LMFDB - Embedded newform 360.2.x.a.53.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(53,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("360.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.x (of order $4$, degree $2$, 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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.18
Character	$\chi$	$=$	360.53
Dual form			360.2.x.a.197.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.803348 + 1.16389i) q^{2} +(-0.709264 + 1.87001i) q^{4} +(-1.29263 + 1.82458i) q^{5} +(-0.306649 + 0.306649i) q^{7} +(-2.74627 + 0.676767i) q^{8} +O(q^{10})$	\(q+(0.803348 + 1.16389i) q^{2} +(-0.709264 + 1.87001i) q^{4} +(-1.29263 + 1.82458i) q^{5} +(-0.306649 + 0.306649i) q^{7} +(-2.74627 + 0.676767i) q^{8} +(-3.16204 - 0.0386996i) q^{10} -4.06731 q^{11} +(-0.625224 + 0.625224i) q^{13} +(-0.603251 - 0.110559i) q^{14} +(-2.99389 - 2.65267i) q^{16} +(3.57491 + 3.57491i) q^{17} +6.82524 q^{19} +(-2.49518 - 3.71135i) q^{20} +(-3.26747 - 4.73389i) q^{22} +(-1.58940 + 1.58940i) q^{23} +(-1.65821 - 4.71703i) q^{25} +(-1.22996 - 0.225418i) q^{26} +(-0.355942 - 0.790933i) q^{28} +8.50925i q^{29} -2.56730 q^{31} +(0.682268 - 5.61556i) q^{32} +(-1.28889 + 7.03269i) q^{34} +(-0.163123 - 0.955891i) q^{35} +(1.69023 + 1.69023i) q^{37} +(5.48305 + 7.94381i) q^{38} +(2.31509 - 5.88561i) q^{40} -5.19315i q^{41} +(4.18889 - 4.18889i) q^{43} +(2.88480 - 7.60592i) q^{44} +(-3.12673 - 0.573041i) q^{46} +(4.58429 + 4.58429i) q^{47} +6.81193i q^{49} +(4.15796 - 5.71938i) q^{50} +(-0.725727 - 1.61263i) q^{52} +(7.41934 + 7.41934i) q^{53} +(5.25753 - 7.42115i) q^{55} +(0.634611 - 1.04967i) q^{56} +(-9.90380 + 6.83589i) q^{58} -8.79560i q^{59} +6.08412i q^{61} +(-2.06244 - 2.98805i) q^{62} +(7.08397 - 3.71717i) q^{64} +(-0.332590 - 1.94896i) q^{65} +(6.18046 + 6.18046i) q^{67} +(-9.22069 + 4.14957i) q^{68} +(0.981504 - 0.957770i) q^{70} -14.7516i q^{71} +(3.05881 + 3.05881i) q^{73} +(-0.609393 + 3.32507i) q^{74} +(-4.84090 + 12.7633i) q^{76} +(1.24724 - 1.24724i) q^{77} -8.56106i q^{79} +(8.71000 - 2.03369i) q^{80} +(6.04424 - 4.17190i) q^{82} +(-5.13122 - 5.13122i) q^{83} +(-11.1438 + 1.90169i) q^{85} +(8.24053 + 1.51026i) q^{86} +(11.1699 - 2.75262i) q^{88} -9.88328 q^{89} -0.383449i q^{91} +(-1.84489 - 4.09951i) q^{92} +(-1.65282 + 9.01838i) q^{94} +(-8.82252 + 12.4532i) q^{95} +(1.75624 - 1.75624i) q^{97} +(-7.92832 + 5.47235i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) $ 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.803348	+	1.16389i	0.568053	+	0.822992i
$2$	0.803348	+	1.16389i	0.568053	+	0.822992i
$3$		0			0
$3$		0			0
$4$	−0.709264	+	1.87001i	−0.354632	+	0.935006i
$5$	−1.29263	+	1.82458i	−0.578082	+	0.815979i
$5$	−1.29263	+	1.82458i	−0.578082	+	0.815979i
$6$		0			0
$7$	−0.306649	+	0.306649i	−0.115902	+	0.115902i	−0.762679	−	0.646777i	$-0.776117\pi$
$7$	−0.306649	+	0.306649i	−0.115902	+	0.115902i	0.646777	+	0.762679i	$0.276117\pi$
$8$	−2.74627	+	0.676767i	−0.970952	+	0.239273i
$9$		0			0
$10$	−3.16204	−	0.0386996i	−0.999925	−	0.0122379i
$11$	−4.06731			−1.22634			−0.613170	−	0.789951i	$-0.710106\pi$
$11$	−4.06731			−1.22634			−0.613170	+	0.789951i	$0.710106\pi$
$12$		0			0
$13$	−0.625224	+	0.625224i	−0.173406	+	0.173406i	−0.788474	−	0.615068i	$-0.789129\pi$
$13$	−0.625224	+	0.625224i	−0.173406	+	0.173406i	0.615068	+	0.788474i	$0.289129\pi$
$14$	−0.603251	−	0.110559i	−0.161226	−	0.0295481i
$15$		0			0
$16$	−2.99389	−	2.65267i	−0.748472	−	0.663166i
$17$	3.57491	+	3.57491i	0.867044	+	0.867044i	0.992144	−	0.125100i	$-0.0399253\pi$
$17$	3.57491	+	3.57491i	0.867044	+	0.867044i	−0.125100	+	0.992144i	$0.539925\pi$
$18$		0			0
$19$	6.82524			1.56582			0.782909	−	0.622136i	$-0.213735\pi$
$19$	6.82524			1.56582			0.782909	+	0.622136i	$0.213735\pi$
$20$	−2.49518	−	3.71135i	−0.557939	−	0.829882i
$21$		0			0
$22$	−3.26747	−	4.73389i	−0.696626	−	1.00927i
$23$	−1.58940	+	1.58940i	−0.331413	+	0.331413i	−0.853123	−	0.521710i	$-0.825294\pi$
$23$	−1.58940	+	1.58940i	−0.331413	+	0.331413i	0.521710	+	0.853123i	$0.325294\pi$
$24$		0			0
$25$	−1.65821	−	4.71703i	−0.331643	−	0.943405i
$26$	−1.22996	−	0.225418i	−0.241216	−	0.0442080i
$27$		0			0
$28$	−0.355942	−	0.790933i	−0.0672667	−	0.149472i
$29$			8.50925i			1.58013i	0.613025	+	0.790064i	$0.289953\pi$
$29$			8.50925i			1.58013i	−0.613025	+	0.790064i	$0.710047\pi$
$30$		0			0
$31$	−2.56730			−0.461101			−0.230551	−	0.973060i	$-0.574053\pi$
$31$	−2.56730			−0.461101			−0.230551	+	0.973060i	$0.574053\pi$
$32$	0.682268	−	5.61556i	0.120609	−	0.992700i
$33$		0			0
$34$	−1.28889	+	7.03269i	−0.221044	+	1.20610i
$35$	−0.163123	−	0.955891i	−0.0275728	−	0.161575i
$36$		0			0
$37$	1.69023	+	1.69023i	0.277872	+	0.277872i	0.832259	−	0.554387i	$-0.187047\pi$
$37$	1.69023	+	1.69023i	0.277872	+	0.277872i	−0.554387	+	0.832259i	$0.687047\pi$
$38$	5.48305	+	7.94381i	0.889467	+	1.28866i
$39$		0			0
$40$	2.31509	−	5.88561i	0.366048	−	0.930596i
$41$		−	5.19315i		−	0.811033i	−0.914088	−	0.405517i	$-0.867092\pi$
$41$		−	5.19315i		−	0.811033i	0.914088	−	0.405517i	$-0.132908\pi$
$42$		0			0
$43$	4.18889	−	4.18889i	0.638800	−	0.638800i	−0.311460	−	0.950259i	$-0.600818\pi$
$43$	4.18889	−	4.18889i	0.638800	−	0.638800i	0.950259	+	0.311460i	$0.100818\pi$
$44$	2.88480	−	7.60592i	0.434900	−	1.14664i
$45$		0			0
$46$	−3.12673	−	0.573041i	−0.461011	−	0.0844903i
$47$	4.58429	+	4.58429i	0.668688	+	0.668688i	0.957412	−	0.288724i	$-0.0932311\pi$
$47$	4.58429	+	4.58429i	0.668688	+	0.668688i	−0.288724	+	0.957412i	$0.593231\pi$
$48$		0			0
$49$			6.81193i			0.973133i
$50$	4.15796	−	5.71938i	0.588024	−	0.808843i
$51$		0			0
$52$	−0.725727	−	1.61263i	−0.100640	−	0.223631i
$53$	7.41934	+	7.41934i	1.01912	+	1.01912i	0.999814	+	0.0193111i	$0.00614730\pi$
$53$	7.41934	+	7.41934i	1.01912	+	1.01912i	0.0193111	+	0.999814i	$0.493853\pi$
$54$		0			0
$55$	5.25753	−	7.42115i	0.708925	−	1.00067i
$56$	0.634611	−	1.04967i	0.0848034	−	0.140268i
$57$		0			0
$58$	−9.90380	+	6.83589i	−1.30043	+	0.897596i
$59$		−	8.79560i		−	1.14509i	−0.819874	−	0.572545i	$-0.805956\pi$
$59$		−	8.79560i		−	1.14509i	0.819874	−	0.572545i	$-0.194044\pi$
$60$		0			0
$61$			6.08412i			0.778992i	0.921028	+	0.389496i	$0.127351\pi$
$61$			6.08412i			0.778992i	−0.921028	+	0.389496i	$0.872649\pi$
$62$	−2.06244	−	2.98805i	−0.261930	−	0.379483i
$63$		0			0
$64$	7.08397	−	3.71717i	0.885497	−	0.464646i
$65$	−0.332590	−	1.94896i	−0.0412527	−	0.241738i
$66$		0			0
$67$	6.18046	+	6.18046i	0.755063	+	0.755063i	0.975419	−	0.220356i	$-0.0707219\pi$
$67$	6.18046	+	6.18046i	0.755063	+	0.755063i	−0.220356	+	0.975419i	$0.570722\pi$
$68$	−9.22069	+	4.14957i	−1.11817	+	0.503209i
$69$		0			0
$70$	0.981504	−	0.957770i	0.117312	−	0.114475i
$71$		−	14.7516i		−	1.75069i	−0.483500	−	0.875344i	$-0.660635\pi$
$71$		−	14.7516i		−	1.75069i	0.483500	−	0.875344i	$-0.339365\pi$
$72$		0			0
$73$	3.05881	+	3.05881i	0.358007	+	0.358007i	0.863078	−	0.505071i	$-0.168534\pi$
$73$	3.05881	+	3.05881i	0.358007	+	0.358007i	−0.505071	+	0.863078i	$0.668534\pi$
$74$	−0.609393	+	3.32507i	−0.0708405	+	0.386532i
$75$		0			0
$76$	−4.84090	+	12.7633i	−0.555290	+	1.46405i
$77$	1.24724	−	1.24724i	0.142136	−	0.142136i
$78$		0			0
$79$		−	8.56106i		−	0.963194i	−0.876393	−	0.481597i	$-0.840057\pi$
$79$		−	8.56106i		−	0.963194i	0.876393	−	0.481597i	$-0.159943\pi$
$80$	8.71000	−	2.03369i	0.973808	−	0.227373i
$81$		0			0
$82$	6.04424	−	4.17190i	0.667474	−	0.460710i
$83$	−5.13122	−	5.13122i	−0.563224	−	0.563224i	0.366998	−	0.930222i	$-0.380386\pi$
$83$	−5.13122	−	5.13122i	−0.563224	−	0.563224i	−0.930222	+	0.366998i	$0.880386\pi$
$84$		0			0
$85$	−11.1438	+	1.90169i	−1.20871	+	0.206267i
$86$	8.24053	+	1.51026i	0.888599	+	0.162855i
$87$		0			0
$88$	11.1699	−	2.75262i	1.19072	−	0.293430i
$89$	−9.88328			−1.04763			−0.523813	−	0.851833i	$-0.675491\pi$
$89$	−9.88328			−1.04763			−0.523813	+	0.851833i	$0.675491\pi$
$90$		0			0
$91$		−	0.383449i		−	0.0401964i
$92$	−1.84489	−	4.09951i	−0.192343	−	0.427403i
$93$		0			0
$94$	−1.65282	+	9.01838i	−0.170475	+	0.930175i
$95$	−8.82252	+	12.4532i	−0.905171	+	1.27767i
$96$		0			0
$97$	1.75624	−	1.75624i	0.178319	−	0.178319i	−0.612303	−	0.790623i	$-0.709757\pi$
$97$	1.75624	−	1.75624i	0.178319	−	0.178319i	0.790623	+	0.612303i	$0.209757\pi$
$98$	−7.92832	+	5.47235i	−0.800881	+	0.552791i
$99$		0			0
$100$	9.99700	+	0.244739i	0.999700	+	0.0244739i
$101$	−1.88077			−0.187143			−0.0935716	−	0.995613i	$-0.529828\pi$
$101$	−1.88077			−0.187143			−0.0935716	+	0.995613i	$0.529828\pi$
$102$		0			0
$103$	10.7376	+	10.7376i	1.05800	+	1.05800i	0.998211	+	0.0597943i	$0.0190445\pi$
$103$	10.7376	+	10.7376i	1.05800	+	1.05800i	0.0597943	+	0.998211i	$0.480956\pi$
$104$	1.29390	−	2.14016i	0.126878	−	0.209860i
$105$		0			0
$106$	−2.67496	+	14.5956i	−0.259815	+	1.41765i
$107$	9.59725	−	9.59725i	0.927801	−	0.927801i	−0.0697628	−	0.997564i	$-0.522224\pi$
$107$	9.59725	−	9.59725i	0.927801	−	0.927801i	0.997564	+	0.0697628i	$0.0222242\pi$
$108$		0			0
$109$	−3.12119			−0.298956			−0.149478	−	0.988765i	$-0.547759\pi$
$109$	−3.12119			−0.298956			−0.149478	+	0.988765i	$0.547759\pi$
$110$	12.8610	+	0.157403i	1.22625	+	0.0150078i
$111$		0			0
$112$	1.73151	−	0.104636i	0.163612	−	0.00988715i
$113$	5.85646	−	5.85646i	0.550929	−	0.550929i	−0.375780	−	0.926709i	$-0.622625\pi$
$113$	5.85646	−	5.85646i	0.550929	−	0.550929i	0.926709	+	0.375780i	$0.122625\pi$
$114$		0			0
$115$	−0.845488	−	4.95451i	−0.0788421	−	0.462010i
$116$	−15.9124	−	6.03531i	−1.47743	−	0.560364i
$117$		0			0
$118$	10.2371	−	7.06592i	0.942399	−	0.650471i
$119$	−2.19249			−0.200985
$120$		0			0
$121$	5.54302			0.503911
$122$	−7.08123	+	4.88767i	−0.641104	+	0.442509i
$123$		0			0
$124$	1.82090	−	4.80088i	0.163521	−	0.431132i
$125$	10.7501	+	3.07182i	0.961515	+	0.274752i
$126$		0			0
$127$	−14.7376	+	14.7376i	−1.30775	+	1.30775i	−0.384712	+	0.923037i	$0.625699\pi$
$127$	−14.7376	+	14.7376i	−1.30775	+	1.30775i	−0.923037	+	0.384712i	$0.874301\pi$
$128$	10.0173	+	5.25876i	0.885409	+	0.464813i
$129$		0			0
$130$	2.00118	−	1.95279i	0.175515	−	0.171271i
$131$	−5.86888			−0.512766			−0.256383	−	0.966575i	$-0.582531\pi$
$131$	−5.86888			−0.512766			−0.256383	+	0.966575i	$0.582531\pi$
$132$		0			0
$133$	−2.09295	+	2.09295i	−0.181482	+	0.181482i
$134$	−2.22830	+	12.1584i	−0.192495	+	1.05033i
$135$		0			0
$136$	−12.2370	−	7.39829i	−1.04932	−	0.634398i
$137$	13.4582	+	13.4582i	1.14981	+	1.14981i	0.986589	+	0.163222i	$0.0521887\pi$
$137$	13.4582	+	13.4582i	1.14981	+	1.14981i	0.163222	+	0.986589i	$0.447811\pi$
$138$		0			0
$139$	−16.0990			−1.36550			−0.682752	−	0.730650i	$-0.739217\pi$
$139$	−16.0990			−1.36550			−0.682752	+	0.730650i	$0.739217\pi$
$140$	1.90322	+	0.372937i	0.160852	+	0.0315189i
$141$		0			0
$142$	17.1691	−	11.8506i	1.44080	−	0.994483i
$143$	2.54298	−	2.54298i	0.212655	−	0.212655i
$144$		0			0
$145$	−15.5258	−	10.9993i	−1.28935	−	0.913443i
$146$	−1.10282	+	6.01740i	−0.0912701	+	0.498004i
$147$		0			0
$148$	−4.35956	+	1.96193i	−0.358354	+	0.161269i
$149$		−	4.56103i		−	0.373654i	−0.982393	−	0.186827i	$-0.940180\pi$
$149$		−	4.56103i		−	0.373654i	0.982393	−	0.186827i	$-0.0598204\pi$
$150$		0			0
$151$	−12.4433			−1.01262			−0.506309	−	0.862352i	$-0.668991\pi$
$151$	−12.4433			−1.01262			−0.506309	+	0.862352i	$0.668991\pi$
$152$	−18.7439	+	4.61910i	−1.52033	+	0.374658i
$153$		0			0
$154$	2.45361	+	0.449677i	0.197717	+	0.0362360i
$155$	3.31857	−	4.68426i	0.266554	−	0.376249i
$156$		0			0
$157$	−13.4700	−	13.4700i	−1.07502	−	1.07502i	−0.996948	−	0.0780736i	$-0.975123\pi$
$157$	−13.4700	−	13.4700i	−1.07502	−	1.07502i	−0.0780736	−	0.996948i	$-0.524877\pi$
$158$	9.96410	−	6.87751i	0.792701	−	0.547145i
$159$		0			0
$160$	9.36414	+	8.50370i	0.740300	+	0.672276i
$161$		−	0.974777i		−	0.0768232i
$162$		0			0
$163$	6.23902	−	6.23902i	0.488678	−	0.488678i	−0.419211	−	0.907889i	$-0.637693\pi$
$163$	6.23902	−	6.23902i	0.488678	−	0.488678i	0.907889	+	0.419211i	$0.137693\pi$
$164$	9.71125	+	3.68331i	0.758321	+	0.287619i
$165$		0			0
$166$	1.85000	−	10.0943i	0.143588	−	0.783470i
$167$	−4.26961	−	4.26961i	−0.330392	−	0.330392i	0.522343	−	0.852735i	$-0.325058\pi$
$167$	−4.26961	−	4.26961i	−0.330392	−	0.330392i	−0.852735	+	0.522343i	$0.825058\pi$
$168$		0			0
$169$			12.2182i			0.939861i
$170$	−11.1657	−	11.4424i	−0.856368	−	0.877590i
$171$		0			0
$172$	4.86224	+	10.8043i	0.370743	+	0.823821i
$173$	−14.0168	−	14.0168i	−1.06568	−	1.06568i	−0.997686	−	0.0679921i	$-0.978341\pi$
$173$	−14.0168	−	14.0168i	−1.06568	−	1.06568i	−0.0679921	−	0.997686i	$-0.521659\pi$
$174$		0			0
$175$	1.95496	+	0.937982i	0.147781	+	0.0709048i
$176$	12.1771	+	10.7892i	0.917882	+	0.813268i
$177$		0			0
$178$	−7.93972	−	11.5030i	−0.595107	−	0.862188i
$179$			16.8624i			1.26036i	0.776451	+	0.630178i	$0.217018\pi$
$179$			16.8624i			1.26036i	−0.776451	+	0.630178i	$0.782982\pi$
$180$		0			0
$181$		−	18.7043i		−	1.39028i	−0.718874	−	0.695140i	$-0.755342\pi$
$181$		−	18.7043i		−	1.39028i	0.718874	−	0.695140i	$-0.244658\pi$
$182$	0.446291	−	0.308043i	0.0330813	−	0.0228337i
$183$		0			0
$184$	3.28927	−	5.44058i	0.242488	−	0.401085i
$185$	−5.26880	+	0.899123i	−0.387370	+	0.0661048i
$186$		0			0
$187$	−14.5403	−	14.5403i	−1.06329	−	1.06329i
$188$	−11.8242	+	5.32121i	−0.862365	+	0.388089i
$189$		0			0
$190$	−21.5817	−	0.264134i	−1.56570	−	0.0191623i
$191$		−	6.52419i		−	0.472074i	−0.971744	−	0.236037i	$-0.924151\pi$
$191$		−	6.52419i		−	0.472074i	0.971744	−	0.236037i	$-0.0758486\pi$
$192$		0			0
$193$	1.52917	+	1.52917i	0.110072	+	0.110072i	0.759998	−	0.649926i	$-0.225200\pi$
$193$	1.52917	+	1.52917i	0.110072	+	0.110072i	−0.649926	+	0.759998i	$0.725200\pi$
$194$	3.45494	+	0.633194i	0.248050	+	0.0454606i
$195$		0			0
$196$	−12.7384	−	4.83146i	−0.909885	−	0.345104i
$197$	3.85488	−	3.85488i	0.274648	−	0.274648i	−0.556320	−	0.830968i	$-0.687787\pi$
$197$	3.85488	−	3.85488i	0.274648	−	0.274648i	0.830968	+	0.556320i	$0.187787\pi$
$198$		0			0
$199$		−	14.3090i		−	1.01434i	−0.861847	−	0.507168i	$-0.830693\pi$
$199$		−	14.3090i		−	1.01434i	0.861847	−	0.507168i	$-0.169307\pi$
$200$	7.74622	+	11.8320i	0.547741	+	0.836648i
$201$		0			0
$202$	−1.51091	−	2.18900i	−0.106307	−	0.154017i
$203$	−2.60935	−	2.60935i	−0.183141	−	0.183141i
$204$		0			0
$205$	9.47533	+	6.71282i	0.661786	+	0.468844i
$206$	−3.87131	+	21.1233i	−0.269727	+	1.47173i
$207$		0			0
$208$	3.53036	−	0.213341i	0.244787	−	0.0147925i
$209$	−27.7604			−1.92023
$210$		0			0
$211$			8.62279i			0.593618i	0.954937	+	0.296809i	$0.0959224\pi$
$211$			8.62279i			0.593618i	−0.954937	+	0.296809i	$0.904078\pi$
$212$	−19.1365	+	8.61198i	−1.31430	+	0.591473i
$213$		0			0
$214$	18.8800	+	3.46018i	1.29061	+	0.236533i
$215$	2.22830	+	13.0577i	0.151968	+	0.890526i
$216$		0			0
$217$	0.787261	−	0.787261i	0.0534427	−	0.0534427i
$218$	−2.50740	−	3.63271i	−0.169823	−	0.246038i
$219$		0			0
$220$	10.1487	+	15.0952i	0.684223	+	1.01772i
$221$	−4.47024			−0.300701
$222$		0			0
$223$	6.87395	+	6.87395i	0.460314	+	0.460314i	0.898758	−	0.438444i	$-0.144470\pi$
$223$	6.87395	+	6.87395i	0.460314	+	0.460314i	−0.438444	+	0.898758i	$0.644470\pi$
$224$	1.51279	+	1.93122i	0.101077	+	0.129035i
$225$		0			0
$226$	11.5210	+	2.11148i	0.766368	+	0.140454i
$227$	−9.19431	+	9.19431i	−0.610248	+	0.610248i	−0.943011	−	0.332763i	$-0.892019\pi$
$227$	−9.19431	+	9.19431i	−0.610248	+	0.610248i	0.332763	+	0.943011i	$0.392019\pi$
$228$		0			0
$229$	2.31517			0.152991			0.0764954	−	0.997070i	$-0.475627\pi$
$229$	2.31517			0.152991			0.0764954	+	0.997070i	$0.475627\pi$
$230$	5.08726	−	4.96424i	0.335444	−	0.327333i
$231$		0			0
$232$	−5.75878	−	23.3687i	−0.378082	−	1.53423i
$233$	13.1377	−	13.1377i	0.860682	−	0.860682i	−0.130735	−	0.991417i	$-0.541734\pi$
$233$	13.1377	−	13.1377i	0.860682	−	0.860682i	0.991417	+	0.130735i	$0.0417338\pi$
$234$		0			0
$235$	−14.2902	+	2.43863i	−0.932191	+	0.159079i
$236$	16.4479	+	6.23840i	1.07067	+	0.406085i
$237$		0			0
$238$	−1.76133	−	2.55181i	−0.114170	−	0.165409i
$239$	12.3925			0.801604			0.400802	−	0.916165i	$-0.368732\pi$
$239$	12.3925			0.801604			0.400802	+	0.916165i	$0.368732\pi$
$240$		0			0
$241$	18.0131			1.16033			0.580164	−	0.814499i	$-0.302988\pi$
$241$	18.0131			1.16033			0.580164	+	0.814499i	$0.302988\pi$
$242$	4.45298	+	6.45145i	0.286248	+	0.414715i
$243$		0			0
$244$	−11.3774	−	4.31525i	−0.728362	−	0.276256i
$245$	−12.4289	−	8.80531i	−0.794056	−	0.562551i
$246$		0			0
$247$	−4.26731	+	4.26731i	−0.271522	+	0.271522i
$248$	7.05050	−	1.73746i	0.447707	−	0.110329i
$249$		0			0
$250$	5.06079	+	14.9796i	0.320073	+	0.947393i
$251$	12.9632			0.818228			0.409114	−	0.912483i	$-0.365838\pi$
$251$	12.9632			0.818228			0.409114	+	0.912483i	$0.365838\pi$
$252$		0			0
$253$	6.46459	−	6.46459i	0.406425	−	0.406425i
$254$	−28.9923	−	5.31347i	−1.81914	−	0.333397i
$255$		0			0
$256$	1.92674	+	15.8836i	0.120421	+	0.992723i
$257$	8.26946	+	8.26946i	0.515835	+	0.515835i	0.916308	−	0.400473i	$-0.131154\pi$
$257$	8.26946	+	8.26946i	0.515835	+	0.515835i	−0.400473	+	0.916308i	$0.631154\pi$
$258$		0			0
$259$	−1.03661			−0.0644120
$260$	3.88047	+	0.760379i	0.240656	+	0.0471567i
$261$		0			0
$262$	−4.71475	−	6.83071i	−0.291278	−	0.422003i
$263$	2.53991	−	2.53991i	0.156617	−	0.156617i	−0.624448	−	0.781066i	$-0.714676\pi$
$263$	2.53991	−	2.53991i	0.156617	−	0.156617i	0.781066	+	0.624448i	$0.214676\pi$
$264$		0			0
$265$	−23.1277	+	3.94674i	−1.42072	+	0.242447i
$266$	−4.11733	−	0.754591i	−0.252450	−	0.0462670i
$267$		0			0
$268$	−15.9411	+	7.17395i	−0.973758	+	0.438219i
$269$		−	1.90816i		−	0.116342i	−0.998307	−	0.0581712i	$-0.981473\pi$
$269$		−	1.90816i		−	0.116342i	0.998307	−	0.0581712i	$-0.0185269\pi$
$270$		0			0
$271$	14.2812			0.867524			0.433762	−	0.901028i	$-0.357186\pi$
$271$	14.2812			0.867524			0.433762	+	0.901028i	$0.357186\pi$
$272$	−1.21984	−	20.1859i	−0.0739639	−	1.22395i
$273$		0			0
$274$	−4.85220	+	26.4754i	−0.293132	+	1.59944i
$275$	6.74447	+	19.1856i	0.406707	+	1.15694i
$276$		0			0
$277$	20.5605	+	20.5605i	1.23536	+	1.23536i	0.961876	+	0.273488i	$0.0881772\pi$
$277$	20.5605	+	20.5605i	1.23536	+	1.23536i	0.273488	+	0.961876i	$0.411823\pi$
$278$	−12.9331	−	18.7375i	−0.775678	−	1.12380i
$279$		0			0
$280$	1.09489	+	2.51474i	0.0654325	+	0.150284i
$281$			9.40066i			0.560796i	0.959884	+	0.280398i	$0.0904665\pi$
$281$			9.40066i			0.560796i	−0.959884	+	0.280398i	$0.909533\pi$
$282$		0			0
$283$	−18.4043	+	18.4043i	−1.09402	+	1.09402i	−0.0989268	+	0.995095i	$0.531541\pi$
$283$	−18.4043	+	18.4043i	−1.09402	+	1.09402i	−0.995095	+	0.0989268i	$0.968459\pi$
$284$	27.5856	+	10.4628i	1.63690	+	0.620850i
$285$		0			0
$286$	5.00264	+	0.916843i	0.295812	+	0.0542141i
$287$	1.59247	+	1.59247i	0.0940008	+	0.0940008i
$288$		0			0
$289$			8.56000i			0.503530i
$290$	0.329304	−	26.9066i	0.0193374	−	1.58001i
$291$		0			0
$292$	−7.88952	+	3.55051i	−0.461699	+	0.207778i
$293$	−10.8096	−	10.8096i	−0.631504	−	0.631504i	0.316941	−	0.948445i	$-0.397344\pi$
$293$	−10.8096	−	10.8096i	−0.631504	−	0.631504i	−0.948445	+	0.316941i	$0.897344\pi$
$294$		0			0
$295$	16.0483	+	11.3695i	0.934369	+	0.661955i
$296$	−5.78571	−	3.49793i	−0.336287	−	0.203313i
$297$		0			0
$298$	5.30852	−	3.66409i	0.307514	−	0.212255i
$299$		−	1.98746i		−	0.114938i
$300$		0			0
$301$			2.56904i			0.148077i
$302$	−9.99627	−	14.4826i	−0.575221	−	0.833377i
$303$		0			0
$304$	−20.4340	−	18.1051i	−1.17197	−	1.03840i
$305$	−11.1010	−	7.86452i	−0.635641	−	0.450321i
$306$		0			0
$307$	23.8171	+	23.8171i	1.35931	+	1.35931i	0.874766	+	0.484546i	$0.161015\pi$
$307$	23.8171	+	23.8171i	1.35931	+	1.35931i	0.484546	+	0.874766i	$0.338985\pi$
$308$	1.44773	+	3.21697i	0.0824919	+	0.183304i
$309$		0			0
$310$	8.11791	+	0.0993535i	0.461066	+	0.00564290i
$311$			0.743382i			0.0421533i	0.999778	+	0.0210767i	$0.00670941\pi$
$311$			0.743382i			0.0421533i	−0.999778	+	0.0210767i	$0.993291\pi$
$312$		0			0
$313$	−16.4757	−	16.4757i	−0.931262	−	0.931262i	0.0665231	−	0.997785i	$-0.478809\pi$
$313$	−16.4757	−	16.4757i	−0.931262	−	0.931262i	−0.997785	+	0.0665231i	$0.978809\pi$
$314$	4.85645	−	26.4986i	0.274065	−	1.49540i
$315$		0			0
$316$	16.0093	+	6.07205i	0.900592	+	0.341580i
$317$	12.0047	−	12.0047i	0.674252	−	0.674252i	−0.284442	−	0.958693i	$-0.591808\pi$
$317$	12.0047	−	12.0047i	0.674252	−	0.674252i	0.958693	+	0.284442i	$0.0918082\pi$
$318$		0			0
$319$		−	34.6098i		−	1.93777i
$320$	−2.37468	+	17.7302i	−0.132749	+	0.991150i
$321$		0			0
$322$	1.13453	−	0.783085i	0.0632249	−	0.0436396i
$323$	24.3997	+	24.3997i	1.35763	+	1.35763i
$324$		0			0
$325$	3.98595	+	1.91244i	0.221101	+	0.106083i
$326$	12.2736	+	2.24941i	0.679773	+	0.124583i
$327$		0			0
$328$	3.51455	+	14.2618i	0.194059	+	0.787475i
$329$	−2.81154			−0.155005
$330$		0			0
$331$		−	20.3586i		−	1.11901i	−0.828827	−	0.559505i	$-0.810991\pi$
$331$		−	20.3586i		−	1.11901i	0.828827	−	0.559505i	$-0.189009\pi$
$332$	13.2348	−	5.95605i	0.726356	−	0.326881i
$333$		0			0
$334$	1.53936	−	8.39932i	0.0842300	−	0.459590i
$335$	−19.2658	+	3.28772i	−1.05260	+	0.179627i
$336$		0			0
$337$	12.3690	−	12.3690i	0.673782	−	0.673782i	−0.284804	−	0.958586i	$-0.591928\pi$
$337$	12.3690	−	12.3690i	0.673782	−	0.673782i	0.958586	+	0.284804i	$0.0919284\pi$
$338$	−14.2206	+	9.81546i	−0.773498	+	0.533890i
$339$		0			0
$340$	4.34770	−	22.1878i	0.235787	−	1.20330i
$341$	10.4420			0.565467
$342$		0			0
$343$	−4.23542	−	4.23542i	−0.228691	−	0.228691i
$344$	−8.66891	+	14.3387i	−0.467396	+	0.773092i
$345$		0			0
$346$	5.05360	−	27.5743i	0.271683	−	1.48241i
$347$	−8.65625	+	8.65625i	−0.464692	+	0.464692i	−0.900190	−	0.435498i	$-0.856572\pi$
$347$	−8.65625	+	8.65625i	−0.464692	+	0.464692i	0.435498	+	0.900190i	$0.356572\pi$
$348$		0			0
$349$	26.6201			1.42494			0.712469	−	0.701703i	$-0.247577\pi$
$349$	26.6201			1.42494			0.712469	+	0.701703i	$0.247577\pi$
$350$	0.478809	+	3.02888i	0.0255934	+	0.161900i
$351$		0			0
$352$	−2.77499	+	22.8402i	−0.147908	+	1.21739i
$353$	2.06573	−	2.06573i	0.109948	−	0.109948i	−0.649993	−	0.759940i	$-0.725228\pi$
$353$	2.06573	−	2.06573i	0.109948	−	0.109948i	0.759940	+	0.649993i	$0.225228\pi$
$354$		0			0
$355$	26.9155	+	19.0683i	1.42852	+	1.01204i
$356$	7.00986	−	18.4819i	0.371522	−	0.979536i
$357$		0			0
$358$	−19.6259	+	13.5464i	−1.03726	+	0.715949i
$359$	25.0314			1.32110			0.660552	−	0.750780i	$-0.270322\pi$
$359$	25.0314			1.32110			0.660552	+	0.750780i	$0.270322\pi$
$360$		0			0
$361$	27.5840			1.45179
$362$	21.7697	−	15.0261i	1.14419	−	0.789753i
$363$		0			0
$364$	0.717054	+	0.271967i	0.0375838	+	0.0142549i
$365$	−9.53497	+	1.62715i	−0.499083	+	0.0851687i
$366$		0			0
$367$	−17.6828	+	17.6828i	−0.923033	+	0.923033i	−0.997243	−	0.0742100i	$-0.976356\pi$
$367$	−17.6828	+	17.6828i	−0.923033	+	0.923033i	0.0742100	+	0.997243i	$0.476356\pi$
$368$	8.97464	−	0.542341i	0.467835	−	0.0282715i
$369$		0			0
$370$	−5.27916	−	5.40998i	−0.274450	−	0.281251i
$371$	−4.55027			−0.236238
$372$		0			0
$373$	17.6344	−	17.6344i	0.913073	−	0.913073i	−0.0834395	−	0.996513i	$-0.526591\pi$
$373$	17.6344	−	17.6344i	0.913073	−	0.913073i	0.996513	+	0.0834395i	$0.0265905\pi$
$374$	5.24234	−	28.6041i	0.271075	−	1.47909i
$375$		0			0
$376$	−15.6922	−	9.48720i	−0.809263	−	0.489265i
$377$	−5.32019	−	5.32019i	−0.274004	−	0.274004i
$378$		0			0
$379$	−17.1117			−0.878971			−0.439486	−	0.898250i	$-0.644839\pi$
$379$	−17.1117			−0.878971			−0.439486	+	0.898250i	$0.644839\pi$
$380$	−17.0302	−	25.3308i	−0.873630	−	1.29944i
$381$		0			0
$382$	7.59342	−	5.24119i	0.388513	−	0.268163i
$383$	7.26450	−	7.26450i	0.371199	−	0.371199i	−0.496715	−	0.867914i	$-0.665461\pi$
$383$	7.26450	−	7.26450i	0.371199	−	0.371199i	0.867914	+	0.496715i	$0.165461\pi$
$384$		0			0
$385$	0.663472	+	3.88791i	0.0338137	+	0.198146i
$386$	−0.551324	+	3.00823i	−0.0280616	+	0.153115i
$387$		0			0
$388$	2.03855	+	4.52983i	0.103492	+	0.229968i
$389$		−	4.30166i		−	0.218103i	−0.994036	−	0.109051i	$-0.965219\pi$
$389$		−	4.30166i		−	0.218103i	0.994036	−	0.109051i	$-0.0347813\pi$
$390$		0			0
$391$	−11.3639			−0.574699
$392$	−4.61009	−	18.7074i	−0.232845	−	0.944866i
$393$		0			0
$394$	7.58344	+	1.38983i	0.382048	+	0.0700187i
$395$	15.6204	+	11.0663i	0.785946	+	0.556805i
$396$		0			0
$397$	9.05589	+	9.05589i	0.454502	+	0.454502i	0.896846	−	0.442344i	$-0.145853\pi$
$397$	9.05589	+	9.05589i	0.454502	+	0.454502i	−0.442344	+	0.896846i	$0.645853\pi$
$398$	16.6540	−	11.4951i	0.834790	−	0.576196i
$399$		0			0
$400$	−7.54818	+	18.5209i	−0.377409	+	0.926047i
$401$			16.9061i			0.844249i	0.906538	+	0.422124i	$0.138715\pi$
$401$			16.9061i			0.844249i	−0.906538	+	0.422124i	$0.861285\pi$
$402$		0			0
$403$	1.60514	−	1.60514i	0.0799577	−	0.0799577i
$404$	1.33396	−	3.51706i	0.0663670	−	0.174980i
$405$		0			0
$406$	0.940773	−	5.13321i	0.0466898	−	0.254757i
$407$	−6.87468	−	6.87468i	−0.340765	−	0.340765i
$408$		0			0
$409$		−	1.92157i		−	0.0950153i	−0.998871	−	0.0475077i	$-0.984872\pi$
$409$		−	1.92157i		−	0.0950153i	0.998871	−	0.0475077i	$-0.0151278\pi$
$410$	−0.200973	+	16.4209i	−0.00992533	+	0.810973i
$411$		0			0
$412$	−27.6952	+	12.4636i	−1.36444	+	0.614038i
$413$	2.69716	+	2.69716i	0.132719	+	0.132719i
$414$		0			0
$415$	15.9951	−	2.72957i	0.785169	−	0.133989i
$416$	3.08441	+	3.93755i	0.151226	+	0.193054i
$417$		0			0
$418$	−22.3013	−	32.3100i	−1.09079	−	1.58033i
$419$			8.33374i			0.407130i	0.979061	+	0.203565i	$0.0652528\pi$
$419$			8.33374i			0.407130i	−0.979061	+	0.203565i	$0.934747\pi$
$420$		0			0
$421$			11.0584i			0.538956i	0.963007	+	0.269478i	$0.0868511\pi$
$421$			11.0584i			0.538956i	−0.963007	+	0.269478i	$0.913149\pi$
$422$	−10.0360	+	6.92710i	−0.488543	+	0.337206i
$423$		0			0
$424$	−25.3967	−	15.3543i	−1.23337	−	0.745672i
$425$	10.9350	−	22.7909i	0.530425	−	1.10552i
$426$		0			0
$427$	−1.86569	−	1.86569i	−0.0902871	−	0.0902871i
$428$	11.1400	+	24.7539i	0.538471	+	1.19653i
$429$		0			0
$430$	−13.4076	+	13.0833i	−0.646570	+	0.630934i
$431$		−	26.6362i		−	1.28302i	−0.767115	−	0.641509i	$-0.778309\pi$
$431$		−	26.6362i		−	1.28302i	0.767115	−	0.641509i	$-0.221691\pi$
$432$		0			0
$433$	−16.5454	−	16.5454i	−0.795123	−	0.795123i	0.187199	−	0.982322i	$-0.440059\pi$
$433$	−16.5454	−	16.5454i	−0.795123	−	0.795123i	−0.982322	+	0.187199i	$0.940059\pi$
$434$	1.54873	+	0.283838i	0.0743412	+	0.0136247i
$435$		0			0
$436$	2.21375	−	5.83666i	0.106019	−	0.279525i
$437$	−10.8481	+	10.8481i	−0.518933	+	0.518933i
$438$		0			0
$439$		−	5.35402i		−	0.255533i	−0.991804	−	0.127767i	$-0.959219\pi$
$439$		−	5.35402i		−	0.255533i	0.991804	−	0.127767i	$-0.0407808\pi$
$440$	−9.41620	+	23.9386i	−0.448900	+	1.14123i
$441$		0			0
$442$	−3.59116	−	5.20286i	−0.170814	−	0.247475i
$443$	−2.73227	−	2.73227i	−0.129814	−	0.129814i	0.639215	−	0.769028i	$-0.279260\pi$
$443$	−2.73227	−	2.73227i	−0.129814	−	0.129814i	−0.769028	+	0.639215i	$0.779260\pi$
$444$		0			0
$445$	12.7754	−	18.0329i	0.605614	−	0.854841i
$446$	−2.47833	+	13.5227i	−0.117352	+	0.640317i
$447$		0			0
$448$	−1.03243	+	3.31216i	−0.0487777	+	0.156485i
$449$	28.9286			1.36522			0.682612	−	0.730781i	$-0.260844\pi$
$449$	28.9286			1.36522			0.682612	+	0.730781i	$0.260844\pi$
$450$		0			0
$451$			21.1222i			0.994603i
$452$	6.79787	+	15.1054i	0.319745	+	0.710500i
$453$		0			0
$454$	−18.0874	−	3.31491i	−0.848882	−	0.155576i
$455$	0.699635	+	0.495658i	0.0327994	+	0.0232368i
$456$		0			0
$457$	10.5512	−	10.5512i	0.493564	−	0.493564i	−0.415863	−	0.909427i	$-0.636520\pi$
$457$	10.5512	−	10.5512i	0.493564	−	0.493564i	0.909427	+	0.415863i	$0.136520\pi$
$458$	1.85989	+	2.69460i	0.0869068	+	0.125910i
$459$		0			0
$460$	9.86466	+	1.93298i	0.459942	+	0.0901257i
$461$	−11.9624			−0.557146			−0.278573	−	0.960415i	$-0.589861\pi$
$461$	−11.9624			−0.557146			−0.278573	+	0.960415i	$0.589861\pi$
$462$		0			0
$463$	8.05265	+	8.05265i	0.374238	+	0.374238i	0.869018	−	0.494780i	$-0.164751\pi$
$463$	8.05265	+	8.05265i	0.374238	+	0.374238i	−0.494780	+	0.869018i	$0.664751\pi$
$464$	22.5722	−	25.4757i	1.04789	−	1.18268i
$465$		0			0
$466$	25.8450	+	4.73666i	1.19725	+	0.219422i
$467$	−13.8717	+	13.8717i	−0.641906	+	0.641906i	−0.951024	−	0.309118i	$-0.899966\pi$
$467$	−13.8717	+	13.8717i	−0.641906	+	0.641906i	0.309118	+	0.951024i	$0.399966\pi$
$468$		0			0
$469$	−3.79046			−0.175027
$470$	−14.3183	−	14.6731i	−0.660454	−	0.676821i
$471$		0			0
$472$	5.95257	+	24.1551i	0.273989	+	1.11183i
$473$	−17.0375	+	17.0375i	−0.783386	+	0.783386i
$474$		0			0
$475$	−11.3177	−	32.1949i	−0.519292	−	1.47720i
$476$	1.55505	−	4.09998i	0.0712757	−	0.187922i
$477$		0			0
$478$	9.95548	+	14.4235i	0.455353	+	0.659713i
$479$	5.00618			0.228738			0.114369	−	0.993438i	$-0.463515\pi$
$479$	5.00618			0.228738			0.114369	+	0.993438i	$0.463515\pi$
$480$		0			0
$481$	−2.11354			−0.0963693
$482$	14.4708	+	20.9653i	0.659128	+	0.954941i
$483$		0			0
$484$	−3.93147	+	10.3655i	−0.178703	+	0.471160i
$485$	0.934240	+	5.47458i	0.0424216	+	0.248588i
$486$		0			0
$487$	−7.84638	+	7.84638i	−0.355554	+	0.355554i	−0.862171	−	0.506617i	$-0.830896\pi$
$487$	−7.84638	+	7.84638i	−0.355554	+	0.355554i	0.506617	+	0.862171i	$0.330896\pi$
$488$	−4.11753	−	16.7086i	−0.186392	−	0.756364i
$489$		0			0
$490$	0.263619	−	21.5396i	0.0119091	−	0.973060i
$491$	−1.65566			−0.0747189			−0.0373594	−	0.999302i	$-0.511895\pi$
$491$	−1.65566			−0.0747189			−0.0373594	+	0.999302i	$0.511895\pi$
$492$		0			0
$493$	−30.4198	+	30.4198i	−1.37004	+	1.37004i
$494$	−8.39480	−	1.53853i	−0.377700	−	0.0692217i
$495$		0			0
$496$	7.68621	+	6.81019i	0.345121	+	0.305787i
$497$	4.52355	+	4.52355i	0.202909	+	0.202909i
$498$		0			0
$499$	28.0466			1.25554			0.627768	−	0.778400i	$-0.283969\pi$
$499$	28.0466			1.25554			0.627768	+	0.778400i	$0.283969\pi$
$500$	−13.3690	+	17.9240i	−0.597879	+	0.801586i
$501$		0			0
$502$	10.4139	+	15.0877i	0.464797	+	0.673395i
$503$	−26.8464	+	26.8464i	−1.19702	+	1.19702i	−0.221965	+	0.975055i	$0.571247\pi$
$503$	−26.8464	+	26.8464i	−1.19702	+	1.19702i	−0.975055	+	0.221965i	$0.928753\pi$
$504$		0			0
$505$	2.43114	−	3.43162i	0.108184	−	0.152705i
$506$	12.7174	+	2.33074i	0.565356	+	0.103614i
$507$		0			0
$508$	−17.1066	−	38.0123i	−0.758983	−	1.68652i
$509$		−	12.0740i		−	0.535170i	−0.963534	−	0.267585i	$-0.913774\pi$
$509$		−	12.0740i		−	0.535170i	0.963534	−	0.267585i	$-0.0862256\pi$
$510$		0			0
$511$	−1.87596			−0.0829878
$512$	−16.9388	+	15.0025i	−0.748598	+	0.663024i
$513$		0			0
$514$	−2.98146	+	16.2680i	−0.131507	+	0.717550i
$515$	−33.4713	+	5.71189i	−1.47492	+	0.251696i
$516$		0			0
$517$	−18.6457	−	18.6457i	−0.820039	−	0.820039i
$518$	−0.832761	−	1.20650i	−0.0365894	−	0.0530106i
$519$		0			0
$520$	2.23237	+	5.12727i	0.0978960	+	0.224846i
$521$			20.1076i			0.880928i	0.897770	+	0.440464i	$0.145186\pi$
$521$			20.1076i			0.880928i	−0.897770	+	0.440464i	$0.854814\pi$
$522$		0			0
$523$	−5.72970	+	5.72970i	−0.250542	+	0.250542i	−0.821193	−	0.570651i	$-0.806691\pi$
$523$	−5.72970	+	5.72970i	−0.250542	+	0.250542i	0.570651	+	0.821193i	$0.306691\pi$
$524$	4.16259	−	10.9749i	0.181843	−	0.479440i
$525$		0			0
$526$	4.99660	+	0.915736i	0.217862	+	0.0399280i
$527$	−9.17788	−	9.17788i	−0.399795	−	0.399795i
$528$		0			0
$529$			17.9476i			0.780331i
$530$	−23.1731	−	23.7474i	−1.00658	−	1.03152i
$531$		0			0
$532$	−2.42939	−	5.39831i	−0.105328	−	0.234046i
$533$	3.24688	+	3.24688i	0.140638	+	0.140638i
$534$		0			0
$535$	5.10529	+	29.9167i	0.220721	+	1.29341i
$536$	−21.1559	−	12.7905i	−0.913797	−	0.552464i
$537$		0			0
$538$	2.22088	−	1.53291i	0.0957489	−	0.0660887i
$539$		−	27.7063i		−	1.19339i
$540$		0			0
$541$		−	33.4356i		−	1.43751i	−0.695263	−	0.718755i	$-0.744712\pi$
$541$		−	33.4356i		−	1.43751i	0.695263	−	0.718755i	$-0.255288\pi$
$542$	11.4728	+	16.6218i	0.492799	+	0.713965i
$543$		0			0
$544$	22.5142	−	17.6361i	0.965288	−	0.756141i
$545$	4.03454	−	5.69487i	0.172821	−	0.243941i
$546$		0			0
$547$	−9.08411	−	9.08411i	−0.388409	−	0.388409i	0.485711	−	0.874119i	$-0.338561\pi$
$547$	−9.08411	−	9.08411i	−0.388409	−	0.388409i	−0.874119	+	0.485711i	$0.838561\pi$
$548$	−34.7124	+	15.6216i	−1.48284	+	0.667320i
$549$		0			0
$550$	−16.9117	+	23.2625i	−0.721118	+	0.991917i
$551$			58.0777i			2.47419i
$552$		0			0
$553$	2.62524	+	2.62524i	0.111637	+	0.111637i
$554$	−7.41287	+	40.4474i	−0.314943	+	1.71845i
$555$		0			0
$556$	11.4185	−	30.1054i	0.484251	−	1.27675i
$557$	−5.55956	+	5.55956i	−0.235566	+	0.235566i	−0.815011	−	0.579445i	$-0.803269\pi$
$557$	−5.55956	+	5.55956i	−0.235566	+	0.235566i	0.579445	+	0.815011i	$0.303269\pi$
$558$		0			0
$559$			5.23799i			0.221543i
$560$	−2.04729	+	3.29454i	−0.0865136	+	0.139220i
$561$		0			0
$562$	−10.9413	+	7.55200i	−0.461531	+	0.318562i
$563$	−6.38203	−	6.38203i	−0.268970	−	0.268970i	0.559715	−	0.828685i	$-0.310911\pi$
$563$	−6.38203	−	6.38203i	−0.268970	−	0.268970i	−0.828685	+	0.559715i	$0.810911\pi$
$564$		0			0
$565$	3.11537	+	18.2558i	0.131064	+	0.768029i
$566$	−36.2056	−	6.63546i	−1.52183	−	0.278909i
$567$		0			0
$568$	9.98337	+	40.5117i	0.418893	+	1.69983i
$569$	−24.2945			−1.01848			−0.509240	−	0.860625i	$-0.670073\pi$
$569$	−24.2945			−1.01848			−0.509240	+	0.860625i	$0.670073\pi$
$570$		0			0
$571$			3.35468i			0.140389i	0.997533	+	0.0701945i	$0.0223620\pi$
$571$			3.35468i			0.140389i	−0.997533	+	0.0701945i	$0.977638\pi$
$572$	2.95176	+	6.55905i	0.123419	+	0.274248i
$573$		0			0
$574$	−0.574149	+	3.13277i	−0.0239645	+	0.130759i
$575$	10.1328	+	4.86168i	0.422568	+	0.202746i
$576$		0			0
$577$	−16.6998	+	16.6998i	−0.695223	+	0.695223i	−0.963376	−	0.268153i	$-0.913587\pi$
$577$	−16.6998	+	16.6998i	−0.695223	+	0.695223i	0.268153	+	0.963376i	$0.413587\pi$
$578$	−9.96287	+	6.87666i	−0.414401	+	0.286031i
$579$		0			0
$580$	31.5808	−	21.2321i	1.31132	−	0.881614i
$581$	3.14697			0.130558
$582$		0			0
$583$	−30.1768	−	30.1768i	−1.24979	−	1.24979i
$584$	−10.4704	−	6.33021i	−0.433269	−	0.261946i
$585$		0			0
$586$	3.89728	−	21.2650i	0.160995	−	0.878450i
$587$	31.8287	−	31.8287i	1.31371	−	1.31371i	0.395050	−	0.918659i	$-0.370727\pi$
$587$	31.8287	−	31.8287i	1.31371	−	1.31371i	0.918659	−	0.395050i	$-0.129273\pi$
$588$		0			0
$589$	−17.5225			−0.722000
$590$	−0.340386	+	27.8120i	−0.0140135	+	1.14500i
$591$		0			0
$592$	−0.576745	−	9.54396i	−0.0237041	−	0.392254i
$593$	8.80387	−	8.80387i	0.361532	−	0.361532i	−0.502845	−	0.864377i	$-0.667713\pi$
$593$	8.80387	−	8.80387i	0.361532	−	0.361532i	0.864377	+	0.502845i	$0.167713\pi$
$594$		0			0
$595$	2.83408	−	4.00038i	0.116186	−	0.163999i
$596$	8.52918	+	3.23498i	0.349369	+	0.132510i
$597$		0			0
$598$	2.31318	−	1.59663i	0.0945931	−	0.0652909i
$599$	36.2251			1.48012			0.740060	−	0.672541i	$-0.234797\pi$
$599$	36.2251			1.48012			0.740060	+	0.672541i	$0.234797\pi$
$600$		0			0
$601$	−5.92157			−0.241546			−0.120773	−	0.992680i	$-0.538537\pi$
$601$	−5.92157			−0.241546			−0.120773	+	0.992680i	$0.538537\pi$
$602$	−2.99007	+	2.06383i	−0.121866	+	0.0841155i
$603$		0			0
$604$	8.82556	−	23.2691i	0.359107	−	0.946804i
$605$	−7.16508	+	10.1137i	−0.291302	+	0.411181i
$606$		0			0
$607$	22.5127	−	22.5127i	0.913763	−	0.913763i	−0.0828026	−	0.996566i	$-0.526387\pi$
$607$	22.5127	−	22.5127i	0.913763	−	0.913763i	0.996566	+	0.0828026i	$0.0263871\pi$
$608$	4.65664	−	38.3276i	0.188852	−	1.55439i
$609$		0			0
$610$	0.235453	−	19.2382i	0.00953321	−	0.778934i
$611$	−5.73242			−0.231909
$612$		0			0
$613$	−17.8351	+	17.8351i	−0.720352	+	0.720352i	−0.968677	−	0.248325i	$-0.920120\pi$
$613$	−17.8351	+	17.8351i	−0.720352	+	0.720352i	0.248325	+	0.968677i	$0.420120\pi$
$614$	−8.58698	+	46.8538i	−0.346542	+	1.89086i
$615$		0			0
$616$	−2.58116	+	4.26934i	−0.103998	+	0.172016i
$617$	−4.87456	−	4.87456i	−0.196242	−	0.196242i	0.602145	−	0.798387i	$-0.294313\pi$
$617$	−4.87456	−	4.87456i	−0.196242	−	0.196242i	−0.798387	+	0.602145i	$0.794313\pi$
$618$		0			0
$619$	−33.3372			−1.33994			−0.669968	−	0.742390i	$-0.733692\pi$
$619$	−33.3372			−1.33994			−0.669968	+	0.742390i	$0.733692\pi$
$620$	6.40587	+	9.52815i	0.257266	+	0.382660i
$621$		0			0
$622$	−0.865213	+	0.597195i	−0.0346919	+	0.0239453i
$623$	3.03070	−	3.03070i	0.121422	−	0.121422i
$624$		0			0
$625$	−19.5007	+	15.6437i	−0.780026	+	0.625747i
$626$	5.94013	−	32.4116i	0.237415	−	1.29543i
$627$		0			0
$628$	34.7428	−	15.6352i	1.38639	−	0.623914i
$629$			12.0848i			0.481854i
$630$		0			0
$631$	−11.3469			−0.451715			−0.225857	−	0.974160i	$-0.572518\pi$
$631$	−11.3469			−0.451715			−0.225857	+	0.974160i	$0.572518\pi$
$632$	5.79384	+	23.5110i	0.230467	+	0.935216i
$633$		0			0
$634$	23.6161	+	4.32816i	0.937914	+	0.171893i
$635$	−7.83971	−	45.9402i	−0.311109	−	1.82308i
$636$		0			0
$637$	−4.25899	−	4.25899i	−0.168747	−	0.168747i
$638$	40.2818	−	27.8037i	1.59477	−	1.10076i
$639$		0			0
$640$	−22.5437	+	11.4797i	−0.891117	+	0.453774i
$641$			0.578269i			0.0228403i	0.999935	+	0.0114201i	$0.00363522\pi$
$641$			0.578269i			0.0228403i	−0.999935	+	0.0114201i	$0.996365\pi$
$642$		0			0
$643$	23.4952	−	23.4952i	0.926559	−	0.926559i	−0.0709229	−	0.997482i	$-0.522594\pi$
$643$	23.4952	−	23.4952i	0.926559	−	0.926559i	0.997482	+	0.0709229i	$0.0225944\pi$
$644$	1.82284	+	0.691374i	0.0718301	+	0.0272440i
$645$		0			0
$646$	−8.79702	+	47.9998i	−0.346114	+	1.88853i
$647$	−25.6996	−	25.6996i	−1.01036	−	1.01036i	−0.999946	−	0.0104099i	$-0.996686\pi$
$647$	−25.6996	−	25.6996i	−1.01036	−	1.01036i	−0.0104099	−	0.999946i	$-0.503314\pi$
$648$		0			0
$649$			35.7744i			1.40427i
$650$	0.976240	+	6.17556i	0.0382913	+	0.242225i
$651$		0			0
$652$	7.24193	+	16.0922i	0.283616	+	0.630218i
$653$	24.0153	+	24.0153i	0.939791	+	0.939791i	0.998288	−	0.0584965i	$-0.0186306\pi$
$653$	24.0153	+	24.0153i	0.939791	+	0.939791i	−0.0584965	+	0.998288i	$0.518631\pi$
$654$		0			0
$655$	7.58629	−	10.7083i	0.296421	−	0.418406i
$656$	−13.7757	+	15.5477i	−0.537850	+	0.607036i
$657$		0			0
$658$	−2.25864	−	3.27231i	−0.0880511	−	0.127568i
$659$			6.25348i			0.243601i	0.992555	+	0.121800i	$0.0388668\pi$
$659$			6.25348i			0.243601i	−0.992555	+	0.121800i	$0.961133\pi$
$660$		0			0
$661$		−	11.0800i		−	0.430960i	−0.976508	−	0.215480i	$-0.930868\pi$
$661$		−	11.0800i		−	0.430960i	0.976508	−	0.215480i	$-0.0691317\pi$
$662$	23.6951	−	16.3550i	0.920937	−	0.635657i
$663$		0			0
$664$	17.5643	+	10.6191i	0.681629	+	0.412100i
$665$	−1.11335	−	6.52419i	−0.0431740	−	0.252997i
$666$		0			0
$667$	−13.5246	−	13.5246i	−0.523675	−	0.523675i
$668$	11.0125	−	4.95594i	0.426086	−	0.191751i
$669$		0			0
$670$	−19.3037	−	19.7820i	−0.745766	−	0.764247i
$671$		−	24.7460i		−	0.955310i
$672$		0			0
$673$	5.39727	+	5.39727i	0.208049	+	0.208049i	0.803438	−	0.595389i	$-0.203002\pi$
$673$	5.39727	+	5.39727i	0.208049	+	0.208049i	−0.595389	+	0.803438i	$0.703002\pi$
$674$	24.3327	+	4.45950i	0.937261	+	0.171774i
$675$		0			0
$676$	−22.8482	−	8.66593i	−0.878775	−	0.333305i
$677$	−7.81449	+	7.81449i	−0.300335	+	0.300335i	−0.841145	−	0.540810i	$-0.818118\pi$
$677$	−7.81449	+	7.81449i	−0.300335	+	0.300335i	0.540810	+	0.841145i	$0.318118\pi$
$678$		0			0
$679$			1.07710i			0.0413353i
$680$	29.3168	−	12.7643i	1.12425	−	0.489488i
$681$		0			0
$682$	8.38857	+	12.1533i	0.321215	+	0.465375i
$683$	−19.2280	−	19.2280i	−0.735740	−	0.735740i	0.236011	−	0.971750i	$-0.424160\pi$
$683$	−19.2280	−	19.2280i	−0.735740	−	0.735740i	−0.971750	+	0.236011i	$0.924160\pi$
$684$		0			0
$685$	−41.9521	+	7.15914i	−1.60291	+	0.273536i
$686$	1.52703	−	8.33206i	0.0583023	−	0.318119i
$687$		0			0
$688$	−23.6528	+	1.42935i	−0.901754	+	0.0544933i
$689$	−9.27750			−0.353445
$690$		0			0
$691$		−	23.0256i		−	0.875936i	−0.898991	−	0.437968i	$-0.855698\pi$
$691$		−	23.0256i		−	0.875936i	0.898991	−	0.437968i	$-0.144302\pi$
$692$	36.1532	−	16.2700i	1.37434	−	0.618492i
$693$		0			0
$694$	−17.0289	−	3.12091i	−0.646407	−	0.118468i
$695$	20.8101	−	29.3741i	0.789373	−	1.11422i
$696$		0			0
$697$	18.5651	−	18.5651i	0.703201	−	0.703201i
$698$	21.3852	+	30.9827i	0.809440	+	1.17271i
$699$		0			0
$700$	−3.14062	+	2.99052i	−0.118704	+	0.113031i
$701$	36.0487			1.36154			0.680771	−	0.732496i	$-0.261645\pi$
$701$	36.0487			1.36154			0.680771	+	0.732496i	$0.261645\pi$
$702$		0			0
$703$	11.5362	+	11.5362i	0.435097	+	0.435097i
$704$	−28.8127	+	15.1189i	−1.08592	+	0.569814i
$705$		0			0
$706$	4.06378	+	0.744776i	0.152942	+	0.0280300i
$707$	0.576735	−	0.576735i	0.0216904	−	0.0216904i
$708$		0			0
$709$	−10.2426			−0.384667			−0.192334	−	0.981330i	$-0.561606\pi$
$709$	−10.2426			−0.384667			−0.192334	+	0.981330i	$0.561606\pi$
$710$	−0.570879	+	46.6450i	−0.0214247	+	1.75056i
$711$		0			0
$712$	27.1421	−	6.68868i	1.01719	−	0.250669i
$713$	4.08047	−	4.08047i	0.152815	−	0.152815i
$714$		0			0
$715$	1.35275	+	7.92702i	0.0505899	+	0.296454i
$716$	−31.5329	−	11.9599i	−1.17844	−	0.446963i
$717$		0			0
$718$	20.1089	+	29.1337i	0.750457	+	1.08726i
$719$	−39.2886			−1.46522			−0.732609	−	0.680650i	$-0.761698\pi$
$719$	−39.2886			−1.46522			−0.732609	+	0.680650i	$0.761698\pi$
$720$		0			0
$721$	−6.58534			−0.245251
$722$	22.1595	+	32.1046i	0.824692	+	1.19481i
$723$		0			0
$724$	34.9773	+	13.2663i	1.29992	+	0.493038i
$725$	40.1383	−	14.1101i	1.49070	−	0.524038i
$726$		0			0
$727$	15.2333	−	15.2333i	0.564970	−	0.564970i	−0.365745	−	0.930715i	$-0.619186\pi$
$727$	15.2333	−	15.2333i	0.564970	−	0.564970i	0.930715	+	0.365745i	$0.119186\pi$
$728$	0.259505	+	1.05305i	0.00961791	+	0.0390287i
$729$		0			0
$730$	−9.55371	−	9.79046i	−0.353599	−	0.362361i
$731$	29.9498			1.10773
$732$		0			0
$733$	12.3754	−	12.3754i	0.457097	−	0.457097i	−0.440604	−	0.897701i	$-0.645236\pi$
$733$	12.3754	−	12.3754i	0.457097	−	0.457097i	0.897701	+	0.440604i	$0.145236\pi$
$734$	−34.7861	−	6.37532i	−1.28398	−	0.235317i
$735$		0			0
$736$	7.84098	+	10.0098i	0.289022	+	0.368965i
$737$	−25.1379	−	25.1379i	−0.925965	−	0.925965i
$738$		0			0
$739$	25.8730			0.951753			0.475876	−	0.879512i	$-0.342131\pi$
$739$	25.8730			0.951753			0.475876	+	0.879512i	$0.342131\pi$
$740$	2.05560	−	10.4904i	0.0755655	−	0.385636i
$741$		0			0
$742$	−3.65545	−	5.29599i	−0.134196	−	0.194422i
$743$	−15.9812	+	15.9812i	−0.586292	+	0.586292i	−0.936625	−	0.350333i	$-0.886068\pi$
$743$	−15.9812	+	15.9812i	−0.586292	+	0.586292i	0.350333	+	0.936625i	$0.386068\pi$
$744$		0			0
$745$	8.32198	+	5.89573i	0.304894	+	0.216003i
$746$	34.6910	+	6.35788i	1.27013	+	0.232778i
$747$		0			0
$748$	37.5034	−	16.8776i	1.37126	−	0.617106i
$749$			5.88597i			0.215069i
$750$		0			0
$751$	−33.3102			−1.21551			−0.607754	−	0.794125i	$-0.707929\pi$
$751$	−33.3102			−1.21551			−0.607754	+	0.794125i	$0.707929\pi$
$752$	−1.56427	−	25.8855i	−0.0570430	−	0.943945i
$753$		0			0
$754$	1.91813	−	10.4661i	0.0698543	−	0.381151i
$755$	16.0845	−	22.7038i	0.585376	−	0.826275i
$756$		0			0
$757$	−35.1121	−	35.1121i	−1.27617	−	1.27617i	−0.942793	−	0.333378i	$-0.891812\pi$
$757$	−35.1121	−	35.1121i	−1.27617	−	1.27617i	−0.333378	−	0.942793i	$-0.608188\pi$
$758$	−13.7467	−	19.9161i	−0.499302	−	0.723386i
$759$		0			0
$760$	15.8011	−	40.1707i	0.573165	−	1.45714i
$761$		−	22.5518i		−	0.817502i	−0.912646	−	0.408751i	$-0.865964\pi$
$761$		−	22.5518i		−	0.817502i	0.912646	−	0.408751i	$-0.134036\pi$
$762$		0			0
$763$	0.957109	−	0.957109i	0.0346497	−	0.0346497i
$764$	12.2003	+	4.62737i	0.441392	+	0.167413i
$765$		0			0
$766$	14.2910	+	2.61913i	0.516354	+	0.0946331i
$767$	5.49922	+	5.49922i	0.198565	+	0.198565i
$768$		0			0
$769$		−	16.8578i		−	0.607907i	−0.952687	−	0.303953i	$-0.901693\pi$
$769$		−	16.8578i		−	0.607907i	0.952687	−	0.303953i	$-0.0983067\pi$
$770$	−3.99208	+	3.89555i	−0.143865	+	0.140386i
$771$		0			0
$772$	−3.94414	+	1.77498i	−0.141953	+	0.0638828i
$773$	−2.59499	−	2.59499i	−0.0933354	−	0.0933354i	0.658897	−	0.752233i	$-0.271023\pi$
$773$	−2.59499	−	2.59499i	−0.0933354	−	0.0933354i	−0.752233	+	0.658897i	$0.771023\pi$
$774$		0			0
$775$	4.25713	+	12.1100i	0.152921	+	0.435005i
$776$	−3.63455	+	6.01168i	−0.130473	+	0.215807i
$777$		0			0
$778$	5.00664	−	3.45573i	0.179497	−	0.123894i
$779$		−	35.4445i		−	1.26993i
$780$		0			0
$781$			59.9992i			2.14694i
$782$	−9.12920	−	13.2263i	−0.326460	−	0.472973i
$783$		0			0
$784$	18.0698	−	20.3942i	0.645349	−	0.728363i
$785$	41.9888	−	7.16540i	1.49864	−	0.255744i
$786$		0			0
$787$	25.1710	+	25.1710i	0.897248	+	0.897248i	0.995192	−	0.0979438i	$-0.0312265\pi$
$787$	25.1710	+	25.1710i	0.897248	+	0.897248i	−0.0979438	+	0.995192i	$0.531227\pi$
$788$	4.47454	+	9.94279i	0.159399	+	0.354197i
$789$		0			0
$790$	−0.331309	+	27.0704i	−0.0117875	+	0.963122i
$791$			3.59176i			0.127708i
$792$		0			0
$793$	−3.80394	−	3.80394i	−0.135082	−	0.135082i
$794$	−3.26500	+	17.8151i	−0.115870	+	0.632233i
$795$		0			0
$796$	26.7579	+	10.1488i	0.948409	+	0.359716i
$797$	0.184398	−	0.184398i	0.00653173	−	0.00653173i	−0.703833	−	0.710365i	$-0.748530\pi$
$797$	0.184398	−	0.184398i	0.00653173	−	0.00653173i	0.710365	+	0.703833i	$0.248530\pi$
$798$		0			0
$799$			32.7769i			1.15956i
$800$	−27.6201	+	6.09352i	−0.976517	+	0.215439i
$801$		0			0
$802$	−19.6767	+	13.5815i	−0.694810	+	0.479578i
$803$	−12.4411	−	12.4411i	−0.439038	−	0.439038i
$804$		0			0
$805$	1.77856	+	1.26003i	0.0626861	+	0.0444101i
$806$	3.15769	+	0.578715i	0.111225	+	0.0203844i
$807$		0			0
$808$	5.16509	−	1.27284i	0.181707	−	0.0447784i
$809$	23.3352			0.820422			0.410211	−	0.911991i	$-0.365455\pi$
$809$	23.3352			0.820422			0.410211	+	0.911991i	$0.365455\pi$
$810$		0			0
$811$		−	4.50503i		−	0.158193i	−0.996867	−	0.0790964i	$-0.974797\pi$
$811$		−	4.50503i		−	0.158193i	0.996867	−	0.0790964i	$-0.0252035\pi$
$812$	6.73024	−	3.02880i	0.236185	−	0.106290i
$813$		0			0
$814$	2.47859	−	13.5241i	0.0868745	−	0.474020i
$815$	3.31887	+	19.4484i	0.116255	+	0.681247i
$816$		0			0
$817$	28.5902	−	28.5902i	1.00024	−	1.00024i
$818$	2.23648	−	1.54369i	0.0781968	−	0.0539737i
$819$		0			0
$820$	−19.2736	+	12.9578i	−0.673062	+	0.452507i
$821$	13.4411			0.469097			0.234549	−	0.972104i	$-0.424639\pi$
$821$	13.4411			0.469097			0.234549	+	0.972104i	$0.424639\pi$
$822$		0			0
$823$	12.1118	+	12.1118i	0.422190	+	0.422190i	0.885957	−	0.463767i	$-0.153503\pi$
$823$	12.1118	+	12.1118i	0.422190	+	0.422190i	−0.463767	+	0.885957i	$0.653503\pi$
$824$	−36.7551	−	22.2214i	−1.28042	−	0.774120i
$825$		0			0
$826$	−0.972431	+	5.30595i	−0.0338352	+	0.184618i
$827$	−3.92415	+	3.92415i	−0.136456	+	0.136456i	−0.772035	−	0.635579i	$-0.780761\pi$
$827$	−3.92415	+	3.92415i	−0.136456	+	0.136456i	0.635579	+	0.772035i	$0.280761\pi$
$828$		0			0
$829$	−7.47321			−0.259555			−0.129778	−	0.991543i	$-0.541426\pi$
$829$	−7.47321			−0.259555			−0.129778	+	0.991543i	$0.541426\pi$
$830$	16.0265	+	16.4237i	0.556290	+	0.570075i
$831$		0			0
$832$	−2.10501	+	6.75313i	−0.0729781	+	0.234123i
$833$	−24.3521	+	24.3521i	−0.843749	+	0.843749i
$834$		0			0
$835$	13.3093	−	2.27123i	0.460587	−	0.0785992i
$836$	19.6895	−	51.9123i	0.680974	−	1.79542i
$837$		0			0
$838$	−9.69953	+	6.69489i	−0.335065	+	0.231271i
$839$	−19.0880			−0.658991			−0.329495	−	0.944157i	$-0.606879\pi$
$839$	−19.0880			−0.658991			−0.329495	+	0.944157i	$0.606879\pi$
$840$		0			0
$841$	−43.4073			−1.49680
$842$	−12.8708	+	8.88378i	−0.443556	+	0.306155i
$843$		0			0
$844$	−16.1247	−	6.11584i	−0.555036	−	0.210516i
$845$	−22.2931	−	15.7936i	−0.766906	−	0.543316i
$846$		0			0
$847$	−1.69976	+	1.69976i	−0.0584045	+	0.0584045i
$848$	−2.53165	−	41.8937i	−0.0869372	−	1.43864i
$849$		0			0
$850$	35.3106	−	5.58195i	1.21115	−	0.191459i
$851$	−5.37290			−0.184181
$852$		0			0
$853$	−0.0201924	+	0.0201924i	−0.000691373	+	0.000691373i	−0.707452	−	0.706761i	$-0.750156\pi$
$853$	−0.0201924	+	0.0201924i	−0.000691373	+	0.000691373i	0.706761	+	0.707452i	$0.250156\pi$
$854$	0.672654	−	3.67025i	0.0230177	−	0.125593i
$855$		0			0
$856$	−19.8615	+	32.8517i	−0.678852	+	1.12285i
$857$	−1.32849	−	1.32849i	−0.0453805	−	0.0453805i	0.684052	−	0.729433i	$-0.260216\pi$
$857$	−1.32849	−	1.32849i	−0.0453805	−	0.0453805i	−0.729433	+	0.684052i	$0.760216\pi$
$858$		0			0
$859$	10.8364			0.369735			0.184867	−	0.982764i	$-0.440814\pi$
$859$	10.8364			0.369735			0.184867	+	0.982764i	$0.440814\pi$
$860$	−25.9984	−	5.09440i	−0.886540	−	0.173718i
$861$		0			0
$862$	31.0015	−	21.3981i	1.05591	−	0.728822i
$863$	−8.57479	+	8.57479i	−0.291889	+	0.291889i	−0.837826	−	0.545937i	$-0.816174\pi$
$863$	−8.57479	+	8.57479i	−0.291889	+	0.291889i	0.545937	+	0.837826i	$0.316174\pi$
$864$		0			0
$865$	43.6934	−	7.45629i	1.48562	−	0.253521i
$866$	5.96527	−	32.5487i	0.202708	−	1.10605i
$867$		0			0
$868$	0.913811	+	2.03056i	0.0310168	+	0.0689218i
$869$			34.8205i			1.18120i
$870$		0			0
$871$	−7.72835			−0.261865
$872$	8.57162	−	2.11232i	0.290272	−	0.0715321i
$873$		0			0
$874$	−21.3407	−	3.91114i	−0.721859	−	0.132296i
$875$	−4.23847	+	2.35453i	−0.143286	+	0.0795975i
$876$		0			0
$877$	6.82619	+	6.82619i	0.230504	+	0.230504i	0.812903	−	0.582399i	$-0.197886\pi$
$877$	6.82619	+	6.82619i	0.230504	+	0.230504i	−0.582399	+	0.812903i	$0.697886\pi$
$878$	6.23147	−	4.30114i	0.210302	−	0.145156i
$879$		0			0
$880$	−35.4263	+	8.27163i	−1.19422	+	0.278837i
$881$			33.3297i			1.12290i	0.827509	+	0.561452i	$0.189757\pi$
$881$			33.3297i			1.12290i	−0.827509	+	0.561452i	$0.810243\pi$
$882$		0			0
$883$	−15.0182	+	15.0182i	−0.505403	+	0.505403i	−0.913112	−	0.407709i	$-0.866328\pi$
$883$	−15.0182	+	15.0182i	−0.505403	+	0.505403i	0.407709	+	0.913112i	$0.366328\pi$
$884$	3.17058	−	8.35941i	0.106638	−	0.281157i
$885$		0			0
$886$	0.985087	−	5.37501i	0.0330947	−	0.180577i
$887$	−37.6074	−	37.6074i	−1.26273	−	1.26273i	−0.949763	−	0.312971i	$-0.898676\pi$
$887$	−37.6074	−	37.6074i	−1.26273	−	1.26273i	−0.312971	−	0.949763i	$-0.601324\pi$
$888$		0			0
$889$		−	9.03853i		−	0.303143i
$890$	31.2513	+	0.382479i	1.04755	+	0.0128207i
$891$		0			0
$892$	−17.7298	+	7.97892i	−0.593638	+	0.267154i
$893$	31.2889	+	31.2889i	1.04704	+	1.04704i
$894$		0			0
$895$	−30.7669	−	21.7969i	−1.02842	−	0.728589i
$896$	−4.68438	+	1.45919i	−0.156494	+	0.0487480i
$897$		0			0
$898$	23.2397	+	33.6696i	0.775520	+	1.12357i
$899$		−	21.8458i		−	0.728598i
$900$		0			0
$901$			53.0470i			1.76725i
$902$	−24.5838	+	16.9684i	−0.818551	+	0.564987i
$903$		0			0
$904$	−12.1200	+	20.0469i	−0.403104	+	0.666749i
$905$	34.1276	+	24.1778i	1.13444	+	0.803696i
$906$		0			0
$907$	−29.6844	−	29.6844i	−0.985654	−	0.985654i	0.0142450	−	0.999899i	$-0.495466\pi$
$907$	−29.6844	−	29.6844i	−0.985654	−	0.985654i	−0.999899	+	0.0142450i	$0.995466\pi$
$908$	−10.6723	−	23.7147i	−0.354172	−	0.786999i
$909$		0			0
$910$	−0.0148393	+	1.21248i	−0.000491918	+	0.0401934i
$911$			9.37413i			0.310579i	0.987869	+	0.155289i	$0.0496310\pi$
$911$			9.37413i			0.310579i	−0.987869	+	0.155289i	$0.950369\pi$
$912$		0			0
$913$	20.8703	+	20.8703i	0.690705	+	0.690705i
$914$	20.7567	+	3.80412i	0.686570	+	0.125829i
$915$		0			0
$916$	−1.64207	+	4.32940i	−0.0542554	+	0.143047i
$917$	1.79969	−	1.79969i	0.0594309	−	0.0594309i
$918$		0			0
$919$			12.2408i			0.403788i	0.979407	+	0.201894i	$0.0647097\pi$
$919$			12.2408i			0.403788i	−0.979407	+	0.201894i	$0.935290\pi$
$920$	5.67498	+	13.0342i	0.187099	+	0.429725i
$921$		0			0
$922$	−9.61000	−	13.9229i	−0.316489	−	0.458527i
$923$	9.22303	+	9.22303i	0.303580	+	0.303580i
$924$		0			0
$925$	5.17009	−	10.7756i	0.169991	−	0.354300i
$926$	−2.90329	+	15.8415i	−0.0954081	+	0.520583i
$927$		0			0
$928$	47.7842	+	5.80558i	1.56859	+	0.190578i
$929$	3.79903			0.124642			0.0623210	−	0.998056i	$-0.480150\pi$
$929$	3.79903			0.124642			0.0623210	+	0.998056i	$0.480150\pi$
$930$		0			0
$931$			46.4931i			1.52375i
$932$	15.2496	+	33.8859i	0.499517	+	1.10997i
$933$		0			0
$934$	−27.2889	−	5.00129i	−0.892920	−	0.163647i
$935$	45.3252	−	7.73476i	1.48229	−	0.252954i
$936$		0			0
$937$	−6.03853	+	6.03853i	−0.197270	+	0.197270i	−0.798829	−	0.601559i	$-0.794547\pi$
$937$	−6.03853	+	6.03853i	−0.197270	+	0.197270i	0.601559	+	0.798829i	$0.294547\pi$
$938$	−3.04506	−	4.41167i	−0.0994248	−	0.144046i
$939$		0			0
$940$	5.57528	−	28.4525i	0.181845	−	0.928019i
$941$	−29.9232			−0.975469			−0.487735	−	0.872992i	$-0.662177\pi$
$941$	−29.9232			−0.975469			−0.487735	+	0.872992i	$0.662177\pi$
$942$		0			0
$943$	8.25400	+	8.25400i	0.268787	+	0.268787i
$944$	−23.3318	+	26.3330i	−0.759385	+	0.857067i
$945$		0			0
$946$	−33.5168	−	6.14269i	−1.08973	−	0.199716i
$947$	−24.1129	+	24.1129i	−0.783564	+	0.783564i	−0.980430	−	0.196867i	$-0.936923\pi$
$947$	−24.1129	+	24.1129i	−0.783564	+	0.783564i	0.196867	+	0.980430i	$0.436923\pi$
$948$		0			0
$949$	−3.82489			−0.124161
$950$	28.3791	−	39.0362i	0.920740	−	1.26650i
$951$		0			0
$952$	6.02116	−	1.48380i	0.195147	−	0.0480903i
$953$	−2.14110	+	2.14110i	−0.0693571	+	0.0693571i	−0.740934	−	0.671577i	$-0.765617\pi$
$953$	−2.14110	+	2.14110i	−0.0693571	+	0.0693571i	0.671577	+	0.740934i	$0.265617\pi$
$954$		0			0
$955$	11.9039	+	8.43336i	0.385202	+	0.272897i
$956$	−8.78955	+	23.1741i	−0.284274	+	0.749504i
$957$		0			0
$958$	4.02170	+	5.82662i	0.129935	+	0.188250i
$959$	−8.25389			−0.266532
$960$		0			0
$961$	−24.4090			−0.787386
$962$	−1.69791	−	2.45992i	−0.0547428	−	0.0793111i
$963$		0			0
$964$	−12.7761	+	33.6848i	−0.411490	+	1.08491i
$965$	−4.76674	+	0.813445i	−0.153447	+	0.0261857i
$966$		0			0
$967$	32.0860	−	32.0860i	1.03182	−	1.03182i	0.0323385	−	0.999477i	$-0.489705\pi$
$967$	32.0860	−	32.0860i	1.03182	−	1.03182i	0.999477	−	0.0323385i	$-0.0102954\pi$
$968$	−15.2226	+	3.75133i	−0.489274	+	0.120572i
$969$		0			0
$970$	−5.62128	+	5.48535i	−0.180488	+	0.176124i
$971$	−43.3908			−1.39248			−0.696239	−	0.717810i	$-0.745144\pi$
$971$	−43.3908			−1.39248			−0.696239	+	0.717810i	$0.745144\pi$
$972$		0			0
$973$	4.93676	−	4.93676i	0.158265	−	0.158265i
$974$	−15.4357	−	2.82892i	−0.494591	−	0.0906446i
$975$		0			0
$976$	16.1391	−	18.2152i	0.516601	−	0.583054i
$977$	−24.5104	−	24.5104i	−0.784156	−	0.784156i	0.196374	−	0.980529i	$-0.437083\pi$
$977$	−24.5104	−	24.5104i	−0.784156	−	0.784156i	−0.980529	+	0.196374i	$0.937083\pi$
$978$		0			0
$979$	40.1984			1.28475
$980$	25.2814	−	16.9970i	0.807586	−	0.542949i
$981$		0			0
$982$	−1.33007	−	1.92700i	−0.0424443	−	0.0614930i
$983$	20.3315	−	20.3315i	0.648473	−	0.648473i	−0.304151	−	0.952624i	$-0.598373\pi$
$983$	20.3315	−	20.3315i	0.648473	−	0.648473i	0.952624	+	0.304151i	$0.0983727\pi$
$984$		0			0
$985$	2.05061	+	12.0165i	0.0653380	+	0.382877i
$986$	−59.8429	−	10.9675i	−1.90579	−	0.349277i
$987$		0			0
$988$	−4.95327	−	11.0066i	−0.157584	−	0.350165i
$989$			13.3157i			0.423413i
$990$		0			0
$991$	3.08590			0.0980269			0.0490135	−	0.998798i	$-0.484392\pi$
$991$	3.08590			0.0980269			0.0490135	+	0.998798i	$0.484392\pi$
$992$	−1.75159	+	14.4168i	−0.0556129	+	0.457735i
$993$		0			0
$994$	−1.63092	+	8.89889i	−0.0517295	+	0.282256i
$995$	26.1079	+	18.4962i	0.827676	+	0.586369i
$996$		0			0
$997$	18.0364	+	18.0364i	0.571217	+	0.571217i	0.932468	−	0.361251i	$-0.117650\pi$
$997$	18.0364	+	18.0364i	0.571217	+	0.571217i	−0.361251	+	0.932468i	$0.617650\pi$
$998$	22.5311	+	32.6430i	0.713211	+	1.03330i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.x.a.53.18	yes	48
3.2	odd	2	inner	360.2.x.a.53.7	yes	48
4.3	odd	2		1440.2.bj.a.593.9		48
5.2	odd	4	inner	360.2.x.a.197.6	yes	48
8.3	odd	2		1440.2.bj.a.593.15		48
8.5	even	2	inner	360.2.x.a.53.19	yes	48
12.11	even	2		1440.2.bj.a.593.16		48
15.2	even	4	inner	360.2.x.a.197.19	yes	48
20.7	even	4		1440.2.bj.a.17.10		48
24.5	odd	2	inner	360.2.x.a.53.6	✓	48
24.11	even	2		1440.2.bj.a.593.10		48
40.27	even	4		1440.2.bj.a.17.16		48
40.37	odd	4	inner	360.2.x.a.197.7	yes	48
60.47	odd	4		1440.2.bj.a.17.15		48
120.77	even	4	inner	360.2.x.a.197.18	yes	48
120.107	odd	4		1440.2.bj.a.17.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.x.a.53.6	✓	48	24.5	odd	2	inner
360.2.x.a.53.7	yes	48	3.2	odd	2	inner
360.2.x.a.53.18	yes	48	1.1	even	1	trivial
360.2.x.a.53.19	yes	48	8.5	even	2	inner
360.2.x.a.197.6	yes	48	5.2	odd	4	inner
360.2.x.a.197.7	yes	48	40.37	odd	4	inner
360.2.x.a.197.18	yes	48	120.77	even	4	inner
360.2.x.a.197.19	yes	48	15.2	even	4	inner
1440.2.bj.a.17.9		48	120.107	odd	4
1440.2.bj.a.17.10		48	20.7	even	4
1440.2.bj.a.17.15		48	60.47	odd	4
1440.2.bj.a.17.16		48	40.27	even	4
1440.2.bj.a.593.9		48	4.3	odd	2
1440.2.bj.a.593.10		48	24.11	even	2
1440.2.bj.a.593.15		48	8.3	odd	2
1440.2.bj.a.593.16		48	12.11	even	2

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.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.803348 + 1.16389i) q^{2} +(-0.709264 + 1.87001i) q^{4} +(-1.29263 + 1.82458i) q^{5} +(-0.306649 + 0.306649i) q^{7} +(-2.74627 + 0.676767i) q^{8} +O(q^{10})\)	\(q+(0.803348 + 1.16389i) q^{2} +(-0.709264 + 1.87001i) q^{4} +(-1.29263 + 1.82458i) q^{5} +(-0.306649 + 0.306649i) q^{7} +(-2.74627 + 0.676767i) q^{8} +(-3.16204 - 0.0386996i) q^{10} -4.06731 q^{11} +(-0.625224 + 0.625224i) q^{13} +(-0.603251 - 0.110559i) q^{14} +(-2.99389 - 2.65267i) q^{16} +(3.57491 + 3.57491i) q^{17} +6.82524 q^{19} +(-2.49518 - 3.71135i) q^{20} +(-3.26747 - 4.73389i) q^{22} +(-1.58940 + 1.58940i) q^{23} +(-1.65821 - 4.71703i) q^{25} +(-1.22996 - 0.225418i) q^{26} +(-0.355942 - 0.790933i) q^{28} +8.50925i q^{29} -2.56730 q^{31} +(0.682268 - 5.61556i) q^{32} +(-1.28889 + 7.03269i) q^{34} +(-0.163123 - 0.955891i) q^{35} +(1.69023 + 1.69023i) q^{37} +(5.48305 + 7.94381i) q^{38} +(2.31509 - 5.88561i) q^{40} -5.19315i q^{41} +(4.18889 - 4.18889i) q^{43} +(2.88480 - 7.60592i) q^{44} +(-3.12673 - 0.573041i) q^{46} +(4.58429 + 4.58429i) q^{47} +6.81193i q^{49} +(4.15796 - 5.71938i) q^{50} +(-0.725727 - 1.61263i) q^{52} +(7.41934 + 7.41934i) q^{53} +(5.25753 - 7.42115i) q^{55} +(0.634611 - 1.04967i) q^{56} +(-9.90380 + 6.83589i) q^{58} -8.79560i q^{59} +6.08412i q^{61} +(-2.06244 - 2.98805i) q^{62} +(7.08397 - 3.71717i) q^{64} +(-0.332590 - 1.94896i) q^{65} +(6.18046 + 6.18046i) q^{67} +(-9.22069 + 4.14957i) q^{68} +(0.981504 - 0.957770i) q^{70} -14.7516i q^{71} +(3.05881 + 3.05881i) q^{73} +(-0.609393 + 3.32507i) q^{74} +(-4.84090 + 12.7633i) q^{76} +(1.24724 - 1.24724i) q^{77} -8.56106i q^{79} +(8.71000 - 2.03369i) q^{80} +(6.04424 - 4.17190i) q^{82} +(-5.13122 - 5.13122i) q^{83} +(-11.1438 + 1.90169i) q^{85} +(8.24053 + 1.51026i) q^{86} +(11.1699 - 2.75262i) q^{88} -9.88328 q^{89} -0.383449i q^{91} +(-1.84489 - 4.09951i) q^{92} +(-1.65282 + 9.01838i) q^{94} +(-8.82252 + 12.4532i) q^{95} +(1.75624 - 1.75624i) q^{97} +(-7.92832 + 5.47235i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Introduction

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