LMFDB - Embedded newform 820.2.u.a.221.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [24] 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.1
Character	$\chi$	$=$	820.221
Dual form			820.2.u.a.141.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.55771 q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.254587 + 0.783539i) q^{7} +3.54189 q^{9} +(1.87777 - 1.36428i) q^{11} +(-0.980451 + 3.01752i) q^{13} +(2.06923 + 1.50339i) q^{15} +(-5.32618 + 3.86970i) q^{17} +(0.947836 + 2.91714i) q^{19} +(-0.651161 - 2.00407i) q^{21} +(2.53799 - 7.81113i) q^{23} +(0.309017 + 0.951057i) q^{25} -1.38599 q^{27} +(-8.11578 - 5.89646i) q^{29} +(7.52831 - 5.46964i) q^{31} +(-4.80279 + 3.48943i) q^{33} +(0.254587 - 0.783539i) q^{35} +(-0.730928 - 0.531051i) q^{37} +(2.50771 - 7.71794i) q^{39} +(5.13251 - 3.82850i) q^{41} +(1.40448 - 4.32254i) q^{43} +(-2.86545 - 2.08187i) q^{45} +(1.68758 - 5.19384i) q^{47} +(5.11400 - 3.71554i) q^{49} +(13.6228 - 9.89758i) q^{51} +(3.59973 + 2.61536i) q^{53} -2.32105 q^{55} +(-2.42429 - 7.46120i) q^{57} +(-1.97221 + 6.06983i) q^{59} +(-3.58776 - 11.0420i) q^{61} +(0.901720 + 2.77521i) q^{63} +(2.56686 - 1.86493i) q^{65} +(-8.95132 - 6.50351i) q^{67} +(-6.49145 + 19.9786i) q^{69} +(6.99837 - 5.08462i) q^{71} -4.08803 q^{73} +(-0.790376 - 2.43253i) q^{75} +(1.54702 + 1.12398i) q^{77} -8.41097 q^{79} -7.08069 q^{81} -4.00591 q^{83} +6.58353 q^{85} +(20.7578 + 15.0814i) q^{87} +(-3.45809 - 10.6429i) q^{89} -2.61396 q^{91} +(-19.2552 + 13.9898i) q^{93} +(0.947836 - 2.91714i) q^{95} +(12.1338 + 8.81569i) q^{97} +(6.65084 - 4.83212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	−2.55771			−1.47670			−0.738348	−	0.674420i	$-0.764394\pi$
$3$	−2.55771			−1.47670			−0.738348	+	0.674420i	$0.764394\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	0.254587	+	0.783539i	0.0962250	+	0.296150i	0.987571	−	0.157174i	$-0.0502382\pi$
$7$	0.254587	+	0.783539i	0.0962250	+	0.296150i	−0.891346	+	0.453324i	$0.850238\pi$
$8$		0			0
$9$	3.54189			1.18063
$10$		0			0
$11$	1.87777	−	1.36428i	0.566168	−	0.411345i	−0.267543	−	0.963546i	$-0.586212\pi$
$11$	1.87777	−	1.36428i	0.566168	−	0.411345i	0.833711	+	0.552201i	$0.186212\pi$
$12$		0			0
$13$	−0.980451	+	3.01752i	−0.271928	+	0.836909i	0.718087	+	0.695953i	$0.245018\pi$
$13$	−0.980451	+	3.01752i	−0.271928	+	0.836909i	−0.990016	+	0.140956i	$0.954982\pi$
$14$		0			0
$15$	2.06923	+	1.50339i	0.534273	+	0.388172i
$16$		0			0
$17$	−5.32618	+	3.86970i	−1.29179	+	0.938540i	−0.999840	−	0.0178937i	$-0.994304\pi$
$17$	−5.32618	+	3.86970i	−1.29179	+	0.938540i	−0.291950	+	0.956434i	$0.594304\pi$
$18$		0			0
$19$	0.947836	+	2.91714i	0.217449	+	0.669238i	0.998971	+	0.0453604i	$0.0144436\pi$
$19$	0.947836	+	2.91714i	0.217449	+	0.669238i	−0.781522	+	0.623878i	$0.785556\pi$
$20$		0			0
$21$	−0.651161	−	2.00407i	−0.142095	−	0.437323i
$22$		0			0
$23$	2.53799	−	7.81113i	0.529207	−	1.62873i	−0.226635	−	0.973980i	$-0.572773\pi$
$23$	2.53799	−	7.81113i	0.529207	−	1.62873i	0.755843	−	0.654753i	$-0.227227\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−1.38599			−0.266735
$28$		0			0
$29$	−8.11578	−	5.89646i	−1.50706	−	1.09494i	−0.967460	−	0.253025i	$-0.918575\pi$
$29$	−8.11578	−	5.89646i	−1.50706	−	1.09494i	−0.539602	−	0.841920i	$-0.681425\pi$
$30$		0			0
$31$	7.52831	−	5.46964i	1.35212	−	0.982376i	0.353222	−	0.935540i	$-0.385086\pi$
$31$	7.52831	−	5.46964i	1.35212	−	0.982376i	0.998903	−	0.0468364i	$-0.0149140\pi$
$32$		0			0
$33$	−4.80279	+	3.48943i	−0.836058	+	0.607432i
$34$		0			0
$35$	0.254587	−	0.783539i	0.0430331	−	0.132442i
$36$		0			0
$37$	−0.730928	−	0.531051i	−0.120164	−	0.0873042i	0.526080	−	0.850435i	$-0.323661\pi$
$37$	−0.730928	−	0.531051i	−0.120164	−	0.0873042i	−0.646244	+	0.763131i	$0.723661\pi$
$38$		0			0
$39$	2.50771	−	7.71794i	0.401555	−	1.23586i
$40$		0			0
$41$	5.13251	−	3.82850i	0.801563	−	0.597911i
$41$	5.13251	−	3.82850i	0.801563	−	0.597911i
$42$		0			0
$43$	1.40448	−	4.32254i	0.214181	−	0.659180i	−0.785030	−	0.619458i	$-0.787353\pi$
$43$	1.40448	−	4.32254i	0.214181	−	0.659180i	0.999211	−	0.0397228i	$-0.0126475\pi$
$44$		0			0
$45$	−2.86545	−	2.08187i	−0.427156	−	0.310347i
$46$		0			0
$47$	1.68758	−	5.19384i	0.246159	−	0.757600i	−0.749285	−	0.662248i	$-0.769602\pi$
$47$	1.68758	−	5.19384i	0.246159	−	0.757600i	0.995444	−	0.0953517i	$-0.0303976\pi$
$48$		0			0
$49$	5.11400	−	3.71554i	0.730571	−	0.530791i
$50$		0			0
$51$	13.6228	−	9.89758i	1.90758	−	1.38594i
$52$		0			0
$53$	3.59973	+	2.61536i	0.494461	+	0.359247i	0.806897	−	0.590692i	$-0.201145\pi$
$53$	3.59973	+	2.61536i	0.494461	+	0.359247i	−0.312436	+	0.949939i	$0.601145\pi$
$54$		0			0
$55$	−2.32105			−0.312970
$56$		0			0
$57$	−2.42429	−	7.46120i	−0.321105	−	0.988261i
$58$		0			0
$59$	−1.97221	+	6.06983i	−0.256759	+	0.790224i	0.736718	+	0.676200i	$0.236374\pi$
$59$	−1.97221	+	6.06983i	−0.256759	+	0.790224i	−0.993478	+	0.114025i	$0.963626\pi$
$60$		0			0
$61$	−3.58776	−	11.0420i	−0.459366	−	1.41378i	−0.865932	−	0.500161i	$-0.833274\pi$
$61$	−3.58776	−	11.0420i	−0.459366	−	1.41378i	0.406567	−	0.913621i	$-0.366726\pi$
$62$		0			0
$63$	0.901720	+	2.77521i	0.113606	+	0.349643i
$64$		0			0
$65$	2.56686	−	1.86493i	0.318379	−	0.231316i
$66$		0			0
$67$	−8.95132	−	6.50351i	−1.09358	−	0.794531i	−0.113578	−	0.993529i	$-0.536231\pi$
$67$	−8.95132	−	6.50351i	−1.09358	−	0.794531i	−0.980000	+	0.198999i	$0.936231\pi$
$68$		0			0
$69$	−6.49145	+	19.9786i	−0.781478	+	2.40514i
$70$		0			0
$71$	6.99837	−	5.08462i	0.830554	−	0.603433i	−0.0891620	−	0.996017i	$-0.528419\pi$
$71$	6.99837	−	5.08462i	0.830554	−	0.603433i	0.919716	+	0.392584i	$0.128419\pi$
$72$		0			0
$73$	−4.08803			−0.478468			−0.239234	−	0.970962i	$-0.576896\pi$
$73$	−4.08803			−0.478468			−0.239234	+	0.970962i	$0.576896\pi$
$74$		0			0
$75$	−0.790376	−	2.43253i	−0.0912648	−	0.280884i
$76$		0			0
$77$	1.54702	+	1.12398i	0.176299	+	0.128089i
$78$		0			0
$79$	−8.41097			−0.946309			−0.473154	−	0.880980i	$-0.656885\pi$
$79$	−8.41097			−0.946309			−0.473154	+	0.880980i	$0.656885\pi$
$80$		0			0
$81$	−7.08069			−0.786744
$82$		0			0
$83$	−4.00591			−0.439706			−0.219853	−	0.975533i	$-0.570558\pi$
$83$	−4.00591			−0.439706			−0.219853	+	0.975533i	$0.570558\pi$
$84$		0			0
$85$	6.58353			0.714084
$86$		0			0
$87$	20.7578	+	15.0814i	2.22547	+	1.61690i
$88$		0			0
$89$	−3.45809	−	10.6429i	−0.366557	−	1.12815i	−0.949000	−	0.315275i	$-0.897903\pi$
$89$	−3.45809	−	10.6429i	−0.366557	−	1.12815i	0.582444	−	0.812871i	$-0.302097\pi$
$90$		0			0
$91$	−2.61396			−0.274017
$92$		0			0
$93$	−19.2552	+	13.9898i	−1.99668	+	1.45067i
$94$		0			0
$95$	0.947836	−	2.91714i	0.0972460	−	0.299292i
$96$		0			0
$97$	12.1338	+	8.81569i	1.23200	+	0.895097i	0.997038	−	0.0769083i	$-0.0245049\pi$
$97$	12.1338	+	8.81569i	1.23200	+	0.895097i	0.234958	+	0.972006i	$0.424505\pi$
$98$		0			0
$99$	6.65084	−	4.83212i	0.668435	−	0.485646i
$100$		0			0
$101$	0.880473	+	2.70982i	0.0876103	+	0.269637i	0.985257	−	0.171078i	$-0.0547250\pi$
$101$	0.880473	+	2.70982i	0.0876103	+	0.269637i	−0.897647	+	0.440715i	$0.854725\pi$
$102$		0			0
$103$	2.94149	+	9.05296i	0.289833	+	0.892015i	0.984908	+	0.173078i	$0.0553712\pi$
$103$	2.94149	+	9.05296i	0.289833	+	0.892015i	−0.695075	+	0.718937i	$0.744629\pi$
$104$		0			0
$105$	−0.651161	+	2.00407i	−0.0635468	+	0.195577i
$106$		0			0
$107$	−3.64567	−	11.2202i	−0.352440	−	1.08470i	−0.957479	−	0.288503i	$-0.906842\pi$
$107$	−3.64567	−	11.2202i	−0.352440	−	1.08470i	0.605039	−	0.796196i	$-0.293158\pi$
$108$		0			0
$109$	11.2203			1.07471			0.537356	−	0.843356i	$-0.319423\pi$
$109$	11.2203			1.07471			0.537356	+	0.843356i	$0.319423\pi$
$110$		0			0
$111$	1.86950	+	1.35827i	0.177445	+	0.128922i
$112$		0			0
$113$	11.5109	−	8.36314i	1.08285	−	0.786738i	0.104674	−	0.994507i	$-0.466620\pi$
$113$	11.5109	−	8.36314i	1.08285	−	0.786738i	0.978178	+	0.207769i	$0.0666202\pi$
$114$		0			0
$115$	−6.64454	+	4.82754i	−0.619607	+	0.450171i
$116$		0			0
$117$	−3.47265	+	10.6877i	−0.321047	+	0.988080i
$118$		0			0
$119$	−4.38804	−	3.18810i	−0.402251	−	0.292253i
$120$		0			0
$121$	−1.73443	+	5.33803i	−0.157675	+	0.485275i
$122$		0			0
$123$	−13.1275	+	9.79219i	−1.18366	+	0.882932i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−1.83286	−	1.33165i	−0.162640	−	0.118165i	0.503488	−	0.864002i	$-0.332050\pi$
$127$	−1.83286	−	1.33165i	−0.162640	−	0.118165i	−0.666128	+	0.745837i	$0.732050\pi$
$128$		0			0
$129$	−3.59225	+	11.0558i	−0.316280	+	0.973409i
$130$		0			0
$131$	16.0806	−	11.6833i	1.40497	−	1.02077i	0.410942	−	0.911662i	$-0.365200\pi$
$131$	16.0806	−	11.6833i	1.40497	−	1.02077i	0.994030	−	0.109110i	$-0.0348000\pi$
$132$		0			0
$133$	−2.04439	+	1.48533i	−0.177271	+	0.128795i
$134$		0			0
$135$	1.12129	+	0.814667i	0.0965055	+	0.0701154i
$136$		0			0
$137$	−10.6119			−0.906639			−0.453319	−	0.891348i	$-0.649760\pi$
$137$	−10.6119			−0.906639			−0.453319	+	0.891348i	$0.649760\pi$
$138$		0			0
$139$	3.49620	+	10.7602i	0.296544	+	0.912668i	0.982699	+	0.185212i	$0.0592973\pi$
$139$	3.49620	+	10.7602i	0.296544	+	0.912668i	−0.686155	+	0.727456i	$0.740703\pi$
$140$		0			0
$141$	−4.31635	+	13.2844i	−0.363502	+	1.11874i
$142$		0			0
$143$	2.27568	+	7.00381i	0.190302	+	0.585688i
$144$		0			0
$145$	3.09995	+	9.54067i	0.257437	+	0.792309i
$146$		0			0
$147$	−13.0801	+	9.50328i	−1.07883	+	0.783817i
$148$		0			0
$149$	6.34283	+	4.60833i	0.519625	+	0.377529i	0.816462	−	0.577398i	$-0.195932\pi$
$149$	6.34283	+	4.60833i	0.519625	+	0.377529i	−0.296838	+	0.954928i	$0.595932\pi$
$150$		0			0
$151$	1.93794	−	5.96438i	0.157708	−	0.485374i	−0.840717	−	0.541474i	$-0.817866\pi$
$151$	1.93794	−	5.96438i	0.157708	−	0.485374i	0.998425	+	0.0560997i	$0.0178665\pi$
$152$		0			0
$153$	−18.8648	+	13.7060i	−1.52512	+	1.10807i
$154$		0			0
$155$	−9.30550			−0.747436
$156$		0			0
$157$	−2.76555	−	8.51149i	−0.220715	−	0.679291i	−0.998698	−	0.0510059i	$-0.983757\pi$
$157$	−2.76555	−	8.51149i	−0.220715	−	0.679291i	0.777983	−	0.628285i	$-0.216243\pi$
$158$		0			0
$159$	−9.20707	−	6.68933i	−0.730168	−	0.530498i
$160$		0			0
$161$	6.76647			0.533272
$162$		0			0
$163$	−7.24829			−0.567730			−0.283865	−	0.958864i	$-0.591617\pi$
$163$	−7.24829			−0.567730			−0.283865	+	0.958864i	$0.591617\pi$
$164$		0			0
$165$	5.93657			0.462162
$166$		0			0
$167$	16.6599			1.28918			0.644592	−	0.764526i	$-0.277027\pi$
$167$	16.6599			1.28918			0.644592	+	0.764526i	$0.277027\pi$
$168$		0			0
$169$	2.37308	+	1.72415i	0.182545	+	0.132627i
$170$		0			0
$171$	3.35713	+	10.3322i	0.256726	+	0.790122i
$172$		0			0
$173$	−14.5215			−1.10405			−0.552023	−	0.833829i	$-0.686144\pi$
$173$	−14.5215			−1.10405			−0.552023	+	0.833829i	$0.686144\pi$
$174$		0			0
$175$	−0.666518	+	0.484254i	−0.0503841	+	0.0366062i
$176$		0			0
$177$	5.04434	−	15.5249i	0.379156	−	1.16692i
$178$		0			0
$179$	−10.3941	−	7.55174i	−0.776890	−	0.564444i	0.127154	−	0.991883i	$-0.459416\pi$
$179$	−10.3941	−	7.55174i	−0.776890	−	0.564444i	−0.904044	+	0.427439i	$0.859416\pi$
$180$		0			0
$181$	−6.04866	+	4.39461i	−0.449594	+	0.326649i	−0.789435	−	0.613834i	$-0.789627\pi$
$181$	−6.04866	+	4.39461i	−0.449594	+	0.326649i	0.339842	+	0.940483i	$0.389627\pi$
$182$		0			0
$183$	9.17646	+	28.2422i	0.678343	+	2.08773i
$184$		0			0
$185$	0.279190	+	0.859258i	0.0205264	+	0.0631739i
$186$		0			0
$187$	−4.72199	+	14.5328i	−0.345306	+	1.06274i
$188$		0			0
$189$	−0.352857	−	1.08598i	−0.0256665	−	0.0789935i
$190$		0			0
$191$	14.1829			1.02624			0.513121	−	0.858316i	$-0.328489\pi$
$191$	14.1829			1.02624			0.513121	+	0.858316i	$0.328489\pi$
$192$		0			0
$193$	−2.51771	−	1.82922i	−0.181229	−	0.131670i	0.493472	−	0.869762i	$-0.335727\pi$
$193$	−2.51771	−	1.82922i	−0.181229	−	0.131670i	−0.674701	+	0.738091i	$0.735727\pi$
$194$		0			0
$195$	−6.56528	+	4.76995i	−0.470149	+	0.341583i
$196$		0			0
$197$	−13.3992	+	9.73508i	−0.954652	+	0.693595i	−0.951903	−	0.306401i	$-0.900875\pi$
$197$	−13.3992	+	9.73508i	−0.954652	+	0.693595i	−0.00274968	+	0.999996i	$0.500875\pi$
$198$		0			0
$199$	1.38628	−	4.26652i	0.0982706	−	0.302446i	−0.889822	−	0.456308i	$-0.849171\pi$
$199$	1.38628	−	4.26652i	0.0982706	−	0.302446i	0.988092	+	0.153863i	$0.0491714\pi$
$200$		0			0
$201$	22.8949	+	16.6341i	1.61488	+	1.17328i
$202$		0			0
$203$	2.55393	−	7.86020i	0.179251	−	0.551678i
$204$		0			0
$205$	−6.40262	+	0.0805086i	−0.447178	+	0.00562296i
$206$		0			0
$207$	8.98928	−	27.6661i	0.624798	−	1.92293i
$208$		0			0
$209$	5.75961	+	4.18460i	0.398400	+	0.289455i
$210$		0			0
$211$	−3.48302	+	10.7196i	−0.239781	+	0.737969i	0.756671	+	0.653796i	$0.226825\pi$
$211$	−3.48302	+	10.7196i	−0.239781	+	0.737969i	−0.996451	+	0.0841726i	$0.973175\pi$
$212$		0			0
$213$	−17.8998	+	13.0050i	−1.22648	+	0.891087i
$214$		0			0
$215$	−3.67697	+	2.67147i	−0.250767	+	0.182193i
$216$		0			0
$217$	6.20229	+	4.50623i	0.421039	+	0.305903i
$218$		0			0
$219$	10.4560			0.706552
$220$		0			0
$221$	−6.45483	−	19.8659i	−0.434199	−	1.33633i
$222$		0			0
$223$	3.28941	−	10.1238i	0.220275	−	0.677938i	−0.778462	−	0.627692i	$-0.784000\pi$
$223$	3.28941	−	10.1238i	0.220275	−	0.677938i	0.998737	−	0.0502454i	$-0.0160003\pi$
$224$		0			0
$225$	1.09450	+	3.36854i	0.0729669	+	0.224569i
$226$		0			0
$227$	−4.33088	−	13.3291i	−0.287451	−	0.884682i	−0.985653	−	0.168782i	$-0.946017\pi$
$227$	−4.33088	−	13.3291i	−0.287451	−	0.884682i	0.698203	−	0.715900i	$-0.253983\pi$
$228$		0			0
$229$	−16.1258	+	11.7161i	−1.06562	+	0.774219i	−0.975120	−	0.221678i	$-0.928847\pi$
$229$	−16.1258	+	11.7161i	−1.06562	+	0.774219i	−0.0905005	+	0.995896i	$0.528847\pi$
$230$		0			0
$231$	−3.95683	−	2.87481i	−0.260341	−	0.189149i
$232$		0			0
$233$	−2.28889	+	7.04448i	−0.149950	+	0.461499i	−0.997614	−	0.0690340i	$-0.978008\pi$
$233$	−2.28889	+	7.04448i	−0.149950	+	0.461499i	0.847664	+	0.530533i	$0.178008\pi$
$234$		0			0
$235$	−4.41815	+	3.20997i	−0.288208	+	0.209395i
$236$		0			0
$237$	21.5128			1.39741
$238$		0			0
$239$	2.71467	+	8.35490i	0.175597	+	0.540433i	0.999660	−	0.0260651i	$-0.00829772\pi$
$239$	2.71467	+	8.35490i	0.175597	+	0.540433i	−0.824063	+	0.566498i	$0.808298\pi$
$240$		0			0
$241$	5.96384	+	4.33298i	0.384165	+	0.279112i	0.763060	−	0.646328i	$-0.223696\pi$
$241$	5.96384	+	4.33298i	0.384165	+	0.279112i	−0.378895	+	0.925439i	$0.623696\pi$
$242$		0			0
$243$	22.2683			1.42852
$244$		0			0
$245$	−6.32125			−0.403850
$246$		0			0
$247$	−9.73184			−0.619222
$248$		0			0
$249$	10.2460			0.649312
$250$		0			0
$251$	−6.62516	−	4.81346i	−0.418177	−	0.303823i	0.358727	−	0.933442i	$-0.383211\pi$
$251$	−6.62516	−	4.81346i	−0.418177	−	0.303823i	−0.776904	+	0.629619i	$0.783211\pi$
$252$		0			0
$253$	−5.89080	−	18.1300i	−0.370351	−	1.13982i
$254$		0			0
$255$	−16.8388			−1.05448
$256$		0			0
$257$	24.0895	−	17.5021i	1.50266	−	1.09175i	0.533357	−	0.845890i	$-0.320930\pi$
$257$	24.0895	−	17.5021i	1.50266	−	1.09175i	0.969306	−	0.245858i	$-0.0790698\pi$
$258$		0			0
$259$	0.230014	−	0.707910i	0.0142924	−	0.0439874i
$260$		0			0
$261$	−28.7452	−	20.8846i	−1.77928	−	1.29272i
$262$		0			0
$263$	1.68689	−	1.22560i	0.104018	−	0.0755735i	−0.534560	−	0.845130i	$-0.679523\pi$
$263$	1.68689	−	1.22560i	0.104018	−	0.0755735i	0.638578	+	0.769557i	$0.279523\pi$
$264$		0			0
$265$	−1.37497	−	4.23174i	−0.0844640	−	0.259953i
$266$		0			0
$267$	8.84480	+	27.2215i	0.541293	+	1.66593i
$268$		0			0
$269$	7.30450	−	22.4809i	0.445363	−	1.37069i	−0.436721	−	0.899597i	$-0.643860\pi$
$269$	7.30450	−	22.4809i	0.445363	−	1.37069i	0.882085	−	0.471091i	$-0.156140\pi$
$270$		0			0
$271$	0.902400	+	2.77730i	0.0548169	+	0.168709i	0.974717	−	0.223445i	$-0.0717302\pi$
$271$	0.902400	+	2.77730i	0.0548169	+	0.168709i	−0.919900	+	0.392154i	$0.871730\pi$
$272$		0			0
$273$	6.68575			0.404640
$274$		0			0
$275$	1.87777	+	1.36428i	0.113234	+	0.0822691i
$276$		0			0
$277$	19.0286	−	13.8251i	1.14332	−	0.830667i	0.155738	−	0.987798i	$-0.450224\pi$
$277$	19.0286	−	13.8251i	1.14332	−	0.830667i	0.987578	+	0.157131i	$0.0502245\pi$
$278$		0			0
$279$	26.6644	−	19.3728i	1.59636	−	1.15982i
$280$		0			0
$281$	0.224932	−	0.692269i	0.0134183	−	0.0412973i	−0.944123	−	0.329593i	$-0.893089\pi$
$281$	0.224932	−	0.692269i	0.0134183	−	0.0412973i	0.957541	+	0.288296i	$0.0930885\pi$
$282$		0			0
$283$	14.2332	+	10.3410i	0.846076	+	0.614710i	0.924061	−	0.382244i	$-0.124849\pi$
$283$	14.2332	+	10.3410i	0.846076	+	0.614710i	−0.0779855	+	0.996954i	$0.524849\pi$
$284$		0			0
$285$	−2.42429	+	7.46120i	−0.143603	+	0.441964i
$286$		0			0
$287$	4.30645	+	3.04683i	0.254202	+	0.179849i
$288$		0			0
$289$	8.14038	−	25.0535i	0.478846	−	1.47374i
$290$		0			0
$291$	−31.0346	−	22.5480i	−1.81928	−	1.32179i
$292$		0			0
$293$	1.13807	−	3.50261i	0.0664867	−	0.204625i	−0.912294	−	0.409536i	$-0.865691\pi$
$293$	1.13807	−	3.50261i	0.0664867	−	0.204625i	0.978781	+	0.204911i	$0.0656906\pi$
$294$		0			0
$295$	5.16331	−	3.75136i	0.300619	−	0.218413i
$296$		0			0
$297$	−2.60257	+	1.89088i	−0.151017	+	0.109720i
$298$		0			0
$299$	21.0819	+	15.3169i	1.21920	+	0.885797i
$300$		0			0
$301$	3.74444			0.215826
$302$		0			0
$303$	−2.25200	−	6.93093i	−0.129374	−	0.398171i
$304$		0			0
$305$	−3.58776	+	11.0420i	−0.205435	+	0.632263i
$306$		0			0
$307$	4.81560	+	14.8209i	0.274841	+	0.845873i	0.989262	+	0.146156i	$0.0466902\pi$
$307$	4.81560	+	14.8209i	0.274841	+	0.845873i	−0.714421	+	0.699716i	$0.753310\pi$
$308$		0			0
$309$	−7.52347	−	23.1549i	−0.427995	−	1.31723i
$310$		0			0
$311$	−27.0475	+	19.6512i	−1.53372	+	1.11432i	−0.579602	+	0.814899i	$0.696792\pi$
$311$	−27.0475	+	19.6512i	−1.53372	+	1.11432i	−0.954122	+	0.299417i	$0.903208\pi$
$312$		0			0
$313$	−16.3605	−	11.8866i	−0.924753	−	0.671872i	0.0199497	−	0.999801i	$-0.493649\pi$
$313$	−16.3605	−	11.8866i	−0.924753	−	0.671872i	−0.944702	+	0.327929i	$0.893649\pi$
$314$		0			0
$315$	0.901720	−	2.77521i	0.0508062	−	0.156365i
$316$		0			0
$317$	9.71307	−	7.05696i	0.545540	−	0.396358i	−0.280598	−	0.959825i	$-0.590533\pi$
$317$	9.71307	−	7.05696i	0.545540	−	0.396358i	0.826139	+	0.563467i	$0.190533\pi$
$318$		0			0
$319$	−23.2840			−1.30365
$320$		0			0
$321$	9.32457	+	28.6981i	0.520447	+	1.60177i
$322$		0			0
$323$	−16.3368	−	11.8694i	−0.909004	−	0.660430i
$324$		0			0
$325$	−3.17281			−0.175996
$326$		0			0
$327$	−28.6983			−1.58702
$328$		0			0
$329$	4.49922			0.248050
$330$		0			0
$331$	−8.74483			−0.480659			−0.240330	−	0.970691i	$-0.577256\pi$
$331$	−8.74483			−0.480659			−0.240330	+	0.970691i	$0.577256\pi$
$332$		0			0
$333$	−2.58887	−	1.88092i	−0.141869	−	0.103074i
$334$		0			0
$335$	3.41910	+	10.5229i	0.186805	+	0.574928i
$336$		0			0
$337$	−13.1398			−0.715768			−0.357884	−	0.933766i	$-0.616502\pi$
$337$	−13.1398			−0.715768			−0.357884	+	0.933766i	$0.616502\pi$
$338$		0			0
$339$	−29.4415	+	21.3905i	−1.59904	+	1.16177i
$340$		0			0
$341$	6.67431	−	20.5414i	0.361434	−	1.11238i
$342$		0			0
$343$	8.87886	+	6.45087i	0.479413	+	0.348314i
$344$		0			0
$345$	16.9948	−	12.3475i	0.914971	−	0.664765i
$346$		0			0
$347$	−6.75719	−	20.7965i	−0.362745	−	1.11641i	−0.951381	−	0.308016i	$-0.900335\pi$
$347$	−6.75719	−	20.7965i	−0.362745	−	1.11641i	0.588636	−	0.808398i	$-0.299665\pi$
$348$		0			0
$349$	10.0196	+	30.8372i	0.536338	+	1.65068i	0.740740	+	0.671792i	$0.234475\pi$
$349$	10.0196	+	30.8372i	0.536338	+	1.65068i	−0.204401	+	0.978887i	$0.565525\pi$
$350$		0			0
$351$	1.35890	−	4.18226i	0.0725327	−	0.223233i
$352$		0			0
$353$	2.41774	+	7.44104i	0.128683	+	0.396047i	0.994554	−	0.104221i	$-0.0332349\pi$
$353$	2.41774	+	7.44104i	0.128683	+	0.396047i	−0.865871	+	0.500268i	$0.833235\pi$
$354$		0			0
$355$	−8.65046			−0.459119
$356$		0			0
$357$	11.2233	+	8.15424i	0.594002	+	0.431568i
$358$		0			0
$359$	14.1852	−	10.3062i	0.748668	−	0.543939i	−0.146746	−	0.989174i	$-0.546880\pi$
$359$	14.1852	−	10.3062i	0.748668	−	0.543939i	0.895414	+	0.445235i	$0.146880\pi$
$360$		0			0
$361$	7.76001	−	5.63798i	0.408422	−	0.296736i
$362$		0			0
$363$	4.43617	−	13.6531i	0.232839	−	0.716604i
$364$		0			0
$365$	3.30729	+	2.40289i	0.173111	+	0.125773i
$366$		0			0
$367$	6.80468	−	20.9426i	0.355201	−	1.09320i	−0.600691	−	0.799481i	$-0.705108\pi$
$367$	6.80468	−	20.9426i	0.355201	−	1.09320i	0.955893	−	0.293716i	$-0.0948921\pi$
$368$		0			0
$369$	18.1788	−	13.5601i	0.946348	−	0.705911i
$370$		0			0
$371$	−1.13279	+	3.48637i	−0.0588115	+	0.181003i
$372$		0			0
$373$	−10.3286	−	7.50415i	−0.534793	−	0.388550i	0.287354	−	0.957824i	$-0.407224\pi$
$373$	−10.3286	−	7.50415i	−0.534793	−	0.388550i	−0.822148	+	0.569274i	$0.807224\pi$
$374$		0			0
$375$	−0.790376	+	2.43253i	−0.0408149	+	0.125615i
$376$		0			0
$377$	25.7498	−	18.7083i	1.32618	−	0.963528i
$378$		0			0
$379$	9.80664	−	7.12494i	0.503733	−	0.365983i	−0.306708	−	0.951804i	$-0.599228\pi$
$379$	9.80664	−	7.12494i	0.503733	−	0.365983i	0.810441	+	0.585820i	$0.199228\pi$
$380$		0			0
$381$	4.68793	+	3.40598i	0.240170	+	0.174494i
$382$		0			0
$383$	9.94539			0.508186			0.254093	−	0.967180i	$-0.418223\pi$
$383$	9.94539			0.508186			0.254093	+	0.967180i	$0.418223\pi$
$384$		0			0
$385$	−0.590910	−	1.81863i	−0.0301155	−	0.0926861i
$386$		0			0
$387$	4.97450	−	15.3099i	0.252868	−	0.778248i
$388$		0			0
$389$	3.22471	+	9.92464i	0.163499	+	0.503199i	0.998923	−	0.0464080i	$-0.0147774\pi$
$389$	3.22471	+	9.92464i	0.163499	+	0.503199i	−0.835423	+	0.549607i	$0.814777\pi$
$390$		0			0
$391$	16.7089	+	51.4248i	0.845006	+	2.60066i
$392$		0			0
$393$	−41.1296	+	29.8824i	−2.07471	+	1.50737i
$394$		0			0
$395$	6.80462	+	4.94385i	0.342378	+	0.248752i
$396$		0			0
$397$	−4.62293	+	14.2279i	−0.232018	+	0.714078i	0.765485	+	0.643454i	$0.222499\pi$
$397$	−4.62293	+	14.2279i	−0.232018	+	0.714078i	−0.997503	+	0.0706243i	$0.977501\pi$
$398$		0			0
$399$	5.22895	−	3.79906i	0.261775	−	0.190191i
$400$		0			0
$401$	−35.4667			−1.77112			−0.885562	−	0.464521i	$-0.846226\pi$
$401$	−35.4667			−1.77112			−0.885562	+	0.464521i	$0.846226\pi$
$402$		0			0
$403$	9.12360	+	28.0795i	0.454479	+	1.39874i
$404$		0			0
$405$	5.72840	+	4.16193i	0.284646	+	0.206808i
$406$		0			0
$407$	−2.09701			−0.103945
$408$		0			0
$409$	−15.5049			−0.766666			−0.383333	−	0.923610i	$-0.625224\pi$
$409$	−15.5049			−0.766666			−0.383333	+	0.923610i	$0.625224\pi$
$410$		0			0
$411$	27.1423			1.33883
$412$		0			0
$413$	−5.25805			−0.258732
$414$		0			0
$415$	3.24085	+	2.35462i	0.159087	+	0.115584i
$416$		0			0
$417$	−8.94227	−	27.5215i	−0.437905	−	1.34773i
$418$		0			0
$419$	−21.6946			−1.05985			−0.529926	−	0.848044i	$-0.677780\pi$
$419$	−21.6946			−1.05985			−0.529926	+	0.848044i	$0.677780\pi$
$420$		0			0
$421$	11.9917	−	8.71246i	0.584439	−	0.424619i	−0.255883	−	0.966708i	$-0.582366\pi$
$421$	11.9917	−	8.71246i	0.584439	−	0.424619i	0.840322	+	0.542088i	$0.182366\pi$
$422$		0			0
$423$	5.97723	−	18.3960i	0.290623	−	0.894445i
$424$		0			0
$425$	−5.32618	−	3.86970i	−0.258358	−	0.187708i
$426$		0			0
$427$	7.73844	−	5.62230i	0.374489	−	0.272082i
$428$		0			0
$429$	−5.82052	−	17.9137i	−0.281017	−	0.864883i
$430$		0			0
$431$	−8.23386	−	25.3412i	−0.396611	−	1.22064i	−0.927700	−	0.373327i	$-0.878217\pi$
$431$	−8.23386	−	25.3412i	−0.396611	−	1.22064i	0.531088	−	0.847316i	$-0.321783\pi$
$432$		0			0
$433$	2.33451	−	7.18487i	0.112189	−	0.345283i	−0.879161	−	0.476525i	$-0.841896\pi$
$433$	2.33451	−	7.18487i	0.112189	−	0.345283i	0.991350	+	0.131242i	$0.0418963\pi$
$434$		0			0
$435$	−7.92878	−	24.4023i	−0.380156	−	1.17000i
$436$		0			0
$437$	25.1918			1.20509
$438$		0			0
$439$	−18.1840	−	13.2115i	−0.867876	−	0.630549i	0.0621405	−	0.998067i	$-0.480207\pi$
$439$	−18.1840	−	13.2115i	−0.867876	−	0.630549i	−0.930016	+	0.367519i	$0.880207\pi$
$440$		0			0
$441$	18.1132	−	13.1600i	0.862534	−	0.626668i
$442$		0			0
$443$	0.0789845	−	0.0573856i	0.00375267	−	0.00272647i	−0.585907	−	0.810378i	$-0.699262\pi$
$443$	0.0789845	−	0.0573856i	0.00375267	−	0.00272647i	0.589660	+	0.807652i	$0.299262\pi$
$444$		0			0
$445$	−3.45809	+	10.6429i	−0.163929	+	0.504522i
$446$		0			0
$447$	−16.2231	−	11.7868i	−0.767327	−	0.557496i
$448$		0			0
$449$	−12.6572	+	38.9549i	−0.597330	+	1.83839i	−0.0545630	+	0.998510i	$0.517377\pi$
$449$	−12.6572	+	38.9549i	−0.597330	+	1.83839i	−0.542767	+	0.839883i	$0.682623\pi$
$450$		0			0
$451$	4.41452	−	14.1912i	0.207871	−	0.668237i
$452$		0			0
$453$	−4.95670	+	15.2552i	−0.232886	+	0.716750i
$454$		0			0
$455$	2.11473	+	1.53644i	0.0991403	+	0.0720296i
$456$		0			0
$457$	−6.18932	+	19.0488i	−0.289524	+	0.891064i	0.695482	+	0.718544i	$0.255191\pi$
$457$	−6.18932	+	19.0488i	−0.289524	+	0.891064i	−0.985006	+	0.172520i	$0.944809\pi$
$458$		0			0
$459$	7.38206	−	5.36338i	0.344565	−	0.250341i
$460$		0			0
$461$	−15.2814	+	11.1026i	−0.711725	+	0.517099i	−0.883730	−	0.467998i	$-0.844976\pi$
$461$	−15.2814	+	11.1026i	−0.711725	+	0.517099i	0.172005	+	0.985096i	$0.444976\pi$
$462$		0			0
$463$	−4.90446	−	3.56330i	−0.227930	−	0.165601i	0.467959	−	0.883750i	$-0.344989\pi$
$463$	−4.90446	−	3.56330i	−0.227930	−	0.165601i	−0.695889	+	0.718150i	$0.744989\pi$
$464$		0			0
$465$	23.8008			1.10374
$466$		0			0
$467$	−10.3802	−	31.9471i	−0.480340	−	1.47833i	−0.838618	−	0.544720i	$-0.816636\pi$
$467$	−10.3802	−	31.9471i	−0.480340	−	1.47833i	0.358278	−	0.933615i	$-0.383364\pi$
$468$		0			0
$469$	2.81687	−	8.66942i	0.130071	−	0.400317i
$470$		0			0
$471$	7.07348	+	21.7699i	0.325929	+	1.00311i
$472$		0			0
$473$	−3.25986	−	10.0328i	−0.149888	−	0.461309i
$474$		0			0
$475$	−2.48147	+	1.80289i	−0.113858	+	0.0827224i
$476$		0			0
$477$	12.7498	+	9.26330i	0.583775	+	0.424137i
$478$		0			0
$479$	−8.10867	+	24.9559i	−0.370494	+	1.14026i	0.575974	+	0.817468i	$0.304623\pi$
$479$	−8.10867	+	24.9559i	−0.370494	+	1.14026i	−0.946468	+	0.322796i	$0.895377\pi$
$480$		0			0
$481$	2.31910	−	1.68492i	0.105742	−	0.0768258i
$482$		0			0
$483$	−17.3067			−0.787481
$484$		0			0
$485$	−4.63468	−	14.2641i	−0.210450	−	0.647699i
$486$		0			0
$487$	2.17097	+	1.57730i	0.0983759	+	0.0714743i	0.635886	−	0.771783i	$-0.280635\pi$
$487$	2.17097	+	1.57730i	0.0983759	+	0.0714743i	−0.537510	+	0.843257i	$0.680635\pi$
$488$		0			0
$489$	18.5390			0.838365
$490$		0			0
$491$	−3.00724			−0.135715			−0.0678575	−	0.997695i	$-0.521616\pi$
$491$	−3.00724			−0.135715			−0.0678575	+	0.997695i	$0.521616\pi$
$492$		0			0
$493$	66.0436			2.97446
$494$		0			0
$495$	−8.22089			−0.369502
$496$		0			0
$497$	5.76569	+	4.18902i	0.258627	+	0.187903i
$498$		0			0
$499$	4.57722	+	14.0872i	0.204905	+	0.630631i	0.999717	+	0.0237766i	$0.00756903\pi$
$499$	4.57722	+	14.0872i	0.204905	+	0.630631i	−0.794813	+	0.606855i	$0.792431\pi$
$500$		0			0
$501$	−42.6113			−1.90373
$502$		0			0
$503$	33.9706	−	24.6811i	1.51467	−	1.10048i	0.550625	−	0.834753i	$-0.314389\pi$
$503$	33.9706	−	24.6811i	1.51467	−	1.10048i	0.964050	−	0.265723i	$-0.0856105\pi$
$504$		0			0
$505$	0.880473	−	2.70982i	0.0391805	−	0.120585i
$506$		0			0
$507$	−6.06966	−	4.40987i	−0.269563	−	0.195849i
$508$		0			0
$509$	−21.4164	+	15.5599i	−0.949264	+	0.689681i	−0.950633	−	0.310318i	$-0.899564\pi$
$509$	−21.4164	+	15.5599i	−0.949264	+	0.689681i	0.00136865	+	0.999999i	$0.499564\pi$
$510$		0			0
$511$	−1.04076	−	3.20314i	−0.0460406	−	0.141698i
$512$		0			0
$513$	−1.31370	−	4.04314i	−0.0580011	−	0.178509i
$514$		0			0
$515$	2.94149	−	9.05296i	0.129617	−	0.398921i
$516$		0			0
$517$	−3.91696	−	12.0552i	−0.172268	−	0.530185i
$518$		0			0
$519$	37.1417			1.63034
$520$		0			0
$521$	4.80316	+	3.48970i	0.210430	+	0.152887i	0.688008	−	0.725703i	$-0.258485\pi$
$521$	4.80316	+	3.48970i	0.210430	+	0.152887i	−0.477578	+	0.878589i	$0.658485\pi$
$522$		0			0
$523$	6.20993	−	4.51178i	0.271541	−	0.197286i	−0.443678	−	0.896186i	$-0.646327\pi$
$523$	6.20993	−	4.51178i	0.271541	−	0.197286i	0.715220	+	0.698900i	$0.246327\pi$
$524$		0			0
$525$	1.70476	−	1.23858i	0.0744019	−	0.0540562i
$526$		0			0
$527$	−18.9313	+	58.2646i	−0.824661	+	2.53805i
$528$		0			0
$529$	−35.9650	−	26.1301i	−1.56369	−	1.13609i
$530$		0			0
$531$	−6.98534	+	21.4987i	−0.303138	+	0.932962i
$532$		0			0
$533$	6.52039	+	19.2411i	0.282430	+	0.833424i
$534$		0			0
$535$	−3.64567	+	11.2202i	−0.157616	+	0.485092i
$536$		0			0
$537$	26.5851	+	19.3152i	1.14723	+	0.833511i
$538$		0			0
$539$	4.53388	−	13.9538i	0.195288	−	0.601034i
$540$		0			0
$541$	−5.66050	+	4.11260i	−0.243364	+	0.176814i	−0.702781	−	0.711407i	$-0.748058\pi$
$541$	−5.66050	+	4.11260i	−0.243364	+	0.176814i	0.459417	+	0.888221i	$0.348058\pi$
$542$		0			0
$543$	15.4707	−	11.2401i	0.663913	−	0.482361i
$544$		0			0
$545$	−9.07743	−	6.59514i	−0.388834	−	0.282505i
$546$		0			0
$547$	−24.3110			−1.03946			−0.519732	−	0.854329i	$-0.673968\pi$
$547$	−24.3110			−1.03946			−0.519732	+	0.854329i	$0.673968\pi$
$548$		0			0
$549$	−12.7074	−	39.1095i	−0.542341	−	1.66915i
$550$		0			0
$551$	9.50837	−	29.2637i	0.405070	−	1.24668i
$552$		0			0
$553$	−2.14133	−	6.59033i	−0.0910585	−	0.280249i
$554$		0			0
$555$	−0.714087	−	2.19773i	−0.0303113	−	0.0932886i
$556$		0			0
$557$	26.0322	−	18.9135i	1.10302	−	0.801392i	0.121471	−	0.992595i	$-0.461239\pi$
$557$	26.0322	−	18.9135i	1.10302	−	0.801392i	0.981551	+	0.191203i	$0.0612389\pi$
$558$		0			0
$559$	11.6663	+	8.47607i	0.493432	+	0.358500i
$560$		0			0
$561$	12.0775	−	37.1707i	0.509912	−	1.56935i
$562$		0			0
$563$	7.54214	−	5.47968i	0.317863	−	0.230941i	−0.417400	−	0.908723i	$-0.637059\pi$
$563$	7.54214	−	5.47968i	0.317863	−	0.230941i	0.735263	+	0.677782i	$0.237059\pi$
$564$		0			0
$565$	−14.2282			−0.598586
$566$		0			0
$567$	−1.80265	−	5.54800i	−0.0757044	−	0.232994i
$568$		0			0
$569$	−24.5198	−	17.8147i	−1.02792	−	0.746830i	−0.0600310	−	0.998197i	$-0.519120\pi$
$569$	−24.5198	−	17.8147i	−1.02792	−	0.746830i	−0.967892	+	0.251367i	$0.919120\pi$
$570$		0			0
$571$	38.8333			1.62512			0.812562	−	0.582875i	$-0.198072\pi$
$571$	38.8333			1.62512			0.812562	+	0.582875i	$0.198072\pi$
$572$		0			0
$573$	−36.2759			−1.51545
$574$		0			0
$575$	8.21311			0.342510
$576$		0			0
$577$	−29.5428			−1.22988			−0.614942	−	0.788572i	$-0.710821\pi$
$577$	−29.5428			−1.22988			−0.614942	+	0.788572i	$0.710821\pi$
$578$		0			0
$579$	6.43958	+	4.67863i	0.267620	+	0.194437i
$580$		0			0
$581$	−1.01985	−	3.13879i	−0.0423107	−	0.130219i
$582$		0			0
$583$	10.3275			0.427723
$584$		0			0
$585$	9.09152	−	6.60537i	0.375888	−	0.273099i
$586$		0			0
$587$	1.92000	−	5.90914i	0.0792467	−	0.243896i	−0.903582	−	0.428414i	$-0.859072\pi$
$587$	1.92000	−	5.90914i	0.0792467	−	0.243896i	0.982829	+	0.184518i	$0.0590724\pi$
$588$		0			0
$589$	23.0913	+	16.7768i	0.951461	+	0.691277i
$590$		0			0
$591$	34.2712	−	24.8995i	1.40973	−	1.02423i
$592$		0			0
$593$	−5.02251	−	15.4577i	−0.206250	−	0.634772i	−0.999660	−	0.0260841i	$-0.991696\pi$
$593$	−5.02251	−	15.4577i	−0.206250	−	0.634772i	0.793410	−	0.608688i	$-0.208304\pi$
$594$		0			0
$595$	1.67608	+	5.15845i	0.0687127	+	0.211476i
$596$		0			0
$597$	−3.54570	+	10.9125i	−0.145116	+	0.446620i
$598$		0			0
$599$	−6.90014	−	21.2365i	−0.281932	−	0.867698i	−0.987301	−	0.158858i	$-0.949219\pi$
$599$	−6.90014	−	21.2365i	−0.281932	−	0.867698i	0.705369	−	0.708840i	$-0.250781\pi$
$600$		0			0
$601$	6.73234			0.274618			0.137309	−	0.990528i	$-0.456155\pi$
$601$	6.73234			0.274618			0.137309	+	0.990528i	$0.456155\pi$
$602$		0			0
$603$	−31.7046	−	23.0347i	−1.29111	−	0.938046i
$604$		0			0
$605$	4.54080	−	3.29908i	0.184610	−	0.134127i
$606$		0			0
$607$	−36.4262	+	26.4652i	−1.47849	+	1.07419i	−0.500454	+	0.865763i	$0.666834\pi$
$607$	−36.4262	+	26.4652i	−1.47849	+	1.07419i	−0.978038	+	0.208425i	$0.933166\pi$
$608$		0			0
$609$	−6.53222	+	20.1041i	−0.264699	+	0.814660i
$610$		0			0
$611$	14.0179	+	10.1846i	0.567105	+	0.412026i
$612$		0			0
$613$	4.20835	−	12.9520i	0.169974	−	0.523125i	−0.829395	−	0.558663i	$-0.811315\pi$
$613$	4.20835	−	12.9520i	0.169974	−	0.523125i	0.999368	+	0.0355381i	$0.0113145\pi$
$614$		0			0
$615$	16.3761	−	0.205918i	0.660346	−	0.00830341i
$616$		0			0
$617$	−7.31769	+	22.5215i	−0.294599	+	0.906683i	0.688757	+	0.724993i	$0.258157\pi$
$617$	−7.31769	+	22.5215i	−0.294599	+	0.906683i	−0.983356	+	0.181690i	$0.941843\pi$
$618$		0			0
$619$	−30.5174	−	22.1722i	−1.22660	−	0.891175i	−0.229967	−	0.973199i	$-0.573862\pi$
$619$	−30.5174	−	22.1722i	−1.22660	−	0.891175i	−0.996630	+	0.0820236i	$0.973862\pi$
$620$		0			0
$621$	−3.51764	+	10.8262i	−0.141158	+	0.434440i
$622$		0			0
$623$	7.45875	−	5.41910i	0.298829	−	0.217112i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−14.7314	−	10.7030i	−0.588316	−	0.427437i
$628$		0			0
$629$	5.94807			0.237165
$630$		0			0
$631$	−3.96306	−	12.1970i	−0.157767	−	0.485556i	0.840664	−	0.541557i	$-0.182165\pi$
$631$	−3.96306	−	12.1970i	−0.157767	−	0.485556i	−0.998431	+	0.0560009i	$0.982165\pi$
$632$		0			0
$633$	8.90855	−	27.4177i	0.354083	−	1.08976i
$634$		0			0
$635$	0.700091	+	2.15466i	0.0277822	+	0.0855050i
$636$		0			0
$637$	6.19768	+	19.0745i	0.245561	+	0.755759i
$638$		0			0
$639$	24.7875	−	18.0091i	0.980577	−	0.712431i
$640$		0			0
$641$	25.9050	+	18.8211i	1.02319	+	0.743389i	0.966934	−	0.255028i	$-0.0820847\pi$
$641$	25.9050	+	18.8211i	1.02319	+	0.743389i	0.0562530	+	0.998417i	$0.482085\pi$
$642$		0			0
$643$	−4.82062	+	14.8363i	−0.190107	+	0.585088i	−0.999999	−	0.00149069i	$-0.999525\pi$
$643$	−4.82062	+	14.8363i	−0.190107	+	0.585088i	0.809892	+	0.586579i	$0.199525\pi$
$644$		0			0
$645$	9.40462	−	6.83286i	0.370307	−	0.269044i
$646$		0			0
$647$	33.8600			1.33118			0.665588	−	0.746320i	$-0.268181\pi$
$647$	33.8600			1.33118			0.665588	+	0.746320i	$0.268181\pi$
$648$		0			0
$649$	4.57759	+	14.0884i	0.179686	+	0.553017i
$650$		0			0
$651$	−15.8637	−	11.5256i	−0.621746	−	0.451725i
$652$		0			0
$653$	8.95555			0.350458			0.175229	−	0.984528i	$-0.443933\pi$
$653$	8.95555			0.350458			0.175229	+	0.984528i	$0.443933\pi$
$654$		0			0
$655$	−19.8768			−0.776649
$656$		0			0
$657$	−14.4794			−0.564894
$658$		0			0
$659$	−5.59706			−0.218030			−0.109015	−	0.994040i	$-0.534770\pi$
$659$	−5.59706			−0.218030			−0.109015	+	0.994040i	$0.534770\pi$
$660$		0			0
$661$	−32.9297	−	23.9248i	−1.28082	−	0.930567i	−0.281238	−	0.959638i	$-0.590745\pi$
$661$	−32.9297	−	23.9248i	−1.28082	−	0.930567i	−0.999577	+	0.0290709i	$0.990745\pi$
$662$		0			0
$663$	16.5096	+	50.8113i	0.641179	+	1.97335i
$664$		0			0
$665$	2.52700			0.0979929
$666$		0			0
$667$	−66.6557	+	48.4282i	−2.58092	+	1.87515i
$668$		0			0
$669$	−8.41337	+	25.8937i	−0.325279	+	1.00111i
$670$		0			0
$671$	−21.8013	−	15.8396i	−0.841631	−	0.611481i
$672$		0			0
$673$	−0.117090	+	0.0850707i	−0.00451348	+	0.00327923i	−0.590040	−	0.807374i	$-0.700888\pi$
$673$	−0.117090	+	0.0850707i	−0.00451348	+	0.00327923i	0.585526	+	0.810653i	$0.300888\pi$
$674$		0			0
$675$	−0.428296	−	1.31816i	−0.0164851	−	0.0507360i
$676$		0			0
$677$	0.997430	+	3.06977i	0.0383343	+	0.117981i	0.968392	−	0.249432i	$-0.0802437\pi$
$677$	0.997430	+	3.06977i	0.0383343	+	0.117981i	−0.930058	+	0.367412i	$0.880244\pi$
$678$		0			0
$679$	−3.81834	+	11.7516i	−0.146534	+	0.450986i
$680$		0			0
$681$	11.0771	+	34.0919i	0.424477	+	1.30641i
$682$		0			0
$683$	−21.7773			−0.833285			−0.416643	−	0.909070i	$-0.636793\pi$
$683$	−21.7773			−0.833285			−0.416643	+	0.909070i	$0.636793\pi$
$684$		0			0
$685$	8.58524	+	6.23754i	0.328025	+	0.238324i
$686$		0			0
$687$	41.2451	−	29.9663i	1.57360	−	1.14329i
$688$		0			0
$689$	−11.4212	+	8.29802i	−0.435115	+	0.316129i
$690$		0			0
$691$	−5.76750	+	17.7505i	−0.219406	+	0.675263i	0.779405	+	0.626520i	$0.215521\pi$
$691$	−5.76750	+	17.7505i	−0.219406	+	0.675263i	−0.998811	+	0.0487426i	$0.984479\pi$
$692$		0			0
$693$	5.47938	+	3.98100i	0.208144	+	0.151226i
$694$		0			0
$695$	3.49620	−	10.7602i	0.132618	−	0.408157i
$696$		0			0
$697$	−12.5215	+	40.2525i	−0.474287	+	1.52467i
$698$		0			0
$699$	5.85432	−	18.0177i	0.221431	−	0.681494i
$700$		0			0
$701$	13.7776	+	10.0100i	0.520374	+	0.378074i	0.816745	−	0.576999i	$-0.195776\pi$
$701$	13.7776	+	10.0100i	0.520374	+	0.378074i	−0.296371	+	0.955073i	$0.595776\pi$
$702$		0			0
$703$	0.856349	−	2.63557i	0.0322978	−	0.0994024i
$704$		0			0
$705$	11.3003	−	8.21018i	0.425596	−	0.309213i
$706$		0			0
$707$	−1.89909	+	1.37977i	−0.0714227	+	0.0518916i
$708$		0			0
$709$	26.9159	+	19.5556i	1.01085	+	0.734425i	0.964387	−	0.264495i	$-0.0852054\pi$
$709$	26.9159	+	19.5556i	1.01085	+	0.734425i	0.0464619	+	0.998920i	$0.485205\pi$
$710$		0			0
$711$	−29.7907			−1.11724
$712$		0			0
$713$	−23.6173	−	72.6865i	−0.884474	−	2.72213i
$714$		0			0
$715$	2.27568	−	7.00381i	0.0851054	−	0.261928i
$716$		0			0
$717$	−6.94334	−	21.3694i	−0.259304	−	0.798055i
$718$		0			0
$719$	3.06324	+	9.42769i	0.114240	+	0.351594i	0.991788	−	0.127895i	$-0.0408221\pi$
$719$	3.06324	+	9.42769i	0.114240	+	0.351594i	−0.877548	+	0.479489i	$0.840822\pi$
$720$		0			0
$721$	−6.34449	+	4.60954i	−0.236281	+	0.171668i
$722$		0			0
$723$	−15.2538	−	11.0825i	−0.567294	−	0.412163i
$724$		0			0
$725$	3.09995	−	9.54067i	0.115129	−	0.354332i
$726$		0			0
$727$	−29.5266	+	21.4524i	−1.09508	+	0.795624i	−0.980250	−	0.197761i	$-0.936633\pi$
$727$	−29.5266	+	21.4524i	−1.09508	+	0.795624i	−0.114832	+	0.993385i	$0.536633\pi$
$728$		0			0
$729$	−35.7139			−1.32274
$730$		0			0
$731$	9.24641	+	28.4575i	0.341991	+	1.05254i
$732$		0			0
$733$	39.6237	+	28.7883i	1.46354	+	1.06332i	0.982424	+	0.186661i	$0.0597667\pi$
$733$	39.6237	+	28.7883i	1.46354	+	1.06332i	0.481111	+	0.876660i	$0.340233\pi$
$734$		0			0
$735$	16.1679			0.596363
$736$		0			0
$737$	−25.6811			−0.945975
$738$		0			0
$739$	27.9886			1.02958			0.514788	−	0.857318i	$-0.327871\pi$
$739$	27.9886			1.02958			0.514788	+	0.857318i	$0.327871\pi$
$740$		0			0
$741$	24.8912			0.914402
$742$		0			0
$743$	35.9814	+	26.1421i	1.32003	+	0.959059i	0.999932	+	0.0116749i	$0.00371632\pi$
$743$	35.9814	+	26.1421i	1.32003	+	0.959059i	0.320099	+	0.947384i	$0.396284\pi$
$744$		0			0
$745$	−2.42274	−	7.45644i	−0.0887625	−	0.273183i
$746$		0			0
$747$	−14.1885			−0.519130
$748$		0			0
$749$	7.86334	−	5.71305i	0.287320	−	0.208750i
$750$		0			0
$751$	7.68289	−	23.6455i	0.280353	−	0.862837i	−0.707401	−	0.706813i	$-0.750132\pi$
$751$	7.68289	−	23.6455i	0.280353	−	0.862837i	0.987753	−	0.156024i	$-0.0498678\pi$
$752$		0			0
$753$	16.9453	+	12.3115i	0.617520	+	0.448654i
$754$		0			0
$755$	−5.07360	+	3.68619i	−0.184647	+	0.134154i
$756$		0			0
$757$	9.63020	+	29.6387i	0.350016	+	1.07724i	0.958843	+	0.283935i	$0.0916401\pi$
$757$	9.63020	+	29.6387i	0.350016	+	1.07724i	−0.608828	+	0.793302i	$0.708360\pi$
$758$		0			0
$759$	15.0670	+	46.3713i	0.546896	+	1.68317i
$760$		0			0
$761$	−0.389601	+	1.19907i	−0.0141230	+	0.0434662i	−0.957870	−	0.287203i	$-0.907274\pi$
$761$	−0.389601	+	1.19907i	−0.0141230	+	0.0434662i	0.943747	+	0.330669i	$0.107274\pi$
$762$		0			0
$763$	2.85655	+	8.79156i	0.103414	+	0.318276i
$764$		0			0
$765$	23.3181			0.843068
$766$		0			0
$767$	−16.3822	−	11.9023i	−0.591526	−	0.429769i
$768$		0			0
$769$	0.0243696	−	0.0177056i	0.000878791	−	0.000638479i	−0.587346	−	0.809336i	$-0.699827\pi$
$769$	0.0243696	−	0.0177056i	0.000878791	−	0.000638479i	0.588225	+	0.808698i	$0.299827\pi$
$770$		0			0
$771$	−61.6140	+	44.7652i	−2.21898	+	1.61218i
$772$		0			0
$773$	−4.24932	+	13.0781i	−0.152837	+	0.470385i	−0.997935	−	0.0642265i	$-0.979542\pi$
$773$	−4.24932	+	13.0781i	−0.152837	+	0.470385i	0.845098	+	0.534611i	$0.179542\pi$
$774$		0			0
$775$	7.52831	+	5.46964i	0.270425	+	0.196475i
$776$		0			0
$777$	−0.588309	+	1.81063i	−0.0211055	+	0.0649560i
$778$		0			0
$779$	16.0330	+	11.3434i	0.574443	+	0.406421i
$780$		0			0
$781$	6.20449	−	19.0955i	0.222014	−	0.683289i
$782$		0			0
$783$	11.2484	+	8.17246i	0.401986	+	0.292060i
$784$		0			0
$785$	−2.76555	+	8.51149i	−0.0987067	+	0.303788i
$786$		0			0
$787$	−11.7108	+	8.50840i	−0.417445	+	0.303292i	−0.776609	−	0.629983i	$-0.783062\pi$
$787$	−11.7108	+	8.50840i	−0.417445	+	0.303292i	0.359164	+	0.933275i	$0.383062\pi$
$788$		0			0
$789$	−4.31457	+	3.13472i	−0.153603	+	0.111599i
$790$		0			0
$791$	9.48337	+	6.89007i	0.337190	+	0.244983i
$792$		0			0
$793$	36.8371			1.30812
$794$		0			0
$795$	3.51679	+	10.8236i	0.124728	+	0.383872i
$796$		0			0
$797$	1.02991	−	3.16975i	0.0364814	−	0.112278i	−0.931157	−	0.364617i	$-0.881200\pi$
$797$	1.02991	−	3.16975i	0.0364814	−	0.112278i	0.967639	+	0.252339i	$0.0811998\pi$
$798$		0			0
$799$	11.1102	+	34.1938i	0.393052	+	1.20969i
$800$		0			0
$801$	−12.2482	−	37.6960i	−0.432768	−	1.33192i
$802$		0			0
$803$	−7.67638	+	5.57722i	−0.270894	+	0.196816i
$804$		0			0
$805$	−5.47419	−	3.97723i	−0.192940	−	0.140179i
$806$		0			0
$807$	−18.6828	+	57.4998i	−0.657666	+	2.02409i
$808$		0			0
$809$	−32.7391	+	23.7864i	−1.15105	+	0.836284i	−0.988620	−	0.150436i	$-0.951932\pi$
$809$	−32.7391	+	23.7864i	−1.15105	+	0.836284i	−0.162427	+	0.986721i	$0.551932\pi$
$810$		0			0
$811$	−26.2206			−0.920729			−0.460365	−	0.887730i	$-0.652281\pi$
$811$	−26.2206			−0.920729			−0.460365	+	0.887730i	$0.652281\pi$
$812$		0			0
$813$	−2.30808	−	7.10353i	−0.0809478	−	0.249132i
$814$		0			0
$815$	5.86399	+	4.26044i	0.205407	+	0.149237i
$816$		0			0
$817$	13.9407			0.487722
$818$		0			0
$819$	−9.25834			−0.323513
$820$		0			0
$821$	17.7603			0.619838			0.309919	−	0.950763i	$-0.399698\pi$
$821$	17.7603			0.619838			0.309919	+	0.950763i	$0.399698\pi$
$822$		0			0
$823$	−38.5826			−1.34490			−0.672452	−	0.740141i	$-0.734759\pi$
$823$	−38.5826			−1.34490			−0.672452	+	0.740141i	$0.734759\pi$
$824$		0			0
$825$	−4.80279	−	3.48943i	−0.167212	−	0.121486i
$826$		0			0
$827$	13.6881	+	42.1277i	0.475983	+	1.46493i	0.844627	+	0.535355i	$0.179822\pi$
$827$	13.6881	+	42.1277i	0.475983	+	1.46493i	−0.368644	+	0.929571i	$0.620178\pi$
$828$		0			0
$829$	30.7334			1.06742			0.533708	−	0.845669i	$-0.320798\pi$
$829$	30.7334			1.06742			0.533708	+	0.845669i	$0.320798\pi$
$830$		0			0
$831$	−48.6696	+	35.3605i	−1.68833	+	1.22664i
$832$		0			0
$833$	−12.8601	+	39.5793i	−0.445576	+	1.37134i
$834$		0			0
$835$	−13.4782	−	9.79247i	−0.466431	−	0.338882i
$836$		0			0
$837$	−10.4342	+	7.58089i	−0.360659	+	0.262034i
$838$		0			0
$839$	8.48044	+	26.1001i	0.292777	+	0.901076i	0.983959	+	0.178395i	$0.0570904\pi$
$839$	8.48044	+	26.1001i	0.292777	+	0.901076i	−0.691182	+	0.722681i	$0.742910\pi$
$840$		0			0
$841$	22.1361	+	68.1280i	0.763315	+	2.34924i
$842$		0			0
$843$	−0.575310	+	1.77062i	−0.0198147	+	0.0609835i
$844$		0			0
$845$	−0.906437	−	2.78973i	−0.0311824	−	0.0959695i
$846$		0			0
$847$	−4.62412			−0.158887
$848$		0			0
$849$	−36.4044	−	26.4494i	−1.24940	−	0.907739i
$850$		0			0
$851$	−6.00319	+	4.36158i	−0.205787	+	0.149513i
$852$		0			0
$853$	34.1719	−	24.8274i	1.17003	−	0.850073i	0.179013	−	0.983847i	$-0.442710\pi$
$853$	34.1719	−	24.8274i	1.17003	−	0.850073i	0.991012	+	0.133774i	$0.0427095\pi$
$854$		0			0
$855$	3.35713	−	10.3322i	0.114811	−	0.353353i
$856$		0			0
$857$	−0.550995	−	0.400322i	−0.0188216	−	0.0136747i	0.578335	−	0.815800i	$-0.303703\pi$
$857$	−0.550995	−	0.400322i	−0.0188216	−	0.0136747i	−0.597156	+	0.802125i	$0.703703\pi$
$858$		0			0
$859$	4.12328	−	12.6901i	0.140684	−	0.432982i	−0.855746	−	0.517395i	$-0.826902\pi$
$859$	4.12328	−	12.6901i	0.140684	−	0.432982i	0.996431	+	0.0844135i	$0.0269016\pi$
$860$		0			0
$861$	−11.0147	−	7.79292i	−0.375378	−	0.265582i
$862$		0			0
$863$	9.97581	−	30.7024i	0.339581	−	1.04512i	−0.624841	−	0.780752i	$-0.714836\pi$
$863$	9.97581	−	30.7024i	0.339581	−	1.04512i	0.964421	−	0.264369i	$-0.0851638\pi$
$864$		0			0
$865$	11.7481	+	8.53550i	0.399448	+	0.290216i
$866$		0			0
$867$	−20.8207	+	64.0796i	−0.707109	+	2.17626i
$868$		0			0
$869$	−15.7939	+	11.4749i	−0.535770	+	0.389260i
$870$		0			0
$871$	28.4008	−	20.6344i	0.962325	−	0.699170i
$872$		0			0
$873$	42.9764	+	31.2242i	1.45453	+	1.05678i
$874$		0			0
$875$	0.823862			0.0278516
$876$		0			0
$877$	−15.7500	−	48.4735i	−0.531840	−	1.63684i	−0.750380	−	0.661007i	$-0.770129\pi$
$877$	−15.7500	−	48.4735i	−0.531840	−	1.63684i	0.218540	−	0.975828i	$-0.429871\pi$
$878$		0			0
$879$	−2.91085	+	8.95868i	−0.0981806	+	0.302169i
$880$		0			0
$881$	9.92077	+	30.5330i	0.334239	+	1.02868i	0.967096	+	0.254413i	$0.0818824\pi$
$881$	9.92077	+	30.5330i	0.334239	+	1.02868i	−0.632856	+	0.774269i	$0.718118\pi$
$882$		0			0
$883$	−9.65896	−	29.7272i	−0.325050	−	1.00040i	−0.971418	−	0.237375i	$-0.923713\pi$
$883$	−9.65896	−	29.7272i	−0.325050	−	1.00040i	0.646368	−	0.763026i	$-0.276287\pi$
$884$		0			0
$885$	−13.2062	+	9.59490i	−0.443923	+	0.322529i
$886$		0			0
$887$	−12.3420	−	8.96700i	−0.414404	−	0.301082i	0.360978	−	0.932574i	$-0.382443\pi$
$887$	−12.3420	−	8.96700i	−0.414404	−	0.301082i	−0.775382	+	0.631492i	$0.782443\pi$
$888$		0			0
$889$	0.576778	−	1.77514i	0.0193445	−	0.0595363i
$890$		0			0
$891$	−13.2959	+	9.66003i	−0.445429	+	0.323623i
$892$		0			0
$893$	16.7507			0.560541
$894$		0			0
$895$	3.97018	+	12.2190i	0.132709	+	0.408435i
$896$		0			0
$897$	−53.9213	−	39.1761i	−1.80038	−	1.30805i
$898$		0			0
$899$	−93.3496			−3.11338
$900$		0			0
$901$	−29.2935			−0.975907
$902$		0			0
$903$	−9.57719			−0.318709
$904$		0			0
$905$	7.47656			0.248529
$906$		0			0
$907$	36.6201	+	26.6061i	1.21595	+	0.883440i	0.995758	−	0.0920157i	$-0.0293310\pi$
$907$	36.6201	+	26.6061i	1.21595	+	0.883440i	0.220194	+	0.975456i	$0.429331\pi$
$908$		0			0
$909$	3.11854	+	9.59787i	0.103435	+	0.318341i
$910$		0			0
$911$	3.37170			0.111709			0.0558547	−	0.998439i	$-0.482212\pi$
$911$	3.37170			0.111709			0.0558547	+	0.998439i	$0.482212\pi$
$912$		0			0
$913$	−7.52217	+	5.46518i	−0.248947	+	0.180871i
$914$		0			0
$915$	9.17646	−	28.2422i	0.303364	−	0.933659i
$916$		0			0
$917$	13.2482	+	9.62540i	0.437495	+	0.317859i
$918$		0			0
$919$	3.26696	−	2.37358i	0.107767	−	0.0782973i	−0.532597	−	0.846369i	$-0.678784\pi$
$919$	3.26696	−	2.37358i	0.107767	−	0.0782973i	0.640364	+	0.768072i	$0.278784\pi$
$920$		0			0
$921$	−12.3169	−	37.9075i	−0.405856	−	1.24910i
$922$		0			0
$923$	8.48136	+	26.1029i	0.279167	+	0.859189i
$924$		0			0
$925$	0.279190	−	0.859258i	0.00917971	−	0.0282522i
$926$		0			0
$927$	10.4184	+	32.0646i	0.342186	+	1.05314i
$928$		0			0
$929$	−44.4464			−1.45824			−0.729119	−	0.684387i	$-0.760070\pi$
$929$	−44.4464			−1.45824			−0.729119	+	0.684387i	$0.760070\pi$
$930$		0			0
$931$	15.6860	+	11.3965i	0.514087	+	0.373506i
$932$		0			0
$933$	69.1798	−	50.2621i	2.26484	−	1.64551i
$934$		0			0
$935$	12.3623	−	8.98176i	0.404291	−	0.293735i
$936$		0			0
$937$	−2.42438	+	7.46148i	−0.0792011	+	0.243756i	−0.982815	−	0.184591i	$-0.940904\pi$
$937$	−2.42438	+	7.46148i	−0.0792011	+	0.243756i	0.903614	+	0.428347i	$0.140904\pi$
$938$		0			0
$939$	41.8456	+	30.4026i	1.36558	+	0.992151i
$940$		0			0
$941$	−13.7359	+	42.2746i	−0.447776	+	1.37811i	0.431634	+	0.902049i	$0.357937\pi$
$941$	−13.7359	+	42.2746i	−0.447776	+	1.37811i	−0.879410	+	0.476064i	$0.842063\pi$
$942$		0			0
$943$	−16.8786	−	49.8073i	−0.549644	−	1.62195i
$944$		0			0
$945$	−0.352857	+	1.08598i	−0.0114784	+	0.0353270i
$946$		0			0
$947$	−24.8044	−	18.0215i	−0.806035	−	0.585619i	0.106643	−	0.994297i	$-0.465990\pi$
$947$	−24.8044	−	18.0215i	−0.806035	−	0.585619i	−0.912678	+	0.408678i	$0.865990\pi$
$948$		0			0
$949$	4.00812	−	12.3357i	0.130109	−	0.400435i
$950$		0			0
$951$	−24.8432	+	18.0497i	−0.805597	+	0.585301i
$952$		0			0
$953$	−0.755634	+	0.549001i	−0.0244774	+	0.0177839i	−0.599957	−	0.800032i	$-0.704816\pi$
$953$	−0.755634	+	0.549001i	−0.0244774	+	0.0177839i	0.575479	+	0.817816i	$0.304816\pi$
$954$		0			0
$955$	−11.4742	−	8.33652i	−0.371298	−	0.269764i
$956$		0			0
$957$	59.5536			1.92510
$958$		0			0
$959$	−2.70167	−	8.31487i	−0.0872413	−	0.268501i
$960$		0			0
$961$	17.1790	−	52.8715i	0.554161	−	1.70553i
$962$		0			0
$963$	−12.9126	−	39.7408i	−0.416101	−	1.28063i
$964$		0			0
$965$	0.961680	+	2.95975i	0.0309576	+	0.0952776i
$966$		0			0
$967$	35.4245	−	25.7374i	1.13918	−	0.827660i	0.152172	−	0.988354i	$-0.451373\pi$
$967$	35.4245	−	25.7374i	1.13918	−	0.827660i	0.987004	+	0.160694i	$0.0513733\pi$
$968$		0			0
$969$	41.7848	+	30.3585i	1.34232	+	0.975254i
$970$		0			0
$971$	5.72303	−	17.6137i	0.183661	−	0.565250i	−0.816262	−	0.577682i	$-0.803957\pi$
$971$	5.72303	−	17.6137i	0.183661	−	0.565250i	0.999923	+	0.0124323i	$0.00395744\pi$
$972$		0			0
$973$	−7.54095	+	5.47882i	−0.241752	+	0.175643i
$974$		0			0
$975$	8.11513			0.259892
$976$		0			0
$977$	−17.1524	−	52.7895i	−0.548752	−	1.68889i	−0.711897	−	0.702284i	$-0.752164\pi$
$977$	−17.1524	−	52.7895i	−0.548752	−	1.68889i	0.163144	−	0.986602i	$-0.447836\pi$
$978$		0			0
$979$	−21.0134	−	15.2671i	−0.671590	−	0.487939i
$980$		0			0
$981$	39.7411			1.26884
$982$		0			0
$983$	33.3719			1.06440			0.532200	−	0.846619i	$-0.321365\pi$
$983$	33.3719			1.06440			0.532200	+	0.846619i	$0.321365\pi$
$984$		0			0
$985$	16.5623			0.527719
$986$		0			0
$987$	−11.5077			−0.366294
$988$		0			0
$989$	−30.1993	−	21.9411i	−0.960283	−	0.697686i
$990$		0			0
$991$	−4.97195	−	15.3021i	−0.157939	−	0.486087i	0.840508	−	0.541800i	$-0.182257\pi$
$991$	−4.97195	−	15.3021i	−0.157939	−	0.486087i	−0.998447	+	0.0557128i	$0.982257\pi$
$992$		0			0
$993$	22.3667			0.709787
$994$		0			0
$995$	−3.62932	+	2.63686i	−0.115057	+	0.0835939i
$996$		0			0
$997$	14.1347	−	43.5020i	0.447649	−	1.37772i	−0.431902	−	0.901920i	$-0.642158\pi$
$997$	14.1347	−	43.5020i	0.447649	−	1.37772i	0.879552	−	0.475803i	$-0.157842\pi$
$998$		0			0
$999$	1.01306	+	0.736033i	0.0320519	+	0.0232871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.a.221.1	yes	24
41.18	even	5	inner	820.2.u.a.141.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.a.141.1	✓	24	41.18	even	5	inner
820.2.u.a.221.1	yes	24	1.1	even	1	trivial

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.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.55771 q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.254587 + 0.783539i) q^{7} +3.54189 q^{9} +(1.87777 - 1.36428i) q^{11} +(-0.980451 + 3.01752i) q^{13} +(2.06923 + 1.50339i) q^{15} +(-5.32618 + 3.86970i) q^{17} +(0.947836 + 2.91714i) q^{19} +(-0.651161 - 2.00407i) q^{21} +(2.53799 - 7.81113i) q^{23} +(0.309017 + 0.951057i) q^{25} -1.38599 q^{27} +(-8.11578 - 5.89646i) q^{29} +(7.52831 - 5.46964i) q^{31} +(-4.80279 + 3.48943i) q^{33} +(0.254587 - 0.783539i) q^{35} +(-0.730928 - 0.531051i) q^{37} +(2.50771 - 7.71794i) q^{39} +(5.13251 - 3.82850i) q^{41} +(1.40448 - 4.32254i) q^{43} +(-2.86545 - 2.08187i) q^{45} +(1.68758 - 5.19384i) q^{47} +(5.11400 - 3.71554i) q^{49} +(13.6228 - 9.89758i) q^{51} +(3.59973 + 2.61536i) q^{53} -2.32105 q^{55} +(-2.42429 - 7.46120i) q^{57} +(-1.97221 + 6.06983i) q^{59} +(-3.58776 - 11.0420i) q^{61} +(0.901720 + 2.77521i) q^{63} +(2.56686 - 1.86493i) q^{65} +(-8.95132 - 6.50351i) q^{67} +(-6.49145 + 19.9786i) q^{69} +(6.99837 - 5.08462i) q^{71} -4.08803 q^{73} +(-0.790376 - 2.43253i) q^{75} +(1.54702 + 1.12398i) q^{77} -8.41097 q^{79} -7.08069 q^{81} -4.00591 q^{83} +6.58353 q^{85} +(20.7578 + 15.0814i) q^{87} +(-3.45809 - 10.6429i) q^{89} -2.61396 q^{91} +(-19.2552 + 13.9898i) q^{93} +(0.947836 - 2.91714i) q^{95} +(12.1338 + 8.81569i) q^{97} +(6.65084 - 4.83212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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