LMFDB - Embedded newform 572.2.bh.a.57.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, degree $8$, 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:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.13
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15330 - 1.56447i) q^{3} +(1.45337 + 0.740531i) q^{5} +(3.81051 - 0.603525i) q^{7} +(1.26211 - 3.88437i) q^{9} +O(q^{10})$	\(q+(2.15330 - 1.56447i) q^{3} +(1.45337 + 0.740531i) q^{5} +(3.81051 - 0.603525i) q^{7} +(1.26211 - 3.88437i) q^{9} +(-3.23867 + 0.714866i) q^{11} +(1.66806 + 3.19650i) q^{13} +(4.28809 - 0.679167i) q^{15} +(0.145227 + 0.446964i) q^{17} +(-8.16749 - 1.29360i) q^{19} +(7.26098 - 7.26098i) q^{21} +5.35491i q^{23} +(-1.37501 - 1.89255i) q^{25} +(-0.891795 - 2.74466i) q^{27} +(-2.70131 + 3.71804i) q^{29} +(-0.970871 - 1.90544i) q^{31} +(-5.85545 + 6.60611i) q^{33} +(5.98502 + 1.94465i) q^{35} +(-1.59193 - 10.0511i) q^{37} +(8.59264 + 4.27340i) q^{39} +(10.2046 + 1.61624i) q^{41} -8.27038 q^{43} +(4.71081 - 4.71081i) q^{45} +(-9.41370 - 1.49098i) q^{47} +(7.49832 - 2.43635i) q^{49} +(1.01198 + 0.735245i) q^{51} +(1.18796 - 3.65618i) q^{53} +(-5.23638 - 1.35937i) q^{55} +(-19.6109 + 9.99224i) q^{57} +(-1.83795 - 11.6044i) q^{59} +(5.60124 - 1.81995i) q^{61} +(2.46496 - 15.5631i) q^{63} +(0.0572070 + 5.88096i) q^{65} +(5.46352 - 5.46352i) q^{67} +(8.37757 + 11.5307i) q^{69} +(0.681911 + 0.347451i) q^{71} +(-10.7535 + 1.70319i) q^{73} +(-5.92165 - 1.92406i) q^{75} +(-11.9095 + 4.67862i) q^{77} +(5.10701 + 1.65937i) q^{79} +(3.69848 + 2.68710i) q^{81} +(-1.29337 + 2.53837i) q^{83} +(-0.119921 + 0.757151i) q^{85} +12.2322i q^{87} +(3.76777 + 3.76777i) q^{89} +(8.28531 + 11.1736i) q^{91} +(-5.07158 - 2.58410i) q^{93} +(-10.9125 - 7.92838i) q^{95} +(4.87455 + 9.56684i) q^{97} +(-1.31075 + 13.4824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.15330	−	1.56447i	1.24321	−	0.903245i	0.245402	−	0.969421i	$-0.421080\pi$
$3$	2.15330	−	1.56447i	1.24321	−	0.903245i	0.997808	+	0.0661767i	$0.0210801\pi$
$4$		0			0
$5$	1.45337	+	0.740531i	0.649969	+	0.331176i	0.747700	−	0.664037i	$-0.231158\pi$
$5$	1.45337	+	0.740531i	0.649969	+	0.331176i	−0.0977306	+	0.995213i	$0.531158\pi$
$6$		0			0
$7$	3.81051	−	0.603525i	1.44024	−	0.228111i	0.613052	−	0.790042i	$-0.289942\pi$
$7$	3.81051	−	0.603525i	1.44024	−	0.228111i	0.827184	+	0.561931i	$0.189942\pi$
$8$		0			0
$9$	1.26211	−	3.88437i	0.420702	−	1.29479i
$10$		0			0
$11$	−3.23867	+	0.714866i	−0.976495	+	0.215540i
$11$	−3.23867	+	0.714866i	−0.976495	+	0.215540i
$12$		0			0
$13$	1.66806	+	3.19650i	0.462636	+	0.886548i
$13$	1.66806	+	3.19650i	0.462636	+	0.886548i
$14$		0			0
$15$	4.28809	−	0.679167i	1.10718	−	0.175360i
$16$		0			0
$17$	0.145227	+	0.446964i	0.0352228	+	0.108405i	0.967122	−	0.254312i	$-0.0818492\pi$
$17$	0.145227	+	0.446964i	0.0352228	+	0.108405i	−0.931899	+	0.362717i	$0.881849\pi$
$18$		0			0
$19$	−8.16749	−	1.29360i	−1.87375	−	0.296773i	−0.887346	−	0.461104i	$-0.847454\pi$
$19$	−8.16749	−	1.29360i	−1.87375	−	0.296773i	−0.986405	+	0.164331i	$0.947454\pi$
$20$		0			0
$21$	7.26098	−	7.26098i	1.58448	−	1.58448i
$22$		0			0
$23$			5.35491i			1.11658i	0.829647	+	0.558288i	$0.188541\pi$
$23$			5.35491i			1.11658i	−0.829647	+	0.558288i	$0.811459\pi$
$24$		0			0
$25$	−1.37501	−	1.89255i	−0.275003	−	0.378509i
$26$		0			0
$27$	−0.891795	−	2.74466i	−0.171626	−	0.528211i
$28$		0			0
$29$	−2.70131	+	3.71804i	−0.501621	+	0.690422i	−0.982478	−	0.186377i	$-0.940326\pi$
$29$	−2.70131	+	3.71804i	−0.501621	+	0.690422i	0.480857	+	0.876799i	$0.340326\pi$
$30$		0			0
$31$	−0.970871	−	1.90544i	−0.174374	−	0.342227i	0.787235	−	0.616654i	$-0.211512\pi$
$31$	−0.970871	−	1.90544i	−0.174374	−	0.342227i	−0.961608	+	0.274426i	$0.911512\pi$
$32$		0			0
$33$	−5.85545	+	6.60611i	−1.01930	+	1.14998i
$34$		0			0
$35$	5.98502	+	1.94465i	1.01165	+	0.328706i
$36$		0			0
$37$	−1.59193	−	10.0511i	−0.261712	−	1.65239i	−0.672090	−	0.740470i	$-0.734603\pi$
$37$	−1.59193	−	10.0511i	−0.261712	−	1.65239i	0.410378	−	0.911916i	$-0.365397\pi$
$38$		0			0
$39$	8.59264	+	4.27340i	1.37592	+	0.684292i
$40$		0			0
$41$	10.2046	+	1.61624i	1.59368	+	0.252415i	0.889272	−	0.457378i	$-0.151211\pi$
$41$	10.2046	+	1.61624i	1.59368	+	0.252415i	0.704411	+	0.709793i	$0.251211\pi$
$42$		0			0
$43$	−8.27038			−1.26122			−0.630611	−	0.776099i	$-0.717195\pi$
$43$	−8.27038			−1.26122			−0.630611	+	0.776099i	$0.717195\pi$
$44$		0			0
$45$	4.71081	−	4.71081i	0.702246	−	0.702246i
$46$		0			0
$47$	−9.41370	−	1.49098i	−1.37313	−	0.217482i	−0.574105	−	0.818782i	$-0.694650\pi$
$47$	−9.41370	−	1.49098i	−1.37313	−	0.217482i	−0.799024	+	0.601300i	$0.794650\pi$
$48$		0			0
$49$	7.49832	−	2.43635i	1.07119	−	0.348050i
$50$		0			0
$51$	1.01198	+	0.735245i	0.141705	+	0.102955i
$52$		0			0
$53$	1.18796	−	3.65618i	0.163179	−	0.502215i	−0.835718	−	0.549159i	$-0.814948\pi$
$53$	1.18796	−	3.65618i	0.163179	−	0.502215i	0.998898	+	0.0469440i	$0.0149482\pi$
$54$		0			0
$55$	−5.23638	−	1.35937i	−0.706073	−	0.183297i
$56$		0			0
$57$	−19.6109	+	9.99224i	−2.59753	+	1.32351i
$58$		0			0
$59$	−1.83795	−	11.6044i	−0.239281	−	1.51076i	−0.755980	−	0.654595i	$-0.772839\pi$
$59$	−1.83795	−	11.6044i	−0.239281	−	1.51076i	0.516698	−	0.856167i	$-0.327161\pi$
$60$		0			0
$61$	5.60124	−	1.81995i	0.717166	−	0.233021i	0.0723717	−	0.997378i	$-0.476943\pi$
$61$	5.60124	−	1.81995i	0.717166	−	0.233021i	0.644794	+	0.764356i	$0.276943\pi$
$62$		0			0
$63$	2.46496	−	15.5631i	0.310555	−	1.96077i
$64$		0			0
$65$	0.0572070	+	5.88096i	0.00709565	+	0.729443i
$66$		0			0
$67$	5.46352	−	5.46352i	0.667475	−	0.667475i	−0.289656	−	0.957131i	$-0.593541\pi$
$67$	5.46352	−	5.46352i	0.667475	−	0.667475i	0.957131	+	0.289656i	$0.0935409\pi$
$68$		0			0
$69$	8.37757	+	11.5307i	1.00854	+	1.38814i
$70$		0			0
$71$	0.681911	+	0.347451i	0.0809279	+	0.0412348i	0.493986	−	0.869470i	$-0.335539\pi$
$71$	0.681911	+	0.347451i	0.0809279	+	0.0412348i	−0.413058	+	0.910705i	$0.635539\pi$
$72$		0			0
$73$	−10.7535	+	1.70319i	−1.25861	+	0.199344i	−0.749874	−	0.661581i	$-0.769886\pi$
$73$	−10.7535	+	1.70319i	−1.25861	+	0.199344i	−0.508733	+	0.860925i	$0.669886\pi$
$74$		0			0
$75$	−5.92165	−	1.92406i	−0.683773	−	0.222171i
$76$		0			0
$77$	−11.9095	+	4.67862i	−1.35722	+	0.533178i
$78$		0			0
$79$	5.10701	+	1.65937i	0.574584	+	0.186694i	0.581873	−	0.813280i	$-0.302320\pi$
$79$	5.10701	+	1.65937i	0.574584	+	0.186694i	−0.00728886	+	0.999973i	$0.502320\pi$
$80$		0			0
$81$	3.69848	+	2.68710i	0.410942	+	0.298567i
$82$		0			0
$83$	−1.29337	+	2.53837i	−0.141965	+	0.278623i	−0.951031	−	0.309096i	$-0.899974\pi$
$83$	−1.29337	+	2.53837i	−0.141965	+	0.278623i	0.809066	+	0.587718i	$0.199974\pi$
$84$		0			0
$85$	−0.119921	+	0.757151i	−0.0130073	+	0.0821246i
$86$		0			0
$87$			12.2322i			1.31143i
$88$		0			0
$89$	3.76777	+	3.76777i	0.399383	+	0.399383i	0.878015	−	0.478633i	$-0.158867\pi$
$89$	3.76777	+	3.76777i	0.399383	+	0.399383i	−0.478633	+	0.878015i	$0.658867\pi$
$90$		0			0
$91$	8.28531	+	11.1736i	0.868536	+	1.17131i
$92$		0			0
$93$	−5.07158	−	2.58410i	−0.525898	−	0.267958i
$94$		0			0
$95$	−10.9125	−	7.92838i	−1.11960	−	0.813434i
$96$		0			0
$97$	4.87455	+	9.56684i	0.494935	+	0.971365i	0.994465	+	0.105068i	$0.0335061\pi$
$97$	4.87455	+	9.56684i	0.494935	+	0.971365i	−0.499530	+	0.866297i	$0.666494\pi$
$98$		0			0
$99$	−1.31075	+	13.4824i	−0.131735	+	1.35503i
$100$		0			0
$101$	−3.96330	+	12.1978i	−0.394363	+	1.21372i	0.535094	+	0.844793i	$0.320276\pi$
$101$	−3.96330	+	12.1978i	−0.394363	+	1.21372i	−0.929457	+	0.368932i	$0.879724\pi$
$102$		0			0
$103$	6.13884	−	8.44939i	0.604878	−	0.832543i	−0.391266	−	0.920278i	$-0.627963\pi$
$103$	6.13884	−	8.44939i	0.604878	−	0.832543i	0.996144	+	0.0877343i	$0.0279627\pi$
$104$		0			0
$105$	15.9299	−	5.17594i	1.55460	−	0.505120i
$106$		0			0
$107$	9.03021	+	12.4290i	0.872984	+	1.20156i	0.978315	+	0.207122i	$0.0664096\pi$
$107$	9.03021	+	12.4290i	0.872984	+	1.20156i	−0.105332	+	0.994437i	$0.533590\pi$
$108$		0			0
$109$	−3.16402	−	3.16402i	−0.303059	−	0.303059i	0.539151	−	0.842209i	$-0.318745\pi$
$109$	−3.16402	−	3.16402i	−0.303059	−	0.303059i	−0.842209	+	0.539151i	$0.818745\pi$
$110$		0			0
$111$	−19.1525	−	19.1525i	−1.81787	−	1.81787i
$112$		0			0
$113$	8.63847	−	6.27621i	0.812638	−	0.590416i	−0.101956	−	0.994789i	$-0.532510\pi$
$113$	8.63847	−	6.27621i	0.812638	−	0.590416i	0.914594	+	0.404373i	$0.132510\pi$
$114$		0			0
$115$	−3.96548	+	7.78269i	−0.369783	+	0.725739i
$116$		0			0
$117$	14.5216	−	2.44503i	1.34253	−	0.226043i
$118$		0			0
$119$	0.823143	+	1.61551i	0.0754574	+	0.148094i
$120$		0			0
$121$	9.97793	−	4.63042i	0.907085	−	0.420948i
$122$		0			0
$123$	24.5020	−	12.4844i	2.20927	−	1.12568i
$124$		0			0
$125$	−1.87277	−	11.8242i	−0.167506	−	1.05759i
$126$		0			0
$127$	2.93597	+	9.03599i	0.260525	+	0.801814i	0.992691	+	0.120687i	$0.0385098\pi$
$127$	2.93597	+	9.03599i	0.260525	+	0.801814i	−0.732165	+	0.681127i	$0.761490\pi$
$128$		0			0
$129$	−17.8086	+	12.9387i	−1.56796	+	1.13919i
$130$		0			0
$131$		−	4.84560i		−	0.423362i	−0.977339	−	0.211681i	$-0.932106\pi$
$131$		−	4.84560i		−	0.423362i	0.977339	−	0.211681i	$-0.0678938\pi$
$132$		0			0
$133$	−31.9030			−2.76634
$134$		0			0
$135$	0.736397	−	4.64943i	0.0633790	−	0.400159i
$136$		0			0
$137$	−7.89908	+	15.5028i	−0.674864	+	1.32450i	0.258656	+	0.965970i	$0.416720\pi$
$137$	−7.89908	+	15.5028i	−0.674864	+	1.32450i	−0.933520	+	0.358526i	$0.883280\pi$
$138$		0			0
$139$	−1.15126	+	1.58457i	−0.0976485	+	0.134402i	−0.855045	−	0.518553i	$-0.826471\pi$
$139$	−1.15126	+	1.58457i	−0.0976485	+	0.134402i	0.757397	+	0.652955i	$0.226471\pi$
$140$		0			0
$141$	−22.6031	+	11.5169i	−1.90353	+	0.969895i
$142$		0			0
$143$	−7.68735	−	9.15995i	−0.642848	−	0.765993i
$144$		0			0
$145$	−6.67934	+	3.40330i	−0.554689	+	0.282628i
$146$		0			0
$147$	12.3346	−	16.9771i	1.01734	−	1.40025i
$148$		0			0
$149$	−5.54065	+	10.8741i	−0.453907	+	0.890843i	0.544728	+	0.838613i	$0.316633\pi$
$149$	−5.54065	+	10.8741i	−0.453907	+	0.890843i	−0.998635	+	0.0522305i	$0.983367\pi$
$150$		0			0
$151$	1.35351	−	8.54571i	0.110147	−	0.695440i	−0.869383	−	0.494139i	$-0.835483\pi$
$151$	1.35351	−	8.54571i	0.110147	−	0.695440i	0.979530	−	0.201300i	$-0.0645168\pi$
$152$		0			0
$153$	1.91946			0.155179
$154$		0			0
$155$		−	3.48828i		−	0.280185i
$156$		0			0
$157$	−10.2106	+	7.41843i	−0.814895	+	0.592056i	−0.915246	−	0.402897i	$-0.868003\pi$
$157$	−10.2106	+	7.41843i	−0.814895	+	0.592056i	0.100351	+	0.994952i	$0.468003\pi$
$158$		0			0
$159$	−3.16192	−	9.73139i	−0.250757	−	0.771749i
$160$		0			0
$161$	3.23182	+	20.4049i	0.254703	+	1.60813i
$162$		0			0
$163$	−6.61055	+	3.36824i	−0.517778	+	0.263821i	−0.693293	−	0.720656i	$-0.743841\pi$
$163$	−6.61055	+	3.36824i	−0.517778	+	0.263821i	0.175515	+	0.984477i	$0.443841\pi$
$164$		0			0
$165$	−13.4022	+	5.26501i	−1.04336	+	0.409880i
$166$		0			0
$167$	1.16220	+	2.28095i	0.0899338	+	0.176505i	0.931592	−	0.363506i	$-0.118420\pi$
$167$	1.16220	+	2.28095i	0.0899338	+	0.176505i	−0.841658	+	0.540011i	$0.818420\pi$
$168$		0			0
$169$	−7.43517	+	10.6639i	−0.571936	+	0.820298i
$170$		0			0
$171$	−15.3331	+	30.0929i	−1.17255	+	2.30126i
$172$		0			0
$173$	5.90250	−	4.28842i	0.448759	−	0.326042i	−0.340347	−	0.940300i	$-0.610544\pi$
$173$	5.90250	−	4.28842i	0.448759	−	0.326042i	0.789105	+	0.614258i	$0.210544\pi$
$174$		0			0
$175$	−6.38170	−	6.38170i	−0.482411	−	0.482411i
$176$		0			0
$177$	−22.1123	−	22.1123i	−1.66207	−	1.66207i
$178$		0			0
$179$	2.34981	+	3.23423i	0.175633	+	0.241738i	0.887753	−	0.460319i	$-0.152265\pi$
$179$	2.34981	+	3.23423i	0.175633	+	0.241738i	−0.712121	+	0.702057i	$0.752265\pi$
$180$		0			0
$181$	3.28281	−	1.06665i	0.244009	−	0.0792834i	−0.184459	−	0.982840i	$-0.559053\pi$
$181$	3.28281	−	1.06665i	0.244009	−	0.0792834i	0.428468	+	0.903557i	$0.359053\pi$
$182$		0			0
$183$	9.21391	−	12.6819i	0.681112	−	0.937470i
$184$		0			0
$185$	5.12946	−	15.7868i	0.377125	−	1.16067i
$186$		0			0
$187$	−0.789862	−	1.34375i	−0.0577604	−	0.0982646i
$188$		0			0
$189$	−5.05467	−	9.92034i	−0.367673	−	0.721599i
$190$		0			0
$191$	−1.95151	−	1.41786i	−0.141206	−	0.102592i	0.514939	−	0.857227i	$-0.327814\pi$
$191$	−1.95151	−	1.41786i	−0.141206	−	0.102592i	−0.656146	+	0.754634i	$0.727814\pi$
$192$		0			0
$193$	6.57369	+	3.34946i	0.473185	+	0.241100i	0.674285	−	0.738471i	$-0.264452\pi$
$193$	6.57369	+	3.34946i	0.473185	+	0.241100i	−0.201101	+	0.979571i	$0.564452\pi$
$194$		0			0
$195$	9.32374	+	12.5740i	0.667687	+	0.900441i
$196$		0			0
$197$	11.7928	+	11.7928i	0.840204	+	0.840204i	0.988885	−	0.148682i	$-0.0475029\pi$
$197$	11.7928	+	11.7928i	0.840204	+	0.840204i	−0.148682	+	0.988885i	$0.547503\pi$
$198$		0			0
$199$		−	20.8713i		−	1.47953i	−0.672868	−	0.739763i	$-0.734938\pi$
$199$		−	20.8713i		−	1.47953i	0.672868	−	0.739763i	$-0.265062\pi$
$200$		0			0
$201$	3.21712	−	20.3121i	0.226918	−	1.43270i
$202$		0			0
$203$	−8.04944	+	15.7979i	−0.564960	+	1.10880i
$204$		0			0
$205$	13.6342	+	9.90580i	0.952251	+	0.691851i
$206$		0			0
$207$	20.8004	+	6.75847i	1.44573	+	0.469746i
$208$		0			0
$209$	27.3765	−	1.64911i	1.89368	−	0.114071i
$210$		0			0
$211$	2.02101	+	0.656667i	0.139132	+	0.0452068i	0.377755	−	0.925905i	$-0.376696\pi$
$211$	2.02101	+	0.656667i	0.139132	+	0.0452068i	−0.238623	+	0.971112i	$0.576696\pi$
$212$		0			0
$213$	2.01193	−	0.318659i	0.137855	−	0.0218342i
$214$		0			0
$215$	−12.0200	−	6.12448i	−0.819755	−	0.417686i
$216$		0			0
$217$	−4.84949	−	6.67475i	−0.329205	−	0.453112i
$218$		0			0
$219$	−20.4910	+	20.4910i	−1.38466	+	1.38466i
$220$		0			0
$221$	−1.18647	+	1.20978i	−0.0798106	+	0.0813786i
$222$		0			0
$223$	0.779338	−	4.92054i	0.0521883	−	0.329504i	−0.947756	−	0.318995i	$-0.896655\pi$
$223$	0.779338	−	4.92054i	0.0521883	−	0.329504i	0.999945	−	0.0105092i	$-0.00334524\pi$
$224$		0			0
$225$	−9.08676	+	2.95247i	−0.605784	+	0.196831i
$226$		0			0
$227$	−2.73508	−	17.2686i	−0.181534	−	1.14616i	−0.895197	−	0.445670i	$-0.852966\pi$
$227$	−2.73508	−	17.2686i	−0.181534	−	1.14616i	0.713664	−	0.700488i	$-0.247034\pi$
$228$		0			0
$229$	1.14946	−	0.585679i	0.0759585	−	0.0387028i	−0.415599	−	0.909548i	$-0.636428\pi$
$229$	1.14946	−	0.585679i	0.0759585	−	0.0387028i	0.491557	+	0.870845i	$0.336428\pi$
$230$		0			0
$231$	−18.3253	+	28.7065i	−1.20571	+	1.88875i
$232$		0			0
$233$	−1.27660	+	3.92896i	−0.0836327	+	0.257395i	−0.984125	−	0.177477i	$-0.943206\pi$
$233$	−1.27660	+	3.92896i	−0.0836327	+	0.257395i	0.900492	+	0.434872i	$0.143206\pi$
$234$		0			0
$235$	−12.5775	−	9.13809i	−0.820466	−	0.596104i
$236$		0			0
$237$	13.5930	−	4.41662i	0.882958	−	0.286891i
$238$		0			0
$239$	−16.2771	−	2.57804i	−1.05288	−	0.166760i	−0.394079	−	0.919077i	$-0.628936\pi$
$239$	−16.2771	−	2.57804i	−1.05288	−	0.166760i	−0.658801	+	0.752317i	$0.728936\pi$
$240$		0			0
$241$	13.5603	−	13.5603i	0.873495	−	0.873495i	−0.119356	−	0.992851i	$-0.538083\pi$
$241$	13.5603	−	13.5603i	0.873495	−	0.873495i	0.992851	+	0.119356i	$0.0380831\pi$
$242$		0			0
$243$	20.8256			1.33596
$244$		0			0
$245$	12.7021	+	2.01181i	0.811505	+	0.128530i
$246$		0			0
$247$	−9.48885	−	28.2652i	−0.603761	−	1.79847i
$248$		0			0
$249$	1.18619	+	7.48931i	0.0751717	+	0.474616i
$250$		0			0
$251$	23.0144	+	7.47783i	1.45266	+	0.471997i	0.925818	−	0.377969i	$-0.123377\pi$
$251$	23.0144	+	7.47783i	1.45266	+	0.471997i	0.526838	+	0.849966i	$0.323377\pi$
$252$		0			0
$253$	−3.82804	−	17.3428i	−0.240667	−	1.09033i
$254$		0			0
$255$	0.926311	+	1.81799i	0.0580078	+	0.113847i
$256$		0			0
$257$	1.28525	−	1.76900i	0.0801720	−	0.110347i	−0.767047	−	0.641590i	$-0.778275\pi$
$257$	1.28525	−	1.76900i	0.0801720	−	0.110347i	0.847219	+	0.531243i	$0.178275\pi$
$258$		0			0
$259$	−12.1321	−	37.3389i	−0.753854	−	2.32013i
$260$		0			0
$261$	11.0329	+	15.1855i	0.682918	+	0.939956i
$262$		0			0
$263$			4.51919i			0.278665i	0.990246	+	0.139333i	$0.0444957\pi$
$263$			4.51919i			0.278665i	−0.990246	+	0.139333i	$0.955504\pi$
$264$		0			0
$265$	4.43407	−	4.43407i	0.272383	−	0.272383i
$266$		0			0
$267$	14.0077	+	2.21860i	0.857257	+	0.135776i
$268$		0			0
$269$	3.21601	+	9.89786i	0.196084	+	0.603483i	0.999962	+	0.00868991i	$0.00276612\pi$
$269$	3.21601	+	9.89786i	0.196084	+	0.603483i	−0.803879	+	0.594793i	$0.797234\pi$
$270$		0			0
$271$	15.2373	−	2.41335i	0.925599	−	0.146600i	0.324601	−	0.945851i	$-0.394770\pi$
$271$	15.2373	−	2.41335i	0.925599	−	0.146600i	0.600998	+	0.799251i	$0.294770\pi$
$272$		0			0
$273$	35.3214	+	11.0980i	2.13775	+	0.671679i
$274$		0			0
$275$	5.80613	+	5.14638i	0.350123	+	0.310338i
$276$		0			0
$277$	0.956352	−	2.94335i	0.0574616	−	0.176849i	−0.918206	−	0.396103i	$-0.870362\pi$
$277$	0.956352	−	2.94335i	0.0574616	−	0.176849i	0.975668	+	0.219254i	$0.0703624\pi$
$278$		0			0
$279$	−8.62678	+	1.36635i	−0.516472	+	0.0818011i
$280$		0			0
$281$	9.40950	+	4.79438i	0.561324	+	0.286009i	0.711541	−	0.702644i	$-0.247997\pi$
$281$	9.40950	+	4.79438i	0.561324	+	0.286009i	−0.150218	+	0.988653i	$0.547997\pi$
$282$		0			0
$283$	9.63340	−	6.99908i	0.572646	−	0.416052i	−0.263419	−	0.964681i	$-0.584850\pi$
$283$	9.63340	−	6.99908i	0.572646	−	0.416052i	0.836066	+	0.548629i	$0.184850\pi$
$284$		0			0
$285$	−35.9015			−2.12662
$286$		0			0
$287$	39.8599			2.35286
$288$		0			0
$289$	13.5746	−	9.86253i	0.798506	−	0.580149i
$290$		0			0
$291$	25.4634	+	12.9742i	1.49269	+	0.760563i
$292$		0			0
$293$	21.3680	−	3.38435i	1.24833	−	0.197716i	0.502926	−	0.864330i	$-0.332257\pi$
$293$	21.3680	−	3.38435i	1.24833	−	0.197716i	0.745403	+	0.666614i	$0.232257\pi$
$294$		0			0
$295$	5.92218	−	18.2266i	0.344802	−	1.06119i
$296$		0			0
$297$	4.85029	+	8.25154i	0.281443	+	0.478803i
$298$		0			0
$299$	−17.1169	+	8.93229i	−0.989898	+	0.516568i
$300$		0			0
$301$	−31.5143	+	4.99138i	−1.81646	+	0.287698i
$302$		0			0
$303$	10.5488	+	32.4660i	0.606014	+	1.86512i
$304$		0			0
$305$	9.48844	+	1.50282i	0.543306	+	0.0860513i
$306$		0			0
$307$	−6.29563	+	6.29563i	−0.359310	+	0.359310i	−0.863559	−	0.504248i	$-0.831770\pi$
$307$	−6.29563	+	6.29563i	−0.359310	+	0.359310i	0.504248	+	0.863559i	$0.331770\pi$
$308$		0			0
$309$		−	27.7981i		−	1.58138i
$310$		0			0
$311$	7.59818	+	10.4580i	0.430853	+	0.593018i	0.968149	−	0.250376i	$-0.0805541\pi$
$311$	7.59818	+	10.4580i	0.430853	+	0.593018i	−0.537296	+	0.843394i	$0.680554\pi$
$312$		0			0
$313$	−1.80784	−	5.56396i	−0.102185	−	0.314494i	0.886874	−	0.462011i	$-0.152872\pi$
$313$	−1.80784	−	5.56396i	−0.102185	−	0.314494i	−0.989059	+	0.147517i	$0.952872\pi$
$314$		0			0
$315$	15.1075	−	20.7937i	0.851210	−	1.17159i
$316$		0			0
$317$	−6.40399	−	12.5685i	−0.359684	−	0.705920i	0.638273	−	0.769810i	$-0.279649\pi$
$317$	−6.40399	−	12.5685i	−0.359684	−	0.705920i	−0.997957	+	0.0638904i	$0.979649\pi$
$318$		0			0
$319$	6.09076	−	13.9726i	0.341017	−	0.782313i
$320$		0			0
$321$	38.8896	+	12.6360i	2.17060	+	0.705272i
$322$		0			0
$323$	−0.607949	−	3.83844i	−0.0338272	−	0.213577i
$324$		0			0
$325$	3.75591	−	7.55210i	0.208340	−	0.418915i
$326$		0			0
$327$	−11.7631	−	1.86309i	−0.650501	−	0.103029i
$328$		0			0
$329$	−36.7708			−2.02724
$330$		0			0
$331$	−15.1490	+	15.1490i	−0.832665	+	0.832665i	−0.987881	−	0.155216i	$-0.950393\pi$
$331$	−15.1490	+	15.1490i	−0.832665	+	0.832665i	0.155216	+	0.987881i	$0.450393\pi$
$332$		0			0
$333$	−41.0512	−	6.50188i	−2.24959	−	0.356301i
$334$		0			0
$335$	11.9864	−	3.89463i	0.654889	−	0.212786i
$336$		0			0
$337$	2.68266	+	1.94906i	0.146134	+	0.106172i	0.658450	−	0.752625i	$-0.271212\pi$
$337$	2.68266	+	1.94906i	0.146134	+	0.106172i	−0.512316	+	0.858797i	$0.671212\pi$
$338$		0			0
$339$	8.78231	−	27.0292i	0.476990	−	1.46802i
$340$		0			0
$341$	4.50646	+	5.47705i	0.244039	+	0.296599i
$342$		0			0
$343$	3.03945	−	1.54868i	0.164115	−	0.0836206i
$344$		0			0
$345$	3.63688	+	22.9623i	0.195803	+	1.23625i
$346$		0			0
$347$	−28.4326	+	9.23832i	−1.52634	+	0.495939i	−0.947570	−	0.319550i	$-0.896468\pi$
$347$	−28.4326	+	9.23832i	−1.52634	+	0.495939i	−0.578773	+	0.815488i	$0.696468\pi$
$348$		0			0
$349$	3.50597	−	22.1358i	0.187670	−	1.18490i	−0.696437	−	0.717618i	$-0.745232\pi$
$349$	3.50597	−	22.1358i	0.187670	−	1.18490i	0.884107	−	0.467285i	$-0.154768\pi$
$350$		0			0
$351$	7.28574	−	7.42888i	0.388884	−	0.396524i
$352$		0			0
$353$	−16.8588	+	16.8588i	−0.897304	+	0.897304i	−0.995197	−	0.0978926i	$-0.968790\pi$
$353$	−16.8588	+	16.8588i	−0.897304	+	0.897304i	0.0978926	+	0.995197i	$0.468790\pi$
$354$		0			0
$355$	0.733773	+	1.00995i	0.0389446	+	0.0536027i
$356$		0			0
$357$	4.29989	+	2.19090i	0.227574	+	0.115955i
$358$		0			0
$359$	−2.27868	+	0.360908i	−0.120264	+	0.0190480i	−0.216276	−	0.976332i	$-0.569391\pi$
$359$	−2.27868	+	0.360908i	−0.120264	+	0.0190480i	0.0960122	+	0.995380i	$0.469391\pi$
$360$		0			0
$361$	46.9645	+	15.2597i	2.47181	+	0.803141i
$362$		0			0
$363$	14.2414	−	25.5808i	0.747478	−	1.34265i
$364$		0			0
$365$	−16.8902	−	5.48795i	−0.884073	−	0.287253i
$366$		0			0
$367$	29.4751	+	21.4149i	1.53859	+	1.11785i	0.951214	+	0.308531i	$0.0998373\pi$
$367$	29.4751	+	21.4149i	1.53859	+	1.11785i	0.587372	+	0.809317i	$0.300163\pi$
$368$		0			0
$369$	19.1573	−	37.5983i	0.997290	−	1.95729i
$370$		0			0
$371$	2.32015	−	14.6489i	0.120456	−	0.760531i
$372$		0			0
$373$			1.21327i			0.0628210i	0.999507	+	0.0314105i	$0.00999991\pi$
$373$			1.21327i			0.0628210i	−0.999507	+	0.0314105i	$0.990000\pi$
$374$		0			0
$375$	−22.5312	−	22.5312i	−1.16351	−	1.16351i
$376$		0			0
$377$	−16.3906	−	2.43283i	−0.844161	−	0.125297i
$378$		0			0
$379$	−24.0377	−	12.2478i	−1.23474	−	0.629129i	−0.290020	−	0.957021i	$-0.593662\pi$
$379$	−24.0377	−	12.2478i	−1.23474	−	0.629129i	−0.944715	+	0.327891i	$0.893662\pi$
$380$		0			0
$381$	20.4585	+	14.8640i	1.04812	+	0.761505i
$382$		0			0
$383$	−5.30830	−	10.4181i	−0.271241	−	0.532341i	0.714700	−	0.699431i	$-0.246563\pi$
$383$	−5.30830	−	10.4181i	−0.271241	−	0.532341i	−0.985942	+	0.167090i	$0.946563\pi$
$384$		0			0
$385$	−20.7737	−	2.01959i	−1.05872	−	0.102928i
$386$		0			0
$387$	−10.4381	+	32.1252i	−0.530599	+	1.63302i
$388$		0			0
$389$	17.3757	−	23.9156i	0.880983	−	1.21257i	−0.0951646	−	0.995462i	$-0.530338\pi$
$389$	17.3757	−	23.9156i	0.880983	−	1.21257i	0.976148	−	0.217108i	$-0.0696623\pi$
$390$		0			0
$391$	−2.39345	+	0.777679i	−0.121042	+	0.0393289i
$392$		0			0
$393$	−7.58077	−	10.4340i	−0.382399	−	0.526328i
$394$		0			0
$395$	6.19359	+	6.19359i	0.311633	+	0.311633i
$396$		0			0
$397$	2.17359	+	2.17359i	0.109089	+	0.109089i	0.759545	−	0.650455i	$-0.225422\pi$
$397$	2.17359	+	2.17359i	0.109089	+	0.109089i	−0.650455	+	0.759545i	$0.725422\pi$
$398$		0			0
$399$	−68.6968	+	49.9112i	−3.43914	+	2.49868i
$400$		0			0
$401$	4.93708	−	9.68956i	0.246546	−	0.483873i	−0.734258	−	0.678871i	$-0.762470\pi$
$401$	4.93708	−	9.68956i	0.246546	−	0.483873i	0.980804	+	0.194997i	$0.0624698\pi$
$402$		0			0
$403$	4.47127	−	6.28177i	0.222730	−	0.312917i
$404$		0			0
$405$	3.38539	+	6.64421i	0.168222	+	0.330153i
$406$		0			0
$407$	12.3409	+	31.4140i	0.611716	+	1.55714i
$408$		0			0
$409$	3.98101	−	2.02843i	0.196848	−	0.100299i	−0.352788	−	0.935703i	$-0.614766\pi$
$409$	3.98101	−	2.02843i	0.196848	−	0.100299i	0.549636	+	0.835404i	$0.314766\pi$
$410$		0			0
$411$	7.24452	+	45.7401i	0.357346	+	2.25619i
$412$		0			0
$413$	−14.0071	−	43.1093i	−0.689243	−	2.12127i
$414$		0			0
$415$	−3.75949	+	2.73143i	−0.184546	+	0.134081i
$416$		0			0
$417$			5.21317i			0.255290i
$418$		0			0
$419$	−14.2235			−0.694862			−0.347431	−	0.937705i	$-0.612946\pi$
$419$	−14.2235			−0.694862			−0.347431	+	0.937705i	$0.612946\pi$
$420$		0			0
$421$	1.64063	−	10.3585i	0.0799593	−	0.504843i	−0.914909	−	0.403661i	$-0.867738\pi$
$421$	1.64063	−	10.3585i	0.0799593	−	0.504843i	0.994868	−	0.101182i	$-0.0322625\pi$
$422$		0			0
$423$	−17.6726	+	34.6845i	−0.859272	+	1.68642i
$424$		0			0
$425$	0.646209	−	0.889431i	0.0313458	−	0.0431437i
$426$		0			0
$427$	20.2452	−	10.3154i	0.979733	−	0.499199i
$428$		0			0
$429$	−30.8836	−	7.69755i	−1.49107	−	0.371641i
$430$		0			0
$431$	10.4344	−	5.31657i	0.502605	−	0.256090i	−0.184257	−	0.982878i	$-0.558988\pi$
$431$	10.4344	−	5.31657i	0.502605	−	0.256090i	0.686862	+	0.726788i	$0.258988\pi$
$432$		0			0
$433$	−11.1260	+	15.3137i	−0.534683	+	0.735928i	−0.987835	−	0.155505i	$-0.950299\pi$
$433$	−11.1260	+	15.3137i	−0.534683	+	0.735928i	0.453152	+	0.891433i	$0.350299\pi$
$434$		0			0
$435$	−9.05831	+	17.7779i	−0.434313	+	0.852386i
$436$		0			0
$437$	6.92713	−	43.7362i	0.331369	−	2.09218i
$438$		0			0
$439$	−29.5111			−1.40849			−0.704243	−	0.709959i	$-0.748714\pi$
$439$	−29.5111			−1.40849			−0.704243	+	0.709959i	$0.748714\pi$
$440$		0			0
$441$		−	32.2012i		−	1.53339i
$442$		0			0
$443$	21.6354	−	15.7190i	1.02793	−	0.746833i	0.0600341	−	0.998196i	$-0.480879\pi$
$443$	21.6354	−	15.7190i	1.02793	−	0.746833i	0.967893	+	0.251364i	$0.0808791\pi$
$444$		0			0
$445$	2.68583	+	8.26613i	0.127320	+	0.391852i
$446$		0			0
$447$	5.08152	+	32.0834i	0.240348	+	1.51749i
$448$		0			0
$449$	−37.3879	+	19.0501i	−1.76444	+	0.899030i	−0.818631	+	0.574320i	$0.805267\pi$
$449$	−37.3879	+	19.0501i	−1.76444	+	0.899030i	−0.945814	+	0.324710i	$0.894733\pi$
$450$		0			0
$451$	−34.2045	+	2.06041i	−1.61063	+	0.0970210i
$452$		0			0
$453$	−10.4550	−	20.5190i	−0.491217	−	0.964067i
$454$		0			0
$455$	3.76729	+	22.3749i	0.176613	+	1.04895i
$456$		0			0
$457$	1.17919	−	2.31430i	0.0551604	−	0.108258i	−0.861781	−	0.507281i	$-0.830651\pi$
$457$	1.17919	−	2.31430i	0.0551604	−	0.108258i	0.916941	+	0.399023i	$0.130651\pi$
$458$		0			0
$459$	1.09725	−	0.797200i	0.0512153	−	0.0372101i
$460$		0			0
$461$	−23.2922	−	23.2922i	−1.08483	−	1.08483i	−0.996052	−	0.0887757i	$-0.971705\pi$
$461$	−23.2922	−	23.2922i	−1.08483	−	1.08483i	−0.0887757	−	0.996052i	$-0.528295\pi$
$462$		0			0
$463$	9.56333	+	9.56333i	0.444446	+	0.444446i	0.893503	−	0.449057i	$-0.148240\pi$
$463$	9.56333	+	9.56333i	0.444446	+	0.444446i	−0.449057	+	0.893503i	$0.648240\pi$
$464$		0			0
$465$	−5.45730	−	7.51132i	−0.253076	−	0.348329i
$466$		0			0
$467$	−14.6868	+	4.77203i	−0.679623	+	0.220823i	−0.628431	−	0.777866i	$-0.716302\pi$
$467$	−14.6868	+	4.77203i	−0.679623	+	0.220823i	−0.0511930	+	0.998689i	$0.516302\pi$
$468$		0			0
$469$	17.5214	−	24.1161i	0.809063	−	1.11358i
$470$		0			0
$471$	−10.3806	+	31.9483i	−0.478314	+	1.47210i
$472$		0			0
$473$	26.7850	−	5.91221i	1.23158	−	0.271844i
$474$		0			0
$475$	8.78222	+	17.2361i	0.402956	+	0.790846i
$476$		0			0
$477$	−12.7026	−	9.22898i	−0.581612	−	0.422566i
$478$		0			0
$479$	10.6722	+	5.43774i	0.487624	+	0.248457i	0.680475	−	0.732771i	$-0.261773\pi$
$479$	10.6722	+	5.43774i	0.487624	+	0.248457i	−0.192851	+	0.981228i	$0.561773\pi$
$480$		0			0
$481$	29.4728	−	21.8544i	1.34384	−	0.996473i
$482$		0			0
$483$	38.8819	+	38.8819i	1.76919	+	1.76919i
$484$		0			0
$485$			17.5140i			0.795268i
$486$		0			0
$487$	3.87988	−	24.4966i	0.175814	−	1.11005i	−0.729086	−	0.684422i	$-0.760054\pi$
$487$	3.87988	−	24.4966i	0.175814	−	1.11005i	0.904900	−	0.425624i	$-0.139946\pi$
$488$		0			0
$489$	−8.96501	+	17.5948i	−0.405412	+	0.795665i
$490$		0			0
$491$	10.5321	+	7.65198i	0.475305	+	0.345329i	0.799505	−	0.600659i	$-0.205095\pi$
$491$	10.5321	+	7.65198i	0.475305	+	0.345329i	−0.324200	+	0.945988i	$0.605095\pi$
$492$		0			0
$493$	−2.05413	−	0.667428i	−0.0925135	−	0.0300594i
$494$		0			0
$495$	−11.8892	+	18.6243i	−0.534378	+	0.837102i
$496$		0			0
$497$	2.80812	+	0.912413i	0.125961	+	0.0409273i
$498$		0			0
$499$	0.992297	−	0.157164i	0.0444213	−	0.00703565i	−0.134184	−	0.990956i	$-0.542841\pi$
$499$	0.992297	−	0.157164i	0.0444213	−	0.00703565i	0.178606	+	0.983921i	$0.442841\pi$
$500$		0			0
$501$	6.07103	+	3.09335i	0.271234	+	0.138200i
$502$		0			0
$503$	−6.92064	−	9.52544i	−0.308576	−	0.424719i	0.626360	−	0.779534i	$-0.284544\pi$
$503$	−6.92064	−	9.52544i	−0.308576	−	0.424719i	−0.934937	+	0.354815i	$0.884544\pi$
$504$		0			0
$505$	−14.7930	+	14.7930i	−0.658280	+	0.658280i
$506$		0			0
$507$	0.673102	+	34.5946i	0.0298935	+	1.53640i
$508$		0			0
$509$	−2.09115	+	13.2030i	−0.0926887	+	0.585213i	0.897006	+	0.442019i	$0.145738\pi$
$509$	−2.09115	+	13.2030i	−0.0926887	+	0.585213i	−0.989695	+	0.143195i	$0.954262\pi$
$510$		0			0
$511$	−39.9485	+	12.9801i	−1.76722	+	0.574204i
$512$		0			0
$513$	3.73323	+	23.5707i	0.164826	+	1.04067i
$514$		0			0
$515$	15.1791	−	7.73413i	0.668870	−	0.340806i
$516$		0			0
$517$	31.5537	−	1.90073i	1.38773	−	0.0835940i
$518$		0			0
$519$	6.00078	−	18.4685i	0.263405	−	0.810678i
$520$		0			0
$521$	−9.31913	−	6.77075i	−0.408279	−	0.296632i	0.364626	−	0.931154i	$-0.381197\pi$
$521$	−9.31913	−	6.77075i	−0.408279	−	0.296632i	−0.772905	+	0.634522i	$0.781197\pi$
$522$		0			0
$523$	−24.6317	+	8.00333i	−1.07707	+	0.349961i	−0.793237	−	0.608912i	$-0.791606\pi$
$523$	−24.6317	+	8.00333i	−1.07707	+	0.349961i	−0.283833	+	0.958874i	$0.591606\pi$
$524$		0			0
$525$	−23.7257	−	3.75778i	−1.03547	−	0.164003i
$526$		0			0
$527$	0.710666	−	0.710666i	0.0309571	−	0.0309571i
$528$		0			0
$529$	−5.67503			−0.246740
$530$		0			0
$531$	−47.3954	−	7.50669i	−2.05678	−	0.325763i
$532$		0			0
$533$	11.8555	+	35.3148i	0.513517	+	1.52965i
$534$		0			0
$535$	3.92020	+	24.7512i	0.169485	+	1.07009i
$536$		0			0
$537$	10.1197	+	3.28809i	0.436697	+	0.141891i
$538$		0			0
$539$	−22.5429	+	13.2508i	−0.970992	+	0.570753i
$540$		0			0
$541$	−6.41721	−	12.5945i	−0.275898	−	0.541479i	0.710929	−	0.703264i	$-0.248275\pi$
$541$	−6.41721	−	12.5945i	−0.275898	−	0.541479i	−0.986826	+	0.161785i	$0.948275\pi$
$542$		0			0
$543$	5.40014	−	7.43266i	0.231742	−	0.318966i
$544$		0			0
$545$	−2.25545	−	6.94157i	−0.0966130	−	0.297344i
$546$		0			0
$547$	−20.9508	−	28.8364i	−0.895793	−	1.23295i	−0.971791	−	0.235846i	$-0.924214\pi$
$547$	−20.9508	−	28.8364i	−0.895793	−	1.23295i	0.0759973	−	0.997108i	$-0.475786\pi$
$548$		0			0
$549$		−	24.0543i		−	1.02661i
$550$		0			0
$551$	26.8726	−	26.8726i	1.14481	−	1.14481i
$552$		0			0
$553$	20.4618	+	3.24083i	0.870123	+	0.137814i
$554$		0			0
$555$	−13.6527	−	42.0187i	−0.579525	−	1.78359i
$556$		0			0
$557$	−17.8594	+	2.82865i	−0.756728	+	0.119854i	−0.522865	−	0.852416i	$-0.675137\pi$
$557$	−17.8594	+	2.82865i	−0.756728	+	0.119854i	−0.233863	+	0.972270i	$0.575137\pi$
$558$		0			0
$559$	−13.7955	−	26.4362i	−0.583486	−	1.11813i
$560$		0			0
$561$	−3.80306	−	1.65779i	−0.160565	−	0.0699918i
$562$		0			0
$563$	−1.88881	+	5.81317i	−0.0796039	+	0.244996i	−0.982937	−	0.183945i	$-0.941113\pi$
$563$	−1.88881	+	5.81317i	−0.0796039	+	0.244996i	0.903333	+	0.428941i	$0.141113\pi$
$564$		0			0
$565$	17.2027	−	2.72463i	0.723721	−	0.114626i
$566$		0			0
$567$	15.7148	+	8.00710i	0.659960	+	0.336267i
$568$		0			0
$569$	−14.6429	+	10.6387i	−0.613860	+	0.445996i	−0.850772	−	0.525536i	$-0.823865\pi$
$569$	−14.6429	+	10.6387i	−0.613860	+	0.445996i	0.236911	+	0.971531i	$0.423865\pi$
$570$		0			0
$571$	−21.1995			−0.887170			−0.443585	−	0.896232i	$-0.646293\pi$
$571$	−21.1995			−0.887170			−0.443585	+	0.896232i	$0.646293\pi$
$572$		0			0
$573$	−6.42038			−0.268215
$574$		0			0
$575$	10.1344	−	7.36308i	0.422634	−	0.307062i
$576$		0			0
$577$	31.0910	+	15.8416i	1.29433	+	0.659496i	0.959214	−	0.282679i	$-0.0912232\pi$
$577$	31.0910	+	15.8416i	1.29433	+	0.659496i	0.335120	+	0.942176i	$0.391223\pi$
$578$		0			0
$579$	19.3953	−	3.07191i	0.806040	−	0.127664i
$580$		0			0
$581$	−3.39641	+	10.4531i	−0.140907	+	0.433666i
$582$		0			0
$583$	−1.23375	+	12.6904i	−0.0510965	+	0.525582i
$584$		0			0
$585$	22.9160	+	7.20018i	0.947460	+	0.297691i
$586$		0			0
$587$	24.6174	−	3.89902i	1.01607	−	0.160930i	0.373881	−	0.927477i	$-0.378027\pi$
$587$	24.6174	−	3.89902i	1.01607	−	0.160930i	0.642188	+	0.766547i	$0.278027\pi$
$588$		0			0
$589$	5.46469	+	16.8186i	0.225169	+	0.692998i
$590$		0			0
$591$	43.8430	+	6.94404i	1.80346	+	0.285640i
$592$		0			0
$593$	−2.36983	+	2.36983i	−0.0973174	+	0.0973174i	−0.754089	−	0.656772i	$-0.771921\pi$
$593$	−2.36983	+	2.36983i	−0.0973174	+	0.0973174i	0.656772	+	0.754089i	$0.271921\pi$
$594$		0			0
$595$			2.95750i			0.121246i
$596$		0			0
$597$	−32.6524	−	44.9422i	−1.33637	−	1.83936i
$598$		0			0
$599$	8.02104	+	24.6862i	0.327731	+	1.00865i	0.970193	+	0.242334i	$0.0779129\pi$
$599$	8.02104	+	24.6862i	0.327731	+	1.00865i	−0.642462	+	0.766317i	$0.722087\pi$
$600$		0			0
$601$	−13.4829	+	18.5576i	−0.549978	+	0.756979i	−0.990009	−	0.141003i	$-0.954967\pi$
$601$	−13.4829	+	18.5576i	−0.549978	+	0.756979i	0.440032	+	0.897982i	$0.354967\pi$
$602$		0			0
$603$	−14.3268	−	28.1179i	−0.583431	−	1.14505i
$604$		0			0
$605$	17.9307	+	0.659233i	0.728985	+	0.0268016i
$606$		0			0
$607$	−35.6702	−	11.5899i	−1.44781	−	0.470421i	−0.523486	−	0.852035i	$-0.675369\pi$
$607$	−35.6702	−	11.5899i	−1.44781	−	0.470421i	−0.924322	+	0.381613i	$0.875369\pi$
$608$		0			0
$609$	7.38242	+	46.6108i	0.299151	+	1.88876i
$610$		0			0
$611$	−10.9367	−	32.5779i	−0.442450	−	1.31796i
$612$		0			0
$613$	21.5916	+	3.41977i	0.872076	+	0.138123i	0.576403	−	0.817166i	$-0.304456\pi$
$613$	21.5916	+	3.41977i	0.872076	+	0.138123i	0.295674	+	0.955289i	$0.404456\pi$
$614$		0			0
$615$	44.8557			1.80876
$616$		0			0
$617$	17.3778	−	17.3778i	0.699604	−	0.699604i	−0.264721	−	0.964325i	$-0.585280\pi$
$617$	17.3778	−	17.3778i	0.699604	−	0.699604i	0.964325	+	0.264721i	$0.0852798\pi$
$618$		0			0
$619$	3.83135	+	0.606827i	0.153995	+	0.0243904i	0.232956	−	0.972487i	$-0.425160\pi$
$619$	3.83135	+	0.606827i	0.153995	+	0.0243904i	−0.0789609	+	0.996878i	$0.525160\pi$
$620$		0			0
$621$	14.6974	−	4.77548i	0.589787	−	0.191633i
$622$		0			0
$623$	16.6310	+	12.0832i	0.666309	+	0.484102i
$624$		0			0
$625$	2.41992	−	7.44775i	0.0967969	−	0.297910i
$626$		0			0
$627$	56.3700	−	46.3807i	2.25120	−	1.85227i
$628$		0			0
$629$	4.26127	−	2.17123i	0.169908	−	0.0865724i
$630$		0			0
$631$	1.09603	+	6.92004i	0.0436321	+	0.275482i	0.999853	−	0.0171646i	$-0.00546393\pi$
$631$	1.09603	+	6.92004i	0.0436321	+	0.275482i	−0.956221	+	0.292647i	$0.905464\pi$
$632$		0			0
$633$	5.37918	−	1.74780i	0.213803	−	0.0694689i
$634$		0			0
$635$	−2.42437	+	15.3069i	−0.0962081	+	0.607434i
$636$		0			0
$637$	20.2954	+	19.9044i	0.804134	+	0.788640i
$638$		0			0
$639$	2.21027	−	2.21027i	0.0874370	−	0.0874370i
$640$		0			0
$641$	5.28776	+	7.27798i	0.208854	+	0.287463i	0.900574	−	0.434703i	$-0.143147\pi$
$641$	5.28776	+	7.27798i	0.208854	+	0.287463i	−0.691720	+	0.722166i	$0.743147\pi$
$642$		0			0
$643$	−7.67285	−	3.90951i	−0.302588	−	0.154176i	0.296104	−	0.955156i	$-0.404312\pi$
$643$	−7.67285	−	3.90951i	−0.302588	−	0.154176i	−0.598692	+	0.800980i	$0.704312\pi$
$644$		0			0
$645$	−35.4641	+	5.61697i	−1.39640	+	0.221168i
$646$		0			0
$647$	−4.63166	−	1.50492i	−0.182089	−	0.0591644i	0.216553	−	0.976271i	$-0.430519\pi$
$647$	−4.63166	−	1.50492i	−0.182089	−	0.0591644i	−0.398642	+	0.917106i	$0.630519\pi$
$648$		0			0
$649$	14.2481	+	36.2689i	0.559287	+	1.42368i
$650$		0			0
$651$	−20.8848	−	6.78590i	−0.818541	−	0.265960i
$652$		0			0
$653$	−34.9671	−	25.4051i	−1.36837	−	0.994179i	−0.997862	−	0.0653496i	$-0.979184\pi$
$653$	−34.9671	−	25.4051i	−1.36837	−	0.994179i	−0.370508	−	0.928829i	$-0.620816\pi$
$654$		0			0
$655$	3.58832	−	7.04247i	0.140207	−	0.275172i
$656$		0			0
$657$	−6.95629	+	43.9203i	−0.271391	+	1.71349i
$658$		0			0
$659$		−	11.2662i		−	0.438867i	−0.975627	−	0.219434i	$-0.929579\pi$
$659$		−	11.2662i		−	0.438867i	0.975627	−	0.219434i	$-0.0704209\pi$
$660$		0			0
$661$	8.28819	+	8.28819i	0.322373	+	0.322373i	0.849677	−	0.527304i	$-0.176797\pi$
$661$	8.28819	+	8.28819i	0.322373	+	0.322373i	−0.527304	+	0.849677i	$0.676797\pi$
$662$		0			0
$663$	−0.662170	+	4.46121i	−0.0257166	+	0.173259i
$664$		0			0
$665$	−46.3670	−	23.6252i	−1.79804	−	0.916145i
$666$		0			0
$667$	−19.9097	−	14.4653i	−0.770908	−	0.560098i
$668$		0			0
$669$	−6.01987	−	11.8147i	−0.232742	−	0.456781i
$670$		0			0
$671$	−16.8395	+	9.89836i	−0.650083	+	0.382122i
$672$		0			0
$673$	5.67946	−	17.4796i	0.218927	−	0.673789i	−0.779924	−	0.625874i	$-0.784742\pi$
$673$	5.67946	−	17.4796i	0.218927	−	0.673789i	0.998851	−	0.0479147i	$-0.0152576\pi$
$674$		0			0
$675$	−3.96817	+	5.46172i	−0.152735	+	0.210222i
$676$		0			0
$677$	−16.8060	+	5.46061i	−0.645908	+	0.209868i	−0.613609	−	0.789610i	$-0.710283\pi$
$677$	−16.8060	+	5.46061i	−0.645908	+	0.209868i	−0.0322989	+	0.999478i	$0.510283\pi$
$678$		0			0
$679$	24.3483	+	33.5126i	0.934402	+	1.28609i
$680$		0			0
$681$	−32.9056	−	32.9056i	−1.26095	−	1.26095i
$682$		0			0
$683$	−34.0121	−	34.0121i	−1.30144	−	1.30144i	−0.927423	−	0.374015i	$-0.877981\pi$
$683$	−34.0121	−	34.0121i	−1.30144	−	1.30144i	−0.374015	−	0.927423i	$-0.622019\pi$
$684$		0			0
$685$	−22.9606	+	16.6819i	−0.877281	+	0.637382i
$686$		0			0
$687$	1.55886	−	3.05944i	0.0594742	−	0.116725i
$688$		0			0
$689$	13.6686	−	2.30139i	0.520730	−	0.0876761i
$690$		0			0
$691$	14.9471	+	29.3352i	0.568613	+	1.11597i	0.978963	+	0.204037i	$0.0654064\pi$
$691$	14.9471	+	29.3352i	0.568613	+	1.11597i	−0.410350	+	0.911928i	$0.634594\pi$
$692$		0			0
$693$	3.14236	+	52.1659i	0.119369	+	1.98162i
$694$		0			0
$695$	−2.84663	+	1.45043i	−0.107979	+	0.0550181i
$696$		0			0
$697$	0.759578	+	4.79579i	0.0287711	+	0.181653i
$698$		0			0
$699$	3.39783	+	10.4574i	0.128518	+	0.395537i
$700$		0			0
$701$	−4.11570	+	2.99023i	−0.155448	+	0.112939i	−0.662790	−	0.748805i	$-0.730628\pi$
$701$	−4.11570	+	2.99023i	−0.155448	+	0.112939i	0.507342	+	0.861745i	$0.330628\pi$
$702$		0			0
$703$			84.1514i			3.17383i
$704$		0			0
$705$	−41.3794			−1.55844
$706$		0			0
$707$	−7.74051	+	48.8717i	−0.291112	+	1.83801i
$708$		0			0
$709$	−16.3766	+	32.1410i	−0.615038	+	1.20708i	0.347945	+	0.937515i	$0.386880\pi$
$709$	−16.3766	+	32.1410i	−0.615038	+	1.20708i	−0.962982	+	0.269564i	$0.913120\pi$
$710$		0			0
$711$	12.8912	−	17.7432i	0.483458	−	0.665423i
$712$		0			0
$713$	10.2035	−	5.19892i	0.382123	−	0.194701i
$714$		0			0
$715$	−4.38937	−	19.0056i	−0.164153	−	0.710768i
$716$		0			0
$717$	−39.0828	+	19.9137i	−1.45958	+	0.743691i
$718$		0			0
$719$	7.15004	−	9.84118i	0.266651	−	0.367014i	−0.654604	−	0.755972i	$-0.727165\pi$
$719$	7.15004	−	9.84118i	0.266651	−	0.367014i	0.921256	+	0.388958i	$0.127165\pi$
$720$		0			0
$721$	18.2927	−	35.9014i	0.681255	−	1.33704i
$722$		0			0
$723$	7.98480	−	50.4140i	0.296958	−	1.87492i
$724$		0			0
$725$	10.7509			0.399278
$726$		0			0
$727$		−	27.3781i		−	1.01540i	−0.861535	−	0.507698i	$-0.830497\pi$
$727$		−	27.3781i		−	1.01540i	0.861535	−	0.507698i	$-0.169503\pi$
$728$		0			0
$729$	33.7483	−	24.5196i	1.24994	−	0.908132i
$730$		0			0
$731$	−1.20108	−	3.69656i	−0.0444237	−	0.136722i
$732$		0			0
$733$	0.557121	+	3.51752i	0.0205777	+	0.129923i	0.995839	−	0.0911344i	$-0.0290493\pi$
$733$	0.557121	+	3.51752i	0.0205777	+	0.129923i	−0.975261	+	0.221057i	$0.929049\pi$
$734$		0			0
$735$	30.4988	−	15.5399i	1.12496	−	0.573198i
$736$		0			0
$737$	−13.7888	+	21.6002i	−0.507918	+	0.795653i
$738$		0			0
$739$	−16.7434	−	32.8608i	−0.615916	−	1.20880i	−0.962627	−	0.270831i	$-0.912702\pi$
$739$	−16.7434	−	32.8608i	−0.615916	−	1.20880i	0.346711	−	0.937972i	$-0.387298\pi$
$740$		0			0
$741$	−64.6522	−	46.0185i	−2.37506	−	1.69053i
$742$		0			0
$743$	−18.7576	+	36.8139i	−0.688150	+	1.35057i	0.237202	+	0.971460i	$0.423770\pi$
$743$	−18.7576	+	36.8139i	−0.688150	+	1.35057i	−0.925352	+	0.379109i	$0.876230\pi$
$744$		0			0
$745$	−16.1053	+	11.7012i	−0.590051	+	0.428697i
$746$		0			0
$747$	8.22760	+	8.22760i	0.301032	+	0.301032i
$748$		0			0
$749$	41.9109	+	41.9109i	1.53139	+	1.53139i
$750$		0			0
$751$	6.69406	+	9.21358i	0.244270	+	0.336208i	0.913494	−	0.406852i	$-0.133374\pi$
$751$	6.69406	+	9.21358i	0.244270	+	0.336208i	−0.669224	+	0.743060i	$0.733374\pi$
$752$		0			0
$753$	61.2558	−	19.9032i	2.23228	−	0.725313i
$754$		0			0
$755$	8.29552	−	11.4178i	0.301905	−	0.415536i
$756$		0			0
$757$	−16.3598	+	50.3502i	−0.594606	+	1.83001i	−0.0379256	+	0.999281i	$0.512075\pi$
$757$	−16.3598	+	50.3502i	−0.594606	+	1.83001i	−0.556680	+	0.830727i	$0.687925\pi$
$758$		0			0
$759$	−35.3751	−	31.3554i	−1.28403	−	1.13813i
$760$		0			0
$761$	−9.86626	−	19.3636i	−0.357652	−	0.701931i	0.640147	−	0.768253i	$-0.278874\pi$
$761$	−9.86626	−	19.3636i	−0.357652	−	0.701931i	−0.997798	+	0.0663220i	$0.978874\pi$
$762$		0			0
$763$	−13.9661	−	10.1470i	−0.505607	−	0.367345i
$764$		0			0
$765$	2.78970	+	1.42142i	0.100862	+	0.0513917i
$766$		0			0
$767$	34.0276	−	25.2318i	1.22866	−	0.911067i
$768$		0			0
$769$	−19.6918	−	19.6918i	−0.710106	−	0.710106i	0.256451	−	0.966557i	$-0.417447\pi$
$769$	−19.6918	−	19.6918i	−0.710106	−	0.710106i	−0.966557	+	0.256451i	$0.917447\pi$
$770$		0			0
$771$		−	5.81993i		−	0.209600i
$772$		0			0
$773$	−0.777232	+	4.90725i	−0.0279551	+	0.176501i	−0.997715	−	0.0675580i	$-0.978479\pi$
$773$	−0.777232	+	4.90725i	−0.0279551	+	0.176501i	0.969760	+	0.244059i	$0.0784792\pi$
$774$		0			0
$775$	−2.27117	+	4.45743i	−0.0815829	+	0.160116i
$776$		0			0
$777$	−84.5396	−	61.4216i	−3.03284	−	2.20349i
$778$		0			0
$779$	−81.2548	−	26.4013i	−2.91126	−	0.945924i
$780$		0			0
$781$	−2.45686	−	0.637803i	−0.0879134	−	0.0228224i
$782$		0			0
$783$	12.6138	+	4.09847i	0.450780	+	0.146467i
$784$		0			0
$785$	−20.3334	+	3.22050i	−0.725731	+	0.114944i
$786$		0			0
$787$	17.4589	+	8.89576i	0.622343	+	0.317100i	0.736576	−	0.676354i	$-0.236441\pi$
$787$	17.4589	+	8.89576i	0.622343	+	0.317100i	−0.114233	+	0.993454i	$0.536441\pi$
$788$		0			0
$789$	7.07012	+	9.73118i	0.251703	+	0.346439i
$790$		0			0
$791$	29.1291	−	29.1291i	1.03571	−	1.03571i
$792$		0			0
$793$	15.1607	+	14.8686i	0.538371	+	0.527998i
$794$		0			0
$795$	2.61094	−	16.4849i	0.0926007	−	0.584658i
$796$		0			0
$797$	1.71701	−	0.557891i	0.0608197	−	0.0197615i	−0.278449	−	0.960451i	$-0.589820\pi$
$797$	1.71701	−	0.557891i	0.0608197	−	0.0197615i	0.339269	+	0.940689i	$0.389820\pi$
$798$		0			0
$799$	−0.700710	−	4.42411i	−0.0247894	−	0.156514i
$800$		0			0
$801$	19.3907	−	9.88007i	0.685138	−	0.349095i
$802$		0			0
$803$	33.6096	−	13.2034i	1.18606	−	0.465938i
$804$		0			0
$805$	−10.4134	+	32.0492i	−0.367025	+	1.12959i
$806$		0			0
$807$	22.4099	+	16.2818i	0.788866	+	0.573145i
$808$		0			0
$809$	−51.1417	+	16.6169i	−1.79804	+	0.584220i	−0.999835	−	0.0181597i	$-0.994219\pi$
$809$	−51.1417	+	16.6169i	−1.79804	+	0.584220i	−0.798210	+	0.602380i	$0.794219\pi$
$810$		0			0
$811$	−10.5854	−	1.67656i	−0.371703	−	0.0588719i	−0.0322113	−	0.999481i	$-0.510255\pi$
$811$	−10.5854	−	1.67656i	−0.371703	−	0.0588719i	−0.339491	+	0.940609i	$0.610255\pi$
$812$		0			0
$813$	29.0349	−	29.0349i	1.01830	−	1.01830i
$814$		0			0
$815$	−12.1019			−0.423911
$816$		0			0
$817$	67.5483	+	10.6986i	2.36321	+	0.374296i
$818$		0			0
$819$	53.8591	−	18.0810i	1.88199	−	0.631800i
$820$		0			0
$821$	−4.20020	−	26.5190i	−0.146588	−	0.925521i	−0.945866	−	0.324559i	$-0.894784\pi$
$821$	−4.20020	−	26.5190i	−0.146588	−	0.925521i	0.799277	−	0.600962i	$-0.205216\pi$
$822$		0			0
$823$	−50.2424	−	16.3248i	−1.75134	−	0.569045i	−0.755096	−	0.655615i	$-0.772410\pi$
$823$	−50.2424	−	16.3248i	−1.75134	−	0.569045i	−0.996246	+	0.0865695i	$0.972410\pi$
$824$		0			0
$825$	20.5537	+	1.99821i	0.715588	+	0.0695687i
$826$		0			0
$827$	17.7145	+	34.7667i	0.615994	+	1.20896i	0.962595	+	0.270944i	$0.0873359\pi$
$827$	17.7145	+	34.7667i	0.615994	+	1.20896i	−0.346601	+	0.938013i	$0.612664\pi$
$828$		0			0
$829$	−1.95920	+	2.69660i	−0.0680457	+	0.0936568i	−0.841683	−	0.539971i	$-0.818435\pi$
$829$	−1.95920	+	2.69660i	−0.0680457	+	0.0936568i	0.773638	+	0.633628i	$0.218435\pi$
$830$		0			0
$831$	−2.54545	−	7.83410i	−0.0883008	−	0.271762i
$832$		0			0
$833$	2.17792	+	2.99765i	0.0754605	+	0.103862i
$834$		0			0
$835$			4.17572i			0.144507i
$836$		0			0
$837$	−4.36398	+	4.36398i	−0.150841	+	0.150841i
$838$		0			0
$839$	29.1693	+	4.61996i	1.00704	+	0.159499i	0.638098	−	0.769956i	$-0.279722\pi$
$839$	29.1693	+	4.61996i	1.00704	+	0.159499i	0.368938	+	0.929454i	$0.379722\pi$
$840$		0			0
$841$	2.43478	+	7.49348i	0.0839579	+	0.258396i
$842$		0			0
$843$	27.7621	−	4.39709i	0.956179	−	0.151444i
$844$		0			0
$845$	−18.7030	+	9.99263i	−0.643404	+	0.343757i
$846$		0			0
$847$	35.2264	−	23.6662i	1.21039	−	0.813180i
$848$		0			0
$849$	9.79381	−	30.1423i	0.336123	−	1.03448i
$850$		0			0
$851$	53.8225	−	8.52465i	1.84501	−	0.292221i
$852$		0			0
$853$	7.63064	+	3.88800i	0.261268	+	0.133123i	0.579719	−	0.814817i	$-0.303162\pi$
$853$	7.63064	+	3.88800i	0.261268	+	0.133123i	−0.318451	+	0.947939i	$0.603162\pi$
$854$		0			0
$855$	−44.5694	+	32.3816i	−1.52424	+	1.10743i
$856$		0			0
$857$	−1.32693			−0.0453271			−0.0226635	−	0.999743i	$-0.507215\pi$
$857$	−1.32693			−0.0453271			−0.0226635	+	0.999743i	$0.507215\pi$
$858$		0			0
$859$	6.97764			0.238074			0.119037	−	0.992890i	$-0.462019\pi$
$859$	6.97764			0.238074			0.119037	+	0.992890i	$0.462019\pi$
$860$		0			0
$861$	85.8305	−	62.3595i	2.92510	−	2.12521i
$862$		0			0
$863$	6.49475	+	3.30924i	0.221084	+	0.112648i	0.561025	−	0.827799i	$-0.310407\pi$
$863$	6.49475	+	3.30924i	0.221084	+	0.112648i	−0.339941	+	0.940447i	$0.610407\pi$
$864$		0			0
$865$	11.7542	−	1.86169i	0.399656	−	0.0632994i
$866$		0			0
$867$	13.8006	−	42.4740i	0.468694	−	1.44249i
$868$		0			0
$869$	−17.7261	−	1.72332i	−0.601318	−	0.0584595i
$870$		0			0
$871$	26.5776	+	8.35065i	0.900547	+	0.282951i
$872$		0			0
$873$	43.3133	−	6.86015i	1.46593	−	0.232181i
$874$		0			0
$875$	−14.2724	−	43.9260i	−0.482496	−	1.48497i
$876$		0			0
$877$	32.9035	+	5.21140i	1.11107	+	0.175976i	0.684880	−	0.728656i	$-0.259855\pi$
$877$	32.9035	+	5.21140i	1.11107	+	0.175976i	0.426192	+	0.904633i	$0.359855\pi$
$878$		0			0
$879$	40.7170	−	40.7170i	1.37335	−	1.37335i
$880$		0			0
$881$			27.4744i			0.925637i	0.886453	+	0.462819i	$0.153162\pi$
$881$			27.4744i			0.925637i	−0.886453	+	0.462819i	$0.846838\pi$
$882$		0			0
$883$	30.6065	+	42.1263i	1.02999	+	1.41766i	0.904953	+	0.425511i	$0.139906\pi$
$883$	30.6065	+	42.1263i	1.02999	+	1.41766i	0.125039	+	0.992152i	$0.460094\pi$
$884$		0			0
$885$	−15.7626	−	48.5124i	−0.529855	−	1.63073i
$886$		0			0
$887$	15.0064	−	20.6546i	0.503867	−	0.693513i	−0.479003	−	0.877813i	$-0.659002\pi$
$887$	15.0064	−	20.6546i	0.503867	−	0.693513i	0.982870	+	0.184300i	$0.0590017\pi$
$888$		0			0
$889$	16.6410	+	32.6597i	0.558120	+	1.09537i
$890$		0			0
$891$	−13.8991	−	6.05872i	−0.465636	−	0.202975i
$892$		0			0
$893$	74.9576	+	24.3552i	2.50836	+	0.815015i
$894$		0			0
$895$	1.02010	+	6.44066i	0.0340982	+	0.215287i
$896$		0			0
$897$	−22.8837	+	46.0128i	−0.764064	+	1.53632i
$898$		0			0
$899$	9.70713	+	1.53746i	0.323751	+	0.0512771i
$900$		0			0
$901$	1.80670			0.0601900
$902$		0			0
$903$	−60.0510	+	60.0510i	−1.99837	+	1.99837i
$904$		0			0
$905$	5.56104	+	0.880782i	0.184855	+	0.0292782i
$906$		0			0
$907$	−8.68138	+	2.82075i	−0.288261	+	0.0936616i	−0.449578	−	0.893241i	$-0.648426\pi$
$907$	−8.68138	+	2.82075i	−0.288261	+	0.0936616i	0.161318	+	0.986903i	$0.448426\pi$
$908$		0			0
$909$	42.3785	+	30.7898i	1.40561	+	1.02123i
$910$		0			0
$911$	−3.24323	+	9.98163i	−0.107453	+	0.330706i	−0.990298	−	0.138958i	$-0.955625\pi$
$911$	−3.24323	+	9.98163i	−0.107453	+	0.330706i	0.882845	+	0.469664i	$0.155625\pi$
$912$		0			0
$913$	2.37419	−	9.14553i	0.0785741	−	0.302673i
$914$		0			0
$915$	22.7826	−	11.6083i	0.753169	−	0.383759i
$916$		0			0
$917$	−2.92444	−	18.4642i	−0.0965735	−	0.609741i
$918$		0			0
$919$	28.6807	−	9.31894i	0.946090	−	0.307403i	0.204964	−	0.978769i	$-0.434292\pi$
$919$	28.6807	−	9.31894i	0.946090	−	0.307403i	0.741126	+	0.671366i	$0.234292\pi$
$920$		0			0
$921$	−3.70710	+	23.4057i	−0.122153	+	0.771243i
$922$		0			0
$923$	0.0268410	+	2.75929i	0.000883482	+	0.0908232i
$924$		0			0
$925$	−16.8332	+	16.8332i	−0.553471	+	0.553471i
$926$		0			0
$927$	−25.0727	−	34.5096i	−0.823494	−	1.13344i
$928$		0			0
$929$	−36.2858	−	18.4886i	−1.19050	−	0.606590i	−0.257434	−	0.966296i	$-0.582877\pi$
$929$	−36.2858	−	18.4886i	−1.19050	−	0.606590i	−0.933066	+	0.359706i	$0.882877\pi$
$930$		0			0
$931$	−64.3942	+	10.1990i	−2.11043	+	0.334260i
$932$		0			0
$933$	32.7223	+	10.6321i	1.07128	+	0.348080i
$934$		0			0
$935$	−0.152877	−	2.53789i	−0.00499962	−	0.0829978i
$936$		0			0
$937$	4.53405	+	1.47320i	0.148121	+	0.0481275i	0.382139	−	0.924105i	$-0.375187\pi$
$937$	4.53405	+	1.47320i	0.148121	+	0.0481275i	−0.234018	+	0.972232i	$0.575187\pi$
$938$		0			0
$939$	−12.5974	−	9.15258i	−0.411102	−	0.298683i
$940$		0			0
$941$	16.7625	−	32.8983i	0.546443	−	1.07246i	−0.438363	−	0.898798i	$-0.644442\pi$
$941$	16.7625	−	32.8983i	0.546443	−	1.07246i	0.984806	−	0.173657i	$-0.0555584\pi$
$942$		0			0
$943$	−8.65482	+	54.6444i	−0.281840	+	1.77947i
$944$		0			0
$945$		−	18.1611i		−	0.590781i
$946$		0			0
$947$	17.2039	+	17.2039i	0.559052	+	0.559052i	0.929038	−	0.369986i	$-0.120637\pi$
$947$	17.2039	+	17.2039i	0.559052	+	0.559052i	−0.369986	+	0.929038i	$0.620637\pi$
$948$		0			0
$949$	−23.3818	−	31.5326i	−0.759004	−	1.02359i
$950$		0			0
$951$	−33.4528	−	17.0451i	−1.08478	−	0.552724i
$952$		0			0
$953$	41.0707	+	29.8396i	1.33041	+	0.966601i	0.999739	+	0.0228550i	$0.00727562\pi$
$953$	41.0707	+	29.8396i	1.33041	+	0.966601i	0.330673	+	0.943745i	$0.392724\pi$
$954$		0			0
$955$	−1.78631	−	3.50583i	−0.0578036	−	0.113446i
$956$		0			0
$957$	−8.74436	−	39.6159i	−0.282665	−	1.28060i
$958$		0			0
$959$	−20.7432	+	63.8409i	−0.669832	+	2.06153i
$960$		0			0
$961$	15.5332	−	21.3797i	0.501072	−	0.689666i
$962$		0			0
$963$	59.6760	−	19.3899i	1.92303	−	0.624831i
$964$		0			0
$965$	7.07366	+	9.73605i	0.227709	+	0.313415i
$966$		0			0
$967$	−20.8205	−	20.8205i	−0.669541	−	0.669541i	0.288069	−	0.957610i	$-0.406987\pi$
$967$	−20.8205	−	20.8205i	−0.669541	−	0.669541i	−0.957610	+	0.288069i	$0.906987\pi$
$968$		0			0
$969$	−7.31421	−	7.31421i	−0.234966	−	0.234966i
$970$		0			0
$971$	−8.31755	+	6.04306i	−0.266923	+	0.193931i	−0.713194	−	0.700967i	$-0.752752\pi$
$971$	−8.31755	+	6.04306i	−0.266923	+	0.193931i	0.446271	+	0.894898i	$0.352752\pi$
$972$		0			0
$973$	−3.43055	+	6.73283i	−0.109978	+	0.215845i
$974$		0			0
$975$	−3.72740	−	22.1380i	−0.119372	−	0.708982i
$976$		0			0
$977$	−3.32690	−	6.52941i	−0.106437	−	0.208894i	0.831645	−	0.555308i	$-0.187399\pi$
$977$	−3.32690	−	6.52941i	−0.106437	−	0.208894i	−0.938082	+	0.346413i	$0.887399\pi$
$978$		0			0
$979$	−14.8960	−	9.50910i	−0.476078	−	0.303912i
$980$		0			0
$981$	−16.2836	+	8.29689i	−0.519894	+	0.264899i
$982$		0			0
$983$	−5.37248	−	33.9205i	−0.171356	−	1.08190i	−0.912057	−	0.410062i	$-0.865507\pi$
$983$	−5.37248	−	33.9205i	−0.171356	−	1.08190i	0.740702	−	0.671834i	$-0.234493\pi$
$984$		0			0
$985$	8.40643	+	25.8723i	0.267851	+	0.824361i
$986$		0			0
$987$	−79.1786	+	57.5266i	−2.52028	+	1.83109i
$988$		0			0
$989$		−	44.2871i		−	1.40825i
$990$		0			0
$991$	51.7759			1.64472			0.822358	−	0.568970i	$-0.192658\pi$
$991$	51.7759			1.64472			0.822358	+	0.568970i	$0.192658\pi$
$992$		0			0
$993$	−8.92029	+	56.3205i	−0.283077	+	1.78728i
$994$		0			0
$995$	15.4558	−	30.3338i	0.489983	−	0.961645i
$996$		0			0
$997$	−4.97077	+	6.84168i	−0.157426	+	0.216678i	−0.880443	−	0.474152i	$-0.842755\pi$
$997$	−4.97077	+	6.84168i	−0.157426	+	0.216678i	0.723017	+	0.690830i	$0.242755\pi$
$998$		0			0
$999$	−26.1671	+	13.3328i	−0.827891	+	0.421832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.13	✓	112
11.6	odd	10	inner	572.2.bh.a.369.13	yes	112
13.8	odd	4	inner	572.2.bh.a.541.13	yes	112
143.138	even	20	inner	572.2.bh.a.281.13	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.13	✓	112	1.1	even	1	trivial
572.2.bh.a.281.13	yes	112	143.138	even	20	inner
572.2.bh.a.369.13	yes	112	11.6	odd	10	inner
572.2.bh.a.541.13	yes	112	13.8	odd	4	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.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.15330 - 1.56447i) q^{3} +(1.45337 + 0.740531i) q^{5} +(3.81051 - 0.603525i) q^{7} +(1.26211 - 3.88437i) q^{9} +O(q^{10})\)	\(q+(2.15330 - 1.56447i) q^{3} +(1.45337 + 0.740531i) q^{5} +(3.81051 - 0.603525i) q^{7} +(1.26211 - 3.88437i) q^{9} +(-3.23867 + 0.714866i) q^{11} +(1.66806 + 3.19650i) q^{13} +(4.28809 - 0.679167i) q^{15} +(0.145227 + 0.446964i) q^{17} +(-8.16749 - 1.29360i) q^{19} +(7.26098 - 7.26098i) q^{21} +5.35491i q^{23} +(-1.37501 - 1.89255i) q^{25} +(-0.891795 - 2.74466i) q^{27} +(-2.70131 + 3.71804i) q^{29} +(-0.970871 - 1.90544i) q^{31} +(-5.85545 + 6.60611i) q^{33} +(5.98502 + 1.94465i) q^{35} +(-1.59193 - 10.0511i) q^{37} +(8.59264 + 4.27340i) q^{39} +(10.2046 + 1.61624i) q^{41} -8.27038 q^{43} +(4.71081 - 4.71081i) q^{45} +(-9.41370 - 1.49098i) q^{47} +(7.49832 - 2.43635i) q^{49} +(1.01198 + 0.735245i) q^{51} +(1.18796 - 3.65618i) q^{53} +(-5.23638 - 1.35937i) q^{55} +(-19.6109 + 9.99224i) q^{57} +(-1.83795 - 11.6044i) q^{59} +(5.60124 - 1.81995i) q^{61} +(2.46496 - 15.5631i) q^{63} +(0.0572070 + 5.88096i) q^{65} +(5.46352 - 5.46352i) q^{67} +(8.37757 + 11.5307i) q^{69} +(0.681911 + 0.347451i) q^{71} +(-10.7535 + 1.70319i) q^{73} +(-5.92165 - 1.92406i) q^{75} +(-11.9095 + 4.67862i) q^{77} +(5.10701 + 1.65937i) q^{79} +(3.69848 + 2.68710i) q^{81} +(-1.29337 + 2.53837i) q^{83} +(-0.119921 + 0.757151i) q^{85} +12.2322i q^{87} +(3.76777 + 3.76777i) q^{89} +(8.28531 + 11.1736i) q^{91} +(-5.07158 - 2.58410i) q^{93} +(-10.9125 - 7.92838i) q^{95} +(4.87455 + 9.56684i) q^{97} +(-1.31075 + 13.4824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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