LMFDB - Embedded newform 1080.2.bm.b.251.1

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			251.1
Character	$\chi$	$=$	1080.251
Dual form			1080.2.bm.b.611.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39113 + 0.254469i) q^{2} +(1.87049 - 0.708000i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.40441 + 1.38819i) q^{7} +(-2.42193 + 1.46090i) q^{8} +O(q^{10})$	\(q+(-1.39113 + 0.254469i) q^{2} +(1.87049 - 0.708000i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.40441 + 1.38819i) q^{7} +(-2.42193 + 1.46090i) q^{8} +(-0.915942 - 1.07752i) q^{10} +(2.70422 + 1.56128i) q^{11} +(3.30414 - 1.90765i) q^{13} +(-3.69810 - 1.31930i) q^{14} +(2.99747 - 2.64862i) q^{16} +3.43533i q^{17} +1.31386 q^{19} +(1.54839 + 1.26589i) q^{20} +(-4.15922 - 1.48381i) q^{22} +(-2.13186 - 3.69249i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.11106 + 3.49459i) q^{26} +(5.48026 + 0.894268i) q^{28} +(-0.266702 + 0.461941i) q^{29} +(-0.413107 + 0.238507i) q^{31} +(-3.49588 + 4.44734i) q^{32} +(-0.874185 - 4.77899i) q^{34} +2.77637i q^{35} +2.26255i q^{37} +(-1.82775 + 0.334338i) q^{38} +(-2.47615 - 1.36700i) q^{40} +(9.97758 - 5.76056i) q^{41} +(-6.25878 + 10.8405i) q^{43} +(6.16360 + 1.00577i) q^{44} +(3.90532 + 4.59424i) q^{46} +(1.52710 - 2.64501i) q^{47} +(0.354125 + 0.613362i) q^{49} +(0.475189 - 1.33199i) q^{50} +(4.82976 - 5.90757i) q^{52} -14.2847 q^{53} +3.12256i q^{55} +(-7.85133 + 0.150515i) q^{56} +(0.253467 - 0.710488i) q^{58} +(8.89170 - 5.13363i) q^{59} +(-10.7109 - 6.18395i) q^{61} +(0.513993 - 0.436918i) q^{62} +(3.73152 - 7.07642i) q^{64} +(3.30414 + 1.90765i) q^{65} +(3.47947 + 6.02663i) q^{67} +(2.43221 + 6.42575i) q^{68} +(-0.706502 - 3.86230i) q^{70} +7.88557 q^{71} +7.92558 q^{73} +(-0.575748 - 3.14750i) q^{74} +(2.45757 - 0.930215i) q^{76} +(4.33470 + 7.50792i) q^{77} +(-0.187206 - 0.108084i) q^{79} +(3.79250 + 1.27158i) q^{80} +(-12.4142 + 10.5527i) q^{82} +(7.86428 + 4.54044i) q^{83} +(-2.97508 + 1.71766i) q^{85} +(5.94820 - 16.6732i) q^{86} +(-8.83031 + 0.169283i) q^{88} +4.82215i q^{89} +10.5927 q^{91} +(-6.60191 - 5.39741i) q^{92} +(-1.45132 + 4.06815i) q^{94} +(0.656931 + 1.13784i) q^{95} +(-4.20125 + 7.27679i) q^{97} +(-0.648716 - 0.763153i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 33 q^{34} + 33 q^{38} - 6 q^{40} - 12 q^{41} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 24 q^{49} - 36 q^{52} - 21 q^{56} - 51 q^{58} + 36 q^{59} + 12 q^{61} - 42 q^{62} - 12 q^{64} - 57 q^{68} - 15 q^{70} - 30 q^{74} + 57 q^{76} - 18 q^{82} + 60 q^{83} - 27 q^{86} + 57 q^{88} + 51 q^{92} + 57 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 + 33 * q^34 + 33 * q^38 - 6 * q^40 - 12 * q^41 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 24 * q^49 - 36 * q^52 - 21 * q^56 - 51 * q^58 + 36 * q^59 + 12 * q^61 - 42 * q^62 - 12 * q^64 - 57 * q^68 - 15 * q^70 - 30 * q^74 + 57 * q^76 - 18 * q^82 + 60 * q^83 - 27 * q^86 + 57 * q^88 + 51 * q^92 + 57 * 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 $

$2$	−1.39113	+	0.254469i	−0.983678	+	0.179937i
$2$	−1.39113	+	0.254469i	−0.983678	+	0.179937i
$3$		0			0
$3$		0			0
$4$	1.87049	−	0.708000i	0.935245	−	0.354000i
$5$	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	0.880039	−	0.474902i	$-0.157516\pi$
$7$	2.40441	+	1.38819i	0.908782	+	0.524685i	0.0287426	+	0.999587i	$0.490850\pi$
$8$	−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	0.0339183	−	0.999425i	$-0.489201\pi$
$13$	3.30414	−	1.90765i	0.916405	−	0.529086i	0.882486	+	0.470338i	$0.155868\pi$
$14$	−3.69810	−	1.31930i	−0.988359	−	0.352598i
$15$		0			0
$16$	2.99747	−	2.64862i	0.749368	−	0.662154i
$17$			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	$0.451844\pi$
$20$	1.54839	+	1.26589i	0.346231	+	0.283062i
$21$		0			0
$22$	−4.15922	−	1.48381i	−0.886748	−	0.316348i
$23$	−2.13186	−	3.69249i	−0.444524	−	0.769937i	0.553495	−	0.832852i	$-0.313294\pi$
$23$	−2.13186	−	3.69249i	−0.444524	−	0.769937i	−0.998019	+	0.0629149i	$0.979960\pi$
$24$		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	−0.889725	−	0.456496i	$-0.849104\pi$
$29$	−0.266702	+	0.461941i	−0.0495253	+	0.0857803i	0.840200	+	0.542277i	$0.182437\pi$
$30$		0			0
$31$	−0.413107	+	0.238507i	−0.0741962	+	0.0428372i	−0.536639	−	0.843812i	$-0.680306\pi$
$31$	−0.413107	+	0.238507i	−0.0741962	+	0.0428372i	0.462443	+	0.886649i	$0.346973\pi$
$32$	−3.49588	+	4.44734i	−0.617991	+	0.786185i
$33$		0			0
$34$	−0.874185	−	4.77899i	−0.149921	−	0.819590i
$35$			2.77637i			0.469293i
$36$		0			0
$37$			2.26255i			0.371960i	0.982554	+	0.185980i	$0.0595460\pi$
$37$			2.26255i			0.371960i	−0.982554	+	0.185980i	$0.940454\pi$
$38$	−1.82775	+	0.334338i	−0.296501	+	0.0542367i
$39$		0			0
$40$	−2.47615	−	1.36700i	−0.391513	−	0.216142i
$41$	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	−0.732892	−	0.680345i	$-0.761830\pi$
$47$	1.52710	−	2.64501i	0.222750	−	0.385814i	0.955642	+	0.294531i	$0.0951634\pi$
$48$		0			0
$49$	0.354125	+	0.613362i	0.0505892	+	0.0876231i
$50$	0.475189	−	1.33199i	0.0672018	−	0.188372i
$51$		0			0
$52$	4.82976	−	5.90757i	0.669767	−	0.819233i
$53$	−14.2847			−1.96215			−0.981075	−	0.193629i	$-0.937974\pi$
$53$	−14.2847			−1.96215			−0.981075	+	0.193629i	$0.937974\pi$
$54$		0			0
$55$			3.12256i			0.421046i
$56$	−7.85133	+	0.150515i	−1.04918	+	0.0201134i
$57$		0			0
$58$	0.253467	−	0.710488i	0.0332819	−	0.0932916i
$59$	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	−0.380289	−	0.924868i	$-0.624175\pi$
$61$	−10.7109	−	6.18395i	−1.37139	−	0.791774i	−0.991103	+	0.133094i	$0.957509\pi$
$62$	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	$0.693577\pi$
$68$	2.43221	+	6.42575i	0.294949	+	0.779236i
$69$		0			0
$70$	−0.706502	−	3.86230i	−0.0844431	−	0.461633i
$71$	7.88557			0.935845			0.467922	−	0.883770i	$-0.345003\pi$
$71$	7.88557			0.935845			0.467922	+	0.883770i	$0.345003\pi$
$72$		0			0
$73$	7.92558			0.927620			0.463810	−	0.885935i	$-0.346482\pi$
$73$	7.92558			0.927620			0.463810	+	0.885935i	$0.346482\pi$
$74$	−0.575748	−	3.14750i	−0.0669294	−	0.365889i
$75$		0			0
$76$	2.45757	−	0.930215i	0.281902	−	0.106703i
$77$	4.33470	+	7.50792i	0.493985	+	0.855606i
$78$		0			0
$79$	−0.187206	−	0.108084i	−0.0210624	−	0.0121604i	0.489432	−	0.872042i	$-0.337204\pi$
$79$	−0.187206	−	0.108084i	−0.0210624	−	0.0121604i	−0.510494	+	0.859881i	$0.670538\pi$
$80$	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
$86$	5.94820	−	16.6732i	0.641411	−	1.79792i
$87$		0			0
$88$	−8.83031	+	0.169283i	−0.941315	+	0.0180456i
$89$			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
$92$	−6.60191	−	5.39741i	−0.688296	−	0.562719i
$93$		0			0
$94$	−1.45132	+	4.06815i	−0.149692	+	0.419598i
$95$	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	−0.805462	−	0.592648i	$-0.798083\pi$
$101$	1.11068	−	1.92376i	0.110517	−	0.191421i	0.915979	+	0.401227i	$0.131416\pi$
$102$		0			0
$103$	12.7933	−	7.38623i	1.26056	−	0.727786i	0.287380	−	0.957817i	$-0.407216\pi$
$103$	12.7933	−	7.38623i	1.26056	−	0.727786i	0.973183	+	0.230030i	$0.0738825\pi$
$104$	−5.21553	+	9.44723i	−0.511424	+	0.926377i
$105$		0			0
$106$	19.8718	−	3.63501i	1.93012	−	0.353063i
$107$			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	$0.290209\pi$
$109$			16.5073i			1.58111i	−0.612389	+	0.790557i	$0.709791\pi$
$110$	−0.794596	−	4.34389i	−0.0757617	−	0.414174i
$111$		0			0
$112$	10.8839	−	2.20731i	1.02843	−	0.208571i
$113$	−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
$122$	16.4739	+	5.87708i	1.49148	+	0.532086i
$123$		0			0
$124$	−0.603849	+	0.738606i	−0.0542273	+	0.0663287i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$			0.554852i			0.0492352i	0.999697	+	0.0246176i	$0.00783681\pi$
$127$			0.554852i			0.0492352i	−0.999697	+	0.0246176i	$0.992163\pi$
$128$	−3.39031	+	10.7938i	−0.299663	+	0.954045i
$129$		0			0
$130$	−5.08193	−	1.81299i	−0.445715	−	0.159009i
$131$	−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	$0.701963\pi$
$140$	1.96567	+	5.19318i	0.166130	+	0.438904i
$141$		0			0
$142$	−10.9699	+	2.00663i	−0.920570	+	0.168393i
$143$	11.9135			0.996257
$144$		0			0
$145$	−0.533403			−0.0442967
$146$	−11.0255	+	2.01682i	−0.912479	+	0.166913i
$147$		0			0
$148$	1.60188	+	4.23207i	0.131674	+	0.347874i
$149$	−5.42917	−	9.40360i	−0.444775	−	0.770373i	0.553261	−	0.833008i	$-0.313383\pi$
$149$	−5.42917	−	9.40360i	−0.444775	−	0.770373i	−0.998037	+	0.0626346i	$0.980050\pi$
$150$		0			0
$151$	9.37631	+	5.41342i	0.763033	+	0.440538i	0.830384	−	0.557192i	$-0.188121\pi$
$151$	9.37631	+	5.41342i	0.763033	+	0.440538i	−0.0673504	+	0.997729i	$0.521455\pi$
$152$	−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	−0.946186	−	0.323625i	$-0.895098\pi$
$157$	−14.2718	+	8.23981i	−1.13901	+	0.657608i	−0.192826	+	0.981233i	$0.561765\pi$
$158$	0.287932	+	0.102720i	0.0229067	+	0.00817198i
$159$		0			0
$160$	−5.59945	−	0.803857i	−0.442675	−	0.0635505i
$161$		−	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	$0.404334\pi$
$164$	14.5845	−	17.8392i	1.13886	−	1.39301i
$165$		0			0
$166$	−12.0956	−	4.31513i	−0.938804	−	0.334919i
$167$	10.6372	+	18.4242i	0.823131	+	1.42570i	0.903340	+	0.428926i	$0.141108\pi$
$167$	10.6372	+	18.4242i	0.823131	+	1.42570i	−0.0802091	+	0.996778i	$0.525559\pi$
$168$		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	$-0.546327\pi$
$173$	10.3166	−	17.8689i	0.784356	−	1.35854i	0.929383	−	0.369116i	$-0.120340\pi$
$174$		0			0
$175$	−2.40441	+	1.38819i	−0.181756	+	0.104937i
$176$	12.2410	−	2.48254i	0.922703	−	0.187128i
$177$		0			0
$178$	−1.22709	−	6.70824i	−0.0919742	−	0.502804i
$179$			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	$-0.808704\pi$
$181$		−	15.2146i		−	1.13089i	0.824785	−	0.565447i	$-0.191296\pi$
$182$	−14.7358	+	2.69551i	−1.09229	+	0.199805i
$183$		0			0
$184$	10.5576	+	5.82852i	0.778316	+	0.429684i
$185$	−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	−0.507850	−	0.861446i	$-0.669559\pi$
$191$	6.80108	−	11.7798i	0.492109	−	0.852358i	0.999959	+	0.00908769i	$0.00289274\pi$
$192$		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	$-0.461143\pi$
$194$	3.99278	−	11.1921i	0.286665	−	0.803542i
$195$		0			0
$196$	1.09665	+	0.896567i	0.0783319	+	0.0640405i
$197$	−5.87131			−0.418314			−0.209157	−	0.977882i	$-0.567072\pi$
$197$	−5.87131			−0.418314			−0.209157	+	0.977882i	$0.567072\pi$
$198$		0			0
$199$		−	17.4689i		−	1.23834i	−0.785259	−	0.619168i	$-0.787470\pi$
$199$		−	17.4689i		−	1.23834i	0.785259	−	0.619168i	$-0.212530\pi$
$200$	−0.0542127	−	2.82791i	−0.00383342	−	0.199963i
$201$		0			0
$202$	−1.05557	+	2.95884i	−0.0742695	+	0.208183i
$203$	−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	$-0.373941\pi$
$212$	−26.7193	+	10.1135i	−1.83509	+	0.694601i
$213$		0			0
$214$	−3.58179	−	19.5809i	−0.244846	−	1.33852i
$215$	−12.5176			−0.853690
$216$		0			0
$217$	−1.32437			−0.0899042
$218$	−4.20060	−	22.9638i	−0.284501	−	1.55531i
$219$		0			0
$220$	2.21077	+	5.84072i	0.149050	+	0.393781i
$221$	6.55339	+	11.3508i	0.440829	+	0.763538i
$222$		0			0
$223$	−7.41753	−	4.28251i	−0.496714	−	0.286778i	0.230641	−	0.973039i	$-0.425918\pi$
$223$	−7.41753	−	4.28251i	−0.496714	−	0.286778i	−0.727356	+	0.686261i	$0.759251\pi$
$224$	−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	−0.274661	−	0.961541i	$-0.588566\pi$
$229$	6.36677	−	3.67586i	0.420728	−	0.242907i	0.695389	+	0.718634i	$0.255232\pi$
$230$	−2.02607	+	5.67923i	−0.133595	+	0.374477i
$231$		0			0
$232$	−0.0289172	−	1.50842i	−0.00189851	−	0.0990323i
$233$		−	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
$236$	12.9972	−	15.8977i	0.846048	−	1.03485i
$237$		0			0
$238$	4.53223	−	12.7042i	0.293781	−	0.823490i
$239$	−2.31092	−	4.00263i	−0.149481	−	0.258908i	0.781555	−	0.623837i	$-0.214427\pi$
$239$	−2.31092	−	4.00263i	−0.149481	−	0.258908i	−0.931036	+	0.364928i	$0.881094\pi$
$240$		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
$248$	0.652081	−	1.18116i	0.0414072	−	0.0750036i
$249$		0			0
$250$	1.39113	−	0.254469i	0.0879828	−	0.0160940i
$251$			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
$254$	−0.141193	−	0.771872i	−0.00885923	−	0.0484316i
$255$		0			0
$256$	1.96967	−	15.8783i	0.123104	−	0.992394i
$257$	−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	−0.926053	−	0.377395i	$-0.876820\pi$
$263$	−2.20868	+	3.82555i	−0.136193	+	0.235893i	0.789860	+	0.613288i	$0.210153\pi$
$264$		0			0
$265$	−7.14233	−	12.3709i	−0.438750	−	0.759937i
$266$	−4.85880	−	1.73338i	−0.297912	−	0.106280i
$267$		0			0
$268$	10.7752	+	8.80928i	0.658199	+	0.538113i
$269$	−24.9314			−1.52010			−0.760048	−	0.649867i	$-0.774825\pi$
$269$	−24.9314			−1.52010			−0.760048	+	0.649867i	$0.774825\pi$
$270$		0			0
$271$		−	21.5066i		−	1.30643i	−0.757172	−	0.653215i	$-0.773420\pi$
$271$		−	21.5066i		−	1.30643i	0.757172	−	0.653215i	$-0.226580\pi$
$272$	9.09886	+	10.2973i	0.551699	+	0.624365i
$273$		0			0
$274$	11.5194	+	4.10957i	0.695914	+	0.248268i
$275$	−2.70422	+	1.56128i	−0.163070	+	0.0941488i
$276$		0			0
$277$	0.693110	+	0.400167i	0.0416449	+	0.0240437i	0.520678	−	0.853753i	$-0.325679\pi$
$277$	0.693110	+	0.400167i	0.0416449	+	0.0240437i	−0.479033	+	0.877797i	$0.659013\pi$
$278$	−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	$0.690008\pi$
$284$	14.7499	−	5.58298i	0.875245	−	0.331289i
$285$		0			0
$286$	−16.5732	+	3.03162i	−0.979996	+	0.179263i
$287$	31.9869			1.88813
$288$		0			0
$289$	5.19853			0.305796
$290$	0.742034	−	0.135735i	0.0435737	−	0.00797062i
$291$		0			0
$292$	14.8247	−	5.61132i	0.867552	−	0.328377i
$293$	−13.4417	−	23.2817i	−0.785273	−	1.36013i	−0.928836	−	0.370491i	$-0.879189\pi$
$293$	−13.4417	−	23.2817i	−0.785273	−	1.36013i	0.143563	−	0.989641i	$-0.454144\pi$
$294$		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
$302$	−14.4212	−	5.14479i	−0.829848	−	0.296049i
$303$		0			0
$304$	3.93827	−	3.47992i	0.225875	−	0.199587i
$305$		−	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	$0.708920\pi$
$308$	13.4236	+	10.9745i	0.764882	+	0.625331i
$309$		0			0
$310$	0.635379	+	0.226672i	0.0360871	+	0.0128741i
$311$	−10.7043	−	18.5404i	−0.606985	−	1.05133i	−0.991734	−	0.128308i	$-0.959045\pi$
$311$	−10.7043	−	18.5404i	−0.606985	−	1.05133i	0.384749	−	0.923021i	$-0.374288\pi$
$312$		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	−0.724010	−	0.689789i	$-0.757703\pi$
$317$	4.19064	−	7.25841i	0.235370	−	0.407673i	0.959380	+	0.282117i	$0.0910365\pi$
$318$		0			0
$319$	−1.44244	+	0.832792i	−0.0807611	+	0.0466274i
$320$	7.99412	−	0.306617i	0.446885	−	0.0171404i
$321$		0			0
$322$	3.01233	+	16.4678i	0.167870	+	0.917712i
$323$			4.51355i			0.251140i
$324$		0			0
$325$			3.81530i			0.211635i
$326$	−10.5158	+	1.92357i	−0.582414	+	0.106537i
$327$		0			0
$328$	−15.7494	+	28.5280i	−0.869616	+	1.57519i
$329$	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	$-0.392979\pi$
$338$	−0.739625	+	2.07322i	−0.0402303	+	0.112769i
$339$		0			0
$340$	−4.34875	+	5.31923i	−0.235844	+	0.288476i
$341$	−1.48951			−0.0806614
$342$		0			0
$343$		−	17.4682i		−	0.943197i
$344$	−0.678610	−	35.3985i	−0.0365882	−	1.90856i
$345$		0			0
$346$	−9.80465	+	27.4832i	−0.527101	+	1.47750i
$347$	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	0.682380	−	0.730998i	$-0.260945\pi$
$349$	7.29528	+	4.21193i	0.390507	+	0.225460i	−0.291873	+	0.956457i	$0.594278\pi$
$350$	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
$356$	3.41408	+	9.01979i	0.180946	+	0.478048i
$357$		0			0
$358$	−1.91050	−	10.4443i	−0.100973	−	0.551998i
$359$	−7.13071			−0.376344			−0.188172	−	0.982136i	$-0.560256\pi$
$359$	−7.13071			−0.376344			−0.188172	+	0.982136i	$0.560256\pi$
$360$		0			0
$361$	−17.2738			−0.909146
$362$	3.87165	+	21.1655i	0.203490	+	1.11244i
$363$		0			0
$364$	19.8135	−	7.49962i	1.03851	−	0.393087i
$365$	3.96279	+	6.86376i	0.207422	+	0.359266i
$366$		0			0
$367$	−29.3780	−	16.9614i	−1.53352	−	0.885379i	−0.999196	−	0.0401004i	$-0.987232\pi$
$367$	−29.3780	−	16.9614i	−1.53352	−	0.885379i	−0.534326	−	0.845279i	$-0.679434\pi$
$368$	−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	−0.264119	−	0.964490i	$-0.585081\pi$
$373$	8.48032	−	4.89612i	0.439095	−	0.253511i	0.703213	+	0.710979i	$0.251748\pi$
$374$	5.09736	−	14.2883i	0.263578	−	0.738829i
$375$		0			0
$376$	0.165576	+	8.63697i	0.00853893	+	0.445418i
$377$			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	$0.365694\pi$
$380$	2.03437	+	1.66321i	0.104361	+	0.0853208i
$381$		0			0
$382$	−6.46360	+	18.1179i	−0.330706	+	0.926995i
$383$	3.70162	+	6.41139i	0.189144	+	0.327607i	0.944965	−	0.327171i	$-0.106095\pi$
$383$	3.70162	+	6.41139i	0.189144	+	0.327607i	−0.755821	+	0.654778i	$0.772762\pi$
$384$		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	$0.395786\pi$
$389$	−13.0021	+	22.5203i	−0.659233	+	1.14182i	−0.980815	+	0.194943i	$0.937548\pi$
$390$		0			0
$391$	12.6849	−	7.32363i	0.641503	−	0.370372i
$392$	−1.75373	−	0.968180i	−0.0885767	−	0.0489005i
$393$		0			0
$394$	8.16777	−	1.49407i	0.411486	−	0.0752701i
$395$		−	0.216167i		−	0.0108766i
$396$		0			0
$397$			26.9039i			1.35027i	0.737694	+	0.675135i	$0.235915\pi$
$397$			26.9039i			1.35027i	−0.737694	+	0.675135i	$0.764085\pi$
$398$	4.44529	+	24.3015i	0.222822	+	1.21812i
$399$		0			0
$400$	0.795033	+	3.92019i	0.0397516	+	0.196010i
$401$	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	$0.800317\pi$
$410$	−15.3460	−	5.47470i	−0.757885	−	0.270376i
$411$		0			0
$412$	18.7003	−	22.8735i	0.921299	−	1.12690i
$413$	28.5057			1.40268
$414$		0			0
$415$			9.08089i			0.445763i
$416$	−3.06695	+	21.3636i	−0.150370	+	1.04743i
$417$		0			0
$418$	−5.46464	−	1.94952i	−0.267284	−	0.0953540i
$419$	−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	0.361135	−	0.932513i	$-0.382389\pi$
$421$	−5.45534	−	3.14964i	−0.265877	−	0.153504i	−0.627013	+	0.779009i	$0.715723\pi$
$422$	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
$428$	9.96549	+	26.3282i	0.481700	+	1.27262i
$429$		0			0
$430$	17.4136	−	3.18533i	0.839756	−	0.153610i
$431$	16.9856			0.818167			0.409084	−	0.912497i	$-0.365848\pi$
$431$	16.9856			0.818167			0.409084	+	0.912497i	$0.365848\pi$
$432$		0			0
$433$	−17.6526			−0.848331			−0.424166	−	0.905585i	$-0.639433\pi$
$433$	−17.6526			−0.848331			−0.424166	+	0.905585i	$0.639433\pi$
$434$	1.84237	−	0.337012i	0.0884368	−	0.0161771i
$435$		0			0
$436$	11.6872	+	30.8768i	0.559714	+	1.47873i
$437$	−2.80097	−	4.85142i	−0.133989	−	0.232075i
$438$		0			0
$439$	33.1600	+	19.1449i	1.58264	+	0.913738i	0.994472	+	0.105000i	$0.0334841\pi$
$439$	33.1600	+	19.1449i	1.58264	+	0.913738i	0.588168	+	0.808738i	$0.299849\pi$
$440$	−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
$446$	11.4085	+	4.07000i	0.540209	+	0.192720i
$447$		0			0
$448$	18.7955	−	11.8346i	0.888004	−	0.559131i
$449$		−	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
$452$	−0.671603	+	0.821479i	−0.0315895	+	0.0386391i
$453$		0			0
$454$	30.7989	+	10.9875i	1.44546	+	0.515671i
$455$	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	−0.971214	−	0.238208i	$-0.923440\pi$
$461$	−5.99710	+	10.3873i	−0.279313	+	0.483784i	0.691901	+	0.721992i	$0.256773\pi$
$462$		0			0
$463$	−21.9062	+	12.6476i	−1.01807	+	0.587782i	−0.913544	−	0.406740i	$-0.866666\pi$
$463$	−21.9062	+	12.6476i	−1.01807	+	0.587782i	−0.104525	+	0.994522i	$0.533332\pi$
$464$	0.424073	+	2.09105i	0.0196871	+	0.0970743i
$465$		0			0
$466$	5.26032	+	28.7571i	0.243680	+	1.33215i
$467$		−	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
$470$	−4.24878	+	0.777198i	−0.195982	+	0.0358495i
$471$		0			0
$472$	−14.0354	+	25.4232i	−0.646031	+	1.17020i
$473$	−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	$0.519016\pi$
$479$	−19.5734	+	33.9022i	−0.894333	+	1.54903i	−0.834628	+	0.550814i	$0.814317\pi$
$480$		0			0
$481$	4.31614	+	7.47578i	0.196799	+	0.340866i
$482$	9.58541	−	26.8686i	0.436603	−	1.22383i
$483$		0			0
$484$	−1.93489	−	1.58188i	−0.0879496	−	0.0719035i
$485$	−8.40251			−0.381538
$486$		0			0
$487$			20.0755i			0.909707i	0.890566	+	0.454854i	$0.150308\pi$
$487$			20.0755i			0.909707i	−0.890566	+	0.454854i	$0.849692\pi$
$488$	34.9753	−	0.670497i	1.58326	−	0.0303520i
$489$		0			0
$490$	0.336552	−	0.943381i	0.0152039	−	0.0426176i
$491$	−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	$0.891665\pi$
$500$	−1.87049	+	0.708000i	−0.0836509	+	0.0316627i
$501$		0			0
$502$	−3.87995	−	21.2109i	−0.173171	−	0.946689i
$503$	9.59614			0.427871			0.213935	−	0.976848i	$-0.431372\pi$
$503$	9.59614			0.427871			0.213935	+	0.976848i	$0.431372\pi$
$504$		0			0
$505$	2.22137			0.0988495
$506$	3.38793	+	18.5211i	0.150612	+	0.823365i
$507$		0			0
$508$	0.392835	+	1.03785i	0.0174293	+	0.0460470i
$509$	−0.164517	−	0.284953i	−0.00729211	−	0.0126303i	0.862356	−	0.506302i	$-0.168988\pi$
$509$	−0.164517	−	0.284953i	−0.00729211	−	0.0126303i	−0.869648	+	0.493672i	$0.835655\pi$
$510$		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
$518$	2.98498	−	8.36712i	0.131152	−	0.367630i
$519$		0			0
$520$	−10.7893	+	0.206838i	−0.473142	+	0.00907043i
$521$			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	$0.370305\pi$
$524$	−7.62648	+	9.32842i	−0.333164	+	0.407514i
$525$		0			0
$526$	2.09908	−	5.88388i	0.0915242	−	0.256549i
$527$	−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
$536$	−17.2314	−	9.51291i	−0.744282	−	0.410895i
$537$		0			0
$538$	34.6829	−	6.34428i	1.49529	−	0.273521i
$539$			2.21155i			0.0952583i
$540$		0			0
$541$		−	3.63353i		−	0.156218i	−0.996945	−	0.0781089i	$-0.975112\pi$
$541$		−	3.63353i		−	0.156218i	0.996945	−	0.0781089i	$-0.0248882\pi$
$542$	5.47276	+	29.9184i	0.235075	+	1.28511i
$543$		0			0
$544$	−15.2780	−	12.0095i	−0.655041	−	0.514903i
$545$	−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
$554$	−1.06604	−	0.380310i	−0.0452916	−	0.0161578i
$555$		0			0
$556$	14.6442	+	11.9724i	0.621054	+	0.507745i
$557$	−32.3117			−1.36909			−0.684544	−	0.728971i	$-0.739999\pi$
$557$	−32.3117			−1.36909			−0.684544	+	0.728971i	$0.739999\pi$
$558$		0			0
$559$			47.7582i			2.01996i
$560$	7.35355	+	8.32210i	0.310744	+	0.351673i
$561$		0			0
$562$	−27.3853	−	9.76974i	−1.15518	−	0.412111i
$563$	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	$-0.492247\pi$
$572$	22.2841	−	8.43476i	0.931744	−	0.352675i
$573$		0			0
$574$	−44.4980	+	8.13968i	−1.85731	+	0.339744i
$575$	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	$0.291956\pi$
$578$	−7.23184	+	1.32287i	−0.300805	+	0.0550240i
$579$		0			0
$580$	−0.997726	+	0.377650i	−0.0414283	+	0.0156811i
$581$	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
$590$	−13.6759	−	4.87888i	−0.563027	−	0.200860i
$591$		0			0
$592$	5.99261	+	6.78192i	0.246295	+	0.278735i
$593$		−	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
$596$	−16.8130	−	13.7455i	−0.688686	−	0.563037i
$597$		0			0
$598$	21.6679	+	7.73006i	0.886068	+	0.316106i
$599$	−9.47635	−	16.4135i	−0.387193	−	0.670638i	0.604878	−	0.796318i	$-0.293222\pi$
$599$	−9.47635	−	16.4135i	−0.387193	−	0.670638i	−0.992071	+	0.125680i	$0.959889\pi$
$600$		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	0.156662	−	0.987652i	$-0.449927\pi$
$607$	26.8628	−	15.5092i	1.09033	−	0.629500i	0.933663	+	0.358153i	$0.116593\pi$
$608$	−4.59311	+	5.84319i	−0.186275	+	0.236973i
$609$		0			0
$610$	3.14725	+	17.2054i	0.127428	+	0.696625i
$611$		−	11.6526i		−	0.471416i
$612$		0			0
$613$		−	43.8644i		−	1.77167i	−0.464002	−	0.885834i	$-0.653587\pi$
$613$		−	43.8644i		−	1.77167i	0.464002	−	0.885834i	$-0.346413\pi$
$614$	29.7478	−	5.44154i	1.20052	−	0.219603i
$615$		0			0
$616$	−21.4667	−	11.8511i	−0.864918	−	0.477494i
$617$	−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
$626$	−2.77338	+	7.77398i	−0.110846	+	0.310711i
$627$		0			0
$628$	−20.8614	+	25.5169i	−0.832461	+	1.01824i
$629$	−7.77258			−0.309913
$630$		0			0
$631$		−	7.35292i		−	0.292715i	−0.989232	−	0.146358i	$-0.953245\pi$
$631$		−	7.35292i		−	0.292715i	0.989232	−	0.146358i	$-0.0467550\pi$
$632$	0.611301	−	0.0117190i	0.0243162	−	0.000466157i
$633$		0			0
$634$	−3.98269	+	11.1638i	−0.158173	+	0.443370i
$635$	−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	$0.965947\pi$
$644$	−8.38108	−	22.1423i	−0.330261	−	0.872528i
$645$		0			0
$646$	−1.14856	−	6.27893i	−0.0451894	−	0.247041i
$647$	−39.5969			−1.55672			−0.778358	−	0.627820i	$-0.783947\pi$
$647$	−39.5969			−1.55672			−0.778358	+	0.627820i	$0.783947\pi$
$648$		0			0
$649$	32.0601			1.25847
$650$	−0.970876	−	5.30758i	−0.0380809	−	0.208180i
$651$		0			0
$652$	14.1393	−	5.35188i	0.553738	−	0.209596i
$653$	22.5179	+	39.0021i	0.881193	+	1.52627i	0.850016	+	0.526757i	$0.176592\pi$
$653$	22.5179	+	39.0021i	0.881193	+	1.52627i	0.0311765	+	0.999514i	$0.490075\pi$
$654$		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	−0.293467	−	0.955969i	$-0.594809\pi$
$661$	9.96758	−	5.75478i	0.387694	−	0.223835i	0.681160	+	0.732134i	$0.261476\pi$
$662$	0.856403	−	2.40056i	0.0332851	−	0.0933005i
$663$		0			0
$664$	−25.6799	+	0.492299i	−0.996574	+	0.0191049i
$665$			3.64777i			0.141455i
$666$		0			0
$667$	2.27428			0.0880606
$668$	32.9411	+	26.9311i	1.27453	+	1.04199i
$669$		0			0
$670$	3.30681	−	9.26925i	0.127753	−	0.358102i
$671$	−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	−0.656129	−	0.754649i	$-0.727807\pi$
$677$	8.46874	−	14.6683i	0.325480	−	0.563748i	0.981609	+	0.190900i	$0.0611407\pi$
$678$		0			0
$679$	−20.2031	+	11.6642i	−0.775323	+	0.447633i
$680$	4.69611	−	8.50637i	0.180087	−	0.326204i
$681$		0			0
$682$	2.07210	−	0.379034i	0.0793448	−	0.0145140i
$683$		−	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
$686$	4.44513	+	24.3006i	0.169716	+	0.927802i
$687$		0			0
$688$	9.95186	+	49.0712i	0.379411	+	1.87082i
$689$	−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
$698$	−11.2205	−	4.00292i	−0.424702	−	0.151513i
$699$		0			0
$700$	−3.51459	+	4.29891i	−0.132839	+	0.162484i
$701$	9.37518			0.354096			0.177048	−	0.984202i	$-0.443345\pi$
$701$	9.37518			0.354096			0.177048	+	0.984202i	$0.443345\pi$
$702$		0			0
$703$			2.97267i			0.112117i
$704$	21.1391	−	13.3102i	0.796711	−	0.501648i
$705$		0			0
$706$	22.9848	+	8.19987i	0.865046	+	0.308606i
$707$	5.34107	−	3.08367i	0.200872	−	0.115973i
$708$		0			0
$709$	−33.2487	−	19.1962i	−1.24868	−	0.720927i	−0.277836	−	0.960629i	$-0.589617\pi$
$709$	−33.2487	−	19.1962i	−1.24868	−	0.720927i	−0.970847	+	0.239702i	$0.922950\pi$
$710$	−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
$716$	5.31551	+	14.0432i	0.198650	+	0.524820i
$717$		0			0
$718$	9.91975	−	1.81455i	0.370202	−	0.0677182i
$719$	12.8804			0.480356			0.240178	−	0.970729i	$-0.422794\pi$
$719$	12.8804			0.480356			0.240178	+	0.970729i	$0.422794\pi$
$720$		0			0
$721$	41.0138			1.52744
$722$	24.0301	−	4.39564i	0.894307	−	0.163589i
$723$		0			0
$724$	−10.7720	−	28.4588i	−0.400337	−	1.05766i
$725$	−0.266702	−	0.461941i	−0.00990505	−	0.0171561i
$726$		0			0
$727$	3.75846	+	2.16995i	0.139393	+	0.0804788i	0.568075	−	0.822977i	$-0.307688\pi$
$727$	3.75846	+	2.16995i	0.139393	+	0.0804788i	−0.428681	+	0.903456i	$0.641022\pi$
$728$	−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	−0.108976	−	0.994044i	$-0.534757\pi$
$733$	18.8815	−	10.9012i	0.697404	−	0.402646i	0.806380	+	0.591398i	$0.201424\pi$
$734$	45.1849	+	16.1197i	1.66780	+	0.594991i
$735$		0			0
$736$	23.8745	+	3.42742i	0.880025	+	0.126336i
$737$			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	$0.699471\pi$
$740$	−2.86414	+	3.50331i	−0.105288	+	0.128784i
$741$		0			0
$742$	52.8261	+	18.8458i	1.93931	+	0.691850i
$743$	−12.2533	−	21.2234i	−0.449532	−	0.778612i	0.548824	−	0.835938i	$-0.315076\pi$
$743$	−12.2533	−	21.2234i	−0.449532	−	0.778612i	−0.998355	+	0.0573263i	$0.981742\pi$
$744$		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	−0.597213	−	0.802083i	$-0.703725\pi$
$751$	−5.51362	+	3.18329i	−0.201195	+	0.116160i	0.396018	+	0.918243i	$0.370392\pi$
$752$	−2.42818	−	11.9730i	−0.0885467	−	0.436611i
$753$		0			0
$754$	−0.517868	−	2.83108i	−0.0188597	−	0.103102i
$755$			10.8268i			0.394029i
$756$		0			0
$757$		−	25.0713i		−	0.911232i	−0.890176	−	0.455616i	$-0.849419\pi$
$757$		−	25.0713i		−	0.911232i	0.890176	−	0.455616i	$-0.150581\pi$
$758$	−22.1820	+	4.05759i	−0.805686	+	0.147378i
$759$		0			0
$760$	−3.25332	−	1.79606i	−0.118010	−	0.0651498i
$761$	−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	$0.970762\pi$
$770$	4.11960	−	11.5475i	0.148460	−	0.416145i
$771$		0			0
$772$	−34.3614	−	28.0923i	−1.23669	−	1.01106i
$773$	32.0701			1.15348			0.576740	−	0.816928i	$-0.304325\pi$
$773$	32.0701			1.15348			0.576740	+	0.816928i	$0.304325\pi$
$774$		0			0
$775$		−	0.477015i		−	0.0171349i
$776$	−0.455523	−	23.7615i	−0.0163523	−	0.852989i
$777$		0			0
$778$	12.3569	−	34.6373i	0.443017	−	1.24181i
$779$	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	$0.580098\pi$
$788$	−10.9822	+	4.15689i	−0.391226	+	0.148083i
$789$		0			0
$790$	0.0550079	+	0.300717i	0.00195709	+	0.0106990i
$791$	−1.47297			−0.0523727
$792$		0			0
$793$	−47.1872			−1.67567
$794$	−6.84622	−	37.4269i	−0.242963	−	1.32823i
$795$		0			0
$796$	−12.3680	−	32.6754i	−0.438371	−	1.15815i
$797$	28.1638	+	48.7811i	0.997612	+	1.72791i	0.558622	+	0.829423i	$0.311330\pi$
$797$	28.1638	+	48.7811i	0.997612	+	1.72791i	0.438990	+	0.898492i	$0.355336\pi$
$798$		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
$806$	0.864821	−	2.42416i	0.0304620	−	0.0853873i
$807$		0			0
$808$	0.120426	+	6.28182i	0.00423658	+	0.220994i
$809$		−	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	$0.952010\pi$
$812$	−1.87469	+	2.29305i	−0.0657889	+	0.0804705i
$813$		0			0
$814$	3.35718	−	9.41042i	0.117669	−	0.329835i
$815$	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	−0.841038	−	0.540976i	$-0.818055\pi$
$821$	1.37477	−	2.38117i	0.0479797	−	0.0831033i	0.889018	+	0.457873i	$0.151388\pi$
$822$		0			0
$823$	−23.4482	+	13.5378i	−0.817353	+	0.471899i	−0.849503	−	0.527584i	$-0.823098\pi$
$823$	−23.4482	+	13.5378i	−0.817353	+	0.471899i	0.0321498	+	0.999483i	$0.489765\pi$
$824$	−20.1940	+	36.5787i	−0.703491	+	1.27428i
$825$		0			0
$826$	−39.6552	+	7.25383i	−1.37978	+	0.252393i
$827$		−	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	$0.175405\pi$
$829$			30.1503i			1.04716i	−0.851975	+	0.523582i	$0.824595\pi$
$830$	−2.31081	−	12.6327i	−0.0802093	−	0.438487i
$831$		0			0
$832$	−1.16984	−	30.4999i	−0.0405567	−	1.05740i
$833$	−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	−0.792686	−	0.609630i	$-0.791318\pi$
$839$	3.81222	−	6.60296i	0.131612	−	0.227959i	0.924298	+	0.381671i	$0.124651\pi$
$840$		0			0
$841$	14.3577	+	24.8683i	0.495094	+	0.857529i
$842$	8.39058	+	2.99335i	0.289159	+	0.103158i
$843$		0			0
$844$	−27.2653	−	22.2908i	−0.938511	−	0.767282i
$845$	1.55649			0.0535448
$846$		0			0
$847$		−	3.46939i		−	0.119210i
$848$	−42.8179	+	37.8346i	−1.47037	+	1.29925i
$849$		0			0
$850$	4.57582	+	1.63243i	0.156949	+	0.0559918i
$851$	8.35443	−	4.82343i	0.286386	−	0.165345i
$852$		0			0
$853$	19.9923	+	11.5426i	0.684525	+	0.395211i	0.801558	−	0.597917i	$-0.204005\pi$
$853$	19.9923	+	11.5426i	0.684525	+	0.395211i	−0.117033	+	0.993128i	$0.537338\pi$
$854$	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	$0.972595\pi$
$860$	−23.4140	+	8.86243i	−0.798410	+	0.302206i
$861$		0			0
$862$	−23.6292	+	4.32231i	−0.804813	+	0.147219i
$863$	−2.55660			−0.0870275			−0.0435138	−	0.999053i	$-0.513855\pi$
$863$	−2.55660			−0.0870275			−0.0435138	+	0.999053i	$0.513855\pi$
$864$		0			0
$865$	20.6332			0.701549
$866$	24.5571	−	4.49205i	0.834485	−	0.152646i
$867$		0			0
$868$	−2.47722	+	0.937655i	−0.0840825	+	0.0318261i
$869$	−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	−0.227743	−	0.973721i	$-0.573135\pi$
$877$	14.8560	−	8.57713i	0.501653	−	0.289629i	0.729396	+	0.684092i	$0.239801\pi$
$878$	−51.0017	−	18.1949i	−1.72122	−	0.614049i
$879$		0			0
$880$	8.27046	+	9.35979i	0.278797	+	0.315518i
$881$		−	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	$0.561812\pi$
$884$	20.2944	+	16.5918i	0.682576	+	0.558042i
$885$		0			0
$886$	−17.4592	−	6.22858i	−0.586553	−	0.209253i
$887$	−23.5408	−	40.7738i	−0.790422	−	1.36905i	−0.925706	−	0.378245i	$-0.876528\pi$
$887$	−23.5408	−	40.7738i	−0.790422	−	1.36905i	0.135283	−	0.990807i	$-0.456806\pi$
$888$		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
$896$	−23.1355	+	21.2463i	−0.772902	+	0.709789i
$897$		0			0
$898$	6.34796	+	34.7030i	0.211834	+	1.15805i
$899$		−	0.254441i		−	0.00848609i
$900$		0			0
$901$		−	49.0725i		−	1.63484i
$902$	−50.0465	+	9.15463i	−1.66636	+	0.304816i
$903$		0			0
$904$	0.725246	−	1.31369i	0.0241213	−	0.0436926i
$905$	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	−0.877372	−	0.479810i	$-0.840706\pi$
$911$	−0.698984	+	1.21068i	−0.0231584	+	0.0401115i	0.854214	+	0.519922i	$0.174039\pi$
$912$		0			0
$913$	14.1778	+	24.5567i	0.469217	+	0.812708i
$914$	−12.6188	+	35.3714i	−0.417392	+	1.16998i
$915$		0			0
$916$	9.30648	−	11.3833i	0.307495	−	0.376116i
$917$	−16.7265			−0.552358
$918$		0			0
$919$		−	7.89210i		−	0.260336i	−0.991492	−	0.130168i	$-0.958448\pi$
$919$		−	7.89210i		−	0.260336i	0.991492	−	0.130168i	$-0.0415517\pi$
$920$	0.231148	+	12.0574i	0.00762072	+	0.397521i
$921$		0			0
$922$	5.69950	−	15.9761i	0.187703	−	0.526146i
$923$	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
$932$	−14.6356	−	38.6663i	−0.479405	−	1.26656i
$933$		0			0
$934$	1.89333	+	10.3504i	0.0619515	+	0.338676i
$935$	−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	$0.560591\pi$
$938$	−4.91651	−	26.8775i	−0.160530	−	0.877583i
$939$		0			0
$940$	5.71284	−	2.16237i	0.186332	−	0.0705287i
$941$	−2.75857	−	4.77799i	−0.0899270	−	0.155758i	0.817553	−	0.575853i	$-0.195330\pi$
$941$	−2.75857	−	4.77799i	−0.0899270	−	0.155758i	−0.907480	+	0.420095i	$0.861997\pi$
$942$		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
$950$	0.624333	−	1.75005i	0.0202560	−	0.0567792i
$951$		0			0
$952$	−0.517067	−	26.9719i	−0.0167582	−	0.874163i
$953$			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
$956$	−7.15641	−	5.85075i	−0.231455	−	0.189227i
$957$		0			0
$958$	18.6021	−	52.1432i	0.601008	−	1.68467i
$959$	−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	−0.105330	−	0.994437i	$-0.533590\pi$
$967$	21.8675	−	12.6252i	0.703213	−	0.406000i	0.808543	+	0.588437i	$0.200257\pi$
$968$	3.09423	+	1.70823i	0.0994522	+	0.0549045i
$969$		0			0
$970$	11.6890	−	2.13818i	0.375311	−	0.0686528i
$971$			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
$974$	−5.10860	−	27.9276i	−0.163690	−	0.894859i
$975$		0			0
$976$	−48.4846	+	9.83288i	−1.55195	+	0.314743i
$977$	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	$0.421609\pi$
$983$	−22.5114	+	38.9908i	−0.718001	+	1.24361i	−0.961791	+	0.273786i	$0.911724\pi$
$984$		0			0
$985$	−2.93566	−	5.08471i	−0.0935378	−	0.162012i
$986$	2.44076	+	0.870743i	0.0777295	+	0.0277301i
$987$		0			0
$988$	6.34563	−	7.76174i	0.201882	−	0.246934i
$989$	53.3713			1.69711
$990$		0			0
$991$			45.4039i			1.44230i	0.692778	+	0.721151i	$0.256387\pi$
$991$			45.4039i			1.44230i	−0.692778	+	0.721151i	$0.743613\pi$
$992$	0.383452	−	2.67102i	0.0121746	−	0.0848049i
$993$		0			0
$994$	−29.1616	−	10.4034i	−0.924950	−	0.329977i
$995$	15.1285	−	8.73444i	0.479605	−	0.276900i
$996$		0			0
$997$	−15.3295	−	8.85052i	−0.485492	−	0.280299i	0.237211	−	0.971458i	$-0.423767\pi$
$997$	−15.3295	−	8.85052i	−0.485492	−	0.280299i	−0.722702	+	0.691160i	$0.757100\pi$
$998$	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.b.251.1		48
3.2	odd	2		360.2.bm.a.11.24	✓	48
4.3	odd	2		4320.2.cc.b.1871.6		48
8.3	odd	2		1080.2.bm.a.251.10		48
8.5	even	2		4320.2.cc.a.1871.19		48
9.4	even	3		360.2.bm.b.131.15	yes	48
9.5	odd	6		1080.2.bm.a.611.10		48
12.11	even	2		1440.2.cc.a.911.24		48
24.5	odd	2		1440.2.cc.b.911.24		48
24.11	even	2		360.2.bm.b.11.15	yes	48
36.23	even	6		4320.2.cc.a.3311.19		48
36.31	odd	6		1440.2.cc.b.1391.24		48
72.5	odd	6		4320.2.cc.b.3311.6		48
72.13	even	6		1440.2.cc.a.1391.24		48
72.59	even	6	inner	1080.2.bm.b.611.1		48
72.67	odd	6		360.2.bm.a.131.24	yes	48

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

\(f(q)\)	\(=\)	\(q+(-1.39113 + 0.254469i) q^{2} +(1.87049 - 0.708000i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.40441 + 1.38819i) q^{7} +(-2.42193 + 1.46090i) q^{8} +O(q^{10})\)	\(q+(-1.39113 + 0.254469i) q^{2} +(1.87049 - 0.708000i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.40441 + 1.38819i) q^{7} +(-2.42193 + 1.46090i) q^{8} +(-0.915942 - 1.07752i) q^{10} +(2.70422 + 1.56128i) q^{11} +(3.30414 - 1.90765i) q^{13} +(-3.69810 - 1.31930i) q^{14} +(2.99747 - 2.64862i) q^{16} +3.43533i q^{17} +1.31386 q^{19} +(1.54839 + 1.26589i) q^{20} +(-4.15922 - 1.48381i) q^{22} +(-2.13186 - 3.69249i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.11106 + 3.49459i) q^{26} +(5.48026 + 0.894268i) q^{28} +(-0.266702 + 0.461941i) q^{29} +(-0.413107 + 0.238507i) q^{31} +(-3.49588 + 4.44734i) q^{32} +(-0.874185 - 4.77899i) q^{34} +2.77637i q^{35} +2.26255i q^{37} +(-1.82775 + 0.334338i) q^{38} +(-2.47615 - 1.36700i) q^{40} +(9.97758 - 5.76056i) q^{41} +(-6.25878 + 10.8405i) q^{43} +(6.16360 + 1.00577i) q^{44} +(3.90532 + 4.59424i) q^{46} +(1.52710 - 2.64501i) q^{47} +(0.354125 + 0.613362i) q^{49} +(0.475189 - 1.33199i) q^{50} +(4.82976 - 5.90757i) q^{52} -14.2847 q^{53} +3.12256i q^{55} +(-7.85133 + 0.150515i) q^{56} +(0.253467 - 0.710488i) q^{58} +(8.89170 - 5.13363i) q^{59} +(-10.7109 - 6.18395i) q^{61} +(0.513993 - 0.436918i) q^{62} +(3.73152 - 7.07642i) q^{64} +(3.30414 + 1.90765i) q^{65} +(3.47947 + 6.02663i) q^{67} +(2.43221 + 6.42575i) q^{68} +(-0.706502 - 3.86230i) q^{70} +7.88557 q^{71} +7.92558 q^{73} +(-0.575748 - 3.14750i) q^{74} +(2.45757 - 0.930215i) q^{76} +(4.33470 + 7.50792i) q^{77} +(-0.187206 - 0.108084i) q^{79} +(3.79250 + 1.27158i) q^{80} +(-12.4142 + 10.5527i) q^{82} +(7.86428 + 4.54044i) q^{83} +(-2.97508 + 1.71766i) q^{85} +(5.94820 - 16.6732i) q^{86} +(-8.83031 + 0.169283i) q^{88} +4.82215i q^{89} +10.5927 q^{91} +(-6.60191 - 5.39741i) q^{92} +(-1.45132 + 4.06815i) q^{94} +(0.656931 + 1.13784i) q^{95} +(-4.20125 + 7.27679i) q^{97} +(-0.648716 - 0.763153i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 + 6 * q^8	\( 48 q + 24 q^{5} + 6 q^{8} - 15 q^{14} + 12 q^{16} + 21 q^{22} - 24 q^{25} + 33 q^{34} + 33 q^{38} - 6 q^{40} - 12 q^{41} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 24 q^{49} - 36 q^{52} - 21 q^{56} - 51 q^{58} + 36 q^{59} + 12 q^{61} - 42 q^{62} - 12 q^{64} - 57 q^{68} - 15 q^{70} - 30 q^{74} + 57 q^{76} - 18 q^{82} + 60 q^{83} - 27 q^{86} + 57 q^{88} + 51 q^{92} + 57 q^{94} - 42 q^{98}+O(q^{100}) \) 48 * q + 24 * q^5 + 6 * q^8 - 15 * q^14 + 12 * q^16 + 21 * q^22 - 24 * q^25 + 33 * q^34 + 33 * q^38 - 6 * q^40 - 12 * q^41 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 24 * q^49 - 36 * q^52 - 21 * q^56 - 51 * q^58 + 36 * q^59 + 12 * q^61 - 42 * q^62 - 12 * q^64 - 57 * q^68 - 15 * q^70 - 30 * q^74 + 57 * q^76 - 18 * q^82 + 60 * q^83 - 27 * q^86 + 57 * q^88 + 51 * q^92 + 57 * q^94 - 42 * q^98

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