LMFDB - Embedded newform 729.2.e.o.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			163.2
Root			$-0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.o.568.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62760 - 0.592396i) q^{2} +(0.766044 - 0.642788i) q^{4} +(0.300767 + 1.70574i) q^{5} +(1.53209 + 1.28558i) q^{7} +(-0.866025 + 1.50000i) q^{8} +O(q^{10})$	\(q+(1.62760 - 0.592396i) q^{2} +(0.766044 - 0.642788i) q^{4} +(0.300767 + 1.70574i) q^{5} +(1.53209 + 1.28558i) q^{7} +(-0.866025 + 1.50000i) q^{8} +(1.50000 + 2.59808i) q^{10} +(0.601535 - 3.41147i) q^{11} +(0.939693 + 0.342020i) q^{13} +(3.25519 + 1.18479i) q^{14} +(-0.868241 + 4.92404i) q^{16} +(2.59808 + 4.50000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.32683 + 1.11334i) q^{20} +(-1.04189 - 5.90885i) q^{22} +(-2.65366 + 2.22668i) q^{23} +(1.87939 - 0.684040i) q^{25} +1.73205 q^{26} +2.00000 q^{28} +(1.62760 - 0.592396i) q^{29} +(6.12836 - 5.14230i) q^{31} +(0.902302 + 5.11721i) q^{32} +(6.89440 + 5.78509i) q^{34} +(-1.73205 + 3.00000i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-0.601535 + 3.41147i) q^{38} +(-2.81908 - 1.02606i) q^{40} +(-6.51038 - 2.36959i) q^{41} +(0.347296 - 1.96962i) q^{43} +(-1.73205 - 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-5.30731 - 4.45336i) q^{47} +(-0.520945 - 2.95442i) q^{49} +(2.65366 - 2.22668i) q^{50} +(0.939693 - 0.342020i) q^{52} +6.00000 q^{55} +(-3.25519 + 1.18479i) q^{56} +(2.29813 - 1.92836i) q^{58} +(-2.40614 - 13.6459i) q^{59} +(-5.36231 - 4.49951i) q^{61} +(6.92820 - 12.0000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.300767 + 1.70574i) q^{65} +(9.39693 + 3.42020i) q^{67} +(4.88279 + 1.77719i) q^{68} +(-1.04189 + 5.90885i) q^{70} +(-5.19615 - 9.00000i) q^{71} +(3.50000 - 6.06218i) q^{73} +(9.28780 + 7.79339i) q^{74} +(0.347296 + 1.96962i) q^{76} +(5.30731 - 4.45336i) q^{77} +(-1.87939 + 0.684040i) q^{79} -8.66025 q^{80} -12.0000 q^{82} +(-13.0208 + 4.73917i) q^{83} +(-6.89440 + 5.78509i) q^{85} +(-0.601535 - 3.41147i) q^{86} +(4.59627 + 3.85673i) q^{88} +(-2.59808 + 4.50000i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-0.601535 + 3.41147i) q^{92} +(-11.2763 - 4.10424i) q^{94} +(-3.25519 - 1.18479i) q^{95} +(0.347296 - 1.96962i) q^{97} +(-2.59808 - 4.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 18 q^{10} - 12 q^{19} + 24 q^{28} + 42 q^{37} - 36 q^{46} + 72 q^{55} - 6 q^{64} + 42 q^{73} - 144 q^{82} + 12 q^{91}+O(q^{100}) $ 12 * q + 18 * q^10 - 12 * q^19 + 24 * q^28 + 42 * q^37 - 36 * q^46 + 72 * q^55 - 6 * q^64 + 42 * q^73 - 144 * q^82 + 12 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.62760	−	0.592396i	1.15088	−	0.418887i	0.305051	−	0.952336i	$-0.401326\pi$
$2$	1.62760	−	0.592396i	1.15088	−	0.418887i	0.845833	+	0.533449i	$0.179104\pi$
$3$		0			0
$3$		0			0
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.300767	+	1.70574i	0.134507	+	0.762829i	0.975202	+	0.221319i	$0.0710361\pi$
$5$	0.300767	+	1.70574i	0.134507	+	0.762829i	−0.840694	+	0.541510i	$0.817853\pi$
$6$		0			0
$7$	1.53209	+	1.28558i	0.579075	+	0.485902i	0.884643	−	0.466268i	$-0.154402\pi$
$7$	1.53209	+	1.28558i	0.579075	+	0.485902i	−0.305568	+	0.952170i	$0.598846\pi$
$8$	−0.866025	+	1.50000i	−0.306186	+	0.530330i
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	0.601535	−	3.41147i	0.181370	−	1.02860i	−0.749162	−	0.662387i	$-0.769544\pi$
$11$	0.601535	−	3.41147i	0.181370	−	1.02860i	0.930532	−	0.366211i	$-0.119345\pi$
$12$		0			0
$13$	0.939693	+	0.342020i	0.260624	+	0.0948593i	0.469027	−	0.883184i	$-0.344605\pi$
$13$	0.939693	+	0.342020i	0.260624	+	0.0948593i	−0.208404	+	0.978043i	$0.566827\pi$
$14$	3.25519	+	1.18479i	0.869986	+	0.316649i
$15$		0			0
$16$	−0.868241	+	4.92404i	−0.217060	+	1.23101i
$17$	2.59808	+	4.50000i	0.630126	+	1.09141i	0.987526	+	0.157459i	$0.0503301\pi$
$17$	2.59808	+	4.50000i	0.630126	+	1.09141i	−0.357400	+	0.933952i	$0.616337\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	1.32683	+	1.11334i	0.296688	+	0.248951i
$21$		0			0
$22$	−1.04189	−	5.90885i	−0.222131	−	1.25977i
$23$	−2.65366	+	2.22668i	−0.553325	+	0.464295i	−0.876065	−	0.482193i	$-0.839841\pi$
$23$	−2.65366	+	2.22668i	−0.553325	+	0.464295i	0.322740	+	0.946488i	$0.395396\pi$
$24$		0			0
$25$	1.87939	−	0.684040i	0.375877	−	0.136808i
$26$	1.73205			0.339683
$27$		0			0
$28$	2.00000			0.377964
$29$	1.62760	−	0.592396i	0.302237	−	0.110005i	−0.186450	−	0.982464i	$-0.559698\pi$
$29$	1.62760	−	0.592396i	0.302237	−	0.110005i	0.488687	+	0.872459i	$0.337476\pi$
$30$		0			0
$31$	6.12836	−	5.14230i	1.10069	−	0.923585i	0.103214	−	0.994659i	$-0.467087\pi$
$31$	6.12836	−	5.14230i	1.10069	−	0.923585i	0.997471	+	0.0710747i	$0.0226429\pi$
$32$	0.902302	+	5.11721i	0.159506	+	0.904604i
$33$		0			0
$34$	6.89440	+	5.78509i	1.18238	+	0.992134i
$35$	−1.73205	+	3.00000i	−0.292770	+	0.507093i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	−0.601535	+	3.41147i	−0.0975819	+	0.553414i
$39$		0			0
$40$	−2.81908	−	1.02606i	−0.445735	−	0.162234i
$41$	−6.51038	−	2.36959i	−1.01675	−	0.370067i	−0.220729	−	0.975335i	$-0.570844\pi$
$41$	−6.51038	−	2.36959i	−1.01675	−	0.370067i	−0.796022	+	0.605268i	$0.793066\pi$
$42$		0			0
$43$	0.347296	−	1.96962i	0.0529622	−	0.300364i	−0.946808	−	0.321799i	$-0.895712\pi$
$43$	0.347296	−	1.96962i	0.0529622	−	0.300364i	0.999770	+	0.0214354i	$0.00682361\pi$
$44$	−1.73205	−	3.00000i	−0.261116	−	0.452267i
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−5.30731	−	4.45336i	−0.774151	−	0.649590i	0.167617	−	0.985852i	$-0.446393\pi$
$47$	−5.30731	−	4.45336i	−0.774151	−	0.649590i	−0.941768	+	0.336262i	$0.890837\pi$
$48$		0			0
$49$	−0.520945	−	2.95442i	−0.0744206	−	0.422060i
$50$	2.65366	−	2.22668i	0.375284	−	0.314900i
$51$		0			0
$52$	0.939693	−	0.342020i	0.130312	−	0.0474297i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$	−3.25519	+	1.18479i	−0.434993	+	0.158325i
$57$		0			0
$58$	2.29813	−	1.92836i	0.301760	−	0.253206i
$59$	−2.40614	−	13.6459i	−0.313253	−	1.77654i	−0.581854	−	0.813293i	$-0.697673\pi$
$59$	−2.40614	−	13.6459i	−0.313253	−	1.77654i	0.268602	−	0.963251i	$-0.413438\pi$
$60$		0			0
$61$	−5.36231	−	4.49951i	−0.686574	−	0.576104i	0.231345	−	0.972872i	$-0.425687\pi$
$61$	−5.36231	−	4.49951i	−0.686574	−	0.576104i	−0.917919	+	0.396768i	$0.870132\pi$
$62$	6.92820	−	12.0000i	0.879883	−	1.52400i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.300767	+	1.70574i	−0.0373056	+	0.211571i
$66$		0			0
$67$	9.39693	+	3.42020i	1.14802	+	0.417844i	0.844803	−	0.535078i	$-0.179718\pi$
$67$	9.39693	+	3.42020i	1.14802	+	0.417844i	0.303215	+	0.952922i	$0.401940\pi$
$68$	4.88279	+	1.77719i	0.592125	+	0.215516i
$69$		0			0
$70$	−1.04189	+	5.90885i	−0.124530	+	0.706242i
$71$	−5.19615	−	9.00000i	−0.616670	−	1.06810i	−0.990089	−	0.140441i	$-0.955148\pi$
$71$	−5.19615	−	9.00000i	−0.616670	−	1.06810i	0.373419	−	0.927663i	$-0.378185\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	9.28780	+	7.79339i	1.07968	+	0.905963i
$75$		0			0
$76$	0.347296	+	1.96962i	0.0398376	+	0.225930i
$77$	5.30731	−	4.45336i	0.604824	−	0.507508i
$78$		0			0
$79$	−1.87939	+	0.684040i	−0.211447	+	0.0769605i	−0.445572	−	0.895246i	$-0.647000\pi$
$79$	−1.87939	+	0.684040i	−0.211447	+	0.0769605i	0.234125	+	0.972207i	$0.424778\pi$
$80$	−8.66025			−0.968246
$81$		0			0
$82$	−12.0000			−1.32518
$83$	−13.0208	+	4.73917i	−1.42921	+	0.520192i	−0.936706	−	0.350116i	$-0.886142\pi$
$83$	−13.0208	+	4.73917i	−1.42921	+	0.520192i	−0.492508	+	0.870308i	$0.663920\pi$
$84$		0			0
$85$	−6.89440	+	5.78509i	−0.747803	+	0.627481i
$86$	−0.601535	−	3.41147i	−0.0648652	−	0.367869i
$87$		0			0
$88$	4.59627	+	3.85673i	0.489964	+	0.411128i
$89$	−2.59808	+	4.50000i	−0.275396	+	0.476999i	−0.970235	−	0.242166i	$-0.922142\pi$
$89$	−2.59808	+	4.50000i	−0.275396	+	0.476999i	0.694839	+	0.719165i	$0.255475\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−0.601535	+	3.41147i	−0.0627144	+	0.355671i
$93$		0			0
$94$	−11.2763	−	4.10424i	−1.16306	−	0.423320i
$95$	−3.25519	−	1.18479i	−0.333976	−	0.121557i
$96$		0			0
$97$	0.347296	−	1.96962i	0.0352626	−	0.199984i	−0.962087	−	0.272743i	$-0.912069\pi$
$97$	0.347296	−	1.96962i	0.0352626	−	0.199984i	0.997350	+	0.0727587i	$0.0231803\pi$
$98$	−2.59808	−	4.50000i	−0.262445	−	0.454569i
$99$		0			0
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−5.30731	−	4.45336i	−0.528097	−	0.443126i	0.339347	−	0.940661i	$-0.389794\pi$
$101$	−5.30731	−	4.45336i	−0.528097	−	0.443126i	−0.867444	+	0.497535i	$0.834239\pi$
$102$		0			0
$103$	1.38919	+	7.87846i	0.136881	+	0.776288i	0.973532	+	0.228552i	$0.0733991\pi$
$103$	1.38919	+	7.87846i	0.136881	+	0.776288i	−0.836651	+	0.547736i	$0.815490\pi$
$104$	−1.32683	+	1.11334i	−0.130106	+	0.109172i
$105$		0			0
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	11.0000			1.05361			0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000			1.05361			0.526804	+	0.849987i	$0.323390\pi$
$110$	9.76557	−	3.55438i	0.931111	−	0.338897i
$111$		0			0
$112$	−7.66044	+	6.42788i	−0.723844	+	0.607377i
$113$	0.300767	+	1.70574i	0.0282938	+	0.160462i	0.995681	−	0.0928398i	$-0.0295945\pi$
$113$	0.300767	+	1.70574i	0.0282938	+	0.160462i	−0.967387	+	0.253302i	$0.918483\pi$
$114$		0			0
$115$	−4.59627	−	3.85673i	−0.428604	−	0.359642i
$116$	0.866025	−	1.50000i	0.0804084	−	0.139272i
$117$		0			0
$118$	−12.0000	−	20.7846i	−1.10469	−	1.91338i
$119$	−1.80460	+	10.2344i	−0.165428	+	0.938188i
$120$		0			0
$121$	−0.939693	−	0.342020i	−0.0854266	−	0.0310927i
$122$	−11.3932	−	4.14677i	−1.03149	−	0.375431i
$123$		0			0
$124$	1.38919	−	7.87846i	0.124753	−	0.707507i
$125$	6.06218	+	10.5000i	0.542218	+	0.939149i
$126$		0			0
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	−9.28780	−	7.79339i	−0.820933	−	0.688844i
$129$		0			0
$130$	0.520945	+	2.95442i	0.0456899	+	0.259120i
$131$	−2.65366	+	2.22668i	−0.231851	+	0.194546i	−0.751310	−	0.659949i	$-0.770578\pi$
$131$	−2.65366	+	2.22668i	−0.231851	+	0.194546i	0.519459	+	0.854495i	$0.326133\pi$
$132$		0			0
$133$	−3.75877	+	1.36808i	−0.325927	+	0.118628i
$134$	17.3205			1.49626
$135$		0			0
$136$	−9.00000			−0.771744
$137$	1.62760	−	0.592396i	0.139055	−	0.0506118i	−0.271555	−	0.962423i	$-0.587538\pi$
$137$	1.62760	−	0.592396i	0.139055	−	0.0506118i	0.410610	+	0.911811i	$0.365316\pi$
$138$		0			0
$139$	6.12836	−	5.14230i	0.519800	−	0.436164i	−0.344762	−	0.938690i	$-0.612040\pi$
$139$	6.12836	−	5.14230i	0.519800	−	0.436164i	0.864562	+	0.502526i	$0.167596\pi$
$140$	0.601535	+	3.41147i	0.0508390	+	0.288322i
$141$		0			0
$142$	−13.7888	−	11.5702i	−1.15713	−	0.970948i
$143$	1.73205	−	3.00000i	0.144841	−	0.250873i
$144$		0			0
$145$	1.50000	+	2.59808i	0.124568	+	0.215758i
$146$	2.10537	−	11.9402i	0.174242	−	0.988175i
$147$		0			0
$148$	6.57785	+	2.39414i	0.540696	+	0.196797i
$149$	8.13798	+	2.96198i	0.666689	+	0.242655i	0.653122	−	0.757253i	$-0.273459\pi$
$149$	8.13798	+	2.96198i	0.666689	+	0.242655i	0.0135674	+	0.999908i	$0.495681\pi$
$150$		0			0
$151$	3.47296	−	19.6962i	0.282626	−	1.60285i	−0.431019	−	0.902343i	$-0.641846\pi$
$151$	3.47296	−	19.6962i	0.282626	−	1.60285i	0.713645	−	0.700508i	$-0.247043\pi$
$152$	−1.73205	−	3.00000i	−0.140488	−	0.243332i
$153$		0			0
$154$	6.00000	−	10.3923i	0.483494	−	0.837436i
$155$	10.6146	+	8.90673i	0.852587	+	0.715405i
$156$		0			0
$157$	2.95202	+	16.7417i	0.235597	+	1.33614i	0.841353	+	0.540486i	$0.181759\pi$
$157$	2.95202	+	16.7417i	0.235597	+	1.33614i	−0.605757	+	0.795650i	$0.707129\pi$
$158$	−2.65366	+	2.22668i	−0.211114	+	0.177145i
$159$		0			0
$160$	−8.45723	+	3.07818i	−0.668603	+	0.243352i
$161$	−6.92820			−0.546019
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−6.51038	+	2.36959i	−0.508375	+	0.185034i
$165$		0			0
$166$	−18.3851	+	15.4269i	−1.42696	+	1.19736i
$167$	3.00767	+	17.0574i	0.232741	+	1.31994i	0.847320	+	0.531083i	$0.178215\pi$
$167$	3.00767	+	17.0574i	0.232741	+	1.31994i	−0.614579	+	0.788856i	$0.710674\pi$
$168$		0			0
$169$	−9.19253	−	7.71345i	−0.707118	−	0.593342i
$170$	−7.79423	+	13.5000i	−0.597790	+	1.03540i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	3.30844	−	18.7631i	0.251536	−	1.42653i	−0.553273	−	0.833000i	$-0.686622\pi$
$173$	3.30844	−	18.7631i	0.251536	−	1.42653i	0.804810	−	0.593533i	$-0.202267\pi$
$174$		0			0
$175$	3.75877	+	1.36808i	0.284136	+	0.103417i
$176$	16.2760	+	5.92396i	1.22685	+	0.446535i
$177$		0			0
$178$	−1.56283	+	8.86327i	−0.117139	+	0.664330i
$179$	10.3923	+	18.0000i	0.776757	+	1.34538i	0.933801	+	0.357792i	$0.116470\pi$
$179$	10.3923	+	18.0000i	0.776757	+	1.34538i	−0.157044	+	0.987592i	$0.550196\pi$
$180$		0			0
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$	2.65366	+	2.22668i	0.196702	+	0.165053i
$183$		0			0
$184$	−1.04189	−	5.90885i	−0.0768091	−	0.435606i
$185$	−9.28780	+	7.79339i	−0.682852	+	0.572981i
$186$		0			0
$187$	16.9145	−	6.15636i	1.23691	−	0.450198i
$188$	−6.92820			−0.505291
$189$		0			0
$190$	−6.00000			−0.435286
$191$	16.2760	−	5.92396i	1.17769	−	0.428643i	0.322302	−	0.946637i	$-0.395543\pi$
$191$	16.2760	−	5.92396i	1.17769	−	0.428643i	0.855384	+	0.517994i	$0.173321\pi$
$192$		0			0
$193$	−0.766044	+	0.642788i	−0.0551411	+	0.0462689i	−0.669942	−	0.742414i	$-0.733681\pi$
$193$	−0.766044	+	0.642788i	−0.0551411	+	0.0462689i	0.614801	+	0.788683i	$0.289236\pi$
$194$	−0.601535	−	3.41147i	−0.0431877	−	0.244930i
$195$		0			0
$196$	−2.29813	−	1.92836i	−0.164152	−	0.137740i
$197$	−2.59808	+	4.50000i	−0.185105	+	0.320612i	−0.943612	−	0.331053i	$-0.892596\pi$
$197$	−2.59808	+	4.50000i	−0.185105	+	0.320612i	0.758507	+	0.651665i	$0.225929\pi$
$198$		0			0
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$	−0.601535	+	3.41147i	−0.0425349	+	0.241228i
$201$		0			0
$202$	−11.2763	−	4.10424i	−0.793399	−	0.288773i
$203$	3.25519	+	1.18479i	0.228470	+	0.0831561i
$204$		0			0
$205$	2.08378	−	11.8177i	0.145537	−	0.825383i
$206$	6.92820	+	12.0000i	0.482711	+	0.836080i
$207$		0			0
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	5.30731	+	4.45336i	0.367114	+	0.308046i
$210$		0			0
$211$	−1.73648	−	9.84808i	−0.119544	−	0.677970i	−0.984399	−	0.175948i	$-0.943701\pi$
$211$	−1.73648	−	9.84808i	−0.119544	−	0.677970i	0.864855	−	0.502022i	$-0.167410\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.46410			0.236250
$216$		0			0
$217$	16.0000			1.08615
$218$	17.9035	−	6.51636i	1.21258	−	0.441344i
$219$		0			0
$220$	4.59627	−	3.85673i	0.309880	−	0.260020i
$221$	0.902302	+	5.11721i	0.0606954	+	0.344221i
$222$		0			0
$223$	1.53209	+	1.28558i	0.102596	+	0.0860885i	0.692643	−	0.721281i	$-0.256446\pi$
$223$	1.53209	+	1.28558i	0.102596	+	0.0860885i	−0.590047	+	0.807369i	$0.700891\pi$
$224$	−5.19615	+	9.00000i	−0.347183	+	0.601338i
$225$		0			0
$226$	1.50000	+	2.59808i	0.0997785	+	0.172821i
$227$	0.601535	−	3.41147i	0.0399253	−	0.226427i	−0.958316	−	0.285711i	$-0.907770\pi$
$227$	0.601535	−	3.41147i	0.0399253	−	0.226427i	0.998241	+	0.0592832i	$0.0188815\pi$
$228$		0			0
$229$	0.939693	+	0.342020i	0.0620966	+	0.0226013i	0.372882	−	0.927879i	$-0.378370\pi$
$229$	0.939693	+	0.342020i	0.0620966	+	0.0226013i	−0.310785	+	0.950480i	$0.600592\pi$
$230$	−9.76557	−	3.55438i	−0.643923	−	0.234369i
$231$		0			0
$232$	−0.520945	+	2.95442i	−0.0342017	+	0.193967i
$233$	−12.9904	−	22.5000i	−0.851028	−	1.47402i	−0.880281	−	0.474452i	$-0.842646\pi$
$233$	−12.9904	−	22.5000i	−0.851028	−	1.47402i	0.0292532	−	0.999572i	$-0.490687\pi$
$234$		0			0
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$	−10.6146	−	8.90673i	−0.690953	−	0.579779i
$237$		0			0
$238$	3.12567	+	17.7265i	0.202607	+	1.14904i
$239$	21.2292	−	17.8135i	1.37321	−	1.15226i	0.401555	−	0.915835i	$-0.368470\pi$
$239$	21.2292	−	17.8135i	1.37321	−	1.15226i	0.971651	−	0.236422i	$-0.0759747\pi$
$240$		0			0
$241$	−27.2511	+	9.91858i	−1.75540	+	0.638912i	−0.999869	−	0.0162041i	$-0.994842\pi$
$241$	−27.2511	+	9.91858i	−1.75540	+	0.638912i	−0.755528	+	0.655116i	$0.772620\pi$
$242$	−1.73205			−0.111340
$243$		0			0
$244$	−7.00000			−0.448129
$245$	4.88279	−	1.77719i	0.311950	−	0.113540i
$246$		0			0
$247$	−1.53209	+	1.28558i	−0.0974845	+	0.0817992i
$248$	2.40614	+	13.6459i	0.152790	+	0.866515i
$249$		0			0
$250$	16.0869	+	13.4985i	1.01743	+	0.853723i
$251$	5.19615	−	9.00000i	0.327978	−	0.568075i	−0.654132	−	0.756380i	$-0.726966\pi$
$251$	5.19615	−	9.00000i	0.327978	−	0.568075i	0.982111	+	0.188305i	$0.0602994\pi$
$252$		0			0
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	−0.601535	+	3.41147i	−0.0377437	+	0.214055i
$255$		0			0
$256$	−17.8542	−	6.49838i	−1.11588	−	0.406149i
$257$	8.13798	+	2.96198i	0.507633	+	0.184763i	0.583124	−	0.812383i	$-0.301830\pi$
$257$	8.13798	+	2.96198i	0.507633	+	0.184763i	−0.0754909	+	0.997146i	$0.524052\pi$
$258$		0			0
$259$	−2.43107	+	13.7873i	−0.151060	+	0.856702i
$260$	0.866025	+	1.50000i	0.0537086	+	0.0930261i
$261$		0			0
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	−5.30731	−	4.45336i	−0.327263	−	0.274606i	0.464321	−	0.885667i	$-0.346299\pi$
$263$	−5.30731	−	4.45336i	−0.327263	−	0.274606i	−0.791583	+	0.611061i	$0.790743\pi$
$264$		0			0
$265$		0			0
$266$	−5.30731	+	4.45336i	−0.325412	+	0.273053i
$267$		0			0
$268$	9.39693	−	3.42020i	0.574009	−	0.208922i
$269$	15.5885			0.950445			0.475223	−	0.879866i	$-0.342368\pi$
$269$	15.5885			0.950445			0.475223	+	0.879866i	$0.342368\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	−24.4139	+	8.88594i	−1.48031	+	0.538789i
$273$		0			0
$274$	2.29813	−	1.92836i	0.138835	−	0.116497i
$275$	−1.20307	−	6.82295i	−0.0725478	−	0.411439i
$276$		0			0
$277$	1.53209	+	1.28558i	0.0920543	+	0.0772427i	0.687653	−	0.726039i	$-0.258641\pi$
$277$	1.53209	+	1.28558i	0.0920543	+	0.0772427i	−0.595599	+	0.803282i	$0.703085\pi$
$278$	6.92820	−	12.0000i	0.415526	−	0.719712i
$279$		0			0
$280$	−3.00000	−	5.19615i	−0.179284	−	0.310530i
$281$	−2.10537	+	11.9402i	−0.125596	+	0.712290i	0.855356	+	0.518040i	$0.173338\pi$
$281$	−2.10537	+	11.9402i	−0.125596	+	0.712290i	−0.980952	+	0.194250i	$0.937773\pi$
$282$		0			0
$283$	26.3114	+	9.57656i	1.56405	+	0.569268i	0.971660	−	0.236384i	$-0.0759622\pi$
$283$	26.3114	+	9.57656i	1.56405	+	0.569268i	0.592390	+	0.805651i	$0.298184\pi$
$284$	−9.76557	−	3.55438i	−0.579480	−	0.210914i
$285$		0			0
$286$	1.04189	−	5.90885i	0.0616082	−	0.349397i
$287$	−6.92820	−	12.0000i	−0.408959	−	0.708338i
$288$		0			0
$289$	−5.00000	+	8.66025i	−0.294118	+	0.509427i
$290$	3.98048	+	3.34002i	0.233742	+	0.196133i
$291$		0			0
$292$	−1.21554	−	6.89365i	−0.0711339	−	0.403421i
$293$	−14.5951	+	12.2467i	−0.852655	+	0.715463i	−0.960373	−	0.278719i	$-0.910090\pi$
$293$	−14.5951	+	12.2467i	−0.852655	+	0.715463i	0.107717	+	0.994182i	$0.465646\pi$
$294$		0			0
$295$	22.5526	−	8.20848i	1.31306	−	0.477916i
$296$	−12.1244			−0.704714
$297$		0			0
$298$	15.0000			0.868927
$299$	−3.25519	+	1.18479i	−0.188253	+	0.0685183i
$300$		0			0
$301$	3.06418	−	2.57115i	0.176616	−	0.148199i
$302$	−6.01535	−	34.1147i	−0.346144	−	1.96308i
$303$		0			0
$304$	−7.66044	−	6.42788i	−0.439357	−	0.368664i
$305$	6.06218	−	10.5000i	0.347119	−	0.601228i
$306$		0			0
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	0.998778	−	0.0494267i	$-0.0157394\pi$
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	−0.542194	+	0.840254i	$0.682406\pi$
$308$	1.20307	−	6.82295i	0.0685513	−	0.388774i
$309$		0			0
$310$	22.5526	+	8.20848i	1.28090	+	0.466211i
$311$	−6.51038	−	2.36959i	−0.369170	−	0.134367i	0.150772	−	0.988569i	$-0.451824\pi$
$311$	−6.51038	−	2.36959i	−0.369170	−	0.134367i	−0.519942	+	0.854202i	$0.674046\pi$
$312$		0			0
$313$	−4.34120	+	24.6202i	−0.245379	+	1.39162i	0.574231	+	0.818694i	$0.305301\pi$
$313$	−4.34120	+	24.6202i	−0.245379	+	1.39162i	−0.819610	+	0.572922i	$0.805810\pi$
$314$	14.7224	+	25.5000i	0.830835	+	1.43905i
$315$		0			0
$316$	−1.00000	+	1.73205i	−0.0562544	+	0.0974355i
$317$	6.63414	+	5.56670i	0.372610	+	0.312657i	0.809793	−	0.586715i	$-0.199579\pi$
$317$	6.63414	+	5.56670i	0.372610	+	0.312657i	−0.437183	+	0.899373i	$0.644024\pi$
$318$		0			0
$319$	−1.04189	−	5.90885i	−0.0583346	−	0.330832i
$320$	1.32683	−	1.11334i	0.0741719	−	0.0622376i
$321$		0			0
$322$	−11.2763	+	4.10424i	−0.628404	+	0.228720i
$323$	−10.3923			−0.578243
$324$		0			0
$325$	2.00000			0.110940
$326$	−26.0415	+	9.47834i	−1.44231	+	0.524957i
$327$		0			0
$328$	9.19253	−	7.71345i	0.507573	−	0.425904i
$329$	−2.40614	−	13.6459i	−0.132655	−	0.752323i
$330$		0			0
$331$	1.53209	+	1.28558i	0.0842112	+	0.0706616i	0.683922	−	0.729556i	$-0.260273\pi$
$331$	1.53209	+	1.28558i	0.0842112	+	0.0706616i	−0.599710	+	0.800217i	$0.704718\pi$
$332$	−6.92820	+	12.0000i	−0.380235	+	0.658586i
$333$		0			0
$334$	15.0000	+	25.9808i	0.820763	+	1.42160i
$335$	−3.00767	+	17.0574i	−0.164327	+	0.931944i
$336$		0			0
$337$	−24.4320	−	8.89252i	−1.33090	−	0.484407i	−0.423962	−	0.905680i	$-0.639361\pi$
$337$	−24.4320	−	8.89252i	−1.33090	−	0.484407i	−0.906934	+	0.421273i	$0.861583\pi$
$338$	−19.5311	−	7.10876i	−1.06235	−	0.386665i
$339$		0			0
$340$	−1.56283	+	8.86327i	−0.0847566	+	0.480678i
$341$	−13.8564	−	24.0000i	−0.750366	−	1.29967i
$342$		0			0
$343$	10.0000	−	17.3205i	0.539949	−	0.935220i
$344$	2.65366	+	2.22668i	0.143076	+	0.120055i
$345$		0			0
$346$	−5.73039	−	32.4987i	−0.308068	−	1.74714i
$347$	−2.65366	+	2.22668i	−0.142456	+	0.119535i	−0.711231	−	0.702959i	$-0.751862\pi$
$347$	−2.65366	+	2.22668i	−0.142456	+	0.119535i	0.568775	+	0.822493i	$0.307417\pi$
$348$		0			0
$349$	−1.87939	+	0.684040i	−0.100601	+	0.0366158i	−0.391830	−	0.920037i	$-0.628158\pi$
$349$	−1.87939	+	0.684040i	−0.100601	+	0.0366158i	0.291229	+	0.956653i	$0.405936\pi$
$350$	6.92820			0.370328
$351$		0			0
$352$	18.0000			0.959403
$353$	−13.0208	+	4.73917i	−0.693025	+	0.252241i	−0.664430	−	0.747350i	$-0.731326\pi$
$353$	−13.0208	+	4.73917i	−0.693025	+	0.252241i	−0.0285953	+	0.999591i	$0.509103\pi$
$354$		0			0
$355$	13.7888	−	11.5702i	0.731834	−	0.614081i
$356$	0.902302	+	5.11721i	0.0478219	+	0.271212i
$357$		0			0
$358$	27.5776	+	23.1404i	1.45752	+	1.22301i
$359$	5.19615	−	9.00000i	0.274242	−	0.475002i	−0.695701	−	0.718331i	$-0.744906\pi$
$359$	5.19615	−	9.00000i	0.274242	−	0.475002i	0.969944	+	0.243329i	$0.0782396\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−0.601535	+	3.41147i	−0.0316160	+	0.179303i
$363$		0			0
$364$	1.87939	+	0.684040i	0.0985066	+	0.0358535i
$365$	11.3932	+	4.14677i	0.596346	+	0.217052i
$366$		0			0
$367$	3.47296	−	19.6962i	0.181287	−	1.02813i	−0.749346	−	0.662178i	$-0.769632\pi$
$367$	3.47296	−	19.6962i	0.181287	−	1.02813i	0.930633	−	0.365953i	$-0.119257\pi$
$368$	−8.66025	−	15.0000i	−0.451447	−	0.781929i
$369$		0			0
$370$	−10.5000	+	18.1865i	−0.545869	+	0.945473i
$371$		0			0
$372$		0			0
$373$	−1.73648	−	9.84808i	−0.0899116	−	0.509914i	−0.996188	−	0.0872291i	$-0.972199\pi$
$373$	−1.73648	−	9.84808i	−0.0899116	−	0.509914i	0.906277	−	0.422685i	$-0.138912\pi$
$374$	23.8829	−	20.0401i	1.23496	−	1.03625i
$375$		0			0
$376$	11.2763	−	4.10424i	0.581531	−	0.211660i
$377$	1.73205			0.0892052
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−3.25519	+	1.18479i	−0.166988	+	0.0607786i
$381$		0			0
$382$	22.9813	−	19.2836i	1.17583	−	0.986636i
$383$	3.00767	+	17.0574i	0.153685	+	0.871591i	0.959978	+	0.280075i	$0.0903593\pi$
$383$	3.00767	+	17.0574i	0.153685	+	0.871591i	−0.806293	+	0.591516i	$0.798530\pi$
$384$		0			0
$385$	9.19253	+	7.71345i	0.468495	+	0.393114i
$386$	−0.866025	+	1.50000i	−0.0440795	+	0.0763480i
$387$		0			0
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−4.81228	+	27.2918i	−0.243992	+	1.38375i	0.578829	+	0.815449i	$0.303510\pi$
$389$	−4.81228	+	27.2918i	−0.243992	+	1.38375i	−0.822821	+	0.568300i	$0.807601\pi$
$390$		0			0
$391$	−16.9145	−	6.15636i	−0.855401	−	0.311341i
$392$	4.88279	+	1.77719i	0.246618	+	0.0897616i
$393$		0			0
$394$	−1.56283	+	8.86327i	−0.0787344	+	0.446525i
$395$	−1.73205	−	3.00000i	−0.0871489	−	0.150946i
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$	−26.5366	−	22.2668i	−1.33016	−	1.11613i
$399$		0			0
$400$	1.73648	+	9.84808i	0.0868241	+	0.492404i
$401$	9.28780	−	7.79339i	0.463810	−	0.389183i	−0.380720	−	0.924690i	$-0.624324\pi$
$401$	9.28780	−	7.79339i	0.463810	−	0.389183i	0.844531	+	0.535507i	$0.179879\pi$
$402$		0			0
$403$	7.51754	−	2.73616i	0.374475	−	0.136298i
$404$	−6.92820			−0.344691
$405$		0			0
$406$	6.00000			0.297775
$407$	22.7863	−	8.29355i	1.12948	−	0.411096i
$408$		0			0
$409$	−14.5548	+	12.2130i	−0.719691	+	0.603892i	−0.927300	−	0.374320i	$-0.877876\pi$
$409$	−14.5548	+	12.2130i	−0.719691	+	0.603892i	0.207609	+	0.978212i	$0.433432\pi$
$410$	−3.60921	−	20.4688i	−0.178246	−	1.01088i
$411$		0			0
$412$	6.12836	+	5.14230i	0.301922	+	0.253343i
$413$	13.8564	−	24.0000i	0.681829	−	1.18096i
$414$		0			0
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$	−0.902302	+	5.11721i	−0.0442390	+	0.250892i
$417$		0			0
$418$	11.2763	+	4.10424i	0.551542	+	0.200745i
$419$	−6.51038	−	2.36959i	−0.318053	−	0.115762i	0.178060	−	0.984020i	$-0.443018\pi$
$419$	−6.51038	−	2.36959i	−0.318053	−	0.115762i	−0.496113	+	0.868258i	$0.665240\pi$
$420$		0			0
$421$	−4.34120	+	24.6202i	−0.211577	+	1.19991i	0.675171	+	0.737662i	$0.264070\pi$
$421$	−4.34120	+	24.6202i	−0.211577	+	1.19991i	−0.886748	+	0.462253i	$0.847041\pi$
$422$	−8.66025	−	15.0000i	−0.421575	−	0.730189i
$423$		0			0
$424$		0			0
$425$	7.96097	+	6.68004i	0.386164	+	0.324030i
$426$		0			0
$427$	−2.43107	−	13.7873i	−0.117648	−	0.667215i
$428$		0			0
$429$		0			0
$430$	5.63816	−	2.05212i	0.271896	−	0.0989621i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$	26.0415	−	9.47834i	1.25003	−	0.454975i
$435$		0			0
$436$	8.42649	−	7.07066i	0.403556	−	0.338623i
$437$	−1.20307	−	6.82295i	−0.0575506	−	0.326386i
$438$		0			0
$439$	15.3209	+	12.8558i	0.731226	+	0.613572i	0.930466	−	0.366379i	$-0.119403\pi$
$439$	15.3209	+	12.8558i	0.731226	+	0.613572i	−0.199239	+	0.979951i	$0.563847\pi$
$440$	−5.19615	+	9.00000i	−0.247717	+	0.429058i
$441$		0			0
$442$	4.50000	+	7.79423i	0.214043	+	0.370734i
$443$	6.01535	−	34.1147i	0.285798	−	1.62084i	−0.416624	−	0.909079i	$-0.636787\pi$
$443$	6.01535	−	34.1147i	0.285798	−	1.62084i	0.702422	−	0.711761i	$-0.252102\pi$
$444$		0			0
$445$	−8.45723	−	3.07818i	−0.400911	−	0.145920i
$446$	3.25519	+	1.18479i	0.154138	+	0.0561016i
$447$		0			0
$448$	0.347296	−	1.96962i	0.0164082	−	0.0930556i
$449$	10.3923	+	18.0000i	0.490443	+	0.849473i	0.999939	−	0.0110003i	$-0.00350158\pi$
$449$	10.3923	+	18.0000i	0.490443	+	0.849473i	−0.509496	+	0.860473i	$0.670168\pi$
$450$		0			0
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$	1.32683	+	1.11334i	0.0624087	+	0.0523671i
$453$		0			0
$454$	−1.04189	−	5.90885i	−0.0488983	−	0.277316i
$455$	−2.65366	+	2.22668i	−0.124405	+	0.104388i
$456$		0			0
$457$	−27.2511	+	9.91858i	−1.27475	+	0.463972i	−0.888693	−	0.458502i	$-0.848386\pi$
$457$	−27.2511	+	9.91858i	−1.27475	+	0.463972i	−0.386059	+	0.922474i	$0.626164\pi$
$458$	1.73205			0.0809334
$459$		0			0
$460$	−6.00000			−0.279751
$461$	−13.0208	+	4.73917i	−0.606437	+	0.220725i	−0.626944	−	0.779065i	$-0.715694\pi$
$461$	−13.0208	+	4.73917i	−0.606437	+	0.220725i	0.0205063	+	0.999790i	$0.493472\pi$
$462$		0			0
$463$	6.12836	−	5.14230i	0.284809	−	0.238983i	−0.489179	−	0.872183i	$-0.662704\pi$
$463$	6.12836	−	5.14230i	0.284809	−	0.238983i	0.773988	+	0.633200i	$0.218259\pi$
$464$	1.50384	+	8.52869i	0.0698139	+	0.395934i
$465$		0			0
$466$	−34.4720	−	28.9254i	−1.59688	−	1.33995i
$467$	−10.3923	+	18.0000i	−0.480899	+	0.832941i	−0.999760	−	0.0219178i	$-0.993023\pi$
$467$	−10.3923	+	18.0000i	−0.480899	+	0.832941i	0.518861	+	0.854858i	$0.326356\pi$
$468$		0			0
$469$	10.0000	+	17.3205i	0.461757	+	0.799787i
$470$	3.60921	−	20.4688i	0.166480	−	0.944157i
$471$		0			0
$472$	22.5526	+	8.20848i	1.03807	+	0.377826i
$473$	−6.51038	−	2.36959i	−0.299348	−	0.108954i
$474$		0			0
$475$	−0.694593	+	3.93923i	−0.0318701	+	0.180744i
$476$	5.19615	+	9.00000i	0.238165	+	0.412514i
$477$		0			0
$478$	24.0000	−	41.5692i	1.09773	−	1.90133i
$479$	18.5756	+	15.5868i	0.848740	+	0.712178i	0.959512	−	0.281668i	$-0.0908877\pi$
$479$	18.5756	+	15.5868i	0.848740	+	0.712178i	−0.110771	+	0.993846i	$0.535332\pi$
$480$		0			0
$481$	1.21554	+	6.89365i	0.0554237	+	0.314324i
$482$	−38.4780	+	32.2869i	−1.75263	+	1.47063i
$483$		0			0
$484$	−0.939693	+	0.342020i	−0.0427133	+	0.0155464i
$485$	3.46410			0.157297
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	11.3932	−	4.14677i	0.515744	−	0.187716i
$489$		0			0
$490$	6.89440	−	5.78509i	0.311457	−	0.261344i
$491$	3.00767	+	17.0574i	0.135734	+	0.769788i	0.974345	+	0.225058i	$0.0722570\pi$
$491$	3.00767	+	17.0574i	0.135734	+	0.769788i	−0.838611	+	0.544731i	$0.816632\pi$
$492$		0			0
$493$	6.89440	+	5.78509i	0.310508	+	0.260547i
$494$	−1.73205	+	3.00000i	−0.0779287	+	0.134976i
$495$		0			0
$496$	20.0000	+	34.6410i	0.898027	+	1.55543i
$497$	3.60921	−	20.4688i	0.161895	−	0.918153i
$498$		0			0
$499$	9.39693	+	3.42020i	0.420664	+	0.153109i	0.543675	−	0.839296i	$-0.317033\pi$
$499$	9.39693	+	3.42020i	0.420664	+	0.153109i	−0.123010	+	0.992405i	$0.539255\pi$
$500$	11.3932	+	4.14677i	0.509518	+	0.185449i
$501$		0			0
$502$	3.12567	−	17.7265i	0.139505	−	0.791174i
$503$	10.3923	+	18.0000i	0.463370	+	0.802580i	0.999126	−	0.0417923i	$-0.0133068\pi$
$503$	10.3923	+	18.0000i	0.463370	+	0.802580i	−0.535756	+	0.844373i	$0.679973\pi$
$504$		0			0
$505$	6.00000	−	10.3923i	0.266996	−	0.462451i
$506$	15.9219	+	13.3601i	0.707816	+	0.593928i
$507$		0			0
$508$	0.347296	+	1.96962i	0.0154088	+	0.0873876i
$509$	21.2292	−	17.8135i	0.940970	−	0.789567i	−0.0367840	−	0.999323i	$-0.511711\pi$
$509$	21.2292	−	17.8135i	0.940970	−	0.789567i	0.977754	+	0.209756i	$0.0672669\pi$
$510$		0			0
$511$	13.1557	−	4.78828i	0.581974	−	0.211821i
$512$	−8.66025			−0.382733
$513$		0			0
$514$	15.0000			0.661622
$515$	−13.0208	+	4.73917i	−0.573763	+	0.208833i
$516$		0			0
$517$	−18.3851	+	15.4269i	−0.808574	+	0.678474i
$518$	4.21074	+	23.8803i	0.185009	+	1.04924i
$519$		0			0
$520$	−2.29813	−	1.92836i	−0.100780	−	0.0845643i
$521$	−10.3923	+	18.0000i	−0.455295	+	0.788594i	−0.998705	−	0.0508731i	$-0.983800\pi$
$521$	−10.3923	+	18.0000i	−0.455295	+	0.788594i	0.543410	+	0.839467i	$0.317133\pi$
$522$		0			0
$523$	−19.0000	−	32.9090i	−0.830812	−	1.43901i	−0.897395	−	0.441228i	$-0.854543\pi$
$523$	−19.0000	−	32.9090i	−0.830812	−	1.43901i	0.0665832	−	0.997781i	$-0.478790\pi$
$524$	−0.601535	+	3.41147i	−0.0262782	+	0.149031i
$525$		0			0
$526$	−11.2763	−	4.10424i	−0.491671	−	0.178953i
$527$	39.0623	+	14.2175i	1.70158	+	0.619324i
$528$		0			0
$529$	−1.91013	+	10.8329i	−0.0830491	+	0.470995i
$530$		0			0
$531$		0			0
$532$	−2.00000	+	3.46410i	−0.0867110	+	0.150188i
$533$	−5.30731	−	4.45336i	−0.229885	−	0.192897i
$534$		0			0
$535$		0			0
$536$	−13.2683	+	11.1334i	−0.573102	+	0.480890i
$537$		0			0
$538$	25.3717	−	9.23454i	1.09385	−	0.398129i
$539$	−10.3923			−0.447628
$540$		0			0
$541$	11.0000			0.472927			0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000			0.472927			0.236463	+	0.971640i	$0.424012\pi$
$542$	3.25519	−	1.18479i	0.139822	−	0.0508912i
$543$		0			0
$544$	−20.6832	+	17.3553i	−0.886785	+	0.744101i
$545$	3.30844	+	18.7631i	0.141718	+	0.803723i
$546$		0			0
$547$	15.3209	+	12.8558i	0.655074	+	0.549672i	0.908606	−	0.417655i	$-0.137148\pi$
$547$	15.3209	+	12.8558i	0.655074	+	0.549672i	−0.253532	+	0.967327i	$0.581592\pi$
$548$	0.866025	−	1.50000i	0.0369948	−	0.0640768i
$549$		0			0
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	−0.601535	+	3.41147i	−0.0256262	+	0.145334i
$552$		0			0
$553$	−3.75877	−	1.36808i	−0.159839	−	0.0581767i
$554$	3.25519	+	1.18479i	0.138300	+	0.0503370i
$555$		0			0
$556$	1.38919	−	7.87846i	0.0589146	−	0.334121i
$557$	18.1865	+	31.5000i	0.770588	+	1.33470i	0.937241	+	0.348682i	$0.113371\pi$
$557$	18.1865	+	31.5000i	0.770588	+	1.33470i	−0.166653	+	0.986016i	$0.553296\pi$
$558$		0			0
$559$	1.00000	−	1.73205i	0.0422955	−	0.0732579i
$560$	−13.2683	−	11.1334i	−0.560687	−	0.470472i
$561$		0			0
$562$	3.64661	+	20.6810i	0.153823	+	0.872374i
$563$	−26.5366	+	22.2668i	−1.11838	+	0.938434i	−0.998522	−	0.0543563i	$-0.982689\pi$
$563$	−26.5366	+	22.2668i	−1.11838	+	0.938434i	−0.119861	+	0.992791i	$0.538245\pi$
$564$		0			0
$565$	−2.81908	+	1.02606i	−0.118599	+	0.0431667i
$566$	48.4974			2.03850
$567$		0			0
$568$	18.0000			0.755263
$569$	30.9243	−	11.2555i	1.29641	−	0.471856i	0.400587	−	0.916259i	$-0.368806\pi$
$569$	30.9243	−	11.2555i	1.29641	−	0.471856i	0.895827	+	0.444402i	$0.146584\pi$
$570$		0			0
$571$	6.12836	−	5.14230i	0.256464	−	0.215199i	−0.505486	−	0.862835i	$-0.668687\pi$
$571$	6.12836	−	5.14230i	0.256464	−	0.215199i	0.761950	+	0.647636i	$0.224242\pi$
$572$	−0.601535	−	3.41147i	−0.0251514	−	0.142641i
$573$		0			0
$574$	−18.3851	−	15.4269i	−0.767378	−	0.643906i
$575$	−3.46410	+	6.00000i	−0.144463	+	0.250217i
$576$		0			0
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−3.00767	+	17.0574i	−0.125103	+	0.709493i
$579$		0			0
$580$	2.81908	+	1.02606i	0.117056	+	0.0426048i
$581$	−26.0415	−	9.47834i	−1.08038	−	0.393228i
$582$		0			0
$583$		0			0
$584$	6.06218	+	10.5000i	0.250855	+	0.434493i
$585$		0			0
$586$	−16.5000	+	28.5788i	−0.681609	+	1.18058i
$587$	−29.1902	−	24.4935i	−1.20481	−	1.01095i	−0.999479	−	0.0322620i	$-0.989729\pi$
$587$	−29.1902	−	24.4935i	−1.20481	−	1.01095i	−0.205330	−	0.978693i	$-0.565827\pi$
$588$		0			0
$589$	2.77837	+	15.7569i	0.114481	+	0.649253i
$590$	31.8439	−	26.7202i	1.31099	−	1.10005i
$591$		0			0
$592$	−32.8892	+	11.9707i	−1.35174	+	0.491993i
$593$	−15.5885			−0.640141			−0.320071	−	0.947394i	$-0.603707\pi$
$593$	−15.5885			−0.640141			−0.320071	+	0.947394i	$0.603707\pi$
$594$		0			0
$595$	−18.0000			−0.737928
$596$	8.13798	−	2.96198i	0.333345	−	0.121327i
$597$		0			0
$598$	−4.59627	+	3.85673i	−0.187955	+	0.157713i
$599$	−2.40614	−	13.6459i	−0.0983122	−	0.557556i	−0.993682	−	0.112233i	$-0.964200\pi$
$599$	−2.40614	−	13.6459i	−0.0983122	−	0.557556i	0.895370	−	0.445323i	$-0.146911\pi$
$600$		0			0
$601$	−19.1511	−	16.0697i	−0.781190	−	0.655496i	0.162358	−	0.986732i	$-0.448090\pi$
$601$	−19.1511	−	16.0697i	−0.781190	−	0.655496i	−0.943548	+	0.331236i	$0.892535\pi$
$602$	3.46410	−	6.00000i	0.141186	−	0.244542i
$603$		0			0
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	0.300767	−	1.70574i	0.0122279	−	0.0693481i
$606$		0			0
$607$	−24.4320	−	8.89252i	−0.991665	−	0.360936i	−0.205300	−	0.978699i	$-0.565817\pi$
$607$	−24.4320	−	8.89252i	−0.991665	−	0.360936i	−0.786365	+	0.617763i	$0.788039\pi$
$608$	−9.76557	−	3.55438i	−0.396046	−	0.144149i
$609$		0			0
$610$	3.64661	−	20.6810i	0.147647	−	0.837348i
$611$	−3.46410	−	6.00000i	−0.140143	−	0.242734i
$612$		0			0
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	−0.286300	−	0.958140i	$-0.592425\pi$
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	0.972924	−	0.231127i	$-0.0742412\pi$
$614$	21.2292	+	17.8135i	0.856743	+	0.718892i
$615$		0			0
$616$	2.08378	+	11.8177i	0.0839578	+	0.476148i
$617$	9.28780	−	7.79339i	0.373913	−	0.313750i	−0.436394	−	0.899755i	$-0.643745\pi$
$617$	9.28780	−	7.79339i	0.373913	−	0.313750i	0.810307	+	0.586006i	$0.199300\pi$
$618$		0			0
$619$	−18.7939	+	6.84040i	−0.755389	+	0.274939i	−0.690871	−	0.722978i	$-0.742773\pi$
$619$	−18.7939	+	6.84040i	−0.755389	+	0.274939i	−0.0645172	+	0.997917i	$0.520551\pi$
$620$	13.8564			0.556487
$621$		0			0
$622$	−12.0000			−0.481156
$623$	−9.76557	+	3.55438i	−0.391249	+	0.142403i
$624$		0			0
$625$	−8.42649	+	7.07066i	−0.337060	+	0.282827i
$626$	7.51919	+	42.6434i	0.300527	+	1.70437i
$627$		0			0
$628$	13.0228	+	10.9274i	0.519665	+	0.436050i
$629$	−18.1865	+	31.5000i	−0.725145	+	1.25599i
$630$		0			0
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	0.595397	−	0.803432i	$-0.296995\pi$
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	−0.993491	+	0.113913i	$0.963661\pi$
$632$	0.601535	−	3.41147i	0.0239278	−	0.135701i
$633$		0			0
$634$	14.0954	+	5.13030i	0.559799	+	0.203750i
$635$	−3.25519	−	1.18479i	−0.129178	−	0.0470171i
$636$		0			0
$637$	0.520945	−	2.95442i	0.0206406	−	0.117059i
$638$	−5.19615	−	9.00000i	−0.205718	−	0.356313i
$639$		0			0
$640$	10.5000	−	18.1865i	0.415049	−	0.718886i
$641$	−17.2488	−	14.4734i	−0.681285	−	0.571666i	0.235096	−	0.971972i	$-0.424459\pi$
$641$	−17.2488	−	14.4734i	−0.681285	−	0.571666i	−0.916382	+	0.400306i	$0.868904\pi$
$642$		0			0
$643$	1.38919	+	7.87846i	0.0547841	+	0.310696i	0.999870	−	0.0161260i	$-0.00513328\pi$
$643$	1.38919	+	7.87846i	0.0547841	+	0.310696i	−0.945086	+	0.326822i	$0.894022\pi$
$644$	−5.30731	+	4.45336i	−0.209137	+	0.175487i
$645$		0			0
$646$	−16.9145	+	6.15636i	−0.665491	+	0.242219i
$647$	31.1769			1.22569			0.612845	−	0.790203i	$-0.290025\pi$
$647$	31.1769			1.22569			0.612845	+	0.790203i	$0.290025\pi$
$648$		0			0
$649$	−48.0000			−1.88416
$650$	3.25519	−	1.18479i	0.127679	−	0.0464714i
$651$		0			0
$652$	−12.2567	+	10.2846i	−0.480010	+	0.402776i
$653$	−2.40614	−	13.6459i	−0.0941595	−	0.534005i	−0.995002	−	0.0998584i	$-0.968161\pi$
$653$	−2.40614	−	13.6459i	−0.0941595	−	0.534005i	0.900842	−	0.434147i	$-0.142950\pi$
$654$		0			0
$655$	−4.59627	−	3.85673i	−0.179591	−	0.150695i
$656$	17.3205	−	30.0000i	0.676252	−	1.17130i
$657$		0			0
$658$	−12.0000	−	20.7846i	−0.467809	−	0.810268i
$659$	0.601535	−	3.41147i	0.0234325	−	0.132892i	−0.970847	−	0.239699i	$-0.922951\pi$
$659$	0.601535	−	3.41147i	0.0234325	−	0.132892i	0.994280	+	0.106806i	$0.0340625\pi$
$660$		0			0
$661$	−15.9748	−	5.81434i	−0.621347	−	0.226152i	0.0121139	−	0.999927i	$-0.496144\pi$
$661$	−15.9748	−	5.81434i	−0.621347	−	0.226152i	−0.633461	+	0.773775i	$0.718366\pi$
$662$	3.25519	+	1.18479i	0.126517	+	0.0460483i
$663$		0			0
$664$	4.16756	−	23.6354i	0.161733	−	0.917231i
$665$	−3.46410	−	6.00000i	−0.134332	−	0.232670i
$666$		0			0
$667$	−3.00000	+	5.19615i	−0.116160	+	0.201196i
$668$	13.2683	+	11.1334i	0.513365	+	0.430764i
$669$		0			0
$670$	5.20945	+	29.5442i	0.201258	+	1.14139i
$671$	−18.5756	+	15.5868i	−0.717103	+	0.601721i
$672$		0			0
$673$	23.4923	−	8.55050i	0.905562	−	0.329598i	0.153083	−	0.988213i	$-0.451080\pi$
$673$	23.4923	−	8.55050i	0.905562	−	0.329598i	0.752479	+	0.658616i	$0.228858\pi$
$674$	−45.0333			−1.73462
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−13.0208	+	4.73917i	−0.500429	+	0.182141i	−0.579887	−	0.814697i	$-0.696903\pi$
$677$	−13.0208	+	4.73917i	−0.500429	+	0.182141i	0.0794582	+	0.996838i	$0.474681\pi$
$678$		0			0
$679$	3.06418	−	2.57115i	0.117592	−	0.0986717i
$680$	−2.70691	−	15.3516i	−0.103805	−	0.588708i
$681$		0			0
$682$	−36.7701	−	30.8538i	−1.40800	−	1.18145i
$683$	−10.3923	+	18.0000i	−0.397650	+	0.688751i	−0.993436	−	0.114393i	$-0.963508\pi$
$683$	−10.3923	+	18.0000i	−0.397650	+	0.688751i	0.595785	+	0.803144i	$0.296841\pi$
$684$		0			0
$685$	1.50000	+	2.59808i	0.0573121	+	0.0992674i
$686$	6.01535	−	34.1147i	0.229667	−	1.30251i
$687$		0			0
$688$	9.39693	+	3.42020i	0.358254	+	0.130394i
$689$		0			0
$690$		0			0
$691$	0.347296	−	1.96962i	0.0132118	−	0.0749277i	−0.977489	−	0.210986i	$-0.932332\pi$
$691$	0.347296	−	1.96962i	0.0132118	−	0.0749277i	0.990701	+	0.136059i	$0.0434436\pi$
$692$	−9.52628	−	16.5000i	−0.362135	−	0.627236i
$693$		0			0
$694$	−3.00000	+	5.19615i	−0.113878	+	0.197243i
$695$	10.6146	+	8.90673i	0.402636	+	0.337851i
$696$		0			0
$697$	−6.25133	−	35.4531i	−0.236786	−	1.34288i
$698$	−2.65366	+	2.22668i	−0.100442	+	0.0842811i
$699$		0			0
$700$	3.75877	−	1.36808i	0.142068	−	0.0517086i
$701$	−46.7654			−1.76630			−0.883152	−	0.469087i	$-0.844583\pi$
$701$	−46.7654			−1.76630			−0.883152	+	0.469087i	$0.844583\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	−3.25519	+	1.18479i	−0.122685	+	0.0446535i
$705$		0			0
$706$	−18.3851	+	15.4269i	−0.691931	+	0.580599i
$707$	−2.40614	−	13.6459i	−0.0904922	−	0.513207i
$708$		0			0
$709$	−19.1511	−	16.0697i	−0.719235	−	0.603510i	0.207939	−	0.978142i	$-0.433325\pi$
$709$	−19.1511	−	16.0697i	−0.719235	−	0.603510i	−0.927174	+	0.374632i	$0.877769\pi$
$710$	15.5885	−	27.0000i	0.585024	−	1.01329i
$711$		0			0
$712$	−4.50000	−	7.79423i	−0.168645	−	0.292101i
$713$	−4.81228	+	27.2918i	−0.180221	+	1.02209i
$714$		0			0
$715$	5.63816	+	2.05212i	0.210855	+	0.0767450i
$716$	19.5311	+	7.10876i	0.729913	+	0.265667i
$717$		0			0
$718$	3.12567	−	17.7265i	0.116649	−	0.661549i
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	0.752717	−	0.658344i	$-0.228743\pi$
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	−0.946501	+	0.322700i	$0.895409\pi$
$720$		0			0
$721$	−8.00000	+	13.8564i	−0.297936	+	0.516040i
$722$	19.9024	+	16.7001i	0.740691	+	0.621514i
$723$		0			0
$724$	0.347296	+	1.96962i	0.0129072	+	0.0732002i
$725$	2.65366	−	2.22668i	0.0985543	−	0.0826969i
$726$		0			0
$727$	31.9495	−	11.6287i	1.18494	−	0.431284i	0.326998	−	0.945025i	$-0.393963\pi$
$727$	31.9495	−	11.6287i	1.18494	−	0.431284i	0.857945	+	0.513741i	$0.171741\pi$
$728$	−3.46410			−0.128388
$729$		0			0
$730$	21.0000			0.777245
$731$	9.76557	−	3.55438i	0.361193	−	0.131463i
$732$		0			0
$733$	−35.2380	+	29.5682i	−1.30155	+	1.09213i	−0.311671	+	0.950190i	$0.600889\pi$
$733$	−35.2380	+	29.5682i	−1.30155	+	1.09213i	−0.989876	+	0.141937i	$0.954667\pi$
$734$	−6.01535	−	34.1147i	−0.222031	−	1.25920i
$735$		0			0
$736$	−13.7888	−	11.5702i	−0.508262	−	0.426482i
$737$	17.3205	−	30.0000i	0.638009	−	1.10506i
$738$		0			0
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	−2.10537	+	11.9402i	−0.0773950	+	0.438929i
$741$		0			0
$742$		0			0
$743$	−6.51038	−	2.36959i	−0.238843	−	0.0869316i	0.219826	−	0.975539i	$-0.429451\pi$
$743$	−6.51038	−	2.36959i	−0.238843	−	0.0869316i	−0.458668	+	0.888608i	$0.651673\pi$
$744$		0			0
$745$	−2.60472	+	14.7721i	−0.0954297	+	0.541208i
$746$	−8.66025	−	15.0000i	−0.317074	−	0.549189i
$747$		0			0
$748$	9.00000	−	15.5885i	0.329073	−	0.569970i
$749$		0			0
$750$		0			0
$751$	−1.73648	−	9.84808i	−0.0633651	−	0.359361i	−0.999960	−	0.00894729i	$-0.997152\pi$
$751$	−1.73648	−	9.84808i	−0.0633651	−	0.359361i	0.936595	−	0.350414i	$-0.113959\pi$
$752$	26.5366	−	22.2668i	0.967689	−	0.811987i
$753$		0			0
$754$	2.81908	−	1.02606i	0.102665	−	0.0373669i
$755$	34.6410			1.26072
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−26.0415	+	9.47834i	−0.945871	+	0.344269i
$759$		0			0
$760$	4.59627	−	3.85673i	0.166724	−	0.139898i
$761$	−5.11305	−	28.9975i	−0.185348	−	1.05116i	−0.925508	−	0.378729i	$-0.876361\pi$
$761$	−5.11305	−	28.9975i	−0.185348	−	1.05116i	0.740160	−	0.672431i	$-0.234750\pi$
$762$		0			0
$763$	16.8530	+	14.1413i	0.610119	+	0.511950i
$764$	8.66025	−	15.0000i	0.313317	−	0.542681i
$765$		0			0
$766$	15.0000	+	25.9808i	0.541972	+	0.938723i
$767$	2.40614	−	13.6459i	0.0868807	−	0.492725i
$768$		0			0
$769$	0.939693	+	0.342020i	0.0338862	+	0.0123336i	0.358908	−	0.933373i	$-0.383149\pi$
$769$	0.939693	+	0.342020i	0.0338862	+	0.0123336i	−0.325021	+	0.945707i	$0.605372\pi$
$770$	19.5311	+	7.10876i	0.703854	+	0.256182i
$771$		0			0
$772$	−0.173648	+	0.984808i	−0.00624973	+	0.0354440i
$773$	−12.9904	−	22.5000i	−0.467232	−	0.809269i	0.532068	−	0.846702i	$-0.321415\pi$
$773$	−12.9904	−	22.5000i	−0.467232	−	0.809269i	−0.999299	+	0.0374331i	$0.988082\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	2.65366	+	2.22668i	0.0952607	+	0.0799332i
$777$		0			0
$778$	8.33511	+	47.2708i	0.298828	+	1.69474i
$779$	10.6146	−	8.90673i	0.380308	−	0.319117i
$780$		0			0
$781$	−33.8289	+	12.3127i	−1.21049	+	0.440584i
$782$	−31.1769			−1.11488
$783$		0			0
$784$	15.0000			0.535714
$785$	−27.6691	+	10.0707i	−0.987553	+	0.359440i
$786$		0			0
$787$	19.9172	−	16.7125i	0.709970	−	0.595735i	−0.214621	−	0.976697i	$-0.568852\pi$
$787$	19.9172	−	16.7125i	0.709970	−	0.595735i	0.924591	+	0.380962i	$0.124407\pi$
$788$	0.902302	+	5.11721i	0.0321432	+	0.182293i
$789$		0			0
$790$	−4.59627	−	3.85673i	−0.163528	−	0.137216i
$791$	−1.73205	+	3.00000i	−0.0615846	+	0.106668i
$792$		0			0
$793$	−3.50000	−	6.06218i	−0.124289	−	0.215274i
$794$	−8.72226	+	49.4664i	−0.309541	+	1.75550i
$795$		0			0
$796$	−18.7939	−	6.84040i	−0.666130	−	0.242452i
$797$	−50.4555	−	18.3643i	−1.78722	−	0.650496i	−0.999401	−	0.0345940i	$-0.988986\pi$
$797$	−50.4555	−	18.3643i	−1.78722	−	0.650496i	−0.787823	−	0.615902i	$-0.788792\pi$
$798$		0			0
$799$	6.25133	−	35.4531i	0.221156	−	1.25424i
$800$	5.19615	+	9.00000i	0.183712	+	0.318198i
$801$		0			0
$802$	10.5000	−	18.1865i	0.370768	−	0.642189i
$803$	−18.5756	−	15.5868i	−0.655518	−	0.550045i
$804$		0			0
$805$	−2.08378	−	11.8177i	−0.0734435	−	0.416519i
$806$	10.6146	−	8.90673i	0.373884	−	0.313726i
$807$		0			0
$808$	11.2763	−	4.10424i	0.396699	−	0.144387i
$809$	46.7654			1.64418			0.822091	−	0.569355i	$-0.192807\pi$
$809$	46.7654			1.64418			0.822091	+	0.569355i	$0.192807\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	3.25519	−	1.18479i	0.114235	−	0.0415781i
$813$		0			0
$814$	32.1739	−	26.9971i	1.12769	−	0.946247i
$815$	−4.81228	−	27.2918i	−0.168567	−	0.955990i
$816$		0			0
$817$	3.06418	+	2.57115i	0.107202	+	0.0899532i
$818$	−16.4545	+	28.5000i	−0.575317	+	0.996479i
$819$		0			0
$820$	−6.00000	−	10.3923i	−0.209529	−	0.362915i
$821$	−2.10537	+	11.9402i	−0.0734780	+	0.416714i	0.925775	+	0.378074i	$0.123414\pi$
$821$	−2.10537	+	11.9402i	−0.0734780	+	0.416714i	−0.999253	+	0.0386400i	$0.987697\pi$
$822$		0			0
$823$	26.3114	+	9.57656i	0.917158	+	0.333818i	0.757107	−	0.653291i	$-0.226612\pi$
$823$	26.3114	+	9.57656i	0.917158	+	0.333818i	0.160050	+	0.987109i	$0.448834\pi$
$824$	−13.0208	−	4.73917i	−0.453600	−	0.165097i
$825$		0			0
$826$	8.33511	−	47.2708i	0.290016	−	1.64476i
$827$	−5.19615	−	9.00000i	−0.180688	−	0.312961i	0.761427	−	0.648251i	$-0.224499\pi$
$827$	−5.19615	−	9.00000i	−0.180688	−	0.312961i	−0.942115	+	0.335290i	$0.891166\pi$
$828$		0			0
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$	−31.8439	−	26.7202i	−1.10532	−	0.927471i
$831$		0			0
$832$	−0.173648	−	0.984808i	−0.00602017	−	0.0341421i
$833$	11.9415	−	10.0201i	0.413747	−	0.347175i
$834$		0			0
$835$	−28.1908	+	10.2606i	−0.975582	+	0.355083i
$836$	6.92820			0.239617
$837$		0			0
$838$	−12.0000			−0.414533
$839$	−42.3175	+	15.4023i	−1.46096	+	0.531747i	−0.945630	−	0.325244i	$-0.894553\pi$
$839$	−42.3175	+	15.4023i	−1.46096	+	0.531747i	−0.515332	+	0.856991i	$0.672331\pi$
$840$		0			0
$841$	−19.9172	+	16.7125i	−0.686798	+	0.576292i
$842$	7.51919	+	42.6434i	0.259128	+	1.46959i
$843$		0			0
$844$	−7.66044	−	6.42788i	−0.263683	−	0.221257i
$845$	10.3923	−	18.0000i	0.357506	−	0.619219i
$846$		0			0
$847$	−1.00000	−	1.73205i	−0.0343604	−	0.0595140i
$848$		0			0
$849$		0			0
$850$	16.9145	+	6.15636i	0.580161	+	0.211161i
$851$	−22.7863	−	8.29355i	−0.781106	−	0.284299i
$852$		0			0
$853$	−5.90404	+	33.4835i	−0.202150	+	1.14645i	0.699711	+	0.714426i	$0.253312\pi$
$853$	−5.90404	+	33.4835i	−0.202150	+	1.14645i	−0.901861	+	0.432026i	$0.857799\pi$
$854$	−12.1244	−	21.0000i	−0.414887	−	0.718605i
$855$		0			0
$856$		0			0
$857$	−17.2488	−	14.4734i	−0.589207	−	0.494403i	0.298749	−	0.954332i	$-0.403431\pi$
$857$	−17.2488	−	14.4734i	−0.589207	−	0.494403i	−0.887956	+	0.459929i	$0.847875\pi$
$858$		0			0
$859$	7.64052	+	43.3315i	0.260691	+	1.47845i	0.781030	+	0.624493i	$0.214694\pi$
$859$	7.64052	+	43.3315i	0.260691	+	1.47845i	−0.520339	+	0.853960i	$0.674194\pi$
$860$	2.65366	−	2.22668i	0.0904889	−	0.0759292i
$861$		0			0
$862$		0			0
$863$	−31.1769			−1.06127			−0.530637	−	0.847599i	$-0.678047\pi$
$863$	−31.1769			−1.06127			−0.530637	+	0.847599i	$0.678047\pi$
$864$		0			0
$865$	33.0000			1.12203
$866$	17.9035	−	6.51636i	0.608387	−	0.221435i
$867$		0			0
$868$	12.2567	−	10.2846i	0.416020	−	0.349082i
$869$	1.20307	+	6.82295i	0.0408113	+	0.231453i
$870$		0			0
$871$	7.66044	+	6.42788i	0.259564	+	0.217800i
$872$	−9.52628	+	16.5000i	−0.322601	+	0.558761i
$873$		0			0
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	−4.21074	+	23.8803i	−0.142349	+	0.807302i
$876$		0			0
$877$	−49.8037	−	18.1271i	−1.68175	−	0.612108i	−0.688203	−	0.725518i	$-0.741600\pi$
$877$	−49.8037	−	18.1271i	−1.68175	−	0.612108i	−0.993548	+	0.113410i	$0.963823\pi$
$878$	32.5519	+	11.8479i	1.09857	+	0.399848i
$879$		0			0
$880$	−5.20945	+	29.5442i	−0.175610	+	0.995936i
$881$	10.3923	+	18.0000i	0.350126	+	0.606435i	0.986271	−	0.165134i	$-0.0528056\pi$
$881$	10.3923	+	18.0000i	0.350126	+	0.606435i	−0.636146	+	0.771569i	$0.719472\pi$
$882$		0			0
$883$	−28.0000	+	48.4974i	−0.942275	+	1.63207i	−0.181158	+	0.983454i	$0.557984\pi$
$883$	−28.0000	+	48.4974i	−0.942275	+	1.63207i	−0.761117	+	0.648614i	$0.775349\pi$
$884$	3.98048	+	3.34002i	0.133878	+	0.112337i
$885$		0			0
$886$	−10.4189	−	59.0885i	−0.350029	−	1.98512i
$887$	−2.65366	+	2.22668i	−0.0891010	+	0.0747647i	−0.686250	−	0.727366i	$-0.740744\pi$
$887$	−2.65366	+	2.22668i	−0.0891010	+	0.0747647i	0.597149	+	0.802130i	$0.296300\pi$
$888$		0			0
$889$	−3.75877	+	1.36808i	−0.126065	+	0.0458839i
$890$	−15.5885			−0.522526
$891$		0			0
$892$	2.00000			0.0669650
$893$	13.0208	−	4.73917i	0.435723	−	0.158590i
$894$		0			0
$895$	−27.5776	+	23.1404i	−0.921818	+	0.773497i
$896$	−4.21074	−	23.8803i	−0.140671	−	0.797785i
$897$		0			0
$898$	27.5776	+	23.1404i	0.920276	+	0.772204i
$899$	6.92820	−	12.0000i	0.231069	−	0.400222i
$900$		0			0
$901$		0			0
$902$	−7.21842	+	40.9377i	−0.240347	+	1.36308i
$903$		0			0
$904$	−2.81908	−	1.02606i	−0.0937611	−	0.0341263i
$905$	−3.25519	−	1.18479i	−0.108206	−	0.0393838i
$906$		0			0
$907$	−9.02971	+	51.2100i	−0.299826	+	1.70040i	0.347084	+	0.937834i	$0.387172\pi$
$907$	−9.02971	+	51.2100i	−0.299826	+	1.70040i	−0.646910	+	0.762566i	$0.723939\pi$
$908$	−1.73205	−	3.00000i	−0.0574801	−	0.0995585i
$909$		0			0
$910$	−3.00000	+	5.19615i	−0.0994490	+	0.172251i
$911$	18.5756	+	15.5868i	0.615437	+	0.516413i	0.896365	−	0.443316i	$-0.146198\pi$
$911$	18.5756	+	15.5868i	0.615437	+	0.516413i	−0.280929	+	0.959729i	$0.590642\pi$
$912$		0			0
$913$	8.33511	+	47.2708i	0.275852	+	1.56443i
$914$	−38.4780	+	32.2869i	−1.27274	+	1.06796i
$915$		0			0
$916$	0.939693	−	0.342020i	0.0310483	−	0.0113007i
$917$	−6.92820			−0.228789
$918$		0			0
$919$	2.00000			0.0659739			0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000			0.0659739			0.0329870	+	0.999456i	$0.489498\pi$
$920$	9.76557	−	3.55438i	0.321961	−	0.117184i
$921$		0			0
$922$	−18.3851	+	15.4269i	−0.605480	+	0.508058i
$923$	−1.80460	−	10.2344i	−0.0593993	−	0.336870i
$924$		0			0
$925$	10.7246	+	8.99903i	0.352623	+	0.295886i
$926$	6.92820	−	12.0000i	0.227675	−	0.394344i
$927$		0			0
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	8.72226	−	49.4664i	0.286168	−	1.62294i	−0.414916	−	0.909860i	$-0.636189\pi$
$929$	8.72226	−	49.4664i	0.286168	−	1.62294i	0.701084	−	0.713079i	$-0.252700\pi$
$930$		0			0
$931$	5.63816	+	2.05212i	0.184783	+	0.0672555i
$932$	−24.4139	−	8.88594i	−0.799705	−	0.291069i
$933$		0			0
$934$	−6.25133	+	35.4531i	−0.204550	+	1.16006i
$935$	15.5885	+	27.0000i	0.509797	+	0.882994i
$936$		0			0
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	−0.586349	−	0.810059i	$-0.699435\pi$
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	0.994706	+	0.102763i	$0.0327685\pi$
$938$	26.5366	+	22.2668i	0.866449	+	0.727037i
$939$		0			0
$940$	−2.08378	−	11.8177i	−0.0679653	−	0.385451i
$941$	−38.4780	+	32.2869i	−1.25435	+	1.05252i	−0.258087	+	0.966122i	$0.583092\pi$
$941$	−38.4780	+	32.2869i	−1.25435	+	1.05252i	−0.996260	+	0.0864006i	$0.972464\pi$
$942$		0			0
$943$	22.5526	−	8.20848i	0.734414	−	0.267305i
$944$	69.2820			2.25494
$945$		0			0
$946$	−12.0000			−0.390154
$947$	16.2760	−	5.92396i	0.528897	−	0.192503i	−0.0637485	−	0.997966i	$-0.520306\pi$
$947$	16.2760	−	5.92396i	0.528897	−	0.192503i	0.592646	+	0.805463i	$0.298083\pi$
$948$		0			0
$949$	5.36231	−	4.49951i	0.174068	−	0.146060i
$950$	1.20307	+	6.82295i	0.0390327	+	0.221366i
$951$		0			0
$952$	−13.7888	−	11.5702i	−0.446898	−	0.374992i
$953$	−2.59808	+	4.50000i	−0.0841599	+	0.145769i	−0.905033	−	0.425341i	$-0.860154\pi$
$953$	−2.59808	+	4.50000i	−0.0841599	+	0.145769i	0.820873	+	0.571111i	$0.193487\pi$
$954$		0			0
$955$	15.0000	+	25.9808i	0.485389	+	0.840718i
$956$	4.81228	−	27.2918i	0.155640	−	0.882680i
$957$		0			0
$958$	39.4671	+	14.3648i	1.27512	+	0.464107i
$959$	3.25519	+	1.18479i	0.105116	+	0.0382589i
$960$		0			0
$961$	5.73039	−	32.4987i	0.184851	−	1.04834i
$962$	6.06218	+	10.5000i	0.195452	+	0.338534i
$963$		0			0
$964$	−14.5000	+	25.1147i	−0.467014	+	0.808891i
$965$	−1.32683	−	1.11334i	−0.0427121	−	0.0358397i
$966$		0			0
$967$	−7.98782	−	45.3012i	−0.256871	−	1.45679i	−0.791224	−	0.611526i	$-0.790556\pi$
$967$	−7.98782	−	45.3012i	−0.256871	−	1.45679i	0.534354	−	0.845261i	$-0.320555\pi$
$968$	1.32683	−	1.11334i	0.0426459	−	0.0357841i
$969$		0			0
$970$	5.63816	−	2.05212i	0.181030	−	0.0658896i
$971$	−31.1769			−1.00051			−0.500257	−	0.865877i	$-0.666761\pi$
$971$	−31.1769			−1.00051			−0.500257	+	0.865877i	$0.666761\pi$
$972$		0			0
$973$	16.0000			0.512936
$974$	−26.0415	+	9.47834i	−0.834424	+	0.303706i
$975$		0			0
$976$	26.8116	−	22.4976i	0.858217	−	0.720130i
$977$	8.42149	+	47.7606i	0.269427	+	1.52800i	0.756125	+	0.654428i	$0.227090\pi$
$977$	8.42149	+	47.7606i	0.269427	+	1.52800i	−0.486697	+	0.873571i	$0.661799\pi$
$978$		0			0
$979$	13.7888	+	11.5702i	0.440692	+	0.369784i
$980$	2.59808	−	4.50000i	0.0829925	−	0.143747i
$981$		0			0
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$	6.01535	−	34.1147i	0.191860	−	1.08809i	−0.724960	−	0.688791i	$-0.758142\pi$
$983$	6.01535	−	34.1147i	0.191860	−	1.08809i	0.916820	−	0.399301i	$-0.130747\pi$
$984$		0			0
$985$	−8.45723	−	3.07818i	−0.269470	−	0.0980790i
$986$	14.6484	+	5.33157i	0.466499	+	0.169792i
$987$		0			0
$988$	−0.347296	+	1.96962i	−0.0110490	+	0.0626618i
$989$	3.46410	+	6.00000i	0.110152	+	0.190789i
$990$		0			0
$991$	17.0000	−	29.4449i	0.540023	−	0.935347i	−0.458879	−	0.888499i	$-0.651749\pi$
$991$	17.0000	−	29.4449i	0.540023	−	0.935347i	0.998902	−	0.0468483i	$-0.0149177\pi$
$992$	31.8439	+	26.7202i	1.01104	+	0.848367i
$993$		0			0
$994$	−6.25133	−	35.4531i	−0.198280	−	1.12450i
$995$	26.5366	−	22.2668i	0.841265	−	0.705906i
$996$		0			0
$997$	6.57785	−	2.39414i	0.208323	−	0.0758232i	−0.235751	−	0.971813i	$-0.575755\pi$
$997$	6.57785	−	2.39414i	0.208323	−	0.0758232i	0.444074	+	0.895990i	$0.353533\pi$
$998$	17.3205			0.548271
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.o.163.2		12
3.2	odd	2	inner	729.2.e.o.163.1		12
9.2	odd	6	inner	729.2.e.o.406.2		12
9.4	even	3	inner	729.2.e.o.649.1		12
9.5	odd	6	inner	729.2.e.o.649.2		12
9.7	even	3	inner	729.2.e.o.406.1		12
27.2	odd	18		81.2.a.a.1.2	yes	2
27.4	even	9	inner	729.2.e.o.568.2		12
27.5	odd	18	inner	729.2.e.o.82.2		12
27.7	even	9		81.2.c.b.55.2		4
27.11	odd	18		81.2.c.b.28.1		4
27.13	even	9	inner	729.2.e.o.325.1		12
27.14	odd	18	inner	729.2.e.o.325.2		12
27.16	even	9		81.2.c.b.28.2		4
27.20	odd	18		81.2.c.b.55.1		4
27.22	even	9	inner	729.2.e.o.82.1		12
27.23	odd	18	inner	729.2.e.o.568.1		12
27.25	even	9		81.2.a.a.1.1	✓	2
108.7	odd	18		1296.2.i.s.865.1		4
108.11	even	18		1296.2.i.s.433.2		4
108.43	odd	18		1296.2.i.s.433.1		4
108.47	even	18		1296.2.i.s.865.2		4
108.79	odd	18		1296.2.a.o.1.2		2
108.83	even	18		1296.2.a.o.1.1		2
135.2	even	36		2025.2.b.k.649.4		4
135.29	odd	18		2025.2.a.j.1.1		2
135.52	odd	36		2025.2.b.k.649.2		4
135.79	even	18		2025.2.a.j.1.2		2
135.83	even	36		2025.2.b.k.649.1		4
135.133	odd	36		2025.2.b.k.649.3		4
189.83	even	18		3969.2.a.i.1.2		2
189.160	odd	18		3969.2.a.i.1.1		2
216.29	odd	18		5184.2.a.br.1.2		2
216.83	even	18		5184.2.a.bq.1.2		2
216.133	even	18		5184.2.a.br.1.1		2
216.187	odd	18		5184.2.a.bq.1.1		2
297.164	even	18		9801.2.a.v.1.1		2
297.241	odd	18		9801.2.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.a.a.1.1	✓	2	27.25	even	9
81.2.a.a.1.2	yes	2	27.2	odd	18
81.2.c.b.28.1		4	27.11	odd	18
81.2.c.b.28.2		4	27.16	even	9
81.2.c.b.55.1		4	27.20	odd	18
81.2.c.b.55.2		4	27.7	even	9
729.2.e.o.82.1		12	27.22	even	9	inner
729.2.e.o.82.2		12	27.5	odd	18	inner
729.2.e.o.163.1		12	3.2	odd	2	inner
729.2.e.o.163.2		12	1.1	even	1	trivial
729.2.e.o.325.1		12	27.13	even	9	inner
729.2.e.o.325.2		12	27.14	odd	18	inner
729.2.e.o.406.1		12	9.7	even	3	inner
729.2.e.o.406.2		12	9.2	odd	6	inner
729.2.e.o.568.1		12	27.23	odd	18	inner
729.2.e.o.568.2		12	27.4	even	9	inner
729.2.e.o.649.1		12	9.4	even	3	inner
729.2.e.o.649.2		12	9.5	odd	6	inner
1296.2.a.o.1.1		2	108.83	even	18
1296.2.a.o.1.2		2	108.79	odd	18
1296.2.i.s.433.1		4	108.43	odd	18
1296.2.i.s.433.2		4	108.11	even	18
1296.2.i.s.865.1		4	108.7	odd	18
1296.2.i.s.865.2		4	108.47	even	18
2025.2.a.j.1.1		2	135.29	odd	18
2025.2.a.j.1.2		2	135.79	even	18
2025.2.b.k.649.1		4	135.83	even	36
2025.2.b.k.649.2		4	135.52	odd	36
2025.2.b.k.649.3		4	135.133	odd	36
2025.2.b.k.649.4		4	135.2	even	36
3969.2.a.i.1.1		2	189.160	odd	18
3969.2.a.i.1.2		2	189.83	even	18
5184.2.a.bq.1.1		2	216.187	odd	18
5184.2.a.bq.1.2		2	216.83	even	18
5184.2.a.br.1.1		2	216.133	even	18
5184.2.a.br.1.2		2	216.29	odd	18
9801.2.a.v.1.1		2	297.164	even	18
9801.2.a.v.1.2		2	297.241	odd	18

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)

\(f(q)\)	\(=\)	\(q+(1.62760 - 0.592396i) q^{2} +(0.766044 - 0.642788i) q^{4} +(0.300767 + 1.70574i) q^{5} +(1.53209 + 1.28558i) q^{7} +(-0.866025 + 1.50000i) q^{8} +O(q^{10})\)	\(q+(1.62760 - 0.592396i) q^{2} +(0.766044 - 0.642788i) q^{4} +(0.300767 + 1.70574i) q^{5} +(1.53209 + 1.28558i) q^{7} +(-0.866025 + 1.50000i) q^{8} +(1.50000 + 2.59808i) q^{10} +(0.601535 - 3.41147i) q^{11} +(0.939693 + 0.342020i) q^{13} +(3.25519 + 1.18479i) q^{14} +(-0.868241 + 4.92404i) q^{16} +(2.59808 + 4.50000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.32683 + 1.11334i) q^{20} +(-1.04189 - 5.90885i) q^{22} +(-2.65366 + 2.22668i) q^{23} +(1.87939 - 0.684040i) q^{25} +1.73205 q^{26} +2.00000 q^{28} +(1.62760 - 0.592396i) q^{29} +(6.12836 - 5.14230i) q^{31} +(0.902302 + 5.11721i) q^{32} +(6.89440 + 5.78509i) q^{34} +(-1.73205 + 3.00000i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-0.601535 + 3.41147i) q^{38} +(-2.81908 - 1.02606i) q^{40} +(-6.51038 - 2.36959i) q^{41} +(0.347296 - 1.96962i) q^{43} +(-1.73205 - 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-5.30731 - 4.45336i) q^{47} +(-0.520945 - 2.95442i) q^{49} +(2.65366 - 2.22668i) q^{50} +(0.939693 - 0.342020i) q^{52} +6.00000 q^{55} +(-3.25519 + 1.18479i) q^{56} +(2.29813 - 1.92836i) q^{58} +(-2.40614 - 13.6459i) q^{59} +(-5.36231 - 4.49951i) q^{61} +(6.92820 - 12.0000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.300767 + 1.70574i) q^{65} +(9.39693 + 3.42020i) q^{67} +(4.88279 + 1.77719i) q^{68} +(-1.04189 + 5.90885i) q^{70} +(-5.19615 - 9.00000i) q^{71} +(3.50000 - 6.06218i) q^{73} +(9.28780 + 7.79339i) q^{74} +(0.347296 + 1.96962i) q^{76} +(5.30731 - 4.45336i) q^{77} +(-1.87939 + 0.684040i) q^{79} -8.66025 q^{80} -12.0000 q^{82} +(-13.0208 + 4.73917i) q^{83} +(-6.89440 + 5.78509i) q^{85} +(-0.601535 - 3.41147i) q^{86} +(4.59627 + 3.85673i) q^{88} +(-2.59808 + 4.50000i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-0.601535 + 3.41147i) q^{92} +(-11.2763 - 4.10424i) q^{94} +(-3.25519 - 1.18479i) q^{95} +(0.347296 - 1.96962i) q^{97} +(-2.59808 - 4.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 18 q^{10} - 12 q^{19} + 24 q^{28} + 42 q^{37} - 36 q^{46} + 72 q^{55} - 6 q^{64} + 42 q^{73} - 144 q^{82} + 12 q^{91}+O(q^{100}) \) 12 * q + 18 * q^10 - 12 * q^19 + 24 * q^28 + 42 * q^37 - 36 * q^46 + 72 * q^55 - 6 * q^64 + 42 * q^73 - 144 * q^82 + 12 * q^91

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