LMFDB - Embedded newform 360.2.bs.a.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(113,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("360.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bs (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			113.1
Character	$\chi$	$=$	360.113
Dual form			360.2.bs.a.137.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72328 - 0.174114i) q^{3} +(-1.74059 + 1.40368i) q^{5} +(-2.54088 - 0.680826i) q^{7} +(2.93937 + 0.600095i) q^{9} +O(q^{10})$	\(q+(-1.72328 - 0.174114i) q^{3} +(-1.74059 + 1.40368i) q^{5} +(-2.54088 - 0.680826i) q^{7} +(2.93937 + 0.600095i) q^{9} +(5.33659 - 3.08108i) q^{11} +(3.45681 - 0.926249i) q^{13} +(3.24393 - 2.11587i) q^{15} +(0.800862 + 0.800862i) q^{17} -8.38516i q^{19} +(4.26010 + 1.61566i) q^{21} +(1.32620 + 4.94943i) q^{23} +(1.05934 - 4.88649i) q^{25} +(-4.96086 - 1.54592i) q^{27} +(0.324362 + 0.561812i) q^{29} +(-0.700374 + 1.21308i) q^{31} +(-9.73289 + 4.38038i) q^{33} +(5.37830 - 2.38155i) q^{35} +(-0.0631533 + 0.0631533i) q^{37} +(-6.11831 + 0.994303i) q^{39} +(7.04010 + 4.06460i) q^{41} +(1.56795 - 5.85166i) q^{43} +(-5.95859 + 3.08142i) q^{45} +(1.59358 - 5.94730i) q^{47} +(-0.0696399 - 0.0402066i) q^{49} +(-1.24067 - 1.51955i) q^{51} +(8.49399 - 8.49399i) q^{53} +(-4.96398 + 12.8538i) q^{55} +(-1.45998 + 14.4500i) q^{57} +(-2.14435 + 3.71412i) q^{59} +(-2.30249 - 3.98802i) q^{61} +(-7.06002 - 3.52597i) q^{63} +(-4.71674 + 6.46449i) q^{65} +(1.61334 + 6.02107i) q^{67} +(-1.42364 - 8.76015i) q^{69} +9.73625i q^{71} +(-2.53137 - 2.53137i) q^{73} +(-2.67635 + 8.23633i) q^{75} +(-15.6573 + 4.19537i) q^{77} +(6.44596 - 3.72158i) q^{79} +(8.27977 + 3.52780i) q^{81} +(-5.50142 - 1.47410i) q^{83} +(-2.51813 - 0.269819i) q^{85} +(-0.461146 - 1.02463i) q^{87} -7.85776 q^{89} -9.41394 q^{91} +(1.41815 - 1.96853i) q^{93} +(11.7701 + 14.5952i) q^{95} +(6.53148 + 1.75011i) q^{97} +(17.5352 - 5.85398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) $ 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.72328	−	0.174114i	−0.994935	−	0.100525i
$3$	−1.72328	−	0.174114i	−0.994935	−	0.100525i
$4$		0			0
$5$	−1.74059	+	1.40368i	−0.778418	+	0.627747i
$5$	−1.74059	+	1.40368i	−0.778418	+	0.627747i
$6$		0			0
$7$	−2.54088	−	0.680826i	−0.960362	−	0.257328i	−0.255608	−	0.966780i	$-0.582276\pi$
$7$	−2.54088	−	0.680826i	−0.960362	−	0.257328i	−0.704753	+	0.709452i	$0.748942\pi$
$8$		0			0
$9$	2.93937	+	0.600095i	0.979789	+	0.200032i
$10$		0			0
$11$	5.33659	−	3.08108i	1.60904	−	0.928982i	0.619459	−	0.785029i	$-0.287352\pi$
$11$	5.33659	−	3.08108i	1.60904	−	0.928982i	0.989585	−	0.143953i	$-0.0459814\pi$
$12$		0			0
$13$	3.45681	−	0.926249i	0.958746	−	0.256895i	0.254676	−	0.967026i	$-0.418031\pi$
$13$	3.45681	−	0.926249i	0.958746	−	0.256895i	0.704069	+	0.710131i	$0.251364\pi$
$14$		0			0
$15$	3.24393	−	2.11587i	0.837579	−	0.546316i
$16$		0			0
$17$	0.800862	+	0.800862i	0.194238	+	0.194238i	0.797524	−	0.603287i	$-0.206143\pi$
$17$	0.800862	+	0.800862i	0.194238	+	0.194238i	−0.603287	+	0.797524i	$0.706143\pi$
$18$		0			0
$19$		−	8.38516i		−	1.92369i	−0.273599	−	0.961844i	$-0.588214\pi$
$19$		−	8.38516i		−	1.92369i	0.273599	−	0.961844i	$-0.411786\pi$
$20$		0			0
$21$	4.26010	+	1.61566i	0.929629	+	0.352565i
$22$		0			0
$23$	1.32620	+	4.94943i	0.276531	+	1.03203i	0.954808	+	0.297222i	$0.0960601\pi$
$23$	1.32620	+	4.94943i	0.276531	+	1.03203i	−0.678277	+	0.734806i	$0.737273\pi$
$24$		0			0
$25$	1.05934	−	4.88649i	0.211868	−	0.977298i
$26$		0			0
$27$	−4.96086	−	1.54592i	−0.954718	−	0.297512i
$28$		0			0
$29$	0.324362	+	0.561812i	0.0602325	+	0.104326i	0.894569	−	0.446929i	$-0.147482\pi$
$29$	0.324362	+	0.561812i	0.0602325	+	0.104326i	−0.834337	+	0.551255i	$0.814149\pi$
$30$		0			0
$31$	−0.700374	+	1.21308i	−0.125791	+	0.217876i	−0.922042	−	0.387090i	$-0.873480\pi$
$31$	−0.700374	+	1.21308i	−0.125791	+	0.217876i	0.796251	+	0.604966i	$0.206813\pi$
$32$		0			0
$33$	−9.73289	+	4.38038i	−1.69428	+	0.762527i
$34$		0			0
$35$	5.37830	−	2.38155i	0.909099	−	0.402555i
$36$		0			0
$37$	−0.0631533	+	0.0631533i	−0.0103823	+	0.0103823i	−0.712279	−	0.701897i	$-0.752337\pi$
$37$	−0.0631533	+	0.0631533i	−0.0103823	+	0.0103823i	0.701897	+	0.712279i	$0.252337\pi$
$38$		0			0
$39$	−6.11831	+	0.994303i	−0.979714	+	0.159216i
$40$		0			0
$41$	7.04010	+	4.06460i	1.09948	+	0.634784i	0.936084	−	0.351777i	$-0.114422\pi$
$41$	7.04010	+	4.06460i	1.09948	+	0.634784i	0.163394	+	0.986561i	$0.447756\pi$
$42$		0			0
$43$	1.56795	−	5.85166i	0.239110	−	0.892370i	−0.737143	−	0.675737i	$-0.763826\pi$
$43$	1.56795	−	5.85166i	0.239110	−	0.892370i	0.976253	−	0.216634i	$-0.0695077\pi$
$44$		0			0
$45$	−5.95859	+	3.08142i	−0.888255	+	0.459351i
$46$		0			0
$47$	1.59358	−	5.94730i	0.232447	−	0.867504i	−0.746836	−	0.665008i	$-0.768428\pi$
$47$	1.59358	−	5.94730i	0.232447	−	0.867504i	0.979283	−	0.202496i	$-0.0649052\pi$
$48$		0			0
$49$	−0.0696399	−	0.0402066i	−0.00994856	−	0.00574381i
$50$		0			0
$51$	−1.24067	−	1.51955i	−0.173728	−	0.212779i
$52$		0			0
$53$	8.49399	−	8.49399i	1.16674	−	1.16674i	0.183771	−	0.982969i	$-0.441170\pi$
$53$	8.49399	−	8.49399i	1.16674	−	1.16674i	0.982969	−	0.183771i	$-0.0588304\pi$
$54$		0			0
$55$	−4.96398	+	12.8538i	−0.669343	+	1.73321i
$56$		0			0
$57$	−1.45998	+	14.4500i	−0.193379	+	1.91394i
$58$		0			0
$59$	−2.14435	+	3.71412i	−0.279170	+	0.483537i	−0.971179	−	0.238352i	$-0.923393\pi$
$59$	−2.14435	+	3.71412i	−0.279170	+	0.483537i	0.692009	+	0.721889i	$0.256726\pi$
$60$		0			0
$61$	−2.30249	−	3.98802i	−0.294803	−	0.510614i	0.680136	−	0.733086i	$-0.261921\pi$
$61$	−2.30249	−	3.98802i	−0.294803	−	0.510614i	−0.974939	+	0.222472i	$0.928587\pi$
$62$		0			0
$63$	−7.06002	−	3.52597i	−0.889479	−	0.444230i
$64$		0			0
$65$	−4.71674	+	6.46449i	−0.585040	+	0.801821i
$66$		0			0
$67$	1.61334	+	6.02107i	0.197101	+	0.735591i	0.991713	+	0.128473i	$0.0410077\pi$
$67$	1.61334	+	6.02107i	0.197101	+	0.735591i	−0.794612	+	0.607118i	$0.792326\pi$
$68$		0			0
$69$	−1.42364	−	8.76015i	−0.171386	−	1.05460i
$70$		0			0
$71$			9.73625i			1.15548i	0.816221	+	0.577740i	$0.196065\pi$
$71$			9.73625i			1.15548i	−0.816221	+	0.577740i	$0.803935\pi$
$72$		0			0
$73$	−2.53137	−	2.53137i	−0.296275	−	0.296275i	0.543278	−	0.839553i	$-0.317183\pi$
$73$	−2.53137	−	2.53137i	−0.296275	−	0.296275i	−0.839553	+	0.543278i	$0.817183\pi$
$74$		0			0
$75$	−2.67635	+	8.23633i	−0.309038	+	0.951050i
$76$		0			0
$77$	−15.6573	+	4.19537i	−1.78432	+	0.478106i
$78$		0			0
$79$	6.44596	−	3.72158i	0.725227	−	0.418710i	−0.0914465	−	0.995810i	$-0.529149\pi$
$79$	6.44596	−	3.72158i	0.725227	−	0.418710i	0.816673	+	0.577100i	$0.195816\pi$
$80$		0			0
$81$	8.27977	+	3.52780i	0.919975	+	0.391978i
$82$		0			0
$83$	−5.50142	−	1.47410i	−0.603860	−	0.161804i	−0.0560799	−	0.998426i	$-0.517860\pi$
$83$	−5.50142	−	1.47410i	−0.603860	−	0.161804i	−0.547780	+	0.836623i	$0.684527\pi$
$84$		0			0
$85$	−2.51813	−	0.269819i	−0.273130	−	0.0292660i
$86$		0			0
$87$	−0.461146	−	1.02463i	−0.0494401	−	0.109852i
$88$		0			0
$89$	−7.85776			−0.832920			−0.416460	−	0.909154i	$-0.636729\pi$
$89$	−7.85776			−0.832920			−0.416460	+	0.909154i	$0.636729\pi$
$90$		0			0
$91$	−9.41394			−0.986849
$92$		0			0
$93$	1.41815	−	1.96853i	0.147056	−	0.204127i
$94$		0			0
$95$	11.7701	+	14.5952i	1.20759	+	1.49743i
$96$		0			0
$97$	6.53148	+	1.75011i	0.663172	+	0.177696i	0.574677	−	0.818380i	$-0.305128\pi$
$97$	6.53148	+	1.75011i	0.663172	+	0.177696i	0.0884947	+	0.996077i	$0.471794\pi$
$98$		0			0
$99$	17.5352	−	5.85398i	1.76235	−	0.588347i
$100$		0			0
$101$	3.38936	−	1.95685i	0.337254	−	0.194714i	−0.321803	−	0.946807i	$-0.604289\pi$
$101$	3.38936	−	1.95685i	0.337254	−	0.194714i	0.659057	+	0.752093i	$0.270956\pi$
$102$		0			0
$103$	−13.8977	+	3.72388i	−1.36938	+	0.366925i	−0.867253	−	0.497868i	$-0.834116\pi$
$103$	−13.8977	+	3.72388i	−1.36938	+	0.366925i	−0.502129	+	0.864793i	$0.667450\pi$
$104$		0			0
$105$	−9.68297	+	3.16763i	−0.944961	+	0.309129i
$106$		0			0
$107$	0.411412	+	0.411412i	0.0397727	+	0.0397727i	0.726713	−	0.686941i	$-0.241047\pi$
$107$	0.411412	+	0.411412i	0.0397727	+	0.0397727i	−0.686941	+	0.726713i	$0.741047\pi$
$108$		0			0
$109$		−	8.97384i		−	0.859538i	−0.902939	−	0.429769i	$-0.858595\pi$
$109$		−	8.97384i		−	0.859538i	0.902939	−	0.429769i	$-0.141405\pi$
$110$		0			0
$111$	0.119826	−	0.0978347i	0.0113734	−	0.00928606i
$112$		0			0
$113$	−3.58897	−	13.3942i	−0.337622	−	1.26002i	−0.900998	−	0.433823i	$-0.857164\pi$
$113$	−3.58897	−	13.3942i	−0.337622	−	1.26002i	0.563376	−	0.826201i	$-0.309502\pi$
$114$		0			0
$115$	−9.25581	−	6.75339i	−0.863108	−	0.629757i
$116$		0			0
$117$	10.7167	−	0.648174i	0.990756	−	0.0599237i
$118$		0			0
$119$	−1.48965	−	2.58014i	−0.136556	−	0.236521i
$120$		0			0
$121$	13.4862	−	23.3587i	1.22601	−	2.12352i
$122$		0			0
$123$	−11.4243	−	8.23022i	−1.03010	−	0.742094i
$124$		0			0
$125$	5.01521	+	9.99238i	0.448574	+	0.893746i
$126$		0			0
$127$	6.82894	−	6.82894i	0.605971	−	0.605971i	−0.335920	−	0.941891i	$-0.609047\pi$
$127$	6.82894	−	6.82894i	0.605971	−	0.605971i	0.941891	+	0.335920i	$0.109047\pi$
$128$		0			0
$129$	−3.72087	+	9.81103i	−0.327604	+	0.863813i
$130$		0			0
$131$	−1.24875	−	0.720966i	−0.109104	−	0.0629911i	0.444455	−	0.895801i	$-0.353397\pi$
$131$	−1.24875	−	0.720966i	−0.109104	−	0.0629911i	−0.553559	+	0.832810i	$0.686731\pi$
$132$		0			0
$133$	−5.70884	+	21.3057i	−0.495019	+	1.84744i
$134$		0			0
$135$	10.8048	−	4.27267i	0.929932	−	0.367733i
$136$		0			0
$137$	−0.145325	+	0.542362i	−0.0124160	+	0.0463371i	−0.971856	−	0.235576i	$-0.924302\pi$
$137$	−0.145325	+	0.542362i	−0.0124160	+	0.0463371i	0.959440	+	0.281913i	$0.0909690\pi$
$138$		0			0
$139$	5.04248	+	2.91128i	0.427698	+	0.246932i	0.698365	−	0.715741i	$-0.253911\pi$
$139$	5.04248	+	2.91128i	0.427698	+	0.246932i	−0.270667	+	0.962673i	$0.587244\pi$
$140$		0			0
$141$	−3.78168	+	9.97139i	−0.318475	+	0.839743i
$142$		0			0
$143$	15.5937	−	15.5937i	1.30401	−	1.30401i
$144$		0			0
$145$	−1.35319	−	0.522585i	−0.112376	−	0.0433983i
$146$		0			0
$147$	0.113008	+	0.0814125i	0.00932077	+	0.00671479i
$148$		0			0
$149$	−3.84151	+	6.65369i	−0.314709	+	0.545091i	−0.979376	−	0.202049i	$-0.935240\pi$
$149$	−3.84151	+	6.65369i	−0.314709	+	0.545091i	0.664667	+	0.747140i	$0.268573\pi$
$150$		0			0
$151$	8.52279	+	14.7619i	0.693575	+	1.20131i	0.970659	+	0.240461i	$0.0772986\pi$
$151$	8.52279	+	14.7619i	0.693575	+	1.20131i	−0.277084	+	0.960846i	$0.589368\pi$
$152$		0			0
$153$	1.87344	+	2.83462i	0.151458	+	0.229166i
$154$		0			0
$155$	−0.483718	−	3.09459i	−0.0388532	−	0.248563i
$156$		0			0
$157$	−1.19633	−	4.46475i	−0.0954773	−	0.356326i	0.901614	−	0.432541i	$-0.142383\pi$
$157$	−1.19633	−	4.46475i	−0.0954773	−	0.356326i	−0.997091	+	0.0762153i	$0.975716\pi$
$158$		0			0
$159$	−16.1164	+	13.1586i	−1.27812	+	1.04354i
$160$		0			0
$161$		−	13.4788i		−	1.06228i
$162$		0			0
$163$	11.7779	+	11.7779i	0.922520	+	0.922520i	0.997207	−	0.0746875i	$-0.0237959\pi$
$163$	11.7779	+	11.7779i	0.922520	+	0.922520i	−0.0746875	+	0.997207i	$0.523796\pi$
$164$		0			0
$165$	10.7923	−	21.2864i	0.840183	−	1.65714i
$166$		0			0
$167$	0.561218	−	0.150378i	0.0434283	−	0.0116366i	−0.237039	−	0.971500i	$-0.576177\pi$
$167$	0.561218	−	0.150378i	0.0434283	−	0.0116366i	0.280468	+	0.959863i	$0.409510\pi$
$168$		0			0
$169$	−0.166748	+	0.0962717i	−0.0128267	+	0.00740552i
$170$		0			0
$171$	5.03189	−	24.6471i	0.384798	−	1.88481i
$172$		0			0
$173$	−4.59483	−	1.23118i	−0.349339	−	0.0936051i	0.0798828	−	0.996804i	$-0.474545\pi$
$173$	−4.59483	−	1.23118i	−0.349339	−	0.0936051i	−0.429222	+	0.903199i	$0.641212\pi$
$174$		0			0
$175$	−6.01851	+	11.6948i	−0.454957	+	0.884040i
$176$		0			0
$177$	4.34198	−	6.02709i	0.326364	−	0.453024i
$178$		0			0
$179$	3.38027			0.252653			0.126327	−	0.991989i	$-0.459681\pi$
$179$	3.38027			0.252653			0.126327	+	0.991989i	$0.459681\pi$
$180$		0			0
$181$	−4.35623			−0.323796			−0.161898	−	0.986807i	$-0.551762\pi$
$181$	−4.35623			−0.323796			−0.161898	+	0.986807i	$0.551762\pi$
$182$		0			0
$183$	3.27345	+	7.27336i	0.241980	+	0.537662i
$184$		0			0
$185$	0.0212770	−	0.198571i	0.00156432	−	0.0145993i
$186$		0			0
$187$	6.74140	+	1.80635i	0.492980	+	0.132094i
$188$		0			0
$189$	11.5524	+	7.30547i	0.840317	+	0.531395i
$190$		0			0
$191$	−15.3224	+	8.84638i	−1.10869	+	0.640101i	−0.938489	−	0.345309i	$-0.887774\pi$
$191$	−15.3224	+	8.84638i	−1.10869	+	0.640101i	−0.170199	+	0.985410i	$0.554441\pi$
$192$		0			0
$193$	19.8730	−	5.32497i	1.43049	−	0.383300i	0.541299	−	0.840830i	$-0.317933\pi$
$193$	19.8730	−	5.32497i	1.43049	−	0.383300i	0.889194	+	0.457530i	$0.151266\pi$
$194$		0			0
$195$	9.25381	−	10.3189i	0.662679	−	0.738949i
$196$		0			0
$197$	−0.624346	−	0.624346i	−0.0444828	−	0.0444828i	0.684516	−	0.728998i	$-0.260014\pi$
$197$	−0.624346	−	0.624346i	−0.0444828	−	0.0444828i	−0.728998	+	0.684516i	$0.760014\pi$
$198$		0			0
$199$			7.11122i			0.504101i	0.967714	+	0.252051i	$0.0811050\pi$
$199$			7.11122i			0.504101i	−0.967714	+	0.252051i	$0.918895\pi$
$200$		0			0
$201$	−1.73188	−	10.6569i	−0.122157	−	0.751679i
$202$		0			0
$203$	−0.441668	−	1.64833i	−0.0309990	−	0.115690i
$204$		0			0
$205$	−17.9594	+	2.80725i	−1.25434	+	0.196067i
$206$		0			0
$207$	0.928051	+	15.3440i	0.0645040	+	1.06648i
$208$		0			0
$209$	−25.8354	−	44.7482i	−1.78707	−	3.09530i
$210$		0			0
$211$	−6.69912	+	11.6032i	−0.461187	+	0.798799i	−0.999020	−	0.0442521i	$-0.985910\pi$
$211$	−6.69912	+	11.6032i	−0.461187	+	0.798799i	0.537834	+	0.843051i	$0.319243\pi$
$212$		0			0
$213$	1.69522	−	16.7783i	0.116155	−	1.14963i
$214$		0			0
$215$	5.48472	+	12.3863i	0.374055	+	0.844737i
$216$		0			0
$217$	2.60546	−	2.60546i	0.176870	−	0.176870i
$218$		0			0
$219$	3.92151	+	4.80301i	0.264991	+	0.324557i
$220$		0			0
$221$	3.51022	+	2.02663i	0.236123	+	0.136326i
$222$		0			0
$223$	0.724558	−	2.70409i	0.0485200	−	0.181079i	−0.937413	−	0.348219i	$-0.886787\pi$
$223$	0.724558	−	2.70409i	0.0485200	−	0.181079i	0.985933	+	0.167140i	$0.0534532\pi$
$224$		0			0
$225$	6.04615	−	13.7275i	0.403077	−	0.915166i
$226$		0			0
$227$	4.75219	−	17.7354i	0.315414	−	1.17714i	−0.608189	−	0.793792i	$-0.708104\pi$
$227$	4.75219	−	17.7354i	0.315414	−	1.17714i	0.923603	−	0.383349i	$-0.125229\pi$
$228$		0			0
$229$	−8.46679	−	4.88830i	−0.559501	−	0.323028i	0.193444	−	0.981111i	$-0.438034\pi$
$229$	−8.46679	−	4.88830i	−0.559501	−	0.323028i	−0.752945	+	0.658083i	$0.771368\pi$
$230$		0			0
$231$	27.7124	−	4.50361i	1.82334	−	0.296316i
$232$		0			0
$233$	−6.43409	+	6.43409i	−0.421511	+	0.421511i	−0.885724	−	0.464212i	$-0.846337\pi$
$233$	−6.43409	+	6.43409i	−0.421511	+	0.421511i	0.464212	+	0.885724i	$0.346337\pi$
$234$		0			0
$235$	5.57437	+	12.5887i	0.363632	+	0.821198i
$236$		0			0
$237$	−11.7562	+	5.29097i	−0.763644	+	0.343686i
$238$		0			0
$239$	−3.98061	+	6.89462i	−0.257484	+	0.445976i	−0.965567	−	0.260153i	$-0.916227\pi$
$239$	−3.98061	+	6.89462i	−0.257484	+	0.445976i	0.708083	+	0.706129i	$0.249560\pi$
$240$		0			0
$241$	6.88496	+	11.9251i	0.443499	+	0.768163i	0.997946	−	0.0640556i	$-0.0204035\pi$
$241$	6.88496	+	11.9251i	0.443499	+	0.768163i	−0.554447	+	0.832219i	$0.687070\pi$
$242$		0			0
$243$	−13.6541	−	7.52100i	−0.875911	−	0.482473i
$244$		0			0
$245$	0.177652	−	0.0277690i	0.0113498	−	0.00177410i
$246$		0			0
$247$	−7.76674	−	28.9859i	−0.494186	−	1.84433i
$248$		0			0
$249$	9.22382	+	3.49816i	0.584536	+	0.221687i
$250$		0			0
$251$			15.1395i			0.955599i	0.878469	+	0.477800i	$0.158566\pi$
$251$			15.1395i			0.955599i	−0.878469	+	0.477800i	$0.841434\pi$
$252$		0			0
$253$	22.3270	+	22.3270i	1.40369	+	1.40369i
$254$		0			0
$255$	4.29246	+	0.903417i	0.268804	+	0.0565741i
$256$		0			0
$257$	−13.2826	+	3.55907i	−0.828548	+	0.222009i	−0.648080	−	0.761572i	$-0.724428\pi$
$257$	−13.2826	+	3.55907i	−0.828548	+	0.222009i	−0.180468	+	0.983581i	$0.557761\pi$
$258$		0			0
$259$	0.203461	−	0.117468i	0.0126425	−	0.00729913i
$260$		0			0
$261$	0.616279	+	1.84602i	0.0381467	+	0.114266i
$262$		0			0
$263$	−1.60721	−	0.430651i	−0.0991049	−	0.0265551i	0.208926	−	0.977931i	$-0.433003\pi$
$263$	−1.60721	−	0.430651i	−0.0991049	−	0.0265551i	−0.308031	+	0.951376i	$0.599670\pi$
$264$		0			0
$265$	−2.86172	+	26.7075i	−0.175794	+	1.64063i
$266$		0			0
$267$	13.5411	+	1.36815i	0.828701	+	0.0837293i
$268$		0			0
$269$	25.6407			1.56334			0.781670	−	0.623692i	$-0.214368\pi$
$269$	25.6407			1.56334			0.781670	+	0.623692i	$0.214368\pi$
$270$		0			0
$271$	3.33314			0.202474			0.101237	−	0.994862i	$-0.467720\pi$
$271$	3.33314			0.202474			0.101237	+	0.994862i	$0.467720\pi$
$272$		0			0
$273$	16.2228	+	1.63910i	0.981850	+	0.0992030i
$274$		0			0
$275$	−9.40241	−	29.3411i	−0.566987	−	1.76934i
$276$		0			0
$277$	13.3972	+	3.58978i	0.804962	+	0.215689i	0.637762	−	0.770234i	$-0.279860\pi$
$277$	13.3972	+	3.58978i	0.804962	+	0.215689i	0.167201	+	0.985923i	$0.446527\pi$
$278$		0			0
$279$	−2.78662	+	3.14541i	−0.166831	+	0.188311i
$280$		0			0
$281$	−9.51966	+	5.49618i	−0.567895	+	0.327875i	−0.756308	−	0.654215i	$-0.772999\pi$
$281$	−9.51966	+	5.49618i	−0.567895	+	0.327875i	0.188413	+	0.982090i	$0.439666\pi$
$282$		0			0
$283$	−9.04353	+	2.42321i	−0.537582	+	0.144045i	−0.517387	−	0.855751i	$-0.673095\pi$
$283$	−9.04353	+	2.42321i	−0.537582	+	0.144045i	−0.0201948	+	0.999796i	$0.506429\pi$
$284$		0			0
$285$	−17.7419	−	27.2009i	−1.05094	−	1.61124i
$286$		0			0
$287$	−15.1207	−	15.1207i	−0.892549	−	0.892549i
$288$		0			0
$289$		−	15.7172i		−	0.924544i
$290$		0			0
$291$	−10.9508	−	4.15314i	−0.641950	−	0.243462i
$292$		0			0
$293$	0.189505	+	0.707241i	0.0110710	+	0.0413174i	0.971240	−	0.238101i	$-0.0765250\pi$
$293$	0.189505	+	0.707241i	0.0110710	+	0.0413174i	−0.960169	+	0.279419i	$0.909858\pi$
$294$		0			0
$295$	−1.48101	−	9.47476i	−0.0862276	−	0.551642i
$296$		0			0
$297$	−31.2372	+	7.03490i	−1.81257	+	0.408207i
$298$		0			0
$299$	9.16881	+	15.8808i	0.530246	+	0.918413i
$300$		0			0
$301$	−7.96793	+	13.8009i	−0.459264	+	0.795469i
$302$		0			0
$303$	−6.18152	+	2.78206i	−0.355119	+	0.159825i
$304$		0			0
$305$	9.60562	+	3.70957i	0.550016	+	0.212409i
$306$		0			0
$307$	2.31491	−	2.31491i	0.132119	−	0.132119i	−0.637955	−	0.770074i	$-0.720219\pi$
$307$	2.31491	−	2.31491i	0.132119	−	0.132119i	0.770074	+	0.637955i	$0.220219\pi$
$308$		0			0
$309$	24.5980	−	3.99749i	1.39933	−	0.227409i
$310$		0			0
$311$	−15.3710	−	8.87444i	−0.871609	−	0.503223i	−0.00372614	−	0.999993i	$-0.501186\pi$
$311$	−15.3710	−	8.87444i	−0.871609	−	0.503223i	−0.867882	+	0.496770i	$0.834519\pi$
$312$		0			0
$313$	−6.22033	+	23.2146i	−0.351594	+	1.31217i	0.533124	+	0.846037i	$0.321018\pi$
$313$	−6.22033	+	23.2146i	−0.351594	+	1.31217i	−0.884717	+	0.466128i	$0.845649\pi$
$314$		0			0
$315$	17.2380	−	3.77275i	0.971250	−	0.212571i
$316$		0			0
$317$	−6.02987	+	22.5038i	−0.338671	+	1.26394i	0.561163	+	0.827706i	$0.310354\pi$
$317$	−6.02987	+	22.5038i	−0.338671	+	1.26394i	−0.899834	+	0.436233i	$0.856312\pi$
$318$		0			0
$319$	3.46198	+	1.99877i	0.193834	+	0.111910i
$320$		0			0
$321$	−0.637345	−	0.780611i	−0.0355731	−	0.0435694i
$322$		0			0
$323$	6.71536	−	6.71536i	0.373652	−	0.373652i
$324$		0			0
$325$	−0.864166	−	17.8729i	−0.0479353	−	0.991409i
$326$		0			0
$327$	−1.56247	+	15.4644i	−0.0864050	+	0.855184i
$328$		0			0
$329$	−8.09816	+	14.0264i	−0.446466	+	0.773302i
$330$		0			0
$331$	−10.3186	−	17.8723i	−0.567162	−	0.982353i	−0.996845	−	0.0793734i	$-0.974708\pi$
$331$	−10.3186	−	17.8723i	−0.567162	−	0.982353i	0.429683	−	0.902980i	$-0.358625\pi$
$332$		0			0
$333$	−0.223529	+	0.147733i	−0.0122493	+	0.00809570i
$334$		0			0
$335$	−11.2599	−	8.21563i	−0.615192	−	0.448868i
$336$		0			0
$337$	2.47106	+	9.22213i	0.134607	+	0.502362i	0.999999	+	0.00126580i	$0.000402917\pi$
$337$	2.47106	+	9.22213i	0.134607	+	0.502362i	−0.865392	+	0.501096i	$0.832930\pi$
$338$		0			0
$339$	3.85267	+	23.7069i	0.209248	+	1.28758i
$340$		0			0
$341$			8.63164i			0.467430i
$342$		0			0
$343$	13.1699	+	13.1699i	0.711110	+	0.711110i
$344$		0			0
$345$	14.7745	+	13.2495i	0.795430	+	0.713331i
$346$		0			0
$347$	2.89721	−	0.776304i	0.155530	−	0.0416742i	−0.180214	−	0.983627i	$-0.557679\pi$
$347$	2.89721	−	0.776304i	0.155530	−	0.0416742i	0.335744	+	0.941953i	$0.391012\pi$
$348$		0			0
$349$	−26.6912	+	15.4102i	−1.42875	+	0.824888i	−0.997022	−	0.0771170i	$-0.975429\pi$
$349$	−26.6912	+	15.4102i	−1.42875	+	0.824888i	−0.431726	+	0.902005i	$0.642095\pi$
$350$		0			0
$351$	−18.5806	−	0.748943i	−0.991762	−	0.0399756i
$352$		0			0
$353$	8.34629	+	2.23638i	0.444228	+	0.119031i	0.473997	−	0.880526i	$-0.342811\pi$
$353$	8.34629	+	2.23638i	0.444228	+	0.119031i	−0.0297694	+	0.999557i	$0.509477\pi$
$354$		0			0
$355$	−13.6666	−	16.9469i	−0.725349	−	0.899447i
$356$		0			0
$357$	2.11783	+	4.70567i	0.112088	+	0.249050i
$358$		0			0
$359$	−36.4319			−1.92280			−0.961400	−	0.275154i	$-0.911271\pi$
$359$	−36.4319			−1.92280			−0.961400	+	0.275154i	$0.911271\pi$
$360$		0			0
$361$	−51.3109			−2.70057
$362$		0			0
$363$	−27.3075	+	37.9054i	−1.43327	+	1.98952i
$364$		0			0
$365$	7.95935	+	0.852847i	0.416611	+	0.0446401i
$366$		0			0
$367$	2.85637	+	0.765362i	0.149101	+	0.0399516i	0.332598	−	0.943069i	$-0.392075\pi$
$367$	2.85637	+	0.765362i	0.149101	+	0.0399516i	−0.183496	+	0.983020i	$0.558742\pi$
$368$		0			0
$369$	18.2543	+	16.1721i	0.950280	+	0.841885i
$370$		0			0
$371$	−27.3651	+	15.7993i	−1.42073	+	0.820257i
$372$		0			0
$373$	−16.3417	+	4.37875i	−0.846141	+	0.226723i	−0.655743	−	0.754984i	$-0.727645\pi$
$373$	−16.3417	+	4.37875i	−0.846141	+	0.226723i	−0.190398	+	0.981707i	$0.560978\pi$
$374$		0			0
$375$	−6.90277	−	18.0929i	−0.356458	−	0.934312i
$376$		0			0
$377$	1.64163	+	1.64163i	0.0845485	+	0.0845485i
$378$		0			0
$379$		−	28.6200i		−	1.47011i	−0.678007	−	0.735055i	$-0.737156\pi$
$379$		−	28.6200i		−	1.47011i	0.678007	−	0.735055i	$-0.262844\pi$
$380$		0			0
$381$	−12.9572	+	10.5791i	−0.663816	+	0.541986i
$382$		0			0
$383$	−0.180708	−	0.674411i	−0.00923375	−	0.0344608i	0.961155	−	0.276008i	$-0.0890117\pi$
$383$	−0.180708	−	0.674411i	−0.00923375	−	0.0344608i	−0.970389	+	0.241547i	$0.922345\pi$
$384$		0			0
$385$	21.3641	−	29.2804i	1.08881	−	1.49227i
$386$		0			0
$387$	8.12033	−	16.2593i	0.412780	−	0.826505i
$388$		0			0
$389$	11.1938	+	19.3882i	0.567546	+	0.983019i	0.996808	+	0.0798388i	$0.0254406\pi$
$389$	11.1938	+	19.3882i	0.567546	+	0.983019i	−0.429261	+	0.903180i	$0.641226\pi$
$390$		0			0
$391$	−2.90171	+	5.02591i	−0.146746	+	0.254171i
$392$		0			0
$393$	2.02641	+	1.45985i	0.102219	+	0.0736397i
$394$		0			0
$395$	−5.99589	+	15.5258i	−0.301686	+	0.781190i
$396$		0			0
$397$	−14.4119	+	14.4119i	−0.723315	+	0.723315i	−0.969279	−	0.245964i	$-0.920895\pi$
$397$	−14.4119	+	14.4119i	−0.723315	+	0.723315i	0.245964	+	0.969279i	$0.420895\pi$
$398$		0			0
$399$	13.5475	−	35.7216i	0.678225	−	1.78832i
$400$		0			0
$401$	21.3370	+	12.3189i	1.06552	+	0.615177i	0.926953	−	0.375177i	$-0.122418\pi$
$401$	21.3370	+	12.3189i	1.06552	+	0.615177i	0.138564	+	0.990353i	$0.455751\pi$
$402$		0			0
$403$	−1.29744	+	4.84211i	−0.0646301	+	0.241203i
$404$		0			0
$405$	−19.3636	+	5.48172i	−0.962187	+	0.272389i
$406$		0			0
$407$	−0.142443	+	0.531604i	−0.00706063	+	0.0263506i
$408$		0			0
$409$	33.7496	+	19.4853i	1.66881	+	0.963488i	0.968281	+	0.249865i	$0.0803864\pi$
$409$	33.7496	+	19.4853i	1.66881	+	0.963488i	0.700530	+	0.713623i	$0.252947\pi$
$410$		0			0
$411$	0.344869	−	0.909337i	0.0170111	−	0.0448543i
$412$		0			0
$413$	7.97719	−	7.97719i	0.392532	−	0.392532i
$414$		0			0
$415$	11.6449	−	5.15645i	0.571627	−	0.253120i
$416$		0			0
$417$	−8.18270	−	5.89491i	−0.400709	−	0.288675i
$418$		0			0
$419$	−5.96480	+	10.3313i	−0.291400	+	0.504719i	−0.974141	−	0.225941i	$-0.927454\pi$
$419$	−5.96480	+	10.3313i	−0.291400	+	0.504719i	0.682741	+	0.730660i	$0.260788\pi$
$420$		0			0
$421$	−14.4601	−	25.0457i	−0.704743	−	1.22065i	−0.966784	−	0.255594i	$-0.917729\pi$
$421$	−14.4601	−	25.0457i	−0.704743	−	1.22065i	0.262041	−	0.965057i	$-0.415604\pi$
$422$		0			0
$423$	8.25305	−	16.5250i	0.401277	−	0.803474i
$424$		0			0
$425$	4.76179	−	3.06502i	0.230981	−	0.148675i
$426$		0			0
$427$	3.13518	+	11.7007i	0.151722	+	0.566235i
$428$		0			0
$429$	−29.5874	+	24.1572i	−1.42849	+	1.16632i
$430$		0			0
$431$		−	13.3062i		−	0.640939i	−0.947259	−	0.320469i	$-0.896159\pi$
$431$		−	13.3062i		−	0.640939i	0.947259	−	0.320469i	$-0.103841\pi$
$432$		0			0
$433$	2.51255	+	2.51255i	0.120746	+	0.120746i	0.764898	−	0.644152i	$-0.222790\pi$
$433$	2.51255	+	2.51255i	0.120746	+	0.120746i	−0.644152	+	0.764898i	$0.722790\pi$
$434$		0			0
$435$	2.24093	+	1.13617i	0.107444	+	0.0544751i
$436$		0			0
$437$	41.5018	−	11.1204i	1.98530	−	0.531959i
$438$		0			0
$439$	−2.38919	+	1.37940i	−0.114030	+	0.0658351i	−0.555930	−	0.831229i	$-0.687638\pi$
$439$	−2.38919	+	1.37940i	−0.114030	+	0.0658351i	0.441900	+	0.897064i	$0.354304\pi$
$440$		0			0
$441$	−0.180570	−	0.159973i	−0.00859855	−	0.00761775i
$442$		0			0
$443$	20.7012	+	5.54688i	0.983545	+	0.263540i	0.714537	−	0.699598i	$-0.246637\pi$
$443$	20.7012	+	5.54688i	0.983545	+	0.263540i	0.269008	+	0.963138i	$0.413304\pi$
$444$		0			0
$445$	13.6772	−	11.0298i	0.648360	−	0.522863i
$446$		0			0
$447$	7.77849	−	10.7973i	0.367910	−	0.510694i
$448$		0			0
$449$	−14.4127			−0.680175			−0.340088	−	0.940394i	$-0.610457\pi$
$449$	−14.4127			−0.680175			−0.340088	+	0.940394i	$0.610457\pi$
$450$		0			0
$451$	50.0935			2.35881
$452$		0			0
$453$	−12.1169	−	26.9228i	−0.569300	−	1.26494i
$454$		0			0
$455$	16.3859	−	13.2142i	0.768181	−	0.619491i
$456$		0			0
$457$	37.9692	+	10.1738i	1.77612	+	0.475911i	0.989868	−	0.141992i	$-0.0453506\pi$
$457$	37.9692	+	10.1738i	1.77612	+	0.475911i	0.786255	+	0.617902i	$0.212017\pi$
$458$		0			0
$459$	−2.73490	−	5.21103i	−0.127654	−	0.243230i
$460$		0			0
$461$	32.0478	−	18.5028i	1.49262	−	0.861762i	0.492651	−	0.870227i	$-0.336028\pi$
$461$	32.0478	−	18.5028i	1.49262	−	0.861762i	0.999964	+	0.00846527i	$0.00269461\pi$
$462$		0			0
$463$	32.6052	−	8.73654i	1.51529	−	0.406022i	0.597104	−	0.802164i	$-0.296318\pi$
$463$	32.6052	−	8.73654i	1.51529	−	0.406022i	0.918189	+	0.396142i	$0.129651\pi$
$464$		0			0
$465$	0.294768	+	5.41706i	0.0136695	+	0.251210i
$466$		0			0
$467$	−11.4422	−	11.4422i	−0.529483	−	0.529483i	0.390935	−	0.920418i	$-0.372152\pi$
$467$	−11.4422	−	11.4422i	−0.529483	−	0.529483i	−0.920418	+	0.390935i	$0.872152\pi$
$468$		0			0
$469$		−	16.3972i		−	0.757153i
$470$		0			0
$471$	1.28422	+	7.90230i	0.0591740	+	0.364119i
$472$		0			0
$473$	−9.66196	−	36.0589i	−0.444257	−	1.65799i
$474$		0			0
$475$	−40.9740	−	8.88275i	−1.88002	−	0.407568i
$476$		0			0
$477$	30.0642	−	19.8698i	1.37654	−	0.909775i
$478$		0			0
$479$	9.83193	+	17.0294i	0.449232	+	0.778093i	0.998336	−	0.0576610i	$-0.0183643\pi$
$479$	9.83193	+	17.0294i	0.449232	+	0.778093i	−0.549104	+	0.835754i	$0.685031\pi$
$480$		0			0
$481$	−0.159813	+	0.276804i	−0.00728685	+	0.0126212i
$482$		0			0
$483$	−2.34686	+	23.2277i	−0.106786	+	1.05690i
$484$		0			0
$485$	−13.8253	+	6.12192i	−0.627773	+	0.277982i
$486$		0			0
$487$	−20.9655	+	20.9655i	−0.950036	+	0.950036i	−0.998810	−	0.0487742i	$-0.984469\pi$
$487$	−20.9655	+	20.9655i	−0.950036	+	0.950036i	0.0487742	+	0.998810i	$0.484469\pi$
$488$		0			0
$489$	−18.2459	−	22.3474i	−0.825110	−	1.01058i
$490$		0			0
$491$	−7.79967	−	4.50314i	−0.351994	−	0.203224i	0.313569	−	0.949565i	$-0.398475\pi$
$491$	−7.79967	−	4.50314i	−0.351994	−	0.203224i	−0.665563	+	0.746341i	$0.731809\pi$
$492$		0			0
$493$	−0.190164	+	0.709703i	−0.00856457	+	0.0319634i
$494$		0			0
$495$	−22.3045	+	34.8032i	−1.00251	+	1.56429i
$496$		0			0
$497$	6.62870	−	24.7386i	0.297338	−	1.10968i
$498$		0			0
$499$	15.8428	+	9.14686i	0.709222	+	0.409470i	0.810773	−	0.585361i	$-0.199047\pi$
$499$	15.8428	+	9.14686i	0.709222	+	0.409470i	−0.101551	+	0.994830i	$0.532380\pi$
$500$		0			0
$501$	−0.993317	+	0.161427i	−0.0443781	+	0.00721201i
$502$		0			0
$503$	18.6921	−	18.6921i	0.833438	−	0.833438i	−0.154547	−	0.987985i	$-0.549392\pi$
$503$	18.6921	−	18.6921i	0.833438	−	0.833438i	0.987985	+	0.154547i	$0.0493919\pi$
$504$		0			0
$505$	−3.15271	+	8.16367i	−0.140294	+	0.363279i
$506$		0			0
$507$	0.304115	−	0.136870i	0.0135062	−	0.00607860i
$508$		0			0
$509$	−4.05713	+	7.02716i	−0.179829	+	0.311473i	−0.941822	−	0.336112i	$-0.890888\pi$
$509$	−4.05713	+	7.02716i	−0.179829	+	0.311473i	0.761993	+	0.647586i	$0.224221\pi$
$510$		0			0
$511$	4.70849	+	8.15534i	0.208291	+	0.360771i
$512$		0			0
$513$	−12.9628	+	41.5976i	−0.572320	+	1.83658i
$514$		0			0
$515$	18.9631	−	25.9898i	0.835615	−	1.14525i
$516$		0			0
$517$	−9.81988	−	36.6483i	−0.431878	−	1.61179i
$518$		0			0
$519$	7.70381	+	2.92170i	0.338160	+	0.128248i
$520$		0			0
$521$			18.0958i			0.792790i	0.918080	+	0.396395i	$0.129739\pi$
$521$			18.0958i			0.792790i	−0.918080	+	0.396395i	$0.870261\pi$
$522$		0			0
$523$	−10.9115	−	10.9115i	−0.477127	−	0.477127i	0.427084	−	0.904212i	$-0.359541\pi$
$523$	−10.9115	−	10.9115i	−0.477127	−	0.477127i	−0.904212	+	0.427084i	$0.859541\pi$
$524$		0			0
$525$	12.4078	−	19.1054i	0.541520	−	0.833828i
$526$		0			0
$527$	−1.53241	+	0.410609i	−0.0667530	+	0.0178864i
$528$		0			0
$529$	−2.81948	+	1.62783i	−0.122586	+	0.0707752i
$530$		0			0
$531$	−8.53185	+	9.63035i	−0.370251	+	0.417921i
$532$		0			0
$533$	28.1011	+	7.52967i	1.21719	+	0.326146i
$534$		0			0
$535$	−1.29360	−	0.138609i	−0.0559270	−	0.00599260i
$536$		0			0
$537$	−5.82514	−	0.588554i	−0.251373	−	0.0253980i
$538$		0			0
$539$	−0.495520			−0.0213436
$540$		0			0
$541$	−44.6319			−1.91888			−0.959438	−	0.281919i	$-0.909029\pi$
$541$	−44.6319			−1.91888			−0.959438	+	0.281919i	$0.909029\pi$
$542$		0			0
$543$	7.50700	+	0.758483i	0.322156	+	0.0325496i
$544$		0			0
$545$	12.5964	+	15.6198i	0.539572	+	0.669079i
$546$		0			0
$547$	9.70069	+	2.59929i	0.414771	+	0.111138i	0.460169	−	0.887831i	$-0.347789\pi$
$547$	9.70069	+	2.59929i	0.414771	+	0.111138i	−0.0453976	+	0.998969i	$0.514455\pi$
$548$		0			0
$549$	−4.37466	−	13.1040i	−0.186706	−	0.559264i
$550$		0			0
$551$	4.71088	−	2.71983i	0.200690	−	0.115869i
$552$		0			0
$553$	−18.9121	+	5.06749i	−0.804226	+	0.215492i
$554$		0			0
$555$	−0.0712404	+	0.338489i	−0.00302398	+	0.0143681i
$556$		0			0
$557$	−20.4994	−	20.4994i	−0.868586	−	0.868586i	0.123730	−	0.992316i	$-0.460514\pi$
$557$	−20.4994	−	20.4994i	−0.868586	−	0.868586i	−0.992316	+	0.123730i	$0.960514\pi$
$558$		0			0
$559$		−	21.6804i		−	0.916983i
$560$		0			0
$561$	−11.3028	−	4.28662i	−0.477204	−	0.180981i
$562$		0			0
$563$	10.1754	+	37.9750i	0.428841	+	1.60046i	0.755390	+	0.655276i	$0.227448\pi$
$563$	10.1754	+	37.9750i	0.428841	+	1.60046i	−0.326549	+	0.945180i	$0.605886\pi$
$564$		0			0
$565$	25.0482	+	18.2761i	1.05379	+	0.768883i
$566$		0			0
$567$	−18.6361	−	14.6008i	−0.782642	−	0.613176i
$568$		0			0
$569$	5.40661	+	9.36453i	0.226657	+	0.392581i	0.956815	−	0.290697i	$-0.0938870\pi$
$569$	5.40661	+	9.36453i	0.226657	+	0.392581i	−0.730158	+	0.683278i	$0.760554\pi$
$570$		0			0
$571$	13.3078	−	23.0499i	0.556916	−	0.964607i	−0.440836	−	0.897588i	$-0.645318\pi$
$571$	13.3078	−	23.0499i	0.556916	−	0.964607i	0.997752	−	0.0670189i	$-0.0213488\pi$
$572$		0			0
$573$	27.9450	−	12.5769i	1.16742	−	0.525408i
$574$		0			0
$575$	25.5902	−	1.23731i	1.06719	−	0.0515992i
$576$		0			0
$577$	19.8079	−	19.8079i	0.824615	−	0.824615i	−0.162151	−	0.986766i	$-0.551843\pi$
$577$	19.8079	−	19.8079i	0.824615	−	0.824615i	0.986766	+	0.162151i	$0.0518431\pi$
$578$		0			0
$579$	−35.1739	+	5.71621i	−1.46178	+	0.237558i
$580$		0			0
$581$	12.9748	+	7.49103i	0.538287	+	0.310780i
$582$		0			0
$583$	19.1583	−	71.4997i	0.793455	−	2.96122i
$584$		0			0
$585$	−17.7435	+	16.1710i	−0.733605	+	0.668590i
$586$		0			0
$587$	−8.17090	+	30.4942i	−0.337249	+	1.25863i	0.564161	+	0.825665i	$0.309200\pi$
$587$	−8.17090	+	30.4942i	−0.337249	+	1.25863i	−0.901410	+	0.432966i	$0.857467\pi$
$588$		0			0
$589$	10.1719	+	5.87275i	0.419126	+	0.241982i
$590$		0			0
$591$	0.967213	+	1.18463i	0.0397858	+	0.0487291i
$592$		0			0
$593$	−28.3282	+	28.3282i	−1.16330	+	1.16330i	−0.179553	+	0.983748i	$0.557465\pi$
$593$	−28.3282	+	28.3282i	−1.16330	+	1.16330i	−0.983748	+	0.179553i	$0.942535\pi$
$594$		0			0
$595$	6.21457	+	2.39999i	0.254773	+	0.0983900i
$596$		0			0
$597$	1.23817	−	12.2546i	0.0506748	−	0.501548i
$598$		0			0
$599$	3.49228	−	6.04880i	0.142691	−	0.247147i	−0.785818	−	0.618457i	$-0.787758\pi$
$599$	3.49228	−	6.04880i	0.142691	−	0.247147i	0.928509	+	0.371310i	$0.121091\pi$
$600$		0			0
$601$	−12.7368	−	22.0608i	−0.519545	−	0.899878i	−0.999742	−	0.0227176i	$-0.992768\pi$
$601$	−12.7368	−	22.0608i	−0.519545	−	0.899878i	0.480197	−	0.877161i	$-0.340565\pi$
$602$		0			0
$603$	1.12899	+	18.6663i	0.0459761	+	0.760151i
$604$		0			0
$605$	9.31431	+	59.5884i	0.378681	+	2.42261i
$606$		0			0
$607$	−11.7235	−	43.7528i	−0.475843	−	1.77587i	−0.618164	−	0.786049i	$-0.712123\pi$
$607$	−11.7235	−	43.7528i	−0.475843	−	1.77587i	0.142321	−	0.989821i	$-0.454543\pi$
$608$		0			0
$609$	0.474119	+	2.91743i	0.0192123	+	0.118220i
$610$		0			0
$611$		−	22.0347i		−	0.891430i
$612$		0			0
$613$	4.02153	+	4.02153i	0.162428	+	0.162428i	0.783641	−	0.621213i	$-0.213360\pi$
$613$	4.02153	+	4.02153i	0.162428	+	0.162428i	−0.621213	+	0.783641i	$0.713360\pi$
$614$		0			0
$615$	31.4378	−	1.71068i	1.26769	−	0.0689812i
$616$		0			0
$617$	−2.74339	+	0.735090i	−0.110445	+	0.0295936i	−0.313618	−	0.949549i	$-0.601541\pi$
$617$	−2.74339	+	0.735090i	−0.110445	+	0.0295936i	0.203173	+	0.979143i	$0.434875\pi$
$618$		0			0
$619$	13.6315	−	7.87017i	0.547897	−	0.316329i	−0.200376	−	0.979719i	$-0.564216\pi$
$619$	13.6315	−	7.87017i	0.547897	−	0.316329i	0.748273	+	0.663390i	$0.230883\pi$
$620$		0			0
$621$	1.07233	−	26.6036i	0.0430312	−	1.06757i
$622$		0			0
$623$	19.9656	+	5.34977i	0.799905	+	0.214334i
$624$		0			0
$625$	−22.7556	−	10.3529i	−0.910224	−	0.414117i
$626$		0			0
$627$	36.7302	+	81.6119i	1.46686	+	3.25926i
$628$		0			0
$629$	−0.101154			−0.00403328
$630$		0			0
$631$	−42.5016			−1.69196			−0.845982	−	0.533212i	$-0.820985\pi$
$631$	−42.5016			−1.69196			−0.845982	+	0.533212i	$0.820985\pi$
$632$		0			0
$633$	13.5647	−	18.8292i	0.539150	−	0.748392i
$634$		0			0
$635$	−2.30075	+	21.4721i	−0.0913023	+	0.852094i
$636$		0			0
$637$	−0.277973	−	0.0744827i	−0.0110137	−	0.00295111i
$638$		0			0
$639$	−5.84268	+	28.6184i	−0.231133	+	1.13213i
$640$		0			0
$641$	17.2917	−	9.98334i	0.682979	−	0.394318i	−0.117997	−	0.993014i	$-0.537647\pi$
$641$	17.2917	−	9.98334i	0.682979	−	0.394318i	0.800977	+	0.598696i	$0.204314\pi$
$642$		0			0
$643$	−11.5315	+	3.08986i	−0.454759	+	0.121852i	−0.478925	−	0.877856i	$-0.658974\pi$
$643$	−11.5315	+	3.08986i	−0.454759	+	0.121852i	0.0241664	+	0.999708i	$0.492307\pi$
$644$		0			0
$645$	−7.29507	−	22.3000i	−0.287243	−	0.878060i
$646$		0			0
$647$	22.0217	+	22.0217i	0.865762	+	0.865762i	0.992000	−	0.126238i	$-0.0402902\pi$
$647$	22.0217	+	22.0217i	0.865762	+	0.865762i	−0.126238	+	0.992000i	$0.540290\pi$
$648$		0			0
$649$			26.4276i			1.03738i
$650$		0			0
$651$	−4.94358	+	4.03629i	−0.193754	+	0.158195i
$652$		0			0
$653$	2.07881	+	7.75822i	0.0813501	+	0.303603i	0.994598	−	0.103802i	$-0.0331007\pi$
$653$	2.07881	+	7.75822i	0.0813501	+	0.303603i	−0.913248	+	0.407404i	$0.866434\pi$
$654$		0			0
$655$	3.18558	−	0.497941i	0.124471	−	0.0194562i
$656$		0			0
$657$	−5.92158	−	8.95971i	−0.231023	−	0.349551i
$658$		0			0
$659$	3.14207	+	5.44223i	0.122398	+	0.211999i	0.920713	−	0.390241i	$-0.127608\pi$
$659$	3.14207	+	5.44223i	0.122398	+	0.211999i	−0.798315	+	0.602240i	$0.794275\pi$
$660$		0			0
$661$	8.93133	−	15.4695i	0.347388	−	0.601694i	−0.638396	−	0.769708i	$-0.720402\pi$
$661$	8.93133	−	15.4695i	0.347388	−	0.601694i	0.985785	+	0.168013i	$0.0537352\pi$
$662$		0			0
$663$	−5.69622	−	4.10362i	−0.221223	−	0.159372i
$664$		0			0
$665$	−19.9697	−	45.0979i	−0.774390	−	1.74882i
$666$		0			0
$667$	−2.35048	+	2.35048i	−0.0910109	+	0.0910109i
$668$		0			0
$669$	−1.71944	+	4.53374i	−0.0664772	+	0.175284i
$670$		0			0
$671$	−24.5749	−	14.1883i	−0.948702	−	0.547733i
$672$		0			0
$673$	11.0168	−	41.1151i	0.424665	−	1.58487i	−0.339990	−	0.940429i	$-0.610424\pi$
$673$	11.0168	−	41.1151i	0.424665	−	1.58487i	0.764654	−	0.644441i	$-0.222910\pi$
$674$		0			0
$675$	−12.8094	+	22.6036i	−0.493032	+	0.870011i
$676$		0			0
$677$	6.40209	−	23.8929i	0.246052	−	0.918280i	−0.726799	−	0.686850i	$-0.758993\pi$
$677$	6.40209	−	23.8929i	0.246052	−	0.918280i	0.972852	−	0.231430i	$-0.0743404\pi$
$678$		0			0
$679$	−15.4042	−	8.89361i	−0.591158	−	0.341306i
$680$		0			0
$681$	−11.2773	+	29.7356i	−0.432148	+	1.13947i
$682$		0			0
$683$	−30.1336	+	30.1336i	−1.15303	+	1.15303i	−0.167090	+	0.985942i	$0.553437\pi$
$683$	−30.1336	+	30.1336i	−1.15303	+	1.15303i	−0.985942	+	0.167090i	$0.946563\pi$
$684$		0			0
$685$	−0.508352	−	1.14802i	−0.0194231	−	0.0438637i
$686$		0			0
$687$	13.7395	+	9.89809i	0.524195	+	0.377636i
$688$		0			0
$689$	21.4946	−	37.2297i	0.818877	−	1.41834i
$690$		0			0
$691$	18.0336	+	31.2351i	0.686030	+	1.18824i	0.973112	+	0.230333i	$0.0739814\pi$
$691$	18.0336	+	31.2351i	0.686030	+	1.18824i	−0.287082	+	0.957906i	$0.592685\pi$
$692$		0			0
$693$	−48.5402	+	2.93585i	−1.84389	+	0.111524i
$694$		0			0
$695$	−12.8634	+	2.01070i	−0.487938	+	0.0762701i
$696$		0			0
$697$	2.38296	+	8.89333i	0.0902611	+	0.336859i
$698$		0			0
$699$	12.2080	−	9.96746i	0.461749	−	0.377004i
$700$		0			0
$701$		−	13.0835i		−	0.494157i	−0.968995	−	0.247078i	$-0.920529\pi$
$701$		−	13.0835i		−	0.494157i	0.968995	−	0.247078i	$-0.0794705\pi$
$702$		0			0
$703$	0.529550	+	0.529550i	0.0199724	+	0.0199724i
$704$		0			0
$705$	−7.41430	−	22.6644i	−0.279239	−	0.853592i
$706$		0			0
$707$	−9.94423	+	2.66455i	−0.373991	+	0.100211i
$708$		0			0
$709$	−44.5001	+	25.6921i	−1.67123	+	0.964888i	−0.704286	+	0.709916i	$0.748733\pi$
$709$	−44.5001	+	25.6921i	−1.67123	+	0.964888i	−0.966948	+	0.254972i	$0.917934\pi$
$710$		0			0
$711$	21.1803	−	7.07090i	0.794325	−	0.265179i
$712$		0			0
$713$	−6.93290	−	1.85767i	−0.259639	−	0.0695701i
$714$		0			0
$715$	−5.25370	+	49.0310i	−0.196477	+	1.83366i
$716$		0			0
$717$	8.06015	−	11.1883i	0.301012	−	0.417833i
$718$		0			0
$719$	8.86775			0.330711			0.165356	−	0.986234i	$-0.447123\pi$
$719$	8.86775			0.330711			0.165356	+	0.986234i	$0.447123\pi$
$720$		0			0
$721$	37.8477			1.40952
$722$		0			0
$723$	−9.78837	−	21.7490i	−0.364033	−	0.808855i
$724$		0			0
$725$	3.08890	−	0.989842i	0.114719	−	0.0367618i
$726$		0			0
$727$	17.9082	+	4.79849i	0.664178	+	0.177966i	0.575131	−	0.818061i	$-0.304951\pi$
$727$	17.9082	+	4.79849i	0.664178	+	0.177966i	0.0890472	+	0.996027i	$0.471618\pi$
$728$		0			0
$729$	22.2203	+	15.3382i	0.822974	+	0.568080i
$730$		0			0
$731$	5.94209	−	3.43066i	0.219776	−	0.126888i
$732$		0			0
$733$	−24.2283	+	6.49196i	−0.894893	+	0.239786i	−0.676822	−	0.736147i	$-0.736643\pi$
$733$	−24.2283	+	6.49196i	−0.894893	+	0.239786i	−0.218071	+	0.975933i	$0.569977\pi$
$734$		0			0
$735$	−0.310979	+	0.0169219i	−0.0114706	+	0.000624172i
$736$		0			0
$737$	27.1612	+	27.1612i	1.00050	+	1.00050i
$738$		0			0
$739$			2.42833i			0.0893276i	0.999002	+	0.0446638i	$0.0142217\pi$
$739$			2.42833i			0.0893276i	−0.999002	+	0.0446638i	$0.985778\pi$
$740$		0			0
$741$	8.33739	+	51.3030i	0.306282	+	1.88466i
$742$		0			0
$743$	−5.45005	−	20.3399i	−0.199943	−	0.746198i	−0.990932	−	0.134367i	$-0.957100\pi$
$743$	−5.45005	−	20.3399i	−0.199943	−	0.746198i	0.790989	−	0.611831i	$-0.209567\pi$
$744$		0			0
$745$	−2.65317	−	16.9736i	−0.0972045	−	0.621866i
$746$		0			0
$747$	−15.2861	−	7.63430i	−0.559289	−	0.279325i
$748$		0			0
$749$	−0.765249	−	1.32545i	−0.0279616	−	0.0484309i
$750$		0			0
$751$	4.17222	−	7.22650i	0.152247	−	0.263699i	−0.779806	−	0.626021i	$-0.784683\pi$
$751$	4.17222	−	7.22650i	0.152247	−	0.263699i	0.932053	+	0.362322i	$0.118016\pi$
$752$		0			0
$753$	2.63601	−	26.0896i	0.0960616	−	0.950759i
$754$		0			0
$755$	−35.5558	−	13.7312i	−1.29401	−	0.499729i
$756$		0			0
$757$	−21.1330	+	21.1330i	−0.768091	+	0.768091i	−0.977770	−	0.209679i	$-0.932758\pi$
$757$	−21.1330	+	21.1330i	−0.768091	+	0.768091i	0.209679	+	0.977770i	$0.432758\pi$
$758$		0			0
$759$	−34.5881	−	42.3630i	−1.25547	−	1.53768i
$760$		0			0
$761$	−4.90482	−	2.83180i	−0.177799	−	0.102653i	0.408459	−	0.912777i	$-0.366066\pi$
$761$	−4.90482	−	2.83180i	−0.177799	−	0.102653i	−0.586258	+	0.810124i	$0.699400\pi$
$762$		0			0
$763$	−6.10962	+	22.8014i	−0.221183	+	0.825467i
$764$		0			0
$765$	−7.23981	−	2.30422i	−0.261756	−	0.0833091i
$766$		0			0
$767$	−3.97240	+	14.8252i	−0.143435	+	0.535306i
$768$		0			0
$769$	23.5176	+	13.5779i	0.848066	+	0.489631i	0.859998	−	0.510298i	$-0.170465\pi$
$769$	23.5176	+	13.5779i	0.848066	+	0.489631i	−0.0119318	+	0.999929i	$0.503798\pi$
$770$		0			0
$771$	23.5093	−	3.82057i	0.846668	−	0.137594i
$772$		0			0
$773$	−14.9420	+	14.9420i	−0.537425	+	0.537425i	−0.922772	−	0.385347i	$-0.874082\pi$
$773$	−14.9420	+	14.9420i	−0.537425	+	0.537425i	0.385347	+	0.922772i	$0.374082\pi$
$774$		0			0
$775$	5.18578	+	4.70744i	0.186279	+	0.169096i
$776$		0			0
$777$	−0.371073	+	0.167005i	−0.0133122	+	0.00599127i
$778$		0			0
$779$	34.0823	−	59.0323i	1.22113	−	2.11505i
$780$		0			0
$781$	29.9982	+	51.9584i	1.07342	+	1.85922i
$782$		0			0
$783$	−0.740602	−	3.28851i	−0.0264669	−	0.117522i
$784$		0			0
$785$	8.34942	+	6.09206i	0.298004	+	0.217435i
$786$		0			0
$787$	2.67468	+	9.98204i	0.0953420	+	0.355821i	0.997071	−	0.0764804i	$-0.0243683\pi$
$787$	2.67468	+	9.98204i	0.0953420	+	0.355821i	−0.901729	+	0.432302i	$0.857702\pi$
$788$		0			0
$789$	2.69469	+	1.02197i	0.0959335	+	0.0363831i
$790$		0			0
$791$			36.4766i			1.29696i
$792$		0			0
$793$	−11.6531	−	11.6531i	−0.413815	−	0.413815i
$794$		0			0
$795$	9.58169	−	45.5261i	0.339828	−	1.61465i
$796$		0			0
$797$	−43.9056	+	11.7645i	−1.55522	+	0.416719i	−0.931145	−	0.364650i	$-0.881189\pi$
$797$	−43.9056	+	11.7645i	−1.55522	+	0.416719i	−0.624070	+	0.781368i	$0.714522\pi$
$798$		0			0
$799$	6.03921	−	3.48674i	0.213652	−	0.123352i
$800$		0			0
$801$	−23.0968	−	4.71540i	−0.816087	−	0.166610i
$802$		0			0
$803$	−21.3083	−	5.70954i	−0.751953	−	0.201485i
$804$		0			0
$805$	18.9200	+	23.4611i	0.666842	+	0.826897i
$806$		0			0
$807$	−44.1860	−	4.46441i	−1.55542	−	0.157155i
$808$		0			0
$809$	−35.7232			−1.25596			−0.627980	−	0.778230i	$-0.716118\pi$
$809$	−35.7232			−1.25596			−0.627980	+	0.778230i	$0.716118\pi$
$810$		0			0
$811$	−0.579168			−0.0203374			−0.0101687	−	0.999948i	$-0.503237\pi$
$811$	−0.579168			−0.0203374			−0.0101687	+	0.999948i	$0.503237\pi$
$812$		0			0
$813$	−5.74393	−	0.580348i	−0.201448	−	0.0203537i
$814$		0			0
$815$	−37.0331	−	3.96812i	−1.29721	−	0.138997i
$816$		0			0
$817$	−49.0671	−	13.1475i	−1.71664	−	0.459973i
$818$		0			0
$819$	−27.6710	−	5.64926i	−0.966905	−	0.197401i
$820$		0			0
$821$	−12.3891	+	7.15286i	−0.432383	+	0.249636i	−0.700361	−	0.713789i	$-0.746978\pi$
$821$	−12.3891	+	7.15286i	−0.432383	+	0.249636i	0.267978	+	0.963425i	$0.413644\pi$
$822$		0			0
$823$	−2.40334	+	0.643973i	−0.0837751	+	0.0224475i	−0.300463	−	0.953793i	$-0.597141\pi$
$823$	−2.40334	+	0.643973i	−0.0837751	+	0.0224475i	0.216688	+	0.976241i	$0.430475\pi$
$824$		0			0
$825$	11.0942	+	52.2000i	0.386252	+	1.81737i
$826$		0			0
$827$	19.5054	+	19.5054i	0.678269	+	0.678269i	0.959608	−	0.281339i	$-0.0907787\pi$
$827$	19.5054	+	19.5054i	0.678269	+	0.678269i	−0.281339	+	0.959608i	$0.590779\pi$
$828$		0			0
$829$		−	40.4705i		−	1.40560i	−0.711388	−	0.702800i	$-0.751933\pi$
$829$		−	40.4705i		−	1.40560i	0.711388	−	0.702800i	$-0.248067\pi$
$830$		0			0
$831$	−22.4621	−	8.51884i	−0.779203	−	0.295515i
$832$		0			0
$833$	−0.0235720	−	0.0879720i	−0.000816722	−	0.00304805i
$834$		0			0
$835$	−0.765770	+	1.04952i	−0.0265006	+	0.0363201i
$836$		0			0
$837$	5.34978	−	4.93522i	0.184915	−	0.170586i
$838$		0			0
$839$	15.3399	+	26.5695i	0.529592	+	0.917280i	0.999404	+	0.0345140i	$0.0109883\pi$
$839$	15.3399	+	26.5695i	0.529592	+	0.917280i	−0.469812	+	0.882766i	$0.655678\pi$
$840$		0			0
$841$	14.2896	−	24.7503i	0.492744	−	0.853458i
$842$		0			0
$843$	17.3620	−	7.81393i	0.597978	−	0.269126i
$844$		0			0
$845$	0.155105	−	0.401631i	0.00533577	−	0.0138165i
$846$		0			0
$847$	−50.1699	+	50.1699i	−1.72386	+	1.72386i
$848$		0			0
$849$	16.0064	−	2.60125i	0.549339	−	0.0892746i
$850$		0			0
$851$	−0.396326	−	0.228819i	−0.0135859	−	0.00784382i
$852$		0			0
$853$	8.83177	−	32.9606i	0.302394	−	1.12855i	−0.632771	−	0.774339i	$-0.718083\pi$
$853$	8.83177	−	32.9606i	0.302394	−	1.12855i	0.935165	−	0.354211i	$-0.115251\pi$
$854$		0			0
$855$	25.8382	+	49.9638i	0.883648	+	1.70872i
$856$		0			0
$857$	−3.59263	+	13.4079i	−0.122722	+	0.458005i	−0.999748	−	0.0224379i	$-0.992857\pi$
$857$	−3.59263	+	13.4079i	−0.122722	+	0.458005i	0.877026	+	0.480442i	$0.159524\pi$
$858$		0			0
$859$	31.1512	+	17.9852i	1.06287	+	0.613646i	0.926224	−	0.376974i	$-0.123035\pi$
$859$	31.1512	+	17.9852i	1.06287	+	0.613646i	0.136643	+	0.990620i	$0.456369\pi$
$860$		0			0
$861$	23.4245	+	28.6900i	0.798304	+	0.977751i
$862$		0			0
$863$	−6.97586	+	6.97586i	−0.237461	+	0.237461i	−0.815798	−	0.578337i	$-0.803702\pi$
$863$	−6.97586	+	6.97586i	−0.237461	+	0.237461i	0.578337	+	0.815798i	$0.303702\pi$
$864$		0			0
$865$	9.72594	−	4.30671i	0.330692	−	0.146432i
$866$		0			0
$867$	−2.73660	+	27.0852i	−0.0929397	+	0.919860i
$868$		0			0
$869$	22.9330	−	39.7211i	0.777948	−	1.34745i
$870$		0			0
$871$	11.1540	+	19.3193i	0.377940	+	0.654611i
$872$		0			0
$873$	18.1482	+	9.06372i	0.614224	+	0.306760i
$874$		0			0
$875$	−5.93995	−	28.8039i	−0.200807	−	0.973750i
$876$		0			0
$877$	5.86149	+	21.8754i	0.197929	+	0.738680i	0.991489	+	0.130188i	$0.0415582\pi$
$877$	5.86149	+	21.8754i	0.197929	+	0.738680i	−0.793561	+	0.608491i	$0.791775\pi$
$878$		0			0
$879$	−0.203428	−	1.25177i	−0.00686146	−	0.0422211i
$880$		0			0
$881$			1.79953i			0.0606276i	0.999540	+	0.0303138i	$0.00965066\pi$
$881$			1.79953i			0.0606276i	−0.999540	+	0.0303138i	$0.990349\pi$
$882$		0			0
$883$	7.73420	+	7.73420i	0.260277	+	0.260277i	0.825166	−	0.564890i	$-0.191081\pi$
$883$	7.73420	+	7.73420i	0.260277	+	0.260277i	−0.564890	+	0.825166i	$0.691081\pi$
$884$		0			0
$885$	0.902496	+	16.5855i	0.0303371	+	0.557515i
$886$		0			0
$887$	48.7751	−	13.0692i	1.63771	−	0.438822i	0.681572	−	0.731751i	$-0.261297\pi$
$887$	48.7751	−	13.0692i	1.63771	−	0.438822i	0.956134	+	0.292929i	$0.0946298\pi$
$888$		0			0
$889$	−22.0008	+	12.7022i	−0.737884	+	0.426018i
$890$		0			0
$891$	55.0552	−	6.68424i	1.84442	−	0.223931i
$892$		0			0
$893$	−49.8691	−	13.3624i	−1.66881	−	0.447155i
$894$		0			0
$895$	−5.88368	+	4.74483i	−0.196670	+	0.158602i
$896$		0			0
$897$	−13.0353	−	28.9635i	−0.435237	−	0.967064i
$898$		0			0
$899$	−0.908699			−0.0303068
$900$		0			0
$901$	13.6050			0.453250
$902$		0			0
$903$	16.1339	−	22.3954i	0.536902	−	0.745272i
$904$		0			0
$905$	7.58244	−	6.11478i	0.252049	−	0.203262i
$906$		0			0
$907$	−54.2321	−	14.5314i	−1.80075	−	0.482509i	−0.806653	−	0.591025i	$-0.798723\pi$
$907$	−54.2321	−	14.5314i	−1.80075	−	0.482509i	−0.994095	+	0.108517i	$0.965390\pi$
$908$		0			0
$909$	11.1369	−	3.71796i	0.369387	−	0.123317i
$910$		0			0
$911$	42.2667	−	24.4027i	1.40036	−	0.808497i	0.405928	−	0.913905i	$-0.366948\pi$
$911$	42.2667	−	24.4027i	1.40036	−	0.808497i	0.994429	+	0.105408i	$0.0336150\pi$
$912$		0			0
$913$	−33.9007	+	9.08366i	−1.12195	+	0.300625i
$914$		0			0
$915$	−15.9072	−	8.06509i	−0.525877	−	0.266624i
$916$		0			0
$917$	2.68207	+	2.68207i	0.0885697	+	0.0885697i
$918$		0			0
$919$		−	7.45262i		−	0.245839i	−0.992417	−	0.122920i	$-0.960774\pi$
$919$		−	7.45262i		−	0.245839i	0.992417	−	0.122920i	$-0.0392257\pi$
$920$		0			0
$921$	−4.39229	+	3.58617i	−0.144731	+	0.118168i
$922$		0			0
$923$	9.01819	+	33.6564i	0.296837	+	1.10781i
$924$		0			0
$925$	0.241697	+	0.375499i	0.00794695	+	0.0123463i
$926$		0			0
$927$	−43.0852	+	2.60591i	−1.41510	+	0.0855894i
$928$		0			0
$929$	0.693384	+	1.20098i	0.0227492	+	0.0394028i	0.877176	−	0.480169i	$-0.159425\pi$
$929$	0.693384	+	1.20098i	0.0227492	+	0.0394028i	−0.854427	+	0.519572i	$0.826091\pi$
$930$		0			0
$931$	−0.337139	+	0.583942i	−0.0110493	+	0.0191379i
$932$		0			0
$933$	24.9433	+	17.9694i	0.816607	+	0.588293i
$934$		0			0
$935$	−14.2696	+	6.31867i	−0.466666	+	0.206643i
$936$		0			0
$937$	29.2796	−	29.2796i	0.956523	−	0.956523i	−0.0425700	−	0.999093i	$-0.513555\pi$
$937$	29.2796	−	29.2796i	0.956523	−	0.956523i	0.999093	+	0.0425700i	$0.0135546\pi$
$938$		0			0
$939$	14.7613	−	38.9221i	0.481718	−	1.27017i
$940$		0			0
$941$	−30.5173	−	17.6192i	−0.994836	−	0.574369i	−0.0881199	−	0.996110i	$-0.528086\pi$
$941$	−30.5173	−	17.6192i	−0.994836	−	0.574369i	−0.906716	+	0.421741i	$0.861419\pi$
$942$		0			0
$943$	−10.7809	+	40.2349i	−0.351075	+	1.31023i
$944$		0			0
$945$	−30.3627	+	3.50012i	−0.987699	+	0.113859i
$946$		0			0
$947$	−8.48135	+	31.6528i	−0.275607	+	1.02858i	0.679827	+	0.733372i	$0.262055\pi$
$947$	−8.48135	+	31.6528i	−0.275607	+	1.02858i	−0.955434	+	0.295206i	$0.904612\pi$
$948$		0			0
$949$	−11.0952	−	6.40579i	−0.360164	−	0.207941i
$950$		0			0
$951$	14.3094	−	37.7304i	0.464013	−	1.22349i
$952$		0			0
$953$	14.2879	−	14.2879i	0.462829	−	0.462829i	−0.436752	−	0.899582i	$-0.643871\pi$
$953$	14.2879	−	14.2879i	0.462829	−	0.462829i	0.899582	+	0.436752i	$0.143871\pi$
$954$		0			0
$955$	14.2525	−	36.9057i	0.461201	−	1.19424i
$956$		0			0
$957$	−5.61793	−	4.04722i	−0.181602	−	0.130828i
$958$		0			0
$959$	0.738509	−	1.27913i	0.0238477	−	0.0413054i
$960$		0			0
$961$	14.5190	+	25.1476i	0.468353	+	0.811212i
$962$		0			0
$963$	0.962406	+	1.45618i	0.0310131	+	0.0469247i
$964$		0			0
$965$	−27.1164	+	37.1641i	−0.872906	+	1.19635i
$966$		0			0
$967$	10.2370	+	38.2050i	0.329200	+	1.22859i	0.910022	+	0.414560i	$0.136064\pi$
$967$	10.2370	+	38.2050i	0.329200	+	1.22859i	−0.580822	+	0.814030i	$0.697269\pi$
$968$		0			0
$969$	−12.7417	+	10.4032i	−0.409321	+	0.334198i
$970$		0			0
$971$		−	4.90527i		−	0.157418i	−0.996898	−	0.0787089i	$-0.974920\pi$
$971$		−	4.90527i		−	0.157418i	0.996898	−	0.0787089i	$-0.0250798\pi$
$972$		0			0
$973$	−10.8303	−	10.8303i	−0.347202	−	0.347202i
$974$		0			0
$975$	−1.62273	+	30.9504i	−0.0519689	+	0.991205i
$976$		0			0
$977$	−12.1864	+	3.26533i	−0.389877	+	0.104467i	−0.448432	−	0.893817i	$-0.648017\pi$
$977$	−12.1864	+	3.26533i	−0.389877	+	0.104467i	0.0585551	+	0.998284i	$0.481351\pi$
$978$		0			0
$979$	−41.9337	+	24.2104i	−1.34021	+	0.773768i
$980$		0			0
$981$	5.38515	−	26.3774i	0.171935	−	0.842166i
$982$		0			0
$983$	−1.30581	−	0.349891i	−0.0416489	−	0.0111598i	0.237934	−	0.971281i	$-0.423530\pi$
$983$	−1.30581	−	0.349891i	−0.0416489	−	0.0111598i	−0.279583	+	0.960121i	$0.590196\pi$
$984$		0			0
$985$	1.96312	+	0.210349i	0.0625501	+	0.00670227i
$986$		0			0
$987$	16.3976	−	22.7614i	0.521941	−	0.724504i
$988$		0			0
$989$	31.0418			0.987072
$990$		0			0
$991$	53.8450			1.71044			0.855222	−	0.518263i	$-0.173421\pi$
$991$	53.8450			1.71044			0.855222	+	0.518263i	$0.173421\pi$
$992$		0			0
$993$	14.6700	+	32.5956i	0.465538	+	1.03439i
$994$		0			0
$995$	−9.98191	−	12.3778i	−0.316448	−	0.392401i
$996$		0			0
$997$	20.2911	+	5.43699i	0.642626	+	0.172191i	0.565393	−	0.824822i	$-0.308725\pi$
$997$	20.2911	+	5.43699i	0.642626	+	0.172191i	0.0772335	+	0.997013i	$0.475391\pi$
$998$		0			0
$999$	0.410924	−	0.215665i	0.0130011	−	0.00682334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bs.a.113.1	✓	72
3.2	odd	2		1080.2.bt.a.233.14		72
4.3	odd	2		720.2.cu.e.113.18		72
5.2	odd	4	inner	360.2.bs.a.257.9	yes	72
9.2	odd	6	inner	360.2.bs.a.353.9	yes	72
9.7	even	3		1080.2.bt.a.953.9		72
15.2	even	4		1080.2.bt.a.17.9		72
20.7	even	4		720.2.cu.e.257.10		72
36.11	even	6		720.2.cu.e.353.10		72
45.2	even	12	inner	360.2.bs.a.137.1	yes	72
45.7	odd	12		1080.2.bt.a.737.14		72
180.47	odd	12		720.2.cu.e.497.18		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.1	✓	72	1.1	even	1	trivial
360.2.bs.a.137.1	yes	72	45.2	even	12	inner
360.2.bs.a.257.9	yes	72	5.2	odd	4	inner
360.2.bs.a.353.9	yes	72	9.2	odd	6	inner
720.2.cu.e.113.18		72	4.3	odd	2
720.2.cu.e.257.10		72	20.7	even	4
720.2.cu.e.353.10		72	36.11	even	6
720.2.cu.e.497.18		72	180.47	odd	12
1080.2.bt.a.17.9		72	15.2	even	4
1080.2.bt.a.233.14		72	3.2	odd	2
1080.2.bt.a.737.14		72	45.7	odd	12
1080.2.bt.a.953.9		72	9.7	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72328 - 0.174114i) q^{3} +(-1.74059 + 1.40368i) q^{5} +(-2.54088 - 0.680826i) q^{7} +(2.93937 + 0.600095i) q^{9} +O(q^{10})\)	\(q+(-1.72328 - 0.174114i) q^{3} +(-1.74059 + 1.40368i) q^{5} +(-2.54088 - 0.680826i) q^{7} +(2.93937 + 0.600095i) q^{9} +(5.33659 - 3.08108i) q^{11} +(3.45681 - 0.926249i) q^{13} +(3.24393 - 2.11587i) q^{15} +(0.800862 + 0.800862i) q^{17} -8.38516i q^{19} +(4.26010 + 1.61566i) q^{21} +(1.32620 + 4.94943i) q^{23} +(1.05934 - 4.88649i) q^{25} +(-4.96086 - 1.54592i) q^{27} +(0.324362 + 0.561812i) q^{29} +(-0.700374 + 1.21308i) q^{31} +(-9.73289 + 4.38038i) q^{33} +(5.37830 - 2.38155i) q^{35} +(-0.0631533 + 0.0631533i) q^{37} +(-6.11831 + 0.994303i) q^{39} +(7.04010 + 4.06460i) q^{41} +(1.56795 - 5.85166i) q^{43} +(-5.95859 + 3.08142i) q^{45} +(1.59358 - 5.94730i) q^{47} +(-0.0696399 - 0.0402066i) q^{49} +(-1.24067 - 1.51955i) q^{51} +(8.49399 - 8.49399i) q^{53} +(-4.96398 + 12.8538i) q^{55} +(-1.45998 + 14.4500i) q^{57} +(-2.14435 + 3.71412i) q^{59} +(-2.30249 - 3.98802i) q^{61} +(-7.06002 - 3.52597i) q^{63} +(-4.71674 + 6.46449i) q^{65} +(1.61334 + 6.02107i) q^{67} +(-1.42364 - 8.76015i) q^{69} +9.73625i q^{71} +(-2.53137 - 2.53137i) q^{73} +(-2.67635 + 8.23633i) q^{75} +(-15.6573 + 4.19537i) q^{77} +(6.44596 - 3.72158i) q^{79} +(8.27977 + 3.52780i) q^{81} +(-5.50142 - 1.47410i) q^{83} +(-2.51813 - 0.269819i) q^{85} +(-0.461146 - 1.02463i) q^{87} -7.85776 q^{89} -9.41394 q^{91} +(1.41815 - 1.96853i) q^{93} +(11.7701 + 14.5952i) q^{95} +(6.53148 + 1.75011i) q^{97} +(17.5352 - 5.85398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) \) 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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