LMFDB - Embedded newform 1080.2.bm.a.251.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(251,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("1080.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.bm (of order $6$, degree $2$, 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.10
Character	$\chi$	$=$	1080.251
Dual form			1080.2.bm.a.611.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.475189 - 1.33199i) q^{2} +(-1.54839 + 1.26589i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.40441 - 1.38819i) q^{7} +(2.42193 + 1.46090i) q^{8} +O(q^{10})$	\(q+(-0.475189 - 1.33199i) q^{2} +(-1.54839 + 1.26589i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.40441 - 1.38819i) q^{7} +(2.42193 + 1.46090i) q^{8} +(-0.915942 + 1.07752i) q^{10} +(2.70422 + 1.56128i) q^{11} +(-3.30414 + 1.90765i) q^{13} +(-0.706502 + 3.86230i) q^{14} +(0.795033 - 3.92019i) q^{16} +3.43533i q^{17} +1.31386 q^{19} +(1.87049 + 0.708000i) q^{20} +(0.794596 - 4.34389i) q^{22} +(2.13186 + 3.69249i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.11106 + 3.49459i) q^{26} +(5.48026 - 0.894268i) q^{28} +(0.266702 - 0.461941i) q^{29} +(0.413107 - 0.238507i) q^{31} +(-5.59945 + 0.803857i) q^{32} +(4.57582 - 1.63243i) q^{34} +2.77637i q^{35} -2.26255i q^{37} +(-0.624333 - 1.75005i) q^{38} +(0.0542127 - 2.82791i) q^{40} +(9.97758 - 5.76056i) q^{41} +(-6.25878 + 10.8405i) q^{43} +(-6.16360 + 1.00577i) q^{44} +(3.90532 - 4.59424i) q^{46} +(-1.52710 + 2.64501i) q^{47} +(0.354125 + 0.613362i) q^{49} +(1.39113 + 0.254469i) q^{50} +(2.70123 - 7.13648i) q^{52} +14.2847 q^{53} -3.12256i q^{55} +(-3.79531 - 6.87471i) q^{56} +(-0.742034 - 0.135735i) q^{58} +(8.89170 - 5.13363i) q^{59} +(10.7109 + 6.18395i) q^{61} +(-0.513993 - 0.436918i) q^{62} +(3.73152 + 7.07642i) q^{64} +(3.30414 + 1.90765i) q^{65} +(3.47947 + 6.02663i) q^{67} +(-4.34875 - 5.31923i) q^{68} +(3.69810 - 1.31930i) q^{70} -7.88557 q^{71} +7.92558 q^{73} +(-3.01369 + 1.07514i) q^{74} +(-2.03437 + 1.66321i) q^{76} +(-4.33470 - 7.50792i) q^{77} +(0.187206 + 0.108084i) q^{79} +(-3.79250 + 1.27158i) q^{80} +(-12.4142 - 10.5527i) q^{82} +(7.86428 + 4.54044i) q^{83} +(2.97508 - 1.71766i) q^{85} +(17.4136 + 3.18533i) q^{86} +(4.26855 + 7.73192i) q^{88} +4.82215i q^{89} +10.5927 q^{91} +(-7.97525 - 3.01871i) q^{92} +(4.24878 + 0.777198i) q^{94} +(-0.656931 - 1.13784i) q^{95} +(-4.20125 + 7.27679i) q^{97} +(0.648716 - 0.763153i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 - 6 * q^8	$ 48 q - 24 q^{5} - 6 q^{8} - 15 q^{14} - 12 q^{16} - 21 q^{22} - 24 q^{25} - 27 q^{34} + 27 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 24 q^{49} + 54 q^{52} - 21 q^{56} + 33 q^{58} + 36 q^{59} - 12 q^{61} + 42 q^{62} - 12 q^{64} - 51 q^{68} + 15 q^{70} - 54 q^{74} - 51 q^{76} - 18 q^{82} + 60 q^{83} - 27 q^{86} - 57 q^{88} + 9 q^{92} - 75 q^{94} + 42 q^{98}+O(q^{100}) $ 48 * q - 24 * q^5 - 6 * q^8 - 15 * q^14 - 12 * q^16 - 21 * q^22 - 24 * q^25 - 27 * q^34 + 27 * q^38 + 12 * q^40 - 12 * q^41 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 24 * q^49 + 54 * q^52 - 21 * q^56 + 33 * q^58 + 36 * q^59 - 12 * q^61 + 42 * q^62 - 12 * q^64 - 51 * q^68 + 15 * q^70 - 54 * q^74 - 51 * q^76 - 18 * q^82 + 60 * q^83 - 27 * q^86 - 57 * q^88 + 9 * q^92 - 75 * q^94 + 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.475189	−	1.33199i	−0.336009	−	0.941859i
$2$	−0.475189	−	1.33199i	−0.336009	−	0.941859i
$3$		0			0
$3$		0			0
$4$	−1.54839	+	1.26589i	−0.774196	+	0.632946i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.40441	−	1.38819i	−0.908782	−	0.524685i	−0.0287426	−	0.999587i	$-0.509150\pi$
$7$	−2.40441	−	1.38819i	−0.908782	−	0.524685i	−0.880039	+	0.474902i	$0.842484\pi$
$8$	2.42193	+	1.46090i	0.856283	+	0.516507i
$9$		0			0
$10$	−0.915942	+	1.07752i	−0.289646	+	0.340742i
$11$	2.70422	+	1.56128i	0.815352	+	0.470744i	0.848811	−	0.528696i	$-0.177319\pi$
$11$	2.70422	+	1.56128i	0.815352	+	0.470744i	−0.0334589	+	0.999440i	$0.510652\pi$
$12$		0			0
$13$	−3.30414	+	1.90765i	−0.916405	+	0.529086i	−0.882486	−	0.470338i	$-0.844132\pi$
$13$	−3.30414	+	1.90765i	−0.916405	+	0.529086i	−0.0339183	+	0.999425i	$0.510799\pi$
$14$	−0.706502	+	3.86230i	−0.188821	+	1.03224i
$15$		0			0
$16$	0.795033	−	3.92019i	0.198758	−	0.980049i
$17$			3.43533i			0.833189i	0.909092	+	0.416594i	$0.136776\pi$
$17$			3.43533i			0.833189i	−0.909092	+	0.416594i	$0.863224\pi$
$18$		0			0
$19$	1.31386			0.301421			0.150710	−	0.988578i	$-0.451844\pi$
$19$	1.31386			0.301421			0.150710	+	0.988578i	$0.451844\pi$
$20$	1.87049	+	0.708000i	0.418254	+	0.158314i
$21$		0			0
$22$	0.794596	−	4.34389i	0.169408	−	0.926121i
$23$	2.13186	+	3.69249i	0.444524	+	0.769937i	0.998019	−	0.0629149i	$-0.0200397\pi$
$23$	2.13186	+	3.69249i	0.444524	+	0.769937i	−0.553495	+	0.832852i	$0.686706\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.11106	+	3.49459i	0.806245	+	0.685346i
$27$		0			0
$28$	5.48026	−	0.894268i	1.03567	−	0.169001i
$29$	0.266702	−	0.461941i	0.0495253	−	0.0857803i	−0.840200	−	0.542277i	$-0.817563\pi$
$29$	0.266702	−	0.461941i	0.0495253	−	0.0857803i	0.889725	+	0.456496i	$0.150896\pi$
$30$		0			0
$31$	0.413107	−	0.238507i	0.0741962	−	0.0428372i	−0.462443	−	0.886649i	$-0.653027\pi$
$31$	0.413107	−	0.238507i	0.0741962	−	0.0428372i	0.536639	+	0.843812i	$0.319694\pi$
$32$	−5.59945	+	0.803857i	−0.989852	+	0.142103i
$33$		0			0
$34$	4.57582	−	1.63243i	0.784746	−	0.279959i
$35$			2.77637i			0.469293i
$36$		0			0
$37$		−	2.26255i		−	0.371960i	−0.982554	−	0.185980i	$-0.940454\pi$
$37$		−	2.26255i		−	0.371960i	0.982554	−	0.185980i	$-0.0595460\pi$
$38$	−0.624333	−	1.75005i	−0.101280	−	0.283896i
$39$		0			0
$40$	0.0542127	−	2.82791i	0.00857178	−	0.447131i
$41$	9.97758	−	5.76056i	1.55824	−	0.899648i	0.560809	−	0.827945i	$-0.310490\pi$
$41$	9.97758	−	5.76056i	1.55824	−	0.899648i	0.997426	−	0.0717028i	$-0.0228433\pi$
$42$		0			0
$43$	−6.25878	+	10.8405i	−0.954454	+	1.65316i	−0.218842	+	0.975760i	$0.570228\pi$
$43$	−6.25878	+	10.8405i	−0.954454	+	1.65316i	−0.735612	+	0.677403i	$0.763105\pi$
$44$	−6.16360	+	1.00577i	−0.929198	+	0.151626i
$45$		0			0
$46$	3.90532	−	4.59424i	0.575808	−	0.677384i
$47$	−1.52710	+	2.64501i	−0.222750	+	0.385814i	−0.955642	−	0.294531i	$-0.904837\pi$
$47$	−1.52710	+	2.64501i	−0.222750	+	0.385814i	0.732892	+	0.680345i	$0.238170\pi$
$48$		0			0
$49$	0.354125	+	0.613362i	0.0505892	+	0.0876231i
$50$	1.39113	+	0.254469i	0.196736	+	0.0359874i
$51$		0			0
$52$	2.70123	−	7.13648i	0.374593	−	0.989651i
$53$	14.2847			1.96215			0.981075	−	0.193629i	$-0.0620257\pi$
$53$	14.2847			1.96215			0.981075	+	0.193629i	$0.0620257\pi$
$54$		0			0
$55$		−	3.12256i		−	0.421046i
$56$	−3.79531	−	6.87471i	−0.507170	−	0.918671i
$57$		0			0
$58$	−0.742034	−	0.135735i	−0.0974338	−	0.0178228i
$59$	8.89170	−	5.13363i	1.15760	−	0.668341i	0.206873	−	0.978368i	$-0.433671\pi$
$59$	8.89170	−	5.13363i	1.15760	−	0.668341i	0.950728	+	0.310026i	$0.100338\pi$
$60$		0			0
$61$	10.7109	+	6.18395i	1.37139	+	0.791774i	0.991103	−	0.133094i	$-0.0424913\pi$
$61$	10.7109	+	6.18395i	1.37139	+	0.791774i	0.380289	+	0.924868i	$0.375825\pi$
$62$	−0.513993	−	0.436918i	−0.0652772	−	0.0554886i
$63$		0			0
$64$	3.73152	+	7.07642i	0.466440	+	0.884553i
$65$	3.30414	+	1.90765i	0.409829	+	0.236615i
$66$		0			0
$67$	3.47947	+	6.02663i	0.425086	+	0.736270i	0.996428	−	0.0844417i	$-0.0269107\pi$
$67$	3.47947	+	6.02663i	0.425086	+	0.736270i	−0.571343	+	0.820711i	$0.693577\pi$
$68$	−4.34875	−	5.31923i	−0.527364	−	0.645051i
$69$		0			0
$70$	3.69810	−	1.31930i	0.442007	−	0.157687i
$71$	−7.88557			−0.935845			−0.467922	−	0.883770i	$-0.654997\pi$
$71$	−7.88557			−0.935845			−0.467922	+	0.883770i	$0.654997\pi$
$72$		0			0
$73$	7.92558			0.927620			0.463810	−	0.885935i	$-0.346482\pi$
$73$	7.92558			0.927620			0.463810	+	0.885935i	$0.346482\pi$
$74$	−3.01369	+	1.07514i	−0.350334	+	0.124982i
$75$		0			0
$76$	−2.03437	+	1.66321i	−0.233359	+	0.190783i
$77$	−4.33470	−	7.50792i	−0.493985	−	0.855606i
$78$		0			0
$79$	0.187206	+	0.108084i	0.0210624	+	0.0121604i	0.510494	−	0.859881i	$-0.329462\pi$
$79$	0.187206	+	0.108084i	0.0210624	+	0.0121604i	−0.489432	+	0.872042i	$0.662796\pi$
$80$	−3.79250	+	1.27158i	−0.424015	+	0.142167i
$81$		0			0
$82$	−12.4142	−	10.5527i	−1.37092	−	1.16535i
$83$	7.86428	+	4.54044i	0.863217	+	0.498378i	0.865088	−	0.501620i	$-0.167262\pi$
$83$	7.86428	+	4.54044i	0.863217	+	0.498378i	−0.00187155	+	0.999998i	$0.500596\pi$
$84$		0			0
$85$	2.97508	−	1.71766i	0.322693	−	0.186307i
$86$	17.4136	+	3.18533i	1.87775	+	0.343483i
$87$		0			0
$88$	4.26855	+	7.73192i	0.455029	+	0.824225i
$89$			4.82215i			0.511147i	0.966790	+	0.255573i	$0.0822642\pi$
$89$			4.82215i			0.511147i	−0.966790	+	0.255573i	$0.917736\pi$
$90$		0			0
$91$	10.5927			1.11042
$92$	−7.97525	−	3.01871i	−0.831477	−	0.314723i
$93$		0			0
$94$	4.24878	+	0.777198i	0.438228	+	0.0801618i
$95$	−0.656931	−	1.13784i	−0.0673997	−	0.116740i
$96$		0			0
$97$	−4.20125	+	7.27679i	−0.426573	+	0.738846i	−0.996566	−	0.0828038i	$-0.973613\pi$
$97$	−4.20125	+	7.27679i	−0.426573	+	0.738846i	0.569993	+	0.821649i	$0.306946\pi$
$98$	0.648716	−	0.763153i	0.0655302	−	0.0770901i
$99$		0			0
$100$	−0.322099	−	1.97389i	−0.0322099	−	0.197389i
$101$	−1.11068	+	1.92376i	−0.110517	+	0.191421i	−0.915979	−	0.401227i	$-0.868584\pi$
$101$	−1.11068	+	1.92376i	−0.110517	+	0.191421i	0.805462	+	0.592648i	$0.201917\pi$
$102$		0			0
$103$	−12.7933	+	7.38623i	−1.26056	+	0.727786i	−0.973183	−	0.230030i	$-0.926117\pi$
$103$	−12.7933	+	7.38623i	−1.26056	+	0.727786i	−0.287380	+	0.957817i	$0.592784\pi$
$104$	−10.7893	−	0.206838i	−1.05798	−	0.0202821i
$105$		0			0
$106$	−6.78791	−	19.0270i	−0.659300	−	1.84807i
$107$			14.0755i			1.36073i	0.732872	+	0.680367i	$0.238180\pi$
$107$			14.0755i			1.36073i	−0.732872	+	0.680367i	$0.761820\pi$
$108$		0			0
$109$		−	16.5073i		−	1.58111i	−0.612389	−	0.790557i	$-0.709791\pi$
$109$		−	16.5073i		−	1.58111i	0.612389	−	0.790557i	$-0.290209\pi$
$110$	−4.15922	+	1.48381i	−0.396566	+	0.141475i
$111$		0			0
$112$	−7.35355	+	8.32210i	−0.694845	+	0.786365i
$113$	−0.459459	+	0.265268i	−0.0432222	+	0.0249544i	−0.521455	−	0.853279i	$-0.674611\pi$
$113$	−0.459459	+	0.265268i	−0.0432222	+	0.0249544i	0.478233	+	0.878233i	$0.341277\pi$
$114$		0			0
$115$	2.13186	−	3.69249i	0.198797	−	0.344326i
$116$	0.171809	+	1.05288i	0.0159521	+	0.0977576i
$117$		0			0
$118$	−11.0632	−	9.40421i	−1.01845	−	0.865728i
$119$	4.76887	−	8.25993i	0.437162	−	0.757187i
$120$		0			0
$121$	−0.624807	−	1.08220i	−0.0568006	−	0.0983816i
$122$	3.14725	−	17.2054i	0.284939	−	1.55770i
$123$		0			0
$124$	−0.337726	+	0.892252i	−0.0303287	+	0.0801266i
$125$	1.00000			0.0894427
$126$		0			0
$127$		−	0.554852i		−	0.0492352i	−0.999697	−	0.0246176i	$-0.992163\pi$
$127$		−	0.554852i		−	0.0492352i	0.999697	−	0.0246176i	$-0.00783681\pi$
$128$	7.65254	−	8.33298i	0.676395	−	0.736539i
$129$		0			0
$130$	0.970876	−	5.30758i	0.0851514	−	0.465505i
$131$	−5.21744	+	3.01229i	−0.455850	+	0.263185i	−0.710298	−	0.703901i	$-0.751440\pi$
$131$	−5.21744	+	3.01229i	−0.455850	+	0.263185i	0.254448	+	0.967087i	$0.418106\pi$
$132$		0			0
$133$	−3.15906	−	1.82389i	−0.273926	−	0.158151i
$134$	6.37400	−	7.49841i	0.550629	−	0.647764i
$135$		0			0
$136$	−5.01868	+	8.32013i	−0.430348	+	0.713445i
$137$	−7.48963	−	4.32414i	−0.639883	−	0.369436i	0.144687	−	0.989478i	$-0.453783\pi$
$137$	−7.48963	−	4.32414i	−0.639883	−	0.369436i	−0.784569	+	0.620041i	$0.787116\pi$
$138$		0			0
$139$	4.72886	+	8.19062i	0.401096	+	0.694719i	0.993859	−	0.110658i	$-0.0352959\pi$
$139$	4.72886	+	8.19062i	0.401096	+	0.694719i	−0.592762	+	0.805378i	$0.701963\pi$
$140$	−3.51459	−	4.29891i	−0.297037	−	0.363324i
$141$		0			0
$142$	3.74713	+	10.5035i	0.314452	+	0.881434i
$143$	−11.9135			−0.996257
$144$		0			0
$145$	−0.533403			−0.0442967
$146$	−3.76615	−	10.5568i	−0.311689	−	0.873687i
$147$		0			0
$148$	2.86414	+	3.50331i	0.235431	+	0.287970i
$149$	5.42917	+	9.40360i	0.444775	+	0.770373i	0.998037	−	0.0626346i	$-0.0199503\pi$
$149$	5.42917	+	9.40360i	0.444775	+	0.770373i	−0.553261	+	0.833008i	$0.686617\pi$
$150$		0			0
$151$	−9.37631	−	5.41342i	−0.763033	−	0.440538i	0.0673504	−	0.997729i	$-0.478545\pi$
$151$	−9.37631	−	5.41342i	−0.763033	−	0.440538i	−0.830384	+	0.557192i	$0.811879\pi$
$152$	3.18209	+	1.91943i	0.258101	+	0.155686i
$153$		0			0
$154$	−7.94067	+	9.34145i	−0.639877	+	0.752755i
$155$	−0.413107	−	0.238507i	−0.0331815	−	0.0191574i
$156$		0			0
$157$	14.2718	−	8.23981i	1.13901	−	0.657608i	0.192826	−	0.981233i	$-0.438235\pi$
$157$	14.2718	−	8.23981i	1.13901	−	0.657608i	0.946186	+	0.323625i	$0.104902\pi$
$158$	0.0550079	−	0.300717i	0.00437620	−	0.0239238i
$159$		0			0
$160$	3.49588	+	4.44734i	0.276374	+	0.351593i
$161$		−	11.8377i		−	0.932940i
$162$		0			0
$163$	7.55915			0.592078			0.296039	−	0.955176i	$-0.404334\pi$
$163$	7.55915			0.592078			0.296039	+	0.955176i	$0.404334\pi$
$164$	−8.15695	+	21.5501i	−0.636951	+	1.68278i
$165$		0			0
$166$	2.31081	−	12.6327i	0.179353	−	0.980488i
$167$	−10.6372	−	18.4242i	−0.823131	−	1.42570i	−0.903340	−	0.428926i	$-0.858892\pi$
$167$	−10.6372	−	18.4242i	−0.823131	−	1.42570i	0.0802091	−	0.996778i	$-0.474441\pi$
$168$		0			0
$169$	0.778243	−	1.34796i	0.0598649	−	0.103689i
$170$	−3.70163	−	3.14656i	−0.283902	−	0.241330i
$171$		0			0
$172$	−4.03189	−	24.7083i	−0.307429	−	1.88399i
$173$	−10.3166	+	17.8689i	−0.784356	+	1.35854i	0.145027	+	0.989428i	$0.453673\pi$
$173$	−10.3166	+	17.8689i	−0.784356	+	1.35854i	−0.929383	+	0.369116i	$0.879660\pi$
$174$		0			0
$175$	2.40441	−	1.38819i	0.181756	−	0.104937i
$176$	8.27046	−	9.35979i	0.623410	−	0.705521i
$177$		0			0
$178$	6.42305	−	2.29143i	0.481428	−	0.171750i
$179$			7.50778i			0.561158i	0.959831	+	0.280579i	$0.0905264\pi$
$179$			7.50778i			0.561158i	−0.959831	+	0.280579i	$0.909474\pi$
$180$		0			0
$181$			15.2146i			1.13089i	0.824785	+	0.565447i	$0.191296\pi$
$181$			15.2146i			1.13089i	−0.824785	+	0.565447i	$0.808704\pi$
$182$	−5.03352	−	14.1093i	−0.373110	−	1.04585i
$183$		0			0
$184$	−0.231148	+	12.0574i	−0.0170404	+	0.888884i
$185$	−1.95942	+	1.13127i	−0.144060	+	0.0831728i
$186$		0			0
$187$	−5.36351	+	9.28987i	−0.392219	+	0.679342i
$188$	−0.983753	−	6.02865i	−0.0717476	−	0.439684i
$189$		0			0
$190$	−1.20342	+	1.41571i	−0.0873054	+	0.102707i
$191$	−6.80108	+	11.7798i	−0.492109	+	0.852358i	−0.999959	−	0.00908769i	$-0.997107\pi$
$191$	−6.80108	+	11.7798i	−0.492109	+	0.852358i	0.507850	+	0.861446i	$0.330441\pi$
$192$		0			0
$193$	−11.0958	−	19.2185i	−0.798696	−	1.38338i	−0.920466	−	0.390823i	$-0.872190\pi$
$193$	−11.0958	−	19.2185i	−0.798696	−	1.38338i	0.121770	−	0.992558i	$-0.461143\pi$
$194$	11.6890	+	2.13818i	0.839221	+	0.153512i
$195$		0			0
$196$	−1.32477	−	0.501441i	−0.0946267	−	0.0358172i
$197$	5.87131			0.418314			0.209157	−	0.977882i	$-0.432928\pi$
$197$	5.87131			0.418314			0.209157	+	0.977882i	$0.432928\pi$
$198$		0			0
$199$			17.4689i			1.23834i	0.785259	+	0.619168i	$0.212530\pi$
$199$			17.4689i			1.23834i	−0.785259	+	0.619168i	$0.787470\pi$
$200$	−2.47615	+	1.36700i	−0.175090	+	0.0966618i
$201$		0			0
$202$	3.09021	+	0.565269i	0.217427	+	0.0397722i
$203$	−1.28252	+	0.740464i	−0.0900153	+	0.0519704i
$204$		0			0
$205$	−9.97758	−	5.76056i	−0.696864	−	0.402335i
$206$	15.9176	+	13.5307i	1.10903	+	0.942729i
$207$		0			0
$208$	4.85145	+	14.4695i	0.336388	+	1.00328i
$209$	3.55297	+	2.05131i	0.245764	+	0.141892i
$210$		0			0
$211$	−8.80440	−	15.2497i	−0.606120	−	1.04983i	−0.991873	−	0.127228i	$-0.959392\pi$
$211$	−8.80440	−	15.2497i	−0.606120	−	1.04983i	0.385754	−	0.922602i	$-0.373941\pi$
$212$	−22.1183	+	18.0829i	−1.51909	+	1.24194i
$213$		0			0
$214$	18.7485	−	6.68854i	1.28162	−	0.457219i
$215$	12.5176			0.853690
$216$		0			0
$217$	−1.32437			−0.0899042
$218$	−21.9876	+	7.84408i	−1.48919	+	0.531268i
$219$		0			0
$220$	3.95283	+	4.83495i	0.266499	+	0.325972i
$221$	−6.55339	−	11.3508i	−0.440829	−	0.763538i
$222$		0			0
$223$	7.41753	+	4.28251i	0.496714	+	0.286778i	0.727356	−	0.686261i	$-0.240749\pi$
$223$	7.41753	+	4.28251i	0.496714	+	0.286778i	−0.230641	+	0.973039i	$0.574082\pi$
$224$	14.5793	+	5.84028i	0.974119	+	0.390220i
$225$		0			0
$226$	0.571664	+	0.485941i	0.0380265	+	0.0323243i
$227$	−20.0247	−	11.5612i	−1.32908	−	0.767347i	−0.343925	−	0.938997i	$-0.611757\pi$
$227$	−20.0247	−	11.5612i	−1.32908	−	0.767347i	−0.985158	+	0.171651i	$0.945090\pi$
$228$		0			0
$229$	−6.36677	+	3.67586i	−0.420728	+	0.242907i	−0.695389	−	0.718634i	$-0.744768\pi$
$229$	−6.36677	+	3.67586i	−0.420728	+	0.242907i	0.274661	+	0.961541i	$0.411434\pi$
$230$	−5.93139	−	1.08499i	−0.391104	−	0.0715418i
$231$		0			0
$232$	1.32078	−	0.729165i	0.0867138	−	0.0478720i
$233$		−	20.6717i		−	1.35425i	−0.735868	−	0.677125i	$-0.763226\pi$
$233$		−	20.6717i		−	1.35425i	0.735868	−	0.677125i	$-0.236774\pi$
$234$		0			0
$235$	3.05419			0.199233
$236$	−7.26922	+	19.2048i	−0.473186	+	1.25013i
$237$		0			0
$238$	−13.2683	−	2.42706i	−0.860053	−	0.157323i
$239$	2.31092	+	4.00263i	0.149481	+	0.258908i	0.931036	−	0.364928i	$-0.118906\pi$
$239$	2.31092	+	4.00263i	0.149481	+	0.258908i	−0.781555	+	0.623837i	$0.785573\pi$
$240$		0			0
$241$	−10.0859	+	17.4693i	−0.649690	+	1.12530i	0.333507	+	0.942748i	$0.391768\pi$
$241$	−10.0859	+	17.4693i	−0.649690	+	1.12530i	−0.983197	+	0.182548i	$0.941565\pi$
$242$	−1.14457	+	1.34648i	−0.0735760	+	0.0865553i
$243$		0			0
$244$	−24.4129	+	3.98369i	−1.56288	+	0.255030i
$245$	0.354125	−	0.613362i	0.0226242	−	0.0391863i
$246$		0			0
$247$	−4.34119	+	2.50639i	−0.276223	+	0.159478i
$248$	1.34895	+	0.0258603i	0.0856586	+	0.00164213i
$249$		0			0
$250$	−0.475189	−	1.33199i	−0.0300536	−	0.0842424i
$251$			15.2472i			0.962397i	0.876612	+	0.481199i	$0.159798\pi$
$251$			15.2472i			0.962397i	−0.876612	+	0.481199i	$0.840202\pi$
$252$		0			0
$253$			13.3137i			0.837027i
$254$	−0.739057	+	0.263659i	−0.0463726	+	0.0165435i
$255$		0			0
$256$	−14.7358	−	6.23336i	−0.920990	−	0.389585i
$257$	−1.24545	+	0.719060i	−0.0776889	+	0.0448537i	−0.538341	−	0.842727i	$-0.680949\pi$
$257$	−1.24545	+	0.719060i	−0.0776889	+	0.0448537i	0.460652	+	0.887581i	$0.347616\pi$
$258$		0			0
$259$	−3.14084	+	5.44009i	−0.195162	+	0.338031i
$260$	−7.53099	+	1.22890i	−0.467052	+	0.0762134i
$261$		0			0
$262$	6.49161	+	5.51817i	0.401053	+	0.340914i
$263$	2.20868	−	3.82555i	0.136193	−	0.235893i	−0.789860	−	0.613288i	$-0.789847\pi$
$263$	2.20868	−	3.82555i	0.136193	−	0.235893i	0.926053	+	0.377395i	$0.123180\pi$
$264$		0			0
$265$	−7.14233	−	12.3709i	−0.438750	−	0.759937i
$266$	−0.928246	+	5.07453i	−0.0569144	+	0.311139i
$267$		0			0
$268$	−13.0167	−	4.92694i	−0.795119	−	0.300961i
$269$	24.9314			1.52010			0.760048	−	0.649867i	$-0.225175\pi$
$269$	24.9314			1.52010			0.760048	+	0.649867i	$0.225175\pi$
$270$		0			0
$271$			21.5066i			1.30643i	0.757172	+	0.653215i	$0.226580\pi$
$271$			21.5066i			1.30643i	−0.757172	+	0.653215i	$0.773420\pi$
$272$	13.4671	+	2.73120i	0.816566	+	0.165603i
$273$		0			0
$274$	−2.20072	+	12.0309i	−0.132951	+	0.726813i
$275$	−2.70422	+	1.56128i	−0.163070	+	0.0941488i
$276$		0			0
$277$	−0.693110	−	0.400167i	−0.0416449	−	0.0240437i	0.479033	−	0.877797i	$-0.340987\pi$
$277$	−0.693110	−	0.400167i	−0.0416449	−	0.0240437i	−0.520678	+	0.853753i	$0.674321\pi$
$278$	8.66272	−	10.1909i	0.519556	−	0.611208i
$279$		0			0
$280$	−4.05601	+	6.72419i	−0.242393	+	0.401847i
$281$	17.8052	+	10.2798i	1.06217	+	0.613244i	0.926032	−	0.377445i	$-0.123197\pi$
$281$	17.8052	+	10.2798i	1.06217	+	0.613244i	0.136139	+	0.990690i	$0.456531\pi$
$282$		0			0
$283$	7.32132	+	12.6809i	0.435207	+	0.753801i	0.997313	−	0.0732645i	$-0.0233417\pi$
$283$	7.32132	+	12.6809i	0.435207	+	0.753801i	−0.562105	+	0.827066i	$0.690008\pi$
$284$	12.2099	−	9.98228i	0.724527	−	0.592339i
$285$		0			0
$286$	5.66116	+	15.8686i	0.334751	+	0.938333i
$287$	−31.9869			−1.88813
$288$		0			0
$289$	5.19853			0.305796
$290$	0.253467	+	0.710488i	0.0148841	+	0.0417213i
$291$		0			0
$292$	−12.2719	+	10.0329i	−0.718159	+	0.587133i
$293$	13.4417	+	23.2817i	0.785273	+	1.36013i	0.928836	+	0.370491i	$0.120811\pi$
$293$	13.4417	+	23.2817i	0.785273	+	1.36013i	−0.143563	+	0.989641i	$0.545856\pi$
$294$		0			0
$295$	−8.89170	−	5.13363i	−0.517695	−	0.298891i
$296$	3.30536	−	5.47974i	0.192120	−	0.318503i
$297$		0			0
$298$	9.94562	−	11.7001i	0.576134	−	0.677768i
$299$	−14.0879	−	8.13368i	−0.814727	−	0.470383i
$300$		0			0
$301$	30.0973	−	17.3767i	1.73478	−	1.00158i
$302$	−2.75510	+	15.0615i	−0.158538	+	0.866694i
$303$		0			0
$304$	1.04456	−	5.15060i	0.0599098	−	0.295407i
$305$		−	12.3679i		−	0.708184i
$306$		0			0
$307$	−21.3839			−1.22044			−0.610221	−	0.792231i	$-0.708920\pi$
$307$	−21.3839			−1.22044			−0.610221	+	0.792231i	$0.708920\pi$
$308$	16.2160	+	6.13793i	0.923994	+	0.349741i
$309$		0			0
$310$	−0.121386	+	0.663590i	−0.00689424	+	0.0376894i
$311$	10.7043	+	18.5404i	0.606985	+	1.05133i	0.991734	+	0.128308i	$0.0409547\pi$
$311$	10.7043	+	18.5404i	0.606985	+	1.05133i	−0.384749	+	0.923021i	$0.625712\pi$
$312$		0			0
$313$	2.91819	−	5.05445i	0.164946	−	0.285694i	−0.771690	−	0.635998i	$-0.780588\pi$
$313$	2.91819	−	5.05445i	0.164946	−	0.285694i	0.936636	+	0.350304i	$0.113922\pi$
$314$	−17.7571	−	15.0944i	−1.00209	−	0.851825i
$315$		0			0
$316$	−0.426691	+	0.0696273i	−0.0240032	+	0.00391684i
$317$	−4.19064	+	7.25841i	−0.235370	+	0.407673i	−0.959380	−	0.282117i	$-0.908964\pi$
$317$	−4.19064	+	7.25841i	−0.235370	+	0.407673i	0.724010	+	0.689789i	$0.242297\pi$
$318$		0			0
$319$	1.44244	−	0.832792i	0.0807611	−	0.0466274i
$320$	4.26260	−	6.76980i	0.238287	−	0.378444i
$321$		0			0
$322$	−15.7677	+	5.62513i	−0.878697	+	0.313476i
$323$			4.51355i			0.251140i
$324$		0			0
$325$		−	3.81530i		−	0.211635i
$326$	−3.59202	−	10.0687i	−0.198944	−	0.557654i
$327$		0			0
$328$	32.5806	+	0.624591i	1.79896	+	0.0344873i
$329$	7.34353	−	4.23979i	0.404862	−	0.233747i
$330$		0			0
$331$	−0.901119	+	1.56078i	−0.0495300	+	0.0857884i	−0.889727	−	0.456492i	$-0.849106\pi$
$331$	−0.901119	+	1.56078i	−0.0495300	+	0.0857884i	0.840197	+	0.542281i	$0.182439\pi$
$332$	−17.9247	+	2.92495i	−0.983745	+	0.160527i
$333$		0			0
$334$	−19.4861	+	22.9236i	−1.06623	+	1.25432i
$335$	3.47947	−	6.02663i	0.190104	−	0.329270i
$336$		0			0
$337$	−11.9797	−	20.7495i	−0.652577	−	1.13030i	−0.982495	−	0.186287i	$-0.940355\pi$
$337$	−11.9797	−	20.7495i	−0.652577	−	1.13030i	0.329918	−	0.944009i	$-0.392979\pi$
$338$	−2.16528	−	0.396078i	−0.117776	−	0.0215438i
$339$		0			0
$340$	−2.43221	+	6.42575i	−0.131905	+	0.348485i
$341$	1.48951			0.0806614
$342$		0			0
$343$			17.4682i			0.943197i
$344$	−30.9953	+	17.1115i	−1.67115	+	0.922593i
$345$		0			0
$346$	28.7035	+	5.25051i	1.54311	+	0.282269i
$347$	15.0256	−	8.67502i	0.806615	−	0.465699i	−0.0391641	−	0.999233i	$-0.512470\pi$
$347$	15.0256	−	8.67502i	0.806615	−	0.465699i	0.845779	+	0.533533i	$0.179136\pi$
$348$		0			0
$349$	−7.29528	−	4.21193i	−0.390507	−	0.225460i	0.291873	−	0.956457i	$-0.405722\pi$
$349$	−7.29528	−	4.21193i	−0.390507	−	0.225460i	−0.682380	+	0.730998i	$0.739055\pi$
$350$	−2.99160	−	2.54300i	−0.159908	−	0.135929i
$351$		0			0
$352$	−16.3972	−	6.56850i	−0.873972	−	0.350102i
$353$	−14.9442	−	8.62801i	−0.795397	−	0.459223i	0.0464619	−	0.998920i	$-0.485205\pi$
$353$	−14.9442	−	8.62801i	−0.795397	−	0.459223i	−0.841859	+	0.539697i	$0.818539\pi$
$354$		0			0
$355$	3.94278	+	6.82910i	0.209261	+	0.362451i
$356$	−6.10432	−	7.46657i	−0.323528	−	0.395728i
$357$		0			0
$358$	10.0003	−	3.56761i	0.528531	−	0.188554i
$359$	7.13071			0.376344			0.188172	−	0.982136i	$-0.439744\pi$
$359$	7.13071			0.376344			0.188172	+	0.982136i	$0.439744\pi$
$360$		0			0
$361$	−17.2738			−0.909146
$362$	20.2657	−	7.22982i	1.06514	−	0.379991i
$363$		0			0
$364$	−16.4016	+	13.4092i	−0.859679	+	0.702833i
$365$	−3.96279	−	6.86376i	−0.207422	−	0.359266i
$366$		0			0
$367$	29.3780	+	16.9614i	1.53352	+	0.885379i	0.999196	+	0.0401004i	$0.0127678\pi$
$367$	29.3780	+	16.9614i	1.53352	+	0.885379i	0.534326	+	0.845279i	$0.320566\pi$
$368$	16.1702	−	5.42166i	0.842929	−	0.282623i
$369$		0			0
$370$	2.43794	+	2.07236i	0.126742	+	0.107737i
$371$	−34.3462	−	19.8298i	−1.78317	−	1.02951i
$372$		0			0
$373$	−8.48032	+	4.89612i	−0.439095	+	0.253511i	−0.703213	−	0.710979i	$-0.748252\pi$
$373$	−8.48032	+	4.89612i	−0.439095	+	0.253511i	0.264119	+	0.964490i	$0.414919\pi$
$374$	14.9227	+	2.72970i	0.771634	+	0.141149i
$375$		0			0
$376$	−7.56262	+	4.17509i	−0.390013	+	0.215314i
$377$			2.03509i			0.104813i
$378$		0			0
$379$	15.9453			0.819054			0.409527	−	0.912298i	$-0.365694\pi$
$379$	15.9453			0.819054			0.409527	+	0.912298i	$0.365694\pi$
$380$	2.45757	+	0.930215i	0.126071	+	0.0477190i
$381$		0			0
$382$	18.9224	+	3.46133i	0.968154	+	0.177097i
$383$	−3.70162	−	6.41139i	−0.189144	−	0.327607i	0.755821	−	0.654778i	$-0.227238\pi$
$383$	−3.70162	−	6.41139i	−0.189144	−	0.327607i	−0.944965	+	0.327171i	$0.893905\pi$
$384$		0			0
$385$	−4.33470	+	7.50792i	−0.220917	+	0.382639i
$386$	−20.3263	+	23.9120i	−1.03458	+	1.21709i
$387$		0			0
$388$	−2.70644	−	16.5856i	−0.137399	−	0.842009i
$389$	13.0021	−	22.5203i	0.659233	−	1.14182i	−0.321582	−	0.946882i	$-0.604214\pi$
$389$	13.0021	−	22.5203i	0.659233	−	1.14182i	0.980815	−	0.194943i	$-0.0624522\pi$
$390$		0			0
$391$	−12.6849	+	7.32363i	−0.641503	+	0.370372i
$392$	−0.0383961	+	2.00286i	−0.00193930	+	0.101160i
$393$		0			0
$394$	−2.78998	−	7.82053i	−0.140557	−	0.393993i
$395$		−	0.216167i		−	0.0108766i
$396$		0			0
$397$		−	26.9039i		−	1.35027i	−0.737694	−	0.675135i	$-0.764085\pi$
$397$		−	26.9039i		−	1.35027i	0.737694	−	0.675135i	$-0.235915\pi$
$398$	23.2684	−	8.30101i	1.16634	−	0.416092i
$399$		0			0
$400$	2.99747	+	2.64862i	0.149874	+	0.132431i
$401$	9.03940	−	5.21890i	0.451406	−	0.260619i	−0.257018	−	0.966407i	$-0.582740\pi$
$401$	9.03940	−	5.21890i	0.451406	−	0.260619i	0.708424	+	0.705787i	$0.249407\pi$
$402$		0			0
$403$	−0.909976	+	1.57613i	−0.0453291	+	0.0785124i
$404$	−0.715500	−	4.38474i	−0.0355975	−	0.218149i
$405$		0			0
$406$	1.59573	+	1.35644i	0.0791947	+	0.0673192i
$407$	3.53247	−	6.11842i	0.175098	−	0.303279i
$408$		0			0
$409$	2.09390	+	3.62675i	0.103537	+	0.179331i	0.913140	−	0.407647i	$-0.133651\pi$
$409$	2.09390	+	3.62675i	0.103537	+	0.179331i	−0.809603	+	0.586978i	$0.800317\pi$
$410$	−2.93177	+	16.0274i	−0.144790	+	0.791536i
$411$		0			0
$412$	10.4589	−	27.6317i	0.515273	−	1.36132i
$413$	−28.5057			−1.40268
$414$		0			0
$415$		−	9.08089i		−	0.445763i
$416$	16.9679	−	13.3378i	0.831920	−	0.653941i
$417$		0			0
$418$	1.04399	−	5.70728i	0.0510632	−	0.279152i
$419$	−2.80884	+	1.62169i	−0.137221	+	0.0792245i	−0.567039	−	0.823691i	$-0.691911\pi$
$419$	−2.80884	+	1.62169i	−0.137221	+	0.0792245i	0.429818	+	0.902916i	$0.358578\pi$
$420$		0			0
$421$	5.45534	+	3.14964i	0.265877	+	0.153504i	0.627013	−	0.779009i	$-0.284277\pi$
$421$	5.45534	+	3.14964i	0.265877	+	0.153504i	−0.361135	+	0.932513i	$0.617611\pi$
$422$	−16.1286	+	18.9738i	−0.785130	+	0.923632i
$423$		0			0
$424$	34.5965	+	20.8685i	1.68016	+	1.01346i
$425$	−2.97508	−	1.71766i	−0.144313	−	0.0833189i
$426$		0			0
$427$	−17.1690	−	29.7375i	−0.830864	−	1.43910i
$428$	−17.8181	−	21.7945i	−0.861272	−	1.05347i
$429$		0			0
$430$	−5.94820	−	16.6732i	−0.286848	−	0.804055i
$431$	−16.9856			−0.818167			−0.409084	−	0.912497i	$-0.634152\pi$
$431$	−16.9856			−0.818167			−0.409084	+	0.912497i	$0.634152\pi$
$432$		0			0
$433$	−17.6526			−0.848331			−0.424166	−	0.905585i	$-0.639433\pi$
$433$	−17.6526			−0.848331			−0.424166	+	0.905585i	$0.639433\pi$
$434$	0.629326	+	1.76405i	0.0302086	+	0.0846770i
$435$		0			0
$436$	20.8965	+	25.5598i	1.00076	+	1.22409i
$437$	2.80097	+	4.85142i	0.133989	+	0.232075i
$438$		0			0
$439$	−33.1600	−	19.1449i	−1.58264	−	0.913738i	−0.994472	−	0.105000i	$-0.966516\pi$
$439$	−33.1600	−	19.1449i	−1.58264	−	0.913738i	−0.588168	−	0.808738i	$-0.700151\pi$
$440$	4.56176	−	7.56263i	0.217473	−	0.360534i
$441$		0			0
$442$	−12.0051	+	14.1228i	−0.571023	+	0.671754i
$443$	11.3515	+	6.55380i	0.539327	+	0.311381i	0.744806	−	0.667281i	$-0.232542\pi$
$443$	11.3515	+	6.55380i	0.539327	+	0.311381i	−0.205479	+	0.978661i	$0.565875\pi$
$444$		0			0
$445$	4.17610	−	2.41107i	0.197966	−	0.114296i
$446$	2.17953	−	11.9151i	0.103204	−	0.564195i
$447$		0			0
$448$	0.851284	−	22.1947i	0.0402194	−	1.04860i
$449$		−	24.9459i		−	1.17727i	−0.808400	−	0.588634i	$-0.799666\pi$
$449$		−	24.9459i		−	1.17727i	0.808400	−	0.588634i	$-0.200334\pi$
$450$		0			0
$451$	35.9754			1.69401
$452$	0.375620	−	0.992365i	0.0176677	−	0.0466769i
$453$		0			0
$454$	−5.88396	+	32.1664i	−0.276148	+	1.50964i
$455$	−5.29634	−	9.17354i	−0.248296	−	0.430062i
$456$		0			0
$457$	13.2777	−	22.9976i	0.621103	−	1.07578i	−0.368178	−	0.929755i	$-0.620018\pi$
$457$	13.2777	−	22.9976i	0.621103	−	1.07578i	0.989281	−	0.146026i	$-0.0466483\pi$
$458$	7.92162	+	6.73375i	0.370153	+	0.314647i
$459$		0			0
$460$	1.37334	+	8.41612i	0.0640324	+	0.392404i
$461$	5.99710	−	10.3873i	0.279313	−	0.483784i	−0.691901	−	0.721992i	$-0.743227\pi$
$461$	5.99710	−	10.3873i	0.279313	−	0.483784i	0.971214	+	0.238208i	$0.0765601\pi$
$462$		0			0
$463$	21.9062	−	12.6476i	1.01807	−	0.587782i	0.104525	−	0.994522i	$-0.466668\pi$
$463$	21.9062	−	12.6476i	1.01807	−	0.587782i	0.913544	+	0.406740i	$0.133334\pi$
$464$	−1.59886	−	1.41278i	−0.0742253	−	0.0655867i
$465$		0			0
$466$	−27.5345	+	9.82297i	−1.27551	+	0.455040i
$467$		−	7.44030i		−	0.344296i	−0.985071	−	0.172148i	$-0.944929\pi$
$467$		−	7.44030i		−	0.344296i	0.985071	−	0.172148i	$-0.0550707\pi$
$468$		0			0
$469$		−	19.3206i		−	0.892144i
$470$	−1.45132	−	4.06815i	−0.0669443	−	0.187650i
$471$		0			0
$472$	29.0348	+	0.556616i	1.33644	+	0.0256203i
$473$	−33.8502	+	19.5434i	−1.55643	+	0.898607i
$474$		0			0
$475$	−0.656931	+	1.13784i	−0.0301421	+	0.0522076i
$476$	3.07210	+	18.8265i	0.140810	+	0.862911i
$477$		0			0
$478$	4.23333	−	4.98012i	0.193628	−	0.227785i
$479$	19.5734	−	33.9022i	0.894333	−	1.54903i	0.0597054	−	0.998216i	$-0.480984\pi$
$479$	19.5734	−	33.9022i	0.894333	−	1.54903i	0.834628	−	0.550814i	$-0.185683\pi$
$480$		0			0
$481$	4.31614	+	7.47578i	0.196799	+	0.340866i
$482$	28.0616	+	5.13310i	1.27817	+	0.233806i
$483$		0			0
$484$	2.33739	+	0.884727i	0.106245	+	0.0402149i
$485$	8.40251			0.381538
$486$		0			0
$487$		−	20.0755i		−	0.909707i	−0.890566	−	0.454854i	$-0.849692\pi$
$487$		−	20.0755i		−	0.909707i	0.890566	−	0.454854i	$-0.150308\pi$
$488$	16.9070	+	30.6247i	0.765343	+	1.38632i
$489$		0			0
$490$	−0.985268	−	0.180228i	−0.0445099	−	0.00814186i
$491$	−18.3558	+	10.5977i	−0.828385	+	0.478268i	−0.853299	−	0.521421i	$-0.825402\pi$
$491$	−18.3558	+	10.5977i	−0.828385	+	0.478268i	0.0249145	+	0.999690i	$0.492069\pi$
$492$		0			0
$493$	1.58692	+	0.916207i	0.0714712	+	0.0412639i
$494$	5.40137	+	4.59141i	0.243019	+	0.206577i
$495$		0			0
$496$	−0.606562	−	1.80908i	−0.0272354	−	0.0812301i
$497$	18.9601	+	10.9466i	0.850479	+	0.491024i
$498$		0			0
$499$	−4.07075	−	7.05075i	−0.182232	−	0.315635i	0.760408	−	0.649445i	$-0.224999\pi$
$499$	−4.07075	−	7.05075i	−0.182232	−	0.315635i	−0.942640	+	0.333810i	$0.891665\pi$
$500$	−1.54839	+	1.26589i	−0.0692462	+	0.0566124i
$501$		0			0
$502$	20.3092	−	7.24532i	0.906442	−	0.323374i
$503$	−9.59614			−0.427871			−0.213935	−	0.976848i	$-0.568628\pi$
$503$	−9.59614			−0.427871			−0.213935	+	0.976848i	$0.568628\pi$
$504$		0			0
$505$	2.22137			0.0988495
$506$	17.7337	−	6.32653i	0.788361	−	0.281249i
$507$		0			0
$508$	0.702383	+	0.859129i	0.0311632	+	0.0381177i
$509$	0.164517	+	0.284953i	0.00729211	+	0.0126303i	0.869648	−	0.493672i	$-0.164345\pi$
$509$	0.164517	+	0.284953i	0.00729211	+	0.0126303i	−0.862356	+	0.506302i	$0.831012\pi$
$510$		0			0
$511$	−19.0564	−	11.0022i	−0.843004	−	0.486708i
$512$	−1.30047	+	22.5900i	−0.0574731	+	0.998347i
$513$		0			0
$514$	1.54960	+	1.31723i	0.0683500	+	0.0581007i
$515$	12.7933	+	7.38623i	0.563741	+	0.325476i
$516$		0			0
$517$	−8.25920	+	4.76845i	−0.363239	+	0.209716i
$518$	8.73863	+	1.59849i	0.383953	+	0.0702337i
$519$		0			0
$520$	5.21553	+	9.44723i	0.228716	+	0.414289i
$521$			14.4490i			0.633021i	0.948589	+	0.316510i	$0.102511\pi$
$521$			14.4490i			0.633021i	−0.948589	+	0.316510i	$0.897489\pi$
$522$		0			0
$523$	18.1246			0.792534			0.396267	−	0.918135i	$-0.370305\pi$
$523$	18.1246			0.792534			0.396267	+	0.918135i	$0.370305\pi$
$524$	4.26541	−	11.2689i	0.186335	−	0.492286i
$525$		0			0
$526$	−6.14513	−	1.12408i	−0.267940	−	0.0490123i
$527$	0.819351	+	1.41916i	0.0356915	+	0.0618194i
$528$		0			0
$529$	2.41035	−	4.17484i	0.104798	−	0.181515i
$530$	−13.0839	+	15.3920i	−0.568330	+	0.668586i
$531$		0			0
$532$	7.20031	−	1.17495i	0.312173	−	0.0509403i
$533$	−21.9782	+	38.0674i	−0.951983	+	1.64888i
$534$		0			0
$535$	12.1898	−	7.03777i	0.527010	−	0.304269i
$536$	−0.377264	+	19.6793i	−0.0162953	+	0.850015i
$537$		0			0
$538$	−11.8471	−	33.2084i	−0.510766	−	1.43172i
$539$			2.21155i			0.0952583i
$540$		0			0
$541$			3.63353i			0.156218i	0.996945	+	0.0781089i	$0.0248882\pi$
$541$			3.63353i			0.156218i	−0.996945	+	0.0781089i	$0.975112\pi$
$542$	28.6465	−	10.2197i	1.23047	−	0.438972i
$543$		0			0
$544$	−2.76151	−	19.2359i	−0.118399	−	0.824734i
$545$	−14.2957	+	8.25365i	−0.612363	+	0.353548i
$546$		0			0
$547$	11.7873	−	20.4162i	0.503987	−	0.872932i	−0.496002	−	0.868321i	$-0.665199\pi$
$547$	11.7873	−	20.4162i	0.503987	−	0.872932i	0.999989	−	0.00461043i	$-0.00146755\pi$
$548$	17.0708	−	2.78561i	0.729228	−	0.118995i
$549$		0			0
$550$	3.36462	+	2.86009i	0.143468	+	0.121954i
$551$	0.350409	−	0.606927i	0.0149279	−	0.0258560i
$552$		0			0
$553$	−0.300081	−	0.519755i	−0.0127607	−	0.0221022i
$554$	−0.203660	+	1.11337i	−0.00865270	+	0.0473026i
$555$		0			0
$556$	−17.6906	−	6.69606i	−0.750247	−	0.283976i
$557$	32.3117			1.36909			0.684544	−	0.728971i	$-0.260001\pi$
$557$	32.3117			1.36909			0.684544	+	0.728971i	$0.260001\pi$
$558$		0			0
$559$		−	47.7582i		−	2.01996i
$560$	10.8839	+	2.20731i	0.459930	+	0.0932758i
$561$		0			0
$562$	5.23181	−	28.6012i	0.220691	−	1.20647i
$563$	13.2429	−	7.64582i	0.558124	−	0.322233i	−0.194268	−	0.980948i	$-0.562233\pi$
$563$	13.2429	−	7.64582i	0.558124	−	0.322233i	0.752392	+	0.658716i	$0.228900\pi$
$564$		0			0
$565$	0.459459	+	0.265268i	0.0193296	+	0.0111599i
$566$	13.4118	−	15.7777i	0.563741	−	0.663188i
$567$		0			0
$568$	−19.0983	−	11.5201i	−0.801348	−	0.483371i
$569$	18.3848	+	10.6145i	0.770730	+	0.444981i	0.833135	−	0.553070i	$-0.186544\pi$
$569$	18.3848	+	10.6145i	0.770730	+	0.444981i	−0.0624050	+	0.998051i	$0.519877\pi$
$570$		0			0
$571$	−20.3971	−	35.3288i	−0.853591	−	1.47846i	−0.877946	−	0.478760i	$-0.841086\pi$
$571$	−20.3971	−	35.3288i	−0.853591	−	1.47846i	0.0243545	−	0.999703i	$-0.492247\pi$
$572$	18.4468	−	15.0812i	0.771298	−	0.630577i
$573$		0			0
$574$	15.1998	+	42.6062i	0.634428	+	1.77835i
$575$	−4.26372			−0.177809
$576$		0			0
$577$	29.2113			1.21608			0.608040	−	0.793906i	$-0.291956\pi$
$577$	29.2113			1.21608			0.608040	+	0.793906i	$0.291956\pi$
$578$	−2.47028	−	6.92439i	−0.102750	−	0.288017i
$579$		0			0
$580$	0.825917	−	0.675231i	0.0342944	−	0.0280375i
$581$	−12.6060	−	21.8342i	−0.522984	−	0.905834i
$582$		0			0
$583$	38.6288	+	22.3024i	1.59984	+	0.923670i
$584$	19.1952	+	11.5785i	0.794305	+	0.479122i
$585$		0			0
$586$	24.6237	−	28.9674i	1.01719	−	1.19663i
$587$	2.09726	+	1.21086i	0.0865634	+	0.0499774i	0.542657	−	0.839954i	$-0.317418\pi$
$587$	2.09726	+	1.21086i	0.0865634	+	0.0499774i	−0.456093	+	0.889932i	$0.650752\pi$
$588$		0			0
$589$	0.542766	−	0.313366i	0.0223643	−	0.0129120i
$590$	−2.61270	+	14.2831i	−0.107563	+	0.588026i
$591$		0			0
$592$	−8.86962	−	1.79880i	−0.364539	−	0.0739301i
$593$		−	7.77622i		−	0.319331i	−0.987171	−	0.159666i	$-0.948958\pi$
$593$		−	7.77622i		−	0.319331i	0.987171	−	0.159666i	$-0.0510416\pi$
$594$		0			0
$595$	−9.53775			−0.391010
$596$	−20.3104	−	7.68771i	−0.831948	−	0.314901i
$597$		0			0
$598$	−4.13954	+	22.6300i	−0.169278	+	0.925410i
$599$	9.47635	+	16.4135i	0.387193	+	0.670638i	0.992071	−	0.125680i	$-0.0401113\pi$
$599$	9.47635	+	16.4135i	0.387193	+	0.670638i	−0.604878	+	0.796318i	$0.706778\pi$
$600$		0			0
$601$	−11.5216	+	19.9560i	−0.469976	+	0.814023i	−0.999411	−	0.0343283i	$-0.989071\pi$
$601$	−11.5216	+	19.9560i	−0.469976	+	0.814023i	0.529434	+	0.848351i	$0.322404\pi$
$602$	−37.4475	−	31.8321i	−1.52625	−	1.29738i
$603$		0			0
$604$	21.3710	−	3.48731i	0.869574	−	0.141897i
$605$	−0.624807	+	1.08220i	−0.0254020	+	0.0439976i
$606$		0			0
$607$	−26.8628	+	15.5092i	−1.09033	+	0.629500i	−0.933663	−	0.358153i	$-0.883407\pi$
$607$	−26.8628	+	15.5092i	−1.09033	+	0.629500i	−0.156662	+	0.987652i	$0.550073\pi$
$608$	−7.35690	+	1.05616i	−0.298362	+	0.0428328i
$609$		0			0
$610$	−16.4739	+	5.87708i	−0.667009	+	0.237956i
$611$		−	11.6526i		−	0.471416i
$612$		0			0
$613$			43.8644i			1.77167i	0.464002	+	0.885834i	$0.346413\pi$
$613$			43.8644i			1.77167i	−0.464002	+	0.885834i	$0.653587\pi$
$614$	10.1614	+	28.4831i	0.410080	+	1.14948i
$615$		0			0
$616$	0.469991	−	24.5162i	0.0189365	−	0.987788i
$617$	−20.2819	+	11.7098i	−0.816520	+	0.471418i	−0.849215	−	0.528047i	$-0.822924\pi$
$617$	−20.2819	+	11.7098i	−0.816520	+	0.471418i	0.0326947	+	0.999465i	$0.489591\pi$
$618$		0			0
$619$	13.1137	−	22.7136i	0.527084	−	0.912935i	−0.472418	−	0.881374i	$-0.656619\pi$
$619$	13.1137	−	22.7136i	0.527084	−	0.912935i	0.999502	−	0.0315610i	$-0.0100479\pi$
$620$	0.941576	−	0.153646i	0.0378146	−	0.00617058i
$621$		0			0
$622$	19.6091	−	23.0682i	0.786251	−	0.924951i
$623$	6.69404	−	11.5944i	0.268191	−	0.464521i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.11916	−	1.48518i	−0.324507	−	0.0593596i
$627$		0			0
$628$	−11.6676	+	30.8250i	−0.465587	+	1.23005i
$629$	7.77258			0.309913
$630$		0			0
$631$			7.35292i			0.292715i	0.989232	+	0.146358i	$0.0467550\pi$
$631$			7.35292i			0.292715i	−0.989232	+	0.146358i	$0.953245\pi$
$632$	0.295502	+	0.535262i	0.0117544	+	0.0212916i
$633$		0			0
$634$	11.6595	+	2.13278i	0.463057	+	0.0847035i
$635$	−0.480516	+	0.277426i	−0.0190687	+	0.0110093i
$636$		0			0
$637$	−2.34016	−	1.35109i	−0.0927204	−	0.0535322i
$638$	−1.79470	−	1.52558i	−0.0710529	−	0.0603983i
$639$		0			0
$640$	−11.0428	−	2.46080i	−0.436507	−	0.0972718i
$641$	−4.75502	−	2.74531i	−0.187812	−	0.108433i	0.403146	−	0.915136i	$-0.367917\pi$
$641$	−4.75502	−	2.74531i	−0.187812	−	0.108433i	−0.590958	+	0.806702i	$0.701250\pi$
$642$		0			0
$643$	−10.2614	−	17.7733i	−0.404670	−	0.700909i	0.589613	−	0.807686i	$-0.299280\pi$
$643$	−10.2614	−	17.7733i	−0.404670	−	0.700909i	−0.994283	+	0.106777i	$0.965947\pi$
$644$	14.9852	+	18.3294i	0.590501	+	0.722278i
$645$		0			0
$646$	6.01200	−	2.14479i	0.236539	−	0.0843855i
$647$	39.5969			1.55672			0.778358	−	0.627820i	$-0.216053\pi$
$647$	39.5969			1.55672			0.778358	+	0.627820i	$0.216053\pi$
$648$		0			0
$649$	32.0601			1.25847
$650$	−5.08193	+	1.81299i	−0.199330	+	0.0711111i
$651$		0			0
$652$	−11.7045	+	9.56907i	−0.458384	+	0.374754i
$653$	−22.5179	−	39.0021i	−0.881193	−	1.52627i	−0.850016	−	0.526757i	$-0.823408\pi$
$653$	−22.5179	−	39.0021i	−0.881193	−	1.52627i	−0.0311765	−	0.999514i	$-0.509925\pi$
$654$		0			0
$655$	5.21744	+	3.01229i	0.203862	+	0.117700i
$656$	−14.6500	−	43.6939i	−0.571986	−	1.70596i
$657$		0			0
$658$	−9.13691	−	7.76680i	−0.356194	−	0.302781i
$659$	22.1927	+	12.8129i	0.864504	+	0.499121i	0.865518	−	0.500878i	$-0.166990\pi$
$659$	22.1927	+	12.8129i	0.864504	+	0.499121i	−0.00101427	+	0.999999i	$0.500323\pi$
$660$		0			0
$661$	−9.96758	+	5.75478i	−0.387694	+	0.223835i	−0.681160	−	0.732134i	$-0.738524\pi$
$661$	−9.96758	+	5.75478i	−0.387694	+	0.223835i	0.293467	+	0.955969i	$0.405191\pi$
$662$	2.50715	+	0.458614i	0.0974431	+	0.0178245i
$663$		0			0
$664$	12.4136	+	22.4856i	0.481741	+	0.872610i
$665$			3.64777i			0.141455i
$666$		0			0
$667$	2.27428			0.0880606
$668$	39.7935	+	15.0623i	1.53966	+	0.582777i
$669$		0			0
$670$	−9.68081	−	1.77084i	−0.374002	−	0.0684135i
$671$	19.3098	+	33.4455i	0.745445	+	1.29115i
$672$		0			0
$673$	23.4948	−	40.6943i	0.905660	−	1.56865i	0.0856300	−	0.996327i	$-0.472710\pi$
$673$	23.4948	−	40.6943i	0.905660	−	1.56865i	0.820029	−	0.572321i	$-0.193957\pi$
$674$	−21.9455	+	25.8168i	−0.845308	+	0.994425i
$675$		0			0
$676$	0.501343	+	3.07234i	0.0192824	+	0.118167i
$677$	−8.46874	+	14.6683i	−0.325480	+	0.563748i	−0.981609	−	0.190900i	$-0.938859\pi$
$677$	−8.46874	+	14.6683i	−0.325480	+	0.563748i	0.656129	+	0.754649i	$0.272193\pi$
$678$		0			0
$679$	20.2031	−	11.6642i	0.775323	−	0.447633i
$680$	9.71478	+	0.186238i	0.372545	+	0.00714191i
$681$		0			0
$682$	−0.707797	−	1.98401i	−0.0271029	−	0.0759716i
$683$		−	2.98462i		−	0.114203i	−0.998368	−	0.0571017i	$-0.981814\pi$
$683$		−	2.98462i		−	0.114203i	0.998368	−	0.0571017i	$-0.0181859\pi$
$684$		0			0
$685$			8.64828i			0.330434i
$686$	23.2675	−	8.30071i	0.888358	−	0.316923i
$687$		0			0
$688$	37.5210	+	33.1542i	1.43047	+	1.26399i
$689$	−47.1986	+	27.2501i	−1.79812	+	1.03815i
$690$		0			0
$691$	4.17425	−	7.23001i	0.158796	−	0.275043i	−0.775639	−	0.631177i	$-0.782572\pi$
$691$	4.17425	−	7.23001i	0.158796	−	0.275043i	0.934435	+	0.356134i	$0.115905\pi$
$692$	−6.64593	−	40.7277i	−0.252640	−	1.54823i
$693$		0			0
$694$	−18.6950	−	15.8916i	−0.709653	−	0.603238i
$695$	4.72886	−	8.19062i	0.179376	−	0.310688i
$696$		0			0
$697$	19.7894	+	34.2762i	0.749577	+	1.29830i
$698$	−2.14361	+	11.7187i	−0.0811370	+	0.443559i
$699$		0			0
$700$	−1.96567	+	5.19318i	−0.0742954	+	0.196284i
$701$	−9.37518			−0.354096			−0.177048	−	0.984202i	$-0.556655\pi$
$701$	−9.37518			−0.354096			−0.177048	+	0.984202i	$0.556655\pi$
$702$		0			0
$703$		−	2.97267i		−	0.112117i
$704$	−0.957431	+	24.9621i	−0.0360845	+	0.940796i
$705$		0			0
$706$	−4.39113	+	24.0054i	−0.165262	+	0.903455i
$707$	5.34107	−	3.08367i	0.200872	−	0.115973i
$708$		0			0
$709$	33.2487	+	19.1962i	1.24868	+	0.720927i	0.970847	−	0.239702i	$-0.0770496\pi$
$709$	33.2487	+	19.1962i	1.24868	+	0.720927i	0.277836	+	0.960629i	$0.410383\pi$
$710$	7.22273	−	8.49686i	0.271064	−	0.318881i
$711$		0			0
$712$	−7.04469	+	11.6789i	−0.264011	+	0.437686i
$713$	1.76137	+	1.01693i	0.0659639	+	0.0380843i
$714$		0			0
$715$	5.95675	+	10.3174i	0.222770	+	0.385848i
$716$	−9.50404	−	11.6250i	−0.355183	−	0.434446i
$717$		0			0
$718$	−3.38843	−	9.49802i	−0.126455	−	0.354463i
$719$	−12.8804			−0.480356			−0.240178	−	0.970729i	$-0.577206\pi$
$719$	−12.8804			−0.480356			−0.240178	+	0.970729i	$0.577206\pi$
$720$		0			0
$721$	41.0138			1.52744
$722$	8.20830	+	23.0085i	0.305481	+	0.856287i
$723$		0			0
$724$	−19.2601	−	23.5582i	−0.715795	−	0.875533i
$725$	0.266702	+	0.461941i	0.00990505	+	0.0171561i
$726$		0			0
$727$	−3.75846	−	2.16995i	−0.139393	−	0.0804788i	0.428681	−	0.903456i	$-0.358978\pi$
$727$	−3.75846	−	2.16995i	−0.139393	−	0.0804788i	−0.568075	+	0.822977i	$0.692312\pi$
$728$	25.6548	+	15.4749i	0.950830	+	0.573538i
$729$		0			0
$730$	−7.25938	+	8.53998i	−0.268682	+	0.316079i
$731$	−37.2407	−	21.5009i	−1.37740	−	0.795241i
$732$		0			0
$733$	−18.8815	+	10.9012i	−0.697404	+	0.402646i	−0.806380	−	0.591398i	$-0.798576\pi$
$733$	−18.8815	+	10.9012i	−0.697404	+	0.402646i	0.108976	+	0.994044i	$0.465243\pi$
$734$	8.63232	−	47.1911i	0.318625	−	1.74186i
$735$		0			0
$736$	−14.9055	−	18.9622i	−0.549423	−	0.698956i
$737$			21.7297i			0.800425i
$738$		0			0
$739$	−31.8843			−1.17288			−0.586441	−	0.809992i	$-0.699471\pi$
$739$	−31.8843			−1.17288			−0.586441	+	0.809992i	$0.699471\pi$
$740$	1.60188	−	4.23207i	0.0588864	−	0.155574i
$741$		0			0
$742$	−10.0921	+	55.1717i	−0.370494	+	2.02542i
$743$	12.2533	+	21.2234i	0.449532	+	0.778612i	0.998355	−	0.0573263i	$-0.0182575\pi$
$743$	12.2533	+	21.2234i	0.449532	+	0.778612i	−0.548824	+	0.835938i	$0.684924\pi$
$744$		0			0
$745$	5.42917	−	9.40360i	0.198909	−	0.344521i
$746$	10.5513	+	8.96912i	0.386312	+	0.328383i
$747$		0			0
$748$	−3.45516	−	21.1740i	−0.126333	−	0.774197i
$749$	19.5395	−	33.8434i	0.713957	−	1.23661i
$750$		0			0
$751$	5.51362	−	3.18329i	0.201195	−	0.116160i	−0.396018	−	0.918243i	$-0.629608\pi$
$751$	5.51362	−	3.18329i	0.201195	−	0.116160i	0.597213	+	0.802083i	$0.296275\pi$
$752$	9.15485	+	8.08938i	0.333843	+	0.294989i
$753$		0			0
$754$	2.71072	−	0.967053i	0.0987186	−	0.0352180i
$755$			10.8268i			0.394029i
$756$		0			0
$757$			25.0713i			0.911232i	0.890176	+	0.455616i	$0.150581\pi$
$757$			25.0713i			0.911232i	−0.890176	+	0.455616i	$0.849419\pi$
$758$	−7.57702	−	21.2390i	−0.275210	−	0.771434i
$759$		0			0
$760$	0.0712281	−	3.71548i	0.00258371	−	0.134775i
$761$	−11.3876	+	6.57465i	−0.412801	+	0.238331i	−0.691993	−	0.721905i	$-0.743267\pi$
$761$	−11.3876	+	6.57465i	−0.412801	+	0.238331i	0.279191	+	0.960235i	$0.409934\pi$
$762$		0			0
$763$	−22.9152	+	39.6903i	−0.829587	+	1.43689i
$764$	−4.38125	−	26.8492i	−0.158508	−	0.971371i
$765$		0			0
$766$	−6.78093	+	7.97713i	−0.245005	+	0.288225i
$767$	−19.5863	+	33.9245i	−0.707221	+	1.22494i
$768$		0			0
$769$	−11.6041	−	20.0990i	−0.418456	−	0.724787i	0.577329	−	0.816512i	$-0.304095\pi$
$769$	−11.6041	−	20.0990i	−0.418456	−	0.724787i	−0.995784	+	0.0917252i	$0.970762\pi$
$770$	12.0603	+	2.20609i	0.434622	+	0.0795021i
$771$		0			0
$772$	41.5093	+	15.7117i	1.49395	+	0.565477i
$773$	−32.0701			−1.15348			−0.576740	−	0.816928i	$-0.695675\pi$
$773$	−32.0701			−1.15348			−0.576740	+	0.816928i	$0.695675\pi$
$774$		0			0
$775$			0.477015i			0.0171349i
$776$	−20.8058	+	11.4863i	−0.746886	+	0.412333i
$777$		0			0
$778$	−36.1753	−	6.61727i	−1.29695	−	0.237241i
$779$	13.1092	−	7.56858i	0.469685	−	0.271172i
$780$		0			0
$781$	−21.3243	−	12.3116i	−0.763043	−	0.440543i
$782$	15.7827	+	13.4161i	0.564389	+	0.479757i
$783$		0			0
$784$	2.68604	−	0.900595i	0.0959299	−	0.0321641i
$785$	−14.2718	−	8.23981i	−0.509381	−	0.294091i
$786$		0			0
$787$	20.0375	+	34.7059i	0.714258	+	1.23713i	0.963245	+	0.268624i	$0.0865690\pi$
$787$	20.0375	+	34.7059i	0.714258	+	1.23713i	−0.248987	+	0.968507i	$0.580098\pi$
$788$	−9.09109	+	7.43245i	−0.323857	+	0.264770i
$789$		0			0
$790$	−0.287932	+	0.102720i	−0.0102442	+	0.00365462i
$791$	1.47297			0.0523727
$792$		0			0
$793$	−47.1872			−1.67567
$794$	−35.8357	+	12.7844i	−1.27176	+	0.453703i
$795$		0			0
$796$	−22.1137	−	27.0487i	−0.783800	−	0.958714i
$797$	−28.1638	−	48.7811i	−0.997612	−	1.72791i	−0.558622	−	0.829423i	$-0.688670\pi$
$797$	−28.1638	−	48.7811i	−0.997612	−	1.72791i	−0.438990	−	0.898492i	$-0.644664\pi$
$798$		0			0
$799$	−9.08646	−	5.24607i	−0.321456	−	0.185593i
$800$	2.10356	−	5.25119i	0.0743722	−	0.185658i
$801$		0			0
$802$	−11.2469	−	9.56042i	−0.397143	−	0.337590i
$803$	21.4325	+	12.3741i	0.756337	+	0.436671i
$804$		0			0
$805$	−10.2517	+	5.91884i	−0.361326	+	0.208612i
$806$	2.53179	+	0.463122i	0.0891786	+	0.0163128i
$807$		0			0
$808$	−5.50043	+	3.03662i	−0.193504	+	0.106828i
$809$		−	17.2021i		−	0.604793i	−0.953182	−	0.302397i	$-0.902213\pi$
$809$		−	17.2021i		−	0.604793i	0.953182	−	0.302397i	$-0.0977867\pi$
$810$		0			0
$811$	−56.3100			−1.97731			−0.988656	−	0.150196i	$-0.952010\pi$
$811$	−56.3100			−1.97731			−0.988656	+	0.150196i	$0.952010\pi$
$812$	1.04850	−	2.77006i	0.0367950	−	0.0972101i
$813$		0			0
$814$	−9.82825	−	1.79781i	−0.344480	−	0.0630132i
$815$	−3.77957	−	6.54641i	−0.132393	−	0.229311i
$816$		0			0
$817$	−8.22317	+	14.2430i	−0.287692	+	0.498298i
$818$	3.83579	−	4.51245i	0.134115	−	0.157774i
$819$		0			0
$820$	22.7414	−	3.71094i	0.794165	−	0.129592i
$821$	−1.37477	+	2.38117i	−0.0479797	+	0.0831033i	−0.889018	−	0.457873i	$-0.848612\pi$
$821$	−1.37477	+	2.38117i	−0.0479797	+	0.0831033i	0.841038	+	0.540976i	$0.181945\pi$
$822$		0			0
$823$	23.4482	−	13.5378i	0.817353	−	0.471899i	−0.0321498	−	0.999483i	$-0.510235\pi$
$823$	23.4482	−	13.5378i	0.817353	−	0.471899i	0.849503	+	0.527584i	$0.176902\pi$
$824$	−41.7751	−	0.800855i	−1.45531	−	0.0278991i
$825$		0			0
$826$	13.5456	+	37.9693i	0.471312	+	1.32112i
$827$		−	29.3670i		−	1.02119i	−0.859821	−	0.510596i	$-0.829425\pi$
$827$		−	29.3670i		−	1.02119i	0.859821	−	0.510596i	$-0.170575\pi$
$828$		0			0
$829$		−	30.1503i		−	1.04716i	−0.851975	−	0.523582i	$-0.824595\pi$
$829$		−	30.1503i		−	1.04716i	0.851975	−	0.523582i	$-0.175405\pi$
$830$	−12.0956	+	4.31513i	−0.419846	+	0.149780i
$831$		0			0
$832$	−25.8288	−	16.2631i	−0.895453	−	0.563821i
$833$	−2.10710	+	1.21653i	−0.0730066	+	0.0421504i
$834$		0			0
$835$	−10.6372	+	18.4242i	−0.368115	+	0.637594i
$836$	−8.09812	+	1.32145i	−0.280079	+	0.0457033i
$837$		0			0
$838$	3.49480	+	2.97074i	0.120726	+	0.102623i
$839$	−3.81222	+	6.60296i	−0.131612	+	0.227959i	−0.924298	−	0.381671i	$-0.875349\pi$
$839$	−3.81222	+	6.60296i	−0.131612	+	0.227959i	0.792686	+	0.609630i	$0.208682\pi$
$840$		0			0
$841$	14.3577	+	24.8683i	0.495094	+	0.857529i
$842$	1.60297	−	8.76313i	0.0552422	−	0.301997i
$843$		0			0
$844$	32.9371	+	12.4670i	1.13374	+	0.429133i
$845$	−1.55649			−0.0535448
$846$		0			0
$847$			3.46939i			0.119210i
$848$	11.3568	−	55.9987i	0.389993	−	1.92300i
$849$		0			0
$850$	−0.874185	+	4.77899i	−0.0299843	+	0.163918i
$851$	8.35443	−	4.82343i	0.286386	−	0.165345i
$852$		0			0
$853$	−19.9923	−	11.5426i	−0.684525	−	0.395211i	0.117033	−	0.993128i	$-0.462662\pi$
$853$	−19.9923	−	11.5426i	−0.684525	−	0.395211i	−0.801558	+	0.597917i	$0.795995\pi$
$854$	−31.4515	+	36.9998i	−1.07625	+	1.26611i
$855$		0			0
$856$	−20.5630	+	34.0900i	−0.702829	+	1.16517i
$857$	−0.537623	−	0.310397i	−0.0183649	−	0.0106030i	0.490789	−	0.871278i	$-0.336708\pi$
$857$	−0.537623	−	0.310397i	−0.0183649	−	0.0106030i	−0.509154	+	0.860675i	$0.670042\pi$
$858$		0			0
$859$	−12.4175	−	21.5077i	−0.423678	−	0.733833i	0.572618	−	0.819823i	$-0.305928\pi$
$859$	−12.4175	−	21.5077i	−0.423678	−	0.733833i	−0.996296	+	0.0859901i	$0.972595\pi$
$860$	−19.3821	+	15.8459i	−0.660923	+	0.540340i
$861$		0			0
$862$	8.07136	+	22.6246i	0.274912	+	0.770598i
$863$	2.55660			0.0870275			0.0435138	−	0.999053i	$-0.486145\pi$
$863$	2.55660			0.0870275			0.0435138	+	0.999053i	$0.486145\pi$
$864$		0			0
$865$	20.6332			0.701549
$866$	8.38833	+	23.5131i	0.285047	+	0.799008i
$867$		0			0
$868$	2.05064	−	1.67651i	0.0696034	−	0.0569045i
$869$	0.337498	+	0.584563i	0.0114488	+	0.0198299i
$870$		0			0
$871$	−22.9934	−	13.2752i	−0.779101	−	0.449814i
$872$	24.1156	−	39.9796i	0.816657	−	1.35388i
$873$		0			0
$874$	5.13106	−	6.03621i	0.173561	−	0.204178i
$875$	−2.40441	−	1.38819i	−0.0812839	−	0.0469293i
$876$		0			0
$877$	−14.8560	+	8.57713i	−0.501653	+	0.289629i	−0.729396	−	0.684092i	$-0.760199\pi$
$877$	−14.8560	+	8.57713i	−0.501653	+	0.289629i	0.227743	+	0.973721i	$0.426865\pi$
$878$	−9.74360	+	53.2662i	−0.328830	+	1.79765i
$879$		0			0
$880$	−12.2410	−	2.48254i	−0.412646	−	0.0836863i
$881$		−	0.662030i		−	0.0223043i	−0.999938	−	0.0111522i	$-0.996450\pi$
$881$		−	0.662030i		−	0.0223043i	0.999938	−	0.0111522i	$-0.00354992\pi$
$882$		0			0
$883$	−11.4683			−0.385939			−0.192969	−	0.981205i	$-0.561812\pi$
$883$	−11.4683			−0.385939			−0.192969	+	0.981205i	$0.561812\pi$
$884$	24.5161	+	9.27961i	0.824567	+	0.312107i
$885$		0			0
$886$	3.33548	−	18.2344i	0.112058	−	0.612596i
$887$	23.5408	+	40.7738i	0.790422	+	1.36905i	0.925706	+	0.378245i	$0.123472\pi$
$887$	23.5408	+	40.7738i	0.790422	+	1.36905i	−0.135283	+	0.990807i	$0.543194\pi$
$888$		0			0
$889$	−0.770239	+	1.33409i	−0.0258330	+	0.0447440i
$890$	−5.19596	−	4.41681i	−0.174169	−	0.148052i
$891$		0			0
$892$	−16.9064	+	2.75879i	−0.566069	+	0.0923710i
$893$	−2.00639	+	3.47518i	−0.0671414	+	0.116292i
$894$		0			0
$895$	6.50193	−	3.75389i	0.217335	−	0.125479i
$896$	−29.9676	+	9.41275i	−1.00115	+	0.314458i
$897$		0			0
$898$	−33.2276	+	11.8540i	−1.10882	+	0.395573i
$899$		−	0.254441i		−	0.00848609i
$900$		0			0
$901$			49.0725i			1.63484i
$902$	−17.0951	−	47.9188i	−0.569204	−	1.59552i
$903$		0			0
$904$	−1.50031	−	0.0287619i	−0.0498996	−	0.000956605i
$905$	13.1762	−	7.60731i	0.437993	−	0.252876i
$906$		0			0
$907$	5.68246	−	9.84232i	0.188683	−	0.326809i	−0.756128	−	0.654423i	$-0.772911\pi$
$907$	5.68246	−	9.84232i	0.188683	−	0.326809i	0.944811	+	0.327615i	$0.106245\pi$
$908$	45.6413	−	7.44773i	1.51466	−	0.247162i
$909$		0			0
$910$	−9.70229	+	11.4138i	−0.321628	+	0.378365i
$911$	0.698984	−	1.21068i	0.0231584	−	0.0401115i	−0.854214	−	0.519922i	$-0.825961\pi$
$911$	0.698984	−	1.21068i	0.0231584	−	0.0401115i	0.877372	+	0.479810i	$0.159294\pi$
$912$		0			0
$913$	14.1778	+	24.5567i	0.469217	+	0.812708i
$914$	−36.9419	−	6.75751i	−1.22193	−	0.223519i
$915$		0			0
$916$	5.20502	−	13.7513i	0.171979	−	0.454356i
$917$	16.7265			0.552358
$918$		0			0
$919$			7.89210i			0.260336i	0.991492	+	0.130168i	$0.0415517\pi$
$919$			7.89210i			0.260336i	−0.991492	+	0.130168i	$0.958448\pi$
$920$	10.5576	−	5.82852i	0.348074	−	0.192161i
$921$		0			0
$922$	−16.6855	−	3.05215i	−0.549507	−	0.100517i
$923$	26.0551	−	15.0429i	0.857612	−	0.495143i
$924$		0			0
$925$	1.95942	+	1.13127i	0.0644254	+	0.0371960i
$926$	−27.2560	−	23.1689i	−0.895688	−	0.761377i
$927$		0			0
$928$	−1.12205	+	2.80100i	−0.0368330	+	0.0919475i
$929$	15.9015	+	9.18072i	0.521710	+	0.301210i	0.737634	−	0.675201i	$-0.235943\pi$
$929$	15.9015	+	9.18072i	0.521710	+	0.301210i	−0.215924	+	0.976410i	$0.569276\pi$
$930$		0			0
$931$	0.465271	+	0.805873i	0.0152486	+	0.0264114i
$932$	26.1682	+	32.0079i	0.857168	+	1.04845i
$933$		0			0
$934$	−9.91039	+	3.53554i	−0.324278	+	0.115687i
$935$	10.7270			0.350811
$936$		0			0
$937$	−11.5833			−0.378411			−0.189205	−	0.981938i	$-0.560591\pi$
$937$	−11.5833			−0.378411			−0.189205	+	0.981938i	$0.560591\pi$
$938$	−25.7349	+	9.18095i	−0.840274	+	0.299769i
$939$		0			0
$940$	−4.72908	+	3.86628i	−0.154246	+	0.126104i
$941$	2.75857	+	4.77799i	0.0899270	+	0.155758i	0.907480	−	0.420095i	$-0.138003\pi$
$941$	2.75857	+	4.77799i	0.0899270	+	0.155758i	−0.817553	+	0.575853i	$0.804670\pi$
$942$		0			0
$943$	42.5416	+	24.5614i	1.38534	+	0.799829i
$944$	−13.0556	−	38.9386i	−0.424924	−	1.26734i
$945$		0			0
$946$	42.1168	+	35.8013i	1.36934	+	1.16400i
$947$	14.0517	+	8.11276i	0.456620	+	0.263629i	0.710622	−	0.703574i	$-0.248414\pi$
$947$	14.0517	+	8.11276i	0.456620	+	0.263629i	−0.254002	+	0.967204i	$0.581747\pi$
$948$		0			0
$949$	−26.1873	+	15.1192i	−0.850075	+	0.490791i
$950$	1.82775	+	0.334338i	0.0593002	+	0.0108473i
$951$		0			0
$952$	23.6169	−	13.0381i	0.765427	−	0.422569i
$953$			0.197221i			0.00638861i	0.999995	+	0.00319431i	$0.00101678\pi$
$953$			0.197221i			0.00638861i	−0.999995	+	0.00319431i	$0.998983\pi$
$954$		0			0
$955$	13.6022			0.440156
$956$	−8.64510	−	3.27226i	−0.279603	−	0.105832i
$957$		0			0
$958$	−54.4584	−	9.96168i	−1.75947	−	0.321847i
$959$	12.0054	+	20.7940i	0.387676	+	0.671474i
$960$		0			0
$961$	−15.3862	+	26.6497i	−0.496330	+	0.859669i
$962$	7.90667	−	9.30146i	0.254921	−	0.299891i
$963$		0			0
$964$	−6.49732	−	39.8170i	−0.209265	−	1.28242i
$965$	−11.0958	+	19.2185i	−0.357188	+	0.618667i
$966$		0			0
$967$	−21.8675	+	12.6252i	−0.703213	+	0.406000i	−0.808543	−	0.588437i	$-0.799743\pi$
$967$	−21.8675	+	12.6252i	−0.703213	+	0.406000i	0.105330	+	0.994437i	$0.466410\pi$
$968$	0.0677450	−	3.53379i	0.00217741	−	0.113580i
$969$		0			0
$970$	−3.99278	−	11.1921i	−0.128200	−	0.359355i
$971$			10.6137i			0.340610i	0.985391	+	0.170305i	$0.0544753\pi$
$971$			10.6137i			0.340610i	−0.985391	+	0.170305i	$0.945525\pi$
$972$		0			0
$973$		−	26.2581i		−	0.841798i
$974$	−26.7403	+	9.53965i	−0.856816	+	0.305670i
$975$		0			0
$976$	32.7578	−	37.0724i	1.04855	−	1.18666i
$977$	24.4452	−	14.1134i	0.782071	−	0.451529i	−0.0550925	−	0.998481i	$-0.517545\pi$
$977$	24.4452	−	14.1134i	0.782071	−	0.451529i	0.837164	+	0.546952i	$0.184212\pi$
$978$		0			0
$979$	−7.52873	+	13.0401i	−0.240619	+	0.416765i
$980$	0.228127	+	1.39801i	0.00728724	+	0.0446577i
$981$		0			0
$982$	22.8385	+	19.4138i	0.728806	+	0.619519i
$983$	22.5114	−	38.9908i	0.718001	−	1.24361i	−0.243790	−	0.969828i	$-0.578391\pi$
$983$	22.5114	−	38.9908i	0.718001	−	1.24361i	0.961791	−	0.273786i	$-0.0882760\pi$
$984$		0			0
$985$	−2.93566	−	5.08471i	−0.0935378	−	0.162012i
$986$	0.466293	−	2.54913i	0.0148498	−	0.0811808i
$987$		0			0
$988$	3.54905	−	9.37635i	0.112910	−	0.298301i
$989$	−53.3713			−1.69711
$990$		0			0
$991$		−	45.4039i		−	1.44230i	−0.692778	−	0.721151i	$-0.743613\pi$
$991$		−	45.4039i		−	1.44230i	0.692778	−	0.721151i	$-0.256387\pi$
$992$	−2.12144	+	1.66759i	−0.0673559	+	0.0529460i
$993$		0			0
$994$	5.57117	−	30.4564i	0.176707	−	0.966019i
$995$	15.1285	−	8.73444i	0.479605	−	0.276900i
$996$		0			0
$997$	15.3295	+	8.85052i	0.485492	+	0.280299i	0.722702	−	0.691160i	$-0.242900\pi$
$997$	15.3295	+	8.85052i	0.485492	+	0.280299i	−0.237211	+	0.971458i	$0.576233\pi$
$998$	−7.45715	+	8.77263i	−0.236052	+	0.277693i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.bm.a.251.10		48
3.2	odd	2		360.2.bm.b.11.15	yes	48
4.3	odd	2		4320.2.cc.a.1871.19		48
8.3	odd	2		1080.2.bm.b.251.1		48
8.5	even	2		4320.2.cc.b.1871.6		48
9.4	even	3		360.2.bm.a.131.24	yes	48
9.5	odd	6		1080.2.bm.b.611.1		48
12.11	even	2		1440.2.cc.b.911.24		48
24.5	odd	2		1440.2.cc.a.911.24		48
24.11	even	2		360.2.bm.a.11.24	✓	48
36.23	even	6		4320.2.cc.b.3311.6		48
36.31	odd	6		1440.2.cc.a.1391.24		48
72.5	odd	6		4320.2.cc.a.3311.19		48
72.13	even	6		1440.2.cc.b.1391.24		48
72.59	even	6	inner	1080.2.bm.a.611.10		48
72.67	odd	6		360.2.bm.b.131.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.24	✓	48	24.11	even	2
360.2.bm.a.131.24	yes	48	9.4	even	3
360.2.bm.b.11.15	yes	48	3.2	odd	2
360.2.bm.b.131.15	yes	48	72.67	odd	6
1080.2.bm.a.251.10		48	1.1	even	1	trivial
1080.2.bm.a.611.10		48	72.59	even	6	inner
1080.2.bm.b.251.1		48	8.3	odd	2
1080.2.bm.b.611.1		48	9.5	odd	6
1440.2.cc.a.911.24		48	24.5	odd	2
1440.2.cc.a.1391.24		48	36.31	odd	6
1440.2.cc.b.911.24		48	12.11	even	2
1440.2.cc.b.1391.24		48	72.13	even	6
4320.2.cc.a.1871.19		48	4.3	odd	2
4320.2.cc.a.3311.19		48	72.5	odd	6
4320.2.cc.b.1871.6		48	8.5	even	2
4320.2.cc.b.3311.6		48	36.23	even	6

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:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.475189 - 1.33199i) q^{2} +(-1.54839 + 1.26589i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.40441 - 1.38819i) q^{7} +(2.42193 + 1.46090i) q^{8} +O(q^{10})\)	\(q+(-0.475189 - 1.33199i) q^{2} +(-1.54839 + 1.26589i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.40441 - 1.38819i) q^{7} +(2.42193 + 1.46090i) q^{8} +(-0.915942 + 1.07752i) q^{10} +(2.70422 + 1.56128i) q^{11} +(-3.30414 + 1.90765i) q^{13} +(-0.706502 + 3.86230i) q^{14} +(0.795033 - 3.92019i) q^{16} +3.43533i q^{17} +1.31386 q^{19} +(1.87049 + 0.708000i) q^{20} +(0.794596 - 4.34389i) q^{22} +(2.13186 + 3.69249i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.11106 + 3.49459i) q^{26} +(5.48026 - 0.894268i) q^{28} +(0.266702 - 0.461941i) q^{29} +(0.413107 - 0.238507i) q^{31} +(-5.59945 + 0.803857i) q^{32} +(4.57582 - 1.63243i) q^{34} +2.77637i q^{35} -2.26255i q^{37} +(-0.624333 - 1.75005i) q^{38} +(0.0542127 - 2.82791i) q^{40} +(9.97758 - 5.76056i) q^{41} +(-6.25878 + 10.8405i) q^{43} +(-6.16360 + 1.00577i) q^{44} +(3.90532 - 4.59424i) q^{46} +(-1.52710 + 2.64501i) q^{47} +(0.354125 + 0.613362i) q^{49} +(1.39113 + 0.254469i) q^{50} +(2.70123 - 7.13648i) q^{52} +14.2847 q^{53} -3.12256i q^{55} +(-3.79531 - 6.87471i) q^{56} +(-0.742034 - 0.135735i) q^{58} +(8.89170 - 5.13363i) q^{59} +(10.7109 + 6.18395i) q^{61} +(-0.513993 - 0.436918i) q^{62} +(3.73152 + 7.07642i) q^{64} +(3.30414 + 1.90765i) q^{65} +(3.47947 + 6.02663i) q^{67} +(-4.34875 - 5.31923i) q^{68} +(3.69810 - 1.31930i) q^{70} -7.88557 q^{71} +7.92558 q^{73} +(-3.01369 + 1.07514i) q^{74} +(-2.03437 + 1.66321i) q^{76} +(-4.33470 - 7.50792i) q^{77} +(0.187206 + 0.108084i) q^{79} +(-3.79250 + 1.27158i) q^{80} +(-12.4142 - 10.5527i) q^{82} +(7.86428 + 4.54044i) q^{83} +(2.97508 - 1.71766i) q^{85} +(17.4136 + 3.18533i) q^{86} +(4.26855 + 7.73192i) q^{88} +4.82215i q^{89} +10.5927 q^{91} +(-7.97525 - 3.01871i) q^{92} +(4.24878 + 0.777198i) q^{94} +(-0.656931 - 1.13784i) q^{95} +(-4.20125 + 7.27679i) q^{97} +(0.648716 - 0.763153i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 - 6 * q^8	\( 48 q - 24 q^{5} - 6 q^{8} - 15 q^{14} - 12 q^{16} - 21 q^{22} - 24 q^{25} - 27 q^{34} + 27 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 24 q^{49} + 54 q^{52} - 21 q^{56} + 33 q^{58} + 36 q^{59} - 12 q^{61} + 42 q^{62} - 12 q^{64} - 51 q^{68} + 15 q^{70} - 54 q^{74} - 51 q^{76} - 18 q^{82} + 60 q^{83} - 27 q^{86} - 57 q^{88} + 9 q^{92} - 75 q^{94} + 42 q^{98}+O(q^{100}) \) 48 * q - 24 * q^5 - 6 * q^8 - 15 * q^14 - 12 * q^16 - 21 * q^22 - 24 * q^25 - 27 * q^34 + 27 * q^38 + 12 * q^40 - 12 * q^41 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 24 * q^49 + 54 * q^52 - 21 * q^56 + 33 * q^58 + 36 * q^59 - 12 * q^61 + 42 * q^62 - 12 * q^64 - 51 * q^68 + 15 * q^70 - 54 * q^74 - 51 * q^76 - 18 * q^82 + 60 * q^83 - 27 * q^86 - 57 * q^88 + 9 * q^92 - 75 * q^94 + 42 * q^98

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