LMFDB - Embedded newform 820.2.x.a.817.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 1])) N = Newforms(chi, 2, names="a")

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			817.20
Character	$\chi$	$=$	820.817
Dual form			820.2.x.a.273.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.52347 - 1.04526i) q^{3} +(1.32280 - 1.80283i) q^{5} +(-0.949785 - 2.29298i) q^{7} +(3.15402 - 3.15402i) q^{9} +(-0.869165 + 2.09835i) q^{11} +(0.524650 - 0.217317i) q^{13} +(1.45364 - 5.93205i) q^{15} +(1.82492 + 0.755905i) q^{17} +(2.21662 + 5.35139i) q^{19} +(-4.79351 - 4.79351i) q^{21} +(-3.20260 - 3.20260i) q^{23} +(-1.50038 - 4.76958i) q^{25} +(1.52656 - 3.68544i) q^{27} +(1.60007 - 3.86291i) q^{29} +3.18030i q^{31} +6.20363i q^{33} +(-5.39024 - 1.32087i) q^{35} +(-4.58425 - 4.58425i) q^{37} +(1.09679 - 1.09679i) q^{39} +(-0.371118 + 6.39236i) q^{41} +0.295330i q^{43} +(-1.51401 - 9.85832i) q^{45} +(1.25279 + 0.518923i) q^{47} +(0.594062 - 0.594062i) q^{49} +5.39524 q^{51} +(1.44291 + 3.48350i) q^{53} +(2.63323 + 4.34266i) q^{55} +(11.1871 + 11.1871i) q^{57} +0.558558i q^{59} +(-9.30634 + 9.30634i) q^{61} +(-10.2278 - 4.23648i) q^{63} +(0.302223 - 1.23332i) q^{65} +(-1.56543 - 0.648422i) q^{67} +(-11.4292 - 4.73413i) q^{69} +(7.96495 + 3.29919i) q^{71} -6.60714i q^{73} +(-8.77160 - 10.4676i) q^{75} +5.63701 q^{77} +(15.2985 + 6.33686i) q^{79} +2.48565i q^{81} +(-4.88232 + 4.88232i) q^{83} +(3.77677 - 2.29010i) q^{85} -11.4204i q^{87} +(1.63251 - 3.94123i) q^{89} +(-0.996609 - 0.996609i) q^{91} +(3.32422 + 8.02539i) q^{93} +(12.5798 + 3.08265i) q^{95} +(-5.18619 + 12.5206i) q^{97} +(3.87688 + 9.35962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.52347	−	1.04526i	1.45693	−	0.603479i	0.493091	−	0.869978i	$-0.335867\pi$
$3$	2.52347	−	1.04526i	1.45693	−	0.603479i	0.963835	+	0.266499i	$0.0858668\pi$
$4$		0			0
$5$	1.32280	−	1.80283i	0.591576	−	0.806250i
$5$	1.32280	−	1.80283i	0.591576	−	0.806250i
$6$		0			0
$7$	−0.949785	−	2.29298i	−0.358985	−	0.866667i	−0.995443	−	0.0953554i	$-0.969601\pi$
$7$	−0.949785	−	2.29298i	−0.358985	−	0.866667i	0.636458	−	0.771311i	$-0.280399\pi$
$8$		0			0
$9$	3.15402	−	3.15402i	1.05134	−	1.05134i
$10$		0			0
$11$	−0.869165	+	2.09835i	−0.262063	+	0.632677i	−0.999066	−	0.0432133i	$-0.986241\pi$
$11$	−0.869165	+	2.09835i	−0.262063	+	0.632677i	0.737003	+	0.675890i	$0.236241\pi$
$12$		0			0
$13$	0.524650	−	0.217317i	0.145512	−	0.0602729i	−0.308739	−	0.951147i	$-0.599907\pi$
$13$	0.524650	−	0.217317i	0.145512	−	0.0602729i	0.454251	+	0.890874i	$0.349907\pi$
$14$		0			0
$15$	1.45364	−	5.93205i	0.375328	−	1.53165i
$16$		0			0
$17$	1.82492	+	0.755905i	0.442607	+	0.183334i	0.592846	−	0.805316i	$-0.298004\pi$
$17$	1.82492	+	0.755905i	0.442607	+	0.183334i	−0.150239	+	0.988650i	$0.548004\pi$
$18$		0			0
$19$	2.21662	+	5.35139i	0.508527	+	1.22769i	0.944731	+	0.327846i	$0.106323\pi$
$19$	2.21662	+	5.35139i	0.508527	+	1.22769i	−0.436204	+	0.899848i	$0.643677\pi$
$20$		0			0
$21$	−4.79351	−	4.79351i	−1.04603	−	1.04603i
$22$		0			0
$23$	−3.20260	−	3.20260i	−0.667788	−	0.667788i	0.289415	−	0.957204i	$-0.406539\pi$
$23$	−3.20260	−	3.20260i	−0.667788	−	0.667788i	−0.957204	+	0.289415i	$0.906539\pi$
$24$		0			0
$25$	−1.50038	−	4.76958i	−0.300077	−	0.953915i
$26$		0			0
$27$	1.52656	−	3.68544i	0.293787	−	0.709263i
$28$		0			0
$29$	1.60007	−	3.86291i	0.297125	−	0.717324i	−0.702857	−	0.711331i	$-0.748093\pi$
$29$	1.60007	−	3.86291i	0.297125	−	0.717324i	0.999982	−	0.00599253i	$-0.00190749\pi$
$30$		0			0
$31$			3.18030i			0.571198i	0.958349	+	0.285599i	$0.0921926\pi$
$31$			3.18030i			0.571198i	−0.958349	+	0.285599i	$0.907807\pi$
$32$		0			0
$33$			6.20363i			1.07991i
$34$		0			0
$35$	−5.39024	−	1.32087i	−0.911116	−	0.223267i
$36$		0			0
$37$	−4.58425	−	4.58425i	−0.753646	−	0.753646i	0.221512	−	0.975158i	$-0.428901\pi$
$37$	−4.58425	−	4.58425i	−0.753646	−	0.753646i	−0.975158	+	0.221512i	$0.928901\pi$
$38$		0			0
$39$	1.09679	−	1.09679i	0.175626	−	0.175626i
$40$		0			0
$41$	−0.371118	+	6.39236i	−0.0579590	+	0.998319i
$41$	−0.371118	+	6.39236i	−0.0579590	+	0.998319i
$42$		0			0
$43$			0.295330i			0.0450374i	0.999746	+	0.0225187i	$0.00716854\pi$
$43$			0.295330i			0.0450374i	−0.999746	+	0.0225187i	$0.992831\pi$
$44$		0			0
$45$	−1.51401	−	9.85832i	−0.225696	−	1.46959i
$46$		0			0
$47$	1.25279	+	0.518923i	0.182738	+	0.0756928i	0.472177	−	0.881504i	$-0.343468\pi$
$47$	1.25279	+	0.518923i	0.182738	+	0.0756928i	−0.289438	+	0.957197i	$0.593468\pi$
$48$		0			0
$49$	0.594062	−	0.594062i	0.0848661	−	0.0848661i
$50$		0			0
$51$	5.39524			0.755485
$52$		0			0
$53$	1.44291	+	3.48350i	0.198199	+	0.478496i	0.991464	−	0.130382i	$-0.0416202\pi$
$53$	1.44291	+	3.48350i	0.198199	+	0.478496i	−0.793265	+	0.608877i	$0.791620\pi$
$54$		0			0
$55$	2.63323	+	4.34266i	0.355065	+	0.585564i
$56$		0			0
$57$	11.1871	+	11.1871i	1.48177	+	1.48177i
$58$		0			0
$59$			0.558558i			0.0727181i	0.999339	+	0.0363590i	$0.0115760\pi$
$59$			0.558558i			0.0727181i	−0.999339	+	0.0363590i	$0.988424\pi$
$60$		0			0
$61$	−9.30634	+	9.30634i	−1.19156	+	1.19156i	−0.214924	+	0.976631i	$0.568950\pi$
$61$	−9.30634	+	9.30634i	−1.19156	+	1.19156i	−0.976631	+	0.214924i	$0.931050\pi$
$62$		0			0
$63$	−10.2278	−	4.23648i	−1.28858	−	0.533747i
$64$		0			0
$65$	0.302223	−	1.23332i	0.0374861	−	0.152975i
$66$		0			0
$67$	−1.56543	−	0.648422i	−0.191247	−	0.0792173i	0.285004	−	0.958526i	$-0.408005\pi$
$67$	−1.56543	−	0.648422i	−0.191247	−	0.0792173i	−0.476252	+	0.879309i	$0.658005\pi$
$68$		0			0
$69$	−11.4292	−	4.73413i	−1.37591	−	0.569922i
$70$		0			0
$71$	7.96495	+	3.29919i	0.945266	+	0.391542i	0.801450	−	0.598062i	$-0.204063\pi$
$71$	7.96495	+	3.29919i	0.945266	+	0.391542i	0.143816	+	0.989604i	$0.454063\pi$
$72$		0			0
$73$		−	6.60714i		−	0.773308i	−0.922225	−	0.386654i	$-0.873631\pi$
$73$		−	6.60714i		−	0.773308i	0.922225	−	0.386654i	$-0.126369\pi$
$74$		0			0
$75$	−8.77160	−	10.4676i	−1.01286	−	1.20869i
$76$		0			0
$77$	5.63701			0.642396
$78$		0			0
$79$	15.2985	+	6.33686i	1.72122	+	0.712953i	0.999791	+	0.0204657i	$0.00651488\pi$
$79$	15.2985	+	6.33686i	1.72122	+	0.712953i	0.721430	+	0.692487i	$0.243485\pi$
$80$		0			0
$81$			2.48565i			0.276183i
$82$		0			0
$83$	−4.88232	+	4.88232i	−0.535905	+	0.535905i	−0.922323	−	0.386419i	$-0.873712\pi$
$83$	−4.88232	+	4.88232i	−0.535905	+	0.535905i	0.386419	+	0.922323i	$0.373712\pi$
$84$		0			0
$85$	3.77677	−	2.29010i	0.409649	−	0.248396i
$86$		0			0
$87$		−	11.4204i		−	1.22440i
$88$		0			0
$89$	1.63251	−	3.94123i	0.173046	−	0.417770i	−0.813433	−	0.581659i	$-0.802404\pi$
$89$	1.63251	−	3.94123i	0.173046	−	0.417770i	0.986479	+	0.163889i	$0.0524039\pi$
$90$		0			0
$91$	−0.996609	−	0.996609i	−0.104473	−	0.104473i
$92$		0			0
$93$	3.32422	+	8.02539i	0.344706	+	0.832194i
$94$		0			0
$95$	12.5798	+	3.08265i	1.29066	+	0.316273i
$96$		0			0
$97$	−5.18619	+	12.5206i	−0.526578	+	1.27127i	0.407174	+	0.913351i	$0.366514\pi$
$97$	−5.18619	+	12.5206i	−0.526578	+	1.27127i	−0.933752	+	0.357921i	$0.883486\pi$
$98$		0			0
$99$	3.87688	+	9.35962i	0.389641	+	0.940677i
$100$		0			0
$101$	−3.39945	+	1.40810i	−0.338258	+	0.140111i	−0.545345	−	0.838211i	$-0.683601\pi$
$101$	−3.39945	+	1.40810i	−0.338258	+	0.140111i	0.207088	+	0.978322i	$0.433601\pi$
$102$		0			0
$103$	1.15561			0.113866			0.0569329	−	0.998378i	$-0.481868\pi$
$103$	1.15561			0.113866			0.0569329	+	0.998378i	$0.481868\pi$
$104$		0			0
$105$	−14.9827	+	2.30101i	−1.46217	+	0.224555i
$106$		0			0
$107$	1.95897	−	1.95897i	0.189381	−	0.189381i	−0.606047	−	0.795428i	$-0.707246\pi$
$107$	1.95897	−	1.95897i	0.189381	−	0.189381i	0.795428	+	0.606047i	$0.207246\pi$
$108$		0			0
$109$	16.9082	−	7.00361i	1.61951	−	0.670824i	0.625514	−	0.780213i	$-0.284889\pi$
$109$	16.9082	−	7.00361i	1.61951	−	0.670824i	0.993999	+	0.109389i	$0.0348894\pi$
$110$		0			0
$111$	−16.3599	−	6.77651i	−1.55282	−	0.643198i
$112$		0			0
$113$	−11.2160	−	11.2160i	−1.05511	−	1.05511i	−0.998390	−	0.0567209i	$-0.981935\pi$
$113$	−11.2160	−	11.2160i	−1.05511	−	1.05511i	−0.0567209	−	0.998390i	$-0.518065\pi$
$114$		0			0
$115$	−10.0101	+	1.53733i	−0.933451	+	0.143357i
$116$		0			0
$117$	0.969335	−	2.34018i	0.0896150	−	0.216350i
$118$		0			0
$119$		−	4.90245i		−	0.449407i
$120$		0			0
$121$	4.13055	+	4.13055i	0.375504	+	0.375504i
$122$		0			0
$123$	5.74515	+	16.5188i	0.518022	+	1.48945i
$124$		0			0
$125$	−10.5834	−	3.60427i	−0.946612	−	0.322376i
$126$		0			0
$127$	0.646133	−	0.646133i	0.0573351	−	0.0573351i	−0.677858	−	0.735193i	$-0.737092\pi$
$127$	0.646133	−	0.646133i	0.0573351	−	0.0573351i	0.735193	+	0.677858i	$0.237092\pi$
$128$		0			0
$129$	0.308696	+	0.745257i	0.0271791	+	0.0656162i
$130$		0			0
$131$	5.41261	+	5.41261i	0.472902	+	0.472902i	0.902852	−	0.429951i	$-0.141469\pi$
$131$	5.41261	+	5.41261i	0.472902	+	0.472902i	−0.429951	+	0.902852i	$0.641469\pi$
$132$		0			0
$133$	10.1653	−	10.1653i	0.881447	−	0.881447i
$134$		0			0
$135$	−4.62488	−	7.62724i	−0.398046	−	0.656448i
$136$		0			0
$137$	0.669422	+	0.277283i	0.0571925	+	0.0236899i	0.411096	−	0.911592i	$-0.365146\pi$
$137$	0.669422	+	0.277283i	0.0571925	+	0.0236899i	−0.353904	+	0.935282i	$0.615146\pi$
$138$		0			0
$139$		−	5.04166i		−	0.427628i	−0.976874	−	0.213814i	$-0.931411\pi$
$139$		−	5.04166i		−	0.427628i	0.976874	−	0.213814i	$-0.0685886\pi$
$140$		0			0
$141$	3.70379			0.311916
$142$		0			0
$143$			1.28978i			0.107857i
$144$		0			0
$145$	−4.84759	−	7.99452i	−0.402570	−	0.663908i
$146$		0			0
$147$	0.878152	−	2.12005i	0.0724288	−	0.174858i
$148$		0			0
$149$	−8.11373	−	19.5883i	−0.664703	−	1.60473i	−0.790347	−	0.612659i	$-0.790100\pi$
$149$	−8.11373	−	19.5883i	−0.664703	−	1.60473i	0.125645	−	0.992075i	$-0.459900\pi$
$150$		0			0
$151$	−5.32915	+	12.8657i	−0.433680	+	1.04700i	0.544411	+	0.838819i	$0.316753\pi$
$151$	−5.32915	+	12.8657i	−0.433680	+	1.04700i	−0.978091	+	0.208178i	$0.933247\pi$
$152$		0			0
$153$	8.13998	−	3.37169i	0.658078	−	0.272585i
$154$		0			0
$155$	5.73353	+	4.20691i	0.460528	+	0.337907i
$156$		0			0
$157$	22.3089	−	9.24064i	1.78044	−	0.737483i	0.787868	−	0.615845i	$-0.211185\pi$
$157$	22.3089	−	9.24064i	1.78044	−	0.737483i	0.992574	−	0.121639i	$-0.0388149\pi$
$158$		0			0
$159$	7.28230	+	7.28230i	0.577524	+	0.577524i
$160$		0			0
$161$	−4.30173	+	10.3853i	−0.339024	+	0.818476i
$162$		0			0
$163$	11.6422	+	11.6422i	0.911889	+	0.911889i	0.996421	−	0.0845316i	$-0.0269394\pi$
$163$	11.6422	+	11.6422i	0.911889	+	0.911889i	−0.0845316	+	0.996421i	$0.526939\pi$
$164$		0			0
$165$	11.1841	+	8.20618i	0.870679	+	0.638850i
$166$		0			0
$167$	1.52301	+	3.67687i	0.117854	+	0.284525i	0.971788	−	0.235857i	$-0.0757896\pi$
$167$	1.52301	+	3.67687i	0.117854	+	0.284525i	−0.853934	+	0.520382i	$0.825790\pi$
$168$		0			0
$169$	−8.96436	+	8.96436i	−0.689566	+	0.689566i
$170$		0			0
$171$	23.8697	+	9.88715i	1.82536	+	0.756089i
$172$		0			0
$173$	7.73026			0.587721			0.293860	−	0.955848i	$-0.405060\pi$
$173$	7.73026			0.587721			0.293860	+	0.955848i	$0.405060\pi$
$174$		0			0
$175$	−9.51152	+	7.97043i	−0.719003	+	0.602508i
$176$		0			0
$177$	0.583836	+	1.40951i	0.0438838	+	0.105945i
$178$		0			0
$179$	−22.3875	+	9.27320i	−1.67332	+	0.693111i	−0.998973	−	0.0453042i	$-0.985574\pi$
$179$	−22.3875	+	9.27320i	−1.67332	+	0.693111i	−0.674346	+	0.738416i	$0.735574\pi$
$180$		0			0
$181$	4.39280	−	1.81956i	0.326514	−	0.135247i	−0.213404	−	0.976964i	$-0.568455\pi$
$181$	4.39280	−	1.81956i	0.326514	−	0.135247i	0.539918	+	0.841717i	$0.318455\pi$
$182$		0			0
$183$	−13.7568	+	33.2118i	−1.01693	+	2.45509i
$184$		0			0
$185$	−14.3287	+	2.20056i	−1.05347	+	0.161788i
$186$		0			0
$187$	−3.17231	+	3.17231i	−0.231982	+	0.231982i
$188$		0			0
$189$	−9.90056			−0.720160
$190$		0			0
$191$	−4.35565	−	10.5155i	−0.315164	−	0.760873i	−0.999497	−	0.0317038i	$-0.989907\pi$
$191$	−4.35565	−	10.5155i	−0.315164	−	0.760873i	0.684333	−	0.729169i	$-0.260093\pi$
$192$		0			0
$193$	22.0947	−	9.15193i	1.59041	−	0.658770i	0.600393	−	0.799705i	$-0.295011\pi$
$193$	22.0947	−	9.15193i	1.59041	−	0.658770i	0.990019	+	0.140934i	$0.0450107\pi$
$194$		0			0
$195$	−0.526486	−	3.42815i	−0.0377024	−	0.245495i
$196$		0			0
$197$	−7.41577			−0.528351			−0.264176	−	0.964475i	$-0.585100\pi$
$197$	−7.41577			−0.528351			−0.264176	+	0.964475i	$0.585100\pi$
$198$		0			0
$199$	−13.4266	+	5.56147i	−0.951785	+	0.394242i	−0.803901	−	0.594763i	$-0.797246\pi$
$199$	−13.4266	+	5.56147i	−0.951785	+	0.394242i	−0.147883	+	0.989005i	$0.547246\pi$
$200$		0			0
$201$	−4.62808			−0.326440
$202$		0			0
$203$	−10.3773			−0.728344
$204$		0			0
$205$	11.0334	+	9.12490i	0.770607	+	0.637310i
$206$		0			0
$207$	−20.2022			−1.40415
$208$		0			0
$209$	−13.1557			−0.909999
$210$		0			0
$211$	−9.64043	+	3.99320i	−0.663675	+	0.274903i	−0.688984	−	0.724777i	$-0.741943\pi$
$211$	−9.64043	+	3.99320i	−0.663675	+	0.274903i	0.0253091	+	0.999680i	$0.491943\pi$
$212$		0			0
$213$	23.5478			1.61347
$214$		0			0
$215$	0.532430	+	0.390664i	0.0363114	+	0.0266430i
$216$		0			0
$217$	7.29237	−	3.02060i	0.495038	−	0.205052i
$218$		0			0
$219$	−6.90616	−	16.6729i	−0.466675	−	1.12665i
$220$		0			0
$221$	1.12171			0.0754546
$222$		0			0
$223$	−19.2171	+	19.2171i	−1.28687	+	1.28687i	−0.350198	+	0.936676i	$0.613886\pi$
$223$	−19.2171	+	19.2171i	−1.28687	+	1.28687i	−0.936676	+	0.350198i	$0.886114\pi$
$224$		0			0
$225$	−19.7756	−	10.3111i	−1.31837	−	0.687407i
$226$		0			0
$227$	−5.04356	+	12.1762i	−0.334753	+	0.808165i	0.663449	+	0.748222i	$0.269092\pi$
$227$	−5.04356	+	12.1762i	−0.334753	+	0.808165i	−0.998202	+	0.0599435i	$0.980908\pi$
$228$		0			0
$229$	−20.4572	+	8.47367i	−1.35185	+	0.559956i	−0.936808	−	0.349845i	$-0.886234\pi$
$229$	−20.4572	+	8.47367i	−1.35185	+	0.559956i	−0.415045	+	0.909801i	$0.636234\pi$
$230$		0			0
$231$	14.2248	−	5.89211i	0.935924	−	0.387673i
$232$		0			0
$233$	−1.83642	−	4.43350i	−0.120308	−	0.290448i	0.852241	−	0.523150i	$-0.175243\pi$
$233$	−1.83642	−	4.43350i	−0.120308	−	0.290448i	−0.972548	+	0.232702i	$0.925243\pi$
$234$		0			0
$235$	2.59273	−	1.57214i	0.169131	−	0.102555i
$236$		0			0
$237$	45.2291			2.93794
$238$		0			0
$239$	−10.1625	−	4.20944i	−0.657356	−	0.272286i	0.0289695	−	0.999580i	$-0.490777\pi$
$239$	−10.1625	−	4.20944i	−0.657356	−	0.272286i	−0.686326	+	0.727295i	$0.740777\pi$
$240$		0			0
$241$	−6.66917	+	6.66917i	−0.429599	+	0.429599i	−0.888492	−	0.458893i	$-0.848246\pi$
$241$	−6.66917	+	6.66917i	−0.429599	+	0.429599i	0.458893	+	0.888492i	$0.348246\pi$
$242$		0			0
$243$	7.17782	+	17.3288i	0.460457	+	1.11164i
$244$		0			0
$245$	−0.285165	−	1.85682i	−0.0182185	−	0.118628i
$246$		0			0
$247$	2.32590	+	2.32590i	0.147993	+	0.147993i
$248$		0			0
$249$	−7.21712	+	17.4237i	−0.457367	+	1.10418i
$250$		0			0
$251$	6.83535	+	6.83535i	0.431443	+	0.431443i	0.889119	−	0.457676i	$-0.151318\pi$
$251$	6.83535	+	6.83535i	0.431443	+	0.431443i	−0.457676	+	0.889119i	$0.651318\pi$
$252$		0			0
$253$	9.50377	−	3.93659i	0.597497	−	0.247491i
$254$		0			0
$255$	7.13684	−	9.72669i	0.446926	−	0.609109i
$256$		0			0
$257$	4.32787	−	1.79266i	0.269965	−	0.111823i	−0.243594	−	0.969877i	$-0.578327\pi$
$257$	4.32787	−	1.79266i	0.269965	−	0.111823i	0.513559	+	0.858054i	$0.328327\pi$
$258$		0			0
$259$	−6.15756	+	14.8657i	−0.382612	+	0.923708i
$260$		0			0
$261$	−7.13705	−	17.2304i	−0.441772	−	1.06653i
$262$		0			0
$263$	5.82029	−	14.0514i	0.358895	−	0.866448i	−0.636561	−	0.771226i	$-0.719644\pi$
$263$	5.82029	−	14.0514i	0.358895	−	0.866448i	0.995456	−	0.0952222i	$-0.0303562\pi$
$264$		0			0
$265$	8.18885	+	2.00666i	0.503037	+	0.123268i
$266$		0			0
$267$		−	11.6520i		−	0.713090i
$268$		0			0
$269$	−21.7159			−1.32404			−0.662021	−	0.749485i	$-0.730301\pi$
$269$	−21.7159			−1.32404			−0.662021	+	0.749485i	$0.730301\pi$
$270$		0			0
$271$			20.1022i			1.22112i	0.791969	+	0.610561i	$0.209056\pi$
$271$			20.1022i			1.22112i	−0.791969	+	0.610561i	$0.790944\pi$
$272$		0			0
$273$	−3.55662	−	1.47320i	−0.215257	−	0.0891622i
$274$		0			0
$275$	11.3123	+	0.997218i	0.682159	+	0.0601345i
$276$		0			0
$277$	−14.8375	+	14.8375i	−0.891496	+	0.891496i	−0.994664	−	0.103168i	$-0.967102\pi$
$277$	−14.8375	+	14.8375i	−0.891496	+	0.891496i	0.103168	+	0.994664i	$0.467102\pi$
$278$		0			0
$279$	10.0307	+	10.0307i	0.600524	+	0.600524i
$280$		0			0
$281$	−11.6260	−	28.0677i	−0.693550	−	1.67438i	−0.737503	−	0.675344i	$-0.763995\pi$
$281$	−11.6260	−	28.0677i	−0.693550	−	1.67438i	0.0439533	−	0.999034i	$-0.486005\pi$
$282$		0			0
$283$	−0.609443	+	0.609443i	−0.0362276	+	0.0362276i	−0.724989	−	0.688761i	$-0.758155\pi$
$283$	−0.609443	+	0.609443i	−0.0362276	+	0.0362276i	0.688761	+	0.724989i	$0.258155\pi$
$284$		0			0
$285$	34.9669	−	5.37012i	2.07126	−	0.318098i
$286$		0			0
$287$	15.0101	−	5.22040i	0.886016	−	0.308150i
$288$		0			0
$289$	−9.26189	−	9.26189i	−0.544817	−	0.544817i
$290$		0			0
$291$			37.0162i			2.16993i
$292$		0			0
$293$	10.2201	−	24.6734i	0.597063	−	1.44144i	−0.279498	−	0.960146i	$-0.590168\pi$
$293$	10.2201	−	24.6734i	0.597063	−	1.44144i	0.876561	−	0.481291i	$-0.159832\pi$
$294$		0			0
$295$	1.00698	+	0.738862i	0.0586289	+	0.0430182i
$296$		0			0
$297$	6.40652	+	6.40652i	0.371744	+	0.371744i
$298$		0			0
$299$	−2.37622	−	0.984263i	−0.137420	−	0.0569214i
$300$		0			0
$301$	0.677188	−	0.280500i	0.0390324	−	0.0161678i
$302$		0			0
$303$	−7.10658	+	7.10658i	−0.408263	+	0.408263i
$304$		0			0
$305$	4.46728	+	29.0882i	0.255796	+	1.66559i
$306$		0			0
$307$	10.4642			0.597222			0.298611	−	0.954375i	$-0.403477\pi$
$307$	10.4642			0.597222			0.298611	+	0.954375i	$0.403477\pi$
$308$		0			0
$309$	2.91615	−	1.20791i	0.165894	−	0.0687156i
$310$		0			0
$311$	−10.1272	−	24.4492i	−0.574261	−	1.38639i	−0.897897	−	0.440206i	$-0.854905\pi$
$311$	−10.1272	−	24.4492i	−0.574261	−	1.38639i	0.323636	−	0.946182i	$-0.395095\pi$
$312$		0			0
$313$	−1.45605	+	3.51522i	−0.0823008	+	0.198692i	−0.959673	−	0.281119i	$-0.909295\pi$
$313$	−1.45605	+	3.51522i	−0.0823008	+	0.198692i	0.877372	+	0.479810i	$0.159295\pi$
$314$		0			0
$315$	−21.1670	+	12.8349i	−1.19262	+	0.723164i
$316$		0			0
$317$	−7.57000	−	18.2756i	−0.425174	−	1.02646i	−0.980798	−	0.195027i	$-0.937521\pi$
$317$	−7.57000	−	18.2756i	−0.425174	−	1.02646i	0.555624	−	0.831434i	$-0.312479\pi$
$318$		0			0
$319$	6.71501	+	6.71501i	0.375968	+	0.375968i
$320$		0			0
$321$	2.89578	−	6.99104i	0.161627	−	0.390202i
$322$		0			0
$323$			11.4414i			0.636617i
$324$		0			0
$325$	−1.82369	−	2.17630i	−0.101160	−	0.120719i
$326$		0			0
$327$	35.3468	−	35.3468i	1.95468	−	1.95468i
$328$		0			0
$329$		−	3.36550i		−	0.185546i
$330$		0			0
$331$	−15.0178	−	6.22056i	−0.825451	−	0.341913i	−0.0703507	−	0.997522i	$-0.522412\pi$
$331$	−15.0178	−	6.22056i	−0.825451	−	0.341913i	−0.755100	+	0.655609i	$0.772412\pi$
$332$		0			0
$333$	−28.9177			−1.58468
$334$		0			0
$335$	−3.23975	+	1.96446i	−0.177006	+	0.107330i
$336$		0			0
$337$			13.2195i			0.720110i	0.932931	+	0.360055i	$0.117242\pi$
$337$			13.2195i			0.720110i	−0.932931	+	0.360055i	$0.882758\pi$
$338$		0			0
$339$	−40.0268	−	16.5796i	−2.17396	−	0.900482i
$340$		0			0
$341$	−6.67338	−	2.76420i	−0.361384	−	0.149690i
$342$		0			0
$343$	−17.9773	−	7.44644i	−0.970683	−	0.402070i
$344$		0			0
$345$	−23.6534	+	14.3426i	−1.27346	+	0.772178i
$346$		0			0
$347$	3.09060	+	1.28017i	0.165912	+	0.0687231i	0.464094	−	0.885786i	$-0.346380\pi$
$347$	3.09060	+	1.28017i	0.165912	+	0.0687231i	−0.298181	+	0.954509i	$0.596380\pi$
$348$		0			0
$349$	14.0112	−	14.0112i	0.750002	−	0.750002i	−0.224477	−	0.974479i	$-0.572067\pi$
$349$	14.0112	−	14.0112i	0.750002	−	0.750002i	0.974479	+	0.224477i	$0.0720675\pi$
$350$		0			0
$351$		−	2.26531i		−	0.120913i
$352$		0			0
$353$	−1.30579	−	1.30579i	−0.0695003	−	0.0695003i	0.671502	−	0.741003i	$-0.265649\pi$
$353$	−1.30579	−	1.30579i	−0.0695003	−	0.0695003i	−0.741003	+	0.671502i	$0.765649\pi$
$354$		0			0
$355$	16.4839	−	9.99527i	0.874877	−	0.530494i
$356$		0			0
$357$	−5.12432	−	12.3712i	−0.271208	−	0.654753i
$358$		0			0
$359$	20.1309			1.06247			0.531233	−	0.847226i	$-0.321729\pi$
$359$	20.1309			1.06247			0.531233	+	0.847226i	$0.321729\pi$
$360$		0			0
$361$	−10.2890	+	10.2890i	−0.541524	+	0.541524i
$362$		0			0
$363$	14.7408	+	6.10584i	0.773691	+	0.320473i
$364$		0			0
$365$	−11.9115	−	8.73995i	−0.623479	−	0.457470i
$366$		0			0
$367$		−	19.8546i		−	1.03640i	−0.855260	−	0.518200i	$-0.826602\pi$
$367$		−	19.8546i		−	1.03640i	0.855260	−	0.518200i	$-0.173398\pi$
$368$		0			0
$369$	18.9911	+	21.3322i	0.988640	+	1.11051i
$370$		0			0
$371$	6.61716	−	6.61716i	0.343546	−	0.343546i
$372$		0			0
$373$	8.58554	+	8.58554i	0.444543	+	0.444543i	0.893535	−	0.448993i	$-0.148217\pi$
$373$	8.58554	+	8.58554i	0.444543	+	0.444543i	−0.448993	+	0.893535i	$0.648217\pi$
$374$		0			0
$375$	−30.4744	+	1.96712i	−1.57369	+	0.101582i
$376$		0			0
$377$		−	2.37439i		−	0.122288i
$378$		0			0
$379$			7.66393i			0.393669i	0.980437	+	0.196835i	$0.0630662\pi$
$379$			7.66393i			0.393669i	−0.980437	+	0.196835i	$0.936934\pi$
$380$		0			0
$381$	0.955124	−	2.30587i	0.0489325	−	0.118133i
$382$		0			0
$383$	−6.93476	+	16.7420i	−0.354350	+	0.855476i	0.641723	+	0.766937i	$0.278220\pi$
$383$	−6.93476	+	16.7420i	−0.354350	+	0.855476i	−0.996073	+	0.0885396i	$0.971780\pi$
$384$		0			0
$385$	7.45665	−	10.1626i	0.380026	−	0.517932i
$386$		0			0
$387$	0.931479	+	0.931479i	0.0473497	+	0.0473497i
$388$		0			0
$389$	−17.2766	−	17.2766i	−0.875961	−	0.875961i	0.117153	−	0.993114i	$-0.462623\pi$
$389$	−17.2766	−	17.2766i	−0.875961	−	0.875961i	−0.993114	+	0.117153i	$0.962623\pi$
$390$		0			0
$391$	−3.42362	−	8.26534i	−0.173140	−	0.417996i
$392$		0			0
$393$	19.3161	+	8.00099i	0.974369	+	0.403597i
$394$		0			0
$395$	31.6612	−	19.1982i	1.59305	−	0.965968i
$396$		0			0
$397$	26.1315	−	10.8240i	1.31150	−	0.543242i	0.386180	−	0.922423i	$-0.373794\pi$
$397$	26.1315	−	10.8240i	1.31150	−	0.543242i	0.925322	+	0.379181i	$0.123794\pi$
$398$		0			0
$399$	15.0266	−	36.2773i	0.752269	−	1.81614i
$400$		0			0
$401$	21.5874	−	21.5874i	1.07803	−	1.07803i	0.0813390	−	0.996686i	$-0.474080\pi$
$401$	21.5874	−	21.5874i	1.07803	−	1.07803i	0.996686	−	0.0813390i	$-0.0259196\pi$
$402$		0			0
$403$	0.691132	+	1.66854i	0.0344278	+	0.0831160i
$404$		0			0
$405$	4.48120	+	3.28802i	0.222672	+	0.163383i
$406$		0			0
$407$	13.6038	−	5.63490i	0.674317	−	0.279311i
$408$		0			0
$409$	20.0737			0.992581			0.496291	−	0.868156i	$-0.334695\pi$
$409$	20.0737			0.992581			0.496291	+	0.868156i	$0.334695\pi$
$410$		0			0
$411$	1.97910			0.0976217
$412$		0			0
$413$	1.28076	−	0.530510i	0.0630223	−	0.0261047i
$414$		0			0
$415$	2.34364	+	15.2603i	0.115045	+	0.749101i
$416$		0			0
$417$	−5.26982	−	12.7225i	−0.258064	−	0.623022i
$418$		0			0
$419$	−1.64729	+	1.64729i	−0.0804754	+	0.0804754i	−0.746199	−	0.665723i	$-0.768123\pi$
$419$	−1.64729	+	1.64729i	−0.0804754	+	0.0804754i	0.665723	+	0.746199i	$0.268123\pi$
$420$		0			0
$421$	−9.57202	+	23.1089i	−0.466512	+	1.12626i	0.499164	+	0.866508i	$0.333641\pi$
$421$	−9.57202	+	23.1089i	−0.466512	+	1.12626i	−0.965675	+	0.259752i	$0.916359\pi$
$422$		0			0
$423$	5.58803	−	2.31464i	0.271700	−	0.112542i
$424$		0			0
$425$	0.867272	−	9.83823i	0.0420689	−	0.477224i
$426$		0			0
$427$	30.1783	+	12.5003i	1.46043	+	0.604930i
$428$		0			0
$429$	1.34815	+	3.25473i	0.0650895	+	0.157140i
$430$		0			0
$431$	19.9917	+	19.9917i	0.962969	+	0.962969i	0.999338	−	0.0363698i	$-0.0115794\pi$
$431$	19.9917	+	19.9917i	0.962969	+	0.962969i	−0.0363698	+	0.999338i	$0.511579\pi$
$432$		0			0
$433$	−5.40420	−	5.40420i	−0.259709	−	0.259709i	0.565226	−	0.824936i	$-0.308789\pi$
$433$	−5.40420	−	5.40420i	−0.259709	−	0.259709i	−0.824936	+	0.565226i	$0.808789\pi$
$434$		0			0
$435$	−20.5891	−	15.1070i	−0.987170	−	0.724323i
$436$		0			0
$437$	10.0394	−	24.2373i	0.480251	−	1.15943i
$438$		0			0
$439$	11.1265	−	26.8618i	0.531040	−	1.28204i	−0.399795	−	0.916605i	$-0.630919\pi$
$439$	11.1265	−	26.8618i	0.531040	−	1.28204i	0.930835	−	0.365440i	$-0.119081\pi$
$440$		0			0
$441$		−	3.74738i		−	0.178446i
$442$		0			0
$443$		−	40.0241i		−	1.90160i	−0.309800	−	0.950802i	$-0.600262\pi$
$443$		−	40.0241i		−	1.90160i	0.309800	−	0.950802i	$-0.399738\pi$
$444$		0			0
$445$	−4.94588	−	8.15662i	−0.234457	−	0.386661i
$446$		0			0
$447$	−40.9495	−	40.9495i	−1.93685	−	1.93685i
$448$		0			0
$449$	25.9798	−	25.9798i	1.22606	−	1.22606i	0.260623	−	0.965441i	$-0.416072\pi$
$449$	25.9798	−	25.9798i	1.22606	−	1.22606i	0.965441	−	0.260623i	$-0.0839279\pi$
$450$		0			0
$451$	−13.0909	−	6.33476i	−0.616424	−	0.298292i
$452$		0			0
$453$			38.0366i			1.78711i
$454$		0			0
$455$	−3.11503	+	0.478398i	−0.146035	+	0.0224276i
$456$		0			0
$457$	−21.7273	−	8.99976i	−1.01636	−	0.420991i	−0.188590	−	0.982056i	$-0.560392\pi$
$457$	−21.7273	−	8.99976i	−1.01636	−	0.420991i	−0.827772	+	0.561065i	$0.810392\pi$
$458$		0			0
$459$	5.57169	−	5.57169i	0.260064	−	0.260064i
$460$		0			0
$461$	−26.3042			−1.22511			−0.612555	−	0.790428i	$-0.709858\pi$
$461$	−26.3042			−1.22511			−0.612555	+	0.790428i	$0.709858\pi$
$462$		0			0
$463$	−9.19993	−	22.2106i	−0.427557	−	1.03221i	−0.980060	−	0.198703i	$-0.936327\pi$
$463$	−9.19993	−	22.2106i	−0.427557	−	1.03221i	0.552503	−	0.833511i	$-0.313673\pi$
$464$		0			0
$465$	18.8657	+	4.62300i	0.874876	+	0.214386i
$466$		0			0
$467$	−26.8274	−	26.8274i	−1.24142	−	1.24142i	−0.959411	−	0.282013i	$-0.908998\pi$
$467$	−26.8274	−	26.8274i	−1.24142	−	1.24142i	−0.282013	−	0.959411i	$-0.591002\pi$
$468$		0			0
$469$			4.20536i			0.194186i
$470$		0			0
$471$	46.6370	−	46.6370i	2.14892	−	2.14892i
$472$		0			0
$473$	−0.619707	−	0.256691i	−0.0284941	−	0.0118027i
$474$		0			0
$475$	22.1981	−	18.6015i	1.01852	−	0.853494i
$476$		0			0
$477$	15.5380	+	6.43606i	0.711438	+	0.294687i
$478$		0			0
$479$	−31.8708	−	13.2013i	−1.45621	−	0.603183i	−0.492545	−	0.870287i	$-0.663933\pi$
$479$	−31.8708	−	13.2013i	−1.45621	−	0.603183i	−0.963668	+	0.267104i	$0.913933\pi$
$480$		0			0
$481$	−3.40136	−	1.40889i	−0.155089	−	0.0642398i
$482$		0			0
$483$			30.7034i			1.39705i
$484$		0			0
$485$	15.7121	+	25.9121i	0.713452	+	1.17661i
$486$		0			0
$487$	−7.09877			−0.321676			−0.160838	−	0.986981i	$-0.551420\pi$
$487$	−7.09877			−0.321676			−0.160838	+	0.986981i	$0.551420\pi$
$488$		0			0
$489$	41.5479	+	17.2097i	1.87886	+	0.778250i
$490$		0			0
$491$		−	8.49502i		−	0.383375i	−0.981456	−	0.191687i	$-0.938604\pi$
$491$		−	8.49502i		−	0.383375i	0.981456	−	0.191687i	$-0.0613960\pi$
$492$		0			0
$493$	5.83999	−	5.83999i	0.263020	−	0.263020i
$494$		0			0
$495$	22.0021	+	5.39158i	0.988923	+	0.242334i
$496$		0			0
$497$		−	21.3970i		−	0.959788i
$498$		0			0
$499$	−14.1912	+	34.2605i	−0.635284	+	1.53371i	0.197610	+	0.980281i	$0.436682\pi$
$499$	−14.1912	+	34.2605i	−0.635284	+	1.53371i	−0.832895	+	0.553432i	$0.813318\pi$
$500$		0			0
$501$	7.68654	+	7.68654i	0.343409	+	0.343409i
$502$		0			0
$503$	−8.52633	−	20.5844i	−0.380170	−	0.917813i	−0.991932	−	0.126771i	$-0.959539\pi$
$503$	−8.52633	−	20.5844i	−0.380170	−	0.917813i	0.611762	−	0.791042i	$-0.290461\pi$
$504$		0			0
$505$	−1.95824	+	7.99126i	−0.0871406	+	0.355606i
$506$		0			0
$507$	−13.2512	+	31.9913i	−0.588509	+	1.42079i
$508$		0			0
$509$	5.09125	+	12.2914i	0.225666	+	0.544805i	0.995641	−	0.0932686i	$-0.0297315\pi$
$509$	5.09125	+	12.2914i	0.225666	+	0.544805i	−0.769975	+	0.638074i	$0.779732\pi$
$510$		0			0
$511$	−15.1501	+	6.27537i	−0.670200	+	0.277606i
$512$		0			0
$513$	23.1060			1.02016
$514$		0			0
$515$	1.52865	−	2.08337i	0.0673602	−	0.0918042i
$516$		0			0
$517$	−2.17777	+	2.17777i	−0.0957781	+	0.0957781i
$518$		0			0
$519$	19.5071	−	8.08010i	0.856266	−	0.354677i
$520$		0			0
$521$	−16.4966	−	6.83314i	−0.722731	−	0.299365i	−0.00917005	−	0.999958i	$-0.502919\pi$
$521$	−16.4966	−	6.83314i	−0.722731	−	0.299365i	−0.713561	+	0.700593i	$0.752919\pi$
$522$		0			0
$523$	−9.16926	−	9.16926i	−0.400944	−	0.400944i	0.477622	−	0.878566i	$-0.341499\pi$
$523$	−9.16926	−	9.16926i	−0.400944	−	0.400944i	−0.878566	+	0.477622i	$0.841499\pi$
$524$		0			0
$525$	−15.6709	+	30.0551i	−0.683934	+	1.31171i
$526$		0			0
$527$	−2.40400	+	5.80378i	−0.104720	+	0.252817i
$528$		0			0
$529$		−	2.48672i		−	0.108118i
$530$		0			0
$531$	1.76171	+	1.76171i	0.0764515	+	0.0764515i
$532$		0			0
$533$	1.19446	+	3.43440i	0.0517379	+	0.148760i
$534$		0			0
$535$	−0.940357	−	6.12303i	−0.0406552	−	0.264721i
$536$		0			0
$537$	−46.8013	+	46.8013i	−2.01963	+	2.01963i
$538$		0			0
$539$	0.730213	+	1.76289i	0.0314525	+	0.0759330i
$540$		0			0
$541$	−12.0018	−	12.0018i	−0.515998	−	0.515998i	0.400360	−	0.916358i	$-0.368885\pi$
$541$	−12.0018	−	12.0018i	−0.515998	−	0.515998i	−0.916358	+	0.400360i	$0.868885\pi$
$542$		0			0
$543$	9.18320	−	9.18320i	0.394089	−	0.394089i
$544$		0			0
$545$	9.73992	−	39.7470i	0.417212	−	1.70257i
$546$		0			0
$547$	12.4768	+	5.16807i	0.533470	+	0.220971i	0.633122	−	0.774052i	$-0.281773\pi$
$547$	12.4768	+	5.16807i	0.533470	+	0.220971i	−0.0996520	+	0.995022i	$0.531773\pi$
$548$		0			0
$549$			58.7049i			2.50546i
$550$		0			0
$551$	24.2187			1.03175
$552$		0			0
$553$		−	41.0980i		−	1.74766i
$554$		0			0
$555$	−33.8579	+	20.5302i	−1.43719	+	0.871458i
$556$		0			0
$557$	−8.75761	+	21.1427i	−0.371072	+	0.895847i	0.622498	+	0.782622i	$0.286118\pi$
$557$	−8.75761	+	21.1427i	−0.371072	+	0.895847i	−0.993569	+	0.113225i	$0.963882\pi$
$558$		0			0
$559$	0.0641803	+	0.154945i	0.00271454	+	0.00655347i
$560$		0			0
$561$	−4.68936	+	11.3211i	−0.197985	+	0.477978i
$562$		0			0
$563$	−22.0541	+	9.13510i	−0.929468	+	0.384998i	−0.795477	−	0.605984i	$-0.792780\pi$
$563$	−22.0541	+	9.13510i	−0.929468	+	0.384998i	−0.133992	+	0.990982i	$0.542780\pi$
$564$		0			0
$565$	−35.0570	+	5.38396i	−1.47486	+	0.226505i
$566$		0			0
$567$	5.69955	−	2.36083i	0.239359	−	0.0991456i
$568$		0			0
$569$	12.5492	+	12.5492i	0.526091	+	0.526091i	0.919405	−	0.393313i	$-0.128671\pi$
$569$	12.5492	+	12.5492i	0.526091	+	0.526091i	−0.393313	+	0.919405i	$0.628671\pi$
$570$		0			0
$571$	4.25403	−	10.2701i	0.178025	−	0.429792i	−0.809527	−	0.587083i	$-0.800276\pi$
$571$	4.25403	−	10.2701i	0.178025	−	0.429792i	0.987552	+	0.157291i	$0.0502762\pi$
$572$		0			0
$573$	−21.9827	−	21.9827i	−0.918341	−	0.918341i
$574$		0			0
$575$	−10.4699	+	20.0802i	−0.436625	+	0.837401i
$576$		0			0
$577$	13.2091	+	31.8895i	0.549901	+	1.32758i	0.917553	+	0.397615i	$0.130162\pi$
$577$	13.2091	+	31.8895i	0.549901	+	1.32758i	−0.367652	+	0.929964i	$0.619838\pi$
$578$		0			0
$579$	46.1893	−	46.1893i	1.91956	−	1.91956i
$580$		0			0
$581$	15.8322	+	6.55793i	0.656832	+	0.272069i
$582$		0			0
$583$	−8.56374			−0.354674
$584$		0			0
$585$	−2.93671	−	4.84314i	−0.121418	−	0.200239i
$586$		0			0
$587$	16.3285	+	39.4204i	0.673948	+	1.62705i	0.774840	+	0.632157i	$0.217830\pi$
$587$	16.3285	+	39.4204i	0.673948	+	1.62705i	−0.100892	+	0.994897i	$0.532170\pi$
$588$		0			0
$589$	−17.0190	+	7.04951i	−0.701256	+	0.290470i
$590$		0			0
$591$	−18.7135	+	7.75137i	−0.769769	+	0.318849i
$592$		0			0
$593$	−15.4839	+	37.3814i	−0.635847	+	1.53507i	0.196317	+	0.980541i	$0.437102\pi$
$593$	−15.4839	+	37.3814i	−0.635847	+	1.53507i	−0.832164	+	0.554530i	$0.812898\pi$
$594$		0			0
$595$	−8.83829	−	6.48498i	−0.362334	−	0.265858i
$596$		0			0
$597$	−28.0684	+	28.0684i	−1.14876	+	1.14876i
$598$		0			0
$599$	−17.5398			−0.716655			−0.358328	−	0.933596i	$-0.616653\pi$
$599$	−17.5398			−0.716655			−0.358328	+	0.933596i	$0.616653\pi$
$600$		0			0
$601$	−3.91884	−	9.46091i	−0.159853	−	0.385918i	0.823578	−	0.567203i	$-0.191974\pi$
$601$	−3.91884	−	9.46091i	−0.159853	−	0.385918i	−0.983431	+	0.181285i	$0.941974\pi$
$602$		0			0
$603$	−6.98254	+	2.89226i	−0.284351	+	0.117782i
$604$		0			0
$605$	12.9106	−	1.98277i	0.524889	−	0.0806110i
$606$		0			0
$607$	32.2107			1.30739			0.653696	−	0.756757i	$-0.273218\pi$
$607$	32.2107			1.30739			0.653696	+	0.756757i	$0.273218\pi$
$608$		0			0
$609$	−26.1868	+	10.8469i	−1.06114	+	0.439540i
$610$		0			0
$611$	0.770048			0.0311528
$612$		0			0
$613$	21.5184			0.869120			0.434560	−	0.900643i	$-0.356904\pi$
$613$	21.5184			0.869120			0.434560	+	0.900643i	$0.356904\pi$
$614$		0			0
$615$	37.3804	+	11.4937i	1.50732	+	0.463470i
$616$		0			0
$617$	−34.8623			−1.40350			−0.701752	−	0.712421i	$-0.747599\pi$
$617$	−34.8623			−1.40350			−0.701752	+	0.712421i	$0.747599\pi$
$618$		0			0
$619$	3.84142			0.154400			0.0771999	−	0.997016i	$-0.475402\pi$
$619$	3.84142			0.154400			0.0771999	+	0.997016i	$0.475402\pi$
$620$		0			0
$621$	−16.6919	+	6.91403i	−0.669825	+	0.277451i
$622$		0			0
$623$	−10.5877			−0.424188
$624$		0			0
$625$	−20.4977	+	14.3124i	−0.819908	+	0.572495i
$626$		0			0
$627$	−33.1980	+	13.7511i	−1.32580	+	0.549165i
$628$		0			0
$629$	−4.90062	−	11.8311i	−0.195400	−	0.471738i
$630$		0			0
$631$	33.6465			1.33945			0.669724	−	0.742610i	$-0.266413\pi$
$631$	33.6465			1.33945			0.669724	+	0.742610i	$0.266413\pi$
$632$		0			0
$633$	−20.1534	+	20.1534i	−0.801027	+	0.801027i
$634$		0			0
$635$	−0.310161	−	2.01958i	−0.0123084	−	0.0801444i
$636$		0			0
$637$	0.182575	−	0.440774i	0.00723387	−	0.0174641i
$638$		0			0
$639$	35.5274	−	14.7159i	1.40544	−	0.582153i
$640$		0			0
$641$	−26.7063	+	11.0621i	−1.05484	+	0.436927i	−0.841616	−	0.540077i	$-0.818395\pi$
$641$	−26.7063	+	11.0621i	−1.05484	+	0.436927i	−0.213220	+	0.977004i	$0.568395\pi$
$642$		0			0
$643$	0.217989	+	0.526272i	0.00859664	+	0.0207541i	0.928120	−	0.372282i	$-0.121425\pi$
$643$	0.217989	+	0.526272i	0.00859664	+	0.0207541i	−0.919523	+	0.393036i	$0.871425\pi$
$644$		0			0
$645$	1.75192	+	0.429303i	0.0689816	+	0.0169038i
$646$		0			0
$647$	20.0557			0.788469			0.394235	−	0.919010i	$-0.371010\pi$
$647$	20.0557			0.788469			0.394235	+	0.919010i	$0.371010\pi$
$648$		0			0
$649$	−1.17205	−	0.485479i	−0.0460070	−	0.0190567i
$650$		0			0
$651$	15.2448	−	15.2448i	0.597490	−	0.597490i
$652$		0			0
$653$	−9.87402	−	23.8380i	−0.386400	−	0.932853i	−0.990696	−	0.136093i	$-0.956545\pi$
$653$	−9.87402	−	23.8380i	−0.386400	−	0.932853i	0.604296	−	0.796760i	$-0.293455\pi$
$654$		0			0
$655$	16.9178	−	2.59819i	0.661034	−	0.101520i
$656$		0			0
$657$	−20.8391	−	20.8391i	−0.813011	−	0.813011i
$658$		0			0
$659$	−6.23462	+	15.0517i	−0.242866	+	0.586331i	−0.997565	−	0.0697400i	$-0.977783\pi$
$659$	−6.23462	+	15.0517i	−0.242866	+	0.586331i	0.754699	+	0.656071i	$0.227783\pi$
$660$		0			0
$661$	−6.55557	−	6.55557i	−0.254982	−	0.254982i	0.568027	−	0.823010i	$-0.307707\pi$
$661$	−6.55557	−	6.55557i	−0.254982	−	0.254982i	−0.823010	+	0.568027i	$0.807707\pi$
$662$		0			0
$663$	2.83061	−	1.17248i	0.109932	−	0.0455352i
$664$		0			0
$665$	−4.87963	−	31.7731i	−0.189224	−	1.23211i
$666$		0			0
$667$	−17.4957	+	7.24697i	−0.677437	+	0.280604i
$668$		0			0
$669$	−28.4070	+	68.5807i	−1.09828	+	2.65148i
$670$		0			0
$671$	−11.4392	−	27.6167i	−0.441606	−	1.06613i
$672$		0			0
$673$	10.1729	−	24.5595i	0.392135	−	0.946698i	−0.597339	−	0.801989i	$-0.703775\pi$
$673$	10.1729	−	24.5595i	0.392135	−	0.946698i	0.989474	−	0.144709i	$-0.0462248\pi$
$674$		0			0
$675$	−19.8684	−	1.75146i	−0.764736	−	0.0674139i
$676$		0			0
$677$			33.3330i			1.28109i	0.767921	+	0.640545i	$0.221291\pi$
$677$			33.3330i			1.28109i	−0.767921	+	0.640545i	$0.778709\pi$
$678$		0			0
$679$	33.6353			1.29080
$680$		0			0
$681$			35.9982i			1.37945i
$682$		0			0
$683$	14.6727	+	6.07764i	0.561436	+	0.232554i	0.645309	−	0.763922i	$-0.276729\pi$
$683$	14.6727	+	6.07764i	0.561436	+	0.232554i	−0.0838724	+	0.996477i	$0.526729\pi$
$684$		0			0
$685$	1.38541	−	0.840061i	0.0529337	−	0.0320971i
$686$		0			0
$687$	−42.7661	+	42.7661i	−1.63163	+	1.63163i
$688$		0			0
$689$	1.51405	+	1.51405i	0.0576806	+	0.0576806i
$690$		0			0
$691$	7.83159	+	18.9071i	0.297928	+	0.719261i	0.999975	+	0.00713041i	$0.00226970\pi$
$691$	7.83159	+	18.9071i	0.297928	+	0.719261i	−0.702047	+	0.712131i	$0.747730\pi$
$692$		0			0
$693$	17.7793	−	17.7793i	0.675378	−	0.675378i
$694$		0			0
$695$	−9.08924	−	6.66912i	−0.344775	−	0.252974i
$696$		0			0
$697$	−5.50928	+	11.3850i	−0.208679	+	0.431238i
$698$		0			0
$699$	−9.26828	−	9.26828i	−0.350559	−	0.350559i
$700$		0			0
$701$			1.26900i			0.0479295i	0.999713	+	0.0239647i	$0.00762894\pi$
$701$			1.26900i			0.0479295i	−0.999713	+	0.0239647i	$0.992371\pi$
$702$		0			0
$703$	14.3706	−	34.6937i	0.541997	−	1.30850i
$704$		0			0
$705$	4.89939	−	6.67730i	0.184522	−	0.251482i
$706$		0			0
$707$	6.45749	+	6.45749i	0.242859	+	0.242859i
$708$		0			0
$709$	17.7782	+	7.36397i	0.667674	+	0.276560i	0.690664	−	0.723176i	$-0.257318\pi$
$709$	17.7782	+	7.36397i	0.667674	+	0.276560i	−0.0229895	+	0.999736i	$0.507318\pi$
$710$		0			0
$711$	68.2386	−	28.2654i	2.55915	−	1.06003i
$712$		0			0
$713$	10.1852	−	10.1852i	0.381439	−	0.381439i
$714$		0			0
$715$	2.32526	+	1.70613i	0.0869597	+	0.0638056i
$716$		0			0
$717$	−30.0447			−1.12204
$718$		0			0
$719$	8.58842	−	3.55744i	0.320294	−	0.132670i	−0.216743	−	0.976229i	$-0.569543\pi$
$719$	8.58842	−	3.55744i	0.320294	−	0.132670i	0.537037	+	0.843558i	$0.319543\pi$
$720$		0			0
$721$	−1.09758	−	2.64980i	−0.0408761	−	0.0986837i
$722$		0			0
$723$	−9.85846	+	23.8004i	−0.366640	+	0.885147i
$724$		0			0
$725$	−20.8251	−	1.83580i	−0.773427	−	0.0681801i
$726$		0			0
$727$	−9.98604	−	24.1084i	−0.370362	−	0.894132i	−0.993689	−	0.112171i	$-0.964219\pi$
$727$	−9.98604	−	24.1084i	−0.370362	−	0.894132i	0.623327	−	0.781961i	$-0.285781\pi$
$728$		0			0
$729$	30.9532	+	30.9532i	1.14641	+	1.14641i
$730$		0			0
$731$	−0.223242	+	0.538953i	−0.00825689	+	0.0199339i
$732$		0			0
$733$			27.0851i			1.00041i	0.865906	+	0.500206i	$0.166743\pi$
$733$			27.0851i			1.00041i	−0.865906	+	0.500206i	$0.833257\pi$
$734$		0			0
$735$	−2.66046	−	4.38756i	−0.0981325	−	0.161838i
$736$		0			0
$737$	2.72123	−	2.72123i	0.100238	−	0.100238i
$738$		0			0
$739$		−	19.9991i		−	0.735680i	−0.929889	−	0.367840i	$-0.880097\pi$
$739$		−	19.9991i		−	0.735680i	0.929889	−	0.367840i	$-0.119903\pi$
$740$		0			0
$741$	8.30049	+	3.43817i	0.304926	+	0.126304i
$742$		0			0
$743$	24.9057			0.913702			0.456851	−	0.889543i	$-0.348977\pi$
$743$	24.9057			0.913702			0.456851	+	0.889543i	$0.348977\pi$
$744$		0			0
$745$	−46.0472	−	11.2838i	−1.68704	−	0.413405i
$746$		0			0
$747$			30.7979i			1.12684i
$748$		0			0
$749$	−6.35250	−	2.63129i	−0.232115	−	0.0961452i
$750$		0			0
$751$	0.790995	+	0.327641i	0.0288638	+	0.0119558i	0.397069	−	0.917789i	$-0.370027\pi$
$751$	0.790995	+	0.327641i	0.0288638	+	0.0119558i	−0.368205	+	0.929745i	$0.620027\pi$
$752$		0			0
$753$	24.3935	+	10.1041i	0.888948	+	0.368214i
$754$		0			0
$755$	16.1453	+	26.6264i	0.587586	+	0.969032i
$756$		0			0
$757$	−18.3811	−	7.61370i	−0.668073	−	0.276725i	0.0227584	−	0.999741i	$-0.492755\pi$
$757$	−18.3811	−	7.61370i	−0.668073	−	0.276725i	−0.690831	+	0.723016i	$0.742755\pi$
$758$		0			0
$759$	19.8677	−	19.8677i	0.721153	−	0.721153i
$760$		0			0
$761$			33.5780i			1.21720i	0.793476	+	0.608601i	$0.208269\pi$
$761$			33.5780i			1.21720i	−0.793476	+	0.608601i	$0.791731\pi$
$762$		0			0
$763$	−32.1183	−	32.1183i	−1.16276	−	1.16276i
$764$		0			0
$765$	4.68901	−	19.1351i	0.169532	−	0.691830i
$766$		0			0
$767$	0.121384	+	0.293047i	0.00438293	+	0.0105813i
$768$		0			0
$769$	6.48872			0.233989			0.116995	−	0.993133i	$-0.462674\pi$
$769$	6.48872			0.233989			0.116995	+	0.993133i	$0.462674\pi$
$770$		0			0
$771$	9.04746	−	9.04746i	0.325836	−	0.325836i
$772$		0			0
$773$	−19.7552	−	8.18288i	−0.710546	−	0.294318i	−0.00201531	−	0.999998i	$-0.500641\pi$
$773$	−19.7552	−	8.18288i	−0.710546	−	0.294318i	−0.708530	+	0.705680i	$0.750641\pi$
$774$		0			0
$775$	15.1687	−	4.77167i	0.544875	−	0.171403i
$776$		0			0
$777$			43.9493i			1.57667i
$778$		0			0
$779$	−35.0306	+	12.1834i	−1.25510	+	0.436517i
$780$		0			0
$781$	−13.8457	+	13.8457i	−0.495439	+	0.495439i
$782$		0			0
$783$	−11.7939	−	11.7939i	−0.421480	−	0.421480i
$784$		0			0
$785$	12.8510	−	52.4426i	0.458670	−	1.87176i
$786$		0			0
$787$		−	48.8135i		−	1.74001i	−0.493040	−	0.870007i	$-0.664114\pi$
$787$		−	48.8135i		−	1.74001i	0.493040	−	0.870007i	$-0.335886\pi$
$788$		0			0
$789$		−	41.5421i		−	1.47894i
$790$		0			0
$791$	−15.0653	+	36.3708i	−0.535660	+	1.29320i
$792$		0			0
$793$	−2.86014	+	6.90499i	−0.101567	+	0.245204i
$794$		0			0
$795$	22.7618	−	3.49569i	0.807277	−	0.123979i
$796$		0			0
$797$	1.84186	+	1.84186i	0.0652419	+	0.0652419i	0.738975	−	0.673733i	$-0.235310\pi$
$797$	1.84186	+	1.84186i	0.0652419	+	0.0652419i	−0.673733	+	0.738975i	$0.735310\pi$
$798$		0			0
$799$	1.89398	+	1.89398i	0.0670044	+	0.0670044i
$800$		0			0
$801$	−7.28177	−	17.5797i	−0.257289	−	0.621150i
$802$		0			0
$803$	13.8641	+	5.74270i	0.489254	+	0.202656i
$804$		0			0
$805$	13.0326	+	21.4930i	0.459337	+	0.757528i
$806$		0			0
$807$	−54.7995	+	22.6987i	−1.92903	+	0.799032i
$808$		0			0
$809$	12.7020	−	30.6653i	0.446578	−	1.07813i	−0.527018	−	0.849854i	$-0.676690\pi$
$809$	12.7020	−	30.6653i	0.446578	−	1.07813i	0.973596	−	0.228280i	$-0.0733100\pi$
$810$		0			0
$811$	−8.24669	+	8.24669i	−0.289581	+	0.289581i	−0.836914	−	0.547334i	$-0.815643\pi$
$811$	−8.24669	+	8.24669i	−0.289581	+	0.289581i	0.547334	+	0.836914i	$0.315643\pi$
$812$		0			0
$813$	21.0120	+	50.7273i	0.736921	+	1.77909i
$814$		0			0
$815$	36.3893	−	5.58857i	1.27466	−	0.195759i
$816$		0			0
$817$	−1.58043	+	0.654635i	−0.0552922	+	0.0229028i
$818$		0			0
$819$	−6.28666			−0.219674
$820$		0			0
$821$	25.6132			0.893906			0.446953	−	0.894557i	$-0.352509\pi$
$821$	25.6132			0.893906			0.446953	+	0.894557i	$0.352509\pi$
$822$		0			0
$823$	−8.95330	+	3.70858i	−0.312092	+	0.129273i	−0.533232	−	0.845969i	$-0.679023\pi$
$823$	−8.95330	+	3.70858i	−0.312092	+	0.129273i	0.221139	+	0.975242i	$0.429023\pi$
$824$		0			0
$825$	29.5887	−	9.30782i	1.03015	−	0.324057i
$826$		0			0
$827$	−0.670040	−	1.61762i	−0.0232996	−	0.0562501i	0.911802	−	0.410631i	$-0.134692\pi$
$827$	−0.670040	−	1.61762i	−0.0232996	−	0.0562501i	−0.935101	+	0.354381i	$0.884692\pi$
$828$		0			0
$829$	2.91568	−	2.91568i	0.101266	−	0.101266i	−0.654659	−	0.755924i	$-0.727188\pi$
$829$	2.91568	−	2.91568i	0.101266	−	0.101266i	0.755924	+	0.654659i	$0.227188\pi$
$830$		0			0
$831$	−21.9329	+	52.9508i	−0.760845	+	1.83684i
$832$		0			0
$833$	1.53317	−	0.635060i	0.0531212	−	0.0220035i
$834$		0			0
$835$	8.64341	+	2.11805i	0.299118	+	0.0732982i
$836$		0			0
$837$	11.7208	+	4.85491i	0.405130	+	0.167810i
$838$		0			0
$839$	11.3314	+	27.3564i	0.391203	+	0.944448i	0.989678	+	0.143307i	$0.0457735\pi$
$839$	11.3314	+	27.3564i	0.391203	+	0.944448i	−0.598475	+	0.801141i	$0.704226\pi$
$840$		0			0
$841$	8.14426	+	8.14426i	0.280837	+	0.280837i
$842$		0			0
$843$	−58.6758	−	58.6758i	−2.02090	−	2.02090i
$844$		0			0
$845$	4.30312	+	28.0193i	0.148032	+	0.963893i
$846$		0			0
$847$	5.54815	−	13.3944i	0.190637	−	0.460237i
$848$		0			0
$849$	−0.900888	+	2.17494i	−0.0309184	+	0.0746436i
$850$		0			0
$851$			29.3630i			1.00655i
$852$		0			0
$853$		−	23.1225i		−	0.791701i	−0.918315	−	0.395850i	$-0.870450\pi$
$853$		−	23.1225i		−	0.791701i	0.918315	−	0.395850i	$-0.129550\pi$
$854$		0			0
$855$	49.3997	−	29.9542i	1.68944	−	1.02441i
$856$		0			0
$857$	21.5664	+	21.5664i	0.736695	+	0.736695i	0.971937	−	0.235242i	$-0.0755883\pi$
$857$	21.5664	+	21.5664i	0.736695	+	0.736695i	−0.235242	+	0.971937i	$0.575588\pi$
$858$		0			0
$859$	17.0661	−	17.0661i	0.582286	−	0.582286i	−0.353245	−	0.935531i	$-0.614922\pi$
$859$	17.0661	−	17.0661i	0.582286	−	0.582286i	0.935531	+	0.353245i	$0.114922\pi$
$860$		0			0
$861$	32.4208	−	28.8629i	1.10490	−	0.983645i
$862$		0			0
$863$		−	42.3869i		−	1.44287i	−0.692484	−	0.721433i	$-0.743484\pi$
$863$		−	42.3869i		−	1.44287i	0.692484	−	0.721433i	$-0.256516\pi$
$864$		0			0
$865$	10.2256	−	13.9363i	0.347681	−	0.473850i
$866$		0			0
$867$	−33.0531	−	13.6911i	−1.12254	−	0.464973i
$868$		0			0
$869$	−26.5939	+	26.5939i	−0.902137	+	0.902137i
$870$		0			0
$871$	−0.962214			−0.0326034
$872$		0			0
$873$	23.1328	+	55.8476i	0.782928	+	1.89016i
$874$		0			0
$875$	1.78745	+	27.6909i	0.0604269	+	0.936125i
$876$		0			0
$877$	37.2642	+	37.2642i	1.25832	+	1.25832i	0.951893	+	0.306432i	$0.0991351\pi$
$877$	37.2642	+	37.2642i	1.25832	+	1.25832i	0.306432	+	0.951893i	$0.400865\pi$
$878$		0			0
$879$		−	72.9453i		−	2.46038i
$880$		0			0
$881$	−5.85422	+	5.85422i	−0.197234	+	0.197234i	−0.798813	−	0.601579i	$-0.794538\pi$
$881$	−5.85422	+	5.85422i	−0.197234	+	0.197234i	0.601579	+	0.798813i	$0.294538\pi$
$882$		0			0
$883$	−2.27217	−	0.941166i	−0.0764648	−	0.0316727i	0.344123	−	0.938924i	$-0.388176\pi$
$883$	−2.27217	−	0.941166i	−0.0764648	−	0.0316727i	−0.420588	+	0.907252i	$0.638176\pi$
$884$		0			0
$885$	3.31340	+	0.811941i	0.111379	+	0.0272931i
$886$		0			0
$887$	−38.8628	−	16.0975i	−1.30488	−	0.540501i	−0.381497	−	0.924370i	$-0.624591\pi$
$887$	−38.8628	−	16.0975i	−1.30488	−	0.540501i	−0.923387	+	0.383870i	$0.874591\pi$
$888$		0			0
$889$	−2.09526	−	0.867886i	−0.0702728	−	0.0291080i
$890$		0			0
$891$	−5.21576	−	2.16044i	−0.174735	−	0.0723774i
$892$		0			0
$893$			7.85443i			0.262839i
$894$		0			0
$895$	−12.8962	+	52.6274i	−0.431074	+	1.75914i
$896$		0			0
$897$	−7.02513			−0.234562
$898$		0			0
$899$	12.2852	+	5.08869i	0.409734	+	0.169717i
$900$		0			0
$901$			7.44781i			0.248122i
$902$		0			0
$903$	1.41567	−	1.41567i	0.0471105	−	0.0471105i
$904$		0			0
$905$	2.53046	−	10.3264i	0.0841153	−	0.343261i
$906$		0			0
$907$			11.6665i			0.387381i	0.981063	+	0.193691i	$0.0620458\pi$
$907$			11.6665i			0.387381i	−0.981063	+	0.193691i	$0.937954\pi$
$908$		0			0
$909$	−6.28077	+	15.1631i	−0.208320	+	0.502929i
$910$		0			0
$911$	−14.7560	−	14.7560i	−0.488889	−	0.488889i	0.419067	−	0.907956i	$-0.362357\pi$
$911$	−14.7560	−	14.7560i	−0.488889	−	0.488889i	−0.907956	+	0.419067i	$0.862357\pi$
$912$		0			0
$913$	−6.00128	−	14.4884i	−0.198613	−	0.479495i
$914$		0			0
$915$	41.6777	+	68.7338i	1.37782	+	2.27227i
$916$		0			0
$917$	7.27021	−	17.5518i	0.240083	−	0.579613i
$918$		0			0
$919$	8.87243	+	21.4199i	0.292675	+	0.706579i	1.00000		0.000309256i	$-9.84392e-5\pi$
$919$	8.87243	+	21.4199i	0.292675	+	0.706579i	−0.707325	+	0.706888i	$0.750098\pi$
$920$		0			0
$921$	26.4060	−	10.9377i	0.870108	−	0.360410i
$922$		0			0
$923$	4.89578			0.161147
$924$		0			0
$925$	−14.9868	+	28.7431i	−0.492763	+	0.945066i
$926$		0			0
$927$	3.64483	−	3.64483i	0.119712	−	0.119712i
$928$		0			0
$929$	46.8801	−	19.4184i	1.53809	−	0.637097i	0.556974	−	0.830530i	$-0.311962\pi$
$929$	46.8801	−	19.4184i	1.53809	−	0.637097i	0.981113	+	0.193434i	$0.0619624\pi$
$930$		0			0
$931$	4.49587	+	1.86225i	0.147346	+	0.0610328i
$932$		0			0
$933$	−51.1114	−	51.1114i	−1.67331	−	1.67331i
$934$		0			0
$935$	1.52279	+	9.91547i	0.0498006	+	0.324271i
$936$		0			0
$937$	17.4772	−	42.1938i	0.570957	−	1.37841i	−0.329785	−	0.944056i	$-0.606976\pi$
$937$	17.4772	−	42.1938i	0.570957	−	1.37841i	0.900742	−	0.434355i	$-0.143024\pi$
$938$		0			0
$939$			10.3925i			0.339146i
$940$		0			0
$941$	5.12402	+	5.12402i	0.167038	+	0.167038i	0.785676	−	0.618638i	$-0.212315\pi$
$941$	5.12402	+	5.12402i	0.167038	+	0.167038i	−0.618638	+	0.785676i	$0.712315\pi$
$942$		0			0
$943$	21.6607	−	19.2836i	0.705370	−	0.627961i
$944$		0			0
$945$	−13.0965	+	17.8490i	−0.426029	+	0.580629i
$946$		0			0
$947$	−42.0766	+	42.0766i	−1.36731	+	1.36731i	−0.503047	+	0.864259i	$0.667788\pi$
$947$	−42.0766	+	42.0766i	−1.36731	+	1.36731i	−0.864259	+	0.503047i	$0.832212\pi$
$948$		0			0
$949$	−1.43584	−	3.46644i	−0.0466095	−	0.112525i
$950$		0			0
$951$	−38.2054	−	38.2054i	−1.23889	−	1.23889i
$952$		0			0
$953$	22.4782	−	22.4782i	0.728141	−	0.728141i	−0.242108	−	0.970249i	$-0.577839\pi$
$953$	22.4782	−	22.4782i	0.728141	−	0.728141i	0.970249	+	0.242108i	$0.0778389\pi$
$954$		0			0
$955$	−24.7193	−	6.05741i	−0.799897	−	0.196013i
$956$		0			0
$957$	23.9640	+	9.92623i	0.774647	+	0.320869i
$958$		0			0
$959$		−	1.79833i		−	0.0580712i
$960$		0			0
$961$	20.8857			0.673733
$962$		0			0
$963$		−	12.3573i		−	0.398208i
$964$		0			0
$965$	12.7276	−	51.9392i	0.409716	−	1.67198i
$966$		0			0
$967$	−17.7311	+	42.8066i	−0.570192	+	1.37657i	0.331199	+	0.943561i	$0.392547\pi$
$967$	−17.7311	+	42.8066i	−0.570192	+	1.37657i	−0.901391	+	0.433005i	$0.857453\pi$
$968$		0			0
$969$	11.9592	+	28.8720i	0.384185	+	0.927504i
$970$		0			0
$971$	3.93390	−	9.49727i	0.126245	−	0.304782i	−0.848102	−	0.529833i	$-0.822255\pi$
$971$	3.93390	−	9.49727i	0.126245	−	0.304782i	0.974347	+	0.225051i	$0.0722548\pi$
$972$		0			0
$973$	−11.5604	+	4.78849i	−0.370611	+	0.153512i
$974$		0			0
$975$	−6.87680	−	3.58560i	−0.220234	−	0.114831i
$976$		0			0
$977$	4.48618	−	1.85824i	0.143526	−	0.0594502i	−0.309764	−	0.950813i	$-0.600250\pi$
$977$	4.48618	−	1.85824i	0.143526	−	0.0594502i	0.453290	+	0.891363i	$0.350250\pi$
$978$		0			0
$979$	6.85117	+	6.85117i	0.218964	+	0.218964i
$980$		0			0
$981$	31.2394	−	75.4185i	0.997396	−	2.40793i
$982$		0			0
$983$	−8.40861	−	8.40861i	−0.268193	−	0.268193i	0.560179	−	0.828372i	$-0.310732\pi$
$983$	−8.40861	−	8.40861i	−0.268193	−	0.268193i	−0.828372	+	0.560179i	$0.810732\pi$
$984$		0			0
$985$	−9.80960	+	13.3694i	−0.312560	+	0.425983i
$986$		0			0
$987$	−3.51781	−	8.49274i	−0.111973	−	0.270327i
$988$		0			0
$989$	0.945824	−	0.945824i	0.0300755	−	0.0300755i
$990$		0			0
$991$	−30.8151	−	12.7640i	−0.978874	−	0.405463i	−0.164866	−	0.986316i	$-0.552719\pi$
$991$	−30.8151	−	12.7640i	−0.978874	−	0.405463i	−0.814008	+	0.580853i	$0.802719\pi$
$992$		0			0
$993$	−44.3990			−1.40896
$994$		0			0
$995$	−7.73434	+	31.5625i	−0.245195	+	1.00060i
$996$		0			0
$997$	−2.13396	−	5.15183i	−0.0675832	−	0.163160i	0.886479	−	0.462769i	$-0.153144\pi$
$997$	−2.13396	−	5.15183i	−0.0675832	−	0.163160i	−0.954062	+	0.299608i	$0.903144\pi$
$998$		0			0
$999$	−23.8931	+	9.89685i	−0.755945	+	0.313123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.817.20	yes	84
5.3	odd	4		820.2.y.a.653.20	yes	84
41.27	odd	8		820.2.y.a.437.20	yes	84
205.68	even	8	inner	820.2.x.a.273.20	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.20	✓	84	205.68	even	8	inner
820.2.x.a.817.20	yes	84	1.1	even	1	trivial
820.2.y.a.437.20	yes	84	41.27	odd	8
820.2.y.a.653.20	yes	84	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.52347 - 1.04526i) q^{3} +(1.32280 - 1.80283i) q^{5} +(-0.949785 - 2.29298i) q^{7} +(3.15402 - 3.15402i) q^{9} +(-0.869165 + 2.09835i) q^{11} +(0.524650 - 0.217317i) q^{13} +(1.45364 - 5.93205i) q^{15} +(1.82492 + 0.755905i) q^{17} +(2.21662 + 5.35139i) q^{19} +(-4.79351 - 4.79351i) q^{21} +(-3.20260 - 3.20260i) q^{23} +(-1.50038 - 4.76958i) q^{25} +(1.52656 - 3.68544i) q^{27} +(1.60007 - 3.86291i) q^{29} +3.18030i q^{31} +6.20363i q^{33} +(-5.39024 - 1.32087i) q^{35} +(-4.58425 - 4.58425i) q^{37} +(1.09679 - 1.09679i) q^{39} +(-0.371118 + 6.39236i) q^{41} +0.295330i q^{43} +(-1.51401 - 9.85832i) q^{45} +(1.25279 + 0.518923i) q^{47} +(0.594062 - 0.594062i) q^{49} +5.39524 q^{51} +(1.44291 + 3.48350i) q^{53} +(2.63323 + 4.34266i) q^{55} +(11.1871 + 11.1871i) q^{57} +0.558558i q^{59} +(-9.30634 + 9.30634i) q^{61} +(-10.2278 - 4.23648i) q^{63} +(0.302223 - 1.23332i) q^{65} +(-1.56543 - 0.648422i) q^{67} +(-11.4292 - 4.73413i) q^{69} +(7.96495 + 3.29919i) q^{71} -6.60714i q^{73} +(-8.77160 - 10.4676i) q^{75} +5.63701 q^{77} +(15.2985 + 6.33686i) q^{79} +2.48565i q^{81} +(-4.88232 + 4.88232i) q^{83} +(3.77677 - 2.29010i) q^{85} -11.4204i q^{87} +(1.63251 - 3.94123i) q^{89} +(-0.996609 - 0.996609i) q^{91} +(3.32422 + 8.02539i) q^{93} +(12.5798 + 3.08265i) q^{95} +(-5.18619 + 12.5206i) q^{97} +(3.87688 + 9.35962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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