LMFDB - Embedded newform 572.2.bh.a.57.9

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			57.9
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.403100 - 0.292869i) q^{3} +(-0.455199 - 0.231936i) q^{5} +(-2.63712 + 0.417678i) q^{7} +(-0.850334 + 2.61706i) q^{9} +O(q^{10})$	\(q+(0.403100 - 0.292869i) q^{3} +(-0.455199 - 0.231936i) q^{5} +(-2.63712 + 0.417678i) q^{7} +(-0.850334 + 2.61706i) q^{9} +(-3.30952 + 0.216900i) q^{11} +(-3.17176 - 1.71462i) q^{13} +(-0.251417 + 0.0398206i) q^{15} +(-1.84689 - 5.68413i) q^{17} +(-1.11834 - 0.177128i) q^{19} +(-0.940695 + 0.940695i) q^{21} +7.01454i q^{23} +(-2.78551 - 3.83393i) q^{25} +(0.885597 + 2.72559i) q^{27} +(0.403264 - 0.555045i) q^{29} +(-0.0263372 - 0.0516897i) q^{31} +(-1.27054 + 1.05669i) q^{33} +(1.29729 + 0.421515i) q^{35} +(1.44055 + 9.09529i) q^{37} +(-1.78069 + 0.237749i) q^{39} +(-0.134643 - 0.0213254i) q^{41} +4.15604 q^{43} +(0.994061 - 0.994061i) q^{45} +(-10.0159 - 1.58636i) q^{47} +(0.122534 - 0.0398138i) q^{49} +(-2.40918 - 1.75037i) q^{51} +(2.30296 - 7.08777i) q^{53} +(1.55680 + 0.668864i) q^{55} +(-0.502678 + 0.256127i) q^{57} +(-1.00339 - 6.33518i) q^{59} +(7.55441 - 2.45458i) q^{61} +(1.14934 - 7.25666i) q^{63} +(1.04610 + 1.51614i) q^{65} +(-9.95536 + 9.95536i) q^{67} +(2.05434 + 2.82756i) q^{69} +(5.25701 + 2.67858i) q^{71} +(-4.90066 + 0.776188i) q^{73} +(-2.24568 - 0.729665i) q^{75} +(8.63701 - 1.95431i) q^{77} +(8.82150 + 2.86628i) q^{79} +(-5.52339 - 4.01298i) q^{81} +(-1.79256 + 3.51810i) q^{83} +(-0.477651 + 3.01577i) q^{85} -0.341842i q^{87} +(4.28948 + 4.28948i) q^{89} +(9.08047 + 3.19687i) q^{91} +(-0.0257548 - 0.0131227i) q^{93} +(0.467986 + 0.340012i) q^{95} +(-8.67157 - 17.0189i) q^{97} +(2.24656 - 8.84566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.403100	−	0.292869i	0.232730	−	0.169088i	−0.465308	−	0.885149i	$-0.654057\pi$
$3$	0.403100	−	0.292869i	0.232730	−	0.169088i	0.698038	+	0.716061i	$0.254057\pi$
$4$		0			0
$5$	−0.455199	−	0.231936i	−0.203571	−	0.103725i	0.349233	−	0.937036i	$-0.386442\pi$
$5$	−0.455199	−	0.231936i	−0.203571	−	0.103725i	−0.552804	+	0.833311i	$0.686442\pi$
$6$		0			0
$7$	−2.63712	+	0.417678i	−0.996736	+	0.157868i	−0.633428	−	0.773801i	$-0.718353\pi$
$7$	−2.63712	+	0.417678i	−0.996736	+	0.157868i	−0.363308	+	0.931669i	$0.618353\pi$
$8$		0			0
$9$	−0.850334	+	2.61706i	−0.283445	+	0.872353i
$10$		0			0
$11$	−3.30952	+	0.216900i	−0.997859	+	0.0653978i
$11$	−3.30952	+	0.216900i	−0.997859	+	0.0653978i
$12$		0			0
$13$	−3.17176	−	1.71462i	−0.879689	−	0.475549i
$13$	−3.17176	−	1.71462i	−0.879689	−	0.475549i
$14$		0			0
$15$	−0.251417	+	0.0398206i	−0.0649157	+	0.0102816i
$16$		0			0
$17$	−1.84689	−	5.68413i	−0.447935	−	1.37860i	−0.879232	−	0.476394i	$-0.841944\pi$
$17$	−1.84689	−	5.68413i	−0.447935	−	1.37860i	0.431297	−	0.902210i	$-0.358056\pi$
$18$		0			0
$19$	−1.11834	−	0.177128i	−0.256565	−	0.0406359i	0.0268268	−	0.999640i	$-0.491460\pi$
$19$	−1.11834	−	0.177128i	−0.256565	−	0.0406359i	−0.283392	+	0.959004i	$0.591460\pi$
$20$		0			0
$21$	−0.940695	+	0.940695i	−0.205277	+	0.205277i
$22$		0			0
$23$			7.01454i			1.46263i	0.682039	+	0.731316i	$0.261094\pi$
$23$			7.01454i			1.46263i	−0.682039	+	0.731316i	$0.738906\pi$
$24$		0			0
$25$	−2.78551	−	3.83393i	−0.557103	−	0.766786i
$26$		0			0
$27$	0.885597	+	2.72559i	0.170433	+	0.524540i
$28$		0			0
$29$	0.403264	−	0.555045i	0.0748842	−	0.103069i	−0.769932	−	0.638126i	$-0.779710\pi$
$29$	0.403264	−	0.555045i	0.0748842	−	0.103069i	0.844816	+	0.535057i	$0.179710\pi$
$30$		0			0
$31$	−0.0263372	−	0.0516897i	−0.00473030	−	0.00928374i	0.888629	−	0.458626i	$-0.151658\pi$
$31$	−0.0263372	−	0.0516897i	−0.00473030	−	0.00928374i	−0.893360	+	0.449342i	$0.851658\pi$
$32$		0			0
$33$	−1.27054	+	1.05669i	−0.221173	+	0.183946i
$34$		0			0
$35$	1.29729	+	0.421515i	0.219282	+	0.0712490i
$36$		0			0
$37$	1.44055	+	9.09529i	0.236825	+	1.49526i	0.763843	+	0.645402i	$0.223310\pi$
$37$	1.44055	+	9.09529i	0.236825	+	1.49526i	−0.527017	+	0.849854i	$0.676690\pi$
$38$		0			0
$39$	−1.78069	+	0.237749i	−0.285139	+	0.0380704i
$40$		0			0
$41$	−0.134643	−	0.0213254i	−0.0210277	−	0.00333046i	0.145912	−	0.989298i	$-0.453388\pi$
$41$	−0.134643	−	0.0213254i	−0.0210277	−	0.00333046i	−0.166939	+	0.985967i	$0.553388\pi$
$42$		0			0
$43$	4.15604			0.633790			0.316895	−	0.948461i	$-0.397360\pi$
$43$	4.15604			0.633790			0.316895	+	0.948461i	$0.397360\pi$
$44$		0			0
$45$	0.994061	−	0.994061i	0.148186	−	0.148186i
$46$		0			0
$47$	−10.0159	−	1.58636i	−1.46097	−	0.231395i	−0.625196	−	0.780468i	$-0.714981\pi$
$47$	−10.0159	−	1.58636i	−1.46097	−	0.231395i	−0.835775	+	0.549073i	$0.814981\pi$
$48$		0			0
$49$	0.122534	−	0.0398138i	0.0175049	−	0.00568768i
$50$		0			0
$51$	−2.40918	−	1.75037i	−0.337353	−	0.245101i
$52$		0			0
$53$	2.30296	−	7.08777i	0.316335	−	0.973580i	−0.658866	−	0.752260i	$-0.728964\pi$
$53$	2.30296	−	7.08777i	0.316335	−	0.973580i	0.975201	−	0.221320i	$-0.0710364\pi$
$54$		0			0
$55$	1.55680	+	0.668864i	0.209919	+	0.0901896i
$56$		0			0
$57$	−0.502678	+	0.256127i	−0.0665814	+	0.0339249i
$58$		0			0
$59$	−1.00339	−	6.33518i	−0.130631	−	0.824770i	−0.962793	−	0.270239i	$-0.912897\pi$
$59$	−1.00339	−	6.33518i	−0.130631	−	0.824770i	0.832163	−	0.554532i	$-0.187103\pi$
$60$		0			0
$61$	7.55441	−	2.45458i	0.967244	−	0.314276i	0.217541	−	0.976051i	$-0.430196\pi$
$61$	7.55441	−	2.45458i	0.967244	−	0.314276i	0.749703	+	0.661775i	$0.230196\pi$
$62$		0			0
$63$	1.14934	−	7.25666i	0.144803	−	0.914253i
$64$		0			0
$65$	1.04610	+	1.51614i	0.129753	+	0.188054i
$66$		0			0
$67$	−9.95536	+	9.95536i	−1.21624	+	1.21624i	−0.247303	+	0.968938i	$0.579544\pi$
$67$	−9.95536	+	9.95536i	−1.21624	+	1.21624i	−0.968938	+	0.247303i	$0.920456\pi$
$68$		0			0
$69$	2.05434	+	2.82756i	0.247314	+	0.340398i
$70$		0			0
$71$	5.25701	+	2.67858i	0.623892	+	0.317889i	0.737204	−	0.675671i	$-0.236146\pi$
$71$	5.25701	+	2.67858i	0.623892	+	0.317889i	−0.113312	+	0.993560i	$0.536146\pi$
$72$		0			0
$73$	−4.90066	+	0.776188i	−0.573579	+	0.0908459i	−0.436484	−	0.899712i	$-0.643776\pi$
$73$	−4.90066	+	0.776188i	−0.573579	+	0.0908459i	−0.137095	+	0.990558i	$0.543776\pi$
$74$		0			0
$75$	−2.24568	−	0.729665i	−0.259309	−	0.0842545i
$76$		0			0
$77$	8.63701	−	1.95431i	0.984279	−	0.222714i
$78$		0			0
$79$	8.82150	+	2.86628i	0.992497	+	0.322482i	0.759863	−	0.650083i	$-0.225266\pi$
$79$	8.82150	+	2.86628i	0.992497	+	0.322482i	0.232633	+	0.972565i	$0.425266\pi$
$80$		0			0
$81$	−5.52339	−	4.01298i	−0.613710	−	0.445886i
$82$		0			0
$83$	−1.79256	+	3.51810i	−0.196759	+	0.386162i	−0.968214	−	0.250122i	$-0.919529\pi$
$83$	−1.79256	+	3.51810i	−0.196759	+	0.386162i	0.771455	+	0.636284i	$0.219529\pi$
$84$		0			0
$85$	−0.477651	+	3.01577i	−0.0518085	+	0.327106i
$86$		0			0
$87$		−	0.341842i		−	0.0366493i
$88$		0			0
$89$	4.28948	+	4.28948i	0.454684	+	0.454684i	0.896906	−	0.442221i	$-0.145809\pi$
$89$	4.28948	+	4.28948i	0.454684	+	0.454684i	−0.442221	+	0.896906i	$0.645809\pi$
$90$		0			0
$91$	9.08047	+	3.19687i	0.951892	+	0.335123i
$92$		0			0
$93$	−0.0257548	−	0.0131227i	−0.00267065	−	0.00136076i
$94$		0			0
$95$	0.467986	+	0.340012i	0.0480144	+	0.0348845i
$96$		0			0
$97$	−8.67157	−	17.0189i	−0.880465	−	1.72801i	−0.657921	−	0.753087i	$-0.728564\pi$
$97$	−8.67157	−	17.0189i	−0.880465	−	1.72801i	−0.222543	−	0.974923i	$-0.571436\pi$
$98$		0			0
$99$	2.24656	−	8.84566i	0.225788	−	0.889022i
$100$		0			0
$101$	2.60046	−	8.00341i	0.258756	−	0.796369i	−0.734311	−	0.678814i	$-0.762494\pi$
$101$	2.60046	−	8.00341i	0.258756	−	0.796369i	0.993066	−	0.117555i	$-0.0375056\pi$
$102$		0			0
$103$	−7.95422	+	10.9480i	−0.783753	+	1.07874i	0.211105	+	0.977463i	$0.432294\pi$
$103$	−7.95422	+	10.9480i	−0.783753	+	1.07874i	−0.994858	+	0.101280i	$0.967706\pi$
$104$		0			0
$105$	0.646385	−	0.210023i	0.0630807	−	0.0204962i
$106$		0			0
$107$	1.83825	+	2.53013i	0.177710	+	0.244597i	0.888575	−	0.458732i	$-0.151696\pi$
$107$	1.83825	+	2.53013i	0.177710	+	0.244597i	−0.710865	+	0.703329i	$0.751696\pi$
$108$		0			0
$109$	4.60173	+	4.60173i	0.440766	+	0.440766i	0.892269	−	0.451504i	$-0.149112\pi$
$109$	4.60173	+	4.60173i	0.440766	+	0.440766i	−0.451504	+	0.892269i	$0.649112\pi$
$110$		0			0
$111$	3.24441	+	3.24441i	0.307946	+	0.307946i
$112$		0			0
$113$	−0.313718	+	0.227929i	−0.0295121	+	0.0214418i	−0.602444	−	0.798162i	$-0.705806\pi$
$113$	−0.313718	+	0.227929i	−0.0295121	+	0.0214418i	0.572931	+	0.819603i	$0.305806\pi$
$114$		0			0
$115$	1.62692	−	3.19301i	0.151711	−	0.297750i
$116$		0			0
$117$	7.18431	−	6.84269i	0.664190	−	0.632607i
$118$		0			0
$119$	7.24459	+	14.2183i	0.664110	+	1.30339i
$120$		0			0
$121$	10.9059	−	1.43567i	0.991446	−	0.130516i
$122$		0			0
$123$	−0.0605201	+	0.0308365i	−0.00545691	+	0.00278044i
$124$		0			0
$125$	0.778337	+	4.91423i	0.0696166	+	0.439542i
$126$		0			0
$127$	2.01531	+	6.20249i	0.178830	+	0.550382i	0.999788	−	0.0206070i	$-0.00655986\pi$
$127$	2.01531	+	6.20249i	0.178830	+	0.550382i	−0.820958	+	0.570989i	$0.806560\pi$
$128$		0			0
$129$	1.67530	−	1.21718i	0.147502	−	0.107166i
$130$		0			0
$131$		−	22.1158i		−	1.93226i	−0.258051	−	0.966131i	$-0.583080\pi$
$131$		−	22.1158i		−	1.93226i	0.258051	−	0.966131i	$-0.416920\pi$
$132$		0			0
$133$	3.02318			0.262143
$134$		0			0
$135$	0.229038	−	1.44609i	0.0197124	−	0.124459i
$136$		0			0
$137$	7.61133	−	14.9381i	0.650280	−	1.27625i	−0.296706	−	0.954969i	$-0.595888\pi$
$137$	7.61133	−	14.9381i	0.650280	−	1.27625i	0.946985	−	0.321277i	$-0.104112\pi$
$138$		0			0
$139$	−7.04882	+	9.70187i	−0.597873	+	0.822902i	−0.995512	−	0.0946406i	$-0.969830\pi$
$139$	−7.04882	+	9.70187i	−0.597873	+	0.822902i	0.397639	+	0.917542i	$0.369830\pi$
$140$		0			0
$141$	−4.50201	+	2.29389i	−0.379137	+	0.193180i
$142$		0			0
$143$	10.8689	+	4.98661i	0.908906	+	0.417002i
$144$		0			0
$145$	−0.312300	+	0.159125i	−0.0259351	+	0.0132146i
$146$		0			0
$147$	0.0377333	−	0.0519354i	0.00311219	−	0.00428356i
$148$		0			0
$149$	1.61094	−	3.16164i	0.131973	−	0.259012i	−0.815558	−	0.578675i	$-0.803570\pi$
$149$	1.61094	−	3.16164i	0.131973	−	0.259012i	0.947531	+	0.319664i	$0.103570\pi$
$150$		0			0
$151$	−1.24232	+	7.84370i	−0.101099	+	0.638311i	0.884153	+	0.467198i	$0.154736\pi$
$151$	−1.24232	+	7.84370i	−0.101099	+	0.638311i	−0.985251	+	0.171113i	$0.945264\pi$
$152$		0			0
$153$	16.4462			1.32959
$154$		0			0
$155$			0.0296377i			0.00238055i
$156$		0			0
$157$	10.3878	−	7.54715i	0.829034	−	0.602328i	−0.0902521	−	0.995919i	$-0.528767\pi$
$157$	10.3878	−	7.54715i	0.829034	−	0.602328i	0.919286	+	0.393591i	$0.128767\pi$
$158$		0			0
$159$	−1.14747	−	3.53154i	−0.0910001	−	0.280069i
$160$		0			0
$161$	−2.92982	−	18.4982i	−0.230902	−	1.45786i
$162$		0			0
$163$	−9.97342	+	5.08171i	−0.781179	+	0.398030i	−0.798634	−	0.601817i	$-0.794444\pi$
$163$	−9.97342	+	5.08171i	−0.781179	+	0.398030i	0.0174552	+	0.999848i	$0.494444\pi$
$164$		0			0
$165$	0.823435	−	0.186320i	0.0641043	−	0.0145050i
$166$		0			0
$167$	−7.28928	−	14.3060i	−0.564062	−	1.10703i	−0.980251	−	0.197755i	$-0.936635\pi$
$167$	−7.28928	−	14.3060i	−0.564062	−	1.10703i	0.416190	−	0.909278i	$-0.363365\pi$
$168$		0			0
$169$	7.12017	+	10.8767i	0.547705	+	0.836671i
$170$		0			0
$171$	1.41452	−	2.77615i	0.108171	−	0.212297i
$172$		0			0
$173$	−15.0006	+	10.8986i	−1.14047	+	0.828602i	−0.987185	−	0.159580i	$-0.948986\pi$
$173$	−15.0006	+	10.8986i	−1.14047	+	0.828602i	−0.153288	+	0.988182i	$0.548986\pi$
$174$		0			0
$175$	8.94708	+	8.94708i	0.676335	+	0.676335i
$176$		0			0
$177$	−2.25985	−	2.25985i	−0.169860	−	0.169860i
$178$		0			0
$179$	10.1466	+	13.9657i	0.758396	+	1.04384i	0.997346	+	0.0728101i	$0.0231967\pi$
$179$	10.1466	+	13.9657i	0.758396	+	1.04384i	−0.238950	+	0.971032i	$0.576803\pi$
$180$		0			0
$181$	−7.79338	+	2.53222i	−0.579277	+	0.188219i	−0.583977	−	0.811770i	$-0.698504\pi$
$181$	−7.79338	+	2.53222i	−0.579277	+	0.188219i	0.00469961	+	0.999989i	$0.498504\pi$
$182$		0			0
$183$	2.32631	−	3.20189i	0.171966	−	0.236691i
$184$		0			0
$185$	1.45378	−	4.47429i	0.106884	−	0.328956i
$186$		0			0
$187$	7.34520	+	18.4112i	0.537134	+	1.34636i
$188$		0			0
$189$	−3.47384	−	6.81780i	−0.252685	−	0.495922i
$190$		0			0
$191$	−16.4921	−	11.9822i	−1.19333	−	0.867002i	−0.199714	−	0.979854i	$-0.564001\pi$
$191$	−16.4921	−	11.9822i	−1.19333	−	0.867002i	−0.993612	+	0.112853i	$0.964001\pi$
$192$		0			0
$193$	−12.5187	−	6.37859i	−0.901115	−	0.459141i	−0.0588882	−	0.998265i	$-0.518756\pi$
$193$	−12.5187	−	6.37859i	−0.901115	−	0.459141i	−0.842227	+	0.539124i	$0.818756\pi$
$194$		0			0
$195$	0.865714	+	0.304783i	0.0619951	+	0.0218260i
$196$		0			0
$197$	10.6732	+	10.6732i	0.760435	+	0.760435i	0.976401	−	0.215966i	$-0.0692901\pi$
$197$	10.6732	+	10.6732i	0.760435	+	0.760435i	−0.215966	+	0.976401i	$0.569290\pi$
$198$		0			0
$199$			13.8086i			0.978864i	0.872042	+	0.489432i	$0.162796\pi$
$199$			13.8086i			0.978864i	−0.872042	+	0.489432i	$0.837204\pi$
$200$		0			0
$201$	−1.09739	+	6.92862i	−0.0774036	+	0.488707i
$202$		0			0
$203$	−0.831623	+	1.63215i	−0.0583685	+	0.114555i
$204$		0			0
$205$	0.0563433	+	0.0409358i	0.00393519	+	0.00285908i
$206$		0			0
$207$	−18.3575	−	5.96470i	−1.27593	−	0.414575i
$208$		0			0
$209$	3.73960	+	0.343641i	0.258674	+	0.0237701i
$210$		0			0
$211$	7.82420	+	2.54224i	0.538640	+	0.175015i	0.565688	−	0.824619i	$-0.308611\pi$
$211$	7.82420	+	2.54224i	0.538640	+	0.175015i	−0.0270478	+	0.999634i	$0.508611\pi$
$212$		0			0
$213$	2.90357	−	0.459880i	0.198949	−	0.0315105i
$214$		0			0
$215$	−1.89183	−	0.963934i	−0.129022	−	0.0657398i
$216$		0			0
$217$	0.0910440	+	0.125311i	0.00618047	+	0.00850668i
$218$		0			0
$219$	−1.74813	+	1.74813i	−0.118128	+	0.118128i
$220$		0			0
$221$	−3.88822	+	21.1954i	−0.261550	+	1.42576i
$222$		0			0
$223$	1.65921	−	10.4758i	0.111109	−	0.701514i	−0.867754	−	0.496995i	$-0.834437\pi$
$223$	1.65921	−	10.4758i	0.111109	−	0.701514i	0.978863	−	0.204519i	$-0.0655631\pi$
$224$		0			0
$225$	12.4022	−	4.02973i	0.826816	−	0.268649i
$226$		0			0
$227$	−3.90278	−	24.6412i	−0.259037	−	1.63549i	−0.683431	−	0.730015i	$-0.739513\pi$
$227$	−3.90278	−	24.6412i	−0.259037	−	1.63549i	0.424394	−	0.905477i	$-0.360487\pi$
$228$		0			0
$229$	−5.05753	+	2.57694i	−0.334211	+	0.170289i	−0.613040	−	0.790052i	$-0.710054\pi$
$229$	−5.05753	+	2.57694i	−0.334211	+	0.170289i	0.278829	+	0.960341i	$0.410054\pi$
$230$		0			0
$231$	2.90922	−	3.31729i	0.191412	−	0.218262i
$232$		0			0
$233$	6.38941	−	19.6646i	0.418584	−	1.28827i	−0.490421	−	0.871486i	$-0.663157\pi$
$233$	6.38941	−	19.6646i	0.418584	−	1.28827i	0.909005	−	0.416785i	$-0.136843\pi$
$234$		0			0
$235$	4.19130	+	3.04516i	0.273410	+	0.198644i
$236$		0			0
$237$	4.39539	−	1.42815i	0.285511	−	0.0927682i
$238$		0			0
$239$	−14.2018	−	2.24935i	−0.918639	−	0.145498i	−0.320830	−	0.947137i	$-0.603962\pi$
$239$	−14.2018	−	2.24935i	−0.918639	−	0.145498i	−0.597809	+	0.801639i	$0.703962\pi$
$240$		0			0
$241$	−15.0221	+	15.0221i	−0.967658	+	0.967658i	−0.999493	−	0.0318350i	$-0.989865\pi$
$241$	−15.0221	+	15.0221i	−0.967658	+	0.967658i	0.0318350	+	0.999493i	$0.489865\pi$
$242$		0			0
$243$	−11.9993			−0.769756
$244$		0			0
$245$	−0.0650118	−	0.0102969i	−0.00415345	−	0.000657842i
$246$		0			0
$247$	3.24341	+	2.47934i	0.206373	+	0.157756i
$248$		0			0
$249$	0.307762	+	1.94313i	0.0195036	+	0.123141i
$250$		0			0
$251$	−2.46880	−	0.802163i	−0.155829	−	0.0506321i	0.230063	−	0.973176i	$-0.426107\pi$
$251$	−2.46880	−	0.802163i	−0.155829	−	0.0506321i	−0.385893	+	0.922544i	$0.626107\pi$
$252$		0			0
$253$	−1.52145	−	23.2148i	−0.0956530	−	1.45950i
$254$		0			0
$255$	0.690685	+	1.35554i	0.0432523	+	0.0848875i
$256$		0			0
$257$	0.432245	−	0.594934i	0.0269627	−	0.0371109i	−0.795323	−	0.606186i	$-0.792699\pi$
$257$	0.432245	−	0.594934i	0.0269627	−	0.0371109i	0.822286	+	0.569075i	$0.192699\pi$
$258$		0			0
$259$	−7.59781	−	23.3837i	−0.472105	−	1.45299i
$260$		0			0
$261$	1.10968	+	1.52734i	0.0686872	+	0.0945399i
$262$		0			0
$263$			3.03629i			0.187226i	0.995609	+	0.0936128i	$0.0298416\pi$
$263$			3.03629i			0.187226i	−0.995609	+	0.0936128i	$0.970158\pi$
$264$		0			0
$265$	−2.69221	+	2.69221i	−0.165381	+	0.165381i
$266$		0			0
$267$	2.98535	+	0.472832i	0.182700	+	0.0289369i
$268$		0			0
$269$	9.56870	+	29.4494i	0.583414	+	1.79556i	0.605548	+	0.795809i	$0.292954\pi$
$269$	9.56870	+	29.4494i	0.583414	+	1.79556i	−0.0221336	+	0.999755i	$0.507046\pi$
$270$		0			0
$271$	−10.5662	+	1.67352i	−0.641850	+	0.101659i	−0.468871	−	0.883267i	$-0.655339\pi$
$271$	−10.5662	+	1.67352i	−0.641850	+	0.101659i	−0.172979	+	0.984926i	$0.555339\pi$
$272$		0			0
$273$	4.59660	−	1.37073i	0.278199	−	0.0829604i
$274$		0			0
$275$	10.0503	+	12.0843i	0.606056	+	0.728711i
$276$		0			0
$277$	−9.83260	+	30.2616i	−0.590784	+	1.81825i	−0.0160996	+	0.999870i	$0.505125\pi$
$277$	−9.83260	+	30.2616i	−0.590784	+	1.81825i	−0.574684	+	0.818375i	$0.694875\pi$
$278$		0			0
$279$	0.157670	−	0.0249725i	0.00943948	−	0.00149507i
$280$		0			0
$281$	−26.3120	−	13.4067i	−1.56964	−	0.799774i	−0.569886	−	0.821724i	$-0.693013\pi$
$281$	−26.3120	−	13.4067i	−1.56964	−	0.799774i	−0.999759	+	0.0219499i	$0.993013\pi$
$282$		0			0
$283$	−15.6885	+	11.3984i	−0.932585	+	0.677562i	−0.946624	−	0.322339i	$-0.895531\pi$
$283$	−15.6885	+	11.3984i	−0.932585	+	0.677562i	0.0140396	+	0.999901i	$0.495531\pi$
$284$		0			0
$285$	0.288224			0.0170729
$286$		0			0
$287$	0.363977			0.0214849
$288$		0			0
$289$	−15.1450	+	11.0035i	−0.890885	+	0.647266i
$290$		0			0
$291$	−8.47982	−	4.32068i	−0.497096	−	0.253283i
$292$		0			0
$293$	−15.2904	+	2.42176i	−0.893273	+	0.141480i	−0.586163	−	0.810194i	$-0.699362\pi$
$293$	−15.2904	+	2.42176i	−0.893273	+	0.141480i	−0.307110	+	0.951674i	$0.599362\pi$
$294$		0			0
$295$	−1.01261	+	3.11649i	−0.0589564	+	0.181449i
$296$		0			0
$297$	−3.52209	−	8.82831i	−0.204372	−	0.512271i
$298$		0			0
$299$	12.0273	−	22.2485i	0.695554	−	1.28666i
$300$		0			0
$301$	−10.9600	+	1.73589i	−0.631722	+	0.100055i
$302$		0			0
$303$	−1.29570	−	3.98776i	−0.0744362	−	0.229091i
$304$		0			0
$305$	−4.00807	−	0.634816i	−0.229501	−	0.0363494i
$306$		0			0
$307$	−3.71196	+	3.71196i	−0.211853	+	0.211853i	−0.805054	−	0.593201i	$-0.797864\pi$
$307$	−3.71196	+	3.71196i	−0.211853	+	0.211853i	0.593201	+	0.805054i	$0.297864\pi$
$308$		0			0
$309$			6.74270i			0.383579i
$310$		0			0
$311$	−4.71495	−	6.48958i	−0.267360	−	0.367990i	0.654136	−	0.756377i	$-0.273032\pi$
$311$	−4.71495	−	6.48958i	−0.267360	−	0.367990i	−0.921496	+	0.388387i	$0.873032\pi$
$312$		0			0
$313$	−5.21752	−	16.0579i	−0.294912	−	0.907645i	−0.983251	−	0.182256i	$-0.941660\pi$
$313$	−5.21752	−	16.0579i	−0.294912	−	0.907645i	0.688340	−	0.725389i	$-0.258340\pi$
$314$		0			0
$315$	−2.20626	+	3.03665i	−0.124309	+	0.171096i
$316$		0			0
$317$	−1.06444	−	2.08909i	−0.0597852	−	0.117335i	0.859180	−	0.511673i	$-0.170974\pi$
$317$	−1.06444	−	2.08909i	−0.0597852	−	0.117335i	−0.918966	+	0.394338i	$0.870974\pi$
$318$		0			0
$319$	−1.21422	+	1.92440i	−0.0679834	+	0.107746i
$320$		0			0
$321$	1.48199	+	0.481529i	0.0827168	+	0.0268763i
$322$		0			0
$323$	1.05863	+	6.68394i	0.0589038	+	0.371904i
$324$		0			0
$325$	2.26127	+	16.9364i	0.125432	+	0.939463i
$326$		0			0
$327$	3.20266	+	0.507251i	0.177107	+	0.0280510i
$328$		0			0
$329$	27.0757			1.49273
$330$		0			0
$331$	−9.09184	+	9.09184i	−0.499733	+	0.499733i	−0.911355	−	0.411622i	$-0.864962\pi$
$331$	−9.09184	+	9.09184i	−0.499733	+	0.499733i	0.411622	+	0.911355i	$0.364962\pi$
$332$		0			0
$333$	−25.0279	−	3.96402i	−1.37152	−	0.217227i
$334$		0			0
$335$	6.84068	−	2.22267i	0.373746	−	0.121437i
$336$		0			0
$337$	−17.4050	−	12.6455i	−0.948113	−	0.688845i	0.00224649	−	0.999997i	$-0.499285\pi$
$337$	−17.4050	−	12.6455i	−0.948113	−	0.688845i	−0.950360	+	0.311153i	$0.899285\pi$
$338$		0			0
$339$	−0.0597061	+	0.183756i	−0.00324279	+	0.00998028i
$340$		0			0
$341$	0.0983752	+	0.165356i	0.00532731	+	0.00895452i
$342$		0			0
$343$	16.3463	−	8.32887i	0.882619	−	0.449717i
$344$		0			0
$345$	−0.279323	−	1.76358i	−0.0150383	−	0.0949478i
$346$		0			0
$347$	4.74097	−	1.54044i	0.254509	−	0.0826949i	−0.178984	−	0.983852i	$-0.557281\pi$
$347$	4.74097	−	1.54044i	0.254509	−	0.0826949i	0.433493	+	0.901157i	$0.357281\pi$
$348$		0			0
$349$	−1.55601	+	9.82424i	−0.0832911	+	0.525879i	0.910400	+	0.413729i	$0.135774\pi$
$349$	−1.55601	+	9.82424i	−0.0832911	+	0.525879i	−0.993691	+	0.112151i	$0.964226\pi$
$350$		0			0
$351$	1.86444	−	10.1634i	0.0995162	−	0.542481i
$352$		0			0
$353$	−12.4105	+	12.4105i	−0.660542	+	0.660542i	−0.955508	−	0.294966i	$-0.904692\pi$
$353$	−12.4105	+	12.4105i	−0.660542	+	0.660542i	0.294966	+	0.955508i	$0.404692\pi$
$354$		0			0
$355$	−1.77173	−	2.43858i	−0.0940336	−	0.129426i
$356$		0			0
$357$	7.08439	+	3.60968i	0.374946	+	0.191044i
$358$		0			0
$359$	−16.3711	+	2.59293i	−0.864033	+	0.136849i	−0.572693	−	0.819770i	$-0.694101\pi$
$359$	−16.3711	+	2.59293i	−0.864033	+	0.136849i	−0.291340	+	0.956619i	$0.594101\pi$
$360$		0			0
$361$	−16.8508	−	5.47514i	−0.886882	−	0.288165i
$362$		0			0
$363$	3.97570	−	3.77272i	0.208670	−	0.198016i
$364$		0			0
$365$	2.41080	+	0.783317i	0.126187	+	0.0410007i
$366$		0			0
$367$	−4.98237	−	3.61991i	−0.260078	−	0.188958i	0.450104	−	0.892976i	$-0.351387\pi$
$367$	−4.98237	−	3.61991i	−0.260078	−	0.188958i	−0.710181	+	0.704019i	$0.751387\pi$
$368$		0			0
$369$	0.170301	−	0.334235i	0.00886553	−	0.0173996i
$370$		0			0
$371$	−3.11276	+	19.6532i	−0.161606	+	1.02034i
$372$		0			0
$373$		−	28.7202i		−	1.48708i	−0.668693	−	0.743538i	$-0.733146\pi$
$373$		−	28.7202i		−	1.48708i	0.668693	−	0.743538i	$-0.266854\pi$
$374$		0			0
$375$	1.75297	+	1.75297i	0.0905230	+	0.0905230i
$376$		0			0
$377$	−2.23075	+	1.06903i	−0.114889	+	0.0550577i
$378$		0			0
$379$	30.4028	+	15.4910i	1.56168	+	0.795718i	0.999510	−	0.0313003i	$-0.00996483\pi$
$379$	30.4028	+	15.4910i	1.56168	+	0.795718i	0.562175	+	0.827018i	$0.309965\pi$
$380$		0			0
$381$	2.62889	+	1.91000i	0.134682	+	0.0978522i
$382$		0			0
$383$	−2.95755	−	5.80452i	−0.151124	−	0.296597i	0.803017	−	0.595957i	$-0.203227\pi$
$383$	−2.95755	−	5.80452i	−0.151124	−	0.296597i	−0.954140	+	0.299360i	$0.903227\pi$
$384$		0			0
$385$	−4.38484	−	1.11363i	−0.223472	−	0.0567559i
$386$		0			0
$387$	−3.53402	+	10.8766i	−0.179644	+	0.552889i
$388$		0			0
$389$	−1.04028	+	1.43182i	−0.0527441	+	0.0725960i	−0.834574	−	0.550895i	$-0.814286\pi$
$389$	−1.04028	+	1.43182i	−0.0527441	+	0.0725960i	0.781830	+	0.623491i	$0.214286\pi$
$390$		0			0
$391$	39.8715	−	12.9550i	2.01639	−	0.655165i
$392$		0			0
$393$	−6.47702	−	8.91485i	−0.326722	−	0.449695i
$394$		0			0
$395$	−3.35075	−	3.35075i	−0.168595	−	0.168595i
$396$		0			0
$397$	23.5939	+	23.5939i	1.18414	+	1.18414i	0.978661	+	0.205482i	$0.0658762\pi$
$397$	23.5939	+	23.5939i	1.18414	+	1.18414i	0.205482	+	0.978661i	$0.434124\pi$
$398$		0			0
$399$	1.21864	−	0.885396i	0.0610084	−	0.0443252i
$400$		0			0
$401$	3.10618	−	6.09623i	0.155115	−	0.304431i	−0.800351	−	0.599532i	$-0.795353\pi$
$401$	3.10618	−	6.09623i	0.155115	−	0.304431i	0.955466	+	0.295101i	$0.0953533\pi$
$402$		0			0
$403$	−0.00509265	+	0.209106i	−0.000253683	+	0.0104163i
$404$		0			0
$405$	1.58349	+	3.10777i	0.0786843	+	0.154427i
$406$		0			0
$407$	−6.74031	−	29.7886i	−0.334105	−	1.47657i
$408$		0			0
$409$	14.7077	−	7.49393i	0.727248	−	0.370551i	−0.0508400	−	0.998707i	$-0.516190\pi$
$409$	14.7077	−	7.49393i	0.727248	−	0.370551i	0.778088	+	0.628156i	$0.216190\pi$
$410$		0			0
$411$	−1.30677	−	8.25065i	−0.0644584	−	0.406975i
$412$		0			0
$413$	5.29213	+	16.2875i	0.260409	+	0.801456i
$414$		0			0
$415$	1.63195	−	1.18568i	0.0801092	−	0.0582027i
$416$		0			0
$417$			5.97520i			0.292607i
$418$		0			0
$419$	13.7196			0.670249			0.335124	−	0.942174i	$-0.391222\pi$
$419$	13.7196			0.670249			0.335124	+	0.942174i	$0.391222\pi$
$420$		0			0
$421$	−2.39759	+	15.1378i	−0.116851	+	0.737769i	0.857791	+	0.513999i	$0.171837\pi$
$421$	−2.39759	+	15.1378i	−0.116851	+	0.737769i	−0.974642	+	0.223770i	$0.928163\pi$
$422$		0			0
$423$	12.6685	−	24.8633i	0.615963	−	1.20889i
$424$		0			0
$425$	−16.6480	+	22.9141i	−0.807548	+	1.11149i
$426$		0			0
$427$	−18.8966	+	9.62832i	−0.914473	+	0.465947i
$428$		0			0
$429$	5.84169	−	1.17307i	0.282039	−	0.0566364i
$430$		0			0
$431$	−28.9030	+	14.7268i	−1.39221	+	0.709366i	−0.979490	−	0.201493i	$-0.935421\pi$
$431$	−28.9030	+	14.7268i	−1.39221	+	0.709366i	−0.412719	+	0.910859i	$0.635421\pi$
$432$		0			0
$433$	−11.0114	+	15.1559i	−0.529176	+	0.728348i	−0.987004	−	0.160693i	$-0.948627\pi$
$433$	−11.0114	+	15.1559i	−0.529176	+	0.728348i	0.457829	+	0.889040i	$0.348627\pi$
$434$		0			0
$435$	−0.0792853	+	0.155606i	−0.00380144	+	0.00746074i
$436$		0			0
$437$	1.24247	−	7.84465i	0.0594354	−	0.375261i
$438$		0			0
$439$	22.0578			1.05276			0.526380	−	0.850250i	$-0.323549\pi$
$439$	22.0578			1.05276			0.526380	+	0.850250i	$0.323549\pi$
$440$		0			0
$441$			0.354534i			0.0168826i
$442$		0			0
$443$	22.2865	−	16.1921i	1.05886	−	0.769308i	0.0849844	−	0.996382i	$-0.472916\pi$
$443$	22.2865	−	16.1921i	1.05886	−	0.769308i	0.973877	+	0.227074i	$0.0729160\pi$
$444$		0			0
$445$	−0.957686	−	2.94746i	−0.0453987	−	0.139723i
$446$		0			0
$447$	−0.276579	−	1.74625i	−0.0130817	−	0.0825947i
$448$		0			0
$449$	19.6203	−	9.99704i	0.925939	−	0.471789i	0.0750762	−	0.997178i	$-0.476080\pi$
$449$	19.6203	−	9.99704i	0.925939	−	0.471789i	0.850862	+	0.525388i	$0.176080\pi$
$450$		0			0
$451$	0.450230	+	0.0413727i	0.0212005	+	0.00194817i
$452$		0			0
$453$	1.79640	+	3.52563i	0.0844021	+	0.165648i
$454$		0			0
$455$	−3.39196	−	3.56130i	−0.159017	−	0.166956i
$456$		0			0
$457$	−14.6455	+	28.7435i	−0.685090	+	1.34456i	0.242203	+	0.970226i	$0.422130\pi$
$457$	−14.6455	+	28.7435i	−0.685090	+	1.34456i	−0.927292	+	0.374338i	$0.877870\pi$
$458$		0			0
$459$	13.8570	−	10.0677i	0.646789	−	0.469920i
$460$		0			0
$461$	5.36729	+	5.36729i	0.249980	+	0.249980i	0.820962	−	0.570983i	$-0.193438\pi$
$461$	5.36729	+	5.36729i	0.249980	+	0.249980i	−0.570983	+	0.820962i	$0.693438\pi$
$462$		0			0
$463$	18.1016	+	18.1016i	0.841252	+	0.841252i	0.989022	−	0.147770i	$-0.0472094\pi$
$463$	18.1016	+	18.1016i	0.841252	+	0.841252i	−0.147770	+	0.989022i	$0.547209\pi$
$464$		0			0
$465$	0.00867995	+	0.0119469i	0.000402523	+	0.000554025i
$466$		0			0
$467$	−15.3040	+	4.97258i	−0.708185	+	0.230103i	−0.640893	−	0.767630i	$-0.721436\pi$
$467$	−15.3040	+	4.97258i	−0.708185	+	0.230103i	−0.0672920	+	0.997733i	$0.521436\pi$
$468$		0			0
$469$	22.0953	−	30.4116i	1.02027	−	1.40428i
$470$		0			0
$471$	1.97698	−	6.08451i	0.0910942	−	0.280359i
$472$		0			0
$473$	−13.7545	+	0.901446i	−0.632434	+	0.0414485i
$474$		0			0
$475$	2.43606	+	4.78104i	0.111774	+	0.219369i
$476$		0			0
$477$	16.5908	+	12.0539i	0.759642	+	0.551912i
$478$		0			0
$479$	−4.83284	−	2.46246i	−0.220818	−	0.112513i	0.340082	−	0.940396i	$-0.389545\pi$
$479$	−4.83284	−	2.46246i	−0.220818	−	0.112513i	−0.560901	+	0.827883i	$0.689545\pi$
$480$		0			0
$481$	11.0259	−	31.3181i	0.502736	−	1.42798i
$482$		0			0
$483$	−6.59854	−	6.59854i	−0.300244	−	0.300244i
$484$		0			0
$485$			9.75825i			0.443099i
$486$		0			0
$487$	0.794974	−	5.01927i	0.0360237	−	0.227445i	−0.963108	−	0.269116i	$-0.913268\pi$
$487$	0.794974	−	5.01927i	0.0360237	−	0.227445i	0.999131	+	0.0416717i	$0.0132683\pi$
$488$		0			0
$489$	−2.53201	+	4.96934i	−0.114501	+	0.224721i
$490$		0			0
$491$	−9.66969	−	7.02544i	−0.436387	−	0.317054i	0.347811	−	0.937565i	$-0.386925\pi$
$491$	−9.66969	−	7.02544i	−0.436387	−	0.317054i	−0.784198	+	0.620511i	$0.786925\pi$
$492$		0			0
$493$	−3.89973	−	1.26710i	−0.175635	−	0.0570672i
$494$		0			0
$495$	−3.07426	+	3.50548i	−0.138178	+	0.157560i
$496$		0			0
$497$	−14.9821	−	4.86799i	−0.672040	−	0.218359i
$498$		0			0
$499$	3.09218	−	0.489753i	0.138425	−	0.0219244i	−0.0868374	−	0.996222i	$-0.527676\pi$
$499$	3.09218	−	0.489753i	0.138425	−	0.0219244i	0.225262	+	0.974298i	$0.427676\pi$
$500$		0			0
$501$	−7.12810	−	3.63195i	−0.318460	−	0.162263i
$502$		0			0
$503$	−4.32601	−	5.95424i	−0.192887	−	0.265487i	0.701609	−	0.712562i	$-0.252465\pi$
$503$	−4.32601	−	5.95424i	−0.192887	−	0.265487i	−0.894496	+	0.447076i	$0.852465\pi$
$504$		0			0
$505$	−3.04001	+	3.04001i	−0.135278	+	0.135278i
$506$		0			0
$507$	6.05559	+	2.29913i	0.268938	+	0.102108i
$508$		0			0
$509$	−2.52626	+	15.9502i	−0.111974	+	0.706978i	0.866278	+	0.499562i	$0.166506\pi$
$509$	−2.52626	+	15.9502i	−0.111974	+	0.706978i	−0.978253	+	0.207417i	$0.933494\pi$
$510$		0			0
$511$	12.5994	−	4.09380i	0.557365	−	0.181099i
$512$		0			0
$513$	−0.507623	−	3.20500i	−0.0224121	−	0.141504i
$514$		0			0
$515$	6.16000	−	3.13868i	0.271442	−	0.138307i
$516$		0			0
$517$	33.4920	+	3.07766i	1.47298	+	0.135355i
$518$		0			0
$519$	−2.85488	+	8.78641i	−0.125315	+	0.385680i
$520$		0			0
$521$	17.4120	+	12.6505i	0.762832	+	0.554230i	0.899778	−	0.436349i	$-0.143729\pi$
$521$	17.4120	+	12.6505i	0.762832	+	0.554230i	−0.136946	+	0.990579i	$0.543729\pi$
$522$		0			0
$523$	11.6458	−	3.78394i	0.509234	−	0.165460i	−0.0431198	−	0.999070i	$-0.513730\pi$
$523$	11.6458	−	3.78394i	0.509234	−	0.165460i	0.552354	+	0.833610i	$0.313730\pi$
$524$		0			0
$525$	6.22688	+	0.986241i	0.271763	+	0.0430431i
$526$		0			0
$527$	−0.245169	+	0.245169i	−0.0106797	+	0.0106797i
$528$		0			0
$529$	−26.2037			−1.13929
$530$		0			0
$531$	17.4328	+	2.76108i	0.756517	+	0.119821i
$532$		0			0
$533$	0.390491	+	0.298500i	0.0169140	+	0.0129295i
$534$		0			0
$535$	−0.249942	−	1.57807i	−0.0108059	−	0.0682259i
$536$		0			0
$537$	8.18021	+	2.65791i	0.353002	+	0.114697i
$538$		0			0
$539$	−0.396895	+	0.158342i	−0.0170955	+	0.00682029i
$540$		0			0
$541$	−8.93253	−	17.5311i	−0.384040	−	0.753720i	0.615364	−	0.788243i	$-0.289009\pi$
$541$	−8.93253	−	17.5311i	−0.384040	−	0.753720i	−0.999404	+	0.0345227i	$0.989009\pi$
$542$		0			0
$543$	−2.39990	+	3.30317i	−0.102989	+	0.141753i
$544$		0			0
$545$	−1.02740	−	3.16201i	−0.0440089	−	0.135446i
$546$		0			0
$547$	−13.7796	−	18.9661i	−0.589175	−	0.810930i	0.405489	−	0.914100i	$-0.367101\pi$
$547$	−13.7796	−	18.9661i	−0.589175	−	0.810930i	−0.994664	+	0.103170i	$0.967101\pi$
$548$		0			0
$549$			21.8576i			0.932858i
$550$		0			0
$551$	−0.549301	+	0.549301i	−0.0234010	+	0.0234010i
$552$		0			0
$553$	−24.4605	−	3.87417i	−1.04017	−	0.164746i
$554$		0			0
$555$	−0.724360	−	2.22935i	−0.0307474	−	0.0946307i
$556$		0			0
$557$	40.7150	−	6.44862i	1.72515	−	0.273237i	0.786369	−	0.617757i	$-0.211958\pi$
$557$	40.7150	−	6.44862i	1.72515	−	0.273237i	0.938779	+	0.344520i	$0.111958\pi$
$558$		0			0
$559$	−13.1820	−	7.12602i	−0.557538	−	0.301399i
$560$		0			0
$561$	8.35291	+	5.27035i	0.352660	+	0.222515i
$562$		0			0
$563$	3.36416	−	10.3538i	0.141783	−	0.436362i	−0.854801	−	0.518957i	$-0.826321\pi$
$563$	3.36416	−	10.3538i	0.141783	−	0.436362i	0.996583	+	0.0825945i	$0.0263206\pi$
$564$		0			0
$565$	0.195669	−	0.0309910i	0.00823186	−	0.00130380i
$566$		0			0
$567$	16.2419	+	8.27569i	0.682098	+	0.347546i
$568$		0			0
$569$	1.68137	−	1.22159i	0.0704867	−	0.0512116i	−0.551984	−	0.833855i	$-0.686129\pi$
$569$	1.68137	−	1.22159i	0.0704867	−	0.0512116i	0.622471	+	0.782643i	$0.286129\pi$
$570$		0			0
$571$	37.0080			1.54874			0.774369	−	0.632734i	$-0.218067\pi$
$571$	37.0080			1.54874			0.774369	+	0.632734i	$0.218067\pi$
$572$		0			0
$573$	−10.1572			−0.424322
$574$		0			0
$575$	26.8933	−	19.5391i	1.12153	−	0.814836i
$576$		0			0
$577$	14.7051	+	7.49264i	0.612183	+	0.311923i	0.732452	−	0.680819i	$-0.238376\pi$
$577$	14.7051	+	7.49264i	0.612183	+	0.311923i	−0.120269	+	0.992741i	$0.538376\pi$
$578$		0			0
$579$	−6.91437	+	1.09513i	−0.287351	+	0.0455120i
$580$		0			0
$581$	3.25776	−	10.0264i	0.135155	−	0.415964i
$582$		0			0
$583$	−6.08435	+	23.9567i	−0.251988	+	0.992184i
$584$		0			0
$585$	−4.85736	+	1.44849i	−0.200827	+	0.0598878i
$586$		0			0
$587$	−0.919842	+	0.145689i	−0.0379659	+	0.00601321i	−0.175389	−	0.984499i	$-0.556118\pi$
$587$	−0.919842	+	0.145689i	−0.0379659	+	0.00601321i	0.137423	+	0.990513i	$0.456118\pi$
$588$		0			0
$589$	0.0202983	+	0.0624718i	0.000836378	+	0.00257411i
$590$		0			0
$591$	7.42822	+	1.17651i	0.305556	+	0.0483953i
$592$		0			0
$593$	8.73616	−	8.73616i	0.358751	−	0.358751i	−0.504601	−	0.863352i	$-0.668361\pi$
$593$	8.73616	−	8.73616i	0.358751	−	0.358751i	0.863352	+	0.504601i	$0.168361\pi$
$594$		0			0
$595$		−	8.15244i		−	0.334218i
$596$		0			0
$597$	4.04410	+	5.56623i	0.165514	+	0.227811i
$598$		0			0
$599$	1.76188	+	5.42252i	0.0719886	+	0.221558i	0.980577	−	0.196134i	$-0.0628389\pi$
$599$	1.76188	+	5.42252i	0.0719886	+	0.221558i	−0.908588	+	0.417693i	$0.862839\pi$
$600$		0			0
$601$	17.0823	−	23.5118i	0.696803	−	0.959066i	−0.303179	−	0.952934i	$-0.598048\pi$
$601$	17.0823	−	23.5118i	0.696803	−	0.959066i	0.999981	−	0.00613271i	$-0.00195211\pi$
$602$		0			0
$603$	−17.5884	−	34.5191i	−0.716254	−	1.40573i
$604$		0			0
$605$	−5.29735	−	1.87595i	−0.215368	−	0.0762683i
$606$		0			0
$607$	−15.3266	−	4.97992i	−0.622088	−	0.202129i	−0.0190210	−	0.999819i	$-0.506055\pi$
$607$	−15.3266	−	4.97992i	−0.622088	−	0.202129i	−0.603067	+	0.797690i	$0.706055\pi$
$608$		0			0
$609$	0.142780	+	0.901476i	0.00578573	+	0.0365297i
$610$		0			0
$611$	29.0481	+	22.2050i	1.17516	+	0.898320i
$612$		0			0
$613$	−18.2212	−	2.88595i	−0.735947	−	0.116563i	−0.222801	−	0.974864i	$-0.571520\pi$
$613$	−18.2212	−	2.88595i	−0.735947	−	0.116563i	−0.513146	+	0.858301i	$0.671520\pi$
$614$		0			0
$615$	0.0347008			0.00139927
$616$		0			0
$617$	16.0427	−	16.0427i	0.645854	−	0.645854i	−0.306134	−	0.951988i	$-0.599036\pi$
$617$	16.0427	−	16.0427i	0.645854	−	0.645854i	0.951988	+	0.306134i	$0.0990357\pi$
$618$		0			0
$619$	1.72045	+	0.272492i	0.0691506	+	0.0109524i	0.190914	−	0.981607i	$-0.438855\pi$
$619$	1.72045	+	0.272492i	0.0691506	+	0.0109524i	−0.121763	+	0.992559i	$0.538855\pi$
$620$		0			0
$621$	−19.1187	+	6.21205i	−0.767208	+	0.249281i
$622$		0			0
$623$	−13.1035	−	9.52025i	−0.524980	−	0.381421i
$624$		0			0
$625$	−6.53667	+	20.1178i	−0.261467	+	0.804712i
$626$		0			0
$627$	1.60807	−	0.956691i	0.0642202	−	0.0382066i
$628$		0			0
$629$	49.0383	−	24.9862i	1.95528	−	0.996267i
$630$		0			0
$631$	−4.76654	−	30.0947i	−0.189753	−	1.19805i	−0.880176	−	0.474647i	$-0.842576\pi$
$631$	−4.76654	−	30.0947i	−0.189753	−	1.19805i	0.690423	−	0.723405i	$-0.257424\pi$
$632$		0			0
$633$	3.89847	−	1.26669i	0.154950	−	0.0503464i
$634$		0			0
$635$	0.521210	−	3.29079i	0.0206836	−	0.130591i
$636$		0			0
$637$	−0.456915	−	0.0838195i	−0.0181036	−	0.00332105i
$638$		0			0
$639$	−11.4802	+	11.4802i	−0.454150	+	0.454150i
$640$		0			0
$641$	8.48228	+	11.6749i	0.335030	+	0.461129i	0.942982	−	0.332845i	$-0.108009\pi$
$641$	8.48228	+	11.6749i	0.335030	+	0.461129i	−0.607952	+	0.793974i	$0.708009\pi$
$642$		0			0
$643$	−33.0474	−	16.8385i	−1.30326	−	0.664045i	−0.342004	−	0.939698i	$-0.611106\pi$
$643$	−33.0474	−	16.8385i	−1.30326	−	0.664045i	−0.961257	+	0.275653i	$0.911106\pi$
$644$		0			0
$645$	−1.04490	+	0.165496i	−0.0411429	+	0.00651640i
$646$		0			0
$647$	41.6683	+	13.5389i	1.63815	+	0.532268i	0.976124	−	0.217213i	$-0.0696965\pi$
$647$	41.6683	+	13.5389i	1.63815	+	0.532268i	0.662027	+	0.749480i	$0.269697\pi$
$648$		0			0
$649$	4.69486	+	20.7488i	0.184289	+	0.814462i
$650$		0			0
$651$	0.0733996	+	0.0238490i	0.00287676	+	0.000934715i
$652$		0			0
$653$	0.142470	+	0.103510i	0.00557526	+	0.00405067i	0.590569	−	0.806987i	$-0.298903\pi$
$653$	0.142470	+	0.103510i	0.00557526	+	0.00405067i	−0.584994	+	0.811038i	$0.698903\pi$
$654$		0			0
$655$	−5.12943	+	10.0671i	−0.200424	+	0.393353i
$656$		0			0
$657$	2.13587	−	13.4853i	0.0833281	−	0.526113i
$658$		0			0
$659$			19.1974i			0.747826i	0.927464	+	0.373913i	$0.121984\pi$
$659$			19.1974i			0.747826i	−0.927464	+	0.373913i	$0.878016\pi$
$660$		0			0
$661$	12.3455	+	12.3455i	0.480183	+	0.480183i	0.905190	−	0.425007i	$-0.139728\pi$
$661$	12.3455	+	12.3455i	0.480183	+	0.480183i	−0.425007	+	0.905190i	$0.639728\pi$
$662$		0			0
$663$	4.64014	+	9.68260i	0.180208	+	0.376041i
$664$		0			0
$665$	−1.37615	−	0.701184i	−0.0533648	−	0.0271907i
$666$		0			0
$667$	3.89338	+	2.82871i	0.150752	+	0.109528i
$668$		0			0
$669$	−2.39922	−	4.70873i	−0.0927592	−	0.182050i
$670$		0			0
$671$	−24.4691	+	9.76204i	−0.944620	+	0.376859i
$672$		0			0
$673$	−6.73875	+	20.7397i	−0.259760	+	0.799458i	0.733095	+	0.680127i	$0.238075\pi$
$673$	−6.73875	+	20.7397i	−0.259760	+	0.799458i	−0.992854	+	0.119332i	$0.961925\pi$
$674$		0			0
$675$	7.98287	−	10.9875i	0.307261	−	0.422908i
$676$		0			0
$677$	−39.8033	+	12.9329i	−1.52976	+	0.497051i	−0.948530	−	0.316686i	$-0.897430\pi$
$677$	−39.8033	+	12.9329i	−1.52976	+	0.497051i	−0.581234	+	0.813737i	$0.697430\pi$
$678$		0			0
$679$	29.9764	+	41.2589i	1.15039	+	1.58337i
$680$		0			0
$681$	−8.78984	−	8.78984i	−0.336828	−	0.336828i
$682$		0			0
$683$	−9.65307	−	9.65307i	−0.369364	−	0.369364i	0.497881	−	0.867245i	$-0.334112\pi$
$683$	−9.65307	−	9.65307i	−0.369364	−	0.369364i	−0.867245	+	0.497881i	$0.834112\pi$
$684$		0			0
$685$	−6.92934	+	5.03446i	−0.264757	+	0.192357i
$686$		0			0
$687$	−1.28398	+	2.51996i	−0.0489870	+	0.0961423i
$688$		0			0
$689$	−19.4573	+	18.5320i	−0.741262	+	0.706015i
$690$		0			0
$691$	3.54210	+	6.95177i	0.134748	+	0.264458i	0.948514	−	0.316735i	$-0.102586\pi$
$691$	3.54210	+	6.95177i	0.134748	+	0.264458i	−0.813766	+	0.581192i	$0.802586\pi$
$692$		0			0
$693$	−2.22980	+	24.2654i	−0.0847033	+	0.921765i
$694$		0			0
$695$	5.45883	−	2.78141i	0.207065	−	0.105505i
$696$		0			0
$697$	0.127454	+	0.804714i	0.00482767	+	0.0304807i
$698$		0			0
$699$	−3.18358	−	9.79805i	−0.120414	−	0.370596i
$700$		0			0
$701$	−34.6267	+	25.1578i	−1.30783	+	0.950195i	−0.999999	−	0.00124556i	$-0.999604\pi$
$701$	−34.6267	+	25.1578i	−1.30783	+	0.950195i	−0.307832	+	0.951441i	$0.599604\pi$
$702$		0			0
$703$		−	10.4268i		−	0.393255i
$704$		0			0
$705$	2.58134			0.0972191
$706$		0			0
$707$	−3.51488	+	22.1921i	−0.132191	+	0.834619i
$708$		0			0
$709$	−5.57954	+	10.9505i	−0.209544	+	0.411253i	−0.971727	−	0.236109i	$-0.924128\pi$
$709$	−5.57954	+	10.9505i	−0.209544	+	0.411253i	0.762183	+	0.647362i	$0.224128\pi$
$710$		0			0
$711$	−15.0024	+	20.6491i	−0.562636	+	0.774402i
$712$		0			0
$713$	0.362579	−	0.184743i	0.0135787	−	0.00691869i
$714$		0			0
$715$	−3.79096	−	4.79080i	−0.141774	−	0.179166i
$716$		0			0
$717$	−6.38351	+	3.25256i	−0.238397	+	0.121469i
$718$		0			0
$719$	−1.57653	+	2.16991i	−0.0587947	+	0.0809240i	−0.837402	−	0.546588i	$-0.815927\pi$
$719$	−1.57653	+	2.16991i	−0.0587947	+	0.0809240i	0.778607	+	0.627512i	$0.215927\pi$
$720$		0			0
$721$	16.4034	−	32.1936i	0.610896	−	1.19895i
$722$		0			0
$723$	−1.65589	+	10.4549i	−0.0615834	+	0.388822i
$724$		0			0
$725$	−3.25130			−0.120750
$726$		0			0
$727$		−	42.5285i		−	1.57729i	−0.614847	−	0.788647i	$-0.710782\pi$
$727$		−	42.5285i		−	1.57729i	0.614847	−	0.788647i	$-0.289218\pi$
$728$		0			0
$729$	11.7332	−	8.52470i	0.434565	−	0.315730i
$730$		0			0
$731$	−7.67573	−	23.6235i	−0.283897	−	0.873746i
$732$		0			0
$733$	2.43037	+	15.3448i	0.0897679	+	0.566772i	0.991045	+	0.133529i	$0.0426309\pi$
$733$	2.43037	+	15.3448i	0.0897679	+	0.566772i	−0.901277	+	0.433243i	$0.857369\pi$
$734$		0			0
$735$	−0.0292218	+	0.0148893i	−0.00107786	+	0.000549199i
$736$		0			0
$737$	30.7882	−	35.1068i	1.13410	−	1.29318i
$738$		0			0
$739$	−12.9932	−	25.5006i	−0.477963	−	0.938056i	−0.996547	−	0.0830290i	$-0.973541\pi$
$739$	−12.9932	−	25.5006i	−0.477963	−	0.938056i	0.518584	−	0.855027i	$-0.326459\pi$
$740$		0			0
$741$	2.03354	+	0.0495257i	0.0747039	+	0.00181937i
$742$		0			0
$743$	16.8264	−	33.0237i	0.617301	−	1.21152i	−0.344761	−	0.938691i	$-0.612040\pi$
$743$	16.8264	−	33.0237i	0.617301	−	1.21152i	0.962062	−	0.272831i	$-0.0879600\pi$
$744$		0			0
$745$	−1.46659	+	1.06554i	−0.0537318	+	0.0390385i
$746$		0			0
$747$	−7.68281	−	7.68281i	−0.281099	−	0.281099i
$748$		0			0
$749$	−5.90445	−	5.90445i	−0.215744	−	0.215744i
$750$		0			0
$751$	−20.9256	−	28.8016i	−0.763586	−	1.05099i	−0.996907	−	0.0785865i	$-0.974959\pi$
$751$	−20.9256	−	28.8016i	−0.763586	−	1.05099i	0.233321	−	0.972400i	$-0.425041\pi$
$752$		0			0
$753$	−1.23010	+	0.399684i	−0.0448274	+	0.0145653i
$754$		0			0
$755$	2.38474	−	3.28231i	0.0867895	−	0.119455i
$756$		0			0
$757$	−4.28960	+	13.2020i	−0.155908	+	0.479836i	−0.998252	−	0.0591050i	$-0.981175\pi$
$757$	−4.28960	+	13.2020i	−0.155908	+	0.479836i	0.842344	+	0.538941i	$0.181175\pi$
$758$		0			0
$759$	−7.41219	−	8.91228i	−0.269045	−	0.323495i
$760$		0			0
$761$	5.77671	+	11.3374i	0.209406	+	0.410982i	0.971690	−	0.236261i	$-0.0759220\pi$
$761$	5.77671	+	11.3374i	0.209406	+	0.410982i	−0.762284	+	0.647243i	$0.775922\pi$
$762$		0			0
$763$	−14.0573	−	10.2133i	−0.508910	−	0.369744i
$764$		0			0
$765$	−7.48629	−	3.81445i	−0.270667	−	0.137912i
$766$		0			0
$767$	−7.67989	+	21.8141i	−0.277305	+	0.787663i
$768$		0			0
$769$	−1.55755	−	1.55755i	−0.0561667	−	0.0561667i	0.678466	−	0.734632i	$-0.262645\pi$
$769$	−1.55755	−	1.55755i	−0.0561667	−	0.0561667i	−0.734632	+	0.678466i	$0.762645\pi$
$770$		0			0
$771$		−	0.366409i		−	0.0131959i
$772$		0			0
$773$	−0.883227	+	5.57647i	−0.0317675	+	0.200572i	−0.998468	−	0.0553401i	$-0.982376\pi$
$773$	−0.883227	+	5.57647i	−0.0317675	+	0.200572i	0.966700	+	0.255912i	$0.0823757\pi$
$774$		0			0
$775$	−0.124812	+	0.244957i	−0.00448338	+	0.00879913i
$776$		0			0
$777$	−9.91102	−	7.20078i	−0.355556	−	0.258326i
$778$		0			0
$779$	0.146800	+	0.0476981i	0.00525964	+	0.00170896i
$780$		0			0
$781$	−17.9792	−	7.72458i	−0.643346	−	0.276407i
$782$		0			0
$783$	1.86995	+	0.607584i	0.0668266	+	0.0217133i
$784$		0			0
$785$	−6.47896	+	1.02617i	−0.231244	+	0.0366254i
$786$		0			0
$787$	−13.2016	−	6.72656i	−0.470587	−	0.239776i	0.202581	−	0.979265i	$-0.435067\pi$
$787$	−13.2016	−	6.72656i	−0.470587	−	0.239776i	−0.673168	+	0.739489i	$0.735067\pi$
$788$		0			0
$789$	0.889235	+	1.22393i	0.0316576	+	0.0435729i
$790$		0			0
$791$	0.732110	−	0.732110i	0.0260308	−	0.0260308i
$792$		0			0
$793$	−28.1695	−	5.16759i	−1.00033	−	0.183507i
$794$		0			0
$795$	−0.296764	+	1.87369i	−0.0105251	+	0.0664531i
$796$		0			0
$797$	2.44717	−	0.795133i	0.0866831	−	0.0281650i	−0.265354	−	0.964151i	$-0.585489\pi$
$797$	2.44717	−	0.795133i	0.0866831	−	0.0281650i	0.352037	+	0.935986i	$0.385489\pi$
$798$		0			0
$799$	9.48114	+	59.8616i	0.335419	+	2.11775i
$800$		0			0
$801$	−14.8733	+	7.57834i	−0.525523	+	0.267767i
$802$		0			0
$803$	16.0505	−	3.63177i	0.566410	−	0.128162i
$804$		0			0
$805$	−2.95673	+	9.09988i	−0.104211	+	0.320729i
$806$		0			0
$807$	12.4820	+	9.06868i	0.439386	+	0.319233i
$808$		0			0
$809$	−45.2130	+	14.6906i	−1.58960	+	0.516494i	−0.964508	−	0.264054i	$-0.914940\pi$
$809$	−45.2130	+	14.6906i	−1.58960	+	0.516494i	−0.625097	+	0.780547i	$0.714940\pi$
$810$		0			0
$811$	51.9383	+	8.22621i	1.82380	+	0.288861i	0.971995	−	0.235000i	$-0.0755089\pi$
$811$	51.9383	+	8.22621i	1.82380	+	0.288861i	0.851804	+	0.523861i	$0.175509\pi$
$812$		0			0
$813$	−3.76910	+	3.76910i	−0.132188	+	0.132188i
$814$		0			0
$815$	5.71853			0.200311
$816$		0			0
$817$	−4.64788	−	0.736151i	−0.162609	−	0.0257547i
$818$		0			0
$819$	−16.0878	+	21.0457i	−0.562154	+	0.735397i
$820$		0			0
$821$	−3.96379	−	25.0264i	−0.138337	−	0.873426i	−0.955064	−	0.296401i	$-0.904213\pi$
$821$	−3.96379	−	25.0264i	−0.138337	−	0.873426i	0.816726	−	0.577025i	$-0.195787\pi$
$822$		0			0
$823$	−4.86017	−	1.57917i	−0.169415	−	0.0550463i	0.223081	−	0.974800i	$-0.428388\pi$
$823$	−4.86017	−	1.57917i	−0.169415	−	0.0550463i	−0.392496	+	0.919754i	$0.628388\pi$
$824$		0			0
$825$	7.59039	+	1.92776i	0.264264	+	0.0671159i
$826$		0			0
$827$	10.5551	+	20.7156i	0.367037	+	0.720351i	0.998483	−	0.0550693i	$-0.0175380\pi$
$827$	10.5551	+	20.7156i	0.367037	+	0.720351i	−0.631445	+	0.775420i	$0.717538\pi$
$828$		0			0
$829$	21.0085	−	28.9157i	0.729656	−	1.00428i	−0.269492	−	0.963003i	$-0.586856\pi$
$829$	21.0085	−	28.9157i	0.729656	−	1.00428i	0.999148	−	0.0412821i	$-0.0131442\pi$
$830$		0			0
$831$	4.89918	+	15.0781i	0.169951	+	0.523054i
$832$		0			0
$833$	−0.452613	−	0.622969i	−0.0156821	−	0.0215846i
$834$		0			0
$835$			8.20274i			0.283867i
$836$		0			0
$837$	0.117561	−	0.117561i	0.00406349	−	0.00406349i
$838$		0			0
$839$	−0.409697	−	0.0648897i	−0.0141443	−	0.00224024i	0.149358	−	0.988783i	$-0.452279\pi$
$839$	−0.409697	−	0.0648897i	−0.0141443	−	0.00224024i	−0.163503	+	0.986543i	$0.552279\pi$
$840$		0			0
$841$	8.81604	+	27.1330i	0.304001	+	0.935620i
$842$		0			0
$843$	−14.5328	+	2.30176i	−0.500535	+	0.0792770i
$844$		0			0
$845$	−0.718397	−	6.60250i	−0.0247136	−	0.227133i
$846$		0			0
$847$	−28.1605	+	8.34120i	−0.967606	+	0.286607i
$848$		0			0
$849$	−2.98580	+	9.18935i	−0.102472	+	0.315378i
$850$		0			0
$851$	−63.7993	+	10.1048i	−2.18701	+	0.346388i
$852$		0			0
$853$	−8.81278	−	4.49034i	−0.301744	−	0.153746i	0.296563	−	0.955013i	$-0.404160\pi$
$853$	−8.81278	−	4.49034i	−0.301744	−	0.153746i	−0.598307	+	0.801267i	$0.704160\pi$
$854$		0			0
$855$	−1.28778	+	0.935624i	−0.0440410	+	0.0319977i
$856$		0			0
$857$	−41.6087			−1.42132			−0.710662	−	0.703533i	$-0.751605\pi$
$857$	−41.6087			−1.42132			−0.710662	+	0.703533i	$0.751605\pi$
$858$		0			0
$859$	21.5457			0.735130			0.367565	−	0.929998i	$-0.380192\pi$
$859$	21.5457			0.735130			0.367565	+	0.929998i	$0.380192\pi$
$860$		0			0
$861$	0.146719	−	0.106597i	0.00500016	−	0.00363283i
$862$		0			0
$863$	−17.9391	−	9.14042i	−0.610653	−	0.311143i	0.121176	−	0.992631i	$-0.461333\pi$
$863$	−17.9391	−	9.14042i	−0.610653	−	0.311143i	−0.731830	+	0.681488i	$0.761333\pi$
$864$		0			0
$865$	9.35602	−	1.48185i	0.318114	−	0.0503843i
$866$		0			0
$867$	−2.88237	+	8.87103i	−0.0978905	+	0.301276i
$868$		0			0
$869$	−29.8167	−	7.57264i	−1.01146	−	0.256884i
$870$		0			0
$871$	48.6457	−	14.5064i	1.64830	−	0.491531i
$872$		0			0
$873$	51.9132	−	8.22225i	1.75700	−	0.278281i
$874$		0			0
$875$	−4.10513	−	12.6343i	−0.138779	−	0.427117i
$876$		0			0
$877$	−4.46392	−	0.707015i	−0.150736	−	0.0238742i	0.0806105	−	0.996746i	$-0.474313\pi$
$877$	−4.46392	−	0.707015i	−0.150736	−	0.0238742i	−0.231346	+	0.972871i	$0.574313\pi$
$878$		0			0
$879$	−5.45428	+	5.45428i	−0.183968	+	0.183968i
$880$		0			0
$881$		−	35.3524i		−	1.19105i	−0.803336	−	0.595527i	$-0.796943\pi$
$881$		−	35.3524i		−	1.19105i	0.803336	−	0.595527i	$-0.203057\pi$
$882$		0			0
$883$	8.47572	+	11.6658i	0.285231	+	0.392586i	0.927458	−	0.373928i	$-0.121989\pi$
$883$	8.47572	+	11.6658i	0.285231	+	0.392586i	−0.642227	+	0.766515i	$0.721989\pi$
$884$		0			0
$885$	0.504542	+	1.55282i	0.0169600	+	0.0521974i
$886$		0			0
$887$	−1.12436	+	1.54755i	−0.0377523	+	0.0519615i	−0.827476	−	0.561501i	$-0.810224\pi$
$887$	−1.12436	+	1.54755i	−0.0377523	+	0.0519615i	0.789724	+	0.613463i	$0.210224\pi$
$888$		0			0
$889$	−7.90526	−	15.5149i	−0.265134	−	0.520354i
$890$		0			0
$891$	19.1502	+	12.0830i	0.641556	+	0.404796i
$892$		0			0
$893$	10.9202	+	3.54820i	0.365431	+	0.118736i
$894$		0			0
$895$	−1.37961	−	8.71053i	−0.0461153	−	0.291161i
$896$		0			0
$897$	−1.66770	−	12.4908i	−0.0556830	−	0.417054i
$898$		0			0
$899$	−0.0393109	−	0.00622624i	−0.00131109	−	0.000207657i
$900$		0			0
$901$	−44.5411			−1.48388
$902$		0			0
$903$	−3.90957	+	3.90957i	−0.130102	+	0.130102i
$904$		0			0
$905$	4.13485	+	0.654896i	0.137447	+	0.0217695i
$906$		0			0
$907$	−33.7453	+	10.9645i	−1.12050	+	0.364071i	−0.809957	−	0.586490i	$-0.800509\pi$
$907$	−33.7453	+	10.9645i	−1.12050	+	0.364071i	−0.310539	+	0.950561i	$0.600509\pi$
$908$		0			0
$909$	18.7341	+	13.6111i	0.621372	+	0.451453i
$910$		0			0
$911$	−3.84628	+	11.8376i	−0.127433	+	0.392198i	−0.994337	−	0.106278i	$-0.966107\pi$
$911$	−3.84628	+	11.8376i	−0.127433	+	0.392198i	0.866904	+	0.498476i	$0.166107\pi$
$912$		0			0
$913$	5.16946	−	12.0321i	0.171084	−	0.398203i
$914$		0			0
$915$	−1.80157	+	0.917945i	−0.0595580	+	0.0303463i
$916$		0			0
$917$	9.23727	+	58.3218i	0.305042	+	1.92596i
$918$		0			0
$919$	−3.39107	+	1.10183i	−0.111861	+	0.0363459i	−0.364413	−	0.931238i	$-0.618730\pi$
$919$	−3.39107	+	1.10183i	−0.111861	+	0.0363459i	0.252552	+	0.967583i	$0.418730\pi$
$920$		0			0
$921$	−0.409172	+	2.58341i	−0.0134827	+	0.0851263i
$922$		0			0
$923$	−12.0812	−	17.5096i	−0.397659	−	0.576335i
$924$		0			0
$925$	30.8580	−	30.8580i	1.01461	−	1.01461i
$926$		0			0
$927$	−21.8879	−	30.1262i	−0.718894	−	0.989473i
$928$		0			0
$929$	25.5929	+	13.0403i	0.839677	+	0.427837i	0.820271	−	0.571975i	$-0.193823\pi$
$929$	25.5929	+	13.0403i	0.839677	+	0.427837i	0.0194059	+	0.999812i	$0.493823\pi$
$930$		0			0
$931$	−0.144087	+	0.0228212i	−0.00472227	+	0.000747934i
$932$		0			0
$933$	−3.80119	−	1.23508i	−0.124445	−	0.0404348i
$934$		0			0
$935$	0.926677	−	10.0844i	0.0303056	−	0.329794i
$936$		0			0
$937$	−50.1827	−	16.3053i	−1.63940	−	0.532672i	−0.662993	−	0.748626i	$-0.730714\pi$
$937$	−50.1827	−	16.3053i	−1.63940	−	0.532672i	−0.976404	+	0.215954i	$0.930714\pi$
$938$		0			0
$939$	−6.80603	−	4.94487i	−0.222106	−	0.161370i
$940$		0			0
$941$	−4.23786	+	8.31727i	−0.138150	+	0.271135i	−0.949708	−	0.313137i	$-0.898620\pi$
$941$	−4.23786	+	8.31727i	−0.138150	+	0.271135i	0.811558	+	0.584272i	$0.198620\pi$
$942$		0			0
$943$	0.149588	−	0.944459i	0.00487124	−	0.0307558i
$944$		0			0
$945$			3.90917i			0.127165i
$946$		0			0
$947$	−29.3506	−	29.3506i	−0.953767	−	0.953767i	0.0452106	−	0.998977i	$-0.485604\pi$
$947$	−29.3506	−	29.3506i	−0.953767	−	0.953767i	−0.998977	+	0.0452106i	$0.985604\pi$
$948$		0			0
$949$	16.8746	+	5.94087i	0.547773	+	0.192849i
$950$		0			0
$951$	−1.04091	−	0.530368i	−0.0337537	−	0.0171984i
$952$		0			0
$953$	15.2561	+	11.0842i	0.494195	+	0.359053i	0.806795	−	0.590831i	$-0.201200\pi$
$953$	15.2561	+	11.0842i	0.494195	+	0.359053i	−0.312601	+	0.949885i	$0.601200\pi$
$954$		0			0
$955$	4.72809	+	9.27939i	0.152997	+	0.300274i
$956$		0			0
$957$	0.0741455	+	1.13133i	0.00239678	+	0.0365708i
$958$		0			0
$959$	−13.8327	+	42.5725i	−0.446680	+	1.37474i
$960$		0			0
$961$	18.2194	−	25.0768i	0.587721	−	0.808929i
$962$		0			0
$963$	−8.18463	+	2.65935i	−0.263746	+	0.0856962i
$964$		0			0
$965$	4.21908	+	5.80706i	0.135817	+	0.186936i
$966$		0			0
$967$	1.29517	+	1.29517i	0.0416500	+	0.0416500i	0.727625	−	0.685975i	$-0.240624\pi$
$967$	1.29517	+	1.29517i	0.0416500	+	0.0416500i	−0.685975	+	0.727625i	$0.740624\pi$
$968$		0			0
$969$	2.38425	+	2.38425i	0.0765932	+	0.0765932i
$970$		0			0
$971$	−31.7544	+	23.0709i	−1.01905	+	0.740380i	−0.966087	−	0.258217i	$-0.916865\pi$
$971$	−31.7544	+	23.0709i	−1.01905	+	0.740380i	−0.0529588	+	0.998597i	$0.516865\pi$
$972$		0			0
$973$	14.5363	−	28.5291i	0.466012	−	0.914601i
$974$		0			0
$975$	5.87166	+	6.16481i	0.188044	+	0.197432i
$976$		0			0
$977$	18.5469	+	36.4004i	0.593369	+	1.16455i	0.971108	+	0.238641i	$0.0767018\pi$
$977$	18.5469	+	36.4004i	0.593369	+	1.16455i	−0.377739	+	0.925912i	$0.623298\pi$
$978$		0			0
$979$	−15.1265	−	13.2658i	−0.483446	−	0.423976i
$980$		0			0
$981$	−15.9560	+	8.12999i	−0.509436	+	0.259570i
$982$		0			0
$983$	−0.938785	−	5.92726i	−0.0299426	−	0.189050i	0.968183	−	0.250241i	$-0.0805100\pi$
$983$	−0.938785	−	5.92726i	−0.0299426	−	0.189050i	−0.998126	+	0.0611914i	$0.980510\pi$
$984$		0			0
$985$	−2.38294	−	7.33394i	−0.0759268	−	0.233679i
$986$		0			0
$987$	10.9142	−	7.92964i	0.347403	−	0.252403i
$988$		0			0
$989$			29.1527i			0.927002i
$990$		0			0
$991$	−48.8657			−1.55227			−0.776135	−	0.630567i	$-0.782822\pi$
$991$	−48.8657			−1.55227			−0.776135	+	0.630567i	$0.782822\pi$
$992$		0			0
$993$	−1.00220	+	6.32763i	−0.0318038	+	0.200801i
$994$		0			0
$995$	3.20270	−	6.28565i	0.101532	−	0.199269i
$996$		0			0
$997$	29.7372	−	40.9298i	0.941787	−	1.29626i	−0.0132930	−	0.999912i	$-0.504231\pi$
$997$	29.7372	−	40.9298i	0.941787	−	1.29626i	0.955080	−	0.296347i	$-0.0957686\pi$
$998$		0			0
$999$	−23.5143	+	11.9811i	−0.743958	+	0.379066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.9	✓	112
11.6	odd	10	inner	572.2.bh.a.369.9	yes	112
13.8	odd	4	inner	572.2.bh.a.541.9	yes	112
143.138	even	20	inner	572.2.bh.a.281.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.9	✓	112	1.1	even	1	trivial
572.2.bh.a.281.9	yes	112	143.138	even	20	inner
572.2.bh.a.369.9	yes	112	11.6	odd	10	inner
572.2.bh.a.541.9	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)

\(f(q)\)	\(=\)	\(q+(0.403100 - 0.292869i) q^{3} +(-0.455199 - 0.231936i) q^{5} +(-2.63712 + 0.417678i) q^{7} +(-0.850334 + 2.61706i) q^{9} +O(q^{10})\)	\(q+(0.403100 - 0.292869i) q^{3} +(-0.455199 - 0.231936i) q^{5} +(-2.63712 + 0.417678i) q^{7} +(-0.850334 + 2.61706i) q^{9} +(-3.30952 + 0.216900i) q^{11} +(-3.17176 - 1.71462i) q^{13} +(-0.251417 + 0.0398206i) q^{15} +(-1.84689 - 5.68413i) q^{17} +(-1.11834 - 0.177128i) q^{19} +(-0.940695 + 0.940695i) q^{21} +7.01454i q^{23} +(-2.78551 - 3.83393i) q^{25} +(0.885597 + 2.72559i) q^{27} +(0.403264 - 0.555045i) q^{29} +(-0.0263372 - 0.0516897i) q^{31} +(-1.27054 + 1.05669i) q^{33} +(1.29729 + 0.421515i) q^{35} +(1.44055 + 9.09529i) q^{37} +(-1.78069 + 0.237749i) q^{39} +(-0.134643 - 0.0213254i) q^{41} +4.15604 q^{43} +(0.994061 - 0.994061i) q^{45} +(-10.0159 - 1.58636i) q^{47} +(0.122534 - 0.0398138i) q^{49} +(-2.40918 - 1.75037i) q^{51} +(2.30296 - 7.08777i) q^{53} +(1.55680 + 0.668864i) q^{55} +(-0.502678 + 0.256127i) q^{57} +(-1.00339 - 6.33518i) q^{59} +(7.55441 - 2.45458i) q^{61} +(1.14934 - 7.25666i) q^{63} +(1.04610 + 1.51614i) q^{65} +(-9.95536 + 9.95536i) q^{67} +(2.05434 + 2.82756i) q^{69} +(5.25701 + 2.67858i) q^{71} +(-4.90066 + 0.776188i) q^{73} +(-2.24568 - 0.729665i) q^{75} +(8.63701 - 1.95431i) q^{77} +(8.82150 + 2.86628i) q^{79} +(-5.52339 - 4.01298i) q^{81} +(-1.79256 + 3.51810i) q^{83} +(-0.477651 + 3.01577i) q^{85} -0.341842i q^{87} +(4.28948 + 4.28948i) q^{89} +(9.08047 + 3.19687i) q^{91} +(-0.0257548 - 0.0131227i) q^{93} +(0.467986 + 0.340012i) q^{95} +(-8.67157 - 17.0189i) q^{97} +(2.24656 - 8.84566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 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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