LMFDB - Embedded newform 820.2.bo.b.61.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(21,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bo (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] 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:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			61.7
Character	$\chi$	$=$	820.61
Dual form			820.2.bo.b.121.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.915716 - 0.915716i) q^{3} +(-0.587785 + 0.809017i) q^{5} +(-3.85694 - 1.96521i) q^{7} +1.32293i q^{9} +(0.298728 - 1.88610i) q^{11} +(-0.991729 - 1.94638i) q^{13} +(0.202586 + 1.27907i) q^{15} +(-5.18836 - 0.821755i) q^{17} +(-2.52870 + 4.96286i) q^{19} +(-5.33144 + 1.73229i) q^{21} +(1.27866 - 3.93532i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(3.95857 + 3.95857i) q^{27} +(-9.75736 + 1.54541i) q^{29} +(3.28016 - 2.38318i) q^{31} +(-1.45358 - 2.00068i) q^{33} +(3.85694 - 1.96521i) q^{35} +(-7.01671 - 5.09794i) q^{37} +(-2.69047 - 0.874188i) q^{39} +(-6.11937 + 1.88503i) q^{41} +(-6.08690 - 1.97775i) q^{43} +(-1.07027 - 0.777597i) q^{45} +(0.329343 - 0.167809i) q^{47} +(6.89947 + 9.49630i) q^{49} +(-5.50356 + 3.99857i) q^{51} +(7.10537 - 1.12538i) q^{53} +(1.35030 + 1.35030i) q^{55} +(2.22900 + 6.86015i) q^{57} +(1.97529 - 6.07933i) q^{59} +(11.4220 - 3.71123i) q^{61} +(2.59983 - 5.10246i) q^{63} +(2.15758 + 0.341727i) q^{65} +(0.679724 + 4.29161i) q^{67} +(-2.43274 - 4.77453i) q^{69} +(-1.61585 + 10.2020i) q^{71} +3.44093i q^{73} +(-1.15387 - 0.587926i) q^{75} +(-4.85875 + 6.68750i) q^{77} +(5.75319 - 5.75319i) q^{79} +3.28108 q^{81} +4.45266 q^{83} +(3.71446 - 3.71446i) q^{85} +(-7.51981 + 10.3501i) q^{87} +(-10.7535 - 5.47918i) q^{89} +9.45603i q^{91} +(0.821384 - 5.18602i) q^{93} +(-2.52870 - 4.96286i) q^{95} +(-0.0847003 - 0.534776i) q^{97} +(2.49517 + 0.395196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) $ 64 * q + 2 * q^3 - 10 * q^7 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 22 * q^23 + 16 * q^25 + 20 * q^27 - 12 * q^29 + 22 * q^31 + 30 * q^33 + 10 * q^35 + 12 * q^37 + 20 * q^39 - 10 * q^41 + 10 * q^43 + 32 * q^45 + 28 * q^47 + 10 * q^49 - 22 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 18 * q^59 - 20 * q^61 + 52 * q^63 - 6 * q^65 - 6 * q^67 - 50 * q^69 + 34 * q^71 + 8 * q^75 - 110 * q^77 - 14 * q^79 - 108 * q^81 + 32 * q^83 - 8 * q^85 - 80 * q^87 - 122 * q^89 + 42 * q^93 + 10 * q^95 - 64 * q^97 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.915716	−	0.915716i	0.528689	−	0.528689i	−0.391492	−	0.920181i	$-0.628041\pi$
$3$	0.915716	−	0.915716i	0.528689	−	0.528689i	0.920181	+	0.391492i	$0.128041\pi$
$4$		0			0
$5$	−0.587785	+	0.809017i	−0.262866	+	0.361803i
$5$	−0.587785	+	0.809017i	−0.262866	+	0.361803i
$6$		0			0
$7$	−3.85694	−	1.96521i	−1.45779	−	0.742780i	−0.467787	−	0.883841i	$-0.654949\pi$
$7$	−3.85694	−	1.96521i	−1.45779	−	0.742780i	−0.990001	+	0.141061i	$0.954949\pi$
$8$		0			0
$9$			1.32293i			0.440976i
$10$		0			0
$11$	0.298728	−	1.88610i	0.0900699	−	0.568679i	−0.900840	−	0.434151i	$-0.857048\pi$
$11$	0.298728	−	1.88610i	0.0900699	−	0.568679i	0.990910	−	0.134528i	$-0.0429517\pi$
$12$		0			0
$13$	−0.991729	−	1.94638i	−0.275056	−	0.539828i	0.711612	−	0.702573i	$-0.247965\pi$
$13$	−0.991729	−	1.94638i	−0.275056	−	0.539828i	−0.986668	+	0.162744i	$0.947965\pi$
$14$		0			0
$15$	0.202586	+	1.27907i	0.0523074	+	0.330256i
$16$		0			0
$17$	−5.18836	−	0.821755i	−1.25836	−	0.199305i	−0.508594	−	0.861006i	$-0.669835\pi$
$17$	−5.18836	−	0.821755i	−1.25836	−	0.199305i	−0.749768	+	0.661701i	$0.769835\pi$
$18$		0			0
$19$	−2.52870	+	4.96286i	−0.580125	+	1.13856i	0.395367	+	0.918523i	$0.370617\pi$
$19$	−2.52870	+	4.96286i	−0.580125	+	1.13856i	−0.975492	+	0.220036i	$0.929383\pi$
$20$		0			0
$21$	−5.33144	+	1.73229i	−1.16342	+	0.378017i
$22$		0			0
$23$	1.27866	−	3.93532i	0.266620	−	0.820571i	−0.724696	−	0.689068i	$-0.758020\pi$
$23$	1.27866	−	3.93532i	0.266620	−	0.820571i	0.991316	−	0.131502i	$-0.0419801\pi$
$24$		0			0
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$		0			0
$27$	3.95857	+	3.95857i	0.761828	+	0.761828i
$28$		0			0
$29$	−9.75736	+	1.54541i	−1.81190	+	0.286976i	−0.968261	−	0.249940i	$-0.919589\pi$
$29$	−9.75736	+	1.54541i	−1.81190	+	0.286976i	−0.843635	+	0.536916i	$0.819589\pi$
$30$		0			0
$31$	3.28016	−	2.38318i	0.589135	−	0.428032i	−0.252871	−	0.967500i	$-0.581375\pi$
$31$	3.28016	−	2.38318i	0.589135	−	0.428032i	0.842006	+	0.539468i	$0.181375\pi$
$32$		0			0
$33$	−1.45358	−	2.00068i	−0.253035	−	0.348273i
$34$		0			0
$35$	3.85694	−	1.96521i	0.651943	−	0.332181i
$36$		0			0
$37$	−7.01671	−	5.09794i	−1.15354	−	0.838096i	−0.164592	−	0.986362i	$-0.552631\pi$
$37$	−7.01671	−	5.09794i	−1.15354	−	0.838096i	−0.988947	+	0.148266i	$0.952631\pi$
$38$		0			0
$39$	−2.69047	−	0.874188i	−0.430820	−	0.139982i
$40$		0			0
$41$	−6.11937	+	1.88503i	−0.955685	+	0.294392i
$41$	−6.11937	+	1.88503i	−0.955685	+	0.294392i
$42$		0			0
$43$	−6.08690	−	1.97775i	−0.928244	−	0.301605i	−0.194399	−	0.980922i	$-0.562276\pi$
$43$	−6.08690	−	1.97775i	−0.928244	−	0.301605i	−0.733844	+	0.679318i	$0.762276\pi$
$44$		0			0
$45$	−1.07027	−	0.777597i	−0.159547	−	0.115917i
$46$		0			0
$47$	0.329343	−	0.167809i	0.0480397	−	0.0244774i	−0.429806	−	0.902921i	$-0.641418\pi$
$47$	0.329343	−	0.167809i	0.0480397	−	0.0244774i	0.477845	+	0.878444i	$0.341418\pi$
$48$		0			0
$49$	6.89947	+	9.49630i	0.985638	+	1.35661i
$50$		0			0
$51$	−5.50356	+	3.99857i	−0.770653	+	0.559912i
$52$		0			0
$53$	7.10537	−	1.12538i	0.975997	−	0.154583i	0.351992	−	0.936003i	$-0.385504\pi$
$53$	7.10537	−	1.12538i	0.975997	−	0.154583i	0.624005	+	0.781420i	$0.285504\pi$
$54$		0			0
$55$	1.35030	+	1.35030i	0.182074	+	0.182074i
$56$		0			0
$57$	2.22900	+	6.86015i	0.295238	+	0.908649i
$58$		0			0
$59$	1.97529	−	6.07933i	0.257161	−	0.791461i	−0.736235	−	0.676726i	$-0.763398\pi$
$59$	1.97529	−	6.07933i	0.257161	−	0.791461i	0.993396	−	0.114735i	$-0.0366018\pi$
$60$		0			0
$61$	11.4220	−	3.71123i	1.46244	−	0.475175i	0.533624	−	0.845722i	$-0.320830\pi$
$61$	11.4220	−	3.71123i	1.46244	−	0.475175i	0.928814	+	0.370547i	$0.120830\pi$
$62$		0			0
$63$	2.59983	−	5.10246i	0.327548	−	0.642849i
$64$		0			0
$65$	2.15758	+	0.341727i	0.267614	+	0.0423860i
$66$		0			0
$67$	0.679724	+	4.29161i	0.0830415	+	0.524304i	0.993784	+	0.111328i	$0.0355105\pi$
$67$	0.679724	+	4.29161i	0.0830415	+	0.524304i	−0.910742	+	0.412975i	$0.864490\pi$
$68$		0			0
$69$	−2.43274	−	4.77453i	−0.292868	−	0.574786i
$70$		0			0
$71$	−1.61585	+	10.2020i	−0.191766	+	1.21076i	0.684529	+	0.728985i	$0.260008\pi$
$71$	−1.61585	+	10.2020i	−0.191766	+	1.21076i	−0.876295	+	0.481775i	$0.839992\pi$
$72$		0			0
$73$			3.44093i			0.402731i	0.979516	+	0.201365i	$0.0645378\pi$
$73$			3.44093i			0.402731i	−0.979516	+	0.201365i	$0.935462\pi$
$74$		0			0
$75$	−1.15387	−	0.587926i	−0.133237	−	0.0678879i
$76$		0			0
$77$	−4.85875	+	6.68750i	−0.553706	+	0.762112i
$78$		0			0
$79$	5.75319	−	5.75319i	0.647284	−	0.647284i	−0.305052	−	0.952336i	$-0.598674\pi$
$79$	5.75319	−	5.75319i	0.647284	−	0.647284i	0.952336	+	0.305052i	$0.0986738\pi$
$80$		0			0
$81$	3.28108			0.364565
$82$		0			0
$83$	4.45266			0.488743			0.244371	−	0.969682i	$-0.421418\pi$
$83$	4.45266			0.488743			0.244371	+	0.969682i	$0.421418\pi$
$84$		0			0
$85$	3.71446	−	3.71446i	0.402889	−	0.402889i
$86$		0			0
$87$	−7.51981	+	10.3501i	−0.806209	+	1.10965i
$88$		0			0
$89$	−10.7535	−	5.47918i	−1.13987	−	0.580792i	−0.220968	−	0.975281i	$-0.570922\pi$
$89$	−10.7535	−	5.47918i	−1.13987	−	0.580792i	−0.918901	+	0.394489i	$0.870922\pi$
$90$		0			0
$91$			9.45603i			0.991261i
$92$		0			0
$93$	0.821384	−	5.18602i	0.0851736	−	0.537765i
$94$		0			0
$95$	−2.52870	−	4.96286i	−0.259440	−	0.509179i
$96$		0			0
$97$	−0.0847003	−	0.534776i	−0.00860001	−	0.0542983i	0.983015	−	0.183525i	$-0.0587507\pi$
$97$	−0.0847003	−	0.534776i	−0.00860001	−	0.0542983i	−0.991615	+	0.129226i	$0.958751\pi$
$98$		0			0
$99$	2.49517	+	0.395196i	0.250774	+	0.0397187i
$100$		0			0
$101$	2.59296	−	5.08897i	0.258009	−	0.506372i	−0.725273	−	0.688462i	$-0.758286\pi$
$101$	2.59296	−	5.08897i	0.258009	−	0.506372i	0.983282	+	0.182090i	$0.0582863\pi$
$102$		0			0
$103$	1.64566	−	0.534709i	0.162152	−	0.0526864i	−0.226816	−	0.973938i	$-0.572832\pi$
$103$	1.64566	−	0.534709i	0.162152	−	0.0526864i	0.388968	+	0.921251i	$0.372832\pi$
$104$		0			0
$105$	1.73229	−	5.33144i	0.169054	−	0.520296i
$106$		0			0
$107$	−3.42898	−	10.5533i	−0.331492	−	1.02023i	−0.968424	−	0.249308i	$-0.919797\pi$
$107$	−3.42898	−	10.5533i	−0.331492	−	1.02023i	0.636932	−	0.770920i	$-0.280203\pi$
$108$		0			0
$109$	−9.19382	−	9.19382i	−0.880608	−	0.880608i	0.112988	−	0.993596i	$-0.463958\pi$
$109$	−9.19382	−	9.19382i	−0.880608	−	0.880608i	−0.993596	+	0.112988i	$0.963958\pi$
$110$		0			0
$111$	−11.0936	+	1.75705i	−1.05296	+	0.166772i
$112$		0			0
$113$	−10.4451	+	7.58879i	−0.982590	+	0.713893i	−0.958286	−	0.285811i	$-0.907737\pi$
$113$	−10.4451	+	7.58879i	−0.982590	+	0.713893i	−0.0243038	+	0.999705i	$0.507737\pi$
$114$		0			0
$115$	2.43216	+	3.34758i	0.226800	+	0.312164i
$116$		0			0
$117$	2.57492	−	1.31199i	0.238051	−	0.121293i
$118$		0			0
$119$	18.3963	+	13.3657i	1.68639	+	1.22523i
$120$		0			0
$121$	6.99350	+	2.27233i	0.635773	+	0.206575i
$122$		0			0
$123$	−3.87746	+	7.32976i	−0.349618	+	0.660902i
$124$		0			0
$125$	0.951057	+	0.309017i	0.0850651	+	0.0276393i
$126$		0			0
$127$	−10.4460	−	7.58945i	−0.926931	−	0.673455i	0.0183081	−	0.999832i	$-0.494172\pi$
$127$	−10.4460	−	7.58945i	−0.926931	−	0.673455i	−0.945240	+	0.326377i	$0.894172\pi$
$128$		0			0
$129$	−7.38494	+	3.76281i	−0.650207	+	0.331297i
$130$		0			0
$131$	6.30977	+	8.68465i	0.551287	+	0.758781i	0.990186	−	0.139755i	$-0.0446315\pi$
$131$	6.30977	+	8.68465i	0.551287	+	0.758781i	−0.438899	+	0.898536i	$0.644632\pi$
$132$		0			0
$133$	19.5061	−	14.1720i	1.69140	−	1.22887i
$134$		0			0
$135$	−5.52935	+	0.875762i	−0.475890	+	0.0753736i
$136$		0			0
$137$	6.87283	+	6.87283i	0.587186	+	0.587186i	0.936868	−	0.349682i	$-0.113711\pi$
$137$	6.87283	+	6.87283i	0.587186	+	0.587186i	−0.349682	+	0.936868i	$0.613711\pi$
$138$		0			0
$139$	−3.23260	−	9.94892i	−0.274185	−	0.843856i	−0.989434	−	0.144986i	$-0.953686\pi$
$139$	−3.23260	−	9.94892i	−0.274185	−	0.843856i	0.715248	−	0.698870i	$-0.246314\pi$
$140$		0			0
$141$	0.147920	−	0.455250i	0.0124571	−	0.0383390i
$142$		0			0
$143$	−3.96731	+	1.28906i	−0.331763	+	0.107796i
$144$		0			0
$145$	4.48497	−	8.80224i	0.372456	−	0.730987i
$146$		0			0
$147$	15.0139	+	2.37796i	1.23832	+	0.196131i
$148$		0			0
$149$	2.23299	+	14.0985i	0.182933	+	1.15500i	0.892731	+	0.450590i	$0.148786\pi$
$149$	2.23299	+	14.0985i	0.182933	+	1.15500i	−0.709798	+	0.704406i	$0.751214\pi$
$150$		0			0
$151$	−0.475263	−	0.932756i	−0.0386763	−	0.0759066i	0.870860	−	0.491532i	$-0.163563\pi$
$151$	−0.475263	−	0.932756i	−0.0386763	−	0.0759066i	−0.909536	+	0.415625i	$0.863563\pi$
$152$		0			0
$153$	1.08712	−	6.86382i	0.0878887	−	0.554907i
$154$		0			0
$155$			4.05451i			0.325666i
$156$		0			0
$157$	−2.12234	−	1.08139i	−0.169381	−	0.0863040i	0.367244	−	0.930124i	$-0.380301\pi$
$157$	−2.12234	−	1.08139i	−0.169381	−	0.0863040i	−0.536626	+	0.843820i	$0.680301\pi$
$158$		0			0
$159$	5.47597	−	7.53703i	0.434273	−	0.597725i
$160$		0			0
$161$	−12.6655	+	12.6655i	−0.998178	+	0.998178i
$162$		0			0
$163$	24.2018			1.89563			0.947815	−	0.318821i	$-0.103287\pi$
$163$	24.2018			1.89563			0.947815	+	0.318821i	$0.103287\pi$
$164$		0			0
$165$	2.47297			0.192521
$166$		0			0
$167$	9.08853	−	9.08853i	0.703291	−	0.703291i	−0.261824	−	0.965116i	$-0.584324\pi$
$167$	9.08853	−	9.08853i	0.703291	−	0.703291i	0.965116	+	0.261824i	$0.0843241\pi$
$168$		0			0
$169$	4.83635	−	6.65666i	0.372027	−	0.512051i
$170$		0			0
$171$	−6.56551	−	3.34529i	−0.502077	−	0.255821i
$172$		0			0
$173$		−	23.4135i		−	1.78009i	−0.455869	−	0.890047i	$-0.650671\pi$
$173$		−	23.4135i		−	1.78009i	0.455869	−	0.890047i	$-0.349329\pi$
$174$		0			0
$175$	−0.677166	+	4.27546i	−0.0511889	+	0.323194i
$176$		0			0
$177$	−3.75813	−	7.37574i	−0.282478	−	0.554395i
$178$		0			0
$179$	1.38124	+	8.72081i	0.103239	+	0.651824i	0.983987	+	0.178239i	$0.0570401\pi$
$179$	1.38124	+	8.72081i	0.103239	+	0.651824i	−0.880748	+	0.473584i	$0.842960\pi$
$180$		0			0
$181$	−18.6995	−	2.96172i	−1.38993	−	0.220143i	−0.583805	−	0.811894i	$-0.698437\pi$
$181$	−18.6995	−	2.96172i	−1.38993	−	0.220143i	−0.806121	+	0.591751i	$0.798437\pi$
$182$		0			0
$183$	7.06088	−	13.8578i	0.521955	−	1.02439i
$184$		0			0
$185$	8.24863	−	2.68014i	0.606452	−	0.197048i
$186$		0			0
$187$	−3.09982	+	9.54026i	−0.226681	+	0.697653i
$188$		0			0
$189$	−7.48857	−	23.0474i	−0.544713	−	1.67645i
$190$		0			0
$191$	7.00396	+	7.00396i	0.506789	+	0.506789i	0.913539	−	0.406750i	$-0.133338\pi$
$191$	7.00396	+	7.00396i	0.506789	+	0.506789i	−0.406750	+	0.913539i	$0.633338\pi$
$192$		0			0
$193$	−8.39411	+	1.32950i	−0.604221	+	0.0956992i	−0.451047	−	0.892500i	$-0.648949\pi$
$193$	−8.39411	+	1.32950i	−0.604221	+	0.0956992i	−0.153174	+	0.988199i	$0.548949\pi$
$194$		0			0
$195$	2.28865	−	1.66280i	0.163894	−	0.119076i
$196$		0			0
$197$	14.1527	+	19.4796i	1.00834	+	1.38786i	0.920064	+	0.391767i	$0.128136\pi$
$197$	14.1527	+	19.4796i	1.00834	+	1.38786i	0.0882774	+	0.996096i	$0.471864\pi$
$198$		0			0
$199$	21.2632	−	10.8341i	1.50731	−	0.768011i	0.511481	−	0.859295i	$-0.329097\pi$
$199$	21.2632	−	10.8341i	1.50731	−	0.768011i	0.995825	+	0.0912840i	$0.0290971\pi$
$200$		0			0
$201$	4.55233	+	3.30746i	0.321097	+	0.233290i
$202$		0			0
$203$	40.6707	+	13.2147i	2.85452	+	0.927490i
$204$		0			0
$205$	2.07186	−	6.05866i	0.144705	−	0.423155i
$206$		0			0
$207$	5.20614	+	1.69158i	0.361852	+	0.117573i
$208$		0			0
$209$	8.60504	+	6.25193i	0.595223	+	0.432455i
$210$		0			0
$211$	−13.8923	+	7.07848i	−0.956385	+	0.487302i	−0.861261	−	0.508163i	$-0.830325\pi$
$211$	−13.8923	+	7.07848i	−0.956385	+	0.487302i	−0.0951238	+	0.995465i	$0.530325\pi$
$212$		0			0
$213$	7.86252	+	10.8218i	0.538731	+	0.741500i
$214$		0			0
$215$	5.17783	−	3.76191i	0.353125	−	0.256560i
$216$		0			0
$217$	−17.3349	+	2.74557i	−1.17677	+	0.186382i
$218$		0			0
$219$	3.15092	+	3.15092i	0.212919	+	0.212919i
$220$		0			0
$221$	3.54600	+	10.9135i	0.238530	+	0.734119i
$222$		0			0
$223$	4.61287	−	14.1970i	0.308901	−	0.950699i	−0.669292	−	0.743000i	$-0.733402\pi$
$223$	4.61287	−	14.1970i	0.308901	−	0.950699i	0.978193	−	0.207699i	$-0.0665976\pi$
$224$		0			0
$225$	1.25818	−	0.408807i	0.0838786	−	0.0272538i
$226$		0			0
$227$	−8.38017	+	16.4470i	−0.556212	+	1.09163i	0.426153	+	0.904651i	$0.359869\pi$
$227$	−8.38017	+	16.4470i	−0.556212	+	1.09163i	−0.982365	+	0.186976i	$0.940131\pi$
$228$		0			0
$229$	−26.5344	−	4.20264i	−1.75344	−	0.277718i	−0.804680	−	0.593708i	$-0.797663\pi$
$229$	−26.5344	−	4.20264i	−1.75344	−	0.277718i	−0.948762	+	0.315990i	$0.897663\pi$
$230$		0			0
$231$	1.67461	+	10.5731i	0.110181	+	0.695659i
$232$		0			0
$233$	1.96657	+	3.85961i	0.128834	+	0.252851i	0.946409	−	0.322971i	$-0.104682\pi$
$233$	1.96657	+	3.85961i	0.128834	+	0.252851i	−0.817574	+	0.575823i	$0.804682\pi$
$234$		0			0
$235$	−0.0578230	+	0.365080i	−0.00377195	+	0.0238152i
$236$		0			0
$237$		−	10.5366i		−	0.684424i
$238$		0			0
$239$	3.70095	+	1.88573i	0.239394	+	0.121978i	0.569572	−	0.821941i	$-0.307109\pi$
$239$	3.70095	+	1.88573i	0.239394	+	0.121978i	−0.330178	+	0.943919i	$0.607109\pi$
$240$		0			0
$241$	2.83202	−	3.89794i	0.182426	−	0.251088i	−0.708004	−	0.706209i	$-0.750404\pi$
$241$	2.83202	−	3.89794i	0.182426	−	0.251088i	0.890430	+	0.455121i	$0.150404\pi$
$242$		0			0
$243$	−8.87119	+	8.87119i	−0.569087	+	0.569087i
$244$		0			0
$245$	−11.7381			−0.749918
$246$		0			0
$247$	12.1674			0.774193
$248$		0			0
$249$	4.07737	−	4.07737i	0.258393	−	0.258393i
$250$		0			0
$251$	−4.62434	+	6.36486i	−0.291886	+	0.401747i	−0.929626	−	0.368505i	$-0.879870\pi$
$251$	−4.62434	+	6.36486i	−0.291886	+	0.401747i	0.637740	+	0.770252i	$0.279870\pi$
$252$		0			0
$253$	−7.04041	−	3.58727i	−0.442627	−	0.225530i
$254$		0			0
$255$		−	6.80277i		−	0.426006i
$256$		0			0
$257$	2.04912	−	12.9377i	0.127821	−	0.807029i	−0.837591	−	0.546298i	$-0.816036\pi$
$257$	2.04912	−	12.9377i	0.127821	−	0.807029i	0.965411	−	0.260731i	$-0.0839636\pi$
$258$		0			0
$259$	17.0445	+	33.4518i	1.05910	+	2.07859i
$260$		0			0
$261$	−2.04447	−	12.9083i	−0.126550	−	0.799003i
$262$		0			0
$263$	−18.2212	−	2.88595i	−1.12357	−	0.177955i	−0.433118	−	0.901337i	$-0.642587\pi$
$263$	−18.2212	−	2.88595i	−1.12357	−	0.177955i	−0.690448	+	0.723382i	$0.742587\pi$
$264$		0			0
$265$	−3.26598	+	6.40984i	−0.200627	+	0.393754i
$266$		0			0
$267$	−14.8645	+	4.82978i	−0.909695	+	0.295578i
$268$		0			0
$269$	−6.34299	+	19.5217i	−0.386739	+	1.19026i	0.548472	+	0.836169i	$0.315210\pi$
$269$	−6.34299	+	19.5217i	−0.386739	+	1.19026i	−0.935211	+	0.354091i	$0.884790\pi$
$270$		0			0
$271$	−3.25302	−	10.0118i	−0.197607	−	0.608171i	−0.999936	−	0.0112896i	$-0.996406\pi$
$271$	−3.25302	−	10.0118i	−0.197607	−	0.608171i	0.802330	−	0.596881i	$-0.203594\pi$
$272$		0			0
$273$	8.65904	+	8.65904i	0.524069	+	0.524069i
$274$		0			0
$275$	−1.88610	+	0.298728i	−0.113736	+	0.0180140i
$276$		0			0
$277$	16.3076	−	11.8482i	0.979828	−	0.711887i	0.0221582	−	0.999754i	$-0.492946\pi$
$277$	16.3076	−	11.8482i	0.979828	−	0.711887i	0.957670	+	0.287867i	$0.0929463\pi$
$278$		0			0
$279$	3.15277	+	4.33942i	0.188752	+	0.259794i
$280$		0			0
$281$	−12.3700	+	6.30284i	−0.737933	+	0.375996i	−0.782203	−	0.623024i	$-0.785904\pi$
$281$	−12.3700	+	6.30284i	−0.737933	+	0.375996i	0.0442695	+	0.999020i	$0.485904\pi$
$282$		0			0
$283$	−2.45387	−	1.78284i	−0.145867	−	0.105979i	0.512458	−	0.858712i	$-0.328735\pi$
$283$	−2.45387	−	1.78284i	−0.145867	−	0.105979i	−0.658326	+	0.752733i	$0.728735\pi$
$284$		0			0
$285$	−6.86015	−	2.22900i	−0.406360	−	0.132034i
$286$		0			0
$287$	27.3065	+	4.75541i	1.61185	+	0.280703i
$288$		0			0
$289$	10.0758	+	3.27384i	0.592696	+	0.192579i
$290$		0			0
$291$	−0.567265	−	0.412142i	−0.0332537	−	0.0241602i
$292$		0			0
$293$	−3.65768	+	1.86368i	−0.213684	+	0.108878i	−0.557557	−	0.830139i	$-0.688261\pi$
$293$	−3.65768	+	1.86368i	−0.213684	+	0.108878i	0.343873	+	0.939016i	$0.388261\pi$
$294$		0			0
$295$	3.75723	+	5.17138i	0.218754	+	0.301090i
$296$		0			0
$297$	8.64879	−	6.28371i	0.501854	−	0.364618i
$298$		0			0
$299$	−8.92770	+	1.41401i	−0.516302	+	0.0817743i
$300$		0			0
$301$	19.5901	+	19.5901i	1.12916	+	1.12916i
$302$		0			0
$303$	−2.28564	−	7.03447i	−0.131306	−	0.404120i
$304$		0			0
$305$	−3.71123	+	11.4220i	−0.212505	+	0.654022i
$306$		0			0
$307$	−18.6384	+	6.05597i	−1.06375	+	0.345632i	−0.788049	−	0.615612i	$-0.788909\pi$
$307$	−18.6384	+	6.05597i	−1.06375	+	0.345632i	−0.275698	+	0.961244i	$0.588909\pi$
$308$		0			0
$309$	1.01732	−	1.99660i	0.0578733	−	0.113583i
$310$		0			0
$311$	−12.5540	−	1.98835i	−0.711870	−	0.112749i	−0.210012	−	0.977699i	$-0.567350\pi$
$311$	−12.5540	−	1.98835i	−0.711870	−	0.112749i	−0.501859	+	0.864950i	$0.667350\pi$
$312$		0			0
$313$	−4.43438	−	27.9976i	−0.250646	−	1.58252i	−0.716457	−	0.697632i	$-0.754237\pi$
$313$	−4.43438	−	27.9976i	−0.250646	−	1.58252i	0.465811	−	0.884884i	$-0.345763\pi$
$314$		0			0
$315$	2.59983	+	5.10246i	0.146484	+	0.287491i
$316$		0			0
$317$	−3.97846	+	25.1190i	−0.223453	+	1.41083i	0.579592	+	0.814907i	$0.303212\pi$
$317$	−3.97846	+	25.1190i	−0.223453	+	1.41083i	−0.803045	+	0.595918i	$0.796788\pi$
$318$		0			0
$319$			18.8650i			1.05624i
$320$		0			0
$321$	−12.8038	−	6.52387i	−0.714640	−	0.364127i
$322$		0			0
$323$	17.1981	−	23.6711i	0.956927	−	1.31710i
$324$		0			0
$325$	−1.54465	+	1.54465i	−0.0856820	+	0.0856820i
$326$		0			0
$327$	−16.8379			−0.931136
$328$		0			0
$329$	−1.60004			−0.0882130
$330$		0			0
$331$	15.8598	−	15.8598i	0.871735	−	0.871735i	−0.120926	−	0.992661i	$-0.538586\pi$
$331$	15.8598	−	15.8598i	0.871735	−	0.871735i	0.992661	+	0.120926i	$0.0385865\pi$
$332$		0			0
$333$	6.74420	−	9.28259i	0.369580	−	0.508683i
$334$		0			0
$335$	−3.87152	−	1.97264i	−0.211524	−	0.107777i
$336$		0			0
$337$		−	32.0658i		−	1.74674i	−0.487060	−	0.873369i	$-0.661931\pi$
$337$		−	32.0658i		−	1.74674i	0.487060	−	0.873369i	$-0.338069\pi$
$338$		0			0
$339$	−2.61554	+	16.5139i	−0.142057	+	0.896912i
$340$		0			0
$341$	−3.51503	−	6.89863i	−0.190349	−	0.373582i
$342$		0			0
$343$	−3.20846	−	20.2574i	−0.173241	−	1.09380i
$344$		0			0
$345$	5.29260	+	0.838266i	0.284944	+	0.0451307i
$346$		0			0
$347$	−0.563956	+	1.10683i	−0.0302747	+	0.0594175i	−0.905648	−	0.424029i	$-0.860615\pi$
$347$	−0.563956	+	1.10683i	−0.0302747	+	0.0594175i	0.875374	+	0.483447i	$0.160615\pi$
$348$		0			0
$349$	−18.2683	+	5.93572i	−0.977877	+	0.317732i	−0.753992	−	0.656884i	$-0.771874\pi$
$349$	−18.2683	+	5.93572i	−0.977877	+	0.317732i	−0.223885	+	0.974615i	$0.571874\pi$
$350$		0			0
$351$	3.77905	−	11.6307i	0.201711	−	0.620802i
$352$		0			0
$353$	−3.49656	−	10.7613i	−0.186103	−	0.572767i	0.813862	−	0.581058i	$-0.197361\pi$
$353$	−3.49656	−	10.7613i	−0.186103	−	0.572767i	−0.999966	+	0.00829062i	$0.997361\pi$
$354$		0			0
$355$	−7.30386	−	7.30386i	−0.387649	−	0.387649i
$356$		0			0
$357$	29.0850	−	4.60661i	1.53934	−	0.243807i
$358$		0			0
$359$	−11.1666	+	8.11302i	−0.589351	+	0.428189i	−0.842083	−	0.539348i	$-0.818671\pi$
$359$	−11.1666	+	8.11302i	−0.589351	+	0.428189i	0.252732	+	0.967536i	$0.418671\pi$
$360$		0			0
$361$	−7.06774	−	9.72791i	−0.371986	−	0.511995i
$362$		0			0
$363$	8.48487	−	4.32326i	0.445340	−	0.226912i
$364$		0			0
$365$	−2.78377	−	2.02253i	−0.145709	−	0.105864i
$366$		0			0
$367$	−22.4237	−	7.28590i	−1.17051	−	0.380321i	−0.341675	−	0.939818i	$-0.610994\pi$
$367$	−22.4237	−	7.28590i	−1.17051	−	0.380321i	−0.828832	+	0.559497i	$0.810994\pi$
$368$		0			0
$369$	−2.49375	−	8.09548i	−0.129820	−	0.421434i
$370$		0			0
$371$	−29.6166	−	9.62302i	−1.53762	−	0.499602i
$372$		0			0
$373$	11.2464	+	8.17096i	0.582314	+	0.423076i	0.839558	−	0.543271i	$-0.182814\pi$
$373$	11.2464	+	8.17096i	0.582314	+	0.423076i	−0.257243	+	0.966347i	$0.582814\pi$
$374$		0			0
$375$	1.15387	−	0.587926i	0.0595856	−	0.0303604i
$376$		0			0
$377$	12.6846	+	17.4589i	0.653291	+	0.899178i
$378$		0			0
$379$	9.56204	−	6.94723i	0.491169	−	0.356855i	−0.314465	−	0.949269i	$-0.601825\pi$
$379$	9.56204	−	6.94723i	0.491169	−	0.356855i	0.805634	+	0.592414i	$0.201825\pi$
$380$		0			0
$381$	−16.5153	+	2.61577i	−0.846107	+	0.134010i
$382$		0			0
$383$	−15.5968	−	15.5968i	−0.796960	−	0.796960i	0.185655	−	0.982615i	$-0.440559\pi$
$383$	−15.5968	−	15.5968i	−0.796960	−	0.796960i	−0.982615	+	0.185655i	$0.940559\pi$
$384$		0			0
$385$	−2.55440	−	7.86163i	−0.130184	−	0.400666i
$386$		0			0
$387$	2.61643	−	8.05253i	0.133000	−	0.409333i
$388$		0			0
$389$	10.5020	−	3.41232i	0.532474	−	0.173011i	−0.0304248	−	0.999537i	$-0.509686\pi$
$389$	10.5020	−	3.41232i	0.532474	−	0.173011i	0.562899	+	0.826526i	$0.309686\pi$
$390$		0			0
$391$	−9.86803	+	19.3671i	−0.499048	+	0.979436i
$392$		0			0
$393$	13.7306	+	2.17472i	0.692619	+	0.109700i
$394$		0			0
$395$	1.27279	+	8.03606i	0.0640409	+	0.404338i
$396$		0			0
$397$	1.17895	+	2.31382i	0.0591698	+	0.116127i	0.918697	−	0.394962i	$-0.129242\pi$
$397$	1.17895	+	2.31382i	0.0591698	+	0.116127i	−0.859528	+	0.511089i	$0.829242\pi$
$398$		0			0
$399$	4.88452	−	30.8397i	0.244532	−	1.54391i
$400$		0			0
$401$		−	6.09768i		−	0.304504i	−0.988342	−	0.152252i	$-0.951347\pi$
$401$		−	6.09768i		−	0.304504i	0.988342	−	0.152252i	$-0.0486525\pi$
$402$		0			0
$403$	−7.89160	−	4.02097i	−0.393109	−	0.200299i
$404$		0			0
$405$	−1.92857	+	2.65445i	−0.0958315	+	0.131901i
$406$		0			0
$407$	−11.7113	+	11.7113i	−0.580507	+	0.580507i
$408$		0			0
$409$	−36.5381			−1.80669			−0.903345	−	0.428914i	$-0.858896\pi$
$409$	−36.5381			−1.80669			−0.903345	+	0.428914i	$0.858896\pi$
$410$		0			0
$411$	12.5871			0.620877
$412$		0			0
$413$	−19.5658	+	19.5658i	−0.962768	+	0.962768i
$414$		0			0
$415$	−2.61721	+	3.60228i	−0.128474	+	0.176829i
$416$		0			0
$417$	−12.0705	−	6.15024i	−0.591096	−	0.301179i
$418$		0			0
$419$			19.6680i			0.960845i	0.877037	+	0.480422i	$0.159517\pi$
$419$			19.6680i			0.960845i	−0.877037	+	0.480422i	$0.840483\pi$
$420$		0			0
$421$	−1.22161	+	7.71292i	−0.0595374	+	0.375905i	0.939872	+	0.341528i	$0.110944\pi$
$421$	−1.22161	+	7.71292i	−0.0595374	+	0.375905i	−0.999409	+	0.0343764i	$0.989056\pi$
$422$		0			0
$423$	0.221999	+	0.435697i	0.0107940	+	0.0211843i
$424$		0			0
$425$	0.821755	+	5.18836i	0.0398610	+	0.251672i
$426$		0			0
$427$	−51.3474	−	8.13263i	−2.48487	−	0.393565i
$428$		0			0
$429$	−2.45252	+	4.81334i	−0.118409	+	0.232390i
$430$		0			0
$431$	−6.97759	+	2.26716i	−0.336099	+	0.109205i	−0.472204	−	0.881489i	$-0.656541\pi$
$431$	−6.97759	+	2.26716i	−0.336099	+	0.109205i	0.136105	+	0.990694i	$0.456541\pi$
$432$		0			0
$433$	−10.8705	+	33.4561i	−0.522405	+	1.60780i	0.246986	+	0.969019i	$0.420560\pi$
$433$	−10.8705	+	33.4561i	−0.522405	+	1.60780i	−0.769391	+	0.638778i	$0.779440\pi$
$434$		0			0
$435$	−3.95340	−	12.1673i	−0.189551	−	0.583378i
$436$		0			0
$437$	16.2971	+	16.2971i	0.779595	+	0.779595i
$438$		0			0
$439$	16.1305	−	2.55481i	0.769865	−	0.121935i	0.240868	−	0.970558i	$-0.422568\pi$
$439$	16.1305	−	2.55481i	0.769865	−	0.121935i	0.528998	+	0.848623i	$0.322568\pi$
$440$		0			0
$441$	−12.5629	+	9.12750i	−0.598234	+	0.434643i
$442$		0			0
$443$	−10.1206	−	13.9298i	−0.480845	−	0.661826i	0.497822	−	0.867279i	$-0.334133\pi$
$443$	−10.1206	−	13.9298i	−0.480845	−	0.661826i	−0.978667	+	0.205453i	$0.934133\pi$
$444$		0			0
$445$	10.7535	−	5.47918i	0.509765	−	0.259738i
$446$		0			0
$447$	14.9550	+	10.8655i	0.707348	+	0.513919i
$448$		0			0
$449$	−19.3540	−	6.28849i	−0.913371	−	0.296772i	−0.185626	−	0.982620i	$-0.559431\pi$
$449$	−19.3540	−	6.28849i	−0.913371	−	0.296772i	−0.727745	+	0.685848i	$0.759431\pi$
$450$		0			0
$451$	1.72731	+	12.1048i	0.0813360	+	0.569994i
$452$		0			0
$453$	−1.28935	−	0.418934i	−0.0605787	−	0.0196832i
$454$		0			0
$455$	−7.65009	−	5.55811i	−0.358642	−	0.260568i
$456$		0			0
$457$	−7.68093	+	3.91363i	−0.359299	+	0.183072i	−0.624316	−	0.781172i	$-0.714622\pi$
$457$	−7.68093	+	3.91363i	−0.359299	+	0.183072i	0.265017	+	0.964244i	$0.414622\pi$
$458$		0			0
$459$	−17.2855	−	23.7915i	−0.806819	−	1.11049i
$460$		0			0
$461$	−28.3237	+	20.5784i	−1.31917	+	0.958430i	−0.319223	+	0.947680i	$0.603422\pi$
$461$	−28.3237	+	20.5784i	−1.31917	+	0.958430i	−0.999942	+	0.0107501i	$0.996578\pi$
$462$		0			0
$463$	−37.6571	+	5.96430i	−1.75007	+	0.277184i	−0.947590	−	0.319490i	$-0.896488\pi$
$463$	−37.6571	+	5.96430i	−1.75007	+	0.277184i	−0.802483	+	0.596675i	$0.796488\pi$
$464$		0			0
$465$	3.71278	+	3.71278i	0.172176	+	0.172176i
$466$		0			0
$467$	−0.419492	−	1.29106i	−0.0194118	−	0.0597433i	0.940881	−	0.338736i	$-0.109999\pi$
$467$	−0.419492	−	1.29106i	−0.0194118	−	0.0597433i	−0.960293	+	0.278993i	$0.909999\pi$
$468$		0			0
$469$	5.81226	−	17.8883i	0.268385	−	0.826005i
$470$		0			0
$471$	−2.93370	+	0.953218i	−0.135178	+	0.0439220i
$472$		0			0
$473$	−5.54856	+	10.8897i	−0.255123	+	0.500707i
$474$		0			0
$475$	5.50138	+	0.871332i	0.252420	+	0.0399795i
$476$		0			0
$477$	1.48880	+	9.39988i	0.0681673	+	0.430391i
$478$		0			0
$479$	−12.1386	−	23.8233i	−0.554626	−	1.08851i	−0.982775	−	0.184806i	$-0.940834\pi$
$479$	−12.1386	−	23.8233i	−0.554626	−	1.08851i	0.428149	−	0.903708i	$-0.359166\pi$
$480$		0			0
$481$	−2.96384	+	18.7129i	−0.135139	+	0.853236i
$482$		0			0
$483$			23.1959i			1.05545i
$484$		0			0
$485$	0.482429	+	0.245810i	0.0219060	+	0.0111616i
$486$		0			0
$487$	−2.53551	+	3.48983i	−0.114895	+	0.158139i	−0.862591	−	0.505902i	$-0.831160\pi$
$487$	−2.53551	+	3.48983i	−0.114895	+	0.158139i	0.747696	+	0.664041i	$0.231160\pi$
$488$		0			0
$489$	22.1620	−	22.1620i	1.00220	−	1.00220i
$490$		0			0
$491$	28.2343			1.27419			0.637097	−	0.770783i	$-0.280135\pi$
$491$	28.2343			1.27419			0.637097	+	0.770783i	$0.280135\pi$
$492$		0			0
$493$	51.8947			2.33722
$494$		0			0
$495$	−1.78634	+	1.78634i	−0.0802901	+	0.0802901i
$496$		0			0
$497$	26.2814	−	36.1733i	1.17888	−	1.62259i
$498$		0			0
$499$	−7.10259	−	3.61895i	−0.317956	−	0.162007i	0.287728	−	0.957712i	$-0.407100\pi$
$499$	−7.10259	−	3.61895i	−0.317956	−	0.162007i	−0.605683	+	0.795706i	$0.707100\pi$
$500$		0			0
$501$		−	16.6450i		−	0.743645i
$502$		0			0
$503$	−0.994793	+	6.28088i	−0.0443556	+	0.280050i	−0.999890	−	0.0148292i	$-0.995280\pi$
$503$	−0.994793	+	6.28088i	−0.0443556	+	0.280050i	0.955534	+	0.294880i	$0.0952795\pi$
$504$		0			0
$505$	2.59296	+	5.08897i	0.115385	+	0.226456i
$506$		0			0
$507$	−1.66689	−	10.5243i	−0.0740292	−	0.467402i
$508$		0			0
$509$	−10.0179	−	1.58669i	−0.444037	−	0.0703286i	−0.0695877	−	0.997576i	$-0.522168\pi$
$509$	−10.0179	−	1.58669i	−0.444037	−	0.0703286i	−0.374450	+	0.927247i	$0.622168\pi$
$510$		0			0
$511$	6.76216	−	13.2715i	0.299140	−	0.587096i
$512$		0			0
$513$	−29.6559	+	9.63580i	−1.30934	+	0.425431i
$514$		0			0
$515$	−0.534709	+	1.64566i	−0.0235621	+	0.0725166i
$516$		0			0
$517$	−0.218119	−	0.671302i	−0.00959287	−	0.0295238i
$518$		0			0
$519$	−21.4401	−	21.4401i	−0.941116	−	0.941116i
$520$		0			0
$521$	−3.51667	+	0.556986i	−0.154068	+	0.0244020i	−0.232992	−	0.972479i	$-0.574852\pi$
$521$	−3.51667	+	0.556986i	−0.154068	+	0.0244020i	0.0789239	+	0.996881i	$0.474852\pi$
$522$		0			0
$523$	−4.98268	+	3.62013i	−0.217877	+	0.158297i	−0.691371	−	0.722500i	$-0.742993\pi$
$523$	−4.98268	+	3.62013i	−0.217877	+	0.158297i	0.473493	+	0.880797i	$0.342993\pi$
$524$		0			0
$525$	3.29501	+	4.53520i	0.143806	+	0.197932i
$526$		0			0
$527$	−18.9771	+	9.66930i	−0.826654	+	0.421201i
$528$		0			0
$529$	4.75564	+	3.45517i	0.206767	+	0.150225i
$530$		0			0
$531$	8.04251	+	2.61317i	0.349015	+	0.113402i
$532$		0			0
$533$	9.73773	+	10.0412i	0.421788	+	0.434931i
$534$		0			0
$535$	10.5533	+	3.42898i	0.456260	+	0.148248i
$536$		0			0
$537$	9.25061	+	6.72096i	0.399193	+	0.290031i
$538$		0			0
$539$	19.9720	−	10.1762i	0.860255	−	0.438322i
$540$		0			0
$541$	14.9913	+	20.6337i	0.644525	+	0.887112i	0.998847	−	0.0480114i	$-0.0152884\pi$
$541$	14.9913	+	20.6337i	0.644525	+	0.887112i	−0.354322	+	0.935123i	$0.615288\pi$
$542$		0			0
$543$	−19.8356	+	14.4114i	−0.851226	+	0.618452i
$544$		0			0
$545$	12.8420	−	2.03397i	0.550089	−	0.0871255i
$546$		0			0
$547$	13.0105	+	13.0105i	0.556291	+	0.556291i	0.928249	−	0.371958i	$-0.121314\pi$
$547$	13.0105	+	13.0105i	0.556291	+	0.556291i	−0.371958	+	0.928249i	$0.621314\pi$
$548$		0			0
$549$	4.90969	+	15.1105i	0.209541	+	0.644900i
$550$		0			0
$551$	17.0038	−	52.3323i	0.724387	−	2.22943i
$552$		0			0
$553$	−33.4959	+	10.8835i	−1.42439	+	0.462813i
$554$		0			0
$555$	5.09916	−	10.0077i	0.216447	−	0.424801i
$556$		0			0
$557$	22.8185	+	3.61409i	0.966849	+	0.153134i	0.619840	−	0.784728i	$-0.287197\pi$
$557$	22.8185	+	3.61409i	0.966849	+	0.153134i	0.347009	+	0.937862i	$0.387197\pi$
$558$		0			0
$559$	2.18710	+	13.8088i	0.0925045	+	0.584050i
$560$		0			0
$561$	5.89762	+	11.5747i	0.248998	+	0.488685i
$562$		0			0
$563$	−6.59889	+	41.6638i	−0.278110	+	1.75592i	0.313401	+	0.949621i	$0.398532\pi$
$563$	−6.59889	+	41.6638i	−0.278110	+	1.75592i	−0.591511	+	0.806297i	$0.701468\pi$
$564$		0			0
$565$		−	12.9108i		−	0.543162i
$566$		0			0
$567$	−12.6549	−	6.44802i	−0.531458	−	0.270791i
$568$		0			0
$569$	−9.65168	+	13.2844i	−0.404619	+	0.556911i	−0.961896	−	0.273416i	$-0.911846\pi$
$569$	−9.65168	+	13.2844i	−0.404619	+	0.556911i	0.557276	+	0.830327i	$0.311846\pi$
$570$		0			0
$571$	24.5287	−	24.5287i	1.02649	−	1.02649i	0.0268534	−	0.999639i	$-0.491451\pi$
$571$	24.5287	−	24.5287i	1.02649	−	1.02649i	0.999639	−	0.0268534i	$-0.00854873\pi$
$572$		0			0
$573$	12.8273			0.535868
$574$		0			0
$575$	−4.13784			−0.172560
$576$		0			0
$577$	−13.8687	+	13.8687i	−0.577362	+	0.577362i	−0.934176	−	0.356814i	$-0.883863\pi$
$577$	−13.8687	+	13.8687i	−0.577362	+	0.577362i	0.356814	+	0.934176i	$0.383863\pi$
$578$		0			0
$579$	−6.46918	+	8.90406i	−0.268850	+	0.370040i
$580$		0			0
$581$	−17.1737	−	8.75042i	−0.712483	−	0.363028i
$582$		0			0
$583$		−	13.7376i		−	0.568953i
$584$		0			0
$585$	−0.452079	+	2.85432i	−0.0186912	+	0.118011i
$586$		0			0
$587$	−6.41684	−	12.5937i	−0.264851	−	0.519800i	0.719833	−	0.694147i	$-0.244218\pi$
$587$	−6.41684	−	12.5937i	−0.264851	−	0.519800i	−0.984684	+	0.174348i	$0.944218\pi$
$588$		0			0
$589$	3.53282	+	22.3054i	0.145567	+	0.919077i
$590$		0			0
$591$	30.7977	+	4.87787i	1.26685	+	0.200649i
$592$		0			0
$593$	7.02404	−	13.7855i	0.288443	−	0.566101i	−0.700631	−	0.713524i	$-0.747098\pi$
$593$	7.02404	−	13.7855i	0.288443	−	0.566101i	0.989074	+	0.147423i	$0.0470979\pi$
$594$		0			0
$595$	−21.6261	+	7.02676i	−0.886585	+	0.288069i
$596$		0			0
$597$	9.55004	−	29.3920i	0.390857	−	1.20293i
$598$		0			0
$599$	−12.3724	−	38.0783i	−0.505522	−	1.55584i	−0.799892	−	0.600144i	$-0.795110\pi$
$599$	−12.3724	−	38.0783i	−0.505522	−	1.55584i	0.294370	−	0.955692i	$-0.404890\pi$
$600$		0			0
$601$	13.4712	+	13.4712i	0.549501	+	0.549501i	0.926297	−	0.376795i	$-0.122974\pi$
$601$	13.4712	+	13.4712i	0.549501	+	0.549501i	−0.376795	+	0.926297i	$0.622974\pi$
$602$		0			0
$603$	−5.67749	+	0.899226i	−0.231205	+	0.0366193i
$604$		0			0
$605$	−5.94903	+	4.32222i	−0.241862	+	0.175723i
$606$		0			0
$607$	−24.1727	−	33.2709i	−0.981141	−	1.35042i	−0.936212	−	0.351435i	$-0.885694\pi$
$607$	−24.1727	−	33.2709i	−0.981141	−	1.35042i	−0.0449288	−	0.998990i	$-0.514306\pi$
$608$		0			0
$609$	49.3437	−	25.1419i	1.99951	−	1.01880i
$610$		0			0
$611$	−0.653239	−	0.474606i	−0.0264272	−	0.0192005i
$612$		0			0
$613$	0.414323	+	0.134622i	0.0167344	+	0.00543732i	0.317372	−	0.948301i	$-0.397200\pi$
$613$	0.414323	+	0.134622i	0.0167344	+	0.00543732i	−0.300638	+	0.953738i	$0.597200\pi$
$614$		0			0
$615$	−3.65079	−	7.44525i	−0.147214	−	0.300221i
$616$		0			0
$617$	−8.47234	−	2.75283i	−0.341083	−	0.110825i	0.133466	−	0.991053i	$-0.457389\pi$
$617$	−8.47234	−	2.75283i	−0.341083	−	0.110825i	−0.474550	+	0.880229i	$0.657389\pi$
$618$		0			0
$619$	38.5059	+	27.9761i	1.54768	+	1.12446i	0.945279	+	0.326264i	$0.105790\pi$
$619$	38.5059	+	27.9761i	1.54768	+	1.12446i	0.602403	+	0.798192i	$0.294210\pi$
$620$		0			0
$621$	20.6399	−	10.5166i	0.828252	−	0.422015i
$622$		0			0
$623$	30.7079	+	42.2658i	1.23029	+	1.69334i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	13.6048	−	2.15478i	0.543322	−	0.0860537i
$628$		0			0
$629$	32.2159	+	32.2159i	1.28453	+	1.28453i
$630$		0			0
$631$	3.43882	+	10.5836i	0.136897	+	0.421326i	0.995880	−	0.0906777i	$-0.0289033\pi$
$631$	3.43882	+	10.5836i	0.136897	+	0.421326i	−0.858983	+	0.512004i	$0.828903\pi$
$632$		0			0
$633$	−6.23952	+	19.2033i	−0.247999	+	0.763261i
$634$		0			0
$635$	12.2800	−	3.99001i	0.487317	−	0.158339i
$636$		0			0
$637$	11.6410	−	22.8467i	0.461233	−	0.905221i
$638$		0			0
$639$	−13.4966	−	2.13765i	−0.533916	−	0.0845640i
$640$		0			0
$641$	−1.85881	−	11.7361i	−0.0734187	−	0.463548i	−0.996818	−	0.0797075i	$-0.974601\pi$
$641$	−1.85881	−	11.7361i	−0.0734187	−	0.463548i	0.923400	−	0.383840i	$-0.125399\pi$
$642$		0			0
$643$	−10.8252	−	21.2457i	−0.426905	−	0.837849i	−0.999834	−	0.0182433i	$-0.994193\pi$
$643$	−10.8252	−	21.2457i	−0.426905	−	0.837849i	0.572928	−	0.819606i	$-0.305807\pi$
$644$		0			0
$645$	1.29658	−	8.18626i	0.0510527	−	0.322334i
$646$		0			0
$647$			20.6096i			0.810248i	0.914262	+	0.405124i	$0.132772\pi$
$647$			20.6096i			0.810248i	−0.914262	+	0.405124i	$0.867228\pi$
$648$		0			0
$649$	−10.8761	−	5.54166i	−0.426925	−	0.217529i
$650$		0			0
$651$	−13.3597	+	18.3880i	−0.523606	+	0.720682i
$652$		0			0
$653$	−25.1200	+	25.1200i	−0.983022	+	0.983022i	−0.999858	−	0.0168363i	$-0.994641\pi$
$653$	−25.1200	+	25.1200i	−0.983022	+	0.983022i	0.0168363	+	0.999858i	$0.494641\pi$
$654$		0			0
$655$	−10.7348			−0.419444
$656$		0			0
$657$	−4.55210			−0.177594
$658$		0			0
$659$	18.6654	−	18.6654i	0.727100	−	0.727100i	−0.242941	−	0.970041i	$-0.578112\pi$
$659$	18.6654	−	18.6654i	0.727100	−	0.727100i	0.970041	+	0.242941i	$0.0781120\pi$
$660$		0			0
$661$	26.7005	−	36.7501i	1.03853	−	1.42941i	0.140185	−	0.990125i	$-0.455230\pi$
$661$	26.7005	−	36.7501i	1.03853	−	1.42941i	0.898346	−	0.439289i	$-0.144770\pi$
$662$		0			0
$663$	13.2408	+	6.74651i	0.514229	+	0.262013i
$664$		0			0
$665$			24.1109i			0.934982i
$666$		0			0
$667$	−6.39468	+	40.3744i	−0.247603	+	1.56330i
$668$		0			0
$669$	−8.77631	−	17.2245i	−0.339312	−	0.665937i
$670$		0			0
$671$	−3.58767	−	22.6516i	−0.138500	−	0.874457i
$672$		0			0
$673$	43.8343	+	6.94267i	1.68969	+	0.267620i	0.925878	−	0.377822i	$-0.123327\pi$
$673$	43.8343	+	6.94267i	1.68969	+	0.267620i	0.763809	+	0.645443i	$0.223327\pi$
$674$		0			0
$675$	2.54156	−	4.98810i	0.0978248	−	0.191992i
$676$		0			0
$677$	−25.7585	+	8.36945i	−0.989980	+	0.321664i	−0.758855	−	0.651260i	$-0.774241\pi$
$677$	−25.7585	+	8.36945i	−0.989980	+	0.321664i	−0.231126	+	0.972924i	$0.574241\pi$
$678$		0			0
$679$	−0.724264	+	2.22906i	−0.0277947	+	0.0855433i
$680$		0			0
$681$	7.38694	+	22.7347i	0.283068	+	0.871194i
$682$		0			0
$683$	−6.62534	−	6.62534i	−0.253512	−	0.253512i	0.568897	−	0.822409i	$-0.307370\pi$
$683$	−6.62534	−	6.62534i	−0.253512	−	0.253512i	−0.822409	+	0.568897i	$0.807370\pi$
$684$		0			0
$685$	−9.59999	+	1.52049i	−0.366797	+	0.0580949i
$686$		0			0
$687$	−28.1464	+	20.4496i	−1.07385	+	0.780200i
$688$		0			0
$689$	−9.23701	−	12.7137i	−0.351902	−	0.484352i
$690$		0			0
$691$	0.304786	−	0.155296i	0.0115946	−	0.00590774i	−0.448184	−	0.893942i	$-0.647929\pi$
$691$	0.304786	−	0.155296i	0.0115946	−	0.00590774i	0.459778	+	0.888034i	$0.347929\pi$
$692$		0			0
$693$	−8.84708	−	6.42778i	−0.336073	−	0.244171i
$694$		0			0
$695$	9.94892	+	3.23260i	0.377384	+	0.122619i
$696$		0			0
$697$	33.2985	−	4.75157i	1.26127	−	0.179979i
$698$		0			0
$699$	5.33513	+	1.73349i	0.201793	+	0.0655665i
$700$		0			0
$701$	−17.5659	−	12.7624i	−0.663454	−	0.482028i	0.204374	−	0.978893i	$-0.434484\pi$
$701$	−17.5659	−	12.7624i	−0.663454	−	0.482028i	−0.867828	+	0.496865i	$0.834484\pi$
$702$		0			0
$703$	43.0435	−	21.9318i	1.62342	−	0.827173i
$704$		0			0
$705$	0.281360	+	0.387259i	0.0105966	+	0.0145850i
$706$		0			0
$707$	−20.0018	+	14.5322i	−0.752246	+	0.546538i
$708$		0			0
$709$	−37.1687	+	5.88695i	−1.39590	+	0.221089i	−0.808637	−	0.588307i	$-0.799795\pi$
$709$	−37.1687	+	5.88695i	−1.39590	+	0.221089i	−0.587263	+	0.809396i	$0.699795\pi$
$710$		0			0
$711$	7.61105	+	7.61105i	0.285437	+	0.285437i
$712$		0			0
$713$	−5.18435	−	15.9558i	−0.194155	−	0.597548i
$714$		0			0
$715$	1.28906	−	3.96731i	0.0482080	−	0.148369i
$716$		0			0
$717$	5.11581	−	1.66223i	0.191053	−	0.0620770i
$718$		0			0
$719$	4.04371	−	7.93624i	0.150805	−	0.295972i	−0.803229	−	0.595671i	$-0.796886\pi$
$719$	4.04371	−	7.93624i	0.150805	−	0.295972i	0.954034	+	0.299699i	$0.0968863\pi$
$720$		0			0
$721$	−7.39805	−	1.17174i	−0.275518	−	0.0436377i
$722$		0			0
$723$	−0.976080	−	6.16273i	−0.0363008	−	0.229194i
$724$		0			0
$725$	4.48497	+	8.80224i	0.166568	+	0.326907i
$726$		0			0
$727$	5.71575	−	36.0878i	0.211985	−	1.33842i	−0.620426	−	0.784265i	$-0.713040\pi$
$727$	5.71575	−	36.0878i	0.211985	−	1.33842i	0.832411	−	0.554158i	$-0.186960\pi$
$728$		0			0
$729$			26.0902i			0.966304i
$730$		0			0
$731$	29.9558	+	15.2632i	1.10796	+	0.564531i
$732$		0			0
$733$	−9.45355	+	13.0117i	−0.349175	+	0.480598i	−0.947093	−	0.320959i	$-0.895995\pi$
$733$	−9.45355	+	13.0117i	−0.349175	+	0.480598i	0.597918	+	0.801557i	$0.295995\pi$
$734$		0			0
$735$	−10.7487	+	10.7487i	−0.396474	+	0.396474i
$736$		0			0
$737$	8.29744			0.305640
$738$		0			0
$739$	32.9645			1.21262			0.606309	−	0.795229i	$-0.292650\pi$
$739$	32.9645			1.21262			0.606309	+	0.795229i	$0.292650\pi$
$740$		0			0
$741$	11.1419	−	11.1419i	0.409307	−	0.409307i
$742$		0			0
$743$	0.224658	−	0.309215i	0.00824191	−	0.0113440i	−0.804876	−	0.593443i	$-0.797768\pi$
$743$	0.224658	−	0.309215i	0.00824191	−	0.0113440i	0.813118	+	0.582099i	$0.197768\pi$
$744$		0			0
$745$	−12.7185	−	6.48038i	−0.465968	−	0.237423i
$746$		0			0
$747$			5.89054i			0.215524i
$748$		0			0
$749$	−7.51411	+	47.4422i	−0.274560	+	1.73350i
$750$		0			0
$751$	−21.6534	−	42.4972i	−0.790143	−	1.55074i	−0.834038	−	0.551708i	$-0.813976\pi$
$751$	−21.6534	−	42.4972i	−0.790143	−	1.55074i	0.0438941	−	0.999036i	$-0.486024\pi$
$752$		0			0
$753$	1.59382	+	10.0630i	0.0580821	+	0.366716i
$754$		0			0
$755$	1.03397	+	0.163764i	0.0376299	+	0.00596000i
$756$		0			0
$757$	5.00260	−	9.81816i	0.181823	−	0.356847i	−0.782048	−	0.623218i	$-0.785825\pi$
$757$	5.00260	−	9.81816i	0.181823	−	0.356847i	0.963870	+	0.266371i	$0.0858248\pi$
$758$		0			0
$759$	−9.73194	+	3.16210i	−0.353247	+	0.114777i
$760$		0			0
$761$	−5.59157	+	17.2091i	−0.202694	+	0.623829i	0.797106	+	0.603840i	$0.206363\pi$
$761$	−5.59157	+	17.2091i	−0.202694	+	0.623829i	−0.999800	+	0.0199895i	$0.993637\pi$
$762$		0			0
$763$	17.3923	+	53.5279i	0.629642	+	1.93784i
$764$		0			0
$765$	4.91395	+	4.91395i	0.177664	+	0.177664i
$766$		0			0
$767$	−13.7916	+	2.18438i	−0.497987	+	0.0788733i
$768$		0			0
$769$	0.0410588	−	0.0298309i	0.00148062	−	0.00107573i	−0.587045	−	0.809555i	$-0.699709\pi$
$769$	0.0410588	−	0.0298309i	0.00148062	−	0.00107573i	0.588525	+	0.808479i	$0.299709\pi$
$770$		0			0
$771$	−9.97081	−	13.7236i	−0.359090	−	0.494245i
$772$		0			0
$773$	−27.4920	+	14.0079i	−0.988817	+	0.503827i	−0.872095	−	0.489337i	$-0.837239\pi$
$773$	−27.4920	+	14.0079i	−0.988817	+	0.503827i	−0.116722	+	0.993165i	$0.537239\pi$
$774$		0			0
$775$	−3.28016	−	2.38318i	−0.117827	−	0.0856063i
$776$		0			0
$777$	46.2403	+	15.0244i	1.65886	+	0.538997i
$778$		0			0
$779$	6.11895	−	35.1363i	0.219234	−	1.25889i
$780$		0			0
$781$	18.7593	+	6.09528i	0.671262	+	0.218106i
$782$		0			0
$783$	−44.7429	−	32.5076i	−1.59898	−	1.16173i
$784$		0			0
$785$	2.12234	−	1.08139i	0.0757495	−	0.0385963i
$786$		0			0
$787$	−10.1379	−	13.9536i	−0.361376	−	0.497392i	0.589155	−	0.808020i	$-0.299461\pi$
$787$	−10.1379	−	13.9536i	−0.361376	−	0.497392i	−0.950532	+	0.310628i	$0.899461\pi$
$788$		0			0
$789$	−19.3281	+	14.0427i	−0.688100	+	0.499934i
$790$		0			0
$791$	55.1996	−	8.74276i	1.96267	−	0.310857i
$792$		0			0
$793$	−18.5510	−	18.5510i	−0.658765	−	0.658765i
$794$		0			0
$795$	2.87889	+	8.86031i	0.102104	+	0.314243i
$796$		0			0
$797$	−0.652460	+	2.00807i	−0.0231113	+	0.0711294i	−0.961947	−	0.273236i	$-0.911906\pi$
$797$	−0.652460	+	2.00807i	−0.0231113	+	0.0711294i	0.938836	+	0.344366i	$0.111906\pi$
$798$		0			0
$799$	−1.84665	+	0.600013i	−0.0653297	+	0.0212269i
$800$		0			0
$801$	7.24856	−	14.2261i	0.256115	−	0.502655i
$802$		0			0
$803$	6.48993	+	1.02790i	0.229024	+	0.0362739i
$804$		0			0
$805$	−2.80200	−	17.6911i	−0.0987576	−	0.623531i
$806$		0			0
$807$	12.0680	+	23.6847i	0.424813	+	0.833742i
$808$		0			0
$809$	2.02776	−	12.8028i	0.0712923	−	0.450122i	−0.926059	−	0.377380i	$-0.876825\pi$
$809$	2.02776	−	12.8028i	0.0712923	−	0.450122i	0.997351	−	0.0727418i	$-0.0231749\pi$
$810$		0			0
$811$		−	24.9827i		−	0.877261i	−0.898668	−	0.438630i	$-0.855464\pi$
$811$		−	24.9827i		−	0.877261i	0.898668	−	0.438630i	$-0.144536\pi$
$812$		0			0
$813$	−12.1468	−	6.18909i	−0.426006	−	0.217061i
$814$		0			0
$815$	−14.2255	+	19.5797i	−0.498296	+	0.685845i
$816$		0			0
$817$	25.2073	−	25.2073i	0.881892	−	0.881892i
$818$		0			0
$819$	−12.5096			−0.437122
$820$		0			0
$821$	47.3895			1.65391			0.826953	−	0.562271i	$-0.190072\pi$
$821$	47.3895			1.65391			0.826953	+	0.562271i	$0.190072\pi$
$822$		0			0
$823$	11.2416	−	11.2416i	0.391856	−	0.391856i	−0.483492	−	0.875349i	$-0.660632\pi$
$823$	11.2416	−	11.2416i	0.391856	−	0.391856i	0.875349	+	0.483492i	$0.160632\pi$
$824$		0			0
$825$	−1.45358	+	2.00068i	−0.0506071	+	0.0696547i
$826$		0			0
$827$	11.4600	+	5.83917i	0.398504	+	0.203048i	0.641745	−	0.766918i	$-0.278211\pi$
$827$	11.4600	+	5.83917i	0.398504	+	0.203048i	−0.243241	+	0.969966i	$0.578211\pi$
$828$		0			0
$829$			18.4458i			0.640648i	0.947308	+	0.320324i	$0.103792\pi$
$829$			18.4458i			0.640648i	−0.947308	+	0.320324i	$0.896208\pi$
$830$		0			0
$831$	4.08358	−	25.7827i	0.141658	−	0.894391i
$832$		0			0
$833$	−27.9933	−	54.9399i	−0.969910	−	1.90356i
$834$		0			0
$835$	2.01067	+	12.6949i	0.0695821	+	0.439324i
$836$		0			0
$837$	22.4188	+	3.55078i	0.774906	+	0.122733i
$838$		0			0
$839$	−8.10859	+	15.9140i	−0.279940	+	0.549412i	−0.987572	−	0.157169i	$-0.949763\pi$
$839$	−8.10859	+	15.9140i	−0.279940	+	0.549412i	0.707632	+	0.706581i	$0.249763\pi$
$840$		0			0
$841$	65.2372	−	21.1968i	2.24956	−	0.730926i
$842$		0			0
$843$	−5.55581	+	17.0990i	−0.191352	+	0.588922i
$844$		0			0
$845$	2.54262	+	7.82537i	0.0874687	+	0.269201i
$846$		0			0
$847$	−22.5080	−	22.5080i	−0.773382	−	0.773382i
$848$		0			0
$849$	−3.87962	+	0.614472i	−0.133148	+	0.0210886i
$850$		0			0
$851$	−29.0340	+	21.0944i	−0.995273	+	0.723108i
$852$		0			0
$853$	−3.58243	−	4.93080i	−0.122660	−	0.168827i	0.743271	−	0.668991i	$-0.233273\pi$
$853$	−3.58243	−	4.93080i	−0.122660	−	0.168827i	−0.865931	+	0.500163i	$0.833273\pi$
$854$		0			0
$855$	6.56551	−	3.34529i	0.224536	−	0.114407i
$856$		0			0
$857$	14.1120	+	10.2530i	0.482057	+	0.350235i	0.802121	−	0.597161i	$-0.203705\pi$
$857$	14.1120	+	10.2530i	0.482057	+	0.350235i	−0.320065	+	0.947396i	$0.603705\pi$
$858$		0			0
$859$	29.8991	+	9.71482i	1.02015	+	0.331465i	0.770887	−	0.636972i	$-0.219813\pi$
$859$	29.8991	+	9.71482i	1.02015	+	0.331465i	0.249258	+	0.968437i	$0.419813\pi$
$860$		0			0
$861$	29.3597	−	20.6504i	1.00057	−	0.703765i
$862$		0			0
$863$	11.4192	+	3.71031i	0.388713	+	0.126301i	0.496852	−	0.867835i	$-0.334489\pi$
$863$	11.4192	+	3.71031i	0.388713	+	0.126301i	−0.108139	+	0.994136i	$0.534489\pi$
$864$		0			0
$865$	18.9419	+	13.7621i	0.644044	+	0.467925i
$866$		0			0
$867$	12.2245	−	6.22870i	0.415166	−	0.211538i
$868$		0			0
$869$	−9.13242	−	12.5697i	−0.309796	−	0.426398i
$870$		0			0
$871$	7.67899	−	5.57912i	0.260193	−	0.189041i
$872$		0			0
$873$	0.707470	−	0.112052i	0.0239442	−	0.00379240i
$874$		0			0
$875$	−3.06089	−	3.06089i	−0.103477	−	0.103477i
$876$		0			0
$877$	−3.84188	−	11.8241i	−0.129731	−	0.399271i	0.865002	−	0.501768i	$-0.167317\pi$
$877$	−3.84188	−	11.8241i	−0.129731	−	0.399271i	−0.994733	+	0.102497i	$0.967317\pi$
$878$		0			0
$879$	−1.64280	+	5.05600i	−0.0554101	+	0.170535i
$880$		0			0
$881$	52.5292	−	17.0678i	1.76975	−	0.575027i	0.771618	−	0.636086i	$-0.219448\pi$
$881$	52.5292	−	17.0678i	1.76975	−	0.575027i	0.998134	+	0.0610583i	$0.0194475\pi$
$882$		0			0
$883$	−12.4528	+	24.4400i	−0.419071	+	0.822473i	0.580893	+	0.813980i	$0.302703\pi$
$883$	−12.4528	+	24.4400i	−0.419071	+	0.822473i	−0.999964	+	0.00849280i	$0.997297\pi$
$884$		0			0
$885$	8.17608	+	1.29496i	0.274836	+	0.0435297i
$886$		0			0
$887$	−7.62159	−	48.1208i	−0.255908	−	1.61574i	−0.696175	−	0.717872i	$-0.745116\pi$
$887$	−7.62159	−	48.1208i	−0.255908	−	1.61574i	0.440267	−	0.897867i	$-0.354884\pi$
$888$		0			0
$889$	25.3747	+	49.8007i	0.851041	+	1.67026i
$890$		0			0
$891$	0.980151	−	6.18843i	0.0328363	−	0.207320i
$892$		0			0
$893$			2.05882i			0.0688959i
$894$		0			0
$895$	−7.86715	−	4.00852i	−0.262970	−	0.133990i
$896$		0			0
$897$	−6.88041	+	9.47008i	−0.229730	+	0.316197i
$898$		0			0
$899$	−28.3228	+	28.3228i	−0.944617	+	0.944617i
$900$		0			0
$901$	−37.7900			−1.25897
$902$		0			0
$903$	35.8780			1.19395
$904$		0			0
$905$	13.3874	−	13.3874i	0.445012	−	0.445012i
$906$		0			0
$907$	32.7376	−	45.0594i	1.08703	−	1.49617i	0.235501	−	0.971874i	$-0.424327\pi$
$907$	32.7376	−	45.0594i	1.08703	−	1.49617i	0.851533	−	0.524300i	$-0.175673\pi$
$908$		0			0
$909$	6.73234	+	3.43030i	0.223298	+	0.113776i
$910$		0			0
$911$			4.99963i			0.165645i	0.996564	+	0.0828225i	$0.0263935\pi$
$911$			4.99963i			0.165645i	−0.996564	+	0.0828225i	$0.973607\pi$
$912$		0			0
$913$	1.33013	−	8.39814i	0.0440210	−	0.277938i
$914$		0			0
$915$	7.06088	+	13.8578i	0.233425	+	0.458123i
$916$		0			0
$917$	−7.26925	−	45.8962i	−0.240052	−	1.51563i
$918$		0			0
$919$	16.8239	+	2.66465i	0.554970	+	0.0878986i	0.427619	−	0.903959i	$-0.359353\pi$
$919$	16.8239	+	2.66465i	0.554970	+	0.0878986i	0.127351	+	0.991858i	$0.459353\pi$
$920$		0			0
$921$	−11.5219	+	22.6130i	−0.379659	+	0.745123i
$922$		0			0
$923$	21.4595	−	6.97262i	0.706349	−	0.229507i
$924$		0			0
$925$	−2.68014	+	8.24863i	−0.0881226	+	0.271213i
$926$		0			0
$927$	0.707381	+	2.17709i	0.0232334	+	0.0715052i
$928$		0			0
$929$	15.2613	+	15.2613i	0.500707	+	0.500707i	0.911658	−	0.410950i	$-0.134803\pi$
$929$	15.2613	+	15.2613i	0.500707	+	0.500707i	−0.410950	+	0.911658i	$0.634803\pi$
$930$		0			0
$931$	−64.5756	+	10.2278i	−2.11638	+	0.335201i
$932$		0			0
$933$	−13.3166	+	9.67511i	−0.435967	+	0.316749i
$934$		0			0
$935$	−5.89620	−	8.11543i	−0.192827	−	0.265403i
$936$		0			0
$937$	−9.07484	+	4.62386i	−0.296462	+	0.151055i	−0.595895	−	0.803062i	$-0.703203\pi$
$937$	−9.07484	+	4.62386i	−0.296462	+	0.151055i	0.299433	+	0.954117i	$0.403203\pi$
$938$		0			0
$939$	−29.6985	−	21.5772i	−0.969173	−	0.704145i
$940$		0			0
$941$	1.00304	+	0.325908i	0.0326983	+	0.0106243i	0.325320	−	0.945604i	$-0.394528\pi$
$941$	1.00304	+	0.325908i	0.0326983	+	0.0106243i	−0.292622	+	0.956228i	$0.594528\pi$
$942$		0			0
$943$	−0.406427	+	26.4920i	−0.0132351	+	0.862697i
$944$		0			0
$945$	23.0474	+	7.48857i	0.749733	+	0.243603i
$946$		0			0
$947$	15.3486	+	11.1514i	0.498764	+	0.362373i	0.808545	−	0.588435i	$-0.200256\pi$
$947$	15.3486	+	11.1514i	0.498764	+	0.362373i	−0.309781	+	0.950808i	$0.600256\pi$
$948$		0			0
$949$	6.69735	−	3.41247i	0.217405	−	0.110774i
$950$		0			0
$951$	19.3588	+	26.6450i	0.627751	+	0.864025i
$952$		0			0
$953$	−34.7680	+	25.2604i	−1.12624	+	0.818265i	−0.985144	−	0.171731i	$-0.945064\pi$
$953$	−34.7680	+	25.2604i	−1.12624	+	0.818265i	−0.141101	+	0.989995i	$0.545064\pi$
$954$		0			0
$955$	−9.78315	+	1.54950i	−0.316575	+	0.0501406i
$956$		0			0
$957$	17.2750	+	17.2750i	0.558420	+	0.558420i
$958$		0			0
$959$	−13.0016	−	40.0147i	−0.419842	−	1.29214i
$960$		0			0
$961$	−4.49959	+	13.8483i	−0.145148	+	0.446720i
$962$		0			0
$963$	13.9613	−	4.53629i	0.449896	−	0.146180i
$964$		0			0
$965$	3.85835	−	7.57243i	0.124205	−	0.243765i
$966$		0			0
$967$	−7.61270	−	1.20573i	−0.244808	−	0.0387737i	0.0328246	−	0.999461i	$-0.489550\pi$
$967$	−7.61270	−	1.20573i	−0.244808	−	0.0387737i	−0.277632	+	0.960687i	$0.589550\pi$
$968$		0			0
$969$	−5.92748	−	37.4246i	−0.190418	−	1.20225i
$970$		0			0
$971$	9.20128	+	18.0585i	0.295283	+	0.579526i	0.990215	−	0.139550i	$-0.0445656\pi$
$971$	9.20128	+	18.0585i	0.295283	+	0.579526i	−0.694932	+	0.719075i	$0.744566\pi$
$972$		0			0
$973$	−7.08377	+	44.7252i	−0.227095	+	1.43382i
$974$		0			0
$975$			2.82893i			0.0905983i
$976$		0			0
$977$	2.11251	+	1.07638i	0.0675851	+	0.0344363i	0.487456	−	0.873147i	$-0.337925\pi$
$977$	2.11251	+	1.07638i	0.0675851	+	0.0344363i	−0.419871	+	0.907584i	$0.637925\pi$
$978$		0			0
$979$	−13.5466	+	18.6453i	−0.432952	+	0.595908i
$980$		0			0
$981$	12.1628	−	12.1628i	0.388327	−	0.388327i
$982$		0			0
$983$	−45.7859			−1.46034			−0.730172	−	0.683263i	$-0.760560\pi$
$983$	−45.7859			−1.46034			−0.730172	+	0.683263i	$0.760560\pi$
$984$		0			0
$985$	−24.0781			−0.767192
$986$		0			0
$987$	−1.46518	+	1.46518i	−0.0466372	+	0.0466372i
$988$		0			0
$989$	−15.5662	+	21.4250i	−0.494976	+	0.681276i
$990$		0			0
$991$	−11.4270	−	5.82237i	−0.362992	−	0.184954i	0.262976	−	0.964802i	$-0.415296\pi$
$991$	−11.4270	−	5.82237i	−0.362992	−	0.184954i	−0.625968	+	0.779849i	$0.715296\pi$
$992$		0			0
$993$		−	29.0462i		−	0.921754i
$994$		0			0
$995$	−3.73318	+	23.5704i	−0.118350	+	0.747232i
$996$		0			0
$997$	20.7692	+	40.7618i	0.657766	+	1.29094i	0.943099	+	0.332511i	$0.107896\pi$
$997$	20.7692	+	40.7618i	0.657766	+	1.29094i	−0.285333	+	0.958428i	$0.592104\pi$
$998$		0			0
$999$	−7.59560	−	47.9567i	−0.240314	−	1.51728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bo.b.61.7	✓	64
41.39	even	20	inner	820.2.bo.b.121.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bo.b.61.7	✓	64	1.1	even	1	trivial
820.2.bo.b.121.7	yes	64	41.39	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bo (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.915716 - 0.915716i) q^{3} +(-0.587785 + 0.809017i) q^{5} +(-3.85694 - 1.96521i) q^{7} +1.32293i q^{9} +(0.298728 - 1.88610i) q^{11} +(-0.991729 - 1.94638i) q^{13} +(0.202586 + 1.27907i) q^{15} +(-5.18836 - 0.821755i) q^{17} +(-2.52870 + 4.96286i) q^{19} +(-5.33144 + 1.73229i) q^{21} +(1.27866 - 3.93532i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(3.95857 + 3.95857i) q^{27} +(-9.75736 + 1.54541i) q^{29} +(3.28016 - 2.38318i) q^{31} +(-1.45358 - 2.00068i) q^{33} +(3.85694 - 1.96521i) q^{35} +(-7.01671 - 5.09794i) q^{37} +(-2.69047 - 0.874188i) q^{39} +(-6.11937 + 1.88503i) q^{41} +(-6.08690 - 1.97775i) q^{43} +(-1.07027 - 0.777597i) q^{45} +(0.329343 - 0.167809i) q^{47} +(6.89947 + 9.49630i) q^{49} +(-5.50356 + 3.99857i) q^{51} +(7.10537 - 1.12538i) q^{53} +(1.35030 + 1.35030i) q^{55} +(2.22900 + 6.86015i) q^{57} +(1.97529 - 6.07933i) q^{59} +(11.4220 - 3.71123i) q^{61} +(2.59983 - 5.10246i) q^{63} +(2.15758 + 0.341727i) q^{65} +(0.679724 + 4.29161i) q^{67} +(-2.43274 - 4.77453i) q^{69} +(-1.61585 + 10.2020i) q^{71} +3.44093i q^{73} +(-1.15387 - 0.587926i) q^{75} +(-4.85875 + 6.68750i) q^{77} +(5.75319 - 5.75319i) q^{79} +3.28108 q^{81} +4.45266 q^{83} +(3.71446 - 3.71446i) q^{85} +(-7.51981 + 10.3501i) q^{87} +(-10.7535 - 5.47918i) q^{89} +9.45603i q^{91} +(0.821384 - 5.18602i) q^{93} +(-2.52870 - 4.96286i) q^{95} +(-0.0847003 - 0.534776i) q^{97} +(2.49517 + 0.395196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) \) 64 * q + 2 * q^3 - 10 * q^7 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 22 * q^23 + 16 * q^25 + 20 * q^27 - 12 * q^29 + 22 * q^31 + 30 * q^33 + 10 * q^35 + 12 * q^37 + 20 * q^39 - 10 * q^41 + 10 * q^43 + 32 * q^45 + 28 * q^47 + 10 * q^49 - 22 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 18 * q^59 - 20 * q^61 + 52 * q^63 - 6 * q^65 - 6 * q^67 - 50 * q^69 + 34 * q^71 + 8 * q^75 - 110 * q^77 - 14 * q^79 - 108 * q^81 + 32 * q^83 - 8 * q^85 - 80 * q^87 - 122 * q^89 + 42 * q^93 + 10 * q^95 - 64 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more