LMFDB - Embedded newform 729.2.e.o.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
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			649.2
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.o.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.300767 - 1.70574i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-1.32683 + 1.11334i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(0.866025 - 1.50000i) q^{8} +O(q^{10})$	\(q+(0.300767 - 1.70574i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-1.32683 + 1.11334i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(0.866025 - 1.50000i) q^{8} +(1.50000 + 2.59808i) q^{10} +(-2.65366 - 2.22668i) q^{11} +(-0.173648 - 0.984808i) q^{13} +(0.601535 + 3.41147i) q^{14} +(-3.83022 - 3.21394i) q^{16} +(-2.59808 - 4.50000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.62760 - 0.592396i) q^{20} +(-4.59627 + 3.85673i) q^{22} +(-3.25519 - 1.18479i) q^{23} +(-0.347296 + 1.96962i) q^{25} -1.73205 q^{26} +2.00000 q^{28} +(0.300767 - 1.70574i) q^{29} +(-7.51754 - 2.73616i) q^{31} +(-3.98048 + 3.34002i) q^{32} +(-8.45723 + 3.07818i) q^{34} +(1.73205 - 3.00000i) q^{35} +(3.50000 + 6.06218i) q^{37} +(2.65366 + 2.22668i) q^{38} +(0.520945 + 2.95442i) q^{40} +(-1.20307 - 6.82295i) q^{41} +(1.53209 + 1.28558i) q^{43} +(1.73205 + 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-6.51038 + 2.36959i) q^{47} +(-2.29813 + 1.92836i) q^{49} +(3.25519 + 1.18479i) q^{50} +(-0.173648 + 0.984808i) q^{52} +6.00000 q^{55} +(-0.601535 + 3.41147i) q^{56} +(-2.81908 - 1.02606i) q^{58} +(10.6146 - 8.90673i) q^{59} +(6.57785 - 2.39414i) q^{61} +(-6.92820 + 12.0000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(1.32683 + 1.11334i) q^{65} +(-1.73648 - 9.84808i) q^{67} +(0.902302 + 5.11721i) q^{68} +(-4.59627 - 3.85673i) q^{70} +(5.19615 + 9.00000i) q^{71} +(3.50000 - 6.06218i) q^{73} +(11.3932 - 4.14677i) q^{74} +(1.53209 - 1.28558i) q^{76} +(6.51038 + 2.36959i) q^{77} +(0.347296 - 1.96962i) q^{79} +8.66025 q^{80} -12.0000 q^{82} +(-2.40614 + 13.6459i) q^{83} +(8.45723 + 3.07818i) q^{85} +(2.65366 - 2.22668i) q^{86} +(-5.63816 + 2.05212i) q^{88} +(2.59808 - 4.50000i) q^{89} +(1.00000 + 1.73205i) q^{91} +(2.65366 + 2.22668i) q^{92} +(2.08378 + 11.8177i) q^{94} +(-0.601535 - 3.41147i) q^{95} +(1.53209 + 1.28558i) q^{97} +(2.59808 + 4.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.300767	−	1.70574i	0.212675	−	1.20614i	−0.672222	−	0.740350i	$-0.734660\pi$
$2$	0.300767	−	1.70574i	0.212675	−	1.20614i	0.884896	−	0.465788i	$-0.154229\pi$
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−1.32683	+	1.11334i	−0.593375	+	0.497901i	−0.889309	−	0.457308i	$-0.848814\pi$
$5$	−1.32683	+	1.11334i	−0.593375	+	0.497901i	0.295933	+	0.955209i	$0.404369\pi$
$6$		0			0
$7$	−1.87939	+	0.684040i	−0.710341	+	0.258543i	−0.671820	−	0.740715i	$-0.734487\pi$
$7$	−1.87939	+	0.684040i	−0.710341	+	0.258543i	−0.0385213	+	0.999258i	$0.512265\pi$
$8$	0.866025	−	1.50000i	0.306186	−	0.530330i
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	−2.65366	−	2.22668i	−0.800107	−	0.671370i	0.148117	−	0.988970i	$-0.452679\pi$
$11$	−2.65366	−	2.22668i	−0.800107	−	0.671370i	−0.948225	+	0.317600i	$0.897123\pi$
$12$		0			0
$13$	−0.173648	−	0.984808i	−0.0481613	−	0.273137i	0.951212	−	0.308539i	$-0.0998399\pi$
$13$	−0.173648	−	0.984808i	−0.0481613	−	0.273137i	−0.999373	+	0.0354021i	$0.988729\pi$
$14$	0.601535	+	3.41147i	0.160767	+	0.911755i
$15$		0			0
$16$	−3.83022	−	3.21394i	−0.957556	−	0.803485i
$17$	−2.59808	−	4.50000i	−0.630126	−	1.09141i	−0.987526	−	0.157459i	$-0.949670\pi$
$17$	−2.59808	−	4.50000i	−0.630126	−	1.09141i	0.357400	−	0.933952i	$-0.383663\pi$
$18$		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	$0.240348\pi$
$20$	1.62760	−	0.592396i	0.363941	−	0.132464i
$21$		0			0
$22$	−4.59627	+	3.85673i	−0.979927	+	0.822257i
$23$	−3.25519	−	1.18479i	−0.678754	−	0.247046i	−0.0204417	−	0.999791i	$-0.506507\pi$
$23$	−3.25519	−	1.18479i	−0.678754	−	0.247046i	−0.658313	+	0.752745i	$0.728729\pi$
$24$		0			0
$25$	−0.347296	+	1.96962i	−0.0694593	+	0.393923i
$26$	−1.73205			−0.339683
$27$		0			0
$28$	2.00000			0.377964
$29$	0.300767	−	1.70574i	0.0558511	−	0.316747i	−0.944064	−	0.329762i	$-0.893032\pi$
$29$	0.300767	−	1.70574i	0.0558511	−	0.316747i	0.999915	+	0.0130143i	$0.00414270\pi$
$30$		0			0
$31$	−7.51754	−	2.73616i	−1.35019	−	0.491429i	−0.437183	−	0.899373i	$-0.644024\pi$
$31$	−7.51754	−	2.73616i	−1.35019	−	0.491429i	−0.913007	+	0.407944i	$0.866246\pi$
$32$	−3.98048	+	3.34002i	−0.703657	+	0.590438i
$33$		0			0
$34$	−8.45723	+	3.07818i	−1.45040	+	0.527904i
$35$	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	$0.638181\pi$
$38$	2.65366	+	2.22668i	0.430480	+	0.361215i
$39$		0			0
$40$	0.520945	+	2.95442i	0.0823686	+	0.467135i
$41$	−1.20307	−	6.82295i	−0.187888	−	1.06557i	−0.922188	−	0.386741i	$-0.873601\pi$
$41$	−1.20307	−	6.82295i	−0.187888	−	1.06557i	0.734300	−	0.678825i	$-0.237510\pi$
$42$		0			0
$43$	1.53209	+	1.28558i	0.233641	+	0.196048i	0.752090	−	0.659060i	$-0.229046\pi$
$43$	1.53209	+	1.28558i	0.233641	+	0.196048i	−0.518449	+	0.855109i	$0.673490\pi$
$44$	1.73205	+	3.00000i	0.261116	+	0.452267i
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−6.51038	+	2.36959i	−0.949637	+	0.345640i	−0.769964	−	0.638087i	$-0.779726\pi$
$47$	−6.51038	+	2.36959i	−0.949637	+	0.345640i	−0.179672	+	0.983726i	$0.557504\pi$
$48$		0			0
$49$	−2.29813	+	1.92836i	−0.328305	+	0.275480i
$50$	3.25519	+	1.18479i	0.460353	+	0.167555i
$51$		0			0
$52$	−0.173648	+	0.984808i	−0.0240807	+	0.136568i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$	−0.601535	+	3.41147i	−0.0803835	+	0.455877i
$57$		0			0
$58$	−2.81908	−	1.02606i	−0.370163	−	0.134728i
$59$	10.6146	−	8.90673i	1.38191	−	1.15956i	0.413405	−	0.910547i	$-0.364339\pi$
$59$	10.6146	−	8.90673i	1.38191	−	1.15956i	0.968501	−	0.249010i	$-0.0801052\pi$
$60$		0			0
$61$	6.57785	−	2.39414i	0.842207	−	0.306538i	0.115348	−	0.993325i	$-0.463202\pi$
$61$	6.57785	−	2.39414i	0.842207	−	0.306538i	0.726859	+	0.686787i	$0.240979\pi$
$62$	−6.92820	+	12.0000i	−0.879883	+	1.52400i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.32683	+	1.11334i	0.164573	+	0.138093i
$66$		0			0
$67$	−1.73648	−	9.84808i	−0.212145	−	1.20313i	−0.885793	−	0.464081i	$-0.846385\pi$
$67$	−1.73648	−	9.84808i	−0.212145	−	1.20313i	0.673648	−	0.739053i	$-0.264727\pi$
$68$	0.902302	+	5.11721i	0.109420	+	0.620553i
$69$		0			0
$70$	−4.59627	−	3.85673i	−0.549359	−	0.460967i
$71$	5.19615	+	9.00000i	0.616670	+	1.06810i	0.990089	+	0.140441i	$0.0448520\pi$
$71$	5.19615	+	9.00000i	0.616670	+	1.06810i	−0.373419	+	0.927663i	$0.621815\pi$
$72$		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	$0.0323196\pi$
$74$	11.3932	−	4.14677i	1.32443	−	0.482053i
$75$		0			0
$76$	1.53209	−	1.28558i	0.175743	−	0.147466i
$77$	6.51038	+	2.36959i	0.741927	+	0.270039i
$78$		0			0
$79$	0.347296	−	1.96962i	0.0390739	−	0.221599i	−0.959018	−	0.283345i	$-0.908556\pi$
$79$	0.347296	−	1.96962i	0.0390739	−	0.221599i	0.998092	+	0.0617461i	$0.0196669\pi$
$80$	8.66025			0.968246
$81$		0			0
$82$	−12.0000			−1.32518
$83$	−2.40614	+	13.6459i	−0.264108	+	1.49783i	0.507455	+	0.861678i	$0.330587\pi$
$83$	−2.40614	+	13.6459i	−0.264108	+	1.49783i	−0.771563	+	0.636153i	$0.780525\pi$
$84$		0			0
$85$	8.45723	+	3.07818i	0.917316	+	0.333876i
$86$	2.65366	−	2.22668i	0.286151	−	0.240109i
$87$		0			0
$88$	−5.63816	+	2.05212i	−0.601029	+	0.218757i
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	−0.694839	−	0.719165i	$-0.744525\pi$
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	0.970235	+	0.242166i	$0.0778579\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	2.65366	+	2.22668i	0.276663	+	0.232148i
$93$		0			0
$94$	2.08378	+	11.8177i	0.214925	+	1.21890i
$95$	−0.601535	−	3.41147i	−0.0617162	−	0.350010i
$96$		0			0
$97$	1.53209	+	1.28558i	0.155560	+	0.130530i	0.717246	−	0.696820i	$-0.245403\pi$
$97$	1.53209	+	1.28558i	0.155560	+	0.130530i	−0.561686	+	0.827351i	$0.689847\pi$
$98$	2.59808	+	4.50000i	0.262445	+	0.454569i
$99$		0			0
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−6.51038	+	2.36959i	−0.647807	+	0.235783i	−0.644963	−	0.764213i	$-0.723127\pi$
$101$	−6.51038	+	2.36959i	−0.647807	+	0.235783i	−0.00284373	+	0.999996i	$0.500905\pi$
$102$		0			0
$103$	6.12836	−	5.14230i	0.603845	−	0.506686i	−0.288834	−	0.957379i	$-0.593268\pi$
$103$	6.12836	−	5.14230i	0.603845	−	0.506686i	0.892679	+	0.450693i	$0.148823\pi$
$104$	−1.62760	−	0.592396i	−0.159599	−	0.0580892i
$105$		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	$0.323390\pi$
$110$	1.80460	−	10.2344i	0.172062	−	0.975814i
$111$		0			0
$112$	9.39693	+	3.42020i	0.887926	+	0.323179i
$113$	−1.32683	+	1.11334i	−0.124817	+	0.104734i	−0.703060	−	0.711131i	$-0.748183\pi$
$113$	−1.32683	+	1.11334i	−0.124817	+	0.104734i	0.578242	+	0.815865i	$0.303739\pi$
$114$		0			0
$115$	5.63816	−	2.05212i	0.525761	−	0.191361i
$116$	−0.866025	+	1.50000i	−0.0804084	+	0.139272i
$117$		0			0
$118$	−12.0000	−	20.7846i	−1.10469	−	1.91338i
$119$	7.96097	+	6.68004i	0.729781	+	0.612359i
$120$		0			0
$121$	0.173648	+	0.984808i	0.0157862	+	0.0895280i
$122$	−2.10537	−	11.9402i	−0.190611	−	1.08101i
$123$		0			0
$124$	6.12836	+	5.14230i	0.550343	+	0.461792i
$125$	−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	$0.194949\pi$
$128$	−11.3932	+	4.14677i	−1.00702	+	0.366526i
$129$		0			0
$130$	2.29813	−	1.92836i	0.201560	−	0.169129i
$131$	−3.25519	−	1.18479i	−0.284407	−	0.103516i	0.195878	−	0.980628i	$-0.437244\pi$
$131$	−3.25519	−	1.18479i	−0.284407	−	0.103516i	−0.480285	+	0.877113i	$0.659467\pi$
$132$		0			0
$133$	0.694593	−	3.93923i	0.0602288	−	0.341575i
$134$	−17.3205			−1.49626
$135$		0			0
$136$	−9.00000			−0.771744
$137$	0.300767	−	1.70574i	0.0256963	−	0.145731i	−0.969260	−	0.246038i	$-0.920871\pi$
$137$	0.300767	−	1.70574i	0.0256963	−	0.145731i	0.994957	+	0.100307i	$0.0319824\pi$
$138$		0			0
$139$	−7.51754	−	2.73616i	−0.637630	−	0.232078i	0.00291916	−	0.999996i	$-0.499071\pi$
$139$	−7.51754	−	2.73616i	−0.637630	−	0.232078i	−0.640549	+	0.767918i	$0.721293\pi$
$140$	−2.65366	+	2.22668i	−0.224275	+	0.188189i
$141$		0			0
$142$	16.9145	−	6.15636i	1.41943	−	0.516630i
$143$	−1.73205	+	3.00000i	−0.144841	+	0.250873i
$144$		0			0
$145$	1.50000	+	2.59808i	0.124568	+	0.215758i
$146$	−9.28780	−	7.79339i	−0.768663	−	0.644985i
$147$		0			0
$148$	−1.21554	−	6.89365i	−0.0999165	−	0.566655i
$149$	1.50384	+	8.52869i	0.123199	+	0.698697i	0.982361	+	0.186993i	$0.0598743\pi$
$149$	1.50384	+	8.52869i	0.123199	+	0.698697i	−0.859162	+	0.511704i	$0.829015\pi$
$150$		0			0
$151$	15.3209	+	12.8558i	1.24680	+	1.04619i	0.996961	+	0.0778978i	$0.0248208\pi$
$151$	15.3209	+	12.8558i	1.24680	+	1.04619i	0.249835	+	0.968288i	$0.419624\pi$
$152$	1.73205	+	3.00000i	0.140488	+	0.243332i
$153$		0			0
$154$	6.00000	−	10.3923i	0.483494	−	0.837436i
$155$	13.0208	−	4.73917i	1.04585	−	0.380659i
$156$		0			0
$157$	13.0228	−	10.9274i	1.03933	−	0.872101i	0.0473976	−	0.998876i	$-0.484907\pi$
$157$	13.0228	−	10.9274i	1.03933	−	0.872101i	0.991931	+	0.126775i	$0.0404628\pi$
$158$	−3.25519	−	1.18479i	−0.258969	−	0.0942570i
$159$		0			0
$160$	1.56283	−	8.86327i	0.123553	−	0.700703i
$161$	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	$0.715557\pi$
$164$	−1.20307	+	6.82295i	−0.0939440	+	0.532783i
$165$		0			0
$166$	22.5526	+	8.20848i	1.75042	+	0.637102i
$167$	−13.2683	+	11.1334i	−1.02673	+	0.861529i	−0.990458	−	0.137813i	$-0.955993\pi$
$167$	−13.2683	+	11.1334i	−1.02673	+	0.861529i	−0.0362720	+	0.999342i	$0.511548\pi$
$168$		0			0
$169$	11.2763	−	4.10424i	0.867409	−	0.315711i
$170$	7.79423	−	13.5000i	0.597790	−	1.03540i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−14.5951	−	12.2467i	−1.10965	−	0.931103i	−0.111610	−	0.993752i	$-0.535601\pi$
$173$	−14.5951	−	12.2467i	−1.10965	−	0.931103i	−0.998036	+	0.0626490i	$0.980045\pi$
$174$		0			0
$175$	−0.694593	−	3.93923i	−0.0525063	−	0.297778i
$176$	3.00767	+	17.0574i	0.226712	+	1.28575i
$177$		0			0
$178$	−6.89440	−	5.78509i	−0.516757	−	0.433611i
$179$	−10.3923	−	18.0000i	−0.776757	−	1.34538i	−0.933801	−	0.357792i	$-0.883530\pi$
$179$	−10.3923	−	18.0000i	−0.776757	−	1.34538i	0.157044	−	0.987592i	$-0.449804\pi$
$180$		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	$0.190348\pi$
$182$	3.25519	−	1.18479i	0.241291	−	0.0878227i
$183$		0			0
$184$	−4.59627	+	3.85673i	−0.338841	+	0.284322i
$185$	−11.3932	−	4.14677i	−0.837642	−	0.304877i
$186$		0			0
$187$	−3.12567	+	17.7265i	−0.228571	+	1.29629i
$188$	6.92820			0.505291
$189$		0			0
$190$	−6.00000			−0.435286
$191$	3.00767	−	17.0574i	0.217628	−	1.23423i	−0.658660	−	0.752440i	$-0.728877\pi$
$191$	3.00767	−	17.0574i	0.217628	−	1.23423i	0.876288	−	0.481788i	$-0.160012\pi$
$192$		0			0
$193$	0.939693	+	0.342020i	0.0676406	+	0.0246191i	0.375619	−	0.926774i	$-0.377430\pi$
$193$	0.939693	+	0.342020i	0.0676406	+	0.0246191i	−0.307978	+	0.951393i	$0.599652\pi$
$194$	2.65366	−	2.22668i	0.190521	−	0.159866i
$195$		0			0
$196$	2.81908	−	1.02606i	0.201363	−	0.0732900i
$197$	2.59808	−	4.50000i	0.185105	−	0.320612i	−0.758507	−	0.651665i	$-0.774071\pi$
$197$	2.59808	−	4.50000i	0.185105	−	0.320612i	0.943612	+	0.331053i	$0.107404\pi$
$198$		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	$-0.417466\pi$
$200$	2.65366	+	2.22668i	0.187642	+	0.157450i
$201$		0			0
$202$	2.08378	+	11.8177i	0.146614	+	0.831490i
$203$	0.601535	+	3.41147i	0.0422195	+	0.239439i
$204$		0			0
$205$	9.19253	+	7.71345i	0.642034	+	0.538731i
$206$	−6.92820	−	12.0000i	−0.482711	−	0.836080i
$207$		0			0
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	6.51038	−	2.36959i	0.450333	−	0.163908i
$210$		0			0
$211$	−7.66044	+	6.42788i	−0.527367	+	0.442513i	−0.867191	−	0.497976i	$-0.834077\pi$
$211$	−7.66044	+	6.42788i	−0.527367	+	0.442513i	0.339824	+	0.940489i	$0.389632\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.46410			−0.236250
$216$		0			0
$217$	16.0000			1.08615
$218$	3.30844	−	18.7631i	0.224076	−	1.27080i
$219$		0			0
$220$	−5.63816	−	2.05212i	−0.380124	−	0.138354i
$221$	−3.98048	+	3.34002i	−0.267756	+	0.224674i
$222$		0			0
$223$	−1.87939	+	0.684040i	−0.125853	+	0.0458067i	−0.404179	−	0.914680i	$-0.632443\pi$
$223$	−1.87939	+	0.684040i	−0.125853	+	0.0458067i	0.278326	+	0.960487i	$0.410220\pi$
$224$	5.19615	−	9.00000i	0.347183	−	0.601338i
$225$		0			0
$226$	1.50000	+	2.59808i	0.0997785	+	0.172821i
$227$	−2.65366	−	2.22668i	−0.176129	−	0.147790i	0.550461	−	0.834861i	$-0.314452\pi$
$227$	−2.65366	−	2.22668i	−0.176129	−	0.147790i	−0.726591	+	0.687071i	$0.758896\pi$
$228$		0			0
$229$	−0.173648	−	0.984808i	−0.0114750	−	0.0650779i	0.978533	−	0.206092i	$-0.0660747\pi$
$229$	−0.173648	−	0.984808i	−0.0114750	−	0.0650779i	−0.990008	+	0.141014i	$0.954964\pi$
$230$	−1.80460	−	10.2344i	−0.118992	−	0.674838i
$231$		0			0
$232$	−2.29813	−	1.92836i	−0.150880	−	0.126603i
$233$	12.9904	+	22.5000i	0.851028	+	1.47402i	0.880281	+	0.474452i	$0.157354\pi$
$233$	12.9904	+	22.5000i	0.851028	+	1.47402i	−0.0292532	+	0.999572i	$0.509313\pi$
$234$		0			0
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$	−13.0208	+	4.73917i	−0.847579	+	0.308494i
$237$		0			0
$238$	13.7888	−	11.5702i	0.893795	−	0.749983i
$239$	26.0415	+	9.47834i	1.68449	+	0.613103i	0.993914	−	0.110160i	$-0.0351364\pi$
$239$	26.0415	+	9.47834i	1.68449	+	0.613103i	0.690572	+	0.723263i	$0.257359\pi$
$240$		0			0
$241$	5.03580	−	28.5594i	0.324384	−	1.83967i	−0.189583	−	0.981865i	$-0.560714\pi$
$241$	5.03580	−	28.5594i	0.324384	−	1.83967i	0.513968	−	0.857810i	$-0.328175\pi$
$242$	1.73205			0.111340
$243$		0			0
$244$	−7.00000			−0.448129
$245$	0.902302	−	5.11721i	0.0576460	−	0.326927i
$246$		0			0
$247$	1.87939	+	0.684040i	0.119582	+	0.0435244i
$248$	−10.6146	+	8.90673i	−0.674029	+	0.565578i
$249$		0			0
$250$	−19.7335	+	7.18242i	−1.24806	+	0.454256i
$251$	−5.19615	+	9.00000i	−0.327978	+	0.568075i	−0.982111	−	0.188305i	$-0.939701\pi$
$251$	−5.19615	+	9.00000i	−0.327978	+	0.568075i	0.654132	+	0.756380i	$0.273034\pi$
$252$		0			0
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	2.65366	+	2.22668i	0.166505	+	0.139714i
$255$		0			0
$256$	3.29932	+	18.7113i	0.206207	+	1.16946i
$257$	1.50384	+	8.52869i	0.0938068	+	0.532005i	0.995106	+	0.0988086i	$0.0315032\pi$
$257$	1.50384	+	8.52869i	0.0938068	+	0.532005i	−0.901300	+	0.433196i	$0.857386\pi$
$258$		0			0
$259$	−10.7246	−	8.99903i	−0.666396	−	0.559172i
$260$	−0.866025	−	1.50000i	−0.0537086	−	0.0930261i
$261$		0			0
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	−6.51038	+	2.36959i	−0.401447	+	0.146115i	−0.534850	−	0.844947i	$-0.679632\pi$
$263$	−6.51038	+	2.36959i	−0.401447	+	0.146115i	0.133403	+	0.991062i	$0.457410\pi$
$264$		0			0
$265$		0			0
$266$	−6.51038	−	2.36959i	−0.399177	−	0.145289i
$267$		0			0
$268$	−1.73648	+	9.84808i	−0.106073	+	0.601567i
$269$	−15.5885			−0.950445			−0.475223	−	0.879866i	$-0.657632\pi$
$269$	−15.5885			−0.950445			−0.475223	+	0.879866i	$0.657632\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	−4.51151	+	25.5861i	−0.273551	+	1.55138i
$273$		0			0
$274$	−2.81908	−	1.02606i	−0.170307	−	0.0619866i
$275$	5.30731	−	4.45336i	0.320043	−	0.268548i
$276$		0			0
$277$	−1.87939	+	0.684040i	−0.112921	+	0.0411000i	−0.397863	−	0.917445i	$-0.630248\pi$
$277$	−1.87939	+	0.684040i	−0.112921	+	0.0411000i	0.284942	+	0.958545i	$0.408026\pi$
$278$	−6.92820	+	12.0000i	−0.415526	+	0.719712i
$279$		0			0
$280$	−3.00000	−	5.19615i	−0.179284	−	0.310530i
$281$	9.28780	+	7.79339i	0.554063	+	0.464914i	0.876314	−	0.481740i	$-0.159995\pi$
$281$	9.28780	+	7.79339i	0.554063	+	0.464914i	−0.322251	+	0.946654i	$0.604439\pi$
$282$		0			0
$283$	−4.86215	−	27.5746i	−0.289025	−	1.63914i	−0.690544	−	0.723290i	$-0.742629\pi$
$283$	−4.86215	−	27.5746i	−0.289025	−	1.63914i	0.401519	−	0.915851i	$-0.368482\pi$
$284$	−1.80460	−	10.2344i	−0.107084	−	0.607301i
$285$		0			0
$286$	4.59627	+	3.85673i	0.271783	+	0.228053i
$287$	6.92820	+	12.0000i	0.408959	+	0.708338i
$288$		0			0
$289$	−5.00000	+	8.66025i	−0.294118	+	0.509427i
$290$	4.88279	−	1.77719i	0.286727	−	0.104360i
$291$		0			0
$292$	−5.36231	+	4.49951i	−0.313806	+	0.263314i
$293$	−17.9035	−	6.51636i	−1.04594	−	0.380690i	−0.238809	−	0.971067i	$-0.576757\pi$
$293$	−17.9035	−	6.51636i	−1.04594	−	0.380690i	−0.807128	+	0.590377i	$0.798979\pi$
$294$		0			0
$295$	−4.16756	+	23.6354i	−0.242645	+	1.37611i
$296$	12.1244			0.704714
$297$		0			0
$298$	15.0000			0.868927
$299$	−0.601535	+	3.41147i	−0.0347877	+	0.197291i
$300$		0			0
$301$	−3.75877	−	1.36808i	−0.216652	−	0.0788549i
$302$	26.5366	−	22.2668i	1.52701	−	1.28131i
$303$		0			0
$304$	9.39693	−	3.42020i	0.538951	−	0.196162i
$305$	−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	$0.682406\pi$
$308$	−5.30731	−	4.45336i	−0.302412	−	0.253754i
$309$		0			0
$310$	−4.16756	−	23.6354i	−0.236701	−	1.34240i
$311$	−1.20307	−	6.82295i	−0.0682198	−	0.386894i	−0.999731	−	0.0231819i	$-0.992620\pi$
$311$	−1.20307	−	6.82295i	−0.0682198	−	0.386894i	0.931511	−	0.363712i	$-0.118491\pi$
$312$		0			0
$313$	−19.1511	−	16.0697i	−1.08248	−	0.908313i	−0.0863600	−	0.996264i	$-0.527524\pi$
$313$	−19.1511	−	16.0697i	−1.08248	−	0.908313i	−0.996125	+	0.0879514i	$0.971968\pi$
$314$	−14.7224	−	25.5000i	−0.830835	−	1.43905i
$315$		0			0
$316$	−1.00000	+	1.73205i	−0.0562544	+	0.0974355i
$317$	8.13798	−	2.96198i	0.457074	−	0.166361i	−0.103214	−	0.994659i	$-0.532913\pi$
$317$	8.13798	−	2.96198i	0.457074	−	0.166361i	0.560288	+	0.828298i	$0.310690\pi$
$318$		0			0
$319$	−4.59627	+	3.85673i	−0.257342	+	0.215935i
$320$	1.62760	+	0.592396i	0.0909853	+	0.0331160i
$321$		0			0
$322$	2.08378	−	11.8177i	0.116124	−	0.658574i
$323$	10.3923			0.578243
$324$		0			0
$325$	2.00000			0.110940
$326$	−4.81228	+	27.2918i	−0.266528	+	1.51155i
$327$		0			0
$328$	−11.2763	−	4.10424i	−0.622630	−	0.226619i
$329$	10.6146	−	8.90673i	0.585203	−	0.491044i
$330$		0			0
$331$	−1.87939	+	0.684040i	−0.103300	+	0.0375983i	−0.393153	−	0.919473i	$-0.628616\pi$
$331$	−1.87939	+	0.684040i	−0.103300	+	0.0375983i	0.289853	+	0.957071i	$0.406394\pi$
$332$	6.92820	−	12.0000i	0.380235	−	0.658586i
$333$		0			0
$334$	15.0000	+	25.9808i	0.820763	+	1.42160i
$335$	13.2683	+	11.1334i	0.724924	+	0.608283i
$336$		0			0
$337$	4.51485	+	25.6050i	0.245940	+	1.39479i	0.818300	+	0.574791i	$0.194917\pi$
$337$	4.51485	+	25.6050i	0.245940	+	1.39479i	−0.572360	+	0.820002i	$0.693972\pi$
$338$	−3.60921	−	20.4688i	−0.196315	−	1.11336i
$339$		0			0
$340$	−6.89440	−	5.78509i	−0.373901	−	0.313740i
$341$	13.8564	+	24.0000i	0.750366	+	1.29967i
$342$		0			0
$343$	10.0000	−	17.3205i	0.539949	−	0.935220i
$344$	3.25519	−	1.18479i	0.175508	−	0.0638797i
$345$		0			0
$346$	−25.2795	+	21.2120i	−1.35903	+	1.14036i
$347$	−3.25519	−	1.18479i	−0.174748	−	0.0636030i	0.253165	−	0.967423i	$-0.418529\pi$
$347$	−3.25519	−	1.18479i	−0.174748	−	0.0636030i	−0.427912	+	0.903820i	$0.640751\pi$
$348$		0			0
$349$	0.347296	−	1.96962i	0.0185903	−	0.105431i	−0.974101	−	0.226115i	$-0.927398\pi$
$349$	0.347296	−	1.96962i	0.0185903	−	0.105431i	0.992691	+	0.120684i	$0.0385087\pi$
$350$	−6.92820			−0.370328
$351$		0			0
$352$	18.0000			0.959403
$353$	−2.40614	+	13.6459i	−0.128066	+	0.726298i	0.851374	+	0.524560i	$0.175770\pi$
$353$	−2.40614	+	13.6459i	−0.128066	+	0.726298i	−0.979440	+	0.201738i	$0.935341\pi$
$354$		0			0
$355$	−16.9145	−	6.15636i	−0.897727	−	0.326746i
$356$	−3.98048	+	3.34002i	−0.210965	+	0.177021i
$357$		0			0
$358$	−33.8289	+	12.3127i	−1.78791	+	0.650748i
$359$	−5.19615	+	9.00000i	−0.274242	+	0.475002i	−0.969944	−	0.243329i	$-0.921760\pi$
$359$	−5.19615	+	9.00000i	−0.274242	+	0.475002i	0.695701	+	0.718331i	$0.255094\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	2.65366	+	2.22668i	0.139473	+	0.117032i
$363$		0			0
$364$	−0.347296	−	1.96962i	−0.0182033	−	0.103236i
$365$	2.10537	+	11.9402i	0.110200	+	0.624977i
$366$		0			0
$367$	15.3209	+	12.8558i	0.799744	+	0.671065i	0.948136	−	0.317864i	$-0.102965\pi$
$367$	15.3209	+	12.8558i	0.799744	+	0.671065i	−0.148393	+	0.988929i	$0.547410\pi$
$368$	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
$373$	−7.66044	+	6.42788i	−0.396643	+	0.332823i	−0.819194	−	0.573516i	$-0.805579\pi$
$373$	−7.66044	+	6.42788i	−0.396643	+	0.332823i	0.422552	+	0.906339i	$0.361135\pi$
$374$	29.2967	+	10.6631i	1.51490	+	0.551377i
$375$		0			0
$376$	−2.08378	+	11.8177i	−0.107463	+	0.609451i
$377$	−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	$0.634797\pi$
$380$	−0.601535	+	3.41147i	−0.0308581	+	0.175005i
$381$		0			0
$382$	−28.1908	−	10.2606i	−1.44237	−	0.524978i
$383$	−13.2683	+	11.1334i	−0.677977	+	0.568891i	−0.915415	−	0.402512i	$-0.868137\pi$
$383$	−13.2683	+	11.1334i	−0.677977	+	0.568891i	0.237437	+	0.971403i	$0.423693\pi$
$384$		0			0
$385$	−11.2763	+	4.10424i	−0.574694	+	0.209172i
$386$	0.866025	−	1.50000i	0.0440795	−	0.0763480i
$387$		0			0
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	21.2292	+	17.8135i	1.07637	+	0.903178i	0.995614	−	0.0935564i	$-0.0298235\pi$
$389$	21.2292	+	17.8135i	1.07637	+	0.903178i	0.0807515	+	0.996734i	$0.474268\pi$
$390$		0			0
$391$	3.12567	+	17.7265i	0.158072	+	0.896470i
$392$	0.902302	+	5.11721i	0.0455732	+	0.258458i
$393$		0			0
$394$	−6.89440	−	5.78509i	−0.347335	−	0.291449i
$395$	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	$0.907240\pi$
$398$	−32.5519	+	11.8479i	−1.63168	+	0.593883i
$399$		0			0
$400$	7.66044	−	6.42788i	0.383022	−	0.321394i
$401$	11.3932	+	4.14677i	0.568948	+	0.207080i	0.610445	−	0.792059i	$-0.290991\pi$
$401$	11.3932	+	4.14677i	0.568948	+	0.207080i	−0.0414974	+	0.999139i	$0.513213\pi$
$402$		0			0
$403$	−1.38919	+	7.87846i	−0.0692003	+	0.392454i
$404$	6.92820			0.344691
$405$		0			0
$406$	6.00000			0.297775
$407$	4.21074	−	23.8803i	0.208719	−	1.18370i
$408$		0			0
$409$	17.8542	+	6.49838i	0.882831	+	0.321324i	0.743352	−	0.668901i	$-0.233235\pi$
$409$	17.8542	+	6.49838i	0.882831	+	0.321324i	0.139480	+	0.990225i	$0.455457\pi$
$410$	15.9219	−	13.3601i	0.786328	−	0.659808i
$411$		0			0
$412$	−7.51754	+	2.73616i	−0.370363	+	0.134801i
$413$	−13.8564	+	24.0000i	−0.681829	+	1.18096i
$414$		0			0
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$	3.98048	+	3.34002i	0.195159	+	0.163758i
$417$		0			0
$418$	−2.08378	−	11.8177i	−0.101921	−	0.578022i
$419$	−1.20307	−	6.82295i	−0.0587738	−	0.333323i	0.941216	−	0.337805i	$-0.109684\pi$
$419$	−1.20307	−	6.82295i	−0.0587738	−	0.333323i	−0.999990	+	0.00448209i	$0.998573\pi$
$420$		0			0
$421$	−19.1511	−	16.0697i	−0.933368	−	0.783189i	0.0430510	−	0.999073i	$-0.486292\pi$
$421$	−19.1511	−	16.0697i	−0.933368	−	0.783189i	−0.976419	+	0.215884i	$0.930737\pi$
$422$	8.66025	+	15.0000i	0.421575	+	0.730189i
$423$		0			0
$424$		0			0
$425$	9.76557	−	3.55438i	0.473700	−	0.172413i
$426$		0			0
$427$	−10.7246	+	8.99903i	−0.519001	+	0.435493i
$428$		0			0
$429$		0			0
$430$	−1.04189	+	5.90885i	−0.0502444	+	0.284950i
$431$		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	$0.414855\pi$
$434$	4.81228	−	27.2918i	0.230997	−	1.31005i
$435$		0			0
$436$	−10.3366	−	3.76222i	−0.495034	−	0.180178i
$437$	5.30731	−	4.45336i	0.253883	−	0.213033i
$438$		0			0
$439$	−18.7939	+	6.84040i	−0.896982	+	0.326475i	−0.749043	−	0.662522i	$-0.769486\pi$
$439$	−18.7939	+	6.84040i	−0.896982	+	0.326475i	−0.147939	+	0.988996i	$0.547264\pi$
$440$	5.19615	−	9.00000i	0.247717	−	0.429058i
$441$		0			0
$442$	4.50000	+	7.79423i	0.214043	+	0.370734i
$443$	−26.5366	−	22.2668i	−1.26079	−	1.05793i	−0.995597	−	0.0937329i	$-0.970120\pi$
$443$	−26.5366	−	22.2668i	−1.26079	−	1.05793i	−0.265193	−	0.964195i	$-0.585436\pi$
$444$		0			0
$445$	1.56283	+	8.86327i	0.0740854	+	0.420159i
$446$	0.601535	+	3.41147i	0.0284835	+	0.161538i
$447$		0			0
$448$	1.53209	+	1.28558i	0.0723844	+	0.0607377i
$449$	−10.3923	−	18.0000i	−0.490443	−	0.849473i	0.509496	−	0.860473i	$-0.329832\pi$
$449$	−10.3923	−	18.0000i	−0.490443	−	0.849473i	−0.999939	+	0.0110003i	$0.996498\pi$
$450$		0			0
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$	1.62760	−	0.592396i	0.0765556	−	0.0278640i
$453$		0			0
$454$	−4.59627	+	3.85673i	−0.215713	+	0.181005i
$455$	−3.25519	−	1.18479i	−0.152606	−	0.0555439i
$456$		0			0
$457$	5.03580	−	28.5594i	0.235565	−	1.33595i	−0.605857	−	0.795574i	$-0.707169\pi$
$457$	5.03580	−	28.5594i	0.235565	−	1.33595i	0.841421	−	0.540380i	$-0.181719\pi$
$458$	−1.73205			−0.0809334
$459$		0			0
$460$	−6.00000			−0.279751
$461$	−2.40614	+	13.6459i	−0.112065	+	0.635553i	0.876096	+	0.482136i	$0.160139\pi$
$461$	−2.40614	+	13.6459i	−0.112065	+	0.635553i	−0.988162	+	0.153417i	$0.950972\pi$
$462$		0			0
$463$	−7.51754	−	2.73616i	−0.349370	−	0.127160i	0.161374	−	0.986893i	$-0.448408\pi$
$463$	−7.51754	−	2.73616i	−0.349370	−	0.127160i	−0.510743	+	0.859733i	$0.670630\pi$
$464$	−6.63414	+	5.56670i	−0.307982	+	0.258428i
$465$		0			0
$466$	42.2862	−	15.3909i	1.95887	−	0.712970i
$467$	10.3923	−	18.0000i	0.480899	−	0.832941i	−0.518861	−	0.854858i	$-0.673644\pi$
$467$	10.3923	−	18.0000i	0.480899	−	0.832941i	0.999760	+	0.0219178i	$0.00697721\pi$
$468$		0			0
$469$	10.0000	+	17.3205i	0.461757	+	0.799787i
$470$	−15.9219	−	13.3601i	−0.734424	−	0.616255i
$471$		0			0
$472$	−4.16756	−	23.6354i	−0.191827	−	1.08791i
$473$	−1.20307	−	6.82295i	−0.0553172	−	0.313719i
$474$		0			0
$475$	−3.06418	−	2.57115i	−0.140594	−	0.117972i
$476$	−5.19615	−	9.00000i	−0.238165	−	0.412514i
$477$		0			0
$478$	24.0000	−	41.5692i	1.09773	−	1.90133i
$479$	22.7863	−	8.29355i	1.04113	−	0.378942i	0.235824	−	0.971796i	$-0.424221\pi$
$479$	22.7863	−	8.29355i	1.04113	−	0.378942i	0.805310	+	0.592854i	$0.201999\pi$
$480$		0			0
$481$	5.36231	−	4.49951i	0.244500	−	0.205160i
$482$	−47.2003	−	17.1795i	−2.14991	−	0.782504i
$483$		0			0
$484$	0.173648	−	0.984808i	0.00789310	−	0.0447640i
$485$	−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	$0.618082\pi$
$488$	2.10537	−	11.9402i	0.0953057	−	0.540506i
$489$		0			0
$490$	−8.45723	−	3.07818i	−0.382059	−	0.139058i
$491$	−13.2683	+	11.1334i	−0.598789	+	0.502444i	−0.891056	−	0.453893i	$-0.850035\pi$
$491$	−13.2683	+	11.1334i	−0.598789	+	0.502444i	0.292267	+	0.956337i	$0.405590\pi$
$492$		0			0
$493$	−8.45723	+	3.07818i	−0.380895	+	0.138634i
$494$	1.73205	−	3.00000i	0.0779287	−	0.134976i
$495$		0			0
$496$	20.0000	+	34.6410i	0.898027	+	1.55543i
$497$	−15.9219	−	13.3601i	−0.714196	−	0.599282i
$498$		0			0
$499$	−1.73648	−	9.84808i	−0.0777356	−	0.440860i	−0.998689	−	0.0511879i	$-0.983699\pi$
$499$	−1.73648	−	9.84808i	−0.0777356	−	0.440860i	0.920953	−	0.389673i	$-0.127412\pi$
$500$	2.10537	+	11.9402i	0.0941551	+	0.533980i
$501$		0			0
$502$	13.7888	+	11.5702i	0.615424	+	0.516402i
$503$	−10.3923	−	18.0000i	−0.463370	−	0.802580i	0.535756	−	0.844373i	$-0.320027\pi$
$503$	−10.3923	−	18.0000i	−0.463370	−	0.802580i	−0.999126	+	0.0417923i	$0.986693\pi$
$504$		0			0
$505$	6.00000	−	10.3923i	0.266996	−	0.462451i
$506$	19.5311	−	7.10876i	0.868265	−	0.316023i
$507$		0			0
$508$	1.53209	−	1.28558i	0.0679755	−	0.0570382i
$509$	26.0415	+	9.47834i	1.15427	+	0.420120i	0.847047	−	0.531517i	$-0.178378\pi$
$509$	26.0415	+	9.47834i	1.15427	+	0.420120i	0.307223	+	0.951638i	$0.400600\pi$
$510$		0			0
$511$	−2.43107	+	13.7873i	−0.107544	+	0.609915i
$512$	8.66025			0.382733
$513$		0			0
$514$	15.0000			0.661622
$515$	−2.40614	+	13.6459i	−0.106027	+	0.601310i
$516$		0			0
$517$	22.5526	+	8.20848i	0.991863	+	0.361009i
$518$	−18.5756	+	15.5868i	−0.816165	+	0.684843i
$519$		0			0
$520$	2.81908	−	1.02606i	0.123625	−	0.0449957i
$521$	10.3923	−	18.0000i	0.455295	−	0.788594i	−0.543410	−	0.839467i	$-0.682867\pi$
$521$	10.3923	−	18.0000i	0.455295	−	0.788594i	0.998705	+	0.0508731i	$0.0162004\pi$
$522$		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	$-0.478790\pi$
$524$	2.65366	+	2.22668i	0.115925	+	0.0972730i
$525$		0			0
$526$	2.08378	+	11.8177i	0.0908570	+	0.515276i
$527$	7.21842	+	40.9377i	0.314439	+	1.78327i
$528$		0			0
$529$	−8.42649	−	7.07066i	−0.366369	−	0.307420i
$530$		0			0
$531$		0			0
$532$	−2.00000	+	3.46410i	−0.0867110	+	0.150188i
$533$	−6.51038	+	2.36959i	−0.281996	+	0.102638i
$534$		0			0
$535$		0			0
$536$	−16.2760	−	5.92396i	−0.703014	−	0.255876i
$537$		0			0
$538$	−4.68850	+	26.5898i	−0.202136	+	1.14637i
$539$	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	$0.424012\pi$
$542$	0.601535	−	3.41147i	0.0258381	−	0.146535i
$543$		0			0
$544$	25.3717	+	9.23454i	1.08780	+	0.395928i
$545$	−14.5951	+	12.2467i	−0.625186	+	0.524593i
$546$		0			0
$547$	−18.7939	+	6.84040i	−0.803567	+	0.292475i	−0.710964	−	0.703229i	$-0.751741\pi$
$547$	−18.7939	+	6.84040i	−0.803567	+	0.292475i	−0.0926033	+	0.995703i	$0.529519\pi$
$548$	−0.866025	+	1.50000i	−0.0369948	+	0.0640768i
$549$		0			0
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	2.65366	+	2.22668i	0.113050	+	0.0948598i
$552$		0			0
$553$	0.694593	+	3.93923i	0.0295371	+	0.167513i
$554$	0.601535	+	3.41147i	0.0255568	+	0.144940i
$555$		0			0
$556$	6.12836	+	5.14230i	0.259900	+	0.218082i
$557$	−18.1865	−	31.5000i	−0.770588	−	1.33470i	−0.937241	−	0.348682i	$-0.886629\pi$
$557$	−18.1865	−	31.5000i	−0.770588	−	1.33470i	0.166653	−	0.986016i	$-0.446704\pi$
$558$		0			0
$559$	1.00000	−	1.73205i	0.0422955	−	0.0732579i
$560$	−16.2760	+	5.92396i	−0.687785	+	0.250333i
$561$		0			0
$562$	16.0869	−	13.4985i	0.678586	−	0.569402i
$563$	−32.5519	−	11.8479i	−1.37190	−	0.499331i	−0.452187	−	0.891923i	$-0.649356\pi$
$563$	−32.5519	−	11.8479i	−1.37190	−	0.499331i	−0.919712	+	0.392593i	$0.871578\pi$
$564$		0			0
$565$	0.520945	−	2.95442i	0.0219163	−	0.124294i
$566$	−48.4974			−2.03850
$567$		0			0
$568$	18.0000			0.755263
$569$	5.71458	−	32.4090i	0.239568	−	1.35866i	−0.593210	−	0.805048i	$-0.702139\pi$
$569$	5.71458	−	32.4090i	0.239568	−	1.35866i	0.832777	−	0.553608i	$-0.186749\pi$
$570$		0			0
$571$	−7.51754	−	2.73616i	−0.314599	−	0.114505i	0.179895	−	0.983686i	$-0.442424\pi$
$571$	−7.51754	−	2.73616i	−0.314599	−	0.114505i	−0.494494	+	0.869181i	$0.664647\pi$
$572$	2.65366	−	2.22668i	0.110955	−	0.0931022i
$573$		0			0
$574$	22.5526	−	8.20848i	0.941328	−	0.342615i
$575$	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	$0.906868\pi$
$578$	13.2683	+	11.1334i	0.551888	+	0.463089i
$579$		0			0
$580$	−0.520945	−	2.95442i	−0.0216310	−	0.122676i
$581$	−4.81228	−	27.2918i	−0.199647	−	1.13225i
$582$		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
$587$	−35.8071	+	13.0327i	−1.47792	+	0.537918i	−0.950238	−	0.311526i	$-0.899160\pi$
$587$	−35.8071	+	13.0327i	−1.47792	+	0.537918i	−0.527679	+	0.849444i	$0.676938\pi$
$588$		0			0
$589$	12.2567	−	10.2846i	0.505029	−	0.423770i
$590$	39.0623	+	14.2175i	1.60817	+	0.585326i
$591$		0			0
$592$	6.07769	−	34.4683i	0.249791	−	1.41664i
$593$	15.5885			0.640141			0.320071	−	0.947394i	$-0.396293\pi$
$593$	15.5885			0.640141			0.320071	+	0.947394i	$0.396293\pi$
$594$		0			0
$595$	−18.0000			−0.737928
$596$	1.50384	−	8.52869i	0.0615996	−	0.349349i
$597$		0			0
$598$	5.63816	+	2.05212i	0.230561	+	0.0839175i
$599$	10.6146	−	8.90673i	0.433702	−	0.363919i	−0.399645	−	0.916670i	$-0.630866\pi$
$599$	10.6146	−	8.90673i	0.433702	−	0.363919i	0.833346	+	0.552751i	$0.186422\pi$
$600$		0			0
$601$	23.4923	−	8.55050i	0.958272	−	0.348782i	0.184916	−	0.982754i	$-0.440799\pi$
$601$	23.4923	−	8.55050i	0.958272	−	0.348782i	0.773356	+	0.633972i	$0.218577\pi$
$602$	−3.46410	+	6.00000i	−0.141186	+	0.244542i
$603$		0			0
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	−1.32683	−	1.11334i	−0.0539432	−	0.0452637i
$606$		0			0
$607$	4.51485	+	25.6050i	0.183252	+	1.03927i	0.928180	+	0.372130i	$0.121373\pi$
$607$	4.51485	+	25.6050i	0.183252	+	1.03927i	−0.744928	+	0.667145i	$0.767516\pi$
$608$	−1.80460	−	10.2344i	−0.0731864	−	0.415061i
$609$		0			0
$610$	16.0869	+	13.4985i	0.651341	+	0.546540i
$611$	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	$-0.0742412\pi$
$614$	26.0415	−	9.47834i	1.05095	−	0.382515i
$615$		0			0
$616$	9.19253	−	7.71345i	0.370378	−	0.310784i
$617$	11.3932	+	4.14677i	0.458672	+	0.166943i	0.561014	−	0.827806i	$-0.310411\pi$
$617$	11.3932	+	4.14677i	0.458672	+	0.166943i	−0.102342	+	0.994749i	$0.532634\pi$
$618$		0			0
$619$	3.47296	−	19.6962i	0.139590	−	0.791655i	−0.831963	−	0.554832i	$-0.812783\pi$
$619$	3.47296	−	19.6962i	0.139590	−	0.791655i	0.971553	−	0.236823i	$-0.0761063\pi$
$620$	−13.8564			−0.556487
$621$		0			0
$622$	−12.0000			−0.481156
$623$	−1.80460	+	10.2344i	−0.0723000	+	0.410033i
$624$		0			0
$625$	10.3366	+	3.76222i	0.413465	+	0.150489i
$626$	−33.1707	+	27.8335i	−1.32577	+	1.11245i
$627$		0			0
$628$	−15.9748	+	5.81434i	−0.637463	+	0.232018i
$629$	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	$0.963661\pi$
$632$	−2.65366	−	2.22668i	−0.105557	−	0.0885726i
$633$		0			0
$634$	−2.60472	−	14.7721i	−0.103447	−	0.586676i
$635$	−0.601535	−	3.41147i	−0.0238712	−	0.135380i
$636$		0			0
$637$	2.29813	+	1.92836i	0.0910554	+	0.0764045i
$638$	5.19615	+	9.00000i	0.205718	+	0.356313i
$639$		0			0
$640$	10.5000	−	18.1865i	0.415049	−	0.718886i
$641$	−21.1587	+	7.70115i	−0.835720	+	0.304177i	−0.724204	−	0.689585i	$-0.757793\pi$
$641$	−21.1587	+	7.70115i	−0.835720	+	0.304177i	−0.111516	+	0.993763i	$0.535571\pi$
$642$		0			0
$643$	6.12836	−	5.14230i	0.241679	−	0.202793i	−0.513900	−	0.857850i	$-0.671800\pi$
$643$	6.12836	−	5.14230i	0.241679	−	0.202793i	0.755579	+	0.655057i	$0.227356\pi$
$644$	−6.51038	−	2.36959i	−0.256545	−	0.0933747i
$645$		0			0
$646$	3.12567	−	17.7265i	0.122978	−	0.697441i
$647$	−31.1769			−1.22569			−0.612845	−	0.790203i	$-0.709975\pi$
$647$	−31.1769			−1.22569			−0.612845	+	0.790203i	$0.709975\pi$
$648$		0			0
$649$	−48.0000			−1.88416
$650$	0.601535	−	3.41147i	0.0235941	−	0.133809i
$651$		0			0
$652$	15.0351	+	5.47232i	0.588819	+	0.214313i
$653$	10.6146	−	8.90673i	0.415382	−	0.348547i	−0.411021	−	0.911626i	$-0.634828\pi$
$653$	10.6146	−	8.90673i	0.415382	−	0.348547i	0.826403	+	0.563079i	$0.190383\pi$
$654$		0			0
$655$	5.63816	−	2.05212i	0.220301	−	0.0801830i
$656$	−17.3205	+	30.0000i	−0.676252	+	1.17130i
$657$		0			0
$658$	−12.0000	−	20.7846i	−0.467809	−	0.810268i
$659$	−2.65366	−	2.22668i	−0.103372	−	0.0867392i	0.589637	−	0.807668i	$-0.299271\pi$
$659$	−2.65366	−	2.22668i	−0.103372	−	0.0867392i	−0.693009	+	0.720929i	$0.743715\pi$
$660$		0			0
$661$	2.95202	+	16.7417i	0.114820	+	0.651178i	0.986839	+	0.161706i	$0.0516995\pi$
$661$	2.95202	+	16.7417i	0.114820	+	0.651178i	−0.872019	+	0.489472i	$0.837189\pi$
$662$	0.601535	+	3.41147i	0.0233793	+	0.132591i
$663$		0			0
$664$	18.3851	+	15.4269i	0.713479	+	0.598680i
$665$	3.46410	+	6.00000i	0.134332	+	0.232670i
$666$		0			0
$667$	−3.00000	+	5.19615i	−0.116160	+	0.201196i
$668$	16.2760	−	5.92396i	0.629736	−	0.229205i
$669$		0			0
$670$	22.9813	−	19.2836i	0.887846	−	0.744992i
$671$	−22.7863	−	8.29355i	−0.879657	−	0.320169i
$672$		0			0
$673$	−4.34120	+	24.6202i	−0.167341	+	0.949039i	0.779277	+	0.626680i	$0.215587\pi$
$673$	−4.34120	+	24.6202i	−0.167341	+	0.949039i	−0.946618	+	0.322359i	$0.895524\pi$
$674$	45.0333			1.73462
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−2.40614	+	13.6459i	−0.0924755	+	0.524454i	0.903016	+	0.429606i	$0.141348\pi$
$677$	−2.40614	+	13.6459i	−0.0924755	+	0.524454i	−0.995492	+	0.0948481i	$0.969763\pi$
$678$		0			0
$679$	−3.75877	−	1.36808i	−0.144248	−	0.0525021i
$680$	11.9415	−	10.0201i	0.457934	−	0.384252i
$681$		0			0
$682$	45.1052	−	16.4170i	1.72717	−	0.628638i
$683$	10.3923	−	18.0000i	0.397650	−	0.688751i	−0.595785	−	0.803144i	$-0.703159\pi$
$683$	10.3923	−	18.0000i	0.397650	−	0.688751i	0.993436	+	0.114393i	$0.0364923\pi$
$684$		0			0
$685$	1.50000	+	2.59808i	0.0573121	+	0.0992674i
$686$	−26.5366	−	22.2668i	−1.01317	−	0.850151i
$687$		0			0
$688$	−1.73648	−	9.84808i	−0.0662027	−	0.375454i
$689$		0			0
$690$		0			0
$691$	1.53209	+	1.28558i	0.0582834	+	0.0489056i	0.671464	−	0.741037i	$-0.265666\pi$
$691$	1.53209	+	1.28558i	0.0582834	+	0.0489056i	−0.613181	+	0.789943i	$0.710110\pi$
$692$	9.52628	+	16.5000i	0.362135	+	0.627236i
$693$		0			0
$694$	−3.00000	+	5.19615i	−0.113878	+	0.197243i
$695$	13.0208	−	4.73917i	0.493906	−	0.179767i
$696$		0			0
$697$	−27.5776	+	23.1404i	−1.04458	+	0.876503i
$698$	−3.25519	−	1.18479i	−0.123211	−	0.0448451i
$699$		0			0
$700$	−0.694593	+	3.93923i	−0.0262531	+	0.148889i
$701$	46.7654			1.76630			0.883152	−	0.469087i	$-0.155417\pi$
$701$	46.7654			1.76630			0.883152	+	0.469087i	$0.155417\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	−0.601535	+	3.41147i	−0.0226712	+	0.128575i
$705$		0			0
$706$	22.5526	+	8.20848i	0.848779	+	0.308930i
$707$	10.6146	−	8.90673i	0.399204	−	0.334972i
$708$		0			0
$709$	23.4923	−	8.55050i	0.882272	−	0.321121i	0.139146	−	0.990272i	$-0.455564\pi$
$709$	23.4923	−	8.55050i	0.882272	−	0.321121i	0.743126	+	0.669151i	$0.233342\pi$
$710$	−15.5885	+	27.0000i	−0.585024	+	1.01329i
$711$		0			0
$712$	−4.50000	−	7.79423i	−0.168645	−	0.292101i
$713$	21.2292	+	17.8135i	0.795042	+	0.667119i
$714$		0			0
$715$	−1.04189	−	5.90885i	−0.0389644	−	0.220978i
$716$	3.60921	+	20.4688i	0.134882	+	0.764957i
$717$		0			0
$718$	13.7888	+	11.5702i	0.514593	+	0.431795i
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	0.946501	−	0.322700i	$-0.104591\pi$
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	−0.752717	+	0.658344i	$0.771257\pi$
$720$		0			0
$721$	−8.00000	+	13.8564i	−0.297936	+	0.516040i
$722$	24.4139	−	8.88594i	0.908592	−	0.330701i
$723$		0			0
$724$	1.53209	−	1.28558i	0.0569396	−	0.0477780i
$725$	3.25519	+	1.18479i	0.120895	+	0.0440021i
$726$		0			0
$727$	−5.90404	+	33.4835i	−0.218969	+	1.24183i	0.654917	+	0.755701i	$0.272704\pi$
$727$	−5.90404	+	33.4835i	−0.218969	+	1.24183i	−0.873885	+	0.486132i	$0.838407\pi$
$728$	3.46410			0.128388
$729$		0			0
$730$	21.0000			0.777245
$731$	1.80460	−	10.2344i	0.0667457	−	0.378534i
$732$		0			0
$733$	43.2259	+	15.7329i	1.59658	+	0.581109i	0.978724	−	0.205180i	$-0.0657779\pi$
$733$	43.2259	+	15.7329i	1.59658	+	0.581109i	0.617859	+	0.786289i	$0.288000\pi$
$734$	26.5366	−	22.2668i	0.979482	−	0.821883i
$735$		0			0
$736$	16.9145	−	6.15636i	0.623476	−	0.226927i
$737$	−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	$0.953241\pi$
$740$	9.28780	+	7.79339i	0.341426	+	0.286491i
$741$		0			0
$742$		0			0
$743$	−1.20307	−	6.82295i	−0.0441364	−	0.250310i	0.954755	−	0.297395i	$-0.0961178\pi$
$743$	−1.20307	−	6.82295i	−0.0441364	−	0.250310i	−0.998891	+	0.0470853i	$0.985007\pi$
$744$		0			0
$745$	−11.4907	−	9.64181i	−0.420985	−	0.353249i
$746$	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
$751$	−7.66044	+	6.42788i	−0.279534	+	0.234557i	−0.771765	−	0.635908i	$-0.780626\pi$
$751$	−7.66044	+	6.42788i	−0.279534	+	0.234557i	0.492231	+	0.870464i	$0.336181\pi$
$752$	32.5519	+	11.8479i	1.18705	+	0.432049i
$753$		0			0
$754$	−0.520945	+	2.95442i	−0.0189717	+	0.107594i
$755$	−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	$0.488428\pi$
$758$	−4.81228	+	27.2918i	−0.174790	+	0.991283i
$759$		0			0
$760$	−5.63816	−	2.05212i	−0.204517	−	0.0744382i
$761$	22.5561	−	18.9268i	0.817657	−	0.686096i	−0.134765	−	0.990878i	$-0.543028\pi$
$761$	22.5561	−	18.9268i	0.817657	−	0.686096i	0.952422	+	0.304782i	$0.0985836\pi$
$762$		0			0
$763$	−20.6732	+	7.52444i	−0.748421	+	0.272403i
$764$	−8.66025	+	15.0000i	−0.313317	+	0.542681i
$765$		0			0
$766$	15.0000	+	25.9808i	0.541972	+	0.938723i
$767$	−10.6146	−	8.90673i	−0.383272	−	0.321603i
$768$		0			0
$769$	−0.173648	−	0.984808i	−0.00626191	−	0.0355131i	0.981517	−	0.191376i	$-0.0612951\pi$
$769$	−0.173648	−	0.984808i	−0.00626191	−	0.0355131i	−0.987779	+	0.155863i	$0.950184\pi$
$770$	3.60921	+	20.4688i	0.130067	+	0.737646i
$771$		0			0
$772$	−0.766044	−	0.642788i	−0.0275705	−	0.0231344i
$773$	12.9904	+	22.5000i	0.467232	+	0.809269i	0.999299	−	0.0374331i	$-0.0119181\pi$
$773$	12.9904	+	22.5000i	0.467232	+	0.809269i	−0.532068	+	0.846702i	$0.678585\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	3.25519	−	1.18479i	0.116855	−	0.0425316i
$777$		0			0
$778$	36.7701	−	30.8538i	1.31827	−	1.10616i
$779$	13.0208	+	4.73917i	0.466517	+	0.169798i
$780$		0			0
$781$	6.25133	−	35.4531i	0.223690	−	1.26861i
$782$	31.1769			1.11488
$783$		0			0
$784$	15.0000			0.535714
$785$	−5.11305	+	28.9975i	−0.182492	+	1.03497i
$786$		0			0
$787$	−24.4320	−	8.89252i	−0.870907	−	0.316984i	−0.132373	−	0.991200i	$-0.542260\pi$
$787$	−24.4320	−	8.89252i	−0.870907	−	0.316984i	−0.738534	+	0.674216i	$0.764482\pi$
$788$	−3.98048	+	3.34002i	−0.141799	+	0.118983i
$789$		0			0
$790$	5.63816	−	2.05212i	0.200597	−	0.0730112i
$791$	1.73205	−	3.00000i	0.0615846	−	0.106668i
$792$		0			0
$793$	−3.50000	−	6.06218i	−0.124289	−	0.215274i
$794$	38.4780	+	32.2869i	1.36553	+	1.14582i
$795$		0			0
$796$	3.47296	+	19.6962i	0.123096	+	0.698112i
$797$	−9.32379	−	52.8778i	−0.330266	−	1.87303i	−0.469741	−	0.882804i	$-0.655653\pi$
$797$	−9.32379	−	52.8778i	−0.330266	−	1.87303i	0.139476	−	0.990225i	$-0.455458\pi$
$798$		0			0
$799$	27.5776	+	23.1404i	0.975625	+	0.818647i
$800$	−5.19615	−	9.00000i	−0.183712	−	0.318198i
$801$		0			0
$802$	10.5000	−	18.1865i	0.370768	−	0.642189i
$803$	−22.7863	+	8.29355i	−0.804112	+	0.292673i
$804$		0			0
$805$	−9.19253	+	7.71345i	−0.323994	+	0.271863i
$806$	13.0208	+	4.73917i	0.458637	+	0.166930i
$807$		0			0
$808$	−2.08378	+	11.8177i	−0.0733071	+	0.415745i
$809$	−46.7654			−1.64418			−0.822091	−	0.569355i	$-0.807193\pi$
$809$	−46.7654			−1.64418			−0.822091	+	0.569355i	$0.807193\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	0.601535	−	3.41147i	0.0211097	−	0.119719i
$813$		0			0
$814$	−39.4671	−	14.3648i	−1.38332	−	0.503488i
$815$	21.2292	−	17.8135i	0.743628	−	0.623978i
$816$		0			0
$817$	−3.75877	+	1.36808i	−0.131503	+	0.0478631i
$818$	16.4545	−	28.5000i	0.575317	−	0.996479i
$819$		0			0
$820$	−6.00000	−	10.3923i	−0.209529	−	0.362915i
$821$	9.28780	+	7.79339i	0.324146	+	0.271991i	0.790310	−	0.612708i	$-0.209920\pi$
$821$	9.28780	+	7.79339i	0.324146	+	0.271991i	−0.466163	+	0.884699i	$0.654364\pi$
$822$		0			0
$823$	−4.86215	−	27.5746i	−0.169484	−	0.961191i	−0.944320	−	0.329029i	$-0.893279\pi$
$823$	−4.86215	−	27.5746i	−0.169484	−	0.961191i	0.774836	−	0.632162i	$-0.217832\pi$
$824$	−2.40614	−	13.6459i	−0.0838218	−	0.475377i
$825$		0			0
$826$	36.7701	+	30.8538i	1.27940	+	1.07354i
$827$	5.19615	+	9.00000i	0.180688	+	0.312961i	0.942115	−	0.335290i	$-0.108834\pi$
$827$	5.19615	+	9.00000i	0.180688	+	0.312961i	−0.761427	+	0.648251i	$0.775501\pi$
$828$		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	$0.177724\pi$
$830$	−39.0623	+	14.2175i	−1.35587	+	0.493497i
$831$		0			0
$832$	−0.766044	+	0.642788i	−0.0265578	+	0.0222847i
$833$	14.6484	+	5.33157i	0.507536	+	0.184728i
$834$		0			0
$835$	5.20945	−	29.5442i	0.180280	−	1.02242i
$836$	−6.92820			−0.239617
$837$		0			0
$838$	−12.0000			−0.414533
$839$	−7.81995	+	44.3492i	−0.269975	+	1.53110i	0.484510	+	0.874786i	$0.338998\pi$
$839$	−7.81995	+	44.3492i	−0.269975	+	1.53110i	−0.754485	+	0.656317i	$0.772113\pi$
$840$		0			0
$841$	24.4320	+	8.89252i	0.842483	+	0.306639i
$842$	−33.1707	+	27.8335i	−1.14314	+	0.959206i
$843$		0			0
$844$	9.39693	−	3.42020i	0.323456	−	0.117728i
$845$	−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
$850$	−3.12567	−	17.7265i	−0.107210	−	0.608015i
$851$	−4.21074	−	23.8803i	−0.144342	−	0.818607i
$852$		0			0
$853$	−26.0455	−	21.8548i	−0.891781	−	0.748293i	0.0767853	−	0.997048i	$-0.475534\pi$
$853$	−26.0455	−	21.8548i	−0.891781	−	0.748293i	−0.968567	+	0.248754i	$0.919979\pi$
$854$	12.1244	+	21.0000i	0.414887	+	0.718605i
$855$		0			0
$856$		0			0
$857$	−21.1587	+	7.70115i	−0.722769	+	0.263066i	−0.677101	−	0.735890i	$-0.736764\pi$
$857$	−21.1587	+	7.70115i	−0.722769	+	0.263066i	−0.0456681	+	0.998957i	$0.514542\pi$
$858$		0			0
$859$	33.7060	−	28.2827i	1.15003	−	0.964992i	0.150312	−	0.988639i	$-0.451972\pi$
$859$	33.7060	−	28.2827i	1.15003	−	0.964992i	0.999720	+	0.0236469i	$0.00752774\pi$
$860$	3.25519	+	1.18479i	0.111001	+	0.0404011i
$861$		0			0
$862$		0			0
$863$	31.1769			1.06127			0.530637	−	0.847599i	$-0.321953\pi$
$863$	31.1769			1.06127			0.530637	+	0.847599i	$0.321953\pi$
$864$		0			0
$865$	33.0000			1.12203
$866$	3.30844	−	18.7631i	0.112425	−	0.637596i
$867$		0			0
$868$	−15.0351	−	5.47232i	−0.510324	−	0.185743i
$869$	−5.30731	+	4.45336i	−0.180038	+	0.151070i
$870$		0			0
$871$	−9.39693	+	3.42020i	−0.318403	+	0.115889i
$872$	9.52628	−	16.5000i	0.322601	−	0.558761i
$873$		0			0
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	18.5756	+	15.5868i	0.627970	+	0.526929i
$876$		0			0
$877$	9.20335	+	52.1948i	0.310775	+	1.76249i	0.594990	+	0.803733i	$0.297156\pi$
$877$	9.20335	+	52.1948i	0.310775	+	1.76249i	−0.284215	+	0.958761i	$0.591733\pi$
$878$	6.01535	+	34.1147i	0.203008	+	1.15132i
$879$		0			0
$880$	−22.9813	−	19.2836i	−0.774701	−	0.650051i
$881$	−10.3923	−	18.0000i	−0.350126	−	0.606435i	0.636146	−	0.771569i	$-0.280528\pi$
$881$	−10.3923	−	18.0000i	−0.350126	−	0.606435i	−0.986271	+	0.165134i	$0.947194\pi$
$882$		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	$0.775349\pi$
$884$	4.88279	−	1.77719i	0.164226	−	0.0597733i
$885$		0			0
$886$	−45.9627	+	38.5673i	−1.54415	+	1.29569i
$887$	−3.25519	−	1.18479i	−0.109299	−	0.0397814i	0.286792	−	0.957993i	$-0.407411\pi$
$887$	−3.25519	−	1.18479i	−0.109299	−	0.0397814i	−0.396091	+	0.918211i	$0.629633\pi$
$888$		0			0
$889$	0.694593	−	3.93923i	0.0232959	−	0.132118i
$890$	15.5885			0.522526
$891$		0			0
$892$	2.00000			0.0669650
$893$	2.40614	−	13.6459i	0.0805184	−	0.456643i
$894$		0			0
$895$	33.8289	+	12.3127i	1.13078	+	0.411569i
$896$	18.5756	−	15.5868i	0.620567	−	0.520717i
$897$		0			0
$898$	−33.8289	+	12.3127i	−1.12889	+	0.410881i
$899$	−6.92820	+	12.0000i	−0.231069	+	0.400222i
$900$		0			0
$901$		0			0
$902$	31.8439	+	26.7202i	1.06028	+	0.889685i
$903$		0			0
$904$	0.520945	+	2.95442i	0.0173264	+	0.0982627i
$905$	−0.601535	−	3.41147i	−0.0199957	−	0.113401i
$906$		0			0
$907$	−39.8343	−	33.4250i	−1.32268	−	1.10986i	−0.985730	−	0.168334i	$-0.946161\pi$
$907$	−39.8343	−	33.4250i	−1.32268	−	1.10986i	−0.336947	−	0.941524i	$-0.609394\pi$
$908$	1.73205	+	3.00000i	0.0574801	+	0.0995585i
$909$		0			0
$910$	−3.00000	+	5.19615i	−0.0994490	+	0.172251i
$911$	22.7863	−	8.29355i	0.754945	−	0.274777i	0.0642599	−	0.997933i	$-0.479531\pi$
$911$	22.7863	−	8.29355i	0.754945	−	0.274777i	0.690685	+	0.723156i	$0.257309\pi$
$912$		0			0
$913$	36.7701	−	30.8538i	1.21691	−	1.02111i
$914$	−47.2003	−	17.1795i	−1.56125	−	0.568247i
$915$		0			0
$916$	−0.173648	+	0.984808i	−0.00573750	+	0.0325390i
$917$	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	$0.489498\pi$
$920$	1.80460	−	10.2344i	0.0594961	−	0.337419i
$921$		0			0
$922$	22.5526	+	8.20848i	0.742731	+	0.270332i
$923$	7.96097	−	6.68004i	0.262038	−	0.219876i
$924$		0			0
$925$	−13.1557	+	4.78828i	−0.432557	+	0.157438i
$926$	−6.92820	+	12.0000i	−0.227675	+	0.394344i
$927$		0			0
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	−38.4780	−	32.2869i	−1.26242	−	1.05930i	−0.995420	−	0.0956026i	$-0.969522\pi$
$929$	−38.4780	−	32.2869i	−1.26242	−	1.05930i	−0.267003	−	0.963696i	$-0.586033\pi$
$930$		0			0
$931$	−1.04189	−	5.90885i	−0.0341465	−	0.193655i
$932$	−4.51151	−	25.5861i	−0.147779	−	0.838099i
$933$		0			0
$934$	−27.5776	−	23.1404i	−0.902367	−	0.757176i
$935$	−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	$0.0327685\pi$
$938$	32.5519	−	11.8479i	1.06286	−	0.386848i
$939$		0			0
$940$	−9.19253	+	7.71345i	−0.299827	+	0.251585i
$941$	−47.2003	−	17.1795i	−1.53868	−	0.560035i	−0.572955	−	0.819587i	$-0.694203\pi$
$941$	−47.2003	−	17.1795i	−1.53868	−	0.560035i	−0.965729	+	0.259551i	$0.916425\pi$
$942$		0			0
$943$	−4.16756	+	23.6354i	−0.135714	+	0.769674i
$944$	−69.2820			−2.25494
$945$		0			0
$946$	−12.0000			−0.390154
$947$	3.00767	−	17.0574i	0.0977363	−	0.554290i	−0.896138	−	0.443775i	$-0.853639\pi$
$947$	3.00767	−	17.0574i	0.0977363	−	0.554290i	0.993874	−	0.110515i	$-0.0352500\pi$
$948$		0			0
$949$	−6.57785	−	2.39414i	−0.213526	−	0.0777171i
$950$	−5.30731	+	4.45336i	−0.172192	+	0.144486i
$951$		0			0
$952$	16.9145	−	6.15636i	0.548201	−	0.199529i
$953$	2.59808	−	4.50000i	0.0841599	−	0.145769i	−0.820873	−	0.571111i	$-0.806513\pi$
$953$	2.59808	−	4.50000i	0.0841599	−	0.145769i	0.905033	+	0.425341i	$0.139846\pi$
$954$		0			0
$955$	15.0000	+	25.9808i	0.485389	+	0.840718i
$956$	−21.2292	−	17.8135i	−0.686603	−	0.576128i
$957$		0			0
$958$	−7.29322	−	41.3619i	−0.235633	−	1.33634i
$959$	0.601535	+	3.41147i	0.0194246	+	0.110162i
$960$		0			0
$961$	25.2795	+	21.2120i	0.815467	+	0.684258i
$962$	−6.06218	−	10.5000i	−0.195452	−	0.338534i
$963$		0			0
$964$	−14.5000	+	25.1147i	−0.467014	+	0.808891i
$965$	−1.62760	+	0.592396i	−0.0523941	+	0.0190699i
$966$		0			0
$967$	−35.2380	+	29.5682i	−1.13318	+	0.950850i	−0.999194	−	0.0401332i	$-0.987222\pi$
$967$	−35.2380	+	29.5682i	−1.13318	+	0.950850i	−0.133985	+	0.990983i	$0.542777\pi$
$968$	1.62760	+	0.592396i	0.0523129	+	0.0190403i
$969$		0			0
$970$	−1.04189	+	5.90885i	−0.0334530	+	0.189722i
$971$	31.1769			1.00051			0.500257	−	0.865877i	$-0.333239\pi$
$971$	31.1769			1.00051			0.500257	+	0.865877i	$0.333239\pi$
$972$		0			0
$973$	16.0000			0.512936
$974$	−4.81228	+	27.2918i	−0.154195	+	0.874485i
$975$		0			0
$976$	−32.8892	−	11.9707i	−1.05276	−	0.383173i
$977$	−37.1512	+	31.1735i	−1.18857	+	0.997330i	−0.188689	+	0.982037i	$0.560424\pi$
$977$	−37.1512	+	31.1735i	−1.18857	+	0.997330i	−0.999883	+	0.0152930i	$0.995132\pi$
$978$		0			0
$979$	−16.9145	+	6.15636i	−0.540589	+	0.196758i
$980$	−2.59808	+	4.50000i	−0.0829925	+	0.143747i
$981$		0			0
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$	−26.5366	−	22.2668i	−0.846385	−	0.710201i	0.112606	−	0.993640i	$-0.464080\pi$
$983$	−26.5366	−	22.2668i	−0.846385	−	0.710201i	−0.958990	+	0.283439i	$0.908525\pi$
$984$		0			0
$985$	1.56283	+	8.86327i	0.0497960	+	0.282407i
$986$	2.70691	+	15.3516i	0.0862055	+	0.488896i
$987$		0			0
$988$	−1.53209	−	1.28558i	−0.0487422	−	0.0408996i
$989$	−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	$-0.0149177\pi$
$992$	39.0623	−	14.2175i	1.24023	−	0.451406i
$993$		0			0
$994$	−27.5776	+	23.1404i	−0.874708	+	0.733967i
$995$	32.5519	+	11.8479i	1.03196	+	0.375604i
$996$		0			0
$997$	−1.21554	+	6.89365i	−0.0384965	+	0.218324i	−0.997987	−	0.0634160i	$-0.979801\pi$
$997$	−1.21554	+	6.89365i	−0.0384965	+	0.218324i	0.959491	+	0.281740i	$0.0909116\pi$
$998$	−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.649.2		12
3.2	odd	2	inner	729.2.e.o.649.1		12
9.2	odd	6	inner	729.2.e.o.163.2		12
9.4	even	3	inner	729.2.e.o.406.2		12
9.5	odd	6	inner	729.2.e.o.406.1		12
9.7	even	3	inner	729.2.e.o.163.1		12
27.2	odd	18		81.2.c.b.55.2		4
27.4	even	9	inner	729.2.e.o.325.2		12
27.5	odd	18	inner	729.2.e.o.568.2		12
27.7	even	9		81.2.c.b.28.1		4
27.11	odd	18		81.2.a.a.1.1	✓	2
27.13	even	9	inner	729.2.e.o.82.2		12
27.14	odd	18	inner	729.2.e.o.82.1		12
27.16	even	9		81.2.a.a.1.2	yes	2
27.20	odd	18		81.2.c.b.28.2		4
27.22	even	9	inner	729.2.e.o.568.1		12
27.23	odd	18	inner	729.2.e.o.325.1		12
27.25	even	9		81.2.c.b.55.1		4
108.7	odd	18		1296.2.i.s.433.2		4
108.11	even	18		1296.2.a.o.1.2		2
108.43	odd	18		1296.2.a.o.1.1		2
108.47	even	18		1296.2.i.s.433.1		4
108.79	odd	18		1296.2.i.s.865.2		4
108.83	even	18		1296.2.i.s.865.1		4
135.38	even	36		2025.2.b.k.649.3		4
135.43	odd	36		2025.2.b.k.649.1		4
135.92	even	36		2025.2.b.k.649.2		4
135.97	odd	36		2025.2.b.k.649.4		4
135.119	odd	18		2025.2.a.j.1.2		2
135.124	even	18		2025.2.a.j.1.1		2
189.97	odd	18		3969.2.a.i.1.2		2
189.146	even	18		3969.2.a.i.1.1		2
216.11	even	18		5184.2.a.bq.1.1		2
216.43	odd	18		5184.2.a.bq.1.2		2
216.173	odd	18		5184.2.a.br.1.1		2
216.205	even	18		5184.2.a.br.1.2		2
297.43	odd	18		9801.2.a.v.1.1		2
297.65	even	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	27.11	odd	18
81.2.a.a.1.2	yes	2	27.16	even	9
81.2.c.b.28.1		4	27.7	even	9
81.2.c.b.28.2		4	27.20	odd	18
81.2.c.b.55.1		4	27.25	even	9
81.2.c.b.55.2		4	27.2	odd	18
729.2.e.o.82.1		12	27.14	odd	18	inner
729.2.e.o.82.2		12	27.13	even	9	inner
729.2.e.o.163.1		12	9.7	even	3	inner
729.2.e.o.163.2		12	9.2	odd	6	inner
729.2.e.o.325.1		12	27.23	odd	18	inner
729.2.e.o.325.2		12	27.4	even	9	inner
729.2.e.o.406.1		12	9.5	odd	6	inner
729.2.e.o.406.2		12	9.4	even	3	inner
729.2.e.o.568.1		12	27.22	even	9	inner
729.2.e.o.568.2		12	27.5	odd	18	inner
729.2.e.o.649.1		12	3.2	odd	2	inner
729.2.e.o.649.2		12	1.1	even	1	trivial
1296.2.a.o.1.1		2	108.43	odd	18
1296.2.a.o.1.2		2	108.11	even	18
1296.2.i.s.433.1		4	108.47	even	18
1296.2.i.s.433.2		4	108.7	odd	18
1296.2.i.s.865.1		4	108.83	even	18
1296.2.i.s.865.2		4	108.79	odd	18
2025.2.a.j.1.1		2	135.124	even	18
2025.2.a.j.1.2		2	135.119	odd	18
2025.2.b.k.649.1		4	135.43	odd	36
2025.2.b.k.649.2		4	135.92	even	36
2025.2.b.k.649.3		4	135.38	even	36
2025.2.b.k.649.4		4	135.97	odd	36
3969.2.a.i.1.1		2	189.146	even	18
3969.2.a.i.1.2		2	189.97	odd	18
5184.2.a.bq.1.1		2	216.11	even	18
5184.2.a.bq.1.2		2	216.43	odd	18
5184.2.a.br.1.1		2	216.173	odd	18
5184.2.a.br.1.2		2	216.205	even	18
9801.2.a.v.1.1		2	297.43	odd	18
9801.2.a.v.1.2		2	297.65	even	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)

\(f(q)\)	\(=\)	\(q+(0.300767 - 1.70574i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-1.32683 + 1.11334i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(0.866025 - 1.50000i) q^{8} +O(q^{10})\)	\(q+(0.300767 - 1.70574i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-1.32683 + 1.11334i) q^{5} +(-1.87939 + 0.684040i) q^{7} +(0.866025 - 1.50000i) q^{8} +(1.50000 + 2.59808i) q^{10} +(-2.65366 - 2.22668i) q^{11} +(-0.173648 - 0.984808i) q^{13} +(0.601535 + 3.41147i) q^{14} +(-3.83022 - 3.21394i) q^{16} +(-2.59808 - 4.50000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(1.62760 - 0.592396i) q^{20} +(-4.59627 + 3.85673i) q^{22} +(-3.25519 - 1.18479i) q^{23} +(-0.347296 + 1.96962i) q^{25} -1.73205 q^{26} +2.00000 q^{28} +(0.300767 - 1.70574i) q^{29} +(-7.51754 - 2.73616i) q^{31} +(-3.98048 + 3.34002i) q^{32} +(-8.45723 + 3.07818i) q^{34} +(1.73205 - 3.00000i) q^{35} +(3.50000 + 6.06218i) q^{37} +(2.65366 + 2.22668i) q^{38} +(0.520945 + 2.95442i) q^{40} +(-1.20307 - 6.82295i) q^{41} +(1.53209 + 1.28558i) q^{43} +(1.73205 + 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-6.51038 + 2.36959i) q^{47} +(-2.29813 + 1.92836i) q^{49} +(3.25519 + 1.18479i) q^{50} +(-0.173648 + 0.984808i) q^{52} +6.00000 q^{55} +(-0.601535 + 3.41147i) q^{56} +(-2.81908 - 1.02606i) q^{58} +(10.6146 - 8.90673i) q^{59} +(6.57785 - 2.39414i) q^{61} +(-6.92820 + 12.0000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(1.32683 + 1.11334i) q^{65} +(-1.73648 - 9.84808i) q^{67} +(0.902302 + 5.11721i) q^{68} +(-4.59627 - 3.85673i) q^{70} +(5.19615 + 9.00000i) q^{71} +(3.50000 - 6.06218i) q^{73} +(11.3932 - 4.14677i) q^{74} +(1.53209 - 1.28558i) q^{76} +(6.51038 + 2.36959i) q^{77} +(0.347296 - 1.96962i) q^{79} +8.66025 q^{80} -12.0000 q^{82} +(-2.40614 + 13.6459i) q^{83} +(8.45723 + 3.07818i) q^{85} +(2.65366 - 2.22668i) q^{86} +(-5.63816 + 2.05212i) q^{88} +(2.59808 - 4.50000i) q^{89} +(1.00000 + 1.73205i) q^{91} +(2.65366 + 2.22668i) q^{92} +(2.08378 + 11.8177i) q^{94} +(-0.601535 - 3.41147i) q^{95} +(1.53209 + 1.28558i) q^{97} +(2.59808 + 4.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 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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