LMFDB - Embedded newform 360.2.w.b.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:	$\Z[a_1, \ldots, a_{5}]$
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.b.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +2.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.00000i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+1.41421 q^{2} +2.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.00000i) q^{7} +2.82843 q^{8} +(3.00000 + 1.00000i) q^{10} -4.24264 q^{11} +(2.00000 + 2.00000i) q^{13} +(-1.41421 + 1.41421i) q^{14} +4.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} -6.00000i q^{19} +(4.24264 + 1.41421i) q^{20} -6.00000 q^{22} +(-1.41421 - 1.41421i) q^{23} +(4.00000 + 3.00000i) q^{25} +(2.82843 + 2.82843i) q^{26} +(-2.00000 + 2.00000i) q^{28} -4.24264 q^{29} +6.00000i q^{31} +5.65685 q^{32} +(-4.00000 - 4.00000i) q^{34} +(-2.82843 + 1.41421i) q^{35} +(8.00000 - 8.00000i) q^{37} -8.48528i q^{38} +(6.00000 + 2.00000i) q^{40} -8.48528 q^{41} +(-2.00000 + 2.00000i) q^{43} -8.48528 q^{44} +(-2.00000 - 2.00000i) q^{46} +(1.41421 - 1.41421i) q^{47} +5.00000i q^{49} +(5.65685 + 4.24264i) q^{50} +(4.00000 + 4.00000i) q^{52} +(-1.41421 - 1.41421i) q^{53} +(-9.00000 - 3.00000i) q^{55} +(-2.82843 + 2.82843i) q^{56} -6.00000 q^{58} -9.89949i q^{59} +8.48528i q^{62} +8.00000 q^{64} +(2.82843 + 5.65685i) q^{65} +(-8.00000 - 8.00000i) q^{67} +(-5.65685 - 5.65685i) q^{68} +(-4.00000 + 2.00000i) q^{70} +14.1421i q^{71} +(-5.00000 + 5.00000i) q^{73} +(11.3137 - 11.3137i) q^{74} -12.0000i q^{76} +(4.24264 - 4.24264i) q^{77} -14.0000 q^{79} +(8.48528 + 2.82843i) q^{80} -12.0000 q^{82} +(-1.41421 + 1.41421i) q^{83} +(-4.00000 - 8.00000i) q^{85} +(-2.82843 + 2.82843i) q^{86} -12.0000 q^{88} +2.82843i q^{89} -4.00000 q^{91} +(-2.82843 - 2.82843i) q^{92} +(2.00000 - 2.00000i) q^{94} +(4.24264 - 12.7279i) q^{95} +(7.00000 + 7.00000i) q^{97} +7.07107i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 12 q^{10} + 8 q^{13} + 16 q^{16} - 24 q^{22} + 16 q^{25} - 8 q^{28} - 16 q^{34} + 32 q^{37} + 24 q^{40} - 8 q^{43} - 8 q^{46} + 16 q^{52} - 36 q^{55} - 24 q^{58} + 32 q^{64} - 32 q^{67} - 16 q^{70} - 20 q^{73} - 56 q^{79} - 48 q^{82} - 16 q^{85} - 48 q^{88} - 16 q^{91} + 8 q^{94} + 28 q^{97}+O(q^{100}) $ 4 * q + 8 * q^4 - 4 * q^7 + 12 * q^10 + 8 * q^13 + 16 * q^16 - 24 * q^22 + 16 * q^25 - 8 * q^28 - 16 * q^34 + 32 * q^37 + 24 * q^40 - 8 * q^43 - 8 * q^46 + 16 * q^52 - 36 * q^55 - 24 * q^58 + 32 * q^64 - 32 * q^67 - 16 * q^70 - 20 * q^73 - 56 * q^79 - 48 * q^82 - 16 * q^85 - 48 * q^88 - 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 $

$2$	1.41421			1.00000
$2$	1.41421			1.00000
$3$		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	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$	2.82843			1.00000
$9$		0			0
$10$	3.00000	+	1.00000i	0.948683	+	0.316228i
$11$	−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	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$	−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
$22$	−6.00000			−1.27920
$23$	−1.41421	−	1.41421i	−0.294884	−	0.294884i	0.544122	−	0.839006i	$-0.316863\pi$
$23$	−1.41421	−	1.41421i	−0.294884	−	0.294884i	−0.839006	+	0.544122i	$0.816863\pi$
$24$		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	$-0.628881\pi$
$29$	−4.24264			−0.787839			−0.393919	+	0.919145i	$0.628881\pi$
$30$		0			0
$31$			6.00000i			1.07763i	0.842424	+	0.538816i	$0.181128\pi$
$31$			6.00000i			1.07763i	−0.842424	+	0.538816i	$0.818872\pi$
$32$	5.65685			1.00000
$33$		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	$-0.369823\pi$
$37$	8.00000	−	8.00000i	1.31519	−	1.31519i	0.917534	−	0.397658i	$-0.130177\pi$
$38$		−	8.48528i		−	1.37649i
$39$		0			0
$40$	6.00000	+	2.00000i	0.948683	+	0.316228i
$41$	−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	−0.596402	−	0.802686i	$-0.703403\pi$
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	0.802686	+	0.596402i	$0.203403\pi$
$48$		0			0
$49$			5.00000i			0.714286i
$50$	5.65685	+	4.24264i	0.800000	+	0.600000i
$51$		0			0
$52$	4.00000	+	4.00000i	0.554700	+	0.554700i
$53$	−1.41421	−	1.41421i	−0.194257	−	0.194257i	0.603276	−	0.797533i	$-0.293862\pi$
$53$	−1.41421	−	1.41421i	−0.194257	−	0.194257i	−0.797533	+	0.603276i	$0.793862\pi$
$54$		0			0
$55$	−9.00000	−	3.00000i	−1.21356	−	0.404520i
$56$	−2.82843	+	2.82843i	−0.377964	+	0.377964i
$57$		0			0
$58$	−6.00000			−0.787839
$59$		−	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			$\pi$
$62$			8.48528i			1.07763i
$63$		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
$70$	−4.00000	+	2.00000i	−0.478091	+	0.239046i
$71$			14.1421i			1.67836i	0.543852	+	0.839181i	$0.316965\pi$
$71$			14.1421i			1.67836i	−0.543852	+	0.839181i	$0.683035\pi$
$72$		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	$-0.788657\pi$
$79$	−14.0000			−1.57512			−0.787562	+	0.616236i	$0.788657\pi$
$80$	8.48528	+	2.82843i	0.948683	+	0.316228i
$81$		0			0
$82$	−12.0000			−1.32518
$83$	−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
$88$	−12.0000			−1.27920
$89$			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	$0.582388\pi$
$98$			7.07107i			0.714286i
$99$		0			0
$100$	8.00000	+	6.00000i	0.800000	+	0.600000i
$101$			1.41421i			0.140720i	0.997522	+	0.0703598i	$0.0224147\pi$
$101$			1.41421i			0.140720i	−0.997522	+	0.0703598i	$0.977585\pi$
$102$		0			0
$103$	5.00000	+	5.00000i	0.492665	+	0.492665i	0.909145	−	0.416480i	$-0.136736\pi$
$103$	5.00000	+	5.00000i	0.492665	+	0.492665i	−0.416480	+	0.909145i	$0.636736\pi$
$104$	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	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	−12.7279	−	4.24264i	−1.21356	−	0.404520i
$111$		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
$118$		−	14.0000i		−	1.28880i
$119$	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	−0.0236286	−	0.999721i	$-0.507522\pi$
$127$	11.0000	−	11.0000i	0.976092	−	0.976092i	0.999721	+	0.0236286i	$0.00752193\pi$
$128$	11.3137			1.00000
$129$		0			0
$130$	4.00000	+	8.00000i	0.350823	+	0.701646i
$131$	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
$142$			20.0000i			1.67836i
$143$	−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	$-0.674574\pi$
$149$	−12.7279			−1.04271			−0.521356	+	0.853339i	$0.674574\pi$
$150$		0			0
$151$			12.0000i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$151$			12.0000i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$152$		−	16.9706i		−	1.37649i
$153$		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	−0.311708	−	0.950178i	$-0.600901\pi$
$157$	8.00000	−	8.00000i	0.638470	−	0.638470i	0.950178	+	0.311708i	$0.100901\pi$
$158$	−19.7990			−1.57512
$159$		0			0
$160$	12.0000	+	4.00000i	0.948683	+	0.316228i
$161$	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	$0.574128\pi$
$167$	−15.5563	+	15.5563i	−1.20379	+	1.20379i	−0.973006	+	0.230781i	$0.925872\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	−5.65685	−	11.3137i	−0.433861	−	0.867722i
$171$		0			0
$172$	−4.00000	+	4.00000i	−0.304997	+	0.304997i
$173$	2.82843	+	2.82843i	0.215041	+	0.215041i	0.806405	−	0.591364i	$-0.201410\pi$
$173$	2.82843	+	2.82843i	0.215041	+	0.215041i	−0.591364	+	0.806405i	$0.701410\pi$
$174$		0			0
$175$	−7.00000	+	1.00000i	−0.529150	+	0.0755929i
$176$	−16.9706			−1.27920
$177$		0			0
$178$			4.00000i			0.299813i
$179$		−	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	$0.350665\pi$
$181$			24.0000i			1.78391i	−0.452128	+	0.891953i	$0.649335\pi$
$182$	−5.65685			−0.419314
$183$		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
$190$	6.00000	−	18.0000i	0.435286	−	1.30586i
$191$		−	11.3137i		−	0.818631i	−0.912393	−	0.409316i	$-0.865768\pi$
$191$		−	11.3137i		−	0.818631i	0.912393	−	0.409316i	$-0.134232\pi$
$192$		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	−0.260235	−	0.965545i	$-0.583800\pi$
$197$	9.89949	−	9.89949i	0.705310	−	0.705310i	0.965545	+	0.260235i	$0.0838002\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$	11.3137	+	8.48528i	0.800000	+	0.600000i
$201$		0			0
$202$			2.00000i			0.140720i
$203$	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
$218$	5.65685			0.383131
$219$		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	0.971921	−	0.235307i	$-0.0756095\pi$
$223$	11.0000	+	11.0000i	0.736614	+	0.736614i	−0.235307	+	0.971921i	$0.575609\pi$
$224$	−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	$-0.729791\pi$
$229$	−20.0000			−1.32164			−0.660819	+	0.750546i	$0.729791\pi$
$230$	−2.82843	−	5.65685i	−0.186501	−	0.373002i
$231$		0			0
$232$	−12.0000			−0.787839
$233$	−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
$238$	8.00000			0.518563
$239$	25.4558			1.64660			0.823301	−	0.567605i	$-0.192130\pi$
$239$	25.4558			1.64660			0.823301	+	0.567605i	$0.192130\pi$
$240$		0			0
$241$	−16.0000			−1.03065			−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000			−1.03065			−0.515325	+	0.856995i	$0.672329\pi$
$242$	9.89949			0.636364
$243$		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
$248$			16.9706i			1.07763i
$249$		0			0
$250$	9.00000	+	13.0000i	0.569210	+	0.822192i
$251$	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
$262$	18.0000			1.11204
$263$	7.07107	+	7.07107i	0.436021	+	0.436021i	0.890670	−	0.454650i	$-0.150236\pi$
$263$	7.07107	+	7.07107i	0.436021	+	0.436021i	−0.454650	+	0.890670i	$0.650236\pi$
$264$		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	$-0.723850\pi$
$269$	−21.2132			−1.29339			−0.646696	+	0.762748i	$0.723850\pi$
$270$		0			0
$271$		−	12.0000i		−	0.728948i	−0.931214	−	0.364474i	$-0.881249\pi$
$271$		−	12.0000i		−	0.728948i	0.931214	−	0.364474i	$-0.118751\pi$
$272$	−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	−0.816989	−	0.576653i	$-0.804359\pi$
$277$	−4.00000	+	4.00000i	−0.240337	+	0.240337i	0.576653	+	0.816989i	$0.304359\pi$
$278$			8.48528i			0.508913i
$279$		0			0
$280$	−8.00000	+	4.00000i	−0.478091	+	0.239046i
$281$	−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
$290$	−12.7279	−	4.24264i	−0.747409	−	0.249136i
$291$		0			0
$292$	−10.0000	+	10.0000i	−0.585206	+	0.585206i
$293$	15.5563	+	15.5563i	0.908812	+	0.908812i	0.996176	−	0.0873648i	$-0.0278446\pi$
$293$	15.5563	+	15.5563i	0.908812	+	0.908812i	−0.0873648	+	0.996176i	$0.527845\pi$
$294$		0			0
$295$	7.00000	−	21.0000i	0.407556	−	1.22267i
$296$	22.6274	−	22.6274i	1.31519	−	1.31519i
$297$		0			0
$298$	−18.0000			−1.04271
$299$		−	5.65685i		−	0.327144i
$300$		0			0
$301$		−	4.00000i		−	0.230556i
$302$			16.9706i			0.976546i
$303$		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
$310$	−6.00000	+	18.0000i	−0.340777	+	1.02233i
$311$			31.1127i			1.76424i	0.471025	+	0.882120i	$0.343884\pi$
$311$			31.1127i			1.76424i	−0.471025	+	0.882120i	$0.656116\pi$
$312$		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	−0.530170	−	0.847891i	$-0.677872\pi$
$317$	5.65685	−	5.65685i	0.317721	−	0.317721i	0.847891	+	0.530170i	$0.177872\pi$
$318$		0			0
$319$	18.0000			1.00781
$320$	16.9706	+	5.65685i	0.948683	+	0.316228i
$321$		0			0
$322$	4.00000			0.222911
$323$	−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
$328$	−24.0000			−1.32518
$329$			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	$0.977254\pi$
$338$		−	7.07107i		−	0.384615i
$339$		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	$-0.679797\pi$
$349$	−20.0000			−1.07058			−0.535288	+	0.844670i	$0.679797\pi$
$350$	−9.89949	+	1.41421i	−0.529150	+	0.0755929i
$351$		0			0
$352$	−24.0000			−1.27920
$353$	−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
$358$		−	14.0000i		−	0.739923i
$359$	8.48528			0.447836			0.223918	−	0.974608i	$-0.428115\pi$
$359$	8.48528			0.447836			0.223918	+	0.974608i	$0.428115\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$			33.9411i			1.78391i
$363$		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	−0.564462	−	0.825459i	$-0.690916\pi$
$367$	5.00000	−	5.00000i	0.260998	−	0.260998i	0.825459	+	0.564462i	$0.190916\pi$
$368$	−5.65685	−	5.65685i	−0.294884	−	0.294884i
$369$		0			0
$370$	32.0000	−	16.0000i	1.66360	−	0.831800i
$371$	2.82843			0.146845
$372$		0			0
$373$	−16.0000	−	16.0000i	−0.828449	−	0.828449i	0.158854	−	0.987302i	$-0.449220\pi$
$373$	−16.0000	−	16.0000i	−0.828449	−	0.828449i	−0.987302	+	0.158854i	$0.949220\pi$
$374$	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
$382$		−	16.0000i		−	0.818631i
$383$	−18.3848	−	18.3848i	−0.939418	−	0.939418i	0.0588487	−	0.998267i	$-0.481257\pi$
$383$	−18.3848	−	18.3848i	−0.939418	−	0.939418i	−0.998267	+	0.0588487i	$0.981257\pi$
$384$		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	$-0.465698\pi$
$389$	4.24264			0.215110			0.107555	+	0.994199i	$0.465698\pi$
$390$		0			0
$391$			8.00000i			0.404577i
$392$			14.1421i			0.714286i
$393$		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	−0.912024	−	0.410138i	$-0.865481\pi$
$397$	−10.0000	+	10.0000i	−0.501886	+	0.501886i	0.410138	+	0.912024i	$0.365481\pi$
$398$	5.65685			0.283552
$399$		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	$-0.0958798\pi$
$410$	−25.4558	−	8.48528i	−1.25717	−	0.419058i
$411$		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
$418$			36.0000i			1.76082i
$419$		−	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	$-0.905539\pi$
$421$		−	12.0000i		−	0.584844i	0.956289	−	0.292422i	$-0.0944612\pi$
$422$	2.82843			0.137686
$423$		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
$430$	−8.00000	+	4.00000i	−0.385794	+	0.192897i
$431$		−	36.7696i		−	1.77113i	−0.464518	−	0.885564i	$-0.653773\pi$
$431$		−	36.7696i		−	1.77113i	0.464518	−	0.885564i	$-0.346227\pi$
$432$		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	$-0.469569\pi$
$439$	4.00000			0.190910			0.0954548	+	0.995434i	$0.469569\pi$
$440$	−25.4558	−	8.48528i	−1.21356	−	0.404520i
$441$		0			0
$442$		−	16.0000i		−	0.761042i
$443$	−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	$0.739469\pi$
$458$	−28.2843			−1.32164
$459$		0			0
$460$	−4.00000	−	8.00000i	−0.186501	−	0.373002i
$461$		−	7.07107i		−	0.329332i	−0.986349	−	0.164666i	$-0.947345\pi$
$461$		−	7.07107i		−	0.329332i	0.986349	−	0.164666i	$-0.0526547\pi$
$462$		0			0
$463$	5.00000	+	5.00000i	0.232370	+	0.232370i	0.813681	−	0.581311i	$-0.197460\pi$
$463$	5.00000	+	5.00000i	0.232370	+	0.232370i	−0.581311	+	0.813681i	$0.697460\pi$
$464$	−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
$470$	5.65685	−	2.82843i	0.260931	−	0.130466i
$471$		0			0
$472$		−	28.0000i		−	1.28880i
$473$	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
$478$	36.0000			1.64660
$479$	25.4558			1.16311			0.581554	−	0.813508i	$-0.302445\pi$
$479$	25.4558			1.16311			0.581554	+	0.813508i	$0.302445\pi$
$480$		0			0
$481$	32.0000			1.45907
$482$	−22.6274			−1.03065
$483$		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	−0.847691	−	0.530491i	$-0.822008\pi$
$487$	−7.00000	+	7.00000i	−0.317200	+	0.317200i	0.530491	+	0.847691i	$0.322008\pi$
$488$		0			0
$489$		0			0
$490$	−5.00000	+	15.0000i	−0.225877	+	0.677631i
$491$	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
$502$	18.0000			0.803379
$503$	24.0416	+	24.0416i	1.07196	+	1.07196i	0.997201	+	0.0747619i	$0.0238197\pi$
$503$	24.0416	+	24.0416i	1.07196	+	1.07196i	0.0747619	+	0.997201i	$0.476180\pi$
$504$		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	$-0.344207\pi$
$509$	21.2132			0.940259			0.470129	+	0.882598i	$0.344207\pi$
$510$		0			0
$511$		−	10.0000i		−	0.442374i
$512$	22.6274			1.00000
$513$		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
$518$			22.6274i			0.994192i
$519$		0			0
$520$	8.00000	+	16.0000i	0.350823	+	0.701646i
$521$	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
$530$	−2.82843	−	5.65685i	−0.122859	−	0.245718i
$531$		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
$538$	−30.0000			−1.29339
$539$		−	21.2132i		−	0.913717i
$540$		0			0
$541$			12.0000i			0.515920i	0.966156	+	0.257960i	$0.0830503\pi$
$541$			12.0000i			0.515920i	−0.966156	+	0.257960i	$0.916950\pi$
$542$		−	16.9706i		−	0.728948i
$543$		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
$550$	−24.0000	−	18.0000i	−1.02336	−	0.767523i
$551$			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	−0.676511	−	0.736433i	$-0.736509\pi$
$557$	1.41421	−	1.41421i	0.0599222	−	0.0599222i	0.736433	+	0.676511i	$0.236509\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	−11.3137	+	5.65685i	−0.478091	+	0.239046i
$561$		0			0
$562$	−24.0000			−1.01238
$563$	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
$568$			40.0000i			1.67836i
$569$			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	$0.683936\pi$
$578$		−	1.41421i		−	0.0588235i
$579$		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
$590$	9.89949	−	29.6985i	0.407556	−	1.22267i
$591$		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
$598$		−	8.00000i		−	0.327144i
$599$	−8.48528			−0.346699			−0.173350	−	0.984860i	$-0.555459\pi$
$599$	−8.48528			−0.346699			−0.173350	+	0.984860i	$0.555459\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		−	5.65685i		−	0.230556i
$603$		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	$0.599099\pi$
$607$	−31.0000	+	31.0000i	−1.25825	+	1.25825i	−0.951927	+	0.306324i	$0.900901\pi$
$608$		−	33.9411i		−	1.37649i
$609$		0			0
$610$		0			0
$611$	5.65685			0.228852
$612$		0			0
$613$	−10.0000	−	10.0000i	−0.403896	−	0.403896i	0.475707	−	0.879604i	$-0.342192\pi$
$613$	−10.0000	−	10.0000i	−0.403896	−	0.403896i	−0.879604	+	0.475707i	$0.842192\pi$
$614$	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
$622$			44.0000i			1.76424i
$623$	−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	$-0.796303\pi$
$631$		−	30.0000i		−	1.19428i	0.802137	−	0.597141i	$-0.203697\pi$
$632$	−39.5980			−1.57512
$633$		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
$638$	25.4558			1.00781
$639$		0			0
$640$	24.0000	+	8.00000i	0.948683	+	0.316228i
$641$	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	−0.832307	−	0.554315i	$-0.812980\pi$
$647$	−7.07107	+	7.07107i	−0.277992	+	0.277992i	0.554315	+	0.832307i	$0.312980\pi$
$648$		0			0
$649$			42.0000i			1.64864i
$650$	2.82843	+	19.7990i	0.110940	+	0.776580i
$651$		0			0
$652$	20.0000	−	20.0000i	0.783260	−	0.783260i
$653$	−5.65685	−	5.65685i	−0.221370	−	0.221370i	0.587705	−	0.809075i	$-0.300031\pi$
$653$	−5.65685	−	5.65685i	−0.221370	−	0.221370i	−0.809075	+	0.587705i	$0.800031\pi$
$654$		0			0
$655$	27.0000	+	9.00000i	1.05498	+	0.351659i
$656$	−33.9411			−1.32518
$657$		0			0
$658$			4.00000i			0.155936i
$659$		−	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	$-0.845426\pi$
$661$		−	24.0000i		−	0.933492i	0.884391	−	0.466746i	$-0.154574\pi$
$662$	2.82843			0.109930
$663$		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
$670$	−16.0000	−	32.0000i	−0.618134	−	1.23627i
$671$		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	−0.122790	−	0.992433i	$-0.539184\pi$
$677$	22.6274	−	22.6274i	0.869642	−	0.869642i	0.992433	+	0.122790i	$0.0391843\pi$
$678$		0			0
$679$	−14.0000			−0.537271
$680$	−11.3137	−	22.6274i	−0.433861	−	0.867722i
$681$		0			0
$682$		−	36.0000i		−	1.37851i
$683$	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
$698$	−28.2843			−1.07058
$699$		0			0
$700$	−14.0000	+	2.00000i	−0.529150	+	0.0755929i
$701$			1.41421i			0.0534141i	0.999643	+	0.0267071i	$0.00850213\pi$
$701$			1.41421i			0.0534141i	−0.999643	+	0.0267071i	$0.991498\pi$
$702$		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	$-0.402864\pi$
$709$	16.0000			0.600893			0.300446	+	0.953799i	$0.402864\pi$
$710$	−14.1421	+	42.4264i	−0.530745	+	1.59223i
$711$		0			0
$712$			8.00000i			0.299813i
$713$	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
$718$	12.0000			0.447836
$719$	−16.9706			−0.632895			−0.316448	−	0.948610i	$-0.602490\pi$
$719$	−16.9706			−0.632895			−0.316448	+	0.948610i	$0.602490\pi$
$720$		0			0
$721$	−10.0000			−0.372419
$722$	−24.0416			−0.894737
$723$		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	$0.552156\pi$
$727$	−31.0000	+	31.0000i	−1.14973	+	1.14973i	−0.986606	+	0.163120i	$0.947844\pi$
$728$	−11.3137			−0.419314
$729$		0			0
$730$	−20.0000	+	10.0000i	−0.740233	+	0.370117i
$731$	11.3137			0.418453
$732$		0			0
$733$	−28.0000	−	28.0000i	−1.03420	−	1.03420i	−0.999394	−	0.0348096i	$-0.988918\pi$
$733$	−28.0000	−	28.0000i	−1.03420	−	1.03420i	−0.0348096	−	0.999394i	$-0.511082\pi$
$734$	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
$742$	4.00000			0.146845
$743$	−9.89949	−	9.89949i	−0.363177	−	0.363177i	0.501804	−	0.864981i	$-0.332670\pi$
$743$	−9.89949	−	9.89949i	−0.363177	−	0.363177i	−0.864981	+	0.501804i	$0.832670\pi$
$744$		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	$0.106514\pi$
$751$			18.0000i			0.656829i	−0.944534	+	0.328415i	$0.893486\pi$
$752$	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	−0.546617	−	0.837382i	$-0.684085\pi$
$757$	8.00000	−	8.00000i	0.290765	−	0.290765i	0.837382	+	0.546617i	$0.184085\pi$
$758$		−	25.4558i		−	0.924598i
$759$		0			0
$760$	12.0000	−	36.0000i	0.435286	−	1.30586i
$761$	−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	$0.965497\pi$
$770$	16.9706	−	8.48528i	0.611577	−	0.305788i
$771$		0			0
$772$	26.0000	−	26.0000i	0.935760	−	0.935760i
$773$	28.2843	+	28.2843i	1.01731	+	1.01731i	0.999847	+	0.0174671i	$0.00556023\pi$
$773$	28.2843	+	28.2843i	1.01731	+	1.01731i	0.0174671	+	0.999847i	$0.494440\pi$
$774$		0			0
$775$	−18.0000	+	24.0000i	−0.646579	+	0.862105i
$776$	19.7990	+	19.7990i	0.710742	+	0.710742i
$777$		0			0
$778$	6.00000			0.215110
$779$			50.9117i			1.82410i
$780$		0			0
$781$		−	60.0000i		−	2.14697i
$782$			11.3137i			0.404577i
$783$		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
$790$	−42.0000	−	14.0000i	−1.49429	−	0.498098i
$791$			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	−0.878498	−	0.477746i	$-0.841454\pi$
$797$	−11.3137	+	11.3137i	−0.400752	+	0.400752i	0.477746	+	0.878498i	$0.341454\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	22.6274	+	16.9706i	0.800000	+	0.600000i
$801$		0			0
$802$	−12.0000			−0.423735
$803$	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
$808$			4.00000i			0.140720i
$809$		−	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
$818$		−	16.9706i		−	0.593362i
$819$		0			0
$820$	−36.0000	−	12.0000i	−1.25717	−	0.419058i
$821$			26.8701i			0.937771i	0.883259	+	0.468886i	$0.155344\pi$
$821$			26.8701i			0.937771i	−0.883259	+	0.468886i	$0.844656\pi$
$822$		0			0
$823$	5.00000	+	5.00000i	0.174289	+	0.174289i	0.788861	−	0.614572i	$-0.210671\pi$
$823$	5.00000	+	5.00000i	0.174289	+	0.174289i	−0.614572	+	0.788861i	$0.710671\pi$
$824$	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	$-0.338368\pi$
$829$	28.0000			0.972480			0.486240	+	0.873825i	$0.338368\pi$
$830$	−5.65685	+	2.82843i	−0.196352	+	0.0981761i
$831$		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
$838$		−	14.0000i		−	0.483622i
$839$	−8.48528			−0.292944			−0.146472	−	0.989215i	$-0.546792\pi$
$839$	−8.48528			−0.292944			−0.146472	+	0.989215i	$0.546792\pi$
$840$		0			0
$841$	−11.0000			−0.379310
$842$		−	16.9706i		−	0.584844i
$843$		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
$850$	−4.00000	−	28.0000i	−0.137199	−	0.960392i
$851$	−22.6274			−0.775658
$852$		0			0
$853$	14.0000	+	14.0000i	0.479351	+	0.479351i	0.904924	−	0.425573i	$-0.139927\pi$
$853$	14.0000	+	14.0000i	0.479351	+	0.479351i	−0.425573	+	0.904924i	$0.639927\pi$
$854$		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
$862$		−	52.0000i		−	1.77113i
$863$	−18.3848	−	18.3848i	−0.625825	−	0.625825i	0.321190	−	0.947015i	$-0.395917\pi$
$863$	−18.3848	−	18.3848i	−0.625825	−	0.625825i	−0.947015	+	0.321190i	$0.895917\pi$
$864$		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
$872$	11.3137			0.383131
$873$		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	−0.771409	−	0.636339i	$-0.780448\pi$
$877$	−4.00000	+	4.00000i	−0.135070	+	0.135070i	0.636339	+	0.771409i	$0.280448\pi$
$878$	5.65685			0.190910
$879$		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	−0.682966	−	0.730450i	$-0.739310\pi$
$887$	1.41421	−	1.41421i	0.0474846	−	0.0474846i	0.730450	+	0.682966i	$0.239310\pi$
$888$		0			0
$889$			22.0000i			0.737856i
$890$	−2.82843	+	8.48528i	−0.0948091	+	0.284427i
$891$		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
$898$			16.0000i			0.533927i
$899$		−	25.4558i		−	0.849000i
$900$		0			0
$901$			8.00000i			0.266519i
$902$	50.9117			1.69517
$903$		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
$910$	−12.0000	−	4.00000i	−0.397796	−	0.132599i
$911$		−	19.7990i		−	0.655970i	−0.944683	−	0.327985i	$-0.893630\pi$
$911$		−	19.7990i		−	0.655970i	0.944683	−	0.327985i	$-0.106370\pi$
$912$		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	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$	−5.65685	−	11.3137i	−0.186501	−	0.373002i
$921$		0			0
$922$		−	10.0000i		−	0.329332i
$923$	−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
$928$	−24.0000			−0.787839
$929$		−	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	$0.698302\pi$
$938$	22.6274			0.738811
$939$		0			0
$940$	8.00000	−	4.00000i	0.260931	−	0.130466i
$941$			9.89949i			0.322714i	0.986896	+	0.161357i	$0.0515871\pi$
$941$			9.89949i			0.322714i	−0.986896	+	0.161357i	$0.948413\pi$
$942$		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
$950$	25.4558	−	33.9411i	0.825897	−	1.10120i
$951$		0			0
$952$	16.0000			0.518563
$953$	−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
$958$	36.0000			1.16311
$959$	−11.3137			−0.365339
$960$		0			0
$961$	−5.00000			−0.161290
$962$	45.2548			1.45907
$963$		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	−0.810644	−	0.585539i	$-0.800883\pi$
$967$	−7.00000	+	7.00000i	−0.225105	+	0.225105i	0.585539	+	0.810644i	$0.300883\pi$
$968$	19.7990			0.636364
$969$		0			0
$970$	14.0000	+	28.0000i	0.449513	+	0.899026i
$971$	−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
$982$	18.0000			0.574403
$983$	−9.89949	−	9.89949i	−0.315745	−	0.315745i	0.531385	−	0.847130i	$-0.321672\pi$
$983$	−9.89949	−	9.89949i	−0.315745	−	0.315745i	−0.847130	+	0.531385i	$0.821672\pi$
$984$		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	$0.193750\pi$
$991$			36.0000i			1.14358i	−0.820401	+	0.571789i	$0.806250\pi$
$992$			33.9411i			1.07763i
$993$		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	−0.963707	−	0.266960i	$-0.913981\pi$
$997$	−22.0000	+	22.0000i	−0.696747	+	0.696747i	0.266960	+	0.963707i	$0.413981\pi$
$998$			25.4558i			0.805791i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +2.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.00000i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+1.41421 q^{2} +2.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.00000i) q^{7} +2.82843 q^{8} +(3.00000 + 1.00000i) q^{10} -4.24264 q^{11} +(2.00000 + 2.00000i) q^{13} +(-1.41421 + 1.41421i) q^{14} +4.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} -6.00000i q^{19} +(4.24264 + 1.41421i) q^{20} -6.00000 q^{22} +(-1.41421 - 1.41421i) q^{23} +(4.00000 + 3.00000i) q^{25} +(2.82843 + 2.82843i) q^{26} +(-2.00000 + 2.00000i) q^{28} -4.24264 q^{29} +6.00000i q^{31} +5.65685 q^{32} +(-4.00000 - 4.00000i) q^{34} +(-2.82843 + 1.41421i) q^{35} +(8.00000 - 8.00000i) q^{37} -8.48528i q^{38} +(6.00000 + 2.00000i) q^{40} -8.48528 q^{41} +(-2.00000 + 2.00000i) q^{43} -8.48528 q^{44} +(-2.00000 - 2.00000i) q^{46} +(1.41421 - 1.41421i) q^{47} +5.00000i q^{49} +(5.65685 + 4.24264i) q^{50} +(4.00000 + 4.00000i) q^{52} +(-1.41421 - 1.41421i) q^{53} +(-9.00000 - 3.00000i) q^{55} +(-2.82843 + 2.82843i) q^{56} -6.00000 q^{58} -9.89949i q^{59} +8.48528i q^{62} +8.00000 q^{64} +(2.82843 + 5.65685i) q^{65} +(-8.00000 - 8.00000i) q^{67} +(-5.65685 - 5.65685i) q^{68} +(-4.00000 + 2.00000i) q^{70} +14.1421i q^{71} +(-5.00000 + 5.00000i) q^{73} +(11.3137 - 11.3137i) q^{74} -12.0000i q^{76} +(4.24264 - 4.24264i) q^{77} -14.0000 q^{79} +(8.48528 + 2.82843i) q^{80} -12.0000 q^{82} +(-1.41421 + 1.41421i) q^{83} +(-4.00000 - 8.00000i) q^{85} +(-2.82843 + 2.82843i) q^{86} -12.0000 q^{88} +2.82843i q^{89} -4.00000 q^{91} +(-2.82843 - 2.82843i) q^{92} +(2.00000 - 2.00000i) q^{94} +(4.24264 - 12.7279i) q^{95} +(7.00000 + 7.00000i) q^{97} +7.07107i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 4 q^{7}+O(q^{10}) \) 4 * q + 8 * q^4 - 4 * q^7	\( 4 q + 8 q^{4} - 4 q^{7} + 12 q^{10} + 8 q^{13} + 16 q^{16} - 24 q^{22} + 16 q^{25} - 8 q^{28} - 16 q^{34} + 32 q^{37} + 24 q^{40} - 8 q^{43} - 8 q^{46} + 16 q^{52} - 36 q^{55} - 24 q^{58} + 32 q^{64} - 32 q^{67} - 16 q^{70} - 20 q^{73} - 56 q^{79} - 48 q^{82} - 16 q^{85} - 48 q^{88} - 16 q^{91} + 8 q^{94} + 28 q^{97}+O(q^{100}) \) 4 * q + 8 * q^4 - 4 * q^7 + 12 * q^10 + 8 * q^13 + 16 * q^16 - 24 * q^22 + 16 * q^25 - 8 * q^28 - 16 * q^34 + 32 * q^37 + 24 * q^40 - 8 * q^43 - 8 * q^46 + 16 * q^52 - 36 * q^55 - 24 * q^58 + 32 * q^64 - 32 * q^67 - 16 * q^70 - 20 * q^73 - 56 * q^79 - 48 * q^82 - 16 * q^85 - 48 * q^88 - 16 * q^91 + 8 * q^94 + 28 * q^97

Introduction

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