LMFDB - Embedded newform 1764.2.j.h.1177.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(589,1764)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1764.589"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1177.6
Root			$1.68442 + 0.403398i$ of defining polynomial
Character	$\chi$	$=$	1764.1177
Dual form			1764.2.j.h.589.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19156 - 1.25705i) q^{3} +(1.80173 + 3.12069i) q^{5} +(-0.160357 - 2.99571i) q^{9} +(3.01334 - 5.21926i) q^{11} +(2.55639 + 4.42780i) q^{13} +(6.06973 + 1.45363i) q^{15} +0.222013 q^{17} +3.42323 q^{19} +(0.509880 + 0.883137i) q^{23} +(-3.99245 + 6.91513i) q^{25} +(-3.95684 - 3.36800i) q^{27} +(-2.83679 + 4.91347i) q^{29} +(-2.52322 - 4.37035i) q^{31} +(-2.97030 - 10.0070i) q^{33} -3.37052 q^{37} +(8.61207 + 2.06249i) q^{39} +(-0.0955808 - 0.165551i) q^{41} +(1.71161 - 2.96460i) q^{43} +(9.05975 - 5.89788i) q^{45} +(-1.03506 + 1.79278i) q^{47} +(0.264542 - 0.279081i) q^{51} +5.30415 q^{53} +21.7169 q^{55} +(4.07899 - 4.30318i) q^{57} +(3.79814 + 6.57858i) q^{59} +(0.891408 - 1.54396i) q^{61} +(-9.21184 + 15.9554i) q^{65} +(-6.49235 - 11.2451i) q^{67} +(1.71770 + 0.411369i) q^{69} +5.89560 q^{71} +12.6104 q^{73} +(3.93542 + 13.2585i) q^{75} +(-6.30763 + 10.9251i) q^{79} +(-8.94857 + 0.960764i) q^{81} +(3.59946 - 6.23444i) q^{83} +(0.400007 + 0.692832i) q^{85} +(2.79627 + 9.42070i) q^{87} -8.89394 q^{89} +(-8.50033 - 2.03573i) q^{93} +(6.16773 + 10.6828i) q^{95} +(2.72991 - 4.72835i) q^{97} +(-16.1186 - 8.19016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} + 2 q^{5} - 5 q^{9} + 2 q^{11} - 2 q^{13} + 7 q^{15} + 4 q^{17} + 14 q^{19} + 11 q^{23} - 9 q^{25} - 9 q^{27} + q^{29} + q^{31} + q^{33} - 20 q^{37} + 22 q^{39} + 33 q^{41} + 7 q^{43}+ \cdots + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 + 2 * q^5 - 5 * q^9 + 2 * q^11 - 2 * q^13 + 7 * q^15 + 4 * q^17 + 14 * q^19 + 11 * q^23 - 9 * q^25 - 9 * q^27 + q^29 + q^31 + q^33 - 20 * q^37 + 22 * q^39 + 33 * q^41 + 7 * q^43 - 5 * q^45 + 3 * q^47 - 7 * q^51 + 30 * q^53 + 28 * q^55 - 18 * q^57 + 14 * q^59 + 10 * q^61 + 15 * q^65 + 6 * q^67 + 43 * q^69 + 2 * q^71 + 42 * q^73 - 43 * q^75 - 10 * q^79 + 7 * q^81 + 25 * q^83 + 8 * q^85 + 26 * q^87 - 12 * q^89 - 38 * q^93 - 28 * q^95 + 18 * q^97 + 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.19156	−	1.25705i	0.687949	−	0.725759i
$3$	1.19156	−	1.25705i	0.687949	−	0.725759i
$4$		0			0
$5$	1.80173	+	3.12069i	0.805757	+	1.39561i	0.915779	+	0.401684i	$0.131575\pi$
$5$	1.80173	+	3.12069i	0.805757	+	1.39561i	−0.110021	+	0.993929i	$0.535092\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.160357	−	2.99571i	−0.0534522	−	0.998570i
$10$		0			0
$11$	3.01334	−	5.21926i	0.908557	−	1.57367i	0.0924872	−	0.995714i	$-0.470518\pi$
$11$	3.01334	−	5.21926i	0.908557	−	1.57367i	0.816070	−	0.577953i	$-0.196148\pi$
$12$		0			0
$13$	2.55639	+	4.42780i	0.709015	+	1.22805i	0.965223	+	0.261429i	$0.0841936\pi$
$13$	2.55639	+	4.42780i	0.709015	+	1.22805i	−0.256207	+	0.966622i	$0.582473\pi$
$14$		0			0
$15$	6.06973	+	1.45363i	1.56720	+	0.375325i
$16$		0			0
$17$	0.222013			0.0538460			0.0269230	−	0.999638i	$-0.491429\pi$
$17$	0.222013			0.0538460			0.0269230	+	0.999638i	$0.491429\pi$
$18$		0			0
$19$	3.42323			0.785343			0.392671	−	0.919679i	$-0.371551\pi$
$19$	3.42323			0.785343			0.392671	+	0.919679i	$0.371551\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.509880	+	0.883137i	0.106317	+	0.184147i	0.914276	−	0.405093i	$-0.132761\pi$
$23$	0.509880	+	0.883137i	0.106317	+	0.184147i	−0.807958	+	0.589240i	$0.799427\pi$
$24$		0			0
$25$	−3.99245	+	6.91513i	−0.798490	+	1.38303i
$26$		0			0
$27$	−3.95684	−	3.36800i	−0.761494	−	0.648172i
$28$		0			0
$29$	−2.83679	+	4.91347i	−0.526779	+	0.912408i	0.472734	+	0.881205i	$0.343267\pi$
$29$	−2.83679	+	4.91347i	−0.526779	+	0.912408i	−0.999513	+	0.0312031i	$0.990066\pi$
$30$		0			0
$31$	−2.52322	−	4.37035i	−0.453184	−	0.784938i	0.545398	−	0.838177i	$-0.316379\pi$
$31$	−2.52322	−	4.37035i	−0.453184	−	0.784938i	−0.998582	+	0.0532395i	$0.983045\pi$
$32$		0			0
$33$	−2.97030	−	10.0070i	−0.517062	−	1.74200i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.37052			−0.554110			−0.277055	−	0.960854i	$-0.589358\pi$
$37$	−3.37052			−0.554110			−0.277055	+	0.960854i	$0.589358\pi$
$38$		0			0
$39$	8.61207	+	2.06249i	1.37904	+	0.330262i
$40$		0			0
$41$	−0.0955808	−	0.165551i	−0.0149272	−	0.0258547i	0.858465	−	0.512872i	$-0.171418\pi$
$41$	−0.0955808	−	0.165551i	−0.0149272	−	0.0258547i	−0.873393	+	0.487017i	$0.838085\pi$
$42$		0			0
$43$	1.71161	−	2.96460i	0.261019	−	0.452098i	−0.705494	−	0.708716i	$-0.749275\pi$
$43$	1.71161	−	2.96460i	0.261019	−	0.452098i	0.966513	+	0.256618i	$0.0826082\pi$
$44$		0			0
$45$	9.05975	−	5.89788i	1.35055	−	0.879204i
$46$		0			0
$47$	−1.03506	+	1.79278i	−0.150980	+	0.261504i	−0.931588	−	0.363516i	$-0.881576\pi$
$47$	−1.03506	+	1.79278i	−0.150980	+	0.261504i	0.780608	+	0.625021i	$0.214909\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.264542	−	0.279081i	0.0370433	−	0.0390792i
$52$		0			0
$53$	5.30415			0.728581			0.364290	−	0.931285i	$-0.381312\pi$
$53$	5.30415			0.728581			0.364290	+	0.931285i	$0.381312\pi$
$54$		0			0
$55$	21.7169			2.92831
$56$		0			0
$57$	4.07899	−	4.30318i	0.540276	−	0.569969i
$58$		0			0
$59$	3.79814	+	6.57858i	0.494476	+	0.856458i	0.999980	−	0.00636650i	$-0.00202653\pi$
$59$	3.79814	+	6.57858i	0.494476	+	0.856458i	−0.505503	+	0.862825i	$0.668693\pi$
$60$		0			0
$61$	0.891408	−	1.54396i	0.114133	−	0.197684i	−0.803300	−	0.595575i	$-0.796924\pi$
$61$	0.891408	−	1.54396i	0.114133	−	0.197684i	0.917433	+	0.397891i	$0.130258\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.21184	+	15.9554i	−1.14259	+	1.97902i
$66$		0			0
$67$	−6.49235	−	11.2451i	−0.793167	−	1.37380i	−0.923997	−	0.382400i	$-0.875098\pi$
$67$	−6.49235	−	11.2451i	−0.793167	−	1.37380i	0.130830	−	0.991405i	$-0.458236\pi$
$68$		0			0
$69$	1.71770	+	0.411369i	0.206787	+	0.0495230i
$70$		0			0
$71$	5.89560			0.699679			0.349839	−	0.936810i	$-0.386236\pi$
$71$	5.89560			0.699679			0.349839	+	0.936810i	$0.386236\pi$
$72$		0			0
$73$	12.6104			1.47593			0.737967	−	0.674837i	$-0.235786\pi$
$73$	12.6104			1.47593			0.737967	+	0.674837i	$0.235786\pi$
$74$		0			0
$75$	3.93542	+	13.2585i	0.454423	+	1.53096i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.30763	+	10.9251i	−0.709664	+	1.22917i	0.255318	+	0.966857i	$0.417820\pi$
$79$	−6.30763	+	10.9251i	−0.709664	+	1.22917i	−0.964982	+	0.262317i	$0.915514\pi$
$80$		0			0
$81$	−8.94857	+	0.960764i	−0.994286	+	0.106752i
$82$		0			0
$83$	3.59946	−	6.23444i	0.395092	−	0.684319i	−0.598021	−	0.801480i	$-0.704046\pi$
$83$	3.59946	−	6.23444i	0.395092	−	0.684319i	0.993113	+	0.117161i	$0.0373795\pi$
$84$		0			0
$85$	0.400007	+	0.692832i	0.0433868	+	0.0751482i
$86$		0			0
$87$	2.79627	+	9.42070i	0.299791	+	1.01001i
$88$		0			0
$89$	−8.89394			−0.942756			−0.471378	−	0.881931i	$-0.656243\pi$
$89$	−8.89394			−0.942756			−0.471378	+	0.881931i	$0.656243\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−8.50033	−	2.03573i	−0.881443	−	0.211095i
$94$		0			0
$95$	6.16773	+	10.6828i	0.632796	+	1.09603i
$96$		0			0
$97$	2.72991	−	4.72835i	0.277181	−	0.480091i	−0.693502	−	0.720454i	$-0.743933\pi$
$97$	2.72991	−	4.72835i	0.277181	−	0.480091i	0.970683	+	0.240364i	$0.0772667\pi$
$98$		0			0
$99$	−16.1186	−	8.19016i	−1.61998	−	0.823142i
$100$		0			0
$101$	−1.98645	+	3.44063i	−0.197659	+	0.342355i	−0.947769	−	0.318958i	$-0.896667\pi$
$101$	−1.98645	+	3.44063i	−0.197659	+	0.342355i	0.750110	+	0.661313i	$0.230001\pi$
$102$		0			0
$103$	1.77894	+	3.08121i	0.175284	+	0.303601i	0.940260	−	0.340458i	$-0.110582\pi$
$103$	1.77894	+	3.08121i	0.175284	+	0.303601i	−0.764975	+	0.644059i	$0.777249\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.46069			0.237884			0.118942	−	0.992901i	$-0.462050\pi$
$107$	2.46069			0.237884			0.118942	+	0.992901i	$0.462050\pi$
$108$		0			0
$109$	5.95255			0.570151			0.285075	−	0.958505i	$-0.407981\pi$
$109$	5.95255			0.570151			0.285075	+	0.958505i	$0.407981\pi$
$110$		0			0
$111$	−4.01619	+	4.23692i	−0.381200	+	0.402150i
$112$		0			0
$113$	3.52974	+	6.11370i	0.332050	+	0.575128i	0.982914	−	0.184067i	$-0.0589263\pi$
$113$	3.52974	+	6.11370i	0.332050	+	0.575128i	−0.650863	+	0.759195i	$0.725593\pi$
$114$		0			0
$115$	−1.83733	+	3.18235i	−0.171332	+	0.296755i
$116$		0			0
$117$	12.8545	−	8.36824i	1.18840	−	0.773644i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−12.6605	−	21.9286i	−1.15095	−	1.99351i
$122$		0			0
$123$	−0.321996	−	0.0771142i	−0.0290334	−	0.00695315i
$124$		0			0
$125$	−10.7560			−0.962042
$126$		0			0
$127$	2.76393			0.245259			0.122629	−	0.992453i	$-0.460867\pi$
$127$	2.76393			0.245259			0.122629	+	0.992453i	$0.460867\pi$
$128$		0			0
$129$	−1.68716	−	5.68410i	−0.148546	−	0.500457i
$130$		0			0
$131$	4.22748	+	7.32221i	0.369357	+	0.639744i	0.989465	−	0.144772i	$-0.0462448\pi$
$131$	4.22748	+	7.32221i	0.369357	+	0.639744i	−0.620108	+	0.784516i	$0.712911\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	3.38132	−	18.4163i	0.291018	−	1.58502i
$136$		0			0
$137$	−9.04286	+	15.6627i	−0.772584	+	1.33815i	0.163559	+	0.986534i	$0.447703\pi$
$137$	−9.04286	+	15.6627i	−0.772584	+	1.33815i	−0.936143	+	0.351621i	$0.885631\pi$
$138$		0			0
$139$	−6.00936	−	10.4085i	−0.509707	−	0.882839i	−0.999937	−	0.0112454i	$-0.996420\pi$
$139$	−6.00936	−	10.4085i	−0.509707	−	0.882839i	0.490230	−	0.871593i	$-0.336913\pi$
$140$		0			0
$141$	1.02028	+	3.43734i	0.0859229	+	0.289477i
$142$		0			0
$143$	30.8131			2.57672
$144$		0			0
$145$	−20.4445			−1.69782
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.49026	+	4.31325i	0.204010	+	0.353355i	0.949817	−	0.312807i	$-0.101269\pi$
$149$	2.49026	+	4.31325i	0.204010	+	0.353355i	−0.745807	+	0.666162i	$0.767936\pi$
$150$		0			0
$151$	0.0921906	−	0.159679i	0.00750237	−	0.0129945i	−0.862250	−	0.506483i	$-0.830945\pi$
$151$	0.0921906	−	0.159679i	0.00750237	−	0.0129945i	0.869752	+	0.493489i	$0.164279\pi$
$152$		0			0
$153$	−0.0356012	−	0.665086i	−0.00287819	−	0.0537690i
$154$		0			0
$155$	9.09232	−	15.7484i	0.730313	−	1.26494i
$156$		0			0
$157$	2.16698	+	3.75332i	0.172944	+	0.299548i	0.939448	−	0.342692i	$-0.111339\pi$
$157$	2.16698	+	3.75332i	0.172944	+	0.299548i	−0.766504	+	0.642240i	$0.778005\pi$
$158$		0			0
$159$	6.32022	−	6.66759i	0.501226	−	0.528774i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−23.7304			−1.85871			−0.929353	−	0.369193i	$-0.879634\pi$
$163$	−23.7304			−1.85871			−0.929353	+	0.369193i	$0.879634\pi$
$164$		0			0
$165$	25.8771	−	27.2993i	2.01453	−	2.12524i
$166$		0			0
$167$	−1.59445	−	2.76166i	−0.123382	−	0.213704i	0.797717	−	0.603032i	$-0.206041\pi$
$167$	−1.59445	−	2.76166i	−0.123382	−	0.213704i	−0.921099	+	0.389328i	$0.872707\pi$
$168$		0			0
$169$	−6.57027	+	11.3800i	−0.505405	+	0.875388i
$170$		0			0
$171$	−0.548937	−	10.2550i	−0.0419783	−	0.784220i
$172$		0			0
$173$	10.6530	−	18.4515i	0.809932	−	1.40284i	−0.102978	−	0.994684i	$-0.532837\pi$
$173$	10.6530	−	18.4515i	0.809932	−	1.40284i	0.912910	−	0.408160i	$-0.133830\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	12.7953	+	3.06433i	0.961757	+	0.230329i
$178$		0			0
$179$	−0.500285			−0.0373931			−0.0186965	−	0.999825i	$-0.505952\pi$
$179$	−0.500285			−0.0373931			−0.0186965	+	0.999825i	$0.505952\pi$
$180$		0			0
$181$	−5.88424			−0.437372			−0.218686	−	0.975795i	$-0.570177\pi$
$181$	−5.88424			−0.437372			−0.218686	+	0.975795i	$0.570177\pi$
$182$		0			0
$183$	−0.878674	−	2.96028i	−0.0649534	−	0.218830i
$184$		0			0
$185$	−6.07276	−	10.5183i	−0.446478	−	0.773323i
$186$		0			0
$187$	0.669001	−	1.15874i	0.0489222	−	0.0847357i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.94466	−	6.83235i	0.285425	−	0.494371i	−0.687287	−	0.726386i	$-0.741198\pi$
$191$	3.94466	−	6.83235i	0.285425	−	0.494371i	0.972712	+	0.232015i	$0.0745318\pi$
$192$		0			0
$193$	−9.50508	−	16.4633i	−0.684190	−	1.18505i	−0.973691	−	0.227875i	$-0.926822\pi$
$193$	−9.50508	−	16.4633i	−0.684190	−	1.18505i	0.289500	−	0.957178i	$-0.406511\pi$
$194$		0			0
$195$	9.08025	+	30.5916i	0.650250	+	2.19071i
$196$		0			0
$197$	−9.72107			−0.692597			−0.346299	−	0.938124i	$-0.612562\pi$
$197$	−9.72107			−0.692597			−0.346299	+	0.938124i	$0.612562\pi$
$198$		0			0
$199$	−15.0916			−1.06982			−0.534908	−	0.844910i	$-0.679654\pi$
$199$	−15.0916			−1.06982			−0.534908	+	0.844910i	$0.679654\pi$
$200$		0			0
$201$	−21.8717	−	5.23800i	−1.54271	−	0.369460i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.344421	−	0.596555i	0.0240554	−	0.0416652i
$206$		0			0
$207$	2.56386	−	1.66907i	0.178201	−	0.116008i
$208$		0			0
$209$	10.3154	−	17.8667i	0.713529	−	1.23587i
$210$		0			0
$211$	−8.75173	−	15.1584i	−0.602494	−	1.04355i	−0.992442	−	0.122713i	$-0.960840\pi$
$211$	−8.75173	−	15.1584i	−0.602494	−	1.04355i	0.389948	−	0.920837i	$-0.372493\pi$
$212$		0			0
$213$	7.02498	−	7.41107i	0.481343	−	0.507798i
$214$		0			0
$215$	12.3355			0.841271
$216$		0			0
$217$		0			0
$218$		0			0
$219$	15.0261	−	15.8519i	1.01537	−	1.07117i
$220$		0			0
$221$	0.567551	+	0.983028i	0.0381776	+	0.0661256i
$222$		0			0
$223$	−5.00337	+	8.66610i	−0.335051	+	0.580325i	−0.983495	−	0.180938i	$-0.942087\pi$
$223$	−5.00337	+	8.66610i	−0.335051	+	0.580325i	0.648444	+	0.761262i	$0.275420\pi$
$224$		0			0
$225$	21.3559	+	10.8513i	1.42373	+	0.723423i
$226$		0			0
$227$	−1.13317	+	1.96270i	−0.0752110	+	0.130269i	−0.901178	−	0.433449i	$-0.857296\pi$
$227$	−1.13317	+	1.96270i	−0.0752110	+	0.130269i	0.825967	+	0.563718i	$0.190630\pi$
$228$		0			0
$229$	−2.51228	−	4.35140i	−0.166016	−	0.287549i	0.770999	−	0.636836i	$-0.219757\pi$
$229$	−2.51228	−	4.35140i	−0.166016	−	0.287549i	−0.937016	+	0.349287i	$0.886424\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.4479			1.01202			0.506011	−	0.862527i	$-0.331119\pi$
$233$	15.4479			1.01202			0.506011	+	0.862527i	$0.331119\pi$
$234$		0			0
$235$	−7.45962			−0.486612
$236$		0			0
$237$	6.21752	+	20.9470i	0.403871	+	1.36065i
$238$		0			0
$239$	−4.62691	−	8.01404i	−0.299290	−	0.518385i	0.676684	−	0.736274i	$-0.263416\pi$
$239$	−4.62691	−	8.01404i	−0.299290	−	0.518385i	−0.975974	+	0.217889i	$0.930083\pi$
$240$		0			0
$241$	−8.16387	+	14.1402i	−0.525881	+	0.910853i	0.473664	+	0.880705i	$0.342931\pi$
$241$	−8.16387	+	14.1402i	−0.525881	+	0.910853i	−0.999545	+	0.0301474i	$0.990402\pi$
$242$		0			0
$243$	−9.45505	+	12.3936i	−0.606542	+	0.795051i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.75111	+	15.1574i	0.556820	+	0.964440i
$248$		0			0
$249$	−3.54804	−	11.9534i	−0.224848	−	0.757518i
$250$		0			0
$251$	−7.54803			−0.476427			−0.238214	−	0.971213i	$-0.576562\pi$
$251$	−7.54803			−0.476427			−0.238214	+	0.971213i	$0.576562\pi$
$252$		0			0
$253$	6.14577			0.386381
$254$		0			0
$255$	1.34756	+	0.322724i	0.0843874	+	0.0202097i
$256$		0			0
$257$	12.6463	+	21.9041i	0.788856	+	1.36634i	0.926668	+	0.375880i	$0.122659\pi$
$257$	12.6463	+	21.9041i	0.788856	+	1.36634i	−0.137813	+	0.990458i	$0.544007\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	15.1742	+	7.71030i	0.939261	+	0.477256i
$262$		0			0
$263$	−11.7490	+	20.3499i	−0.724474	+	1.25483i	0.234716	+	0.972064i	$0.424584\pi$
$263$	−11.7490	+	20.3499i	−0.724474	+	1.25483i	−0.959190	+	0.282762i	$0.908749\pi$
$264$		0			0
$265$	9.55663	+	16.5526i	0.587059	+	1.01682i
$266$		0			0
$267$	−10.5977	+	11.1801i	−0.648568	+	0.684214i
$268$		0			0
$269$	−27.8156			−1.69595			−0.847975	−	0.530037i	$-0.822178\pi$
$269$	−27.8156			−1.69595			−0.847975	+	0.530037i	$0.822178\pi$
$270$		0			0
$271$	−19.1567			−1.16369			−0.581843	−	0.813301i	$-0.697668\pi$
$271$	−19.1567			−1.16369			−0.581843	+	0.813301i	$0.697668\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	24.0612	+	41.6753i	1.45095	+	2.51312i
$276$		0			0
$277$	−13.7905	+	23.8859i	−0.828593	+	1.43516i	0.0705495	+	0.997508i	$0.477525\pi$
$277$	−13.7905	+	23.8859i	−0.828593	+	1.43516i	−0.899142	+	0.437657i	$0.855809\pi$
$278$		0			0
$279$	−12.6877	+	8.25966i	−0.759592	+	0.494493i
$280$		0			0
$281$	0.192591	−	0.333577i	0.0114890	−	0.0198995i	−0.860224	−	0.509917i	$-0.829676\pi$
$281$	0.192591	−	0.333577i	0.0114890	−	0.0198995i	0.871713	+	0.490017i	$0.163010\pi$
$282$		0			0
$283$	−7.49904	−	12.9887i	−0.445772	−	0.772099i	0.552334	−	0.833623i	$-0.313737\pi$
$283$	−7.49904	−	12.9887i	−0.445772	−	0.772099i	−0.998106	+	0.0615239i	$0.980404\pi$
$284$		0			0
$285$	20.7781	+	4.97610i	1.23079	+	0.294759i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−16.9507			−0.997101
$290$		0			0
$291$	−2.69091	−	9.06576i	−0.157744	−	0.531444i
$292$		0			0
$293$	−11.2323	−	19.4550i	−0.656200	−	1.13657i	−0.981592	−	0.190992i	$-0.938830\pi$
$293$	−11.2323	−	19.4550i	−0.656200	−	1.13657i	0.325392	−	0.945579i	$-0.394504\pi$
$294$		0			0
$295$	−13.6865	+	23.7056i	−0.796856	+	1.38019i
$296$		0			0
$297$	−29.5018	+	10.5028i	−1.71187	+	0.609436i
$298$		0			0
$299$	−2.60690	+	4.51529i	−0.150761	+	0.261126i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.95807	+	6.59679i	0.112488	+	0.378976i
$304$		0			0
$305$	6.42430			0.367854
$306$		0			0
$307$	−6.90792			−0.394256			−0.197128	−	0.980378i	$-0.563161\pi$
$307$	−6.90792			−0.394256			−0.197128	+	0.980378i	$0.563161\pi$
$308$		0			0
$309$	5.99296	+	1.43524i	0.340928	+	0.0816480i
$310$		0			0
$311$	11.5890	+	20.0727i	0.657152	+	1.13822i	0.981350	+	0.192231i	$0.0615722\pi$
$311$	11.5890	+	20.0727i	0.657152	+	1.13822i	−0.324198	+	0.945989i	$0.605094\pi$
$312$		0			0
$313$	8.21883	−	14.2354i	0.464556	−	0.804635i	−0.534625	−	0.845089i	$-0.679547\pi$
$313$	8.21883	−	14.2354i	0.464556	−	0.804635i	0.999181	+	0.0404546i	$0.0128806\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.18401	−	12.4431i	0.403494	−	0.698873i	−0.590651	−	0.806927i	$-0.701129\pi$
$317$	7.18401	−	12.4431i	0.403494	−	0.698873i	0.994145	+	0.108055i	$0.0344622\pi$
$318$		0			0
$319$	17.0965	+	29.6119i	0.957218	+	1.65795i
$320$		0			0
$321$	2.93207	−	3.09322i	0.163652	−	0.172646i
$322$		0			0
$323$	0.760001			0.0422876
$324$		0			0
$325$	−40.8251			−2.26457
$326$		0			0
$327$	7.09284	−	7.48266i	0.392235	−	0.413792i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.87582	+	3.24902i	−0.103105	+	0.178582i	−0.912962	−	0.408044i	$-0.866211\pi$
$331$	−1.87582	+	3.24902i	−0.103105	+	0.178582i	0.809858	+	0.586626i	$0.199544\pi$
$332$		0			0
$333$	0.540485	+	10.0971i	0.0296184	+	0.553318i
$334$		0			0
$335$	23.3949	−	40.5211i	1.27820	−	2.21391i
$336$		0			0
$337$	−2.77171	−	4.80074i	−0.150984	−	0.261513i	0.780605	−	0.625024i	$-0.214911\pi$
$337$	−2.77171	−	4.80074i	−0.150984	−	0.261513i	−0.931590	+	0.363512i	$0.881578\pi$
$338$		0			0
$339$	11.8911	+	2.84778i	0.645838	+	0.154670i
$340$		0			0
$341$	−30.4133			−1.64697
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.81108	+	6.10158i	0.0975053	+	0.328498i
$346$		0			0
$347$	−3.77609	−	6.54037i	−0.202711	−	0.351106i	0.746690	−	0.665172i	$-0.231642\pi$
$347$	−3.77609	−	6.54037i	−0.202711	−	0.351106i	−0.949401	+	0.314066i	$0.898309\pi$
$348$		0			0
$349$	9.10179	−	15.7648i	0.487207	−	0.843868i	−0.512684	−	0.858577i	$-0.671349\pi$
$349$	9.10179	−	15.7648i	0.487207	−	0.843868i	0.999892	+	0.0147092i	$0.00468224\pi$
$350$		0			0
$351$	4.79761	−	26.1300i	0.256077	−	1.39472i
$352$		0			0
$353$	−0.266224	+	0.461114i	−0.0141697	+	0.0245426i	−0.873023	−	0.487678i	$-0.837844\pi$
$353$	−0.266224	+	0.461114i	−0.0141697	+	0.0245426i	0.858854	+	0.512221i	$0.171177\pi$
$354$		0			0
$355$	10.6223	+	18.3983i	0.563771	+	0.976481i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.1099			−1.37803			−0.689014	−	0.724748i	$-0.741956\pi$
$359$	−26.1099			−1.37803			−0.689014	+	0.724748i	$0.741956\pi$
$360$		0			0
$361$	−7.28150			−0.383237
$362$		0			0
$363$	−42.6511	−	10.2144i	−2.23860	−	0.536118i
$364$		0			0
$365$	22.7205	+	39.3530i	1.18924	+	2.05983i
$366$		0			0
$367$	10.5921	−	18.3461i	0.552904	−	0.957658i	−0.445159	−	0.895451i	$-0.646853\pi$
$367$	10.5921	−	18.3461i	0.552904	−	0.957658i	0.998063	−	0.0622062i	$-0.0198137\pi$
$368$		0			0
$369$	−0.480615	+	0.312880i	−0.0250198	+	0.0162879i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−9.00427	−	15.5959i	−0.466223	−	0.807523i	0.533032	−	0.846095i	$-0.321052\pi$
$373$	−9.00427	−	15.5959i	−0.466223	−	0.807523i	−0.999256	+	0.0385721i	$0.987719\pi$
$374$		0			0
$375$	−12.8164	+	13.5208i	−0.661836	+	0.698211i
$376$		0			0
$377$	−29.0078			−1.49398
$378$		0			0
$379$	−15.9120			−0.817343			−0.408672	−	0.912681i	$-0.634008\pi$
$379$	−15.9120			−0.817343			−0.408672	+	0.912681i	$0.634008\pi$
$380$		0			0
$381$	3.29339	−	3.47440i	0.168725	−	0.177999i
$382$		0			0
$383$	−0.154293	−	0.267243i	−0.00788400	−	0.0136555i	0.862056	−	0.506812i	$-0.169176\pi$
$383$	−0.154293	−	0.267243i	−0.00788400	−	0.0136555i	−0.869940	+	0.493157i	$0.835843\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.15556	−	4.65211i	−0.465404	−	0.236480i
$388$		0			0
$389$	−2.38753	+	4.13533i	−0.121053	+	0.209669i	−0.920183	−	0.391488i	$-0.871960\pi$
$389$	−2.38753	+	4.13533i	−0.121053	+	0.209669i	0.799130	+	0.601158i	$0.205294\pi$
$390$		0			0
$391$	0.113200	+	0.196068i	0.00572476	+	0.00991557i
$392$		0			0
$393$	14.2417	+	3.41071i	0.718399	+	0.172048i
$394$		0			0
$395$	−45.4585			−2.28727
$396$		0			0
$397$	−9.50058			−0.476820			−0.238410	−	0.971165i	$-0.576626\pi$
$397$	−9.50058			−0.476820			−0.238410	+	0.971165i	$0.576626\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.67088	+	16.7505i	0.482941	+	0.836478i	0.999808	−	0.0195874i	$-0.00623526\pi$
$401$	9.67088	+	16.7505i	0.482941	+	0.836478i	−0.516867	+	0.856066i	$0.672902\pi$
$402$		0			0
$403$	12.9007	−	22.3446i	0.642629	−	1.11307i
$404$		0			0
$405$	−19.1211	−	26.1946i	−0.950137	−	1.30162i
$406$		0			0
$407$	−10.1565	+	17.5916i	−0.503441	+	0.871985i
$408$		0			0
$409$	−5.34036	−	9.24977i	−0.264064	−	0.457372i	0.703254	−	0.710939i	$-0.251730\pi$
$409$	−5.34036	−	9.24977i	−0.264064	−	0.457372i	−0.967318	+	0.253567i	$0.918396\pi$
$410$		0			0
$411$	8.91368	+	30.0304i	0.439679	+	1.48129i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	25.9410			1.27339
$416$		0			0
$417$	−20.2446	−	4.84833i	−0.991381	−	0.237424i
$418$		0			0
$419$	17.5274	+	30.3583i	0.856267	+	1.48310i	0.875464	+	0.483283i	$0.160556\pi$
$419$	17.5274	+	30.3583i	0.856267	+	1.48310i	−0.0191966	+	0.999816i	$0.506111\pi$
$420$		0			0
$421$	15.8653	−	27.4795i	0.773226	−	1.33927i	−0.162560	−	0.986699i	$-0.551975\pi$
$421$	15.8653	−	27.4795i	0.773226	−	1.33927i	0.935786	−	0.352568i	$-0.114692\pi$
$422$		0			0
$423$	5.53664	+	2.81327i	0.269201	+	0.136786i
$424$		0			0
$425$	−0.886375	+	1.53525i	−0.0429955	+	0.0744704i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	36.7158	−	38.7337i	1.77265	−	1.87008i
$430$		0			0
$431$	34.9536			1.68366			0.841829	−	0.539745i	$-0.181479\pi$
$431$	34.9536			1.68366			0.841829	+	0.539745i	$0.181479\pi$
$432$		0			0
$433$	28.3369			1.36178			0.680891	−	0.732385i	$-0.261593\pi$
$433$	28.3369			1.36178			0.680891	+	0.732385i	$0.261593\pi$
$434$		0			0
$435$	−24.3609	+	25.6998i	−1.16802	+	1.23221i
$436$		0			0
$437$	1.74543	+	3.02318i	0.0834955	+	0.144618i
$438$		0			0
$439$	−4.85457	+	8.40837i	−0.231696	+	0.401310i	−0.958307	−	0.285739i	$-0.907761\pi$
$439$	−4.85457	+	8.40837i	−0.231696	+	0.401310i	0.726611	+	0.687049i	$0.241094\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.03961	−	8.72885i	0.239439	−	0.414720i	−0.721114	−	0.692816i	$-0.756370\pi$
$443$	5.03961	−	8.72885i	0.239439	−	0.414720i	0.960553	+	0.278096i	$0.0897032\pi$
$444$		0			0
$445$	−16.0245	−	27.7552i	−0.759633	−	1.31572i
$446$		0			0
$447$	8.38927	+	2.00913i	0.396799	+	0.0950285i
$448$		0			0
$449$	−28.9202			−1.36483			−0.682414	−	0.730966i	$-0.739070\pi$
$449$	−28.9202			−1.36483			−0.682414	+	0.730966i	$0.739070\pi$
$450$		0			0
$451$	−1.15207			−0.0542489
$452$		0			0
$453$	−0.0908736	−	0.306156i	−0.00426961	−	0.0143845i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.10680	−	7.11318i	0.192108	−	0.332741i	−0.753841	−	0.657057i	$-0.771801\pi$
$457$	4.10680	−	7.11318i	0.192108	−	0.332741i	0.945949	+	0.324317i	$0.105134\pi$
$458$		0			0
$459$	−0.878469	−	0.747739i	−0.0410034	−	0.0349015i
$460$		0			0
$461$	−14.0516	+	24.3381i	−0.654448	+	1.13354i	0.327584	+	0.944822i	$0.393766\pi$
$461$	−14.0516	+	24.3381i	−0.654448	+	1.13354i	−0.982032	+	0.188715i	$0.939568\pi$
$462$		0			0
$463$	1.54897	+	2.68289i	0.0719866	+	0.124684i	0.899772	−	0.436361i	$-0.143733\pi$
$463$	1.54897	+	2.68289i	0.0719866	+	0.124684i	−0.827785	+	0.561045i	$0.810399\pi$
$464$		0			0
$465$	−8.96243	−	30.1947i	−0.415623	−	1.40024i
$466$		0			0
$467$	11.5191			0.533040			0.266520	−	0.963829i	$-0.414126\pi$
$467$	11.5191			0.533040			0.266520	+	0.963829i	$0.414126\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.30021	+	1.74831i	0.336376	+	0.0805579i
$472$		0			0
$473$	−10.3154	−	17.8667i	−0.474301	−	0.821513i
$474$		0			0
$475$	−13.6671	+	23.6721i	−0.627088	+	1.08615i
$476$		0			0
$477$	−0.850555	−	15.8897i	−0.0389442	−	0.727539i
$478$		0			0
$479$	−20.3542	+	35.2545i	−0.930007	+	1.61082i	−0.146704	+	0.989180i	$0.546867\pi$
$479$	−20.3542	+	35.2545i	−0.930007	+	1.61082i	−0.783303	+	0.621640i	$0.786467\pi$
$480$		0			0
$481$	−8.61637	−	14.9240i	−0.392873	−	0.680475i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	19.6742			0.893361
$486$		0			0
$487$	−33.5910			−1.52215			−0.761077	−	0.648662i	$-0.775329\pi$
$487$	−33.5910			−1.52215			−0.761077	+	0.648662i	$0.775329\pi$
$488$		0			0
$489$	−28.2762	+	29.8303i	−1.27869	+	1.34897i
$490$		0			0
$491$	−3.22990	−	5.59435i	−0.145763	−	0.252469i	0.783894	−	0.620894i	$-0.213230\pi$
$491$	−3.22990	−	5.59435i	−0.145763	−	0.252469i	−0.929657	+	0.368425i	$0.879897\pi$
$492$		0			0
$493$	−0.629804	+	1.09085i	−0.0283650	+	0.0491295i
$494$		0			0
$495$	−3.48245	−	65.0576i	−0.156524	−	2.92412i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6.00584	+	10.4024i	0.268859	+	0.465677i	0.968567	−	0.248752i	$-0.0800203\pi$
$499$	6.00584	+	10.4024i	0.268859	+	0.465677i	−0.699709	+	0.714428i	$0.746687\pi$
$500$		0			0
$501$	−5.37144	−	1.28639i	−0.239978	−	0.0574718i
$502$		0			0
$503$	−34.3935			−1.53353			−0.766765	−	0.641928i	$-0.778135\pi$
$503$	−34.3935			−1.53353			−0.766765	+	0.641928i	$0.778135\pi$
$504$		0			0
$505$	−14.3162			−0.637060
$506$		0			0
$507$	6.47641	+	21.8192i	0.287627	+	0.969025i
$508$		0			0
$509$	−15.7523	−	27.2838i	−0.698208	−	1.20933i	−0.969087	−	0.246718i	$-0.920648\pi$
$509$	−15.7523	−	27.2838i	−0.698208	−	1.20933i	0.270879	−	0.962613i	$-0.412686\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−13.5452	−	11.5294i	−0.598034	−	0.509037i
$514$		0			0
$515$	−6.41033	+	11.1030i	−0.282473	+	0.489258i
$516$		0			0
$517$	6.23801	+	10.8045i	0.274347	+	0.475183i
$518$		0			0
$519$	−10.5008	−	35.3775i	−0.460934	−	1.55290i
$520$		0			0
$521$	26.6390			1.16708			0.583539	−	0.812085i	$-0.301668\pi$
$521$	26.6390			1.16708			0.583539	+	0.812085i	$0.301668\pi$
$522$		0			0
$523$	30.4012			1.32935			0.664676	−	0.747132i	$-0.268570\pi$
$523$	30.4012			1.32935			0.664676	+	0.747132i	$0.268570\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.560188	−	0.970273i	−0.0244022	−	0.0422658i
$528$		0			0
$529$	10.9800	−	19.0180i	0.477393	−	0.826869i
$530$		0			0
$531$	19.0985	−	12.4331i	0.828803	−	0.539549i
$532$		0			0
$533$	0.488684	−	0.846425i	0.0211672	−	0.0366627i
$534$		0			0
$535$	4.43350	+	7.67904i	0.191677	+	0.331994i
$536$		0			0
$537$	−0.596121	+	0.628884i	−0.0257245	+	0.0271383i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.51710			0.108219			0.0541094	−	0.998535i	$-0.482768\pi$
$541$	2.51710			0.108219			0.0541094	+	0.998535i	$0.482768\pi$
$542$		0			0
$543$	−7.01144	+	7.39679i	−0.300890	+	0.317427i
$544$		0			0
$545$	10.7249	+	18.5760i	0.459403	+	0.795710i
$546$		0			0
$547$	9.25785	−	16.0351i	0.395837	−	0.685610i	−0.597370	−	0.801965i	$-0.703788\pi$
$547$	9.25785	−	16.0351i	0.395837	−	0.685610i	0.993208	+	0.116355i	$0.0371211\pi$
$548$		0			0
$549$	−4.76821	−	2.42282i	−0.203502	−	0.103403i
$550$		0			0
$551$	−9.71099	+	16.8199i	−0.413702	+	0.716553i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−20.4582	−	4.89948i	−0.868401	−	0.207971i
$556$		0			0
$557$	24.4247			1.03491			0.517454	−	0.855711i	$-0.326880\pi$
$557$	24.4247			1.03491			0.517454	+	0.855711i	$0.326880\pi$
$558$		0			0
$559$	17.5022			0.740265
$560$		0			0
$561$	−0.659443	−	2.22168i	−0.0278417	−	0.0937995i
$562$		0			0
$563$	12.3700	+	21.4255i	0.521334	+	0.902976i	0.999692	+	0.0248116i	$0.00789858\pi$
$563$	12.3700	+	21.4255i	0.521334	+	0.902976i	−0.478359	+	0.878165i	$0.658768\pi$
$564$		0			0
$565$	−12.7193	+	22.0304i	−0.535104	+	0.926828i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.35982	+	14.4796i	−0.350462	+	0.607018i	−0.986330	−	0.164780i	$-0.947309\pi$
$569$	−8.35982	+	14.4796i	−0.350462	+	0.607018i	0.635869	+	0.771797i	$0.280642\pi$
$570$		0			0
$571$	14.8135	+	25.6578i	0.619926	+	1.07374i	0.989499	+	0.144542i	$0.0461708\pi$
$571$	14.8135	+	25.6578i	0.619926	+	1.07374i	−0.369573	+	0.929202i	$0.620496\pi$
$572$		0			0
$573$	−3.88831	−	13.0998i	−0.162436	−	0.547252i
$574$		0			0
$575$	−8.14267			−0.339573
$576$		0			0
$577$	30.6682			1.27673			0.638367	−	0.769732i	$-0.279610\pi$
$577$	30.6682			1.27673			0.638367	+	0.769732i	$0.279610\pi$
$578$		0			0
$579$	−32.0211	−	7.66866i	−1.33075	−	0.318698i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	15.9832	−	27.6837i	0.661957	−	1.14654i
$584$		0			0
$585$	49.2749	+	25.0375i	2.03727	+	1.03517i
$586$		0			0
$587$	−7.88611	+	13.6591i	−0.325495	+	0.563773i	−0.981612	−	0.190885i	$-0.938864\pi$
$587$	−7.88611	+	13.6591i	−0.325495	+	0.563773i	0.656118	+	0.754658i	$0.272197\pi$
$588$		0			0
$589$	−8.63757	−	14.9607i	−0.355905	−	0.616445i
$590$		0			0
$591$	−11.5833	+	12.2199i	−0.476472	+	0.502659i
$592$		0			0
$593$	−3.06678			−0.125938			−0.0629688	−	0.998015i	$-0.520057\pi$
$593$	−3.06678			−0.125938			−0.0629688	+	0.998015i	$0.520057\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−17.9826	+	18.9709i	−0.735979	+	0.776429i
$598$		0			0
$599$	−16.1696	−	28.0066i	−0.660673	−	1.14432i	−0.980439	−	0.196822i	$-0.936938\pi$
$599$	−16.1696	−	28.0066i	−0.660673	−	1.14432i	0.319766	−	0.947496i	$-0.396396\pi$
$600$		0			0
$601$	14.9839	−	25.9529i	0.611208	−	1.05864i	−0.379830	−	0.925056i	$-0.624017\pi$
$601$	14.9839	−	25.9529i	0.611208	−	1.05864i	0.991037	−	0.133586i	$-0.0426493\pi$
$602$		0			0
$603$	−32.6459	+	21.2524i	−1.32944	+	0.865466i
$604$		0			0
$605$	45.6215	−	79.0187i	1.85478	−	3.21257i
$606$		0			0
$607$	−10.1275	−	17.5414i	−0.411064	−	0.711984i	0.583942	−	0.811795i	$-0.301509\pi$
$607$	−10.1275	−	17.5414i	−0.411064	−	0.711984i	−0.995006	+	0.0998113i	$0.968176\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.5841			−0.428188
$612$		0			0
$613$	−25.0839			−1.01313			−0.506564	−	0.862202i	$-0.669085\pi$
$613$	−25.0839			−1.01313			−0.506564	+	0.862202i	$0.669085\pi$
$614$		0			0
$615$	−0.339501	−	1.14379i	−0.0136900	−	0.0461220i
$616$		0			0
$617$	−21.0472	−	36.4548i	−0.847328	−	1.46762i	−0.883584	−	0.468273i	$-0.844877\pi$
$617$	−21.0472	−	36.4548i	−0.847328	−	1.46762i	0.0362561	−	0.999343i	$-0.488457\pi$
$618$		0			0
$619$	−7.41252	+	12.8389i	−0.297934	+	0.516037i	−0.975663	−	0.219275i	$-0.929631\pi$
$619$	−7.41252	+	12.8389i	−0.297934	+	0.516037i	0.677729	+	0.735312i	$0.262964\pi$
$620$		0			0
$621$	0.956897	−	5.21171i	0.0383989	−	0.209139i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.582932	+	1.00967i	0.0233173	+	0.0403867i
$626$		0			0
$627$	−10.1680	−	34.2563i	−0.406071	−	1.36806i
$628$		0			0
$629$	−0.748299			−0.0298366
$630$		0			0
$631$	20.6414			0.821722			0.410861	−	0.911698i	$-0.365228\pi$
$631$	20.6414			0.821722			0.410861	+	0.911698i	$0.365228\pi$
$632$		0			0
$633$	−29.4832	−	7.06086i	−1.17185	−	0.280644i
$634$		0			0
$635$	4.97984	+	8.62534i	0.197619	+	0.342286i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.945398	−	17.6615i	−0.0373994	−	0.698679i
$640$		0			0
$641$	−0.776633	+	1.34517i	−0.0306752	+	0.0531309i	−0.880955	−	0.473199i	$-0.843099\pi$
$641$	−0.776633	+	1.34517i	−0.0306752	+	0.0531309i	0.850280	+	0.526330i	$0.176432\pi$
$642$		0			0
$643$	10.7061	+	18.5435i	0.422206	+	0.731282i	0.996155	−	0.0876087i	$-0.0279225\pi$
$643$	10.7061	+	18.5435i	0.422206	+	0.731282i	−0.573949	+	0.818891i	$0.694589\pi$
$644$		0			0
$645$	14.6985	−	15.5063i	0.578752	−	0.610560i
$646$		0			0
$647$	−29.5274			−1.16084			−0.580422	−	0.814316i	$-0.697112\pi$
$647$	−29.5274			−1.16084			−0.580422	+	0.814316i	$0.697112\pi$
$648$		0			0
$649$	45.7805			1.79704
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.03041	−	13.9091i	−0.314254	−	0.544304i	0.665025	−	0.746822i	$-0.268421\pi$
$653$	−8.03041	−	13.9091i	−0.314254	−	0.544304i	−0.979279	+	0.202517i	$0.935088\pi$
$654$		0			0
$655$	−15.2335	+	26.3853i	−0.595224	+	1.03096i
$656$		0			0
$657$	−2.02216	−	37.7771i	−0.0788919	−	1.47382i
$658$		0			0
$659$	14.2100	−	24.6124i	0.553543	−	0.958764i	−0.444473	−	0.895792i	$-0.646609\pi$
$659$	14.2100	−	24.6124i	0.553543	−	0.958764i	0.998015	−	0.0629717i	$-0.0200578\pi$
$660$		0			0
$661$	16.9884	+	29.4248i	0.660773	+	1.14449i	0.980413	+	0.196953i	$0.0631047\pi$
$661$	16.9884	+	29.4248i	0.660773	+	1.14449i	−0.319640	+	0.947539i	$0.603562\pi$
$662$		0			0
$663$	1.91199	+	0.457898i	0.0742555	+	0.0177833i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.78569			−0.224023
$668$		0			0
$669$	4.93190	+	16.6157i	0.190678	+	0.642400i
$670$		0			0
$671$	−5.37224	−	9.30499i	−0.207393	−	0.359215i
$672$		0			0
$673$	−0.807019	+	1.39780i	−0.0311083	+	0.0538812i	−0.881160	−	0.472817i	$-0.843237\pi$
$673$	−0.807019	+	1.39780i	−0.0311083	+	0.0538812i	0.850052	+	0.526699i	$0.176570\pi$
$674$		0			0
$675$	39.0876	−	13.9155i	1.50448	−	0.535606i
$676$		0			0
$677$	−13.3479	+	23.1193i	−0.513002	+	0.888545i	0.486884	+	0.873466i	$0.338133\pi$
$677$	−13.3479	+	23.1193i	−0.513002	+	0.888545i	−0.999886	+	0.0150790i	$0.995200\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.11698	+	3.76313i	0.0428027	+	0.144204i
$682$		0			0
$683$	35.2366			1.34829			0.674146	−	0.738598i	$-0.264512\pi$
$683$	35.2366			1.34829			0.674146	+	0.738598i	$0.264512\pi$
$684$		0			0
$685$	−65.1711			−2.49006
$686$		0			0
$687$	−8.46347	−	2.02690i	−0.322902	−	0.0773310i
$688$		0			0
$689$	13.5595	+	23.4857i	0.516575	+	0.894734i
$690$		0			0
$691$	−14.3904	+	24.9248i	−0.547435	+	0.948185i	0.451014	+	0.892517i	$0.351062\pi$
$691$	−14.3904	+	24.9248i	−0.547435	+	0.948185i	−0.998449	+	0.0556685i	$0.982271\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.6545	−	37.5066i	0.821401	−	1.42271i
$696$		0			0
$697$	−0.0212202	−	0.0367544i	−0.000803771	−	0.00139217i
$698$		0			0
$699$	18.4071	−	19.4188i	0.696220	−	0.734485i
$700$		0			0
$701$	17.2044			0.649800			0.324900	−	0.945748i	$-0.394669\pi$
$701$	17.2044			0.649800			0.324900	+	0.945748i	$0.394669\pi$
$702$		0			0
$703$	−11.5381			−0.435166
$704$		0			0
$705$	−8.88860	+	9.37713i	−0.334764	+	0.353163i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−22.8211	+	39.5272i	−0.857063	+	1.48448i	0.0176546	+	0.999844i	$0.494380\pi$
$709$	−22.8211	+	39.5272i	−0.857063	+	1.48448i	−0.874718	+	0.484633i	$0.838953\pi$
$710$		0			0
$711$	33.7400	+	17.1439i	1.26535	+	0.642947i
$712$		0			0
$713$	2.57308	−	4.45670i	0.0963626	−	0.166905i
$714$		0			0
$715$	55.5169	+	96.1581i	2.07621	+	3.59611i
$716$		0			0
$717$	−15.5873	−	3.73297i	−0.582118	−	0.139410i
$718$		0			0
$719$	22.3713			0.834309			0.417155	−	0.908836i	$-0.363027\pi$
$719$	22.3713			0.834309			0.417155	+	0.908836i	$0.363027\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	8.04724	+	27.1114i	0.299280	+	1.00828i
$724$		0			0
$725$	−22.6515	−	39.2336i	−0.841256	−	1.45710i
$726$		0			0
$727$	18.3031	−	31.7019i	0.678824	−	1.17576i	−0.296512	−	0.955029i	$-0.595823\pi$
$727$	18.3031	−	31.7019i	0.678824	−	1.17576i	0.975335	−	0.220728i	$-0.0708433\pi$
$728$		0			0
$729$	4.31313	+	26.6533i	0.159746	+	0.987158i
$730$		0			0
$731$	0.380000	−	0.658180i	0.0140548	−	0.0243437i
$732$		0			0
$733$	−19.9734	−	34.5950i	−0.737736	−	1.27780i	−0.953513	−	0.301353i	$-0.902562\pi$
$733$	−19.9734	−	34.5950i	−0.737736	−	1.27780i	0.215777	−	0.976443i	$-0.430772\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−78.2547			−2.88255
$738$		0			0
$739$	−10.8428			−0.398859			−0.199430	−	0.979912i	$-0.563909\pi$
$739$	−10.8428			−0.398859			−0.199430	+	0.979912i	$0.563909\pi$
$740$		0			0
$741$	29.4811	+	7.06036i	1.08302	+	0.259369i
$742$		0			0
$743$	−2.74353	−	4.75194i	−0.100651	−	0.174332i	0.811302	−	0.584627i	$-0.198759\pi$
$743$	−2.74353	−	4.75194i	−0.100651	−	0.174332i	−0.911953	+	0.410295i	$0.865426\pi$
$744$		0			0
$745$	−8.97353	+	15.5426i	−0.328765	+	0.569437i
$746$		0			0
$747$	−19.2538	−	9.78320i	−0.704459	−	0.357949i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	13.5621	+	23.4902i	0.494888	+	0.857171i	0.999983	−	0.00589323i	$-0.00187588\pi$
$751$	13.5621	+	23.4902i	0.494888	+	0.857171i	−0.505095	+	0.863064i	$0.668543\pi$
$752$		0			0
$753$	−8.99395	+	9.48826i	−0.327758	+	0.345771i
$754$		0			0
$755$	0.664410			0.0241804
$756$		0			0
$757$	−36.5294			−1.32768			−0.663842	−	0.747872i	$-0.731075\pi$
$757$	−36.5294			−1.32768			−0.663842	+	0.747872i	$0.731075\pi$
$758$		0			0
$759$	7.32307	−	7.72555i	0.265811	−	0.280420i
$760$		0			0
$761$	26.4394	+	45.7944i	0.958429	+	1.66005i	0.726319	+	0.687358i	$0.241230\pi$
$761$	26.4394	+	45.7944i	0.958429	+	1.66005i	0.232110	+	0.972690i	$0.425437\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.01138	−	1.30940i	0.0727216	−	0.0473416i
$766$		0			0
$767$	−19.4191	+	33.6348i	−0.701183	+	1.21448i
$768$		0			0
$769$	−22.9381	−	39.7299i	−0.827169	−	1.43270i	−0.900250	−	0.435372i	$-0.856617\pi$
$769$	−22.9381	−	39.7299i	−0.827169	−	1.43270i	0.0730816	−	0.997326i	$-0.476717\pi$
$770$		0			0
$771$	42.6034	+	10.2030i	1.53432	+	0.367452i
$772$		0			0
$773$	15.2245			0.547586			0.273793	−	0.961789i	$-0.411722\pi$
$773$	15.2245			0.547586			0.273793	+	0.961789i	$0.411722\pi$
$774$		0			0
$775$	40.2954			1.44745
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.327195	−	0.566718i	−0.0117230	−	0.0203048i
$780$		0			0
$781$	17.7655	−	30.7707i	0.635698	−	1.10106i
$782$		0			0
$783$	27.7733	−	9.88748i	0.992537	−	0.353350i
$784$		0			0
$785$	−7.80862	+	13.5249i	−0.278702	+	0.482725i
$786$		0			0
$787$	10.5617	+	18.2935i	0.376485	+	0.652091i	0.990548	−	0.137166i	$-0.0437993\pi$
$787$	10.5617	+	18.2935i	0.376485	+	0.652091i	−0.614063	+	0.789257i	$0.710466\pi$
$788$		0			0
$789$	11.5811	+	39.0172i	0.412300	+	1.38905i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	9.11515			0.323689
$794$		0			0
$795$	32.1948	+	7.71025i	1.14183	+	0.273454i
$796$		0			0
$797$	27.0532	+	46.8575i	0.958272	+	1.65978i	0.726695	+	0.686960i	$0.241055\pi$
$797$	27.0532	+	46.8575i	0.958272	+	1.65978i	0.231577	+	0.972817i	$0.425611\pi$
$798$		0			0
$799$	−0.229798	+	0.398021i	−0.00812965	+	0.0140810i
$800$		0			0
$801$	1.42620	+	26.6437i	0.0503924	+	0.941408i
$802$		0			0
$803$	37.9994	−	65.8169i	1.34097	−	2.32263i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−33.1441	+	34.9657i	−1.16673	+	1.23085i
$808$		0			0
$809$	−54.6561			−1.92161			−0.960803	−	0.277233i	$-0.910582\pi$
$809$	−54.6561			−1.92161			−0.960803	+	0.277233i	$0.910582\pi$
$810$		0			0
$811$	12.7853			0.448954			0.224477	−	0.974479i	$-0.427933\pi$
$811$	12.7853			0.448954			0.224477	+	0.974479i	$0.427933\pi$
$812$		0			0
$813$	−22.8264	+	24.0809i	−0.800556	+	0.844555i
$814$		0			0
$815$	−42.7557	−	74.0550i	−1.49767	−	2.59403i
$816$		0			0
$817$	5.85925	−	10.1485i	0.204989	−	0.355052i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.7302	+	30.7095i	−0.618787	+	1.07177i	0.370921	+	0.928664i	$0.379042\pi$
$821$	−17.7302	+	30.7095i	−0.618787	+	1.07177i	−0.989707	+	0.143105i	$0.954291\pi$
$822$		0			0
$823$	−3.95726	−	6.85417i	−0.137941	−	0.238921i	0.788776	−	0.614681i	$-0.210715\pi$
$823$	−3.95726	−	6.85417i	−0.137941	−	0.238921i	−0.926717	+	0.375760i	$0.877382\pi$
$824$		0			0
$825$	81.0585	+	19.4125i	2.82209	+	0.675857i
$826$		0			0
$827$	45.6562			1.58762			0.793811	−	0.608164i	$-0.208094\pi$
$827$	45.6562			1.58762			0.793811	+	0.608164i	$0.208094\pi$
$828$		0			0
$829$	42.0886			1.46180			0.730898	−	0.682487i	$-0.239102\pi$
$829$	42.0886			1.46180			0.730898	+	0.682487i	$0.239102\pi$
$830$		0			0
$831$	13.5935	+	45.7970i	0.471554	+	1.58868i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	5.74552	−	9.95154i	0.198832	−	0.344387i
$836$		0			0
$837$	−4.73536	+	25.7910i	−0.163678	+	0.891467i
$838$		0			0
$839$	10.3598	−	17.9437i	0.357660	−	0.619485i	−0.629910	−	0.776668i	$-0.716908\pi$
$839$	10.3598	−	17.9437i	0.357660	−	0.619485i	0.987569	+	0.157183i	$0.0502414\pi$
$840$		0			0
$841$	−1.59479	−	2.76225i	−0.0549926	−	0.0952500i
$842$		0			0
$843$	−0.189840	−	0.639575i	−0.00653842	−	0.0220281i
$844$		0			0
$845$	−47.3514			−1.62894
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−25.2631	−	6.05019i	−0.867026	−	0.207642i
$850$		0			0
$851$	−1.71856	−	2.97663i	−0.0589115	−	0.102038i
$852$		0			0
$853$	−7.75942	+	13.4397i	−0.265678	+	0.460167i	−0.967741	−	0.251947i	$-0.918929\pi$
$853$	−7.75942	+	13.4397i	−0.265678	+	0.460167i	0.702063	+	0.712115i	$0.252262\pi$
$854$		0			0
$855$	31.0136	−	20.1898i	1.06064	−	0.690476i
$856$		0			0
$857$	1.24091	−	2.14933i	0.0423888	−	0.0734196i	−0.844053	−	0.536260i	$-0.819837\pi$
$857$	1.24091	−	2.14933i	0.0423888	−	0.0734196i	0.886441	+	0.462841i	$0.153170\pi$
$858$		0			0
$859$	17.5198	+	30.3452i	0.597768	+	1.03537i	0.993150	+	0.116848i	$0.0372791\pi$
$859$	17.5198	+	30.3452i	0.597768	+	1.03537i	−0.395382	+	0.918517i	$0.629388\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	28.9556			0.985661			0.492831	−	0.870125i	$-0.335962\pi$
$863$	28.9556			0.985661			0.492831	+	0.870125i	$0.335962\pi$
$864$		0			0
$865$	76.7752			2.61044
$866$		0			0
$867$	−20.1978	+	21.3079i	−0.685954	+	0.723655i
$868$		0			0
$869$	38.0141	+	65.8424i	1.28954	+	2.23355i
$870$		0			0
$871$	33.1940	−	57.4936i	1.12473	−	1.94810i
$872$		0			0
$873$	−14.6025	−	7.41981i	−0.494220	−	0.251122i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.79611	−	16.9674i	−0.330791	−	0.572947i	0.651876	−	0.758325i	$-0.273982\pi$
$877$	−9.79611	−	16.9674i	−0.330791	−	0.572947i	−0.982667	+	0.185379i	$0.940649\pi$
$878$		0			0
$879$	−37.8399	−	9.06219i	−1.27631	−	0.305660i
$880$		0			0
$881$	15.9010			0.535717			0.267858	−	0.963458i	$-0.413684\pi$
$881$	15.9010			0.535717			0.267858	+	0.963458i	$0.413684\pi$
$882$		0			0
$883$	0.329844			0.0111001			0.00555007	−	0.999985i	$-0.498233\pi$
$883$	0.329844			0.0111001			0.00555007	+	0.999985i	$0.498233\pi$
$884$		0			0
$885$	13.4909	+	45.4513i	0.453493	+	1.52783i
$886$		0			0
$887$	−6.31301	−	10.9345i	−0.211970	−	0.367143i	0.740361	−	0.672210i	$-0.234655\pi$
$887$	−6.31301	−	10.9345i	−0.211970	−	0.367143i	−0.952331	+	0.305066i	$0.901321\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−21.9506	+	49.6001i	−0.735374	+	1.66166i
$892$		0			0
$893$	−3.54326	+	6.13711i	−0.118571	+	0.205371i
$894$		0			0
$895$	−0.901378	−	1.56123i	−0.0301297	−	0.0521862i
$896$		0			0
$897$	2.56966	+	8.65726i	0.0857985	+	0.289057i
$898$		0			0
$899$	28.6314			0.954912
$900$		0			0
$901$	1.17759			0.0392312
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−10.6018	−	18.3629i	−0.352416	−	0.610402i
$906$		0			0
$907$	4.94626	−	8.56717i	0.164238	−	0.284468i	−0.772147	−	0.635445i	$-0.780817\pi$
$907$	4.94626	−	8.56717i	0.164238	−	0.284468i	0.936384	+	0.350976i	$0.114150\pi$
$908$		0			0
$909$	10.6257	+	5.39910i	0.352431	+	0.179077i
$910$		0			0
$911$	29.8185	−	51.6472i	0.987932	−	1.71115i	0.359828	−	0.933019i	$-0.382835\pi$
$911$	29.8185	−	51.6472i	0.987932	−	1.71115i	0.628104	−	0.778130i	$-0.283831\pi$
$912$		0			0
$913$	−21.6928	−	37.5730i	−0.717927	−	1.24349i
$914$		0			0
$915$	7.65496	−	8.07568i	0.253065	−	0.266974i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−7.69518			−0.253841			−0.126920	−	0.991913i	$-0.540509\pi$
$919$	−7.69518			−0.253841			−0.126920	+	0.991913i	$0.540509\pi$
$920$		0			0
$921$	−8.23122	+	8.68361i	−0.271228	+	0.286135i
$922$		0			0
$923$	15.0715	+	26.1045i	0.496083	+	0.859241i
$924$		0			0
$925$	13.4566	−	23.3076i	0.442452	−	0.766349i
$926$		0			0
$927$	8.94516	−	5.82328i	0.293798	−	0.191262i
$928$		0			0
$929$	13.8357	−	23.9642i	0.453936	−	0.786240i	−0.544690	−	0.838637i	$-0.683353\pi$
$929$	13.8357	−	23.9642i	0.453936	−	0.786240i	0.998626	+	0.0523969i	$0.0166861\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	39.0415	+	9.34995i	1.27816	+	0.306104i
$934$		0			0
$935$	4.82143			0.157678
$936$		0			0
$937$	−44.7712			−1.46261			−0.731305	−	0.682051i	$-0.761088\pi$
$937$	−44.7712			−1.46261			−0.731305	+	0.682051i	$0.761088\pi$
$938$		0			0
$939$	−8.10142	−	27.2939i	−0.264380	−	0.890703i
$940$		0			0
$941$	20.0046	+	34.6490i	0.652132	+	1.12953i	0.982605	+	0.185710i	$0.0594586\pi$
$941$	20.0046	+	34.6490i	0.652132	+	1.12953i	−0.330472	+	0.943816i	$0.607208\pi$
$942$		0			0
$943$	0.0974694	−	0.168822i	0.00317404	−	0.00549760i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.4634	−	38.9078i	0.729963	−	1.26433i	−0.226935	−	0.973910i	$-0.572871\pi$
$947$	22.4634	−	38.9078i	0.729963	−	1.26433i	0.956898	−	0.290423i	$-0.0937961\pi$
$948$		0			0
$949$	32.2371	+	55.8362i	1.04646	+	1.81252i
$950$		0			0
$951$	−7.08138	−	23.8574i	−0.229630	−	0.773629i
$952$		0			0
$953$	−40.8038			−1.32176			−0.660882	−	0.750490i	$-0.729818\pi$
$953$	−40.8038			−1.32176			−0.660882	+	0.750490i	$0.729818\pi$
$954$		0			0
$955$	28.4288			0.919935
$956$		0			0
$957$	57.5952	+	13.7934i	1.86179	+	0.445876i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	2.76670	−	4.79206i	0.0892483	−	0.154583i
$962$		0			0
$963$	−0.394588	−	7.37152i	−0.0127154	−	0.237544i
$964$		0			0
$965$	34.2511	−	59.3247i	1.10258	−	1.90973i
$966$		0			0
$967$	−9.63289	−	16.6847i	−0.309773	−	0.536542i	0.668540	−	0.743677i	$-0.266920\pi$
$967$	−9.63289	−	16.6847i	−0.309773	−	0.536542i	−0.978313	+	0.207134i	$0.933586\pi$
$968$		0			0
$969$	0.905588	−	0.955360i	0.0290917	−	0.0306906i
$970$		0			0
$971$	−59.7368			−1.91705			−0.958523	−	0.285017i	$-0.908001\pi$
$971$	−59.7368			−1.91705			−0.958523	+	0.285017i	$0.908001\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−48.6456	+	51.3192i	−1.55791	+	1.64353i
$976$		0			0
$977$	29.7758	+	51.5732i	0.952613	+	1.64997i	0.739739	+	0.672893i	$0.234949\pi$
$977$	29.7758	+	51.5732i	0.952613	+	1.64997i	0.212873	+	0.977080i	$0.431718\pi$
$978$		0			0
$979$	−26.8005	+	46.4198i	−0.856548	+	1.48358i
$980$		0			0
$981$	−0.954530	−	17.8321i	−0.0304758	−	0.569336i
$982$		0			0
$983$	−4.06414	+	7.03930i	−0.129626	+	0.224519i	−0.923532	−	0.383522i	$-0.874711\pi$
$983$	−4.06414	+	7.03930i	−0.129626	+	0.224519i	0.793906	+	0.608041i	$0.208044\pi$
$984$		0			0
$985$	−17.5147	−	30.3364i	−0.558066	−	0.966598i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.49087			0.111003
$990$		0			0
$991$	55.3622			1.75864			0.879320	−	0.476232i	$-0.157998\pi$
$991$	55.3622			1.75864			0.879320	+	0.476232i	$0.157998\pi$
$992$		0			0
$993$	1.84903	+	6.22942i	0.0586770	+	0.197685i
$994$		0			0
$995$	−27.1910	−	47.0962i	−0.862013	−	1.49305i
$996$		0			0
$997$	−4.83187	+	8.36904i	−0.153027	+	0.265050i	−0.932339	−	0.361586i	$-0.882235\pi$
$997$	−4.83187	+	8.36904i	−0.153027	+	0.265050i	0.779312	+	0.626636i	$0.215569\pi$
$998$		0			0
$999$	13.3366	+	11.3519i	0.421952	+	0.359159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.j.h.1177.6		14
3.2	odd	2		5292.2.j.g.3529.2		14
7.2	even	3		1764.2.i.i.1537.5		14
7.3	odd	6		252.2.l.b.205.7	yes	14
7.4	even	3		1764.2.l.i.961.1		14
7.5	odd	6		252.2.i.b.25.3	✓	14
7.6	odd	2		1764.2.j.g.1177.2		14
9.4	even	3	inner	1764.2.j.h.589.6		14
9.5	odd	6		5292.2.j.g.1765.2		14
21.2	odd	6		5292.2.i.i.2125.2		14
21.5	even	6		756.2.i.b.613.6		14
21.11	odd	6		5292.2.l.i.3313.6		14
21.17	even	6		756.2.l.b.289.2		14
21.20	even	2		5292.2.j.h.3529.6		14
28.3	even	6		1008.2.t.j.961.1		14
28.19	even	6		1008.2.q.j.529.5		14
63.4	even	3		1764.2.i.i.373.5		14
63.5	even	6		756.2.l.b.361.2		14
63.13	odd	6		1764.2.j.g.589.2		14
63.23	odd	6		5292.2.l.i.361.6		14
63.31	odd	6		252.2.i.b.121.3	yes	14
63.32	odd	6		5292.2.i.i.1549.2		14
63.38	even	6		2268.2.k.f.1297.6		14
63.40	odd	6		252.2.l.b.193.7	yes	14
63.41	even	6		5292.2.j.h.1765.6		14
63.47	even	6		2268.2.k.f.1621.6		14
63.52	odd	6		2268.2.k.e.1297.2		14
63.58	even	3		1764.2.l.i.949.1		14
63.59	even	6		756.2.i.b.37.6		14
63.61	odd	6		2268.2.k.e.1621.2		14
84.47	odd	6		3024.2.q.j.2881.6		14
84.59	odd	6		3024.2.t.j.289.2		14
252.31	even	6		1008.2.q.j.625.5		14
252.59	odd	6		3024.2.q.j.2305.6		14
252.103	even	6		1008.2.t.j.193.1		14
252.131	odd	6		3024.2.t.j.1873.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.3	✓	14	7.5	odd	6
252.2.i.b.121.3	yes	14	63.31	odd	6
252.2.l.b.193.7	yes	14	63.40	odd	6
252.2.l.b.205.7	yes	14	7.3	odd	6
756.2.i.b.37.6		14	63.59	even	6
756.2.i.b.613.6		14	21.5	even	6
756.2.l.b.289.2		14	21.17	even	6
756.2.l.b.361.2		14	63.5	even	6
1008.2.q.j.529.5		14	28.19	even	6
1008.2.q.j.625.5		14	252.31	even	6
1008.2.t.j.193.1		14	252.103	even	6
1008.2.t.j.961.1		14	28.3	even	6
1764.2.i.i.373.5		14	63.4	even	3
1764.2.i.i.1537.5		14	7.2	even	3
1764.2.j.g.589.2		14	63.13	odd	6
1764.2.j.g.1177.2		14	7.6	odd	2
1764.2.j.h.589.6		14	9.4	even	3	inner
1764.2.j.h.1177.6		14	1.1	even	1	trivial
1764.2.l.i.949.1		14	63.58	even	3
1764.2.l.i.961.1		14	7.4	even	3
2268.2.k.e.1297.2		14	63.52	odd	6
2268.2.k.e.1621.2		14	63.61	odd	6
2268.2.k.f.1297.6		14	63.38	even	6
2268.2.k.f.1621.6		14	63.47	even	6
3024.2.q.j.2305.6		14	252.59	odd	6
3024.2.q.j.2881.6		14	84.47	odd	6
3024.2.t.j.289.2		14	84.59	odd	6
3024.2.t.j.1873.2		14	252.131	odd	6
5292.2.i.i.1549.2		14	63.32	odd	6
5292.2.i.i.2125.2		14	21.2	odd	6
5292.2.j.g.1765.2		14	9.5	odd	6
5292.2.j.g.3529.2		14	3.2	odd	2
5292.2.j.h.1765.6		14	63.41	even	6
5292.2.j.h.3529.6		14	21.20	even	2
5292.2.l.i.361.6		14	63.23	odd	6
5292.2.l.i.3313.6		14	21.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19156 - 1.25705i) q^{3} +(1.80173 + 3.12069i) q^{5} +(-0.160357 - 2.99571i) q^{9} +(3.01334 - 5.21926i) q^{11} +(2.55639 + 4.42780i) q^{13} +(6.06973 + 1.45363i) q^{15} +0.222013 q^{17} +3.42323 q^{19} +(0.509880 + 0.883137i) q^{23} +(-3.99245 + 6.91513i) q^{25} +(-3.95684 - 3.36800i) q^{27} +(-2.83679 + 4.91347i) q^{29} +(-2.52322 - 4.37035i) q^{31} +(-2.97030 - 10.0070i) q^{33} -3.37052 q^{37} +(8.61207 + 2.06249i) q^{39} +(-0.0955808 - 0.165551i) q^{41} +(1.71161 - 2.96460i) q^{43} +(9.05975 - 5.89788i) q^{45} +(-1.03506 + 1.79278i) q^{47} +(0.264542 - 0.279081i) q^{51} +5.30415 q^{53} +21.7169 q^{55} +(4.07899 - 4.30318i) q^{57} +(3.79814 + 6.57858i) q^{59} +(0.891408 - 1.54396i) q^{61} +(-9.21184 + 15.9554i) q^{65} +(-6.49235 - 11.2451i) q^{67} +(1.71770 + 0.411369i) q^{69} +5.89560 q^{71} +12.6104 q^{73} +(3.93542 + 13.2585i) q^{75} +(-6.30763 + 10.9251i) q^{79} +(-8.94857 + 0.960764i) q^{81} +(3.59946 - 6.23444i) q^{83} +(0.400007 + 0.692832i) q^{85} +(2.79627 + 9.42070i) q^{87} -8.89394 q^{89} +(-8.50033 - 2.03573i) q^{93} +(6.16773 + 10.6828i) q^{95} +(2.72991 - 4.72835i) q^{97} +(-16.1186 - 8.19016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} + 2 q^{5} - 5 q^{9} + 2 q^{11} - 2 q^{13} + 7 q^{15} + 4 q^{17} + 14 q^{19} + 11 q^{23} - 9 q^{25} - 9 q^{27} + q^{29} + q^{31} + q^{33} - 20 q^{37} + 22 q^{39} + 33 q^{41} + 7 q^{43}+ \cdots + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 + 2 * q^5 - 5 * q^9 + 2 * q^11 - 2 * q^13 + 7 * q^15 + 4 * q^17 + 14 * q^19 + 11 * q^23 - 9 * q^25 - 9 * q^27 + q^29 + q^31 + q^33 - 20 * q^37 + 22 * q^39 + 33 * q^41 + 7 * q^43 - 5 * q^45 + 3 * q^47 - 7 * q^51 + 30 * q^53 + 28 * q^55 - 18 * q^57 + 14 * q^59 + 10 * q^61 + 15 * q^65 + 6 * q^67 + 43 * q^69 + 2 * q^71 + 42 * q^73 - 43 * q^75 - 10 * q^79 + 7 * q^81 + 25 * q^83 + 8 * q^85 + 26 * q^87 - 12 * q^89 - 38 * q^93 - 28 * q^95 + 18 * q^97 + 7 * q^99

Introduction

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