LMFDB - Embedded newform 756.2.bi.c.559.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(307,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,6,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.32
Character	$\chi$	$=$	756.559
Dual form			756.2.bi.c.307.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13617 - 0.842090i) q^{2} +(0.581768 - 1.91352i) q^{4} +(1.43245 - 0.827025i) q^{5} +(-0.0302588 - 2.64558i) q^{7} +(-0.950366 - 2.66398i) q^{8} +(0.931077 - 2.14589i) q^{10} +(-4.24842 - 2.45282i) q^{11} +(0.876334 - 0.505952i) q^{13} +(-2.26220 - 2.98035i) q^{14} +(-3.32309 - 2.22644i) q^{16} +7.66107i q^{17} +2.85119 q^{19} +(-0.749173 - 3.22215i) q^{20} +(-6.89242 + 0.790723i) q^{22} +(-1.98118 + 1.14384i) q^{23} +(-1.13206 + 1.96079i) q^{25} +(0.569608 - 1.31280i) q^{26} +(-5.07996 - 1.48121i) q^{28} +(4.19857 - 7.27213i) q^{29} +(-0.348784 - 0.604112i) q^{31} +(-5.65047 + 0.268722i) q^{32} +(6.45131 + 8.70428i) q^{34} +(-2.23130 - 3.76463i) q^{35} +3.97490 q^{37} +(3.23944 - 2.40096i) q^{38} +(-3.56453 - 3.03004i) q^{40} +(6.69947 - 3.86794i) q^{41} +(6.70811 + 3.87293i) q^{43} +(-7.16511 + 6.70244i) q^{44} +(-1.28775 + 2.96793i) q^{46} +(3.70722 - 6.42109i) q^{47} +(-6.99817 + 0.160104i) q^{49} +(0.364945 + 3.18108i) q^{50} +(-0.458324 - 1.97123i) q^{52} +8.61878 q^{53} -8.11418 q^{55} +(-7.01902 + 2.59488i) q^{56} +(-1.35350 - 11.7980i) q^{58} +(2.54378 + 4.40596i) q^{59} +(-5.12759 - 2.96042i) q^{61} +(-0.904996 - 0.392667i) q^{62} +(-6.19361 + 5.06352i) q^{64} +(0.836869 - 1.44950i) q^{65} +(-2.18590 + 1.26203i) q^{67} +(14.6596 + 4.45696i) q^{68} +(-5.70530 - 2.39830i) q^{70} -1.00362i q^{71} +5.89658i q^{73} +(4.51617 - 3.34723i) q^{74} +(1.65873 - 5.45580i) q^{76} +(-6.36058 + 11.3137i) q^{77} +(-4.90752 - 2.83336i) q^{79} +(-6.60149 - 0.440989i) q^{80} +(4.35458 - 10.0362i) q^{82} +(-1.20736 + 2.09120i) q^{83} +(6.33589 + 10.9741i) q^{85} +(10.8829 - 1.24853i) q^{86} +(-2.49673 + 13.6488i) q^{88} -8.19734i q^{89} +(-1.36505 - 2.30310i) q^{91} +(1.03616 + 4.45647i) q^{92} +(-1.19511 - 10.4173i) q^{94} +(4.08418 - 2.35800i) q^{95} +(8.82136 + 5.09301i) q^{97} +(-7.81629 + 6.07500i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56}+ \cdots - 20 q^{98}+O(q^{100}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Character values

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

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

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 $

$2$	1.13617	−	0.842090i	0.803394	−	0.595448i
$2$	1.13617	−	0.842090i	0.803394	−	0.595448i
$3$		0			0
$3$		0			0
$4$	0.581768	−	1.91352i	0.290884	−	0.956758i
$5$	1.43245	−	0.827025i	0.640611	−	0.369857i	−0.144239	−	0.989543i	$-0.546073\pi$
$5$	1.43245	−	0.827025i	0.640611	−	0.369857i	0.784850	+	0.619686i	$0.212740\pi$
$6$		0			0
$7$	−0.0302588	−	2.64558i	−0.0114368	−	0.999935i
$7$	−0.0302588	−	2.64558i	−0.0114368	−	0.999935i
$8$	−0.950366	−	2.66398i	−0.336005	−	0.941860i
$9$		0			0
$10$	0.931077	−	2.14589i	0.294432	−	0.678591i
$11$	−4.24842	−	2.45282i	−1.28095	−	0.739554i	−0.303924	−	0.952696i	$-0.598297\pi$
$11$	−4.24842	−	2.45282i	−1.28095	−	0.739554i	−0.977021	+	0.213142i	$0.931630\pi$
$12$		0			0
$13$	0.876334	−	0.505952i	0.243051	−	0.140326i	−0.373527	−	0.927619i	$-0.621852\pi$
$13$	0.876334	−	0.505952i	0.243051	−	0.140326i	0.616578	+	0.787294i	$0.288518\pi$
$14$	−2.26220	−	2.98035i	−0.604597	−	0.796531i
$15$		0			0
$16$	−3.32309	−	2.22644i	−0.830773	−	0.556611i
$17$			7.66107i			1.85808i	0.369976	+	0.929041i	$0.379366\pi$
$17$			7.66107i			1.85808i	−0.369976	+	0.929041i	$0.620634\pi$
$18$		0			0
$19$	2.85119			0.654108			0.327054	−	0.945006i	$-0.393944\pi$
$19$	2.85119			0.654108			0.327054	+	0.945006i	$0.393944\pi$
$20$	−0.749173	−	3.22215i	−0.167520	−	0.720495i
$21$		0			0
$22$	−6.89242	+	0.790723i	−1.46947	+	0.168583i
$23$	−1.98118	+	1.14384i	−0.413105	+	0.238506i	−0.692123	−	0.721780i	$-0.743324\pi$
$23$	−1.98118	+	1.14384i	−0.413105	+	0.238506i	0.279018	+	0.960286i	$0.409991\pi$
$24$		0			0
$25$	−1.13206	+	1.96079i	−0.226412	+	0.392157i
$26$	0.569608	−	1.31280i	0.111709	−	0.257461i
$27$		0			0
$28$	−5.07996	−	1.48121i	−0.960023	−	0.279923i
$29$	4.19857	−	7.27213i	0.779654	−	1.35040i	−0.152486	−	0.988306i	$-0.548728\pi$
$29$	4.19857	−	7.27213i	0.779654	−	1.35040i	0.932141	−	0.362096i	$-0.117939\pi$
$30$		0			0
$31$	−0.348784	−	0.604112i	−0.0626435	−	0.108502i	0.833003	−	0.553269i	$-0.186620\pi$
$31$	−0.348784	−	0.604112i	−0.0626435	−	0.108502i	−0.895646	+	0.444767i	$0.853286\pi$
$32$	−5.65047	+	0.268722i	−0.998871	+	0.0475038i
$33$		0			0
$34$	6.45131	+	8.70428i	1.10639	+	1.49277i
$35$	−2.23130	−	3.76463i	−0.377159	−	0.636339i
$36$		0			0
$37$	3.97490			0.653470			0.326735	−	0.945116i	$-0.394051\pi$
$37$	3.97490			0.653470			0.326735	+	0.945116i	$0.394051\pi$
$38$	3.23944	−	2.40096i	0.525506	−	0.389487i
$39$		0			0
$40$	−3.56453	−	3.03004i	−0.563602	−	0.479092i
$41$	6.69947	−	3.86794i	1.04628	−	0.604071i	0.124675	−	0.992198i	$-0.460211\pi$
$41$	6.69947	−	3.86794i	1.04628	−	0.604071i	0.921606	+	0.388127i	$0.126878\pi$
$42$		0			0
$43$	6.70811	+	3.87293i	1.02298	+	0.590617i	0.914965	−	0.403533i	$-0.132218\pi$
$43$	6.70811	+	3.87293i	1.02298	+	0.590617i	0.108013	+	0.994150i	$0.465551\pi$
$44$	−7.16511	+	6.70244i	−1.08018	+	1.01043i
$45$		0			0
$46$	−1.28775	+	2.96793i	−0.189868	+	0.437597i
$47$	3.70722	−	6.42109i	0.540754	−	0.936613i	−0.458107	−	0.888897i	$-0.651472\pi$
$47$	3.70722	−	6.42109i	0.540754	−	0.936613i	0.998861	−	0.0477158i	$-0.0151942\pi$
$48$		0			0
$49$	−6.99817	+	0.160104i	−0.999738	+	0.0228720i
$50$	0.364945	+	3.18108i	0.0516110	+	0.449873i
$51$		0			0
$52$	−0.458324	−	1.97123i	−0.0635581	−	0.273360i
$53$	8.61878			1.18388			0.591940	−	0.805982i	$-0.298362\pi$
$53$	8.61878			1.18388			0.591940	+	0.805982i	$0.298362\pi$
$54$		0			0
$55$	−8.11418			−1.09412
$56$	−7.01902	+	2.59488i	−0.937956	+	0.346755i
$57$		0			0
$58$	−1.35350	−	11.7980i	−0.177724	−	1.54915i
$59$	2.54378	+	4.40596i	0.331172	+	0.573607i	0.982742	−	0.184981i	$-0.0592225\pi$
$59$	2.54378	+	4.40596i	0.331172	+	0.573607i	−0.651570	+	0.758589i	$0.725889\pi$
$60$		0			0
$61$	−5.12759	−	2.96042i	−0.656521	−	0.379042i	0.134429	−	0.990923i	$-0.457080\pi$
$61$	−5.12759	−	2.96042i	−0.656521	−	0.379042i	−0.790950	+	0.611881i	$0.790413\pi$
$62$	−0.904996	−	0.392667i	−0.114935	−	0.0498687i
$63$		0			0
$64$	−6.19361	+	5.06352i	−0.774201	+	0.632940i
$65$	0.836869	−	1.44950i	0.103801	−	0.179788i
$66$		0			0
$67$	−2.18590	+	1.26203i	−0.267051	+	0.154182i	−0.627547	−	0.778579i	$-0.715941\pi$
$67$	−2.18590	+	1.26203i	−0.267051	+	0.154182i	0.360496	+	0.932761i	$0.382607\pi$
$68$	14.6596	+	4.45696i	1.77774	+	0.540486i
$69$		0			0
$70$	−5.70530	−	2.39830i	−0.681914	−	0.286652i
$71$		−	1.00362i		−	0.119108i	−0.998225	−	0.0595539i	$-0.981032\pi$
$71$		−	1.00362i		−	0.119108i	0.998225	−	0.0595539i	$-0.0189678\pi$
$72$		0			0
$73$			5.89658i			0.690142i	0.938577	+	0.345071i	$0.112145\pi$
$73$			5.89658i			0.690142i	−0.938577	+	0.345071i	$0.887855\pi$
$74$	4.51617	−	3.34723i	0.524994	−	0.389107i
$75$		0			0
$76$	1.65873	−	5.45580i	0.190269	−	0.625823i
$77$	−6.36058	+	11.3137i	−0.724856	+	1.28932i
$78$		0			0
$79$	−4.90752	−	2.83336i	−0.552139	−	0.318778i	0.197845	−	0.980233i	$-0.436606\pi$
$79$	−4.90752	−	2.83336i	−0.552139	−	0.318778i	−0.749984	+	0.661456i	$0.769939\pi$
$80$	−6.60149	−	0.440989i	−0.738069	−	0.0493041i
$81$		0			0
$82$	4.35458	−	10.0362i	0.480883	−	1.10831i
$83$	−1.20736	+	2.09120i	−0.132525	+	0.229539i	−0.924649	−	0.380820i	$-0.875642\pi$
$83$	−1.20736	+	2.09120i	−0.132525	+	0.229539i	0.792125	+	0.610359i	$0.208975\pi$
$84$		0			0
$85$	6.33589	+	10.9741i	0.687224	+	1.19031i
$86$	10.8829	−	1.24853i	1.17354	−	0.134632i
$87$		0			0
$88$	−2.49673	+	13.6488i	−0.266152	+	1.45497i
$89$		−	8.19734i		−	0.868916i	−0.900692	−	0.434458i	$-0.856940\pi$
$89$		−	8.19734i		−	0.868916i	0.900692	−	0.434458i	$-0.143060\pi$
$90$		0			0
$91$	−1.36505	−	2.30310i	−0.143096	−	0.241431i
$92$	1.03616	+	4.45647i	0.108027	+	0.464619i
$93$		0			0
$94$	−1.19511	−	10.4173i	−0.123266	−	1.07446i
$95$	4.08418	−	2.35800i	0.419028	−	0.241926i
$96$		0			0
$97$	8.82136	+	5.09301i	0.895673	+	0.517117i	0.875794	−	0.482685i	$-0.160338\pi$
$97$	8.82136	+	5.09301i	0.895673	+	0.517117i	0.0198794	+	0.999802i	$0.493672\pi$
$98$	−7.81629	+	6.07500i	−0.789565	+	0.613667i
$99$		0			0
$100$	3.09340	+	3.30694i	0.309340	+	0.330694i
$101$	0.846450	+	0.488698i	0.0842249	+	0.0486273i	0.541521	−	0.840687i	$-0.317849\pi$
$101$	0.846450	+	0.488698i	0.0842249	+	0.0486273i	−0.457296	+	0.889315i	$0.651182\pi$
$102$		0			0
$103$	6.53514	+	11.3192i	0.643926	+	1.11531i	0.984548	+	0.175113i	$0.0560290\pi$
$103$	6.53514	+	11.3192i	0.643926	+	1.11531i	−0.340622	+	0.940200i	$0.610638\pi$
$104$	−2.18068	−	1.85370i	−0.213834	−	0.181770i
$105$		0			0
$106$	9.79241	−	7.25779i	0.951122	−	0.704939i
$107$		−	1.03143i		−	0.0997116i	−0.998756	−	0.0498558i	$-0.984124\pi$
$107$		−	1.03143i		−	0.0997116i	0.998756	−	0.0498558i	$-0.0158762\pi$
$108$		0			0
$109$	−0.842410			−0.0806882			−0.0403441	−	0.999186i	$-0.512845\pi$
$109$	−0.842410			−0.0806882			−0.0403441	+	0.999186i	$0.512845\pi$
$110$	−9.21910	+	6.83288i	−0.879007	+	0.651489i
$111$		0			0
$112$	−5.78968	+	8.85887i	−0.547073	+	0.837085i
$113$	−3.19162	−	5.52804i	−0.300242	−	0.520035i	0.675949	−	0.736949i	$-0.263734\pi$
$113$	−3.19162	−	5.52804i	−0.300242	−	0.520035i	−0.976191	+	0.216914i	$0.930401\pi$
$114$		0			0
$115$	−1.89196	+	3.27697i	−0.176426	+	0.305579i
$116$	−11.4728	−	12.2647i	−1.06522	−	1.13875i
$117$		0			0
$118$	6.60039	+	2.86383i	0.607615	+	0.263637i
$119$	20.2680	−	0.231815i	1.85796	−	0.0212505i
$120$		0			0
$121$	6.53269	+	11.3149i	0.593881	+	1.02863i
$122$	−8.31875	+	0.954356i	−0.753145	+	0.0864034i
$123$		0			0
$124$	−1.35889	+	0.315952i	−0.122032	+	0.0283733i
$125$			12.0152i			1.07467i
$126$		0			0
$127$		−	17.9070i		−	1.58899i	−0.607272	−	0.794494i	$-0.707736\pi$
$127$		−	17.9070i		−	1.58899i	0.607272	−	0.794494i	$-0.292264\pi$
$128$	−2.77306	+	10.9686i	−0.245106	+	0.969496i
$129$		0			0
$130$	−0.269784	−	2.35160i	−0.0236616	−	0.206249i
$131$	5.02346	+	8.70089i	0.438902	+	0.760200i	0.997605	−	0.0691675i	$-0.0220343\pi$
$131$	5.02346	+	8.70089i	0.438902	+	0.760200i	−0.558703	+	0.829368i	$0.688701\pi$
$132$		0			0
$133$	−0.0862737	−	7.54305i	−0.00748088	−	0.654065i
$134$	−1.42081	+	3.27461i	−0.122740	+	0.282883i
$135$		0			0
$136$	20.4090	−	7.28082i	1.75005	−	0.624325i
$137$	−1.97707	+	3.42439i	−0.168913	+	0.292566i	−0.938038	−	0.346533i	$-0.887359\pi$
$137$	−1.97707	+	3.42439i	−0.168913	+	0.292566i	0.769125	+	0.639098i	$0.220692\pi$
$138$		0			0
$139$	4.85060	+	8.40148i	0.411422	+	0.712605i	0.995046	−	0.0994201i	$-0.0316988\pi$
$139$	4.85060	+	8.40148i	0.411422	+	0.712605i	−0.583623	+	0.812025i	$0.698365\pi$
$140$	−8.50178	+	2.07949i	−0.718532	+	0.175749i
$141$		0			0
$142$	−0.845139	−	1.14028i	−0.0709225	−	0.0956905i
$143$	−4.96404			−0.415114
$144$		0			0
$145$		−	13.8893i		−	1.15344i
$146$	4.96545	+	6.69952i	0.410944	+	0.554456i
$147$		0			0
$148$	2.31247	−	7.60605i	0.190084	−	0.625213i
$149$	3.46856	+	6.00773i	0.284156	+	0.492172i	0.972404	−	0.233303i	$-0.0749534\pi$
$149$	3.46856	+	6.00773i	0.284156	+	0.492172i	−0.688248	+	0.725475i	$0.741620\pi$
$150$		0			0
$151$	10.8500	+	6.26427i	0.882964	+	0.509779i	0.871635	−	0.490156i	$-0.163060\pi$
$151$	10.8500	+	6.26427i	0.882964	+	0.509779i	0.0113294	+	0.999936i	$0.496394\pi$
$152$	−2.70967	−	7.59552i	−0.219784	−	0.616078i
$153$		0			0
$154$	2.30048	+	18.2105i	0.185378	+	1.46745i
$155$	−0.999232	−	0.576907i	−0.0802602	−	0.0463383i
$156$		0			0
$157$	−1.44619	+	0.834956i	−0.115418	+	0.0666367i	−0.556598	−	0.830782i	$-0.687894\pi$
$157$	−1.44619	+	0.834956i	−0.115418	+	0.0666367i	0.441180	+	0.897419i	$0.354560\pi$
$158$	−7.96173	+	0.913397i	−0.633401	+	0.0726659i
$159$		0			0
$160$	−7.87177	+	5.05801i	−0.622318	+	0.399871i
$161$	3.08606	+	5.20676i	0.243215	+	0.410350i
$162$		0			0
$163$			7.06914i			0.553698i	0.960913	+	0.276849i	$0.0892901\pi$
$163$			7.06914i			0.553698i	−0.960913	+	0.276849i	$0.910710\pi$
$164$	−3.50383	−	15.0698i	−0.273603	−	1.17675i
$165$		0			0
$166$	0.389218	+	3.39266i	0.0302092	+	0.263322i
$167$	−0.578614	−	1.00219i	−0.0447745	−	0.0775518i	0.842770	−	0.538274i	$-0.180924\pi$
$167$	−0.578614	−	1.00219i	−0.0447745	−	0.0775518i	−0.887544	+	0.460723i	$0.847590\pi$
$168$		0			0
$169$	−5.98803	+	10.3716i	−0.460617	+	0.797813i
$170$	16.4398	+	7.13305i	1.26088	+	0.547080i
$171$		0			0
$172$	11.3135	−	10.5829i	0.862645	−	0.806942i
$173$	−1.30347	−	0.752561i	−0.0991013	−	0.0572162i	0.449630	−	0.893215i	$-0.351556\pi$
$173$	−1.30347	−	0.752561i	−0.0991013	−	0.0572162i	−0.548732	+	0.835999i	$0.684889\pi$
$174$		0			0
$175$	5.22167	+	2.93562i	0.394721	+	0.221912i
$176$	8.65680	+	17.6098i	0.652531	+	1.32739i
$177$		0			0
$178$	−6.90290	−	9.31357i	−0.517394	−	0.698082i
$179$		−	1.28088i		−	0.0957374i	−0.998854	−	0.0478687i	$-0.984757\pi$
$179$		−	1.28088i		−	0.0957374i	0.998854	−	0.0478687i	$-0.0152429\pi$
$180$		0			0
$181$			26.6202i			1.97866i	0.145683	+	0.989331i	$0.453462\pi$
$181$			26.6202i			1.97866i	−0.145683	+	0.989331i	$0.546538\pi$
$182$	−3.49035	−	1.46722i	−0.258722	−	0.108757i
$183$		0			0
$184$	4.93001	+	4.19077i	0.363445	+	0.308948i
$185$	5.69385	−	3.28734i	0.418620	−	0.241690i
$186$		0			0
$187$	18.7913	−	32.5474i	1.37415	−	2.38010i
$188$	−10.1301	−	10.8294i	−0.738815	−	0.789816i
$189$		0			0
$190$	2.65468	−	6.11835i	0.192591	−	0.443872i
$191$	−7.44229	−	4.29681i	−0.538506	−	0.310906i	0.205968	−	0.978559i	$-0.433966\pi$
$191$	−7.44229	−	4.29681i	−0.538506	−	0.310906i	−0.744473	+	0.667653i	$0.767299\pi$
$192$		0			0
$193$	−3.80654	−	6.59312i	−0.274001	−	0.474583i	0.695882	−	0.718156i	$-0.255014\pi$
$193$	−3.80654	−	6.59312i	−0.274001	−	0.474583i	−0.969882	+	0.243573i	$0.921680\pi$
$194$	14.3113	−	1.64185i	1.02749	−	0.117878i
$195$		0			0
$196$	−3.76495	+	13.4843i	−0.268925	+	0.963161i
$197$	−14.3946			−1.02557			−0.512786	−	0.858517i	$-0.671386\pi$
$197$	−14.3946			−1.02557			−0.512786	+	0.858517i	$0.671386\pi$
$198$		0			0
$199$	−21.9194			−1.55382			−0.776911	−	0.629610i	$-0.783215\pi$
$199$	−21.9194			−1.55382			−0.776911	+	0.629610i	$0.783215\pi$
$200$	6.29937	+	1.15232i	0.445433	+	0.0814816i
$201$		0			0
$202$	1.37324	−	0.157543i	0.0966208	−	0.0110847i
$203$	−19.3660	−	10.8876i	−1.35923	−	0.764159i
$204$		0			0
$205$	6.39776	−	11.0813i	0.446839	−	0.773948i
$206$	16.9568	+	7.35736i	1.18144	+	0.512611i
$207$		0			0
$208$	−4.03861	−	0.269785i	−0.280027	−	0.0187062i
$209$	−12.1130	−	6.99347i	−0.837876	−	0.483748i
$210$		0			0
$211$	−1.45464	+	0.839838i	−0.100142	+	0.0578168i	−0.549234	−	0.835668i	$-0.685081\pi$
$211$	−1.45464	+	0.839838i	−0.100142	+	0.0578168i	0.449093	+	0.893485i	$0.351747\pi$
$212$	5.01413	−	16.4922i	0.344372	−	1.13269i
$213$		0			0
$214$	−0.868553	−	1.17188i	−0.0593731	−	0.0801077i
$215$	12.8120			0.873774
$216$		0			0
$217$	−1.58767	+	0.941016i	−0.107778	+	0.0638803i
$218$	−0.957121	+	0.709385i	−0.0648244	+	0.0480456i
$219$		0			0
$220$	−4.72057	+	15.5266i	−0.318261	+	1.04680i
$221$	3.87613	+	6.71366i	0.260737	+	0.451609i
$222$		0			0
$223$	−4.09002	+	7.08413i	−0.273888	+	0.474388i	−0.969854	−	0.243687i	$-0.921643\pi$
$223$	−4.09002	+	7.08413i	−0.273888	+	0.474388i	0.695966	+	0.718075i	$0.254977\pi$
$224$	0.881903	+	14.9406i	0.0589246	+	0.998262i
$225$		0			0
$226$	−8.28133	−	3.59317i	−0.550866	−	0.239014i
$227$	−13.5064	+	23.3937i	−0.896450	+	1.55270i	−0.0644498	+	0.997921i	$0.520529\pi$
$227$	−13.5064	+	23.3937i	−0.896450	+	1.55270i	−0.832000	+	0.554776i	$0.812804\pi$
$228$		0			0
$229$	10.4216	−	6.01689i	0.688677	−	0.397608i	−0.114439	−	0.993430i	$-0.536507\pi$
$229$	10.4216	−	6.01689i	0.688677	−	0.397608i	0.803116	+	0.595823i	$0.203174\pi$
$230$	0.609916	+	5.31640i	0.0402167	+	0.350553i
$231$		0			0
$232$	−23.3630	−	4.27372i	−1.53386	−	0.280584i
$233$	−12.9746			−0.849992			−0.424996	−	0.905195i	$-0.639724\pi$
$233$	−12.9746			−0.849992			−0.424996	+	0.905195i	$0.639724\pi$
$234$		0			0
$235$		−	12.2639i		−	0.800005i
$236$	9.91077	−	2.30433i	0.645136	−	0.149999i
$237$		0			0
$238$	22.8327	−	17.3308i	1.48002	−	1.12339i
$239$	−5.65067	+	3.26242i	−0.365512	+	0.211028i	−0.671496	−	0.741008i	$-0.734348\pi$
$239$	−5.65067	+	3.26242i	−0.365512	+	0.211028i	0.305984	+	0.952037i	$0.401015\pi$
$240$		0			0
$241$	−20.0162	−	11.5564i	−1.28936	−	0.744410i	−0.310817	−	0.950470i	$-0.600603\pi$
$241$	−20.0162	−	11.5564i	−1.28936	−	0.744410i	−0.978539	+	0.206059i	$0.933936\pi$
$242$	16.9505	+	7.35460i	1.08962	+	0.472772i
$243$		0			0
$244$	−8.64787	+	8.08945i	−0.553623	+	0.517874i
$245$	−9.89211	+	6.01700i	−0.631984	+	0.384412i
$246$		0			0
$247$	2.49859	−	1.44256i	0.158982	−	0.0917881i
$248$	−1.27787	+	1.50328i	−0.0811449	+	0.0954586i
$249$		0			0
$250$	10.1179	+	13.6513i	0.639912	+	0.863386i
$251$	−5.55147			−0.350406			−0.175203	−	0.984532i	$-0.556058\pi$
$251$	−5.55147			−0.350406			−0.175203	+	0.984532i	$0.556058\pi$
$252$		0			0
$253$	11.2225			0.705553
$254$	−15.0793	−	20.3454i	−0.946159	−	1.27658i
$255$		0			0
$256$	6.08589	+	14.7974i	0.380368	+	0.924835i
$257$	16.9652	−	9.79486i	1.05826	−	0.610987i	0.133309	−	0.991074i	$-0.457440\pi$
$257$	16.9652	−	9.79486i	1.05826	−	0.610987i	0.924950	+	0.380088i	$0.124106\pi$
$258$		0			0
$259$	−0.120276	−	10.5159i	−0.00747359	−	0.653428i
$260$	−2.28678	−	2.44464i	−0.141820	−	0.151610i
$261$		0			0
$262$	13.0344	+	5.65549i	0.805270	+	0.349397i
$263$	11.4745	+	6.62480i	0.707548	+	0.408503i	0.810152	−	0.586219i	$-0.199384\pi$
$263$	11.4745	+	6.62480i	0.707548	+	0.408503i	−0.102605	+	0.994722i	$0.532718\pi$
$264$		0			0
$265$	12.3460	−	7.12794i	0.758406	−	0.437866i
$266$	−6.44995	−	8.49754i	−0.395472	−	0.521017i
$267$		0			0
$268$	1.14323	+	4.91697i	0.0698339	+	0.300352i
$269$		−	23.5318i		−	1.43476i	−0.696683	−	0.717379i	$-0.745342\pi$
$269$		−	23.5318i		−	1.43476i	0.696683	−	0.717379i	$-0.254658\pi$
$270$		0			0
$271$	20.2947			1.23281			0.616406	−	0.787428i	$-0.288588\pi$
$271$	20.2947			1.23281			0.616406	+	0.787428i	$0.288588\pi$
$272$	17.0569	−	25.4584i	1.03423	−	1.54364i
$273$		0			0
$274$	0.637354	+	5.55557i	0.0385040	+	0.335624i
$275$	9.61892	−	5.55349i	0.580043	−	0.334888i
$276$		0			0
$277$	9.44902	−	16.3662i	0.567736	−	0.983348i	−0.429053	−	0.903279i	$-0.641153\pi$
$277$	9.44902	−	16.3662i	0.567736	−	0.983348i	0.996789	−	0.0800689i	$-0.0255140\pi$
$278$	12.5859	+	5.46088i	0.754853	+	0.327522i
$279$		0			0
$280$	−7.90836	+	9.52193i	−0.472615	+	0.569044i
$281$	1.06714	−	1.84834i	0.0636602	−	0.110263i	−0.832439	−	0.554117i	$-0.813056\pi$
$281$	1.06714	−	1.84834i	0.0636602	−	0.110263i	0.896099	+	0.443854i	$0.146389\pi$
$282$		0			0
$283$	0.122715	+	0.212549i	0.00729468	+	0.0126347i	0.869650	−	0.493669i	$-0.164345\pi$
$283$	0.122715	+	0.212549i	0.00729468	+	0.0126347i	−0.862355	+	0.506304i	$0.831011\pi$
$284$	−1.92044	−	0.583874i	−0.113957	−	0.0346465i
$285$		0			0
$286$	−5.64000	+	4.18017i	−0.333500	+	0.247179i
$287$	−10.4357	−	17.6069i	−0.615997	−	1.03930i
$288$		0			0
$289$	−41.6920			−2.45247
$290$	−11.6960	−	15.7806i	−0.686814	−	0.926668i
$291$		0			0
$292$	11.2832	+	3.43044i	0.660299	+	0.200751i
$293$	−9.64296	+	5.56736i	−0.563347	+	0.325249i	−0.754488	−	0.656314i	$-0.772115\pi$
$293$	−9.64296	+	5.56736i	−0.563347	+	0.325249i	0.191141	+	0.981563i	$0.438781\pi$
$294$		0			0
$295$	7.28768	+	4.20754i	0.424305	+	0.244973i
$296$	−3.77762	−	10.5891i	−0.219569	−	0.615478i
$297$		0			0
$298$	8.99993	+	3.90496i	0.521352	+	0.226208i
$299$	−1.15745	+	2.00476i	−0.0669371	+	0.115939i
$300$		0			0
$301$	10.0432	−	17.8640i	0.578878	−	1.02967i
$302$	17.6026	−	2.01943i	1.01291	−	0.116205i
$303$		0			0
$304$	−9.47477	−	6.34802i	−0.543415	−	0.364084i
$305$	−9.79335			−0.560765
$306$		0			0
$307$	−23.3864			−1.33473			−0.667366	−	0.744730i	$-0.732578\pi$
$307$	−23.3864			−1.33473			−0.667366	+	0.744730i	$0.732578\pi$
$308$	17.9486	+	18.7531i	1.02272	+	1.06855i
$309$		0			0
$310$	−1.62111	+	0.185979i	−0.0920726	+	0.0105629i
$311$	15.3325	+	26.5567i	0.869428	+	1.50589i	0.862582	+	0.505918i	$0.168846\pi$
$311$	15.3325	+	26.5567i	0.869428	+	1.50589i	0.00684678	+	0.999977i	$0.497821\pi$
$312$		0			0
$313$	−13.6566	−	7.88467i	−0.771919	−	0.445668i	0.0616396	−	0.998098i	$-0.480367\pi$
$313$	−13.6566	−	7.88467i	−0.771919	−	0.445668i	−0.833559	+	0.552431i	$0.813700\pi$
$314$	−0.940006	+	2.16647i	−0.0530476	+	0.122261i
$315$		0			0
$316$	−8.27672	+	7.74227i	−0.465602	+	0.435537i
$317$	3.31354	−	5.73923i	0.186107	−	0.322347i	−0.757842	−	0.652438i	$-0.773746\pi$
$317$	3.31354	−	5.73923i	0.186107	−	0.322347i	0.943949	+	0.330091i	$0.107080\pi$
$318$		0			0
$319$	−35.6745	+	20.5967i	−1.99739	+	1.15319i
$320$	−4.68437	+	12.3755i	−0.261864	+	0.691811i
$321$		0			0
$322$	7.89085	+	3.31703i	0.439740	+	0.184851i
$323$			21.8432i			1.21539i
$324$		0			0
$325$			2.29107i			0.127086i
$326$	5.95285	+	8.03175i	0.329698	+	0.444837i
$327$		0			0
$328$	−16.6711	−	14.1713i	−0.920506	−	0.782479i
$329$	−17.0997	−	9.61345i	−0.942736	−	0.530006i
$330$		0			0
$331$	6.89178	+	3.97897i	0.378807	+	0.218704i	0.677299	−	0.735708i	$-0.263150\pi$
$331$	6.89178	+	3.97897i	0.378807	+	0.218704i	−0.298492	+	0.954412i	$0.596484\pi$
$332$	3.29915	+	3.52689i	0.181064	+	0.193563i
$333$		0			0
$334$	−1.50134	−	0.651413i	−0.0821496	−	0.0356437i
$335$	−2.08746	+	3.61559i	−0.114050	+	0.197541i
$336$		0			0
$337$	−16.0246	−	27.7555i	−0.872918	−	1.51194i	−0.858964	−	0.512036i	$-0.828891\pi$
$337$	−16.0246	−	27.7555i	−0.872918	−	1.51194i	−0.0139542	−	0.999903i	$-0.504442\pi$
$338$	1.93037	+	16.8263i	0.104999	+	0.915232i
$339$		0			0
$340$	24.6851	−	5.73947i	1.33874	−	0.311266i
$341$			3.42203i			0.185313i
$342$		0			0
$343$	0.635325	+	18.5094i	0.0343043	+	0.999411i
$344$	3.94226	−	21.5510i	0.212552	−	1.16195i
$345$		0			0
$346$	−2.11469	+	0.242605i	−0.113687	+	0.0130425i
$347$	−2.35072	+	1.35719i	−0.126193	+	0.0728576i	−0.561768	−	0.827295i	$-0.689879\pi$
$347$	−2.35072	+	1.35719i	−0.126193	+	0.0728576i	0.435575	+	0.900153i	$0.356545\pi$
$348$		0			0
$349$	−0.192902	−	0.111372i	−0.0103258	−	0.00596160i	0.494828	−	0.868991i	$-0.335231\pi$
$349$	−0.192902	−	0.111372i	−0.0103258	−	0.00596160i	−0.505154	+	0.863029i	$0.668564\pi$
$350$	8.40476	−	1.06175i	0.449253	−	0.0567527i
$351$		0			0
$352$	24.6647	+	12.7180i	1.31463	+	0.677869i
$353$	24.5385	+	14.1673i	1.30605	+	0.754049i	0.981435	−	0.191796i	$-0.0614312\pi$
$353$	24.5385	+	14.1673i	1.30605	+	0.754049i	0.324617	+	0.945846i	$0.394765\pi$
$354$		0			0
$355$	−0.830019	−	1.43763i	−0.0440528	−	0.0763017i
$356$	−15.6857	−	4.76895i	−0.831343	−	0.252754i
$357$		0			0
$358$	−1.07862	−	1.45530i	−0.0570066	−	0.0769148i
$359$			21.8680i			1.15415i	0.816691	+	0.577075i	$0.195806\pi$
$359$			21.8680i			1.15415i	−0.816691	+	0.577075i	$0.804194\pi$
$360$		0			0
$361$	−10.8707			−0.572143
$362$	22.4166	+	30.2451i	1.17819	+	1.58965i
$363$		0			0
$364$	−5.20116	+	1.27218i	−0.272615	+	0.0666803i
$365$	4.87662	+	8.44655i	0.255254	+	0.442113i
$366$		0			0
$367$	−3.75833	+	6.50962i	−0.196183	+	0.339800i	−0.947288	−	0.320384i	$-0.896188\pi$
$367$	−3.75833	+	6.50962i	−0.196183	+	0.339800i	0.751104	+	0.660183i	$0.229521\pi$
$368$	9.13034	+	0.609920i	0.475952	+	0.0317943i
$369$		0			0
$370$	3.70094	−	8.52972i	0.192403	−	0.443439i
$371$	−0.260794	−	22.8017i	−0.0135398	−	1.18380i
$372$		0			0
$373$	5.04377	+	8.73606i	0.261156	+	0.452336i	0.966549	−	0.256480i	$-0.0825629\pi$
$373$	5.04377	+	8.73606i	0.261156	+	0.452336i	−0.705393	+	0.708816i	$0.749230\pi$
$374$	−6.05778	−	52.8033i	−0.313240	−	2.73040i
$375$		0			0
$376$	−20.6289	−	3.77358i	−1.06385	−	0.194607i
$377$		−	8.49709i		−	0.437622i
$378$		0			0
$379$			20.7129i			1.06395i	0.846761	+	0.531974i	$0.178550\pi$
$379$			20.7129i			1.06395i	−0.846761	+	0.531974i	$0.821450\pi$
$380$	−2.13603	−	9.18696i	−0.109576	−	0.471281i
$381$		0			0
$382$	−12.0740	+	1.38517i	−0.617761	+	0.0708716i
$383$	−12.6923	−	21.9837i	−0.648545	−	1.12331i	−0.983471	−	0.181068i	$-0.942045\pi$
$383$	−12.6923	−	21.9837i	−0.648545	−	1.12331i	0.334926	−	0.942245i	$-0.391289\pi$
$384$		0			0
$385$	0.245526	+	21.4667i	0.0125132	+	1.09404i
$386$	−9.87688	−	4.28546i	−0.502720	−	0.218124i
$387$		0			0
$388$	14.8776	−	13.9169i	0.755293	−	0.706522i
$389$	−15.9336	+	27.5978i	−0.807865	+	1.39926i	0.106475	+	0.994315i	$0.466043\pi$
$389$	−15.9336	+	27.5978i	−0.807865	+	1.39926i	−0.914340	+	0.404947i	$0.867290\pi$
$390$		0			0
$391$	−8.76301	−	15.1780i	−0.443164	−	0.767583i
$392$	7.07734	+	18.4908i	0.357460	+	0.933929i
$393$		0			0
$394$	−16.3547	+	12.1215i	−0.823938	+	0.610674i
$395$	−9.37303			−0.471608
$396$		0			0
$397$		−	10.3571i		−	0.519806i	−0.965635	−	0.259903i	$-0.916309\pi$
$397$		−	10.3571i		−	0.519806i	0.965635	−	0.259903i	$-0.0836906\pi$
$398$	−24.9041	+	18.4581i	−1.24833	+	0.925220i
$399$		0			0
$400$	8.12752	−	3.99540i	0.406376	−	0.199770i
$401$	−9.69923	−	16.7996i	−0.484356	−	0.838930i	0.515482	−	0.856900i	$-0.327613\pi$
$401$	−9.69923	−	16.7996i	−0.484356	−	0.838930i	−0.999839	+	0.0179704i	$0.994280\pi$
$402$		0			0
$403$	−0.611303	−	0.352936i	−0.0304512	−	0.0175810i
$404$	1.42757	−	1.33539i	0.0710242	−	0.0664380i
$405$		0			0
$406$	−31.1715	+	3.93779i	−1.54701	+	0.195429i
$407$	−16.8870	−	9.74974i	−0.837060	−	0.483277i
$408$		0			0
$409$	14.1825	−	8.18830i	0.701282	−	0.404885i	−0.106543	−	0.994308i	$-0.533978\pi$
$409$	14.1825	−	8.18830i	0.701282	−	0.404885i	0.807825	+	0.589423i	$0.200645\pi$
$410$	−2.06246	−	17.9777i	−0.101858	−	0.887855i
$411$		0			0
$412$	25.4614	−	5.91995i	1.25439	−	0.291655i
$413$	11.5793	−	6.86310i	0.569782	−	0.337711i
$414$		0			0
$415$			3.99405i			0.196060i
$416$	−4.81574	+	3.09435i	−0.236111	+	0.151713i
$417$		0			0
$418$	−19.6516	+	2.25450i	−0.961192	+	0.110271i
$419$	−10.4437	−	18.0890i	−0.510209	−	0.883707i	−0.999930	−	0.0118282i	$-0.996235\pi$
$419$	−10.4437	−	18.0890i	−0.510209	−	0.883707i	0.489722	−	0.871879i	$-0.337098\pi$
$420$		0			0
$421$	−2.68795	+	4.65567i	−0.131003	+	0.226904i	−0.924063	−	0.382239i	$-0.875153\pi$
$421$	−2.68795	+	4.65567i	−0.131003	+	0.226904i	0.793061	+	0.609143i	$0.208486\pi$
$422$	−0.945502	+	2.17914i	−0.0460263	+	0.106079i
$423$		0			0
$424$	−8.19100	−	22.9603i	−0.397790	−	1.11505i
$425$	−15.0217	−	8.67279i	−0.728660	−	0.420692i
$426$		0			0
$427$	−7.67685	+	13.6550i	−0.371509	+	0.660813i
$428$	−1.97365	−	0.600050i	−0.0953999	−	0.0290045i
$429$		0			0
$430$	14.5567	−	10.7889i	0.701985	−	0.520287i
$431$			0.569062i			0.0274108i	0.999906	+	0.0137054i	$0.00436270\pi$
$431$			0.569062i			0.0274108i	−0.999906	+	0.0137054i	$0.995637\pi$
$432$		0			0
$433$		−	29.1119i		−	1.39903i	−0.714619	−	0.699514i	$-0.753400\pi$
$433$		−	29.1119i		−	1.39903i	0.714619	−	0.699514i	$-0.246600\pi$
$434$	−1.01145	+	2.40612i	−0.0485510	+	0.115497i
$435$		0			0
$436$	−0.490087	+	1.61196i	−0.0234709	+	0.0771991i
$437$	−5.64873	+	3.26129i	−0.270215	+	0.156009i
$438$		0			0
$439$	−0.679870	+	1.17757i	−0.0324484	+	0.0562023i	−0.881794	−	0.471636i	$-0.843664\pi$
$439$	−0.679870	+	1.17757i	−0.0324484	+	0.0562023i	0.849345	+	0.527838i	$0.176997\pi$
$440$	7.71145	+	21.6160i	0.367629	+	1.03050i
$441$		0			0
$442$	10.0575	+	4.36381i	0.478384	+	0.207565i
$443$	−3.04716	−	1.75928i	−0.144775	−	0.0835858i	0.425863	−	0.904788i	$-0.359971\pi$
$443$	−3.04716	−	1.75928i	−0.144775	−	0.0835858i	−0.570638	+	0.821202i	$0.693304\pi$
$444$		0			0
$445$	−6.77940	−	11.7423i	−0.321374	−	0.556637i
$446$	1.31851	+	11.4929i	0.0624333	+	0.544207i
$447$		0			0
$448$	13.5833	+	16.2325i	0.641753	+	0.766912i
$449$	−13.2772			−0.626591			−0.313295	−	0.949656i	$-0.601433\pi$
$449$	−13.2772			−0.626591			−0.313295	+	0.949656i	$0.601433\pi$
$450$		0			0
$451$	−37.9495			−1.78697
$452$	−12.4348	+	2.89118i	−0.584883	+	0.135989i
$453$		0			0
$454$	4.35408	+	37.9529i	0.204347	+	1.78122i
$455$	−3.86009	−	2.17014i	−0.180964	−	0.101738i
$456$		0			0
$457$	11.7494	−	20.3506i	0.549614	−	0.951959i	−0.448687	−	0.893689i	$-0.648108\pi$
$457$	11.7494	−	20.3506i	0.549614	−	0.951959i	0.998301	−	0.0582701i	$-0.0185584\pi$
$458$	6.77391	−	15.6121i	0.316524	−	0.729507i
$459$		0			0
$460$	5.16986	+	5.52674i	0.241046	+	0.257685i
$461$	13.3984	+	7.73555i	0.624024	+	0.360280i	0.778434	−	0.627726i	$-0.216014\pi$
$461$	13.3984	+	7.73555i	0.624024	+	0.360280i	−0.154410	+	0.988007i	$0.549348\pi$
$462$		0			0
$463$	−18.2044	+	10.5103i	−0.846031	+	0.488456i	−0.859310	−	0.511456i	$-0.829106\pi$
$463$	−18.2044	+	10.5103i	−0.846031	+	0.488456i	0.0132786	+	0.999912i	$0.495773\pi$
$464$	−30.1432	+	14.8181i	−1.39936	+	0.687913i
$465$		0			0
$466$	−14.7413	+	10.9258i	−0.682878	+	0.506126i
$467$	29.6578			1.37240			0.686199	−	0.727414i	$-0.259278\pi$
$467$	29.6578			1.37240			0.686199	+	0.727414i	$0.259278\pi$
$468$		0			0
$469$	3.40495	+	5.74479i	0.157226	+	0.265270i
$470$	−10.3273	−	13.9338i	−0.476361	−	0.642720i
$471$		0			0
$472$	9.31988	−	10.9639i	0.428982	−	0.504653i
$473$	−18.9992	−	32.9076i	−0.873586	−	1.51310i
$474$		0			0
$475$	−3.22772	+	5.59057i	−0.148098	+	0.256513i
$476$	11.3477	−	38.9179i	0.520119	−	1.78380i
$477$		0			0
$478$	−3.67288	+	8.46504i	−0.167994	+	0.387182i
$479$	−2.16539	+	3.75057i	−0.0989393	+	0.171368i	−0.911246	−	0.411863i	$-0.864878\pi$
$479$	−2.16539	+	3.75057i	−0.0989393	+	0.171368i	0.812307	+	0.583231i	$0.198212\pi$
$480$		0			0
$481$	3.48334	−	2.01111i	0.158827	−	0.0916987i
$482$	−32.4733	+	3.72545i	−1.47912	+	0.169690i
$483$		0			0
$484$	25.4518	−	5.91773i	1.15690	−	0.268988i
$485$	16.8482			0.765037
$486$		0			0
$487$		−	33.3117i		−	1.50950i	−0.656015	−	0.754748i	$-0.727759\pi$
$487$		−	33.3117i		−	1.50950i	0.656015	−	0.754748i	$-0.272241\pi$
$488$	−3.01341	+	16.4733i	−0.136411	+	0.745711i
$489$		0			0
$490$	−6.17227	+	15.1664i	−0.278835	+	0.685148i
$491$	27.8604	−	16.0852i	1.25732	−	0.725916i	0.284770	−	0.958596i	$-0.408083\pi$
$491$	27.8604	−	16.0852i	1.25732	−	0.725916i	0.972553	+	0.232680i	$0.0747495\pi$
$492$		0			0
$493$	55.7123	+	32.1655i	2.50916	+	1.44866i
$494$	1.62406	−	3.74304i	0.0730699	−	0.168407i
$495$		0			0
$496$	−0.185980	+	2.78407i	−0.00835075	+	0.125008i
$497$	−2.65516	+	0.0303684i	−0.119100	+	0.00136221i
$498$		0			0
$499$	29.5577	−	17.0652i	1.32319	−	0.763941i	0.338950	−	0.940805i	$-0.389928\pi$
$499$	29.5577	−	17.0652i	1.32319	−	0.763941i	0.984235	+	0.176863i	$0.0565950\pi$
$500$	22.9913	+	6.99007i	1.02820	+	0.312605i
$501$		0			0
$502$	−6.30742	+	4.67484i	−0.281514	+	0.208648i
$503$	−9.76180			−0.435257			−0.217629	−	0.976032i	$-0.569832\pi$
$503$	−9.76180			−0.435257			−0.217629	+	0.976032i	$0.569832\pi$
$504$		0			0
$505$	1.61666			0.0719405
$506$	12.7507	−	9.45037i	0.566837	−	0.420120i
$507$		0			0
$508$	−34.2653	−	10.4177i	−1.52028	−	0.462211i
$509$	−12.0256	+	6.94300i	−0.533027	+	0.307743i	−0.742248	−	0.670125i	$-0.766240\pi$
$509$	−12.0256	+	6.94300i	−0.533027	+	0.307743i	0.209221	+	0.977868i	$0.432907\pi$
$510$		0			0
$511$	15.5999	−	0.178424i	0.690097	−	0.00789300i
$512$	19.3753	+	11.6875i	0.856276	+	0.516518i
$513$		0			0
$514$	11.0272	−	25.4149i	0.486389	−	1.12100i
$515$	18.7225	+	10.8094i	0.825012	+	0.476321i
$516$		0			0
$517$	−31.4996	+	18.1863i	−1.38535	+	0.799833i
$518$	−8.99201	−	11.8466i	−0.395086	−	0.520510i
$519$		0			0
$520$	−4.65677	−	0.851849i	−0.204213	−	0.0373561i
$521$		−	15.9160i		−	0.697291i	−0.937255	−	0.348646i	$-0.886642\pi$
$521$		−	15.9160i		−	0.697291i	0.937255	−	0.348646i	$-0.113358\pi$
$522$		0			0
$523$	28.0511			1.22659			0.613294	−	0.789855i	$-0.289844\pi$
$523$	28.0511			1.22659			0.613294	+	0.789855i	$0.289844\pi$
$524$	19.5718	−	4.55058i	0.854997	−	0.198793i
$525$		0			0
$526$	18.6157	−	2.13565i	0.811682	−	0.0931189i
$527$	4.62815	−	2.67206i	0.201605	−	0.116397i
$528$		0			0
$529$	−8.88328	+	15.3863i	−0.386229	+	0.668969i
$530$	8.02475	−	18.4950i	0.348573	−	0.803370i
$531$		0			0
$532$	−14.4839	−	4.22321i	−0.627958	−	0.183100i
$533$	3.91398	−	6.77921i	0.169533	−	0.293640i
$534$		0			0
$535$	−0.853014	−	1.47746i	−0.0368790	−	0.0638763i
$536$	5.43944	+	4.62382i	0.234948	+	0.199718i
$537$		0			0
$538$	−19.8159	−	26.7361i	−0.854324	−	1.15268i
$539$	30.1238	+	16.4851i	1.29753	+	0.710063i
$540$		0			0
$541$	4.98478			0.214313			0.107156	−	0.994242i	$-0.465825\pi$
$541$	4.98478			0.214313			0.107156	+	0.994242i	$0.465825\pi$
$542$	23.0582	−	17.0899i	0.990434	−	0.734076i
$543$		0			0
$544$	−2.05870	−	43.2886i	−0.0882661	−	1.85598i
$545$	−1.20671	+	0.696694i	−0.0516897	+	0.0298431i
$546$		0			0
$547$	−24.9146	−	14.3844i	−1.06527	−	0.615034i	−0.138384	−	0.990379i	$-0.544191\pi$
$547$	−24.9146	−	14.3844i	−1.06527	−	0.615034i	−0.926885	+	0.375345i	$0.877524\pi$
$548$	5.40243	+	5.77536i	0.230780	+	0.246711i
$549$		0			0
$550$	6.25220	−	14.4097i	0.266595	−	0.614432i
$551$	11.9709	−	20.7342i	0.509978	−	0.883308i
$552$		0			0
$553$	−7.34738	+	13.0690i	−0.312442	+	0.555749i
$554$	−3.04610	−	26.5517i	−0.129417	−	1.12807i
$555$		0			0
$556$	18.8983	−	4.39399i	0.801467	−	0.186347i
$557$	24.8923			1.05472			0.527360	−	0.849642i	$-0.323182\pi$
$557$	24.8923			1.05472			0.527360	+	0.849642i	$0.323182\pi$
$558$		0			0
$559$	7.83806			0.331515
$560$	−0.966917	+	17.4781i	−0.0408597	+	0.738584i
$561$		0			0
$562$	−0.344017	−	2.99866i	−0.0145115	−	0.126491i
$563$	5.94575	+	10.2983i	0.250584	+	0.434024i	0.963687	−	0.267036i	$-0.0860442\pi$
$563$	5.94575	+	10.2983i	0.250584	+	0.434024i	−0.713103	+	0.701059i	$0.752711\pi$
$564$		0			0
$565$	−9.14366	−	5.27909i	−0.384677	−	0.222093i
$566$	0.318411	+	0.138155i	0.0133838	+	0.00580708i
$567$		0			0
$568$	−2.67363	+	0.953807i	−0.112183	+	0.0400208i
$569$	−2.96159	+	5.12962i	−0.124156	+	0.215045i	−0.921403	−	0.388609i	$-0.872956\pi$
$569$	−2.96159	+	5.12962i	−0.124156	+	0.215045i	0.797247	+	0.603654i	$0.206289\pi$
$570$		0			0
$571$	28.8922	−	16.6809i	1.20910	−	0.698074i	0.246537	−	0.969133i	$-0.420707\pi$
$571$	28.8922	−	16.6809i	1.20910	−	0.698074i	0.962563	+	0.271059i	$0.0873739\pi$
$572$	−2.88792	+	9.49877i	−0.120750	+	0.397164i
$573$		0			0
$574$	−26.6833	−	11.2167i	−1.11374	−	0.468176i
$575$		−	5.17956i		−	0.216003i
$576$		0			0
$577$			29.0803i			1.21063i	0.795987	+	0.605314i	$0.206952\pi$
$577$			29.0803i			1.21063i	−0.795987	+	0.605314i	$0.793048\pi$
$578$	−47.3692	+	35.1084i	−1.97030	+	1.46032i
$579$		0			0
$580$	−26.5774	−	8.08034i	−1.10357	−	0.335518i
$581$	5.56897	+	3.13088i	0.231040	+	0.129891i
$582$		0			0
$583$	−36.6162	−	21.1403i	−1.51649	−	0.875544i
$584$	15.7084	−	5.60391i	0.650018	−	0.231891i
$585$		0			0
$586$	−6.26782	+	14.4457i	−0.258921	+	0.596747i
$587$	−7.47781	+	12.9519i	−0.308642	+	0.534584i	−0.978066	−	0.208297i	$-0.933208\pi$
$587$	−7.47781	+	12.9519i	−0.308642	+	0.534584i	0.669423	+	0.742881i	$0.266541\pi$
$588$		0			0
$589$	−0.994450	−	1.72244i	−0.0409756	−	0.0709718i
$590$	11.8232	−	1.35640i	0.486753	−	0.0558420i
$591$		0			0
$592$	−13.2090	−	8.84991i	−0.542886	−	0.363729i
$593$		−	15.6604i		−	0.643096i	−0.946893	−	0.321548i	$-0.895797\pi$
$593$		−	15.6604i		−	0.643096i	0.946893	−	0.321548i	$-0.104203\pi$
$594$		0			0
$595$	28.8411	−	17.0942i	1.18237	−	0.700793i
$596$	13.5138	−	3.14205i	0.553546	−	0.128703i
$597$		0			0
$598$	0.373130	+	3.25243i	0.0152584	+	0.133002i
$599$	−33.5225	+	19.3542i	−1.36969	+	0.790791i	−0.990888	−	0.134686i	$-0.956997\pi$
$599$	−33.5225	+	19.3542i	−1.36969	+	0.790791i	−0.378803	+	0.925477i	$0.623664\pi$
$600$		0			0
$601$	−22.3109	−	12.8812i	−0.910081	−	0.525435i	−0.0296235	−	0.999561i	$-0.509431\pi$
$601$	−22.3109	−	12.8812i	−0.910081	−	0.525435i	−0.880457	+	0.474126i	$0.842764\pi$
$602$	−3.63238	−	28.7538i	−0.148045	−	1.17192i
$603$		0			0
$604$	18.2990	−	17.1174i	0.744576	−	0.696496i
$605$	18.7155	+	10.8054i	0.760893	+	0.439302i
$606$		0			0
$607$	3.14595	+	5.44895i	0.127690	+	0.221166i	0.922781	−	0.385324i	$-0.125910\pi$
$607$	3.14595	+	5.44895i	0.127690	+	0.221166i	−0.795091	+	0.606490i	$0.792577\pi$
$608$	−16.1106	+	0.766178i	−0.653369	+	0.0310726i
$609$		0			0
$610$	−11.1269	+	8.24688i	−0.450516	+	0.333906i
$611$		−	7.50270i		−	0.303527i
$612$		0			0
$613$	22.1645			0.895217			0.447608	−	0.894230i	$-0.352276\pi$
$613$	22.1645			0.895217			0.447608	+	0.894230i	$0.352276\pi$
$614$	−26.5710	+	19.6935i	−1.07232	+	0.794764i
$615$		0			0
$616$	36.1845	+	6.19230i	1.45791	+	0.249495i
$617$	20.1769	+	34.9474i	0.812291	+	1.40693i	0.911257	+	0.411838i	$0.135113\pi$
$617$	20.1769	+	34.9474i	0.812291	+	1.40693i	−0.0989666	+	0.995091i	$0.531554\pi$
$618$		0			0
$619$	−19.4800	+	33.7403i	−0.782966	+	1.35614i	0.147241	+	0.989101i	$0.452961\pi$
$619$	−19.4800	+	33.7403i	−0.782966	+	1.35614i	−0.930207	+	0.367035i	$0.880373\pi$
$620$	−1.68524	+	1.57642i	−0.0676809	+	0.0633106i
$621$		0			0
$622$	39.7836	+	17.2616i	1.59518	+	0.692127i
$623$	−21.6867	+	0.248042i	−0.868859	+	0.00993759i
$624$		0			0
$625$	4.27658	+	7.40725i	0.171063	+	0.296290i
$626$	−22.1559	+	2.54180i	−0.885527	+	0.101591i
$627$		0			0
$628$	0.756357	+	3.25305i	0.0301819	+	0.129811i
$629$			30.4520i			1.21420i
$630$		0			0
$631$		−	1.06032i		−	0.0422108i	−0.999777	−	0.0211054i	$-0.993281\pi$
$631$		−	1.06032i		−	0.0422108i	0.999777	−	0.0211054i	$-0.00671856\pi$
$632$	−2.88408	+	15.7663i	−0.114722	+	0.627149i
$633$		0			0
$634$	−1.06820	−	9.31104i	−0.0424235	−	0.369789i
$635$	−14.8095	−	25.6508i	−0.587698	−	1.01792i
$636$		0			0
$637$	−6.05173	+	3.68104i	−0.239778	+	0.145848i
$638$	−23.1881	+	53.4425i	−0.918024	+	2.11581i
$639$		0			0
$640$	5.09904	+	18.0053i	0.201557	+	0.711724i
$641$	13.7294	−	23.7800i	0.542278	−	0.939253i	−0.456495	−	0.889726i	$-0.650895\pi$
$641$	13.7294	−	23.7800i	0.542278	−	0.939253i	0.998773	−	0.0495272i	$-0.0157714\pi$
$642$		0			0
$643$	−0.0203966	−	0.0353280i	−0.000804364	−	0.00139320i	0.865623	−	0.500696i	$-0.166923\pi$
$643$	−0.0203966	−	0.0353280i	−0.000804364	−	0.00139320i	−0.866427	+	0.499303i	$0.833589\pi$
$644$	11.7586	−	2.87609i	0.463353	−	0.113334i
$645$		0			0
$646$	18.3939	+	24.8176i	0.723699	+	0.976434i
$647$	12.6901			0.498899			0.249449	−	0.968388i	$-0.419750\pi$
$647$	12.6901			0.498899			0.249449	+	0.968388i	$0.419750\pi$
$648$		0			0
$649$		−	24.9578i		−	0.979680i
$650$	1.92929	+	2.60305i	0.0756729	+	0.102100i
$651$		0			0
$652$	13.5269	+	4.11260i	0.529755	+	0.161062i
$653$	3.40787	+	5.90260i	0.133360	+	0.230987i	0.924970	−	0.380041i	$-0.124090\pi$
$653$	3.40787	+	5.90260i	0.133360	+	0.230987i	−0.791610	+	0.611027i	$0.790757\pi$
$654$		0			0
$655$	14.3917	+	8.30905i	0.562330	+	0.324661i
$656$	−30.8747	−	2.06248i	−1.20545	−	0.0805261i
$657$		0			0
$658$	−27.5235	+	3.47696i	−1.07298	+	0.135546i
$659$	−21.9583	−	12.6776i	−0.855375	−	0.493851i	0.00708581	−	0.999975i	$-0.497744\pi$
$659$	−21.9583	−	12.6776i	−0.855375	−	0.493851i	−0.862461	+	0.506124i	$0.831078\pi$
$660$		0			0
$661$	−27.4120	+	15.8263i	−1.06620	+	0.615572i	−0.927141	−	0.374712i	$-0.877742\pi$
$661$	−27.4120	+	15.8263i	−1.06620	+	0.615572i	−0.139061	+	0.990284i	$0.544408\pi$
$662$	11.1809	−	1.28271i	0.434558	−	0.0498540i
$663$		0			0
$664$	6.71835	+	1.22897i	0.260723	+	0.0476932i
$665$	−6.36187	−	10.7337i	−0.246703	−	0.416234i
$666$		0			0
$667$			19.2099i			0.743810i
$668$	−2.25433	+	0.524147i	−0.0872225	+	0.0202798i
$669$		0			0
$670$	0.672941	+	5.86576i	0.0259980	+	0.226614i
$671$	14.5228	+	25.1541i	0.560645	+	0.971065i
$672$		0			0
$673$	−2.22066	+	3.84630i	−0.0856002	+	0.148264i	−0.905647	−	0.424033i	$-0.860614\pi$
$673$	−2.22066	+	3.84630i	−0.0856002	+	0.148264i	0.820047	+	0.572297i	$0.193947\pi$
$674$	−41.5794	−	18.0408i	−1.60158	−	0.694905i
$675$		0			0
$676$	16.3625	+	17.4920i	0.629328	+	0.672770i
$677$	−5.61421	−	3.24137i	−0.215772	−	0.124576i	0.388219	−	0.921567i	$-0.373090\pi$
$677$	−5.61421	−	3.24137i	−0.215772	−	0.124576i	−0.603991	+	0.796991i	$0.706424\pi$
$678$		0			0
$679$	13.2070	−	23.4917i	0.506840	−	0.901529i
$680$	23.2134	−	27.3081i	0.890192	−	1.04722i
$681$		0			0
$682$	2.88165	+	3.88801i	0.110344	+	0.148879i
$683$		−	28.5921i		−	1.09405i	−0.837117	−	0.547024i	$-0.815761\pi$
$683$		−	28.5921i		−	1.09405i	0.837117	−	0.547024i	$-0.184239\pi$
$684$		0			0
$685$			6.54035i			0.249894i
$686$	16.3084	+	20.4948i	0.622657	+	0.782495i
$687$		0			0
$688$	−13.6688	−	27.8054i	−0.521119	−	1.06007i
$689$	7.55293	−	4.36069i	0.287744	−	0.166129i
$690$		0			0
$691$	−4.98156	+	8.62831i	−0.189507	+	0.328236i	−0.945086	−	0.326822i	$-0.894022\pi$
$691$	−4.98156	+	8.62831i	−0.189507	+	0.328236i	0.755579	+	0.655058i	$0.227356\pi$
$692$	−2.19836	+	2.05640i	−0.0835690	+	0.0781728i
$693$		0			0
$694$	−1.52794	+	3.52151i	−0.0579999	+	0.133675i
$695$	13.8965	+	8.02313i	0.527123	+	0.304335i
$696$		0			0
$697$	29.6326	+	51.3251i	1.12241	+	1.94408i
$698$	−0.312954	+	0.0359032i	−0.0118455	+	0.00135896i
$699$		0			0
$700$	8.65516	−	8.28389i	0.327134	−	0.313102i
$701$	13.0365			0.492382			0.246191	−	0.969221i	$-0.420821\pi$
$701$	13.0365			0.492382			0.246191	+	0.969221i	$0.420821\pi$
$702$		0			0
$703$	11.3332			0.427440
$704$	38.7329	−	6.32010i	1.45980	−	0.238198i
$705$		0			0
$706$	39.8101	−	4.56715i	1.49827	−	0.171887i
$707$	1.26728	−	2.25414i	0.0476608	−	0.0847755i
$708$		0			0
$709$	−1.46945	+	2.54516i	−0.0551862	+	0.0955853i	−0.892299	−	0.451445i	$-0.850909\pi$
$709$	−1.46945	+	2.54516i	−0.0551862	+	0.0955853i	0.837113	+	0.547031i	$0.184242\pi$
$710$	−2.15366	−	0.934447i	−0.0808254	−	0.0350692i
$711$		0			0
$712$	−21.8376	+	7.79047i	−0.818397	+	0.291960i
$713$	1.38201	+	0.797904i	0.0517567	+	0.0298817i
$714$		0			0
$715$	−7.11073	+	4.10538i	−0.265926	+	0.153533i
$716$	−2.45098	−	0.745174i	−0.0915975	−	0.0278485i
$717$		0			0
$718$	18.4148	+	24.8458i	0.687235	+	0.927236i
$719$	−52.8108			−1.96951			−0.984754	−	0.173951i	$-0.944347\pi$
$719$	−52.8108			−1.96951			−0.984754	+	0.173951i	$0.944347\pi$
$720$		0			0
$721$	29.7481	−	17.6317i	1.10788	−	0.656640i
$722$	−12.3510	+	9.15413i	−0.459656	+	0.340681i
$723$		0			0
$724$	50.9382	+	15.4868i	1.89310	+	0.575561i
$725$	9.50606	+	16.4650i	0.353046	+	0.611494i
$726$		0			0
$727$	13.3309	−	23.0897i	0.494414	−	0.856351i	−0.505565	−	0.862789i	$-0.668716\pi$
$727$	13.3309	−	23.0897i	0.494414	−	0.856351i	0.999979	+	0.00643778i	$0.00204922\pi$
$728$	−4.83812	+	5.82526i	−0.179313	+	0.215899i
$729$		0			0
$730$	12.6534	+	5.49017i	0.468324	+	0.203200i
$731$	−29.6708	+	51.3913i	−1.09741	+	1.90078i
$732$		0			0
$733$	−23.6033	+	13.6274i	−0.871807	+	0.503338i	−0.867948	−	0.496654i	$-0.834562\pi$
$733$	−23.6033	+	13.6274i	−0.871807	+	0.503338i	−0.00385894	+	0.999993i	$0.501228\pi$
$734$	1.21158	+	10.5609i	0.0447203	+	0.389810i
$735$		0			0
$736$	10.8872	−	6.99560i	0.401309	−	0.257861i
$737$	12.3822			0.456103
$738$		0			0
$739$			42.7029i			1.57085i	0.618957	+	0.785425i	$0.287556\pi$
$739$			42.7029i			1.57085i	−0.618957	+	0.785425i	$0.712444\pi$
$740$	−2.97789	−	12.8077i	−0.109469	−	0.470822i
$741$		0			0
$742$	−19.4974	−	25.6870i	−0.715771	−	0.942998i
$743$	31.9011	−	18.4181i	1.17034	−	0.675695i	0.216578	−	0.976265i	$-0.430510\pi$
$743$	31.9011	−	18.4181i	1.17034	−	0.675695i	0.953760	+	0.300571i	$0.0971772\pi$
$744$		0			0
$745$	9.93708	+	5.73718i	0.364067	+	0.210194i
$746$	13.0871	+	5.67835i	0.479154	+	0.207899i
$747$		0			0
$748$	−51.3479	−	54.8924i	−1.87746	−	2.00707i
$749$	−2.72872	+	0.0312097i	−0.0997051	+	0.00114038i
$750$		0			0
$751$	20.8062	−	12.0125i	0.759228	−	0.438341i	−0.0697904	−	0.997562i	$-0.522233\pi$
$751$	20.8062	−	12.0125i	0.759228	−	0.438341i	0.829019	+	0.559221i	$0.188900\pi$
$752$	−26.6156	+	13.0840i	−0.970573	+	0.477123i
$753$		0			0
$754$	−7.15532	−	9.65414i	−0.260581	−	0.351583i
$755$	20.7228			0.754181
$756$		0			0
$757$	45.4741			1.65279			0.826393	−	0.563094i	$-0.190389\pi$
$757$	45.4741			1.65279			0.826393	+	0.563094i	$0.190389\pi$
$758$	17.4421	+	23.5333i	0.633525	+	0.854769i
$759$		0			0
$760$	−10.1632	−	8.63923i	−0.368656	−	0.313378i
$761$	−33.8844	+	19.5632i	−1.22831	+	0.709164i	−0.966676	−	0.256003i	$-0.917594\pi$
$761$	−33.8844	+	19.5632i	−1.22831	+	0.709164i	−0.261633	+	0.965167i	$0.584261\pi$
$762$		0			0
$763$	0.0254903	+	2.22866i	0.000922812	+	0.0806829i
$764$	−12.5517	+	11.7412i	−0.454105	+	0.424782i
$765$		0			0
$766$	−32.9328	−	14.2892i	−1.18991	−	0.516288i
$767$	4.45841	+	2.57406i	0.160984	+	0.0929440i
$768$		0			0
$769$	−14.2130	+	8.20587i	−0.512534	+	0.295911i	−0.733874	−	0.679285i	$-0.762290\pi$
$769$	−14.2130	+	8.20587i	−0.512534	+	0.295911i	0.221341	+	0.975196i	$0.428957\pi$
$770$	18.3559	+	24.1831i	0.661500	+	0.871498i
$771$		0			0
$772$	−14.8306	+	3.44821i	−0.533763	+	0.124104i
$773$			43.6024i			1.56827i	0.620591	+	0.784134i	$0.286893\pi$
$773$			43.6024i			1.56827i	−0.620591	+	0.784134i	$0.713107\pi$
$774$		0			0
$775$	1.57938			0.0567330
$776$	5.18418	−	28.3402i	0.186101	−	1.01735i
$777$		0			0
$778$	5.13655	+	44.7733i	0.184154	+	1.60520i
$779$	19.1015	−	11.0282i	0.684380	−	0.395127i
$780$		0			0
$781$	−2.46170	+	4.26379i	−0.0880866	+	0.152571i
$782$	−22.7375	−	9.86553i	−0.813091	−	0.352790i
$783$		0			0
$784$	23.6120	+	15.0490i	0.843287	+	0.537464i
$785$	−1.38106	+	2.39206i	−0.0492921	+	0.0853764i
$786$		0			0
$787$	2.89125	+	5.00779i	0.103062	+	0.178508i	0.912945	−	0.408083i	$-0.133803\pi$
$787$	2.89125	+	5.00779i	0.103062	+	0.178508i	−0.809883	+	0.586592i	$0.800469\pi$
$788$	−8.37431	+	27.5443i	−0.298322	+	0.981224i
$789$		0			0
$790$	−10.6494	+	7.89294i	−0.378887	+	0.280818i
$791$	−14.5283	+	8.61095i	−0.516567	+	0.306170i
$792$		0			0
$793$	−5.99131			−0.212758
$794$	−8.72159	−	11.7674i	−0.309517	−	0.417609i
$795$		0			0
$796$	−12.7520	+	41.9431i	−0.451982	+	1.48663i
$797$	−11.1404	+	6.43191i	−0.394613	+	0.227830i	−0.684157	−	0.729335i	$-0.739830\pi$
$797$	−11.1404	+	6.43191i	−0.394613	+	0.227830i	0.289544	+	0.957165i	$0.406496\pi$
$798$		0			0
$799$	49.1924	+	28.4013i	1.74030	+	1.00476i
$800$	5.86976	−	11.3836i	0.207527	−	0.402470i
$801$		0			0
$802$	−25.1667	−	10.9195i	−0.888668	−	0.385582i
$803$	14.4633	−	25.0511i	0.510398	−	0.884035i
$804$		0			0
$805$	8.72674	+	4.90617i	0.307577	+	0.172920i
$806$	−0.991749	+	0.113777i	−0.0349329	+	0.00400762i
$807$		0			0
$808$	0.497446	−	2.71937i	0.0175001	−	0.0956671i
$809$	−11.6895			−0.410980			−0.205490	−	0.978659i	$-0.565879\pi$
$809$	−11.6895			−0.410980			−0.205490	+	0.978659i	$0.565879\pi$
$810$		0			0
$811$	23.0355			0.808885			0.404443	−	0.914563i	$-0.367466\pi$
$811$	23.0355			0.808885			0.404443	+	0.914563i	$0.367466\pi$
$812$	−32.1001	+	30.7232i	−1.12649	+	1.07817i
$813$		0			0
$814$	−27.3967	+	3.14305i	−0.960255	+	0.110164i
$815$	5.84635	+	10.1262i	0.204789	+	0.354705i
$816$		0			0
$817$	19.1261	+	11.0425i	0.669138	+	0.386327i
$818$	9.21851	−	21.2463i	0.322318	−	0.742859i
$819$		0			0
$820$	−17.4821	−	18.6889i	−0.610503	−	0.652646i
$821$	−5.85488	+	10.1410i	−0.204337	+	0.353922i	−0.949921	−	0.312489i	$-0.898837\pi$
$821$	−5.85488	+	10.1410i	−0.204337	+	0.353922i	0.745584	+	0.666411i	$0.232170\pi$
$822$		0			0
$823$	30.7319	−	17.7431i	1.07125	−	0.618484i	0.142724	−	0.989763i	$-0.454414\pi$
$823$	30.7319	−	17.7431i	1.07125	−	0.618484i	0.928521	+	0.371279i	$0.121081\pi$
$824$	23.9434	−	28.1669i	0.834106	−	0.981239i
$825$		0			0
$826$	7.37677	−	17.5485i	0.256671	−	0.610591i
$827$			28.8739i			1.00405i	0.864854	+	0.502023i	$0.167411\pi$
$827$			28.8739i			1.00405i	−0.864854	+	0.502023i	$0.832589\pi$
$828$		0			0
$829$		−	31.4981i		−	1.09397i	−0.837141	−	0.546987i	$-0.815775\pi$
$829$		−	31.4981i		−	1.09397i	0.837141	−	0.546987i	$-0.184225\pi$
$830$	3.36335	+	4.53793i	0.116744	+	0.157514i
$831$		0			0
$832$	−2.86577	+	7.57100i	−0.0993528	+	0.262477i
$833$	−1.22657	−	53.6135i	−0.0424981	−	1.85760i
$834$		0			0
$835$	−1.65767	−	0.957057i	−0.0573661	−	0.0331203i
$836$	−20.4291	+	19.1099i	−0.706555	+	0.660931i
$837$		0			0
$838$	−27.0984	−	11.7577i	−0.936100	−	0.406162i
$839$	−7.70959	+	13.3534i	−0.266165	+	0.461011i	−0.967868	−	0.251458i	$-0.919090\pi$
$839$	−7.70959	+	13.3534i	−0.266165	+	0.461011i	0.701703	+	0.712469i	$0.252423\pi$
$840$		0			0
$841$	−20.7559	−	35.9503i	−0.715722	−	1.23967i
$842$	0.866522	+	7.55314i	0.0298623	+	0.260298i
$843$		0			0
$844$	0.760780	+	3.27207i	0.0261871	+	0.112629i
$845$			19.8090i			0.681450i
$846$		0			0
$847$	29.7369	−	17.6251i	1.02177	−	0.605606i
$848$	−28.6410	−	19.1892i	−0.983536	−	0.658961i
$849$		0			0
$850$	−24.3705	+	2.79587i	−0.835901	+	0.0958975i
$851$	−7.87501	+	4.54664i	−0.269952	+	0.155857i
$852$		0			0
$853$	9.82218	+	5.67084i	0.336305	+	0.194166i	0.658637	−	0.752461i	$-0.271133\pi$
$853$	9.82218	+	5.67084i	0.336305	+	0.194166i	−0.322332	+	0.946627i	$0.604467\pi$
$854$	2.77654	+	21.9790i	0.0950112	+	0.752107i
$855$		0			0
$856$	−2.74770	+	0.980232i	−0.0939144	+	0.0335036i
$857$	0.268417	+	0.154971i	0.00916895	+	0.00529370i	0.504577	−	0.863366i	$-0.331648\pi$
$857$	0.268417	+	0.154971i	0.00916895	+	0.00529370i	−0.495409	+	0.868660i	$0.664982\pi$
$858$		0			0
$859$	−9.88124	−	17.1148i	−0.337144	−	0.583950i	0.646751	−	0.762702i	$-0.276127\pi$
$859$	−9.88124	−	17.1148i	−0.337144	−	0.583950i	−0.983894	+	0.178752i	$0.942794\pi$
$860$	7.45363	−	24.5161i	0.254167	−	0.835991i
$861$		0			0
$862$	0.479202	+	0.646552i	0.0163217	+	0.0220216i
$863$		−	23.9730i		−	0.816051i	−0.912970	−	0.408026i	$-0.866217\pi$
$863$		−	23.9730i		−	0.816051i	0.912970	−	0.408026i	$-0.133783\pi$
$864$		0			0
$865$	−2.48955			−0.0846472
$866$	−24.5148	−	33.0761i	−0.833048	−	1.12397i
$867$		0			0
$868$	0.876993	+	3.58549i	0.0297671	+	0.121699i
$869$	13.8995	+	24.0746i	0.471507	+	0.816674i
$870$		0			0
$871$	−1.27705	+	2.21192i	−0.0432713	+	0.0749481i
$872$	0.800598	+	2.24416i	0.0271117	+	0.0759970i
$873$		0			0
$874$	−3.67161	+	8.46212i	−0.124194	+	0.286236i
$875$	31.7872	−	0.363567i	1.07460	−	0.0122908i
$876$		0			0
$877$	15.6916	+	27.1787i	0.529868	+	0.917759i	0.999393	+	0.0348396i	$0.0110920\pi$
$877$	15.6916	+	27.1787i	0.529868	+	0.917759i	−0.469524	+	0.882919i	$0.655575\pi$
$878$	0.219171	+	1.91043i	0.00739667	+	0.0644739i
$879$		0			0
$880$	26.9642	+	18.0658i	0.908962	+	0.608997i
$881$			2.85106i			0.0960548i	0.998846	+	0.0480274i	$0.0152935\pi$
$881$			2.85106i			0.0960548i	−0.998846	+	0.0480274i	$0.984707\pi$
$882$		0			0
$883$		−	58.5844i		−	1.97152i	−0.168153	−	0.985761i	$-0.553780\pi$
$883$		−	58.5844i		−	1.97152i	0.168153	−	0.985761i	$-0.446220\pi$
$884$	15.1017	−	3.51125i	0.507925	−	0.118096i
$885$		0			0
$886$	−4.94356	+	0.567142i	−0.166082	+	0.0190535i
$887$	11.7716	+	20.3891i	0.395253	+	0.684598i	0.993133	−	0.116987i	$-0.0373237\pi$
$887$	11.7716	+	20.3891i	0.395253	+	0.684598i	−0.597881	+	0.801585i	$0.703990\pi$
$888$		0			0
$889$	−47.3743	+	0.541845i	−1.58888	+	0.0181729i
$890$	−17.5906	−	7.63235i	−0.589638	−	0.255837i
$891$		0			0
$892$	11.1762	+	11.9476i	0.374205	+	0.400037i
$893$	10.5700	−	18.3078i	0.353711	−	0.612646i
$894$		0			0
$895$	−1.05932	−	1.83479i	−0.0354091	−	0.0613304i
$896$	29.1022	+	7.00444i	0.972236	+	0.234002i
$897$		0			0
$898$	−15.0852	+	11.1806i	−0.503399	+	0.373102i
$899$	−5.85758			−0.195361
$900$		0			0
$901$			66.0291i			2.19975i
$902$	−43.1171	+	31.9569i	−1.43564	+	1.06405i
$903$		0			0
$904$	−11.6934	+	13.7561i	−0.388917	+	0.457520i
$905$	22.0156	+	38.1321i	0.731822	+	1.26755i
$906$		0			0
$907$	−16.2312	−	9.37107i	−0.538947	−	0.311161i	0.205705	−	0.978614i	$-0.434051\pi$
$907$	−16.2312	−	9.37107i	−0.538947	−	0.311161i	−0.744652	+	0.667453i	$0.767385\pi$
$908$	36.9067	+	39.4544i	1.22479	+	1.30934i
$909$		0			0
$910$	−6.21317	+	0.784890i	−0.205965	+	0.0260189i
$911$	27.7633	+	16.0291i	0.919838	+	0.531069i	0.883583	−	0.468274i	$-0.155124\pi$
$911$	27.7633	+	16.0291i	0.919838	+	0.531069i	0.0362544	+	0.999343i	$0.488457\pi$
$912$		0			0
$913$	10.2587	−	5.92286i	0.339513	−	0.196018i
$914$	−3.78768	−	33.0158i	−0.125285	−	1.09206i
$915$		0			0
$916$	−5.45050	−	23.4423i	−0.180089	−	0.774555i
$917$	22.8669	−	13.5532i	0.755131	−	0.447567i
$918$		0			0
$919$			40.9560i			1.35101i	0.737354	+	0.675507i	$0.236075\pi$
$919$			40.9560i			1.35101i	−0.737354	+	0.675507i	$0.763925\pi$
$920$	10.5279	+	1.92583i	0.347093	+	0.0634927i
$921$		0			0
$922$	21.7369	−	2.49373i	0.715865	−	0.0821265i
$923$	−0.507783	−	0.879506i	−0.0167139	−	0.0289493i
$924$		0			0
$925$	−4.49983	+	7.79394i	−0.147954	+	0.256263i
$926$	−11.8327	+	27.2713i	−0.388846	+	0.896190i
$927$		0			0
$928$	−21.7697	+	42.2192i	−0.714625	+	1.38591i
$929$	20.6442	+	11.9189i	0.677314	+	0.391047i	0.798842	−	0.601540i	$-0.205446\pi$
$929$	20.6442	+	11.9189i	0.677314	+	0.391047i	−0.121528	+	0.992588i	$0.538779\pi$
$930$		0			0
$931$	−19.9531	+	0.456488i	−0.653937	+	0.0149608i
$932$	−7.54818	+	24.8270i	−0.247249	+	0.813237i
$933$		0			0
$934$	33.6963	−	24.9745i	1.10258	−	0.817191i
$935$		−	62.1633i		−	2.03296i
$936$		0			0
$937$			28.7675i			0.939794i	0.882721	+	0.469897i	$0.155709\pi$
$937$			28.7675i			0.939794i	−0.882721	+	0.469897i	$0.844291\pi$
$938$	8.70623	+	3.65979i	0.284269	+	0.119496i
$939$		0			0
$940$	−23.4671	−	7.13471i	−0.765412	−	0.232709i
$941$	35.9743	−	20.7698i	1.17273	−	0.677075i	0.218407	−	0.975858i	$-0.429914\pi$
$941$	35.9743	−	20.7698i	1.17273	−	0.677075i	0.954321	+	0.298783i	$0.0965807\pi$
$942$		0			0
$943$	−8.84858	+	15.3262i	−0.288149	+	0.499089i
$944$	1.35640	−	20.3050i	0.0441472	−	0.660872i
$945$		0			0
$946$	−49.2976	−	21.3896i	−1.60280	−	0.695437i
$947$	−11.5666	−	6.67800i	−0.375865	−	0.217006i	0.300152	−	0.953891i	$-0.402962\pi$
$947$	−11.5666	−	6.67800i	−0.375865	−	0.217006i	−0.676018	+	0.736885i	$0.736296\pi$
$948$		0			0
$949$	2.98338	+	5.16737i	0.0968447	+	0.167740i
$950$	1.04053	+	9.06987i	0.0337592	+	0.294266i
$951$		0			0
$952$	−19.8795	−	53.7732i	−0.644299	−	1.74280i
$953$	6.70188			0.217095			0.108548	−	0.994091i	$-0.465380\pi$
$953$	6.70188			0.217095			0.108548	+	0.994091i	$0.465380\pi$
$954$		0			0
$955$	−14.2143			−0.459963
$956$	2.95531	+	12.7106i	0.0955815	+	0.411091i
$957$		0			0
$958$	0.698063	+	6.08475i	0.0225534	+	0.196589i
$959$	9.11932	+	5.12688i	0.294478	+	0.165556i
$960$		0			0
$961$	15.2567	−	26.4254i	0.492152	−	0.852432i
$962$	2.26414	−	5.21825i	0.0729987	−	0.168243i
$963$		0			0
$964$	−33.7581	+	31.5782i	−1.08727	+	1.01707i
$965$	−10.9053	−	6.29620i	−0.351055	−	0.202682i
$966$		0			0
$967$	18.7298	−	10.8137i	0.602311	−	0.347744i	−0.167639	−	0.985848i	$-0.553614\pi$
$967$	18.7298	−	10.8137i	0.602311	−	0.347744i	0.769950	+	0.638104i	$0.220281\pi$
$968$	23.9344	−	28.1563i	0.769280	−	0.904978i
$969$		0			0
$970$	19.1424	−	14.1877i	0.614626	−	0.455540i
$971$	25.7885			0.827592			0.413796	−	0.910370i	$-0.364203\pi$
$971$	25.7885			0.827592			0.413796	+	0.910370i	$0.364203\pi$
$972$		0			0
$973$	22.0800	−	13.0869i	0.707853	−	0.419545i
$974$	−28.0514	−	37.8478i	−0.898826	−	1.21272i
$975$		0			0
$976$	10.4483	+	21.2540i	0.334440	+	0.680325i
$977$	−18.8498	−	32.6488i	−0.603058	−	1.04453i	−0.992355	−	0.123414i	$-0.960616\pi$
$977$	−18.8498	−	32.6488i	−0.603058	−	1.04453i	0.389298	−	0.921112i	$-0.372718\pi$
$978$		0			0
$979$	−20.1066	+	34.8257i	−0.642610	+	1.11303i
$980$	5.75872	+	22.4292i	0.183956	+	0.716475i
$981$		0			0
$982$	18.1090	−	41.7365i	0.577881	−	1.33187i
$983$	23.1492	−	40.0956i	0.738345	−	1.27885i	−0.214895	−	0.976637i	$-0.568941\pi$
$983$	23.1492	−	40.0956i	0.738345	−	1.27885i	0.953240	−	0.302214i	$-0.0977258\pi$
$984$		0			0
$985$	−20.6195	+	11.9047i	−0.656992	+	0.379315i
$986$	90.3850	−	10.3693i	2.87844	−	0.330225i
$987$		0			0
$988$	−1.30677	−	5.62034i	−0.0415738	−	0.178807i
$989$	−17.7200			−0.563463
$990$		0			0
$991$			12.6519i			0.401900i	0.979602	+	0.200950i	$0.0644028\pi$
$991$			12.6519i			0.401900i	−0.979602	+	0.200950i	$0.935597\pi$
$992$	2.13313	+	3.31979i	0.0677270	+	0.105403i
$993$		0			0
$994$	−2.99114	+	2.27038i	−0.0948731	+	0.0720122i
$995$	−31.3984	+	18.1279i	−0.995395	+	0.574692i
$996$		0			0
$997$	−12.9778	−	7.49276i	−0.411012	−	0.237298i	0.280212	−	0.959938i	$-0.409595\pi$
$997$	−12.9778	−	7.49276i	−0.411012	−	0.237298i	−0.691225	+	0.722640i	$0.742928\pi$
$998$	19.2122	−	44.2792i	0.608152	−	1.40163i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bi.c.559.32		80
3.2	odd	2		252.2.bi.c.223.10	yes	80
4.3	odd	2	inner	756.2.bi.c.559.22		80
7.6	odd	2	inner	756.2.bi.c.559.31		80
9.4	even	3	inner	756.2.bi.c.307.21		80
9.5	odd	6		252.2.bi.c.139.20	yes	80
12.11	even	2		252.2.bi.c.223.19	yes	80
21.20	even	2		252.2.bi.c.223.9	yes	80
28.27	even	2	inner	756.2.bi.c.559.21		80
36.23	even	6		252.2.bi.c.139.9	✓	80
36.31	odd	6	inner	756.2.bi.c.307.31		80
63.13	odd	6	inner	756.2.bi.c.307.22		80
63.41	even	6		252.2.bi.c.139.19	yes	80
84.83	odd	2		252.2.bi.c.223.20	yes	80
252.139	even	6	inner	756.2.bi.c.307.32		80
252.167	odd	6		252.2.bi.c.139.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.9	✓	80	36.23	even	6
252.2.bi.c.139.10	yes	80	252.167	odd	6
252.2.bi.c.139.19	yes	80	63.41	even	6
252.2.bi.c.139.20	yes	80	9.5	odd	6
252.2.bi.c.223.9	yes	80	21.20	even	2
252.2.bi.c.223.10	yes	80	3.2	odd	2
252.2.bi.c.223.19	yes	80	12.11	even	2
252.2.bi.c.223.20	yes	80	84.83	odd	2
756.2.bi.c.307.21		80	9.4	even	3	inner
756.2.bi.c.307.22		80	63.13	odd	6	inner
756.2.bi.c.307.31		80	36.31	odd	6	inner
756.2.bi.c.307.32		80	252.139	even	6	inner
756.2.bi.c.559.21		80	28.27	even	2	inner
756.2.bi.c.559.22		80	4.3	odd	2	inner
756.2.bi.c.559.31		80	7.6	odd	2	inner
756.2.bi.c.559.32		80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.13617 - 0.842090i) q^{2} +(0.581768 - 1.91352i) q^{4} +(1.43245 - 0.827025i) q^{5} +(-0.0302588 - 2.64558i) q^{7} +(-0.950366 - 2.66398i) q^{8} +(0.931077 - 2.14589i) q^{10} +(-4.24842 - 2.45282i) q^{11} +(0.876334 - 0.505952i) q^{13} +(-2.26220 - 2.98035i) q^{14} +(-3.32309 - 2.22644i) q^{16} +7.66107i q^{17} +2.85119 q^{19} +(-0.749173 - 3.22215i) q^{20} +(-6.89242 + 0.790723i) q^{22} +(-1.98118 + 1.14384i) q^{23} +(-1.13206 + 1.96079i) q^{25} +(0.569608 - 1.31280i) q^{26} +(-5.07996 - 1.48121i) q^{28} +(4.19857 - 7.27213i) q^{29} +(-0.348784 - 0.604112i) q^{31} +(-5.65047 + 0.268722i) q^{32} +(6.45131 + 8.70428i) q^{34} +(-2.23130 - 3.76463i) q^{35} +3.97490 q^{37} +(3.23944 - 2.40096i) q^{38} +(-3.56453 - 3.03004i) q^{40} +(6.69947 - 3.86794i) q^{41} +(6.70811 + 3.87293i) q^{43} +(-7.16511 + 6.70244i) q^{44} +(-1.28775 + 2.96793i) q^{46} +(3.70722 - 6.42109i) q^{47} +(-6.99817 + 0.160104i) q^{49} +(0.364945 + 3.18108i) q^{50} +(-0.458324 - 1.97123i) q^{52} +8.61878 q^{53} -8.11418 q^{55} +(-7.01902 + 2.59488i) q^{56} +(-1.35350 - 11.7980i) q^{58} +(2.54378 + 4.40596i) q^{59} +(-5.12759 - 2.96042i) q^{61} +(-0.904996 - 0.392667i) q^{62} +(-6.19361 + 5.06352i) q^{64} +(0.836869 - 1.44950i) q^{65} +(-2.18590 + 1.26203i) q^{67} +(14.6596 + 4.45696i) q^{68} +(-5.70530 - 2.39830i) q^{70} -1.00362i q^{71} +5.89658i q^{73} +(4.51617 - 3.34723i) q^{74} +(1.65873 - 5.45580i) q^{76} +(-6.36058 + 11.3137i) q^{77} +(-4.90752 - 2.83336i) q^{79} +(-6.60149 - 0.440989i) q^{80} +(4.35458 - 10.0362i) q^{82} +(-1.20736 + 2.09120i) q^{83} +(6.33589 + 10.9741i) q^{85} +(10.8829 - 1.24853i) q^{86} +(-2.49673 + 13.6488i) q^{88} -8.19734i q^{89} +(-1.36505 - 2.30310i) q^{91} +(1.03616 + 4.45647i) q^{92} +(-1.19511 - 10.4173i) q^{94} +(4.08418 - 2.35800i) q^{95} +(8.82136 + 5.09301i) q^{97} +(-7.81629 + 6.07500i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56}+ \cdots - 20 q^{98}+O(q^{100}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Introduction

L-functions

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