LMFDB - Embedded newform 810.2.p.a.199.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(19,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16, 9]))

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

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

chi := DirichletCharacter("810.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.p (of order $18$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.10
Character	$\chi$	$=$	810.199
Dual form			810.2.p.a.289.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(-1.90411 + 1.17233i) q^{5} +(0.531122 - 0.0936511i) q^{7} +(-0.866025 + 0.500000i) q^{8} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(-1.90411 + 1.17233i) q^{5} +(0.531122 - 0.0936511i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.12200 - 0.705079i) q^{10} +(-3.82525 - 1.39228i) q^{11} +(-1.58330 + 1.88690i) q^{13} +(0.413139 + 0.346665i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-3.71596 - 2.14541i) q^{17} +(1.08914 + 1.88645i) q^{19} +(-0.823871 - 2.07876i) q^{20} +(-1.39228 - 3.82525i) q^{22} +(-4.39867 - 0.775604i) q^{23} +(2.25130 - 4.46449i) q^{25} -2.46317 q^{26} +0.539315i q^{28} +(0.558330 - 0.468495i) q^{29} +(-1.28782 + 7.30358i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-0.745092 - 4.22563i) q^{34} +(-0.901527 + 0.800971i) q^{35} +(-6.45946 - 3.72937i) q^{37} +(-0.745018 + 2.04692i) q^{38} +(1.06285 - 1.96732i) q^{40} +(5.82235 + 4.88553i) q^{41} +(2.73291 - 7.50862i) q^{43} +(2.03537 - 3.52537i) q^{44} +(-2.23326 - 3.86812i) q^{46} +(-9.13513 + 1.61077i) q^{47} +(-6.30453 + 2.29466i) q^{49} +(4.86710 - 1.14512i) q^{50} +(-1.58330 - 1.88690i) q^{52} -0.116236i q^{53} +(8.91592 - 1.83339i) q^{55} +(-0.413139 + 0.346665i) q^{56} +(0.717776 + 0.126563i) q^{58} +(10.2609 - 3.73464i) q^{59} +(-1.35199 - 7.66749i) q^{61} +(-6.42266 + 3.70813i) q^{62} +(0.500000 - 0.866025i) q^{64} +(0.802714 - 5.44902i) q^{65} +(-6.14767 + 7.32650i) q^{67} +(2.75808 - 3.28696i) q^{68} +(-1.19307 - 0.175755i) q^{70} +(-6.98968 + 12.1065i) q^{71} +(-2.27739 + 1.31485i) q^{73} +(-1.29520 - 7.34543i) q^{74} +(-2.04692 + 0.745018i) q^{76} +(-2.16206 - 0.381230i) q^{77} +(-4.10029 + 3.44055i) q^{79} +(2.19024 - 0.450382i) q^{80} +7.60054i q^{82} +(9.14477 + 10.8983i) q^{83} +(9.59072 - 0.271214i) q^{85} +(7.50862 - 2.73291i) q^{86} +(4.00891 - 0.706878i) q^{88} +(4.79299 + 8.30170i) q^{89} +(-0.664214 + 1.15045i) q^{91} +(1.52764 - 4.19716i) q^{92} +(-7.10587 - 5.96254i) q^{94} +(-4.28539 - 2.31519i) q^{95} +(-0.646954 + 1.77749i) q^{97} +(-5.81028 - 3.35457i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{5}+O(q^{10}) $ 108 * q - 6 * q^5	$ 108 q - 6 q^{5} + 12 q^{11} - 6 q^{14} - 12 q^{20} - 18 q^{25} + 72 q^{26} - 6 q^{29} + 36 q^{31} - 18 q^{35} + 12 q^{41} + 12 q^{44} + 18 q^{49} + 12 q^{50} + 6 q^{56} + 84 q^{59} - 18 q^{61} + 54 q^{64} + 6 q^{65} + 48 q^{74} - 72 q^{79} + 36 q^{86} + 132 q^{89} - 36 q^{94} + 18 q^{95}+O(q^{100}) $ 108 * q - 6 * q^5 + 12 * q^11 - 6 * q^14 - 12 * q^20 - 18 * q^25 + 72 * q^26 - 6 * q^29 + 36 * q^31 - 18 * q^35 + 12 * q^41 + 12 * q^44 + 18 * q^49 + 12 * q^50 + 6 * q^56 + 84 * q^59 - 18 * q^61 + 54 * q^64 + 6 * q^65 + 48 * q^74 - 72 * q^79 + 36 * q^86 + 132 * q^89 - 36 * q^94 + 18 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$3$		0			0
$3$		0			0
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	−1.90411	+	1.17233i	−0.851546	+	0.524281i
$5$	−1.90411	+	1.17233i	−0.851546	+	0.524281i
$6$		0			0
$7$	0.531122	−	0.0936511i	0.200745	−	0.0353968i	−0.0723713	−	0.997378i	$-0.523057\pi$
$7$	0.531122	−	0.0936511i	0.200745	−	0.0353968i	0.273116	+	0.961981i	$0.411946\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$		0			0
$10$	−2.12200	−	0.705079i	−0.671034	−	0.222965i
$11$	−3.82525	−	1.39228i	−1.15336	−	0.419788i	−0.306637	−	0.951826i	$-0.599204\pi$
$11$	−3.82525	−	1.39228i	−1.15336	−	0.419788i	−0.846720	+	0.532039i	$0.821426\pi$
$12$		0			0
$13$	−1.58330	+	1.88690i	−0.439128	+	0.523332i	−0.939533	−	0.342459i	$-0.888740\pi$
$13$	−1.58330	+	1.88690i	−0.439128	+	0.523332i	0.500405	+	0.865792i	$0.333185\pi$
$14$	0.413139	+	0.346665i	0.110416	+	0.0926502i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−3.71596	−	2.14541i	−0.901252	−	0.520338i	−0.0236455	−	0.999720i	$-0.507527\pi$
$17$	−3.71596	−	2.14541i	−0.901252	−	0.520338i	−0.877606	+	0.479383i	$0.840861\pi$
$18$		0			0
$19$	1.08914	+	1.88645i	0.249867	+	0.432782i	0.963489	−	0.267749i	$-0.0862799\pi$
$19$	1.08914	+	1.88645i	0.249867	+	0.432782i	−0.713622	+	0.700531i	$0.752947\pi$
$20$	−0.823871	−	2.07876i	−0.184223	−	0.464825i
$21$		0			0
$22$	−1.39228	−	3.82525i	−0.296835	−	0.815547i
$23$	−4.39867	−	0.775604i	−0.917185	−	0.161725i	−0.304921	−	0.952378i	$-0.598630\pi$
$23$	−4.39867	−	0.775604i	−0.917185	−	0.161725i	−0.612264	+	0.790653i	$0.709741\pi$
$24$		0			0
$25$	2.25130	−	4.46449i	0.450260	−	0.892898i
$26$	−2.46317			−0.483068
$27$		0			0
$28$			0.539315i			0.101921i
$29$	0.558330	−	0.468495i	0.103679	−	0.0869973i	−0.589474	−	0.807787i	$-0.700665\pi$
$29$	0.558330	−	0.468495i	0.103679	−	0.0869973i	0.693154	+	0.720790i	$0.256221\pi$
$30$		0			0
$31$	−1.28782	+	7.30358i	−0.231299	+	1.31176i	0.618970	+	0.785414i	$0.287550\pi$
$31$	−1.28782	+	7.30358i	−0.231299	+	1.31176i	−0.850269	+	0.526348i	$0.823561\pi$
$32$	−0.342020	−	0.939693i	−0.0604612	−	0.166116i
$33$		0			0
$34$	−0.745092	−	4.22563i	−0.127782	−	0.724689i
$35$	−0.901527	+	0.800971i	−0.152386	+	0.135389i
$36$		0			0
$37$	−6.45946	−	3.72937i	−1.06193	−	0.613105i	−0.135964	−	0.990714i	$-0.543413\pi$
$37$	−6.45946	−	3.72937i	−1.06193	−	0.613105i	−0.925965	+	0.377609i	$0.876746\pi$
$38$	−0.745018	+	2.04692i	−0.120858	+	0.332054i
$39$		0			0
$40$	1.06285	−	1.96732i	0.168051	−	0.311061i
$41$	5.82235	+	4.88553i	0.909298	+	0.762992i	0.971985	−	0.235042i	$-0.0755226\pi$
$41$	5.82235	+	4.88553i	0.909298	+	0.762992i	−0.0626873	+	0.998033i	$0.519967\pi$
$42$		0			0
$43$	2.73291	−	7.50862i	0.416765	−	1.14505i	−0.536759	−	0.843736i	$-0.680351\pi$
$43$	2.73291	−	7.50862i	0.416765	−	1.14505i	0.953524	−	0.301317i	$-0.0974264\pi$
$44$	2.03537	−	3.52537i	0.306844	−	0.531470i
$45$		0			0
$46$	−2.23326	−	3.86812i	−0.329276	−	0.570324i
$47$	−9.13513	+	1.61077i	−1.33250	+	0.234955i	−0.794126	−	0.607753i	$-0.792071\pi$
$47$	−9.13513	+	1.61077i	−1.33250	+	0.234955i	−0.538370	+	0.842708i	$0.680960\pi$
$48$		0			0
$49$	−6.30453	+	2.29466i	−0.900647	+	0.327809i
$50$	4.86710	−	1.14512i	0.688312	−	0.161945i
$51$		0			0
$52$	−1.58330	−	1.88690i	−0.219564	−	0.261666i
$53$		−	0.116236i		−	0.0159662i	−0.999968	−	0.00798309i	$-0.997459\pi$
$53$		−	0.116236i		−	0.0159662i	0.999968	−	0.00798309i	$-0.00254112\pi$
$54$		0			0
$55$	8.91592	−	1.83339i	1.20222	−	0.247214i
$56$	−0.413139	+	0.346665i	−0.0552081	+	0.0463251i
$57$		0			0
$58$	0.717776	+	0.126563i	0.0942486	+	0.0166186i
$59$	10.2609	−	3.73464i	1.33585	−	0.486209i	0.427346	−	0.904088i	$-0.359449\pi$
$59$	10.2609	−	3.73464i	1.33585	−	0.486209i	0.908503	+	0.417879i	$0.137226\pi$
$60$		0			0
$61$	−1.35199	−	7.66749i	−0.173104	−	0.981721i	−0.940310	−	0.340320i	$-0.889465\pi$
$61$	−1.35199	−	7.66749i	−0.173104	−	0.981721i	0.767206	−	0.641401i	$-0.221647\pi$
$62$	−6.42266	+	3.70813i	−0.815679	+	0.470932i
$63$		0			0
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	0.802714	−	5.44902i	0.0995645	−	0.675867i
$66$		0			0
$67$	−6.14767	+	7.32650i	−0.751057	+	0.895075i	−0.997247	−	0.0741468i	$-0.976377\pi$
$67$	−6.14767	+	7.32650i	−0.751057	+	0.895075i	0.246190	+	0.969221i	$0.420821\pi$
$68$	2.75808	−	3.28696i	0.334467	−	0.398602i
$69$		0			0
$70$	−1.19307	−	0.175755i	−0.142599	−	0.0210068i
$71$	−6.98968	+	12.1065i	−0.829522	+	1.43677i	0.0688910	+	0.997624i	$0.478054\pi$
$71$	−6.98968	+	12.1065i	−0.829522	+	1.43677i	−0.898413	+	0.439151i	$0.855279\pi$
$72$		0			0
$73$	−2.27739	+	1.31485i	−0.266548	+	0.153892i	−0.627318	−	0.778763i	$-0.715847\pi$
$73$	−2.27739	+	1.31485i	−0.266548	+	0.153892i	0.360770	+	0.932655i	$0.382514\pi$
$74$	−1.29520	−	7.34543i	−0.150564	−	0.853889i
$75$		0			0
$76$	−2.04692	+	0.745018i	−0.234798	+	0.0854594i
$77$	−2.16206	−	0.381230i	−0.246390	−	0.0434452i
$78$		0			0
$79$	−4.10029	+	3.44055i	−0.461318	+	0.387092i	−0.843616	−	0.536947i	$-0.819577\pi$
$79$	−4.10029	+	3.44055i	−0.461318	+	0.387092i	0.382297	+	0.924039i	$0.375133\pi$
$80$	2.19024	−	0.450382i	0.244876	−	0.0503542i
$81$		0			0
$82$			7.60054i			0.839339i
$83$	9.14477	+	10.8983i	1.00377	+	1.19624i	0.980501	+	0.196515i	$0.0629626\pi$
$83$	9.14477	+	10.8983i	1.00377	+	1.19624i	0.0232678	+	0.999729i	$0.492593\pi$
$84$		0			0
$85$	9.59072	−	0.271214i	1.04026	−	0.0294173i
$86$	7.50862	−	2.73291i	0.809675	−	0.294698i
$87$		0			0
$88$	4.00891	−	0.706878i	0.427351	−	0.0753535i
$89$	4.79299	+	8.30170i	0.508056	+	0.879979i	0.999956	+	0.00932743i	$0.00296906\pi$
$89$	4.79299	+	8.30170i	0.508056	+	0.879979i	−0.491900	+	0.870651i	$0.663698\pi$
$90$		0			0
$91$	−0.664214	+	1.15045i	−0.0696285	+	0.120600i
$92$	1.52764	−	4.19716i	0.159268	−	0.437584i
$93$		0			0
$94$	−7.10587	−	5.96254i	−0.732915	−	0.614989i
$95$	−4.28539	−	2.31519i	−0.439672	−	0.237533i
$96$		0			0
$97$	−0.646954	+	1.77749i	−0.0656882	+	0.180477i	−0.968194	−	0.250201i	$-0.919503\pi$
$97$	−0.646954	+	1.77749i	−0.0656882	+	0.180477i	0.902506	+	0.430678i	$0.141726\pi$
$98$	−5.81028	−	3.35457i	−0.586927	−	0.338863i
$99$		0			0
$100$	4.00573	+	2.99235i	0.400573	+	0.299235i
$101$	0.0649104	+	0.368125i	0.00645883	+	0.0366298i	0.987867	−	0.155303i	$-0.0496355\pi$
$101$	0.0649104	+	0.368125i	0.00645883	+	0.0366298i	−0.981408	+	0.191933i	$0.938524\pi$
$102$		0			0
$103$	−1.47527	−	4.05326i	−0.145362	−	0.399380i	0.845549	−	0.533898i	$-0.179273\pi$
$103$	−1.47527	−	4.05326i	−0.145362	−	0.399380i	−0.990911	+	0.134519i	$0.957051\pi$
$104$	0.427726	−	2.42575i	0.0419420	−	0.237865i
$105$		0			0
$106$	0.0890416	−	0.0747148i	0.00864849	−	0.00725694i
$107$		−	4.30890i		−	0.416557i	−0.978070	−	0.208279i	$-0.933214\pi$
$107$		−	4.30890i		−	0.416557i	0.978070	−	0.208279i	$-0.0667860\pi$
$108$		0			0
$109$	19.7643			1.89308			0.946538	−	0.322594i	$-0.104555\pi$
$109$	19.7643			1.89308			0.946538	+	0.322594i	$0.104555\pi$
$110$	7.13550	+	5.65151i	0.680344	+	0.538850i
$111$		0			0
$112$	−0.531122	−	0.0936511i	−0.0501863	−	0.00884920i
$113$	6.31294	+	17.3447i	0.593871	+	1.63165i	0.763255	+	0.646097i	$0.223600\pi$
$113$	6.31294	+	17.3447i	0.593871	+	1.63165i	−0.169384	+	0.985550i	$0.554178\pi$
$114$		0			0
$115$	9.28482	−	3.67984i	0.865814	−	0.343147i
$116$	0.364424	+	0.631201i	0.0338360	+	0.0586056i
$117$		0			0
$118$	9.45645	+	5.45968i	0.870537	+	0.502605i
$119$	−2.17454	−	0.791470i	−0.199340	−	0.0725539i
$120$		0			0
$121$	4.26763	+	3.58097i	0.387966	+	0.325543i
$122$	5.00460	−	5.96425i	0.453095	−	0.539978i
$123$		0			0
$124$	−6.96900	−	2.53651i	−0.625834	−	0.227785i
$125$	0.947111	+	11.1402i	0.0847122	+	0.996405i
$126$		0			0
$127$	−8.44545	+	4.87598i	−0.749413	+	0.432674i	−0.825482	−	0.564429i	$-0.809096\pi$
$127$	−8.44545	+	4.87598i	−0.749413	+	0.432674i	0.0760690	+	0.997103i	$0.475763\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$		0			0
$130$	4.69016	−	2.88765i	0.411355	−	0.253263i
$131$	0.846116	−	4.79856i	0.0739255	−	0.419253i	−0.925276	−	0.379295i	$-0.876167\pi$
$131$	0.846116	−	4.79856i	0.0739255	−	0.419253i	0.999201	−	0.0399576i	$-0.0127223\pi$
$132$		0			0
$133$	0.755136	+	0.899936i	0.0654786	+	0.0780343i
$134$	−9.56407			−0.826210
$135$		0			0
$136$	4.29082			0.367934
$137$	−4.54631	−	5.41808i	−0.388417	−	0.462898i	0.536035	−	0.844196i	$-0.319922\pi$
$137$	−4.54631	−	5.41808i	−0.388417	−	0.462898i	−0.924452	+	0.381298i	$0.875477\pi$
$138$		0			0
$139$	0.148126	−	0.840064i	0.0125639	−	0.0712533i	−0.977881	−	0.209161i	$-0.932927\pi$
$139$	0.148126	−	0.840064i	0.0125639	−	0.0712533i	0.990445	+	0.137908i	$0.0440378\pi$
$140$	−0.632254	−	1.02692i	−0.0534352	−	0.0867904i
$141$		0			0
$142$	−13.7670	+	2.42749i	−1.15530	+	0.203710i
$143$	8.68361	−	5.01348i	0.726160	−	0.419248i
$144$		0			0
$145$	−0.513896	+	1.54661i	−0.0426767	+	0.128439i
$146$	−2.47111	−	0.899411i	−0.204511	−	0.0744358i
$147$		0			0
$148$	4.79439	−	5.71373i	0.394096	−	0.469666i
$149$	3.89120	+	3.26511i	0.318780	+	0.267488i	0.788110	−	0.615535i	$-0.211060\pi$
$149$	3.89120	+	3.26511i	0.318780	+	0.267488i	−0.469330	+	0.883023i	$0.655504\pi$
$150$		0			0
$151$	3.86669	+	1.40736i	0.314667	+	0.114529i	0.494525	−	0.869163i	$-0.335342\pi$
$151$	3.86669	+	1.40736i	0.314667	+	0.114529i	−0.179859	+	0.983692i	$0.557564\pi$
$152$	−1.88645	−	1.08914i	−0.153011	−	0.0883412i
$153$		0			0
$154$	−1.09771	−	1.90129i	−0.0884559	−	0.153210i
$155$	−6.11003	−	15.4166i	−0.490770	−	1.23829i
$156$		0			0
$157$	4.11379	+	11.3026i	0.328317	+	0.902042i	0.988538	+	0.150971i	$0.0482401\pi$
$157$	4.11379	+	11.3026i	0.328317	+	0.902042i	−0.660222	+	0.751071i	$0.729538\pi$
$158$	−5.27123	−	0.929460i	−0.419356	−	0.0739439i
$159$		0			0
$160$	1.75287	+	1.38832i	0.138577	+	0.109757i
$161$	−2.40886			−0.189845
$162$		0			0
$163$		−	1.98122i		−	0.155181i	−0.996985	−	0.0775905i	$-0.975277\pi$
$163$		−	1.98122i		−	0.155181i	0.996985	−	0.0775905i	$-0.0247227\pi$
$164$	−5.82235	+	4.88553i	−0.454649	+	0.381496i
$165$		0			0
$166$	−2.47045	+	14.0106i	−0.191744	+	1.08743i
$167$	−3.70137	−	10.1694i	−0.286421	−	0.786934i	−0.996560	−	0.0828733i	$-0.973590\pi$
$167$	−3.70137	−	10.1694i	−0.286421	−	0.786934i	0.710139	−	0.704061i	$-0.248632\pi$
$168$		0			0
$169$	1.20386	+	6.82745i	0.0926049	+	0.525188i
$170$	6.37256	+	7.17259i	0.488753	+	0.550112i
$171$		0			0
$172$	6.91998	+	3.99525i	0.527643	+	0.304635i
$173$	8.31946	−	22.8575i	0.632517	−	1.73783i	−0.0415308	−	0.999137i	$-0.513223\pi$
$173$	8.31946	−	22.8575i	0.632517	−	1.73783i	0.674047	−	0.738688i	$-0.264554\pi$
$174$		0			0
$175$	0.777610	−	2.58202i	0.0587818	−	0.195183i
$176$	3.11837	+	2.61663i	0.235056	+	0.197236i
$177$		0			0
$178$	−3.27860	+	9.00788i	−0.245741	+	0.675169i
$179$	−2.57674	+	4.46304i	−0.192594	+	0.333583i	−0.946109	−	0.323848i	$-0.895023\pi$
$179$	−2.57674	+	4.46304i	−0.192594	+	0.333583i	0.753515	+	0.657431i	$0.228357\pi$
$180$		0			0
$181$	−4.22810	−	7.32328i	−0.314272	−	0.544335i	0.665011	−	0.746834i	$-0.268427\pi$
$181$	−4.22810	−	7.32328i	−0.314272	−	0.544335i	−0.979282	+	0.202499i	$0.935094\pi$
$182$	−1.30825	+	0.230679i	−0.0969736	+	0.0170991i
$183$		0			0
$184$	4.19716	−	1.52764i	0.309419	−	0.112619i
$185$	16.6716	−	0.471453i	1.22572	−	0.0346619i
$186$		0			0
$187$	11.2275	+	13.3804i	0.821033	+	0.978470i
$188$		−	9.27606i		−	0.676526i
$189$		0			0
$190$	−0.981060	−	4.77097i	−0.0711736	−	0.346123i
$191$	−16.3395	+	13.7105i	−1.18229	+	0.992057i	−0.182326	+	0.983238i	$0.558363\pi$
$191$	−16.3395	+	13.7105i	−1.18229	+	0.992057i	−0.999961	+	0.00881893i	$0.997193\pi$
$192$		0			0
$193$	−10.8998	−	1.92193i	−0.784585	−	0.138344i	−0.233016	−	0.972473i	$-0.574860\pi$
$193$	−10.8998	−	1.92193i	−0.784585	−	0.138344i	−0.551569	+	0.834129i	$0.685971\pi$
$194$	−1.77749	+	0.646954i	−0.127616	+	0.0464486i
$195$		0			0
$196$	−1.16503	−	6.60721i	−0.0832164	−	0.471944i
$197$	6.79514	−	3.92318i	0.484134	−	0.279515i	−0.238004	−	0.971264i	$-0.576493\pi$
$197$	6.79514	−	3.92318i	0.484134	−	0.279515i	0.722138	+	0.691749i	$0.243160\pi$
$198$		0			0
$199$	−4.94805	+	8.57027i	−0.350758	+	0.607530i	−0.986382	−	0.164468i	$-0.947409\pi$
$199$	−4.94805	+	8.57027i	−0.350758	+	0.607530i	0.635625	+	0.771998i	$0.280743\pi$
$200$	0.282562	+	4.99201i	0.0199802	+	0.352988i
$201$		0			0
$202$	−0.240277	+	0.286351i	−0.0169058	+	0.0201476i
$203$	0.252666	−	0.301116i	0.0177337	−	0.0211342i
$204$		0			0
$205$	−16.8139	−	2.47691i	−1.17433	−	0.172995i
$206$	2.15669	−	3.73550i	0.150264	−	0.260265i
$207$		0			0
$208$	2.13317	−	1.23159i	0.147909	−	0.0853952i
$209$	−1.53978	−	8.73254i	−0.106509	−	0.604043i
$210$		0			0
$211$	−25.3811	+	9.23797i	−1.74731	+	0.635968i	−0.999606	−	0.0280677i	$-0.991065\pi$
$211$	−25.3811	+	9.23797i	−1.74731	+	0.635968i	−0.747701	+	0.664035i	$0.768842\pi$
$212$	0.114470	+	0.0201841i	0.00786181	+	0.00138625i
$213$		0			0
$214$	3.30081	−	2.76971i	0.225639	−	0.189333i
$215$	3.59878	+	17.5011i	0.245435	+	1.19357i
$216$		0			0
$217$			3.99970i			0.271517i
$218$	12.7042	+	15.1403i	0.860439	+	1.02543i
$219$		0			0
$220$	0.257304	+	9.09883i	0.0173474	+	0.613443i
$221$	9.93164	−	3.61482i	0.668074	−	0.243159i
$222$		0			0
$223$	19.6897	−	3.47182i	1.31852	−	0.232490i	0.530260	−	0.847835i	$-0.322094\pi$
$223$	19.6897	−	3.47182i	1.31852	−	0.232490i	0.788258	+	0.615345i	$0.210983\pi$
$224$	−0.269658	−	0.467061i	−0.0180173	−	0.0312068i
$225$		0			0
$226$	−9.22890	+	15.9849i	−0.613897	+	1.06330i
$227$	8.25698	−	22.6859i	0.548035	−	1.50571i	−0.288325	−	0.957533i	$-0.593098\pi$
$227$	8.25698	−	22.6859i	0.548035	−	1.50571i	0.836360	−	0.548181i	$-0.184680\pi$
$228$		0			0
$229$	9.12526	+	7.65700i	0.603014	+	0.505989i	0.892413	−	0.451220i	$-0.149011\pi$
$229$	9.12526	+	7.65700i	0.603014	+	0.505989i	−0.289399	+	0.957209i	$0.593455\pi$
$230$	8.78709	+	4.74723i	0.579403	+	0.313023i
$231$		0			0
$232$	−0.249281	+	0.684894i	−0.0163661	+	0.0449655i
$233$	12.9249	+	7.46217i	0.846735	+	0.488863i	0.859548	−	0.511055i	$-0.170745\pi$
$233$	12.9249	+	7.46217i	0.846735	+	0.488863i	−0.0128126	+	0.999918i	$0.504078\pi$
$234$		0			0
$235$	15.5060	−	13.7765i	1.01150	−	0.898677i
$236$	1.89613	+	10.7535i	0.123427	+	0.699992i
$237$		0			0
$238$	−0.791470	−	2.17454i	−0.0513034	−	0.140955i
$239$	−2.21754	+	12.5763i	−0.143441	+	0.813492i	0.825165	+	0.564891i	$0.191082\pi$
$239$	−2.21754	+	12.5763i	−0.143441	+	0.813492i	−0.968606	+	0.248601i	$0.920029\pi$
$240$		0			0
$241$	18.6632	−	15.6602i	1.20220	−	1.00877i	0.202635	−	0.979254i	$-0.435050\pi$
$241$	18.6632	−	15.6602i	1.20220	−	1.00877i	0.999564	−	0.0295107i	$-0.00939492\pi$
$242$			5.57100i			0.358117i
$243$		0			0
$244$	7.78577			0.498433
$245$	9.31445	−	11.7603i	0.595078	−	0.751336i
$246$		0			0
$247$	−5.28398	−	0.931709i	−0.336212	−	0.0592832i
$248$	−2.53651	−	6.96900i	−0.161068	−	0.442532i
$249$		0			0
$250$	−7.92506	+	7.88628i	−0.501225	+	0.498772i
$251$	−12.1853	−	21.1055i	−0.769128	−	1.33217i	−0.938036	−	0.346537i	$-0.887357\pi$
$251$	−12.1853	−	21.1055i	−0.769128	−	1.33217i	0.168908	−	0.985632i	$-0.445976\pi$
$252$		0			0
$253$	15.7462	+	9.09105i	0.989952	+	0.571549i
$254$	−9.16385	−	3.33537i	−0.574991	−	0.209280i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−18.8110	+	22.4180i	−1.17340	+	1.39840i	−0.273738	+	0.961804i	$0.588260\pi$
$257$	−18.8110	+	22.4180i	−1.17340	+	1.39840i	−0.899658	+	0.436595i	$0.856184\pi$
$258$		0			0
$259$	−3.78002	−	1.37582i	−0.234879	−	0.0854890i
$260$	5.22684	+	1.73673i	0.324155	+	0.107708i
$261$		0			0
$262$	4.21979	−	2.43630i	0.260699	−	0.150515i
$263$	−8.78743	+	1.54946i	−0.541856	+	0.0955439i	−0.437876	−	0.899035i	$-0.644269\pi$
$263$	−8.78743	+	1.54946i	−0.541856	+	0.0955439i	−0.103980	+	0.994579i	$0.533158\pi$
$264$		0			0
$265$	0.136266	+	0.221326i	0.00837076	+	0.0135959i
$266$	−0.203999	+	1.15694i	−0.0125080	+	0.0709362i
$267$		0			0
$268$	−6.14767	−	7.32650i	−0.375528	−	0.447537i
$269$	9.14408			0.557525			0.278762	−	0.960360i	$-0.410076\pi$
$269$	9.14408			0.557525			0.278762	+	0.960360i	$0.410076\pi$
$270$		0			0
$271$	−20.6295			−1.25315			−0.626576	−	0.779360i	$-0.715544\pi$
$271$	−20.6295			−1.25315			−0.626576	+	0.779360i	$0.715544\pi$
$272$	2.75808	+	3.28696i	0.167233	+	0.199301i
$273$		0			0
$274$	1.22818	−	6.96535i	0.0741970	−	0.420792i
$275$	−14.8276	+	13.9434i	−0.894138	+	0.840816i
$276$		0			0
$277$	−18.2145	+	3.21170i	−1.09440	+	0.192972i	−0.691575	−	0.722305i	$-0.743083\pi$
$277$	−18.2145	+	3.21170i	−1.09440	+	0.192972i	−0.402825	+	0.915277i	$0.631972\pi$
$278$	0.738740	−	0.426512i	0.0443067	−	0.0255805i
$279$		0			0
$280$	0.380260	−	1.14442i	0.0227249	−	0.0683924i
$281$	19.2451	+	7.00466i	1.14807	+	0.417863i	0.844821	−	0.535049i	$-0.179707\pi$
$281$	19.2451	+	7.00466i	1.14807	+	0.417863i	0.303247	+	0.952912i	$0.401929\pi$
$282$		0			0
$283$	−8.84939	+	10.5463i	−0.526042	+	0.626912i	−0.961998	−	0.273056i	$-0.911966\pi$
$283$	−8.84939	+	10.5463i	−0.526042	+	0.626912i	0.435957	+	0.899968i	$0.356410\pi$
$284$	−10.7088	−	8.98576i	−0.635451	−	0.533207i
$285$		0			0
$286$	9.42226	+	3.42942i	0.557150	+	0.202786i
$287$	3.54991	+	2.04954i	0.209545	+	0.120981i
$288$		0			0
$289$	0.705549	+	1.22205i	0.0415029	+	0.0718851i
$290$	−1.51510	+	0.600477i	−0.0889698	+	0.0352612i
$291$		0			0
$292$	−0.899411	−	2.47111i	−0.0526340	−	0.144611i
$293$	−12.2060	−	2.15225i	−0.713081	−	0.125736i	−0.194672	−	0.980868i	$-0.562364\pi$
$293$	−12.2060	−	2.15225i	−0.713081	−	0.125736i	−0.518409	+	0.855133i	$0.673476\pi$
$294$		0			0
$295$	−15.1596	+	19.1403i	−0.882626	+	1.11439i
$296$	7.45874			0.433531
$297$		0			0
$298$			5.07960i			0.294254i
$299$	8.42789	−	7.07184i	0.487397	−	0.408975i
$300$		0			0
$301$	0.748319	−	4.24393i	0.0431324	−	0.244616i
$302$	1.40736	+	3.86669i	0.0809845	+	0.222503i
$303$		0			0
$304$	−0.378255	−	2.14519i	−0.0216944	−	0.123035i
$305$	11.5631	+	13.0148i	0.662103	+	0.745225i
$306$		0			0
$307$	−27.7691	−	16.0325i	−1.58486	−	0.915022i	−0.994134	−	0.108152i	$-0.965507\pi$
$307$	−27.7691	−	16.0325i	−1.58486	−	0.915022i	−0.590730	−	0.806870i	$-0.701160\pi$
$308$	0.750877	−	2.06302i	0.0427852	−	0.117551i
$309$		0			0
$310$	7.88234	−	14.5902i	0.447687	−	0.828665i
$311$	1.12523	+	0.944177i	0.0638058	+	0.0535394i	0.674133	−	0.738610i	$-0.264518\pi$
$311$	1.12523	+	0.944177i	0.0638058	+	0.0535394i	−0.610327	+	0.792150i	$0.708962\pi$
$312$		0			0
$313$	6.17591	−	16.9682i	0.349083	−	0.959097i	−0.633577	−	0.773680i	$-0.718414\pi$
$313$	6.17591	−	16.9682i	0.349083	−	0.959097i	0.982660	−	0.185418i	$-0.0593638\pi$
$314$	−6.01396	+	10.4165i	−0.339388	+	0.587837i
$315$		0			0
$316$	−2.67627	−	4.63544i	−0.150552	−	0.260764i
$317$	−32.8188	+	5.78683i	−1.84329	+	0.325021i	−0.982831	−	0.184507i	$-0.940931\pi$
$317$	−32.8188	+	5.78683i	−1.84329	+	0.325021i	−0.860454	+	0.509528i	$0.829820\pi$
$318$		0			0
$319$	−2.78803	+	1.01476i	−0.156100	+	0.0568157i
$320$	0.0632081	+	2.23517i	0.00353344	+	0.124950i
$321$		0			0
$322$	−1.54839	−	1.84530i	−0.0862883	−	0.102834i
$323$		−	9.34662i		−	0.520060i
$324$		0			0
$325$	4.85957	+	11.3166i	0.269560	+	0.627732i
$326$	1.51770	−	1.27350i	0.0840577	−	0.0705328i
$327$		0			0
$328$	−7.48507	−	1.31982i	−0.413294	−	0.0728748i
$329$	−4.70102	+	1.71103i	−0.259176	+	0.0943322i
$330$		0			0
$331$	−1.59511	−	9.04632i	−0.0876752	−	0.497231i	−0.996747	−	0.0805917i	$-0.974319\pi$
$331$	−1.59511	−	9.04632i	−0.0876752	−	0.497231i	0.909072	−	0.416639i	$-0.136792\pi$
$332$	−12.3207	+	7.11337i	−0.676187	+	0.390397i
$333$		0			0
$334$	5.41104	−	9.37220i	0.296079	−	0.512824i
$335$	3.11680	−	21.1576i	0.170289	−	1.15596i
$336$		0			0
$337$	14.9760	−	17.8477i	0.815796	−	0.972228i	−0.184147	−	0.982899i	$-0.558952\pi$
$337$	14.9760	−	17.8477i	0.815796	−	0.972228i	0.999943	+	0.0106706i	$0.00339663\pi$
$338$	−4.45630	+	5.31081i	−0.242391	+	0.288870i
$339$		0			0
$340$	−1.39832	+	9.49211i	−0.0758344	+	0.514782i
$341$	15.0948	−	26.1450i	0.817432	−	1.41583i
$342$		0			0
$343$	−6.40300	+	3.69677i	−0.345729	+	0.199607i
$344$	1.38754	+	7.86911i	0.0748109	+	0.424274i
$345$		0			0
$346$	22.8575	−	8.31946i	1.22883	−	0.447257i
$347$	−13.3920	−	2.36136i	−0.718918	−	0.126765i	−0.197792	−	0.980244i	$-0.563377\pi$
$347$	−13.3920	−	2.36136i	−0.718918	−	0.126765i	−0.521127	+	0.853479i	$0.674488\pi$
$348$		0			0
$349$	−3.05394	+	2.56256i	−0.163474	+	0.137171i	−0.720855	−	0.693086i	$-0.756251\pi$
$349$	−3.05394	+	2.56256i	−0.163474	+	0.137171i	0.557381	+	0.830257i	$0.311806\pi$
$350$	2.47778	−	1.06401i	0.132443	−	0.0568737i
$351$		0			0
$352$			4.07075i			0.216972i
$353$	3.51345	+	4.18717i	0.187002	+	0.222861i	0.851398	−	0.524521i	$-0.175755\pi$
$353$	3.51345	+	4.18717i	0.187002	+	0.222861i	−0.664396	+	0.747381i	$0.731311\pi$
$354$		0			0
$355$	−0.883608	−	31.2463i	−0.0468971	−	1.65838i
$356$	−9.00788	+	3.27860i	−0.477417	+	0.173765i
$357$		0			0
$358$	−5.07518	+	0.894891i	−0.268232	+	0.0472965i
$359$	−3.16078	−	5.47463i	−0.166820	−	0.288940i	0.770480	−	0.637464i	$-0.220016\pi$
$359$	−3.16078	−	5.47463i	−0.166820	−	0.288940i	−0.937300	+	0.348524i	$0.886683\pi$
$360$		0			0
$361$	7.12754	−	12.3453i	0.375133	−	0.649750i
$362$	2.89219	−	7.94622i	0.152010	−	0.417644i
$363$		0			0
$364$	−1.01763	−	0.853897i	−0.0533385	−	0.0447563i
$365$	2.79497	−	5.17347i	0.146295	−	0.270792i
$366$		0			0
$367$	−6.32341	+	17.3734i	−0.330079	+	0.906886i	0.658011	+	0.753009i	$0.271398\pi$
$367$	−6.32341	+	17.3734i	−0.330079	+	0.906886i	−0.988090	+	0.153877i	$0.950824\pi$
$368$	3.86812	+	2.23326i	0.201640	+	0.116417i
$369$		0			0
$370$	11.0774	+	12.4681i	0.575889	+	0.648188i
$371$	−0.0108856	−	0.0617353i	−0.000565152	−	0.00320514i
$372$		0			0
$373$	1.21721	+	3.34426i	0.0630248	+	0.173159i	0.967208	−	0.253986i	$-0.0817416\pi$
$373$	1.21721	+	3.34426i	0.0630248	+	0.173159i	−0.904183	+	0.427145i	$0.859519\pi$
$374$	−3.03308	+	17.2015i	−0.156837	+	0.889467i
$375$		0			0
$376$	7.10587	−	5.96254i	0.366457	−	0.307494i
$377$			1.79528i			0.0924617i
$378$		0			0
$379$	1.04628			0.0537435			0.0268718	−	0.999639i	$-0.491445\pi$
$379$	1.04628			0.0537435			0.0268718	+	0.999639i	$0.491445\pi$
$380$	3.02416	−	3.81826i	0.155136	−	0.195872i
$381$		0			0
$382$	−21.0057	−	3.70387i	−1.07475	−	0.189507i
$383$	−2.58954	−	7.11469i	−0.132319	−	0.363544i	0.855785	−	0.517332i	$-0.173075\pi$
$383$	−2.58954	−	7.11469i	−0.132319	−	0.363544i	−0.988104	+	0.153788i	$0.950853\pi$
$384$		0			0
$385$	4.56374	−	1.80874i	0.232590	−	0.0921819i
$386$	−5.53398	−	9.58513i	−0.281672	−	0.487870i
$387$		0			0
$388$	−1.63815	−	0.945783i	−0.0831642	−	0.0480149i
$389$	18.9188	+	6.88588i	0.959221	+	0.349128i	0.773728	−	0.633518i	$-0.218390\pi$
$389$	18.9188	+	6.88588i	0.959221	+	0.349128i	0.185493	+	0.982646i	$0.440612\pi$
$390$		0			0
$391$	14.6813	+	12.3190i	0.742463	+	0.623001i
$392$	4.31255	−	5.13950i	0.217817	−	0.259584i
$393$		0			0
$394$	7.37316	+	2.68361i	0.371454	+	0.135198i
$395$	3.77396	−	11.3581i	0.189889	−	0.571487i
$396$		0			0
$397$	11.5545	−	6.67099i	0.579903	−	0.334807i	−0.181192	−	0.983448i	$-0.557995\pi$
$397$	11.5545	−	6.67099i	0.579903	−	0.334807i	0.761095	+	0.648640i	$0.224662\pi$
$398$	−9.74575	+	1.71844i	−0.488510	+	0.0861375i
$399$		0			0
$400$	−3.64247	+	3.42526i	−0.182124	+	0.171263i
$401$	5.09876	−	28.9165i	0.254620	−	1.44402i	−0.542426	−	0.840103i	$-0.682494\pi$
$401$	5.09876	−	28.9165i	0.254620	−	1.44402i	0.797046	−	0.603918i	$-0.206395\pi$
$402$		0			0
$403$	−11.7421	−	13.9937i	−0.584917	−	0.697077i
$404$	−0.373804			−0.0185975
$405$		0			0
$406$	0.393079			0.0195082
$407$	19.5168	+	23.2592i	0.967409	+	1.15291i
$408$		0			0
$409$	5.26607	−	29.8654i	0.260391	−	1.47675i	−0.521456	−	0.853278i	$-0.674611\pi$
$409$	5.26607	−	29.8654i	0.260391	−	1.47675i	0.781847	−	0.623470i	$-0.214278\pi$
$410$	−8.91031	−	14.4723i	−0.440049	−	0.714735i
$411$		0			0
$412$	4.24786	−	0.749012i	0.209277	−	0.0369012i
$413$	5.10001	−	2.94449i	0.250955	−	0.144889i
$414$		0			0
$415$	−30.1891	−	10.0310i	−1.48192	−	0.492401i
$416$	2.31463	+	0.842455i	0.113484	+	0.0413048i
$417$		0			0
$418$	5.69976	−	6.79271i	0.278784	−	0.332242i
$419$	−31.0303	−	26.0375i	−1.51593	−	1.27202i	−0.851074	−	0.525046i	$-0.824048\pi$
$419$	−31.0303	−	26.0375i	−1.51593	−	1.27202i	−0.664857	−	0.746971i	$-0.731507\pi$
$420$		0			0
$421$	25.0173	+	9.10554i	1.21927	+	0.443777i	0.869909	−	0.493213i	$-0.164178\pi$
$421$	25.0173	+	9.10554i	1.21927	+	0.443777i	0.349358	+	0.936989i	$0.386400\pi$
$422$	−23.3914	−	13.5050i	−1.13867	−	0.657413i
$423$		0			0
$424$	0.0581178	+	0.100663i	0.00282245	+	0.00488863i
$425$	−17.9439	+	11.7599i	−0.870406	+	0.570438i
$426$		0			0
$427$	−1.43614	−	3.94576i	−0.0694996	−	0.190949i
$428$	4.24344	+	0.748233i	0.205114	+	0.0361672i
$429$		0			0
$430$	−11.0934	+	14.0063i	−0.534971	+	0.675445i
$431$	−23.7321			−1.14314			−0.571568	−	0.820555i	$-0.693665\pi$
$431$	−23.7321			−1.14314			−0.571568	+	0.820555i	$0.693665\pi$
$432$		0			0
$433$		−	18.7982i		−	0.903385i	−0.892174	−	0.451693i	$-0.850820\pi$
$433$		−	18.7982i		−	0.903385i	0.892174	−	0.451693i	$-0.149180\pi$
$434$	−3.06395	+	2.57096i	−0.147074	+	0.123410i
$435$		0			0
$436$	−3.43203	+	19.4640i	−0.164365	+	0.932157i
$437$	−3.32764	−	9.14261i	−0.159183	−	0.437350i
$438$		0			0
$439$	3.18217	+	18.0470i	0.151877	+	0.861336i	0.961586	+	0.274504i	$0.0885138\pi$
$439$	3.18217	+	18.0470i	0.151877	+	0.861336i	−0.809709	+	0.586831i	$0.800375\pi$
$440$	−6.80472	+	6.04572i	−0.324402	+	0.288219i
$441$		0			0
$442$	9.15305	+	5.28451i	0.435366	+	0.251359i
$443$	−5.75361	+	15.8079i	−0.273362	+	0.751057i	0.724713	+	0.689050i	$0.241972\pi$
$443$	−5.75361	+	15.8079i	−0.273362	+	0.751057i	−0.998076	+	0.0620063i	$0.980250\pi$
$444$		0			0
$445$	−18.8587	−	10.1884i	−0.893989	−	0.482978i
$446$	15.3158	+	12.8515i	0.725226	+	0.608537i
$447$		0			0
$448$	0.184457	−	0.506791i	0.00871476	−	0.0239436i
$449$	2.86531	−	4.96287i	0.135222	−	0.234212i	−0.790460	−	0.612514i	$-0.790158\pi$
$449$	2.86531	−	4.96287i	0.135222	−	0.234212i	0.925682	+	0.378302i	$0.123492\pi$
$450$		0			0
$451$	−15.4699	−	26.7947i	−0.728451	−	1.26171i
$452$	−18.1774	+	3.20516i	−0.854992	+	0.150758i
$453$		0			0
$454$	22.6859	−	8.25698i	1.06470	−	0.387519i
$455$	−0.0839673	−	2.96927i	−0.00393645	−	0.139201i
$456$		0			0
$457$	−5.68883	−	6.77968i	−0.266112	−	0.317140i	0.616397	−	0.787436i	$-0.288592\pi$
$457$	−5.68883	−	6.77968i	−0.266112	−	0.317140i	−0.882509	+	0.470296i	$0.844147\pi$
$458$			11.9122i			0.556620i
$459$		0			0
$460$	2.01164	+	9.78276i	0.0937932	+	0.456124i
$461$	−15.8273	+	13.2806i	−0.737149	+	0.618541i	−0.932070	−	0.362277i	$-0.881999\pi$
$461$	−15.8273	+	13.2806i	−0.737149	+	0.618541i	0.194921	+	0.980819i	$0.437555\pi$
$462$		0			0
$463$	−8.62824	−	1.52139i	−0.400988	−	0.0707050i	−0.0304826	−	0.999535i	$-0.509704\pi$
$463$	−8.62824	−	1.52139i	−0.400988	−	0.0707050i	−0.370505	+	0.928830i	$0.620816\pi$
$464$	−0.684894	+	0.249281i	−0.0317954	+	0.0115726i
$465$		0			0
$466$	2.59158	+	14.6976i	0.120053	+	0.680853i
$467$	−2.14140	+	1.23634i	−0.0990924	+	0.0572110i	−0.548727	−	0.836001i	$-0.684887\pi$
$467$	−2.14140	+	1.23634i	−0.0990924	+	0.0572110i	0.449635	+	0.893212i	$0.351554\pi$
$468$		0			0
$469$	−2.57902	+	4.46700i	−0.119088	+	0.206267i
$470$	20.5204	+	3.02294i	0.946537	+	0.139438i
$471$		0			0
$472$	−7.01884	+	8.36472i	−0.323068	+	0.385018i
$473$	−20.9082	+	24.9174i	−0.961358	+	1.14570i
$474$		0			0
$475$	10.8740	−	0.615501i	0.498934	−	0.0282411i
$476$	1.15705	−	2.00407i	0.0530333	−	0.0918565i
$477$		0			0
$478$	−11.0594	+	6.38515i	−0.505845	+	0.292050i
$479$	2.95115	+	16.7368i	0.134841	+	0.764724i	0.974970	+	0.222336i	$0.0713683\pi$
$479$	2.95115	+	16.7368i	0.134841	+	0.764724i	−0.840129	+	0.542387i	$0.817521\pi$
$480$		0			0
$481$	17.2642	−	6.28366i	0.787180	−	0.286510i
$482$	23.9929	+	4.23059i	1.09285	+	0.192698i
$483$		0			0
$484$	−4.26763	+	3.58097i	−0.193983	+	0.162771i
$485$	−0.851927	−	4.14299i	−0.0386840	−	0.188123i
$486$		0			0
$487$		−	29.0344i		−	1.31567i	−0.753160	−	0.657837i	$-0.771471\pi$
$487$		−	29.0344i		−	1.31567i	0.753160	−	0.657837i	$-0.228529\pi$
$488$	5.00460	+	5.96425i	0.226548	+	0.269989i
$489$		0			0
$490$	14.9961	−	0.424072i	0.677455	−	0.0191576i
$491$	20.2892	−	7.38465i	0.915637	−	0.333265i	0.159136	−	0.987257i	$-0.449129\pi$
$491$	20.2892	−	7.38465i	0.915637	−	0.333265i	0.756501	+	0.653992i	$0.226907\pi$
$492$		0			0
$493$	−3.07984	+	0.543060i	−0.138709	+	0.0244582i
$494$	−2.68275	−	4.64666i	−0.120703	−	0.209063i
$495$		0			0
$496$	3.70813	−	6.42266i	0.166500	−	0.288386i
$497$	−2.57859	+	7.08461i	−0.115665	+	0.317788i
$498$		0			0
$499$	1.39359	+	1.16936i	0.0623856	+	0.0523477i	0.673447	−	0.739235i	$-0.264813\pi$
$499$	1.39359	+	1.16936i	0.0623856	+	0.0523477i	−0.611062	+	0.791583i	$0.709257\pi$
$500$	−11.1354	−	1.00174i	−0.497989	−	0.0447994i
$501$		0			0
$502$	8.33522	−	22.9008i	0.372019	−	1.02211i
$503$	−17.3370	−	10.0095i	−0.773018	−	0.446302i	0.0609321	−	0.998142i	$-0.480593\pi$
$503$	−17.3370	−	10.0095i	−0.773018	−	0.446302i	−0.833950	+	0.551840i	$0.813926\pi$
$504$		0			0
$505$	−0.555160	−	0.624856i	−0.0247043	−	0.0278057i
$506$	3.15729	+	17.9059i	0.140359	+	0.796013i
$507$		0			0
$508$	−3.33537	−	9.16385i	−0.147983	−	0.406580i
$509$	−3.77631	+	21.4165i	−0.167382	+	0.949270i	0.779192	+	0.626785i	$0.215629\pi$
$509$	−3.77631	+	21.4165i	−0.167382	+	0.949270i	−0.946574	+	0.322485i	$0.895482\pi$
$510$		0			0
$511$	−1.08643	+	0.911626i	−0.0480610	+	0.0403279i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−29.2647			−1.29081
$515$	7.56082	+	5.98837i	0.333170	+	0.263879i
$516$		0			0
$517$	37.1868	+	6.55704i	1.63548	+	0.288378i
$518$	−1.37582	−	3.78002i	−0.0604498	−	0.166085i
$519$		0			0
$520$	2.02934	+	5.12034i	0.0889923	+	0.224542i
$521$	−15.2692	−	26.4470i	−0.668954	−	1.15866i	−0.978197	−	0.207679i	$-0.933409\pi$
$521$	−15.2692	−	26.4470i	−0.668954	−	1.15866i	0.309243	−	0.950983i	$-0.399924\pi$
$522$		0			0
$523$	30.0364	+	17.3415i	1.31340	+	0.758291i	0.982657	−	0.185430i	$-0.0593678\pi$
$523$	30.0364	+	17.3415i	1.31340	+	0.758291i	0.330742	+	0.943721i	$0.392701\pi$
$524$	4.57874	+	1.66652i	0.200023	+	0.0728024i
$525$		0			0
$526$	−6.83541	−	5.73559i	−0.298038	−	0.250084i
$527$	20.4546	−	24.3769i	0.891018	−	1.06187i
$528$		0			0
$529$	−2.86622	−	1.04322i	−0.124618	−	0.0453574i
$530$	−0.0819552	+	0.246651i	−0.00355991	+	0.0107139i
$531$		0			0
$532$	−1.01739	+	0.587391i	−0.0441095	+	0.0254666i
$533$	−18.4370	+	3.25094i	−0.798596	+	0.140814i
$534$		0			0
$535$	5.05144	+	8.20464i	0.218393	+	0.354717i
$536$	1.66078	−	9.41877i	0.0717349	−	0.406829i
$537$		0			0
$538$	5.87770	+	7.00477i	0.253406	+	0.301997i
$539$	27.3112			1.17638
$540$		0			0
$541$	−35.7367			−1.53644			−0.768221	−	0.640185i	$-0.778858\pi$
$541$	−35.7367			−1.53644			−0.768221	+	0.640185i	$0.778858\pi$
$542$	−13.2604	−	15.8031i	−0.569582	−	0.678802i
$543$		0			0
$544$	−0.745092	+	4.22563i	−0.0319456	+	0.181172i
$545$	−37.6334	+	23.1702i	−1.61204	+	0.992502i
$546$		0			0
$547$	−13.5618	+	2.39131i	−0.579860	+	0.102245i	−0.455883	−	0.890040i	$-0.650676\pi$
$547$	−13.5618	+	2.39131i	−0.579860	+	0.102245i	−0.123978	+	0.992285i	$0.539565\pi$
$548$	6.12522	−	3.53640i	0.261657	−	0.151068i
$549$		0			0
$550$	−20.2122	−	2.39598i	−0.861852	−	0.102165i
$551$	1.49189	+	0.543005i	0.0635568	+	0.0231328i
$552$		0			0
$553$	−1.85554	+	2.21135i	−0.0789056	+	0.0940361i
$554$	−14.1683	−	11.8886i	−0.601955	−	0.505100i
$555$		0			0
$556$	0.801580	+	0.291751i	0.0339946	+	0.0123730i
$557$	19.9184	+	11.4999i	0.843970	+	0.487266i	0.858612	−	0.512626i	$-0.171327\pi$
$557$	19.9184	+	11.4999i	0.843970	+	0.487266i	−0.0146417	+	0.999893i	$0.504661\pi$
$558$		0			0
$559$	9.84100	+	17.0451i	0.416230	+	0.720931i
$560$	1.12111	−	0.444326i	0.0473754	−	0.0187762i
$561$		0			0
$562$	7.00466	+	19.2451i	0.295474	+	0.811807i
$563$	21.2374	+	3.74472i	0.895048	+	0.157821i	0.602207	−	0.798340i	$-0.294288\pi$
$563$	21.2374	+	3.74472i	0.895048	+	0.157821i	0.292841	+	0.956161i	$0.405399\pi$
$564$		0			0
$565$	−32.3542	−	25.6254i	−1.36115	−	1.07807i
$566$	−13.7672			−0.578679
$567$		0			0
$568$		−	13.9794i		−	0.586561i
$569$	11.3258	−	9.50345i	0.474801	−	0.398405i	−0.373741	−	0.927533i	$-0.621925\pi$
$569$	11.3258	−	9.50345i	0.474801	−	0.398405i	0.848542	+	0.529128i	$0.177481\pi$
$570$		0			0
$571$	1.39101	−	7.88879i	0.0582118	−	0.330136i	−0.941769	−	0.336259i	$-0.890838\pi$
$571$	1.39101	−	7.88879i	0.0582118	−	0.330136i	0.999981	+	0.00612376i	$0.00194927\pi$
$572$	3.42942	+	9.42226i	0.143391	+	0.393965i
$573$		0			0
$574$	0.711799	+	4.03681i	0.0297099	+	0.168493i
$575$	−13.3654	+	17.8917i	−0.557375	+	0.746135i
$576$		0			0
$577$	5.43636	+	3.13868i	0.226319	+	0.130665i	0.608873	−	0.793268i	$-0.291622\pi$
$577$	5.43636	+	3.13868i	0.226319	+	0.130665i	−0.382554	+	0.923933i	$0.624955\pi$
$578$	−0.482624	+	1.32600i	−0.0200745	+	0.0551542i
$579$		0			0
$580$	−1.43388	−	0.774655i	−0.0595386	−	0.0321658i
$581$	5.87762	+	4.93191i	0.243845	+	0.204610i
$582$		0			0
$583$	−0.161832	+	0.444631i	−0.00670241	+	0.0184147i
$584$	1.31485	−	2.27739i	0.0544089	−	0.0942390i
$585$		0			0
$586$	−6.19714	−	10.7338i	−0.256002	−	0.443408i
$587$	26.5118	−	4.67475i	1.09426	−	0.192947i	0.402746	−	0.915312i	$-0.368056\pi$
$587$	26.5118	−	4.67475i	1.09426	−	0.192947i	0.691513	+	0.722364i	$0.256945\pi$
$588$		0			0
$589$	−15.1805	+	5.52524i	−0.625500	+	0.227663i
$590$	−24.4067	+	0.690192i	−1.00481	+	0.0284148i
$591$		0			0
$592$	4.79439	+	5.71373i	0.197048	+	0.234833i
$593$		−	11.9452i		−	0.490529i	−0.969456	−	0.245264i	$-0.921125\pi$
$593$		−	11.9452i		−	0.490529i	0.969456	−	0.245264i	$-0.0788747\pi$
$594$		0			0
$595$	5.06844	−	1.04223i	0.207786	−	0.0427272i
$596$	−3.89120	+	3.26511i	−0.159390	+	0.133744i
$597$		0			0
$598$	10.8347	+	1.91045i	0.443063	+	0.0781240i
$599$	−2.09601	+	0.762886i	−0.0856408	+	0.0311707i	−0.384485	−	0.923131i	$-0.625621\pi$
$599$	−2.09601	+	0.762886i	−0.0856408	+	0.0311707i	0.298844	+	0.954302i	$0.403399\pi$
$600$		0			0
$601$	5.05104	+	28.6459i	0.206036	+	1.16849i	0.895801	+	0.444456i	$0.146603\pi$
$601$	5.05104	+	28.6459i	0.206036	+	1.16849i	−0.689764	+	0.724034i	$0.742286\pi$
$602$	3.73205	−	2.15470i	0.152107	−	0.0878190i
$603$		0			0
$604$	−2.05742	+	3.56356i	−0.0837153	+	0.144999i
$605$	−12.3241	−	1.81551i	−0.501047	−	0.0738110i
$606$		0			0
$607$	−11.4898	+	13.6930i	−0.466355	+	0.555781i	−0.947041	−	0.321112i	$-0.895943\pi$
$607$	−11.4898	+	13.6930i	−0.466355	+	0.555781i	0.480686	+	0.876893i	$0.340388\pi$
$608$	1.40018	−	1.66866i	0.0567846	−	0.0676733i
$609$		0			0
$610$	−2.53728	+	17.2236i	−0.102731	+	0.697364i
$611$	11.4243	−	19.7874i	0.462177	−	0.800513i
$612$		0			0
$613$	−39.7223	+	22.9337i	−1.60437	+	0.926284i	−0.613772	+	0.789483i	$0.710349\pi$
$613$	−39.7223	+	22.9337i	−1.60437	+	0.926284i	−0.990599	+	0.136800i	$0.956318\pi$
$614$	−5.56802	−	31.5778i	−0.224707	−	1.27438i
$615$		0			0
$616$	2.06302	−	0.750877i	0.0831213	−	0.0302537i
$617$	−1.67563	−	0.295459i	−0.0674583	−	0.0118947i	0.139817	−	0.990177i	$-0.455349\pi$
$617$	−1.67563	−	0.295459i	−0.0674583	−	0.0118947i	−0.207275	+	0.978283i	$0.566460\pi$
$618$		0			0
$619$	−16.5836	+	13.9153i	−0.666550	+	0.559302i	−0.912042	−	0.410097i	$-0.865495\pi$
$619$	−16.5836	+	13.9153i	−0.666550	+	0.559302i	0.245492	+	0.969399i	$0.421050\pi$
$620$	16.2434	−	3.34014i	0.652350	−	0.134143i
$621$		0			0
$622$			1.46888i			0.0588967i
$623$	3.32313	+	3.96035i	0.133138	+	0.158668i
$624$		0			0
$625$	−14.8633	−	20.1018i	−0.594532	−	0.804072i
$626$	16.9682	−	6.17591i	0.678184	−	0.246839i
$627$		0			0
$628$	−11.8452	+	2.08863i	−0.472675	+	0.0833453i
$629$	16.0020	+	27.7164i	0.638043	+	1.10512i
$630$		0			0
$631$	6.44066	−	11.1555i	0.256398	−	0.444095i	−0.708876	−	0.705333i	$-0.750797\pi$
$631$	6.44066	−	11.1555i	0.256398	−	0.444095i	0.965274	+	0.261238i	$0.0841307\pi$
$632$	1.83068	−	5.02975i	0.0728205	−	0.200073i
$633$		0			0
$634$	−25.5285	−	21.4209i	−1.01386	−	0.850733i
$635$	10.3649	−	19.1853i	0.411317	−	0.761344i
$636$		0			0
$637$	5.65215	−	15.5292i	0.223946	−	0.615287i
$638$	−2.56946	−	1.48348i	−0.101726	−	0.0587315i
$639$		0			0
$640$	−1.67161	+	1.48516i	−0.0660763	+	0.0587062i
$641$	2.61920	+	14.8542i	0.103452	+	0.586706i	0.991827	+	0.127588i	$0.0407235\pi$
$641$	2.61920	+	14.8542i	0.103452	+	0.586706i	−0.888375	+	0.459118i	$0.848165\pi$
$642$		0			0
$643$	7.44994	+	20.4685i	0.293797	+	0.807200i	0.995503	+	0.0947334i	$0.0301999\pi$
$643$	7.44994	+	20.4685i	0.293797	+	0.807200i	−0.701706	+	0.712467i	$0.747578\pi$
$644$	0.418295	−	2.37227i	0.0164831	−	0.0934805i
$645$		0			0
$646$	7.15993	−	6.00789i	0.281704	−	0.236377i
$647$		−	7.76918i		−	0.305438i	−0.988270	−	0.152719i	$-0.951197\pi$
$647$		−	7.76918i		−	0.305438i	0.988270	−	0.152719i	$-0.0488030\pi$
$648$		0			0
$649$	−44.4500			−1.74482
$650$	−5.54534	+	10.9968i	−0.217506	+	0.431330i
$651$		0			0
$652$	1.95112	+	0.344035i	0.0764118	+	0.0134735i
$653$	−7.67233	−	21.0796i	−0.300241	−	0.824907i	−0.994457	−	0.105140i	$-0.966471\pi$
$653$	−7.67233	−	21.0796i	−0.300241	−	0.824907i	0.694216	−	0.719767i	$-0.255751\pi$
$654$		0			0
$655$	4.01438	+	10.1289i	0.156855	+	0.395770i
$656$	−3.80027	−	6.58226i	−0.148376	−	0.256994i
$657$		0			0
$658$	−4.33248	−	2.50136i	−0.168898	−	0.0975132i
$659$	17.0727	+	6.21395i	0.665057	+	0.242061i	0.652418	−	0.757859i	$-0.273755\pi$
$659$	17.0727	+	6.21395i	0.665057	+	0.242061i	0.0126389	+	0.999920i	$0.495977\pi$
$660$		0			0
$661$	33.8258	+	28.3832i	1.31567	+	1.10398i	0.987204	+	0.159465i	$0.0509768\pi$
$661$	33.8258	+	28.3832i	1.31567	+	1.10398i	0.328468	+	0.944515i	$0.393468\pi$
$662$	5.90457	−	7.03679i	0.229487	−	0.273493i
$663$		0			0
$664$	−13.3688	−	4.86583i	−0.518808	−	0.188831i
$665$	−2.49288	−	0.828314i	−0.0966699	−	0.0321206i
$666$		0			0
$667$	−2.81928	+	1.62771i	−0.109163	+	0.0630252i
$668$	10.6577	−	1.87924i	0.412358	−	0.0727098i
$669$		0			0
$670$	18.2111	−	11.2122i	0.703555	−	0.433166i
$671$	−5.50359	+	31.2124i	−0.212464	+	1.20494i
$672$		0			0
$673$	18.4578	+	21.9972i	0.711497	+	0.847929i	0.993775	−	0.111404i	$-0.0355347\pi$
$673$	18.4578	+	21.9972i	0.711497	+	0.847929i	−0.282279	+	0.959332i	$0.591090\pi$
$674$	23.2986			0.897427
$675$		0			0
$676$	−6.93277			−0.266645
$677$	24.4113	+	29.0923i	0.938203	+	1.11811i	0.992822	+	0.119599i	$0.0381610\pi$
$677$	24.4113	+	29.0923i	0.938203	+	1.11811i	−0.0546194	+	0.998507i	$0.517395\pi$
$678$		0			0
$679$	−0.177147	+	1.00465i	−0.00679829	+	0.0385550i
$680$	−8.17020	+	5.03024i	−0.313313	+	0.192901i
$681$		0			0
$682$	29.7310	−	5.24239i	1.13846	−	0.200741i
$683$	−35.7083	+	20.6162i	−1.36634	+	0.788856i	−0.990458	−	0.137812i	$-0.955993\pi$
$683$	−35.7083	+	20.6162i	−1.36634	+	0.788856i	−0.375880	+	0.926668i	$0.622660\pi$
$684$		0			0
$685$	15.0084	+	4.98688i	0.573443	+	0.190539i
$686$	−6.94766	−	2.52874i	−0.265263	−	0.0965478i
$687$		0			0
$688$	−5.13620	+	6.12108i	−0.195816	+	0.233364i
$689$	0.219325	+	0.184036i	0.00835562	+	0.00701120i
$690$		0			0
$691$	−0.00336697	−	0.00122548i	−0.000128086	−	4.66193e-5i	0.341956	−	0.939716i	$-0.388911\pi$
$691$	−0.00336697	−	0.00122548i	−0.000128086	−	4.66193e-5i	−0.342084	+	0.939669i	$0.611133\pi$
$692$	21.0656	+	12.1622i	0.800794	+	0.462339i
$693$		0			0
$694$	−6.79928	−	11.7767i	−0.258097	−	0.447037i
$695$	0.702781	+	1.77323i	0.0266580	+	0.0672625i
$696$		0			0
$697$	−11.1541	−	30.6457i	−0.422493	−	1.16079i
$698$	−3.92607	−	0.692272i	−0.148604	−	0.0262029i
$699$		0			0
$700$	2.40777	+	1.21416i	0.0910050	+	0.0458909i
$701$	−11.4392			−0.432052			−0.216026	−	0.976388i	$-0.569310\pi$
$701$	−11.4392			−0.432052			−0.216026	+	0.976388i	$0.569310\pi$
$702$		0			0
$703$		−	16.2473i		−	0.612778i
$704$	−3.11837	+	2.61663i	−0.117528	+	0.0986178i
$705$		0			0
$706$	−0.949154	+	5.38292i	−0.0357219	+	0.202589i
$707$	0.0689507	+	0.189441i	0.00259316	+	0.00712464i
$708$		0			0
$709$	0.817504	+	4.63629i	0.0307020	+	0.174120i	0.996303	−	0.0859085i	$-0.0273793\pi$
$709$	0.817504	+	4.63629i	0.0307020	+	0.174120i	−0.965601	+	0.260028i	$0.916268\pi$
$710$	23.3681	−	20.7616i	0.876989	−	0.779170i
$711$		0			0
$712$	−8.30170	−	4.79299i	−0.311120	−	0.179625i
$713$	11.3294	−	31.1272i	0.424288	−	1.16572i
$714$		0			0
$715$	−10.6571	+	19.7263i	−0.398554	+	0.737721i
$716$	−3.94779	−	3.31259i	−0.147536	−	0.123797i
$717$		0			0
$718$	2.16210	−	5.94032i	0.0806889	−	0.221691i
$719$	8.53531	−	14.7836i	0.318313	−	0.551335i	−0.661823	−	0.749660i	$-0.730217\pi$
$719$	8.53531	−	14.7836i	0.318313	−	0.551335i	0.980136	+	0.198325i	$0.0635502\pi$
$720$		0			0
$721$	−1.16314	−	2.01461i	−0.0433175	−	0.0750282i
$722$	14.0385	−	2.47537i	0.522459	−	0.0921236i
$723$		0			0
$724$	7.94622	−	2.89219i	0.295319	−	0.107487i
$725$	−0.834621	−	3.54738i	−0.0309971	−	0.131746i
$726$		0			0
$727$	19.5543	+	23.3039i	0.725229	+	0.864294i	0.995128	−	0.0985945i	$-0.0314347\pi$
$727$	19.5543	+	23.3039i	0.725229	+	0.864294i	−0.269899	+	0.962889i	$0.586990\pi$
$728$		−	1.32843i		−	0.0492348i
$729$		0			0
$730$	5.75968	−	1.18437i	0.213175	−	0.0438355i
$731$	−26.2644	+	22.0385i	−0.971425	+	0.815122i
$732$		0			0
$733$	45.0180	+	7.93788i	1.66278	+	0.293192i	0.924465	−	0.381268i	$-0.124512\pi$
$733$	45.0180	+	7.93788i	1.66278	+	0.293192i	0.738311	+	0.674460i	$0.235623\pi$
$734$	−17.3734	+	6.32341i	−0.641265	+	0.233401i
$735$		0			0
$736$	0.775604	+	4.39867i	0.0285891	+	0.162137i
$737$	33.7169	−	19.4665i	1.24198	−	0.717056i
$738$		0			0
$739$	−2.88611	+	4.99888i	−0.106167	+	0.183887i	−0.914214	−	0.405231i	$-0.867191\pi$
$739$	−2.88611	+	4.99888i	−0.106167	+	0.183887i	0.808047	+	0.589118i	$0.200525\pi$
$740$	−2.43070	+	16.5002i	−0.0893544	+	0.606559i
$741$		0			0
$742$	0.0402948	−	0.0480215i	0.00147927	−	0.00176293i
$743$	19.3095	−	23.0121i	0.708395	−	0.844233i	−0.285053	−	0.958512i	$-0.592011\pi$
$743$	19.3095	−	23.0121i	0.708395	−	0.844233i	0.993449	+	0.114279i	$0.0364557\pi$
$744$		0			0
$745$	−11.2371	−	1.65537i	−0.411694	−	0.0606482i
$746$	−1.77944	+	3.08209i	−0.0651501	+	0.112843i
$747$		0			0
$748$	−15.1267	+	8.73342i	−0.553088	+	0.319325i
$749$	−0.403533	−	2.28855i	−0.0147448	−	0.0836218i
$750$		0			0
$751$	−16.7944	+	6.11265i	−0.612835	+	0.223054i	−0.629743	−	0.776803i	$-0.716840\pi$
$751$	−16.7944	+	6.11265i	−0.612835	+	0.223054i	0.0169082	+	0.999857i	$0.494618\pi$
$752$	9.13513	+	1.61077i	0.333124	+	0.0587388i
$753$		0			0
$754$	−1.37527	+	1.15398i	−0.0500842	+	0.0420256i
$755$	−9.01250	+	1.85325i	−0.327999	+	0.0674467i
$756$		0			0
$757$			34.8600i			1.26701i	0.773739	+	0.633504i	$0.218384\pi$
$757$			34.8600i			1.26701i	−0.773739	+	0.633504i	$0.781616\pi$
$758$	0.672533	+	0.801493i	0.0244275	+	0.0291115i
$759$		0			0
$760$	4.86885	−	0.137685i	0.176612	−	0.00499437i
$761$	−17.5585	+	6.39077i	−0.636495	+	0.231665i	−0.640056	−	0.768328i	$-0.721089\pi$
$761$	−17.5585	+	6.39077i	−0.636495	+	0.231665i	0.00356090	+	0.999994i	$0.498867\pi$
$762$		0			0
$763$	10.4972	−	1.85095i	0.380026	−	0.0670088i
$764$	−10.6649	−	18.4721i	−0.385842	−	0.668297i
$765$		0			0
$766$	3.78565	−	6.55694i	0.136781	−	0.236912i
$767$	−9.19908	+	25.2743i	−0.332160	+	0.912601i
$768$		0			0
$769$	20.4455	+	17.1558i	0.737282	+	0.618653i	0.932106	−	0.362185i	$-0.117969\pi$
$769$	20.4455	+	17.1558i	0.737282	+	0.618653i	−0.194824	+	0.980838i	$0.562414\pi$
$770$	4.31909	+	2.33339i	0.155649	+	0.0840897i
$771$		0			0
$772$	3.78546	−	10.4005i	0.136242	−	0.374321i
$773$	−13.3630	−	7.71514i	−0.480634	−	0.277494i	0.240047	−	0.970761i	$-0.422837\pi$
$773$	−13.3630	−	7.71514i	−0.480634	−	0.277494i	−0.720681	+	0.693267i	$0.756171\pi$
$774$		0			0
$775$	29.7075	+	22.1920i	1.06712	+	0.797160i
$776$	−0.328467	−	1.86283i	−0.0117913	−	0.0668717i
$777$		0			0
$778$	6.88588	+	18.9188i	0.246871	+	0.678271i
$779$	−2.87494	+	16.3046i	−0.103006	+	0.584173i
$780$		0			0
$781$	43.5929	−	36.5788i	1.55988	−	1.30889i
$782$			19.1650i			0.685340i
$783$		0			0
$784$	6.70914			0.239612
$785$	−21.0834	−	16.6986i	−0.752500	−	0.596000i
$786$		0			0
$787$	33.9745	+	5.99062i	1.21106	+	0.213542i	0.742473	−	0.669876i	$-0.233653\pi$
$787$	33.9745	+	5.99062i	1.21106	+	0.213542i	0.468586	+	0.883418i	$0.344764\pi$
$788$	2.68361	+	7.37316i	0.0955997	+	0.262658i
$789$		0			0
$790$	11.1266	−	4.40981i	0.395868	−	0.156894i
$791$	4.97728	+	8.62091i	0.176972	+	0.306524i
$792$		0			0
$793$	16.6084	+	9.58886i	0.589781	+	0.340510i
$794$	12.5374	+	4.56323i	0.444934	+	0.161943i
$795$		0			0
$796$	−7.58085	−	6.36108i	−0.268696	−	0.225463i
$797$	3.57242	−	4.25745i	0.126542	−	0.150806i	−0.699054	−	0.715069i	$-0.746395\pi$
$797$	3.57242	−	4.25745i	0.126542	−	0.150806i	0.825595	+	0.564263i	$0.190840\pi$
$798$		0			0
$799$	37.4015	+	13.6130i	1.32317	+	0.481595i
$800$	−4.96524	−	0.588584i	−0.175548	−	0.0208096i
$801$		0			0
$802$	25.4288	−	14.6813i	0.897920	−	0.518415i
$803$	10.5422	−	1.85888i	0.372027	−	0.0655984i
$804$		0			0
$805$	4.58675	−	2.82398i	0.161662	−	0.0995321i
$806$	3.17212	−	17.9900i	0.111733	−	0.633671i
$807$		0			0
$808$	−0.240277	−	0.286351i	−0.00845291	−	0.0100738i
$809$	−1.58313			−0.0556599			−0.0278299	−	0.999613i	$-0.508860\pi$
$809$	−1.58313			−0.0556599			−0.0278299	+	0.999613i	$0.508860\pi$
$810$		0			0
$811$	−22.1659			−0.778351			−0.389175	−	0.921164i	$-0.627240\pi$
$811$	−22.1659			−0.778351			−0.389175	+	0.921164i	$0.627240\pi$
$812$	0.252666	+	0.301116i	0.00886685	+	0.0105671i
$813$		0			0
$814$	−5.27242	+	29.9014i	−0.184798	+	1.04804i
$815$	2.32264	+	3.77247i	0.0813584	+	0.132144i
$816$		0			0
$817$	17.1412	−	3.02245i	0.599694	−	0.105742i
$818$	26.2632	−	15.1631i	0.918271	−	0.530164i
$819$		0			0
$820$	5.35897	−	16.1283i	0.187144	−	0.563225i
$821$	−9.63738	−	3.50772i	−0.336347	−	0.122420i	0.168325	−	0.985732i	$-0.446164\pi$
$821$	−9.63738	−	3.50772i	−0.336347	−	0.122420i	−0.504672	+	0.863311i	$0.668386\pi$
$822$		0			0
$823$	−14.3467	+	17.0977i	−0.500093	+	0.595988i	−0.955755	−	0.294165i	$-0.904958\pi$
$823$	−14.3467	+	17.0977i	−0.500093	+	0.595988i	0.455661	+	0.890153i	$0.349403\pi$
$824$	3.30425	+	2.77259i	0.115109	+	0.0965878i
$825$		0			0
$826$	5.53383	+	2.01415i	0.192547	+	0.0700813i
$827$	6.88573	+	3.97548i	0.239440	+	0.138241i	0.614920	−	0.788590i	$-0.289188\pi$
$827$	6.88573	+	3.97548i	0.239440	+	0.138241i	−0.375479	+	0.926831i	$0.622522\pi$
$828$		0			0
$829$	2.41490	+	4.18273i	0.0838731	+	0.145272i	0.904910	−	0.425602i	$-0.139938\pi$
$829$	2.41490	+	4.18273i	0.0838731	+	0.145272i	−0.821037	+	0.570874i	$0.806604\pi$
$830$	−11.7210	−	29.5739i	−0.406841	−	1.02653i
$831$		0			0
$832$	0.842455	+	2.31463i	0.0292069	+	0.0802452i
$833$	28.3503	+	4.99893i	0.982281	+	0.173203i
$834$		0			0
$835$	18.9697	+	15.0245i	0.656475	+	0.519946i
$836$	8.86726			0.306680
$837$		0			0
$838$		−	40.5072i		−	1.39930i
$839$	12.7392	−	10.6895i	0.439807	−	0.369042i	−0.395830	−	0.918324i	$-0.629543\pi$
$839$	12.7392	−	10.6895i	0.439807	−	0.369042i	0.835637	+	0.549282i	$0.185099\pi$
$840$		0			0
$841$	−4.94355	+	28.0363i	−0.170467	+	0.966768i
$842$	9.10554	+	25.0173i	0.313798	+	0.862152i
$843$		0			0
$844$	−4.69024	−	26.5997i	−0.161445	−	0.915598i
$845$	−10.2963	−	11.5889i	−0.354203	−	0.398671i
$846$		0			0
$847$	2.60199	+	1.50226i	0.0894056	+	0.0516183i
$848$	−0.0397549	+	0.109226i	−0.00136519	+	0.00375083i
$849$		0			0
$850$	−20.5427	−	6.18670i	−0.704609	−	0.212202i
$851$	25.5205	+	21.4142i	0.874832	+	0.734071i
$852$		0			0
$853$	−16.5267	+	45.4068i	−0.565865	+	1.55470i	0.245034	+	0.969514i	$0.421201\pi$
$853$	−16.5267	+	45.4068i	−0.565865	+	1.55470i	−0.810899	+	0.585186i	$0.801021\pi$
$854$	2.09949	−	3.63643i	0.0718432	−	0.124436i
$855$		0			0
$856$	2.15445	+	3.73162i	0.0736376	+	0.127544i
$857$	5.42516	−	0.956602i	0.185320	−	0.0326769i	−0.0802178	−	0.996777i	$-0.525562\pi$
$857$	5.42516	−	0.956602i	0.185320	−	0.0326769i	0.265538	+	0.964100i	$0.414450\pi$
$858$		0			0
$859$	22.5455	−	8.20589i	0.769242	−	0.279981i	0.0725627	−	0.997364i	$-0.476882\pi$
$859$	22.5455	−	8.20589i	0.769242	−	0.279981i	0.696679	+	0.717383i	$0.254660\pi$
$860$	−17.8602	+	0.505064i	−0.609027	+	0.0172225i
$861$		0			0
$862$	−15.2547	−	18.1799i	−0.519577	−	0.619208i
$863$			20.5253i			0.698689i	0.936994	+	0.349344i	$0.113596\pi$
$863$			20.5253i			0.698689i	−0.936994	+	0.349344i	$0.886404\pi$
$864$		0			0
$865$	10.9553	+	53.2764i	0.372491	+	1.81145i
$866$	14.4003	−	12.0833i	0.489341	−	0.410606i
$867$		0			0
$868$	−3.93893	−	0.694540i	−0.133696	−	0.0235742i
$869$	20.4748	−	7.45223i	0.694561	−	0.252800i
$870$		0			0
$871$	−4.09080	−	23.2001i	−0.138611	−	0.786104i
$872$	−17.1164	+	9.88214i	−0.579633	+	0.334652i
$873$		0			0
$874$	4.86468	−	8.42588i	0.164550	−	0.285010i
$875$	1.54632	+	5.82808i	0.0522751	+	0.197025i
$876$		0			0
$877$	28.4839	−	33.9458i	0.961833	−	1.14627i	−0.0273565	−	0.999626i	$-0.508709\pi$
$877$	28.4839	−	33.9458i	0.961833	−	1.14627i	0.989190	−	0.146642i	$-0.0468466\pi$
$878$	−11.7793	+	14.0381i	−0.397533	+	0.473762i
$879$		0			0
$880$	−9.00528	−	1.32660i	−0.303568	−	0.0447197i
$881$	−3.94879	+	6.83950i	−0.133038	+	0.230429i	−0.924846	−	0.380341i	$-0.875807\pi$
$881$	−3.94879	+	6.83950i	−0.133038	+	0.230429i	0.791808	+	0.610770i	$0.209140\pi$
$882$		0			0
$883$	8.09566	−	4.67403i	0.272441	−	0.157294i	−0.357556	−	0.933892i	$-0.616390\pi$
$883$	8.09566	−	4.67403i	0.272441	−	0.157294i	0.629996	+	0.776598i	$0.283056\pi$
$884$	1.83529	+	10.4085i	0.0617276	+	0.350074i
$885$		0			0
$886$	−15.8079	+	5.75361i	−0.531077	+	0.193296i
$887$	−1.37077	−	0.241704i	−0.0460260	−	0.00811563i	0.150588	−	0.988597i	$-0.451883\pi$
$887$	−1.37077	−	0.241704i	−0.0460260	−	0.00811563i	−0.196614	+	0.980481i	$0.562995\pi$
$888$		0			0
$889$	−4.02892	+	3.38067i	−0.135126	+	0.113384i
$890$	−4.31735	−	20.9956i	−0.144718	−	0.703775i
$891$		0			0
$892$			19.9934i			0.669429i
$893$	−12.9881	−	15.4786i	−0.434630	−	0.517972i
$894$		0			0
$895$	−0.325741	−	11.5189i	−0.0108883	−	0.385035i
$896$	0.506791	−	0.184457i	0.0169307	−	0.00616226i
$897$		0			0
$898$	5.64357	−	0.995113i	0.188328	−	0.0332073i
$899$	2.70266	+	4.68115i	0.0901388	+	0.156125i
$900$		0			0
$901$	−0.249373	+	0.431926i	−0.00830781	+	0.0143896i
$902$	10.5821	−	29.0740i	0.352344	−	0.968057i
$903$		0			0
$904$	−14.1395	−	11.8644i	−0.470272	−	0.394605i
$905$	16.6361	+	8.98764i	0.553001	+	0.298759i
$906$		0			0
$907$	1.20927	−	3.32245i	0.0401532	−	0.110320i	−0.917996	−	0.396590i	$-0.870193\pi$
$907$	1.20927	−	3.32245i	0.0401532	−	0.110320i	0.958149	+	0.286270i	$0.0924156\pi$
$908$	20.9074	+	12.0709i	0.693837	+	0.400587i
$909$		0			0
$910$	2.22062	−	1.97293i	0.0736127	−	0.0654020i
$911$	8.19262	+	46.4627i	0.271434	+	1.53938i	0.750067	+	0.661362i	$0.230021\pi$
$911$	8.19262	+	46.4627i	0.271434	+	1.53938i	−0.478633	+	0.878015i	$0.658868\pi$
$912$		0			0
$913$	−19.8076	−	54.4208i	−0.655535	−	1.80107i
$914$	1.53683	−	8.71579i	0.0508338	−	0.288293i
$915$		0			0
$916$	−9.12526	+	7.65700i	−0.301507	+	0.252995i
$917$		−	2.62786i		−	0.0867797i
$918$		0			0
$919$	29.2135			0.963666			0.481833	−	0.876263i	$-0.339971\pi$
$919$	29.2135			0.963666			0.481833	+	0.876263i	$0.339971\pi$
$920$	−6.20097	+	7.82925i	−0.204440	+	0.258123i
$921$		0			0
$922$	−20.3471	−	3.58775i	−0.670097	−	0.118156i
$923$	−11.7770	−	32.3570i	−0.387644	−	1.06504i
$924$		0			0
$925$	−31.1919	+	20.4423i	−1.02558	+	0.672137i
$926$	−4.38067	−	7.58754i	−0.143958	−	0.249342i
$927$		0			0
$928$	−0.631201	−	0.364424i	−0.0207202	−	0.0119628i
$929$	−11.0326	−	4.01553i	−0.361967	−	0.131745i	0.154633	−	0.987972i	$-0.450580\pi$
$929$	−11.0326	−	4.01553i	−0.361967	−	0.131745i	−0.516600	+	0.856227i	$0.672803\pi$
$930$		0			0
$931$	−11.1953	−	9.39397i	−0.366911	−	0.307875i
$932$	−9.59318	+	11.4327i	−0.314235	+	0.374491i
$933$		0			0
$934$	−2.32356	−	0.845707i	−0.0760292	−	0.0276724i
$935$	−37.0645	−	12.3155i	−1.21214	−	0.402760i
$936$		0			0
$937$	22.2280	−	12.8334i	0.726159	−	0.419248i	−0.0908566	−	0.995864i	$-0.528961\pi$
$937$	22.2280	−	12.8334i	0.726159	−	0.419248i	0.817015	+	0.576616i	$0.195627\pi$
$938$	−5.07969	+	0.895686i	−0.165858	+	0.0292452i
$939$		0			0
$940$	10.8746	+	17.6627i	0.354689	+	0.576093i
$941$	3.73531	−	21.1840i	0.121768	−	0.690578i	−0.861408	−	0.507914i	$-0.830417\pi$
$941$	3.73531	−	21.1840i	0.121768	−	0.690578i	0.983175	−	0.182664i	$-0.0584721\pi$
$942$		0			0
$943$	−21.8213	−	26.0057i	−0.710600	−	0.846861i
$944$	−10.9194			−0.355395
$945$		0			0
$946$	−32.5273			−1.05755
$947$	13.8601	+	16.5178i	0.450392	+	0.536756i	0.942690	−	0.333671i	$-0.108287\pi$
$947$	13.8601	+	16.5178i	0.450392	+	0.536756i	−0.492298	+	0.870427i	$0.663843\pi$
$948$		0			0
$949$	1.12479	−	6.37901i	0.0365123	−	0.207071i
$950$	7.46119	+	7.93435i	0.242073	+	0.257424i
$951$		0			0
$952$	2.27895	−	0.401840i	0.0738611	−	0.0130237i
$953$	−2.26739	+	1.30908i	−0.0734480	+	0.0424052i	−0.536274	−	0.844044i	$-0.680169\pi$
$953$	−2.26739	+	1.30908i	−0.0734480	+	0.0424052i	0.462826	+	0.886449i	$0.346835\pi$
$954$		0			0
$955$	15.0392	−	45.2616i	0.486655	−	1.46463i
$956$	−12.0002	−	4.36770i	−0.388113	−	0.141261i
$957$		0			0
$958$	−10.9242	+	13.0189i	−0.352944	+	0.420622i
$959$	−2.92205	−	2.45189i	−0.0943580	−	0.0791758i
$960$		0			0
$961$	−22.5534	−	8.20875i	−0.727528	−	0.264798i
$962$	15.9108	+	9.18609i	0.512984	+	0.296172i
$963$		0			0
$964$	12.1815	+	21.0990i	0.392340	+	0.679553i
$965$	23.0076	−	9.11857i	0.740641	−	0.293537i
$966$		0			0
$967$	4.40078	+	12.0910i	0.141520	+	0.388822i	0.990122	−	0.140209i	$-0.0447776\pi$
$967$	4.40078	+	12.0910i	0.141520	+	0.388822i	−0.848602	+	0.529031i	$0.822555\pi$
$968$	−5.48636	−	0.967393i	−0.176338	−	0.0310932i
$969$		0			0
$970$	2.62610	−	3.31568i	0.0843191	−	0.106460i
$971$	−15.9136			−0.510691			−0.255345	−	0.966850i	$-0.582189\pi$
$971$	−15.9136			−0.510691			−0.255345	+	0.966850i	$0.582189\pi$
$972$		0			0
$973$		−	0.460049i		−	0.0147485i
$974$	22.2417	−	18.6630i	0.712668	−	0.598000i
$975$		0			0
$976$	−1.35199	+	7.66749i	−0.0432760	+	0.245430i
$977$	11.4374	+	31.4239i	0.365914	+	1.00534i	0.976900	+	0.213699i	$0.0685512\pi$
$977$	11.4374	+	31.4239i	0.365914	+	1.00534i	−0.610985	+	0.791642i	$0.709227\pi$
$978$		0			0
$979$	−6.77612	−	38.4293i	−0.216566	−	1.22821i
$980$	9.96416	+	11.2151i	0.318293	+	0.358253i
$981$		0			0
$982$	18.6986	+	10.7956i	0.596696	+	0.344503i
$983$	−5.52588	+	15.1822i	−0.176248	+	0.484238i	−0.996089	−	0.0883534i	$-0.971840\pi$
$983$	−5.52588	+	15.1822i	−0.176248	+	0.484238i	0.819841	+	0.572591i	$0.194062\pi$
$984$		0			0
$985$	−8.33948	+	15.4363i	−0.265718	+	0.491841i
$986$	−2.39569	−	2.01023i	−0.0762944	−	0.0640186i
$987$		0			0
$988$	1.83511	−	5.04192i	0.0583826	−	0.160405i
$989$	−17.8449	+	30.9082i	−0.567434	+	0.982825i
$990$		0			0
$991$	17.0726	+	29.5706i	0.542329	+	0.939342i	0.998770	+	0.0495881i	$0.0157909\pi$
$991$	17.0726	+	29.5706i	0.542329	+	0.939342i	−0.456440	+	0.889754i	$0.650876\pi$
$992$	7.30358	−	1.28782i	0.231889	−	0.0408883i
$993$		0			0
$994$	−7.08461	+	2.57859i	−0.224710	+	0.0817878i
$995$	−0.625513	−	22.1195i	−0.0198301	−	0.701235i
$996$		0			0
$997$	5.26635	+	6.27619i	0.166787	+	0.198769i	0.842964	−	0.537971i	$-0.180809\pi$
$997$	5.26635	+	6.27619i	0.166787	+	0.198769i	−0.676177	+	0.736740i	$0.736364\pi$
$998$			1.81920i			0.0575858i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.p.a.199.10		108
3.2	odd	2		270.2.p.a.49.5	✓	108
5.4	even	2	inner	810.2.p.a.199.1		108
15.14	odd	2		270.2.p.a.49.14	yes	108
27.11	odd	18		270.2.p.a.259.14	yes	108
27.16	even	9	inner	810.2.p.a.289.1		108
135.119	odd	18		270.2.p.a.259.5	yes	108
135.124	even	18	inner	810.2.p.a.289.10		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.p.a.49.5	✓	108	3.2	odd	2
270.2.p.a.49.14	yes	108	15.14	odd	2
270.2.p.a.259.5	yes	108	135.119	odd	18
270.2.p.a.259.14	yes	108	27.11	odd	18
810.2.p.a.199.1		108	5.4	even	2	inner
810.2.p.a.199.10		108	1.1	even	1	trivial
810.2.p.a.289.1		108	27.16	even	9	inner
810.2.p.a.289.10		108	135.124	even	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.p (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(-1.90411 + 1.17233i) q^{5} +(0.531122 - 0.0936511i) q^{7} +(-0.866025 + 0.500000i) q^{8} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(-1.90411 + 1.17233i) q^{5} +(0.531122 - 0.0936511i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.12200 - 0.705079i) q^{10} +(-3.82525 - 1.39228i) q^{11} +(-1.58330 + 1.88690i) q^{13} +(0.413139 + 0.346665i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-3.71596 - 2.14541i) q^{17} +(1.08914 + 1.88645i) q^{19} +(-0.823871 - 2.07876i) q^{20} +(-1.39228 - 3.82525i) q^{22} +(-4.39867 - 0.775604i) q^{23} +(2.25130 - 4.46449i) q^{25} -2.46317 q^{26} +0.539315i q^{28} +(0.558330 - 0.468495i) q^{29} +(-1.28782 + 7.30358i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-0.745092 - 4.22563i) q^{34} +(-0.901527 + 0.800971i) q^{35} +(-6.45946 - 3.72937i) q^{37} +(-0.745018 + 2.04692i) q^{38} +(1.06285 - 1.96732i) q^{40} +(5.82235 + 4.88553i) q^{41} +(2.73291 - 7.50862i) q^{43} +(2.03537 - 3.52537i) q^{44} +(-2.23326 - 3.86812i) q^{46} +(-9.13513 + 1.61077i) q^{47} +(-6.30453 + 2.29466i) q^{49} +(4.86710 - 1.14512i) q^{50} +(-1.58330 - 1.88690i) q^{52} -0.116236i q^{53} +(8.91592 - 1.83339i) q^{55} +(-0.413139 + 0.346665i) q^{56} +(0.717776 + 0.126563i) q^{58} +(10.2609 - 3.73464i) q^{59} +(-1.35199 - 7.66749i) q^{61} +(-6.42266 + 3.70813i) q^{62} +(0.500000 - 0.866025i) q^{64} +(0.802714 - 5.44902i) q^{65} +(-6.14767 + 7.32650i) q^{67} +(2.75808 - 3.28696i) q^{68} +(-1.19307 - 0.175755i) q^{70} +(-6.98968 + 12.1065i) q^{71} +(-2.27739 + 1.31485i) q^{73} +(-1.29520 - 7.34543i) q^{74} +(-2.04692 + 0.745018i) q^{76} +(-2.16206 - 0.381230i) q^{77} +(-4.10029 + 3.44055i) q^{79} +(2.19024 - 0.450382i) q^{80} +7.60054i q^{82} +(9.14477 + 10.8983i) q^{83} +(9.59072 - 0.271214i) q^{85} +(7.50862 - 2.73291i) q^{86} +(4.00891 - 0.706878i) q^{88} +(4.79299 + 8.30170i) q^{89} +(-0.664214 + 1.15045i) q^{91} +(1.52764 - 4.19716i) q^{92} +(-7.10587 - 5.96254i) q^{94} +(-4.28539 - 2.31519i) q^{95} +(-0.646954 + 1.77749i) q^{97} +(-5.81028 - 3.35457i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{5}+O(q^{10}) \) 108 * q - 6 * q^5	\( 108 q - 6 q^{5} + 12 q^{11} - 6 q^{14} - 12 q^{20} - 18 q^{25} + 72 q^{26} - 6 q^{29} + 36 q^{31} - 18 q^{35} + 12 q^{41} + 12 q^{44} + 18 q^{49} + 12 q^{50} + 6 q^{56} + 84 q^{59} - 18 q^{61} + 54 q^{64} + 6 q^{65} + 48 q^{74} - 72 q^{79} + 36 q^{86} + 132 q^{89} - 36 q^{94} + 18 q^{95}+O(q^{100}) \) 108 * q - 6 * q^5 + 12 * q^11 - 6 * q^14 - 12 * q^20 - 18 * q^25 + 72 * q^26 - 6 * q^29 + 36 * q^31 - 18 * q^35 + 12 * q^41 + 12 * q^44 + 18 * q^49 + 12 * q^50 + 6 * q^56 + 84 * q^59 - 18 * q^61 + 54 * q^64 + 6 * q^65 + 48 * q^74 - 72 * q^79 + 36 * q^86 + 132 * q^89 - 36 * q^94 + 18 * q^95

Introduction

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