LMFDB - Embedded newform 544.2.cc.c.175.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(79,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.cc (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [112,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			175.14
Character	$\chi$	$=$	544.175
Dual form			544.2.cc.c.143.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72164 + 2.57662i) q^{3} +(2.84924 + 0.566749i) q^{5} +(1.07350 - 0.213532i) q^{7} +(-2.52687 + 6.10039i) q^{9} +(-1.65107 - 1.10321i) q^{11} +(3.43124 - 3.43124i) q^{13} +(3.44507 + 8.31714i) q^{15} +(-2.78526 - 3.04012i) q^{17} +(0.843066 + 2.03534i) q^{19} +(2.39837 + 2.39837i) q^{21} +(-3.88838 - 2.59813i) q^{23} +(3.17755 + 1.31619i) q^{25} +(-10.9508 + 2.17824i) q^{27} +(0.598581 - 3.00927i) q^{29} +(-5.36812 - 8.03396i) q^{31} -6.15351i q^{33} +3.17967 q^{35} +(-3.54311 + 2.36743i) q^{37} +(14.7484 + 2.93363i) q^{39} +(0.251769 + 1.26573i) q^{41} +(-0.398138 + 0.961190i) q^{43} +(-10.6570 + 15.9494i) q^{45} +(-4.54349 + 4.54349i) q^{47} +(-5.36035 + 2.22033i) q^{49} +(3.03799 - 12.4106i) q^{51} +(-0.113637 + 0.0470698i) q^{53} +(-4.07905 - 4.07905i) q^{55} +(-3.79284 + 5.67639i) q^{57} +(2.61174 + 1.08182i) q^{59} +(2.10581 + 10.5866i) q^{61} +(-1.40996 + 7.08833i) q^{63} +(11.7211 - 7.83176i) q^{65} +2.27343i q^{67} -14.4919i q^{69} +(0.572331 - 0.382419i) q^{71} +(-2.44907 + 12.3123i) q^{73} +(2.07930 + 10.4533i) q^{75} +(-2.00799 - 0.831737i) q^{77} +(7.26595 - 10.8743i) q^{79} +(-10.4587 - 10.4587i) q^{81} +(0.181706 - 0.0752650i) q^{83} +(-6.21290 - 10.2406i) q^{85} +(8.78428 - 3.63857i) q^{87} +(5.16813 - 5.16813i) q^{89} +(2.95075 - 4.41611i) q^{91} +(11.4585 - 27.6632i) q^{93} +(1.24857 + 6.27698i) q^{95} +(15.5086 + 3.08484i) q^{97} +(10.9020 - 7.28451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 16 q^{3} - 16 q^{9} + 16 q^{11} - 16 q^{17} + 16 q^{19} - 16 q^{25} - 32 q^{27} + 32 q^{35} - 16 q^{41} + 96 q^{43} - 16 q^{49} + 16 q^{51} + 32 q^{57} + 16 q^{59} + 64 q^{65} - 96 q^{73} + 16 q^{75}+ \cdots - 48 q^{99}+O(q^{100}) $ 112 * q + 16 * q^3 - 16 * q^9 + 16 * q^11 - 16 * q^17 + 16 * q^19 - 16 * q^25 - 32 * q^27 + 32 * q^35 - 16 * q^41 + 96 * q^43 - 16 * q^49 + 16 * q^51 + 32 * q^57 + 16 * q^59 + 64 * q^65 - 96 * q^73 + 16 * q^75 - 96 * q^81 - 128 * q^83 - 16 * q^89 + 16 * q^91 - 16 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

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
$3$	1.72164	+	2.57662i	0.993990	+	1.48761i	0.868606	+	0.495504i	$0.165016\pi$
$3$	1.72164	+	2.57662i	0.993990	+	1.48761i	0.125385	+	0.992108i	$0.459984\pi$
$4$		0			0
$5$	2.84924	+	0.566749i	1.27422	+	0.253458i	0.785433	−	0.618947i	$-0.212440\pi$
$5$	2.84924	+	0.566749i	1.27422	+	0.253458i	0.488785	+	0.872404i	$0.337440\pi$
$6$		0			0
$7$	1.07350	−	0.213532i	0.405744	−	0.0807075i	0.0120009	−	0.999928i	$-0.496180\pi$
$7$	1.07350	−	0.213532i	0.405744	−	0.0807075i	0.393743	+	0.919220i	$0.371180\pi$
$8$		0			0
$9$	−2.52687	+	6.10039i	−0.842289	+	2.03346i
$10$		0			0
$11$	−1.65107	−	1.10321i	−0.497816	−	0.332630i	0.281184	−	0.959654i	$-0.409273\pi$
$11$	−1.65107	−	1.10321i	−0.497816	−	0.332630i	−0.779000	+	0.627024i	$0.784273\pi$
$12$		0			0
$13$	3.43124	−	3.43124i	0.951654	−	0.951654i	−0.0472302	−	0.998884i	$-0.515039\pi$
$13$	3.43124	−	3.43124i	0.951654	−	0.951654i	0.998884	+	0.0472302i	$0.0150394\pi$
$14$		0			0
$15$	3.44507	+	8.31714i	0.889514	+	2.14748i
$16$		0			0
$17$	−2.78526	−	3.04012i	−0.675526	−	0.737336i
$17$	−2.78526	−	3.04012i	−0.675526	−	0.737336i
$18$		0			0
$19$	0.843066	+	2.03534i	0.193413	+	0.466939i	0.990600	−	0.136793i	$-0.0436795\pi$
$19$	0.843066	+	2.03534i	0.193413	+	0.466939i	−0.797187	+	0.603732i	$0.793680\pi$
$20$		0			0
$21$	2.39837	+	2.39837i	0.523367	+	0.523367i
$22$		0			0
$23$	−3.88838	−	2.59813i	−0.810783	−	0.541748i	0.0796709	−	0.996821i	$-0.474613\pi$
$23$	−3.88838	−	2.59813i	−0.810783	−	0.541748i	−0.890454	+	0.455073i	$0.849613\pi$
$24$		0			0
$25$	3.17755	+	1.31619i	0.635511	+	0.263237i
$26$		0			0
$27$	−10.9508	+	2.17824i	−2.10747	+	0.419203i
$28$		0			0
$29$	0.598581	−	3.00927i	0.111154	−	0.558807i	−0.884569	−	0.466410i	$-0.845547\pi$
$29$	0.598581	−	3.00927i	0.111154	−	0.558807i	0.995722	−	0.0923970i	$-0.0294529\pi$
$30$		0			0
$31$	−5.36812	−	8.03396i	−0.964143	−	1.44294i	−0.895377	−	0.445308i	$-0.853094\pi$
$31$	−5.36812	−	8.03396i	−0.964143	−	1.44294i	−0.0687653	−	0.997633i	$-0.521906\pi$
$32$		0			0
$33$		−	6.15351i		−	1.07119i
$34$		0			0
$35$	3.17967			0.537462
$36$		0			0
$37$	−3.54311	+	2.36743i	−0.582484	+	0.389203i	−0.811615	−	0.584192i	$-0.801411\pi$
$37$	−3.54311	+	2.36743i	−0.582484	+	0.389203i	0.229131	+	0.973396i	$0.426411\pi$
$38$		0			0
$39$	14.7484	+	2.93363i	2.36163	+	0.469757i
$40$		0			0
$41$	0.251769	+	1.26573i	0.0393198	+	0.197674i	0.995452	−	0.0952603i	$-0.0303683\pi$
$41$	0.251769	+	1.26573i	0.0393198	+	0.197674i	−0.956133	+	0.292934i	$0.905368\pi$
$42$		0			0
$43$	−0.398138	+	0.961190i	−0.0607155	+	0.146580i	−0.951326	−	0.308187i	$-0.900278\pi$
$43$	−0.398138	+	0.961190i	−0.0607155	+	0.146580i	0.890610	+	0.454767i	$0.150278\pi$
$44$		0			0
$45$	−10.6570	+	15.9494i	−1.58866	+	2.37759i
$46$		0			0
$47$	−4.54349	+	4.54349i	−0.662736	+	0.662736i	−0.956024	−	0.293288i	$-0.905250\pi$
$47$	−4.54349	+	4.54349i	−0.662736	+	0.662736i	0.293288	+	0.956024i	$0.405250\pi$
$48$		0			0
$49$	−5.36035	+	2.22033i	−0.765765	+	0.317190i
$50$		0			0
$51$	3.03799	−	12.4106i	0.425404	−	1.73783i
$52$		0			0
$53$	−0.113637	+	0.0470698i	−0.0156092	+	0.00646553i	−0.390474	−	0.920614i	$-0.627689\pi$
$53$	−0.113637	+	0.0470698i	−0.0156092	+	0.00646553i	0.374865	+	0.927079i	$0.377689\pi$
$54$		0			0
$55$	−4.07905	−	4.07905i	−0.550019	−	0.550019i
$56$		0			0
$57$	−3.79284	+	5.67639i	−0.502374	+	0.751856i
$58$		0			0
$59$	2.61174	+	1.08182i	0.340019	+	0.140841i	0.546158	−	0.837682i	$-0.316090\pi$
$59$	2.61174	+	1.08182i	0.340019	+	0.140841i	−0.206139	+	0.978523i	$0.566090\pi$
$60$		0			0
$61$	2.10581	+	10.5866i	0.269621	+	1.35548i	0.843761	+	0.536719i	$0.180336\pi$
$61$	2.10581	+	10.5866i	0.269621	+	1.35548i	−0.574140	+	0.818757i	$0.694664\pi$
$62$		0			0
$63$	−1.40996	+	7.08833i	−0.177638	+	0.893045i
$64$		0			0
$65$	11.7211	−	7.83176i	1.45382	−	0.971410i
$66$		0			0
$67$			2.27343i			0.277743i	0.990310	+	0.138872i	$0.0443476\pi$
$67$			2.27343i			0.277743i	−0.990310	+	0.138872i	$0.955652\pi$
$68$		0			0
$69$		−	14.4919i		−	1.74462i
$70$		0			0
$71$	0.572331	−	0.382419i	0.0679231	−	0.0453848i	−0.521145	−	0.853468i	$-0.674495\pi$
$71$	0.572331	−	0.382419i	0.0679231	−	0.0453848i	0.589068	+	0.808083i	$0.299495\pi$
$72$		0			0
$73$	−2.44907	+	12.3123i	−0.286642	+	1.44105i	0.522099	+	0.852885i	$0.325149\pi$
$73$	−2.44907	+	12.3123i	−0.286642	+	1.44105i	−0.808742	+	0.588164i	$0.799851\pi$
$74$		0			0
$75$	2.07930	+	10.4533i	0.240097	+	1.20705i
$76$		0			0
$77$	−2.00799	−	0.831737i	−0.228832	−	0.0947853i
$78$		0			0
$79$	7.26595	−	10.8743i	0.817483	−	1.22345i	−0.154405	−	0.988008i	$-0.549346\pi$
$79$	7.26595	−	10.8743i	0.817483	−	1.22345i	0.971888	−	0.235443i	$-0.0756540\pi$
$80$		0			0
$81$	−10.4587	−	10.4587i	−1.16207	−	1.16207i
$82$		0			0
$83$	0.181706	−	0.0752650i	0.0199448	−	0.00826141i	−0.372689	−	0.927956i	$-0.621564\pi$
$83$	0.181706	−	0.0752650i	0.0199448	−	0.00826141i	0.392634	+	0.919695i	$0.371564\pi$
$84$		0			0
$85$	−6.21290	−	10.2406i	−0.673883	−	1.11074i
$86$		0			0
$87$	8.78428	−	3.63857i	0.941774	−	0.390095i
$88$		0			0
$89$	5.16813	−	5.16813i	0.547820	−	0.547820i	−0.377990	−	0.925810i	$-0.623384\pi$
$89$	5.16813	−	5.16813i	0.547820	−	0.547820i	0.925810	+	0.377990i	$0.123384\pi$
$90$		0			0
$91$	2.95075	−	4.41611i	0.309322	−	0.462934i
$92$		0			0
$93$	11.4585	−	27.6632i	1.18819	−	2.86854i
$94$		0			0
$95$	1.24857	+	6.27698i	0.128100	+	0.644005i
$96$		0			0
$97$	15.5086	+	3.08484i	1.57466	+	0.313219i	0.903663	−	0.428245i	$-0.140868\pi$
$97$	15.5086	+	3.08484i	1.57466	+	0.313219i	0.670993	+	0.741464i	$0.265868\pi$
$98$		0			0
$99$	10.9020	−	7.28451i	1.09570	−	0.732121i
$100$		0			0
$101$	−6.93385			−0.689944			−0.344972	−	0.938613i	$-0.612112\pi$
$101$	−6.93385			−0.689944			−0.344972	+	0.938613i	$0.612112\pi$
$102$		0			0
$103$		−	1.42621i		−	0.140528i	−0.997528	−	0.0702642i	$-0.977616\pi$
$103$		−	1.42621i		−	0.140528i	0.997528	−	0.0702642i	$-0.0223842\pi$
$104$		0			0
$105$	5.47425	+	8.19280i	0.534233	+	0.799536i
$106$		0			0
$107$	−1.47646	+	7.42265i	−0.142735	+	0.717575i	0.841437	+	0.540355i	$0.181710\pi$
$107$	−1.47646	+	7.42265i	−0.142735	+	0.717575i	−0.984171	+	0.177219i	$0.943290\pi$
$108$		0			0
$109$	7.31548	−	1.45514i	0.700695	−	0.139377i	0.168129	−	0.985765i	$-0.446228\pi$
$109$	7.31548	−	1.45514i	0.700695	−	0.139377i	0.532567	+	0.846388i	$0.321228\pi$
$110$		0			0
$111$	−12.1999	−	5.05338i	−1.15797	−	0.479646i
$112$		0			0
$113$	−6.02876	−	4.02829i	−0.567138	−	0.378950i	0.238693	−	0.971095i	$-0.423281\pi$
$113$	−6.02876	−	4.02829i	−0.567138	−	0.378950i	−0.805831	+	0.592145i	$0.798281\pi$
$114$		0			0
$115$	−9.60643	−	9.60643i	−0.895804	−	0.895804i
$116$		0			0
$117$	12.2616	+	29.6022i	1.13359	+	2.73672i
$118$		0			0
$119$	−3.63914	−	2.66882i	−0.333599	−	0.244650i
$120$		0			0
$121$	−2.70056	−	6.51972i	−0.245505	−	0.592702i
$122$		0			0
$123$	−2.82785	+	2.82785i	−0.254978	+	0.254978i
$124$		0			0
$125$	−3.76967	−	2.51882i	−0.337170	−	0.225290i
$126$		0			0
$127$	4.60400	−	11.1150i	0.408539	−	0.986300i	−0.576984	−	0.816756i	$-0.695770\pi$
$127$	4.60400	−	11.1150i	0.408539	−	0.986300i	0.985523	−	0.169544i	$-0.0542296\pi$
$128$		0			0
$129$	−3.16207	+	0.628975i	−0.278405	+	0.0553782i
$130$		0			0
$131$	1.18604	+	0.235918i	0.103625	+	0.0206122i	0.246630	−	0.969110i	$-0.420677\pi$
$131$	1.18604	+	0.235918i	0.103625	+	0.0206122i	−0.143006	+	0.989722i	$0.545677\pi$
$132$		0			0
$133$	1.33964	+	2.00491i	0.116162	+	0.173848i
$134$		0			0
$135$	−32.4358			−2.79163
$136$		0			0
$137$	−7.10936			−0.607394			−0.303697	−	0.952769i	$-0.598221\pi$
$137$	−7.10936			−0.607394			−0.303697	+	0.952769i	$0.598221\pi$
$138$		0			0
$139$	10.3226	+	15.4488i	0.875550	+	1.31035i	0.949718	+	0.313108i	$0.101370\pi$
$139$	10.3226	+	15.4488i	0.875550	+	1.31035i	−0.0741672	+	0.997246i	$0.523630\pi$
$140$		0			0
$141$	−19.5291	−	3.88458i	−1.64465	−	0.327141i
$142$		0			0
$143$	−9.45058	+	1.87984i	−0.790298	+	0.157200i
$144$		0			0
$145$	3.41100	−	8.23488i	0.283268	−	0.683869i
$146$		0			0
$147$	−14.9496	−	9.98898i	−1.23302	−	0.823877i
$148$		0			0
$149$	−10.5928	+	10.5928i	−0.867798	+	0.867798i	−0.992228	−	0.124430i	$-0.960290\pi$
$149$	−10.5928	+	10.5928i	−0.867798	+	0.867798i	0.124430	+	0.992228i	$0.460290\pi$
$150$		0			0
$151$	4.25657	+	10.2763i	0.346395	+	0.836272i	0.997040	+	0.0768894i	$0.0244988\pi$
$151$	4.25657	+	10.2763i	0.346395	+	0.836272i	−0.650644	+	0.759382i	$0.725501\pi$
$152$		0			0
$153$	25.5839	−	9.30924i	2.06833	−	0.752608i
$154$		0			0
$155$	−10.7418	−	25.9330i	−0.862803	−	2.08299i
$156$		0			0
$157$	4.32762	+	4.32762i	0.345382	+	0.345382i	0.858386	−	0.513004i	$-0.171468\pi$
$157$	4.32762	+	4.32762i	0.345382	+	0.345382i	−0.513004	+	0.858386i	$0.671468\pi$
$158$		0			0
$159$	−0.316922	−	0.211761i	−0.0251336	−	0.0167937i
$160$		0			0
$161$	−4.72895	−	1.95880i	−0.372694	−	0.154375i
$162$		0			0
$163$	23.4802	−	4.67051i	1.83911	−	0.365823i	0.851707	−	0.524018i	$-0.175568\pi$
$163$	23.4802	−	4.67051i	1.83911	−	0.365823i	0.987408	+	0.158195i	$0.0505676\pi$
$164$		0			0
$165$	3.48749	−	17.5328i	0.271501	−	1.36493i
$166$		0			0
$167$	0.314811	+	0.471148i	0.0243608	+	0.0364586i	0.843450	−	0.537207i	$-0.180521\pi$
$167$	0.314811	+	0.471148i	0.0243608	+	0.0364586i	−0.819089	+	0.573666i	$0.805521\pi$
$168$		0			0
$169$		−	10.5468i		−	0.811290i
$170$		0			0
$171$	−14.5467			−1.11241
$172$		0			0
$173$	7.47726	−	4.99615i	0.568486	−	0.379850i	−0.237856	−	0.971301i	$-0.576445\pi$
$173$	7.47726	−	4.99615i	0.568486	−	0.379850i	0.806341	+	0.591451i	$0.201445\pi$
$174$		0			0
$175$	3.69215	+	0.734414i	0.279100	+	0.0555165i
$176$		0			0
$177$	1.70905	+	8.59196i	0.128460	+	0.645811i
$178$		0			0
$179$	4.40207	−	10.6275i	0.329027	−	0.794340i	−0.669639	−	0.742687i	$-0.733551\pi$
$179$	4.40207	−	10.6275i	0.329027	−	0.794340i	0.998665	−	0.0516532i	$-0.0164490\pi$
$180$		0			0
$181$	2.33686	−	3.49735i	0.173697	−	0.259956i	−0.734399	−	0.678718i	$-0.762536\pi$
$181$	2.33686	−	3.49735i	0.173697	−	0.259956i	0.908096	+	0.418762i	$0.137536\pi$
$182$		0			0
$183$	−23.6522	+	23.6522i	−1.74842	+	1.74842i
$184$		0			0
$185$	−11.4369	+	4.73732i	−0.840858	+	0.348295i
$186$		0			0
$187$	1.24478	+	8.09217i	0.0910274	+	0.591758i
$188$		0			0
$189$	−11.2905	+	4.67668i	−0.821263	+	0.340178i
$190$		0			0
$191$	10.1812	+	10.1812i	0.736687	+	0.736687i	0.971935	−	0.235248i	$-0.0755902\pi$
$191$	10.1812	+	10.1812i	0.736687	+	0.736687i	−0.235248	+	0.971935i	$0.575590\pi$
$192$		0			0
$193$	0.284175	−	0.425297i	0.0204553	−	0.0306136i	−0.821101	−	0.570783i	$-0.806640\pi$
$193$	0.284175	−	0.425297i	0.0204553	−	0.0306136i	0.841556	+	0.540169i	$0.181640\pi$
$194$		0			0
$195$	40.3589	+	16.7172i	2.89016	+	1.19714i
$196$		0			0
$197$	−2.96479	−	14.9050i	−0.211232	−	1.06194i	−0.930245	−	0.366940i	$-0.880406\pi$
$197$	−2.96479	−	14.9050i	−0.211232	−	1.06194i	0.719012	−	0.694997i	$-0.244594\pi$
$198$		0			0
$199$	−0.0927723	+	0.466398i	−0.00657645	+	0.0330621i	−0.983934	−	0.178532i	$-0.942865\pi$
$199$	−0.0927723	+	0.466398i	−0.00657645	+	0.0330621i	0.977358	+	0.211594i	$0.0678653\pi$
$200$		0			0
$201$	−5.85776	+	3.91403i	−0.413174	+	0.276074i
$202$		0			0
$203$		−	3.35826i		−	0.235704i
$204$		0			0
$205$			3.74906i			0.261845i
$206$		0			0
$207$	25.6750	−	17.1555i	1.78454	−	1.19239i
$208$		0			0
$209$	0.853448	−	4.29057i	0.0590342	−	0.296785i
$210$		0			0
$211$	−1.02148	−	5.13534i	−0.0703218	−	0.353531i	0.929564	−	0.368661i	$-0.120184\pi$
$211$	−1.02148	−	5.13534i	−0.0703218	−	0.353531i	−0.999886	+	0.0151300i	$0.995184\pi$
$212$		0			0
$213$	1.97070	+	0.816289i	0.135030	+	0.0559312i
$214$		0			0
$215$	−1.67914	+	2.51301i	−0.114517	+	0.171386i
$216$		0			0
$217$	−7.47817	−	7.47817i	−0.507652	−	0.507652i
$218$		0			0
$219$	−35.9406	+	14.8871i	−2.42864	+	1.00598i
$220$		0			0
$221$	−19.9883	−	0.874457i	−1.34456	−	0.0588223i
$222$		0			0
$223$	5.56999	−	2.30717i	0.372994	−	0.154499i	−0.188308	−	0.982110i	$-0.560300\pi$
$223$	5.56999	−	2.30717i	0.372994	−	0.154499i	0.561303	+	0.827611i	$0.310300\pi$
$224$		0			0
$225$	−16.0585	+	16.0585i	−1.07057	+	1.07057i
$226$		0			0
$227$	−6.86470	+	10.2737i	−0.455626	+	0.681893i	−0.986165	−	0.165768i	$-0.946990\pi$
$227$	−6.86470	+	10.2737i	−0.455626	+	0.681893i	0.530539	+	0.847661i	$0.321990\pi$
$228$		0			0
$229$	−2.89813	+	6.99670i	−0.191514	+	0.462355i	−0.990246	−	0.139332i	$-0.955505\pi$
$229$	−2.89813	+	6.99670i	−0.191514	+	0.462355i	0.798732	+	0.601687i	$0.205505\pi$
$230$		0			0
$231$	−1.31397	−	6.60578i	−0.0864530	−	0.434629i
$232$		0			0
$233$	−19.4553	−	3.86991i	−1.27456	−	0.253526i	−0.488986	−	0.872292i	$-0.662633\pi$
$233$	−19.4553	−	3.86991i	−1.27456	−	0.253526i	−0.785576	+	0.618765i	$0.787633\pi$
$234$		0			0
$235$	−15.5205	+	10.3705i	−1.01245	+	0.676494i
$236$		0			0
$237$	40.5282			2.63259
$238$		0			0
$239$			24.9953i			1.61681i	0.588625	+	0.808406i	$0.299669\pi$
$239$			24.9953i			1.61681i	−0.588625	+	0.808406i	$0.700331\pi$
$240$		0			0
$241$	8.78732	+	13.1511i	0.566041	+	0.847140i	0.998513	−	0.0545072i	$-0.0173588\pi$
$241$	8.78732	+	13.1511i	0.566041	+	0.847140i	−0.432473	+	0.901647i	$0.642359\pi$
$242$		0			0
$243$	2.40720	−	12.1018i	0.154422	−	0.776332i
$244$		0			0
$245$	−16.5313	+	3.28828i	−1.05615	+	0.210080i
$246$		0			0
$247$	9.87650	+	4.09098i	0.628427	+	0.260303i
$248$		0			0
$249$	0.506762	+	0.338607i	0.0321147	+	0.0214584i
$250$		0			0
$251$	−11.8712	−	11.8712i	−0.749301	−	0.749301i	0.225047	−	0.974348i	$-0.427747\pi$
$251$	−11.8712	−	11.8712i	−0.749301	−	0.749301i	−0.974348	+	0.225047i	$0.927747\pi$
$252$		0			0
$253$	3.55370	+	8.57939i	0.223419	+	0.539382i
$254$		0			0
$255$	15.6896	−	33.6388i	0.982523	−	2.10655i
$256$		0			0
$257$	8.73779	+	21.0949i	0.545048	+	1.31586i	0.921122	+	0.389273i	$0.127274\pi$
$257$	8.73779	+	21.0949i	0.545048	+	1.31586i	−0.376074	+	0.926590i	$0.622726\pi$
$258$		0			0
$259$	−3.29800	+	3.29800i	−0.204928	+	0.204928i
$260$		0			0
$261$	16.8452	+	11.2556i	1.04269	+	0.696704i
$262$		0			0
$263$	7.24757	−	17.4972i	0.446904	−	1.07892i	−0.526571	−	0.850131i	$-0.676523\pi$
$263$	7.24757	−	17.4972i	0.446904	−	1.07892i	0.973475	−	0.228791i	$-0.0734774\pi$
$264$		0			0
$265$	−0.350454	+	0.0697097i	−0.0215282	+	0.00428223i
$266$		0			0
$267$	22.2140	+	4.41863i	1.35947	+	0.270416i
$268$		0			0
$269$	13.3618	+	19.9973i	0.814681	+	1.21926i	0.972756	+	0.231830i	$0.0744712\pi$
$269$	13.3618	+	19.9973i	0.814681	+	1.21926i	−0.158075	+	0.987427i	$0.550529\pi$
$270$		0			0
$271$	−6.93459			−0.421246			−0.210623	−	0.977567i	$-0.567549\pi$
$271$	−6.93459			−0.421246			−0.210623	+	0.977567i	$0.567549\pi$
$272$		0			0
$273$	16.4588			0.996129
$274$		0			0
$275$	−3.79434	−	5.67862i	−0.228807	−	0.342434i
$276$		0			0
$277$	19.9019	+	3.95873i	1.19579	+	0.237857i	0.752543	−	0.658543i	$-0.228827\pi$
$277$	19.9019	+	3.95873i	1.19579	+	0.237857i	0.443245	+	0.896400i	$0.353827\pi$
$278$		0			0
$279$	62.5748	−	12.4469i	3.74626	−	0.745177i
$280$		0			0
$281$	7.51376	−	18.1398i	0.448233	−	1.08213i	−0.524750	−	0.851256i	$-0.675841\pi$
$281$	7.51376	−	18.1398i	0.448233	−	1.08213i	0.972984	−	0.230874i	$-0.0741587\pi$
$282$		0			0
$283$	8.45289	+	5.64804i	0.502472	+	0.335741i	0.780837	−	0.624734i	$-0.214793\pi$
$283$	8.45289	+	5.64804i	0.502472	+	0.335741i	−0.278366	+	0.960475i	$0.589793\pi$
$284$		0			0
$285$	−14.0238	+	14.0238i	−0.830698	+	0.830698i
$286$		0			0
$287$	0.540548	+	1.30500i	0.0319075	+	0.0770316i
$288$		0			0
$289$	−1.48461	+	16.9351i	−0.0873299	+	0.996179i
$290$		0			0
$291$	18.7517	+	45.2707i	1.09925	+	2.65381i
$292$		0			0
$293$	−12.6074	−	12.6074i	−0.736534	−	0.736534i	0.235371	−	0.971906i	$-0.424369\pi$
$293$	−12.6074	−	12.6074i	−0.736534	−	0.736534i	−0.971906	+	0.235371i	$0.924369\pi$
$294$		0			0
$295$	6.82835	+	4.56256i	0.397562	+	0.265642i
$296$		0			0
$297$	20.4835	+	8.48455i	1.18857	+	0.492324i
$298$		0			0
$299$	−22.2568	+	4.42714i	−1.28714	+	0.256028i
$300$		0			0
$301$	−0.222155	+	1.11685i	−0.0128048	+	0.0643742i
$302$		0			0
$303$	−11.9376	−	17.8659i	−0.685798	−	1.02637i
$304$		0			0
$305$			31.3572i			1.79551i
$306$		0			0
$307$	9.55065			0.545084			0.272542	−	0.962144i	$-0.412136\pi$
$307$	9.55065			0.545084			0.272542	+	0.962144i	$0.412136\pi$
$308$		0			0
$309$	3.67480	−	2.45542i	0.209052	−	0.139684i
$310$		0			0
$311$	−15.6177	−	3.10656i	−0.885599	−	0.176157i	−0.268723	−	0.963217i	$-0.586602\pi$
$311$	−15.6177	−	3.10656i	−0.885599	−	0.176157i	−0.616875	+	0.787061i	$0.711602\pi$
$312$		0			0
$313$	0.316223	+	1.58976i	0.0178740	+	0.0898584i	0.988693	−	0.149956i	$-0.0479133\pi$
$313$	0.316223	+	1.58976i	0.0178740	+	0.0898584i	−0.970819	+	0.239815i	$0.922913\pi$
$314$		0			0
$315$	−8.03460	+	19.3972i	−0.452698	+	1.09291i
$316$		0			0
$317$	−0.260456	+	0.389800i	−0.0146287	+	0.0218933i	−0.838712	−	0.544575i	$-0.816691\pi$
$317$	−0.260456	+	0.389800i	−0.0146287	+	0.0218933i	0.824083	+	0.566469i	$0.191691\pi$
$318$		0			0
$319$	−4.30815	+	4.30815i	−0.241210	+	0.241210i
$320$		0			0
$321$	−21.6673	+	8.97488i	−1.20935	+	0.500929i
$322$		0			0
$323$	3.83951	−	8.23198i	0.213636	−	0.458040i
$324$		0			0
$325$	15.4191	−	6.38679i	0.855297	−	0.354276i
$326$		0			0
$327$	16.3440	+	16.3440i	0.903823	+	0.903823i
$328$		0			0
$329$	−3.90725	+	5.84761i	−0.215413	+	0.322389i
$330$		0			0
$331$	−23.3026	−	9.65226i	−1.28083	−	0.530536i	−0.364588	−	0.931169i	$-0.618790\pi$
$331$	−23.3026	−	9.65226i	−1.28083	−	0.530536i	−0.916239	+	0.400633i	$0.868790\pi$
$332$		0			0
$333$	−5.48930	−	27.5966i	−0.300812	−	1.51228i
$334$		0			0
$335$	−1.28846	+	6.47754i	−0.0703962	+	0.353906i
$336$		0			0
$337$	4.75051	−	3.17419i	0.258777	−	0.172909i	−0.419414	−	0.907795i	$-0.637764\pi$
$337$	4.75051	−	3.17419i	0.258777	−	0.172909i	0.678191	+	0.734886i	$0.262764\pi$
$338$		0			0
$339$		−	22.4691i		−	1.22035i
$340$		0			0
$341$			19.1868i			1.03902i
$342$		0			0
$343$	−11.6507	+	7.78475i	−0.629078	+	0.420337i
$344$		0			0
$345$	8.21328	−	41.2909i	0.442188	−	2.22303i
$346$		0			0
$347$	5.22360	+	26.2608i	0.280418	+	1.40976i	0.822182	+	0.569225i	$0.192757\pi$
$347$	5.22360	+	26.2608i	0.280418	+	1.40976i	−0.541764	+	0.840531i	$0.682243\pi$
$348$		0			0
$349$	−5.23539	−	2.16857i	−0.280244	−	0.116081i	0.238134	−	0.971232i	$-0.423464\pi$
$349$	−5.23539	−	2.16857i	−0.280244	−	0.116081i	−0.518378	+	0.855151i	$0.673464\pi$
$350$		0			0
$351$	−30.1006	+	45.0487i	−1.60665	+	2.40452i
$352$		0			0
$353$	−17.2667	−	17.2667i	−0.919016	−	0.919016i	0.0779424	−	0.996958i	$-0.475165\pi$
$353$	−17.2667	−	17.2667i	−0.919016	−	0.919016i	−0.996958	+	0.0779424i	$0.975165\pi$
$354$		0			0
$355$	1.84744	−	0.765235i	0.0980520	−	0.0406145i
$356$		0			0
$357$	0.611229	−	13.9714i	0.0323497	−	0.739446i
$358$		0			0
$359$	−33.2447	+	13.7704i	−1.75459	+	0.726774i	−0.757309	+	0.653057i	$0.773486\pi$
$359$	−33.2447	+	13.7704i	−1.75459	+	0.726774i	−0.997279	+	0.0737173i	$0.976514\pi$
$360$		0			0
$361$	10.0032	−	10.0032i	0.526483	−	0.526483i
$362$		0			0
$363$	12.1494	−	18.1829i	0.637681	−	0.954357i
$364$		0			0
$365$	−13.9560	+	33.6927i	−0.730490	+	1.76356i
$366$		0			0
$367$	2.88416	+	14.4997i	0.150552	+	0.756876i	0.980110	+	0.198455i	$0.0635924\pi$
$367$	2.88416	+	14.4997i	0.150552	+	0.756876i	−0.829558	+	0.558421i	$0.811408\pi$
$368$		0			0
$369$	−8.35764	−	1.66244i	−0.435081	−	0.0865431i
$370$		0			0
$371$	−0.111938	+	0.0747944i	−0.00581151	+	0.00388313i
$372$		0			0
$373$	2.68975			0.139270			0.0696349	−	0.997573i	$-0.477817\pi$
$373$	2.68975			0.139270			0.0696349	+	0.997573i	$0.477817\pi$
$374$		0			0
$375$		−	14.0495i		−	0.725514i
$376$		0			0
$377$	−8.27164	−	12.3794i	−0.426011	−	0.637571i
$378$		0			0
$379$	1.19273	−	5.99624i	0.0612662	−	0.308006i	−0.937986	−	0.346673i	$-0.887311\pi$
$379$	1.19273	−	5.99624i	0.0612662	−	0.308006i	0.999252	+	0.0386673i	$0.0123112\pi$
$380$		0			0
$381$	36.5657	−	7.27336i	1.87332	−	0.372626i
$382$		0			0
$383$	11.7055	+	4.84857i	0.598122	+	0.247750i	0.661141	−	0.750262i	$-0.270073\pi$
$383$	11.7055	+	4.84857i	0.598122	+	0.247750i	−0.0630184	+	0.998012i	$0.520073\pi$
$384$		0			0
$385$	−5.24986	−	3.50784i	−0.267558	−	0.178776i
$386$		0			0
$387$	−4.85760	−	4.85760i	−0.246925	−	0.246925i
$388$		0			0
$389$	7.98630	+	19.2806i	0.404921	+	0.977567i	0.986453	+	0.164043i	$0.0524536\pi$
$389$	7.98630	+	19.2806i	0.404921	+	0.977567i	−0.581532	+	0.813524i	$0.697546\pi$
$390$		0			0
$391$	2.93154	+	19.0576i	0.148254	+	0.963784i
$392$		0			0
$393$	1.43406	+	3.46214i	0.0723390	+	0.174642i
$394$		0			0
$395$	26.8654	−	26.8654i	1.35174	−	1.35174i
$396$		0			0
$397$	−32.1873	−	21.5068i	−1.61543	−	1.07940i	−0.939563	−	0.342376i	$-0.888768\pi$
$397$	−32.1873	−	21.5068i	−1.61543	−	1.07940i	−0.675870	−	0.737021i	$-0.736232\pi$
$398$		0			0
$399$	−2.85952	+	6.90349i	−0.143155	+	0.345607i
$400$		0			0
$401$	3.73319	−	0.742577i	0.186427	−	0.0370825i	−0.100994	−	0.994887i	$-0.532202\pi$
$401$	3.73319	−	0.742577i	0.186427	−	0.0370825i	0.287421	+	0.957804i	$0.407202\pi$
$402$		0			0
$403$	−45.9857	−	9.14712i	−2.29071	−	0.455651i
$404$		0			0
$405$	−23.8718	−	35.7267i	−1.18620	−	1.77527i
$406$		0			0
$407$	8.46170			0.419431
$408$		0			0
$409$	−25.4900			−1.26040			−0.630200	−	0.776433i	$-0.717027\pi$
$409$	−25.4900			−1.26040			−0.630200	+	0.776433i	$0.717027\pi$
$410$		0			0
$411$	−12.2398	−	18.3181i	−0.603744	−	0.903566i
$412$		0			0
$413$	3.03470	+	0.603639i	0.149328	+	0.0297032i
$414$		0			0
$415$	0.560380	−	0.111466i	0.0275080	−	0.00547167i
$416$		0			0
$417$	−22.0340	+	53.1948i	−1.07901	+	2.60496i
$418$		0			0
$419$	0.997962	+	0.666817i	0.0487537	+	0.0325762i	0.579708	−	0.814824i	$-0.303167\pi$
$419$	0.997962	+	0.666817i	0.0487537	+	0.0325762i	−0.530955	+	0.847400i	$0.678167\pi$
$420$		0			0
$421$	−4.37164	+	4.37164i	−0.213061	+	0.213061i	−0.805566	−	0.592506i	$-0.798139\pi$
$421$	−4.37164	+	4.37164i	−0.213061	+	0.213061i	0.592506	+	0.805566i	$0.298139\pi$
$422$		0			0
$423$	−16.2363	−	39.1978i	−0.789435	−	1.90586i
$424$		0			0
$425$	−4.84897	−	13.3261i	−0.235210	−	0.646409i
$426$		0			0
$427$	4.52116	+	10.9150i	0.218794	+	0.528216i
$428$		0			0
$429$	−21.1142	−	21.1142i	−1.01940	−	1.01940i
$430$		0			0
$431$	−14.6489	−	9.78805i	−0.705610	−	0.471474i	0.150272	−	0.988645i	$-0.451985\pi$
$431$	−14.6489	−	9.78805i	−0.705610	−	0.471474i	−0.855882	+	0.517171i	$0.826985\pi$
$432$		0			0
$433$	27.3362	+	11.3230i	1.31369	+	0.544150i	0.925960	−	0.377622i	$-0.123258\pi$
$433$	27.3362	+	11.3230i	1.31369	+	0.544150i	0.387733	+	0.921772i	$0.373258\pi$
$434$		0			0
$435$	27.0907	−	5.38867i	1.29890	−	0.258367i
$436$		0			0
$437$	2.00993	−	10.1046i	0.0961478	−	0.483368i
$438$		0			0
$439$	−10.6237	−	15.8995i	−0.507043	−	0.758843i	0.486330	−	0.873775i	$-0.338335\pi$
$439$	−10.6237	−	15.8995i	−0.507043	−	0.758843i	−0.993373	+	0.114932i	$0.963335\pi$
$440$		0			0
$441$		−	38.3107i		−	1.82432i
$442$		0			0
$443$	6.76589			0.321457			0.160729	−	0.986999i	$-0.448616\pi$
$443$	6.76589			0.321457			0.160729	+	0.986999i	$0.448616\pi$
$444$		0			0
$445$	17.6542	−	11.7962i	0.836892	−	0.559193i
$446$		0			0
$447$	−45.5307	−	9.05663i	−2.15353	−	0.428364i
$448$		0			0
$449$	−1.84456	−	9.27321i	−0.0870500	−	0.437630i	−0.999590	−	0.0286418i	$-0.990882\pi$
$449$	−1.84456	−	9.27321i	−0.0870500	−	0.437630i	0.912540	−	0.408988i	$-0.134118\pi$
$450$		0			0
$451$	0.980677	−	2.36756i	0.0461783	−	0.111484i
$452$		0			0
$453$	−19.1498	+	28.6596i	−0.899734	+	1.34655i
$454$		0			0
$455$	10.9102	−	10.9102i	0.511478	−	0.511478i
$456$		0			0
$457$	−21.8728	+	9.06001i	−1.02317	+	0.423809i	−0.830241	−	0.557404i	$-0.811797\pi$
$457$	−21.8728	+	9.06001i	−1.02317	+	0.423809i	−0.192925	+	0.981214i	$0.561797\pi$
$458$		0			0
$459$	37.1229	+	27.2246i	1.73275	+	1.27074i
$460$		0			0
$461$	27.7787	−	11.5063i	1.29378	−	0.535903i	0.373673	−	0.927560i	$-0.378098\pi$
$461$	27.7787	−	11.5063i	1.29378	−	0.535903i	0.920111	+	0.391657i	$0.128098\pi$
$462$		0			0
$463$	−14.9625	−	14.9625i	−0.695368	−	0.695368i	0.268040	−	0.963408i	$-0.413624\pi$
$463$	−14.9625	−	14.9625i	−0.695368	−	0.695368i	−0.963408	+	0.268040i	$0.913624\pi$
$464$		0			0
$465$	48.3260	−	72.3249i	2.24106	−	3.35399i
$466$		0			0
$467$	−33.3168	−	13.8003i	−1.54172	−	0.638601i	−0.559924	−	0.828544i	$-0.689170\pi$
$467$	−33.3168	−	13.8003i	−1.54172	−	0.638601i	−0.981795	+	0.189943i	$0.939170\pi$
$468$		0			0
$469$	0.485450	+	2.44052i	0.0224160	+	0.112693i
$470$		0			0
$471$	−3.70002	+	18.6012i	−0.170488	+	0.857100i
$472$		0			0
$473$	1.71775	−	1.14776i	0.0789821	−	0.0527742i
$474$		0			0
$475$			7.57704i			0.347659i
$476$		0			0
$477$		−	0.812166i		−	0.0371865i
$478$		0			0
$479$	14.6280	−	9.77412i	0.668371	−	0.446591i	−0.174536	−	0.984651i	$-0.555843\pi$
$479$	14.6280	−	9.77412i	0.668371	−	0.446591i	0.842907	+	0.538060i	$0.180843\pi$
$480$		0			0
$481$	−4.03404	+	20.2805i	−0.183936	+	0.924710i
$482$		0			0
$483$	−3.09449	−	15.5571i	−0.140804	−	0.707871i
$484$		0			0
$485$	42.4392	+	17.5789i	1.92707	+	0.798217i
$486$		0			0
$487$	8.20327	−	12.2771i	0.371726	−	0.556327i	−0.597697	−	0.801722i	$-0.703918\pi$
$487$	8.20327	−	12.2771i	0.371726	−	0.556327i	0.969423	+	0.245395i	$0.0789176\pi$
$488$		0			0
$489$	52.4587	+	52.4587i	2.37226	+	2.37226i
$490$		0			0
$491$	−18.3182	+	7.58764i	−0.826688	+	0.342425i	−0.755591	−	0.655044i	$-0.772650\pi$
$491$	−18.3182	+	7.58764i	−0.826688	+	0.342425i	−0.0710973	+	0.997469i	$0.522650\pi$
$492$		0			0
$493$	−10.8157	+	6.56185i	−0.487116	+	0.295531i
$494$		0			0
$495$	35.1910	−	14.5766i	1.58172	−	0.655169i
$496$		0			0
$497$	0.532737	−	0.532737i	0.0238965	−	0.0238965i
$498$		0			0
$499$	2.45869	−	3.67969i	0.110066	−	0.164725i	−0.772347	−	0.635201i	$-0.780917\pi$
$499$	2.45869	−	3.67969i	0.110066	−	0.164725i	0.882413	+	0.470475i	$0.155917\pi$
$500$		0			0
$501$	−0.671978	+	1.62230i	−0.0300218	+	0.0724789i
$502$		0			0
$503$	−5.36414	−	26.9673i	−0.239175	−	1.20241i	−0.894500	−	0.447067i	$-0.852468\pi$
$503$	−5.36414	−	26.9673i	−0.239175	−	1.20241i	0.655325	−	0.755347i	$-0.272532\pi$
$504$		0			0
$505$	−19.7562	−	3.92975i	−0.879139	−	0.174872i
$506$		0			0
$507$	27.1750	−	18.1578i	1.20688	−	0.806414i
$508$		0			0
$509$	−32.6513			−1.44724			−0.723621	−	0.690197i	$-0.757524\pi$
$509$	−32.6513			−1.44724			−0.723621	+	0.690197i	$0.757524\pi$
$510$		0			0
$511$			13.7402i			0.607832i
$512$		0			0
$513$	−13.6657	−	20.4521i	−0.603355	−	0.902984i
$514$		0			0
$515$	0.808302	−	4.06361i	0.0356180	−	0.179064i
$516$		0			0
$517$	12.5140	−	2.48920i	0.550367	−	0.109475i
$518$		0			0
$519$	25.7463	+	10.6645i	1.13014	+	0.468119i
$520$		0			0
$521$	−0.761700	−	0.508952i	−0.0333707	−	0.0222976i	0.538773	−	0.842451i	$-0.318888\pi$
$521$	−0.761700	−	0.508952i	−0.0333707	−	0.0222976i	−0.572144	+	0.820153i	$0.693888\pi$
$522$		0			0
$523$	27.5393	+	27.5393i	1.20421	+	1.20421i	0.972874	+	0.231334i	$0.0743090\pi$
$523$	27.5393	+	27.5393i	1.20421	+	1.20421i	0.231334	+	0.972874i	$0.425691\pi$
$524$		0			0
$525$	4.46425	+	10.7777i	0.194836	+	0.470375i
$526$		0			0
$527$	−9.47253	+	38.6964i	−0.412630	+	1.68564i
$528$		0			0
$529$	−0.432517	−	1.04419i	−0.0188051	−	0.0453995i
$530$		0			0
$531$	−13.1990	+	13.1990i	−0.572789	+	0.572789i
$532$		0			0
$533$	5.20690	+	3.47914i	0.225536	+	0.150698i
$534$		0			0
$535$	−8.41356	+	20.3121i	−0.363750	+	0.878170i
$536$		0			0
$537$	34.9619	−	6.95436i	1.50872	−	0.300103i
$538$		0			0
$539$	11.2998	+	2.24767i	0.486717	+	0.0968141i
$540$		0			0
$541$	−10.6957	−	16.0073i	−0.459845	−	0.688206i	0.527002	−	0.849864i	$-0.323316\pi$
$541$	−10.6957	−	16.0073i	−0.459845	−	0.688206i	−0.986847	+	0.161658i	$0.948316\pi$
$542$		0			0
$543$	13.0346			0.559367
$544$		0			0
$545$	21.6682			0.928165
$546$		0			0
$547$	−5.75904	−	8.61902i	−0.246239	−	0.368522i	0.687676	−	0.726018i	$-0.258631\pi$
$547$	−5.75904	−	8.61902i	−0.246239	−	0.368522i	−0.933915	+	0.357495i	$0.883631\pi$
$548$		0			0
$549$	−69.9035	−	13.9047i	−2.98341	−	0.593437i
$550$		0			0
$551$	6.62953	−	1.31870i	0.282428	−	0.0561783i
$552$		0			0
$553$	5.47798	−	13.2250i	0.232948	−	0.562385i
$554$		0			0
$555$	−31.8965	−	21.3126i	−1.35393	−	0.904669i
$556$		0			0
$557$	12.2722	−	12.2722i	0.519988	−	0.519988i	−0.397580	−	0.917568i	$-0.630150\pi$
$557$	12.2722	−	12.2722i	0.519988	−	0.519988i	0.917568	+	0.397580i	$0.130150\pi$
$558$		0			0
$559$	1.93196	+	4.66418i	0.0817134	+	0.197274i
$560$		0			0
$561$	−18.7074	+	17.1392i	−0.789826	+	0.723616i
$562$		0			0
$563$	13.9907	+	33.7766i	0.589639	+	1.42352i	0.883848	+	0.467774i	$0.154944\pi$
$563$	13.9907	+	33.7766i	0.589639	+	1.42352i	−0.294209	+	0.955741i	$0.595056\pi$
$564$		0			0
$565$	−14.8944	−	14.8944i	−0.626610	−	0.626610i
$566$		0			0
$567$	−13.4606	−	8.99410i	−0.565293	−	0.377717i
$568$		0			0
$569$	−26.4641	−	10.9618i	−1.10943	−	0.459543i	−0.248691	−	0.968583i	$-0.580000\pi$
$569$	−26.4641	−	10.9618i	−1.10943	−	0.459543i	−0.860743	+	0.509040i	$0.830000\pi$
$570$		0			0
$571$	15.6422	−	3.11143i	0.654607	−	0.130209i	0.143397	−	0.989665i	$-0.454197\pi$
$571$	15.6422	−	3.11143i	0.654607	−	0.130209i	0.511210	+	0.859456i	$0.329197\pi$
$572$		0			0
$573$	−8.70471	+	43.7616i	−0.363645	+	1.82817i
$574$		0			0
$575$	−8.93591	−	13.3735i	−0.372653	−	0.557715i
$576$		0			0
$577$			0.533016i			0.0221898i	0.999938	+	0.0110949i	$0.00353168\pi$
$577$			0.533016i			0.0221898i	−0.999938	+	0.0110949i	$0.996468\pi$
$578$		0			0
$579$	1.58508			0.0658735
$580$		0			0
$581$	0.178989	−	0.119597i	0.00742573	−	0.00496172i
$582$		0			0
$583$	0.239550	+	0.0476494i	0.00992113	+	0.00197344i
$584$		0			0
$585$	18.1593	+	91.2929i	0.750794	+	3.77450i
$586$		0			0
$587$	−2.81261	+	6.79025i	−0.116089	+	0.280264i	−0.971235	−	0.238124i	$-0.923468\pi$
$587$	−2.81261	+	6.79025i	−0.116089	+	0.280264i	0.855146	+	0.518388i	$0.173468\pi$
$588$		0			0
$589$	11.8262	−	17.6991i	0.487289	−	0.729279i
$590$		0			0
$591$	33.3002	−	33.3002i	1.36979	−	1.36979i
$592$		0			0
$593$	41.6870	−	17.2673i	1.71188	−	0.709085i	0.711905	−	0.702276i	$-0.247833\pi$
$593$	41.6870	−	17.2673i	1.71188	−	0.709085i	0.999977	−	0.00680847i	$-0.00216722\pi$
$594$		0			0
$595$	−8.85622	−	9.66657i	−0.363070	−	0.396291i
$596$		0			0
$597$	−1.36145	+	0.563931i	−0.0557204	+	0.0230802i
$598$		0			0
$599$	−19.8695	−	19.8695i	−0.811847	−	0.811847i	0.173064	−	0.984911i	$-0.444633\pi$
$599$	−19.8695	−	19.8695i	−0.811847	−	0.811847i	−0.984911	+	0.173064i	$0.944633\pi$
$600$		0			0
$601$	−8.28776	+	12.4035i	−0.338065	+	0.505950i	−0.961084	−	0.276257i	$-0.910906\pi$
$601$	−8.28776	+	12.4035i	−0.338065	+	0.505950i	0.623019	+	0.782207i	$0.285906\pi$
$602$		0			0
$603$	−13.8688	−	5.74465i	−0.564781	−	0.233940i
$604$		0			0
$605$	−3.99949	−	20.1068i	−0.162602	−	0.817457i
$606$		0			0
$607$	−4.45355	+	22.3895i	−0.180764	+	0.908762i	0.778800	+	0.627272i	$0.215829\pi$
$607$	−4.45355	+	22.3895i	−0.180764	+	0.908762i	−0.959564	+	0.281490i	$0.909171\pi$
$608$		0			0
$609$	8.65296	−	5.78172i	0.350636	−	0.234287i
$610$		0			0
$611$			31.1796i			1.26139i
$612$		0			0
$613$		−	2.66972i		−	0.107829i	−0.998546	−	0.0539146i	$-0.982830\pi$
$613$		−	2.66972i		−	0.107829i	0.998546	−	0.0539146i	$-0.0171699\pi$
$614$		0			0
$615$	−9.65989	+	6.45453i	−0.389524	+	0.260272i
$616$		0			0
$617$	1.85421	−	9.32176i	0.0746478	−	0.375280i	−0.925345	−	0.379127i	$-0.876224\pi$
$617$	1.85421	−	9.32176i	0.0746478	−	0.375280i	0.999993	+	0.00384677i	$0.00122447\pi$
$618$		0			0
$619$	2.23331	+	11.2276i	0.0897645	+	0.451276i	0.999360	+	0.0357809i	$0.0113918\pi$
$619$	2.23331	+	11.2276i	0.0897645	+	0.451276i	−0.909595	+	0.415496i	$0.863608\pi$
$620$		0			0
$621$	48.2401	+	19.9817i	1.93581	+	0.801837i
$622$		0			0
$623$	4.44441	−	6.65153i	0.178062	−	0.266488i
$624$		0			0
$625$	−21.4731	−	21.4731i	−0.858926	−	0.858926i
$626$		0			0
$627$	12.5245	−	5.18782i	0.500180	−	0.207181i
$628$		0			0
$629$	17.0658	+	4.17755i	0.680457	+	0.166570i
$630$		0			0
$631$	38.2174	−	15.8302i	1.52141	−	0.630188i	0.543536	−	0.839386i	$-0.317085\pi$
$631$	38.2174	−	15.8302i	1.52141	−	0.630188i	0.977873	+	0.209198i	$0.0670852\pi$
$632$		0			0
$633$	11.4732	−	11.4732i	0.456018	−	0.456018i
$634$		0			0
$635$	19.4173	−	29.0601i	0.770553	−	1.15321i
$636$		0			0
$637$	−10.7742	+	26.0111i	−0.426888	+	1.03060i
$638$		0			0
$639$	0.886704	+	4.45776i	0.0350775	+	0.176346i
$640$		0			0
$641$	6.51603	+	1.29612i	0.257368	+	0.0511936i	0.322088	−	0.946710i	$-0.395615\pi$
$641$	6.51603	+	1.29612i	0.257368	+	0.0511936i	−0.0647200	+	0.997903i	$0.520615\pi$
$642$		0			0
$643$	30.6722	−	20.4945i	1.20959	−	0.808224i	0.223546	−	0.974693i	$-0.428237\pi$
$643$	30.6722	−	20.4945i	1.20959	−	0.808224i	0.986047	+	0.166470i	$0.0532369\pi$
$644$		0			0
$645$	−9.36596			−0.368784
$646$		0			0
$647$		−	9.05916i		−	0.356153i	−0.984017	−	0.178076i	$-0.943013\pi$
$647$		−	9.05916i		−	0.356153i	0.984017	−	0.178076i	$-0.0569874\pi$
$648$		0			0
$649$	−3.11869	−	4.66745i	−0.122419	−	0.183214i
$650$		0			0
$651$	6.39367	−	32.1431i	0.250588	−	1.25979i
$652$		0			0
$653$	−21.1507	+	4.20713i	−0.827690	+	0.164638i	−0.590717	−	0.806879i	$-0.701155\pi$
$653$	−21.1507	+	4.20713i	−0.827690	+	0.164638i	−0.236973	+	0.971516i	$0.576155\pi$
$654$		0			0
$655$	3.24560	+	1.34437i	0.126816	+	0.0525290i
$656$		0			0
$657$	−68.9216	−	46.0519i	−2.68889	−	1.79666i
$658$		0			0
$659$	−2.23049	−	2.23049i	−0.0868876	−	0.0868876i	0.662327	−	0.749215i	$-0.269569\pi$
$659$	−2.23049	−	2.23049i	−0.0868876	−	0.0868876i	−0.749215	+	0.662327i	$0.769569\pi$
$660$		0			0
$661$	−19.0064	−	45.8854i	−0.739262	−	1.78474i	−0.608864	−	0.793275i	$-0.708374\pi$
$661$	−19.0064	−	45.8854i	−0.739262	−	1.78474i	−0.130398	−	0.991462i	$-0.541626\pi$
$662$		0			0
$663$	−32.1595	−	53.0076i	−1.24897	−	2.05865i
$664$		0			0
$665$	2.68067	+	6.47172i	0.103952	+	0.250962i
$666$		0			0
$667$	−10.1460	+	10.1460i	−0.392854	+	0.392854i
$668$		0			0
$669$	15.5342	+	10.3796i	0.600588	+	0.401300i
$670$		0			0
$671$	8.20241	−	19.8024i	0.316650	−	0.764462i
$672$		0			0
$673$	18.7405	−	3.72773i	0.722395	−	0.143693i	0.179819	−	0.983700i	$-0.442449\pi$
$673$	18.7405	−	3.72773i	0.722395	−	0.143693i	0.542576	+	0.840006i	$0.317449\pi$
$674$		0			0
$675$	−37.6636	−	7.49176i	−1.44967	−	0.288358i
$676$		0			0
$677$	1.45451	+	2.17683i	0.0559015	+	0.0836624i	0.858367	−	0.513035i	$-0.171479\pi$
$677$	1.45451	+	2.17683i	0.0559015	+	0.0836624i	−0.802466	+	0.596698i	$0.796479\pi$
$678$		0			0
$679$	17.3071			0.664187
$680$		0			0
$681$	−38.2901			−1.46728
$682$		0			0
$683$	−4.97072	−	7.43922i	−0.190200	−	0.284654i	0.724098	−	0.689697i	$-0.242256\pi$
$683$	−4.97072	−	7.43922i	−0.190200	−	0.284654i	−0.914297	+	0.405044i	$0.867256\pi$
$684$		0			0
$685$	−20.2563	−	4.02922i	−0.773952	−	0.153949i
$686$		0			0
$687$	−23.0174	+	4.57844i	−0.878168	+	0.174678i
$688$		0			0
$689$	−0.228406	+	0.551421i	−0.00870158	+	0.0210075i
$690$		0			0
$691$	23.1673	+	15.4799i	0.881326	+	0.588883i	0.911792	−	0.410652i	$-0.134699\pi$
$691$	23.1673	+	15.4799i	0.881326	+	0.588883i	−0.0304657	+	0.999536i	$0.509699\pi$
$692$		0			0
$693$	10.1478	−	10.1478i	0.385485	−	0.385485i
$694$		0			0
$695$	20.6559	+	49.8677i	0.783523	+	1.89159i
$696$		0			0
$697$	3.14672	−	4.29080i	0.119191	−	0.162526i
$698$		0			0
$699$	−23.5239	−	56.7916i	−0.889754	−	2.14806i
$700$		0			0
$701$	3.36707	+	3.36707i	0.127173	+	0.127173i	0.767828	−	0.640656i	$-0.221337\pi$
$701$	3.36707	+	3.36707i	0.127173	+	0.127173i	−0.640656	+	0.767828i	$0.721337\pi$
$702$		0			0
$703$	−7.80561	−	5.21554i	−0.294394	−	0.196708i
$704$		0			0
$705$	−53.4415	−	22.1362i	−2.01272	−	0.833697i
$706$		0			0
$707$	−7.44348	+	1.48060i	−0.279941	+	0.0556837i
$708$		0			0
$709$	−7.32212	+	36.8108i	−0.274988	+	1.38246i	0.558309	+	0.829633i	$0.311450\pi$
$709$	−7.32212	+	36.8108i	−0.274988	+	1.38246i	−0.833297	+	0.552825i	$0.813550\pi$
$710$		0			0
$711$	47.9772	+	71.8030i	1.79929	+	2.69282i
$712$		0			0
$713$			45.1861i			1.69223i
$714$		0			0
$715$	−27.9924			−1.04685
$716$		0			0
$717$	−64.4034	+	43.0330i	−2.40519	+	1.60710i
$718$		0			0
$719$	−13.3199	−	2.64949i	−0.496749	−	0.0988095i	−0.0596434	−	0.998220i	$-0.518996\pi$
$719$	−13.3199	−	2.64949i	−0.496749	−	0.0988095i	−0.437105	+	0.899410i	$0.643996\pi$
$720$		0			0
$721$	−0.304541	−	1.53103i	−0.0113417	−	0.0570186i
$722$		0			0
$723$	−18.7569	+	45.2831i	−0.697576	+	1.68410i
$724$		0			0
$725$	5.86278	−	8.77427i	0.217738	−	0.325868i
$726$		0			0
$727$	−32.7732	+	32.7732i	−1.21549	+	1.21549i	−0.246294	+	0.969195i	$0.579213\pi$
$727$	−32.7732	+	32.7732i	−1.21549	+	1.21549i	−0.969195	+	0.246294i	$0.920787\pi$
$728$		0			0
$729$	−5.66863	+	2.34802i	−0.209949	+	0.0869638i
$730$		0			0
$731$	4.03105	−	1.46678i	0.149094	−	0.0542509i
$732$		0			0
$733$	25.2869	−	10.4742i	0.933994	−	0.386873i	0.136802	−	0.990598i	$-0.456318\pi$
$733$	25.2869	−	10.4742i	0.933994	−	0.386873i	0.797192	+	0.603726i	$0.206318\pi$
$734$		0			0
$735$	−36.9336	−	36.9336i	−1.36232	−	1.36232i
$736$		0			0
$737$	2.50807	−	3.75359i	0.0923859	−	0.138265i
$738$		0			0
$739$	−8.84951	−	3.66559i	−0.325534	−	0.134841i	0.213930	−	0.976849i	$-0.431373\pi$
$739$	−8.84951	−	3.66559i	−0.325534	−	0.134841i	−0.539465	+	0.842008i	$0.681373\pi$
$740$		0			0
$741$	6.46290	+	32.4912i	0.237421	+	1.19359i
$742$		0			0
$743$	−1.10893	+	5.57494i	−0.0406825	+	0.204525i	−0.995781	−	0.0917645i	$-0.970749\pi$
$743$	−1.10893	+	5.57494i	−0.0406825	+	0.204525i	0.955098	+	0.296289i	$0.0957493\pi$
$744$		0			0
$745$	−36.1850	+	24.1780i	−1.32571	+	0.885814i
$746$		0			0
$747$			1.29866i			0.0475156i
$748$		0			0
$749$			8.28348i			0.302672i
$750$		0			0
$751$	−30.2193	+	20.1919i	−1.10272	+	0.736812i	−0.967213	−	0.253965i	$-0.918265\pi$
$751$	−30.2193	+	20.1919i	−1.10272	+	0.736812i	−0.135503	+	0.990777i	$0.543265\pi$
$752$		0			0
$753$	10.1496	−	51.0254i	0.369871	−	1.85947i
$754$		0			0
$755$	6.30393	+	31.6920i	0.229423	+	1.15339i
$756$		0			0
$757$	−32.6522	−	13.5250i	−1.18676	−	0.491574i	−0.300065	−	0.953919i	$-0.597008\pi$
$757$	−32.6522	−	13.5250i	−1.18676	−	0.491574i	−0.886700	+	0.462345i	$0.847008\pi$
$758$		0			0
$759$	−15.9876	+	23.9272i	−0.580314	+	0.868502i
$760$		0			0
$761$	19.7187	+	19.7187i	0.714801	+	0.714801i	0.967536	−	0.252735i	$-0.0813299\pi$
$761$	19.7187	+	19.7187i	0.714801	+	0.714801i	−0.252735	+	0.967536i	$0.581330\pi$
$762$		0			0
$763$	7.54243	−	3.12418i	0.273054	−	0.113103i
$764$		0			0
$765$	78.1706	−	12.0246i	2.82626	−	0.434751i
$766$		0			0
$767$	12.6735	−	5.24952i	0.457612	−	0.189549i
$768$		0			0
$769$	26.9749	−	26.9749i	0.972738	−	0.972738i	−0.0268997	−	0.999638i	$-0.508563\pi$
$769$	26.9749	−	26.9749i	0.972738	−	0.972738i	0.999638	+	0.0268997i	$0.00856346\pi$
$770$		0			0
$771$	−39.3101	+	58.8318i	−1.41572	+	2.11878i
$772$		0			0
$773$	7.59170	−	18.3280i	0.273054	−	0.659212i	−0.726556	−	0.687107i	$-0.758880\pi$
$773$	7.59170	−	18.3280i	0.273054	−	0.659212i	0.999611	+	0.0278950i	$0.00888042\pi$
$774$		0			0
$775$	−6.48331	−	32.5938i	−0.232887	−	1.17080i
$776$		0			0
$777$	−14.1757	−	2.81972i	−0.508550	−	0.101157i
$778$		0			0
$779$	−2.36394	+	1.57953i	−0.0846968	+	0.0565926i
$780$		0			0
$781$	−1.36685			−0.0489096
$782$		0			0
$783$			34.2576i			1.22427i
$784$		0			0
$785$	9.87775	+	14.7831i	0.352552	+	0.527631i
$786$		0			0
$787$	3.17472	−	15.9604i	0.113166	−	0.568926i	−0.882044	−	0.471168i	$-0.843833\pi$
$787$	3.17472	−	15.9604i	0.113166	−	0.568926i	0.995210	−	0.0977587i	$-0.0311673\pi$
$788$		0			0
$789$	57.5613	−	11.4497i	2.04924	−	0.407618i
$790$		0			0
$791$	−7.33204	−	3.03703i	−0.260697	−	0.107984i
$792$		0			0
$793$	43.5507	+	29.0996i	1.54653	+	1.03336i
$794$		0			0
$795$	−0.782972	−	0.782972i	−0.0277691	−	0.0277691i
$796$		0			0
$797$	−5.34141	−	12.8953i	−0.189203	−	0.456775i	0.800604	−	0.599194i	$-0.204512\pi$
$797$	−5.34141	−	12.8953i	−0.189203	−	0.456775i	−0.989807	+	0.142418i	$0.954512\pi$
$798$		0			0
$799$	26.4675	+	1.15792i	0.936354	+	0.0409641i
$800$		0			0
$801$	18.4684	+	44.5868i	0.652550	+	1.57540i
$802$		0			0
$803$	17.6267	−	17.6267i	0.622032	−	0.622032i
$804$		0			0
$805$	−12.3638	−	8.26120i	−0.435765	−	0.291169i
$806$		0			0
$807$	−28.5212	+	68.8564i	−1.00400	+	2.42386i
$808$		0			0
$809$	−5.23056	+	1.04042i	−0.183897	+	0.0365793i	−0.286179	−	0.958176i	$-0.592385\pi$
$809$	−5.23056	+	1.04042i	−0.183897	+	0.0365793i	0.102283	+	0.994755i	$0.467385\pi$
$810$		0			0
$811$	−13.4158	−	2.66857i	−0.471093	−	0.0937062i	−0.0461659	−	0.998934i	$-0.514700\pi$
$811$	−13.4158	−	2.66857i	−0.471093	−	0.0937062i	−0.424927	+	0.905228i	$0.639700\pi$
$812$		0			0
$813$	−11.9389	−	17.8678i	−0.418715	−	0.626651i
$814$		0			0
$815$	69.5478			2.43615
$816$		0			0
$817$	−2.29201			−0.0801872
$818$		0			0
$819$	19.4838	+	29.1596i	0.680820	+	1.01892i
$820$		0			0
$821$	17.1412	+	3.40959i	0.598231	+	0.118996i	0.484912	−	0.874563i	$-0.338852\pi$
$821$	17.1412	+	3.40959i	0.598231	+	0.118996i	0.113319	+	0.993559i	$0.463852\pi$
$822$		0			0
$823$	37.8016	−	7.51921i	1.31768	−	0.262103i	0.514322	−	0.857597i	$-0.328044\pi$
$823$	37.8016	−	7.51921i	1.31768	−	0.262103i	0.803360	+	0.595494i	$0.203044\pi$
$824$		0			0
$825$	8.09916	−	19.5531i	0.281977	−	0.680752i
$826$		0			0
$827$	27.6757	+	18.4923i	0.962379	+	0.643041i	0.934271	−	0.356564i	$-0.116052\pi$
$827$	27.6757	+	18.4923i	0.962379	+	0.643041i	0.0281083	+	0.999605i	$0.491052\pi$
$828$		0			0
$829$	11.3108	−	11.3108i	0.392840	−	0.392840i	−0.482859	−	0.875698i	$-0.660402\pi$
$829$	11.3108	−	11.3108i	0.392840	−	0.392840i	0.875698	+	0.482859i	$0.160402\pi$
$830$		0			0
$831$	24.0638	+	58.0951i	0.834763	+	2.01530i
$832$		0			0
$833$	21.6801	+	10.1119i	0.751170	+	0.350356i
$834$		0			0
$835$	0.629950	+	1.52083i	0.0218003	+	0.0526306i
$836$		0			0
$837$	76.2849	+	76.2849i	2.63679	+	2.63679i
$838$		0			0
$839$	−38.1022	−	25.4591i	−1.31544	−	0.878946i	−0.317833	−	0.948147i	$-0.602955\pi$
$839$	−38.1022	−	25.4591i	−1.31544	−	0.878946i	−0.997603	+	0.0692008i	$0.977955\pi$
$840$		0			0
$841$	18.0951	+	7.49524i	0.623969	+	0.258457i
$842$		0			0
$843$	59.6754	−	11.8702i	2.05533	−	0.408831i
$844$		0			0
$845$	5.97737	−	30.0503i	0.205628	−	1.03376i
$846$		0			0
$847$	−4.29121	−	6.42226i	−0.147448	−	0.220671i
$848$		0			0
$849$			31.5038i			1.08121i
$850$		0			0
$851$	19.9279			0.683118
$852$		0			0
$853$	19.7290	−	13.1825i	0.675509	−	0.451361i	−0.169913	−	0.985459i	$-0.554349\pi$
$853$	19.7290	−	13.1825i	0.675509	−	0.451361i	0.845423	+	0.534098i	$0.179349\pi$
$854$		0			0
$855$	−41.4470	−	8.24432i	−1.41746	−	0.281950i
$856$		0			0
$857$	−2.43308	−	12.2319i	−0.0831123	−	0.417834i	−0.999832	−	0.0183038i	$-0.994173\pi$
$857$	−2.43308	−	12.2319i	−0.0831123	−	0.417834i	0.916720	−	0.399530i	$-0.130827\pi$
$858$		0			0
$859$	0.425098	−	1.02628i	0.0145041	−	0.0350161i	−0.916462	−	0.400123i	$-0.868967\pi$
$859$	0.425098	−	1.02628i	0.0145041	−	0.0350161i	0.930966	+	0.365107i	$0.118967\pi$
$860$		0			0
$861$	−2.43185	+	3.63953i	−0.0828774	+	0.124035i
$862$		0			0
$863$	4.69476	−	4.69476i	0.159812	−	0.159812i	−0.622672	−	0.782483i	$-0.713953\pi$
$863$	4.69476	−	4.69476i	0.159812	−	0.159812i	0.782483	+	0.622672i	$0.213953\pi$
$864$		0			0
$865$	24.1361	−	9.99748i	0.820650	−	0.339925i
$866$		0			0
$867$	−46.1911	+	25.3308i	−1.56873	+	0.860280i
$868$		0			0
$869$	−23.9932	+	9.93830i	−0.813913	+	0.337134i
$870$		0			0
$871$	7.80067	+	7.80067i	0.264316	+	0.264316i
$872$		0			0
$873$	−58.0068	+	86.8133i	−1.96323	+	2.93819i
$874$		0			0
$875$	−4.58459	−	1.89900i	−0.154987	−	0.0641979i
$876$		0			0
$877$	−1.00715	−	5.06328i	−0.0340090	−	0.170975i	0.960048	−	0.279835i	$-0.0902798\pi$
$877$	−1.00715	−	5.06328i	−0.0340090	−	0.170975i	−0.994057	+	0.108860i	$0.965280\pi$
$878$		0			0
$879$	10.7791	−	54.1901i	0.363569	−	1.82779i
$880$		0			0
$881$	−18.0545	+	12.0636i	−0.608271	+	0.406433i	−0.821205	−	0.570633i	$-0.806698\pi$
$881$	−18.0545	+	12.0636i	−0.608271	+	0.406433i	0.212935	+	0.977066i	$0.431698\pi$
$882$		0			0
$883$		−	29.6365i		−	0.997346i	−0.866790	−	0.498673i	$-0.833821\pi$
$883$		−	29.6365i		−	0.997346i	0.866790	−	0.498673i	$-0.166179\pi$
$884$		0			0
$885$			25.4491i			0.855463i
$886$		0			0
$887$	35.1208	−	23.4670i	1.17924	−	0.787944i	0.197901	−	0.980222i	$-0.436588\pi$
$887$	35.1208	−	23.4670i	1.17924	−	0.787944i	0.981340	+	0.192278i	$0.0615875\pi$
$888$		0			0
$889$	2.56897	−	12.9151i	0.0861604	−	0.433158i
$890$		0			0
$891$	5.72989	+	28.8061i	0.191958	+	0.965041i
$892$		0			0
$893$	−13.0780	−	5.41709i	−0.437639	−	0.181276i
$894$		0			0
$895$	18.5657	−	27.7855i	0.620583	−	0.928768i
$896$		0			0
$897$	−49.7252	−	49.7252i	−1.66028	−	1.66028i
$898$		0			0
$899$	−27.3896	+	11.3451i	−0.913494	+	0.378381i
$900$		0			0
$901$	0.459605	+	0.214366i	0.0153117	+	0.00714158i
$902$		0			0
$903$	−3.26017	+	1.35041i	−0.108492	+	0.0449387i
$904$		0			0
$905$	8.64038	−	8.64038i	0.287216	−	0.287216i
$906$		0			0
$907$	21.5907	−	32.3127i	0.716907	−	1.07293i	−0.276801	−	0.960927i	$-0.589274\pi$
$907$	21.5907	−	32.3127i	0.716907	−	1.07293i	0.993708	−	0.112000i	$-0.0357256\pi$
$908$		0			0
$909$	17.5209	−	42.2992i	0.581132	−	1.40298i
$910$		0			0
$911$	−10.4388	−	52.4794i	−0.345853	−	1.73872i	−0.626966	−	0.779047i	$-0.715703\pi$
$911$	−10.4388	−	52.4794i	−0.345853	−	1.73872i	0.281113	−	0.959675i	$-0.409297\pi$
$912$		0			0
$913$	−0.383042	−	0.0761918i	−0.0126768	−	0.00252158i
$914$		0			0
$915$	−80.7956	+	53.9859i	−2.67102	+	1.78472i
$916$		0			0
$917$	1.32359			0.0437087
$918$		0			0
$919$			13.3692i			0.441010i	0.975386	+	0.220505i	$0.0707706\pi$
$919$			13.3692i			0.441010i	−0.975386	+	0.220505i	$0.929229\pi$
$920$		0			0
$921$	16.4428	+	24.6084i	0.541809	+	0.810874i
$922$		0			0
$923$	0.651631	−	3.27597i	0.0214487	−	0.107830i
$924$		0			0
$925$	−14.3744	+	2.85925i	−0.472628	+	0.0940115i
$926$		0			0
$927$	8.70043	+	3.60384i	0.285760	+	0.118366i
$928$		0			0
$929$	42.4970	+	28.3956i	1.39428	+	0.931629i	0.999920	+	0.0126737i	$0.00403428\pi$
$929$	42.4970	+	28.3956i	1.39428	+	0.931629i	0.394362	+	0.918955i	$0.370966\pi$
$930$		0			0
$931$	−9.03827	−	9.03827i	−0.296217	−	0.296217i
$932$		0			0
$933$	−18.8837	−	45.5893i	−0.618224	−	1.49253i
$934$		0			0
$935$	−1.03955	+	23.7620i	−0.0339970	+	0.777101i
$936$		0			0
$937$	−8.11589	−	19.5935i	−0.265135	−	0.640092i	0.734107	−	0.679034i	$-0.237601\pi$
$937$	−8.11589	−	19.5935i	−0.265135	−	0.640092i	−0.999241	+	0.0389423i	$0.987601\pi$
$938$		0			0
$939$	−3.55178	+	3.55178i	−0.115908	+	0.115908i
$940$		0			0
$941$	31.9559	+	21.3522i	1.04173	+	0.696063i	0.953916	−	0.300074i	$-0.0970114\pi$
$941$	31.9559	+	21.3522i	1.04173	+	0.696063i	0.0878157	+	0.996137i	$0.472011\pi$
$942$		0			0
$943$	2.30956	−	5.57577i	0.0752096	−	0.181572i
$944$		0			0
$945$	−34.8198	+	6.92609i	−1.13269	+	0.225306i
$946$		0			0
$947$	36.5017	+	7.26065i	1.18615	+	0.235939i	0.748455	−	0.663185i	$-0.230796\pi$
$947$	36.5017	+	7.26065i	1.18615	+	0.235939i	0.437692	+	0.899125i	$0.355796\pi$
$948$		0			0
$949$	33.8432	+	50.6499i	1.09860	+	1.64416i
$950$		0			0
$951$	−1.45278			−0.0471095
$952$		0			0
$953$	−14.7363			−0.477355			−0.238678	−	0.971099i	$-0.576714\pi$
$953$	−14.7363			−0.477355			−0.238678	+	0.971099i	$0.576714\pi$
$954$		0			0
$955$	23.2385	+	34.7789i	0.751981	+	1.12542i
$956$		0			0
$957$	−18.5176	−	3.68337i	−0.598588	−	0.119067i
$958$		0			0
$959$	−7.63189	+	1.51808i	−0.246447	+	0.0490213i
$960$		0			0
$961$	−23.8646	+	57.6142i	−0.769825	+	1.85852i
$962$		0			0
$963$	−41.5503	−	27.7630i	−1.33894	−	0.894651i
$964$		0			0
$965$	1.05072	−	1.05072i	0.0338238	−	0.0338238i
$966$		0			0
$967$	−7.82515	−	18.8916i	−0.251640	−	0.607512i	0.746697	−	0.665164i	$-0.231639\pi$
$967$	−7.82515	−	18.8916i	−0.251640	−	0.607512i	−0.998337	+	0.0576521i	$0.981639\pi$
$968$		0			0
$969$	27.8210	−	4.27957i	0.893738	−	0.137479i
$970$		0			0
$971$	11.5844	+	27.9672i	0.371761	+	0.897511i	0.993452	+	0.114248i	$0.0364460\pi$
$971$	11.5844	+	27.9672i	0.371761	+	0.897511i	−0.621691	+	0.783263i	$0.713554\pi$
$972$		0			0
$973$	14.3801	+	14.3801i	0.461005	+	0.461005i
$974$		0			0
$975$	43.0025	+	28.7333i	1.37718	+	0.920203i
$976$		0			0
$977$	−4.59670	−	1.90401i	−0.147061	−	0.0609148i	0.307939	−	0.951406i	$-0.400361\pi$
$977$	−4.59670	−	1.90401i	−0.147061	−	0.0609148i	−0.455000	+	0.890491i	$0.650361\pi$
$978$		0			0
$979$	−14.2345	+	2.83141i	−0.454935	+	0.0904923i
$980$		0			0
$981$	−9.60831	+	48.3042i	−0.306770	+	1.54223i
$982$		0			0
$983$	21.0890	+	31.5619i	0.672635	+	1.00667i	0.998130	+	0.0611260i	$0.0194691\pi$
$983$	21.0890	+	31.5619i	0.672635	+	1.00667i	−0.325495	+	0.945544i	$0.605531\pi$
$984$		0			0
$985$		−	44.1482i		−	1.40668i
$986$		0			0
$987$	−21.7939			−0.693709
$988$		0			0
$989$	4.04541	−	2.70306i	0.128637	−	0.0859522i
$990$		0			0
$991$	33.9143	+	6.74598i	1.07732	+	0.214293i	0.701695	−	0.712477i	$-0.252427\pi$
$991$	33.9143	+	6.74598i	1.07732	+	0.214293i	0.375629	+	0.926770i	$0.377427\pi$
$992$		0			0
$993$	−15.2486	−	76.6597i	−0.483898	−	2.43272i
$994$		0			0
$995$	−0.528660	+	1.27630i	−0.0167597	+	0.0404614i
$996$		0			0
$997$	−12.3285	+	18.4509i	−0.390447	+	0.584345i	−0.973669	−	0.227968i	$-0.926792\pi$
$997$	−12.3285	+	18.4509i	−0.390447	+	0.584345i	0.583222	+	0.812313i	$0.301792\pi$
$998$		0			0
$999$	33.6429	−	33.6429i	1.06442	−	1.06442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.cc.c.175.14		112
4.3	odd	2		136.2.s.c.107.9	yes	112
8.3	odd	2	inner	544.2.cc.c.175.13		112
8.5	even	2		136.2.s.c.107.3	yes	112
17.7	odd	16	inner	544.2.cc.c.143.13		112
68.7	even	16		136.2.s.c.75.3	✓	112
136.75	even	16	inner	544.2.cc.c.143.14		112
136.109	odd	16		136.2.s.c.75.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.75.3	✓	112	68.7	even	16
136.2.s.c.75.9	yes	112	136.109	odd	16
136.2.s.c.107.3	yes	112	8.5	even	2
136.2.s.c.107.9	yes	112	4.3	odd	2
544.2.cc.c.143.13		112	17.7	odd	16	inner
544.2.cc.c.143.14		112	136.75	even	16	inner
544.2.cc.c.175.13		112	8.3	odd	2	inner
544.2.cc.c.175.14		112	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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.cc (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.72164 + 2.57662i) q^{3} +(2.84924 + 0.566749i) q^{5} +(1.07350 - 0.213532i) q^{7} +(-2.52687 + 6.10039i) q^{9} +(-1.65107 - 1.10321i) q^{11} +(3.43124 - 3.43124i) q^{13} +(3.44507 + 8.31714i) q^{15} +(-2.78526 - 3.04012i) q^{17} +(0.843066 + 2.03534i) q^{19} +(2.39837 + 2.39837i) q^{21} +(-3.88838 - 2.59813i) q^{23} +(3.17755 + 1.31619i) q^{25} +(-10.9508 + 2.17824i) q^{27} +(0.598581 - 3.00927i) q^{29} +(-5.36812 - 8.03396i) q^{31} -6.15351i q^{33} +3.17967 q^{35} +(-3.54311 + 2.36743i) q^{37} +(14.7484 + 2.93363i) q^{39} +(0.251769 + 1.26573i) q^{41} +(-0.398138 + 0.961190i) q^{43} +(-10.6570 + 15.9494i) q^{45} +(-4.54349 + 4.54349i) q^{47} +(-5.36035 + 2.22033i) q^{49} +(3.03799 - 12.4106i) q^{51} +(-0.113637 + 0.0470698i) q^{53} +(-4.07905 - 4.07905i) q^{55} +(-3.79284 + 5.67639i) q^{57} +(2.61174 + 1.08182i) q^{59} +(2.10581 + 10.5866i) q^{61} +(-1.40996 + 7.08833i) q^{63} +(11.7211 - 7.83176i) q^{65} +2.27343i q^{67} -14.4919i q^{69} +(0.572331 - 0.382419i) q^{71} +(-2.44907 + 12.3123i) q^{73} +(2.07930 + 10.4533i) q^{75} +(-2.00799 - 0.831737i) q^{77} +(7.26595 - 10.8743i) q^{79} +(-10.4587 - 10.4587i) q^{81} +(0.181706 - 0.0752650i) q^{83} +(-6.21290 - 10.2406i) q^{85} +(8.78428 - 3.63857i) q^{87} +(5.16813 - 5.16813i) q^{89} +(2.95075 - 4.41611i) q^{91} +(11.4585 - 27.6632i) q^{93} +(1.24857 + 6.27698i) q^{95} +(15.5086 + 3.08484i) q^{97} +(10.9020 - 7.28451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 16 q^{3} - 16 q^{9} + 16 q^{11} - 16 q^{17} + 16 q^{19} - 16 q^{25} - 32 q^{27} + 32 q^{35} - 16 q^{41} + 96 q^{43} - 16 q^{49} + 16 q^{51} + 32 q^{57} + 16 q^{59} + 64 q^{65} - 96 q^{73} + 16 q^{75}+ \cdots - 48 q^{99}+O(q^{100}) \) 112 * q + 16 * q^3 - 16 * q^9 + 16 * q^11 - 16 * q^17 + 16 * q^19 - 16 * q^25 - 32 * q^27 + 32 * q^35 - 16 * q^41 + 96 * q^43 - 16 * q^49 + 16 * q^51 + 32 * q^57 + 16 * q^59 + 64 * q^65 - 96 * q^73 + 16 * q^75 - 96 * q^81 - 128 * q^83 - 16 * q^89 + 16 * q^91 - 16 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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