LMFDB - Embedded newform 729.2.e.p.325.2

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			325.2
Root			$1.39273 - 0.245576i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.p.406.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87642 - 1.57450i) q^{2} +(0.694593 - 3.93923i) q^{4} +(2.30177 - 0.837775i) q^{5} +(0.347296 + 1.96962i) q^{7} +(-2.44949 - 4.24264i) q^{8} +O(q^{10})$	\(q+(1.87642 - 1.57450i) q^{2} +(0.694593 - 3.93923i) q^{4} +(2.30177 - 0.837775i) q^{5} +(0.347296 + 1.96962i) q^{7} +(-2.44949 - 4.24264i) q^{8} +(3.00000 - 5.19615i) q^{10} +(-2.30177 - 0.837775i) q^{11} +(-0.766044 - 0.642788i) q^{13} +(3.75284 + 3.14900i) q^{14} +(-3.75877 - 1.36808i) q^{16} +(3.67423 - 6.36396i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-1.70140 - 9.64911i) q^{20} +(-5.63816 + 2.05212i) q^{22} +(-0.425349 + 2.41228i) q^{23} +(0.766044 - 0.642788i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(-3.75284 + 3.14900i) q^{29} +(-0.173648 + 0.984808i) q^{31} +(-3.12567 - 17.7265i) q^{34} +(2.44949 + 4.24264i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(2.30177 + 0.837775i) q^{38} +(-9.19253 - 7.71345i) q^{40} +(3.75284 + 3.14900i) q^{41} +(-10.3366 - 3.76222i) q^{43} +(-4.89898 + 8.48528i) q^{44} +(3.00000 + 5.19615i) q^{46} +(1.70140 + 9.64911i) q^{47} +(2.81908 - 1.02606i) q^{49} +(0.425349 - 2.41228i) q^{50} +(-3.06418 + 2.57115i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(7.50567 - 6.29801i) q^{56} +(-2.08378 + 11.8177i) q^{58} +(2.30177 - 0.837775i) q^{59} +(0.868241 + 4.92404i) q^{61} +(1.22474 + 2.12132i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-2.30177 - 0.837775i) q^{65} +(-5.36231 - 4.49951i) q^{67} +(-22.5170 - 18.8940i) q^{68} +(11.2763 + 4.10424i) q^{70} +(-3.67423 + 6.36396i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(3.40280 + 19.2982i) q^{74} +(3.75877 - 1.36808i) q^{76} +(0.850699 - 4.82455i) q^{77} +(-5.36231 + 4.49951i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(-9.38209 + 7.87251i) q^{83} +(3.12567 - 17.7265i) q^{85} +(-25.3194 + 9.21552i) q^{86} +(2.08378 + 11.8177i) q^{88} +(1.00000 - 1.73205i) q^{91} +(9.20707 + 3.35110i) q^{92} +(18.3851 + 15.4269i) q^{94} +(1.87642 + 1.57450i) q^{95} +(6.57785 + 2.39414i) q^{97} +(3.67423 - 6.36396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	1.87642	−	1.57450i	1.32683	−	1.11334i	0.342020	−	0.939693i	$-0.388889\pi$
$2$	1.87642	−	1.57450i	1.32683	−	1.11334i	0.984808	−	0.173648i	$-0.0555556\pi$
$3$		0			0
$3$		0			0
$4$	0.694593	−	3.93923i	0.347296	−	1.96962i
$5$	2.30177	−	0.837775i	1.02938	−	0.374664i	0.228536	−	0.973535i	$-0.426606\pi$
$5$	2.30177	−	0.837775i	1.02938	−	0.374664i	0.800845	+	0.598871i	$0.204384\pi$
$6$		0			0
$7$	0.347296	+	1.96962i	0.131266	+	0.744445i	0.977388	+	0.211455i	$0.0678203\pi$
$7$	0.347296	+	1.96962i	0.131266	+	0.744445i	−0.846122	+	0.532989i	$0.821069\pi$
$8$	−2.44949	−	4.24264i	−0.866025	−	1.50000i
$9$		0			0
$10$	3.00000	−	5.19615i	0.948683	−	1.64317i
$11$	−2.30177	−	0.837775i	−0.694009	−	0.252599i	−0.0291582	−	0.999575i	$-0.509283\pi$
$11$	−2.30177	−	0.837775i	−0.694009	−	0.252599i	−0.664851	+	0.746976i	$0.731505\pi$
$12$		0			0
$13$	−0.766044	−	0.642788i	−0.212463	−	0.178277i	0.530346	−	0.847781i	$-0.322062\pi$
$13$	−0.766044	−	0.642788i	−0.212463	−	0.178277i	−0.742808	+	0.669504i	$0.766507\pi$
$14$	3.75284	+	3.14900i	1.00299	+	0.841607i
$15$		0			0
$16$	−3.75877	−	1.36808i	−0.939693	−	0.342020i
$17$	3.67423	−	6.36396i	0.891133	−	1.54349i	0.0526138	−	0.998615i	$-0.483245\pi$
$17$	3.67423	−	6.36396i	0.891133	−	1.54349i	0.838519	−	0.544872i	$-0.183422\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−1.70140	−	9.64911i	−0.380444	−	2.15761i
$21$		0			0
$22$	−5.63816	+	2.05212i	−1.20206	+	0.437514i
$23$	−0.425349	+	2.41228i	−0.0886915	+	0.502994i	0.907807	+	0.419387i	$0.137755\pi$
$23$	−0.425349	+	2.41228i	−0.0886915	+	0.502994i	−0.996499	+	0.0836069i	$0.973356\pi$
$24$		0			0
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	−2.44949			−0.480384
$27$		0			0
$28$	8.00000			1.51186
$29$	−3.75284	+	3.14900i	−0.696884	+	0.584755i	−0.920885	−	0.389834i	$-0.872533\pi$
$29$	−3.75284	+	3.14900i	−0.696884	+	0.584755i	0.224001	+	0.974589i	$0.428088\pi$
$30$		0			0
$31$	−0.173648	+	0.984808i	−0.0311881	+	0.176877i	−0.996423	−	0.0845082i	$-0.973068\pi$
$31$	−0.173648	+	0.984808i	−0.0311881	+	0.176877i	0.965235	+	0.261385i	$0.0841792\pi$
$32$		0			0
$33$		0			0
$34$	−3.12567	−	17.7265i	−0.536048	−	3.04008i
$35$	2.44949	+	4.24264i	0.414039	+	0.717137i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	2.30177	+	0.837775i	0.373396	+	0.135905i
$39$		0			0
$40$	−9.19253	−	7.71345i	−1.45347	−	1.21960i
$41$	3.75284	+	3.14900i	0.586095	+	0.491792i	0.886942	−	0.461881i	$-0.152825\pi$
$41$	3.75284	+	3.14900i	0.586095	+	0.491792i	−0.300848	+	0.953672i	$0.597270\pi$
$42$		0			0
$43$	−10.3366	−	3.76222i	−1.57632	−	0.573733i	−0.601920	−	0.798556i	$-0.705597\pi$
$43$	−10.3366	−	3.76222i	−1.57632	−	0.573733i	−0.974400	+	0.224823i	$0.927820\pi$
$44$	−4.89898	+	8.48528i	−0.738549	+	1.27920i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	1.70140	+	9.64911i	0.248174	+	1.40747i	0.813003	+	0.582259i	$0.197831\pi$
$47$	1.70140	+	9.64911i	0.248174	+	1.40747i	−0.564829	+	0.825208i	$0.691058\pi$
$48$		0			0
$49$	2.81908	−	1.02606i	0.402725	−	0.146580i
$50$	0.425349	−	2.41228i	0.0601535	−	0.341147i
$51$		0			0
$52$	−3.06418	+	2.57115i	−0.424925	+	0.356554i
$53$	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
$56$	7.50567	−	6.29801i	1.00299	−	0.841607i
$57$		0			0
$58$	−2.08378	+	11.8177i	−0.273613	+	1.55174i
$59$	2.30177	−	0.837775i	0.299665	−	0.109069i	−0.187812	−	0.982205i	$-0.560140\pi$
$59$	2.30177	−	0.837775i	0.299665	−	0.109069i	0.487477	+	0.873136i	$0.337917\pi$
$60$		0			0
$61$	0.868241	+	4.92404i	0.111167	+	0.630459i	0.988577	+	0.150717i	$0.0481583\pi$
$61$	0.868241	+	4.92404i	0.111167	+	0.630459i	−0.877410	+	0.479741i	$0.840731\pi$
$62$	1.22474	+	2.12132i	0.155543	+	0.269408i
$63$		0			0
$64$	4.00000	−	6.92820i	0.500000	−	0.866025i
$65$	−2.30177	−	0.837775i	−0.285499	−	0.103913i
$66$		0			0
$67$	−5.36231	−	4.49951i	−0.655111	−	0.549703i	0.253506	−	0.967334i	$-0.418416\pi$
$67$	−5.36231	−	4.49951i	−0.655111	−	0.549703i	−0.908617	+	0.417631i	$0.862861\pi$
$68$	−22.5170	−	18.8940i	−2.73059	−	2.29124i
$69$		0			0
$70$	11.2763	+	4.10424i	1.34778	+	0.490551i
$71$	−3.67423	+	6.36396i	−0.436051	+	0.755263i	−0.997381	−	0.0723293i	$-0.976957\pi$
$71$	−3.67423	+	6.36396i	−0.436051	+	0.755263i	0.561329	+	0.827592i	$0.310290\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	3.40280	+	19.2982i	0.395567	+	2.24337i
$75$		0			0
$76$	3.75877	−	1.36808i	0.431161	−	0.156930i
$77$	0.850699	−	4.82455i	0.0969461	−	0.549809i
$78$		0			0
$79$	−5.36231	+	4.49951i	−0.603307	+	0.506235i	−0.892507	−	0.451034i	$-0.851055\pi$
$79$	−5.36231	+	4.49951i	−0.603307	+	0.506235i	0.289200	+	0.957269i	$0.406611\pi$
$80$	−9.79796			−1.09545
$81$		0			0
$82$	12.0000			1.32518
$83$	−9.38209	+	7.87251i	−1.02982	+	0.864120i	−0.990829	−	0.135120i	$-0.956858\pi$
$83$	−9.38209	+	7.87251i	−1.02982	+	0.864120i	−0.0389889	+	0.999240i	$0.512414\pi$
$84$		0			0
$85$	3.12567	−	17.7265i	0.339026	−	1.92271i
$86$	−25.3194	+	9.21552i	−2.73027	+	0.993735i
$87$		0			0
$88$	2.08378	+	11.8177i	0.222131	+	1.25977i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	1.00000	−	1.73205i	0.104828	−	0.181568i
$92$	9.20707	+	3.35110i	0.959903	+	0.349376i
$93$		0			0
$94$	18.3851	+	15.4269i	1.89627	+	1.59116i
$95$	1.87642	+	1.57450i	0.192516	+	0.161540i
$96$		0			0
$97$	6.57785	+	2.39414i	0.667879	+	0.243088i	0.653635	−	0.756810i	$-0.273243\pi$
$97$	6.57785	+	2.39414i	0.667879	+	0.243088i	0.0142448	+	0.999899i	$0.495466\pi$
$98$	3.67423	−	6.36396i	0.371154	−	0.642857i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−0.850699	−	4.82455i	−0.0846477	−	0.480061i	−0.997432	−	0.0716191i	$-0.977183\pi$
$101$	−0.850699	−	4.82455i	−0.0846477	−	0.480061i	0.912784	−	0.408442i	$-0.133928\pi$
$102$		0			0
$103$	6.57785	−	2.39414i	0.648135	−	0.235902i	0.00302937	−	0.999995i	$-0.499036\pi$
$103$	6.57785	−	2.39414i	0.648135	−	0.235902i	0.645105	+	0.764094i	$0.276813\pi$
$104$	−0.850699	+	4.82455i	−0.0834179	+	0.473086i
$105$		0			0
$106$	13.7888	−	11.5702i	1.33929	−	1.12379i
$107$	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	$0.515250\pi$
$110$	−11.2585	+	9.44701i	−1.07346	+	0.900737i
$111$		0			0
$112$	1.38919	−	7.87846i	0.131266	−	0.744445i
$113$	9.20707	−	3.35110i	0.866128	−	0.315245i	0.129530	−	0.991575i	$-0.458653\pi$
$113$	9.20707	−	3.35110i	0.866128	−	0.315245i	0.736598	+	0.676331i	$0.236431\pi$
$114$		0			0
$115$	1.04189	+	5.90885i	0.0971567	+	0.551003i
$116$	9.79796	+	16.9706i	0.909718	+	1.57568i
$117$		0			0
$118$	3.00000	−	5.19615i	0.276172	−	0.478345i
$119$	13.8106	+	5.02665i	1.26602	+	0.460792i
$120$		0			0
$121$	−3.83022	−	3.21394i	−0.348202	−	0.292176i
$122$	9.38209	+	7.87251i	0.849415	+	0.712743i
$123$		0			0
$124$	3.75877	+	1.36808i	0.337548	+	0.122857i
$125$	−4.89898	+	8.48528i	−0.438178	+	0.758947i
$126$		0			0
$127$	9.50000	+	16.4545i	0.842989	+	1.46010i	0.887357	+	0.461084i	$0.152539\pi$
$127$	9.50000	+	16.4545i	0.842989	+	1.46010i	−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−3.40280	−	19.2982i	−0.300767	−	1.70574i
$129$		0			0
$130$	−5.63816	+	2.05212i	−0.494499	+	0.179983i
$131$	2.12675	−	12.0614i	0.185815	−	1.05381i	−0.739089	−	0.673607i	$-0.764744\pi$
$131$	2.12675	−	12.0614i	0.185815	−	1.05381i	0.924904	−	0.380200i	$-0.124145\pi$
$132$		0			0
$133$	−1.53209	+	1.28558i	−0.132849	+	0.111474i
$134$	−17.1464			−1.48123
$135$		0			0
$136$	−36.0000			−3.08697
$137$	7.50567	−	6.29801i	0.641253	−	0.538075i	−0.263150	−	0.964755i	$-0.584761\pi$
$137$	7.50567	−	6.29801i	0.641253	−	0.538075i	0.904403	+	0.426680i	$0.140317\pi$
$138$		0			0
$139$	−1.73648	+	9.84808i	−0.147286	+	0.835303i	0.818216	+	0.574910i	$0.194963\pi$
$139$	−1.73648	+	9.84808i	−0.147286	+	0.835303i	−0.965503	+	0.260393i	$0.916148\pi$
$140$	18.4141	−	6.70220i	1.55628	−	0.566439i
$141$		0			0
$142$	3.12567	+	17.7265i	0.262300	+	1.48758i
$143$	1.22474	+	2.12132i	0.102418	+	0.177394i
$144$		0			0
$145$	−6.00000	+	10.3923i	−0.498273	+	0.863034i
$146$	−25.3194	−	9.21552i	−2.09545	−	0.762682i
$147$		0			0
$148$	24.5134	+	20.5692i	2.01499	+	1.69078i
$149$	9.38209	+	7.87251i	0.768611	+	0.644941i	0.940353	−	0.340201i	$-0.110495\pi$
$149$	9.38209	+	7.87251i	0.768611	+	0.644941i	−0.171742	+	0.985142i	$0.554940\pi$
$150$		0			0
$151$	−4.69846	−	1.71010i	−0.382356	−	0.139166i	0.143689	−	0.989623i	$-0.454103\pi$
$151$	−4.69846	−	1.71010i	−0.382356	−	0.139166i	−0.526045	+	0.850457i	$0.676326\pi$
$152$	2.44949	−	4.24264i	0.198680	−	0.344124i
$153$		0			0
$154$	−6.00000	−	10.3923i	−0.483494	−	0.837436i
$155$	0.425349	+	2.41228i	0.0341649	+	0.193759i
$156$		0			0
$157$	−15.9748	+	5.81434i	−1.27493	+	0.464035i	−0.888751	−	0.458391i	$-0.848426\pi$
$157$	−15.9748	+	5.81434i	−1.27493	+	0.464035i	−0.386175	+	0.922426i	$0.626204\pi$
$158$	−2.97745	+	16.8859i	−0.236873	+	1.34337i
$159$		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	$0.628089\pi$
$164$	15.0113	−	12.5960i	1.17219	−	0.983583i
$165$		0			0
$166$	−5.20945	+	29.5442i	−0.404331	+	2.29308i
$167$	−4.60353	+	1.67555i	−0.356232	+	0.129658i	−0.513936	−	0.857829i	$-0.671813\pi$
$167$	−4.60353	+	1.67555i	−0.356232	+	0.129658i	0.157704	+	0.987486i	$0.449591\pi$
$168$		0			0
$169$	−2.08378	−	11.8177i	−0.160291	−	0.909053i
$170$	−22.0454	−	38.1838i	−1.69081	−	2.92856i
$171$		0			0
$172$	−22.0000	+	38.1051i	−1.67748	+	2.90549i
$173$	−9.20707	−	3.35110i	−0.700001	−	0.254779i	−0.0325894	−	0.999469i	$-0.510375\pi$
$173$	−9.20707	−	3.35110i	−0.700001	−	0.254779i	−0.667411	+	0.744689i	$0.732598\pi$
$174$		0			0
$175$	1.53209	+	1.28558i	0.115815	+	0.0971804i
$176$	7.50567	+	6.29801i	0.565761	+	0.474730i
$177$		0			0
$178$		0			0
$179$	7.34847	−	12.7279i	0.549250	−	0.951330i	−0.449076	−	0.893494i	$-0.648247\pi$
$179$	7.34847	−	12.7279i	0.549250	−	0.951330i	0.998326	−	0.0578359i	$-0.0184200\pi$
$180$		0			0
$181$	−4.00000	−	6.92820i	−0.297318	−	0.514969i	0.678204	−	0.734874i	$-0.262759\pi$
$181$	−4.00000	−	6.92820i	−0.297318	−	0.514969i	−0.975521	+	0.219905i	$0.929425\pi$
$182$	−0.850699	−	4.82455i	−0.0630580	−	0.357620i
$183$		0			0
$184$	11.2763	−	4.10424i	0.831301	−	0.302569i
$185$	−3.40280	+	19.2982i	−0.250178	+	1.41883i
$186$		0			0
$187$	−13.7888	+	11.5702i	−1.00834	+	0.846095i
$188$	39.1918			2.85836
$189$		0			0
$190$	6.00000			0.435286
$191$	7.50567	−	6.29801i	0.543091	−	0.455708i	−0.329502	−	0.944155i	$-0.606881\pi$
$191$	7.50567	−	6.29801i	0.543091	−	0.455708i	0.872594	+	0.488447i	$0.162436\pi$
$192$		0			0
$193$	1.91013	−	10.8329i	0.137494	−	0.779768i	−0.835596	−	0.549344i	$-0.814878\pi$
$193$	1.91013	−	10.8329i	0.137494	−	0.779768i	0.973090	−	0.230424i	$-0.0740113\pi$
$194$	16.1124	−	5.86442i	1.15680	−	0.421041i
$195$		0			0
$196$	−2.08378	−	11.8177i	−0.148841	−	0.844121i
$197$	−7.34847	−	12.7279i	−0.523557	−	0.906827i	−0.999624	−	0.0274180i	$-0.991271\pi$
$197$	−7.34847	−	12.7279i	−0.523557	−	0.906827i	0.476067	−	0.879409i	$-0.342062\pi$
$198$		0			0
$199$	0.500000	−	0.866025i	0.0354441	−	0.0613909i	−0.847759	−	0.530381i	$-0.822049\pi$
$199$	0.500000	−	0.866025i	0.0354441	−	0.0613909i	0.883203	+	0.468990i	$0.155382\pi$
$200$	−4.60353	−	1.67555i	−0.325519	−	0.118479i
$201$		0			0
$202$	−9.19253	−	7.71345i	−0.646784	−	0.542717i
$203$	−7.50567	−	6.29801i	−0.526795	−	0.442033i
$204$		0			0
$205$	11.2763	+	4.10424i	0.787572	+	0.286653i
$206$	8.57321	−	14.8492i	0.597324	−	1.03460i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	−0.425349	−	2.41228i	−0.0294220	−	0.166861i
$210$		0			0
$211$	0.939693	−	0.342020i	0.0646911	−	0.0235456i	−0.309472	−	0.950909i	$-0.600152\pi$
$211$	0.939693	−	0.342020i	0.0646911	−	0.0235456i	0.374163	+	0.927363i	$0.377930\pi$
$212$	5.10419	−	28.9473i	0.350557	−	1.98811i
$213$		0			0
$214$	27.5776	−	23.1404i	1.88517	−	1.58184i
$215$	−26.9444			−1.83759
$216$		0			0
$217$	−2.00000			−0.135769
$218$	−1.87642	+	1.57450i	−0.127087	+	0.106639i
$219$		0			0
$220$	−4.16756	+	23.6354i	−0.280977	+	1.59350i
$221$	−6.90530	+	2.51332i	−0.464501	+	0.169065i
$222$		0			0
$223$	−1.21554	−	6.89365i	−0.0813984	−	0.461633i	−0.998076	−	0.0620053i	$-0.980250\pi$
$223$	−1.21554	−	6.89365i	−0.0813984	−	0.461633i	0.916677	−	0.399628i	$-0.130861\pi$
$224$		0			0
$225$		0			0
$226$	12.0000	−	20.7846i	0.798228	−	1.38257i
$227$	−9.20707	−	3.35110i	−0.611095	−	0.222420i	0.0178875	−	0.999840i	$-0.494306\pi$
$227$	−9.20707	−	3.35110i	−0.611095	−	0.222420i	−0.628982	+	0.777420i	$0.716528\pi$
$228$		0			0
$229$	−0.766044	−	0.642788i	−0.0506216	−	0.0424766i	0.617126	−	0.786864i	$-0.288297\pi$
$229$	−0.766044	−	0.642788i	−0.0506216	−	0.0424766i	−0.667747	+	0.744388i	$0.732741\pi$
$230$	11.2585	+	9.44701i	0.742364	+	0.622917i
$231$		0			0
$232$	22.5526	+	8.20848i	1.48065	+	0.538913i
$233$	3.67423	−	6.36396i	0.240707	−	0.416917i	−0.720209	−	0.693757i	$-0.755954\pi$
$233$	3.67423	−	6.36396i	0.240707	−	0.416917i	0.960916	+	0.276840i	$0.0892873\pi$
$234$		0			0
$235$	12.0000	+	20.7846i	0.782794	+	1.35584i
$236$	−1.70140	−	9.64911i	−0.110752	−	0.628103i
$237$		0			0
$238$	33.8289	−	12.3127i	2.19280	−	0.798115i
$239$	−0.425349	+	2.41228i	−0.0275136	+	0.156037i	−0.995469	−	0.0950838i	$-0.969688\pi$
$239$	−0.425349	+	2.41228i	−0.0275136	+	0.156037i	0.967956	+	0.251121i	$0.0807992\pi$
$240$		0			0
$241$	−12.2567	+	10.2846i	−0.789524	+	0.662489i	−0.945628	−	0.325251i	$-0.894551\pi$
$241$	−12.2567	+	10.2846i	−0.789524	+	0.662489i	0.156103	+	0.987741i	$0.450107\pi$
$242$	−12.2474			−0.787296
$243$		0			0
$244$	20.0000			1.28037
$245$	5.62925	−	4.72350i	0.359640	−	0.301774i
$246$		0			0
$247$	0.173648	−	0.984808i	0.0110490	−	0.0626618i
$248$	4.60353	−	1.67555i	0.292325	−	0.106398i
$249$		0			0
$250$	4.16756	+	23.6354i	0.263579	+	1.49483i
$251$	3.67423	+	6.36396i	0.231916	+	0.401690i	0.958372	−	0.285523i	$-0.0921673\pi$
$251$	3.67423	+	6.36396i	0.231916	+	0.401690i	−0.726456	+	0.687213i	$0.758834\pi$
$252$		0			0
$253$	3.00000	−	5.19615i	0.188608	−	0.326679i
$254$	43.7336	+	15.9177i	2.74409	+	0.998767i
$255$		0			0
$256$	−24.5134	−	20.5692i	−1.53209	−	1.28558i
$257$	−13.1349	−	11.0215i	−0.819334	−	0.687503i	0.133482	−	0.991051i	$-0.457384\pi$
$257$	−13.1349	−	11.0215i	−0.819334	−	0.687503i	−0.952816	+	0.303548i	$0.901829\pi$
$258$		0			0
$259$	−15.0351	−	5.47232i	−0.934235	−	0.340034i
$260$	−4.89898	+	8.48528i	−0.303822	+	0.526235i
$261$		0			0
$262$	−15.0000	−	25.9808i	−0.926703	−	1.60510i
$263$	−4.67884	−	26.5350i	−0.288510	−	1.63622i	−0.692472	−	0.721445i	$-0.743478\pi$
$263$	−4.67884	−	26.5350i	−0.288510	−	1.63622i	0.403962	−	0.914776i	$-0.367633\pi$
$264$		0			0
$265$	16.9145	−	6.15636i	1.03905	−	0.378182i
$266$	−0.850699	+	4.82455i	−0.0521597	+	0.295812i
$267$		0			0
$268$	−21.4492	+	17.9981i	−1.31022	+	1.09941i
$269$	−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	$0.568196\pi$
$272$	−22.5170	+	18.8940i	−1.36529	+	1.14562i
$273$		0			0
$274$	4.16756	−	23.6354i	0.251771	−	1.42787i
$275$	−2.30177	+	0.837775i	−0.138802	+	0.0505197i
$276$		0			0
$277$	1.91013	+	10.8329i	0.114769	+	0.650885i	0.986865	+	0.161550i	$0.0516493\pi$
$277$	1.91013	+	10.8329i	0.114769	+	0.650885i	−0.872096	+	0.489335i	$0.837240\pi$
$278$	12.2474	+	21.2132i	0.734553	+	1.27228i
$279$		0			0
$280$	12.0000	−	20.7846i	0.717137	−	1.24212i
$281$	11.5088	+	4.18887i	0.686560	+	0.249887i	0.661661	−	0.749803i	$-0.269852\pi$
$281$	11.5088	+	4.18887i	0.686560	+	0.249887i	0.0248982	+	0.999690i	$0.492074\pi$
$282$		0			0
$283$	13.0228	+	10.9274i	0.774122	+	0.649566i	0.941761	−	0.336283i	$-0.109170\pi$
$283$	13.0228	+	10.9274i	0.774122	+	0.649566i	−0.167639	+	0.985849i	$0.553614\pi$
$284$	22.5170	+	18.8940i	1.33614	+	1.12115i
$285$		0			0
$286$	5.63816	+	2.05212i	0.333391	+	0.121344i
$287$	−4.89898	+	8.48528i	−0.289178	+	0.500870i
$288$		0			0
$289$	−18.5000	−	32.0429i	−1.08824	−	1.88488i
$290$	5.10419	+	28.9473i	0.299729	+	1.69985i
$291$		0			0
$292$	−41.3465	+	15.0489i	−2.41962	+	0.880669i
$293$	0.850699	−	4.82455i	0.0496984	−	0.281853i	−0.949823	−	0.312788i	$-0.898737\pi$
$293$	0.850699	−	4.82455i	0.0496984	−	0.281853i	0.999521	+	0.0309343i	$0.00984827\pi$
$294$		0			0
$295$	4.59627	−	3.85673i	0.267605	−	0.224547i
$296$	39.1918			2.27798
$297$		0			0
$298$	30.0000			1.73785
$299$	1.87642	−	1.57450i	0.108516	−	0.0910558i
$300$		0			0
$301$	3.82026	−	21.6658i	0.220196	−	1.24879i
$302$	−11.5088	+	4.18887i	−0.662259	+	0.241043i
$303$		0			0
$304$	−0.694593	−	3.93923i	−0.0398376	−	0.225930i
$305$	6.12372	+	10.6066i	0.350643	+	0.607332i
$306$		0			0
$307$	−1.00000	+	1.73205i	−0.0570730	+	0.0988534i	−0.893150	−	0.449758i	$-0.851510\pi$
$307$	−1.00000	+	1.73205i	−0.0570730	+	0.0988534i	0.836077	+	0.548612i	$0.184843\pi$
$308$	−18.4141	−	6.70220i	−1.04924	−	0.381893i
$309$		0			0
$310$	4.59627	+	3.85673i	0.261050	+	0.219047i
$311$	−18.7642	−	15.7450i	−1.06402	−	0.892818i	−0.0695218	−	0.997580i	$-0.522147\pi$
$311$	−18.7642	−	15.7450i	−1.06402	−	0.892818i	−0.994497	+	0.104762i	$0.966592\pi$
$312$		0			0
$313$	15.0351	+	5.47232i	0.849833	+	0.309314i	0.729972	−	0.683477i	$-0.239533\pi$
$313$	15.0351	+	5.47232i	0.849833	+	0.309314i	0.119861	+	0.992791i	$0.461755\pi$
$314$	−20.8207	+	36.0624i	−1.17498	+	2.03512i
$315$		0			0
$316$	14.0000	+	24.2487i	0.787562	+	1.36410i
$317$	1.70140	+	9.64911i	0.0955600	+	0.541948i	0.994574	+	0.104029i	$0.0331733\pi$
$317$	1.70140	+	9.64911i	0.0955600	+	0.541948i	−0.899014	+	0.437919i	$0.855716\pi$
$318$		0			0
$319$	11.2763	−	4.10424i	0.631352	−	0.229793i
$320$	3.40280	−	19.2982i	0.190222	−	1.07880i
$321$		0			0
$322$	−9.19253	+	7.71345i	−0.512280	+	0.429854i
$323$	7.34847			0.408880
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−18.7642	+	15.7450i	−1.03925	+	0.872036i
$327$		0			0
$328$	4.16756	−	23.6354i	0.230115	−	1.30505i
$329$	−18.4141	+	6.70220i	−1.01520	+	0.369504i
$330$		0			0
$331$	−1.21554	−	6.89365i	−0.0668120	−	0.378910i	−0.999819	−	0.0190501i	$-0.993936\pi$
$331$	−1.21554	−	6.89365i	−0.0668120	−	0.378910i	0.933007	−	0.359859i	$-0.117175\pi$
$332$	24.4949	+	42.4264i	1.34433	+	2.32845i
$333$		0			0
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−16.1124	−	5.86442i	−0.880313	−	0.320408i
$336$		0			0
$337$	−21.4492	−	17.9981i	−1.16841	−	0.980416i	−0.168429	−	0.985714i	$-0.553869\pi$
$337$	−21.4492	−	17.9981i	−1.16841	−	0.980416i	−0.999986	+	0.00529739i	$0.998314\pi$
$338$	−22.5170	−	18.8940i	−1.22476	−	1.02770i
$339$		0			0
$340$	−67.6579	−	24.6255i	−3.66926	−	1.33550i
$341$	1.22474	−	2.12132i	0.0663237	−	0.114876i
$342$		0			0
$343$	10.0000	+	17.3205i	0.539949	+	0.935220i
$344$	9.35769	+	53.0701i	0.504533	+	2.86135i
$345$		0			0
$346$	−22.5526	+	8.20848i	−1.21244	+	0.441291i
$347$	−4.25349	+	24.1228i	−0.228340	+	1.29498i	0.627857	+	0.778328i	$0.283932\pi$
$347$	−4.25349	+	24.1228i	−0.228340	+	1.29498i	−0.856197	+	0.516650i	$0.827179\pi$
$348$		0			0
$349$	15.3209	−	12.8558i	0.820108	−	0.688153i	−0.132889	−	0.991131i	$-0.542425\pi$
$349$	15.3209	−	12.8558i	0.820108	−	0.688153i	0.952997	+	0.302978i	$0.0979810\pi$
$350$	4.89898			0.261861
$351$		0			0
$352$		0			0
$353$	1.87642	−	1.57450i	0.0998717	−	0.0838023i	−0.591485	−	0.806316i	$-0.701458\pi$
$353$	1.87642	−	1.57450i	0.0998717	−	0.0838023i	0.691356	+	0.722514i	$0.257014\pi$
$354$		0			0
$355$	−3.12567	+	17.7265i	−0.165893	+	0.940827i
$356$		0			0
$357$		0			0
$358$	−6.25133	−	35.4531i	−0.330393	−	1.87375i
$359$	−14.6969	−	25.4558i	−0.775675	−	1.34351i	−0.934414	−	0.356188i	$-0.884076\pi$
$359$	−14.6969	−	25.4558i	−0.775675	−	1.34351i	0.158740	−	0.987320i	$-0.449257\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−18.4141	−	6.70220i	−0.967826	−	0.352260i
$363$		0			0
$364$	−6.12836	−	5.14230i	−0.321213	−	0.269530i
$365$	−20.6406	−	17.3195i	−1.08038	−	0.906545i
$366$		0			0
$367$	−4.69846	−	1.71010i	−0.245258	−	0.0892665i	0.216466	−	0.976290i	$-0.430547\pi$
$367$	−4.69846	−	1.71010i	−0.245258	−	0.0892665i	−0.461724	+	0.887024i	$0.652769\pi$
$368$	4.89898	−	8.48528i	0.255377	−	0.442326i
$369$		0			0
$370$	24.0000	+	41.5692i	1.24770	+	2.16108i
$371$	2.55210	+	14.4737i	0.132498	+	0.751435i
$372$		0			0
$373$	−32.8892	+	11.9707i	−1.70294	+	0.619820i	−0.996155	−	0.0876084i	$-0.972078\pi$
$373$	−32.8892	+	11.9707i	−1.70294	+	0.619820i	−0.706785	+	0.707428i	$0.749855\pi$
$374$	−7.65629	+	43.4210i	−0.395897	+	2.24525i
$375$		0			0
$376$	36.7701	−	30.8538i	1.89627	−	1.59116i
$377$	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	$0.434129\pi$
$380$	7.50567	−	6.29801i	0.385033	−	0.323081i
$381$		0			0
$382$	4.16756	−	23.6354i	0.213231	−	1.20929i
$383$	−32.2247	+	11.7288i	−1.64661	+	0.599316i	−0.988176	−	0.153324i	$-0.951002\pi$
$383$	−32.2247	+	11.7288i	−1.64661	+	0.599316i	−0.658432	+	0.752641i	$0.728780\pi$
$384$		0			0
$385$	−2.08378	−	11.8177i	−0.106199	−	0.602285i
$386$	−13.4722	−	23.3345i	−0.685717	−	1.18770i
$387$		0			0
$388$	14.0000	−	24.2487i	0.710742	−	1.23104i
$389$	25.3194	+	9.21552i	1.28375	+	0.467246i	0.891670	−	0.452687i	$-0.149534\pi$
$389$	25.3194	+	9.21552i	1.28375	+	0.467246i	0.392077	+	0.919932i	$0.371757\pi$
$390$		0			0
$391$	13.7888	+	11.5702i	0.697330	+	0.585129i
$392$	−11.2585	−	9.44701i	−0.568641	−	0.477146i
$393$		0			0
$394$	−33.8289	−	12.3127i	−1.70428	−	0.620306i
$395$	−8.57321	+	14.8492i	−0.431365	+	0.747146i
$396$		0			0
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−0.425349	−	2.41228i	−0.0213208	−	0.120916i
$399$		0			0
$400$	−3.75877	+	1.36808i	−0.187939	+	0.0684040i
$401$	5.95489	−	33.7719i	0.297373	−	1.68649i	−0.360024	−	0.932943i	$-0.617232\pi$
$401$	5.95489	−	33.7719i	0.297373	−	1.68649i	0.657398	−	0.753544i	$-0.271657\pi$
$402$		0			0
$403$	0.766044	−	0.642788i	0.0381594	−	0.0320195i
$404$	−19.5959			−0.974933
$405$		0			0
$406$	−24.0000			−1.19110
$407$	15.0113	−	12.5960i	0.744085	−	0.624361i
$408$		0			0
$409$	−4.86215	+	27.5746i	−0.240418	+	1.36348i	0.590480	+	0.807052i	$0.298938\pi$
$409$	−4.86215	+	27.5746i	−0.240418	+	1.36348i	−0.830898	+	0.556425i	$0.812173\pi$
$410$	27.6212	−	10.0533i	1.36411	−	0.496497i
$411$		0			0
$412$	−4.86215	−	27.5746i	−0.239541	−	1.35850i
$413$	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
$418$	−4.59627	−	3.85673i	−0.224811	−	0.188639i
$419$	26.2699	+	22.0430i	1.28337	+	1.07687i	0.992771	+	0.120026i	$0.0382978\pi$
$419$	26.2699	+	22.0430i	1.28337	+	1.07687i	0.290596	+	0.956846i	$0.406147\pi$
$420$		0			0
$421$	−1.87939	−	0.684040i	−0.0915956	−	0.0333381i	0.295816	−	0.955245i	$-0.404409\pi$
$421$	−1.87939	−	0.684040i	−0.0915956	−	0.0333381i	−0.387412	+	0.921907i	$0.626631\pi$
$422$	1.22474	−	2.12132i	0.0596196	−	0.103264i
$423$		0			0
$424$	−18.0000	−	31.1769i	−0.874157	−	1.51408i
$425$	−1.27605	−	7.23683i	−0.0618974	−	0.351038i
$426$		0			0
$427$	−9.39693	+	3.42020i	−0.454749	+	0.165515i
$428$	10.2084	−	57.8946i	0.493441	−	2.79844i
$429$		0			0
$430$	−50.5589	+	42.4240i	−2.43817	+	2.04587i
$431$	−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	$0.366058\pi$
$434$	−3.75284	+	3.14900i	−0.180142	+	0.151157i
$435$		0			0
$436$	−0.694593	+	3.93923i	−0.0332650	+	0.188655i
$437$	−2.30177	+	0.837775i	−0.110108	+	0.0400762i
$438$		0			0
$439$	2.43107	+	13.7873i	0.116029	+	0.658032i	0.986236	+	0.165346i	$0.0528740\pi$
$439$	2.43107	+	13.7873i	0.116029	+	0.658032i	−0.870207	+	0.492687i	$0.836015\pi$
$440$	14.6969	+	25.4558i	0.700649	+	1.21356i
$441$		0			0
$442$	−9.00000	+	15.5885i	−0.428086	+	0.741467i
$443$	11.5088	+	4.18887i	0.546801	+	0.199019i	0.600625	−	0.799531i	$-0.294919\pi$
$443$	11.5088	+	4.18887i	0.546801	+	0.199019i	−0.0538234	+	0.998550i	$0.517141\pi$
$444$		0			0
$445$		0			0
$446$	−13.1349	−	11.0215i	−0.621957	−	0.521884i
$447$		0			0
$448$	15.0351	+	5.47232i	0.710341	+	0.258543i
$449$	−11.0227	+	19.0919i	−0.520194	+	0.901002i	0.479531	+	0.877525i	$0.340807\pi$
$449$	−11.0227	+	19.0919i	−0.520194	+	0.901002i	−0.999724	+	0.0234766i	$0.992526\pi$
$450$		0			0
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	−6.80559	−	38.5964i	−0.320108	−	1.81542i
$453$		0			0
$454$	−22.5526	+	8.20848i	−1.05845	+	0.385243i
$455$	0.850699	−	4.82455i	0.0398814	−	0.226179i
$456$		0			0
$457$	22.2153	−	18.6408i	1.03919	−	0.871982i	0.0472719	−	0.998882i	$-0.484947\pi$
$457$	22.2153	−	18.6408i	1.03919	−	0.871982i	0.991915	+	0.126900i	$0.0405028\pi$
$458$	−2.44949			−0.114457
$459$		0			0
$460$	24.0000			1.11901
$461$	−20.6406	+	17.3195i	−0.961328	+	0.806650i	−0.981169	−	0.193153i	$-0.938129\pi$
$461$	−20.6406	+	17.3195i	−0.961328	+	0.806650i	0.0198402	+	0.999803i	$0.493684\pi$
$462$		0			0
$463$	−3.29932	+	18.7113i	−0.153332	+	0.869590i	0.806963	+	0.590603i	$0.201110\pi$
$463$	−3.29932	+	18.7113i	−0.153332	+	0.869590i	−0.960295	+	0.278987i	$0.910001\pi$
$464$	18.4141	−	6.70220i	0.854855	−	0.311142i
$465$		0			0
$466$	−3.12567	−	17.7265i	−0.144794	−	0.821166i
$467$	−7.34847	−	12.7279i	−0.340047	−	0.588978i	0.644394	−	0.764693i	$-0.277110\pi$
$467$	−7.34847	−	12.7279i	−0.340047	−	0.588978i	−0.984441	+	0.175715i	$0.943776\pi$
$468$		0			0
$469$	7.00000	−	12.1244i	0.323230	−	0.559851i
$470$	55.2424	+	20.1066i	2.54814	+	0.927448i
$471$		0			0
$472$	−9.19253	−	7.71345i	−0.423121	−	0.355040i
$473$	20.6406	+	17.3195i	0.949056	+	0.796352i
$474$		0			0
$475$	0.939693	+	0.342020i	0.0431161	+	0.0156930i
$476$	29.3939	−	50.9117i	1.34727	−	2.33353i
$477$		0			0
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	−4.67884	−	26.5350i	−0.213782	−	1.21242i	−0.883008	−	0.469358i	$-0.844485\pi$
$479$	−4.67884	−	26.5350i	−0.213782	−	1.21242i	0.669226	−	0.743059i	$-0.266626\pi$
$480$		0			0
$481$	7.51754	−	2.73616i	0.342770	−	0.124758i
$482$	−6.80559	+	38.5964i	−0.309986	+	1.75802i
$483$		0			0
$484$	−15.3209	+	12.8558i	−0.696404	+	0.584352i
$485$	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	$0.208518\pi$
$488$	18.7642	−	15.7450i	0.849415	−	0.712743i
$489$		0			0
$490$	3.12567	−	17.7265i	0.141203	−	0.800803i
$491$	36.8283	−	13.4044i	1.66204	−	0.604932i	0.671356	−	0.741135i	$-0.265712\pi$
$491$	36.8283	−	13.4044i	1.66204	−	0.604932i	0.990681	+	0.136203i	$0.0434899\pi$
$492$		0			0
$493$	6.25133	+	35.4531i	0.281546	+	1.59673i
$494$	−1.22474	−	2.12132i	−0.0551039	−	0.0954427i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	−13.8106	−	5.02665i	−0.619490	−	0.225476i
$498$		0			0
$499$	1.53209	+	1.28558i	0.0685857	+	0.0575503i	0.676436	−	0.736501i	$-0.263524\pi$
$499$	1.53209	+	1.28558i	0.0685857	+	0.0575503i	−0.607850	+	0.794052i	$0.707968\pi$
$500$	30.0227	+	25.1920i	1.34266	+	1.12662i
$501$		0			0
$502$	16.9145	+	6.15636i	0.754930	+	0.274772i
$503$	7.34847	−	12.7279i	0.327652	−	0.567510i	−0.654393	−	0.756154i	$-0.727076\pi$
$503$	7.34847	−	12.7279i	0.327652	−	0.567510i	0.982045	+	0.188644i	$0.0604093\pi$
$504$		0			0
$505$	−6.00000	−	10.3923i	−0.266996	−	0.462451i
$506$	−2.55210	−	14.4737i	−0.113455	−	0.643433i
$507$		0			0
$508$	71.4166	−	25.9935i	3.16860	−	1.15328i
$509$	−1.70140	+	9.64911i	−0.0754131	+	0.427689i	0.923603	+	0.383349i	$0.125229\pi$
$509$	−1.70140	+	9.64911i	−0.0754131	+	0.427689i	−0.999017	+	0.0443397i	$0.985882\pi$
$510$		0			0
$511$	16.8530	−	14.1413i	0.745532	−	0.625575i
$512$	−39.1918			−1.73205
$513$		0			0
$514$	−42.0000			−1.85254
$515$	13.1349	−	11.0215i	0.578794	−	0.485666i
$516$		0			0
$517$	4.16756	−	23.6354i	0.183289	−	1.03948i
$518$	−36.8283	+	13.4044i	−1.61814	+	0.588955i
$519$		0			0
$520$	2.08378	+	11.8177i	0.0913797	+	0.518240i
$521$	−11.0227	−	19.0919i	−0.482913	−	0.836431i	0.516894	−	0.856049i	$-0.327088\pi$
$521$	−11.0227	−	19.0919i	−0.482913	−	0.836431i	−0.999808	+	0.0196188i	$0.993755\pi$
$522$		0			0
$523$	12.5000	−	21.6506i	0.546587	−	0.946716i	−0.451918	−	0.892059i	$-0.649260\pi$
$523$	12.5000	−	21.6506i	0.546587	−	0.946716i	0.998505	−	0.0546569i	$-0.0174065\pi$
$524$	−46.0353	−	16.7555i	−2.01106	−	0.731967i
$525$		0			0
$526$	−50.5589	−	42.4240i	−2.20447	−	1.84977i
$527$	5.62925	+	4.72350i	0.245214	+	0.205759i
$528$		0			0
$529$	15.9748	+	5.81434i	0.694555	+	0.252797i
$530$	22.0454	−	38.1838i	0.957591	−	1.65860i
$531$		0			0
$532$	4.00000	+	6.92820i	0.173422	+	0.300376i
$533$	−0.850699	−	4.82455i	−0.0368479	−	0.208975i
$534$		0			0
$535$	33.8289	−	12.3127i	1.46255	−	0.532326i
$536$	−5.95489	+	33.7719i	−0.257212	+	1.45872i
$537$		0			0
$538$	−41.3664	+	34.7105i	−1.78343	+	1.49648i
$539$	−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	$0.705592\pi$
$542$	−13.1349	+	11.0215i	−0.564193	+	0.473414i
$543$		0			0
$544$		0			0
$545$	−2.30177	+	0.837775i	−0.0985969	+	0.0358863i
$546$		0			0
$547$	−2.25743	−	12.8025i	−0.0965206	−	0.547395i	−0.994271	−	0.106891i	$-0.965911\pi$
$547$	−2.25743	−	12.8025i	−0.0965206	−	0.547395i	0.897750	−	0.440505i	$-0.145201\pi$
$548$	−19.5959	−	33.9411i	−0.837096	−	1.44989i
$549$		0			0
$550$	−3.00000	+	5.19615i	−0.127920	+	0.221565i
$551$	−4.60353	−	1.67555i	−0.196117	−	0.0713808i
$552$		0			0
$553$	−10.7246	−	8.99903i	−0.456057	−	0.382678i
$554$	20.6406	+	17.3195i	0.876935	+	0.735836i
$555$		0			0
$556$	37.5877	+	13.6808i	1.59407	+	0.580195i
$557$	−3.67423	+	6.36396i	−0.155682	+	0.269650i	−0.933307	−	0.359079i	$-0.883091\pi$
$557$	−3.67423	+	6.36396i	−0.155682	+	0.269650i	0.777625	+	0.628728i	$0.216424\pi$
$558$		0			0
$559$	5.50000	+	9.52628i	0.232625	+	0.402919i
$560$	−3.40280	−	19.2982i	−0.143794	−	0.815498i
$561$		0			0
$562$	28.1908	−	10.2606i	1.18916	−	0.432817i
$563$	2.12675	−	12.0614i	0.0896317	−	0.508327i	−0.906629	−	0.421929i	$-0.861353\pi$
$563$	2.12675	−	12.0614i	0.0896317	−	0.508327i	0.996261	−	0.0863979i	$-0.0275356\pi$
$564$		0			0
$565$	18.3851	−	15.4269i	0.773466	−	0.649015i
$566$	41.6413			1.75032
$567$		0			0
$568$	36.0000			1.51053
$569$	−9.38209	+	7.87251i	−0.393318	+	0.330033i	−0.817904	−	0.575355i	$-0.804864\pi$
$569$	−9.38209	+	7.87251i	−0.393318	+	0.330033i	0.424586	+	0.905387i	$0.360420\pi$
$570$		0			0
$571$	−1.73648	+	9.84808i	−0.0726695	+	0.412129i	0.926673	+	0.375869i	$0.122656\pi$
$571$	−1.73648	+	9.84808i	−0.0726695	+	0.412129i	−0.999342	+	0.0362604i	$0.988455\pi$
$572$	9.20707	−	3.35110i	0.384967	−	0.140117i
$573$		0			0
$574$	4.16756	+	23.6354i	0.173950	+	0.986522i
$575$	1.22474	+	2.12132i	0.0510754	+	0.0884652i
$576$		0			0
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	−0.479337	−	0.877631i	$-0.659123\pi$
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	0.999719	−	0.0236970i	$-0.00754370\pi$
$578$	−85.1654	−	30.9977i	−3.54241	−	1.28933i
$579$		0			0
$580$	36.7701	+	30.8538i	1.52680	+	1.28113i
$581$	−18.7642	−	15.7450i	−0.778469	−	0.653213i
$582$		0			0
$583$	−16.9145	−	6.15636i	−0.700526	−	0.254970i
$584$	−26.9444	+	46.6690i	−1.11497	+	1.93118i
$585$		0			0
$586$	−6.00000	−	10.3923i	−0.247858	−	0.429302i
$587$	0.425349	+	2.41228i	0.0175560	+	0.0995653i	0.992327	−	0.123644i	$-0.0394579\pi$
$587$	0.425349	+	2.41228i	0.0175560	+	0.0995653i	−0.974771	+	0.223209i	$0.928347\pi$
$588$		0			0
$589$	−0.939693	+	0.342020i	−0.0387194	+	0.0140927i
$590$	2.55210	−	14.4737i	0.105068	−	0.595871i
$591$		0			0
$592$	24.5134	−	20.5692i	1.00750	−	0.845389i
$593$	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
$596$	37.5284	−	31.4900i	1.53722	−	1.28988i
$597$		0			0
$598$	1.04189	−	5.90885i	0.0426060	−	0.241631i
$599$	36.8283	−	13.4044i	1.50476	−	0.547689i	0.547474	−	0.836823i	$-0.315589\pi$
$599$	36.8283	−	13.4044i	1.50476	−	0.547689i	0.957289	+	0.289134i	$0.0933673\pi$
$600$		0			0
$601$	−1.21554	−	6.89365i	−0.0495828	−	0.281198i	0.949928	−	0.312468i	$-0.101156\pi$
$601$	−1.21554	−	6.89365i	−0.0495828	−	0.281198i	−0.999511	+	0.0312703i	$0.990045\pi$
$602$	−26.9444	−	46.6690i	−1.09817	−	1.90209i
$603$		0			0
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−11.5088	−	4.18887i	−0.467901	−	0.170302i
$606$		0			0
$607$	33.7060	+	28.2827i	1.36808	+	1.14796i	0.973393	+	0.229143i	$0.0735924\pi$
$607$	33.7060	+	28.2827i	1.36808	+	1.14796i	0.394690	+	0.918814i	$0.370852\pi$
$608$		0			0
$609$		0			0
$610$	28.1908	+	10.2606i	1.14141	+	0.415440i
$611$	4.89898	−	8.48528i	0.198191	−	0.343278i
$612$		0			0
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$	0.850699	+	4.82455i	0.0343314	+	0.194703i
$615$		0			0
$616$	−22.5526	+	8.20848i	−0.908671	+	0.330729i
$617$	−4.25349	+	24.1228i	−0.171239	+	0.971146i	0.771156	+	0.636646i	$0.219679\pi$
$617$	−4.25349	+	24.1228i	−0.171239	+	0.971146i	−0.942396	+	0.334500i	$0.891432\pi$
$618$		0			0
$619$	−37.5362	+	31.4966i	−1.50871	+	1.26595i	−0.642481	+	0.766302i	$0.722095\pi$
$619$	−37.5362	+	31.4966i	−1.50871	+	1.26595i	−0.866226	+	0.499653i	$0.833461\pi$
$620$	9.79796			0.393496
$621$		0			0
$622$	−60.0000			−2.40578
$623$		0			0
$624$		0			0
$625$	−5.03580	+	28.5594i	−0.201432	+	1.14238i
$626$	36.8283	−	13.4044i	1.47195	−	0.535747i
$627$		0			0
$628$	11.8081	+	66.9669i	0.471194	+	2.67227i
$629$	29.3939	+	50.9117i	1.17201	+	2.02998i
$630$		0			0
$631$	−22.0000	+	38.1051i	−0.875806	+	1.51694i	−0.0199047	+	0.999802i	$0.506336\pi$
$631$	−22.0000	+	38.1051i	−0.875806	+	1.51694i	−0.855901	+	0.517139i	$0.826997\pi$
$632$	32.2247	+	11.7288i	1.28183	+	0.466549i
$633$		0			0
$634$	18.3851	+	15.4269i	0.730164	+	0.612681i
$635$	35.6519	+	29.9155i	1.41480	+	1.18716i
$636$		0			0
$637$	−2.81908	−	1.02606i	−0.111696	−	0.0406540i
$638$	14.6969	−	25.4558i	0.581857	−	1.00781i
$639$		0			0
$640$	−24.0000	−	41.5692i	−0.948683	−	1.64317i
$641$	2.97745	+	16.8859i	0.117602	+	0.666954i	0.985429	+	0.170088i	$0.0544051\pi$
$641$	2.97745	+	16.8859i	0.117602	+	0.666954i	−0.867827	+	0.496867i	$0.834484\pi$
$642$		0			0
$643$	−35.7083	+	12.9968i	−1.40820	+	0.512542i	−0.930601	−	0.366036i	$-0.880715\pi$
$643$	−35.7083	+	12.9968i	−1.40820	+	0.512542i	−0.477598	+	0.878578i	$0.658492\pi$
$644$	−3.40280	+	19.2982i	−0.134089	+	0.760456i
$645$		0			0
$646$	13.7888	−	11.5702i	0.542513	−	0.455223i
$647$	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
$650$	−1.87642	+	1.57450i	−0.0735992	+	0.0617570i
$651$		0			0
$652$	−6.94593	+	39.3923i	−0.272023	+	1.54272i
$653$	9.20707	−	3.35110i	0.360300	−	0.131139i	−0.155526	−	0.987832i	$-0.549707\pi$
$653$	9.20707	−	3.35110i	0.360300	−	0.131139i	0.515826	+	0.856693i	$0.327485\pi$
$654$		0			0
$655$	−5.20945	−	29.5442i	−0.203550	−	1.15439i
$656$	−9.79796	−	16.9706i	−0.382546	−	0.662589i
$657$		0			0
$658$	−24.0000	+	41.5692i	−0.935617	+	1.62054i
$659$	18.4141	+	6.70220i	0.717313	+	0.261081i	0.674785	−	0.738015i	$-0.264236\pi$
$659$	18.4141	+	6.70220i	0.717313	+	0.261081i	0.0425284	+	0.999095i	$0.486459\pi$
$660$		0			0
$661$	8.42649	+	7.07066i	0.327752	+	0.275017i	0.791783	−	0.610802i	$-0.209153\pi$
$661$	8.42649	+	7.07066i	0.327752	+	0.275017i	−0.464031	+	0.885819i	$0.653597\pi$
$662$	−13.1349	−	11.0215i	−0.510503	−	0.428363i
$663$		0			0
$664$	56.3816	+	20.5212i	2.18803	+	0.796377i
$665$	−2.44949	+	4.24264i	−0.0949871	+	0.164523i
$666$		0			0
$667$	−6.00000	−	10.3923i	−0.232321	−	0.402392i
$668$	3.40280	+	19.2982i	0.131658	+	0.746670i
$669$		0			0
$670$	−39.4671	+	14.3648i	−1.52475	+	0.554962i
$671$	2.12675	−	12.0614i	0.0821022	−	0.465625i
$672$		0			0
$673$	22.2153	−	18.6408i	0.856336	−	0.718552i	−0.104839	−	0.994489i	$-0.533433\pi$
$673$	22.2153	−	18.6408i	0.856336	−	0.718552i	0.961176	+	0.275938i	$0.0889883\pi$
$674$	−68.5857			−2.64182
$675$		0			0
$676$	−48.0000			−1.84615
$677$	35.6519	−	29.9155i	1.37022	−	1.14975i	0.397538	−	0.917586i	$-0.369865\pi$
$677$	35.6519	−	29.9155i	1.37022	−	1.14975i	0.972677	−	0.232162i	$-0.0745798\pi$
$678$		0			0
$679$	−2.43107	+	13.7873i	−0.0932961	+	0.529108i
$680$	−82.8636	+	30.1599i	−3.17768	+	1.15658i
$681$		0			0
$682$	−1.04189	−	5.90885i	−0.0398960	−	0.226261i
$683$	11.0227	+	19.0919i	0.421772	+	0.730531i	0.996113	−	0.0880857i	$-0.0280749\pi$
$683$	11.0227	+	19.0919i	0.421772	+	0.730531i	−0.574341	+	0.818616i	$0.694742\pi$
$684$		0			0
$685$	12.0000	−	20.7846i	0.458496	−	0.794139i
$686$	46.0353	+	16.7555i	1.75764	+	0.639728i
$687$		0			0
$688$	33.7060	+	28.2827i	1.28503	+	1.07827i
$689$	−5.62925	−	4.72350i	−0.214457	−	0.179951i
$690$		0			0
$691$	−44.1656	−	16.0749i	−1.68014	−	0.611520i	−0.686808	−	0.726839i	$-0.740989\pi$
$691$	−44.1656	−	16.0749i	−1.68014	−	0.611520i	−0.993329	+	0.115319i	$0.963211\pi$
$692$	−19.5959	+	33.9411i	−0.744925	+	1.29025i
$693$		0			0
$694$	30.0000	+	51.9615i	1.13878	+	1.97243i
$695$	4.25349	+	24.1228i	0.161344	+	0.915029i
$696$		0			0
$697$	33.8289	−	12.3127i	1.28136	−	0.466378i
$698$	8.50699	−	48.2455i	0.321994	−	1.82612i
$699$		0			0
$700$	6.12836	−	5.14230i	0.231630	−	0.194361i
$701$	−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
$704$	−15.0113	+	12.5960i	−0.565761	+	0.474730i
$705$		0			0
$706$	1.04189	−	5.90885i	0.0392120	−	0.222382i
$707$	9.20707	−	3.35110i	0.346267	−	0.126031i
$708$		0			0
$709$	−1.21554	−	6.89365i	−0.0456505	−	0.258897i	0.953438	−	0.301590i	$-0.0975173\pi$
$709$	−1.21554	−	6.89365i	−0.0456505	−	0.258897i	−0.999088	+	0.0426932i	$0.986406\pi$
$710$	22.0454	+	38.1838i	0.827349	+	1.43301i
$711$		0			0
$712$		0			0
$713$	−2.30177	−	0.837775i	−0.0862019	−	0.0313749i
$714$		0			0
$715$	4.59627	+	3.85673i	0.171891	+	0.144233i
$716$	−45.0340	−	37.7880i	−1.68300	−	1.41221i
$717$		0			0
$718$	−67.6579	−	24.6255i	−2.52497	−	0.919014i
$719$	18.3712	−	31.8198i	0.685129	−	1.18668i	−0.288267	−	0.957550i	$-0.593079\pi$
$719$	18.3712	−	31.8198i	0.685129	−	1.18668i	0.973396	−	0.229128i	$-0.0735876\pi$
$720$		0			0
$721$	7.00000	+	12.1244i	0.260694	+	0.451535i
$722$	−7.65629	−	43.4210i	−0.284938	−	1.61596i
$723$		0			0
$724$	−30.0702	+	10.9446i	−1.11755	+	0.406755i
$725$	−0.850699	+	4.82455i	−0.0315942	+	0.179179i
$726$		0			0
$727$	10.7246	−	8.99903i	0.397754	−	0.333755i	−0.421871	−	0.906656i	$-0.638626\pi$
$727$	10.7246	−	8.99903i	0.397754	−	0.333755i	0.819625	+	0.572901i	$0.194182\pi$
$728$	−9.79796			−0.363137
$729$		0			0
$730$	−66.0000			−2.44277
$731$	−61.9218	+	51.9586i	−2.29026	+	1.92176i
$732$		0			0
$733$	2.95202	−	16.7417i	0.109035	−	0.618370i	−0.880496	−	0.474053i	$-0.842790\pi$
$733$	2.95202	−	16.7417i	0.109035	−	0.618370i	0.989532	−	0.144317i	$-0.0460984\pi$
$734$	−11.5088	+	4.18887i	−0.424799	+	0.154614i
$735$		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	−0.856683	−	0.515844i	$-0.827478\pi$
$739$	0.500000	−	0.866025i	0.0183928	−	0.0318573i	0.875075	+	0.483987i	$0.160812\pi$
$740$	73.6566	+	26.8088i	2.70767	+	0.985511i
$741$		0			0
$742$	27.5776	+	23.1404i	1.01241	+	0.849509i
$743$	−24.3934	−	20.4685i	−0.894908	−	0.750917i	0.0742802	−	0.997237i	$-0.476334\pi$
$743$	−24.3934	−	20.4685i	−0.894908	−	0.750917i	−0.969189	+	0.246320i	$0.920779\pi$
$744$		0			0
$745$	28.1908	+	10.2606i	1.03283	+	0.375919i
$746$	−42.8661	+	74.2462i	−1.56944	+	2.71835i
$747$		0			0
$748$	36.0000	+	62.3538i	1.31629	+	2.27988i
$749$	5.10419	+	28.9473i	0.186503	+	1.05771i
$750$		0			0
$751$	−24.4320	+	8.89252i	−0.891537	+	0.324493i	−0.746856	−	0.664986i	$-0.768438\pi$
$751$	−24.4320	+	8.89252i	−0.891537	+	0.324493i	−0.144680	+	0.989478i	$0.546215\pi$
$752$	6.80559	−	38.5964i	0.248174	−	1.40747i
$753$		0			0
$754$	9.19253	−	7.71345i	0.334772	−	0.280907i
$755$	−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	$0.540602\pi$
$758$	15.0113	−	12.5960i	0.545237	−	0.457508i
$759$		0			0
$760$	2.08378	−	11.8177i	0.0755866	−	0.428673i
$761$	2.30177	−	0.837775i	0.0834390	−	0.0303693i	−0.299963	−	0.953951i	$-0.596974\pi$
$761$	2.30177	−	0.837775i	0.0834390	−	0.0303693i	0.383402	+	0.923581i	$0.374752\pi$
$762$		0			0
$763$	−0.347296	−	1.96962i	−0.0125730	−	0.0713049i
$764$	−19.5959	−	33.9411i	−0.708955	−	1.22795i
$765$		0			0
$766$	−42.0000	+	72.7461i	−1.51752	+	2.62842i
$767$	−2.30177	−	0.837775i	−0.0831120	−	0.0302503i
$768$		0			0
$769$	−28.3436	−	23.7831i	−1.02210	−	0.857642i	−0.0322082	−	0.999481i	$-0.510254\pi$
$769$	−28.3436	−	23.7831i	−1.02210	−	0.857642i	−0.989890	+	0.141839i	$0.954698\pi$
$770$	−22.5170	−	18.8940i	−0.811457	−	0.680893i
$771$		0			0
$772$	−41.3465	−	15.0489i	−1.48809	−	0.541621i
$773$	22.0454	−	38.1838i	0.792918	−	1.37337i	−0.131235	−	0.991351i	$-0.541894\pi$
$773$	22.0454	−	38.1838i	0.792918	−	1.37337i	0.924153	−	0.382023i	$-0.124773\pi$
$774$		0			0
$775$	0.500000	+	0.866025i	0.0179605	+	0.0311086i
$776$	−5.95489	−	33.7719i	−0.213768	−	1.21234i
$777$		0			0
$778$	62.0197	−	22.5733i	2.22351	−	0.809293i
$779$	−0.850699	+	4.82455i	−0.0304794	+	0.172858i
$780$		0			0
$781$	13.7888	−	11.5702i	0.493402	−	0.414013i
$782$	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)

\(f(q)\)	\(=\)	\(q+(1.87642 - 1.57450i) q^{2} +(0.694593 - 3.93923i) q^{4} +(2.30177 - 0.837775i) q^{5} +(0.347296 + 1.96962i) q^{7} +(-2.44949 - 4.24264i) q^{8} +O(q^{10})\)	\(q+(1.87642 - 1.57450i) q^{2} +(0.694593 - 3.93923i) q^{4} +(2.30177 - 0.837775i) q^{5} +(0.347296 + 1.96962i) q^{7} +(-2.44949 - 4.24264i) q^{8} +(3.00000 - 5.19615i) q^{10} +(-2.30177 - 0.837775i) q^{11} +(-0.766044 - 0.642788i) q^{13} +(3.75284 + 3.14900i) q^{14} +(-3.75877 - 1.36808i) q^{16} +(3.67423 - 6.36396i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-1.70140 - 9.64911i) q^{20} +(-5.63816 + 2.05212i) q^{22} +(-0.425349 + 2.41228i) q^{23} +(0.766044 - 0.642788i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(-3.75284 + 3.14900i) q^{29} +(-0.173648 + 0.984808i) q^{31} +(-3.12567 - 17.7265i) q^{34} +(2.44949 + 4.24264i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(2.30177 + 0.837775i) q^{38} +(-9.19253 - 7.71345i) q^{40} +(3.75284 + 3.14900i) q^{41} +(-10.3366 - 3.76222i) q^{43} +(-4.89898 + 8.48528i) q^{44} +(3.00000 + 5.19615i) q^{46} +(1.70140 + 9.64911i) q^{47} +(2.81908 - 1.02606i) q^{49} +(0.425349 - 2.41228i) q^{50} +(-3.06418 + 2.57115i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(7.50567 - 6.29801i) q^{56} +(-2.08378 + 11.8177i) q^{58} +(2.30177 - 0.837775i) q^{59} +(0.868241 + 4.92404i) q^{61} +(1.22474 + 2.12132i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-2.30177 - 0.837775i) q^{65} +(-5.36231 - 4.49951i) q^{67} +(-22.5170 - 18.8940i) q^{68} +(11.2763 + 4.10424i) q^{70} +(-3.67423 + 6.36396i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(3.40280 + 19.2982i) q^{74} +(3.75877 - 1.36808i) q^{76} +(0.850699 - 4.82455i) q^{77} +(-5.36231 + 4.49951i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(-9.38209 + 7.87251i) q^{83} +(3.12567 - 17.7265i) q^{85} +(-25.3194 + 9.21552i) q^{86} +(2.08378 + 11.8177i) q^{88} +(1.00000 - 1.73205i) q^{91} +(9.20707 + 3.35110i) q^{92} +(18.3851 + 15.4269i) q^{94} +(1.87642 + 1.57450i) q^{95} +(6.57785 + 2.39414i) q^{97} +(3.67423 - 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 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

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