LMFDB - Embedded newform 972.2.l.b.215.9

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)

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);

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")

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,-3,0,0,6,12] 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			215.9
Character	$\chi$	$=$	972.215
Dual form			972.2.l.b.755.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.117341 + 1.40934i) q^{2} +(-1.97246 - 0.330746i) q^{4} +(0.194411 - 0.231690i) q^{5} +(-0.166049 + 0.456215i) q^{7} +(0.697584 - 2.74105i) q^{8} +(0.303717 + 0.301177i) q^{10} +(0.0318926 - 0.0267611i) q^{11} +(-0.749815 + 4.25241i) q^{13} +(-0.623477 - 0.287551i) q^{14} +(3.78121 + 1.30477i) q^{16} +(2.14427 + 1.23800i) q^{17} +(6.55326 - 3.78353i) q^{19} +(-0.460098 + 0.392699i) q^{20} +(0.0339731 + 0.0480877i) q^{22} +(-6.17265 + 2.24666i) q^{23} +(0.852356 + 4.83395i) q^{25} +(-5.90510 - 1.55572i) q^{26} +(0.478416 - 0.844947i) q^{28} +(-6.91801 + 1.21983i) q^{29} +(1.22825 + 3.37459i) q^{31} +(-2.28255 + 5.17590i) q^{32} +(-1.99636 + 2.87673i) q^{34} +(0.0734187 + 0.127165i) q^{35} +(-3.36015 + 5.81994i) q^{37} +(4.56330 + 9.67972i) q^{38} +(-0.499456 - 0.694513i) q^{40} +(6.22846 + 1.09825i) q^{41} +(1.55474 + 1.85287i) q^{43} +(-0.0717582 + 0.0422369i) q^{44} +(-2.44200 - 8.96296i) q^{46} +(-6.75922 - 2.46015i) q^{47} +(5.18175 + 4.34801i) q^{49} +(-6.91269 + 0.634036i) q^{50} +(2.88545 - 8.13973i) q^{52} +9.90799i q^{53} -0.0125918i q^{55} +(1.13468 + 0.773397i) q^{56} +(-0.907388 - 9.89295i) q^{58} +(-3.33471 - 2.79816i) q^{59} +(7.07970 + 2.57680i) q^{61} +(-4.90006 + 1.33504i) q^{62} +(-7.02675 - 3.82423i) q^{64} +(0.839468 + 1.00044i) q^{65} +(-10.9694 - 1.93421i) q^{67} +(-3.82003 - 3.15111i) q^{68} +(-0.187833 + 0.0885501i) q^{70} +(-1.68932 + 2.92598i) q^{71} +(0.315477 + 0.546421i) q^{73} +(-7.80798 - 5.41850i) q^{74} +(-14.1775 + 5.29540i) q^{76} +(0.00691309 + 0.0189936i) q^{77} +(2.98154 - 0.525727i) q^{79} +(1.03741 - 0.622407i) q^{80} +(-2.27865 + 8.64913i) q^{82} +(0.999837 + 5.67036i) q^{83} +(0.703701 - 0.256126i) q^{85} +(-2.79375 + 1.97374i) q^{86} +(-0.0511058 - 0.106088i) q^{88} +(-9.00521 + 5.19916i) q^{89} +(-1.81551 - 1.04819i) q^{91} +(12.9184 - 2.38987i) q^{92} +(4.26032 - 9.23734i) q^{94} +(0.397420 - 2.25388i) q^{95} +(-2.55186 + 2.14126i) q^{97} +(-6.73584 + 6.79263i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 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 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Character values

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

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	−0.117341	+	1.40934i	−0.0829726	+	0.996552i
$2$	−0.117341	+	1.40934i	−0.0829726	+	0.996552i
$3$		0			0
$3$		0			0
$4$	−1.97246	−	0.330746i	−0.986231	−	0.165373i
$5$	0.194411	−	0.231690i	0.0869431	−	0.103615i	−0.720819	−	0.693123i	$-0.756234\pi$
$5$	0.194411	−	0.231690i	0.0869431	−	0.103615i	0.807762	+	0.589509i	$0.200679\pi$
$6$		0			0
$7$	−0.166049	+	0.456215i	−0.0627605	+	0.172433i	−0.967109	−	0.254361i	$-0.918135\pi$
$7$	−0.166049	+	0.456215i	−0.0627605	+	0.172433i	0.904349	+	0.426794i	$0.140357\pi$
$8$	0.697584	−	2.74105i	0.246633	−	0.969109i
$9$		0			0
$10$	0.303717	+	0.301177i	0.0960436	+	0.0952405i
$11$	0.0318926	−	0.0267611i	0.00961599	−	0.00806878i	−0.637967	−	0.770064i	$-0.720224\pi$
$11$	0.0318926	−	0.0267611i	0.00961599	−	0.00806878i	0.647583	+	0.761995i	$0.275780\pi$
$12$		0			0
$13$	−0.749815	+	4.25241i	−0.207961	+	1.17941i	0.684750	+	0.728778i	$0.259911\pi$
$13$	−0.749815	+	4.25241i	−0.207961	+	1.17941i	−0.892711	+	0.450629i	$0.851200\pi$
$14$	−0.623477	−	0.287551i	−0.166631	−	0.0768514i
$15$		0			0
$16$	3.78121	+	1.30477i	0.945303	+	0.326192i
$17$	2.14427	+	1.23800i	0.520062	+	0.300258i	0.736960	−	0.675936i	$-0.236261\pi$
$17$	2.14427	+	1.23800i	0.520062	+	0.300258i	−0.216898	+	0.976194i	$0.569594\pi$
$18$		0			0
$19$	6.55326	−	3.78353i	1.50342	−	0.868001i	0.503430	−	0.864036i	$-0.332071\pi$
$19$	6.55326	−	3.78353i	1.50342	−	0.868001i	0.999992	−	0.00396479i	$-0.00126203\pi$
$20$	−0.460098	+	0.392699i	−0.102881	+	0.0878101i
$21$		0			0
$22$	0.0339731	+	0.0480877i	0.00724309	+	0.0102523i
$23$	−6.17265	+	2.24666i	−1.28709	+	0.468461i	−0.892769	−	0.450514i	$-0.851241\pi$
$23$	−6.17265	+	2.24666i	−1.28709	+	0.468461i	−0.394316	+	0.918975i	$0.629019\pi$
$24$		0			0
$25$	0.852356	+	4.83395i	0.170471	+	0.966791i
$26$	−5.90510	−	1.55572i	−1.15809	−	0.305103i
$27$		0			0
$28$	0.478416	−	0.844947i	0.0904122	−	0.159680i
$29$	−6.91801	+	1.21983i	−1.28464	+	0.226517i	−0.773950	−	0.633246i	$-0.781722\pi$
$29$	−6.91801	+	1.21983i	−1.28464	+	0.226517i	−0.510692	+	0.859764i	$0.670611\pi$
$30$		0			0
$31$	1.22825	+	3.37459i	0.220600	+	0.606094i	0.999786	−	0.0206992i	$-0.00658924\pi$
$31$	1.22825	+	3.37459i	0.220600	+	0.606094i	−0.779186	+	0.626793i	$0.784367\pi$
$32$	−2.28255	+	5.17590i	−0.403502	+	0.914979i
$33$		0			0
$34$	−1.99636	+	2.87673i	−0.342374	+	0.493356i
$35$	0.0734187	+	0.127165i	0.0124100	+	0.0214948i
$36$		0			0
$37$	−3.36015	+	5.81994i	−0.552405	+	0.956793i	0.445696	+	0.895184i	$0.352956\pi$
$37$	−3.36015	+	5.81994i	−0.552405	+	0.956793i	−0.998100	+	0.0616082i	$0.980377\pi$
$38$	4.56330	+	9.67972i	0.740265	+	1.57026i
$39$		0			0
$40$	−0.499456	−	0.694513i	−0.0789710	−	0.109812i
$41$	6.22846	+	1.09825i	0.972722	+	0.171517i	0.637355	−	0.770571i	$-0.280029\pi$
$41$	6.22846	+	1.09825i	0.972722	+	0.171517i	0.335367	+	0.942088i	$0.391140\pi$
$42$		0			0
$43$	1.55474	+	1.85287i	0.237096	+	0.282560i	0.871452	−	0.490481i	$-0.163179\pi$
$43$	1.55474	+	1.85287i	0.237096	+	0.282560i	−0.634356	+	0.773041i	$0.718735\pi$
$44$	−0.0717582	+	0.0422369i	−0.0108179	+	0.00636745i
$45$		0			0
$46$	−2.44200	−	8.96296i	−0.360053	−	1.32152i
$47$	−6.75922	−	2.46015i	−0.985933	−	0.358850i	−0.201789	−	0.979429i	$-0.564675\pi$
$47$	−6.75922	−	2.46015i	−0.985933	−	0.358850i	−0.784144	+	0.620579i	$0.786898\pi$
$48$		0			0
$49$	5.18175	+	4.34801i	0.740250	+	0.621144i
$50$	−6.91269	+	0.634036i	−0.977601	+	0.0896663i
$51$		0			0
$52$	2.88545	−	8.13973i	0.400140	−	1.12878i
$53$			9.90799i			1.36097i	0.732763	+	0.680484i	$0.238230\pi$
$53$			9.90799i			1.36097i	−0.732763	+	0.680484i	$0.761770\pi$
$54$		0			0
$55$		−	0.0125918i		−	0.00169788i
$56$	1.13468	+	0.773397i	0.151628	+	0.103350i
$57$		0			0
$58$	−0.907388	−	9.89295i	−0.119146	−	1.29901i
$59$	−3.33471	−	2.79816i	−0.434143	−	0.364289i	0.399369	−	0.916790i	$-0.369229\pi$
$59$	−3.33471	−	2.79816i	−0.434143	−	0.364289i	−0.833512	+	0.552501i	$0.813674\pi$
$60$		0			0
$61$	7.07970	+	2.57680i	0.906462	+	0.329925i	0.752839	−	0.658204i	$-0.228684\pi$
$61$	7.07970	+	2.57680i	0.906462	+	0.329925i	0.153623	+	0.988130i	$0.450906\pi$
$62$	−4.90006	+	1.33504i	−0.622308	+	0.169550i
$63$		0			0
$64$	−7.02675	−	3.82423i	−0.878344	−	0.478029i
$65$	0.839468	+	1.00044i	0.104123	+	0.124089i
$66$		0			0
$67$	−10.9694	−	1.93421i	−1.34013	−	0.236301i	−0.542810	−	0.839856i	$-0.682639\pi$
$67$	−10.9694	−	1.93421i	−1.34013	−	0.236301i	−0.797322	+	0.603554i	$0.793751\pi$
$68$	−3.82003	−	3.15111i	−0.463247	−	0.382128i
$69$		0			0
$70$	−0.187833	+	0.0885501i	−0.0224504	+	0.0105838i
$71$	−1.68932	+	2.92598i	−0.200485	+	0.347250i	−0.948685	−	0.316223i	$-0.897585\pi$
$71$	−1.68932	+	2.92598i	−0.200485	+	0.347250i	0.748200	+	0.663473i	$0.230918\pi$
$72$		0			0
$73$	0.315477	+	0.546421i	0.0369237	+	0.0639538i	0.883897	−	0.467682i	$-0.154911\pi$
$73$	0.315477	+	0.546421i	0.0369237	+	0.0639538i	−0.846973	+	0.531636i	$0.821577\pi$
$74$	−7.80798	−	5.41850i	−0.907659	−	0.629887i
$75$		0			0
$76$	−14.1775	+	5.29540i	−1.62627	+	0.607424i
$77$	0.00691309	+	0.0189936i	0.000787820	+	0.00216452i
$78$		0			0
$79$	2.98154	−	0.525727i	0.335450	−	0.0591489i	−0.00338622	−	0.999994i	$-0.501078\pi$
$79$	2.98154	−	0.525727i	0.335450	−	0.0591489i	0.338836	+	0.940845i	$0.389967\pi$
$80$	1.03741	−	0.622407i	0.115986	−	0.0695873i
$81$		0			0
$82$	−2.27865	+	8.64913i	−0.251635	+	0.955136i
$83$	0.999837	+	5.67036i	0.109746	+	0.622403i	0.989218	+	0.146451i	$0.0467852\pi$
$83$	0.999837	+	5.67036i	0.109746	+	0.622403i	−0.879471	+	0.475952i	$0.842104\pi$
$84$		0			0
$85$	0.703701	−	0.256126i	0.0763270	−	0.0277808i
$86$	−2.79375	+	1.97374i	−0.301258	+	0.212834i
$87$		0			0
$88$	−0.0511058	−	0.106088i	−0.00544790	−	0.0113090i
$89$	−9.00521	+	5.19916i	−0.954550	+	0.551110i	−0.894491	−	0.447085i	$-0.852462\pi$
$89$	−9.00521	+	5.19916i	−0.954550	+	0.551110i	−0.0600588	+	0.998195i	$0.519129\pi$
$90$		0			0
$91$	−1.81551	−	1.04819i	−0.190317	−	0.109880i
$92$	12.9184	−	2.38987i	1.34683	−	0.249161i
$93$		0			0
$94$	4.26032	−	9.23734i	0.439418	−	0.952759i
$95$	0.397420	−	2.25388i	0.0407745	−	0.231244i
$96$		0			0
$97$	−2.55186	+	2.14126i	−0.259102	+	0.217412i	−0.763080	−	0.646304i	$-0.776314\pi$
$97$	−2.55186	+	2.14126i	−0.259102	+	0.217412i	0.503978	+	0.863717i	$0.331869\pi$
$98$	−6.73584	+	6.79263i	−0.680422	+	0.686160i
$99$		0			0
$100$	−0.0824291	−	9.81670i	−0.00824291	−	0.981670i
$101$	5.71163	−	15.6926i	0.568329	−	1.56147i	−0.238784	−	0.971073i	$-0.576749\pi$
$101$	5.71163	−	15.6926i	0.568329	−	1.56147i	0.807113	−	0.590397i	$-0.201029\pi$
$102$		0			0
$103$	10.2156	−	12.1745i	1.00657	−	1.19959i	0.0267664	−	0.999642i	$-0.491479\pi$
$103$	10.2156	−	12.1745i	1.00657	−	1.19959i	0.979807	−	0.199946i	$-0.0640766\pi$
$104$	11.1330	+	5.02170i	1.09168	+	0.492418i
$105$		0			0
$106$	−13.9637	−	1.16261i	−1.35627	−	0.112923i
$107$	1.00162			0.0968302			0.0484151	−	0.998827i	$-0.484583\pi$
$107$	1.00162			0.0968302			0.0484151	+	0.998827i	$0.484583\pi$
$108$		0			0
$109$	7.26618			0.695973			0.347987	−	0.937499i	$-0.386865\pi$
$109$	7.26618			0.695973			0.347987	+	0.937499i	$0.386865\pi$
$110$	0.0177462	+	0.00147754i	0.00169203	+	0.000140878i
$111$		0			0
$112$	−1.22312	+	1.50839i	−0.115574	+	0.142530i
$113$	9.30051	−	11.0839i	0.874918	−	1.04269i	−0.123812	−	0.992306i	$-0.539512\pi$
$113$	9.30051	−	11.0839i	0.874918	−	1.04269i	0.998730	−	0.0503815i	$-0.0160437\pi$
$114$		0			0
$115$	−0.679501	+	1.86691i	−0.0633638	+	0.174091i
$116$	14.0490	−	0.117967i	1.30441	−	0.0109529i
$117$		0			0
$118$	4.33485	−	4.37140i	0.399055	−	0.402420i
$119$	−0.920846	+	0.772682i	−0.0844138	+	0.0708316i
$120$		0			0
$121$	−1.90983	+	10.8312i	−0.173621	+	0.984653i
$122$	−4.46232	+	9.67531i	−0.403999	+	0.875962i
$123$		0			0
$124$	−1.30654	−	7.06249i	−0.117331	−	0.634230i
$125$	2.59533	+	1.49841i	0.232133	+	0.134022i
$126$		0			0
$127$	−7.70348	+	4.44760i	−0.683573	+	0.394661i	−0.801200	−	0.598397i	$-0.795805\pi$
$127$	−7.70348	+	4.44760i	−0.683573	+	0.394661i	0.117627	+	0.993058i	$0.462471\pi$
$128$	6.21415	−	9.45433i	0.549259	−	0.835652i
$129$		0			0
$130$	−1.50846	+	1.06570i	−0.132301	+	0.0934682i
$131$	18.2616	−	6.64668i	1.59552	−	0.580723i	0.617020	−	0.786948i	$-0.288340\pi$
$131$	18.2616	−	6.64668i	1.59552	−	0.580723i	0.978505	+	0.206224i	$0.0661176\pi$
$132$		0			0
$133$	0.637942	+	3.61795i	0.0553166	+	0.313716i
$134$	4.01312	−	15.2327i	0.346681	−	1.31590i
$135$		0			0
$136$	4.88922	−	5.01396i	0.419247	−	0.429943i
$137$	−15.1042	+	2.66328i	−1.29044	+	0.227540i	−0.776408	−	0.630231i	$-0.782960\pi$
$137$	−15.1042	+	2.66328i	−1.29044	+	0.227540i	−0.514033	+	0.857770i	$0.671849\pi$
$138$		0			0
$139$	3.05591	+	8.39605i	0.259199	+	0.712144i	0.999217	+	0.0395570i	$0.0125947\pi$
$139$	3.05591	+	8.39605i	0.259199	+	0.712144i	−0.740018	+	0.672587i	$0.765183\pi$
$140$	−0.102756	−	0.275111i	−0.00868450	−	0.0232511i
$141$		0			0
$142$	−3.92547	−	2.72415i	−0.329418	−	0.228606i
$143$	0.0898857	+	0.155687i	0.00751662	+	0.0130192i
$144$		0			0
$145$	−1.06231	+	1.83998i	−0.0882203	+	0.152802i
$146$	−0.807110	+	0.380495i	−0.0667969	+	0.0314900i
$147$		0			0
$148$	8.55268	−	10.3683i	0.703026	−	0.852266i
$149$	1.69578	+	0.299012i	0.138924	+	0.0244960i	0.242678	−	0.970107i	$-0.421974\pi$
$149$	1.69578	+	0.299012i	0.138924	+	0.0244960i	−0.103754	+	0.994603i	$0.533085\pi$
$150$		0			0
$151$	−0.387667	−	0.462003i	−0.0315479	−	0.0375973i	0.750040	−	0.661393i	$-0.230034\pi$
$151$	−0.387667	−	0.462003i	−0.0315479	−	0.0375973i	−0.781588	+	0.623795i	$0.785590\pi$
$152$	−5.79941	−	20.6022i	−0.470394	−	1.67106i
$153$		0			0
$154$	−0.0275795	+	0.00751415i	−0.00222242	+	0.000605507i
$155$	1.02064	+	0.371484i	0.0819800	+	0.0298383i
$156$		0			0
$157$	−7.94651	−	6.66791i	−0.634201	−	0.532157i	0.268031	−	0.963410i	$-0.413627\pi$
$157$	−7.94651	−	6.66791i	−0.634201	−	0.532157i	−0.902231	+	0.431253i	$0.858072\pi$
$158$	0.391069	+	4.26369i	0.0311118	+	0.339201i
$159$		0			0
$160$	0.755451	+	1.53509i	0.0597237	+	0.121360i
$161$		−	3.18911i		−	0.251337i
$162$		0			0
$163$			5.70430i			0.446795i	0.974727	+	0.223397i	$0.0717148\pi$
$163$			5.70430i			0.446795i	−0.974727	+	0.223397i	$0.928285\pi$
$164$	−11.9222	−	4.22629i	−0.930964	−	0.330017i
$165$		0			0
$166$	−8.10877	+	0.743742i	−0.629363	+	0.0577256i
$167$	4.02217	+	3.37500i	0.311245	+	0.261165i	0.785006	−	0.619488i	$-0.212660\pi$
$167$	4.02217	+	3.37500i	0.311245	+	0.261165i	−0.473761	+	0.880653i	$0.657104\pi$
$168$		0			0
$169$	−5.30479	−	1.93079i	−0.408061	−	0.148522i
$170$	0.278395	+	1.02181i	0.0213519	+	0.0783689i
$171$		0			0
$172$	−2.45384	−	4.16894i	−0.187104	−	0.317879i
$173$	−0.891706	−	1.06269i	−0.0677952	−	0.0807951i	0.731081	−	0.682291i	$-0.239016\pi$
$173$	−0.891706	−	1.06269i	−0.0677952	−	0.0807951i	−0.798876	+	0.601496i	$0.794572\pi$
$174$		0			0
$175$	−2.34686	−	0.413814i	−0.177406	−	0.0312814i
$176$	0.155510	−	0.0595769i	0.0117220	−	0.00449078i
$177$		0			0
$178$	−6.27069	−	13.3015i	−0.470008	−	0.996986i
$179$	5.77179	−	9.99703i	0.431403	−	0.747213i	−0.565591	−	0.824686i	$-0.691352\pi$
$179$	5.77179	−	9.99703i	0.431403	−	0.747213i	0.996994	+	0.0774732i	$0.0246852\pi$
$180$		0			0
$181$	8.57298	+	14.8488i	0.637225	+	1.10371i	0.986039	+	0.166514i	$0.0532510\pi$
$181$	8.57298	+	14.8488i	0.637225	+	1.10371i	−0.348814	+	0.937192i	$0.613416\pi$
$182$	1.69028	−	2.43567i	0.125292	−	0.180544i
$183$		0			0
$184$	1.85228	+	18.4868i	0.136552	+	1.36286i
$185$	0.695173	+	1.90997i	0.0511101	+	0.140424i
$186$		0			0
$187$	0.101517	−	0.0179001i	0.00742363	−	0.00130899i
$188$	12.5186	+	7.08814i	0.913014	+	0.516956i
$189$		0			0
$190$	3.12985	+	0.824572i	0.227063	+	0.0598208i
$191$	2.87475	+	16.3035i	0.208010	+	1.17968i	0.892633	+	0.450785i	$0.148856\pi$
$191$	2.87475	+	16.3035i	0.208010	+	1.17968i	−0.684623	+	0.728898i	$0.740033\pi$
$192$		0			0
$193$	8.27219	−	3.01083i	0.595445	−	0.216724i	−0.0266776	−	0.999644i	$-0.508493\pi$
$193$	8.27219	−	3.01083i	0.595445	−	0.216724i	0.622123	+	0.782920i	$0.286271\pi$
$194$	−2.71832	−	3.84769i	−0.195164	−	0.276248i
$195$		0			0
$196$	−8.78272	−	10.2901i	−0.627337	−	0.735009i
$197$	10.8232	−	6.24879i	0.771122	−	0.445208i	−0.0621526	−	0.998067i	$-0.519797\pi$
$197$	10.8232	−	6.24879i	0.771122	−	0.445208i	0.833275	+	0.552859i	$0.186463\pi$
$198$		0			0
$199$	−3.88531	−	2.24318i	−0.275422	−	0.159015i	0.355927	−	0.934514i	$-0.384165\pi$
$199$	−3.88531	−	2.24318i	−0.275422	−	0.159015i	−0.631349	+	0.775499i	$0.717499\pi$
$200$	13.8447	+	1.03573i	0.978969	+	0.0732373i
$201$		0			0
$202$	21.4459	+	9.89100i	1.50893	+	0.695928i
$203$	0.592221	−	3.35865i	0.0415658	−	0.235731i
$204$		0			0
$205$	1.46533	−	1.22956i	0.102343	−	0.0858761i
$206$	15.9592	+	15.8258i	1.11193	+	1.10264i
$207$		0			0
$208$	−8.38363	+	15.1009i	−0.581300	+	1.04706i
$209$	0.107749	−	0.296039i	0.00745319	−	0.0204775i
$210$		0			0
$211$	14.4269	−	17.1933i	0.993188	−	1.18363i	0.0102029	−	0.999948i	$-0.496752\pi$
$211$	14.4269	−	17.1933i	0.993188	−	1.18363i	0.982985	−	0.183687i	$-0.0588033\pi$
$212$	3.27703	−	19.5431i	0.225067	−	1.34223i
$213$		0			0
$214$	−0.117531	+	1.41162i	−0.00803426	+	0.0964963i
$215$	0.731549			0.0498912
$216$		0			0
$217$	−1.74349			−0.118356
$218$	−0.852621	+	10.2405i	−0.0577468	+	0.693574i
$219$		0			0
$220$	−0.00416470	+	0.0248369i	−0.000280784	+	0.00167451i
$221$	−6.87228	+	8.19006i	−0.462279	+	0.550923i
$222$		0			0
$223$	6.26467	−	17.2121i	0.419514	−	1.15260i	−0.532468	−	0.846450i	$-0.678735\pi$
$223$	6.26467	−	17.2121i	0.419514	−	1.15260i	0.951982	−	0.306154i	$-0.0990423\pi$
$224$	−1.98231	−	1.90079i	−0.132449	−	0.127002i
$225$		0			0
$226$	14.5296	+	14.4082i	0.966498	+	0.958416i
$227$	15.0169	−	12.6007i	0.996709	−	0.836338i	0.0101841	−	0.999948i	$-0.496758\pi$
$227$	15.0169	−	12.6007i	0.996709	−	0.836338i	0.986525	+	0.163610i	$0.0523138\pi$
$228$		0			0
$229$	0.984254	−	5.58198i	0.0650413	−	0.368868i	−0.934863	−	0.355010i	$-0.884478\pi$
$229$	0.984254	−	5.58198i	0.0650413	−	0.368868i	0.999904	−	0.0138580i	$-0.00441128\pi$
$230$	−2.55138	−	1.17671i	−0.168233	−	0.0775901i
$231$		0			0
$232$	−1.48227	+	19.8136i	−0.0973155	+	1.30083i
$233$	−6.50499	−	3.75566i	−0.426156	−	0.246041i	0.271552	−	0.962424i	$-0.412463\pi$
$233$	−6.50499	−	3.75566i	−0.426156	−	0.246041i	−0.697708	+	0.716383i	$0.745797\pi$
$234$		0			0
$235$	−1.88406	+	1.08776i	−0.122902	+	0.0709577i
$236$	5.65212	+	6.62220i	0.367922	+	0.431069i
$237$		0			0
$238$	−0.980916	−	1.38845i	−0.0635833	−	0.0899999i
$239$	−6.08140	+	2.21345i	−0.393373	+	0.143176i	−0.531131	−	0.847290i	$-0.678233\pi$
$239$	−6.08140	+	2.21345i	−0.393373	+	0.143176i	0.137758	+	0.990466i	$0.456010\pi$
$240$		0			0
$241$	−0.120498	−	0.683378i	−0.00776195	−	0.0440202i	0.980681	−	0.195615i	$-0.0626703\pi$
$241$	−0.120498	−	0.683378i	−0.00776195	−	0.0440202i	−0.988443	+	0.151595i	$0.951559\pi$
$242$	−15.0407	−	3.96253i	−0.966852	−	0.254721i
$243$		0			0
$244$	−13.1122	−	7.42422i	−0.839420	−	0.475287i
$245$	2.01478	−	0.355259i	0.128719	−	0.0226967i
$246$		0			0
$247$	11.1754	+	30.7041i	0.711073	+	1.95366i
$248$	10.1067	−	1.01264i	0.641779	−	0.0643028i
$249$		0			0
$250$	−2.41631	+	3.48187i	−0.152821	+	0.220213i
$251$	−1.09113	−	1.88989i	−0.0688715	−	0.119289i	0.829533	−	0.558457i	$-0.188607\pi$
$251$	−1.09113	−	1.88989i	−0.0688715	−	0.119289i	−0.898405	+	0.439168i	$0.855273\pi$
$252$		0			0
$253$	−0.136739	+	0.236839i	−0.00859670	+	0.0148899i
$254$	−5.36424	−	11.3787i	−0.336582	−	0.713962i
$255$		0			0
$256$	12.5952	+	9.86722i	0.787197	+	0.616701i
$257$	−14.1712	−	2.49877i	−0.883977	−	0.155869i	−0.286812	−	0.957987i	$-0.592595\pi$
$257$	−14.1712	−	2.49877i	−0.883977	−	0.155869i	−0.597166	+	0.802118i	$0.703706\pi$
$258$		0			0
$259$	−2.09720	−	2.49934i	−0.130314	−	0.155302i
$260$	−1.32493	−	2.25098i	−0.0821686	−	0.139600i
$261$		0			0
$262$	7.22458	+	26.5167i	0.446336	+	1.63821i
$263$	9.62617	+	3.50364i	0.593575	+	0.216044i	0.621301	−	0.783572i	$-0.286604\pi$
$263$	9.62617	+	3.50364i	0.593575	+	0.216044i	−0.0277260	+	0.999616i	$0.508827\pi$
$264$		0			0
$265$	2.29558	+	1.92622i	0.141016	+	0.118327i
$266$	−5.17377	+	0.474541i	−0.317224	+	0.0290960i
$267$		0			0
$268$	20.9971	+	7.44326i	1.28260	+	0.454669i
$269$		−	3.15222i		−	0.192194i	−0.995372	−	0.0960971i	$-0.969364\pi$
$269$		−	3.15222i		−	0.192194i	0.995372	−	0.0960971i	$-0.0306359\pi$
$270$		0			0
$271$			3.33151i			0.202375i	0.994867	+	0.101188i	$0.0322642\pi$
$271$			3.33151i			0.202375i	−0.994867	+	0.101188i	$0.967736\pi$
$272$	6.49265	+	7.47891i	0.393675	+	0.453475i
$273$		0			0
$274$	−1.98112	−	21.5995i	−0.119684	−	1.30487i
$275$	0.156546	+	0.131358i	0.00944007	+	0.00792116i
$276$		0			0
$277$	−3.92367	−	1.42810i	−0.235750	−	0.0858061i	0.221443	−	0.975173i	$-0.428923\pi$
$277$	−3.92367	−	1.42810i	−0.235750	−	0.0858061i	−0.457194	+	0.889367i	$0.651145\pi$
$278$	−12.1915	+	3.32161i	−0.731195	+	0.199217i
$279$		0			0
$280$	0.399782	−	0.112537i	0.0238915	−	0.00672534i
$281$	12.6165	+	15.0357i	0.752635	+	0.896955i	0.997358	−	0.0726377i	$-0.0231417\pi$
$281$	12.6165	+	15.0357i	0.752635	+	0.896955i	−0.244724	+	0.969593i	$0.578697\pi$
$282$		0			0
$283$	−15.1640	−	2.67383i	−0.901407	−	0.158942i	−0.296308	−	0.955092i	$-0.595755\pi$
$283$	−15.1640	−	2.67383i	−0.901407	−	0.158942i	−0.605099	+	0.796150i	$0.706867\pi$
$284$	4.29987	−	5.21265i	0.255150	−	0.309314i
$285$		0			0
$286$	−0.229962	+	0.108411i	−0.0135979	+	0.00641046i
$287$	−1.53526	+	2.65916i	−0.0906238	+	0.156965i
$288$		0			0
$289$	−5.43473	−	9.41323i	−0.319690	−	0.553720i
$290$	−2.46850	−	1.71306i	−0.144955	−	0.100595i
$291$		0			0
$292$	−0.441539	−	1.18214i	−0.0258391	−	0.0691794i
$293$	−6.36906	−	17.4989i	−0.372085	−	1.02229i	−0.974554	−	0.224152i	$-0.928039\pi$
$293$	−6.36906	−	17.4989i	−0.372085	−	1.02229i	0.602469	−	0.798142i	$-0.294184\pi$
$294$		0			0
$295$	−1.29661	+	0.228627i	−0.0754915	+	0.0133112i
$296$	13.6088	+	13.2702i	0.790995	+	0.771317i
$297$		0			0
$298$	−0.620393	+	2.35484i	−0.0359384	+	0.136412i
$299$	−4.92538	−	27.9332i	−0.284842	−	1.61542i
$300$		0			0
$301$	−1.10347	+	0.401630i	−0.0636030	+	0.0231496i
$302$	0.696608	−	0.492141i	0.0400853	−	0.0283196i
$303$		0			0
$304$	29.7159	−	5.75584i	1.70432	−	0.330120i
$305$	1.97339	−	1.13934i	0.112996	−	0.0652382i
$306$		0			0
$307$	17.7533	+	10.2499i	1.01323	+	0.584990i	0.912136	−	0.409887i	$-0.134432\pi$
$307$	17.7533	+	10.2499i	1.01323	+	0.584990i	0.101096	+	0.994877i	$0.467765\pi$
$308$	−0.00735376	−	0.0397506i	−0.000419019	−	0.00226500i
$309$		0			0
$310$	−0.643309	+	1.39484i	−0.0365375	+	0.0792216i
$311$	−3.47790	+	19.7241i	−0.197213	+	1.11845i	0.712018	+	0.702161i	$0.247782\pi$
$311$	−3.47790	+	19.7241i	−0.197213	+	1.11845i	−0.909231	+	0.416292i	$0.863330\pi$
$312$		0			0
$313$	−13.5141	+	11.3397i	−0.763863	+	0.640957i	−0.939129	−	0.343564i	$-0.888366\pi$
$313$	−13.5141	+	11.3397i	−0.763863	+	0.640957i	0.175266	+	0.984521i	$0.443921\pi$
$314$	10.3298	−	10.4169i	0.582944	−	0.587859i
$315$		0			0
$316$	−6.05487	+	0.0508417i	−0.340613	+	0.00286007i
$317$	−1.46957	+	4.03761i	−0.0825392	+	0.226775i	−0.974096	−	0.226134i	$-0.927391\pi$
$317$	−1.46957	+	4.03761i	−0.0825392	+	0.226775i	0.891557	+	0.452908i	$0.149614\pi$
$318$		0			0
$319$	−0.187990	+	0.224037i	−0.0105254	+	0.0125437i
$320$	−2.25211	+	0.884556i	−0.125897	+	0.0494482i
$321$		0			0
$322$	4.49453	+	0.374214i	0.250470	+	0.0208541i
$323$	18.7360			1.04250
$324$		0			0
$325$	−21.1951			−1.17569
$326$	−8.03928	−	0.669348i	−0.445254	−	0.0370718i
$327$		0			0
$328$	7.35522	−	16.3064i	0.406124	−	0.900371i
$329$	2.24472	−	2.67515i	0.123755	−	0.147486i
$330$		0			0
$331$	−6.88468	+	18.9155i	−0.378416	+	1.03969i	0.593597	+	0.804763i	$0.297707\pi$
$331$	−6.88468	+	18.9155i	−0.378416	+	1.03969i	−0.972013	+	0.234927i	$0.924515\pi$
$332$	−0.0966917	−	11.5153i	−0.00530664	−	0.631982i
$333$		0			0
$334$	−5.22848	+	5.27257i	−0.286090	+	0.288502i
$335$	−2.58072	+	2.16548i	−0.141000	+	0.118313i
$336$		0			0
$337$	2.29367	−	13.0081i	0.124944	−	0.708595i	−0.856397	−	0.516319i	$-0.827302\pi$
$337$	2.29367	−	13.0081i	0.124944	−	0.708595i	0.981341	−	0.192276i	$-0.0615869\pi$
$338$	3.34360	−	7.24968i	0.181868	−	0.394330i
$339$		0			0
$340$	−1.47274	+	0.272453i	−0.0798703	+	0.0147758i
$341$	0.129480	+	0.0747552i	0.00701173	+	0.00404822i
$342$		0			0
$343$	−5.78720	+	3.34124i	−0.312480	+	0.180410i
$344$	6.16338	−	2.96910i	0.332307	−	0.160083i
$345$		0			0
$346$	1.60233	−	1.13202i	0.0861417	−	0.0608576i
$347$	−16.7772	+	6.10639i	−0.900645	+	0.327808i	−0.750511	−	0.660858i	$-0.770193\pi$
$347$	−16.7772	+	6.10639i	−0.900645	+	0.327808i	−0.150134	+	0.988666i	$0.547971\pi$
$348$		0			0
$349$	−2.27001	−	12.8739i	−0.121511	−	0.689123i	−0.983319	−	0.181889i	$-0.941779\pi$
$349$	−2.27001	−	12.8739i	−0.121511	−	0.689123i	0.861808	−	0.507234i	$-0.169332\pi$
$350$	0.858586	−	3.25895i	0.0458933	−	0.174198i
$351$		0			0
$352$	0.0657163	+	0.226157i	0.00350269	+	0.0120542i
$353$	21.1607	−	3.73120i	1.12627	−	0.198592i	0.420678	−	0.907210i	$-0.361792\pi$
$353$	21.1607	−	3.73120i	1.12627	−	0.198592i	0.705592	+	0.708618i	$0.250681\pi$
$354$		0			0
$355$	0.349499	+	0.960240i	0.0185495	+	0.0509642i
$356$	19.4820	−	7.27671i	1.03255	−	0.385665i
$357$		0			0
$358$	13.4119	+	9.30745i	0.708842	+	0.491914i
$359$	9.46695	+	16.3972i	0.499647	+	0.865413i	1.00000		0.000407927i	$-0.000129847\pi$
$359$	9.46695	+	16.3972i	0.499647	+	0.865413i	−0.500353	+	0.865821i	$0.666797\pi$
$360$		0			0
$361$	19.1302	−	33.1344i	1.00685	−	1.74392i
$362$	−21.9330	+	10.3398i	−1.15277	+	0.543450i
$363$		0			0
$364$	3.23434	+	2.66798i	0.169526	+	0.139840i
$365$	0.187932	+	0.0331375i	0.00983682	+	0.00173450i
$366$		0			0
$367$	−15.3111	−	18.2471i	−0.799233	−	0.952489i	0.200396	−	0.979715i	$-0.435777\pi$
$367$	−15.3111	−	18.2471i	−0.799233	−	0.952489i	−0.999629	+	0.0272258i	$0.991333\pi$
$368$	−26.2715	+	0.441225i	−1.36949	+	0.0230004i
$369$		0			0
$370$	−2.77337	+	0.755615i	−0.144180	+	0.0392825i
$371$	−4.52018	−	1.64521i	−0.234676	−	0.0854151i
$372$		0			0
$373$	−16.6039	−	13.9323i	−0.859717	−	0.721388i	0.102190	−	0.994765i	$-0.467415\pi$
$373$	−16.6039	−	13.9323i	−0.859717	−	0.721388i	−0.961907	+	0.273377i	$0.911859\pi$
$374$	0.0133152	+	0.145172i	0.000688514	+	0.00750664i
$375$		0			0
$376$	−11.4585	+	16.8112i	−0.590929	+	0.866972i
$377$		−	30.3329i		−	1.56222i
$378$		0			0
$379$		−	33.6783i		−	1.72994i	−0.501825	−	0.864969i	$-0.667338\pi$
$379$		−	33.6783i		−	1.72994i	0.501825	−	0.864969i	$-0.332662\pi$
$380$	−1.52936	+	4.31425i	−0.0784545	+	0.221317i
$381$		0			0
$382$	−23.3145	+	2.13842i	−1.19287	+	0.109411i
$383$	1.15170	+	0.966388i	0.0588490	+	0.0493801i	0.671738	−	0.740789i	$-0.265548\pi$
$383$	1.15170	+	0.966388i	0.0588490	+	0.0493801i	−0.612889	+	0.790169i	$0.709993\pi$
$384$		0			0
$385$	0.00574459	+	0.00209086i	0.000292772	+	0.000106560i
$386$	3.27261	+	12.0116i	0.166571	+	0.611374i
$387$		0			0
$388$	5.74166	−	3.37954i	0.291489	−	0.171570i
$389$	−2.48223	−	2.95820i	−0.125854	−	0.149987i	0.699438	−	0.714693i	$-0.253434\pi$
$389$	−2.48223	−	2.95820i	−0.125854	−	0.149987i	−0.825292	+	0.564707i	$0.808989\pi$
$390$		0			0
$391$	−16.0172	−	2.82426i	−0.810024	−	0.142829i
$392$	15.5328	−	11.1704i	0.784526	−	0.564188i
$393$		0			0
$394$	7.53664	+	15.9868i	0.379690	+	0.805403i
$395$	0.457839	−	0.793000i	0.0230364	−	0.0399002i
$396$		0			0
$397$	−9.80431	−	16.9816i	−0.492064	−	0.852280i	0.507894	−	0.861419i	$-0.330424\pi$
$397$	−9.80431	−	16.9816i	−0.492064	−	0.852280i	−0.999958	+	0.00913954i	$0.997091\pi$
$398$	3.61731	−	5.21249i	0.181319	−	0.261279i
$399$		0			0
$400$	−3.08425	+	19.3903i	−0.154212	+	0.969517i
$401$	7.41930	+	20.3844i	0.370502	+	1.01795i	0.975168	+	0.221467i	$0.0710845\pi$
$401$	7.41930	+	20.3844i	0.370502	+	1.01795i	−0.604666	+	0.796479i	$0.706693\pi$
$402$		0			0
$403$	−15.2711	+	2.69271i	−0.760708	+	0.134133i
$404$	−16.4562	+	29.0639i	−0.818728	+	1.44598i
$405$		0			0
$406$	4.66398	+	1.22875i	0.231470	+	0.0609817i
$407$	0.0485842	+	0.275535i	0.00240823	+	0.0136577i
$408$		0			0
$409$	10.3343	−	3.76139i	0.510999	−	0.185989i	−0.0736354	−	0.997285i	$-0.523460\pi$
$409$	10.3343	−	3.76139i	0.510999	−	0.185989i	0.584635	+	0.811297i	$0.301238\pi$
$410$	1.56092	+	2.20942i	0.0770883	+	0.109116i
$411$		0			0
$412$	−24.1766	+	20.6349i	−1.19109	+	1.01661i
$413$	1.83029	−	1.05672i	0.0900626	−	0.0519976i
$414$		0			0
$415$	1.50814	+	0.870727i	0.0740319	+	0.0427423i
$416$	−20.2986	−	13.5873i	−0.995220	−	0.666173i
$417$		0			0
$418$	0.404576	+	0.186593i	0.0197884	+	0.00912656i
$419$	4.20531	−	23.8495i	0.205443	−	1.16512i	−0.691298	−	0.722569i	$-0.742961\pi$
$419$	4.20531	−	23.8495i	0.205443	−	1.16512i	0.896741	−	0.442555i	$-0.145928\pi$
$420$		0			0
$421$	28.0468	−	23.5341i	1.36692	−	1.14698i	0.393141	−	0.919478i	$-0.371388\pi$
$421$	28.0468	−	23.5341i	1.36692	−	1.14698i	0.973777	−	0.227503i	$-0.0730561\pi$
$422$	22.5383	+	22.3498i	1.09715	+	1.08797i
$423$		0			0
$424$	27.1583	+	6.91165i	1.31893	+	0.335660i
$425$	−4.15673	+	11.4205i	−0.201631	+	0.553977i
$426$		0			0
$427$	−2.35115	+	2.80199i	−0.113780	+	0.135598i
$428$	−1.97566	−	0.331282i	−0.0954969	−	0.0160131i
$429$		0			0
$430$	−0.0858408	+	1.03100i	−0.00413961	+	0.0497192i
$431$	−38.5608			−1.85741			−0.928705	−	0.370820i	$-0.879077\pi$
$431$	−38.5608			−1.85741			−0.928705	+	0.370820i	$0.879077\pi$
$432$		0			0
$433$	−6.56251			−0.315374			−0.157687	−	0.987489i	$-0.550404\pi$
$433$	−6.56251			−0.315374			−0.157687	+	0.987489i	$0.550404\pi$
$434$	0.204583	−	2.45716i	0.00982029	−	0.117948i
$435$		0			0
$436$	−14.3323	−	2.40326i	−0.686391	−	0.115095i
$437$	−31.9507	+	38.0773i	−1.52841	+	1.82149i
$438$		0			0
$439$	0.624030	−	1.71451i	0.0297833	−	0.0818291i	−0.923910	−	0.382610i	$-0.875025\pi$
$439$	0.624030	−	1.71451i	0.0297833	−	0.0818291i	0.953693	+	0.300781i	$0.0972474\pi$
$440$	−0.0345149	−	0.00878386i	−0.00164543	−	0.000418754i
$441$		0			0
$442$	−10.7362	−	10.6464i	−0.510667	−	0.506397i
$443$	−1.33656	+	1.12150i	−0.0635017	+	0.0532843i	−0.673986	−	0.738744i	$-0.735419\pi$
$443$	−1.33656	+	1.12150i	−0.0635017	+	0.0532843i	0.610484	+	0.792028i	$0.290975\pi$
$444$		0			0
$445$	−0.546118	+	3.09719i	−0.0258885	+	0.146821i
$446$	23.5225	+	10.8487i	1.11382	+	0.513702i
$447$		0			0
$448$	2.91146	−	2.57070i	0.137553	−	0.121454i
$449$	−8.00158	−	4.61971i	−0.377618	−	0.218018i	0.299164	−	0.954202i	$-0.403292\pi$
$449$	−8.00158	−	4.61971i	−0.377618	−	0.218018i	−0.676781	+	0.736184i	$0.736626\pi$
$450$		0			0
$451$	0.228032	−	0.131654i	0.0107376	−	0.00619937i
$452$	−22.0109	+	18.7865i	−1.03530	+	0.883643i
$453$		0			0
$454$	15.9965	+	22.6425i	0.750755	+	1.06267i
$455$	−0.595808	+	0.216857i	−0.0279319	+	0.0101664i
$456$		0			0
$457$	−4.78964	−	27.1634i	−0.224050	−	1.27065i	−0.864493	−	0.502645i	$-0.832360\pi$
$457$	−4.78964	−	27.1634i	−0.224050	−	1.27065i	0.640443	−	0.768006i	$-0.278751\pi$
$458$	7.75140	+	2.04214i	0.362199	+	0.0954229i
$459$		0			0
$460$	1.95776	−	3.45767i	0.0912812	−	0.161215i
$461$	20.4199	−	3.60059i	0.951052	−	0.167696i	0.323463	−	0.946241i	$-0.395153\pi$
$461$	20.4199	−	3.60059i	0.951052	−	0.167696i	0.627589	+	0.778545i	$0.284042\pi$
$462$		0			0
$463$	3.27860	+	9.00787i	0.152369	+	0.418631i	0.992268	−	0.124112i	$-0.0396081\pi$
$463$	3.27860	+	9.00787i	0.152369	+	0.418631i	−0.839899	+	0.542743i	$0.817386\pi$
$464$	−27.7501	−	4.41396i	−1.28827	−	0.204913i
$465$		0			0
$466$	6.05629	−	8.72703i	0.280552	−	0.404272i
$467$	−8.74737	−	15.1509i	−0.404780	−	0.701099i	0.589516	−	0.807757i	$-0.299319\pi$
$467$	−8.74737	−	15.1509i	−0.404780	−	0.701099i	−0.994296	+	0.106657i	$0.965985\pi$
$468$		0			0
$469$	2.70388	−	4.68326i	0.124854	−	0.216253i
$470$	−1.31194	−	2.78291i	−0.0605155	−	0.128366i
$471$		0			0
$472$	−9.99614	+	7.18868i	−0.460110	+	0.330886i
$473$	0.0991696	+	0.0174863i	0.00455982	+	0.000804020i
$474$		0			0
$475$	23.8751	+	28.4533i	1.09547	+	1.30552i
$476$	2.07190	−	1.21952i	0.0949652	−	0.0558966i
$477$		0			0
$478$	−2.40590	−	8.83047i	−0.110043	−	0.403896i
$479$	−24.6167	−	8.95976i	−1.12477	−	0.409382i	−0.288378	−	0.957517i	$-0.593116\pi$
$479$	−24.6167	−	8.95976i	−1.12477	−	0.409382i	−0.836390	+	0.548135i	$0.815338\pi$
$480$		0			0
$481$	−22.2293	−	18.6526i	−1.01357	−	0.850486i
$482$	0.977249	−	0.0896339i	0.0445125	−	0.00408271i
$483$		0			0
$484$	7.34944	−	20.7324i	0.334065	−	0.942383i
$485$			1.00752i			0.0457493i
$486$		0			0
$487$			7.10957i			0.322166i	0.986941	+	0.161083i	$0.0514986\pi$
$487$			7.10957i			0.322166i	−0.986941	+	0.161083i	$0.948501\pi$
$488$	12.0018	−	17.6083i	0.543297	−	0.797090i
$489$		0			0
$490$	0.264264	+	2.88119i	0.0119382	+	0.130159i
$491$	15.1317	+	12.6970i	0.682883	+	0.573006i	0.916847	−	0.399239i	$-0.130726\pi$
$491$	15.1317	+	12.6970i	0.682883	+	0.573006i	−0.233965	+	0.972245i	$0.575170\pi$
$492$		0			0
$493$	−16.3442	−	5.94882i	−0.736108	−	0.267921i
$494$	−44.5838	+	12.1470i	−2.00592	+	0.546521i
$495$		0			0
$496$	0.241218	+	14.3626i	0.0108310	+	0.644901i
$497$	−1.05437	−	1.25655i	−0.0472949	−	0.0563639i
$498$		0			0
$499$	−38.9262	−	6.86374i	−1.74258	−	0.307263i	−0.790350	−	0.612655i	$-0.790101\pi$
$499$	−38.9262	−	6.86374i	−1.74258	−	0.307263i	−0.952227	+	0.305392i	$0.901212\pi$
$500$	−4.62359	−	3.81396i	−0.206773	−	0.170565i
$501$		0			0
$502$	2.79153	−	1.31601i	0.124592	−	0.0587363i
$503$	−19.5426	+	33.8489i	−0.871364	+	1.50925i	−0.0107769	+	0.999942i	$0.503430\pi$
$503$	−19.5426	+	33.8489i	−0.871364	+	1.50925i	−0.860587	+	0.509304i	$0.829903\pi$
$504$		0			0
$505$	−2.52541	−	4.37413i	−0.112379	−	0.194646i
$506$	−0.317740	−	0.220502i	−0.0141253	−	0.00980251i
$507$		0			0
$508$	16.6658	−	6.22483i	0.739427	−	0.276182i
$509$	5.04413	+	13.8586i	0.223577	+	0.614273i	0.999870	−	0.0160989i	$-0.00512466\pi$
$509$	5.04413	+	13.8586i	0.223577	+	0.614273i	−0.776293	+	0.630372i	$0.782902\pi$
$510$		0			0
$511$	−0.301670	+	0.0531926i	−0.0133451	+	0.00235310i
$512$	−15.3842	+	16.5930i	−0.679891	+	0.733314i
$513$		0			0
$514$	5.18448	−	19.6788i	0.228677	−	0.867996i
$515$	−0.834679	−	4.73370i	−0.0367804	−	0.208592i
$516$		0			0
$517$	−0.281406	+	0.102423i	−0.0123762	+	0.00450457i
$518$	3.76851	−	2.66238i	0.165579	−	0.116978i
$519$		0			0
$520$	3.32786	−	1.60314i	0.145936	−	0.0703023i
$521$	10.1293	−	5.84816i	0.443773	−	0.256213i	−0.261424	−	0.965224i	$-0.584192\pi$
$521$	10.1293	−	5.84816i	0.443773	−	0.256213i	0.705197	+	0.709012i	$0.250859\pi$
$522$		0			0
$523$	−6.89969	−	3.98354i	−0.301702	−	0.174188i	0.341505	−	0.939880i	$-0.389063\pi$
$523$	−6.89969	−	3.98354i	−0.301702	−	0.174188i	−0.643207	+	0.765692i	$0.722397\pi$
$524$	−38.2187	+	7.07037i	−1.66959	+	0.308871i
$525$		0			0
$526$	−6.06736	+	13.1554i	−0.264549	+	0.573603i
$527$	−1.54403	+	8.75661i	−0.0672588	+	0.381444i
$528$		0			0
$529$	15.4351	−	12.9515i	0.671089	−	0.563111i
$530$	−2.98406	+	3.00922i	−0.129619	+	0.130712i
$531$		0			0
$532$	−0.0616937	−	7.34727i	−0.00267476	−	0.318544i
$533$	−9.34038	+	25.6625i	−0.404577	+	1.11157i
$534$		0			0
$535$	0.194726	−	0.232065i	0.00841872	−	0.0100330i
$536$	−12.9539	+	28.7186i	−0.559522	+	1.24045i
$537$		0			0
$538$	4.44254	+	0.369885i	0.191531	+	0.0159469i
$539$	0.281617			0.0121301
$540$		0			0
$541$	8.41220			0.361669			0.180834	−	0.983514i	$-0.442120\pi$
$541$	8.41220			0.361669			0.180834	+	0.983514i	$0.442120\pi$
$542$	−4.69523	−	0.390923i	−0.201677	−	0.0167916i
$543$		0			0
$544$	−11.3022	+	8.27275i	−0.484576	+	0.354691i
$545$	1.41262	−	1.68350i	0.0605101	−	0.0721132i
$546$		0			0
$547$	−5.97901	+	16.4272i	−0.255644	+	0.702376i	0.743780	+	0.668425i	$0.233031\pi$
$547$	−5.97901	+	16.4272i	−0.255644	+	0.702376i	−0.999424	+	0.0339508i	$0.989191\pi$
$548$	30.6734	−	0.257559i	1.31030	−	0.0110024i
$549$		0			0
$550$	−0.203496	+	0.205212i	−0.00867711	+	0.00875028i
$551$	−40.7203	+	34.1684i	−1.73474	+	1.45562i
$552$		0			0
$553$	−0.255237	+	1.44752i	−0.0108538	+	0.0615549i
$554$	2.47308	−	5.36220i	0.105071	−	0.227818i
$555$		0			0
$556$	−3.25071	−	17.5716i	−0.137861	−	0.745203i
$557$	−0.688812	−	0.397686i	−0.0291859	−	0.0168505i	0.485336	−	0.874328i	$-0.338697\pi$
$557$	−0.688812	−	0.397686i	−0.0291859	−	0.0168505i	−0.514522	+	0.857477i	$0.672031\pi$
$558$		0			0
$559$	−9.04493	+	5.22209i	−0.382560	+	0.220871i
$560$	0.111691	+	0.576632i	0.00471981	+	0.0243672i
$561$		0			0
$562$	−22.6708	+	16.0165i	−0.956310	+	0.675617i
$563$	5.88781	−	2.14299i	0.248142	−	0.0903162i	−0.214955	−	0.976624i	$-0.568960\pi$
$563$	5.88781	−	2.14299i	0.248142	−	0.0903162i	0.463097	+	0.886308i	$0.346738\pi$
$564$		0			0
$565$	−0.759910	−	4.30967i	−0.0319697	−	0.181309i
$566$	5.54768	−	21.0575i	0.233187	−	0.885111i
$567$		0			0
$568$	6.84184	+	6.67163i	0.287077	+	0.279935i
$569$	5.33693	−	0.941045i	0.223736	−	0.0394507i	−0.0606563	−	0.998159i	$-0.519319\pi$
$569$	5.33693	−	0.941045i	0.223736	−	0.0394507i	0.284392	+	0.958708i	$0.408208\pi$
$570$		0			0
$571$	−10.4263	−	28.6461i	−0.436328	−	1.19880i	−0.941863	−	0.335996i	$-0.890927\pi$
$571$	−10.4263	−	28.6461i	−0.436328	−	1.19880i	0.505535	−	0.862806i	$-0.331295\pi$
$572$	−0.125803	−	0.336815i	−0.00526010	−	0.0140830i
$573$		0			0
$574$	−3.56750	−	2.47573i	−0.148904	−	0.103335i
$575$	−16.1215	−	27.9233i	−0.672315	−	1.16448i
$576$		0			0
$577$	−9.67484	+	16.7573i	−0.402769	+	0.697616i	−0.994059	−	0.108843i	$-0.965286\pi$
$577$	−9.67484	+	16.7573i	−0.402769	+	0.697616i	0.591290	+	0.806459i	$0.298619\pi$
$578$	13.9041	−	6.55481i	0.578336	−	0.272644i
$579$		0			0
$580$	2.70394	−	3.27794i	0.112275	−	0.136109i
$581$	−2.75293	−	0.485415i	−0.114211	−	0.0201384i
$582$		0			0
$583$	0.265149	+	0.315992i	0.0109813	+	0.0130871i
$584$	1.71784	−	0.483564i	0.0710848	−	0.0200100i
$585$		0			0
$586$	25.4091	−	6.92282i	1.04964	−	0.285979i
$587$	40.6493	+	14.7951i	1.67778	+	0.610660i	0.993002	−	0.118096i	$-0.0376791\pi$
$587$	40.6493	+	14.7951i	1.67778	+	0.610660i	0.684773	+	0.728756i	$0.259901\pi$
$588$		0			0
$589$	20.8169	+	17.4675i	0.857746	+	0.719734i
$590$	−0.170067	−	1.85419i	−0.00700156	−	0.0763356i
$591$		0			0
$592$	−20.2991	+	17.6222i	−0.834288	+	0.724269i
$593$			32.7916i			1.34659i	0.739375	+	0.673294i	$0.235121\pi$
$593$			32.7916i			1.34659i	−0.739375	+	0.673294i	$0.764879\pi$
$594$		0			0
$595$			0.363568i			0.0149048i
$596$	−3.24596	−	1.15066i	−0.132960	−	0.0471329i
$597$		0			0
$598$	39.9453	−	3.66381i	1.63348	−	0.149824i
$599$	−28.7904	−	24.1580i	−1.17634	−	0.987070i	−0.999996	−	0.00274159i	$-0.999127\pi$
$599$	−28.7904	−	24.1580i	−1.17634	−	0.987070i	−0.176347	−	0.984328i	$-0.556428\pi$
$600$		0			0
$601$	−9.38452	−	3.41569i	−0.382802	−	0.139329i	0.143449	−	0.989658i	$-0.454181\pi$
$601$	−9.38452	−	3.41569i	−0.382802	−	0.139329i	−0.526251	+	0.850329i	$0.676403\pi$
$602$	−0.436550	−	1.60229i	−0.0177925	−	0.0653044i
$603$		0			0
$604$	0.611852	+	1.03950i	0.0248959	+	0.0422968i
$605$	2.13818	+	2.54819i	0.0869294	+	0.103598i
$606$		0			0
$607$	28.5897	+	5.04113i	1.16042	+	0.204613i	0.720520	−	0.693434i	$-0.243903\pi$
$607$	28.5897	+	5.04113i	1.16042	+	0.204613i	0.439899	+	0.898047i	$0.355014\pi$
$608$	4.62502	+	42.5551i	0.187569	+	1.72584i
$609$		0			0
$610$	1.37415	+	2.91486i	0.0556377	+	0.118019i
$611$	15.5298	−	26.8983i	0.628266	−	1.08819i
$612$		0			0
$613$	−10.6465	−	18.4402i	−0.430007	−	0.744794i	0.566866	−	0.823810i	$-0.308156\pi$
$613$	−10.6465	−	18.4402i	−0.430007	−	0.744794i	−0.996873	+	0.0790155i	$0.974822\pi$
$614$	−16.5287	+	23.8176i	−0.667043	+	0.961200i
$615$		0			0
$616$	0.0568848	−	0.00569956i	0.00229195	−	0.000229642i
$617$	−0.850396	−	2.33644i	−0.0342357	−	0.0940617i	0.921397	−	0.388622i	$-0.127049\pi$
$617$	−0.850396	−	2.33644i	−0.0342357	−	0.0940617i	−0.955633	+	0.294561i	$0.904827\pi$
$618$		0			0
$619$	13.1393	−	2.31682i	0.528114	−	0.0931207i	0.0967674	−	0.995307i	$-0.469150\pi$
$619$	13.1393	−	2.31682i	0.528114	−	0.0931207i	0.431347	+	0.902186i	$0.358039\pi$
$620$	−1.89031	−	1.07031i	−0.0759168	−	0.0429847i
$621$		0			0
$622$	−27.3899	−	7.21598i	−1.09823	−	0.289334i
$623$	−0.876632	−	4.97163i	−0.0351215	−	0.199184i
$624$		0			0
$625$	−22.2108	+	8.08407i	−0.888432	+	0.323363i
$626$	−14.3957	−	20.3766i	−0.575367	−	0.814411i
$627$		0			0
$628$	13.4688	+	15.7805i	0.537464	+	0.629710i
$629$	−14.4101	+	8.31969i	−0.574570	+	0.331728i
$630$		0			0
$631$	−33.1235	−	19.1238i	−1.31862	−	0.761308i	−0.335117	−	0.942176i	$-0.608776\pi$
$631$	−33.1235	−	19.1238i	−1.31862	−	0.761308i	−0.983507	+	0.180868i	$0.942109\pi$
$632$	0.638831	−	8.53931i	0.0254113	−	0.339676i
$633$		0			0
$634$	−5.51791	−	2.54489i	−0.219144	−	0.101071i
$635$	−0.467175	+	2.64948i	−0.0185393	+	0.105141i
$636$		0			0
$637$	−22.3749	+	18.7747i	−0.886525	+	0.743882i
$638$	−0.293685	−	0.291229i	−0.0116271	−	0.0115299i
$639$		0			0
$640$	−0.982372	−	3.27778i	−0.0388317	−	0.129566i
$641$	−4.86140	+	13.3566i	−0.192014	+	0.527553i	−0.997918	−	0.0644923i	$-0.979457\pi$
$641$	−4.86140	+	13.3566i	−0.192014	+	0.527553i	0.805905	+	0.592046i	$0.201679\pi$
$642$		0			0
$643$	0.409458	−	0.487973i	0.0161474	−	0.0192438i	−0.757910	−	0.652359i	$-0.773780\pi$
$643$	0.409458	−	0.487973i	0.0161474	−	0.0192438i	0.774058	+	0.633115i	$0.218224\pi$
$644$	−1.05479	+	6.29040i	−0.0415644	+	0.247876i
$645$		0			0
$646$	−2.19850	+	26.4053i	−0.0864988	+	1.03890i
$647$	−7.26586			−0.285650			−0.142825	−	0.989748i	$-0.545619\pi$
$647$	−7.26586			−0.285650			−0.142825	+	0.989748i	$0.545619\pi$
$648$		0			0
$649$	−0.181235			−0.00711408
$650$	2.48705	−	29.8710i	0.0975502	−	1.17164i
$651$		0			0
$652$	1.88667	−	11.2515i	0.0738879	−	0.440643i
$653$	20.4733	−	24.3991i	0.801182	−	0.954811i	−0.198498	−	0.980101i	$-0.563606\pi$
$653$	20.4733	−	24.3991i	0.801182	−	0.954811i	0.999680	+	0.0252900i	$0.00805092\pi$
$654$		0			0
$655$	2.01029	−	5.52322i	0.0785484	−	0.215810i
$656$	22.1182	+	12.2794i	0.863570	+	0.479430i
$657$		0			0
$658$	3.50679	+	3.47747i	0.136709	+	0.135566i
$659$	11.3095	−	9.48984i	0.440557	−	0.369672i	−0.395360	−	0.918526i	$-0.629380\pi$
$659$	11.3095	−	9.48984i	0.440557	−	0.369672i	0.835918	+	0.548854i	$0.184936\pi$
$660$		0			0
$661$	3.47979	−	19.7349i	0.135348	−	0.767598i	−0.839268	−	0.543717i	$-0.817016\pi$
$661$	3.47979	−	19.7349i	0.135348	−	0.767598i	0.974617	−	0.223880i	$-0.0718725\pi$
$662$	−25.8505	−	11.9224i	−1.00471	−	0.463377i
$663$		0			0
$664$	16.2402	+	1.21494i	0.630243	+	0.0471489i
$665$	0.962265	+	0.555564i	0.0373150	+	0.0215438i
$666$		0			0
$667$	39.9619	−	23.0720i	1.54733	−	0.893352i
$668$	−6.81731	−	7.98738i	−0.263770	−	0.309041i
$669$		0			0
$670$	−2.74906	−	3.89120i	−0.106206	−	0.150330i
$671$	0.294748	−	0.107280i	0.0113786	−	0.00414148i
$672$		0			0
$673$	6.03662	+	34.2354i	0.232695	+	1.31968i	0.847415	+	0.530932i	$0.178158\pi$
$673$	6.03662	+	34.2354i	0.232695	+	1.31968i	−0.614720	+	0.788745i	$0.710731\pi$
$674$	18.0636	+	4.75894i	0.695784	+	0.183307i
$675$		0			0
$676$	9.82490	+	5.56294i	0.377881	+	0.213959i
$677$	33.0938	−	5.83534i	1.27190	−	0.224270i	0.503363	−	0.864075i	$-0.332096\pi$
$677$	33.0938	−	5.83534i	1.27190	−	0.224270i	0.768537	+	0.639805i	$0.220985\pi$
$678$		0			0
$679$	−0.553144	−	1.51975i	−0.0212277	−	0.0583227i
$680$	−0.211165	−	2.10755i	−0.00809782	−	0.0808209i
$681$		0			0
$682$	−0.120549	+	0.173709i	−0.00461605	+	0.00665166i
$683$	12.3153	+	21.3308i	0.471233	+	0.816200i	0.999459	−	0.0329044i	$-0.0104757\pi$
$683$	12.3153	+	21.3308i	0.471233	+	0.816200i	−0.528225	+	0.849104i	$0.677142\pi$
$684$		0			0
$685$	−2.31937	+	4.01726i	−0.0886185	+	0.153492i
$686$	−4.02986	−	8.54818i	−0.153861	−	0.326371i
$687$		0			0
$688$	3.46125	+	9.03467i	0.131959	+	0.344444i
$689$	−42.1329	−	7.42916i	−1.60514	−	0.283029i
$690$		0			0
$691$	9.45010	+	11.2622i	0.359499	+	0.428434i	0.915232	−	0.402926i	$-0.132007\pi$
$691$	9.45010	+	11.2622i	0.359499	+	0.428434i	−0.555733	+	0.831361i	$0.687562\pi$
$692$	1.40737	+	2.39105i	0.0535003	+	0.0908942i
$693$		0			0
$694$	−6.63731	−	24.3612i	−0.251949	−	0.924739i
$695$	2.53938	+	0.924260i	0.0963243	+	0.0350592i
$696$		0			0
$697$	11.9959	+	10.0657i	0.454376	+	0.381267i
$698$	18.4100	−	1.68858i	0.696829	−	0.0639136i
$699$		0			0
$700$	4.49222	+	1.59245i	0.169790	+	0.0601888i
$701$		−	32.3443i		−	1.22163i	−0.791775	−	0.610813i	$-0.790843\pi$
$701$		−	32.3443i		−	1.22163i	0.791775	−	0.610813i	$-0.209157\pi$
$702$		0			0
$703$			50.8528i			1.91795i
$704$	−0.326442	+	0.0660789i	−0.0123033	+	0.00249044i
$705$		0			0
$706$	2.77550	+	30.2604i	0.104457	+	1.13886i
$707$	6.21078	+	5.21147i	0.233581	+	0.195997i
$708$		0			0
$709$	36.8919	+	13.4276i	1.38551	+	0.504283i	0.923842	−	0.382773i	$-0.125031\pi$
$709$	36.8919	+	13.4276i	1.38551	+	0.504283i	0.461663	+	0.887056i	$0.347253\pi$
$710$	−1.39431	+	0.379886i	−0.0523276	+	0.0142569i
$711$		0			0
$712$	7.96929	+	28.3106i	0.298662	+	1.06099i
$713$	−15.1631	−	18.0707i	−0.567863	−	0.676752i
$714$		0			0
$715$	0.0535457	+	0.00944156i	0.00200250	+	0.000353094i
$716$	−14.6911	+	17.8098i	−0.549032	+	0.665582i
$717$		0			0
$718$	−24.2201	+	11.4181i	−0.903886	+	0.426118i
$719$	−0.482259	+	0.835298i	−0.0179852	+	0.0311514i	−0.874878	−	0.484343i	$-0.839059\pi$
$719$	−0.482259	+	0.835298i	−0.0179852	+	0.0311514i	0.856893	+	0.515495i	$0.172392\pi$
$720$		0			0
$721$	3.85790	+	6.68207i	0.143676	+	0.248853i
$722$	44.4528	+	30.8489i	1.65436	+	1.14808i
$723$		0			0
$724$	−11.9987	−	32.1243i	−0.445928	−	1.19389i
$725$	−11.7932	−	32.4016i	−0.437989	−	1.20337i
$726$		0			0
$727$	20.6400	−	3.63939i	0.765495	−	0.134977i	0.222751	−	0.974875i	$-0.428496\pi$
$727$	20.6400	−	3.63939i	0.765495	−	0.134977i	0.542744	+	0.839898i	$0.317385\pi$
$728$	−4.13960	+	4.24521i	−0.153424	+	0.157338i
$729$		0			0
$730$	−0.0687541	+	0.260972i	−0.00254470	+	0.00965899i
$731$	1.03994	+	5.89782i	0.0384637	+	0.218139i
$732$		0			0
$733$	−1.68677	+	0.613933i	−0.0623022	+	0.0226761i	−0.372983	−	0.927838i	$-0.621665\pi$
$733$	−1.68677	+	0.613933i	−0.0623022	+	0.0226761i	0.310681	+	0.950514i	$0.399443\pi$
$734$	27.5129	−	19.4374i	1.01552	−	0.717447i
$735$		0			0
$736$	2.46089	−	37.0771i	0.0907095	−	1.36668i
$737$	−0.401606	+	0.231867i	−0.0147934	+	0.00854095i
$738$		0			0
$739$	17.1448	+	9.89858i	0.630683	+	0.364125i	0.781017	−	0.624510i	$-0.214701\pi$
$739$	17.1448	+	9.89858i	0.630683	+	0.364125i	−0.150333	+	0.988635i	$0.548035\pi$
$740$	−0.739486	−	3.99727i	−0.0271840	−	0.146943i
$741$		0			0
$742$	2.84906	−	6.17740i	0.104592	−	0.226780i
$743$	−6.72417	+	38.1347i	−0.246686	+	1.39903i	0.569858	+	0.821743i	$0.306998\pi$
$743$	−6.72417	+	38.1347i	−0.246686	+	1.39903i	−0.816544	+	0.577283i	$0.804113\pi$
$744$		0			0
$745$	0.398956	−	0.334764i	0.0146166	−	0.0122648i
$746$	21.5837	−	21.7656i	0.790234	−	0.796897i
$747$		0			0
$748$	−0.206158	+	0.00173107i	−0.00753789	+	6.32943e-5i
$749$	−0.166318	+	0.456954i	−0.00607712	+	0.0166967i
$750$		0			0
$751$	14.8195	−	17.6612i	0.540770	−	0.644465i	−0.424590	−	0.905386i	$-0.639582\pi$
$751$	14.8195	−	17.6612i	0.540770	−	0.644465i	0.965360	+	0.260921i	$0.0840261\pi$
$752$	−22.3481	−	18.1216i	−0.814952	−	0.660826i
$753$		0			0
$754$	42.7493	+	3.55929i	1.55684	+	0.129622i
$755$	−0.182408			−0.00663851
$756$		0			0
$757$	33.3070			1.21056			0.605281	−	0.796012i	$-0.293061\pi$
$757$	33.3070			1.21056			0.605281	+	0.796012i	$0.293061\pi$
$758$	47.4641	+	3.95185i	1.72397	+	0.143538i
$759$		0			0
$760$	−5.90078	−	2.66162i	−0.214044	−	0.0965472i
$761$	10.2052	−	12.1621i	0.369940	−	0.440877i	−0.548673	−	0.836037i	$-0.684867\pi$
$761$	10.2052	−	12.1621i	0.369940	−	0.440877i	0.918612	+	0.395161i	$0.129311\pi$
$762$		0			0
$763$	−1.20654	+	3.31494i	−0.0436797	+	0.120009i
$764$	−0.278010	−	33.1089i	−0.0100580	−	1.19784i
$765$		0			0
$766$	−1.49711	+	1.50973i	−0.0540927	+	0.0545488i
$767$	14.3993	−	12.0825i	0.519930	−	0.436273i
$768$		0			0
$769$	−3.82683	+	21.7030i	−0.137999	+	0.782631i	0.834725	+	0.550666i	$0.185626\pi$
$769$	−3.82683	+	21.7030i	−0.137999	+	0.782631i	−0.972724	+	0.231964i	$0.925485\pi$
$770$	−0.00362080	+	0.00785072i	−0.000130485	+	0.000282920i
$771$		0			0
$772$	−17.3124	+	3.20275i	−0.623087	+	0.115270i
$773$	18.9410	+	10.9356i	0.681261	+	0.393326i	0.800330	−	0.599560i	$-0.204658\pi$
$773$	18.9410	+	10.9356i	0.681261	+	0.393326i	−0.119069	+	0.992886i	$0.537991\pi$
$774$		0			0
$775$	−15.2657	+	8.81366i	−0.548360	+	0.316596i
$776$	4.08918	+	8.48849i	0.146793	+	0.304719i
$777$		0			0
$778$	4.46037	−	3.15118i	0.159912	−	0.112975i
$779$	44.9720	−	16.3685i	1.61129	−	0.586461i
$780$		0			0
$781$	0.0244257	+	0.138525i	0.000874022	+	0.00495682i
$782$	5.85981	−	22.2422i	0.209546	−	0.795380i
$783$		0			0
$784$	13.9202	+	23.2017i	0.497149	+	0.828633i
$785$	−3.08977	+	0.544811i	−0.110279	+	0.0194451i
$786$		0			0
$787$	−1.15642	−	3.17723i	−0.0412218	−	0.113256i	0.917374	−	0.398027i	$-0.130305\pi$
$787$	−1.15642	−	3.17723i	−0.0412218	−	0.113256i	−0.958596	+	0.284771i	$0.908083\pi$
$788$	−23.4151	+	8.74576i	−0.834130	+	0.311555i
$789$		0			0
$790$	1.06388	+	0.738301i	0.0378512	+	0.0262676i
$791$	3.51231	+	6.08351i	0.124884	+	0.216305i
$792$		0			0
$793$	−16.2661	+	28.1737i	−0.577625	+	1.00048i
$794$	25.0832	−	11.8249i	0.890169	−	0.419651i
$795$		0			0
$796$	6.92170	+	5.70965i	0.245333	+	0.202373i
$797$	47.1233	+	8.30912i	1.66919	+	0.294324i	0.926776	−	0.375613i	$-0.122568\pi$
$797$	47.1233	+	8.30912i	1.66919	+	0.294324i	0.742418	+	0.669937i	$0.233679\pi$
$798$		0			0
$799$	−11.4479	−	13.6431i	−0.404999	−	0.482659i
$800$	−26.9656	−	6.62203i	−0.953378	−	0.234124i
$801$		0			0
$802$	−29.5990	+	8.06437i	−1.04518	+	0.284763i
$803$	0.0246842	+	0.00898432i	0.000871087	+	0.000317050i
$804$		0			0
$805$	−0.738884	−	0.619997i	−0.0260422	−	0.0218520i
$806$	−2.00301	−	21.8381i	−0.0705529	−	0.769214i
$807$		0			0
$808$	−39.0299	−	26.6028i	−1.37307	−	0.935882i
$809$			17.3637i			0.610473i	0.952277	+	0.305237i	$0.0987356\pi$
$809$			17.3637i			0.610473i	−0.952277	+	0.305237i	$0.901264\pi$
$810$		0			0
$811$			13.7618i			0.483242i	0.970371	+	0.241621i	$0.0776791\pi$
$811$			13.7618i			0.483242i	−0.970371	+	0.241621i	$0.922321\pi$
$812$	−2.27900	+	6.42894i	−0.0799771	+	0.225612i
$813$		0			0
$814$	−0.394022	+	0.0361400i	−0.0138105	+	0.00126671i
$815$	1.32163	+	1.10898i	0.0462946	+	0.0388458i
$816$		0			0
$817$	17.1990	+	6.25993i	0.601717	+	0.219007i
$818$	4.08842	+	15.0059i	0.142948	+	0.524669i
$819$		0			0
$820$	−3.29698	+	1.94061i	−0.115136	+	0.0677689i
$821$	−17.1467	−	20.4347i	−0.598425	−	0.713175i	0.378777	−	0.925488i	$-0.376345\pi$
$821$	−17.1467	−	20.4347i	−0.598425	−	0.713175i	−0.977202	+	0.212313i	$0.931900\pi$
$822$		0			0
$823$	43.4440	+	7.66035i	1.51436	+	0.267023i	0.868214	−	0.496190i	$-0.165268\pi$
$823$	43.4440	+	7.66035i	1.51436	+	0.267023i	0.646148	+	0.763212i	$0.276379\pi$
$824$	−26.2447	−	36.4942i	−0.914277	−	1.27134i
$825$		0			0
$826$	1.27450	+	2.70349i	0.0443456	+	0.0940664i
$827$	5.67028	−	9.82121i	0.197175	−	0.341517i	−0.750436	−	0.660943i	$-0.770157\pi$
$827$	5.67028	−	9.82121i	0.197175	−	0.341517i	0.947611	+	0.319426i	$0.103490\pi$
$828$		0			0
$829$	14.5329	+	25.1717i	0.504747	+	0.874248i	0.999985	+	0.00549015i	$0.00174758\pi$
$829$	14.5329	+	25.1717i	0.504747	+	0.874248i	−0.495238	+	0.868757i	$0.664919\pi$
$830$	−1.40412	+	2.02331i	−0.0487375	+	0.0702301i
$831$		0			0
$832$	21.5310	−	27.0132i	0.746452	−	0.936514i
$833$	5.72827	+	15.7383i	0.198473	+	0.545299i
$834$		0			0
$835$	1.56391	−	0.275759i	0.0541212	−	0.00954303i
$836$	−0.310446	+	0.548289i	−0.0107370	+	0.0189630i
$837$		0			0
$838$	33.1185	+	8.72523i	1.14406	+	0.301408i
$839$	2.04353	+	11.5894i	0.0705503	+	0.400111i	0.999549	+	0.0300279i	$0.00955962\pi$
$839$	2.04353	+	11.5894i	0.0705503	+	0.400111i	−0.928999	+	0.370083i	$0.879329\pi$
$840$		0			0
$841$	19.1198	−	6.95904i	0.659304	−	0.239967i
$842$	29.8764	+	42.2889i	1.02961	+	1.45737i
$843$		0			0
$844$	−34.1431	+	29.1415i	−1.17525	+	1.00309i
$845$	−1.47865	+	0.853700i	−0.0508672	+	0.0293682i
$846$		0			0
$847$	−4.62422	−	2.66980i	−0.158890	−	0.0917353i
$848$	−12.9276	+	37.4642i	−0.443937	+	1.28653i
$849$		0			0
$850$	−15.6076	−	7.19833i	−0.535337	−	0.246901i
$851$	7.66556	−	43.4735i	0.262772	−	1.49025i
$852$		0			0
$853$	−33.4958	+	28.1063i	−1.14687	+	0.962342i	−0.999642	−	0.0267597i	$-0.991481\pi$
$853$	−33.4958	+	28.1063i	−1.14687	+	0.962342i	−0.147233	+	0.989102i	$0.547037\pi$
$854$	−3.67306	−	3.64235i	−0.125690	−	0.124639i
$855$		0			0
$856$	0.698713	−	2.74549i	0.0238815	−	0.0938390i
$857$	1.39456	−	3.83152i	0.0476372	−	0.130882i	−0.913593	−	0.406631i	$-0.866704\pi$
$857$	1.39456	−	3.83152i	0.0476372	−	0.130882i	0.961230	+	0.275749i	$0.0889258\pi$
$858$		0			0
$859$	−25.0149	+	29.8116i	−0.853499	+	1.01716i	0.146112	+	0.989268i	$0.453324\pi$
$859$	−25.0149	+	29.8116i	−0.853499	+	1.01716i	−0.999611	+	0.0278919i	$0.991121\pi$
$860$	−1.44295	−	0.241957i	−0.0492043	−	0.00825067i
$861$		0			0
$862$	4.52477	−	54.3452i	0.154114	−	1.85100i
$863$	48.5663			1.65322			0.826608	−	0.562778i	$-0.190268\pi$
$863$	48.5663			1.65322			0.826608	+	0.562778i	$0.190268\pi$
$864$		0			0
$865$	−0.419573			−0.0142659
$866$	0.770052	−	9.24879i	0.0261674	−	0.314287i
$867$		0			0
$868$	3.43897	+	0.576652i	0.116726	+	0.0195729i
$869$	0.0810203	−	0.0965562i	0.00274843	−	0.00327545i
$870$		0			0
$871$	16.4501	−	45.1963i	0.557391	−	1.53142i
$872$	5.06877	−	19.9170i	0.171650	−	0.674474i
$873$		0			0
$874$	−49.9147	−	49.4973i	−1.68839	−	1.67427i
$875$	−1.11455	+	0.935219i	−0.0376787	+	0.0316162i
$876$		0			0
$877$	−2.95518	+	16.7597i	−0.0997895	+	0.565934i	0.893385	+	0.449293i	$0.148324\pi$
$877$	−2.95518	+	16.7597i	−0.0997895	+	0.565934i	−0.993174	+	0.116641i	$0.962787\pi$
$878$	2.34310	+	1.08065i	0.0790757	+	0.0364702i
$879$		0			0
$880$	0.0164294	−	0.0476125i	0.000553836	−	0.00160502i
$881$	2.59611	+	1.49886i	0.0874651	+	0.0504980i	0.543095	−	0.839672i	$-0.317252\pi$
$881$	2.59611	+	1.49886i	0.0874651	+	0.0504980i	−0.455630	+	0.890169i	$0.650586\pi$
$882$		0			0
$883$	17.0858	−	9.86450i	0.574984	−	0.331967i	−0.184154	−	0.982897i	$-0.558954\pi$
$883$	17.0858	−	9.86450i	0.574984	−	0.331967i	0.759137	+	0.650931i	$0.225621\pi$
$884$	16.2641	−	13.8816i	0.547022	−	0.466889i
$885$		0			0
$886$	−1.42374	−	2.01526i	−0.0478316	−	0.0677039i
$887$	−43.7296	+	15.9163i	−1.46830	+	0.534416i	−0.947637	−	0.319349i	$-0.896536\pi$
$887$	−43.7296	+	15.9163i	−1.46830	+	0.534416i	−0.520658	+	0.853765i	$0.674313\pi$
$888$		0			0
$889$	−0.749912	−	4.25296i	−0.0251512	−	0.142640i
$890$	−4.30090	−	1.13309i	−0.144166	−	0.0379813i
$891$		0			0
$892$	−18.0497	+	31.8781i	−0.604347	+	1.06736i
$893$	−53.6030	+	9.45165i	−1.79376	+	0.316287i
$894$		0			0
$895$	−1.19411	−	3.28079i	−0.0399147	−	0.109665i
$896$	3.28136	+	4.40487i	0.109622	+	0.147156i
$897$		0			0
$898$	7.44965	−	10.7348i	0.248598	−	0.358226i
$899$	−12.6135	−	21.8472i	−0.420683	−	0.728645i
$900$		0			0
$901$	−12.2661	+	21.2454i	−0.408642	+	0.707788i
$902$	0.158788	+	0.336823i	0.00528706	+	0.0112150i
$903$		0			0
$904$	−23.8937	−	33.2252i	−0.794694	−	1.10505i
$905$	5.10700	+	0.900503i	0.169763	+	0.0299337i
$906$		0			0
$907$	−22.3588	−	26.6461i	−0.742411	−	0.884771i	0.254190	−	0.967154i	$-0.418191\pi$
$907$	−22.3588	−	26.6461i	−0.742411	−	0.884771i	−0.996601	+	0.0823838i	$0.973747\pi$
$908$	−33.7880	+	19.8876i	−1.12129	+	0.659994i
$909$		0			0
$910$	−0.235711	−	0.865141i	−0.00781375	−	0.0286791i
$911$	28.1223	+	10.2357i	0.931735	+	0.339124i	0.762897	−	0.646520i	$-0.223776\pi$
$911$	28.1223	+	10.2357i	0.931735	+	0.339124i	0.168838	+	0.985644i	$0.445999\pi$
$912$		0			0
$913$	0.183633	+	0.154086i	0.00607735	+	0.00509950i
$914$	38.8444	−	3.56284i	1.28486	−	0.117848i
$915$		0			0
$916$	−3.78762	+	10.6847i	−0.125147	+	0.353033i
$917$			9.43490i			0.311568i
$918$		0			0
$919$		−	52.7647i		−	1.74055i	−0.492569	−	0.870273i	$-0.663942\pi$
$919$		−	52.7647i		−	1.74055i	0.492569	−	0.870273i	$-0.336058\pi$
$920$	4.64330	+	3.16488i	0.153085	+	0.104343i
$921$		0			0
$922$	2.67834	+	29.2011i	0.0882065	+	0.961686i
$923$	−11.1758	−	9.37762i	−0.367856	−	0.308668i
$924$		0			0
$925$	−30.9974	−	11.2821i	−1.01919	−	0.370954i
$926$	−13.0798	+	3.56365i	−0.429830	+	0.117109i
$927$		0			0
$928$	9.47698	−	38.5913i	0.311097	−	1.26682i
$929$	−35.7471	−	42.6017i	−1.17282	−	1.39772i	−0.900132	−	0.435617i	$-0.856530\pi$
$929$	−35.7471	−	42.6017i	−1.17282	−	1.39772i	−0.272692	−	0.962101i	$-0.587914\pi$
$930$		0			0
$931$	50.4082	+	8.88832i	1.65206	+	0.291303i
$932$	11.5887	+	9.55940i	0.379600	+	0.313128i
$933$		0			0
$934$	22.3791	−	10.5502i	0.732268	−	0.345212i
$935$	0.0155887	−	0.0270003i	0.000509803	−	0.000883005i
$936$		0			0
$937$	9.12048	+	15.7971i	0.297953	+	0.516070i	0.975667	−	0.219255i	$-0.0703628\pi$
$937$	9.12048	+	15.7971i	0.297953	+	0.516070i	−0.677715	+	0.735325i	$0.737029\pi$
$938$	6.28301	+	4.36022i	0.205148	+	0.142366i
$939$		0			0
$940$	4.07600	−	1.52242i	0.132945	−	0.0496559i
$941$	−5.96053	−	16.3764i	−0.194308	−	0.533856i	0.803830	−	0.594859i	$-0.202792\pi$
$941$	−5.96053	−	16.3764i	−0.194308	−	0.533856i	−0.998138	+	0.0610030i	$0.980570\pi$
$942$		0			0
$943$	−40.9134	+	7.21414i	−1.33232	+	0.234925i
$944$	−8.95832	−	14.9315i	−0.291568	−	0.485978i
$945$		0			0
$946$	−0.0362807	+	0.137712i	−0.00117959	+	0.00447739i
$947$	−7.47101	−	42.3702i	−0.242775	−	1.37685i	−0.825603	−	0.564251i	$-0.809165\pi$
$947$	−7.47101	−	42.3702i	−0.242775	−	1.37685i	0.582828	−	0.812596i	$-0.301946\pi$
$948$		0			0
$949$	−2.56016	+	0.931821i	−0.0831063	+	0.0302482i
$950$	−42.9018	+	30.3094i	−1.39192	+	0.983365i
$951$		0			0
$952$	1.47560	+	3.06310i	0.0478243	+	0.0992756i
$953$	17.5809	−	10.1503i	0.569502	−	0.328802i	−0.187449	−	0.982274i	$-0.560022\pi$
$953$	17.5809	−	10.1503i	0.569502	−	0.328802i	0.756950	+	0.653472i	$0.226688\pi$
$954$		0			0
$955$	4.33625	+	2.50353i	0.140318	+	0.0810124i
$956$	12.7274	−	2.35454i	0.411634	−	0.0761513i
$957$		0			0
$958$	15.5159	−	33.6419i	0.501295	−	1.08692i
$959$	1.29301	−	7.33301i	0.0417534	−	0.236795i
$960$		0			0
$961$	13.8681	−	11.6367i	0.447359	−	0.375379i
$962$	28.8962	−	29.1399i	0.931652	−	0.939507i
$963$		0			0
$964$	0.0116530	+	1.38779i	0.000375319	+	0.0446977i
$965$	0.910624	−	2.50192i	0.0293140	−	0.0805396i
$966$		0			0
$967$	−30.0283	+	35.7863i	−0.965644	+	1.15081i	0.0228793	+	0.999738i	$0.492717\pi$
$967$	−30.0283	+	35.7863i	−0.965644	+	1.15081i	−0.988523	+	0.151071i	$0.951728\pi$
$968$	28.3566	+	12.7906i	0.911415	+	0.411105i
$969$		0			0
$970$	−1.41994	−	0.118224i	−0.0455916	−	0.00379594i
$971$	29.3788			0.942809			0.471405	−	0.881917i	$-0.343747\pi$
$971$	29.3788			0.942809			0.471405	+	0.881917i	$0.343747\pi$
$972$		0			0
$973$	−4.33784			−0.139065
$974$	−10.0198	−	0.834245i	−0.321055	−	0.0267309i
$975$		0			0
$976$	23.4077	+	18.9808i	0.749263	+	0.607560i
$977$	12.0038	−	14.3055i	0.384035	−	0.457675i	−0.539049	−	0.842275i	$-0.681216\pi$
$977$	12.0038	−	14.3055i	0.384035	−	0.457675i	0.923083	+	0.384600i	$0.125661\pi$
$978$		0			0
$979$	−0.148065	+	0.406804i	−0.00473217	+	0.0130015i
$980$	−4.09157	+	0.0343562i	−0.130700	+	0.00109747i
$981$		0			0
$982$	−19.6699	+	19.8357i	−0.627691	+	0.632984i
$983$	−20.0449	+	16.8196i	−0.639332	+	0.536463i	−0.903813	−	0.427928i	$-0.859244\pi$
$983$	−20.0449	+	16.8196i	−0.639332	+	0.536463i	0.264481	+	0.964391i	$0.414799\pi$
$984$		0			0
$985$	0.656370	−	3.72246i	0.0209137	−	0.118607i
$986$	10.3017	−	22.3365i	0.328074	−	0.711339i
$987$		0			0
$988$	−11.8878	−	64.2590i	−0.378200	−	2.04435i
$989$	−13.7596	−	7.94413i	−0.437531	−	0.252609i
$990$		0			0
$991$	−25.5875	+	14.7730i	−0.812815	+	0.469279i	−0.847932	−	0.530105i	$-0.822153\pi$
$991$	−25.5875	+	14.7730i	−0.812815	+	0.469279i	0.0351178	+	0.999383i	$0.488819\pi$
$992$	−20.2701	−	1.34537i	−0.643576	−	0.0427155i
$993$		0			0
$994$	1.89462	−	1.33852i	0.0600937	−	0.0424552i
$995$	−1.27507	+	0.464087i	−0.0404224	+	0.0147125i
$996$		0			0
$997$	6.87604	+	38.9959i	0.217766	+	1.23501i	0.876041	+	0.482236i	$0.160175\pi$
$997$	6.87604	+	38.9959i	0.217766	+	1.23501i	−0.658275	+	0.752778i	$0.728714\pi$
$998$	14.2410	−	54.0548i	0.450790	−	1.71107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.b.215.9		96
3.2	odd	2		972.2.l.c.215.8		96
4.3	odd	2	inner	972.2.l.b.215.7		96
9.2	odd	6		972.2.l.d.863.3		96
9.4	even	3		324.2.l.a.179.3		96
9.5	odd	6		108.2.l.a.23.14	yes	96
9.7	even	3		972.2.l.a.863.14		96
12.11	even	2		972.2.l.c.215.10		96
27.2	odd	18	inner	972.2.l.b.755.7		96
27.7	even	9		972.2.l.d.107.12		96
27.11	odd	18		324.2.l.a.143.16		96
27.16	even	9		108.2.l.a.47.1	yes	96
27.20	odd	18		972.2.l.a.107.5		96
27.25	even	9		972.2.l.c.755.10		96
36.7	odd	6		972.2.l.a.863.5		96
36.11	even	6		972.2.l.d.863.12		96
36.23	even	6		108.2.l.a.23.1	✓	96
36.31	odd	6		324.2.l.a.179.16		96
108.7	odd	18		972.2.l.d.107.3		96
108.11	even	18		324.2.l.a.143.3		96
108.43	odd	18		108.2.l.a.47.14	yes	96
108.47	even	18		972.2.l.a.107.14		96
108.79	odd	18		972.2.l.c.755.8		96
108.83	even	18	inner	972.2.l.b.755.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.1	✓	96	36.23	even	6
108.2.l.a.23.14	yes	96	9.5	odd	6
108.2.l.a.47.1	yes	96	27.16	even	9
108.2.l.a.47.14	yes	96	108.43	odd	18
324.2.l.a.143.3		96	108.11	even	18
324.2.l.a.143.16		96	27.11	odd	18
324.2.l.a.179.3		96	9.4	even	3
324.2.l.a.179.16		96	36.31	odd	6
972.2.l.a.107.5		96	27.20	odd	18
972.2.l.a.107.14		96	108.47	even	18
972.2.l.a.863.5		96	36.7	odd	6
972.2.l.a.863.14		96	9.7	even	3
972.2.l.b.215.7		96	4.3	odd	2	inner
972.2.l.b.215.9		96	1.1	even	1	trivial
972.2.l.b.755.7		96	27.2	odd	18	inner
972.2.l.b.755.9		96	108.83	even	18	inner
972.2.l.c.215.8		96	3.2	odd	2
972.2.l.c.215.10		96	12.11	even	2
972.2.l.c.755.8		96	108.79	odd	18
972.2.l.c.755.10		96	27.25	even	9
972.2.l.d.107.3		96	108.7	odd	18
972.2.l.d.107.12		96	27.7	even	9
972.2.l.d.863.3		96	9.2	odd	6
972.2.l.d.863.12		96	36.11	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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.117341 + 1.40934i) q^{2} +(-1.97246 - 0.330746i) q^{4} +(0.194411 - 0.231690i) q^{5} +(-0.166049 + 0.456215i) q^{7} +(0.697584 - 2.74105i) q^{8} +(0.303717 + 0.301177i) q^{10} +(0.0318926 - 0.0267611i) q^{11} +(-0.749815 + 4.25241i) q^{13} +(-0.623477 - 0.287551i) q^{14} +(3.78121 + 1.30477i) q^{16} +(2.14427 + 1.23800i) q^{17} +(6.55326 - 3.78353i) q^{19} +(-0.460098 + 0.392699i) q^{20} +(0.0339731 + 0.0480877i) q^{22} +(-6.17265 + 2.24666i) q^{23} +(0.852356 + 4.83395i) q^{25} +(-5.90510 - 1.55572i) q^{26} +(0.478416 - 0.844947i) q^{28} +(-6.91801 + 1.21983i) q^{29} +(1.22825 + 3.37459i) q^{31} +(-2.28255 + 5.17590i) q^{32} +(-1.99636 + 2.87673i) q^{34} +(0.0734187 + 0.127165i) q^{35} +(-3.36015 + 5.81994i) q^{37} +(4.56330 + 9.67972i) q^{38} +(-0.499456 - 0.694513i) q^{40} +(6.22846 + 1.09825i) q^{41} +(1.55474 + 1.85287i) q^{43} +(-0.0717582 + 0.0422369i) q^{44} +(-2.44200 - 8.96296i) q^{46} +(-6.75922 - 2.46015i) q^{47} +(5.18175 + 4.34801i) q^{49} +(-6.91269 + 0.634036i) q^{50} +(2.88545 - 8.13973i) q^{52} +9.90799i q^{53} -0.0125918i q^{55} +(1.13468 + 0.773397i) q^{56} +(-0.907388 - 9.89295i) q^{58} +(-3.33471 - 2.79816i) q^{59} +(7.07970 + 2.57680i) q^{61} +(-4.90006 + 1.33504i) q^{62} +(-7.02675 - 3.82423i) q^{64} +(0.839468 + 1.00044i) q^{65} +(-10.9694 - 1.93421i) q^{67} +(-3.82003 - 3.15111i) q^{68} +(-0.187833 + 0.0885501i) q^{70} +(-1.68932 + 2.92598i) q^{71} +(0.315477 + 0.546421i) q^{73} +(-7.80798 - 5.41850i) q^{74} +(-14.1775 + 5.29540i) q^{76} +(0.00691309 + 0.0189936i) q^{77} +(2.98154 - 0.525727i) q^{79} +(1.03741 - 0.622407i) q^{80} +(-2.27865 + 8.64913i) q^{82} +(0.999837 + 5.67036i) q^{83} +(0.703701 - 0.256126i) q^{85} +(-2.79375 + 1.97374i) q^{86} +(-0.0511058 - 0.106088i) q^{88} +(-9.00521 + 5.19916i) q^{89} +(-1.81551 - 1.04819i) q^{91} +(12.9184 - 2.38987i) q^{92} +(4.26032 - 9.23734i) q^{94} +(0.397420 - 2.25388i) q^{95} +(-2.55186 + 2.14126i) q^{97} +(-6.73584 + 6.79263i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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