LMFDB - Embedded newform 729.2.e.p.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	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			649.2
Root			$-0.483690 - 1.32893i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.p.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.425349 - 2.41228i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-1.87642 + 1.57450i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(-2.44949 + 4.24264i) q^{8} +O(q^{10})$	\(q+(0.425349 - 2.41228i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-1.87642 + 1.57450i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(-2.44949 + 4.24264i) q^{8} +(3.00000 + 5.19615i) q^{10} +(1.87642 + 1.57450i) q^{11} +(-0.173648 - 0.984808i) q^{13} +(0.850699 + 4.82455i) q^{14} +(3.06418 + 2.57115i) q^{16} +(3.67423 + 6.36396i) q^{17} +(0.500000 - 0.866025i) q^{19} +(9.20707 - 3.35110i) q^{20} +(4.59627 - 3.85673i) q^{22} +(2.30177 + 0.837775i) q^{23} +(0.173648 - 0.984808i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(-0.850699 + 4.82455i) q^{29} +(0.939693 + 0.342020i) q^{31} +(16.9145 - 6.15636i) q^{34} +(2.44949 - 4.24264i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(-1.87642 - 1.57450i) q^{38} +(-2.08378 - 11.8177i) q^{40} +(0.850699 + 4.82455i) q^{41} +(8.42649 + 7.07066i) q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-9.20707 + 3.35110i) q^{47} +(-2.29813 + 1.92836i) q^{49} +(-2.30177 - 0.837775i) q^{50} +(-0.694593 + 3.93923i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(1.70140 - 9.64911i) q^{56} +(11.2763 + 4.10424i) q^{58} +(-1.87642 + 1.57450i) q^{59} +(-4.69846 + 1.71010i) q^{61} +(1.22474 - 2.12132i) q^{62} +(4.00000 + 6.92820i) q^{64} +(1.87642 + 1.57450i) q^{65} +(-1.21554 - 6.89365i) q^{67} +(-5.10419 - 28.9473i) q^{68} +(-9.19253 - 7.71345i) q^{70} +(-3.67423 - 6.36396i) q^{71} +(-5.50000 + 9.52628i) q^{73} +(-18.4141 + 6.70220i) q^{74} +(-3.06418 + 2.57115i) q^{76} +(-4.60353 - 1.67555i) q^{77} +(-1.21554 + 6.89365i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(-2.12675 + 12.0614i) q^{83} +(-16.9145 - 6.15636i) q^{85} +(20.6406 - 17.3195i) q^{86} +(-11.2763 + 4.10424i) q^{88} +(1.00000 + 1.73205i) q^{91} +(-7.50567 - 6.29801i) q^{92} +(4.16756 + 23.6354i) q^{94} +(0.425349 + 2.41228i) q^{95} +(-5.36231 - 4.49951i) q^{97} +(3.67423 + 6.36396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.425349	−	2.41228i	0.300767	−	1.70574i	−0.342020	−	0.939693i	$-0.611111\pi$
$2$	0.425349	−	2.41228i	0.300767	−	1.70574i	0.642788	−	0.766044i	$-0.277778\pi$
$3$		0			0
$3$		0			0
$4$	−3.75877	−	1.36808i	−1.87939	−	0.684040i
$5$	−1.87642	+	1.57450i	−0.839160	+	0.704139i	−0.957375	−	0.288849i	$-0.906727\pi$
$5$	−1.87642	+	1.57450i	−0.839160	+	0.704139i	0.118215	+	0.992988i	$0.462283\pi$
$6$		0			0
$7$	−1.87939	+	0.684040i	−0.710341	+	0.258543i	−0.671820	−	0.740715i	$-0.734487\pi$
$7$	−1.87939	+	0.684040i	−0.710341	+	0.258543i	−0.0385213	+	0.999258i	$0.512265\pi$
$8$	−2.44949	+	4.24264i	−0.866025	+	1.50000i
$9$		0			0
$10$	3.00000	+	5.19615i	0.948683	+	1.64317i
$11$	1.87642	+	1.57450i	0.565761	+	0.474730i	0.880236	−	0.474536i	$-0.157384\pi$
$11$	1.87642	+	1.57450i	0.565761	+	0.474730i	−0.314475	+	0.949266i	$0.601828\pi$
$12$		0			0
$13$	−0.173648	−	0.984808i	−0.0481613	−	0.273137i	0.951212	−	0.308539i	$-0.0998399\pi$
$13$	−0.173648	−	0.984808i	−0.0481613	−	0.273137i	−0.999373	+	0.0354021i	$0.988729\pi$
$14$	0.850699	+	4.82455i	0.227359	+	1.28942i
$15$		0			0
$16$	3.06418	+	2.57115i	0.766044	+	0.642788i
$17$	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	$0.130073\pi$
$20$	9.20707	−	3.35110i	2.05876	−	0.749329i
$21$		0			0
$22$	4.59627	−	3.85673i	0.979927	−	0.822257i
$23$	2.30177	+	0.837775i	0.479952	+	0.174688i	0.570655	−	0.821190i	$-0.306689\pi$
$23$	2.30177	+	0.837775i	0.479952	+	0.174688i	−0.0907034	+	0.995878i	$0.528912\pi$
$24$		0			0
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−2.44949			−0.480384
$27$		0			0
$28$	8.00000			1.51186
$29$	−0.850699	+	4.82455i	−0.157971	+	0.895897i	0.798048	+	0.602593i	$0.205866\pi$
$29$	−0.850699	+	4.82455i	−0.157971	+	0.895897i	−0.956019	+	0.293304i	$0.905245\pi$
$30$		0			0
$31$	0.939693	+	0.342020i	0.168774	+	0.0614286i	0.425025	−	0.905182i	$-0.360265\pi$
$31$	0.939693	+	0.342020i	0.168774	+	0.0614286i	−0.256251	+	0.966610i	$0.582487\pi$
$32$		0			0
$33$		0			0
$34$	16.9145	−	6.15636i	2.90081	−	1.05581i
$35$	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	$-0.395093\pi$
$38$	−1.87642	−	1.57450i	−0.304395	−	0.255418i
$39$		0			0
$40$	−2.08378	−	11.8177i	−0.329474	−	1.86854i
$41$	0.850699	+	4.82455i	0.132857	+	0.753469i	0.976328	+	0.216294i	$0.0693971\pi$
$41$	0.850699	+	4.82455i	0.132857	+	0.753469i	−0.843471	+	0.537174i	$0.819492\pi$
$42$		0			0
$43$	8.42649	+	7.07066i	1.28503	+	1.07827i	0.992530	+	0.122000i	$0.0389307\pi$
$43$	8.42649	+	7.07066i	1.28503	+	1.07827i	0.292497	+	0.956266i	$0.405514\pi$
$44$	−4.89898	−	8.48528i	−0.738549	−	1.27920i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−9.20707	+	3.35110i	−1.34299	+	0.488808i	−0.910753	−	0.412952i	$-0.864498\pi$
$47$	−9.20707	+	3.35110i	−1.34299	+	0.488808i	−0.432236	+	0.901760i	$0.642275\pi$
$48$		0			0
$49$	−2.29813	+	1.92836i	−0.328305	+	0.275480i
$50$	−2.30177	−	0.837775i	−0.325519	−	0.118479i
$51$		0			0
$52$	−0.694593	+	3.93923i	−0.0963227	+	0.546273i
$53$	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
$56$	1.70140	−	9.64911i	0.227359	−	1.28942i
$57$		0			0
$58$	11.2763	+	4.10424i	1.48065	+	0.538913i
$59$	−1.87642	+	1.57450i	−0.244289	+	0.204983i	−0.756708	−	0.653753i	$-0.773194\pi$
$59$	−1.87642	+	1.57450i	−0.244289	+	0.204983i	0.512420	+	0.858735i	$0.328749\pi$
$60$		0			0
$61$	−4.69846	+	1.71010i	−0.601577	+	0.218956i	−0.624814	−	0.780774i	$-0.714825\pi$
$61$	−4.69846	+	1.71010i	−0.601577	+	0.218956i	0.0232370	+	0.999730i	$0.492603\pi$
$62$	1.22474	−	2.12132i	0.155543	−	0.269408i
$63$		0			0
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	1.87642	+	1.57450i	0.232741	+	0.195293i
$66$		0			0
$67$	−1.21554	−	6.89365i	−0.148502	−	0.842194i	−0.964489	−	0.264124i	$-0.914917\pi$
$67$	−1.21554	−	6.89365i	−0.148502	−	0.842194i	0.815987	−	0.578070i	$-0.196194\pi$
$68$	−5.10419	−	28.9473i	−0.618974	−	3.51038i
$69$		0			0
$70$	−9.19253	−	7.71345i	−1.09872	−	0.921934i
$71$	−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	$0.944054\pi$
$74$	−18.4141	+	6.70220i	−2.14060	+	0.779115i
$75$		0			0
$76$	−3.06418	+	2.57115i	−0.351485	+	0.294931i
$77$	−4.60353	−	1.67555i	−0.524621	−	0.190947i
$78$		0			0
$79$	−1.21554	+	6.89365i	−0.136759	+	0.775597i	0.836860	+	0.547417i	$0.184389\pi$
$79$	−1.21554	+	6.89365i	−0.136759	+	0.775597i	−0.973619	+	0.228180i	$0.926722\pi$
$80$	−9.79796			−1.09545
$81$		0			0
$82$	12.0000			1.32518
$83$	−2.12675	+	12.0614i	−0.233441	+	1.32391i	0.612432	+	0.790524i	$0.290191\pi$
$83$	−2.12675	+	12.0614i	−0.233441	+	1.32391i	−0.845872	+	0.533385i	$0.820920\pi$
$84$		0			0
$85$	−16.9145	−	6.15636i	−1.83463	−	0.667751i
$86$	20.6406	−	17.3195i	2.22573	−	1.86761i
$87$		0			0
$88$	−11.2763	+	4.10424i	−1.20206	+	0.437514i
$89$		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
$92$	−7.50567	−	6.29801i	−0.782520	−	0.656613i
$93$		0			0
$94$	4.16756	+	23.6354i	0.429851	+	2.43780i
$95$	0.425349	+	2.41228i	0.0436399	+	0.247494i
$96$		0			0
$97$	−5.36231	−	4.49951i	−0.544460	−	0.456856i	0.328600	−	0.944469i	$-0.393423\pi$
$97$	−5.36231	−	4.49951i	−0.544460	−	0.456856i	−0.873060	+	0.487613i	$0.837868\pi$
$98$	3.67423	+	6.36396i	0.371154	+	0.642857i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	4.60353	−	1.67555i	0.458069	−	0.166723i	−0.102671	−	0.994715i	$-0.532739\pi$
$101$	4.60353	−	1.67555i	0.458069	−	0.166723i	0.560740	+	0.827992i	$0.310517\pi$
$102$		0			0
$103$	−5.36231	+	4.49951i	−0.528364	+	0.443350i	−0.867536	−	0.497374i	$-0.834298\pi$
$103$	−5.36231	+	4.49951i	−0.528364	+	0.443350i	0.339172	+	0.940724i	$0.389853\pi$
$104$	4.60353	+	1.67555i	0.451414	+	0.164301i
$105$		0			0
$106$	3.12567	−	17.7265i	0.303592	−	1.72175i
$107$	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	$0.515250\pi$
$110$	−2.55210	+	14.4737i	−0.243333	+	1.38001i
$111$		0			0
$112$	−7.51754	−	2.73616i	−0.710341	−	0.258543i
$113$	−7.50567	+	6.29801i	−0.706074	+	0.592467i	−0.923495	−	0.383611i	$-0.874680\pi$
$113$	−7.50567	+	6.29801i	−0.706074	+	0.592467i	0.217420	+	0.976078i	$0.430236\pi$
$114$		0			0
$115$	−5.63816	+	2.05212i	−0.525761	+	0.191361i
$116$	9.79796	−	16.9706i	0.909718	−	1.57568i
$117$		0			0
$118$	3.00000	+	5.19615i	0.276172	+	0.478345i
$119$	−11.2585	−	9.44701i	−1.03207	−	0.866006i
$120$		0			0
$121$	−0.868241	−	4.92404i	−0.0789310	−	0.447640i
$122$	2.12675	+	12.0614i	0.192547	+	1.09199i
$123$		0			0
$124$	−3.06418	−	2.57115i	−0.275171	−	0.230896i
$125$	−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	$-0.152539\pi$
$128$	18.4141	−	6.70220i	1.62760	−	0.592396i
$129$		0			0
$130$	4.59627	−	3.85673i	0.403119	−	0.338257i
$131$	−11.5088	−	4.18887i	−1.00553	−	0.365984i	−0.213816	−	0.976874i	$-0.568589\pi$
$131$	−11.5088	−	4.18887i	−1.00553	−	0.365984i	−0.791715	+	0.610890i	$0.790812\pi$
$132$		0			0
$133$	−0.347296	+	1.96962i	−0.0301144	+	0.170787i
$134$	−17.1464			−1.48123
$135$		0			0
$136$	−36.0000			−3.08697
$137$	1.70140	−	9.64911i	0.145360	−	0.824379i	−0.821717	−	0.569896i	$-0.806984\pi$
$137$	1.70140	−	9.64911i	0.145360	−	0.824379i	0.967077	−	0.254483i	$-0.0819053\pi$
$138$		0			0
$139$	9.39693	+	3.42020i	0.797037	+	0.290098i	0.708258	−	0.705954i	$-0.249481\pi$
$139$	9.39693	+	3.42020i	0.797037	+	0.290098i	0.0887789	+	0.996051i	$0.471704\pi$
$140$	−15.0113	+	12.5960i	−1.26869	+	1.06456i
$141$		0			0
$142$	−16.9145	+	6.15636i	−1.41943	+	0.516630i
$143$	1.22474	−	2.12132i	0.102418	−	0.177394i
$144$		0			0
$145$	−6.00000	−	10.3923i	−0.498273	−	0.863034i
$146$	20.6406	+	17.3195i	1.70823	+	1.43337i
$147$		0			0
$148$	5.55674	+	31.5138i	0.456761	+	2.59042i
$149$	2.12675	+	12.0614i	0.174230	+	0.988107i	0.939029	+	0.343838i	$0.111727\pi$
$149$	2.12675	+	12.0614i	0.174230	+	0.988107i	−0.764799	+	0.644269i	$0.777162\pi$
$150$		0			0
$151$	3.83022	+	3.21394i	0.311699	+	0.261547i	0.785194	−	0.619250i	$-0.212563\pi$
$151$	3.83022	+	3.21394i	0.311699	+	0.261547i	−0.473495	+	0.880797i	$0.657008\pi$
$152$	2.44949	+	4.24264i	0.198680	+	0.344124i
$153$		0			0
$154$	−6.00000	+	10.3923i	−0.483494	+	0.837436i
$155$	−2.30177	+	0.837775i	−0.184882	+	0.0672917i
$156$		0			0
$157$	13.0228	−	10.9274i	1.03933	−	0.872101i	0.0473976	−	0.998876i	$-0.484907\pi$
$157$	13.0228	−	10.9274i	1.03933	−	0.872101i	0.991931	+	0.126775i	$0.0404628\pi$
$158$	16.1124	+	5.86442i	1.28183	+	0.466549i
$159$		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	$0.628089\pi$
$164$	3.40280	−	19.2982i	0.265714	−	1.50694i
$165$		0			0
$166$	28.1908	+	10.2606i	2.18803	+	0.796377i
$167$	3.75284	−	3.14900i	0.290403	−	0.243677i	−0.485933	−	0.873996i	$-0.661520\pi$
$167$	3.75284	−	3.14900i	0.290403	−	0.243677i	0.776336	+	0.630319i	$0.217076\pi$
$168$		0			0
$169$	11.2763	−	4.10424i	0.867409	−	0.315711i
$170$	−22.0454	+	38.1838i	−1.69081	+	2.92856i
$171$		0			0
$172$	−22.0000	−	38.1051i	−1.67748	−	2.90549i
$173$	7.50567	+	6.29801i	0.570646	+	0.478829i	0.881860	−	0.471511i	$-0.156291\pi$
$173$	7.50567	+	6.29801i	0.570646	+	0.478829i	−0.311214	+	0.950340i	$0.600736\pi$
$174$		0			0
$175$	0.347296	+	1.96962i	0.0262531	+	0.148889i
$176$	1.70140	+	9.64911i	0.128248	+	0.727329i
$177$		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	$0.262759\pi$
$182$	4.60353	−	1.67555i	0.341237	−	0.124200i
$183$		0			0
$184$	−9.19253	+	7.71345i	−0.677683	+	0.568643i
$185$	18.4141	+	6.70220i	1.35383	+	0.492755i
$186$		0			0
$187$	−3.12567	+	17.7265i	−0.228571	+	1.29629i
$188$	39.1918			2.85836
$189$		0			0
$190$	6.00000			0.435286
$191$	1.70140	−	9.64911i	0.123109	−	0.698185i	−0.859304	−	0.511465i	$-0.829103\pi$
$191$	1.70140	−	9.64911i	0.123109	−	0.698185i	0.982413	−	0.186720i	$-0.0597858\pi$
$192$		0			0
$193$	−10.3366	−	3.76222i	−0.744046	−	0.270811i	−0.0579479	−	0.998320i	$-0.518456\pi$
$193$	−10.3366	−	3.76222i	−0.744046	−	0.270811i	−0.686098	+	0.727509i	$0.740678\pi$
$194$	−13.1349	+	11.0215i	−0.943033	+	0.791298i
$195$		0			0
$196$	11.2763	−	4.10424i	0.805451	−	0.293160i
$197$	−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	$0.822049\pi$
$200$	3.75284	+	3.14900i	0.265366	+	0.222668i
$201$		0			0
$202$	−2.08378	−	11.8177i	−0.146614	−	0.831490i
$203$	−1.70140	−	9.64911i	−0.119415	−	0.677234i
$204$		0			0
$205$	−9.19253	−	7.71345i	−0.642034	−	0.538731i
$206$	8.57321	+	14.8492i	0.597324	+	1.03460i
$207$		0			0
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$	2.30177	−	0.837775i	0.159217	−	0.0579501i
$210$		0			0
$211$	−0.766044	+	0.642788i	−0.0527367	+	0.0442513i	−0.668775	−	0.743465i	$-0.733181\pi$
$211$	−0.766044	+	0.642788i	−0.0527367	+	0.0442513i	0.616038	+	0.787716i	$0.288737\pi$
$212$	−27.6212	−	10.0533i	−1.89703	−	0.690463i
$213$		0			0
$214$	6.25133	−	35.4531i	0.427332	−	2.42352i
$215$	−26.9444			−1.83759
$216$		0			0
$217$	−2.00000			−0.135769
$218$	−0.425349	+	2.41228i	−0.0288083	+	0.163380i
$219$		0			0
$220$	22.5526	+	8.20848i	1.52050	+	0.553416i
$221$	5.62925	−	4.72350i	0.378665	−	0.317737i
$222$		0			0
$223$	6.57785	−	2.39414i	0.440485	−	0.160324i	−0.112251	−	0.993680i	$-0.535806\pi$
$223$	6.57785	−	2.39414i	0.440485	−	0.160324i	0.552736	+	0.833356i	$0.313584\pi$
$224$		0			0
$225$		0			0
$226$	12.0000	+	20.7846i	0.798228	+	1.38257i
$227$	7.50567	+	6.29801i	0.498169	+	0.418013i	0.856943	−	0.515411i	$-0.172361\pi$
$227$	7.50567	+	6.29801i	0.498169	+	0.418013i	−0.358774	+	0.933424i	$0.616805\pi$
$228$		0			0
$229$	−0.173648	−	0.984808i	−0.0114750	−	0.0650779i	0.978533	−	0.206092i	$-0.0660747\pi$
$229$	−0.173648	−	0.984808i	−0.0114750	−	0.0650779i	−0.990008	+	0.141014i	$0.954964\pi$
$230$	2.55210	+	14.4737i	0.168280	+	0.954365i
$231$		0			0
$232$	−18.3851	−	15.4269i	−1.20704	−	1.01283i
$233$	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
$236$	9.20707	−	3.35110i	0.599329	−	0.218138i
$237$		0			0
$238$	−27.5776	+	23.1404i	−1.78759	+	1.49997i
$239$	2.30177	+	0.837775i	0.148889	+	0.0541911i	0.415390	−	0.909644i	$-0.363645\pi$
$239$	2.30177	+	0.837775i	0.148889	+	0.0541911i	−0.266501	+	0.963835i	$0.585867\pi$
$240$		0			0
$241$	−2.77837	+	15.7569i	−0.178971	+	1.01499i	0.754490	+	0.656312i	$0.227884\pi$
$241$	−2.77837	+	15.7569i	−0.178971	+	1.01499i	−0.933460	+	0.358681i	$0.883227\pi$
$242$	−12.2474			−0.787296
$243$		0			0
$244$	20.0000			1.28037
$245$	1.27605	−	7.23683i	0.0815237	−	0.462344i
$246$		0			0
$247$	−0.939693	−	0.342020i	−0.0597912	−	0.0217622i
$248$	−3.75284	+	3.14900i	−0.238305	+	0.199962i
$249$		0			0
$250$	−22.5526	+	8.20848i	−1.42635	+	0.519150i
$251$	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
$254$	−35.6519	−	29.9155i	−2.23700	−	1.87707i
$255$		0			0
$256$	−5.55674	−	31.5138i	−0.347296	−	1.96962i
$257$	−2.97745	−	16.8859i	−0.185728	−	1.05332i	−0.925017	−	0.379927i	$-0.875949\pi$
$257$	−2.97745	−	16.8859i	−0.185728	−	1.05332i	0.739289	−	0.673389i	$-0.235162\pi$
$258$		0			0
$259$	12.2567	+	10.2846i	0.761595	+	0.639054i
$260$	−4.89898	−	8.48528i	−0.303822	−	0.526235i
$261$		0			0
$262$	−15.0000	+	25.9808i	−0.926703	+	1.60510i
$263$	25.3194	−	9.21552i	1.56126	−	0.568254i	0.590238	−	0.807229i	$-0.299034\pi$
$263$	25.3194	−	9.21552i	1.56126	−	0.568254i	0.971026	+	0.238976i	$0.0768116\pi$
$264$		0			0
$265$	−13.7888	+	11.5702i	−0.847039	+	0.710750i
$266$	4.60353	+	1.67555i	0.282261	+	0.102735i
$267$		0			0
$268$	−4.86215	+	27.5746i	−0.297003	+	1.68439i
$269$	−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	$0.568196\pi$
$272$	−5.10419	+	28.9473i	−0.309487	+	1.75519i
$273$		0			0
$274$	−22.5526	−	8.20848i	−1.36245	−	0.495893i
$275$	1.87642	−	1.57450i	0.113152	−	0.0949460i
$276$		0			0
$277$	−10.3366	+	3.76222i	−0.621067	+	0.226050i	−0.633339	−	0.773875i	$-0.718316\pi$
$277$	−10.3366	+	3.76222i	−0.621067	+	0.226050i	0.0122715	+	0.999925i	$0.496094\pi$
$278$	12.2474	−	21.2132i	0.734553	−	1.27228i
$279$		0			0
$280$	12.0000	+	20.7846i	0.717137	+	1.24212i
$281$	−9.38209	−	7.87251i	−0.559689	−	0.469634i	0.318517	−	0.947917i	$-0.396815\pi$
$281$	−9.38209	−	7.87251i	−0.559689	−	0.469634i	−0.878206	+	0.478283i	$0.841259\pi$
$282$		0			0
$283$	2.95202	+	16.7417i	0.175479	+	0.995193i	0.937589	+	0.347745i	$0.113052\pi$
$283$	2.95202	+	16.7417i	0.175479	+	0.995193i	−0.762110	+	0.647448i	$0.775836\pi$
$284$	5.10419	+	28.9473i	0.302878	+	1.71771i
$285$		0			0
$286$	−4.59627	−	3.85673i	−0.271783	−	0.228053i
$287$	−4.89898	−	8.48528i	−0.289178	−	0.500870i
$288$		0			0
$289$	−18.5000	+	32.0429i	−1.08824	+	1.88488i
$290$	−27.6212	+	10.0533i	−1.62197	+	0.590350i
$291$		0			0
$292$	33.7060	−	28.2827i	1.97249	−	1.65512i
$293$	−4.60353	−	1.67555i	−0.268941	−	0.0978867i	0.204029	−	0.978965i	$-0.434596\pi$
$293$	−4.60353	−	1.67555i	−0.268941	−	0.0978867i	−0.472971	+	0.881078i	$0.656818\pi$
$294$		0			0
$295$	1.04189	−	5.90885i	0.0606611	−	0.344026i
$296$	39.1918			2.27798
$297$		0			0
$298$	30.0000			1.73785
$299$	0.425349	−	2.41228i	0.0245986	−	0.139506i
$300$		0			0
$301$	−20.6732	−	7.52444i	−1.19159	−	0.433702i
$302$	9.38209	−	7.87251i	0.539879	−	0.453012i
$303$		0			0
$304$	3.75877	−	1.36808i	0.215580	−	0.0784648i
$305$	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	$0.851510\pi$
$308$	15.0113	+	12.5960i	0.855351	+	0.717724i
$309$		0			0
$310$	1.04189	+	5.90885i	0.0591753	+	0.335600i
$311$	−4.25349	−	24.1228i	−0.241194	−	1.36788i	−0.829169	−	0.558998i	$-0.811186\pi$
$311$	−4.25349	−	24.1228i	−0.241194	−	1.36788i	0.587976	−	0.808879i	$-0.299925\pi$
$312$		0			0
$313$	−12.2567	−	10.2846i	−0.692790	−	0.581320i	0.226922	−	0.973913i	$-0.427134\pi$
$313$	−12.2567	−	10.2846i	−0.692790	−	0.581320i	−0.919712	+	0.392593i	$0.871578\pi$
$314$	−20.8207	−	36.0624i	−1.17498	−	2.03512i
$315$		0			0
$316$	14.0000	−	24.2487i	0.787562	−	1.36410i
$317$	−9.20707	+	3.35110i	−0.517121	+	0.188216i	−0.587378	−	0.809312i	$-0.699840\pi$
$317$	−9.20707	+	3.35110i	−0.517121	+	0.188216i	0.0702579	+	0.997529i	$0.477618\pi$
$318$		0			0
$319$	−9.19253	+	7.71345i	−0.514683	+	0.431870i
$320$	−18.4141	−	6.70220i	−1.02938	−	0.374664i
$321$		0			0
$322$	−2.08378	+	11.8177i	−0.116124	+	0.658574i
$323$	7.34847			0.408880
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−4.25349	+	24.1228i	−0.235579	+	1.33604i
$327$		0			0
$328$	−22.5526	−	8.20848i	−1.24526	−	0.453238i
$329$	15.0113	−	12.5960i	0.827602	−	0.694441i
$330$		0			0
$331$	6.57785	−	2.39414i	0.361551	−	0.131594i	−0.154856	−	0.987937i	$-0.549491\pi$
$331$	6.57785	−	2.39414i	0.361551	−	0.131594i	0.516407	+	0.856343i	$0.327269\pi$
$332$	24.4949	−	42.4264i	1.34433	−	2.32845i
$333$		0			0
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	13.1349	+	11.0215i	0.717638	+	0.602170i
$336$		0			0
$337$	−4.86215	−	27.5746i	−0.264858	−	1.50209i	−0.769439	−	0.638721i	$-0.779464\pi$
$337$	−4.86215	−	27.5746i	−0.264858	−	1.50209i	0.504581	−	0.863365i	$-0.331647\pi$
$338$	−5.10419	−	28.9473i	−0.277632	−	1.57453i
$339$		0			0
$340$	55.1552	+	46.2807i	2.99121	+	2.50992i
$341$	1.22474	+	2.12132i	0.0663237	+	0.114876i
$342$		0			0
$343$	10.0000	−	17.3205i	0.539949	−	0.935220i
$344$	−50.6389	+	18.4310i	−2.73027	+	0.993735i
$345$		0			0
$346$	18.3851	−	15.4269i	0.988387	−	0.829355i
$347$	23.0177	+	8.37775i	1.23565	+	0.449741i	0.875530	−	0.483164i	$-0.160512\pi$
$347$	23.0177	+	8.37775i	1.23565	+	0.449741i	0.360123	+	0.932905i	$0.382735\pi$
$348$		0			0
$349$	3.47296	−	19.6962i	0.185903	−	1.05431i	−0.738886	−	0.673831i	$-0.764648\pi$
$349$	3.47296	−	19.6962i	0.185903	−	1.05431i	0.924789	−	0.380480i	$-0.124241\pi$
$350$	4.89898			0.261861
$351$		0			0
$352$		0			0
$353$	0.425349	−	2.41228i	0.0226391	−	0.128393i	−0.971394	−	0.237475i	$-0.923680\pi$
$353$	0.425349	−	2.41228i	0.0226391	−	0.128393i	0.994033	+	0.109083i	$0.0347913\pi$
$354$		0			0
$355$	16.9145	+	6.15636i	0.897727	+	0.326746i
$356$		0			0
$357$		0			0
$358$	33.8289	−	12.3127i	1.78791	−	0.650748i
$359$	−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
$362$	15.0113	+	12.5960i	0.788979	+	0.662032i
$363$		0			0
$364$	−1.38919	−	7.87846i	−0.0728131	−	0.412944i
$365$	−4.67884	−	26.5350i	−0.244902	−	1.38891i
$366$		0			0
$367$	3.83022	+	3.21394i	0.199936	+	0.167766i	0.737259	−	0.675610i	$-0.236120\pi$
$367$	3.83022	+	3.21394i	0.199936	+	0.167766i	−0.537323	+	0.843377i	$0.680564\pi$
$368$	4.89898	+	8.48528i	0.255377	+	0.442326i
$369$		0			0
$370$	24.0000	−	41.5692i	1.24770	−	2.16108i
$371$	−13.8106	+	5.02665i	−0.717011	+	0.260971i
$372$		0			0
$373$	26.8116	−	22.4976i	1.38825	−	1.16488i	0.422206	−	0.906500i	$-0.361256\pi$
$373$	26.8116	−	22.4976i	1.38825	−	1.16488i	0.966043	−	0.258380i	$-0.0831887\pi$
$374$	41.4318	+	15.0799i	2.14239	+	0.779765i
$375$		0			0
$376$	8.33511	−	47.2708i	0.429851	−	2.43780i
$377$	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	$0.434129\pi$
$380$	1.70140	−	9.64911i	0.0872799	−	0.494989i
$381$		0			0
$382$	−22.5526	−	8.20848i	−1.15389	−	0.419983i
$383$	26.2699	−	22.0430i	1.34233	−	1.12635i	0.361305	−	0.932448i	$-0.382331\pi$
$383$	26.2699	−	22.0430i	1.34233	−	1.12635i	0.981022	−	0.193898i	$-0.0621132\pi$
$384$		0			0
$385$	11.2763	−	4.10424i	0.574694	−	0.209172i
$386$	−13.4722	+	23.3345i	−0.685717	+	1.18770i
$387$		0			0
$388$	14.0000	+	24.2487i	0.710742	+	1.23104i
$389$	−20.6406	−	17.3195i	−1.04652	−	0.878134i	−0.0537965	−	0.998552i	$-0.517132\pi$
$389$	−20.6406	−	17.3195i	−1.04652	−	0.878134i	−0.992723	+	0.120417i	$0.961577\pi$
$390$		0			0
$391$	3.12567	+	17.7265i	0.158072	+	0.896470i
$392$	−2.55210	−	14.4737i	−0.128900	−	0.731030i
$393$		0			0
$394$	27.5776	+	23.1404i	1.38934	+	1.16579i
$395$	−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	$0.158678\pi$
$398$	2.30177	−	0.837775i	0.115377	−	0.0419939i
$399$		0			0
$400$	3.06418	−	2.57115i	0.153209	−	0.128558i
$401$	−32.2247	−	11.7288i	−1.60923	−	0.585711i	−0.627940	−	0.778262i	$-0.716102\pi$
$401$	−32.2247	−	11.7288i	−1.60923	−	0.585711i	−0.981287	+	0.192551i	$0.938324\pi$
$402$		0			0
$403$	0.173648	−	0.984808i	0.00865003	−	0.0490568i
$404$	−19.5959			−0.974933
$405$		0			0
$406$	−24.0000			−1.19110
$407$	3.40280	−	19.2982i	0.168670	−	0.956577i
$408$		0			0
$409$	26.3114	+	9.57656i	1.30101	+	0.473531i	0.897327	−	0.441366i	$-0.145506\pi$
$409$	26.3114	+	9.57656i	1.30101	+	0.473531i	0.403688	+	0.914897i	$0.367728\pi$
$410$	−22.5170	+	18.8940i	−1.11204	+	0.933109i
$411$		0			0
$412$	26.3114	−	9.57656i	1.29627	−	0.471803i
$413$	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
$418$	−1.04189	−	5.90885i	−0.0509605	−	0.289011i
$419$	5.95489	+	33.7719i	0.290916	+	1.64986i	0.683355	+	0.730086i	$0.260520\pi$
$419$	5.95489	+	33.7719i	0.290916	+	1.64986i	−0.392440	+	0.919778i	$0.628369\pi$
$420$		0			0
$421$	1.53209	+	1.28558i	0.0746694	+	0.0626551i	0.679358	−	0.733807i	$-0.262258\pi$
$421$	1.53209	+	1.28558i	0.0746694	+	0.0626551i	−0.604689	+	0.796462i	$0.706703\pi$
$422$	1.22474	+	2.12132i	0.0596196	+	0.103264i
$423$		0			0
$424$	−18.0000	+	31.1769i	−0.874157	+	1.51408i
$425$	6.90530	−	2.51332i	0.334956	−	0.121914i
$426$		0			0
$427$	7.66044	−	6.42788i	0.370715	−	0.311067i
$428$	−55.2424	−	20.1066i	−2.67024	−	0.971889i
$429$		0			0
$430$	−11.4608	+	64.9973i	−0.552688	+	3.13445i
$431$	−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	$0.366058\pi$
$434$	−0.850699	+	4.82455i	−0.0408349	+	0.231586i
$435$		0			0
$436$	3.75877	+	1.36808i	0.180012	+	0.0655192i
$437$	1.87642	−	1.57450i	0.0897612	−	0.0753186i
$438$		0			0
$439$	−13.1557	+	4.78828i	−0.627887	+	0.228532i	−0.636311	−	0.771432i	$-0.719541\pi$
$439$	−13.1557	+	4.78828i	−0.627887	+	0.228532i	0.00842428	+	0.999965i	$0.497318\pi$
$440$	14.6969	−	25.4558i	0.700649	−	1.21356i
$441$		0			0
$442$	−9.00000	−	15.5885i	−0.428086	−	0.741467i
$443$	−9.38209	−	7.87251i	−0.445757	−	0.374034i	0.392102	−	0.919922i	$-0.371748\pi$
$443$	−9.38209	−	7.87251i	−0.445757	−	0.374034i	−0.837858	+	0.545888i	$0.816193\pi$
$444$		0			0
$445$		0			0
$446$	−2.97745	−	16.8859i	−0.140986	−	0.799572i
$447$		0			0
$448$	−12.2567	−	10.2846i	−0.579075	−	0.485902i
$449$	−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
$452$	36.8283	−	13.4044i	1.73226	−	0.630490i
$453$		0			0
$454$	18.3851	−	15.4269i	0.862854	−	0.724020i
$455$	−4.60353	−	1.67555i	−0.215817	−	0.0785510i
$456$		0			0
$457$	5.03580	−	28.5594i	0.235565	−	1.33595i	−0.605857	−	0.795574i	$-0.707169\pi$
$457$	5.03580	−	28.5594i	0.235565	−	1.33595i	0.841421	−	0.540380i	$-0.181719\pi$
$458$	−2.44949			−0.114457
$459$		0			0
$460$	24.0000			1.11901
$461$	−4.67884	+	26.5350i	−0.217915	+	1.23586i	0.657860	+	0.753141i	$0.271462\pi$
$461$	−4.67884	+	26.5350i	−0.217915	+	1.23586i	−0.875775	+	0.482719i	$0.839649\pi$
$462$		0			0
$463$	17.8542	+	6.49838i	0.829753	+	0.302005i	0.721758	−	0.692146i	$-0.243335\pi$
$463$	17.8542	+	6.49838i	0.829753	+	0.302005i	0.107996	+	0.994151i	$0.465557\pi$
$464$	−15.0113	+	12.5960i	−0.696884	+	0.584755i
$465$		0			0
$466$	16.9145	−	6.15636i	0.783548	−	0.285188i
$467$	−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
$470$	−45.0340	−	37.7880i	−2.07727	−	1.74303i
$471$		0			0
$472$	−2.08378	−	11.8177i	−0.0959137	−	0.543953i
$473$	4.67884	+	26.5350i	0.215133	+	1.22008i
$474$		0			0
$475$	−0.766044	−	0.642788i	−0.0351485	−	0.0294931i
$476$	29.3939	+	50.9117i	1.34727	+	2.33353i
$477$		0			0
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	25.3194	−	9.21552i	1.15687	−	0.421068i	0.308895	−	0.951096i	$-0.400041\pi$
$479$	25.3194	−	9.21552i	1.15687	−	0.421068i	0.847980	+	0.530028i	$0.177819\pi$
$480$		0			0
$481$	−6.12836	+	5.14230i	−0.279429	+	0.234469i
$482$	36.8283	+	13.4044i	1.67748	+	0.610554i
$483$		0			0
$484$	−3.47296	+	19.6962i	−0.157862	+	0.895280i
$485$	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	$0.208518\pi$
$488$	4.25349	−	24.1228i	0.192547	−	1.09199i
$489$		0			0
$490$	−16.9145	−	6.15636i	−0.764118	−	0.278116i
$491$	−30.0227	+	25.1920i	−1.35490	+	1.13690i	−0.377385	+	0.926056i	$0.623177\pi$
$491$	−30.0227	+	25.1920i	−1.35490	+	1.13690i	−0.977520	+	0.210844i	$0.932379\pi$
$492$		0			0
$493$	−33.8289	+	12.3127i	−1.52358	+	0.554537i
$494$	−1.22474	+	2.12132i	−0.0551039	+	0.0954427i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	11.2585	+	9.44701i	0.505013	+	0.423756i
$498$		0			0
$499$	0.347296	+	1.96962i	0.0155471	+	0.0881721i	0.991594	−	0.129388i	$-0.0413013\pi$
$499$	0.347296	+	1.96962i	0.0155471	+	0.0881721i	−0.976047	+	0.217560i	$0.930190\pi$
$500$	6.80559	+	38.5964i	0.304355	+	1.72608i
$501$		0			0
$502$	−13.7888	−	11.5702i	−0.615424	−	0.516402i
$503$	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
$506$	13.8106	−	5.02665i	0.613956	−	0.223462i
$507$		0			0
$508$	−58.2194	+	48.8519i	−2.58307	+	2.16745i
$509$	9.20707	+	3.35110i	0.408096	+	0.148535i	0.537908	−	0.843004i	$-0.319215\pi$
$509$	9.20707	+	3.35110i	0.408096	+	0.148535i	−0.129811	+	0.991539i	$0.541437\pi$
$510$		0			0
$511$	3.82026	−	21.6658i	0.168998	−	0.958437i
$512$	−39.1918			−1.73205
$513$		0			0
$514$	−42.0000			−1.85254
$515$	2.97745	−	16.8859i	0.131202	−	0.744083i
$516$		0			0
$517$	−22.5526	−	8.20848i	−0.991863	−	0.361009i
$518$	30.0227	−	25.1920i	1.31912	−	1.10687i
$519$		0			0
$520$	−11.2763	+	4.10424i	−0.494499	+	0.179983i
$521$	−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	$0.649260\pi$
$524$	37.5284	+	31.4900i	1.63943	+	1.37565i
$525$		0			0
$526$	−11.4608	−	64.9973i	−0.499714	−	2.83402i
$527$	1.27605	+	7.23683i	0.0555855	+	0.315241i
$528$		0			0
$529$	−13.0228	−	10.9274i	−0.566207	−	0.475104i
$530$	22.0454	+	38.1838i	0.957591	+	1.65860i
$531$		0			0
$532$	4.00000	−	6.92820i	0.173422	−	0.300376i
$533$	4.60353	−	1.67555i	0.199401	−	0.0725761i
$534$		0			0
$535$	−27.5776	+	23.1404i	−1.19228	+	1.00044i
$536$	32.2247	+	11.7288i	1.39190	+	0.506609i
$537$		0			0
$538$	−9.37700	+	53.1796i	−0.404271	+	2.29274i
$539$	−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	$0.705592\pi$
$542$	−2.97745	+	16.8859i	−0.127892	+	0.725313i
$543$		0			0
$544$		0			0
$545$	1.87642	−	1.57450i	0.0803769	−	0.0674442i
$546$		0			0
$547$	12.2160	−	4.44626i	0.522319	−	0.190108i	−0.0673867	−	0.997727i	$-0.521466\pi$
$547$	12.2160	−	4.44626i	0.522319	−	0.190108i	0.589705	+	0.807619i	$0.299244\pi$
$548$	−19.5959	+	33.9411i	−0.837096	+	1.44989i
$549$		0			0
$550$	−3.00000	−	5.19615i	−0.127920	−	0.221565i
$551$	3.75284	+	3.14900i	0.159876	+	0.134152i
$552$		0			0
$553$	−2.43107	−	13.7873i	−0.103380	−	0.586296i
$554$	4.67884	+	26.5350i	0.198785	+	1.12737i
$555$		0			0
$556$	−30.6418	−	25.7115i	−1.29950	−	1.09041i
$557$	−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
$560$	18.4141	−	6.70220i	0.778139	−	0.283220i
$561$		0			0
$562$	−22.9813	+	19.2836i	−0.969409	+	0.813431i
$563$	−11.5088	−	4.18887i	−0.485040	−	0.176540i	0.0879135	−	0.996128i	$-0.471980\pi$
$563$	−11.5088	−	4.18887i	−0.485040	−	0.176540i	−0.572953	+	0.819588i	$0.694202\pi$
$564$		0			0
$565$	4.16756	−	23.6354i	0.175330	−	0.994348i
$566$	41.6413			1.75032
$567$		0			0
$568$	36.0000			1.51053
$569$	−2.12675	+	12.0614i	−0.0891579	+	0.505639i	0.907224	+	0.420648i	$0.138197\pi$
$569$	−2.12675	+	12.0614i	−0.0891579	+	0.505639i	−0.996382	+	0.0849912i	$0.972914\pi$
$570$		0			0
$571$	9.39693	+	3.42020i	0.393249	+	0.143131i	0.531074	−	0.847326i	$-0.321789\pi$
$571$	9.39693	+	3.42020i	0.393249	+	0.143131i	−0.137824	+	0.990457i	$0.544011\pi$
$572$	−7.50567	+	6.29801i	−0.313828	+	0.263333i
$573$		0			0
$574$	−22.5526	+	8.20848i	−0.941328	+	0.342615i
$575$	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	$0.659123\pi$
$578$	69.4275	+	58.2566i	2.88780	+	2.42315i
$579$		0			0
$580$	8.33511	+	47.2708i	0.346097	+	1.96281i
$581$	−4.25349	−	24.1228i	−0.176465	−	1.00078i
$582$		0			0
$583$	13.7888	+	11.5702i	0.571074	+	0.479188i
$584$	−26.9444	−	46.6690i	−1.11497	−	1.93118i
$585$		0			0
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$	−2.30177	+	0.837775i	−0.0950041	+	0.0345787i	−0.389085	−	0.921202i	$-0.627209\pi$
$587$	−2.30177	+	0.837775i	−0.0950041	+	0.0345787i	0.294081	+	0.955781i	$0.404987\pi$
$588$		0			0
$589$	0.766044	−	0.642788i	0.0315643	−	0.0264856i
$590$	−13.8106	−	5.02665i	−0.568574	−	0.206944i
$591$		0			0
$592$	5.55674	−	31.5138i	0.228381	−	1.29521i
$593$	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
$596$	8.50699	−	48.2455i	0.348460	−	1.97621i
$597$		0			0
$598$	−5.63816	−	2.05212i	−0.230561	−	0.0839175i
$599$	−30.0227	+	25.1920i	−1.22669	+	1.02932i	−0.228247	+	0.973603i	$0.573299\pi$
$599$	−30.0227	+	25.1920i	−1.22669	+	1.02932i	−0.998447	+	0.0557151i	$0.982256\pi$
$600$		0			0
$601$	6.57785	−	2.39414i	0.268316	−	0.0976590i	−0.204359	−	0.978896i	$-0.565511\pi$
$601$	6.57785	−	2.39414i	0.268316	−	0.0976590i	0.472675	+	0.881237i	$0.343289\pi$
$602$	−26.9444	+	46.6690i	−1.09817	+	1.90209i
$603$		0			0
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	9.38209	+	7.87251i	0.381436	+	0.320063i
$606$		0			0
$607$	7.64052	+	43.3315i	0.310119	+	1.75877i	0.598372	+	0.801219i	$0.295815\pi$
$607$	7.64052	+	43.3315i	0.310119	+	1.75877i	−0.288253	+	0.957554i	$0.593074\pi$
$608$		0			0
$609$		0			0
$610$	−22.9813	−	19.2836i	−0.930487	−	0.780771i
$611$	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	$0.237972\pi$
$614$	−4.60353	+	1.67555i	−0.185784	+	0.0676197i
$615$		0			0
$616$	18.3851	−	15.4269i	0.740755	−	0.621568i
$617$	23.0177	+	8.37775i	0.926657	+	0.337275i	0.760884	−	0.648888i	$-0.224766\pi$
$617$	23.0177	+	8.37775i	0.926657	+	0.337275i	0.165773	+	0.986164i	$0.446988\pi$
$618$		0			0
$619$	−8.50876	+	48.2556i	−0.341996	+	1.93956i	0.000400419		1.00000i	$0.499873\pi$
$619$	−8.50876	+	48.2556i	−0.341996	+	1.93956i	−0.342396	+	0.939556i	$0.611239\pi$
$620$	9.79796			0.393496
$621$		0			0
$622$	−60.0000			−2.40578
$623$		0			0
$624$		0			0
$625$	27.2511	+	9.91858i	1.09004	+	0.396743i
$626$	−30.0227	+	25.1920i	−1.19995	+	1.00688i
$627$		0			0
$628$	−63.8991	+	23.2574i	−2.54985	+	0.928070i
$629$	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	$-0.506336\pi$
$632$	−26.2699	−	22.0430i	−1.04496	−	0.876824i
$633$		0			0
$634$	4.16756	+	23.6354i	0.165515	+	0.938681i
$635$	8.08164	+	45.8333i	0.320710	+	1.81884i
$636$		0			0
$637$	2.29813	+	1.92836i	0.0910554	+	0.0764045i
$638$	14.6969	+	25.4558i	0.581857	+	1.00781i
$639$		0			0
$640$	−24.0000	+	41.5692i	−0.948683	+	1.64317i
$641$	−16.1124	+	5.86442i	−0.636400	+	0.231631i	−0.640015	−	0.768363i	$-0.721072\pi$
$641$	−16.1124	+	5.86442i	−0.636400	+	0.231631i	0.00361428	+	0.999993i	$0.498850\pi$
$642$		0			0
$643$	29.1097	−	24.4259i	1.14797	−	0.963265i	0.148304	−	0.988942i	$-0.452619\pi$
$643$	29.1097	−	24.4259i	1.14797	−	0.963265i	0.999670	+	0.0256772i	$0.00817422\pi$
$644$	18.4141	+	6.70220i	0.725619	+	0.264104i
$645$		0			0
$646$	3.12567	−	17.7265i	0.122978	−	0.697441i
$647$	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
$650$	−0.425349	+	2.41228i	−0.0166836	+	0.0946173i
$651$		0			0
$652$	37.5877	+	13.6808i	1.47205	+	0.535782i
$653$	−7.50567	+	6.29801i	−0.293720	+	0.246460i	−0.777725	−	0.628605i	$-0.783626\pi$
$653$	−7.50567	+	6.29801i	−0.293720	+	0.246460i	0.484005	+	0.875065i	$0.339182\pi$
$654$		0			0
$655$	28.1908	−	10.2606i	1.10150	−	0.400915i
$656$	−9.79796	+	16.9706i	−0.382546	+	0.662589i
$657$		0			0
$658$	−24.0000	−	41.5692i	−0.935617	−	1.62054i
$659$	−15.0113	−	12.5960i	−0.584759	−	0.490671i	0.301747	−	0.953388i	$-0.402430\pi$
$659$	−15.0113	−	12.5960i	−0.584759	−	0.490671i	−0.886506	+	0.462717i	$0.846875\pi$
$660$		0			0
$661$	1.91013	+	10.8329i	0.0742954	+	0.421350i	0.999157	+	0.0410470i	$0.0130693\pi$
$661$	1.91013	+	10.8329i	0.0742954	+	0.421350i	−0.924862	+	0.380303i	$0.875820\pi$
$662$	−2.97745	−	16.8859i	−0.115722	−	0.656291i
$663$		0			0
$664$	−45.9627	−	38.5673i	−1.78370	−	1.49670i
$665$	−2.44949	−	4.24264i	−0.0949871	−	0.164523i
$666$		0			0
$667$	−6.00000	+	10.3923i	−0.232321	+	0.402392i
$668$	−18.4141	+	6.70220i	−0.712464	+	0.259316i
$669$		0			0
$670$	32.1739	−	26.9971i	1.24298	−	1.04299i
$671$	−11.5088	−	4.18887i	−0.444294	−	0.161710i
$672$		0			0
$673$	5.03580	−	28.5594i	0.194116	−	1.10088i	−0.719557	−	0.694434i	$-0.755655\pi$
$673$	5.03580	−	28.5594i	0.194116	−	1.10088i	0.913672	−	0.406451i	$-0.133234\pi$
$674$	−68.5857			−2.64182
$675$		0			0
$676$	−48.0000			−1.84615
$677$	8.08164	−	45.8333i	0.310603	−	1.76152i	−0.285281	−	0.958444i	$-0.592087\pi$
$677$	8.08164	−	45.8333i	0.310603	−	1.76152i	0.595883	−	0.803071i	$-0.296802\pi$
$678$		0			0
$679$	13.1557	+	4.78828i	0.504869	+	0.183757i
$680$	67.5510	−	56.6821i	2.59046	−	2.17366i
$681$		0			0
$682$	5.63816	−	2.05212i	0.215896	−	0.0785798i
$683$	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
$686$	−37.5284	−	31.4900i	−1.43284	−	1.20230i
$687$		0			0
$688$	7.64052	+	43.3315i	0.291292	+	1.65200i
$689$	−1.27605	−	7.23683i	−0.0486136	−	0.275701i
$690$		0			0
$691$	36.0041	+	30.2110i	1.36966	+	1.14928i	0.972865	+	0.231374i	$0.0743221\pi$
$691$	36.0041	+	30.2110i	1.36966	+	1.14928i	0.396795	+	0.917907i	$0.370122\pi$
$692$	−19.5959	−	33.9411i	−0.744925	−	1.29025i
$693$		0			0
$694$	30.0000	−	51.9615i	1.13878	−	1.97243i
$695$	−23.0177	+	8.37775i	−0.873110	+	0.317786i
$696$		0			0
$697$	−27.5776	+	23.1404i	−1.04458	+	0.876503i
$698$	−46.0353	−	16.7555i	−1.74246	−	0.634205i
$699$		0			0
$700$	1.38919	−	7.87846i	0.0525063	−	0.297778i
$701$	−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
$704$	−3.40280	+	19.2982i	−0.128248	+	0.727329i
$705$		0			0
$706$	−5.63816	−	2.05212i	−0.212195	−	0.0772326i
$707$	−7.50567	+	6.29801i	−0.282280	+	0.236861i
$708$		0			0
$709$	6.57785	−	2.39414i	0.247036	−	0.0899139i	−0.215534	−	0.976496i	$-0.569149\pi$
$709$	6.57785	−	2.39414i	0.247036	−	0.0899139i	0.462571	+	0.886582i	$0.346927\pi$
$710$	22.0454	−	38.1838i	0.827349	−	1.43301i
$711$		0			0
$712$		0			0
$713$	1.87642	+	1.57450i	0.0702724	+	0.0589656i
$714$		0			0
$715$	1.04189	+	5.90885i	0.0389644	+	0.220978i
$716$	−10.2084	−	57.8946i	−0.381505	−	2.16362i
$717$		0			0
$718$	55.1552	+	46.2807i	2.05837	+	1.72718i
$719$	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
$722$	41.4318	−	15.0799i	1.54193	−	0.561218i
$723$		0			0
$724$	24.5134	−	20.5692i	0.911034	−	0.764448i
$725$	4.60353	+	1.67555i	0.170971	+	0.0622284i
$726$		0			0
$727$	2.43107	−	13.7873i	0.0901636	−	0.511343i	−0.905959	−	0.423366i	$-0.860849\pi$
$727$	2.43107	−	13.7873i	0.0901636	−	0.511343i	0.996122	−	0.0879774i	$-0.0280403\pi$
$728$	−9.79796			−0.363137
$729$		0			0
$730$	−66.0000			−2.44277
$731$	−14.0365	+	79.6051i	−0.519160	+	2.94430i
$732$		0			0
$733$	−15.9748	−	5.81434i	−0.590042	−	0.214758i	0.0297060	−	0.999559i	$-0.490543\pi$
$733$	−15.9748	−	5.81434i	−0.590042	−	0.214758i	−0.619748	+	0.784801i	$0.712765\pi$
$734$	9.38209	−	7.87251i	0.346299	−	0.290580i
$735$		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	$0.827478\pi$
$740$	−60.0454	−	50.3841i	−2.20731	−	1.85215i
$741$		0			0
$742$	6.25133	+	35.4531i	0.229494	+	1.30152i
$743$	−5.52954	−	31.3596i	−0.202859	−	1.15047i	−0.900773	−	0.434290i	$-0.856999\pi$
$743$	−5.52954	−	31.3596i	−0.202859	−	1.15047i	0.697914	−	0.716182i	$-0.254112\pi$
$744$		0			0
$745$	−22.9813	−	19.2836i	−0.841971	−	0.706497i
$746$	−42.8661	−	74.2462i	−1.56944	−	2.71835i
$747$		0			0
$748$	36.0000	−	62.3538i	1.31629	−	2.27988i
$749$	−27.6212	+	10.0533i	−1.00926	+	0.367340i
$750$		0			0
$751$	19.9172	−	16.7125i	0.726787	−	0.609847i	−0.202466	−	0.979289i	$-0.564896\pi$
$751$	19.9172	−	16.7125i	0.726787	−	0.609847i	0.929254	+	0.369442i	$0.120451\pi$
$752$	−36.8283	−	13.4044i	−1.34299	−	0.488808i
$753$		0			0
$754$	2.08378	−	11.8177i	0.0758867	−	0.430375i
$755$	−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	$0.540602\pi$
$758$	3.40280	−	19.2982i	0.123595	−	0.700943i
$759$		0			0
$760$	−11.2763	−	4.10424i	−0.409035	−	0.148876i
$761$	−1.87642	+	1.57450i	−0.0680201	+	0.0570756i	−0.676164	−	0.736751i	$-0.736359\pi$
$761$	−1.87642	+	1.57450i	−0.0680201	+	0.0570756i	0.608144	+	0.793827i	$0.291914\pi$
$762$		0			0
$763$	1.87939	−	0.684040i	0.0680383	−	0.0247639i
$764$	−19.5959	+	33.9411i	−0.708955	+	1.22795i
$765$		0			0
$766$	−42.0000	−	72.7461i	−1.51752	−	2.62842i
$767$	1.87642	+	1.57450i	0.0677535	+	0.0568520i
$768$		0			0
$769$	−6.42498	−	36.4379i	−0.231691	−	1.31398i	−0.849472	−	0.527634i	$-0.823079\pi$
$769$	−6.42498	−	36.4379i	−0.231691	−	1.31398i	0.617781	−	0.786350i	$-0.288032\pi$
$770$	−5.10419	−	28.9473i	−0.183942	−	1.04319i
$771$		0			0
$772$	33.7060	+	28.2827i	1.21310	+	1.01792i
$773$	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
$776$	32.2247	−	11.7288i	1.15680	−	0.421041i
$777$		0			0
$778$	−50.5589	+	42.4240i	−1.81263	+	1.52097i
$779$	4.60353	+	1.67555i	0.164939	+	0.0600328i
$780$		0			0
$781$	3.12567	−	17.7265i	0.111845	−	0.634305i
$782$	44.0908			1.57668
$783$

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)

\(f(q)\)	\(=\)	\(q+(0.425349 - 2.41228i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-1.87642 + 1.57450i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(-2.44949 + 4.24264i) q^{8} +O(q^{10})\)	\(q+(0.425349 - 2.41228i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-1.87642 + 1.57450i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(-2.44949 + 4.24264i) q^{8} +(3.00000 + 5.19615i) q^{10} +(1.87642 + 1.57450i) q^{11} +(-0.173648 - 0.984808i) q^{13} +(0.850699 + 4.82455i) q^{14} +(3.06418 + 2.57115i) q^{16} +(3.67423 + 6.36396i) q^{17} +(0.500000 - 0.866025i) q^{19} +(9.20707 - 3.35110i) q^{20} +(4.59627 - 3.85673i) q^{22} +(2.30177 + 0.837775i) q^{23} +(0.173648 - 0.984808i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(-0.850699 + 4.82455i) q^{29} +(0.939693 + 0.342020i) q^{31} +(16.9145 - 6.15636i) q^{34} +(2.44949 - 4.24264i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(-1.87642 - 1.57450i) q^{38} +(-2.08378 - 11.8177i) q^{40} +(0.850699 + 4.82455i) q^{41} +(8.42649 + 7.07066i) q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-9.20707 + 3.35110i) q^{47} +(-2.29813 + 1.92836i) q^{49} +(-2.30177 - 0.837775i) q^{50} +(-0.694593 + 3.93923i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(1.70140 - 9.64911i) q^{56} +(11.2763 + 4.10424i) q^{58} +(-1.87642 + 1.57450i) q^{59} +(-4.69846 + 1.71010i) q^{61} +(1.22474 - 2.12132i) q^{62} +(4.00000 + 6.92820i) q^{64} +(1.87642 + 1.57450i) q^{65} +(-1.21554 - 6.89365i) q^{67} +(-5.10419 - 28.9473i) q^{68} +(-9.19253 - 7.71345i) q^{70} +(-3.67423 - 6.36396i) q^{71} +(-5.50000 + 9.52628i) q^{73} +(-18.4141 + 6.70220i) q^{74} +(-3.06418 + 2.57115i) q^{76} +(-4.60353 - 1.67555i) q^{77} +(-1.21554 + 6.89365i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(-2.12675 + 12.0614i) q^{83} +(-16.9145 - 6.15636i) q^{85} +(20.6406 - 17.3195i) q^{86} +(-11.2763 + 4.10424i) q^{88} +(1.00000 + 1.73205i) q^{91} +(-7.50567 - 6.29801i) q^{92} +(4.16756 + 23.6354i) q^{94} +(0.425349 + 2.41228i) q^{95} +(-5.36231 - 4.49951i) q^{97} +(3.67423 + 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 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

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