LMFDB - Embedded newform 512.2.k.a.497.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] 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("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			497.3
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98529 + 1.06116i) q^{3} +(-0.212591 - 0.259043i) q^{5} +(0.792164 - 0.529307i) q^{7} +(1.14862 - 1.71903i) q^{9} +(-2.34047 + 0.709975i) q^{11} +(-2.81226 - 2.30796i) q^{13} +(0.696942 + 0.288683i) q^{15} +(-1.82571 + 0.756236i) q^{17} +(-0.157890 - 1.60309i) q^{19} +(-1.01100 + 1.89144i) q^{21} +(7.27219 - 1.44653i) q^{23} +(0.953543 - 4.79379i) q^{25} +(0.205763 - 2.08914i) q^{27} +(1.10598 - 3.64593i) q^{29} +(-7.16783 - 7.16783i) q^{31} +(3.89313 - 3.89313i) q^{33} +(-0.305520 - 0.0926785i) q^{35} +(0.968069 + 0.0953465i) q^{37} +(8.03228 + 1.59772i) q^{39} +(-2.34900 - 11.8092i) q^{41} +(-7.65676 - 4.09262i) q^{43} +(-0.689487 + 0.0679086i) q^{45} +(1.74223 + 4.20612i) q^{47} +(-2.33143 + 5.62856i) q^{49} +(2.82209 - 3.43873i) q^{51} +(2.50640 + 8.26251i) q^{53} +(0.681478 + 0.455349i) q^{55} +(2.01459 + 3.01505i) q^{57} +(2.07085 - 1.69950i) q^{59} +(3.63666 + 6.80371i) q^{61} -1.96972i q^{63} +1.21915i q^{65} +(-5.45136 - 10.1988i) q^{67} +(-12.9024 + 10.5887i) q^{69} +(-1.79285 - 2.68319i) q^{71} +(2.04993 + 1.36972i) q^{73} +(3.19392 + 10.5289i) q^{75} +(-1.47825 + 1.80125i) q^{77} +(-4.58780 + 11.0759i) q^{79} +(4.18196 + 10.0961i) q^{81} +(7.11006 - 0.700280i) q^{83} +(0.584028 + 0.312169i) q^{85} +(1.67322 + 8.41187i) q^{87} +(-13.6682 - 2.71877i) q^{89} +(-3.44939 - 0.339735i) q^{91} +(21.8365 + 6.62402i) q^{93} +(-0.381702 + 0.381702i) q^{95} +(-10.5511 - 10.5511i) q^{97} +(-1.46784 + 4.83883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.98529	+	1.06116i	−1.14621	+	0.612662i	−0.931401	−	0.363994i	$-0.881413\pi$
$3$	−1.98529	+	1.06116i	−1.14621	+	0.612662i	−0.214809	+	0.976656i	$0.568913\pi$
$4$		0			0
$5$	−0.212591	−	0.259043i	−0.0950736	−	0.115847i	0.723300	−	0.690533i	$-0.242624\pi$
$5$	−0.212591	−	0.259043i	−0.0950736	−	0.115847i	−0.818374	+	0.574686i	$0.805124\pi$
$6$		0			0
$7$	0.792164	−	0.529307i	0.299410	−	0.200059i	−0.396786	−	0.917911i	$-0.629874\pi$
$7$	0.792164	−	0.529307i	0.299410	−	0.200059i	0.696196	+	0.717852i	$0.254874\pi$
$8$		0			0
$9$	1.14862	−	1.71903i	0.382872	−	0.573009i
$10$		0			0
$11$	−2.34047	+	0.709975i	−0.705680	+	0.214066i	−0.622672	−	0.782483i	$-0.713953\pi$
$11$	−2.34047	+	0.709975i	−0.705680	+	0.214066i	−0.0830081	+	0.996549i	$0.526453\pi$
$12$		0			0
$13$	−2.81226	−	2.30796i	−0.779980	−	0.640113i	0.157750	−	0.987479i	$-0.449576\pi$
$13$	−2.81226	−	2.30796i	−0.779980	−	0.640113i	−0.937730	+	0.347366i	$0.887076\pi$
$14$		0			0
$15$	0.696942	+	0.288683i	0.179950	+	0.0745376i
$16$		0			0
$17$	−1.82571	+	0.756236i	−0.442801	+	0.183414i	−0.592933	−	0.805252i	$-0.702030\pi$
$17$	−1.82571	+	0.756236i	−0.442801	+	0.183414i	0.150132	+	0.988666i	$0.452030\pi$
$18$		0			0
$19$	−0.157890	−	1.60309i	−0.0362225	−	0.367773i	−0.996159	−	0.0875572i	$-0.972094\pi$
$19$	−0.157890	−	1.60309i	−0.0362225	−	0.367773i	0.959937	−	0.280216i	$-0.0904061\pi$
$20$		0			0
$21$	−1.01100	+	1.89144i	−0.220618	+	0.412747i
$22$		0			0
$23$	7.27219	−	1.44653i	1.51636	−	0.301622i	0.634419	−	0.772990i	$-0.281240\pi$
$23$	7.27219	−	1.44653i	1.51636	−	0.301622i	0.881937	+	0.471368i	$0.156240\pi$
$24$		0			0
$25$	0.953543	−	4.79379i	0.190709	−	0.958757i
$26$		0			0
$27$	0.205763	−	2.08914i	0.0395990	−	0.402056i
$28$		0			0
$29$	1.10598	−	3.64593i	0.205376	−	0.677032i	−0.792377	−	0.610031i	$-0.791157\pi$
$29$	1.10598	−	3.64593i	0.205376	−	0.677032i	0.997753	−	0.0670011i	$-0.0213431\pi$
$30$		0			0
$31$	−7.16783	−	7.16783i	−1.28738	−	1.28738i	−0.936372	−	0.351008i	$-0.885839\pi$
$31$	−7.16783	−	7.16783i	−1.28738	−	1.28738i	−0.351008	−	0.936372i	$-0.614161\pi$
$32$		0			0
$33$	3.89313	−	3.89313i	0.677707	−	0.677707i
$34$		0			0
$35$	−0.305520	−	0.0926785i	−0.0516423	−	0.0156655i
$36$		0			0
$37$	0.968069	+	0.0953465i	0.159150	+	0.0156749i	0.177278	−	0.984161i	$-0.443271\pi$
$37$	0.968069	+	0.0953465i	0.159150	+	0.0156749i	−0.0181285	+	0.999836i	$0.505771\pi$
$38$		0			0
$39$	8.03228	+	1.59772i	1.28619	+	0.255840i
$40$		0			0
$41$	−2.34900	−	11.8092i	−0.366852	−	1.84429i	−0.517473	−	0.855699i	$-0.673127\pi$
$41$	−2.34900	−	11.8092i	−0.366852	−	1.84429i	0.150621	−	0.988592i	$-0.451873\pi$
$42$		0			0
$43$	−7.65676	−	4.09262i	−1.16764	−	0.624119i	−0.230504	−	0.973071i	$-0.574038\pi$
$43$	−7.65676	−	4.09262i	−1.16764	−	0.624119i	−0.937141	+	0.348952i	$0.886538\pi$
$44$		0			0
$45$	−0.689487	+	0.0679086i	−0.102783	+	0.0101232i
$46$		0			0
$47$	1.74223	+	4.20612i	0.254130	+	0.613525i	0.998530	−	0.0542099i	$-0.0172640\pi$
$47$	1.74223	+	4.20612i	0.254130	+	0.613525i	−0.744399	+	0.667735i	$0.767264\pi$
$48$		0			0
$49$	−2.33143	+	5.62856i	−0.333061	+	0.804080i
$50$		0			0
$51$	2.82209	−	3.43873i	0.395172	−	0.481518i
$52$		0			0
$53$	2.50640	+	8.26251i	0.344281	+	1.13494i	0.942667	+	0.333735i	$0.108309\pi$
$53$	2.50640	+	8.26251i	0.344281	+	1.13494i	−0.598386	+	0.801208i	$0.704191\pi$
$54$		0			0
$55$	0.681478	+	0.455349i	0.0918905	+	0.0613992i
$56$		0			0
$57$	2.01459	+	3.01505i	0.266839	+	0.399353i
$58$		0			0
$59$	2.07085	−	1.69950i	0.269601	−	0.221256i	−0.489872	−	0.871794i	$-0.662957\pi$
$59$	2.07085	−	1.69950i	0.269601	−	0.221256i	0.759474	+	0.650538i	$0.225457\pi$
$60$		0			0
$61$	3.63666	+	6.80371i	0.465626	+	0.871125i	0.999670	+	0.0256689i	$0.00817157\pi$
$61$	3.63666	+	6.80371i	0.465626	+	0.871125i	−0.534044	+	0.845457i	$0.679328\pi$
$62$		0			0
$63$		−	1.96972i		−	0.248162i
$64$		0			0
$65$			1.21915i			0.151217i
$66$		0			0
$67$	−5.45136	−	10.1988i	−0.665990	−	1.24598i	−0.957230	−	0.289329i	$-0.906568\pi$
$67$	−5.45136	−	10.1988i	−0.665990	−	1.24598i	0.291240	−	0.956650i	$-0.405932\pi$
$68$		0			0
$69$	−12.9024	+	10.5887i	−1.55327	+	1.27474i
$70$		0			0
$71$	−1.79285	−	2.68319i	−0.212772	−	0.318436i	0.709697	−	0.704507i	$-0.248832\pi$
$71$	−1.79285	−	2.68319i	−0.212772	−	0.318436i	−0.922469	+	0.386071i	$0.873832\pi$
$72$		0			0
$73$	2.04993	+	1.36972i	0.239926	+	0.160314i	0.669721	−	0.742613i	$-0.266414\pi$
$73$	2.04993	+	1.36972i	0.239926	+	0.160314i	−0.429794	+	0.902927i	$0.641414\pi$
$74$		0			0
$75$	3.19392	+	10.5289i	0.368802	+	1.21578i
$76$		0			0
$77$	−1.47825	+	1.80125i	−0.168462	+	0.205271i
$78$		0			0
$79$	−4.58780	+	11.0759i	−0.516168	+	1.24614i	0.424072	+	0.905628i	$0.360600\pi$
$79$	−4.58780	+	11.0759i	−0.516168	+	1.24614i	−0.940240	+	0.340512i	$0.889400\pi$
$80$		0			0
$81$	4.18196	+	10.0961i	0.464662	+	1.12179i
$82$		0			0
$83$	7.11006	−	0.700280i	0.780431	−	0.0768657i	0.300047	−	0.953924i	$-0.402997\pi$
$83$	7.11006	−	0.700280i	0.780431	−	0.0768657i	0.480384	+	0.877059i	$0.340497\pi$
$84$		0			0
$85$	0.584028	+	0.312169i	0.0633467	+	0.0338595i
$86$		0			0
$87$	1.67322	+	8.41187i	0.179389	+	0.901847i
$88$		0			0
$89$	−13.6682	−	2.71877i	−1.44882	−	0.288189i	−0.592893	−	0.805281i	$-0.702014\pi$
$89$	−13.6682	−	2.71877i	−1.44882	−	0.288189i	−0.855930	+	0.517092i	$0.827014\pi$
$90$		0			0
$91$	−3.44939	−	0.339735i	−0.361594	−	0.0356139i
$92$		0			0
$93$	21.8365	+	6.62402i	2.26434	+	0.686879i
$94$		0			0
$95$	−0.381702	+	0.381702i	−0.0391618	+	0.0391618i
$96$		0			0
$97$	−10.5511	−	10.5511i	−1.07131	−	1.07131i	−0.997254	−	0.0740512i	$-0.976407\pi$
$97$	−10.5511	−	10.5511i	−1.07131	−	1.07131i	−0.0740512	−	0.997254i	$-0.523593\pi$
$98$		0			0
$99$	−1.46784	+	4.83883i	−0.147524	+	0.486321i
$100$		0			0
$101$	0.241180	−	2.44874i	0.0239983	−	0.243658i	−0.975700	−	0.219109i	$-0.929685\pi$
$101$	0.241180	−	2.44874i	0.0239983	−	0.243658i	0.999699	−	0.0245493i	$-0.00781508\pi$
$102$		0			0
$103$	−0.902073	+	4.53503i	−0.0888839	+	0.446850i	0.910556	+	0.413386i	$0.135654\pi$
$103$	−0.902073	+	4.53503i	−0.0888839	+	0.446850i	−0.999440	+	0.0334639i	$0.989346\pi$
$104$		0			0
$105$	0.704894	−	0.140212i	0.0687906	−	0.0136833i
$106$		0			0
$107$	−3.99011	+	7.46498i	−0.385739	+	0.721667i	−0.997596	−	0.0693019i	$-0.977923\pi$
$107$	−3.99011	+	7.46498i	−0.385739	+	0.721667i	0.611857	+	0.790968i	$0.290423\pi$
$108$		0			0
$109$	−0.550234	−	5.58662i	−0.0527029	−	0.535101i	−0.984897	−	0.173142i	$-0.944608\pi$
$109$	−0.550234	−	5.58662i	−0.0527029	−	0.535101i	0.932194	−	0.361959i	$-0.117892\pi$
$110$		0			0
$111$	−2.02308	+	0.837987i	−0.192022	+	0.0795382i
$112$		0			0
$113$	7.49280	+	3.10362i	0.704864	+	0.291964i	0.706177	−	0.708035i	$-0.250418\pi$
$113$	7.49280	+	3.10362i	0.704864	+	0.291964i	−0.00131364	+	0.999999i	$0.500418\pi$
$114$		0			0
$115$	−1.92071	−	1.57629i	−0.179107	−	0.146990i
$116$		0			0
$117$	−7.19765	+	2.18338i	−0.665423	+	0.201854i
$118$		0			0
$119$	−1.04598	+	1.56543i	−0.0958853	+	0.143502i
$120$		0			0
$121$	−4.17241	+	2.78791i	−0.379310	+	0.253447i
$122$		0			0
$123$	17.1950	+	20.9521i	1.55042	+	1.88919i
$124$		0			0
$125$	−2.92221	+	1.56195i	−0.261370	+	0.139705i
$126$		0			0
$127$	5.64761			0.501144			0.250572	−	0.968098i	$-0.419381\pi$
$127$	5.64761			0.501144			0.250572	+	0.968098i	$0.419381\pi$
$128$		0			0
$129$	19.5439			1.72074
$130$		0			0
$131$	−9.16751	+	4.90014i	−0.800969	+	0.428127i	−0.820475	−	0.571683i	$-0.806291\pi$
$131$	−9.16751	+	4.90014i	−0.800969	+	0.428127i	0.0195057	+	0.999810i	$0.493791\pi$
$132$		0			0
$133$	−0.973600	−	1.18633i	−0.0844218	−	0.102868i
$134$		0			0
$135$	−0.584921	+	0.390832i	−0.0503420	+	0.0336374i
$136$		0			0
$137$	−2.63082	+	3.93731i	−0.224766	+	0.336387i	−0.926664	−	0.375891i	$-0.877337\pi$
$137$	−2.63082	+	3.93731i	−0.224766	+	0.336387i	0.701897	+	0.712278i	$0.252337\pi$
$138$		0			0
$139$	−6.81590	+	2.06758i	−0.578117	+	0.175370i	−0.565783	−	0.824554i	$-0.691426\pi$
$139$	−6.81590	+	2.06758i	−0.578117	+	0.175370i	−0.0123340	+	0.999924i	$0.503926\pi$
$140$		0			0
$141$	−7.92221	−	6.50159i	−0.667170	−	0.547532i
$142$		0			0
$143$	8.22061	+	3.40509i	0.687442	+	0.284748i
$144$		0			0
$145$	−1.17957	+	0.488596i	−0.0979583	+	0.0405756i
$146$		0			0
$147$	−1.34425	−	13.6484i	−0.110872	−	1.12570i
$148$		0			0
$149$	7.01271	−	13.1199i	0.574504	−	1.07482i	−0.412015	−	0.911177i	$-0.635175\pi$
$149$	7.01271	−	13.1199i	0.574504	−	1.07482i	0.986519	−	0.163644i	$-0.0523250\pi$
$150$		0			0
$151$	−9.87098	+	1.96346i	−0.803289	+	0.159784i	−0.579626	−	0.814882i	$-0.696801\pi$
$151$	−9.87098	+	1.96346i	−0.803289	+	0.159784i	−0.223663	+	0.974667i	$0.571801\pi$
$152$		0			0
$153$	−0.797057	+	4.00708i	−0.0644383	+	0.323953i
$154$		0			0
$155$	−0.332959	+	3.38059i	−0.0267439	+	0.271536i
$156$		0			0
$157$	2.12049	−	6.99032i	0.169234	−	0.557888i	−0.830766	−	0.556622i	$-0.812097\pi$
$157$	2.12049	−	6.99032i	0.169234	−	0.557888i	0.999999	−	0.00126599i	$-0.000402977\pi$
$158$		0			0
$159$	−13.7438	−	13.7438i	−1.08995	−	1.08995i
$160$		0			0
$161$	4.99511	−	4.99511i	0.393670	−	0.393670i
$162$		0			0
$163$	16.4166	+	4.97992i	1.28585	+	0.390058i	0.857933	−	0.513761i	$-0.171748\pi$
$163$	16.4166	+	4.97992i	1.28585	+	0.390058i	0.427915	+	0.903819i	$0.359248\pi$
$164$		0			0
$165$	−1.83613	−	0.180843i	−0.142943	−	0.0140786i
$166$		0			0
$167$	21.3192	+	4.24066i	1.64973	+	0.328152i	0.930408	−	0.366525i	$-0.119453\pi$
$167$	21.3192	+	4.24066i	1.64973	+	0.328152i	0.719322	+	0.694677i	$0.244453\pi$
$168$		0			0
$169$	0.0459389	+	0.230950i	0.00353376	+	0.0177654i
$170$		0			0
$171$	−2.93710	−	1.56991i	−0.224606	−	0.120054i
$172$		0			0
$173$	10.4715	−	1.03135i	0.796135	−	0.0784124i	0.308233	−	0.951311i	$-0.400262\pi$
$173$	10.4715	−	1.03135i	0.796135	−	0.0784124i	0.487902	+	0.872898i	$0.337762\pi$
$174$		0			0
$175$	−1.78202	−	4.30218i	−0.134708	−	0.325214i
$176$		0			0
$177$	−2.30779	+	5.57151i	−0.173464	+	0.418780i
$178$		0			0
$179$	7.64464	−	9.31502i	0.571387	−	0.696237i	−0.404494	−	0.914541i	$-0.632552\pi$
$179$	7.64464	−	9.31502i	0.571387	−	0.696237i	0.975881	+	0.218303i	$0.0700523\pi$
$180$		0			0
$181$	−7.03798	−	23.2011i	−0.523129	−	1.72452i	−0.676581	−	0.736368i	$-0.736539\pi$
$181$	−7.03798	−	23.2011i	−0.523129	−	1.72452i	0.153452	−	0.988156i	$-0.450961\pi$
$182$		0			0
$183$	−14.4397	−	9.64828i	−1.06741	−	0.713221i
$184$		0			0
$185$	−0.181104	−	0.271041i	−0.0133150	−	0.0199274i
$186$		0			0
$187$	3.73613	−	3.06616i	0.273213	−	0.224220i
$188$		0			0
$189$	−0.942801	−	1.76386i	−0.0685786	−	0.128302i
$190$		0			0
$191$			2.59963i			0.188103i	0.995567	+	0.0940515i	$0.0299818\pi$
$191$			2.59963i			0.188103i	−0.995567	+	0.0940515i	$0.970018\pi$
$192$		0			0
$193$			19.4382i			1.39919i	0.714540	+	0.699595i	$0.246636\pi$
$193$			19.4382i			1.39919i	−0.714540	+	0.699595i	$0.753364\pi$
$194$		0			0
$195$	−1.29371	−	2.42036i	−0.0926446	−	0.173326i
$196$		0			0
$197$	−12.0265	+	9.86986i	−0.856850	+	0.703198i	−0.956471	−	0.291827i	$-0.905737\pi$
$197$	−12.0265	+	9.86986i	−0.856850	+	0.703198i	0.0996215	+	0.995025i	$0.468237\pi$
$198$		0			0
$199$	−10.9772	−	16.4285i	−0.778153	−	1.16459i	−0.982604	−	0.185711i	$-0.940541\pi$
$199$	−10.9772	−	16.4285i	−0.778153	−	1.16459i	0.204451	−	0.978877i	$-0.434459\pi$
$200$		0			0
$201$	21.6451	+	14.4628i	1.52673	+	1.02013i
$202$		0			0
$203$	−1.05370	−	3.47358i	−0.0739552	−	0.243797i
$204$		0			0
$205$	−2.55972	+	3.11903i	−0.178779	+	0.217842i
$206$		0			0
$207$	5.86634	−	14.1626i	0.407739	−	0.984368i
$208$		0			0
$209$	1.50769	+	3.63988i	0.104289	+	0.251776i
$210$		0			0
$211$	4.37815	−	0.431211i	0.301405	−	0.0296858i	0.0538155	−	0.998551i	$-0.482862\pi$
$211$	4.37815	−	0.431211i	0.301405	−	0.0296858i	0.247589	+	0.968865i	$0.420362\pi$
$212$		0			0
$213$	6.40664	+	3.42442i	0.438976	+	0.234637i
$214$		0			0
$215$	0.567593	+	2.85348i	0.0387095	+	0.194606i
$216$		0			0
$217$	−9.47208	−	1.88411i	−0.643007	−	0.127902i
$218$		0			0
$219$	−5.52321	−	0.543989i	−0.373224	−	0.0367593i
$220$		0			0
$221$	6.87974	+	2.08695i	0.462782	+	0.140383i
$222$		0			0
$223$	1.23977	−	1.23977i	0.0830214	−	0.0830214i	−0.664377	−	0.747398i	$-0.731303\pi$
$223$	1.23977	−	1.23977i	0.0830214	−	0.0830214i	0.747398	+	0.664377i	$0.231303\pi$
$224$		0			0
$225$	−7.14539	−	7.14539i	−0.476359	−	0.476359i
$226$		0			0
$227$	−3.94145	+	12.9932i	−0.261603	+	0.862389i	0.723485	+	0.690340i	$0.242539\pi$
$227$	−3.94145	+	12.9932i	−0.261603	+	0.862389i	−0.985088	+	0.172050i	$0.944961\pi$
$228$		0			0
$229$	0.156386	−	1.58782i	0.0103343	−	0.104926i	−0.988634	−	0.150344i	$-0.951962\pi$
$229$	0.156386	−	1.58782i	0.0103343	−	0.104926i	0.998968	+	0.0454179i	$0.0144620\pi$
$230$		0			0
$231$	1.02334	−	5.14466i	0.0673306	−	0.338494i
$232$		0			0
$233$	−4.28801	+	0.852938i	−0.280917	+	0.0558778i	−0.333538	−	0.942737i	$-0.608242\pi$
$233$	−4.28801	+	0.852938i	−0.280917	+	0.0558778i	0.0526209	+	0.998615i	$0.483242\pi$
$234$		0			0
$235$	0.719182	−	1.34549i	0.0469142	−	0.0877704i
$236$		0			0
$237$	−2.64522	−	26.8574i	−0.171826	−	1.74458i
$238$		0			0
$239$	−12.0420	+	4.98797i	−0.778933	+	0.322645i	−0.736485	−	0.676454i	$-0.763516\pi$
$239$	−12.0420	+	4.98797i	−0.778933	+	0.322645i	−0.0424483	+	0.999099i	$0.513516\pi$
$240$		0			0
$241$	−1.86200	−	0.771266i	−0.119942	−	0.0496816i	0.321905	−	0.946772i	$-0.395677\pi$
$241$	−1.86200	−	0.771266i	−0.119942	−	0.0496816i	−0.441847	+	0.897090i	$0.645677\pi$
$242$		0			0
$243$	−14.1478	−	11.6108i	−0.907584	−	0.744835i
$244$		0			0
$245$	1.95368	−	0.592642i	0.124816	−	0.0378625i
$246$		0			0
$247$	−3.25583	+	4.87270i	−0.207164	+	0.310042i
$248$		0			0
$249$	−13.3725	+	8.93519i	−0.847445	+	0.566245i
$250$		0			0
$251$	8.29747	+	10.1105i	0.523732	+	0.638169i	0.965947	−	0.258740i	$-0.0833072\pi$
$251$	8.29747	+	10.1105i	0.523732	+	0.638169i	−0.442215	+	0.896909i	$0.645807\pi$
$252$		0			0
$253$	−15.9934	+	8.54863i	−1.00549	+	0.537448i
$254$		0			0
$255$	−1.49073			−0.0933531
$256$		0			0
$257$	−19.2312			−1.19961			−0.599805	−	0.800146i	$-0.704755\pi$
$257$	−19.2312			−1.19961			−0.599805	+	0.800146i	$0.704755\pi$
$258$		0			0
$259$	0.817337	−	0.436876i	0.0507869	−	0.0271462i
$260$		0			0
$261$	−4.99710	−	6.08899i	−0.309313	−	0.376899i
$262$		0			0
$263$	9.83832	−	6.57376i	0.606657	−	0.405355i	−0.213953	−	0.976844i	$-0.568634\pi$
$263$	9.83832	−	6.57376i	0.606657	−	0.405355i	0.820610	+	0.571489i	$0.193634\pi$
$264$		0			0
$265$	1.60750	−	2.40580i	0.0987482	−	0.147787i
$266$		0			0
$267$	30.0204	−	9.10658i	1.83722	−	0.557314i
$268$		0			0
$269$	12.2545	+	10.0570i	0.747172	+	0.613188i	0.928973	−	0.370147i	$-0.120693\pi$
$269$	12.2545	+	10.0570i	0.747172	+	0.613188i	−0.181801	+	0.983335i	$0.558193\pi$
$270$		0			0
$271$	2.99583	+	1.24092i	0.181984	+	0.0753802i	0.471815	−	0.881698i	$-0.343599\pi$
$271$	2.99583	+	1.24092i	0.181984	+	0.0753802i	−0.289831	+	0.957078i	$0.593599\pi$
$272$		0			0
$273$	7.20857	−	2.98589i	0.436282	−	0.180714i
$274$		0			0
$275$	1.17173	+	11.8967i	0.0706577	+	0.717400i
$276$		0			0
$277$	4.28434	−	8.01543i	0.257421	−	0.481601i	−0.719700	−	0.694285i	$-0.755721\pi$
$277$	4.28434	−	8.01543i	0.257421	−	0.481601i	0.977121	+	0.212684i	$0.0682206\pi$
$278$		0			0
$279$	−20.5548	+	4.08860i	−1.23058	+	0.244778i
$280$		0			0
$281$	3.45353	−	17.3621i	0.206020	−	1.03573i	−0.729909	−	0.683545i	$-0.760437\pi$
$281$	3.45353	−	17.3621i	0.206020	−	1.03573i	0.935929	−	0.352189i	$-0.114563\pi$
$282$		0			0
$283$	1.26031	−	12.7962i	0.0749177	−	0.760652i	−0.882185	−	0.470903i	$-0.843928\pi$
$283$	1.26031	−	12.7962i	0.0749177	−	0.760652i	0.957103	−	0.289749i	$-0.0935719\pi$
$284$		0			0
$285$	0.352743	−	1.16284i	0.0208947	−	0.0688806i
$286$		0			0
$287$	−8.11150	−	8.11150i	−0.478807	−	0.478807i
$288$		0			0
$289$	−9.25947	+	9.25947i	−0.544675	+	0.544675i
$290$		0			0
$291$	32.1436	+	9.75065i	1.88429	+	0.571593i
$292$		0			0
$293$	27.6406	+	2.72236i	1.61478	+	0.159042i	0.864695	−	0.502298i	$-0.167512\pi$
$293$	27.6406	+	2.72236i	1.61478	+	0.159042i	0.750087	+	0.661340i	$0.230012\pi$
$294$		0			0
$295$	−0.880486	−	0.175140i	−0.0512639	−	0.0101970i
$296$		0			0
$297$	1.00166	+	5.03567i	0.0581221	+	0.292199i
$298$		0			0
$299$	−23.7898	−	12.7159i	−1.37580	−	0.735380i
$300$		0			0
$301$	−8.23167	+	0.810748i	−0.474465	+	0.0467308i
$302$		0			0
$303$	2.11969	+	5.11739i	0.121773	+	0.293987i
$304$		0			0
$305$	0.989331	−	2.38846i	0.0566489	−	0.136763i
$306$		0			0
$307$	6.25726	−	7.62450i	0.357121	−	0.435153i	−0.563198	−	0.826322i	$-0.690429\pi$
$307$	6.25726	−	7.62450i	0.357121	−	0.435153i	0.920319	+	0.391169i	$0.127929\pi$
$308$		0			0
$309$	−3.02152	−	9.96061i	−0.171888	−	0.566639i
$310$		0			0
$311$	−11.0505	−	7.38374i	−0.626619	−	0.418693i	0.201309	−	0.979528i	$-0.435480\pi$
$311$	−11.0505	−	7.38374i	−0.626619	−	0.418693i	−0.827928	+	0.560834i	$0.810480\pi$
$312$		0			0
$313$	1.33684	+	2.00073i	0.0755629	+	0.113088i	0.867326	−	0.497740i	$-0.165837\pi$
$313$	1.33684	+	2.00073i	0.0755629	+	0.113088i	−0.791763	+	0.610828i	$0.790837\pi$
$314$		0			0
$315$	−0.510243	+	0.418745i	−0.0287489	+	0.0235936i
$316$		0			0
$317$	−3.45253	−	6.45922i	−0.193913	−	0.362786i	0.766109	−	0.642711i	$-0.222190\pi$
$317$	−3.45253	−	6.45922i	−0.193913	−	0.362786i	−0.960022	+	0.279925i	$0.909690\pi$
$318$		0			0
$319$			9.31843i			0.521732i
$320$		0			0
$321$		−	19.0543i		−	1.06351i
$322$		0			0
$323$	1.50057	+	2.80738i	0.0834941	+	0.156207i
$324$		0			0
$325$	−13.7455	+	11.2806i	−0.762462	+	0.625736i
$326$		0			0
$327$	7.02068	+	10.5072i	0.388245	+	0.581049i
$328$		0			0
$329$	3.60646	+	2.40976i	0.198831	+	0.132854i
$330$		0			0
$331$	−9.31359	−	30.7028i	−0.511921	−	1.68758i	−0.707353	−	0.706861i	$-0.750111\pi$
$331$	−9.31359	−	30.7028i	−0.511921	−	1.68758i	0.195431	−	0.980717i	$-0.437389\pi$
$332$		0			0
$333$	1.27584	−	1.55462i	0.0699158	−	0.0851927i
$334$		0			0
$335$	−1.48301	+	3.58030i	−0.0810255	+	0.195613i
$336$		0			0
$337$	−2.11817	−	5.11372i	−0.115384	−	0.278562i	0.855628	−	0.517591i	$-0.173171\pi$
$337$	−2.11817	−	5.11372i	−0.115384	−	0.278562i	−0.971012	+	0.239029i	$0.923171\pi$
$338$		0			0
$339$	−18.1689	+	1.78948i	−0.986797	+	0.0971910i
$340$		0			0
$341$	21.8651	+	11.6871i	1.18406	+	0.632894i
$342$		0			0
$343$	2.43344	+	12.2337i	0.131393	+	0.660560i
$344$		0			0
$345$	5.48588	+	1.09121i	0.295350	+	0.0587487i
$346$		0			0
$347$	22.1503	+	2.18162i	1.18909	+	0.117115i	0.673149	−	0.739507i	$-0.264941\pi$
$347$	22.1503	+	2.18162i	1.18909	+	0.117115i	0.515944	+	0.856622i	$0.327441\pi$
$348$		0			0
$349$	−19.5904	−	5.94269i	−1.04865	−	0.318105i	−0.281494	−	0.959563i	$-0.590830\pi$
$349$	−19.5904	−	5.94269i	−1.04865	−	0.318105i	−0.767158	+	0.641458i	$0.778330\pi$
$350$		0			0
$351$	−5.40032	+	5.40032i	−0.288248	+	0.288248i
$352$		0			0
$353$	−12.4918	−	12.4918i	−0.664872	−	0.664872i	0.291652	−	0.956524i	$-0.405795\pi$
$353$	−12.4918	−	12.4918i	−0.664872	−	0.664872i	−0.956524	+	0.291652i	$0.905795\pi$
$354$		0			0
$355$	−0.313918	+	1.03485i	−0.0166610	+	0.0549240i
$356$		0			0
$357$	0.415416	−	4.21779i	0.0219862	−	0.223229i
$358$		0			0
$359$	4.39055	−	22.0728i	0.231724	−	1.16496i	−0.673225	−	0.739437i	$-0.735092\pi$
$359$	4.39055	−	22.0728i	0.231724	−	1.16496i	0.904950	−	0.425519i	$-0.139908\pi$
$360$		0			0
$361$	16.0900	−	3.20049i	0.846840	−	0.168447i
$362$		0			0
$363$	5.32503	−	9.96243i	0.279491	−	0.522892i
$364$		0			0
$365$	−0.0809806	−	0.822210i	−0.00423872	−	0.0430364i
$366$		0			0
$367$	−8.79474	+	3.64290i	−0.459082	+	0.190158i	−0.600225	−	0.799831i	$-0.704922\pi$
$367$	−8.79474	+	3.64290i	−0.459082	+	0.190158i	0.141143	+	0.989989i	$0.454922\pi$
$368$		0			0
$369$	−22.9985	−	9.52628i	−1.19725	−	0.495918i
$370$		0			0
$371$	6.35889	+	5.21860i	0.330137	+	0.270936i
$372$		0			0
$373$	35.2348	−	10.6884i	1.82439	−	0.553422i	0.824465	−	0.565913i	$-0.191476\pi$
$373$	35.2348	−	10.6884i	1.82439	−	0.553422i	0.999922	+	0.0124909i	$0.00397609\pi$
$374$		0			0
$375$	4.14396	−	6.20187i	0.213993	−	0.320263i
$376$		0			0
$377$	−11.5250	+	7.70074i	−0.593566	+	0.396608i
$378$		0			0
$379$	−11.3438	−	13.8224i	−0.582690	−	0.710009i	0.395326	−	0.918541i	$-0.370632\pi$
$379$	−11.3438	−	13.8224i	−0.582690	−	0.710009i	−0.978016	+	0.208532i	$0.933132\pi$
$380$		0			0
$381$	−11.2122	+	5.99302i	−0.574416	+	0.307032i
$382$		0			0
$383$	22.3035			1.13966			0.569829	−	0.821763i	$-0.307009\pi$
$383$	22.3035			1.13966			0.569829	+	0.821763i	$0.307009\pi$
$384$		0			0
$385$	0.780862			0.0397964
$386$		0			0
$387$	−15.8300	+	8.46132i	−0.804685	+	0.430113i
$388$		0			0
$389$	24.1574	+	29.4359i	1.22483	+	1.49246i	0.814123	+	0.580692i	$0.197218\pi$
$389$	24.1574	+	29.4359i	1.22483	+	1.49246i	0.410707	+	0.911767i	$0.365282\pi$
$390$		0			0
$391$	−12.1830	+	8.14043i	−0.616122	+	0.411679i
$392$		0			0
$393$	13.0004	−	19.4564i	0.655782	−	0.981446i
$394$		0			0
$395$	3.84447	−	1.16621i	0.193436	−	0.0586782i
$396$		0			0
$397$	5.05789	+	4.15091i	0.253848	+	0.208328i	0.752707	−	0.658355i	$-0.228747\pi$
$397$	5.05789	+	4.15091i	0.253848	+	0.208328i	−0.498859	+	0.866683i	$0.666247\pi$
$398$		0			0
$399$	3.19177	+	1.32208i	0.159789	+	0.0661866i
$400$		0			0
$401$	20.1808	−	8.35915i	1.00778	−	0.417436i	0.183136	−	0.983088i	$-0.441375\pi$
$401$	20.1808	−	8.35915i	1.00778	−	0.417436i	0.824644	+	0.565651i	$0.191375\pi$
$402$		0			0
$403$	3.61472	+	36.7009i	0.180062	+	1.82820i
$404$		0			0
$405$	1.72629	−	3.22966i	0.0857799	−	0.160483i
$406$		0			0
$407$	−2.33344	+	0.464149i	−0.115664	+	0.0230070i
$408$		0			0
$409$	5.10569	−	25.6680i	0.252460	−	1.26920i	−0.621580	−	0.783350i	$-0.713509\pi$
$409$	5.10569	−	25.6680i	0.252460	−	1.26920i	0.874041	−	0.485853i	$-0.161491\pi$
$410$		0			0
$411$	1.04484	−	10.6084i	0.0515382	−	0.523276i
$412$		0			0
$413$	0.740893	−	2.44240i	0.0364569	−	0.120182i
$414$		0			0
$415$	−1.69294	−	1.69294i	−0.0831031	−	0.0831031i
$416$		0			0
$417$	11.3375	−	11.3375i	0.555201	−	0.555201i
$418$		0			0
$419$	−25.3170	−	7.67983i	−1.23682	−	0.375184i	−0.396881	−	0.917870i	$-0.629907\pi$
$419$	−25.3170	−	7.67983i	−1.23682	−	0.375184i	−0.839936	+	0.542686i	$0.817407\pi$
$420$		0			0
$421$	−20.7637	−	2.04505i	−1.01196	−	0.0996694i	−0.421577	−	0.906792i	$-0.638523\pi$
$421$	−20.7637	−	2.04505i	−1.01196	−	0.0996694i	−0.590383	+	0.807123i	$0.701023\pi$
$422$		0			0
$423$	9.23158	+	1.83628i	0.448855	+	0.0892828i
$424$		0			0
$425$	1.88433	+	9.47319i	0.0914037	+	0.459517i
$426$		0			0
$427$	6.48208	+	3.46474i	0.313690	+	0.167671i
$428$		0			0
$429$	−19.9337	+	1.96330i	−0.962407	+	0.0947889i
$430$		0			0
$431$	3.82955	+	9.24536i	0.184463	+	0.445333i	0.988877	−	0.148736i	$-0.0475205\pi$
$431$	3.82955	+	9.24536i	0.184463	+	0.445333i	−0.804414	+	0.594069i	$0.797520\pi$
$432$		0			0
$433$	−11.3803	+	27.4745i	−0.546904	+	1.32034i	0.372866	+	0.927885i	$0.378375\pi$
$433$	−11.3803	+	27.4745i	−0.546904	+	1.32034i	−0.919770	+	0.392457i	$0.871625\pi$
$434$		0			0
$435$	1.82332	−	2.22172i	0.0874216	−	0.106524i
$436$		0			0
$437$	−3.46711	−	11.4295i	−0.165855	−	0.546749i
$438$		0			0
$439$	3.20918	+	2.14431i	0.153166	+	0.102342i	0.629792	−	0.776764i	$-0.283140\pi$
$439$	3.20918	+	2.14431i	0.153166	+	0.102342i	−0.476626	+	0.879106i	$0.658140\pi$
$440$		0			0
$441$	6.99773	+	10.4728i	0.333225	+	0.498707i
$442$		0			0
$443$	−22.8422	+	18.7461i	−1.08527	+	0.890654i	−0.994450	−	0.105213i	$-0.966447\pi$
$443$	−22.8422	+	18.7461i	−1.08527	+	0.890654i	−0.0908157	+	0.995868i	$0.528947\pi$
$444$		0			0
$445$	2.20145	+	4.11863i	0.104359	+	0.195242i
$446$		0			0
$447$			33.4884i			1.58395i
$448$		0			0
$449$			32.1926i			1.51926i	0.650354	+	0.759632i	$0.274621\pi$
$449$			32.1926i			1.51926i	−0.650354	+	0.759632i	$0.725379\pi$
$450$		0			0
$451$	13.8820	+	25.9715i	0.653679	+	1.22295i
$452$		0			0
$453$	17.5133	−	14.3728i	0.822844	−	0.675291i
$454$		0			0
$455$	0.645303	+	0.965764i	0.0302523	+	0.0452757i
$456$		0			0
$457$	21.5886	+	14.4250i	1.00987	+	0.674775i	0.946329	−	0.323204i	$-0.104760\pi$
$457$	21.5886	+	14.4250i	1.00987	+	0.674775i	0.0635431	+	0.997979i	$0.479760\pi$
$458$		0			0
$459$	1.20422	+	3.96978i	0.0562082	+	0.185294i
$460$		0			0
$461$	−20.1466	+	24.5487i	−0.938321	+	1.14335i	0.0511604	+	0.998690i	$0.483708\pi$
$461$	−20.1466	+	24.5487i	−0.938321	+	1.14335i	−0.989482	+	0.144657i	$0.953792\pi$
$462$		0			0
$463$	14.3990	−	34.7624i	0.669180	−	1.61554i	−0.113804	−	0.993503i	$-0.536304\pi$
$463$	14.3990	−	34.7624i	0.669180	−	1.61554i	0.782985	−	0.622041i	$-0.213696\pi$
$464$		0			0
$465$	−2.92633	−	7.06479i	−0.135705	−	0.327622i
$466$		0			0
$467$	−36.0818	+	3.55375i	−1.66967	+	0.164448i	−0.888187	−	0.459483i	$-0.848035\pi$
$467$	−36.0818	+	3.55375i	−1.66967	+	0.164448i	−0.781480	+	0.623931i	$0.785535\pi$
$468$		0			0
$469$	−9.71666	−	5.19366i	−0.448674	−	0.239821i
$470$		0			0
$471$	3.20806	+	16.1280i	0.147820	+	0.743140i
$472$		0			0
$473$	20.8261	+	4.14257i	0.957586	+	0.190476i
$474$		0			0
$475$	−7.83541	−	0.771720i	−0.359513	−	0.0354089i
$476$		0			0
$477$	17.0824	+	5.18188i	0.782148	+	0.237262i
$478$		0			0
$479$	15.6299	−	15.6299i	0.714150	−	0.714150i	−0.253251	−	0.967401i	$-0.581500\pi$
$479$	15.6299	−	15.6299i	0.714150	−	0.714150i	0.967401	+	0.253251i	$0.0814997\pi$
$480$		0			0
$481$	−2.50240	−	2.50240i	−0.114100	−	0.114100i
$482$		0			0
$483$	−4.61614	+	15.2174i	−0.210042	+	0.692414i
$484$		0			0
$485$	−0.490120	+	4.97627i	−0.0222552	+	0.225961i
$486$		0			0
$487$	−3.86259	+	19.4185i	−0.175031	+	0.879938i	0.789050	+	0.614329i	$0.210573\pi$
$487$	−3.86259	+	19.4185i	−0.175031	+	0.879938i	−0.964081	+	0.265609i	$0.914427\pi$
$488$		0			0
$489$	−37.8763	+	7.53406i	−1.71282	+	0.340702i
$490$		0			0
$491$	−8.68630	+	16.2509i	−0.392007	+	0.733394i	−0.998075	−	0.0620192i	$-0.980246\pi$
$491$	−8.68630	+	16.2509i	−0.392007	+	0.733394i	0.606068	+	0.795413i	$0.292746\pi$
$492$		0			0
$493$	0.737978	+	7.49281i	0.0332368	+	0.337459i
$494$		0			0
$495$	1.56551	−	0.648457i	0.0703646	−	0.0291460i
$496$		0			0
$497$	−2.84047	−	1.17656i	−0.127412	−	0.0527759i
$498$		0			0
$499$	16.8715	+	13.8461i	0.755274	+	0.619837i	0.931176	−	0.364571i	$-0.118784\pi$
$499$	16.8715	+	13.8461i	0.755274	+	0.619837i	−0.175902	+	0.984408i	$0.556284\pi$
$500$		0			0
$501$	−46.8249	+	14.2042i	−2.09198	+	0.634596i
$502$		0			0
$503$	18.4681	−	27.6395i	0.823453	−	1.23238i	−0.146529	−	0.989206i	$-0.546810\pi$
$503$	18.4681	−	27.6395i	0.823453	−	1.23238i	0.969982	−	0.243178i	$-0.0781898\pi$
$504$		0			0
$505$	−0.685601	+	0.458104i	−0.0305088	+	0.0203853i
$506$		0			0
$507$	−0.336278	−	0.409756i	−0.0149346	−	0.0181979i
$508$		0			0
$509$	−6.19498	+	3.31129i	−0.274588	+	0.146770i	−0.602943	−	0.797784i	$-0.706006\pi$
$509$	−6.19498	+	3.31129i	−0.274588	+	0.146770i	0.328356	+	0.944554i	$0.393506\pi$
$510$		0			0
$511$	2.34888			0.103909
$512$		0			0
$513$	−3.38156			−0.149300
$514$		0			0
$515$	1.36654	−	0.730430i	0.0602169	−	0.0321866i
$516$		0			0
$517$	−7.06388	−	8.60737i	−0.310669	−	0.378552i
$518$		0			0
$519$	−19.6946	+	13.1595i	−0.864497	+	0.577639i
$520$		0			0
$521$	0.697488	−	1.04386i	0.0305575	−	0.0457325i	−0.815876	−	0.578226i	$-0.803745\pi$
$521$	0.697488	−	1.04386i	0.0305575	−	0.0457325i	0.846434	+	0.532494i	$0.178745\pi$
$522$		0			0
$523$	1.15058	−	0.349024i	0.0503112	−	0.0152617i	−0.265029	−	0.964241i	$-0.585381\pi$
$523$	1.15058	−	0.349024i	0.0503112	−	0.0152617i	0.315340	+	0.948979i	$0.397881\pi$
$524$		0			0
$525$	8.10315	+	6.65008i	0.353650	+	0.290233i
$526$		0			0
$527$	18.5070	+	7.66585i	0.806177	+	0.333929i
$528$		0			0
$529$	29.5430	−	12.2371i	1.28448	−	0.532049i
$530$		0			0
$531$	−0.542876	−	5.51191i	−0.0235588	−	0.239197i
$532$		0			0
$533$	−20.6492	+	38.6320i	−0.894417	+	1.67334i
$534$		0			0
$535$	2.78201	−	0.553376i	0.120277	−	0.0239245i
$536$		0			0
$537$	−5.29211	+	26.6053i	−0.228372	+	1.14810i
$538$		0			0
$539$	1.46051	−	14.8288i	0.0629084	−	0.638720i
$540$		0			0
$541$	−13.2951	+	43.8282i	−0.571603	+	1.88432i	−0.118265	+	0.992982i	$0.537733\pi$
$541$	−13.2951	+	43.8282i	−0.571603	+	1.88432i	−0.453337	+	0.891339i	$0.649767\pi$
$542$		0			0
$543$	38.5926	+	38.5926i	1.65617	+	1.65617i
$544$		0			0
$545$	−1.33020	+	1.33020i	−0.0569795	+	0.0569795i
$546$		0			0
$547$	−9.28357	−	2.81614i	−0.396937	−	0.120410i	0.0855044	−	0.996338i	$-0.472750\pi$
$547$	−9.28357	−	2.81614i	−0.396937	−	0.120410i	−0.482441	+	0.875928i	$0.660250\pi$
$548$		0			0
$549$	15.8729	+	1.56334i	0.677438	+	0.0667218i
$550$		0			0
$551$	−6.01936	−	1.19733i	−0.256434	−	0.0510078i
$552$		0			0
$553$	2.22828	+	11.2023i	0.0947561	+	0.476371i
$554$		0			0
$555$	0.647163	+	0.345916i	0.0274706	+	0.0146833i
$556$		0			0
$557$	−5.96670	+	0.587669i	−0.252817	+	0.0249003i	−0.223632	−	0.974674i	$-0.571791\pi$
$557$	−5.96670	+	0.587669i	−0.252817	+	0.0249003i	−0.0291854	+	0.999574i	$0.509291\pi$
$558$		0			0
$559$	12.0872	+	29.1810i	0.511233	+	1.23423i
$560$		0			0
$561$	−4.16362	+	10.0519i	−0.175788	+	0.424391i
$562$		0			0
$563$	10.9206	−	13.3068i	0.460247	−	0.560813i	−0.490236	−	0.871590i	$-0.663089\pi$
$563$	10.9206	−	13.3068i	0.460247	−	0.560813i	0.950483	+	0.310777i	$0.100589\pi$
$564$		0			0
$565$	−0.788932	−	2.60076i	−0.0331906	−	0.109415i
$566$		0			0
$567$	8.65677	+	5.78427i	0.363550	+	0.242916i
$568$		0			0
$569$	−2.17077	−	3.24879i	−0.0910036	−	0.136196i	0.783174	−	0.621802i	$-0.213599\pi$
$569$	−2.17077	−	3.24879i	−0.0910036	−	0.136196i	−0.874178	+	0.485606i	$0.838599\pi$
$570$		0			0
$571$	2.07416	−	1.70222i	0.0868010	−	0.0712357i	−0.589992	−	0.807409i	$-0.700869\pi$
$571$	2.07416	−	1.70222i	0.0868010	−	0.0712357i	0.676793	+	0.736173i	$0.263369\pi$
$572$		0			0
$573$	−2.75863	−	5.16104i	−0.115244	−	0.215605i
$574$		0			0
$575$		−	36.2406i		−	1.51134i
$576$		0			0
$577$		−	39.0335i		−	1.62499i	−0.582971	−	0.812493i	$-0.698110\pi$
$577$		−	39.0335i		−	1.62499i	0.582971	−	0.812493i	$-0.301890\pi$
$578$		0			0
$579$	−20.6270	−	38.5905i	−0.857230	−	1.60377i
$580$		0			0
$581$	5.26167	−	4.31815i	0.218291	−	0.179147i
$582$		0			0
$583$	−11.7324	−	17.5587i	−0.485904	−	0.727207i
$584$		0			0
$585$	2.09575	+	1.40033i	0.0866484	+	0.0578966i
$586$		0			0
$587$	0.172486	+	0.568609i	0.00711924	+	0.0234690i	0.960428	−	0.278528i	$-0.0898466\pi$
$587$	0.172486	+	0.568609i	0.00711924	+	0.0234690i	−0.953309	+	0.301997i	$0.902347\pi$
$588$		0			0
$589$	−10.3589	+	12.6224i	−0.426832	+	0.520096i
$590$		0			0
$591$	13.4025	−	32.3566i	0.551307	−	1.33097i
$592$		0			0
$593$	−14.8160	−	35.7689i	−0.608418	−	1.46885i	−0.864720	−	0.502255i	$-0.832504\pi$
$593$	−14.8160	−	35.7689i	−0.608418	−	1.46885i	0.256301	−	0.966597i	$-0.417496\pi$
$594$		0			0
$595$	0.627880	−	0.0618407i	0.0257406	−	0.00253522i
$596$		0			0
$597$	39.2263	+	20.9669i	1.60543	+	0.858118i
$598$		0			0
$599$	−1.03501	−	5.20335i	−0.0422894	−	0.212603i	0.953863	−	0.300243i	$-0.0970676\pi$
$599$	−1.03501	−	5.20335i	−0.0422894	−	0.212603i	−0.996152	+	0.0876395i	$0.972068\pi$
$600$		0			0
$601$	32.6187	+	6.48826i	1.33054	+	0.264661i	0.808620	−	0.588331i	$-0.200215\pi$
$601$	32.6187	+	6.48826i	1.33054	+	0.264661i	0.521923	+	0.852993i	$0.325215\pi$
$602$		0			0
$603$	−23.7935	−	2.34345i	−0.968946	−	0.0954329i
$604$		0			0
$605$	1.60921	+	0.488147i	0.0654235	+	0.0198460i
$606$		0			0
$607$	6.29388	−	6.29388i	0.255461	−	0.255461i	−0.567744	−	0.823205i	$-0.692184\pi$
$607$	6.29388	−	6.29388i	0.255461	−	0.255461i	0.823205	+	0.567744i	$0.192184\pi$
$608$		0			0
$609$	5.77793	+	5.77793i	0.234134	+	0.234134i
$610$		0			0
$611$	4.80795	−	15.8497i	0.194509	−	0.641209i
$612$		0			0
$613$	3.40477	−	34.5692i	0.137517	−	1.39624i	−0.640482	−	0.767973i	$-0.721265\pi$
$613$	3.40477	−	34.5692i	0.137517	−	1.39624i	0.777999	−	0.628265i	$-0.216235\pi$
$614$		0			0
$615$	1.77200	−	8.90846i	0.0714540	−	0.359224i
$616$		0			0
$617$	−14.8154	+	2.94696i	−0.596445	+	0.118640i	−0.484076	−	0.875026i	$-0.660844\pi$
$617$	−14.8154	+	2.94696i	−0.596445	+	0.118640i	−0.112370	+	0.993666i	$0.535844\pi$
$618$		0			0
$619$	−20.8273	+	38.9652i	−0.837121	+	1.56614i	−0.0128715	+	0.999917i	$0.504097\pi$
$619$	−20.8273	+	38.9652i	−0.837121	+	1.56614i	−0.824250	+	0.566226i	$0.808403\pi$
$620$		0			0
$621$	−1.52566	−	15.4903i	−0.0612226	−	0.621603i
$622$		0			0
$623$	−12.2665	+	5.08095i	−0.491447	+	0.203564i
$624$		0			0
$625$	−21.5524	−	8.92729i	−0.862096	−	0.357092i
$626$		0			0
$627$	−6.85571	−	5.62634i	−0.273791	−	0.224694i
$628$		0			0
$629$	−1.83952	+	0.558013i	−0.0733466	+	0.0222494i
$630$		0			0
$631$	1.42383	−	2.13091i	0.0566817	−	0.0848302i	−0.802046	−	0.597262i	$-0.796255\pi$
$631$	1.42383	−	2.13091i	0.0566817	−	0.0848302i	0.858728	+	0.512432i	$0.171255\pi$
$632$		0			0
$633$	−8.23434	+	5.50201i	−0.327286	+	0.218685i
$634$		0			0
$635$	−1.20063	−	1.46297i	−0.0476456	−	0.0580563i
$636$		0			0
$637$	19.5471	−	10.4481i	0.774483	−	0.413970i
$638$		0			0
$639$	−6.67178			−0.263932
$640$		0			0
$641$	28.0900			1.10949			0.554744	−	0.832021i	$-0.312816\pi$
$641$	28.0900			1.10949			0.554744	+	0.832021i	$0.312816\pi$
$642$		0			0
$643$	−3.60833	+	1.92869i	−0.142299	+	0.0760602i	−0.541010	−	0.841016i	$-0.681958\pi$
$643$	−3.60833	+	1.92869i	−0.142299	+	0.0760602i	0.398711	+	0.917077i	$0.369458\pi$
$644$		0			0
$645$	−4.15485	−	5.06270i	−0.163597	−	0.199343i
$646$		0			0
$647$	−13.0443	+	8.71591i	−0.512824	+	0.342658i	−0.784905	−	0.619616i	$-0.787288\pi$
$647$	−13.0443	+	8.71591i	−0.512824	+	0.342658i	0.272081	+	0.962274i	$0.412288\pi$
$648$		0			0
$649$	−3.64016	+	5.44788i	−0.142889	+	0.213848i
$650$		0			0
$651$	20.8042	−	6.31089i	0.815382	−	0.247343i
$652$		0			0
$653$	26.5729	+	21.8078i	1.03988	+	0.853406i	0.989385	−	0.145319i	$-0.0464208\pi$
$653$	26.5729	+	21.8078i	1.03988	+	0.853406i	0.0504928	+	0.998724i	$0.483921\pi$
$654$		0			0
$655$	3.21827	+	1.33305i	0.125748	+	0.0520867i
$656$		0			0
$657$	4.70917	−	1.95060i	0.183722	−	0.0761002i
$658$		0			0
$659$	1.27374	+	12.9325i	0.0496177	+	0.503777i	0.987589	+	0.157063i	$0.0502026\pi$
$659$	1.27374	+	12.9325i	0.0496177	+	0.503777i	−0.937971	+	0.346714i	$0.887297\pi$
$660$		0			0
$661$	−1.34649	+	2.51910i	−0.0523723	+	0.0979817i	−0.906746	−	0.421678i	$-0.861441\pi$
$661$	−1.34649	+	2.51910i	−0.0523723	+	0.0979817i	0.854373	+	0.519660i	$0.173941\pi$
$662$		0			0
$663$	−15.8729	+	3.15732i	−0.616452	+	0.122620i
$664$		0			0
$665$	−0.100333	+	0.504408i	−0.00389075	+	0.0195601i
$666$		0			0
$667$	2.76896	−	28.1137i	0.107215	−	1.08857i
$668$		0			0
$669$	−1.14572	+	3.77692i	−0.0442959	+	0.146024i
$670$		0			0
$671$	−13.3420	−	13.3420i	−0.515061	−	0.515061i
$672$		0			0
$673$	17.8773	−	17.8773i	0.689118	−	0.689118i	−0.272919	−	0.962037i	$-0.587989\pi$
$673$	17.8773	−	17.8773i	0.689118	−	0.689118i	0.962037	+	0.272919i	$0.0879891\pi$
$674$		0			0
$675$	−9.81870	−	2.97847i	−0.377922	−	0.114641i
$676$		0			0
$677$	−30.5205	−	3.00601i	−1.17300	−	0.115530i	−0.507312	−	0.861762i	$-0.669361\pi$
$677$	−30.5205	−	3.00601i	−1.17300	−	0.115530i	−0.665686	+	0.746232i	$0.731861\pi$
$678$		0			0
$679$	−13.9430	−	2.77344i	−0.535084	−	0.106435i
$680$		0			0
$681$	−5.96296	−	29.9778i	−0.228501	−	1.14875i
$682$		0			0
$683$	9.92330	+	5.30412i	0.379705	+	0.202956i	0.650197	−	0.759766i	$-0.274686\pi$
$683$	9.92330	+	5.30412i	0.379705	+	0.202956i	−0.270492	+	0.962722i	$0.587186\pi$
$684$		0			0
$685$	1.57922	−	0.155540i	0.0603389	−	0.00594286i
$686$		0			0
$687$	1.37446	+	3.31823i	0.0524388	+	0.126598i
$688$		0			0
$689$	12.0209	−	29.0210i	0.457959	−	1.10561i
$690$		0			0
$691$	3.45694	−	4.21230i	0.131508	−	0.160243i	−0.703093	−	0.711098i	$-0.748198\pi$
$691$	3.45694	−	4.21230i	0.131508	−	0.160243i	0.834601	+	0.550855i	$0.185698\pi$
$692$		0			0
$693$	1.39845	+	4.61009i	0.0531229	+	0.175123i
$694$		0			0
$695$	1.98459	+	1.32606i	0.0752799	+	0.0503004i
$696$		0			0
$697$	13.2192	+	19.7839i	0.500712	+	0.749368i
$698$		0			0
$699$	7.60786	−	6.24361i	0.287756	−	0.236155i
$700$		0			0
$701$	−13.2608	−	24.8092i	−0.500853	−	0.937030i	−0.997607	−	0.0691388i	$-0.977975\pi$
$701$	−13.2608	−	24.8092i	−0.500853	−	0.937030i	0.496754	−	0.867891i	$-0.334525\pi$
$702$		0			0
$703$		−	1.56695i		−	0.0590987i
$704$		0			0
$705$			3.43437i			0.129346i
$706$		0			0
$707$	−1.10508	−	2.06746i	−0.0415608	−	0.0777548i
$708$		0			0
$709$	33.8638	−	27.7913i	1.27178	−	1.04373i	0.275178	−	0.961393i	$-0.411263\pi$
$709$	33.8638	−	27.7913i	1.27178	−	1.04373i	0.996605	−	0.0823324i	$-0.0262369\pi$
$710$		0			0
$711$	13.7702	+	20.6086i	0.516423	+	0.772882i
$712$		0			0
$713$	−62.4943	−	41.7573i	−2.34043	−	1.56382i
$714$		0			0
$715$	−0.865564	−	2.85338i	−0.0323703	−	0.106710i
$716$		0			0
$717$	18.6139	−	22.6811i	0.695149	−	0.847041i
$718$		0			0
$719$	−10.9176	+	26.3573i	−0.407156	+	0.982963i	0.578726	+	0.815522i	$0.303550\pi$
$719$	−10.9176	+	26.3573i	−0.407156	+	0.982963i	−0.985882	+	0.167440i	$0.946450\pi$
$720$		0			0
$721$	1.68583	+	4.06996i	0.0627837	+	0.151573i
$722$		0			0
$723$	4.51506	−	0.444694i	0.167917	−	0.0165384i
$724$		0			0
$725$	−16.4232	−	8.77839i	−0.609943	−	0.326021i
$726$		0			0
$727$	−0.486066	−	2.44362i	−0.0180272	−	0.0906287i	0.970724	−	0.240196i	$-0.0772118\pi$
$727$	−0.486066	−	2.44362i	−0.0180272	−	0.0906287i	−0.988751	+	0.149568i	$0.952212\pi$
$728$		0			0
$729$	8.25455	+	1.64193i	0.305724	+	0.0608123i
$730$		0			0
$731$	17.0740	+	1.68165i	0.631507	+	0.0621980i
$732$		0			0
$733$	3.62879	+	1.10078i	0.134032	+	0.0406583i	0.356588	−	0.934262i	$-0.383940\pi$
$733$	3.62879	+	1.10078i	0.134032	+	0.0406583i	−0.222556	+	0.974920i	$0.571440\pi$
$734$		0			0
$735$	−3.24974	+	3.24974i	−0.119868	+	0.119868i
$736$		0			0
$737$	19.9997	+	19.9997i	0.736697	+	0.736697i
$738$		0			0
$739$	10.8262	−	35.6893i	0.398250	−	1.31285i	−0.497179	−	0.867648i	$-0.665631\pi$
$739$	10.8262	−	35.6893i	0.398250	−	1.31285i	0.895429	−	0.445205i	$-0.146869\pi$
$740$		0			0
$741$	1.29306	−	13.1287i	0.0475019	−	0.482295i
$742$		0			0
$743$	4.97247	−	24.9983i	0.182422	−	0.917099i	−0.775779	−	0.631005i	$-0.782643\pi$
$743$	4.97247	−	24.9983i	0.182422	−	0.917099i	0.958201	−	0.286094i	$-0.0923571\pi$
$744$		0			0
$745$	−4.88945	+	0.972572i	−0.179136	+	0.0356323i
$746$		0			0
$747$	6.96294	−	13.0267i	0.254761	−	0.476624i
$748$		0			0
$749$	0.790441	+	8.02548i	0.0288821	+	0.293245i
$750$		0			0
$751$	19.4112	−	8.04037i	0.708323	−	0.293397i	0.000712746	−	1.00000i	$-0.499773\pi$
$751$	19.4112	−	8.04037i	0.708323	−	0.293397i	0.707611	+	0.706603i	$0.249773\pi$
$752$		0			0
$753$	−27.2018	−	11.2674i	−0.991289	−	0.410605i
$754$		0			0
$755$	2.60710	+	2.13959i	0.0948822	+	0.0778678i
$756$		0			0
$757$	−6.81930	+	2.06861i	−0.247852	+	0.0751850i	−0.411766	−	0.911290i	$-0.635088\pi$
$757$	−6.81930	+	2.06861i	−0.247852	+	0.0751850i	0.163914	+	0.986475i	$0.447588\pi$
$758$		0			0
$759$	22.6801	−	33.9431i	0.823234	−	1.23206i
$760$		0			0
$761$	19.7593	−	13.2028i	0.716275	−	0.478599i	−0.143255	−	0.989686i	$-0.545757\pi$
$761$	19.7593	−	13.2028i	0.716275	−	0.478599i	0.859529	+	0.511086i	$0.170757\pi$
$762$		0			0
$763$	−3.39291	−	4.13428i	−0.122832	−	0.149671i
$764$		0			0
$765$	1.20745	−	0.645397i	0.0436555	−	0.0233344i
$766$		0			0
$767$	−9.74613			−0.351912
$768$		0			0
$769$	−38.7313			−1.39669			−0.698344	−	0.715762i	$-0.746079\pi$
$769$	−38.7313			−1.39669			−0.698344	+	0.715762i	$0.746079\pi$
$770$		0			0
$771$	38.1796	−	20.4074i	1.37501	−	0.734956i
$772$		0			0
$773$	2.77436	+	3.38056i	0.0997867	+	0.121590i	0.820509	−	0.571633i	$-0.193690\pi$
$773$	2.77436	+	3.38056i	0.0997867	+	0.121590i	−0.720723	+	0.693223i	$0.756190\pi$
$774$		0			0
$775$	−41.1959	+	27.5262i	−1.47980	+	0.988771i
$776$		0			0
$777$	−1.15906	+	1.73465i	−0.0415810	+	0.0622304i
$778$		0			0
$779$	−18.5603	+	5.63021i	−0.664992	+	0.201723i
$780$		0			0
$781$	6.10113	+	5.00707i	0.218315	+	0.179167i
$782$		0			0
$783$	−7.38930	−	3.06075i	−0.264072	−	0.109382i
$784$		0			0
$785$	−2.26159	+	0.936781i	−0.0807196	+	0.0334352i
$786$		0			0
$787$	2.97998	+	30.2562i	0.106225	+	1.07852i	0.889529	+	0.456879i	$0.151033\pi$
$787$	2.97998	+	30.2562i	0.106225	+	1.07852i	−0.783304	+	0.621639i	$0.786467\pi$
$788$		0			0
$789$	−12.5561	+	23.4909i	−0.447011	+	0.836298i
$790$		0			0
$791$	7.57830	−	1.50742i	0.269453	−	0.0535976i
$792$		0			0
$793$	5.47547	−	27.5270i	0.194440	−	0.977514i
$794$		0			0
$795$	−0.638426	+	6.48204i	−0.0226426	+	0.229894i
$796$		0			0
$797$	12.4603	−	41.0761i	0.441366	−	1.45499i	−0.400997	−	0.916079i	$-0.631336\pi$
$797$	12.4603	−	41.0761i	0.441366	−	1.45499i	0.842363	−	0.538910i	$-0.181164\pi$
$798$		0			0
$799$	−6.36163	−	6.36163i	−0.225058	−	0.225058i
$800$		0			0
$801$	−20.3731	+	20.3731i	−0.719849	+	0.719849i
$802$		0			0
$803$	−5.77028	−	1.75040i	−0.203629	−	0.0617701i
$804$		0			0
$805$	−2.35586	−	0.232032i	−0.0830332	−	0.00817806i
$806$		0			0
$807$	−35.0010	−	6.96213i	−1.23209	−	0.245079i
$808$		0			0
$809$	−0.218606	−	1.09901i	−0.00768578	−	0.0386390i	0.976752	−	0.214372i	$-0.0687705\pi$
$809$	−0.218606	−	1.09901i	−0.00768578	−	0.0386390i	−0.984438	+	0.175733i	$0.943770\pi$
$810$		0			0
$811$	23.6341	+	12.6327i	0.829905	+	0.443594i	0.830911	−	0.556406i	$-0.187820\pi$
$811$	23.6341	+	12.6327i	0.829905	+	0.443594i	−0.00100525	+	0.999999i	$0.500320\pi$
$812$		0			0
$813$	−7.26442	+	0.715483i	−0.254774	+	0.0250931i
$814$		0			0
$815$	−2.20001	−	5.31129i	−0.0770629	−	0.186046i
$816$		0			0
$817$	−5.35190	+	12.9206i	−0.187239	+	0.452036i
$818$		0			0
$819$	−4.54604	+	5.53937i	−0.158852	+	0.193561i
$820$		0			0
$821$	−1.99541	−	6.57798i	−0.0696402	−	0.229573i	0.915211	−	0.402975i	$-0.132024\pi$
$821$	−1.99541	−	6.57798i	−0.0696402	−	0.229573i	−0.984851	+	0.173402i	$0.944524\pi$
$822$		0			0
$823$	25.8856	+	17.2962i	0.902314	+	0.602907i	0.917830	−	0.396973i	$-0.129939\pi$
$823$	25.8856	+	17.2962i	0.902314	+	0.602907i	−0.0155165	+	0.999880i	$0.504939\pi$
$824$		0			0
$825$	−14.9506	−	22.3751i	−0.520512	−	0.779001i
$826$		0			0
$827$	−8.73951	+	7.17233i	−0.303903	+	0.249406i	−0.773967	−	0.633226i	$-0.781731\pi$
$827$	−8.73951	+	7.17233i	−0.303903	+	0.249406i	0.470065	+	0.882632i	$0.344231\pi$
$828$		0			0
$829$	−4.25119	−	7.95341i	−0.147650	−	0.276233i	0.797214	−	0.603697i	$-0.206306\pi$
$829$	−4.25119	−	7.95341i	−0.147650	−	0.276233i	−0.944864	+	0.327463i	$0.893806\pi$
$830$		0			0
$831$			20.4594i			0.709728i
$832$		0			0
$833$		−	12.0393i		−	0.417135i
$834$		0			0
$835$	−3.43376	−	6.42412i	−0.118830	−	0.222316i
$836$		0			0
$837$	−16.4495	+	13.4998i	−0.568578	+	0.466620i
$838$		0			0
$839$	5.00659	+	7.49289i	0.172847	+	0.258683i	0.907771	−	0.419466i	$-0.137783\pi$
$839$	5.00659	+	7.49289i	0.172847	+	0.258683i	−0.734925	+	0.678149i	$0.762783\pi$
$840$		0			0
$841$	12.0430	+	8.04688i	0.415276	+	0.277479i
$842$		0			0
$843$	11.5677	+	38.1336i	0.398412	+	1.31339i
$844$		0			0
$845$	0.0500598	−	0.0609981i	0.00172211	−	0.00209840i
$846$		0			0
$847$	−1.82957	+	4.41697i	−0.0628647	+	0.151769i
$848$		0			0
$849$	11.0767	+	26.7415i	0.380151	+	0.917767i
$850$		0			0
$851$	7.17790	−	0.706962i	0.246055	−	0.0242343i
$852$		0			0
$853$	7.72001	+	4.12643i	0.264328	+	0.141286i	0.598237	−	0.801319i	$-0.295868\pi$
$853$	7.72001	+	4.12643i	0.264328	+	0.141286i	−0.333909	+	0.942605i	$0.608368\pi$
$854$		0			0
$855$	0.217727	+	1.09459i	0.00744609	+	0.0374340i
$856$		0			0
$857$	−0.938777	−	0.186734i	−0.0320680	−	0.00637872i	0.179030	−	0.983844i	$-0.442704\pi$
$857$	−0.938777	−	0.186734i	−0.0320680	−	0.00637872i	−0.211098	+	0.977465i	$0.567704\pi$
$858$		0			0
$859$	0.141007	+	0.0138880i	0.00481111	+	0.000473853i	0.100422	−	0.994945i	$-0.467981\pi$
$859$	0.141007	+	0.0138880i	0.00481111	+	0.000473853i	−0.0956113	+	0.995419i	$0.530481\pi$
$860$		0			0
$861$	24.7113	+	7.49610i	0.842160	+	0.255466i
$862$		0			0
$863$	−9.00152	+	9.00152i	−0.306415	+	0.306415i	−0.843517	−	0.537102i	$-0.819519\pi$
$863$	−9.00152	+	9.00152i	−0.306415	+	0.306415i	0.537102	+	0.843517i	$0.319519\pi$
$864$		0			0
$865$	−2.49332	−	2.49332i	−0.0847753	−	0.0847753i
$866$		0			0
$867$	8.55698	−	28.2086i	0.290610	−	0.958013i
$868$		0			0
$869$	2.87400	−	29.1802i	0.0974937	−	0.989870i
$870$		0			0
$871$	−8.20774	+	41.2631i	−0.278109	+	1.39815i
$872$		0			0
$873$	−30.2569	+	6.01847i	−1.02404	+	0.203694i
$874$		0			0
$875$	−1.48812	+	2.78407i	−0.0503075	+	0.0941188i
$876$		0			0
$877$	0.299332	+	3.03917i	0.0101077	+	0.102625i	0.998915	−	0.0465741i	$-0.0148304\pi$
$877$	0.299332	+	3.03917i	0.0101077	+	0.102625i	−0.988807	+	0.149199i	$0.952330\pi$
$878$		0			0
$879$	−57.7636	+	23.9265i	−1.94832	+	0.807020i
$880$		0			0
$881$	24.9060	+	10.3164i	0.839103	+	0.347568i	0.760500	−	0.649338i	$-0.224954\pi$
$881$	24.9060	+	10.3164i	0.839103	+	0.347568i	0.0786033	+	0.996906i	$0.474954\pi$
$882$		0			0
$883$	−8.11127	−	6.65675i	−0.272966	−	0.224018i	0.487944	−	0.872875i	$-0.337747\pi$
$883$	−8.11127	−	6.65675i	−0.272966	−	0.224018i	−0.760910	+	0.648858i	$0.775247\pi$
$884$		0			0
$885$	1.93388	−	0.586635i	0.0650065	−	0.0197195i
$886$		0			0
$887$	0.709984	−	1.06257i	0.0238389	−	0.0356775i	−0.819359	−	0.573281i	$-0.805670\pi$
$887$	0.709984	−	1.06257i	0.0238389	−	0.0356775i	0.843198	+	0.537604i	$0.180670\pi$
$888$		0			0
$889$	4.47383	−	2.98932i	0.150048	−	0.100259i
$890$		0			0
$891$	−16.9558	−	20.6607i	−0.568041	−	0.692159i
$892$		0			0
$893$	6.46768	−	3.45705i	0.216433	−	0.115686i
$894$		0			0
$895$	−4.03817			−0.134981
$896$		0			0
$897$	60.7234			2.02749
$898$		0			0
$899$	−34.0609	+	18.2059i	−1.13599	+	0.607202i
$900$		0			0
$901$	−10.8244	−	13.1895i	−0.360613	−	0.439408i
$902$		0			0
$903$	15.4819	−	10.3447i	0.515207	−	0.344250i
$904$		0			0
$905$	−4.51387	+	6.75548i	−0.150046	+	0.224560i
$906$		0			0
$907$	27.9154	−	8.46806i	0.926917	−	0.281177i	0.209490	−	0.977811i	$-0.432820\pi$
$907$	27.9154	−	8.46806i	0.926917	−	0.281177i	0.717427	+	0.696634i	$0.245320\pi$
$908$		0			0
$909$	−3.93242	−	3.22726i	−0.130430	−	0.107041i
$910$		0			0
$911$	−53.6149	−	22.2080i	−1.77634	−	0.735784i	−0.993536	−	0.113515i	$-0.963789\pi$
$911$	−53.6149	−	22.2080i	−1.77634	−	0.735784i	−0.782803	−	0.622269i	$-0.786211\pi$
$912$		0			0
$913$	−16.1437	+	6.68696i	−0.534280	+	0.221306i
$914$		0			0
$915$	0.570426	+	5.79163i	0.0188577	+	0.191465i
$916$		0			0
$917$	−4.66849	+	8.73414i	−0.154167	+	0.288427i
$918$		0			0
$919$	33.0705	−	6.57814i	1.09090	−	0.216993i	0.383310	−	0.923620i	$-0.374784\pi$
$919$	33.0705	−	6.57814i	1.09090	−	0.216993i	0.707586	+	0.706627i	$0.249784\pi$
$920$		0			0
$921$	−4.33168	+	21.7768i	−0.142734	+	0.717571i
$922$		0			0
$923$	−1.15074	+	11.6837i	−0.0378771	+	0.384572i
$924$		0			0
$925$	1.38017	−	4.54980i	0.0453796	−	0.149597i
$926$		0			0
$927$	6.75970	+	6.75970i	0.222018	+	0.222018i
$928$		0			0
$929$	−21.7009	+	21.7009i	−0.711983	+	0.711983i	−0.966950	−	0.254967i	$-0.917935\pi$
$929$	−21.7009	+	21.7009i	−0.711983	+	0.711983i	0.254967	+	0.966950i	$0.417935\pi$
$930$		0			0
$931$	9.39117	+	2.84878i	0.307783	+	0.0933651i
$932$		0			0
$933$	29.7739	+	2.93247i	0.974754	+	0.0960049i
$934$		0			0
$935$	−1.58854	−	0.315979i	−0.0519507	−	0.0103336i
$936$		0			0
$937$	1.87575	+	9.43002i	0.0612780	+	0.308065i	0.999253	−	0.0386367i	$-0.0123015\pi$
$937$	1.87575	+	9.43002i	0.0612780	+	0.308065i	−0.937975	+	0.346702i	$0.887302\pi$
$938$		0			0
$939$	−4.77712	−	2.55343i	−0.155896	−	0.0833279i
$940$		0			0
$941$	14.2234	−	1.40088i	0.463669	−	0.0456675i	0.136514	−	0.990638i	$-0.456410\pi$
$941$	14.2234	−	1.40088i	0.463669	−	0.0456675i	0.327155	+	0.944971i	$0.393910\pi$
$942$		0			0
$943$	−34.1647	−	82.4810i	−1.11256	−	2.68595i
$944$		0			0
$945$	−0.256483	+	0.619206i	−0.00834340	+	0.0201428i
$946$		0			0
$947$	0.634218	−	0.772797i	0.0206093	−	0.0251125i	−0.762604	−	0.646866i	$-0.776079\pi$
$947$	0.634218	−	0.772797i	0.0206093	−	0.0251125i	0.783213	+	0.621753i	$0.213579\pi$
$948$		0			0
$949$	−2.60367	−	8.58317i	−0.0845189	−	0.278621i
$950$		0			0
$951$	13.7086	+	9.15977i	0.444531	+	0.297026i
$952$		0			0
$953$	9.38542	+	14.0463i	0.304024	+	0.455004i	0.951752	−	0.306868i	$-0.0992809\pi$
$953$	9.38542	+	14.0463i	0.304024	+	0.455004i	−0.647729	+	0.761871i	$0.724281\pi$
$954$		0			0
$955$	0.673417	−	0.552659i	0.0217913	−	0.0178836i
$956$		0			0
$957$	−9.88836	−	18.4998i	−0.319645	−	0.598014i
$958$		0			0
$959$			4.51151i			0.145684i
$960$		0			0
$961$			71.7556i			2.31470i
$962$		0			0
$963$	8.24938	+	15.4335i	0.265833	+	0.497338i
$964$		0			0
$965$	5.03532	−	4.13238i	0.162093	−	0.133026i
$966$		0			0
$967$	−11.8328	−	17.7090i	−0.380516	−	0.569482i	0.590936	−	0.806718i	$-0.298758\pi$
$967$	−11.8328	−	17.7090i	−0.380516	−	0.569482i	−0.971452	+	0.237236i	$0.923758\pi$
$968$		0			0
$969$	−5.95816	−	3.98111i	−0.191404	−	0.127892i
$970$		0			0
$971$	−2.98496	−	9.84008i	−0.0957918	−	0.315783i	0.895929	−	0.444198i	$-0.146511\pi$
$971$	−2.98496	−	9.84008i	−0.0957918	−	0.315783i	−0.991721	+	0.128414i	$0.959011\pi$
$972$		0			0
$973$	−4.30493	+	5.24557i	−0.138010	+	0.168165i
$974$		0			0
$975$	15.3182	−	36.9815i	0.490577	−	1.18436i
$976$		0			0
$977$	−3.03498	−	7.32709i	−0.0970976	−	0.234414i	0.867866	−	0.496799i	$-0.165491\pi$
$977$	−3.03498	−	7.32709i	−0.0970976	−	0.234414i	−0.964963	+	0.262384i	$0.915491\pi$
$978$		0			0
$979$	33.9203	−	3.34085i	1.08410	−	0.106774i
$980$		0			0
$981$	−10.2356	−	5.47102i	−0.326796	−	0.174676i
$982$		0			0
$983$	−5.67893	−	28.5499i	−0.181130	−	0.910601i	−0.959266	−	0.282505i	$-0.908835\pi$
$983$	−5.67893	−	28.5499i	−0.181130	−	0.910601i	0.778136	−	0.628096i	$-0.216165\pi$
$984$		0			0
$985$	5.11343	+	1.01712i	0.162928	+	0.0324083i
$986$		0			0
$987$	−9.71703	−	0.957043i	−0.309296	−	0.0304630i
$988$		0			0
$989$	−61.6015	−	18.6866i	−1.95881	−	0.594199i
$990$		0			0
$991$	25.1199	−	25.1199i	0.797960	−	0.797960i	−0.184813	−	0.982774i	$-0.559168\pi$
$991$	25.1199	−	25.1199i	0.797960	−	0.797960i	0.982774	+	0.184813i	$0.0591681\pi$
$992$		0			0
$993$	51.0708	+	51.0708i	1.62068	+	1.62068i
$994$		0			0
$995$	−1.92204	+	6.33612i	−0.0609328	+	0.200869i
$996$		0			0
$997$	−5.42076	+	55.0379i	−0.171677	+	1.74307i	0.394599	+	0.918853i	$0.370884\pi$
$997$	−5.42076	+	55.0379i	−0.171677	+	1.74307i	−0.566276	+	0.824215i	$0.691616\pi$
$998$		0			0
$999$	0.398385	−	2.00282i	0.0126043	−	0.0633663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.3		240
4.3	odd	2		128.2.k.a.101.10	✓	240
128.19	odd	32		128.2.k.a.109.10	yes	240
128.109	even	32	inner	512.2.k.a.273.3		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.10	✓	240	4.3	odd	2
128.2.k.a.109.10	yes	240	128.19	odd	32
512.2.k.a.273.3		240	128.109	even	32	inner
512.2.k.a.497.3		240	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.98529 + 1.06116i) q^{3} +(-0.212591 - 0.259043i) q^{5} +(0.792164 - 0.529307i) q^{7} +(1.14862 - 1.71903i) q^{9} +(-2.34047 + 0.709975i) q^{11} +(-2.81226 - 2.30796i) q^{13} +(0.696942 + 0.288683i) q^{15} +(-1.82571 + 0.756236i) q^{17} +(-0.157890 - 1.60309i) q^{19} +(-1.01100 + 1.89144i) q^{21} +(7.27219 - 1.44653i) q^{23} +(0.953543 - 4.79379i) q^{25} +(0.205763 - 2.08914i) q^{27} +(1.10598 - 3.64593i) q^{29} +(-7.16783 - 7.16783i) q^{31} +(3.89313 - 3.89313i) q^{33} +(-0.305520 - 0.0926785i) q^{35} +(0.968069 + 0.0953465i) q^{37} +(8.03228 + 1.59772i) q^{39} +(-2.34900 - 11.8092i) q^{41} +(-7.65676 - 4.09262i) q^{43} +(-0.689487 + 0.0679086i) q^{45} +(1.74223 + 4.20612i) q^{47} +(-2.33143 + 5.62856i) q^{49} +(2.82209 - 3.43873i) q^{51} +(2.50640 + 8.26251i) q^{53} +(0.681478 + 0.455349i) q^{55} +(2.01459 + 3.01505i) q^{57} +(2.07085 - 1.69950i) q^{59} +(3.63666 + 6.80371i) q^{61} -1.96972i q^{63} +1.21915i q^{65} +(-5.45136 - 10.1988i) q^{67} +(-12.9024 + 10.5887i) q^{69} +(-1.79285 - 2.68319i) q^{71} +(2.04993 + 1.36972i) q^{73} +(3.19392 + 10.5289i) q^{75} +(-1.47825 + 1.80125i) q^{77} +(-4.58780 + 11.0759i) q^{79} +(4.18196 + 10.0961i) q^{81} +(7.11006 - 0.700280i) q^{83} +(0.584028 + 0.312169i) q^{85} +(1.67322 + 8.41187i) q^{87} +(-13.6682 - 2.71877i) q^{89} +(-3.44939 - 0.339735i) q^{91} +(21.8365 + 6.62402i) q^{93} +(-0.381702 + 0.381702i) q^{95} +(-10.5511 - 10.5511i) q^{97} +(-1.46784 + 4.83883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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