LMFDB - Embedded newform 756.2.bf.d.271.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.16
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.d.703.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41359 - 0.0418553i) q^{2} +(1.99650 - 0.118333i) q^{4} +(-1.51137 - 0.872592i) q^{5} +(1.00609 - 2.44699i) q^{7} +(2.81728 - 0.250838i) q^{8} +O(q^{10})$	\(q+(1.41359 - 0.0418553i) q^{2} +(1.99650 - 0.118333i) q^{4} +(-1.51137 - 0.872592i) q^{5} +(1.00609 - 2.44699i) q^{7} +(2.81728 - 0.250838i) q^{8} +(-2.17299 - 1.17023i) q^{10} +(-2.72676 + 1.57430i) q^{11} -3.39927i q^{13} +(1.31979 - 3.50117i) q^{14} +(3.97199 - 0.472502i) q^{16} +(3.59390 - 2.07494i) q^{17} +(2.67253 - 4.62896i) q^{19} +(-3.12071 - 1.56328i) q^{20} +(-3.78864 + 2.33955i) q^{22} +(7.05875 + 4.07537i) q^{23} +(-0.977168 - 1.69250i) q^{25} +(-0.142277 - 4.80518i) q^{26} +(1.71910 - 5.00447i) q^{28} -7.25396 q^{29} +(1.20251 + 2.08280i) q^{31} +(5.59501 - 0.834175i) q^{32} +(4.99347 - 3.08355i) q^{34} +(-3.65581 + 2.82041i) q^{35} +(-4.00014 + 6.92844i) q^{37} +(3.58413 - 6.65533i) q^{38} +(-4.47684 - 2.07923i) q^{40} -0.0436357i q^{41} +5.38348i q^{43} +(-5.25768 + 3.46574i) q^{44} +(10.1488 + 5.46547i) q^{46} +(-1.52872 + 2.64782i) q^{47} +(-4.97556 - 4.92380i) q^{49} +(-1.45216 - 2.35161i) q^{50} +(-0.402245 - 6.78662i) q^{52} +(-2.03636 - 3.52708i) q^{53} +5.49487 q^{55} +(2.22065 - 7.14624i) q^{56} +(-10.2542 + 0.303617i) q^{58} +(3.89522 + 6.74671i) q^{59} +(-1.01994 - 0.588861i) q^{61} +(1.78703 + 2.89391i) q^{62} +(7.87416 - 1.41337i) q^{64} +(-2.96617 + 5.13756i) q^{65} +(7.53828 - 4.35223i) q^{67} +(6.92968 - 4.56789i) q^{68} +(-5.04978 + 4.13993i) q^{70} +10.7539i q^{71} +(14.4866 - 8.36382i) q^{73} +(-5.36458 + 9.96143i) q^{74} +(4.78794 - 9.55794i) q^{76} +(1.10892 + 8.25626i) q^{77} +(2.56615 + 1.48157i) q^{79} +(-6.41547 - 2.75180i) q^{80} +(-0.00182638 - 0.0616832i) q^{82} -7.83867 q^{83} -7.24230 q^{85} +(0.225327 + 7.61006i) q^{86} +(-7.28716 + 5.11922i) q^{88} +(-4.07523 - 2.35284i) q^{89} +(-8.31798 - 3.41998i) q^{91} +(14.5750 + 7.30118i) q^{92} +(-2.05016 + 3.80693i) q^{94} +(-8.07838 + 4.66405i) q^{95} +11.9465i q^{97} +(-7.23950 - 6.75201i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{7}+O(q^{10}) $ 32 * q + 2 * q^7	$ 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) $ 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.41359	−	0.0418553i	0.999562	−	0.0295962i
$2$	1.41359	−	0.0418553i	0.999562	−	0.0295962i
$3$		0			0
$3$		0			0
$4$	1.99650	−	0.118333i	0.998248	−	0.0591664i
$5$	−1.51137	−	0.872592i	−0.675907	−	0.390235i	0.122404	−	0.992480i	$-0.460940\pi$
$5$	−1.51137	−	0.872592i	−0.675907	−	0.390235i	−0.798311	+	0.602245i	$0.794273\pi$
$6$		0			0
$7$	1.00609	−	2.44699i	0.380267	−	0.924877i
$7$	1.00609	−	2.44699i	0.380267	−	0.924877i
$8$	2.81728	−	0.250838i	0.996060	−	0.0886848i
$9$		0			0
$10$	−2.17299	−	1.17023i	−0.687160	−	0.370060i
$11$	−2.72676	+	1.57430i	−0.822150	+	0.474668i	−0.851157	−	0.524911i	$-0.824099\pi$
$11$	−2.72676	+	1.57430i	−0.822150	+	0.474668i	0.0290075	+	0.999579i	$0.490765\pi$
$12$		0			0
$13$		−	3.39927i		−	0.942787i	−0.881923	−	0.471394i	$-0.843751\pi$
$13$		−	3.39927i		−	0.942787i	0.881923	−	0.471394i	$-0.156249\pi$
$14$	1.31979	−	3.50117i	0.352728	−	0.935726i
$15$		0			0
$16$	3.97199	−	0.472502i	0.992999	−	0.118125i
$17$	3.59390	−	2.07494i	0.871649	−	0.503247i	0.00375343	−	0.999993i	$-0.498805\pi$
$17$	3.59390	−	2.07494i	0.871649	−	0.503247i	0.867896	+	0.496746i	$0.165472\pi$
$18$		0			0
$19$	2.67253	−	4.62896i	0.613120	−	1.06196i	−0.377591	−	0.925973i	$-0.623247\pi$
$19$	2.67253	−	4.62896i	0.613120	−	1.06196i	0.990711	−	0.135983i	$-0.0434193\pi$
$20$	−3.12071	−	1.56328i	−0.697811	−	0.349560i
$21$		0			0
$22$	−3.78864	+	2.33955i	−0.807741	+	0.498793i
$23$	7.05875	+	4.07537i	1.47185	+	0.849774i	0.999499	−	0.0316366i	$-0.0100719\pi$
$23$	7.05875	+	4.07537i	1.47185	+	0.849774i	0.472352	+	0.881410i	$0.343405\pi$
$24$		0			0
$25$	−0.977168	−	1.69250i	−0.195434	−	0.338501i
$26$	−0.142277	−	4.80518i	−0.0279029	−	0.942374i
$27$		0			0
$28$	1.71910	−	5.00447i	0.324879	−	0.945755i
$29$	−7.25396			−1.34703			−0.673514	−	0.739175i	$-0.735216\pi$
$29$	−7.25396			−1.34703			−0.673514	+	0.739175i	$0.735216\pi$
$30$		0			0
$31$	1.20251	+	2.08280i	0.215977	+	0.374083i	0.953574	−	0.301158i	$-0.0973731\pi$
$31$	1.20251	+	2.08280i	0.215977	+	0.374083i	−0.737598	+	0.675241i	$0.764040\pi$
$32$	5.59501	−	0.834175i	0.989068	−	0.147463i
$33$		0			0
$34$	4.99347	−	3.08355i	0.856373	−	0.528824i
$35$	−3.65581	+	2.82041i	−0.617944	+	0.476737i
$36$		0			0
$37$	−4.00014	+	6.92844i	−0.657619	+	1.13903i	0.323612	+	0.946190i	$0.395103\pi$
$37$	−4.00014	+	6.92844i	−0.657619	+	1.13903i	−0.981230	+	0.192839i	$0.938231\pi$
$38$	3.58413	−	6.65533i	0.581422	−	1.07964i
$39$		0			0
$40$	−4.47684	−	2.07923i	−0.707851	−	0.328755i
$41$		−	0.0436357i		−	0.00681475i	−0.999994	−	0.00340738i	$-0.998915\pi$
$41$		−	0.0436357i		−	0.00681475i	0.999994	−	0.00340738i	$-0.00108460\pi$
$42$		0			0
$43$			5.38348i			0.820973i	0.911867	+	0.410487i	$0.134641\pi$
$43$			5.38348i			0.820973i	−0.911867	+	0.410487i	$0.865359\pi$
$44$	−5.25768	+	3.46574i	−0.792625	+	0.522480i
$45$		0			0
$46$	10.1488	+	5.46547i	1.49636	+	0.805840i
$47$	−1.52872	+	2.64782i	−0.222987	+	0.386224i	−0.955713	−	0.294299i	$-0.904914\pi$
$47$	−1.52872	+	2.64782i	−0.222987	+	0.386224i	0.732727	+	0.680523i	$0.238247\pi$
$48$		0			0
$49$	−4.97556	−	4.92380i	−0.710794	−	0.703401i
$50$	−1.45216	−	2.35161i	−0.205366	−	0.332568i
$51$		0			0
$52$	−0.402245	−	6.78662i	−0.0557813	−	0.941135i
$53$	−2.03636	−	3.52708i	−0.279715	−	0.484481i	0.691599	−	0.722282i	$-0.256907\pi$
$53$	−2.03636	−	3.52708i	−0.279715	−	0.484481i	−0.971314	+	0.237801i	$0.923573\pi$
$54$		0			0
$55$	5.49487			0.740929
$56$	2.22065	−	7.14624i	0.296746	−	0.954956i
$57$		0			0
$58$	−10.2542	+	0.303617i	−1.34644	+	0.0398668i
$59$	3.89522	+	6.74671i	0.507114	+	0.878347i	0.999966	+	0.00823426i	$0.00262108\pi$
$59$	3.89522	+	6.74671i	0.507114	+	0.878347i	−0.492852	+	0.870113i	$0.664046\pi$
$60$		0			0
$61$	−1.01994	−	0.588861i	−0.130589	−	0.0753959i	0.433282	−	0.901258i	$-0.357355\pi$
$61$	−1.01994	−	0.588861i	−0.130589	−	0.0753959i	−0.563872	+	0.825862i	$0.690689\pi$
$62$	1.78703	+	2.89391i	0.226954	+	0.367527i
$63$		0			0
$64$	7.87416	−	1.41337i	0.984270	−	0.176671i
$65$	−2.96617	+	5.13756i	−0.367908	+	0.637236i
$66$		0			0
$67$	7.53828	−	4.35223i	0.920948	−	0.531710i	0.0370107	−	0.999315i	$-0.488216\pi$
$67$	7.53828	−	4.35223i	0.920948	−	0.531710i	0.883937	+	0.467605i	$0.154883\pi$
$68$	6.92968	−	4.56789i	0.840347	−	0.553938i
$69$		0			0
$70$	−5.04978	+	4.13993i	−0.603564	+	0.494817i
$71$			10.7539i			1.27625i	0.769932	+	0.638126i	$0.220290\pi$
$71$			10.7539i			1.27625i	−0.769932	+	0.638126i	$0.779710\pi$
$72$		0			0
$73$	14.4866	−	8.36382i	1.69552	−	0.978911i	0.745619	−	0.666372i	$-0.232154\pi$
$73$	14.4866	−	8.36382i	1.69552	−	0.978911i	0.949905	−	0.312539i	$-0.101180\pi$
$74$	−5.36458	+	9.96143i	−0.623620	+	1.15799i
$75$		0			0
$76$	4.78794	−	9.55794i	0.549214	−	1.09637i
$77$	1.10892	+	8.25626i	0.126373	+	0.940888i
$78$		0			0
$79$	2.56615	+	1.48157i	0.288714	+	0.166689i	0.637362	−	0.770565i	$-0.280026\pi$
$79$	2.56615	+	1.48157i	0.288714	+	0.166689i	−0.348648	+	0.937254i	$0.613359\pi$
$80$	−6.41547	−	2.75180i	−0.717271	−	0.307661i
$81$		0			0
$82$	−0.00182638	−	0.0616832i	−0.000201690	−	0.00681177i
$83$	−7.83867			−0.860405			−0.430203	−	0.902732i	$-0.641558\pi$
$83$	−7.83867			−0.860405			−0.430203	+	0.902732i	$0.641558\pi$
$84$		0			0
$85$	−7.24230			−0.785538
$86$	0.225327	+	7.61006i	0.0242977	+	0.820614i
$87$		0			0
$88$	−7.28716	+	5.11922i	−0.776814	+	0.545710i
$89$	−4.07523	−	2.35284i	−0.431974	−	0.249400i	0.268213	−	0.963360i	$-0.413567\pi$
$89$	−4.07523	−	2.35284i	−0.431974	−	0.249400i	−0.700187	+	0.713959i	$0.746900\pi$
$90$		0			0
$91$	−8.31798	−	3.41998i	−0.871962	−	0.358511i
$92$	14.5750	+	7.30118i	1.51955	+	0.761201i
$93$		0			0
$94$	−2.05016	+	3.80693i	−0.211458	+	0.392654i
$95$	−8.07838	+	4.66405i	−0.828824	+	0.478522i
$96$		0			0
$97$			11.9465i			1.21299i	0.795089	+	0.606493i	$0.207424\pi$
$97$			11.9465i			1.21299i	−0.795089	+	0.606493i	$0.792576\pi$
$98$	−7.23950	−	6.75201i	−0.731300	−	0.682056i
$99$		0			0
$100$	−2.15119	−	3.26345i	−0.215119	−	0.326345i
$101$	−13.1592	+	7.59749i	−1.30939	+	0.755978i	−0.981995	−	0.188908i	$-0.939505\pi$
$101$	−13.1592	+	7.59749i	−1.30939	+	0.755978i	−0.327398	+	0.944886i	$0.606172\pi$
$102$		0			0
$103$	−7.14374	+	12.3733i	−0.703894	+	1.21918i	0.263195	+	0.964743i	$0.415224\pi$
$103$	−7.14374	+	12.3733i	−0.703894	+	1.21918i	−0.967089	+	0.254437i	$0.918110\pi$
$104$	−0.852667	−	9.57669i	−0.0836108	−	0.939072i
$105$		0			0
$106$	−3.02621	−	4.90062i	−0.293932	−	0.475990i
$107$	11.2621	+	6.50215i	1.08874	+	0.628586i	0.933242	−	0.359249i	$-0.116967\pi$
$107$	11.2621	+	6.50215i	1.08874	+	0.628586i	0.155502	+	0.987836i	$0.450301\pi$
$108$		0			0
$109$	4.52814	+	7.84297i	0.433717	+	0.751220i	0.997190	−	0.0749144i	$-0.0238683\pi$
$109$	4.52814	+	7.84297i	0.433717	+	0.751220i	−0.563473	+	0.826135i	$0.690535\pi$
$110$	7.76752	−	0.229989i	0.740604	−	0.0219286i
$111$		0			0
$112$	2.83999	−	10.1948i	0.268353	−	0.963321i
$113$	−12.2941			−1.15653			−0.578265	−	0.815849i	$-0.696270\pi$
$113$	−12.2941			−1.15653			−0.578265	+	0.815849i	$0.696270\pi$
$114$		0			0
$115$	−7.11227	−	12.3188i	−0.663223	−	1.14874i
$116$	−14.4825	+	0.858382i	−1.34467	+	0.0796987i
$117$		0			0
$118$	5.78864	+	9.37408i	0.532888	+	0.862954i
$119$	−1.46157	−	10.8818i	−0.133982	−	0.997537i
$120$		0			0
$121$	−0.543179	+	0.940814i	−0.0493799	+	0.0855286i
$122$	−1.46642	−	0.789720i	−0.132764	−	0.0714979i
$123$		0			0
$124$	2.64727	+	4.01601i	0.237731	+	0.360649i
$125$			12.1366i			1.08553i
$126$		0			0
$127$			4.04936i			0.359322i	0.983729	+	0.179661i	$0.0575002\pi$
$127$			4.04936i			0.359322i	−0.983729	+	0.179661i	$0.942500\pi$
$128$	11.0717	−	2.32750i	0.978610	−	0.205724i
$129$		0			0
$130$	−3.97793	+	7.38658i	−0.348887	+	0.647845i
$131$	6.81934	−	11.8114i	0.595808	−	1.03197i	−0.397624	−	0.917549i	$-0.630165\pi$
$131$	6.81934	−	11.8114i	0.595808	−	1.03197i	0.993432	−	0.114422i	$-0.0365016\pi$
$132$		0			0
$133$	−8.63822	−	11.1968i	−0.749028	−	0.970888i
$134$	10.4739	−	6.46780i	0.904808	−	0.558733i
$135$		0			0
$136$	9.60456	−	6.74718i	0.823585	−	0.578566i
$137$	−2.24543	−	3.88919i	−0.191840	−	0.332276i	0.754020	−	0.656851i	$-0.228112\pi$
$137$	−2.24543	−	3.88919i	−0.191840	−	0.332276i	−0.945860	+	0.324575i	$0.894779\pi$
$138$		0			0
$139$	−11.2927			−0.957836			−0.478918	−	0.877860i	$-0.658971\pi$
$139$	−11.2927			−0.957836			−0.478918	+	0.877860i	$0.658971\pi$
$140$	−6.96506	+	6.06354i	−0.588655	+	0.512463i
$141$		0			0
$142$	0.450107	+	15.2016i	0.0377721	+	1.27569i
$143$	5.35145	+	9.26899i	0.447511	+	0.775112i
$144$		0			0
$145$	10.9634	+	6.32975i	0.910465	+	0.525657i
$146$	20.1281	−	12.4294i	1.66581	−	1.02866i
$147$		0			0
$148$	−7.16640	+	14.3060i	−0.589074	+	1.17594i
$149$	9.21596	−	15.9625i	0.755001	−	1.30770i	−0.190373	−	0.981712i	$-0.560970\pi$
$149$	9.21596	−	15.9625i	0.755001	−	1.30770i	0.945374	−	0.325988i	$-0.105697\pi$
$150$		0			0
$151$	−2.52537	+	1.45802i	−0.205511	+	0.118652i	−0.599224	−	0.800582i	$-0.704524\pi$
$151$	−2.52537	+	1.45802i	−0.205511	+	0.118652i	0.393712	+	0.919234i	$0.371191\pi$
$152$	6.36815	−	13.7115i	0.516525	−	1.11215i
$153$		0			0
$154$	1.91313	+	11.6246i	0.154164	+	0.936736i
$155$		−	4.19719i		−	0.337127i
$156$		0			0
$157$	1.83218	−	1.05781i	0.146224	−	0.0844225i	−0.425103	−	0.905145i	$-0.639762\pi$
$157$	1.83218	−	1.05781i	0.146224	−	0.0844225i	0.571327	+	0.820722i	$0.306429\pi$
$158$	3.68951	+	1.98693i	0.293521	+	0.158071i
$159$		0			0
$160$	−9.18404	−	3.62141i	−0.726062	−	0.286298i
$161$	17.0742	−	13.1725i	1.34563	−	1.03814i
$162$		0			0
$163$	−1.05056	−	0.606543i	−0.0822865	−	0.0475081i	0.458292	−	0.888802i	$-0.348461\pi$
$163$	−1.05056	−	0.606543i	−0.0822865	−	0.0475081i	−0.540579	+	0.841293i	$0.681795\pi$
$164$	−0.00516353	−	0.0871185i	−0.000403204	−	0.00680281i
$165$		0			0
$166$	−11.0807	+	0.328090i	−0.860028	+	0.0254647i
$167$	−12.5840			−0.973777			−0.486888	−	0.873464i	$-0.661868\pi$
$167$	−12.5840			−0.973777			−0.486888	+	0.873464i	$0.661868\pi$
$168$		0			0
$169$	1.44498			0.111153
$170$	−10.2377	+	0.303129i	−0.785194	+	0.0232489i
$171$		0			0
$172$	0.637042	+	10.7481i	0.0485740	+	0.819535i
$173$	−6.28324	−	3.62763i	−0.477706	−	0.275804i	0.241754	−	0.970338i	$-0.422277\pi$
$173$	−6.28324	−	3.62763i	−0.477706	−	0.275804i	−0.719460	+	0.694534i	$0.755611\pi$
$174$		0			0
$175$	−5.12467	+	0.688307i	−0.387388	+	0.0520311i
$176$	−10.0868	+	7.54150i	−0.760323	+	0.568462i
$177$		0			0
$178$	−5.85920	−	3.15539i	−0.439166	−	0.236506i
$179$	1.52858	−	0.882525i	0.114251	−	0.0659630i	−0.441785	−	0.897121i	$-0.645655\pi$
$179$	1.52858	−	0.882525i	0.114251	−	0.0659630i	0.556037	+	0.831158i	$0.312321\pi$
$180$		0			0
$181$			1.28610i			0.0955948i	0.998857	+	0.0477974i	$0.0152202\pi$
$181$			1.28610i			0.0955948i	−0.998857	+	0.0477974i	$0.984780\pi$
$182$	−11.9014	−	4.48631i	−0.882190	−	0.332547i
$183$		0			0
$184$	20.9088	+	9.71087i	1.54141	+	0.715895i
$185$	12.0914	−	6.98097i	0.888978	−	0.513251i
$186$		0			0
$187$	−6.53315	+	11.3157i	−0.477751	+	0.827489i
$188$	−2.73876	+	5.46726i	−0.199744	+	0.398741i
$189$		0			0
$190$	−11.2243	+	6.93120i	−0.814299	+	0.502842i
$191$	2.68691	+	1.55129i	0.194418	+	0.112247i	0.594049	−	0.804429i	$-0.297528\pi$
$191$	2.68691	+	1.55129i	0.194418	+	0.112247i	−0.399631	+	0.916676i	$0.630862\pi$
$192$		0			0
$193$	9.62484	+	16.6707i	0.692811	+	1.19998i	0.970913	+	0.239432i	$0.0769613\pi$
$193$	9.62484	+	16.6707i	0.692811	+	1.19998i	−0.278102	+	0.960551i	$0.589705\pi$
$194$	0.500025	+	16.8875i	0.0358997	+	1.21245i
$195$		0			0
$196$	−10.5163	−	9.24159i	−0.751166	−	0.660113i
$197$	16.1765			1.15253			0.576264	−	0.817263i	$-0.304510\pi$
$197$	16.1765			1.15253			0.576264	+	0.817263i	$0.304510\pi$
$198$		0			0
$199$	3.03212	+	5.25179i	0.214941	+	0.372289i	0.953254	−	0.302169i	$-0.0977106\pi$
$199$	3.03212	+	5.25179i	0.214941	+	0.372289i	−0.738313	+	0.674458i	$0.764377\pi$
$200$	−3.17750	−	4.52315i	−0.224683	−	0.319835i
$201$		0			0
$202$	−18.2838	+	11.2905i	−1.28645	+	0.794400i
$203$	−7.29816	+	17.7504i	−0.512230	+	1.24583i
$204$		0			0
$205$	−0.0380762	+	0.0659498i	−0.00265935	+	0.00460614i
$206$	−9.58046	+	17.7899i	−0.667502	+	1.23948i
$207$		0			0
$208$	−1.60616	−	13.5019i	−0.111367	−	0.936186i
$209$			16.8294i			1.16412i
$210$		0			0
$211$			4.15702i			0.286181i	0.989710	+	0.143091i	$0.0457040\pi$
$211$			4.15702i			0.286181i	−0.989710	+	0.143091i	$0.954296\pi$
$212$	−4.48295	−	6.80083i	−0.307890	−	0.467083i
$213$		0			0
$214$	16.1921	+	8.72002i	1.10687	+	0.596088i
$215$	4.69758	−	8.13645i	0.320372	−	0.554901i
$216$		0			0
$217$	6.30644	−	0.847035i	0.428109	−	0.0575004i
$218$	6.72922	+	10.8972i	0.455760	+	0.738055i
$219$		0			0
$220$	10.9705	−	0.650223i	0.739631	−	0.0438381i
$221$	−7.05328	−	12.2166i	−0.474455	−	0.821780i
$222$		0			0
$223$	−0.863765			−0.0578420			−0.0289210	−	0.999582i	$-0.509207\pi$
$223$	−0.863765			−0.0578420			−0.0289210	+	0.999582i	$0.509207\pi$
$224$	3.58788	−	14.5302i	0.239725	−	0.970841i
$225$		0			0
$226$	−17.3788	+	0.514572i	−1.15602	+	0.0342289i
$227$	−2.80804	−	4.86367i	−0.186376	−	0.322813i	0.757663	−	0.652646i	$-0.226341\pi$
$227$	−2.80804	−	4.86367i	−0.186376	−	0.322813i	−0.944039	+	0.329833i	$0.893008\pi$
$228$		0			0
$229$	−24.7154	−	14.2694i	−1.63324	−	0.942950i	−0.983086	−	0.183145i	$-0.941372\pi$
$229$	−24.7154	−	14.2694i	−1.63324	−	0.942950i	−0.650152	−	0.759805i	$-0.725295\pi$
$230$	−10.5695	−	17.1161i	−0.696930	−	1.12860i
$231$		0			0
$232$	−20.4365	+	1.81957i	−1.34172	+	0.119461i
$233$	10.7308	−	18.5863i	0.703000	−	1.21763i	−0.264409	−	0.964411i	$-0.585177\pi$
$233$	10.7308	−	18.5863i	0.703000	−	1.21763i	0.967409	−	0.253221i	$-0.0814899\pi$
$234$		0			0
$235$	4.62093	−	2.66790i	0.301436	−	0.174034i
$236$	8.57514	+	13.0089i	0.558194	+	0.846805i
$237$		0			0
$238$	−2.52153	−	15.3213i	−0.163446	−	0.993134i
$239$		−	22.3476i		−	1.44555i	−0.691086	−	0.722773i	$-0.742867\pi$
$239$		−	22.3476i		−	1.44555i	0.691086	−	0.722773i	$-0.257133\pi$
$240$		0			0
$241$	18.9331	−	10.9310i	1.21959	−	0.704130i	0.254759	−	0.967005i	$-0.418004\pi$
$241$	18.9331	−	10.9310i	1.21959	−	0.704130i	0.964830	+	0.262875i	$0.0846706\pi$
$242$	−0.728457	+	1.35266i	−0.0468270	+	0.0869525i
$243$		0			0
$244$	−2.10598	−	1.05497i	−0.134822	−	0.0675373i
$245$	3.22345	+	11.7833i	0.205939	+	0.752810i
$246$		0			0
$247$	−15.7351	−	9.08464i	−1.00120	−	0.578042i
$248$	3.91025	+	5.56621i	0.248301	+	0.353455i
$249$		0			0
$250$	0.507980	+	17.1562i	0.0321275	+	1.08505i
$251$	−6.30849			−0.398189			−0.199094	−	0.979980i	$-0.563800\pi$
$251$	−6.30849			−0.398189			−0.199094	+	0.979980i	$0.563800\pi$
$252$		0			0
$253$	−25.6634			−1.61344
$254$	0.169487	+	5.72415i	0.0106346	+	0.359165i
$255$		0			0
$256$	15.5535	−	3.75355i	0.972093	−	0.234597i
$257$	23.3700	+	13.4927i	1.45778	+	0.841650i	0.998902	−	0.0468481i	$-0.0149177\pi$
$257$	23.3700	+	13.4927i	1.45778	+	0.841650i	0.458879	+	0.888499i	$0.348251\pi$
$258$		0			0
$259$	12.9293	+	16.7590i	0.803390	+	1.04135i
$260$	−5.31401	+	10.6081i	−0.329561	+	0.657887i
$261$		0			0
$262$	9.14541	−	16.9820i	0.565005	−	1.04915i
$263$	18.0702	−	10.4328i	1.11426	−	0.643316i	0.174327	−	0.984688i	$-0.444225\pi$
$263$	18.0702	−	10.4328i	1.11426	−	0.643316i	0.939928	+	0.341372i	$0.110892\pi$
$264$		0			0
$265$			7.10764i			0.436619i
$266$	−12.6796	−	15.4662i	−0.777435	−	0.948294i
$267$		0			0
$268$	14.5351	−	9.58124i	0.887875	−	0.585267i
$269$	8.27930	−	4.78006i	0.504798	−	0.291445i	−0.225895	−	0.974152i	$-0.572531\pi$
$269$	8.27930	−	4.78006i	0.504798	−	0.291445i	0.730693	+	0.682707i	$0.239197\pi$
$270$		0			0
$271$	7.03688	−	12.1882i	0.427460	−	0.740383i	−0.569187	−	0.822208i	$-0.692742\pi$
$271$	7.03688	−	12.1882i	0.427460	−	0.740383i	0.996647	+	0.0818258i	$0.0260751\pi$
$272$	13.2945	−	9.93978i	0.806100	−	0.602688i
$273$		0			0
$274$	−3.33691	−	5.40376i	−0.201590	−	0.326453i
$275$	5.32901	+	3.07670i	0.321351	+	0.185532i
$276$		0			0
$277$	3.53991	+	6.13130i	0.212692	+	0.368394i	0.952556	−	0.304362i	$-0.0984434\pi$
$277$	3.53991	+	6.13130i	0.212692	+	0.368394i	−0.739864	+	0.672757i	$0.765110\pi$
$278$	−15.9633	+	0.472660i	−0.957416	+	0.0283483i
$279$		0			0
$280$	−9.59197	+	8.86292i	−0.573230	+	0.529660i
$281$	−33.0322			−1.97054			−0.985268	−	0.171019i	$-0.945294\pi$
$281$	−33.0322			−1.97054			−0.985268	+	0.171019i	$0.945294\pi$
$282$		0			0
$283$	3.23766	+	5.60778i	0.192459	+	0.333348i	0.946064	−	0.323978i	$-0.105021\pi$
$283$	3.23766	+	5.60778i	0.192459	+	0.333348i	−0.753606	+	0.657327i	$0.771687\pi$
$284$	1.27254	+	21.4701i	0.0755112	+	1.27402i
$285$		0			0
$286$	7.95274	+	12.8786i	0.470255	+	0.761528i
$287$	−0.106776	−	0.0439016i	−0.00630281	−	0.00259143i
$288$		0			0
$289$	0.110758	−	0.191839i	0.00651518	−	0.0112846i
$290$	15.7628	+	8.48882i	0.925623	+	0.498481i
$291$		0			0
$292$	27.9327	−	18.4126i	1.63464	−	1.07751i
$293$			18.9712i			1.10831i	0.832414	+	0.554154i	$0.186958\pi$
$293$			18.9712i			1.10831i	−0.832414	+	0.554154i	$0.813042\pi$
$294$		0			0
$295$		−	13.5957i		−	0.791574i
$296$	−9.53160	+	20.5228i	−0.554013	+	1.19286i
$297$		0			0
$298$	12.3595	−	22.9503i	0.715967	−	1.32947i
$299$	13.8533	−	23.9946i	0.801155	−	1.38764i
$300$		0			0
$301$	13.1733	+	5.41628i	0.759299	+	0.312189i
$302$	−3.50882	+	2.16675i	−0.201910	+	0.124682i
$303$		0			0
$304$	8.42808	−	19.6490i	0.483384	−	1.12695i
$305$	1.02767	+	1.77998i	0.0588442	+	0.101921i
$306$		0			0
$307$	−6.30262			−0.359709			−0.179855	−	0.983693i	$-0.557563\pi$
$307$	−6.30262			−0.359709			−0.179855	+	0.983693i	$0.557563\pi$
$308$	3.19094	+	16.3524i	0.181821	+	0.931763i
$309$		0			0
$310$	−0.175675	−	5.93313i	−0.00997765	−	0.336979i
$311$	−14.3143	−	24.7931i	−0.811691	−	1.40589i	−0.911680	−	0.410901i	$-0.865214\pi$
$311$	−14.3143	−	24.7931i	−0.811691	−	1.40589i	0.0999893	−	0.994989i	$-0.468119\pi$
$312$		0			0
$313$	2.56163	+	1.47896i	0.144792	+	0.0835956i	0.570646	−	0.821196i	$-0.306693\pi$
$313$	2.56163	+	1.47896i	0.144792	+	0.0835956i	−0.425854	+	0.904792i	$0.640026\pi$
$314$	2.54569	−	1.57200i	0.143661	−	0.0887132i
$315$		0			0
$316$	5.29863	+	2.65428i	0.298071	+	0.149315i
$317$	7.24576	−	12.5500i	0.406963	−	0.704880i	−0.587585	−	0.809162i	$-0.699921\pi$
$317$	7.24576	−	12.5500i	0.406963	−	0.704880i	0.994548	+	0.104283i	$0.0332546\pi$
$318$		0			0
$319$	19.7798	−	11.4199i	1.10746	−	0.639391i
$320$	−13.1341	−	4.73480i	−0.734218	−	0.264684i
$321$		0			0
$322$	23.5846	−	19.3352i	1.31432	−	1.07751i
$323$		−	22.1814i		−	1.23420i
$324$		0			0
$325$	−5.75327	+	3.32165i	−0.319134	+	0.184252i
$326$	−1.51046	−	0.813434i	−0.0836565	−	0.0450519i
$327$		0			0
$328$	−0.0109455	−	0.122934i	−0.000604365	−	0.00678790i
$329$	4.94116	+	6.40472i	0.272415	+	0.353103i
$330$		0			0
$331$	26.9846	+	15.5796i	1.48321	+	0.856330i	0.999818	−	0.0190761i	$-0.00607248\pi$
$331$	26.9846	+	15.5796i	1.48321	+	0.856330i	0.483389	+	0.875406i	$0.339406\pi$
$332$	−15.6499	+	0.927571i	−0.858898	+	0.0509071i
$333$		0			0
$334$	−17.7886	+	0.526706i	−0.973350	+	0.0288201i
$335$	−15.1909			−0.829967
$336$		0			0
$337$	−2.65831			−0.144807			−0.0724036	−	0.997375i	$-0.523067\pi$
$337$	−2.65831			−0.144807			−0.0724036	+	0.997375i	$0.523067\pi$
$338$	2.04262	−	0.0604802i	0.111104	−	0.00328969i
$339$		0			0
$340$	−14.4592	+	0.857002i	−0.784162	+	0.0464774i
$341$	−6.55790	−	3.78621i	−0.355130	−	0.205035i
$342$		0			0
$343$	−17.0544	+	7.22135i	−0.920850	+	0.389916i
$344$	1.35038	+	15.1668i	0.0728078	+	0.817738i
$345$		0			0
$346$	−9.03379	−	4.86501i	−0.485660	−	0.261545i
$347$	−4.73026	+	2.73102i	−0.253933	+	0.146609i	−0.621564	−	0.783363i	$-0.713502\pi$
$347$	−4.73026	+	2.73102i	−0.253933	+	0.146609i	0.367631	+	0.929972i	$0.380169\pi$
$348$		0			0
$349$			5.66488i			0.303234i	0.988439	+	0.151617i	$0.0484480\pi$
$349$			5.66488i			0.303234i	−0.988439	+	0.151617i	$0.951552\pi$
$350$	−7.21539	+	1.18748i	−0.385679	+	0.0634735i
$351$		0			0
$352$	−13.9430	+	11.0828i	−0.743166	+	0.590715i
$353$	4.49048	−	2.59258i	0.239004	−	0.137989i	−0.375715	−	0.926735i	$-0.622603\pi$
$353$	4.49048	−	2.59258i	0.239004	−	0.137989i	0.614719	+	0.788746i	$0.289269\pi$
$354$		0			0
$355$	9.38375	−	16.2531i	0.498038	−	0.862627i
$356$	−8.41460	−	4.21519i	−0.445973	−	0.223405i
$357$		0			0
$358$	2.12385	−	1.31151i	0.112249	−	0.0693155i
$359$	−2.38293	−	1.37579i	−0.125766	−	0.0726113i	0.435797	−	0.900045i	$-0.356467\pi$
$359$	−2.38293	−	1.37579i	−0.125766	−	0.0726113i	−0.561563	+	0.827434i	$0.689800\pi$
$360$		0			0
$361$	−4.78483	−	8.28757i	−0.251833	−	0.436188i
$362$	0.0538299	+	1.81802i	0.00282924	+	0.0955529i
$363$		0			0
$364$	−17.0115	−	5.84368i	−0.891646	−	0.306292i
$365$	−29.1928			−1.52802
$366$		0			0
$367$	−15.7346	−	27.2531i	−0.821340	−	1.42260i	−0.904685	−	0.426081i	$-0.859894\pi$
$367$	−15.7346	−	27.2531i	−0.821340	−	1.42260i	0.0833450	−	0.996521i	$-0.473440\pi$
$368$	29.9629	+	12.8521i	1.56193	+	0.669961i
$369$		0			0
$370$	16.8001	−	10.3744i	0.873398	−	0.539337i
$371$	−10.6795	+	1.43439i	−0.554452	+	0.0744699i
$372$		0			0
$373$	1.14632	−	1.98548i	0.0593540	−	0.102804i	−0.834822	−	0.550521i	$-0.814429\pi$
$373$	1.14632	−	1.98548i	0.0593540	−	0.102804i	0.894176	+	0.447716i	$0.147763\pi$
$374$	−8.76159	+	16.2693i	−0.453051	+	0.841266i
$375$		0			0
$376$	−3.64266	+	7.84312i	−0.187856	+	0.404478i
$377$			24.6582i			1.26996i
$378$		0			0
$379$			7.27551i			0.373718i	0.982387	+	0.186859i	$0.0598307\pi$
$379$			7.27551i			0.373718i	−0.982387	+	0.186859i	$0.940169\pi$
$380$	−15.5765	+	10.2677i	−0.799060	+	0.526722i
$381$		0			0
$382$	3.86313	+	2.08043i	0.197655	+	0.106444i
$383$	−6.41999	+	11.1197i	−0.328046	+	0.568193i	−0.982124	−	0.188235i	$-0.939723\pi$
$383$	−6.41999	+	11.1197i	−0.328046	+	0.568193i	0.654078	+	0.756427i	$0.273057\pi$
$384$		0			0
$385$	5.52835	−	13.4459i	0.281751	−	0.685268i
$386$	14.3034	+	23.1628i	0.728022	+	1.17895i
$387$		0			0
$388$	1.41366	+	23.8512i	0.0717679	+	1.21086i
$389$	14.0867	+	24.3988i	0.714223	+	1.23707i	0.963259	+	0.268576i	$0.0865530\pi$
$389$	14.0867	+	24.3988i	0.714223	+	1.23707i	−0.249036	+	0.968494i	$0.580114\pi$
$390$		0			0
$391$	33.8246			1.71058
$392$	−15.2526	−	12.6237i	−0.770374	−	0.637592i
$393$		0			0
$394$	22.8670	−	0.677073i	1.15202	−	0.0341104i
$395$	−2.58561	−	4.47840i	−0.130096	−	0.225333i
$396$		0			0
$397$	−25.5945	−	14.7770i	−1.28455	−	0.741635i	−0.306873	−	0.951751i	$-0.599283\pi$
$397$	−25.5945	−	14.7770i	−1.28455	−	0.741635i	−0.977676	+	0.210116i	$0.932616\pi$
$398$	4.50600	+	7.29699i	0.225866	+	0.365765i
$399$		0			0
$400$	−4.68102	−	6.26090i	−0.234051	−	0.313045i
$401$	−6.40446	+	11.0929i	−0.319824	+	0.553951i	−0.980451	−	0.196763i	$-0.936957\pi$
$401$	−6.40446	+	11.0929i	−0.319824	+	0.553951i	0.660627	+	0.750714i	$0.270290\pi$
$402$		0			0
$403$	7.08001	−	4.08764i	0.352680	−	0.203620i
$404$	−25.3733	+	16.7255i	−1.26237	+	0.832126i
$405$		0			0
$406$	−9.57369	+	25.3973i	−0.475134	+	1.26045i
$407$		−	25.1896i		−	1.24860i
$408$		0			0
$409$	25.2149	−	14.5579i	1.24680	−	0.719840i	0.276329	−	0.961063i	$-0.410882\pi$
$409$	25.2149	−	14.5579i	1.24680	−	0.719840i	0.970470	+	0.241223i	$0.0775486\pi$
$410$	−0.0510639	+	0.0948200i	−0.00252187	+	0.00468283i
$411$		0			0
$412$	−12.7983	+	25.5486i	−0.630526	+	1.25869i
$413$	20.4281	−	2.74375i	1.00520	−	0.135011i
$414$		0			0
$415$	11.8471	+	6.83995i	0.581554	+	0.335760i
$416$	−2.83558	−	19.0189i	−0.139026	−	0.932480i
$417$		0			0
$418$	0.704400	+	23.7900i	0.0344533	+	1.16361i
$419$	35.4929			1.73394			0.866971	−	0.498359i	$-0.166064\pi$
$419$	35.4929			1.73394			0.866971	+	0.498359i	$0.166064\pi$
$420$		0			0
$421$	−36.4676			−1.77732			−0.888660	−	0.458567i	$-0.848363\pi$
$421$	−36.4676			−1.77732			−0.888660	+	0.458567i	$0.848363\pi$
$422$	0.173993	+	5.87634i	0.00846986	+	0.286056i
$423$		0			0
$424$	−6.62172	−	9.42597i	−0.321579	−	0.457766i
$425$	−7.02369	−	4.05513i	−0.340699	−	0.196703i
$426$		0			0
$427$	−2.46709	+	1.90333i	−0.119391	+	0.0921086i
$428$	23.2541	+	11.6488i	1.12403	+	0.563068i
$429$		0			0
$430$	6.29992	−	11.6983i	0.303809	−	0.564140i
$431$	21.5079	−	12.4176i	1.03600	−	0.598134i	0.117301	−	0.993096i	$-0.462576\pi$
$431$	21.5079	−	12.4176i	1.03600	−	0.598134i	0.918697	+	0.394962i	$0.129242\pi$
$432$		0			0
$433$		−	17.3503i		−	0.833801i	−0.908952	−	0.416900i	$-0.863116\pi$
$433$		−	17.3503i		−	0.833801i	0.908952	−	0.416900i	$-0.136884\pi$
$434$	8.87930	−	1.46132i	0.426220	−	0.0701456i
$435$		0			0
$436$	9.96850	+	15.1226i	0.477404	+	0.724243i
$437$	37.7294	−	21.7831i	1.80484	−	1.04203i
$438$		0			0
$439$	−6.74162	+	11.6768i	−0.321760	+	0.557304i	−0.980851	−	0.194758i	$-0.937608\pi$
$439$	−6.74162	+	11.6768i	−0.321760	+	0.557304i	0.659091	+	0.752063i	$0.270941\pi$
$440$	15.4806	−	1.37833i	0.738009	−	0.0657091i
$441$		0			0
$442$	−10.4818	−	16.9741i	−0.498568	−	0.807378i
$443$	−24.9668	−	14.4146i	−1.18621	−	0.684858i	−0.228766	−	0.973481i	$-0.573469\pi$
$443$	−24.9668	−	14.4146i	−1.18621	−	0.684858i	−0.957443	+	0.288624i	$0.906802\pi$
$444$		0			0
$445$	4.10613	+	7.11203i	0.194649	+	0.337142i
$446$	−1.22101	+	0.0361531i	−0.0578166	+	0.00171190i
$447$		0			0
$448$	4.46364	−	20.6900i	0.210887	−	0.977510i
$449$	4.75749			0.224520			0.112260	−	0.993679i	$-0.464191\pi$
$449$	4.75749			0.224520			0.112260	+	0.993679i	$0.464191\pi$
$450$		0			0
$451$	0.0686956	+	0.118984i	0.00323475	+	0.00560275i
$452$	−24.5451	+	1.45479i	−1.15450	+	0.0684277i
$453$		0			0
$454$	−4.17300	−	6.75772i	−0.195849	−	0.317156i
$455$	9.58733	+	12.4271i	0.449461	+	0.582590i
$456$		0			0
$457$	3.50860	−	6.07707i	0.164125	−	0.284273i	−0.772219	−	0.635356i	$-0.780853\pi$
$457$	3.50860	−	6.07707i	0.164125	−	0.284273i	0.936344	+	0.351083i	$0.114187\pi$
$458$	−35.5347	−	19.1367i	−1.66043	−	0.894199i
$459$		0			0
$460$	−15.6573	−	23.7528i	−0.730027	−	1.10748i
$461$		−	9.12188i		−	0.424848i	−0.977178	−	0.212424i	$-0.931864\pi$
$461$		−	9.12188i		−	0.424848i	0.977178	−	0.212424i	$-0.0681359\pi$
$462$		0			0
$463$			3.92320i			0.182326i	0.995836	+	0.0911632i	$0.0290585\pi$
$463$			3.92320i			0.182326i	−0.995836	+	0.0911632i	$0.970942\pi$
$464$	−28.8127	+	3.42751i	−1.33760	+	0.159118i
$465$		0			0
$466$	14.3911	−	26.7227i	0.666655	−	1.23790i
$467$	−15.4364	+	26.7366i	−0.714311	+	1.23722i	0.248913	+	0.968526i	$0.419927\pi$
$467$	−15.4364	+	26.7366i	−0.714311	+	1.23722i	−0.963225	+	0.268698i	$0.913407\pi$
$468$		0			0
$469$	−3.06567	−	22.8249i	−0.141559	−	1.05396i
$470$	6.42045	−	3.96473i	0.296153	−	0.182879i
$471$		0			0
$472$	12.6663	+	18.0303i	0.583012	+	0.829913i
$473$	−8.47520	−	14.6795i	−0.389690	−	0.674963i
$474$		0			0
$475$	−10.4460			−0.479297
$476$	−4.20569	−	21.5526i	−0.192768	−	0.987862i
$477$		0			0
$478$	−0.935364	−	31.5904i	−0.0427826	−	1.44491i
$479$	20.2431	+	35.0622i	0.924933	+	1.60203i	0.791669	+	0.610950i	$0.209212\pi$
$479$	20.2431	+	35.0622i	0.924933	+	1.60203i	0.133264	+	0.991081i	$0.457454\pi$
$480$		0			0
$481$	23.5516	+	13.5975i	1.07386	+	0.619994i
$482$	26.3062	−	16.2445i	1.19821	−	0.739917i
$483$		0			0
$484$	−0.973126	+	1.94261i	−0.0442330	+	0.0883003i
$485$	10.4244	−	18.0556i	0.473349	−	0.819865i
$486$		0			0
$487$	−18.2669	+	10.5464i	−0.827751	+	0.477902i	−0.853082	−	0.521777i	$-0.825269\pi$
$487$	−18.2669	+	10.5464i	−0.827751	+	0.477902i	0.0253310	+	0.999679i	$0.491936\pi$
$488$	−3.02116	−	1.40315i	−0.136761	−	0.0635175i
$489$		0			0
$490$	5.04985	+	16.5219i	0.228129	+	0.746385i
$491$		−	9.42666i		−	0.425419i	−0.977115	−	0.212710i	$-0.931771\pi$
$491$		−	9.42666i		−	0.425419i	0.977115	−	0.212710i	$-0.0682288\pi$
$492$		0			0
$493$	−26.0700	+	15.0515i	−1.17414	+	0.677888i
$494$	−22.6232	−	12.1834i	−1.01787	−	0.548157i
$495$		0			0
$496$	5.76048	+	7.70470i	0.258653	+	0.345951i
$497$	26.3147	+	10.8194i	1.18038	+	0.485317i
$498$		0			0
$499$	6.44025	+	3.71828i	0.288305	+	0.166453i	0.637177	−	0.770717i	$-0.280102\pi$
$499$	6.44025	+	3.71828i	0.288305	+	0.166453i	−0.348872	+	0.937170i	$0.613435\pi$
$500$	1.43616	+	24.2307i	0.0642268	+	1.08363i
$501$		0			0
$502$	−8.91765	+	0.264044i	−0.398014	+	0.0117848i
$503$	−28.9841			−1.29234			−0.646168	−	0.763195i	$-0.723629\pi$
$503$	−28.9841			−1.29234			−0.646168	+	0.763195i	$0.723629\pi$
$504$		0			0
$505$	26.5180			1.18004
$506$	−36.2776	+	1.07415i	−1.61274	+	0.0477517i
$507$		0			0
$508$	0.479172	+	8.08453i	0.0212598	+	0.358693i
$509$	3.35237	+	1.93549i	0.148591	+	0.0857892i	0.572452	−	0.819938i	$-0.305992\pi$
$509$	3.35237	+	1.93549i	0.148591	+	0.0857892i	−0.423861	+	0.905727i	$0.639325\pi$
$510$		0			0
$511$	−5.89139	−	43.8633i	−0.260620	−	1.94040i
$512$	21.8292	−	5.95699i	0.964724	−	0.263264i
$513$		0			0
$514$	33.6005	+	18.0950i	1.48205	+	0.798137i
$515$	21.5937	−	12.4671i	0.951533	−	0.549368i
$516$		0			0
$517$		−	9.62663i		−	0.423379i
$518$	18.9783	+	23.1492i	0.833858	+	1.01712i
$519$		0			0
$520$	−7.06785	+	15.2180i	−0.309946	+	0.667353i
$521$	−22.5775	+	13.0351i	−0.989138	+	0.571079i	−0.905017	−	0.425376i	$-0.860142\pi$
$521$	−22.5775	+	13.0351i	−0.989138	+	0.571079i	−0.0841215	+	0.996456i	$0.526808\pi$
$522$		0			0
$523$	16.5356	−	28.6406i	0.723053	−	1.25237i	−0.236717	−	0.971579i	$-0.576071\pi$
$523$	16.5356	−	28.6406i	0.723053	−	1.25237i	0.959770	−	0.280786i	$-0.0905953\pi$
$524$	12.2171	−	24.3885i	0.533707	−	1.06541i
$525$		0			0
$526$	25.1072	−	15.5041i	1.09473	−	0.676012i
$527$	8.64339	+	4.99026i	0.376512	+	0.217379i
$528$		0			0
$529$	21.7173	+	37.6155i	0.944230	+	1.63545i
$530$	0.297492	+	10.0473i	0.0129222	+	0.436427i
$531$		0			0
$532$	−18.5711	−	21.3322i	−0.805160	−	0.924869i
$533$	−0.148329			−0.00642486
$534$		0			0
$535$	−11.3474	−	19.6543i	−0.490593	−	0.849731i
$536$	20.1458	−	14.1524i	0.870165	−	0.611289i
$537$		0			0
$538$	11.5035	−	7.10359i	0.495951	−	0.306258i
$539$	21.3187	+	5.59304i	0.918261	+	0.240909i
$540$		0			0
$541$	−17.9702	+	31.1253i	−0.772598	+	1.33818i	0.163536	+	0.986537i	$0.447710\pi$
$541$	−17.9702	+	31.1253i	−0.772598	+	1.33818i	−0.936135	+	0.351642i	$0.885623\pi$
$542$	9.43715	−	17.5237i	0.405360	−	0.752709i
$543$		0			0
$544$	18.3771	−	14.6073i	0.787910	−	0.626281i
$545$		−	15.8049i		−	0.677006i
$546$		0			0
$547$		−	15.9365i		−	0.681394i	−0.940173	−	0.340697i	$-0.889337\pi$
$547$		−	15.9365i		−	0.681394i	0.940173	−	0.340697i	$-0.110663\pi$
$548$	−4.94321	−	7.49905i	−0.211163	−	0.320344i
$549$		0			0
$550$	7.66183	+	4.12616i	0.326701	+	0.175940i
$551$	−19.3864	+	33.5783i	−0.825890	+	1.43048i
$552$		0			0
$553$	6.20717	−	4.78876i	0.263956	−	0.203639i
$554$	5.26062	+	8.51901i	0.223502	+	0.361938i
$555$		0			0
$556$	−22.5459	+	1.33630i	−0.956158	+	0.0566717i
$557$	−14.5279	−	25.1631i	−0.615568	−	1.06620i	−0.990285	−	0.139056i	$-0.955593\pi$
$557$	−14.5279	−	25.1631i	−0.615568	−	1.06620i	0.374716	−	0.927140i	$-0.377740\pi$
$558$		0			0
$559$	18.2999			0.774003
$560$	−13.1882	+	12.9300i	−0.557303	+	0.546394i
$561$		0			0
$562$	−46.6941	+	1.38257i	−1.96967	+	0.0583203i
$563$	−14.1540	−	24.5154i	−0.596520	−	1.03320i	−0.993331	−	0.115302i	$-0.963216\pi$
$563$	−14.1540	−	24.5154i	−0.596520	−	1.03320i	0.396811	−	0.917900i	$-0.370117\pi$
$564$		0			0
$565$	18.5810	+	10.7277i	0.781707	+	0.451319i
$566$	4.81145	+	7.79162i	0.202240	+	0.327506i
$567$		0			0
$568$	2.69749	+	30.2967i	0.113184	+	1.27122i
$569$	11.1284	−	19.2749i	0.466525	−	0.808046i	−0.532743	−	0.846277i	$-0.678839\pi$
$569$	11.1284	−	19.2749i	0.466525	−	0.808046i	0.999269	+	0.0382310i	$0.0121723\pi$
$570$		0			0
$571$	−21.1885	+	12.2332i	−0.886712	+	0.511943i	−0.872866	−	0.487961i	$-0.837741\pi$
$571$	−21.1885	+	12.2332i	−0.886712	+	0.511943i	−0.0138464	+	0.999904i	$0.504408\pi$
$572$	11.7810	+	17.8723i	0.492588	+	0.747277i
$573$		0			0
$574$	−0.152776	−	0.0575898i	−0.00637674	−	0.00240375i
$575$		−	15.9293i		−	0.664297i
$576$		0			0
$577$	−11.3480	+	6.55179i	−0.472425	+	0.272755i	−0.717254	−	0.696811i	$-0.754601\pi$
$577$	−11.3480	+	6.55179i	−0.472425	+	0.272755i	0.244829	+	0.969566i	$0.421268\pi$
$578$	0.148537	−	0.275818i	0.00617834	−	0.0114725i
$579$		0			0
$580$	22.6375	+	11.3400i	0.939971	+	0.470867i
$581$	−7.88642	+	19.1812i	−0.327184	+	0.795769i
$582$		0			0
$583$	11.1053	+	6.41166i	0.459936	+	0.265544i
$584$	38.7148	−	27.1970i	1.60203	−	1.12542i
$585$		0			0
$586$	0.794045	+	26.8176i	0.0328017	+	1.10782i
$587$	−35.2610			−1.45538			−0.727688	−	0.685908i	$-0.759405\pi$
$587$	−35.2610			−1.45538			−0.727688	+	0.685908i	$0.759405\pi$
$588$		0			0
$589$	12.8549			0.529679
$590$	−0.569053	−	19.2189i	−0.0234276	−	0.791228i
$591$		0			0
$592$	−12.6148	+	29.4098i	−0.518466	+	1.20874i
$593$	−20.4717	−	11.8193i	−0.840670	−	0.485361i	0.0168218	−	0.999859i	$-0.494645\pi$
$593$	−20.4717	−	11.8193i	−0.840670	−	0.485361i	−0.857492	+	0.514497i	$0.827979\pi$
$594$		0			0
$595$	−7.28643	+	17.7219i	−0.298714	+	0.726526i
$596$	16.5107	−	32.9596i	0.676306	−	1.35008i
$597$		0			0
$598$	18.5786	−	34.4984i	0.759736	−	1.41075i
$599$	11.0108	−	6.35709i	0.449889	−	0.259744i	−0.257894	−	0.966173i	$-0.583029\pi$
$599$	11.0108	−	6.35709i	0.449889	−	0.259744i	0.707783	+	0.706429i	$0.249695\pi$
$600$		0			0
$601$		−	30.7523i		−	1.25441i	−0.778853	−	0.627207i	$-0.784198\pi$
$601$		−	30.7523i		−	1.25441i	0.778853	−	0.627207i	$-0.215802\pi$
$602$	18.8485	+	7.10505i	0.768206	+	0.289580i
$603$		0			0
$604$	−4.86936	+	3.20977i	−0.198131	+	0.130604i
$605$	1.64189	−	0.947947i	0.0667524	−	0.0385395i
$606$		0			0
$607$	−7.15640	+	12.3952i	−0.290469	+	0.503107i	−0.973921	−	0.226889i	$-0.927145\pi$
$607$	−7.15640	+	12.3952i	−0.290469	+	0.503107i	0.683452	+	0.729996i	$0.260478\pi$
$608$	11.0915	−	28.1284i	0.449819	−	1.14076i
$609$		0			0
$610$	1.52721	+	2.47315i	0.0618349	+	0.100135i
$611$	9.00064	+	5.19652i	0.364127	+	0.210229i
$612$		0			0
$613$	−10.3934	−	18.0019i	−0.419785	−	0.727090i	0.576132	−	0.817357i	$-0.304561\pi$
$613$	−10.3934	−	18.0019i	−0.419785	−	0.727090i	−0.995918	+	0.0902669i	$0.971228\pi$
$614$	−8.90934	+	0.263798i	−0.359552	+	0.0106460i
$615$		0			0
$616$	5.19512	+	22.9820i	0.209318	+	0.925973i
$617$	−10.6737			−0.429707			−0.214853	−	0.976646i	$-0.568927\pi$
$617$	−10.6737			−0.429707			−0.214853	+	0.976646i	$0.568927\pi$
$618$		0			0
$619$	13.2341	+	22.9222i	0.531924	+	0.921319i	0.999305	+	0.0372635i	$0.0118641\pi$
$619$	13.2341	+	22.9222i	0.531924	+	0.921319i	−0.467382	+	0.884056i	$0.654803\pi$
$620$	−0.496665	−	8.37968i	−0.0199466	−	0.336536i
$621$		0			0
$622$	−21.2724	−	34.4483i	−0.852944	−	1.38125i
$623$	−9.85743	+	7.60489i	−0.394930	+	0.304684i
$624$		0			0
$625$	5.70445	−	9.88040i	0.228178	−	0.395216i
$626$	3.68300	+	1.98343i	0.147202	+	0.0792737i
$627$		0			0
$628$	3.53277	−	2.32872i	0.140973	−	0.0929262i
$629$			33.2002i			1.32378i
$630$		0			0
$631$			44.3235i			1.76449i	0.470790	+	0.882245i	$0.343969\pi$
$631$			44.3235i			1.76449i	−0.470790	+	0.882245i	$0.656031\pi$
$632$	7.60120	+	3.53030i	0.302360	+	0.140428i
$633$		0			0
$634$	9.71728	−	18.0439i	0.385923	−	0.716616i
$635$	3.53344	−	6.12009i	0.140220	−	0.242868i
$636$		0			0
$637$	−16.7373	+	16.9132i	−0.663157	+	0.670127i
$638$	27.4827	−	16.9710i	1.08805	−	0.671888i
$639$		0			0
$640$	−18.7644	−	6.14336i	−0.741730	−	0.242838i
$641$	−15.4218	−	26.7113i	−0.609123	−	1.05503i	−0.991385	−	0.130979i	$-0.958188\pi$
$641$	−15.4218	−	26.7113i	−0.609123	−	1.05503i	0.382262	−	0.924054i	$-0.375145\pi$
$642$		0			0
$643$	−7.23732			−0.285412			−0.142706	−	0.989765i	$-0.545580\pi$
$643$	−7.23732			−0.285412			−0.142706	+	0.989765i	$0.545580\pi$
$644$	32.5298	−	28.3193i	1.28185	−	1.11594i
$645$		0			0
$646$	−0.928407	−	31.3554i	−0.0365277	−	1.23366i
$647$	11.8777	+	20.5727i	0.466960	+	0.808798i	0.999288	−	0.0377401i	$-0.0120159\pi$
$647$	11.8777	+	20.5727i	0.466960	+	0.808798i	−0.532328	+	0.846538i	$0.678683\pi$
$648$		0			0
$649$	−21.2427	−	12.2645i	−0.833847	−	0.481422i
$650$	−7.99376	+	4.93627i	−0.313541	+	0.193617i
$651$		0			0
$652$	−2.16922	−	1.08664i	−0.0849532	−	0.0425563i
$653$	9.03318	−	15.6459i	0.353495	−	0.612272i	−0.633364	−	0.773854i	$-0.718326\pi$
$653$	9.03318	−	15.6459i	0.353495	−	0.612272i	0.986859	+	0.161582i	$0.0516596\pi$
$654$		0			0
$655$	−20.6131	+	11.9010i	−0.805422	+	0.465010i
$656$	−0.0206179	−	0.173321i	−0.000804996	−	0.00676704i
$657$		0			0
$658$	7.25287	+	8.84686i	0.282746	+	0.344886i
$659$			11.2889i			0.439752i	0.975528	+	0.219876i	$0.0705653\pi$
$659$			11.2889i			0.439752i	−0.975528	+	0.219876i	$0.929435\pi$
$660$		0			0
$661$	−33.7023	+	19.4580i	−1.31087	+	0.756830i	−0.982240	−	0.187630i	$-0.939919\pi$
$661$	−33.7023	+	19.4580i	−1.31087	+	0.756830i	−0.328628	+	0.944460i	$0.606586\pi$
$662$	38.7973	+	20.8937i	1.50790	+	0.812057i
$663$		0			0
$664$	−22.0837	+	1.96624i	−0.857015	+	0.0763048i
$665$	3.28531	+	24.4602i	0.127399	+	0.948526i
$666$		0			0
$667$	−51.2039	−	29.5626i	−1.98262	−	1.14467i
$668$	−25.1239	+	1.48910i	−0.972071	+	0.0576149i
$669$		0			0
$670$	−21.4737	+	0.635819i	−0.829603	+	0.0245638i
$671$	3.70817			0.143152
$672$		0			0
$673$	28.6507			1.10440			0.552201	−	0.833711i	$-0.313788\pi$
$673$	28.6507			1.10440			0.552201	+	0.833711i	$0.313788\pi$
$674$	−3.75777	+	0.111264i	−0.144744	+	0.00428574i
$675$		0			0
$676$	2.88491	−	0.170989i	0.110958	−	0.00657650i
$677$	−20.0975	−	11.6033i	−0.772410	−	0.445951i	0.0613234	−	0.998118i	$-0.480468\pi$
$677$	−20.0975	−	11.6033i	−0.772410	−	0.445951i	−0.833734	+	0.552167i	$0.813801\pi$
$678$		0			0
$679$	29.2331	+	12.0193i	1.12186	+	0.461259i
$680$	−20.4036	+	1.81665i	−0.782443	+	0.0696653i
$681$		0			0
$682$	−9.42869	−	5.07768i	−0.361043	−	0.194434i
$683$	−22.0570	+	12.7346i	−0.843987	+	0.487276i	−0.858617	−	0.512617i	$-0.828676\pi$
$683$	−22.0570	+	12.7346i	−0.843987	+	0.487276i	0.0146307	+	0.999893i	$0.495343\pi$
$684$		0			0
$685$			7.83736i			0.299450i
$686$	−23.8057	+	10.9219i	−0.908907	+	0.416999i
$687$		0			0
$688$	2.54370	+	21.3832i	0.0969778	+	0.815225i
$689$	−11.9895	+	6.92213i	−0.456763	+	0.263712i
$690$		0			0
$691$	−22.9300	+	39.7160i	−0.872299	+	1.51087i	−0.0126863	+	0.999920i	$0.504038\pi$
$691$	−22.9300	+	39.7160i	−0.872299	+	1.51087i	−0.859613	+	0.510946i	$0.829295\pi$
$692$	−12.9737	−	6.49904i	−0.493188	−	0.247057i
$693$		0			0
$694$	−6.57236	+	4.05853i	−0.249483	+	0.154060i
$695$	17.0675	+	9.85393i	0.647408	+	0.373781i
$696$		0			0
$697$	−0.0905415	−	0.156822i	−0.00342950	−	0.00594008i
$698$	0.237105	+	8.00784i	0.00897456	+	0.303101i
$699$		0			0
$700$	−10.1499	+	1.98062i	−0.383631	+	0.0748604i
$701$	−36.4203			−1.37557			−0.687787	−	0.725912i	$-0.741418\pi$
$701$	−36.4203			−1.37557			−0.687787	+	0.725912i	$0.741418\pi$
$702$		0			0
$703$	21.3810	+	37.0329i	0.806399	+	1.39672i
$704$	−19.2459	+	16.2502i	−0.725357	+	0.612452i
$705$		0			0
$706$	6.23920	−	3.85280i	0.234815	−	0.145002i
$707$	5.35160	+	39.8443i	0.201268	+	1.49850i
$708$		0			0
$709$	15.5549	−	26.9419i	0.584177	−	1.01182i	−0.410801	−	0.911725i	$-0.634751\pi$
$709$	15.5549	−	26.9419i	0.584177	−	1.01182i	0.994977	−	0.100099i	$-0.0319159\pi$
$710$	12.5845	−	23.3681i	0.472289	−	0.876989i
$711$		0			0
$712$	−12.0713	−	5.60638i	−0.452390	−	0.210108i
$713$			19.6027i			0.734125i
$714$		0			0
$715$		−	18.6785i		−	0.698538i
$716$	2.94737	−	1.94284i	0.110148	−	0.0726073i
$717$		0			0
$718$	−3.42608	−	1.84507i	−0.127860	−	0.0688573i
$719$	9.22256	−	15.9739i	0.343943	−	0.595727i	−0.641218	−	0.767359i	$-0.721571\pi$
$719$	9.22256	−	15.9739i	0.343943	−	0.595727i	0.985161	+	0.171632i	$0.0549038\pi$
$720$		0			0
$721$	23.0902	+	29.9294i	0.859923	+	1.11463i
$722$	−7.11068	−	11.5150i	−0.264632	−	0.428543i
$723$		0			0
$724$	0.152187	+	2.56769i	0.00565600	+	0.0954273i
$725$	7.08834	+	12.2774i	0.263254	+	0.455970i
$726$		0			0
$727$	−21.2825			−0.789324			−0.394662	−	0.918826i	$-0.629138\pi$
$727$	−21.2825			−0.789324			−0.394662	+	0.918826i	$0.629138\pi$
$728$	−24.2920	−	7.54857i	−0.900320	−	0.279769i
$729$		0			0
$730$	−41.2668	+	1.22187i	−1.52735	+	0.0452236i
$731$	11.1704	+	19.3477i	0.413152	+	0.715601i
$732$		0			0
$733$	18.0418	+	10.4164i	0.666388	+	0.384740i	0.794707	−	0.606993i	$-0.207625\pi$
$733$	18.0418	+	10.4164i	0.666388	+	0.384740i	−0.128318	+	0.991733i	$0.540958\pi$
$734$	−23.3830	−	37.8663i	−0.863084	−	1.39767i
$735$		0			0
$736$	42.8934	+	16.9135i	1.58107	+	0.623441i
$737$	−13.7034	+	23.7350i	−0.504771	+	0.874290i
$738$		0			0
$739$	2.80080	−	1.61704i	0.103029	−	0.0594839i	−0.447600	−	0.894234i	$-0.647721\pi$
$739$	2.80080	−	1.61704i	0.103029	−	0.0594839i	0.550629	+	0.834750i	$0.314388\pi$
$740$	23.3144	−	15.3683i	0.857053	−	0.564950i
$741$		0			0
$742$	−15.0364	+	2.47464i	−0.552005	+	0.0908469i
$743$			26.3203i			0.965597i	0.875732	+	0.482798i	$0.160380\pi$
$743$			26.3203i			0.965597i	−0.875732	+	0.482798i	$0.839620\pi$
$744$		0			0
$745$	−27.8575	+	16.0835i	−1.02062	+	0.589255i
$746$	1.53732	−	2.85464i	0.0562854	−	0.104516i
$747$		0			0
$748$	−11.7044	+	23.3649i	−0.427954	+	0.854306i
$749$	27.2414	−	21.0164i	0.995378	−	0.767923i
$750$		0			0
$751$	−16.6938	−	9.63819i	−0.609166	−	0.351702i	0.163473	−	0.986548i	$-0.447730\pi$
$751$	−16.6938	−	9.63819i	−0.609166	−	0.351702i	−0.772639	+	0.634845i	$0.781064\pi$
$752$	−4.82097	+	11.2394i	−0.175803	+	0.409860i
$753$		0			0
$754$	1.03207	+	34.8566i	0.0375859	+	1.26940i
$755$	5.08903			0.185209
$756$		0			0
$757$	−2.35122			−0.0854567			−0.0427283	−	0.999087i	$-0.513605\pi$
$757$	−2.35122			−0.0854567			−0.0427283	+	0.999087i	$0.513605\pi$
$758$	0.304518	+	10.2846i	0.0110606	+	0.373554i
$759$		0			0
$760$	−21.5892	+	15.1663i	−0.783121	+	0.550140i
$761$	−14.0951	−	8.13782i	−0.510948	−	0.294996i	0.222275	−	0.974984i	$-0.428652\pi$
$761$	−14.0951	−	8.13782i	−0.510948	−	0.294996i	−0.733223	+	0.679988i	$0.761985\pi$
$762$		0			0
$763$	23.7474	−	3.18958i	0.859715	−	0.115470i
$764$	5.54798	+	2.77919i	0.200719	+	0.100548i
$765$		0			0
$766$	−8.60984	+	15.9875i	−0.311086	+	0.577653i
$767$	22.9339	−	13.2409i	0.828095	−	0.478101i
$768$		0			0
$769$			27.1545i			0.979216i	0.871943	+	0.489608i	$0.162860\pi$
$769$			27.1545i			0.979216i	−0.871943	+	0.489608i	$0.837140\pi$
$770$	7.25206	−	19.2385i	0.261346	−	0.693306i
$771$		0			0
$772$	21.1886	+	32.1441i	0.762596	+	1.15689i
$773$	−7.84184	+	4.52749i	−0.282051	+	0.162842i	−0.634352	−	0.773045i	$-0.718733\pi$
$773$	−7.84184	+	4.52749i	−0.282051	+	0.162842i	0.352300	+	0.935887i	$0.385400\pi$
$774$		0			0
$775$	2.35010	−	4.07050i	0.0844182	−	0.146217i
$776$	2.99665	+	33.6567i	0.107573	+	1.20821i
$777$		0			0
$778$	20.9341	+	33.9004i	0.750522	+	1.21539i
$779$	−0.201988	−	0.116618i	−0.00723696	−	0.00417826i
$780$		0			0
$781$	−16.9298	−	29.3233i	−0.605796	−	1.04927i
$782$	47.8143	−	1.41574i	1.70983	−	0.0506267i
$783$		0			0
$784$	−22.0894	−	17.2064i	−0.788907	−	0.614513i
$785$	−3.69215			−0.131778
$786$		0			0
$787$	−7.86884	−	13.6292i	−0.280494	−	0.485830i	0.691013	−	0.722843i	$-0.257165\pi$
$787$	−7.86884	−	13.6292i	−0.280494	−	0.485830i	−0.971506	+	0.237013i	$0.923832\pi$
$788$	32.2964	−	1.91421i	1.15051	−	0.0681910i
$789$		0			0
$790$	−3.84244	−	6.22242i	−0.136708	−	0.221384i
$791$	−12.3690	+	30.0836i	−0.439791	+	1.06965i
$792$		0			0
$793$	−2.00169	+	3.46704i	−0.0710823	+	0.123118i
$794$	−36.7987	−	19.8174i	−1.30594	−	0.703292i
$795$		0			0
$796$	6.67508	+	10.1264i	0.236592	+	0.358920i
$797$			51.7070i			1.83156i	0.401684	+	0.915778i	$0.368425\pi$
$797$			51.7070i			1.83156i	−0.401684	+	0.915778i	$0.631575\pi$
$798$		0			0
$799$			12.6880i			0.448869i
$800$	−6.87911	−	8.65445i	−0.243213	−	0.305981i
$801$		0			0
$802$	−8.58902	+	15.9489i	−0.303289	+	0.563174i
$803$	−26.3343	+	45.6123i	−0.929316	+	1.60962i
$804$		0			0
$805$	−37.2997	+	5.00981i	−1.31464	+	0.176573i
$806$	9.83717	−	6.07460i	0.346499	−	0.213969i
$807$		0			0
$808$	−35.1675	+	24.7051i	−1.23719	+	0.869123i
$809$	−3.30849	−	5.73047i	−0.116320	−	0.201473i	0.801986	−	0.597342i	$-0.203777\pi$
$809$	−3.30849	−	5.73047i	−0.116320	−	0.201473i	−0.918307	+	0.395870i	$0.870443\pi$
$810$		0			0
$811$	−17.9160			−0.629117			−0.314558	−	0.949238i	$-0.601856\pi$
$811$	−17.9160			−0.629117			−0.314558	+	0.949238i	$0.601856\pi$
$812$	−12.4703	+	36.3022i	−0.437622	+	1.27396i
$813$		0			0
$814$	−1.05432	−	35.6079i	−0.0369538	−	1.24806i
$815$	1.05853	+	1.83343i	0.0370786	+	0.0642221i
$816$		0			0
$817$	24.9199	+	14.3875i	0.871837	+	0.503355i
$818$	35.0344	−	21.6343i	1.22495	−	0.756425i
$819$		0			0
$820$	−0.0682149	+	0.136174i	−0.00238217	+	0.00475541i
$821$	4.57063	−	7.91656i	0.159516	−	0.276290i	−0.775178	−	0.631743i	$-0.782340\pi$
$821$	4.57063	−	7.91656i	0.159516	−	0.276290i	0.934694	+	0.355453i	$0.115673\pi$
$822$		0			0
$823$	−19.2435	+	11.1103i	−0.670787	+	0.387279i	−0.796375	−	0.604803i	$-0.793252\pi$
$823$	−19.2435	+	11.1103i	−0.670787	+	0.387279i	0.125588	+	0.992083i	$0.459918\pi$
$824$	−17.0222	+	36.6511i	−0.592998	+	1.27680i
$825$		0			0
$826$	28.7622	−	4.73358i	1.00077	−	0.164702i
$827$		−	5.08679i		−	0.176885i	−0.996081	−	0.0884425i	$-0.971811\pi$
$827$		−	5.08679i		−	0.176885i	0.996081	−	0.0884425i	$-0.0281890\pi$
$828$		0			0
$829$	36.4476	−	21.0430i	1.26588	−	0.730855i	0.291673	−	0.956518i	$-0.405788\pi$
$829$	36.4476	−	21.0430i	1.26588	−	0.730855i	0.974205	+	0.225663i	$0.0724548\pi$
$830$	17.0333	+	9.17305i	0.591236	+	0.318401i
$831$		0			0
$832$	−4.80441	−	26.7664i	−0.166563	−	0.927957i
$833$	−28.0983	−	7.37169i	−0.973547	−	0.255414i
$834$		0			0
$835$	19.0191	+	10.9807i	0.658182	+	0.380002i
$836$	1.99147	+	33.5999i	0.0688765	+	1.16208i
$837$		0			0
$838$	50.1726	−	1.48557i	1.73318	−	0.0513180i
$839$	−13.2905			−0.458838			−0.229419	−	0.973328i	$-0.573683\pi$
$839$	−13.2905			−0.458838			−0.229419	+	0.973328i	$0.573683\pi$
$840$		0			0
$841$	23.6200			0.814483
$842$	−51.5503	+	1.52636i	−1.77654	+	0.0526018i
$843$		0			0
$844$	0.491912	+	8.29947i	0.0169323	+	0.285680i
$845$	−2.18391	−	1.26088i	−0.0751288	−	0.0433756i
$846$		0			0
$847$	1.75568	+	2.27570i	0.0603258	+	0.0781941i
$848$	−9.75495	−	13.0473i	−0.334987	−	0.448048i
$849$		0			0
$850$	−10.0984	−	5.43833i	−0.346371	−	0.186533i
$851$	−56.4719	+	32.6041i	−1.93583	+	1.11765i
$852$		0			0
$853$		−	4.72501i		−	0.161781i	−0.996723	−	0.0808905i	$-0.974224\pi$
$853$		−	4.72501i		−	0.161781i	0.996723	−	0.0808905i	$-0.0257764\pi$
$854$	−3.40780	+	2.79380i	−0.116612	+	0.0956017i
$855$		0			0
$856$	33.3594	+	15.4934i	1.14020	+	0.529555i
$857$	−1.37578	+	0.794304i	−0.0469956	+	0.0271329i	−0.523314	−	0.852140i	$-0.675304\pi$
$857$	−1.37578	+	0.794304i	−0.0469956	+	0.0271329i	0.476318	+	0.879273i	$0.341971\pi$
$858$		0			0
$859$	5.30022	−	9.18026i	0.180841	−	0.313226i	−0.761326	−	0.648369i	$-0.775451\pi$
$859$	5.30022	−	9.18026i	0.180841	−	0.313226i	0.942167	+	0.335143i	$0.108785\pi$
$860$	8.41590	−	16.8003i	0.286980	−	0.572884i
$861$		0			0
$862$	29.8837	−	18.4536i	1.01784	−	0.628534i
$863$	−33.6848	−	19.4479i	−1.14664	−	0.662015i	−0.198576	−	0.980085i	$-0.563632\pi$
$863$	−33.6848	−	19.4479i	−1.14664	−	0.662015i	−0.948067	+	0.318070i	$0.896965\pi$
$864$		0			0
$865$	6.33089	+	10.9654i	0.215257	+	0.372835i
$866$	−0.726200	−	24.5262i	−0.0246773	−	0.833435i
$867$		0			0
$868$	12.4906	−	2.43736i	0.423957	−	0.0827294i
$869$	−9.32971			−0.316489
$870$		0			0
$871$	−14.7944	−	25.6246i	−0.501289	−	0.868258i
$872$	14.7244	+	20.9600i	0.498630	+	0.709796i
$873$		0			0
$874$	52.4224	−	32.3716i	1.77321	−	1.09499i
$875$	29.6982	+	12.2105i	1.00398	+	0.412791i
$876$		0			0
$877$	−19.3555	+	33.5247i	−0.653589	+	1.13205i	0.328656	+	0.944450i	$0.393404\pi$
$877$	−19.3555	+	33.5247i	−0.653589	+	1.13205i	−0.982245	+	0.187600i	$0.939929\pi$
$878$	−9.04117	+	16.7885i	−0.305125	+	0.566583i
$879$		0			0
$880$	21.8256	−	2.59634i	0.735741	−	0.0875225i
$881$			7.38217i			0.248712i	0.992238	+	0.124356i	$0.0396864\pi$
$881$			7.38217i			0.248712i	−0.992238	+	0.124356i	$0.960314\pi$
$882$		0			0
$883$		−	44.5978i		−	1.50084i	−0.660963	−	0.750418i	$-0.729852\pi$
$883$		−	44.5978i		−	1.50084i	0.660963	−	0.750418i	$-0.270148\pi$
$884$	−15.5275	−	23.5558i	−0.522245	−	0.792268i
$885$		0			0
$886$	−35.8962	−	19.3314i	−1.20596	−	0.649451i
$887$	6.05823	−	10.4932i	0.203415	−	0.352326i	−0.746211	−	0.665709i	$-0.768129\pi$
$887$	6.05823	−	10.4932i	0.203415	−	0.352326i	0.949627	+	0.313383i	$0.101462\pi$
$888$		0			0
$889$	9.90875	+	4.07403i	0.332329	+	0.136639i
$890$	6.10208	+	9.88165i	0.204542	+	0.331234i
$891$		0			0
$892$	−1.72450	+	0.102212i	−0.0577407	+	0.00342230i
$893$	8.17109	+	14.1528i	0.273435	+	0.473604i
$894$		0			0
$895$	−3.08033			−0.102964
$896$	5.44379	−	29.4341i	0.181864	−	0.983324i
$897$		0			0
$898$	6.72516	−	0.199126i	0.224422	−	0.00664493i
$899$	−8.72295	−	15.1086i	−0.290927	−	0.503900i
$900$		0			0
$901$	−14.6369	−	8.45065i	−0.487627	−	0.281532i
$902$	0.102088	+	0.165320i	0.00339915	+	0.00550456i
$903$		0			0
$904$	−34.6359	+	3.08383i	−1.15197	+	0.102567i
$905$	1.12224	−	1.94377i	0.0373044	−	0.0646131i
$906$		0			0
$907$	18.9570	−	10.9448i	0.629458	−	0.363418i	−0.151084	−	0.988521i	$-0.548276\pi$
$907$	18.9570	−	10.9448i	0.629458	−	0.363418i	0.780542	+	0.625103i	$0.214943\pi$
$908$	−6.18177	−	9.37801i	−0.205149	−	0.311220i
$909$		0			0
$910$	14.0727	+	17.1655i	0.466507	+	0.569032i
$911$			8.74240i			0.289649i	0.989457	+	0.144824i	$0.0462617\pi$
$911$			8.74240i			0.289649i	−0.989457	+	0.144824i	$0.953738\pi$
$912$		0			0
$913$	21.3742	−	12.3404i	0.707382	−	0.408407i
$914$	4.70537	−	8.73736i	0.155640	−	0.289006i
$915$		0			0
$916$	−51.0327	−	25.5642i	−1.68617	−	0.844665i
$917$	−22.0416	−	28.5703i	−0.727879	−	0.943474i
$918$		0			0
$919$	−35.4621	−	20.4740i	−1.16979	−	0.675376i	−0.216156	−	0.976359i	$-0.569352\pi$
$919$	−35.4621	−	20.4740i	−1.16979	−	0.675376i	−0.953630	+	0.300982i	$0.902685\pi$
$920$	−23.1273	−	32.9215i	−0.762485	−	1.08539i
$921$		0			0
$922$	−0.381799	−	12.8946i	−0.0125739	−	0.424662i
$923$	36.5553			1.20323
$924$		0			0
$925$	15.6352			0.514083
$926$	0.164206	+	5.54581i	0.00539616	+	0.182246i
$927$		0			0
$928$	−40.5860	+	6.05107i	−1.33230	+	0.198636i
$929$	38.8035	+	22.4032i	1.27310	+	0.735026i	0.975571	−	0.219686i	$-0.0705033\pi$
$929$	38.8035	+	22.4032i	1.27310	+	0.735026i	0.297532	+	0.954712i	$0.403837\pi$
$930$		0			0
$931$	−36.0894	+	9.87262i	−1.18278	+	0.323562i
$932$	19.2247	−	38.3774i	0.629725	−	1.25709i
$933$		0			0
$934$	−20.7017	+	38.4408i	−0.677381	+	1.25782i
$935$	19.7480	−	11.4015i	0.645830	−	0.372870i
$936$		0			0
$937$		−	5.99648i		−	0.195896i	−0.995192	−	0.0979482i	$-0.968772\pi$
$937$		−	5.99648i		−	0.195896i	0.995192	−	0.0979482i	$-0.0312279\pi$
$938$	−5.28895	−	32.1368i	−0.172690	−	1.04930i
$939$		0			0
$940$	8.90997	−	5.87325i	0.290611	−	0.191564i
$941$	−1.79932	+	1.03884i	−0.0586560	+	0.0338651i	−0.529041	−	0.848596i	$-0.677448\pi$
$941$	−1.79932	+	1.03884i	−0.0586560	+	0.0338651i	0.470385	+	0.882461i	$0.344115\pi$
$942$		0			0
$943$	0.177832	−	0.308014i	0.00579100	−	0.0100303i
$944$	18.6596	+	24.9574i	0.607319	+	0.812295i
$945$		0			0
$946$	−12.5949	−	20.3961i	−0.409496	−	0.663134i
$947$	49.0666	+	28.3286i	1.59445	+	0.920557i	0.992530	+	0.122002i	$0.0389315\pi$
$947$	49.0666	+	28.3286i	1.59445	+	0.920557i	0.601922	+	0.798555i	$0.294402\pi$
$948$		0			0
$949$	−28.4309	−	49.2437i	−0.922905	−	1.59852i
$950$	−14.7665	+	0.437222i	−0.479087	+	0.0141853i
$951$		0			0
$952$	−6.84723	−	30.2906i	−0.221920	−	0.981724i
$953$	−23.0343			−0.746154			−0.373077	−	0.927800i	$-0.621697\pi$
$953$	−23.0343			−0.746154			−0.373077	+	0.927800i	$0.621697\pi$
$954$		0			0
$955$	−2.70728	−	4.68915i	−0.0876057	−	0.151737i
$956$	−2.64445	−	44.6169i	−0.0855277	−	1.44301i
$957$		0			0
$958$	30.0831	+	48.7164i	0.971942	+	1.57395i
$959$	−11.7759	+	1.58166i	−0.380265	+	0.0510744i
$960$		0			0
$961$	12.6080	−	21.8376i	0.406708	−	0.704439i
$962$	33.8616	+	18.2356i	1.09174	+	0.587941i
$963$		0			0
$964$	36.5064	−	24.0642i	1.17579	−	0.775055i
$965$		−	33.5942i		−	1.08144i
$966$		0			0
$967$			11.5096i			0.370125i	0.982727	+	0.185062i	$0.0592487\pi$
$967$			11.5096i			0.370125i	−0.982727	+	0.185062i	$0.940751\pi$
$968$	−1.29430	+	2.78679i	−0.0416003	+	0.0895708i
$969$		0			0
$970$	13.9802	−	25.9597i	0.448877	−	0.833515i
$971$	3.02418	−	5.23804i	0.0970507	−	0.168097i	−0.813412	−	0.581688i	$-0.802392\pi$
$971$	3.02418	−	5.23804i	0.0970507	−	0.168097i	0.910463	+	0.413591i	$0.135726\pi$
$972$		0			0
$973$	−11.3615	+	27.6332i	−0.364234	+	0.885880i
$974$	−25.3805	+	15.6729i	−0.813244	+	0.502191i
$975$		0			0
$976$	−4.32942	−	1.85703i	−0.138581	−	0.0594421i
$977$	−21.5504	−	37.3264i	−0.689459	−	1.19418i	−0.972013	−	0.234926i	$-0.924515\pi$
$977$	−21.5504	−	37.3264i	−0.689459	−	1.19418i	0.282554	−	0.959251i	$-0.408818\pi$
$978$		0			0
$979$	14.8162			0.473529
$980$	7.82996	+	23.1439i	0.250119	+	0.739306i
$981$		0			0
$982$	−0.394555	−	13.3255i	−0.0125908	−	0.425233i
$983$	19.4666	+	33.7172i	0.620889	+	1.07541i	0.989321	+	0.145756i	$0.0465614\pi$
$983$	19.4666	+	33.7172i	0.620889	+	1.07541i	−0.368432	+	0.929655i	$0.620105\pi$
$984$		0			0
$985$	−24.4488	−	14.1155i	−0.779002	−	0.449757i
$986$	−36.2225	+	22.3679i	−1.15356	+	0.712340i
$987$		0			0
$988$	−32.4900	−	16.2755i	−1.03364	−	0.517792i
$989$	−21.9397	+	38.0007i	−0.697641	+	1.20835i
$990$		0			0
$991$	36.3252	−	20.9724i	1.15391	−	0.666209i	0.204072	−	0.978956i	$-0.434582\pi$
$991$	36.3252	−	20.9724i	1.15391	−	0.666209i	0.949837	+	0.312747i	$0.101249\pi$
$992$	8.46547	+	10.6502i	0.268779	+	0.338145i
$993$		0			0
$994$	37.6511	+	14.1928i	1.19422	+	0.450170i
$995$		−	10.5832i		−	0.335511i
$996$		0			0
$997$	9.81396	−	5.66609i	0.310811	−	0.179447i	−0.336478	−	0.941691i	$-0.609236\pi$
$997$	9.81396	−	5.66609i	0.310811	−	0.179447i	0.647289	+	0.762244i	$0.275903\pi$
$998$	9.25953	+	4.98658i	0.293105	+	0.157847i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.d.271.16	yes	32
3.2	odd	2	inner	756.2.bf.d.271.1	yes	32
4.3	odd	2		756.2.bf.a.271.7	✓	32
7.3	odd	6		756.2.bf.a.703.7	yes	32
12.11	even	2		756.2.bf.a.271.10	yes	32
21.17	even	6		756.2.bf.a.703.10	yes	32
28.3	even	6	inner	756.2.bf.d.703.16	yes	32
84.59	odd	6	inner	756.2.bf.d.703.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.a.271.7	✓	32	4.3	odd	2
756.2.bf.a.271.10	yes	32	12.11	even	2
756.2.bf.a.703.7	yes	32	7.3	odd	6
756.2.bf.a.703.10	yes	32	21.17	even	6
756.2.bf.d.271.1	yes	32	3.2	odd	2	inner
756.2.bf.d.271.16	yes	32	1.1	even	1	trivial
756.2.bf.d.703.1	yes	32	84.59	odd	6	inner
756.2.bf.d.703.16	yes	32	28.3	even	6	inner

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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41359 - 0.0418553i) q^{2} +(1.99650 - 0.118333i) q^{4} +(-1.51137 - 0.872592i) q^{5} +(1.00609 - 2.44699i) q^{7} +(2.81728 - 0.250838i) q^{8} +O(q^{10})\)	\(q+(1.41359 - 0.0418553i) q^{2} +(1.99650 - 0.118333i) q^{4} +(-1.51137 - 0.872592i) q^{5} +(1.00609 - 2.44699i) q^{7} +(2.81728 - 0.250838i) q^{8} +(-2.17299 - 1.17023i) q^{10} +(-2.72676 + 1.57430i) q^{11} -3.39927i q^{13} +(1.31979 - 3.50117i) q^{14} +(3.97199 - 0.472502i) q^{16} +(3.59390 - 2.07494i) q^{17} +(2.67253 - 4.62896i) q^{19} +(-3.12071 - 1.56328i) q^{20} +(-3.78864 + 2.33955i) q^{22} +(7.05875 + 4.07537i) q^{23} +(-0.977168 - 1.69250i) q^{25} +(-0.142277 - 4.80518i) q^{26} +(1.71910 - 5.00447i) q^{28} -7.25396 q^{29} +(1.20251 + 2.08280i) q^{31} +(5.59501 - 0.834175i) q^{32} +(4.99347 - 3.08355i) q^{34} +(-3.65581 + 2.82041i) q^{35} +(-4.00014 + 6.92844i) q^{37} +(3.58413 - 6.65533i) q^{38} +(-4.47684 - 2.07923i) q^{40} -0.0436357i q^{41} +5.38348i q^{43} +(-5.25768 + 3.46574i) q^{44} +(10.1488 + 5.46547i) q^{46} +(-1.52872 + 2.64782i) q^{47} +(-4.97556 - 4.92380i) q^{49} +(-1.45216 - 2.35161i) q^{50} +(-0.402245 - 6.78662i) q^{52} +(-2.03636 - 3.52708i) q^{53} +5.49487 q^{55} +(2.22065 - 7.14624i) q^{56} +(-10.2542 + 0.303617i) q^{58} +(3.89522 + 6.74671i) q^{59} +(-1.01994 - 0.588861i) q^{61} +(1.78703 + 2.89391i) q^{62} +(7.87416 - 1.41337i) q^{64} +(-2.96617 + 5.13756i) q^{65} +(7.53828 - 4.35223i) q^{67} +(6.92968 - 4.56789i) q^{68} +(-5.04978 + 4.13993i) q^{70} +10.7539i q^{71} +(14.4866 - 8.36382i) q^{73} +(-5.36458 + 9.96143i) q^{74} +(4.78794 - 9.55794i) q^{76} +(1.10892 + 8.25626i) q^{77} +(2.56615 + 1.48157i) q^{79} +(-6.41547 - 2.75180i) q^{80} +(-0.00182638 - 0.0616832i) q^{82} -7.83867 q^{83} -7.24230 q^{85} +(0.225327 + 7.61006i) q^{86} +(-7.28716 + 5.11922i) q^{88} +(-4.07523 - 2.35284i) q^{89} +(-8.31798 - 3.41998i) q^{91} +(14.5750 + 7.30118i) q^{92} +(-2.05016 + 3.80693i) q^{94} +(-8.07838 + 4.66405i) q^{95} +11.9465i q^{97} +(-7.23950 - 6.75201i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{7}+O(q^{10}) \) 32 * q + 2 * q^7	\( 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) \) 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more