LMFDB - Embedded newform 360.2.w.a.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (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:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	360.307
Dual form			360.2.w.a.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -2.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(1.00000 - 1.00000i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+1.41421i q^{2} -2.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(1.00000 - 1.00000i) q^{7} -2.82843i q^{8} +(1.00000 - 3.00000i) q^{10} -4.24264 q^{11} +(-2.00000 - 2.00000i) q^{13} +(1.41421 + 1.41421i) q^{14} +4.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} -6.00000i q^{19} +(4.24264 + 1.41421i) q^{20} -6.00000i q^{22} +(1.41421 + 1.41421i) q^{23} +(4.00000 + 3.00000i) q^{25} +(2.82843 - 2.82843i) q^{26} +(-2.00000 + 2.00000i) q^{28} +4.24264 q^{29} -6.00000i q^{31} +5.65685i q^{32} +(4.00000 - 4.00000i) q^{34} +(-2.82843 + 1.41421i) q^{35} +(-8.00000 + 8.00000i) q^{37} +8.48528 q^{38} +(-2.00000 + 6.00000i) q^{40} -8.48528 q^{41} +(-2.00000 + 2.00000i) q^{43} +8.48528 q^{44} +(-2.00000 + 2.00000i) q^{46} +(-1.41421 + 1.41421i) q^{47} +5.00000i q^{49} +(-4.24264 + 5.65685i) q^{50} +(4.00000 + 4.00000i) q^{52} +(1.41421 + 1.41421i) q^{53} +(9.00000 + 3.00000i) q^{55} +(-2.82843 - 2.82843i) q^{56} +6.00000i q^{58} -9.89949i q^{59} +8.48528 q^{62} -8.00000 q^{64} +(2.82843 + 5.65685i) q^{65} +(-8.00000 - 8.00000i) q^{67} +(5.65685 + 5.65685i) q^{68} +(-2.00000 - 4.00000i) q^{70} -14.1421i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-11.3137 - 11.3137i) q^{74} +12.0000i q^{76} +(-4.24264 + 4.24264i) q^{77} +14.0000 q^{79} +(-8.48528 - 2.82843i) q^{80} -12.0000i q^{82} +(-1.41421 + 1.41421i) q^{83} +(4.00000 + 8.00000i) q^{85} +(-2.82843 - 2.82843i) q^{86} +12.0000i q^{88} +2.82843i q^{89} -4.00000 q^{91} +(-2.82843 - 2.82843i) q^{92} +(-2.00000 - 2.00000i) q^{94} +(-4.24264 + 12.7279i) q^{95} +(7.00000 + 7.00000i) q^{97} -7.07107 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} + 4 q^{7}+O(q^{10}) $ 4 * q - 8 * q^4 + 4 * q^7	$ 4 q - 8 q^{4} + 4 q^{7} + 4 q^{10} - 8 q^{13} + 16 q^{16} + 16 q^{25} - 8 q^{28} + 16 q^{34} - 32 q^{37} - 8 q^{40} - 8 q^{43} - 8 q^{46} + 16 q^{52} + 36 q^{55} - 32 q^{64} - 32 q^{67} - 8 q^{70} - 20 q^{73} + 56 q^{79} + 16 q^{85} - 16 q^{91} - 8 q^{94} + 28 q^{97}+O(q^{100}) $ 4 * q - 8 * q^4 + 4 * q^7 + 4 * q^10 - 8 * q^13 + 16 * q^16 + 16 * q^25 - 8 * q^28 + 16 * q^34 - 32 * q^37 - 8 * q^40 - 8 * q^43 - 8 * q^46 + 16 * q^52 + 36 * q^55 - 32 * q^64 - 32 * q^67 - 8 * q^70 - 20 * q^73 + 56 * q^79 + 16 * q^85 - 16 * q^91 - 8 * q^94 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			1.41421i			1.00000i
$2$			1.41421i			1.00000i
$3$		0			0
$3$		0			0
$4$	−2.00000			−1.00000
$5$	−2.12132	−	0.707107i	−0.948683	−	0.316228i
$5$	−2.12132	−	0.707107i	−0.948683	−	0.316228i
$6$		0			0
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	1.00000	−	3.00000i	0.316228	−	0.948683i
$11$	−4.24264			−1.27920			−0.639602	−	0.768706i	$-0.720901\pi$
$11$	−4.24264			−1.27920			−0.639602	+	0.768706i	$0.720901\pi$
$12$		0			0
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	0.373094	−	0.927794i	$-0.378297\pi$
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	−0.927794	+	0.373094i	$0.878297\pi$
$14$	1.41421	+	1.41421i	0.377964	+	0.377964i
$15$		0			0
$16$	4.00000			1.00000
$17$	−2.82843	−	2.82843i	−0.685994	−	0.685994i	0.275350	−	0.961344i	$-0.411206\pi$
$17$	−2.82843	−	2.82843i	−0.685994	−	0.685994i	−0.961344	+	0.275350i	$0.911206\pi$
$18$		0			0
$19$		−	6.00000i		−	1.37649i	−0.725476	−	0.688247i	$-0.758380\pi$
$19$		−	6.00000i		−	1.37649i	0.725476	−	0.688247i	$-0.241620\pi$
$20$	4.24264	+	1.41421i	0.948683	+	0.316228i
$21$		0			0
$22$		−	6.00000i		−	1.27920i
$23$	1.41421	+	1.41421i	0.294884	+	0.294884i	0.839006	−	0.544122i	$-0.183137\pi$
$23$	1.41421	+	1.41421i	0.294884	+	0.294884i	−0.544122	+	0.839006i	$0.683137\pi$
$24$		0			0
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$	2.82843	−	2.82843i	0.554700	−	0.554700i
$27$		0			0
$28$	−2.00000	+	2.00000i	−0.377964	+	0.377964i
$29$	4.24264			0.787839			0.393919	−	0.919145i	$-0.371119\pi$
$29$	4.24264			0.787839			0.393919	+	0.919145i	$0.371119\pi$
$30$		0			0
$31$		−	6.00000i		−	1.07763i	−0.842424	−	0.538816i	$-0.818872\pi$
$31$		−	6.00000i		−	1.07763i	0.842424	−	0.538816i	$-0.181128\pi$
$32$			5.65685i			1.00000i
$33$		0			0
$34$	4.00000	−	4.00000i	0.685994	−	0.685994i
$35$	−2.82843	+	1.41421i	−0.478091	+	0.239046i
$36$		0			0
$37$	−8.00000	+	8.00000i	−1.31519	+	1.31519i	−0.397658	+	0.917534i	$0.630177\pi$
$37$	−8.00000	+	8.00000i	−1.31519	+	1.31519i	−0.917534	+	0.397658i	$0.869823\pi$
$38$	8.48528			1.37649
$39$		0			0
$40$	−2.00000	+	6.00000i	−0.316228	+	0.948683i
$41$	−8.48528			−1.32518			−0.662589	−	0.748983i	$-0.730542\pi$
$41$	−8.48528			−1.32518			−0.662589	+	0.748983i	$0.730542\pi$
$42$		0			0
$43$	−2.00000	+	2.00000i	−0.304997	+	0.304997i	−0.842965	−	0.537968i	$-0.819192\pi$
$43$	−2.00000	+	2.00000i	−0.304997	+	0.304997i	0.537968	+	0.842965i	$0.319192\pi$
$44$	8.48528			1.27920
$45$		0			0
$46$	−2.00000	+	2.00000i	−0.294884	+	0.294884i
$47$	−1.41421	+	1.41421i	−0.206284	+	0.206284i	−0.802686	−	0.596402i	$-0.796597\pi$
$47$	−1.41421	+	1.41421i	−0.206284	+	0.206284i	0.596402	+	0.802686i	$0.296597\pi$
$48$		0			0
$49$			5.00000i			0.714286i
$50$	−4.24264	+	5.65685i	−0.600000	+	0.800000i
$51$		0			0
$52$	4.00000	+	4.00000i	0.554700	+	0.554700i
$53$	1.41421	+	1.41421i	0.194257	+	0.194257i	0.797533	−	0.603276i	$-0.206138\pi$
$53$	1.41421	+	1.41421i	0.194257	+	0.194257i	−0.603276	+	0.797533i	$0.706138\pi$
$54$		0			0
$55$	9.00000	+	3.00000i	1.21356	+	0.404520i
$56$	−2.82843	−	2.82843i	−0.377964	−	0.377964i
$57$		0			0
$58$			6.00000i			0.787839i
$59$		−	9.89949i		−	1.28880i	−0.764687	−	0.644402i	$-0.777106\pi$
$59$		−	9.89949i		−	1.28880i	0.764687	−	0.644402i	$-0.222894\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	8.48528			1.07763
$63$		0			0
$64$	−8.00000			−1.00000
$65$	2.82843	+	5.65685i	0.350823	+	0.701646i
$66$		0			0
$67$	−8.00000	−	8.00000i	−0.977356	−	0.977356i	0.0223937	−	0.999749i	$-0.492871\pi$
$67$	−8.00000	−	8.00000i	−0.977356	−	0.977356i	−0.999749	+	0.0223937i	$0.992871\pi$
$68$	5.65685	+	5.65685i	0.685994	+	0.685994i
$69$		0			0
$70$	−2.00000	−	4.00000i	−0.239046	−	0.478091i
$71$		−	14.1421i		−	1.67836i	−0.543852	−	0.839181i	$-0.683035\pi$
$71$		−	14.1421i		−	1.67836i	0.543852	−	0.839181i	$-0.316965\pi$
$72$		0			0
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	0.351123	+	0.936329i	$0.385800\pi$
$74$	−11.3137	−	11.3137i	−1.31519	−	1.31519i
$75$		0			0
$76$			12.0000i			1.37649i
$77$	−4.24264	+	4.24264i	−0.483494	+	0.483494i
$78$		0			0
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	−8.48528	−	2.82843i	−0.948683	−	0.316228i
$81$		0			0
$82$		−	12.0000i		−	1.32518i
$83$	−1.41421	+	1.41421i	−0.155230	+	0.155230i	−0.780449	−	0.625219i	$-0.785010\pi$
$83$	−1.41421	+	1.41421i	−0.155230	+	0.155230i	0.625219	+	0.780449i	$0.285010\pi$
$84$		0			0
$85$	4.00000	+	8.00000i	0.433861	+	0.867722i
$86$	−2.82843	−	2.82843i	−0.304997	−	0.304997i
$87$		0			0
$88$			12.0000i			1.27920i
$89$			2.82843i			0.299813i	0.988700	+	0.149906i	$0.0478972\pi$
$89$			2.82843i			0.299813i	−0.988700	+	0.149906i	$0.952103\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$	−2.82843	−	2.82843i	−0.294884	−	0.294884i
$93$		0			0
$94$	−2.00000	−	2.00000i	−0.206284	−	0.206284i
$95$	−4.24264	+	12.7279i	−0.435286	+	1.30586i
$96$		0			0
$97$	7.00000	+	7.00000i	0.710742	+	0.710742i	0.966691	−	0.255948i	$-0.0823876\pi$
$97$	7.00000	+	7.00000i	0.710742	+	0.710742i	−0.255948	+	0.966691i	$0.582388\pi$
$98$	−7.07107			−0.714286
$99$		0			0
$100$	−8.00000	−	6.00000i	−0.800000	−	0.600000i
$101$		−	1.41421i		−	0.140720i	−0.997522	−	0.0703598i	$-0.977585\pi$
$101$		−	1.41421i		−	0.140720i	0.997522	−	0.0703598i	$-0.0224147\pi$
$102$		0			0
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$104$	−5.65685	+	5.65685i	−0.554700	+	0.554700i
$105$		0			0
$106$	−2.00000	+	2.00000i	−0.194257	+	0.194257i
$107$	9.89949	+	9.89949i	0.957020	+	0.957020i	0.999114	−	0.0420934i	$-0.0134027\pi$
$107$	9.89949	+	9.89949i	0.957020	+	0.957020i	−0.0420934	+	0.999114i	$0.513403\pi$
$108$		0			0
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	−4.24264	+	12.7279i	−0.404520	+	1.21356i
$111$		0			0
$112$	4.00000	−	4.00000i	0.377964	−	0.377964i
$113$	11.3137	−	11.3137i	1.06430	−	1.06430i	0.0665190	−	0.997785i	$-0.478811\pi$
$113$	11.3137	−	11.3137i	1.06430	−	1.06430i	0.997785	−	0.0665190i	$-0.0211893\pi$
$114$		0			0
$115$	−2.00000	−	4.00000i	−0.186501	−	0.373002i
$116$	−8.48528			−0.787839
$117$		0			0
$118$	14.0000			1.28880
$119$	−5.65685			−0.518563
$120$		0			0
$121$	7.00000			0.636364
$122$		0			0
$123$		0			0
$124$			12.0000i			1.07763i
$125$	−6.36396	−	9.19239i	−0.569210	−	0.822192i
$126$		0			0
$127$	−11.0000	+	11.0000i	−0.976092	+	0.976092i	−0.999721	−	0.0236286i	$-0.992478\pi$
$127$	−11.0000	+	11.0000i	−0.976092	+	0.976092i	0.0236286	+	0.999721i	$0.492478\pi$
$128$		−	11.3137i		−	1.00000i
$129$		0			0
$130$	−8.00000	+	4.00000i	−0.701646	+	0.350823i
$131$	12.7279			1.11204			0.556022	−	0.831168i	$-0.312327\pi$
$131$	12.7279			1.11204			0.556022	+	0.831168i	$0.312327\pi$
$132$		0			0
$133$	−6.00000	−	6.00000i	−0.520266	−	0.520266i
$134$	11.3137	−	11.3137i	0.977356	−	0.977356i
$135$		0			0
$136$	−8.00000	+	8.00000i	−0.685994	+	0.685994i
$137$	5.65685	+	5.65685i	0.483298	+	0.483298i	0.906183	−	0.422885i	$-0.138983\pi$
$137$	5.65685	+	5.65685i	0.483298	+	0.483298i	−0.422885	+	0.906183i	$0.638983\pi$
$138$		0			0
$139$			6.00000i			0.508913i	0.967084	+	0.254457i	$0.0818966\pi$
$139$			6.00000i			0.508913i	−0.967084	+	0.254457i	$0.918103\pi$
$140$	5.65685	−	2.82843i	0.478091	−	0.239046i
$141$		0			0
$142$	20.0000			1.67836
$143$	8.48528	+	8.48528i	0.709575	+	0.709575i
$144$		0			0
$145$	−9.00000	−	3.00000i	−0.747409	−	0.249136i
$146$	−7.07107	−	7.07107i	−0.585206	−	0.585206i
$147$		0			0
$148$	16.0000	−	16.0000i	1.31519	−	1.31519i
$149$	12.7279			1.04271			0.521356	−	0.853339i	$-0.325426\pi$
$149$	12.7279			1.04271			0.521356	+	0.853339i	$0.325426\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	−16.9706			−1.37649
$153$		0			0
$154$	−6.00000	−	6.00000i	−0.483494	−	0.483494i
$155$	−4.24264	+	12.7279i	−0.340777	+	1.02233i
$156$		0			0
$157$	−8.00000	+	8.00000i	−0.638470	+	0.638470i	−0.950178	−	0.311708i	$-0.899099\pi$
$157$	−8.00000	+	8.00000i	−0.638470	+	0.638470i	0.311708	+	0.950178i	$0.399099\pi$
$158$			19.7990i			1.57512i
$159$		0			0
$160$	4.00000	−	12.0000i	0.316228	−	0.948683i
$161$	2.82843			0.222911
$162$		0			0
$163$	10.0000	−	10.0000i	0.783260	−	0.783260i	−0.197119	−	0.980380i	$-0.563159\pi$
$163$	10.0000	−	10.0000i	0.783260	−	0.783260i	0.980380	+	0.197119i	$0.0631586\pi$
$164$	16.9706			1.32518
$165$		0			0
$166$	−2.00000	−	2.00000i	−0.155230	−	0.155230i
$167$	15.5563	−	15.5563i	1.20379	−	1.20379i	0.230781	−	0.973006i	$-0.425872\pi$
$167$	15.5563	−	15.5563i	1.20379	−	1.20379i	0.973006	−	0.230781i	$-0.0741280\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	−11.3137	+	5.65685i	−0.867722	+	0.433861i
$171$		0			0
$172$	4.00000	−	4.00000i	0.304997	−	0.304997i
$173$	−2.82843	−	2.82843i	−0.215041	−	0.215041i	0.591364	−	0.806405i	$-0.298590\pi$
$173$	−2.82843	−	2.82843i	−0.215041	−	0.215041i	−0.806405	+	0.591364i	$0.798590\pi$
$174$		0			0
$175$	7.00000	−	1.00000i	0.529150	−	0.0755929i
$176$	−16.9706			−1.27920
$177$		0			0
$178$	−4.00000			−0.299813
$179$		−	9.89949i		−	0.739923i	−0.929047	−	0.369961i	$-0.879371\pi$
$179$		−	9.89949i		−	0.739923i	0.929047	−	0.369961i	$-0.120629\pi$
$180$		0			0
$181$		−	24.0000i		−	1.78391i	−0.452128	−	0.891953i	$-0.649335\pi$
$181$		−	24.0000i		−	1.78391i	0.452128	−	0.891953i	$-0.350665\pi$
$182$		−	5.65685i		−	0.419314i
$183$		0			0
$184$	4.00000	−	4.00000i	0.294884	−	0.294884i
$185$	22.6274	−	11.3137i	1.66360	−	0.831800i
$186$		0			0
$187$	12.0000	+	12.0000i	0.877527	+	0.877527i
$188$	2.82843	−	2.82843i	0.206284	−	0.206284i
$189$		0			0
$190$	−18.0000	−	6.00000i	−1.30586	−	0.435286i
$191$			11.3137i			0.818631i	0.912393	+	0.409316i	$0.134232\pi$
$191$			11.3137i			0.818631i	−0.912393	+	0.409316i	$0.865768\pi$
$192$		0			0
$193$	13.0000	−	13.0000i	0.935760	−	0.935760i	−0.0622972	−	0.998058i	$-0.519843\pi$
$193$	13.0000	−	13.0000i	0.935760	−	0.935760i	0.998058	+	0.0622972i	$0.0198427\pi$
$194$	−9.89949	+	9.89949i	−0.710742	+	0.710742i
$195$		0			0
$196$		−	10.0000i		−	0.714286i
$197$	−9.89949	+	9.89949i	−0.705310	+	0.705310i	−0.965545	−	0.260235i	$-0.916200\pi$
$197$	−9.89949	+	9.89949i	−0.705310	+	0.705310i	0.260235	+	0.965545i	$0.416200\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	8.48528	−	11.3137i	0.600000	−	0.800000i
$201$		0			0
$202$	2.00000			0.140720
$203$	4.24264	−	4.24264i	0.297775	−	0.297775i
$204$		0			0
$205$	18.0000	+	6.00000i	1.25717	+	0.419058i
$206$	7.07107	−	7.07107i	0.492665	−	0.492665i
$207$		0			0
$208$	−8.00000	−	8.00000i	−0.554700	−	0.554700i
$209$			25.4558i			1.76082i
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	−2.82843	−	2.82843i	−0.194257	−	0.194257i
$213$		0			0
$214$	−14.0000	+	14.0000i	−0.957020	+	0.957020i
$215$	5.65685	−	2.82843i	0.385794	−	0.192897i
$216$		0			0
$217$	−6.00000	−	6.00000i	−0.407307	−	0.407307i
$218$		−	5.65685i		−	0.383131i
$219$		0			0
$220$	−18.0000	−	6.00000i	−1.21356	−	0.404520i
$221$			11.3137i			0.761042i
$222$		0			0
$223$	−11.0000	−	11.0000i	−0.736614	−	0.736614i	0.235307	−	0.971921i	$-0.424391\pi$
$223$	−11.0000	−	11.0000i	−0.736614	−	0.736614i	−0.971921	+	0.235307i	$0.924391\pi$
$224$	5.65685	+	5.65685i	0.377964	+	0.377964i
$225$		0			0
$226$	16.0000	+	16.0000i	1.06430	+	1.06430i
$227$	5.65685	+	5.65685i	0.375459	+	0.375459i	0.869461	−	0.494002i	$-0.164466\pi$
$227$	5.65685	+	5.65685i	0.375459	+	0.375459i	−0.494002	+	0.869461i	$0.664466\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	5.65685	−	2.82843i	0.373002	−	0.186501i
$231$		0			0
$232$		−	12.0000i		−	0.787839i
$233$	−5.65685	+	5.65685i	−0.370593	+	0.370593i	−0.867693	−	0.497100i	$-0.834398\pi$
$233$	−5.65685	+	5.65685i	−0.370593	+	0.370593i	0.497100	+	0.867693i	$0.334398\pi$
$234$		0			0
$235$	4.00000	−	2.00000i	0.260931	−	0.130466i
$236$			19.7990i			1.28880i
$237$		0			0
$238$		−	8.00000i		−	0.518563i
$239$	−25.4558			−1.64660			−0.823301	−	0.567605i	$-0.807870\pi$
$239$	−25.4558			−1.64660			−0.823301	+	0.567605i	$0.807870\pi$
$240$		0			0
$241$	−16.0000			−1.03065			−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000			−1.03065			−0.515325	+	0.856995i	$0.672329\pi$
$242$			9.89949i			0.636364i
$243$		0			0
$244$		0			0
$245$	3.53553	−	10.6066i	0.225877	−	0.677631i
$246$		0			0
$247$	−12.0000	+	12.0000i	−0.763542	+	0.763542i
$248$	−16.9706			−1.07763
$249$		0			0
$250$	13.0000	−	9.00000i	0.822192	−	0.569210i
$251$	12.7279			0.803379			0.401690	−	0.915776i	$-0.368423\pi$
$251$	12.7279			0.803379			0.401690	+	0.915776i	$0.368423\pi$
$252$		0			0
$253$	−6.00000	−	6.00000i	−0.377217	−	0.377217i
$254$	−15.5563	−	15.5563i	−0.976092	−	0.976092i
$255$		0			0
$256$	16.0000			1.00000
$257$	−19.7990	−	19.7990i	−1.23503	−	1.23503i	−0.962009	−	0.273018i	$-0.911978\pi$
$257$	−19.7990	−	19.7990i	−1.23503	−	1.23503i	−0.273018	−	0.962009i	$-0.588022\pi$
$258$		0			0
$259$			16.0000i			0.994192i
$260$	−5.65685	−	11.3137i	−0.350823	−	0.701646i
$261$		0			0
$262$			18.0000i			1.11204i
$263$	−7.07107	−	7.07107i	−0.436021	−	0.436021i	0.454650	−	0.890670i	$-0.349764\pi$
$263$	−7.07107	−	7.07107i	−0.436021	−	0.436021i	−0.890670	+	0.454650i	$0.849764\pi$
$264$		0			0
$265$	−2.00000	−	4.00000i	−0.122859	−	0.245718i
$266$	8.48528	−	8.48528i	0.520266	−	0.520266i
$267$		0			0
$268$	16.0000	+	16.0000i	0.977356	+	0.977356i
$269$	21.2132			1.29339			0.646696	−	0.762748i	$-0.276150\pi$
$269$	21.2132			1.29339			0.646696	+	0.762748i	$0.276150\pi$
$270$		0			0
$271$			12.0000i			0.728948i	0.931214	+	0.364474i	$0.118751\pi$
$271$			12.0000i			0.728948i	−0.931214	+	0.364474i	$0.881249\pi$
$272$	−11.3137	−	11.3137i	−0.685994	−	0.685994i
$273$		0			0
$274$	−8.00000	+	8.00000i	−0.483298	+	0.483298i
$275$	−16.9706	−	12.7279i	−1.02336	−	0.767523i
$276$		0			0
$277$	4.00000	−	4.00000i	0.240337	−	0.240337i	−0.576653	−	0.816989i	$-0.695641\pi$
$277$	4.00000	−	4.00000i	0.240337	−	0.240337i	0.816989	+	0.576653i	$0.195641\pi$
$278$	−8.48528			−0.508913
$279$		0			0
$280$	4.00000	+	8.00000i	0.239046	+	0.478091i
$281$	−16.9706			−1.01238			−0.506189	−	0.862422i	$-0.668946\pi$
$281$	−16.9706			−1.01238			−0.506189	+	0.862422i	$0.668946\pi$
$282$		0			0
$283$	−8.00000	+	8.00000i	−0.475551	+	0.475551i	−0.903705	−	0.428155i	$-0.859164\pi$
$283$	−8.00000	+	8.00000i	−0.475551	+	0.475551i	0.428155	+	0.903705i	$0.359164\pi$
$284$			28.2843i			1.67836i
$285$		0			0
$286$	−12.0000	+	12.0000i	−0.709575	+	0.709575i
$287$	−8.48528	+	8.48528i	−0.500870	+	0.500870i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	4.24264	−	12.7279i	0.249136	−	0.747409i
$291$		0			0
$292$	10.0000	−	10.0000i	0.585206	−	0.585206i
$293$	−15.5563	−	15.5563i	−0.908812	−	0.908812i	0.0873648	−	0.996176i	$-0.472155\pi$
$293$	−15.5563	−	15.5563i	−0.908812	−	0.908812i	−0.996176	+	0.0873648i	$0.972155\pi$
$294$		0			0
$295$	−7.00000	+	21.0000i	−0.407556	+	1.22267i
$296$	22.6274	+	22.6274i	1.31519	+	1.31519i
$297$		0			0
$298$			18.0000i			1.04271i
$299$		−	5.65685i		−	0.327144i
$300$		0			0
$301$			4.00000i			0.230556i
$302$	16.9706			0.976546
$303$		0			0
$304$		−	24.0000i		−	1.37649i
$305$		0			0
$306$		0			0
$307$	10.0000	+	10.0000i	0.570730	+	0.570730i	0.932332	−	0.361602i	$-0.117770\pi$
$307$	10.0000	+	10.0000i	0.570730	+	0.570730i	−0.361602	+	0.932332i	$0.617770\pi$
$308$	8.48528	−	8.48528i	0.483494	−	0.483494i
$309$		0			0
$310$	−18.0000	−	6.00000i	−1.02233	−	0.340777i
$311$		−	31.1127i		−	1.76424i	−0.471025	−	0.882120i	$-0.656116\pi$
$311$		−	31.1127i		−	1.76424i	0.471025	−	0.882120i	$-0.343884\pi$
$312$		0			0
$313$	1.00000	−	1.00000i	0.0565233	−	0.0565233i	−0.678280	−	0.734803i	$-0.737274\pi$
$313$	1.00000	−	1.00000i	0.0565233	−	0.0565233i	0.734803	+	0.678280i	$0.237274\pi$
$314$	−11.3137	−	11.3137i	−0.638470	−	0.638470i
$315$		0			0
$316$	−28.0000			−1.57512
$317$	−5.65685	+	5.65685i	−0.317721	+	0.317721i	−0.847891	−	0.530170i	$-0.822128\pi$
$317$	−5.65685	+	5.65685i	−0.317721	+	0.317721i	0.530170	+	0.847891i	$0.322128\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$	16.9706	+	5.65685i	0.948683	+	0.316228i
$321$		0			0
$322$			4.00000i			0.222911i
$323$	−16.9706	+	16.9706i	−0.944267	+	0.944267i
$324$		0			0
$325$	−2.00000	−	14.0000i	−0.110940	−	0.776580i
$326$	14.1421	+	14.1421i	0.783260	+	0.783260i
$327$		0			0
$328$			24.0000i			1.32518i
$329$			2.82843i			0.155936i
$330$		0			0
$331$	2.00000			0.109930			0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000			0.109930			0.0549650	+	0.998488i	$0.482495\pi$
$332$	2.82843	−	2.82843i	0.155230	−	0.155230i
$333$		0			0
$334$	22.0000	+	22.0000i	1.20379	+	1.20379i
$335$	11.3137	+	22.6274i	0.618134	+	1.23627i
$336$		0			0
$337$	−17.0000	−	17.0000i	−0.926049	−	0.926049i	0.0713988	−	0.997448i	$-0.477254\pi$
$337$	−17.0000	−	17.0000i	−0.926049	−	0.926049i	−0.997448	+	0.0713988i	$0.977254\pi$
$338$	7.07107			0.384615
$339$		0			0
$340$	−8.00000	−	16.0000i	−0.433861	−	0.867722i
$341$			25.4558i			1.37851i
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	5.65685	+	5.65685i	0.304997	+	0.304997i
$345$		0			0
$346$	4.00000	−	4.00000i	0.215041	−	0.215041i
$347$	−11.3137	−	11.3137i	−0.607352	−	0.607352i	0.334901	−	0.942253i	$-0.391297\pi$
$347$	−11.3137	−	11.3137i	−0.607352	−	0.607352i	−0.942253	+	0.334901i	$0.891297\pi$
$348$		0			0
$349$	20.0000			1.07058			0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000			1.07058			0.535288	+	0.844670i	$0.320203\pi$
$350$	1.41421	+	9.89949i	0.0755929	+	0.529150i
$351$		0			0
$352$		−	24.0000i		−	1.27920i
$353$	−5.65685	+	5.65685i	−0.301084	+	0.301084i	−0.841438	−	0.540354i	$-0.818290\pi$
$353$	−5.65685	+	5.65685i	−0.301084	+	0.301084i	0.540354	+	0.841438i	$0.318290\pi$
$354$		0			0
$355$	−10.0000	+	30.0000i	−0.530745	+	1.59223i
$356$		−	5.65685i		−	0.299813i
$357$		0			0
$358$	14.0000			0.739923
$359$	−8.48528			−0.447836			−0.223918	−	0.974608i	$-0.571885\pi$
$359$	−8.48528			−0.447836			−0.223918	+	0.974608i	$0.571885\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$	33.9411			1.78391
$363$		0			0
$364$	8.00000			0.419314
$365$	14.1421	−	7.07107i	0.740233	−	0.370117i
$366$		0			0
$367$	−5.00000	+	5.00000i	−0.260998	+	0.260998i	−0.825459	−	0.564462i	$-0.809084\pi$
$367$	−5.00000	+	5.00000i	−0.260998	+	0.260998i	0.564462	+	0.825459i	$0.309084\pi$
$368$	5.65685	+	5.65685i	0.294884	+	0.294884i
$369$		0			0
$370$	16.0000	+	32.0000i	0.831800	+	1.66360i
$371$	2.82843			0.146845
$372$		0			0
$373$	16.0000	+	16.0000i	0.828449	+	0.828449i	0.987302	−	0.158854i	$-0.0507798\pi$
$373$	16.0000	+	16.0000i	0.828449	+	0.828449i	−0.158854	+	0.987302i	$0.550780\pi$
$374$	−16.9706	+	16.9706i	−0.877527	+	0.877527i
$375$		0			0
$376$	4.00000	+	4.00000i	0.206284	+	0.206284i
$377$	−8.48528	−	8.48528i	−0.437014	−	0.437014i
$378$		0			0
$379$		−	18.0000i		−	0.924598i	−0.886724	−	0.462299i	$-0.847025\pi$
$379$		−	18.0000i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$380$	8.48528	−	25.4558i	0.435286	−	1.30586i
$381$		0			0
$382$	−16.0000			−0.818631
$383$	18.3848	+	18.3848i	0.939418	+	0.939418i	0.998267	−	0.0588487i	$-0.0187430\pi$
$383$	18.3848	+	18.3848i	0.939418	+	0.939418i	−0.0588487	+	0.998267i	$0.518743\pi$
$384$		0			0
$385$	12.0000	−	6.00000i	0.611577	−	0.305788i
$386$	18.3848	+	18.3848i	0.935760	+	0.935760i
$387$		0			0
$388$	−14.0000	−	14.0000i	−0.710742	−	0.710742i
$389$	−4.24264			−0.215110			−0.107555	−	0.994199i	$-0.534302\pi$
$389$	−4.24264			−0.215110			−0.107555	+	0.994199i	$0.534302\pi$
$390$		0			0
$391$		−	8.00000i		−	0.404577i
$392$	14.1421			0.714286
$393$		0			0
$394$	−14.0000	−	14.0000i	−0.705310	−	0.705310i
$395$	−29.6985	−	9.89949i	−1.49429	−	0.498098i
$396$		0			0
$397$	10.0000	−	10.0000i	0.501886	−	0.501886i	−0.410138	−	0.912024i	$-0.634519\pi$
$397$	10.0000	−	10.0000i	0.501886	−	0.501886i	0.912024	+	0.410138i	$0.134519\pi$
$398$		−	5.65685i		−	0.283552i
$399$		0			0
$400$	16.0000	+	12.0000i	0.800000	+	0.600000i
$401$	−8.48528			−0.423735			−0.211867	−	0.977298i	$-0.567954\pi$
$401$	−8.48528			−0.423735			−0.211867	+	0.977298i	$0.567954\pi$
$402$		0			0
$403$	−12.0000	+	12.0000i	−0.597763	+	0.597763i
$404$			2.82843i			0.140720i
$405$		0			0
$406$	6.00000	+	6.00000i	0.297775	+	0.297775i
$407$	33.9411	−	33.9411i	1.68240	−	1.68240i
$408$		0			0
$409$		−	12.0000i		−	0.593362i	−0.954977	−	0.296681i	$-0.904120\pi$
$409$		−	12.0000i		−	0.593362i	0.954977	−	0.296681i	$-0.0958798\pi$
$410$	−8.48528	+	25.4558i	−0.419058	+	1.25717i
$411$		0			0
$412$	10.0000	+	10.0000i	0.492665	+	0.492665i
$413$	−9.89949	−	9.89949i	−0.487122	−	0.487122i
$414$		0			0
$415$	4.00000	−	2.00000i	0.196352	−	0.0981761i
$416$	11.3137	−	11.3137i	0.554700	−	0.554700i
$417$		0			0
$418$	−36.0000			−1.76082
$419$		−	9.89949i		−	0.483622i	−0.970323	−	0.241811i	$-0.922259\pi$
$419$		−	9.89949i		−	0.483622i	0.970323	−	0.241811i	$-0.0777414\pi$
$420$		0			0
$421$			12.0000i			0.584844i	0.956289	+	0.292422i	$0.0944612\pi$
$421$			12.0000i			0.584844i	−0.956289	+	0.292422i	$0.905539\pi$
$422$			2.82843i			0.137686i
$423$		0			0
$424$	4.00000	−	4.00000i	0.194257	−	0.194257i
$425$	−2.82843	−	19.7990i	−0.137199	−	0.960392i
$426$		0			0
$427$		0			0
$428$	−19.7990	−	19.7990i	−0.957020	−	0.957020i
$429$		0			0
$430$	4.00000	+	8.00000i	0.192897	+	0.385794i
$431$			36.7696i			1.77113i	0.464518	+	0.885564i	$0.346227\pi$
$431$			36.7696i			1.77113i	−0.464518	+	0.885564i	$0.653773\pi$
$432$		0			0
$433$	−23.0000	+	23.0000i	−1.10531	+	1.10531i	−0.111551	+	0.993759i	$0.535582\pi$
$433$	−23.0000	+	23.0000i	−1.10531	+	1.10531i	−0.993759	+	0.111551i	$0.964418\pi$
$434$	8.48528	−	8.48528i	0.407307	−	0.407307i
$435$		0			0
$436$	8.00000			0.383131
$437$	8.48528	−	8.48528i	0.405906	−	0.405906i
$438$		0			0
$439$	−4.00000			−0.190910			−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000			−0.190910			−0.0954548	+	0.995434i	$0.530431\pi$
$440$	8.48528	−	25.4558i	0.404520	−	1.21356i
$441$		0			0
$442$	−16.0000			−0.761042
$443$	−22.6274	+	22.6274i	−1.07506	+	1.07506i	−0.0781168	+	0.996944i	$0.524891\pi$
$443$	−22.6274	+	22.6274i	−1.07506	+	1.07506i	−0.996944	+	0.0781168i	$0.975109\pi$
$444$		0			0
$445$	2.00000	−	6.00000i	0.0948091	−	0.284427i
$446$	15.5563	−	15.5563i	0.736614	−	0.736614i
$447$		0			0
$448$	−8.00000	+	8.00000i	−0.377964	+	0.377964i
$449$			11.3137i			0.533927i	0.963707	+	0.266963i	$0.0860203\pi$
$449$			11.3137i			0.533927i	−0.963707	+	0.266963i	$0.913980\pi$
$450$		0			0
$451$	36.0000			1.69517
$452$	−22.6274	+	22.6274i	−1.06430	+	1.06430i
$453$		0			0
$454$	−8.00000	+	8.00000i	−0.375459	+	0.375459i
$455$	8.48528	+	2.82843i	0.397796	+	0.132599i
$456$		0			0
$457$	1.00000	+	1.00000i	0.0467780	+	0.0467780i	0.730109	−	0.683331i	$-0.239469\pi$
$457$	1.00000	+	1.00000i	0.0467780	+	0.0467780i	−0.683331	+	0.730109i	$0.739469\pi$
$458$			28.2843i			1.32164i
$459$		0			0
$460$	4.00000	+	8.00000i	0.186501	+	0.373002i
$461$			7.07107i			0.329332i	0.986349	+	0.164666i	$0.0526547\pi$
$461$			7.07107i			0.329332i	−0.986349	+	0.164666i	$0.947345\pi$
$462$		0			0
$463$	−5.00000	−	5.00000i	−0.232370	−	0.232370i	0.581311	−	0.813681i	$-0.302540\pi$
$463$	−5.00000	−	5.00000i	−0.232370	−	0.232370i	−0.813681	+	0.581311i	$0.802540\pi$
$464$	16.9706			0.787839
$465$		0			0
$466$	−8.00000	−	8.00000i	−0.370593	−	0.370593i
$467$	9.89949	+	9.89949i	0.458094	+	0.458094i	0.898029	−	0.439935i	$-0.144999\pi$
$467$	9.89949	+	9.89949i	0.458094	+	0.458094i	−0.439935	+	0.898029i	$0.644999\pi$
$468$		0			0
$469$	−16.0000			−0.738811
$470$	2.82843	+	5.65685i	0.130466	+	0.260931i
$471$		0			0
$472$	−28.0000			−1.28880
$473$	8.48528	−	8.48528i	0.390154	−	0.390154i
$474$		0			0
$475$	18.0000	−	24.0000i	0.825897	−	1.10120i
$476$	11.3137			0.518563
$477$		0			0
$478$		−	36.0000i		−	1.64660i
$479$	−25.4558			−1.16311			−0.581554	−	0.813508i	$-0.697555\pi$
$479$	−25.4558			−1.16311			−0.581554	+	0.813508i	$0.697555\pi$
$480$		0			0
$481$	32.0000			1.45907
$482$		−	22.6274i		−	1.03065i
$483$		0			0
$484$	−14.0000			−0.636364
$485$	−9.89949	−	19.7990i	−0.449513	−	0.899026i
$486$		0			0
$487$	7.00000	−	7.00000i	0.317200	−	0.317200i	−0.530491	−	0.847691i	$-0.677992\pi$
$487$	7.00000	−	7.00000i	0.317200	−	0.317200i	0.847691	+	0.530491i	$0.177992\pi$
$488$		0			0
$489$		0			0
$490$	15.0000	+	5.00000i	0.677631	+	0.225877i
$491$	12.7279			0.574403			0.287202	−	0.957870i	$-0.407275\pi$
$491$	12.7279			0.574403			0.287202	+	0.957870i	$0.407275\pi$
$492$		0			0
$493$	−12.0000	−	12.0000i	−0.540453	−	0.540453i
$494$	−16.9706	−	16.9706i	−0.763542	−	0.763542i
$495$		0			0
$496$		−	24.0000i		−	1.07763i
$497$	−14.1421	−	14.1421i	−0.634361	−	0.634361i
$498$		0			0
$499$			18.0000i			0.805791i	0.915246	+	0.402895i	$0.131996\pi$
$499$			18.0000i			0.805791i	−0.915246	+	0.402895i	$0.868004\pi$
$500$	12.7279	+	18.3848i	0.569210	+	0.822192i
$501$		0			0
$502$			18.0000i			0.803379i
$503$	−24.0416	−	24.0416i	−1.07196	−	1.07196i	−0.997201	−	0.0747619i	$-0.976180\pi$
$503$	−24.0416	−	24.0416i	−1.07196	−	1.07196i	−0.0747619	−	0.997201i	$-0.523820\pi$
$504$		0			0
$505$	−1.00000	+	3.00000i	−0.0444994	+	0.133498i
$506$	8.48528	−	8.48528i	0.377217	−	0.377217i
$507$		0			0
$508$	22.0000	−	22.0000i	0.976092	−	0.976092i
$509$	−21.2132			−0.940259			−0.470129	−	0.882598i	$-0.655793\pi$
$509$	−21.2132			−0.940259			−0.470129	+	0.882598i	$0.655793\pi$
$510$		0			0
$511$			10.0000i			0.442374i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	28.0000	−	28.0000i	1.23503	−	1.23503i
$515$	7.07107	+	14.1421i	0.311588	+	0.623177i
$516$		0			0
$517$	6.00000	−	6.00000i	0.263880	−	0.263880i
$518$	−22.6274			−0.994192
$519$		0			0
$520$	16.0000	−	8.00000i	0.701646	−	0.350823i
$521$	16.9706			0.743494			0.371747	−	0.928334i	$-0.378759\pi$
$521$	16.9706			0.743494			0.371747	+	0.928334i	$0.378759\pi$
$522$		0			0
$523$	4.00000	−	4.00000i	0.174908	−	0.174908i	−0.614224	−	0.789132i	$-0.710531\pi$
$523$	4.00000	−	4.00000i	0.174908	−	0.174908i	0.789132	+	0.614224i	$0.210531\pi$
$524$	−25.4558			−1.11204
$525$		0			0
$526$	10.0000	−	10.0000i	0.436021	−	0.436021i
$527$	−16.9706	+	16.9706i	−0.739249	+	0.739249i
$528$		0			0
$529$		−	19.0000i		−	0.826087i
$530$	5.65685	−	2.82843i	0.245718	−	0.122859i
$531$		0			0
$532$	12.0000	+	12.0000i	0.520266	+	0.520266i
$533$	16.9706	+	16.9706i	0.735077	+	0.735077i
$534$		0			0
$535$	−14.0000	−	28.0000i	−0.605273	−	1.21055i
$536$	−22.6274	+	22.6274i	−0.977356	+	0.977356i
$537$		0			0
$538$			30.0000i			1.29339i
$539$		−	21.2132i		−	0.913717i
$540$		0			0
$541$		−	12.0000i		−	0.515920i	−0.966156	−	0.257960i	$-0.916950\pi$
$541$		−	12.0000i		−	0.515920i	0.966156	−	0.257960i	$-0.0830503\pi$
$542$	−16.9706			−0.728948
$543$		0			0
$544$	16.0000	−	16.0000i	0.685994	−	0.685994i
$545$	8.48528	+	2.82843i	0.363470	+	0.121157i
$546$		0			0
$547$	−26.0000	−	26.0000i	−1.11168	−	1.11168i	−0.992923	−	0.118756i	$-0.962109\pi$
$547$	−26.0000	−	26.0000i	−1.11168	−	1.11168i	−0.118756	−	0.992923i	$-0.537891\pi$
$548$	−11.3137	−	11.3137i	−0.483298	−	0.483298i
$549$		0			0
$550$	18.0000	−	24.0000i	0.767523	−	1.02336i
$551$		−	25.4558i		−	1.08446i
$552$		0			0
$553$	14.0000	−	14.0000i	0.595341	−	0.595341i
$554$	5.65685	+	5.65685i	0.240337	+	0.240337i
$555$		0			0
$556$		−	12.0000i		−	0.508913i
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	−0.736433	−	0.676511i	$-0.763491\pi$
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	0.676511	+	0.736433i	$0.263491\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	−11.3137	+	5.65685i	−0.478091	+	0.239046i
$561$		0			0
$562$		−	24.0000i		−	1.01238i
$563$	11.3137	−	11.3137i	0.476816	−	0.476816i	−0.427296	−	0.904112i	$-0.640534\pi$
$563$	11.3137	−	11.3137i	0.476816	−	0.476816i	0.904112	+	0.427296i	$0.140534\pi$
$564$		0			0
$565$	−32.0000	+	16.0000i	−1.34625	+	0.673125i
$566$	−11.3137	−	11.3137i	−0.475551	−	0.475551i
$567$		0			0
$568$	−40.0000			−1.67836
$569$			36.7696i			1.54146i	0.637162	+	0.770730i	$0.280108\pi$
$569$			36.7696i			1.54146i	−0.637162	+	0.770730i	$0.719892\pi$
$570$		0			0
$571$	−34.0000			−1.42286			−0.711428	−	0.702759i	$-0.751951\pi$
$571$	−34.0000			−1.42286			−0.711428	+	0.702759i	$0.751951\pi$
$572$	−16.9706	−	16.9706i	−0.709575	−	0.709575i
$573$		0			0
$574$	−12.0000	−	12.0000i	−0.500870	−	0.500870i
$575$	1.41421	+	9.89949i	0.0589768	+	0.412837i
$576$		0			0
$577$	7.00000	+	7.00000i	0.291414	+	0.291414i	0.837639	−	0.546225i	$-0.183936\pi$
$577$	7.00000	+	7.00000i	0.291414	+	0.291414i	−0.546225	+	0.837639i	$0.683936\pi$
$578$	1.41421			0.0588235
$579$		0			0
$580$	18.0000	+	6.00000i	0.747409	+	0.249136i
$581$			2.82843i			0.117343i
$582$		0			0
$583$	−6.00000	−	6.00000i	−0.248495	−	0.248495i
$584$	14.1421	+	14.1421i	0.585206	+	0.585206i
$585$		0			0
$586$	22.0000	−	22.0000i	0.908812	−	0.908812i
$587$	18.3848	+	18.3848i	0.758821	+	0.758821i	0.976108	−	0.217287i	$-0.0697207\pi$
$587$	18.3848	+	18.3848i	0.758821	+	0.758821i	−0.217287	+	0.976108i	$0.569721\pi$
$588$		0			0
$589$	−36.0000			−1.48335
$590$	−29.6985	−	9.89949i	−1.22267	−	0.407556i
$591$		0			0
$592$	−32.0000	+	32.0000i	−1.31519	+	1.31519i
$593$	2.82843	−	2.82843i	0.116150	−	0.116150i	−0.646643	−	0.762793i	$-0.723828\pi$
$593$	2.82843	−	2.82843i	0.116150	−	0.116150i	0.762793	+	0.646643i	$0.223828\pi$
$594$		0			0
$595$	12.0000	+	4.00000i	0.491952	+	0.163984i
$596$	−25.4558			−1.04271
$597$		0			0
$598$	8.00000			0.327144
$599$	8.48528			0.346699			0.173350	−	0.984860i	$-0.444541\pi$
$599$	8.48528			0.346699			0.173350	+	0.984860i	$0.444541\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$	−5.65685			−0.230556
$603$		0			0
$604$			24.0000i			0.976546i
$605$	−14.8492	−	4.94975i	−0.603708	−	0.201236i
$606$		0			0
$607$	31.0000	−	31.0000i	1.25825	−	1.25825i	0.306324	−	0.951927i	$-0.400901\pi$
$607$	31.0000	−	31.0000i	1.25825	−	1.25825i	0.951927	−	0.306324i	$-0.0990990\pi$
$608$	33.9411			1.37649
$609$		0			0
$610$		0			0
$611$	5.65685			0.228852
$612$		0			0
$613$	10.0000	+	10.0000i	0.403896	+	0.403896i	0.879604	−	0.475707i	$-0.157808\pi$
$613$	10.0000	+	10.0000i	0.403896	+	0.403896i	−0.475707	+	0.879604i	$0.657808\pi$
$614$	−14.1421	+	14.1421i	−0.570730	+	0.570730i
$615$		0			0
$616$	12.0000	+	12.0000i	0.483494	+	0.483494i
$617$	5.65685	+	5.65685i	0.227736	+	0.227736i	0.811746	−	0.584010i	$-0.198517\pi$
$617$	5.65685	+	5.65685i	0.227736	+	0.227736i	−0.584010	+	0.811746i	$0.698517\pi$
$618$		0			0
$619$		−	30.0000i		−	1.20580i	−0.797816	−	0.602901i	$-0.794011\pi$
$619$		−	30.0000i		−	1.20580i	0.797816	−	0.602901i	$-0.205989\pi$
$620$	8.48528	−	25.4558i	0.340777	−	1.02233i
$621$		0			0
$622$	44.0000			1.76424
$623$	2.82843	+	2.82843i	0.113319	+	0.113319i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	1.41421	+	1.41421i	0.0565233	+	0.0565233i
$627$		0			0
$628$	16.0000	−	16.0000i	0.638470	−	0.638470i
$629$	45.2548			1.80443
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$		−	39.5980i		−	1.57512i
$633$		0			0
$634$	−8.00000	−	8.00000i	−0.317721	−	0.317721i
$635$	31.1127	−	15.5563i	1.23467	−	0.617335i
$636$		0			0
$637$	10.0000	−	10.0000i	0.396214	−	0.396214i
$638$		−	25.4558i		−	1.00781i
$639$		0			0
$640$	−8.00000	+	24.0000i	−0.316228	+	0.948683i
$641$	16.9706			0.670297			0.335148	−	0.942165i	$-0.391214\pi$
$641$	16.9706			0.670297			0.335148	+	0.942165i	$0.391214\pi$
$642$		0			0
$643$	10.0000	−	10.0000i	0.394362	−	0.394362i	−0.481877	−	0.876239i	$-0.660045\pi$
$643$	10.0000	−	10.0000i	0.394362	−	0.394362i	0.876239	+	0.481877i	$0.160045\pi$
$644$	−5.65685			−0.222911
$645$		0			0
$646$	−24.0000	−	24.0000i	−0.944267	−	0.944267i
$647$	7.07107	−	7.07107i	0.277992	−	0.277992i	−0.554315	−	0.832307i	$-0.687020\pi$
$647$	7.07107	−	7.07107i	0.277992	−	0.277992i	0.832307	+	0.554315i	$0.187020\pi$
$648$		0			0
$649$			42.0000i			1.64864i
$650$	19.7990	−	2.82843i	0.776580	−	0.110940i
$651$		0			0
$652$	−20.0000	+	20.0000i	−0.783260	+	0.783260i
$653$	5.65685	+	5.65685i	0.221370	+	0.221370i	0.809075	−	0.587705i	$-0.199969\pi$
$653$	5.65685	+	5.65685i	0.221370	+	0.221370i	−0.587705	+	0.809075i	$0.699969\pi$
$654$		0			0
$655$	−27.0000	−	9.00000i	−1.05498	−	0.351659i
$656$	−33.9411			−1.32518
$657$		0			0
$658$	−4.00000			−0.155936
$659$		−	1.41421i		−	0.0550899i	−0.999621	−	0.0275450i	$-0.991231\pi$
$659$		−	1.41421i		−	0.0550899i	0.999621	−	0.0275450i	$-0.00876895\pi$
$660$		0			0
$661$			24.0000i			0.933492i	0.884391	+	0.466746i	$0.154574\pi$
$661$			24.0000i			0.933492i	−0.884391	+	0.466746i	$0.845426\pi$
$662$			2.82843i			0.109930i
$663$		0			0
$664$	4.00000	+	4.00000i	0.155230	+	0.155230i
$665$	8.48528	+	16.9706i	0.329045	+	0.658090i
$666$		0			0
$667$	6.00000	+	6.00000i	0.232321	+	0.232321i
$668$	−31.1127	+	31.1127i	−1.20379	+	1.20379i
$669$		0			0
$670$	−32.0000	+	16.0000i	−1.23627	+	0.618134i
$671$		0			0
$672$		0			0
$673$	−5.00000	+	5.00000i	−0.192736	+	0.192736i	−0.796877	−	0.604141i	$-0.793516\pi$
$673$	−5.00000	+	5.00000i	−0.192736	+	0.192736i	0.604141	+	0.796877i	$0.293516\pi$
$674$	24.0416	−	24.0416i	0.926049	−	0.926049i
$675$		0			0
$676$			10.0000i			0.384615i
$677$	−22.6274	+	22.6274i	−0.869642	+	0.869642i	−0.992433	−	0.122790i	$-0.960816\pi$
$677$	−22.6274	+	22.6274i	−0.869642	+	0.869642i	0.122790	+	0.992433i	$0.460816\pi$
$678$		0			0
$679$	14.0000			0.537271
$680$	22.6274	−	11.3137i	0.867722	−	0.433861i
$681$		0			0
$682$	−36.0000			−1.37851
$683$	15.5563	−	15.5563i	0.595247	−	0.595247i	−0.343797	−	0.939044i	$-0.611713\pi$
$683$	15.5563	−	15.5563i	0.595247	−	0.595247i	0.939044	+	0.343797i	$0.111713\pi$
$684$		0			0
$685$	−8.00000	−	16.0000i	−0.305664	−	0.611329i
$686$	−16.9706	+	16.9706i	−0.647939	+	0.647939i
$687$		0			0
$688$	−8.00000	+	8.00000i	−0.304997	+	0.304997i
$689$		−	5.65685i		−	0.215509i
$690$		0			0
$691$	−22.0000			−0.836919			−0.418460	−	0.908235i	$-0.637430\pi$
$691$	−22.0000			−0.836919			−0.418460	+	0.908235i	$0.637430\pi$
$692$	5.65685	+	5.65685i	0.215041	+	0.215041i
$693$		0			0
$694$	16.0000	−	16.0000i	0.607352	−	0.607352i
$695$	4.24264	−	12.7279i	0.160933	−	0.482798i
$696$		0			0
$697$	24.0000	+	24.0000i	0.909065	+	0.909065i
$698$			28.2843i			1.07058i
$699$		0			0
$700$	−14.0000	+	2.00000i	−0.529150	+	0.0755929i
$701$		−	1.41421i		−	0.0534141i	−0.999643	−	0.0267071i	$-0.991498\pi$
$701$		−	1.41421i		−	0.0534141i	0.999643	−	0.0267071i	$-0.00850213\pi$
$702$		0			0
$703$	48.0000	+	48.0000i	1.81035	+	1.81035i
$704$	33.9411			1.27920
$705$		0			0
$706$	−8.00000	−	8.00000i	−0.301084	−	0.301084i
$707$	−1.41421	−	1.41421i	−0.0531870	−	0.0531870i
$708$		0			0
$709$	−16.0000			−0.600893			−0.300446	−	0.953799i	$-0.597136\pi$
$709$	−16.0000			−0.600893			−0.300446	+	0.953799i	$0.597136\pi$
$710$	−42.4264	−	14.1421i	−1.59223	−	0.530745i
$711$		0			0
$712$	8.00000			0.299813
$713$	8.48528	−	8.48528i	0.317776	−	0.317776i
$714$		0			0
$715$	−12.0000	−	24.0000i	−0.448775	−	0.897549i
$716$			19.7990i			0.739923i
$717$		0			0
$718$		−	12.0000i		−	0.447836i
$719$	16.9706			0.632895			0.316448	−	0.948610i	$-0.397510\pi$
$719$	16.9706			0.632895			0.316448	+	0.948610i	$0.397510\pi$
$720$		0			0
$721$	−10.0000			−0.372419
$722$		−	24.0416i		−	0.894737i
$723$		0			0
$724$			48.0000i			1.78391i
$725$	16.9706	+	12.7279i	0.630271	+	0.472703i
$726$		0			0
$727$	31.0000	−	31.0000i	1.14973	−	1.14973i	0.163120	−	0.986606i	$-0.447844\pi$
$727$	31.0000	−	31.0000i	1.14973	−	1.14973i	0.986606	−	0.163120i	$-0.0521558\pi$
$728$			11.3137i			0.419314i
$729$		0			0
$730$	10.0000	+	20.0000i	0.370117	+	0.740233i
$731$	11.3137			0.418453
$732$		0			0
$733$	28.0000	+	28.0000i	1.03420	+	1.03420i	0.999394	+	0.0348096i	$0.0110825\pi$
$733$	28.0000	+	28.0000i	1.03420	+	1.03420i	0.0348096	+	0.999394i	$0.488918\pi$
$734$	−7.07107	−	7.07107i	−0.260998	−	0.260998i
$735$		0			0
$736$	−8.00000	+	8.00000i	−0.294884	+	0.294884i
$737$	33.9411	+	33.9411i	1.25024	+	1.25024i
$738$		0			0
$739$			6.00000i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$739$			6.00000i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$740$	−45.2548	+	22.6274i	−1.66360	+	0.831800i
$741$		0			0
$742$			4.00000i			0.146845i
$743$	9.89949	+	9.89949i	0.363177	+	0.363177i	0.864981	−	0.501804i	$-0.167330\pi$
$743$	9.89949	+	9.89949i	0.363177	+	0.363177i	−0.501804	+	0.864981i	$0.667330\pi$
$744$		0			0
$745$	−27.0000	−	9.00000i	−0.989203	−	0.329734i
$746$	−22.6274	+	22.6274i	−0.828449	+	0.828449i
$747$		0			0
$748$	−24.0000	−	24.0000i	−0.877527	−	0.877527i
$749$	19.7990			0.723439
$750$		0			0
$751$		−	18.0000i		−	0.656829i	−0.944534	−	0.328415i	$-0.893486\pi$
$751$		−	18.0000i		−	0.656829i	0.944534	−	0.328415i	$-0.106514\pi$
$752$	−5.65685	+	5.65685i	−0.206284	+	0.206284i
$753$		0			0
$754$	12.0000	−	12.0000i	0.437014	−	0.437014i
$755$	−8.48528	+	25.4558i	−0.308811	+	0.926433i
$756$		0			0
$757$	−8.00000	+	8.00000i	−0.290765	+	0.290765i	−0.837382	−	0.546617i	$-0.815915\pi$
$757$	−8.00000	+	8.00000i	−0.290765	+	0.290765i	0.546617	+	0.837382i	$0.315915\pi$
$758$	25.4558			0.924598
$759$		0			0
$760$	36.0000	+	12.0000i	1.30586	+	0.435286i
$761$	−16.9706			−0.615182			−0.307591	−	0.951519i	$-0.599523\pi$
$761$	−16.9706			−0.615182			−0.307591	+	0.951519i	$0.599523\pi$
$762$		0			0
$763$	−4.00000	+	4.00000i	−0.144810	+	0.144810i
$764$		−	22.6274i		−	0.818631i
$765$		0			0
$766$	−26.0000	+	26.0000i	−0.939418	+	0.939418i
$767$	−19.7990	+	19.7990i	−0.714900	+	0.714900i
$768$		0			0
$769$			6.00000i			0.216366i	0.994131	+	0.108183i	$0.0345032\pi$
$769$			6.00000i			0.216366i	−0.994131	+	0.108183i	$0.965497\pi$
$770$	8.48528	+	16.9706i	0.305788	+	0.611577i
$771$		0			0
$772$	−26.0000	+	26.0000i	−0.935760	+	0.935760i
$773$	−28.2843	−	28.2843i	−1.01731	−	1.01731i	−0.999847	−	0.0174671i	$-0.994440\pi$
$773$	−28.2843	−	28.2843i	−1.01731	−	1.01731i	−0.0174671	−	0.999847i	$-0.505560\pi$
$774$		0			0
$775$	18.0000	−	24.0000i	0.646579	−	0.862105i
$776$	19.7990	−	19.7990i	0.710742	−	0.710742i
$777$		0			0
$778$		−	6.00000i		−	0.215110i
$779$			50.9117i			1.82410i
$780$		0			0
$781$			60.0000i			2.14697i
$782$	11.3137			0.404577
$783$		0			0
$784$			20.0000i			0.714286i
$785$	22.6274	−	11.3137i	0.807607	−	0.403804i
$786$		0			0
$787$	−20.0000	−	20.0000i	−0.712923	−	0.712923i	0.254223	−	0.967146i	$-0.418180\pi$
$787$	−20.0000	−	20.0000i	−0.712923	−	0.712923i	−0.967146	+	0.254223i	$0.918180\pi$
$788$	19.7990	−	19.7990i	0.705310	−	0.705310i
$789$		0			0
$790$	14.0000	−	42.0000i	0.498098	−	1.49429i
$791$		−	22.6274i		−	0.804538i
$792$		0			0
$793$		0			0
$794$	14.1421	+	14.1421i	0.501886	+	0.501886i
$795$		0			0
$796$	8.00000			0.283552
$797$	11.3137	−	11.3137i	0.400752	−	0.400752i	−0.477746	−	0.878498i	$-0.658546\pi$
$797$	11.3137	−	11.3137i	0.400752	−	0.400752i	0.878498	+	0.477746i	$0.158546\pi$
$798$		0			0
$799$	8.00000			0.283020
$800$	−16.9706	+	22.6274i	−0.600000	+	0.800000i
$801$		0			0
$802$		−	12.0000i		−	0.423735i
$803$	21.2132	−	21.2132i	0.748598	−	0.748598i
$804$		0			0
$805$	−6.00000	−	2.00000i	−0.211472	−	0.0704907i
$806$	−16.9706	−	16.9706i	−0.597763	−	0.597763i
$807$		0			0
$808$	−4.00000			−0.140720
$809$		−	39.5980i		−	1.39219i	−0.717949	−	0.696095i	$-0.754919\pi$
$809$		−	39.5980i		−	1.39219i	0.717949	−	0.696095i	$-0.245081\pi$
$810$		0			0
$811$	−22.0000			−0.772524			−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000			−0.772524			−0.386262	+	0.922389i	$0.626234\pi$
$812$	−8.48528	+	8.48528i	−0.297775	+	0.297775i
$813$		0			0
$814$	48.0000	+	48.0000i	1.68240	+	1.68240i
$815$	−28.2843	+	14.1421i	−0.990755	+	0.495377i
$816$		0			0
$817$	12.0000	+	12.0000i	0.419827	+	0.419827i
$818$	16.9706			0.593362
$819$		0			0
$820$	−36.0000	−	12.0000i	−1.25717	−	0.419058i
$821$		−	26.8701i		−	0.937771i	−0.883259	−	0.468886i	$-0.844656\pi$
$821$		−	26.8701i		−	0.937771i	0.883259	−	0.468886i	$-0.155344\pi$
$822$		0			0
$823$	−5.00000	−	5.00000i	−0.174289	−	0.174289i	0.614572	−	0.788861i	$-0.289329\pi$
$823$	−5.00000	−	5.00000i	−0.174289	−	0.174289i	−0.788861	+	0.614572i	$0.789329\pi$
$824$	−14.1421	+	14.1421i	−0.492665	+	0.492665i
$825$		0			0
$826$	14.0000	−	14.0000i	0.487122	−	0.487122i
$827$	5.65685	+	5.65685i	0.196708	+	0.196708i	0.798587	−	0.601879i	$-0.205581\pi$
$827$	5.65685	+	5.65685i	0.196708	+	0.196708i	−0.601879	+	0.798587i	$0.705581\pi$
$828$		0			0
$829$	−28.0000			−0.972480			−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000			−0.972480			−0.486240	+	0.873825i	$0.661632\pi$
$830$	2.82843	+	5.65685i	0.0981761	+	0.196352i
$831$		0			0
$832$	16.0000	+	16.0000i	0.554700	+	0.554700i
$833$	14.1421	−	14.1421i	0.489996	−	0.489996i
$834$		0			0
$835$	−44.0000	+	22.0000i	−1.52268	+	0.761341i
$836$		−	50.9117i		−	1.76082i
$837$		0			0
$838$	14.0000			0.483622
$839$	8.48528			0.292944			0.146472	−	0.989215i	$-0.453208\pi$
$839$	8.48528			0.292944			0.146472	+	0.989215i	$0.453208\pi$
$840$		0			0
$841$	−11.0000			−0.379310
$842$	−16.9706			−0.584844
$843$		0			0
$844$	−4.00000			−0.137686
$845$	−3.53553	+	10.6066i	−0.121626	+	0.364878i
$846$		0			0
$847$	7.00000	−	7.00000i	0.240523	−	0.240523i
$848$	5.65685	+	5.65685i	0.194257	+	0.194257i
$849$		0			0
$850$	28.0000	−	4.00000i	0.960392	−	0.137199i
$851$	−22.6274			−0.775658
$852$		0			0
$853$	−14.0000	−	14.0000i	−0.479351	−	0.479351i	0.425573	−	0.904924i	$-0.360073\pi$
$853$	−14.0000	−	14.0000i	−0.479351	−	0.479351i	−0.904924	+	0.425573i	$0.860073\pi$
$854$		0			0
$855$		0			0
$856$	28.0000	−	28.0000i	0.957020	−	0.957020i
$857$	−19.7990	−	19.7990i	−0.676321	−	0.676321i	0.282845	−	0.959166i	$-0.408722\pi$
$857$	−19.7990	−	19.7990i	−0.676321	−	0.676321i	−0.959166	+	0.282845i	$0.908722\pi$
$858$		0			0
$859$		−	6.00000i		−	0.204717i	−0.994748	−	0.102359i	$-0.967361\pi$
$859$		−	6.00000i		−	0.204717i	0.994748	−	0.102359i	$-0.0326389\pi$
$860$	−11.3137	+	5.65685i	−0.385794	+	0.192897i
$861$		0			0
$862$	−52.0000			−1.77113
$863$	18.3848	+	18.3848i	0.625825	+	0.625825i	0.947015	−	0.321190i	$-0.104083\pi$
$863$	18.3848	+	18.3848i	0.625825	+	0.625825i	−0.321190	+	0.947015i	$0.604083\pi$
$864$		0			0
$865$	4.00000	+	8.00000i	0.136004	+	0.272008i
$866$	−32.5269	−	32.5269i	−1.10531	−	1.10531i
$867$		0			0
$868$	12.0000	+	12.0000i	0.407307	+	0.407307i
$869$	−59.3970			−2.01490
$870$		0			0
$871$			32.0000i			1.08428i
$872$			11.3137i			0.383131i
$873$		0			0
$874$	12.0000	+	12.0000i	0.405906	+	0.405906i
$875$	−15.5563	−	2.82843i	−0.525901	−	0.0956183i
$876$		0			0
$877$	4.00000	−	4.00000i	0.135070	−	0.135070i	−0.636339	−	0.771409i	$-0.719552\pi$
$877$	4.00000	−	4.00000i	0.135070	−	0.135070i	0.771409	+	0.636339i	$0.219552\pi$
$878$		−	5.65685i		−	0.190910i
$879$		0			0
$880$	36.0000	+	12.0000i	1.21356	+	0.404520i
$881$	−25.4558			−0.857629			−0.428815	−	0.903393i	$-0.641069\pi$
$881$	−25.4558			−0.857629			−0.428815	+	0.903393i	$0.641069\pi$
$882$		0			0
$883$	34.0000	−	34.0000i	1.14419	−	1.14419i	0.156516	−	0.987675i	$-0.449974\pi$
$883$	34.0000	−	34.0000i	1.14419	−	1.14419i	0.987675	−	0.156516i	$-0.0500262\pi$
$884$		−	22.6274i		−	0.761042i
$885$		0			0
$886$	−32.0000	−	32.0000i	−1.07506	−	1.07506i
$887$	−1.41421	+	1.41421i	−0.0474846	+	0.0474846i	−0.730450	−	0.682966i	$-0.760690\pi$
$887$	−1.41421	+	1.41421i	−0.0474846	+	0.0474846i	0.682966	+	0.730450i	$0.260690\pi$
$888$		0			0
$889$			22.0000i			0.737856i
$890$	8.48528	+	2.82843i	0.284427	+	0.0948091i
$891$		0			0
$892$	22.0000	+	22.0000i	0.736614	+	0.736614i
$893$	8.48528	+	8.48528i	0.283949	+	0.283949i
$894$		0			0
$895$	−7.00000	+	21.0000i	−0.233984	+	0.701953i
$896$	−11.3137	−	11.3137i	−0.377964	−	0.377964i
$897$		0			0
$898$	−16.0000			−0.533927
$899$		−	25.4558i		−	0.849000i
$900$		0			0
$901$		−	8.00000i		−	0.266519i
$902$			50.9117i			1.69517i
$903$		0			0
$904$	−32.0000	−	32.0000i	−1.06430	−	1.06430i
$905$	−16.9706	+	50.9117i	−0.564121	+	1.69236i
$906$		0			0
$907$	28.0000	+	28.0000i	0.929725	+	0.929725i	0.997688	−	0.0679631i	$-0.0216500\pi$
$907$	28.0000	+	28.0000i	0.929725	+	0.929725i	−0.0679631	+	0.997688i	$0.521650\pi$
$908$	−11.3137	−	11.3137i	−0.375459	−	0.375459i
$909$		0			0
$910$	−4.00000	+	12.0000i	−0.132599	+	0.397796i
$911$			19.7990i			0.655970i	0.944683	+	0.327985i	$0.106370\pi$
$911$			19.7990i			0.655970i	−0.944683	+	0.327985i	$0.893630\pi$
$912$		0			0
$913$	6.00000	−	6.00000i	0.198571	−	0.198571i
$914$	−1.41421	+	1.41421i	−0.0467780	+	0.0467780i
$915$		0			0
$916$	−40.0000			−1.32164
$917$	12.7279	−	12.7279i	0.420313	−	0.420313i
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$	−11.3137	+	5.65685i	−0.373002	+	0.186501i
$921$		0			0
$922$	−10.0000			−0.329332
$923$	−28.2843	+	28.2843i	−0.930988	+	0.930988i
$924$		0			0
$925$	−56.0000	+	8.00000i	−1.84127	+	0.263038i
$926$	7.07107	−	7.07107i	0.232370	−	0.232370i
$927$		0			0
$928$			24.0000i			0.787839i
$929$		−	39.5980i		−	1.29917i	−0.760290	−	0.649584i	$-0.774943\pi$
$929$		−	39.5980i		−	1.29917i	0.760290	−	0.649584i	$-0.225057\pi$
$930$		0			0
$931$	30.0000			0.983210
$932$	11.3137	−	11.3137i	0.370593	−	0.370593i
$933$		0			0
$934$	−14.0000	+	14.0000i	−0.458094	+	0.458094i
$935$	−16.9706	−	33.9411i	−0.554997	−	1.10999i
$936$		0			0
$937$	7.00000	+	7.00000i	0.228680	+	0.228680i	0.812141	−	0.583461i	$-0.198302\pi$
$937$	7.00000	+	7.00000i	0.228680	+	0.228680i	−0.583461	+	0.812141i	$0.698302\pi$
$938$		−	22.6274i		−	0.738811i
$939$		0			0
$940$	−8.00000	+	4.00000i	−0.260931	+	0.130466i
$941$		−	9.89949i		−	0.322714i	−0.986896	−	0.161357i	$-0.948413\pi$
$941$		−	9.89949i		−	0.322714i	0.986896	−	0.161357i	$-0.0515871\pi$
$942$		0			0
$943$	−12.0000	−	12.0000i	−0.390774	−	0.390774i
$944$		−	39.5980i		−	1.28880i
$945$		0			0
$946$	12.0000	+	12.0000i	0.390154	+	0.390154i
$947$	−11.3137	−	11.3137i	−0.367646	−	0.367646i	0.498972	−	0.866618i	$-0.333711\pi$
$947$	−11.3137	−	11.3137i	−0.367646	−	0.367646i	−0.866618	+	0.498972i	$0.833711\pi$
$948$		0			0
$949$	20.0000			0.649227
$950$	33.9411	+	25.4558i	1.10120	+	0.825897i
$951$		0			0
$952$			16.0000i			0.518563i
$953$	−14.1421	+	14.1421i	−0.458109	+	0.458109i	−0.898034	−	0.439926i	$-0.855005\pi$
$953$	−14.1421	+	14.1421i	−0.458109	+	0.458109i	0.439926	+	0.898034i	$0.355005\pi$
$954$		0			0
$955$	8.00000	−	24.0000i	0.258874	−	0.776622i
$956$	50.9117			1.64660
$957$		0			0
$958$		−	36.0000i		−	1.16311i
$959$	11.3137			0.365339
$960$		0			0
$961$	−5.00000			−0.161290
$962$			45.2548i			1.45907i
$963$		0			0
$964$	32.0000			1.03065
$965$	−36.7696	+	18.3848i	−1.18365	+	0.591827i
$966$		0			0
$967$	7.00000	−	7.00000i	0.225105	−	0.225105i	−0.585539	−	0.810644i	$-0.699117\pi$
$967$	7.00000	−	7.00000i	0.225105	−	0.225105i	0.810644	+	0.585539i	$0.199117\pi$
$968$		−	19.7990i		−	0.636364i
$969$		0			0
$970$	28.0000	−	14.0000i	0.899026	−	0.449513i
$971$	−29.6985			−0.953070			−0.476535	−	0.879156i	$-0.658107\pi$
$971$	−29.6985			−0.953070			−0.476535	+	0.879156i	$0.658107\pi$
$972$		0			0
$973$	6.00000	+	6.00000i	0.192351	+	0.192351i
$974$	9.89949	+	9.89949i	0.317200	+	0.317200i
$975$		0			0
$976$		0			0
$977$	22.6274	+	22.6274i	0.723915	+	0.723915i	0.969400	−	0.245485i	$-0.0789473\pi$
$977$	22.6274	+	22.6274i	0.723915	+	0.723915i	−0.245485	+	0.969400i	$0.578947\pi$
$978$		0			0
$979$		−	12.0000i		−	0.383522i
$980$	−7.07107	+	21.2132i	−0.225877	+	0.677631i
$981$		0			0
$982$			18.0000i			0.574403i
$983$	9.89949	+	9.89949i	0.315745	+	0.315745i	0.847130	−	0.531385i	$-0.178328\pi$
$983$	9.89949	+	9.89949i	0.315745	+	0.315745i	−0.531385	+	0.847130i	$0.678328\pi$
$984$		0			0
$985$	28.0000	−	14.0000i	0.892154	−	0.446077i
$986$	16.9706	−	16.9706i	0.540453	−	0.540453i
$987$		0			0
$988$	24.0000	−	24.0000i	0.763542	−	0.763542i
$989$	−5.65685			−0.179878
$990$		0			0
$991$		−	36.0000i		−	1.14358i	−0.820401	−	0.571789i	$-0.806250\pi$
$991$		−	36.0000i		−	1.14358i	0.820401	−	0.571789i	$-0.193750\pi$
$992$	33.9411			1.07763
$993$		0			0
$994$	20.0000	−	20.0000i	0.634361	−	0.634361i
$995$	8.48528	+	2.82843i	0.269002	+	0.0896672i
$996$		0			0
$997$	22.0000	−	22.0000i	0.696747	−	0.696747i	−0.266960	−	0.963707i	$-0.586019\pi$
$997$	22.0000	−	22.0000i	0.696747	−	0.696747i	0.963707	+	0.266960i	$0.0860193\pi$
$998$	−25.4558			−0.805791
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.a.307.2	yes	4
3.2	odd	2	inner	360.2.w.a.307.1	yes	4
4.3	odd	2		1440.2.bi.a.847.1		4
5.3	odd	4		360.2.w.b.163.2	yes	4
8.3	odd	2		360.2.w.b.307.2	yes	4
8.5	even	2		1440.2.bi.b.847.2		4
12.11	even	2		1440.2.bi.a.847.2		4
15.8	even	4		360.2.w.b.163.1	yes	4
20.3	even	4		1440.2.bi.b.1423.2		4
24.5	odd	2		1440.2.bi.b.847.1		4
24.11	even	2		360.2.w.b.307.1	yes	4
40.3	even	4	inner	360.2.w.a.163.1	✓	4
40.13	odd	4		1440.2.bi.a.1423.1		4
60.23	odd	4		1440.2.bi.b.1423.1		4
120.53	even	4		1440.2.bi.a.1423.2		4
120.83	odd	4	inner	360.2.w.a.163.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.w.a.163.1	✓	4	40.3	even	4	inner
360.2.w.a.163.2	yes	4	120.83	odd	4	inner
360.2.w.a.307.1	yes	4	3.2	odd	2	inner
360.2.w.a.307.2	yes	4	1.1	even	1	trivial
360.2.w.b.163.1	yes	4	15.8	even	4
360.2.w.b.163.2	yes	4	5.3	odd	4
360.2.w.b.307.1	yes	4	24.11	even	2
360.2.w.b.307.2	yes	4	8.3	odd	2
1440.2.bi.a.847.1		4	4.3	odd	2
1440.2.bi.a.847.2		4	12.11	even	2
1440.2.bi.a.1423.1		4	40.13	odd	4
1440.2.bi.a.1423.2		4	120.53	even	4
1440.2.bi.b.847.1		4	24.5	odd	2
1440.2.bi.b.847.2		4	8.5	even	2
1440.2.bi.b.1423.1		4	60.23	odd	4
1440.2.bi.b.1423.2		4	20.3	even	4

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

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(1.00000 - 1.00000i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(1.00000 - 1.00000i) q^{7} -2.82843i q^{8} +(1.00000 - 3.00000i) q^{10} -4.24264 q^{11} +(-2.00000 - 2.00000i) q^{13} +(1.41421 + 1.41421i) q^{14} +4.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} -6.00000i q^{19} +(4.24264 + 1.41421i) q^{20} -6.00000i q^{22} +(1.41421 + 1.41421i) q^{23} +(4.00000 + 3.00000i) q^{25} +(2.82843 - 2.82843i) q^{26} +(-2.00000 + 2.00000i) q^{28} +4.24264 q^{29} -6.00000i q^{31} +5.65685i q^{32} +(4.00000 - 4.00000i) q^{34} +(-2.82843 + 1.41421i) q^{35} +(-8.00000 + 8.00000i) q^{37} +8.48528 q^{38} +(-2.00000 + 6.00000i) q^{40} -8.48528 q^{41} +(-2.00000 + 2.00000i) q^{43} +8.48528 q^{44} +(-2.00000 + 2.00000i) q^{46} +(-1.41421 + 1.41421i) q^{47} +5.00000i q^{49} +(-4.24264 + 5.65685i) q^{50} +(4.00000 + 4.00000i) q^{52} +(1.41421 + 1.41421i) q^{53} +(9.00000 + 3.00000i) q^{55} +(-2.82843 - 2.82843i) q^{56} +6.00000i q^{58} -9.89949i q^{59} +8.48528 q^{62} -8.00000 q^{64} +(2.82843 + 5.65685i) q^{65} +(-8.00000 - 8.00000i) q^{67} +(5.65685 + 5.65685i) q^{68} +(-2.00000 - 4.00000i) q^{70} -14.1421i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-11.3137 - 11.3137i) q^{74} +12.0000i q^{76} +(-4.24264 + 4.24264i) q^{77} +14.0000 q^{79} +(-8.48528 - 2.82843i) q^{80} -12.0000i q^{82} +(-1.41421 + 1.41421i) q^{83} +(4.00000 + 8.00000i) q^{85} +(-2.82843 - 2.82843i) q^{86} +12.0000i q^{88} +2.82843i q^{89} -4.00000 q^{91} +(-2.82843 - 2.82843i) q^{92} +(-2.00000 - 2.00000i) q^{94} +(-4.24264 + 12.7279i) q^{95} +(7.00000 + 7.00000i) q^{97} -7.07107 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) 4 * q - 8 * q^4 + 4 * q^7	\( 4 q - 8 q^{4} + 4 q^{7} + 4 q^{10} - 8 q^{13} + 16 q^{16} + 16 q^{25} - 8 q^{28} + 16 q^{34} - 32 q^{37} - 8 q^{40} - 8 q^{43} - 8 q^{46} + 16 q^{52} + 36 q^{55} - 32 q^{64} - 32 q^{67} - 8 q^{70} - 20 q^{73} + 56 q^{79} + 16 q^{85} - 16 q^{91} - 8 q^{94} + 28 q^{97}+O(q^{100}) \) 4 * q - 8 * q^4 + 4 * q^7 + 4 * q^10 - 8 * q^13 + 16 * q^16 + 16 * q^25 - 8 * q^28 + 16 * q^34 - 32 * q^37 - 8 * q^40 - 8 * q^43 - 8 * q^46 + 16 * q^52 + 36 * q^55 - 32 * q^64 - 32 * q^67 - 8 * q^70 - 20 * q^73 + 56 * q^79 + 16 * q^85 - 16 * q^91 - 8 * q^94 + 28 * q^97

Introduction

L-functions

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