LMFDB - Embedded newform 702.2.t.a.415.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(181,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.181"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.5
Character	$\chi$	$=$	702.415
Dual form			702.2.t.a.181.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.548308 + 0.316566i) q^{5} +(2.15366 - 1.24342i) q^{7} +1.00000i q^{8} -0.633132 q^{10} +(-4.20891 + 2.43002i) q^{11} +(3.35794 - 1.31310i) q^{13} +(-1.24342 + 2.15366i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.27837 q^{17} +4.86004i q^{19} +(0.548308 - 0.316566i) q^{20} +(2.43002 - 4.20891i) q^{22} +(1.77384 - 3.07238i) q^{23} +(-2.29957 - 3.98298i) q^{25} +(-2.25152 + 2.81615i) q^{26} -2.48683i q^{28} +(-0.415447 - 0.719576i) q^{29} +(3.73461 + 2.15618i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.43723 + 3.13918i) q^{34} +1.57449 q^{35} -7.81310i q^{37} +(-2.43002 - 4.20891i) q^{38} +(-0.316566 + 0.548308i) q^{40} +(0.0678657 + 0.0391823i) q^{41} +(4.84370 + 8.38954i) q^{43} +4.86004i q^{44} +3.54768i q^{46} +(4.30069 - 2.48301i) q^{47} +(-0.407830 + 0.706382i) q^{49} +(3.98298 + 2.29957i) q^{50} +(0.541797 - 3.56461i) q^{52} +6.36026 q^{53} -3.07704 q^{55} +(1.24342 + 2.15366i) q^{56} +(0.719576 + 0.415447i) q^{58} +(7.86994 + 4.54371i) q^{59} +(5.28535 + 9.15449i) q^{61} -4.31236 q^{62} -1.00000 q^{64} +(2.25687 + 0.343029i) q^{65} +(6.82824 + 3.94228i) q^{67} +(3.13918 - 5.43723i) q^{68} +(-1.36355 + 0.787247i) q^{70} -12.3085i q^{71} -1.05367i q^{73} +(3.90655 + 6.76635i) q^{74} +(4.20891 + 2.43002i) q^{76} +(-6.04305 + 10.4669i) q^{77} +(-1.68838 - 2.92436i) q^{79} -0.633132i q^{80} -0.0783645 q^{82} +(-13.1755 + 7.60686i) q^{83} +(3.44248 + 1.98752i) q^{85} +(-8.38954 - 4.84370i) q^{86} +(-2.43002 - 4.20891i) q^{88} -0.595093i q^{89} +(5.59914 - 7.00329i) q^{91} +(-1.77384 - 3.07238i) q^{92} +(-2.48301 + 4.30069i) q^{94} +(-1.53852 + 2.66480i) q^{95} +(-14.7770 + 8.53151i) q^{97} -0.815659i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.548308	+	0.316566i	0.245211	+	0.141573i	0.617569	−	0.786516i	$-0.288117\pi$
$5$	0.548308	+	0.316566i	0.245211	+	0.141573i	−0.372358	+	0.928089i	$0.621451\pi$
$6$		0			0
$7$	2.15366	−	1.24342i	0.814007	−	0.469967i	−0.0343382	−	0.999410i	$-0.510932\pi$
$7$	2.15366	−	1.24342i	0.814007	−	0.469967i	0.848346	+	0.529443i	$0.177599\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.633132			−0.200214
$11$	−4.20891	+	2.43002i	−1.26904	+	0.732678i	−0.974805	−	0.223057i	$-0.928396\pi$
$11$	−4.20891	+	2.43002i	−1.26904	+	0.732678i	−0.294230	+	0.955735i	$0.595063\pi$
$12$		0			0
$13$	3.35794	−	1.31310i	0.931326	−	0.364187i
$13$	3.35794	−	1.31310i	0.931326	−	0.364187i
$14$	−1.24342	+	2.15366i	−0.332317	+	0.575590i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.27837			1.52273			0.761364	−	0.648325i	$-0.224530\pi$
$17$	6.27837			1.52273			0.761364	+	0.648325i	$0.224530\pi$
$18$		0			0
$19$			4.86004i			1.11497i	0.830187	+	0.557484i	$0.188233\pi$
$19$			4.86004i			1.11497i	−0.830187	+	0.557484i	$0.811767\pi$
$20$	0.548308	−	0.316566i	0.122605	−	0.0707863i
$21$		0			0
$22$	2.43002	−	4.20891i	0.518082	−	0.897344i
$23$	1.77384	−	3.07238i	0.369871	−	0.640636i	−0.619674	−	0.784859i	$-0.712735\pi$
$23$	1.77384	−	3.07238i	0.369871	−	0.640636i	0.989545	+	0.144224i	$0.0460685\pi$
$24$		0			0
$25$	−2.29957	−	3.98298i	−0.459914	−	0.796595i
$26$	−2.25152	+	2.81615i	−0.441559	+	0.552292i
$27$		0			0
$28$		−	2.48683i		−	0.469967i
$29$	−0.415447	−	0.719576i	−0.0771466	−	0.133622i	0.824871	−	0.565321i	$-0.191248\pi$
$29$	−0.415447	−	0.719576i	−0.0771466	−	0.133622i	−0.902018	+	0.431699i	$0.857914\pi$
$30$		0			0
$31$	3.73461	+	2.15618i	0.670756	+	0.387261i	0.796363	−	0.604819i	$-0.206755\pi$
$31$	3.73461	+	2.15618i	0.670756	+	0.387261i	−0.125607	+	0.992080i	$0.540088\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−5.43723	+	3.13918i	−0.932477	+	0.538366i
$35$	1.57449			0.266138
$36$		0			0
$37$		−	7.81310i		−	1.28447i	−0.766509	−	0.642233i	$-0.778008\pi$
$37$		−	7.81310i		−	1.28447i	0.766509	−	0.642233i	$-0.221992\pi$
$38$	−2.43002	−	4.20891i	−0.394201	−	0.682776i
$39$		0			0
$40$	−0.316566	+	0.548308i	−0.0500535	+	0.0866952i
$41$	0.0678657	+	0.0391823i	0.0105988	+	0.00611924i	0.505290	−	0.862950i	$-0.331386\pi$
$41$	0.0678657	+	0.0391823i	0.0105988	+	0.00611924i	−0.494691	+	0.869069i	$0.664719\pi$
$42$		0			0
$43$	4.84370	+	8.38954i	0.738658	+	1.27939i	0.953100	+	0.302656i	$0.0978733\pi$
$43$	4.84370	+	8.38954i	0.738658	+	1.27939i	−0.214442	+	0.976737i	$0.568793\pi$
$44$			4.86004i			0.732678i
$45$		0			0
$46$			3.54768i			0.523077i
$47$	4.30069	−	2.48301i	0.627320	−	0.362184i	−0.152393	−	0.988320i	$-0.548698\pi$
$47$	4.30069	−	2.48301i	0.627320	−	0.362184i	0.779714	+	0.626136i	$0.215365\pi$
$48$		0			0
$49$	−0.407830	+	0.706382i	−0.0582614	+	0.100912i
$50$	3.98298	+	2.29957i	0.563278	+	0.325209i
$51$		0			0
$52$	0.541797	−	3.56461i	0.0751337	−	0.494323i
$53$	6.36026			0.873649			0.436824	−	0.899547i	$-0.356103\pi$
$53$	6.36026			0.873649			0.436824	+	0.899547i	$0.356103\pi$
$54$		0			0
$55$	−3.07704			−0.414909
$56$	1.24342	+	2.15366i	0.166159	+	0.287795i
$57$		0			0
$58$	0.719576	+	0.415447i	0.0944849	+	0.0545509i
$59$	7.86994	+	4.54371i	1.02458	+	0.591541i	0.915427	−	0.402484i	$-0.131853\pi$
$59$	7.86994	+	4.54371i	1.02458	+	0.591541i	0.109152	+	0.994025i	$0.465187\pi$
$60$		0			0
$61$	5.28535	+	9.15449i	0.676719	+	1.17211i	0.975963	+	0.217935i	$0.0699322\pi$
$61$	5.28535	+	9.15449i	0.676719	+	1.17211i	−0.299244	+	0.954177i	$0.596734\pi$
$62$	−4.31236			−0.547670
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.25687	+	0.343029i	0.279930	+	0.0425475i
$66$		0			0
$67$	6.82824	+	3.94228i	0.834202	+	0.481627i	0.855289	−	0.518151i	$-0.173380\pi$
$67$	6.82824	+	3.94228i	0.834202	+	0.481627i	−0.0210874	+	0.999778i	$0.506713\pi$
$68$	3.13918	−	5.43723i	0.380682	−	0.659361i
$69$		0			0
$70$	−1.36355	+	0.787247i	−0.162976	+	0.0940940i
$71$		−	12.3085i		−	1.46075i	−0.683048	−	0.730374i	$-0.739346\pi$
$71$		−	12.3085i		−	1.46075i	0.683048	−	0.730374i	$-0.260654\pi$
$72$		0			0
$73$		−	1.05367i		−	0.123323i	−0.998097	−	0.0616615i	$-0.980360\pi$
$73$		−	1.05367i		−	0.123323i	0.998097	−	0.0616615i	$-0.0196399\pi$
$74$	3.90655	+	6.76635i	0.454127	+	0.786572i
$75$		0			0
$76$	4.20891	+	2.43002i	0.482796	+	0.278742i
$77$	−6.04305	+	10.4669i	−0.688669	+	1.19281i
$78$		0			0
$79$	−1.68838	−	2.92436i	−0.189958	−	0.329017i	0.755278	−	0.655404i	$-0.227502\pi$
$79$	−1.68838	−	2.92436i	−0.189958	−	0.329017i	−0.945236	+	0.326388i	$0.894168\pi$
$80$		−	0.633132i		−	0.0707863i
$81$		0			0
$82$	−0.0783645			−0.00865391
$83$	−13.1755	+	7.60686i	−1.44620	+	0.834961i	−0.998252	−	0.0591005i	$-0.981177\pi$
$83$	−13.1755	+	7.60686i	−1.44620	+	0.834961i	−0.447943	+	0.894062i	$0.647843\pi$
$84$		0			0
$85$	3.44248	+	1.98752i	0.373390	+	0.215577i
$86$	−8.38954	−	4.84370i	−0.904667	−	0.522310i
$87$		0			0
$88$	−2.43002	−	4.20891i	−0.259041	−	0.448672i
$89$		−	0.595093i		−	0.0630797i	−0.999502	−	0.0315398i	$-0.989959\pi$
$89$		−	0.595093i		−	0.0630797i	0.999502	−	0.0315398i	$-0.0100411\pi$
$90$		0			0
$91$	5.59914	−	7.00329i	0.586950	−	0.734144i
$92$	−1.77384	−	3.07238i	−0.184936	−	0.320318i
$93$		0			0
$94$	−2.48301	+	4.30069i	−0.256103	+	0.443583i
$95$	−1.53852	+	2.66480i	−0.157849	+	0.273403i
$96$		0			0
$97$	−14.7770	+	8.53151i	−1.50038	+	0.866244i	−0.500378	+	0.865807i	$0.666806\pi$
$97$	−14.7770	+	8.53151i	−1.50038	+	0.866244i	−1.00000		0.000436560i	$0.999861\pi$
$98$		−	0.815659i		−	0.0823940i
$99$		0			0
$100$	−4.59914			−0.459914
$101$	−2.53762	−	4.39529i	−0.252503	−	0.437348i	0.711712	−	0.702472i	$-0.247920\pi$
$101$	−2.53762	−	4.39529i	−0.252503	−	0.437348i	−0.964214	+	0.265124i	$0.914587\pi$
$102$		0			0
$103$	0.538522	−	0.932747i	0.0530621	−	0.0919063i	−0.838274	−	0.545249i	$-0.816435\pi$
$103$	0.538522	−	0.932747i	0.0530621	−	0.0919063i	0.891336	+	0.453342i	$0.149769\pi$
$104$	1.31310	+	3.35794i	0.128760	+	0.329273i
$105$		0			0
$106$	−5.50815	+	3.18013i	−0.534998	+	0.308881i
$107$	9.16763			0.886268			0.443134	−	0.896455i	$-0.353867\pi$
$107$	9.16763			0.886268			0.443134	+	0.896455i	$0.353867\pi$
$108$		0			0
$109$		−	9.90028i		−	0.948275i	−0.880451	−	0.474138i	$-0.842760\pi$
$109$		−	9.90028i		−	0.948275i	0.880451	−	0.474138i	$-0.157240\pi$
$110$	2.66480	−	1.53852i	0.254079	−	0.146692i
$111$		0			0
$112$	−2.15366	−	1.24342i	−0.203502	−	0.117492i
$113$	3.31088	−	5.73460i	0.311461	−	0.539466i	−0.667218	−	0.744863i	$-0.732515\pi$
$113$	3.31088	−	5.73460i	0.311461	−	0.539466i	0.978679	+	0.205396i	$0.0658484\pi$
$114$		0			0
$115$	1.94522	−	1.12307i	0.181393	−	0.104727i
$116$	−0.830894			−0.0771466
$117$		0			0
$118$	−9.08742			−0.836565
$119$	13.5215	−	7.80663i	1.23951	−	0.715632i
$120$		0			0
$121$	6.30997	−	10.9292i	0.573634	−	0.993563i
$122$	−9.15449	−	5.28535i	−0.828808	−	0.478513i
$123$		0			0
$124$	3.73461	−	2.15618i	0.335378	−	0.193630i
$125$		−	6.07752i		−	0.543590i
$126$		0			0
$127$	−17.8088			−1.58028			−0.790138	−	0.612929i	$-0.789991\pi$
$127$	−17.8088			−1.58028			−0.790138	+	0.612929i	$0.789991\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.12602	+	0.831363i	−0.186464	+	0.0729154i
$131$	−6.02780	+	10.4404i	−0.526651	+	0.912186i	0.472867	+	0.881134i	$0.343219\pi$
$131$	−6.02780	+	10.4404i	−0.526651	+	0.912186i	−0.999518	+	0.0310522i	$0.990114\pi$
$132$		0			0
$133$	6.04305	+	10.4669i	0.523999	+	0.907593i
$134$	−7.88457			−0.681123
$135$		0			0
$136$			6.27837i			0.538366i
$137$	0.263943	−	0.152388i	0.0225502	−	0.0130194i	−0.488683	−	0.872462i	$-0.662522\pi$
$137$	0.263943	−	0.152388i	0.0225502	−	0.0130194i	0.511233	+	0.859442i	$0.329189\pi$
$138$		0			0
$139$	−4.09109	+	7.08598i	−0.347002	+	0.601025i	−0.985715	−	0.168420i	$-0.946134\pi$
$139$	−4.09109	+	7.08598i	−0.347002	+	0.601025i	0.638714	+	0.769445i	$0.279467\pi$
$140$	0.787247	−	1.36355i	0.0665345	−	0.115241i
$141$		0			0
$142$	6.15424	+	10.6595i	0.516452	+	0.894522i
$143$	−10.9424	+	13.6866i	−0.915053	+	1.14453i
$144$		0			0
$145$		−	0.526066i		−	0.0436874i
$146$	0.526836	+	0.912507i	0.0436013	+	0.0755196i
$147$		0			0
$148$	−6.76635	−	3.90655i	−0.556190	−	0.321117i
$149$	−15.9905	−	9.23210i	−1.30999	−	0.756323i	−0.327895	−	0.944714i	$-0.606339\pi$
$149$	−15.9905	−	9.23210i	−1.30999	−	0.756323i	−0.982094	+	0.188391i	$0.939673\pi$
$150$		0			0
$151$	4.61608	−	2.66510i	0.375651	−	0.216882i	−0.300273	−	0.953853i	$-0.597078\pi$
$151$	4.61608	−	2.66510i	0.375651	−	0.216882i	0.675925	+	0.736971i	$0.263745\pi$
$152$	−4.86004			−0.394201
$153$		0			0
$154$		−	12.0861i		−	0.973926i
$155$	1.36515	+	2.36450i	0.109651	+	0.189921i
$156$		0			0
$157$	1.46920	−	2.54473i	0.117255	−	0.203092i	−0.801424	−	0.598097i	$-0.795924\pi$
$157$	1.46920	−	2.54473i	0.117255	−	0.203092i	0.918679	+	0.395005i	$0.129257\pi$
$158$	2.92436	+	1.68838i	0.232650	+	0.134320i
$159$		0			0
$160$	0.316566	+	0.548308i	0.0250267	+	0.0433476i
$161$		−	8.82249i		−	0.695310i
$162$		0			0
$163$		−	7.41051i		−	0.580436i	−0.956961	−	0.290218i	$-0.906272\pi$
$163$		−	7.41051i		−	0.580436i	0.956961	−	0.290218i	$-0.0937278\pi$
$164$	0.0678657	−	0.0391823i	0.00529942	−	0.00305962i
$165$		0			0
$166$	7.60686	−	13.1755i	0.590407	−	1.02261i
$167$	−0.0771631	−	0.0445501i	−0.00597106	−	0.00344739i	0.497011	−	0.867744i	$-0.334431\pi$
$167$	−0.0771631	−	0.0445501i	−0.00597106	−	0.00344739i	−0.502983	+	0.864297i	$0.667764\pi$
$168$		0			0
$169$	9.55156	−	8.81860i	0.734735	−	0.678354i
$170$	−3.97504			−0.304871
$171$		0			0
$172$	9.68740			0.738658
$173$	−3.79919	−	6.58039i	−0.288847	−	0.500298i	0.684688	−	0.728836i	$-0.259939\pi$
$173$	−3.79919	−	6.58039i	−0.288847	−	0.500298i	−0.973535	+	0.228539i	$0.926605\pi$
$174$		0			0
$175$	−9.90500	−	5.71865i	−0.748747	−	0.432290i
$176$	4.20891	+	2.43002i	0.317259	+	0.183169i
$177$		0			0
$178$	0.297546	+	0.515365i	0.0223020	+	0.0386283i
$179$	−23.7909			−1.77822			−0.889109	−	0.457695i	$-0.848675\pi$
$179$	−23.7909			−1.77822			−0.889109	+	0.457695i	$0.848675\pi$
$180$		0			0
$181$	−1.63229			−0.121327			−0.0606637	−	0.998158i	$-0.519322\pi$
$181$	−1.63229			−0.121327			−0.0606637	+	0.998158i	$0.519322\pi$
$182$	−1.34736	+	8.86460i	−0.0998728	+	0.657088i
$183$		0			0
$184$	3.07238	+	1.77384i	0.226499	+	0.130769i
$185$	2.47336	−	4.28399i	0.181845	−	0.314965i
$186$		0			0
$187$	−26.4251	+	15.2565i	−1.93240	+	1.11567i
$188$		−	4.96601i		−	0.362184i
$189$		0			0
$190$		−	3.07704i		−	0.223232i
$191$	−1.58316	−	2.74212i	−0.114554	−	0.198413i	0.803048	−	0.595915i	$-0.203210\pi$
$191$	−1.58316	−	2.74212i	−0.114554	−	0.198413i	−0.917601	+	0.397502i	$0.869877\pi$
$192$		0			0
$193$	−14.2560	−	8.23071i	−1.02617	−	0.592459i	−0.110285	−	0.993900i	$-0.535176\pi$
$193$	−14.2560	−	8.23071i	−1.02617	−	0.592459i	−0.915885	+	0.401441i	$0.868510\pi$
$194$	8.53151	−	14.7770i	0.612527	−	1.06093i
$195$		0			0
$196$	0.407830	+	0.706382i	0.0291307	+	0.0504558i
$197$		−	11.4351i		−	0.814719i	−0.913268	−	0.407360i	$-0.866450\pi$
$197$		−	11.4351i		−	0.814719i	0.913268	−	0.407360i	$-0.133550\pi$
$198$		0			0
$199$	−13.1983			−0.935602			−0.467801	−	0.883834i	$-0.654954\pi$
$199$	−13.1983			−0.935602			−0.467801	+	0.883834i	$0.654954\pi$
$200$	3.98298	−	2.29957i	0.281639	−	0.162604i
$201$		0			0
$202$	4.39529	+	2.53762i	0.309251	+	0.178546i
$203$	−1.78946	−	1.03315i	−0.125596	−	0.0725128i
$204$		0			0
$205$	0.0248075	+	0.0429679i	0.00173263	+	0.00300101i
$206$			1.07704i			0.0750412i
$207$		0			0
$208$	−2.81615	−	2.25152i	−0.195265	−	0.156115i
$209$	−11.8100	−	20.4555i	−0.816913	−	1.41493i
$210$		0			0
$211$	−4.63857	+	8.03423i	−0.319332	+	0.553099i	−0.980349	−	0.197272i	$-0.936792\pi$
$211$	−4.63857	+	8.03423i	−0.319332	+	0.553099i	0.661017	+	0.750371i	$0.270125\pi$
$212$	3.18013	−	5.50815i	0.218412	−	0.378301i
$213$		0			0
$214$	−7.93940	+	4.58381i	−0.542726	+	0.313343i
$215$			6.13341i			0.418295i
$216$		0			0
$217$	10.7241			0.728000
$218$	4.95014	+	8.57390i	0.335266	+	0.580698i
$219$		0			0
$220$	−1.53852	+	2.66480i	−0.103727	+	0.179661i
$221$	21.0824	−	8.24410i	1.41816	−	0.554558i
$222$		0			0
$223$	−12.1351	+	7.00623i	−0.812630	+	0.469172i	−0.847868	−	0.530207i	$-0.822114\pi$
$223$	−12.1351	+	7.00623i	−0.812630	+	0.469172i	0.0352386	+	0.999379i	$0.488781\pi$
$224$	2.48683			0.166159
$225$		0			0
$226$			6.62175i			0.440472i
$227$	2.40085	−	1.38613i	0.159350	−	0.0920010i	−0.418204	−	0.908353i	$-0.637340\pi$
$227$	2.40085	−	1.38613i	0.159350	−	0.0920010i	0.577555	+	0.816352i	$0.304007\pi$
$228$		0			0
$229$	−14.4165	−	8.32339i	−0.952671	−	0.550025i	−0.0587614	−	0.998272i	$-0.518715\pi$
$229$	−14.4165	−	8.32339i	−0.952671	−	0.550025i	−0.893910	+	0.448247i	$0.852048\pi$
$230$	−1.12307	+	1.94522i	−0.0740534	+	0.128264i
$231$		0			0
$232$	0.719576	−	0.415447i	0.0472425	−	0.0272754i
$233$	5.45324			0.357254			0.178627	−	0.983917i	$-0.442835\pi$
$233$	5.45324			0.357254			0.178627	+	0.983917i	$0.442835\pi$
$234$		0			0
$235$	3.14414			0.205101
$236$	7.86994	−	4.54371i	0.512289	−	0.295770i
$237$		0			0
$238$	−7.80663	+	13.5215i	−0.506029	+	0.876467i
$239$	−11.8000	−	6.81272i	−0.763277	−	0.440678i	0.0671938	−	0.997740i	$-0.478595\pi$
$239$	−11.8000	−	6.81272i	−0.763277	−	0.440678i	−0.830471	+	0.557062i	$0.811929\pi$
$240$		0			0
$241$	16.3780	−	9.45585i	1.05500	−	0.609105i	0.130956	−	0.991388i	$-0.458195\pi$
$241$	16.3780	−	9.45585i	1.05500	−	0.609105i	0.924045	+	0.382283i	$0.124862\pi$
$242$			12.6199i			0.811241i
$243$		0			0
$244$	10.5707			0.676719
$245$	−0.447233	+	0.258210i	−0.0285727	+	0.0164964i
$246$		0			0
$247$	6.38169	+	16.3197i	0.406058	+	1.03840i
$248$	−2.15618	+	3.73461i	−0.136917	+	0.237148i
$249$		0			0
$250$	3.03876	+	5.26329i	0.192188	+	0.332880i
$251$	2.07524			0.130988			0.0654940	−	0.997853i	$-0.479138\pi$
$251$	2.07524			0.130988			0.0654940	+	0.997853i	$0.479138\pi$
$252$		0			0
$253$			17.2419i			1.08399i
$254$	15.4229	−	8.90441i	0.967718	−	0.558712i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.5009	+	21.6522i	−0.779785	+	1.35063i	0.152280	+	0.988337i	$0.451338\pi$
$257$	−12.5009	+	21.6522i	−0.779785	+	1.35063i	−0.932065	+	0.362290i	$0.881995\pi$
$258$		0			0
$259$	−9.71494	−	16.8268i	−0.603657	−	1.04557i
$260$	1.42551	−	1.78299i	0.0884061	−	0.110576i
$261$		0			0
$262$		−	12.0556i		−	0.744797i
$263$	12.6267	+	21.8701i	0.778596	+	1.34857i	0.932751	+	0.360521i	$0.117401\pi$
$263$	12.6267	+	21.8701i	0.778596	+	1.34857i	−0.154155	+	0.988047i	$0.549266\pi$
$264$		0			0
$265$	3.48738	+	2.01344i	0.214228	+	0.123685i
$266$	−10.4669	−	6.04305i	−0.641765	−	0.370523i
$267$		0			0
$268$	6.82824	−	3.94228i	0.417101	−	0.240813i
$269$	23.7793			1.44985			0.724925	−	0.688828i	$-0.241874\pi$
$269$	23.7793			1.44985			0.724925	+	0.688828i	$0.241874\pi$
$270$		0			0
$271$			14.2050i			0.862894i	0.902138	+	0.431447i	$0.141997\pi$
$271$			14.2050i			0.862894i	−0.902138	+	0.431447i	$0.858003\pi$
$272$	−3.13918	−	5.43723i	−0.190341	−	0.329680i
$273$		0			0
$274$	−0.152388	+	0.263943i	−0.00920609	+	0.0159454i
$275$	19.3574	+	11.1760i	1.16730	+	0.673938i
$276$		0			0
$277$	−4.06786	−	7.04574i	−0.244414	−	0.423337i	0.717553	−	0.696504i	$-0.245262\pi$
$277$	−4.06786	−	7.04574i	−0.244414	−	0.423337i	−0.961967	+	0.273167i	$0.911929\pi$
$278$		−	8.18218i		−	0.490735i
$279$		0			0
$280$			1.57449i			0.0940940i
$281$	−28.6610	+	16.5474i	−1.70977	+	0.987138i	−0.774949	+	0.632023i	$0.782225\pi$
$281$	−28.6610	+	16.5474i	−1.70977	+	0.987138i	−0.934823	+	0.355114i	$0.884442\pi$
$282$		0			0
$283$	5.92146	−	10.2563i	0.351994	−	0.609672i	−0.634604	−	0.772837i	$-0.718837\pi$
$283$	5.92146	−	10.2563i	0.351994	−	0.609672i	0.986599	+	0.163165i	$0.0521703\pi$
$284$	−10.6595	−	6.15424i	−0.632522	−	0.365187i
$285$		0			0
$286$	2.63315	−	17.3241i	0.155701	−	1.02440i
$287$	0.194879			0.0115034
$288$		0			0
$289$	22.4179			1.31870
$290$	0.263033	+	0.455586i	0.0154458	+	0.0267530i
$291$		0			0
$292$	−0.912507	−	0.526836i	−0.0534004	−	0.0308308i
$293$	12.8880	+	7.44091i	0.752927	+	0.434702i	0.826750	−	0.562569i	$-0.190187\pi$
$293$	12.8880	+	7.44091i	0.752927	+	0.434702i	−0.0738237	+	0.997271i	$0.523520\pi$
$294$		0			0
$295$	2.87677	+	4.98271i	0.167492	+	0.290104i
$296$	7.81310			0.454127
$297$		0			0
$298$	18.4642			1.06960
$299$	1.92212	−	12.6461i	0.111159	−	0.731343i
$300$		0			0
$301$	20.8634	+	12.0455i	1.20255	+	0.694290i
$302$	−2.66510	+	4.61608i	−0.153359	+	0.265626i
$303$		0			0
$304$	4.20891	−	2.43002i	0.241398	−	0.139371i
$305$			6.69264i			0.383220i
$306$		0			0
$307$			23.7291i			1.35429i	0.735849	+	0.677145i	$0.236783\pi$
$307$			23.7291i			1.35429i	−0.735849	+	0.677145i	$0.763217\pi$
$308$	6.04305	+	10.4669i	0.344335	+	0.596405i
$309$		0			0
$310$	−2.36450	−	1.36515i	−0.134295	−	0.0775350i
$311$	−4.38513	+	7.59527i	−0.248658	+	0.430688i	−0.963154	−	0.268952i	$-0.913323\pi$
$311$	−4.38513	+	7.59527i	−0.248658	+	0.430688i	0.714496	+	0.699640i	$0.246656\pi$
$312$		0			0
$313$	−5.14061	−	8.90380i	−0.290565	−	0.503273i	0.683379	−	0.730064i	$-0.260510\pi$
$313$	−5.14061	−	8.90380i	−0.290565	−	0.503273i	−0.973943	+	0.226791i	$0.927176\pi$
$314$			2.93840i			0.165824i
$315$		0			0
$316$	−3.37676			−0.189958
$317$	−5.03088	+	2.90458i	−0.282562	+	0.163137i	−0.634583	−	0.772855i	$-0.718828\pi$
$317$	−5.03088	+	2.90458i	−0.282562	+	0.163137i	0.352020	+	0.935992i	$0.385495\pi$
$318$		0			0
$319$	3.49716	+	2.01909i	0.195804	+	0.113047i
$320$	−0.548308	−	0.316566i	−0.0306514	−	0.0176966i
$321$		0			0
$322$	4.41124	+	7.64050i	0.245829	+	0.425788i
$323$			30.5131i			1.69779i
$324$		0			0
$325$	−12.9519	−	10.3550i	−0.718440	−	0.574394i
$326$	3.70526	+	6.41769i	0.205215	+	0.355443i
$327$		0			0
$328$	−0.0391823	+	0.0678657i	−0.00216348	+	0.00374725i
$329$	6.17482	−	10.6951i	0.340429	−	0.589640i
$330$		0			0
$331$	9.26705	−	5.35033i	0.509363	−	0.294081i	−0.223209	−	0.974771i	$-0.571653\pi$
$331$	9.26705	−	5.35033i	0.509363	−	0.294081i	0.732572	+	0.680690i	$0.238320\pi$
$332$			15.2137i			0.834961i
$333$		0			0
$334$	0.0891003			0.00487535
$335$	2.49599	+	4.32317i	0.136370	+	0.236200i
$336$		0			0
$337$	−0.977254	+	1.69265i	−0.0532344	+	0.0922047i	−0.891415	−	0.453189i	$-0.850286\pi$
$337$	−0.977254	+	1.69265i	−0.0532344	+	0.0922047i	0.838180	+	0.545393i	$0.183620\pi$
$338$	−3.86259	+	12.4129i	−0.210097	+	0.675173i
$339$		0			0
$340$	3.44248	−	1.98752i	0.186695	−	0.107788i
$341$	−20.9582			−1.13495
$342$		0			0
$343$			19.4362i			1.04946i
$344$	−8.38954	+	4.84370i	−0.452334	+	0.261155i
$345$		0			0
$346$	6.58039	+	3.79919i	0.353764	+	0.204246i
$347$	2.17035	−	3.75915i	0.116510	−	0.201802i	−0.801872	−	0.597496i	$-0.796162\pi$
$347$	2.17035	−	3.75915i	0.116510	−	0.201802i	0.918383	+	0.395694i	$0.129496\pi$
$348$		0			0
$349$	24.2212	−	13.9841i	1.29653	−	0.748552i	0.316727	−	0.948517i	$-0.397416\pi$
$349$	24.2212	−	13.9841i	1.29653	−	0.748552i	0.979803	+	0.199964i	$0.0640827\pi$
$350$	11.4373			0.611350
$351$		0			0
$352$	−4.86004			−0.259041
$353$	−14.5560	+	8.40389i	−0.774736	+	0.447294i	−0.834561	−	0.550915i	$-0.814279\pi$
$353$	−14.5560	+	8.40389i	−0.774736	+	0.447294i	0.0598256	+	0.998209i	$0.480946\pi$
$354$		0			0
$355$	3.89645	−	6.74884i	0.206802	−	0.358191i
$356$	−0.515365	−	0.297546i	−0.0273143	−	0.0157699i
$357$		0			0
$358$	20.6036	−	11.8955i	1.08893	−	0.628695i
$359$		−	20.0302i		−	1.05715i	−0.848886	−	0.528576i	$-0.822726\pi$
$359$		−	20.0302i		−	1.05715i	0.848886	−	0.528576i	$-0.177274\pi$
$360$		0			0
$361$	−4.61995			−0.243155
$362$	1.41361	−	0.816146i	0.0742975	−	0.0428957i
$363$		0			0
$364$	−3.26545	−	8.35064i	−0.171156	−	0.437693i
$365$	0.333557	−	0.577737i	0.0174592	−	0.0302402i
$366$		0			0
$367$	−16.8691	−	29.2181i	−0.880560	−	1.52517i	−0.850720	−	0.525620i	$-0.823834\pi$
$367$	−16.8691	−	29.2181i	−0.880560	−	1.52517i	−0.0298400	−	0.999555i	$-0.509500\pi$
$368$	−3.54768			−0.184936
$369$		0			0
$370$			4.94673i			0.257168i
$371$	13.6978	−	7.90845i	0.711156	−	0.410586i
$372$		0			0
$373$	−6.98145	+	12.0922i	−0.361486	+	0.626112i	−0.988206	−	0.153133i	$-0.951064\pi$
$373$	−6.98145	+	12.0922i	−0.361486	+	0.626112i	0.626720	+	0.779245i	$0.284397\pi$
$374$	15.2565	−	26.4251i	0.788897	−	1.36641i
$375$		0			0
$376$	2.48301	+	4.30069i	0.128051	+	0.221791i
$377$	−2.33992	−	1.87077i	−0.120512	−	0.0963496i
$378$		0			0
$379$		−	29.7828i		−	1.52984i	−0.644124	−	0.764921i	$-0.722778\pi$
$379$		−	29.7828i		−	1.52984i	0.644124	−	0.764921i	$-0.277222\pi$
$380$	1.53852	+	2.66480i	0.0789245	+	0.136701i
$381$		0			0
$382$	2.74212	+	1.58316i	0.140299	+	0.0810018i
$383$	−2.06820	−	1.19408i	−0.105680	−	0.0610146i	0.446228	−	0.894919i	$-0.352767\pi$
$383$	−2.06820	−	1.19408i	−0.105680	−	0.0610146i	−0.551909	+	0.833905i	$0.686100\pi$
$384$		0			0
$385$	−6.62691	+	3.82605i	−0.337739	+	0.194993i
$386$	16.4614			0.837864
$387$		0			0
$388$			17.0630i			0.866244i
$389$	12.3362	+	21.3670i	0.625473	+	1.08335i	0.988449	+	0.151552i	$0.0484271\pi$
$389$	12.3362	+	21.3670i	0.625473	+	1.08335i	−0.362977	+	0.931798i	$0.618240\pi$
$390$		0			0
$391$	11.1368	−	19.2895i	0.563213	−	0.975514i
$392$	−0.706382	−	0.407830i	−0.0356777	−	0.0205985i
$393$		0			0
$394$	5.71756	+	9.90311i	0.288047	+	0.498911i
$395$		−	2.13794i		−	0.107571i
$396$		0			0
$397$			9.36279i			0.469905i	0.972007	+	0.234952i	$0.0754934\pi$
$397$			9.36279i			0.469905i	−0.972007	+	0.234952i	$0.924507\pi$
$398$	11.4301	−	6.59914i	0.572937	−	0.330785i
$399$		0			0
$400$	−2.29957	+	3.98298i	−0.114979	+	0.199149i
$401$	5.99814	+	3.46303i	0.299533	+	0.172935i	0.642233	−	0.766509i	$-0.278008\pi$
$401$	5.99814	+	3.46303i	0.299533	+	0.172935i	−0.342700	+	0.939445i	$0.611341\pi$
$402$		0			0
$403$	15.3719	+	2.33642i	0.765728	+	0.116385i
$404$	−5.07524			−0.252503
$405$		0			0
$406$	2.06630			0.102549
$407$	18.9860	+	32.8847i	0.941100	+	1.63003i
$408$		0			0
$409$	−16.1011	−	9.29599i	−0.796149	−	0.459657i	0.0459735	−	0.998943i	$-0.485361\pi$
$409$	−16.1011	−	9.29599i	−0.796149	−	0.459657i	−0.842123	+	0.539286i	$0.818694\pi$
$410$	−0.0429679	−	0.0248075i	−0.00212203	−	0.00122516i
$411$		0			0
$412$	−0.538522	−	0.932747i	−0.0265311	−	0.0459532i
$413$	22.5989			1.11202
$414$		0			0
$415$	−9.63229			−0.472831
$416$	3.56461	+	0.541797i	0.174769	+	0.0265638i
$417$		0			0
$418$	20.4555	+	11.8100i	1.00051	+	0.577645i
$419$	−0.455614	+	0.789146i	−0.0222582	+	0.0385523i	−0.876940	−	0.480600i	$-0.840419\pi$
$419$	−0.455614	+	0.789146i	−0.0222582	+	0.0385523i	0.854682	+	0.519152i	$0.173752\pi$
$420$		0			0
$421$	−34.0472	+	19.6572i	−1.65936	+	0.958033i	−0.686351	+	0.727270i	$0.740789\pi$
$421$	−34.0472	+	19.6572i	−1.65936	+	0.958033i	−0.973010	+	0.230763i	$0.925878\pi$
$422$		−	9.27713i		−	0.451604i
$423$		0			0
$424$			6.36026i			0.308881i
$425$	−14.4376	−	25.0066i	−0.700324	−	1.21300i
$426$		0			0
$427$	22.7657	+	13.1438i	1.10171	+	0.636072i
$428$	4.58381	−	7.93940i	0.221567	−	0.383765i
$429$		0			0
$430$	−3.06670	−	5.31168i	−0.147890	−	0.256152i
$431$			38.0100i			1.83088i	0.402457	+	0.915439i	$0.368156\pi$
$431$			38.0100i			1.83088i	−0.402457	+	0.915439i	$0.631844\pi$
$432$		0			0
$433$	37.5218			1.80318			0.901592	−	0.432587i	$-0.142399\pi$
$433$	37.5218			1.80318			0.901592	+	0.432587i	$0.142399\pi$
$434$	−9.28735	+	5.36206i	−0.445807	+	0.257387i
$435$		0			0
$436$	−8.57390	−	4.95014i	−0.410615	−	0.237069i
$437$	14.9319	+	8.62093i	0.714289	+	0.412395i
$438$		0			0
$439$	−5.41124	−	9.37255i	−0.258265	−	0.447327i	0.707513	−	0.706701i	$-0.249817\pi$
$439$	−5.41124	−	9.37255i	−0.258265	−	0.447327i	−0.965777	+	0.259373i	$0.916484\pi$
$440$		−	3.07704i		−	0.146692i
$441$		0			0
$442$	−14.1358	+	17.6808i	−0.672373	+	0.840990i
$443$	−10.5311	−	18.2403i	−0.500346	−	0.866625i	−1.00000		0.000399639i	$-0.999873\pi$
$443$	−10.5311	−	18.2403i	−0.500346	−	0.866625i	0.499654	−	0.866225i	$-0.333461\pi$
$444$		0			0
$445$	0.188386	−	0.326294i	0.00893036	−	0.0154678i
$446$	7.00623	−	12.1351i	0.331755	−	0.574616i
$447$		0			0
$448$	−2.15366	+	1.24342i	−0.101751	+	0.0587459i
$449$			12.0811i			0.570140i	0.958507	+	0.285070i	$0.0920169\pi$
$449$			12.0811i			0.570140i	−0.958507	+	0.285070i	$0.907983\pi$
$450$		0			0
$451$	−0.380854			−0.0179337
$452$	−3.31088	−	5.73460i	−0.155730	−	0.269733i
$453$		0			0
$454$	−1.38613	+	2.40085i	−0.0650545	+	0.112678i
$455$	5.28706	−	2.06746i	0.247861	−	0.0969241i
$456$		0			0
$457$	24.6389	−	14.2252i	1.15256	−	0.665429i	0.203048	−	0.979169i	$-0.434915\pi$
$457$	24.6389	−	14.2252i	1.15256	−	0.665429i	0.949509	+	0.313740i	$0.101582\pi$
$458$	16.6468			0.777853
$459$		0			0
$460$		−	2.24615i		−	0.104727i
$461$	−14.9740	+	8.64522i	−0.697407	+	0.402648i	−0.806381	−	0.591396i	$-0.798577\pi$
$461$	−14.9740	+	8.64522i	−0.697407	+	0.402648i	0.108974	+	0.994045i	$0.465244\pi$
$462$		0			0
$463$	−20.5804	−	11.8821i	−0.956452	−	0.552208i	−0.0613728	−	0.998115i	$-0.519548\pi$
$463$	−20.5804	−	11.8821i	−0.956452	−	0.552208i	−0.895079	+	0.445907i	$0.852881\pi$
$464$	−0.415447	+	0.719576i	−0.0192867	+	0.0334055i
$465$		0			0
$466$	−4.72264	+	2.72662i	−0.218772	+	0.126308i
$467$	−30.5214			−1.41236			−0.706182	−	0.708030i	$-0.749584\pi$
$467$	−30.5214			−1.41236			−0.706182	+	0.708030i	$0.749584\pi$
$468$		0			0
$469$	19.6076			0.905395
$470$	−2.72291	+	1.57207i	−0.125598	+	0.0725142i
$471$		0			0
$472$	−4.54371	+	7.86994i	−0.209141	+	0.362243i
$473$	−40.7735	−	23.5406i	−1.87477	−	1.08240i
$474$		0			0
$475$	19.3574	−	11.1760i	0.888179	−	0.512790i
$476$		−	15.6133i		−	0.715632i
$477$		0			0
$478$	13.6254			0.623213
$479$	19.7570	−	11.4067i	0.902719	−	0.521185i	0.0246377	−	0.999696i	$-0.492157\pi$
$479$	19.7570	−	11.4067i	0.902719	−	0.521185i	0.878081	+	0.478511i	$0.158823\pi$
$480$		0			0
$481$	−10.2594	−	26.2360i	−0.467786	−	1.19626i
$482$	−9.45585	+	16.3780i	−0.430702	+	0.745998i
$483$		0			0
$484$	−6.30997	−	10.9292i	−0.286817	−	0.496782i
$485$	−10.8031			−0.490545
$486$		0			0
$487$			21.9090i			0.992792i	0.868096	+	0.496396i	$0.165344\pi$
$487$			21.9090i			0.992792i	−0.868096	+	0.496396i	$0.834656\pi$
$488$	−9.15449	+	5.28535i	−0.414404	+	0.239256i
$489$		0			0
$490$	0.258210	−	0.447233i	0.0116647	−	0.0202039i
$491$	−12.8330	+	22.2274i	−0.579145	+	1.00311i	0.416433	+	0.909167i	$0.363280\pi$
$491$	−12.8330	+	22.2274i	−0.579145	+	1.00311i	−0.995578	+	0.0939422i	$0.970053\pi$
$492$		0			0
$493$	−2.60833	−	4.51776i	−0.117473	−	0.203470i
$494$	−13.6866	−	10.9424i	−0.615788	−	0.492324i
$495$		0			0
$496$		−	4.31236i		−	0.193630i
$497$	−15.3046	−	26.5083i	−0.686504	−	1.18906i
$498$		0			0
$499$	−30.0035	−	17.3226i	−1.34314	−	0.775464i	−0.355876	−	0.934533i	$-0.615817\pi$
$499$	−30.0035	−	17.3226i	−1.34314	−	0.775464i	−0.987267	+	0.159069i	$0.949151\pi$
$500$	−5.26329	−	3.03876i	−0.235382	−	0.135898i
$501$		0			0
$502$	−1.79721	+	1.03762i	−0.0802135	+	0.0463113i
$503$	16.8864			0.752928			0.376464	−	0.926431i	$-0.377140\pi$
$503$	16.8864			0.752928			0.376464	+	0.926431i	$0.377140\pi$
$504$		0			0
$505$		−	3.21330i		−	0.142990i
$506$	−8.62093	−	14.9319i	−0.383247	−	0.663803i
$507$		0			0
$508$	−8.90441	+	15.4229i	−0.395069	+	0.684280i
$509$	10.0617	+	5.80914i	0.445978	+	0.257485i	0.706130	−	0.708082i	$-0.250439\pi$
$509$	10.0617	+	5.80914i	0.445978	+	0.257485i	−0.260152	+	0.965568i	$0.583773\pi$
$510$		0			0
$511$	−1.31015	−	2.26925i	−0.0579578	−	0.100386i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	25.0018i		−	1.10278i
$515$	0.590552	−	0.340955i	0.0260228	−	0.0150243i
$516$		0			0
$517$	−12.0675	+	20.9015i	−0.530728	+	0.919248i
$518$	16.8268	+	9.71494i	0.739326	+	0.426850i
$519$		0			0
$520$	−0.343029	+	2.25687i	−0.0150428	+	0.0989703i
$521$	32.5005			1.42387			0.711937	−	0.702243i	$-0.247818\pi$
$521$	32.5005			1.42387			0.711937	+	0.702243i	$0.247818\pi$
$522$		0			0
$523$	−23.8182			−1.04150			−0.520749	−	0.853710i	$-0.674347\pi$
$523$	−23.8182			−1.04150			−0.520749	+	0.853710i	$0.674347\pi$
$524$	6.02780	+	10.4404i	0.263325	+	0.456093i
$525$		0			0
$526$	−21.8701	−	12.6267i	−0.953581	−	0.550550i
$527$	23.4473	+	13.5373i	1.02138	+	0.589693i
$528$		0			0
$529$	5.20698	+	9.01876i	0.226391	+	0.392120i
$530$	−4.02688			−0.174917
$531$		0			0
$532$	12.0861			0.523999
$533$	0.279339	+	0.0424576i	0.0120995	+	0.00183904i
$534$		0			0
$535$	5.02669	+	2.90216i	0.217323	+	0.125471i
$536$	−3.94228	+	6.82824i	−0.170281	+	0.294935i
$537$		0			0
$538$	−20.5935	+	11.8897i	−0.887848	+	0.512600i
$539$		−	3.96413i		−	0.170747i
$540$		0			0
$541$			32.5049i			1.39750i	0.715368	+	0.698748i	$0.246259\pi$
$541$			32.5049i			1.39750i	−0.715368	+	0.698748i	$0.753741\pi$
$542$	−7.10251	−	12.3019i	−0.305079	−	0.528412i
$543$		0			0
$544$	5.43723	+	3.13918i	0.233119	+	0.134591i
$545$	3.13409	−	5.42841i	0.134250	−	0.232527i
$546$		0			0
$547$	4.78240	+	8.28337i	0.204481	+	0.354171i	0.949967	−	0.312350i	$-0.101116\pi$
$547$	4.78240	+	8.28337i	0.204481	+	0.354171i	−0.745486	+	0.666521i	$0.767783\pi$
$548$		−	0.304776i		−	0.0130194i
$549$		0			0
$550$	−22.3520			−0.953093
$551$	3.49716	−	2.01909i	0.148984	−	0.0860161i
$552$		0			0
$553$	−7.27240	−	4.19872i	−0.309254	−	0.178548i
$554$	7.04574	+	4.06786i	0.299345	+	0.172827i
$555$		0			0
$556$	4.09109	+	7.08598i	0.173501	+	0.300512i
$557$		−	34.6218i		−	1.46697i	−0.679703	−	0.733487i	$-0.737891\pi$
$557$		−	34.6218i		−	1.46697i	0.679703	−	0.733487i	$-0.262109\pi$
$558$		0			0
$559$	27.2811	+	21.8113i	1.15387	+	0.922521i
$560$	−0.787247	−	1.36355i	−0.0332673	−	0.0576206i
$561$		0			0
$562$	16.5474	−	28.6610i	0.698012	−	1.20899i
$563$	3.42757	−	5.93673i	0.144455	−	0.250203i	−0.784715	−	0.619857i	$-0.787190\pi$
$563$	3.42757	−	5.93673i	0.144455	−	0.250203i	0.929169	+	0.369654i	$0.120524\pi$
$564$		0			0
$565$	3.63076	−	2.09622i	0.152747	−	0.0881887i
$566$			11.8429i			0.497795i
$567$		0			0
$568$	12.3085			0.516452
$569$	−10.6617	−	18.4665i	−0.446960	−	0.774158i	0.551226	−	0.834356i	$-0.314160\pi$
$569$	−10.6617	−	18.4665i	−0.446960	−	0.774158i	−0.998186	+	0.0601979i	$0.980827\pi$
$570$		0			0
$571$	−4.72379	+	8.18185i	−0.197685	+	0.342400i	−0.947777	−	0.318933i	$-0.896675\pi$
$571$	−4.72379	+	8.18185i	−0.197685	+	0.342400i	0.750093	+	0.661333i	$0.230009\pi$
$572$	6.38169	+	16.3197i	0.266832	+	0.682362i
$573$		0			0
$574$	−0.168771	+	0.0974397i	−0.00704435	+	0.00406706i
$575$	−16.3163			−0.680436
$576$		0			0
$577$		−	25.5692i		−	1.06446i	−0.846599	−	0.532231i	$-0.821354\pi$
$577$		−	25.5692i		−	1.06446i	0.846599	−	0.532231i	$-0.178646\pi$
$578$	−19.4145	+	11.2090i	−0.807536	+	0.466231i
$579$		0			0
$580$	−0.455586	−	0.263033i	−0.0189172	−	0.0109218i
$581$	−18.9170	+	32.7652i	−0.784809	+	1.35933i
$582$		0			0
$583$	−26.7698	+	15.4555i	−1.10869	+	0.640103i
$584$	1.05367			0.0436013
$585$		0			0
$586$	−14.8818			−0.614762
$587$	−6.72060	+	3.88014i	−0.277389	+	0.160151i	−0.632241	−	0.774772i	$-0.717865\pi$
$587$	−6.72060	+	3.88014i	−0.277389	+	0.160151i	0.354852	+	0.934923i	$0.384531\pi$
$588$		0			0
$589$	−10.4791	+	18.1503i	−0.431784	+	0.747872i
$590$	−4.98271	−	2.87677i	−0.205135	−	0.118435i
$591$		0			0
$592$	−6.76635	+	3.90655i	−0.278095	+	0.160558i
$593$			4.65405i			0.191119i	0.995424	+	0.0955594i	$0.0304640\pi$
$593$			4.65405i			0.191119i	−0.995424	+	0.0955594i	$0.969536\pi$
$594$		0			0
$595$	9.88525			0.405256
$596$	−15.9905	+	9.23210i	−0.654995	+	0.378161i
$597$		0			0
$598$	4.65845	+	11.9129i	0.190498	+	0.487155i
$599$	13.2758	−	22.9943i	0.542433	−	0.939521i	−0.456331	−	0.889810i	$-0.650837\pi$
$599$	13.2758	−	22.9943i	0.542433	−	0.939521i	0.998764	−	0.0497107i	$-0.0158299\pi$
$600$		0			0
$601$	16.7970	+	29.0933i	0.685165	+	1.18674i	0.973385	+	0.229176i	$0.0736033\pi$
$601$	16.7970	+	29.0933i	0.685165	+	1.18674i	−0.288220	+	0.957564i	$0.593063\pi$
$602$	−24.0910			−0.981874
$603$		0			0
$604$		−	5.33019i		−	0.216882i
$605$	6.91962	−	3.99505i	0.281323	−	0.162422i
$606$		0			0
$607$	7.17582	−	12.4289i	0.291258	−	0.504473i	−0.682850	−	0.730559i	$-0.739260\pi$
$607$	7.17582	−	12.4289i	0.291258	−	0.504473i	0.974107	+	0.226086i	$0.0725929\pi$
$608$	−2.43002	+	4.20891i	−0.0985502	+	0.170694i
$609$		0			0
$610$	−3.34632	−	5.79600i	−0.135489	−	0.234673i
$611$	11.1811	−	13.9850i	0.452337	−	0.565773i
$612$		0			0
$613$		−	32.5357i		−	1.31410i	−0.753845	−	0.657052i	$-0.771803\pi$
$613$		−	32.5357i		−	1.31410i	0.753845	−	0.657052i	$-0.228197\pi$
$614$	−11.8645	−	20.5500i	−0.478814	−	0.829330i
$615$		0			0
$616$	−10.4669	−	6.04305i	−0.421722	−	0.243481i
$617$	−17.4197	−	10.0573i	−0.701292	−	0.404891i	0.106537	−	0.994309i	$-0.466024\pi$
$617$	−17.4197	−	10.0573i	−0.701292	−	0.404891i	−0.807828	+	0.589418i	$0.799357\pi$
$618$		0			0
$619$	12.2002	−	7.04379i	0.490367	−	0.283114i	−0.234359	−	0.972150i	$-0.575299\pi$
$619$	12.2002	−	7.04379i	0.490367	−	0.283114i	0.724727	+	0.689036i	$0.241966\pi$
$620$	2.73029			0.109651
$621$		0			0
$622$		−	8.77026i		−	0.351655i
$623$	−0.739948	−	1.28163i	−0.0296454	−	0.0513473i
$624$		0			0
$625$	−9.57392	+	16.5825i	−0.382957	+	0.663301i
$626$	8.90380	+	5.14061i	0.355867	+	0.205460i
$627$		0			0
$628$	−1.46920	−	2.54473i	−0.0586275	−	0.101546i
$629$		−	49.0535i		−	1.95589i
$630$		0			0
$631$		−	15.6969i		−	0.624885i	−0.949937	−	0.312443i	$-0.898853\pi$
$631$		−	15.6969i		−	0.624885i	0.949937	−	0.312443i	$-0.101147\pi$
$632$	2.92436	−	1.68838i	0.116325	−	0.0671602i
$633$		0			0
$634$	2.90458	−	5.03088i	0.115356	−	0.199802i
$635$	−9.76472	−	5.63766i	−0.387501	−	0.223724i
$636$		0			0
$637$	−0.441921	+	2.90751i	−0.0175096	+	0.115200i
$638$	−4.03818			−0.159873
$639$		0			0
$640$	0.633132			0.0250267
$641$	−6.43804	−	11.1510i	−0.254287	−	0.440439i	0.710414	−	0.703784i	$-0.248508\pi$
$641$	−6.43804	−	11.1510i	−0.254287	−	0.440439i	−0.964702	+	0.263345i	$0.915174\pi$
$642$		0			0
$643$	−29.3762	−	16.9604i	−1.15849	−	0.668852i	−0.207545	−	0.978225i	$-0.566547\pi$
$643$	−29.3762	−	16.9604i	−1.15849	−	0.668852i	−0.950941	+	0.309373i	$0.899881\pi$
$644$	−7.64050	−	4.41124i	−0.301078	−	0.173827i
$645$		0			0
$646$	−15.2565	−	26.4251i	−0.600261	−	1.03968i
$647$	4.53172			0.178160			0.0890802	−	0.996024i	$-0.471607\pi$
$647$	4.53172			0.178160			0.0890802	+	0.996024i	$0.471607\pi$
$648$		0			0
$649$	−44.1652			−1.73364
$650$	16.3942	+	2.49180i	0.643032	+	0.0977365i
$651$		0			0
$652$	−6.41769	−	3.70526i	−0.251336	−	0.145109i
$653$	2.39149	−	4.14217i	0.0935861	−	0.162096i	−0.815432	−	0.578854i	$-0.803500\pi$
$653$	2.39149	−	4.14217i	0.0935861	−	0.162096i	0.909018	+	0.416758i	$0.136834\pi$
$654$		0			0
$655$	−6.61018	+	3.81639i	−0.258281	+	0.149119i
$656$		−	0.0783645i		−	0.00305962i
$657$		0			0
$658$			12.3496i			0.481439i
$659$	−9.88260	−	17.1172i	−0.384972	−	0.666790i	0.606794	−	0.794859i	$-0.292455\pi$
$659$	−9.88260	−	17.1172i	−0.384972	−	0.666790i	−0.991765	+	0.128069i	$0.959122\pi$
$660$		0			0
$661$	23.8446	+	13.7667i	0.927449	+	0.535463i	0.886004	−	0.463678i	$-0.153471\pi$
$661$	23.8446	+	13.7667i	0.927449	+	0.535463i	0.0414449	+	0.999141i	$0.486804\pi$
$662$	−5.35033	+	9.26705i	−0.207947	+	0.360174i
$663$		0			0
$664$	−7.60686	−	13.1755i	−0.295203	−	0.511307i
$665$			7.65210i			0.296736i
$666$		0			0
$667$	−2.94775			−0.114137
$668$	−0.0771631	+	0.0445501i	−0.00298553	+	0.00172370i
$669$		0			0
$670$	−4.32317	−	2.49599i	−0.167019	−	0.0964283i
$671$	−44.4911	−	25.6870i	−1.71756	−	0.991635i
$672$		0			0
$673$	−21.7825	−	37.7284i	−0.839653	−	1.45432i	−0.890185	−	0.455600i	$-0.849425\pi$
$673$	−21.7825	−	37.7284i	−0.839653	−	1.45432i	0.0505315	−	0.998722i	$-0.483908\pi$
$674$		−	1.95451i		−	0.0752848i
$675$		0			0
$676$	−2.86136	−	12.6812i	−0.110052	−	0.487738i
$677$	24.1766	+	41.8751i	0.929181	+	1.60939i	0.784694	+	0.619883i	$0.212820\pi$
$677$	24.1766	+	41.8751i	0.929181	+	1.60939i	0.144487	+	0.989507i	$0.453847\pi$
$678$		0			0
$679$	−21.2164	+	36.7480i	−0.814212	+	1.41026i
$680$	−1.98752	+	3.44248i	−0.0762178	+	0.132013i
$681$		0			0
$682$	18.1503	−	10.4791i	0.695012	−	0.401266i
$683$		−	25.6842i		−	0.982779i	−0.870940	−	0.491390i	$-0.836489\pi$
$683$		−	25.6842i		−	0.982779i	0.870940	−	0.491390i	$-0.163511\pi$
$684$		0			0
$685$	0.192963			0.00737275
$686$	−9.71812	−	16.8323i	−0.371040	−	0.642659i
$687$		0			0
$688$	4.84370	−	8.38954i	0.184664	−	0.319848i
$689$	21.3574	−	8.35163i	0.813651	−	0.318172i
$690$		0			0
$691$	−3.65761	+	2.11172i	−0.139142	+	0.0803338i	−0.567955	−	0.823060i	$-0.692265\pi$
$691$	−3.65761	+	2.11172i	−0.139142	+	0.0803338i	0.428813	+	0.903393i	$0.358932\pi$
$692$	−7.59838			−0.288847
$693$		0			0
$694$			4.34070i			0.164771i
$695$	−4.48636	+	2.59020i	−0.170177	+	0.0982519i
$696$		0			0
$697$	0.426086	+	0.246001i	0.0161391	+	0.00931794i
$698$	−13.9841	+	24.2212i	−0.529306	+	0.916785i
$699$		0			0
$700$	−9.90500	+	5.71865i	−0.374374	+	0.216145i
$701$	7.76144			0.293145			0.146573	−	0.989200i	$-0.453176\pi$
$701$	7.76144			0.293145			0.146573	+	0.989200i	$0.453176\pi$
$702$		0			0
$703$	37.9720			1.43214
$704$	4.20891	−	2.43002i	0.158629	−	0.0915847i
$705$		0			0
$706$	8.40389	−	14.5560i	0.316285	−	0.547821i
$707$	−10.9303	−	6.31064i	−0.411078	−	0.237336i
$708$		0			0
$709$	37.1354	−	21.4401i	1.39465	−	0.805200i	0.400822	−	0.916156i	$-0.368725\pi$
$709$	37.1354	−	21.4401i	1.39465	−	0.805200i	0.993825	+	0.110956i	$0.0353912\pi$
$710$			7.79289i			0.292462i
$711$		0			0
$712$	0.595093			0.0223020
$713$	13.2492	−	7.64943i	0.496186	−	0.286473i
$714$		0			0
$715$	−10.3325	+	4.04045i	−0.386415	+	0.151104i
$716$	−11.8955	+	20.6036i	−0.444555	+	0.769991i
$717$		0			0
$718$	10.0151	+	17.3467i	0.373760	+	0.647371i
$719$	0.181195			0.00675742			0.00337871	−	0.999994i	$-0.498925\pi$
$719$	0.181195			0.00675742			0.00337871	+	0.999994i	$0.498925\pi$
$720$		0			0
$721$		−	2.67843i		−	0.0997499i
$722$	4.00099	−	2.30997i	0.148902	−	0.0859683i
$723$		0			0
$724$	−0.816146	+	1.41361i	−0.0303318	+	0.0525363i
$725$	−1.91070	+	3.30943i	−0.0709617	+	0.122909i
$726$		0			0
$727$	16.1693	+	28.0061i	0.599688	+	1.03869i	0.992867	+	0.119228i	$0.0380420\pi$
$727$	16.1693	+	28.0061i	0.599688	+	1.03869i	−0.393179	+	0.919462i	$0.628625\pi$
$728$	7.00329	+	5.59914i	0.259559	+	0.207518i
$729$		0			0
$730$			0.667114i			0.0246910i
$731$	30.4105	+	52.6726i	1.12477	+	1.94817i
$732$		0			0
$733$	40.0538	+	23.1251i	1.47942	+	0.854143i	0.999729	−	0.0232941i	$-0.00741540\pi$
$733$	40.0538	+	23.1251i	1.47942	+	0.854143i	0.479691	+	0.877437i	$0.340749\pi$
$734$	29.2181	+	16.8691i	1.07846	+	0.622650i
$735$		0			0
$736$	3.07238	−	1.77384i	0.113249	−	0.0653846i
$737$	−38.3193			−1.41151
$738$		0			0
$739$		−	8.94056i		−	0.328884i	−0.986387	−	0.164442i	$-0.947418\pi$
$739$		−	8.94056i		−	0.328884i	0.986387	−	0.164442i	$-0.0525823\pi$
$740$	−2.47336	−	4.28399i	−0.0909226	−	0.157483i
$741$		0			0
$742$	−7.90845	+	13.6978i	−0.290328	+	0.502864i
$743$	−13.6805	−	7.89847i	−0.501891	−	0.289767i	0.227603	−	0.973754i	$-0.426911\pi$
$743$	−13.6805	−	7.89847i	−0.501891	−	0.289767i	−0.729494	+	0.683987i	$0.760244\pi$
$744$		0			0
$745$	−5.84513	−	10.1241i	−0.214149	−	0.370917i
$746$		−	13.9629i		−	0.511218i
$747$		0			0
$748$			30.5131i			1.11567i
$749$	19.7440	−	11.3992i	0.721429	−	0.416517i
$750$		0			0
$751$	−23.7961	+	41.2161i	−0.868333	+	1.50400i	−0.00463416	+	0.999989i	$0.501475\pi$
$751$	−23.7961	+	41.2161i	−0.868333	+	1.50400i	−0.863699	+	0.504008i	$0.831858\pi$
$752$	−4.30069	−	2.48301i	−0.156830	−	0.0905459i
$753$		0			0
$754$	2.96182	+	0.450176i	0.107863	+	0.0163944i
$755$	3.37471			0.122818
$756$		0			0
$757$	−36.6710			−1.33283			−0.666414	−	0.745582i	$-0.732172\pi$
$757$	−36.6710			−1.33283			−0.666414	+	0.745582i	$0.732172\pi$
$758$	14.8914	+	25.7927i	0.540881	+	0.936833i
$759$		0			0
$760$	−2.66480	−	1.53852i	−0.0966624	−	0.0558081i
$761$	19.9038	+	11.4915i	0.721514	+	0.416566i	0.815310	−	0.579025i	$-0.196567\pi$
$761$	19.9038	+	11.4915i	0.721514	+	0.416566i	−0.0937959	+	0.995591i	$0.529900\pi$
$762$		0			0
$763$	−12.3102	−	21.3219i	−0.445658	−	0.771903i
$764$	−3.16633			−0.114554
$765$		0			0
$766$	2.38816			0.0862876
$767$	32.3931	+	4.92353i	1.16965	+	0.177778i
$768$		0			0
$769$	−1.49286	−	0.861901i	−0.0538338	−	0.0310810i	0.472842	−	0.881147i	$-0.343228\pi$
$769$	−1.49286	−	0.861901i	−0.0538338	−	0.0310810i	−0.526675	+	0.850067i	$0.676562\pi$
$770$	3.82605	−	6.62691i	0.137881	−	0.238817i
$771$		0			0
$772$	−14.2560	+	8.23071i	−0.513085	+	0.296230i
$773$			7.86189i			0.282772i	0.989955	+	0.141386i	$0.0451559\pi$
$773$			7.86189i			0.282772i	−0.989955	+	0.141386i	$0.954844\pi$
$774$		0			0
$775$		−	19.8331i		−	0.712428i
$776$	−8.53151	−	14.7770i	−0.306263	−	0.530464i
$777$		0			0
$778$	−21.3670	−	12.3362i	−0.766044	−	0.442276i
$779$	−0.190427	+	0.329830i	−0.00682276	+	0.0118174i
$780$		0			0
$781$	29.9098	+	51.8053i	1.07026	+	1.85374i
$782$			22.2736i			0.796504i
$783$		0			0
$784$	0.815659			0.0291307
$785$	1.61115	−	0.930198i	0.0575044	−	0.0332002i
$786$		0			0
$787$	22.7512	+	13.1354i	0.810991	+	0.468226i	0.847300	−	0.531115i	$-0.178227\pi$
$787$	22.7512	+	13.1354i	0.810991	+	0.468226i	−0.0363089	+	0.999341i	$0.511560\pi$
$788$	−9.90311	−	5.71756i	−0.352784	−	0.203680i
$789$		0			0
$790$	1.06897	+	1.85151i	0.0380322	+	0.0658737i
$791$		−	16.4672i		−	0.585506i
$792$		0			0
$793$	29.7686	+	23.8001i	1.05711	+	0.845166i
$794$	−4.68139	−	8.10841i	−0.166136	−	0.287757i
$795$		0			0
$796$	−6.59914	+	11.4301i	−0.233900	+	0.405127i
$797$	5.38194	−	9.32179i	0.190638	−	0.330195i	−0.754824	−	0.655928i	$-0.772278\pi$
$797$	5.38194	−	9.32179i	0.190638	−	0.330195i	0.945462	+	0.325733i	$0.105611\pi$
$798$		0			0
$799$	27.0013	−	15.5892i	0.955238	−	0.551507i
$800$		−	4.59914i		−	0.162604i
$801$		0			0
$802$	−6.92606			−0.244568
$803$	2.56044	+	4.43482i	0.0903560	+	0.156501i
$804$		0			0
$805$	2.79290	−	4.83744i	0.0984368	−	0.170498i
$806$	−14.4806	+	5.66254i	−0.510059	+	0.199454i
$807$		0			0
$808$	4.39529	−	2.53762i	0.154626	−	0.0892732i
$809$	−2.05900			−0.0723905			−0.0361952	−	0.999345i	$-0.511524\pi$
$809$	−2.05900			−0.0723905			−0.0361952	+	0.999345i	$0.511524\pi$
$810$		0			0
$811$			12.5483i			0.440630i	0.975429	+	0.220315i	$0.0707086\pi$
$811$			12.5483i			0.440630i	−0.975429	+	0.220315i	$0.929291\pi$
$812$	−1.78946	+	1.03315i	−0.0627979	+	0.0362564i
$813$		0			0
$814$	−32.8847	−	18.9860i	−1.15261	−	0.665458i
$815$	2.34592	−	4.06325i	0.0821739	−	0.142329i
$816$		0			0
$817$	−40.7735	+	23.5406i	−1.42648	+	0.823580i
$818$	18.5920			0.650053
$819$		0			0
$820$	0.0496151			0.00173263
$821$	23.7509	−	13.7126i	0.828911	−	0.478572i	−0.0245686	−	0.999698i	$-0.507821\pi$
$821$	23.7509	−	13.7126i	0.828911	−	0.478572i	0.853480	+	0.521126i	$0.174488\pi$
$822$		0			0
$823$	1.97058	−	3.41315i	0.0686902	−	0.118975i	−0.829635	−	0.558306i	$-0.811451\pi$
$823$	1.97058	−	3.41315i	0.0686902	−	0.118975i	0.898325	+	0.439332i	$0.144785\pi$
$824$	0.932747	+	0.538522i	0.0324938	+	0.0187603i
$825$		0			0
$826$	−19.5712	+	11.2995i	−0.680970	+	0.393158i
$827$			31.5551i			1.09728i	0.836060	+	0.548639i	$0.184854\pi$
$827$			31.5551i			1.09728i	−0.836060	+	0.548639i	$0.815146\pi$
$828$		0			0
$829$	−48.2865			−1.67706			−0.838529	−	0.544857i	$-0.816584\pi$
$829$	−48.2865			−1.67706			−0.838529	+	0.544857i	$0.816584\pi$
$830$	8.34181	−	4.81615i	0.289548	−	0.167171i
$831$		0			0
$832$	−3.35794	+	1.31310i	−0.116416	+	0.0455234i
$833$	−2.56050	+	4.43492i	−0.0887162	+	0.153661i
$834$		0			0
$835$	−0.0282061	−	0.0488544i	−0.000976113	−	0.00169068i
$836$	−23.6199			−0.816913
$837$		0			0
$838$		−	0.911227i		−	0.0314778i
$839$	−18.8067	+	10.8581i	−0.649279	+	0.374862i	−0.788180	−	0.615445i	$-0.788976\pi$
$839$	−18.8067	+	10.8581i	−0.649279	+	0.374862i	0.138901	+	0.990306i	$0.455643\pi$
$840$		0			0
$841$	14.1548	−	24.5168i	0.488097	−	0.845408i
$842$	19.6572	−	34.0472i	0.677431	−	1.17335i
$843$		0			0
$844$	4.63857	+	8.03423i	0.159666	+	0.276550i
$845$	8.02887	−	1.81162i	0.276201	−	0.0623215i
$846$		0			0
$847$		−	31.3837i		−	1.07836i
$848$	−3.18013	−	5.50815i	−0.109206	−	0.189150i
$849$		0			0
$850$	25.0066	+	14.4376i	0.857719	+	0.495204i
$851$	−24.0048	−	13.8592i	−0.822875	−	0.475087i
$852$		0			0
$853$	12.8491	−	7.41846i	0.439946	−	0.254003i	−0.263629	−	0.964624i	$-0.584919\pi$
$853$	12.8491	−	7.41846i	0.439946	−	0.254003i	0.703575	+	0.710621i	$0.251586\pi$
$854$	−26.2876			−0.899541
$855$		0			0
$856$			9.16763i			0.313343i
$857$	4.26503	+	7.38725i	0.145691	+	0.252344i	0.929630	−	0.368493i	$-0.120126\pi$
$857$	4.26503	+	7.38725i	0.145691	+	0.252344i	−0.783940	+	0.620837i	$0.786793\pi$
$858$		0			0
$859$	10.1420	−	17.5665i	0.346042	−	0.599362i	−0.639500	−	0.768791i	$-0.720859\pi$
$859$	10.1420	−	17.5665i	0.346042	−	0.599362i	0.985543	+	0.169428i	$0.0541921\pi$
$860$	5.31168	+	3.06670i	0.181127	+	0.104574i
$861$		0			0
$862$	−19.0050	−	32.9176i	−0.647313	−	1.12118i
$863$			17.3161i			0.589447i	0.955583	+	0.294723i	$0.0952275\pi$
$863$			17.3161i			0.589447i	−0.955583	+	0.294723i	$0.904772\pi$
$864$		0			0
$865$		−	4.81078i		−	0.163571i
$866$	−32.4949	+	18.7609i	−1.10422	+	0.637522i
$867$		0			0
$868$	5.36206	−	9.28735i	0.182000	−	0.315233i
$869$	14.2125	+	8.20560i	0.482126	+	0.278356i
$870$		0			0
$871$	28.1054	+	4.27183i	0.952316	+	0.144745i
$872$	9.90028			0.335266
$873$		0			0
$874$	−17.2419			−0.583214
$875$	−7.55690	−	13.0889i	−0.255470	−	0.442487i
$876$		0			0
$877$	−7.51181	−	4.33695i	−0.253656	−	0.146448i	0.367781	−	0.929912i	$-0.380118\pi$
$877$	−7.51181	−	4.33695i	−0.253656	−	0.146448i	−0.621437	+	0.783464i	$0.713451\pi$
$878$	9.37255	+	5.41124i	0.316308	+	0.182621i
$879$		0			0
$880$	1.53852	+	2.66480i	0.0518636	+	0.0898303i
$881$	−2.08434			−0.0702232			−0.0351116	−	0.999383i	$-0.511179\pi$
$881$	−2.08434			−0.0702232			−0.0351116	+	0.999383i	$0.511179\pi$
$882$		0			0
$883$	22.5903			0.760224			0.380112	−	0.924941i	$-0.375885\pi$
$883$	22.5903			0.760224			0.380112	+	0.924941i	$0.375885\pi$
$884$	3.40160	−	22.3799i	0.114408	−	0.752719i
$885$		0			0
$886$	18.2403	+	10.5311i	0.612796	+	0.353798i
$887$	26.4409	−	45.7970i	0.887799	−	1.53771i	0.0453268	−	0.998972i	$-0.485567\pi$
$887$	26.4409	−	45.7970i	0.887799	−	1.53771i	0.842472	−	0.538740i	$-0.181100\pi$
$888$		0			0
$889$	−38.3541	+	22.1438i	−1.28636	+	0.742678i
$890$			0.376772i			0.0126294i
$891$		0			0
$892$			14.0125i			0.469172i
$893$	12.0675	+	20.9015i	0.403823	+	0.699443i
$894$		0			0
$895$	−13.0448	−	7.53140i	−0.436039	−	0.251747i
$896$	1.24342	−	2.15366i	0.0415396	−	0.0719488i
$897$		0			0
$898$	−6.04053	−	10.4625i	−0.201575	−	0.349138i
$899$		−	3.58311i		−	0.119503i
$900$		0			0
$901$	39.9320			1.33033
$902$	0.329830	−	0.190427i	0.0109821	−	0.00634053i
$903$		0			0
$904$	5.73460	+	3.31088i	0.190730	+	0.110118i
$905$	−0.894999	−	0.516728i	−0.0297508	−	0.0171766i
$906$		0			0
$907$	27.8451	+	48.2290i	0.924580	+	1.60142i	0.792236	+	0.610215i	$0.208917\pi$
$907$	27.8451	+	48.2290i	0.924580	+	1.60142i	0.132344	+	0.991204i	$0.457750\pi$
$908$		−	2.77227i		−	0.0920010i
$909$		0			0
$910$	−3.54500	+	4.43400i	−0.117516	+	0.146986i
$911$	−19.2465	−	33.3359i	−0.637665	−	1.10447i	−0.985944	−	0.167078i	$-0.946567\pi$
$911$	−19.2465	−	33.3359i	−0.637665	−	1.10447i	0.348278	−	0.937391i	$-0.386766\pi$
$912$		0			0
$913$	36.9696	−	64.0332i	1.22352	−	2.11919i
$914$	−14.2252	+	24.6389i	−0.470529	+	0.814981i
$915$		0			0
$916$	−14.4165	+	8.32339i	−0.476336	+	0.275012i
$917$			29.9802i			0.990035i
$918$		0			0
$919$	−26.0262			−0.858525			−0.429263	−	0.903180i	$-0.641227\pi$
$919$	−26.0262			−0.858525			−0.429263	+	0.903180i	$0.641227\pi$
$920$	1.12307	+	1.94522i	0.0370267	+	0.0641321i
$921$		0			0
$922$	8.64522	−	14.9740i	0.284715	−	0.493141i
$923$	−16.1622	−	41.3312i	−0.531986	−	1.36043i
$924$		0			0
$925$	−31.1194	+	17.9668i	−1.02320	+	0.590745i
$926$	23.7642			0.780940
$927$		0			0
$928$		−	0.830894i		−	0.0272754i
$929$	1.69730	−	0.979934i	0.0556865	−	0.0321506i	−0.471898	−	0.881653i	$-0.656431\pi$
$929$	1.69730	−	0.979934i	0.0556865	−	0.0321506i	0.527585	+	0.849502i	$0.323098\pi$
$930$		0			0
$931$	−3.43304	−	1.98207i	−0.112513	−	0.0649596i
$932$	2.72662	−	4.72264i	0.0893134	−	0.154695i
$933$		0			0
$934$	26.4323	−	15.2607i	0.864893	−	0.499346i
$935$	−19.3188			−0.631793
$936$		0			0
$937$	−42.2865			−1.38144			−0.690720	−	0.723122i	$-0.742706\pi$
$937$	−42.2865			−1.38144			−0.690720	+	0.723122i	$0.742706\pi$
$938$	−16.9807	+	9.80380i	−0.554439	+	0.320105i
$939$		0			0
$940$	1.57207	−	2.72291i	0.0512753	−	0.0888114i
$941$	50.0947	+	28.9222i	1.63304	+	0.942836i	0.983148	+	0.182810i	$0.0585192\pi$
$941$	50.0947	+	28.9222i	1.63304	+	0.942836i	0.649892	+	0.760027i	$0.274814\pi$
$942$		0			0
$943$	0.240766	−	0.139006i	0.00784041	−	0.00452666i
$944$		−	9.08742i		−	0.295770i
$945$		0			0
$946$	47.0811			1.53074
$947$	−14.8043	+	8.54727i	−0.481075	+	0.277749i	−0.720864	−	0.693076i	$-0.756255\pi$
$947$	−14.8043	+	8.54727i	−0.481075	+	0.277749i	0.239789	+	0.970825i	$0.422922\pi$
$948$		0			0
$949$	−1.38357	−	3.53817i	−0.0449127	−	0.114854i
$950$	−11.1760	+	19.3574i	−0.362597	+	0.628037i
$951$		0			0
$952$	7.80663	+	13.5215i	0.253014	+	0.438234i
$953$	−19.8333			−0.642465			−0.321233	−	0.947000i	$-0.604097\pi$
$953$	−19.8333			−0.642465			−0.321233	+	0.947000i	$0.604097\pi$
$954$		0			0
$955$		−	2.00470i		−	0.0648707i
$956$	−11.8000	+	6.81272i	−0.381639	+	0.220339i
$957$		0			0
$958$	−11.4067	+	19.7570i	−0.368533	+	0.638319i
$959$	0.378963	−	0.656383i	0.0122374	−	0.0211957i
$960$		0			0
$961$	−6.20179	−	10.7418i	−0.200058	−	0.346510i
$962$	22.0028	+	17.5913i	0.709400	+	0.567167i
$963$		0			0
$964$		−	18.9117i		−	0.609105i
$965$	−5.21113	−	9.02593i	−0.167752	−	0.290555i
$966$		0			0
$967$	19.0476	+	10.9971i	0.612530	+	0.353644i	0.773955	−	0.633241i	$-0.218276\pi$
$967$	19.0476	+	10.9971i	0.612530	+	0.353644i	−0.161425	+	0.986885i	$0.551609\pi$
$968$	10.9292	+	6.30997i	0.351278	+	0.202810i
$969$		0			0
$970$	9.35580	−	5.40157i	0.300397	−	0.173434i
$971$	16.0662			0.515589			0.257794	−	0.966200i	$-0.417004\pi$
$971$	16.0662			0.515589			0.257794	+	0.966200i	$0.417004\pi$
$972$		0			0
$973$			20.3477i			0.652318i
$974$	−10.9545	−	18.9738i	−0.351005	−	0.607958i
$975$		0			0
$976$	5.28535	−	9.15449i	0.169180	−	0.293028i
$977$	1.21231	+	0.699926i	0.0387851	+	0.0223926i	0.519267	−	0.854612i	$-0.326205\pi$
$977$	1.21231	+	0.699926i	0.0387851	+	0.0223926i	−0.480482	+	0.877005i	$0.659538\pi$
$978$		0			0
$979$	1.44609	+	2.50469i	0.0462171	+	0.0800504i
$980$			0.516420i			0.0164964i
$981$		0			0
$982$		−	25.6660i		−	0.819035i
$983$	11.4778	−	6.62671i	0.366085	−	0.211359i	−0.305662	−	0.952140i	$-0.598878\pi$
$983$	11.4778	−	6.62671i	0.366085	−	0.211359i	0.671747	+	0.740781i	$0.265544\pi$
$984$		0			0
$985$	3.61997	−	6.26998i	0.115342	−	0.199778i
$986$	4.51776	+	2.60833i	0.143875	+	0.0830662i
$987$		0			0
$988$	17.3241	+	2.63315i	0.551154	+	0.0837717i
$989$	34.3678			1.09283
$990$		0			0
$991$	5.66549			0.179970			0.0899851	−	0.995943i	$-0.471318\pi$
$991$	5.66549			0.179970			0.0899851	+	0.995943i	$0.471318\pi$
$992$	2.15618	+	3.73461i	0.0684587	+	0.118574i
$993$		0			0
$994$	26.5083	+	15.3046i	0.840792	+	0.485431i
$995$	−7.23673	−	4.17813i	−0.229420	−	0.132456i
$996$		0			0
$997$	−2.82880	−	4.89963i	−0.0895891	−	0.155173i	0.817748	−	0.575576i	$-0.195222\pi$
$997$	−2.82880	−	4.89963i	−0.0895891	−	0.155173i	−0.907338	+	0.420403i	$0.861889\pi$
$998$	34.6451			1.09667
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.t.a.415.5		28
3.2	odd	2		234.2.t.a.103.8	yes	28
9.2	odd	6		234.2.t.a.25.1	✓	28
9.4	even	3		2106.2.b.d.649.3		14
9.5	odd	6		2106.2.b.c.649.12		14
9.7	even	3	inner	702.2.t.a.181.10		28
13.12	even	2	inner	702.2.t.a.415.10		28
39.38	odd	2		234.2.t.a.103.1	yes	28
117.25	even	6	inner	702.2.t.a.181.5		28
117.38	odd	6		234.2.t.a.25.8	yes	28
117.77	odd	6		2106.2.b.c.649.3		14
117.103	even	6		2106.2.b.d.649.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.1	✓	28	9.2	odd	6
234.2.t.a.25.8	yes	28	117.38	odd	6
234.2.t.a.103.1	yes	28	39.38	odd	2
234.2.t.a.103.8	yes	28	3.2	odd	2
702.2.t.a.181.5		28	117.25	even	6	inner
702.2.t.a.181.10		28	9.7	even	3	inner
702.2.t.a.415.5		28	1.1	even	1	trivial
702.2.t.a.415.10		28	13.12	even	2	inner
2106.2.b.c.649.3		14	117.77	odd	6
2106.2.b.c.649.12		14	9.5	odd	6
2106.2.b.d.649.3		14	9.4	even	3
2106.2.b.d.649.12		14	117.103	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.548308 + 0.316566i) q^{5} +(2.15366 - 1.24342i) q^{7} +1.00000i q^{8} -0.633132 q^{10} +(-4.20891 + 2.43002i) q^{11} +(3.35794 - 1.31310i) q^{13} +(-1.24342 + 2.15366i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.27837 q^{17} +4.86004i q^{19} +(0.548308 - 0.316566i) q^{20} +(2.43002 - 4.20891i) q^{22} +(1.77384 - 3.07238i) q^{23} +(-2.29957 - 3.98298i) q^{25} +(-2.25152 + 2.81615i) q^{26} -2.48683i q^{28} +(-0.415447 - 0.719576i) q^{29} +(3.73461 + 2.15618i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.43723 + 3.13918i) q^{34} +1.57449 q^{35} -7.81310i q^{37} +(-2.43002 - 4.20891i) q^{38} +(-0.316566 + 0.548308i) q^{40} +(0.0678657 + 0.0391823i) q^{41} +(4.84370 + 8.38954i) q^{43} +4.86004i q^{44} +3.54768i q^{46} +(4.30069 - 2.48301i) q^{47} +(-0.407830 + 0.706382i) q^{49} +(3.98298 + 2.29957i) q^{50} +(0.541797 - 3.56461i) q^{52} +6.36026 q^{53} -3.07704 q^{55} +(1.24342 + 2.15366i) q^{56} +(0.719576 + 0.415447i) q^{58} +(7.86994 + 4.54371i) q^{59} +(5.28535 + 9.15449i) q^{61} -4.31236 q^{62} -1.00000 q^{64} +(2.25687 + 0.343029i) q^{65} +(6.82824 + 3.94228i) q^{67} +(3.13918 - 5.43723i) q^{68} +(-1.36355 + 0.787247i) q^{70} -12.3085i q^{71} -1.05367i q^{73} +(3.90655 + 6.76635i) q^{74} +(4.20891 + 2.43002i) q^{76} +(-6.04305 + 10.4669i) q^{77} +(-1.68838 - 2.92436i) q^{79} -0.633132i q^{80} -0.0783645 q^{82} +(-13.1755 + 7.60686i) q^{83} +(3.44248 + 1.98752i) q^{85} +(-8.38954 - 4.84370i) q^{86} +(-2.43002 - 4.20891i) q^{88} -0.595093i q^{89} +(5.59914 - 7.00329i) q^{91} +(-1.77384 - 3.07238i) q^{92} +(-2.48301 + 4.30069i) q^{94} +(-1.53852 + 2.66480i) q^{95} +(-14.7770 + 8.53151i) q^{97} -0.815659i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more