LMFDB - Embedded newform 820.2.bq.a.569.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(49,820)] 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, 10, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bq (of order $20$, degree $8$, 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:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			569.6
Character	$\chi$	$=$	820.569
Dual form			820.2.bq.a.49.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37884 - 1.37884i) q^{3} +(-2.23133 - 0.145551i) q^{5} +(-0.0463388 - 0.292571i) q^{7} +0.802406i q^{9} +(1.40198 + 0.714346i) q^{11} +(-3.46233 - 0.548380i) q^{13} +(2.87595 + 3.27734i) q^{15} +(-3.94420 - 2.00967i) q^{17} +(0.467063 + 2.94892i) q^{19} +(-0.339516 + 0.467303i) q^{21} +(-1.12543 - 1.54902i) q^{23} +(4.95763 + 0.649542i) q^{25} +(-3.03013 + 3.03013i) q^{27} +(4.61197 + 9.05151i) q^{29} +(-0.629522 - 1.93747i) q^{31} +(-0.948143 - 2.91808i) q^{33} +(0.0608129 + 0.659567i) q^{35} +(9.17488 + 2.98110i) q^{37} +(4.01788 + 5.53014i) q^{39} +(0.449547 + 6.38732i) q^{41} +(-6.88192 + 5.00000i) q^{43} +(0.116791 - 1.79043i) q^{45} +(-0.920552 + 5.81214i) q^{47} +(6.57394 - 2.13600i) q^{49} +(2.66741 + 8.20945i) q^{51} +(6.34023 - 3.23051i) q^{53} +(-3.02431 - 1.79800i) q^{55} +(3.42208 - 4.71009i) q^{57} +(-7.47962 + 5.43426i) q^{59} +(3.99337 - 5.49640i) q^{61} +(0.234761 - 0.0371825i) q^{63} +(7.64578 + 1.72756i) q^{65} +(6.17845 + 12.1259i) q^{67} +(-0.584066 + 3.68765i) q^{69} +(-11.0761 - 5.64356i) q^{71} -7.00586 q^{73} +(-5.94017 - 7.73140i) q^{75} +(0.144031 - 0.443282i) q^{77} +(-1.93786 + 1.93786i) q^{79} +10.7634 q^{81} -6.08123i q^{83} +(8.50829 + 5.05831i) q^{85} +(6.12141 - 18.8398i) q^{87} +(-8.22569 + 1.30282i) q^{89} +1.03839i q^{91} +(-1.80345 + 3.53947i) q^{93} +(-0.612952 - 6.64798i) q^{95} +(-2.14160 - 4.20314i) q^{97} +(-0.573196 + 1.12496i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Character values

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

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

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
$3$	−1.37884	−	1.37884i	−0.796074	−	0.796074i	0.186400	−	0.982474i	$-0.440318\pi$
$3$	−1.37884	−	1.37884i	−0.796074	−	0.796074i	−0.982474	+	0.186400i	$0.940318\pi$
$4$		0			0
$5$	−2.23133	−	0.145551i	−0.997879	−	0.0650922i
$5$	−2.23133	−	0.145551i	−0.997879	−	0.0650922i
$6$		0			0
$7$	−0.0463388	−	0.292571i	−0.0175144	−	0.110582i	0.977382	−	0.211480i	$-0.0678283\pi$
$7$	−0.0463388	−	0.292571i	−0.0175144	−	0.110582i	−0.994897	+	0.100898i	$0.967828\pi$
$8$		0			0
$9$			0.802406i			0.267469i
$10$		0			0
$11$	1.40198	+	0.714346i	0.422714	+	0.215384i	0.652390	−	0.757884i	$-0.273767\pi$
$11$	1.40198	+	0.714346i	0.422714	+	0.215384i	−0.229676	+	0.973267i	$0.573767\pi$
$12$		0			0
$13$	−3.46233	−	0.548380i	−0.960278	−	0.152093i	−0.343433	−	0.939177i	$-0.611590\pi$
$13$	−3.46233	−	0.548380i	−0.960278	−	0.152093i	−0.616846	+	0.787084i	$0.711590\pi$
$14$		0			0
$15$	2.87595	+	3.27734i	0.742568	+	0.846204i
$16$		0			0
$17$	−3.94420	−	2.00967i	−0.956610	−	0.487417i	−0.0952727	−	0.995451i	$-0.530372\pi$
$17$	−3.94420	−	2.00967i	−0.956610	−	0.487417i	−0.861337	+	0.508034i	$0.830372\pi$
$18$		0			0
$19$	0.467063	+	2.94892i	0.107152	+	0.676528i	0.981534	+	0.191290i	$0.0612671\pi$
$19$	0.467063	+	2.94892i	0.107152	+	0.676528i	−0.874382	+	0.485238i	$0.838733\pi$
$20$		0			0
$21$	−0.339516	+	0.467303i	−0.0740884	+	0.101974i
$22$		0			0
$23$	−1.12543	−	1.54902i	−0.234669	−	0.322994i	0.675400	−	0.737452i	$-0.263971\pi$
$23$	−1.12543	−	1.54902i	−0.234669	−	0.322994i	−0.910068	+	0.414458i	$0.863971\pi$
$24$		0			0
$25$	4.95763	+	0.649542i	0.991526	+	0.129908i
$26$		0			0
$27$	−3.03013	+	3.03013i	−0.583149	+	0.583149i
$28$		0			0
$29$	4.61197	+	9.05151i	0.856422	+	1.68082i	0.724186	+	0.689605i	$0.242216\pi$
$29$	4.61197	+	9.05151i	0.856422	+	1.68082i	0.132236	+	0.991218i	$0.457784\pi$
$30$		0			0
$31$	−0.629522	−	1.93747i	−0.113065	−	0.347980i	0.878473	−	0.477792i	$-0.158563\pi$
$31$	−0.629522	−	1.93747i	−0.113065	−	0.347980i	−0.991539	+	0.129812i	$0.958563\pi$
$32$		0			0
$33$	−0.948143	−	2.91808i	−0.165050	−	0.507973i
$34$		0			0
$35$	0.0608129	+	0.659567i	0.0102793	+	0.111487i
$36$		0			0
$37$	9.17488	+	2.98110i	1.50834	+	0.490089i	0.942437	−	0.334383i	$-0.108528\pi$
$37$	9.17488	+	2.98110i	1.50834	+	0.490089i	0.565903	+	0.824472i	$0.308528\pi$
$38$		0			0
$39$	4.01788	+	5.53014i	0.643376	+	0.885530i
$40$		0			0
$41$	0.449547	+	6.38732i	0.0702074	+	0.997532i
$41$	0.449547	+	6.38732i	0.0702074	+	0.997532i
$42$		0			0
$43$	−6.88192	+	5.00000i	−1.04948	+	0.762494i	−0.972114	−	0.234509i	$-0.924652\pi$
$43$	−6.88192	+	5.00000i	−1.04948	+	0.762494i	−0.0773684	+	0.997003i	$0.524652\pi$
$44$		0			0
$45$	0.116791	−	1.79043i	0.0174101	−	0.266901i
$46$		0			0
$47$	−0.920552	+	5.81214i	−0.134276	+	0.847788i	0.824962	+	0.565189i	$0.191197\pi$
$47$	−0.920552	+	5.81214i	−0.134276	+	0.847788i	−0.959238	+	0.282599i	$0.908803\pi$
$48$		0			0
$49$	6.57394	−	2.13600i	0.939135	−	0.305143i
$50$		0			0
$51$	2.66741	+	8.20945i	0.373512	+	1.14955i
$52$		0			0
$53$	6.34023	−	3.23051i	0.870898	−	0.443744i	0.0393679	−	0.999225i	$-0.487466\pi$
$53$	6.34023	−	3.23051i	0.870898	−	0.443744i	0.831530	+	0.555480i	$0.187466\pi$
$54$		0			0
$55$	−3.02431	−	1.79800i	−0.407798	−	0.242442i
$56$		0			0
$57$	3.42208	−	4.71009i	0.453266	−	0.623867i
$58$		0			0
$59$	−7.47962	+	5.43426i	−0.973764	+	0.707481i	−0.956306	−	0.292367i	$-0.905557\pi$
$59$	−7.47962	+	5.43426i	−0.973764	+	0.707481i	−0.0174575	+	0.999848i	$0.505557\pi$
$60$		0			0
$61$	3.99337	−	5.49640i	0.511299	−	0.703742i	−0.472839	−	0.881149i	$-0.656771\pi$
$61$	3.99337	−	5.49640i	0.511299	−	0.703742i	0.984138	+	0.177406i	$0.0567707\pi$
$62$		0			0
$63$	0.234761	−	0.0371825i	0.0295771	−	0.00468455i
$64$		0			0
$65$	7.64578	+	1.72756i	0.948342	+	0.214277i
$66$		0			0
$67$	6.17845	+	12.1259i	0.754817	+	1.48141i	0.872633	+	0.488377i	$0.162411\pi$
$67$	6.17845	+	12.1259i	0.754817	+	1.48141i	−0.117815	+	0.993036i	$0.537589\pi$
$68$		0			0
$69$	−0.584066	+	3.68765i	−0.0703133	+	0.443940i
$70$		0			0
$71$	−11.0761	−	5.64356i	−1.31449	−	0.669767i	−0.350717	−	0.936482i	$-0.614062\pi$
$71$	−11.0761	−	5.64356i	−1.31449	−	0.669767i	−0.963776	+	0.266714i	$0.914062\pi$
$72$		0			0
$73$	−7.00586			−0.819974			−0.409987	−	0.912091i	$-0.634467\pi$
$73$	−7.00586			−0.819974			−0.409987	+	0.912091i	$0.634467\pi$
$74$		0			0
$75$	−5.94017	−	7.73140i	−0.685912	−	0.892745i
$76$		0			0
$77$	0.144031	−	0.443282i	0.0164139	−	0.0505167i
$78$		0			0
$79$	−1.93786	+	1.93786i	−0.218026	+	0.218026i	−0.807666	−	0.589640i	$-0.799270\pi$
$79$	−1.93786	+	1.93786i	−0.218026	+	0.218026i	0.589640	+	0.807666i	$0.299270\pi$
$80$		0			0
$81$	10.7634			1.19593
$82$		0			0
$83$		−	6.08123i		−	0.667502i	−0.942661	−	0.333751i	$-0.891686\pi$
$83$		−	6.08123i		−	0.667502i	0.942661	−	0.333751i	$-0.108314\pi$
$84$		0			0
$85$	8.50829	+	5.05831i	0.922854	+	0.548651i
$86$		0			0
$87$	6.12141	−	18.8398i	0.656284	−	2.01984i
$88$		0			0
$89$	−8.22569	+	1.30282i	−0.871922	+	0.138099i	−0.576331	−	0.817216i	$-0.695516\pi$
$89$	−8.22569	+	1.30282i	−0.871922	+	0.138099i	−0.295590	+	0.955315i	$0.595516\pi$
$90$		0			0
$91$			1.03839i			0.108853i
$92$		0			0
$93$	−1.80345	+	3.53947i	−0.187009	+	0.367026i
$94$		0			0
$95$	−0.612952	−	6.64798i	−0.0628876	−	0.682068i
$96$		0			0
$97$	−2.14160	−	4.20314i	−0.217447	−	0.426764i	0.756355	−	0.654161i	$-0.226978\pi$
$97$	−2.14160	−	4.20314i	−0.217447	−	0.426764i	−0.973802	+	0.227398i	$0.926978\pi$
$98$		0			0
$99$	−0.573196	+	1.12496i	−0.0576083	+	0.113063i
$100$		0			0
$101$	0.115937	+	0.731999i	0.0115362	+	0.0728366i	0.992785	−	0.119910i	$-0.0382605\pi$
$101$	0.115937	+	0.731999i	0.0115362	+	0.0728366i	−0.981249	+	0.192746i	$0.938261\pi$
$102$		0			0
$103$	4.37118	+	3.17584i	0.430705	+	0.312925i	0.781931	−	0.623365i	$-0.214235\pi$
$103$	4.37118	+	3.17584i	0.430705	+	0.312925i	−0.351226	+	0.936291i	$0.614235\pi$
$104$		0			0
$105$	0.825586	−	0.993289i	0.0805690	−	0.0969351i
$106$		0			0
$107$	−5.93155	+	8.16408i	−0.573424	+	0.789251i	−0.992955	−	0.118490i	$-0.962195\pi$
$107$	−5.93155	+	8.16408i	−0.573424	+	0.789251i	0.419531	+	0.907741i	$0.362195\pi$
$108$		0			0
$109$	1.51484	+	1.51484i	0.145095	+	0.145095i	0.775923	−	0.630828i	$-0.217285\pi$
$109$	1.51484	+	1.51484i	0.145095	+	0.145095i	−0.630828	+	0.775923i	$0.717285\pi$
$110$		0			0
$111$	−8.54024	−	16.7612i	−0.810603	−	1.59090i
$112$		0			0
$113$	−14.7113	+	4.77998i	−1.38392	+	0.449663i	−0.903956	−	0.427626i	$-0.859350\pi$
$113$	−14.7113	+	4.77998i	−1.38392	+	0.449663i	−0.479963	+	0.877289i	$0.659350\pi$
$114$		0			0
$115$	2.28574	+	3.62018i	0.213146	+	0.337584i
$116$		0			0
$117$	0.440023	−	2.77820i	0.0406801	−	0.256844i
$118$		0			0
$119$	−0.405203	+	1.24709i	−0.0371449	+	0.114320i
$120$		0			0
$121$	−5.01037	−	6.89618i	−0.455488	−	0.626926i
$122$		0			0
$123$	8.18725	−	9.42696i	0.738220	−	0.850000i
$124$		0			0
$125$	−10.9675	−	2.17092i	−0.980967	−	0.194173i
$126$		0			0
$127$	−10.9732	−	3.56541i	−0.973714	−	0.316379i	−0.221400	−	0.975183i	$-0.571063\pi$
$127$	−10.9732	−	3.56541i	−0.973714	−	0.316379i	−0.752314	+	0.658804i	$0.771063\pi$
$128$		0			0
$129$	16.3833	+	2.59486i	1.44247	+	0.228464i
$130$		0			0
$131$	−13.5762	+	4.41118i	−1.18616	+	0.385406i	−0.834651	−	0.550779i	$-0.814331\pi$
$131$	−13.5762	+	4.41118i	−1.18616	+	0.385406i	−0.351507	+	0.936185i	$0.614331\pi$
$132$		0			0
$133$	0.841126	−	0.273298i	0.0729349	−	0.0236980i
$134$		0			0
$135$	7.20225	−	6.32018i	0.619871	−	0.543954i
$136$		0			0
$137$	−2.13593	+	2.13593i	−0.182484	+	0.182484i	−0.792438	−	0.609953i	$-0.791188\pi$
$137$	−2.13593	+	2.13593i	−0.182484	+	0.182484i	0.609953	+	0.792438i	$0.291188\pi$
$138$		0			0
$139$	13.3692	+	9.71327i	1.13396	+	0.823869i	0.986266	−	0.165164i	$-0.0528154\pi$
$139$	13.3692	+	9.71327i	1.13396	+	0.823869i	0.147692	+	0.989033i	$0.452815\pi$
$140$		0			0
$141$	9.28331	−	6.74472i	0.781796	−	0.568008i
$142$		0			0
$143$	−4.46240	−	3.24212i	−0.373165	−	0.271120i
$144$		0			0
$145$	−8.97336	−	20.8681i	−0.745197	−	1.73300i
$146$		0			0
$147$	−12.0096	−	6.11922i	−0.990538	−	0.504704i
$148$		0			0
$149$	2.04211	−	1.04051i	0.167296	−	0.0852416i	−0.368337	−	0.929692i	$-0.620073\pi$
$149$	2.04211	−	1.04051i	0.167296	−	0.0852416i	0.535633	+	0.844451i	$0.320073\pi$
$150$		0			0
$151$	0.532183	−	3.36007i	0.0433084	−	0.273439i	−0.956526	−	0.291648i	$-0.905796\pi$
$151$	0.532183	−	3.36007i	0.0433084	−	0.273439i	0.999834	+	0.0182092i	$0.00579647\pi$
$152$		0			0
$153$	1.61257	−	3.16485i	0.130369	−	0.255863i
$154$		0			0
$155$	1.12267	+	4.41475i	0.0901749	+	0.354601i
$156$		0			0
$157$	2.22566	+	14.0523i	0.177627	+	1.12149i	0.901888	+	0.431969i	$0.142181\pi$
$157$	2.22566	+	14.0523i	0.177627	+	1.12149i	−0.724261	+	0.689526i	$0.757819\pi$
$158$		0			0
$159$	−13.1965	−	4.28781i	−1.04655	−	0.340046i
$160$		0			0
$161$	−0.401049	+	0.401049i	−0.0316071	+	0.0316071i
$162$		0			0
$163$		−	10.2991i		−	0.806687i	−0.915049	−	0.403344i	$-0.867848\pi$
$163$		−	10.2991i		−	0.806687i	0.915049	−	0.403344i	$-0.132152\pi$
$164$		0			0
$165$	1.69089	+	6.64920i	0.131635	+	0.517639i
$166$		0			0
$167$	7.85177	+	7.85177i	0.607588	+	0.607588i	0.942315	−	0.334727i	$-0.108644\pi$
$167$	7.85177	+	7.85177i	0.607588	+	0.607588i	−0.334727	+	0.942315i	$0.608644\pi$
$168$		0			0
$169$	−0.676704	−	0.219874i	−0.0520542	−	0.0169134i
$170$		0			0
$171$	−2.36623	+	0.374774i	−0.180950	+	0.0286597i
$172$		0			0
$173$	−0.653351			−0.0496733			−0.0248367	−	0.999692i	$-0.507907\pi$
$173$	−0.653351			−0.0496733			−0.0248367	+	0.999692i	$0.507907\pi$
$174$		0			0
$175$	−0.0396931	−	1.48056i	−0.00300052	−	0.111920i
$176$		0			0
$177$	17.8062	+	2.82022i	1.33840	+	0.211981i
$178$		0			0
$179$	−20.3513	+	10.3695i	−1.52112	+	0.775052i	−0.997060	−	0.0766264i	$-0.975585\pi$
$179$	−20.3513	+	10.3695i	−1.52112	+	0.775052i	−0.524065	+	0.851678i	$0.675585\pi$
$180$		0			0
$181$	2.75939	−	5.41560i	0.205104	−	0.402539i	−0.765425	−	0.643525i	$-0.777471\pi$
$181$	2.75939	−	5.41560i	0.205104	−	0.402539i	0.970528	+	0.240987i	$0.0774711\pi$
$182$		0			0
$183$	−13.0849	+	2.07244i	−0.967263	+	0.153199i
$184$		0			0
$185$	−20.0382	−	7.98721i	−1.47324	−	0.587231i
$186$		0			0
$187$	−4.09411	−	5.63505i	−0.299391	−	0.412076i
$188$		0			0
$189$	1.02694	+	0.746118i	0.0746991	+	0.0542721i
$190$		0			0
$191$	−9.47076	−	9.47076i	−0.685280	−	0.685280i	0.275905	−	0.961185i	$-0.411023\pi$
$191$	−9.47076	−	9.47076i	−0.685280	−	0.685280i	−0.961185	+	0.275905i	$0.911023\pi$
$192$		0			0
$193$	12.6082	−	6.42421i	0.907559	−	0.462424i	0.0630773	−	0.998009i	$-0.479909\pi$
$193$	12.6082	−	6.42421i	0.907559	−	0.462424i	0.844482	+	0.535584i	$0.179909\pi$
$194$		0			0
$195$	−8.16028	−	12.9243i	−0.584370	−	0.925531i
$196$		0			0
$197$	−3.17745	−	9.77919i	−0.226384	−	0.696738i	−0.998148	−	0.0608294i	$-0.980625\pi$
$197$	−3.17745	−	9.77919i	−0.226384	−	0.696738i	0.771764	−	0.635909i	$-0.219375\pi$
$198$		0			0
$199$	0.362611	+	0.0574320i	0.0257048	+	0.00407125i	0.169274	−	0.985569i	$-0.445858\pi$
$199$	0.362611	+	0.0574320i	0.0257048	+	0.00407125i	−0.143569	+	0.989640i	$0.545858\pi$
$200$		0			0
$201$	8.20057	−	25.2388i	0.578424	−	1.78021i
$202$		0			0
$203$	2.43450	−	1.76877i	0.170868	−	0.124143i
$204$		0			0
$205$	−0.0734068	−	14.3176i	−0.00512696	−	0.999987i
$206$		0			0
$207$	1.24294	−	0.903052i	0.0863906	−	0.0627665i
$208$		0			0
$209$	−1.45173	+	4.46798i	−0.100419	+	0.309057i
$210$		0			0
$211$	−2.59599	−	0.411165i	−0.178716	−	0.0283058i	0.0664352	−	0.997791i	$-0.478837\pi$
$211$	−2.59599	−	0.411165i	−0.178716	−	0.0283058i	−0.245151	+	0.969485i	$0.578837\pi$
$212$		0			0
$213$	7.49062	+	23.0538i	0.513249	+	1.57962i
$214$		0			0
$215$	16.0835	−	10.1550i	1.09689	−	0.692563i
$216$		0			0
$217$	−0.537676	+	0.273960i	−0.0364999	+	0.0185976i
$218$		0			0
$219$	9.65997	+	9.65997i	0.652760	+	0.652760i
$220$		0			0
$221$	12.5541	+	9.12107i	0.844479	+	0.613550i
$222$		0			0
$223$	10.7385	+	14.7802i	0.719101	+	0.989758i	0.999553	+	0.0298896i	$0.00951557\pi$
$223$	10.7385	+	14.7802i	0.719101	+	0.989758i	−0.280452	+	0.959868i	$0.590484\pi$
$224$		0			0
$225$	−0.521196	+	3.97803i	−0.0347464	+	0.265202i
$226$		0			0
$227$	−6.40775	+	1.01489i	−0.425297	+	0.0673604i	−0.365414	−	0.930845i	$-0.619073\pi$
$227$	−6.40775	+	1.01489i	−0.425297	+	0.0673604i	−0.0598828	+	0.998205i	$0.519073\pi$
$228$		0			0
$229$	−0.430823	+	0.845537i	−0.0284696	+	0.0558747i	−0.904803	−	0.425830i	$-0.859982\pi$
$229$	−0.430823	+	0.845537i	−0.0284696	+	0.0558747i	0.876334	+	0.481705i	$0.159982\pi$
$230$		0			0
$231$	−0.809812	+	0.412620i	−0.0532817	+	0.0271484i
$232$		0			0
$233$	16.1650	+	2.56028i	1.05900	+	0.167730i	0.661556	−	0.749895i	$-0.269896\pi$
$233$	16.1650	+	2.56028i	1.05900	+	0.167730i	0.397447	+	0.917625i	$0.369896\pi$
$234$		0			0
$235$	2.90001	−	12.8348i	0.189176	−	0.837249i
$236$		0			0
$237$	5.34399			0.347129
$238$		0			0
$239$	6.26820	−	0.992785i	0.405456	−	0.0642179i	0.0496243	−	0.998768i	$-0.484198\pi$
$239$	6.26820	−	0.992785i	0.405456	−	0.0642179i	0.355832	+	0.934550i	$0.384198\pi$
$240$		0			0
$241$	−13.9836	−	4.54355i	−0.900764	−	0.292676i	−0.178212	−	0.983992i	$-0.557031\pi$
$241$	−13.9836	−	4.54355i	−0.900764	−	0.292676i	−0.722552	+	0.691316i	$0.757031\pi$
$242$		0			0
$243$	−5.75057	−	5.75057i	−0.368899	−	0.368899i
$244$		0			0
$245$	−14.9795	+	3.80928i	−0.957006	+	0.243366i
$246$		0			0
$247$		−	10.4663i		−	0.665952i
$248$		0			0
$249$	−8.38505	+	8.38505i	−0.531381	+	0.531381i
$250$		0			0
$251$	−23.1253	−	7.51385i	−1.45965	−	0.474270i	−0.531690	−	0.846939i	$-0.678443\pi$
$251$	−23.1253	−	7.51385i	−1.45965	−	0.474270i	−0.927964	+	0.372669i	$0.878443\pi$
$252$		0			0
$253$	−0.471297	−	2.97565i	−0.0296302	−	0.187078i
$254$		0			0
$255$	−4.75697	−	18.7062i	−0.297893	−	1.17143i
$256$		0			0
$257$	3.15544	−	6.19290i	0.196831	−	0.386302i	−0.771404	−	0.636346i	$-0.780445\pi$
$257$	3.15544	−	6.19290i	0.196831	−	0.386302i	0.968235	+	0.250044i	$0.0804450\pi$
$258$		0			0
$259$	0.447032	−	2.82245i	0.0277772	−	0.175378i
$260$		0			0
$261$	−7.26298	+	3.70067i	−0.449567	+	0.229066i
$262$		0			0
$263$	25.6443	+	13.0664i	1.58129	+	0.805709i	0.999968	−	0.00796322i	$-0.00253480\pi$
$263$	25.6443	+	13.0664i	1.58129	+	0.805709i	0.581324	+	0.813672i	$0.302535\pi$
$264$		0			0
$265$	−14.6173	+	6.28549i	−0.897935	+	0.386115i
$266$		0			0
$267$	13.1383	+	9.54554i	0.804051	+	0.584178i
$268$		0			0
$269$	−1.46737	+	1.06611i	−0.0894673	+	0.0650018i	−0.631620	−	0.775278i	$-0.717610\pi$
$269$	−1.46737	+	1.06611i	−0.0894673	+	0.0650018i	0.542152	+	0.840280i	$0.317610\pi$
$270$		0			0
$271$	4.24101	+	3.08128i	0.257623	+	0.187174i	0.709099	−	0.705109i	$-0.249102\pi$
$271$	4.24101	+	3.08128i	0.257623	+	0.187174i	−0.451475	+	0.892284i	$0.649102\pi$
$272$		0			0
$273$	1.43178	−	1.43178i	0.0866550	−	0.0866550i
$274$		0			0
$275$	6.48652	+	4.45211i	0.391152	+	0.268472i
$276$		0			0
$277$	16.0008	−	5.19897i	0.961395	−	0.312376i	0.214057	−	0.976821i	$-0.431332\pi$
$277$	16.0008	−	5.19897i	0.961395	−	0.312376i	0.747337	+	0.664445i	$0.231332\pi$
$278$		0			0
$279$	1.55464	−	0.505132i	0.0930736	−	0.0302414i
$280$		0			0
$281$	16.8922	+	2.67546i	1.00770	+	0.159605i	0.638401	−	0.769704i	$-0.279596\pi$
$281$	16.8922	+	2.67546i	1.00770	+	0.159605i	0.369304	+	0.929309i	$0.379596\pi$
$282$		0			0
$283$	17.6319	+	5.72897i	1.04811	+	0.340552i	0.781926	−	0.623371i	$-0.214237\pi$
$283$	17.6319	+	5.72897i	1.04811	+	0.340552i	0.266184	+	0.963922i	$0.414237\pi$
$284$		0			0
$285$	−8.32134	+	10.0117i	−0.492914	+	0.593040i
$286$		0			0
$287$	1.84792	−	0.427505i	0.109079	−	0.0252348i
$288$		0			0
$289$	1.52560	+	2.09981i	0.0897414	+	0.123518i
$290$		0			0
$291$	−2.84252	+	8.74839i	−0.166632	+	0.512840i
$292$		0			0
$293$	1.02513	−	6.47241i	0.0598886	−	0.378122i	−0.939480	−	0.342603i	$-0.888692\pi$
$293$	1.02513	−	6.47241i	0.0598886	−	0.378122i	0.999369	−	0.0355192i	$-0.0113085\pi$
$294$		0			0
$295$	17.4804	−	11.0369i	1.01775	−	0.642596i
$296$		0			0
$297$	−6.41276	+	2.08363i	−0.372106	+	0.120905i
$298$		0			0
$299$	3.04716	+	5.98040i	0.176222	+	0.345855i
$300$		0			0
$301$	1.78176	+	1.78176i	0.102699	+	0.102699i
$302$		0			0
$303$	0.849451	−	1.16917i	0.0487997	−	0.0671670i
$304$		0			0
$305$	−9.71052	+	11.6830i	−0.556023	+	0.668968i
$306$		0			0
$307$	−5.49138	−	3.98972i	−0.313409	−	0.227705i	0.419949	−	0.907548i	$-0.362048\pi$
$307$	−5.49138	−	3.98972i	−0.313409	−	0.227705i	−0.733358	+	0.679843i	$0.762048\pi$
$308$		0			0
$309$	−1.64817	−	10.4061i	−0.0937612	−	0.591985i
$310$		0			0
$311$	5.73879	−	11.2630i	0.325417	−	0.638667i	−0.669108	−	0.743165i	$-0.733324\pi$
$311$	5.73879	−	11.2630i	0.325417	−	0.638667i	0.994525	+	0.104498i	$0.0333237\pi$
$312$		0			0
$313$	9.08612	+	17.8325i	0.513578	+	1.00795i	0.991568	+	0.129588i	$0.0413656\pi$
$313$	9.08612	+	17.8325i	0.513578	+	1.00795i	−0.477990	+	0.878365i	$0.658634\pi$
$314$		0			0
$315$	−0.529240	+	0.0487966i	−0.0298193	+	0.00274938i
$316$		0			0
$317$	−7.43766	+	14.5972i	−0.417741	+	0.819862i	0.582236	+	0.813020i	$0.302178\pi$
$317$	−7.43766	+	14.5972i	−0.417741	+	0.819862i	−0.999977	+	0.00684242i	$0.997822\pi$
$318$		0			0
$319$			15.9846i			0.894967i
$320$		0			0
$321$	19.4356	−	3.07830i	1.08479	−	0.171814i
$322$		0			0
$323$	4.08417	−	12.5698i	0.227249	−	0.699401i
$324$		0			0
$325$	−16.8088	−	4.96759i	−0.932383	−	0.275552i
$326$		0			0
$327$		−	4.17744i		−	0.231013i
$328$		0			0
$329$	1.74312			0.0961015
$330$		0			0
$331$	−17.9626	+	17.9626i	−0.987313	+	0.987313i	−0.999921	−	0.0126077i	$-0.995987\pi$
$331$	−17.9626	+	17.9626i	−0.987313	+	0.987313i	0.0126077	+	0.999921i	$0.495987\pi$
$332$		0			0
$333$	−2.39205	+	7.36197i	−0.131084	+	0.403434i
$334$		0			0
$335$	−12.0212	−	27.9561i	−0.656788	−	1.52740i
$336$		0			0
$337$	−32.1929			−1.75366			−0.876829	−	0.480802i	$-0.840345\pi$
$337$	−32.1929			−1.75366			−0.876829	+	0.480802i	$0.840345\pi$
$338$		0			0
$339$	26.8753	+	13.6937i	1.45967	+	0.743738i
$340$		0			0
$341$	0.501444	−	3.16600i	0.0271547	−	0.171448i
$342$		0			0
$343$	−1.87092	−	3.67190i	−0.101020	−	0.198264i
$344$		0			0
$345$	1.83998	−	8.14333i	0.0990612	−	0.438422i
$346$		0			0
$347$	−23.1637	+	3.66877i	−1.24349	+	0.196950i	−0.743296	−	0.668962i	$-0.766739\pi$
$347$	−23.1637	+	3.66877i	−1.24349	+	0.196950i	−0.500196	+	0.865912i	$0.666739\pi$
$348$		0			0
$349$	−10.4885	+	14.4362i	−0.561439	+	0.772754i	−0.991509	−	0.130041i	$-0.958489\pi$
$349$	−10.4885	+	14.4362i	−0.561439	+	0.772754i	0.430070	+	0.902796i	$0.358489\pi$
$350$		0			0
$351$	12.1530	−	8.82967i	0.648679	−	0.471293i
$352$		0			0
$353$	−20.4960	+	28.2103i	−1.09089	+	1.50148i	−0.243954	+	0.969787i	$0.578445\pi$
$353$	−20.4960	+	28.2103i	−1.09089	+	1.50148i	−0.846936	+	0.531695i	$0.821555\pi$
$354$		0			0
$355$	23.8930	+	14.2048i	1.26811	+	0.753910i
$356$		0			0
$357$	2.27824	−	1.16082i	0.120577	−	0.0614373i
$358$		0			0
$359$	1.02286	+	3.14804i	0.0539845	+	0.166147i	0.974414	−	0.224762i	$-0.0721606\pi$
$359$	1.02286	+	3.14804i	0.0539845	+	0.166147i	−0.920429	+	0.390909i	$0.872161\pi$
$360$		0			0
$361$	9.59210	−	3.11666i	0.504848	−	0.164035i
$362$		0			0
$363$	−2.60024	+	16.4172i	−0.136477	+	0.861682i
$364$		0			0
$365$	15.6324	+	1.01971i	0.818235	+	0.0533739i
$366$		0			0
$367$	−27.8405	+	20.2273i	−1.45326	+	1.05586i	−0.468209	+	0.883618i	$0.655100\pi$
$367$	−27.8405	+	20.2273i	−1.45326	+	1.05586i	−0.985055	+	0.172240i	$0.944900\pi$
$368$		0			0
$369$	−5.12523	+	0.360719i	−0.266809	+	0.0187783i
$370$		0			0
$371$	−1.23895	−	1.70527i	−0.0643232	−	0.0885333i
$372$		0			0
$373$	−27.3609	−	8.89011i	−1.41670	−	0.460312i	−0.502145	−	0.864784i	$-0.667456\pi$
$373$	−27.3609	−	8.89011i	−1.41670	−	0.460312i	−0.914551	+	0.404471i	$0.867456\pi$
$374$		0			0
$375$	12.1291	+	18.1159i	0.626346	+	0.935499i
$376$		0			0
$377$	−11.0045	−	33.8685i	−0.566762	−	1.74431i
$378$		0			0
$379$	3.50430	+	10.7851i	0.180004	+	0.553994i	0.999827	−	0.0186228i	$-0.00592815\pi$
$379$	3.50430	+	10.7851i	0.180004	+	0.553994i	−0.819823	+	0.572617i	$0.805928\pi$
$380$		0			0
$381$	10.2142	+	20.0464i	0.523288	+	1.02701i
$382$		0			0
$383$	9.02383	−	9.02383i	0.461096	−	0.461096i	−0.437918	−	0.899015i	$-0.644284\pi$
$383$	9.02383	−	9.02383i	0.461096	−	0.461096i	0.899015	+	0.437918i	$0.144284\pi$
$384$		0			0
$385$	−0.385900	+	0.968143i	−0.0196673	+	0.0493411i
$386$		0			0
$387$	−4.01203	−	5.52209i	−0.203943	−	0.280704i
$388$		0			0
$389$	−9.36158	+	12.8851i	−0.474651	+	0.653301i	−0.977466	−	0.211093i	$-0.932298\pi$
$389$	−9.36158	+	12.8851i	−0.474651	+	0.653301i	0.502815	+	0.864394i	$0.332298\pi$
$390$		0			0
$391$	1.32590	+	8.37140i	0.0670537	+	0.423360i
$392$		0			0
$393$	24.8017	+	12.6371i	1.25108	+	0.637458i
$394$		0			0
$395$	4.60604	−	4.04193i	0.231755	−	0.203372i
$396$		0			0
$397$	32.5611	+	5.15717i	1.63420	+	0.258831i	0.904980	−	0.425453i	$-0.139885\pi$
$397$	32.5611	+	5.15717i	1.63420	+	0.258831i	0.729215	+	0.684284i	$0.239885\pi$
$398$		0			0
$399$	−1.53661	−	0.782944i	−0.0769269	−	0.0391962i
$400$		0			0
$401$			30.5887i			1.52752i	0.645497	+	0.763762i	$0.276650\pi$
$401$			30.5887i			1.52752i	−0.645497	+	0.763762i	$0.723350\pi$
$402$		0			0
$403$	1.11715	+	7.05338i	0.0556490	+	0.351354i
$404$		0			0
$405$	−24.0166	−	1.56661i	−1.19339	−	0.0778457i
$406$		0			0
$407$	10.7335	+	10.7335i	0.532039	+	0.532039i
$408$		0			0
$409$	25.3561			1.25378			0.626889	−	0.779109i	$-0.284328\pi$
$409$	25.3561			1.25378			0.626889	+	0.779109i	$0.284328\pi$
$410$		0			0
$411$	5.89020			0.290542
$412$		0			0
$413$	1.93651	+	1.93651i	0.0952892	+	0.0952892i
$414$		0			0
$415$	−0.885127	+	13.5692i	−0.0434492	+	0.666086i
$416$		0			0
$417$	−5.04091	−	31.8270i	−0.246854	−	1.55858i
$418$		0			0
$419$		−	17.9606i		−	0.877433i	−0.898626	−	0.438716i	$-0.855433\pi$
$419$		−	17.9606i		−	0.877433i	0.898626	−	0.438716i	$-0.144567\pi$
$420$		0			0
$421$	−0.0592811	−	0.0302052i	−0.00288918	−	0.00147211i	0.452545	−	0.891741i	$-0.350516\pi$
$421$	−0.0592811	−	0.0302052i	−0.00288918	−	0.00147211i	−0.455434	+	0.890269i	$0.650516\pi$
$422$		0			0
$423$	−4.66369	−	0.738657i	−0.226757	−	0.0359147i
$424$		0			0
$425$	−18.2485	−	12.5251i	−0.885184	−	0.607558i
$426$		0			0
$427$	−1.79314	−	0.913650i	−0.0867760	−	0.0442146i
$428$		0			0
$429$	1.68257	+	10.6233i	0.0812352	+	0.512899i
$430$		0			0
$431$	−3.84273	+	5.28907i	−0.185098	+	0.254766i	−0.891475	−	0.453071i	$-0.850329\pi$
$431$	−3.84273	+	5.28907i	−0.185098	+	0.254766i	0.706377	+	0.707836i	$0.250329\pi$
$432$		0			0
$433$	−11.1873	−	15.3979i	−0.537625	−	0.739978i	0.450643	−	0.892704i	$-0.351195\pi$
$433$	−11.1873	−	15.3979i	−0.537625	−	0.739978i	−0.988269	+	0.152726i	$0.951195\pi$
$434$		0			0
$435$	−16.4010	+	41.1467i	−0.786368	+	1.97283i
$436$		0			0
$437$	4.04229	−	4.04229i	0.193369	−	0.193369i
$438$		0			0
$439$	−13.6078	−	26.7068i	−0.649465	−	1.27465i	−0.947397	−	0.320060i	$-0.896297\pi$
$439$	−13.6078	−	26.7068i	−0.649465	−	1.27465i	0.297932	−	0.954587i	$-0.403703\pi$
$440$		0			0
$441$	1.71394	+	5.27497i	0.0816163	+	0.251189i
$442$		0			0
$443$	−7.93182	−	24.4116i	−0.376852	−	1.15983i	−0.942220	−	0.334994i	$-0.891266\pi$
$443$	−7.93182	−	24.4116i	−0.376852	−	1.15983i	0.565368	−	0.824839i	$-0.308734\pi$
$444$		0			0
$445$	18.5438	−	1.70977i	0.879062	−	0.0810507i
$446$		0			0
$447$	−4.25043	−	1.38105i	−0.201039	−	0.0653214i
$448$		0			0
$449$	−2.60909	−	3.59111i	−0.123131	−	0.169475i	0.743002	−	0.669290i	$-0.233401\pi$
$449$	−2.60909	−	3.59111i	−0.123131	−	0.169475i	−0.866132	+	0.499815i	$0.833401\pi$
$450$		0			0
$451$	−3.93250	+	9.27606i	−0.185174	+	0.436792i
$452$		0			0
$453$	−5.36680	+	3.89921i	−0.252154	+	0.183201i
$454$		0			0
$455$	0.151138	−	2.31699i	0.00708548	−	0.108622i
$456$		0			0
$457$	0.373752	−	2.35978i	0.0174834	−	0.110386i	−0.977403	−	0.211383i	$-0.932203\pi$
$457$	0.373752	−	2.35978i	0.0174834	−	0.110386i	0.994887	+	0.100997i	$0.0322033\pi$
$458$		0			0
$459$	18.0410	−	5.86189i	0.842083	−	0.273609i
$460$		0			0
$461$	4.68644	+	14.4234i	0.218269	+	0.671763i	0.998905	+	0.0467775i	$0.0148952\pi$
$461$	4.68644	+	14.4234i	0.218269	+	0.671763i	−0.780636	+	0.624986i	$0.785105\pi$
$462$		0			0
$463$	−3.72998	+	1.90052i	−0.173347	+	0.0883246i	−0.538511	−	0.842619i	$-0.681013\pi$
$463$	−3.72998	+	1.90052i	−0.173347	+	0.0883246i	0.365164	+	0.930943i	$0.381013\pi$
$464$		0			0
$465$	4.53926	−	7.63522i	0.210503	−	0.354075i
$466$		0			0
$467$	−1.25860	+	1.73232i	−0.0582412	+	0.0801621i	−0.837144	−	0.546982i	$-0.815776\pi$
$467$	−1.25860	+	1.73232i	−0.0582412	+	0.0801621i	0.778903	+	0.627145i	$0.215776\pi$
$468$		0			0
$469$	3.26138	−	2.36953i	0.150597	−	0.109415i
$470$		0			0
$471$	16.3070	−	22.4447i	0.751389	−	1.03420i
$472$		0			0
$473$	−13.2201	+	2.09385i	−0.607859	+	0.0962755i
$474$		0			0
$475$	0.400079	+	14.9230i	0.0183569	+	0.684715i
$476$		0			0
$477$	2.59218	+	5.08744i	0.118688	+	0.232938i
$478$		0			0
$479$	−0.976152	+	6.16318i	−0.0446015	+	0.281603i	−0.999901	−	0.0140353i	$-0.995532\pi$
$479$	−0.976152	+	6.16318i	−0.0446015	+	0.281603i	0.955300	+	0.295638i	$0.0955323\pi$
$480$		0			0
$481$	−30.1317	−	15.3529i	−1.37389	−	0.700031i
$482$		0			0
$483$	1.10596			0.0503231
$484$		0			0
$485$	4.16685	+	9.69028i	0.189207	+	0.440013i
$486$		0			0
$487$	−8.18513	+	25.1913i	−0.370904	+	1.14152i	0.575297	+	0.817945i	$0.304886\pi$
$487$	−8.18513	+	25.1913i	−0.370904	+	1.14152i	−0.946201	+	0.323580i	$0.895114\pi$
$488$		0			0
$489$	−14.2008	+	14.2008i	−0.642183	+	0.642183i
$490$		0			0
$491$	−7.71268			−0.348068			−0.174034	−	0.984740i	$-0.555680\pi$
$491$	−7.71268			−0.348068			−0.174034	+	0.984740i	$0.555680\pi$
$492$		0			0
$493$		−	44.9695i		−	2.02533i
$494$		0			0
$495$	1.44272	−	2.42672i	0.0648457	−	0.109073i
$496$		0			0
$497$	−1.13789	+	3.50207i	−0.0510414	+	0.157089i
$498$		0			0
$499$	10.8473	−	1.71805i	0.485593	−	0.0769103i	0.0911621	−	0.995836i	$-0.470942\pi$
$499$	10.8473	−	1.71805i	0.485593	−	0.0769103i	0.394431	+	0.918926i	$0.370942\pi$
$500$		0			0
$501$		−	21.6527i		−	0.967371i
$502$		0			0
$503$	−0.807477	+	1.58476i	−0.0360036	+	0.0706611i	−0.908308	−	0.418303i	$-0.862625\pi$
$503$	−0.807477	+	1.58476i	−0.0360036	+	0.0706611i	0.872304	+	0.488964i	$0.162625\pi$
$504$		0			0
$505$	−0.152151	−	1.65020i	−0.00677062	−	0.0734330i
$506$		0			0
$507$	0.629895	+	1.23624i	0.0279746	+	0.0549033i
$508$		0			0
$509$	−15.1790	+	29.7904i	−0.672796	+	1.32044i	0.261937	+	0.965085i	$0.415639\pi$
$509$	−15.1790	+	29.7904i	−0.672796	+	1.32044i	−0.934733	+	0.355352i	$0.884361\pi$
$510$		0			0
$511$	0.324643	+	2.04971i	0.0143613	+	0.0906740i
$512$		0			0
$513$	−10.3509	−	7.52035i	−0.457002	−	0.332032i
$514$		0			0
$515$	−9.29127	−	7.72257i	−0.409422	−	0.340297i
$516$		0			0
$517$	−5.44248	+	7.49093i	−0.239360	+	0.329451i
$518$		0			0
$519$	0.900867	+	0.900867i	0.0395437	+	0.0395437i
$520$		0			0
$521$	5.93523	+	11.6485i	0.260027	+	0.510332i	0.983701	−	0.179810i	$-0.0575481\pi$
$521$	5.93523	+	11.6485i	0.260027	+	0.510332i	−0.723674	+	0.690142i	$0.757548\pi$
$522$		0			0
$523$	24.3643	−	7.91643i	1.06537	−	0.346161i	0.276690	−	0.960959i	$-0.410762\pi$
$523$	24.3643	−	7.91643i	1.06537	−	0.346161i	0.788685	+	0.614798i	$0.210762\pi$
$524$		0			0
$525$	−1.98673	+	2.09619i	−0.0867078	+	0.0914851i
$526$		0			0
$527$	−1.41071	+	8.90690i	−0.0614517	+	0.387991i
$528$		0			0
$529$	5.97451	−	18.3877i	0.259762	−	0.799464i
$530$		0			0
$531$	−4.36048	−	6.00169i	−0.189229	−	0.260451i
$532$		0			0
$533$	1.94620	−	22.3616i	0.0842992	−	0.968587i
$534$		0			0
$535$	14.4235	−	17.3534i	0.623582	−	0.750252i
$536$		0			0
$537$	42.3590	+	13.7633i	1.82793	+	0.593930i
$538$		0			0
$539$	10.7424	+	1.70143i	0.462708	+	0.0732858i
$540$		0			0
$541$	21.8517	−	7.10005i	0.939478	−	0.305255i	0.201045	−	0.979582i	$-0.435566\pi$
$541$	21.8517	−	7.10005i	0.939478	−	0.305255i	0.738433	+	0.674327i	$0.235566\pi$
$542$		0			0
$543$	−11.2720	+	3.66250i	−0.483728	+	0.157173i
$544$		0			0
$545$	−3.15961	−	3.60058i	−0.135343	−	0.154232i
$546$		0			0
$547$	3.13537	−	3.13537i	0.134059	−	0.134059i	−0.636893	−	0.770952i	$-0.719781\pi$
$547$	3.13537	−	3.13537i	0.134059	−	0.134059i	0.770952	+	0.636893i	$0.219781\pi$
$548$		0			0
$549$	4.41035	+	3.20430i	0.188229	+	0.136756i
$550$		0			0
$551$	−24.5381	+	17.8280i	−1.04536	+	0.759496i
$552$		0			0
$553$	0.656759	+	0.477163i	0.0279282	+	0.0202910i
$554$		0			0
$555$	16.6165	+	38.6426i	0.705329	+	1.64029i
$556$		0			0
$557$	12.0564	+	6.14306i	0.510847	+	0.260290i	0.690360	−	0.723466i	$-0.257452\pi$
$557$	12.0564	+	6.14306i	0.510847	+	0.260290i	−0.179513	+	0.983756i	$0.557452\pi$
$558$		0			0
$559$	26.5694	−	13.5378i	1.12377	−	0.572587i
$560$		0			0
$561$	−2.12472	+	13.4150i	−0.0897058	+	0.566380i
$562$		0			0
$563$	−21.1809	+	41.5699i	−0.892669	+	1.75196i	−0.283390	+	0.959005i	$0.591459\pi$
$563$	−21.1809	+	41.5699i	−0.892669	+	1.75196i	−0.609278	+	0.792956i	$0.708541\pi$
$564$		0			0
$565$	33.5213	−	8.52446i	1.41025	−	0.358627i
$566$		0			0
$567$	−0.498761	−	3.14905i	−0.0209460	−	0.132248i
$568$		0			0
$569$	−21.6384	−	7.03073i	−0.907128	−	0.294744i	−0.181952	−	0.983307i	$-0.558242\pi$
$569$	−21.6384	−	7.03073i	−0.907128	−	0.294744i	−0.725176	+	0.688564i	$0.758242\pi$
$570$		0			0
$571$	−18.2775	+	18.2775i	−0.764891	+	0.764891i	−0.977202	−	0.212311i	$-0.931901\pi$
$571$	−18.2775	+	18.2775i	−0.764891	+	0.764891i	0.212311	+	0.977202i	$0.431901\pi$
$572$		0			0
$573$			26.1173i			1.09107i
$574$		0			0
$575$	−4.57331	−	8.41049i	−0.190720	−	0.350742i
$576$		0			0
$577$	19.6049	+	19.6049i	0.816163	+	0.816163i	0.985550	−	0.169387i	$-0.0541787\pi$
$577$	19.6049	+	19.6049i	0.816163	+	0.816163i	−0.169387	+	0.985550i	$0.554179\pi$
$578$		0			0
$579$	−26.2427	−	8.52676i	−1.09061	−	0.354360i
$580$		0			0
$581$	−1.77919	+	0.281797i	−0.0738134	+	0.0116909i
$582$		0			0
$583$	11.1966			0.463716
$584$		0			0
$585$	−1.38620	+	6.13502i	−0.0573124	+	0.253652i
$586$		0			0
$587$	26.9234	+	4.26425i	1.11125	+	0.176004i	0.684958	−	0.728583i	$-0.259821\pi$
$587$	26.9234	+	4.26425i	1.11125	+	0.176004i	0.426289	+	0.904587i	$0.359821\pi$
$588$		0			0
$589$	5.41941	−	2.76133i	0.223303	−	0.113778i
$590$		0			0
$591$	−9.10275	+	17.8651i	−0.374437	+	0.734874i
$592$		0			0
$593$	5.99460	−	0.949451i	0.246169	−	0.0389893i	−0.0321306	−	0.999484i	$-0.510229\pi$
$593$	5.99460	−	0.949451i	0.246169	−	0.0389893i	0.278299	+	0.960494i	$0.410229\pi$
$594$		0			0
$595$	1.08565	−	2.72368i	0.0445075	−	0.111660i
$596$		0			0
$597$	−0.420794	−	0.579173i	−0.0172219	−	0.0237040i
$598$		0			0
$599$	30.8534	+	22.4163i	1.26064	+	0.915906i	0.998789	−	0.0492029i	$-0.0156681\pi$
$599$	30.8534	+	22.4163i	1.26064	+	0.915906i	0.261848	+	0.965109i	$0.415668\pi$
$600$		0			0
$601$	6.64339	+	6.64339i	0.270989	+	0.270989i	0.829498	−	0.558509i	$-0.188626\pi$
$601$	6.64339	+	6.64339i	0.270989	+	0.270989i	−0.558509	+	0.829498i	$0.688626\pi$
$602$		0			0
$603$	−9.72988	+	4.95762i	−0.396231	+	0.201890i
$604$		0			0
$605$	10.1760	+	16.1169i	0.413714	+	0.655245i
$606$		0			0
$607$	0.163156	+	0.502141i	0.00662228	+	0.0203813i	0.954313	−	0.298809i	$-0.0965892\pi$
$607$	0.163156	+	0.502141i	0.00662228	+	0.0203813i	−0.947691	+	0.319190i	$0.896589\pi$
$608$		0			0
$609$	−5.79564	−	0.917939i	−0.234851	−	0.0371967i
$610$		0			0
$611$	6.37452	−	19.6187i	0.257885	−	0.793690i
$612$		0			0
$613$	20.6035	−	14.9693i	0.832169	−	0.604606i	−0.0880030	−	0.996120i	$-0.528049\pi$
$613$	20.6035	−	14.9693i	0.832169	−	0.604606i	0.920172	+	0.391514i	$0.128049\pi$
$614$		0			0
$615$	−19.6405	+	19.8430i	−0.791982	+	0.800145i
$616$		0			0
$617$	−5.33859	+	3.87871i	−0.214924	+	0.156151i	−0.690039	−	0.723773i	$-0.742406\pi$
$617$	−5.33859	+	3.87871i	−0.214924	+	0.156151i	0.475115	+	0.879924i	$0.342406\pi$
$618$		0			0
$619$	14.5396	−	44.7482i	0.584395	−	1.79858i	−0.0172922	−	0.999850i	$-0.505505\pi$
$619$	14.5396	−	44.7482i	0.584395	−	1.79858i	0.601687	−	0.798732i	$-0.294495\pi$
$620$		0			0
$621$	8.10395	+	1.28354i	0.325200	+	0.0515067i
$622$		0			0
$623$	0.762337	+	2.34623i	0.0305424	+	0.0939998i
$624$		0			0
$625$	24.1562	+	6.44037i	0.966248	+	0.257615i
$626$		0			0
$627$	8.16235	−	4.15892i	0.325973	−	0.166091i
$628$		0			0
$629$	−30.1965	−	30.1965i	−1.20401	−	1.20401i
$630$		0			0
$631$	9.73371	+	7.07195i	0.387493	+	0.281530i	0.764427	−	0.644710i	$-0.223022\pi$
$631$	9.73371	+	7.07195i	0.387493	+	0.281530i	−0.376935	+	0.926240i	$0.623022\pi$
$632$		0			0
$633$	3.01253	+	4.14639i	0.119737	+	0.164804i
$634$		0			0
$635$	23.9658	+	9.55274i	0.951055	+	0.379089i
$636$		0			0
$637$	−23.9325	+	3.79054i	−0.948241	+	0.150187i
$638$		0			0
$639$	4.52843	−	8.88754i	0.179142	−	0.351586i
$640$		0			0
$641$	30.2660	−	15.4213i	1.19543	−	0.609105i	0.261035	−	0.965329i	$-0.415936\pi$
$641$	30.2660	−	15.4213i	1.19543	−	0.609105i	0.934400	+	0.356225i	$0.115936\pi$
$642$		0			0
$643$	−41.4158	−	6.55961i	−1.63328	−	0.258686i	−0.728650	−	0.684887i	$-0.759852\pi$
$643$	−41.4158	−	6.55961i	−1.63328	−	0.258686i	−0.904629	+	0.426201i	$0.859852\pi$
$644$		0			0
$645$	−36.1788	−	8.17457i	−1.42454	−	0.321873i
$646$		0			0
$647$	5.43559			0.213695			0.106847	−	0.994275i	$-0.465924\pi$
$647$	5.43559			0.213695			0.106847	+	0.994275i	$0.465924\pi$
$648$		0			0
$649$	−14.3683	+	2.27571i	−0.564003	+	0.0893293i
$650$		0			0
$651$	1.11912	+	0.363623i	0.0438617	+	0.0142515i
$652$		0			0
$653$	−24.6719	−	24.6719i	−0.965486	−	0.965486i	0.0339379	−	0.999424i	$-0.489195\pi$
$653$	−24.6719	−	24.6719i	−0.965486	−	0.965486i	−0.999424	+	0.0339379i	$0.989195\pi$
$654$		0			0
$655$	30.9350	−	7.86675i	1.20873	−	0.307379i
$656$		0			0
$657$		−	5.62154i		−	0.219317i
$658$		0			0
$659$	−23.4890	+	23.4890i	−0.915002	+	0.915002i	−0.996660	−	0.0816582i	$-0.973978\pi$
$659$	−23.4890	+	23.4890i	−0.915002	+	0.915002i	0.0816582	+	0.996660i	$0.473978\pi$
$660$		0			0
$661$	−1.20546	−	0.391678i	−0.0468870	−	0.0152345i	0.285480	−	0.958385i	$-0.407847\pi$
$661$	−1.20546	−	0.391678i	−0.0468870	−	0.0152345i	−0.332367	+	0.943150i	$0.607847\pi$
$662$		0			0
$663$	−4.73357	−	29.8866i	−0.183837	−	1.16070i
$664$		0			0
$665$	−1.91660	+	0.487391i	−0.0743227	+	0.0189002i
$666$		0			0
$667$	8.83053	−	17.3309i	0.341920	−	0.671055i
$668$		0			0
$669$	5.57295	−	35.1862i	0.215463	−	1.36038i
$670$		0			0
$671$	9.52498	−	4.85322i	0.367708	−	0.187356i
$672$		0			0
$673$	20.6627	+	10.5282i	0.796489	+	0.405831i	0.804363	−	0.594138i	$-0.202507\pi$
$673$	20.6627	+	10.5282i	0.796489	+	0.405831i	−0.00787448	+	0.999969i	$0.502507\pi$
$674$		0			0
$675$	−16.9905	+	13.0541i	−0.653964	+	0.502452i
$676$		0			0
$677$	−32.3842	−	23.5285i	−1.24462	−	0.904272i	−0.246727	−	0.969085i	$-0.579355\pi$
$677$	−32.3842	−	23.5285i	−1.24462	−	0.904272i	−0.997897	+	0.0648127i	$0.979355\pi$
$678$		0			0
$679$	−1.13048	+	0.821340i	−0.0433838	+	0.0315201i
$680$		0			0
$681$	10.2346	+	7.43590i	0.392192	+	0.284944i
$682$		0			0
$683$	−2.23439	+	2.23439i	−0.0854966	+	0.0854966i	−0.748562	−	0.663065i	$-0.769255\pi$
$683$	−2.23439	+	2.23439i	−0.0854966	+	0.0854966i	0.663065	+	0.748562i	$0.269255\pi$
$684$		0			0
$685$	5.07683	−	4.45506i	0.193976	−	0.170219i
$686$		0			0
$687$	1.75990	−	0.571826i	0.0671443	−	0.0218165i
$688$		0			0
$689$	−23.7235	+	7.70824i	−0.903795	+	0.293661i
$690$		0			0
$691$	−32.4411	−	5.13817i	−1.23412	−	0.195465i	−0.494911	−	0.868944i	$-0.664799\pi$
$691$	−32.4411	−	5.13817i	−1.23412	−	0.195465i	−0.739207	+	0.673479i	$0.764799\pi$
$692$		0			0
$693$	0.355692	+	0.115571i	0.0135116	+	0.00439019i
$694$		0			0
$695$	−28.4172	−	23.6194i	−1.07793	−	0.895934i
$696$		0			0
$697$	11.0633	−	26.0963i	0.419053	−	0.988469i
$698$		0			0
$699$	−18.7587	−	25.8192i	−0.709520	−	0.976571i
$700$		0			0
$701$	5.53530	−	17.0359i	0.209065	−	0.643437i	−0.790457	−	0.612518i	$-0.790157\pi$
$701$	5.53530	−	17.0359i	0.209065	−	0.643437i	0.999522	−	0.0309187i	$-0.00984331\pi$
$702$		0			0
$703$	−4.50577	+	28.4483i	−0.169938	+	1.07295i
$704$		0			0
$705$	−21.6958	+	13.6985i	−0.817111	+	0.515915i
$706$		0			0
$707$	0.208789	−	0.0678398i	0.00785234	−	0.00255138i
$708$		0			0
$709$	3.40113	+	6.67510i	0.127732	+	0.250688i	0.946012	−	0.324132i	$-0.105072\pi$
$709$	3.40113	+	6.67510i	0.127732	+	0.250688i	−0.818280	+	0.574820i	$0.805072\pi$
$710$		0			0
$711$	−1.55495	−	1.55495i	−0.0583150	−	0.0583150i
$712$		0			0
$713$	−2.29270	+	3.15563i	−0.0858622	+	0.118179i
$714$		0			0
$715$	9.48518	+	7.88374i	0.354726	+	0.294835i
$716$		0			0
$717$	−10.0117	−	7.27396i	−0.373895	−	0.271651i
$718$		0			0
$719$	−6.26414	−	39.5502i	−0.233613	−	1.47497i	−0.773801	−	0.633429i	$-0.781647\pi$
$719$	−6.26414	−	39.5502i	−0.233613	−	1.47497i	0.540188	−	0.841544i	$-0.318353\pi$
$720$		0			0
$721$	0.726606	−	1.42605i	0.0270602	−	0.0531087i
$722$		0			0
$723$	13.0163	+	25.5460i	0.484083	+	0.950067i
$724$		0			0
$725$	16.9851	+	47.8697i	0.630812	+	1.77784i
$726$		0			0
$727$	8.57435	−	16.8281i	0.318005	−	0.624120i	−0.675570	−	0.737296i	$-0.736102\pi$
$727$	8.57435	−	16.8281i	0.318005	−	0.624120i	0.993575	+	0.113176i	$0.0361024\pi$
$728$		0			0
$729$		−	16.4319i		−	0.608587i
$730$		0			0
$731$	37.1920	−	5.89064i	1.37560	−	0.217873i
$732$		0			0
$733$	1.60113	−	4.92778i	0.0591391	−	0.182012i	−0.917123	−	0.398605i	$-0.869495\pi$
$733$	1.60113	−	4.92778i	0.0591391	−	0.182012i	0.976262	+	0.216593i	$0.0694945\pi$
$734$		0			0
$735$	25.9068	+	15.4020i	0.955585	+	0.568110i
$736$		0			0
$737$			21.4138i			0.788789i
$738$		0			0
$739$	13.8728			0.510318			0.255159	−	0.966899i	$-0.417872\pi$
$739$	13.8728			0.510318			0.255159	+	0.966899i	$0.417872\pi$
$740$		0			0
$741$	−14.4313	+	14.4313i	−0.530148	+	0.530148i
$742$		0			0
$743$	14.1618	−	43.5855i	0.519546	−	1.59900i	−0.255309	−	0.966859i	$-0.582177\pi$
$743$	14.1618	−	43.5855i	0.519546	−	1.59900i	0.774855	−	0.632139i	$-0.217823\pi$
$744$		0			0
$745$	−4.70805	+	2.02448i	−0.172490	+	0.0741711i
$746$		0			0
$747$	4.87961			0.178536
$748$		0			0
$749$	2.66344	+	1.35709i	0.0973198	+	0.0495869i
$750$		0			0
$751$	2.27831	−	14.3847i	0.0831367	−	0.524904i	−0.910612	−	0.413263i	$-0.864389\pi$
$751$	2.27831	−	14.3847i	0.0831367	−	0.524904i	0.993749	−	0.111642i	$-0.0356109\pi$
$752$		0			0
$753$	21.5257	+	42.2465i	0.784439	+	1.53955i
$754$		0			0
$755$	−1.67653	+	7.41995i	−0.0610153	+	0.270040i
$756$		0			0
$757$	−45.8347	+	7.25951i	−1.66589	+	0.263851i	−0.917013	−	0.398857i	$-0.869407\pi$
$757$	−45.8347	+	7.25951i	−1.66589	+	0.263851i	−0.748878	+	0.662708i	$0.769407\pi$
$758$		0			0
$759$	−3.45311	+	4.75279i	−0.125340	+	0.172516i
$760$		0			0
$761$	10.4251	−	7.57428i	0.377910	−	0.274567i	−0.382574	−	0.923925i	$-0.624962\pi$
$761$	10.4251	−	7.57428i	0.377910	−	0.274567i	0.760483	+	0.649358i	$0.224962\pi$
$762$		0			0
$763$	0.373003	−	0.513394i	0.0135036	−	0.0185861i
$764$		0			0
$765$	−4.05882	+	6.82710i	−0.146747	+	0.246834i
$766$		0			0
$767$	28.8770	−	14.7136i	1.04269	−	0.531276i
$768$		0			0
$769$	−10.5422	−	32.4456i	−0.380162	−	1.17002i	−0.939930	−	0.341368i	$-0.889110\pi$
$769$	−10.5422	−	32.4456i	−0.380162	−	1.17002i	0.559768	−	0.828650i	$-0.310890\pi$
$770$		0			0
$771$	−12.8899	+	4.18817i	−0.464217	+	0.150833i
$772$		0			0
$773$	8.15973	−	51.5185i	0.293485	−	1.85299i	−0.195507	−	0.980702i	$-0.562635\pi$
$773$	8.15973	−	51.5185i	0.293485	−	1.85299i	0.488992	−	0.872288i	$-0.337365\pi$
$774$		0			0
$775$	−1.86247	−	10.0142i	−0.0669019	−	0.359719i
$776$		0			0
$777$	−4.50809	+	3.27532i	−0.161727	+	0.117501i
$778$		0			0
$779$	−18.6257	+	4.30896i	−0.667336	+	0.154384i
$780$		0			0
$781$	−11.4971	−	15.8244i	−0.411398	−	0.566240i
$782$		0			0
$783$	−41.4022	−	13.4524i	−1.47959	−	0.480749i
$784$		0			0
$785$	−2.92086	−	31.6792i	−0.104250	−	1.13068i
$786$		0			0
$787$	14.8657	+	45.7520i	0.529906	+	1.63088i	0.754405	+	0.656410i	$0.227926\pi$
$787$	14.8657	+	45.7520i	0.529906	+	1.63088i	−0.224498	+	0.974474i	$0.572074\pi$
$788$		0			0
$789$	−17.3429	−	53.3758i	−0.617422	−	1.90023i
$790$		0			0
$791$	2.08019	+	4.08260i	0.0739629	+	0.145160i
$792$		0			0
$793$	−16.8405	+	16.8405i	−0.598024	+	0.598024i
$794$		0			0
$795$	28.8217	+	11.4883i	1.02220	+	0.407447i
$796$		0			0
$797$	1.13056	+	1.55608i	0.0400463	+	0.0551190i	0.828571	−	0.559885i	$-0.189155\pi$
$797$	1.13056	+	1.55608i	0.0400463	+	0.0551190i	−0.788524	+	0.615004i	$0.789155\pi$
$798$		0			0
$799$	15.3113	−	21.0742i	0.541676	−	0.745553i
$800$		0			0
$801$	−1.04539	−	6.60034i	−0.0369371	−	0.233212i
$802$		0			0
$803$	−9.82210	−	5.00461i	−0.346614	−	0.176609i
$804$		0			0
$805$	0.953243	−	0.836497i	0.0335974	−	0.0294826i
$806$		0			0
$807$	3.49327	+	0.553279i	0.122969	+	0.0194763i
$808$		0			0
$809$	−6.90702	−	3.51930i	−0.242838	−	0.123732i	0.328336	−	0.944561i	$-0.393512\pi$
$809$	−6.90702	−	3.51930i	−0.242838	−	0.123732i	−0.571174	+	0.820829i	$0.693512\pi$
$810$		0			0
$811$			5.55756i			0.195152i	0.995228	+	0.0975762i	$0.0311090\pi$
$811$			5.55756i			0.195152i	−0.995228	+	0.0975762i	$0.968891\pi$
$812$		0			0
$813$	−1.59909	−	10.0963i	−0.0560826	−	0.354092i
$814$		0			0
$815$	−1.49904	+	22.9806i	−0.0525090	+	0.804976i
$816$		0			0
$817$	−17.9589	−	17.9589i	−0.628302	−	0.628302i
$818$		0			0
$819$	−0.833211			−0.0291147
$820$		0			0
$821$	−12.6761			−0.442400			−0.221200	−	0.975228i	$-0.570997\pi$
$821$	−12.6761			−0.442400			−0.221200	+	0.975228i	$0.570997\pi$
$822$		0			0
$823$	11.6812	+	11.6812i	0.407181	+	0.407181i	0.880754	−	0.473573i	$-0.157036\pi$
$823$	11.6812	+	11.6812i	0.407181	+	0.407181i	−0.473573	+	0.880754i	$0.657036\pi$
$824$		0			0
$825$	−2.80512	−	15.0826i	−0.0976619	−	0.525110i
$826$		0			0
$827$	−4.68495	−	29.5796i	−0.162912	−	1.02858i	−0.924683	−	0.380738i	$-0.875670\pi$
$827$	−4.68495	−	29.5796i	−0.162912	−	1.02858i	0.761772	−	0.647846i	$-0.224330\pi$
$828$		0			0
$829$		−	49.0999i		−	1.70531i	−0.522473	−	0.852656i	$-0.674991\pi$
$829$		−	49.0999i		−	1.70531i	0.522473	−	0.852656i	$-0.325009\pi$
$830$		0			0
$831$	−29.2311	−	14.8940i	−1.01402	−	0.516667i
$832$		0			0
$833$	−30.2216	−	4.78664i	−1.04712	−	0.165847i
$834$		0			0
$835$	−16.3770	−	18.6627i	−0.566751	−	0.645849i
$836$		0			0
$837$	7.77832	+	3.96325i	0.268858	+	0.136990i
$838$		0			0
$839$	−7.43431	−	46.9384i	−0.256661	−	1.62049i	−0.693157	−	0.720787i	$-0.743781\pi$
$839$	−7.43431	−	46.9384i	−0.256661	−	1.62049i	0.436496	−	0.899706i	$-0.356219\pi$
$840$		0			0
$841$	−43.6137	+	60.0292i	−1.50392	+	2.06997i
$842$		0			0
$843$	−19.6026	−	26.9807i	−0.675150	−	0.929265i
$844$		0			0
$845$	1.47794	+	0.589106i	0.0508428	+	0.0202659i
$846$		0			0
$847$	−1.78545	+	1.78545i	−0.0613488	+	0.0613488i
$848$		0			0
$849$	−16.4123	−	32.2110i	−0.563269	−	1.10548i
$850$		0			0
$851$	−5.70790	−	17.5671i	−0.195664	−	0.602193i
$852$		0			0
$853$	−13.2385	−	40.7438i	−0.453276	−	1.39504i	−0.873147	−	0.487456i	$-0.837925\pi$
$853$	−13.2385	−	40.7438i	−0.453276	−	1.39504i	0.419871	−	0.907584i	$-0.362075\pi$
$854$		0			0
$855$	5.33438	−	0.491837i	0.182432	−	0.0168205i
$856$		0			0
$857$	28.6940	+	9.32326i	0.980170	+	0.318476i	0.754914	−	0.655823i	$-0.227678\pi$
$857$	28.6940	+	9.32326i	0.980170	+	0.318476i	0.225255	+	0.974300i	$0.427678\pi$
$858$		0			0
$859$	16.3269	+	22.4720i	0.557067	+	0.766736i	0.990950	−	0.134233i	$-0.0428570\pi$
$859$	16.3269	+	22.4720i	0.557067	+	0.766736i	−0.433883	+	0.900969i	$0.642857\pi$
$860$		0			0
$861$	−3.13745	−	1.95852i	−0.106924	−	0.0667462i
$862$		0			0
$863$	−21.1117	+	15.3386i	−0.718651	+	0.522131i	−0.885953	−	0.463775i	$-0.846495\pi$
$863$	−21.1117	+	15.3386i	−0.718651	+	0.522131i	0.167302	+	0.985906i	$0.446495\pi$
$864$		0			0
$865$	1.45784	+	0.0950956i	0.0495680	+	0.00323335i
$866$		0			0
$867$	0.791744	−	4.99887i	0.0268890	−	0.169771i
$868$		0			0
$869$	−4.10114	+	1.33254i	−0.139122	+	0.0452034i
$870$		0			0
$871$	−14.7423	−	45.3720i	−0.499522	−	1.53737i
$872$		0			0
$873$	3.37262	−	1.71844i	0.114146	−	0.0581603i
$874$		0			0
$875$	−0.126928	+	3.30939i	−0.00429095	+	0.111878i
$876$		0			0
$877$	−12.1600	+	16.7369i	−0.410615	+	0.565163i	−0.963368	−	0.268182i	$-0.913577\pi$
$877$	−12.1600	+	16.7369i	−0.410615	+	0.565163i	0.552753	+	0.833345i	$0.313577\pi$
$878$		0			0
$879$	−10.3379	+	7.51093i	−0.348689	+	0.253337i
$880$		0			0
$881$	−12.1871	+	16.7742i	−0.410595	+	0.565136i	−0.963363	−	0.268199i	$-0.913571\pi$
$881$	−12.1871	+	16.7742i	−0.410595	+	0.565136i	0.552768	+	0.833335i	$0.313571\pi$
$882$		0			0
$883$	−25.3334	+	4.01242i	−0.852537	+	0.135029i	−0.567384	−	0.823453i	$-0.692044\pi$
$883$	−25.3334	+	4.01242i	−0.852537	+	0.135029i	−0.285153	+	0.958482i	$0.592044\pi$
$884$		0			0
$885$	−39.3209	−	8.88454i	−1.32176	−	0.298651i
$886$		0			0
$887$	4.70911	+	9.24214i	0.158116	+	0.310321i	0.956451	−	0.291894i	$-0.0942853\pi$
$887$	4.70911	+	9.24214i	0.158116	+	0.310321i	−0.798335	+	0.602214i	$0.794285\pi$
$888$		0			0
$889$	−0.534652	+	3.37566i	−0.0179317	+	0.113216i
$890$		0			0
$891$	15.0901	+	7.68877i	0.505536	+	0.257583i
$892$		0			0
$893$	−17.5695			−0.587940
$894$		0			0
$895$	46.9196	−	20.1756i	1.56835	−	0.674395i
$896$		0			0
$897$	4.04446	−	12.4476i	0.135041	−	0.415612i
$898$		0			0
$899$	14.6337	−	14.6337i	0.488060	−	0.488060i
$900$		0			0
$901$	−31.4994			−1.04940
$902$		0			0
$903$		−	4.91352i		−	0.163512i
$904$		0			0
$905$	−6.94534	+	11.6823i	−0.230871	+	0.388334i
$906$		0			0
$907$	3.30509	−	10.1720i	0.109744	−	0.337757i	−0.881071	−	0.472985i	$-0.843177\pi$
$907$	3.30509	−	10.1720i	0.109744	−	0.337757i	0.990815	+	0.135228i	$0.0431767\pi$
$908$		0			0
$909$	−0.587360	+	0.0930287i	−0.0194815	+	0.00308557i
$910$		0			0
$911$		−	44.8426i		−	1.48570i	−0.669457	−	0.742850i	$-0.733473\pi$
$911$		−	44.8426i		−	1.48570i	0.669457	−	0.742850i	$-0.266527\pi$
$912$		0			0
$913$	4.34410	−	8.52579i	0.143769	−	0.282162i
$914$		0			0
$915$	29.4983	−	2.71978i	0.975184	−	0.0899132i
$916$		0			0
$917$	1.91969	+	3.76760i	0.0633937	+	0.124417i
$918$		0			0
$919$	−11.3492	+	22.2740i	−0.374375	+	0.734752i	−0.998931	−	0.0462282i	$-0.985280\pi$
$919$	−11.3492	+	22.2740i	−0.374375	+	0.734752i	0.624556	+	0.780980i	$0.285280\pi$
$920$		0			0
$921$	2.07055	+	13.0729i	0.0682269	+	0.430768i
$922$		0			0
$923$	35.2544	+	25.6138i	1.16041	+	0.843089i
$924$		0			0
$925$	43.5493	+	20.7386i	1.43189	+	0.681882i
$926$		0			0
$927$	−2.54832	+	3.50746i	−0.0836977	+	0.115200i
$928$		0			0
$929$	11.5532	+	11.5532i	0.379049	+	0.379049i	0.870759	−	0.491710i	$-0.163628\pi$
$929$	11.5532	+	11.5532i	0.379049	+	0.379049i	−0.491710	+	0.870759i	$0.663628\pi$
$930$		0			0
$931$	9.36935	+	18.3884i	0.307068	+	0.602655i
$932$		0			0
$933$	−23.4428	+	7.61702i	−0.767482	+	0.249370i
$934$		0			0
$935$	8.31510	+	13.1695i	0.271933	+	0.430690i
$936$		0			0
$937$	−7.34460	+	46.3720i	−0.239938	+	1.51491i	0.513902	+	0.857849i	$0.328199\pi$
$937$	−7.34460	+	46.3720i	−0.239938	+	1.51491i	−0.753840	+	0.657058i	$0.771801\pi$
$938$		0			0
$939$	12.0599	−	37.1165i	0.393560	−	1.21125i
$940$		0			0
$941$	22.8327	+	31.4265i	0.744324	+	1.02447i	0.998358	+	0.0572790i	$0.0182425\pi$
$941$	22.8327	+	31.4265i	0.744324	+	1.02447i	−0.254034	+	0.967195i	$0.581758\pi$
$942$		0			0
$943$	9.38817	−	7.88485i	0.305721	−	0.256766i
$944$		0			0
$945$	−2.18285	−	1.81430i	−0.0710080	−	0.0590193i
$946$		0			0
$947$	−19.4193	−	6.30973i	−0.631044	−	0.205039i	−0.0240063	−	0.999712i	$-0.507642\pi$
$947$	−19.4193	−	6.30973i	−0.631044	−	0.205039i	−0.607037	+	0.794673i	$0.707642\pi$
$948$		0			0
$949$	24.2566	+	3.84187i	0.787403	+	0.124712i
$950$		0			0
$951$	30.3826	−	9.87191i	0.985224	−	0.320119i
$952$		0			0
$953$	20.1690	−	6.55332i	0.653339	−	0.212283i	0.0364532	−	0.999335i	$-0.488394\pi$
$953$	20.1690	−	6.55332i	0.653339	−	0.212283i	0.616886	+	0.787053i	$0.288394\pi$
$954$		0			0
$955$	19.7539	+	22.5108i	0.639220	+	0.728433i
$956$		0			0
$957$	22.0402	−	22.0402i	0.712460	−	0.712460i
$958$		0			0
$959$	0.723887	+	0.525934i	0.0233755	+	0.0169833i
$960$		0			0
$961$	21.7220	−	15.7820i	0.700711	−	0.509096i
$962$		0			0
$963$	−6.55090	−	4.75951i	−0.211100	−	0.153373i
$964$		0			0
$965$	−29.0681	+	12.4994i	−0.935735	+	0.402369i
$966$		0			0
$967$	17.9657	+	9.15397i	0.577738	+	0.294372i	0.718338	−	0.695694i	$-0.244903\pi$
$967$	17.9657	+	9.15397i	0.577738	+	0.294372i	−0.140600	+	0.990066i	$0.544903\pi$
$968$		0			0
$969$	−22.9631	+	11.7003i	−0.737682	+	0.375868i
$970$		0			0
$971$	−0.697362	+	4.40297i	−0.0223794	+	0.141298i	−0.996348	−	0.0853847i	$-0.972788\pi$
$971$	−0.697362	+	4.40297i	−0.0223794	+	0.141298i	0.973969	+	0.226683i	$0.0727881\pi$
$972$		0			0
$973$	2.22231	−	4.36154i	0.0712441	−	0.139825i
$974$		0			0
$975$	16.3271	+	30.0261i	0.522886	+	0.961606i
$976$		0			0
$977$	7.87632	+	49.7291i	0.251986	+	1.59098i	0.711422	+	0.702765i	$0.248051\pi$
$977$	7.87632	+	49.7291i	0.251986	+	1.59098i	−0.459436	+	0.888211i	$0.651949\pi$
$978$		0			0
$979$	−12.4630	−	4.04946i	−0.398318	−	0.129421i
$980$		0			0
$981$	−1.21552	+	1.21552i	−0.0388084	+	0.0388084i
$982$		0			0
$983$		−	34.6761i		−	1.10600i	−0.833183	−	0.552998i	$-0.813484\pi$
$983$		−	34.6761i		−	1.10600i	0.833183	−	0.552998i	$-0.186516\pi$
$984$		0			0
$985$	5.66656	+	22.2830i	0.180552	+	0.709996i
$986$		0			0
$987$	−2.40349	−	2.40349i	−0.0765039	−	0.0765039i
$988$		0			0
$989$	15.4902	+	5.03308i	0.492561	+	0.160043i
$990$		0			0
$991$	−43.1288	+	6.83093i	−1.37003	+	0.216992i	−0.797711	−	0.603039i	$-0.793956\pi$
$991$	−43.1288	+	6.83093i	−1.37003	+	0.216992i	−0.572319	+	0.820031i	$0.693956\pi$
$992$		0			0
$993$	49.5351			1.57195
$994$		0			0
$995$	−0.800745	−	0.180928i	−0.0253853	−	0.00573580i
$996$		0			0
$997$	−26.5331	−	4.20244i	−0.840313	−	0.133092i	−0.278582	−	0.960412i	$-0.589864\pi$
$997$	−26.5331	−	4.20244i	−0.840313	−	0.133092i	−0.561731	+	0.827320i	$0.689864\pi$
$998$		0			0
$999$	−36.8342	+	18.7680i	−1.16538	+	0.593792i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bq.a.569.6	yes	176
5.4	even	2	inner	820.2.bq.a.569.17	yes	176
41.8	even	20	inner	820.2.bq.a.49.17	yes	176
205.49	even	20	inner	820.2.bq.a.49.6	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bq.a.49.6	✓	176	205.49	even	20	inner
820.2.bq.a.49.17	yes	176	41.8	even	20	inner
820.2.bq.a.569.6	yes	176	1.1	even	1	trivial
820.2.bq.a.569.17	yes	176	5.4	even	2	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.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37884 - 1.37884i) q^{3} +(-2.23133 - 0.145551i) q^{5} +(-0.0463388 - 0.292571i) q^{7} +0.802406i q^{9} +(1.40198 + 0.714346i) q^{11} +(-3.46233 - 0.548380i) q^{13} +(2.87595 + 3.27734i) q^{15} +(-3.94420 - 2.00967i) q^{17} +(0.467063 + 2.94892i) q^{19} +(-0.339516 + 0.467303i) q^{21} +(-1.12543 - 1.54902i) q^{23} +(4.95763 + 0.649542i) q^{25} +(-3.03013 + 3.03013i) q^{27} +(4.61197 + 9.05151i) q^{29} +(-0.629522 - 1.93747i) q^{31} +(-0.948143 - 2.91808i) q^{33} +(0.0608129 + 0.659567i) q^{35} +(9.17488 + 2.98110i) q^{37} +(4.01788 + 5.53014i) q^{39} +(0.449547 + 6.38732i) q^{41} +(-6.88192 + 5.00000i) q^{43} +(0.116791 - 1.79043i) q^{45} +(-0.920552 + 5.81214i) q^{47} +(6.57394 - 2.13600i) q^{49} +(2.66741 + 8.20945i) q^{51} +(6.34023 - 3.23051i) q^{53} +(-3.02431 - 1.79800i) q^{55} +(3.42208 - 4.71009i) q^{57} +(-7.47962 + 5.43426i) q^{59} +(3.99337 - 5.49640i) q^{61} +(0.234761 - 0.0371825i) q^{63} +(7.64578 + 1.72756i) q^{65} +(6.17845 + 12.1259i) q^{67} +(-0.584066 + 3.68765i) q^{69} +(-11.0761 - 5.64356i) q^{71} -7.00586 q^{73} +(-5.94017 - 7.73140i) q^{75} +(0.144031 - 0.443282i) q^{77} +(-1.93786 + 1.93786i) q^{79} +10.7634 q^{81} -6.08123i q^{83} +(8.50829 + 5.05831i) q^{85} +(6.12141 - 18.8398i) q^{87} +(-8.22569 + 1.30282i) q^{89} +1.03839i q^{91} +(-1.80345 + 3.53947i) q^{93} +(-0.612952 - 6.64798i) q^{95} +(-2.14160 - 4.20314i) q^{97} +(-0.573196 + 1.12496i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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