LMFDB - Embedded newform 820.2.x.a.273.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] 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, 6, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (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			273.7
Character	$\chi$	$=$	820.273
Dual form			820.2.x.a.817.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03141 - 0.427224i) q^{3} +(0.661175 - 2.13608i) q^{5} +(1.80577 - 4.35952i) q^{7} +(-1.24003 - 1.24003i) q^{9} +(-0.166356 - 0.401618i) q^{11} +(0.389100 + 0.161171i) q^{13} +(-1.59453 + 1.92071i) q^{15} +(-2.80926 + 1.16364i) q^{17} +(-0.838825 + 2.02510i) q^{19} +(-3.72499 + 3.72499i) q^{21} +(2.60933 - 2.60933i) q^{23} +(-4.12569 - 2.82465i) q^{25} +(2.03088 + 4.90299i) q^{27} +(0.255143 + 0.615970i) q^{29} +7.81564i q^{31} +0.485304i q^{33} +(-8.11836 - 6.73968i) q^{35} +(-3.42297 + 3.42297i) q^{37} +(-0.332466 - 0.332466i) q^{39} +(-1.54273 - 6.21450i) q^{41} -0.269822i q^{43} +(-3.46869 + 1.82893i) q^{45} +(4.37677 - 1.81292i) q^{47} +(-10.7948 - 10.7948i) q^{49} +3.39464 q^{51} +(1.93975 - 4.68297i) q^{53} +(-0.967879 + 0.0898093i) q^{55} +(1.73035 - 1.73035i) q^{57} -3.56822i q^{59} +(-2.86341 - 2.86341i) q^{61} +(-7.64516 + 3.16673i) q^{63} +(0.601537 - 0.724588i) q^{65} +(12.6703 - 5.24823i) q^{67} +(-3.80606 + 1.57652i) q^{69} +(0.878331 - 0.363817i) q^{71} -4.54719i q^{73} +(3.04853 + 4.67597i) q^{75} -2.05126 q^{77} +(-12.8604 + 5.32695i) q^{79} -0.663629i q^{81} +(-2.66851 - 2.66851i) q^{83} +(0.628204 + 6.77019i) q^{85} -0.744321i q^{87} +(-3.99780 - 9.65153i) q^{89} +(1.40525 - 1.40525i) q^{91} +(3.33903 - 8.06114i) q^{93} +(3.77117 + 3.13075i) q^{95} +(3.02699 + 7.30780i) q^{97} +(-0.291733 + 0.704305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.03141	−	0.427224i	−0.595485	−	0.246658i	0.0645231	−	0.997916i	$-0.479447\pi$
$3$	−1.03141	−	0.427224i	−0.595485	−	0.246658i	−0.660009	+	0.751258i	$0.729447\pi$
$4$		0			0
$5$	0.661175	−	2.13608i	0.295687	−	0.955285i
$5$	0.661175	−	2.13608i	0.295687	−	0.955285i
$6$		0			0
$7$	1.80577	−	4.35952i	0.682517	−	1.64774i	−0.0768194	−	0.997045i	$-0.524476\pi$
$7$	1.80577	−	4.35952i	0.682517	−	1.64774i	0.759337	−	0.650698i	$-0.225524\pi$
$8$		0			0
$9$	−1.24003	−	1.24003i	−0.413344	−	0.413344i
$10$		0			0
$11$	−0.166356	−	0.401618i	−0.0501581	−	0.121092i	0.896814	−	0.442407i	$-0.145875\pi$
$11$	−0.166356	−	0.401618i	−0.0501581	−	0.121092i	−0.946973	+	0.321315i	$0.895875\pi$
$12$		0			0
$13$	0.389100	+	0.161171i	0.107917	+	0.0447007i	0.435989	−	0.899952i	$-0.356399\pi$
$13$	0.389100	+	0.161171i	0.107917	+	0.0447007i	−0.328072	+	0.944653i	$0.606399\pi$
$14$		0			0
$15$	−1.59453	+	1.92071i	−0.411706	+	0.495925i
$16$		0			0
$17$	−2.80926	+	1.16364i	−0.681347	+	0.282223i	−0.696390	−	0.717664i	$-0.745211\pi$
$17$	−2.80926	+	1.16364i	−0.681347	+	0.282223i	0.0150431	+	0.999887i	$0.495211\pi$
$18$		0			0
$19$	−0.838825	+	2.02510i	−0.192440	+	0.464590i	−0.990419	−	0.138094i	$-0.955902\pi$
$19$	−0.838825	+	2.02510i	−0.192440	+	0.464590i	0.797980	+	0.602685i	$0.205902\pi$
$20$		0			0
$21$	−3.72499	+	3.72499i	−0.812858	+	0.812858i
$22$		0			0
$23$	2.60933	−	2.60933i	0.544082	−	0.544082i	−0.380641	−	0.924723i	$-0.624297\pi$
$23$	2.60933	−	2.60933i	0.544082	−	0.544082i	0.924723	+	0.380641i	$0.124297\pi$
$24$		0			0
$25$	−4.12569	−	2.82465i	−0.825139	−	0.564930i
$26$		0			0
$27$	2.03088	+	4.90299i	0.390844	+	0.943581i
$28$		0			0
$29$	0.255143	+	0.615970i	0.0473789	+	0.114383i	0.945797	−	0.324758i	$-0.105283\pi$
$29$	0.255143	+	0.615970i	0.0473789	+	0.114383i	−0.898418	+	0.439141i	$0.855283\pi$
$30$		0			0
$31$			7.81564i			1.40373i	0.712310	+	0.701865i	$0.247649\pi$
$31$			7.81564i			1.40373i	−0.712310	+	0.701865i	$0.752351\pi$
$32$		0			0
$33$			0.485304i			0.0844806i
$34$		0			0
$35$	−8.11836	−	6.73968i	−1.37225	−	1.13921i
$36$		0			0
$37$	−3.42297	+	3.42297i	−0.562733	+	0.562733i	−0.930083	−	0.367350i	$-0.880265\pi$
$37$	−3.42297	+	3.42297i	−0.562733	+	0.562733i	0.367350	+	0.930083i	$0.380265\pi$
$38$		0			0
$39$	−0.332466	−	0.332466i	−0.0532372	−	0.0532372i
$40$		0			0
$41$	−1.54273	−	6.21450i	−0.240934	−	0.970541i
$41$	−1.54273	−	6.21450i	−0.240934	−	0.970541i
$42$		0			0
$43$		−	0.269822i		−	0.0411474i	−0.999788	−	0.0205737i	$-0.993451\pi$
$43$		−	0.269822i		−	0.0411474i	0.999788	−	0.0205737i	$-0.00654928\pi$
$44$		0			0
$45$	−3.46869	+	1.82893i	−0.517082	+	0.272641i
$46$		0			0
$47$	4.37677	−	1.81292i	0.638418	−	0.264441i	−0.0399071	−	0.999203i	$-0.512706\pi$
$47$	4.37677	−	1.81292i	0.638418	−	0.264441i	0.678325	+	0.734762i	$0.262706\pi$
$48$		0			0
$49$	−10.7948	−	10.7948i	−1.54212	−	1.54212i
$50$		0			0
$51$	3.39464			0.475345
$52$		0			0
$53$	1.93975	−	4.68297i	0.266445	−	0.643256i	−0.732866	−	0.680373i	$-0.761818\pi$
$53$	1.93975	−	4.68297i	0.266445	−	0.643256i	0.999311	+	0.0371176i	$0.0118176\pi$
$54$		0			0
$55$	−0.967879	+	0.0898093i	−0.130509	+	0.0121099i
$56$		0			0
$57$	1.73035	−	1.73035i	0.229190	−	0.229190i
$58$		0			0
$59$		−	3.56822i		−	0.464542i	−0.972651	−	0.232271i	$-0.925384\pi$
$59$		−	3.56822i		−	0.464542i	0.972651	−	0.232271i	$-0.0746156\pi$
$60$		0			0
$61$	−2.86341	−	2.86341i	−0.366623	−	0.366623i	0.499621	−	0.866244i	$-0.333473\pi$
$61$	−2.86341	−	2.86341i	−0.366623	−	0.366623i	−0.866244	+	0.499621i	$0.833473\pi$
$62$		0			0
$63$	−7.64516	+	3.16673i	−0.963199	+	0.398970i
$64$		0			0
$65$	0.601537	−	0.724588i	0.0746115	−	0.0898741i
$66$		0			0
$67$	12.6703	−	5.24823i	1.54793	−	0.641173i	0.564988	−	0.825099i	$-0.308881\pi$
$67$	12.6703	−	5.24823i	1.54793	−	0.641173i	0.982940	+	0.183926i	$0.0588806\pi$
$68$		0			0
$69$	−3.80606	+	1.57652i	−0.458195	+	0.189791i
$70$		0			0
$71$	0.878331	−	0.363817i	0.104239	−	0.0431771i	−0.329955	−	0.943997i	$-0.607033\pi$
$71$	0.878331	−	0.363817i	0.104239	−	0.0431771i	0.434193	+	0.900820i	$0.357033\pi$
$72$		0			0
$73$		−	4.54719i		−	0.532208i	−0.963944	−	0.266104i	$-0.914264\pi$
$73$		−	4.54719i		−	0.532208i	0.963944	−	0.266104i	$-0.0857365\pi$
$74$		0			0
$75$	3.04853	+	4.67597i	0.352014	+	0.539935i
$76$		0			0
$77$	−2.05126			−0.233763
$78$		0			0
$79$	−12.8604	+	5.32695i	−1.44691	+	0.599329i	−0.961462	−	0.274938i	$-0.911343\pi$
$79$	−12.8604	+	5.32695i	−1.44691	+	0.599329i	−0.485446	+	0.874267i	$0.661343\pi$
$80$		0			0
$81$		−	0.663629i		−	0.0737366i
$82$		0			0
$83$	−2.66851	−	2.66851i	−0.292907	−	0.292907i	0.545320	−	0.838228i	$-0.316408\pi$
$83$	−2.66851	−	2.66851i	−0.292907	−	0.292907i	−0.838228	+	0.545320i	$0.816408\pi$
$84$		0			0
$85$	0.628204	+	6.77019i	0.0681383	+	0.734330i
$86$		0			0
$87$		−	0.744321i		−	0.0797996i
$88$		0			0
$89$	−3.99780	−	9.65153i	−0.423765	−	1.02306i	−0.981227	−	0.192857i	$-0.938225\pi$
$89$	−3.99780	−	9.65153i	−0.423765	−	1.02306i	0.557461	−	0.830203i	$-0.311775\pi$
$90$		0			0
$91$	1.40525	−	1.40525i	0.147310	−	0.147310i
$92$		0			0
$93$	3.33903	−	8.06114i	0.346242	−	0.835901i
$94$		0			0
$95$	3.77117	+	3.13075i	0.386914	+	0.321208i
$96$		0			0
$97$	3.02699	+	7.30780i	0.307344	+	0.741995i	0.999789	+	0.0205242i	$0.00653350\pi$
$97$	3.02699	+	7.30780i	0.307344	+	0.741995i	−0.692445	+	0.721471i	$0.743466\pi$
$98$		0			0
$99$	−0.291733	+	0.704305i	−0.0293202	+	0.0707853i
$100$		0			0
$101$	−14.1968	−	5.88049i	−1.41263	−	0.585130i	−0.459632	−	0.888109i	$-0.652019\pi$
$101$	−14.1968	−	5.88049i	−1.41263	−	0.585130i	−0.952997	+	0.302979i	$0.902019\pi$
$102$		0			0
$103$	7.22797			0.712193			0.356096	−	0.934449i	$-0.384107\pi$
$103$	7.22797			0.712193			0.356096	+	0.934449i	$0.384107\pi$
$104$		0			0
$105$	5.49401	+	10.4197i	0.536160	+	1.01686i
$106$		0			0
$107$	9.23838	+	9.23838i	0.893108	+	0.893108i	0.994814	−	0.101706i	$-0.0324302\pi$
$107$	9.23838	+	9.23838i	0.893108	+	0.893108i	−0.101706	+	0.994814i	$0.532430\pi$
$108$		0			0
$109$	7.54137	+	3.12374i	0.722332	+	0.299200i	0.713397	−	0.700760i	$-0.247156\pi$
$109$	7.54137	+	3.12374i	0.722332	+	0.299200i	0.00893549	+	0.999960i	$0.497156\pi$
$110$		0			0
$111$	4.99287	−	2.06811i	0.473902	−	0.196297i
$112$		0			0
$113$	0.904176	−	0.904176i	0.0850577	−	0.0850577i	−0.663298	−	0.748356i	$-0.730844\pi$
$113$	0.904176	−	0.904176i	0.0850577	−	0.0850577i	0.748356	+	0.663298i	$0.230844\pi$
$114$		0			0
$115$	−3.84851	−	7.29896i	−0.358876	−	0.680631i
$116$		0			0
$117$	−0.282640	−	0.682354i	−0.0261301	−	0.0630836i
$118$		0			0
$119$			14.3483i			1.31531i
$120$		0			0
$121$	7.64455	−	7.64455i	0.694959	−	0.694959i
$122$		0			0
$123$	−1.06379	+	7.06879i	−0.0959190	+	0.637372i
$124$		0			0
$125$	−8.76149	+	6.94523i	−0.783652	+	0.621201i
$126$		0			0
$127$	12.6063	+	12.6063i	1.11862	+	1.11862i	0.991943	+	0.126682i	$0.0404326\pi$
$127$	12.6063	+	12.6063i	1.11862	+	1.11862i	0.126682	+	0.991943i	$0.459567\pi$
$128$		0			0
$129$	−0.115274	+	0.278297i	−0.0101493	+	0.0245027i
$130$		0			0
$131$	9.99646	−	9.99646i	0.873395	−	0.873395i	−0.119446	−	0.992841i	$-0.538112\pi$
$131$	9.99646	−	9.99646i	0.873395	−	0.873395i	0.992841	+	0.119446i	$0.0381119\pi$
$132$		0			0
$133$	7.31374	+	7.31374i	0.634182	+	0.634182i
$134$		0			0
$135$	11.8160	−	1.09640i	1.01696	−	0.0943631i
$136$		0			0
$137$	−17.8478	+	7.39279i	−1.52484	+	0.631609i	−0.978554	−	0.205991i	$-0.933958\pi$
$137$	−17.8478	+	7.39279i	−1.52484	+	0.631609i	−0.546285	+	0.837599i	$0.683958\pi$
$138$		0			0
$139$			15.6004i			1.32321i	0.749852	+	0.661605i	$0.230125\pi$
$139$			15.6004i			1.32321i	−0.749852	+	0.661605i	$0.769875\pi$
$140$		0			0
$141$	−5.28877			−0.445395
$142$		0			0
$143$		−	0.183081i		−	0.0153100i
$144$		0			0
$145$	1.48446	−	0.137742i	0.123277	−	0.0114389i
$146$		0			0
$147$	6.52210	+	15.7457i	0.537933	+	1.29869i
$148$		0			0
$149$	1.72600	−	4.16693i	0.141399	−	0.341368i	−0.837276	−	0.546780i	$-0.815853\pi$
$149$	1.72600	−	4.16693i	0.141399	−	0.341368i	0.978676	+	0.205412i	$0.0658534\pi$
$150$		0			0
$151$	−5.48465	−	13.2411i	−0.446334	−	1.07755i	−0.973685	−	0.227899i	$-0.926814\pi$
$151$	−5.48465	−	13.2411i	−0.446334	−	1.07755i	0.527350	−	0.849648i	$-0.323186\pi$
$152$		0			0
$153$	4.92652	+	2.04063i	0.398286	+	0.164975i
$154$		0			0
$155$	16.6949	+	5.16751i	1.34096	+	0.415064i
$156$		0			0
$157$	15.5756	+	6.45163i	1.24307	+	0.514896i	0.904673	−	0.426107i	$-0.140115\pi$
$157$	15.5756	+	6.45163i	1.24307	+	0.514896i	0.338397	+	0.941003i	$0.390115\pi$
$158$		0			0
$159$	−4.00136	+	4.00136i	−0.317329	+	0.317329i
$160$		0			0
$161$	−6.66356	−	16.0872i	−0.525162	−	1.26785i
$162$		0			0
$163$	13.1064	−	13.1064i	1.02657	−	1.02657i	0.0269349	−	0.999637i	$-0.491425\pi$
$163$	13.1064	−	13.1064i	1.02657	−	1.02657i	0.999637	−	0.0269349i	$-0.00857468\pi$
$164$		0			0
$165$	1.03665	+	0.320871i	0.0807031	+	0.0249798i
$166$		0			0
$167$	4.60706	−	11.1224i	0.356505	−	0.860680i	−0.639281	−	0.768973i	$-0.720768\pi$
$167$	4.60706	−	11.1224i	0.356505	−	0.860680i	0.995786	−	0.0917065i	$-0.0292322\pi$
$168$		0			0
$169$	−9.06697	−	9.06697i	−0.697459	−	0.697459i
$170$		0			0
$171$	3.55136	−	1.47102i	0.271579	−	0.112492i
$172$		0			0
$173$	18.3401			1.39437			0.697185	−	0.716891i	$-0.254436\pi$
$173$	18.3401			1.39437			0.697185	+	0.716891i	$0.254436\pi$
$174$		0			0
$175$	−19.7642	+	12.8854i	−1.49403	+	0.974042i
$176$		0			0
$177$	−1.52443	+	3.68030i	−0.114583	+	0.276628i
$178$		0			0
$179$	−2.77798	−	1.15068i	−0.207636	−	0.0860058i	0.276441	−	0.961031i	$-0.410845\pi$
$179$	−2.77798	−	1.15068i	−0.207636	−	0.0860058i	−0.484078	+	0.875025i	$0.660845\pi$
$180$		0			0
$181$	17.3480	+	7.18576i	1.28946	+	0.534113i	0.918825	−	0.394664i	$-0.129139\pi$
$181$	17.3480	+	7.18576i	1.28946	+	0.534113i	0.370638	+	0.928777i	$0.379139\pi$
$182$		0			0
$183$	1.73004	+	4.17668i	0.127888	+	0.308749i
$184$		0			0
$185$	5.04856	+	9.57493i	0.371178	+	0.703963i
$186$		0			0
$187$	0.934673	+	0.934673i	0.0683501	+	0.0683501i
$188$		0			0
$189$	25.0420			1.82154
$190$		0			0
$191$	3.14818	−	7.60038i	0.227794	−	0.549944i	−0.768114	−	0.640313i	$-0.778805\pi$
$191$	3.14818	−	7.60038i	0.227794	−	0.549944i	0.995908	+	0.0903690i	$0.0288046\pi$
$192$		0			0
$193$	−14.9160	−	6.17841i	−1.07368	−	0.444732i	−0.225390	−	0.974269i	$-0.572366\pi$
$193$	−14.9160	−	6.17841i	−1.07368	−	0.444732i	−0.848287	+	0.529537i	$0.822366\pi$
$194$		0			0
$195$	−0.929994	+	0.490357i	−0.0665983	+	0.0351152i
$196$		0			0
$197$	−13.0916			−0.932741			−0.466370	−	0.884590i	$-0.654439\pi$
$197$	−13.0916			−0.932741			−0.466370	+	0.884590i	$0.654439\pi$
$198$		0			0
$199$	−5.47635	−	2.26838i	−0.388208	−	0.160801i	0.180038	−	0.983660i	$-0.442378\pi$
$199$	−5.47635	−	2.26838i	−0.388208	−	0.160801i	−0.568246	+	0.822858i	$0.692378\pi$
$200$		0			0
$201$	−15.3105			−1.07992
$202$		0			0
$203$	3.14606			0.220810
$204$		0			0
$205$	−14.2947	−	0.813468i	−0.998385	−	0.0568151i
$206$		0			0
$207$	−6.47130			−0.449786
$208$		0			0
$209$	0.952860			0.0659107
$210$		0			0
$211$	−8.81195	−	3.65003i	−0.606640	−	0.251278i	0.0581512	−	0.998308i	$-0.481479\pi$
$211$	−8.81195	−	3.65003i	−0.606640	−	0.251278i	−0.664791	+	0.747029i	$0.731479\pi$
$212$		0			0
$213$	−1.06135			−0.0727227
$214$		0			0
$215$	−0.576361	−	0.178399i	−0.0393075	−	0.0121667i
$216$		0			0
$217$	34.0724	+	14.1133i	2.31299	+	0.958071i
$218$		0			0
$219$	−1.94267	+	4.69002i	−0.131273	+	0.316922i
$220$		0			0
$221$	−1.28063			−0.0861444
$222$		0			0
$223$	−10.6232	−	10.6232i	−0.711379	−	0.711379i	0.255444	−	0.966824i	$-0.417778\pi$
$223$	−10.6232	−	10.6232i	−0.711379	−	0.711379i	−0.966824	+	0.255444i	$0.917778\pi$
$224$		0			0
$225$	1.61334	+	8.61865i	0.107556	+	0.574577i
$226$		0			0
$227$	0.505854	+	1.22124i	0.0335747	+	0.0810565i	0.939778	−	0.341787i	$-0.111032\pi$
$227$	0.505854	+	1.22124i	0.0335747	+	0.0810565i	−0.906203	+	0.422843i	$0.861032\pi$
$228$		0			0
$229$	15.4663	+	6.40634i	1.02204	+	0.423343i	0.829833	−	0.558011i	$-0.188435\pi$
$229$	15.4663	+	6.40634i	1.02204	+	0.423343i	0.192207	+	0.981354i	$0.438435\pi$
$230$		0			0
$231$	2.11569	+	0.876348i	0.139202	+	0.0576595i
$232$		0			0
$233$	−2.50981	+	6.05922i	−0.164423	+	0.396953i	−0.984520	−	0.175272i	$-0.943919\pi$
$233$	−2.50981	+	6.05922i	−0.164423	+	0.396953i	0.820097	+	0.572225i	$0.193919\pi$
$234$		0			0
$235$	−0.978729	−	10.5478i	−0.0638452	−	0.688063i
$236$		0			0
$237$	15.5402			1.00944
$238$		0			0
$239$	16.3221	−	6.76083i	1.05579	−	0.437322i	0.213834	−	0.976870i	$-0.431405\pi$
$239$	16.3221	−	6.76083i	1.05579	−	0.437322i	0.841955	+	0.539548i	$0.181405\pi$
$240$		0			0
$241$	5.17206	+	5.17206i	0.333162	+	0.333162i	0.853786	−	0.520624i	$-0.174301\pi$
$241$	5.17206	+	5.17206i	0.333162	+	0.333162i	−0.520624	+	0.853786i	$0.674301\pi$
$242$		0			0
$243$	5.80913	−	14.0245i	0.372656	−	0.899672i
$244$		0			0
$245$	−30.1959	+	15.9214i	−1.92915	+	1.01718i
$246$		0			0
$247$	−0.652774	+	0.652774i	−0.0415350	+	0.0415350i
$248$		0			0
$249$	1.61228	+	3.89239i	0.102174	+	0.246670i
$250$		0			0
$251$	7.75236	−	7.75236i	0.489324	−	0.489324i	−0.418769	−	0.908093i	$-0.637538\pi$
$251$	7.75236	−	7.75236i	0.489324	−	0.489324i	0.908093	+	0.418769i	$0.137538\pi$
$252$		0			0
$253$	−1.48203	−	0.613876i	−0.0931743	−	0.0385940i
$254$		0			0
$255$	2.24445	−	7.25123i	0.140553	−	0.454090i
$256$		0			0
$257$	−3.27835	−	1.35794i	−0.204498	−	0.0847058i	0.278084	−	0.960557i	$-0.410301\pi$
$257$	−3.27835	−	1.35794i	−0.204498	−	0.0847058i	−0.482582	+	0.875851i	$0.660301\pi$
$258$		0			0
$259$	8.74140	+	21.1036i	0.543164	+	1.31131i
$260$		0			0
$261$	0.447437	−	1.08021i	0.0276956	−	0.0668632i
$262$		0			0
$263$	−10.8637	−	26.2274i	−0.669887	−	1.61725i	−0.781797	−	0.623533i	$-0.785697\pi$
$263$	−10.8637	−	26.2274i	−0.669887	−	1.61725i	0.111910	−	0.993718i	$-0.464303\pi$
$264$		0			0
$265$	−8.72070	−	7.23973i	−0.535708	−	0.444733i
$266$		0			0
$267$			11.6627i			0.713743i
$268$		0			0
$269$	−7.78640			−0.474745			−0.237373	−	0.971419i	$-0.576286\pi$
$269$	−7.78640			−0.474745			−0.237373	+	0.971419i	$0.576286\pi$
$270$		0			0
$271$			30.9889i			1.88244i	0.337794	+	0.941220i	$0.390319\pi$
$271$			30.9889i			1.88244i	−0.337794	+	0.941220i	$0.609681\pi$
$272$		0			0
$273$	−2.04975	+	0.849035i	−0.124057	+	0.0513859i
$274$		0			0
$275$	−0.448098	+	2.12685i	−0.0270213	+	0.128254i
$276$		0			0
$277$	−13.7728	−	13.7728i	−0.827529	−	0.827529i	0.159645	−	0.987174i	$-0.448965\pi$
$277$	−13.7728	−	13.7728i	−0.827529	−	0.827529i	−0.987174	+	0.159645i	$0.948965\pi$
$278$		0			0
$279$	9.69165	−	9.69165i	0.580224	−	0.580224i
$280$		0			0
$281$	−0.621868	+	1.50132i	−0.0370976	+	0.0895614i	−0.941342	−	0.337453i	$-0.890435\pi$
$281$	−0.621868	+	1.50132i	−0.0370976	+	0.0895614i	0.904245	+	0.427014i	$0.140435\pi$
$282$		0			0
$283$	15.8621	+	15.8621i	0.942902	+	0.942902i	0.998456	−	0.0555536i	$-0.0176924\pi$
$283$	15.8621	+	15.8621i	0.942902	+	0.942902i	−0.0555536	+	0.998456i	$0.517692\pi$
$284$		0			0
$285$	−2.55210	−	4.84022i	−0.151173	−	0.286710i
$286$		0			0
$287$	−29.8780	−	4.49639i	−1.76364	−	0.265413i
$288$		0			0
$289$	−5.48290	+	5.48290i	−0.322523	+	0.322523i
$290$		0			0
$291$		−	8.83055i		−	0.517656i
$292$		0			0
$293$	−1.23733	−	2.98718i	−0.0722857	−	0.174513i	0.883607	−	0.468229i	$-0.155108\pi$
$293$	−1.23733	−	2.98718i	−0.0722857	−	0.174513i	−0.955893	+	0.293716i	$0.905108\pi$
$294$		0			0
$295$	−7.62200	−	2.35922i	−0.443770	−	0.137359i
$296$		0			0
$297$	1.63128	−	1.63128i	0.0946564	−	0.0946564i
$298$		0			0
$299$	1.43584	−	0.594743i	0.0830366	−	0.0343949i
$300$		0			0
$301$	−1.17629	−	0.487236i	−0.0678003	−	0.0280838i
$302$		0			0
$303$	12.1304	+	12.1304i	0.696873	+	0.696873i
$304$		0			0
$305$	−8.00971	+	4.22327i	−0.458634	+	0.241824i
$306$		0			0
$307$	10.6833			0.609729			0.304864	−	0.952396i	$-0.401389\pi$
$307$	10.6833			0.609729			0.304864	+	0.952396i	$0.401389\pi$
$308$		0			0
$309$	−7.45501	−	3.08797i	−0.424101	−	0.175668i
$310$		0			0
$311$	−6.62338	+	15.9903i	−0.375578	+	0.906725i	0.617206	+	0.786802i	$0.288265\pi$
$311$	−6.62338	+	15.9903i	−0.375578	+	0.906725i	−0.992783	+	0.119923i	$0.961735\pi$
$312$		0			0
$313$	0.899901	+	2.17255i	0.0508654	+	0.122800i	0.947270	−	0.320437i	$-0.103830\pi$
$313$	0.899901	+	2.17255i	0.0508654	+	0.122800i	−0.896404	+	0.443237i	$0.853830\pi$
$314$		0			0
$315$	1.70960	+	18.4244i	0.0963251	+	1.03810i
$316$		0			0
$317$	10.1117	−	24.4119i	0.567932	−	1.37111i	−0.335363	−	0.942089i	$-0.608859\pi$
$317$	10.1117	−	24.4119i	0.567932	−	1.37111i	0.903295	−	0.429020i	$-0.141141\pi$
$318$		0			0
$319$	0.204940	−	0.204940i	0.0114744	−	0.0114744i
$320$		0			0
$321$	−5.58171	−	13.4754i	−0.311541	−	0.752126i
$322$		0			0
$323$		−	6.66513i		−	0.370858i
$324$		0			0
$325$	−1.15006	−	1.76401i	−0.0637938	−	0.0978498i
$326$		0			0
$327$	−6.44372	−	6.44372i	−0.356338	−	0.356338i
$328$		0			0
$329$		−	22.3543i		−	1.23243i
$330$		0			0
$331$	−13.5314	+	5.60490i	−0.743755	+	0.308073i	−0.722190	−	0.691694i	$-0.756865\pi$
$331$	−13.5314	+	5.60490i	−0.743755	+	0.308073i	−0.0215641	+	0.999767i	$0.506865\pi$
$332$		0			0
$333$	8.48919			0.465205
$334$		0			0
$335$	−2.83333	−	30.5349i	−0.154801	−	1.66830i
$336$		0			0
$337$			6.33503i			0.345091i	0.985002	+	0.172545i	$0.0551992\pi$
$337$			6.33503i			0.345091i	−0.985002	+	0.172545i	$0.944801\pi$
$338$		0			0
$339$	−1.31886	+	0.546291i	−0.0716308	+	0.0296705i
$340$		0			0
$341$	3.13890	−	1.30018i	0.169981	−	0.0704084i
$342$		0			0
$343$	−36.0367	+	14.9269i	−1.94580	+	0.805976i
$344$		0			0
$345$	0.851106	+	9.17240i	0.0458220	+	0.493826i
$346$		0			0
$347$	2.14069	−	0.886701i	0.114918	−	0.0476006i	−0.324484	−	0.945891i	$-0.605191\pi$
$347$	2.14069	−	0.886701i	0.114918	−	0.0476006i	0.439402	+	0.898291i	$0.355191\pi$
$348$		0			0
$349$	3.51068	+	3.51068i	0.187922	+	0.187922i	0.794797	−	0.606875i	$-0.207577\pi$
$349$	3.51068	+	3.51068i	0.187922	+	0.187922i	−0.606875	+	0.794797i	$0.707577\pi$
$350$		0			0
$351$			2.23507i			0.119299i
$352$		0			0
$353$	24.6843	−	24.6843i	1.31381	−	1.31381i	0.395228	−	0.918583i	$-0.370665\pi$
$353$	24.6843	−	24.6843i	1.31381	−	1.31381i	0.918583	−	0.395228i	$-0.129335\pi$
$354$		0			0
$355$	−0.196411	−	2.11673i	−0.0104244	−	0.112345i
$356$		0			0
$357$	6.12994	−	14.7990i	0.324431	−	0.783246i
$358$		0			0
$359$	−9.98691			−0.527089			−0.263544	−	0.964647i	$-0.584892\pi$
$359$	−9.98691			−0.527089			−0.263544	+	0.964647i	$0.584892\pi$
$360$		0			0
$361$	10.0376	+	10.0376i	0.528296	+	0.528296i
$362$		0			0
$363$	−11.1506	+	4.61874i	−0.585256	+	0.242421i
$364$		0			0
$365$	−9.71317	−	3.00649i	−0.508411	−	0.157367i
$366$		0			0
$367$		−	8.75431i		−	0.456971i	−0.973547	−	0.228486i	$-0.926623\pi$
$367$		−	8.75431i		−	0.456971i	0.973547	−	0.228486i	$-0.0733774\pi$
$368$		0			0
$369$	−5.79314	+	9.61922i	−0.301579	+	0.500756i
$370$		0			0
$371$	−16.9128	−	16.9128i	−0.878067	−	0.878067i
$372$		0			0
$373$	18.4099	−	18.4099i	0.953228	−	0.953228i	−0.0457261	−	0.998954i	$-0.514560\pi$
$373$	18.4099	−	18.4099i	0.953228	−	0.953228i	0.998954	+	0.0457261i	$0.0145602\pi$
$374$		0			0
$375$	12.0039	−	3.42027i	0.619877	−	0.176622i
$376$		0			0
$377$			0.280796i			0.0144617i
$378$		0			0
$379$		−	8.68435i		−	0.446085i	−0.974809	−	0.223042i	$-0.928401\pi$
$379$		−	8.68435i		−	0.446085i	0.974809	−	0.223042i	$-0.0715988\pi$
$380$		0			0
$381$	−7.61654	−	18.3879i	−0.390207	−	0.942043i
$382$		0			0
$383$	10.3419	+	24.9675i	0.528445	+	1.27578i	0.932541	+	0.361063i	$0.117586\pi$
$383$	10.3419	+	24.9675i	0.528445	+	1.27578i	−0.404096	+	0.914717i	$0.632414\pi$
$384$		0			0
$385$	−1.35624	+	4.38166i	−0.0691205	+	0.223310i
$386$		0			0
$387$	−0.334587	+	0.334587i	−0.0170080	+	0.0170080i
$388$		0			0
$389$	−19.7477	+	19.7477i	−1.00125	+	1.00125i	−0.00124717	+	0.999999i	$0.500397\pi$
$389$	−19.7477	+	19.7477i	−1.00125	+	1.00125i	−0.999999	+	0.00124717i	$0.999603\pi$
$390$		0			0
$391$	−4.29398	+	10.3666i	−0.217156	+	0.524261i
$392$		0			0
$393$	−14.5812	+	6.03973i	−0.735524	+	0.304664i
$394$		0			0
$395$	2.87583	+	30.9929i	0.144699	+	1.55942i
$396$		0			0
$397$	−0.215919	−	0.0894366i	−0.0108367	−	0.00448869i	0.377259	−	0.926108i	$-0.376867\pi$
$397$	−0.215919	−	0.0894366i	−0.0108367	−	0.00448869i	−0.388095	+	0.921619i	$0.626867\pi$
$398$		0			0
$399$	−4.41886	−	10.6681i	−0.221220	−	0.534072i
$400$		0			0
$401$	−19.7095	−	19.7095i	−0.984246	−	0.984246i	0.0156322	−	0.999878i	$-0.495024\pi$
$401$	−19.7095	−	19.7095i	−0.984246	−	0.984246i	−0.999878	+	0.0156322i	$0.995024\pi$
$402$		0			0
$403$	−1.25965	+	3.04107i	−0.0627477	+	0.151486i
$404$		0			0
$405$	−1.41757	−	0.438775i	−0.0704395	−	0.0218029i
$406$		0			0
$407$	1.94416	+	0.805296i	0.0963682	+	0.0399170i
$408$		0			0
$409$	−10.1126			−0.500034			−0.250017	−	0.968241i	$-0.580436\pi$
$409$	−10.1126			−0.500034			−0.250017	+	0.968241i	$0.580436\pi$
$410$		0			0
$411$	21.5668			1.06381
$412$		0			0
$413$	−15.5557	−	6.44338i	−0.765446	−	0.317058i
$414$		0			0
$415$	−7.46452	+	3.93581i	−0.366419	+	0.193201i
$416$		0			0
$417$	6.66488	−	16.0905i	0.326381	−	0.787953i
$418$		0			0
$419$	24.9878	+	24.9878i	1.22073	+	1.22073i	0.967371	+	0.253363i	$0.0815367\pi$
$419$	24.9878	+	24.9878i	1.22073	+	1.22073i	0.253363	+	0.967371i	$0.418463\pi$
$420$		0			0
$421$	7.56934	+	18.2740i	0.368907	+	0.890620i	0.993930	+	0.110014i	$0.0350895\pi$
$421$	7.56934	+	18.2740i	0.368907	+	0.890620i	−0.625023	+	0.780606i	$0.714911\pi$
$422$		0			0
$423$	−7.67542	−	3.17926i	−0.373191	−	0.154581i
$424$		0			0
$425$	14.8770	+	3.13438i	0.721642	+	0.152040i
$426$		0			0
$427$	−17.6538	+	7.31243i	−0.854326	+	0.353873i
$428$		0			0
$429$	−0.0782168	+	0.188832i	−0.00377634	+	0.00911690i
$430$		0			0
$431$	27.4763	−	27.4763i	1.32349	−	1.32349i	0.412557	−	0.910932i	$-0.364636\pi$
$431$	27.4763	−	27.4763i	1.32349	−	1.32349i	0.910932	−	0.412557i	$-0.135364\pi$
$432$		0			0
$433$	−1.02997	+	1.02997i	−0.0494970	+	0.0494970i	−0.731422	−	0.681925i	$-0.761143\pi$
$433$	−1.02997	+	1.02997i	−0.0494970	+	0.0494970i	0.681925	+	0.731422i	$0.261143\pi$
$434$		0			0
$435$	−1.58993	−	0.492127i	−0.0762314	−	0.0235957i
$436$		0			0
$437$	3.09538	+	7.47292i	0.148072	+	0.357478i
$438$		0			0
$439$	−10.6934	−	25.8160i	−0.510366	−	1.23213i	−0.943671	−	0.330885i	$-0.892653\pi$
$439$	−10.6934	−	25.8160i	−0.510366	−	1.23213i	0.433305	−	0.901247i	$-0.357347\pi$
$440$		0			0
$441$			26.7719i			1.27485i
$442$		0			0
$443$		−	19.5219i		−	0.927513i	−0.885963	−	0.463757i	$-0.846501\pi$
$443$		−	19.5219i		−	0.927513i	0.885963	−	0.463757i	$-0.153499\pi$
$444$		0			0
$445$	−23.2597	+	2.15826i	−1.10262	+	0.102312i
$446$		0			0
$447$	−3.56043	+	3.56043i	−0.168402	+	0.168402i
$448$		0			0
$449$	9.50363	+	9.50363i	0.448504	+	0.448504i	0.894857	−	0.446353i	$-0.147277\pi$
$449$	9.50363	+	9.50363i	0.448504	+	0.448504i	−0.446353	+	0.894857i	$0.647277\pi$
$450$		0			0
$451$	−2.23921	+	1.65340i	−0.105440	+	0.0778558i
$452$		0			0
$453$			16.0002i			0.751755i
$454$		0			0
$455$	−2.07262	−	3.93085i	−0.0971658	−	0.184281i
$456$		0			0
$457$	5.66806	−	2.34779i	0.265141	−	0.109825i	−0.246153	−	0.969231i	$-0.579166\pi$
$457$	5.66806	−	2.34779i	0.265141	−	0.109825i	0.511294	+	0.859406i	$0.329166\pi$
$458$		0			0
$459$	−11.4106	−	11.4106i	−0.532600	−	0.532600i
$460$		0			0
$461$	28.3368			1.31978			0.659888	−	0.751364i	$-0.270604\pi$
$461$	28.3368			1.31978			0.659888	+	0.751364i	$0.270604\pi$
$462$		0			0
$463$	−7.43559	+	17.9511i	−0.345561	+	0.834259i	0.651572	+	0.758587i	$0.274110\pi$
$463$	−7.43559	+	17.9511i	−0.345561	+	0.834259i	−0.997133	+	0.0756715i	$0.975890\pi$
$464$		0			0
$465$	−15.0116	−	12.4623i	−0.696145	−	0.577924i
$466$		0			0
$467$	−4.25833	+	4.25833i	−0.197052	+	0.197052i	−0.798735	−	0.601683i	$-0.794497\pi$
$467$	−4.25833	+	4.25833i	−0.197052	+	0.197052i	0.601683	+	0.798735i	$0.294497\pi$
$468$		0			0
$469$		−	64.7137i		−	2.98820i
$470$		0			0
$471$	−13.3086	−	13.3086i	−0.613227	−	0.613227i
$472$		0			0
$473$	−0.108365	+	0.0448863i	−0.00498263	+	0.00206387i
$474$		0			0
$475$	9.18094	−	5.98556i	0.421250	−	0.274637i
$476$		0			0
$477$	−8.21239	+	3.40168i	−0.376020	+	0.155752i
$478$		0			0
$479$	−6.09390	+	2.52417i	−0.278437	+	0.115332i	−0.517532	−	0.855664i	$-0.673149\pi$
$479$	−6.09390	+	2.52417i	−0.278437	+	0.115332i	0.239095	+	0.970996i	$0.423149\pi$
$480$		0			0
$481$	−1.88356	+	0.780197i	−0.0858830	+	0.0355739i
$482$		0			0
$483$			19.4394i			0.884523i
$484$		0			0
$485$	17.6114	−	1.63416i	0.799694	−	0.0742035i
$486$		0			0
$487$	3.88897			0.176226			0.0881129	−	0.996110i	$-0.471916\pi$
$487$	3.88897			0.176226			0.0881129	+	0.996110i	$0.471916\pi$
$488$		0			0
$489$	−19.1175	+	7.91871i	−0.864521	+	0.358096i
$490$		0			0
$491$			10.8724i			0.490665i	0.969439	+	0.245332i	$0.0788971\pi$
$491$			10.8724i			0.490665i	−0.969439	+	0.245332i	$0.921103\pi$
$492$		0			0
$493$	−1.43353	−	1.43353i	−0.0645629	−	0.0645629i
$494$		0			0
$495$	1.31157	+	1.08883i	0.0589506	+	0.0489395i
$496$		0			0
$497$		−	4.48607i		−	0.201228i
$498$		0			0
$499$	−2.94056	−	7.09914i	−0.131638	−	0.317801i	0.844293	−	0.535881i	$-0.180021\pi$
$499$	−2.94056	−	7.09914i	−0.131638	−	0.317801i	−0.975931	+	0.218080i	$0.930021\pi$
$500$		0			0
$501$	−9.50355	+	9.50355i	−0.424587	+	0.424587i
$502$		0			0
$503$	10.0261	−	24.2050i	0.447040	−	1.07925i	−0.526386	−	0.850246i	$-0.676453\pi$
$503$	10.0261	−	24.2050i	0.447040	−	1.07925i	0.973426	−	0.229004i	$-0.0735468\pi$
$504$		0			0
$505$	−21.9477	+	26.4374i	−0.976662	+	1.17645i
$506$		0			0
$507$	5.47814	+	13.2254i	0.243293	+	0.587361i
$508$		0			0
$509$	4.91124	−	11.8568i	0.217687	−	0.525542i	−0.776879	−	0.629649i	$-0.783199\pi$
$509$	4.91124	−	11.8568i	0.217687	−	0.525542i	0.994566	+	0.104107i	$0.0331985\pi$
$510$		0			0
$511$	−19.8236	−	8.21118i	−0.876942	−	0.363241i
$512$		0			0
$513$	−11.6326			−0.513592
$514$		0			0
$515$	4.77896	−	15.4395i	0.210586	−	0.680347i
$516$		0			0
$517$	−1.45620	−	1.45620i	−0.0640436	−	0.0640436i
$518$		0			0
$519$	−18.9162	−	7.83533i	−0.830327	−	0.343933i
$520$		0			0
$521$	24.5155	−	10.1546i	1.07404	−	0.444883i	0.225627	−	0.974214i	$-0.427557\pi$
$521$	24.5155	−	10.1546i	1.07404	−	0.444883i	0.848416	+	0.529330i	$0.177557\pi$
$522$		0			0
$523$	−14.2135	+	14.2135i	−0.621513	+	0.621513i	−0.945918	−	0.324405i	$-0.894836\pi$
$523$	−14.2135	+	14.2135i	−0.621513	+	0.621513i	0.324405	+	0.945918i	$0.394836\pi$
$524$		0			0
$525$	25.8899	−	4.84637i	1.12993	−	0.211513i
$526$		0			0
$527$	−9.09455	−	21.9562i	−0.396165	−	0.956427i
$528$		0			0
$529$			9.38284i			0.407949i
$530$		0			0
$531$	−4.42470	+	4.42470i	−0.192016	+	0.192016i
$532$		0			0
$533$	0.401317	−	2.66671i	0.0173829	−	0.115508i
$534$		0			0
$535$	25.8421	−	13.6258i	1.11725	−	0.589093i
$536$		0			0
$537$	2.37365	+	2.37365i	0.102430	+	0.102430i
$538$		0			0
$539$	−2.53962	+	6.13118i	−0.109389	+	0.264089i
$540$		0			0
$541$	24.3581	−	24.3581i	1.04724	−	1.04724i	0.0484099	−	0.998828i	$-0.484585\pi$
$541$	24.3581	−	24.3581i	1.04724	−	1.04724i	0.998828	−	0.0484099i	$-0.0154154\pi$
$542$		0			0
$543$	−14.8229	−	14.8229i	−0.636113	−	0.636113i
$544$		0			0
$545$	11.6587	−	14.0437i	0.499405	−	0.601564i
$546$		0			0
$547$	3.80124	−	1.57453i	0.162529	−	0.0673219i	−0.299935	−	0.953960i	$-0.596965\pi$
$547$	3.80124	−	1.57453i	0.162529	−	0.0673219i	0.462465	+	0.886638i	$0.346965\pi$
$548$		0			0
$549$			7.10145i			0.303083i
$550$		0			0
$551$	−1.46142			−0.0622587
$552$		0			0
$553$			65.6844i			2.79318i
$554$		0			0
$555$	−1.11650	−	12.0326i	−0.0473927	−	0.510754i
$556$		0			0
$557$	−15.6599	−	37.8063i	−0.663531	−	1.60190i	−0.792231	−	0.610221i	$-0.791080\pi$
$557$	−15.6599	−	37.8063i	−0.663531	−	1.60190i	0.128700	−	0.991684i	$-0.458920\pi$
$558$		0			0
$559$	0.0434873	−	0.104988i	0.00183932	−	0.00444051i
$560$		0			0
$561$	−0.564717	−	1.36335i	−0.0238424	−	0.0575606i
$562$		0			0
$563$	−15.7601	−	6.52805i	−0.664209	−	0.275124i	0.0249996	−	0.999687i	$-0.492042\pi$
$563$	−15.7601	−	6.52805i	−0.664209	−	0.275124i	−0.689208	+	0.724563i	$0.742042\pi$
$564$		0			0
$565$	−1.33358	−	2.52921i	−0.0561039	−	0.106405i
$566$		0			0
$567$	−2.89310	−	1.19836i	−0.121499	−	0.0503265i
$568$		0			0
$569$	−12.0334	+	12.0334i	−0.504468	+	0.504468i	−0.912823	−	0.408355i	$-0.866103\pi$
$569$	−12.0334	+	12.0334i	−0.504468	+	0.504468i	0.408355	+	0.912823i	$0.366103\pi$
$570$		0			0
$571$	−0.909472	−	2.19566i	−0.0380602	−	0.0918855i	0.903706	−	0.428153i	$-0.140835\pi$
$571$	−0.909472	−	2.19566i	−0.0380602	−	0.0918855i	−0.941767	+	0.336267i	$0.890835\pi$
$572$		0			0
$573$	−6.49413	+	6.49413i	−0.271296	+	0.271296i
$574$		0			0
$575$	−18.1357	+	3.39485i	−0.756312	+	0.141575i
$576$		0			0
$577$	0.498804	−	1.20422i	0.0207655	−	0.0501323i	−0.913157	−	0.407609i	$-0.866363\pi$
$577$	0.498804	−	1.20422i	0.0207655	−	0.0501323i	0.933922	+	0.357476i	$0.116363\pi$
$578$		0			0
$579$	12.7450	+	12.7450i	0.529662	+	0.529662i
$580$		0			0
$581$	−16.4522	+	6.81471i	−0.682550	+	0.282722i
$582$		0			0
$583$	−2.20345			−0.0912577
$584$		0			0
$585$	−1.64444	+	0.152587i	−0.0679892	+	0.00630870i
$586$		0			0
$587$	−8.32346	+	20.0946i	−0.343546	+	0.829393i	0.653806	+	0.756662i	$0.273171\pi$
$587$	−8.32346	+	20.0946i	−0.343546	+	0.829393i	−0.997352	+	0.0727307i	$0.976829\pi$
$588$		0			0
$589$	−15.8275	−	6.55595i	−0.652159	−	0.270133i
$590$		0			0
$591$	13.5029	+	5.59307i	0.555434	+	0.230068i
$592$		0			0
$593$	−12.5243	−	30.2363i	−0.514312	−	1.24166i	−0.941352	−	0.337425i	$-0.890444\pi$
$593$	−12.5243	−	30.2363i	−0.514312	−	1.24166i	0.427041	−	0.904232i	$-0.359556\pi$
$594$		0			0
$595$	30.6491	+	9.48674i	1.25649	+	0.388918i
$596$		0			0
$597$	4.67926	+	4.67926i	0.191510	+	0.191510i
$598$		0			0
$599$	−16.2896			−0.665573			−0.332787	−	0.943002i	$-0.607989\pi$
$599$	−16.2896			−0.665573			−0.332787	+	0.943002i	$0.607989\pi$
$600$		0			0
$601$	−9.57060	+	23.1055i	−0.390393	+	0.942492i	0.599461	+	0.800404i	$0.295382\pi$
$601$	−9.57060	+	23.1055i	−0.390393	+	0.942492i	−0.989854	+	0.142088i	$0.954618\pi$
$602$		0			0
$603$	−22.2196	−	9.20366i	−0.904852	−	0.374802i
$604$		0			0
$605$	−11.2750	−	21.3838i	−0.458394	−	0.869374i
$606$		0			0
$607$	−3.58240			−0.145405			−0.0727026	−	0.997354i	$-0.523162\pi$
$607$	−3.58240			−0.145405			−0.0727026	+	0.997354i	$0.523162\pi$
$608$		0			0
$609$	−3.24488	−	1.34407i	−0.131489	−	0.0544646i
$610$		0			0
$611$	1.99519			0.0807169
$612$		0			0
$613$	34.9087			1.40995			0.704975	−	0.709233i	$-0.250958\pi$
$613$	34.9087			1.40995			0.704975	+	0.709233i	$0.250958\pi$
$614$		0			0
$615$	14.3962	+	6.94606i	0.580510	+	0.280092i
$616$		0			0
$617$	41.0127			1.65111			0.825555	−	0.564321i	$-0.190862\pi$
$617$	41.0127			1.65111			0.825555	+	0.564321i	$0.190862\pi$
$618$		0			0
$619$	31.2587			1.25639			0.628196	−	0.778055i	$-0.283793\pi$
$619$	31.2587			1.25639			0.628196	+	0.778055i	$0.283793\pi$
$620$		0			0
$621$	18.0927	+	7.49426i	0.726036	+	0.300734i
$622$		0			0
$623$	−49.2951			−1.97497
$624$		0			0
$625$	9.04271	+	23.3073i	0.361708	+	0.932291i
$626$		0			0
$627$	−0.982790	−	0.407085i	−0.0392489	−	0.0162574i
$628$		0			0
$629$	5.63294	−	13.5991i	0.224600	−	0.542232i
$630$		0			0
$631$	−14.3299			−0.570465			−0.285232	−	0.958458i	$-0.592071\pi$
$631$	−14.3299			−0.570465			−0.285232	+	0.958458i	$0.592071\pi$
$632$		0			0
$633$	7.52936	+	7.52936i	0.299265	+	0.299265i
$634$		0			0
$635$	35.2630	−	18.5931i	1.39937	−	0.737843i
$636$		0			0
$637$	−2.46046	−	5.94009i	−0.0974871	−	0.235355i
$638$		0			0
$639$	−1.54030	−	0.638015i	−0.0609335	−	0.0252395i
$640$		0			0
$641$	5.36857	+	2.22373i	0.212046	+	0.0878322i	0.486178	−	0.873860i	$-0.338391\pi$
$641$	5.36857	+	2.22373i	0.212046	+	0.0878322i	−0.274132	+	0.961692i	$0.588391\pi$
$642$		0			0
$643$	12.5986	−	30.4157i	0.496841	−	1.19948i	−0.454335	−	0.890831i	$-0.650123\pi$
$643$	12.5986	−	30.4157i	0.496841	−	1.19948i	0.951176	−	0.308649i	$-0.0998768\pi$
$644$		0			0
$645$	0.518249	+	0.430239i	0.0204060	+	0.0169406i
$646$		0			0
$647$	−23.0484			−0.906126			−0.453063	−	0.891478i	$-0.649669\pi$
$647$	−23.0484			−0.906126			−0.453063	+	0.891478i	$0.649669\pi$
$648$		0			0
$649$	−1.43306	+	0.593592i	−0.0562525	+	0.0233005i
$650$		0			0
$651$	−29.1131	−	29.1131i	−1.14103	−	1.14103i
$652$		0			0
$653$	−10.2779	+	24.8130i	−0.402205	+	0.971008i	0.584925	+	0.811087i	$0.301124\pi$
$653$	−10.2779	+	24.8130i	−0.402205	+	0.971008i	−0.987130	+	0.159921i	$0.948876\pi$
$654$		0			0
$655$	−14.7438	−	27.9627i	−0.576090	−	1.09259i
$656$		0			0
$657$	−5.63866	+	5.63866i	−0.219985	+	0.219985i
$658$		0			0
$659$	15.3127	+	36.9681i	0.596498	+	1.44007i	0.877128	+	0.480257i	$0.159457\pi$
$659$	15.3127	+	36.9681i	0.596498	+	1.44007i	−0.280630	+	0.959816i	$0.590543\pi$
$660$		0			0
$661$	−30.9218	+	30.9218i	−1.20272	+	1.20272i	−0.229383	+	0.973336i	$0.573671\pi$
$661$	−30.9218	+	30.9218i	−1.20272	+	1.20272i	−0.973336	+	0.229383i	$0.926329\pi$
$662$		0			0
$663$	1.32086	+	0.547116i	0.0512978	+	0.0212482i
$664$		0			0
$665$	20.4584	−	10.7871i	0.793343	−	0.418305i
$666$		0			0
$667$	2.27302	+	0.941515i	0.0880116	+	0.0364556i
$668$		0			0
$669$	6.41837	+	15.4953i	0.248149	+	0.599084i
$670$		0			0
$671$	−0.673653	+	1.62634i	−0.0260061	+	0.0627843i
$672$		0			0
$673$	10.5272	+	25.4149i	0.405794	+	0.979673i	0.986232	+	0.165369i	$0.0528814\pi$
$673$	10.5272	+	25.4149i	0.405794	+	0.979673i	−0.580438	+	0.814305i	$0.697119\pi$
$674$		0			0
$675$	5.47042	−	25.9648i	0.210557	−	0.999384i
$676$		0			0
$677$			34.9508i			1.34327i	0.740883	+	0.671634i	$0.234407\pi$
$677$			34.9508i			1.34327i	−0.740883	+	0.671634i	$0.765593\pi$
$678$		0			0
$679$	37.3245			1.43238
$680$		0			0
$681$		−	1.47571i		−	0.0565494i
$682$		0			0
$683$	37.1326	−	15.3808i	1.42084	−	0.588531i	0.465768	−	0.884907i	$-0.345778\pi$
$683$	37.1326	−	15.3808i	1.42084	−	0.588531i	0.955071	+	0.296376i	$0.0957782\pi$
$684$		0			0
$685$	3.99110	+	43.0123i	0.152492	+	1.64341i
$686$		0			0
$687$	−13.2151	−	13.2151i	−0.504189	−	0.504189i
$688$		0			0
$689$	1.50952	−	1.50952i	0.0575080	−	0.0575080i
$690$		0			0
$691$	−6.19650	+	14.9597i	−0.235726	+	0.569093i	−0.996832	−	0.0795345i	$-0.974657\pi$
$691$	−6.19650	+	14.9597i	−0.235726	+	0.569093i	0.761106	+	0.648627i	$0.224657\pi$
$692$		0			0
$693$	2.54363	+	2.54363i	0.0966244	+	0.0966244i
$694$		0			0
$695$	33.3238	+	10.3146i	1.26404	+	0.391256i
$696$		0			0
$697$	11.5654	+	15.6630i	0.438069	+	0.593278i
$698$		0			0
$699$	5.17729	−	5.17729i	0.195823	−	0.195823i
$700$		0			0
$701$			51.1728i			1.93277i	0.257102	+	0.966384i	$0.417232\pi$
$701$			51.1728i			1.93277i	−0.257102	+	0.966384i	$0.582768\pi$
$702$		0			0
$703$	−4.06059	−	9.80313i	−0.153148	−	0.369732i
$704$		0			0
$705$	−3.49681	+	11.2973i	−0.131697	+	0.425479i
$706$		0			0
$707$	−51.2722	+	51.2722i	−1.92829	+	1.92829i
$708$		0			0
$709$	−13.6171	+	5.64041i	−0.511403	+	0.211830i	−0.623436	−	0.781875i	$-0.714264\pi$
$709$	−13.6171	+	5.64041i	−0.511403	+	0.211830i	0.112033	+	0.993704i	$0.464264\pi$
$710$		0			0
$711$	22.5529	+	9.34171i	0.845800	+	0.350342i
$712$		0			0
$713$	20.3936	+	20.3936i	0.763745	+	0.763745i
$714$		0			0
$715$	−0.391077	−	0.121049i	−0.0146254	−	0.00452697i
$716$		0			0
$717$	−19.7232			−0.736576
$718$		0			0
$719$	−25.6832	−	10.6383i	−0.957823	−	0.396743i	−0.151657	−	0.988433i	$-0.548461\pi$
$719$	−25.6832	−	10.6383i	−0.957823	−	0.396743i	−0.806166	+	0.591690i	$0.798461\pi$
$720$		0			0
$721$	13.0521	−	31.5105i	0.486084	−	1.17351i
$722$		0			0
$723$	−3.12489	−	7.54415i	−0.116216	−	0.280570i
$724$		0			0
$725$	0.687257	−	3.26199i	0.0255241	−	0.121147i
$726$		0			0
$727$	−10.1029	+	24.3905i	−0.374695	+	0.904593i	0.618246	+	0.785984i	$0.287843\pi$
$727$	−10.1029	+	24.3905i	−0.374695	+	0.904593i	−0.992941	+	0.118609i	$0.962157\pi$
$728$		0			0
$729$	−13.3910	+	13.3910i	−0.495962	+	0.495962i
$730$		0			0
$731$	0.313974	+	0.758000i	0.0116127	+	0.0280356i
$732$		0			0
$733$			42.7291i			1.57823i	0.614243	+	0.789117i	$0.289462\pi$
$733$			42.7291i			1.57823i	−0.614243	+	0.789117i	$0.710538\pi$
$734$		0			0
$735$	37.9464	−	3.52104i	1.39968	−	0.129876i
$736$		0			0
$737$	−4.21556	−	4.21556i	−0.155282	−	0.155282i
$738$		0			0
$739$			7.24292i			0.266435i	0.991087	+	0.133218i	$0.0425309\pi$
$739$			7.24292i			0.266435i	−0.991087	+	0.133218i	$0.957469\pi$
$740$		0			0
$741$	0.952159	−	0.394397i	0.0349784	−	0.0144885i
$742$		0			0
$743$	41.7474			1.53157			0.765783	−	0.643100i	$-0.222352\pi$
$743$	41.7474			1.53157			0.765783	+	0.643100i	$0.222352\pi$
$744$		0			0
$745$	−7.75971	−	6.44194i	−0.284294	−	0.236015i
$746$		0			0
$747$			6.61808i			0.242143i
$748$		0			0
$749$	56.9573	−	23.5925i	2.08117	−	0.862051i
$750$		0			0
$751$	30.4138	−	12.5978i	1.10982	−	0.459701i	0.248942	−	0.968518i	$-0.419917\pi$
$751$	30.4138	−	12.5978i	1.10982	−	0.459701i	0.860875	+	0.508817i	$0.169917\pi$
$752$		0			0
$753$	−11.3079	+	4.68387i	−0.412081	+	0.170690i
$754$		0			0
$755$	−31.9104	+	2.96096i	−1.16134	+	0.107760i
$756$		0			0
$757$	41.2537	−	17.0878i	1.49939	−	0.621068i	0.526055	−	0.850451i	$-0.323671\pi$
$757$	41.2537	−	17.0878i	1.49939	−	0.621068i	0.973336	+	0.229383i	$0.0736707\pi$
$758$		0			0
$759$	1.26632	+	1.26632i	0.0459644	+	0.0459644i
$760$		0			0
$761$			24.7884i			0.898578i	0.893386	+	0.449289i	$0.148323\pi$
$761$			24.7884i			0.898578i	−0.893386	+	0.449289i	$0.851677\pi$
$762$		0			0
$763$	27.2360	−	27.2360i	0.986009	−	0.986009i
$764$		0			0
$765$	7.61625	−	9.17424i	0.275366	−	0.331695i
$766$		0			0
$767$	0.575092	−	1.38839i	0.0207654	−	0.0501320i
$768$		0			0
$769$	11.7479			0.423641			0.211820	−	0.977309i	$-0.432061\pi$
$769$	11.7479			0.423641			0.211820	+	0.977309i	$0.432061\pi$
$770$		0			0
$771$	2.80118	+	2.80118i	0.100882	+	0.100882i
$772$		0			0
$773$	−13.1080	+	5.42950i	−0.471461	+	0.195285i	−0.605747	−	0.795657i	$-0.707126\pi$
$773$	−13.1080	+	5.42950i	−0.471461	+	0.195285i	0.134287	+	0.990943i	$0.457126\pi$
$774$		0			0
$775$	22.0765	−	32.2449i	0.793009	−	1.15827i
$776$		0			0
$777$		−	25.5010i		−	0.914844i
$778$		0			0
$779$	13.8791	+	2.08868i	0.497269	+	0.0748348i
$780$		0			0
$781$	−0.292231	−	0.292231i	−0.0104568	−	0.0104568i
$782$		0			0
$783$	−2.50193	+	2.50193i	−0.0894116	+	0.0894116i
$784$		0			0
$785$	24.0794	−	29.0051i	0.859432	−	1.03524i
$786$		0			0
$787$		−	2.91744i		−	0.103996i	−0.998647	−	0.0519978i	$-0.983441\pi$
$787$		−	2.91744i		−	0.103996i	0.998647	−	0.0519978i	$-0.0165589\pi$
$788$		0			0
$789$			31.6925i			1.12828i
$790$		0			0
$791$	−2.30904	−	5.57451i	−0.0820999	−	0.198207i
$792$		0			0
$793$	−0.652657	−	1.57565i	−0.0231765	−	0.0559531i
$794$		0			0
$795$	5.90164	+	11.1928i	0.209309	+	0.396969i
$796$		0			0
$797$	18.2595	−	18.2595i	0.646786	−	0.646786i	−0.305429	−	0.952215i	$-0.598800\pi$
$797$	18.2595	−	18.2595i	0.646786	−	0.646786i	0.952215	+	0.305429i	$0.0987998\pi$
$798$		0			0
$799$	−10.1859	+	10.1859i	−0.360352	+	0.360352i
$800$		0			0
$801$	−7.01082	+	16.9256i	−0.247715	+	0.598037i
$802$		0			0
$803$	−1.82623	+	0.756450i	−0.0644463	+	0.0266945i
$804$		0			0
$805$	−38.7695	+	3.59741i	−1.36644	+	0.126792i
$806$		0			0
$807$	8.03098	+	3.32654i	0.282704	+	0.117100i
$808$		0			0
$809$	−6.42188	−	15.5038i	−0.225781	−	0.545084i	0.769874	−	0.638195i	$-0.220319\pi$
$809$	−6.42188	−	15.5038i	−0.225781	−	0.545084i	−0.995656	+	0.0931112i	$0.970319\pi$
$810$		0			0
$811$	−9.87507	−	9.87507i	−0.346761	−	0.346761i	0.512141	−	0.858901i	$-0.328853\pi$
$811$	−9.87507	−	9.87507i	−0.346761	−	0.346761i	−0.858901	+	0.512141i	$0.828853\pi$
$812$		0			0
$813$	13.2392	−	31.9623i	0.464319	−	1.12097i
$814$		0			0
$815$	−19.3307	−	36.6620i	−0.677125	−	1.28421i
$816$		0			0
$817$	0.546416	+	0.226333i	0.0191167	+	0.00791839i
$818$		0			0
$819$	−3.48512			−0.121780
$820$		0			0
$821$	−18.0844			−0.631150			−0.315575	−	0.948901i	$-0.602197\pi$
$821$	−18.0844			−0.631150			−0.315575	+	0.948901i	$0.602197\pi$
$822$		0			0
$823$	−7.13807	−	2.95668i	−0.248817	−	0.103064i	0.254789	−	0.966997i	$-0.417994\pi$
$823$	−7.13807	−	2.95668i	−0.248817	−	0.103064i	−0.503607	+	0.863933i	$0.667994\pi$
$824$		0			0
$825$	1.37081	−	2.00222i	0.0477256	−	0.0697082i
$826$		0			0
$827$	−17.1995	+	41.5234i	−0.598087	+	1.44391i	0.277442	+	0.960742i	$0.410513\pi$
$827$	−17.1995	+	41.5234i	−0.598087	+	1.44391i	−0.875529	+	0.483166i	$0.839487\pi$
$828$		0			0
$829$	19.5197	+	19.5197i	0.677947	+	0.677947i	0.959535	−	0.281589i	$-0.0908613\pi$
$829$	19.5197	+	19.5197i	0.677947	+	0.677947i	−0.281589	+	0.959535i	$0.590861\pi$
$830$		0			0
$831$	8.32136	+	20.0895i	0.288665	+	0.696899i
$832$		0			0
$833$	42.8868	+	17.7643i	1.48594	+	0.615496i
$834$		0			0
$835$	−20.7124	−	17.1949i	−0.716781	−	0.595056i
$836$		0			0
$837$	−38.3200	+	15.8727i	−1.32453	+	0.548639i
$838$		0			0
$839$	12.2038	−	29.4625i	0.421321	−	1.01716i	−0.560638	−	0.828061i	$-0.689444\pi$
$839$	12.2038	−	29.4625i	0.421321	−	1.01716i	0.981958	−	0.189097i	$-0.0605560\pi$
$840$		0			0
$841$	20.1918	−	20.1918i	0.696268	−	0.696268i
$842$		0			0
$843$	1.28280	−	1.28280i	0.0441821	−	0.0441821i
$844$		0			0
$845$	−25.3626	+	13.3729i	−0.872501	+	0.460043i
$846$		0			0
$847$	−19.5222	−	47.1309i	−0.670792	−	1.61944i
$848$		0			0
$849$	−9.58365	−	23.1370i	−0.328910	−	0.794059i
$850$		0			0
$851$			17.8633i			0.612346i
$852$		0			0
$853$			5.89080i			0.201697i	0.994902	+	0.100849i	$0.0321558\pi$
$853$			5.89080i			0.201697i	−0.994902	+	0.100849i	$0.967844\pi$
$854$		0			0
$855$	−0.794151	−	8.55860i	−0.0271594	−	0.292698i
$856$		0			0
$857$	39.1868	−	39.1868i	1.33860	−	1.33860i	0.441175	−	0.897421i	$-0.354562\pi$
$857$	39.1868	−	39.1868i	1.33860	−	1.33860i	0.897421	−	0.441175i	$-0.145438\pi$
$858$		0			0
$859$	33.8316	+	33.8316i	1.15432	+	1.15432i	0.985678	+	0.168640i	$0.0539375\pi$
$859$	33.8316	+	33.8316i	1.15432	+	1.15432i	0.168640	+	0.985678i	$0.446063\pi$
$860$		0			0
$861$	28.8956	+	17.4023i	0.984758	+	0.593067i
$862$		0			0
$863$			3.51029i			0.119491i	0.998214	+	0.0597457i	$0.0190290\pi$
$863$			3.51029i			0.119491i	−0.998214	+	0.0597457i	$0.980971\pi$
$864$		0			0
$865$	12.1260	−	39.1759i	0.412296	−	1.33202i
$866$		0			0
$867$	7.99755	−	3.31269i	0.271611	−	0.112505i
$868$		0			0
$869$	4.27880	+	4.27880i	0.145148	+	0.145148i
$870$		0			0
$871$	5.77589			0.195709
$872$		0			0
$873$	5.30834	−	12.8155i	0.179660	−	0.433738i
$874$		0			0
$875$	14.4566	+	50.7374i	0.488723	+	1.71524i
$876$		0			0
$877$	−16.3231	+	16.3231i	−0.551193	+	0.551193i	−0.926785	−	0.375592i	$-0.877439\pi$
$877$	−16.3231	+	16.3231i	−0.551193	+	0.551193i	0.375592	+	0.926785i	$0.377439\pi$
$878$		0			0
$879$			3.60963i			0.121750i
$880$		0			0
$881$	35.7057	+	35.7057i	1.20295	+	1.20295i	0.973264	+	0.229690i	$0.0737713\pi$
$881$	35.7057	+	35.7057i	1.20295	+	1.20295i	0.229690	+	0.973264i	$0.426229\pi$
$882$		0			0
$883$	−22.7354	+	9.41729i	−0.765106	+	0.316917i	−0.730888	−	0.682497i	$-0.760894\pi$
$883$	−22.7354	+	9.41729i	−0.765106	+	0.316917i	−0.0342176	+	0.999414i	$0.510894\pi$
$884$		0			0
$885$	6.85350	+	5.68963i	0.230378	+	0.191255i
$886$		0			0
$887$	−2.15511	+	0.892674i	−0.0723614	+	0.0299731i	−0.418571	−	0.908184i	$-0.637469\pi$
$887$	−2.15511	+	0.892674i	−0.0723614	+	0.0299731i	0.346209	+	0.938157i	$0.387469\pi$
$888$		0			0
$889$	77.7213	−	32.1932i	2.60669	−	1.07973i
$890$		0			0
$891$	−0.266525	+	0.110398i	−0.00892893	+	0.00369849i
$892$		0			0
$893$			10.3841i			0.347492i
$894$		0			0
$895$	−4.29468	+	5.17320i	−0.143555	+	0.172921i
$896$		0			0
$897$	−1.73503			−0.0579308
$898$		0			0
$899$	−4.81420	+	1.99411i	−0.160563	+	0.0665072i
$900$		0			0
$901$			15.4129i			0.513477i
$902$		0			0
$903$	1.00508	+	1.00508i	0.0334470	+	0.0334470i
$904$		0			0
$905$	26.8194	−	32.3056i	0.891507	−	1.07387i
$906$		0			0
$907$		−	30.2223i		−	1.00352i	−0.865008	−	0.501758i	$-0.832687\pi$
$907$		−	30.2223i		−	1.00352i	0.865008	−	0.501758i	$-0.167313\pi$
$908$		0			0
$909$	10.3124	+	24.8964i	0.342042	+	0.825762i
$910$		0			0
$911$	−29.4076	+	29.4076i	−0.974316	+	0.974316i	−0.999678	−	0.0253621i	$-0.991926\pi$
$911$	−29.4076	+	29.4076i	−0.974316	+	0.974316i	0.0253621	+	0.999678i	$0.491926\pi$
$912$		0			0
$913$	−0.627800	+	1.51564i	−0.0207772	+	0.0501605i
$914$		0			0
$915$	10.0656	−	0.933984i	0.332758	−	0.0308766i
$916$		0			0
$917$	−25.5284	−	61.6311i	−0.843023	−	2.03524i
$918$		0			0
$919$	15.2321	−	36.7736i	0.502462	−	1.21305i	−0.445677	−	0.895194i	$-0.647037\pi$
$919$	15.2321	−	36.7736i	0.502462	−	1.21305i	0.948139	−	0.317856i	$-0.102963\pi$
$920$		0			0
$921$	−11.0189	−	4.56417i	−0.363085	−	0.150395i
$922$		0			0
$923$	0.400396			0.0131792
$924$		0			0
$925$	23.7908	−	4.45344i	0.782237	−	0.146428i
$926$		0			0
$927$	−8.96291	−	8.96291i	−0.294381	−	0.294381i
$928$		0			0
$929$	−38.2675	−	15.8509i	−1.25552	−	0.520052i	−0.346985	−	0.937871i	$-0.612795\pi$
$929$	−38.2675	−	15.8509i	−1.25552	−	0.520052i	−0.908530	+	0.417819i	$0.862795\pi$
$930$		0			0
$931$	30.9156	−	12.8057i	1.01322	−	0.419689i
$932$		0			0
$933$	13.6629	−	13.6629i	0.447302	−	0.447302i
$934$		0			0
$935$	2.61452	−	1.37856i	0.0855040	−	0.0450836i
$936$		0			0
$937$	1.35356	+	3.26779i	0.0442190	+	0.106754i	0.944446	−	0.328667i	$-0.106599\pi$
$937$	1.35356	+	3.26779i	0.0442190	+	0.106754i	−0.900227	+	0.435421i	$0.856599\pi$
$938$		0			0
$939$		−	2.62525i		−	0.0856720i
$940$		0			0
$941$	−37.7304	+	37.7304i	−1.22998	+	1.22998i	−0.266003	+	0.963972i	$0.585703\pi$
$941$	−37.7304	+	37.7304i	−1.22998	+	1.22998i	−0.963972	+	0.266003i	$0.914297\pi$
$942$		0			0
$943$	−20.2411	−	12.1902i	−0.659142	−	0.396966i
$944$		0			0
$945$	16.5571	−	53.4917i	0.538604	−	1.74009i
$946$		0			0
$947$	−8.64029	−	8.64029i	−0.280772	−	0.280772i	0.552645	−	0.833417i	$-0.313619\pi$
$947$	−8.64029	−	8.64029i	−0.280772	−	0.280772i	−0.833417	+	0.552645i	$0.813619\pi$
$948$		0			0
$949$	0.732873	−	1.76931i	0.0237901	−	0.0574343i
$950$		0			0
$951$	−20.8587	+	20.8587i	−0.676391	+	0.676391i
$952$		0			0
$953$	−1.65636	−	1.65636i	−0.0536546	−	0.0536546i	0.679770	−	0.733425i	$-0.262079\pi$
$953$	−1.65636	−	1.65636i	−0.0536546	−	0.0536546i	−0.733425	+	0.679770i	$0.762079\pi$
$954$		0			0
$955$	−14.1535	−	11.7500i	−0.457998	−	0.380220i
$956$		0			0
$957$	−0.298933	+	0.123822i	−0.00966312	+	0.00400260i
$958$		0			0
$959$			91.1574i			2.94363i
$960$		0			0
$961$	−30.0842			−0.970459
$962$		0			0
$963$		−	22.9118i		−	0.738322i
$964$		0			0
$965$	−23.0597	+	27.7768i	−0.742317	+	0.894166i
$966$		0			0
$967$	−12.2078	−	29.4721i	−0.392575	−	0.947759i	−0.989377	−	0.145371i	$-0.953562\pi$
$967$	−12.2078	−	29.4721i	−0.392575	−	0.947759i	0.596802	−	0.802388i	$-0.296438\pi$
$968$		0			0
$969$	−2.84751	+	6.87449i	−0.0914751	+	0.220840i
$970$		0			0
$971$	20.9957	+	50.6880i	0.673783	+	1.62666i	0.775127	+	0.631805i	$0.217686\pi$
$971$	20.9957	+	50.6880i	0.673783	+	1.62666i	−0.101344	+	0.994851i	$0.532314\pi$
$972$		0			0
$973$	68.0103	+	28.1708i	2.18031	+	0.903114i
$974$		0			0
$975$	0.432553	+	2.31076i	0.0138528	+	0.0740034i
$976$		0			0
$977$	−36.7788	−	15.2343i	−1.17666	−	0.487387i	−0.293269	−	0.956030i	$-0.594743\pi$
$977$	−36.7788	−	15.2343i	−1.17666	−	0.487387i	−0.883388	+	0.468643i	$0.844743\pi$
$978$		0			0
$979$	−3.21117	+	3.21117i	−0.102629	+	0.102629i
$980$		0			0
$981$	−5.47801	−	13.2251i	−0.174899	−	0.422244i
$982$		0			0
$983$	−28.5291	+	28.5291i	−0.909937	+	0.909937i	−0.996267	−	0.0863301i	$-0.972486\pi$
$983$	−28.5291	+	28.5291i	−0.909937	+	0.909937i	0.0863301	+	0.996267i	$0.472486\pi$
$984$		0			0
$985$	−8.65587	+	27.9648i	−0.275799	+	0.891033i
$986$		0			0
$987$	−9.55032	+	23.0565i	−0.303990	+	0.733897i
$988$		0			0
$989$	−0.704052	−	0.704052i	−0.0223876	−	0.0223876i
$990$		0			0
$991$	−46.5910	+	19.2986i	−1.48001	+	0.613041i	−0.969117	−	0.246603i	$-0.920686\pi$
$991$	−46.5910	+	19.2986i	−1.48001	+	0.613041i	−0.510894	+	0.859643i	$0.670686\pi$
$992$		0			0
$993$	16.3510			0.518884
$994$		0			0
$995$	−8.46628	+	10.1981i	−0.268399	+	0.323303i
$996$		0			0
$997$	0.996401	−	2.40553i	0.0315563	−	0.0761838i	−0.907316	−	0.420450i	$-0.861872\pi$
$997$	0.996401	−	2.40553i	0.0315563	−	0.0761838i	0.938872	+	0.344266i	$0.111872\pi$
$998$		0			0
$999$	−23.7344	−	9.83113i	−0.750924	−	0.311043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.273.7	✓	84
5.2	odd	4		820.2.y.a.437.7	yes	84
41.38	odd	8		820.2.y.a.653.7	yes	84
205.202	even	8	inner	820.2.x.a.817.7	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.7	✓	84	1.1	even	1	trivial
820.2.x.a.817.7	yes	84	205.202	even	8	inner
820.2.y.a.437.7	yes	84	5.2	odd	4
820.2.y.a.653.7	yes	84	41.38	odd	8

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.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03141 - 0.427224i) q^{3} +(0.661175 - 2.13608i) q^{5} +(1.80577 - 4.35952i) q^{7} +(-1.24003 - 1.24003i) q^{9} +(-0.166356 - 0.401618i) q^{11} +(0.389100 + 0.161171i) q^{13} +(-1.59453 + 1.92071i) q^{15} +(-2.80926 + 1.16364i) q^{17} +(-0.838825 + 2.02510i) q^{19} +(-3.72499 + 3.72499i) q^{21} +(2.60933 - 2.60933i) q^{23} +(-4.12569 - 2.82465i) q^{25} +(2.03088 + 4.90299i) q^{27} +(0.255143 + 0.615970i) q^{29} +7.81564i q^{31} +0.485304i q^{33} +(-8.11836 - 6.73968i) q^{35} +(-3.42297 + 3.42297i) q^{37} +(-0.332466 - 0.332466i) q^{39} +(-1.54273 - 6.21450i) q^{41} -0.269822i q^{43} +(-3.46869 + 1.82893i) q^{45} +(4.37677 - 1.81292i) q^{47} +(-10.7948 - 10.7948i) q^{49} +3.39464 q^{51} +(1.93975 - 4.68297i) q^{53} +(-0.967879 + 0.0898093i) q^{55} +(1.73035 - 1.73035i) q^{57} -3.56822i q^{59} +(-2.86341 - 2.86341i) q^{61} +(-7.64516 + 3.16673i) q^{63} +(0.601537 - 0.724588i) q^{65} +(12.6703 - 5.24823i) q^{67} +(-3.80606 + 1.57652i) q^{69} +(0.878331 - 0.363817i) q^{71} -4.54719i q^{73} +(3.04853 + 4.67597i) q^{75} -2.05126 q^{77} +(-12.8604 + 5.32695i) q^{79} -0.663629i q^{81} +(-2.66851 - 2.66851i) q^{83} +(0.628204 + 6.77019i) q^{85} -0.744321i q^{87} +(-3.99780 - 9.65153i) q^{89} +(1.40525 - 1.40525i) q^{91} +(3.33903 - 8.06114i) q^{93} +(3.77117 + 3.13075i) q^{95} +(3.02699 + 7.30780i) q^{97} +(-0.291733 + 0.704305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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