LMFDB - Embedded newform 680.2.cg.b.57.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(57,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 0, 4, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.57"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cg (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			57.8
Character	$\chi$	$=$	680.57
Dual form			680.2.cg.b.513.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.203615 - 0.304732i) q^{3} +(-0.154785 + 2.23070i) q^{5} +(-0.0416810 + 0.209544i) q^{7} +(1.09665 + 2.64754i) q^{9} +(0.615902 - 3.09635i) q^{11} -0.714977i q^{13} +(0.648250 + 0.501374i) q^{15} +(0.794784 + 4.04578i) q^{17} +(-1.90886 + 4.60839i) q^{19} +(0.0553680 + 0.0553680i) q^{21} +(1.23743 - 0.826823i) q^{23} +(-4.95208 - 0.690557i) q^{25} +(2.10845 + 0.419397i) q^{27} +(-3.31238 + 4.95733i) q^{29} +(1.79308 + 9.01444i) q^{31} +(-0.818149 - 0.818149i) q^{33} +(-0.460980 - 0.125412i) q^{35} +(3.37529 + 2.25530i) q^{37} +(-0.217876 - 0.145580i) q^{39} +(-0.771819 - 1.15511i) q^{41} +(2.51533 - 6.07255i) q^{43} +(-6.07563 + 2.03650i) q^{45} +1.76827 q^{47} +(6.42499 + 2.66132i) q^{49} +(1.39471 + 0.581586i) q^{51} +(-9.97479 + 4.13169i) q^{53} +(6.81170 + 1.85316i) q^{55} +(1.01565 + 1.52003i) q^{57} +(13.3351 - 5.52358i) q^{59} +(8.64444 - 5.77603i) q^{61} +(-0.600487 + 0.119444i) q^{63} +(1.59490 + 0.110667i) q^{65} +(5.05623 - 5.05623i) q^{67} -0.545438i q^{69} +(-13.7274 + 2.73054i) q^{71} +(-1.01438 - 5.09964i) q^{73} +(-1.21876 + 1.36845i) q^{75} +(0.623151 + 0.258118i) q^{77} +(-3.41105 - 0.678501i) q^{79} +(-5.52191 + 5.52191i) q^{81} +(-1.17245 - 2.83055i) q^{83} +(-9.14795 + 1.14670i) q^{85} +(0.836205 + 2.01878i) q^{87} +(-4.73379 + 4.73379i) q^{89} +(0.149819 + 0.0298009i) q^{91} +(3.11209 + 1.28907i) q^{93} +(-9.98449 - 4.97141i) q^{95} +(-1.17426 - 5.90341i) q^{97} +(8.87314 - 1.76498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 16 q^{15} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 48 q^{33} - 32 q^{35} - 16 q^{37} - 16 q^{41} + 48 q^{43} - 24 q^{45} - 16 q^{47} - 80 q^{49} + 32 q^{51} - 8 q^{53} + 24 q^{55} - 80 q^{59} - 24 q^{61}+ \cdots + 48 q^{99}+O(q^{100}) $ 112 * q + 16 * q^15 - 24 * q^27 - 8 * q^29 + 16 * q^31 - 48 * q^33 - 32 * q^35 - 16 * q^37 - 16 * q^41 + 48 * q^43 - 24 * q^45 - 16 * q^47 - 80 * q^49 + 32 * q^51 - 8 * q^53 + 24 * q^55 - 80 * q^59 - 24 * q^61 - 72 * q^63 + 16 * q^65 - 48 * q^67 - 40 * q^71 - 16 * q^73 + 16 * q^75 + 24 * q^77 + 40 * q^79 - 24 * q^83 + 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^93 - 8 * q^95 + 64 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.203615	−	0.304732i	0.117557	−	0.175937i	−0.768024	−	0.640421i	$-0.778760\pi$
$3$	0.203615	−	0.304732i	0.117557	−	0.175937i	0.885582	+	0.464484i	$0.153760\pi$
$4$		0			0
$5$	−0.154785	+	2.23070i	−0.0692218	+	0.997601i
$5$	−0.154785	+	2.23070i	−0.0692218	+	0.997601i
$6$		0			0
$7$	−0.0416810	+	0.209544i	−0.0157539	+	0.0792003i	−0.987862	−	0.155331i	$-0.950356\pi$
$7$	−0.0416810	+	0.209544i	−0.0157539	+	0.0792003i	0.972109	+	0.234531i	$0.0753556\pi$
$8$		0			0
$9$	1.09665	+	2.64754i	0.365549	+	0.882514i
$10$		0			0
$11$	0.615902	−	3.09635i	0.185701	−	0.933584i	−0.769730	−	0.638370i	$-0.779609\pi$
$11$	0.615902	−	3.09635i	0.185701	−	0.933584i	0.955431	−	0.295214i	$-0.0953910\pi$
$12$		0			0
$13$		−	0.714977i		−	0.198299i	−0.995073	−	0.0991495i	$-0.968388\pi$
$13$		−	0.714977i		−	0.198299i	0.995073	−	0.0991495i	$-0.0316122\pi$
$14$		0			0
$15$	0.648250	+	0.501374i	0.167378	+	0.129454i
$16$		0			0
$17$	0.794784	+	4.04578i	0.192763	+	0.981245i
$17$	0.794784	+	4.04578i	0.192763	+	0.981245i
$18$		0			0
$19$	−1.90886	+	4.60839i	−0.437922	+	1.05724i	0.538743	+	0.842470i	$0.318899\pi$
$19$	−1.90886	+	4.60839i	−0.437922	+	1.05724i	−0.976665	+	0.214767i	$0.931101\pi$
$20$		0			0
$21$	0.0553680	+	0.0553680i	0.0120823	+	0.0120823i
$22$		0			0
$23$	1.23743	−	0.826823i	0.258022	−	0.172405i	−0.419831	−	0.907602i	$-0.637911\pi$
$23$	1.23743	−	0.826823i	0.258022	−	0.172405i	0.677853	+	0.735198i	$0.262911\pi$
$24$		0			0
$25$	−4.95208	−	0.690557i	−0.990417	−	0.138111i
$26$		0			0
$27$	2.10845	+	0.419397i	0.405772	+	0.0807130i
$28$		0			0
$29$	−3.31238	+	4.95733i	−0.615094	+	0.920553i	−0.999997	−	0.00240386i	$-0.999235\pi$
$29$	−3.31238	+	4.95733i	−0.615094	+	0.920553i	0.384903	+	0.922957i	$0.374235\pi$
$30$		0			0
$31$	1.79308	+	9.01444i	0.322047	+	1.61904i	0.714753	+	0.699377i	$0.246539\pi$
$31$	1.79308	+	9.01444i	0.322047	+	1.61904i	−0.392706	+	0.919664i	$0.628461\pi$
$32$		0			0
$33$	−0.818149	−	0.818149i	−0.142421	−	0.142421i
$34$		0			0
$35$	−0.460980	−	0.125412i	−0.0779198	−	0.0211985i
$36$		0			0
$37$	3.37529	+	2.25530i	0.554894	+	0.370768i	0.801175	−	0.598430i	$-0.204209\pi$
$37$	3.37529	+	2.25530i	0.554894	+	0.370768i	−0.246281	+	0.969198i	$0.579209\pi$
$38$		0			0
$39$	−0.217876	−	0.145580i	−0.0348881	−	0.0233115i
$40$		0			0
$41$	−0.771819	−	1.15511i	−0.120538	−	0.180398i	0.766294	−	0.642490i	$-0.222099\pi$
$41$	−0.771819	−	1.15511i	−0.120538	−	0.180398i	−0.886832	+	0.462093i	$0.847099\pi$
$42$		0			0
$43$	2.51533	−	6.07255i	0.383585	−	0.926056i	−0.607682	−	0.794181i	$-0.707900\pi$
$43$	2.51533	−	6.07255i	0.383585	−	0.926056i	0.991266	−	0.131875i	$-0.0420997\pi$
$44$		0			0
$45$	−6.07563	+	2.03650i	−0.905701	+	0.303583i
$46$		0			0
$47$	1.76827			0.257928			0.128964	−	0.991649i	$-0.458835\pi$
$47$	1.76827			0.257928			0.128964	+	0.991649i	$0.458835\pi$
$48$		0			0
$49$	6.42499	+	2.66132i	0.917855	+	0.380188i
$50$		0			0
$51$	1.39471	+	0.581586i	0.195298	+	0.0814384i
$52$		0			0
$53$	−9.97479	+	4.13169i	−1.37014	+	0.567532i	−0.941827	−	0.336097i	$-0.890893\pi$
$53$	−9.97479	+	4.13169i	−1.37014	+	0.567532i	−0.428316	+	0.903629i	$0.640893\pi$
$54$		0			0
$55$	6.81170	+	1.85316i	0.918490	+	0.249880i
$56$		0			0
$57$	1.01565	+	1.52003i	0.134526	+	0.201333i
$58$		0			0
$59$	13.3351	−	5.52358i	1.73608	−	0.719109i	0.737017	−	0.675874i	$-0.236234\pi$
$59$	13.3351	−	5.52358i	1.73608	−	0.719109i	0.999065	−	0.0432346i	$-0.0137663\pi$
$60$		0			0
$61$	8.64444	−	5.77603i	1.10681	−	0.739545i	0.138763	−	0.990326i	$-0.455687\pi$
$61$	8.64444	−	5.77603i	1.10681	−	0.739545i	0.968044	+	0.250781i	$0.0806873\pi$
$62$		0			0
$63$	−0.600487	+	0.119444i	−0.0756543	+	0.0150486i
$64$		0			0
$65$	1.59490	+	0.110667i	0.197823	+	0.0137266i
$66$		0			0
$67$	5.05623	−	5.05623i	0.617717	−	0.617717i	−0.327229	−	0.944945i	$-0.606115\pi$
$67$	5.05623	−	5.05623i	0.617717	−	0.617717i	0.944945	+	0.327229i	$0.106115\pi$
$68$		0			0
$69$		−	0.545438i		−	0.0656630i
$70$		0			0
$71$	−13.7274	+	2.73054i	−1.62914	+	0.324056i	−0.923230	−	0.384248i	$-0.874461\pi$
$71$	−13.7274	+	2.73054i	−1.62914	+	0.324056i	−0.705908	+	0.708304i	$0.749461\pi$
$72$		0			0
$73$	−1.01438	−	5.09964i	−0.118724	−	0.596868i	−0.993641	−	0.112595i	$-0.964084\pi$
$73$	−1.01438	−	5.09964i	−0.118724	−	0.596868i	0.874917	−	0.484274i	$-0.160916\pi$
$74$		0			0
$75$	−1.21876	+	1.36845i	−0.140730	+	0.158015i
$76$		0			0
$77$	0.623151	+	0.258118i	0.0710147	+	0.0294152i
$78$		0			0
$79$	−3.41105	−	0.678501i	−0.383773	−	0.0763373i	−0.000566588	−	1.00000i	$-0.500180\pi$
$79$	−3.41105	−	0.678501i	−0.383773	−	0.0763373i	−0.383207	+	0.923663i	$0.625180\pi$
$80$		0			0
$81$	−5.52191	+	5.52191i	−0.613545	+	0.613545i
$82$		0			0
$83$	−1.17245	−	2.83055i	−0.128693	−	0.310693i	0.846379	−	0.532581i	$-0.178778\pi$
$83$	−1.17245	−	2.83055i	−0.128693	−	0.310693i	−0.975072	+	0.221888i	$0.928778\pi$
$84$		0			0
$85$	−9.14795	+	1.14670i	−0.992235	+	0.124378i
$86$		0			0
$87$	0.836205	+	2.01878i	0.0896506	+	0.216436i
$88$		0			0
$89$	−4.73379	+	4.73379i	−0.501781	+	0.501781i	−0.911991	−	0.410210i	$-0.865455\pi$
$89$	−4.73379	+	4.73379i	−0.501781	+	0.501781i	0.410210	+	0.911991i	$0.365455\pi$
$90$		0			0
$91$	0.149819	+	0.0298009i	0.0157053	+	0.00312399i
$92$		0			0
$93$	3.11209	+	1.28907i	0.322708	+	0.133670i
$94$		0			0
$95$	−9.98449	−	4.97141i	−1.02439	−	0.510055i
$96$		0			0
$97$	−1.17426	−	5.90341i	−0.119228	−	0.599400i	−0.993487	−	0.113941i	$-0.963652\pi$
$97$	−1.17426	−	5.90341i	−0.119228	−	0.599400i	0.874259	−	0.485459i	$-0.161348\pi$
$98$		0			0
$99$	8.87314	−	1.76498i	0.891784	−	0.177387i
$100$		0			0
$101$			0.137150i			0.0136469i	0.999977	+	0.00682344i	$0.00217199\pi$
$101$			0.137150i			0.0136469i	−0.999977	+	0.00682344i	$0.997828\pi$
$102$		0			0
$103$	11.9995	−	11.9995i	1.18234	−	1.18234i	0.203206	−	0.979136i	$-0.434864\pi$
$103$	11.9995	−	11.9995i	1.18234	−	1.18234i	0.979136	−	0.203206i	$-0.0651361\pi$
$104$		0			0
$105$	−0.132080	+	0.114939i	−0.0128897	+	0.0112169i
$106$		0			0
$107$	5.07386	−	1.00925i	0.490508	−	0.0975681i	0.0563616	−	0.998410i	$-0.482050\pi$
$107$	5.07386	−	1.00925i	0.490508	−	0.0975681i	0.434146	+	0.900842i	$0.357050\pi$
$108$		0			0
$109$	−5.33339	+	3.56366i	−0.510847	+	0.341337i	−0.784130	−	0.620597i	$-0.786890\pi$
$109$	−5.33339	+	3.56366i	−0.510847	+	0.341337i	0.273283	+	0.961934i	$0.411890\pi$
$110$		0			0
$111$	1.37452	−	0.569345i	0.130464	−	0.0540399i
$112$		0			0
$113$	−2.38105	−	3.56349i	−0.223990	−	0.335225i	0.702405	−	0.711777i	$-0.252109\pi$
$113$	−2.38105	−	3.56349i	−0.223990	−	0.335225i	−0.926395	+	0.376552i	$0.877109\pi$
$114$		0			0
$115$	1.65286	+	2.88832i	0.154130	+	0.269337i
$116$		0			0
$117$	1.89293	−	0.784078i	0.175002	−	0.0724880i
$118$		0			0
$119$	−0.880897	−	0.00208940i	−0.0807517	−	0.000191535i
$120$		0			0
$121$	0.954639	+	0.395424i	0.0867853	+	0.0359477i
$122$		0			0
$123$	−0.509153			−0.0459088
$124$		0			0
$125$	2.30694	−	10.9397i	0.206339	−	0.978481i
$126$		0			0
$127$	−2.07251	+	5.00348i	−0.183906	+	0.443987i	−0.988765	−	0.149478i	$-0.952241\pi$
$127$	−2.07251	+	5.00348i	−0.183906	+	0.443987i	0.804859	+	0.593466i	$0.202241\pi$
$128$		0			0
$129$	−1.33834	−	2.00297i	−0.117834	−	0.176351i
$130$		0			0
$131$	−11.5174	−	7.69569i	−1.00628	−	0.672376i	−0.0608334	−	0.998148i	$-0.519376\pi$
$131$	−11.5174	−	7.69569i	−1.00628	−	0.672376i	−0.945448	+	0.325772i	$0.894376\pi$
$132$		0			0
$133$	−0.886099	−	0.592073i	−0.0768346	−	0.0513392i
$134$		0			0
$135$	−1.26191	+	4.63842i	−0.108608	+	0.399211i
$136$		0			0
$137$	−3.13581	−	3.13581i	−0.267910	−	0.267910i	0.560347	−	0.828258i	$-0.310668\pi$
$137$	−3.13581	−	3.13581i	−0.267910	−	0.267910i	−0.828258	+	0.560347i	$0.810668\pi$
$138$		0			0
$139$	−2.47875	−	12.4615i	−0.210245	−	1.05697i	−0.931344	−	0.364140i	$-0.881363\pi$
$139$	−2.47875	−	12.4615i	−0.210245	−	1.05697i	0.721100	−	0.692831i	$-0.243637\pi$
$140$		0			0
$141$	0.360046	−	0.538847i	0.0303214	−	0.0453791i
$142$		0			0
$143$	−2.21382	−	0.440356i	−0.185129	−	0.0368244i
$144$		0			0
$145$	−10.5456	−	8.15626i	−0.875767	−	0.677341i
$146$		0			0
$147$	2.11921	−	1.41601i	0.174790	−	0.116791i
$148$		0			0
$149$	12.0150	+	12.0150i	0.984307	+	0.984307i	0.999879	−	0.0155714i	$-0.00495672\pi$
$149$	12.0150	+	12.0150i	0.984307	+	0.984307i	−0.0155714	+	0.999879i	$0.504957\pi$
$150$		0			0
$151$	−4.01773	+	9.69966i	−0.326958	+	0.789347i	0.671857	+	0.740681i	$0.265497\pi$
$151$	−4.01773	+	9.69966i	−0.326958	+	0.789347i	−0.998815	+	0.0486659i	$0.984503\pi$
$152$		0			0
$153$	−9.83977	+	6.54102i	−0.795498	+	0.528810i
$154$		0			0
$155$	−20.3861	+	2.60454i	−1.63745	+	0.209202i
$156$		0			0
$157$		−	12.4709i		−	0.995286i	−0.867382	−	0.497643i	$-0.834199\pi$
$157$		−	12.4709i		−	0.995286i	0.867382	−	0.497643i	$-0.165801\pi$
$158$		0			0
$159$	−0.771962	+	3.88091i	−0.0612205	+	0.307776i
$160$		0			0
$161$	0.121679	+	0.293759i	0.00958965	+	0.0231515i
$162$		0			0
$163$	3.96915	−	19.9543i	0.310888	−	1.56294i	−0.437215	−	0.899357i	$-0.644035\pi$
$163$	3.96915	−	19.9543i	0.310888	−	1.56294i	0.748103	−	0.663583i	$-0.230965\pi$
$164$		0			0
$165$	1.95169	−	1.69841i	0.151939	−	0.132221i
$166$		0			0
$167$	−0.575887	+	0.861876i	−0.0445635	+	0.0666940i	−0.853082	−	0.521776i	$-0.825270\pi$
$167$	−0.575887	+	0.861876i	−0.0445635	+	0.0666940i	0.808519	+	0.588470i	$0.200270\pi$
$168$		0			0
$169$	12.4888			0.960678
$170$		0			0
$171$	−14.2943			−1.09311
$172$		0			0
$173$	14.2056	−	21.2601i	1.08003	−	1.61638i	0.344636	−	0.938736i	$-0.388002\pi$
$173$	14.2056	−	21.2601i	1.08003	−	1.61638i	0.735393	−	0.677641i	$-0.236998\pi$
$174$		0			0
$175$	0.351110	−	1.00890i	0.0265414	−	0.0762655i
$176$		0			0
$177$	1.03202	−	5.18832i	0.0775714	−	0.389978i
$178$		0			0
$179$	−3.87179	−	9.34732i	−0.289391	−	0.698651i	0.710597	−	0.703599i	$-0.248425\pi$
$179$	−3.87179	−	9.34732i	−0.289391	−	0.698651i	−0.999988	+	0.00494798i	$0.998425\pi$
$180$		0			0
$181$	−1.95886	+	9.84785i	−0.145601	+	0.731985i	0.837139	+	0.546990i	$0.184227\pi$
$181$	−1.95886	+	9.84785i	−0.145601	+	0.731985i	−0.982740	+	0.184994i	$0.940773\pi$
$182$		0			0
$183$		−	3.81033i		−	0.281667i
$184$		0			0
$185$	−5.55334	+	7.18018i	−0.408290	+	0.527898i
$186$		0			0
$187$	13.0166	+	0.0308741i	0.951871	+	0.00225774i
$188$		0			0
$189$	−0.175765	+	0.424334i	−0.0127850	+	0.0308657i
$190$		0			0
$191$	8.70008	+	8.70008i	0.629516	+	0.629516i	0.947946	−	0.318430i	$-0.103156\pi$
$191$	8.70008	+	8.70008i	0.629516	+	0.629516i	−0.318430	+	0.947946i	$0.603156\pi$
$192$		0			0
$193$	10.2967	−	6.88005i	0.741175	−	0.495237i	−0.126749	−	0.991935i	$-0.540454\pi$
$193$	10.2967	−	6.88005i	0.741175	−	0.495237i	0.867924	+	0.496698i	$0.165454\pi$
$194$		0			0
$195$	0.358471	−	0.463484i	0.0256706	−	0.0331908i
$196$		0			0
$197$	−18.2417	−	3.62850i	−1.29967	−	0.258520i	−0.503710	−	0.863873i	$-0.668032\pi$
$197$	−18.2417	−	3.62850i	−1.29967	−	0.258520i	−0.795957	+	0.605353i	$0.793032\pi$
$198$		0			0
$199$	1.36562	−	2.04379i	0.0968061	−	0.144880i	−0.779905	−	0.625898i	$-0.784733\pi$
$199$	1.36562	−	2.04379i	0.0968061	−	0.144880i	0.876711	+	0.481017i	$0.159733\pi$
$200$		0			0
$201$	−0.511268	−	2.57032i	−0.0360621	−	0.181296i
$202$		0			0
$203$	−0.900717	−	0.900717i	−0.0632180	−	0.0632180i
$204$		0			0
$205$	2.69617	−	1.54291i	0.188309	−	0.107761i
$206$		0			0
$207$	3.54607	+	2.36941i	0.246469	+	0.164685i
$208$		0			0
$209$	13.0935	+	8.74880i	0.905697	+	0.605167i
$210$		0			0
$211$	−5.61721	−	8.40675i	−0.386705	−	0.578744i	0.586138	−	0.810211i	$-0.300648\pi$
$211$	−5.61721	−	8.40675i	−0.386705	−	0.578744i	−0.972843	+	0.231467i	$0.925648\pi$
$212$		0			0
$213$	−1.96302	+	4.73915i	−0.134504	+	0.324721i
$214$		0			0
$215$	13.1567	+	6.55090i	0.897282	+	0.446768i
$216$		0			0
$217$	−1.96366			−0.133302
$218$		0			0
$219$	−1.76057	−	0.729251i	−0.118968	−	0.0492782i
$220$		0			0
$221$	2.89264	−	0.568252i	0.194580	−	0.0382248i
$222$		0			0
$223$	−6.00934	+	2.48915i	−0.402415	+	0.166686i	−0.574705	−	0.818360i	$-0.694883\pi$
$223$	−6.00934	+	2.48915i	−0.402415	+	0.166686i	0.172290	+	0.985046i	$0.444883\pi$
$224$		0			0
$225$	−3.60241	−	13.8681i	−0.240161	−	0.924543i
$226$		0			0
$227$	−4.71714	−	7.05969i	−0.313087	−	0.468568i	0.641236	−	0.767344i	$-0.278422\pi$
$227$	−4.71714	−	7.05969i	−0.313087	−	0.468568i	−0.954323	+	0.298775i	$0.903422\pi$
$228$		0			0
$229$	15.1257	−	6.26528i	0.999536	−	0.414021i	0.177909	−	0.984047i	$-0.443067\pi$
$229$	15.1257	−	6.26528i	0.999536	−	0.414021i	0.821627	+	0.570025i	$0.193067\pi$
$230$		0			0
$231$	0.205540	−	0.137337i	0.0135235	−	0.00903613i
$232$		0			0
$233$	15.4108	−	3.06540i	1.00959	−	0.200821i	0.337531	−	0.941314i	$-0.390408\pi$
$233$	15.4108	−	3.06540i	1.00959	−	0.200821i	0.672063	+	0.740494i	$0.265408\pi$
$234$		0			0
$235$	−0.273701	+	3.94448i	−0.0178543	+	0.257310i
$236$		0			0
$237$	−0.901304	+	0.901304i	−0.0585460	+	0.0585460i
$238$		0			0
$239$			7.99538i			0.517178i	0.965987	+	0.258589i	$0.0832575\pi$
$239$			7.99538i			0.517178i	−0.965987	+	0.258589i	$0.916742\pi$
$240$		0			0
$241$	22.1394	−	4.40380i	1.42613	−	0.283674i	0.579113	−	0.815247i	$-0.303399\pi$
$241$	22.1394	−	4.40380i	1.42613	−	0.283674i	0.847012	+	0.531573i	$0.178399\pi$
$242$		0			0
$243$	1.81655	+	9.13240i	0.116532	+	0.585844i
$244$		0			0
$245$	−6.93110	+	13.9203i	−0.442812	+	0.889336i
$246$		0			0
$247$	3.29489	+	1.36479i	0.209649	+	0.0868395i
$248$		0			0
$249$	−1.10129	−	0.219060i	−0.0697912	−	0.0138823i
$250$		0			0
$251$	−4.52118	+	4.52118i	−0.285374	+	0.285374i	−0.835248	−	0.549874i	$-0.814676\pi$
$251$	−4.52118	+	4.52118i	−0.285374	+	0.285374i	0.549874	+	0.835248i	$0.314676\pi$
$252$		0			0
$253$	−1.79800	−	4.34075i	−0.113039	−	0.272901i
$254$		0			0
$255$	−1.51323	+	3.02116i	−0.0947619	+	0.189192i
$256$		0			0
$257$	7.61837	+	18.3924i	0.475221	+	1.14729i	0.961826	+	0.273663i	$0.0882352\pi$
$257$	7.61837	+	18.3924i	0.475221	+	1.14729i	−0.486605	+	0.873622i	$0.661765\pi$
$258$		0			0
$259$	−0.613270	+	0.613270i	−0.0381067	+	0.0381067i
$260$		0			0
$261$	−16.7573	−	3.33323i	−1.03725	−	0.206322i
$262$		0			0
$263$	1.02175	+	0.423221i	0.0630035	+	0.0260969i	0.413963	−	0.910294i	$-0.364144\pi$
$263$	1.02175	+	0.423221i	0.0630035	+	0.0260969i	−0.350959	+	0.936391i	$0.614144\pi$
$264$		0			0
$265$	−7.67264	−	22.8903i	−0.471327	−	1.40614i
$266$		0			0
$267$	0.478665	+	2.40641i	0.0292938	+	0.147270i
$268$		0			0
$269$	−4.10222	+	0.815983i	−0.250117	+	0.0497514i	−0.318556	−	0.947904i	$-0.603198\pi$
$269$	−4.10222	+	0.815983i	−0.250117	+	0.0497514i	0.0684394	+	0.997655i	$0.478198\pi$
$270$		0			0
$271$		−	1.66787i		−	0.101316i	−0.998716	−	0.0506580i	$-0.983868\pi$
$271$		−	1.66787i		−	0.101316i	0.998716	−	0.0506580i	$-0.0161318\pi$
$272$		0			0
$273$	0.0395868	−	0.0395868i	0.00239590	−	0.00239590i
$274$		0			0
$275$	−5.18820	+	14.9081i	−0.312860	+	0.898990i
$276$		0			0
$277$	12.9415	−	2.57423i	0.777580	−	0.154670i	0.209683	−	0.977770i	$-0.432757\pi$
$277$	12.9415	−	2.57423i	0.777580	−	0.154670i	0.567898	+	0.823099i	$0.307757\pi$
$278$		0			0
$279$	−21.8997	+	14.6329i	−1.31110	+	0.876051i
$280$		0			0
$281$	8.15533	−	3.37805i	0.486506	−	0.201517i	−0.125927	−	0.992039i	$-0.540191\pi$
$281$	8.15533	−	3.37805i	0.486506	−	0.201517i	0.612434	+	0.790522i	$0.290191\pi$
$282$		0			0
$283$	−12.9056	−	19.3146i	−0.767159	−	1.14813i	−0.985068	−	0.172165i	$-0.944924\pi$
$283$	−12.9056	−	19.3146i	−0.767159	−	1.14813i	0.217909	−	0.975969i	$-0.430076\pi$
$284$		0			0
$285$	−3.54794	+	2.03034i	−0.210162	+	0.120267i
$286$		0			0
$287$	0.274217	−	0.113584i	0.0161865	−	0.00670467i
$288$		0			0
$289$	−15.7366	+	6.43104i	−0.925684	+	0.378296i
$290$		0			0
$291$	−2.03805	−	0.844190i	−0.119473	−	0.0494873i
$292$		0			0
$293$	−17.9425			−1.04821			−0.524107	−	0.851653i	$-0.675601\pi$
$293$	−17.9425			−1.04821			−0.524107	+	0.851653i	$0.675601\pi$
$294$		0			0
$295$	10.2574	+	30.6016i	0.597209	+	1.78170i
$296$		0			0
$297$	2.59720	−	6.27020i	0.150705	−	0.363834i
$298$		0			0
$299$	−0.591160	−	0.884733i	−0.0341876	−	0.0511654i
$300$		0			0
$301$	1.16763	+	0.780184i	0.0673010	+	0.0449691i
$302$		0			0
$303$	0.0417938	+	0.0279258i	0.00240099	+	0.00160429i
$304$		0			0
$305$	11.5466	+	20.1772i	0.661156	+	1.15534i
$306$		0			0
$307$	17.4618	+	17.4618i	0.996596	+	0.996596i	0.999994	−	0.00339870i	$-0.00108184\pi$
$307$	17.4618	+	17.4618i	0.996596	+	0.996596i	−0.00339870	+	0.999994i	$0.501082\pi$
$308$		0			0
$309$	−1.21334	−	6.09989i	−0.0690247	−	0.347011i
$310$		0			0
$311$	−15.9963	+	23.9402i	−0.907067	+	1.35752i	0.0267010	+	0.999643i	$0.491500\pi$
$311$	−15.9963	+	23.9402i	−0.907067	+	1.35752i	−0.933768	+	0.357878i	$0.883500\pi$
$312$		0			0
$313$	−12.9263	−	2.57120i	−0.730638	−	0.145333i	−0.184267	−	0.982876i	$-0.558991\pi$
$313$	−12.9263	−	2.57120i	−0.730638	−	0.145333i	−0.546371	+	0.837543i	$0.683991\pi$
$314$		0			0
$315$	−0.173499	−	1.35800i	−0.00977555	−	0.0765145i
$316$		0			0
$317$	4.58967	−	3.06672i	0.257781	−	0.172244i	−0.419964	−	0.907541i	$-0.637957\pi$
$317$	4.58967	−	3.06672i	0.257781	−	0.172244i	0.677745	+	0.735297i	$0.262957\pi$
$318$		0			0
$319$	13.3095	+	13.3095i	0.745190	+	0.745190i
$320$		0			0
$321$	0.725563	−	1.75167i	0.0404970	−	0.0977684i
$322$		0			0
$323$	−20.1617	−	4.06014i	−1.12182	−	0.225912i
$324$		0			0
$325$	−0.493733	+	3.54063i	−0.0273874	+	0.196399i
$326$		0			0
$327$			2.35087i			0.130004i
$328$		0			0
$329$	−0.0737031	+	0.370530i	−0.00406338	+	0.0204280i
$330$		0			0
$331$	1.40867	+	3.40083i	0.0774274	+	0.186926i	0.957854	−	0.287257i	$-0.0927434\pi$
$331$	1.40867	+	3.40083i	0.0774274	+	0.186926i	−0.880426	+	0.474183i	$0.842743\pi$
$332$		0			0
$333$	−2.26949	+	11.4095i	−0.124367	+	0.625236i
$334$		0			0
$335$	10.4963	+	12.0616i	0.573475	+	0.658994i
$336$		0			0
$337$	2.71279	−	4.05997i	0.147775	−	0.221161i	−0.750196	−	0.661215i	$-0.770041\pi$
$337$	2.71279	−	4.05997i	0.147775	−	0.221161i	0.897971	+	0.440055i	$0.145041\pi$
$338$		0			0
$339$	−1.57073			−0.0853102
$340$		0			0
$341$	29.0162			1.57132
$342$		0			0
$343$	−1.65635	+	2.47890i	−0.0894342	+	0.133848i
$344$		0			0
$345$	1.21671	+	0.0844254i	0.0655055	+	0.00454531i
$346$		0			0
$347$	−3.75381	+	18.8717i	−0.201515	+	1.01309i	0.739096	+	0.673600i	$0.235253\pi$
$347$	−3.75381	+	18.8717i	−0.201515	+	1.01309i	−0.940611	+	0.339486i	$0.889747\pi$
$348$		0			0
$349$	−8.60216	−	20.7675i	−0.460463	−	1.11166i	−0.968207	−	0.250149i	$-0.919521\pi$
$349$	−8.60216	−	20.7675i	−0.460463	−	1.11166i	0.507744	−	0.861508i	$-0.330479\pi$
$350$		0			0
$351$	0.299859	−	1.50750i	0.0160053	−	0.0804641i
$352$		0			0
$353$			25.9994i			1.38381i	0.721990	+	0.691903i	$0.243228\pi$
$353$			25.9994i			1.38381i	−0.721990	+	0.691903i	$0.756772\pi$
$354$		0			0
$355$	−3.96625	−	31.0443i	−0.210507	−	1.64766i
$356$		0			0
$357$	−0.180001	+	0.268012i	−0.00952666	+	0.0141847i
$358$		0			0
$359$	−5.43081	+	13.1111i	−0.286627	+	0.691980i	−0.999961	−	0.00884497i	$-0.997185\pi$
$359$	−5.43081	+	13.1111i	−0.286627	+	0.691980i	0.713333	+	0.700825i	$0.247185\pi$
$360$		0			0
$361$	−4.15850	−	4.15850i	−0.218868	−	0.218868i
$362$		0			0
$363$	0.314878	−	0.210394i	0.0165268	−	0.0110428i
$364$		0			0
$365$	11.5328	−	1.47344i	0.603655	−	0.0771234i
$366$		0			0
$367$	−14.3779	−	2.85995i	−0.750521	−	0.149288i	−0.195015	−	0.980800i	$-0.562476\pi$
$367$	−14.3779	−	2.85995i	−0.750521	−	0.149288i	−0.555506	+	0.831512i	$0.687476\pi$
$368$		0			0
$369$	2.21179	−	3.31017i	0.115141	−	0.172321i
$370$		0			0
$371$	−0.450014	−	2.26237i	−0.0233636	−	0.117457i
$372$		0			0
$373$	22.5092	+	22.5092i	1.16548	+	1.16548i	0.983256	+	0.182228i	$0.0583310\pi$
$373$	22.5092	+	22.5092i	1.16548	+	1.16548i	0.182228	+	0.983256i	$0.441669\pi$
$374$		0			0
$375$	−2.86396	−	2.93050i	−0.147894	−	0.151330i
$376$		0			0
$377$	3.54438	+	2.36828i	0.182545	+	0.121972i
$378$		0			0
$379$	13.2509	+	8.85395i	0.680651	+	0.454797i	0.847226	−	0.531232i	$-0.178271\pi$
$379$	13.2509	+	8.85395i	0.680651	+	0.454797i	−0.166575	+	0.986029i	$0.553271\pi$
$380$		0			0
$381$	1.10273	+	1.65035i	0.0564944	+	0.0845498i
$382$		0			0
$383$	10.0191	−	24.1883i	0.511953	−	1.23596i	−0.430793	−	0.902451i	$-0.641766\pi$
$383$	10.0191	−	24.1883i	0.511953	−	1.23596i	0.942746	−	0.333512i	$-0.108234\pi$
$384$		0			0
$385$	−0.672238	+	1.35011i	−0.0342604	+	0.0688081i
$386$		0			0
$387$	18.8358			0.957476
$388$		0			0
$389$	27.6421	+	11.4497i	1.40151	+	0.580524i	0.950143	−	0.311815i	$-0.100937\pi$
$389$	27.6421	+	11.4497i	1.40151	+	0.580524i	0.451366	+	0.892339i	$0.350937\pi$
$390$		0			0
$391$	4.32863	+	4.34921i	0.218908	+	0.219949i
$392$		0			0
$393$	−4.69025	+	1.94276i	−0.236592	+	0.0979995i
$394$		0			0
$395$	2.04151	−	7.50403i	0.102720	−	0.377569i
$396$		0			0
$397$	19.0599	+	28.5252i	0.956591	+	1.43164i	0.901313	+	0.433168i	$0.142604\pi$
$397$	19.0599	+	28.5252i	0.956591	+	1.43164i	0.0552774	+	0.998471i	$0.482396\pi$
$398$		0			0
$399$	−0.360847	+	0.149468i	−0.0180649	+	0.00748274i
$400$		0			0
$401$	4.67166	−	3.12150i	0.233292	−	0.155881i	−0.433430	−	0.901187i	$-0.642697\pi$
$401$	4.67166	−	3.12150i	0.233292	−	0.155881i	0.666722	+	0.745307i	$0.267697\pi$
$402$		0			0
$403$	6.44512	−	1.28201i	0.321054	−	0.0638616i
$404$		0			0
$405$	−11.4630	−	13.1724i	−0.569603	−	0.654544i
$406$		0			0
$407$	9.06202	−	9.06202i	0.449188	−	0.449188i
$408$		0			0
$409$			2.64200i			0.130639i	0.997864	+	0.0653193i	$0.0208066\pi$
$409$			2.64200i			0.130639i	−0.997864	+	0.0653193i	$0.979193\pi$
$410$		0			0
$411$	−1.59408	+	0.317082i	−0.0786302	+	0.0156405i
$412$		0			0
$413$	0.601615	+	3.02452i	0.0296035	+	0.148827i
$414$		0			0
$415$	6.49559	−	2.17727i	0.318856	−	0.106878i
$416$		0			0
$417$	−4.30213	−	1.78200i	−0.210676	−	0.0872649i
$418$		0			0
$419$	−15.6573	−	3.11444i	−0.764911	−	0.152150i	−0.202809	−	0.979218i	$-0.565007\pi$
$419$	−15.6573	−	3.11444i	−0.764911	−	0.152150i	−0.562102	+	0.827068i	$0.690007\pi$
$420$		0			0
$421$	9.77083	−	9.77083i	0.476201	−	0.476201i	−0.427713	−	0.903915i	$-0.640681\pi$
$421$	9.77083	−	9.77083i	0.476201	−	0.476201i	0.903915	+	0.427713i	$0.140681\pi$
$422$		0			0
$423$	1.93917	+	4.68156i	0.0942855	+	0.227625i
$424$		0			0
$425$	−1.14200	−	20.5839i	−0.0553949	−	0.998465i
$426$		0			0
$427$	0.850026	+	2.05214i	0.0411356	+	0.0993102i
$428$		0			0
$429$	−0.584958	+	0.584958i	−0.0282420	+	0.0282420i
$430$		0			0
$431$	−23.5888	−	4.69210i	−1.13623	−	0.226010i	−0.409087	−	0.912495i	$-0.634153\pi$
$431$	−23.5888	−	4.69210i	−1.13623	−	0.226010i	−0.727144	+	0.686485i	$0.759153\pi$
$432$		0			0
$433$	30.2129	+	12.5146i	1.45194	+	0.601412i	0.962659	−	0.270715i	$-0.0872602\pi$
$433$	30.2129	+	12.5146i	1.45194	+	0.601412i	0.489278	+	0.872128i	$0.337260\pi$
$434$		0			0
$435$	−4.63273	+	1.55285i	−0.222122	+	0.0744535i
$436$		0			0
$437$	1.44825	+	7.28084i	0.0692792	+	0.348290i
$438$		0			0
$439$	−24.4788	+	4.86914i	−1.16831	+	0.232392i	−0.740868	−	0.671651i	$-0.765586\pi$
$439$	−24.4788	+	4.86914i	−1.16831	+	0.232392i	−0.427443	+	0.904042i	$0.640586\pi$
$440$		0			0
$441$			19.9289i			0.948997i
$442$		0			0
$443$	−28.4943	+	28.4943i	−1.35381	+	1.35381i	−0.472448	+	0.881358i	$0.656630\pi$
$443$	−28.4943	+	28.4943i	−1.35381	+	1.35381i	−0.881358	+	0.472448i	$0.843370\pi$
$444$		0			0
$445$	−9.82697	−	11.2924i	−0.465843	−	0.535311i
$446$		0			0
$447$	6.10779	−	1.21492i	0.288889	−	0.0574635i
$448$		0			0
$449$	−5.00378	+	3.34342i	−0.236143	+	0.157786i	−0.668012	−	0.744151i	$-0.732854\pi$
$449$	−5.00378	+	3.34342i	−0.236143	+	0.157786i	0.431869	+	0.901937i	$0.357854\pi$
$450$		0			0
$451$	−4.05198	+	1.67839i	−0.190800	+	0.0790321i
$452$		0			0
$453$	2.13772	+	3.19933i	0.100439	+	0.150318i
$454$		0			0
$455$	−0.0896668	+	0.329590i	−0.00420365	+	0.0154514i
$456$		0			0
$457$	−33.1823	+	13.7446i	−1.55220	+	0.642944i	−0.983713	−	0.179746i	$-0.942472\pi$
$457$	−33.1823	+	13.7446i	−1.55220	+	0.642944i	−0.568491	+	0.822690i	$0.692472\pi$
$458$		0			0
$459$	−0.0210237	+	8.86366i	−0.000981301	+	0.413720i
$460$		0			0
$461$	5.00522	+	2.07323i	0.233116	+	0.0965599i	0.496184	−	0.868218i	$-0.334734\pi$
$461$	5.00522	+	2.07323i	0.233116	+	0.0965599i	−0.263068	+	0.964777i	$0.584734\pi$
$462$		0			0
$463$	36.5808			1.70005			0.850027	−	0.526739i	$-0.176585\pi$
$463$	36.5808			1.70005			0.850027	+	0.526739i	$0.176585\pi$
$464$		0			0
$465$	−3.35723	+	6.74262i	−0.155688	+	0.312681i
$466$		0			0
$467$	4.15531	−	10.0318i	0.192285	−	0.464217i	−0.798105	−	0.602518i	$-0.794164\pi$
$467$	4.15531	−	10.0318i	0.192285	−	0.464217i	0.990390	+	0.138301i	$0.0441642\pi$
$468$		0			0
$469$	0.848756	+	1.27025i	0.0391919	+	0.0586548i
$470$		0			0
$471$	−3.80028	−	2.53927i	−0.175108	−	0.117003i
$472$		0			0
$473$	−17.2535	−	11.5284i	−0.793319	−	0.530079i
$474$		0			0
$475$	12.6352	−	21.5030i	0.579742	−	0.986623i
$476$		0			0
$477$	−21.8777	−	21.8777i	−1.00171	−	1.00171i
$478$		0			0
$479$	0.139646	+	0.702046i	0.00638057	+	0.0320773i	0.983844	−	0.179026i	$-0.0572945\pi$
$479$	0.139646	+	0.702046i	0.00638057	+	0.0320773i	−0.977464	+	0.211103i	$0.932294\pi$
$480$		0			0
$481$	1.61248	−	2.41325i	0.0735229	−	0.110035i
$482$		0			0
$483$	0.114293	+	0.0227344i	0.00520053	+	0.00103445i
$484$		0			0
$485$	13.3505	−	1.70567i	0.606216	−	0.0774506i
$486$		0			0
$487$	−12.3264	+	8.23626i	−0.558564	+	0.373221i	−0.802574	−	0.596552i	$-0.796537\pi$
$487$	−12.3264	+	8.23626i	−0.558564	+	0.373221i	0.244010	+	0.969773i	$0.421537\pi$
$488$		0			0
$489$	−5.27253	−	5.27253i	−0.238432	−	0.238432i
$490$		0			0
$491$	7.12490	−	17.2010i	0.321542	−	0.776272i	−0.677623	−	0.735410i	$-0.736990\pi$
$491$	7.12490	−	17.2010i	0.321542	−	0.776272i	0.999165	−	0.0408619i	$-0.0130104\pi$
$492$		0			0
$493$	−22.6889	−	9.46115i	−1.02186	−	0.426109i
$494$		0			0
$495$	2.56372	+	20.0665i	0.115231	+	0.901924i
$496$		0			0
$497$		−	2.99030i		−	0.134133i
$498$		0			0
$499$	8.09099	−	40.6762i	0.362203	−	1.82092i	−0.183599	−	0.983001i	$-0.558775\pi$
$499$	8.09099	−	40.6762i	0.362203	−	1.82092i	0.545802	−	0.837914i	$-0.316225\pi$
$500$		0			0
$501$	0.145382	+	0.350982i	0.00649517	+	0.0156807i
$502$		0			0
$503$	4.16599	−	20.9439i	0.185752	−	0.933841i	−0.769635	−	0.638484i	$-0.779562\pi$
$503$	4.16599	−	20.9439i	0.185752	−	0.933841i	0.955387	−	0.295356i	$-0.0954383\pi$
$504$		0			0
$505$	−0.305940	−	0.0212286i	−0.0136142	−	0.000944662i
$506$		0			0
$507$	2.54291	−	3.80574i	0.112935	−	0.169019i
$508$		0			0
$509$	−9.69310			−0.429639			−0.214820	−	0.976654i	$-0.568916\pi$
$509$	−9.69310			−0.429639			−0.214820	+	0.976654i	$0.568916\pi$
$510$		0			0
$511$	1.11088			0.0491425
$512$		0			0
$513$	−5.95748	+	8.91600i	−0.263029	+	0.393651i
$514$		0			0
$515$	24.9099	+	28.6246i	1.09766	+	1.26135i
$516$		0			0
$517$	1.08908	−	5.47517i	0.0478976	−	0.240798i
$518$		0			0
$519$	−3.58617	−	8.65778i	−0.157415	−	0.380034i
$520$		0			0
$521$	2.36122	−	11.8707i	0.103447	−	0.520063i	−0.893963	−	0.448140i	$-0.852086\pi$
$521$	2.36122	−	11.8707i	0.103447	−	0.520063i	0.997410	−	0.0719228i	$-0.0229135\pi$
$522$		0			0
$523$		−	0.482638i		−	0.0211043i	−0.999944	−	0.0105521i	$-0.996641\pi$
$523$		−	0.482638i		−	0.0211043i	0.999944	−	0.0105521i	$-0.00335891\pi$
$524$		0			0
$525$	−0.235952	−	0.312422i	−0.0102978	−	0.0136352i
$526$		0			0
$527$	−35.0453	+	14.4190i	−1.52660	+	0.628099i
$528$		0			0
$529$	−7.95413	+	19.2030i	−0.345832	+	0.834911i
$530$		0			0
$531$	29.2478	+	29.2478i	1.26925	+	1.26925i
$532$		0			0
$533$	−0.825876	+	0.551833i	−0.0357727	+	0.0239025i
$534$		0			0
$535$	1.46599	+	11.4745i	0.0633802	+	0.496085i
$536$		0			0
$537$	−3.63678	−	0.723401i	−0.156939	−	0.0312171i
$538$		0			0
$539$	12.1975	−	18.2549i	0.525384	−	0.786293i
$540$		0			0
$541$	−3.94954	−	19.8557i	−0.169804	−	0.853661i	−0.967939	−	0.251184i	$-0.919180\pi$
$541$	−3.94954	−	19.8557i	−0.169804	−	0.853661i	0.798136	−	0.602478i	$-0.205820\pi$
$542$		0			0
$543$	2.60210	+	2.60210i	0.111667	+	0.111667i
$544$		0			0
$545$	−7.12395	−	12.4488i	−0.305156	−	0.533249i
$546$		0			0
$547$	−7.87301	−	5.26058i	−0.336626	−	0.224926i	0.375755	−	0.926719i	$-0.377383\pi$
$547$	−7.87301	−	5.26058i	−0.336626	−	0.224926i	−0.712381	+	0.701793i	$0.752383\pi$
$548$		0			0
$549$	24.7722	+	16.5522i	1.05725	+	0.706433i
$550$		0			0
$551$	−16.5224	−	24.7276i	−0.703880	−	1.05343i
$552$		0			0
$553$	0.284352	−	0.686486i	0.0120919	−	0.0291924i
$554$		0			0
$555$	1.05729	+	3.15428i	0.0448793	+	0.133892i
$556$		0			0
$557$	−33.3761			−1.41419			−0.707096	−	0.707117i	$-0.749995\pi$
$557$	−33.3761			−1.41419			−0.707096	+	0.707117i	$0.749995\pi$
$558$		0			0
$559$	−4.34174	−	1.79841i	−0.183636	−	0.0760645i
$560$		0			0
$561$	2.65980	−	3.96030i	0.112297	−	0.167204i
$562$		0			0
$563$	−3.68426	+	1.52607i	−0.155273	+	0.0643162i	−0.458966	−	0.888454i	$-0.651780\pi$
$563$	−3.68426	+	1.52607i	−0.155273	+	0.0643162i	0.303693	+	0.952770i	$0.401780\pi$
$564$		0			0
$565$	8.31764	−	4.75984i	0.349926	−	0.200248i
$566$		0			0
$567$	−0.926926	−	1.38724i	−0.0389272	−	0.0582587i
$568$		0			0
$569$	5.98773	−	2.48020i	0.251019	−	0.103975i	−0.253626	−	0.967302i	$-0.581623\pi$
$569$	5.98773	−	2.48020i	0.251019	−	0.103975i	0.504645	+	0.863327i	$0.331623\pi$
$570$		0			0
$571$	30.1443	−	20.1418i	1.26150	−	0.842907i	0.268762	−	0.963207i	$-0.413386\pi$
$571$	30.1443	−	20.1418i	1.26150	−	0.842907i	0.992738	+	0.120300i	$0.0383855\pi$
$572$		0			0
$573$	4.42266	−	0.879722i	0.184759	−	0.0367509i
$574$		0			0
$575$	−6.69882	+	3.23998i	−0.279360	+	0.135117i
$576$		0			0
$577$	25.4339	−	25.4339i	1.05883	−	1.05883i	0.0606679	−	0.998158i	$-0.480677\pi$
$577$	25.4339	−	25.4339i	1.05883	−	1.05883i	0.998158	−	0.0606679i	$-0.0193231\pi$
$578$		0			0
$579$		−	4.53863i		−	0.188619i
$580$		0			0
$581$	0.641994	−	0.127701i	0.0266344	−	0.00529791i
$582$		0			0
$583$	6.64967	+	33.4301i	0.275401	+	1.38453i
$584$		0			0
$585$	1.45605	+	4.34393i	0.0602002	+	0.179600i
$586$		0			0
$587$	−19.6419	−	8.13595i	−0.810709	−	0.335807i	−0.0614721	−	0.998109i	$-0.519580\pi$
$587$	−19.6419	−	8.13595i	−0.810709	−	0.335807i	−0.749237	+	0.662302i	$0.769580\pi$
$588$		0			0
$589$	−44.9648	−	8.94406i	−1.85274	−	0.368533i
$590$		0			0
$591$	−4.82001	+	4.82001i	−0.198269	+	0.198269i
$592$		0			0
$593$	−5.95021	−	14.3651i	−0.244346	−	0.589903i	0.753359	−	0.657609i	$-0.228432\pi$
$593$	−5.95021	−	14.3651i	−0.244346	−	0.589903i	−0.997705	+	0.0677057i	$0.978432\pi$
$594$		0			0
$595$	0.141010	−	1.96470i	0.00578085	−	0.0805448i
$596$		0			0
$597$	−0.344748	−	0.832294i	−0.0141096	−	0.0340635i
$598$		0			0
$599$	31.7543	−	31.7543i	1.29744	−	1.29744i	0.367368	−	0.930076i	$-0.380259\pi$
$599$	31.7543	−	31.7543i	1.29744	−	1.29744i	0.930076	−	0.367368i	$-0.119741\pi$
$600$		0			0
$601$	−6.59373	−	1.31157i	−0.268964	−	0.0535002i	0.0587658	−	0.998272i	$-0.481283\pi$
$601$	−6.59373	−	1.31157i	−0.268964	−	0.0535002i	−0.327730	+	0.944772i	$0.606283\pi$
$602$		0			0
$603$	18.9315	+	7.84168i	0.770950	+	0.319338i
$604$		0			0
$605$	−1.02984	+	2.06831i	−0.0418689	+	0.0840888i
$606$		0			0
$607$	−4.05210	−	20.3713i	−0.164470	−	0.826845i	−0.971629	−	0.236511i	$-0.923996\pi$
$607$	−4.05210	−	20.3713i	−0.164470	−	0.826845i	0.807159	−	0.590334i	$-0.201004\pi$
$608$		0			0
$609$	−0.457877	+	0.0910775i	−0.0185541	+	0.00369064i
$610$		0			0
$611$		−	1.26427i		−	0.0511469i
$612$		0			0
$613$	−12.2026	+	12.2026i	−0.492858	+	0.492858i	−0.909206	−	0.416348i	$-0.863310\pi$
$613$	−12.2026	+	12.2026i	−0.492858	+	0.492858i	0.416348	+	0.909206i	$0.363310\pi$
$614$		0			0
$615$	0.0788090	−	1.13577i	0.00317789	−	0.0457986i
$616$		0			0
$617$	−24.4757	+	4.86852i	−0.985354	+	0.195999i	−0.661367	−	0.750062i	$-0.730023\pi$
$617$	−24.4757	+	4.86852i	−0.985354	+	0.195999i	−0.323987	+	0.946061i	$0.605023\pi$
$618$		0			0
$619$	−4.39049	+	2.93363i	−0.176469	+	0.117913i	−0.640668	−	0.767818i	$-0.721342\pi$
$619$	−4.39049	+	2.93363i	−0.176469	+	0.117913i	0.464199	+	0.885731i	$0.346342\pi$
$620$		0			0
$621$	2.95583	−	1.22434i	0.118613	−	0.0491312i
$622$		0			0
$623$	−0.794631	−	1.18925i	−0.0318362	−	0.0476462i
$624$		0			0
$625$	24.0463	+	6.83940i	0.961850	+	0.273576i
$626$		0			0
$627$	5.33208	−	2.20862i	0.212943	−	0.0882038i
$628$		0			0
$629$	−6.44180	+	15.4481i	−0.256851	+	0.615958i
$630$		0			0
$631$	−0.510927	−	0.211633i	−0.0203397	−	0.00842496i	0.372490	−	0.928036i	$-0.378504\pi$
$631$	−0.510927	−	0.211633i	−0.0203397	−	0.00842496i	−0.392830	+	0.919611i	$0.628504\pi$
$632$		0			0
$633$	−3.70555			−0.147283
$634$		0			0
$635$	−10.8405	−	5.39762i	−0.430192	−	0.214198i
$636$		0			0
$637$	1.90278	−	4.59372i	0.0753909	−	0.182010i
$638$		0			0
$639$	−22.2833	−	33.3493i	−0.881514	−	1.31928i
$640$		0			0
$641$	−0.975837	−	0.652033i	−0.0385432	−	0.0257538i	0.536149	−	0.844123i	$-0.319878\pi$
$641$	−0.975837	−	0.652033i	−0.0385432	−	0.0257538i	−0.574693	+	0.818369i	$0.694878\pi$
$642$		0			0
$643$	34.2475	+	22.8834i	1.35059	+	0.902434i	0.999426	−	0.0338804i	$-0.0107865\pi$
$643$	34.2475	+	22.8834i	1.35059	+	0.902434i	0.351162	+	0.936315i	$0.385787\pi$
$644$		0			0
$645$	4.67518	−	2.67541i	0.184085	−	0.105344i
$646$		0			0
$647$	−31.8920	−	31.8920i	−1.25380	−	1.25380i	−0.954001	−	0.299803i	$-0.903079\pi$
$647$	−31.8920	−	31.8920i	−1.25380	−	1.25380i	−0.299803	−	0.954001i	$-0.596921\pi$
$648$		0			0
$649$	−8.88981	−	44.6921i	−0.348956	−	1.75432i
$650$		0			0
$651$	−0.399832	+	0.598391i	−0.0156707	+	0.0234528i
$652$		0			0
$653$	−9.37037	−	1.86388i	−0.366691	−	0.0729394i	0.00830571	−	0.999966i	$-0.497356\pi$
$653$	−9.37037	−	1.86388i	−0.366691	−	0.0729394i	−0.374997	+	0.927026i	$0.622356\pi$
$654$		0			0
$655$	18.9495	−	24.5008i	0.740420	−	0.957325i
$656$		0			0
$657$	12.3891	−	8.27813i	0.483345	−	0.322961i
$658$		0			0
$659$	−10.6988	−	10.6988i	−0.416765	−	0.416765i	0.467322	−	0.884087i	$-0.345219\pi$
$659$	−10.6988	−	10.6988i	−0.416765	−	0.416765i	−0.884087	+	0.467322i	$0.845219\pi$
$660$		0			0
$661$	−6.12835	+	14.7952i	−0.238365	+	0.575465i	−0.997114	−	0.0759186i	$-0.975811\pi$
$661$	−6.12835	+	14.7952i	−0.238365	+	0.575465i	0.758749	+	0.651384i	$0.225811\pi$
$662$		0			0
$663$	0.415821	−	0.997184i	0.0161491	−	0.0387274i
$664$		0			0
$665$	1.45789	−	1.88498i	0.0565347	−	0.0730965i
$666$		0			0
$667$			8.87310i			0.343568i
$668$		0			0
$669$	−0.465070	+	2.33807i	−0.0179807	+	0.0903949i
$670$		0			0
$671$	−12.5605	−	30.3237i	−0.484892	−	1.17063i
$672$		0			0
$673$	−8.15674	+	41.0067i	−0.314419	+	1.58069i	0.423560	+	0.905868i	$0.360780\pi$
$673$	−8.15674	+	41.0067i	−0.314419	+	1.58069i	−0.737979	+	0.674823i	$0.764220\pi$
$674$		0			0
$675$	−10.1516	−	3.53290i	−0.390736	−	0.135981i
$676$		0			0
$677$	−7.12682	+	10.6660i	−0.273906	+	0.409929i	−0.942764	−	0.333461i	$-0.891783\pi$
$677$	−7.12682	+	10.6660i	−0.273906	+	0.409929i	0.668858	+	0.743390i	$0.266783\pi$
$678$		0			0
$679$	1.28597			0.0493510
$680$		0			0
$681$	−3.11180			−0.119244
$682$		0			0
$683$	−7.84481	+	11.7406i	−0.300173	+	0.449241i	−0.950641	−	0.310293i	$-0.899573\pi$
$683$	−7.84481	+	11.7406i	−0.300173	+	0.449241i	0.650468	+	0.759534i	$0.274573\pi$
$684$		0			0
$685$	7.48044	−	6.50969i	0.285813	−	0.248723i
$686$		0			0
$687$	1.17060	−	5.88500i	0.0446612	−	0.224527i
$688$		0			0
$689$	2.95407	+	7.13175i	0.112541	+	0.271698i
$690$		0			0
$691$	−4.77936	+	24.0275i	−0.181815	+	0.914047i	0.776888	+	0.629639i	$0.216797\pi$
$691$	−4.77936	+	24.0275i	−0.181815	+	0.914047i	−0.958703	+	0.284408i	$0.908203\pi$
$692$		0			0
$693$			1.93288i			0.0734242i
$694$		0			0
$695$	28.1816	−	3.60050i	1.06899	−	0.136575i
$696$		0			0
$697$	4.05988	−	4.04067i	0.153779	−	0.153051i
$698$		0			0
$699$	2.20375	−	5.32032i	0.0833534	−	0.201233i
$700$		0			0
$701$	−7.61190	−	7.61190i	−0.287497	−	0.287497i	0.548592	−	0.836090i	$-0.315164\pi$
$701$	−7.61190	−	7.61190i	−0.287497	−	0.287497i	−0.836090	+	0.548592i	$0.815164\pi$
$702$		0			0
$703$	−16.8362	+	11.2496i	−0.634990	+	0.424287i
$704$		0			0
$705$	1.14628	+	0.886562i	0.0431714	+	0.0333899i
$706$		0			0
$707$	−0.0287389	−	0.00571653i	−0.00108084	−	0.000214992i
$708$		0			0
$709$	13.3104	−	19.9204i	0.499882	−	0.748127i	−0.492634	−	0.870236i	$-0.663966\pi$
$709$	13.3104	−	19.9204i	0.499882	−	0.748127i	0.992517	+	0.122110i	$0.0389660\pi$
$710$		0			0
$711$	−1.94437	−	9.77498i	−0.0729194	−	0.366591i
$712$		0			0
$713$	9.67216	+	9.67216i	0.362225	+	0.362225i
$714$		0			0
$715$	1.32497	−	4.87021i	0.0495510	−	0.182136i
$716$		0			0
$717$	2.43645	+	1.62798i	0.0909908	+	0.0607981i
$718$		0			0
$719$	2.45078	+	1.63756i	0.0913986	+	0.0610706i	0.600430	−	0.799677i	$-0.294996\pi$
$719$	2.45078	+	1.63756i	0.0913986	+	0.0610706i	−0.509031	+	0.860748i	$0.669996\pi$
$720$		0			0
$721$	2.01427	+	3.01457i	0.0750154	+	0.112268i
$722$		0			0
$723$	3.16595	−	7.64327i	0.117743	−	0.284256i
$724$		0			0
$725$	19.8265	−	22.2617i	0.736338	−	0.826780i
$726$		0			0
$727$	31.3857			1.16403			0.582015	−	0.813178i	$-0.302265\pi$
$727$	31.3857			1.16403			0.582015	+	0.813178i	$0.302265\pi$
$728$		0			0
$729$	−18.4913	−	7.65937i	−0.684865	−	0.283680i
$730$		0			0
$731$	26.5674	+	5.35011i	0.982629	+	0.197881i
$732$		0			0
$733$	−34.3242	+	14.2175i	−1.26779	+	0.525137i	−0.912292	−	0.409540i	$-0.865689\pi$
$733$	−34.3242	+	14.2175i	−1.26779	+	0.525137i	−0.355500	+	0.934676i	$0.615689\pi$
$734$		0			0
$735$	2.83069	+	4.94652i	0.104411	+	0.182455i
$736$		0			0
$737$	−12.5417	−	18.7700i	−0.461980	−	0.691401i
$738$		0			0
$739$	33.5869	−	13.9122i	1.23552	−	0.511767i	0.333205	−	0.942854i	$-0.391870\pi$
$739$	33.5869	−	13.9122i	1.23552	−	0.511767i	0.902310	+	0.431087i	$0.141870\pi$
$740$		0			0
$741$	1.08679	−	0.726167i	0.0399241	−	0.0266764i
$742$		0			0
$743$	37.7240	−	7.50377i	1.38396	−	0.275287i	0.553724	−	0.832700i	$-0.313206\pi$
$743$	37.7240	−	7.50377i	1.38396	−	0.275287i	0.830235	+	0.557414i	$0.188206\pi$
$744$		0			0
$745$	−28.6617	+	24.9422i	−1.05008	+	0.913811i
$746$		0			0
$747$	6.20823	−	6.20823i	0.227147	−	0.227147i
$748$		0			0
$749$			1.10526i			0.0403855i
$750$		0			0
$751$	−20.3177	+	4.04144i	−0.741404	+	0.147474i	−0.551321	−	0.834294i	$-0.685876\pi$
$751$	−20.3177	+	4.04144i	−0.741404	+	0.147474i	−0.190083	+	0.981768i	$0.560876\pi$
$752$		0			0
$753$	0.457166	+	2.29833i	0.0166601	+	0.0837557i
$754$		0			0
$755$	−21.0152	−	10.4637i	−0.764821	−	0.380814i
$756$		0			0
$757$	−20.5037	−	8.49289i	−0.745218	−	0.308679i	−0.0224293	−	0.999748i	$-0.507140\pi$
$757$	−20.5037	−	8.49289i	−0.745218	−	0.308679i	−0.722789	+	0.691069i	$0.757140\pi$
$758$		0			0
$759$	−1.68887	−	0.335936i	−0.0613019	−	0.0121937i
$760$		0			0
$761$	21.7021	−	21.7021i	0.786700	−	0.786700i	−0.194252	−	0.980952i	$-0.562228\pi$
$761$	21.7021	−	21.7021i	0.786700	−	0.786700i	0.980952	+	0.194252i	$0.0622279\pi$
$762$		0			0
$763$	−0.524444	−	1.26612i	−0.0189861	−	0.0458366i
$764$		0			0
$765$	−13.0680	−	22.9621i	−0.472476	−	0.830195i
$766$		0			0
$767$	−3.94923	−	9.53429i	−0.142598	−	0.344263i
$768$		0			0
$769$	−19.6699	+	19.6699i	−0.709314	+	0.709314i	−0.966391	−	0.257077i	$-0.917241\pi$
$769$	−19.6699	+	19.6699i	−0.709314	+	0.709314i	0.257077	+	0.966391i	$0.417241\pi$
$770$		0			0
$771$	7.15596	+	1.42341i	0.257716	+	0.0512628i
$772$		0			0
$773$	34.5080	+	14.2937i	1.24117	+	0.514109i	0.904079	−	0.427365i	$-0.140558\pi$
$773$	34.5080	+	14.2937i	1.24117	+	0.514109i	0.337088	+	0.941473i	$0.390558\pi$
$774$		0			0
$775$	−2.65451	−	45.8785i	−0.0953529	−	1.64800i
$776$		0			0
$777$	0.0620117	+	0.311754i	0.00222466	+	0.0111841i
$778$		0			0
$779$	6.79648	−	1.35190i	0.243509	−	0.0484370i
$780$		0			0
$781$			44.1864i			1.58111i
$782$		0			0
$783$	−9.06309	+	9.06309i	−0.323888	+	0.323888i
$784$		0			0
$785$	27.8189	+	1.93030i	0.992899	+	0.0688955i
$786$		0			0
$787$	−22.1283	+	4.40160i	−0.788790	+	0.156900i	−0.573017	−	0.819543i	$-0.694227\pi$
$787$	−22.1283	+	4.40160i	−0.788790	+	0.156900i	−0.215773	+	0.976444i	$0.569227\pi$
$788$		0			0
$789$	0.337012	−	0.225184i	0.0119979	−	0.00801677i
$790$		0			0
$791$	0.845954	−	0.350406i	0.0300787	−	0.0124590i
$792$		0			0
$793$	−4.12973	−	6.18058i	−0.146651	−	0.219479i
$794$		0			0
$795$	−8.53768	−	2.32272i	−0.302800	−	0.0823785i
$796$		0			0
$797$	5.32803	−	2.20694i	0.188729	−	0.0781739i	−0.286318	−	0.958135i	$-0.592431\pi$
$797$	5.32803	−	2.20694i	0.188729	−	0.0781739i	0.475046	+	0.879961i	$0.342431\pi$
$798$		0			0
$799$	1.40539	+	7.15402i	0.0497191	+	0.253091i
$800$		0			0
$801$	−17.7242	−	7.34161i	−0.626254	−	0.259403i
$802$		0			0
$803$	−16.4150			−0.579274
$804$		0			0
$805$	−0.674124	+	0.225960i	−0.0237597	+	0.00796406i
$806$		0			0
$807$	−0.586620	+	1.41623i	−0.0206500	+	0.0498535i
$808$		0			0
$809$	−6.70196	−	10.0302i	−0.235628	−	0.352643i	0.694745	−	0.719256i	$-0.255517\pi$
$809$	−6.70196	−	10.0302i	−0.235628	−	0.352643i	−0.930373	+	0.366613i	$0.880517\pi$
$810$		0			0
$811$	11.4181	+	7.62930i	0.400942	+	0.267901i	0.739652	−	0.672990i	$-0.234990\pi$
$811$	11.4181	+	7.62930i	0.400942	+	0.267901i	−0.338709	+	0.940891i	$0.609990\pi$
$812$		0			0
$813$	−0.508254	−	0.339604i	−0.0178252	−	0.0119104i
$814$		0			0
$815$	43.8977	+	11.9426i	1.53767	+	0.418332i
$816$		0			0
$817$	23.1833	+	23.1833i	0.811080	+	0.811080i
$818$		0			0
$819$	0.0853999	+	0.429334i	0.00298411	+	0.0150022i
$820$		0			0
$821$	0.131017	−	0.196081i	0.00457252	−	0.00684327i	−0.829176	−	0.558987i	$-0.811190\pi$
$821$	0.131017	−	0.196081i	0.00457252	−	0.00684327i	0.833749	+	0.552144i	$0.186190\pi$
$822$		0			0
$823$	−28.9033	−	5.74923i	−1.00751	−	0.200406i	−0.336363	−	0.941732i	$-0.609197\pi$
$823$	−28.9033	−	5.74923i	−1.00751	−	0.200406i	−0.671144	+	0.741327i	$0.734197\pi$
$824$		0			0
$825$	3.48656	+	4.61652i	0.121387	+	0.160727i
$826$		0			0
$827$	−31.5114	+	21.0552i	−1.09576	+	0.732161i	−0.965782	−	0.259356i	$-0.916490\pi$
$827$	−31.5114	+	21.0552i	−1.09576	+	0.732161i	−0.129975	+	0.991517i	$0.541490\pi$
$828$		0			0
$829$	2.75038	+	2.75038i	0.0955245	+	0.0955245i	0.753254	−	0.657730i	$-0.228483\pi$
$829$	2.75038	+	2.75038i	0.0955245	+	0.0955245i	−0.657730	+	0.753254i	$0.728483\pi$
$830$		0			0
$831$	1.85064	−	4.46784i	0.0641981	−	0.154988i
$832$		0			0
$833$	−5.66062	+	28.1092i	−0.196129	+	0.973927i
$834$		0			0
$835$	−1.83345	−	1.41804i	−0.0634492	−	0.0490733i
$836$		0			0
$837$			19.7585i			0.682955i
$838$		0			0
$839$	−4.72643	+	23.7614i	−0.163174	+	0.820333i	0.809313	+	0.587378i	$0.199840\pi$
$839$	−4.72643	+	23.7614i	−0.163174	+	0.820333i	−0.972487	+	0.232955i	$0.925160\pi$
$840$		0			0
$841$	−2.50543	−	6.04864i	−0.0863940	−	0.208574i
$842$		0			0
$843$	0.631151	−	3.17301i	0.0217380	−	0.109284i
$844$		0			0
$845$	−1.93308	+	27.8588i	−0.0664998	+	0.958373i
$846$		0			0
$847$	−0.122649	+	0.183558i	−0.00421428	+	0.00630711i
$848$		0			0
$849$	−8.51356			−0.292185
$850$		0			0
$851$	6.04141			0.207097
$852$		0			0
$853$	−1.66200	+	2.48735i	−0.0569057	+	0.0851654i	−0.858831	−	0.512258i	$-0.828809\pi$
$853$	−1.66200	+	2.48735i	−0.0569057	+	0.0851654i	0.801926	+	0.597424i	$0.203809\pi$
$854$		0			0
$855$	2.21253	−	31.8863i	0.0756669	−	1.09049i
$856$		0			0
$857$	−9.27959	+	46.6516i	−0.316985	+	1.59359i	0.413398	+	0.910551i	$0.364342\pi$
$857$	−9.27959	+	46.6516i	−0.316985	+	1.59359i	−0.730382	+	0.683039i	$0.760658\pi$
$858$		0			0
$859$	−14.2348	−	34.3659i	−0.485686	−	1.17255i	−0.956870	−	0.290515i	$-0.906173\pi$
$859$	−14.2348	−	34.3659i	−0.485686	−	1.17255i	0.471184	−	0.882035i	$-0.343827\pi$
$860$		0			0
$861$	0.0212220	−	0.106690i	0.000723243	−	0.00363599i
$862$		0			0
$863$			33.5405i			1.14173i	0.821043	+	0.570866i	$0.193392\pi$
$863$			33.5405i			1.14173i	−0.821043	+	0.570866i	$0.806608\pi$
$864$		0			0
$865$	45.2263	+	34.9791i	1.53774	+	1.18933i
$866$		0			0
$867$	−1.24448	+	6.10491i	−0.0422647	+	0.207334i
$868$		0			0
$869$	−4.20175	+	10.1439i	−0.142535	+	0.344109i
$870$		0			0
$871$	−3.61509	−	3.61509i	−0.122493	−	0.122493i
$872$		0			0
$873$	14.3418	−	9.58287i	0.485395	−	0.324331i
$874$		0			0
$875$	2.19621	+	0.939385i	0.0742454	+	0.0317570i
$876$		0			0
$877$	−21.1097	−	4.19898i	−0.712824	−	0.141789i	−0.174659	−	0.984629i	$-0.555882\pi$
$877$	−21.1097	−	4.19898i	−0.712824	−	0.141789i	−0.538165	+	0.842840i	$0.680882\pi$
$878$		0			0
$879$	−3.65337	+	5.46766i	−0.123225	+	0.184420i
$880$		0			0
$881$	−6.35305	−	31.9389i	−0.214040	−	1.07605i	−0.927062	−	0.374909i	$-0.877674\pi$
$881$	−6.35305	−	31.9389i	−0.214040	−	1.07605i	0.713022	−	0.701142i	$-0.247326\pi$
$882$		0			0
$883$	−35.8879	−	35.8879i	−1.20772	−	1.20772i	−0.971763	−	0.235961i	$-0.924176\pi$
$883$	−35.8879	−	35.8879i	−1.20772	−	1.20772i	−0.235961	−	0.971763i	$-0.575824\pi$
$884$		0			0
$885$	11.4139	+	3.10520i	0.383673	+	0.104380i
$886$		0			0
$887$	−20.2573	−	13.5355i	−0.680172	−	0.454476i	0.166886	−	0.985976i	$-0.446629\pi$
$887$	−20.2573	−	13.5355i	−0.680172	−	0.454476i	−0.847058	+	0.531500i	$0.821629\pi$
$888$		0			0
$889$	−0.962068	−	0.642833i	−0.0322667	−	0.0215599i
$890$		0			0
$891$	13.6968	+	20.4987i	0.458860	+	0.686732i
$892$		0			0
$893$	−3.37537	+	8.14887i	−0.112952	+	0.272691i
$894$		0			0
$895$	21.4504	−	7.18999i	0.717008	−	0.240335i
$896$		0			0
$897$	−0.389976			−0.0130209
$898$		0			0
$899$	−50.6269	−	20.9704i	−1.68850	−	0.699401i
$900$		0			0
$901$	−24.6437	−	37.0720i	−0.821001	−	1.23505i
$902$		0			0
$903$	0.475494	−	0.196956i	0.0158235	−	0.00655429i
$904$		0			0
$905$	−21.6644	−	5.89393i	−0.720150	−	0.195921i
$906$		0			0
$907$	3.54822	+	5.31029i	0.117817	+	0.176325i	0.885691	−	0.464276i	$-0.153685\pi$
$907$	3.54822	+	5.31029i	0.117817	+	0.176325i	−0.767874	+	0.640601i	$0.778685\pi$
$908$		0			0
$909$	−0.363109	+	0.150405i	−0.0120436	+	0.00498861i
$910$		0			0
$911$	38.8770	−	25.9768i	1.28805	−	0.860648i	0.292629	−	0.956226i	$-0.405470\pi$
$911$	38.8770	−	25.9768i	1.28805	−	0.860648i	0.995422	+	0.0955779i	$0.0304699\pi$
$912$		0			0
$913$	−9.48647	+	1.88698i	−0.313956	+	0.0624498i
$914$		0			0
$915$	8.49971	+	0.589780i	0.280992	+	0.0194975i
$916$		0			0
$917$	2.09265	−	2.09265i	0.0691053	−	0.0691053i
$918$		0			0
$919$			35.3651i			1.16659i	0.812262	+	0.583293i	$0.198236\pi$
$919$			35.3651i			1.16659i	−0.812262	+	0.583293i	$0.801764\pi$
$920$		0			0
$921$	8.87664	−	1.76567i	0.292495	−	0.0581809i
$922$		0			0
$923$	1.95227	+	9.81475i	0.0642599	+	0.323056i
$924$		0			0
$925$	−15.1573	−	13.4992i	−0.498369	−	0.443852i
$926$		0			0
$927$	44.9283	+	18.6099i	1.47564	+	0.611229i
$928$		0			0
$929$	17.6853	+	3.51782i	0.580235	+	0.115416i	0.476477	−	0.879187i	$-0.341913\pi$
$929$	17.6853	+	3.51782i	0.580235	+	0.115416i	0.103757	+	0.994603i	$0.466913\pi$
$930$		0			0
$931$	−24.5288	+	24.5288i	−0.803898	+	0.803898i
$932$		0			0
$933$	4.03824	+	9.74917i	0.132206	+	0.319173i
$934$		0			0
$935$	−2.08365	+	29.0315i	−0.0681426	+	0.949432i
$936$		0			0
$937$	1.13871	+	2.74909i	0.0372000	+	0.0898089i	0.941388	−	0.337327i	$-0.109523\pi$
$937$	1.13871	+	2.74909i	0.0372000	+	0.0898089i	−0.904188	+	0.427136i	$0.859523\pi$
$938$		0			0
$939$	−3.41552	+	3.41552i	−0.111461	+	0.111461i
$940$		0			0
$941$	16.8693	+	3.35552i	0.549925	+	0.109387i	0.462229	−	0.886761i	$-0.347050\pi$
$941$	16.8693	+	3.35552i	0.549925	+	0.109387i	0.0876955	+	0.996147i	$0.472050\pi$
$942$		0			0
$943$	−1.91014	−	0.791206i	−0.0622028	−	0.0257652i
$944$		0			0
$945$	−0.919357	−	0.457759i	−0.0299067	−	0.0148909i
$946$		0			0
$947$	10.8064	+	54.3275i	0.351161	+	1.76541i	0.603101	+	0.797665i	$0.293932\pi$
$947$	10.8064	+	54.3275i	0.351161	+	1.76541i	−0.251940	+	0.967743i	$0.581068\pi$
$948$		0			0
$949$	−3.64613	+	0.725260i	−0.118358	+	0.0235429i
$950$		0			0
$951$		−	2.02305i		−	0.0656019i
$952$		0			0
$953$	42.2935	−	42.2935i	1.37002	−	1.37002i	0.509621	−	0.860399i	$-0.329786\pi$
$953$	42.2935	−	42.2935i	1.37002	−	1.37002i	0.860399	−	0.509621i	$-0.170214\pi$
$954$		0			0
$955$	−20.7540	+	18.0607i	−0.671582	+	0.584430i
$956$		0			0
$957$	6.76586	−	1.34581i	0.218709	−	0.0435039i
$958$		0			0
$959$	0.787795	−	0.526388i	0.0254392	−	0.0169980i
$960$		0			0
$961$	−49.4047	+	20.4641i	−1.59370	+	0.660133i
$962$		0			0
$963$	8.23627	+	12.3265i	0.265410	+	0.397214i
$964$		0			0
$965$	13.7536	+	24.0339i	0.442744	+	0.773678i
$966$		0			0
$967$	34.3415	−	14.2247i	1.10435	−	0.457436i	0.245361	−	0.969432i	$-0.421094\pi$
$967$	34.3415	−	14.2247i	1.10435	−	0.457436i	0.858988	+	0.511996i	$0.171094\pi$
$968$		0			0
$969$	−5.34248	+	5.31719i	−0.171625	+	0.170813i
$970$		0			0
$971$	27.8647	+	11.5419i	0.894221	+	0.370399i	0.781995	−	0.623284i	$-0.214202\pi$
$971$	27.8647	+	11.5419i	0.894221	+	0.370399i	0.112226	+	0.993683i	$0.464202\pi$
$972$		0			0
$973$	2.71456			0.0870247
$974$		0			0
$975$	0.978410	+	0.871382i	0.0313342	+	0.0279066i
$976$		0			0
$977$	−4.67854	+	11.2950i	−0.149680	+	0.361359i	−0.980880	−	0.194615i	$-0.937654\pi$
$977$	−4.67854	+	11.2950i	−0.149680	+	0.361359i	0.831200	+	0.555973i	$0.187654\pi$
$978$		0			0
$979$	11.7419	+	17.5730i	0.375273	+	0.561636i
$980$		0			0
$981$	−15.2838	−	10.2123i	−0.487974	−	0.326054i
$982$		0			0
$983$	35.7659	+	23.8980i	1.14075	+	0.762227i	0.974618	−	0.223876i	$-0.0718710\pi$
$983$	35.7659	+	23.8980i	1.14075	+	0.762227i	0.166136	+	0.986103i	$0.446871\pi$
$984$		0			0
$985$	10.9176	−	40.1302i	0.347865	−	1.27866i
$986$		0			0
$987$	0.0979054	+	0.0979054i	0.00311636	+	0.00311636i
$988$		0			0
$989$	−1.90838	−	9.59409i	−0.0606830	−	0.305074i
$990$		0			0
$991$	5.57528	−	8.34399i	0.177104	−	0.265056i	−0.732288	−	0.680995i	$-0.761547\pi$
$991$	5.57528	−	8.34399i	0.177104	−	0.265056i	0.909392	+	0.415940i	$0.136547\pi$
$992$		0			0
$993$	1.32317	+	0.263194i	0.0419894	+	0.00835221i
$994$		0			0
$995$	4.34772	+	3.36264i	0.137832	+	0.106603i
$996$		0			0
$997$	9.63345	−	6.43687i	0.305094	−	0.203858i	−0.393593	−	0.919285i	$-0.628768\pi$
$997$	9.63345	−	6.43687i	0.305094	−	0.203858i	0.698687	+	0.715427i	$0.253768\pi$
$998$		0			0
$999$	6.17077	+	6.17077i	0.195235	+	0.195235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cg.b.57.8	✓	112
5.3	odd	4		680.2.cq.b.193.8	yes	112
17.3	odd	16		680.2.cq.b.377.8	yes	112
85.3	even	16	inner	680.2.cg.b.513.8	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cg.b.57.8	✓	112	1.1	even	1	trivial
680.2.cg.b.513.8	yes	112	85.3	even	16	inner
680.2.cq.b.193.8	yes	112	5.3	odd	4
680.2.cq.b.377.8	yes	112	17.3	odd	16

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cg (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203615 - 0.304732i) q^{3} +(-0.154785 + 2.23070i) q^{5} +(-0.0416810 + 0.209544i) q^{7} +(1.09665 + 2.64754i) q^{9} +(0.615902 - 3.09635i) q^{11} -0.714977i q^{13} +(0.648250 + 0.501374i) q^{15} +(0.794784 + 4.04578i) q^{17} +(-1.90886 + 4.60839i) q^{19} +(0.0553680 + 0.0553680i) q^{21} +(1.23743 - 0.826823i) q^{23} +(-4.95208 - 0.690557i) q^{25} +(2.10845 + 0.419397i) q^{27} +(-3.31238 + 4.95733i) q^{29} +(1.79308 + 9.01444i) q^{31} +(-0.818149 - 0.818149i) q^{33} +(-0.460980 - 0.125412i) q^{35} +(3.37529 + 2.25530i) q^{37} +(-0.217876 - 0.145580i) q^{39} +(-0.771819 - 1.15511i) q^{41} +(2.51533 - 6.07255i) q^{43} +(-6.07563 + 2.03650i) q^{45} +1.76827 q^{47} +(6.42499 + 2.66132i) q^{49} +(1.39471 + 0.581586i) q^{51} +(-9.97479 + 4.13169i) q^{53} +(6.81170 + 1.85316i) q^{55} +(1.01565 + 1.52003i) q^{57} +(13.3351 - 5.52358i) q^{59} +(8.64444 - 5.77603i) q^{61} +(-0.600487 + 0.119444i) q^{63} +(1.59490 + 0.110667i) q^{65} +(5.05623 - 5.05623i) q^{67} -0.545438i q^{69} +(-13.7274 + 2.73054i) q^{71} +(-1.01438 - 5.09964i) q^{73} +(-1.21876 + 1.36845i) q^{75} +(0.623151 + 0.258118i) q^{77} +(-3.41105 - 0.678501i) q^{79} +(-5.52191 + 5.52191i) q^{81} +(-1.17245 - 2.83055i) q^{83} +(-9.14795 + 1.14670i) q^{85} +(0.836205 + 2.01878i) q^{87} +(-4.73379 + 4.73379i) q^{89} +(0.149819 + 0.0298009i) q^{91} +(3.11209 + 1.28907i) q^{93} +(-9.98449 - 4.97141i) q^{95} +(-1.17426 - 5.90341i) q^{97} +(8.87314 - 1.76498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 16 q^{15} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 48 q^{33} - 32 q^{35} - 16 q^{37} - 16 q^{41} + 48 q^{43} - 24 q^{45} - 16 q^{47} - 80 q^{49} + 32 q^{51} - 8 q^{53} + 24 q^{55} - 80 q^{59} - 24 q^{61}+ \cdots + 48 q^{99}+O(q^{100}) \) 112 * q + 16 * q^15 - 24 * q^27 - 8 * q^29 + 16 * q^31 - 48 * q^33 - 32 * q^35 - 16 * q^37 - 16 * q^41 + 48 * q^43 - 24 * q^45 - 16 * q^47 - 80 * q^49 + 32 * q^51 - 8 * q^53 + 24 * q^55 - 80 * q^59 - 24 * q^61 - 72 * q^63 + 16 * q^65 - 48 * q^67 - 40 * q^71 - 16 * q^73 + 16 * q^75 + 24 * q^77 + 40 * q^79 - 24 * q^83 + 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^93 - 8 * q^95 + 64 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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