LMFDB - Embedded newform 729.2.e.n.325.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
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 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			325.2
Root			$0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.n.406.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32683 - 1.11334i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-3.25519 + 1.18479i) q^{5} +(-0.173648 - 0.984808i) q^{7} +(0.866025 + 1.50000i) q^{8} +(-3.00000 + 5.19615i) q^{10} +(3.25519 + 1.18479i) q^{11} +(3.83022 + 3.21394i) q^{13} +(-1.32683 - 1.11334i) q^{14} +(4.69846 + 1.71010i) q^{16} +(0.500000 + 0.866025i) q^{19} +(0.601535 + 3.41147i) q^{20} +(5.63816 - 2.05212i) q^{22} +(-1.20307 + 6.82295i) q^{23} +(5.36231 - 4.49951i) q^{25} +8.66025 q^{26} -1.00000 q^{28} +(-2.65366 + 2.22668i) q^{29} +(0.868241 - 4.92404i) q^{31} +(4.88279 - 1.77719i) q^{32} +(1.73205 + 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.62760 + 0.592396i) q^{38} +(-4.59627 - 3.85673i) q^{40} +(2.65366 + 2.22668i) q^{41} +(0.939693 + 0.342020i) q^{43} +(1.73205 - 3.00000i) q^{44} +(6.00000 + 10.3923i) q^{46} +(-0.601535 - 3.41147i) q^{47} +(5.63816 - 2.05212i) q^{49} +(2.10537 - 11.9402i) q^{50} +(3.83022 - 3.21394i) q^{52} -10.3923 q^{53} -12.0000 q^{55} +(1.32683 - 1.11334i) q^{56} +(-1.04189 + 5.90885i) q^{58} +(-3.25519 + 1.18479i) q^{59} +(0.347296 + 1.96962i) q^{61} +(-4.33013 - 7.50000i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-16.2760 - 5.92396i) q^{65} +(6.12836 + 5.14230i) q^{67} +(5.63816 + 2.05212i) q^{70} +(-5.19615 + 9.00000i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(-0.300767 - 1.70574i) q^{74} +(0.939693 - 0.342020i) q^{76} +(0.601535 - 3.41147i) q^{77} +(-0.766044 + 0.642788i) q^{79} -17.3205 q^{80} +6.00000 q^{82} +(5.30731 - 4.45336i) q^{83} +(1.62760 - 0.592396i) q^{86} +(1.04189 + 5.90885i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(2.50000 - 4.33013i) q^{91} +(6.51038 + 2.36959i) q^{92} +(-4.59627 - 3.85673i) q^{94} +(-2.65366 - 2.22668i) q^{95} +(-15.9748 - 5.81434i) q^{97} +(5.19615 - 9.00000i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 36 q^{10} + 6 q^{19} - 12 q^{28} + 6 q^{37} + 72 q^{46} - 144 q^{55} - 6 q^{64} - 12 q^{73} + 72 q^{82} + 30 q^{91}+O(q^{100})$ 12 * q - 36 * q^10 + 6 * q^19 - 12 * q^28 + 6 * q^37 + 72 * q^46 - 144 * q^55 - 6 * q^64 - 12 * q^73 + 72 * q^82 + 30 * q^91

Character values

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

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

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.32683	−	1.11334i	0.938209	−	0.787251i	−0.0390637	−	0.999237i	$-0.512438\pi$
$2$	1.32683	−	1.11334i	0.938209	−	0.787251i	0.977273	+	0.211986i	$0.0679931\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−3.25519	+	1.18479i	−1.45577	+	0.529855i	−0.944195	−	0.329386i	$-0.893158\pi$
$5$	−3.25519	+	1.18479i	−1.45577	+	0.529855i	−0.511570	+	0.859241i	$0.670936\pi$
$6$		0			0
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i	−0.999878	−	0.0155920i	$-0.995037\pi$
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i	0.934246	−	0.356630i	$-0.116074\pi$
$8$	0.866025	+	1.50000i	0.306186	+	0.530330i
$9$		0			0
$10$	−3.00000	+	5.19615i	−0.948683	+	1.64317i
$11$	3.25519	+	1.18479i	0.981477	+	0.357228i	0.782414	−	0.622758i	$-0.213988\pi$
$11$	3.25519	+	1.18479i	0.981477	+	0.357228i	0.199063	+	0.979987i	$0.436210\pi$
$12$		0			0
$13$	3.83022	+	3.21394i	1.06231	+	0.891386i	0.994334	−	0.106301i	$-0.0339006\pi$
$13$	3.83022	+	3.21394i	1.06231	+	0.891386i	0.0679785	+	0.997687i	$0.478345\pi$
$14$	−1.32683	−	1.11334i	−0.354610	−	0.297553i
$15$		0			0
$16$	4.69846	+	1.71010i	1.17462	+	0.427525i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	0.601535	+	3.41147i	0.134507	+	0.762829i
$21$		0			0
$22$	5.63816	−	2.05212i	1.20206	−	0.437514i
$23$	−1.20307	+	6.82295i	−0.250857	+	1.42268i	0.555629	+	0.831430i	$0.312478\pi$
$23$	−1.20307	+	6.82295i	−0.250857	+	1.42268i	−0.806486	+	0.591253i	$0.798634\pi$
$24$		0			0
$25$	5.36231	−	4.49951i	1.07246	−	0.899903i
$26$	8.66025			1.69842
$27$		0			0
$28$	−1.00000			−0.188982
$29$	−2.65366	+	2.22668i	−0.492772	+	0.413484i	−0.855018	−	0.518598i	$-0.826454\pi$
$29$	−2.65366	+	2.22668i	−0.492772	+	0.413484i	0.362247	+	0.932082i	$0.382010\pi$
$30$		0			0
$31$	0.868241	−	4.92404i	0.155941	−	0.884383i	−0.801980	−	0.597351i	$-0.796220\pi$
$31$	0.868241	−	4.92404i	0.155941	−	0.884383i	0.957921	−	0.287033i	$-0.0926689\pi$
$32$	4.88279	−	1.77719i	0.863163	−	0.314166i
$33$		0			0
$34$		0			0
$35$	1.73205	+	3.00000i	0.292770	+	0.507093i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	1.62760	+	0.592396i	0.264031	+	0.0960994i
$39$		0			0
$40$	−4.59627	−	3.85673i	−0.726734	−	0.609802i
$41$	2.65366	+	2.22668i	0.414431	+	0.347749i	0.826040	−	0.563611i	$-0.190588\pi$
$41$	2.65366	+	2.22668i	0.414431	+	0.347749i	−0.411609	+	0.911361i	$0.635033\pi$
$42$		0			0
$43$	0.939693	+	0.342020i	0.143302	+	0.0521576i	0.412675	−	0.910878i	$-0.364594\pi$
$43$	0.939693	+	0.342020i	0.143302	+	0.0521576i	−0.269374	+	0.963036i	$0.586817\pi$
$44$	1.73205	−	3.00000i	0.261116	−	0.452267i
$45$		0			0
$46$	6.00000	+	10.3923i	0.884652	+	1.53226i
$47$	−0.601535	−	3.41147i	−0.0877429	−	0.497615i	−0.996731	−	0.0807925i	$-0.974255\pi$
$47$	−0.601535	−	3.41147i	−0.0877429	−	0.497615i	0.908988	−	0.416822i	$-0.136856\pi$
$48$		0			0
$49$	5.63816	−	2.05212i	0.805451	−	0.293160i
$50$	2.10537	−	11.9402i	0.297745	−	1.68859i
$51$		0			0
$52$	3.83022	−	3.21394i	0.531156	−	0.445693i
$53$	−10.3923			−1.42749			−0.713746	−	0.700404i	$-0.753003\pi$
$53$	−10.3923			−1.42749			−0.713746	+	0.700404i	$0.753003\pi$
$54$		0			0
$55$	−12.0000			−1.61808
$56$	1.32683	−	1.11334i	0.177305	−	0.148776i
$57$		0			0
$58$	−1.04189	+	5.90885i	−0.136807	+	0.775870i
$59$	−3.25519	+	1.18479i	−0.423790	+	0.154247i	−0.545106	−	0.838367i	$-0.683511\pi$
$59$	−3.25519	+	1.18479i	−0.423790	+	0.154247i	0.121316	+	0.992614i	$0.461288\pi$
$60$		0			0
$61$	0.347296	+	1.96962i	0.0444667	+	0.252183i	0.998936	−	0.0461272i	$-0.0146880\pi$
$61$	0.347296	+	1.96962i	0.0444667	+	0.252183i	−0.954469	+	0.298311i	$0.903577\pi$
$62$	−4.33013	−	7.50000i	−0.549927	−	0.952501i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−16.2760	−	5.92396i	−2.01878	−	0.734777i
$66$		0			0
$67$	6.12836	+	5.14230i	0.748698	+	0.628232i	0.935158	−	0.354230i	$-0.115257\pi$
$67$	6.12836	+	5.14230i	0.748698	+	0.628232i	−0.186460	+	0.982462i	$0.559702\pi$
$68$		0			0
$69$		0			0
$70$	5.63816	+	2.05212i	0.673889	+	0.245275i
$71$	−5.19615	+	9.00000i	−0.616670	+	1.06810i	0.373419	+	0.927663i	$0.378185\pi$
$71$	−5.19615	+	9.00000i	−0.616670	+	1.06810i	−0.990089	+	0.140441i	$0.955148\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−0.300767	−	1.70574i	−0.0349635	−	0.198288i
$75$		0			0
$76$	0.939693	−	0.342020i	0.107790	−	0.0392324i
$77$	0.601535	−	3.41147i	0.0685513	−	0.388774i
$78$		0			0
$79$	−0.766044	+	0.642788i	−0.0861867	+	0.0723193i	−0.684863	−	0.728672i	$-0.740138\pi$
$79$	−0.766044	+	0.642788i	−0.0861867	+	0.0723193i	0.598676	+	0.800991i	$0.295694\pi$
$80$	−17.3205			−1.93649
$81$		0			0
$82$	6.00000			0.662589
$83$	5.30731	−	4.45336i	0.582553	−	0.488820i	−0.303231	−	0.952917i	$-0.598065\pi$
$83$	5.30731	−	4.45336i	0.582553	−	0.488820i	0.885784	+	0.464097i	$0.153621\pi$
$84$		0			0
$85$		0			0
$86$	1.62760	−	0.592396i	0.175508	−	0.0638797i
$87$		0			0
$88$	1.04189	+	5.90885i	0.111066	+	0.629885i
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		0			0
$91$	2.50000	−	4.33013i	0.262071	−	0.453921i
$92$	6.51038	+	2.36959i	0.678754	+	0.247046i
$93$		0			0
$94$	−4.59627	−	3.85673i	−0.474069	−	0.397791i
$95$	−2.65366	−	2.22668i	−0.272259	−	0.228453i
$96$		0			0
$97$	−15.9748	−	5.81434i	−1.62199	−	0.590357i	−0.638232	−	0.769844i	$-0.720334\pi$
$97$	−15.9748	−	5.81434i	−1.62199	−	0.590357i	−0.983760	+	0.179487i	$0.942556\pi$
$98$	5.19615	−	9.00000i	0.524891	−	0.909137i
$99$		0			0
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	−2.40614	−	13.6459i	−0.239420	−	1.35782i	−0.833103	−	0.553118i	$-0.813438\pi$
$101$	−2.40614	−	13.6459i	−0.239420	−	1.35782i	0.593683	−	0.804699i	$-0.297673\pi$
$102$		0			0
$103$	−7.51754	+	2.73616i	−0.740725	+	0.269602i	−0.684698	−	0.728827i	$-0.740066\pi$
$103$	−7.51754	+	2.73616i	−0.740725	+	0.269602i	−0.0560277	+	0.998429i	$0.517844\pi$
$104$	−1.50384	+	8.52869i	−0.147463	+	0.836306i
$105$		0			0
$106$	−13.7888	+	11.5702i	−1.33929	+	1.12379i
$107$	10.3923			1.00466			0.502331	−	0.864675i	$-0.332476\pi$
$107$	10.3923			1.00466			0.502331	+	0.864675i	$0.332476\pi$
$108$		0			0
$109$	17.0000			1.62830			0.814152	−	0.580651i	$-0.197202\pi$
$109$	17.0000			1.62830			0.814152	+	0.580651i	$0.197202\pi$
$110$	−15.9219	+	13.3601i	−1.51810	+	1.27383i
$111$		0			0
$112$	0.868241	−	4.92404i	0.0820411	−	0.465278i
$113$	16.2760	−	5.92396i	1.53111	−	0.557280i	0.567219	−	0.823567i	$-0.308019\pi$
$113$	16.2760	−	5.92396i	1.53111	−	0.557280i	0.963894	+	0.266287i	$0.0857970\pi$
$114$		0			0
$115$	−4.16756	−	23.6354i	−0.388627	−	2.20401i
$116$	1.73205	+	3.00000i	0.160817	+	0.278543i
$117$		0			0
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$		0			0
$120$		0			0
$121$	0.766044	+	0.642788i	0.0696404	+	0.0584352i
$122$	2.65366	+	2.22668i	0.240251	+	0.201594i
$123$		0			0
$124$	−4.69846	−	1.71010i	−0.421934	−	0.153572i
$125$	−3.46410	+	6.00000i	−0.309839	+	0.536656i
$126$		0			0
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	−0.945745	−	0.324910i	$-0.894666\pi$
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	0.191492	−	0.981494i	$-0.438667\pi$
$128$	2.10537	+	11.9402i	0.186090	+	1.05537i
$129$		0			0
$130$	−28.1908	+	10.2606i	−2.47249	+	0.899915i
$131$	0.601535	−	3.41147i	0.0525564	−	0.298062i	−0.947188	−	0.320679i	$-0.896089\pi$
$131$	0.601535	−	3.41147i	0.0525564	−	0.298062i	0.999744	+	0.0226174i	$0.00719995\pi$
$132$		0			0
$133$	0.766044	−	0.642788i	0.0664245	−	0.0557368i
$134$	13.8564			1.19701
$135$		0			0
$136$		0			0
$137$	5.30731	−	4.45336i	0.453434	−	0.380476i	−0.387274	−	0.921965i	$-0.626583\pi$
$137$	5.30731	−	4.45336i	0.453434	−	0.380476i	0.840708	+	0.541488i	$0.182139\pi$
$138$		0			0
$139$	−2.25743	+	12.8025i	−0.191472	+	1.08589i	0.725881	+	0.687820i	$0.241432\pi$
$139$	−2.25743	+	12.8025i	−0.191472	+	1.08589i	−0.917353	+	0.398074i	$0.869679\pi$
$140$	3.25519	−	1.18479i	0.275114	−	0.100133i
$141$		0			0
$142$	3.12567	+	17.7265i	0.262300	+	1.48758i
$143$	8.66025	+	15.0000i	0.724207	+	1.25436i
$144$		0			0
$145$	6.00000	−	10.3923i	0.498273	−	0.863034i
$146$	−3.25519	−	1.18479i	−0.269402	−	0.0980541i
$147$		0			0
$148$	−0.766044	−	0.642788i	−0.0629685	−	0.0528368i
$149$	−5.30731	−	4.45336i	−0.434792	−	0.364834i	0.398964	−	0.916966i	$-0.369370\pi$
$149$	−5.30731	−	4.45336i	−0.434792	−	0.364834i	−0.833756	+	0.552133i	$0.813814\pi$
$150$		0			0
$151$	15.0351	+	5.47232i	1.22354	+	0.445331i	0.871380	−	0.490609i	$-0.163226\pi$
$151$	15.0351	+	5.47232i	1.22354	+	0.445331i	0.352158	+	0.935941i	$0.385448\pi$
$152$	−0.866025	+	1.50000i	−0.0702439	+	0.121666i
$153$		0			0
$154$	−3.00000	−	5.19615i	−0.241747	−	0.418718i
$155$	3.00767	+	17.0574i	0.241582	+	1.37008i
$156$		0			0
$157$	12.2160	−	4.44626i	0.974943	−	0.354850i	0.195071	−	0.980789i	$-0.437506\pi$
$157$	12.2160	−	4.44626i	0.974943	−	0.354850i	0.779872	+	0.625939i	$0.215284\pi$
$158$	−0.300767	+	1.70574i	−0.0239278	+	0.135701i
$159$		0			0
$160$	−13.7888	+	11.5702i	−1.09010	+	0.914703i
$161$	6.92820			0.546019
$162$		0			0
$163$	−1.00000			−0.0783260			−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000			−0.0783260			−0.0391630	+	0.999233i	$0.512469\pi$
$164$	2.65366	−	2.22668i	0.207216	−	0.173875i
$165$		0			0
$166$	2.08378	−	11.8177i	0.161733	−	0.917231i
$167$	−22.7863	+	8.29355i	−1.76326	+	0.641774i	−0.999991	−	0.00430705i	$-0.998629\pi$
$167$	−22.7863	+	8.29355i	−1.76326	+	0.641774i	−0.763269	+	0.646081i	$0.776407\pi$
$168$		0			0
$169$	2.08378	+	11.8177i	0.160291	+	0.909053i
$170$		0			0
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	13.0208	+	4.73917i	0.989950	+	0.360312i	0.785701	−	0.618606i	$-0.212302\pi$
$173$	13.0208	+	4.73917i	0.989950	+	0.360312i	0.204249	+	0.978919i	$0.434525\pi$
$174$		0			0
$175$	−5.36231	−	4.49951i	−0.405353	−	0.340131i
$176$	13.2683	+	11.1334i	1.00013	+	0.839212i
$177$		0			0
$178$	−16.9145	−	6.15636i	−1.26779	−	0.461439i
$179$	10.3923	−	18.0000i	0.776757	−	1.34538i	−0.157044	−	0.987592i	$-0.550196\pi$
$179$	10.3923	−	18.0000i	0.776757	−	1.34538i	0.933801	−	0.357792i	$-0.116470\pi$
$180$		0			0
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	−0.987184	−	0.159589i	$-0.948983\pi$
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	0.355383	−	0.934721i	$-0.384350\pi$
$182$	−1.50384	−	8.52869i	−0.111472	−	0.632188i
$183$		0			0
$184$	−11.2763	+	4.10424i	−0.831301	+	0.302569i
$185$	−0.601535	+	3.41147i	−0.0442257	+	0.250817i
$186$		0			0
$187$		0			0
$188$	−3.46410			−0.252646
$189$		0			0
$190$	−6.00000			−0.435286
$191$	5.30731	−	4.45336i	0.384024	−	0.322234i	−0.430256	−	0.902707i	$-0.641577\pi$
$191$	5.30731	−	4.45336i	0.384024	−	0.322234i	0.814280	+	0.580473i	$0.197132\pi$
$192$		0			0
$193$	−1.73648	+	9.84808i	−0.124995	+	0.708880i	0.856316	+	0.516452i	$0.172747\pi$
$193$	−1.73648	+	9.84808i	−0.124995	+	0.708880i	−0.981311	+	0.192428i	$0.938364\pi$
$194$	−27.6691	+	10.0707i	−1.98653	+	0.723037i
$195$		0			0
$196$	−1.04189	−	5.90885i	−0.0744206	−	0.422060i
$197$	5.19615	+	9.00000i	0.370211	+	0.641223i	0.989598	−	0.143862i	$-0.0459522\pi$
$197$	5.19615	+	9.00000i	0.370211	+	0.641223i	−0.619387	+	0.785086i	$0.712619\pi$
$198$		0			0
$199$	9.50000	−	16.4545i	0.673437	−	1.16643i	−0.303486	−	0.952836i	$-0.598151\pi$
$199$	9.50000	−	16.4545i	0.673437	−	1.16643i	0.976923	−	0.213591i	$-0.0685161\pi$
$200$	11.3932	+	4.14677i	0.805619	+	0.293221i
$201$		0			0
$202$	−18.3851	−	15.4269i	−1.29357	−	1.08543i
$203$	2.65366	+	2.22668i	0.186250	+	0.156282i
$204$		0			0
$205$	−11.2763	−	4.10424i	−0.787572	−	0.286653i
$206$	−6.92820	+	12.0000i	−0.482711	+	0.836080i
$207$		0			0
$208$	12.5000	+	21.6506i	0.866719	+	1.50120i
$209$	0.601535	+	3.41147i	0.0416090	+	0.235977i
$210$		0			0
$211$	−4.69846	+	1.71010i	−0.323456	+	0.117728i	−0.498644	−	0.866807i	$-0.666169\pi$
$211$	−4.69846	+	1.71010i	−0.323456	+	0.117728i	0.175189	+	0.984535i	$0.443946\pi$
$212$	−1.80460	+	10.2344i	−0.123941	+	0.702903i
$213$		0			0
$214$	13.7888	−	11.5702i	0.942583	−	0.790921i
$215$	−3.46410			−0.236250
$216$		0			0
$217$	−5.00000			−0.339422
$218$	22.5561	−	18.9268i	1.52769	−	1.28188i
$219$		0			0
$220$	−2.08378	+	11.8177i	−0.140488	+	0.796749i
$221$		0			0
$222$		0			0
$223$	−3.29932	−	18.7113i	−0.220938	−	1.25300i	−0.870299	−	0.492524i	$-0.836074\pi$
$223$	−3.29932	−	18.7113i	−0.220938	−	1.25300i	0.649360	−	0.760481i	$-0.275037\pi$
$224$	−2.59808	−	4.50000i	−0.173591	−	0.300669i
$225$		0			0
$226$	15.0000	−	25.9808i	0.997785	−	1.72821i
$227$	13.0208	+	4.73917i	0.864218	+	0.314550i	0.735824	−	0.677173i	$-0.236795\pi$
$227$	13.0208	+	4.73917i	0.864218	+	0.314550i	0.128395	+	0.991723i	$0.459018\pi$
$228$		0			0
$229$	3.83022	+	3.21394i	0.253108	+	0.212383i	0.760509	−	0.649327i	$-0.224949\pi$
$229$	3.83022	+	3.21394i	0.253108	+	0.212383i	−0.507401	+	0.861710i	$0.669394\pi$
$230$	−31.8439	−	26.7202i	−2.09972	−	1.76188i
$231$		0			0
$232$	−5.63816	−	2.05212i	−0.370163	−	0.134728i
$233$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$233$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$234$		0			0
$235$	6.00000	+	10.3923i	0.391397	+	0.677919i
$236$	0.601535	+	3.41147i	0.0391566	+	0.222068i
$237$		0			0
$238$		0			0
$239$	−1.20307	+	6.82295i	−0.0778201	+	0.441340i	0.920856	+	0.389903i	$0.127491\pi$
$239$	−1.20307	+	6.82295i	−0.0778201	+	0.441340i	−0.998676	+	0.0514372i	$0.983620\pi$
$240$		0			0
$241$	−14.5548	+	12.2130i	−0.937560	+	0.786706i	−0.977159	−	0.212509i	$-0.931836\pi$
$241$	−14.5548	+	12.2130i	−0.937560	+	0.786706i	0.0395991	+	0.999216i	$0.487392\pi$
$242$	1.73205			0.111340
$243$		0			0
$244$	2.00000			0.128037
$245$	−15.9219	+	13.3601i	−1.01722	+	0.853545i
$246$		0			0
$247$	−0.868241	+	4.92404i	−0.0552448	+	0.313309i
$248$	8.13798	−	2.96198i	0.516762	−	0.188086i
$249$		0			0
$250$	2.08378	+	11.8177i	0.131790	+	0.747417i
$251$	−10.3923	−	18.0000i	−0.655956	−	1.13615i	−0.981653	−	0.190676i	$-0.938932\pi$
$251$	−10.3923	−	18.0000i	−0.655956	−	1.13615i	0.325697	−	0.945474i	$-0.394401\pi$
$252$		0			0
$253$	−12.0000	+	20.7846i	−0.754434	+	1.30672i
$254$	−27.6691	−	10.0707i	−1.73612	−	0.631894i
$255$		0			0
$256$	14.5548	+	12.2130i	0.909678	+	0.763310i
$257$	2.65366	+	2.22668i	0.165531	+	0.138897i	0.721790	−	0.692112i	$-0.243320\pi$
$257$	2.65366	+	2.22668i	0.165531	+	0.138897i	−0.556260	+	0.831009i	$0.687764\pi$
$258$		0			0
$259$	−0.939693	−	0.342020i	−0.0583897	−	0.0212521i
$260$	−8.66025	+	15.0000i	−0.537086	+	0.930261i
$261$		0			0
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−2.40614	−	13.6459i	−0.148369	−	0.841442i	−0.964600	−	0.263717i	$-0.915052\pi$
$263$	−2.40614	−	13.6459i	−0.148369	−	0.841442i	0.816231	−	0.577725i	$-0.196060\pi$
$264$		0			0
$265$	33.8289	−	12.3127i	2.07809	−	0.756365i
$266$	0.300767	−	1.70574i	0.0184412	−	0.104585i
$267$		0			0
$268$	6.12836	−	5.14230i	0.374349	−	0.314116i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$		0			0
$273$		0			0
$274$	2.08378	−	11.8177i	0.125886	−	0.713933i
$275$	22.7863	−	8.29355i	1.37407	−	0.500120i
$276$		0			0
$277$	2.95202	+	16.7417i	0.177370	+	1.00591i	0.935373	+	0.353663i	$0.115064\pi$
$277$	2.95202	+	16.7417i	0.177370	+	1.00591i	−0.758003	+	0.652251i	$0.773825\pi$
$278$	11.2583	+	19.5000i	0.675230	+	1.16953i
$279$		0			0
$280$	−3.00000	+	5.19615i	−0.179284	+	0.310530i
$281$	13.0208	+	4.73917i	0.776754	+	0.282715i	0.699818	−	0.714321i	$-0.253264\pi$
$281$	13.0208	+	4.73917i	0.776754	+	0.282715i	0.0769353	+	0.997036i	$0.475487\pi$
$282$		0			0
$283$	−9.95858	−	8.35624i	−0.591976	−	0.496727i	0.296879	−	0.954915i	$-0.404054\pi$
$283$	−9.95858	−	8.35624i	−0.591976	−	0.496727i	−0.888855	+	0.458188i	$0.848499\pi$
$284$	7.96097	+	6.68004i	0.472397	+	0.396388i
$285$		0			0
$286$	28.1908	+	10.2606i	1.66696	+	0.606722i
$287$	1.73205	−	3.00000i	0.102240	−	0.177084i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−3.60921	−	20.4688i	−0.211940	−	1.20197i
$291$		0			0
$292$	−1.87939	+	0.684040i	−0.109983	+	0.0400304i
$293$	2.40614	−	13.6459i	0.140568	−	0.797202i	−0.830251	−	0.557390i	$-0.811803\pi$
$293$	2.40614	−	13.6459i	0.140568	−	0.797202i	0.970819	−	0.239812i	$-0.0770859\pi$
$294$		0			0
$295$	9.19253	−	7.71345i	0.535210	−	0.449094i
$296$	1.73205			0.100673
$297$		0			0
$298$	−12.0000			−0.695141
$299$	−26.5366	+	22.2668i	−1.53465	+	1.28772i
$300$		0			0
$301$	0.173648	−	0.984808i	0.0100089	−	0.0567634i
$302$	26.0415	−	9.47834i	1.49852	−	0.545417i
$303$		0			0
$304$	0.868241	+	4.92404i	0.0497970	+	0.282413i
$305$	−3.46410	−	6.00000i	−0.198354	−	0.343559i
$306$		0			0
$307$	−10.0000	+	17.3205i	−0.570730	+	0.988534i	0.425761	+	0.904836i	$0.360006\pi$
$307$	−10.0000	+	17.3205i	−0.570730	+	0.988534i	−0.996491	+	0.0836980i	$0.973327\pi$
$308$	−3.25519	−	1.18479i	−0.185482	−	0.0675098i
$309$		0			0
$310$	22.9813	+	19.2836i	1.30525	+	1.09524i
$311$	10.6146	+	8.90673i	0.601900	+	0.505054i	0.892056	−	0.451925i	$-0.149263\pi$
$311$	10.6146	+	8.90673i	0.601900	+	0.505054i	−0.290156	+	0.956979i	$0.593707\pi$
$312$		0			0
$313$	0.939693	+	0.342020i	0.0531146	+	0.0193321i	0.368441	−	0.929651i	$-0.379892\pi$
$313$	0.939693	+	0.342020i	0.0531146	+	0.0193321i	−0.315326	+	0.948983i	$0.602114\pi$
$314$	11.2583	−	19.5000i	0.635344	−	1.10045i
$315$		0			0
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	4.81228	+	27.2918i	0.270285	+	1.53286i	0.753553	+	0.657387i	$0.228338\pi$
$317$	4.81228	+	27.2918i	0.270285	+	1.53286i	−0.483268	+	0.875472i	$0.660550\pi$
$318$		0			0
$319$	−11.2763	+	4.10424i	−0.631352	+	0.229793i
$320$	0.601535	−	3.41147i	0.0336268	−	0.190707i
$321$		0			0
$322$	9.19253	−	7.71345i	0.512280	−	0.429854i
$323$		0			0
$324$		0			0
$325$	35.0000			1.94145
$326$	−1.32683	+	1.11334i	−0.0734862	+	0.0616622i
$327$		0			0
$328$	−1.04189	+	5.90885i	−0.0575287	+	0.326261i
$329$	−3.25519	+	1.18479i	−0.179464	+	0.0653197i
$330$		0			0
$331$	−3.29932	−	18.7113i	−0.181347	−	1.02847i	−0.930560	−	0.366140i	$-0.880679\pi$
$331$	−3.29932	−	18.7113i	−0.181347	−	1.02847i	0.749213	−	0.662329i	$-0.230432\pi$
$332$	−3.46410	−	6.00000i	−0.190117	−	0.329293i
$333$		0			0
$334$	−21.0000	+	36.3731i	−1.14907	+	1.99025i
$335$	−26.0415	−	9.47834i	−1.42280	−	0.517857i
$336$		0			0
$337$	3.83022	+	3.21394i	0.208645	+	0.175074i	0.741122	−	0.671370i	$-0.234294\pi$
$337$	3.83022	+	3.21394i	0.208645	+	0.175074i	−0.532476	+	0.846445i	$0.678738\pi$
$338$	15.9219	+	13.3601i	0.866039	+	0.726693i
$339$		0			0
$340$		0			0
$341$	8.66025	−	15.0000i	0.468979	−	0.812296i
$342$		0			0
$343$	−6.50000	−	11.2583i	−0.350967	−	0.607893i
$344$	0.300767	+	1.70574i	0.0162163	+	0.0919672i
$345$		0			0
$346$	22.5526	−	8.20848i	1.21244	−	0.441291i
$347$	4.21074	−	23.8803i	0.226045	−	1.28196i	−0.634634	−	0.772813i	$-0.718849\pi$
$347$	4.21074	−	23.8803i	0.226045	−	1.28196i	0.860678	−	0.509149i	$-0.170040\pi$
$348$		0			0
$349$	−0.766044	+	0.642788i	−0.0410054	+	0.0344076i	−0.663060	−	0.748566i	$-0.730743\pi$
$349$	−0.766044	+	0.642788i	−0.0410054	+	0.0344076i	0.622055	+	0.782974i	$0.286298\pi$
$350$	−12.1244			−0.648074
$351$		0			0
$352$	18.0000			0.959403
$353$	13.2683	−	11.1334i	0.706199	−	0.592572i	−0.217331	−	0.976098i	$-0.569735\pi$
$353$	13.2683	−	11.1334i	0.706199	−	0.592572i	0.923530	+	0.383527i	$0.125291\pi$
$354$		0			0
$355$	6.25133	−	35.4531i	0.331786	−	1.88165i
$356$	−9.76557	+	3.55438i	−0.517574	+	0.188382i
$357$		0			0
$358$	−6.25133	−	35.4531i	−0.330393	−	1.87375i
$359$	−15.5885	−	27.0000i	−0.822727	−	1.42501i	−0.903644	−	0.428285i	$-0.859118\pi$
$359$	−15.5885	−	27.0000i	−0.822727	−	1.42501i	0.0809166	−	0.996721i	$-0.474215\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−27.6691	−	10.0707i	−1.45426	−	0.529306i
$363$		0			0
$364$	−3.83022	−	3.21394i	−0.200758	−	0.168456i
$365$	5.30731	+	4.45336i	0.277797	+	0.233100i
$366$		0			0
$367$	15.0351	+	5.47232i	0.784825	+	0.285653i	0.703183	−	0.711009i	$-0.251761\pi$
$367$	15.0351	+	5.47232i	0.784825	+	0.285653i	0.0816418	+	0.996662i	$0.473984\pi$
$368$	−17.3205	+	30.0000i	−0.902894	+	1.56386i
$369$		0			0
$370$	3.00000	+	5.19615i	0.155963	+	0.270135i
$371$	1.80460	+	10.2344i	0.0936904	+	0.531345i
$372$		0			0
$373$	−21.6129	+	7.86646i	−1.11908	+	0.407310i	−0.834315	−	0.551289i	$-0.814136\pi$
$373$	−21.6129	+	7.86646i	−1.11908	+	0.407310i	−0.284761	+	0.958599i	$0.591914\pi$
$374$		0			0
$375$		0			0
$376$	4.59627	−	3.85673i	0.237034	−	0.198895i
$377$	−17.3205			−0.892052
$378$		0			0
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$	−2.65366	+	2.22668i	−0.136130	+	0.114226i
$381$		0			0
$382$	2.08378	−	11.8177i	0.106615	−	0.604646i
$383$	16.2760	−	5.92396i	0.831662	−	0.302700i	0.109121	−	0.994028i	$-0.465196\pi$
$383$	16.2760	−	5.92396i	0.831662	−	0.302700i	0.722541	+	0.691328i	$0.242974\pi$
$384$		0			0
$385$	2.08378	+	11.8177i	0.106199	+	0.602285i
$386$	8.66025	+	15.0000i	0.440795	+	0.763480i
$387$		0			0
$388$	−8.50000	+	14.7224i	−0.431522	+	0.747418i
$389$	−6.51038	−	2.36959i	−0.330089	−	0.120143i	0.171659	−	0.985156i	$-0.445087\pi$
$389$	−6.51038	−	2.36959i	−0.330089	−	0.120143i	−0.501748	+	0.865014i	$0.667310\pi$
$390$		0			0
$391$		0			0
$392$	7.96097	+	6.68004i	0.402090	+	0.337393i
$393$		0			0
$394$	16.9145	+	6.15636i	0.852139	+	0.310153i
$395$	1.73205	−	3.00000i	0.0871489	−	0.150946i
$396$		0			0
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−5.71458	−	32.4090i	−0.286446	−	1.62452i
$399$		0			0
$400$	32.8892	−	11.9707i	1.64446	−	0.598535i
$401$	0.601535	−	3.41147i	0.0300392	−	0.170361i	−0.966097	−	0.258178i	$-0.916878\pi$
$401$	0.601535	−	3.41147i	0.0300392	−	0.170361i	0.996137	+	0.0878170i	$0.0279891\pi$
$402$		0			0
$403$	19.1511	−	16.0697i	0.953985	−	0.800488i
$404$	−13.8564			−0.689382
$405$		0			0
$406$	6.00000			0.297775
$407$	2.65366	−	2.22668i	0.131537	−	0.110373i
$408$		0			0
$409$	0.868241	−	4.92404i	0.0429317	−	0.243478i	−0.955788	−	0.294055i	$-0.904995\pi$
$409$	0.868241	−	4.92404i	0.0429317	−	0.243478i	0.998720	+	0.0505773i	$0.0161061\pi$
$410$	−19.5311	+	7.10876i	−0.964574	+	0.351076i
$411$		0			0
$412$	1.38919	+	7.87846i	0.0684403	+	0.388144i
$413$	1.73205	+	3.00000i	0.0852286	+	0.147620i
$414$		0			0
$415$	−12.0000	+	20.7846i	−0.589057	+	1.02028i
$416$	24.4139	+	8.88594i	1.19699	+	0.435669i
$417$		0			0
$418$	4.59627	+	3.85673i	0.224811	+	0.188639i
$419$	−29.1902	−	24.4935i	−1.42604	−	1.19659i	−0.948010	−	0.318239i	$-0.896908\pi$
$419$	−29.1902	−	24.4935i	−1.42604	−	1.19659i	−0.478025	−	0.878346i	$-0.658647\pi$
$420$		0			0
$421$	17.8542	+	6.49838i	0.870159	+	0.316712i	0.738231	−	0.674548i	$-0.235661\pi$
$421$	17.8542	+	6.49838i	0.870159	+	0.316712i	0.131927	+	0.991259i	$0.457883\pi$
$422$	−4.33013	+	7.50000i	−0.210787	+	0.365094i
$423$		0			0
$424$	−9.00000	−	15.5885i	−0.437079	−	0.757042i
$425$		0			0
$426$		0			0
$427$	1.87939	−	0.684040i	0.0909498	−	0.0331030i
$428$	1.80460	−	10.2344i	0.0872289	−	0.494699i
$429$		0			0
$430$	−4.59627	+	3.85673i	−0.221652	+	0.185988i
$431$	−20.7846			−1.00116			−0.500580	−	0.865690i	$-0.666880\pi$
$431$	−20.7846			−1.00116			−0.500580	+	0.865690i	$0.666880\pi$
$432$		0			0
$433$	−1.00000			−0.0480569			−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000			−0.0480569			−0.0240285	+	0.999711i	$0.507649\pi$
$434$	−6.63414	+	5.56670i	−0.318449	+	0.267210i
$435$		0			0
$436$	2.95202	−	16.7417i	0.141376	−	0.801784i
$437$	−6.51038	+	2.36959i	−0.311434	+	0.113353i
$438$		0			0
$439$	3.47296	+	19.6962i	0.165756	+	0.940046i	0.948282	+	0.317429i	$0.102820\pi$
$439$	3.47296	+	19.6962i	0.165756	+	0.940046i	−0.782527	+	0.622617i	$0.786069\pi$
$440$	−10.3923	−	18.0000i	−0.495434	−	0.858116i
$441$		0			0
$442$		0			0
$443$	13.0208	+	4.73917i	0.618635	+	0.225165i	0.632277	−	0.774742i	$-0.282120\pi$
$443$	13.0208	+	4.73917i	0.618635	+	0.225165i	−0.0136422	+	0.999907i	$0.504343\pi$
$444$		0			0
$445$	27.5776	+	23.1404i	1.30730	+	1.09696i
$446$	−25.2097	−	21.1535i	−1.19372	−	1.00165i
$447$		0			0
$448$	0.939693	+	0.342020i	0.0443963	+	0.0161589i
$449$	5.19615	−	9.00000i	0.245222	−	0.424736i	−0.716972	−	0.697102i	$-0.754473\pi$
$449$	5.19615	−	9.00000i	0.245222	−	0.424736i	0.962194	+	0.272365i	$0.0878059\pi$
$450$		0			0
$451$	6.00000	+	10.3923i	0.282529	+	0.489355i
$452$	−3.00767	−	17.0574i	−0.141469	−	0.802311i
$453$		0			0
$454$	22.5526	−	8.20848i	1.05845	−	0.385243i
$455$	−3.00767	+	17.0574i	−0.141002	+	0.799662i
$456$		0			0
$457$	13.0228	−	10.9274i	0.609179	−	0.511162i	−0.285202	−	0.958467i	$-0.592061\pi$
$457$	13.0228	−	10.9274i	0.609179	−	0.511162i	0.894381	+	0.447306i	$0.147616\pi$
$458$	8.66025			0.404667
$459$		0			0
$460$	−24.0000			−1.11901
$461$	21.2292	−	17.8135i	0.988745	−	0.829655i	0.00335908	−	0.999994i	$-0.498931\pi$
$461$	21.2292	−	17.8135i	0.988745	−	0.829655i	0.985385	+	0.170339i	$0.0544863\pi$
$462$		0			0
$463$	−5.38309	+	30.5290i	−0.250174	+	1.41880i	0.557990	+	0.829847i	$0.311573\pi$
$463$	−5.38309	+	30.5290i	−0.250174	+	1.41880i	−0.808164	+	0.588957i	$0.799539\pi$
$464$	−16.2760	+	5.92396i	−0.755592	+	0.275013i
$465$		0			0
$466$		0			0
$467$	5.19615	+	9.00000i	0.240449	+	0.416470i	0.960842	−	0.277096i	$-0.0893719\pi$
$467$	5.19615	+	9.00000i	0.240449	+	0.416470i	−0.720393	+	0.693566i	$0.756039\pi$
$468$		0			0
$469$	4.00000	−	6.92820i	0.184703	−	0.319915i
$470$	19.5311	+	7.10876i	0.900905	+	0.327902i
$471$		0			0
$472$	−4.59627	−	3.85673i	−0.211560	−	0.177520i
$473$	2.65366	+	2.22668i	0.122015	+	0.102383i
$474$		0			0
$475$	6.57785	+	2.39414i	0.301812	+	0.109851i
$476$		0			0
$477$		0			0
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	−2.40614	−	13.6459i	−0.109939	−	0.623497i	−0.989132	−	0.147030i	$-0.953028\pi$
$479$	−2.40614	−	13.6459i	−0.109939	−	0.623497i	0.879193	−	0.476466i	$-0.158083\pi$
$480$		0			0
$481$	4.69846	−	1.71010i	0.214231	−	0.0779739i
$482$	−5.71458	+	32.4090i	−0.260292	+	1.47619i
$483$		0			0
$484$	0.766044	−	0.642788i	0.0348202	−	0.0292176i
$485$	58.8897			2.67404
$486$		0			0
$487$	−19.0000			−0.860972			−0.430486	−	0.902597i	$-0.641658\pi$
$487$	−19.0000			−0.860972			−0.430486	+	0.902597i	$0.641658\pi$
$488$	−2.65366	+	2.22668i	−0.120125	+	0.100797i
$489$		0			0
$490$	−6.25133	+	35.4531i	−0.282407	+	1.60161i
$491$	35.8071	−	13.0327i	1.61595	−	0.588158i	0.633347	−	0.773868i	$-0.281681\pi$
$491$	35.8071	−	13.0327i	1.61595	−	0.588158i	0.982605	+	0.185710i	$0.0594584\pi$
$492$		0			0
$493$		0			0
$494$	4.33013	+	7.50000i	0.194822	+	0.337441i
$495$		0			0
$496$	12.5000	−	21.6506i	0.561267	−	0.972142i
$497$	9.76557	+	3.55438i	0.438046	+	0.159436i
$498$		0			0
$499$	−21.4492	−	17.9981i	−0.960200	−	0.805704i	0.0207856	−	0.999784i	$-0.493383\pi$
$499$	−21.4492	−	17.9981i	−0.960200	−	0.805704i	−0.980986	+	0.194080i	$0.937828\pi$
$500$	5.30731	+	4.45336i	0.237350	+	0.199160i
$501$		0			0
$502$	−33.8289	−	12.3127i	−1.50986	−	0.549544i
$503$	−20.7846	+	36.0000i	−0.926740	+	1.60516i	−0.138001	+	0.990432i	$0.544068\pi$
$503$	−20.7846	+	36.0000i	−0.926740	+	1.60516i	−0.788739	+	0.614729i	$0.789266\pi$
$504$		0			0
$505$	24.0000	+	41.5692i	1.06799	+	1.84981i
$506$	7.21842	+	40.9377i	0.320898	+	1.81990i
$507$		0			0
$508$	−15.9748	+	5.81434i	−0.708766	+	0.257970i
$509$	−4.81228	+	27.2918i	−0.213301	+	1.20969i	0.670531	+	0.741882i	$0.266066\pi$
$509$	−4.81228	+	27.2918i	−0.213301	+	1.20969i	−0.883831	+	0.467806i	$0.845045\pi$
$510$		0			0
$511$	−1.53209	+	1.28558i	−0.0677756	+	0.0568705i
$512$	8.66025			0.382733
$513$		0			0
$514$	6.00000			0.264649
$515$	21.2292	−	17.8135i	0.935472	−	0.784955i
$516$		0			0
$517$	2.08378	−	11.8177i	0.0916445	−	0.519742i
$518$	−1.62760	+	0.592396i	−0.0715124	+	0.0260284i
$519$		0			0
$520$	−5.20945	−	29.5442i	−0.228449	−	1.29560i
$521$	10.3923	+	18.0000i	0.455295	+	0.788594i	0.998705	−	0.0508731i	$-0.0162004\pi$
$521$	10.3923	+	18.0000i	0.455295	+	0.788594i	−0.543410	+	0.839467i	$0.682867\pi$
$522$		0			0
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	−3.25519	−	1.18479i	−0.142204	−	0.0517579i
$525$		0			0
$526$	−18.3851	−	15.4269i	−0.801627	−	0.672645i
$527$		0			0
$528$		0			0
$529$	−23.4923	−	8.55050i	−1.02141	−	0.371761i
$530$	31.1769	−	54.0000i	1.35424	−	2.34561i
$531$		0			0
$532$	−0.500000	−	0.866025i	−0.0216777	−	0.0375470i
$533$	3.00767	+	17.0574i	0.130277	+	0.738837i
$534$		0			0
$535$	−33.8289	+	12.3127i	−1.46255	+	0.532326i
$536$	−2.40614	+	13.6459i	−0.103929	+	0.589413i
$537$		0			0
$538$		0			0
$539$	20.7846			0.895257
$540$		0			0
$541$	17.0000			0.730887			0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000			0.730887			0.365444	+	0.930834i	$0.380917\pi$
$542$	−21.2292	+	17.8135i	−0.911874	+	0.765153i
$543$		0			0
$544$		0			0
$545$	−55.3382	+	20.1415i	−2.37043	+	0.862766i
$546$		0			0
$547$	3.47296	+	19.6962i	0.148493	+	0.842147i	0.964496	+	0.264098i	$0.0850744\pi$
$547$	3.47296	+	19.6962i	0.148493	+	0.842147i	−0.816003	+	0.578048i	$0.803815\pi$
$548$	−3.46410	−	6.00000i	−0.147979	−	0.256307i
$549$		0			0
$550$	21.0000	−	36.3731i	0.895443	−	1.55095i
$551$	−3.25519	−	1.18479i	−0.138676	−	0.0504739i
$552$		0			0
$553$	0.766044	+	0.642788i	0.0325755	+	0.0273341i
$554$	22.5561	+	18.9268i	0.958316	+	0.804122i
$555$		0			0
$556$	12.2160	+	4.44626i	0.518074	+	0.188564i
$557$	−5.19615	+	9.00000i	−0.220168	+	0.381342i	−0.954859	−	0.297060i	$-0.903994\pi$
$557$	−5.19615	+	9.00000i	−0.220168	+	0.381342i	0.734691	+	0.678402i	$0.237327\pi$
$558$		0			0
$559$	2.50000	+	4.33013i	0.105739	+	0.183145i
$560$	3.00767	+	17.0574i	0.127097	+	0.720805i
$561$		0			0
$562$	22.5526	−	8.20848i	0.951325	−	0.346254i
$563$	6.01535	−	34.1147i	0.253517	−	1.43776i	−0.546335	−	0.837567i	$-0.683977\pi$
$563$	6.01535	−	34.1147i	0.253517	−	1.43776i	0.799851	−	0.600198i	$-0.204912\pi$
$564$		0			0
$565$	−45.9627	+	38.5673i	−1.93366	+	1.62254i
$566$	−22.5167			−0.946446
$567$		0			0
$568$	−18.0000			−0.755263
$569$	−18.5756	+	15.5868i	−0.778729	+	0.653431i	−0.942928	−	0.332996i	$-0.891941\pi$
$569$	−18.5756	+	15.5868i	−0.778729	+	0.653431i	0.164199	+	0.986427i	$0.447496\pi$
$570$		0			0
$571$	7.11958	−	40.3771i	0.297945	−	1.68973i	−0.357041	−	0.934089i	$-0.616214\pi$
$571$	7.11958	−	40.3771i	0.297945	−	1.68973i	0.654986	−	0.755641i	$-0.272675\pi$
$572$	16.2760	−	5.92396i	0.680532	−	0.247693i
$573$		0			0
$574$	−1.04189	−	5.90885i	−0.0434876	−	0.246630i
$575$	24.2487	+	42.0000i	1.01124	+	1.75152i
$576$		0			0
$577$	17.0000	−	29.4449i	0.707719	−	1.22581i	−0.257982	−	0.966150i	$-0.583058\pi$
$577$	17.0000	−	29.4449i	0.707719	−	1.22581i	0.965701	−	0.259656i	$-0.0836092\pi$
$578$	27.6691	+	10.0707i	1.15088	+	0.418887i
$579$		0			0
$580$	−9.19253	−	7.71345i	−0.381699	−	0.320284i
$581$	−5.30731	−	4.45336i	−0.220184	−	0.184757i
$582$		0			0
$583$	−33.8289	−	12.3127i	−1.40105	−	0.509941i
$584$	1.73205	−	3.00000i	0.0716728	−	0.124141i
$585$		0			0
$586$	−12.0000	−	20.7846i	−0.495715	−	0.858604i
$587$	1.20307	+	6.82295i	0.0496560	+	0.281613i	0.999518	−	0.0310575i	$-0.00988749\pi$
$587$	1.20307	+	6.82295i	0.0496560	+	0.281613i	−0.949862	+	0.312671i	$0.898776\pi$
$588$		0			0
$589$	4.69846	−	1.71010i	0.193597	−	0.0704635i
$590$	3.60921	−	20.4688i	0.148589	−	0.842689i
$591$		0			0
$592$	3.83022	−	3.21394i	0.157421	−	0.132092i
$593$	20.7846			0.853522			0.426761	−	0.904365i	$-0.359655\pi$
$593$	20.7846			0.853522			0.426761	+	0.904365i	$0.359655\pi$
$594$		0			0
$595$		0			0
$596$	−5.30731	+	4.45336i	−0.217396	+	0.182417i
$597$		0			0
$598$	−10.4189	+	59.0885i	−0.426060	+	2.41631i
$599$	−22.7863	+	8.29355i	−0.931024	+	0.338865i	−0.762616	−	0.646852i	$-0.776085\pi$
$599$	−22.7863	+	8.29355i	−0.931024	+	0.338865i	−0.168409	+	0.985717i	$0.553863\pi$
$600$		0			0
$601$	6.07769	+	34.4683i	0.247914	+	1.40599i	0.813627	+	0.581388i	$0.197490\pi$
$601$	6.07769	+	34.4683i	0.247914	+	1.40599i	−0.565713	+	0.824602i	$0.691399\pi$
$602$	−0.866025	−	1.50000i	−0.0352966	−	0.0611354i
$603$		0			0
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$	−3.25519	−	1.18479i	−0.132342	−	0.0481687i
$606$		0			0
$607$	−9.95858	−	8.35624i	−0.404206	−	0.339169i	0.417911	−	0.908488i	$-0.362763\pi$
$607$	−9.95858	−	8.35624i	−0.404206	−	0.339169i	−0.822117	+	0.569319i	$0.807207\pi$
$608$	3.98048	+	3.34002i	0.161430	+	0.135456i
$609$		0			0
$610$	−11.2763	−	4.10424i	−0.456565	−	0.166176i
$611$	8.66025	−	15.0000i	0.350356	−	0.606835i
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	6.01535	+	34.1147i	0.242760	+	1.37676i
$615$		0			0
$616$	5.63816	−	2.05212i	0.227168	−	0.0826823i
$617$	−1.20307	+	6.82295i	−0.0484338	+	0.274682i	−0.999401	−	0.0346105i	$-0.988981\pi$
$617$	−1.20307	+	6.82295i	−0.0484338	+	0.274682i	0.950967	+	0.309292i	$0.100092\pi$
$618$		0			0
$619$	15.3209	−	12.8558i	0.615799	−	0.516716i	−0.280681	−	0.959801i	$-0.590560\pi$
$619$	15.3209	−	12.8558i	0.615799	−	0.516716i	0.896480	+	0.443085i	$0.146116\pi$
$620$	17.3205			0.695608
$621$		0			0
$622$	24.0000			0.962312
$623$	−7.96097	+	6.68004i	−0.318949	+	0.267630i
$624$		0			0
$625$	−1.91013	+	10.8329i	−0.0764052	+	0.433315i
$626$	1.62760	−	0.592396i	0.0650518	−	0.0236769i
$627$		0			0
$628$	−2.25743	−	12.8025i	−0.0900811	−	0.510875i
$629$		0			0
$630$		0			0
$631$	−8.50000	+	14.7224i	−0.338380	+	0.586091i	−0.984128	−	0.177459i	$-0.943212\pi$
$631$	−8.50000	+	14.7224i	−0.338380	+	0.586091i	0.645748	+	0.763550i	$0.276545\pi$
$632$	−1.62760	−	0.592396i	−0.0647423	−	0.0235643i
$633$		0			0
$634$	36.7701	+	30.8538i	1.46033	+	1.22536i
$635$	45.1121	+	37.8536i	1.79022	+	1.50217i
$636$		0			0
$637$	28.1908	+	10.2606i	1.11696	+	0.406540i
$638$	−10.3923	+	18.0000i	−0.411435	+	0.712627i
$639$		0			0
$640$	−21.0000	−	36.3731i	−0.830098	−	1.43777i
$641$	−7.81995	−	44.3492i	−0.308870	−	1.75169i	−0.604707	−	0.796448i	$-0.706710\pi$
$641$	−7.81995	−	44.3492i	−0.308870	−	1.75169i	0.295837	−	0.955238i	$-0.404401\pi$
$642$		0			0
$643$	−41.3465	+	15.0489i	−1.63055	+	0.593470i	−0.985350	−	0.170547i	$-0.945447\pi$
$643$	−41.3465	+	15.0489i	−1.63055	+	0.593470i	−0.645196	+	0.764017i	$0.723224\pi$
$644$	1.20307	−	6.82295i	0.0474076	−	0.268862i
$645$		0			0
$646$		0			0
$647$	−20.7846			−0.817127			−0.408564	−	0.912730i	$-0.633970\pi$
$647$	−20.7846			−0.817127			−0.408564	+	0.912730i	$0.633970\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$	46.4390	−	38.9669i	1.82149	−	1.52841i
$651$		0			0
$652$	−0.173648	+	0.984808i	−0.00680059	+	0.0385680i
$653$	16.2760	−	5.92396i	0.636927	−	0.231823i	−0.00331633	−	0.999995i	$-0.501056\pi$
$653$	16.2760	−	5.92396i	0.636927	−	0.231823i	0.640244	+	0.768172i	$0.278833\pi$
$654$		0			0
$655$	2.08378	+	11.8177i	0.0814199	+	0.461755i
$656$	8.66025	+	15.0000i	0.338126	+	0.585652i
$657$		0			0
$658$	−3.00000	+	5.19615i	−0.116952	+	0.202567i
$659$	−26.0415	−	9.47834i	−1.01443	−	0.369224i	−0.219300	−	0.975658i	$-0.570377\pi$
$659$	−26.0415	−	9.47834i	−1.01443	−	0.369224i	−0.795134	+	0.606434i	$0.792600\pi$
$660$		0			0
$661$	−7.66044	−	6.42788i	−0.297957	−	0.250015i	0.481536	−	0.876426i	$-0.340079\pi$
$661$	−7.66044	−	6.42788i	−0.297957	−	0.250015i	−0.779493	+	0.626411i	$0.784523\pi$
$662$	−25.2097	−	21.1535i	−0.979804	−	0.822153i
$663$		0			0
$664$	11.2763	+	4.10424i	0.437606	+	0.159275i
$665$	−1.73205	+	3.00000i	−0.0671660	+	0.116335i
$666$		0			0
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$	4.21074	+	23.8803i	0.162919	+	0.923957i
$669$		0			0
$670$	−45.1052	+	16.4170i	−1.74257	+	0.634243i
$671$	−1.20307	+	6.82295i	−0.0464440	+	0.263397i
$672$		0			0
$673$	−28.3436	+	23.7831i	−1.09257	+	0.916773i	−0.996903	−	0.0786409i	$-0.974942\pi$
$673$	−28.3436	+	23.7831i	−1.09257	+	0.916773i	−0.0956642	+	0.995414i	$0.530497\pi$
$674$	8.66025			0.333581
$675$		0			0
$676$	12.0000			0.461538
$677$	13.2683	−	11.1334i	0.509941	−	0.427892i	−0.351167	−	0.936313i	$-0.614215\pi$
$677$	13.2683	−	11.1334i	0.509941	−	0.427892i	0.861109	+	0.508421i	$0.169771\pi$
$678$		0			0
$679$	−2.95202	+	16.7417i	−0.113288	+	0.642489i
$680$		0			0
$681$		0			0
$682$	−5.20945	−	29.5442i	−0.199480	−	1.13131i
$683$	−20.7846	−	36.0000i	−0.795301	−	1.37750i	−0.922648	−	0.385643i	$-0.873979\pi$
$683$	−20.7846	−	36.0000i	−0.795301	−	1.37750i	0.127347	−	0.991858i	$-0.459354\pi$
$684$		0			0
$685$	−12.0000	+	20.7846i	−0.458496	+	0.794139i
$686$	−21.1587	−	7.70115i	−0.807844	−	0.294031i
$687$		0			0
$688$	3.83022	+	3.21394i	0.146026	+	0.122530i
$689$	−39.8048	−	33.4002i	−1.51644	−	1.27245i
$690$		0			0
$691$	−15.9748	−	5.81434i	−0.607709	−	0.221188i	0.0197915	−	0.999804i	$-0.493700\pi$
$691$	−15.9748	−	5.81434i	−0.607709	−	0.221188i	−0.627501	+	0.778616i	$0.715922\pi$
$692$	6.92820	−	12.0000i	0.263371	−	0.456172i
$693$		0			0
$694$	−21.0000	−	36.3731i	−0.797149	−	1.38070i
$695$	−7.81995	−	44.3492i	−0.296628	−	1.68226i
$696$		0			0
$697$		0			0
$698$	−0.300767	+	1.70574i	−0.0113842	+	0.0645631i
$699$		0			0
$700$	−5.36231	+	4.49951i	−0.202676	+	0.170066i
$701$	−41.5692			−1.57005			−0.785024	−	0.619466i	$-0.787349\pi$
$701$	−41.5692			−1.57005			−0.785024	+	0.619466i	$0.787349\pi$
$702$		0			0
$703$	1.00000			0.0377157
$704$	−2.65366	+	2.22668i	−0.100013	+	0.0839212i
$705$		0			0
$706$	5.20945	−	29.5442i	0.196060	−	1.11191i
$707$	−13.0208	+	4.73917i	−0.489696	+	0.178235i
$708$		0			0
$709$	−3.29932	−	18.7113i	−0.123908	−	0.702719i	−0.981950	−	0.189140i	$-0.939430\pi$
$709$	−3.29932	−	18.7113i	−0.123908	−	0.702719i	0.858042	−	0.513580i	$-0.171681\pi$
$710$	−31.1769	−	54.0000i	−1.17005	−	2.02658i
$711$		0			0
$712$	9.00000	−	15.5885i	0.337289	−	0.584202i
$713$	32.5519	+	11.8479i	1.21908	+	0.443708i
$714$		0			0
$715$	−45.9627	−	38.5673i	−1.71891	−	1.44233i
$716$	−15.9219	−	13.3601i	−0.595031	−	0.499290i
$717$		0			0
$718$	−50.7434	−	18.4691i	−1.89373	−	0.689260i
$719$	−5.19615	+	9.00000i	−0.193784	+	0.335643i	−0.946501	−	0.322700i	$-0.895409\pi$
$719$	−5.19615	+	9.00000i	−0.193784	+	0.335643i	0.752717	+	0.658344i	$0.228743\pi$
$720$		0			0
$721$	4.00000	+	6.92820i	0.148968	+	0.258020i
$722$	−5.41381	−	30.7033i	−0.201481	−	1.14266i
$723$		0			0
$724$	−15.9748	+	5.81434i	−0.593698	+	0.216088i
$725$	−4.21074	+	23.8803i	−0.156383	+	0.886893i
$726$		0			0
$727$	−12.2567	+	10.2846i	−0.454576	+	0.381435i	−0.841131	−	0.540832i	$-0.818110\pi$
$727$	−12.2567	+	10.2846i	−0.454576	+	0.381435i	0.386555	+	0.922267i	$0.373665\pi$
$728$	8.66025			0.320970
$729$		0			0
$730$	12.0000			0.444140
$731$		0			0
$732$		0			0
$733$	7.11958	−	40.3771i	0.262968	−	1.49136i	−0.511793	−	0.859109i	$-0.671019\pi$
$733$	7.11958	−	40.3771i	0.262968	−	1.49136i	0.774761	−	0.632254i	$-0.217870\pi$
$734$	26.0415	−	9.47834i	0.961210	−	0.349852i
$735$		0			0
$736$	6.25133	+	35.4531i	0.230427	+	1.30682i
$737$	13.8564	+	24.0000i	0.510407	+	0.884051i
$738$		0			0
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	−0.636691	−	0.771119i	$-0.719697\pi$
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	0.986154	+	0.165831i	$0.0530307\pi$
$740$	3.25519	+	1.18479i	0.119663	+	0.0435538i
$741$		0			0
$742$	13.7888	+	11.5702i	0.506203	+	0.424755i
$743$	−5.30731	−	4.45336i	−0.194706	−	0.163378i	0.540223	−	0.841522i	$-0.318340\pi$
$743$	−5.30731	−	4.45336i	−0.194706	−	0.163378i	−0.734929	+	0.678144i	$0.762785\pi$
$744$		0			0
$745$	22.5526	+	8.20848i	0.826264	+	0.300736i
$746$	−19.9186	+	34.5000i	−0.729271	+	1.26313i
$747$		0			0
$748$		0			0
$749$	−1.80460	−	10.2344i	−0.0659388	−	0.373958i
$750$		0			0
$751$	−4.69846	+	1.71010i	−0.171449	+	0.0624025i	−0.426319	−	0.904573i	$-0.640190\pi$
$751$	−4.69846	+	1.71010i	−0.171449	+	0.0624025i	0.254869	+	0.966976i	$0.417968\pi$
$752$	3.00767	−	17.0574i	0.109679	−	0.622018i
$753$		0			0
$754$	−22.9813	+	19.2836i	−0.836931	+	0.702268i
$755$	−55.4256			−2.01715
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	−25.2097	+	21.1535i	−0.915659	+	0.768329i
$759$		0			0
$760$	1.04189	−	5.90885i	0.0377933	−	0.214336i
$761$	26.0415	−	9.47834i	0.944005	−	0.343590i	0.176259	−	0.984344i	$-0.443601\pi$
$761$	26.0415	−	9.47834i	0.944005	−	0.343590i	0.767746	+	0.640754i	$0.221378\pi$
$762$		0			0
$763$	−2.95202	−	16.7417i	−0.106870	−	0.606091i
$764$	−3.46410	−	6.00000i	−0.125327	−	0.217072i
$765$		0			0
$766$	15.0000	−	25.9808i	0.541972	−	0.938723i
$767$	−16.2760	−	5.92396i	−0.587691	−	0.213902i
$768$		0			0
$769$	−9.95858	−	8.35624i	−0.359115	−	0.301334i	0.445323	−	0.895370i	$-0.353089\pi$
$769$	−9.95858	−	8.35624i	−0.359115	−	0.301334i	−0.804438	+	0.594037i	$0.797533\pi$
$770$	15.9219	+	13.3601i	0.573787	+	0.481464i
$771$		0			0
$772$	9.39693	+	3.42020i	0.338203	+	0.123096i
$773$	−10.3923	+	18.0000i	−0.373785	+	0.647415i	−0.990144	−	0.140050i	$-0.955274\pi$
$773$	−10.3923	+	18.0000i	−0.373785	+	0.647415i	0.616359	+	0.787465i	$0.288607\pi$
$774$		0			0
$775$	−17.5000	−	30.3109i	−0.628619	−	1.08880i
$776$	−5.11305	−	28.9975i	−0.183548	−	1.04095i
$777$		0			0
$778$	−11.2763	+	4.10424i	−0.404275	+	0.147144i
$779$	−0.601535	+	3.41147i	−0.0215522	+	0.122229i
$780$		0			0
$781$	−27.5776	+	23.1404i	−0.986804	+	0.828027i
$782$		0			0
$783$		0			0
$784$	30.0000			1.07143
$785$	−34.4975	+	28.9469i	−1.23127	+	1.03316i
$786$		0			0
$787$	−4.86215	+	27.5746i	−0.173317	+	0.982929i	0.766752	+	0.641944i	$0.221872\pi$
$787$	−4.86215	+	27.5746i	−0.173317	+	0.982929i	−0.940069	+	0.340985i	$0.889239\pi$
$788$	9.76557	−	3.55438i	0.347884	−	0.126619i
$789$		0			0
$790$	−1.04189	−	5.90885i	−0.0370687	−	0.210227i
$791$	−8.66025	−	15.0000i	−0.307923	−	0.533339i
$792$		0			0
$793$	−5.00000	+	8.66025i	−0.177555	+	0.307535i
$794$	1.62760	+	0.592396i	0.0577612	+	0.0210234i
$795$		0			0
$796$	−14.5548	−	12.2130i	−0.515883	−	0.432877i
$797$	10.6146	+	8.90673i	0.375989	+	0.315492i	0.811125	−	0.584872i	$-0.198855\pi$
$797$	10.6146	+	8.90673i	0.375989	+	0.315492i	−0.435136	+	0.900365i	$0.643300\pi$
$798$		0			0
$799$		0			0
$800$	18.1865	−	31.5000i	0.642991	−	1.11369i
$801$		0			0
$802$	−3.00000	−	5.19615i	−0.105934	−	0.183483i
$803$	−1.20307	−	6.82295i	−0.0424554	−	0.240777i
$804$		0			0
$805$	−22.5526	+	8.20848i	−0.794876	+	0.289311i
$806$	7.51919	−	42.6434i	0.264852	−	1.50205i
$807$		0			0
$808$	18.3851	−	15.4269i	0.646784	−	0.542717i
$809$	−31.1769			−1.09612			−0.548061	−	0.836438i	$-0.684634\pi$
$809$	−31.1769			−1.09612			−0.548061	+	0.836438i	$0.684634\pi$
$810$		0			0
$811$	35.0000			1.22902			0.614508	−	0.788911i	$-0.289355\pi$
$811$	35.0000			1.22902			0.614508	+	0.788911i	$0.289355\pi$
$812$	2.65366	−	2.22668i	0.0931251	−	0.0781412i
$813$		0			0
$814$	1.04189	−	5.90885i	0.0365182	−	0.207105i
$815$	3.25519	−	1.18479i	0.114024	−	0.0415015i
$816$		0			0
$817$	0.173648	+	0.984808i	0.00607518	+	0.0344541i
$818$	−4.33013	−	7.50000i	−0.151399	−	0.262231i
$819$		0			0
$820$	−6.00000	+	10.3923i	−0.209529	+	0.362915i
$821$	−35.8071	−	13.0327i	−1.24968	−	0.454845i	−0.369384	−	0.929277i	$-0.620431\pi$
$821$	−35.8071	−	13.0327i	−1.24968	−	0.454845i	−0.880292	+	0.474432i	$0.842654\pi$
$822$		0			0
$823$	17.6190	+	14.7841i	0.614161	+	0.515342i	0.895962	−	0.444131i	$-0.146487\pi$
$823$	17.6190	+	14.7841i	0.614161	+	0.515342i	−0.281801	+	0.959473i	$0.590932\pi$
$824$	−10.6146	−	8.90673i	−0.369778	−	0.310281i
$825$		0			0
$826$	5.63816	+	2.05212i	0.196177	+	0.0714024i
$827$	5.19615	−	9.00000i	0.180688	−	0.312961i	−0.761427	−	0.648251i	$-0.775501\pi$
$827$	5.19615	−	9.00000i	0.180688	−	0.312961i	0.942115	+	0.335290i	$0.108834\pi$
$828$		0			0
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	0.982501	−	0.186256i	$-0.0596352\pi$
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	−0.652553	+	0.757743i	$0.726302\pi$
$830$	7.21842	+	40.9377i	0.250555	+	1.42097i
$831$		0			0
$832$	−4.69846	+	1.71010i	−0.162890	+	0.0592871i
$833$		0			0
$834$		0			0
$835$	64.3477	−	53.9942i	2.22685	−	1.86854i
$836$	3.46410			0.119808
$837$		0			0
$838$	−66.0000			−2.27993
$839$	−2.65366	+	2.22668i	−0.0916144	+	0.0768736i	−0.687445	−	0.726237i	$-0.741268\pi$
$839$	−2.65366	+	2.22668i	−0.0916144	+	0.0768736i	0.595830	+	0.803110i	$0.296823\pi$
$840$		0			0
$841$	−2.95202	+	16.7417i	−0.101794	+	0.577301i
$842$	30.9243	−	11.2555i	1.06572	−	0.387891i
$843$		0			0
$844$	0.868241	+	4.92404i	0.0298861	+	0.169492i
$845$	−20.7846	−	36.0000i	−0.715012	−	1.23844i
$846$		0			0
$847$	0.500000	−	0.866025i	0.0171802	−	0.0297570i
$848$	−48.8279	−	17.7719i	−1.67676	−	0.610289i
$849$		0			0
$850$		0			0
$851$	5.30731	+	4.45336i	0.181932	+	0.152659i
$852$		0			0
$853$	−1.87939	−	0.684040i	−0.0643489	−	0.0234211i	0.309645	−	0.950852i	$-0.399790\pi$
$853$	−1.87939	−	0.684040i	−0.0643489	−	0.0234211i	−0.373994	+	0.927431i	$0.622012\pi$
$854$	1.73205	−	3.00000i	0.0592696	−	0.102658i
$855$		0			0
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	6.61688	+	37.5262i	0.226028	+	1.28187i	0.860709	+	0.509097i	$0.170020\pi$
$857$	6.61688	+	37.5262i	0.226028	+	1.28187i	−0.634681	+	0.772774i	$0.718868\pi$
$858$		0			0
$859$	46.0449	−	16.7590i	1.57103	−	0.571809i	0.597803	−	0.801643i	$-0.296040\pi$
$859$	46.0449	−	16.7590i	1.57103	−	0.571809i	0.973230	+	0.229834i	$0.0738182\pi$
$860$	−0.601535	+	3.41147i	−0.0205122	+	0.116330i
$861$		0			0
$862$	−27.5776	+	23.1404i	−0.939297	+	0.788164i
$863$	10.3923			0.353758			0.176879	−	0.984233i	$-0.443400\pi$
$863$	10.3923			0.353758			0.176879	+	0.984233i	$0.443400\pi$
$864$		0			0
$865$	−48.0000			−1.63205
$866$	−1.32683	+	1.11334i	−0.0450874	+	0.0378329i
$867$		0			0
$868$	−0.868241	+	4.92404i	−0.0294700	+	0.167133i
$869$	−3.25519	+	1.18479i	−0.110425	+	0.0401913i
$870$		0			0
$871$	6.94593	+	39.3923i	0.235354	+	1.33476i
$872$	14.7224	+	25.5000i	0.498564	+	0.863539i
$873$		0			0
$874$	−6.00000	+	10.3923i	−0.202953	+	0.351525i
$875$	6.51038	+	2.36959i	0.220091	+	0.0801066i
$876$		0			0
$877$	17.6190	+	14.7841i	0.594952	+	0.499224i	0.889819	−	0.456314i	$-0.150831\pi$
$877$	17.6190	+	14.7841i	0.594952	+	0.499224i	−0.294867	+	0.955538i	$0.595275\pi$
$878$	26.5366	+	22.2668i	0.895565	+	0.751469i
$879$		0			0
$880$	−56.3816	−	20.5212i	−1.90062	−	0.691770i
$881$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$881$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$882$		0			0
$883$	9.50000	+	16.4545i	0.319700	+	0.553737i	0.980425	−	0.196891i	$-0.0630844\pi$
$883$	9.50000	+	16.4545i	0.319700	+	0.553737i	−0.660725	+	0.750628i	$0.729751\pi$
$884$		0			0
$885$		0			0
$886$	22.5526	−	8.20848i	0.757670	−	0.275769i
$887$	2.40614	−	13.6459i	0.0807903	−	0.458184i	−0.917396	−	0.397977i	$-0.869713\pi$
$887$	2.40614	−	13.6459i	0.0807903	−	0.458184i	0.998186	−	0.0602078i	$-0.0191763\pi$
$888$		0			0
$889$	−13.0228	+	10.9274i	−0.436769	+	0.366493i
$890$	62.3538			2.09011
$891$		0			0
$892$	−19.0000			−0.636167
$893$	2.65366	−	2.22668i	0.0888012	−	0.0745131i
$894$		0			0
$895$	−12.5027	+	70.9062i	−0.417918	+	2.37013i
$896$	11.3932	−	4.14677i	0.380619	−	0.138534i
$897$		0			0
$898$	−3.12567	−	17.7265i	−0.104305	−	0.591542i
$899$	8.66025	+	15.0000i	0.288836	+	0.500278i
$900$		0			0
$901$		0			0
$902$	19.5311	+	7.10876i	0.650316	+	0.236696i
$903$		0			0
$904$	22.9813	+	19.2836i	0.764348	+	0.641364i
$905$	45.1121	+	37.8536i	1.49958	+	1.25830i
$906$		0			0
$907$	34.7686	+	12.6547i	1.15447	+	0.420194i	0.847120	−	0.531402i	$-0.178334\pi$
$907$	34.7686	+	12.6547i	1.15447	+	0.420194i	0.307353	+	0.951595i	$0.400557\pi$
$908$	6.92820	−	12.0000i	0.229920	−	0.398234i
$909$		0			0
$910$	15.0000	+	25.9808i	0.497245	+	0.861254i
$911$	4.81228	+	27.2918i	0.159438	+	0.904217i	0.954616	+	0.297841i	$0.0962665\pi$
$911$	4.81228	+	27.2918i	0.159438	+	0.904217i	−0.795178	+	0.606377i	$0.792622\pi$
$912$		0			0
$913$	22.5526	−	8.20848i	0.746383	−	0.271661i
$914$	5.11305	−	28.9975i	0.169125	−	0.959153i
$915$		0			0
$916$	3.83022	−	3.21394i	0.126554	−	0.106192i
$917$	−3.46410			−0.114395
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	31.8439	−	26.7202i	1.04986	−	0.880938i
$921$		0			0
$922$	8.33511	−	47.2708i	0.274502	−	1.55678i
$923$	−48.8279	+	17.7719i	−1.60719	+	0.584969i
$924$		0			0
$925$	−1.21554	−	6.89365i	−0.0399666	−	0.226662i
$926$	26.8468	+	46.5000i	0.882240	+	1.52808i
$927$		0			0
$928$	−9.00000	+	15.5885i	−0.295439	+	0.511716i
$929$	−6.51038	−	2.36959i	−0.213599	−	0.0777436i	0.233005	−	0.972476i	$-0.425144\pi$
$929$	−6.51038	−	2.36959i	−0.213599	−	0.0777436i	−0.446603	+	0.894732i	$0.647366\pi$
$930$		0			0
$931$	4.59627	+	3.85673i	0.150637	+	0.126399i
$932$		0			0
$933$		0			0
$934$	16.9145	+	6.15636i	0.553458	+	0.201442i
$935$		0			0
$936$		0			0
$937$	18.5000	+	32.0429i	0.604369	+	1.04680i	0.992151	+	0.125046i	$0.0399079\pi$
$937$	18.5000	+	32.0429i	0.604369	+	1.04680i	−0.387782	+	0.921751i	$0.626759\pi$
$938$	−2.40614	−	13.6459i	−0.0785632	−	0.445554i
$939$		0			0
$940$	11.2763	−	4.10424i	0.367793	−	0.133866i
$941$	0.601535	−	3.41147i	0.0196095	−	0.111211i	−0.973432	−	0.228977i	$-0.926462\pi$
$941$	0.601535	−	3.41147i	0.0196095	−	0.111211i	0.993041	+	0.117766i	$0.0375732\pi$
$942$		0			0
$943$	−18.3851	+	15.4269i	−0.598700	+	0.502369i
$944$	−17.3205			−0.563735
$945$		0			0
$946$	6.00000			0.195077
$947$	−10.6146	+	8.90673i	−0.344929	+	0.289430i	−0.798750	−	0.601663i	$-0.794505\pi$
$947$	−10.6146	+	8.90673i	−0.344929	+	0.289430i	0.453821	+	0.891093i	$0.350061\pi$
$948$		0			0
$949$	1.73648	−	9.84808i	0.0563686	−	0.319682i
$950$	11.3932	−	4.14677i	0.369643	−	0.134539i
$951$		0			0
$952$		0			0
$953$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$953$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$954$		0			0
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$	6.51038	+	2.36959i	0.210561	+	0.0766379i
$957$		0			0
$958$	−18.3851	−	15.4269i	−0.593995	−	0.498421i
$959$	−5.30731	−	4.45336i	−0.171382	−	0.143807i
$960$		0			0
$961$	5.63816	+	2.05212i	0.181876	+	0.0661974i
$962$	4.33013	−	7.50000i	0.139609	−	0.241810i
$963$		0			0
$964$	9.50000	+	16.4545i	0.305974	+	0.529963i
$965$	−6.01535	−	34.1147i	−0.193641	−	1.09819i
$966$		0			0
$967$	−7.51754	+	2.73616i	−0.241748	+	0.0879890i	−0.460053	−	0.887892i	$-0.652169\pi$
$967$	−7.51754	+	2.73616i	−0.241748	+	0.0879890i	0.218305	+	0.975881i	$0.429947\pi$
$968$	−0.300767	+	1.70574i	−0.00966703	+	0.0548245i
$969$		0			0
$970$	78.1365	−	65.5643i	2.50881	−	2.10514i
$971$	51.9615			1.66752			0.833762	−	0.552124i	$-0.186182\pi$
$971$	51.9615			1.66752			0.833762	+	0.552124i	$0.186182\pi$
$972$		0			0
$973$	13.0000			0.416761
$974$	−25.2097	+	21.1535i	−0.807772	+	0.677801i
$975$		0			0
$976$	−1.73648	+	9.84808i	−0.0555834	+	0.315229i
$977$	−3.25519	+	1.18479i	−0.104143	+	0.0379049i	−0.393566	−	0.919296i	$-0.628759\pi$
$977$	−3.25519	+	1.18479i	−0.104143	+	0.0379049i	0.289423	+	0.957201i	$0.406537\pi$
$978$		0			0
$979$	−6.25133	−	35.4531i	−0.199794	−	1.13309i
$980$	10.3923	+	18.0000i	0.331970	+	0.574989i
$981$		0			0
$982$	33.0000	−	57.1577i	1.05307	−	1.82397i
$983$	−6.51038	−	2.36959i	−0.207649	−	0.0755780i	0.236102	−	0.971728i	$-0.424130\pi$
$983$	−6.51038	−	2.36959i	−0.207649	−	0.0755780i	−0.443751	+	0.896150i	$0.646352\pi$
$984$		0			0
$985$	−27.5776	−	23.1404i	−0.878695	−	0.737313i
$986$		0			0
$987$		0			0
$988$	4.69846	+	1.71010i	0.149478	+	0.0544056i
$989$	−3.46410	+	6.00000i	−0.110152	+	0.190789i
$990$		0			0
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	−4.51151	−	25.5861i	−0.143241	−	0.812358i
$993$		0			0
$994$	16.9145	−	6.15636i	0.536494	−	0.195268i
$995$	−11.4292	+	64.8180i	−0.362329	+	2.05487i
$996$		0			0
$997$	1.53209	−	1.28558i	0.0485217	−	0.0407146i	−0.618204	−	0.786017i	$-0.712140\pi$
$997$	1.53209	−	1.28558i	0.0485217	−	0.0407146i	0.666726	+	0.745303i	$0.267695\pi$
$998$	−48.4974			−1.53516
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.n.325.2		12
3.2	odd	2	inner	729.2.e.n.325.1		12
9.2	odd	6	inner	729.2.e.n.568.2		12
9.4	even	3	inner	729.2.e.n.82.2		12
9.5	odd	6	inner	729.2.e.n.82.1		12
9.7	even	3	inner	729.2.e.n.568.1		12
27.2	odd	18	inner	729.2.e.n.163.2		12
27.4	even	9		243.2.a.c.1.2	yes	2
27.5	odd	18		243.2.c.d.82.2		4
27.7	even	9	inner	729.2.e.n.649.2		12
27.11	odd	18	inner	729.2.e.n.406.1		12
27.13	even	9		243.2.c.d.163.1		4
27.14	odd	18		243.2.c.d.163.2		4
27.16	even	9	inner	729.2.e.n.406.2		12
27.20	odd	18	inner	729.2.e.n.649.1		12
27.22	even	9		243.2.c.d.82.1		4
27.23	odd	18		243.2.a.c.1.1	✓	2
27.25	even	9	inner	729.2.e.n.163.1		12
108.23	even	18		3888.2.a.ba.1.1		2
108.31	odd	18		3888.2.a.ba.1.2		2
135.4	even	18		6075.2.a.bm.1.1		2
135.104	odd	18		6075.2.a.bm.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.c.1.1	✓	2	27.23	odd	18
243.2.a.c.1.2	yes	2	27.4	even	9
243.2.c.d.82.1		4	27.22	even	9
243.2.c.d.82.2		4	27.5	odd	18
243.2.c.d.163.1		4	27.13	even	9
243.2.c.d.163.2		4	27.14	odd	18
729.2.e.n.82.1		12	9.5	odd	6	inner
729.2.e.n.82.2		12	9.4	even	3	inner
729.2.e.n.163.1		12	27.25	even	9	inner
729.2.e.n.163.2		12	27.2	odd	18	inner
729.2.e.n.325.1		12	3.2	odd	2	inner
729.2.e.n.325.2		12	1.1	even	1	trivial
729.2.e.n.406.1		12	27.11	odd	18	inner
729.2.e.n.406.2		12	27.16	even	9	inner
729.2.e.n.568.1		12	9.7	even	3	inner
729.2.e.n.568.2		12	9.2	odd	6	inner
729.2.e.n.649.1		12	27.20	odd	18	inner
729.2.e.n.649.2		12	27.7	even	9	inner
3888.2.a.ba.1.1		2	108.23	even	18
3888.2.a.ba.1.2		2	108.31	odd	18
6075.2.a.bm.1.1		2	135.4	even	18
6075.2.a.bm.1.2		2	135.104	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	729.2.e.n.325.2

Level	$729$
Weight	$2$
Character	729.325
Analytic conductor	$5.821$
Analytic rank	$0$
Dimension	$12$
Inner twists	$12$