LMFDB - Embedded newform 810.2.f.b.647.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [810,2,Mod(323,810)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("810.323"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(810, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	810.647
Dual form			810.2.f.b.323.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.41421 + 1.73205i) q^{5} +(3.22474 + 3.22474i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.224745 - 2.22474i) q^{10} +0.635674i q^{11} +(2.44949 - 2.44949i) q^{13} -4.56048 q^{14} -1.00000 q^{16} +(0.317837 - 0.317837i) q^{17} +6.44949i q^{19} +(1.73205 + 1.41421i) q^{20} +(-0.449490 - 0.449490i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.00000 - 4.89898i) q^{25} +3.46410i q^{26} +(3.22474 - 3.22474i) q^{28} +0.317837 q^{29} +0.449490 q^{31} +(0.707107 - 0.707107i) q^{32} +0.449490i q^{34} +(-10.1459 + 1.02494i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-4.56048 - 4.56048i) q^{38} +(-2.22474 + 0.224745i) q^{40} +7.38891i q^{41} +(-2.44949 + 2.44949i) q^{43} +0.635674 q^{44} +1.00000 q^{46} +(-6.36396 + 6.36396i) q^{47} +13.7980i q^{49} +(4.17121 + 2.75699i) q^{50} +(-2.44949 - 2.44949i) q^{52} +(3.78194 + 3.78194i) q^{53} +(-1.10102 - 0.898979i) q^{55} +4.56048i q^{56} +(-0.224745 + 0.224745i) q^{58} +8.97809 q^{59} -0.550510 q^{61} +(-0.317837 + 0.317837i) q^{62} +1.00000i q^{64} +(0.778539 + 7.70674i) q^{65} +(-4.67423 - 4.67423i) q^{67} +(-0.317837 - 0.317837i) q^{68} +(6.44949 - 7.89898i) q^{70} +6.29253i q^{71} +(-6.89898 + 6.89898i) q^{73} +4.24264 q^{74} +6.44949 q^{76} +(-2.04989 + 2.04989i) q^{77} +2.44949i q^{79} +(1.41421 - 1.73205i) q^{80} +(-5.22474 - 5.22474i) q^{82} +(-3.85337 - 3.85337i) q^{83} +(0.101021 + 1.00000i) q^{85} -3.46410i q^{86} +(-0.449490 + 0.449490i) q^{88} -8.02458 q^{89} +15.7980 q^{91} +(-0.707107 + 0.707107i) q^{92} -9.00000i q^{94} +(-11.1708 - 9.12096i) q^{95} +(1.89898 + 1.89898i) q^{97} +(-9.75663 - 9.75663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{7} + 8 q^{10} - 8 q^{16} + 16 q^{22} - 8 q^{25} + 16 q^{28} - 16 q^{31} - 24 q^{37} - 8 q^{40} + 8 q^{46} - 48 q^{55} + 8 q^{58} - 24 q^{61} - 8 q^{67} + 32 q^{70} - 16 q^{73} + 32 q^{76} - 32 q^{82}+ \cdots - 24 q^{97}+O(q^{100}) $ 8 * q + 16 * q^7 + 8 * q^10 - 8 * q^16 + 16 * q^22 - 8 * q^25 + 16 * q^28 - 16 * q^31 - 24 * q^37 - 8 * q^40 + 8 * q^46 - 48 * q^55 + 8 * q^58 - 24 * q^61 - 8 * q^67 + 32 * q^70 - 16 * q^73 + 32 * q^76 - 32 * q^82 + 40 * q^85 + 16 * q^88 + 48 * q^91 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.41421	+	1.73205i	−0.632456	+	0.774597i
$5$	−1.41421	+	1.73205i	−0.632456	+	0.774597i
$6$		0			0
$7$	3.22474	+	3.22474i	1.21884	+	1.21884i	0.968039	+	0.250800i	$0.0806937\pi$
$7$	3.22474	+	3.22474i	1.21884	+	1.21884i	0.250800	+	0.968039i	$0.419306\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−0.224745	−	2.22474i	−0.0710706	−	0.703526i
$11$			0.635674i			0.191663i	0.995398	+	0.0958315i	$0.0305510\pi$
$11$			0.635674i			0.191663i	−0.995398	+	0.0958315i	$0.969449\pi$
$12$		0			0
$13$	2.44949	−	2.44949i	0.679366	−	0.679366i	−0.280491	−	0.959857i	$-0.590497\pi$
$13$	2.44949	−	2.44949i	0.679366	−	0.679366i	0.959857	+	0.280491i	$0.0904971\pi$
$14$	−4.56048			−1.21884
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.317837	−	0.317837i	0.0770869	−	0.0770869i	−0.667512	−	0.744599i	$-0.732641\pi$
$17$	0.317837	−	0.317837i	0.0770869	−	0.0770869i	0.744599	+	0.667512i	$0.232641\pi$
$18$		0			0
$19$			6.44949i			1.47961i	0.672819	+	0.739807i	$0.265083\pi$
$19$			6.44949i			1.47961i	−0.672819	+	0.739807i	$0.734917\pi$
$20$	1.73205	+	1.41421i	0.387298	+	0.316228i
$21$		0			0
$22$	−0.449490	−	0.449490i	−0.0958315	−	0.0958315i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i	0.629532	−	0.776974i	$-0.283247\pi$
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i	−0.776974	+	0.629532i	$0.783247\pi$
$24$		0			0
$25$	−1.00000	−	4.89898i	−0.200000	−	0.979796i
$26$			3.46410i			0.679366i
$27$		0			0
$28$	3.22474	−	3.22474i	0.609419	−	0.609419i
$29$	0.317837			0.0590209			0.0295104	−	0.999564i	$-0.490605\pi$
$29$	0.317837			0.0590209			0.0295104	+	0.999564i	$0.490605\pi$
$30$		0			0
$31$	0.449490			0.0807307			0.0403654	−	0.999185i	$-0.487148\pi$
$31$	0.449490			0.0807307			0.0403654	+	0.999185i	$0.487148\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			0.449490i			0.0770869i
$35$	−10.1459	+	1.02494i	−1.71497	+	0.173247i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$	−4.56048	−	4.56048i	−0.739807	−	0.739807i
$39$		0			0
$40$	−2.22474	+	0.224745i	−0.351763	+	0.0355353i
$41$			7.38891i			1.15395i	0.816761	+	0.576977i	$0.195768\pi$
$41$			7.38891i			1.15395i	−0.816761	+	0.576977i	$0.804232\pi$
$42$		0			0
$43$	−2.44949	+	2.44949i	−0.373544	+	0.373544i	−0.868766	−	0.495222i	$-0.835087\pi$
$43$	−2.44949	+	2.44949i	−0.373544	+	0.373544i	0.495222	+	0.868766i	$0.335087\pi$
$44$	0.635674			0.0958315
$45$		0			0
$46$	1.00000			0.147442
$47$	−6.36396	+	6.36396i	−0.928279	+	0.928279i	−0.997595	−	0.0693157i	$-0.977918\pi$
$47$	−6.36396	+	6.36396i	−0.928279	+	0.928279i	0.0693157	+	0.997595i	$0.477918\pi$
$48$		0			0
$49$			13.7980i			1.97114i
$50$	4.17121	+	2.75699i	0.589898	+	0.389898i
$51$		0			0
$52$	−2.44949	−	2.44949i	−0.339683	−	0.339683i
$53$	3.78194	+	3.78194i	0.519489	+	0.519489i	0.917417	−	0.397928i	$-0.130270\pi$
$53$	3.78194	+	3.78194i	0.519489	+	0.519489i	−0.397928	+	0.917417i	$0.630270\pi$
$54$		0			0
$55$	−1.10102	−	0.898979i	−0.148462	−	0.121218i
$56$			4.56048i			0.609419i
$57$		0			0
$58$	−0.224745	+	0.224745i	−0.0295104	+	0.0295104i
$59$	8.97809			1.16885			0.584424	−	0.811448i	$-0.301321\pi$
$59$	8.97809			1.16885			0.584424	+	0.811448i	$0.301321\pi$
$60$		0			0
$61$	−0.550510			−0.0704856			−0.0352428	−	0.999379i	$-0.511220\pi$
$61$	−0.550510			−0.0704856			−0.0352428	+	0.999379i	$0.511220\pi$
$62$	−0.317837	+	0.317837i	−0.0403654	+	0.0403654i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	0.778539	+	7.70674i	0.0965659	+	0.955904i
$66$		0			0
$67$	−4.67423	−	4.67423i	−0.571049	−	0.571049i	0.361373	−	0.932421i	$-0.382308\pi$
$67$	−4.67423	−	4.67423i	−0.571049	−	0.571049i	−0.932421	+	0.361373i	$0.882308\pi$
$68$	−0.317837	−	0.317837i	−0.0385434	−	0.0385434i
$69$		0			0
$70$	6.44949	−	7.89898i	0.770861	−	0.944109i
$71$			6.29253i			0.746786i	0.927673	+	0.373393i	$0.121806\pi$
$71$			6.29253i			0.746786i	−0.927673	+	0.373393i	$0.878194\pi$
$72$		0			0
$73$	−6.89898	+	6.89898i	−0.807464	+	0.807464i	−0.984249	−	0.176785i	$-0.943430\pi$
$73$	−6.89898	+	6.89898i	−0.807464	+	0.807464i	0.176785	+	0.984249i	$0.443430\pi$
$74$	4.24264			0.493197
$75$		0			0
$76$	6.44949			0.739807
$77$	−2.04989	+	2.04989i	−0.233606	+	0.233606i
$78$		0			0
$79$			2.44949i			0.275589i	0.990461	+	0.137795i	$0.0440014\pi$
$79$			2.44949i			0.275589i	−0.990461	+	0.137795i	$0.955999\pi$
$80$	1.41421	−	1.73205i	0.158114	−	0.193649i
$81$		0			0
$82$	−5.22474	−	5.22474i	−0.576977	−	0.576977i
$83$	−3.85337	−	3.85337i	−0.422962	−	0.422962i	0.463260	−	0.886222i	$-0.346680\pi$
$83$	−3.85337	−	3.85337i	−0.422962	−	0.422962i	−0.886222	+	0.463260i	$0.846680\pi$
$84$		0			0
$85$	0.101021	+	1.00000i	0.0109572	+	0.108465i
$86$		−	3.46410i		−	0.373544i
$87$		0			0
$88$	−0.449490	+	0.449490i	−0.0479158	+	0.0479158i
$89$	−8.02458			−0.850604			−0.425302	−	0.905052i	$-0.639832\pi$
$89$	−8.02458			−0.850604			−0.425302	+	0.905052i	$0.639832\pi$
$90$		0			0
$91$	15.7980			1.65608
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$		0			0
$94$		−	9.00000i		−	0.928279i
$95$	−11.1708	−	9.12096i	−1.14610	−	0.935790i
$96$		0			0
$97$	1.89898	+	1.89898i	0.192812	+	0.192812i	0.796910	−	0.604098i	$-0.206466\pi$
$97$	1.89898	+	1.89898i	0.192812	+	0.192812i	−0.604098	+	0.796910i	$0.706466\pi$
$98$	−9.75663	−	9.75663i	−0.985568	−	0.985568i
$99$		0			0
$100$	−4.89898	+	1.00000i	−0.489898	+	0.100000i
$101$		−	12.5851i		−	1.25226i	−0.779719	−	0.626130i	$-0.784638\pi$
$101$		−	12.5851i		−	1.25226i	0.779719	−	0.626130i	$-0.215362\pi$
$102$		0			0
$103$	−6.89898	+	6.89898i	−0.679777	+	0.679777i	−0.959950	−	0.280173i	$-0.909608\pi$
$103$	−6.89898	+	6.89898i	−0.679777	+	0.679777i	0.280173	+	0.959950i	$0.409608\pi$
$104$	3.46410			0.339683
$105$		0			0
$106$	−5.34847			−0.519489
$107$	13.6100	−	13.6100i	1.31573	−	1.31573i	0.398606	−	0.917122i	$-0.369494\pi$
$107$	13.6100	−	13.6100i	1.31573	−	1.31573i	0.917122	−	0.398606i	$-0.130506\pi$
$108$		0			0
$109$		−	5.65153i		−	0.541318i	−0.962675	−	0.270659i	$-0.912758\pi$
$109$		−	5.65153i		−	0.541318i	0.962675	−	0.270659i	$-0.0872417\pi$
$110$	1.41421	−	0.142865i	0.134840	−	0.0136216i
$111$		0			0
$112$	−3.22474	−	3.22474i	−0.304710	−	0.304710i
$113$	−4.09978	−	4.09978i	−0.385674	−	0.385674i	0.487467	−	0.873141i	$-0.337921\pi$
$113$	−4.09978	−	4.09978i	−0.385674	−	0.385674i	−0.873141	+	0.487467i	$0.837921\pi$
$114$		0			0
$115$	2.22474	−	0.224745i	0.207459	−	0.0209576i
$116$		−	0.317837i		−	0.0295104i
$117$		0			0
$118$	−6.34847	+	6.34847i	−0.584424	+	0.584424i
$119$	2.04989			0.187913
$120$		0			0
$121$	10.5959			0.963265
$122$	0.389270	−	0.389270i	0.0352428	−	0.0352428i
$123$		0			0
$124$		−	0.449490i		−	0.0403654i
$125$	9.89949	+	5.19615i	0.885438	+	0.464758i
$126$		0			0
$127$	1.87628	+	1.87628i	0.166493	+	0.166493i	0.785436	−	0.618943i	$-0.212439\pi$
$127$	1.87628	+	1.87628i	0.166493	+	0.166493i	−0.618943	+	0.785436i	$0.712439\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−6.00000	−	4.89898i	−0.526235	−	0.429669i
$131$		−	3.60697i		−	0.315142i	−0.987508	−	0.157571i	$-0.949634\pi$
$131$		−	3.60697i		−	0.315142i	0.987508	−	0.157571i	$-0.0503663\pi$
$132$		0			0
$133$	−20.7980	+	20.7980i	−1.80341	+	1.80341i
$134$	6.61037			0.571049
$135$		0			0
$136$	0.449490			0.0385434
$137$	15.4135	−	15.4135i	1.31686	−	1.31686i	0.400617	−	0.916245i	$-0.368796\pi$
$137$	15.4135	−	15.4135i	1.31686	−	1.31686i	0.916245	−	0.400617i	$-0.131204\pi$
$138$		0			0
$139$			3.10102i			0.263025i	0.991315	+	0.131513i	$0.0419834\pi$
$139$			3.10102i			0.263025i	−0.991315	+	0.131513i	$0.958017\pi$
$140$	1.02494	+	10.1459i	0.0866236	+	0.857485i
$141$		0			0
$142$	−4.44949	−	4.44949i	−0.373393	−	0.373393i
$143$	1.55708	+	1.55708i	0.130209	+	0.130209i
$144$		0			0
$145$	−0.449490	+	0.550510i	−0.0373281	+	0.0457174i
$146$		−	9.75663i		−	0.807464i
$147$		0			0
$148$	−3.00000	+	3.00000i	−0.246598	+	0.246598i
$149$	−4.41761			−0.361905			−0.180952	−	0.983492i	$-0.557918\pi$
$149$	−4.41761			−0.361905			−0.180952	+	0.983492i	$0.557918\pi$
$150$		0			0
$151$	17.5959			1.43194			0.715968	−	0.698133i	$-0.245986\pi$
$151$	17.5959			1.43194			0.715968	+	0.698133i	$0.245986\pi$
$152$	−4.56048	+	4.56048i	−0.369904	+	0.369904i
$153$		0			0
$154$		−	2.89898i		−	0.233606i
$155$	−0.635674	+	0.778539i	−0.0510586	+	0.0625338i
$156$		0			0
$157$	−10.3485	−	10.3485i	−0.825898	−	0.825898i	0.161049	−	0.986946i	$-0.448512\pi$
$157$	−10.3485	−	10.3485i	−0.825898	−	0.825898i	−0.986946	+	0.161049i	$0.948512\pi$
$158$	−1.73205	−	1.73205i	−0.137795	−	0.137795i
$159$		0			0
$160$	0.224745	+	2.22474i	0.0177676	+	0.175882i
$161$		−	4.56048i		−	0.359416i
$162$		0			0
$163$	4.44949	−	4.44949i	0.348511	−	0.348511i	−0.511044	−	0.859555i	$-0.670741\pi$
$163$	4.44949	−	4.44949i	0.348511	−	0.348511i	0.859555	+	0.511044i	$0.170741\pi$
$164$	7.38891			0.576977
$165$		0			0
$166$	5.44949			0.422962
$167$	6.22110	−	6.22110i	0.481403	−	0.481403i	−0.424177	−	0.905579i	$-0.639436\pi$
$167$	6.22110	−	6.22110i	0.481403	−	0.481403i	0.905579	+	0.424177i	$0.139436\pi$
$168$		0			0
$169$			1.00000i			0.0769231i
$170$	−0.778539	−	0.635674i	−0.0597112	−	0.0487540i
$171$		0			0
$172$	2.44949	+	2.44949i	0.186772	+	0.186772i
$173$	9.12096	+	9.12096i	0.693453	+	0.693453i	0.962990	−	0.269537i	$-0.0868705\pi$
$173$	9.12096	+	9.12096i	0.693453	+	0.693453i	−0.269537	+	0.962990i	$0.586871\pi$
$174$		0			0
$175$	12.5732	−	19.0227i	0.950446	−	1.43798i
$176$		−	0.635674i		−	0.0479158i
$177$		0			0
$178$	5.67423	−	5.67423i	0.425302	−	0.425302i
$179$	10.6780			0.798114			0.399057	−	0.916926i	$-0.369338\pi$
$179$	10.6780			0.798114			0.399057	+	0.916926i	$0.369338\pi$
$180$		0			0
$181$	−15.4495			−1.14835			−0.574176	−	0.818732i	$-0.694677\pi$
$181$	−15.4495			−1.14835			−0.574176	+	0.818732i	$0.694677\pi$
$182$	−11.1708	+	11.1708i	−0.828038	+	0.828038i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	9.43879	−	0.953512i	0.693954	−	0.0701036i
$186$		0			0
$187$	0.202041	+	0.202041i	0.0147747	+	0.0147747i
$188$	6.36396	+	6.36396i	0.464140	+	0.464140i
$189$		0			0
$190$	14.3485	−	1.44949i	1.04095	−	0.105157i
$191$			17.4634i			1.26361i	0.775129	+	0.631803i	$0.217685\pi$
$191$			17.4634i			1.26361i	−0.775129	+	0.631803i	$0.782315\pi$
$192$		0			0
$193$	−12.2474	+	12.2474i	−0.881591	+	0.881591i	−0.993696	−	0.112106i	$-0.964240\pi$
$193$	−12.2474	+	12.2474i	−0.881591	+	0.881591i	0.112106	+	0.993696i	$0.464240\pi$
$194$	−2.68556			−0.192812
$195$		0			0
$196$	13.7980			0.985568
$197$	6.92820	−	6.92820i	0.493614	−	0.493614i	−0.415829	−	0.909443i	$-0.636508\pi$
$197$	6.92820	−	6.92820i	0.493614	−	0.493614i	0.909443	+	0.415829i	$0.136508\pi$
$198$		0			0
$199$			8.44949i			0.598968i	0.954101	+	0.299484i	$0.0968146\pi$
$199$			8.44949i			0.598968i	−0.954101	+	0.299484i	$0.903185\pi$
$200$	2.75699	−	4.17121i	0.194949	−	0.294949i
$201$		0			0
$202$	8.89898	+	8.89898i	0.626130	+	0.626130i
$203$	1.02494	+	1.02494i	0.0719370	+	0.0719370i
$204$		0			0
$205$	−12.7980	−	10.4495i	−0.893848	−	0.729824i
$206$		−	9.75663i		−	0.679777i
$207$		0			0
$208$	−2.44949	+	2.44949i	−0.169842	+	0.169842i
$209$	−4.09978			−0.283587
$210$		0			0
$211$	9.10102			0.626540			0.313270	−	0.949664i	$-0.398576\pi$
$211$	9.10102			0.626540			0.313270	+	0.949664i	$0.398576\pi$
$212$	3.78194	−	3.78194i	0.259745	−	0.259745i
$213$		0			0
$214$			19.2474i			1.31573i
$215$	−0.778539	−	7.70674i	−0.0530959	−	0.525595i
$216$		0			0
$217$	1.44949	+	1.44949i	0.0983978	+	0.0983978i
$218$	3.99624	+	3.99624i	0.270659	+	0.270659i
$219$		0			0
$220$	−0.898979	+	1.10102i	−0.0606092	+	0.0742308i
$221$		−	1.55708i		−	0.104740i
$222$		0			0
$223$	18.1237	−	18.1237i	1.21365	−	1.21365i	0.243838	−	0.969816i	$-0.421593\pi$
$223$	18.1237	−	18.1237i	1.21365	−	1.21365i	0.969816	−	0.243838i	$-0.0784067\pi$
$224$	4.56048			0.304710
$225$		0			0
$226$	5.79796			0.385674
$227$	17.6062	−	17.6062i	1.16857	−	1.16857i	0.186021	−	0.982546i	$-0.440441\pi$
$227$	17.6062	−	17.6062i	1.16857	−	1.16857i	0.982546	−	0.186021i	$-0.0595593\pi$
$228$		0			0
$229$		−	1.65153i		−	0.109136i	−0.998510	−	0.0545681i	$-0.982622\pi$
$229$		−	1.65153i		−	0.109136i	0.998510	−	0.0545681i	$-0.0173782\pi$
$230$	−1.41421	+	1.73205i	−0.0932505	+	0.114208i
$231$		0			0
$232$	0.224745	+	0.224745i	0.0147552	+	0.0147552i
$233$	−14.4600	−	14.4600i	−0.947304	−	0.947304i	0.0513751	−	0.998679i	$-0.483640\pi$
$233$	−14.4600	−	14.4600i	−0.947304	−	0.947304i	−0.998679	+	0.0513751i	$0.983640\pi$
$234$		0			0
$235$	−2.02270	−	20.0227i	−0.131947	−	1.30614i
$236$		−	8.97809i		−	0.584424i
$237$		0			0
$238$	−1.44949	+	1.44949i	−0.0939565	+	0.0939565i
$239$	16.9706			1.09773			0.548867	−	0.835910i	$-0.315059\pi$
$239$	16.9706			1.09773			0.548867	+	0.835910i	$0.315059\pi$
$240$		0			0
$241$	19.0000			1.22390			0.611949	−	0.790897i	$-0.290386\pi$
$241$	19.0000			1.22390			0.611949	+	0.790897i	$0.290386\pi$
$242$	−7.49245	+	7.49245i	−0.481633	+	0.481633i
$243$		0			0
$244$			0.550510i			0.0352428i
$245$	−23.8988	−	19.5133i	−1.52684	−	1.24666i
$246$		0			0
$247$	15.7980	+	15.7980i	1.00520	+	1.00520i
$248$	0.317837	+	0.317837i	0.0201827	+	0.0201827i
$249$		0			0
$250$	−10.6742	+	3.32577i	−0.675098	+	0.210340i
$251$			2.68556i			0.169511i	0.996402	+	0.0847556i	$0.0270110\pi$
$251$			2.68556i			0.169511i	−0.996402	+	0.0847556i	$0.972989\pi$
$252$		0			0
$253$	0.449490	−	0.449490i	0.0282592	−	0.0282592i
$254$	−2.65345			−0.166493
$255$		0			0
$256$	1.00000			0.0625000
$257$	12.7600	−	12.7600i	0.795949	−	0.795949i	−0.186505	−	0.982454i	$-0.559716\pi$
$257$	12.7600	−	12.7600i	0.795949	−	0.795949i	0.982454	+	0.186505i	$0.0597161\pi$
$258$		0			0
$259$		−	19.3485i		−	1.20226i
$260$	7.70674	−	0.778539i	0.477952	−	0.0482829i
$261$		0			0
$262$	2.55051	+	2.55051i	0.157571	+	0.157571i
$263$	−11.8065	−	11.8065i	−0.728021	−	0.728021i	0.242204	−	0.970225i	$-0.422130\pi$
$263$	−11.8065	−	11.8065i	−0.728021	−	0.728021i	−0.970225	+	0.242204i	$0.922130\pi$
$264$		0			0
$265$	−11.8990	+	1.20204i	−0.730948	+	0.0738408i
$266$		−	29.4128i		−	1.80341i
$267$		0			0
$268$	−4.67423	+	4.67423i	−0.285524	+	0.285524i
$269$	−15.0956			−0.920398			−0.460199	−	0.887816i	$-0.652222\pi$
$269$	−15.0956			−0.920398			−0.460199	+	0.887816i	$0.652222\pi$
$270$		0			0
$271$	28.0454			1.70364			0.851819	−	0.523837i	$-0.175500\pi$
$271$	28.0454			1.70364			0.851819	+	0.523837i	$0.175500\pi$
$272$	−0.317837	+	0.317837i	−0.0192717	+	0.0192717i
$273$		0			0
$274$			21.7980i			1.31686i
$275$	3.11416	−	0.635674i	0.187791	−	0.0383326i
$276$		0			0
$277$	−19.8990	−	19.8990i	−1.19561	−	1.19561i	−0.975467	−	0.220147i	$-0.929346\pi$
$277$	−19.8990	−	19.8990i	−1.19561	−	1.19561i	−0.220147	−	0.975467i	$-0.570654\pi$
$278$	−2.19275	−	2.19275i	−0.131513	−	0.131513i
$279$		0			0
$280$	−7.89898	−	6.44949i	−0.472054	−	0.385431i
$281$			17.1455i			1.02282i	0.859338	+	0.511408i	$0.170876\pi$
$281$			17.1455i			1.02282i	−0.859338	+	0.511408i	$0.829124\pi$
$282$		0			0
$283$	17.1237	−	17.1237i	1.01790	−	1.01790i	0.0180629	−	0.999837i	$-0.494250\pi$
$283$	17.1237	−	17.1237i	1.01790	−	1.01790i	0.999837	−	0.0180629i	$-0.00574991\pi$
$284$	6.29253			0.373393
$285$		0			0
$286$	−2.20204			−0.130209
$287$	−23.8273	+	23.8273i	−1.40648	+	1.40648i
$288$		0			0
$289$			16.7980i			0.988115i
$290$	−0.0714323	−	0.707107i	−0.00419465	−	0.0415227i
$291$		0			0
$292$	6.89898	+	6.89898i	0.403732	+	0.403732i
$293$	15.5885	+	15.5885i	0.910687	+	0.910687i	0.996326	−	0.0856388i	$-0.0272931\pi$
$293$	15.5885	+	15.5885i	0.910687	+	0.910687i	−0.0856388	+	0.996326i	$0.527293\pi$
$294$		0			0
$295$	−12.6969	+	15.5505i	−0.739244	+	0.905386i
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	3.12372	−	3.12372i	0.180952	−	0.180952i
$299$	−3.46410			−0.200334
$300$		0			0
$301$	−15.7980			−0.910579
$302$	−12.4422	+	12.4422i	−0.715968	+	0.715968i
$303$		0			0
$304$		−	6.44949i		−	0.369904i
$305$	0.778539	−	0.953512i	0.0445790	−	0.0545979i
$306$		0			0
$307$	−6.67423	−	6.67423i	−0.380919	−	0.380919i	0.490514	−	0.871433i	$-0.336809\pi$
$307$	−6.67423	−	6.67423i	−0.380919	−	0.380919i	−0.871433	+	0.490514i	$0.836809\pi$
$308$	2.04989	+	2.04989i	0.116803	+	0.116803i
$309$		0			0
$310$	−0.101021	−	1.00000i	−0.00573758	−	0.0567962i
$311$			27.5057i			1.55971i	0.625962	+	0.779853i	$0.284706\pi$
$311$			27.5057i			1.55971i	−0.625962	+	0.779853i	$0.715294\pi$
$312$		0			0
$313$	8.44949	−	8.44949i	0.477593	−	0.477593i	−0.426768	−	0.904361i	$-0.640348\pi$
$313$	8.44949	−	8.44949i	0.477593	−	0.477593i	0.904361	+	0.426768i	$0.140348\pi$
$314$	14.6349			0.825898
$315$		0			0
$316$	2.44949			0.137795
$317$	−7.70674	+	7.70674i	−0.432854	+	0.432854i	−0.889598	−	0.456744i	$-0.849015\pi$
$317$	−7.70674	+	7.70674i	−0.432854	+	0.432854i	0.456744	+	0.889598i	$0.349015\pi$
$318$		0			0
$319$			0.202041i			0.0113121i
$320$	−1.73205	−	1.41421i	−0.0968246	−	0.0790569i
$321$		0			0
$322$	3.22474	+	3.22474i	0.179708	+	0.179708i
$323$	2.04989	+	2.04989i	0.114059	+	0.114059i
$324$		0			0
$325$	−14.4495	−	9.55051i	−0.801513	−	0.529767i
$326$			6.29253i			0.348511i
$327$		0			0
$328$	−5.22474	+	5.22474i	−0.288488	+	0.288488i
$329$	−41.0443			−2.26285
$330$		0			0
$331$	0.449490			0.0247062			0.0123531	−	0.999924i	$-0.496068\pi$
$331$	0.449490			0.0247062			0.0123531	+	0.999924i	$0.496068\pi$
$332$	−3.85337	+	3.85337i	−0.211481	+	0.211481i
$333$		0			0
$334$			8.79796i			0.481403i
$335$	14.7064	−	1.48565i	0.803495	−	0.0811695i
$336$		0			0
$337$	−2.20204	−	2.20204i	−0.119953	−	0.119953i	0.644582	−	0.764535i	$-0.277031\pi$
$337$	−2.20204	−	2.20204i	−0.119953	−	0.119953i	−0.764535	+	0.644582i	$0.777031\pi$
$338$	−0.707107	−	0.707107i	−0.0384615	−	0.0384615i
$339$		0			0
$340$	1.00000	−	0.101021i	0.0542326	−	0.00547861i
$341$			0.285729i			0.0154731i
$342$		0			0
$343$	−21.9217	+	21.9217i	−1.18366	+	1.18366i
$344$	−3.46410			−0.186772
$345$		0			0
$346$	−12.8990			−0.693453
$347$	−16.8277	+	16.8277i	−0.903358	+	0.903358i	−0.995725	−	0.0923669i	$-0.970557\pi$
$347$	−16.8277	+	16.8277i	−0.903358	+	0.903358i	0.0923669	+	0.995725i	$0.470557\pi$
$348$		0			0
$349$			29.0454i			1.55477i	0.629028	+	0.777383i	$0.283453\pi$
$349$			29.0454i			1.55477i	−0.629028	+	0.777383i	$0.716547\pi$
$350$	4.56048	+	22.3417i	0.243768	+	1.19421i
$351$		0			0
$352$	0.449490	+	0.449490i	0.0239579	+	0.0239579i
$353$	24.2487	+	24.2487i	1.29063	+	1.29063i	0.934398	+	0.356231i	$0.115938\pi$
$353$	24.2487	+	24.2487i	1.29063	+	1.29063i	0.356231	+	0.934398i	$0.384062\pi$
$354$		0			0
$355$	−10.8990	−	8.89898i	−0.578458	−	0.472309i
$356$			8.02458i			0.425302i
$357$		0			0
$358$	−7.55051	+	7.55051i	−0.399057	+	0.399057i
$359$	3.32124			0.175288			0.0876441	−	0.996152i	$-0.472066\pi$
$359$	3.32124			0.175288			0.0876441	+	0.996152i	$0.472066\pi$
$360$		0			0
$361$	−22.5959			−1.18926
$362$	10.9244	−	10.9244i	0.574176	−	0.574176i
$363$		0			0
$364$		−	15.7980i		−	0.828038i
$365$	−2.19275	−	21.7060i	−0.114774	−	1.13614i
$366$		0			0
$367$	−2.89898	−	2.89898i	−0.151325	−	0.151325i	0.627384	−	0.778710i	$-0.284126\pi$
$367$	−2.89898	−	2.89898i	−0.151325	−	0.151325i	−0.778710	+	0.627384i	$0.784126\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$		0			0
$370$	−6.00000	+	7.34847i	−0.311925	+	0.382029i
$371$			24.3916i			1.26635i
$372$		0			0
$373$	−0.348469	+	0.348469i	−0.0180431	+	0.0180431i	−0.716071	−	0.698028i	$-0.754061\pi$
$373$	−0.348469	+	0.348469i	−0.0180431	+	0.0180431i	0.698028	+	0.716071i	$0.254061\pi$
$374$	−0.285729			−0.0147747
$375$		0			0
$376$	−9.00000			−0.464140
$377$	0.778539	−	0.778539i	0.0400968	−	0.0400968i
$378$		0			0
$379$		−	21.3485i		−	1.09660i	−0.836283	−	0.548299i	$-0.815276\pi$
$379$		−	21.3485i		−	1.09660i	0.836283	−	0.548299i	$-0.184724\pi$
$380$	−9.12096	+	11.1708i	−0.467895	+	0.573052i
$381$		0			0
$382$	−12.3485	−	12.3485i	−0.631803	−	0.631803i
$383$	−5.79972	−	5.79972i	−0.296352	−	0.296352i	0.543231	−	0.839583i	$-0.317201\pi$
$383$	−5.79972	−	5.79972i	−0.296352	−	0.296352i	−0.839583	+	0.543231i	$0.817201\pi$
$384$		0			0
$385$	−0.651531	−	6.44949i	−0.0332051	−	0.328696i
$386$		−	17.3205i		−	0.881591i
$387$		0			0
$388$	1.89898	−	1.89898i	0.0964061	−	0.0964061i
$389$	−36.8017			−1.86592			−0.932959	−	0.359982i	$-0.882783\pi$
$389$	−36.8017			−1.86592			−0.932959	+	0.359982i	$0.882783\pi$
$390$		0			0
$391$	−0.449490			−0.0227317
$392$	−9.75663	+	9.75663i	−0.492784	+	0.492784i
$393$		0			0
$394$			9.79796i			0.493614i
$395$	−4.24264	−	3.46410i	−0.213470	−	0.174298i
$396$		0			0
$397$	10.5505	+	10.5505i	0.529515	+	0.529515i	0.920428	−	0.390913i	$-0.127841\pi$
$397$	10.5505	+	10.5505i	0.529515	+	0.529515i	−0.390913	+	0.920428i	$0.627841\pi$
$398$	−5.97469	−	5.97469i	−0.299484	−	0.299484i
$399$		0			0
$400$	1.00000	+	4.89898i	0.0500000	+	0.244949i
$401$			8.83523i			0.441210i	0.975363	+	0.220605i	$0.0708032\pi$
$401$			8.83523i			0.441210i	−0.975363	+	0.220605i	$0.929197\pi$
$402$		0			0
$403$	1.10102	−	1.10102i	0.0548457	−	0.0548457i
$404$	−12.5851			−0.626130
$405$		0			0
$406$	−1.44949			−0.0719370
$407$	1.90702	−	1.90702i	0.0945276	−	0.0945276i
$408$		0			0
$409$		−	28.8990i		−	1.42896i	−0.699655	−	0.714481i	$-0.746663\pi$
$409$		−	28.8990i		−	1.42896i	0.699655	−	0.714481i	$-0.253337\pi$
$410$	16.4384	−	1.66062i	0.811836	−	0.0820121i
$411$		0			0
$412$	6.89898	+	6.89898i	0.339888	+	0.339888i
$413$	28.9521	+	28.9521i	1.42464	+	1.42464i
$414$		0			0
$415$	12.1237	−	1.22474i	0.595130	−	0.0601204i
$416$		−	3.46410i		−	0.169842i
$417$		0			0
$418$	2.89898	−	2.89898i	0.141794	−	0.141794i
$419$	−5.02118			−0.245301			−0.122650	−	0.992450i	$-0.539139\pi$
$419$	−5.02118			−0.245301			−0.122650	+	0.992450i	$0.539139\pi$
$420$		0			0
$421$	−5.10102			−0.248609			−0.124304	−	0.992244i	$-0.539670\pi$
$421$	−5.10102			−0.248609			−0.124304	+	0.992244i	$0.539670\pi$
$422$	−6.43539	+	6.43539i	−0.313270	+	0.313270i
$423$		0			0
$424$			5.34847i			0.259745i
$425$	−1.87492	−	1.23924i	−0.0909468	−	0.0601120i
$426$		0			0
$427$	−1.77526	−	1.77526i	−0.0859106	−	0.0859106i
$428$	−13.6100	−	13.6100i	−0.657864	−	0.657864i
$429$		0			0
$430$	6.00000	+	4.89898i	0.289346	+	0.236250i
$431$		−	15.5563i		−	0.749323i	−0.927162	−	0.374661i	$-0.877759\pi$
$431$		−	15.5563i		−	0.749323i	0.927162	−	0.374661i	$-0.122241\pi$
$432$		0			0
$433$	13.4495	−	13.4495i	0.646341	−	0.646341i	−0.305766	−	0.952107i	$-0.598912\pi$
$433$	13.4495	−	13.4495i	0.646341	−	0.646341i	0.952107	+	0.305766i	$0.0989124\pi$
$434$	−2.04989			−0.0983978
$435$		0			0
$436$	−5.65153			−0.270659
$437$	4.56048	−	4.56048i	0.218157	−	0.218157i
$438$		0			0
$439$			29.7980i			1.42218i	0.703102	+	0.711089i	$0.251798\pi$
$439$			29.7980i			1.42218i	−0.703102	+	0.711089i	$0.748202\pi$
$440$	−0.142865	−	1.41421i	−0.00681080	−	0.0674200i
$441$		0			0
$442$	1.10102	+	1.10102i	0.0523702	+	0.0523702i
$443$	3.85337	+	3.85337i	0.183079	+	0.183079i	0.792696	−	0.609617i	$-0.208677\pi$
$443$	3.85337	+	3.85337i	0.183079	+	0.183079i	−0.609617	+	0.792696i	$0.708677\pi$
$444$		0			0
$445$	11.3485	−	13.8990i	0.537969	−	0.658875i
$446$			25.6308i			1.21365i
$447$		0			0
$448$	−3.22474	+	3.22474i	−0.152355	+	0.152355i
$449$	0.921404			0.0434837			0.0217419	−	0.999764i	$-0.493079\pi$
$449$	0.921404			0.0434837			0.0217419	+	0.999764i	$0.493079\pi$
$450$		0			0
$451$	−4.69694			−0.221170
$452$	−4.09978	+	4.09978i	−0.192837	+	0.192837i
$453$		0			0
$454$			24.8990i			1.16857i
$455$	−22.3417	+	27.3629i	−1.04739	+	1.28279i
$456$		0			0
$457$	−10.3485	−	10.3485i	−0.484081	−	0.484081i	0.422351	−	0.906432i	$-0.361205\pi$
$457$	−10.3485	−	10.3485i	−0.484081	−	0.484081i	−0.906432	+	0.422351i	$0.861205\pi$
$458$	1.16781	+	1.16781i	0.0545681	+	0.0545681i
$459$		0			0
$460$	−0.224745	−	2.22474i	−0.0104788	−	0.103729i
$461$		−	33.0518i		−	1.53938i	−0.638420	−	0.769689i	$-0.720411\pi$
$461$		−	33.0518i		−	1.53938i	0.638420	−	0.769689i	$-0.279589\pi$
$462$		0			0
$463$	−8.65153	+	8.65153i	−0.402071	+	0.402071i	−0.878962	−	0.476891i	$-0.841763\pi$
$463$	−8.65153	+	8.65153i	−0.402071	+	0.402071i	0.476891	+	0.878962i	$0.341763\pi$
$464$	−0.317837			−0.0147552
$465$		0			0
$466$	20.4495			0.947304
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	−0.638630	−	0.769514i	$-0.720499\pi$
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	0.769514	+	0.638630i	$0.220499\pi$
$468$		0			0
$469$		−	30.1464i		−	1.39203i
$470$	15.5885	+	12.7279i	0.719042	+	0.587095i
$471$		0			0
$472$	6.34847	+	6.34847i	0.292212	+	0.292212i
$473$	−1.55708	−	1.55708i	−0.0715945	−	0.0715945i
$474$		0			0
$475$	31.5959	−	6.44949i	1.44972	−	0.295923i
$476$		−	2.04989i		−	0.0939565i
$477$		0			0
$478$	−12.0000	+	12.0000i	−0.548867	+	0.548867i
$479$	7.07107			0.323085			0.161543	−	0.986866i	$-0.448353\pi$
$479$	7.07107			0.323085			0.161543	+	0.986866i	$0.448353\pi$
$480$		0			0
$481$	−14.6969			−0.670123
$482$	−13.4350	+	13.4350i	−0.611949	+	0.611949i
$483$		0			0
$484$		−	10.5959i		−	0.481633i
$485$	−5.97469	+	0.603566i	−0.271297	+	0.0274065i
$486$		0			0
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	0.380861	−	0.924632i	$-0.375628\pi$
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	−0.924632	+	0.380861i	$0.875628\pi$
$488$	−0.389270	−	0.389270i	−0.0176214	−	0.0176214i
$489$		0			0
$490$	30.6969	−	3.10102i	1.38675	−	0.140090i
$491$		−	27.9985i		−	1.26356i	−0.775149	−	0.631778i	$-0.782325\pi$
$491$		−	27.9985i		−	1.26356i	0.775149	−	0.631778i	$-0.217675\pi$
$492$		0			0
$493$	0.101021	−	0.101021i	0.00454974	−	0.00454974i
$494$	−22.3417			−1.00520
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	−20.2918	+	20.2918i	−0.910212	+	0.910212i
$498$		0			0
$499$			0.898979i			0.0402438i	0.999798	+	0.0201219i	$0.00640544\pi$
$499$			0.898979i			0.0402438i	−0.999798	+	0.0201219i	$0.993595\pi$
$500$	5.19615	−	9.89949i	0.232379	−	0.442719i
$501$		0			0
$502$	−1.89898	−	1.89898i	−0.0847556	−	0.0847556i
$503$	4.02834	+	4.02834i	0.179615	+	0.179615i	0.791188	−	0.611573i	$-0.209463\pi$
$503$	4.02834	+	4.02834i	0.179615	+	0.179615i	−0.611573	+	0.791188i	$0.709463\pi$
$504$		0			0
$505$	21.7980	+	17.7980i	0.969996	+	0.791999i
$506$			0.635674i			0.0282592i
$507$		0			0
$508$	1.87628	−	1.87628i	0.0832463	−	0.0832463i
$509$	8.45317			0.374680			0.187340	−	0.982295i	$-0.440013\pi$
$509$	8.45317			0.374680			0.187340	+	0.982295i	$0.440013\pi$
$510$		0			0
$511$	−44.4949			−1.96834
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			18.0454i			0.795949i
$515$	−2.19275	−	21.7060i	−0.0966242	−	0.956481i
$516$		0			0
$517$	−4.04541	−	4.04541i	−0.177917	−	0.177917i
$518$	13.6814	+	13.6814i	0.601128	+	0.601128i
$519$		0			0
$520$	−4.89898	+	6.00000i	−0.214834	+	0.263117i
$521$			29.4449i			1.29000i	0.764181	+	0.645001i	$0.223143\pi$
$521$			29.4449i			1.29000i	−0.764181	+	0.645001i	$0.776857\pi$
$522$		0			0
$523$	4.22474	−	4.22474i	0.184735	−	0.184735i	−0.608680	−	0.793416i	$-0.708301\pi$
$523$	4.22474	−	4.22474i	0.184735	−	0.184735i	0.793416	+	0.608680i	$0.208301\pi$
$524$	−3.60697			−0.157571
$525$		0			0
$526$	16.6969			0.728021
$527$	0.142865	−	0.142865i	0.00622328	−	0.00622328i
$528$		0			0
$529$		−	22.0000i		−	0.956522i
$530$	7.56388	−	9.26382i	0.328554	−	0.402395i
$531$		0			0
$532$	20.7980	+	20.7980i	0.901706	+	0.901706i
$533$	18.0990	+	18.0990i	0.783957	+	0.783957i
$534$		0			0
$535$	4.32577	+	42.8207i	0.187019	+	1.85130i
$536$		−	6.61037i		−	0.285524i
$537$		0			0
$538$	10.6742	−	10.6742i	0.460199	−	0.460199i
$539$	−8.77101			−0.377794
$540$		0			0
$541$	27.9444			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$541$	27.9444			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$542$	−19.8311	+	19.8311i	−0.851819	+	0.851819i
$543$		0			0
$544$		−	0.449490i		−	0.0192717i
$545$	9.78874	+	7.99247i	0.419303	+	0.342360i
$546$		0			0
$547$	−2.87628	−	2.87628i	−0.122981	−	0.122981i	0.642938	−	0.765918i	$-0.277715\pi$
$547$	−2.87628	−	2.87628i	−0.122981	−	0.122981i	−0.765918	+	0.642938i	$0.777715\pi$
$548$	−15.4135	−	15.4135i	−0.658431	−	0.658431i
$549$		0			0
$550$	−1.75255	+	2.65153i	−0.0747290	+	0.113062i
$551$			2.04989i			0.0873282i
$552$		0			0
$553$	−7.89898	+	7.89898i	−0.335899	+	0.335899i
$554$	28.1414			1.19561
$555$		0			0
$556$	3.10102			0.131513
$557$	−7.88171	+	7.88171i	−0.333959	+	0.333959i	−0.854088	−	0.520129i	$-0.825884\pi$
$557$	−7.88171	+	7.88171i	−0.333959	+	0.333959i	0.520129	+	0.854088i	$0.325884\pi$
$558$		0			0
$559$			12.0000i			0.507546i
$560$	10.1459	−	1.02494i	0.428743	−	0.0433118i
$561$		0			0
$562$	−12.1237	−	12.1237i	−0.511408	−	0.511408i
$563$	13.8957	+	13.8957i	0.585635	+	0.585635i	0.936446	−	0.350811i	$-0.114094\pi$
$563$	13.8957	+	13.8957i	0.585635	+	0.585635i	−0.350811	+	0.936446i	$0.614094\pi$
$564$		0			0
$565$	12.8990	−	1.30306i	0.542664	−	0.0548202i
$566$			24.2166i			1.01790i
$567$		0			0
$568$	−4.44949	+	4.44949i	−0.186696	+	0.186696i
$569$	19.1633			0.803368			0.401684	−	0.915778i	$-0.368425\pi$
$569$	19.1633			0.803368			0.401684	+	0.915778i	$0.368425\pi$
$570$		0			0
$571$	36.8990			1.54417			0.772087	−	0.635517i	$-0.219213\pi$
$571$	36.8990			1.54417			0.772087	+	0.635517i	$0.219213\pi$
$572$	1.55708	−	1.55708i	0.0651047	−	0.0651047i
$573$		0			0
$574$		−	33.6969i		−	1.40648i
$575$	−2.75699	+	4.17121i	−0.114975	+	0.173951i
$576$		0			0
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	0.258336	−	0.966055i	$-0.416826\pi$
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	−0.966055	+	0.258336i	$0.916826\pi$
$578$	−11.8780	−	11.8780i	−0.494058	−	0.494058i
$579$		0			0
$580$	0.550510	+	0.449490i	0.0228587	+	0.0186640i
$581$		−	24.8523i		−	1.03105i
$582$		0			0
$583$	−2.40408	+	2.40408i	−0.0995669	+	0.0995669i
$584$	−9.75663			−0.403732
$585$		0			0
$586$	−22.0454			−0.910687
$587$	9.22450	−	9.22450i	0.380736	−	0.380736i	−0.490631	−	0.871367i	$-0.663234\pi$
$587$	9.22450	−	9.22450i	0.380736	−	0.380736i	0.871367	+	0.490631i	$0.163234\pi$
$588$		0			0
$589$			2.89898i			0.119450i
$590$	−2.01778	−	19.9740i	−0.0830707	−	0.822315i
$591$		0			0
$592$	3.00000	+	3.00000i	0.123299	+	0.123299i
$593$	−7.24604	−	7.24604i	−0.297559	−	0.297559i	0.542498	−	0.840057i	$-0.317479\pi$
$593$	−7.24604	−	7.24604i	−0.297559	−	0.297559i	−0.840057	+	0.542498i	$0.817479\pi$
$594$		0			0
$595$	−2.89898	+	3.55051i	−0.118847	+	0.145557i
$596$			4.41761i			0.180952i
$597$		0			0
$598$	2.44949	−	2.44949i	0.100167	−	0.100167i
$599$	−19.9419			−0.814802			−0.407401	−	0.913249i	$-0.633565\pi$
$599$	−19.9419			−0.814802			−0.407401	+	0.913249i	$0.633565\pi$
$600$		0			0
$601$	5.30306			0.216316			0.108158	−	0.994134i	$-0.465505\pi$
$601$	5.30306			0.216316			0.108158	+	0.994134i	$0.465505\pi$
$602$	11.1708	−	11.1708i	0.455290	−	0.455290i
$603$		0			0
$604$		−	17.5959i		−	0.715968i
$605$	−14.9849	+	18.3527i	−0.609222	+	0.746142i
$606$		0			0
$607$	8.32577	+	8.32577i	0.337932	+	0.337932i	0.855589	−	0.517656i	$-0.173195\pi$
$607$	8.32577	+	8.32577i	0.337932	+	0.337932i	−0.517656	+	0.855589i	$0.673195\pi$
$608$	4.56048	+	4.56048i	0.184952	+	0.184952i
$609$		0			0
$610$	0.123724	+	1.22474i	0.00500945	+	0.0495885i
$611$			31.1769i			1.26128i
$612$		0			0
$613$	6.79796	−	6.79796i	0.274567	−	0.274567i	−0.556369	−	0.830936i	$-0.687806\pi$
$613$	6.79796	−	6.79796i	0.274567	−	0.274567i	0.830936	+	0.556369i	$0.187806\pi$
$614$	9.43879			0.380919
$615$		0			0
$616$	−2.89898			−0.116803
$617$	11.9494	−	11.9494i	0.481064	−	0.481064i	−0.424407	−	0.905471i	$-0.639518\pi$
$617$	11.9494	−	11.9494i	0.481064	−	0.481064i	0.905471	+	0.424407i	$0.139518\pi$
$618$		0			0
$619$		−	48.7423i		−	1.95912i	−0.201151	−	0.979560i	$-0.564468\pi$
$619$		−	48.7423i		−	1.95912i	0.201151	−	0.979560i	$-0.435532\pi$
$620$	0.778539	+	0.635674i	0.0312669	+	0.0255293i
$621$		0			0
$622$	−19.4495	−	19.4495i	−0.779853	−	0.779853i
$623$	−25.8772	−	25.8772i	−1.03675	−	1.03675i
$624$		0			0
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$			11.9494i			0.477593i
$627$		0			0
$628$	−10.3485	+	10.3485i	−0.412949	+	0.412949i
$629$	−1.90702			−0.0760380
$630$		0			0
$631$	−3.10102			−0.123450			−0.0617248	−	0.998093i	$-0.519660\pi$
$631$	−3.10102			−0.123450			−0.0617248	+	0.998093i	$0.519660\pi$
$632$	−1.73205	+	1.73205i	−0.0688973	+	0.0688973i
$633$		0			0
$634$		−	10.8990i		−	0.432854i
$635$	−5.90326	+	0.596350i	−0.234264	+	0.0236654i
$636$		0			0
$637$	33.7980	+	33.7980i	1.33912	+	1.33912i
$638$	−0.142865	−	0.142865i	−0.00565606	−	0.00565606i
$639$		0			0
$640$	2.22474	−	0.224745i	0.0879408	−	0.00888382i
$641$		−	19.3383i		−	0.763816i	−0.924200	−	0.381908i	$-0.875267\pi$
$641$		−	19.3383i		−	0.763816i	0.924200	−	0.381908i	$-0.124733\pi$
$642$		0			0
$643$	4.47219	−	4.47219i	0.176366	−	0.176366i	−0.613404	−	0.789770i	$-0.710200\pi$
$643$	4.47219	−	4.47219i	0.176366	−	0.176366i	0.789770	+	0.613404i	$0.210200\pi$
$644$	−4.56048			−0.179708
$645$		0			0
$646$	−2.89898			−0.114059
$647$	23.5416	−	23.5416i	0.925516	−	0.925516i	−0.0718961	−	0.997412i	$-0.522905\pi$
$647$	23.5416	−	23.5416i	0.925516	−	0.925516i	0.997412	+	0.0718961i	$0.0229050\pi$
$648$		0			0
$649$			5.70714i			0.224025i
$650$	16.9706	−	3.46410i	0.665640	−	0.135873i
$651$		0			0
$652$	−4.44949	−	4.44949i	−0.174255	−	0.174255i
$653$	18.7026	+	18.7026i	0.731890	+	0.731890i	0.970994	−	0.239104i	$-0.0768537\pi$
$653$	18.7026	+	18.7026i	0.731890	+	0.731890i	−0.239104	+	0.970994i	$0.576854\pi$
$654$		0			0
$655$	6.24745	+	5.10102i	0.244108	+	0.199313i
$656$		−	7.38891i		−	0.288488i
$657$		0			0
$658$	29.0227	−	29.0227i	1.13142	−	1.13142i
$659$	−11.3137			−0.440720			−0.220360	−	0.975419i	$-0.570723\pi$
$659$	−11.3137			−0.440720			−0.220360	+	0.975419i	$0.570723\pi$
$660$		0			0
$661$	−1.30306			−0.0506832			−0.0253416	−	0.999679i	$-0.508067\pi$
$661$	−1.30306			−0.0506832			−0.0253416	+	0.999679i	$0.508067\pi$
$662$	−0.317837	+	0.317837i	−0.0123531	+	0.0123531i
$663$		0			0
$664$		−	5.44949i		−	0.211481i
$665$	−6.61037	−	65.4359i	−0.256339	−	2.53749i
$666$		0			0
$667$	−0.224745	−	0.224745i	−0.00870216	−	0.00870216i
$668$	−6.22110	−	6.22110i	−0.240701	−	0.240701i
$669$		0			0
$670$	−9.34847	+	11.4495i	−0.361163	+	0.442332i
$671$		−	0.349945i		−	0.0135095i
$672$		0			0
$673$	−16.4495	+	16.4495i	−0.634081	+	0.634081i	−0.949089	−	0.315008i	$-0.897993\pi$
$673$	−16.4495	+	16.4495i	−0.634081	+	0.634081i	0.315008	+	0.949089i	$0.397993\pi$
$674$	3.11416			0.119953
$675$		0			0
$676$	1.00000			0.0384615
$677$	−32.2412	+	32.2412i	−1.23913	+	1.23913i	−0.278772	+	0.960357i	$0.589927\pi$
$677$	−32.2412	+	32.2412i	−1.23913	+	1.23913i	−0.960357	+	0.278772i	$0.910073\pi$
$678$		0			0
$679$			12.2474i			0.470014i
$680$	−0.635674	+	0.778539i	−0.0243770	+	0.0298556i
$681$		0			0
$682$	−0.202041	−	0.202041i	−0.00773655	−	0.00773655i
$683$	−13.8564	−	13.8564i	−0.530201	−	0.530201i	0.390431	−	0.920632i	$-0.372326\pi$
$683$	−13.8564	−	13.8564i	−0.530201	−	0.530201i	−0.920632	+	0.390431i	$0.872326\pi$
$684$		0			0
$685$	4.89898	+	48.4949i	0.187180	+	1.85289i
$686$		−	31.0019i		−	1.18366i
$687$		0			0
$688$	2.44949	−	2.44949i	0.0933859	−	0.0933859i
$689$	18.5276			0.705847
$690$		0			0
$691$	−20.9444			−0.796762			−0.398381	−	0.917220i	$-0.630428\pi$
$691$	−20.9444			−0.796762			−0.398381	+	0.917220i	$0.630428\pi$
$692$	9.12096	−	9.12096i	0.346727	−	0.346727i
$693$		0			0
$694$		−	23.7980i		−	0.903358i
$695$	−5.37113	−	4.38551i	−0.203738	−	0.166352i
$696$		0			0
$697$	2.34847	+	2.34847i	0.0889546	+	0.0889546i
$698$	−20.5382	−	20.5382i	−0.777383	−	0.777383i
$699$		0			0
$700$	−19.0227	−	12.5732i	−0.718991	−	0.475223i
$701$		−	21.1024i		−	0.797028i	−0.917162	−	0.398514i	$-0.869526\pi$
$701$		−	21.1024i		−	0.797028i	0.917162	−	0.398514i	$-0.130474\pi$
$702$		0			0
$703$	19.3485	−	19.3485i	0.729741	−	0.729741i
$704$	−0.635674			−0.0239579
$705$		0			0
$706$	−34.2929			−1.29063
$707$	40.5836	−	40.5836i	1.52630	−	1.52630i
$708$		0			0
$709$			29.6515i			1.11359i	0.830651	+	0.556793i	$0.187968\pi$
$709$			29.6515i			1.11359i	−0.830651	+	0.556793i	$0.812032\pi$
$710$	13.9993	−	1.41421i	0.525383	−	0.0530745i
$711$		0			0
$712$	−5.67423	−	5.67423i	−0.212651	−	0.212651i
$713$	−0.317837	−	0.317837i	−0.0119031	−	0.0119031i
$714$		0			0
$715$	−4.89898	+	0.494897i	−0.183211	+	0.0185081i
$716$		−	10.6780i		−	0.399057i
$717$		0			0
$718$	−2.34847	+	2.34847i	−0.0876441	+	0.0876441i
$719$	32.5269			1.21305			0.606525	−	0.795065i	$-0.292563\pi$
$719$	32.5269			1.21305			0.606525	+	0.795065i	$0.292563\pi$
$720$		0			0
$721$	−44.4949			−1.65708
$722$	15.9777	−	15.9777i	0.594629	−	0.594629i
$723$		0			0
$724$			15.4495i			0.574176i
$725$	−0.317837	−	1.55708i	−0.0118042	−	0.0578284i
$726$		0			0
$727$	34.1691	+	34.1691i	1.26726	+	1.26726i	0.947496	+	0.319767i	$0.103605\pi$
$727$	34.1691	+	34.1691i	1.26726	+	1.26726i	0.319767	+	0.947496i	$0.396395\pi$
$728$	11.1708	+	11.1708i	0.414019	+	0.414019i
$729$		0			0
$730$	16.8990	+	13.7980i	0.625459	+	0.510685i
$731$			1.55708i			0.0575906i
$732$		0			0
$733$	24.1464	−	24.1464i	0.891869	−	0.891869i	−0.102830	−	0.994699i	$-0.532790\pi$
$733$	24.1464	−	24.1464i	0.891869	−	0.891869i	0.994699	+	0.102830i	$0.0327898\pi$
$734$	4.09978			0.151325
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	2.97129	−	2.97129i	0.109449	−	0.109449i
$738$		0			0
$739$			28.9444i			1.06474i	0.846513	+	0.532368i	$0.178698\pi$
$739$			28.9444i			1.06474i	−0.846513	+	0.532368i	$0.821302\pi$
$740$	−0.953512	−	9.43879i	−0.0350518	−	0.346977i
$741$		0			0
$742$	−17.2474	−	17.2474i	−0.633174	−	0.633174i
$743$	−6.99964	−	6.99964i	−0.256792	−	0.256792i	0.566956	−	0.823748i	$-0.308121\pi$
$743$	−6.99964	−	6.99964i	−0.256792	−	0.256792i	−0.823748	+	0.566956i	$0.808121\pi$
$744$		0			0
$745$	6.24745	−	7.65153i	0.228889	−	0.280330i
$746$		−	0.492810i		−	0.0180431i
$747$		0			0
$748$	0.202041	−	0.202041i	0.00738735	−	0.00738735i
$749$	87.7776			3.20732
$750$		0			0
$751$	20.6969			0.755242			0.377621	−	0.925960i	$-0.376742\pi$
$751$	20.6969			0.755242			0.377621	+	0.925960i	$0.376742\pi$
$752$	6.36396	−	6.36396i	0.232070	−	0.232070i
$753$		0			0
$754$			1.10102i			0.0400968i
$755$	−24.8844	+	30.4770i	−0.905636	+	1.10917i
$756$		0			0
$757$	22.0454	+	22.0454i	0.801254	+	0.801254i	0.983292	−	0.182038i	$-0.0582693\pi$
$757$	22.0454	+	22.0454i	0.801254	+	0.801254i	−0.182038	+	0.983292i	$0.558269\pi$
$758$	15.0956	+	15.0956i	0.548299	+	0.548299i
$759$		0			0
$760$	−1.44949	−	14.3485i	−0.0525785	−	0.520474i
$761$		−	6.46750i		−	0.234447i	−0.993106	−	0.117223i	$-0.962601\pi$
$761$		−	6.46750i		−	0.234447i	0.993106	−	0.117223i	$-0.0373993\pi$
$762$		0			0
$763$	18.2247	−	18.2247i	0.659780	−	0.659780i
$764$	17.4634			0.631803
$765$		0			0
$766$	8.20204			0.296352
$767$	21.9917	−	21.9917i	0.794076	−	0.794076i
$768$		0			0
$769$		−	9.69694i		−	0.349681i	−0.984597	−	0.174840i	$-0.944059\pi$
$769$		−	9.69694i		−	0.349681i	0.984597	−	0.174840i	$-0.0559409\pi$
$770$	5.02118	+	4.09978i	0.180951	+	0.147746i
$771$		0			0
$772$	12.2474	+	12.2474i	0.440795	+	0.440795i
$773$	30.8270	+	30.8270i	1.10877	+	1.10877i	0.993313	+	0.115456i	$0.0368331\pi$
$773$	30.8270	+	30.8270i	1.10877	+	1.10877i	0.115456	+	0.993313i	$0.463167\pi$
$774$		0			0
$775$	−0.449490	−	2.20204i	−0.0161461	−	0.0790996i
$776$			2.68556i			0.0964061i
$777$		0			0
$778$	26.0227	−	26.0227i	0.932959	−	0.932959i
$779$	−47.6547			−1.70741
$780$		0			0
$781$	−4.00000			−0.143131
$782$	0.317837	−	0.317837i	0.0113658	−	0.0113658i
$783$		0			0
$784$		−	13.7980i		−	0.492784i
$785$	32.5590	−	3.28913i	1.16208	−	0.117394i
$786$		0			0
$787$	−6.89898	−	6.89898i	−0.245922	−	0.245922i	0.573373	−	0.819295i	$-0.305635\pi$
$787$	−6.89898	−	6.89898i	−0.245922	−	0.245922i	−0.819295	+	0.573373i	$0.805635\pi$
$788$	−6.92820	−	6.92820i	−0.246807	−	0.246807i
$789$		0			0
$790$	5.44949	−	0.550510i	0.193884	−	0.0195863i
$791$		−	26.4415i		−	0.940150i
$792$		0			0
$793$	−1.34847	+	1.34847i	−0.0478855	+	0.0478855i
$794$	−14.9207			−0.529515
$795$		0			0
$796$	8.44949			0.299484
$797$	−28.1414	+	28.1414i	−0.996820	+	0.996820i	−0.999995	−	0.00317519i	$-0.998989\pi$
$797$	−28.1414	+	28.1414i	−0.996820	+	0.996820i	0.00317519	+	0.999995i	$0.498989\pi$
$798$		0			0
$799$			4.04541i			0.143116i
$800$	−4.17121	−	2.75699i	−0.147474	−	0.0974745i
$801$		0			0
$802$	−6.24745	−	6.24745i	−0.220605	−	0.220605i
$803$	−4.38551	−	4.38551i	−0.154761	−	0.154761i
$804$		0			0
$805$	7.89898	+	6.44949i	0.278402	+	0.227315i
$806$			1.55708i			0.0548457i
$807$		0			0
$808$	8.89898	−	8.89898i	0.313065	−	0.313065i
$809$	−19.4490			−0.683792			−0.341896	−	0.939738i	$-0.611069\pi$
$809$	−19.4490			−0.683792			−0.341896	+	0.939738i	$0.611069\pi$
$810$		0			0
$811$	−39.6413			−1.39200			−0.695998	−	0.718044i	$-0.745038\pi$
$811$	−39.6413			−1.39200			−0.695998	+	0.718044i	$0.745038\pi$
$812$	1.02494	−	1.02494i	0.0359685	−	0.0359685i
$813$		0			0
$814$			2.69694i			0.0945276i
$815$	1.41421	+	13.9993i	0.0495377	+	0.490373i
$816$		0			0
$817$	−15.7980	−	15.7980i	−0.552701	−	0.552701i
$818$	20.4347	+	20.4347i	0.714481	+	0.714481i
$819$		0			0
$820$	−10.4495	+	12.7980i	−0.364912	+	0.446924i
$821$		−	22.3096i		−	0.778610i	−0.921109	−	0.389305i	$-0.872715\pi$
$821$		−	22.3096i		−	0.778610i	0.921109	−	0.389305i	$-0.127285\pi$
$822$		0			0
$823$	2.37117	−	2.37117i	0.0826539	−	0.0826539i	−0.664571	−	0.747225i	$-0.731386\pi$
$823$	2.37117	−	2.37117i	0.0826539	−	0.0826539i	0.747225	+	0.664571i	$0.231386\pi$
$824$	−9.75663			−0.339888
$825$		0			0
$826$	−40.9444			−1.42464
$827$	31.5662	−	31.5662i	1.09766	−	1.09766i	0.102980	−	0.994683i	$-0.467162\pi$
$827$	31.5662	−	31.5662i	1.09766	−	1.09766i	0.994683	−	0.102980i	$-0.0328379\pi$
$828$		0			0
$829$		−	10.5505i		−	0.366434i	−0.983072	−	0.183217i	$-0.941349\pi$
$829$		−	10.5505i		−	0.366434i	0.983072	−	0.183217i	$-0.0586512\pi$
$830$	−7.70674	+	9.43879i	−0.267505	+	0.327625i
$831$		0			0
$832$	2.44949	+	2.44949i	0.0849208	+	0.0849208i
$833$	4.38551	+	4.38551i	0.151949	+	0.151949i
$834$		0			0
$835$	1.97730	+	19.5732i	0.0684272	+	0.677359i
$836$			4.09978i			0.141794i
$837$		0			0
$838$	3.55051	−	3.55051i	0.122650	−	0.122650i
$839$	−0.492810			−0.0170137			−0.00850684	−	0.999964i	$-0.502708\pi$
$839$	−0.492810			−0.0170137			−0.00850684	+	0.999964i	$0.502708\pi$
$840$		0			0
$841$	−28.8990			−0.996517
$842$	3.60697	−	3.60697i	0.124304	−	0.124304i
$843$		0			0
$844$		−	9.10102i		−	0.313270i
$845$	−1.73205	−	1.41421i	−0.0595844	−	0.0486504i
$846$		0			0
$847$	34.1691	+	34.1691i	1.17407	+	1.17407i
$848$	−3.78194	−	3.78194i	−0.129872	−	0.129872i
$849$		0			0
$850$	2.20204	−	0.449490i	0.0755294	−	0.0154174i
$851$			4.24264i			0.145436i
$852$		0			0
$853$	−1.75255	+	1.75255i	−0.0600062	+	0.0600062i	−0.736473	−	0.676467i	$-0.763510\pi$
$853$	−1.75255	+	1.75255i	−0.0600062	+	0.0600062i	0.676467	+	0.736473i	$0.263510\pi$
$854$	2.51059			0.0859106
$855$		0			0
$856$	19.2474			0.657864
$857$	11.1708	−	11.1708i	0.381589	−	0.381589i	−0.490086	−	0.871674i	$-0.663034\pi$
$857$	11.1708	−	11.1708i	0.381589	−	0.381589i	0.871674	+	0.490086i	$0.163034\pi$
$858$		0			0
$859$		−	46.4949i		−	1.58639i	−0.608971	−	0.793193i	$-0.708417\pi$
$859$		−	46.4949i		−	1.58639i	0.608971	−	0.793193i	$-0.291583\pi$
$860$	−7.70674	+	0.778539i	−0.262798	+	0.0265480i
$861$		0			0
$862$	11.0000	+	11.0000i	0.374661	+	0.374661i
$863$	−20.7132	−	20.7132i	−0.705085	−	0.705085i	0.260413	−	0.965497i	$-0.416141\pi$
$863$	−20.7132	−	20.7132i	−0.705085	−	0.705085i	−0.965497	+	0.260413i	$0.916141\pi$
$864$		0			0
$865$	−28.6969	+	2.89898i	−0.975725	+	0.0985683i
$866$			19.0205i			0.646341i
$867$		0			0
$868$	1.44949	−	1.44949i	0.0491989	−	0.0491989i
$869$	−1.55708			−0.0528203
$870$		0			0
$871$	−22.8990			−0.775902
$872$	3.99624	−	3.99624i	0.135330	−	0.135330i
$873$		0			0
$874$			6.44949i			0.218157i
$875$	15.1671	+	48.6796i	0.512741	+	1.64567i
$876$		0			0
$877$	30.2474	+	30.2474i	1.02138	+	1.02138i	0.999766	+	0.0216175i	$0.00688159\pi$
$877$	30.2474	+	30.2474i	1.02138	+	1.02138i	0.0216175	+	0.999766i	$0.493118\pi$
$878$	−21.0703	−	21.0703i	−0.711089	−	0.711089i
$879$		0			0
$880$	1.10102	+	0.898979i	0.0371154	+	0.0303046i
$881$			54.8365i			1.84749i	0.383010	+	0.923744i	$0.374887\pi$
$881$			54.8365i			1.84749i	−0.383010	+	0.923744i	$0.625113\pi$
$882$		0			0
$883$	6.27015	−	6.27015i	0.211007	−	0.211007i	−0.593688	−	0.804695i	$-0.702329\pi$
$883$	6.27015	−	6.27015i	0.211007	−	0.211007i	0.804695	+	0.593688i	$0.202329\pi$
$884$	−1.55708			−0.0523702
$885$		0			0
$886$	−5.44949			−0.183079
$887$	5.79972	−	5.79972i	0.194735	−	0.194735i	−0.603003	−	0.797739i	$-0.706029\pi$
$887$	5.79972	−	5.79972i	0.194735	−	0.194735i	0.797739	+	0.603003i	$0.206029\pi$
$888$		0			0
$889$			12.1010i			0.405855i
$890$	1.80348	+	17.8526i	0.0604529	+	0.598422i
$891$		0			0
$892$	−18.1237	−	18.1237i	−0.606827	−	0.606827i
$893$	−41.0443	−	41.0443i	−1.37350	−	1.37350i
$894$		0			0
$895$	−15.1010	+	18.4949i	−0.504771	+	0.618216i
$896$		−	4.56048i		−	0.152355i
$897$		0			0
$898$	−0.651531	+	0.651531i	−0.0217419	+	0.0217419i
$899$	0.142865			0.00476480
$900$		0			0
$901$	2.40408			0.0800916
$902$	3.32124	−	3.32124i	0.110585	−	0.110585i
$903$		0			0
$904$		−	5.79796i		−	0.192837i
$905$	21.8489	−	26.7593i	0.726281	−	0.889509i
$906$		0			0
$907$	−2.67423	−	2.67423i	−0.0887965	−	0.0887965i	0.661313	−	0.750110i	$-0.269999\pi$
$907$	−2.67423	−	2.67423i	−0.0887965	−	0.0887965i	−0.750110	+	0.661313i	$0.769999\pi$
$908$	−17.6062	−	17.6062i	−0.584284	−	0.584284i
$909$		0			0
$910$	−3.55051	−	35.1464i	−0.117698	−	1.16509i
$911$			7.07107i			0.234275i	0.993116	+	0.117137i	$0.0373718\pi$
$911$			7.07107i			0.234275i	−0.993116	+	0.117137i	$0.962628\pi$
$912$		0			0
$913$	2.44949	−	2.44949i	0.0810663	−	0.0810663i
$914$	14.6349			0.484081
$915$		0			0
$916$	−1.65153			−0.0545681
$917$	11.6315	−	11.6315i	0.384107	−	0.384107i
$918$		0			0
$919$			12.6515i			0.417335i	0.977987	+	0.208668i	$0.0669127\pi$
$919$			12.6515i			0.417335i	−0.977987	+	0.208668i	$0.933087\pi$
$920$	1.73205	+	1.41421i	0.0571040	+	0.0466252i
$921$		0			0
$922$	23.3712	+	23.3712i	0.769689	+	0.769689i
$923$	15.4135	+	15.4135i	0.507341	+	0.507341i
$924$		0			0
$925$	−11.6969	+	17.6969i	−0.384593	+	0.581872i
$926$		−	12.2351i		−	0.402071i
$927$		0			0
$928$	0.224745	−	0.224745i	0.00737761	−	0.00737761i
$929$	−42.2049			−1.38470			−0.692349	−	0.721563i	$-0.743424\pi$
$929$	−42.2049			−1.38470			−0.692349	+	0.721563i	$0.743424\pi$
$930$		0			0
$931$	−88.9898			−2.91652
$932$	−14.4600	+	14.4600i	−0.473652	+	0.473652i
$933$		0			0
$934$			4.00000i			0.130884i
$935$	−0.635674	+	0.0642162i	−0.0207888	+	0.00210009i
$936$		0			0
$937$	−3.10102	−	3.10102i	−0.101306	−	0.101306i	0.654637	−	0.755943i	$-0.272821\pi$
$937$	−3.10102	−	3.10102i	−0.101306	−	0.101306i	−0.755943	+	0.654637i	$0.772821\pi$
$938$	21.3167	+	21.3167i	0.696016	+	0.696016i
$939$		0			0
$940$	−20.0227	+	2.02270i	−0.653069	+	0.0659733i
$941$			31.7805i			1.03601i	0.855376	+	0.518007i	$0.173326\pi$
$941$			31.7805i			1.03601i	−0.855376	+	0.518007i	$0.826674\pi$
$942$		0			0
$943$	5.22474	−	5.22474i	0.170141	−	0.170141i
$944$	−8.97809			−0.292212
$945$		0			0
$946$	2.20204			0.0715945
$947$	2.15343	−	2.15343i	0.0699770	−	0.0699770i	−0.671252	−	0.741229i	$-0.734243\pi$
$947$	2.15343	−	2.15343i	0.0699770	−	0.0699770i	0.741229	+	0.671252i	$0.234243\pi$
$948$		0			0
$949$			33.7980i			1.09713i
$950$	−17.7812	+	26.9022i	−0.576899	+	0.872822i
$951$		0			0
$952$	1.44949	+	1.44949i	0.0469782	+	0.0469782i
$953$	−5.79972	−	5.79972i	−0.187871	−	0.187871i	0.606904	−	0.794775i	$-0.292411\pi$
$953$	−5.79972	−	5.79972i	−0.187871	−	0.187871i	−0.794775	+	0.606904i	$0.792411\pi$
$954$		0			0
$955$	−30.2474	−	24.6969i	−0.978784	−	0.799174i
$956$		−	16.9706i		−	0.548867i
$957$		0			0
$958$	−5.00000	+	5.00000i	−0.161543	+	0.161543i
$959$	99.4091			3.21009
$960$		0			0
$961$	−30.7980			−0.993483
$962$	10.3923	−	10.3923i	0.335061	−	0.335061i
$963$		0			0
$964$		−	19.0000i		−	0.611949i
$965$	−3.89270	−	38.5337i	−0.125310	−	1.24044i
$966$		0			0
$967$	−28.3258	−	28.3258i	−0.910895	−	0.910895i	0.0854475	−	0.996343i	$-0.472768\pi$
$967$	−28.3258	−	28.3258i	−0.910895	−	0.910895i	−0.996343	+	0.0854475i	$0.972768\pi$
$968$	7.49245	+	7.49245i	0.240816	+	0.240816i
$969$		0			0
$970$	3.79796	−	4.65153i	0.121945	−	0.149352i
$971$		−	21.4989i		−	0.689934i	−0.938615	−	0.344967i	$-0.887890\pi$
$971$		−	21.4989i		−	0.689934i	0.938615	−	0.344967i	$-0.112110\pi$
$972$		0			0
$973$	−10.0000	+	10.0000i	−0.320585	+	0.320585i
$974$	16.9706			0.543772
$975$		0			0
$976$	0.550510			0.0176214
$977$	−4.59259	+	4.59259i	−0.146930	+	0.146930i	−0.776745	−	0.629815i	$-0.783131\pi$
$977$	−4.59259	+	4.59259i	−0.146930	+	0.146930i	0.629815	+	0.776745i	$0.283131\pi$
$978$		0			0
$979$		−	5.10102i		−	0.163029i
$980$	−19.5133	+	23.8988i	−0.623328	+	0.763418i
$981$		0			0
$982$	19.7980	+	19.7980i	0.631778	+	0.631778i
$983$	19.2347	+	19.2347i	0.613493	+	0.613493i	0.943855	−	0.330361i	$-0.107171\pi$
$983$	19.2347	+	19.2347i	0.613493	+	0.613493i	−0.330361	+	0.943855i	$0.607171\pi$
$984$		0			0
$985$	2.20204	+	21.7980i	0.0701629	+	0.694541i
$986$			0.142865i			0.00454974i
$987$		0			0
$988$	15.7980	−	15.7980i	0.502600	−	0.502600i
$989$	3.46410			0.110152
$990$		0			0
$991$	16.7423			0.531838			0.265919	−	0.963995i	$-0.414325\pi$
$991$	16.7423			0.531838			0.265919	+	0.963995i	$0.414325\pi$
$992$	0.317837	−	0.317837i	0.0100913	−	0.0100913i
$993$		0			0
$994$		−	28.6969i		−	0.910212i
$995$	−14.6349	−	11.9494i	−0.463959	−	0.378821i
$996$		0			0
$997$	−4.75255	−	4.75255i	−0.150515	−	0.150515i	0.627833	−	0.778348i	$-0.283942\pi$
$997$	−4.75255	−	4.75255i	−0.150515	−	0.150515i	−0.778348	+	0.627833i	$0.783942\pi$
$998$	−0.635674	−	0.635674i	−0.0201219	−	0.0201219i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.f.b.647.2		8
3.2	odd	2	inner	810.2.f.b.647.3		8
5.3	odd	4	inner	810.2.f.b.323.4		8
9.2	odd	6		90.2.l.a.77.1	yes	8
9.4	even	3		90.2.l.a.47.1	yes	8
9.5	odd	6		270.2.m.a.197.2		8
9.7	even	3		270.2.m.a.17.2		8
15.8	even	4	inner	810.2.f.b.323.1		8
36.11	even	6		720.2.cu.a.257.1		8
36.31	odd	6		720.2.cu.a.497.1		8
45.2	even	12		450.2.p.a.293.2		8
45.4	even	6		450.2.p.a.407.2		8
45.7	odd	12		1350.2.q.g.1043.1		8
45.13	odd	12		90.2.l.a.83.1	yes	8
45.14	odd	6		1350.2.q.g.1007.1		8
45.22	odd	12		450.2.p.a.443.2		8
45.23	even	12		270.2.m.a.143.2		8
45.29	odd	6		450.2.p.a.257.2		8
45.32	even	12		1350.2.q.g.143.1		8
45.34	even	6		1350.2.q.g.557.1		8
45.38	even	12		90.2.l.a.23.1	✓	8
45.43	odd	12		270.2.m.a.233.2		8
180.83	odd	12		720.2.cu.a.113.1		8
180.103	even	12		720.2.cu.a.353.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.1	✓	8	45.38	even	12
90.2.l.a.47.1	yes	8	9.4	even	3
90.2.l.a.77.1	yes	8	9.2	odd	6
90.2.l.a.83.1	yes	8	45.13	odd	12
270.2.m.a.17.2		8	9.7	even	3
270.2.m.a.143.2		8	45.23	even	12
270.2.m.a.197.2		8	9.5	odd	6
270.2.m.a.233.2		8	45.43	odd	12
450.2.p.a.257.2		8	45.29	odd	6
450.2.p.a.293.2		8	45.2	even	12
450.2.p.a.407.2		8	45.4	even	6
450.2.p.a.443.2		8	45.22	odd	12
720.2.cu.a.113.1		8	180.83	odd	12
720.2.cu.a.257.1		8	36.11	even	6
720.2.cu.a.353.1		8	180.103	even	12
720.2.cu.a.497.1		8	36.31	odd	6
810.2.f.b.323.1		8	15.8	even	4	inner
810.2.f.b.323.4		8	5.3	odd	4	inner
810.2.f.b.647.2		8	1.1	even	1	trivial
810.2.f.b.647.3		8	3.2	odd	2	inner
1350.2.q.g.143.1		8	45.32	even	12
1350.2.q.g.557.1		8	45.34	even	6
1350.2.q.g.1007.1		8	45.14	odd	6
1350.2.q.g.1043.1		8	45.7	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.41421 + 1.73205i) q^{5} +(3.22474 + 3.22474i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.224745 - 2.22474i) q^{10} +0.635674i q^{11} +(2.44949 - 2.44949i) q^{13} -4.56048 q^{14} -1.00000 q^{16} +(0.317837 - 0.317837i) q^{17} +6.44949i q^{19} +(1.73205 + 1.41421i) q^{20} +(-0.449490 - 0.449490i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.00000 - 4.89898i) q^{25} +3.46410i q^{26} +(3.22474 - 3.22474i) q^{28} +0.317837 q^{29} +0.449490 q^{31} +(0.707107 - 0.707107i) q^{32} +0.449490i q^{34} +(-10.1459 + 1.02494i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-4.56048 - 4.56048i) q^{38} +(-2.22474 + 0.224745i) q^{40} +7.38891i q^{41} +(-2.44949 + 2.44949i) q^{43} +0.635674 q^{44} +1.00000 q^{46} +(-6.36396 + 6.36396i) q^{47} +13.7980i q^{49} +(4.17121 + 2.75699i) q^{50} +(-2.44949 - 2.44949i) q^{52} +(3.78194 + 3.78194i) q^{53} +(-1.10102 - 0.898979i) q^{55} +4.56048i q^{56} +(-0.224745 + 0.224745i) q^{58} +8.97809 q^{59} -0.550510 q^{61} +(-0.317837 + 0.317837i) q^{62} +1.00000i q^{64} +(0.778539 + 7.70674i) q^{65} +(-4.67423 - 4.67423i) q^{67} +(-0.317837 - 0.317837i) q^{68} +(6.44949 - 7.89898i) q^{70} +6.29253i q^{71} +(-6.89898 + 6.89898i) q^{73} +4.24264 q^{74} +6.44949 q^{76} +(-2.04989 + 2.04989i) q^{77} +2.44949i q^{79} +(1.41421 - 1.73205i) q^{80} +(-5.22474 - 5.22474i) q^{82} +(-3.85337 - 3.85337i) q^{83} +(0.101021 + 1.00000i) q^{85} -3.46410i q^{86} +(-0.449490 + 0.449490i) q^{88} -8.02458 q^{89} +15.7980 q^{91} +(-0.707107 + 0.707107i) q^{92} -9.00000i q^{94} +(-11.1708 - 9.12096i) q^{95} +(1.89898 + 1.89898i) q^{97} +(-9.75663 - 9.75663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{7} + 8 q^{10} - 8 q^{16} + 16 q^{22} - 8 q^{25} + 16 q^{28} - 16 q^{31} - 24 q^{37} - 8 q^{40} + 8 q^{46} - 48 q^{55} + 8 q^{58} - 24 q^{61} - 8 q^{67} + 32 q^{70} - 16 q^{73} + 32 q^{76} - 32 q^{82}+ \cdots - 24 q^{97}+O(q^{100}) \) 8 * q + 16 * q^7 + 8 * q^10 - 8 * q^16 + 16 * q^22 - 8 * q^25 + 16 * q^28 - 16 * q^31 - 24 * q^37 - 8 * q^40 + 8 * q^46 - 48 * q^55 + 8 * q^58 - 24 * q^61 - 8 * q^67 + 32 * q^70 - 16 * q^73 + 32 * q^76 - 32 * q^82 + 40 * q^85 + 16 * q^88 + 48 * q^91 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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