LMFDB - Embedded newform 572.2.bq.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(49,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 12, 25]))

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

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

chi := DirichletCharacter("572.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bq (of order $30$, 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 $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	572.49
Dual form			572.2.bq.a.537.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292873 + 2.78650i) q^{3} +(-1.71678 - 0.557815i) q^{5} +(-3.86952 + 0.406703i) q^{7} +(-4.74434 - 1.00844i) q^{9} +O(q^{10})$	\(q+(-0.292873 + 2.78650i) q^{3} +(-1.71678 - 0.557815i) q^{5} +(-3.86952 + 0.406703i) q^{7} +(-4.74434 - 1.00844i) q^{9} +(0.904947 - 3.19078i) q^{11} +(3.58902 - 0.344834i) q^{13} +(2.05715 - 4.62043i) q^{15} +(-2.32330 - 2.58028i) q^{17} +(-1.10750 - 2.48749i) q^{19} -10.9015i q^{21} +(3.43989 + 5.95807i) q^{23} +(-1.40891 - 1.02364i) q^{25} +(1.60205 - 4.93061i) q^{27} +(-5.46290 - 2.43224i) q^{29} +(3.93081 - 1.27720i) q^{31} +(8.62606 + 3.45612i) q^{33} +(6.86998 + 1.46026i) q^{35} +(0.675247 - 1.51663i) q^{37} +(-0.0902480 + 10.1018i) q^{39} +(-11.3221 - 1.19000i) q^{41} +(-5.73984 + 9.94170i) q^{43} +(7.58246 + 4.37774i) q^{45} +(4.27130 - 5.87894i) q^{47} +(7.96077 - 1.69211i) q^{49} +(7.87037 - 5.71816i) q^{51} +(-2.92102 - 8.98997i) q^{53} +(-3.33346 + 4.97307i) q^{55} +(7.25573 - 2.35753i) q^{57} +(-11.2018 + 1.17735i) q^{59} +(-3.83137 - 4.25517i) q^{61} +(18.7685 + 1.97265i) q^{63} +(-6.35391 - 1.41001i) q^{65} +(-0.952298 + 0.549810i) q^{67} +(-17.6096 + 7.84029i) q^{69} +(5.47524 - 4.92993i) q^{71} +(-6.68651 - 9.20320i) q^{73} +(3.26499 - 3.62614i) q^{75} +(-2.20401 + 12.7148i) q^{77} +(-0.282152 - 0.868375i) q^{79} +(-0.0230681 - 0.0102706i) q^{81} +(-3.62583 - 1.17811i) q^{83} +(2.54926 + 5.72574i) q^{85} +(8.37736 - 14.5100i) q^{87} +(5.62162 - 3.24564i) q^{89} +(-13.7476 + 2.79401i) q^{91} +(2.40768 + 11.3272i) q^{93} +(0.513776 + 4.88825i) q^{95} +(-3.48552 + 16.3981i) q^{97} +(-7.51109 + 14.2256i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 20 q^{9}+O(q^{10}) $ 112 * q + 20 * q^9	$ 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) $ 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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
$3$	−0.292873	+	2.78650i	−0.169090	+	1.60878i	0.500286	+	0.865860i	$0.333228\pi$
$3$	−0.292873	+	2.78650i	−0.169090	+	1.60878i	−0.669376	+	0.742924i	$0.733438\pi$
$4$		0			0
$5$	−1.71678	−	0.557815i	−0.767767	−	0.249463i	−0.101158	−	0.994870i	$-0.532255\pi$
$5$	−1.71678	−	0.557815i	−0.767767	−	0.249463i	−0.666609	+	0.745408i	$0.732255\pi$
$6$		0			0
$7$	−3.86952	+	0.406703i	−1.46254	+	0.153719i	−0.802115	−	0.597170i	$-0.796292\pi$
$7$	−3.86952	+	0.406703i	−1.46254	+	0.153719i	−0.660428	+	0.750889i	$0.729625\pi$
$8$		0			0
$9$	−4.74434	−	1.00844i	−1.58145	−	0.336147i
$10$		0			0
$11$	0.904947	−	3.19078i	0.272852	−	0.962056i
$11$	0.904947	−	3.19078i	0.272852	−	0.962056i
$12$		0			0
$13$	3.58902	−	0.344834i	0.995416	−	0.0956397i
$13$	3.58902	−	0.344834i	0.995416	−	0.0956397i
$14$		0			0
$15$	2.05715	−	4.62043i	0.531153	−	1.19299i
$16$		0			0
$17$	−2.32330	−	2.58028i	−0.563482	−	0.625810i	0.392317	−	0.919830i	$-0.371673\pi$
$17$	−2.32330	−	2.58028i	−0.563482	−	0.625810i	−0.955799	+	0.294020i	$0.905007\pi$
$18$		0			0
$19$	−1.10750	−	2.48749i	−0.254078	−	0.570669i	0.740803	−	0.671723i	$-0.234445\pi$
$19$	−1.10750	−	2.48749i	−0.254078	−	0.570669i	−0.994881	+	0.101054i	$0.967779\pi$
$20$		0			0
$21$		−	10.9015i		−	2.37891i
$22$		0			0
$23$	3.43989	+	5.95807i	0.717267	+	1.24234i	0.962078	+	0.272773i	$0.0879407\pi$
$23$	3.43989	+	5.95807i	0.717267	+	1.24234i	−0.244811	+	0.969571i	$0.578726\pi$
$24$		0			0
$25$	−1.40891	−	1.02364i	−0.281783	−	0.204727i
$26$		0			0
$27$	1.60205	−	4.93061i	0.308315	−	0.948897i
$28$		0			0
$29$	−5.46290	−	2.43224i	−1.01444	−	0.451656i	−0.168933	−	0.985628i	$-0.554032\pi$
$29$	−5.46290	−	2.43224i	−1.01444	−	0.451656i	−0.845502	+	0.533972i	$0.820699\pi$
$30$		0			0
$31$	3.93081	−	1.27720i	0.705994	−	0.229391i	0.0660537	−	0.997816i	$-0.478959\pi$
$31$	3.93081	−	1.27720i	0.705994	−	0.229391i	0.639940	+	0.768425i	$0.278959\pi$
$32$		0			0
$33$	8.62606	+	3.45612i	1.50160	+	0.601634i
$34$		0			0
$35$	6.86998	+	1.46026i	1.16124	+	0.246829i
$36$		0			0
$37$	0.675247	−	1.51663i	0.111010	−	0.249332i	−0.849494	−	0.527598i	$-0.823093\pi$
$37$	0.675247	−	1.51663i	0.111010	−	0.249332i	0.960504	+	0.278265i	$0.0897595\pi$
$38$		0			0
$39$	−0.0902480	+	10.1018i	−0.0144512	+	1.61758i
$40$		0			0
$41$	−11.3221	−	1.19000i	−1.76821	−	0.185846i	−0.836235	−	0.548372i	$-0.815248\pi$
$41$	−11.3221	−	1.19000i	−1.76821	−	0.185846i	−0.931974	+	0.362526i	$0.881915\pi$
$42$		0			0
$43$	−5.73984	+	9.94170i	−0.875318	+	1.51609i	−0.0188934	+	0.999822i	$0.506014\pi$
$43$	−5.73984	+	9.94170i	−0.875318	+	1.51609i	−0.856424	+	0.516273i	$0.827319\pi$
$44$		0			0
$45$	7.58246	+	4.37774i	1.13033	+	0.652595i
$46$		0			0
$47$	4.27130	−	5.87894i	0.623033	−	0.857532i	−0.374536	−	0.927212i	$-0.622198\pi$
$47$	4.27130	−	5.87894i	0.623033	−	0.857532i	0.997569	+	0.0696806i	$0.0221980\pi$
$48$		0			0
$49$	7.96077	−	1.69211i	1.13725	−	0.241731i
$50$		0			0
$51$	7.87037	−	5.71816i	1.10207	−	0.800703i
$52$		0			0
$53$	−2.92102	−	8.98997i	−0.401233	−	1.23487i	−0.924000	−	0.382392i	$-0.875101\pi$
$53$	−2.92102	−	8.98997i	−0.401233	−	1.23487i	0.522768	−	0.852475i	$-0.324899\pi$
$54$		0			0
$55$	−3.33346	+	4.97307i	−0.449483	+	0.670568i
$56$		0			0
$57$	7.25573	−	2.35753i	0.961045	−	0.312263i
$58$		0			0
$59$	−11.2018	+	1.17735i	−1.45834	+	0.153278i	−0.800254	−	0.599661i	$-0.795302\pi$
$59$	−11.2018	+	1.17735i	−1.45834	+	0.153278i	−0.658090	+	0.752939i	$0.728635\pi$
$60$		0			0
$61$	−3.83137	−	4.25517i	−0.490557	−	0.544819i	0.446138	−	0.894964i	$-0.352799\pi$
$61$	−3.83137	−	4.25517i	−0.490557	−	0.544819i	−0.936695	+	0.350145i	$0.886132\pi$
$62$		0			0
$63$	18.7685	+	1.97265i	2.36461	+	0.248530i
$64$		0			0
$65$	−6.35391	−	1.41001i	−0.788106	−	0.174890i
$66$		0			0
$67$	−0.952298	+	0.549810i	−0.116342	+	0.0671700i	−0.557042	−	0.830485i	$-0.688064\pi$
$67$	−0.952298	+	0.549810i	−0.116342	+	0.0671700i	0.440700	+	0.897655i	$0.354730\pi$
$68$		0			0
$69$	−17.6096	+	7.84029i	−2.11995	+	0.943861i
$70$		0			0
$71$	5.47524	−	4.92993i	0.649792	−	0.585075i	−0.276899	−	0.960899i	$-0.589307\pi$
$71$	5.47524	−	4.92993i	0.649792	−	0.585075i	0.926691	+	0.375824i	$0.122640\pi$
$72$		0			0
$73$	−6.68651	−	9.20320i	−0.782597	−	1.07715i	−0.994991	−	0.0999683i	$-0.968126\pi$
$73$	−6.68651	−	9.20320i	−0.782597	−	1.07715i	0.212393	−	0.977184i	$-0.431874\pi$
$74$		0			0
$75$	3.26499	−	3.62614i	0.377009	−	0.418710i
$76$		0			0
$77$	−2.20401	+	12.7148i	−0.251170	+	1.44899i
$78$		0			0
$79$	−0.282152	−	0.868375i	−0.0317446	−	0.0976998i	0.933929	−	0.357459i	$-0.116357\pi$
$79$	−0.282152	−	0.868375i	−0.0317446	−	0.0976998i	−0.965673	+	0.259759i	$0.916357\pi$
$80$		0			0
$81$	−0.0230681	−	0.0102706i	−0.00256312	−	0.00114118i
$82$		0			0
$83$	−3.62583	−	1.17811i	−0.397987	−	0.129314i	0.103184	−	0.994662i	$-0.467097\pi$
$83$	−3.62583	−	1.17811i	−0.397987	−	0.129314i	−0.501171	+	0.865348i	$0.667097\pi$
$84$		0			0
$85$	2.54926	+	5.72574i	0.276506	+	0.621044i
$86$		0			0
$87$	8.37736	−	14.5100i	0.898148	−	1.55564i
$88$		0			0
$89$	5.62162	−	3.24564i	0.595890	−	0.344037i	−0.171533	−	0.985178i	$-0.554872\pi$
$89$	5.62162	−	3.24564i	0.595890	−	0.344037i	0.767423	+	0.641141i	$0.221539\pi$
$90$		0			0
$91$	−13.7476	+	2.79401i	−1.44114	+	0.292892i
$92$		0			0
$93$	2.40768	+	11.3272i	0.249665	+	1.17458i
$94$		0			0
$95$	0.513776	+	4.88825i	0.0527123	+	0.501524i
$96$		0			0
$97$	−3.48552	+	16.3981i	−0.353901	+	1.66497i	0.336603	+	0.941647i	$0.390722\pi$
$97$	−3.48552	+	16.3981i	−0.353901	+	1.66497i	−0.690504	+	0.723328i	$0.742611\pi$
$98$		0			0
$99$	−7.51109	+	14.2256i	−0.754893	+	1.42972i
$100$		0			0
$101$	0.423728	−	0.470597i	0.0421625	−	0.0468262i	−0.721695	−	0.692212i	$-0.756637\pi$
$101$	0.423728	−	0.470597i	0.0421625	−	0.0468262i	0.763857	+	0.645385i	$0.223303\pi$
$102$		0			0
$103$	−14.7702	+	10.7312i	−1.45535	+	1.05737i	−0.470803	+	0.882238i	$0.656036\pi$
$103$	−14.7702	+	10.7312i	−1.45535	+	1.05737i	−0.984545	+	0.175134i	$0.943964\pi$
$104$		0			0
$105$	−6.08104	+	18.7155i	−0.593448	+	1.82645i
$106$		0			0
$107$	0.676336	−	6.43490i	0.0653838	−	0.622086i	−0.911938	−	0.410327i	$-0.865414\pi$
$107$	0.676336	−	6.43490i	0.0653838	−	0.622086i	0.977322	−	0.211758i	$-0.0679189\pi$
$108$		0			0
$109$			10.4914i			1.00489i	0.864609	+	0.502445i	$0.167566\pi$
$109$			10.4914i			1.00489i	−0.864609	+	0.502445i	$0.832434\pi$
$110$		0			0
$111$	4.02832	+	2.32575i	0.382351	+	0.220751i
$112$		0			0
$113$	2.98095	−	1.32720i	0.280424	−	0.124853i	−0.261705	−	0.965148i	$-0.584285\pi$
$113$	2.98095	−	1.32720i	0.280424	−	0.124853i	0.542130	+	0.840295i	$0.317618\pi$
$114$		0			0
$115$	−2.58203	−	12.1475i	−0.240776	−	1.13276i
$116$		0			0
$117$	−17.3753	−	1.98331i	−1.60635	−	0.183357i
$118$		0			0
$119$	10.0395	+	9.03957i	0.920315	+	0.828656i
$120$		0			0
$121$	−9.36214	−	5.77497i	−0.851104	−	0.524997i
$122$		0			0
$123$	6.63184	−	31.2004i	0.597973	−	2.81324i
$124$		0			0
$125$	7.15293	+	9.84517i	0.639778	+	0.880578i
$126$		0			0
$127$	1.05147	−	0.223497i	0.0933028	−	0.0198321i	−0.161024	−	0.986951i	$-0.551480\pi$
$127$	1.05147	−	0.223497i	0.0933028	−	0.0198321i	0.254326	+	0.967118i	$0.418146\pi$
$128$		0			0
$129$	−26.0215	−	18.9057i	−2.29106	−	1.66455i
$130$		0			0
$131$	−0.490797			−0.0428811			−0.0214406	−	0.999770i	$-0.506825\pi$
$131$	−0.490797			−0.0428811			−0.0214406	+	0.999770i	$0.506825\pi$
$132$		0			0
$133$	5.29717	+	9.17497i	0.459323	+	0.795571i
$134$		0			0
$135$	−5.50074	+	7.57112i	−0.473429	+	0.651618i
$136$		0			0
$137$	6.48162	−	5.83608i	0.553762	−	0.498610i	−0.344072	−	0.938943i	$-0.611806\pi$
$137$	6.48162	−	5.83608i	0.553762	−	0.498610i	0.897834	+	0.440334i	$0.145140\pi$
$138$		0			0
$139$	1.64258	+	15.6281i	0.139322	+	1.32556i	0.811145	+	0.584845i	$0.198845\pi$
$139$	1.64258	+	15.6281i	0.139322	+	1.32556i	−0.671824	+	0.740711i	$0.734489\pi$
$140$		0			0
$141$	15.1307	+	13.6237i	1.27423	+	1.14733i
$142$		0			0
$143$	2.14759	−	11.7638i	0.179590	−	0.983742i
$144$		0			0
$145$	8.02185	+	7.22291i	0.666179	+	0.599830i
$146$		0			0
$147$	2.38358	+	22.6782i	0.196594	+	1.87047i
$148$		0			0
$149$	1.41767	−	1.27647i	0.116140	−	0.104573i	−0.609015	−	0.793159i	$-0.708435\pi$
$149$	1.41767	−	1.27647i	0.116140	−	0.104573i	0.725155	+	0.688586i	$0.241768\pi$
$150$		0			0
$151$	4.13051	−	5.68516i	0.336136	−	0.462652i	−0.607172	−	0.794571i	$-0.707696\pi$
$151$	4.13051	−	5.68516i	0.336136	−	0.462652i	0.943308	+	0.331919i	$0.107696\pi$
$152$		0			0
$153$	8.42045	+	14.5846i	0.680753	+	1.17910i
$154$		0			0
$155$	−7.46077			−0.599263
$156$		0			0
$157$	14.7916	+	10.7467i	1.18050	+	0.857681i	0.992228	−	0.124436i	$-0.0397121\pi$
$157$	14.7916	+	10.7467i	1.18050	+	0.857681i	0.188270	+	0.982117i	$0.439712\pi$
$158$		0			0
$159$	25.9060	−	5.50649i	2.05448	−	0.436693i
$160$		0			0
$161$	−15.7339	−	21.6559i	−1.24001	−	1.70672i
$162$		0			0
$163$	−0.663374	+	3.12093i	−0.0519595	+	0.244450i	−0.996461	−	0.0840571i	$-0.973212\pi$
$163$	−0.663374	+	3.12093i	−0.0519595	+	0.244450i	0.944501	+	0.328507i	$0.106546\pi$
$164$		0			0
$165$	−12.8812	−	10.7451i	−1.00280	−	0.836508i
$166$		0			0
$167$	−0.369676	−	0.332858i	−0.0286064	−	0.0257573i	0.654703	−	0.755886i	$-0.272794\pi$
$167$	−0.369676	−	0.332858i	−0.0286064	−	0.0257573i	−0.683310	+	0.730128i	$0.739460\pi$
$168$		0			0
$169$	12.7622	−	2.47523i	0.981706	−	0.190403i
$170$		0			0
$171$	2.74588	+	12.9184i	0.209983	+	0.987891i
$172$		0			0
$173$	8.22704	−	3.66291i	0.625490	−	0.278486i	−0.0694148	−	0.997588i	$-0.522113\pi$
$173$	8.22704	−	3.66291i	0.625490	−	0.278486i	0.694905	+	0.719102i	$0.255447\pi$
$174$		0			0
$175$	5.86814	+	3.38797i	0.443590	+	0.256107i
$176$		0			0
$177$		−	31.5585i		−	2.37208i
$178$		0			0
$179$	−0.866892	+	8.24793i	−0.0647946	+	0.616479i	0.913151	+	0.407621i	$0.133641\pi$
$179$	−0.866892	+	8.24793i	−0.0647946	+	0.616479i	−0.977946	+	0.208858i	$0.933025\pi$
$180$		0			0
$181$	−7.36793	+	22.6762i	−0.547654	+	1.68551i	0.166941	+	0.985967i	$0.446611\pi$
$181$	−7.36793	+	22.6762i	−0.547654	+	1.68551i	−0.714595	+	0.699538i	$0.753389\pi$
$182$		0			0
$183$	12.9791	−	9.42988i	0.959444	−	0.697077i
$184$		0			0
$185$	−2.00525	+	2.22705i	−0.147429	+	0.163736i
$186$		0			0
$187$	−10.3356	+	5.07811i	−0.755811	+	0.371348i
$188$		0			0
$189$	−4.19389	+	19.7307i	−0.305060	+	1.43520i
$190$		0			0
$191$	1.20374	+	11.4528i	0.0870995	+	0.828696i	0.947646	+	0.319324i	$0.103456\pi$
$191$	1.20374	+	11.4528i	0.0870995	+	0.828696i	−0.860546	+	0.509373i	$0.829878\pi$
$192$		0			0
$193$	−1.20496	−	5.66887i	−0.0867346	−	0.408054i	−1.00000		0.000688659i	$-0.999781\pi$
$193$	−1.20496	−	5.66887i	−0.0867346	−	0.408054i	0.913265	−	0.407366i	$-0.133553\pi$
$194$		0			0
$195$	5.78987	−	17.2922i	0.414621	−	1.23832i
$196$		0			0
$197$	8.18233	−	4.72407i	0.582967	−	0.336576i	−0.179345	−	0.983786i	$-0.557398\pi$
$197$	8.18233	−	4.72407i	0.582967	−	0.336576i	0.762312	+	0.647210i	$0.224064\pi$
$198$		0			0
$199$	−3.28143	+	5.68360i	−0.232614	+	0.402900i	−0.958577	−	0.284835i	$-0.908061\pi$
$199$	−3.28143	+	5.68360i	−0.232614	+	0.402900i	0.725962	+	0.687734i	$0.241395\pi$
$200$		0			0
$201$	−1.25314	−	2.81460i	−0.0883897	−	0.198527i
$202$		0			0
$203$	22.1280	+	7.18983i	1.55308	+	0.504627i
$204$		0			0
$205$	18.7737	+	8.35858i	1.31121	+	0.583788i
$206$		0			0
$207$	−10.3117	−	31.7361i	−0.716711	−	2.20581i
$208$		0			0
$209$	−8.93926	+	1.28275i	−0.618341	+	0.0887295i
$210$		0			0
$211$	4.32356	−	4.80179i	0.297646	−	0.330569i	−0.575708	−	0.817655i	$-0.695274\pi$
$211$	4.32356	−	4.80179i	0.297646	−	0.330569i	0.873354	+	0.487086i	$0.161940\pi$
$212$		0			0
$213$	12.1337	+	16.7006i	0.831387	+	1.14431i
$214$		0			0
$215$	15.3997	−	13.8659i	1.05025	−	0.945648i
$216$		0			0
$217$	−14.6909	+	6.54082i	−0.997284	+	0.444019i
$218$		0			0
$219$	27.6030	−	15.9366i	1.86524	−	1.07689i
$220$		0			0
$221$	−9.22813	−	8.45954i	−0.620751	−	0.569050i
$222$		0			0
$223$	−10.2982	−	1.08238i	−0.689617	−	0.0724816i	−0.246763	−	0.969076i	$-0.579367\pi$
$223$	−10.2982	−	1.08238i	−0.689617	−	0.0724816i	−0.442853	+	0.896594i	$0.646034\pi$
$224$		0			0
$225$	5.65210	+	6.27729i	0.376806	+	0.418486i
$226$		0			0
$227$	−17.8288	+	1.87388i	−1.18334	+	0.124374i	−0.675686	−	0.737189i	$-0.736153\pi$
$227$	−17.8288	+	1.87388i	−1.18334	+	0.124374i	−0.507650	+	0.861563i	$0.669486\pi$
$228$		0			0
$229$	−15.0474	+	4.88919i	−0.994359	+	0.323087i	−0.760609	−	0.649210i	$-0.775100\pi$
$229$	−15.0474	+	4.88919i	−0.994359	+	0.323087i	−0.233750	+	0.972297i	$0.575100\pi$
$230$		0			0
$231$	−34.7844	−	9.86530i	−2.28864	−	0.649089i
$232$		0			0
$233$	1.18387	+	3.64357i	0.0775578	+	0.238698i	0.982317	−	0.187225i	$-0.0599493\pi$
$233$	1.18387	+	3.64357i	0.0775578	+	0.238698i	−0.904759	+	0.425923i	$0.859949\pi$
$234$		0			0
$235$	−10.6122	+	7.71024i	−0.692266	+	0.502961i
$236$		0			0
$237$	2.50236	−	0.531892i	0.162546	−	0.0345501i
$238$		0			0
$239$	6.17250	−	8.49572i	0.399266	−	0.549542i	−0.561294	−	0.827617i	$-0.689696\pi$
$239$	6.17250	−	8.49572i	0.399266	−	0.549542i	0.960560	+	0.278074i	$0.0896962\pi$
$240$		0			0
$241$	−10.0416	−	5.79753i	−0.646838	−	0.373452i	0.140406	−	0.990094i	$-0.455159\pi$
$241$	−10.0416	−	5.79753i	−0.646838	−	0.373452i	−0.787244	+	0.616642i	$0.788493\pi$
$242$		0			0
$243$	7.81191	−	13.5306i	0.501134	−	0.867989i
$244$		0			0
$245$	−14.6108	−	1.53565i	−0.933448	−	0.0981093i
$246$		0			0
$247$	−4.83262	−	8.54575i	−0.307492	−	0.543753i
$248$		0			0
$249$	4.34469	−	9.75834i	0.275334	−	0.618410i
$250$		0			0
$251$	−25.0049	−	5.31496i	−1.57830	−	0.335478i	−0.666304	−	0.745680i	$-0.732125\pi$
$251$	−25.0049	−	5.31496i	−1.57830	−	0.335478i	−0.911994	+	0.410203i	$0.865458\pi$
$252$		0			0
$253$	22.1238	−	5.58420i	1.39091	−	0.351076i
$254$		0			0
$255$	−16.7014	+	5.42660i	−1.04588	+	0.339827i
$256$		0			0
$257$	−12.3384	−	5.49340i	−0.769647	−	0.342669i	−0.0159346	−	0.999873i	$-0.505072\pi$
$257$	−12.3384	−	5.49340i	−0.769647	−	0.342669i	−0.753713	+	0.657204i	$0.771739\pi$
$258$		0			0
$259$	−1.99607	+	6.14326i	−0.124030	+	0.381724i
$260$		0			0
$261$	23.4651	+	17.0484i	1.45245	+	1.05527i
$262$		0			0
$263$	−4.90956	−	8.50360i	−0.302736	−	0.524354i	0.674019	−	0.738714i	$-0.264567\pi$
$263$	−4.90956	−	8.50360i	−0.302736	−	0.524354i	−0.976755	+	0.214360i	$0.931233\pi$
$264$		0			0
$265$			17.0632i			1.04818i
$266$		0			0
$267$	7.39755	+	16.6152i	0.452723	+	1.01683i
$268$		0			0
$269$	−10.9053	−	12.1115i	−0.664906	−	0.738453i	0.312478	−	0.949925i	$-0.398841\pi$
$269$	−10.9053	−	12.1115i	−0.664906	−	0.738453i	−0.977384	+	0.211472i	$0.932174\pi$
$270$		0			0
$271$	11.1240	−	24.9848i	0.675733	−	1.51772i	−0.170756	−	0.985313i	$-0.554621\pi$
$271$	11.1240	−	24.9848i	0.675733	−	1.51772i	0.846488	−	0.532407i	$-0.178712\pi$
$272$		0			0
$273$	−3.75922	−	39.1258i	−0.227518	−	2.36800i
$274$		0			0
$275$	−4.54119	+	3.56920i	−0.273844	+	0.215231i
$276$		0			0
$277$	1.55187	+	0.329861i	0.0932429	+	0.0198194i	0.254297	−	0.967126i	$-0.418156\pi$
$277$	1.55187	+	0.329861i	0.0932429	+	0.0198194i	−0.161054	+	0.986946i	$0.551489\pi$
$278$		0			0
$279$	−19.9371	+	2.09547i	−1.19360	+	0.125453i
$280$		0			0
$281$	1.43918	+	0.467617i	0.0858541	+	0.0278957i	0.351629	−	0.936139i	$-0.385628\pi$
$281$	1.43918	+	0.467617i	0.0858541	+	0.0278957i	−0.265775	+	0.964035i	$0.585628\pi$
$282$		0			0
$283$	−2.12974	+	20.2631i	−0.126600	+	1.20452i	0.728128	+	0.685441i	$0.240390\pi$
$283$	−2.12974	+	20.2631i	−0.126600	+	1.20452i	−0.854728	+	0.519076i	$0.826276\pi$
$284$		0			0
$285$	−13.7716			−0.815757
$286$		0			0
$287$	44.2949			2.61465
$288$		0			0
$289$	0.516836	−	4.91736i	0.0304021	−	0.289257i
$290$		0			0
$291$	−44.6724	−	14.5150i	−2.61874	−	0.850882i
$292$		0			0
$293$	15.6673	−	1.64670i	0.915296	−	0.0962015i	0.364844	−	0.931069i	$-0.381122\pi$
$293$	15.6673	−	1.64670i	0.915296	−	0.0962015i	0.550452	+	0.834867i	$0.314456\pi$
$294$		0			0
$295$	19.8877	+	4.22726i	1.15791	+	0.246120i
$296$		0			0
$297$	−14.2827	−	9.57374i	−0.828768	−	0.555525i
$298$		0			0
$299$	14.4004	+	20.1975i	0.832797	+	1.16805i
$300$		0			0
$301$	18.1671	−	40.8040i	1.04714	−	2.35191i
$302$		0			0
$303$	1.18722	+	1.31854i	0.0682040	+	0.0757482i
$304$		0			0
$305$	4.20402	+	9.44238i	0.240721	+	0.540669i
$306$		0			0
$307$			12.2065i			0.696662i	0.937372	+	0.348331i	$0.113252\pi$
$307$			12.2065i			0.696662i	−0.937372	+	0.348331i	$0.886748\pi$
$308$		0			0
$309$	−25.5765	−	44.2999i	−1.45500	−	2.52013i
$310$		0			0
$311$	12.0652	+	8.76586i	0.684153	+	0.497066i	0.874733	−	0.484605i	$-0.161037\pi$
$311$	12.0652	+	8.76586i	0.684153	+	0.497066i	−0.190580	+	0.981672i	$0.561037\pi$
$312$		0			0
$313$	−3.73881	+	11.5069i	−0.211330	+	0.650408i	0.788064	+	0.615594i	$0.211084\pi$
$313$	−3.73881	+	11.5069i	−0.211330	+	0.650408i	−0.999394	+	0.0348137i	$0.988916\pi$
$314$		0			0
$315$	−31.1210	−	13.8559i	−1.75347	−	0.780694i
$316$		0			0
$317$	−8.52961	+	2.77144i	−0.479070	+	0.155659i	−0.538590	−	0.842568i	$-0.681043\pi$
$317$	−8.52961	+	2.77144i	−0.479070	+	0.155659i	0.0595200	+	0.998227i	$0.481043\pi$
$318$		0			0
$319$	−12.7044	+	15.2299i	−0.711309	+	0.852709i
$320$		0			0
$321$	17.7328	+	3.76921i	0.989746	+	0.210377i
$322$		0			0
$323$	−3.84537	+	8.63683i	−0.213962	+	0.480566i
$324$		0			0
$325$	−5.40961	−	3.18801i	−0.300071	−	0.176839i
$326$		0			0
$327$	−29.2341	−	3.07263i	−1.61665	−	0.169917i
$328$		0			0
$329$	−14.1369	+	24.4859i	−0.779393	+	1.34995i
$330$		0			0
$331$	−12.3933	−	7.15525i	−0.681195	−	0.393288i	0.119110	−	0.992881i	$-0.461996\pi$
$331$	−12.3933	−	7.15525i	−0.681195	−	0.393288i	−0.800305	+	0.599593i	$0.795329\pi$
$332$		0			0
$333$	−4.73304	+	6.51447i	−0.259369	+	0.356991i
$334$		0			0
$335$	1.94158	−	0.412695i	0.106080	−	0.0225479i
$336$		0			0
$337$	25.0662	−	18.2117i	1.36544	−	0.992052i	0.367365	−	0.930077i	$-0.380260\pi$
$337$	25.0662	−	18.2117i	1.36544	−	0.992052i	0.998078	−	0.0619757i	$-0.0197401\pi$
$338$		0			0
$339$	2.82521	+	8.69511i	0.153444	+	0.472253i
$340$		0			0
$341$	−0.518082	−	13.6981i	−0.0280557	−	0.741795i
$342$		0			0
$343$	−4.21336	+	1.36900i	−0.227500	+	0.0739193i
$344$		0			0
$345$	34.6052	−	3.63715i	1.86308	−	0.195818i
$346$		0			0
$347$	−12.1345	−	13.4768i	−0.651416	−	0.723471i	0.323454	−	0.946244i	$-0.395156\pi$
$347$	−12.1345	−	13.4768i	−0.651416	−	0.723471i	−0.974870	+	0.222773i	$0.928489\pi$
$348$		0			0
$349$	−25.1005	−	2.63816i	−1.34360	−	0.141218i	−0.594723	−	0.803931i	$-0.702738\pi$
$349$	−25.1005	−	2.63816i	−1.34360	−	0.141218i	−0.748873	+	0.662713i	$0.769405\pi$
$350$		0			0
$351$	4.04956	−	18.2485i	0.216150	−	0.974034i
$352$		0			0
$353$	28.2915	−	16.3341i	1.50580	−	0.869376i	0.505826	−	0.862635i	$-0.331188\pi$
$353$	28.2915	−	16.3341i	1.50580	−	0.869376i	0.999977	−	0.00674047i	$-0.00214557\pi$
$354$		0			0
$355$	−12.1498	+	5.40943i	−0.644843	+	0.287103i
$356$		0			0
$357$	−28.1290	+	25.3275i	−1.48874	+	1.34047i
$358$		0			0
$359$	−3.18842	−	4.38848i	−0.168278	−	0.231615i	0.716546	−	0.697540i	$-0.245722\pi$
$359$	−3.18842	−	4.38848i	−0.168278	−	0.231615i	−0.884825	+	0.465924i	$0.845722\pi$
$360$		0			0
$361$	7.75244	−	8.60996i	0.408023	−	0.453156i
$362$		0			0
$363$	18.8338	−	24.3962i	0.988521	−	1.28047i
$364$		0			0
$365$	6.34558	+	19.5297i	0.332143	+	1.02223i
$366$		0			0
$367$	27.2944	+	12.1522i	1.42476	+	0.634342i	0.967009	−	0.254741i	$-0.0819901\pi$
$367$	27.2944	+	12.1522i	1.42476	+	0.634342i	0.457746	+	0.889083i	$0.348657\pi$
$368$		0			0
$369$	52.5157	+	17.0634i	2.73386	+	0.888284i
$370$		0			0
$371$	14.9592	+	33.5989i	0.776643	+	1.74437i
$372$		0			0
$373$	8.78995	−	15.2246i	0.455126	−	0.788302i	−0.543569	−	0.839364i	$-0.682927\pi$
$373$	8.78995	−	15.2246i	0.455126	−	0.788302i	0.998695	+	0.0510624i	$0.0162607\pi$
$374$		0			0
$375$	−29.5284	+	17.0482i	−1.52484	+	0.880367i
$376$		0			0
$377$	−20.4452	−	6.84557i	−1.05298	−	0.352565i
$378$		0			0
$379$	3.81850	+	17.9647i	0.196143	+	0.922782i	0.960563	+	0.278063i	$0.0896924\pi$
$379$	3.81850	+	17.9647i	0.196143	+	0.922782i	−0.764419	+	0.644719i	$0.776974\pi$
$380$		0			0
$381$	0.314826	+	2.99537i	0.0161290	+	0.153457i
$382$		0			0
$383$	−1.71407	+	8.06409i	−0.0875851	+	0.412056i	0.912411	+	0.409275i	$0.134218\pi$
$383$	−1.71407	+	8.06409i	−0.0875851	+	0.412056i	−0.999996	+	0.00278044i	$0.999115\pi$
$384$		0			0
$385$	10.8763	−	20.5991i	0.554309	−	1.04983i
$386$		0			0
$387$	37.2574	−	41.3785i	1.89390	−	2.10339i
$388$		0			0
$389$	19.7799	−	14.3709i	1.00288	−	0.728636i	0.0401774	−	0.999193i	$-0.487208\pi$
$389$	19.7799	−	14.3709i	1.00288	−	0.728636i	0.962704	+	0.270557i	$0.0872077\pi$
$390$		0			0
$391$	7.38161	−	22.7182i	0.373304	−	1.14891i
$392$		0			0
$393$	0.143741	−	1.36760i	0.00725077	−	0.0689865i
$394$		0			0
$395$			1.64820i			0.0829297i
$396$		0			0
$397$	7.96291	+	4.59739i	0.399647	+	0.230736i	0.686332	−	0.727289i	$-0.259220\pi$
$397$	7.96291	+	4.59739i	0.399647	+	0.230736i	−0.286685	+	0.958025i	$0.592553\pi$
$398$		0			0
$399$	−27.1174	+	12.0735i	−1.35757	+	0.604429i
$400$		0			0
$401$	4.34879	+	20.4595i	0.217168	+	1.02170i	0.942734	+	0.333544i	$0.108245\pi$
$401$	4.34879	+	20.4595i	0.217168	+	1.02170i	−0.725566	+	0.688153i	$0.758422\pi$
$402$		0			0
$403$	13.6673	−	5.93936i	0.680819	−	0.295861i
$404$		0			0
$405$	0.0338737	+	0.0305000i	0.00168320	+	0.00151556i
$406$		0			0
$407$	−4.22817	−	3.52703i	−0.209583	−	0.174829i
$408$		0			0
$409$	7.67966	−	36.1299i	0.379735	−	1.78651i	−0.208714	−	0.977977i	$-0.566928\pi$
$409$	7.67966	−	36.1299i	0.379735	−	1.78651i	0.588449	−	0.808534i	$-0.299739\pi$
$410$		0			0
$411$	14.3639	+	19.7702i	0.708520	+	0.975194i
$412$		0			0
$413$	42.8666	−	9.11158i	2.10933	−	0.448352i
$414$		0			0
$415$	5.56759	+	4.04509i	0.273302	+	0.198566i
$416$		0			0
$417$	−44.0286			−2.15609
$418$		0			0
$419$	−13.1718	−	22.8142i	−0.643483	−	1.11455i	−0.984650	−	0.174542i	$-0.944155\pi$
$419$	−13.1718	−	22.8142i	−0.643483	−	1.11455i	0.341167	−	0.940003i	$-0.389178\pi$
$420$		0			0
$421$	−19.6934	+	27.1056i	−0.959796	+	1.32105i	−0.0127606	+	0.999919i	$0.504062\pi$
$421$	−19.6934	+	27.1056i	−0.959796	+	1.32105i	−0.947036	+	0.321128i	$0.895938\pi$
$422$		0			0
$423$	−26.1931	+	23.5844i	−1.27355	+	1.14671i
$424$		0			0
$425$	0.632055	+	6.01360i	0.0306592	+	0.291703i
$426$		0			0
$427$	16.5562	+	14.9072i	0.801210	+	0.721412i
$428$		0			0
$429$	32.1509	+	9.42954i	1.55226	+	0.455263i
$430$		0			0
$431$	7.26108	+	6.53791i	0.349754	+	0.314920i	0.825217	−	0.564816i	$-0.191053\pi$
$431$	7.26108	+	6.53791i	0.349754	+	0.314920i	−0.475463	+	0.879736i	$0.657719\pi$
$432$		0			0
$433$	−0.718209	−	6.83330i	−0.0345149	−	0.328387i	−0.998132	−	0.0610997i	$-0.980539\pi$
$433$	−0.718209	−	6.83330i	−0.0345149	−	0.328387i	0.963617	−	0.267288i	$-0.0861274\pi$
$434$		0			0
$435$	−22.4760	+	20.2375i	−1.07764	+	0.970312i
$436$		0			0
$437$	11.0109	−	15.1553i	0.526725	−	0.724975i
$438$		0			0
$439$	−0.761832	−	1.31953i	−0.0363603	−	0.0629778i	0.847273	−	0.531158i	$-0.178243\pi$
$439$	−0.761832	−	1.31953i	−0.0363603	−	0.0629778i	−0.883633	+	0.468180i	$0.844910\pi$
$440$		0			0
$441$	−39.4750			−1.87976
$442$		0			0
$443$	0.211659	+	0.153779i	0.0100562	+	0.00730628i	0.592802	−	0.805348i	$-0.298022\pi$
$443$	0.211659	+	0.153779i	0.0100562	+	0.00730628i	−0.582746	+	0.812655i	$0.698022\pi$
$444$		0			0
$445$	−11.4615	+	2.43622i	−0.543329	+	0.115488i
$446$		0			0
$447$	3.14169	+	4.32417i	0.148597	+	0.204526i
$448$		0			0
$449$	4.23577	−	19.9277i	0.199898	−	0.940448i	−0.757758	−	0.652535i	$-0.773705\pi$
$449$	4.23577	−	19.9277i	0.199898	−	0.940448i	0.957657	−	0.287913i	$-0.0929613\pi$
$450$		0			0
$451$	−14.0429	+	35.0493i	−0.661253	+	1.65041i
$452$		0			0
$453$	14.6320	+	13.1747i	0.687470	+	0.619000i
$454$		0			0
$455$	25.1601	+	2.87190i	1.17952	+	0.134637i
$456$		0			0
$457$	1.74210	+	8.19592i	0.0814918	+	0.383389i	0.999926	−	0.0121856i	$-0.00387889\pi$
$457$	1.74210	+	8.19592i	0.0814918	+	0.383389i	−0.918434	+	0.395574i	$0.870546\pi$
$458$		0			0
$459$	−16.4444	+	7.32152i	−0.767559	+	0.341739i
$460$		0			0
$461$	−27.2094	−	15.7093i	−1.26727	−	0.731657i	−0.292797	−	0.956175i	$-0.594586\pi$
$461$	−27.2094	−	15.7093i	−1.26727	−	0.731657i	−0.974470	+	0.224517i	$0.927919\pi$
$462$		0			0
$463$		−	29.5580i		−	1.37368i	−0.726810	−	0.686838i	$-0.758998\pi$
$463$		−	29.5580i		−	1.37368i	0.726810	−	0.686838i	$-0.241002\pi$
$464$		0			0
$465$	2.18505	−	20.7894i	0.101329	−	0.964085i
$466$		0			0
$467$	11.5381	−	35.5106i	0.533919	−	1.64323i	−0.212053	−	0.977258i	$-0.568015\pi$
$467$	11.5381	−	35.5106i	0.533919	−	1.64323i	0.745973	−	0.665977i	$-0.231985\pi$
$468$		0			0
$469$	3.46133	−	2.51480i	0.159829	−	0.116123i
$470$		0			0
$471$	−34.2777	+	38.0693i	−1.57943	+	1.75414i
$472$		0			0
$473$	26.5275	+	27.3113i	1.21974	+	1.25577i
$474$		0			0
$475$	−0.985908	+	4.63833i	−0.0452366	+	0.212821i
$476$		0			0
$477$	4.79246	+	45.5972i	0.219431	+	2.08775i
$478$		0			0
$479$	4.12994	+	19.4298i	0.188702	+	0.887771i	0.965980	+	0.258615i	$0.0832661\pi$
$479$	4.12994	+	19.4298i	0.188702	+	0.887771i	−0.777279	+	0.629156i	$0.783401\pi$
$480$		0			0
$481$	1.90049	−	5.67607i	0.0866550	−	0.258806i
$482$		0			0
$483$	64.9521	−	37.5001i	2.95542	−	1.70631i
$484$		0			0
$485$	15.1310	−	26.2076i	0.687063	−	1.19003i
$486$		0			0
$487$	−2.51748	−	5.65436i	−0.114078	−	0.256224i	0.847479	−	0.530829i	$-0.178119\pi$
$487$	−2.51748	−	5.65436i	−0.114078	−	0.256224i	−0.961557	+	0.274606i	$0.911453\pi$
$488$		0			0
$489$	−8.50217	−	2.76252i	−0.384482	−	0.124926i
$490$		0			0
$491$	−35.8262	−	15.9509i	−1.61681	−	0.719852i	−0.618966	−	0.785418i	$-0.712448\pi$
$491$	−35.8262	−	15.9509i	−1.61681	−	0.719852i	−0.997848	+	0.0655654i	$0.979115\pi$
$492$		0			0
$493$	6.41607	+	19.7466i	0.288965	+	0.889344i
$494$		0			0
$495$	20.8301	−	20.2324i	0.936244	−	0.909377i
$496$		0			0
$497$	−19.1816	+	21.3033i	−0.860411	+	0.955583i
$498$		0			0
$499$	−0.0735456	−	0.101227i	−0.00329235	−	0.00453153i	0.807368	−	0.590049i	$-0.200891\pi$
$499$	−0.0735456	−	0.101227i	−0.00329235	−	0.00453153i	−0.810660	+	0.585517i	$0.800891\pi$
$500$		0			0
$501$	1.03578	−	0.932617i	0.0462751	−	0.0416663i
$502$		0			0
$503$	−31.9067	+	14.2058i	−1.42265	+	0.633404i	−0.966539	−	0.256520i	$-0.917424\pi$
$503$	−31.9067	+	14.2058i	−1.42265	+	0.633404i	−0.456109	+	0.889924i	$0.650757\pi$
$504$		0			0
$505$	−0.989953	+	0.571550i	−0.0440523	+	0.0254336i
$506$		0			0
$507$	3.15954	+	36.2867i	0.140320	+	1.61155i
$508$		0			0
$509$	−24.3324	−	2.55744i	−1.07852	−	0.113357i	−0.451430	−	0.892306i	$-0.649086\pi$
$509$	−24.3324	−	2.55744i	−1.07852	−	0.113357i	−0.627086	+	0.778950i	$0.715753\pi$
$510$		0			0
$511$	29.6166	+	32.8926i	1.31016	+	1.45508i
$512$		0			0
$513$	−14.0391	+	1.47557i	−0.619842	+	0.0651481i
$514$		0			0
$515$	31.3431	−	10.1840i	1.38114	−	0.448760i
$516$		0			0
$517$	−14.8931	−	18.9489i	−0.654998	−	0.833372i
$518$		0			0
$519$	7.79722	+	23.9974i	0.342260	+	1.05337i
$520$		0			0
$521$	16.8000	−	12.2059i	0.736023	−	0.534752i	−0.155440	−	0.987845i	$-0.549680\pi$
$521$	16.8000	−	12.2059i	0.736023	−	0.534752i	0.891463	+	0.453093i	$0.149680\pi$
$522$		0			0
$523$	6.94859	−	1.47697i	0.303840	−	0.0645833i	−0.0534685	−	0.998570i	$-0.517028\pi$
$523$	6.94859	−	1.47697i	0.303840	−	0.0645833i	0.357309	+	0.933986i	$0.383694\pi$
$524$		0			0
$525$	−11.1592	+	15.3593i	−0.487027	+	0.670335i
$526$		0			0
$527$	−12.4280	−	7.17528i	−0.541370	−	0.312560i
$528$		0			0
$529$	−12.1657	+	21.0717i	−0.528945	+	0.916160i
$530$		0			0
$531$	54.3323	+	5.71055i	2.35782	+	0.247817i
$532$		0			0
$533$	−41.0455	−	0.366695i	−1.77788	−	0.0158833i
$534$		0			0
$535$	−4.75061	+	10.6700i	−0.205387	+	0.461306i
$536$		0			0
$537$	−22.7289	−	4.83118i	−0.980826	−	0.208481i
$538$		0			0
$539$	1.80491	−	26.9323i	0.0777430	−	1.16006i
$540$		0			0
$541$	3.56541	−	1.15847i	0.153289	−	0.0498066i	−0.231367	−	0.972866i	$-0.574320\pi$
$541$	3.56541	−	1.15847i	0.153289	−	0.0498066i	0.384656	+	0.923060i	$0.374320\pi$
$542$		0			0
$543$	−61.0292	−	27.1719i	−2.61901	−	1.16606i
$544$		0			0
$545$	5.85224	−	18.0113i	0.250682	−	0.771521i
$546$		0			0
$547$	21.5045	+	15.6240i	0.919467	+	0.668032i	0.943391	−	0.331682i	$-0.107616\pi$
$547$	21.5045	+	15.6240i	0.919467	+	0.668032i	−0.0239240	+	0.999714i	$0.507616\pi$
$548$		0			0
$549$	13.8863	+	24.0517i	0.592651	+	1.02650i
$550$		0			0
$551$			16.2826i			0.693663i
$552$		0			0
$553$	1.44496	+	3.24544i	0.0614462	+	0.138010i
$554$		0			0
$555$	−5.61840	−	6.23986i	−0.238488	−	0.264867i
$556$		0			0
$557$	−9.28933	+	20.8642i	−0.393601	+	0.884043i	0.602688	+	0.797977i	$0.294096\pi$
$557$	−9.28933	+	20.8642i	−0.393601	+	0.884043i	−0.996289	+	0.0860664i	$0.972570\pi$
$558$		0			0
$559$	−17.1722	+	37.6603i	−0.726306	+	1.59286i
$560$		0			0
$561$	−11.1231	−	30.2872i	−0.469618	−	1.27873i
$562$		0			0
$563$	−21.0369	−	4.47154i	−0.886601	−	0.188453i	−0.257967	−	0.966154i	$-0.583053\pi$
$563$	−21.0369	−	4.47154i	−0.886601	−	0.188453i	−0.628635	+	0.777701i	$0.716386\pi$
$564$		0			0
$565$	−5.85797	+	0.615697i	−0.246446	+	0.0259026i
$566$		0			0
$567$	0.0934396	+	0.0303604i	0.00392410	+	0.00127502i
$568$		0			0
$569$	−3.51684	+	33.4605i	−0.147434	+	1.40274i	0.631376	+	0.775477i	$0.282490\pi$
$569$	−3.51684	+	33.4605i	−0.147434	+	1.40274i	−0.778810	+	0.627260i	$0.784176\pi$
$570$		0			0
$571$	−13.8425			−0.579291			−0.289645	−	0.957134i	$-0.593537\pi$
$571$	−13.8425			−0.579291			−0.289645	+	0.957134i	$0.593537\pi$
$572$		0			0
$573$	−32.2658			−1.34792
$574$		0			0
$575$	1.25238	−	11.9156i	0.0522279	−	0.496915i
$576$		0			0
$577$	−4.42753	−	1.43859i	−0.184320	−	0.0598893i	0.215403	−	0.976525i	$-0.430894\pi$
$577$	−4.42753	−	1.43859i	−0.184320	−	0.0598893i	−0.399723	+	0.916636i	$0.630894\pi$
$578$		0			0
$579$	16.1492	−	1.69735i	0.671137	−	0.0705394i
$580$		0			0
$581$	14.5094	+	3.08407i	0.601951	+	0.127949i
$582$		0			0
$583$	−31.3284	+	1.18488i	−1.29749	+	0.0490727i
$584$		0			0
$585$	28.7232	+	13.0971i	1.18756	+	0.541499i
$586$		0			0
$587$	−8.54629	+	19.1953i	−0.352743	+	0.792274i	0.646818	+	0.762645i	$0.276099\pi$
$587$	−8.54629	+	19.1953i	−0.352743	+	0.792274i	−0.999561	+	0.0296296i	$0.990567\pi$
$588$		0			0
$589$	−7.53039	−	8.36334i	−0.310284	−	0.344605i
$590$		0			0
$591$	10.7672	+	24.1836i	0.442904	+	0.994779i
$592$		0			0
$593$		−	14.4302i		−	0.592578i	−0.955098	−	0.296289i	$-0.904251\pi$
$593$		−	14.4302i		−	0.592578i	0.955098	−	0.296289i	$-0.0957491\pi$
$594$		0			0
$595$	−12.1931	−	21.1191i	−0.499869	−	0.865798i
$596$		0			0
$597$	−14.8763	−	10.8083i	−0.608846	−	0.442352i
$598$		0			0
$599$	7.92595	−	24.3936i	0.323845	−	0.996694i	−0.648114	−	0.761544i	$-0.724442\pi$
$599$	7.92595	−	24.3936i	0.323845	−	0.996694i	0.971959	−	0.235150i	$-0.0755582\pi$
$600$		0			0
$601$	33.3016	+	14.8268i	1.35840	+	0.604799i	0.951210	−	0.308544i	$-0.0998416\pi$
$601$	33.3016	+	14.8268i	1.35840	+	0.604799i	0.407191	+	0.913343i	$0.366508\pi$
$602$		0			0
$603$	5.07248	−	1.64815i	0.206567	−	0.0671178i
$604$		0			0
$605$	12.8514	+	15.1367i	0.522482	+	0.615394i
$606$		0			0
$607$	−8.85635	−	1.88248i	−0.359468	−	0.0764073i	0.0246375	−	0.999696i	$-0.492157\pi$
$607$	−8.85635	−	1.88248i	−0.359468	−	0.0764073i	−0.384106	+	0.923289i	$0.625490\pi$
$608$		0			0
$609$	−26.5151	+	59.5540i	−1.07445	+	2.41325i
$610$		0			0
$611$	13.3025	−	22.5725i	0.538163	−	0.913188i
$612$		0			0
$613$	30.4127	+	3.19650i	1.22836	+	0.129105i	0.696392	−	0.717661i	$-0.254787\pi$
$613$	30.4127	+	3.19650i	1.22836	+	0.129105i	0.531964	+	0.846767i	$0.321454\pi$
$614$		0			0
$615$	−28.7894	+	49.8648i	−1.16090	+	2.01074i
$616$		0			0
$617$	13.0455	+	7.53181i	0.525191	+	0.303219i	0.739056	−	0.673644i	$-0.235272\pi$
$617$	13.0455	+	7.53181i	0.525191	+	0.303219i	−0.213865	+	0.976863i	$0.568605\pi$
$618$		0			0
$619$	−15.5603	+	21.4169i	−0.625420	+	0.860817i	−0.997733	−	0.0672904i	$-0.978565\pi$
$619$	−15.5603	+	21.4169i	−0.625420	+	0.860817i	0.372314	+	0.928107i	$0.378565\pi$
$620$		0			0
$621$	34.8878	−	7.41564i	1.40000	−	0.297579i
$622$		0			0
$623$	−20.4330	+	14.8454i	−0.818629	+	0.594769i
$624$		0			0
$625$	−4.09743	−	12.6106i	−0.163897	−	0.504424i
$626$		0			0
$627$	−0.956308	−	25.2849i	−0.0381913	−	1.00978i
$628$		0			0
$629$	−5.48213	+	1.78125i	−0.218587	+	0.0710232i
$630$		0			0
$631$	−8.59564	+	0.903438i	−0.342187	+	0.0359653i	−0.274063	−	0.961712i	$-0.588368\pi$
$631$	−8.59564	+	0.903438i	−0.342187	+	0.0359653i	−0.0681235	+	0.997677i	$0.521701\pi$
$632$		0			0
$633$	12.1139	+	13.4539i	0.481486	+	0.534744i
$634$		0			0
$635$	−1.92981	−	0.202831i	−0.0765821	−	0.00804911i
$636$		0			0
$637$	27.9879	−	8.81818i	1.10892	−	0.349389i
$638$		0			0
$639$	−30.9480	+	17.8678i	−1.22428	+	0.706840i
$640$		0			0
$641$	14.2686	−	6.35279i	0.563576	−	0.250920i	−0.105116	−	0.994460i	$-0.533521\pi$
$641$	14.2686	−	6.35279i	0.563576	−	0.250920i	0.668692	+	0.743540i	$0.266855\pi$
$642$		0			0
$643$	−32.4287	+	29.1989i	−1.27886	+	1.15149i	−0.298476	+	0.954417i	$0.596478\pi$
$643$	−32.4287	+	29.1989i	−1.27886	+	1.15149i	−0.980388	+	0.197077i	$0.936855\pi$
$644$		0			0
$645$	34.1272	+	46.9721i	1.34376	+	1.84952i
$646$		0			0
$647$	−11.6892	+	12.9822i	−0.459551	+	0.510383i	−0.927731	−	0.373250i	$-0.878243\pi$
$647$	−11.6892	+	12.9822i	−0.459551	+	0.510383i	0.468180	+	0.883633i	$0.344910\pi$
$648$		0			0
$649$	−6.38032	+	36.8078i	−0.250450	+	1.44483i
$650$		0			0
$651$	−13.9234	−	42.8518i	−0.545701	−	1.67949i
$652$		0			0
$653$	−23.9392	−	10.6584i	−0.936815	−	0.417097i	−0.119205	−	0.992870i	$-0.538035\pi$
$653$	−23.9392	−	10.6584i	−0.936815	−	0.417097i	−0.817610	+	0.575773i	$0.804701\pi$
$654$		0			0
$655$	0.842589	+	0.273774i	0.0329227	+	0.0106972i
$656$		0			0
$657$	22.4422	+	50.4061i	0.875555	+	1.96653i
$658$		0			0
$659$	6.22805	−	10.7873i	0.242610	−	0.420213i	−0.718847	−	0.695169i	$-0.755330\pi$
$659$	6.22805	−	10.7873i	0.242610	−	0.420213i	0.961457	+	0.274955i	$0.0886631\pi$
$660$		0			0
$661$	12.5359	−	7.23760i	0.487589	−	0.281510i	−0.235984	−	0.971757i	$-0.575831\pi$
$661$	12.5359	−	7.23760i	0.487589	−	0.281510i	0.723574	+	0.690247i	$0.242498\pi$
$662$		0			0
$663$	26.2751	−	23.2366i	1.02044	−	0.902434i
$664$		0			0
$665$	−3.97613	−	18.7062i	−0.154188	−	0.725397i
$666$		0			0
$667$	−4.30034	−	40.9150i	−0.166510	−	1.58424i
$668$		0			0
$669$	6.03211	−	28.3788i	0.233215	−	1.09719i
$670$		0			0
$671$	−17.0445	+	8.37436i	−0.657995	+	0.323289i
$672$		0			0
$673$	−23.5819	+	26.1904i	−0.909017	+	1.00957i	0.0908894	+	0.995861i	$0.471029\pi$
$673$	−23.5819	+	26.1904i	−0.909017	+	1.00957i	−0.999906	+	0.0137043i	$0.995638\pi$
$674$		0			0
$675$	−7.30431	+	5.30689i	−0.281143	+	0.204262i
$676$		0			0
$677$	−10.8042	+	33.2518i	−0.415237	+	1.27797i	0.496801	+	0.867864i	$0.334508\pi$
$677$	−10.8042	+	33.2518i	−0.415237	+	1.27797i	−0.912038	+	0.410105i	$0.865492\pi$
$678$		0			0
$679$	6.81816	−	64.8704i	0.261657	−	2.48950i
$680$		0			0
$681$		−	50.2286i		−	1.92476i
$682$		0			0
$683$	23.5351	+	13.5880i	0.900545	+	0.519930i	0.877377	−	0.479802i	$-0.159291\pi$
$683$	23.5351	+	13.5880i	0.900545	+	0.519930i	0.0231680	+	0.999732i	$0.492625\pi$
$684$		0			0
$685$	−14.3830	+	6.40371i	−0.549545	+	0.244673i
$686$		0			0
$687$	−9.21674	−	43.3614i	−0.351641	−	1.65434i
$688$		0			0
$689$	−13.5836	−	31.2579i	−0.517496	−	1.19083i
$690$		0			0
$691$	2.43748	+	2.19472i	0.0927262	+	0.0834910i	0.714190	−	0.699952i	$-0.246795\pi$
$691$	2.43748	+	2.19472i	0.0927262	+	0.0834910i	−0.621464	+	0.783443i	$0.713462\pi$
$692$		0			0
$693$	23.2788	−	58.1010i	0.884287	−	2.20707i
$694$		0			0
$695$	5.89764	−	27.7462i	0.223710	−	1.05247i
$696$		0			0
$697$	23.2340	+	31.9788i	0.880049	+	1.21128i
$698$		0			0
$699$	−10.4995	+	2.23174i	−0.397129	+	0.0844123i
$700$		0			0
$701$	33.1569	+	24.0899i	1.25232	+	0.909863i	0.998354	−	0.0573499i	$-0.0182650\pi$
$701$	33.1569	+	24.0899i	1.25232	+	0.909863i	0.253965	+	0.967213i	$0.418265\pi$
$702$		0			0
$703$	−4.52044			−0.170492
$704$		0			0
$705$	−18.3765	−	31.8291i	−0.692100	−	1.19875i
$706$		0			0
$707$	−1.44823	+	1.99332i	−0.0544663	+	0.0749665i
$708$		0			0
$709$	−5.99563	+	5.39849i	−0.225171	+	0.202745i	−0.773992	−	0.633195i	$-0.781743\pi$
$709$	−5.99563	+	5.39849i	−0.225171	+	0.202745i	0.548822	+	0.835939i	$0.315077\pi$
$710$		0			0
$711$	0.462921	+	4.40440i	0.0173609	+	0.165178i
$712$		0			0
$713$	21.1312	+	19.0266i	0.791369	+	0.712552i
$714$		0			0
$715$	−10.2490	+	18.9979i	−0.383290	+	0.710483i
$716$		0			0
$717$	21.8655	+	19.6878i	0.816583	+	0.735255i
$718$		0			0
$719$	3.18324	+	30.2865i	0.118715	+	1.12949i	0.877975	+	0.478707i	$0.158894\pi$
$719$	3.18324	+	30.2865i	0.118715	+	1.12949i	−0.759260	+	0.650787i	$0.774439\pi$
$720$		0			0
$721$	52.7891	−	47.5315i	1.96597	−	1.77017i
$722$		0			0
$723$	19.0957	−	26.2830i	0.710177	−	0.977475i
$724$		0			0
$725$	5.20703	+	9.01884i	0.193384	+	0.334951i
$726$		0			0
$727$	4.53607			0.168233			0.0841167	−	0.996456i	$-0.473193\pi$
$727$	4.53607			0.168233			0.0841167	+	0.996456i	$0.473193\pi$
$728$		0			0
$729$	35.3538	+	25.6861i	1.30940	+	0.951336i
$730$		0			0
$731$	38.9877	−	8.28709i	1.44201	−	0.306509i
$732$		0			0
$733$	2.10284	+	2.89431i	0.0776701	+	0.106904i	0.846084	−	0.533049i	$-0.178954\pi$
$733$	2.10284	+	2.89431i	0.0776701	+	0.106904i	−0.768414	+	0.639953i	$0.778954\pi$
$734$		0			0
$735$	8.55819	−	40.2631i	0.315674	−	1.48513i
$736$		0			0
$737$	0.892542	+	3.53612i	0.0328772	+	0.130255i
$738$		0			0
$739$	−25.6305	−	23.0778i	−0.942832	−	0.848930i	0.0458514	−	0.998948i	$-0.485400\pi$
$739$	−25.6305	−	23.0778i	−0.942832	−	0.848930i	−0.988683	+	0.150019i	$0.952067\pi$
$740$		0			0
$741$	25.2280	−	10.9633i	0.926775	−	0.402745i
$742$		0			0
$743$	1.73664	+	8.17024i	0.0637111	+	0.299737i	0.998454	−	0.0555883i	$-0.0177034\pi$
$743$	1.73664	+	8.17024i	0.0637111	+	0.299737i	−0.934743	+	0.355325i	$0.884370\pi$
$744$		0			0
$745$	−3.14586	+	1.40063i	−0.115255	+	0.0513150i
$746$		0			0
$747$	16.0142	+	9.24578i	0.585927	+	0.338285i
$748$		0			0
$749$			25.1751i			0.919878i
$750$		0			0
$751$	4.83467	−	45.9988i	0.176419	−	1.67852i	−0.445379	−	0.895342i	$-0.646931\pi$
$751$	4.83467	−	45.9988i	0.176419	−	1.67852i	0.621799	−	0.783177i	$-0.286402\pi$
$752$		0			0
$753$	22.1334	−	68.1196i	0.806586	−	2.48242i
$754$		0			0
$755$	−10.2624	+	7.45610i	−0.373488	+	0.271355i
$756$		0			0
$757$	23.5929	−	26.2026i	0.857500	−	0.952350i	−0.141795	−	0.989896i	$-0.545287\pi$
$757$	23.5929	−	26.2026i	0.857500	−	0.952350i	0.999295	+	0.0375458i	$0.0119540\pi$
$758$		0			0
$759$	9.08091	+	63.2834i	0.329616	+	2.29704i
$760$		0			0
$761$	6.78322	−	31.9126i	0.245892	−	1.15683i	−0.665857	−	0.746080i	$-0.731934\pi$
$761$	6.78322	−	31.9126i	0.245892	−	1.15683i	0.911748	−	0.410750i	$-0.134733\pi$
$762$		0			0
$763$	−4.26687	−	40.5965i	−0.154471	−	1.46969i
$764$		0			0
$765$	−6.32051	−	29.7357i	−0.228519	−	1.07510i
$766$		0			0
$767$	−39.7974	+	8.08829i	−1.43700	+	0.292051i
$768$		0			0
$769$	−18.7055	+	10.7996i	−0.674539	+	0.389445i	−0.797794	−	0.602930i	$-0.794000\pi$
$769$	−18.7055	+	10.7996i	−0.674539	+	0.389445i	0.123256	+	0.992375i	$0.460667\pi$
$770$		0			0
$771$	18.9209	−	32.7720i	0.681420	−	1.18025i
$772$		0			0
$773$	−20.0544	−	45.0430i	−0.721308	−	1.62008i	−0.783025	−	0.621990i	$-0.786324\pi$
$773$	−20.0544	−	45.0430i	−0.721308	−	1.62008i	0.0617173	−	0.998094i	$-0.480342\pi$
$774$		0			0
$775$	−6.84555	−	2.22425i	−0.245900	−	0.0798976i
$776$		0			0
$777$	−16.5336	−	7.36122i	−0.593139	−	0.264082i
$778$		0			0
$779$	9.57909	+	29.4814i	0.343207	+	1.05628i
$780$		0			0
$781$	−10.7755	−	21.9316i	−0.385578	−	0.784775i
$782$		0			0
$783$	−20.7443	+	23.0389i	−0.741341	+	0.823342i
$784$		0			0
$785$	−19.3992	−	26.7007i	−0.692387	−	0.952989i
$786$		0			0
$787$	−32.9114	+	29.6336i	−1.17317	+	1.05632i	−0.175754	+	0.984434i	$0.556236\pi$
$787$	−32.9114	+	29.6336i	−1.17317	+	1.05632i	−0.997413	+	0.0718897i	$0.977097\pi$
$788$		0			0
$789$	25.1331	−	11.1900i	0.894763	−	0.398374i
$790$		0			0
$791$	−10.9951	+	6.34801i	−0.390940	+	0.225709i
$792$		0			0
$793$	−15.2182	−	13.9507i	−0.540415	−	0.495404i
$794$		0			0
$795$	−47.5465	−	4.99733i	−1.68630	−	0.177237i
$796$		0			0
$797$	12.1040	+	13.4429i	0.428746	+	0.476171i	0.918347	−	0.395776i	$-0.129524\pi$
$797$	12.1040	+	13.4429i	0.428746	+	0.476171i	−0.489601	+	0.871947i	$0.662857\pi$
$798$		0			0
$799$	−25.0928	+	2.63736i	−0.887720	+	0.0933031i
$800$		0			0
$801$	−29.9439	+	9.72937i	−1.05802	+	0.343770i
$802$		0			0
$803$	−35.4163	+	13.0068i	−1.24981	+	0.458999i
$804$		0			0
$805$	14.9317	+	45.9550i	0.526272	+	1.61970i
$806$		0			0
$807$	36.9426	−	26.8404i	1.30044	−	0.944826i
$808$		0			0
$809$	16.5680	−	3.52164i	0.582501	−	0.123814i	0.0927691	−	0.995688i	$-0.470428\pi$
$809$	16.5680	−	3.52164i	0.582501	−	0.123814i	0.489731	+	0.871873i	$0.337095\pi$
$810$		0			0
$811$	26.9964	−	37.1574i	0.947972	−	1.30477i	−0.00445038	−	0.999990i	$-0.501417\pi$
$811$	26.9964	−	37.1574i	0.947972	−	1.30477i	0.952422	−	0.304781i	$-0.0985834\pi$
$812$		0			0
$813$	66.3622	+	38.3143i	2.32743	+	1.34374i
$814$		0			0
$815$	2.87977	−	4.98791i	0.100874	−	0.174719i
$816$		0			0
$817$	31.0867	+	3.26735i	1.08759	+	0.114310i
$818$		0			0
$819$	68.0408	+	0.607867i	2.37754	+	0.0212406i
$820$		0			0
$821$	−15.2291	+	34.2051i	−0.531499	+	1.19377i	0.425839	+	0.904799i	$0.359979\pi$
$821$	−15.2291	+	34.2051i	−0.531499	+	1.19377i	−0.957339	+	0.288968i	$0.906688\pi$
$822$		0			0
$823$	−21.7431	−	4.62165i	−0.757918	−	0.161100i	−0.187285	−	0.982306i	$-0.559969\pi$
$823$	−21.7431	−	4.62165i	−0.757918	−	0.161100i	−0.570633	+	0.821205i	$0.693302\pi$
$824$		0			0
$825$	−8.61556	−	13.6993i	−0.299955	−	0.476949i
$826$		0			0
$827$	−22.0959	+	7.17941i	−0.768351	+	0.249652i	−0.666859	−	0.745184i	$-0.732362\pi$
$827$	−22.0959	+	7.17941i	−0.768351	+	0.249652i	−0.101492	+	0.994836i	$0.532362\pi$
$828$		0			0
$829$	−0.180416	−	0.0803264i	−0.00626611	−	0.00278985i	0.403601	−	0.914935i	$-0.367758\pi$
$829$	−0.180416	−	0.0803264i	−0.00626611	−	0.00278985i	−0.409867	+	0.912145i	$0.634425\pi$
$830$		0			0
$831$	−1.37366	+	4.22768i	−0.0476516	+	0.146657i
$832$		0			0
$833$	−22.8614	−	16.6097i	−0.792099	−	0.575494i
$834$		0			0
$835$	0.448979	+	0.777655i	0.0155376	+	0.0269119i
$836$		0			0
$837$		−	21.4274i		−	0.740640i
$838$		0			0
$839$	−7.46918	−	16.7760i	−0.257865	−	0.579173i	0.737500	−	0.675347i	$-0.236006\pi$
$839$	−7.46918	−	16.7760i	−0.257865	−	0.579173i	−0.995365	+	0.0961738i	$0.969340\pi$
$840$		0			0
$841$	4.52272	+	5.02298i	0.155956	+	0.173206i
$842$		0			0
$843$	−1.72451	+	3.87331i	−0.0593952	+	0.133404i
$844$		0			0
$845$	−23.2906	−	2.86951i	−0.801220	−	0.0987141i
$846$		0			0
$847$	38.5757	+	18.5388i	1.32548	+	0.637000i
$848$		0			0
$849$	−55.8393	−	11.8690i	−1.91640	−	0.407344i
$850$		0			0
$851$	11.3590	−	1.19388i	0.389380	−	0.0409255i
$852$		0			0
$853$	−36.5566	−	11.8780i	−1.25167	−	0.406694i	−0.393154	−	0.919473i	$-0.628616\pi$
$853$	−36.5566	−	11.8780i	−1.25167	−	0.406694i	−0.858521	+	0.512779i	$0.828616\pi$
$854$		0			0
$855$	2.49198	−	23.7096i	0.0852241	−	0.810853i
$856$		0			0
$857$	−10.6731			−0.364586			−0.182293	−	0.983244i	$-0.558352\pi$
$857$	−10.6731			−0.364586			−0.182293	+	0.983244i	$0.558352\pi$
$858$		0			0
$859$	40.2917			1.37474			0.687368	−	0.726310i	$-0.258766\pi$
$859$	40.2917			1.37474			0.687368	+	0.726310i	$0.258766\pi$
$860$		0			0
$861$	−12.9728	+	123.428i	−0.442111	+	4.20640i
$862$		0			0
$863$	16.6956	+	5.42474i	0.568326	+	0.184660i	0.579064	−	0.815282i	$-0.303418\pi$
$863$	16.6956	+	5.42474i	0.568326	+	0.184660i	−0.0107383	+	0.999942i	$0.503418\pi$
$864$		0			0
$865$	−16.1672	+	1.69924i	−0.549702	+	0.0577760i
$866$		0			0
$867$	13.5509	+	2.88032i	0.460211	+	0.0978209i
$868$		0			0
$869$	−3.02612	+	0.114452i	−0.102654	+	0.00388252i
$870$		0			0
$871$	−3.22823	+	2.30167i	−0.109384	+	0.0779889i
$872$		0			0
$873$	33.0731	−	74.2833i	1.11935	−	2.51411i
$874$		0			0
$875$	−31.6825	−	35.1870i	−1.07106	−	1.18954i
$876$		0			0
$877$	1.79607	+	4.03404i	0.0606490	+	0.136220i	0.941327	−	0.337495i	$-0.109579\pi$
$877$	1.79607	+	4.03404i	0.0606490	+	0.136220i	−0.880678	+	0.473715i	$0.842913\pi$
$878$		0			0
$879$			44.1393i			1.48878i
$880$		0			0
$881$	1.47266	+	2.55073i	0.0496153	+	0.0859363i	0.889766	−	0.456416i	$-0.150867\pi$
$881$	1.47266	+	2.55073i	0.0496153	+	0.0859363i	−0.840151	+	0.542352i	$0.817534\pi$
$882$		0			0
$883$	−5.33376	−	3.87520i	−0.179495	−	0.130411i	0.494410	−	0.869229i	$-0.335384\pi$
$883$	−5.33376	−	3.87520i	−0.179495	−	0.130411i	−0.673905	+	0.738818i	$0.735384\pi$
$884$		0			0
$885$	−17.6038	+	54.1789i	−0.591745	+	1.82120i
$886$		0			0
$887$	23.7700	+	10.5831i	0.798119	+	0.355345i	0.764938	−	0.644104i	$-0.222770\pi$
$887$	23.7700	+	10.5831i	0.798119	+	0.355345i	0.0331808	+	0.999449i	$0.489436\pi$
$888$		0			0
$889$	−3.97779	+	1.29246i	−0.133411	+	0.0433478i
$890$		0			0
$891$	−0.0536465	+	0.0643109i	−0.00179723	+	0.00215450i
$892$		0			0
$893$	−19.3543	−	4.11388i	−0.647666	−	0.137666i
$894$		0			0
$895$	6.08908	−	13.6763i	0.203536	−	0.457148i
$896$		0			0
$897$	−60.4976	+	34.2114i	−2.01996	+	1.14228i
$898$		0			0
$899$	−24.5801	−	2.58347i	−0.819791	−	0.0861635i
$900$		0			0
$901$	−16.4103	+	28.4234i	−0.546705	+	0.946920i
$902$		0			0
$903$	108.380	+	62.5730i	3.60665	+	2.08230i
$904$		0			0
$905$	25.2982	−	34.8200i	0.840941	−	1.15746i
$906$		0			0
$907$	35.6165	−	7.57052i	1.18263	−	0.251375i	0.425693	−	0.904867i	$-0.360030\pi$
$907$	35.6165	−	7.57052i	1.18263	−	0.251375i	0.756933	+	0.653492i	$0.226697\pi$
$908$		0			0
$909$	−2.48488	+	1.80537i	−0.0824183	+	0.0598804i
$910$		0			0
$911$	9.26003	+	28.4994i	0.306798	+	0.944229i	0.979000	+	0.203860i	$0.0653488\pi$
$911$	9.26003	+	28.4994i	0.306798	+	0.944229i	−0.672202	+	0.740368i	$0.734651\pi$
$912$		0			0
$913$	−7.04026	+	10.5031i	−0.232999	+	0.347602i
$914$		0			0
$915$	−27.5424	+	8.94907i	−0.910524	+	0.295847i
$916$		0			0
$917$	1.89915	−	0.199609i	0.0627154	−	0.00659166i
$918$		0			0
$919$	−15.0670	−	16.7336i	−0.497013	−	0.551989i	0.441487	−	0.897268i	$-0.354451\pi$
$919$	−15.0670	−	16.7336i	−0.497013	−	0.551989i	−0.938500	+	0.345278i	$0.887784\pi$
$920$		0			0
$921$	−34.0134	−	3.57495i	−1.12078	−	0.117799i
$922$		0			0
$923$	17.9508	−	19.5817i	0.590857	−	0.644539i
$924$		0			0
$925$	−2.50384	+	1.44559i	−0.0823258	+	0.0475308i
$926$		0			0
$927$	80.8965	−	36.0174i	2.65699	−	1.18297i
$928$		0			0
$929$	−37.1032	+	33.4078i	−1.21732	+	1.09608i	−0.224743	+	0.974418i	$0.572154\pi$
$929$	−37.1032	+	33.4078i	−1.21732	+	1.09608i	−0.992572	+	0.121658i	$0.961179\pi$
$930$		0			0
$931$	−13.0257	−	17.9283i	−0.426899	−	0.587577i
$932$		0			0
$933$	−27.9596	+	31.0523i	−0.915356	+	1.01661i
$934$		0			0
$935$	20.5765	−	2.95265i	0.672924	−	0.0965619i
$936$		0			0
$937$	−2.16925	−	6.67627i	−0.0708663	−	0.218104i	0.909350	−	0.416031i	$-0.136579\pi$
$937$	−2.16925	−	6.67627i	−0.0708663	−	0.218104i	−0.980217	+	0.197927i	$0.936579\pi$
$938$		0			0
$939$	−30.9689	−	13.7882i	−1.01063	−	0.449962i
$940$		0			0
$941$	−10.3632	−	3.36721i	−0.337831	−	0.109768i	0.135188	−	0.990820i	$-0.456836\pi$
$941$	−10.3632	−	3.36721i	−0.337831	−	0.109768i	−0.473020	+	0.881052i	$0.656836\pi$
$942$		0			0
$943$	−31.8566	−	71.5511i	−1.03739	−	2.33002i
$944$		0			0
$945$	18.2061	−	31.5338i	0.592243	−	1.02579i
$946$		0			0
$947$	10.0510	−	5.80293i	0.326613	−	0.188570i	−0.327724	−	0.944774i	$-0.606281\pi$
$947$	10.0510	−	5.80293i	0.326613	−	0.188570i	0.654336	+	0.756204i	$0.272948\pi$
$948$		0			0
$949$	−27.1716	−	30.7247i	−0.882028	−	0.997368i
$950$		0			0
$951$	−5.22451	−	24.5794i	−0.169416	−	0.797042i
$952$		0			0
$953$	−1.01168	−	9.62547i	−0.0327714	−	0.311799i	−0.998612	−	0.0526635i	$-0.983229\pi$
$953$	−1.01168	−	9.62547i	−0.0327714	−	0.311799i	0.965841	−	0.259136i	$-0.0834378\pi$
$954$		0			0
$955$	4.32200	−	20.3334i	0.139857	−	0.657974i
$956$		0			0
$957$	−38.7172	−	39.8611i	−1.25155	−	1.28853i
$958$		0			0
$959$	−22.7072	+	25.2189i	−0.733255	+	0.814362i
$960$		0			0
$961$	−11.2595	+	8.18051i	−0.363210	+	0.263888i
$962$		0			0
$963$	−9.69799	+	29.8474i	−0.312514	+	0.961818i
$964$		0			0
$965$	−1.09354	+	10.4043i	−0.0352023	+	0.334928i
$966$		0			0
$967$			4.61146i			0.148294i	0.997247	+	0.0741472i	$0.0236235\pi$
$967$			4.61146i			0.148294i	−0.997247	+	0.0741472i	$0.976377\pi$
$968$		0			0
$969$	−22.9403	−	13.2446i	−0.736949	−	0.425478i
$970$		0			0
$971$	11.8680	−	5.28398i	0.380863	−	0.169571i	−0.207370	−	0.978263i	$-0.566490\pi$
$971$	11.8680	−	5.28398i	0.380863	−	0.169571i	0.588233	+	0.808692i	$0.299824\pi$
$972$		0			0
$973$	−12.7120	−	59.8052i	−0.407527	−	1.91727i
$974$		0			0
$975$	10.4677	−	14.1402i	0.335235	−	0.452848i
$976$		0			0
$977$	19.4524	+	17.5150i	0.622338	+	0.560356i	0.918817	−	0.394683i	$-0.129146\pi$
$977$	19.4524	+	17.5150i	0.622338	+	0.560356i	−0.296479	+	0.955039i	$0.595812\pi$
$978$		0			0
$979$	−5.26886	−	20.8745i	−0.168394	−	0.667151i
$980$		0			0
$981$	10.5799	−	49.7746i	0.337791	−	1.58918i
$982$		0			0
$983$	−19.8975	−	27.3865i	−0.634631	−	0.873494i	0.363684	−	0.931522i	$-0.381519\pi$
$983$	−19.8975	−	27.3865i	−0.634631	−	0.873494i	−0.998315	+	0.0580281i	$0.981519\pi$
$984$		0			0
$985$	−16.6824	+	3.54595i	−0.531546	+	0.112984i
$986$		0			0
$987$	−64.0894	−	46.5637i	−2.03999	−	1.48214i
$988$		0			0
$989$	−78.9778			−2.51135
$990$		0			0
$991$	−9.35374	−	16.2012i	−0.297131	−	0.514647i	0.678347	−	0.734742i	$-0.262697\pi$
$991$	−9.35374	−	16.2012i	−0.297131	−	0.514647i	−0.975478	+	0.220095i	$0.929363\pi$
$992$		0			0
$993$	23.5677	−	32.4382i	0.747899	−	1.02940i
$994$		0			0
$995$	8.80388	−	7.92705i	0.279102	−	0.251304i
$996$		0			0
$997$	−2.40677	−	22.8989i	−0.0762231	−	0.725215i	−0.964173	−	0.265274i	$-0.914537\pi$
$997$	−2.40677	−	22.8989i	−0.0762231	−	0.725215i	0.887950	−	0.459940i	$-0.152129\pi$
$998$		0			0
$999$	−6.39613	−	5.75911i	−0.202365	−	0.182210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bq.a.49.2	✓	112
11.9	even	5	inner	572.2.bq.a.361.13	yes	112
13.4	even	6	inner	572.2.bq.a.225.13	yes	112
143.108	even	30	inner	572.2.bq.a.537.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bq.a.49.2	✓	112	1.1	even	1	trivial
572.2.bq.a.225.13	yes	112	13.4	even	6	inner
572.2.bq.a.361.13	yes	112	11.9	even	5	inner
572.2.bq.a.537.2	yes	112	143.108	even	30	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.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292873 + 2.78650i) q^{3} +(-1.71678 - 0.557815i) q^{5} +(-3.86952 + 0.406703i) q^{7} +(-4.74434 - 1.00844i) q^{9} +O(q^{10})\)	\(q+(-0.292873 + 2.78650i) q^{3} +(-1.71678 - 0.557815i) q^{5} +(-3.86952 + 0.406703i) q^{7} +(-4.74434 - 1.00844i) q^{9} +(0.904947 - 3.19078i) q^{11} +(3.58902 - 0.344834i) q^{13} +(2.05715 - 4.62043i) q^{15} +(-2.32330 - 2.58028i) q^{17} +(-1.10750 - 2.48749i) q^{19} -10.9015i q^{21} +(3.43989 + 5.95807i) q^{23} +(-1.40891 - 1.02364i) q^{25} +(1.60205 - 4.93061i) q^{27} +(-5.46290 - 2.43224i) q^{29} +(3.93081 - 1.27720i) q^{31} +(8.62606 + 3.45612i) q^{33} +(6.86998 + 1.46026i) q^{35} +(0.675247 - 1.51663i) q^{37} +(-0.0902480 + 10.1018i) q^{39} +(-11.3221 - 1.19000i) q^{41} +(-5.73984 + 9.94170i) q^{43} +(7.58246 + 4.37774i) q^{45} +(4.27130 - 5.87894i) q^{47} +(7.96077 - 1.69211i) q^{49} +(7.87037 - 5.71816i) q^{51} +(-2.92102 - 8.98997i) q^{53} +(-3.33346 + 4.97307i) q^{55} +(7.25573 - 2.35753i) q^{57} +(-11.2018 + 1.17735i) q^{59} +(-3.83137 - 4.25517i) q^{61} +(18.7685 + 1.97265i) q^{63} +(-6.35391 - 1.41001i) q^{65} +(-0.952298 + 0.549810i) q^{67} +(-17.6096 + 7.84029i) q^{69} +(5.47524 - 4.92993i) q^{71} +(-6.68651 - 9.20320i) q^{73} +(3.26499 - 3.62614i) q^{75} +(-2.20401 + 12.7148i) q^{77} +(-0.282152 - 0.868375i) q^{79} +(-0.0230681 - 0.0102706i) q^{81} +(-3.62583 - 1.17811i) q^{83} +(2.54926 + 5.72574i) q^{85} +(8.37736 - 14.5100i) q^{87} +(5.62162 - 3.24564i) q^{89} +(-13.7476 + 2.79401i) q^{91} +(2.40768 + 11.3272i) q^{93} +(0.513776 + 4.88825i) q^{95} +(-3.48552 + 16.3981i) q^{97} +(-7.51109 + 14.2256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 20 q^{9}+O(q^{10}) \) 112 * q + 20 * q^9	\( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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