LMFDB - Embedded newform 820.2.y.a.653.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] 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, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (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			653.20
Character	$\chi$	$=$	820.653
Dual form			820.2.y.a.437.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04526 + 2.52347i) q^{3} +(-1.80283 + 1.32280i) q^{5} +(-2.29298 + 0.949785i) q^{7} +(-3.15402 + 3.15402i) q^{9} +(-0.869165 + 2.09835i) q^{11} +(0.217317 + 0.524650i) q^{13} +(-5.22247 - 3.16672i) q^{15} +(0.755905 - 1.82492i) q^{17} +(-2.21662 - 5.35139i) q^{19} +(-4.79351 - 4.79351i) q^{21} +(3.20260 - 3.20260i) q^{23} +(1.50038 - 4.76958i) q^{25} +(-3.68544 - 1.52656i) q^{27} +(-1.60007 + 3.86291i) q^{29} +3.18030i q^{31} -6.20363 q^{33} +(2.87748 - 4.74547i) q^{35} +(-4.58425 + 4.58425i) q^{37} +(-1.09679 + 1.09679i) q^{39} +(-0.371118 + 6.39236i) q^{41} -0.295330 q^{43} +(1.51401 - 9.85832i) q^{45} +(0.518923 - 1.25279i) q^{47} +(-0.594062 + 0.594062i) q^{49} +5.39524 q^{51} +(-3.48350 + 1.44291i) q^{53} +(-1.20875 - 4.93270i) q^{55} +(11.1871 - 11.1871i) q^{57} -0.558558i q^{59} +(-9.30634 + 9.30634i) q^{61} +(4.23648 - 10.2278i) q^{63} +(-1.08579 - 0.658386i) q^{65} +(-0.648422 + 1.56543i) q^{67} +(11.4292 + 4.73413i) q^{69} +(7.96495 + 3.29919i) q^{71} +6.60714 q^{73} +(13.6042 - 1.19925i) q^{75} -5.63701i q^{77} +(-15.2985 - 6.33686i) q^{79} +2.48565i q^{81} +(-4.88232 - 4.88232i) q^{83} +(1.05124 + 4.28993i) q^{85} -11.4204 q^{87} +(-1.63251 + 3.94123i) q^{89} +(-0.996609 - 0.996609i) q^{91} +(-8.02539 + 3.32422i) q^{93} +(11.0750 + 6.71549i) q^{95} +(12.5206 + 5.18619i) q^{97} +(-3.87688 - 9.35962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.04526	+	2.52347i	0.603479	+	1.45693i	0.869978	+	0.493091i	$0.164133\pi$
$3$	1.04526	+	2.52347i	0.603479	+	1.45693i	−0.266499	+	0.963835i	$0.585867\pi$
$4$		0			0
$5$	−1.80283	+	1.32280i	−0.806250	+	0.591576i
$5$	−1.80283	+	1.32280i	−0.806250	+	0.591576i
$6$		0			0
$7$	−2.29298	+	0.949785i	−0.866667	+	0.358985i	−0.771311	−	0.636458i	$-0.780399\pi$
$7$	−2.29298	+	0.949785i	−0.866667	+	0.358985i	−0.0953554	+	0.995443i	$0.530399\pi$
$8$		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
$13$	0.217317	+	0.524650i	0.0602729	+	0.145512i	0.951147	−	0.308739i	$-0.0999070\pi$
$13$	0.217317	+	0.524650i	0.0602729	+	0.145512i	−0.890874	+	0.454251i	$0.849907\pi$
$14$		0			0
$15$	−5.22247	−	3.16672i	−1.34844	−	0.817643i
$16$		0			0
$17$	0.755905	−	1.82492i	0.183334	−	0.442607i	−0.805316	−	0.592846i	$-0.798004\pi$
$17$	0.755905	−	1.82492i	0.183334	−	0.442607i	0.988650	+	0.150239i	$0.0480042\pi$
$18$		0			0
$19$	−2.21662	−	5.35139i	−0.508527	−	1.22769i	−0.944731	−	0.327846i	$-0.893677\pi$
$19$	−2.21662	−	5.35139i	−0.508527	−	1.22769i	0.436204	−	0.899848i	$-0.356323\pi$
$20$		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	$-0.593461\pi$
$23$	3.20260	−	3.20260i	0.667788	−	0.667788i	0.957204	+	0.289415i	$0.0934609\pi$
$24$		0			0
$25$	1.50038	−	4.76958i	0.300077	−	0.953915i
$26$		0			0
$27$	−3.68544	−	1.52656i	−0.709263	−	0.293787i
$28$		0			0
$29$	−1.60007	+	3.86291i	−0.297125	+	0.717324i	0.702857	+	0.711331i	$0.251907\pi$
$29$	−1.60007	+	3.86291i	−0.297125	+	0.717324i	−0.999982	+	0.00599253i	$0.998093\pi$
$30$		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
$33$	−6.20363			−1.07991
$34$		0			0
$35$	2.87748	−	4.74547i	0.486383	−	0.802130i
$36$		0			0
$37$	−4.58425	+	4.58425i	−0.753646	+	0.753646i	−0.975158	−	0.221512i	$-0.928901\pi$
$37$	−4.58425	+	4.58425i	−0.753646	+	0.753646i	0.221512	+	0.975158i	$0.428901\pi$
$38$		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
$43$	−0.295330			−0.0450374			−0.0225187	−	0.999746i	$-0.507169\pi$
$43$	−0.295330			−0.0450374			−0.0225187	+	0.999746i	$0.507169\pi$
$44$		0			0
$45$	1.51401	−	9.85832i	0.225696	−	1.46959i
$46$		0			0
$47$	0.518923	−	1.25279i	0.0756928	−	0.182738i	−0.881504	−	0.472177i	$-0.843468\pi$
$47$	0.518923	−	1.25279i	0.0756928	−	0.182738i	0.957197	+	0.289438i	$0.0934685\pi$
$48$		0			0
$49$	−0.594062	+	0.594062i	−0.0848661	+	0.0848661i
$50$		0			0
$51$	5.39524			0.755485
$52$		0			0
$53$	−3.48350	+	1.44291i	−0.478496	+	0.198199i	−0.608877	−	0.793265i	$-0.708380\pi$
$53$	−3.48350	+	1.44291i	−0.478496	+	0.198199i	0.130382	+	0.991464i	$0.458380\pi$
$54$		0			0
$55$	−1.20875	−	4.93270i	−0.162988	−	0.665125i
$56$		0			0
$57$	11.1871	−	11.1871i	1.48177	−	1.48177i
$58$		0			0
$59$		−	0.558558i		−	0.0727181i	−0.999339	−	0.0363590i	$-0.988424\pi$
$59$		−	0.558558i		−	0.0727181i	0.999339	−	0.0363590i	$-0.0115760\pi$
$60$		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
$63$	4.23648	−	10.2278i	0.533747	−	1.28858i
$64$		0			0
$65$	−1.08579	−	0.658386i	−0.134676	−	0.0816627i
$66$		0			0
$67$	−0.648422	+	1.56543i	−0.0792173	+	0.191247i	−0.958526	−	0.285004i	$-0.908005\pi$
$67$	−0.648422	+	1.56543i	−0.0792173	+	0.191247i	0.879309	+	0.476252i	$0.158005\pi$
$68$		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
$73$	6.60714			0.773308			0.386654	−	0.922225i	$-0.373631\pi$
$73$	6.60714			0.773308			0.386654	+	0.922225i	$0.373631\pi$
$74$		0			0
$75$	13.6042	−	1.19925i	1.57087	−	0.138478i
$76$		0			0
$77$		−	5.63701i		−	0.642396i
$78$		0			0
$79$	−15.2985	−	6.33686i	−1.72122	−	0.712953i	−0.999791	−	0.0204657i	$-0.993485\pi$
$79$	−15.2985	−	6.33686i	−1.72122	−	0.712953i	−0.721430	−	0.692487i	$-0.756515\pi$
$80$		0			0
$81$			2.48565i			0.276183i
$82$		0			0
$83$	−4.88232	−	4.88232i	−0.535905	−	0.535905i	0.386419	−	0.922323i	$-0.373712\pi$
$83$	−4.88232	−	4.88232i	−0.535905	−	0.535905i	−0.922323	+	0.386419i	$0.873712\pi$
$84$		0			0
$85$	1.05124	+	4.28993i	0.114023	+	0.465308i
$86$		0			0
$87$	−11.4204			−1.22440
$88$		0			0
$89$	−1.63251	+	3.94123i	−0.173046	+	0.417770i	−0.986479	−	0.163889i	$-0.947596\pi$
$89$	−1.63251	+	3.94123i	−0.173046	+	0.417770i	0.813433	+	0.581659i	$0.197596\pi$
$90$		0			0
$91$	−0.996609	−	0.996609i	−0.104473	−	0.104473i
$92$		0			0
$93$	−8.02539	+	3.32422i	−0.832194	+	0.344706i
$94$		0			0
$95$	11.0750	+	6.71549i	1.13627	+	0.688995i
$96$		0			0
$97$	12.5206	+	5.18619i	1.27127	+	0.526578i	0.913351	−	0.407174i	$-0.133486\pi$
$97$	12.5206	+	5.18619i	1.27127	+	0.526578i	0.357921	+	0.933752i	$0.383486\pi$
$98$		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
$103$			1.15561i			0.113866i	0.998378	+	0.0569329i	$0.0181321\pi$
$103$			1.15561i			0.113866i	−0.998378	+	0.0569329i	$0.981868\pi$
$104$		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	$-0.292754\pi$
$107$	−1.95897	−	1.95897i	−0.189381	−	0.189381i	−0.795428	+	0.606047i	$0.792754\pi$
$108$		0			0
$109$	−16.9082	+	7.00361i	−1.61951	+	0.670824i	−0.993999	−	0.109389i	$-0.965111\pi$
$109$	−16.9082	+	7.00361i	−1.61951	+	0.670824i	−0.625514	+	0.780213i	$0.715111\pi$
$110$		0			0
$111$	−16.3599	−	6.77651i	−1.55282	−	0.643198i
$112$		0			0
$113$	11.2160	−	11.2160i	1.05511	−	1.05511i	0.0567209	−	0.998390i	$-0.481935\pi$
$113$	11.2160	−	11.2160i	1.05511	−	1.05511i	0.998390	−	0.0567209i	$-0.0180645\pi$
$114$		0			0
$115$	−1.53733	+	10.0101i	−0.143357	+	0.933451i
$116$		0			0
$117$	−2.34018	−	0.969335i	−0.216350	−	0.0896150i
$118$		0			0
$119$			4.90245i			0.449407i
$120$		0			0
$121$	4.13055	+	4.13055i	0.375504	+	0.375504i
$122$		0			0
$123$	−16.5188	+	5.74515i	−1.48945	+	0.518022i
$124$		0			0
$125$	3.60427	+	10.5834i	0.322376	+	0.946612i
$126$		0			0
$127$	−0.646133	−	0.646133i	−0.0573351	−	0.0573351i	0.677858	−	0.735193i	$-0.262908\pi$
$127$	−0.646133	−	0.646133i	−0.0573351	−	0.0573351i	−0.735193	+	0.677858i	$0.762908\pi$
$128$		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
$135$	8.66356	−	2.12299i	0.745640	−	0.182718i
$136$		0			0
$137$	0.277283	−	0.669422i	0.0236899	−	0.0571925i	−0.911592	−	0.411096i	$-0.865146\pi$
$137$	0.277283	−	0.669422i	0.0236899	−	0.0571925i	0.935282	+	0.353904i	$0.115146\pi$
$138$		0			0
$139$			5.04166i			0.427628i	0.976874	+	0.213814i	$0.0685886\pi$
$139$			5.04166i			0.427628i	−0.976874	+	0.213814i	$0.931411\pi$
$140$		0			0
$141$	3.70379			0.311916
$142$		0			0
$143$	−1.28978			−0.107857
$144$		0			0
$145$	−2.22522	−	9.08074i	−0.184794	−	0.754114i
$146$		0			0
$147$	−2.12005	−	0.878152i	−0.174858	−	0.0724288i
$148$		0			0
$149$	8.11373	+	19.5883i	0.664703	+	1.60473i	0.790347	+	0.612659i	$0.209900\pi$
$149$	8.11373	+	19.5883i	0.664703	+	1.60473i	−0.125645	+	0.992075i	$0.540100\pi$
$150$		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
$153$	3.37169	+	8.13998i	0.272585	+	0.658078i
$154$		0			0
$155$	−4.20691	−	5.73353i	−0.337907	−	0.460528i
$156$		0			0
$157$	−9.24064	−	22.3089i	−0.737483	−	1.78044i	−0.615845	−	0.787868i	$-0.711185\pi$
$157$	−9.24064	−	22.3089i	−0.737483	−	1.78044i	−0.121639	−	0.992574i	$-0.538815\pi$
$158$		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	$-0.973061\pi$
$163$	−11.6422	+	11.6422i	−0.911889	+	0.911889i	0.0845316	+	0.996421i	$0.473061\pi$
$164$		0			0
$165$	11.1841	−	8.20618i	0.870679	−	0.638850i
$166$		0			0
$167$	3.67687	−	1.52301i	0.284525	−	0.117854i	−0.235857	−	0.971788i	$-0.575790\pi$
$167$	3.67687	−	1.52301i	0.284525	−	0.117854i	0.520382	+	0.853934i	$0.325790\pi$
$168$		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
$173$			7.73026i			0.587721i	0.955848	+	0.293860i	$0.0949401\pi$
$173$			7.73026i			0.587721i	−0.955848	+	0.293860i	$0.905060\pi$
$174$		0			0
$175$	1.08972	+	12.3616i	0.0823747	+	0.934449i
$176$		0			0
$177$	1.40951	−	0.583836i	0.105945	−	0.0438838i
$178$		0			0
$179$	22.3875	−	9.27320i	1.67332	−	0.693111i	0.674346	−	0.738416i	$-0.264426\pi$
$179$	22.3875	−	9.27320i	1.67332	−	0.693111i	0.998973	+	0.0453042i	$0.0144257\pi$
$180$		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
$183$	−33.2118	−	13.7568i	−2.45509	−	1.01693i
$184$		0			0
$185$	2.20056	−	14.3287i	0.161788	−	1.05347i
$186$		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
$193$	9.15193	+	22.0947i	0.658770	+	1.59041i	0.799705	+	0.600393i	$0.204989\pi$
$193$	9.15193	+	22.0947i	0.658770	+	1.59041i	−0.140934	+	0.990019i	$0.545011\pi$
$194$		0			0
$195$	0.526486	−	3.42815i	0.0377024	−	0.245495i
$196$		0			0
$197$			7.41577i			0.528351i	0.964475	+	0.264176i	$0.0850999\pi$
$197$			7.41577i			0.528351i	−0.964475	+	0.264176i	$0.914900\pi$
$198$		0			0
$199$	13.4266	−	5.56147i	0.951785	−	0.394242i	0.147883	−	0.989005i	$-0.452754\pi$
$199$	13.4266	−	5.56147i	0.951785	−	0.394242i	0.803901	+	0.594763i	$0.202754\pi$
$200$		0			0
$201$	−4.62808			−0.326440
$202$		0			0
$203$		−	10.3773i		−	0.728344i
$204$		0			0
$205$	−7.78677	−	12.0152i	−0.543852	−	0.839181i
$206$		0			0
$207$			20.2022i			1.40415i
$208$		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
$213$			23.5478i			1.61347i
$214$		0			0
$215$	0.532430	−	0.390664i	0.0363114	−	0.0266430i
$216$		0			0
$217$	−3.02060	−	7.29237i	−0.205052	−	0.495038i
$218$		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	−0.936676	−	0.350198i	$-0.886114\pi$
$223$	−19.2171	−	19.2171i	−1.28687	−	1.28687i	−0.350198	−	0.936676i	$-0.613886\pi$
$224$		0			0
$225$	10.3111	+	19.7756i	0.687407	+	1.31837i
$226$		0			0
$227$	12.1762	+	5.04356i	0.808165	+	0.334753i	0.748222	−	0.663449i	$-0.230908\pi$
$227$	12.1762	+	5.04356i	0.808165	+	0.334753i	0.0599435	+	0.998202i	$0.480908\pi$
$228$		0			0
$229$	20.4572	−	8.47367i	1.35185	−	0.559956i	0.415045	−	0.909801i	$-0.363766\pi$
$229$	20.4572	−	8.47367i	1.35185	−	0.559956i	0.936808	+	0.349845i	$0.113766\pi$
$230$		0			0
$231$	14.2248	−	5.89211i	0.935924	−	0.387673i
$232$		0			0
$233$	4.43350	−	1.83642i	0.290448	−	0.120308i	−0.232702	−	0.972548i	$-0.574757\pi$
$233$	4.43350	−	1.83642i	0.290448	−	0.120308i	0.523150	+	0.852241i	$0.324757\pi$
$234$		0			0
$235$	0.721667	+	2.94500i	0.0470764	+	0.192111i
$236$		0			0
$237$		−	45.2291i		−	2.93794i
$238$		0			0
$239$	10.1625	+	4.20944i	0.657356	+	0.272286i	0.686326	−	0.727295i	$-0.259223\pi$
$239$	10.1625	+	4.20944i	0.657356	+	0.272286i	−0.0289695	+	0.999580i	$0.509223\pi$
$240$		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
$243$	−17.3288	+	7.17782i	−1.11164	+	0.460457i
$244$		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
$253$	3.93659	+	9.50377i	0.247491	+	0.597497i
$254$		0			0
$255$	−9.72669	+	7.13684i	−0.609109	+	0.446926i
$256$		0			0
$257$	−1.79266	−	4.32787i	−0.111823	−	0.269965i	0.858054	−	0.513559i	$-0.171673\pi$
$257$	−1.79266	−	4.32787i	−0.111823	−	0.269965i	−0.969877	+	0.243594i	$0.921673\pi$
$258$		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
$263$	14.0514	+	5.82029i	0.866448	+	0.358895i	0.771226	−	0.636561i	$-0.219644\pi$
$263$	14.0514	+	5.82029i	0.866448	+	0.358895i	0.0952222	+	0.995456i	$0.469644\pi$
$264$		0			0
$265$	4.37147	−	7.20931i	0.268537	−	0.442864i
$266$		0			0
$267$	−11.6520			−0.713090
$268$		0			0
$269$	21.7159			1.32404			0.662021	−	0.749485i	$-0.269699\pi$
$269$	21.7159			1.32404			0.662021	+	0.749485i	$0.269699\pi$
$270$		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
$273$	1.47320	−	3.55662i	0.0891622	−	0.215257i
$274$		0			0
$275$	8.70416	+	7.29388i	0.524881	+	0.439838i
$276$		0			0
$277$	14.8375	+	14.8375i	0.891496	+	0.891496i	0.994664	−	0.103168i	$-0.0328979\pi$
$277$	14.8375	+	14.8375i	0.891496	+	0.891496i	−0.103168	+	0.994664i	$0.532898\pi$
$278$		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	0.688761	−	0.724989i	$-0.258155\pi$
$283$	−0.609443	−	0.609443i	−0.0362276	−	0.0362276i	−0.724989	+	0.688761i	$0.758155\pi$
$284$		0			0
$285$	−5.37012	+	34.9669i	−0.318098	+	2.07126i
$286$		0			0
$287$	−5.22040	−	15.0101i	−0.308150	−	0.886016i
$288$		0			0
$289$	9.26189	+	9.26189i	0.544817	+	0.544817i
$290$		0			0
$291$			37.0162i			2.16993i
$292$		0			0
$293$	24.6734	+	10.2201i	1.44144	+	0.597063i	0.960146	−	0.279498i	$-0.0901682\pi$
$293$	24.6734	+	10.2201i	1.44144	+	0.597063i	0.481291	+	0.876561i	$0.340168\pi$
$294$		0			0
$295$	0.738862	+	1.00698i	0.0430182	+	0.0586289i
$296$		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
$307$		−	10.4642i		−	0.597222i	−0.954375	−	0.298611i	$-0.903477\pi$
$307$		−	10.4642i		−	0.597222i	0.954375	−	0.298611i	$-0.0965232\pi$
$308$		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
$313$	−3.51522	−	1.45605i	−0.198692	−	0.0823008i	0.281119	−	0.959673i	$-0.409295\pi$
$313$	−3.51522	−	1.45605i	−0.198692	−	0.0823008i	−0.479810	+	0.877372i	$0.659295\pi$
$314$		0			0
$315$	5.89168	+	24.0430i	0.331959	+	1.35467i
$316$		0			0
$317$	−18.2756	+	7.57000i	−1.02646	+	0.425174i	−0.831434	−	0.555624i	$-0.812479\pi$
$317$	−18.2756	+	7.57000i	−1.02646	+	0.425174i	−0.195027	+	0.980798i	$0.562479\pi$
$318$		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
$323$	−11.4414			−0.636617
$324$		0			0
$325$	2.82841	−	0.249334i	0.156892	−	0.0138306i
$326$		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
$333$		−	28.9177i		−	1.58468i
$334$		0			0
$335$	−0.901760	−	3.67993i	−0.0492684	−	0.201056i
$336$		0			0
$337$	13.2195			0.720110			0.360055	−	0.932931i	$-0.382758\pi$
$337$	13.2195			0.720110			0.360055	+	0.932931i	$0.382758\pi$
$338$		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
$343$	7.44644	−	17.9773i	0.402070	−	0.970683i
$344$		0			0
$345$	−26.8672	+	6.58376i	−1.44648	+	0.354458i
$346$		0			0
$347$	1.28017	−	3.09060i	0.0687231	−	0.165912i	−0.885786	−	0.464094i	$-0.846380\pi$
$347$	1.28017	−	3.09060i	0.0687231	−	0.165912i	0.954509	+	0.298181i	$0.0963801\pi$
$348$		0			0
$349$	−14.0112	+	14.0112i	−0.750002	+	0.750002i	−0.974479	−	0.224477i	$-0.927933\pi$
$349$	−14.0112	+	14.0112i	−0.750002	+	0.750002i	0.224477	+	0.974479i	$0.427933\pi$
$350$		0			0
$351$		−	2.26531i		−	0.120913i
$352$		0			0
$353$	1.30579	−	1.30579i	0.0695003	−	0.0695003i	−0.671502	−	0.741003i	$-0.734351\pi$
$353$	1.30579	−	1.30579i	0.0695003	−	0.0695003i	0.741003	+	0.671502i	$0.234351\pi$
$354$		0			0
$355$	−18.7236	+	4.58819i	−0.993747	+	0.243516i
$356$		0			0
$357$	−12.3712	+	5.12432i	−0.654753	+	0.271208i
$358$		0			0
$359$	−20.1309			−1.06247			−0.531233	−	0.847226i	$-0.678271\pi$
$359$	−20.1309			−1.06247			−0.531233	+	0.847226i	$0.678271\pi$
$360$		0			0
$361$	−10.2890	+	10.2890i	−0.541524	+	0.541524i
$362$		0			0
$363$	−6.10584	+	14.7408i	−0.320473	+	0.773691i
$364$		0			0
$365$	−11.9115	+	8.73995i	−0.623479	+	0.457470i
$366$		0			0
$367$	−19.8546			−1.03640			−0.518200	−	0.855260i	$-0.673398\pi$
$367$	−19.8546			−1.03640			−0.518200	+	0.855260i	$0.673398\pi$
$368$		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	$-0.851783\pi$
$373$	−8.58554	+	8.58554i	−0.444543	+	0.444543i	0.448993	+	0.893535i	$0.351783\pi$
$374$		0			0
$375$	−22.9396	+	20.1577i	−1.18460	+	1.04094i
$376$		0			0
$377$	−2.37439			−0.122288
$378$		0			0
$379$		−	7.66393i		−	0.393669i	−0.980437	−	0.196835i	$-0.936934\pi$
$379$		−	7.66393i		−	0.393669i	0.980437	−	0.196835i	$-0.0630662\pi$
$380$		0			0
$381$	0.955124	−	2.30587i	0.0489325	−	0.118133i
$382$		0			0
$383$	−16.7420	−	6.93476i	−0.855476	−	0.354350i	−0.0885396	−	0.996073i	$-0.528220\pi$
$383$	−16.7420	−	6.93476i	−0.855476	−	0.354350i	−0.766937	+	0.641723i	$0.778220\pi$
$384$		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	0.993114	−	0.117153i	$-0.0373768\pi$
$389$	17.2766	+	17.2766i	0.875961	+	0.875961i	−0.117153	+	0.993114i	$0.537377\pi$
$390$		0			0
$391$	−3.42362	−	8.26534i	−0.173140	−	0.417996i
$392$		0			0
$393$	−8.00099	+	19.3161i	−0.403597	+	0.974369i
$394$		0			0
$395$	35.9631	−	8.81268i	1.80950	−	0.443414i
$396$		0			0
$397$	−10.8240	−	26.1315i	−0.543242	−	1.31150i	−0.922423	−	0.386180i	$-0.873794\pi$
$397$	−10.8240	−	26.1315i	−0.543242	−	1.31150i	0.379181	−	0.925322i	$-0.376206\pi$
$398$		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
$403$	−1.66854	+	0.691132i	−0.0831160	+	0.0344278i
$404$		0			0
$405$	−3.28802	−	4.48120i	−0.163383	−	0.222672i
$406$		0			0
$407$	−5.63490	−	13.6038i	−0.279311	−	0.674317i
$408$		0			0
$409$	−20.0737			−0.992581			−0.496291	−	0.868156i	$-0.665305\pi$
$409$	−20.0737			−0.992581			−0.496291	+	0.868156i	$0.665305\pi$
$410$		0			0
$411$	1.97910			0.0976217
$412$		0			0
$413$	0.530510	+	1.28076i	0.0261047	+	0.0630223i
$414$		0			0
$415$	15.2603	+	2.34364i	0.749101	+	0.115045i
$416$		0			0
$417$	−12.7225	+	5.26982i	−0.623022	+	0.258064i
$418$		0			0
$419$	1.64729	−	1.64729i	0.0804754	−	0.0804754i	−0.665723	−	0.746199i	$-0.731877\pi$
$419$	1.64729	−	1.64729i	0.0804754	−	0.0804754i	0.746199	+	0.665723i	$0.231877\pi$
$420$		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
$423$	2.31464	+	5.58803i	0.112542	+	0.271700i
$424$		0			0
$425$	−7.56993	−	6.34342i	−0.367196	−	0.307701i
$426$		0			0
$427$	12.5003	−	30.1783i	0.604930	−	1.46043i
$428$		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	$-0.691211\pi$
$433$	5.40420	−	5.40420i	0.259709	−	0.259709i	0.824936	+	0.565226i	$0.191211\pi$
$434$		0			0
$435$	20.5891	−	15.1070i	0.987170	−	0.724323i
$436$		0			0
$437$	−24.2373	−	10.0394i	−1.15943	−	0.480251i
$438$		0			0
$439$	−11.1265	+	26.8618i	−0.531040	+	1.28204i	0.399795	+	0.916605i	$0.369081\pi$
$439$	−11.1265	+	26.8618i	−0.531040	+	1.28204i	−0.930835	+	0.365440i	$0.880919\pi$
$440$		0			0
$441$		−	3.74738i		−	0.178446i
$442$		0			0
$443$	40.0241			1.90160			0.950802	−	0.309800i	$-0.100262\pi$
$443$	40.0241			1.90160			0.950802	+	0.309800i	$0.100262\pi$
$444$		0			0
$445$	−2.27034	−	9.26486i	−0.107624	−	0.439197i
$446$		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	$0.583928\pi$
$449$	−25.9798	+	25.9798i	−1.22606	+	1.22606i	−0.965441	+	0.260623i	$0.916072\pi$
$450$		0			0
$451$	−13.0909	−	6.33476i	−0.616424	−	0.298292i
$452$		0			0
$453$	−38.0366			−1.78711
$454$		0			0
$455$	3.11503	+	0.478398i	0.146035	+	0.0224276i
$456$		0			0
$457$	−8.99976	+	21.7273i	−0.420991	+	1.01636i	0.561065	+	0.827772i	$0.310392\pi$
$457$	−8.99976	+	21.7273i	−0.420991	+	1.01636i	−0.982056	+	0.188590i	$0.939608\pi$
$458$		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
$463$	22.2106	−	9.19993i	1.03221	−	0.427557i	0.198703	−	0.980060i	$-0.436327\pi$
$463$	22.2106	−	9.19993i	1.03221	−	0.427557i	0.833511	+	0.552503i	$0.186327\pi$
$464$		0			0
$465$	10.0711	−	16.6090i	0.467036	−	0.770225i
$466$		0			0
$467$	−26.8274	+	26.8274i	−1.24142	+	1.24142i	−0.282013	+	0.959411i	$0.591002\pi$
$467$	−26.8274	+	26.8274i	−1.24142	+	1.24142i	−0.959411	+	0.282013i	$0.908998\pi$
$468$		0			0
$469$		−	4.20536i		−	0.194186i
$470$		0			0
$471$	46.6370	−	46.6370i	2.14892	−	2.14892i
$472$		0			0
$473$	0.256691	−	0.619707i	0.0118027	−	0.0284941i
$474$		0			0
$475$	−28.8496	+	2.54319i	−1.32371	+	0.116690i
$476$		0			0
$477$	6.43606	−	15.5380i	0.294687	−	0.711438i
$478$		0			0
$479$	31.8708	+	13.2013i	1.45621	+	0.603183i	0.963668	−	0.267104i	$-0.0860668\pi$
$479$	31.8708	+	13.2013i	1.45621	+	0.603183i	0.492545	+	0.870287i	$0.336067\pi$
$480$		0			0
$481$	−3.40136	−	1.40889i	−0.155089	−	0.0642398i
$482$		0			0
$483$	−30.7034			−1.39705
$484$		0			0
$485$	−29.4328	+	7.21244i	−1.33647	+	0.327500i
$486$		0			0
$487$			7.09877i			0.321676i	0.986981	+	0.160838i	$0.0514197\pi$
$487$			7.09877i			0.321676i	−0.986981	+	0.160838i	$0.948580\pi$
$488$		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
$495$	19.3703	+	11.7454i	0.870630	+	0.527918i
$496$		0			0
$497$	−21.3970			−0.959788
$498$		0			0
$499$	14.1912	−	34.2605i	0.635284	−	1.53371i	−0.197610	−	0.980281i	$-0.563318\pi$
$499$	14.1912	−	34.2605i	0.635284	−	1.53371i	0.832895	−	0.553432i	$-0.186682\pi$
$500$		0			0
$501$	7.68654	+	7.68654i	0.343409	+	0.343409i
$502$		0			0
$503$	20.5844	−	8.52633i	0.917813	−	0.380170i	0.126771	−	0.991932i	$-0.459539\pi$
$503$	20.5844	−	8.52633i	0.917813	−	0.380170i	0.791042	+	0.611762i	$0.209539\pi$
$504$		0			0
$505$	4.26599	−	7.03536i	0.189834	−	0.313069i
$506$		0			0
$507$	31.9913	+	13.2512i	1.42079	+	0.588509i
$508$		0			0
$509$	−5.09125	−	12.2914i	−0.225666	−	0.544805i	0.769975	−	0.638074i	$-0.220268\pi$
$509$	−5.09125	−	12.2914i	−0.225666	−	0.544805i	−0.995641	+	0.0932686i	$0.970268\pi$
$510$		0			0
$511$	−15.1501	+	6.27537i	−0.670200	+	0.277606i
$512$		0			0
$513$			23.1060i			1.02016i
$514$		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	$-0.658501\pi$
$523$	9.16926	−	9.16926i	0.400944	−	0.400944i	0.878566	+	0.477622i	$0.158501\pi$
$524$		0			0
$525$	−30.0551	+	15.6709i	−1.31171	+	0.683934i
$526$		0			0
$527$	5.80378	+	2.40400i	0.252817	+	0.104720i
$528$		0			0
$529$			2.48672i			0.108118i
$530$		0			0
$531$	1.76171	+	1.76171i	0.0764515	+	0.0764515i
$532$		0			0
$533$	−3.43440	+	1.19446i	−0.148760	+	0.0517379i
$534$		0			0
$535$	6.12303	+	0.940357i	0.264721	+	0.0406552i
$536$		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
$545$	21.2182	−	34.9925i	0.908888	−	1.49892i
$546$		0			0
$547$	5.16807	−	12.4768i	0.220971	−	0.533470i	−0.774052	−	0.633122i	$-0.781773\pi$
$547$	5.16807	−	12.4768i	0.220971	−	0.533470i	0.995022	+	0.0996520i	$0.0317730\pi$
$548$		0			0
$549$		−	58.7049i		−	2.50546i
$550$		0			0
$551$	24.2187			1.03175
$552$		0			0
$553$	41.0980			1.74766
$554$		0			0
$555$	38.4582	−	9.42409i	1.63246	−	0.400030i
$556$		0			0
$557$	21.1427	+	8.75761i	0.895847	+	0.371072i	0.782622	−	0.622498i	$-0.213882\pi$
$557$	21.1427	+	8.75761i	0.895847	+	0.371072i	0.113225	+	0.993569i	$0.463882\pi$
$558$		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
$563$	−9.13510	−	22.0541i	−0.384998	−	0.929468i	−0.990982	−	0.133992i	$-0.957220\pi$
$563$	−9.13510	−	22.0541i	−0.384998	−	0.929468i	0.605984	−	0.795477i	$-0.292780\pi$
$564$		0			0
$565$	−5.38396	+	35.0570i	−0.226505	+	1.47486i
$566$		0			0
$567$	−2.36083	−	5.69955i	−0.0991456	−	0.239359i
$568$		0			0
$569$	−12.5492	−	12.5492i	−0.526091	−	0.526091i	0.393313	−	0.919405i	$-0.371329\pi$
$569$	−12.5492	−	12.5492i	−0.526091	−	0.526091i	−0.919405	+	0.393313i	$0.871329\pi$
$570$		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
$577$	31.8895	−	13.2091i	1.32758	−	0.549901i	0.397615	−	0.917553i	$-0.369838\pi$
$577$	31.8895	−	13.2091i	1.32758	−	0.549901i	0.929964	+	0.367652i	$0.119838\pi$
$578$		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
$583$		−	8.56374i		−	0.354674i
$584$		0			0
$585$	5.50118	−	1.34805i	0.227446	−	0.0557352i
$586$		0			0
$587$	39.4204	−	16.3285i	1.62705	−	0.673948i	0.632157	−	0.774840i	$-0.282170\pi$
$587$	39.4204	−	16.3285i	1.62705	−	0.673948i	0.994897	+	0.100892i	$0.0321698\pi$
$588$		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
$593$	−37.3814	−	15.4839i	−1.53507	−	0.635847i	−0.554530	−	0.832164i	$-0.687102\pi$
$593$	−37.3814	−	15.4839i	−1.53507	−	0.635847i	−0.980541	+	0.196317i	$0.937102\pi$
$594$		0			0
$595$	−6.48498	−	8.83829i	−0.265858	−	0.362334i
$596$		0			0
$597$	28.0684	+	28.0684i	1.14876	+	1.14876i
$598$		0			0
$599$	17.5398			0.716655			0.358328	−	0.933596i	$-0.383347\pi$
$599$	17.5398			0.716655			0.358328	+	0.933596i	$0.383347\pi$
$600$		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
$603$	−2.89226	−	6.98254i	−0.117782	−	0.284351i
$604$		0			0
$605$	−12.9106	−	1.98277i	−0.524889	−	0.0806110i
$606$		0			0
$607$		−	32.2107i		−	1.30739i	−0.756757	−	0.653696i	$-0.773218\pi$
$607$		−	32.2107i		−	1.30739i	0.756757	−	0.653696i	$-0.226782\pi$
$608$		0			0
$609$	26.1868	−	10.8469i	1.06114	−	0.439540i
$610$		0			0
$611$	0.770048			0.0311528
$612$		0			0
$613$			21.5184i			0.869120i	0.900643	+	0.434560i	$0.143096\pi$
$613$			21.5184i			0.869120i	−0.900643	+	0.434560i	$0.856904\pi$
$614$		0			0
$615$	22.1810	−	32.2087i	0.894423	−	1.29878i
$616$		0			0
$617$			34.8623i			1.40350i	0.712421	+	0.701752i	$0.247599\pi$
$617$			34.8623i			1.40350i	−0.712421	+	0.701752i	$0.752401\pi$
$618$		0			0
$619$	−3.84142			−0.154400			−0.0771999	−	0.997016i	$-0.524598\pi$
$619$	−3.84142			−0.154400			−0.0771999	+	0.997016i	$0.524598\pi$
$620$		0			0
$621$	−16.6919	+	6.91403i	−0.669825	+	0.277451i
$622$		0			0
$623$		−	10.5877i		−	0.424188i
$624$		0			0
$625$	−20.4977	−	14.3124i	−0.819908	−	0.572495i
$626$		0			0
$627$	13.7511	+	33.1980i	0.549165	+	1.32580i
$628$		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
$635$	2.01958	+	0.310161i	0.0801444	+	0.0123084i
$636$		0			0
$637$	−0.440774	−	0.182575i	−0.0174641	−	0.00723387i
$638$		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
$643$	−0.526272	+	0.217989i	−0.0207541	+	0.00859664i	−0.393036	−	0.919523i	$-0.628575\pi$
$643$	−0.526272	+	0.217989i	−0.0207541	+	0.00859664i	0.372282	+	0.928120i	$0.378575\pi$
$644$		0			0
$645$	1.54235	+	0.935228i	0.0607301	+	0.0368246i
$646$		0			0
$647$		−	20.0557i		−	0.788469i	−0.919010	−	0.394235i	$-0.871010\pi$
$647$		−	20.0557i		−	0.788469i	0.919010	−	0.394235i	$-0.128990\pi$
$648$		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
$653$	23.8380	−	9.87402i	0.932853	−	0.386400i	0.136093	−	0.990696i	$-0.456545\pi$
$653$	23.8380	−	9.87402i	0.932853	−	0.386400i	0.796760	+	0.604296i	$0.206545\pi$
$654$		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	−0.754699	−	0.656071i	$-0.772217\pi$
$659$	6.23462	−	15.0517i	0.242866	−	0.586331i	0.997565	+	0.0697400i	$0.0222170\pi$
$660$		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
$663$	1.17248	+	2.83061i	0.0455352	+	0.109932i
$664$		0			0
$665$	−31.7731	−	4.87963i	−1.23211	−	0.189224i
$666$		0			0
$667$	7.24697	+	17.4957i	0.280604	+	0.677437i
$668$		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
$673$	24.5595	+	10.1729i	0.946698	+	0.392135i	0.801989	−	0.597339i	$-0.203775\pi$
$673$	24.5595	+	10.1729i	0.946698	+	0.392135i	0.144709	+	0.989474i	$0.453775\pi$
$674$		0			0
$675$	−12.8106	+	15.2876i	−0.493081	+	0.588419i
$676$		0			0
$677$	33.3330			1.28109			0.640545	−	0.767921i	$-0.278709\pi$
$677$	33.3330			1.28109			0.640545	+	0.767921i	$0.278709\pi$
$678$		0			0
$679$	−33.6353			−1.29080
$680$		0			0
$681$			35.9982i			1.37945i
$682$		0			0
$683$	−6.07764	+	14.6727i	−0.232554	+	0.561436i	−0.996477	−	0.0838724i	$-0.973271\pi$
$683$	−6.07764	+	14.6727i	−0.232554	+	0.561436i	0.763922	+	0.645309i	$0.223271\pi$
$684$		0			0
$685$	0.385618	+	1.57364i	0.0147337	+	0.0601258i
$686$		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
$695$	−6.66912	−	9.08924i	−0.252974	−	0.344775i
$696$		0			0
$697$	11.3850	+	5.50928i	0.431238	+	0.208679i
$698$		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
$703$	34.6937	+	14.3706i	1.30850	+	0.541997i
$704$		0			0
$705$	−6.67730	+	4.89939i	−0.251482	+	0.184522i
$706$		0			0
$707$	6.45749	−	6.45749i	0.242859	−	0.242859i
$708$		0			0
$709$	−17.7782	−	7.36397i	−0.667674	−	0.276560i	0.0229895	−	0.999736i	$-0.492682\pi$
$709$	−17.7782	−	7.36397i	−0.667674	−	0.276560i	−0.690664	+	0.723176i	$0.742682\pi$
$710$		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
$717$			30.0447i			1.12204i
$718$		0			0
$719$	−8.58842	+	3.55744i	−0.320294	+	0.132670i	−0.537037	−	0.843558i	$-0.680457\pi$
$719$	−8.58842	+	3.55744i	−0.320294	+	0.132670i	0.216743	+	0.976229i	$0.430457\pi$
$720$		0			0
$721$	−1.09758	−	2.64980i	−0.0408761	−	0.0986837i
$722$		0			0
$723$	−23.8004	−	9.85846i	−0.885147	−	0.366640i
$724$		0			0
$725$	16.0237	+	13.4275i	0.595106	+	0.498685i
$726$		0			0
$727$	−24.1084	+	9.98604i	−0.894132	+	0.370362i	−0.781961	−	0.623327i	$-0.785781\pi$
$727$	−24.1084	+	9.98604i	−0.894132	+	0.370362i	−0.112171	+	0.993689i	$0.535781\pi$
$728$		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
$733$	−27.0851			−1.00041			−0.500206	−	0.865906i	$-0.666743\pi$
$733$	−27.0851			−1.00041			−0.500206	+	0.865906i	$0.666743\pi$
$734$		0			0
$735$	4.98370	−	1.22125i	0.183827	−	0.0450463i
$736$		0			0
$737$	−2.72123	−	2.72123i	−0.100238	−	0.100238i
$738$		0			0
$739$			19.9991i			0.735680i	0.929889	+	0.367840i	$0.119903\pi$
$739$			19.9991i			0.735680i	−0.929889	+	0.367840i	$0.880097\pi$
$740$		0			0
$741$	8.30049	+	3.43817i	0.304926	+	0.126304i
$742$		0			0
$743$			24.9057i			0.913702i	0.889543	+	0.456851i	$0.151023\pi$
$743$			24.9057i			0.913702i	−0.889543	+	0.456851i	$0.848977\pi$
$744$		0			0
$745$	−40.5391	−	24.5814i	−1.48524	−	0.900594i
$746$		0			0
$747$	30.7979			1.12684
$748$		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
$753$	−10.1041	+	24.3935i	−0.368214	+	0.888948i
$754$		0			0
$755$	−7.41126	−	30.2441i	−0.269723	−	1.10070i
$756$		0			0
$757$	−7.61370	+	18.3811i	−0.276725	+	0.668073i	−0.999741	−	0.0227584i	$-0.992755\pi$
$757$	−7.61370	+	18.3811i	−0.276725	+	0.668073i	0.723016	+	0.690831i	$0.242755\pi$
$758$		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
$765$	−16.8462	−	10.2149i	−0.609075	−	0.369321i
$766$		0			0
$767$	0.293047	−	0.121384i	0.0105813	−	0.00438293i
$768$		0			0
$769$	−6.48872			−0.233989			−0.116995	−	0.993133i	$-0.537326\pi$
$769$	−6.48872			−0.233989			−0.116995	+	0.993133i	$0.537326\pi$
$770$		0			0
$771$	9.04746	−	9.04746i	0.325836	−	0.325836i
$772$		0			0
$773$	8.18288	−	19.7552i	0.294318	−	0.710546i	−0.705680	−	0.708530i	$-0.749359\pi$
$773$	8.18288	−	19.7552i	0.294318	−	0.710546i	0.999998	−	0.00201531i	$-0.000641494\pi$
$774$		0			0
$775$	15.1687	+	4.77167i	0.544875	+	0.171403i
$776$		0			0
$777$	43.9493			1.57667
$778$		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
$785$	46.1695	+	27.9955i	1.64786	+	0.999204i
$786$		0			0
$787$	−48.8135			−1.74001			−0.870007	−	0.493040i	$-0.835886\pi$
$787$	−48.8135			−1.74001			−0.870007	+	0.493040i	$0.835886\pi$
$788$		0			0
$789$			41.5421i			1.47894i
$790$		0			0
$791$	−15.0653	+	36.3708i	−0.535660	+	1.29320i
$792$		0			0
$793$	−6.90499	−	2.86014i	−0.245204	−	0.101567i
$794$		0			0
$795$	22.7618	+	3.49569i	0.807277	+	0.123979i
$796$		0			0
$797$	1.84186	−	1.84186i	0.0652419	−	0.0652419i	−0.673733	−	0.738975i	$-0.735310\pi$
$797$	1.84186	−	1.84186i	0.0652419	−	0.0652419i	0.738975	+	0.673733i	$0.235310\pi$
$798$		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
$803$	−5.74270	+	13.8641i	−0.202656	+	0.489254i
$804$		0			0
$805$	−5.98242	−	24.4132i	−0.210852	−	0.860454i
$806$		0			0
$807$	22.6987	+	54.7995i	0.799032	+	1.92903i
$808$		0			0
$809$	−12.7020	+	30.6653i	−0.446578	+	1.07813i	0.527018	+	0.849854i	$0.323310\pi$
$809$	−12.7020	+	30.6653i	−0.446578	+	1.07813i	−0.973596	+	0.228280i	$0.926690\pi$
$810$		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
$813$	−50.7273	+	21.0120i	−1.77909	+	0.736921i
$814$		0			0
$815$	5.58857	−	36.3893i	0.195759	−	1.27466i
$816$		0			0
$817$	0.654635	+	1.58043i	0.0229028	+	0.0552922i
$818$		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
$823$	−3.70858	−	8.95330i	−0.129273	−	0.312092i	0.845969	−	0.533232i	$-0.179023\pi$
$823$	−3.70858	−	8.95330i	−0.129273	−	0.312092i	−0.975242	+	0.221139i	$0.929023\pi$
$824$		0			0
$825$	−9.30782	+	29.5887i	−0.324057	+	1.03015i
$826$		0			0
$827$	−1.61762	+	0.670040i	−0.0562501	+	0.0232996i	−0.410631	−	0.911802i	$-0.634692\pi$
$827$	−1.61762	+	0.670040i	−0.0562501	+	0.0232996i	0.354381	+	0.935101i	$0.384692\pi$
$828$		0			0
$829$	−2.91568	+	2.91568i	−0.101266	+	0.101266i	−0.755924	−	0.654659i	$-0.772812\pi$
$829$	−2.91568	+	2.91568i	−0.101266	+	0.101266i	0.654659	+	0.755924i	$0.272812\pi$
$830$		0			0
$831$	−21.9329	+	52.9508i	−0.760845	+	1.83684i
$832$		0			0
$833$	0.635060	+	1.53317i	0.0220035	+	0.0531212i
$834$		0			0
$835$	−4.61413	+	7.60950i	−0.159679	+	0.263338i
$836$		0			0
$837$	4.85491	−	11.7208i	0.167810	−	0.405130i
$838$		0			0
$839$	−11.3314	−	27.3564i	−0.391203	−	0.944448i	−0.989678	−	0.143307i	$-0.954226\pi$
$839$	−11.3314	−	27.3564i	−0.391203	−	0.944448i	0.598475	−	0.801141i	$-0.295774\pi$
$840$		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
$847$	−13.3944	−	5.54815i	−0.460237	−	0.190637i
$848$		0			0
$849$	0.900888	−	2.17494i	0.0309184	−	0.0746436i
$850$		0			0
$851$			29.3630i			1.00655i
$852$		0			0
$853$	23.1225			0.791701			0.395850	−	0.918315i	$-0.370450\pi$
$853$	23.1225			0.791701			0.395850	+	0.918315i	$0.370450\pi$
$854$		0			0
$855$	−56.1117	+	13.7501i	−1.91898	+	0.470242i
$856$		0			0
$857$	21.5664	−	21.5664i	0.736695	−	0.736695i	−0.235242	−	0.971937i	$-0.575588\pi$
$857$	21.5664	−	21.5664i	0.736695	−	0.736695i	0.971937	+	0.235242i	$0.0755883\pi$
$858$		0			0
$859$	−17.0661	+	17.0661i	−0.582286	+	0.582286i	−0.935531	−	0.353245i	$-0.885078\pi$
$859$	−17.0661	+	17.0661i	−0.582286	+	0.582286i	0.353245	+	0.935531i	$0.385078\pi$
$860$		0			0
$861$	32.4208	−	28.8629i	1.10490	−	0.983645i
$862$		0			0
$863$	42.3869			1.44287			0.721433	−	0.692484i	$-0.243484\pi$
$863$	42.3869			1.44287			0.721433	+	0.692484i	$0.243484\pi$
$864$		0			0
$865$	−10.2256	−	13.9363i	−0.347681	−	0.473850i
$866$		0			0
$867$	−13.6911	+	33.0531i	−0.464973	+	1.12254i
$868$		0			0
$869$	26.5939	−	26.5939i	0.902137	−	0.902137i
$870$		0			0
$871$	−0.962214			−0.0326034
$872$		0			0
$873$	−55.8476	+	23.1328i	−1.89016	+	0.782928i
$874$		0			0
$875$	−18.3165	−	20.8444i	−0.619212	−	0.704669i
$876$		0			0
$877$	37.2642	−	37.2642i	1.25832	−	1.25832i	0.306432	−	0.951893i	$-0.400865\pi$
$877$	37.2642	−	37.2642i	1.25832	−	1.25832i	0.951893	−	0.306432i	$-0.0991351\pi$
$878$		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
$883$	0.941166	−	2.27217i	0.0316727	−	0.0764648i	−0.907252	−	0.420588i	$-0.861824\pi$
$883$	0.941166	−	2.27217i	0.0316727	−	0.0764648i	0.938924	+	0.344123i	$0.111824\pi$
$884$		0			0
$885$	−1.76880	+	2.91705i	−0.0594574	+	0.0980557i
$886$		0			0
$887$	−16.0975	+	38.8628i	−0.540501	+	1.30488i	0.383870	+	0.923387i	$0.374591\pi$
$887$	−16.0975	+	38.8628i	−0.540501	+	1.30488i	−0.924370	+	0.381497i	$0.875409\pi$
$888$		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
$893$	−7.85443			−0.262839
$894$		0			0
$895$	−28.0942	+	46.3322i	−0.939085	+	1.54872i
$896$		0			0
$897$			7.02513i			0.234562i
$898$		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
$905$	−5.51255	+	9.09116i	−0.183243	+	0.302200i
$906$		0			0
$907$	11.6665			0.387381			0.193691	−	0.981063i	$-0.437954\pi$
$907$	11.6665			0.387381			0.193691	+	0.981063i	$0.437954\pi$
$908$		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
$913$	14.4884	−	6.00128i	0.479495	−	0.198613i
$914$		0			0
$915$	78.0727	−	19.1316i	2.58100	−	0.632470i
$916$		0			0
$917$	−17.5518	−	7.27021i	−0.579613	−	0.240083i
$918$		0			0
$919$	−8.87243	−	21.4199i	−0.292675	−	0.706579i	0.707325	−	0.706888i	$-0.249902\pi$
$919$	−8.87243	−	21.4199i	−0.292675	−	0.706579i	−1.00000		0.000309256i	$0.999902\pi$
$920$		0			0
$921$	26.4060	−	10.9377i	0.870108	−	0.360410i
$922$		0			0
$923$			4.89578i			0.161147i
$924$		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	−0.981113	−	0.193434i	$-0.938038\pi$
$929$	−46.8801	+	19.4184i	−1.53809	+	0.637097i	−0.556974	+	0.830530i	$0.688038\pi$
$930$		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
$935$	−9.91547	−	1.52279i	−0.324271	−	0.0498006i
$936$		0			0
$937$	−42.1938	−	17.4772i	−1.37841	−	0.570957i	−0.434355	−	0.900742i	$-0.643024\pi$
$937$	−42.1938	−	17.4772i	−1.37841	−	0.570957i	−0.944056	+	0.329785i	$0.893024\pi$
$938$		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
$943$	19.2836	+	21.6607i	0.627961	+	0.705370i
$944$		0			0
$945$	−17.8490	+	13.0965i	−0.580629	+	0.426029i
$946$		0			0
$947$	42.0766	+	42.0766i	1.36731	+	1.36731i	0.864259	+	0.503047i	$0.167788\pi$
$947$	42.0766	+	42.0766i	1.36731	+	1.36731i	0.503047	+	0.864259i	$0.332212\pi$
$948$		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	0.970249	−	0.242108i	$-0.0778389\pi$
$953$	22.4782	+	22.4782i	0.728141	+	0.728141i	−0.242108	+	0.970249i	$0.577839\pi$
$954$		0			0
$955$	21.7624	+	13.1959i	0.704215	+	0.427010i
$956$		0			0
$957$	9.92623	−	23.9640i	0.320869	−	0.774647i
$958$		0			0
$959$			1.79833i			0.0580712i
$960$		0			0
$961$	20.8857			0.673733
$962$		0			0
$963$	12.3573			0.398208
$964$		0			0
$965$	−45.7263	−	27.7268i	−1.47198	−	0.892557i
$966$		0			0
$967$	42.8066	+	17.7311i	1.37657	+	0.570192i	0.943561	−	0.331199i	$-0.107453\pi$
$967$	42.8066	+	17.7311i	1.37657	+	0.570192i	0.433005	+	0.901391i	$0.357453\pi$
$968$		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
$973$	−4.78849	−	11.5604i	−0.153512	−	0.370611i
$974$		0			0
$975$	3.58560	+	6.87680i	0.114831	+	0.220234i
$976$		0			0
$977$	−1.85824	−	4.48618i	−0.0594502	−	0.143526i	0.891363	−	0.453290i	$-0.149750\pi$
$977$	−1.85824	−	4.48618i	−0.0594502	−	0.143526i	−0.950813	+	0.309764i	$0.899750\pi$
$978$		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	$-0.689268\pi$
$983$	8.40861	−	8.40861i	0.268193	−	0.268193i	0.828372	+	0.560179i	$0.189268\pi$
$984$		0			0
$985$	−9.80960	−	13.3694i	−0.312560	−	0.425983i
$986$		0			0
$987$	−8.49274	+	3.51781i	−0.270327	+	0.111973i
$988$		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
$993$		−	44.3990i		−	1.40896i
$994$		0			0
$995$	−16.8491	+	27.7871i	−0.534152	+	0.880910i
$996$		0			0
$997$	−5.15183	+	2.13396i	−0.163160	+	0.0675832i	−0.462769	−	0.886479i	$-0.653144\pi$
$997$	−5.15183	+	2.13396i	−0.163160	+	0.0675832i	0.299608	+	0.954062i	$0.403144\pi$
$998$		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.y.a.653.20	yes	84
5.2	odd	4		820.2.x.a.817.20	yes	84
41.27	odd	8		820.2.x.a.273.20	✓	84
205.27	even	8	inner	820.2.y.a.437.20	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.20	✓	84	41.27	odd	8
820.2.x.a.817.20	yes	84	5.2	odd	4
820.2.y.a.437.20	yes	84	205.27	even	8	inner
820.2.y.a.653.20	yes	84	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.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04526 + 2.52347i) q^{3} +(-1.80283 + 1.32280i) q^{5} +(-2.29298 + 0.949785i) q^{7} +(-3.15402 + 3.15402i) q^{9} +(-0.869165 + 2.09835i) q^{11} +(0.217317 + 0.524650i) q^{13} +(-5.22247 - 3.16672i) q^{15} +(0.755905 - 1.82492i) q^{17} +(-2.21662 - 5.35139i) q^{19} +(-4.79351 - 4.79351i) q^{21} +(3.20260 - 3.20260i) q^{23} +(1.50038 - 4.76958i) q^{25} +(-3.68544 - 1.52656i) q^{27} +(-1.60007 + 3.86291i) q^{29} +3.18030i q^{31} -6.20363 q^{33} +(2.87748 - 4.74547i) q^{35} +(-4.58425 + 4.58425i) q^{37} +(-1.09679 + 1.09679i) q^{39} +(-0.371118 + 6.39236i) q^{41} -0.295330 q^{43} +(1.51401 - 9.85832i) q^{45} +(0.518923 - 1.25279i) q^{47} +(-0.594062 + 0.594062i) q^{49} +5.39524 q^{51} +(-3.48350 + 1.44291i) q^{53} +(-1.20875 - 4.93270i) q^{55} +(11.1871 - 11.1871i) q^{57} -0.558558i q^{59} +(-9.30634 + 9.30634i) q^{61} +(4.23648 - 10.2278i) q^{63} +(-1.08579 - 0.658386i) q^{65} +(-0.648422 + 1.56543i) q^{67} +(11.4292 + 4.73413i) q^{69} +(7.96495 + 3.29919i) q^{71} +6.60714 q^{73} +(13.6042 - 1.19925i) q^{75} -5.63701i q^{77} +(-15.2985 - 6.33686i) q^{79} +2.48565i q^{81} +(-4.88232 - 4.88232i) q^{83} +(1.05124 + 4.28993i) q^{85} -11.4204 q^{87} +(-1.63251 + 3.94123i) q^{89} +(-0.996609 - 0.996609i) q^{91} +(-8.02539 + 3.32422i) q^{93} +(11.0750 + 6.71549i) q^{95} +(12.5206 + 5.18619i) q^{97} +(-3.87688 - 9.35962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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