i	0.00428356	−	0.0242933i
$800$	34.1558	+	59.1596i	1.20759	+	2.09161i
$801$		0			0
$802$	−36.5205	+	63.2554i	−1.28958	+	2.23363i
$803$	−7.81028	−	6.55361i	−0.275619	−	0.231272i
$804$		0			0
$805$	−0.783119	−	4.44129i	−0.0276013	−	0.156535i
$806$	30.6411	−	25.7110i	1.07929	−	0.905630i
$807$		0			0
$808$	−1.04411	+	0.380025i	−0.0367317	+	0.0133692i
$809$	42.7873			1.50432			0.752161	−	0.658979i	$-0.229012\pi$
$809$	42.7873			1.50432			0.752161	+	0.658979i	$0.229012\pi$
$810$		0			0
$811$	−31.2098			−1.09592			−0.547962	−	0.836503i	$-0.684596\pi$
$811$	−31.2098			−1.09592			−0.547962	+	0.836503i	$0.684596\pi$
$812$	14.4790	−	5.26991i	0.508112	−	0.184938i
$813$		0			0
$814$	7.92649	−	6.65111i	0.277823	−	0.233121i
$815$	−1.78265	−	10.1099i	−0.0624437	−	0.354136i
$816$		0			0
$817$	−5.07604	−	4.25930i	−0.177588	−	0.149014i
$818$	3.33770	−	5.78106i	0.116700	−	0.202130i
$819$		0			0
$820$	−8.69119	−	15.0536i	−0.303509	−	0.525694i
$821$	4.73210	−	26.8371i	0.165152	−	0.936621i	−0.783757	−	0.621068i	$-0.786699\pi$
$821$	4.73210	−	26.8371i	0.165152	−	0.936621i	0.948908	−	0.315553i	$-0.102190\pi$
$822$		0			0
$823$	13.5697	+	4.93897i	0.473010	+	0.172162i	0.567515	−	0.823363i	$-0.307905\pi$
$823$	13.5697	+	4.93897i	0.473010	+	0.172162i	−0.0945054	+	0.995524i	$0.530127\pi$
$824$	−3.04130	−	1.10694i	−0.105949	−	0.0385622i
$825$		0			0
$826$	−10.6873	+	60.6108i	−0.371859	+	2.10892i
$827$	−3.51379	−	6.08606i	−0.122186	−	0.211633i	0.798443	−	0.602070i	$-0.205657\pi$
$827$	−3.51379	−	6.08606i	−0.122186	−	0.211633i	−0.920630	+	0.390437i	$0.872324\pi$
$828$		0			0
$829$	21.0403	−	36.4429i	0.730760	−	1.26571i	−0.225799	−	0.974174i	$-0.572499\pi$
$829$	21.0403	−	36.4429i	0.730760	−	1.26571i	0.956559	−	0.291539i	$-0.0941673\pi$
$830$	−63.1340	−	52.9757i	−2.19141	−	1.83881i
$831$		0			0
$832$	5.73989	+	32.5525i	0.198995	+	1.12856i
$833$	−3.35061	+	2.81150i	−0.116092	+	0.0974127i
$834$		0			0
$835$	13.3157	−	4.84651i	0.460808	−	0.167720i
$836$	−25.4938			−0.881723
$837$		0			0
$838$	−40.6851			−1.40544
$839$	37.5137	−	13.6539i	1.29512	−	0.471384i	0.399715	−	0.916640i	$-0.369109\pi$
$839$	37.5137	−	13.6539i	1.29512	−	0.471384i	0.895404	+	0.445255i	$0.146887\pi$
$840$		0			0
$841$	−12.8701	+	10.7993i	−0.443795	+	0.372388i
$842$	9.41685	+	53.4056i	0.324526	+	1.84048i
$843$		0			0
$844$	−8.60607	−	7.22135i	−0.296233	−	0.248569i
$845$	17.1183	−	29.6498i	0.588887	−	1.01998i
$846$		0			0
$847$	−7.34002	−	12.7133i	−0.252206	−	0.436834i
$848$	3.42550	−	19.4270i	0.117632	−	0.667124i
$849$		0			0
$850$	−47.2747	−	17.2066i	−1.62151	−	0.590181i
$851$	1.17614	+	0.428081i	0.0403177	+	0.0146744i
$852$		0			0
$853$	−4.07744	+	23.1243i	−0.139609	+	0.791761i	0.831930	+	0.554881i	$0.187236\pi$
$853$	−4.07744	+	23.1243i	−0.139609	+	0.791761i	−0.971539	+	0.236880i	$0.923875\pi$
$854$	−8.49524	−	14.7142i	−0.290701	−	0.503509i
$855$		0			0
$856$	−1.38191	+	2.39354i	−0.0472328	+	0.0818095i
$857$	−6.15495	−	5.16462i	−0.210249	−	0.176420i	0.531582	−	0.847007i	$-0.321598\pi$
$857$	−6.15495	−	5.16462i	−0.210249	−	0.176420i	−0.741831	+	0.670587i	$0.766042\pi$
$858$		0			0
$859$	−4.21894	−	23.9268i	−0.143948	−	0.816372i	−0.968205	−	0.250156i	$-0.919518\pi$
$859$	−4.21894	−	23.9268i	−0.143948	−	0.816372i	0.824257	−	0.566216i	$-0.191593\pi$
$860$	−5.67128	+	4.75877i	−0.193389	+	0.162273i
$861$		0			0
$862$	4.77719	−	1.73875i	0.162712	−	0.0592222i
$863$	10.2828			0.350029			0.175015	−	0.984566i	$-0.444003\pi$
$863$	10.2828			0.350029			0.175015	+	0.984566i	$0.444003\pi$
$864$		0			0
$865$	−26.0205			−0.884725
$866$	49.9979	−	18.1977i	1.69900	−	0.618385i
$867$		0			0
$868$	14.5496	−	12.2086i	0.493847	−	0.414387i
$869$	−4.84245	−	27.4629i	−0.164269	−	0.931616i
$870$		0			0
$871$	−51.6657	−	43.3527i	−1.75063	−	1.46895i
$872$	1.73470	−	3.00459i	0.0587443	−	0.101748i
$873$		0			0
$874$	−3.18273	−	5.51266i	−0.107658	−	0.186468i
$875$	5.58613	−	31.6805i	0.188846	−	1.07100i
$876$		0			0
$877$	24.6459	+	8.97037i	0.832233	+	0.302908i	0.722775	−	0.691083i	$-0.242866\pi$
$877$	24.6459	+	8.97037i	0.832233	+	0.302908i	0.109458	+	0.993991i	$0.465089\pi$
$878$	−21.6734	−	7.88847i	−0.731442	−	0.266223i
$879$		0			0
$880$	5.91875	−	33.5669i	0.199521	−	1.13154i
$881$	−19.6163	−	33.9764i	−0.660890	−	1.14469i	−0.980382	−	0.197106i	$-0.936846\pi$
$881$	−19.6163	−	33.9764i	−0.660890	−	1.14469i	0.319492	−	0.947589i	$-0.396488\pi$
$882$		0			0
$883$	−3.89915	+	6.75352i	−0.131217	+	0.227274i	−0.924146	−	0.382040i	$-0.875222\pi$
$883$	−3.89915	+	6.75352i	−0.131217	+	0.227274i	0.792929	+	0.609314i	$0.208555\pi$
$884$	−19.9320	−	16.7249i	−0.670385	−	0.562520i
$885$		0			0
$886$	0.711667	+	4.03606i	0.0239089	+	0.135594i
$887$	17.5095	−	14.6922i	0.587912	−	0.493317i	−0.299623	−	0.954058i	$-0.596861\pi$
$887$	17.5095	−	14.6922i	0.587912	−	0.493317i	0.887535	+	0.460741i	$0.152416\pi$
$888$		0			0
$889$	13.4363	−	4.89041i	0.450639	−	0.164019i
$890$	5.09840			0.170899
$891$		0			0
$892$	−16.7297			−0.560151
$893$	1.39003	−	0.505930i	0.0465156	−	0.0169303i
$894$		0			0
$895$	−40.7918	+	34.2284i	−1.36352	+	1.14413i
$896$	−0.773249	−	4.38532i	−0.0258324	−	0.146503i
$897$		0			0
$898$	15.9192	+	13.3578i	0.531231	+	0.445756i
$899$	7.51887	−	13.0231i	0.250768	−	0.434343i
$900$		0			0
$901$	6.84936	+	11.8634i	0.228185	+	0.395228i
$902$	−1.86170	+	10.5582i	−0.0619880	+	0.351551i
$903$		0			0
$904$	−1.04829	−	0.381545i	−0.0348655	−	0.0126900i
$905$	45.9162	+	16.7121i	1.52631	+	0.555530i
$906$		0			0
$907$	−6.57233	+	37.2735i	−0.218231	+	1.23765i	0.656981	+	0.753907i	$0.271833\pi$
$907$	−6.57233	+	37.2735i	−0.218231	+	1.23765i	−0.875212	+	0.483740i	$0.839278\pi$
$908$	−10.0251	−	17.3640i	−0.332694	−	0.576243i
$909$		0			0
$910$	40.3619	−	69.9089i	1.33798	−	2.31746i
$911$	40.3740	+	33.8778i	1.33765	+	1.12242i	0.982223	+	0.187717i	$0.0601088\pi$
$911$	40.3740	+	33.8778i	1.33765	+	1.12242i	0.355427	+	0.934704i	$0.384336\pi$
$912$		0			0
$913$	4.27626	+	24.2518i	0.141523	+	0.802619i
$914$	−11.9338	+	10.0137i	−0.394736	+	0.331223i
$915$		0			0
$916$	14.6074	−	5.31666i	0.482642	−	0.175667i
$917$	24.2908			0.802152
$918$		0			0
$919$	−49.1052			−1.61983			−0.809916	−	0.586545i	$-0.800488\pi$
$919$	−49.1052			−1.61983			−0.809916	+	0.586545i	$0.800488\pi$
$920$	0.428901	−	0.156107i	0.0141404	−	0.00514670i
$921$		0			0
$922$	−58.9837	+	49.4932i	−1.94252	+	1.62997i
$923$	0.985408	+	5.58853i	0.0324351	+	0.183949i
$924$		0			0
$925$	16.0758	+	13.4892i	0.528569	+	0.443522i
$926$	−23.3329	+	40.4138i	−0.766766	+	1.32808i
$927$		0			0
$928$	13.7087	+	23.7442i	0.450011	+	0.779442i
$929$	3.11711	−	17.6780i	0.102269	−	0.579996i	−0.890007	−	0.455947i	$-0.849301\pi$
$929$	3.11711	−	17.6780i	0.102269	−	0.579996i	0.992276	−	0.124049i	$-0.0395881\pi$
$930$		0			0
$931$	−8.71941	−	3.17360i	−0.285767	−	0.104011i
$932$	22.4982	+	8.18866i	0.736952	+	0.268229i
$933$		0			0
$934$	−11.8733	+	67.3368i	−0.388506	+	2.20333i
$935$	11.8347	+	20.4982i	0.387035	+	0.670364i
$936$		0			0
$937$	14.8990	−	25.8058i	0.486729	−	0.843039i	−0.513155	−	0.858296i	$-0.671523\pi$
$937$	14.8990	−	25.8058i	0.486729	−	0.843039i	0.999884	+	0.0152572i	$0.00485672\pi$
$938$	−50.6404	−	42.4923i	−1.65347	−	1.38742i
$939$		0			0
$940$	−0.286989	−	1.62760i	−0.00936055	−	0.0530863i
$941$	−22.9900	+	19.2909i	−0.749451	+	0.628864i	−0.935358	−	0.353703i	$-0.884922\pi$
$941$	−22.9900	+	19.2909i	−0.749451	+	0.628864i	0.185907	+	0.982567i	$0.440478\pi$
$942$		0			0
$943$	−1.21864	+	0.443547i	−0.0396843	+	0.0144439i
$944$	−56.2663			−1.83131
$945$		0			0
$946$	4.56624			0.148461
$947$	−42.8512	+	15.5966i	−1.39248	+	0.506820i	−0.925937	−	0.377679i	$-0.876722\pi$
$947$	−42.8512	+	15.5966i	−1.39248	+	0.506820i	−0.466541	+	0.884499i	$0.654500\pi$
$948$		0			0
$949$	16.9106	−	14.1897i	0.548941	−	0.460616i
$950$	−18.5329	−	105.105i	−0.601288	−	3.41007i
$951$		0			0
$952$	1.25380	+	1.05207i	0.0406360	+	0.0340977i
$953$	6.59786	−	11.4278i	0.213726	−	0.370184i	−0.739152	−	0.673539i	$-0.764773\pi$
$953$	6.59786	−	11.4278i	0.213726	−	0.370184i	0.952878	+	0.303355i	$0.0981068\pi$
$954$		0			0
$955$	−24.8444	−	43.0317i	−0.803945	−	1.39247i
$956$	−4.90036	+	27.7913i	−0.158489	+	0.898836i
$957$		0			0
$958$	11.9966	+	4.36640i	0.387592	+	0.141072i
$959$	−42.0958	−	15.3216i	−1.35934	−	0.494760i
$960$		0			0
$961$	−2.16426	+	12.2741i	−0.0698148	+	0.395939i
$962$	11.2018	+	19.4021i	0.361162	+	0.625550i
$963$		0			0
$964$	−0.747626	+	1.29493i	−0.0240794	+	0.0417068i
$965$	−42.5489	−	35.7028i	−1.36970	−	1.14931i
$966$		0			0
$967$	−3.49984	−	19.8486i	−0.112547	−	0.638287i	−0.987935	−	0.154866i	$-0.950505\pi$
$967$	−3.49984	−	19.8486i	−0.112547	−	0.638287i	0.875388	−	0.483421i	$-0.160606\pi$
$968$	1.13814	−	0.955012i	0.0365812	−	0.0306953i
$969$		0			0
$970$	−48.5506	+	17.6710i	−1.55886	+	0.567380i
$971$	−26.5839			−0.853118			−0.426559	−	0.904460i	$-0.640274\pi$
$971$	−26.5839			−0.853118			−0.426559	+	0.904460i	$0.640274\pi$
$972$		0			0
$973$	54.7006			1.75362
$974$	−36.9848	+	13.4614i	−1.18507	+	0.431330i
$975$		0			0
$976$	11.8990	−	9.98443i	0.380877	−	0.319594i
$977$	2.50124	+	14.1853i	0.0800219	+	0.453827i	0.998320	+	0.0579375i	$0.0184524\pi$
$977$	2.50124	+	14.1853i	0.0800219	+	0.453827i	−0.918298	+	0.395889i	$0.870436\pi$
$978$		0			0
$979$	−1.16700	−	0.979232i	−0.0372976	−	0.0312964i
$980$	−5.18355	+	8.97818i	−0.165583	+	0.286797i
$981$		0			0
$982$	25.8286	+	44.7365i	0.824225	+	1.42760i
$983$	−7.46481	+	42.3350i	−0.238090	+	1.35028i	0.597916	+	0.801558i	$0.295995\pi$
$983$	−7.46481	+	42.3350i	−0.238090	+	1.35028i	−0.836007	+	0.548719i	$0.815116\pi$
$984$		0			0
$985$	77.6425	+	28.2596i	2.47390	+	0.900425i
$986$	−18.9741	−	6.90601i	−0.604259	−	0.219932i
$987$		0			0
$988$	9.58512	−	54.3599i	0.304943	−	1.72942i
$989$	0.276170	+	0.478340i	0.00878169	+	0.0152103i
$990$		0			0
$991$	7.78968	−	13.4921i	0.247447	−	0.428591i	−0.715370	−	0.698746i	$-0.753742\pi$
$991$	7.78968	−	13.4921i	0.247447	−	0.428591i	0.962817	+	0.270155i	$0.0870750\pi$
$992$	25.8897	+	21.7240i	0.821999	+	0.689739i
$993$		0			0
$994$	0.965852	+	5.47762i	0.0306350	+	0.173739i
$995$	25.8072	−	21.6548i	0.818144	−	0.686504i
$996$		0			0
$997$	−38.1690	+	13.8924i	−1.20882	+	0.439976i	−0.866295	−	0.499532i	$-0.833505\pi$
$997$	−38.1690	+	13.8924i	−1.20882	+	0.439976i	−0.342528	+	0.939508i	$0.611283\pi$
$998$	12.4426			0.393863
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.r.163.1		12
3.2	odd	2	inner	729.2.e.r.163.2		12
9.2	odd	6		729.2.e.q.406.1		12
9.4	even	3		729.2.e.m.649.2		12
9.5	odd	6		729.2.e.m.649.1		12
9.7	even	3		729.2.e.q.406.2		12
27.2	odd	18		729.2.a.c.1.1	✓	6
27.4	even	9	inner	729.2.e.r.568.1		12
27.5	odd	18		729.2.e.m.82.1		12
27.7	even	9		729.2.c.c.487.1		12
27.11	odd	18		729.2.c.c.244.6		12
27.13	even	9		729.2.e.q.325.2		12
27.14	odd	18		729.2.e.q.325.1		12
27.16	even	9		729.2.c.c.244.1		12
27.20	odd	18		729.2.c.c.487.6		12
27.22	even	9		729.2.e.m.82.2		12
27.23	odd	18	inner	729.2.e.r.568.2		12
27.25	even	9		729.2.a.c.1.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.1	✓	6	27.2	odd	18
729.2.a.c.1.6	yes	6	27.25	even	9
729.2.c.c.244.1		12	27.16	even	9
729.2.c.c.244.6		12	27.11	odd	18
729.2.c.c.487.1		12	27.7	even	9
729.2.c.c.487.6		12	27.20	odd	18
729.2.e.m.82.1		12	27.5	odd	18
729.2.e.m.82.2		12	27.22	even	9
729.2.e.m.649.1		12	9.5	odd	6
729.2.e.m.649.2		12	9.4	even	3
729.2.e.q.325.1		12	27.14	odd	18
729.2.e.q.325.2		12	27.13	even	9
729.2.e.q.406.1		12	9.2	odd	6
729.2.e.q.406.2		12	9.7	even	3
729.2.e.r.163.1		12	1.1	even	1	trivial
729.2.e.r.163.2		12	3.2	odd	2	inner
729.2.e.r.568.1		12	27.4	even	9	inner
729.2.e.r.568.2		12	27.23	odd	18	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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.85083 + 0.673648i) q^{2} +(1.43969 - 1.20805i) q^{4} +(-0.642788 - 3.64543i) q^{5} +(-1.79813 - 1.50881i) q^{7} +(0.118782 - 0.205737i) q^{8} +O(q^{10})\)	\(q+(-1.85083 + 0.673648i) q^{2} +(1.43969 - 1.20805i) q^{4} +(-0.642788 - 3.64543i) q^{5} +(-1.79813 - 1.50881i) q^{7} +(0.118782 - 0.205737i) q^{8} +(3.64543 + 6.31407i) q^{10} +(0.378297 - 2.14543i) q^{11} +(4.43242 + 1.61327i) q^{13} +(4.34445 + 1.58125i) q^{14} +(-0.733956 + 4.16247i) q^{16} +(-1.46756 - 2.54189i) q^{17} +(3.11334 - 5.39246i) q^{19} +(-5.32926 - 4.47178i) q^{20} +(0.745100 + 4.22567i) q^{22} +(-0.397600 + 0.333626i) q^{23} +(-8.17752 + 2.97637i) q^{25} -9.29044 q^{26} -4.41147 q^{28} +(-3.28212 + 1.19459i) q^{29} +(-3.29813 + 2.76746i) q^{31} +(-1.36310 - 7.73055i) q^{32} +(4.42855 + 3.71599i) q^{34} +(-4.34445 + 7.52481i) q^{35} +(-1.20574 - 2.08840i) q^{37} +(-2.12965 + 12.0778i) q^{38} +(-0.826352 - 0.300767i) q^{40} +(2.34791 + 0.854570i) q^{41} +(0.184793 - 1.04801i) q^{43} +(-2.04715 - 3.54576i) q^{44} +(0.511144 - 0.885328i) q^{46} +(0.181985 + 0.152704i) q^{47} +(-0.258770 - 1.46756i) q^{49} +(13.1302 - 11.0175i) q^{50} +(8.33022 - 3.03195i) q^{52} -4.66717 q^{53} -8.06418 q^{55} +(-0.524005 + 0.190722i) q^{56} +(5.26991 - 4.42198i) q^{58} +(2.31164 + 13.1099i) q^{59} +(-2.81521 - 2.36224i) q^{61} +(4.24000 - 7.34389i) q^{62} +(3.50387 + 6.06888i) q^{64} +(3.03195 - 17.1951i) q^{65} +(-13.4363 - 4.89041i) q^{67} +(-5.18355 - 1.88666i) q^{68} +(2.97178 - 16.8538i) q^{70} +(0.601535 + 1.04189i) q^{71} +(2.34002 - 4.05304i) q^{73} +(3.63846 + 3.05303i) q^{74} +(-2.03209 - 11.5245i) q^{76} +(-3.91728 + 3.28699i) q^{77} +(12.0287 - 4.37808i) q^{79} +15.6458 q^{80} -4.92127 q^{82} +(-10.6222 + 3.86618i) q^{83} +(-8.32295 + 6.98378i) q^{85} +(0.363970 + 2.06418i) q^{86} +(-0.396459 - 0.332669i) q^{88} +(0.349643 - 0.605600i) q^{89} +(-5.53596 - 9.58856i) q^{91} +(-0.169386 + 0.960637i) q^{92} +(-0.439693 - 0.160035i) q^{94} +(-21.6591 - 7.88326i) q^{95} +(-1.23055 + 6.97881i) q^{97} +(1.46756 + 2.54189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) \) 12 * q + 6 * q^4 + 6 * q^7	\( 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 + 6 * q^7 + 12 * q^10 + 6 * q^13 - 18 * q^16 + 24 * q^19 + 6 * q^22 - 48 * q^25 - 12 * q^28 - 12 * q^31 + 54 * q^34 + 6 * q^37 - 12 * q^40 - 12 * q^43 - 6 * q^46 + 42 * q^49 + 54 * q^52 - 60 * q^55 + 6 * q^58 - 48 * q^61 - 6 * q^64 - 66 * q^67 + 6 * q^70 - 12 * q^73 - 6 * q^76 + 42 * q^79 - 24 * q^82 - 18 * q^85 - 24 * q^88 + 6 * q^94 + 60 * q^97

Introduction

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