LMFDB - Embedded newform 820.2.y.a.137.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			137.17
Character	$\chi$	$=$	820.137
Dual form			820.2.y.a.413.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.07085 + 0.857774i) q^{3} +(2.22915 - 0.175717i) q^{5} +(0.0957430 - 0.231144i) q^{7} +(1.43132 + 1.43132i) q^{9} +(-3.00068 + 1.24292i) q^{11} +(-0.159938 - 0.0662484i) q^{13} +(4.76697 + 1.54823i) q^{15} +(2.76943 - 1.14714i) q^{17} +(5.11603 + 2.11913i) q^{19} +(0.396538 - 0.396538i) q^{21} +(6.52881 + 6.52881i) q^{23} +(4.93825 - 0.783399i) q^{25} +(-0.837022 - 2.02075i) q^{27} +(-5.48777 + 2.27311i) q^{29} -4.49794i q^{31} -7.28009 q^{33} +(0.172810 - 0.532079i) q^{35} +(-2.67648 - 2.67648i) q^{37} +(-0.274381 - 0.274381i) q^{39} +(-6.25145 - 1.38541i) q^{41} -6.29767 q^{43} +(3.44214 + 2.93913i) q^{45} +(0.626265 - 0.259407i) q^{47} +(4.90549 + 4.90549i) q^{49} +6.71907 q^{51} +(4.65277 - 11.2328i) q^{53} +(-6.47056 + 3.29793i) q^{55} +(8.77679 + 8.77679i) q^{57} -2.87123i q^{59} +(-6.75796 - 6.75796i) q^{61} +(0.467880 - 0.193802i) q^{63} +(-0.368167 - 0.119574i) q^{65} +(-10.4995 + 4.34904i) q^{67} +(7.91994 + 19.1204i) q^{69} +(-2.27489 - 5.49206i) q^{71} -5.86285 q^{73} +(10.8983 + 2.61360i) q^{75} +0.812589i q^{77} +(5.51307 + 13.3097i) q^{79} -10.9752i q^{81} +(-1.54246 + 1.54246i) q^{83} +(5.97192 - 3.04378i) q^{85} -13.3142 q^{87} +(-5.80891 + 2.40613i) q^{89} +(-0.0306259 + 0.0306259i) q^{91} +(3.85822 - 9.31456i) q^{93} +(11.7768 + 3.82489i) q^{95} +(-2.76542 - 6.67632i) q^{97} +(-6.07395 - 2.51591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.07085	+	0.857774i	1.19561	+	0.495236i	0.889576	−	0.456786i	$-0.151000\pi$
$3$	2.07085	+	0.857774i	1.19561	+	0.495236i	0.306029	+	0.952022i	$0.401000\pi$
$4$		0			0
$5$	2.22915	−	0.175717i	0.996908	−	0.0785829i
$5$	2.22915	−	0.175717i	0.996908	−	0.0785829i
$6$		0			0
$7$	0.0957430	−	0.231144i	0.0361874	−	0.0873642i	−0.904753	−	0.425938i	$-0.859944\pi$
$7$	0.0957430	−	0.231144i	0.0361874	−	0.0873642i	0.940940	+	0.338573i	$0.109944\pi$
$8$		0			0
$9$	1.43132	+	1.43132i	0.477107	+	0.477107i
$10$		0			0
$11$	−3.00068	+	1.24292i	−0.904738	+	0.374755i	−0.786040	−	0.618176i	$-0.787872\pi$
$11$	−3.00068	+	1.24292i	−0.904738	+	0.374755i	−0.118698	+	0.992930i	$0.537872\pi$
$12$		0			0
$13$	−0.159938	−	0.0662484i	−0.0443588	−	0.0183740i	0.360394	−	0.932800i	$-0.382642\pi$
$13$	−0.159938	−	0.0662484i	−0.0443588	−	0.0183740i	−0.404753	+	0.914426i	$0.632642\pi$
$14$		0			0
$15$	4.76697	+	1.54823i	1.23083	+	0.399750i
$16$		0			0
$17$	2.76943	−	1.14714i	0.671687	−	0.278222i	−0.0206602	−	0.999787i	$-0.506577\pi$
$17$	2.76943	−	1.14714i	0.671687	−	0.278222i	0.692347	+	0.721565i	$0.256577\pi$
$18$		0			0
$19$	5.11603	+	2.11913i	1.17370	+	0.486161i	0.882413	−	0.470475i	$-0.155918\pi$
$19$	5.11603	+	2.11913i	1.17370	+	0.486161i	0.291284	+	0.956637i	$0.405918\pi$
$20$		0			0
$21$	0.396538	−	0.396538i	0.0865318	−	0.0865318i
$22$		0			0
$23$	6.52881	+	6.52881i	1.36135	+	1.36135i	0.872198	+	0.489152i	$0.162694\pi$
$23$	6.52881	+	6.52881i	1.36135	+	1.36135i	0.489152	+	0.872198i	$0.337306\pi$
$24$		0			0
$25$	4.93825	−	0.783399i	0.987649	−	0.156680i
$26$		0			0
$27$	−0.837022	−	2.02075i	−0.161085	−	0.388894i
$28$		0			0
$29$	−5.48777	+	2.27311i	−1.01905	+	0.422106i	−0.828750	−	0.559620i	$-0.810947\pi$
$29$	−5.48777	+	2.27311i	−1.01905	+	0.422106i	−0.190304	+	0.981725i	$0.560947\pi$
$30$		0			0
$31$		−	4.49794i		−	0.807854i	−0.914791	−	0.403927i	$-0.867645\pi$
$31$		−	4.49794i		−	0.807854i	0.914791	−	0.403927i	$-0.132355\pi$
$32$		0			0
$33$	−7.28009			−1.26730
$34$		0			0
$35$	0.172810	−	0.532079i	0.0292102	−	0.0899378i
$36$		0			0
$37$	−2.67648	−	2.67648i	−0.440011	−	0.440011i	0.452005	−	0.892016i	$-0.350709\pi$
$37$	−2.67648	−	2.67648i	−0.440011	−	0.440011i	−0.892016	+	0.452005i	$0.850709\pi$
$38$		0			0
$39$	−0.274381	−	0.274381i	−0.0439361	−	0.0439361i
$40$		0			0
$41$	−6.25145	−	1.38541i	−0.976313	−	0.216365i
$41$	−6.25145	−	1.38541i	−0.976313	−	0.216365i
$42$		0			0
$43$	−6.29767			−0.960386			−0.480193	−	0.877163i	$-0.659433\pi$
$43$	−6.29767			−0.960386			−0.480193	+	0.877163i	$0.659433\pi$
$44$		0			0
$45$	3.44214	+	2.93913i	0.513124	+	0.438139i
$46$		0			0
$47$	0.626265	−	0.259407i	0.0913501	−	0.0378385i	−0.336540	−	0.941669i	$-0.609257\pi$
$47$	0.626265	−	0.259407i	0.0913501	−	0.0378385i	0.427891	+	0.903831i	$0.359257\pi$
$48$		0			0
$49$	4.90549	+	4.90549i	0.700784	+	0.700784i
$50$		0			0
$51$	6.71907			0.940858
$52$		0			0
$53$	4.65277	−	11.2328i	0.639107	−	1.54294i	−0.188764	−	0.982022i	$-0.560448\pi$
$53$	4.65277	−	11.2328i	0.639107	−	1.54294i	0.827871	−	0.560918i	$-0.189552\pi$
$54$		0			0
$55$	−6.47056	+	3.29793i	−0.872491	+	0.444693i
$56$		0			0
$57$	8.77679	+	8.77679i	1.16251	+	1.16251i
$58$		0			0
$59$		−	2.87123i		−	0.373802i	−0.982379	−	0.186901i	$-0.940156\pi$
$59$		−	2.87123i		−	0.373802i	0.982379	−	0.186901i	$-0.0598444\pi$
$60$		0			0
$61$	−6.75796	−	6.75796i	−0.865268	−	0.865268i	0.126676	−	0.991944i	$-0.459569\pi$
$61$	−6.75796	−	6.75796i	−0.865268	−	0.865268i	−0.991944	+	0.126676i	$0.959569\pi$
$62$		0			0
$63$	0.467880	−	0.193802i	0.0589473	−	0.0244168i
$64$		0			0
$65$	−0.368167	−	0.119574i	−0.0456655	−	0.0148314i
$66$		0			0
$67$	−10.4995	+	4.34904i	−1.28272	+	0.531320i	−0.916807	−	0.399330i	$-0.869243\pi$
$67$	−10.4995	+	4.34904i	−1.28272	+	0.531320i	−0.365912	+	0.930650i	$0.619243\pi$
$68$		0			0
$69$	7.91994	+	19.1204i	0.953448	+	2.30183i
$70$		0			0
$71$	−2.27489	−	5.49206i	−0.269979	−	0.651787i	0.729503	−	0.683978i	$-0.239752\pi$
$71$	−2.27489	−	5.49206i	−0.269979	−	0.651787i	−0.999482	+	0.0321907i	$0.989752\pi$
$72$		0			0
$73$	−5.86285			−0.686195			−0.343098	−	0.939300i	$-0.611476\pi$
$73$	−5.86285			−0.686195			−0.343098	+	0.939300i	$0.611476\pi$
$74$		0			0
$75$	10.8983	+	2.61360i	1.25843	+	0.301792i
$76$		0			0
$77$			0.812589i			0.0926031i
$78$		0			0
$79$	5.51307	+	13.3097i	0.620269	+	1.49746i	0.851388	+	0.524536i	$0.175761\pi$
$79$	5.51307	+	13.3097i	0.620269	+	1.49746i	−0.231120	+	0.972925i	$0.574239\pi$
$80$		0			0
$81$		−	10.9752i		−	1.21947i
$82$		0			0
$83$	−1.54246	+	1.54246i	−0.169307	+	0.169307i	−0.786675	−	0.617368i	$-0.788199\pi$
$83$	−1.54246	+	1.54246i	−0.169307	+	0.169307i	0.617368	+	0.786675i	$0.288199\pi$
$84$		0			0
$85$	5.97192	−	3.04378i	0.647746	−	0.330144i
$86$		0			0
$87$	−13.3142			−1.42743
$88$		0			0
$89$	−5.80891	+	2.40613i	−0.615743	+	0.255049i	−0.668682	−	0.743549i	$-0.733141\pi$
$89$	−5.80891	+	2.40613i	−0.615743	+	0.255049i	0.0529389	+	0.998598i	$0.483141\pi$
$90$		0			0
$91$	−0.0306259	+	0.0306259i	−0.00321046	+	0.00321046i
$92$		0			0
$93$	3.85822	−	9.31456i	0.400079	−	0.965875i
$94$		0			0
$95$	11.7768	+	3.82489i	1.20827	+	0.392425i
$96$		0			0
$97$	−2.76542	−	6.67632i	−0.280786	−	0.677878i	0.719068	−	0.694940i	$-0.244569\pi$
$97$	−2.76542	−	6.67632i	−0.280786	−	0.677878i	−0.999854	+	0.0170616i	$0.994569\pi$
$98$		0			0
$99$	−6.07395	−	2.51591i	−0.610454	−	0.252859i
$100$		0			0
$101$	−5.26260	+	12.7050i	−0.523648	+	1.26420i	0.411974	+	0.911196i	$0.364840\pi$
$101$	−5.26260	+	12.7050i	−0.523648	+	1.26420i	−0.935622	+	0.353003i	$0.885160\pi$
$102$		0			0
$103$		−	5.35305i		−	0.527452i	−0.964598	−	0.263726i	$-0.915049\pi$
$103$		−	5.35305i		−	0.527452i	0.964598	−	0.263726i	$-0.0849514\pi$
$104$		0			0
$105$	0.814267	−	0.953623i	0.0794643	−	0.0930641i
$106$		0			0
$107$	−5.13335	+	5.13335i	−0.496260	+	0.496260i	−0.910272	−	0.414012i	$-0.864127\pi$
$107$	−5.13335	+	5.13335i	−0.496260	+	0.496260i	0.414012	+	0.910272i	$0.364127\pi$
$108$		0			0
$109$	6.11798	−	14.7701i	0.585996	−	1.41472i	−0.301304	−	0.953528i	$-0.597422\pi$
$109$	6.11798	−	14.7701i	0.585996	−	1.41472i	0.887301	−	0.461192i	$-0.152578\pi$
$110$		0			0
$111$	−3.24677	−	7.83840i	−0.308170	−	0.743988i
$112$		0			0
$113$	0.751818	+	0.751818i	0.0707251	+	0.0707251i	0.741585	−	0.670859i	$-0.234075\pi$
$113$	0.751818	+	0.751818i	0.0707251	+	0.0707251i	−0.670859	+	0.741585i	$0.734075\pi$
$114$		0			0
$115$	15.7009	+	13.4065i	1.46412	+	1.25016i
$116$		0			0
$117$	−0.134100	−	0.323745i	−0.0123975	−	0.0299302i
$118$		0			0
$119$		−	0.749968i		−	0.0687495i
$120$		0			0
$121$	−0.318972	+	0.318972i	−0.0289974	+	0.0289974i
$122$		0			0
$123$	−11.7574	−	8.23131i	−1.06013	−	0.742192i
$124$		0			0
$125$	10.8705	−	2.61405i	0.972283	−	0.233808i
$126$		0			0
$127$	4.29375	−	4.29375i	0.381009	−	0.381009i	−0.490457	−	0.871466i	$-0.663170\pi$
$127$	4.29375	−	4.29375i	0.381009	−	0.381009i	0.871466	+	0.490457i	$0.163170\pi$
$128$		0			0
$129$	−13.0415	−	5.40198i	−1.14824	−	0.475618i
$130$		0			0
$131$	0.502255	−	0.502255i	0.0438822	−	0.0438822i	−0.684825	−	0.728707i	$-0.740121\pi$
$131$	0.502255	−	0.502255i	0.0438822	−	0.0438822i	0.728707	+	0.684825i	$0.240121\pi$
$132$		0			0
$133$	0.979647	−	0.979647i	0.0849462	−	0.0849462i
$134$		0			0
$135$	−2.22093	−	4.35748i	−0.191147	−	0.375032i
$136$		0			0
$137$	−16.1542	+	6.69127i	−1.38014	+	0.571674i	−0.944520	−	0.328455i	$-0.893472\pi$
$137$	−16.1542	+	6.69127i	−1.38014	+	0.571674i	−0.435623	+	0.900129i	$0.643472\pi$
$138$		0			0
$139$		−	10.9375i		−	0.927704i	−0.885913	−	0.463852i	$-0.846467\pi$
$139$		−	10.9375i		−	0.927704i	0.885913	−	0.463852i	$-0.153533\pi$
$140$		0			0
$141$	1.51941			0.127958
$142$		0			0
$143$	0.562263			0.0470188
$144$		0			0
$145$	−11.8337	+	6.03140i	−0.982732	+	0.500880i
$146$		0			0
$147$	5.95073	+	14.3663i	0.490808	+	1.18491i
$148$		0			0
$149$	7.72747	+	3.20082i	0.633059	+	0.262221i	0.676052	−	0.736854i	$-0.263689\pi$
$149$	7.72747	+	3.20082i	0.633059	+	0.262221i	−0.0429934	+	0.999075i	$0.513689\pi$
$150$		0			0
$151$	3.16216	−	1.30981i	0.257333	−	0.106591i	−0.250288	−	0.968172i	$-0.580525\pi$
$151$	3.16216	−	1.30981i	0.257333	−	0.106591i	0.507621	+	0.861581i	$0.330525\pi$
$152$		0			0
$153$	5.60587	+	2.32203i	0.453208	+	0.187725i
$154$		0			0
$155$	−0.790364	−	10.0266i	−0.0634836	−	0.805356i
$156$		0			0
$157$	−7.86134	−	3.25627i	−0.627403	−	0.259879i	0.0462460	−	0.998930i	$-0.485274\pi$
$157$	−7.86134	−	3.25627i	−0.627403	−	0.259879i	−0.673649	+	0.739051i	$0.735274\pi$
$158$		0			0
$159$	19.2704	−	19.2704i	1.52824	−	1.52824i
$160$		0			0
$161$	2.13418	−	0.884007i	0.168197	−	0.0696695i
$162$		0			0
$163$	11.0842	+	11.0842i	0.868179	+	0.868179i	0.992271	−	0.124092i	$-0.0396017\pi$
$163$	11.0842	+	11.0842i	0.868179	+	0.868179i	−0.124092	+	0.992271i	$0.539602\pi$
$164$		0			0
$165$	−16.2284	+	1.27923i	−1.26338	+	0.0995882i
$166$		0			0
$167$	−4.94477	+	11.9377i	−0.382638	+	0.923769i	0.608816	+	0.793311i	$0.291645\pi$
$167$	−4.94477	+	11.9377i	−0.382638	+	0.923769i	−0.991454	+	0.130458i	$0.958355\pi$
$168$		0			0
$169$	−9.17120	−	9.17120i	−0.705477	−	0.705477i
$170$		0			0
$171$	4.28952	+	10.3558i	0.328028	+	0.791930i
$172$		0			0
$173$			9.88179i			0.751299i	0.926762	+	0.375649i	$0.122580\pi$
$173$			9.88179i			0.751299i	−0.926762	+	0.375649i	$0.877420\pi$
$174$		0			0
$175$	0.291724	−	1.21645i	0.0220523	−	0.0919550i
$176$		0			0
$177$	2.46286	−	5.94588i	0.185120	−	0.446920i
$178$		0			0
$179$	3.46037	−	8.35406i	0.258640	−	0.624412i	−0.740209	−	0.672377i	$-0.765274\pi$
$179$	3.46037	−	8.35406i	0.258640	−	0.624412i	0.998849	+	0.0479647i	$0.0152735\pi$
$180$		0			0
$181$	0.839831	−	2.02753i	0.0624242	−	0.150705i	−0.889589	−	0.456761i	$-0.849009\pi$
$181$	0.839831	−	2.02753i	0.0624242	−	0.150705i	0.952014	+	0.306056i	$0.0990094\pi$
$182$		0			0
$183$	−8.19792	−	19.7915i	−0.606008	−	1.46303i
$184$		0			0
$185$	−6.43659	−	5.49598i	−0.473227	−	0.404073i
$186$		0			0
$187$	−6.88437	+	6.88437i	−0.503435	+	0.503435i
$188$		0			0
$189$	−0.547223			−0.0398046
$190$		0			0
$191$	12.1736	+	5.04247i	0.880850	+	0.364860i	0.776826	−	0.629715i	$-0.216828\pi$
$191$	12.1736	+	5.04247i	0.880850	+	0.364860i	0.104024	+	0.994575i	$0.466828\pi$
$192$		0			0
$193$	−19.3761	−	8.02585i	−1.39472	−	0.577713i	−0.446346	−	0.894860i	$-0.647275\pi$
$193$	−19.3761	−	8.02585i	−1.39472	−	0.577713i	−0.948376	+	0.317147i	$0.897275\pi$
$194$		0			0
$195$	−0.659851	−	0.563424i	−0.0472529	−	0.0403476i
$196$		0			0
$197$		−	12.7028i		−	0.905039i	−0.891754	−	0.452520i	$-0.850525\pi$
$197$		−	12.7028i		−	0.905039i	0.891754	−	0.452520i	$-0.149475\pi$
$198$		0			0
$199$	−4.34463	+	10.4889i	−0.307983	+	0.743536i	0.691788	+	0.722101i	$0.256823\pi$
$199$	−4.34463	+	10.4889i	−0.307983	+	0.743536i	−0.999770	+	0.0214350i	$0.993177\pi$
$200$		0			0
$201$	−25.4734			−1.79675
$202$		0			0
$203$			1.48610i			0.104304i
$204$		0			0
$205$	−14.1789	−	1.98981i	−0.990296	−	0.138974i
$206$		0			0
$207$			18.6896i			1.29902i
$208$		0			0
$209$	−17.9854			−1.24408
$210$		0			0
$211$	9.70134	−	23.4211i	0.667868	−	1.61237i	−0.117304	−	0.993096i	$-0.537425\pi$
$211$	9.70134	−	23.4211i	0.667868	−	1.61237i	0.785171	−	0.619279i	$-0.212575\pi$
$212$		0			0
$213$		−	13.3246i		−	0.912984i
$214$		0			0
$215$	−14.0385	+	1.10661i	−0.957416	+	0.0754699i
$216$		0			0
$217$	−1.03967	−	0.430646i	−0.0705776	−	0.0292342i
$218$		0			0
$219$	−12.1411	−	5.02900i	−0.820418	−	0.339828i
$220$		0			0
$221$	−0.518934			−0.0349073
$222$		0			0
$223$	−5.89652	+	5.89652i	−0.394860	+	0.394860i	−0.876416	−	0.481555i	$-0.840072\pi$
$223$	−5.89652	+	5.89652i	−0.394860	+	0.394860i	0.481555	+	0.876416i	$0.340072\pi$
$224$		0			0
$225$	8.18951	+	5.94692i	0.545967	+	0.396461i
$226$		0			0
$227$	3.33248	+	8.04531i	0.221184	+	0.533986i	0.995051	−	0.0993621i	$-0.0316802\pi$
$227$	3.33248	+	8.04531i	0.221184	+	0.533986i	−0.773867	+	0.633348i	$0.781680\pi$
$228$		0			0
$229$	3.60205	−	8.69612i	0.238030	−	0.574656i	−0.759049	−	0.651034i	$-0.774336\pi$
$229$	3.60205	−	8.69612i	0.238030	−	0.574656i	0.997079	+	0.0763779i	$0.0243355\pi$
$230$		0			0
$231$	−0.697018	+	1.68275i	−0.0458604	+	0.110717i
$232$		0			0
$233$	0.0477648	−	0.115314i	0.00312917	−	0.00755449i	−0.922307	−	0.386457i	$-0.873699\pi$
$233$	0.0477648	−	0.115314i	0.00312917	−	0.00755449i	0.925436	+	0.378903i	$0.123699\pi$
$234$		0			0
$235$	1.35046	−	0.688304i	0.0880942	−	0.0449000i
$236$		0			0
$237$			32.2914i			2.09755i
$238$		0			0
$239$	4.34880	+	10.4989i	0.281300	+	0.679119i	0.999866	−	0.0163397i	$-0.00520132\pi$
$239$	4.34880	+	10.4989i	0.281300	+	0.679119i	−0.718566	+	0.695458i	$0.755201\pi$
$240$		0			0
$241$	1.45287	+	1.45287i	0.0935878	+	0.0935878i	0.752351	−	0.658763i	$-0.228920\pi$
$241$	1.45287	+	1.45287i	0.0935878	+	0.0935878i	−0.658763	+	0.752351i	$0.728920\pi$
$242$		0			0
$243$	6.90319	−	16.6658i	0.442840	−	1.06911i
$244$		0			0
$245$	11.7971	+	10.0731i	0.753686	+	0.643547i
$246$		0			0
$247$	−0.677858	−	0.677858i	−0.0431311	−	0.0431311i
$248$		0			0
$249$	−4.51729	+	1.87112i	−0.286272	+	0.118578i
$250$		0			0
$251$	17.7813	−	17.7813i	1.12235	−	1.12235i	0.130959	−	0.991388i	$-0.458194\pi$
$251$	17.7813	−	17.7813i	1.12235	−	1.12235i	0.991388	−	0.130959i	$-0.0418055\pi$
$252$		0			0
$253$	−27.7056	−	11.4760i	−1.74184	−	0.721493i
$254$		0			0
$255$	14.9778	−	1.18065i	0.937948	−	0.0739353i
$256$		0			0
$257$	−8.67753	−	3.59435i	−0.541290	−	0.224210i	0.0952501	−	0.995453i	$-0.469635\pi$
$257$	−8.67753	−	3.59435i	−0.541290	−	0.224210i	−0.636540	+	0.771244i	$0.719635\pi$
$258$		0			0
$259$	−0.874907	+	0.362398i	−0.0543641	+	0.0225183i
$260$		0			0
$261$	−11.1083	−	4.60121i	−0.687587	−	0.284808i
$262$		0			0
$263$	10.2897	+	24.8414i	0.634487	+	1.53179i	0.833925	+	0.551877i	$0.186088\pi$
$263$	10.2897	+	24.8414i	0.634487	+	1.53179i	−0.199438	+	0.979910i	$0.563912\pi$
$264$		0			0
$265$	8.39795	−	25.8571i	0.515882	−	1.58839i
$266$		0			0
$267$	−14.0933			−0.862495
$268$		0			0
$269$	15.0810			0.919507			0.459753	−	0.888047i	$-0.347938\pi$
$269$	15.0810			0.919507			0.459753	+	0.888047i	$0.347938\pi$
$270$		0			0
$271$		−	2.29249i		−	0.139259i	−0.997573	−	0.0696294i	$-0.977818\pi$
$271$		−	2.29249i		−	0.139259i	0.997573	−	0.0696294i	$-0.0221817\pi$
$272$		0			0
$273$	−0.0896916	+	0.0371515i	−0.00542838	+	0.00224851i
$274$		0			0
$275$	−13.8444	+	8.48858i	−0.834847	+	0.511880i
$276$		0			0
$277$	5.60574	−	5.60574i	0.336816	−	0.336816i	−0.518351	−	0.855168i	$-0.673454\pi$
$277$	5.60574	−	5.60574i	0.336816	−	0.336816i	0.855168	+	0.518351i	$0.173454\pi$
$278$		0			0
$279$	6.43800	−	6.43800i	0.385433	−	0.385433i
$280$		0			0
$281$	5.22285	+	2.16337i	0.311569	+	0.129056i	0.532988	−	0.846123i	$-0.321069\pi$
$281$	5.22285	+	2.16337i	0.311569	+	0.129056i	−0.221419	+	0.975179i	$0.571069\pi$
$282$		0			0
$283$	−15.7011	+	15.7011i	−0.933331	+	0.933331i	−0.997912	−	0.0645813i	$-0.979429\pi$
$283$	−15.7011	+	15.7011i	−0.933331	+	0.933331i	0.0645813	+	0.997912i	$0.479429\pi$
$284$		0			0
$285$	21.1070	+	18.0226i	1.25027	+	1.06757i
$286$		0			0
$287$	−0.918762	+	1.31234i	−0.0542328	+	0.0774651i
$288$		0			0
$289$	−5.66697	+	5.66697i	−0.333351	+	0.333351i
$290$		0			0
$291$		−	16.1978i		−	0.949530i
$292$		0			0
$293$	2.35697	+	5.69024i	0.137696	+	0.332427i	0.977653	−	0.210226i	$-0.0674199\pi$
$293$	2.35697	+	5.69024i	0.137696	+	0.332427i	−0.839957	+	0.542653i	$0.817420\pi$
$294$		0			0
$295$	−0.504523	−	6.40041i	−0.0293745	−	0.372646i
$296$		0			0
$297$	5.02326	+	5.02326i	0.291479	+	0.291479i
$298$		0			0
$299$	−0.611681	−	1.47673i	−0.0353744	−	0.0854014i
$300$		0			0
$301$	−0.602958	+	1.45567i	−0.0347539	+	0.0839034i
$302$		0			0
$303$	−21.7961	+	21.7961i	−1.25215	+	1.25215i
$304$		0			0
$305$	−16.2520	−	13.8770i	−0.930588	−	0.794597i
$306$		0			0
$307$			4.62519i			0.263974i	0.991251	+	0.131987i	$0.0421356\pi$
$307$			4.62519i			0.263974i	−0.991251	+	0.131987i	$0.957864\pi$
$308$		0			0
$309$	4.59171	−	11.0854i	0.261213	−	0.630624i
$310$		0			0
$311$	18.9657	+	7.85583i	1.07544	+	0.445463i	0.848909	−	0.528540i	$-0.177260\pi$
$311$	18.9657	+	7.85583i	1.07544	+	0.445463i	0.226535	+	0.974003i	$0.427260\pi$
$312$		0			0
$313$	−7.42460	−	17.9246i	−0.419663	−	1.01316i	−0.982445	−	0.186551i	$-0.940269\pi$
$313$	−7.42460	−	17.9246i	−0.419663	−	1.01316i	0.562782	−	0.826605i	$-0.309731\pi$
$314$		0			0
$315$	1.00892	−	0.514229i	0.0568463	−	0.0289735i
$316$		0			0
$317$	−10.9861	+	26.5228i	−0.617041	+	1.48967i	0.238082	+	0.971245i	$0.423481\pi$
$317$	−10.9861	+	26.5228i	−0.617041	+	1.48967i	−0.855123	+	0.518424i	$0.826519\pi$
$318$		0			0
$319$	13.6417	−	13.6417i	0.763790	−	0.763790i
$320$		0			0
$321$	−15.0337	+	6.22714i	−0.839097	+	0.347565i
$322$		0			0
$323$	16.5994			0.923617
$324$		0			0
$325$	−0.841712	−	0.201856i	−0.0466898	−	0.0111970i
$326$		0			0
$327$	25.3388	−	25.3388i	1.40124	−	1.40124i
$328$		0			0
$329$		−	0.169594i		−	0.00935001i
$330$		0			0
$331$	−4.22960	−	10.2111i	−0.232480	−	0.561255i	0.763988	−	0.645230i	$-0.223239\pi$
$331$	−4.22960	−	10.2111i	−0.232480	−	0.561255i	−0.996468	+	0.0839747i	$0.973239\pi$
$332$		0			0
$333$		−	7.66180i		−	0.419864i
$334$		0			0
$335$	−22.6408	+	11.5396i	−1.23700	+	0.630476i
$336$		0			0
$337$	8.80269			0.479513			0.239757	−	0.970833i	$-0.422932\pi$
$337$	8.80269			0.479513			0.239757	+	0.970833i	$0.422932\pi$
$338$		0			0
$339$	0.912012	+	2.20179i	0.0495337	+	0.119585i
$340$		0			0
$341$	5.59059	+	13.4969i	0.302747	+	0.730896i
$342$		0			0
$343$	3.22155	−	1.33441i	0.173947	−	0.0720513i
$344$		0			0
$345$	21.0145	+	41.2307i	1.13138	+	2.21979i
$346$		0			0
$347$	−32.9940	+	13.6666i	−1.77121	+	0.733659i	−0.776597	+	0.629998i	$0.783056\pi$
$347$	−32.9940	+	13.6666i	−1.77121	+	0.733659i	−0.994613	+	0.103661i	$0.966944\pi$
$348$		0			0
$349$	−7.82835	−	7.82835i	−0.419042	−	0.419042i	0.465832	−	0.884873i	$-0.345755\pi$
$349$	−7.82835	−	7.82835i	−0.419042	−	0.419042i	−0.884873	+	0.465832i	$0.845755\pi$
$350$		0			0
$351$			0.378646i			0.0202106i
$352$		0			0
$353$	−11.9845	−	11.9845i	−0.637870	−	0.637870i	0.312160	−	0.950030i	$-0.398948\pi$
$353$	−11.9845	−	11.9845i	−0.637870	−	0.637870i	−0.950030	+	0.312160i	$0.898948\pi$
$354$		0			0
$355$	−6.03611	−	11.8429i	−0.320364	−	0.628556i
$356$		0			0
$357$	0.643303	−	1.55307i	0.0340472	−	0.0821973i
$358$		0			0
$359$	32.2936			1.70439			0.852196	−	0.523223i	$-0.175270\pi$
$359$	32.2936			1.70439			0.852196	+	0.523223i	$0.175270\pi$
$360$		0			0
$361$	8.24801	+	8.24801i	0.434106	+	0.434106i
$362$		0			0
$363$	−0.934148	+	0.386937i	−0.0490301	+	0.0203089i
$364$		0			0
$365$	−13.0692	+	1.03020i	−0.684073	+	0.0539232i
$366$		0			0
$367$	12.7327			0.664643			0.332322	−	0.943166i	$-0.392168\pi$
$367$	12.7327			0.664643			0.332322	+	0.943166i	$0.392168\pi$
$368$		0			0
$369$	−6.96486	−	10.9308i	−0.362576	−	0.569034i
$370$		0			0
$371$	−2.15092	−	2.15092i	−0.111670	−	0.111670i
$372$		0			0
$373$	0.724553	+	0.724553i	0.0375160	+	0.0375160i	0.725616	−	0.688100i	$-0.241555\pi$
$373$	0.724553	+	0.724553i	0.0375160	+	0.0375160i	−0.688100	+	0.725616i	$0.741555\pi$
$374$		0			0
$375$	24.7533	+	3.91109i	1.27826	+	0.201968i
$376$		0			0
$377$	1.02829			0.0529597
$378$		0			0
$379$		−	24.6126i		−	1.26427i	−0.774860	−	0.632133i	$-0.782180\pi$
$379$		−	24.6126i		−	1.26427i	0.774860	−	0.632133i	$-0.217820\pi$
$380$		0			0
$381$	12.5748	−	5.20864i	0.644225	−	0.266847i
$382$		0			0
$383$	10.6421	+	25.6923i	0.543785	+	1.31281i	0.922034	+	0.387110i	$0.126526\pi$
$383$	10.6421	+	25.6923i	0.543785	+	1.31281i	−0.378249	+	0.925704i	$0.623474\pi$
$384$		0			0
$385$	0.142785	+	1.81139i	0.00727702	+	0.0923167i
$386$		0			0
$387$	−9.01399	−	9.01399i	−0.458207	−	0.458207i
$388$		0			0
$389$	10.5624	−	10.5624i	0.535533	−	0.535533i	−0.386681	−	0.922214i	$-0.626379\pi$
$389$	10.5624	−	10.5624i	0.535533	−	0.535533i	0.922214	+	0.386681i	$0.126379\pi$
$390$		0			0
$391$	25.5706	+	10.5917i	1.29316	+	0.535644i
$392$		0			0
$393$	1.47092	−	0.609273i	0.0741979	−	0.0307338i
$394$		0			0
$395$	14.6282	+	28.7007i	0.736025	+	1.44409i
$396$		0			0
$397$	20.8168	+	8.62260i	1.04477	+	0.432756i	0.838020	−	0.545639i	$-0.183713\pi$
$397$	20.8168	+	8.62260i	1.04477	+	0.432756i	0.206745	+	0.978395i	$0.433713\pi$
$398$		0			0
$399$	2.86902	−	1.18839i	0.143631	−	0.0594937i
$400$		0			0
$401$	−14.3525	−	14.3525i	−0.716729	−	0.716729i	0.251205	−	0.967934i	$-0.419173\pi$
$401$	−14.3525	−	14.3525i	−0.716729	−	0.716729i	−0.967934	+	0.251205i	$0.919173\pi$
$402$		0			0
$403$	−0.297982	+	0.719392i	−0.0148435	+	0.0358355i
$404$		0			0
$405$	−1.92853	−	24.4655i	−0.0958294	−	1.21570i
$406$		0			0
$407$	11.3579	+	4.70460i	0.562990	+	0.233198i
$408$		0			0
$409$	27.7714			1.37321			0.686603	−	0.727033i	$-0.259101\pi$
$409$	27.7714			1.37321			0.686603	+	0.727033i	$0.259101\pi$
$410$		0			0
$411$	−39.1924			−1.93322
$412$		0			0
$413$	−0.663667	−	0.274900i	−0.0326569	−	0.0135269i
$414$		0			0
$415$	−3.16735	+	3.70942i	−0.155479	+	0.182088i
$416$		0			0
$417$	9.38188	−	22.6499i	0.459432	−	1.10917i
$418$		0			0
$419$	24.0432	+	24.0432i	1.17459	+	1.17459i	0.981104	+	0.193482i	$0.0619780\pi$
$419$	24.0432	+	24.0432i	1.17459	+	1.17459i	0.193482	+	0.981104i	$0.438022\pi$
$420$		0			0
$421$	15.8131	−	6.55002i	0.770685	−	0.319228i	0.0375352	−	0.999295i	$-0.488049\pi$
$421$	15.8131	−	6.55002i	0.770685	−	0.319228i	0.733150	+	0.680067i	$0.238049\pi$
$422$		0			0
$423$	1.26768	+	0.525091i	0.0616368	+	0.0255308i
$424$		0			0
$425$	12.7775	−	7.83442i	0.619799	−	0.380025i
$426$		0			0
$427$	−2.20909	+	0.915035i	−0.106905	+	0.0442816i
$428$		0			0
$429$	1.16436	+	0.482295i	0.0562160	+	0.0232854i
$430$		0			0
$431$	−0.981291	+	0.981291i	−0.0472671	+	0.0472671i	−0.730345	−	0.683078i	$-0.760641\pi$
$431$	−0.981291	+	0.981291i	−0.0472671	+	0.0472671i	0.683078	+	0.730345i	$0.260641\pi$
$432$		0			0
$433$	10.1296	+	10.1296i	0.486798	+	0.486798i	0.907294	−	0.420496i	$-0.138144\pi$
$433$	10.1296	+	10.1296i	0.486798	+	0.486798i	−0.420496	+	0.907294i	$0.638144\pi$
$434$		0			0
$435$	−29.6793	+	2.33952i	−1.42301	+	0.112171i
$436$		0			0
$437$	19.5662	+	47.2370i	0.935978	+	2.25965i
$438$		0			0
$439$	−28.9551	+	11.9936i	−1.38195	+	0.572424i	−0.945003	−	0.327061i	$-0.893942\pi$
$439$	−28.9551	+	11.9936i	−1.38195	+	0.572424i	−0.436951	+	0.899485i	$0.643942\pi$
$440$		0			0
$441$			14.0426i			0.668697i
$442$		0			0
$443$	28.0480			1.33260			0.666300	−	0.745683i	$-0.267877\pi$
$443$	28.0480			1.33260			0.666300	+	0.745683i	$0.267877\pi$
$444$		0			0
$445$	−12.5261	+	6.38435i	−0.593796	+	0.302647i
$446$		0			0
$447$	13.2568	+	13.2568i	0.627027	+	0.627027i
$448$		0			0
$449$	24.9077	+	24.9077i	1.17547	+	1.17547i	0.980886	+	0.194581i	$0.0623348\pi$
$449$	24.9077	+	24.9077i	1.17547	+	1.17547i	0.194581	+	0.980886i	$0.437665\pi$
$450$		0			0
$451$	20.4805	−	3.61289i	0.964391	−	0.170124i
$452$		0			0
$453$	7.67187			0.360456
$454$		0			0
$455$	−0.0628882	+	0.0736512i	−0.00294825	+	0.00345282i
$456$		0			0
$457$	14.8029	−	6.13156i	0.692450	−	0.286822i	−0.00857035	−	0.999963i	$-0.502728\pi$
$457$	14.8029	−	6.13156i	0.692450	−	0.286822i	0.701021	+	0.713141i	$0.252728\pi$
$458$		0			0
$459$	−4.63616	−	4.63616i	−0.216397	−	0.216397i
$460$		0			0
$461$	27.2669			1.26994			0.634972	−	0.772535i	$-0.281012\pi$
$461$	27.2669			1.26994			0.634972	+	0.772535i	$0.281012\pi$
$462$		0			0
$463$	4.94752	−	11.9444i	0.229931	−	0.555102i	−0.766238	−	0.642557i	$-0.777873\pi$
$463$	4.94752	−	11.9444i	0.229931	−	0.555102i	0.996168	+	0.0874552i	$0.0278735\pi$
$464$		0			0
$465$	6.96383	−	21.4415i	0.322940	−	0.994328i
$466$		0			0
$467$	0.962372	+	0.962372i	0.0445333	+	0.0445333i	0.729023	−	0.684489i	$-0.239975\pi$
$467$	0.962372	+	0.962372i	0.0445333	+	0.0445333i	−0.684489	+	0.729023i	$0.739975\pi$
$468$		0			0
$469$			2.84329i			0.131291i
$470$		0			0
$471$	−13.4865	−	13.4865i	−0.621425	−	0.621425i
$472$		0			0
$473$	18.8973	−	7.82751i	0.868897	−	0.359909i
$474$		0			0
$475$	26.9243	+	6.45689i	1.23537	+	0.296262i
$476$		0			0
$477$	22.7373	−	9.41810i	1.04107	−	0.431225i
$478$		0			0
$479$	5.38950	+	13.0114i	0.246253	+	0.594507i	0.997880	−	0.0650815i	$-0.0207307\pi$
$479$	5.38950	+	13.0114i	0.246253	+	0.594507i	−0.751627	+	0.659588i	$0.770731\pi$
$480$		0			0
$481$	0.250758	+	0.605383i	0.0114336	+	0.0276031i
$482$		0			0
$483$	5.17785			0.235600
$484$		0			0
$485$	−7.33769	−	14.3966i	−0.333188	−	0.653717i
$486$		0			0
$487$		−	38.5997i		−	1.74912i	−0.484917	−	0.874560i	$-0.661150\pi$
$487$		−	38.5997i		−	1.74912i	0.484917	−	0.874560i	$-0.338850\pi$
$488$		0			0
$489$	13.4459	+	32.4614i	0.608046	+	1.46795i
$490$		0			0
$491$			30.4438i			1.37391i	0.726699	+	0.686956i	$0.241053\pi$
$491$			30.4438i			1.37391i	−0.726699	+	0.686956i	$0.758947\pi$
$492$		0			0
$493$	−12.5905	+	12.5905i	−0.567045	+	0.567045i
$494$		0			0
$495$	−13.9818	−	4.54106i	−0.628437	−	0.204105i
$496$		0			0
$497$	−1.48726			−0.0667127
$498$		0			0
$499$	15.7034	−	6.50457i	0.702981	−	0.291184i	−0.00241537	−	0.999997i	$-0.500769\pi$
$499$	15.7034	−	6.50457i	0.702981	−	0.291184i	0.705397	+	0.708813i	$0.250769\pi$
$500$		0			0
$501$	−20.4797	+	20.4797i	−0.914967	+	0.914967i
$502$		0			0
$503$	−9.30853	+	22.4728i	−0.415047	+	1.00201i	0.568715	+	0.822534i	$0.307441\pi$
$503$	−9.30853	+	22.4728i	−0.415047	+	1.00201i	−0.983762	+	0.179477i	$0.942559\pi$
$504$		0			0
$505$	−9.49865	+	29.2462i	−0.422685	+	1.30144i
$506$		0			0
$507$	−11.1254	−	26.8590i	−0.494094	−	1.19285i
$508$		0			0
$509$	−17.1288	−	7.09498i	−0.759220	−	0.314479i	−0.0307229	−	0.999528i	$-0.509781\pi$
$509$	−17.1288	−	7.09498i	−0.759220	−	0.314479i	−0.728497	+	0.685049i	$0.759781\pi$
$510$		0			0
$511$	−0.561327	+	1.35516i	−0.0248316	+	0.0599489i
$512$		0			0
$513$		−	12.1120i		−	0.534757i
$514$		0			0
$515$	−0.940620	−	11.9328i	−0.0414487	−	0.525821i
$516$		0			0
$517$	−1.55680	+	1.55680i	−0.0684678	+	0.0684678i
$518$		0			0
$519$	−8.47634	+	20.4637i	−0.372070	+	0.898257i
$520$		0			0
$521$	0.504954	+	1.21907i	0.0221224	+	0.0534083i	0.934555	−	0.355819i	$-0.115798\pi$
$521$	0.504954	+	1.21907i	0.0221224	+	0.0534083i	−0.912432	+	0.409228i	$0.865798\pi$
$522$		0			0
$523$	−24.9780	−	24.9780i	−1.09221	−	1.09221i	−0.995292	−	0.0969193i	$-0.969101\pi$
$523$	−24.9780	−	24.9780i	−1.09221	−	1.09221i	−0.0969193	−	0.995292i	$-0.530899\pi$
$524$		0			0
$525$	1.64756	−	2.26885i	0.0719053	−	0.0990209i
$526$		0			0
$527$	−5.15976	−	12.4568i	−0.224763	−	0.542625i
$528$		0			0
$529$			62.2507i			2.70655i
$530$		0			0
$531$	4.10965	−	4.10965i	0.178343	−	0.178343i
$532$		0			0
$533$	0.908063	+	0.635729i	0.0393326	+	0.0275365i
$534$		0			0
$535$	−10.5410	+	12.3450i	−0.455728	+	0.533723i
$536$		0			0
$537$	14.3318	−	14.3318i	0.618463	−	0.618463i
$538$		0			0
$539$	−20.8169	−	8.62264i	−0.896648	−	0.371404i
$540$		0			0
$541$	10.9802	−	10.9802i	0.472077	−	0.472077i	−0.430509	−	0.902586i	$-0.641666\pi$
$541$	10.9802	−	10.9802i	0.472077	−	0.472077i	0.902586	+	0.430509i	$0.141666\pi$
$542$		0			0
$543$	3.47833	−	3.47833i	0.149269	−	0.149269i
$544$		0			0
$545$	11.0426	−	33.9999i	0.473011	−	1.45639i
$546$		0			0
$547$	13.6892	−	5.67026i	0.585309	−	0.242443i	−0.0703220	−	0.997524i	$-0.522403\pi$
$547$	13.6892	−	5.67026i	0.585309	−	0.242443i	0.655631	+	0.755081i	$0.272403\pi$
$548$		0			0
$549$		−	19.3456i		−	0.825651i
$550$		0			0
$551$	−32.8926			−1.40127
$552$		0			0
$553$	3.60430			0.153270
$554$		0			0
$555$	−8.61489	−	16.9025i	−0.365682	−	0.717471i
$556$		0			0
$557$	−10.0925	−	24.3654i	−0.427633	−	1.03240i	−0.980036	−	0.198820i	$-0.936289\pi$
$557$	−10.0925	−	24.3654i	−0.427633	−	1.03240i	0.552403	−	0.833577i	$-0.313711\pi$
$558$		0			0
$559$	1.00724	+	0.417211i	0.0426016	+	0.0176461i
$560$		0			0
$561$	−20.1617	+	8.35127i	−0.851229	+	0.352591i
$562$		0			0
$563$	−33.6106	−	13.9220i	−1.41652	−	0.586741i	−0.462534	−	0.886601i	$-0.653060\pi$
$563$	−33.6106	−	13.9220i	−1.41652	−	0.586741i	−0.953983	+	0.299861i	$0.903060\pi$
$564$		0			0
$565$	1.80802	+	1.54381i	0.0760641	+	0.0649486i
$566$		0			0
$567$	−2.53686	−	1.05080i	−0.106538	−	0.0441295i
$568$		0			0
$569$	−27.3236	+	27.3236i	−1.14547	+	1.14547i	−0.158031	+	0.987434i	$0.550515\pi$
$569$	−27.3236	+	27.3236i	−1.14547	+	1.14547i	−0.987434	+	0.158031i	$0.949485\pi$
$570$		0			0
$571$	−24.9063	+	10.3165i	−1.04230	+	0.431733i	−0.837136	−	0.546995i	$-0.815772\pi$
$571$	−24.9063	+	10.3165i	−1.04230	+	0.431733i	−0.205160	+	0.978728i	$0.565772\pi$
$572$		0			0
$573$	20.8844	+	20.8844i	0.872457	+	0.872457i
$574$		0			0
$575$	37.3555	+	27.1262i	1.55783	+	1.13124i
$576$		0			0
$577$	−6.91737	+	16.7000i	−0.287974	+	0.695230i	−0.999976	−	0.00694702i	$-0.997789\pi$
$577$	−6.91737	+	16.7000i	−0.287974	+	0.695230i	0.712002	+	0.702177i	$0.247789\pi$
$578$		0			0
$579$	−33.2406	−	33.2406i	−1.38143	−	1.38143i
$580$		0			0
$581$	0.208851	+	0.504211i	0.00866460	+	0.0209182i
$582$		0			0
$583$			39.4889i			1.63546i
$584$		0			0
$585$	−0.355816	−	0.698114i	−0.0147112	−	0.0288635i
$586$		0			0
$587$	3.04789	−	7.35826i	0.125800	−	0.303708i	−0.848414	−	0.529333i	$-0.822442\pi$
$587$	3.04789	−	7.35826i	0.125800	−	0.303708i	0.974214	+	0.225625i	$0.0724423\pi$
$588$		0			0
$589$	9.53172	−	23.0116i	0.392748	−	0.948177i
$590$		0			0
$591$	10.8962	−	26.3057i	0.448208	−	1.08207i
$592$		0			0
$593$	12.0588	+	29.1125i	0.495195	+	1.19551i	0.952044	+	0.305962i	$0.0989782\pi$
$593$	12.0588	+	29.1125i	0.495195	+	1.19551i	−0.456848	+	0.889545i	$0.651022\pi$
$594$		0			0
$595$	−0.131782	−	1.67179i	−0.00540254	−	0.0685369i
$596$		0			0
$597$	−17.9942	+	17.9942i	−0.736452	+	0.736452i
$598$		0			0
$599$	−6.24271			−0.255070			−0.127535	−	0.991834i	$-0.540707\pi$
$599$	−6.24271			−0.255070			−0.127535	+	0.991834i	$0.540707\pi$
$600$		0			0
$601$	6.78171	+	2.80907i	0.276632	+	0.114585i	0.516686	−	0.856175i	$-0.327165\pi$
$601$	6.78171	+	2.80907i	0.276632	+	0.114585i	−0.240055	+	0.970759i	$0.577165\pi$
$602$		0			0
$603$	−21.2530	−	8.80329i	−0.865490	−	0.358498i
$604$		0			0
$605$	−0.654989	+	0.767086i	−0.0266291	+	0.0311865i
$606$		0			0
$607$		−	12.0268i		−	0.488151i	−0.969756	−	0.244076i	$-0.921515\pi$
$607$		−	12.0268i		−	0.488151i	0.969756	−	0.244076i	$-0.0784845\pi$
$608$		0			0
$609$	−1.27474	+	3.07749i	−0.0516549	+	0.124706i
$610$		0			0
$611$	−0.117349			−0.00474743
$612$		0			0
$613$			4.93404i			0.199284i	0.995023	+	0.0996421i	$0.0317698\pi$
$613$			4.93404i			0.199284i	−0.995023	+	0.0996421i	$0.968230\pi$
$614$		0			0
$615$	−27.6555	−	16.2829i	−1.11518	−	0.656588i
$616$		0			0
$617$			20.9156i			0.842031i	0.907053	+	0.421016i	$0.138326\pi$
$617$			20.9156i			0.842031i	−0.907053	+	0.421016i	$0.861674\pi$
$618$		0			0
$619$	−25.4726			−1.02383			−0.511916	−	0.859036i	$-0.671064\pi$
$619$	−25.4726			−1.02383			−0.511916	+	0.859036i	$0.671064\pi$
$620$		0			0
$621$	7.72833	−	18.6578i	0.310127	−	0.748714i
$622$		0			0
$623$			1.57306i			0.0630235i
$624$		0			0
$625$	23.7726	−	7.73724i	0.950903	−	0.309489i
$626$		0			0
$627$	−37.2452	−	15.4274i	−1.48743	−	0.616113i
$628$		0			0
$629$	−10.4826	−	4.34205i	−0.417970	−	0.173129i
$630$		0			0
$631$	1.59357			0.0634390			0.0317195	−	0.999497i	$-0.489902\pi$
$631$	1.59357			0.0634390			0.0317195	+	0.999497i	$0.489902\pi$
$632$		0			0
$633$	40.1800	−	40.1800i	1.59701	−	1.59701i
$634$		0			0
$635$	8.81694	−	10.3259i	0.349890	−	0.409771i
$636$		0			0
$637$	−0.459592	−	1.10955i	−0.0182097	−	0.0439621i
$638$		0			0
$639$	4.60481	−	11.1170i	0.182163	−	0.439781i
$640$		0			0
$641$	7.96987	−	19.2410i	0.314791	−	0.759973i	−0.684723	−	0.728803i	$-0.740077\pi$
$641$	7.96987	−	19.2410i	0.314791	−	0.759973i	0.999514	−	0.0311693i	$-0.00992311\pi$
$642$		0			0
$643$	−17.2129	+	41.5557i	−0.678812	+	1.63880i	0.0873714	+	0.996176i	$0.472153\pi$
$643$	−17.2129	+	41.5557i	−0.678812	+	1.63880i	−0.766184	+	0.642622i	$0.777847\pi$
$644$		0			0
$645$	−30.0208	−	9.75022i	−1.18207	−	0.383915i
$646$		0			0
$647$		−	22.9558i		−	0.902484i	−0.892402	−	0.451242i	$-0.850981\pi$
$647$		−	22.9558i		−	0.902484i	0.892402	−	0.451242i	$-0.149019\pi$
$648$		0			0
$649$	3.56871	+	8.61562i	0.140084	+	0.338193i
$650$		0			0
$651$	−1.78361	−	1.78361i	−0.0699051	−	0.0699051i
$652$		0			0
$653$	15.5738	−	37.5984i	0.609449	−	1.47134i	−0.254151	−	0.967164i	$-0.581796\pi$
$653$	15.5738	−	37.5984i	0.609449	−	1.47134i	0.863601	−	0.504176i	$-0.168204\pi$
$654$		0			0
$655$	1.03135	−	1.20786i	0.0402981	−	0.0471949i
$656$		0			0
$657$	−8.39162	−	8.39162i	−0.327388	−	0.327388i
$658$		0			0
$659$	−27.0533	+	11.2058i	−1.05385	+	0.436517i	−0.841263	−	0.540626i	$-0.818187\pi$
$659$	−27.0533	+	11.2058i	−1.05385	+	0.436517i	−0.212582	+	0.977143i	$0.568187\pi$
$660$		0			0
$661$	−19.5944	+	19.5944i	−0.762133	+	0.762133i	−0.976708	−	0.214575i	$-0.931163\pi$
$661$	−19.5944	+	19.5944i	−0.762133	+	0.762133i	0.214575	+	0.976708i	$0.431163\pi$
$662$		0			0
$663$	−1.07463	−	0.445128i	−0.0417353	−	0.0172873i
$664$		0			0
$665$	2.01164	−	2.35592i	0.0780082	−	0.0913588i
$666$		0			0
$667$	−50.6693	−	20.9879i	−1.96192	−	0.812655i
$668$		0			0
$669$	−17.2687	+	7.15293i	−0.667646	+	0.276548i
$670$		0			0
$671$	28.6781	+	11.8788i	1.10710	+	0.458578i
$672$		0			0
$673$	7.24261	+	17.4852i	0.279182	+	0.674006i	0.999813	−	0.0193129i	$-0.00614788\pi$
$673$	7.24261	+	17.4852i	0.279182	+	0.674006i	−0.720631	+	0.693319i	$0.756148\pi$
$674$		0			0
$675$	−5.71648	−	9.32324i	−0.220027	−	0.358852i
$676$		0			0
$677$	31.3949			1.20660			0.603302	−	0.797512i	$-0.293851\pi$
$677$	31.3949			1.20660			0.603302	+	0.797512i	$0.293851\pi$
$678$		0			0
$679$	−1.80796			−0.0693832
$680$		0			0
$681$			19.5191i			0.747975i
$682$		0			0
$683$	−37.6121	+	15.5794i	−1.43919	+	0.596130i	−0.959601	−	0.281365i	$-0.909213\pi$
$683$	−37.6121	+	15.5794i	−1.43919	+	0.596130i	−0.479585	+	0.877495i	$0.659213\pi$
$684$		0			0
$685$	−34.8343	+	17.7544i	−1.33095	+	0.678362i
$686$		0			0
$687$	14.9186	−	14.9186i	0.569181	−	0.569181i
$688$		0			0
$689$	−1.48831	+	1.48831i	−0.0567000	+	0.0567000i
$690$		0			0
$691$	−13.0122	−	5.38984i	−0.495008	−	0.205039i	0.121191	−	0.992629i	$-0.461329\pi$
$691$	−13.0122	−	5.38984i	−0.495008	−	0.205039i	−0.616200	+	0.787590i	$0.711329\pi$
$692$		0			0
$693$	−1.16308	+	1.16308i	−0.0441816	+	0.0441816i
$694$		0			0
$695$	−1.92190	−	24.3813i	−0.0729017	−	0.924835i
$696$		0			0
$697$	−18.9022	+	3.33447i	−0.715973	+	0.126302i
$698$		0			0
$699$	0.197827	−	0.197827i	0.00748251	−	0.00748251i
$700$		0			0
$701$			18.8015i			0.710124i	0.934843	+	0.355062i	$0.115540\pi$
$701$			18.8015i			0.710124i	−0.934843	+	0.355062i	$0.884460\pi$
$702$		0			0
$703$	−8.02114	−	19.3648i	−0.302523	−	0.730356i
$704$		0			0
$705$	3.38701	−	0.266986i	0.127562	−	0.0100553i
$706$		0			0
$707$	2.43284	+	2.43284i	0.0914962	+	0.0914962i
$708$		0			0
$709$	−8.12773	−	19.6221i	−0.305243	−	0.736923i	−0.999846	−	0.0175293i	$-0.994420\pi$
$709$	−8.12773	−	19.6221i	−0.305243	−	0.736923i	0.694603	−	0.719393i	$-0.255580\pi$
$710$		0			0
$711$	−11.1595	+	26.9414i	−0.418514	+	1.01038i
$712$		0			0
$713$	29.3662	−	29.3662i	1.09977	−	1.09977i
$714$		0			0
$715$	1.25337	−	0.0987991i	0.0468734	−	0.00369488i
$716$		0			0
$717$			25.4720i			0.951268i
$718$		0			0
$719$	−5.69223	+	13.7423i	−0.212284	+	0.512500i	−0.993774	−	0.111419i	$-0.964460\pi$
$719$	−5.69223	+	13.7423i	−0.212284	+	0.512500i	0.781489	+	0.623919i	$0.214460\pi$
$720$		0			0
$721$	−1.23733	−	0.512517i	−0.0460804	−	0.0190871i
$722$		0			0
$723$	1.76244	+	4.25492i	0.0655460	+	0.158242i
$724$		0			0
$725$	−25.3192	+	15.5243i	−0.940332	+	0.576557i
$726$		0			0
$727$	4.97936	−	12.0212i	0.184674	−	0.445843i	−0.804245	−	0.594298i	$-0.797430\pi$
$727$	4.97936	−	12.0212i	0.184674	−	0.445843i	0.988919	+	0.148455i	$0.0474300\pi$
$728$		0			0
$729$	5.30898	−	5.30898i	0.196629	−	0.196629i
$730$		0			0
$731$	−17.4410	+	7.22430i	−0.645078	+	0.267200i
$732$		0			0
$733$	43.4827			1.60607			0.803036	−	0.595931i	$-0.203217\pi$
$733$	43.4827			1.60607			0.803036	+	0.595931i	$0.203217\pi$
$734$		0			0
$735$	15.7895	+	30.9791i	0.582404	+	1.14268i
$736$		0			0
$737$	26.1001	−	26.1001i	0.961410	−	0.961410i
$738$		0			0
$739$			1.05826i			0.0389289i	0.999811	+	0.0194644i	$0.00619612\pi$
$739$			1.05826i			0.0389289i	−0.999811	+	0.0194644i	$0.993804\pi$
$740$		0			0
$741$	−0.822293	−	1.98519i	−0.0302077	−	0.0729278i
$742$		0			0
$743$		−	15.2753i		−	0.560397i	−0.959942	−	0.280198i	$-0.909600\pi$
$743$		−	15.2753i		−	0.560397i	0.959942	−	0.280198i	$-0.0904003\pi$
$744$		0			0
$745$	17.7881	+	5.77728i	0.651707	+	0.211663i
$746$		0			0
$747$	−4.41552			−0.161555
$748$		0			0
$749$	0.695061	+	1.67803i	0.0253970	+	0.0613137i
$750$		0			0
$751$	2.06773	+	4.99193i	0.0754524	+	0.182158i	0.957105	−	0.289740i	$-0.0935689\pi$
$751$	2.06773	+	4.99193i	0.0754524	+	0.182158i	−0.881653	+	0.471898i	$0.843569\pi$
$752$		0			0
$753$	52.0748	−	21.5701i	1.89771	−	0.786057i
$754$		0			0
$755$	6.81878	−	3.47541i	0.248161	−	0.126483i
$756$		0			0
$757$	47.6790	−	19.7493i	1.73292	−	0.717800i	0.733655	−	0.679522i	$-0.237813\pi$
$757$	47.6790	−	19.7493i	1.73292	−	0.717800i	0.999267	−	0.0382776i	$-0.0121871\pi$
$758$		0			0
$759$	−47.5303	−	47.5303i	−1.72524	−	1.72524i
$760$		0			0
$761$			23.3761i			0.847382i	0.905807	+	0.423691i	$0.139266\pi$
$761$			23.3761i			0.847382i	−0.905807	+	0.423691i	$0.860734\pi$
$762$		0			0
$763$	−2.82827	−	2.82827i	−0.102390	−	0.102390i
$764$		0			0
$765$	12.9044	+	4.19111i	0.466558	+	0.151530i
$766$		0			0
$767$	−0.190214	+	0.459218i	−0.00686824	+	0.0165814i
$768$		0			0
$769$	0.970937			0.0350129			0.0175065	−	0.999847i	$-0.494427\pi$
$769$	0.970937			0.0350129			0.0175065	+	0.999847i	$0.494427\pi$
$770$		0			0
$771$	−14.8867	−	14.8867i	−0.536132	−	0.536132i
$772$		0			0
$773$	−11.6334	+	4.81869i	−0.418423	+	0.173316i	−0.581954	−	0.813222i	$-0.697712\pi$
$773$	−11.6334	+	4.81869i	−0.418423	+	0.173316i	0.163531	+	0.986538i	$0.447712\pi$
$774$		0			0
$775$	−3.52368	−	22.2120i	−0.126574	−	0.797877i
$776$		0			0
$777$	−2.12266			−0.0761498
$778$		0			0
$779$	−29.0467	−	20.3354i	−1.04071	−	0.728592i
$780$		0			0
$781$	13.6524	+	13.6524i	0.488521	+	0.488521i
$782$		0			0
$783$	9.18677	+	9.18677i	0.328308	+	0.328308i
$784$		0			0
$785$	−18.0963	−	5.87736i	−0.645885	−	0.209772i
$786$		0			0
$787$	−26.6939			−0.951535			−0.475768	−	0.879571i	$-0.657830\pi$
$787$	−26.6939			−0.951535			−0.475768	+	0.879571i	$0.657830\pi$
$788$		0			0
$789$			60.2690i			2.14563i
$790$		0			0
$791$	0.245759	−	0.101797i	0.00873820	−	0.00361948i
$792$		0			0
$793$	0.633150	+	1.52856i	0.0224838	+	0.0542807i
$794$		0			0
$795$	39.5705	−	46.3427i	1.40342	−	1.64361i
$796$		0			0
$797$	−37.5630	−	37.5630i	−1.33055	−	1.33055i	−0.904877	−	0.425672i	$-0.860038\pi$
$797$	−37.5630	−	37.5630i	−1.33055	−	1.33055i	−0.425672	−	0.904877i	$-0.639962\pi$
$798$		0			0
$799$	1.43682	−	1.43682i	0.0508312	−	0.0508312i
$800$		0			0
$801$	−11.7583	−	4.87047i	−0.415461	−	0.172089i
$802$		0			0
$803$	17.5925	−	7.28706i	0.620827	−	0.257155i
$804$		0			0
$805$	4.60208	−	2.34560i	0.162202	−	0.0826715i
$806$		0			0
$807$	31.2306	+	12.9361i	1.09937	+	0.455373i
$808$		0			0
$809$	34.9150	−	14.4623i	1.22755	−	0.508466i	0.327744	−	0.944766i	$-0.393712\pi$
$809$	34.9150	−	14.4623i	1.22755	−	0.508466i	0.899801	+	0.436300i	$0.143712\pi$
$810$		0			0
$811$	−1.42303	−	1.42303i	−0.0499693	−	0.0499693i	0.681681	−	0.731650i	$-0.261249\pi$
$811$	−1.42303	−	1.42303i	−0.0499693	−	0.0499693i	−0.731650	+	0.681681i	$0.761249\pi$
$812$		0			0
$813$	1.96644	−	4.74740i	0.0689660	−	0.166499i
$814$		0			0
$815$	26.6560	+	22.7606i	0.933718	+	0.797270i
$816$		0			0
$817$	−32.2191	−	13.3456i	−1.12720	−	0.466903i
$818$		0			0
$819$	−0.0876708			−0.00306347
$820$		0			0
$821$	−16.8467			−0.587954			−0.293977	−	0.955813i	$-0.594979\pi$
$821$	−16.8467			−0.587954			−0.293977	+	0.955813i	$0.594979\pi$
$822$		0			0
$823$	29.2851	+	12.1303i	1.02081	+	0.422835i	0.829389	−	0.558672i	$-0.188689\pi$
$823$	29.2851	+	12.1303i	1.02081	+	0.422835i	0.191426	+	0.981507i	$0.438689\pi$
$824$		0			0
$825$	−35.9509	+	5.70322i	−1.25165	+	0.198561i
$826$		0			0
$827$	−5.30999	+	12.8195i	−0.184647	+	0.445776i	−0.988914	−	0.148492i	$-0.952558\pi$
$827$	−5.30999	+	12.8195i	−0.184647	+	0.445776i	0.804267	+	0.594268i	$0.202558\pi$
$828$		0			0
$829$	32.0783	+	32.0783i	1.11413	+	1.11413i	0.992586	+	0.121541i	$0.0387834\pi$
$829$	32.0783	+	32.0783i	1.11413	+	1.11413i	0.121541	+	0.992586i	$0.461217\pi$
$830$		0			0
$831$	16.4171	−	6.80019i	0.569503	−	0.235896i
$832$		0			0
$833$	19.2127	+	7.95816i	0.665680	+	0.275734i
$834$		0			0
$835$	−8.92499	+	27.4799i	−0.308862	+	0.950981i
$836$		0			0
$837$	−9.08922	+	3.76488i	−0.314169	+	0.130133i
$838$		0			0
$839$	18.0712	+	7.48535i	0.623888	+	0.258423i	0.672154	−	0.740412i	$-0.265369\pi$
$839$	18.0712	+	7.48535i	0.623888	+	0.258423i	−0.0482655	+	0.998835i	$0.515369\pi$
$840$		0			0
$841$	4.44249	−	4.44249i	0.153189	−	0.153189i
$842$		0			0
$843$	8.96004	+	8.96004i	0.308600	+	0.308600i
$844$		0			0
$845$	−22.0555	−	18.8325i	−0.758733	−	0.647857i
$846$		0			0
$847$	0.0431891	+	0.104268i	0.00148400	+	0.00358268i
$848$		0			0
$849$	−45.9825	+	19.0466i	−1.57811	+	0.653677i
$850$		0			0
$851$		−	34.9485i		−	1.19802i
$852$		0			0
$853$	−42.6895			−1.46166			−0.730830	−	0.682560i	$-0.760867\pi$
$853$	−42.6895			−1.46166			−0.730830	+	0.682560i	$0.760867\pi$
$854$		0			0
$855$	11.3817	+	22.3310i	0.389246	+	0.763703i
$856$		0			0
$857$	0.314016	+	0.314016i	0.0107266	+	0.0107266i	0.712450	−	0.701723i	$-0.247586\pi$
$857$	0.314016	+	0.314016i	0.0107266	+	0.0107266i	−0.701723	+	0.712450i	$0.747586\pi$
$858$		0			0
$859$	15.4113	+	15.4113i	0.525825	+	0.525825i	0.919325	−	0.393500i	$-0.128736\pi$
$859$	15.4113	+	15.4113i	0.525825	+	0.525825i	−0.393500	+	0.919325i	$0.628736\pi$
$860$		0			0
$861$	−3.02831	+	1.92957i	−0.103205	+	0.0657597i
$862$		0			0
$863$	−28.6000			−0.973556			−0.486778	−	0.873526i	$-0.661828\pi$
$863$	−28.6000			−0.973556			−0.486778	+	0.873526i	$0.661828\pi$
$864$		0			0
$865$	1.73640	+	22.0280i	0.0590392	+	0.748975i
$866$		0			0
$867$	−16.5964	+	6.87446i	−0.563644	+	0.233469i
$868$		0			0
$869$	−33.0859	−	33.0859i	−1.12236	−	1.12236i
$870$		0			0
$871$	1.96739			0.0666623
$872$		0			0
$873$	5.59775	−	13.5142i	0.189455	−	0.457385i
$874$		0			0
$875$	0.436548	−	2.76292i	0.0147580	−	0.0934036i
$876$		0			0
$877$	0.740530	+	0.740530i	0.0250059	+	0.0250059i	0.719499	−	0.694493i	$-0.244371\pi$
$877$	0.740530	+	0.740530i	0.0250059	+	0.0250059i	−0.694493	+	0.719499i	$0.744371\pi$
$878$		0			0
$879$			13.8054i			0.465644i
$880$		0			0
$881$	17.1395	+	17.1395i	0.577445	+	0.577445i	0.934199	−	0.356753i	$-0.116116\pi$
$881$	17.1395	+	17.1395i	0.577445	+	0.577445i	−0.356753	+	0.934199i	$0.616116\pi$
$882$		0			0
$883$	15.9689	−	6.61454i	0.537397	−	0.222597i	−0.0974428	−	0.995241i	$-0.531066\pi$
$883$	15.9689	−	6.61454i	0.537397	−	0.222597i	0.634839	+	0.772644i	$0.281066\pi$
$884$		0			0
$885$	4.44531	−	13.6870i	0.149427	−	0.460085i
$886$		0			0
$887$	−1.98882	+	0.823794i	−0.0667779	+	0.0276603i	−0.415822	−	0.909446i	$-0.636506\pi$
$887$	−1.98882	+	0.823794i	−0.0667779	+	0.0276603i	0.349044	+	0.937106i	$0.386506\pi$
$888$		0			0
$889$	−0.581378	−	1.40357i	−0.0194988	−	0.0470743i
$890$		0			0
$891$	13.6413	+	32.9331i	0.457002	+	1.10330i
$892$		0			0
$893$	3.75371			0.125613
$894$		0			0
$895$	6.24574	−	19.2305i	0.208772	−	0.642806i
$896$		0			0
$897$		−	3.58276i		−	0.119625i
$898$		0			0
$899$	10.2243	+	24.6837i	0.341000	+	0.823247i
$900$		0			0
$901$		−	36.4458i		−	1.21419i
$902$		0			0
$903$	−2.49727	+	2.49727i	−0.0831039	+	0.0831039i
$904$		0			0
$905$	1.51584	−	4.66725i	0.0503883	−	0.155145i
$906$		0			0
$907$	12.7735			0.424139			0.212069	−	0.977255i	$-0.431980\pi$
$907$	12.7735			0.424139			0.212069	+	0.977255i	$0.431980\pi$
$908$		0			0
$909$	−25.7175	+	10.6525i	−0.852994	+	0.353322i
$910$		0			0
$911$	−27.7653	+	27.7653i	−0.919905	+	0.919905i	−0.997022	−	0.0771166i	$-0.975429\pi$
$911$	−27.7653	+	27.7653i	−0.919905	+	0.919905i	0.0771166	+	0.997022i	$0.475429\pi$
$912$		0			0
$913$	2.71127	−	6.54559i	0.0897300	−	0.216627i
$914$		0			0
$915$	−21.7521	−	42.6778i	−0.719103	−	1.41089i
$916$		0			0
$917$	−0.0680059	−	0.164181i	−0.00224575	−	0.00542172i
$918$		0			0
$919$	46.1563	+	19.1186i	1.52256	+	0.630664i	0.978102	−	0.208126i	$-0.0667366\pi$
$919$	46.1563	+	19.1186i	1.52256	+	0.630664i	0.544455	+	0.838790i	$0.316737\pi$
$920$		0			0
$921$	−3.96737	+	9.57807i	−0.130729	+	0.315608i
$922$		0			0
$923$			1.02910i			0.0338731i
$924$		0			0
$925$	−15.3139	−	11.1204i	−0.503517	−	0.365636i
$926$		0			0
$927$	7.66193	−	7.66193i	0.251651	−	0.251651i
$928$		0			0
$929$	3.83864	−	9.26730i	0.125942	−	0.304050i	−0.848315	−	0.529492i	$-0.822383\pi$
$929$	3.83864	−	9.26730i	0.125942	−	0.304050i	0.974257	+	0.225442i	$0.0723825\pi$
$930$		0			0
$931$	14.7013	+	35.4920i	0.481814	+	1.16320i
$932$		0			0
$933$	32.5365	+	32.5365i	1.06520	+	1.06520i
$934$		0			0
$935$	−14.1366	+	16.5560i	−0.462317	+	0.541440i
$936$		0			0
$937$	−4.70130	−	11.3499i	−0.153585	−	0.370786i	0.828295	−	0.560293i	$-0.189311\pi$
$937$	−4.70130	−	11.3499i	−0.153585	−	0.370786i	−0.981880	+	0.189506i	$0.939311\pi$
$938$		0			0
$939$		−	43.4877i		−	1.41917i
$940$		0			0
$941$	−13.5648	+	13.5648i	−0.442201	+	0.442201i	−0.892751	−	0.450550i	$-0.851228\pi$
$941$	−13.5648	+	13.5648i	−0.442201	+	0.442201i	0.450550	+	0.892751i	$0.351228\pi$
$942$		0			0
$943$	−31.7695	−	49.8596i	−1.03456	−	1.62365i
$944$		0			0
$945$	−1.21984	+	0.0961563i	−0.0396815	+	0.00312796i
$946$		0			0
$947$	22.0861	−	22.0861i	0.717703	−	0.717703i	−0.250432	−	0.968134i	$-0.580573\pi$
$947$	22.0861	−	22.0861i	0.717703	−	0.717703i	0.968134	+	0.250432i	$0.0805725\pi$
$948$		0			0
$949$	0.937692	+	0.388405i	0.0304388	+	0.0126082i
$950$		0			0
$951$	−45.5011	+	45.5011i	−1.47548	+	1.47548i
$952$		0			0
$953$	17.9119	−	17.9119i	0.580222	−	0.580222i	−0.354742	−	0.934964i	$-0.615431\pi$
$953$	17.9119	−	17.9119i	0.580222	−	0.580222i	0.934964	+	0.354742i	$0.115431\pi$
$954$		0			0
$955$	28.0228	+	9.10133i	0.906798	+	0.294512i
$956$		0			0
$957$	39.9515	−	16.5484i	1.29145	−	0.534935i
$958$		0			0
$959$			4.37458i			0.141262i
$960$		0			0
$961$	10.7685			0.347371
$962$		0			0
$963$	−14.6949			−0.473538
$964$		0			0
$965$	−44.6026	−	14.4861i	−1.43581	−	0.466325i
$966$		0			0
$967$	−9.37236	−	22.6269i	−0.301395	−	0.727632i	−0.999927	−	0.0120533i	$-0.996163\pi$
$967$	−9.37236	−	22.6269i	−0.301395	−	0.727632i	0.698532	−	0.715578i	$-0.253837\pi$
$968$		0			0
$969$	34.3749	+	14.2386i	1.10428	+	0.457409i
$970$		0			0
$971$	41.7787	−	17.3053i	1.34074	−	0.555353i	0.407041	−	0.913410i	$-0.366561\pi$
$971$	41.7787	−	17.3053i	1.34074	−	0.555353i	0.933700	+	0.358057i	$0.116561\pi$
$972$		0			0
$973$	−2.52813	−	1.04719i	−0.0810481	−	0.0335712i
$974$		0			0
$975$	−1.56991	−	1.14001i	−0.0502774	−	0.0365096i
$976$		0			0
$977$	−6.10784	−	2.52995i	−0.195407	−	0.0809403i	0.282834	−	0.959169i	$-0.408725\pi$
$977$	−6.10784	−	2.52995i	−0.195407	−	0.0809403i	−0.478241	+	0.878229i	$0.658725\pi$
$978$		0			0
$979$	14.4400	−	14.4400i	0.461505	−	0.461505i
$980$		0			0
$981$	29.8975	−	12.3840i	0.954555	−	0.395390i
$982$		0			0
$983$	20.7699	+	20.7699i	0.662458	+	0.662458i	0.955959	−	0.293501i	$-0.0948204\pi$
$983$	20.7699	+	20.7699i	0.662458	+	0.662458i	−0.293501	+	0.955959i	$0.594820\pi$
$984$		0			0
$985$	−2.23210	−	28.3166i	−0.0711206	−	0.902241i
$986$		0			0
$987$	0.145473	−	0.351203i	0.00463046	−	0.0111789i
$988$		0			0
$989$	−41.1163	−	41.1163i	−1.30742	−	1.30742i
$990$		0			0
$991$	0.446779	+	1.07862i	0.0141924	+	0.0342635i	0.930817	−	0.365486i	$-0.119097\pi$
$991$	0.446779	+	1.07862i	0.0141924	+	0.0342635i	−0.916624	+	0.399749i	$0.869097\pi$
$992$		0			0
$993$		−	24.7738i		−	0.786172i
$994$		0			0
$995$	−7.84178	+	24.1447i	−0.248601	+	0.765439i
$996$		0			0
$997$	−12.1635	+	29.3653i	−0.385222	+	0.930007i	0.605716	+	0.795681i	$0.292887\pi$
$997$	−12.1635	+	29.3653i	−0.385222	+	0.930007i	−0.990937	+	0.134326i	$0.957113\pi$
$998$		0			0
$999$	−3.16823	+	7.64877i	−0.100238	+	0.241996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.y.a.137.17	yes	84
5.3	odd	4		820.2.x.a.793.5	yes	84
41.3	odd	8		820.2.x.a.577.5	✓	84
205.3	even	8	inner	820.2.y.a.413.17	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.5	✓	84	41.3	odd	8
820.2.x.a.793.5	yes	84	5.3	odd	4
820.2.y.a.137.17	yes	84	1.1	even	1	trivial
820.2.y.a.413.17	yes	84	205.3	even	8	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.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.07085 + 0.857774i) q^{3} +(2.22915 - 0.175717i) q^{5} +(0.0957430 - 0.231144i) q^{7} +(1.43132 + 1.43132i) q^{9} +(-3.00068 + 1.24292i) q^{11} +(-0.159938 - 0.0662484i) q^{13} +(4.76697 + 1.54823i) q^{15} +(2.76943 - 1.14714i) q^{17} +(5.11603 + 2.11913i) q^{19} +(0.396538 - 0.396538i) q^{21} +(6.52881 + 6.52881i) q^{23} +(4.93825 - 0.783399i) q^{25} +(-0.837022 - 2.02075i) q^{27} +(-5.48777 + 2.27311i) q^{29} -4.49794i q^{31} -7.28009 q^{33} +(0.172810 - 0.532079i) q^{35} +(-2.67648 - 2.67648i) q^{37} +(-0.274381 - 0.274381i) q^{39} +(-6.25145 - 1.38541i) q^{41} -6.29767 q^{43} +(3.44214 + 2.93913i) q^{45} +(0.626265 - 0.259407i) q^{47} +(4.90549 + 4.90549i) q^{49} +6.71907 q^{51} +(4.65277 - 11.2328i) q^{53} +(-6.47056 + 3.29793i) q^{55} +(8.77679 + 8.77679i) q^{57} -2.87123i q^{59} +(-6.75796 - 6.75796i) q^{61} +(0.467880 - 0.193802i) q^{63} +(-0.368167 - 0.119574i) q^{65} +(-10.4995 + 4.34904i) q^{67} +(7.91994 + 19.1204i) q^{69} +(-2.27489 - 5.49206i) q^{71} -5.86285 q^{73} +(10.8983 + 2.61360i) q^{75} +0.812589i q^{77} +(5.51307 + 13.3097i) q^{79} -10.9752i q^{81} +(-1.54246 + 1.54246i) q^{83} +(5.97192 - 3.04378i) q^{85} -13.3142 q^{87} +(-5.80891 + 2.40613i) q^{89} +(-0.0306259 + 0.0306259i) q^{91} +(3.85822 - 9.31456i) q^{93} +(11.7768 + 3.82489i) q^{95} +(-2.76542 - 6.67632i) q^{97} +(-6.07395 - 2.51591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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