LMFDB - Embedded newform 756.2.bp.a.193.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(193,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 12]))

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

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

chi := DirichletCharacter("756.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bp (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.11
Character	$\chi$	$=$	756.193
Dual form			756.2.bp.a.709.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.513768 + 1.65410i) q^{3} +(-0.633570 + 0.230601i) q^{5} +(1.95184 - 1.78614i) q^{7} +(-2.47208 - 1.69965i) q^{9} +O(q^{10})$	\(q+(-0.513768 + 1.65410i) q^{3} +(-0.633570 + 0.230601i) q^{5} +(1.95184 - 1.78614i) q^{7} +(-2.47208 - 1.69965i) q^{9} +(-2.98516 - 1.08651i) q^{11} +(-4.11055 + 1.49612i) q^{13} +(-0.0559281 - 1.16646i) q^{15} +(-2.71093 - 4.69546i) q^{17} +(-3.70030 + 6.40911i) q^{19} +(1.95166 + 4.14620i) q^{21} +(1.20350 - 6.82538i) q^{23} +(-3.48199 + 2.92173i) q^{25} +(4.08146 - 3.21585i) q^{27} +(1.59498 + 0.580527i) q^{29} +(-4.59328 + 1.67182i) q^{31} +(3.33087 - 4.37953i) q^{33} +(-0.824743 + 1.58174i) q^{35} +3.07669 q^{37} +(-0.362857 - 7.56792i) q^{39} +(0.0621882 - 0.0226347i) q^{41} +(-1.14344 - 6.48479i) q^{43} +(1.95818 + 0.506781i) q^{45} +(-6.66677 - 2.42651i) q^{47} +(0.619380 - 6.97254i) q^{49} +(9.15954 - 2.07176i) q^{51} +(-2.30032 + 3.98428i) q^{53} +2.14186 q^{55} +(-8.70020 - 9.41346i) q^{57} +(-10.6128 - 8.90518i) q^{59} +(12.5030 + 4.55073i) q^{61} +(-7.86093 + 1.09806i) q^{63} +(2.25932 - 1.89579i) q^{65} +(0.00391736 - 0.0222165i) q^{67} +(10.6715 + 5.49737i) q^{69} +(0.368370 - 0.638035i) q^{71} -4.14191 q^{73} +(-3.04390 - 7.26065i) q^{75} +(-7.76722 + 3.21123i) q^{77} +(-1.41066 - 8.00026i) q^{79} +(3.22240 + 8.40334i) q^{81} +(9.62674 + 3.50385i) q^{83} +(2.80034 + 2.34976i) q^{85} +(-1.77970 + 2.34000i) q^{87} +(1.48426 - 2.57082i) q^{89} +(-5.35087 + 10.2622i) q^{91} +(-0.405469 - 8.45666i) q^{93} +(0.866456 - 4.91391i) q^{95} +(3.23076 + 18.3225i) q^{97} +(5.53288 + 7.75965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.513768	+	1.65410i	−0.296624	+	0.954994i
$3$	−0.513768	+	1.65410i	−0.296624	+	0.954994i
$4$		0			0
$5$	−0.633570	+	0.230601i	−0.283341	+	0.103128i	−0.479781	−	0.877388i	$-0.659284\pi$
$5$	−0.633570	+	0.230601i	−0.283341	+	0.103128i	0.196440	+	0.980516i	$0.437062\pi$
$6$		0			0
$7$	1.95184	−	1.78614i	0.737727	−	0.675099i
$7$	1.95184	−	1.78614i	0.737727	−	0.675099i
$8$		0			0
$9$	−2.47208	−	1.69965i	−0.824028	−	0.566549i
$10$		0			0
$11$	−2.98516	−	1.08651i	−0.900059	−	0.327595i	−0.149783	−	0.988719i	$-0.547857\pi$
$11$	−2.98516	−	1.08651i	−0.900059	−	0.327595i	−0.750276	+	0.661124i	$0.770080\pi$
$12$		0			0
$13$	−4.11055	+	1.49612i	−1.14006	+	0.414949i	−0.841936	−	0.539578i	$-0.818584\pi$
$13$	−4.11055	+	1.49612i	−1.14006	+	0.414949i	−0.298127	+	0.954526i	$0.596362\pi$
$14$		0			0
$15$	−0.0559281	−	1.16646i	−0.0144406	−	0.301179i
$16$		0			0
$17$	−2.71093	−	4.69546i	−0.657496	−	1.13882i	−0.981262	−	0.192679i	$-0.938282\pi$
$17$	−2.71093	−	4.69546i	−0.657496	−	1.13882i	0.323766	−	0.946137i	$-0.395051\pi$
$18$		0			0
$19$	−3.70030	+	6.40911i	−0.848908	+	1.47035i	0.0332765	+	0.999446i	$0.489406\pi$
$19$	−3.70030	+	6.40911i	−0.848908	+	1.47035i	−0.882184	+	0.470905i	$0.843928\pi$
$20$		0			0
$21$	1.95166	+	4.14620i	0.425888	+	0.904776i
$22$		0			0
$23$	1.20350	−	6.82538i	0.250947	−	1.42319i	−0.555319	−	0.831637i	$-0.687404\pi$
$23$	1.20350	−	6.82538i	0.250947	−	1.42319i	0.806266	−	0.591553i	$-0.201485\pi$
$24$		0			0
$25$	−3.48199	+	2.92173i	−0.696398	+	0.584347i
$26$		0			0
$27$	4.08146	−	3.21585i	0.785478	−	0.618890i
$28$		0			0
$29$	1.59498	+	0.580527i	0.296181	+	0.107801i	0.485837	−	0.874050i	$-0.338515\pi$
$29$	1.59498	+	0.580527i	0.296181	+	0.107801i	−0.189656	+	0.981851i	$0.560737\pi$
$30$		0			0
$31$	−4.59328	+	1.67182i	−0.824977	+	0.300267i	−0.719796	−	0.694186i	$-0.755764\pi$
$31$	−4.59328	+	1.67182i	−0.824977	+	0.300267i	−0.105181	+	0.994453i	$0.533542\pi$
$32$		0			0
$33$	3.33087	−	4.37953i	0.579830	−	0.762379i
$34$		0			0
$35$	−0.824743	+	1.58174i	−0.139407	+	0.267364i
$36$		0			0
$37$	3.07669			0.505805			0.252902	−	0.967492i	$-0.418615\pi$
$37$	3.07669			0.505805			0.252902	+	0.967492i	$0.418615\pi$
$38$		0			0
$39$	−0.362857	−	7.56792i	−0.0581037	−	1.21184i
$40$		0			0
$41$	0.0621882	−	0.0226347i	0.00971217	−	0.00353494i	−0.337159	−	0.941448i	$-0.609466\pi$
$41$	0.0621882	−	0.0226347i	0.00971217	−	0.00353494i	0.346872	+	0.937913i	$0.387244\pi$
$42$		0			0
$43$	−1.14344	−	6.48479i	−0.174373	−	0.988921i	−0.938865	−	0.344287i	$-0.888121\pi$
$43$	−1.14344	−	6.48479i	−0.174373	−	0.988921i	0.764491	−	0.644634i	$-0.222990\pi$
$44$		0			0
$45$	1.95818	+	0.506781i	0.291908	+	0.0755464i
$46$		0			0
$47$	−6.66677	−	2.42651i	−0.972449	−	0.353942i	−0.193549	−	0.981091i	$-0.562000\pi$
$47$	−6.66677	−	2.42651i	−0.972449	−	0.353942i	−0.778900	+	0.627148i	$0.784222\pi$
$48$		0			0
$49$	0.619380	−	6.97254i	0.0884828	−	0.996078i
$50$		0			0
$51$	9.15954	−	2.07176i	1.28259	−	0.290104i
$52$		0			0
$53$	−2.30032	+	3.98428i	−0.315974	+	0.547283i	−0.979644	−	0.200743i	$-0.935665\pi$
$53$	−2.30032	+	3.98428i	−0.315974	+	0.547283i	0.663670	+	0.748025i	$0.268998\pi$
$54$		0			0
$55$	2.14186			0.288808
$56$		0			0
$57$	−8.70020	−	9.41346i	−1.15237	−	1.24684i
$58$		0			0
$59$	−10.6128	−	8.90518i	−1.38167	−	1.15936i	−0.968591	−	0.248658i	$-0.920010\pi$
$59$	−10.6128	−	8.90518i	−1.38167	−	1.15936i	−0.413074	−	0.910697i	$-0.635545\pi$
$60$		0			0
$61$	12.5030	+	4.55073i	1.60085	+	0.582661i	0.979601	−	0.200953i	$-0.0644040\pi$
$61$	12.5030	+	4.55073i	1.60085	+	0.582661i	0.621247	+	0.783614i	$0.286626\pi$
$62$		0			0
$63$	−7.86093	+	1.09806i	−0.990384	+	0.138342i
$64$		0			0
$65$	2.25932	−	1.89579i	0.280234	−	0.235144i
$66$		0			0
$67$	0.00391736	−	0.0222165i	0.000478582	−	0.00271417i	−0.984568	−	0.175005i	$-0.944006\pi$
$67$	0.00391736	−	0.0222165i	0.000478582	−	0.00271417i	0.985046	+	0.172291i	$0.0551169\pi$
$68$		0			0
$69$	10.6715	+	5.49737i	1.28470	+	0.661805i
$70$		0			0
$71$	0.368370	−	0.638035i	0.0437174	−	0.0757208i	−0.843339	−	0.537382i	$-0.819413\pi$
$71$	0.368370	−	0.638035i	0.0437174	−	0.0757208i	0.887056	+	0.461662i	$0.152747\pi$
$72$		0			0
$73$	−4.14191			−0.484774			−0.242387	−	0.970180i	$-0.577930\pi$
$73$	−4.14191			−0.484774			−0.242387	+	0.970180i	$0.577930\pi$
$74$		0			0
$75$	−3.04390	−	7.26065i	−0.351480	−	0.838387i
$76$		0			0
$77$	−7.76722	+	3.21123i	−0.885157	+	0.365953i
$78$		0			0
$79$	−1.41066	−	8.00026i	−0.158712	−	0.900099i	−0.955313	−	0.295595i	$-0.904482\pi$
$79$	−1.41066	−	8.00026i	−0.158712	−	0.900099i	0.796602	−	0.604505i	$-0.206629\pi$
$80$		0			0
$81$	3.22240	+	8.40334i	0.358045	+	0.933704i
$82$		0			0
$83$	9.62674	+	3.50385i	1.05667	+	0.384597i	0.811177	−	0.584801i	$-0.198827\pi$
$83$	9.62674	+	3.50385i	1.05667	+	0.384597i	0.245495	+	0.969398i	$0.421050\pi$
$84$		0			0
$85$	2.80034	+	2.34976i	0.303739	+	0.254868i
$86$		0			0
$87$	−1.77970	+	2.34000i	−0.190804	+	0.250875i
$88$		0			0
$89$	1.48426	−	2.57082i	0.157332	−	0.272507i	−0.776574	−	0.630026i	$-0.783044\pi$
$89$	1.48426	−	2.57082i	0.157332	−	0.272507i	0.933906	+	0.357520i	$0.116377\pi$
$90$		0			0
$91$	−5.35087	+	10.2622i	−0.560924	+	1.07577i
$92$		0			0
$93$	−0.405469	−	8.45666i	−0.0420452	−	0.876915i
$94$		0			0
$95$	0.866456	−	4.91391i	0.0888965	−	0.504157i
$96$		0			0
$97$	3.23076	+	18.3225i	0.328034	+	1.86037i	0.487438	+	0.873158i	$0.337932\pi$
$97$	3.23076	+	18.3225i	0.328034	+	1.86037i	−0.159404	+	0.987213i	$0.550957\pi$
$98$		0			0
$99$	5.53288	+	7.75965i	0.556076	+	0.779875i
$100$		0			0
$101$	1.16961	+	6.63317i	0.116380	+	0.660025i	0.986058	+	0.166405i	$0.0532158\pi$
$101$	1.16961	+	6.63317i	0.116380	+	0.660025i	−0.869677	+	0.493621i	$0.835673\pi$
$102$		0			0
$103$	1.45117	−	0.528181i	0.142988	−	0.0520433i	−0.269535	−	0.962991i	$-0.586870\pi$
$103$	1.45117	−	0.528181i	0.142988	−	0.0520433i	0.412523	+	0.910947i	$0.364648\pi$
$104$		0			0
$105$	−2.19263	−	2.17686i	−0.213979	−	0.212439i
$106$		0			0
$107$	−3.52226	−	6.10074i	−0.340510	−	0.589781i	0.644018	−	0.765011i	$-0.277266\pi$
$107$	−3.52226	−	6.10074i	−0.340510	−	0.589781i	−0.984527	+	0.175230i	$0.943933\pi$
$108$		0			0
$109$	−3.39453	+	5.87950i	−0.325137	+	0.563154i	−0.981540	−	0.191257i	$-0.938744\pi$
$109$	−3.39453	+	5.87950i	−0.325137	+	0.563154i	0.656403	+	0.754410i	$0.272077\pi$
$110$		0			0
$111$	−1.58071	+	5.08915i	−0.150034	+	0.483041i
$112$		0			0
$113$	−3.65974	+	20.7554i	−0.344279	+	1.95251i	−0.0426128	+	0.999092i	$0.513568\pi$
$113$	−3.65974	+	20.7554i	−0.344279	+	1.95251i	−0.301667	+	0.953414i	$0.597543\pi$
$114$		0			0
$115$	0.811437	+	4.60189i	0.0756668	+	0.429128i
$116$		0			0
$117$	12.7045	+	3.28795i	1.17453	+	0.303972i
$118$		0			0
$119$	−13.6781	−	4.32270i	−1.25387	−	0.396261i
$120$		0			0
$121$	−0.695822	−	0.583864i	−0.0632565	−	0.0530785i
$122$		0			0
$123$	0.00548963	+	0.114494i	0.000494984	+	0.0103236i
$124$		0			0
$125$	3.21791	−	5.57358i	0.287818	−	0.498516i
$126$		0			0
$127$	1.50749	+	2.61105i	0.133768	+	0.231693i	0.925126	−	0.379660i	$-0.123959\pi$
$127$	1.50749	+	2.61105i	0.133768	+	0.231693i	−0.791358	+	0.611353i	$0.790626\pi$
$128$		0			0
$129$	11.3139	+	1.44031i	0.996137	+	0.126812i
$130$		0			0
$131$	−1.34286	+	7.61572i	−0.117326	+	0.665388i	0.868246	+	0.496133i	$0.165247\pi$
$131$	−1.34286	+	7.61572i	−0.117326	+	0.665388i	−0.985572	+	0.169255i	$0.945864\pi$
$132$		0			0
$133$	4.22519	+	19.1188i	0.366370	+	1.65781i
$134$		0			0
$135$	−1.84432	+	2.97865i	−0.158733	+	0.256362i
$136$		0			0
$137$	13.9866	−	11.7362i	1.19496	−	1.00269i	0.195197	−	0.980764i	$-0.437465\pi$
$137$	13.9866	−	11.7362i	1.19496	−	1.00269i	0.999760	−	0.0219235i	$-0.00697902\pi$
$138$		0			0
$139$	−9.07671	−	7.61627i	−0.769877	−	0.646003i	0.170801	−	0.985306i	$-0.445365\pi$
$139$	−9.07671	−	7.61627i	−0.769877	−	0.646003i	−0.940677	+	0.339302i	$0.889809\pi$
$140$		0			0
$141$	7.43886	−	9.78084i	0.626465	−	0.823695i
$142$		0			0
$143$	13.8962			1.16206
$144$		0			0
$145$	−1.14440			−0.0950376
$146$		0			0
$147$	11.2151	+	4.60679i	0.925002	+	0.379961i
$148$		0			0
$149$	−17.0103	−	14.2733i	−1.39353	−	1.16931i	−0.963885	−	0.266319i	$-0.914193\pi$
$149$	−17.0103	−	14.2733i	−1.39353	−	1.16931i	−0.429649	−	0.902996i	$-0.641363\pi$
$150$		0			0
$151$	−13.7365	−	4.99969i	−1.11786	−	0.406869i	−0.283991	−	0.958827i	$-0.591659\pi$
$151$	−13.7365	−	4.99969i	−1.11786	−	0.406869i	−0.833872	+	0.551958i	$0.813881\pi$
$152$		0			0
$153$	−1.27899	+	16.2152i	−0.103400	+	1.31092i
$154$		0			0
$155$	2.52464	−	2.11843i	0.202784	−	0.170156i
$156$		0			0
$157$	7.62101	+	6.39479i	0.608223	+	0.510359i	0.894077	−	0.447914i	$-0.147833\pi$
$157$	7.62101	+	6.39479i	0.608223	+	0.510359i	−0.285854	+	0.958273i	$0.592277\pi$
$158$		0			0
$159$	−5.40856	−	5.85196i	−0.428926	−	0.464090i
$160$		0			0
$161$	−9.84207	−	15.4717i	−0.775664	−	1.21934i
$162$		0			0
$163$	−1.31148	−	2.27156i	−0.102723	−	0.177922i	0.810082	−	0.586316i	$-0.199422\pi$
$163$	−1.31148	−	2.27156i	−0.102723	−	0.177922i	−0.912806	+	0.408394i	$0.866089\pi$
$164$		0			0
$165$	−1.10042	+	3.54284i	−0.0856674	+	0.275810i
$166$		0			0
$167$	−3.30659	+	18.7526i	−0.255872	+	1.45112i	0.537953	+	0.842975i	$0.319198\pi$
$167$	−3.30659	+	18.7526i	−0.255872	+	1.45112i	−0.793825	+	0.608147i	$0.791913\pi$
$168$		0			0
$169$	4.69970	−	3.94352i	0.361516	−	0.303348i
$170$		0			0
$171$	20.0407	−	9.55466i	1.53255	−	0.730663i
$172$		0			0
$173$	−15.3178	+	12.8531i	−1.16459	+	0.977206i	−0.999958	−	0.00914901i	$-0.997088\pi$
$173$	−15.3178	+	12.8531i	−1.16459	+	0.977206i	−0.164631	+	0.986355i	$0.552643\pi$
$174$		0			0
$175$	−1.57765	+	11.9221i	−0.119259	+	0.901226i
$176$		0			0
$177$	20.1825	−	12.9794i	1.51701	−	0.975590i
$178$		0			0
$179$	−2.78736	−	4.82784i	−0.208337	−	0.360850i	0.742854	−	0.669454i	$-0.233472\pi$
$179$	−2.78736	−	4.82784i	−0.208337	−	0.360850i	−0.951191	+	0.308604i	$0.900138\pi$
$180$		0			0
$181$	7.94317	+	13.7580i	0.590411	+	1.02262i	0.994177	+	0.107760i	$0.0343677\pi$
$181$	7.94317	+	13.7580i	0.590411	+	1.02262i	−0.403766	+	0.914862i	$0.632299\pi$
$182$		0			0
$183$	−13.9510	+	18.3432i	−1.03129	+	1.35597i
$184$		0			0
$185$	−1.94930	+	0.709487i	−0.143315	+	0.0521625i
$186$		0			0
$187$	2.99088	+	16.9621i	0.218715	+	1.24039i
$188$		0			0
$189$	2.22240	−	13.5669i	0.161656	−	0.986847i
$190$		0			0
$191$	3.02889	+	17.1777i	0.219163	+	1.24293i	0.873535	+	0.486760i	$0.161822\pi$
$191$	3.02889	+	17.1777i	0.219163	+	1.24293i	−0.654373	+	0.756172i	$0.727067\pi$
$192$		0			0
$193$	−0.694452	+	0.252760i	−0.0499878	+	0.0181941i	−0.366893	−	0.930263i	$-0.619578\pi$
$193$	−0.694452	+	0.252760i	−0.0499878	+	0.0181941i	0.316905	+	0.948457i	$0.397356\pi$
$194$		0			0
$195$	1.97506	+	4.71113i	0.141437	+	0.337371i
$196$		0			0
$197$	−11.6309	−	20.1452i	−0.828665	−	1.43529i	−0.899086	−	0.437772i	$-0.855768\pi$
$197$	−11.6309	−	20.1452i	−0.828665	−	1.43529i	0.0704215	−	0.997517i	$-0.477566\pi$
$198$		0			0
$199$	−3.08637	−	5.34575i	−0.218787	−	0.378950i	0.735650	−	0.677361i	$-0.236877\pi$
$199$	−3.08637	−	5.34575i	−0.218787	−	0.378950i	−0.954437	+	0.298411i	$0.903543\pi$
$200$		0			0
$201$	0.0347356	+	0.0178938i	0.00245006	+	0.00126213i
$202$		0			0
$203$	4.15006	−	1.71577i	0.291277	−	0.120424i
$204$		0			0
$205$	−0.0341810	+	0.0286813i	−0.00238731	+	0.00200319i
$206$		0			0
$207$	−14.5759	+	14.8274i	−1.01309	+	1.03058i
$208$		0			0
$209$	18.0095	−	15.1118i	1.24575	−	1.04530i
$210$		0			0
$211$	0.316246	−	1.79352i	0.0217713	−	0.123471i	−0.971985	−	0.235042i	$-0.924477\pi$
$211$	0.316246	−	1.79352i	0.0217713	−	0.123471i	0.993756	+	0.111571i	$0.0355883\pi$
$212$		0			0
$213$	0.866116	+	0.937122i	0.0593453	+	0.0642105i
$214$		0			0
$215$	2.21985	+	3.84489i	0.151392	+	0.262219i
$216$		0			0
$217$	−5.97925	+	11.4674i	−0.405898	+	0.778456i
$218$		0			0
$219$	2.12798	−	6.85113i	0.143796	−	0.462957i
$220$		0			0
$221$	18.1684	+	15.2451i	1.22214	+	1.02549i
$222$		0			0
$223$	10.9488	−	9.18715i	0.733187	−	0.615217i	−0.197812	−	0.980240i	$-0.563383\pi$
$223$	10.9488	−	9.18715i	0.733187	−	0.615217i	0.930998	+	0.365023i	$0.118939\pi$
$224$		0			0
$225$	13.5737	−	1.30463i	0.904912	−	0.0869752i
$226$		0			0
$227$	17.6517	+	6.42470i	1.17159	+	0.426422i	0.853223	−	0.521546i	$-0.174645\pi$
$227$	17.6517	+	6.42470i	1.17159	+	0.426422i	0.318363	+	0.947969i	$0.396867\pi$
$228$		0			0
$229$	−2.95379	−	2.47853i	−0.195192	−	0.163786i	0.539954	−	0.841695i	$-0.318442\pi$
$229$	−2.95379	−	2.47853i	−0.195192	−	0.163786i	−0.735146	+	0.677909i	$0.762886\pi$
$230$		0			0
$231$	−1.32114	−	14.4976i	−0.0869245	−	0.953870i
$232$		0			0
$233$	18.4541			1.20897			0.604485	−	0.796617i	$-0.293379\pi$
$233$	18.4541			1.20897			0.604485	+	0.796617i	$0.293379\pi$
$234$		0			0
$235$	4.78342			0.312036
$236$		0			0
$237$	13.9580	+	1.77690i	0.906667	+	0.115422i
$238$		0			0
$239$	−3.93658	−	3.30318i	−0.254636	−	0.213665i	0.506530	−	0.862223i	$-0.330928\pi$
$239$	−3.93658	−	3.30318i	−0.254636	−	0.213665i	−0.761166	+	0.648558i	$0.775373\pi$
$240$		0			0
$241$	11.0068	−	9.23577i	0.709008	−	0.594928i	−0.215313	−	0.976545i	$-0.569077\pi$
$241$	11.0068	−	9.23577i	0.709008	−	0.594928i	0.924321	+	0.381617i	$0.124633\pi$
$242$		0			0
$243$	−15.5555	+	1.01281i	−0.997887	+	0.0649716i
$244$		0			0
$245$	1.21545	+	4.56043i	0.0776524	+	0.291355i
$246$		0			0
$247$	5.62150	−	31.8811i	0.357687	−	2.02855i
$248$		0			0
$249$	−10.7416	+	14.1234i	−0.680722	+	0.895034i
$250$		0			0
$251$	−8.29992	−	14.3759i	−0.523886	−	0.907398i	−0.999613	−	0.0278048i	$-0.991148\pi$
$251$	−8.29992	−	14.3759i	−0.523886	−	0.907398i	0.475727	−	0.879593i	$-0.342185\pi$
$252$		0			0
$253$	−11.0085	+	19.0672i	−0.692096	+	1.19875i
$254$		0			0
$255$	−5.32547	+	3.42480i	−0.333494	+	0.214469i
$256$		0			0
$257$	−17.2774	−	14.4975i	−1.07773	−	0.904327i	−0.0820042	−	0.996632i	$-0.526132\pi$
$257$	−17.2774	−	14.4975i	−1.07773	−	0.904327i	−0.995731	+	0.0923050i	$0.970577\pi$
$258$		0			0
$259$	6.00522	−	5.49541i	0.373146	−	0.341468i
$260$		0			0
$261$	−2.95625	−	4.14602i	−0.182987	−	0.256632i
$262$		0			0
$263$	3.74889	+	21.2610i	0.231167	+	1.31101i	0.850538	+	0.525913i	$0.176276\pi$
$263$	3.74889	+	21.2610i	0.231167	+	1.31101i	−0.619372	+	0.785098i	$0.712613\pi$
$264$		0			0
$265$	0.538640	−	3.05478i	0.0330884	−	0.187653i
$266$		0			0
$267$	3.48983	+	3.77593i	0.213574	+	0.231083i
$268$		0			0
$269$	−5.53074	+	9.57952i	−0.337215	+	0.584074i	−0.983908	−	0.178677i	$-0.942818\pi$
$269$	−5.53074	+	9.57952i	−0.337215	+	0.584074i	0.646693	+	0.762751i	$0.276152\pi$
$270$		0			0
$271$	−4.55943	−	7.89717i	−0.276966	−	0.479719i	0.693663	−	0.720299i	$-0.255996\pi$
$271$	−4.55943	−	7.89717i	−0.276966	−	0.479719i	−0.970629	+	0.240581i	$0.922662\pi$
$272$		0			0
$273$	−14.2256	−	14.1233i	−0.860975	−	0.854779i
$274$		0			0
$275$	13.5688	−	4.93863i	0.818228	−	0.297811i
$276$		0			0
$277$	−0.108884	−	0.617513i	−0.00654222	−	0.0371028i	0.981362	−	0.192169i	$-0.0615521\pi$
$277$	−0.108884	−	0.617513i	−0.00654222	−	0.0371028i	−0.987904	+	0.155066i	$0.950441\pi$
$278$		0			0
$279$	14.1965	+	3.67408i	0.849920	+	0.219961i
$280$		0			0
$281$	0.364119	+	2.06502i	0.0217215	+	0.123189i	0.993740	−	0.111714i	$-0.0356340\pi$
$281$	0.364119	+	2.06502i	0.0217215	+	0.123189i	−0.972019	+	0.234903i	$0.924523\pi$
$282$		0			0
$283$	1.68840	−	9.57537i	0.100365	−	0.569197i	−0.892606	−	0.450837i	$-0.851125\pi$
$283$	1.68840	−	9.57537i	0.100365	−	0.569197i	0.992971	−	0.118359i	$-0.0377634\pi$
$284$		0			0
$285$	7.68294	+	3.95782i	0.455098	+	0.234441i
$286$		0			0
$287$	0.0809528	−	0.155256i	0.00477850	−	0.00916449i
$288$		0			0
$289$	−6.19824	+	10.7357i	−0.364602	+	0.631509i
$290$		0			0
$291$	−31.9671	−	4.06954i	−1.87395	−	0.238561i
$292$		0			0
$293$	−17.3738	−	14.5784i	−1.01499	−	0.851677i	−0.0259992	−	0.999662i	$-0.508277\pi$
$293$	−17.3738	−	14.5784i	−1.01499	−	0.851677i	−0.988990	+	0.147985i	$0.952721\pi$
$294$		0			0
$295$	8.77748	+	3.19474i	0.511045	+	0.186005i
$296$		0			0
$297$	−15.6779	+	5.16527i	−0.909721	+	0.299719i
$298$		0			0
$299$	5.26454	+	29.8567i	0.304456	+	1.72666i
$300$		0			0
$301$	−13.8146	−	10.6149i	−0.796260	−	0.611835i
$302$		0			0
$303$	−11.5728	−	1.47327i	−0.664842	−	0.0846370i
$304$		0			0
$305$	−8.97095			−0.513675
$306$		0			0
$307$	−9.71647	+	16.8294i	−0.554548	+	0.960505i	0.443391	+	0.896329i	$0.353775\pi$
$307$	−9.71647	+	16.8294i	−0.554548	+	0.960505i	−0.997939	+	0.0641767i	$0.979558\pi$
$308$		0			0
$309$	0.128101	+	2.67174i	0.00728741	+	0.151990i
$310$		0			0
$311$	2.60879	−	14.7952i	0.147931	−	0.838959i	−0.817036	−	0.576587i	$-0.804384\pi$
$311$	2.60879	−	14.7952i	0.147931	−	0.838959i	0.964967	−	0.262372i	$-0.0845047\pi$
$312$		0			0
$313$	21.3951	−	17.9526i	1.20932	−	1.01474i	0.210010	−	0.977699i	$-0.432650\pi$
$313$	21.3951	−	17.9526i	1.20932	−	1.01474i	0.999314	−	0.0370436i	$-0.0117940\pi$
$314$		0			0
$315$	4.72724	−	2.50843i	0.266350	−	0.141334i
$316$		0			0
$317$	−9.00160	−	3.27631i	−0.505580	−	0.184016i	0.0766219	−	0.997060i	$-0.475587\pi$
$317$	−9.00160	−	3.27631i	−0.505580	−	0.184016i	−0.582202	+	0.813044i	$0.697809\pi$
$318$		0			0
$319$	−4.13053	−	3.46593i	−0.231265	−	0.194055i
$320$		0			0
$321$	11.9008	−	2.69180i	0.664241	−	0.150242i
$322$		0			0
$323$	40.1250			2.23261
$324$		0			0
$325$	9.94163	−	17.2194i	0.551463	−	0.955161i
$326$		0			0
$327$	−7.98127	−	8.63559i	−0.441365	−	0.477549i
$328$		0			0
$329$	−17.3466	+	7.17166i	−0.956348	+	0.395386i
$330$		0			0
$331$	6.16261	+	2.24301i	0.338727	+	0.123287i	0.505783	−	0.862661i	$-0.331204\pi$
$331$	6.16261	+	2.24301i	0.338727	+	0.123287i	−0.167055	+	0.985947i	$0.553426\pi$
$332$		0			0
$333$	−7.60584	−	5.22929i	−0.416797	−	0.286563i
$334$		0			0
$335$	0.00264121	+	0.0149790i	0.000144305	+	0.000818392i
$336$		0			0
$337$	23.9409	−	8.71378i	1.30414	−	0.474670i	0.405800	−	0.913962i	$-0.366993\pi$
$337$	23.9409	−	8.71378i	1.30414	−	0.474670i	0.898344	+	0.439292i	$0.144771\pi$
$338$		0			0
$339$	−32.4512	−	16.7170i	−1.76251	−	0.907945i
$340$		0			0
$341$	15.5281			0.840894
$342$		0			0
$343$	−11.2450	−	14.7156i	−0.607175	−	0.794568i
$344$		0			0
$345$	−8.02886	−	1.02211i	−0.432259	−	0.0550283i
$346$		0			0
$347$	−24.2674	+	8.83260i	−1.30274	+	0.474159i	−0.897888	−	0.440223i	$-0.854899\pi$
$347$	−24.2674	+	8.83260i	−1.30274	+	0.474159i	−0.404852	+	0.914382i	$0.632677\pi$
$348$		0			0
$349$	−0.801528	−	0.291732i	−0.0429048	−	0.0156161i	0.320479	−	0.947256i	$-0.396156\pi$
$349$	−0.801528	−	0.291732i	−0.0429048	−	0.0156161i	−0.363383	+	0.931640i	$0.618378\pi$
$350$		0			0
$351$	−11.9658	+	19.3253i	−0.638686	+	1.03151i
$352$		0			0
$353$	3.44182	−	2.88803i	0.183190	−	0.153715i	−0.546581	−	0.837406i	$-0.684071\pi$
$353$	3.44182	−	2.88803i	0.183190	−	0.153715i	0.729771	+	0.683692i	$0.239627\pi$
$354$		0			0
$355$	−0.0862568	+	0.489186i	−0.00457803	+	0.0259633i
$356$		0			0
$357$	14.1775	−	20.4040i	0.750354	−	1.07989i
$358$		0			0
$359$	12.6760	−	21.9555i	0.669015	−	1.15877i	−0.309165	−	0.951008i	$-0.600050\pi$
$359$	12.6760	−	21.9555i	0.669015	−	1.15877i	0.978180	−	0.207759i	$-0.0666171\pi$
$360$		0			0
$361$	−17.8845	−	30.9768i	−0.941288	−	1.63036i
$362$		0			0
$363$	1.32326	−	0.850988i	0.0694531	−	0.0446653i
$364$		0			0
$365$	2.62419	−	0.955128i	0.137357	−	0.0499937i
$366$		0			0
$367$	1.56476	+	0.569528i	0.0816800	+	0.0297291i	0.382537	−	0.923940i	$-0.375050\pi$
$367$	1.56476	+	0.569528i	0.0816800	+	0.0297291i	−0.300857	+	0.953669i	$0.597273\pi$
$368$		0			0
$369$	−0.192205	−	0.0497432i	−0.0100058	−	0.00258953i
$370$		0			0
$371$	2.62662	+	11.8854i	0.136368	+	0.617059i
$372$		0			0
$373$	−18.6289	+	6.78037i	−0.964568	+	0.351074i	−0.775822	−	0.630952i	$-0.782665\pi$
$373$	−18.6289	+	6.78037i	−0.964568	+	0.351074i	−0.188746	+	0.982026i	$0.560442\pi$
$374$		0			0
$375$	7.56599	+	8.18627i	0.390706	+	0.422737i
$376$		0			0
$377$	−7.42480			−0.382397
$378$		0			0
$379$	6.42449			0.330004			0.165002	−	0.986293i	$-0.447237\pi$
$379$	6.42449			0.330004			0.165002	+	0.986293i	$0.447237\pi$
$380$		0			0
$381$	−5.09343	+	1.15206i	−0.260944	+	0.0590219i
$382$		0			0
$383$	−28.9245	+	10.5277i	−1.47797	+	0.537939i	−0.950253	−	0.311479i	$-0.899176\pi$
$383$	−28.9245	+	10.5277i	−1.47797	+	0.537939i	−0.527721	+	0.849418i	$0.676953\pi$
$384$		0			0
$385$	4.18057	−	3.82566i	0.213061	−	0.194974i
$386$		0			0
$387$	−8.19516	+	17.9744i	−0.416583	+	0.913690i
$388$		0			0
$389$	1.11163	+	0.404601i	0.0563620	+	0.0205141i	0.370047	−	0.929013i	$-0.379341\pi$
$389$	1.11163	+	0.404601i	0.0563620	+	0.0205141i	−0.313685	+	0.949527i	$0.601564\pi$
$390$		0			0
$391$	−35.3109	+	12.8521i	−1.78575	+	0.649959i
$392$		0			0
$393$	−11.9072	−	6.13393i	−0.600640	−	0.309416i
$394$		0			0
$395$	2.73862	+	4.74342i	0.137795	+	0.238668i
$396$		0			0
$397$	−11.5177	+	19.9492i	−0.578055	+	1.00122i	0.417647	+	0.908609i	$0.362855\pi$
$397$	−11.5177	+	19.9492i	−0.578055	+	1.00122i	−0.995702	+	0.0926116i	$0.970479\pi$
$398$		0			0
$399$	−33.7952	−	2.83378i	−1.69188	−	0.141866i
$400$		0			0
$401$	0.0551597	−	0.312826i	0.00275454	−	0.0156218i	−0.983400	−	0.181454i	$-0.941920\pi$
$401$	0.0551597	−	0.312826i	0.00275454	−	0.0156218i	0.986154	+	0.165832i	$0.0530309\pi$
$402$		0			0
$403$	16.3797	−	13.7442i	0.815930	−	0.684646i
$404$		0			0
$405$	−3.97944	−	4.58102i	−0.197740	−	0.227633i
$406$		0			0
$407$	−9.18441	−	3.34285i	−0.455254	−	0.165699i
$408$		0			0
$409$	6.37450	−	2.32013i	0.315199	−	0.114723i	−0.179576	−	0.983744i	$-0.557473\pi$
$409$	6.37450	−	2.32013i	0.315199	−	0.114723i	0.494775	+	0.869021i	$0.335250\pi$
$410$		0			0
$411$	12.2269	+	29.1649i	0.603108	+	1.43860i
$412$		0			0
$413$	−36.6204	+	1.57444i	−1.80197	+	0.0774732i
$414$		0			0
$415$	−6.90720			−0.339061
$416$		0			0
$417$	17.2614	−	11.1008i	0.845294	−	0.543608i
$418$		0			0
$419$	17.9737	−	6.54191i	0.878075	−	0.319593i	0.136642	−	0.990620i	$-0.456369\pi$
$419$	17.9737	−	6.54191i	0.878075	−	0.319593i	0.741433	+	0.671027i	$0.234147\pi$
$420$		0			0
$421$	1.63432	+	9.26870i	0.0796520	+	0.451729i	0.998383	+	0.0568449i	$0.0181040\pi$
$421$	1.63432	+	9.26870i	0.0796520	+	0.451729i	−0.918731	+	0.394884i	$0.870785\pi$
$422$		0			0
$423$	12.3566	+	17.3297i	0.600800	+	0.842598i
$424$		0			0
$425$	23.1583	+	8.42893i	1.12334	+	0.408863i
$426$		0			0
$427$	32.5322	−	13.4499i	1.57434	−	0.650886i
$428$		0			0
$429$	−7.13942	+	22.9857i	−0.344695	+	1.10976i
$430$		0			0
$431$	0.894264	−	1.54891i	0.0430752	−	0.0746084i	−0.843684	−	0.536840i	$-0.819618\pi$
$431$	0.894264	−	1.54891i	0.0430752	−	0.0746084i	0.886759	+	0.462232i	$0.152951\pi$
$432$		0			0
$433$	−27.5799			−1.32541			−0.662704	−	0.748882i	$-0.730591\pi$
$433$	−27.5799			−1.32541			−0.662704	+	0.748882i	$0.730591\pi$
$434$		0			0
$435$	0.587959	−	1.89296i	0.0281905	−	0.0907604i
$436$		0			0
$437$	39.2913	+	32.9693i	1.87956	+	1.57714i
$438$		0			0
$439$	−12.2783	−	4.46894i	−0.586012	−	0.213291i	0.0319625	−	0.999489i	$-0.489824\pi$
$439$	−12.2783	−	4.46894i	−0.586012	−	0.213291i	−0.617974	+	0.786198i	$0.712047\pi$
$440$		0			0
$441$	−13.3820	+	16.1840i	−0.637239	+	0.770666i
$442$		0			0
$443$	19.1779	−	16.0921i	0.911168	−	0.764561i	−0.0611731	−	0.998127i	$-0.519484\pi$
$443$	19.1779	−	16.0921i	0.911168	−	0.764561i	0.972341	+	0.233567i	$0.0750397\pi$
$444$		0			0
$445$	−0.347553	+	1.97107i	−0.0164756	+	0.0934376i
$446$		0			0
$447$	32.3488	−	20.8035i	1.53004	−	0.983971i
$448$		0			0
$449$	−18.0765	+	31.3094i	−0.853081	+	1.47758i	0.0253329	+	0.999679i	$0.491935\pi$
$449$	−18.0765	+	31.3094i	−0.853081	+	1.47758i	−0.878414	+	0.477901i	$0.841398\pi$
$450$		0			0
$451$	−0.210234			−0.00989955
$452$		0			0
$453$	15.3274	−	20.1529i	0.720142	−	0.946865i
$454$		0			0
$455$	1.02367	−	7.73576i	0.0479906	−	0.362658i
$456$		0			0
$457$	1.89023	+	10.7200i	0.0884210	+	0.501460i	0.996566	+	0.0828043i	$0.0263876\pi$
$457$	1.89023	+	10.7200i	0.0884210	+	0.501460i	−0.908145	+	0.418656i	$0.862501\pi$
$458$		0			0
$459$	−26.1644	−	10.4464i	−1.22125	−	0.487597i
$460$		0			0
$461$	−4.72740	−	1.72063i	−0.220177	−	0.0801378i	0.229577	−	0.973291i	$-0.426266\pi$
$461$	−4.72740	−	1.72063i	−0.220177	−	0.0801378i	−0.449753	+	0.893153i	$0.648488\pi$
$462$		0			0
$463$	−24.0241	−	20.1586i	−1.11649	−	0.936849i	−0.118071	−	0.993005i	$-0.537671\pi$
$463$	−24.0241	−	20.1586i	−1.11649	−	0.936849i	−0.998422	+	0.0561558i	$0.982116\pi$
$464$		0			0
$465$	2.20700	+	5.26439i	0.102347	+	0.244130i
$466$		0			0
$467$	6.08425	−	10.5382i	0.281546	−	0.487651i	−0.690220	−	0.723600i	$-0.742486\pi$
$467$	6.08425	−	10.5382i	0.281546	−	0.487651i	0.971766	+	0.235948i	$0.0758196\pi$
$468$		0			0
$469$	−0.0320357	−	0.0503600i	−0.00147927	−	0.00232541i
$470$		0			0
$471$	−14.4930	+	9.32046i	−0.667804	+	0.429464i
$472$		0			0
$473$	−3.63242	+	20.6005i	−0.167019	+	0.947211i
$474$		0			0
$475$	−5.84132	−	33.1277i	−0.268018	−	1.52001i
$476$		0			0
$477$	12.4585	−	5.93974i	0.570434	−	0.271962i
$478$		0			0
$479$	−4.60067	−	26.0917i	−0.210210	−	1.19216i	−0.889028	−	0.457854i	$-0.848618\pi$
$479$	−4.60067	−	26.0917i	−0.210210	−	1.19216i	0.678817	−	0.734307i	$-0.262493\pi$
$480$		0			0
$481$	−12.6469	+	4.60310i	−0.576649	+	0.209883i
$482$		0			0
$483$	30.6482	−	8.33089i	1.39454	−	0.379069i
$484$		0			0
$485$	−6.27210	−	10.8636i	−0.284801	−	0.493290i
$486$		0			0
$487$	18.9239	−	32.7772i	0.857524	−	1.48528i	−0.0167590	−	0.999860i	$-0.505335\pi$
$487$	18.9239	−	32.7772i	0.857524	−	1.48528i	0.874283	−	0.485416i	$-0.161332\pi$
$488$		0			0
$489$	4.43118	−	1.00227i	0.200385	−	0.0453242i
$490$		0			0
$491$	0.481876	−	2.73285i	0.0217468	−	0.123332i	−0.972002	−	0.234973i	$-0.924500\pi$
$491$	0.481876	−	2.73285i	0.0217468	−	0.123332i	0.993749	+	0.111641i	$0.0356108\pi$
$492$		0			0
$493$	−1.59804	−	9.06295i	−0.0719722	−	0.408175i
$494$		0			0
$495$	−5.29485	−	3.64040i	−0.237986	−	0.163624i
$496$		0			0
$497$	−0.420623	−	1.90331i	−0.0188675	−	0.0853749i
$498$		0			0
$499$	−22.9389	−	19.2480i	−1.02688	−	0.861659i	−0.0364077	−	0.999337i	$-0.511591\pi$
$499$	−22.9389	−	19.2480i	−1.02688	−	0.861659i	−0.990477	+	0.137678i	$0.956036\pi$
$500$		0			0
$501$	−29.3199	−	15.1039i	−1.30992	−	0.674794i
$502$		0			0
$503$	16.4780	−	28.5407i	0.734716	−	1.27257i	−0.220131	−	0.975470i	$-0.570649\pi$
$503$	16.4780	−	28.5407i	0.734716	−	1.27257i	0.954848	−	0.297096i	$-0.0960181\pi$
$504$		0			0
$505$	−2.27064	−	3.93287i	−0.101042	−	0.175010i
$506$		0			0
$507$	4.10841	+	9.79983i	0.182461	+	0.435226i
$508$		0			0
$509$	1.19000	−	6.74883i	0.0527459	−	0.299137i	−0.947011	−	0.321202i	$-0.895913\pi$
$509$	1.19000	−	6.74883i	0.0527459	−	0.299137i	0.999757	+	0.0220655i	$0.00702423\pi$
$510$		0			0
$511$	−8.08436	+	7.39805i	−0.357631	+	0.327270i
$512$		0			0
$513$	5.50809	+	38.0581i	0.243188	+	1.68031i
$514$		0			0
$515$	−0.797617	+	0.669280i	−0.0351472	+	0.0294920i
$516$		0			0
$517$	17.2650	+	14.4870i	0.759312	+	0.637138i
$518$		0			0
$519$	−13.3906	−	31.9406i	−0.587781	−	1.40204i
$520$		0			0
$521$	22.2630			0.975359			0.487679	−	0.873023i	$-0.337844\pi$
$521$	22.2630			0.975359			0.487679	+	0.873023i	$0.337844\pi$
$522$		0			0
$523$	39.8662			1.74323			0.871614	−	0.490192i	$-0.163073\pi$
$523$	39.8662			1.74323			0.871614	+	0.490192i	$0.163073\pi$
$524$		0			0
$525$	−18.9098	−	8.73479i	−0.825290	−	0.381217i
$526$		0			0
$527$	20.3020	+	17.0354i	0.884368	+	0.742073i
$528$		0			0
$529$	−23.5245	−	8.56220i	−1.02280	−	0.372270i
$530$		0			0
$531$	11.1000	+	40.0523i	0.481700	+	1.73812i
$532$		0			0
$533$	−0.221764	+	0.186082i	−0.00960566	+	0.00806010i
$534$		0			0
$535$	3.63844	+	3.05301i	0.157303	+	0.131993i
$536$		0			0
$537$	9.41778	−	2.13017i	0.406407	−	0.0919237i
$538$		0			0
$539$	−9.42468	+	20.1412i	−0.405950	+	0.867542i
$540$		0			0
$541$	−6.90010	−	11.9513i	−0.296658	−	0.513827i	0.678711	−	0.734405i	$-0.262539\pi$
$541$	−6.90010	−	11.9513i	−0.296658	−	0.513827i	−0.975369	+	0.220578i	$0.929206\pi$
$542$		0			0
$543$	−26.8380	+	6.07038i	−1.15173	+	0.260505i
$544$		0			0
$545$	0.794857	−	4.50786i	0.0340479	−	0.193095i
$546$		0			0
$547$	17.7763	−	14.9161i	0.760060	−	0.637766i	−0.178083	−	0.984016i	$-0.556989\pi$
$547$	17.7763	−	14.9161i	0.760060	−	0.637766i	0.938142	+	0.346250i	$0.112545\pi$
$548$		0			0
$549$	−23.1739	−	32.5005i	−0.989038	−	1.38709i
$550$		0			0
$551$	−9.62258	+	8.07431i	−0.409936	+	0.343977i
$552$		0			0
$553$	−17.0430	−	13.0956i	−0.724742	−	0.556881i
$554$		0			0
$555$	−0.172073	−	3.58885i	−0.00730411	−	0.152338i
$556$		0			0
$557$	6.78854	+	11.7581i	0.287640	+	0.498207i	0.973246	−	0.229766i	$-0.0737961\pi$
$557$	6.78854	+	11.7581i	0.287640	+	0.498207i	−0.685606	+	0.727973i	$0.740463\pi$
$558$		0			0
$559$	14.4022	+	24.9453i	0.609148	+	1.05508i
$560$		0			0
$561$	−29.5937	−	3.76739i	−1.24945	−	0.159059i
$562$		0			0
$563$	−8.97354	+	3.26610i	−0.378189	+	0.137650i	−0.524118	−	0.851645i	$-0.675605\pi$
$563$	−8.97354	+	3.26610i	−0.378189	+	0.137650i	0.145929	+	0.989295i	$0.453383\pi$
$564$		0			0
$565$	−2.46751	−	13.9940i	−0.103809	−	0.588730i
$566$		0			0
$567$	21.2992	+	10.6463i	0.894482	+	0.447103i
$568$		0			0
$569$	1.24364	+	7.05302i	0.0521360	+	0.295678i	0.999716	−	0.0238415i	$-0.00758970\pi$
$569$	1.24364	+	7.05302i	0.0521360	+	0.295678i	−0.947580	+	0.319519i	$0.896479\pi$
$570$		0			0
$571$	11.9070	−	4.33379i	0.498292	−	0.181364i	−0.0806335	−	0.996744i	$-0.525694\pi$
$571$	11.9070	−	4.33379i	0.498292	−	0.181364i	0.578926	+	0.815380i	$0.303472\pi$
$572$		0			0
$573$	−29.9697	−	3.81526i	−1.25200	−	0.159385i
$574$		0			0
$575$	15.7514	+	27.2822i	0.656878	+	1.13775i
$576$		0			0
$577$	11.2863	+	19.5485i	0.469856	+	0.813814i	0.999406	−	0.0344645i	$-0.0109726\pi$
$577$	11.2863	+	19.5485i	0.469856	+	0.813814i	−0.529550	+	0.848279i	$0.677639\pi$
$578$		0			0
$579$	−0.0613024	−	1.27855i	−0.00254764	−	0.0531348i
$580$		0			0
$581$	25.0482	−	10.3558i	1.03918	−	0.429630i
$582$		0			0
$583$	11.1958	−	9.39438i	0.463682	−	0.389075i
$584$		0			0
$585$	−8.80741	+	0.846519i	−0.364141	+	0.0349993i
$586$		0			0
$587$	16.0262	−	13.4476i	0.661471	−	0.555040i	−0.249056	−	0.968489i	$-0.580120\pi$
$587$	16.0262	−	13.4476i	0.661471	−	0.555040i	0.910527	+	0.413449i	$0.135676\pi$
$588$		0			0
$589$	6.28166	−	35.6250i	0.258831	−	1.46790i
$590$		0			0
$591$	39.2978	−	8.88861i	1.61649	−	0.365628i
$592$		0			0
$593$	−8.90303	−	15.4205i	−0.365604	−	0.633244i	0.623269	−	0.782007i	$-0.285804\pi$
$593$	−8.90303	−	15.4205i	−0.365604	−	0.633244i	−0.988873	+	0.148763i	$0.952471\pi$
$594$		0			0
$595$	9.66284	−	0.415440i	0.396138	−	0.0170314i
$596$		0			0
$597$	10.4281	−	2.35869i	0.426793	−	0.0965346i
$598$		0			0
$599$	32.5181	+	27.2859i	1.32865	+	1.11487i	0.984390	+	0.175999i	$0.0563156\pi$
$599$	32.5181	+	27.2859i	1.32865	+	1.11487i	0.344263	+	0.938873i	$0.388129\pi$
$600$		0			0
$601$	−21.6651	+	18.1792i	−0.883737	+	0.741544i	−0.966944	−	0.254989i	$-0.917928\pi$
$601$	−21.6651	+	18.1792i	−0.883737	+	0.741544i	0.0832066	+	0.996532i	$0.473484\pi$
$602$		0			0
$603$	−0.0474442	+	0.0482629i	−0.00193208	+	0.00196542i
$604$		0			0
$605$	0.575492	+	0.209462i	0.0233971	+	0.00851583i
$606$		0			0
$607$	−3.53043	−	2.96239i	−0.143296	−	0.120240i	0.568322	−	0.822806i	$-0.307593\pi$
$607$	−3.53043	−	2.96239i	−0.143296	−	0.120240i	−0.711618	+	0.702567i	$0.752037\pi$
$608$		0			0
$609$	0.705890	+	7.74612i	0.0286041	+	0.313889i
$610$		0			0
$611$	31.0345			1.25552
$612$		0			0
$613$	39.5542			1.59758			0.798789	−	0.601612i	$-0.205475\pi$
$613$	39.5542			1.59758			0.798789	+	0.601612i	$0.205475\pi$
$614$		0			0
$615$	−0.0298806	−	0.0712743i	−0.00120490	−	0.00287406i
$616$		0			0
$617$	−4.87383	−	4.08963i	−0.196213	−	0.164642i	0.539388	−	0.842057i	$-0.318656\pi$
$617$	−4.87383	−	4.08963i	−0.196213	−	0.164642i	−0.735601	+	0.677415i	$0.763100\pi$
$618$		0			0
$619$	−0.982237	+	0.824195i	−0.0394794	+	0.0331272i	−0.662314	−	0.749226i	$-0.730425\pi$
$619$	−0.982237	+	0.824195i	−0.0394794	+	0.0331272i	0.622834	+	0.782354i	$0.285981\pi$
$620$		0			0
$621$	−17.0373	−	31.7278i	−0.683685	−	1.27319i
$622$		0			0
$623$	−1.69481	−	7.66895i	−0.0679010	−	0.307250i
$624$		0			0
$625$	3.19301	−	18.1085i	0.127721	−	0.724339i
$626$		0			0
$627$	15.7437	+	37.5535i	0.628742	+	1.49974i
$628$		0			0
$629$	−8.34068	−	14.4465i	−0.332565	−	0.576019i
$630$		0			0
$631$	−10.1063	+	17.5046i	−0.402326	+	0.696848i	−0.994006	−	0.109324i	$-0.965131\pi$
$631$	−10.1063	+	17.5046i	−0.402326	+	0.696848i	0.591681	+	0.806173i	$0.298465\pi$
$632$		0			0
$633$	2.80418	+	1.44456i	0.111456	+	0.0574159i
$634$		0			0
$635$	−1.55721	−	1.30665i	−0.0617960	−	0.0518530i
$636$		0			0
$637$	7.88576	+	29.5877i	0.312445	+	1.17231i
$638$		0			0
$639$	−1.99507	+	0.951178i	−0.0789239	+	0.0376280i
$640$		0			0
$641$	−0.907778	−	5.14827i	−0.0358551	−	0.203344i	0.961618	−	0.274392i	$-0.0884767\pi$
$641$	−0.907778	−	5.14827i	−0.0358551	−	0.203344i	−0.997473	+	0.0710481i	$0.977366\pi$
$642$		0			0
$643$	−4.03581	+	22.8882i	−0.159157	+	0.902622i	0.795730	+	0.605652i	$0.207087\pi$
$643$	−4.03581	+	22.8882i	−0.159157	+	0.902622i	−0.954887	+	0.296971i	$0.904024\pi$
$644$		0			0
$645$	−7.50032	+	1.69647i	−0.295325	+	0.0667983i
$646$		0			0
$647$	−18.5926	+	32.2034i	−0.730952	+	1.26605i	0.225524	+	0.974238i	$0.427590\pi$
$647$	−18.5926	+	32.2034i	−0.730952	+	1.26605i	−0.956477	+	0.291809i	$0.905743\pi$
$648$		0			0
$649$	22.0053	+	38.1142i	0.863782	+	1.49611i
$650$		0			0
$651$	−15.8962	−	15.7818i	−0.623022	−	0.618539i
$652$		0			0
$653$	−24.0564	+	8.75583i	−0.941401	+	0.342642i	−0.766719	−	0.641983i	$-0.778112\pi$
$653$	−24.0564	+	8.75583i	−0.941401	+	0.342642i	−0.174682	+	0.984625i	$0.555890\pi$
$654$		0			0
$655$	−0.905396	−	5.13476i	−0.0353768	−	0.200632i
$656$		0			0
$657$	10.2392	+	7.03979i	0.399468	+	0.274648i
$658$		0			0
$659$	4.61991	+	26.2008i	0.179966	+	1.02064i	0.932254	+	0.361804i	$0.117839\pi$
$659$	4.61991	+	26.2008i	0.179966	+	1.02064i	−0.752288	+	0.658834i	$0.771050\pi$
$660$		0			0
$661$	5.54694	−	31.4583i	0.215751	−	1.22358i	−0.663848	−	0.747868i	$-0.731078\pi$
$661$	5.54694	−	31.4583i	0.215751	−	1.22358i	0.879599	−	0.475717i	$-0.157811\pi$
$662$		0			0
$663$	−34.5512	+	22.2199i	−1.34186	+	0.862947i
$664$		0			0
$665$	−7.08577	−	11.1388i	−0.274775	−	0.431944i
$666$		0			0
$667$	5.88188	−	10.1877i	0.227747	−	0.394470i
$668$		0			0
$669$	9.57129	+	22.8305i	0.370048	+	0.882677i
$670$		0			0
$671$	−32.3791	−	27.1693i	−1.24998	−	1.04886i
$672$		0			0
$673$	36.7973	+	13.3931i	1.41843	+	0.516266i	0.933592	−	0.358337i	$-0.116656\pi$
$673$	36.7973	+	13.3931i	1.41843	+	0.516266i	0.484838	+	0.874604i	$0.338878\pi$
$674$		0			0
$675$	−4.81574	+	23.1225i	−0.185358	+	0.889985i
$676$		0			0
$677$	1.13637	+	6.44465i	0.0436741	+	0.247688i	0.998827	−	0.0484256i	$-0.0154204\pi$
$677$	1.13637	+	6.44465i	0.0436741	+	0.247688i	−0.955153	+	0.296114i	$0.904309\pi$
$678$		0			0
$679$	39.0326	+	29.9921i	1.49793	+	1.15099i
$680$		0			0
$681$	−19.6960	+	25.8969i	−0.754752	+	0.992371i
$682$		0			0
$683$	25.2774			0.967215			0.483607	−	0.875285i	$-0.339326\pi$
$683$	25.2774			0.967215			0.483607	+	0.875285i	$0.339326\pi$
$684$		0			0
$685$	−6.15513	+	10.6610i	−0.235176	+	0.407336i
$686$		0			0
$687$	5.61729	−	3.61248i	0.214313	−	0.137825i
$688$		0			0
$689$	3.49465	−	19.8191i	0.133136	−	0.755049i
$690$		0			0
$691$	3.65383	−	3.06593i	0.138998	−	0.116633i	−0.570638	−	0.821202i	$-0.693304\pi$
$691$	3.65383	−	3.06593i	0.138998	−	0.116633i	0.709636	+	0.704569i	$0.248859\pi$
$692$		0			0
$693$	24.6592	+	5.26310i	0.936725	+	0.199929i
$694$		0			0
$695$	7.50705	+	2.73234i	0.284759	+	0.103644i
$696$		0			0
$697$	−0.274868	−	0.230641i	−0.0104114	−	0.00873617i
$698$		0			0
$699$	−9.48114	+	30.5249i	−0.358610	+	1.15456i
$700$		0			0
$701$	−10.5836			−0.399736			−0.199868	−	0.979823i	$-0.564051\pi$
$701$	−10.5836			−0.399736			−0.199868	+	0.979823i	$0.564051\pi$
$702$		0			0
$703$	−11.3847	+	19.7188i	−0.429381	+	0.743710i
$704$		0			0
$705$	−2.45757	+	7.91225i	−0.0925575	+	0.297993i
$706$		0			0
$707$	14.1307	+	10.8578i	0.531439	+	0.408350i
$708$		0			0
$709$	−14.7927	−	5.38409i	−0.555550	−	0.202204i	0.0489608	−	0.998801i	$-0.484409\pi$
$709$	−14.7927	−	5.38409i	−0.555550	−	0.202204i	−0.604511	+	0.796597i	$0.706631\pi$
$710$		0			0
$711$	−10.1103	+	22.1749i	−0.379167	+	0.831625i
$712$		0			0
$713$	5.88278	+	33.3629i	0.220312	+	1.24945i
$714$		0			0
$715$	−8.80422	+	3.20447i	−0.329259	+	0.119841i
$716$		0			0
$717$	7.48627	−	4.81442i	0.279580	−	0.179798i
$718$		0			0
$719$	1.59259			0.0593935			0.0296967	−	0.999559i	$-0.490546\pi$
$719$	1.59259			0.0593935			0.0296967	+	0.999559i	$0.490546\pi$
$720$		0			0
$721$	1.88904	−	3.62292i	0.0703515	−	0.134925i
$722$		0			0
$723$	9.62195	+	22.9513i	0.357844	+	0.853569i
$724$		0			0
$725$	−7.24986	+	2.63873i	−0.269253	+	0.0980001i
$726$		0			0
$727$	−41.1359	−	14.9722i	−1.52565	−	0.555290i	−0.563096	−	0.826392i	$-0.690390\pi$
$727$	−41.1359	−	14.9722i	−1.52565	−	0.555290i	−0.962551	+	0.271102i	$0.912612\pi$
$728$		0			0
$729$	6.31665	−	26.2507i	0.233950	−	0.972249i
$730$		0			0
$731$	−27.3493	+	22.9488i	−1.01155	+	0.848791i
$732$		0			0
$733$	0.130040	−	0.737494i	0.00480314	−	0.0272400i	−0.982312	−	0.187252i	$-0.940042\pi$
$733$	0.130040	−	0.737494i	0.00480314	−	0.0272400i	0.987115	+	0.160012i	$0.0511532\pi$
$734$		0			0
$735$	−8.16786	−	0.332522i	−0.301276	−	0.0122653i
$736$		0			0
$737$	−0.0358323	+	0.0620634i	−0.00131990	+	0.00228614i
$738$		0			0
$739$	−21.6570	−	37.5110i	−0.796666	−	1.37987i	−0.921776	−	0.387723i	$-0.873262\pi$
$739$	−21.6570	−	37.5110i	−0.796666	−	1.37987i	0.125110	−	0.992143i	$-0.460072\pi$
$740$		0			0
$741$	49.8463	+	25.6780i	1.83115	+	0.943305i
$742$		0			0
$743$	13.4355	−	4.89012i	0.492900	−	0.179401i	−0.0835977	−	0.996500i	$-0.526641\pi$
$743$	13.4355	−	4.89012i	0.492900	−	0.179401i	0.576498	+	0.817099i	$0.304419\pi$
$744$		0			0
$745$	14.0686	+	5.12056i	0.515435	+	0.187603i
$746$		0			0
$747$	−17.8428	−	25.0238i	−0.652834	−	0.915575i
$748$		0			0
$749$	−17.7717	−	5.61641i	−0.649364	−	0.205219i
$750$		0			0
$751$	17.2481	−	6.27779i	0.629392	−	0.229080i	−0.00757466	−	0.999971i	$-0.502411\pi$
$751$	17.2481	−	6.27779i	0.629392	−	0.229080i	0.636967	+	0.770891i	$0.280189\pi$
$752$		0			0
$753$	28.0434	−	6.34302i	1.02196	−	0.231152i
$754$		0			0
$755$	9.85599			0.358696
$756$		0			0
$757$	−9.92793			−0.360837			−0.180418	−	0.983590i	$-0.557745\pi$
$757$	−9.92793			−0.360837			−0.180418	+	0.983590i	$0.557745\pi$
$758$		0			0
$759$	−25.8833	−	28.0052i	−0.939503	−	1.01653i
$760$		0			0
$761$	−6.78484	+	2.46948i	−0.245950	+	0.0895186i	−0.462054	−	0.886852i	$-0.652887\pi$
$761$	−6.78484	+	2.46948i	−0.245950	+	0.0895186i	0.216104	+	0.976370i	$0.430665\pi$
$762$		0			0
$763$	3.87604	+	17.5390i	0.140322	+	0.634954i
$764$		0			0
$765$	−2.92891	−	10.5684i	−0.105895	−	0.382101i
$766$		0			0
$767$	56.9476	+	20.7272i	2.05626	+	0.748417i
$768$		0			0
$769$	−5.04359	+	1.83572i	−0.181877	+	0.0661977i	−0.431353	−	0.902183i	$-0.641964\pi$
$769$	−5.04359	+	1.83572i	−0.181877	+	0.0661977i	0.249477	+	0.968381i	$0.419741\pi$
$770$		0			0
$771$	32.8568	−	21.1302i	1.18331	−	0.760985i
$772$		0			0
$773$	−6.22385	−	10.7800i	−0.223856	−	0.387731i	0.732119	−	0.681176i	$-0.238531\pi$
$773$	−6.22385	−	10.7800i	−0.223856	−	0.387731i	−0.955976	+	0.293446i	$0.905198\pi$
$774$		0			0
$775$	11.1091	−	19.2416i	0.399052	−	0.691178i
$776$		0			0
$777$	6.00466	+	12.7566i	0.215416	+	0.457640i
$778$		0			0
$779$	−0.0850471	+	0.482326i	−0.00304713	+	0.0172811i
$780$		0			0
$781$	−1.79287	+	1.50440i	−0.0641540	+	0.0538316i
$782$		0			0
$783$	8.37675	−	2.75983i	0.299361	−	0.0986282i
$784$		0			0
$785$	−6.30309	−	2.29414i	−0.224967	−	0.0818812i
$786$		0			0
$787$	−28.0207	+	10.1987i	−0.998830	+	0.363544i	−0.789133	−	0.614222i	$-0.789470\pi$
$787$	−28.0207	+	10.1987i	−0.998830	+	0.363544i	−0.209697	+	0.977767i	$0.567248\pi$
$788$		0			0
$789$	−37.0939	−	4.72220i	−1.32058	−	0.168115i
$790$		0			0
$791$	29.9289	+	47.0481i	1.06415	+	1.67284i
$792$		0			0
$793$	−58.2028			−2.06684
$794$		0			0
$795$	4.77617	+	2.46041i	0.169393	+	0.0872617i
$796$		0			0
$797$	−3.92080	+	1.42706i	−0.138882	+	0.0505489i	−0.410526	−	0.911849i	$-0.634655\pi$
$797$	−3.92080	+	1.42706i	−0.138882	+	0.0505489i	0.271644	+	0.962398i	$0.412433\pi$
$798$		0			0
$799$	6.67956	+	37.8817i	0.236306	+	1.34016i
$800$		0			0
$801$	−8.03872	+	3.83256i	−0.284034	+	0.135417i
$802$		0			0
$803$	12.3643	+	4.50022i	0.436325	+	0.158809i
$804$		0			0
$805$	9.80343	+	7.53281i	0.345525	+	0.265497i
$806$		0			0
$807$	−13.0040	−	14.0700i	−0.457761	−	0.495289i
$808$		0			0
$809$	14.1046	−	24.4298i	0.495890	−	0.858907i	−0.504098	−	0.863646i	$-0.668175\pi$
$809$	14.1046	−	24.4298i	0.495890	−	0.858907i	0.999989	+	0.00473902i	$0.00150848\pi$
$810$		0			0
$811$	7.93998			0.278810			0.139405	−	0.990235i	$-0.455481\pi$
$811$	7.93998			0.278810			0.139405	+	0.990235i	$0.455481\pi$
$812$		0			0
$813$	15.4052	−	3.48444i	0.540283	−	0.122205i
$814$		0			0
$815$	1.35474	+	1.13676i	0.0474545	+	0.0398190i
$816$		0			0
$817$	45.7928	+	16.6672i	1.60209	+	0.583112i
$818$		0			0
$819$	30.6700	−	16.2745i	1.07170	−	0.568678i
$820$		0			0
$821$	2.79747	−	2.34736i	0.0976325	−	0.0819234i	−0.592665	−	0.805449i	$-0.701924\pi$
$821$	2.79747	−	2.34736i	0.0976325	−	0.0819234i	0.690297	+	0.723526i	$0.257480\pi$
$822$		0			0
$823$	−3.28459	+	18.6278i	−0.114493	+	0.649325i	0.872506	+	0.488603i	$0.162493\pi$
$823$	−3.28459	+	18.6278i	−0.114493	+	0.649325i	−0.987000	+	0.160722i	$0.948618\pi$
$824$		0			0
$825$	1.19778	+	24.9814i	0.0417012	+	0.869741i
$826$		0			0
$827$	−19.2281	+	33.3040i	−0.668626	+	1.15809i	0.309662	+	0.950847i	$0.399784\pi$
$827$	−19.2281	+	33.3040i	−0.668626	+	1.15809i	−0.978288	+	0.207248i	$0.933549\pi$
$828$		0			0
$829$	−14.4991			−0.503573			−0.251787	−	0.967783i	$-0.581018\pi$
$829$	−14.4991			−0.503573			−0.251787	+	0.967783i	$0.581018\pi$
$830$		0			0
$831$	1.07737	+	0.137153i	0.0373735	+	0.00475780i
$832$		0			0
$833$	−34.4184	+	15.9938i	−1.19253	+	0.554151i
$834$		0			0
$835$	−2.22941	−	12.6436i	−0.0771519	−	0.437550i
$836$		0			0
$837$	−13.3710	+	21.5947i	−0.462168	+	0.746423i
$838$		0			0
$839$	−39.7509	−	14.4681i	−1.37235	−	0.499495i	−0.452501	−	0.891764i	$-0.649468\pi$
$839$	−39.7509	−	14.4681i	−1.37235	−	0.499495i	−0.919851	+	0.392268i	$0.871690\pi$
$840$		0			0
$841$	−20.0083	−	16.7890i	−0.689942	−	0.578930i
$842$		0			0
$843$	−3.60282	−	0.458653i	−0.124088	−	0.0157969i
$844$		0			0
$845$	−2.06821	+	3.58225i	−0.0711487	+	0.123233i
$846$		0			0
$847$	−2.40100	+	0.103228i	−0.0824993	+	0.00354694i
$848$		0			0
$849$	14.9712	+	7.71229i	0.513809	+	0.264685i
$850$		0			0
$851$	3.70279	−	20.9996i	0.126930	−	0.719856i
$852$		0			0
$853$	1.36437	+	7.73770i	0.0467150	+	0.264934i	0.999215	−	0.0396032i	$-0.0126094\pi$
$853$	1.36437	+	7.73770i	0.0467150	+	0.264934i	−0.952501	+	0.304537i	$0.901498\pi$
$854$		0			0
$855$	−10.4939	+	10.6749i	−0.358883	+	0.365075i
$856$		0			0
$857$	0.720534	+	4.08635i	0.0246130	+	0.139587i	0.994638	−	0.103418i	$-0.0329779\pi$
$857$	0.720534	+	4.08635i	0.0246130	+	0.139587i	−0.970025	+	0.243005i	$0.921867\pi$
$858$		0			0
$859$	−10.6899	+	3.89081i	−0.364735	+	0.132753i	−0.517885	−	0.855450i	$-0.673281\pi$
$859$	−10.6899	+	3.89081i	−0.364735	+	0.132753i	0.153150	+	0.988203i	$0.451058\pi$
$860$		0			0
$861$	0.215218	+	0.213670i	0.00733462	+	0.00728185i
$862$		0			0
$863$	13.1388	+	22.7570i	0.447249	+	0.774659i	0.998206	−	0.0598753i	$-0.0190703\pi$
$863$	13.1388	+	22.7570i	0.447249	+	0.774659i	−0.550956	+	0.834534i	$0.685737\pi$
$864$		0			0
$865$	6.74094	−	11.6757i	0.229199	−	0.396984i
$866$		0			0
$867$	−14.5734	−	15.7681i	−0.494938	−	0.535514i
$868$		0			0
$869$	−4.48130	+	25.4147i	−0.152018	+	0.862135i
$870$		0			0
$871$	0.0171360	+	0.0971828i	0.000580630	+	0.00329291i
$872$		0			0
$873$	23.1551	−	50.7860i	0.783682	−	1.71885i
$874$		0			0
$875$	−3.67437	−	16.6264i	−0.124216	−	0.562075i
$876$		0			0
$877$	38.4767	+	32.2858i	1.29927	+	1.09021i	0.990271	+	0.139151i	$0.0444374\pi$
$877$	38.4767	+	32.2858i	1.29927	+	1.09021i	0.308996	+	0.951063i	$0.400007\pi$
$878$		0			0
$879$	33.0402	−	21.2481i	1.11442	−	0.716681i
$880$		0			0
$881$	23.9664	−	41.5110i	0.807448	−	1.39854i	−0.107179	−	0.994240i	$-0.534182\pi$
$881$	23.9664	−	41.5110i	0.807448	−	1.39854i	0.914626	−	0.404301i	$-0.132485\pi$
$882$		0			0
$883$	2.37566	+	4.11476i	0.0799472	+	0.138473i	0.903227	−	0.429163i	$-0.141191\pi$
$883$	2.37566	+	4.11476i	0.0799472	+	0.138473i	−0.823280	+	0.567636i	$0.807858\pi$
$884$		0			0
$885$	−9.79401	+	12.8775i	−0.329222	+	0.432871i
$886$		0			0
$887$	0.859272	−	4.87317i	0.0288515	−	0.163625i	−0.966978	−	0.254861i	$-0.917970\pi$
$887$	0.859272	−	4.87317i	0.0288515	−	0.163625i	0.995829	+	0.0912353i	$0.0290816\pi$
$888$		0			0
$889$	7.60609	+	2.40376i	0.255100	+	0.0806196i
$890$		0			0
$891$	−0.489086	−	28.5865i	−0.0163850	−	0.957683i
$892$		0			0
$893$	40.2208	−	33.7493i	1.34594	−	1.12938i
$894$		0			0
$895$	2.87929	+	2.41601i	0.0962441	+	0.0807584i
$896$		0			0
$897$	−52.0906	−	6.63134i	−1.73926	−	0.221414i
$898$		0			0
$899$	−8.29674			−0.276712
$900$		0			0
$901$	24.9440			0.831006
$902$		0			0
$903$	24.6556	−	17.3971i	0.820488	−	0.578938i
$904$		0			0
$905$	−8.20515	−	6.88494i	−0.272749	−	0.228863i
$906$		0			0
$907$	−14.8612	−	5.40905i	−0.493460	−	0.179605i	0.0832904	−	0.996525i	$-0.473457\pi$
$907$	−14.8612	−	5.40905i	−0.493460	−	0.179605i	−0.576750	+	0.816921i	$0.695679\pi$
$908$		0			0
$909$	8.38268	−	18.3857i	0.278036	−	0.609815i
$910$		0			0
$911$	6.82179	−	5.72416i	0.226016	−	0.189650i	−0.522747	−	0.852488i	$-0.675093\pi$
$911$	6.82179	−	5.72416i	0.226016	−	0.189650i	0.748763	+	0.662838i	$0.230648\pi$
$912$		0			0
$913$	−24.9304	−	20.9191i	−0.825075	−	0.692320i
$914$		0			0
$915$	4.60899	−	14.8388i	0.152368	−	0.490557i
$916$		0			0
$917$	10.9817	+	17.2632i	0.362649	+	0.570082i
$918$		0			0
$919$	−5.44059	−	9.42338i	−0.179469	−	0.310849i	0.762230	−	0.647306i	$-0.224104\pi$
$919$	−5.44059	−	9.42338i	−0.179469	−	0.310849i	−0.941699	+	0.336458i	$0.890771\pi$
$920$		0			0
$921$	−22.8455	−	24.7184i	−0.752785	−	0.814499i
$922$		0			0
$923$	−0.559627	+	3.17380i	−0.0184203	+	0.104467i
$924$		0			0
$925$	−10.7130	+	8.98927i	−0.352241	+	0.295565i
$926$		0			0
$927$	−4.48513	−	1.16076i	−0.147311	−	0.0381244i
$928$		0			0
$929$	−25.2997	+	21.2289i	−0.830055	+	0.696499i	−0.955304	−	0.295626i	$-0.904472\pi$
$929$	−25.2997	+	21.2289i	−0.830055	+	0.696499i	0.125248	+	0.992125i	$0.460027\pi$
$930$		0			0
$931$	42.3959	+	29.7702i	1.38947	+	0.975679i
$932$		0			0
$933$	23.1324	+	11.9165i	0.757321	+	0.390129i
$934$		0			0
$935$	−5.80642	−	10.0570i	−0.189890	−	0.328899i
$936$		0			0
$937$	−27.1366	−	47.0020i	−0.886514	−	1.53549i	−0.843968	−	0.536393i	$-0.819786\pi$
$937$	−27.1366	−	47.0020i	−0.886514	−	1.53549i	−0.0425464	−	0.999094i	$-0.513547\pi$
$938$		0			0
$939$	18.7033	+	44.6131i	0.610359	+	1.45589i
$940$		0			0
$941$	−21.5507	+	7.84382i	−0.702534	+	0.255701i	−0.668492	−	0.743719i	$-0.733060\pi$
$941$	−21.5507	+	7.84382i	−0.702534	+	0.255701i	−0.0340413	+	0.999420i	$0.510838\pi$
$942$		0			0
$943$	−0.0796467	−	0.451699i	−0.00259365	−	0.0147093i
$944$		0			0
$945$	1.72049	+	9.10808i	0.0559675	+	0.296286i
$946$		0			0
$947$	1.53295	+	8.69381i	0.0498143	+	0.282511i	0.999532	−	0.0305973i	$-0.00974093\pi$
$947$	1.53295	+	8.69381i	0.0498143	+	0.282511i	−0.949718	+	0.313108i	$0.898630\pi$
$948$		0			0
$949$	17.0256	−	6.19679i	0.552673	−	0.201156i
$950$		0			0
$951$	10.0441	−	13.2063i	0.325702	−	0.428243i
$952$		0			0
$953$	−10.4867	−	18.1635i	−0.339697	−	0.588373i	0.644678	−	0.764454i	$-0.276991\pi$
$953$	−10.4867	−	18.1635i	−0.339697	−	0.588373i	−0.984376	+	0.176081i	$0.943658\pi$
$954$		0			0
$955$	−5.88020	−	10.1848i	−0.190279	−	0.329572i
$956$		0			0
$957$	7.85512	−	5.05162i	0.253920	−	0.163296i
$958$		0			0
$959$	6.33719	−	47.8892i	0.204639	−	1.54642i
$960$		0			0
$961$	−5.44416	+	4.56819i	−0.175618	+	0.147361i
$962$		0			0
$963$	−1.66177	+	21.0681i	−0.0535496	+	0.678911i
$964$		0			0
$965$	0.381698	−	0.320282i	0.0122873	−	0.0103103i
$966$		0			0
$967$	−2.39335	+	13.5733i	−0.0769649	+	0.436489i	0.921838	+	0.387575i	$0.126687\pi$
$967$	−2.39335	+	13.5733i	−0.0769649	+	0.436489i	−0.998803	+	0.0489143i	$0.984424\pi$
$968$		0			0
$969$	−20.6149	+	66.3707i	−0.662247	+	2.13213i
$970$		0			0
$971$	−16.5476	−	28.6613i	−0.531037	−	0.919783i	−0.999344	−	0.0362174i	$-0.988469\pi$
$971$	−16.5476	−	28.6613i	−0.531037	−	0.919783i	0.468307	−	0.883566i	$-0.344864\pi$
$972$		0			0
$973$	−31.3201	+	1.34656i	−1.00408	+	0.0431688i
$974$		0			0
$975$	23.3749	+	25.2912i	0.748596	+	0.809968i
$976$		0			0
$977$	30.8398	+	25.8776i	0.986651	+	0.827899i	0.985079	−	0.172100i	$-0.0550552\pi$
$977$	30.8398	+	25.8776i	0.986651	+	0.827899i	0.00157187	+	0.999999i	$0.499500\pi$
$978$		0			0
$979$	−7.22399	+	6.06164i	−0.230880	+	0.193731i
$980$		0			0
$981$	18.3846	−	8.76512i	0.586976	−	0.279849i
$982$		0			0
$983$	−49.9337	−	18.1744i	−1.59264	−	0.579673i	−0.614735	−	0.788734i	$-0.710737\pi$
$983$	−49.9337	−	18.1744i	−1.59264	−	0.579673i	−0.977903	+	0.209061i	$0.932959\pi$
$984$		0			0
$985$	12.0145	+	10.0813i	0.382813	+	0.321218i
$986$		0			0
$987$	−2.95051	−	32.3775i	−0.0939156	−	1.03059i
$988$		0			0
$989$	−45.6373			−1.45118
$990$		0			0
$991$	3.06967			0.0975111			0.0487556	−	0.998811i	$-0.484474\pi$
$991$	3.06967			0.0975111			0.0487556	+	0.998811i	$0.484474\pi$
$992$		0			0
$993$	−6.87630	+	9.04117i	−0.218213	+	0.286913i
$994$		0			0
$995$	3.18817	+	2.67519i	0.101072	+	0.0848092i
$996$		0			0
$997$	29.1272	−	24.4406i	0.922466	−	0.774041i	−0.0519831	−	0.998648i	$-0.516554\pi$
$997$	29.1272	−	24.4406i	0.922466	−	0.774041i	0.974449	+	0.224607i	$0.0721097\pi$
$998$		0			0
$999$	12.5574	−	9.89417i	0.397298	−	0.313038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bp.a.193.11	✓	144
7.2	even	3		756.2.bq.a.625.6	yes	144
27.7	even	9		756.2.bq.a.277.6	yes	144
189.142	even	9	inner	756.2.bp.a.709.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.11	✓	144	1.1	even	1	trivial
756.2.bp.a.709.11	yes	144	189.142	even	9	inner
756.2.bq.a.277.6	yes	144	27.7	even	9
756.2.bq.a.625.6	yes	144	7.2	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.513768 + 1.65410i) q^{3} +(-0.633570 + 0.230601i) q^{5} +(1.95184 - 1.78614i) q^{7} +(-2.47208 - 1.69965i) q^{9} +O(q^{10})\)	\(q+(-0.513768 + 1.65410i) q^{3} +(-0.633570 + 0.230601i) q^{5} +(1.95184 - 1.78614i) q^{7} +(-2.47208 - 1.69965i) q^{9} +(-2.98516 - 1.08651i) q^{11} +(-4.11055 + 1.49612i) q^{13} +(-0.0559281 - 1.16646i) q^{15} +(-2.71093 - 4.69546i) q^{17} +(-3.70030 + 6.40911i) q^{19} +(1.95166 + 4.14620i) q^{21} +(1.20350 - 6.82538i) q^{23} +(-3.48199 + 2.92173i) q^{25} +(4.08146 - 3.21585i) q^{27} +(1.59498 + 0.580527i) q^{29} +(-4.59328 + 1.67182i) q^{31} +(3.33087 - 4.37953i) q^{33} +(-0.824743 + 1.58174i) q^{35} +3.07669 q^{37} +(-0.362857 - 7.56792i) q^{39} +(0.0621882 - 0.0226347i) q^{41} +(-1.14344 - 6.48479i) q^{43} +(1.95818 + 0.506781i) q^{45} +(-6.66677 - 2.42651i) q^{47} +(0.619380 - 6.97254i) q^{49} +(9.15954 - 2.07176i) q^{51} +(-2.30032 + 3.98428i) q^{53} +2.14186 q^{55} +(-8.70020 - 9.41346i) q^{57} +(-10.6128 - 8.90518i) q^{59} +(12.5030 + 4.55073i) q^{61} +(-7.86093 + 1.09806i) q^{63} +(2.25932 - 1.89579i) q^{65} +(0.00391736 - 0.0222165i) q^{67} +(10.6715 + 5.49737i) q^{69} +(0.368370 - 0.638035i) q^{71} -4.14191 q^{73} +(-3.04390 - 7.26065i) q^{75} +(-7.76722 + 3.21123i) q^{77} +(-1.41066 - 8.00026i) q^{79} +(3.22240 + 8.40334i) q^{81} +(9.62674 + 3.50385i) q^{83} +(2.80034 + 2.34976i) q^{85} +(-1.77970 + 2.34000i) q^{87} +(1.48426 - 2.57082i) q^{89} +(-5.35087 + 10.2622i) q^{91} +(-0.405469 - 8.45666i) q^{93} +(0.866456 - 4.91391i) q^{95} +(3.23076 + 18.3225i) q^{97} +(5.53288 + 7.75965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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