LMFDB - Embedded newform 360.2.k.e.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("360.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.k (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.3
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.2.k.e.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} -1.00000i q^{5} +0.732051 q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} -1.00000i q^{5} +0.732051 q^{7} +(2.00000 - 2.00000i) q^{8} +(-0.366025 - 1.36603i) q^{10} -2.00000i q^{11} +3.46410i q^{13} +(1.00000 - 0.267949i) q^{14} +(2.00000 - 3.46410i) q^{16} -3.46410 q^{17} -0.535898i q^{19} +(-1.00000 - 1.73205i) q^{20} +(-0.732051 - 2.73205i) q^{22} +6.19615 q^{23} -1.00000 q^{25} +(1.26795 + 4.73205i) q^{26} +(1.26795 - 0.732051i) q^{28} +6.92820i q^{29} -5.46410 q^{31} +(1.46410 - 5.46410i) q^{32} +(-4.73205 + 1.26795i) q^{34} -0.732051i q^{35} +2.00000i q^{37} +(-0.196152 - 0.732051i) q^{38} +(-2.00000 - 2.00000i) q^{40} -1.46410 q^{41} +5.26795i q^{43} +(-2.00000 - 3.46410i) q^{44} +(8.46410 - 2.26795i) q^{46} -3.26795 q^{47} -6.46410 q^{49} +(-1.36603 + 0.366025i) q^{50} +(3.46410 + 6.00000i) q^{52} +11.4641i q^{53} -2.00000 q^{55} +(1.46410 - 1.46410i) q^{56} +(2.53590 + 9.46410i) q^{58} -7.46410i q^{59} +8.92820i q^{61} +(-7.46410 + 2.00000i) q^{62} -8.00000i q^{64} +3.46410 q^{65} -10.7321i q^{67} +(-6.00000 + 3.46410i) q^{68} +(-0.267949 - 1.00000i) q^{70} -5.46410 q^{71} +7.46410 q^{73} +(0.732051 + 2.73205i) q^{74} +(-0.535898 - 0.928203i) q^{76} -1.46410i q^{77} -1.07180 q^{79} +(-3.46410 - 2.00000i) q^{80} +(-2.00000 + 0.535898i) q^{82} +1.26795i q^{83} +3.46410i q^{85} +(1.92820 + 7.19615i) q^{86} +(-4.00000 - 4.00000i) q^{88} -8.92820 q^{89} +2.53590i q^{91} +(10.7321 - 6.19615i) q^{92} +(-4.46410 + 1.19615i) q^{94} -0.535898 q^{95} -14.3923 q^{97} +(-8.83013 + 2.36603i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^7 + 8 * q^8	$ 4 q + 2 q^{2} - 4 q^{7} + 8 q^{8} + 2 q^{10} + 4 q^{14} + 8 q^{16} - 4 q^{20} + 4 q^{22} + 4 q^{23} - 4 q^{25} + 12 q^{26} + 12 q^{28} - 8 q^{31} - 8 q^{32} - 12 q^{34} + 20 q^{38} - 8 q^{40} + 8 q^{41} - 8 q^{44} + 20 q^{46} - 20 q^{47} - 12 q^{49} - 2 q^{50} - 8 q^{55} - 8 q^{56} + 24 q^{58} - 16 q^{62} - 24 q^{68} - 8 q^{70} - 8 q^{71} + 16 q^{73} - 4 q^{74} - 16 q^{76} - 32 q^{79} - 8 q^{82} - 20 q^{86} - 16 q^{88} - 8 q^{89} + 36 q^{92} - 4 q^{94} - 16 q^{95} - 16 q^{97} - 18 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^7 + 8 * q^8 + 2 * q^10 + 4 * q^14 + 8 * q^16 - 4 * q^20 + 4 * q^22 + 4 * q^23 - 4 * q^25 + 12 * q^26 + 12 * q^28 - 8 * q^31 - 8 * q^32 - 12 * q^34 + 20 * q^38 - 8 * q^40 + 8 * q^41 - 8 * q^44 + 20 * q^46 - 20 * q^47 - 12 * q^49 - 2 * q^50 - 8 * q^55 - 8 * q^56 + 24 * q^58 - 16 * q^62 - 24 * q^68 - 8 * q^70 - 8 * q^71 + 16 * q^73 - 4 * q^74 - 16 * q^76 - 32 * q^79 - 8 * q^82 - 20 * q^86 - 16 * q^88 - 8 * q^89 + 36 * q^92 - 4 * q^94 - 16 * q^95 - 16 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	0.732051			0.276689			0.138345	−	0.990384i	$-0.455822\pi$
$7$	0.732051			0.276689			0.138345	+	0.990384i	$0.455822\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	−0.366025	−	1.36603i	−0.115747	−	0.431975i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		0			0
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$	1.00000	−	0.267949i	0.267261	−	0.0716124i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−3.46410			−0.840168			−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410			−0.840168			−0.420084	+	0.907485i	$0.637999\pi$
$18$		0			0
$19$		−	0.535898i		−	0.122944i	−0.998109	−	0.0614718i	$-0.980421\pi$
$19$		−	0.535898i		−	0.122944i	0.998109	−	0.0614718i	$-0.0195794\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$		0			0
$22$	−0.732051	−	2.73205i	−0.156074	−	0.582475i
$23$	6.19615			1.29199			0.645994	−	0.763343i	$-0.276443\pi$
$23$	6.19615			1.29199			0.645994	+	0.763343i	$0.276443\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	1.26795	+	4.73205i	0.248665	+	0.928032i
$27$		0			0
$28$	1.26795	−	0.732051i	0.239620	−	0.138345i
$29$			6.92820i			1.28654i	0.765641	+	0.643268i	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$		0			0
$31$	−5.46410			−0.981382			−0.490691	−	0.871334i	$-0.663256\pi$
$31$	−5.46410			−0.981382			−0.490691	+	0.871334i	$0.663256\pi$
$32$	1.46410	−	5.46410i	0.258819	−	0.965926i
$33$		0			0
$34$	−4.73205	+	1.26795i	−0.811540	+	0.217451i
$35$		−	0.732051i		−	0.123739i
$36$		0			0
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−0.196152	−	0.732051i	−0.0318201	−	0.118754i
$39$		0			0
$40$	−2.00000	−	2.00000i	−0.316228	−	0.316228i
$41$	−1.46410			−0.228654			−0.114327	−	0.993443i	$-0.536471\pi$
$41$	−1.46410			−0.228654			−0.114327	+	0.993443i	$0.536471\pi$
$42$		0			0
$43$			5.26795i			0.803355i	0.915781	+	0.401677i	$0.131573\pi$
$43$			5.26795i			0.803355i	−0.915781	+	0.401677i	$0.868427\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$		0			0
$46$	8.46410	−	2.26795i	1.24796	−	0.334391i
$47$	−3.26795			−0.476679			−0.238340	−	0.971182i	$-0.576603\pi$
$47$	−3.26795			−0.476679			−0.238340	+	0.971182i	$0.576603\pi$
$48$		0			0
$49$	−6.46410			−0.923443
$50$	−1.36603	+	0.366025i	−0.193185	+	0.0517638i
$51$		0			0
$52$	3.46410	+	6.00000i	0.480384	+	0.832050i
$53$			11.4641i			1.57472i	0.616496	+	0.787358i	$0.288551\pi$
$53$			11.4641i			1.57472i	−0.616496	+	0.787358i	$0.711449\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	1.46410	−	1.46410i	0.195649	−	0.195649i
$57$		0			0
$58$	2.53590	+	9.46410i	0.332980	+	1.24270i
$59$		−	7.46410i		−	0.971743i	−0.874030	−	0.485872i	$-0.838502\pi$
$59$		−	7.46410i		−	0.971743i	0.874030	−	0.485872i	$-0.161498\pi$
$60$		0			0
$61$			8.92820i			1.14314i	0.820554	+	0.571570i	$0.193665\pi$
$61$			8.92820i			1.14314i	−0.820554	+	0.571570i	$0.806335\pi$
$62$	−7.46410	+	2.00000i	−0.947942	+	0.254000i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	3.46410			0.429669
$66$		0			0
$67$		−	10.7321i		−	1.31113i	−0.755139	−	0.655564i	$-0.772431\pi$
$67$		−	10.7321i		−	1.31113i	0.755139	−	0.655564i	$-0.227569\pi$
$68$	−6.00000	+	3.46410i	−0.727607	+	0.420084i
$69$		0			0
$70$	−0.267949	−	1.00000i	−0.0320261	−	0.119523i
$71$	−5.46410			−0.648470			−0.324235	−	0.945977i	$-0.605107\pi$
$71$	−5.46410			−0.648470			−0.324235	+	0.945977i	$0.605107\pi$
$72$		0			0
$73$	7.46410			0.873607			0.436804	−	0.899557i	$-0.356111\pi$
$73$	7.46410			0.873607			0.436804	+	0.899557i	$0.356111\pi$
$74$	0.732051	+	2.73205i	0.0850992	+	0.317594i
$75$		0			0
$76$	−0.535898	−	0.928203i	−0.0614718	−	0.106472i
$77$		−	1.46410i		−	0.166850i
$78$		0			0
$79$	−1.07180			−0.120587			−0.0602933	−	0.998181i	$-0.519204\pi$
$79$	−1.07180			−0.120587			−0.0602933	+	0.998181i	$0.519204\pi$
$80$	−3.46410	−	2.00000i	−0.387298	−	0.223607i
$81$		0			0
$82$	−2.00000	+	0.535898i	−0.220863	+	0.0591801i
$83$			1.26795i			0.139176i	0.997576	+	0.0695878i	$0.0221684\pi$
$83$			1.26795i			0.139176i	−0.997576	+	0.0695878i	$0.977832\pi$
$84$		0			0
$85$			3.46410i			0.375735i
$86$	1.92820	+	7.19615i	0.207924	+	0.775981i
$87$		0			0
$88$	−4.00000	−	4.00000i	−0.426401	−	0.426401i
$89$	−8.92820			−0.946388			−0.473194	−	0.880958i	$-0.656899\pi$
$89$	−8.92820			−0.946388			−0.473194	+	0.880958i	$0.656899\pi$
$90$		0			0
$91$			2.53590i			0.265834i
$92$	10.7321	−	6.19615i	1.11889	−	0.645994i
$93$		0			0
$94$	−4.46410	+	1.19615i	−0.460437	+	0.123374i
$95$	−0.535898			−0.0549820
$96$		0			0
$97$	−14.3923			−1.46132			−0.730659	−	0.682743i	$-0.760787\pi$
$97$	−14.3923			−1.46132			−0.730659	+	0.682743i	$0.760787\pi$
$98$	−8.83013	+	2.36603i	−0.891978	+	0.239005i
$99$		0			0
$100$	−1.73205	+	1.00000i	−0.173205	+	0.100000i
$101$			2.92820i			0.291367i	0.989331	+	0.145684i	$0.0465381\pi$
$101$			2.92820i			0.291367i	−0.989331	+	0.145684i	$0.953462\pi$
$102$		0			0
$103$	15.6603			1.54305			0.771525	−	0.636199i	$-0.219494\pi$
$103$	15.6603			1.54305			0.771525	+	0.636199i	$0.219494\pi$
$104$	6.92820	+	6.92820i	0.679366	+	0.679366i
$105$		0			0
$106$	4.19615	+	15.6603i	0.407566	+	1.52106i
$107$			2.73205i			0.264117i	0.991242	+	0.132059i	$0.0421587\pi$
$107$			2.73205i			0.264117i	−0.991242	+	0.132059i	$0.957841\pi$
$108$		0			0
$109$		−	16.9282i		−	1.62143i	−0.585443	−	0.810714i	$-0.699079\pi$
$109$		−	16.9282i		−	1.62143i	0.585443	−	0.810714i	$-0.300921\pi$
$110$	−2.73205	+	0.732051i	−0.260491	+	0.0697983i
$111$		0			0
$112$	1.46410	−	2.53590i	0.138345	−	0.239620i
$113$	12.9282			1.21618			0.608092	−	0.793867i	$-0.291935\pi$
$113$	12.9282			1.21618			0.608092	+	0.793867i	$0.291935\pi$
$114$		0			0
$115$		−	6.19615i		−	0.577794i
$116$	6.92820	+	12.0000i	0.643268	+	1.11417i
$117$		0			0
$118$	−2.73205	−	10.1962i	−0.251506	−	0.938632i
$119$	−2.53590			−0.232465
$120$		0			0
$121$	7.00000			0.636364
$122$	3.26795	+	12.1962i	0.295866	+	1.10419i
$123$		0			0
$124$	−9.46410	+	5.46410i	−0.849901	+	0.490691i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	16.7321			1.48473			0.742365	−	0.669996i	$-0.233704\pi$
$127$	16.7321			1.48473			0.742365	+	0.669996i	$0.233704\pi$
$128$	−2.92820	−	10.9282i	−0.258819	−	0.965926i
$129$		0			0
$130$	4.73205	−	1.26795i	0.415028	−	0.111207i
$131$		−	19.8564i		−	1.73486i	−0.497557	−	0.867431i	$-0.665770\pi$
$131$		−	19.8564i		−	1.73486i	0.497557	−	0.867431i	$-0.334230\pi$
$132$		0			0
$133$		−	0.392305i		−	0.0340171i
$134$	−3.92820	−	14.6603i	−0.339345	−	1.26645i
$135$		0			0
$136$	−6.92820	+	6.92820i	−0.594089	+	0.594089i
$137$	−4.92820			−0.421045			−0.210522	−	0.977589i	$-0.567516\pi$
$137$	−4.92820			−0.421045			−0.210522	+	0.977589i	$0.567516\pi$
$138$		0			0
$139$			0.535898i			0.0454543i	0.999742	+	0.0227272i	$0.00723490\pi$
$139$			0.535898i			0.0454543i	−0.999742	+	0.0227272i	$0.992765\pi$
$140$	−0.732051	−	1.26795i	−0.0618696	−	0.107161i
$141$		0			0
$142$	−7.46410	+	2.00000i	−0.626373	+	0.167836i
$143$	6.92820			0.579365
$144$		0			0
$145$	6.92820			0.575356
$146$	10.1962	−	2.73205i	0.843840	−	0.226106i
$147$		0			0
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$		−	7.85641i		−	0.643622i	−0.946804	−	0.321811i	$-0.895708\pi$
$149$		−	7.85641i		−	0.643622i	0.946804	−	0.321811i	$-0.104292\pi$
$150$		0			0
$151$	−12.3923			−1.00847			−0.504236	−	0.863566i	$-0.668226\pi$
$151$	−12.3923			−1.00847			−0.504236	+	0.863566i	$0.668226\pi$
$152$	−1.07180	−	1.07180i	−0.0869342	−	0.0869342i
$153$		0			0
$154$	−0.535898	−	2.00000i	−0.0431839	−	0.161165i
$155$			5.46410i			0.438887i
$156$		0			0
$157$			3.07180i			0.245156i	0.992459	+	0.122578i	$0.0391162\pi$
$157$			3.07180i			0.245156i	−0.992459	+	0.122578i	$0.960884\pi$
$158$	−1.46410	+	0.392305i	−0.116478	+	0.0312101i
$159$		0			0
$160$	−5.46410	−	1.46410i	−0.431975	−	0.115747i
$161$	4.53590			0.357479
$162$		0			0
$163$			0.196152i			0.0153638i	0.999970	+	0.00768192i	$0.00244526\pi$
$163$			0.196152i			0.0153638i	−0.999970	+	0.00768192i	$0.997555\pi$
$164$	−2.53590	+	1.46410i	−0.198020	+	0.114327i
$165$		0			0
$166$	0.464102	+	1.73205i	0.0360213	+	0.134433i
$167$	9.80385			0.758645			0.379322	−	0.925265i	$-0.376157\pi$
$167$	9.80385			0.758645			0.379322	+	0.925265i	$0.376157\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	1.26795	+	4.73205i	0.0972473	+	0.362932i
$171$		0			0
$172$	5.26795	+	9.12436i	0.401677	+	0.695726i
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$		0			0
$175$	−0.732051			−0.0553378
$176$	−6.92820	−	4.00000i	−0.522233	−	0.301511i
$177$		0			0
$178$	−12.1962	+	3.26795i	−0.914140	+	0.244943i
$179$		−	8.53590i		−	0.638003i	−0.947754	−	0.319002i	$-0.896652\pi$
$179$		−	8.53590i		−	0.638003i	0.947754	−	0.319002i	$-0.103348\pi$
$180$		0			0
$181$		−	16.0000i		−	1.18927i	−0.803996	−	0.594635i	$-0.797296\pi$
$181$		−	16.0000i		−	1.18927i	0.803996	−	0.594635i	$-0.202704\pi$
$182$	0.928203	+	3.46410i	0.0688030	+	0.256776i
$183$		0			0
$184$	12.3923	−	12.3923i	0.913573	−	0.913573i
$185$	2.00000			0.147043
$186$		0			0
$187$			6.92820i			0.506640i
$188$	−5.66025	+	3.26795i	−0.412816	+	0.238340i
$189$		0			0
$190$	−0.732051	+	0.196152i	−0.0531085	+	0.0142304i
$191$	−15.3205			−1.10855			−0.554277	−	0.832333i	$-0.687005\pi$
$191$	−15.3205			−1.10855			−0.554277	+	0.832333i	$0.687005\pi$
$192$		0			0
$193$	0.535898			0.0385748			0.0192874	−	0.999814i	$-0.493860\pi$
$193$	0.535898			0.0385748			0.0192874	+	0.999814i	$0.493860\pi$
$194$	−19.6603	+	5.26795i	−1.41152	+	0.378217i
$195$		0			0
$196$	−11.1962	+	6.46410i	−0.799725	+	0.461722i
$197$		−	19.4641i		−	1.38676i	−0.720572	−	0.693380i	$-0.756121\pi$
$197$		−	19.4641i		−	1.38676i	0.720572	−	0.693380i	$-0.243879\pi$
$198$		0			0
$199$	−1.85641			−0.131597			−0.0657986	−	0.997833i	$-0.520959\pi$
$199$	−1.85641			−0.131597			−0.0657986	+	0.997833i	$0.520959\pi$
$200$	−2.00000	+	2.00000i	−0.141421	+	0.141421i
$201$		0			0
$202$	1.07180	+	4.00000i	0.0754114	+	0.281439i
$203$			5.07180i			0.355970i
$204$		0			0
$205$			1.46410i			0.102257i
$206$	21.3923	−	5.73205i	1.49047	−	0.399371i
$207$		0			0
$208$	12.0000	+	6.92820i	0.832050	+	0.480384i
$209$	−1.07180			−0.0741377
$210$		0			0
$211$		−	26.7846i		−	1.84393i	−0.387275	−	0.921964i	$-0.626584\pi$
$211$		−	26.7846i		−	1.84393i	0.387275	−	0.921964i	$-0.373416\pi$
$212$	11.4641	+	19.8564i	0.787358	+	1.36374i
$213$		0			0
$214$	1.00000	+	3.73205i	0.0683586	+	0.255118i
$215$	5.26795			0.359271
$216$		0			0
$217$	−4.00000			−0.271538
$218$	−6.19615	−	23.1244i	−0.419656	−	1.56618i
$219$		0			0
$220$	−3.46410	+	2.00000i	−0.233550	+	0.134840i
$221$		−	12.0000i		−	0.807207i
$222$		0			0
$223$	−5.80385			−0.388654			−0.194327	−	0.980937i	$-0.562252\pi$
$223$	−5.80385			−0.388654			−0.194327	+	0.980937i	$0.562252\pi$
$224$	1.07180	−	4.00000i	0.0716124	−	0.267261i
$225$		0			0
$226$	17.6603	−	4.73205i	1.17474	−	0.314771i
$227$			10.0526i			0.667212i	0.942713	+	0.333606i	$0.108265\pi$
$227$			10.0526i			0.667212i	−0.942713	+	0.333606i	$0.891735\pi$
$228$		0			0
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$	−2.26795	−	8.46410i	−0.149544	−	0.558106i
$231$		0			0
$232$	13.8564	+	13.8564i	0.909718	+	0.909718i
$233$	5.32051			0.348558			0.174279	−	0.984696i	$-0.444241\pi$
$233$	5.32051			0.348558			0.174279	+	0.984696i	$0.444241\pi$
$234$		0			0
$235$			3.26795i			0.213177i
$236$	−7.46410	−	12.9282i	−0.485872	−	0.841554i
$237$		0			0
$238$	−3.46410	+	0.928203i	−0.224544	+	0.0601665i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	16.3923			1.05592			0.527961	−	0.849269i	$-0.322957\pi$
$241$	16.3923			1.05592			0.527961	+	0.849269i	$0.322957\pi$
$242$	9.56218	−	2.56218i	0.614680	−	0.164703i
$243$		0			0
$244$	8.92820	+	15.4641i	0.571570	+	0.989988i
$245$			6.46410i			0.412976i
$246$		0			0
$247$	1.85641			0.118120
$248$	−10.9282	+	10.9282i	−0.693942	+	0.693942i
$249$		0			0
$250$	0.366025	+	1.36603i	0.0231495	+	0.0863950i
$251$			24.9282i			1.57345i	0.617301	+	0.786727i	$0.288226\pi$
$251$			24.9282i			1.57345i	−0.617301	+	0.786727i	$0.711774\pi$
$252$		0			0
$253$		−	12.3923i		−	0.779098i
$254$	22.8564	−	6.12436i	1.43414	−	0.384276i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	2.00000			0.124757			0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000			0.124757			0.0623783	+	0.998053i	$0.480131\pi$
$258$		0			0
$259$			1.46410i			0.0909748i
$260$	6.00000	−	3.46410i	0.372104	−	0.214834i
$261$		0			0
$262$	−7.26795	−	27.1244i	−0.449015	−	1.67575i
$263$	11.6603			0.719002			0.359501	−	0.933145i	$-0.382947\pi$
$263$	11.6603			0.719002			0.359501	+	0.933145i	$0.382947\pi$
$264$		0			0
$265$	11.4641			0.704234
$266$	−0.143594	−	0.535898i	−0.00880428	−	0.0328580i
$267$		0			0
$268$	−10.7321	−	18.5885i	−0.655564	−	1.13547i
$269$		−	8.92820i		−	0.544362i	−0.962246	−	0.272181i	$-0.912255\pi$
$269$		−	8.92820i		−	0.544362i	0.962246	−	0.272181i	$-0.0877450\pi$
$270$		0			0
$271$	−19.3205			−1.17364			−0.586819	−	0.809718i	$-0.699620\pi$
$271$	−19.3205			−1.17364			−0.586819	+	0.809718i	$0.699620\pi$
$272$	−6.92820	+	12.0000i	−0.420084	+	0.727607i
$273$		0			0
$274$	−6.73205	+	1.80385i	−0.406698	+	0.108974i
$275$			2.00000i			0.120605i
$276$		0			0
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$	0.196152	+	0.732051i	0.0117644	+	0.0439055i
$279$		0			0
$280$	−1.46410	−	1.46410i	−0.0874968	−	0.0874968i
$281$	−10.5359			−0.628519			−0.314260	−	0.949337i	$-0.601756\pi$
$281$	−10.5359			−0.628519			−0.314260	+	0.949337i	$0.601756\pi$
$282$		0			0
$283$			9.66025i			0.574242i	0.957894	+	0.287121i	$0.0926983\pi$
$283$			9.66025i			0.574242i	−0.957894	+	0.287121i	$0.907302\pi$
$284$	−9.46410	+	5.46410i	−0.561591	+	0.324235i
$285$		0			0
$286$	9.46410	−	2.53590i	0.559624	−	0.149951i
$287$	−1.07180			−0.0632662
$288$		0			0
$289$	−5.00000			−0.294118
$290$	9.46410	−	2.53590i	0.555751	−	0.148913i
$291$		0			0
$292$	12.9282	−	7.46410i	0.756566	−	0.436804i
$293$		−	15.8564i		−	0.926341i	−0.886269	−	0.463171i	$-0.846712\pi$
$293$		−	15.8564i		−	0.926341i	0.886269	−	0.463171i	$-0.153288\pi$
$294$		0			0
$295$	−7.46410			−0.434577
$296$	4.00000	+	4.00000i	0.232495	+	0.232495i
$297$		0			0
$298$	−2.87564	−	10.7321i	−0.166582	−	0.621691i
$299$			21.4641i			1.24130i
$300$		0			0
$301$			3.85641i			0.222280i
$302$	−16.9282	+	4.53590i	−0.974109	+	0.261012i
$303$		0			0
$304$	−1.85641	−	1.07180i	−0.106472	−	0.0614718i
$305$	8.92820			0.511227
$306$		0			0
$307$			24.9808i			1.42573i	0.701303	+	0.712864i	$0.252602\pi$
$307$			24.9808i			1.42573i	−0.701303	+	0.712864i	$0.747398\pi$
$308$	−1.46410	−	2.53590i	−0.0834249	−	0.144496i
$309$		0			0
$310$	2.00000	+	7.46410i	0.113592	+	0.423932i
$311$	−31.3205			−1.77602			−0.888012	−	0.459821i	$-0.847914\pi$
$311$	−31.3205			−1.77602			−0.888012	+	0.459821i	$0.847914\pi$
$312$		0			0
$313$	−4.14359			−0.234210			−0.117105	−	0.993120i	$-0.537361\pi$
$313$	−4.14359			−0.234210			−0.117105	+	0.993120i	$0.537361\pi$
$314$	1.12436	+	4.19615i	0.0634511	+	0.236803i
$315$		0			0
$316$	−1.85641	+	1.07180i	−0.104431	+	0.0602933i
$317$			8.53590i			0.479424i	0.970844	+	0.239712i	$0.0770530\pi$
$317$			8.53590i			0.479424i	−0.970844	+	0.239712i	$0.922947\pi$
$318$		0			0
$319$	13.8564			0.775810
$320$	−8.00000			−0.447214
$321$		0			0
$322$	6.19615	−	1.66025i	0.345298	−	0.0925223i
$323$			1.85641i			0.103293i
$324$		0			0
$325$		−	3.46410i		−	0.192154i
$326$	0.0717968	+	0.267949i	0.00397646	+	0.0148403i
$327$		0			0
$328$	−2.92820	+	2.92820i	−0.161683	+	0.161683i
$329$	−2.39230			−0.131892
$330$		0			0
$331$			14.0000i			0.769510i	0.923019	+	0.384755i	$0.125714\pi$
$331$			14.0000i			0.769510i	−0.923019	+	0.384755i	$0.874286\pi$
$332$	1.26795	+	2.19615i	0.0695878	+	0.120530i
$333$		0			0
$334$	13.3923	−	3.58846i	0.732794	−	0.196352i
$335$	−10.7321			−0.586355
$336$		0			0
$337$	−19.8564			−1.08165			−0.540824	−	0.841136i	$-0.681887\pi$
$337$	−19.8564			−1.08165			−0.540824	+	0.841136i	$0.681887\pi$
$338$	1.36603	−	0.366025i	0.0743020	−	0.0199092i
$339$		0			0
$340$	3.46410	+	6.00000i	0.187867	+	0.325396i
$341$			10.9282i			0.591795i
$342$		0			0
$343$	−9.85641			−0.532196
$344$	10.5359	+	10.5359i	0.568058	+	0.568058i
$345$		0			0
$346$	0.732051	+	2.73205i	0.0393553	+	0.146876i
$347$		−	1.66025i		−	0.0891271i	−0.999007	−	0.0445636i	$-0.985810\pi$
$347$		−	1.66025i		−	0.0891271i	0.999007	−	0.0445636i	$-0.0141897\pi$
$348$		0			0
$349$			28.0000i			1.49881i	0.662114	+	0.749403i	$0.269659\pi$
$349$			28.0000i			1.49881i	−0.662114	+	0.749403i	$0.730341\pi$
$350$	−1.00000	+	0.267949i	−0.0534522	+	0.0143225i
$351$		0			0
$352$	−10.9282	−	2.92820i	−0.582475	−	0.156074i
$353$	−12.9282			−0.688099			−0.344049	−	0.938952i	$-0.611799\pi$
$353$	−12.9282			−0.688099			−0.344049	+	0.938952i	$0.611799\pi$
$354$		0			0
$355$			5.46410i			0.290004i
$356$	−15.4641	+	8.92820i	−0.819596	+	0.473194i
$357$		0			0
$358$	−3.12436	−	11.6603i	−0.165127	−	0.616264i
$359$	−18.9282			−0.998992			−0.499496	−	0.866316i	$-0.666482\pi$
$359$	−18.9282			−0.998992			−0.499496	+	0.866316i	$0.666482\pi$
$360$		0			0
$361$	18.7128			0.984885
$362$	−5.85641	−	21.8564i	−0.307806	−	1.14875i
$363$		0			0
$364$	2.53590	+	4.39230i	0.132917	+	0.230219i
$365$		−	7.46410i		−	0.390689i
$366$		0			0
$367$	2.87564			0.150107			0.0750537	−	0.997179i	$-0.476087\pi$
$367$	2.87564			0.150107			0.0750537	+	0.997179i	$0.476087\pi$
$368$	12.3923	−	21.4641i	0.645994	−	1.11889i
$369$		0			0
$370$	2.73205	−	0.732051i	0.142033	−	0.0380575i
$371$			8.39230i			0.435707i
$372$		0			0
$373$			25.7128i			1.33136i	0.746238	+	0.665679i	$0.231858\pi$
$373$			25.7128i			1.33136i	−0.746238	+	0.665679i	$0.768142\pi$
$374$	2.53590	+	9.46410i	0.131128	+	0.489377i
$375$		0			0
$376$	−6.53590	+	6.53590i	−0.337063	+	0.337063i
$377$	−24.0000			−1.23606
$378$		0			0
$379$			36.2487i			1.86197i	0.365056	+	0.930986i	$0.381050\pi$
$379$			36.2487i			1.86197i	−0.365056	+	0.930986i	$0.618950\pi$
$380$	−0.928203	+	0.535898i	−0.0476158	+	0.0274910i
$381$		0			0
$382$	−20.9282	+	5.60770i	−1.07078	+	0.286915i
$383$	−21.1244			−1.07940			−0.539702	−	0.841856i	$-0.681463\pi$
$383$	−21.1244			−1.07940			−0.539702	+	0.841856i	$0.681463\pi$
$384$		0			0
$385$	−1.46410			−0.0746175
$386$	0.732051	−	0.196152i	0.0372604	−	0.00998390i
$387$		0			0
$388$	−24.9282	+	14.3923i	−1.26554	+	0.730659i
$389$			6.78461i			0.343993i	0.985098	+	0.171997i	$0.0550218\pi$
$389$			6.78461i			0.343993i	−0.985098	+	0.171997i	$0.944978\pi$
$390$		0			0
$391$	−21.4641			−1.08549
$392$	−12.9282	+	12.9282i	−0.652973	+	0.652973i
$393$		0			0
$394$	−7.12436	−	26.5885i	−0.358920	−	1.33951i
$395$			1.07180i			0.0539279i
$396$		0			0
$397$		−	32.2487i		−	1.61852i	−0.587453	−	0.809258i	$-0.699869\pi$
$397$		−	32.2487i		−	1.61852i	0.587453	−	0.809258i	$-0.300131\pi$
$398$	−2.53590	+	0.679492i	−0.127113	+	0.0340599i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	7.85641			0.392330			0.196165	−	0.980571i	$-0.437151\pi$
$401$	7.85641			0.392330			0.196165	+	0.980571i	$0.437151\pi$
$402$		0			0
$403$		−	18.9282i		−	0.942881i
$404$	2.92820	+	5.07180i	0.145684	+	0.252331i
$405$		0			0
$406$	1.85641	+	6.92820i	0.0921319	+	0.343841i
$407$	4.00000			0.198273
$408$		0			0
$409$	−11.3205			−0.559763			−0.279882	−	0.960035i	$-0.590295\pi$
$409$	−11.3205			−0.559763			−0.279882	+	0.960035i	$0.590295\pi$
$410$	0.535898	+	2.00000i	0.0264661	+	0.0987730i
$411$		0			0
$412$	27.1244	−	15.6603i	1.33632	−	0.771525i
$413$		−	5.46410i		−	0.268871i
$414$		0			0
$415$	1.26795			0.0622412
$416$	18.9282	+	5.07180i	0.928032	+	0.248665i
$417$		0			0
$418$	−1.46410	+	0.392305i	−0.0716116	+	0.0191883i
$419$			18.3923i			0.898523i	0.893400	+	0.449261i	$0.148313\pi$
$419$			18.3923i			0.898523i	−0.893400	+	0.449261i	$0.851687\pi$
$420$		0			0
$421$		−	0.143594i		−	0.00699832i	−0.999994	−	0.00349916i	$-0.998886\pi$
$421$		−	0.143594i		−	0.00699832i	0.999994	−	0.00349916i	$-0.00111382\pi$
$422$	−9.80385	−	36.5885i	−0.477244	−	1.78110i
$423$		0			0
$424$	22.9282	+	22.9282i	1.11349	+	1.11349i
$425$	3.46410			0.168034
$426$		0			0
$427$			6.53590i			0.316294i
$428$	2.73205	+	4.73205i	0.132059	+	0.228732i
$429$		0			0
$430$	7.19615	−	1.92820i	0.347029	−	0.0929862i
$431$	21.4641			1.03389			0.516945	−	0.856019i	$-0.327069\pi$
$431$	21.4641			1.03389			0.516945	+	0.856019i	$0.327069\pi$
$432$		0			0
$433$	−19.4641			−0.935385			−0.467693	−	0.883891i	$-0.654915\pi$
$433$	−19.4641			−0.935385			−0.467693	+	0.883891i	$0.654915\pi$
$434$	−5.46410	+	1.46410i	−0.262285	+	0.0702791i
$435$		0			0
$436$	−16.9282	−	29.3205i	−0.810714	−	1.40420i
$437$		−	3.32051i		−	0.158841i
$438$		0			0
$439$	40.7846			1.94654			0.973272	−	0.229657i	$-0.0737605\pi$
$439$	40.7846			1.94654			0.973272	+	0.229657i	$0.0737605\pi$
$440$	−4.00000	+	4.00000i	−0.190693	+	0.190693i
$441$		0			0
$442$	−4.39230	−	16.3923i	−0.208921	−	0.779702i
$443$			20.9808i			0.996826i	0.866940	+	0.498413i	$0.166084\pi$
$443$			20.9808i			0.996826i	−0.866940	+	0.498413i	$0.833916\pi$
$444$		0			0
$445$			8.92820i			0.423237i
$446$	−7.92820	+	2.12436i	−0.375411	+	0.100591i
$447$		0			0
$448$		−	5.85641i		−	0.276689i
$449$	23.3205			1.10056			0.550281	−	0.834979i	$-0.314520\pi$
$449$	23.3205			1.10056			0.550281	+	0.834979i	$0.314520\pi$
$450$		0			0
$451$			2.92820i			0.137884i
$452$	22.3923	−	12.9282i	1.05325	−	0.608092i
$453$		0			0
$454$	3.67949	+	13.7321i	0.172687	+	0.644477i
$455$	2.53590			0.118885
$456$		0			0
$457$	−26.7846			−1.25293			−0.626466	−	0.779449i	$-0.715499\pi$
$457$	−26.7846			−1.25293			−0.626466	+	0.779449i	$0.715499\pi$
$458$	1.46410	+	5.46410i	0.0684130	+	0.255321i
$459$		0			0
$460$	−6.19615	−	10.7321i	−0.288897	−	0.500384i
$461$		−	10.9282i		−	0.508977i	−0.967076	−	0.254489i	$-0.918093\pi$
$461$		−	10.9282i		−	0.508977i	0.967076	−	0.254489i	$-0.0819071\pi$
$462$		0			0
$463$	−11.2679			−0.523666			−0.261833	−	0.965113i	$-0.584327\pi$
$463$	−11.2679			−0.523666			−0.261833	+	0.965113i	$0.584327\pi$
$464$	24.0000	+	13.8564i	1.11417	+	0.643268i
$465$		0			0
$466$	7.26795	−	1.94744i	0.336681	−	0.0902135i
$467$		−	25.6603i		−	1.18741i	−0.804681	−	0.593707i	$-0.797664\pi$
$467$		−	25.6603i		−	1.18741i	0.804681	−	0.593707i	$-0.202336\pi$
$468$		0			0
$469$		−	7.85641i		−	0.362775i
$470$	1.19615	+	4.46410i	0.0551744	+	0.205914i
$471$		0			0
$472$	−14.9282	−	14.9282i	−0.687126	−	0.687126i
$473$	10.5359			0.484441
$474$		0			0
$475$			0.535898i			0.0245887i
$476$	−4.39230	+	2.53590i	−0.201321	+	0.116233i
$477$		0			0
$478$	27.3205	−	7.32051i	1.24961	−	0.334832i
$479$	−5.85641			−0.267586			−0.133793	−	0.991009i	$-0.542716\pi$
$479$	−5.85641			−0.267586			−0.133793	+	0.991009i	$0.542716\pi$
$480$		0			0
$481$	−6.92820			−0.315899
$482$	22.3923	−	6.00000i	1.01994	−	0.273293i
$483$		0			0
$484$	12.1244	−	7.00000i	0.551107	−	0.318182i
$485$			14.3923i			0.653521i
$486$		0			0
$487$	6.58846			0.298551			0.149276	−	0.988796i	$-0.452306\pi$
$487$	6.58846			0.298551			0.149276	+	0.988796i	$0.452306\pi$
$488$	17.8564	+	17.8564i	0.808322	+	0.808322i
$489$		0			0
$490$	2.36603	+	8.83013i	0.106886	+	0.398904i
$491$		−	16.9282i		−	0.763959i	−0.924171	−	0.381980i	$-0.875242\pi$
$491$		−	16.9282i		−	0.763959i	0.924171	−	0.381980i	$-0.124758\pi$
$492$		0			0
$493$		−	24.0000i		−	1.08091i
$494$	2.53590	−	0.679492i	0.114095	−	0.0305718i
$495$		0			0
$496$	−10.9282	+	18.9282i	−0.490691	+	0.849901i
$497$	−4.00000			−0.179425
$498$		0			0
$499$		−	31.4641i		−	1.40853i	−0.709939	−	0.704263i	$-0.751277\pi$
$499$		−	31.4641i		−	1.40853i	0.709939	−	0.704263i	$-0.248723\pi$
$500$	1.00000	+	1.73205i	0.0447214	+	0.0774597i
$501$		0			0
$502$	9.12436	+	34.0526i	0.407240	+	1.51984i
$503$	0.339746			0.0151485			0.00757426	−	0.999971i	$-0.497589\pi$
$503$	0.339746			0.0151485			0.00757426	+	0.999971i	$0.497589\pi$
$504$		0			0
$505$	2.92820			0.130303
$506$	−4.53590	−	16.9282i	−0.201645	−	0.752550i
$507$		0			0
$508$	28.9808	−	16.7321i	1.28581	−	0.742365i
$509$		−	1.85641i		−	0.0822838i	−0.999153	−	0.0411419i	$-0.986900\pi$
$509$		−	1.85641i		−	0.0822838i	0.999153	−	0.0411419i	$-0.0130996\pi$
$510$		0			0
$511$	5.46410			0.241718
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	2.73205	−	0.732051i	0.120506	−	0.0322894i
$515$		−	15.6603i		−	0.690073i
$516$		0			0
$517$			6.53590i			0.287448i
$518$	0.535898	+	2.00000i	0.0235460	+	0.0878750i
$519$		0			0
$520$	6.92820	−	6.92820i	0.303822	−	0.303822i
$521$	43.8564			1.92138			0.960692	−	0.277616i	$-0.0895444\pi$
$521$	43.8564			1.92138			0.960692	+	0.277616i	$0.0895444\pi$
$522$		0			0
$523$			11.8038i			0.516146i	0.966125	+	0.258073i	$0.0830875\pi$
$523$			11.8038i			0.516146i	−0.966125	+	0.258073i	$0.916912\pi$
$524$	−19.8564	−	34.3923i	−0.867431	−	1.50243i
$525$		0			0
$526$	15.9282	−	4.26795i	0.694503	−	0.186091i
$527$	18.9282			0.824525
$528$		0			0
$529$	15.3923			0.669231
$530$	15.6603	−	4.19615i	0.680238	−	0.182269i
$531$		0			0
$532$	−0.392305	−	0.679492i	−0.0170086	−	0.0294597i
$533$		−	5.07180i		−	0.219684i
$534$		0			0
$535$	2.73205			0.118117
$536$	−21.4641	−	21.4641i	−0.927108	−	0.927108i
$537$		0			0
$538$	−3.26795	−	12.1962i	−0.140891	−	0.525813i
$539$			12.9282i			0.556857i
$540$		0			0
$541$			26.9282i			1.15773i	0.815422	+	0.578867i	$0.196505\pi$
$541$			26.9282i			1.15773i	−0.815422	+	0.578867i	$0.803495\pi$
$542$	−26.3923	+	7.07180i	−1.13365	+	0.303760i
$543$		0			0
$544$	−5.07180	+	18.9282i	−0.217451	+	0.811540i
$545$	−16.9282			−0.725125
$546$		0			0
$547$		−	33.2679i		−	1.42243i	−0.702972	−	0.711217i	$-0.748144\pi$
$547$		−	33.2679i		−	1.42243i	0.702972	−	0.711217i	$-0.251856\pi$
$548$	−8.53590	+	4.92820i	−0.364636	+	0.210522i
$549$		0			0
$550$	0.732051	+	2.73205i	0.0312148	+	0.116495i
$551$	3.71281			0.158171
$552$		0			0
$553$	−0.784610			−0.0333650
$554$	−0.732051	−	2.73205i	−0.0311019	−	0.116074i
$555$		0			0
$556$	0.535898	+	0.928203i	0.0227272	+	0.0393646i
$557$			14.7846i			0.626444i	0.949680	+	0.313222i	$0.101408\pi$
$557$			14.7846i			0.626444i	−0.949680	+	0.313222i	$0.898592\pi$
$558$		0			0
$559$	−18.2487			−0.771838
$560$	−2.53590	−	1.46410i	−0.107161	−	0.0618696i
$561$		0			0
$562$	−14.3923	+	3.85641i	−0.607103	+	0.162673i
$563$		−	22.0526i		−	0.929405i	−0.885467	−	0.464702i	$-0.846161\pi$
$563$		−	22.0526i		−	0.929405i	0.885467	−	0.464702i	$-0.153839\pi$
$564$		0			0
$565$		−	12.9282i		−	0.543894i
$566$	3.53590	+	13.1962i	0.148625	+	0.554676i
$567$		0			0
$568$	−10.9282	+	10.9282i	−0.458537	+	0.458537i
$569$	13.4641			0.564445			0.282222	−	0.959349i	$-0.408928\pi$
$569$	13.4641			0.564445			0.282222	+	0.959349i	$0.408928\pi$
$570$		0			0
$571$		−	6.78461i		−	0.283927i	−0.989872	−	0.141964i	$-0.954658\pi$
$571$		−	6.78461i		−	0.283927i	0.989872	−	0.141964i	$-0.0453416\pi$
$572$	12.0000	−	6.92820i	0.501745	−	0.289683i
$573$		0			0
$574$	−1.46410	+	0.392305i	−0.0611104	+	0.0163745i
$575$	−6.19615			−0.258397
$576$		0			0
$577$	39.5692			1.64729			0.823644	−	0.567107i	$-0.191937\pi$
$577$	39.5692			1.64729			0.823644	+	0.567107i	$0.191937\pi$
$578$	−6.83013	+	1.83013i	−0.284096	+	0.0761232i
$579$		0			0
$580$	12.0000	−	6.92820i	0.498273	−	0.287678i
$581$			0.928203i			0.0385084i
$582$		0			0
$583$	22.9282			0.949589
$584$	14.9282	−	14.9282i	0.617733	−	0.617733i
$585$		0			0
$586$	−5.80385	−	21.6603i	−0.239755	−	0.894777i
$587$		−	3.80385i		−	0.157002i	−0.996914	−	0.0785008i	$-0.974987\pi$
$587$		−	3.80385i		−	0.157002i	0.996914	−	0.0785008i	$-0.0250133\pi$
$588$		0			0
$589$			2.92820i			0.120655i
$590$	−10.1962	+	2.73205i	−0.419769	+	0.112477i
$591$		0			0
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$	−32.6410			−1.34041			−0.670203	−	0.742178i	$-0.733793\pi$
$593$	−32.6410			−1.34041			−0.670203	+	0.742178i	$0.733793\pi$
$594$		0			0
$595$			2.53590i			0.103962i
$596$	−7.85641	−	13.6077i	−0.321811	−	0.557393i
$597$		0			0
$598$	7.85641	+	29.3205i	0.321272	+	1.19900i
$599$	34.6410			1.41539			0.707697	−	0.706516i	$-0.249734\pi$
$599$	34.6410			1.41539			0.707697	+	0.706516i	$0.249734\pi$
$600$		0			0
$601$	18.5359			0.756095			0.378048	−	0.925786i	$-0.376596\pi$
$601$	18.5359			0.756095			0.378048	+	0.925786i	$0.376596\pi$
$602$	1.41154	+	5.26795i	0.0575302	+	0.214706i
$603$		0			0
$604$	−21.4641	+	12.3923i	−0.873362	+	0.504236i
$605$		−	7.00000i		−	0.284590i
$606$		0			0
$607$	30.9808			1.25747			0.628735	−	0.777619i	$-0.283573\pi$
$607$	30.9808			1.25747			0.628735	+	0.777619i	$0.283573\pi$
$608$	−2.92820	−	0.784610i	−0.118754	−	0.0318201i
$609$		0			0
$610$	12.1962	−	3.26795i	0.493808	−	0.132315i
$611$		−	11.3205i		−	0.457979i
$612$		0			0
$613$		−	26.3923i		−	1.06598i	−0.846123	−	0.532988i	$-0.821069\pi$
$613$		−	26.3923i		−	1.06598i	0.846123	−	0.532988i	$-0.178931\pi$
$614$	9.14359	+	34.1244i	0.369005	+	1.37715i
$615$		0			0
$616$	−2.92820	−	2.92820i	−0.117981	−	0.117981i
$617$	20.5359			0.826744			0.413372	−	0.910562i	$-0.364351\pi$
$617$	20.5359			0.826744			0.413372	+	0.910562i	$0.364351\pi$
$618$		0			0
$619$		−	1.32051i		−	0.0530757i	−0.999648	−	0.0265379i	$-0.991552\pi$
$619$		−	1.32051i		−	0.0530757i	0.999648	−	0.0265379i	$-0.00844825\pi$
$620$	5.46410	+	9.46410i	0.219444	+	0.380087i
$621$		0			0
$622$	−42.7846	+	11.4641i	−1.71551	+	0.459669i
$623$	−6.53590			−0.261855
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.66025	+	1.51666i	−0.226229	+	0.0606179i
$627$		0			0
$628$	3.07180	+	5.32051i	0.122578	+	0.212311i
$629$		−	6.92820i		−	0.276246i
$630$		0			0
$631$	−23.3205			−0.928375			−0.464187	−	0.885737i	$-0.653654\pi$
$631$	−23.3205			−0.928375			−0.464187	+	0.885737i	$0.653654\pi$
$632$	−2.14359	+	2.14359i	−0.0852676	+	0.0852676i
$633$		0			0
$634$	3.12436	+	11.6603i	0.124084	+	0.463088i
$635$		−	16.7321i		−	0.663991i
$636$		0			0
$637$		−	22.3923i		−	0.887215i
$638$	18.9282	−	5.07180i	0.749375	−	0.200794i
$639$		0			0
$640$	−10.9282	+	2.92820i	−0.431975	+	0.115747i
$641$	−0.392305			−0.0154951			−0.00774755	−	0.999970i	$-0.502466\pi$
$641$	−0.392305			−0.0154951			−0.00774755	+	0.999970i	$0.502466\pi$
$642$		0			0
$643$		−	39.1244i		−	1.54291i	−0.636281	−	0.771457i	$-0.719528\pi$
$643$		−	39.1244i		−	1.54291i	0.636281	−	0.771457i	$-0.280472\pi$
$644$	7.85641	−	4.53590i	0.309586	−	0.178739i
$645$		0			0
$646$	0.679492	+	2.53590i	0.0267343	+	0.0997736i
$647$	−16.7321			−0.657805			−0.328902	−	0.944364i	$-0.606679\pi$
$647$	−16.7321			−0.657805			−0.328902	+	0.944364i	$0.606679\pi$
$648$		0			0
$649$	−14.9282			−0.585983
$650$	−1.26795	−	4.73205i	−0.0497331	−	0.185606i
$651$		0			0
$652$	0.196152	+	0.339746i	0.00768192	+	0.0133055i
$653$			12.2487i			0.479329i	0.970856	+	0.239665i	$0.0770375\pi$
$653$			12.2487i			0.479329i	−0.970856	+	0.239665i	$0.922963\pi$
$654$		0			0
$655$	−19.8564			−0.775854
$656$	−2.92820	+	5.07180i	−0.114327	+	0.198020i
$657$		0			0
$658$	−3.26795	+	0.875644i	−0.127398	+	0.0341362i
$659$		−	17.3205i		−	0.674711i	−0.941377	−	0.337356i	$-0.890468\pi$
$659$		−	17.3205i		−	0.674711i	0.941377	−	0.337356i	$-0.109532\pi$
$660$		0			0
$661$			8.14359i			0.316749i	0.987379	+	0.158375i	$0.0506253\pi$
$661$			8.14359i			0.316749i	−0.987379	+	0.158375i	$0.949375\pi$
$662$	5.12436	+	19.1244i	0.199164	+	0.743289i
$663$		0			0
$664$	2.53590	+	2.53590i	0.0984119	+	0.0984119i
$665$	−0.392305			−0.0152129
$666$		0			0
$667$			42.9282i			1.66219i
$668$	16.9808	−	9.80385i	0.657005	−	0.379322i
$669$		0			0
$670$	−14.6603	+	3.92820i	−0.566375	+	0.151760i
$671$	17.8564			0.689339
$672$		0			0
$673$	12.5359			0.483223			0.241612	−	0.970373i	$-0.422324\pi$
$673$	12.5359			0.483223			0.241612	+	0.970373i	$0.422324\pi$
$674$	−27.1244	+	7.26795i	−1.04479	+	0.279951i
$675$		0			0
$676$	1.73205	−	1.00000i	0.0666173	−	0.0384615i
$677$			17.6077i			0.676719i	0.941017	+	0.338359i	$0.109872\pi$
$677$			17.6077i			0.676719i	−0.941017	+	0.338359i	$0.890128\pi$
$678$		0			0
$679$	−10.5359			−0.404331
$680$	6.92820	+	6.92820i	0.265684	+	0.265684i
$681$		0			0
$682$	4.00000	+	14.9282i	0.153168	+	0.571630i
$683$		−	16.9808i		−	0.649751i	−0.945757	−	0.324875i	$-0.894678\pi$
$683$		−	16.9808i		−	0.649751i	0.945757	−	0.324875i	$-0.105322\pi$
$684$		0			0
$685$			4.92820i			0.188297i
$686$	−13.4641	+	3.60770i	−0.514062	+	0.137742i
$687$		0			0
$688$	18.2487	+	10.5359i	0.695726	+	0.401677i
$689$	−39.7128			−1.51294
$690$		0			0
$691$		−	18.0000i		−	0.684752i	−0.939563	−	0.342376i	$-0.888768\pi$
$691$		−	18.0000i		−	0.684752i	0.939563	−	0.342376i	$-0.111232\pi$
$692$	2.00000	+	3.46410i	0.0760286	+	0.131685i
$693$		0			0
$694$	−0.607695	−	2.26795i	−0.0230678	−	0.0860902i
$695$	0.535898			0.0203278
$696$		0			0
$697$	5.07180			0.192108
$698$	10.2487	+	38.2487i	0.387919	+	1.44774i
$699$		0			0
$700$	−1.26795	+	0.732051i	−0.0479240	+	0.0276689i
$701$			19.0718i			0.720332i	0.932888	+	0.360166i	$0.117280\pi$
$701$			19.0718i			0.720332i	−0.932888	+	0.360166i	$0.882720\pi$
$702$		0			0
$703$	1.07180			0.0404236
$704$	−16.0000			−0.603023
$705$		0			0
$706$	−17.6603	+	4.73205i	−0.664652	+	0.178093i
$707$			2.14359i			0.0806181i
$708$		0			0
$709$			12.7846i			0.480136i	0.970756	+	0.240068i	$0.0771698\pi$
$709$			12.7846i			0.480136i	−0.970756	+	0.240068i	$0.922830\pi$
$710$	2.00000	+	7.46410i	0.0750587	+	0.280123i
$711$		0			0
$712$	−17.8564	+	17.8564i	−0.669197	+	0.669197i
$713$	−33.8564			−1.26793
$714$		0			0
$715$		−	6.92820i		−	0.259100i
$716$	−8.53590	−	14.7846i	−0.319002	−	0.552527i
$717$		0			0
$718$	−25.8564	+	6.92820i	−0.964953	+	0.258558i
$719$	1.85641			0.0692323			0.0346161	−	0.999401i	$-0.488979\pi$
$719$	1.85641			0.0692323			0.0346161	+	0.999401i	$0.488979\pi$
$720$		0			0
$721$	11.4641			0.426945
$722$	25.5622	−	6.84936i	0.951326	−	0.254907i
$723$		0			0
$724$	−16.0000	−	27.7128i	−0.594635	−	1.02994i
$725$		−	6.92820i		−	0.257307i
$726$		0			0
$727$	−24.0526			−0.892060			−0.446030	−	0.895018i	$-0.647163\pi$
$727$	−24.0526			−0.892060			−0.446030	+	0.895018i	$0.647163\pi$
$728$	5.07180	+	5.07180i	0.187973	+	0.187973i
$729$		0			0
$730$	−2.73205	−	10.1962i	−0.101118	−	0.377377i
$731$		−	18.2487i		−	0.674953i
$732$		0			0
$733$			35.0718i			1.29541i	0.761893	+	0.647703i	$0.224270\pi$
$733$			35.0718i			1.29541i	−0.761893	+	0.647703i	$0.775730\pi$
$734$	3.92820	−	1.05256i	0.144993	−	0.0388507i
$735$		0			0
$736$	9.07180	−	33.8564i	0.334391	−	1.24796i
$737$	−21.4641			−0.790640
$738$		0			0
$739$		−	29.3205i		−	1.07857i	−0.842123	−	0.539286i	$-0.818694\pi$
$739$		−	29.3205i		−	1.07857i	0.842123	−	0.539286i	$-0.181306\pi$
$740$	3.46410	−	2.00000i	0.127343	−	0.0735215i
$741$		0			0
$742$	3.07180	+	11.4641i	0.112769	+	0.420860i
$743$	−10.9808			−0.402845			−0.201423	−	0.979504i	$-0.564556\pi$
$743$	−10.9808			−0.402845			−0.201423	+	0.979504i	$0.564556\pi$
$744$		0			0
$745$	−7.85641			−0.287836
$746$	9.41154	+	35.1244i	0.344581	+	1.28599i
$747$		0			0
$748$	6.92820	+	12.0000i	0.253320	+	0.438763i
$749$			2.00000i			0.0730784i
$750$		0			0
$751$	26.2487			0.957829			0.478915	−	0.877862i	$-0.341030\pi$
$751$	26.2487			0.957829			0.478915	+	0.877862i	$0.341030\pi$
$752$	−6.53590	+	11.3205i	−0.238340	+	0.412816i
$753$		0			0
$754$	−32.7846	+	8.78461i	−1.19395	+	0.319917i
$755$			12.3923i			0.451002i
$756$		0			0
$757$			19.0718i			0.693176i	0.938017	+	0.346588i	$0.112660\pi$
$757$			19.0718i			0.693176i	−0.938017	+	0.346588i	$0.887340\pi$
$758$	13.2679	+	49.5167i	0.481914	+	1.79853i
$759$		0			0
$760$	−1.07180	+	1.07180i	−0.0388782	+	0.0388782i
$761$	5.71281			0.207089			0.103545	−	0.994625i	$-0.466982\pi$
$761$	5.71281			0.207089			0.103545	+	0.994625i	$0.466982\pi$
$762$		0			0
$763$		−	12.3923i		−	0.448632i
$764$	−26.5359	+	15.3205i	−0.960035	+	0.554277i
$765$		0			0
$766$	−28.8564	+	7.73205i	−1.04262	+	0.279370i
$767$	25.8564			0.933621
$768$		0			0
$769$	12.9282			0.466203			0.233101	−	0.972452i	$-0.425113\pi$
$769$	12.9282			0.466203			0.233101	+	0.972452i	$0.425113\pi$
$770$	−2.00000	+	0.535898i	−0.0720750	+	0.0193124i
$771$		0			0
$772$	0.928203	−	0.535898i	0.0334068	−	0.0192874i
$773$		−	22.3923i		−	0.805395i	−0.915333	−	0.402698i	$-0.868073\pi$
$773$		−	22.3923i		−	0.805395i	0.915333	−	0.402698i	$-0.131927\pi$
$774$		0			0
$775$	5.46410			0.196276
$776$	−28.7846	+	28.7846i	−1.03331	+	1.03331i
$777$		0			0
$778$	2.48334	+	9.26795i	0.0890320	+	0.332272i
$779$			0.784610i			0.0281116i
$780$		0			0
$781$			10.9282i			0.391042i
$782$	−29.3205	+	7.85641i	−1.04850	+	0.280945i
$783$		0			0
$784$	−12.9282	+	22.3923i	−0.461722	+	0.799725i
$785$	3.07180			0.109637
$786$		0			0
$787$		−	16.5885i		−	0.591315i	−0.955294	−	0.295657i	$-0.904461\pi$
$787$		−	16.5885i		−	0.591315i	0.955294	−	0.295657i	$-0.0955387\pi$
$788$	−19.4641	−	33.7128i	−0.693380	−	1.20097i
$789$		0			0
$790$	0.392305	+	1.46410i	0.0139576	+	0.0520904i
$791$	9.46410			0.336505
$792$		0			0
$793$	−30.9282			−1.09829
$794$	−11.8038	−	44.0526i	−0.418903	−	1.56337i
$795$		0			0
$796$	−3.21539	+	1.85641i	−0.113966	+	0.0657986i
$797$			50.1051i			1.77481i	0.460986	+	0.887407i	$0.347496\pi$
$797$			50.1051i			1.77481i	−0.460986	+	0.887407i	$0.652504\pi$
$798$		0			0
$799$	11.3205			0.400491
$800$	−1.46410	+	5.46410i	−0.0517638	+	0.193185i
$801$		0			0
$802$	10.7321	−	2.87564i	0.378962	−	0.101543i
$803$		−	14.9282i		−	0.526805i
$804$		0			0
$805$		−	4.53590i		−	0.159869i
$806$	−6.92820	−	25.8564i	−0.244036	−	0.910753i
$807$		0			0
$808$	5.85641	+	5.85641i	0.206028	+	0.206028i
$809$	−23.8564			−0.838747			−0.419373	−	0.907814i	$-0.637750\pi$
$809$	−23.8564			−0.838747			−0.419373	+	0.907814i	$0.637750\pi$
$810$		0			0
$811$			28.9282i			1.01581i	0.861414	+	0.507903i	$0.169579\pi$
$811$			28.9282i			1.01581i	−0.861414	+	0.507903i	$0.830421\pi$
$812$	5.07180	+	8.78461i	0.177985	+	0.308279i
$813$		0			0
$814$	5.46410	−	1.46410i	0.191517	−	0.0513167i
$815$	0.196152			0.00687092
$816$		0			0
$817$	2.82309			0.0987673
$818$	−15.4641	+	4.14359i	−0.540690	+	0.144877i
$819$		0			0
$820$	1.46410	+	2.53590i	0.0511286	+	0.0885574i
$821$			34.7846i			1.21399i	0.794705	+	0.606996i	$0.207625\pi$
$821$			34.7846i			1.21399i	−0.794705	+	0.606996i	$0.792375\pi$
$822$		0			0
$823$	−9.12436			−0.318055			−0.159028	−	0.987274i	$-0.550836\pi$
$823$	−9.12436			−0.318055			−0.159028	+	0.987274i	$0.550836\pi$
$824$	31.3205	−	31.3205i	1.09110	−	1.09110i
$825$		0			0
$826$	−2.00000	−	7.46410i	−0.0695889	−	0.259709i
$827$			23.1244i			0.804113i	0.915615	+	0.402056i	$0.131704\pi$
$827$			23.1244i			0.804113i	−0.915615	+	0.402056i	$0.868296\pi$
$828$		0			0
$829$		−	28.9282i		−	1.00472i	−0.864659	−	0.502359i	$-0.832466\pi$
$829$		−	28.9282i		−	1.00472i	0.864659	−	0.502359i	$-0.167534\pi$
$830$	1.73205	−	0.464102i	0.0601204	−	0.0161092i
$831$		0			0
$832$	27.7128			0.960769
$833$	22.3923			0.775847
$834$		0			0
$835$		−	9.80385i		−	0.339276i
$836$	−1.85641	+	1.07180i	−0.0642052	+	0.0370689i
$837$		0			0
$838$	6.73205	+	25.1244i	0.232555	+	0.867906i
$839$	−24.7846			−0.855660			−0.427830	−	0.903859i	$-0.640722\pi$
$839$	−24.7846			−0.855660			−0.427830	+	0.903859i	$0.640722\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	−0.0525589	−	0.196152i	−0.00181130	−	0.00675986i
$843$		0			0
$844$	−26.7846	−	46.3923i	−0.921964	−	1.59689i
$845$		−	1.00000i		−	0.0344010i
$846$		0			0
$847$	5.12436			0.176075
$848$	39.7128	+	22.9282i	1.36374	+	0.787358i
$849$		0			0
$850$	4.73205	−	1.26795i	0.162308	−	0.0434903i
$851$			12.3923i			0.424803i
$852$		0			0
$853$			21.6077i			0.739833i	0.929065	+	0.369917i	$0.120614\pi$
$853$			21.6077i			0.739833i	−0.929065	+	0.369917i	$0.879386\pi$
$854$	2.39230	+	8.92820i	0.0818630	+	0.305517i
$855$		0			0
$856$	5.46410	+	5.46410i	0.186759	+	0.186759i
$857$	19.8564			0.678282			0.339141	−	0.940736i	$-0.389864\pi$
$857$	19.8564			0.678282			0.339141	+	0.940736i	$0.389864\pi$
$858$		0			0
$859$		−	28.2487i		−	0.963834i	−0.876217	−	0.481917i	$-0.839941\pi$
$859$		−	28.2487i		−	0.963834i	0.876217	−	0.481917i	$-0.160059\pi$
$860$	9.12436	−	5.26795i	0.311138	−	0.179636i
$861$		0			0
$862$	29.3205	−	7.85641i	0.998660	−	0.267590i
$863$	−47.6603			−1.62237			−0.811187	−	0.584787i	$-0.801178\pi$
$863$	−47.6603			−1.62237			−0.811187	+	0.584787i	$0.801178\pi$
$864$		0			0
$865$	2.00000			0.0680020
$866$	−26.5885	+	7.12436i	−0.903513	+	0.242095i
$867$		0			0
$868$	−6.92820	+	4.00000i	−0.235159	+	0.135769i
$869$			2.14359i			0.0727164i
$870$		0			0
$871$	37.1769			1.25969
$872$	−33.8564	−	33.8564i	−1.14652	−	1.14652i
$873$		0			0
$874$	−1.21539	−	4.53590i	−0.0411112	−	0.153429i
$875$			0.732051i			0.0247478i
$876$		0			0
$877$			1.71281i			0.0578376i	0.999582	+	0.0289188i	$0.00920642\pi$
$877$			1.71281i			0.0578376i	−0.999582	+	0.0289188i	$0.990794\pi$
$878$	55.7128	−	14.9282i	1.88022	−	0.503802i
$879$		0			0
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	−9.46410			−0.318854			−0.159427	−	0.987210i	$-0.550965\pi$
$881$	−9.46410			−0.318854			−0.159427	+	0.987210i	$0.550965\pi$
$882$		0			0
$883$			27.9090i			0.939211i	0.882876	+	0.469606i	$0.155604\pi$
$883$			27.9090i			0.939211i	−0.882876	+	0.469606i	$0.844396\pi$
$884$	−12.0000	−	20.7846i	−0.403604	−	0.699062i
$885$		0			0
$886$	7.67949	+	28.6603i	0.257998	+	0.962860i
$887$	13.9090			0.467017			0.233509	−	0.972355i	$-0.424979\pi$
$887$	13.9090			0.467017			0.233509	+	0.972355i	$0.424979\pi$
$888$		0			0
$889$	12.2487			0.410809
$890$	3.26795	+	12.1962i	0.109542	+	0.408816i
$891$		0			0
$892$	−10.0526	+	5.80385i	−0.336585	+	0.194327i
$893$			1.75129i			0.0586046i
$894$		0			0
$895$	−8.53590			−0.285324
$896$	−2.14359	−	8.00000i	−0.0716124	−	0.267261i
$897$		0			0
$898$	31.8564	−	8.53590i	1.06306	−	0.284847i
$899$		−	37.8564i		−	1.26258i
$900$		0			0
$901$		−	39.7128i		−	1.32303i
$902$	1.07180	+	4.00000i	0.0356869	+	0.133185i
$903$		0			0
$904$	25.8564	−	25.8564i	0.859971	−	0.859971i
$905$	−16.0000			−0.531858
$906$		0			0
$907$		−	4.87564i		−	0.161893i	−0.996718	−	0.0809466i	$-0.974206\pi$
$907$		−	4.87564i		−	0.161893i	0.996718	−	0.0809466i	$-0.0257943\pi$
$908$	10.0526	+	17.4115i	0.333606	+	0.577822i
$909$		0			0
$910$	3.46410	−	0.928203i	0.114834	−	0.0307696i
$911$	49.1769			1.62930			0.814652	−	0.579950i	$-0.196928\pi$
$911$	49.1769			1.62930			0.814652	+	0.579950i	$0.196928\pi$
$912$		0			0
$913$	2.53590			0.0839260
$914$	−36.5885	+	9.80385i	−1.21024	+	0.324282i
$915$		0			0
$916$	4.00000	+	6.92820i	0.132164	+	0.228914i
$917$		−	14.5359i		−	0.480018i
$918$		0			0
$919$	−38.9282			−1.28412			−0.642061	−	0.766653i	$-0.721921\pi$
$919$	−38.9282			−1.28412			−0.642061	+	0.766653i	$0.721921\pi$
$920$	−12.3923	−	12.3923i	−0.408562	−	0.408562i
$921$		0			0
$922$	−4.00000	−	14.9282i	−0.131733	−	0.491634i
$923$		−	18.9282i		−	0.623029i
$924$		0			0
$925$		−	2.00000i		−	0.0657596i
$926$	−15.3923	+	4.12436i	−0.505823	+	0.135535i
$927$		0			0
$928$	37.8564	+	10.1436i	1.24270	+	0.332980i
$929$	17.4641			0.572979			0.286489	−	0.958083i	$-0.407512\pi$
$929$	17.4641			0.572979			0.286489	+	0.958083i	$0.407512\pi$
$930$		0			0
$931$			3.46410i			0.113531i
$932$	9.21539	−	5.32051i	0.301860	−	0.174279i
$933$		0			0
$934$	−9.39230	−	35.0526i	−0.307326	−	1.14695i
$935$	6.92820			0.226576
$936$		0			0
$937$	4.24871			0.138799			0.0693997	−	0.997589i	$-0.477892\pi$
$937$	4.24871			0.138799			0.0693997	+	0.997589i	$0.477892\pi$
$938$	−2.87564	−	10.7321i	−0.0938931	−	0.350414i
$939$		0			0
$940$	3.26795	+	5.66025i	0.106589	+	0.184617i
$941$		−	32.0000i		−	1.04317i	−0.853199	−	0.521585i	$-0.825341\pi$
$941$		−	32.0000i		−	1.04317i	0.853199	−	0.521585i	$-0.174659\pi$
$942$		0			0
$943$	−9.07180			−0.295418
$944$	−25.8564	−	14.9282i	−0.841554	−	0.485872i
$945$		0			0
$946$	14.3923	−	3.85641i	0.467934	−	0.125383i
$947$		−	3.12436i		−	0.101528i	−0.998711	−	0.0507640i	$-0.983834\pi$
$947$		−	3.12436i		−	0.101528i	0.998711	−	0.0507640i	$-0.0161656\pi$
$948$		0			0
$949$			25.8564i			0.839334i
$950$	0.196152	+	0.732051i	0.00636402	+	0.0237509i
$951$		0			0
$952$	−5.07180	+	5.07180i	−0.164378	+	0.164378i
$953$	17.2154			0.557661			0.278831	−	0.960340i	$-0.410053\pi$
$953$	17.2154			0.557661			0.278831	+	0.960340i	$0.410053\pi$
$954$		0			0
$955$			15.3205i			0.495760i
$956$	34.6410	−	20.0000i	1.12037	−	0.646846i
$957$		0			0
$958$	−8.00000	+	2.14359i	−0.258468	+	0.0692564i
$959$	−3.60770			−0.116499
$960$		0			0
$961$	−1.14359			−0.0368901
$962$	−9.46410	+	2.53590i	−0.305135	+	0.0817606i
$963$		0			0
$964$	28.3923	−	16.3923i	0.914455	−	0.527961i
$965$		−	0.535898i		−	0.0172512i
$966$		0			0
$967$	16.3397			0.525451			0.262725	−	0.964871i	$-0.415379\pi$
$967$	16.3397			0.525451			0.262725	+	0.964871i	$0.415379\pi$
$968$	14.0000	−	14.0000i	0.449977	−	0.449977i
$969$		0			0
$970$	5.26795	+	19.6603i	0.169144	+	0.631253i
$971$			36.9282i			1.18508i	0.805540	+	0.592541i	$0.201875\pi$
$971$			36.9282i			1.18508i	−0.805540	+	0.592541i	$0.798125\pi$
$972$		0			0
$973$			0.392305i			0.0125767i
$974$	9.00000	−	2.41154i	0.288379	−	0.0772708i
$975$		0			0
$976$	30.9282	+	17.8564i	0.989988	+	0.571570i
$977$	24.5359			0.784973			0.392486	−	0.919758i	$-0.371615\pi$
$977$	24.5359			0.784973			0.392486	+	0.919758i	$0.371615\pi$
$978$		0			0
$979$			17.8564i			0.570693i
$980$	6.46410	+	11.1962i	0.206488	+	0.357648i
$981$		0			0
$982$	−6.19615	−	23.1244i	−0.197727	−	0.737928i
$983$	48.7321			1.55431			0.777156	−	0.629309i	$-0.216662\pi$
$983$	48.7321			1.55431			0.777156	+	0.629309i	$0.216662\pi$
$984$		0			0
$985$	−19.4641			−0.620178
$986$	−8.78461	−	32.7846i	−0.279759	−	1.04407i
$987$		0			0
$988$	3.21539	−	1.85641i	0.102295	−	0.0590602i
$989$			32.6410i			1.03792i
$990$		0			0
$991$	41.4641			1.31715			0.658575	−	0.752515i	$-0.271159\pi$
$991$	41.4641			1.31715			0.658575	+	0.752515i	$0.271159\pi$
$992$	−8.00000	+	29.8564i	−0.254000	+	0.947942i
$993$		0			0
$994$	−5.46410	+	1.46410i	−0.173311	+	0.0464385i
$995$			1.85641i			0.0588520i
$996$		0			0
$997$			11.1769i			0.353976i	0.984213	+	0.176988i	$0.0566354\pi$
$997$			11.1769i			0.353976i	−0.984213	+	0.176988i	$0.943365\pi$
$998$	−11.5167	−	42.9808i	−0.364554	−	1.36053i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.k.e.181.3		4
3.2	odd	2		40.2.d.a.21.2	yes	4
4.3	odd	2		1440.2.k.e.721.1		4
5.2	odd	4		1800.2.d.l.1549.4		4
5.3	odd	4		1800.2.d.p.1549.1		4
5.4	even	2		1800.2.k.j.901.2		4
8.3	odd	2		1440.2.k.e.721.3		4
8.5	even	2	inner	360.2.k.e.181.4		4
12.11	even	2		160.2.d.a.81.4		4
15.2	even	4		200.2.f.e.149.1		4
15.8	even	4		200.2.f.c.149.4		4
15.14	odd	2		200.2.d.f.101.3		4
20.3	even	4		7200.2.d.o.2449.3		4
20.7	even	4		7200.2.d.n.2449.2		4
20.19	odd	2		7200.2.k.j.3601.4		4
24.5	odd	2		40.2.d.a.21.1	✓	4
24.11	even	2		160.2.d.a.81.1		4
40.3	even	4		7200.2.d.n.2449.3		4
40.13	odd	4		1800.2.d.l.1549.3		4
40.19	odd	2		7200.2.k.j.3601.3		4
40.27	even	4		7200.2.d.o.2449.2		4
40.29	even	2		1800.2.k.j.901.1		4
40.37	odd	4		1800.2.d.p.1549.2		4
48.5	odd	4		1280.2.a.a.1.1		2
48.11	even	4		1280.2.a.n.1.2		2
48.29	odd	4		1280.2.a.o.1.2		2
48.35	even	4		1280.2.a.d.1.1		2
60.23	odd	4		800.2.f.c.49.2		4
60.47	odd	4		800.2.f.e.49.3		4
60.59	even	2		800.2.d.e.401.1		4
120.29	odd	2		200.2.d.f.101.4		4
120.53	even	4		200.2.f.e.149.2		4
120.59	even	2		800.2.d.e.401.4		4
120.77	even	4		200.2.f.c.149.3		4
120.83	odd	4		800.2.f.e.49.4		4
120.107	odd	4		800.2.f.c.49.1		4
240.29	odd	4		6400.2.a.z.1.1		2
240.59	even	4		6400.2.a.be.1.1		2
240.149	odd	4		6400.2.a.ce.1.2		2
240.179	even	4		6400.2.a.cj.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.d.a.21.1	✓	4	24.5	odd	2
40.2.d.a.21.2	yes	4	3.2	odd	2
160.2.d.a.81.1		4	24.11	even	2
160.2.d.a.81.4		4	12.11	even	2
200.2.d.f.101.3		4	15.14	odd	2
200.2.d.f.101.4		4	120.29	odd	2
200.2.f.c.149.3		4	120.77	even	4
200.2.f.c.149.4		4	15.8	even	4
200.2.f.e.149.1		4	15.2	even	4
200.2.f.e.149.2		4	120.53	even	4
360.2.k.e.181.3		4	1.1	even	1	trivial
360.2.k.e.181.4		4	8.5	even	2	inner
800.2.d.e.401.1		4	60.59	even	2
800.2.d.e.401.4		4	120.59	even	2
800.2.f.c.49.1		4	120.107	odd	4
800.2.f.c.49.2		4	60.23	odd	4
800.2.f.e.49.3		4	60.47	odd	4
800.2.f.e.49.4		4	120.83	odd	4
1280.2.a.a.1.1		2	48.5	odd	4
1280.2.a.d.1.1		2	48.35	even	4
1280.2.a.n.1.2		2	48.11	even	4
1280.2.a.o.1.2		2	48.29	odd	4
1440.2.k.e.721.1		4	4.3	odd	2
1440.2.k.e.721.3		4	8.3	odd	2
1800.2.d.l.1549.3		4	40.13	odd	4
1800.2.d.l.1549.4		4	5.2	odd	4
1800.2.d.p.1549.1		4	5.3	odd	4
1800.2.d.p.1549.2		4	40.37	odd	4
1800.2.k.j.901.1		4	40.29	even	2
1800.2.k.j.901.2		4	5.4	even	2
6400.2.a.z.1.1		2	240.29	odd	4
6400.2.a.be.1.1		2	240.59	even	4
6400.2.a.ce.1.2		2	240.149	odd	4
6400.2.a.cj.1.2		2	240.179	even	4
7200.2.d.n.2449.2		4	20.7	even	4
7200.2.d.n.2449.3		4	40.3	even	4
7200.2.d.o.2449.2		4	40.27	even	4
7200.2.d.o.2449.3		4	20.3	even	4
7200.2.k.j.3601.3		4	40.19	odd	2
7200.2.k.j.3601.4		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} -1.00000i q^{5} +0.732051 q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} -1.00000i q^{5} +0.732051 q^{7} +(2.00000 - 2.00000i) q^{8} +(-0.366025 - 1.36603i) q^{10} -2.00000i q^{11} +3.46410i q^{13} +(1.00000 - 0.267949i) q^{14} +(2.00000 - 3.46410i) q^{16} -3.46410 q^{17} -0.535898i q^{19} +(-1.00000 - 1.73205i) q^{20} +(-0.732051 - 2.73205i) q^{22} +6.19615 q^{23} -1.00000 q^{25} +(1.26795 + 4.73205i) q^{26} +(1.26795 - 0.732051i) q^{28} +6.92820i q^{29} -5.46410 q^{31} +(1.46410 - 5.46410i) q^{32} +(-4.73205 + 1.26795i) q^{34} -0.732051i q^{35} +2.00000i q^{37} +(-0.196152 - 0.732051i) q^{38} +(-2.00000 - 2.00000i) q^{40} -1.46410 q^{41} +5.26795i q^{43} +(-2.00000 - 3.46410i) q^{44} +(8.46410 - 2.26795i) q^{46} -3.26795 q^{47} -6.46410 q^{49} +(-1.36603 + 0.366025i) q^{50} +(3.46410 + 6.00000i) q^{52} +11.4641i q^{53} -2.00000 q^{55} +(1.46410 - 1.46410i) q^{56} +(2.53590 + 9.46410i) q^{58} -7.46410i q^{59} +8.92820i q^{61} +(-7.46410 + 2.00000i) q^{62} -8.00000i q^{64} +3.46410 q^{65} -10.7321i q^{67} +(-6.00000 + 3.46410i) q^{68} +(-0.267949 - 1.00000i) q^{70} -5.46410 q^{71} +7.46410 q^{73} +(0.732051 + 2.73205i) q^{74} +(-0.535898 - 0.928203i) q^{76} -1.46410i q^{77} -1.07180 q^{79} +(-3.46410 - 2.00000i) q^{80} +(-2.00000 + 0.535898i) q^{82} +1.26795i q^{83} +3.46410i q^{85} +(1.92820 + 7.19615i) q^{86} +(-4.00000 - 4.00000i) q^{88} -8.92820 q^{89} +2.53590i q^{91} +(10.7321 - 6.19615i) q^{92} +(-4.46410 + 1.19615i) q^{94} -0.535898 q^{95} -14.3923 q^{97} +(-8.83013 + 2.36603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^7 + 8 * q^8	\( 4 q + 2 q^{2} - 4 q^{7} + 8 q^{8} + 2 q^{10} + 4 q^{14} + 8 q^{16} - 4 q^{20} + 4 q^{22} + 4 q^{23} - 4 q^{25} + 12 q^{26} + 12 q^{28} - 8 q^{31} - 8 q^{32} - 12 q^{34} + 20 q^{38} - 8 q^{40} + 8 q^{41} - 8 q^{44} + 20 q^{46} - 20 q^{47} - 12 q^{49} - 2 q^{50} - 8 q^{55} - 8 q^{56} + 24 q^{58} - 16 q^{62} - 24 q^{68} - 8 q^{70} - 8 q^{71} + 16 q^{73} - 4 q^{74} - 16 q^{76} - 32 q^{79} - 8 q^{82} - 20 q^{86} - 16 q^{88} - 8 q^{89} + 36 q^{92} - 4 q^{94} - 16 q^{95} - 16 q^{97} - 18 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^7 + 8 * q^8 + 2 * q^10 + 4 * q^14 + 8 * q^16 - 4 * q^20 + 4 * q^22 + 4 * q^23 - 4 * q^25 + 12 * q^26 + 12 * q^28 - 8 * q^31 - 8 * q^32 - 12 * q^34 + 20 * q^38 - 8 * q^40 + 8 * q^41 - 8 * q^44 + 20 * q^46 - 20 * q^47 - 12 * q^49 - 2 * q^50 - 8 * q^55 - 8 * q^56 + 24 * q^58 - 16 * q^62 - 24 * q^68 - 8 * q^70 - 8 * q^71 + 16 * q^73 - 4 * q^74 - 16 * q^76 - 32 * q^79 - 8 * q^82 - 20 * q^86 - 16 * q^88 - 8 * q^89 + 36 * q^92 - 4 * q^94 - 16 * q^95 - 16 * q^97 - 18 * q^98

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