LMFDB - Embedded newform 820.2.bo.b.21.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			21.8
Character	$\chi$	$=$	820.21
Dual form			820.2.bo.b.781.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.27233 + 2.27233i) q^{3} +(0.587785 - 0.809017i) q^{5} +(1.91674 - 3.76182i) q^{7} +7.32700i q^{9} +(-3.64371 - 0.577108i) q^{11} +(3.28988 - 1.67628i) q^{13} +(3.17400 - 0.502712i) q^{15} +(0.0641329 - 0.404919i) q^{17} +(6.17966 + 3.14869i) q^{19} +(12.9036 - 4.19263i) q^{21} +(-2.14607 + 6.60491i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(-9.83239 + 9.83239i) q^{27} +(1.02160 + 6.45011i) q^{29} +(6.57947 - 4.78026i) q^{31} +(-6.96835 - 9.59112i) q^{33} +(-1.91674 - 3.76182i) q^{35} +(0.512250 + 0.372171i) q^{37} +(11.2848 + 3.66664i) q^{39} +(-6.19552 - 1.61726i) q^{41} +(-6.50749 - 2.11441i) q^{43} +(5.92767 + 4.30670i) q^{45} +(-5.43784 - 10.6724i) q^{47} +(-6.36291 - 8.75779i) q^{49} +(1.06584 - 0.774380i) q^{51} +(-1.00821 - 6.36559i) q^{53} +(-2.60861 + 2.60861i) q^{55} +(6.88736 + 21.1971i) q^{57} +(-1.43206 + 4.40742i) q^{59} +(-12.5977 + 4.09325i) q^{61} +(27.5629 + 14.0440i) q^{63} +(0.577606 - 3.64686i) q^{65} +(4.92336 - 0.779784i) q^{67} +(-19.8851 + 10.1320i) q^{69} +(5.43321 + 0.860536i) q^{71} +3.15849i q^{73} +(1.45893 - 2.86331i) q^{75} +(-9.15505 + 12.6008i) q^{77} +(-5.88894 - 5.88894i) q^{79} -22.7039 q^{81} -2.45844 q^{83} +(-0.289890 - 0.289890i) q^{85} +(-12.3354 + 16.9782i) q^{87} +(0.951082 - 1.86660i) q^{89} -15.5889i q^{91} +(25.8131 + 4.08839i) q^{93} +(6.17966 - 3.14869i) q^{95} +(-11.3855 + 1.80329i) q^{97} +(4.22847 - 26.6975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) $ 64 * q + 2 * q^3 - 10 * q^7 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 22 * q^23 + 16 * q^25 + 20 * q^27 - 12 * q^29 + 22 * q^31 + 30 * q^33 + 10 * q^35 + 12 * q^37 + 20 * q^39 - 10 * q^41 + 10 * q^43 + 32 * q^45 + 28 * q^47 + 10 * q^49 - 22 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 18 * q^59 - 20 * q^61 + 52 * q^63 - 6 * q^65 - 6 * q^67 - 50 * q^69 + 34 * q^71 + 8 * q^75 - 110 * q^77 - 14 * q^79 - 108 * q^81 + 32 * q^83 - 8 * q^85 - 80 * q^87 - 122 * q^89 + 42 * q^93 + 10 * q^95 - 64 * q^97 - 54 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.27233	+	2.27233i	1.31193	+	1.31193i	0.919990	+	0.391943i	$0.128197\pi$
$3$	2.27233	+	2.27233i	1.31193	+	1.31193i	0.391943	+	0.919990i	$0.371803\pi$
$4$		0			0
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$6$		0			0
$7$	1.91674	−	3.76182i	0.724461	−	1.42184i	−0.174881	−	0.984590i	$-0.555954\pi$
$7$	1.91674	−	3.76182i	0.724461	−	1.42184i	0.899342	−	0.437246i	$-0.144046\pi$
$8$		0			0
$9$			7.32700i			2.44233i
$10$		0			0
$11$	−3.64371	−	0.577108i	−1.09862	−	0.174004i	−0.419302	−	0.907847i	$-0.637725\pi$
$11$	−3.64371	−	0.577108i	−1.09862	−	0.174004i	−0.679320	+	0.733843i	$0.737725\pi$
$12$		0			0
$13$	3.28988	−	1.67628i	0.912448	−	0.464916i	0.0662617	−	0.997802i	$-0.478893\pi$
$13$	3.28988	−	1.67628i	0.912448	−	0.464916i	0.846187	+	0.532887i	$0.178893\pi$
$14$		0			0
$15$	3.17400	−	0.502712i	0.819523	−	0.129800i
$16$		0			0
$17$	0.0641329	−	0.404919i	0.0155545	−	0.0982073i	−0.978690	−	0.205345i	$-0.934168\pi$
$17$	0.0641329	−	0.404919i	0.0155545	−	0.0982073i	0.994244	+	0.107137i	$0.0341685\pi$
$18$		0			0
$19$	6.17966	+	3.14869i	1.41771	+	0.722360i	0.983913	−	0.178650i	$-0.0571731\pi$
$19$	6.17966	+	3.14869i	1.41771	+	0.722360i	0.433798	+	0.901010i	$0.357173\pi$
$20$		0			0
$21$	12.9036	−	4.19263i	2.81580	−	0.914908i
$22$		0			0
$23$	−2.14607	+	6.60491i	−0.447486	+	1.37722i	0.432249	+	0.901754i	$0.357720\pi$
$23$	−2.14607	+	6.60491i	−0.447486	+	1.37722i	−0.879734	+	0.475465i	$0.842280\pi$
$24$		0			0
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$		0			0
$27$	−9.83239	+	9.83239i	−1.89224	+	1.89224i
$28$		0			0
$29$	1.02160	+	6.45011i	0.189706	+	1.19776i	0.880266	+	0.474481i	$0.157364\pi$
$29$	1.02160	+	6.45011i	0.189706	+	1.19776i	−0.690560	+	0.723275i	$0.742636\pi$
$30$		0			0
$31$	6.57947	−	4.78026i	1.18171	−	0.858561i	0.189344	−	0.981911i	$-0.439364\pi$
$31$	6.57947	−	4.78026i	1.18171	−	0.858561i	0.992363	+	0.123350i	$0.0393637\pi$
$32$		0			0
$33$	−6.96835	−	9.59112i	−1.21303	−	1.66960i
$34$		0			0
$35$	−1.91674	−	3.76182i	−0.323989	−	0.635864i
$36$		0			0
$37$	0.512250	+	0.372171i	0.0842134	+	0.0611846i	0.629095	−	0.777328i	$-0.283426\pi$
$37$	0.512250	+	0.372171i	0.0842134	+	0.0611846i	−0.544882	+	0.838513i	$0.683426\pi$
$38$		0			0
$39$	11.2848	+	3.66664i	1.80701	+	0.587133i
$40$		0			0
$41$	−6.19552	−	1.61726i	−0.967578	−	0.252573i
$41$	−6.19552	−	1.61726i	−0.967578	−	0.252573i
$42$		0			0
$43$	−6.50749	−	2.11441i	−0.992384	−	0.322445i	−0.232566	−	0.972581i	$-0.574712\pi$
$43$	−6.50749	−	2.11441i	−0.992384	−	0.322445i	−0.759818	+	0.650136i	$0.774712\pi$
$44$		0			0
$45$	5.92767	+	4.30670i	0.883645	+	0.642005i
$46$		0			0
$47$	−5.43784	−	10.6724i	−0.793191	−	1.55673i	−0.830236	−	0.557412i	$-0.811795\pi$
$47$	−5.43784	−	10.6724i	−0.793191	−	1.55673i	0.0370451	−	0.999314i	$-0.488205\pi$
$48$		0			0
$49$	−6.36291	−	8.75779i	−0.908987	−	1.25111i
$50$		0			0
$51$	1.06584	−	0.774380i	0.149248	−	0.108435i
$52$		0			0
$53$	−1.00821	−	6.36559i	−0.138488	−	0.874381i	−0.954904	−	0.296916i	$-0.904042\pi$
$53$	−1.00821	−	6.36559i	−0.138488	−	0.874381i	0.816415	−	0.577465i	$-0.195958\pi$
$54$		0			0
$55$	−2.60861	+	2.60861i	−0.351745	+	0.351745i
$56$		0			0
$57$	6.88736	+	21.1971i	0.912254	+	2.80763i
$58$		0			0
$59$	−1.43206	+	4.40742i	−0.186438	+	0.573797i	−0.999970	−	0.00772284i	$-0.997542\pi$
$59$	−1.43206	+	4.40742i	−0.186438	+	0.573797i	0.813532	+	0.581520i	$0.197542\pi$
$60$		0			0
$61$	−12.5977	+	4.09325i	−1.61298	+	0.524087i	−0.970270	−	0.242026i	$-0.922188\pi$
$61$	−12.5977	+	4.09325i	−1.61298	+	0.524087i	−0.642706	+	0.766113i	$0.722188\pi$
$62$		0			0
$63$	27.5629	+	14.0440i	3.47260	+	1.76938i
$64$		0			0
$65$	0.577606	−	3.64686i	0.0716432	−	0.452337i
$66$		0			0
$67$	4.92336	−	0.779784i	0.601485	−	0.0952658i	0.151736	−	0.988421i	$-0.451514\pi$
$67$	4.92336	−	0.779784i	0.601485	−	0.0952658i	0.449749	+	0.893155i	$0.351514\pi$
$68$		0			0
$69$	−19.8851	+	10.1320i	−2.39389	+	1.21975i
$70$		0			0
$71$	5.43321	+	0.860536i	0.644803	+	0.102127i	0.470267	−	0.882524i	$-0.344157\pi$
$71$	5.43321	+	0.860536i	0.644803	+	0.102127i	0.174536	+	0.984651i	$0.444157\pi$
$72$		0			0
$73$			3.15849i			0.369674i	0.982769	+	0.184837i	$0.0591757\pi$
$73$			3.15849i			0.369674i	−0.982769	+	0.184837i	$0.940824\pi$
$74$		0			0
$75$	1.45893	−	2.86331i	0.168462	−	0.330626i
$76$		0			0
$77$	−9.15505	+	12.6008i	−1.04331	+	1.43600i
$78$		0			0
$79$	−5.88894	−	5.88894i	−0.662557	−	0.662557i	0.293425	−	0.955982i	$-0.405205\pi$
$79$	−5.88894	−	5.88894i	−0.662557	−	0.662557i	−0.955982	+	0.293425i	$0.905205\pi$
$80$		0			0
$81$	−22.7039			−2.52266
$82$		0			0
$83$	−2.45844			−0.269849			−0.134925	−	0.990856i	$-0.543079\pi$
$83$	−2.45844			−0.269849			−0.134925	+	0.990856i	$0.543079\pi$
$84$		0			0
$85$	−0.289890	−	0.289890i	−0.0314430	−	0.0314430i
$86$		0			0
$87$	−12.3354	+	16.9782i	−1.32249	+	1.82026i
$88$		0			0
$89$	0.951082	−	1.86660i	0.100815	−	0.197860i	−0.835090	−	0.550113i	$-0.814585\pi$
$89$	0.951082	−	1.86660i	0.100815	−	0.197860i	0.935905	+	0.352254i	$0.114585\pi$
$90$		0			0
$91$		−	15.5889i		−	1.63416i
$92$		0			0
$93$	25.8131	+	4.08839i	2.67669	+	0.423947i
$94$		0			0
$95$	6.17966	−	3.14869i	0.634020	−	0.323049i
$96$		0			0
$97$	−11.3855	+	1.80329i	−1.15602	+	0.183096i	−0.704861	−	0.709345i	$-0.748991\pi$
$97$	−11.3855	+	1.80329i	−1.15602	+	0.183096i	−0.451163	+	0.892441i	$0.648991\pi$
$98$		0			0
$99$	4.22847	−	26.6975i	0.424977	−	2.68320i
$100$		0			0
$101$	−2.07375	−	1.05663i	−0.206346	−	0.105138i	0.347764	−	0.937582i	$-0.386941\pi$
$101$	−2.07375	−	1.05663i	−0.206346	−	0.105138i	−0.554109	+	0.832444i	$0.686941\pi$
$102$		0			0
$103$	9.22180	−	2.99634i	0.908651	−	0.295238i	0.182848	−	0.983141i	$-0.441468\pi$
$103$	9.22180	−	2.99634i	0.908651	−	0.295238i	0.725803	+	0.687903i	$0.241468\pi$
$104$		0			0
$105$	4.19263	−	12.9036i	0.409159	−	1.25926i
$106$		0			0
$107$	−3.01151	−	9.26848i	−0.291134	−	0.896018i	−0.984493	−	0.175425i	$-0.943870\pi$
$107$	−3.01151	−	9.26848i	−0.291134	−	0.896018i	0.693359	−	0.720592i	$-0.256130\pi$
$108$		0			0
$109$	−8.90213	+	8.90213i	−0.852669	+	0.852669i	−0.990461	−	0.137792i	$-0.955999\pi$
$109$	−8.90213	+	8.90213i	−0.852669	+	0.852669i	0.137792	+	0.990461i	$0.455999\pi$
$110$		0			0
$111$	0.318305	+	2.00970i	0.0302122	+	0.190752i
$112$		0			0
$113$	1.70237	−	1.23684i	0.160145	−	0.116352i	−0.504827	−	0.863221i	$-0.668444\pi$
$113$	1.70237	−	1.23684i	0.160145	−	0.116352i	0.664972	+	0.746869i	$0.268444\pi$
$114$		0			0
$115$	4.08206	+	5.61848i	0.380654	+	0.523926i
$116$		0			0
$117$	12.2821	+	24.1049i	1.13548	+	2.22850i
$118$		0			0
$119$	−1.40031	−	1.01738i	−0.128366	−	0.0932633i
$120$		0			0
$121$	2.48198	+	0.806444i	0.225634	+	0.0733131i
$122$		0			0
$123$	−10.4033	−	17.7532i	−0.938038	−	1.60076i
$124$		0			0
$125$	−0.951057	−	0.309017i	−0.0850651	−	0.0276393i
$126$		0			0
$127$	10.3782	+	7.54023i	0.920920	+	0.669088i	0.943753	−	0.330652i	$-0.107269\pi$
$127$	10.3782	+	7.54023i	0.920920	+	0.669088i	−0.0228328	+	0.999739i	$0.507269\pi$
$128$		0			0
$129$	−9.98255	−	19.5919i	−0.878914	−	1.72497i
$130$		0			0
$131$	0.421661	+	0.580367i	0.0368407	+	0.0507069i	0.827040	−	0.562143i	$-0.190023\pi$
$131$	0.421661	+	0.580367i	0.0368407	+	0.0507069i	−0.790199	+	0.612850i	$0.790023\pi$
$132$		0			0
$133$	23.6897	−	17.2115i	2.05415	−	1.49243i
$134$		0			0
$135$	2.17524	+	13.7339i	0.187215	+	1.18203i
$136$		0			0
$137$	6.06271	−	6.06271i	0.517973	−	0.517973i	−0.398985	−	0.916958i	$-0.630637\pi$
$137$	6.06271	−	6.06271i	0.517973	−	0.517973i	0.916958	+	0.398985i	$0.130637\pi$
$138$		0			0
$139$	1.42063	+	4.37226i	0.120497	+	0.370850i	0.993054	−	0.117662i	$-0.0375399\pi$
$139$	1.42063	+	4.37226i	0.120497	+	0.370850i	−0.872557	+	0.488512i	$0.837540\pi$
$140$		0			0
$141$	11.8946	−	36.6078i	1.00171	−	3.08293i
$142$		0			0
$143$	−12.9548	+	4.20926i	−1.08333	+	0.351996i
$144$		0			0
$145$	5.81873	+	2.96479i	0.483219	+	0.246213i
$146$		0			0
$147$	5.44197	−	34.3593i	0.448846	−	2.83390i
$148$		0			0
$149$	2.84386	−	0.450423i	0.232978	−	0.0369001i	−0.0388536	−	0.999245i	$-0.512371\pi$
$149$	2.84386	−	0.450423i	0.232978	−	0.0369001i	0.271832	+	0.962345i	$0.412371\pi$
$150$		0			0
$151$	−12.4594	+	6.34838i	−1.01393	+	0.516624i	−0.880305	−	0.474408i	$-0.842662\pi$
$151$	−12.4594	+	6.34838i	−1.01393	+	0.516624i	−0.133626	+	0.991032i	$0.542662\pi$
$152$		0			0
$153$	2.96684	+	0.469902i	0.239855	+	0.0379893i
$154$		0			0
$155$		−	8.13267i		−	0.653232i
$156$		0			0
$157$	3.99416	−	7.83898i	0.318769	−	0.625618i	−0.674908	−	0.737902i	$-0.735817\pi$
$157$	3.99416	−	7.83898i	0.318769	−	0.625618i	0.993676	+	0.112284i	$0.0358166\pi$
$158$		0			0
$159$	12.1738	−	16.7557i	0.965442	−	1.32882i
$160$		0			0
$161$	20.7331	+	20.7331i	1.63399	+	1.63399i
$162$		0			0
$163$	2.70984			0.212251			0.106125	−	0.994353i	$-0.466156\pi$
$163$	2.70984			0.212251			0.106125	+	0.994353i	$0.466156\pi$
$164$		0			0
$165$	−11.8553			−0.922932
$166$		0			0
$167$	−14.0294	−	14.0294i	−1.08563	−	1.08563i	−0.995973	−	0.0896551i	$-0.971424\pi$
$167$	−14.0294	−	14.0294i	−1.08563	−	1.08563i	−0.0896551	−	0.995973i	$-0.528576\pi$
$168$		0			0
$169$	0.372191	−	0.512277i	0.0286301	−	0.0394060i
$170$		0			0
$171$	−23.0705	+	45.2784i	−1.76424	+	3.46252i
$172$		0			0
$173$			24.3013i			1.84759i	0.382883	+	0.923797i	$0.374931\pi$
$173$			24.3013i			1.84759i	−0.382883	+	0.923797i	$0.625069\pi$
$174$		0			0
$175$	−4.17001	−	0.660465i	−0.315223	−	0.0499265i
$176$		0			0
$177$	−13.2692	+	6.76101i	−0.997377	+	0.508189i
$178$		0			0
$179$	−7.51613	+	1.19044i	−0.561782	+	0.0889776i	−0.430866	−	0.902416i	$-0.641792\pi$
$179$	−7.51613	+	1.19044i	−0.561782	+	0.0889776i	−0.130916	+	0.991393i	$0.541792\pi$
$180$		0			0
$181$	−0.637260	+	4.02350i	−0.0473672	+	0.299064i	−0.999987	−	0.00509903i	$-0.998377\pi$
$181$	−0.637260	+	4.02350i	−0.0473672	+	0.299064i	0.952620	+	0.304164i	$0.0983769\pi$
$182$		0			0
$183$	−37.9275	−	19.3250i	−2.80368	−	1.42855i
$184$		0			0
$185$	0.602186	−	0.195662i	0.0442736	−	0.0143854i
$186$		0			0
$187$	−0.467364	+	1.43840i	−0.0341770	+	0.105186i
$188$		0			0
$189$	18.1415	+	55.8339i	1.31960	+	4.06132i
$190$		0			0
$191$	7.73422	−	7.73422i	0.559629	−	0.559629i	−0.369573	−	0.929202i	$-0.620496\pi$
$191$	7.73422	−	7.73422i	0.559629	−	0.559629i	0.929202	+	0.369573i	$0.120496\pi$
$192$		0			0
$193$	1.41861	+	8.95673i	0.102113	+	0.644719i	0.984659	+	0.174492i	$0.0558282\pi$
$193$	1.41861	+	8.95673i	0.102113	+	0.644719i	−0.882545	+	0.470228i	$0.844172\pi$
$194$		0			0
$195$	9.59939	−	6.97437i	0.687427	−	0.499445i
$196$		0			0
$197$	9.31438	+	12.8201i	0.663622	+	0.913397i	0.999595	−	0.0284747i	$-0.00906499\pi$
$197$	9.31438	+	12.8201i	0.663622	+	0.913397i	−0.335973	+	0.941872i	$0.609065\pi$
$198$		0			0
$199$	−9.48628	−	18.6179i	−0.672464	−	1.31979i	−0.934926	−	0.354843i	$-0.884534\pi$
$199$	−9.48628	−	18.6179i	−0.672464	−	1.31979i	0.262461	−	0.964942i	$-0.415466\pi$
$200$		0			0
$201$	12.9595	+	9.41560i	0.914090	+	0.664125i
$202$		0			0
$203$	26.2223	+	8.52015i	1.84045	+	0.597997i
$204$		0			0
$205$	−4.95002	+	4.06168i	−0.345725	+	0.283680i
$206$		0			0
$207$	−48.3942	−	15.7242i	−3.36363	−	1.09291i
$208$		0			0
$209$	−20.6998	−	15.0393i	−1.43183	−	1.04029i
$210$		0			0
$211$	−6.13155	−	12.0338i	−0.422113	−	0.828444i	−0.999925	−	0.0122739i	$-0.996093\pi$
$211$	−6.13155	−	12.0338i	−0.422113	−	0.828444i	0.577811	−	0.816170i	$-0.303907\pi$
$212$		0			0
$213$	10.3906	+	14.3015i	0.711955	+	0.979922i
$214$		0			0
$215$	−5.53561	+	4.02185i	−0.377525	+	0.274288i
$216$		0			0
$217$	−5.37135	−	33.9133i	−0.364631	−	2.30219i
$218$		0			0
$219$	−7.17715	+	7.17715i	−0.484987	+	0.484987i
$220$		0			0
$221$	−0.467767	−	1.43964i	−0.0314654	−	0.0968406i
$222$		0			0
$223$	−2.79750	+	8.60982i	−0.187334	+	0.576556i	−0.999981	−	0.00620111i	$-0.998026\pi$
$223$	−2.79750	+	8.60982i	−0.187334	+	0.576556i	0.812646	+	0.582757i	$0.198026\pi$
$224$		0			0
$225$	6.96839	−	2.26417i	0.464559	−	0.150945i
$226$		0			0
$227$	5.17182	+	2.63517i	0.343266	+	0.174903i	0.617121	−	0.786868i	$-0.288299\pi$
$227$	5.17182	+	2.63517i	0.343266	+	0.174903i	−0.273855	+	0.961771i	$0.588299\pi$
$228$		0			0
$229$	4.17130	−	26.3365i	0.275647	−	1.74037i	−0.329412	−	0.944186i	$-0.606851\pi$
$229$	4.17130	−	26.3365i	0.275647	−	1.74037i	0.605059	−	0.796180i	$-0.293149\pi$
$230$		0			0
$231$	−49.4366	+	7.82999i	−3.25269	+	0.515176i
$232$		0			0
$233$	6.51369	−	3.31889i	0.426726	−	0.217428i	−0.227419	−	0.973797i	$-0.573029\pi$
$233$	6.51369	−	3.31889i	0.426726	−	0.217428i	0.654145	+	0.756369i	$0.273029\pi$
$234$		0			0
$235$	−11.8304	−	1.87375i	−0.771731	−	0.122230i
$236$		0			0
$237$		−	26.7633i		−	1.73846i
$238$		0			0
$239$	5.06444	−	9.93953i	0.327592	−	0.642935i	−0.667198	−	0.744880i	$-0.732507\pi$
$239$	5.06444	−	9.93953i	0.327592	−	0.642935i	0.994790	+	0.101945i	$0.0325066\pi$
$240$		0			0
$241$	−13.5734	+	18.6821i	−0.874338	+	1.20342i	0.103620	+	0.994617i	$0.466958\pi$
$241$	−13.5734	+	18.6821i	−0.874338	+	1.20342i	−0.977957	+	0.208805i	$0.933042\pi$
$242$		0			0
$243$	−22.0937	−	22.0937i	−1.41731	−	1.41731i
$244$		0			0
$245$	−10.8252			−0.691598
$246$		0			0
$247$	25.6084			1.62942
$248$		0			0
$249$	−5.58640	−	5.58640i	−0.354024	−	0.354024i
$250$		0			0
$251$	8.43729	−	11.6129i	0.532557	−	0.733002i	−0.454960	−	0.890512i	$-0.650347\pi$
$251$	8.43729	−	11.6129i	0.532557	−	0.733002i	0.987517	+	0.157510i	$0.0503465\pi$
$252$		0			0
$253$	11.6314	−	22.8279i	0.731260	−	1.43518i
$254$		0			0
$255$		−	1.31745i		−	0.0825021i
$256$		0			0
$257$	−19.2823	−	3.05401i	−1.20280	−	0.190504i	−0.477306	−	0.878737i	$-0.658387\pi$
$257$	−19.2823	−	3.05401i	−1.20280	−	0.190504i	−0.725490	+	0.688233i	$0.758387\pi$
$258$		0			0
$259$	2.38190	−	1.21364i	0.148004	−	0.0754117i
$260$		0			0
$261$	−47.2600	+	7.48525i	−2.92532	+	0.463325i
$262$		0			0
$263$	−1.03565	+	6.53882i	−0.0638607	+	0.403201i	0.934964	+	0.354741i	$0.115431\pi$
$263$	−1.03565	+	6.53882i	−0.0638607	+	0.403201i	−0.998825	+	0.0484593i	$0.984569\pi$
$264$		0			0
$265$	−5.74248	−	2.92594i	−0.352758	−	0.179739i
$266$		0			0
$267$	6.40272	−	2.08037i	0.391840	−	0.127317i
$268$		0			0
$269$	−8.25958	+	25.4204i	−0.503596	+	1.54991i	0.299523	+	0.954089i	$0.403172\pi$
$269$	−8.25958	+	25.4204i	−0.503596	+	1.54991i	−0.803119	+	0.595819i	$0.796828\pi$
$270$		0			0
$271$	−3.74087	−	11.5132i	−0.227242	−	0.699379i	−0.998056	−	0.0623190i	$-0.980150\pi$
$271$	−3.74087	−	11.5132i	−0.227242	−	0.699379i	0.770814	−	0.637060i	$-0.219850\pi$
$272$		0			0
$273$	35.4233	−	35.4233i	2.14391	−	2.14391i
$274$		0			0
$275$	0.577108	+	3.64371i	0.0348009	+	0.219724i
$276$		0			0
$277$	7.00313	−	5.08807i	0.420777	−	0.305712i	−0.357173	−	0.934038i	$-0.616259\pi$
$277$	7.00313	−	5.08807i	0.420777	−	0.305712i	0.777950	+	0.628326i	$0.216259\pi$
$278$		0			0
$279$	35.0250	+	48.2078i	2.09689	+	2.88612i
$280$		0			0
$281$	2.79157	+	5.47877i	0.166531	+	0.326836i	0.959158	−	0.282871i	$-0.0912870\pi$
$281$	2.79157	+	5.47877i	0.166531	+	0.326836i	−0.792627	+	0.609707i	$0.791287\pi$
$282$		0			0
$283$	12.5306	+	9.10403i	0.744869	+	0.541179i	0.894232	−	0.447604i	$-0.147722\pi$
$283$	12.5306	+	9.10403i	0.744869	+	0.541179i	−0.149364	+	0.988782i	$0.547722\pi$
$284$		0			0
$285$	21.1971	+	6.88736i	1.25561	+	0.407972i
$286$		0			0
$287$	−17.9591	+	20.2066i	−1.06009	+	1.19276i
$288$		0			0
$289$	16.0081	+	5.20135i	0.941654	+	0.305962i
$290$		0			0
$291$	−29.9694	−	21.7740i	−1.75684	−	1.27642i
$292$		0			0
$293$	3.61686	+	7.09848i	0.211299	+	0.414698i	0.972194	−	0.234177i	$-0.0752397\pi$
$293$	3.61686	+	7.09848i	0.211299	+	0.414698i	−0.760895	+	0.648875i	$0.775240\pi$
$294$		0			0
$295$	2.72393	+	3.74917i	0.158594	+	0.218285i
$296$		0			0
$297$	41.5008	−	30.1521i	2.40812	−	1.74960i
$298$		0			0
$299$	4.01137	+	25.3268i	0.231983	+	1.46468i
$300$		0			0
$301$	−20.4273	+	20.4273i	−1.17741	+	1.17741i
$302$		0			0
$303$	−2.31124	−	7.11325i	−0.132777	−	0.408646i
$304$		0			0
$305$	−4.09325	+	12.5977i	−0.234379	+	0.721345i
$306$		0			0
$307$	16.3856	−	5.32399i	0.935173	−	0.303856i	0.198497	−	0.980102i	$-0.436394\pi$
$307$	16.3856	−	5.32399i	0.935173	−	0.303856i	0.736677	+	0.676245i	$0.236394\pi$
$308$		0			0
$309$	27.7637	+	14.1463i	1.57942	+	0.804755i
$310$		0			0
$311$	−2.53328	+	15.9945i	−0.143649	+	0.906964i	0.805605	+	0.592453i	$0.201840\pi$
$311$	−2.53328	+	15.9945i	−0.143649	+	0.906964i	−0.949254	+	0.314511i	$0.898160\pi$
$312$		0			0
$313$	−25.3553	+	4.01588i	−1.43316	+	0.226991i	−0.824241	−	0.566239i	$-0.808398\pi$
$313$	−25.3553	+	4.01588i	−1.43316	+	0.226991i	−0.608922	+	0.793230i	$0.708398\pi$
$314$		0			0
$315$	27.5629	−	14.0440i	1.55299	−	0.791289i
$316$		0			0
$317$	6.31800	+	1.00067i	0.354854	+	0.0562034i	0.331317	−	0.943520i	$-0.392507\pi$
$317$	6.31800	+	1.00067i	0.354854	+	0.0562034i	0.0235374	+	0.999723i	$0.492507\pi$
$318$		0			0
$319$		−	24.0919i		−	1.34889i
$320$		0			0
$321$	14.2179	−	27.9042i	0.793567	−	1.55746i
$322$		0			0
$323$	1.67128	−	2.30033i	0.0929928	−	0.127994i
$324$		0			0
$325$	−2.61086	−	2.61086i	−0.144825	−	0.144825i
$326$		0			0
$327$	−40.4572			−2.23729
$328$		0			0
$329$	−50.5705			−2.78804
$330$		0			0
$331$	11.8848	+	11.8848i	0.653248	+	0.653248i	0.953774	−	0.300526i	$-0.0971622\pi$
$331$	11.8848	+	11.8848i	0.653248	+	0.653248i	−0.300526	+	0.953774i	$0.597162\pi$
$332$		0			0
$333$	−2.72690	+	3.75326i	−0.149433	+	0.205677i
$334$		0			0
$335$	2.26302	−	4.44143i	0.123642	−	0.242661i
$336$		0			0
$337$			10.2602i			0.558909i	0.960159	+	0.279455i	$0.0901537\pi$
$337$			10.2602i			0.558909i	−0.960159	+	0.279455i	$0.909846\pi$
$338$		0			0
$339$	6.67886	+	1.05783i	0.362746	+	0.0574533i
$340$		0			0
$341$	−26.7324	+	13.6209i	−1.44764	+	0.737611i
$342$		0			0
$343$	−15.9512	+	2.52643i	−0.861285	+	0.136414i
$344$		0			0
$345$	−3.49125	+	22.0429i	−0.187962	+	1.18675i
$346$		0			0
$347$	20.9223	+	10.6604i	1.12317	+	0.572282i	0.914047	−	0.405609i	$-0.132940\pi$
$347$	20.9223	+	10.6604i	1.12317	+	0.572282i	0.209119	+	0.977890i	$0.432940\pi$
$348$		0			0
$349$	−14.2515	+	4.63060i	−0.762866	+	0.247870i	−0.664508	−	0.747281i	$-0.731359\pi$
$349$	−14.2515	+	4.63060i	−0.762866	+	0.247870i	−0.0983576	+	0.995151i	$0.531359\pi$
$350$		0			0
$351$	−15.8656	+	48.8292i	−0.846841	+	2.60631i
$352$		0			0
$353$	0.402375	+	1.23838i	0.0214163	+	0.0659125i	0.961193	−	0.275875i	$-0.0889676\pi$
$353$	0.402375	+	1.23838i	0.0214163	+	0.0659125i	−0.939777	+	0.341788i	$0.888968\pi$
$354$		0			0
$355$	3.88975	−	3.88975i	0.206446	−	0.206446i
$356$		0			0
$357$	−0.870132	−	5.49380i	−0.0460523	−	0.290763i
$358$		0			0
$359$	27.5627	−	20.0255i	1.45470	−	1.05690i	0.470001	−	0.882666i	$-0.344254\pi$
$359$	27.5627	−	20.0255i	1.45470	−	1.05690i	0.984703	−	0.174239i	$-0.0557464\pi$
$360$		0			0
$361$	17.1060	+	23.5444i	0.900315	+	1.23918i
$362$		0			0
$363$	3.80737	+	7.47239i	0.199835	+	0.392199i
$364$		0			0
$365$	2.55528	+	1.85652i	0.133749	+	0.0971745i
$366$		0			0
$367$	7.78450	+	2.52934i	0.406348	+	0.132030i	0.505057	−	0.863086i	$-0.331471\pi$
$367$	7.78450	+	2.52934i	0.406348	+	0.132030i	−0.0987095	+	0.995116i	$0.531471\pi$
$368$		0			0
$369$	11.8496	−	45.3946i	0.616867	−	2.36315i
$370$		0			0
$371$	−25.8787	−	8.40850i	−1.34356	−	0.436548i
$372$		0			0
$373$	9.95850	+	7.23528i	0.515632	+	0.374628i	0.814956	−	0.579523i	$-0.196761\pi$
$373$	9.95850	+	7.23528i	0.515632	+	0.374628i	−0.299324	+	0.954152i	$0.596761\pi$
$374$		0			0
$375$	−1.45893	−	2.86331i	−0.0753387	−	0.147861i
$376$		0			0
$377$	14.1731	+	19.5076i	0.729952	+	1.00469i
$378$		0			0
$379$	−2.32363	+	1.68822i	−0.119357	+	0.0867179i	−0.645862	−	0.763454i	$-0.723502\pi$
$379$	−2.32363	+	1.68822i	−0.119357	+	0.0867179i	0.526505	+	0.850172i	$0.323502\pi$
$380$		0			0
$381$	6.44890	+	40.7168i	0.330387	+	2.08598i
$382$		0			0
$383$	3.72754	−	3.72754i	0.190468	−	0.190468i	−0.605430	−	0.795898i	$-0.706999\pi$
$383$	3.72754	−	3.72754i	0.190468	−	0.190468i	0.795898	+	0.605430i	$0.206999\pi$
$384$		0			0
$385$	4.81309	+	14.8132i	0.245298	+	0.754949i
$386$		0			0
$387$	15.4923	−	47.6804i	0.787518	−	2.42373i
$388$		0			0
$389$	−25.6732	+	8.34171i	−1.30168	+	0.422942i	−0.876166	−	0.482010i	$-0.839907\pi$
$389$	−25.6732	+	8.34171i	−1.30168	+	0.422942i	−0.425515	+	0.904951i	$0.639907\pi$
$390$		0			0
$391$	2.53682	+	1.29258i	0.128293	+	0.0653683i
$392$		0			0
$393$	−0.360632	+	2.27694i	−0.0181915	+	0.114857i
$394$		0			0
$395$	−8.22568	+	1.30282i	−0.413879	+	0.0655520i
$396$		0			0
$397$	27.7456	−	14.1371i	1.39251	−	0.709520i	0.412967	−	0.910746i	$-0.364493\pi$
$397$	27.7456	−	14.1371i	1.39251	−	0.709520i	0.979545	+	0.201226i	$0.0644926\pi$
$398$		0			0
$399$	92.9411	+	14.7204i	4.65288	+	0.736943i
$400$		0			0
$401$		−	14.5533i		−	0.726757i	−0.931642	−	0.363379i	$-0.881623\pi$
$401$		−	14.5533i		−	0.726757i	0.931642	−	0.363379i	$-0.118377\pi$
$402$		0			0
$403$	13.6326	−	26.7555i	0.679089	−	1.33279i
$404$		0			0
$405$	−13.3450	+	18.3679i	−0.663120	+	0.912707i
$406$		0			0
$407$	−1.65171	−	1.65171i	−0.0818722	−	0.0818722i
$408$		0			0
$409$	−6.76561			−0.334538			−0.167269	−	0.985911i	$-0.553495\pi$
$409$	−6.76561			−0.334538			−0.167269	+	0.985911i	$0.553495\pi$
$410$		0			0
$411$	27.5530			1.35909
$412$		0			0
$413$	13.8350	+	13.8350i	0.680778	+	0.680778i
$414$		0			0
$415$	−1.44504	+	1.98892i	−0.0709340	+	0.0976323i
$416$		0			0
$417$	−6.70708	+	13.1634i	−0.328447	+	0.644614i
$418$		0			0
$419$		−	16.2325i		−	0.793008i	−0.918033	−	0.396504i	$-0.870223\pi$
$419$		−	16.2325i		−	0.793008i	0.918033	−	0.396504i	$-0.129777\pi$
$420$		0			0
$421$	25.4488	+	4.03070i	1.24030	+	0.196444i	0.741905	−	0.670505i	$-0.233923\pi$
$421$	25.4488	+	4.03070i	1.24030	+	0.196444i	0.498396	+	0.866950i	$0.333923\pi$
$422$		0			0
$423$	78.1965	−	39.8431i	3.80204	−	1.93724i
$424$		0			0
$425$	−0.404919	+	0.0641329i	−0.0196415	+	0.00311090i
$426$		0			0
$427$	−8.74855	+	55.2362i	−0.423372	+	2.67307i
$428$		0			0
$429$	−39.0024	−	19.8727i	−1.88305	−	0.959464i
$430$		0			0
$431$	−1.79076	+	0.581854i	−0.0862580	+	0.0280269i	−0.351828	−	0.936065i	$-0.614440\pi$
$431$	−1.79076	+	0.581854i	−0.0862580	+	0.0280269i	0.265570	+	0.964092i	$0.414440\pi$
$432$		0			0
$433$	3.22537	−	9.92667i	0.155001	−	0.477045i	−0.843160	−	0.537663i	$-0.819307\pi$
$433$	3.22537	−	9.92667i	0.155001	−	0.477045i	0.998161	+	0.0606180i	$0.0193071\pi$
$434$		0			0
$435$	6.48510	+	19.9591i	0.310937	+	0.956966i
$436$		0			0
$437$	−34.0588	+	34.0588i	−1.62925	+	1.62925i
$438$		0			0
$439$	−4.01237	−	25.3331i	−0.191500	−	1.20908i	−0.876812	−	0.480834i	$-0.840334\pi$
$439$	−4.01237	−	25.3331i	−0.191500	−	1.20908i	0.685311	−	0.728250i	$-0.259666\pi$
$440$		0			0
$441$	64.1683	−	46.6210i	3.05563	−	2.22005i
$442$		0			0
$443$	−10.5671	−	14.5443i	−0.502056	−	0.691021i	0.480498	−	0.876996i	$-0.340456\pi$
$443$	−10.5671	−	14.5443i	−0.502056	−	0.691021i	−0.982555	+	0.185975i	$0.940456\pi$
$444$		0			0
$445$	−0.951082	−	1.86660i	−0.0450856	−	0.0884855i
$446$		0			0
$447$	7.48571	+	5.43869i	0.354062	+	0.257241i
$448$		0			0
$449$	11.1010	+	3.60694i	0.523889	+	0.170222i	0.559010	−	0.829161i	$-0.311181\pi$
$449$	11.1010	+	3.60694i	0.523889	+	0.170222i	−0.0351205	+	0.999383i	$0.511181\pi$
$450$		0			0
$451$	21.6414	+	9.46830i	1.01905	+	0.445845i
$452$		0			0
$453$	−42.7375	−	13.8863i	−2.00799	−	0.652434i
$454$		0			0
$455$	−12.6117	−	9.16295i	−0.591246	−	0.429566i
$456$		0			0
$457$	15.6379	+	30.6912i	0.731512	+	1.43567i	0.893585	+	0.448894i	$0.148182\pi$
$457$	15.6379	+	30.6912i	0.731512	+	1.43567i	−0.162073	+	0.986779i	$0.551818\pi$
$458$		0			0
$459$	3.35074	+	4.61190i	0.156399	+	0.215265i
$460$		0			0
$461$	−4.74767	+	3.44939i	−0.221121	+	0.160654i	−0.692831	−	0.721100i	$-0.743637\pi$
$461$	−4.74767	+	3.44939i	−0.221121	+	0.160654i	0.471710	+	0.881754i	$0.343637\pi$
$462$		0			0
$463$	−0.672543	−	4.24627i	−0.0312557	−	0.197341i	0.967120	−	0.254322i	$-0.0818524\pi$
$463$	−0.672543	−	4.24627i	−0.0312557	−	0.197341i	−0.998375	+	0.0569815i	$0.981852\pi$
$464$		0			0
$465$	18.4801	−	18.4801i	0.856996	−	0.856996i
$466$		0			0
$467$	−7.10554	−	21.8686i	−0.328805	−	1.01196i	−0.969694	−	0.244324i	$-0.921434\pi$
$467$	−7.10554	−	21.8686i	−0.328805	−	1.01196i	0.640888	−	0.767634i	$-0.278566\pi$
$468$		0			0
$469$	6.50342	−	20.0155i	0.300300	−	0.924229i
$470$		0			0
$471$	26.8888	−	8.73671i	1.23897	−	0.402566i
$472$		0			0
$473$	22.4912	+	11.4598i	1.03415	+	0.526924i
$474$		0			0
$475$	1.08497	−	6.85020i	0.0497816	−	0.314309i
$476$		0			0
$477$	46.6407	−	7.38716i	2.13553	−	0.338235i
$478$		0			0
$479$	−22.6718	+	11.5519i	−1.03590	+	0.527819i	−0.887355	−	0.461086i	$-0.847460\pi$
$479$	−22.6718	+	11.5519i	−1.03590	+	0.527819i	−0.148548	+	0.988905i	$0.547460\pi$
$480$		0			0
$481$	2.30910	+	0.365726i	0.105286	+	0.0166757i
$482$		0			0
$483$			94.2248i			4.28738i
$484$		0			0
$485$	−5.23335	+	10.2710i	−0.237634	+	0.466383i
$486$		0			0
$487$	−13.1505	+	18.1001i	−0.595904	+	0.820192i	−0.995326	−	0.0965756i	$-0.969211\pi$
$487$	−13.1505	+	18.1001i	−0.595904	+	0.820192i	0.399421	+	0.916767i	$0.369211\pi$
$488$		0			0
$489$	6.15765	+	6.15765i	0.278459	+	0.278459i
$490$		0			0
$491$	43.4585			1.96126			0.980628	−	0.195880i	$-0.0627564\pi$
$491$	43.4585			1.96126			0.980628	+	0.195880i	$0.0627564\pi$
$492$		0			0
$493$	2.67729			0.120579
$494$		0			0
$495$	−19.1133	−	19.1133i	−0.859079	−	0.859079i
$496$		0			0
$497$	13.6513	−	18.7893i	0.612343	−	0.842817i
$498$		0			0
$499$	20.0752	−	39.3998i	0.898690	−	1.76378i	0.322206	−	0.946670i	$-0.395576\pi$
$499$	20.0752	−	39.3998i	0.898690	−	1.76378i	0.576484	−	0.817109i	$-0.304424\pi$
$500$		0			0
$501$		−	63.7590i		−	2.84854i
$502$		0			0
$503$	−2.28970	−	0.362653i	−0.102093	−	0.0161699i	0.105179	−	0.994453i	$-0.466458\pi$
$503$	−2.28970	−	0.362653i	−0.102093	−	0.0161699i	−0.207272	+	0.978283i	$0.566458\pi$
$504$		0			0
$505$	−2.07375	+	1.05663i	−0.0922805	+	0.0470193i
$506$		0			0
$507$	2.00981	−	0.318322i	0.0892587	−	0.0141372i
$508$		0			0
$509$	1.36666	−	8.62877i	0.0605762	−	0.382463i	−0.938711	−	0.344706i	$-0.887979\pi$
$509$	1.36666	−	8.62877i	0.0605762	−	0.382463i	0.999287	−	0.0377573i	$-0.0120214\pi$
$510$		0			0
$511$	11.8817	+	6.05403i	0.525615	+	0.267814i
$512$		0			0
$513$	−91.7200	+	29.8016i	−4.04954	+	1.31577i
$514$		0			0
$515$	2.99634	−	9.22180i	0.132035	−	0.406361i
$516$		0			0
$517$	13.6548	+	42.0253i	0.600539	+	1.84827i
$518$		0			0
$519$	−55.2207	+	55.2207i	−2.42392	+	2.42392i
$520$		0			0
$521$	1.73654	+	10.9641i	0.0760791	+	0.480344i	0.996082	+	0.0884331i	$0.0281859\pi$
$521$	1.73654	+	10.9641i	0.0760791	+	0.480344i	−0.920003	+	0.391911i	$0.871814\pi$
$522$		0			0
$523$	18.2536	−	13.2621i	0.798176	−	0.579909i	−0.112202	−	0.993685i	$-0.535790\pi$
$523$	18.2536	−	13.2621i	0.798176	−	0.579909i	0.910379	+	0.413776i	$0.135790\pi$
$524$		0			0
$525$	−7.97486	−	10.9765i	−0.348052	−	0.479052i
$526$		0			0
$527$	−1.51366	−	2.97072i	−0.0659361	−	0.129407i
$528$		0			0
$529$	−20.4119	−	14.8301i	−0.887474	−	0.644787i
$530$		0			0
$531$	−32.2932	−	10.4927i	−1.40140	−	0.455344i
$532$		0			0
$533$	−23.0935	+	5.06483i	−1.00029	+	0.219382i
$534$		0			0
$535$	−9.26848	−	3.01151i	−0.400711	−	0.130199i
$536$		0			0
$537$	−19.7842	−	14.3741i	−0.853753	−	0.620288i
$538$		0			0
$539$	18.1304	+	35.5830i	0.780933	+	1.53267i
$540$		0			0
$541$	−4.48873	−	6.17821i	−0.192986	−	0.265622i	0.701548	−	0.712622i	$-0.252492\pi$
$541$	−4.48873	−	6.17821i	−0.192986	−	0.265622i	−0.894534	+	0.447000i	$0.852492\pi$
$542$		0			0
$543$	−10.5908	+	7.69467i	−0.454495	+	0.330210i
$544$		0			0
$545$	1.96943	+	12.4345i	0.0843612	+	0.532636i
$546$		0			0
$547$	−21.6382	+	21.6382i	−0.925183	+	0.925183i	−0.997390	−	0.0722070i	$-0.976996\pi$
$547$	−21.6382	+	21.6382i	−0.925183	+	0.925183i	0.0722070	+	0.997390i	$0.476996\pi$
$548$		0			0
$549$	−29.9913	−	92.3036i	−1.28000	−	3.93942i
$550$		0			0
$551$	−13.9963	+	43.0762i	−0.596263	+	1.83511i
$552$		0			0
$553$	−33.4407	+	10.8656i	−1.42205	+	0.462050i
$554$		0			0
$555$	1.81298	+	0.923758i	0.0769566	+	0.0392113i
$556$		0			0
$557$	1.57446	−	9.94075i	0.0667120	−	0.421203i	−0.931618	−	0.363438i	$-0.881603\pi$
$557$	1.57446	−	9.94075i	0.0667120	−	0.421203i	0.998330	−	0.0577647i	$-0.0183973\pi$
$558$		0			0
$559$	−24.9532	+	3.95220i	−1.05541	+	0.167160i
$560$		0			0
$561$	−4.33053	+	2.20651i	−0.182835	+	0.0931591i
$562$		0			0
$563$	17.3837	+	2.75331i	0.732637	+	0.116038i	0.511596	−	0.859226i	$-0.329054\pi$
$563$	17.3837	+	2.75331i	0.732637	+	0.116038i	0.221041	+	0.975264i	$0.429054\pi$
$564$		0			0
$565$		−	2.10424i		−	0.0885260i
$566$		0			0
$567$	−43.5176	+	85.4082i	−1.82757	+	3.58681i
$568$		0			0
$569$	−21.4876	+	29.5751i	−0.900805	+	1.23985i	0.0694049	+	0.997589i	$0.477890\pi$
$569$	−21.4876	+	29.5751i	−0.900805	+	1.23985i	−0.970210	+	0.242264i	$0.922110\pi$
$570$		0			0
$571$	−7.82512	−	7.82512i	−0.327471	−	0.327471i	0.524153	−	0.851624i	$-0.324382\pi$
$571$	−7.82512	−	7.82512i	−0.327471	−	0.327471i	−0.851624	+	0.524153i	$0.824382\pi$
$572$		0			0
$573$	35.1495			1.46839
$574$		0			0
$575$	6.94482			0.289619
$576$		0			0
$577$	3.60766	+	3.60766i	0.150189	+	0.150189i	0.778202	−	0.628014i	$-0.216132\pi$
$577$	3.60766	+	3.60766i	0.150189	+	0.150189i	−0.628014	+	0.778202i	$0.716132\pi$
$578$		0			0
$579$	−17.1291	+	23.5762i	−0.711862	+	0.979794i
$580$		0			0
$581$	−4.71221	+	9.24822i	−0.195495	+	0.383681i
$582$		0			0
$583$			23.7762i			0.984711i
$584$		0			0
$585$	26.7205	+	4.23212i	1.10476	+	0.174977i
$586$		0			0
$587$	4.64215	−	2.36529i	0.191602	−	0.0976261i	−0.355558	−	0.934654i	$-0.615709\pi$
$587$	4.64215	−	2.36529i	0.191602	−	0.0976261i	0.547160	+	0.837028i	$0.315709\pi$
$588$		0			0
$589$	55.7105	−	8.82367i	2.29551	−	0.363573i
$590$		0			0
$591$	−7.96626	+	50.2970i	−0.327688	+	2.06894i
$592$		0			0
$593$	−13.7216	−	6.99150i	−0.563478	−	0.287107i	0.148958	−	0.988844i	$-0.452408\pi$
$593$	−13.7216	−	6.99150i	−0.563478	−	0.287107i	−0.712436	+	0.701737i	$0.752408\pi$
$594$		0			0
$595$	−1.64616	+	0.534870i	−0.0674860	+	0.0219275i
$596$		0			0
$597$	20.7500	−	63.8620i	0.849242	−	2.61370i
$598$		0			0
$599$	−3.71599	−	11.4366i	−0.151831	−	0.467288i	0.845995	−	0.533191i	$-0.179007\pi$
$599$	−3.71599	−	11.4366i	−0.151831	−	0.467288i	−0.997826	+	0.0659027i	$0.979007\pi$
$600$		0			0
$601$	−7.25146	+	7.25146i	−0.295793	+	0.295793i	−0.839364	−	0.543570i	$-0.817072\pi$
$601$	−7.25146	+	7.25146i	−0.295793	+	0.295793i	0.543570	+	0.839364i	$0.317072\pi$
$602$		0			0
$603$	5.71348	+	36.0735i	0.232671	+	1.46903i
$604$		0			0
$605$	2.11130	−	1.53395i	0.0858364	−	0.0623638i
$606$		0			0
$607$	6.91662	+	9.51991i	0.280737	+	0.386401i	0.925978	−	0.377578i	$-0.123243\pi$
$607$	6.91662	+	9.51991i	0.280737	+	0.386401i	−0.645241	+	0.763979i	$0.723243\pi$
$608$		0			0
$609$	40.2253	+	78.9465i	1.63001	+	3.19907i
$610$		0			0
$611$	−35.7797	−	25.9955i	−1.44749	−	1.05166i
$612$		0			0
$613$	−9.55967	−	3.10612i	−0.386111	−	0.125455i	0.109528	−	0.993984i	$-0.465066\pi$
$613$	−9.55967	−	3.10612i	−0.386111	−	0.125455i	−0.495639	+	0.868529i	$0.665066\pi$
$614$		0			0
$615$	−20.4776	−	2.01861i	−0.825737	−	0.0813981i
$616$		0			0
$617$	−40.2350	−	13.0731i	−1.61980	−	0.526305i	−0.647904	−	0.761722i	$-0.724354\pi$
$617$	−40.2350	−	13.0731i	−1.61980	−	0.526305i	−0.971894	+	0.235417i	$0.924354\pi$
$618$		0			0
$619$	−23.6995	−	17.2187i	−0.952563	−	0.692078i	−0.00115171	−	0.999999i	$-0.500367\pi$
$619$	−23.6995	−	17.2187i	−0.952563	−	0.692078i	−0.951412	+	0.307921i	$0.900367\pi$
$620$		0			0
$621$	−43.8411	−	86.0430i	−1.75928	−	3.45279i
$622$		0			0
$623$	−5.19885	−	7.15561i	−0.208288	−	0.286683i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−12.8626	−	81.2110i	−0.513681	−	3.24326i
$628$		0			0
$629$	0.183551	−	0.183551i	0.00731867	−	0.00731867i
$630$		0			0
$631$	0.561861	+	1.72923i	0.0223673	+	0.0688395i	0.961617	−	0.274395i	$-0.0884775\pi$
$631$	0.561861	+	1.72923i	0.0223673	+	0.0688395i	−0.939250	+	0.343234i	$0.888478\pi$
$632$		0			0
$633$	13.4120	−	41.2779i	0.533079	−	1.64065i
$634$		0			0
$635$	12.2004	−	3.96414i	0.484156	−	0.157312i
$636$		0			0
$637$	−35.6137	−	18.1461i	−1.41107	−	0.718974i
$638$		0			0
$639$	−6.30515	+	39.8091i	−0.249428	+	1.57482i
$640$		0			0
$641$	6.64091	−	1.05182i	0.262300	−	0.0415442i	−0.0238992	−	0.999714i	$-0.507608\pi$
$641$	6.64091	−	1.05182i	0.262300	−	0.0415442i	0.286199	+	0.958170i	$0.407608\pi$
$642$		0			0
$643$	24.1798	−	12.3202i	0.953559	−	0.485863i	0.0932540	−	0.995642i	$-0.470273\pi$
$643$	24.1798	−	12.3202i	0.953559	−	0.485863i	0.860305	+	0.509780i	$0.170273\pi$
$644$		0			0
$645$	−21.7177	−	3.43975i	−0.855135	−	0.135440i
$646$		0			0
$647$			42.9895i			1.69009i	0.534695	+	0.845045i	$0.320427\pi$
$647$			42.9895i			1.69009i	−0.534695	+	0.845045i	$0.679573\pi$
$648$		0			0
$649$	7.76156	−	15.2329i	0.304668	−	0.597944i
$650$		0			0
$651$	64.8569	−	89.2679i	2.54194	−	3.49869i
$652$		0			0
$653$	6.00403	+	6.00403i	0.234956	+	0.234956i	0.814758	−	0.579802i	$-0.196870\pi$
$653$	6.00403	+	6.00403i	0.234956	+	0.234956i	−0.579802	+	0.814758i	$0.696870\pi$
$654$		0			0
$655$	0.717373			0.0280301
$656$		0			0
$657$	−23.1423			−0.902867
$658$		0			0
$659$	6.87859	+	6.87859i	0.267952	+	0.267952i	0.828275	−	0.560323i	$-0.189323\pi$
$659$	6.87859	+	6.87859i	0.267952	+	0.267952i	−0.560323	+	0.828275i	$0.689323\pi$
$660$		0			0
$661$	5.72943	−	7.88588i	0.222849	−	0.306725i	−0.682923	−	0.730490i	$-0.739292\pi$
$661$	5.72943	−	7.88588i	0.222849	−	0.306725i	0.905772	+	0.423765i	$0.139292\pi$
$662$		0			0
$663$	2.20842	−	4.33426i	0.0857678	−	0.168329i
$664$		0			0
$665$		−	29.2820i		−	1.13551i
$666$		0			0
$667$	−44.7949	−	7.09481i	−1.73446	−	0.274712i
$668$		0			0
$669$	−25.9212	+	13.2075i	−1.00217	+	0.510632i
$670$		0			0
$671$	48.2648	−	7.64440i	1.86324	−	0.295109i
$672$		0			0
$673$	−3.95044	+	24.9421i	−0.152278	+	0.961446i	0.786667	+	0.617378i	$0.211805\pi$
$673$	−3.95044	+	24.9421i	−0.152278	+	0.961446i	−0.938945	+	0.344068i	$0.888195\pi$
$674$		0			0
$675$	12.3895	+	6.31278i	0.476873	+	0.242979i
$676$		0			0
$677$	25.0321	−	8.13344i	0.962063	−	0.312593i	0.214456	−	0.976734i	$-0.431202\pi$
$677$	25.0321	−	8.13344i	0.962063	−	0.312593i	0.747608	+	0.664140i	$0.231202\pi$
$678$		0			0
$679$	−15.0395	+	46.2868i	−0.577162	+	1.77632i
$680$		0			0
$681$	5.76410	+	17.7401i	0.220881	+	0.679802i
$682$		0			0
$683$	−24.3441	+	24.3441i	−0.931502	+	0.931502i	−0.997800	−	0.0662979i	$-0.978881\pi$
$683$	−24.3441	+	24.3441i	−0.931502	+	0.931502i	0.0662979	+	0.997800i	$0.478881\pi$
$684$		0			0
$685$	−1.34126	−	8.46841i	−0.0512471	−	0.323561i
$686$		0			0
$687$	69.3239	−	50.3668i	2.64487	−	1.92161i
$688$		0			0
$689$	−13.9874	−	19.2520i	−0.532877	−	0.733442i
$690$		0			0
$691$	18.5908	+	36.4865i	0.707228	+	1.38801i	0.912405	+	0.409288i	$0.134223\pi$
$691$	18.5908	+	36.4865i	0.707228	+	1.38801i	−0.205177	+	0.978725i	$0.565777\pi$
$692$		0			0
$693$	−92.3264	−	67.0790i	−3.50719	−	2.54812i
$694$		0			0
$695$	4.37226	+	1.42063i	0.165849	+	0.0538877i
$696$		0			0
$697$	−1.05219	+	2.40497i	−0.0398547	+	0.0910946i
$698$		0			0
$699$	22.3429	+	7.25964i	0.845086	+	0.274585i
$700$		0			0
$701$	−0.363350	−	0.263989i	−0.0137235	−	0.00997073i	0.580902	−	0.813973i	$-0.302700\pi$
$701$	−0.363350	−	0.263989i	−0.0137235	−	0.00997073i	−0.594626	+	0.804003i	$0.702700\pi$
$702$		0			0
$703$	1.99368	+	3.91281i	0.0751929	+	0.147574i
$704$		0			0
$705$	−22.6249	−	31.1404i	−0.852101	−	1.17282i
$706$		0			0
$707$	−7.94969	+	5.77578i	−0.298979	+	0.217221i
$708$		0			0
$709$	−0.0782035	−	0.493757i	−0.00293699	−	0.0185435i	0.986176	−	0.165699i	$-0.0529881\pi$
$709$	−0.0782035	−	0.493757i	−0.00293699	−	0.0185435i	−0.989113	+	0.147156i	$0.952988\pi$
$710$		0			0
$711$	43.1483	−	43.1483i	1.61819	−	1.61819i
$712$		0			0
$713$	17.4533	+	53.7156i	0.653630	+	2.01166i
$714$		0			0
$715$	−4.20926	+	12.9548i	−0.157417	+	0.484481i
$716$		0			0
$717$	34.0940	−	11.0778i	1.27327	−	0.413709i
$718$		0			0
$719$	14.1999	+	7.23521i	0.529567	+	0.269828i	0.698264	−	0.715840i	$-0.253956\pi$
$719$	14.1999	+	7.23521i	0.529567	+	0.269828i	−0.168697	+	0.985668i	$0.553956\pi$
$720$		0			0
$721$	6.40412	−	40.4340i	0.238502	−	1.50584i
$722$		0			0
$723$	−73.2953	+	11.6088i	−2.72588	+	0.431737i
$724$		0			0
$725$	5.81873	−	2.96479i	0.216102	−	0.110110i
$726$		0			0
$727$	21.6988	+	3.43675i	0.804764	+	0.127462i	0.545246	−	0.838276i	$-0.316436\pi$
$727$	21.6988	+	3.43675i	0.804764	+	0.127462i	0.259518	+	0.965738i	$0.416436\pi$
$728$		0			0
$729$		−	32.2969i		−	1.19618i
$730$		0			0
$731$	−1.27351	+	2.49941i	−0.0471025	+	0.0924438i
$732$		0			0
$733$	14.2820	−	19.6575i	0.527518	−	0.726067i	−0.459231	−	0.888317i	$-0.651875\pi$
$733$	14.2820	−	19.6575i	0.527518	−	0.726067i	0.986750	+	0.162250i	$0.0518751\pi$
$734$		0			0
$735$	−24.5985	−	24.5985i	−0.907330	−	0.907330i
$736$		0			0
$737$	−18.3894			−0.677381
$738$		0			0
$739$	−25.6217			−0.942509			−0.471255	−	0.881997i	$-0.656199\pi$
$739$	−25.6217			−0.942509			−0.471255	+	0.881997i	$0.656199\pi$
$740$		0			0
$741$	58.1908	+	58.1908i	2.13769	+	2.13769i
$742$		0			0
$743$	−14.3477	+	19.7479i	−0.526364	+	0.724479i	−0.986571	−	0.163333i	$-0.947775\pi$
$743$	−14.3477	+	19.7479i	−0.526364	+	0.724479i	0.460206	+	0.887812i	$0.347775\pi$
$744$		0			0
$745$	1.30718	−	2.56548i	0.0478913	−	0.0939921i
$746$		0			0
$747$		−	18.0130i		−	0.659061i
$748$		0			0
$749$	−40.6387	−	6.43653i	−1.48490	−	0.235186i
$750$		0			0
$751$	18.4311	−	9.39112i	0.672561	−	0.342687i	−0.0841347	−	0.996454i	$-0.526813\pi$
$751$	18.4311	−	9.39112i	0.672561	−	0.342687i	0.756695	+	0.653768i	$0.226813\pi$
$752$		0			0
$753$	45.5608	−	7.21612i	1.66033	−	0.262970i
$754$		0			0
$755$	−2.18750	+	13.8113i	−0.0796114	+	0.502646i
$756$		0			0
$757$	35.9492	+	18.3170i	1.30660	+	0.665744i	0.962011	−	0.273012i	$-0.0880197\pi$
$757$	35.9492	+	18.3170i	1.30660	+	0.665744i	0.344585	+	0.938755i	$0.388020\pi$
$758$		0			0
$759$	78.3030	−	25.4422i	2.84222	−	0.923493i
$760$		0			0
$761$	1.77525	−	5.46367i	0.0643529	−	0.198058i	−0.913710	−	0.406366i	$-0.866796\pi$
$761$	1.77525	−	5.46367i	0.0643529	−	0.198058i	0.978063	+	0.208308i	$0.0667957\pi$
$762$		0			0
$763$	16.4251	+	50.5513i	0.594629	+	1.83008i
$764$		0			0
$765$	2.12402	−	2.12402i	0.0767943	−	0.0767943i
$766$		0			0
$767$	2.67676	+	16.9004i	0.0966522	+	0.610238i
$768$		0			0
$769$	−37.2880	+	27.0913i	−1.34464	+	0.976937i	−0.345379	+	0.938463i	$0.612249\pi$
$769$	−37.2880	+	27.0913i	−1.34464	+	0.976937i	−0.999260	+	0.0384734i	$0.987751\pi$
$770$		0			0
$771$	−36.8760	−	50.7555i	−1.32806	−	1.82792i
$772$		0			0
$773$	−6.76644	−	13.2799i	−0.243372	−	0.477644i	0.736718	−	0.676201i	$-0.236375\pi$
$773$	−6.76644	−	13.2799i	−0.243372	−	0.477644i	−0.980090	+	0.198556i	$0.936375\pi$
$774$		0			0
$775$	−6.57947	−	4.78026i	−0.236342	−	0.171712i
$776$		0			0
$777$	8.17025	+	2.65467i	0.293106	+	0.0952359i
$778$		0			0
$779$	−33.1940	−	29.5019i	−1.18930	−	1.05701i
$780$		0			0
$781$	−19.3004	−	6.27109i	−0.690624	−	0.224397i
$782$		0			0
$783$	−73.4648	−	53.3753i	−2.62542	−	1.90748i
$784$		0			0
$785$	−3.99416	−	7.83898i	−0.142558	−	0.279785i
$786$		0			0
$787$	−2.72667	−	3.75294i	−0.0971953	−	0.133778i	0.757649	−	0.652662i	$-0.226348\pi$
$787$	−2.72667	−	3.75294i	−0.0971953	−	0.133778i	−0.854845	+	0.518884i	$0.826348\pi$
$788$		0			0
$789$	−17.2117	+	12.5050i	−0.612753	+	0.445191i
$790$		0			0
$791$	−1.38978	−	8.77471i	−0.0494148	−	0.311993i
$792$		0			0
$793$	−34.5836	+	34.5836i	−1.22810	+	1.22810i
$794$		0			0
$795$	−6.40012	−	19.6976i	−0.226989	−	0.698600i
$796$		0			0
$797$	8.11775	−	24.9839i	0.287545	−	0.884974i	−0.698079	−	0.716021i	$-0.745962\pi$
$797$	8.11775	−	24.9839i	0.287545	−	0.884974i	0.985624	−	0.168953i	$-0.0540385\pi$
$798$		0			0
$799$	−4.67019	+	1.51744i	−0.165219	+	0.0536831i
$800$		0			0
$801$	13.6766	+	6.96858i	0.483239	+	0.246223i
$802$		0			0
$803$	1.82279	−	11.5087i	0.0643249	−	0.406131i
$804$		0			0
$805$	28.9600	−	4.58681i	1.02071	−	0.161664i
$806$		0			0
$807$	−76.5321	+	38.9951i	−2.69406	+	1.37269i
$808$		0			0
$809$	7.20014	+	1.14039i	0.253143	+	0.0400940i	0.281716	−	0.959498i	$-0.409096\pi$
$809$	7.20014	+	1.14039i	0.253143	+	0.0400940i	−0.0285730	+	0.999592i	$0.509096\pi$
$810$		0			0
$811$		−	34.9205i		−	1.22623i	−0.789996	−	0.613113i	$-0.789917\pi$
$811$		−	34.9205i		−	1.22623i	0.789996	−	0.613113i	$-0.210083\pi$
$812$		0			0
$813$	17.6614	−	34.6624i	0.619412	−	1.21566i
$814$		0			0
$815$	1.59280	−	2.19230i	0.0557934	−	0.0767931i
$816$		0			0
$817$	−33.5565	−	33.5565i	−1.17399	−	1.17399i
$818$		0			0
$819$	114.220			3.99118
$820$		0			0
$821$	50.5976			1.76587			0.882934	−	0.469497i	$-0.155565\pi$
$821$	50.5976			1.76587			0.882934	+	0.469497i	$0.155565\pi$
$822$		0			0
$823$	7.77724	+	7.77724i	0.271098	+	0.271098i	0.829542	−	0.558444i	$-0.188602\pi$
$823$	7.77724	+	7.77724i	0.271098	+	0.271098i	−0.558444	+	0.829542i	$0.688602\pi$
$824$		0			0
$825$	−6.96835	+	9.59112i	−0.242607	+	0.333920i
$826$		0			0
$827$	3.57390	−	7.01418i	0.124277	−	0.243907i	−0.820483	−	0.571671i	$-0.806295\pi$
$827$	3.57390	−	7.01418i	0.124277	−	0.243907i	0.944759	+	0.327764i	$0.106295\pi$
$828$		0			0
$829$			29.8851i			1.03795i	0.854789	+	0.518976i	$0.173686\pi$
$829$			29.8851i			1.03795i	−0.854789	+	0.518976i	$0.826314\pi$
$830$		0			0
$831$	27.4752	+	4.35165i	0.953105	+	0.150957i
$832$		0			0
$833$	−3.95427	+	2.01480i	−0.137007	+	0.0698087i
$834$		0			0
$835$	−19.5963	+	3.10375i	−0.678158	+	0.107410i
$836$		0			0
$837$	−17.6905	+	111.693i	−0.611473	+	3.86069i
$838$		0			0
$839$	−5.07517	−	2.58593i	−0.175214	−	0.0892761i	0.364184	−	0.931327i	$-0.381348\pi$
$839$	−5.07517	−	2.58593i	−0.175214	−	0.0892761i	−0.539398	+	0.842051i	$0.681348\pi$
$840$		0			0
$841$	−12.9797	+	4.21735i	−0.447575	+	0.145426i
$842$		0			0
$843$	−6.10621	+	18.7930i	−0.210309	+	0.647264i
$844$		0			0
$845$	−0.195673	−	0.602218i	−0.00673134	−	0.0207169i
$846$		0			0
$847$	7.79102	−	7.79102i	0.267702	−	0.267702i
$848$		0			0
$849$	7.78636	+	49.1612i	0.267227	+	1.68721i
$850$		0			0
$851$	−3.55748	+	2.58466i	−0.121949	+	0.0886011i
$852$		0			0
$853$	8.69633	+	11.9695i	0.297756	+	0.409827i	0.931514	−	0.363705i	$-0.118488\pi$
$853$	8.69633	+	11.9695i	0.297756	+	0.409827i	−0.633758	+	0.773532i	$0.718488\pi$
$854$		0			0
$855$	23.0705	+	45.2784i	0.788994	+	1.54849i
$856$		0			0
$857$	−25.0954	−	18.2328i	−0.857241	−	0.622822i	0.0698921	−	0.997555i	$-0.477735\pi$
$857$	−25.0954	−	18.2328i	−0.857241	−	0.622822i	−0.927133	+	0.374733i	$0.877735\pi$
$858$		0			0
$859$	−38.8258	−	12.6153i	−1.32472	−	0.430428i	−0.440607	−	0.897700i	$-0.645237\pi$
$859$	−38.8258	−	12.6153i	−1.32472	−	0.430428i	−0.884113	+	0.467272i	$0.845237\pi$
$860$		0			0
$861$	−86.7251	+	5.10712i	−2.95558	+	0.174050i
$862$		0			0
$863$	29.5131	+	9.58938i	1.00464	+	0.326426i	0.764717	−	0.644366i	$-0.222879\pi$
$863$	29.5131	+	9.58938i	1.00464	+	0.326426i	0.239920	+	0.970793i	$0.422879\pi$
$864$		0			0
$865$	19.6602	+	14.2839i	0.668466	+	0.485669i
$866$		0			0
$867$	24.5566	+	48.1950i	0.833985	+	1.63679i
$868$		0			0
$869$	18.0591	+	24.8562i	0.612612	+	0.843188i
$870$		0			0
$871$	14.8901	−	10.8183i	0.504533	−	0.366565i
$872$		0			0
$873$	−13.2127	−	83.4217i	−0.447182	−	2.82340i
$874$		0			0
$875$	−2.98540	+	2.98540i	−0.100925	+	0.100925i
$876$		0			0
$877$	6.70806	+	20.6453i	0.226515	+	0.697142i	0.998134	+	0.0610571i	$0.0194472\pi$
$877$	6.70806	+	20.6453i	0.226515	+	0.697142i	−0.771619	+	0.636085i	$0.780553\pi$
$878$		0			0
$879$	−7.91141	+	24.3488i	−0.266845	+	0.821266i
$880$		0			0
$881$	1.81516	−	0.589782i	0.0611544	−	0.0198703i	−0.278280	−	0.960500i	$-0.589764\pi$
$881$	1.81516	−	0.589782i	0.0611544	−	0.0198703i	0.339434	+	0.940630i	$0.389764\pi$
$882$		0			0
$883$	−25.5826	−	13.0350i	−0.860924	−	0.438663i	−0.0329683	−	0.999456i	$-0.510496\pi$
$883$	−25.5826	−	13.0350i	−0.860924	−	0.438663i	−0.827955	+	0.560794i	$0.810496\pi$
$884$		0			0
$885$	−2.32969	+	14.7091i	−0.0783116	+	0.494440i
$886$		0			0
$887$	32.9819	−	5.22381i	1.10742	−	0.175398i	0.424171	−	0.905582i	$-0.360565\pi$
$887$	32.9819	−	5.22381i	1.10742	−	0.175398i	0.683251	+	0.730183i	$0.260565\pi$
$888$		0			0
$889$	48.2575	−	24.5884i	1.61850	−	0.824669i
$890$		0			0
$891$	82.7266	+	13.1026i	2.77145	+	0.438954i
$892$		0			0
$893$		−	83.0737i		−	2.77996i
$894$		0			0
$895$	−3.45479	+	6.78040i	−0.115481	+	0.226644i
$896$		0			0
$897$	−48.4357	+	66.6660i	−1.61722	+	2.22591i
$898$		0			0
$899$	37.5548	+	37.5548i	1.25252	+	1.25252i
$900$		0			0
$901$	−2.64221			−0.0880247
$902$		0			0
$903$	−92.8351			−3.08936
$904$		0			0
$905$	2.88051	+	2.88051i	0.0957514	+	0.0957514i
$906$		0			0
$907$	−11.0044	+	15.1463i	−0.365396	+	0.502924i	−0.951642	−	0.307209i	$-0.900605\pi$
$907$	−11.0044	+	15.1463i	−0.365396	+	0.502924i	0.586247	+	0.810133i	$0.300605\pi$
$908$		0			0
$909$	7.74190	−	15.1943i	0.256783	−	0.503965i
$910$		0			0
$911$		−	26.6553i		−	0.883129i	−0.897230	−	0.441564i	$-0.854424\pi$
$911$		−	26.6553i		−	0.883129i	0.897230	−	0.441564i	$-0.145576\pi$
$912$		0			0
$913$	8.95786	+	1.41879i	0.296462	+	0.0469549i
$914$		0			0
$915$	−37.9275	+	19.3250i	−1.25384	+	0.638866i
$916$		0			0
$917$	2.99145	−	0.473800i	0.0987865	−	0.0156462i
$918$		0			0
$919$	0.614022	−	3.87678i	0.0202547	−	0.127883i	−0.975489	−	0.220048i	$-0.929379\pi$
$919$	0.614022	−	3.87678i	0.0202547	−	0.127883i	0.995744	+	0.0921646i	$0.0293786\pi$
$920$		0			0
$921$	49.3313	+	25.1356i	1.62552	+	0.828245i
$922$		0			0
$923$	19.3171	−	6.27651i	0.635830	−	0.206594i
$924$		0			0
$925$	0.195662	−	0.602186i	0.00643333	−	0.0197998i
$926$		0			0
$927$	21.9542	+	67.5681i	0.721071	+	2.21923i
$928$		0			0
$929$	40.8411	−	40.8411i	1.33995	−	1.33995i	0.443855	−	0.896099i	$-0.353611\pi$
$929$	40.8411	−	40.8411i	1.33995	−	1.33995i	0.896099	−	0.443855i	$-0.146389\pi$
$930$		0			0
$931$	−11.7450	−	74.1550i	−0.384927	−	2.43033i
$932$		0			0
$933$	−42.1012	+	30.5883i	−1.37833	+	1.00142i
$934$		0			0
$935$	0.888979	+	1.22357i	0.0290727	+	0.0400152i
$936$		0			0
$937$	−0.542268	−	1.06426i	−0.0177151	−	0.0347679i	0.881979	−	0.471288i	$-0.156211\pi$
$937$	−0.542268	−	1.06426i	−0.0177151	−	0.0347679i	−0.899694	+	0.436520i	$0.856211\pi$
$938$		0			0
$939$	−66.7410	−	48.4902i	−2.17801	−	1.58242i
$940$		0			0
$941$	−56.2849	−	18.2881i	−1.83484	−	0.596175i	−0.998877	−	0.0473842i	$-0.984912\pi$
$941$	−56.2849	−	18.2881i	−1.83484	−	0.596175i	−0.835960	−	0.548790i	$-0.815088\pi$
$942$		0			0
$943$	23.9778	−	37.4501i	0.780826	−	1.21954i
$944$		0			0
$945$	55.8339	+	18.1415i	1.81628	+	0.590144i
$946$		0			0
$947$	35.9036	+	26.0855i	1.16671	+	0.847664i	0.990611	−	0.136708i	$-0.0436523\pi$
$947$	35.9036	+	26.0855i	1.16671	+	0.847664i	0.176098	+	0.984373i	$0.443652\pi$
$948$		0			0
$949$	5.29451	+	10.3911i	0.171867	+	0.337308i
$950$		0			0
$951$	12.0827	+	16.6305i	0.391810	+	0.539280i
$952$		0			0
$953$	−34.6106	+	25.1461i	−1.12115	+	0.814561i	−0.984383	−	0.176043i	$-0.943670\pi$
$953$	−34.6106	+	25.1461i	−1.12115	+	0.814561i	−0.136765	+	0.990604i	$0.543670\pi$
$954$		0			0
$955$	−1.71106	−	10.8032i	−0.0553685	−	0.349583i
$956$		0			0
$957$	54.7449	−	54.7449i	1.76965	−	1.76965i
$958$		0			0
$959$	−11.1862	−	34.4275i	−0.361221	−	1.11172i
$960$		0			0
$961$	10.8590	−	33.4205i	0.350289	−	1.07808i
$962$		0			0
$963$	67.9101	−	22.0653i	2.18837	−	0.711046i
$964$		0			0
$965$	8.07998	+	4.11695i	0.260104	+	0.132529i
$966$		0			0
$967$	5.73376	−	36.2015i	0.184385	−	1.16416i	−0.705748	−	0.708463i	$-0.749389\pi$
$967$	5.73376	−	36.2015i	0.184385	−	1.16416i	0.890133	−	0.455700i	$-0.150611\pi$
$968$		0			0
$969$	9.02483	−	1.42939i	0.289919	−	0.0459187i
$970$		0			0
$971$	−5.35736	+	2.72971i	−0.171926	+	0.0876006i	−0.537836	−	0.843050i	$-0.680758\pi$
$971$	−5.35736	+	2.72971i	−0.171926	+	0.0876006i	0.365910	+	0.930650i	$0.380758\pi$
$972$		0			0
$973$	19.1707	+	3.03633i	0.614583	+	0.0973404i
$974$		0			0
$975$		−	11.8655i		−	0.380000i
$976$		0			0
$977$	7.53287	−	14.7841i	0.240998	−	0.472985i	−0.738549	−	0.674199i	$-0.764489\pi$
$977$	7.53287	−	14.7841i	0.240998	−	0.472985i	0.979547	+	0.201214i	$0.0644888\pi$
$978$		0			0
$979$	−4.54270	+	6.25250i	−0.145185	+	0.199831i
$980$		0			0
$981$	−65.2259	−	65.2259i	−2.08250	−	2.08250i
$982$		0			0
$983$	43.0090			1.37177			0.685887	−	0.727708i	$-0.259414\pi$
$983$	43.0090			1.37177			0.685887	+	0.727708i	$0.259414\pi$
$984$		0			0
$985$	15.8466			0.504913
$986$		0			0
$987$	−114.913	−	114.913i	−3.65772	−	3.65772i
$988$		0			0
$989$	27.9310	−	38.4438i	0.888155	−	1.22244i
$990$		0			0
$991$	−12.5058	+	24.5440i	−0.397260	+	0.779666i	−0.999831	−	0.0183994i	$-0.994143\pi$
$991$	−12.5058	+	24.5440i	−0.397260	+	0.779666i	0.602571	+	0.798065i	$0.294143\pi$
$992$		0			0
$993$			54.0124i			1.71403i
$994$		0			0
$995$	−20.6381	−	3.26875i	−0.654271	−	0.103626i
$996$		0			0
$997$	31.7331	−	16.1688i	1.00500	−	0.512072i	0.127595	−	0.991826i	$-0.459274\pi$
$997$	31.7331	−	16.1688i	1.00500	−	0.512072i	0.877403	+	0.479754i	$0.159274\pi$
$998$		0			0
$999$	−8.69598	+	1.37731i	−0.275129	+	0.0435761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bo.b.21.8	✓	64
41.2	even	20	inner	820.2.bo.b.781.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bo.b.21.8	✓	64	1.1	even	1	trivial
820.2.bo.b.781.8	yes	64	41.2	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.27233 + 2.27233i) q^{3} +(0.587785 - 0.809017i) q^{5} +(1.91674 - 3.76182i) q^{7} +7.32700i q^{9} +(-3.64371 - 0.577108i) q^{11} +(3.28988 - 1.67628i) q^{13} +(3.17400 - 0.502712i) q^{15} +(0.0641329 - 0.404919i) q^{17} +(6.17966 + 3.14869i) q^{19} +(12.9036 - 4.19263i) q^{21} +(-2.14607 + 6.60491i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(-9.83239 + 9.83239i) q^{27} +(1.02160 + 6.45011i) q^{29} +(6.57947 - 4.78026i) q^{31} +(-6.96835 - 9.59112i) q^{33} +(-1.91674 - 3.76182i) q^{35} +(0.512250 + 0.372171i) q^{37} +(11.2848 + 3.66664i) q^{39} +(-6.19552 - 1.61726i) q^{41} +(-6.50749 - 2.11441i) q^{43} +(5.92767 + 4.30670i) q^{45} +(-5.43784 - 10.6724i) q^{47} +(-6.36291 - 8.75779i) q^{49} +(1.06584 - 0.774380i) q^{51} +(-1.00821 - 6.36559i) q^{53} +(-2.60861 + 2.60861i) q^{55} +(6.88736 + 21.1971i) q^{57} +(-1.43206 + 4.40742i) q^{59} +(-12.5977 + 4.09325i) q^{61} +(27.5629 + 14.0440i) q^{63} +(0.577606 - 3.64686i) q^{65} +(4.92336 - 0.779784i) q^{67} +(-19.8851 + 10.1320i) q^{69} +(5.43321 + 0.860536i) q^{71} +3.15849i q^{73} +(1.45893 - 2.86331i) q^{75} +(-9.15505 + 12.6008i) q^{77} +(-5.88894 - 5.88894i) q^{79} -22.7039 q^{81} -2.45844 q^{83} +(-0.289890 - 0.289890i) q^{85} +(-12.3354 + 16.9782i) q^{87} +(0.951082 - 1.86660i) q^{89} -15.5889i q^{91} +(25.8131 + 4.08839i) q^{93} +(6.17966 - 3.14869i) q^{95} +(-11.3855 + 1.80329i) q^{97} +(4.22847 - 26.6975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) \) 64 * q + 2 * q^3 - 10 * q^7 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 22 * q^23 + 16 * q^25 + 20 * q^27 - 12 * q^29 + 22 * q^31 + 30 * q^33 + 10 * q^35 + 12 * q^37 + 20 * q^39 - 10 * q^41 + 10 * q^43 + 32 * q^45 + 28 * q^47 + 10 * q^49 - 22 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 18 * q^59 - 20 * q^61 + 52 * q^63 - 6 * q^65 - 6 * q^67 - 50 * q^69 + 34 * q^71 + 8 * q^75 - 110 * q^77 - 14 * q^79 - 108 * q^81 + 32 * q^83 - 8 * q^85 - 80 * q^87 - 122 * q^89 + 42 * q^93 + 10 * q^95 - 64 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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