LMFDB - Embedded newform 972.2.l.a.107.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,-3,0,3,-6,0,0,9,0,-3,0,0,6,-33] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	972.107
Dual form			972.2.l.a.863.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.06904 - 0.925831i) q^{2} +(0.285675 + 1.97949i) q^{4} +(-1.17862 + 3.23823i) q^{5} +(2.88522 + 0.508742i) q^{7} +(1.52728 - 2.38064i) q^{8} +(4.25804 - 2.37058i) q^{10} +(2.45635 - 0.894038i) q^{11} +(4.15529 - 3.48670i) q^{13} +(-2.61340 - 3.21509i) q^{14} +(-3.83678 + 1.13098i) q^{16} +(-1.15583 + 0.667320i) q^{17} +(-0.0790760 - 0.0456546i) q^{19} +(-6.74675 - 1.40799i) q^{20} +(-3.45365 - 1.31840i) q^{22} +(0.147416 + 0.836038i) q^{23} +(-5.26677 - 4.41934i) q^{25} +(-7.67024 - 0.119685i) q^{26} +(-0.182815 + 5.85661i) q^{28} +(0.322160 - 0.383935i) q^{29} +(6.56230 - 1.15711i) q^{31} +(5.14875 + 2.34314i) q^{32} +(1.85345 + 0.356716i) q^{34} +(-5.04800 + 8.74340i) q^{35} +(2.75869 + 4.77819i) q^{37} +(0.0422667 + 0.122017i) q^{38} +(5.90897 + 7.75154i) q^{40} +(1.83593 + 2.18798i) q^{41} +(1.94395 + 5.34095i) q^{43} +(2.47146 + 4.60692i) q^{44} +(0.616436 - 1.03024i) q^{46} +(1.14746 - 6.50759i) q^{47} +(1.48783 + 0.541527i) q^{49} +(1.53880 + 9.60057i) q^{50} +(8.08896 + 7.22929i) q^{52} +7.37249i q^{53} +9.00795i q^{55} +(5.61766 - 6.09167i) q^{56} +(-0.699859 + 0.112175i) q^{58} +(2.86152 + 1.04151i) q^{59} +(-0.421082 + 2.38808i) q^{61} +(-8.08663 - 4.83859i) q^{62} +(-3.33485 - 7.27178i) q^{64} +(6.39324 + 17.5653i) q^{65} +(-3.09917 - 3.69345i) q^{67} +(-1.65115 - 2.09732i) q^{68} +(13.4914 - 4.67341i) q^{70} +(-5.91940 - 10.2527i) q^{71} +(-5.83049 + 10.0987i) q^{73} +(1.47466 - 7.66214i) q^{74} +(0.0677828 - 0.169573i) q^{76} +(7.54195 - 1.32985i) q^{77} +(1.08439 - 1.29232i) q^{79} +(0.859714 - 13.7574i) q^{80} +(0.0630204 - 4.03879i) q^{82} +(-1.65438 - 1.38819i) q^{83} +(-0.798649 - 4.52937i) q^{85} +(2.86667 - 7.50943i) q^{86} +(1.62315 - 7.21311i) q^{88} +(12.5801 + 7.26310i) q^{89} +(13.7628 - 7.94593i) q^{91} +(-1.61282 + 0.530644i) q^{92} +(-7.25160 + 5.89449i) q^{94} +(0.241041 - 0.202257i) q^{95} +(-6.20195 + 2.25733i) q^{97} +(-1.08919 - 1.95639i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} - 33 q^{14} + 3 q^{16} + 18 q^{17} + 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 30 q^{29} - 33 q^{32} + 15 q^{34} - 6 q^{37} + 63 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 - 33 * q^14 + 3 * q^16 + 18 * q^17 + 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 30 * q^29 - 33 * q^32 + 15 * q^34 - 6 * q^37 + 63 * q^38 + 33 * q^40 + 24 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 21 * q^50 + 57 * q^52 + 18 * q^56 + 57 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 - 30 * q^65 + 102 * q^68 + 51 * q^70 - 6 * q^73 - 75 * q^74 + 27 * q^76 + 42 * q^77 - 12 * q^82 - 24 * q^85 + 111 * q^86 + 27 * q^88 - 147 * q^92 + 30 * q^94 - 12 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	−1.06904	−	0.925831i	−0.755923	−	0.654661i
$2$	−1.06904	−	0.925831i	−0.755923	−	0.654661i
$3$		0			0
$3$		0			0
$4$	0.285675	+	1.97949i	0.142838	+	0.989746i
$5$	−1.17862	+	3.23823i	−0.527095	+	1.44818i	0.335381	+	0.942082i	$0.391135\pi$
$5$	−1.17862	+	3.23823i	−0.527095	+	1.44818i	−0.862476	+	0.506098i	$0.831087\pi$
$6$		0			0
$7$	2.88522	+	0.508742i	1.09051	+	0.192287i	0.689859	−	0.723944i	$-0.257672\pi$
$7$	2.88522	+	0.508742i	1.09051	+	0.192287i	0.400652	+	0.916230i	$0.368784\pi$
$8$	1.52728	−	2.38064i	0.539974	−	0.841682i
$9$		0			0
$10$	4.25804	−	2.37058i	1.34651	−	0.749644i
$11$	2.45635	−	0.894038i	0.740617	−	0.269563i	0.0559651	−	0.998433i	$-0.482176\pi$
$11$	2.45635	−	0.894038i	0.740617	−	0.269563i	0.684652	+	0.728870i	$0.259954\pi$
$12$		0			0
$13$	4.15529	−	3.48670i	1.15247	−	0.967037i	0.152695	−	0.988273i	$-0.451205\pi$
$13$	4.15529	−	3.48670i	1.15247	−	0.967037i	0.999774	+	0.0212368i	$0.00676040\pi$
$14$	−2.61340	−	3.21509i	−0.698459	−	0.859269i
$15$		0			0
$16$	−3.83678	+	1.13098i	−0.959195	+	0.282746i
$17$	−1.15583	+	0.667320i	−0.280330	+	0.161849i	−0.633573	−	0.773683i	$-0.718412\pi$
$17$	−1.15583	+	0.667320i	−0.280330	+	0.161849i	0.353243	+	0.935532i	$0.385079\pi$
$18$		0			0
$19$	−0.0790760	−	0.0456546i	−0.0181413	−	0.0104739i	0.490902	−	0.871215i	$-0.336667\pi$
$19$	−0.0790760	−	0.0456546i	−0.0181413	−	0.0104739i	−0.509043	+	0.860741i	$0.670001\pi$
$20$	−6.74675	−	1.40799i	−1.50862	−	0.314835i
$21$		0			0
$22$	−3.45365	−	1.31840i	−0.736321	−	0.281085i
$23$	0.147416	+	0.836038i	0.0307384	+	0.174326i	0.996312	−	0.0858037i	$-0.0273458\pi$
$23$	0.147416	+	0.836038i	0.0307384	+	0.174326i	−0.965574	+	0.260130i	$0.916235\pi$
$24$		0			0
$25$	−5.26677	−	4.41934i	−1.05335	−	0.883869i
$26$	−7.67024	−	0.119685i	−1.50426	−	0.0234721i
$27$		0			0
$28$	−0.182815	+	5.85661i	−0.0345487	+	1.10679i
$29$	0.322160	−	0.383935i	0.0598236	−	0.0712950i	−0.735303	−	0.677739i	$-0.762960\pi$
$29$	0.322160	−	0.383935i	0.0598236	−	0.0712950i	0.795126	+	0.606444i	$0.207404\pi$
$30$		0			0
$31$	6.56230	−	1.15711i	1.17862	−	0.207823i	0.450186	−	0.892935i	$-0.351358\pi$
$31$	6.56230	−	1.15711i	1.17862	−	0.207823i	0.728438	+	0.685111i	$0.240246\pi$
$32$	5.14875	+	2.34314i	0.910180	+	0.414213i
$33$		0			0
$34$	1.85345	+	0.356716i	0.317864	+	0.0611762i
$35$	−5.04800	+	8.74340i	−0.853268	+	1.47790i
$36$		0			0
$37$	2.75869	+	4.77819i	0.453526	+	0.785530i	0.998602	−	0.0528563i	$-0.0168325\pi$
$37$	2.75869	+	4.77819i	0.453526	+	0.785530i	−0.545076	+	0.838387i	$0.683499\pi$
$38$	0.0422667	+	0.122017i	0.00685657	+	0.0197938i
$39$		0			0
$40$	5.90897	+	7.75154i	0.934290	+	1.22563i
$41$	1.83593	+	2.18798i	0.286725	+	0.341705i	0.890111	−	0.455744i	$-0.150627\pi$
$41$	1.83593	+	2.18798i	0.286725	+	0.341705i	−0.603386	+	0.797449i	$0.706182\pi$
$42$		0			0
$43$	1.94395	+	5.34095i	0.296449	+	0.814487i	0.995086	+	0.0990112i	$0.0315680\pi$
$43$	1.94395	+	5.34095i	0.296449	+	0.814487i	−0.698637	+	0.715476i	$0.746210\pi$
$44$	2.47146	+	4.60692i	0.372587	+	0.694519i
$45$		0			0
$46$	0.616436	−	1.03024i	0.0908886	−	0.151900i
$47$	1.14746	−	6.50759i	0.167375	−	0.949229i	−0.779207	−	0.626766i	$-0.784378\pi$
$47$	1.14746	−	6.50759i	0.167375	−	0.949229i	0.946582	−	0.322463i	$-0.104511\pi$
$48$		0			0
$49$	1.48783	+	0.541527i	0.212548	+	0.0773611i
$50$	1.53880	+	9.60057i	0.217619	+	1.35773i
$51$		0			0
$52$	8.08896	+	7.22929i	1.12174	+	1.00252i
$53$			7.37249i			1.01269i	0.862331	+	0.506345i	$0.169004\pi$
$53$			7.37249i			1.01269i	−0.862331	+	0.506345i	$0.830996\pi$
$54$		0			0
$55$			9.00795i			1.21463i
$56$	5.61766	−	6.09167i	0.750692	−	0.814033i
$57$		0			0
$58$	−0.699859	+	0.112175i	−0.0918960	+	0.0147293i
$59$	2.86152	+	1.04151i	0.372538	+	0.135593i	0.521502	−	0.853250i	$-0.325372\pi$
$59$	2.86152	+	1.04151i	0.372538	+	0.135593i	−0.148965	+	0.988843i	$0.547594\pi$
$60$		0			0
$61$	−0.421082	+	2.38808i	−0.0539141	+	0.305762i	−0.999826	−	0.0186620i	$-0.994059\pi$
$61$	−0.421082	+	2.38808i	−0.0539141	+	0.305762i	0.945912	+	0.324424i	$0.105170\pi$
$62$	−8.08663	−	4.83859i	−1.02700	−	0.614501i
$63$		0			0
$64$	−3.33485	−	7.27178i	−0.416856	−	0.908973i
$65$	6.39324	+	17.5653i	0.792983	+	2.17870i
$66$		0			0
$67$	−3.09917	−	3.69345i	−0.378624	−	0.451227i	0.542755	−	0.839891i	$-0.317381\pi$
$67$	−3.09917	−	3.69345i	−0.378624	−	0.451227i	−0.921380	+	0.388664i	$0.872937\pi$
$68$	−1.65115	−	2.09732i	−0.200231	−	0.254338i
$69$		0			0
$70$	13.4914	−	4.67341i	1.61253	−	0.558579i
$71$	−5.91940	−	10.2527i	−0.702504	−	1.21677i	−0.967585	−	0.252546i	$-0.918732\pi$
$71$	−5.91940	−	10.2527i	−0.702504	−	1.21677i	0.265081	−	0.964226i	$-0.414601\pi$
$72$		0			0
$73$	−5.83049	+	10.0987i	−0.682408	+	1.18197i	0.291836	+	0.956468i	$0.405734\pi$
$73$	−5.83049	+	10.0987i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927600\pi$
$74$	1.47466	−	7.66214i	0.171426	−	0.890706i
$75$		0			0
$76$	0.0677828	−	0.169573i	0.00777522	−	0.0194513i
$77$	7.54195	−	1.32985i	0.859484	−	0.151550i
$78$		0			0
$79$	1.08439	−	1.29232i	0.122003	−	0.145398i	−0.701586	−	0.712585i	$-0.747524\pi$
$79$	1.08439	−	1.29232i	0.122003	−	0.145398i	0.823589	+	0.567188i	$0.191969\pi$
$80$	0.859714	−	13.7574i	0.0961190	−	1.53812i
$81$		0			0
$82$	0.0630204	−	4.03879i	0.00695944	−	0.446010i
$83$	−1.65438	−	1.38819i	−0.181592	−	0.152374i	0.547461	−	0.836831i	$-0.315595\pi$
$83$	−1.65438	−	1.38819i	−0.181592	−	0.152374i	−0.729052	+	0.684458i	$0.760039\pi$
$84$		0			0
$85$	−0.798649	−	4.52937i	−0.0866257	−	0.491279i
$86$	2.86667	−	7.50943i	0.309121	−	0.809763i
$87$		0			0
$88$	1.62315	−	7.21311i	0.173028	−	0.768921i
$89$	12.5801	+	7.26310i	1.33348	+	0.769887i	0.985832	−	0.167737i	$-0.0536458\pi$
$89$	12.5801	+	7.26310i	1.33348	+	0.769887i	0.347652	+	0.937624i	$0.386979\pi$
$90$		0			0
$91$	13.7628	−	7.94593i	1.44273	−	0.832960i
$92$	−1.61282	+	0.530644i	−0.168148	+	0.0553235i
$93$		0			0
$94$	−7.25160	+	5.89449i	−0.747945	+	0.607970i
$95$	0.241041	−	0.202257i	0.0247302	−	0.0207511i
$96$		0			0
$97$	−6.20195	+	2.25733i	−0.629713	+	0.229197i	−0.637106	−	0.770776i	$-0.719869\pi$
$97$	−6.20195	+	2.25733i	−0.629713	+	0.229197i	0.00739349	+	0.999973i	$0.497647\pi$
$98$	−1.08919	−	1.95639i	−0.110024	−	0.197626i
$99$		0			0
$100$	7.24347	−	11.6880i	0.724347	−	1.16880i
$101$	−8.11999	−	1.43177i	−0.807970	−	0.142467i	−0.245620	−	0.969366i	$-0.578991\pi$
$101$	−8.11999	−	1.43177i	−0.807970	−	0.142467i	−0.562350	+	0.826899i	$0.690103\pi$
$102$		0			0
$103$	−5.50544	+	15.1261i	−0.542467	+	1.49042i	0.301206	+	0.953559i	$0.402611\pi$
$103$	−5.50544	+	15.1261i	−0.542467	+	1.49042i	−0.843673	+	0.536857i	$0.819611\pi$
$104$	−1.95429	−	15.2174i	−0.191633	−	1.49219i
$105$		0			0
$106$	6.82568	−	7.88146i	0.662969	−	0.765515i
$107$	9.71808			0.939482			0.469741	−	0.882804i	$-0.344347\pi$
$107$	9.71808			0.939482			0.469741	+	0.882804i	$0.344347\pi$
$108$		0			0
$109$	−4.69860			−0.450044			−0.225022	−	0.974354i	$-0.572245\pi$
$109$	−4.69860			−0.450044			−0.225022	+	0.974354i	$0.572245\pi$
$110$	8.33984	−	9.62983i	0.795172	−	0.918168i
$111$		0			0
$112$	−11.6453	+	1.31121i	−1.10038	+	0.123898i
$113$	0.193057	−	0.530421i	0.0181613	−	0.0498978i	−0.930281	−	0.366848i	$-0.880437\pi$
$113$	0.193057	−	0.530421i	0.0181613	−	0.0498978i	0.948442	+	0.316951i	$0.102659\pi$
$114$		0			0
$115$	−2.88103	−	0.508003i	−0.268658	−	0.0473716i
$116$	0.852030	+	0.528032i	0.0791090	+	0.0490266i
$117$		0			0
$118$	−2.09480	−	3.76269i	−0.192842	−	0.346383i
$119$	−3.67432	+	1.33734i	−0.336825	+	0.122594i
$120$		0			0
$121$	−3.19214	+	2.67853i	−0.290195	+	0.243502i
$122$	2.66111	−	2.16309i	0.240925	−	0.195837i
$123$		0			0
$124$	4.16518	+	12.6595i	0.374044	+	1.13685i
$125$	5.59652	−	3.23116i	0.500568	−	0.289003i
$126$		0			0
$127$	−9.63141	−	5.56070i	−0.854649	−	0.493432i	0.00756758	−	0.999971i	$-0.497591\pi$
$127$	−9.63141	−	5.56070i	−0.854649	−	0.493432i	−0.862217	+	0.506539i	$0.830924\pi$
$128$	−3.16736	+	10.8613i	−0.279958	+	0.960012i
$129$		0			0
$130$	9.42787	−	24.6970i	0.826879	−	2.16607i
$131$	0.538705	+	3.05515i	0.0470669	+	0.266930i	0.999255	−	0.0385813i	$-0.0122839\pi$
$131$	0.538705	+	3.05515i	0.0470669	+	0.266930i	−0.952189	+	0.305511i	$0.901173\pi$
$132$		0			0
$133$	−0.204925	−	0.171953i	−0.0177693	−	0.0149102i
$134$	−0.106382	+	6.81774i	−0.00919004	+	0.588963i
$135$		0			0
$136$	−0.176631	+	3.77080i	−0.0151459	+	0.323343i
$137$	11.0998	−	13.2282i	0.948321	−	1.13017i	−0.0430492	−	0.999073i	$-0.513707\pi$
$137$	11.0998	−	13.2282i	0.948321	−	1.13017i	0.991370	−	0.131092i	$-0.0418483\pi$
$138$		0			0
$139$	11.0200	−	1.94313i	0.934705	−	0.164814i	0.314504	−	0.949256i	$-0.398162\pi$
$139$	11.0200	−	1.94313i	0.934705	−	0.164814i	0.620201	+	0.784443i	$0.287051\pi$
$140$	−18.7496	−	7.49471i	−1.58463	−	0.633418i
$141$		0			0
$142$	−3.16421	+	16.4409i	−0.265535	+	1.37969i
$143$	7.08959	−	12.2795i	0.592862	−	1.02687i
$144$		0			0
$145$	0.863567	+	1.49574i	0.0717153	+	0.124215i
$146$	15.5827	−	5.39784i	1.28963	−	0.446728i
$147$		0			0
$148$	−8.67031	+	6.82582i	−0.712695	+	0.561079i
$149$	11.7321	+	13.9817i	0.961128	+	1.14543i	0.989310	+	0.145825i	$0.0465836\pi$
$149$	11.7321	+	13.9817i	0.961128	+	1.14543i	−0.0281824	+	0.999603i	$0.508972\pi$
$150$		0			0
$151$	−6.58373	−	18.0887i	−0.535776	−	1.47203i	−0.852098	−	0.523382i	$-0.824670\pi$
$151$	−6.58373	−	18.0887i	−0.535776	−	1.47203i	0.316322	−	0.948652i	$-0.397552\pi$
$152$	−0.229458	+	0.118524i	−0.0186115	+	0.00961357i
$153$		0			0
$154$	−9.29382	−	5.56091i	−0.748918	−	0.448111i
$155$	−3.98747	+	22.6140i	−0.320281	+	1.81640i
$156$		0			0
$157$	15.8245	+	5.75965i	1.26293	+	0.459670i	0.884752	−	0.466061i	$-0.154327\pi$
$157$	15.8245	+	5.75965i	1.26293	+	0.459670i	0.378181	+	0.925732i	$0.376550\pi$
$158$	−2.35572	+	0.377580i	−0.187411	+	0.0300386i
$159$		0			0
$160$	−13.6561	+	13.9112i	−1.07961	+	1.09978i
$161$			2.48715i			0.196015i
$162$		0			0
$163$		−	8.02606i		−	0.628650i	−0.949315	−	0.314325i	$-0.898222\pi$
$163$		−	8.02606i		−	0.628650i	0.949315	−	0.314325i	$-0.101778\pi$
$164$	−3.80661	+	4.25927i	−0.297246	+	0.332593i
$165$		0			0
$166$	0.483363	+	3.01570i	0.0375162	+	0.234064i
$167$	−1.22693	−	0.446565i	−0.0949425	−	0.0345563i	0.294112	−	0.955771i	$-0.404976\pi$
$167$	−1.22693	−	0.446565i	−0.0949425	−	0.0345563i	−0.389055	+	0.921215i	$0.627198\pi$
$168$		0			0
$169$	2.85191	−	16.1740i	0.219378	−	1.24415i
$170$	−3.33964	+	5.58147i	−0.256139	+	0.428079i
$171$		0			0
$172$	−10.0170	+	5.37381i	−0.763792	+	0.409749i
$173$	3.91642	+	10.7603i	0.297760	+	0.818089i	0.994873	+	0.101128i	$0.0322452\pi$
$173$	3.91642	+	10.7603i	0.297760	+	0.818089i	−0.697113	+	0.716961i	$0.745533\pi$
$174$		0			0
$175$	−12.9475	−	15.4302i	−0.978738	−	1.16641i
$176$	−8.41333	+	6.20832i	−0.634178	+	0.467970i
$177$		0			0
$178$	−6.72413	−	19.4115i	−0.503995	−	1.45495i
$179$	10.7064	+	18.5441i	0.800237	+	1.38605i	0.919460	+	0.393184i	$0.128627\pi$
$179$	10.7064	+	18.5441i	0.800237	+	1.38605i	−0.119222	+	0.992868i	$0.538040\pi$
$180$		0			0
$181$	7.31416	−	12.6685i	0.543657	−	0.941641i	−0.455033	−	0.890474i	$-0.650373\pi$
$181$	7.31416	−	12.6685i	0.543657	−	0.941641i	0.998690	−	0.0511670i	$-0.0162941\pi$
$182$	−22.0695	−	4.24749i	−1.63590	−	0.314845i
$183$		0			0
$184$	2.21545	+	0.925918i	0.163325	+	0.0682596i
$185$	−18.7243	+	3.30161i	−1.37664	+	0.242739i
$186$		0			0
$187$	−2.24252	+	2.67253i	−0.163989	+	0.195435i
$188$	13.2095	+	0.412337i	0.963403	+	0.0300728i
$189$		0			0
$190$	−0.444937	−	0.00694269i	−0.0322791	−	0.000503676i
$191$	1.47232	+	1.23543i	0.106534	+	0.0893924i	0.694499	−	0.719494i	$-0.255626\pi$
$191$	1.47232	+	1.23543i	0.106534	+	0.0893924i	−0.587965	+	0.808886i	$0.700071\pi$
$192$		0			0
$193$	−1.08729	−	6.16635i	−0.0782651	−	0.443863i	−0.998608	−	0.0527503i	$-0.983201\pi$
$193$	−1.08729	−	6.16635i	−0.0782651	−	0.443863i	0.920343	−	0.391113i	$-0.127910\pi$
$194$	8.72001	+	3.32879i	0.626060	+	0.238994i
$195$		0			0
$196$	−0.646912	+	3.09986i	−0.0462080	+	0.221418i
$197$	−13.1022	−	7.56456i	−0.933494	−	0.538953i	−0.0455788	−	0.998961i	$-0.514513\pi$
$197$	−13.1022	−	7.56456i	−0.933494	−	0.538953i	−0.887915	+	0.460008i	$0.847847\pi$
$198$		0			0
$199$	−22.4427	+	12.9573i	−1.59092	+	0.918517i	−0.597769	+	0.801669i	$0.703946\pi$
$199$	−22.4427	+	12.9573i	−1.59092	+	0.918517i	−0.993150	+	0.116849i	$0.962721\pi$
$200$	−18.5647	+	5.78869i	−1.31272	+	0.409322i
$201$		0			0
$202$	7.35498	+	9.04836i	0.517495	+	0.636640i
$203$	1.12483	−	0.943842i	0.0789473	−	0.0662447i
$204$		0			0
$205$	−9.24905	+	3.36638i	−0.645982	+	0.235118i
$206$	19.8897	−	11.0732i	1.38578	−	0.771507i
$207$		0			0
$208$	−11.9995	+	18.0773i	−0.832017	+	1.25343i
$209$	−0.235055	−	0.0414466i	−0.0162591	−	0.00286692i
$210$		0			0
$211$	−5.96780	+	16.3964i	−0.410840	+	1.12877i	0.545905	+	0.837847i	$0.316186\pi$
$211$	−5.96780	+	16.3964i	−0.410840	+	1.12877i	−0.956745	+	0.290928i	$0.906036\pi$
$212$	−14.5938	+	2.10614i	−1.00231	+	0.144650i
$213$		0			0
$214$	−10.3890	−	8.99730i	−0.710176	−	0.615042i
$215$	−19.5864			−1.33578
$216$		0			0
$217$	19.5224			1.32526
$218$	5.02297	+	4.35011i	0.340199	+	0.294627i
$219$		0			0
$220$	−17.8312	+	2.57335i	−1.20218	+	0.173495i
$221$	−2.47607	+	6.80295i	−0.166558	+	0.457616i
$222$		0			0
$223$	−17.4075	−	3.06941i	−1.16569	−	0.205543i	−0.442874	−	0.896584i	$-0.646041\pi$
$223$	−17.4075	−	3.06941i	−1.16569	−	0.205543i	−0.722816	+	0.691041i	$0.757152\pi$
$224$	13.6632	+	9.37988i	0.912914	+	0.626720i
$225$		0			0
$226$	−0.697465	+	0.388300i	−0.0463947	+	0.0258294i
$227$	−8.76686	+	3.19088i	−0.581877	+	0.211786i	−0.616153	−	0.787626i	$-0.711310\pi$
$227$	−8.76686	+	3.19088i	−0.581877	+	0.211786i	0.0342759	+	0.999412i	$0.489088\pi$
$228$		0			0
$229$	12.8827	−	10.8099i	0.851311	−	0.714335i	−0.108767	−	0.994067i	$-0.534690\pi$
$229$	12.8827	−	10.8099i	0.851311	−	0.714335i	0.960078	+	0.279732i	$0.0902457\pi$
$230$	2.60960	+	3.21042i	0.172072	+	0.211689i
$231$		0			0
$232$	−0.421982	−	1.35332i	−0.0277045	−	0.0888499i
$233$	−15.2659	+	8.81379i	−1.00010	+	0.577410i	−0.908279	−	0.418365i	$-0.862603\pi$
$233$	−15.2659	+	8.81379i	−1.00010	+	0.577410i	−0.0918250	+	0.995775i	$0.529270\pi$
$234$		0			0
$235$	19.7206	+	11.3857i	1.28643	+	0.742722i
$236$	−1.24419	+	5.96188i	−0.0809899	+	0.388085i
$237$		0			0
$238$	5.16614	+	1.97213i	0.334871	+	0.127834i
$239$	−1.60006	−	9.07439i	−0.103499	−	0.586974i	−0.991809	−	0.127729i	$-0.959231\pi$
$239$	−1.60006	−	9.07439i	−0.103499	−	0.586974i	0.888310	−	0.459245i	$-0.151880\pi$
$240$		0			0
$241$	4.76992	+	4.00244i	0.307257	+	0.257820i	0.783357	−	0.621572i	$-0.213506\pi$
$241$	4.76992	+	4.00244i	0.307257	+	0.257820i	−0.476100	+	0.879391i	$0.657950\pi$
$242$	5.89238	+	0.0919433i	0.378776	+	0.00591034i
$243$		0			0
$244$	−4.84747	−	0.151315i	−0.310328	−	0.00968692i
$245$	−3.50718	+	4.17970i	−0.224066	+	0.267031i
$246$		0			0
$247$	−0.487767	+	0.0860066i	−0.0310359	+	0.00547247i
$248$	7.26780	−	17.3897i	0.461506	−	1.10425i
$249$		0			0
$250$	−8.97439	−	1.72721i	−0.567590	−	0.109239i
$251$	14.1765	−	24.5545i	0.894814	−	1.54986i	0.0607805	−	0.998151i	$-0.480641\pi$
$251$	14.1765	−	24.5545i	0.894814	−	1.54986i	0.834034	−	0.551713i	$-0.186026\pi$
$252$		0			0
$253$	1.10955	+	1.92181i	0.0697571	+	0.120823i
$254$	5.14806	+	14.8616i	0.323018	+	0.932502i
$255$		0			0
$256$	13.4417	−	8.67868i	0.840109	−	0.542417i
$257$	−10.6047	−	12.6382i	−0.661505	−	0.788351i	0.326096	−	0.945337i	$-0.394267\pi$
$257$	−10.6047	−	12.6382i	−0.661505	−	0.788351i	−0.987601	+	0.156986i	$0.949822\pi$
$258$		0			0
$259$	5.52857	+	15.1896i	0.343528	+	0.943837i
$260$	−32.9439	+	17.6733i	−2.04310	+	1.09605i
$261$		0			0
$262$	2.25266	−	3.76481i	0.139170	−	0.232591i
$263$	4.20521	−	23.8489i	0.259304	−	1.47059i	−0.525473	−	0.850810i	$-0.676111\pi$
$263$	4.20521	−	23.8489i	0.259304	−	1.47059i	0.784777	−	0.619778i	$-0.212777\pi$
$264$		0			0
$265$	−23.8738	−	8.68936i	−1.46656	−	0.533783i
$266$	0.0598734	+	0.373550i	0.00367108	+	0.0229038i
$267$		0			0
$268$	6.42580	−	7.18992i	0.392518	−	0.439194i
$269$		−	12.1956i		−	0.743578i	−0.928317	−	0.371789i	$-0.878745\pi$
$269$		−	12.1956i		−	0.743578i	0.928317	−	0.371789i	$-0.121255\pi$
$270$		0			0
$271$		−	25.0009i		−	1.51870i	−0.650683	−	0.759349i	$-0.725517\pi$
$271$		−	25.0009i		−	1.51870i	0.650683	−	0.759349i	$-0.274483\pi$
$272$	3.67994	−	3.86759i	0.223129	−	0.234507i
$273$		0			0
$274$	−24.1132	+	3.86492i	−1.45673	+	0.233488i
$275$	−16.8881	−	6.14676i	−1.01839	−	0.370664i
$276$		0			0
$277$	−1.51731	+	8.60510i	−0.0911664	+	0.517030i	0.904688	+	0.426074i	$0.140104\pi$
$277$	−1.51731	+	8.60510i	−0.0911664	+	0.517030i	−0.995855	+	0.0909566i	$0.971008\pi$
$278$	−13.5798	−	8.12539i	−0.814462	−	0.487329i
$279$		0			0
$280$	13.1051	+	25.3710i	0.783182	+	1.51621i
$281$	−7.48611	−	20.5679i	−0.446584	−	1.22698i	−0.935087	−	0.354417i	$-0.884679\pi$
$281$	−7.48611	−	20.5679i	−0.446584	−	1.22698i	0.488504	−	0.872562i	$-0.337543\pi$
$282$		0			0
$283$	−19.3494	−	23.0597i	−1.15020	−	1.37076i	−0.917270	−	0.398266i	$-0.869612\pi$
$283$	−19.3494	−	23.0597i	−1.15020	−	1.37076i	−0.232933	−	0.972493i	$-0.574832\pi$
$284$	18.6041	−	14.6464i	1.10395	−	0.869101i
$285$		0			0
$286$	−18.9478	+	6.56350i	−1.12041	+	0.388108i
$287$	4.18396	+	7.24682i	0.246971	+	0.427766i
$288$		0			0
$289$	−7.60937	+	13.1798i	−0.447610	+	0.775283i
$290$	0.461619	−	2.39852i	0.0271072	−	0.140846i
$291$		0			0
$292$	−21.6560	−	8.65647i	−1.26732	−	0.506581i
$293$	13.0378	−	2.29891i	0.761675	−	0.134304i	0.220699	−	0.975342i	$-0.429166\pi$
$293$	13.0378	−	2.29891i	0.761675	−	0.134304i	0.540976	+	0.841038i	$0.318055\pi$
$294$		0			0
$295$	−6.74528	+	8.03871i	−0.392725	+	0.468032i
$296$	15.5884	+	0.730189i	0.906059	+	0.0424413i
$297$		0			0
$298$	0.402716	−	25.8089i	0.0233287	−	1.49507i
$299$	3.52757	+	2.95998i	0.204005	+	0.171180i
$300$		0			0
$301$	2.89155	+	16.3988i	0.166666	+	0.945211i
$302$	−9.70878	+	25.4328i	−0.558678	+	1.46350i
$303$		0			0
$304$	0.355032	+	0.0857327i	0.0203625	+	0.00491711i
$305$	−7.23685	−	4.17820i	−0.414381	−	0.239243i
$306$		0			0
$307$	−11.4064	+	6.58546i	−0.650995	+	0.375852i	−0.788837	−	0.614602i	$-0.789317\pi$
$307$	−11.4064	+	6.58546i	−0.650995	+	0.375852i	0.137842	+	0.990454i	$0.455983\pi$
$308$	4.78697	+	14.5493i	0.272763	+	0.829024i
$309$		0			0
$310$	25.1995	−	20.4835i	1.43124	−	1.16338i
$311$	−4.73104	+	3.96982i	−0.268273	+	0.225108i	−0.766993	−	0.641655i	$-0.778248\pi$
$311$	−4.73104	+	3.96982i	−0.268273	+	0.225108i	0.498720	+	0.866763i	$0.333804\pi$
$312$		0			0
$313$	20.1441	−	7.33187i	1.13861	−	0.414422i	0.297201	−	0.954815i	$-0.403947\pi$
$313$	20.1441	−	7.33187i	1.13861	−	0.414422i	0.841413	+	0.540393i	$0.181724\pi$
$314$	−11.5845	−	20.8081i	−0.653752	−	1.17427i
$315$		0			0
$316$	2.86792	+	1.77735i	0.161333	+	0.0999838i
$317$	−14.4792	−	2.55307i	−0.813231	−	0.143395i	−0.248460	−	0.968642i	$-0.579924\pi$
$317$	−14.4792	−	2.55307i	−0.813231	−	0.143395i	−0.564771	+	0.825247i	$0.691036\pi$
$318$		0			0
$319$	0.448084	−	1.23110i	0.0250879	−	0.0689285i
$320$	27.4782	−	2.22835i	1.53608	−	0.124568i
$321$		0			0
$322$	2.30268	−	2.65885i	0.128323	−	0.148172i
$323$	0.121865			0.00678074
$324$		0			0
$325$	−37.2939			−2.06869
$326$	−7.43077	+	8.58015i	−0.411552	+	0.475210i
$327$		0			0
$328$	8.01276	−	1.02904i	0.442431	−	0.0568190i
$329$	6.62137	−	18.1921i	0.365048	−	1.00296i
$330$		0			0
$331$	26.1208	+	4.60580i	1.43573	+	0.253158i	0.836741	−	0.547600i	$-0.184458\pi$
$331$	26.1208	+	4.60580i	1.43573	+	0.253158i	0.598989	+	0.800757i	$0.295569\pi$
$332$	2.27529	−	3.67140i	0.124873	−	0.201494i
$333$		0			0
$334$	0.898186	+	1.61332i	0.0491466	+	0.0882770i
$335$	15.6130	−	5.68266i	0.853029	−	0.310477i
$336$		0			0
$337$	−11.8198	+	9.91801i	−0.643867	+	0.540269i	−0.905203	−	0.424979i	$-0.860281\pi$
$337$	−11.8198	+	9.91801i	−0.643867	+	0.540269i	0.261336	+	0.965248i	$0.415837\pi$
$338$	−18.0232	+	14.6502i	−0.980330	+	0.796865i
$339$		0			0
$340$	8.73769	−	2.87485i	0.473868	−	0.155911i
$341$	15.0848	−	8.70922i	0.816888	−	0.471631i
$342$		0			0
$343$	−13.7433	−	7.93471i	−0.742069	−	0.428434i
$344$	15.6838	+	3.52928i	0.845614	+	0.190286i
$345$		0			0
$346$	5.77540	−	15.1291i	0.310487	−	0.813344i
$347$	−3.73769	−	21.1975i	−0.200650	−	1.13794i	−0.904140	−	0.427237i	$-0.859487\pi$
$347$	−3.73769	−	21.1975i	−0.200650	−	1.13794i	0.703490	−	0.710705i	$-0.251624\pi$
$348$		0			0
$349$	9.68359	+	8.12550i	0.518351	+	0.434948i	0.864056	−	0.503395i	$-0.167916\pi$
$349$	9.68359	+	8.12550i	0.518351	+	0.434948i	−0.345706	+	0.938343i	$0.612360\pi$
$350$	−0.444436	+	28.4826i	−0.0237561	+	1.52246i
$351$		0			0
$352$	14.7420	+	1.15240i	0.785751	+	0.0614231i
$353$	−7.19217	+	8.57129i	−0.382800	+	0.456204i	−0.922696	−	0.385528i	$-0.874019\pi$
$353$	−7.19217	+	8.57129i	−0.382800	+	0.456204i	0.539896	+	0.841732i	$0.318464\pi$
$354$		0			0
$355$	40.1773	−	7.08435i	2.13239	−	0.375998i
$356$	−10.7834	+	26.9770i	−0.571521	+	1.42978i
$357$		0			0
$358$	5.72313	−	29.7367i	0.302477	−	1.57163i
$359$	−16.1699	+	28.0070i	−0.853413	+	1.47816i	0.0246959	+	0.999695i	$0.492138\pi$
$359$	−16.1699	+	28.0070i	−0.853413	+	1.47816i	−0.878109	+	0.478460i	$0.841195\pi$
$360$		0			0
$361$	−9.49583	−	16.4473i	−0.499781	−	0.865645i
$362$	−19.5480	+	6.77140i	−1.02742	+	0.355897i
$363$		0			0
$364$	19.6606	+	24.9733i	1.03049	+	1.30896i
$365$	−25.8300	−	30.7830i	−1.35201	−	1.61126i
$366$		0			0
$367$	0.227944	+	0.626272i	0.0118986	+	0.0326911i	0.945500	−	0.325623i	$-0.105574\pi$
$367$	0.227944	+	0.626272i	0.0118986	+	0.0326911i	−0.933601	+	0.358314i	$0.883352\pi$
$368$	−1.51115	−	3.04097i	−0.0787741	−	0.158521i
$369$		0			0
$370$	23.0737	+	13.8060i	1.19955	+	0.717741i
$371$	−3.75070	+	21.2713i	−0.194727	+	1.10435i
$372$		0			0
$373$	−19.5747	−	7.12459i	−1.01354	−	0.368897i	−0.218747	−	0.975782i	$-0.570197\pi$
$373$	−19.5747	−	7.12459i	−1.01354	−	0.368897i	−0.794790	+	0.606884i	$0.792419\pi$
$374$	4.87164	−	0.780837i	0.251907	−	0.0403761i
$375$		0			0
$376$	−13.7397	−	12.6706i	−0.708571	−	0.653435i
$377$		−	2.71864i		−	0.140017i
$378$		0			0
$379$			19.1904i			0.985744i	0.870102	+	0.492872i	$0.164053\pi$
$379$			19.1904i			0.985744i	−0.870102	+	0.492872i	$0.835947\pi$
$380$	0.469226	+	0.419358i	0.0240708	+	0.0215126i
$381$		0			0
$382$	−0.430172	−	2.68384i	−0.0220095	−	0.137317i
$383$	7.45399	+	2.71303i	0.380881	+	0.138629i	0.525363	−	0.850878i	$-0.323929\pi$
$383$	7.45399	+	2.71303i	0.380881	+	0.138629i	−0.144482	+	0.989507i	$0.546152\pi$
$384$		0			0
$385$	−4.58273	+	25.9899i	−0.233557	+	1.32457i
$386$	−4.54664	+	7.59870i	−0.231418	+	0.386763i
$387$		0			0
$388$	−6.24010	−	11.6319i	−0.316793	−	0.590518i
$389$	−4.22261	−	11.6015i	−0.214095	−	0.588220i	0.785433	−	0.618947i	$-0.212440\pi$
$389$	−4.22261	−	11.6015i	−0.214095	−	0.588220i	−0.999528	+	0.0307262i	$0.990218\pi$
$390$		0			0
$391$	−0.728293	−	0.867946i	−0.0368314	−	0.0438939i
$392$	3.56151	−	2.71493i	0.179884	−	0.137125i
$393$		0			0
$394$	7.00323	+	20.2172i	0.352817	+	1.01853i
$395$	2.90676	+	5.03465i	0.146255	+	0.253321i
$396$		0			0
$397$	11.5959	−	20.0847i	0.581982	−	1.00802i	−0.413263	−	0.910612i	$-0.635611\pi$
$397$	11.5959	−	20.0847i	0.581982	−	1.00802i	0.995244	−	0.0974099i	$-0.0310558\pi$
$398$	35.9883	+	6.92631i	1.80393	+	0.347185i
$399$		0			0
$400$	25.2056	+	10.9994i	1.26028	+	0.549971i
$401$	6.69261	−	1.18009i	0.334213	−	0.0589308i	−0.00402354	−	0.999992i	$-0.501281\pi$
$401$	6.69261	−	1.18009i	0.334213	−	0.0589308i	0.338236	+	0.941061i	$0.390170\pi$
$402$		0			0
$403$	23.2338	−	27.6889i	1.15736	−	1.37928i
$404$	0.514503	−	16.4825i	0.0255975	−	0.820034i
$405$		0			0
$406$	−2.07632	−	0.0323984i	−0.103046	−	0.00160790i
$407$	11.0482	+	9.27054i	0.547639	+	0.459523i
$408$		0			0
$409$	3.15472	+	17.8913i	0.155991	+	0.884668i	0.957874	+	0.287187i	$0.0927202\pi$
$409$	3.15472	+	17.8913i	0.155991	+	0.884668i	−0.801884	+	0.597480i	$0.796169\pi$
$410$	13.0043	+	4.96427i	0.642235	+	0.245168i
$411$		0			0
$412$	−31.5147	−	6.57683i	−1.55262	−	0.324017i
$413$	7.72625	+	4.46075i	0.380184	+	0.219499i
$414$		0			0
$415$	6.44516	−	3.72111i	0.316380	−	0.182662i
$416$	29.5644	−	8.21572i	1.44951	−	0.402809i
$417$		0			0
$418$	0.212910	+	0.261929i	0.0104138	+	0.0128114i
$419$	3.77003	−	3.16343i	0.184178	−	0.154544i	−0.546037	−	0.837761i	$-0.683864\pi$
$419$	3.77003	−	3.16343i	0.184178	−	0.154544i	0.730215	+	0.683217i	$0.239420\pi$
$420$		0			0
$421$	11.0588	−	4.02508i	0.538974	−	0.196171i	−0.0581667	−	0.998307i	$-0.518525\pi$
$421$	11.0588	−	4.02508i	0.538974	−	0.196171i	0.597141	+	0.802136i	$0.296303\pi$
$422$	21.5601	−	12.0032i	1.04953	−	0.584305i
$423$		0			0
$424$	17.5512	+	11.2598i	0.852362	+	0.546826i
$425$	9.03662	+	1.59340i	0.438340	+	0.0772912i
$426$		0			0
$427$	−2.42983	+	6.67591i	−0.117588	+	0.323070i
$428$	2.77622	+	19.2369i	0.134193	+	0.929849i
$429$		0			0
$430$	20.9386	+	18.1337i	1.00975	+	0.874484i
$431$	4.40894			0.212371			0.106186	−	0.994346i	$-0.466136\pi$
$431$	4.40894			0.212371			0.106186	+	0.994346i	$0.466136\pi$
$432$		0			0
$433$	28.5232			1.37074			0.685369	−	0.728196i	$-0.259641\pi$
$433$	28.5232			1.37074			0.685369	+	0.728196i	$0.259641\pi$
$434$	−20.8701	−	18.0744i	−1.00180	−	0.867599i
$435$		0			0
$436$	−1.34228	−	9.30085i	−0.0642833	−	0.445430i
$437$	0.0265119	−	0.0728408i	0.00126824	−	0.00348445i
$438$		0			0
$439$	−4.76337	−	0.839911i	−0.227343	−	0.0400867i	0.0588159	−	0.998269i	$-0.481267\pi$
$439$	−4.76337	−	0.839911i	−0.227343	−	0.0400867i	−0.286159	+	0.958182i	$0.592379\pi$
$440$	21.4447	+	13.7576i	1.02233	+	0.655870i
$441$		0			0
$442$	8.94538	−	4.98017i	0.425488	−	0.236883i
$443$	6.82844	−	2.48535i	0.324429	−	0.118083i	−0.174671	−	0.984627i	$-0.555886\pi$
$443$	6.82844	−	2.48535i	0.324429	−	0.118083i	0.499100	+	0.866544i	$0.333664\pi$
$444$		0			0
$445$	−38.3467	+	32.1767i	−1.81781	+	1.52532i
$446$	15.7675	+	19.3977i	0.746611	+	0.918506i
$447$		0			0
$448$	−5.92231	−	22.6773i	−0.279803	−	1.07140i
$449$	5.50442	−	3.17798i	0.259769	−	0.149978i	−0.364460	−	0.931219i	$-0.618746\pi$
$449$	5.50442	−	3.17798i	0.259769	−	0.149978i	0.624229	+	0.781241i	$0.285413\pi$
$450$		0			0
$451$	6.46583	+	3.73305i	0.304464	+	0.175782i
$452$	1.10512	+	0.230627i	0.0519802	+	0.0108478i
$453$		0			0
$454$	12.3263	+	4.70547i	0.578502	+	0.220839i
$455$	9.50970	+	53.9322i	0.445822	+	2.52838i
$456$		0			0
$457$	−0.684966	−	0.574755i	−0.0320413	−	0.0268859i	0.626626	−	0.779320i	$-0.284435\pi$
$457$	−0.684966	−	0.574755i	−0.0320413	−	0.0268859i	−0.658668	+	0.752434i	$0.728880\pi$
$458$	−23.7801	−	0.371060i	−1.11117	−	0.0173385i
$459$		0			0
$460$	0.182549	−	5.84810i	0.00851140	−	0.272669i
$461$	8.42157	−	10.0364i	0.392232	−	0.467443i	−0.533403	−	0.845861i	$-0.679087\pi$
$461$	8.42157	−	10.0364i	0.392232	−	0.467443i	0.925635	+	0.378418i	$0.123532\pi$
$462$		0			0
$463$	−1.32810	+	0.234180i	−0.0617220	+	0.0108833i	−0.204424	−	0.978882i	$-0.565532\pi$
$463$	−1.32810	+	0.234180i	−0.0617220	+	0.0108833i	0.142702	+	0.989766i	$0.454421\pi$
$464$	−0.801832	+	1.83743i	−0.0372241	+	0.0853007i
$465$		0			0
$466$	24.4799	+	4.71141i	1.13401	+	0.218252i
$467$	−9.81172	+	16.9944i	−0.454032	+	0.786407i	−0.998632	−	0.0522890i	$-0.983348\pi$
$467$	−9.81172	+	16.9944i	−0.454032	+	0.786407i	0.544600	+	0.838696i	$0.316682\pi$
$468$		0			0
$469$	−7.06278	−	12.2331i	−0.326129	−	0.564872i
$470$	−10.5408	−	30.4297i	−0.486212	−	1.40362i
$471$		0			0
$472$	6.84978	−	5.22156i	0.315287	−	0.240342i
$473$	9.55002	+	11.3813i	0.439111	+	0.523312i
$474$		0			0
$475$	0.214712	+	0.589916i	0.00985166	+	0.0270672i
$476$	−3.69693	−	6.89125i	−0.169448	−	0.315860i
$477$		0			0
$478$	−6.69083	+	11.1822i	−0.306031	+	0.511464i
$479$	3.30994	−	18.7716i	0.151235	−	0.857698i	−0.810912	−	0.585168i	$-0.801029\pi$
$479$	3.30994	−	18.7716i	0.151235	−	0.857698i	0.962147	−	0.272530i	$-0.0878603\pi$
$480$		0			0
$481$	28.1233	+	10.2360i	1.28231	+	0.466723i
$482$	−1.39364	−	8.69488i	−0.0634783	−	0.396041i
$483$		0			0
$484$	−6.21404	−	5.55363i	−0.282456	−	0.252438i
$485$		−	22.7439i		−	1.03275i
$486$		0			0
$487$			12.7440i			0.577486i	0.957407	+	0.288743i	$0.0932373\pi$
$487$			12.7440i			0.577486i	−0.957407	+	0.288743i	$0.906763\pi$
$488$	5.04203	+	4.64970i	0.228242	+	0.210482i
$489$		0			0
$490$	7.61899	−	1.22119i	0.344191	−	0.0551677i
$491$	23.2409	+	8.45899i	1.04885	+	0.381749i	0.808227	−	0.588871i	$-0.200427\pi$
$491$	23.2409	+	8.45899i	1.04885	+	0.381749i	0.240619	+	0.970620i	$0.422650\pi$
$492$		0			0
$493$	−0.116155	+	0.658748i	−0.00523136	+	0.0296685i
$494$	0.601068	+	0.359646i	0.0270433	+	0.0161812i
$495$		0			0
$496$	−23.8694	+	11.8614i	−1.07177	+	0.532595i
$497$	−11.8628	−	32.5928i	−0.532119	−	1.46199i
$498$		0			0
$499$	25.3958	+	30.2655i	1.13687	+	1.35487i	0.926074	+	0.377341i	$0.123161\pi$
$499$	25.3958	+	30.2655i	1.13687	+	1.35487i	0.210797	+	0.977530i	$0.432394\pi$
$500$	7.99484	+	10.1552i	0.357540	+	0.454155i
$501$		0			0
$502$	−37.8885	+	13.1245i	−1.69105	+	0.585777i
$503$	−18.2058	−	31.5334i	−0.811757	−	1.40600i	−0.911633	−	0.411005i	$-0.865178\pi$
$503$	−18.2058	−	31.5334i	−0.811757	−	1.40600i	0.0998757	−	0.995000i	$-0.468155\pi$
$504$		0			0
$505$	14.2068	−	24.6069i	0.632194	−	1.09499i
$506$	0.593112	−	3.08174i	0.0263671	−	0.137000i
$507$		0			0
$508$	8.25590	−	20.6539i	0.366296	−	0.916366i
$509$	−3.56810	+	0.629152i	−0.158153	+	0.0278867i	−0.252164	−	0.967685i	$-0.581142\pi$
$509$	−3.56810	+	0.629152i	−0.158153	+	0.0278867i	0.0940109	+	0.995571i	$0.470031\pi$
$510$		0			0
$511$	−21.9599	+	26.1708i	−0.971449	+	1.15773i
$512$	−22.4047	−	3.16697i	−0.990157	−	0.139961i
$513$		0			0
$514$	−0.364019	+	23.3289i	−0.0160562	+	1.02899i
$515$	−42.4929	−	35.6558i	−1.87246	−	1.57118i
$516$		0			0
$517$	−2.99946	−	17.0108i	−0.131916	−	0.748133i
$518$	8.15277	−	21.3568i	0.358212	−	0.938362i
$519$		0			0
$520$	51.5807	+	11.6071i	2.26197	+	0.509004i
$521$	−18.0443	−	10.4179i	−0.790534	−	0.456415i	0.0496162	−	0.998768i	$-0.484200\pi$
$521$	−18.0443	−	10.4179i	−0.790534	−	0.456415i	−0.840151	+	0.542353i	$0.817534\pi$
$522$		0			0
$523$	19.0780	−	11.0147i	0.834223	−	0.481639i	−0.0210733	−	0.999778i	$-0.506708\pi$
$523$	19.0780	−	11.0147i	0.834223	−	0.481639i	0.855296	+	0.518139i	$0.173375\pi$
$524$	−5.89375	+	1.93914i	−0.257470	+	0.0847119i
$525$		0			0
$526$	−26.5756	+	21.6021i	−1.15875	+	0.941894i
$527$	−6.81276	+	5.71658i	−0.296768	+	0.249018i
$528$		0			0
$529$	20.9357	−	7.61997i	0.910248	−	0.331303i
$530$	17.4771	+	31.3924i	0.759157	+	1.36360i
$531$		0			0
$532$	0.281837	−	0.454771i	0.0122192	−	0.0197168i
$533$	15.2577	+	2.69034i	0.660883	+	0.116531i
$534$		0			0
$535$	−11.4539	+	31.4694i	−0.495196	+	1.36054i
$536$	−13.5261	+	1.73708i	−0.584237	+	0.0750303i
$537$		0			0
$538$	−11.2910	+	13.0375i	−0.486792	+	0.562087i
$539$	4.13879			0.178270
$540$		0			0
$541$	−13.2610			−0.570135			−0.285067	−	0.958507i	$-0.592016\pi$
$541$	−13.2610			−0.570135			−0.285067	+	0.958507i	$0.592016\pi$
$542$	−23.1466	+	26.7269i	−0.994233	+	1.14802i
$543$		0			0
$544$	−7.51472	+	0.727585i	−0.322191	+	0.0311950i
$545$	5.53786	−	15.2152i	0.237216	−	0.651746i
$546$		0			0
$547$	14.0853	+	2.48362i	0.602245	+	0.106192i	0.466454	−	0.884546i	$-0.345531\pi$
$547$	14.0853	+	2.48362i	0.602245	+	0.106192i	0.135791	+	0.990738i	$0.456642\pi$
$548$	29.3561	+	18.1930i	1.25403	+	0.777167i
$549$		0			0
$550$	12.3631	+	22.2066i	0.527165	+	0.946893i
$551$	−0.0430035	+	0.0156520i	−0.00183201	+	0.000666798i
$552$		0			0
$553$	3.78615	−	3.17696i	0.161004	−	0.135098i
$554$	9.58892	−	7.79439i	0.407394	−	0.331152i
$555$		0			0
$556$	6.99455	+	21.2589i	0.296635	+	0.901579i
$557$	−6.40425	+	3.69750i	−0.271357	+	0.156668i	−0.629504	−	0.776997i	$-0.716742\pi$
$557$	−6.40425	+	3.69750i	−0.271357	+	0.156668i	0.358147	+	0.933665i	$0.383409\pi$
$558$		0			0
$559$	26.6999	+	15.4152i	1.12929	+	0.651994i
$560$	9.47942	−	39.2557i	0.400579	−	1.65886i
$561$		0			0
$562$	−11.0395	+	28.9187i	−0.465673	+	1.21986i
$563$	−3.67837	−	20.8611i	−0.155025	−	0.879189i	−0.958763	−	0.284206i	$-0.908270\pi$
$563$	−3.67837	−	20.8611i	−0.155025	−	0.879189i	0.803739	−	0.594983i	$-0.202841\pi$
$564$		0			0
$565$	1.49008	+	1.25033i	0.0626883	+	0.0526017i
$566$	−0.664189	+	42.5660i	−0.0279180	+	1.78918i
$567$		0			0
$568$	−33.4485	−	1.56679i	−1.40347	−	0.0657409i
$569$	2.86471	−	3.41403i	0.120095	−	0.143124i	−0.702647	−	0.711539i	$-0.747999\pi$
$569$	2.86471	−	3.41403i	0.120095	−	0.143124i	0.822742	+	0.568415i	$0.192443\pi$
$570$		0			0
$571$	2.11796	−	0.373453i	0.0886338	−	0.0156285i	−0.129155	−	0.991624i	$-0.541227\pi$
$571$	2.11796	−	0.373453i	0.0886338	−	0.0156285i	0.217789	+	0.975996i	$0.430115\pi$
$572$	26.3326	+	10.5258i	1.10102	+	0.440107i
$573$		0			0
$574$	2.23653	−	11.6207i	0.0933511	−	0.485041i
$575$	2.91833	−	5.05470i	0.121703	−	0.210796i
$576$		0			0
$577$	−16.0706	−	27.8351i	−0.669028	−	1.15879i	−0.978176	−	0.207777i	$-0.933377\pi$
$577$	−16.0706	−	27.8351i	−0.669028	−	1.15879i	0.309148	−	0.951014i	$-0.399956\pi$
$578$	20.3370	−	7.04471i	0.845906	−	0.293021i
$579$		0			0
$580$	−2.71411	+	2.13672i	−0.112697	+	0.0887225i
$581$	−4.06702	−	4.84689i	−0.168728	−	0.201083i
$582$		0			0
$583$	6.59129	+	18.1094i	0.272983	+	0.750015i
$584$	15.1366	+	29.3038i	0.626356	+	1.21260i
$585$		0			0
$586$	−16.0663	−	9.61316i	−0.663691	−	0.397116i
$587$	6.25991	−	35.5017i	0.258374	−	1.46531i	−0.528887	−	0.848692i	$-0.677391\pi$
$587$	6.25991	−	35.5017i	0.258374	−	1.46531i	0.787261	−	0.616620i	$-0.211498\pi$
$588$		0			0
$589$	−0.571748	−	0.208099i	−0.0235585	−	0.00857459i
$590$	14.6534	−	2.34868i	0.603272	−	0.0966938i
$591$		0			0
$592$	−15.9886	−	15.2128i	−0.657126	−	0.625244i
$593$		−	4.09387i		−	0.168115i	−0.996461	−	0.0840576i	$-0.973212\pi$
$593$		−	4.09387i		−	0.168115i	0.996461	−	0.0840576i	$-0.0267880\pi$
$594$		0			0
$595$		−	13.4745i		−	0.552402i
$596$	−24.3252	+	27.2178i	−0.996397	+	1.11488i
$597$		0			0
$598$	−1.03066	−	6.43026i	−0.0421467	−	0.262953i
$599$	7.94531	+	2.89186i	0.324637	+	0.118158i	0.499197	−	0.866488i	$-0.333628\pi$
$599$	7.94531	+	2.89186i	0.324637	+	0.118158i	−0.174561	+	0.984646i	$0.555851\pi$
$600$		0			0
$601$	5.07141	−	28.7614i	0.206867	−	1.17320i	−0.687607	−	0.726083i	$-0.741339\pi$
$601$	5.07141	−	28.7614i	0.206867	−	1.17320i	0.894474	−	0.447120i	$-0.147550\pi$
$602$	12.0913	−	20.2080i	0.492806	−	0.823616i
$603$		0			0
$604$	33.9255	−	18.1999i	1.38041	−	0.740544i
$605$	−4.91136	−	13.4939i	−0.199675	−	0.548603i
$606$		0			0
$607$	−24.9423	−	29.7251i	−1.01238	−	1.20651i	−0.978323	−	0.207085i	$-0.933602\pi$
$607$	−24.9423	−	29.7251i	−1.01238	−	1.20651i	−0.0340554	−	0.999420i	$-0.510842\pi$
$608$	−0.300168	−	0.420351i	−0.0121734	−	0.0170475i
$609$		0			0
$610$	3.86815	+	11.1667i	0.156617	+	0.452128i
$611$	−17.9220	−	31.0417i	−0.725045	−	1.25581i
$612$		0			0
$613$	−0.677216	+	1.17297i	−0.0273525	+	0.0473759i	−0.879378	−	0.476125i	$-0.842041\pi$
$613$	−0.677216	+	1.17297i	−0.0273525	+	0.0473759i	0.852025	+	0.523501i	$0.175374\pi$
$614$	18.2908	+	3.52026i	0.738157	+	0.142066i
$615$		0			0
$616$	8.35276	−	19.9857i	0.336542	−	0.805245i
$617$	−21.8700	+	3.85627i	−0.880453	+	0.155248i	−0.595559	−	0.803311i	$-0.703069\pi$
$617$	−21.8700	+	3.85627i	−0.880453	+	0.155248i	−0.284894	+	0.958559i	$0.591958\pi$
$618$		0			0
$619$	1.42295	−	1.69581i	0.0571934	−	0.0681604i	−0.736689	−	0.676231i	$-0.763612\pi$
$619$	1.42295	−	1.69581i	0.0571934	−	0.0681604i	0.793883	+	0.608071i	$0.208056\pi$
$620$	−45.9034	−	1.43288i	−1.84353	−	0.0575459i
$621$		0			0
$622$	8.73303	+	0.136268i	0.350163	+	0.00546386i
$623$	32.6012	+	27.3557i	1.30614	+	1.09598i
$624$		0			0
$625$	−2.10235	−	11.9230i	−0.0840939	−	0.476920i
$626$	−28.3229	−	10.8120i	−1.13201	−	0.432136i
$627$		0			0
$628$	−6.88051	+	32.9699i	−0.274562	+	1.31564i
$629$	−6.37717	−	3.68186i	−0.254274	−	0.146805i
$630$		0			0
$631$	10.3534	−	5.97752i	0.412161	−	0.237961i	−0.279557	−	0.960129i	$-0.590187\pi$
$631$	10.3534	−	5.97752i	0.412161	−	0.237961i	0.691718	+	0.722168i	$0.256854\pi$
$632$	−1.42039	−	4.55526i	−0.0565000	−	0.181199i
$633$		0			0
$634$	13.1150	+	16.1346i	0.520865	+	0.640786i
$635$	29.3586	−	24.6348i	1.16506	−	0.977601i
$636$		0			0
$637$	8.07052	−	2.93743i	0.319766	−	0.116385i
$638$	−1.61881	+	0.901242i	−0.0640893	+	0.0356805i
$639$		0			0
$640$	−31.4383	−	23.0580i	−1.24271	−	0.911447i
$641$	13.2770	+	2.34110i	0.524412	+	0.0924680i	0.429586	−	0.903026i	$-0.358659\pi$
$641$	13.2770	+	2.34110i	0.524412	+	0.0924680i	0.0948258	+	0.995494i	$0.469771\pi$
$642$		0			0
$643$	9.44529	−	25.9507i	0.372486	−	1.02340i	−0.601911	−	0.798563i	$-0.705594\pi$
$643$	9.44529	−	25.9507i	0.372486	−	1.02340i	0.974397	−	0.224833i	$-0.0721838\pi$
$644$	−4.92330	+	0.710518i	−0.194005	+	0.0279983i
$645$		0			0
$646$	−0.130278	−	0.112826i	−0.00512571	−	0.00443909i
$647$	−15.2634			−0.600064			−0.300032	−	0.953929i	$-0.596997\pi$
$647$	−15.2634			−0.600064			−0.300032	+	0.953929i	$0.596997\pi$
$648$		0			0
$649$	7.96003			0.312458
$650$	39.8685	+	34.5278i	1.56377	+	1.35429i
$651$		0			0
$652$	15.8875	−	2.29285i	0.622204	−	0.0897949i
$653$	−10.4641	+	28.7499i	−0.409493	+	1.12507i	0.547966	+	0.836501i	$0.315402\pi$
$653$	−10.4641	+	28.7499i	−0.409493	+	1.12507i	−0.957458	+	0.288571i	$0.906820\pi$
$654$		0			0
$655$	−10.5282	−	1.85641i	−0.411371	−	0.0725358i
$656$	−9.51864	−	6.31838i	−0.371641	−	0.246691i
$657$		0			0
$658$	−23.9212	+	13.3177i	−0.932547	+	0.519178i
$659$	−39.2583	+	14.2888i	−1.52929	+	0.556614i	−0.963446	−	0.267901i	$-0.913670\pi$
$659$	−39.2583	+	14.2888i	−1.52929	+	0.556614i	−0.565839	+	0.824516i	$0.691448\pi$
$660$		0			0
$661$	25.0624	−	21.0298i	0.974812	−	0.817965i	−0.00848622	−	0.999964i	$-0.502701\pi$
$661$	25.0624	−	21.0298i	0.974812	−	0.817965i	0.983299	+	0.181999i	$0.0582568\pi$
$662$	−23.6599	−	29.1072i	−0.919568	−	1.13128i
$663$		0			0
$664$	−5.83147	+	1.81832i	−0.226305	+	0.0705647i
$665$	0.798352	−	0.460929i	0.0309588	−	0.0178741i
$666$		0			0
$667$	0.368476	+	0.212740i	0.0142674	+	0.00823731i
$668$	0.533469	−	2.55627i	0.0206405	−	0.0989049i
$669$		0			0
$670$	−21.9520	−	8.38001i	−0.848081	−	0.323748i
$671$	1.10071	+	6.24241i	0.0424923	+	0.240986i
$672$		0			0
$673$	21.7229	+	18.2276i	0.837354	+	0.702624i	0.956967	−	0.290197i	$-0.0937208\pi$
$673$	21.7229	+	18.2276i	0.837354	+	0.702624i	−0.119613	+	0.992821i	$0.538165\pi$
$674$	21.8182	+	0.340446i	0.840407	+	0.0131135i
$675$		0			0
$676$	32.8310	+	1.02482i	1.26273	+	0.0394163i
$677$	−25.8861	+	30.8498i	−0.994883	+	1.18566i	−0.0122822	+	0.999925i	$0.503910\pi$
$677$	−25.8861	+	30.8498i	−0.994883	+	1.18566i	−0.982601	+	0.185731i	$0.940535\pi$
$678$		0			0
$679$	−19.0424	+	3.35769i	−0.730780	+	0.128856i
$680$	−12.0025	−	5.01631i	−0.460276	−	0.192367i
$681$		0			0
$682$	−24.1895	−	4.65551i	−0.926262	−	0.178269i
$683$	−2.35647	+	4.08153i	−0.0901678	+	0.156175i	−0.907582	−	0.419876i	$-0.862074\pi$
$683$	−2.35647	+	4.08153i	−0.0901678	+	0.156175i	0.817414	+	0.576051i	$0.195407\pi$
$684$		0			0
$685$	29.7536	+	51.5348i	1.13683	+	1.96904i
$686$	7.34590	+	21.2065i	0.280468	+	0.809667i
$687$		0			0
$688$	−13.4990	−	18.2935i	−0.514646	−	0.697432i
$689$	25.7057	+	30.6348i	0.979308	+	1.16709i
$690$		0			0
$691$	−16.6235	−	45.6728i	−0.632389	−	1.73748i	−0.674408	−	0.738359i	$-0.735601\pi$
$691$	−16.6235	−	45.6728i	−0.632389	−	1.73748i	0.0420184	−	0.999117i	$-0.486621\pi$
$692$	−20.1811	+	10.8265i	−0.767169	+	0.411561i
$693$		0			0
$694$	−15.6296	+	26.1214i	−0.593291	+	0.991553i
$695$	−6.69611	+	37.9755i	−0.253998	+	1.44049i
$696$		0			0
$697$	−3.58211	−	1.30378i	−0.135682	−	0.0493843i
$698$	−2.82927	−	17.6518i	−0.107090	−	0.668131i
$699$		0			0
$700$	26.8452	−	30.0375i	1.01465	−	1.13531i
$701$			5.10945i			0.192981i	0.995334	+	0.0964906i	$0.0307618\pi$
$701$			5.10945i			0.192981i	−0.995334	+	0.0964906i	$0.969238\pi$
$702$		0			0
$703$		−	0.503788i		−	0.0190007i
$704$	−14.6928	−	14.8805i	−0.553756	−	0.560832i
$705$		0			0
$706$	15.6242	−	2.50429i	0.588026	−	0.0942502i
$707$	−22.6996	−	8.26197i	−0.853705	−	0.310723i
$708$		0			0
$709$	−1.58766	+	9.00406i	−0.0596258	+	0.338155i	−0.999998	−	0.00199245i	$-0.999366\pi$
$709$	−1.58766	+	9.00406i	−0.0596258	+	0.338155i	0.940372	+	0.340147i	$0.110477\pi$
$710$	−49.5099	−	29.6240i	−1.85807	−	1.11177i
$711$		0			0
$712$	36.5040	−	18.8558i	1.36805	−	0.706650i
$713$	1.93478	+	5.31576i	0.0724580	+	0.199077i
$714$		0			0
$715$	31.4080	+	37.4306i	1.17459	+	1.39983i
$716$	−33.6494	+	26.4909i	−1.25754	+	0.990012i
$717$		0			0
$718$	43.2160	−	14.9700i	1.61281	−	0.558674i
$719$	11.2528	+	19.4904i	0.419658	+	0.726869i	0.995905	−	0.0904064i	$-0.0288166\pi$
$719$	11.2528	+	19.4904i	0.419658	+	0.726869i	−0.576247	+	0.817276i	$0.695483\pi$
$720$		0			0
$721$	−23.5797	+	40.8412i	−0.878153	+	1.52101i
$722$	−5.07599	+	26.3742i	−0.188909	+	0.981548i
$723$		0			0
$724$	27.1667	+	10.8592i	1.00964	+	0.403580i
$725$	−3.39348	+	0.598363i	−0.126031	+	0.0222226i
$726$		0			0
$727$	11.2656	−	13.4258i	0.417817	−	0.497934i	−0.515550	−	0.856860i	$-0.672412\pi$
$727$	11.2656	−	13.4258i	0.417817	−	0.497934i	0.933366	+	0.358925i	$0.116857\pi$
$728$	2.10318	−	44.8997i	0.0779491	−	1.66409i
$729$		0			0
$730$	−0.886643	+	56.8224i	−0.0328161	+	2.10309i
$731$	−5.81100	−	4.87601i	−0.214928	−	0.180346i
$732$		0			0
$733$	−3.90323	−	22.1363i	−0.144169	−	0.817623i	−0.968031	−	0.250832i	$-0.919296\pi$
$733$	−3.90323	−	22.1363i	−0.144169	−	0.817623i	0.823862	−	0.566791i	$-0.191815\pi$
$734$	0.336141	−	0.880545i	0.0124072	−	0.0325015i
$735$		0			0
$736$	−1.19995	+	4.64997i	−0.0442307	+	0.171400i
$737$	−10.9147	−	6.30162i	−0.402049	−	0.232123i
$738$		0			0
$739$	7.76664	−	4.48407i	0.285700	−	0.164949i	−0.350301	−	0.936637i	$-0.613921\pi$
$739$	7.76664	−	4.48407i	0.285700	−	0.164949i	0.636001	+	0.771688i	$0.280587\pi$
$740$	−11.8846	−	36.1215i	−0.436886	−	1.32785i
$741$		0			0
$742$	23.7032	−	19.2672i	0.870173	−	0.707323i
$743$	−36.3720	+	30.5197i	−1.33436	+	1.11966i	−0.351321	+	0.936255i	$0.614267\pi$
$743$	−36.3720	+	30.5197i	−1.33436	+	1.11966i	−0.983038	+	0.183404i	$0.941288\pi$
$744$		0			0
$745$	−59.1037	+	21.5120i	−2.16539	+	0.788138i
$746$	14.3298	+	25.7393i	0.524653	+	0.942381i
$747$		0			0
$748$	−5.93088	−	3.67557i	−0.216854	−	0.134392i
$749$	28.0388	+	4.94400i	1.02452	+	0.180650i
$750$		0			0
$751$	4.76596	−	13.0944i	0.173912	−	0.477820i	−0.821858	−	0.569692i	$-0.807063\pi$
$751$	4.76596	−	13.0944i	0.173912	−	0.477820i	0.995771	+	0.0918713i	$0.0292848\pi$
$752$	2.95742	+	26.2659i	0.107846	+	0.957820i
$753$		0			0
$754$	−2.51700	+	2.90632i	−0.0916636	+	0.105842i
$755$	66.3349			2.41418
$756$		0			0
$757$	12.8098			0.465582			0.232791	−	0.972527i	$-0.425214\pi$
$757$	12.8098			0.465582			0.232791	+	0.972527i	$0.425214\pi$
$758$	17.7671	−	20.5152i	0.645328	−	0.745146i
$759$		0			0
$760$	−0.113365	−	0.882732i	−0.00411216	−	0.0320201i
$761$	10.5995	−	29.1218i	0.384230	−	1.05566i	−0.585326	−	0.810798i	$-0.699034\pi$
$761$	10.5995	−	29.1218i	0.384230	−	1.05566i	0.969557	−	0.244867i	$-0.0787442\pi$
$762$		0			0
$763$	−13.5565	−	2.39038i	−0.490778	−	0.0865375i
$764$	−2.02491	+	3.26739i	−0.0732587	+	0.118210i
$765$		0			0
$766$	−5.45678	−	9.80146i	−0.197161	−	0.354141i
$767$	15.5218	−	5.64949i	0.560461	−	0.203991i
$768$		0			0
$769$	13.1158	−	11.0054i	0.472966	−	0.396866i	−0.374909	−	0.927062i	$-0.622326\pi$
$769$	13.1158	−	11.0054i	0.472966	−	0.396866i	0.847875	+	0.530196i	$0.177882\pi$
$770$	28.9614	−	23.5413i	1.04370	−	0.848371i
$771$		0			0
$772$	11.8956	−	3.91386i	0.428133	−	0.140863i
$773$	−37.1476	+	21.4472i	−1.33610	+	0.771401i	−0.986227	−	0.165395i	$-0.947110\pi$
$773$	−37.1476	+	21.4472i	−1.33610	+	0.771401i	−0.349877	+	0.936795i	$0.613777\pi$
$774$		0			0
$775$	−39.6758	−	22.9068i	−1.42520	−	0.822838i
$776$	−4.09823	+	18.2121i	−0.147118	+	0.653778i
$777$		0			0
$778$	−6.22692	+	16.3119i	−0.223246	+	0.584808i
$779$	−0.0452870	−	0.256836i	−0.00162258	−	0.00920209i
$780$		0			0
$781$	−23.7064	−	19.8920i	−0.848282	−	0.711793i
$782$	−0.0249994	+	1.60214i	−0.000893978	+	0.0572924i
$783$		0			0
$784$	−6.32095	−	0.395004i	−0.225748	−	0.0141073i
$785$	−37.3022	+	44.4550i	−1.33137	+	1.58667i
$786$		0			0
$787$	5.86911	−	1.03488i	0.209211	−	0.0368896i	−0.0680603	−	0.997681i	$-0.521681\pi$
$787$	5.86911	−	1.03488i	0.209211	−	0.0368896i	0.277271	+	0.960792i	$0.410570\pi$
$788$	11.2310	−	28.0967i	0.400088	−	1.00090i
$789$		0			0
$790$	1.55381	−	8.07339i	0.0552819	−	0.287238i
$791$	0.826860	−	1.43216i	0.0293998	−	0.0509219i
$792$		0			0
$793$	6.57679	+	11.3913i	0.233549	+	0.404518i
$794$	−30.9915	+	10.7354i	−1.09985	+	0.380986i
$795$		0			0
$796$	−32.0602	−	40.7235i	−1.13634	−	1.44341i
$797$	−26.5934	−	31.6928i	−0.941987	−	1.12262i	−0.992297	−	0.123883i	$-0.960465\pi$
$797$	−26.5934	−	31.6928i	−0.941987	−	1.12262i	0.0503097	−	0.998734i	$-0.483979\pi$
$798$		0			0
$799$	3.01637	+	8.28740i	0.106711	+	0.293187i
$800$	−16.7621	−	35.0949i	−0.592631	−	1.24079i
$801$		0			0
$802$	−8.24720	−	4.93467i	−0.291219	−	0.174249i
$803$	−5.29310	+	30.0186i	−0.186789	+	1.05934i
$804$		0			0
$805$	−8.05397	−	2.93140i	−0.283865	−	0.103318i
$806$	−50.4730	+	8.08992i	−1.77783	+	0.284955i
$807$		0			0
$808$	−15.8100	+	17.1440i	−0.556194	+	0.603125i
$809$			45.8780i			1.61298i	0.591245	+	0.806492i	$0.298637\pi$
$809$			45.8780i			1.61298i	−0.591245	+	0.806492i	$0.701363\pi$
$810$		0			0
$811$			25.4302i			0.892974i	0.894790	+	0.446487i	$0.147325\pi$
$811$			25.4302i			0.892974i	−0.894790	+	0.446487i	$0.852675\pi$
$812$	2.18966	+	1.95695i	0.0768421	+	0.0686756i
$813$		0			0
$814$	−3.22797	−	20.1393i	−0.113140	−	0.705882i
$815$	25.9902	+	9.45967i	0.910398	+	0.331358i
$816$		0			0
$817$	0.0901192	−	0.511091i	0.00315287	−	0.0178808i
$818$	13.1918	−	22.0472i	0.461241	−	0.770861i
$819$		0			0
$820$	−9.30595	−	17.3467i	−0.324978	−	0.605774i
$821$	−2.68201	−	7.36876i	−0.0936027	−	0.257171i	0.884052	−	0.467389i	$-0.154805\pi$
$821$	−2.68201	−	7.36876i	−0.0936027	−	0.257171i	−0.977655	+	0.210217i	$0.932583\pi$
$822$		0			0
$823$	−5.63305	−	6.71321i	−0.196356	−	0.234008i	0.658878	−	0.752250i	$-0.271031\pi$
$823$	−5.63305	−	6.71321i	−0.196356	−	0.234008i	−0.855234	+	0.518242i	$0.826587\pi$
$824$	27.6013	+	36.2082i	0.961538	+	1.26137i
$825$		0			0
$826$	−4.12974	−	11.9219i	−0.143692	−	0.414816i
$827$	9.57006	+	16.5758i	0.332784	+	0.576398i	0.983057	−	0.183303i	$-0.0586788\pi$
$827$	9.57006	+	16.5758i	0.332784	+	0.576398i	−0.650273	+	0.759701i	$0.725345\pi$
$828$		0			0
$829$	−0.0258029	+	0.0446919i	−0.000896172	+	0.00155222i	−0.866473	−	0.499224i	$-0.833619\pi$
$829$	−0.0258029	+	0.0446919i	−0.000896172	+	0.00155222i	0.865577	+	0.500776i	$0.166952\pi$
$830$	−10.3352	−	1.98912i	−0.358741	−	0.0690434i
$831$		0			0
$832$	−39.2118	−	18.5887i	−1.35942	−	0.644448i
$833$	−2.08106	+	0.366947i	−0.0721044	+	0.0127140i
$834$		0			0
$835$	2.89216	−	3.44674i	0.100087	−	0.119280i
$836$	0.0148937	−	0.477130i	0.000515109	−	0.0165019i
$837$		0			0
$838$	−6.95909	−	0.108588i	−0.240398	−	0.00375111i
$839$	−8.24125	−	6.91523i	−0.284520	−	0.238740i	0.489347	−	0.872089i	$-0.337235\pi$
$839$	−8.24125	−	6.91523i	−0.284520	−	0.238740i	−0.773866	+	0.633349i	$0.781680\pi$
$840$		0			0
$841$	4.99218	+	28.3120i	0.172144	+	0.976278i
$842$	−15.5488	−	5.93564i	−0.535848	−	0.204556i
$843$		0			0
$844$	−34.1614	−	7.12917i	−1.17588	−	0.245396i
$845$	49.0137	+	28.2981i	1.68612	+	0.973484i
$846$		0			0
$847$	−10.5727	+	6.10416i	−0.363283	+	0.209741i
$848$	−8.33818	−	28.2866i	−0.286334	−	0.971367i
$849$		0			0
$850$	−8.18525	−	10.0698i	−0.280752	−	0.345391i
$851$	−3.58808	+	3.01075i	−0.122998	+	0.103207i
$852$		0			0
$853$	−37.1684	+	13.5282i	−1.27262	+	0.463196i	−0.887985	−	0.459872i	$-0.847895\pi$
$853$	−37.1684	+	13.5282i	−1.27262	+	0.463196i	−0.384636	+	0.923068i	$0.625673\pi$
$854$	8.77834	−	4.88717i	0.300389	−	0.167236i
$855$		0			0
$856$	14.8422	−	23.1352i	0.507296	−	0.790745i
$857$	−10.1029	−	1.78141i	−0.345108	−	0.0608519i	−0.00159234	−	0.999999i	$-0.500507\pi$
$857$	−10.1029	−	1.78141i	−0.345108	−	0.0608519i	−0.343516	+	0.939147i	$0.611618\pi$
$858$		0			0
$859$	1.21231	−	3.33080i	0.0413636	−	0.113645i	−0.917291	−	0.398217i	$-0.869629\pi$
$859$	1.21231	−	3.33080i	0.0413636	−	0.113645i	0.958655	+	0.284572i	$0.0918513\pi$
$860$	−5.59535	−	38.7711i	−0.190800	−	1.32208i
$861$		0			0
$862$	−4.71332	−	4.08193i	−0.160536	−	0.139031i
$863$	−6.36151			−0.216548			−0.108274	−	0.994121i	$-0.534532\pi$
$863$	−6.36151			−0.216548			−0.108274	+	0.994121i	$0.534532\pi$
$864$		0			0
$865$	−39.4602			−1.34169
$866$	−30.4924	−	26.4077i	−1.03617	−	0.897369i
$867$		0			0
$868$	5.57706	+	38.6444i	0.189298	+	1.31168i
$869$	1.50825	−	4.14388i	0.0511638	−	0.140571i
$870$		0			0
$871$	−25.7559	−	4.54146i	−0.872706	−	0.153882i
$872$	−7.17607	+	11.1857i	−0.243012	+	0.378794i
$873$		0			0
$874$	−0.0957804	+	0.0533239i	−0.00323982	+	0.00180371i
$875$	17.7910	−	6.47541i	0.601447	−	0.218909i
$876$		0			0
$877$	−12.5094	+	10.4966i	−0.422412	+	0.354446i	−0.829080	−	0.559130i	$-0.811135\pi$
$877$	−12.5094	+	10.4966i	−0.422412	+	0.354446i	0.406668	+	0.913576i	$0.366691\pi$
$878$	4.31460	+	5.30797i	0.145611	+	0.179135i
$879$		0			0
$880$	−10.1879	−	34.5615i	−0.343433	−	1.16507i
$881$	43.1593	−	24.9180i	1.45407	−	0.839509i	0.455364	−	0.890306i	$-0.349509\pi$
$881$	43.1593	−	24.9180i	1.45407	−	0.839509i	0.998709	+	0.0507963i	$0.0161759\pi$
$882$		0			0
$883$	−38.2077	−	22.0592i	−1.28579	−	0.742352i	−0.307890	−	0.951422i	$-0.599623\pi$
$883$	−38.2077	−	22.0592i	−1.28579	−	0.742352i	−0.977901	+	0.209070i	$0.932956\pi$
$884$	−14.1737	−	2.95793i	−0.476714	−	0.0994858i
$885$		0			0
$886$	−9.60086	−	3.66505i	−0.322547	−	0.123130i
$887$	0.417367	+	2.36700i	0.0140138	+	0.0794762i	0.991013	−	0.133769i	$-0.0427079\pi$
$887$	0.417367	+	2.36700i	0.0140138	+	0.0794762i	−0.976999	+	0.213245i	$0.931597\pi$
$888$		0			0
$889$	−24.9598	−	20.9437i	−0.837124	−	0.702431i
$890$	70.7842	+	1.10450i	2.37269	+	0.0370229i
$891$		0			0
$892$	1.10298	−	35.3348i	0.0369305	−	1.18310i
$893$	−0.387838	+	0.462207i	−0.0129785	+	0.0154672i
$894$		0			0
$895$	−72.6689	+	12.8135i	−2.42905	+	0.428308i
$896$	−14.6641	+	29.7259i	−0.489895	+	0.993072i
$897$		0			0
$898$	−8.82668	−	1.69879i	−0.294550	−	0.0566892i
$899$	1.66986	−	2.89227i	0.0556928	−	0.0964627i
$900$		0			0
$901$	−4.91981	−	8.52136i	−0.163903	−	0.283888i
$902$	−3.45603	−	9.97703i	−0.115073	−	0.332199i
$903$		0			0
$904$	−0.967886	−	1.26970i	−0.0321914	−	0.0422295i
$905$	32.4029	+	38.6163i	1.07711	+	1.28365i
$906$		0			0
$907$	12.0002	+	32.9702i	0.398459	+	1.09476i	0.963035	+	0.269376i	$0.0868176\pi$
$907$	12.0002	+	32.9702i	0.398459	+	1.09476i	−0.564576	+	0.825381i	$0.690960\pi$
$908$	−8.82079	−	16.4424i	−0.292728	−	0.545660i
$909$		0			0
$910$	39.7659	−	66.4598i	1.31823	−	2.20312i
$911$	1.87566	−	10.6374i	0.0621434	−	0.352433i	−0.937842	−	0.347062i	$-0.887179\pi$
$911$	1.87566	−	10.6374i	0.0621434	−	0.352433i	0.999986	−	0.00537068i	$-0.00170955\pi$
$912$		0			0
$913$	−5.30483	−	1.93080i	−0.175564	−	0.0639001i
$914$	0.200128	+	1.24860i	0.00661963	+	0.0412999i
$915$		0			0
$916$	25.0783	+	22.4131i	0.828610	+	0.740548i
$917$			9.08884i			0.300140i
$918$		0			0
$919$			20.9319i			0.690481i	0.938514	+	0.345241i	$0.112203\pi$
$919$			20.9319i			0.690481i	−0.938514	+	0.345241i	$0.887797\pi$
$920$	−5.60950	+	6.08282i	−0.184940	+	0.200545i
$921$		0			0
$922$	−18.2950	+	2.93236i	−0.602514	+	0.0965722i
$923$	−60.3449	−	21.9637i	−1.98628	−	0.722946i
$924$		0			0
$925$	6.58709	−	37.3573i	0.216582	−	1.22830i
$926$	1.63660	+	0.979249i	0.0537819	+	0.0321801i
$927$		0			0
$928$	2.55834	−	1.22192i	0.0839816	−	0.0401115i
$929$	11.5040	+	31.6070i	0.377435	+	1.03699i	0.972416	+	0.233254i	$0.0749373\pi$
$929$	11.5040	+	31.6070i	0.377435	+	1.03699i	−0.594981	+	0.803740i	$0.702840\pi$
$930$		0			0
$931$	−0.0929288	−	0.110748i	−0.00304562	−	0.00362963i
$932$	−21.8079	−	27.7009i	−0.714342	−	0.907373i
$933$		0			0
$934$	26.2230	−	9.08363i	0.858043	−	0.297226i
$935$	−6.01119	−	10.4117i	−0.196587	−	0.340498i
$936$		0			0
$937$	−12.5767	+	21.7834i	−0.410862	+	0.711634i	−0.994984	−	0.100032i	$-0.968106\pi$
$937$	−12.5767	+	21.7834i	−0.410862	+	0.711634i	0.584122	+	0.811666i	$0.301439\pi$
$938$	−3.77541	+	19.6166i	−0.123271	+	0.640504i
$939$		0			0
$940$	−16.9042	+	42.2895i	−0.551355	+	1.37933i
$941$	40.7896	−	7.19230i	1.32970	−	0.234462i	0.536747	−	0.843743i	$-0.319653\pi$
$941$	40.7896	−	7.19230i	1.32970	−	0.234462i	0.792955	+	0.609281i	$0.208542\pi$
$942$		0			0
$943$	−1.55859	+	1.85745i	−0.0507546	+	0.0604870i
$944$	−12.1569	−	0.759701i	−0.395675	−	0.0247262i
$945$		0			0
$946$	0.327815	−	21.0087i	0.0106582	−	0.683052i
$947$	43.3100	+	36.3414i	1.40739	+	1.18094i	0.957706	+	0.287748i	$0.0929067\pi$
$947$	43.3100	+	36.3414i	1.40739	+	1.18094i	0.449681	+	0.893189i	$0.351538\pi$
$948$		0			0
$949$	10.9838	+	62.2922i	0.356549	+	2.02209i
$950$	0.316628	−	0.829429i	0.0102728	−	0.0269102i
$951$		0			0
$952$	−2.42798	+	10.7897i	−0.0786914	+	0.349697i
$953$	31.8569	+	18.3926i	1.03195	+	0.595795i	0.917542	−	0.397639i	$-0.130170\pi$
$953$	31.8569	+	18.3926i	1.03195	+	0.595795i	0.114405	+	0.993434i	$0.463504\pi$
$954$		0			0
$955$	−5.73591	+	3.31163i	−0.185610	+	0.107162i
$956$	17.5056	−	5.75964i	0.566171	−	0.186280i
$957$		0			0
$958$	−20.9178	+	17.0031i	−0.675823	+	0.549345i
$959$	38.7552	−	32.5195i	1.25147	−	1.05011i
$960$		0			0
$961$	12.5945	−	4.58401i	0.406273	−	0.147871i
$962$	−20.5880	−	36.9801i	−0.663783	−	1.19229i
$963$		0			0
$964$	−6.56014	+	10.5854i	−0.211288	+	0.340933i
$965$	21.2496	+	3.74687i	0.684047	+	0.120616i
$966$		0			0
$967$	15.4066	−	42.3293i	0.495444	−	1.36122i	−0.400192	−	0.916431i	$-0.631057\pi$
$967$	15.4066	−	42.3293i	0.495444	−	1.36122i	0.895636	−	0.444789i	$-0.146721\pi$
$968$	1.50131	+	11.6902i	0.0482538	+	0.375737i
$969$		0			0
$970$	−21.0570	+	24.3140i	−0.676099	+	0.780676i
$971$	−40.1053			−1.28704			−0.643520	−	0.765429i	$-0.722527\pi$
$971$	−40.1053			−1.28704			−0.643520	+	0.765429i	$0.722527\pi$
$972$		0			0
$973$	32.7837			1.05100
$974$	11.7988	−	13.6238i	0.378058	−	0.436535i
$975$		0			0
$976$	−1.08528	−	9.63876i	−0.0347389	−	0.308529i
$977$	−12.5629	+	34.5163i	−0.401923	+	1.10427i	0.559411	+	0.828890i	$0.311027\pi$
$977$	−12.5629	+	34.5163i	−0.401923	+	1.10427i	−0.961334	+	0.275384i	$0.911195\pi$
$978$		0			0
$979$	37.3945	+	6.59366i	1.19513	+	0.210734i
$980$	−9.27559	−	5.74840i	−0.296298	−	0.183626i
$981$		0			0
$982$	−17.0137	−	30.5601i	−0.542930	−	0.975211i
$983$	17.7958	−	6.47713i	0.567597	−	0.206588i	−0.0422506	−	0.999107i	$-0.513453\pi$
$983$	17.7958	−	6.47713i	0.567597	−	0.206588i	0.609848	+	0.792519i	$0.291231\pi$
$984$		0			0
$985$	39.9383	−	33.5122i	1.27254	−	1.06779i
$986$	0.734063	−	0.596686i	0.0233773	−	0.0190023i
$987$		0			0
$988$	−0.309592	−	0.940962i	−0.00984945	−	0.0299360i
$989$	−4.17867	+	2.41256i	−0.132874	+	0.0767148i
$990$		0			0
$991$	−30.3997	−	17.5513i	−0.965680	−	0.557535i	−0.0677633	−	0.997701i	$-0.521586\pi$
$991$	−30.3997	−	17.5513i	−0.965680	−	0.557535i	−0.897916	+	0.440166i	$0.854920\pi$
$992$	36.4990	+	9.41874i	1.15884	+	0.299045i
$993$		0			0
$994$	−17.4936	+	45.8258i	−0.554864	+	1.45351i
$995$	−15.5073	−	87.9462i	−0.491614	−	2.78808i
$996$		0			0
$997$	18.3914	+	15.4322i	0.582460	+	0.488742i	0.885754	−	0.464155i	$-0.153642\pi$
$997$	18.3914	+	15.4322i	0.582460	+	0.488742i	−0.303294	+	0.952897i	$0.598086\pi$
$998$	0.871737	−	55.8671i	0.0275944	−	1.76844i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.a.107.4		96
3.2	odd	2		972.2.l.d.107.13		96
4.3	odd	2	inner	972.2.l.a.107.12		96
9.2	odd	6		972.2.l.c.755.9		96
9.4	even	3		324.2.l.a.143.15		96
9.5	odd	6		108.2.l.a.47.2	yes	96
9.7	even	3		972.2.l.b.755.8		96
12.11	even	2		972.2.l.d.107.5		96
27.4	even	9		972.2.l.c.215.7		96
27.5	odd	18	inner	972.2.l.a.863.12		96
27.13	even	9		108.2.l.a.23.15	yes	96
27.14	odd	18		324.2.l.a.179.2		96
27.22	even	9		972.2.l.d.863.5		96
27.23	odd	18		972.2.l.b.215.10		96
36.7	odd	6		972.2.l.b.755.10		96
36.11	even	6		972.2.l.c.755.7		96
36.23	even	6		108.2.l.a.47.15	yes	96
36.31	odd	6		324.2.l.a.143.2		96
108.23	even	18		972.2.l.b.215.8		96
108.31	odd	18		972.2.l.c.215.9		96
108.59	even	18	inner	972.2.l.a.863.4		96
108.67	odd	18		108.2.l.a.23.2	✓	96
108.95	even	18		324.2.l.a.179.15		96
108.103	odd	18		972.2.l.d.863.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.2	✓	96	108.67	odd	18
108.2.l.a.23.15	yes	96	27.13	even	9
108.2.l.a.47.2	yes	96	9.5	odd	6
108.2.l.a.47.15	yes	96	36.23	even	6
324.2.l.a.143.2		96	36.31	odd	6
324.2.l.a.143.15		96	9.4	even	3
324.2.l.a.179.2		96	27.14	odd	18
324.2.l.a.179.15		96	108.95	even	18
972.2.l.a.107.4		96	1.1	even	1	trivial
972.2.l.a.107.12		96	4.3	odd	2	inner
972.2.l.a.863.4		96	108.59	even	18	inner
972.2.l.a.863.12		96	27.5	odd	18	inner
972.2.l.b.215.8		96	108.23	even	18
972.2.l.b.215.10		96	27.23	odd	18
972.2.l.b.755.8		96	9.7	even	3
972.2.l.b.755.10		96	36.7	odd	6
972.2.l.c.215.7		96	27.4	even	9
972.2.l.c.215.9		96	108.31	odd	18
972.2.l.c.755.7		96	36.11	even	6
972.2.l.c.755.9		96	9.2	odd	6
972.2.l.d.107.5		96	12.11	even	2
972.2.l.d.107.13		96	3.2	odd	2
972.2.l.d.863.5		96	27.22	even	9
972.2.l.d.863.13		96	108.103	odd	18

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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06904 - 0.925831i) q^{2} +(0.285675 + 1.97949i) q^{4} +(-1.17862 + 3.23823i) q^{5} +(2.88522 + 0.508742i) q^{7} +(1.52728 - 2.38064i) q^{8} +(4.25804 - 2.37058i) q^{10} +(2.45635 - 0.894038i) q^{11} +(4.15529 - 3.48670i) q^{13} +(-2.61340 - 3.21509i) q^{14} +(-3.83678 + 1.13098i) q^{16} +(-1.15583 + 0.667320i) q^{17} +(-0.0790760 - 0.0456546i) q^{19} +(-6.74675 - 1.40799i) q^{20} +(-3.45365 - 1.31840i) q^{22} +(0.147416 + 0.836038i) q^{23} +(-5.26677 - 4.41934i) q^{25} +(-7.67024 - 0.119685i) q^{26} +(-0.182815 + 5.85661i) q^{28} +(0.322160 - 0.383935i) q^{29} +(6.56230 - 1.15711i) q^{31} +(5.14875 + 2.34314i) q^{32} +(1.85345 + 0.356716i) q^{34} +(-5.04800 + 8.74340i) q^{35} +(2.75869 + 4.77819i) q^{37} +(0.0422667 + 0.122017i) q^{38} +(5.90897 + 7.75154i) q^{40} +(1.83593 + 2.18798i) q^{41} +(1.94395 + 5.34095i) q^{43} +(2.47146 + 4.60692i) q^{44} +(0.616436 - 1.03024i) q^{46} +(1.14746 - 6.50759i) q^{47} +(1.48783 + 0.541527i) q^{49} +(1.53880 + 9.60057i) q^{50} +(8.08896 + 7.22929i) q^{52} +7.37249i q^{53} +9.00795i q^{55} +(5.61766 - 6.09167i) q^{56} +(-0.699859 + 0.112175i) q^{58} +(2.86152 + 1.04151i) q^{59} +(-0.421082 + 2.38808i) q^{61} +(-8.08663 - 4.83859i) q^{62} +(-3.33485 - 7.27178i) q^{64} +(6.39324 + 17.5653i) q^{65} +(-3.09917 - 3.69345i) q^{67} +(-1.65115 - 2.09732i) q^{68} +(13.4914 - 4.67341i) q^{70} +(-5.91940 - 10.2527i) q^{71} +(-5.83049 + 10.0987i) q^{73} +(1.47466 - 7.66214i) q^{74} +(0.0677828 - 0.169573i) q^{76} +(7.54195 - 1.32985i) q^{77} +(1.08439 - 1.29232i) q^{79} +(0.859714 - 13.7574i) q^{80} +(0.0630204 - 4.03879i) q^{82} +(-1.65438 - 1.38819i) q^{83} +(-0.798649 - 4.52937i) q^{85} +(2.86667 - 7.50943i) q^{86} +(1.62315 - 7.21311i) q^{88} +(12.5801 + 7.26310i) q^{89} +(13.7628 - 7.94593i) q^{91} +(-1.61282 + 0.530644i) q^{92} +(-7.25160 + 5.89449i) q^{94} +(0.241041 - 0.202257i) q^{95} +(-6.20195 + 2.25733i) q^{97} +(-1.08919 - 1.95639i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} - 33 q^{14} + 3 q^{16} + 18 q^{17} + 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 30 q^{29} - 33 q^{32} + 15 q^{34} - 6 q^{37} + 63 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 - 33 * q^14 + 3 * q^16 + 18 * q^17 + 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 30 * q^29 - 33 * q^32 + 15 * q^34 - 6 * q^37 + 63 * q^38 + 33 * q^40 + 24 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 21 * q^50 + 57 * q^52 + 18 * q^56 + 57 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 - 30 * q^65 + 102 * q^68 + 51 * q^70 - 6 * q^73 - 75 * q^74 + 27 * q^76 + 42 * q^77 - 12 * q^82 - 24 * q^85 + 111 * q^86 + 27 * q^88 - 147 * q^92 + 30 * q^94 - 12 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

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