LMFDB - Embedded newform 1053.2.e.i.703.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1053,2,Mod(352,1053)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1053, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1053.352"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1053 = 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1053.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-2,0,0,-4] 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:	$8.40824733284$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			703.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1053.703
Dual form			1053.2.e.i.352.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{7} -1.73205 q^{8} +(1.73205 - 3.00000i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-1.73205 - 3.00000i) q^{14} +(2.50000 - 4.33013i) q^{16} -6.92820 q^{17} +2.00000 q^{19} +(3.00000 + 5.19615i) q^{22} +(-3.46410 - 6.00000i) q^{23} +(2.50000 - 4.33013i) q^{25} +1.73205 q^{26} +2.00000 q^{28} +(-3.46410 + 6.00000i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(2.59808 + 4.50000i) q^{32} +(6.00000 - 10.3923i) q^{34} +2.00000 q^{37} +(-1.73205 + 3.00000i) q^{38} +(-3.46410 - 6.00000i) q^{41} +(-4.00000 + 6.92820i) q^{43} -3.46410 q^{44} +12.0000 q^{46} +(5.19615 - 9.00000i) q^{47} +(1.50000 + 2.59808i) q^{49} +(4.33013 + 7.50000i) q^{50} +(-0.500000 + 0.866025i) q^{52} +(1.73205 - 3.00000i) q^{56} +(-6.00000 - 10.3923i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(5.00000 - 8.66025i) q^{61} +3.46410 q^{62} +1.00000 q^{64} +(-7.00000 - 12.1244i) q^{67} +(3.46410 + 6.00000i) q^{68} +3.46410 q^{71} -10.0000 q^{73} +(-1.73205 + 3.00000i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(3.46410 + 6.00000i) q^{77} +(2.00000 - 3.46410i) q^{79} +12.0000 q^{82} +(-5.19615 + 9.00000i) q^{83} +(-6.92820 - 12.0000i) q^{86} +(-3.00000 + 5.19615i) q^{88} +6.92820 q^{89} +2.00000 q^{91} +(-3.46410 + 6.00000i) q^{92} +(9.00000 + 15.5885i) q^{94} +(5.00000 - 8.66025i) q^{97} -5.19615 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} - 4 q^{7} - 2 q^{13} + 10 q^{16} + 8 q^{19} + 12 q^{22} + 10 q^{25} + 8 q^{28} - 4 q^{31} + 24 q^{34} + 8 q^{37} - 16 q^{43} + 48 q^{46} + 6 q^{49} - 2 q^{52} - 24 q^{58} + 20 q^{61} + 4 q^{64}+ \cdots + 20 q^{97}+O(q^{100}) $ 4 * q - 2 * q^4 - 4 * q^7 - 2 * q^13 + 10 * q^16 + 8 * q^19 + 12 * q^22 + 10 * q^25 + 8 * q^28 - 4 * q^31 + 24 * q^34 + 8 * q^37 - 16 * q^43 + 48 * q^46 + 6 * q^49 - 2 * q^52 - 24 * q^58 + 20 * q^61 + 4 * q^64 - 28 * q^67 - 40 * q^73 - 4 * q^76 + 8 * q^79 + 48 * q^82 - 12 * q^88 + 8 * q^91 + 36 * q^94 + 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times$.

$n$	$326$	$730$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.866025	+	1.50000i	−0.612372	+	1.06066i	0.378467	+	0.925615i	$0.376451\pi$
$2$	−0.866025	+	1.50000i	−0.612372	+	1.06066i	−0.990839	+	0.135045i	$0.956882\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	−1.73205			−0.612372
$9$		0			0
$10$		0			0
$11$	1.73205	−	3.00000i	0.522233	−	0.904534i	−0.477432	−	0.878668i	$-0.658432\pi$
$11$	1.73205	−	3.00000i	0.522233	−	0.904534i	0.999665	−	0.0258656i	$-0.00823419\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−1.73205	−	3.00000i	−0.462910	−	0.801784i
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−6.92820			−1.68034			−0.840168	−	0.542326i	$-0.817544\pi$
$17$	−6.92820			−1.68034			−0.840168	+	0.542326i	$0.817544\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$		0			0
$21$		0			0
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	−3.46410	−	6.00000i	−0.722315	−	1.25109i	−0.960070	−	0.279761i	$-0.909745\pi$
$23$	−3.46410	−	6.00000i	−0.722315	−	1.25109i	0.237754	−	0.971325i	$-0.423589\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	1.73205			0.339683
$27$		0			0
$28$	2.00000			0.377964
$29$	−3.46410	+	6.00000i	−0.643268	+	1.11417i	0.341431	+	0.939907i	$0.389088\pi$
$29$	−3.46410	+	6.00000i	−0.643268	+	1.11417i	−0.984699	+	0.174265i	$0.944245\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	2.59808	+	4.50000i	0.459279	+	0.795495i
$33$		0			0
$34$	6.00000	−	10.3923i	1.02899	−	1.78227i
$35$		0			0
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−1.73205	+	3.00000i	−0.280976	+	0.486664i
$39$		0			0
$40$		0			0
$41$	−3.46410	−	6.00000i	−0.541002	−	0.937043i	−0.998847	−	0.0480106i	$-0.984712\pi$
$41$	−3.46410	−	6.00000i	−0.541002	−	0.937043i	0.457845	−	0.889032i	$-0.348621\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	12.0000			1.76930
$47$	5.19615	−	9.00000i	0.757937	−	1.31278i	−0.185964	−	0.982556i	$-0.559541\pi$
$47$	5.19615	−	9.00000i	0.757937	−	1.31278i	0.943901	−	0.330228i	$-0.107126\pi$
$48$		0			0
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	4.33013	+	7.50000i	0.612372	+	1.06066i
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$		0			0
$56$	1.73205	−	3.00000i	0.231455	−	0.400892i
$57$		0			0
$58$	−6.00000	−	10.3923i	−0.787839	−	1.36458i
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	0.730974	−	0.682406i	$-0.239066\pi$
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	−0.956467	+	0.291839i	$0.905733\pi$
$60$		0			0
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	3.46410			0.439941
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$	3.46410	+	6.00000i	0.420084	+	0.727607i
$69$		0			0
$70$		0			0
$71$	3.46410			0.411113			0.205557	−	0.978645i	$-0.434100\pi$
$71$	3.46410			0.411113			0.205557	+	0.978645i	$0.434100\pi$
$72$		0			0
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$	−1.73205	+	3.00000i	−0.201347	+	0.348743i
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	3.46410	+	6.00000i	0.394771	+	0.683763i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$		0			0
$82$	12.0000			1.32518
$83$	−5.19615	+	9.00000i	−0.570352	+	0.987878i	0.426178	+	0.904639i	$0.359860\pi$
$83$	−5.19615	+	9.00000i	−0.570352	+	0.987878i	−0.996530	+	0.0832389i	$0.973474\pi$
$84$		0			0
$85$		0			0
$86$	−6.92820	−	12.0000i	−0.747087	−	1.29399i
$87$		0			0
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	6.92820			0.734388			0.367194	−	0.930144i	$-0.380318\pi$
$89$	6.92820			0.734388			0.367194	+	0.930144i	$0.380318\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$	−3.46410	+	6.00000i	−0.361158	+	0.625543i
$93$		0			0
$94$	9.00000	+	15.5885i	0.928279	+	1.60783i
$95$		0			0
$96$		0			0
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	−5.19615			−0.524891
$99$		0			0
$100$	−5.00000			−0.500000
$101$	6.92820	−	12.0000i	0.689382	−	1.19404i	−0.282656	−	0.959221i	$-0.591216\pi$
$101$	6.92820	−	12.0000i	0.689382	−	1.19404i	0.972038	−	0.234823i	$-0.0754512\pi$
$102$		0			0
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	0.866025	+	1.50000i	0.0849208	+	0.147087i
$105$		0			0
$106$		0			0
$107$	6.92820			0.669775			0.334887	−	0.942258i	$-0.391302\pi$
$107$	6.92820			0.669775			0.334887	+	0.942258i	$0.391302\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$		0			0
$112$	5.00000	+	8.66025i	0.472456	+	0.818317i
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$		0			0
$115$		0			0
$116$	6.92820			0.643268
$117$		0			0
$118$	6.00000			0.552345
$119$	6.92820	−	12.0000i	0.635107	−	1.10004i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	8.66025	+	15.0000i	0.784063	+	1.35804i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	−6.06218	+	10.5000i	−0.535826	+	0.928078i
$129$		0			0
$130$		0			0
$131$	10.3923	+	18.0000i	0.907980	+	1.57267i	0.816866	+	0.576827i	$0.195709\pi$
$131$	10.3923	+	18.0000i	0.907980	+	1.57267i	0.0911134	+	0.995841i	$0.470957\pi$
$132$		0			0
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$	24.2487			2.09477
$135$		0			0
$136$	12.0000			1.02899
$137$	3.46410	−	6.00000i	0.295958	−	0.512615i	−0.679249	−	0.733908i	$-0.737694\pi$
$137$	3.46410	−	6.00000i	0.295958	−	0.512615i	0.975207	+	0.221293i	$0.0710278\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−3.46410			−0.289683
$144$		0			0
$145$		0			0
$146$	8.66025	−	15.0000i	0.716728	−	1.24141i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−6.92820	−	12.0000i	−0.567581	−	0.983078i	−0.996804	−	0.0798802i	$-0.974546\pi$
$149$	−6.92820	−	12.0000i	−0.567581	−	0.983078i	0.429224	−	0.903198i	$-0.358787\pi$
$150$		0			0
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	0.426948	+	0.904276i	$0.359589\pi$
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	−0.996600	+	0.0823900i	$0.973745\pi$
$152$	−3.46410			−0.280976
$153$		0			0
$154$	−12.0000			−0.966988
$155$		0			0
$156$		0			0
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$158$	3.46410	+	6.00000i	0.275589	+	0.477334i
$159$		0			0
$160$		0			0
$161$	13.8564			1.09204
$162$		0			0
$163$	14.0000			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$164$	−3.46410	+	6.00000i	−0.270501	+	0.468521i
$165$		0			0
$166$	−9.00000	−	15.5885i	−0.698535	−	1.20990i
$167$	−8.66025	−	15.0000i	−0.670151	−	1.16073i	−0.977861	−	0.209255i	$-0.932896\pi$
$167$	−8.66025	−	15.0000i	−0.670151	−	1.16073i	0.307711	−	0.951480i	$-0.400437\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$		0			0
$172$	8.00000			0.609994
$173$	−6.92820	+	12.0000i	−0.526742	+	0.912343i	0.472773	+	0.881184i	$0.343253\pi$
$173$	−6.92820	+	12.0000i	−0.526742	+	0.912343i	−0.999514	+	0.0311588i	$0.990080\pi$
$174$		0			0
$175$	5.00000	+	8.66025i	0.377964	+	0.654654i
$176$	−8.66025	−	15.0000i	−0.652791	−	1.13067i
$177$		0			0
$178$	−6.00000	+	10.3923i	−0.449719	+	0.778936i
$179$	−13.8564			−1.03568			−0.517838	−	0.855479i	$-0.673263\pi$
$179$	−13.8564			−1.03568			−0.517838	+	0.855479i	$0.673263\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−1.73205	+	3.00000i	−0.128388	+	0.222375i
$183$		0			0
$184$	6.00000	+	10.3923i	0.442326	+	0.766131i
$185$		0			0
$186$		0			0
$187$	−12.0000	+	20.7846i	−0.877527	+	1.51992i
$188$	−10.3923			−0.757937
$189$		0			0
$190$		0			0
$191$	−6.92820	+	12.0000i	−0.501307	+	0.868290i	0.498692	+	0.866779i	$0.333814\pi$
$191$	−6.92820	+	12.0000i	−0.501307	+	0.868290i	−0.999999	+	0.00151007i	$0.999519\pi$
$192$		0			0
$193$	−13.0000	−	22.5167i	−0.935760	−	1.62078i	−0.773272	−	0.634074i	$-0.781381\pi$
$193$	−13.0000	−	22.5167i	−0.935760	−	1.62078i	−0.162488	−	0.986710i	$-0.551952\pi$
$194$	8.66025	+	15.0000i	0.621770	+	1.07694i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	−13.8564			−0.987228			−0.493614	−	0.869681i	$-0.664324\pi$
$197$	−13.8564			−0.987228			−0.493614	+	0.869681i	$0.664324\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−4.33013	+	7.50000i	−0.306186	+	0.530330i
$201$		0			0
$202$	12.0000	+	20.7846i	0.844317	+	1.46240i
$203$	−6.92820	−	12.0000i	−0.486265	−	0.842235i
$204$		0			0
$205$		0			0
$206$	−6.92820			−0.482711
$207$		0			0
$208$	−5.00000			−0.346688
$209$	3.46410	−	6.00000i	0.239617	−	0.415029i
$210$		0			0
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$		0			0
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$		0			0
$216$		0			0
$217$	4.00000			0.271538
$218$	8.66025	−	15.0000i	0.586546	−	1.01593i
$219$		0			0
$220$		0			0
$221$	3.46410	+	6.00000i	0.233021	+	0.403604i
$222$		0			0
$223$	−1.00000	+	1.73205i	−0.0669650	+	0.115987i	−0.897564	−	0.440884i	$-0.854665\pi$
$223$	−1.00000	+	1.73205i	−0.0669650	+	0.115987i	0.830599	+	0.556871i	$0.187998\pi$
$224$	−10.3923			−0.694365
$225$		0			0
$226$	−12.0000			−0.798228
$227$	−1.73205	+	3.00000i	−0.114960	+	0.199117i	−0.917764	−	0.397127i	$-0.870007\pi$
$227$	−1.73205	+	3.00000i	−0.114960	+	0.199117i	0.802804	+	0.596244i	$0.203341\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$		0			0
$232$	6.00000	−	10.3923i	0.393919	−	0.682288i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$		0			0
$236$	−1.73205	+	3.00000i	−0.112747	+	0.195283i
$237$		0			0
$238$	12.0000	+	20.7846i	0.777844	+	1.34727i
$239$	5.19615	+	9.00000i	0.336111	+	0.582162i	0.983698	−	0.179830i	$-0.0575549\pi$
$239$	5.19615	+	9.00000i	0.336111	+	0.582162i	−0.647586	+	0.761992i	$0.724222\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	1.73205			0.111340
$243$		0			0
$244$	−10.0000			−0.640184
$245$		0			0
$246$		0			0
$247$	−1.00000	−	1.73205i	−0.0636285	−	0.110208i
$248$	1.73205	+	3.00000i	0.109985	+	0.190500i
$249$		0			0
$250$		0			0
$251$	−6.92820			−0.437304			−0.218652	−	0.975803i	$-0.570166\pi$
$251$	−6.92820			−0.437304			−0.218652	+	0.975803i	$0.570166\pi$
$252$		0			0
$253$	−24.0000			−1.50887
$254$	13.8564	−	24.0000i	0.869428	−	1.50589i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−13.8564	−	24.0000i	−0.864339	−	1.49708i	−0.867702	−	0.497085i	$-0.834404\pi$
$257$	−13.8564	−	24.0000i	−0.864339	−	1.49708i	0.00336324	−	0.999994i	$-0.498929\pi$
$258$		0			0
$259$	−2.00000	+	3.46410i	−0.124274	+	0.215249i
$260$		0			0
$261$		0			0
$262$	−36.0000			−2.22409
$263$	−3.46410	+	6.00000i	−0.213606	+	0.369976i	−0.952840	−	0.303472i	$-0.901854\pi$
$263$	−3.46410	+	6.00000i	−0.213606	+	0.369976i	0.739235	+	0.673448i	$0.235187\pi$
$264$		0			0
$265$		0			0
$266$	−3.46410	−	6.00000i	−0.212398	−	0.367884i
$267$		0			0
$268$	−7.00000	+	12.1244i	−0.427593	+	0.740613i
$269$	−6.92820			−0.422420			−0.211210	−	0.977441i	$-0.567740\pi$
$269$	−6.92820			−0.422420			−0.211210	+	0.977441i	$0.567740\pi$
$270$		0			0
$271$	−22.0000			−1.33640			−0.668202	−	0.743980i	$-0.732936\pi$
$271$	−22.0000			−1.33640			−0.668202	+	0.743980i	$0.732936\pi$
$272$	−17.3205	+	30.0000i	−1.05021	+	1.81902i
$273$		0			0
$274$	6.00000	+	10.3923i	0.362473	+	0.627822i
$275$	−8.66025	−	15.0000i	−0.522233	−	0.904534i
$276$		0			0
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−6.92820			−0.415526
$279$		0			0
$280$		0			0
$281$	10.3923	−	18.0000i	0.619953	−	1.07379i	−0.369541	−	0.929214i	$-0.620485\pi$
$281$	10.3923	−	18.0000i	0.619953	−	1.07379i	0.989494	−	0.144575i	$-0.0461817\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−1.73205	−	3.00000i	−0.102778	−	0.178017i
$285$		0			0
$286$	3.00000	−	5.19615i	0.177394	−	0.307255i
$287$	13.8564			0.817918
$288$		0			0
$289$	31.0000			1.82353
$290$		0			0
$291$		0			0
$292$	5.00000	+	8.66025i	0.292603	+	0.506803i
$293$	−6.92820	−	12.0000i	−0.404750	−	0.701047i	0.589542	−	0.807737i	$-0.299308\pi$
$293$	−6.92820	−	12.0000i	−0.404750	−	0.701047i	−0.994292	+	0.106690i	$0.965975\pi$
$294$		0			0
$295$		0			0
$296$	−3.46410			−0.201347
$297$		0			0
$298$	24.0000			1.39028
$299$	−3.46410	+	6.00000i	−0.200334	+	0.346989i
$300$		0			0
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$	−12.1244	−	21.0000i	−0.697678	−	1.20841i
$303$		0			0
$304$	5.00000	−	8.66025i	0.286770	−	0.496700i
$305$		0			0
$306$		0			0
$307$	26.0000			1.48390			0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000			1.48390			0.741949	+	0.670456i	$0.233902\pi$
$308$	3.46410	−	6.00000i	0.197386	−	0.341882i
$309$		0			0
$310$		0			0
$311$	10.3923	+	18.0000i	0.589294	+	1.02069i	0.994325	+	0.106384i	$0.0339272\pi$
$311$	10.3923	+	18.0000i	0.589294	+	1.02069i	−0.405032	+	0.914303i	$0.632739\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	3.46410			0.195491
$315$		0			0
$316$	−4.00000			−0.225018
$317$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$317$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$318$		0			0
$319$	12.0000	+	20.7846i	0.671871	+	1.16371i
$320$		0			0
$321$		0			0
$322$	−12.0000	+	20.7846i	−0.668734	+	1.15828i
$323$	−13.8564			−0.770991
$324$		0			0
$325$	−5.00000			−0.277350
$326$	−12.1244	+	21.0000i	−0.671506	+	1.16308i
$327$		0			0
$328$	6.00000	+	10.3923i	0.331295	+	0.573819i
$329$	10.3923	+	18.0000i	0.572946	+	0.992372i
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$	10.3923			0.570352
$333$		0			0
$334$	30.0000			1.64153
$335$		0			0
$336$		0			0
$337$	−1.00000	−	1.73205i	−0.0544735	−	0.0943508i	0.837503	−	0.546433i	$-0.184015\pi$
$337$	−1.00000	−	1.73205i	−0.0544735	−	0.0943508i	−0.891976	+	0.452082i	$0.850681\pi$
$338$	−0.866025	−	1.50000i	−0.0471056	−	0.0815892i
$339$		0			0
$340$		0			0
$341$	−6.92820			−0.375183
$342$		0			0
$343$	−20.0000			−1.07990
$344$	6.92820	−	12.0000i	0.373544	−	0.646997i
$345$		0			0
$346$	−12.0000	−	20.7846i	−0.645124	−	1.11739i
$347$	13.8564	+	24.0000i	0.743851	+	1.28839i	0.950730	+	0.310021i	$0.100336\pi$
$347$	13.8564	+	24.0000i	0.743851	+	1.28839i	−0.206879	+	0.978367i	$0.566331\pi$
$348$		0			0
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$	−17.3205			−0.925820
$351$		0			0
$352$	18.0000			0.959403
$353$	−3.46410	+	6.00000i	−0.184376	+	0.319348i	−0.943366	−	0.331754i	$-0.892360\pi$
$353$	−3.46410	+	6.00000i	−0.184376	+	0.319348i	0.758990	+	0.651102i	$0.225693\pi$
$354$		0			0
$355$		0			0
$356$	−3.46410	−	6.00000i	−0.183597	−	0.317999i
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	−10.3923			−0.548485			−0.274242	−	0.961661i	$-0.588427\pi$
$359$	−10.3923			−0.548485			−0.274242	+	0.961661i	$0.588427\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$	8.66025	−	15.0000i	0.455173	−	0.788382i
$363$		0			0
$364$	−1.00000	−	1.73205i	−0.0524142	−	0.0907841i
$365$		0			0
$366$		0			0
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	−34.6410			−1.80579
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	−20.7846	−	36.0000i	−1.07475	−	1.86152i
$375$		0			0
$376$	−9.00000	+	15.5885i	−0.464140	+	0.803913i
$377$	6.92820			0.356821
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$		0			0
$381$		0			0
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	8.66025	+	15.0000i	0.442518	+	0.766464i	0.997876	−	0.0651476i	$-0.0207518\pi$
$383$	8.66025	+	15.0000i	0.442518	+	0.766464i	−0.555357	+	0.831612i	$0.687419\pi$
$384$		0			0
$385$		0			0
$386$	45.0333			2.29214
$387$		0			0
$388$	−10.0000			−0.507673
$389$	−10.3923	+	18.0000i	−0.526911	+	0.912636i	0.472597	+	0.881278i	$0.343316\pi$
$389$	−10.3923	+	18.0000i	−0.526911	+	0.912636i	−0.999508	+	0.0313578i	$0.990017\pi$
$390$		0			0
$391$	24.0000	+	41.5692i	1.21373	+	2.10225i
$392$	−2.59808	−	4.50000i	−0.131223	−	0.227284i
$393$		0			0
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$		0			0
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	13.8564	−	24.0000i	0.694559	−	1.20301i
$399$		0			0
$400$	−12.5000	−	21.6506i	−0.625000	−	1.08253i
$401$	17.3205	+	30.0000i	0.864945	+	1.49813i	0.867102	+	0.498131i	$0.165980\pi$
$401$	17.3205	+	30.0000i	0.864945	+	1.49813i	−0.00215698	+	0.999998i	$0.500687\pi$
$402$		0			0
$403$	−1.00000	+	1.73205i	−0.0498135	+	0.0862796i
$404$	−13.8564			−0.689382
$405$		0			0
$406$	24.0000			1.19110
$407$	3.46410	−	6.00000i	0.171709	−	0.297409i
$408$		0			0
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$		0			0
$411$		0			0
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	6.92820			0.340915
$414$		0			0
$415$		0			0
$416$	2.59808	−	4.50000i	0.127381	−	0.220631i
$417$		0			0
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$	−3.46410	−	6.00000i	−0.169232	−	0.293119i	0.768918	−	0.639348i	$-0.220796\pi$
$419$	−3.46410	−	6.00000i	−0.169232	−	0.293119i	−0.938150	+	0.346228i	$0.887462\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	13.8564			0.674519
$423$		0			0
$424$		0			0
$425$	−17.3205	+	30.0000i	−0.840168	+	1.45521i
$426$		0			0
$427$	10.0000	+	17.3205i	0.483934	+	0.838198i
$428$	−3.46410	−	6.00000i	−0.167444	−	0.290021i
$429$		0			0
$430$		0			0
$431$	38.1051			1.83546			0.917729	−	0.397206i	$-0.130020\pi$
$431$	38.1051			1.83546			0.917729	+	0.397206i	$0.130020\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	−3.46410	+	6.00000i	−0.166282	+	0.288009i
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	−6.92820	−	12.0000i	−0.331421	−	0.574038i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−10.3923	+	18.0000i	−0.493753	+	0.855206i	−0.999974	−	0.00719811i	$-0.997709\pi$
$443$	−10.3923	+	18.0000i	−0.493753	+	0.855206i	0.506221	+	0.862404i	$0.331042\pi$
$444$		0			0
$445$		0			0
$446$	−1.73205	−	3.00000i	−0.0820150	−	0.142054i
$447$		0			0
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	−6.92820			−0.326962			−0.163481	−	0.986546i	$-0.552272\pi$
$449$	−6.92820			−0.326962			−0.163481	+	0.986546i	$0.552272\pi$
$450$		0			0
$451$	−24.0000			−1.13012
$452$	3.46410	−	6.00000i	0.162938	−	0.282216i
$453$		0			0
$454$	−3.00000	−	5.19615i	−0.140797	−	0.243868i
$455$		0			0
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	24.2487			1.13307
$459$		0			0
$460$		0			0
$461$	13.8564	−	24.0000i	0.645357	−	1.11779i	−0.338862	−	0.940836i	$-0.610042\pi$
$461$	13.8564	−	24.0000i	0.645357	−	1.11779i	0.984219	−	0.176955i	$-0.0566248\pi$
$462$		0			0
$463$	−1.00000	−	1.73205i	−0.0464739	−	0.0804952i	0.841853	−	0.539707i	$-0.181465\pi$
$463$	−1.00000	−	1.73205i	−0.0464739	−	0.0804952i	−0.888327	+	0.459212i	$0.848132\pi$
$464$	17.3205	+	30.0000i	0.804084	+	1.39272i
$465$		0			0
$466$		0			0
$467$	20.7846			0.961797			0.480899	−	0.876776i	$-0.340311\pi$
$467$	20.7846			0.961797			0.480899	+	0.876776i	$0.340311\pi$
$468$		0			0
$469$	28.0000			1.29292
$470$		0			0
$471$		0			0
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	13.8564	+	24.0000i	0.637118	+	1.10352i
$474$		0			0
$475$	5.00000	−	8.66025i	0.229416	−	0.397360i
$476$	−13.8564			−0.635107
$477$		0			0
$478$	−18.0000			−0.823301
$479$	1.73205	−	3.00000i	0.0791394	−	0.137073i	−0.823739	−	0.566969i	$-0.808116\pi$
$479$	1.73205	−	3.00000i	0.0791394	−	0.137073i	0.902879	+	0.429895i	$0.141449\pi$
$480$		0			0
$481$	−1.00000	−	1.73205i	−0.0455961	−	0.0789747i
$482$	8.66025	+	15.0000i	0.394464	+	0.683231i
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$		0			0
$486$		0			0
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−8.66025	+	15.0000i	−0.392031	+	0.679018i
$489$		0			0
$490$		0			0
$491$	−3.46410	−	6.00000i	−0.156333	−	0.270776i	0.777211	−	0.629240i	$-0.216634\pi$
$491$	−3.46410	−	6.00000i	−0.156333	−	0.270776i	−0.933544	+	0.358464i	$0.883301\pi$
$492$		0			0
$493$	24.0000	−	41.5692i	1.08091	−	1.87218i
$494$	3.46410			0.155857
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−3.46410	+	6.00000i	−0.155386	+	0.269137i
$498$		0			0
$499$	−7.00000	−	12.1244i	−0.313363	−	0.542761i	0.665725	−	0.746197i	$-0.268122\pi$
$499$	−7.00000	−	12.1244i	−0.313363	−	0.542761i	−0.979088	+	0.203436i	$0.934789\pi$
$500$		0			0
$501$		0			0
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	−6.92820			−0.308913			−0.154457	−	0.988000i	$-0.549363\pi$
$503$	−6.92820			−0.308913			−0.154457	+	0.988000i	$0.549363\pi$
$504$		0			0
$505$		0			0
$506$	20.7846	−	36.0000i	0.923989	−	1.60040i
$507$		0			0
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	6.92820	+	12.0000i	0.307087	+	0.531891i	0.977724	−	0.209895i	$-0.0673123\pi$
$509$	6.92820	+	12.0000i	0.307087	+	0.531891i	−0.670637	+	0.741786i	$0.733979\pi$
$510$		0			0
$511$	10.0000	−	17.3205i	0.442374	−	0.766214i
$512$	8.66025			0.382733
$513$		0			0
$514$	48.0000			2.11719
$515$		0			0
$516$		0			0
$517$	−18.0000	−	31.1769i	−0.791639	−	1.37116i
$518$	−3.46410	−	6.00000i	−0.152204	−	0.263625i
$519$		0			0
$520$		0			0
$521$	20.7846			0.910590			0.455295	−	0.890341i	$-0.349534\pi$
$521$	20.7846			0.910590			0.455295	+	0.890341i	$0.349534\pi$
$522$		0			0
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	10.3923	−	18.0000i	0.453990	−	0.786334i
$525$		0			0
$526$	−6.00000	−	10.3923i	−0.261612	−	0.453126i
$527$	6.92820	+	12.0000i	0.301797	+	0.522728i
$528$		0			0
$529$	−12.5000	+	21.6506i	−0.543478	+	0.941332i
$530$		0			0
$531$		0			0
$532$	4.00000			0.173422
$533$	−3.46410	+	6.00000i	−0.150047	+	0.259889i
$534$		0			0
$535$		0			0
$536$	12.1244	+	21.0000i	0.523692	+	0.907062i
$537$		0			0
$538$	6.00000	−	10.3923i	0.258678	−	0.448044i
$539$	10.3923			0.447628
$540$		0			0
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	19.0526	−	33.0000i	0.818377	−	1.41747i
$543$		0			0
$544$	−18.0000	−	31.1769i	−0.771744	−	1.33670i
$545$		0			0
$546$		0			0
$547$	2.00000	−	3.46410i	0.0855138	−	0.148114i	−0.820096	−	0.572226i	$-0.806080\pi$
$547$	2.00000	−	3.46410i	0.0855138	−	0.148114i	0.905610	+	0.424111i	$0.139413\pi$
$548$	−6.92820			−0.295958
$549$		0			0
$550$	30.0000			1.27920
$551$	−6.92820	+	12.0000i	−0.295151	+	0.511217i
$552$		0			0
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	−1.73205	−	3.00000i	−0.0735878	−	0.127458i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	27.7128			1.17423			0.587115	−	0.809504i	$-0.300264\pi$
$557$	27.7128			1.17423			0.587115	+	0.809504i	$0.300264\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$		0			0
$562$	18.0000	+	31.1769i	0.759284	+	1.31512i
$563$	−6.92820	−	12.0000i	−0.291989	−	0.505740i	0.682291	−	0.731081i	$-0.260984\pi$
$563$	−6.92820	−	12.0000i	−0.291989	−	0.505740i	−0.974280	+	0.225341i	$0.927650\pi$
$564$		0			0
$565$		0			0
$566$	−6.92820			−0.291214
$567$		0			0
$568$	−6.00000			−0.251754
$569$	6.92820	−	12.0000i	0.290445	−	0.503066i	−0.683470	−	0.729979i	$-0.739530\pi$
$569$	6.92820	−	12.0000i	0.290445	−	0.503066i	0.973915	+	0.226913i	$0.0728632\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	1.73205	+	3.00000i	0.0724207	+	0.125436i
$573$		0			0
$574$	−12.0000	+	20.7846i	−0.500870	+	0.867533i
$575$	−34.6410			−1.44463
$576$		0			0
$577$	26.0000			1.08239			0.541197	−	0.840896i	$-0.317971\pi$
$577$	26.0000			1.08239			0.541197	+	0.840896i	$0.317971\pi$
$578$	−26.8468	+	46.5000i	−1.11668	+	1.93415i
$579$		0			0
$580$		0			0
$581$	−10.3923	−	18.0000i	−0.431145	−	0.746766i
$582$		0			0
$583$		0			0
$584$	17.3205			0.716728
$585$		0			0
$586$	24.0000			0.991431
$587$	22.5167	−	39.0000i	0.929362	−	1.60970i	0.144971	−	0.989436i	$-0.453691\pi$
$587$	22.5167	−	39.0000i	0.929362	−	1.60970i	0.784391	−	0.620266i	$-0.212975\pi$
$588$		0			0
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$		0			0
$591$		0			0
$592$	5.00000	−	8.66025i	0.205499	−	0.355934i
$593$	20.7846			0.853522			0.426761	−	0.904365i	$-0.359655\pi$
$593$	20.7846			0.853522			0.426761	+	0.904365i	$0.359655\pi$
$594$		0			0
$595$		0			0
$596$	−6.92820	+	12.0000i	−0.283790	+	0.491539i
$597$		0			0
$598$	−6.00000	−	10.3923i	−0.245358	−	0.424973i
$599$	−10.3923	−	18.0000i	−0.424618	−	0.735460i	0.571767	−	0.820416i	$-0.306258\pi$
$599$	−10.3923	−	18.0000i	−0.424618	−	0.735460i	−0.996385	+	0.0849563i	$0.972925\pi$
$600$		0			0
$601$	17.0000	−	29.4449i	0.693444	−	1.20108i	−0.277258	−	0.960796i	$-0.589426\pi$
$601$	17.0000	−	29.4449i	0.693444	−	1.20108i	0.970702	−	0.240285i	$-0.0772411\pi$
$602$	27.7128			1.12949
$603$		0			0
$604$	14.0000			0.569652
$605$		0			0
$606$		0			0
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	0.911621	+	0.411033i	$0.134832\pi$
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	−0.0998457	+	0.995003i	$0.531835\pi$
$608$	5.19615	+	9.00000i	0.210732	+	0.364998i
$609$		0			0
$610$		0			0
$611$	−10.3923			−0.420428
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	−22.5167	+	39.0000i	−0.908698	+	1.57391i
$615$		0			0
$616$	−6.00000	−	10.3923i	−0.241747	−	0.418718i
$617$	3.46410	+	6.00000i	0.139459	+	0.241551i	0.927292	−	0.374338i	$-0.122130\pi$
$617$	3.46410	+	6.00000i	0.139459	+	0.241551i	−0.787833	+	0.615889i	$0.788797\pi$
$618$		0			0
$619$	−13.0000	+	22.5167i	−0.522514	+	0.905021i	0.477143	+	0.878826i	$0.341672\pi$
$619$	−13.0000	+	22.5167i	−0.522514	+	0.905021i	−0.999657	+	0.0261952i	$0.991661\pi$
$620$		0			0
$621$		0			0
$622$	−36.0000			−1.44347
$623$	−6.92820	+	12.0000i	−0.277573	+	0.480770i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−12.1244	−	21.0000i	−0.484587	−	0.839329i
$627$		0			0
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	−13.8564			−0.552491
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$	−3.46410	+	6.00000i	−0.137795	+	0.238667i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.50000	−	2.59808i	0.0594322	−	0.102940i
$638$	−41.5692			−1.64574
$639$		0			0
$640$		0			0
$641$	−17.3205	+	30.0000i	−0.684119	+	1.18493i	0.289594	+	0.957150i	$0.406480\pi$
$641$	−17.3205	+	30.0000i	−0.684119	+	1.18493i	−0.973713	+	0.227779i	$0.926854\pi$
$642$		0			0
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	0.694347	−	0.719640i	$-0.255693\pi$
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	−0.970400	+	0.241502i	$0.922360\pi$
$644$	−6.92820	−	12.0000i	−0.273009	−	0.472866i
$645$		0			0
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	−13.8564			−0.544752			−0.272376	−	0.962191i	$-0.587809\pi$
$647$	−13.8564			−0.544752			−0.272376	+	0.962191i	$0.587809\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$	4.33013	−	7.50000i	0.169842	−	0.294174i
$651$		0			0
$652$	−7.00000	−	12.1244i	−0.274141	−	0.474826i
$653$	17.3205	+	30.0000i	0.677804	+	1.17399i	0.975641	+	0.219374i	$0.0704015\pi$
$653$	17.3205	+	30.0000i	0.677804	+	1.17399i	−0.297837	+	0.954617i	$0.596265\pi$
$654$		0			0
$655$		0			0
$656$	−34.6410			−1.35250
$657$		0			0
$658$	−36.0000			−1.40343
$659$	−6.92820	+	12.0000i	−0.269884	+	0.467454i	−0.968832	−	0.247720i	$-0.920319\pi$
$659$	−6.92820	+	12.0000i	−0.269884	+	0.467454i	0.698947	+	0.715173i	$0.253652\pi$
$660$		0			0
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	−0.999979	−	0.00652642i	$-0.997923\pi$
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	0.494337	−	0.869270i	$-0.335411\pi$
$662$	8.66025	+	15.0000i	0.336590	+	0.582992i
$663$		0			0
$664$	9.00000	−	15.5885i	0.349268	−	0.604949i
$665$		0			0
$666$		0			0
$667$	48.0000			1.85857
$668$	−8.66025	+	15.0000i	−0.335075	+	0.580367i
$669$		0			0
$670$		0			0
$671$	−17.3205	−	30.0000i	−0.668651	−	1.15814i
$672$		0			0
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	−0.753420	−	0.657539i	$-0.771597\pi$
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	0.946156	+	0.323711i	$0.104931\pi$
$674$	3.46410			0.133432
$675$		0			0
$676$	1.00000			0.0384615
$677$	20.7846	−	36.0000i	0.798817	−	1.38359i	−0.121569	−	0.992583i	$-0.538793\pi$
$677$	20.7846	−	36.0000i	0.798817	−	1.38359i	0.920387	−	0.391009i	$-0.127874\pi$
$678$		0			0
$679$	10.0000	+	17.3205i	0.383765	+	0.664700i
$680$		0			0
$681$		0			0
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	−17.3205			−0.662751			−0.331375	−	0.943499i	$-0.607513\pi$
$683$	−17.3205			−0.662751			−0.331375	+	0.943499i	$0.607513\pi$
$684$		0			0
$685$		0			0
$686$	17.3205	−	30.0000i	0.661300	−	1.14541i
$687$		0			0
$688$	20.0000	+	34.6410i	0.762493	+	1.32068i
$689$		0			0
$690$		0			0
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	−0.755110	−	0.655598i	$-0.772417\pi$
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	0.945319	+	0.326146i	$0.105750\pi$
$692$	13.8564			0.526742
$693$		0			0
$694$	−48.0000			−1.82206
$695$		0			0
$696$		0			0
$697$	24.0000	+	41.5692i	0.909065	+	1.57455i
$698$	−22.5167	−	39.0000i	−0.852268	−	1.47617i
$699$		0			0
$700$	5.00000	−	8.66025i	0.188982	−	0.327327i
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$		0			0
$703$	4.00000			0.150863
$704$	1.73205	−	3.00000i	0.0652791	−	0.113067i
$705$		0			0
$706$	−6.00000	−	10.3923i	−0.225813	−	0.391120i
$707$	13.8564	+	24.0000i	0.521124	+	0.902613i
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$		0			0
$711$		0			0
$712$	−12.0000			−0.449719
$713$	−6.92820	+	12.0000i	−0.259463	+	0.449404i
$714$		0			0
$715$		0			0
$716$	6.92820	+	12.0000i	0.258919	+	0.448461i
$717$		0			0
$718$	9.00000	−	15.5885i	0.335877	−	0.581756i
$719$	34.6410			1.29189			0.645946	−	0.763383i	$-0.276463\pi$
$719$	34.6410			1.29189			0.645946	+	0.763383i	$0.276463\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	12.9904	−	22.5000i	0.483452	−	0.837363i
$723$		0			0
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	17.3205	+	30.0000i	0.643268	+	1.11417i
$726$		0			0
$727$	−16.0000	+	27.7128i	−0.593407	+	1.02781i	0.400362	+	0.916357i	$0.368884\pi$
$727$	−16.0000	+	27.7128i	−0.593407	+	1.02781i	−0.993770	+	0.111454i	$0.964449\pi$
$728$	−3.46410			−0.128388
$729$		0			0
$730$		0			0
$731$	27.7128	−	48.0000i	1.02500	−	1.77534i
$732$		0			0
$733$	17.0000	+	29.4449i	0.627909	+	1.08757i	0.987971	+	0.154642i	$0.0494225\pi$
$733$	17.0000	+	29.4449i	0.627909	+	1.08757i	−0.360061	+	0.932929i	$0.617244\pi$
$734$	−6.92820	−	12.0000i	−0.255725	−	0.442928i
$735$		0			0
$736$	18.0000	−	31.1769i	0.663489	−	1.14920i
$737$	−48.4974			−1.78643
$738$		0			0
$739$	−22.0000			−0.809283			−0.404642	−	0.914475i	$-0.632604\pi$
$739$	−22.0000			−0.809283			−0.404642	+	0.914475i	$0.632604\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	12.1244	+	21.0000i	0.444799	+	0.770415i	0.998038	−	0.0626075i	$-0.0199416\pi$
$743$	12.1244	+	21.0000i	0.444799	+	0.770415i	−0.553239	+	0.833023i	$0.686608\pi$
$744$		0			0
$745$		0			0
$746$	45.0333			1.64879
$747$		0			0
$748$	24.0000			0.877527
$749$	−6.92820	+	12.0000i	−0.253151	+	0.438470i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	−25.9808	−	45.0000i	−0.947421	−	1.64098i
$753$		0			0
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$		0			0
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−1.73205	+	3.00000i	−0.0629109	+	0.108965i
$759$		0			0
$760$		0			0
$761$	−17.3205	−	30.0000i	−0.627868	−	1.08750i	−0.987979	−	0.154590i	$-0.950594\pi$
$761$	−17.3205	−	30.0000i	−0.627868	−	1.08750i	0.360111	−	0.932910i	$-0.382739\pi$
$762$		0			0
$763$	10.0000	−	17.3205i	0.362024	−	0.627044i
$764$	13.8564			0.501307
$765$		0			0
$766$	−30.0000			−1.08394
$767$	−1.73205	+	3.00000i	−0.0625407	+	0.108324i
$768$		0			0
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.825518	−	0.564376i	$-0.809117\pi$
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.0760054	−	0.997107i	$-0.524217\pi$
$770$		0			0
$771$		0			0
$772$	−13.0000	+	22.5167i	−0.467880	+	0.810392i
$773$	13.8564			0.498380			0.249190	−	0.968455i	$-0.419836\pi$
$773$	13.8564			0.498380			0.249190	+	0.968455i	$0.419836\pi$
$774$		0			0
$775$	−10.0000			−0.359211
$776$	−8.66025	+	15.0000i	−0.310885	+	0.538469i
$777$		0			0
$778$	−18.0000	−	31.1769i	−0.645331	−	1.11775i
$779$	−6.92820	−	12.0000i	−0.248229	−	0.429945i
$780$		0			0
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$	−83.1384			−2.97302
$783$		0			0
$784$	15.0000			0.535714
$785$		0			0
$786$		0			0
$787$	11.0000	+	19.0526i	0.392108	+	0.679150i	0.992727	−	0.120384i	$-0.0384127\pi$
$787$	11.0000	+	19.0526i	0.392108	+	0.679150i	−0.600620	+	0.799535i	$0.705079\pi$
$788$	6.92820	+	12.0000i	0.246807	+	0.427482i
$789$		0			0
$790$		0			0
$791$	−13.8564			−0.492677
$792$		0			0
$793$	−10.0000			−0.355110
$794$	−1.73205	+	3.00000i	−0.0614682	+	0.106466i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	−17.3205	−	30.0000i	−0.613524	−	1.06265i	−0.990642	−	0.136489i	$-0.956418\pi$
$797$	−17.3205	−	30.0000i	−0.613524	−	1.06265i	0.377118	−	0.926165i	$-0.376915\pi$
$798$		0			0
$799$	−36.0000	+	62.3538i	−1.27359	+	2.20592i
$800$	25.9808			0.918559
$801$		0			0
$802$	−60.0000			−2.11867
$803$	−17.3205	+	30.0000i	−0.611227	+	1.05868i
$804$		0			0
$805$		0			0
$806$	−1.73205	−	3.00000i	−0.0610089	−	0.105670i
$807$		0			0
$808$	−12.0000	+	20.7846i	−0.422159	+	0.731200i
$809$	6.92820			0.243583			0.121791	−	0.992556i	$-0.461136\pi$
$809$	6.92820			0.243583			0.121791	+	0.992556i	$0.461136\pi$
$810$		0			0
$811$	26.0000			0.912983			0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000			0.912983			0.456492	+	0.889728i	$0.349106\pi$
$812$	−6.92820	+	12.0000i	−0.243132	+	0.421117i
$813$		0			0
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$		0			0
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	−17.3205			−0.605597
$819$		0			0
$820$		0			0
$821$	−13.8564	+	24.0000i	−0.483592	+	0.837606i	−0.999822	−	0.0188439i	$-0.994001\pi$
$821$	−13.8564	+	24.0000i	−0.483592	+	0.837606i	0.516231	+	0.856450i	$0.327335\pi$
$822$		0			0
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	−3.46410	−	6.00000i	−0.120678	−	0.209020i
$825$		0			0
$826$	−6.00000	+	10.3923i	−0.208767	+	0.361595i
$827$	10.3923			0.361376			0.180688	−	0.983540i	$-0.442168\pi$
$827$	10.3923			0.361376			0.180688	+	0.983540i	$0.442168\pi$
$828$		0			0
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$		0			0
$831$		0			0
$832$	−0.500000	−	0.866025i	−0.0173344	−	0.0300240i
$833$	−10.3923	−	18.0000i	−0.360072	−	0.623663i
$834$		0			0
$835$		0			0
$836$	−6.92820			−0.239617
$837$		0			0
$838$	12.0000			0.414533
$839$	−12.1244	+	21.0000i	−0.418579	+	0.725001i	−0.995797	−	0.0915899i	$-0.970805\pi$
$839$	−12.1244	+	21.0000i	−0.418579	+	0.725001i	0.577218	+	0.816590i	$0.304138\pi$
$840$		0			0
$841$	−9.50000	−	16.4545i	−0.327586	−	0.567396i
$842$	8.66025	+	15.0000i	0.298452	+	0.516934i
$843$		0			0
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$		0			0
$846$		0			0
$847$	2.00000			0.0687208
$848$		0			0
$849$		0			0
$850$	−30.0000	−	51.9615i	−1.02899	−	1.78227i
$851$	−6.92820	−	12.0000i	−0.237496	−	0.411355i
$852$		0			0
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	0.927491	−	0.373845i	$-0.121961\pi$
$854$	−34.6410			−1.18539
$855$		0			0
$856$	−12.0000			−0.410152
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	0.974249	+	0.225475i	$0.0723932\pi$
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	−0.291858	+	0.956462i	$0.594273\pi$
$860$		0			0
$861$		0			0
$862$	−33.0000	+	57.1577i	−1.12398	+	1.94680i
$863$	−31.1769			−1.06127			−0.530637	−	0.847599i	$-0.678047\pi$
$863$	−31.1769			−1.06127			−0.530637	+	0.847599i	$0.678047\pi$
$864$		0			0
$865$		0			0
$866$	−1.73205	+	3.00000i	−0.0588575	+	0.101944i
$867$		0			0
$868$	−2.00000	−	3.46410i	−0.0678844	−	0.117579i
$869$	−6.92820	−	12.0000i	−0.235023	−	0.407072i
$870$		0			0
$871$	−7.00000	+	12.1244i	−0.237186	+	0.410818i
$872$	17.3205			0.586546
$873$		0			0
$874$	24.0000			0.811812
$875$		0			0
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	24.2487	+	42.0000i	0.818354	+	1.41743i
$879$		0			0
$880$		0			0
$881$	−13.8564			−0.466834			−0.233417	−	0.972377i	$-0.574991\pi$
$881$	−13.8564			−0.466834			−0.233417	+	0.972377i	$0.574991\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	3.46410	−	6.00000i	0.116510	−	0.201802i
$885$		0			0
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−13.8564	−	24.0000i	−0.465253	−	0.805841i	0.533960	−	0.845510i	$-0.320703\pi$
$887$	−13.8564	−	24.0000i	−0.465253	−	0.805841i	−0.999213	+	0.0396684i	$0.987370\pi$
$888$		0			0
$889$	16.0000	−	27.7128i	0.536623	−	0.929458i
$890$		0			0
$891$		0			0
$892$	2.00000			0.0669650
$893$	10.3923	−	18.0000i	0.347765	−	0.602347i
$894$		0			0
$895$		0			0
$896$	−12.1244	−	21.0000i	−0.405046	−	0.701561i
$897$		0			0
$898$	6.00000	−	10.3923i	0.200223	−	0.346796i
$899$	13.8564			0.462137
$900$		0			0
$901$		0			0
$902$	20.7846	−	36.0000i	0.692052	−	1.19867i
$903$		0			0
$904$	−6.00000	−	10.3923i	−0.199557	−	0.345643i
$905$		0			0
$906$		0			0
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	0.226173	+	0.974087i	$0.427379\pi$
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	−0.956671	+	0.291172i	$0.905955\pi$
$908$	3.46410			0.114960
$909$		0			0
$910$		0			0
$911$	20.7846	−	36.0000i	0.688625	−	1.19273i	−0.283658	−	0.958926i	$-0.591548\pi$
$911$	20.7846	−	36.0000i	0.688625	−	1.19273i	0.972283	−	0.233808i	$-0.0751186\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	8.66025	+	15.0000i	0.286456	+	0.496156i
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	−41.5692			−1.37274
$918$		0			0
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$		0			0
$921$		0			0
$922$	24.0000	+	41.5692i	0.790398	+	1.36901i
$923$	−1.73205	−	3.00000i	−0.0570111	−	0.0987462i
$924$		0			0
$925$	5.00000	−	8.66025i	0.164399	−	0.284747i
$926$	3.46410			0.113837
$927$		0			0
$928$	−36.0000			−1.18176
$929$	24.2487	−	42.0000i	0.795574	−	1.37798i	−0.126899	−	0.991916i	$-0.540503\pi$
$929$	24.2487	−	42.0000i	0.795574	−	1.37798i	0.922474	−	0.386060i	$-0.126164\pi$
$930$		0			0
$931$	3.00000	+	5.19615i	0.0983210	+	0.170297i
$932$		0			0
$933$		0			0
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$		0			0
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	−24.2487	+	42.0000i	−0.791748	+	1.37135i
$939$		0			0
$940$		0			0
$941$	−20.7846	−	36.0000i	−0.677559	−	1.17357i	−0.975714	−	0.219049i	$-0.929705\pi$
$941$	−20.7846	−	36.0000i	−0.677559	−	1.17357i	0.298155	−	0.954517i	$-0.403629\pi$
$942$		0			0
$943$	−24.0000	+	41.5692i	−0.781548	+	1.35368i
$944$	−17.3205			−0.563735
$945$		0			0
$946$	−48.0000			−1.56061
$947$	−8.66025	+	15.0000i	−0.281420	+	0.487435i	−0.971735	−	0.236075i	$-0.924139\pi$
$947$	−8.66025	+	15.0000i	−0.281420	+	0.487435i	0.690314	+	0.723510i	$0.257472\pi$
$948$		0			0
$949$	5.00000	+	8.66025i	0.162307	+	0.281124i
$950$	8.66025	+	15.0000i	0.280976	+	0.486664i
$951$		0			0
$952$	−12.0000	+	20.7846i	−0.388922	+	0.673633i
$953$	−27.7128			−0.897706			−0.448853	−	0.893606i	$-0.648167\pi$
$953$	−27.7128			−0.897706			−0.448853	+	0.893606i	$0.648167\pi$
$954$		0			0
$955$		0			0
$956$	5.19615	−	9.00000i	0.168056	−	0.291081i
$957$		0			0
$958$	3.00000	+	5.19615i	0.0969256	+	0.167880i
$959$	6.92820	+	12.0000i	0.223723	+	0.387500i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	3.46410			0.111687
$963$		0			0
$964$	−10.0000			−0.322078
$965$		0			0
$966$		0			0
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	0.849499	−	0.527591i	$-0.176905\pi$
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	−0.881656	+	0.471892i	$0.843571\pi$
$968$	0.866025	+	1.50000i	0.0278351	+	0.0482118i
$969$		0			0
$970$		0			0
$971$	55.4256			1.77869			0.889346	−	0.457234i	$-0.151160\pi$
$971$	55.4256			1.77869			0.889346	+	0.457234i	$0.151160\pi$
$972$		0			0
$973$	−8.00000			−0.256468
$974$	−1.73205	+	3.00000i	−0.0554985	+	0.0961262i
$975$		0			0
$976$	−25.0000	−	43.3013i	−0.800230	−	1.38604i
$977$	−3.46410	−	6.00000i	−0.110826	−	0.191957i	0.805277	−	0.592898i	$-0.202016\pi$
$977$	−3.46410	−	6.00000i	−0.110826	−	0.191957i	−0.916104	+	0.400941i	$0.868683\pi$
$978$		0			0
$979$	12.0000	−	20.7846i	0.383522	−	0.664279i
$980$		0			0
$981$		0			0
$982$	12.0000			0.382935
$983$	−5.19615	+	9.00000i	−0.165732	+	0.287055i	−0.936915	−	0.349558i	$-0.886332\pi$
$983$	−5.19615	+	9.00000i	−0.165732	+	0.287055i	0.771183	+	0.636613i	$0.219665\pi$
$984$		0			0
$985$		0			0
$986$	41.5692	+	72.0000i	1.32383	+	2.29295i
$987$		0			0
$988$	−1.00000	+	1.73205i	−0.0318142	+	0.0551039i
$989$	55.4256			1.76243
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	5.19615	−	9.00000i	0.164978	−	0.285750i
$993$		0			0
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$		0			0
$996$		0			0
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$	24.2487			0.767580
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1053.2.e.i.703.1		4
3.2	odd	2	inner	1053.2.e.i.703.2		4
9.2	odd	6		117.2.a.b.1.1	✓	2
9.4	even	3	inner	1053.2.e.i.352.1		4
9.5	odd	6	inner	1053.2.e.i.352.2		4
9.7	even	3		117.2.a.b.1.2	yes	2
36.7	odd	6		1872.2.a.v.1.2		2
36.11	even	6		1872.2.a.v.1.1		2
45.2	even	12		2925.2.c.s.2224.2		4
45.7	odd	12		2925.2.c.s.2224.4		4
45.29	odd	6		2925.2.a.y.1.2		2
45.34	even	6		2925.2.a.y.1.1		2
45.38	even	12		2925.2.c.s.2224.3		4
45.43	odd	12		2925.2.c.s.2224.1		4
63.20	even	6		5733.2.a.t.1.1		2
63.34	odd	6		5733.2.a.t.1.2		2
72.11	even	6		7488.2.a.cj.1.2		2
72.29	odd	6		7488.2.a.cq.1.1		2
72.43	odd	6		7488.2.a.cj.1.1		2
72.61	even	6		7488.2.a.cq.1.2		2
117.25	even	6		1521.2.a.j.1.1		2
117.34	odd	12		1521.2.b.i.1351.3		4
117.38	odd	6		1521.2.a.j.1.2		2
117.47	even	12		1521.2.b.i.1351.1		4
117.70	odd	12		1521.2.b.i.1351.2		4
117.83	even	12		1521.2.b.i.1351.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.a.b.1.1	✓	2	9.2	odd	6
117.2.a.b.1.2	yes	2	9.7	even	3
1053.2.e.i.352.1		4	9.4	even	3	inner
1053.2.e.i.352.2		4	9.5	odd	6	inner
1053.2.e.i.703.1		4	1.1	even	1	trivial
1053.2.e.i.703.2		4	3.2	odd	2	inner
1521.2.a.j.1.1		2	117.25	even	6
1521.2.a.j.1.2		2	117.38	odd	6
1521.2.b.i.1351.1		4	117.47	even	12
1521.2.b.i.1351.2		4	117.70	odd	12
1521.2.b.i.1351.3		4	117.34	odd	12
1521.2.b.i.1351.4		4	117.83	even	12
1872.2.a.v.1.1		2	36.11	even	6
1872.2.a.v.1.2		2	36.7	odd	6
2925.2.a.y.1.1		2	45.34	even	6
2925.2.a.y.1.2		2	45.29	odd	6
2925.2.c.s.2224.1		4	45.43	odd	12
2925.2.c.s.2224.2		4	45.2	even	12
2925.2.c.s.2224.3		4	45.38	even	12
2925.2.c.s.2224.4		4	45.7	odd	12
5733.2.a.t.1.1		2	63.20	even	6
5733.2.a.t.1.2		2	63.34	odd	6
7488.2.a.cj.1.1		2	72.43	odd	6
7488.2.a.cj.1.2		2	72.11	even	6
7488.2.a.cq.1.1		2	72.29	odd	6
7488.2.a.cq.1.2		2	72.61	even	6

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:	\( N \)	\(=\)	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1053.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{7} -1.73205 q^{8} +(1.73205 - 3.00000i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-1.73205 - 3.00000i) q^{14} +(2.50000 - 4.33013i) q^{16} -6.92820 q^{17} +2.00000 q^{19} +(3.00000 + 5.19615i) q^{22} +(-3.46410 - 6.00000i) q^{23} +(2.50000 - 4.33013i) q^{25} +1.73205 q^{26} +2.00000 q^{28} +(-3.46410 + 6.00000i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(2.59808 + 4.50000i) q^{32} +(6.00000 - 10.3923i) q^{34} +2.00000 q^{37} +(-1.73205 + 3.00000i) q^{38} +(-3.46410 - 6.00000i) q^{41} +(-4.00000 + 6.92820i) q^{43} -3.46410 q^{44} +12.0000 q^{46} +(5.19615 - 9.00000i) q^{47} +(1.50000 + 2.59808i) q^{49} +(4.33013 + 7.50000i) q^{50} +(-0.500000 + 0.866025i) q^{52} +(1.73205 - 3.00000i) q^{56} +(-6.00000 - 10.3923i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(5.00000 - 8.66025i) q^{61} +3.46410 q^{62} +1.00000 q^{64} +(-7.00000 - 12.1244i) q^{67} +(3.46410 + 6.00000i) q^{68} +3.46410 q^{71} -10.0000 q^{73} +(-1.73205 + 3.00000i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(3.46410 + 6.00000i) q^{77} +(2.00000 - 3.46410i) q^{79} +12.0000 q^{82} +(-5.19615 + 9.00000i) q^{83} +(-6.92820 - 12.0000i) q^{86} +(-3.00000 + 5.19615i) q^{88} +6.92820 q^{89} +2.00000 q^{91} +(-3.46410 + 6.00000i) q^{92} +(9.00000 + 15.5885i) q^{94} +(5.00000 - 8.66025i) q^{97} -5.19615 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} - 4 q^{7} - 2 q^{13} + 10 q^{16} + 8 q^{19} + 12 q^{22} + 10 q^{25} + 8 q^{28} - 4 q^{31} + 24 q^{34} + 8 q^{37} - 16 q^{43} + 48 q^{46} + 6 q^{49} - 2 q^{52} - 24 q^{58} + 20 q^{61} + 4 q^{64}+ \cdots + 20 q^{97}+O(q^{100}) \) 4 * q - 2 * q^4 - 4 * q^7 - 2 * q^13 + 10 * q^16 + 8 * q^19 + 12 * q^22 + 10 * q^25 + 8 * q^28 - 4 * q^31 + 24 * q^34 + 8 * q^37 - 16 * q^43 + 48 * q^46 + 6 * q^49 - 2 * q^52 - 24 * q^58 + 20 * q^61 + 4 * q^64 - 28 * q^67 - 40 * q^73 - 4 * q^76 + 8 * q^79 + 48 * q^82 - 12 * q^88 + 8 * q^91 + 36 * q^94 + 20 * q^97

Introduction

L-functions

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