LMFDB - Embedded newform 729.2.e.r.568.2

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			568.2
Root			$0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.r.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	1.85083	+	0.673648i	1.30874	+	0.476341i	0.899832	−	0.436236i	$-0.143689\pi$
$2$	1.85083	+	0.673648i	1.30874	+	0.476341i	0.408904	+	0.912577i	$0.365911\pi$
$3$		0			0
$3$		0			0
$4$	1.43969	+	1.20805i	0.719846	+	0.604023i
$5$	0.642788	−	3.64543i	0.287463	−	1.63029i	−0.408888	−	0.912585i	$-0.634083\pi$
$5$	0.642788	−	3.64543i	0.287463	−	1.63029i	0.696351	−	0.717701i	$-0.254806\pi$
$6$		0			0
$7$	−1.79813	+	1.50881i	−0.679631	+	0.570278i	−0.915898	−	0.401410i	$-0.868520\pi$
$7$	−1.79813	+	1.50881i	−0.679631	+	0.570278i	0.236268	+	0.971688i	$0.424076\pi$
$8$	−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	−0.987211	−	0.159420i	$-0.949038\pi$
$11$	−0.378297	−	2.14543i	−0.114061	−	0.646871i	0.873150	−	0.487452i	$-0.162073\pi$
$12$		0			0
$13$	4.43242	−	1.61327i	1.22933	−	0.447440i	0.355963	−	0.934500i	$-0.384153\pi$
$13$	4.43242	−	1.61327i	1.22933	−	0.447440i	0.873369	+	0.487060i	$0.161931\pi$
$14$	−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	$-0.717496\pi$
$17$	1.46756	−	2.54189i	0.355936	−	0.616499i	0.987278	+	0.159006i	$0.0508289\pi$
$18$		0			0
$19$	3.11334	+	5.39246i	0.714249	+	1.23712i	0.963248	+	0.268612i	$0.0865651\pi$
$19$	3.11334	+	5.39246i	0.714249	+	1.23712i	−0.248999	+	0.968504i	$0.580102\pi$
$20$	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	$-0.260545\pi$
$23$	0.397600	+	0.333626i	0.0829053	+	0.0695658i	−0.600393	+	0.799705i	$0.704989\pi$
$24$		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	$-0.283762\pi$
$29$	3.28212	+	1.19459i	0.609474	+	0.221830i	−0.0187992	+	0.999823i	$0.505984\pi$
$30$		0			0
$31$	−3.29813	−	2.76746i	−0.592362	−	0.497051i	0.296618	−	0.954996i	$-0.404141\pi$
$31$	−3.29813	−	2.76746i	−0.592362	−	0.497051i	−0.888980	+	0.457945i	$0.848586\pi$
$32$	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	−0.947952	−	0.318413i	$-0.896850\pi$
$37$	−1.20574	+	2.08840i	−0.198222	+	0.343330i	0.749730	+	0.661744i	$0.230183\pi$
$38$	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	$-0.673617\pi$
$41$	−2.34791	+	0.854570i	−0.366682	+	0.133461i	0.152106	+	0.988364i	$0.451394\pi$
$42$		0			0
$43$	0.184793	+	1.04801i	0.0281806	+	0.159820i	0.995651	−	0.0931655i	$-0.0296986\pi$
$43$	0.184793	+	1.04801i	0.0281806	+	0.159820i	−0.967470	+	0.252986i	$0.918587\pi$
$44$	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	$-0.727738\pi$
$47$	−0.181985	+	0.152704i	−0.0265453	+	0.0222741i	0.629418	+	0.777067i	$0.283293\pi$
$48$		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	$-0.396135\pi$
$53$	4.66717			0.641085			0.320543	+	0.947234i	$0.396135\pi$
$54$		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	0.341035	+	0.940051i	$0.389223\pi$
$59$	−2.31164	+	13.1099i	−0.300949	+	1.70677i	−0.641984	+	0.766718i	$0.721889\pi$
$60$		0			0
$61$	−2.81521	+	2.36224i	−0.360450	+	0.302454i	−0.804970	−	0.593315i	$-0.797819\pi$
$61$	−2.81521	+	2.36224i	−0.360450	+	0.302454i	0.444520	+	0.895769i	$0.353374\pi$
$62$	−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	−0.987301	−	0.158860i	$-0.949218\pi$
$67$	−13.4363	+	4.89041i	−1.64150	+	0.597459i	−0.654203	+	0.756319i	$0.726996\pi$
$68$	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	$-0.856077\pi$
$71$	−0.601535	+	1.04189i	−0.0713891	+	0.123649i	0.828121	+	0.560549i	$0.189410\pi$
$72$		0			0
$73$	2.34002	+	4.05304i	0.273879	+	0.474372i	0.969852	−	0.243696i	$-0.0783599\pi$
$73$	2.34002	+	4.05304i	0.273879	+	0.474372i	−0.695973	+	0.718068i	$0.745027\pi$
$74$	−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	0.913986	−	0.405745i	$-0.132988\pi$
$79$	12.0287	+	4.37808i	1.35333	+	0.492573i	0.439346	+	0.898318i	$0.355210\pi$
$80$	−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	$-0.175865\pi$
$83$	10.6222	+	3.86618i	1.16594	+	0.424369i	0.314726	+	0.949183i	$0.398087\pi$
$84$		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	$-0.178467\pi$
$89$	−0.349643	−	0.605600i	−0.0370621	−	0.0641935i	−0.883961	+	0.467560i	$0.845133\pi$
$90$		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	−0.981341	−	0.192274i	$-0.938414\pi$
$97$	−1.23055	−	6.97881i	−0.124944	−	0.708591i	0.856398	−	0.516317i	$-0.172697\pi$
$98$	−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	$-0.647468\pi$
$101$	3.58288	−	3.00640i	0.356510	−	0.299148i	0.803398	+	0.595442i	$0.203023\pi$
$102$		0			0
$103$	−2.36571	+	13.4166i	−0.233101	+	1.32198i	0.613476	+	0.789713i	$0.289771\pi$
$103$	−2.36571	+	13.4166i	−0.233101	+	1.32198i	−0.846577	+	0.532267i	$0.821340\pi$
$104$	−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	$-0.309898\pi$
$107$	11.6340			1.12470			0.562350	+	0.826900i	$0.309898\pi$
$108$		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	−0.922131	−	0.386877i	$-0.873554\pi$
$113$	0.815422	−	4.62449i	0.0767084	−	0.435035i	0.998840	−	0.0481580i	$-0.0153351\pi$
$114$		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	0.698663	−	0.715451i	$-0.253779\pi$
$127$	−3.04576	−	5.27541i	−0.270267	−	0.468117i	−0.968930	+	0.247334i	$0.920445\pi$
$128$	−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	$-0.128463\pi$
$131$	7.92734	+	6.65183i	0.692615	+	0.581173i	−0.227047	+	0.973884i	$0.572907\pi$
$132$		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	$-0.692293\pi$
$137$	−17.9337	−	6.52734i	−1.53218	−	0.557668i	−0.964154	+	0.265342i	$0.914515\pi$
$138$		0			0
$139$	−17.8516	−	14.9793i	−1.51416	−	1.27053i	−0.855138	−	0.518400i	$-0.826528\pi$
$139$	−17.8516	−	14.9793i	−1.51416	−	1.27053i	−0.659018	−	0.752128i	$-0.729028\pi$
$140$	−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	$-0.830172\pi$
$149$	−14.5708	+	5.30335i	−1.19369	+	0.434467i	−0.332671	+	0.943043i	$0.607950\pi$
$150$		0			0
$151$	−1.02481	−	5.81201i	−0.0833983	−	0.472975i	−0.997691	−	0.0679204i	$-0.978364\pi$
$151$	−1.02481	−	5.81201i	−0.0833983	−	0.472975i	0.914292	−	0.405055i	$-0.132748\pi$
$152$	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	−0.992054	−	0.125810i	$-0.959847\pi$
$157$	−0.210485	+	1.19372i	−0.0167985	+	0.0952691i	0.975256	+	0.221079i	$0.0709580\pi$
$158$	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	$-0.991764\pi$
$167$	−0.664738	+	3.76991i	−0.0514389	+	0.291725i	0.948226	+	0.317595i	$0.102875\pi$
$168$		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	−0.995398	−	0.0958248i	$-0.969451\pi$
$173$	−1.22064	−	6.92262i	−0.0928039	−	0.526317i	0.902594	−	0.430492i	$-0.141660\pi$
$174$		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	−0.461425	−	0.887179i	$-0.652662\pi$
$179$	7.19269	−	12.4581i	0.537607	−	0.931163i	0.999032	−	0.0439838i	$-0.0140050\pi$
$180$		0			0
$181$	−6.60014	−	11.4318i	−0.490584	−	0.849717i	0.509357	−	0.860555i	$-0.329883\pi$
$181$	−6.60014	−	11.4318i	−0.490584	−	0.849717i	−0.999941	+	0.0108384i	$0.996550\pi$
$182$	−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	$-0.550302\pi$
$191$	−12.6138	−	4.59105i	−0.912703	−	0.332197i	−0.755332	+	0.655343i	$0.772524\pi$
$192$		0			0
$193$	11.4945	+	9.64506i	0.827395	+	0.694267i	0.954691	−	0.297598i	$-0.0961855\pi$
$193$	11.4945	+	9.64506i	0.827395	+	0.694267i	−0.127296	+	0.991865i	$0.540630\pi$
$194$	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	0.922739	+	0.385426i	$0.125946\pi$
$197$	11.1606	+	19.3307i	0.795158	+	1.37725i	−0.127580	+	0.991828i	$0.540721\pi$
$198$		0			0
$199$	4.55051	−	7.88171i	0.322577	−	0.558720i	−0.658442	−	0.752631i	$-0.728784\pi$
$199$	4.55051	−	7.88171i	0.322577	−	0.558720i	0.981019	+	0.193912i	$0.0621176\pi$
$200$	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	0.928005	+	0.372568i	$0.121523\pi$
$211$	−1.03802	+	5.88690i	−0.0714602	+	0.405271i	−0.999465	+	0.0327028i	$0.989589\pi$
$212$	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	−0.841893	−	0.539645i	$-0.818558\pi$
$223$	−6.81908	+	5.72189i	−0.456639	+	0.383166i	0.385253	+	0.922811i	$0.374114\pi$
$224$	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	−0.982499	−	0.186266i	$-0.940361\pi$
$227$	−1.85256	−	10.5064i	−0.122959	−	0.697334i	0.859540	−	0.511068i	$-0.170750\pi$
$228$		0			0
$229$	7.77244	−	2.82894i	0.513617	−	0.186941i	−0.0721913	−	0.997391i	$-0.522999\pi$
$229$	7.77244	−	2.82894i	0.513617	−	0.186941i	0.585809	+	0.810449i	$0.300777\pi$
$230$	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	$-0.970353\pi$
$233$	−6.36965	+	11.0326i	−0.417290	+	0.722767i	0.578376	+	0.815770i	$0.303687\pi$
$234$		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	$-0.116365\pi$
$239$	11.5026	+	9.65183i	0.744041	+	0.624325i	−0.189878	+	0.981808i	$0.560809\pi$
$240$		0			0
$241$	−0.747626	−	0.272114i	−0.0481588	−	0.0175284i	0.317828	−	0.948148i	$-0.397046\pi$
$241$	−0.747626	−	0.272114i	−0.0481588	−	0.0175284i	−0.365987	+	0.930620i	$0.619269\pi$
$242$	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	$-0.251187\pi$
$251$	−4.15749	−	7.20099i	−0.262419	−	0.454522i	−0.966884	+	0.255216i	$0.917853\pi$
$252$		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	$-0.316435\pi$
$257$	24.0752	−	8.76264i	1.50177	−	0.546599i	0.956517	+	0.291675i	$0.0942126\pi$
$258$		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	0.340622	−	0.940200i	$-0.389362\pi$
$263$	21.4990	−	18.0398i	1.32569	−	1.11238i	0.985065	−	0.172183i	$-0.0550821\pi$
$264$		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	$-0.871631\pi$
$269$	−30.1710			−1.83956			−0.919778	+	0.392439i	$0.871631\pi$
$270$		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	−0.0107242	−	0.999942i	$-0.503414\pi$
$277$	16.1800	−	13.5767i	0.972165	−	0.815743i	0.982889	+	0.184199i	$0.0589692\pi$
$278$	−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	$-0.0721526\pi$
$281$	−0.303415	−	1.72075i	−0.0181002	−	0.102651i	−0.992519	+	0.122086i	$0.961041\pi$
$282$		0			0
$283$	6.84864	−	2.49270i	0.407109	−	0.148176i	−0.130345	−	0.991469i	$-0.541608\pi$
$283$	6.84864	−	2.49270i	0.407109	−	0.148176i	0.537454	+	0.843293i	$0.319386\pi$
$284$	−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	$-0.425785\pi$
$293$	−11.7595	−	9.86736i	−0.686995	−	0.576458i	−0.918041	+	0.396485i	$0.870230\pi$
$294$		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	−0.999693	−	0.0247861i	$-0.992110\pi$
$307$	−8.38191	+	14.5179i	−0.478381	+	0.828580i	0.521312	+	0.853366i	$0.325443\pi$
$308$	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	$-0.761220\pi$
$311$	−15.0568	+	5.48024i	−0.853794	+	0.310756i	−0.122208	+	0.992505i	$0.538998\pi$
$312$		0			0
$313$	5.97447	+	33.8829i	0.337697	+	1.91517i	0.398789	+	0.917043i	$0.369431\pi$
$313$	5.97447	+	33.8829i	0.337697	+	1.91517i	−0.0610920	+	0.998132i	$0.519458\pi$
$314$	−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	$-0.570766\pi$
$317$	12.4950	−	10.4846i	0.701791	−	0.588872i	0.922283	+	0.386516i	$0.126322\pi$
$318$		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	−0.345545	+	0.938402i	$0.612306\pi$
$331$	−24.1917	+	20.2992i	−1.32969	+	1.11575i	−0.984149	+	0.177343i	$0.943250\pi$
$332$	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	−0.491109	−	0.871098i	$-0.663408\pi$
$337$	−5.64290	+	2.05385i	−0.307389	+	0.111880i	0.183720	+	0.982979i	$0.441186\pi$
$338$	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	$-0.489903\pi$
$347$	−17.6423	−	14.8037i	−0.947089	−	0.794702i	−0.978805	+	0.204795i	$0.934347\pi$
$348$		0			0
$349$	10.8687	+	3.95589i	0.581789	+	0.211754i	0.616114	−	0.787657i	$-0.288706\pi$
$349$	10.8687	+	3.95589i	0.581789	+	0.211754i	−0.0343254	+	0.999411i	$0.510928\pi$
$350$	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	$-0.406981\pi$
$353$	−2.00589	−	0.730085i	−0.106763	−	0.0388585i	−0.394849	+	0.918746i	$0.629203\pi$
$354$		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	0.985601	+	0.169087i	$0.0540818\pi$
$359$	12.1118	+	20.9782i	0.639234	+	1.10719i	−0.346367	+	0.938099i	$0.612585\pi$
$360$		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	0.969261	−	0.246036i	$-0.0791282\pi$
$367$	−0.492259	−	2.79174i	−0.0256957	−	0.145728i	−0.994956	+	0.100308i	$0.968017\pi$
$368$	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	0.525689	+	0.850677i	$0.323807\pi$
$373$	−5.00686	+	28.3953i	−0.259246	+	1.47025i	−0.784935	+	0.619578i	$0.787304\pi$
$374$	−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	$-0.949912\pi$
$383$	−0.116735	+	0.662037i	−0.00596488	+	0.0338285i	0.981680	+	0.190537i	$0.0610229\pi$
$384$		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	$-0.0211181\pi$
$389$	0.739620	+	4.19459i	0.0375002	+	0.212674i	−0.960300	+	0.278970i	$0.910007\pi$
$390$		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	0.955553	−	0.294818i	$-0.0952591\pi$
$397$	4.43242	+	7.67717i	0.222457	+	0.385306i	−0.733097	+	0.680124i	$0.761926\pi$
$398$	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	−0.952072	−	0.305874i	$-0.901051\pi$
$401$	−28.4079	−	23.8371i	−1.41862	−	1.19037i	−0.466552	−	0.884494i	$-0.654504\pi$
$402$		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	0.576339	−	0.817211i	$-0.304481\pi$
$409$	−2.59627	−	2.17853i	−0.128377	−	0.107721i	−0.704716	+	0.709490i	$0.748925\pi$
$410$	−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	$-0.779458\pi$
$419$	−19.4106	+	7.06489i	−0.948272	+	0.345143i	−0.178845	+	0.983877i	$0.557236\pi$
$420$		0			0
$421$	4.78106	+	27.1147i	0.233015	+	1.32149i	0.846755	+	0.531983i	$0.178553\pi$
$421$	4.78106	+	27.1147i	0.233015	+	1.32149i	−0.613740	+	0.789508i	$0.710336\pi$
$422$	−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	$-0.480200\pi$
$431$	2.58110			0.124327			0.0621636	+	0.998066i	$0.480200\pi$
$432$		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	−0.403112	−	0.915151i	$-0.632072\pi$
$439$	8.97044	−	7.52709i	0.428136	−	0.359248i	0.831248	+	0.555902i	$0.187627\pi$
$440$	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	$-0.0712961\pi$
$443$	−0.361323	−	2.04916i	−0.0171670	−	0.0973587i	−0.992187	+	0.124757i	$0.960185\pi$
$444$		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	$-0.753244\pi$
$449$	5.27541	−	9.13728i	0.248962	−	0.431215i	0.963238	+	0.268649i	$0.0865772\pi$
$450$		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	0.509954	−	0.860202i	$-0.329663\pi$
$457$	7.43242	+	2.70518i	0.347674	+	0.126543i	−0.162280	+	0.986745i	$0.551885\pi$
$458$	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	$-0.753089\pi$
$461$	−36.7352	−	13.3705i	−1.71093	−	0.622727i	−0.996994	+	0.0774846i	$0.975311\pi$
$462$		0			0
$463$	18.1498	+	15.2295i	0.843491	+	0.707773i	0.958346	−	0.285609i	$-0.0921959\pi$
$463$	18.1498	+	15.2295i	0.843491	+	0.707773i	−0.114855	+	0.993382i	$0.536640\pi$
$464$	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	−0.917490	−	0.397758i	$-0.869788\pi$
$467$	−17.3576	−	30.0642i	−0.803214	−	1.39121i	0.114277	−	0.993449i	$-0.463545\pi$
$468$		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	$-0.674913\pi$
$479$	4.96529	−	4.16637i	0.226870	−	0.190366i	0.749136	+	0.662416i	$0.230469\pi$
$480$		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	−0.691068	−	0.722789i	$-0.742860\pi$
$491$	4.55428	−	25.8286i	0.205532	−	1.16563i	0.896600	−	0.442840i	$-0.146029\pi$
$492$		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	−0.471456	−	0.881890i	$-0.656271\pi$
$499$	−5.93629	+	2.16063i	−0.265745	+	0.0967232i	0.205711	+	0.978613i	$0.434049\pi$
$500$	−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	$-0.995093\pi$
$503$	−10.9131	+	18.9020i	−0.486589	+	0.842798i	0.513292	+	0.858214i	$0.328426\pi$
$504$		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	$-0.500822\pi$
$509$	−22.2866	−	18.7007i	−0.987837	−	0.828893i	−0.985253	+	0.171103i	$0.945267\pi$
$510$		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	$-0.263650\pi$
$521$	−6.84743	−	11.8601i	−0.299991	−	0.519600i	−0.976134	+	0.217171i	$0.930317\pi$
$522$		0			0
$523$	−6.57532	+	11.3888i	−0.287519	+	0.497997i	−0.973217	−	0.229889i	$-0.926164\pi$
$523$	−6.57532	+	11.3888i	−0.287519	+	0.497997i	0.685698	+	0.727886i	$0.259497\pi$
$524$	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	−0.990582	−	0.136921i	$-0.956279\pi$
$547$	−24.0371	+	20.1696i	−1.02775	+	0.862388i	−0.0371720	+	0.999309i	$0.511835\pi$
$548$	−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	−0.121324	+	0.992613i	$0.538714\pi$
$557$	−21.7196	+	37.6195i	−0.920290	+	1.59399i	−0.798966	+	0.601376i	$0.794619\pi$
$558$		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	$-0.0420546\pi$
$563$	24.5269	+	20.5805i	1.03369	+	0.867366i	0.0424018	+	0.999101i	$0.486499\pi$
$564$		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	$-0.434225\pi$
$569$	−6.36355	−	2.31614i	−0.266774	−	0.0970977i	−0.471944	+	0.881629i	$0.656447\pi$
$570$		0			0
$571$	−16.2041	−	13.5969i	−0.678122	−	0.569012i	0.237335	−	0.971428i	$-0.423726\pi$
$571$	−16.2041	−	13.5969i	−0.678122	−	0.569012i	−0.915457	+	0.402416i	$0.868171\pi$
$572$	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	−0.962982	−	0.269567i	$-0.913120\pi$
$577$	−5.95811	+	10.3198i	−0.248039	+	0.429617i	0.714942	+	0.699183i	$0.246453\pi$
$578$	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	$-0.721369\pi$
$587$	0.0994798	−	0.0834734i	0.00410597	−	0.00344532i	0.644838	+	0.764319i	$0.276925\pi$
$588$		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	$-0.681285\pi$
$593$	−26.2622			−1.07846			−0.539230	+	0.842158i	$0.681285\pi$
$594$		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	0.715500	+	0.698613i	$0.246199\pi$
$599$	−4.79185	+	27.1759i	−0.195790	+	1.11038i	−0.911290	+	0.411766i	$0.864912\pi$
$600$		0			0
$601$	1.02094	−	0.856674i	0.0416452	−	0.0349445i	−0.621728	−	0.783234i	$-0.713569\pi$
$601$	1.02094	−	0.856674i	0.0416452	−	0.0349445i	0.663373	+	0.748289i	$0.269124\pi$
$602$	−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	−0.0911037	−	0.995841i	$-0.529039\pi$
$607$	11.8068	−	4.29731i	0.479221	−	0.174422i	0.570325	+	0.821419i	$0.306817\pi$
$608$	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	0.972047	−	0.234787i	$-0.0754393\pi$
$613$	6.99912	+	12.1228i	0.282692	+	0.489637i	−0.689355	+	0.724424i	$0.742106\pi$
$614$	−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	$-0.438610\pi$
$617$	−18.4209	−	15.4569i	−0.741596	−	0.622273i	−0.933266	+	0.359187i	$0.883054\pi$
$618$		0			0
$619$	−6.45723	−	2.35024i	−0.259538	−	0.0944642i	0.208974	−	0.977921i	$-0.432988\pi$
$619$	−6.45723	−	2.35024i	−0.259538	−	0.0944642i	−0.468512	+	0.883457i	$0.655210\pi$
$620$	−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	−0.262814	−	0.964847i	$-0.584651\pi$
$631$	17.6887	−	30.6377i	0.704175	−	1.21967i	0.966989	−	0.254820i	$-0.0820161\pi$
$632$	−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	$-0.598608\pi$
$641$	14.6879	−	12.3246i	0.580136	−	0.486792i	0.884992	+	0.465606i	$0.154164\pi$
$642$		0			0
$643$	3.36468	−	19.0820i	0.132690	−	0.752521i	−0.843751	−	0.536735i	$-0.819657\pi$
$643$	3.36468	−	19.0820i	0.132690	−	0.752521i	0.976441	−	0.215786i	$-0.0692315\pi$
$644$	−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	$-0.555159\pi$
$647$	−8.77141			−0.344840			−0.172420	+	0.985024i	$0.555159\pi$
$648$		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	0.643609	+	0.765354i	$0.277436\pi$
$653$	−5.69729	+	32.3109i	−0.222952	+	1.26442i	−0.866562	+	0.499070i	$0.833675\pi$
$654$		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	−0.980608	−	0.195978i	$-0.937212\pi$
$659$	−3.23882	−	18.3682i	−0.126166	−	0.715525i	0.854442	−	0.519547i	$-0.173899\pi$
$660$		0			0
$661$	−34.2117	+	12.4520i	−1.33068	+	0.484329i	−0.906866	−	0.421420i	$-0.861532\pi$
$661$	−34.2117	+	12.4520i	−1.33068	+	0.484329i	−0.423816	+	0.905748i	$0.639310\pi$
$662$	−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	−0.490793	−	0.871276i	$-0.663293\pi$
$673$	−37.0146	−	13.4722i	−1.42681	−	0.519316i	−0.936015	+	0.351960i	$0.885515\pi$
$674$	−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	$-0.180583\pi$
$677$	29.7651	+	10.8336i	1.14397	+	0.416370i	0.300623	+	0.953743i	$0.402806\pi$
$678$		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	−0.997818	−	0.0660187i	$-0.978970\pi$
$683$	−14.5328	−	25.1716i	−0.556083	−	0.963164i	0.441735	−	0.897145i	$-0.354363\pi$
$684$		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	0.997376	−	0.0723898i	$-0.0230626\pi$
$691$	0.930303	+	5.27601i	0.0353904	+	0.200709i	−0.961986	+	0.273099i	$0.911951\pi$
$692$	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	$-0.339016\pi$
$701$	25.6536			0.968922			0.484461	+	0.874813i	$0.339016\pi$
$702$		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	−0.707761	−	0.706452i	$-0.750294\pi$
$709$	−3.59311	+	3.01498i	−0.134942	+	0.113230i	0.572818	+	0.819682i	$0.305850\pi$
$710$	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	−0.229052	−	0.973414i	$-0.573562\pi$
$719$	19.5335	−	33.8330i	0.728476	−	1.26176i	0.957527	−	0.288343i	$-0.0931042\pi$
$720$		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	0.523696	−	0.851905i	$-0.324553\pi$
$727$	10.1725	+	3.70247i	0.377276	+	0.137317i	−0.146420	+	0.989223i	$0.546775\pi$
$728$	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	0.593234	−	0.805030i	$-0.297851\pi$
$733$	−2.61406	−	2.19345i	−0.0965524	−	0.0810171i	−0.689786	+	0.724013i	$0.742295\pi$
$734$	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	−0.999826	−	0.0186653i	$-0.994058\pi$
$739$	−13.1505	+	22.7773i	−0.483748	+	0.837877i	0.516077	+	0.856542i	$0.327392\pi$
$740$	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	$-0.432956\pi$
$743$	27.1984	−	9.89940i	0.997811	−	0.363174i	0.788740	+	0.614727i	$0.210734\pi$
$744$		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	0.859106	+	0.511797i	$0.171020\pi$
$751$	−3.37716	+	19.1528i	−0.123234	+	0.698897i	−0.982341	+	0.187100i	$0.940091\pi$
$752$	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	0.934882	+	0.354959i	$0.115505\pi$
$761$	−1.79373	+	10.1728i	−0.0650228	+	0.368763i	−0.999905	+	0.0138038i	$0.995606\pi$
$762$		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	−0.961173	−	0.275947i	$-0.911009\pi$
$769$	−42.1536	+	15.3427i	−1.52010	+	0.553271i	−0.558926	+	0.829217i	$0.688786\pi$
$770$	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	−0.164247	−	0.986419i	$-0.552519\pi$
$773$	21.4677	−	37.1832i	0.772141	−	1.33739i	0.936388	−	0.350968i	$-0.114147\pi$
$774$		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	0.649283	−	0.760547i	$-0.275069\pi$
$787$	0.365715	+	0.306871i	0.0130363	+	0.0109388i	−0.636246	+	0.771486i	$0.719514\pi$
$788$	−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	$-0.546001\pi$
$797$	10.7773	−	3.92262i	0.381752	−	0.138946i	0.525766	+	0.850629i	$0.323779\pi$
$798$		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	$-0.770988\pi$
$809$	−42.7873			−1.50432			−0.752161	+	0.658979i	$0.770988\pi$
$810$		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	−0.948908	−	0.315553i	$-0.897810\pi$
$821$	−4.73210	−	26.8371i	−0.165152	−	0.936621i	0.783757	−	0.621068i	$-0.213301\pi$
$822$		0			0
$823$	13.5697	−	4.93897i	0.473010	−	0.172162i	−0.0945054	−	0.995524i	$-0.530127\pi$
$823$	13.5697	−	4.93897i	0.473010	−	0.172162i	0.567515	+	0.823363i	$0.307905\pi$
$824$	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	$-0.794343\pi$
$827$	3.51379	−	6.08606i	0.122186	−	0.211633i	0.920630	+	0.390437i	$0.127676\pi$
$828$		0			0
$829$	21.0403	+	36.4429i	0.730760	+	1.26571i	0.956559	+	0.291539i	$0.0941673\pi$
$829$	21.0403	+	36.4429i	0.730760	+	1.26571i	−0.225799	+	0.974174i	$0.572499\pi$
$830$	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	$-0.630891\pi$
$839$	−37.5137	−	13.6539i	−1.29512	−	0.471384i	−0.895404	+	0.445255i	$0.853113\pi$
$840$		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	−0.971539	−	0.236880i	$-0.923875\pi$
$853$	−4.07744	−	23.1243i	−0.139609	−	0.791761i	0.831930	−	0.554881i	$-0.187236\pi$
$854$	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	$-0.678402\pi$
$857$	6.15495	−	5.16462i	0.210249	−	0.176420i	0.741831	+	0.670587i	$0.233958\pi$
$858$		0			0
$859$	−4.21894	+	23.9268i	−0.143948	+	0.816372i	0.824257	+	0.566216i	$0.191593\pi$
$859$	−4.21894	+	23.9268i	−0.143948	+	0.816372i	−0.968205	+	0.250156i	$0.919518\pi$
$860$	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	$-0.555997\pi$
$863$	−10.2828			−0.350029			−0.175015	+	0.984566i	$0.555997\pi$
$864$		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	0.109458	−	0.993991i	$-0.465089\pi$
$877$	24.6459	−	8.97037i	0.832233	−	0.302908i	0.722775	+	0.691083i	$0.242866\pi$
$878$	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	−0.319492	−	0.947589i	$-0.603512\pi$
$881$	19.6163	−	33.9764i	0.660890	−	1.14469i	0.980382	−	0.197106i	$-0.0631543\pi$
$882$		0			0
$883$	−3.89915	−	6.75352i	−0.131217	−	0.227274i	0.792929	−	0.609314i	$-0.208555\pi$
$883$	−3.89915	−	6.75352i	−0.131217	−	0.227274i	−0.924146	+	0.382040i	$0.875222\pi$
$884$	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	$-0.403139\pi$
$887$	−17.5095	−	14.6922i	−0.587912	−	0.493317i	−0.887535	+	0.460741i	$0.847584\pi$
$888$		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	−0.875212	−	0.483740i	$-0.839278\pi$
$907$	−6.57233	−	37.2735i	−0.218231	−	1.23765i	0.656981	−	0.753907i	$-0.271833\pi$
$908$	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	−0.355427	+	0.934704i	$0.615664\pi$
$911$	−40.3740	+	33.8778i	−1.33765	+	1.12242i	−0.982223	+	0.187717i	$0.939891\pi$
$912$		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	−0.992276	−	0.124049i	$-0.960412\pi$
$929$	−3.11711	−	17.6780i	−0.102269	−	0.579996i	0.890007	−	0.455947i	$-0.150699\pi$
$930$		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	0.999884	−	0.0152572i	$-0.00485672\pi$
$937$	14.8990	+	25.8058i	0.486729	+	0.843039i	−0.513155	+	0.858296i	$0.671523\pi$
$938$	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	$-0.115078\pi$
$941$	22.9900	+	19.2909i	0.749451	+	0.628864i	−0.185907	+	0.982567i	$0.559522\pi$
$942$		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	$-0.123278\pi$
$947$	42.8512	+	15.5966i	1.39248	+	0.506820i	0.466541	+	0.884499i	$0.345500\pi$
$948$		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	$-0.235227\pi$
$953$	−6.59786	−	11.4278i	−0.213726	−	0.370184i	−0.952878	+	0.303355i	$0.901893\pi$
$954$		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	0.875388	+	0.483421i	$0.160606\pi$
$967$	−3.49984	+	19.8486i	−0.112547	+	0.638287i	−0.987935	+	0.154866i	$0.950505\pi$
$968$	−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	$-0.359726\pi$
$971$	26.5839			0.853118			0.426559	+	0.904460i	$0.359726\pi$
$972$		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	0.918298	+	0.395889i	$0.129564\pi$
$977$	−2.50124	+	14.1853i	−0.0800219	+	0.453827i	−0.998320	+	0.0579375i	$0.981548\pi$
$978$		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	0.836007	+	0.548719i	$0.184884\pi$
$983$	7.46481	+	42.3350i	0.238090	+	1.35028i	−0.597916	+	0.801558i	$0.704005\pi$
$984$		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	0.962817	−	0.270155i	$-0.0870750\pi$
$991$	7.78968	+	13.4921i	0.247447	+	0.428591i	−0.715370	+	0.698746i	$0.753742\pi$
$992$	−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	−0.342528	−	0.939508i	$-0.611283\pi$
$997$	−38.1690	−	13.8924i	−1.20882	−	0.439976i	−0.866295	+	0.499532i	$0.833505\pi$
$998$	−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.568.2		12
3.2	odd	2	inner	729.2.e.r.568.1		12
9.2	odd	6		729.2.e.m.82.2		12
9.4	even	3		729.2.e.q.325.1		12
9.5	odd	6		729.2.e.q.325.2		12
9.7	even	3		729.2.e.m.82.1		12
27.2	odd	18		729.2.e.q.406.2		12
27.4	even	9		729.2.c.c.244.6		12
27.5	odd	18		729.2.c.c.487.1		12
27.7	even	9	inner	729.2.e.r.163.2		12
27.11	odd	18		729.2.e.m.649.2		12
27.13	even	9		729.2.a.c.1.1	✓	6
27.14	odd	18		729.2.a.c.1.6	yes	6
27.16	even	9		729.2.e.m.649.1		12
27.20	odd	18	inner	729.2.e.r.163.1		12
27.22	even	9		729.2.c.c.487.6		12
27.23	odd	18		729.2.c.c.244.1		12
27.25	even	9		729.2.e.q.406.1		12

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

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)

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

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