LMFDB - Embedded newform 702.2.t.a.415.10

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			415.10
Character	$\chi$	$=$	702.415
Dual form			702.2.t.a.181.10

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.548308 - 0.316566i) q^{5} +(-2.15366 + 1.24342i) q^{7} -1.00000i q^{8} -0.633132 q^{10} +(4.20891 - 2.43002i) q^{11} +(-0.541797 - 3.56461i) q^{13} +(-1.24342 + 2.15366i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.27837 q^{17} -4.86004i q^{19} +(-0.548308 + 0.316566i) q^{20} +(2.43002 - 4.20891i) q^{22} +(1.77384 - 3.07238i) q^{23} +(-2.29957 - 3.98298i) q^{25} +(-2.25152 - 2.81615i) q^{26} +2.48683i q^{28} +(-0.415447 - 0.719576i) q^{29} +(-3.73461 - 2.15618i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.43723 - 3.13918i) q^{34} +1.57449 q^{35} +7.81310i q^{37} +(-2.43002 - 4.20891i) q^{38} +(-0.316566 + 0.548308i) q^{40} +(-0.0678657 - 0.0391823i) q^{41} +(4.84370 + 8.38954i) q^{43} -4.86004i q^{44} -3.54768i q^{46} +(-4.30069 + 2.48301i) q^{47} +(-0.407830 + 0.706382i) q^{49} +(-3.98298 - 2.29957i) q^{50} +(-3.35794 - 1.31310i) q^{52} +6.36026 q^{53} -3.07704 q^{55} +(1.24342 + 2.15366i) q^{56} +(-0.719576 - 0.415447i) q^{58} +(-7.86994 - 4.54371i) q^{59} +(5.28535 + 9.15449i) q^{61} -4.31236 q^{62} -1.00000 q^{64} +(-0.831363 + 2.12602i) q^{65} +(-6.82824 - 3.94228i) q^{67} +(3.13918 - 5.43723i) q^{68} +(1.36355 - 0.787247i) q^{70} +12.3085i q^{71} +1.05367i q^{73} +(3.90655 + 6.76635i) q^{74} +(-4.20891 - 2.43002i) q^{76} +(-6.04305 + 10.4669i) q^{77} +(-1.68838 - 2.92436i) q^{79} +0.633132i q^{80} -0.0783645 q^{82} +(13.1755 - 7.60686i) q^{83} +(-3.44248 - 1.98752i) q^{85} +(8.38954 + 4.84370i) q^{86} +(-2.43002 - 4.20891i) q^{88} +0.595093i q^{89} +(5.59914 + 7.00329i) q^{91} +(-1.77384 - 3.07238i) q^{92} +(-2.48301 + 4.30069i) q^{94} +(-1.53852 + 2.66480i) q^{95} +(14.7770 - 8.53151i) q^{97} +0.815659i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100})$ 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	0.372358	−	0.928089i	$-0.378549\pi$
$5$	−0.548308	−	0.316566i	−0.245211	−	0.141573i	−0.617569	+	0.786516i	$0.711883\pi$
$6$		0			0
$7$	−2.15366	+	1.24342i	−0.814007	+	0.469967i	−0.848346	−	0.529443i	$-0.822401\pi$
$7$	−2.15366	+	1.24342i	−0.814007	+	0.469967i	0.0343382	+	0.999410i	$0.489068\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.633132			−0.200214
$11$	4.20891	−	2.43002i	1.26904	−	0.732678i	0.294230	−	0.955735i	$-0.404937\pi$
$11$	4.20891	−	2.43002i	1.26904	−	0.732678i	0.974805	+	0.223057i	$0.0716035\pi$
$12$		0			0
$13$	−0.541797	−	3.56461i	−0.150267	−	0.988645i
$13$	−0.541797	−	3.56461i	−0.150267	−	0.988645i
$14$	−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	$-0.811767\pi$
$19$		−	4.86004i		−	1.11497i	0.830187	−	0.557484i	$-0.188233\pi$
$20$	−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	0.125607	−	0.992080i	$-0.459912\pi$
$31$	−3.73461	−	2.15618i	−0.670756	−	0.387261i	−0.796363	+	0.604819i	$0.793245\pi$
$32$	−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	$0.221992\pi$
$37$			7.81310i			1.28447i	−0.766509	+	0.642233i	$0.778008\pi$
$38$	−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	0.494691	−	0.869069i	$-0.335281\pi$
$41$	−0.0678657	−	0.0391823i	−0.0105988	−	0.00611924i	−0.505290	+	0.862950i	$0.668614\pi$
$42$		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	−0.779714	−	0.626136i	$-0.784635\pi$
$47$	−4.30069	+	2.48301i	−0.627320	+	0.362184i	0.152393	+	0.988320i	$0.451302\pi$
$48$		0			0
$49$	−0.407830	+	0.706382i	−0.0582614	+	0.100912i
$50$	−3.98298	−	2.29957i	−0.563278	−	0.325209i
$51$		0			0
$52$	−3.35794	−	1.31310i	−0.465663	−	0.182094i
$53$	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	−0.109152	−	0.994025i	$-0.534813\pi$
$59$	−7.86994	−	4.54371i	−1.02458	−	0.591541i	−0.915427	+	0.402484i	$0.868147\pi$
$60$		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
$65$	−0.831363	+	2.12602i	−0.103118	+	0.263700i
$66$		0			0
$67$	−6.82824	−	3.94228i	−0.834202	−	0.481627i	0.0210874	−	0.999778i	$-0.493287\pi$
$67$	−6.82824	−	3.94228i	−0.834202	−	0.481627i	−0.855289	+	0.518151i	$0.826620\pi$
$68$	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	$0.260654\pi$
$71$			12.3085i			1.46075i	−0.683048	+	0.730374i	$0.739346\pi$
$72$		0			0
$73$			1.05367i			0.123323i	0.998097	+	0.0616615i	$0.0196399\pi$
$73$			1.05367i			0.123323i	−0.998097	+	0.0616615i	$0.980360\pi$
$74$	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	0.447943	−	0.894062i	$-0.352157\pi$
$83$	13.1755	−	7.60686i	1.44620	−	0.834961i	0.998252	+	0.0591005i	$0.0188232\pi$
$84$		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	$0.0100411\pi$
$89$			0.595093i			0.0630797i	−0.999502	+	0.0315398i	$0.989959\pi$
$90$		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	$-0.333194\pi$
$97$	14.7770	−	8.53151i	1.50038	−	0.866244i	1.00000		0.000436560i	$-0.000138961\pi$
$98$			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	$0.149769\pi$
$104$	−3.56461	+	0.541797i	−0.349539	+	0.0531275i
$105$		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	$0.157240\pi$
$109$			9.90028i			0.948275i	−0.880451	+	0.474138i	$0.842760\pi$
$110$	−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
$130$	0.343029	+	2.25687i	0.0300856	+	0.197941i
$131$	−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	−0.511233	−	0.859442i	$-0.670811\pi$
$137$	−0.263943	+	0.152388i	−0.0225502	+	0.0130194i	0.488683	+	0.872462i	$0.337478\pi$
$138$		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	0.982094	−	0.188391i	$-0.0603273\pi$
$149$	15.9905	+	9.23210i	1.30999	+	0.756323i	0.327895	+	0.944714i	$0.393661\pi$
$150$		0			0
$151$	−4.61608	+	2.66510i	−0.375651	+	0.216882i	−0.675925	−	0.736971i	$-0.736255\pi$
$151$	−4.61608	+	2.66510i	−0.375651	+	0.216882i	0.300273	+	0.953853i	$0.402922\pi$
$152$	−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	$0.0937278\pi$
$163$			7.41051i			0.580436i	−0.956961	+	0.290218i	$0.906272\pi$
$164$	−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	0.502983	−	0.864297i	$-0.332236\pi$
$167$	0.0771631	+	0.0445501i	0.00597106	+	0.00344739i	−0.497011	+	0.867744i	$0.665569\pi$
$168$		0			0
$169$	−12.4129	+	3.86259i	−0.954839	+	0.297122i
$170$	−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	$0.519322\pi$
$182$	8.35064	+	3.26545i	0.618991	+	0.242051i
$183$		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	0.915885	−	0.401441i	$-0.131490\pi$
$193$	14.2560	+	8.23071i	1.02617	+	0.592459i	0.110285	+	0.993900i	$0.464824\pi$
$194$	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	$0.133550\pi$
$197$			11.4351i			0.814719i	−0.913268	+	0.407360i	$0.866450\pi$
$198$		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
$221$	−3.40160	−	22.3799i	−0.228816	−	1.50544i
$222$		0			0
$223$	12.1351	−	7.00623i	0.812630	−	0.469172i	−0.0352386	−	0.999379i	$-0.511219\pi$
$223$	12.1351	−	7.00623i	0.812630	−	0.469172i	0.847868	+	0.530207i	$0.177886\pi$
$224$	2.48683			0.166159
$225$		0			0
$226$		−	6.62175i		−	0.440472i
$227$	−2.40085	+	1.38613i	−0.159350	+	0.0920010i	−0.577555	−	0.816352i	$-0.695993\pi$
$227$	−2.40085	+	1.38613i	−0.159350	+	0.0920010i	0.418204	+	0.908353i	$0.362660\pi$
$228$		0			0
$229$	14.4165	+	8.32339i	0.952671	+	0.550025i	0.893910	−	0.448247i	$-0.147952\pi$
$229$	14.4165	+	8.32339i	0.952671	+	0.550025i	0.0587614	+	0.998272i	$0.481285\pi$
$230$	−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	0.830471	−	0.557062i	$-0.188071\pi$
$239$	11.8000	+	6.81272i	0.763277	+	0.440678i	−0.0671938	+	0.997740i	$0.521405\pi$
$240$		0			0
$241$	−16.3780	+	9.45585i	−1.05500	+	0.609105i	−0.924045	−	0.382283i	$-0.875138\pi$
$241$	−16.3780	+	9.45585i	−1.05500	+	0.609105i	−0.130956	+	0.991388i	$0.541805\pi$
$242$		−	12.6199i		−	0.811241i
$243$		0			0
$244$	10.5707			0.676719
$245$	0.447233	−	0.258210i	0.0285727	−	0.0164964i
$246$		0			0
$247$	−17.3241	+	2.63315i	−1.10231	+	0.167543i
$248$	−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	$-0.858003\pi$
$271$		−	14.2050i		−	0.862894i	0.902138	−	0.431447i	$-0.141997\pi$
$272$	−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	$-0.217775\pi$
$281$	28.6610	−	16.5474i	1.70977	−	0.987138i	0.934823	−	0.355114i	$-0.115558\pi$
$282$		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
$286$	−16.3197	−	6.38169i	−0.965005	−	0.377358i
$287$	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	0.0738237	−	0.997271i	$-0.476480\pi$
$293$	−12.8880	−	7.44091i	−0.752927	−	0.434702i	−0.826750	+	0.562569i	$0.809813\pi$
$294$		0			0
$295$	2.87677	+	4.98271i	0.167492	+	0.290104i
$296$	7.81310			0.454127
$297$		0			0
$298$	18.4642			1.06960
$299$	−11.9129	−	4.65845i	−0.688941	−	0.269405i
$300$		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	$-0.763217\pi$
$307$		−	23.7291i		−	1.35429i	0.735849	−	0.677145i	$-0.236783\pi$
$308$	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	−0.352020	−	0.935992i	$-0.614505\pi$
$317$	5.03088	−	2.90458i	0.282562	−	0.163137i	0.634583	+	0.772855i	$0.281172\pi$
$318$		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	−0.732572	−	0.680690i	$-0.761680\pi$
$331$	−9.26705	+	5.35033i	−0.509363	+	0.294081i	0.223209	+	0.974771i	$0.428347\pi$
$332$		−	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	$0.183620\pi$
$338$	−8.81860	+	9.55156i	−0.479669	+	0.519536i
$339$		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	−0.979803	−	0.199964i	$-0.935917\pi$
$349$	−24.2212	+	13.9841i	−1.29653	+	0.748552i	−0.316727	+	0.948517i	$0.602584\pi$
$350$	11.4373			0.611350
$351$		0			0
$352$	−4.86004			−0.259041
$353$	14.5560	−	8.40389i	0.774736	−	0.447294i	−0.0598256	−	0.998209i	$-0.519054\pi$
$353$	14.5560	−	8.40389i	0.774736	−	0.447294i	0.834561	+	0.550915i	$0.185721\pi$
$354$		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	$0.177274\pi$
$359$			20.0302i			1.05715i	−0.848886	+	0.528576i	$0.822726\pi$
$360$		0			0
$361$	−4.61995			−0.243155
$362$	−1.41361	+	0.816146i	−0.0742975	+	0.0428957i
$363$		0			0
$364$	8.86460	−	1.34736i	0.464631	−	0.0706207i
$365$	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	$0.277222\pi$
$379$			29.7828i			1.52984i	−0.644124	+	0.764921i	$0.722778\pi$
$380$	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	0.551909	−	0.833905i	$-0.313900\pi$
$383$	2.06820	+	1.19408i	0.105680	+	0.0610146i	−0.446228	+	0.894919i	$0.647233\pi$
$384$		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	$-0.924507\pi$
$397$		−	9.36279i		−	0.469905i	0.972007	−	0.234952i	$-0.0754934\pi$
$398$	−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	0.342700	−	0.939445i	$-0.388659\pi$
$401$	−5.99814	−	3.46303i	−0.299533	−	0.172935i	−0.642233	+	0.766509i	$0.721992\pi$
$402$		0			0
$403$	−5.66254	+	14.4806i	−0.282071	+	0.721332i
$404$	−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	0.842123	−	0.539286i	$-0.181306\pi$
$409$	16.1011	+	9.29599i	0.796149	+	0.459657i	−0.0459735	+	0.998943i	$0.514639\pi$
$410$	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
$416$	−1.31310	+	3.35794i	−0.0643798	+	0.164637i
$417$		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	$-0.259211\pi$
$421$	34.0472	−	19.6572i	1.65936	−	0.958033i	0.973010	−	0.230763i	$-0.0741221\pi$
$422$			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	$-0.631844\pi$
$431$		−	38.0100i		−	1.83088i	0.402457	−	0.915439i	$-0.368156\pi$
$432$		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	$-0.907983\pi$
$449$		−	12.0811i		−	0.570140i	0.958507	−	0.285070i	$-0.0920169\pi$
$450$		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
$455$	−0.853055	−	5.61246i	−0.0399918	−	0.263116i
$456$		0			0
$457$	−24.6389	+	14.2252i	−1.15256	+	0.665429i	−0.949509	−	0.313740i	$-0.898418\pi$
$457$	−24.6389	+	14.2252i	−1.15256	+	0.665429i	−0.203048	+	0.979169i	$0.565085\pi$
$458$	16.6468			0.777853
$459$		0			0
$460$			2.24615i			0.104727i
$461$	14.9740	−	8.64522i	0.697407	−	0.402648i	−0.108974	−	0.994045i	$-0.534756\pi$
$461$	14.9740	−	8.64522i	0.697407	−	0.402648i	0.806381	+	0.591396i	$0.201423\pi$
$462$		0			0
$463$	20.5804	+	11.8821i	0.956452	+	0.552208i	0.895079	−	0.445907i	$-0.147119\pi$
$463$	20.5804	+	11.8821i	0.956452	+	0.552208i	0.0613728	+	0.998115i	$0.480452\pi$
$464$	−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	−0.878081	−	0.478511i	$-0.841177\pi$
$479$	−19.7570	+	11.4067i	−0.902719	+	0.521185i	−0.0246377	+	0.999696i	$0.507843\pi$
$480$		0			0
$481$	27.8507	−	4.23311i	1.26988	−	0.193013i
$482$	−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	$-0.834656\pi$
$487$		−	21.9090i		−	0.992792i	0.868096	−	0.496396i	$-0.165344\pi$
$488$	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	0.987267	−	0.159069i	$-0.0508493\pi$
$499$	30.0035	+	17.3226i	1.34314	+	0.775464i	0.355876	+	0.934533i	$0.384183\pi$
$500$	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	0.260152	−	0.965568i	$-0.416227\pi$
$509$	−10.0617	−	5.80914i	−0.445978	−	0.257485i	−0.706130	+	0.708082i	$0.749561\pi$
$510$		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
$520$	2.12602	+	0.831363i	0.0932322	+	0.0364577i
$521$	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
$533$	−0.102900	+	0.263144i	−0.00445710	+	0.0113980i
$534$		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	$-0.753741\pi$
$541$		−	32.5049i		−	1.39750i	0.715368	−	0.698748i	$-0.246259\pi$
$542$	−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	$0.262109\pi$
$557$			34.6218i			1.46697i	−0.679703	+	0.733487i	$0.737891\pi$
$558$		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	$0.230009\pi$
$572$	−17.3241	+	2.63315i	−0.724359	+	0.110098i
$573$		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	$0.178646\pi$
$577$			25.5692i			1.06446i	−0.846599	+	0.532231i	$0.821354\pi$
$578$	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	−0.354852	−	0.934923i	$-0.615469\pi$
$587$	6.72060	−	3.88014i	0.277389	−	0.160151i	0.632241	+	0.774772i	$0.282135\pi$
$588$		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	$-0.969536\pi$
$593$		−	4.65405i		−	0.191119i	0.995424	−	0.0955594i	$-0.0304640\pi$
$594$		0			0
$595$	9.88525			0.405256
$596$	15.9905	−	9.23210i	0.654995	−	0.378161i
$597$		0			0
$598$	−12.6461	+	1.92212i	−0.517138	+	0.0786014i
$599$	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	$0.228197\pi$
$613$			32.5357i			1.31410i	−0.753845	+	0.657052i	$0.771803\pi$
$614$	−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	0.807828	−	0.589418i	$-0.200643\pi$
$617$	17.4197	+	10.0573i	0.701292	+	0.404891i	−0.106537	+	0.994309i	$0.533976\pi$
$618$		0			0
$619$	−12.2002	+	7.04379i	−0.490367	+	0.283114i	−0.724727	−	0.689036i	$-0.758034\pi$
$619$	−12.2002	+	7.04379i	−0.490367	+	0.283114i	0.234359	+	0.972150i	$0.424701\pi$
$620$	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	$0.101147\pi$
$631$			15.6969i			0.624885i	−0.949937	+	0.312443i	$0.898853\pi$
$632$	−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
$637$	2.73894	+	1.07104i	0.108521	+	0.0424361i
$638$	−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	0.950941	−	0.309373i	$-0.100119\pi$
$643$	29.3762	+	16.9604i	1.15849	+	0.668852i	0.207545	+	0.978225i	$0.433453\pi$
$644$	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
$650$	−6.03912	+	15.4437i	−0.236874	+	0.605750i
$651$		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	−0.0414449	−	0.999141i	$-0.513196\pi$
$661$	−23.8446	−	13.7667i	−0.927449	−	0.535463i	−0.886004	+	0.463678i	$0.846529\pi$
$662$	−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	$0.163511\pi$
$683$			25.6842i			0.982779i	−0.870940	+	0.491390i	$0.836489\pi$
$684$		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
$689$	−3.44597	−	22.6719i	−0.131281	−	0.863729i
$690$		0			0
$691$	3.65761	−	2.11172i	0.139142	−	0.0803338i	−0.428813	−	0.903393i	$-0.641068\pi$
$691$	3.65761	−	2.11172i	0.139142	−	0.0803338i	0.567955	+	0.823060i	$0.307735\pi$
$692$	−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	−0.993825	−	0.110956i	$-0.964609\pi$
$709$	−37.1354	+	21.4401i	−1.39465	+	0.805200i	−0.400822	+	0.916156i	$0.631275\pi$
$710$		−	7.79289i		−	0.292462i
$711$		0			0
$712$	0.595093			0.0223020
$713$	−13.2492	+	7.64943i	−0.496186	+	0.286473i
$714$		0			0
$715$	1.66713	+	10.9685i	0.0623472	+	0.410197i
$716$	−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	−0.479691	−	0.877437i	$-0.659251\pi$
$733$	−40.0538	−	23.1251i	−1.47942	−	0.854143i	−0.999729	+	0.0232941i	$0.992585\pi$
$734$	−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	$0.0525823\pi$
$739$			8.94056i			0.328884i	−0.986387	+	0.164442i	$0.947418\pi$
$740$	−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	0.729494	−	0.683987i	$-0.239756\pi$
$743$	13.6805	+	7.89847i	0.501891	+	0.289767i	−0.227603	+	0.973754i	$0.573089\pi$
$744$		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
$754$	−1.09104	+	2.79010i	−0.0397335	+	0.101609i
$755$	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	0.0937959	−	0.995591i	$-0.470100\pi$
$761$	−19.9038	−	11.4915i	−0.721514	−	0.416566i	−0.815310	+	0.579025i	$0.803433\pi$
$762$		0			0
$763$	−12.3102	−	21.3219i	−0.445658	−	0.771903i
$764$	−3.16633			−0.114554
$765$		0			0
$766$	2.38816			0.0862876
$767$	−11.9327	+	30.5150i	−0.430863	+	1.10183i
$768$		0			0
$769$	1.49286	+	0.861901i	0.0538338	+	0.0310810i	0.526675	−	0.850067i	$-0.323438\pi$
$769$	1.49286	+	0.861901i	0.0538338	+	0.0310810i	−0.472842	+	0.881147i	$0.656772\pi$
$770$	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	$-0.954844\pi$
$773$		−	7.86189i		−	0.282772i	0.989955	−	0.141386i	$-0.0451559\pi$
$774$		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	0.0363089	−	0.999341i	$-0.488440\pi$
$787$	−22.7512	−	13.1354i	−0.810991	−	0.468226i	−0.847300	+	0.531115i	$0.821773\pi$
$788$	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
$806$	2.33642	+	15.3719i	0.0822969	+	0.541451i
$807$		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	$-0.929291\pi$
$811$		−	12.5483i		−	0.440630i	0.975429	−	0.220315i	$-0.0707086\pi$
$812$	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	−0.853480	−	0.521126i	$-0.825512\pi$
$821$	−23.7509	+	13.7126i	−0.828911	+	0.478572i	0.0245686	+	0.999698i	$0.492179\pi$
$822$		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	$-0.815146\pi$
$827$		−	31.5551i		−	1.09728i	0.836060	−	0.548639i	$-0.184854\pi$
$828$		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
$832$	0.541797	+	3.56461i	0.0187834	+	0.123581i
$833$	−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	−0.138901	−	0.990306i	$-0.544357\pi$
$839$	18.8067	−	10.8581i	0.649279	−	0.374862i	0.788180	+	0.615445i	$0.211024\pi$
$840$		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	−0.703575	−	0.710621i	$-0.748414\pi$
$853$	−12.8491	+	7.41846i	−0.439946	+	0.254003i	0.263629	+	0.964624i	$0.415081\pi$
$854$	−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	$-0.904772\pi$
$863$		−	17.3161i		−	0.589447i	0.955583	−	0.294723i	$-0.0952275\pi$
$864$		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
$871$	−10.3532	+	26.4759i	−0.350805	+	0.897102i
$872$	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	0.621437	−	0.783464i	$-0.286549\pi$
$877$	7.51181	+	4.33695i	0.253656	+	0.146448i	−0.367781	+	0.929912i	$0.619882\pi$
$878$	−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	$0.375885\pi$
$884$	−21.0824	−	8.24410i	−0.709078	−	0.277279i
$885$		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
$923$	43.8750	−	6.66869i	1.44416	−	0.219503i
$924$		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	−0.527585	−	0.849502i	$-0.676902\pi$
$929$	−1.69730	+	0.979934i	−0.0556865	+	0.0321506i	0.471898	+	0.881653i	$0.343569\pi$
$930$		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	$-0.941481\pi$
$941$	−50.0947	−	28.9222i	−1.63304	−	0.942836i	−0.649892	−	0.760027i	$-0.725186\pi$
$942$		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	−0.239789	−	0.970825i	$-0.577078\pi$
$947$	14.8043	−	8.54727i	0.481075	−	0.277749i	0.720864	+	0.693076i	$0.243745\pi$
$948$		0			0
$949$	3.75593	−	0.570876i	0.121923	−	0.0185314i
$950$	−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	0.161425	−	0.986885i	$-0.448391\pi$
$967$	−19.0476	−	10.9971i	−0.612530	−	0.353644i	−0.773955	+	0.633241i	$0.781724\pi$
$968$	−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	0.480482	−	0.877005i	$-0.340462\pi$
$977$	−1.21231	−	0.699926i	−0.0387851	−	0.0223926i	−0.519267	+	0.854612i	$0.673795\pi$
$978$		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	−0.671747	−	0.740781i	$-0.734456\pi$
$983$	−11.4778	+	6.62671i	−0.366085	+	0.211359i	0.305662	+	0.952140i	$0.401122\pi$
$984$		0			0
$985$	3.61997	−	6.26998i	0.115342	−	0.199778i
$986$	−4.51776	−	2.60833i	−0.143875	−	0.0830662i
$987$		0			0
$988$	−6.38169	+	16.3197i	−0.203029	+	0.519199i
$989$	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

Display

a_p

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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

)

Twists

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

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

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	702.2.t.a.415.10

Level	$702$
Weight	$2$
Character	702.415
Analytic conductor	$5.605$
Analytic rank	$0$
Dimension	$28$
Inner twists	$4$