LMFDB - Embedded newform 729.2.e.p.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.101559956668416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{6} + 64 $ x^12 - 8*x^6 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			163.1
Root			$-0.909039 + 1.08335i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.p.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30177 + 0.837775i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-0.425349 - 2.41228i) q^{5} +(1.53209 + 1.28558i) q^{7} +(-2.44949 + 4.24264i) q^{8} +O(q^{10})$	\(q+(-2.30177 + 0.837775i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-0.425349 - 2.41228i) q^{5} +(1.53209 + 1.28558i) q^{7} +(-2.44949 + 4.24264i) q^{8} +(3.00000 + 5.19615i) q^{10} +(0.425349 - 2.41228i) q^{11} +(0.939693 + 0.342020i) q^{13} +(-4.60353 - 1.67555i) q^{14} +(0.694593 - 3.93923i) q^{16} +(3.67423 + 6.36396i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-7.50567 - 6.29801i) q^{20} +(1.04189 + 5.90885i) q^{22} +(-1.87642 + 1.57450i) q^{23} +(-0.939693 + 0.342020i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(4.60353 - 1.67555i) q^{29} +(-0.766044 + 0.642788i) q^{31} +(-13.7888 - 11.5702i) q^{34} +(2.44949 - 4.24264i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(-0.425349 + 2.41228i) q^{38} +(11.2763 + 4.10424i) q^{40} +(-4.60353 - 1.67555i) q^{41} +(1.91013 - 10.8329i) q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.00000 - 5.19615i) q^{46} +(7.50567 + 6.29801i) q^{47} +(-0.520945 - 2.95442i) q^{49} +(1.87642 - 1.57450i) q^{50} +(3.75877 - 1.36808i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(-9.20707 + 3.35110i) q^{56} +(-9.19253 + 7.71345i) q^{58} +(-0.425349 - 2.41228i) q^{59} +(3.83022 + 3.21394i) q^{61} +(1.22474 - 2.12132i) q^{62} +(4.00000 + 6.92820i) q^{64} +(0.425349 - 2.41228i) q^{65} +(6.57785 + 2.39414i) q^{67} +(27.6212 + 10.0533i) q^{68} +(-2.08378 + 11.8177i) q^{70} +(-3.67423 - 6.36396i) q^{71} +(-5.50000 + 9.52628i) q^{73} +(15.0113 + 12.5960i) q^{74} +(-0.694593 - 3.93923i) q^{76} +(3.75284 - 3.14900i) q^{77} +(6.57785 - 2.39414i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(11.5088 - 4.18887i) q^{83} +(13.7888 - 11.5702i) q^{85} +(4.67884 + 26.5350i) q^{86} +(9.19253 + 7.71345i) q^{88} +(1.00000 + 1.73205i) q^{91} +(-1.70140 + 9.64911i) q^{92} +(-22.5526 - 8.20848i) q^{94} +(-2.30177 - 0.837775i) q^{95} +(-1.21554 + 6.89365i) q^{97} +(3.67423 + 6.36396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 36 q^{10} + 6 q^{19} + 96 q^{28} - 48 q^{37} + 36 q^{46} - 72 q^{55} + 48 q^{64} - 66 q^{73} + 144 q^{82} + 12 q^{91}+O(q^{100}) $ 12 * q + 36 * q^10 + 6 * q^19 + 96 * q^28 - 48 * q^37 + 36 * q^46 - 72 * q^55 + 48 * q^64 - 66 * q^73 + 144 * q^82 + 12 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.30177	+	0.837775i	−1.62760	+	0.592396i	−0.984808	−	0.173648i	$-0.944444\pi$
$2$	−2.30177	+	0.837775i	−1.62760	+	0.592396i	−0.642788	+	0.766044i	$0.722222\pi$
$3$		0			0
$3$		0			0
$4$	3.06418	−	2.57115i	1.53209	−	1.28558i
$5$	−0.425349	−	2.41228i	−0.190222	−	1.07880i	−0.919060	−	0.394117i	$-0.871050\pi$
$5$	−0.425349	−	2.41228i	−0.190222	−	1.07880i	0.728838	−	0.684686i	$-0.240061\pi$
$6$		0			0
$7$	1.53209	+	1.28558i	0.579075	+	0.485902i	0.884643	−	0.466268i	$-0.154402\pi$
$7$	1.53209	+	1.28558i	0.579075	+	0.485902i	−0.305568	+	0.952170i	$0.598846\pi$
$8$	−2.44949	+	4.24264i	−0.866025	+	1.50000i
$9$		0			0
$10$	3.00000	+	5.19615i	0.948683	+	1.64317i
$11$	0.425349	−	2.41228i	0.128248	−	0.727329i	−0.851078	−	0.525039i	$-0.824051\pi$
$11$	0.425349	−	2.41228i	0.128248	−	0.727329i	0.979326	−	0.202290i	$-0.0648382\pi$
$12$		0			0
$13$	0.939693	+	0.342020i	0.260624	+	0.0948593i	0.469027	−	0.883184i	$-0.344605\pi$
$13$	0.939693	+	0.342020i	0.260624	+	0.0948593i	−0.208404	+	0.978043i	$0.566827\pi$
$14$	−4.60353	−	1.67555i	−1.23035	−	0.447809i
$15$		0			0
$16$	0.694593	−	3.93923i	0.173648	−	0.984808i
$17$	3.67423	+	6.36396i	0.891133	+	1.54349i	0.838519	+	0.544872i	$0.183422\pi$
$17$	3.67423	+	6.36396i	0.891133	+	1.54349i	0.0526138	+	0.998615i	$0.483245\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	−7.50567	−	6.29801i	−1.67832	−	1.40828i
$21$		0			0
$22$	1.04189	+	5.90885i	0.222131	+	1.25977i
$23$	−1.87642	+	1.57450i	−0.391260	+	0.328306i	−0.817104	−	0.576490i	$-0.804422\pi$
$23$	−1.87642	+	1.57450i	−0.391260	+	0.328306i	0.425844	+	0.904797i	$0.359977\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−2.44949			−0.480384
$27$		0			0
$28$	8.00000			1.51186
$29$	4.60353	−	1.67555i	0.854855	−	0.311142i	0.122837	−	0.992427i	$-0.460801\pi$
$29$	4.60353	−	1.67555i	0.854855	−	0.311142i	0.732018	+	0.681285i	$0.238579\pi$
$30$		0			0
$31$	−0.766044	+	0.642788i	−0.137586	+	0.115448i	−0.708983	−	0.705225i	$-0.750846\pi$
$31$	−0.766044	+	0.642788i	−0.137586	+	0.115448i	0.571398	+	0.820673i	$0.306401\pi$
$32$		0			0
$33$		0			0
$34$	−13.7888	−	11.5702i	−2.36476	−	1.98427i
$35$	2.44949	−	4.24264i	0.414039	−	0.717137i
$36$		0			0
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	−0.425349	+	2.41228i	−0.0690008	+	0.391323i
$39$		0			0
$40$	11.2763	+	4.10424i	1.78294	+	0.648938i
$41$	−4.60353	−	1.67555i	−0.718951	−	0.261677i	−0.0434708	−	0.999055i	$-0.513842\pi$
$41$	−4.60353	−	1.67555i	−0.718951	−	0.261677i	−0.675481	+	0.737378i	$0.736064\pi$
$42$		0			0
$43$	1.91013	−	10.8329i	0.291292	−	1.65200i	−0.390610	−	0.920556i	$-0.627736\pi$
$43$	1.91013	−	10.8329i	0.291292	−	1.65200i	0.681902	−	0.731443i	$-0.261153\pi$
$44$	−4.89898	−	8.48528i	−0.738549	−	1.27920i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	7.50567	+	6.29801i	1.09481	+	0.918659i	0.997066	−	0.0765524i	$-0.0243912\pi$
$47$	7.50567	+	6.29801i	1.09481	+	0.918659i	0.0977492	+	0.995211i	$0.468836\pi$
$48$		0			0
$49$	−0.520945	−	2.95442i	−0.0744206	−	0.422060i
$50$	1.87642	−	1.57450i	0.265366	−	0.222668i
$51$		0			0
$52$	3.75877	−	1.36808i	0.521248	−	0.189719i
$53$	7.34847			1.00939			0.504695	−	0.863298i	$-0.331605\pi$
$53$	7.34847			1.00939			0.504695	+	0.863298i	$0.331605\pi$
$54$		0			0
$55$	−6.00000			−0.809040
$56$	−9.20707	+	3.35110i	−1.23035	+	0.447809i
$57$		0			0
$58$	−9.19253	+	7.71345i	−1.20704	+	1.01283i
$59$	−0.425349	−	2.41228i	−0.0553758	−	0.314052i	0.944521	−	0.328452i	$-0.106527\pi$
$59$	−0.425349	−	2.41228i	−0.0553758	−	0.314052i	−0.999896	+	0.0144007i	$0.995416\pi$
$60$		0			0
$61$	3.83022	+	3.21394i	0.490410	+	0.411503i	0.854173	−	0.519989i	$-0.174064\pi$
$61$	3.83022	+	3.21394i	0.490410	+	0.411503i	−0.363763	+	0.931491i	$0.618508\pi$
$62$	1.22474	−	2.12132i	0.155543	−	0.269408i
$63$		0			0
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	0.425349	−	2.41228i	0.0527581	−	0.299206i
$66$		0			0
$67$	6.57785	+	2.39414i	0.803612	+	0.292491i	0.710982	−	0.703210i	$-0.248251\pi$
$67$	6.57785	+	2.39414i	0.803612	+	0.292491i	0.0926296	+	0.995701i	$0.470473\pi$
$68$	27.6212	+	10.0533i	3.34956	+	1.21914i
$69$		0			0
$70$	−2.08378	+	11.8177i	−0.249059	+	1.41248i
$71$	−3.67423	−	6.36396i	−0.436051	−	0.755263i	0.561329	−	0.827592i	$-0.310290\pi$
$71$	−3.67423	−	6.36396i	−0.436051	−	0.755263i	−0.997381	+	0.0723293i	$0.976957\pi$
$72$		0			0
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$	15.0113	+	12.5960i	1.74503	+	1.46426i
$75$		0			0
$76$	−0.694593	−	3.93923i	−0.0796752	−	0.451861i
$77$	3.75284	−	3.14900i	0.427675	−	0.358862i
$78$		0			0
$79$	6.57785	−	2.39414i	0.740066	−	0.269362i	0.0556465	−	0.998451i	$-0.482278\pi$
$79$	6.57785	−	2.39414i	0.740066	−	0.269362i	0.684419	+	0.729089i	$0.260056\pi$
$80$	−9.79796			−1.09545
$81$		0			0
$82$	12.0000			1.32518
$83$	11.5088	−	4.18887i	1.26326	−	0.459789i	0.378398	−	0.925643i	$-0.376475\pi$
$83$	11.5088	−	4.18887i	1.26326	−	0.459789i	0.884861	+	0.465854i	$0.154253\pi$
$84$		0			0
$85$	13.7888	−	11.5702i	1.49561	−	1.25496i
$86$	4.67884	+	26.5350i	0.504533	+	2.86135i
$87$		0			0
$88$	9.19253	+	7.71345i	0.979927	+	0.822257i
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−1.70140	+	9.64911i	−0.177383	+	1.00599i
$93$		0			0
$94$	−22.5526	−	8.20848i	−2.32613	−	0.846640i
$95$	−2.30177	−	0.837775i	−0.236156	−	0.0859539i
$96$		0			0
$97$	−1.21554	+	6.89365i	−0.123419	+	0.699945i	0.858815	+	0.512286i	$0.171201\pi$
$97$	−1.21554	+	6.89365i	−0.123419	+	0.699945i	−0.982234	+	0.187659i	$0.939910\pi$
$98$	3.67423	+	6.36396i	0.371154	+	0.642857i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−3.75284	−	3.14900i	−0.373421	−	0.313338i	0.436692	−	0.899611i	$-0.356150\pi$
$101$	−3.75284	−	3.14900i	−0.373421	−	0.313338i	−0.810113	+	0.586274i	$0.800594\pi$
$102$		0			0
$103$	−1.21554	−	6.89365i	−0.119770	−	0.679252i	−0.984277	−	0.176631i	$-0.943480\pi$
$103$	−1.21554	−	6.89365i	−0.119770	−	0.679252i	0.864507	−	0.502621i	$-0.167631\pi$
$104$	−3.75284	+	3.14900i	−0.367996	+	0.308785i
$105$		0			0
$106$	−16.9145	+	6.15636i	−1.64288	+	0.597959i
$107$	14.6969			1.42081			0.710403	−	0.703795i	$-0.248513\pi$
$107$	14.6969			1.42081			0.710403	+	0.703795i	$0.248513\pi$
$108$		0			0
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$	13.8106	−	5.02665i	1.31679	−	0.479272i
$111$		0			0
$112$	6.12836	−	5.14230i	0.579075	−	0.485902i
$113$	−1.70140	−	9.64911i	−0.160054	−	0.907712i	−0.954019	−	0.299747i	$-0.903098\pi$
$113$	−1.70140	−	9.64911i	−0.160054	−	0.907712i	0.793965	−	0.607964i	$-0.208014\pi$
$114$		0			0
$115$	4.59627	+	3.85673i	0.428604	+	0.359642i
$116$	9.79796	−	16.9706i	0.909718	−	1.57568i
$117$		0			0
$118$	3.00000	+	5.19615i	0.276172	+	0.478345i
$119$	−2.55210	+	14.4737i	−0.233950	+	1.32680i
$120$		0			0
$121$	4.69846	+	1.71010i	0.427133	+	0.155464i
$122$	−11.5088	−	4.18887i	−1.04196	−	0.379243i
$123$		0			0
$124$	−0.694593	+	3.93923i	−0.0623763	+	0.353753i
$125$	−4.89898	−	8.48528i	−0.438178	−	0.758947i
$126$		0			0
$127$	9.50000	−	16.4545i	0.842989	−	1.46010i	−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	9.50000	−	16.4545i	0.842989	−	1.46010i	0.887357	−	0.461084i	$-0.152539\pi$
$128$	−15.0113	−	12.5960i	−1.32683	−	1.11334i
$129$		0			0
$130$	1.04189	+	5.90885i	0.0913797	+	0.518240i
$131$	9.38209	−	7.87251i	0.819717	−	0.687824i	−0.133189	−	0.991091i	$-0.542522\pi$
$131$	9.38209	−	7.87251i	0.819717	−	0.687824i	0.952906	+	0.303266i	$0.0980772\pi$
$132$		0			0
$133$	1.87939	−	0.684040i	0.162963	−	0.0593138i
$134$	−17.1464			−1.48123
$135$		0			0
$136$	−36.0000			−3.08697
$137$	−9.20707	+	3.35110i	−0.786613	+	0.286304i	−0.703927	−	0.710272i	$-0.748572\pi$
$137$	−9.20707	+	3.35110i	−0.786613	+	0.286304i	−0.0826857	+	0.996576i	$0.526350\pi$
$138$		0			0
$139$	−7.66044	+	6.42788i	−0.649750	+	0.545205i	−0.906995	−	0.421141i	$-0.861630\pi$
$139$	−7.66044	+	6.42788i	−0.649750	+	0.545205i	0.257245	+	0.966346i	$0.417185\pi$
$140$	−3.40280	−	19.2982i	−0.287589	−	1.63100i
$141$		0			0
$142$	13.7888	+	11.5702i	1.15713	+	0.970948i
$143$	1.22474	−	2.12132i	0.102418	−	0.177394i
$144$		0			0
$145$	−6.00000	−	10.3923i	−0.498273	−	0.863034i
$146$	4.67884	−	26.5350i	0.387224	−	2.19606i
$147$		0			0
$148$	−30.0702	−	10.9446i	−2.47175	−	0.899644i
$149$	−11.5088	−	4.18887i	−0.942841	−	0.343166i	−0.175554	−	0.984470i	$-0.556172\pi$
$149$	−11.5088	−	4.18887i	−0.942841	−	0.343166i	−0.767287	+	0.641304i	$0.778394\pi$
$150$		0			0
$151$	0.868241	−	4.92404i	0.0706564	−	0.400713i	−0.928883	−	0.370373i	$-0.879230\pi$
$151$	0.868241	−	4.92404i	0.0706564	−	0.400713i	0.999540	−	0.0303398i	$-0.00965894\pi$
$152$	2.44949	+	4.24264i	0.198680	+	0.344124i
$153$		0			0
$154$	−6.00000	+	10.3923i	−0.483494	+	0.837436i
$155$	1.87642	+	1.57450i	0.150718	+	0.126467i
$156$		0			0
$157$	2.95202	+	16.7417i	0.235597	+	1.33614i	0.841353	+	0.540486i	$0.181759\pi$
$157$	2.95202	+	16.7417i	0.235597	+	1.33614i	−0.605757	+	0.795650i	$0.707129\pi$
$158$	−13.1349	+	11.0215i	−1.04496	+	0.876824i
$159$		0			0
$160$		0			0
$161$	−4.89898			−0.386094
$162$		0			0
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	−18.4141	+	6.70220i	−1.43790	+	0.523354i
$165$		0			0
$166$	−22.9813	+	19.2836i	−1.78370	+	1.49670i
$167$	0.850699	+	4.82455i	0.0658291	+	0.373335i	0.999869	+	0.0161673i	$0.00514645\pi$
$167$	0.850699	+	4.82455i	0.0658291	+	0.373335i	−0.934040	+	0.357168i	$0.883742\pi$
$168$		0			0
$169$	−9.19253	−	7.71345i	−0.707118	−	0.593342i
$170$	−22.0454	+	38.1838i	−1.69081	+	2.92856i
$171$		0			0
$172$	−22.0000	−	38.1051i	−1.67748	−	2.90549i
$173$	1.70140	−	9.64911i	0.129355	−	0.733608i	−0.849271	−	0.527958i	$-0.822958\pi$
$173$	1.70140	−	9.64911i	0.129355	−	0.733608i	0.978626	−	0.205650i	$-0.0659309\pi$
$174$		0			0
$175$	−1.87939	−	0.684040i	−0.142068	−	0.0517086i
$176$	−9.20707	−	3.35110i	−0.694009	−	0.252599i
$177$		0			0
$178$		0			0
$179$	7.34847	+	12.7279i	0.549250	+	0.951330i	0.998326	+	0.0578359i	$0.0184200\pi$
$179$	7.34847	+	12.7279i	0.549250	+	0.951330i	−0.449076	+	0.893494i	$0.648247\pi$
$180$		0			0
$181$	−4.00000	+	6.92820i	−0.297318	+	0.514969i	−0.975521	−	0.219905i	$-0.929425\pi$
$181$	−4.00000	+	6.92820i	−0.297318	+	0.514969i	0.678204	+	0.734874i	$0.262759\pi$
$182$	−3.75284	−	3.14900i	−0.278179	−	0.233420i
$183$		0			0
$184$	−2.08378	−	11.8177i	−0.153618	−	0.871212i
$185$	−15.0113	+	12.5960i	−1.10366	+	0.926077i
$186$		0			0
$187$	16.9145	−	6.15636i	1.23691	−	0.450198i
$188$	39.1918			2.85836
$189$		0			0
$190$	6.00000			0.435286
$191$	−9.20707	+	3.35110i	−0.666200	+	0.242477i	−0.652911	−	0.757435i	$-0.726452\pi$
$191$	−9.20707	+	3.35110i	−0.666200	+	0.242477i	−0.0132892	+	0.999912i	$0.504230\pi$
$192$		0			0
$193$	8.42649	−	7.07066i	0.606552	−	0.508958i	−0.286992	−	0.957933i	$-0.592655\pi$
$193$	8.42649	−	7.07066i	0.606552	−	0.508958i	0.893544	+	0.448975i	$0.148211\pi$
$194$	−2.97745	−	16.8859i	−0.213768	−	1.21234i
$195$		0			0
$196$	−9.19253	−	7.71345i	−0.656610	−	0.550961i
$197$	−7.34847	+	12.7279i	−0.523557	+	0.906827i	0.476067	+	0.879409i	$0.342062\pi$
$197$	−7.34847	+	12.7279i	−0.523557	+	0.906827i	−0.999624	+	0.0274180i	$0.991271\pi$
$198$		0			0
$199$	0.500000	+	0.866025i	0.0354441	+	0.0613909i	0.883203	−	0.468990i	$-0.155382\pi$
$199$	0.500000	+	0.866025i	0.0354441	+	0.0613909i	−0.847759	+	0.530381i	$0.822049\pi$
$200$	0.850699	−	4.82455i	0.0601535	−	0.341147i
$201$		0			0
$202$	11.2763	+	4.10424i	0.793399	+	0.288773i
$203$	9.20707	+	3.35110i	0.646210	+	0.235201i
$204$		0			0
$205$	−2.08378	+	11.8177i	−0.145537	+	0.825383i
$206$	8.57321	+	14.8492i	0.597324	+	1.03460i
$207$		0			0
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$	−1.87642	−	1.57450i	−0.129795	−	0.108911i
$210$		0			0
$211$	−0.173648	−	0.984808i	−0.0119544	−	0.0677970i	0.978247	−	0.207444i	$-0.0665144\pi$
$211$	−0.173648	−	0.984808i	−0.0119544	−	0.0677970i	−0.990201	+	0.139647i	$0.955403\pi$
$212$	22.5170	−	18.8940i	1.54648	−	1.29765i
$213$		0			0
$214$	−33.8289	+	12.3127i	−2.31250	+	0.841681i
$215$	−26.9444			−1.83759
$216$		0			0
$217$	−2.00000			−0.135769
$218$	2.30177	−	0.837775i	0.155895	−	0.0567413i
$219$		0			0
$220$	−18.3851	+	15.4269i	−1.23952	+	1.04008i
$221$	1.27605	+	7.23683i	0.0858363	+	0.486802i
$222$		0			0
$223$	−5.36231	−	4.49951i	−0.359087	−	0.301310i	0.445340	−	0.895362i	$-0.353083\pi$
$223$	−5.36231	−	4.49951i	−0.359087	−	0.301310i	−0.804427	+	0.594052i	$0.797527\pi$
$224$		0			0
$225$		0			0
$226$	12.0000	+	20.7846i	0.798228	+	1.38257i
$227$	1.70140	−	9.64911i	0.112926	−	0.640434i	−0.874831	−	0.484429i	$-0.839027\pi$
$227$	1.70140	−	9.64911i	0.112926	−	0.640434i	0.987756	−	0.156005i	$-0.0498615\pi$
$228$		0			0
$229$	0.939693	+	0.342020i	0.0620966	+	0.0226013i	0.372882	−	0.927879i	$-0.378370\pi$
$229$	0.939693	+	0.342020i	0.0620966	+	0.0226013i	−0.310785	+	0.950480i	$0.600592\pi$
$230$	−13.8106	−	5.02665i	−0.910644	−	0.331447i
$231$		0			0
$232$	−4.16756	+	23.6354i	−0.273613	+	1.55174i
$233$	3.67423	+	6.36396i	0.240707	+	0.416917i	0.960916	−	0.276840i	$-0.0892873\pi$
$233$	3.67423	+	6.36396i	0.240707	+	0.416917i	−0.720209	+	0.693757i	$0.755954\pi$
$234$		0			0
$235$	12.0000	−	20.7846i	0.782794	−	1.35584i
$236$	−7.50567	−	6.29801i	−0.488578	−	0.409965i
$237$		0			0
$238$	−6.25133	−	35.4531i	−0.405214	−	2.29808i
$239$	−1.87642	+	1.57450i	−0.121375	+	0.101846i	−0.701455	−	0.712714i	$-0.747466\pi$
$239$	−1.87642	+	1.57450i	−0.121375	+	0.101846i	0.580080	+	0.814560i	$0.303021\pi$
$240$		0			0
$241$	15.0351	−	5.47232i	0.968495	−	0.352503i	0.191138	−	0.981563i	$-0.438782\pi$
$241$	15.0351	−	5.47232i	0.968495	−	0.352503i	0.777357	+	0.629060i	$0.216560\pi$
$242$	−12.2474			−0.787296
$243$		0			0
$244$	20.0000			1.28037
$245$	−6.90530	+	2.51332i	−0.441164	+	0.160570i
$246$		0			0
$247$	0.766044	−	0.642788i	0.0487422	−	0.0408996i
$248$	−0.850699	−	4.82455i	−0.0540194	−	0.306359i
$249$		0			0
$250$	18.3851	+	15.4269i	1.16277	+	0.975683i
$251$	3.67423	−	6.36396i	0.231916	−	0.401690i	−0.726456	−	0.687213i	$-0.758834\pi$
$251$	3.67423	−	6.36396i	0.231916	−	0.401690i	0.958372	+	0.285523i	$0.0921673\pi$
$252$		0			0
$253$	3.00000	+	5.19615i	0.188608	+	0.326679i
$254$	−8.08164	+	45.8333i	−0.507087	+	2.87583i
$255$		0			0
$256$	30.0702	+	10.9446i	1.87939	+	0.684040i
$257$	16.1124	+	5.86442i	1.00506	+	0.365813i	0.791535	−	0.611124i	$-0.209282\pi$
$257$	16.1124	+	5.86442i	1.00506	+	0.365813i	0.213528	+	0.976937i	$0.431505\pi$
$258$		0			0
$259$	2.77837	−	15.7569i	0.172640	−	0.979088i
$260$	−4.89898	−	8.48528i	−0.303822	−	0.526235i
$261$		0			0
$262$	−15.0000	+	25.9808i	−0.926703	+	1.60510i
$263$	−20.6406	−	17.3195i	−1.27275	−	1.06797i	−0.994200	−	0.107547i	$-0.965701\pi$
$263$	−20.6406	−	17.3195i	−1.27275	−	1.06797i	−0.278554	−	0.960421i	$-0.589855\pi$
$264$		0			0
$265$	−3.12567	−	17.7265i	−0.192008	−	1.08893i
$266$	−3.75284	+	3.14900i	−0.230101	+	0.193078i
$267$		0			0
$268$	26.3114	−	9.57656i	1.60722	−	0.584982i
$269$	−22.0454			−1.34413			−0.672066	−	0.740491i	$-0.734593\pi$
$269$	−22.0454			−1.34413			−0.672066	+	0.740491i	$0.734593\pi$
$270$		0			0
$271$	−7.00000			−0.425220			−0.212610	−	0.977137i	$-0.568196\pi$
$271$	−7.00000			−0.425220			−0.212610	+	0.977137i	$0.568196\pi$
$272$	27.6212	−	10.0533i	1.67478	−	0.609571i
$273$		0			0
$274$	18.3851	−	15.4269i	1.11068	−	0.931973i
$275$	0.425349	+	2.41228i	0.0256495	+	0.145466i
$276$		0			0
$277$	8.42649	+	7.07066i	0.506299	+	0.424835i	0.859824	−	0.510590i	$-0.170573\pi$
$277$	8.42649	+	7.07066i	0.506299	+	0.424835i	−0.353526	+	0.935425i	$0.615017\pi$
$278$	12.2474	−	21.2132i	0.734553	−	1.27228i
$279$		0			0
$280$	12.0000	+	20.7846i	0.717137	+	1.24212i
$281$	−2.12675	+	12.0614i	−0.126871	+	0.719522i	0.853308	+	0.521407i	$0.174593\pi$
$281$	−2.12675	+	12.0614i	−0.126871	+	0.719522i	−0.980179	+	0.198114i	$0.936518\pi$
$282$		0			0
$283$	−15.9748	−	5.81434i	−0.949602	−	0.345627i	−0.179651	−	0.983730i	$-0.557497\pi$
$283$	−15.9748	−	5.81434i	−0.949602	−	0.345627i	−0.769951	+	0.638104i	$0.779719\pi$
$284$	−27.6212	−	10.0533i	−1.63902	−	0.596553i
$285$		0			0
$286$	−1.04189	+	5.90885i	−0.0616082	+	0.349397i
$287$	−4.89898	−	8.48528i	−0.289178	−	0.500870i
$288$		0			0
$289$	−18.5000	+	32.0429i	−1.08824	+	1.88488i
$290$	22.5170	+	18.8940i	1.32224	+	1.10950i
$291$		0			0
$292$	7.64052	+	43.3315i	0.447128	+	2.53579i
$293$	3.75284	−	3.14900i	0.219243	−	0.183967i	−0.526551	−	0.850144i	$-0.676515\pi$
$293$	3.75284	−	3.14900i	0.219243	−	0.183967i	0.745794	+	0.666177i	$0.232070\pi$
$294$		0			0
$295$	−5.63816	+	2.05212i	−0.328266	+	0.119479i
$296$	39.1918			2.27798
$297$		0			0
$298$	30.0000			1.73785
$299$	−2.30177	+	0.837775i	−0.133115	+	0.0484498i
$300$		0			0
$301$	16.8530	−	14.1413i	0.971389	−	0.815093i
$302$	2.12675	+	12.0614i	0.122381	+	0.694055i
$303$		0			0
$304$	−3.06418	−	2.57115i	−0.175743	−	0.147466i
$305$	6.12372	−	10.6066i	0.350643	−	0.607332i
$306$		0			0
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	0.836077	−	0.548612i	$-0.184843\pi$
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	−0.893150	+	0.449758i	$0.851510\pi$
$308$	3.40280	−	19.2982i	0.193892	−	1.09962i
$309$		0			0
$310$	−5.63816	−	2.05212i	−0.320226	−	0.116553i
$311$	23.0177	+	8.37775i	1.30521	+	0.475059i	0.898691	−	0.438583i	$-0.144519\pi$
$311$	23.0177	+	8.37775i	1.30521	+	0.475059i	0.406522	+	0.913641i	$0.366742\pi$
$312$		0			0
$313$	−2.77837	+	15.7569i	−0.157043	+	0.890634i	0.799852	+	0.600198i	$0.204911\pi$
$313$	−2.77837	+	15.7569i	−0.157043	+	0.890634i	−0.956894	+	0.290436i	$0.906200\pi$
$314$	−20.8207	−	36.0624i	−1.17498	−	2.03512i
$315$		0			0
$316$	14.0000	−	24.2487i	0.787562	−	1.36410i
$317$	7.50567	+	6.29801i	0.421561	+	0.353731i	0.828756	−	0.559610i	$-0.189049\pi$
$317$	7.50567	+	6.29801i	0.421561	+	0.353731i	−0.407196	+	0.913341i	$0.633493\pi$
$318$		0			0
$319$	−2.08378	−	11.8177i	−0.116669	−	0.661664i
$320$	15.0113	−	12.5960i	0.839160	−	0.704139i
$321$		0			0
$322$	11.2763	−	4.10424i	0.628404	−	0.228720i
$323$	7.34847			0.408880
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	23.0177	−	8.37775i	1.27483	−	0.464001i
$327$		0			0
$328$	18.3851	−	15.4269i	1.01515	−	0.851808i
$329$	3.40280	+	19.2982i	0.187602	+	1.06394i
$330$		0			0
$331$	−5.36231	−	4.49951i	−0.294739	−	0.247316i	0.483411	−	0.875393i	$-0.339398\pi$
$331$	−5.36231	−	4.49951i	−0.294739	−	0.247316i	−0.778151	+	0.628078i	$0.783842\pi$
$332$	24.4949	−	42.4264i	1.34433	−	2.32845i
$333$		0			0
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	2.97745	−	16.8859i	0.162675	−	0.922577i
$336$		0			0
$337$	26.3114	+	9.57656i	1.43327	+	0.521669i	0.937868	−	0.346993i	$-0.112797\pi$
$337$	26.3114	+	9.57656i	1.43327	+	0.521669i	0.495405	+	0.868662i	$0.335020\pi$
$338$	27.6212	+	10.0533i	1.50240	+	0.546827i
$339$		0			0
$340$	12.5027	−	70.9062i	0.678052	−	3.84543i
$341$	1.22474	+	2.12132i	0.0663237	+	0.114876i
$342$		0			0
$343$	10.0000	−	17.3205i	0.539949	−	0.935220i
$344$	41.2812	+	34.6390i	2.22573	+	1.86761i
$345$		0			0
$346$	4.16756	+	23.6354i	0.224049	+	1.27065i
$347$	−18.7642	+	15.7450i	−1.00731	+	0.845237i	−0.987981	−	0.154576i	$-0.950599\pi$
$347$	−18.7642	+	15.7450i	−1.00731	+	0.845237i	−0.0193331	+	0.999813i	$0.506154\pi$
$348$		0			0
$349$	−18.7939	+	6.84040i	−1.00601	+	0.366158i	−0.791900	−	0.610651i	$-0.790908\pi$
$349$	−18.7939	+	6.84040i	−1.00601	+	0.366158i	−0.214112	+	0.976809i	$0.568686\pi$
$350$	4.89898			0.261861
$351$		0			0
$352$		0			0
$353$	−2.30177	+	0.837775i	−0.122511	+	0.0445903i	−0.402548	−	0.915399i	$-0.631875\pi$
$353$	−2.30177	+	0.837775i	−0.122511	+	0.0445903i	0.280037	+	0.959989i	$0.409653\pi$
$354$		0			0
$355$	−13.7888	+	11.5702i	−0.731834	+	0.614081i
$356$		0			0
$357$		0			0
$358$	−27.5776	−	23.1404i	−1.45752	−	1.22301i
$359$	−14.6969	+	25.4558i	−0.775675	+	1.34351i	0.158740	+	0.987320i	$0.449257\pi$
$359$	−14.6969	+	25.4558i	−0.775675	+	1.34351i	−0.934414	+	0.356188i	$0.884076\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	3.40280	−	19.2982i	0.178847	−	1.01429i
$363$		0			0
$364$	7.51754	+	2.73616i	0.394026	+	0.143414i
$365$	25.3194	+	9.21552i	1.32528	+	0.482363i
$366$		0			0
$367$	0.868241	−	4.92404i	0.0453218	−	0.257033i	−0.953725	−	0.300680i	$-0.902787\pi$
$367$	0.868241	−	4.92404i	0.0453218	−	0.257033i	0.999047	+	0.0436469i	$0.0138976\pi$
$368$	4.89898	+	8.48528i	0.255377	+	0.442326i
$369$		0			0
$370$	24.0000	−	41.5692i	1.24770	−	2.16108i
$371$	11.2585	+	9.44701i	0.584513	+	0.490464i
$372$		0			0
$373$	6.07769	+	34.4683i	0.314691	+	1.78470i	0.573949	+	0.818891i	$0.305411\pi$
$373$	6.07769	+	34.4683i	0.314691	+	1.78470i	−0.259258	+	0.965808i	$0.583478\pi$
$374$	−33.7755	+	28.3410i	−1.74649	+	1.46548i
$375$		0			0
$376$	−45.1052	+	16.4170i	−2.32613	+	0.846640i
$377$	4.89898			0.252310
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	−9.20707	+	3.35110i	−0.472313	+	0.171908i
$381$		0			0
$382$	18.3851	−	15.4269i	0.940662	−	0.789309i
$383$	5.95489	+	33.7719i	0.304281	+	1.72566i	0.626871	+	0.779123i	$0.284335\pi$
$383$	5.95489	+	33.7719i	0.304281	+	1.72566i	−0.322590	+	0.946539i	$0.604554\pi$
$384$		0			0
$385$	−9.19253	−	7.71345i	−0.468495	−	0.393114i
$386$	−13.4722	+	23.3345i	−0.685717	+	1.18770i
$387$		0			0
$388$	14.0000	+	24.2487i	0.710742	+	1.23104i
$389$	−4.67884	+	26.5350i	−0.237227	+	1.34538i	0.600646	+	0.799515i	$0.294910\pi$
$389$	−4.67884	+	26.5350i	−0.237227	+	1.34538i	−0.837873	+	0.545865i	$0.816201\pi$
$390$		0			0
$391$	−16.9145	−	6.15636i	−0.855401	−	0.311341i
$392$	13.8106	+	5.02665i	0.697541	+	0.253884i
$393$		0			0
$394$	6.25133	−	35.4531i	0.314938	−	1.78610i
$395$	−8.57321	−	14.8492i	−0.431365	−	0.747146i
$396$		0			0
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	0.878300	+	0.478110i	$0.158678\pi$
$398$	−1.87642	−	1.57450i	−0.0940563	−	0.0789226i
$399$		0			0
$400$	0.694593	+	3.93923i	0.0347296	+	0.196962i
$401$	26.2699	−	22.0430i	1.31185	−	1.10078i	0.323889	−	0.946095i	$-0.395009\pi$
$401$	26.2699	−	22.0430i	1.31185	−	1.10078i	0.987964	−	0.154681i	$-0.0494350\pi$
$402$		0			0
$403$	−0.939693	+	0.342020i	−0.0468094	+	0.0170372i
$404$	−19.5959			−0.974933
$405$		0			0
$406$	−24.0000			−1.19110
$407$	−18.4141	+	6.70220i	−0.912755	+	0.332216i
$408$		0			0
$409$	−21.4492	+	17.9981i	−1.06060	+	0.889946i	−0.994168	−	0.107845i	$-0.965605\pi$
$409$	−21.4492	+	17.9981i	−1.06060	+	0.889946i	−0.0664291	+	0.997791i	$0.521161\pi$
$410$	−5.10419	−	28.9473i	−0.252078	−	1.42961i
$411$		0			0
$412$	−21.4492	−	17.9981i	−1.05673	−	0.886700i
$413$	2.44949	−	4.24264i	0.120532	−	0.208767i
$414$		0			0
$415$	−15.0000	−	25.9808i	−0.736321	−	1.27535i
$416$		0			0
$417$		0			0
$418$	5.63816	+	2.05212i	0.275771	+	0.100373i
$419$	−32.2247	−	11.7288i	−1.57428	−	0.572992i	−0.600331	−	0.799752i	$-0.704965\pi$
$419$	−32.2247	−	11.7288i	−1.57428	−	0.572992i	−0.973951	+	0.226760i	$0.927187\pi$
$420$		0			0
$421$	0.347296	−	1.96962i	0.0169262	−	0.0959932i	−0.975174	−	0.221438i	$-0.928925\pi$
$421$	0.347296	−	1.96962i	0.0169262	−	0.0959932i	0.992101	+	0.125445i	$0.0400359\pi$
$422$	1.22474	+	2.12132i	0.0596196	+	0.103264i
$423$		0			0
$424$	−18.0000	+	31.1769i	−0.874157	+	1.51408i
$425$	−5.62925	−	4.72350i	−0.273059	−	0.229124i
$426$		0			0
$427$	1.73648	+	9.84808i	0.0840342	+	0.476582i
$428$	45.0340	−	37.7880i	2.17680	−	1.82655i
$429$		0			0
$430$	62.0197	−	22.5733i	2.99086	−	1.08858i
$431$	−7.34847			−0.353963			−0.176982	−	0.984214i	$-0.556633\pi$
$431$	−7.34847			−0.353963			−0.176982	+	0.984214i	$0.556633\pi$
$432$		0			0
$433$	17.0000			0.816968			0.408484	−	0.912766i	$-0.366058\pi$
$433$	17.0000			0.816968			0.408484	+	0.912766i	$0.366058\pi$
$434$	4.60353	−	1.67555i	0.220977	−	0.0804290i
$435$		0			0
$436$	−3.06418	+	2.57115i	−0.146748	+	0.123136i
$437$	0.425349	+	2.41228i	0.0203472	+	0.115395i
$438$		0			0
$439$	10.7246	+	8.99903i	0.511858	+	0.429500i	0.861783	−	0.507278i	$-0.169348\pi$
$439$	10.7246	+	8.99903i	0.511858	+	0.429500i	−0.349924	+	0.936778i	$0.613793\pi$
$440$	14.6969	−	25.4558i	0.700649	−	1.21356i
$441$		0			0
$442$	−9.00000	−	15.5885i	−0.428086	−	0.741467i
$443$	−2.12675	+	12.0614i	−0.101045	+	0.573054i	0.891682	+	0.452663i	$0.149526\pi$
$443$	−2.12675	+	12.0614i	−0.101045	+	0.573054i	−0.992727	+	0.120391i	$0.961585\pi$
$444$		0			0
$445$		0			0
$446$	16.1124	+	5.86442i	0.762943	+	0.277689i
$447$		0			0
$448$	−2.77837	+	15.7569i	−0.131266	+	0.744445i
$449$	−11.0227	−	19.0919i	−0.520194	−	0.901002i	−0.999724	−	0.0234766i	$-0.992526\pi$
$449$	−11.0227	−	19.0919i	−0.520194	−	0.901002i	0.479531	−	0.877525i	$-0.340807\pi$
$450$		0			0
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$	−30.0227	−	25.1920i	−1.41215	−	1.18493i
$453$		0			0
$454$	4.16756	+	23.6354i	0.195593	+	1.10926i
$455$	3.75284	−	3.14900i	0.175936	−	0.147628i
$456$		0			0
$457$	−27.2511	+	9.91858i	−1.27475	+	0.463972i	−0.888693	−	0.458502i	$-0.848386\pi$
$457$	−27.2511	+	9.91858i	−1.27475	+	0.463972i	−0.386059	+	0.922474i	$0.626164\pi$
$458$	−2.44949			−0.114457
$459$		0			0
$460$	24.0000			1.11901
$461$	25.3194	−	9.21552i	1.17924	−	0.429210i	0.323309	−	0.946293i	$-0.395205\pi$
$461$	25.3194	−	9.21552i	1.17924	−	0.429210i	0.855935	+	0.517084i	$0.172982\pi$
$462$		0			0
$463$	−14.5548	+	12.2130i	−0.676421	+	0.567585i	−0.914958	−	0.403549i	$-0.867777\pi$
$463$	−14.5548	+	12.2130i	−0.676421	+	0.567585i	0.238537	+	0.971133i	$0.423332\pi$
$464$	−3.40280	−	19.2982i	−0.157971	−	0.895897i
$465$		0			0
$466$	−13.7888	−	11.5702i	−0.638754	−	0.535978i
$467$	−7.34847	+	12.7279i	−0.340047	+	0.588978i	−0.984441	−	0.175715i	$-0.943776\pi$
$467$	−7.34847	+	12.7279i	−0.340047	+	0.588978i	0.644394	+	0.764693i	$0.277110\pi$
$468$		0			0
$469$	7.00000	+	12.1244i	0.323230	+	0.559851i
$470$	−10.2084	+	57.8946i	−0.470878	+	2.67048i
$471$		0			0
$472$	11.2763	+	4.10424i	0.519034	+	0.188913i
$473$	−25.3194	−	9.21552i	−1.16419	−	0.423730i
$474$		0			0
$475$	−0.173648	+	0.984808i	−0.00796752	+	0.0451861i
$476$	29.3939	+	50.9117i	1.34727	+	2.33353i
$477$		0			0
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	−20.6406	−	17.3195i	−0.943093	−	0.791349i	0.0350279	−	0.999386i	$-0.488848\pi$
$479$	−20.6406	−	17.3195i	−0.943093	−	0.791349i	−0.978121	+	0.208037i	$0.933292\pi$
$480$		0			0
$481$	−1.38919	−	7.87846i	−0.0633414	−	0.359227i
$482$	−30.0227	+	25.1920i	−1.36750	+	1.14747i
$483$		0			0
$484$	18.7939	−	6.84040i	0.854266	−	0.310927i
$485$	17.1464			0.778579
$486$		0			0
$487$	35.0000			1.58600			0.793001	−	0.609221i	$-0.208518\pi$
$487$	35.0000			1.58600			0.793001	+	0.609221i	$0.208518\pi$
$488$	−23.0177	+	8.37775i	−1.04196	+	0.379243i
$489$		0			0
$490$	13.7888	−	11.5702i	0.622914	−	0.522687i
$491$	−6.80559	−	38.5964i	−0.307132	−	1.74183i	−0.613296	−	0.789853i	$-0.710157\pi$
$491$	−6.80559	−	38.5964i	−0.307132	−	1.74183i	0.306164	−	0.951979i	$-0.400954\pi$
$492$		0			0
$493$	27.5776	+	23.1404i	1.24203	+	1.04219i
$494$	−1.22474	+	2.12132i	−0.0551039	+	0.0954427i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	2.55210	−	14.4737i	0.114477	−	0.649232i
$498$		0			0
$499$	−1.87939	−	0.684040i	−0.0841328	−	0.0306218i	0.299611	−	0.954061i	$-0.403143\pi$
$499$	−1.87939	−	0.684040i	−0.0841328	−	0.0306218i	−0.383744	+	0.923440i	$0.625365\pi$
$500$	−36.8283	−	13.4044i	−1.64701	−	0.599463i
$501$		0			0
$502$	−3.12567	+	17.7265i	−0.139505	+	0.791174i
$503$	7.34847	+	12.7279i	0.327652	+	0.567510i	0.982045	−	0.188644i	$-0.0604093\pi$
$503$	7.34847	+	12.7279i	0.327652	+	0.567510i	−0.654393	+	0.756154i	$0.727076\pi$
$504$		0			0
$505$	−6.00000	+	10.3923i	−0.266996	+	0.462451i
$506$	−11.2585	−	9.44701i	−0.500502	−	0.419971i
$507$		0			0
$508$	−13.1973	−	74.8454i	−0.585534	−	3.32073i
$509$	−7.50567	+	6.29801i	−0.332683	+	0.279154i	−0.793792	−	0.608189i	$-0.791896\pi$
$509$	−7.50567	+	6.29801i	−0.332683	+	0.279154i	0.461109	+	0.887344i	$0.347452\pi$
$510$		0			0
$511$	−20.6732	+	7.52444i	−0.914530	+	0.332862i
$512$	−39.1918			−1.73205
$513$		0			0
$514$	−42.0000			−1.85254
$515$	−16.1124	+	5.86442i	−0.709996	+	0.258417i
$516$		0			0
$517$	18.3851	−	15.4269i	0.808574	−	0.678474i
$518$	6.80559	+	38.5964i	0.299020	+	1.69583i
$519$		0			0
$520$	9.19253	+	7.71345i	0.403119	+	0.338257i
$521$	−11.0227	+	19.0919i	−0.482913	+	0.836431i	−0.999808	−	0.0196188i	$-0.993755\pi$
$521$	−11.0227	+	19.0919i	−0.482913	+	0.836431i	0.516894	+	0.856049i	$0.327088\pi$
$522$		0			0
$523$	12.5000	+	21.6506i	0.546587	+	0.946716i	0.998505	+	0.0546569i	$0.0174065\pi$
$523$	12.5000	+	21.6506i	0.546587	+	0.946716i	−0.451918	+	0.892059i	$0.649260\pi$
$524$	8.50699	−	48.2455i	0.371630	−	2.10762i
$525$		0			0
$526$	62.0197	+	22.5733i	2.70419	+	0.984244i
$527$	−6.90530	−	2.51332i	−0.300800	−	0.109482i
$528$		0			0
$529$	−2.95202	+	16.7417i	−0.128349	+	0.727901i
$530$	22.0454	+	38.1838i	0.957591	+	1.65860i
$531$		0			0
$532$	4.00000	−	6.92820i	0.173422	−	0.300376i
$533$	−3.75284	−	3.14900i	−0.162553	−	0.136398i
$534$		0			0
$535$	−6.25133	−	35.4531i	−0.270269	−	1.53277i
$536$	−26.2699	+	22.0430i	−1.13468	+	0.952114i
$537$		0			0
$538$	50.7434	−	18.4691i	2.18770	−	0.796259i
$539$	−7.34847			−0.316521
$540$		0			0
$541$	−28.0000			−1.20381			−0.601907	−	0.798566i	$-0.705592\pi$
$541$	−28.0000			−1.20381			−0.601907	+	0.798566i	$0.705592\pi$
$542$	16.1124	−	5.86442i	0.692086	−	0.251899i
$543$		0			0
$544$		0			0
$545$	0.425349	+	2.41228i	0.0182200	+	0.103331i
$546$		0			0
$547$	−9.95858	−	8.35624i	−0.425798	−	0.357287i	0.404565	−	0.914509i	$-0.367423\pi$
$547$	−9.95858	−	8.35624i	−0.425798	−	0.357287i	−0.830364	+	0.557222i	$0.811867\pi$
$548$	−19.5959	+	33.9411i	−0.837096	+	1.44989i
$549$		0			0
$550$	−3.00000	−	5.19615i	−0.127920	−	0.221565i
$551$	0.850699	−	4.82455i	0.0362410	−	0.205533i
$552$		0			0
$553$	13.1557	+	4.78828i	0.559437	+	0.203618i
$554$	−25.3194	−	9.21552i	−1.07572	−	0.391530i
$555$		0			0
$556$	−6.94593	+	39.3923i	−0.294573	+	1.67061i
$557$	−3.67423	−	6.36396i	−0.155682	−	0.269650i	0.777625	−	0.628728i	$-0.216424\pi$
$557$	−3.67423	−	6.36396i	−0.155682	−	0.269650i	−0.933307	+	0.359079i	$0.883091\pi$
$558$		0			0
$559$	5.50000	−	9.52628i	0.232625	−	0.402919i
$560$	−15.0113	−	12.5960i	−0.634345	−	0.532279i
$561$		0			0
$562$	−5.20945	−	29.5442i	−0.219747	−	1.24625i
$563$	9.38209	−	7.87251i	0.395408	−	0.331787i	−0.423308	−	0.905986i	$-0.639131\pi$
$563$	9.38209	−	7.87251i	0.395408	−	0.331787i	0.818715	+	0.574199i	$0.194687\pi$
$564$		0			0
$565$	−22.5526	+	8.20848i	−0.948796	+	0.345333i
$566$	41.6413			1.75032
$567$		0			0
$568$	36.0000			1.51053
$569$	11.5088	−	4.18887i	0.482476	−	0.175607i	−0.0893199	−	0.996003i	$-0.528469\pi$
$569$	11.5088	−	4.18887i	0.482476	−	0.175607i	0.571795	+	0.820396i	$0.306247\pi$
$570$		0			0
$571$	−7.66044	+	6.42788i	−0.320580	+	0.268998i	−0.788848	−	0.614588i	$-0.789322\pi$
$571$	−7.66044	+	6.42788i	−0.320580	+	0.268998i	0.468269	+	0.883586i	$0.344878\pi$
$572$	−1.70140	−	9.64911i	−0.0711390	−	0.403449i
$573$		0			0
$574$	18.3851	+	15.4269i	0.767378	+	0.643906i
$575$	1.22474	−	2.12132i	0.0510754	−	0.0884652i
$576$		0			0
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	0.999719	+	0.0236970i	$0.00754370\pi$
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	−0.479337	+	0.877631i	$0.659123\pi$
$578$	15.7379	−	89.2542i	0.654612	−	3.71249i
$579$		0			0
$580$	−45.1052	−	16.4170i	−1.87289	−	0.681677i
$581$	23.0177	+	8.37775i	0.954934	+	0.347568i
$582$		0			0
$583$	3.12567	−	17.7265i	0.129452	−	0.734158i
$584$	−26.9444	−	46.6690i	−1.11497	−	1.93118i
$585$		0			0
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$	1.87642	+	1.57450i	0.0774481	+	0.0649866i	0.680690	−	0.732572i	$-0.261680\pi$
$587$	1.87642	+	1.57450i	0.0774481	+	0.0649866i	−0.603242	+	0.797558i	$0.706125\pi$
$588$		0			0
$589$	0.173648	+	0.984808i	0.00715505	+	0.0405783i
$590$	11.2585	−	9.44701i	0.463505	−	0.388927i
$591$		0			0
$592$	−30.0702	+	10.9446i	−1.23588	+	0.449822i
$593$	7.34847			0.301765			0.150883	−	0.988552i	$-0.451788\pi$
$593$	7.34847			0.301765			0.150883	+	0.988552i	$0.451788\pi$
$594$		0			0
$595$	36.0000			1.47586
$596$	−46.0353	+	16.7555i	−1.88568	+	0.686332i
$597$		0			0
$598$	4.59627	−	3.85673i	0.187955	−	0.157713i
$599$	−6.80559	−	38.5964i	−0.278069	−	1.57701i	−0.729042	−	0.684469i	$-0.760034\pi$
$599$	−6.80559	−	38.5964i	−0.278069	−	1.57701i	0.450973	−	0.892538i	$-0.351077\pi$
$600$		0			0
$601$	−5.36231	−	4.49951i	−0.218733	−	0.183539i	0.526836	−	0.849967i	$-0.323378\pi$
$601$	−5.36231	−	4.49951i	−0.218733	−	0.183539i	−0.745570	+	0.666428i	$0.767822\pi$
$602$	−26.9444	+	46.6690i	−1.09817	+	1.90209i
$603$		0			0
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	2.12675	−	12.0614i	0.0864646	−	0.490365i
$606$		0			0
$607$	−41.3465	−	15.0489i	−1.67820	−	0.610815i	−0.685140	−	0.728411i	$-0.740259\pi$
$607$	−41.3465	−	15.0489i	−1.67820	−	0.610815i	−0.993062	+	0.117596i	$0.962481\pi$
$608$		0			0
$609$		0			0
$610$	−5.20945	+	29.5442i	−0.210924	+	1.19621i
$611$	4.89898	+	8.48528i	0.198191	+	0.343278i
$612$		0			0
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	−0.955458	−	0.295126i	$-0.904638\pi$
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	0.733316	+	0.679888i	$0.237972\pi$
$614$	3.75284	+	3.14900i	0.151452	+	0.127083i
$615$		0			0
$616$	4.16756	+	23.6354i	0.167916	+	0.952297i
$617$	−18.7642	+	15.7450i	−0.755417	+	0.633870i	−0.936930	−	0.349518i	$-0.886345\pi$
$617$	−18.7642	+	15.7450i	−0.755417	+	0.633870i	0.181512	+	0.983389i	$0.441901\pi$
$618$		0			0
$619$	46.0449	−	16.7590i	1.85070	−	0.673601i	0.865825	−	0.500347i	$-0.166794\pi$
$619$	46.0449	−	16.7590i	1.85070	−	0.673601i	0.984877	−	0.173254i	$-0.0554281\pi$
$620$	9.79796			0.393496
$621$		0			0
$622$	−60.0000			−2.40578
$623$		0			0
$624$		0			0
$625$	−22.2153	+	18.6408i	−0.888612	+	0.745634i
$626$	−6.80559	−	38.5964i	−0.272006	−	1.54262i
$627$		0			0
$628$	52.0910	+	43.7096i	2.07866	+	1.74420i
$629$	29.3939	−	50.9117i	1.17201	−	2.02998i
$630$		0			0
$631$	−22.0000	−	38.1051i	−0.875806	−	1.51694i	−0.855901	−	0.517139i	$-0.826997\pi$
$631$	−22.0000	−	38.1051i	−0.875806	−	1.51694i	−0.0199047	−	0.999802i	$-0.506336\pi$
$632$	−5.95489	+	33.7719i	−0.236873	+	1.34337i
$633$		0			0
$634$	−22.5526	−	8.20848i	−0.895679	−	0.326001i
$635$	−43.7336	−	15.9177i	−1.73551	−	0.631676i
$636$		0			0
$637$	0.520945	−	2.95442i	0.0206406	−	0.117059i
$638$	14.6969	+	25.4558i	0.581857	+	1.00781i
$639$		0			0
$640$	−24.0000	+	41.5692i	−0.948683	+	1.64317i
$641$	13.1349	+	11.0215i	0.518798	+	0.435324i	0.864213	−	0.503127i	$-0.167817\pi$
$641$	13.1349	+	11.0215i	0.518798	+	0.435324i	−0.345414	+	0.938450i	$0.612262\pi$
$642$		0			0
$643$	6.59863	+	37.4227i	0.260225	+	1.47581i	0.782297	+	0.622906i	$0.214048\pi$
$643$	6.59863	+	37.4227i	0.260225	+	1.47581i	−0.522072	+	0.852901i	$0.674841\pi$
$644$	−15.0113	+	12.5960i	−0.591530	+	0.496352i
$645$		0			0
$646$	−16.9145	+	6.15636i	−0.665491	+	0.242219i
$647$	36.7423			1.44449			0.722245	−	0.691637i	$-0.243110\pi$
$647$	36.7423			1.44449			0.722245	+	0.691637i	$0.243110\pi$
$648$		0			0
$649$	−6.00000			−0.235521
$650$	2.30177	−	0.837775i	0.0902827	−	0.0328602i
$651$		0			0
$652$	−30.6418	+	25.7115i	−1.20002	+	1.00694i
$653$	−1.70140	−	9.64911i	−0.0665808	−	0.377599i	−0.999831	−	0.0183721i	$-0.994152\pi$
$653$	−1.70140	−	9.64911i	−0.0665808	−	0.377599i	0.933250	−	0.359227i	$-0.116959\pi$
$654$		0			0
$655$	−22.9813	−	19.2836i	−0.897955	−	0.753474i
$656$	−9.79796	+	16.9706i	−0.382546	+	0.662589i
$657$		0			0
$658$	−24.0000	−	41.5692i	−0.935617	−	1.62054i
$659$	−3.40280	+	19.2982i	−0.132554	+	0.751752i	0.843978	+	0.536378i	$0.180208\pi$
$659$	−3.40280	+	19.2982i	−0.132554	+	0.751752i	−0.976532	+	0.215373i	$0.930903\pi$
$660$		0			0
$661$	−10.3366	−	3.76222i	−0.402048	−	0.146333i	0.133078	−	0.991106i	$-0.457514\pi$
$661$	−10.3366	−	3.76222i	−0.402048	−	0.146333i	−0.535126	+	0.844772i	$0.679736\pi$
$662$	16.1124	+	5.86442i	0.626225	+	0.227927i
$663$		0			0
$664$	−10.4189	+	59.0885i	−0.404331	+	2.29308i
$665$	−2.44949	−	4.24264i	−0.0949871	−	0.164523i
$666$		0			0
$667$	−6.00000	+	10.3923i	−0.232321	+	0.402392i
$668$	15.0113	+	12.5960i	0.580806	+	0.487354i
$669$		0			0
$670$	7.29322	+	41.3619i	0.281762	+	1.59795i
$671$	9.38209	−	7.87251i	0.362192	−	0.303915i
$672$		0			0
$673$	−27.2511	+	9.91858i	−1.05045	+	0.382333i	−0.808833	−	0.588038i	$-0.799901\pi$
$673$	−27.2511	+	9.91858i	−1.05045	+	0.382333i	−0.241619	+	0.970371i	$0.577678\pi$
$674$	−68.5857			−2.64182
$675$		0			0
$676$	−48.0000			−1.84615
$677$	−43.7336	+	15.9177i	−1.68082	+	0.611768i	−0.993422	−	0.114515i	$-0.963469\pi$
$677$	−43.7336	+	15.9177i	−1.68082	+	0.611768i	−0.687397	+	0.726282i	$0.741247\pi$
$678$		0			0
$679$	−10.7246	+	8.99903i	−0.411573	+	0.345351i
$680$	15.3126	+	86.8420i	0.587211	+	3.33024i
$681$		0			0
$682$	−4.59627	−	3.85673i	−0.176000	−	0.147682i
$683$	11.0227	−	19.0919i	0.421772	−	0.730531i	−0.574341	−	0.818616i	$-0.694742\pi$
$683$	11.0227	−	19.0919i	0.421772	−	0.730531i	0.996113	+	0.0880857i	$0.0280749\pi$
$684$		0			0
$685$	12.0000	+	20.7846i	0.458496	+	0.794139i
$686$	−8.50699	+	48.2455i	−0.324798	+	1.84202i
$687$		0			0
$688$	−41.3465	−	15.0489i	−1.57632	−	0.573733i
$689$	6.90530	+	2.51332i	0.263071	+	0.0957500i
$690$		0			0
$691$	8.16146	−	46.2860i	0.310477	−	1.76080i	−0.286057	−	0.958213i	$-0.592345\pi$
$691$	8.16146	−	46.2860i	0.310477	−	1.76080i	0.596533	−	0.802588i	$-0.296544\pi$
$692$	−19.5959	−	33.9411i	−0.744925	−	1.29025i
$693$		0			0
$694$	30.0000	−	51.9615i	1.13878	−	1.97243i
$695$	18.7642	+	15.7450i	0.711766	+	0.597243i
$696$		0			0
$697$	−6.25133	−	35.4531i	−0.236786	−	1.34288i
$698$	37.5284	−	31.4900i	1.42047	−	1.19192i
$699$		0			0
$700$	−7.51754	+	2.73616i	−0.284136	+	0.103417i
$701$	−14.6969			−0.555096			−0.277548	−	0.960712i	$-0.589522\pi$
$701$	−14.6969			−0.555096			−0.277548	+	0.960712i	$0.589522\pi$
$702$		0			0
$703$	−8.00000			−0.301726
$704$	18.4141	−	6.70220i	0.694009	−	0.252599i
$705$		0			0
$706$	4.59627	−	3.85673i	0.172983	−	0.145150i
$707$	−1.70140	−	9.64911i	−0.0639876	−	0.362892i
$708$		0			0
$709$	−5.36231	−	4.49951i	−0.201386	−	0.168983i	0.536518	−	0.843889i	$-0.319740\pi$
$709$	−5.36231	−	4.49951i	−0.201386	−	0.168983i	−0.737903	+	0.674906i	$0.764184\pi$
$710$	22.0454	−	38.1838i	0.827349	−	1.43301i
$711$		0			0
$712$		0			0
$713$	0.425349	−	2.41228i	0.0159295	−	0.0903405i
$714$		0			0
$715$	−5.63816	−	2.05212i	−0.210855	−	0.0767450i
$716$	55.2424	+	20.1066i	2.06451	+	0.751419i
$717$		0			0
$718$	12.5027	−	70.9062i	0.466595	−	2.64619i
$719$	18.3712	+	31.8198i	0.685129	+	1.18668i	0.973396	+	0.229128i	$0.0735876\pi$
$719$	18.3712	+	31.8198i	0.685129	+	1.18668i	−0.288267	+	0.957550i	$0.593079\pi$
$720$		0			0
$721$	7.00000	−	12.1244i	0.260694	−	0.451535i
$722$	−33.7755	−	28.3410i	−1.25699	−	1.05474i
$723$		0			0
$724$	5.55674	+	31.5138i	0.206515	+	1.17120i
$725$	−3.75284	+	3.14900i	−0.139377	+	0.116951i
$726$		0			0
$727$	−13.1557	+	4.78828i	−0.487918	+	0.177588i	−0.574252	−	0.818679i	$-0.694707\pi$
$727$	−13.1557	+	4.78828i	−0.487918	+	0.177588i	0.0863341	+	0.996266i	$0.472485\pi$
$728$	−9.79796			−0.363137
$729$		0			0
$730$	−66.0000			−2.44277
$731$	75.9583	−	27.6466i	2.80942	−	1.02255i
$732$		0			0
$733$	13.0228	−	10.9274i	0.481006	−	0.403612i	−0.369784	−	0.929118i	$-0.620568\pi$
$733$	13.0228	−	10.9274i	0.481006	−	0.403612i	0.850790	+	0.525506i	$0.176124\pi$
$734$	2.12675	+	12.0614i	0.0784997	+	0.445194i
$735$		0			0
$736$		0			0
$737$	8.57321	−	14.8492i	0.315798	−	0.546979i
$738$		0			0
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	0.875075	−	0.483987i	$-0.160812\pi$
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	−0.856683	+	0.515844i	$0.827478\pi$
$740$	−13.6112	+	77.1928i	−0.500357	+	2.83767i
$741$		0			0
$742$	−33.8289	−	12.3127i	−1.24190	−	0.452014i
$743$	29.9230	+	10.8911i	1.09777	+	0.399555i	0.826493	−	0.562947i	$-0.190333\pi$
$743$	29.9230	+	10.8911i	1.09777	+	0.399555i	0.271275	+	0.962502i	$0.412555\pi$
$744$		0			0
$745$	−5.20945	+	29.5442i	−0.190859	+	1.08242i
$746$	−42.8661	−	74.2462i	−1.56944	−	2.71835i
$747$		0			0
$748$	36.0000	−	62.3538i	1.31629	−	2.27988i
$749$	22.5170	+	18.8940i	0.822754	+	0.690372i
$750$		0			0
$751$	4.51485	+	25.6050i	0.164749	+	0.934340i	0.949323	+	0.314304i	$0.101771\pi$
$751$	4.51485	+	25.6050i	0.164749	+	0.934340i	−0.784573	+	0.620036i	$0.787118\pi$
$752$	30.0227	−	25.1920i	1.09481	−	0.918659i
$753$		0			0
$754$	−11.2763	+	4.10424i	−0.410659	+	0.149468i
$755$	−12.2474			−0.445730
$756$		0			0
$757$	−7.00000			−0.254419			−0.127210	−	0.991876i	$-0.540602\pi$
$757$	−7.00000			−0.254419			−0.127210	+	0.991876i	$0.540602\pi$
$758$	−18.4141	+	6.70220i	−0.668832	+	0.243435i
$759$		0			0
$760$	9.19253	−	7.71345i	0.333448	−	0.279796i
$761$	−0.425349	−	2.41228i	−0.0154189	−	0.0874450i	0.976127	−	0.217199i	$-0.0696922\pi$
$761$	−0.425349	−	2.41228i	−0.0154189	−	0.0874450i	−0.991546	+	0.129754i	$0.958581\pi$
$762$		0			0
$763$	−1.53209	−	1.28558i	−0.0554653	−	0.0465409i
$764$	−19.5959	+	33.9411i	−0.708955	+	1.22795i
$765$		0			0
$766$	−42.0000	−	72.7461i	−1.51752	−	2.62842i
$767$	0.425349	−	2.41228i	0.0153585	−	0.0871023i
$768$		0			0
$769$	34.7686	+	12.6547i	1.25379	+	0.456342i	0.881680	−	0.471847i	$-0.156413\pi$
$769$	34.7686	+	12.6547i	1.25379	+	0.456342i	0.372109	+	0.928189i	$0.378635\pi$
$770$	27.6212	+	10.0533i	0.995399	+	0.362296i
$771$		0			0
$772$	7.64052	−	43.3315i	0.274988	−	1.55954i
$773$	22.0454	+	38.1838i	0.792918	+	1.37337i	0.924153	+	0.382023i	$0.124773\pi$
$773$	22.0454	+	38.1838i	0.792918	+	1.37337i	−0.131235	+	0.991351i	$0.541894\pi$
$774$		0			0
$775$	0.500000	−	0.866025i	0.0179605	−	0.0311086i
$776$	−26.2699	−	22.0430i	−0.943033	−	0.791298i
$777$		0			0
$778$	−11.4608	−	64.9973i	−0.410889	−	2.33027i
$779$	−3.75284	+	3.14900i	−0.134459	+	0.112825i
$780$		0			0
$781$	−16.9145	+	6.15636i	−0.605247	+	0.220292i
$782$	44.0908			1.57668

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)

\(f(q)\)	\(=\)	\(q+(-2.30177 + 0.837775i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-0.425349 - 2.41228i) q^{5} +(1.53209 + 1.28558i) q^{7} +(-2.44949 + 4.24264i) q^{8} +O(q^{10})\)	\(q+(-2.30177 + 0.837775i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-0.425349 - 2.41228i) q^{5} +(1.53209 + 1.28558i) q^{7} +(-2.44949 + 4.24264i) q^{8} +(3.00000 + 5.19615i) q^{10} +(0.425349 - 2.41228i) q^{11} +(0.939693 + 0.342020i) q^{13} +(-4.60353 - 1.67555i) q^{14} +(0.694593 - 3.93923i) q^{16} +(3.67423 + 6.36396i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-7.50567 - 6.29801i) q^{20} +(1.04189 + 5.90885i) q^{22} +(-1.87642 + 1.57450i) q^{23} +(-0.939693 + 0.342020i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(4.60353 - 1.67555i) q^{29} +(-0.766044 + 0.642788i) q^{31} +(-13.7888 - 11.5702i) q^{34} +(2.44949 - 4.24264i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(-0.425349 + 2.41228i) q^{38} +(11.2763 + 4.10424i) q^{40} +(-4.60353 - 1.67555i) q^{41} +(1.91013 - 10.8329i) q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.00000 - 5.19615i) q^{46} +(7.50567 + 6.29801i) q^{47} +(-0.520945 - 2.95442i) q^{49} +(1.87642 - 1.57450i) q^{50} +(3.75877 - 1.36808i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(-9.20707 + 3.35110i) q^{56} +(-9.19253 + 7.71345i) q^{58} +(-0.425349 - 2.41228i) q^{59} +(3.83022 + 3.21394i) q^{61} +(1.22474 - 2.12132i) q^{62} +(4.00000 + 6.92820i) q^{64} +(0.425349 - 2.41228i) q^{65} +(6.57785 + 2.39414i) q^{67} +(27.6212 + 10.0533i) q^{68} +(-2.08378 + 11.8177i) q^{70} +(-3.67423 - 6.36396i) q^{71} +(-5.50000 + 9.52628i) q^{73} +(15.0113 + 12.5960i) q^{74} +(-0.694593 - 3.93923i) q^{76} +(3.75284 - 3.14900i) q^{77} +(6.57785 - 2.39414i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(11.5088 - 4.18887i) q^{83} +(13.7888 - 11.5702i) q^{85} +(4.67884 + 26.5350i) q^{86} +(9.19253 + 7.71345i) q^{88} +(1.00000 + 1.73205i) q^{91} +(-1.70140 + 9.64911i) q^{92} +(-22.5526 - 8.20848i) q^{94} +(-2.30177 - 0.837775i) q^{95} +(-1.21554 + 6.89365i) q^{97} +(3.67423 + 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 36 q^{10} + 6 q^{19} + 96 q^{28} - 48 q^{37} + 36 q^{46} - 72 q^{55} + 48 q^{64} - 66 q^{73} + 144 q^{82} + 12 q^{91}+O(q^{100}) \) 12 * q + 36 * q^10 + 6 * q^19 + 96 * q^28 - 48 * q^37 + 36 * q^46 - 72 * q^55 + 48 * q^64 - 66 * q^73 + 144 * q^82 + 12 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more