LMFDB - Embedded newform 572.2.bc.a.197.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(197,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.7
Character	$\chi$	$=$	572.197
Dual form			572.2.bc.a.241.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.308749 - 0.534769i) q^{3} +(-1.59856 + 1.59856i) q^{5} +(-0.412876 - 1.54087i) q^{7} +(1.30935 - 2.26786i) q^{9} +O(q^{10})$	\(q+(-0.308749 - 0.534769i) q^{3} +(-1.59856 + 1.59856i) q^{5} +(-0.412876 - 1.54087i) q^{7} +(1.30935 - 2.26786i) q^{9} +(0.0702351 + 3.31588i) q^{11} +(2.31396 + 2.76506i) q^{13} +(1.34842 + 0.361307i) q^{15} +(3.96153 - 6.86158i) q^{17} +(2.77762 - 0.744262i) q^{19} +(-0.696536 + 0.696536i) q^{21} +(4.54615 - 2.62472i) q^{23} -0.110810i q^{25} -3.46953 q^{27} +(8.12214 - 4.68932i) q^{29} +(-2.55707 + 2.55707i) q^{31} +(1.75154 - 1.06133i) q^{33} +(3.12319 + 1.80318i) q^{35} +(-1.30446 + 4.86830i) q^{37} +(0.764236 - 2.09114i) q^{39} +(1.58788 - 5.92607i) q^{41} +(-2.44212 + 4.22987i) q^{43} +(1.53224 + 5.71839i) q^{45} +(3.60099 + 3.60099i) q^{47} +(3.85835 - 2.22762i) q^{49} -4.89247 q^{51} -0.552512 q^{53} +(-5.41292 - 5.18837i) q^{55} +(-1.25560 - 1.25560i) q^{57} +(9.91459 - 2.65661i) q^{59} +(-0.768571 - 0.443735i) q^{61} +(-4.03508 - 1.08120i) q^{63} +(-8.11915 - 0.721112i) q^{65} +(-13.4069 - 3.59236i) q^{67} +(-2.80724 - 1.62076i) q^{69} +(-1.19653 - 4.46550i) q^{71} +(3.46658 - 3.46658i) q^{73} +(-0.0592576 + 0.0342124i) q^{75} +(5.08036 - 1.47727i) q^{77} +8.67614i q^{79} +(-2.85683 - 4.94818i) q^{81} +(-9.70994 - 9.70994i) q^{83} +(4.63590 + 17.3014i) q^{85} +(-5.01540 - 2.89564i) q^{87} +(-1.78516 + 6.66231i) q^{89} +(3.30524 - 4.70715i) q^{91} +(2.15694 + 0.577949i) q^{93} +(-3.25046 + 5.62996i) q^{95} +(2.86040 + 10.6752i) q^{97} +(7.61191 + 4.18236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^9	$ 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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
$3$	−0.308749	−	0.534769i	−0.178256	−	0.308749i	0.763027	−	0.646366i	$-0.223712\pi$
$3$	−0.308749	−	0.534769i	−0.178256	−	0.308749i	−0.941283	+	0.337618i	$0.890379\pi$
$4$		0			0
$5$	−1.59856	+	1.59856i	−0.714899	+	0.714899i	−0.967556	−	0.252657i	$-0.918696\pi$
$5$	−1.59856	+	1.59856i	−0.714899	+	0.714899i	0.252657	+	0.967556i	$0.418696\pi$
$6$		0			0
$7$	−0.412876	−	1.54087i	−0.156052	−	0.582396i	−0.999013	−	0.0444202i	$-0.985856\pi$
$7$	−0.412876	−	1.54087i	−0.156052	−	0.582396i	0.842960	−	0.537976i	$-0.180811\pi$
$8$		0			0
$9$	1.30935	−	2.26786i	0.436449	−	0.755953i
$10$		0			0
$11$	0.0702351	+	3.31588i	0.0211767	+	0.999776i
$11$	0.0702351	+	3.31588i	0.0211767	+	0.999776i
$12$		0			0
$13$	2.31396	+	2.76506i	0.641778	+	0.766891i
$13$	2.31396	+	2.76506i	0.641778	+	0.766891i
$14$		0			0
$15$	1.34842	+	0.361307i	0.348159	+	0.0932890i
$16$		0			0
$17$	3.96153	−	6.86158i	0.960813	−	1.66418i	0.240347	−	0.970687i	$-0.422739\pi$
$17$	3.96153	−	6.86158i	0.960813	−	1.66418i	0.720466	−	0.693490i	$-0.243928\pi$
$18$		0			0
$19$	2.77762	−	0.744262i	0.637230	−	0.170745i	0.0742818	−	0.997237i	$-0.476334\pi$
$19$	2.77762	−	0.744262i	0.637230	−	0.170745i	0.562949	+	0.826492i	$0.309667\pi$
$20$		0			0
$21$	−0.696536	+	0.696536i	−0.151997	+	0.151997i
$22$		0			0
$23$	4.54615	−	2.62472i	0.947938	−	0.547292i	0.0554985	−	0.998459i	$-0.482325\pi$
$23$	4.54615	−	2.62472i	0.947938	−	0.547292i	0.892440	+	0.451166i	$0.148992\pi$
$24$		0			0
$25$		−	0.110810i		−	0.0221620i
$26$		0			0
$27$	−3.46953			−0.667712
$28$		0			0
$29$	8.12214	−	4.68932i	1.50824	−	0.870784i	0.508289	−	0.861187i	$-0.330278\pi$
$29$	8.12214	−	4.68932i	1.50824	−	0.870784i	0.999954	−	0.00959769i	$-0.00305509\pi$
$30$		0			0
$31$	−2.55707	+	2.55707i	−0.459264	+	0.459264i	−0.898414	−	0.439150i	$-0.855280\pi$
$31$	−2.55707	+	2.55707i	−0.459264	+	0.459264i	0.439150	+	0.898414i	$0.355280\pi$
$32$		0			0
$33$	1.75154	−	1.06133i	0.304905	−	0.184754i
$34$		0			0
$35$	3.12319	+	1.80318i	0.527916	+	0.304792i
$36$		0			0
$37$	−1.30446	+	4.86830i	−0.214451	+	0.800343i	0.771908	+	0.635735i	$0.219303\pi$
$37$	−1.30446	+	4.86830i	−0.214451	+	0.800343i	−0.986359	+	0.164609i	$0.947364\pi$
$38$		0			0
$39$	0.764236	−	2.09114i	0.122376	−	0.334851i
$40$		0			0
$41$	1.58788	−	5.92607i	0.247986	−	0.925496i	−0.723873	−	0.689933i	$-0.757640\pi$
$41$	1.58788	−	5.92607i	0.247986	−	0.925496i	0.971859	−	0.235563i	$-0.0756934\pi$
$42$		0			0
$43$	−2.44212	+	4.22987i	−0.372419	+	0.645049i	−0.989937	−	0.141508i	$-0.954805\pi$
$43$	−2.44212	+	4.22987i	−0.372419	+	0.645049i	0.617518	+	0.786557i	$0.288138\pi$
$44$		0			0
$45$	1.53224	+	5.71839i	0.228413	+	0.852447i
$46$		0			0
$47$	3.60099	+	3.60099i	0.525258	+	0.525258i	0.919155	−	0.393896i	$-0.128873\pi$
$47$	3.60099	+	3.60099i	0.525258	+	0.525258i	−0.393896	+	0.919155i	$0.628873\pi$
$48$		0			0
$49$	3.85835	−	2.22762i	0.551193	−	0.318231i
$50$		0			0
$51$	−4.89247			−0.685083
$52$		0			0
$53$	−0.552512			−0.0758934			−0.0379467	−	0.999280i	$-0.512082\pi$
$53$	−0.552512			−0.0758934			−0.0379467	+	0.999280i	$0.512082\pi$
$54$		0			0
$55$	−5.41292	−	5.18837i	−0.729878	−	0.699600i
$56$		0			0
$57$	−1.25560	−	1.25560i	−0.166308	−	0.166308i
$58$		0			0
$59$	9.91459	−	2.65661i	1.29077	−	0.345861i	0.452817	−	0.891603i	$-0.350419\pi$
$59$	9.91459	−	2.65661i	1.29077	−	0.345861i	0.837953	+	0.545743i	$0.183752\pi$
$60$		0			0
$61$	−0.768571	−	0.443735i	−0.0984054	−	0.0568144i	0.449990	−	0.893034i	$-0.351428\pi$
$61$	−0.768571	−	0.443735i	−0.0984054	−	0.0568144i	−0.548395	+	0.836219i	$0.684761\pi$
$62$		0			0
$63$	−4.03508	−	1.08120i	−0.508373	−	0.136218i
$64$		0			0
$65$	−8.11915	−	0.721112i	−1.00706	−	0.0894430i
$66$		0			0
$67$	−13.4069	−	3.59236i	−1.63791	−	0.438877i	−0.681718	−	0.731615i	$-0.738767\pi$
$67$	−13.4069	−	3.59236i	−1.63791	−	0.438877i	−0.956193	+	0.292738i	$0.905434\pi$
$68$		0			0
$69$	−2.80724	−	1.62076i	−0.337952	−	0.195117i
$70$		0			0
$71$	−1.19653	−	4.46550i	−0.142002	−	0.529958i	−0.999871	−	0.0160891i	$-0.994878\pi$
$71$	−1.19653	−	4.46550i	−0.142002	−	0.529958i	0.857869	−	0.513869i	$-0.171788\pi$
$72$		0			0
$73$	3.46658	−	3.46658i	0.405733	−	0.405733i	−0.474515	−	0.880248i	$-0.657376\pi$
$73$	3.46658	−	3.46658i	0.405733	−	0.405733i	0.880248	+	0.474515i	$0.157376\pi$
$74$		0			0
$75$	−0.0592576	+	0.0342124i	−0.00684248	+	0.00395051i
$76$		0			0
$77$	5.08036	−	1.47727i	0.578960	−	0.168351i
$78$		0			0
$79$			8.67614i			0.976142i	0.872804	+	0.488071i	$0.162299\pi$
$79$			8.67614i			0.976142i	−0.872804	+	0.488071i	$0.837701\pi$
$80$		0			0
$81$	−2.85683	−	4.94818i	−0.317426	−	0.549798i
$82$		0			0
$83$	−9.70994	−	9.70994i	−1.06580	−	1.06580i	−0.997677	−	0.0681280i	$-0.978297\pi$
$83$	−9.70994	−	9.70994i	−1.06580	−	1.06580i	−0.0681280	−	0.997677i	$-0.521703\pi$
$84$		0			0
$85$	4.63590	+	17.3014i	0.502834	+	1.87660i
$86$		0			0
$87$	−5.01540	−	2.89564i	−0.537707	−	0.310445i
$88$		0			0
$89$	−1.78516	+	6.66231i	−0.189227	+	0.706203i	0.804460	+	0.594007i	$0.202455\pi$
$89$	−1.78516	+	6.66231i	−0.189227	+	0.706203i	−0.993686	+	0.112196i	$0.964212\pi$
$90$		0			0
$91$	3.30524	−	4.70715i	0.346483	−	0.493444i
$92$		0			0
$93$	2.15694	+	0.577949i	0.223664	+	0.0599305i
$94$		0			0
$95$	−3.25046	+	5.62996i	−0.333490	+	0.577621i
$96$		0			0
$97$	2.86040	+	10.6752i	0.290430	+	1.08390i	0.944780	+	0.327706i	$0.106276\pi$
$97$	2.86040	+	10.6752i	0.290430	+	1.08390i	−0.654350	+	0.756192i	$0.727058\pi$
$98$		0			0
$99$	7.61191	+	4.18236i	0.765026	+	0.420343i
$100$		0			0
$101$	9.36279	+	16.2168i	0.931632	+	1.61363i	0.780532	+	0.625115i	$0.214948\pi$
$101$	9.36279	+	16.2168i	0.931632	+	1.61363i	0.151100	+	0.988519i	$0.451719\pi$
$102$		0			0
$103$		−	4.63938i		−	0.457132i	−0.973528	−	0.228566i	$-0.926596\pi$
$103$		−	4.63938i		−	0.457132i	0.973528	−	0.228566i	$-0.0734037\pi$
$104$		0			0
$105$		−	2.22691i		−	0.217325i
$106$		0			0
$107$	−15.6248	+	9.02098i	−1.51051	+	0.872092i	−0.510582	+	0.859829i	$0.670570\pi$
$107$	−15.6248	+	9.02098i	−1.51051	+	0.872092i	−0.999925	+	0.0122625i	$0.996097\pi$
$108$		0			0
$109$	5.57579	+	5.57579i	0.534064	+	0.534064i	0.921779	−	0.387715i	$-0.126736\pi$
$109$	5.57579	+	5.57579i	0.534064	+	0.534064i	−0.387715	+	0.921779i	$0.626736\pi$
$110$		0			0
$111$	3.00616	−	0.805499i	0.285332	−	0.0764546i
$112$		0			0
$113$	−2.06089	+	3.56957i	−0.193873	+	0.335797i	−0.946530	−	0.322615i	$-0.895438\pi$
$113$	−2.06089	+	3.56957i	−0.193873	+	0.335797i	0.752658	+	0.658412i	$0.228771\pi$
$114$		0			0
$115$	−3.07153	+	11.4631i	−0.286421	+	1.06894i
$116$		0			0
$117$	9.30055	−	1.62731i	0.859837	−	0.150445i
$118$		0			0
$119$	−12.2085	−	3.27124i	−1.11915	−	0.299874i
$120$		0			0
$121$	−10.9901	+	0.465782i	−0.999103	+	0.0423439i
$122$		0			0
$123$	−3.65933	+	0.980515i	−0.329951	+	0.0884100i
$124$		0			0
$125$	−7.81568	−	7.81568i	−0.699056	−	0.699056i
$126$		0			0
$127$	−4.10559	−	7.11110i	−0.364313	−	0.631008i	0.624353	−	0.781142i	$-0.285363\pi$
$127$	−4.10559	−	7.11110i	−0.364313	−	0.631008i	−0.988666	+	0.150134i	$0.952029\pi$
$128$		0			0
$129$	3.01600			0.265544
$130$		0			0
$131$		−	9.78278i		−	0.854725i	−0.904080	−	0.427363i	$-0.859443\pi$
$131$		−	9.78278i		−	0.854725i	0.904080	−	0.427363i	$-0.140557\pi$
$132$		0			0
$133$	−2.29363	−	3.97268i	−0.198883	−	0.344475i
$134$		0			0
$135$	5.54627	−	5.54627i	0.477347	−	0.477347i
$136$		0			0
$137$	11.2039	−	3.00207i	0.957211	−	0.256484i	0.253791	−	0.967259i	$-0.418322\pi$
$137$	11.2039	−	3.00207i	0.957211	−	0.256484i	0.703419	+	0.710775i	$0.251656\pi$
$138$		0			0
$139$	−7.82696	−	4.51890i	−0.663874	−	0.383288i	0.129877	−	0.991530i	$-0.458542\pi$
$139$	−7.82696	−	4.51890i	−0.663874	−	0.383288i	−0.793752	+	0.608242i	$0.791875\pi$
$140$		0			0
$141$	0.813895	−	3.03750i	0.0685423	−	0.255803i
$142$		0			0
$143$	−9.00610	+	7.86703i	−0.753128	+	0.657874i
$144$		0			0
$145$	−5.48758	+	20.4799i	−0.455719	+	1.70076i
$146$		0			0
$147$	−2.38252	−	1.37555i	−0.196507	−	0.113453i
$148$		0			0
$149$	−10.0008	+	2.67971i	−0.819300	+	0.219531i	−0.644040	−	0.764992i	$-0.722743\pi$
$149$	−10.0008	+	2.67971i	−0.819300	+	0.219531i	−0.175259	+	0.984522i	$0.556076\pi$
$150$		0			0
$151$	−13.6435	+	13.6435i	−1.11030	+	1.11030i	−0.117186	+	0.993110i	$0.537387\pi$
$151$	−13.6435	+	13.6435i	−1.11030	+	1.11030i	−0.993110	+	0.117186i	$0.962613\pi$
$152$		0			0
$153$	−10.3741	−	17.9684i	−0.838693	−	1.45266i
$154$		0			0
$155$		−	8.17529i		−	0.656655i
$156$		0			0
$157$	2.05004			0.163611			0.0818055	−	0.996648i	$-0.473931\pi$
$157$	2.05004			0.163611			0.0818055	+	0.996648i	$0.473931\pi$
$158$		0			0
$159$	0.170587	+	0.295466i	0.0135285	+	0.0234320i
$160$		0			0
$161$	−5.92136	−	5.92136i	−0.466669	−	0.466669i
$162$		0			0
$163$	20.5349	−	5.50230i	1.60842	−	0.430974i	0.660846	−	0.750522i	$-0.270198\pi$
$163$	20.5349	−	5.50230i	1.60842	−	0.430974i	0.947570	+	0.319548i	$0.103531\pi$
$164$		0			0
$165$	−1.10334	+	4.49656i	−0.0858953	+	0.350057i
$166$		0			0
$167$	1.46311	+	0.392040i	0.113219	+	0.0303370i	0.314984	−	0.949097i	$-0.398001\pi$
$167$	1.46311	+	0.392040i	0.113219	+	0.0303370i	−0.201765	+	0.979434i	$0.564668\pi$
$168$		0			0
$169$	−2.29115	+	12.7965i	−0.176242	+	0.984347i
$170$		0			0
$171$	1.94900	−	7.27375i	0.149043	−	0.556238i
$172$		0			0
$173$	6.36319	−	11.0214i	0.483784	−	0.837939i	−0.516043	−	0.856563i	$-0.672595\pi$
$173$	6.36319	−	11.0214i	0.483784	−	0.837939i	0.999827	+	0.0186245i	$0.00592869\pi$
$174$		0			0
$175$	−0.170744	+	0.0457507i	−0.0129070	+	0.00345843i
$176$		0			0
$177$	−4.48179	−	4.48179i	−0.336872	−	0.336872i
$178$		0			0
$179$	−10.9128	+	6.30050i	−0.815660	+	0.470922i	−0.848918	−	0.528525i	$-0.822745\pi$
$179$	−10.9128	+	6.30050i	−0.815660	+	0.470922i	0.0332573	+	0.999447i	$0.489412\pi$
$180$		0			0
$181$		−	3.58739i		−	0.266649i	−0.991072	−	0.133324i	$-0.957435\pi$
$181$		−	3.58739i		−	0.266649i	0.991072	−	0.133324i	$-0.0425652\pi$
$182$		0			0
$183$			0.548010i			0.0405101i
$184$		0			0
$185$	−5.69703	−	9.86754i	−0.418854	−	0.725476i
$186$		0			0
$187$	23.0304	+	12.6541i	1.68415	+	0.925356i
$188$		0			0
$189$	1.43249	+	5.34611i	0.104198	+	0.388872i
$190$		0			0
$191$	−11.0469	+	19.1338i	−0.799328	+	1.38448i	0.120727	+	0.992686i	$0.461478\pi$
$191$	−11.0469	+	19.1338i	−0.799328	+	1.38448i	−0.920054	+	0.391790i	$0.871856\pi$
$192$		0			0
$193$	−15.8550	−	4.24834i	−1.14127	−	0.305802i	−0.361808	−	0.932253i	$-0.617840\pi$
$193$	−15.8550	−	4.24834i	−1.14127	−	0.305802i	−0.779461	+	0.626450i	$0.784507\pi$
$194$		0			0
$195$	2.12115	+	4.56451i	0.151899	+	0.326871i
$196$		0			0
$197$	6.62441	−	24.7227i	0.471970	−	1.76142i	−0.160709	−	0.987002i	$-0.551378\pi$
$197$	6.62441	−	24.7227i	0.471970	−	1.76142i	0.632679	−	0.774414i	$-0.281955\pi$
$198$		0			0
$199$	7.31623	+	4.22403i	0.518634	+	0.299433i	0.736376	−	0.676573i	$-0.236536\pi$
$199$	7.31623	+	4.22403i	0.518634	+	0.299433i	−0.217742	+	0.976006i	$0.569869\pi$
$200$		0			0
$201$	2.21827	+	8.27871i	0.156465	+	0.583935i
$202$		0			0
$203$	−10.5791	−	10.5791i	−0.742506	−	0.742506i
$204$		0			0
$205$	6.93486	+	12.0115i	0.484351	+	0.838921i
$206$		0			0
$207$		−	13.7467i		−	0.955462i
$208$		0			0
$209$	2.66297	+	9.15799i	0.184201	+	0.633472i
$210$		0			0
$211$	22.0984	−	12.7585i	1.52132	−	0.878332i	0.521632	−	0.853170i	$-0.325323\pi$
$211$	22.0984	−	12.7585i	1.52132	−	0.878332i	0.999683	−	0.0251617i	$-0.00801007\pi$
$212$		0			0
$213$	−2.01858	+	2.01858i	−0.138311	+	0.138311i
$214$		0			0
$215$	−2.85784	−	10.6656i	−0.194903	−	0.727388i
$216$		0			0
$217$	4.99588	+	2.88437i	0.339143	+	0.195804i
$218$		0			0
$219$	−2.92412	−	0.783516i	−0.197594	−	0.0529451i
$220$		0			0
$221$	28.1395	−	4.92355i	1.89287	−	0.331193i
$222$		0			0
$223$	−10.3157	−	2.76409i	−0.690791	−	0.185097i	−0.103689	−	0.994610i	$-0.533065\pi$
$223$	−10.3157	−	2.76409i	−0.690791	−	0.185097i	−0.587102	+	0.809513i	$0.699731\pi$
$224$		0			0
$225$	−0.251301	−	0.145089i	−0.0167534	−	0.00967258i
$226$		0			0
$227$	−9.79499	+	2.62456i	−0.650116	+	0.174198i	−0.568782	−	0.822489i	$-0.692585\pi$
$227$	−9.79499	+	2.62456i	−0.650116	+	0.174198i	−0.0813349	+	0.996687i	$0.525918\pi$
$228$		0			0
$229$	−0.435123	−	0.435123i	−0.0287538	−	0.0287538i	0.692584	−	0.721337i	$-0.256472\pi$
$229$	−0.435123	−	0.435123i	−0.0287538	−	0.0287538i	−0.721337	+	0.692584i	$0.756472\pi$
$230$		0			0
$231$	−2.35855	−	2.26071i	−0.155181	−	0.148744i
$232$		0			0
$233$	2.67193			0.175044			0.0875219	−	0.996163i	$-0.472105\pi$
$233$	2.67193			0.175044			0.0875219	+	0.996163i	$0.472105\pi$
$234$		0			0
$235$	−11.5128			−0.751014
$236$		0			0
$237$	4.63973	−	2.67875i	0.301383	−	0.174003i
$238$		0			0
$239$	14.6542	+	14.6542i	0.947903	+	0.947903i	0.998709	−	0.0508059i	$-0.0161790\pi$
$239$	14.6542	+	14.6542i	0.947903	+	0.947903i	−0.0508059	+	0.998709i	$0.516179\pi$
$240$		0			0
$241$	−3.76225	−	14.0409i	−0.242348	−	0.904455i	−0.974698	−	0.223527i	$-0.928243\pi$
$241$	−3.76225	−	14.0409i	−0.242348	−	0.904455i	0.732350	−	0.680929i	$-0.238424\pi$
$242$		0			0
$243$	−6.96838	+	12.0696i	−0.447022	+	0.774265i
$244$		0			0
$245$	−2.60683	+	9.72881i	−0.166544	+	0.621551i
$246$		0			0
$247$	8.48525	+	5.95811i	0.539903	+	0.379105i
$248$		0			0
$249$	−2.19464	+	8.19050i	−0.139080	+	0.519052i
$250$		0			0
$251$	19.7581	+	11.4073i	1.24712	+	0.720025i	0.970534	−	0.240965i	$-0.0774638\pi$
$251$	19.7581	+	11.4073i	1.24712	+	0.720025i	0.276585	+	0.960989i	$0.410797\pi$
$252$		0			0
$253$	9.02257	+	14.8902i	0.567244	+	0.936136i
$254$		0			0
$255$	7.82093	−	7.82093i	0.489766	−	0.489766i
$256$		0			0
$257$	20.6779	−	11.9384i	1.28985	−	0.744695i	0.311223	−	0.950337i	$-0.399261\pi$
$257$	20.6779	−	11.9384i	1.28985	−	0.744695i	0.978627	+	0.205642i	$0.0659281\pi$
$258$		0			0
$259$	8.04002			0.499582
$260$		0			0
$261$		−	24.5598i		−	1.52021i
$262$		0			0
$263$	10.8094	−	6.24080i	0.666536	−	0.384824i	−0.128227	−	0.991745i	$-0.540929\pi$
$263$	10.8094	−	6.24080i	0.666536	−	0.384824i	0.794763	+	0.606920i	$0.207595\pi$
$264$		0			0
$265$	0.883225	−	0.883225i	0.0542561	−	0.0542561i
$266$		0			0
$267$	4.11396	−	1.10233i	0.251770	−	0.0674616i
$268$		0			0
$269$	−8.42796	+	14.5977i	−0.513862	+	0.890035i	0.486009	+	0.873954i	$0.338452\pi$
$269$	−8.42796	+	14.5977i	−0.513862	+	0.890035i	−0.999871	+	0.0160812i	$0.994881\pi$
$270$		0			0
$271$	4.75147	+	1.27315i	0.288631	+	0.0773386i	0.400230	−	0.916415i	$-0.368930\pi$
$271$	4.75147	+	1.27315i	0.288631	+	0.0773386i	−0.111598	+	0.993753i	$0.535597\pi$
$272$		0			0
$273$	−3.53773	−	0.314208i	−0.214113	−	0.0190167i
$274$		0			0
$275$	0.367432	−	0.00778274i	0.0221570	−	0.000469317i
$276$		0			0
$277$	−6.38704	+	11.0627i	−0.383760	+	0.664692i	−0.991596	−	0.129370i	$-0.958704\pi$
$277$	−6.38704	+	11.0627i	−0.383760	+	0.664692i	0.607836	+	0.794062i	$0.292038\pi$
$278$		0			0
$279$	2.45098	+	9.14718i	0.146736	+	0.547627i
$280$		0			0
$281$	6.41048	−	6.41048i	0.382417	−	0.382417i	−0.489555	−	0.871972i	$-0.662841\pi$
$281$	6.41048	−	6.41048i	0.382417	−	0.382417i	0.871972	+	0.489555i	$0.162841\pi$
$282$		0			0
$283$	2.21151	+	3.83044i	0.131461	+	0.227696i	0.924240	−	0.381813i	$-0.124700\pi$
$283$	2.21151	+	3.83044i	0.131461	+	0.227696i	−0.792779	+	0.609509i	$0.791367\pi$
$284$		0			0
$285$	4.01430			0.237786
$286$		0			0
$287$	−9.78692			−0.577704
$288$		0			0
$289$	−22.8875	−	39.6423i	−1.34632	−	2.33190i
$290$		0			0
$291$	4.82559	−	4.82559i	0.282881	−	0.282881i
$292$		0			0
$293$	−2.08482	−	7.78066i	−0.121797	−	0.454551i	0.877909	−	0.478828i	$-0.158938\pi$
$293$	−2.08482	−	7.78066i	−0.121797	−	0.454551i	−0.999705	+	0.0242772i	$0.992272\pi$
$294$		0			0
$295$	−11.6023	+	20.0959i	−0.675515	+	1.17003i
$296$		0			0
$297$	−0.243683	−	11.5046i	−0.0141399	−	0.667562i
$298$		0			0
$299$	17.7772	+	6.49689i	1.02808	+	0.375725i
$300$		0			0
$301$	7.52599	+	2.01658i	0.433791	+	0.116234i
$302$		0			0
$303$	5.78150	−	10.0138i	0.332138	−	0.575280i
$304$		0			0
$305$	1.93795	−	0.519271i	0.110967	−	0.0297334i
$306$		0			0
$307$	9.28199	−	9.28199i	0.529751	−	0.529751i	−0.390747	−	0.920498i	$-0.627783\pi$
$307$	9.28199	−	9.28199i	0.529751	−	0.529751i	0.920498	+	0.390747i	$0.127783\pi$
$308$		0			0
$309$	−2.48100	+	1.43240i	−0.141139	+	0.0814866i
$310$		0			0
$311$			2.20389i			0.124971i	0.998046	+	0.0624856i	$0.0199027\pi$
$311$			2.20389i			0.124971i	−0.998046	+	0.0624856i	$0.980097\pi$
$312$		0			0
$313$	−12.4064			−0.701253			−0.350626	−	0.936515i	$-0.614031\pi$
$313$	−12.4064			−0.701253			−0.350626	+	0.936515i	$0.614031\pi$
$314$		0			0
$315$	8.17870	−	4.72197i	0.460817	−	0.266053i
$316$		0			0
$317$	−17.8203	+	17.8203i	−1.00089	+	1.00089i	−0.000886049		1.00000i	$0.500282\pi$
$317$	−17.8203	+	17.8203i	−1.00089	+	1.00089i	−1.00000		0.000886049i	$0.999718\pi$
$318$		0			0
$319$	16.1197	+	26.6027i	0.902529	+	1.48946i
$320$		0			0
$321$	9.64828	+	5.57044i	0.538514	+	0.310911i
$322$		0			0
$323$	5.89684	−	22.0073i	0.328109	−	1.22452i
$324$		0			0
$325$	0.306396	−	0.256410i	0.0169958	−	0.0142231i
$326$		0			0
$327$	1.26024	−	4.70327i	0.0696914	−	0.260092i
$328$		0			0
$329$	4.06191	−	7.03543i	0.223940	−	0.387876i
$330$		0			0
$331$	2.06735	+	7.71544i	0.113632	+	0.424079i	0.999181	−	0.0404666i	$-0.0128844\pi$
$331$	2.06735	+	7.71544i	0.113632	+	0.424079i	−0.885549	+	0.464545i	$0.846218\pi$
$332$		0			0
$333$	9.33262	+	9.33262i	0.511425	+	0.511425i
$334$		0			0
$335$	27.1744	−	15.6891i	1.48469	−	0.857188i
$336$		0			0
$337$	−11.1128			−0.605355			−0.302677	−	0.953093i	$-0.597880\pi$
$337$	−11.1128			−0.605355			−0.302677	+	0.953093i	$0.597880\pi$
$338$		0			0
$339$	2.54519			0.138236
$340$		0			0
$341$	−8.65855	−	8.29935i	−0.468887	−	0.449435i
$342$		0			0
$343$	−12.9215	−	12.9215i	−0.697695	−	0.697695i
$344$		0			0
$345$	7.07843	−	1.89666i	0.381090	−	0.102113i
$346$		0			0
$347$	−20.9771	−	12.1111i	−1.12611	−	0.650159i	−0.183155	−	0.983084i	$-0.558631\pi$
$347$	−20.9771	−	12.1111i	−1.12611	−	0.650159i	−0.942953	+	0.332925i	$0.891964\pi$
$348$		0			0
$349$	29.2938	+	7.84925i	1.56806	+	0.420161i	0.935205	−	0.354108i	$-0.115215\pi$
$349$	29.2938	+	7.84925i	1.56806	+	0.420161i	0.632857	+	0.774269i	$0.281882\pi$
$350$		0			0
$351$	−8.02837	−	9.59347i	−0.428523	−	0.512062i
$352$		0			0
$353$	0.747091	+	0.200182i	0.0397636	+	0.0106546i	0.278646	−	0.960394i	$-0.410114\pi$
$353$	0.747091	+	0.200182i	0.0397636	+	0.0106546i	−0.238882	+	0.971049i	$0.576781\pi$
$354$		0			0
$355$	9.05112	+	5.22567i	0.480383	+	0.277350i
$356$		0			0
$357$	2.01999	+	7.53869i	0.106909	+	0.398990i
$358$		0			0
$359$	0.598765	−	0.598765i	0.0316016	−	0.0316016i	−0.691129	−	0.722731i	$-0.742887\pi$
$359$	0.598765	−	0.598765i	0.0316016	−	0.0316016i	0.722731	+	0.691129i	$0.242887\pi$
$360$		0			0
$361$	−9.29322	+	5.36544i	−0.489117	+	0.282392i
$362$		0			0
$363$	3.64228	+	5.73337i	0.191170	+	0.300924i
$364$		0			0
$365$			11.0831i			0.580116i
$366$		0			0
$367$	−6.07967	−	10.5303i	−0.317356	−	0.549677i	0.662579	−	0.748992i	$-0.269462\pi$
$367$	−6.07967	−	10.5303i	−0.317356	−	0.549677i	−0.979936	+	0.199315i	$0.936128\pi$
$368$		0			0
$369$	−11.3604	−	11.3604i	−0.591398	−	0.591398i
$370$		0			0
$371$	0.228119	+	0.851351i	0.0118433	+	0.0442000i
$372$		0			0
$373$	−11.2555	−	6.49839i	−0.582790	−	0.336474i	0.179452	−	0.983767i	$-0.442568\pi$
$373$	−11.2555	−	6.49839i	−0.582790	−	0.336474i	−0.762241	+	0.647293i	$0.775901\pi$
$374$		0			0
$375$	−1.76650	+	6.59266i	−0.0912216	+	0.340444i
$376$		0			0
$377$	31.7606	+	11.6073i	1.63575	+	0.597807i
$378$		0			0
$379$	−16.4201	−	4.39976i	−0.843444	−	0.226000i	−0.188874	−	0.982001i	$-0.560484\pi$
$379$	−16.4201	−	4.39976i	−0.843444	−	0.226000i	−0.654570	+	0.756001i	$0.727150\pi$
$380$		0			0
$381$	−2.53519	+	4.39108i	−0.129882	+	0.224962i
$382$		0			0
$383$	−2.48712	−	9.28205i	−0.127086	−	0.474291i	0.872820	−	0.488043i	$-0.162289\pi$
$383$	−2.48712	−	9.28205i	−0.127086	−	0.474291i	−0.999905	+	0.0137522i	$0.995622\pi$
$384$		0			0
$385$	−5.75976	+	10.4828i	−0.293545	+	0.534252i
$386$		0			0
$387$	6.39517	+	11.0768i	0.325085	+	0.563063i
$388$		0			0
$389$		−	4.88750i		−	0.247806i	−0.992294	−	0.123903i	$-0.960459\pi$
$389$		−	4.88750i		−	0.247806i	0.992294	−	0.123903i	$-0.0395412\pi$
$390$		0			0
$391$		−	41.5917i		−	2.10338i
$392$		0			0
$393$	−5.23152	+	3.02042i	−0.263895	+	0.152360i
$394$		0			0
$395$	−13.8694	−	13.8694i	−0.697843	−	0.697843i
$396$		0			0
$397$	−25.8059	+	6.91468i	−1.29516	+	0.347038i	−0.839619	−	0.543176i	$-0.817222\pi$
$397$	−25.8059	+	6.91468i	−1.29516	+	0.347038i	−0.455544	+	0.890213i	$0.650555\pi$
$398$		0			0
$399$	−1.41631	+	2.45312i	−0.0709042	+	0.122810i
$400$		0			0
$401$	−4.55545	+	17.0012i	−0.227488	+	0.848998i	0.753904	+	0.656985i	$0.228168\pi$
$401$	−4.55545	+	17.0012i	−0.227488	+	0.848998i	−0.981392	+	0.192014i	$0.938498\pi$
$402$		0			0
$403$	−12.9874	−	1.15350i	−0.646951	−	0.0574597i
$404$		0			0
$405$	12.4768	+	3.34315i	0.619977	+	0.166122i
$406$		0			0
$407$	−16.2343	−	3.98350i	−0.804705	−	0.197455i
$408$		0			0
$409$	−16.4120	+	4.39759i	−0.811522	+	0.217447i	−0.640637	−	0.767844i	$-0.721329\pi$
$409$	−16.4120	+	4.39759i	−0.811522	+	0.217447i	−0.170886	+	0.985291i	$0.554663\pi$
$410$		0			0
$411$	−5.06459	−	5.06459i	−0.249818	−	0.249818i
$412$		0			0
$413$	−8.18699	−	14.1803i	−0.402856	−	0.697766i
$414$		0			0
$415$	31.0439			1.52389
$416$		0			0
$417$			5.58082i			0.273294i
$418$		0			0
$419$	−2.48358	−	4.30170i	−0.121331	−	0.210152i	0.798962	−	0.601382i	$-0.205383\pi$
$419$	−2.48358	−	4.30170i	−0.121331	−	0.210152i	−0.920293	+	0.391230i	$0.872050\pi$
$420$		0			0
$421$	5.49830	−	5.49830i	0.267971	−	0.267971i	−0.560311	−	0.828282i	$-0.689318\pi$
$421$	5.49830	−	5.49830i	0.267971	−	0.267971i	0.828282	+	0.560311i	$0.189318\pi$
$422$		0			0
$423$	12.8815	−	3.45158i	0.626319	−	0.167822i
$424$		0			0
$425$	−0.760330	−	0.438977i	−0.0368814	−	0.0212935i
$426$		0			0
$427$	−0.366415	+	1.36748i	−0.0177321	+	0.0661769i
$428$		0			0
$429$	6.98766	+	2.38724i	0.337368	+	0.115257i
$430$		0			0
$431$	−3.28575	+	12.2626i	−0.158269	+	0.590668i	0.840534	+	0.541758i	$0.182241\pi$
$431$	−3.28575	+	12.2626i	−0.158269	+	0.590668i	−0.998803	+	0.0489095i	$0.984425\pi$
$432$		0			0
$433$	23.6708	+	13.6663i	1.13755	+	0.656762i	0.945822	−	0.324687i	$-0.105259\pi$
$433$	23.6708	+	13.6663i	1.13755	+	0.656762i	0.191724	+	0.981449i	$0.438592\pi$
$434$		0			0
$435$	12.6463	−	3.38857i	0.606344	−	0.162469i
$436$		0			0
$437$	10.6740	−	10.6740i	0.510607	−	0.510607i
$438$		0			0
$439$	11.8235	+	20.4789i	0.564306	+	0.977406i	0.997114	+	0.0759201i	$0.0241894\pi$
$439$	11.8235	+	20.4789i	0.564306	+	0.977406i	−0.432808	+	0.901486i	$0.642477\pi$
$440$		0			0
$441$		−	11.6669i		−	0.555568i
$442$		0			0
$443$	−16.8217			−0.799224			−0.399612	−	0.916684i	$-0.630855\pi$
$443$	−16.8217			−0.799224			−0.399612	+	0.916684i	$0.630855\pi$
$444$		0			0
$445$	−7.79643	−	13.5038i	−0.369586	−	0.640142i
$446$		0			0
$447$	4.52077	+	4.52077i	0.213825	+	0.213825i
$448$		0			0
$449$	8.41406	−	2.25454i	0.397084	−	0.106398i	−0.0547506	−	0.998500i	$-0.517436\pi$
$449$	8.41406	−	2.25454i	0.397084	−	0.106398i	0.451835	+	0.892102i	$0.350770\pi$
$450$		0			0
$451$	19.7617	+	4.84902i	0.930540	+	0.228331i
$452$		0			0
$453$	11.5086	+	3.08371i	0.540720	+	0.144885i
$454$		0			0
$455$	2.24106	+	12.8083i	0.105062	+	0.600463i
$456$		0			0
$457$	−4.33359	+	16.1732i	−0.202717	+	0.756550i	0.787416	+	0.616421i	$0.211418\pi$
$457$	−4.33359	+	16.1732i	−0.202717	+	0.756550i	−0.990133	+	0.140128i	$0.955248\pi$
$458$		0			0
$459$	−13.7447	+	23.8065i	−0.641546	+	1.11119i
$460$		0			0
$461$	11.9931	−	3.21354i	0.558573	−	0.149669i	0.0315225	−	0.999503i	$-0.489964\pi$
$461$	11.9931	−	3.21354i	0.558573	−	0.149669i	0.527051	+	0.849834i	$0.323298\pi$
$462$		0			0
$463$	13.7029	+	13.7029i	0.636829	+	0.636829i	0.949772	−	0.312943i	$-0.101315\pi$
$463$	13.7029	+	13.7029i	0.636829	+	0.636829i	−0.312943	+	0.949772i	$0.601315\pi$
$464$		0			0
$465$	−4.37189	+	2.52411i	−0.202741	+	0.117053i
$466$		0			0
$467$			17.1937i			0.795632i	0.917465	+	0.397816i	$0.130232\pi$
$467$			17.1937i			0.795632i	−0.917465	+	0.397816i	$0.869768\pi$
$468$		0			0
$469$			22.1415i			1.02240i
$470$		0			0
$471$	−0.632947	−	1.09630i	−0.0291647	−	0.0505147i
$472$		0			0
$473$	−14.1973	−	7.80069i	−0.652791	−	0.358676i
$474$		0			0
$475$	−0.0824715	−	0.307788i	−0.00378405	−	0.0141223i
$476$		0			0
$477$	−0.723431	+	1.25302i	−0.0331236	+	0.0573718i
$478$		0			0
$479$	11.6911	+	3.13261i	0.534178	+	0.143133i	0.515817	−	0.856699i	$-0.327488\pi$
$479$	11.6911	+	3.13261i	0.534178	+	0.143133i	0.0183613	+	0.999831i	$0.494155\pi$
$480$		0			0
$481$	−16.4796	+	7.65816i	−0.751406	+	0.349182i
$482$		0			0
$483$	−1.33835	+	4.99477i	−0.0608968	+	0.227270i
$484$		0			0
$485$	−21.6374	−	12.4924i	−0.982506	−	0.567250i
$486$		0			0
$487$	7.37560	+	27.5261i	0.334220	+	1.24733i	0.904712	+	0.426023i	$0.140086\pi$
$487$	7.37560	+	27.5261i	0.334220	+	1.24733i	−0.570492	+	0.821303i	$0.693247\pi$
$488$		0			0
$489$	−9.28258	−	9.28258i	−0.419773	−	0.419773i
$490$		0			0
$491$	−2.81829	−	4.88141i	−0.127187	−	0.220295i	0.795398	−	0.606087i	$-0.207262\pi$
$491$	−2.81829	−	4.88141i	−0.127187	−	0.220295i	−0.922586	+	0.385792i	$0.873928\pi$
$492$		0			0
$493$		−	74.3076i		−	3.34664i
$494$		0			0
$495$	−18.8539	+	5.48235i	−0.847419	+	0.246413i
$496$		0			0
$497$	−6.38676	+	3.68740i	−0.286485	+	0.165402i
$498$		0			0
$499$	−11.1318	+	11.1318i	−0.498328	+	0.498328i	−0.910917	−	0.412589i	$-0.864624\pi$
$499$	−11.1318	+	11.1318i	−0.498328	+	0.498328i	0.412589	+	0.910917i	$0.364624\pi$
$500$		0			0
$501$	−0.242084	−	0.903469i	−0.0108155	−	0.0403640i
$502$		0			0
$503$	−21.1411	−	12.2058i	−0.942634	−	0.544230i	−0.0518492	−	0.998655i	$-0.516512\pi$
$503$	−21.1411	−	12.2058i	−0.942634	−	0.544230i	−0.890785	+	0.454425i	$0.849845\pi$
$504$		0			0
$505$	−40.8906	−	10.9566i	−1.81961	−	0.487563i
$506$		0			0
$507$	7.55056	−	2.72567i	0.335332	−	0.121051i
$508$		0			0
$509$	5.45419	+	1.46145i	0.241753	+	0.0647775i	0.377661	−	0.925944i	$-0.376728\pi$
$509$	5.45419	+	1.46145i	0.241753	+	0.0647775i	−0.135908	+	0.990721i	$0.543395\pi$
$510$		0			0
$511$	−6.77284	−	3.91030i	−0.299613	−	0.172981i
$512$		0			0
$513$	−9.63705	+	2.58224i	−0.425486	+	0.114009i
$514$		0			0
$515$	7.41635	+	7.41635i	0.326803	+	0.326803i
$516$		0			0
$517$	−11.6875	+	12.1934i	−0.514017	+	0.536264i
$518$		0			0
$519$	−7.85850			−0.344950
$520$		0			0
$521$	−27.4063			−1.20069			−0.600347	−	0.799740i	$-0.704971\pi$
$521$	−27.4063			−1.20069			−0.600347	+	0.799740i	$0.704971\pi$
$522$		0			0
$523$	−9.60712	+	5.54667i	−0.420090	+	0.242539i	−0.695116	−	0.718898i	$-0.744647\pi$
$523$	−9.60712	+	5.54667i	−0.420090	+	0.242539i	0.275026	+	0.961437i	$0.411314\pi$
$524$		0			0
$525$	0.0771831	+	0.0771831i	0.00336854	+	0.00336854i
$526$		0			0
$527$	7.41562	+	27.6755i	0.323030	+	1.20556i
$528$		0			0
$529$	2.27834	−	3.94619i	0.0990581	−	0.171574i
$530$		0			0
$531$	6.95685	−	25.9633i	0.301901	−	1.12671i
$532$		0			0
$533$	20.0603	−	9.32210i	0.868906	−	0.403785i
$534$		0			0
$535$	10.5566	−	39.3979i	0.456403	−	1.70332i
$536$		0			0
$537$	6.73862	+	3.89055i	0.290793	+	0.167889i
$538$		0			0
$539$	7.65751	+	12.6374i	0.329832	+	0.544330i
$540$		0			0
$541$	−28.1391	+	28.1391i	−1.20980	+	1.20980i	−0.238704	+	0.971092i	$0.576723\pi$
$541$	−28.1391	+	28.1391i	−1.20980	+	1.20980i	−0.971092	+	0.238704i	$0.923277\pi$
$542$		0			0
$543$	−1.91842	+	1.10760i	−0.0823274	+	0.0475318i
$544$		0			0
$545$	−17.8265			−0.763604
$546$		0			0
$547$			29.1930i			1.24820i	0.781343	+	0.624102i	$0.214535\pi$
$547$			29.1930i			1.24820i	−0.781343	+	0.624102i	$0.785465\pi$
$548$		0			0
$549$	−2.01265	+	1.16201i	−0.0858980	+	0.0495932i
$550$		0			0
$551$	19.0702	−	19.0702i	0.812416	−	0.812416i
$552$		0			0
$553$	13.3688	−	3.58217i	0.568501	−	0.152329i
$554$		0			0
$555$	−3.51790	+	6.09318i	−0.149327	+	0.258641i
$556$		0			0
$557$	−30.2311	−	8.10041i	−1.28093	−	0.343225i	−0.446724	−	0.894672i	$-0.647410\pi$
$557$	−30.2311	−	8.10041i	−1.28093	−	0.343225i	−0.834210	+	0.551446i	$0.814076\pi$
$558$		0			0
$559$	−17.3468	+	3.03516i	−0.733693	+	0.128373i
$560$		0			0
$561$	−0.343623	−	16.2229i	−0.0145078	−	0.684930i
$562$		0			0
$563$	1.09129	−	1.89018i	0.0459926	−	0.0796615i	−0.842113	−	0.539302i	$-0.818688\pi$
$563$	1.09129	−	1.89018i	0.0459926	−	0.0796615i	0.888105	+	0.459640i	$0.152022\pi$
$564$		0			0
$565$	−2.41172	−	9.00065i	−0.101462	−	0.378660i
$566$		0			0
$567$	−6.44500	+	6.44500i	−0.270665	+	0.270665i
$568$		0			0
$569$	−4.08896	−	7.08229i	−0.171418	−	0.296905i	0.767498	−	0.641052i	$-0.221502\pi$
$569$	−4.08896	−	7.08229i	−0.171418	−	0.296905i	−0.938916	+	0.344147i	$0.888168\pi$
$570$		0			0
$571$	−31.3537			−1.31211			−0.656056	−	0.754712i	$-0.727777\pi$
$571$	−31.3537			−1.31211			−0.656056	+	0.754712i	$0.727777\pi$
$572$		0			0
$573$	13.6429			0.569940
$574$		0			0
$575$	−0.290845	−	0.503758i	−0.0121291	−	0.0210082i
$576$		0			0
$577$	−3.05790	+	3.05790i	−0.127302	+	0.127302i	−0.767887	−	0.640585i	$-0.778692\pi$
$577$	−3.05790	+	3.05790i	−0.127302	+	0.127302i	0.640585	+	0.767887i	$0.278692\pi$
$578$		0			0
$579$	2.62334	+	9.79044i	0.109022	+	0.406877i
$580$		0			0
$581$	−10.9528	+	18.9708i	−0.454399	+	0.787041i
$582$		0			0
$583$	−0.0388057	−	1.83206i	−0.00160717	−	0.0758763i
$584$		0			0
$585$	−12.2662	+	17.4689i	−0.507144	+	0.722249i
$586$		0			0
$587$	−12.7313	−	3.41134i	−0.525476	−	0.140801i	−0.0136776	−	0.999906i	$-0.504354\pi$
$587$	−12.7313	−	3.41134i	−0.525476	−	0.140801i	−0.511798	+	0.859106i	$0.671021\pi$
$588$		0			0
$589$	−5.19945	+	9.00572i	−0.214240	+	0.371074i
$590$		0			0
$591$	−15.2662	+	4.09056i	−0.627966	+	0.168263i
$592$		0			0
$593$	−3.52027	+	3.52027i	−0.144560	+	0.144560i	−0.775683	−	0.631123i	$-0.782594\pi$
$593$	−3.52027	+	3.52027i	−0.144560	+	0.144560i	0.631123	+	0.775683i	$0.282594\pi$
$594$		0			0
$595$	24.7453	−	14.2867i	1.01446	−	0.585697i
$596$		0			0
$597$		−	5.21665i		−	0.213503i
$598$		0			0
$599$	−32.1694			−1.31440			−0.657202	−	0.753714i	$-0.728260\pi$
$599$	−32.1694			−1.31440			−0.657202	+	0.753714i	$0.728260\pi$
$600$		0			0
$601$	0.467979	−	0.270188i	0.0190893	−	0.0110212i	−0.490425	−	0.871483i	$-0.663158\pi$
$601$	0.467979	−	0.270188i	0.0190893	−	0.0110212i	0.509514	+	0.860462i	$0.329825\pi$
$602$		0			0
$603$	−25.7012	+	25.7012i	−1.04664	+	1.04664i
$604$		0			0
$605$	16.8238	−	18.3130i	0.683986	−	0.744530i
$606$		0			0
$607$	−22.5794	−	13.0362i	−0.916468	−	0.529123i	−0.0339612	−	0.999423i	$-0.510812\pi$
$607$	−22.5794	−	13.0362i	−0.916468	−	0.529123i	−0.882506	+	0.470300i	$0.844146\pi$
$608$		0			0
$609$	−2.39108	+	8.92364i	−0.0968915	+	0.361604i
$610$		0			0
$611$	−1.62441	+	18.2895i	−0.0657165	+	0.739915i
$612$		0			0
$613$	−8.12314	+	30.3160i	−0.328091	+	1.22445i	0.583078	+	0.812416i	$0.301848\pi$
$613$	−8.12314	+	30.3160i	−0.328091	+	1.22445i	−0.911168	+	0.412034i	$0.864818\pi$
$614$		0			0
$615$	4.28226	−	7.41709i	0.172677	−	0.299086i
$616$		0			0
$617$	−5.30975	−	19.8163i	−0.213763	−	0.797773i	−0.986598	−	0.163167i	$-0.947829\pi$
$617$	−5.30975	−	19.8163i	−0.213763	−	0.797773i	0.772836	−	0.634606i	$-0.218838\pi$
$618$		0			0
$619$	10.3400	+	10.3400i	0.415601	+	0.415601i	0.883684	−	0.468083i	$-0.155055\pi$
$619$	10.3400	+	10.3400i	0.415601	+	0.415601i	−0.468083	+	0.883684i	$0.655055\pi$
$620$		0			0
$621$	−15.7730	+	9.10656i	−0.632949	+	0.365434i
$622$		0			0
$623$	11.0028			0.440819
$624$		0			0
$625$	25.5418			1.02167
$626$		0			0
$627$	4.07522	−	4.25159i	0.162749	−	0.169792i
$628$		0			0
$629$	28.2366	+	28.2366i	1.12587	+	1.12587i
$630$		0			0
$631$	41.8613	−	11.2167i	1.66647	−	0.446530i	0.702317	−	0.711865i	$-0.252149\pi$
$631$	41.8613	−	11.2167i	1.66647	−	0.446530i	0.964156	+	0.265334i	$0.0854824\pi$
$632$		0			0
$633$	−13.6457	−	7.87835i	−0.542368	−	0.313136i
$634$		0			0
$635$	17.9306	+	4.80449i	0.711554	+	0.190660i
$636$		0			0
$637$	15.0876	+	5.51395i	0.597792	+	0.218471i
$638$		0			0
$639$	−11.6938	−	3.13334i	−0.462600	−	0.123953i
$640$		0			0
$641$	−39.9582	−	23.0699i	−1.57825	−	0.911206i	−0.995103	−	0.0988418i	$-0.968486\pi$
$641$	−39.9582	−	23.0699i	−1.57825	−	0.911206i	−0.583151	−	0.812364i	$-0.698180\pi$
$642$		0			0
$643$	0.673989	+	2.51536i	0.0265795	+	0.0991961i	0.977941	−	0.208880i	$-0.0669817\pi$
$643$	0.673989	+	2.51536i	0.0265795	+	0.0991961i	−0.951362	+	0.308076i	$0.900315\pi$
$644$		0			0
$645$	−4.82127	+	4.82127i	−0.189837	+	0.189837i
$646$		0			0
$647$	33.7464	−	19.4835i	1.32671	−	0.765975i	0.341919	−	0.939730i	$-0.388923\pi$
$647$	33.7464	−	19.4835i	1.32671	−	0.765975i	0.984789	+	0.173754i	$0.0555899\pi$
$648$		0			0
$649$	9.50534	+	32.6890i	0.373117	+	1.28316i
$650$		0			0
$651$		−	3.56219i		−	0.139613i
$652$		0			0
$653$	10.4088	+	18.0286i	0.407328	+	0.705513i	0.994589	−	0.103885i	$-0.0331273\pi$
$653$	10.4088	+	18.0286i	0.407328	+	0.705513i	−0.587261	+	0.809397i	$0.699794\pi$
$654$		0			0
$655$	15.6384	+	15.6384i	0.611043	+	0.611043i
$656$		0			0
$657$	−3.32275	−	12.4007i	−0.129633	−	0.483797i
$658$		0			0
$659$	38.6720	+	22.3273i	1.50645	+	0.869748i	0.999972	+	0.00749469i	$0.00238565\pi$
$659$	38.6720	+	22.3273i	1.50645	+	0.869748i	0.506477	+	0.862254i	$0.330948\pi$
$660$		0			0
$661$	−8.20143	+	30.6081i	−0.318999	+	1.19052i	0.601210	+	0.799091i	$0.294685\pi$
$661$	−8.20143	+	30.6081i	−0.318999	+	1.19052i	−0.920209	+	0.391428i	$0.871981\pi$
$662$		0			0
$663$	−11.3210	−	13.5280i	−0.439671	−	0.525384i
$664$		0			0
$665$	10.0171	+	2.68407i	0.388446	+	0.104084i
$666$		0			0
$667$	24.6163	−	42.6367i	0.953147	−	1.65090i
$668$		0			0
$669$	1.70682	+	6.36993i	0.0659894	+	0.246276i
$670$		0			0
$671$	1.41739	−	2.57966i	0.0547178	−	0.0995865i
$672$		0			0
$673$	−13.7532	−	23.8213i	−0.530149	−	0.918245i	−0.999381	−	0.0351699i	$-0.988803\pi$
$673$	−13.7532	−	23.8213i	−0.530149	−	0.918245i	0.469233	−	0.883075i	$-0.344531\pi$
$674$		0			0
$675$			0.384458i			0.0147978i
$676$		0			0
$677$			1.98782i			0.0763981i	0.999270	+	0.0381991i	$0.0121621\pi$
$677$			1.98782i			0.0763981i	−0.999270	+	0.0381991i	$0.987838\pi$
$678$		0			0
$679$	15.2681	−	8.81503i	0.585935	−	0.338290i
$680$		0			0
$681$	4.42772	+	4.42772i	0.169671	+	0.169671i
$682$		0			0
$683$	−14.7083	+	3.94107i	−0.562797	+	0.150801i	−0.528991	−	0.848628i	$-0.677429\pi$
$683$	−14.7083	+	3.94107i	−0.562797	+	0.150801i	−0.0338057	+	0.999428i	$0.510763\pi$
$684$		0			0
$685$	−13.1111	+	22.7091i	−0.500949	+	0.867669i
$686$		0			0
$687$	−0.0983465	+	0.367034i	−0.00375215	+	0.0140032i
$688$		0			0
$689$	−1.27849	−	1.52773i	−0.0487067	−	0.0582019i
$690$		0			0
$691$	−39.6897	−	10.6348i	−1.50987	−	0.404567i	−0.593475	−	0.804852i	$-0.702245\pi$
$691$	−39.6897	−	10.6348i	−1.50987	−	0.404567i	−0.916391	+	0.400285i	$0.868911\pi$
$692$		0			0
$693$	3.30172	−	13.4558i	0.125422	−	0.511143i
$694$		0			0
$695$	19.7356	−	5.28815i	0.748615	−	0.200591i
$696$		0			0
$697$	−34.3717	−	34.3717i	−1.30192	−	1.30192i
$698$		0			0
$699$	−0.824954	−	1.42886i	−0.0312026	−	0.0540445i
$700$		0			0
$701$	−24.9157			−0.941053			−0.470526	−	0.882386i	$-0.655936\pi$
$701$	−24.9157			−0.941053			−0.470526	+	0.882386i	$0.655936\pi$
$702$		0			0
$703$			14.4932i			0.546620i
$704$		0			0
$705$	3.55457	+	6.15669i	0.133873	+	0.231875i
$706$		0			0
$707$	21.1224	−	21.1224i	0.794390	−	0.794390i
$708$		0			0
$709$	29.7121	−	7.96134i	1.11586	−	0.298994i	0.346654	−	0.937993i	$-0.387318\pi$
$709$	29.7121	−	7.96134i	1.11586	−	0.298994i	0.769208	+	0.638999i	$0.220651\pi$
$710$		0			0
$711$	19.6763	+	11.3601i	0.737917	+	0.426037i
$712$		0			0
$713$	−4.91324	+	18.3365i	−0.184002	+	0.686705i
$714$		0			0
$715$	1.82087	−	26.9728i	0.0680968	−	1.00872i
$716$		0			0
$717$	3.31214	−	12.3611i	0.123694	−	0.461633i
$718$		0			0
$719$	19.8579	+	11.4650i	0.740576	+	0.427572i	0.822279	−	0.569085i	$-0.192702\pi$
$719$	19.8579	+	11.4650i	0.740576	+	0.427572i	−0.0817026	+	0.996657i	$0.526036\pi$
$720$		0			0
$721$	−7.14871	+	1.91549i	−0.266232	+	0.0713366i
$722$		0			0
$723$	−6.34705	+	6.34705i	−0.236049	+	0.236049i
$724$		0			0
$725$	−0.519623	−	0.900013i	−0.0192983	−	0.0334256i
$726$		0			0
$727$			6.18064i			0.229227i	0.993410	+	0.114614i	$0.0365630\pi$
$727$			6.18064i			0.229227i	−0.993410	+	0.114614i	$0.963437\pi$
$728$		0			0
$729$	−8.53507			−0.316114
$730$		0			0
$731$	19.3491	+	33.5136i	0.715651	+	1.23954i
$732$		0			0
$733$	−10.4406	−	10.4406i	−0.385632	−	0.385632i	0.487494	−	0.873126i	$-0.337911\pi$
$733$	−10.4406	−	10.4406i	−0.385632	−	0.385632i	−0.873126	+	0.487494i	$0.837911\pi$
$734$		0			0
$735$	6.00752	−	1.60971i	0.221591	−	0.0593750i
$736$		0			0
$737$	10.9702	−	44.7079i	0.404093	−	1.64684i
$738$		0			0
$739$	−3.47729	−	0.931738i	−0.127914	−	0.0342745i	0.194294	−	0.980943i	$-0.437758\pi$
$739$	−3.47729	−	0.931738i	−0.127914	−	0.0342745i	−0.322208	+	0.946669i	$0.604425\pi$
$740$		0			0
$741$	0.566399	−	6.37720i	0.0208072	−	0.234272i
$742$		0			0
$743$	6.21374	−	23.1900i	0.227960	−	0.850759i	−0.753237	−	0.657749i	$-0.771509\pi$
$743$	6.21374	−	23.1900i	0.227960	−	0.850759i	0.981197	−	0.193009i	$-0.0618247\pi$
$744$		0			0
$745$	11.7033	−	20.2707i	0.428774	−	0.742659i
$746$		0			0
$747$	−34.7345	+	9.30707i	−1.27087	+	0.340528i
$748$		0			0
$749$	20.3513	+	20.3513i	0.743621	+	0.743621i
$750$		0			0
$751$	−6.98146	+	4.03075i	−0.254757	+	0.147084i	−0.621941	−	0.783064i	$-0.713655\pi$
$751$	−6.98146	+	4.03075i	−0.254757	+	0.147084i	0.367183	+	0.930149i	$0.380322\pi$
$752$		0			0
$753$		−	14.0880i		−	0.513395i
$754$		0			0
$755$		−	43.6201i		−	1.58750i
$756$		0			0
$757$	15.3065	+	26.5117i	0.556326	+	0.963585i	0.997799	+	0.0663104i	$0.0211227\pi$
$757$	15.3065	+	26.5117i	0.556326	+	0.963585i	−0.441473	+	0.897275i	$0.645544\pi$
$758$		0			0
$759$	5.17708	−	9.42230i	0.187916	−	0.342008i
$760$		0			0
$761$	7.66291	+	28.5984i	0.277780	+	1.03669i	0.953955	+	0.299949i	$0.0969697\pi$
$761$	7.66291	+	28.5984i	0.277780	+	1.03669i	−0.676175	+	0.736741i	$0.736364\pi$
$762$		0			0
$763$	6.28948	−	10.8937i	0.227694	−	0.394378i
$764$		0			0
$765$	45.3072	+	12.1400i	1.63809	+	0.438924i
$766$		0			0
$767$	30.2877	+	21.2672i	1.09362	+	0.767914i
$768$		0			0
$769$	5.76573	−	21.5180i	0.207918	−	0.775959i	−0.780623	−	0.625002i	$-0.785098\pi$
$769$	5.76573	−	21.5180i	0.207918	−	0.775959i	0.988540	−	0.150956i	$-0.0482353\pi$
$770$		0			0
$771$	−12.7685	−	7.37192i	−0.459847	−	0.265493i
$772$		0			0
$773$	−0.950854	−	3.54863i	−0.0341998	−	0.127635i	0.946715	−	0.322071i	$-0.104379\pi$
$773$	−0.950854	−	3.54863i	−0.0341998	−	0.127635i	−0.980915	+	0.194436i	$0.937712\pi$
$774$		0			0
$775$	0.283349	+	0.283349i	0.0101782	+	0.0101782i
$776$		0			0
$777$	−2.48234	−	4.29955i	−0.0890536	−	0.154245i
$778$		0			0
$779$		−	17.6422i		−	0.632097i
$780$		0			0
$781$	14.7230	−	4.28118i	0.526832	−	0.153193i
$782$		0			0
$783$	−28.1800	+	16.2697i	−1.00707	+	0.581433i
$784$		0			0
$785$	−3.27712	+	3.27712i	−0.116965	+	0.116965i
$786$		0			0
$787$	−6.02629	−	22.4904i	−0.214814	−	0.801696i	−0.986232	−	0.165368i	$-0.947119\pi$
$787$	−6.02629	−	22.4904i	−0.214814	−	0.801696i	0.771418	−	0.636329i	$-0.219548\pi$
$788$		0			0
$789$	−6.67477	−	3.85368i	−0.237628	−	0.137195i
$790$		0			0
$791$	6.35115	+	1.70179i	0.225821	+	0.0605086i
$792$		0			0
$793$	−0.551490	−	3.15193i	−0.0195840	−	0.111928i
$794$		0			0
$795$	−0.745016	−	0.199626i	−0.0264230	−	0.00708002i
$796$		0			0
$797$	−26.1728	−	15.1109i	−0.927090	−	0.535256i	−0.0411998	−	0.999151i	$-0.513118\pi$
$797$	−26.1728	−	15.1109i	−0.927090	−	0.535256i	−0.885890	+	0.463895i	$0.846451\pi$
$798$		0			0
$799$	38.9739	−	10.4430i	1.37880	−	0.369448i
$800$		0			0
$801$	12.7718	+	12.7718i	0.451268	+	0.451268i
$802$		0			0
$803$	11.7383	+	11.2513i	0.414234	+	0.397050i
$804$		0			0
$805$	18.9314			0.667243
$806$		0			0
$807$	10.4085			0.366396
$808$		0			0
$809$	0.609725	−	0.352025i	0.0214368	−	0.0123765i	−0.489243	−	0.872147i	$-0.662727\pi$
$809$	0.609725	−	0.352025i	0.0214368	−	0.0123765i	0.510680	+	0.859771i	$0.329394\pi$
$810$		0			0
$811$	−30.7285	−	30.7285i	−1.07902	−	1.07902i	−0.996597	−	0.0824268i	$-0.973733\pi$
$811$	−30.7285	−	30.7285i	−1.07902	−	1.07902i	−0.0824268	−	0.996597i	$-0.526267\pi$
$812$		0			0
$813$	−0.786169	−	2.93402i	−0.0275721	−	0.102901i
$814$		0			0
$815$	−24.0305	+	41.6221i	−0.841753	+	1.45796i
$816$		0			0
$817$	−3.63515	+	13.5666i	−0.127178	+	0.474634i
$818$		0			0
$819$	−6.34745	−	13.6591i	−0.221798	−	0.477288i
$820$		0			0
$821$	−6.03853	+	22.5361i	−0.210746	+	0.786515i	0.776875	+	0.629655i	$0.216804\pi$
$821$	−6.03853	+	22.5361i	−0.210746	+	0.786515i	−0.987621	+	0.156860i	$0.949863\pi$
$822$		0			0
$823$	12.6651	+	7.31220i	0.441477	+	0.254887i	0.704224	−	0.709978i	$-0.251295\pi$
$823$	12.6651	+	7.31220i	0.441477	+	0.254887i	−0.262747	+	0.964865i	$0.584628\pi$
$824$		0			0
$825$	−0.117606	−	0.194088i	−0.00409452	−	0.00675729i
$826$		0			0
$827$	22.5166	−	22.5166i	0.782978	−	0.782978i	−0.197354	−	0.980332i	$-0.563235\pi$
$827$	22.5166	−	22.5166i	0.782978	−	0.782978i	0.980332	+	0.197354i	$0.0632349\pi$
$828$		0			0
$829$	−31.3470	+	18.0982i	−1.08873	+	0.628577i	−0.933238	−	0.359260i	$-0.883029\pi$
$829$	−31.3470	+	18.0982i	−1.08873	+	0.628577i	−0.155490	+	0.987837i	$0.549696\pi$
$830$		0			0
$831$	7.88796			0.273630
$832$		0			0
$833$		−	35.2992i		−	1.22304i
$834$		0			0
$835$	−2.96558	+	1.71218i	−0.102628	+	0.0592524i
$836$		0			0
$837$	8.87184	−	8.87184i	0.306656	−	0.306656i
$838$		0			0
$839$	−32.9143	+	8.81935i	−1.13633	+	0.304478i	−0.777473	−	0.628916i	$-0.783499\pi$
$839$	−32.9143	+	8.81935i	−1.13633	+	0.304478i	−0.358853	+	0.933394i	$0.616832\pi$
$840$		0			0
$841$	29.4794	−	51.0598i	1.01653	−	1.76068i
$842$		0			0
$843$	−5.40735	−	1.44889i	−0.186239	−	0.0499026i
$844$		0			0
$845$	−16.7935	−	24.1186i	−0.577713	−	0.829704i
$846$		0			0
$847$	5.25527	+	16.7421i	0.180573	+	0.575266i
$848$		0			0
$849$	1.36560	−	2.36529i	0.0468673	−	0.0811765i
$850$		0			0
$851$	6.84767	+	25.5559i	0.234735	+	0.876044i
$852$		0			0
$853$	26.1650	−	26.1650i	0.895873	−	0.895873i	−0.0991946	−	0.995068i	$-0.531627\pi$
$853$	26.1650	−	26.1650i	0.895873	−	0.895873i	0.995068	+	0.0991946i	$0.0316266\pi$
$854$		0			0
$855$	8.51196	+	14.7431i	0.291103	+	0.504205i
$856$		0			0
$857$	40.9318			1.39820			0.699102	−	0.715022i	$-0.253583\pi$
$857$	40.9318			1.39820			0.699102	+	0.715022i	$0.253583\pi$
$858$		0			0
$859$	28.5843			0.975285			0.487642	−	0.873043i	$-0.337857\pi$
$859$	28.5843			0.975285			0.487642	+	0.873043i	$0.337857\pi$
$860$		0			0
$861$	3.02170	+	5.23374i	0.102979	+	0.178365i
$862$		0			0
$863$	−20.1875	+	20.1875i	−0.687189	+	0.687189i	−0.961610	−	0.274421i	$-0.911514\pi$
$863$	−20.1875	+	20.1875i	−0.687189	+	0.687189i	0.274421	+	0.961610i	$0.411514\pi$
$864$		0			0
$865$	7.44639	+	27.7903i	0.253185	+	0.944898i
$866$		0			0
$867$	−14.1330	+	24.4790i	−0.479981	+	0.831351i
$868$		0			0
$869$	−28.7691	+	0.609370i	−0.975923	+	0.0206714i
$870$		0			0
$871$	−21.0899	−	45.3835i	−0.714604	−	1.53776i
$872$		0			0
$873$	27.9550	+	7.49052i	0.946133	+	0.253516i
$874$		0			0
$875$	−8.81607	+	15.2699i	−0.298038	+	0.516216i
$876$		0			0
$877$	7.23700	−	1.93915i	0.244376	−	0.0654804i	−0.134552	−	0.990907i	$-0.542959\pi$
$877$	7.23700	−	1.93915i	0.244376	−	0.0654804i	0.378928	+	0.925426i	$0.376293\pi$
$878$		0			0
$879$	−3.51716	+	3.51716i	−0.118631	+	0.118631i
$880$		0			0
$881$	−18.2804	+	10.5542i	−0.615884	+	0.355581i	−0.775265	−	0.631637i	$-0.782384\pi$
$881$	−18.2804	+	10.5542i	−0.615884	+	0.355581i	0.159381	+	0.987217i	$0.449050\pi$
$882$		0			0
$883$			41.2775i			1.38910i	0.719446	+	0.694549i	$0.244396\pi$
$883$			41.2775i			1.38910i	−0.719446	+	0.694549i	$0.755604\pi$
$884$		0			0
$885$	14.3288			0.481659
$886$		0			0
$887$	−24.5052	+	14.1481i	−0.822804	+	0.475046i	−0.851382	−	0.524546i	$-0.824235\pi$
$887$	−24.5052	+	14.1481i	−0.822804	+	0.475046i	0.0285787	+	0.999592i	$0.490902\pi$
$888$		0			0
$889$	−9.26221	+	9.26221i	−0.310644	+	0.310644i
$890$		0			0
$891$	16.2069	−	9.82045i	0.542952	−	0.328997i
$892$		0			0
$893$	12.6823	+	7.32211i	0.424396	+	0.245025i
$894$		0			0
$895$	7.37304	−	27.5165i	0.246453	−	0.919777i
$896$		0			0
$897$	−2.01434	−	11.5126i	−0.0672569	−	0.384393i
$898$		0			0
$899$	−8.77797	+	32.7598i	−0.292762	+	1.09260i
$900$		0			0
$901$	−2.18879	+	3.79110i	−0.0729193	+	0.126300i
$902$		0			0
$903$	−1.24524	−	4.64728i	−0.0414388	−	0.154652i
$904$		0			0
$905$	5.73467	+	5.73467i	0.190627	+	0.190627i
$906$		0			0
$907$	32.9676	−	19.0339i	1.09467	−	0.632009i	0.159856	−	0.987140i	$-0.448897\pi$
$907$	32.9676	−	19.0339i	1.09467	−	0.632009i	0.934816	+	0.355131i	$0.115564\pi$
$908$		0			0
$909$	49.0366			1.62644
$910$		0			0
$911$	14.9949			0.496803			0.248402	−	0.968657i	$-0.420095\pi$
$911$	14.9949			0.496803			0.248402	+	0.968657i	$0.420095\pi$
$912$		0			0
$913$	31.5150	−	32.8790i	1.04300	−	1.08814i
$914$		0			0
$915$	−0.876029	−	0.876029i	−0.0289606	−	0.0289606i
$916$		0			0
$917$	−15.0740	+	4.03907i	−0.497788	+	0.133382i
$918$		0			0
$919$	22.6799	+	13.0942i	0.748139	+	0.431939i	0.825021	−	0.565102i	$-0.191163\pi$
$919$	22.6799	+	13.0942i	0.748139	+	0.431939i	−0.0768818	+	0.997040i	$0.524496\pi$
$920$		0			0
$921$	−7.82952	−	2.09791i	−0.257991	−	0.0691286i
$922$		0			0
$923$	9.57868	−	13.6415i	0.315286	−	0.449015i
$924$		0			0
$925$	0.539456	+	0.144547i	0.0177372	+	0.00475267i
$926$		0			0
$927$	−10.5215	−	6.07457i	−0.345570	−	0.199515i
$928$		0			0
$929$	3.48651	+	13.0118i	0.114389	+	0.426904i	0.999240	−	0.0389683i	$-0.0124071\pi$
$929$	3.48651	+	13.0118i	0.114389	+	0.426904i	−0.884852	+	0.465873i	$0.845740\pi$
$930$		0			0
$931$	9.05911	−	9.05911i	0.296900	−	0.296900i
$932$		0			0
$933$	1.17857	−	0.680448i	0.0385847	−	0.0222769i
$934$		0			0
$935$	−57.0439	+	16.5873i	−1.86553	+	0.542462i
$936$		0			0
$937$		−	29.5538i		−	0.965481i	−0.875763	−	0.482741i	$-0.839641\pi$
$937$		−	29.5538i		−	0.965481i	0.875763	−	0.482741i	$-0.160359\pi$
$938$		0			0
$939$	3.83047	+	6.63457i	0.125003	+	0.216511i
$940$		0			0
$941$	4.72620	+	4.72620i	0.154070	+	0.154070i	0.779933	−	0.625863i	$-0.215253\pi$
$941$	4.72620	+	4.72620i	0.154070	+	0.154070i	−0.625863	+	0.779933i	$0.715253\pi$
$942$		0			0
$943$	−8.33551	−	31.1086i	−0.271442	−	1.01303i
$944$		0			0
$945$	−10.8360	−	6.25618i	−0.352496	−	0.203513i
$946$		0			0
$947$	−5.51280	+	20.5741i	−0.179142	+	0.668567i	0.816667	+	0.577109i	$0.195819\pi$
$947$	−5.51280	+	20.5741i	−0.179142	+	0.668567i	−0.995809	+	0.0914578i	$0.970847\pi$
$948$		0			0
$949$	17.6069	+	1.56378i	0.571543	+	0.0507623i
$950$		0			0
$951$	15.0317	+	4.02773i	0.487436	+	0.130608i
$952$		0			0
$953$	−26.8957	+	46.5847i	−0.871236	+	1.50903i	−0.0105170	+	0.999945i	$0.503348\pi$
$953$	−26.8957	+	46.5847i	−0.871236	+	1.50903i	−0.860719	+	0.509080i	$0.829986\pi$
$954$		0			0
$955$	−12.9274	−	48.2459i	−0.418322	−	1.56120i
$956$		0			0
$957$	9.24935	−	16.8338i	0.298989	−	0.544161i
$958$		0			0
$959$	−9.25161	−	16.0243i	−0.298750	−	0.517450i
$960$		0			0
$961$			17.9228i			0.578153i
$962$		0			0
$963$			47.2465i			1.52250i
$964$		0			0
$965$	32.1365	−	18.5540i	1.03451	−	0.597275i
$966$		0			0
$967$	7.57259	+	7.57259i	0.243518	+	0.243518i	0.818304	−	0.574786i	$-0.194915\pi$
$967$	7.57259	+	7.57259i	0.243518	+	0.243518i	−0.574786	+	0.818304i	$0.694915\pi$
$968$		0			0
$969$	−13.5894	+	3.64128i	−0.436556	+	0.116975i
$970$		0			0
$971$	20.6594	−	35.7831i	0.662991	−	1.14833i	−0.316834	−	0.948481i	$-0.602620\pi$
$971$	20.6594	−	35.7831i	0.662991	−	1.14833i	0.979826	−	0.199854i	$-0.0640467\pi$
$972$		0			0
$973$	−3.73149	+	13.9261i	−0.119626	+	0.446451i
$974$		0			0
$975$	−0.231719	−	0.0846848i	−0.00742096	−	0.00271209i
$976$		0			0
$977$	13.4990	+	3.61705i	0.431872	+	0.115720i	0.468205	−	0.883620i	$-0.344901\pi$
$977$	13.4990	+	3.61705i	0.431872	+	0.115720i	−0.0363327	+	0.999340i	$0.511568\pi$
$978$		0			0
$979$	−22.2168	−	5.45145i	−0.710052	−	0.174229i
$980$		0			0
$981$	19.9458	−	5.34445i	0.636819	−	0.170635i
$982$		0			0
$983$	−36.0451	−	36.0451i	−1.14966	−	1.14966i	−0.986619	−	0.163040i	$-0.947870\pi$
$983$	−36.0451	−	36.0451i	−1.14966	−	1.14966i	−0.163040	−	0.986619i	$-0.552130\pi$
$984$		0			0
$985$	28.9312	+	50.1103i	0.921824	+	1.59665i
$986$		0			0
$987$	−5.01644			−0.159675
$988$		0			0
$989$			25.6395i			0.815289i
$990$		0			0
$991$	−26.7436	−	46.3213i	−0.849538	−	1.47144i	−0.881621	−	0.471958i	$-0.843547\pi$
$991$	−26.7436	−	46.3213i	−0.849538	−	1.47144i	0.0320829	−	0.999485i	$-0.489786\pi$
$992$		0			0
$993$	3.48768	−	3.48768i	0.110678	−	0.110678i
$994$		0			0
$995$	−18.4478	+	4.94308i	−0.584836	+	0.156706i
$996$		0			0
$997$	4.84603	+	2.79785i	0.153475	+	0.0886090i	0.574771	−	0.818314i	$-0.305091\pi$
$997$	4.84603	+	2.79785i	0.153475	+	0.0886090i	−0.421296	+	0.906923i	$0.638425\pi$
$998$		0			0
$999$	4.52585	−	16.8907i	0.143192	−	0.534399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bc.a.197.7	✓	56
11.10	odd	2	inner	572.2.bc.a.197.8	yes	56
13.7	odd	12	inner	572.2.bc.a.241.8	yes	56
143.98	even	12	inner	572.2.bc.a.241.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.7	✓	56	1.1	even	1	trivial
572.2.bc.a.197.8	yes	56	11.10	odd	2	inner
572.2.bc.a.241.7	yes	56	143.98	even	12	inner
572.2.bc.a.241.8	yes	56	13.7	odd	12	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.308749 - 0.534769i) q^{3} +(-1.59856 + 1.59856i) q^{5} +(-0.412876 - 1.54087i) q^{7} +(1.30935 - 2.26786i) q^{9} +O(q^{10})\)	\(q+(-0.308749 - 0.534769i) q^{3} +(-1.59856 + 1.59856i) q^{5} +(-0.412876 - 1.54087i) q^{7} +(1.30935 - 2.26786i) q^{9} +(0.0702351 + 3.31588i) q^{11} +(2.31396 + 2.76506i) q^{13} +(1.34842 + 0.361307i) q^{15} +(3.96153 - 6.86158i) q^{17} +(2.77762 - 0.744262i) q^{19} +(-0.696536 + 0.696536i) q^{21} +(4.54615 - 2.62472i) q^{23} -0.110810i q^{25} -3.46953 q^{27} +(8.12214 - 4.68932i) q^{29} +(-2.55707 + 2.55707i) q^{31} +(1.75154 - 1.06133i) q^{33} +(3.12319 + 1.80318i) q^{35} +(-1.30446 + 4.86830i) q^{37} +(0.764236 - 2.09114i) q^{39} +(1.58788 - 5.92607i) q^{41} +(-2.44212 + 4.22987i) q^{43} +(1.53224 + 5.71839i) q^{45} +(3.60099 + 3.60099i) q^{47} +(3.85835 - 2.22762i) q^{49} -4.89247 q^{51} -0.552512 q^{53} +(-5.41292 - 5.18837i) q^{55} +(-1.25560 - 1.25560i) q^{57} +(9.91459 - 2.65661i) q^{59} +(-0.768571 - 0.443735i) q^{61} +(-4.03508 - 1.08120i) q^{63} +(-8.11915 - 0.721112i) q^{65} +(-13.4069 - 3.59236i) q^{67} +(-2.80724 - 1.62076i) q^{69} +(-1.19653 - 4.46550i) q^{71} +(3.46658 - 3.46658i) q^{73} +(-0.0592576 + 0.0342124i) q^{75} +(5.08036 - 1.47727i) q^{77} +8.67614i q^{79} +(-2.85683 - 4.94818i) q^{81} +(-9.70994 - 9.70994i) q^{83} +(4.63590 + 17.3014i) q^{85} +(-5.01540 - 2.89564i) q^{87} +(-1.78516 + 6.66231i) q^{89} +(3.30524 - 4.70715i) q^{91} +(2.15694 + 0.577949i) q^{93} +(-3.25046 + 5.62996i) q^{95} +(2.86040 + 10.6752i) q^{97} +(7.61191 + 4.18236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^9	\( 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more