LMFDB - Embedded newform 972.2.l.c.755.10

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,-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			755.10
Character	$\chi$	$=$	972.755
Dual form			972.2.l.c.215.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.592286 - 1.28421i) q^{2} +(-1.29839 - 1.52124i) q^{4} +(-0.194411 - 0.231690i) q^{5} +(0.166049 + 0.456215i) q^{7} +(-2.72261 + 0.766402i) q^{8} +(-0.412685 + 0.112438i) q^{10} +(0.0318926 + 0.0267611i) q^{11} +(-0.749815 - 4.25241i) q^{13} +(0.684225 + 0.0569684i) q^{14} +(-0.628345 + 3.95034i) q^{16} +(-2.14427 + 1.23800i) q^{17} +(-6.55326 - 3.78353i) q^{19} +(-0.100034 + 0.596570i) q^{20} +(0.0532565 - 0.0251066i) q^{22} +(-6.17265 - 2.24666i) q^{23} +(0.852356 - 4.83395i) q^{25} +(-5.90510 - 1.55572i) q^{26} +(0.478416 - 0.844947i) q^{28} +(6.91801 + 1.21983i) q^{29} +(-1.22825 + 3.37459i) q^{31} +(4.70091 + 3.14666i) q^{32} +(0.319825 + 3.48694i) q^{34} +(0.0734187 - 0.127165i) q^{35} +(-3.36015 - 5.81994i) q^{37} +(-8.74026 + 6.17484i) q^{38} +(0.706873 + 0.481805i) q^{40} +(-6.22846 + 1.09825i) q^{41} +(-1.55474 + 1.85287i) q^{43} +(-0.000699143 - 0.0832628i) q^{44} +(-6.54116 + 6.59631i) q^{46} +(-6.75922 + 2.46015i) q^{47} +(5.18175 - 4.34801i) q^{49} +(-5.70297 - 3.95769i) q^{50} +(-5.49539 + 6.66196i) q^{52} +9.90799i q^{53} -0.0125918i q^{55} +(-0.801731 - 1.11484i) q^{56} +(5.66396 - 8.16169i) q^{58} +(-3.33471 + 2.79816i) q^{59} +(7.07970 - 2.57680i) q^{61} +(3.60621 + 3.57605i) q^{62} +(6.82526 - 4.17323i) q^{64} +(-0.839468 + 1.00044i) q^{65} +(10.9694 - 1.93421i) q^{67} +(4.66740 + 1.65455i) q^{68} +(-0.119822 - 0.169603i) q^{70} +(-1.68932 - 2.92598i) q^{71} +(0.315477 - 0.546421i) q^{73} +(-9.46420 + 0.868063i) q^{74} +(2.75306 + 14.8816i) q^{76} +(-0.00691309 + 0.0189936i) q^{77} +(-2.98154 - 0.525727i) q^{79} +(1.03741 - 0.622407i) q^{80} +(-2.27865 + 8.64913i) q^{82} +(0.999837 - 5.67036i) q^{83} +(0.703701 + 0.256126i) q^{85} +(1.45862 + 3.09404i) q^{86} +(-0.107341 - 0.0484176i) q^{88} +(9.00521 + 5.19916i) q^{89} +(1.81551 - 1.04819i) q^{91} +(4.59682 + 12.3071i) q^{92} +(-0.844035 + 10.1374i) q^{94} +(0.397420 + 2.25388i) q^{95} +(-2.55186 - 2.14126i) q^{97} +(-2.51468 - 9.22972i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.592286	−	1.28421i	0.418810	−	0.908074i
$2$	0.592286	−	1.28421i	0.418810	−	0.908074i
$3$		0			0
$3$		0			0
$4$	−1.29839	−	1.52124i	−0.649197	−	0.760620i
$5$	−0.194411	−	0.231690i	−0.0869431	−	0.103615i	0.720819	−	0.693123i	$-0.243766\pi$
$5$	−0.194411	−	0.231690i	−0.0869431	−	0.103615i	−0.807762	+	0.589509i	$0.799321\pi$
$6$		0			0
$7$	0.166049	+	0.456215i	0.0627605	+	0.172433i	0.967109	−	0.254361i	$-0.0818651\pi$
$7$	0.166049	+	0.456215i	0.0627605	+	0.172433i	−0.904349	+	0.426794i	$0.859643\pi$
$8$	−2.72261	+	0.766402i	−0.962589	+	0.270964i
$9$		0			0
$10$	−0.412685	+	0.112438i	−0.130503	+	0.0355559i
$11$	0.0318926	+	0.0267611i	0.00961599	+	0.00806878i	0.647583	−	0.761995i	$-0.275780\pi$
$11$	0.0318926	+	0.0267611i	0.00961599	+	0.00806878i	−0.637967	+	0.770064i	$0.720224\pi$
$12$		0			0
$13$	−0.749815	−	4.25241i	−0.207961	−	1.17941i	−0.892711	−	0.450629i	$-0.851200\pi$
$13$	−0.749815	−	4.25241i	−0.207961	−	1.17941i	0.684750	−	0.728778i	$-0.259911\pi$
$14$	0.684225	+	0.0569684i	0.182867	+	0.0152254i
$15$		0			0
$16$	−0.628345	+	3.95034i	−0.157086	+	0.987585i
$17$	−2.14427	+	1.23800i	−0.520062	+	0.300258i	−0.736960	−	0.675936i	$-0.763739\pi$
$17$	−2.14427	+	1.23800i	−0.520062	+	0.300258i	0.216898	+	0.976194i	$0.430406\pi$
$18$		0			0
$19$	−6.55326	−	3.78353i	−1.50342	−	0.868001i	−0.999992	−	0.00396479i	$-0.998738\pi$
$19$	−6.55326	−	3.78353i	−1.50342	−	0.868001i	−0.503430	−	0.864036i	$-0.667929\pi$
$20$	−0.100034	+	0.596570i	−0.0223683	+	0.133397i
$21$		0			0
$22$	0.0532565	−	0.0251066i	0.0113543	−	0.00535275i
$23$	−6.17265	−	2.24666i	−1.28709	−	0.468461i	−0.394316	−	0.918975i	$-0.629019\pi$
$23$	−6.17265	−	2.24666i	−1.28709	−	0.468461i	−0.892769	+	0.450514i	$0.851241\pi$
$24$		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	$-0.218278\pi$
$29$	6.91801	+	1.21983i	1.28464	+	0.226517i	0.510692	+	0.859764i	$0.329389\pi$
$30$		0			0
$31$	−1.22825	+	3.37459i	−0.220600	+	0.606094i	−0.999786	−	0.0206992i	$-0.993411\pi$
$31$	−1.22825	+	3.37459i	−0.220600	+	0.606094i	0.779186	+	0.626793i	$0.215633\pi$
$32$	4.70091	+	3.14666i	0.831011	+	0.556256i
$33$		0			0
$34$	0.319825	+	3.48694i	0.0548495	+	0.598006i
$35$	0.0734187	−	0.127165i	0.0124100	−	0.0214948i
$36$		0			0
$37$	−3.36015	−	5.81994i	−0.552405	−	0.956793i	−0.998100	−	0.0616082i	$-0.980377\pi$
$37$	−3.36015	−	5.81994i	−0.552405	−	0.956793i	0.445696	−	0.895184i	$-0.352956\pi$
$38$	−8.74026	+	6.17484i	−1.41786	+	1.00169i
$39$		0			0
$40$	0.706873	+	0.481805i	0.111766	+	0.0761801i
$41$	−6.22846	+	1.09825i	−0.972722	+	0.171517i	−0.637355	−	0.770571i	$-0.719971\pi$
$41$	−6.22846	+	1.09825i	−0.972722	+	0.171517i	−0.335367	+	0.942088i	$0.608860\pi$
$42$		0			0
$43$	−1.55474	+	1.85287i	−0.237096	+	0.282560i	−0.871452	−	0.490481i	$-0.836821\pi$
$43$	−1.55474	+	1.85287i	−0.237096	+	0.282560i	0.634356	+	0.773041i	$0.281265\pi$
$44$	−0.000699143	−	0.0832628i	−0.000105400	−	0.0125523i
$45$		0			0
$46$	−6.54116	+	6.59631i	−0.964441	+	0.972573i
$47$	−6.75922	+	2.46015i	−0.985933	+	0.358850i	−0.784144	−	0.620579i	$-0.786898\pi$
$47$	−6.75922	+	2.46015i	−0.985933	+	0.358850i	−0.201789	+	0.979429i	$0.564675\pi$
$48$		0			0
$49$	5.18175	−	4.34801i	0.740250	−	0.621144i
$50$	−5.70297	−	3.95769i	−0.806522	−	0.559702i
$51$		0			0
$52$	−5.49539	+	6.66196i	−0.762073	+	0.923847i
$53$			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
$56$	−0.801731	−	1.11484i	−0.107136	−	0.148977i
$57$		0			0
$58$	5.66396	−	8.16169i	0.743715	−	1.07168i
$59$	−3.33471	+	2.79816i	−0.434143	+	0.364289i	−0.833512	−	0.552501i	$-0.813674\pi$
$59$	−3.33471	+	2.79816i	−0.434143	+	0.364289i	0.399369	+	0.916790i	$0.369229\pi$
$60$		0			0
$61$	7.07970	−	2.57680i	0.906462	−	0.329925i	0.153623	−	0.988130i	$-0.450906\pi$
$61$	7.07970	−	2.57680i	0.906462	−	0.329925i	0.752839	+	0.658204i	$0.228684\pi$
$62$	3.60621	+	3.57605i	0.457989	+	0.454159i
$63$		0			0
$64$	6.82526	−	4.17323i	0.853157	−	0.521654i
$65$	−0.839468	+	1.00044i	−0.104123	+	0.124089i
$66$		0			0
$67$	10.9694	−	1.93421i	1.34013	−	0.236301i	0.542810	−	0.839856i	$-0.317361\pi$
$67$	10.9694	−	1.93421i	1.34013	−	0.236301i	0.797322	+	0.603554i	$0.206249\pi$
$68$	4.66740	+	1.65455i	0.566005	+	0.200643i
$69$		0			0
$70$	−0.119822	−	0.169603i	−0.0143214	−	0.0202715i
$71$	−1.68932	−	2.92598i	−0.200485	−	0.347250i	0.748200	−	0.663473i	$-0.230918\pi$
$71$	−1.68932	−	2.92598i	−0.200485	−	0.347250i	−0.948685	+	0.316223i	$0.897585\pi$
$72$		0			0
$73$	0.315477	−	0.546421i	0.0369237	−	0.0639538i	−0.846973	−	0.531636i	$-0.821577\pi$
$73$	0.315477	−	0.546421i	0.0369237	−	0.0639538i	0.883897	+	0.467682i	$0.154911\pi$
$74$	−9.46420	+	0.868063i	−1.10019	+	0.100910i
$75$		0			0
$76$	2.75306	+	14.8816i	0.315798	+	1.70704i
$77$	−0.00691309	+	0.0189936i	−0.000787820	+	0.00216452i
$78$		0			0
$79$	−2.98154	−	0.525727i	−0.335450	−	0.0591489i	0.00338622	−	0.999994i	$-0.498922\pi$
$79$	−2.98154	−	0.525727i	−0.335450	−	0.0591489i	−0.338836	+	0.940845i	$0.610033\pi$
$80$	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	−0.879471	−	0.475952i	$-0.842104\pi$
$83$	0.999837	−	5.67036i	0.109746	−	0.622403i	0.989218	−	0.146451i	$-0.0467852\pi$
$84$		0			0
$85$	0.703701	+	0.256126i	0.0763270	+	0.0277808i
$86$	1.45862	+	3.09404i	0.157287	+	0.333639i
$87$		0			0
$88$	−0.107341	−	0.0484176i	−0.0114426	−	0.00516133i
$89$	9.00521	+	5.19916i	0.954550	+	0.551110i	0.894491	−	0.447085i	$-0.147538\pi$
$89$	9.00521	+	5.19916i	0.954550	+	0.551110i	0.0600588	+	0.998195i	$0.480871\pi$
$90$		0			0
$91$	1.81551	−	1.04819i	0.190317	−	0.109880i
$92$	4.59682	+	12.3071i	0.479251	+	1.28311i
$93$		0			0
$94$	−0.844035	+	10.1374i	−0.0870556	+	1.04559i
$95$	0.397420	+	2.25388i	0.0407745	+	0.231244i
$96$		0			0
$97$	−2.55186	−	2.14126i	−0.259102	−	0.217412i	0.503978	−	0.863717i	$-0.331869\pi$
$97$	−2.55186	−	2.14126i	−0.259102	−	0.217412i	−0.763080	+	0.646304i	$0.776314\pi$
$98$	−2.51468	−	9.22972i	−0.254021	−	0.932343i
$99$		0			0
$100$	−8.46030	+	4.97974i	−0.846030	+	0.497974i
$101$	−5.71163	−	15.6926i	−0.568329	−	1.56147i	−0.807113	−	0.590397i	$-0.798971\pi$
$101$	−5.71163	−	15.6926i	−0.568329	−	1.56147i	0.238784	−	0.971073i	$-0.423251\pi$
$102$		0			0
$103$	−10.2156	−	12.1745i	−1.00657	−	1.19959i	−0.979807	−	0.199946i	$-0.935923\pi$
$103$	−10.2156	−	12.1745i	−1.00657	−	1.19959i	−0.0267664	−	0.999642i	$-0.508521\pi$
$104$	5.30051	+	11.0030i	0.519758	+	1.07893i
$105$		0			0
$106$	12.7240	+	5.86837i	1.23586	+	0.569986i
$107$	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	$0.386865\pi$
$110$	−0.0161706	−	0.00745798i	−0.00154180	−	0.000711090i
$111$		0			0
$112$	−1.90654	+	0.369288i	−0.180151	+	0.0348945i
$113$	−9.30051	−	11.0839i	−0.874918	−	1.04269i	−0.998730	−	0.0503815i	$-0.983956\pi$
$113$	−9.30051	−	11.0839i	−0.874918	−	1.04269i	0.123812	−	0.992306i	$-0.460488\pi$
$114$		0			0
$115$	0.679501	+	1.86691i	0.0633638	+	0.174091i
$116$	−7.12665	−	12.1078i	−0.661693	−	1.12418i
$117$		0			0
$118$	1.61832	+	5.93979i	0.148978	+	0.546802i
$119$	−0.920846	−	0.772682i	−0.0844138	−	0.0708316i
$120$		0			0
$121$	−1.90983	−	10.8312i	−0.173621	−	0.984653i
$122$	0.884054	−	10.6180i	0.0800385	−	0.961311i
$123$		0			0
$124$	6.72831	−	2.51308i	0.604221	−	0.225682i
$125$	−2.59533	+	1.49841i	−0.232133	+	0.134022i
$126$		0			0
$127$	7.70348	+	4.44760i	0.683573	+	0.394661i	0.801200	−	0.598397i	$-0.204195\pi$
$127$	7.70348	+	4.44760i	0.683573	+	0.394661i	−0.117627	+	0.993058i	$0.537529\pi$
$128$	−1.31681	−	11.2368i	−0.116390	−	0.993204i
$129$		0			0
$130$	0.787569	+	1.67060i	0.0690744	+	0.146521i
$131$	18.2616	+	6.64668i	1.59552	+	0.580723i	0.978505	−	0.206224i	$-0.0661176\pi$
$131$	18.2616	+	6.64668i	1.59552	+	0.580723i	0.617020	+	0.786948i	$0.288340\pi$
$132$		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	$-0.217040\pi$
$137$	15.1042	+	2.66328i	1.29044	+	0.227540i	0.514033	+	0.857770i	$0.328151\pi$
$138$		0			0
$139$	−3.05591	+	8.39605i	−0.259199	+	0.712144i	0.740018	+	0.672587i	$0.234817\pi$
$139$	−3.05591	+	8.39605i	−0.259199	+	0.712144i	−0.999217	+	0.0395570i	$0.987405\pi$
$140$	−0.288775	+	0.0534227i	−0.0244059	+	0.00451504i
$141$		0			0
$142$	−4.75814	+	0.436420i	−0.399294	+	0.0366235i
$143$	0.0898857	−	0.155687i	0.00751662	−	0.0130192i
$144$		0			0
$145$	−1.06231	−	1.83998i	−0.0882203	−	0.152802i
$146$	−0.514868	−	0.728776i	−0.0426108	−	0.0603139i
$147$		0			0
$148$	−4.49074	+	12.6682i	−0.369137	+	1.04132i
$149$	−1.69578	+	0.299012i	−0.138924	+	0.0244960i	−0.242678	−	0.970107i	$-0.578026\pi$
$149$	−1.69578	+	0.299012i	−0.138924	+	0.0244960i	0.103754	+	0.994603i	$0.466915\pi$
$150$		0			0
$151$	0.387667	−	0.462003i	0.0315479	−	0.0375973i	−0.750040	−	0.661393i	$-0.769966\pi$
$151$	0.387667	−	0.462003i	0.0315479	−	0.0375973i	0.781588	+	0.623795i	$0.214410\pi$
$152$	20.7417	+	5.27866i	1.68238	+	0.428155i
$153$		0			0
$154$	0.0202972	+	0.0201275i	0.00163560	+	0.00162192i
$155$	1.02064	−	0.371484i	0.0819800	−	0.0298383i
$156$		0			0
$157$	−7.94651	+	6.66791i	−0.634201	+	0.532157i	−0.902231	−	0.431253i	$-0.858072\pi$
$157$	−7.94651	+	6.66791i	−0.634201	+	0.532157i	0.268031	+	0.963410i	$0.413627\pi$
$158$	−2.44107	+	3.51755i	−0.194201	+	0.279841i
$159$		0			0
$160$	−0.184858	−	1.70090i	−0.0146143	−	0.134468i
$161$		−	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	$0.928285\pi$
$164$	9.75769	+	8.04903i	0.761947	+	0.628523i
$165$		0			0
$166$	−6.68975	−	4.64248i	−0.519225	−	0.360326i
$167$	4.02217	−	3.37500i	0.311245	−	0.261165i	−0.473761	−	0.880653i	$-0.657104\pi$
$167$	4.02217	−	3.37500i	0.311245	−	0.261165i	0.785006	+	0.619488i	$0.212660\pi$
$168$		0			0
$169$	−5.30479	+	1.93079i	−0.408061	+	0.148522i
$170$	0.745712	−	0.752000i	0.0571935	−	0.0576758i
$171$		0			0
$172$	4.83733	−	0.0406182i	0.368843	−	0.00309711i
$173$	0.891706	−	1.06269i	0.0677952	−	0.0807951i	−0.731081	−	0.682291i	$-0.760984\pi$
$173$	0.891706	−	1.06269i	0.0677952	−	0.0807951i	0.798876	+	0.601496i	$0.205428\pi$
$174$		0			0
$175$	2.34686	−	0.413814i	0.177406	−	0.0312814i
$176$	−0.125755	+	0.109172i	−0.00947914	+	0.00822911i
$177$		0			0
$178$	12.0105	−	8.48520i	0.900223	−	0.635992i
$179$	5.77179	+	9.99703i	0.431403	+	0.747213i	0.996994	−	0.0774732i	$-0.0246852\pi$
$179$	5.77179	+	9.99703i	0.431403	+	0.747213i	−0.565591	+	0.824686i	$0.691352\pi$
$180$		0			0
$181$	8.57298	−	14.8488i	0.637225	−	1.10371i	−0.348814	−	0.937192i	$-0.613416\pi$
$181$	8.57298	−	14.8488i	0.637225	−	1.10371i	0.986039	−	0.166514i	$-0.0532510\pi$
$182$	−0.270789	−	2.95232i	−0.0200722	−	0.218841i
$183$		0			0
$184$	18.5276	+	1.38606i	1.36587	+	0.102182i
$185$	−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	−0.684623	−	0.728898i	$-0.740033\pi$
$191$	2.87475	−	16.3035i	0.208010	−	1.17968i	0.892633	−	0.450785i	$-0.148856\pi$
$192$		0			0
$193$	8.27219	+	3.01083i	0.595445	+	0.216724i	0.622123	−	0.782920i	$-0.286271\pi$
$193$	8.27219	+	3.01083i	0.595445	+	0.216724i	−0.0266776	+	0.999644i	$0.508493\pi$
$194$	−4.26126	+	2.00888i	−0.305941	+	0.144229i
$195$		0			0
$196$	−13.3423	−	2.23726i	−0.953023	−	0.159805i
$197$	−10.8232	−	6.24879i	−0.771122	−	0.445208i	0.0621526	−	0.998067i	$-0.480203\pi$
$197$	−10.8232	−	6.24879i	−0.771122	−	0.445208i	−0.833275	+	0.552859i	$0.813537\pi$
$198$		0			0
$199$	3.88531	−	2.24318i	0.275422	−	0.159015i	−0.355927	−	0.934514i	$-0.615835\pi$
$199$	3.88531	−	2.24318i	0.275422	−	0.159015i	0.631349	+	0.775499i	$0.282501\pi$
$200$	1.38411	+	13.8142i	0.0978716	+	0.976814i
$201$		0			0
$202$	−23.5355	−	1.95956i	−1.65595	−	0.137874i
$203$	0.592221	+	3.35865i	0.0415658	+	0.235731i
$204$		0			0
$205$	1.46533	+	1.22956i	0.102343	+	0.0858761i
$206$	−21.6852	+	5.90821i	−1.51088	+	0.411644i
$207$		0			0
$208$	17.2696	−	0.290040i	1.19743	−	0.0201107i
$209$	−0.107749	−	0.296039i	−0.00745319	−	0.0204775i
$210$		0			0
$211$	−14.4269	−	17.1933i	−0.993188	−	1.18363i	−0.982985	−	0.183687i	$-0.941197\pi$
$211$	−14.4269	−	17.1933i	−0.993188	−	1.18363i	−0.0102029	−	0.999948i	$-0.503248\pi$
$212$	15.0724	−	12.8645i	1.03518	−	0.883536i
$213$		0			0
$214$	0.593245	−	1.28629i	0.0405534	−	0.0879290i
$215$	0.731549			0.0498912
$216$		0			0
$217$	−1.74349			−0.118356
$218$	4.30366	−	9.33130i	0.291480	−	0.631995i
$219$		0			0
$220$	−0.0191552	+	0.0163492i	−0.00129144	+	0.00110226i
$221$	6.87228	+	8.19006i	0.462279	+	0.550923i
$222$		0			0
$223$	−6.26467	−	17.2121i	−0.419514	−	1.15260i	−0.951982	−	0.306154i	$-0.900958\pi$
$223$	−6.26467	−	17.2121i	−0.419514	−	1.15260i	0.532468	−	0.846450i	$-0.321265\pi$
$224$	−0.654974	+	2.66712i	−0.0437623	+	0.178205i
$225$		0			0
$226$	−19.7426	+	5.37896i	−1.31326	+	0.357803i
$227$	15.0169	+	12.6007i	0.996709	+	0.836338i	0.986525	−	0.163610i	$-0.0523138\pi$
$227$	15.0169	+	12.6007i	0.996709	+	0.836338i	0.0101841	+	0.999948i	$0.496758\pi$
$228$		0			0
$229$	0.984254	+	5.58198i	0.0650413	+	0.368868i	0.999904	+	0.0138580i	$0.00441128\pi$
$229$	0.984254	+	5.58198i	0.0650413	+	0.368868i	−0.934863	+	0.355010i	$0.884478\pi$
$230$	2.79997	+	0.233125i	0.184625	+	0.0153718i
$231$		0			0
$232$	−19.7700	+	1.98084i	−1.29796	+	0.130049i
$233$	6.50499	−	3.75566i	0.426156	−	0.246041i	−0.271552	−	0.962424i	$-0.587537\pi$
$233$	6.50499	−	3.75566i	0.426156	−	0.246041i	0.697708	+	0.716383i	$0.254203\pi$
$234$		0			0
$235$	1.88406	+	1.08776i	0.122902	+	0.0709577i
$236$	8.58644	+	1.43979i	0.558930	+	0.0937224i
$237$		0			0
$238$	−1.53769	+	0.724912i	−0.0996737	+	0.0469891i
$239$	−6.08140	−	2.21345i	−0.393373	−	0.143176i	0.137758	−	0.990466i	$-0.456010\pi$
$239$	−6.08140	−	2.21345i	−0.393373	−	0.143176i	−0.531131	+	0.847290i	$0.678233\pi$
$240$		0			0
$241$	−0.120498	+	0.683378i	−0.00776195	+	0.0440202i	−0.988443	−	0.151595i	$-0.951559\pi$
$241$	−0.120498	+	0.683378i	−0.00776195	+	0.0440202i	0.980681	+	0.195615i	$0.0626703\pi$
$242$	−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
$248$	0.757760	−	10.1290i	0.0481178	−	0.643195i
$249$		0			0
$250$	0.387102	+	4.22044i	0.0244825	+	0.266924i
$251$	−1.09113	+	1.88989i	−0.0688715	+	0.119289i	−0.898405	−	0.439168i	$-0.855273\pi$
$251$	−1.09113	+	1.88989i	−0.0688715	+	0.119289i	0.829533	+	0.558457i	$0.188607\pi$
$252$		0			0
$253$	−0.136739	−	0.236839i	−0.00859670	−	0.0148899i
$254$	10.2743	−	7.25863i	0.644668	−	0.455447i
$255$		0			0
$256$	−15.2104	−	4.96436i	−0.950648	−	0.310272i
$257$	14.1712	−	2.49877i	0.883977	−	0.155869i	0.286812	−	0.957987i	$-0.407405\pi$
$257$	14.1712	−	2.49877i	0.883977	−	0.155869i	0.597166	+	0.802118i	$0.296294\pi$
$258$		0			0
$259$	2.09720	−	2.49934i	0.130314	−	0.155302i
$260$	2.61187	−	0.0219314i	0.161981	−	0.00136013i
$261$		0			0
$262$	19.3518	−	19.5150i	1.19556	−	1.20564i
$263$	9.62617	−	3.50364i	0.593575	−	0.216044i	−0.0277260	−	0.999616i	$-0.508827\pi$
$263$	9.62617	−	3.50364i	0.593575	−	0.216044i	0.621301	+	0.783572i	$0.286604\pi$
$264$		0			0
$265$	2.29558	−	1.92622i	0.141016	−	0.118327i
$266$	−4.26836	−	2.96211i	−0.261710	−	0.181619i
$267$		0			0
$268$	−17.1851	−	14.1758i	−1.04974	−	0.865925i
$269$		−	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	$0.967736\pi$
$272$	−3.54316	−	9.24849i	−0.214836	−	0.560772i
$273$		0			0
$274$	12.3662	−	17.8196i	0.747072	−	1.07652i
$275$	0.156546	−	0.131358i	0.00944007	−	0.00792116i
$276$		0			0
$277$	−3.92367	+	1.42810i	−0.235750	+	0.0858061i	−0.457194	−	0.889367i	$-0.651145\pi$
$277$	−3.92367	+	1.42810i	−0.235750	+	0.0858061i	0.221443	+	0.975173i	$0.428923\pi$
$278$	8.97233	+	8.89730i	0.538124	+	0.533625i
$279$		0			0
$280$	−0.102431	+	0.402489i	−0.00612145	+	0.0240533i
$281$	−12.6165	+	15.0357i	−0.752635	+	0.896955i	−0.997358	−	0.0726377i	$-0.976858\pi$
$281$	−12.6165	+	15.0357i	−0.752635	+	0.896955i	0.244724	+	0.969593i	$0.421303\pi$
$282$		0			0
$283$	15.1640	−	2.67383i	0.901407	−	0.158942i	0.296308	−	0.955092i	$-0.404245\pi$
$283$	15.1640	−	2.67383i	0.901407	−	0.158942i	0.605099	+	0.796150i	$0.293133\pi$
$284$	−2.25772	+	6.36893i	−0.133971	+	0.377927i
$285$		0			0
$286$	−0.146696	−	0.207643i	−0.00867433	−	0.0122782i
$287$	−1.53526	−	2.65916i	−0.0906238	−	0.156965i
$288$		0			0
$289$	−5.43473	+	9.41323i	−0.319690	+	0.553720i
$290$	−2.99212	+	0.274439i	−0.175703	+	0.0161156i
$291$		0			0
$292$	−1.24085	+	0.229555i	−0.0726153	+	0.0134337i
$293$	6.36906	−	17.4989i	0.372085	−	1.02229i	−0.602469	−	0.798142i	$-0.705816\pi$
$293$	6.36906	−	17.4989i	0.372085	−	1.02229i	0.974554	−	0.224152i	$-0.0719613\pi$
$294$		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
$302$	−0.363700	−	0.771484i	−0.0209286	−	0.0443939i
$303$		0			0
$304$	19.0639	−	23.5103i	1.09339	−	1.34841i
$305$	−1.97339	−	1.13934i	−0.112996	−	0.0652382i
$306$		0			0
$307$	−17.7533	+	10.2499i	−1.01323	+	0.584990i	−0.912136	−	0.409887i	$-0.865568\pi$
$307$	−17.7533	+	10.2499i	−1.01323	+	0.584990i	−0.101096	+	0.994877i	$0.532235\pi$
$308$	0.0378697	−	0.0141447i	0.00215783	−	0.000805966i
$309$		0			0
$310$	0.127449	−	1.53075i	0.00723864	−	0.0869405i
$311$	−3.47790	−	19.7241i	−0.197213	−	1.11845i	−0.909231	−	0.416292i	$-0.863330\pi$
$311$	−3.47790	−	19.7241i	−0.197213	−	1.11845i	0.712018	−	0.702161i	$-0.247782\pi$
$312$		0			0
$313$	−13.5141	−	11.3397i	−0.763863	−	0.640957i	0.175266	−	0.984521i	$-0.443921\pi$
$313$	−13.5141	−	11.3397i	−0.763863	−	0.640957i	−0.939129	+	0.343564i	$0.888366\pi$
$314$	3.85640	+	14.1543i	0.217629	+	0.798774i
$315$		0			0
$316$	3.07146	+	5.21825i	0.172783	+	0.293549i
$317$	1.46957	+	4.03761i	0.0825392	+	0.226775i	0.974096	−	0.226134i	$-0.0726087\pi$
$317$	1.46957	+	4.03761i	0.0825392	+	0.226775i	−0.891557	+	0.452908i	$0.850386\pi$
$318$		0			0
$319$	0.187990	+	0.224037i	0.0105254	+	0.0125437i
$320$	−2.29380	−	0.770020i	−0.128227	−	0.0430455i
$321$		0			0
$322$	−4.09549	−	1.88887i	−0.228233	−	0.105262i
$323$	18.7360			1.04250
$324$		0			0
$325$	−21.1951			−1.17569
$326$	7.32552	+	3.37858i	0.405723	+	0.187122i
$327$		0			0
$328$	16.1160	−	7.76360i	0.889857	−	0.428673i
$329$	−2.24472	−	2.67515i	−0.123755	−	0.147486i
$330$		0			0
$331$	6.88468	+	18.9155i	0.378416	+	1.03969i	0.972013	+	0.234927i	$0.0754852\pi$
$331$	6.88468	+	18.9155i	0.378416	+	1.03969i	−0.593597	+	0.804763i	$0.702293\pi$
$332$	−9.92416	+	5.84137i	−0.544659	+	0.320587i
$333$		0			0
$334$	−1.95194	−	7.16428i	−0.106805	−	0.392012i
$335$	−2.58072	−	2.16548i	−0.141000	−	0.118313i
$336$		0			0
$337$	2.29367	+	13.0081i	0.124944	+	0.708595i	0.981341	+	0.192276i	$0.0615869\pi$
$337$	2.29367	+	13.0081i	0.124944	+	0.708595i	−0.856397	+	0.516319i	$0.827302\pi$
$338$	−0.662418	+	7.95605i	−0.0360308	+	0.432752i
$339$		0			0
$340$	−0.524051	−	1.40305i	−0.0284207	−	0.0760911i
$341$	−0.129480	+	0.0747552i	−0.00701173	+	0.00404822i
$342$		0			0
$343$	5.78720	+	3.34124i	0.312480	+	0.180410i
$344$	2.81292	−	6.23620i	0.151662	−	0.336234i
$345$		0			0
$346$	−0.836578	−	1.77456i	−0.0449747	−	0.0954008i
$347$	−16.7772	−	6.10639i	−0.900645	−	0.327808i	−0.150134	−	0.988666i	$-0.547971\pi$
$347$	−16.7772	−	6.10639i	−0.900645	−	0.327808i	−0.750511	+	0.660858i	$0.770193\pi$
$348$		0			0
$349$	−2.27001	+	12.8739i	−0.121511	+	0.689123i	0.861808	+	0.507234i	$0.169332\pi$
$349$	−2.27001	+	12.8739i	−0.121511	+	0.689123i	−0.983319	+	0.181889i	$0.941779\pi$
$350$	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	$-0.638208\pi$
$353$	−21.1607	−	3.73120i	−1.12627	−	0.198592i	−0.705592	+	0.708618i	$0.749319\pi$
$354$		0			0
$355$	−0.349499	+	0.960240i	−0.0185495	+	0.0509642i
$356$	−3.78314	−	20.4496i	−0.200506	−	1.08383i
$357$		0			0
$358$	16.2568	−	1.49109i	0.859200	−	0.0788065i
$359$	9.46695	−	16.3972i	0.499647	−	0.865413i	−0.500353	−	0.865821i	$-0.666797\pi$
$359$	9.46695	−	16.3972i	0.499647	−	0.865413i	1.00000		0.000407927i	$0.000129847\pi$
$360$		0			0
$361$	19.1302	+	33.1344i	1.00685	+	1.74392i
$362$	−13.9914	−	19.8043i	−0.735371	−	1.04089i
$363$		0			0
$364$	−3.95179	−	1.40087i	−0.207130	−	0.0734255i
$365$	−0.187932	+	0.0331375i	−0.00983682	+	0.00173450i
$366$		0			0
$367$	15.3111	−	18.2471i	0.799233	−	0.952489i	−0.200396	−	0.979715i	$-0.564223\pi$
$367$	15.3111	−	18.2471i	0.799233	−	0.952489i	0.999629	+	0.0272258i	$0.00866731\pi$
$368$	12.7536	−	22.9724i	0.664828	−	1.19752i
$369$		0			0
$370$	2.04106	+	2.02400i	0.106110	+	0.105223i
$371$	−4.52018	+	1.64521i	−0.234676	+	0.0854151i
$372$		0			0
$373$	−16.6039	+	13.9323i	−0.859717	+	0.721388i	−0.961907	−	0.273377i	$-0.911859\pi$
$373$	−16.6039	+	13.9323i	−0.859717	+	0.721388i	0.102190	+	0.994765i	$0.467415\pi$
$374$	−0.0831144	+	0.119767i	−0.00429774	+	0.00619299i
$375$		0			0
$376$	16.5173	−	11.8783i	0.851813	−	0.612578i
$377$		−	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	$-0.332662\pi$
$380$	2.91269	−	3.53100i	0.149418	−	0.181136i
$381$		0			0
$382$	−19.2345	−	13.3482i	−0.984123	−	0.682951i
$383$	1.15170	−	0.966388i	0.0588490	−	0.0493801i	−0.612889	−	0.790169i	$-0.709993\pi$
$383$	1.15170	−	0.966388i	0.0588490	−	0.0493801i	0.671738	+	0.740789i	$0.265548\pi$
$384$		0			0
$385$	0.00574459	−	0.00209086i	0.000292772	−	0.000106560i
$386$	8.76604	−	8.83996i	0.446180	−	0.449942i
$387$		0			0
$388$	0.0559413	+	6.66219i	0.00283999	+	0.338222i
$389$	2.48223	−	2.95820i	0.125854	−	0.149987i	−0.699438	−	0.714693i	$-0.746566\pi$
$389$	2.48223	−	2.95820i	0.125854	−	0.149987i	0.825292	+	0.564707i	$0.191011\pi$
$390$		0			0
$391$	16.0172	−	2.82426i	0.810024	−	0.142829i
$392$	−10.7756	+	15.8092i	−0.544249	+	0.798487i
$393$		0			0
$394$	−14.4352	+	10.1982i	−0.727235	+	0.513779i
$395$	0.457839	+	0.793000i	0.0230364	+	0.0399002i
$396$		0			0
$397$	−9.80431	+	16.9816i	−0.492064	+	0.852280i	−0.999958	−	0.00913954i	$-0.997091\pi$
$397$	−9.80431	+	16.9816i	−0.492064	+	0.852280i	0.507894	+	0.861419i	$0.330424\pi$
$398$	−0.579506	−	6.31816i	−0.0290480	−	0.316701i
$399$		0			0
$400$	18.5602	+	6.40449i	0.928009	+	0.320224i
$401$	−7.41930	+	20.3844i	−0.370502	+	1.01795i	0.604666	+	0.796479i	$0.293307\pi$
$401$	−7.41930	+	20.3844i	−0.370502	+	1.01795i	−0.975168	+	0.221467i	$0.928915\pi$
$402$		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	0.584635	−	0.811297i	$-0.301238\pi$
$409$	10.3343	+	3.76139i	0.510999	+	0.185989i	−0.0736354	+	0.997285i	$0.523460\pi$
$410$	2.44691	−	1.15354i	0.120844	−	0.0569694i
$411$		0			0
$412$	−5.25644	+	31.3477i	−0.258966	+	1.54439i
$413$	−1.83029	−	1.05672i	−0.0900626	−	0.0519976i
$414$		0			0
$415$	−1.50814	+	0.870727i	−0.0740319	+	0.0427423i
$416$	9.85608	−	22.3496i	0.483234	−	1.09578i
$417$		0			0
$418$	−0.443995	−	0.0369669i	−0.0217165	−	0.00180811i
$419$	4.20531	+	23.8495i	0.205443	+	1.16512i	0.896741	+	0.442555i	$0.145928\pi$
$419$	4.20531	+	23.8495i	0.205443	+	1.16512i	−0.691298	+	0.722569i	$0.742961\pi$
$420$		0			0
$421$	28.0468	+	23.5341i	1.36692	+	1.14698i	0.973777	+	0.227503i	$0.0730561\pi$
$421$	28.0468	+	23.5341i	1.36692	+	1.14698i	0.393141	+	0.919478i	$0.371388\pi$
$422$	−30.6247	+	8.34381i	−1.49078	+	0.406170i
$423$		0			0
$424$	−7.59351	−	26.9756i	−0.368773	−	1.31005i
$425$	4.15673	+	11.4205i	0.201631	+	0.553977i
$426$		0			0
$427$	2.35115	+	2.80199i	0.113780	+	0.135598i
$428$	−1.30050	−	1.52370i	−0.0628619	−	0.0736510i
$429$		0			0
$430$	0.433287	−	0.939463i	0.0208949	−	0.0453049i
$431$	−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	$0.550404\pi$
$434$	−1.03264	+	2.23901i	−0.0495685	+	0.107476i
$435$		0			0
$436$	−9.43436	−	11.0536i	−0.451824	−	0.529372i
$437$	31.9507	+	38.0773i	1.52841	+	1.82149i
$438$		0			0
$439$	−0.624030	−	1.71451i	−0.0297833	−	0.0818291i	0.923910	−	0.382610i	$-0.124975\pi$
$439$	−0.624030	−	1.71451i	−0.0297833	−	0.0818291i	−0.953693	+	0.300781i	$0.902753\pi$
$440$	0.00965041	+	0.0342827i	0.000460065	+	0.00163437i
$441$		0			0
$442$	14.5881	−	3.97459i	0.693886	−	0.189052i
$443$	−1.33656	−	1.12150i	−0.0635017	−	0.0532843i	0.610484	−	0.792028i	$-0.290975\pi$
$443$	−1.33656	−	1.12150i	−0.0635017	−	0.0532843i	−0.673986	+	0.738744i	$0.735419\pi$
$444$		0			0
$445$	−0.546118	−	3.09719i	−0.0258885	−	0.146821i
$446$	−25.8144	−	2.14930i	−1.22235	−	0.101772i
$447$		0			0
$448$	3.03722	+	2.42083i	0.143495	+	0.114373i
$449$	8.00158	−	4.61971i	0.377618	−	0.218018i	−0.299164	−	0.954202i	$-0.596708\pi$
$449$	8.00158	−	4.61971i	0.377618	−	0.218018i	0.676781	+	0.736184i	$0.263374\pi$
$450$		0			0
$451$	−0.228032	−	0.131654i	−0.0107376	−	0.00619937i
$452$	−4.78558	+	28.5396i	−0.225095	+	1.34239i
$453$		0			0
$454$	25.0763	−	11.8217i	1.17689	−	0.554819i
$455$	−0.595808	−	0.216857i	−0.0279319	−	0.0101664i
$456$		0			0
$457$	−4.78964	+	27.1634i	−0.224050	+	1.27065i	0.640443	+	0.768006i	$0.278751\pi$
$457$	−4.78964	+	27.1634i	−0.224050	+	1.27065i	−0.864493	+	0.502645i	$0.832360\pi$
$458$	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	$-0.604847\pi$
$461$	−20.4199	−	3.60059i	−0.951052	−	0.167696i	−0.627589	+	0.778545i	$0.715958\pi$
$462$		0			0
$463$	−3.27860	+	9.00787i	−0.152369	+	0.418631i	−0.992268	−	0.124112i	$-0.960392\pi$
$463$	−3.27860	+	9.00787i	−0.152369	+	0.418631i	0.839899	+	0.542743i	$0.182614\pi$
$464$	−9.16565	+	26.5620i	−0.425505	+	1.23311i
$465$		0			0
$466$	−0.970240	−	10.5782i	−0.0449455	−	0.490026i
$467$	−8.74737	+	15.1509i	−0.404780	+	0.701099i	−0.994296	−	0.106657i	$-0.965985\pi$
$467$	−8.74737	+	15.1509i	−0.404780	+	0.701099i	0.589516	+	0.807757i	$0.299319\pi$
$468$		0			0
$469$	2.70388	+	4.68326i	0.124854	+	0.216253i
$470$	2.51281	−	1.77526i	0.115907	−	0.0818866i
$471$		0			0
$472$	6.93463	−	10.1740i	0.319192	−	0.468298i
$473$	−0.0991696	+	0.0174863i	−0.00455982	+	0.000804020i
$474$		0			0
$475$	−23.8751	+	28.4533i	−1.09547	+	1.30552i
$476$	0.0201866	+	2.40407i	0.000925251	+	0.110191i
$477$		0			0
$478$	−6.44446	+	6.49880i	−0.294763	+	0.297248i
$479$	−24.6167	+	8.95976i	−1.12477	+	0.409382i	−0.836390	−	0.548135i	$-0.815338\pi$
$479$	−24.6167	+	8.95976i	−1.12477	+	0.409382i	−0.288378	+	0.957517i	$0.593116\pi$
$480$		0			0
$481$	−22.2293	+	18.6526i	−1.01357	+	0.850486i
$482$	0.806231	+	0.559500i	0.0367228	+	0.0254845i
$483$		0			0
$484$	−13.9971	+	16.9684i	−0.636233	+	0.771293i
$485$			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	$0.948501\pi$
$488$	−17.3004	+	12.4415i	−0.783153	+	0.563201i
$489$		0			0
$490$	−1.64955	+	2.37698i	−0.0745192	+	0.107381i
$491$	15.1317	−	12.6970i	0.682883	−	0.573006i	−0.233965	−	0.972245i	$-0.575170\pi$
$491$	15.1317	−	12.6970i	0.682883	−	0.573006i	0.916847	+	0.399239i	$0.130726\pi$
$492$		0			0
$493$	−16.3442	+	5.94882i	−0.736108	+	0.267921i
$494$	32.8115	+	32.5372i	1.47626	+	1.46392i
$495$		0			0
$496$	−12.5590	−	6.97241i	−0.563916	−	0.313071i
$497$	1.05437	−	1.25655i	0.0472949	−	0.0563639i
$498$		0			0
$499$	38.9262	−	6.86374i	1.74258	−	0.307263i	0.790350	−	0.612655i	$-0.209899\pi$
$499$	38.9262	−	6.86374i	1.74258	−	0.307263i	0.952227	+	0.305392i	$0.0987875\pi$
$500$	5.64921	+	2.00259i	0.252640	+	0.0895585i
$501$		0			0
$502$	1.78076	+	2.52060i	0.0794792	+	0.112500i
$503$	−19.5426	−	33.8489i	−0.871364	−	1.50925i	−0.860587	−	0.509304i	$-0.829903\pi$
$503$	−19.5426	−	33.8489i	−0.871364	−	1.50925i	−0.0107769	−	0.999942i	$-0.503430\pi$
$504$		0			0
$505$	−2.52541	+	4.37413i	−0.112379	+	0.194646i
$506$	−0.385139	+	0.0353252i	−0.0171215	+	0.00157040i
$507$		0			0
$508$	−3.23627	−	17.4936i	−0.143586	−	0.776152i
$509$	−5.04413	+	13.8586i	−0.223577	+	0.614273i	−0.999870	−	0.0160989i	$-0.994875\pi$
$509$	−5.04413	+	13.8586i	−0.223577	+	0.614273i	0.776293	+	0.630372i	$0.217098\pi$
$510$		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
$518$	−1.96754	−	4.17357i	−0.0864489	−	0.183376i
$519$		0			0
$520$	1.51881	−	3.36718i	0.0666042	−	0.147661i
$521$	−10.1293	−	5.84816i	−0.443773	−	0.256213i	0.261424	−	0.965224i	$-0.415808\pi$
$521$	−10.1293	−	5.84816i	−0.443773	−	0.256213i	−0.705197	+	0.709012i	$0.749141\pi$
$522$		0			0
$523$	6.89969	−	3.98354i	0.301702	−	0.174188i	−0.341505	−	0.939880i	$-0.610937\pi$
$523$	6.89969	−	3.98354i	0.301702	−	0.174188i	0.643207	+	0.765692i	$0.277603\pi$
$524$	−13.5996	−	36.4103i	−0.594100	−	1.59059i
$525$		0			0
$526$	1.20204	−	14.4372i	0.0524113	−	0.629491i
$527$	−1.54403	−	8.75661i	−0.0672588	−	0.381444i
$528$		0			0
$529$	15.4351	+	12.9515i	0.671089	+	0.563111i
$530$	−1.11403	−	4.08888i	−0.0483905	−	0.177610i
$531$		0			0
$532$	−6.33207	+	3.72706i	−0.274530	+	0.161589i
$533$	9.34038	+	25.6625i	0.404577	+	1.11157i
$534$		0			0
$535$	−0.194726	−	0.232065i	−0.00841872	−	0.0100330i
$536$	−28.3832	+	13.6731i	−1.22597	+	0.590588i
$537$		0			0
$538$	−4.04811	−	1.86702i	−0.174527	−	0.0804928i
$539$	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	$0.442120\pi$
$542$	4.27836	+	1.97321i	0.183772	+	0.0847566i
$543$		0			0
$544$	−13.9756	−	0.927588i	−0.599198	−	0.0397700i
$545$	−1.41262	−	1.68350i	−0.0605101	−	0.0721132i
$546$		0			0
$547$	5.97901	+	16.4272i	0.255644	+	0.702376i	0.999424	+	0.0339508i	$0.0108090\pi$
$547$	5.97901	+	16.4272i	0.255644	+	0.702376i	−0.743780	+	0.668425i	$0.766969\pi$
$548$	−15.5597	−	26.4351i	−0.664679	−	1.12925i
$549$		0			0
$550$	−0.0759708	−	0.278839i	−0.00323941	−	0.0118897i
$551$	−40.7203	−	34.1684i	−1.73474	−	1.45562i
$552$		0			0
$553$	−0.255237	−	1.44752i	−0.0108538	−	0.0615549i
$554$	−0.489955	+	5.88466i	−0.0208162	+	0.250015i
$555$		0			0
$556$	16.7402	−	6.25261i	0.709943	−	0.265170i
$557$	0.688812	−	0.397686i	0.0291859	−	0.0168505i	−0.485336	−	0.874328i	$-0.661303\pi$
$557$	0.688812	−	0.397686i	0.0291859	−	0.0168505i	0.514522	+	0.857477i	$0.327969\pi$
$558$		0			0
$559$	9.04493	+	5.22209i	0.382560	+	0.220871i
$560$	0.456212	+	0.369932i	0.0192785	+	0.0156325i
$561$		0			0
$562$	11.8365	+	25.1076i	0.499291	+	1.05910i
$563$	5.88781	+	2.14299i	0.248142	+	0.0903162i	0.463097	−	0.886308i	$-0.346738\pi$
$563$	5.88781	+	2.14299i	0.248142	+	0.0903162i	−0.214955	+	0.976624i	$0.568960\pi$
$564$		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	$-0.480681\pi$
$569$	−5.33693	−	0.941045i	−0.223736	−	0.0394507i	−0.284392	+	0.958708i	$0.591792\pi$
$570$		0			0
$571$	10.4263	−	28.6461i	0.436328	−	1.19880i	−0.505535	−	0.862806i	$-0.668705\pi$
$571$	10.4263	−	28.6461i	0.436328	−	1.19880i	0.941863	−	0.335996i	$-0.109073\pi$
$572$	−0.353544	+	0.0654048i	−0.0147824	+	0.00273471i
$573$		0			0
$574$	−4.32423	+	0.396621i	−0.180490	+	0.0165547i
$575$	−16.1215	+	27.9233i	−0.672315	+	1.16448i
$576$		0			0
$577$	−9.67484	−	16.7573i	−0.402769	−	0.697616i	0.591290	−	0.806459i	$-0.298619\pi$
$577$	−9.67484	−	16.7573i	−0.402769	−	0.697616i	−0.994059	+	0.108843i	$0.965286\pi$
$578$	8.86966	+	12.5547i	0.368929	+	0.522205i
$579$		0			0
$580$	−1.41975	+	4.00505i	−0.0589520	+	0.166301i
$581$	2.75293	−	0.485415i	0.114211	−	0.0201384i
$582$		0			0
$583$	−0.265149	+	0.315992i	−0.0109813	+	0.0130871i
$584$	−0.440143	+	1.72948i	−0.0182132	+	0.0715662i
$585$		0			0
$586$	−18.6999	−	18.5436i	−0.772486	−	0.766027i
$587$	40.6493	−	14.7951i	1.67778	−	0.610660i	0.684773	−	0.728756i	$-0.259901\pi$
$587$	40.6493	−	14.7951i	1.67778	−	0.610660i	0.993002	+	0.118096i	$0.0376791\pi$
$588$		0			0
$589$	20.8169	−	17.4675i	0.857746	−	0.719734i
$590$	1.06157	−	1.52971i	0.0437041	−	0.0629770i
$591$		0			0
$592$	25.1021	−	9.61678i	1.03169	−	0.395247i
$593$			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
$596$	2.65666	+	2.19145i	0.108821	+	0.0897654i
$597$		0			0
$598$	32.9549	+	22.8697i	1.34763	+	0.935211i
$599$	−28.7904	+	24.1580i	−1.17634	+	0.987070i	−0.176347	+	0.984328i	$0.556428\pi$
$599$	−28.7904	+	24.1580i	−1.17634	+	0.987070i	−0.999996	+	0.00274159i	$0.999127\pi$
$600$		0			0
$601$	−9.38452	+	3.41569i	−0.382802	+	0.139329i	−0.526251	−	0.850329i	$-0.676403\pi$
$601$	−9.38452	+	3.41569i	−0.382802	+	0.139329i	0.143449	+	0.989658i	$0.454181\pi$
$602$	−1.16935	+	1.17921i	−0.0476591	+	0.0480609i
$603$		0			0
$604$	−1.20616	+	0.0101279i	−0.0490781	+	0.000412100i
$605$	−2.13818	+	2.54819i	−0.0869294	+	0.103598i
$606$		0			0
$607$	−28.5897	+	5.04113i	−1.16042	+	0.204613i	−0.720520	−	0.693434i	$-0.756097\pi$
$607$	−28.5897	+	5.04113i	−1.16042	+	0.204613i	−0.439899	+	0.898047i	$0.644986\pi$
$608$	−18.9008	−	38.4069i	−0.766529	−	1.55761i
$609$		0			0
$610$	−2.63196	+	1.85943i	−0.106565	+	0.0752862i
$611$	15.5298	+	26.8983i	0.628266	+	1.08819i
$612$		0			0
$613$	−10.6465	+	18.4402i	−0.430007	+	0.744794i	−0.996873	−	0.0790155i	$-0.974822\pi$
$613$	−10.6465	+	18.4402i	−0.430007	+	0.744794i	0.566866	+	0.823810i	$0.308156\pi$
$614$	2.64796	+	28.8698i	0.106863	+	1.16509i
$615$		0			0
$616$	0.00426498	−	0.0570103i	0.000171841	−	0.00229701i
$617$	0.850396	−	2.33644i	0.0342357	−	0.0940617i	−0.921397	−	0.388622i	$-0.872951\pi$
$617$	0.850396	−	2.33644i	0.0342357	−	0.0940617i	0.955633	+	0.294561i	$0.0951733\pi$
$618$		0			0
$619$	−13.1393	−	2.31682i	−0.528114	−	0.0931207i	−0.0967674	−	0.995307i	$-0.530850\pi$
$619$	−13.1393	−	2.31682i	−0.528114	−	0.0931207i	−0.431347	+	0.902186i	$0.641961\pi$
$620$	−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
$626$	−22.5668	+	10.6386i	−0.901950	+	0.425205i
$627$		0			0
$628$	20.4612	+	3.43097i	0.816491	+	0.136911i
$629$	14.4101	+	8.31969i	0.574570	+	0.331728i
$630$		0			0
$631$	33.1235	−	19.1238i	1.31862	−	0.761308i	0.335117	−	0.942176i	$-0.391224\pi$
$631$	33.1235	−	19.1238i	1.31862	−	0.761308i	0.983507	+	0.180868i	$0.0578908\pi$
$632$	8.52051	−	0.853710i	0.338928	−	0.0339588i
$633$		0			0
$634$	6.05554	+	0.504183i	0.240496	+	0.0200237i
$635$	−0.467175	−	2.64948i	−0.0185393	−	0.105141i
$636$		0			0
$637$	−22.3749	−	18.7747i	−0.886525	−	0.743882i
$638$	0.399055	−	0.108724i	0.0157987	−	0.00430443i
$639$		0			0
$640$	−2.34745	+	2.48965i	−0.0927913	+	0.0984120i
$641$	4.86140	+	13.3566i	0.192014	+	0.527553i	0.997918	−	0.0644923i	$-0.0205428\pi$
$641$	4.86140	+	13.3566i	0.192014	+	0.527553i	−0.805905	+	0.592046i	$0.798321\pi$
$642$		0			0
$643$	−0.409458	−	0.487973i	−0.0161474	−	0.0192438i	0.757910	−	0.652359i	$-0.226220\pi$
$643$	−0.409458	−	0.487973i	−0.0161474	−	0.0192438i	−0.774058	+	0.633115i	$0.781776\pi$
$644$	−4.85140	+	4.14072i	−0.191172	+	0.163167i
$645$		0			0
$646$	11.0971	−	24.0609i	0.436608	−	0.946665i
$647$	−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
$650$	−12.5535	+	27.2189i	−0.492391	+	1.06761i
$651$		0			0
$652$	8.67761	−	7.40642i	0.339841	−	0.290058i
$653$	−20.4733	−	24.3991i	−0.801182	−	0.954811i	0.198498	−	0.980101i	$-0.436394\pi$
$653$	−20.4733	−	24.3991i	−0.801182	−	0.954811i	−0.999680	+	0.0252900i	$0.991949\pi$
$654$		0			0
$655$	−2.01029	−	5.52322i	−0.0785484	−	0.215810i
$656$	−0.424819	−	25.2946i	−0.0165864	−	0.987588i
$657$		0			0
$658$	−4.76497	+	1.29824i	−0.185758	+	0.0506105i
$659$	11.3095	+	9.48984i	0.440557	+	0.369672i	0.835918	−	0.548854i	$-0.184936\pi$
$659$	11.3095	+	9.48984i	0.440557	+	0.369672i	−0.395360	+	0.918526i	$0.629380\pi$
$660$		0			0
$661$	3.47979	+	19.7349i	0.135348	+	0.767598i	0.974617	+	0.223880i	$0.0718725\pi$
$661$	3.47979	+	19.7349i	0.135348	+	0.767598i	−0.839268	+	0.543717i	$0.817016\pi$
$662$	28.3692	+	2.36201i	1.10260	+	0.0918022i
$663$		0			0
$664$	1.62360	+	16.2045i	0.0630080	+	0.628856i
$665$	−0.962265	+	0.555564i	−0.0373150	+	0.0215438i
$666$		0			0
$667$	−39.9619	−	23.0720i	−1.54733	−	0.893352i
$668$	−10.3566	−	1.73661i	−0.400707	−	0.0671913i
$669$		0			0
$670$	−4.30945	+	2.03160i	−0.166489	+	0.0784876i
$671$	0.294748	+	0.107280i	0.0113786	+	0.00414148i
$672$		0			0
$673$	6.03662	−	34.2354i	0.232695	−	1.31968i	−0.614720	−	0.788745i	$-0.710731\pi$
$673$	6.03662	−	34.2354i	0.232695	−	1.31968i	0.847415	−	0.530932i	$-0.178158\pi$
$674$	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	$-0.667904\pi$
$677$	−33.0938	−	5.83534i	−1.27190	−	0.224270i	−0.768537	+	0.639805i	$0.779015\pi$
$678$		0			0
$679$	0.553144	−	1.51975i	0.0212277	−	0.0583227i
$680$	−2.11220	−	0.158015i	−0.0809992	−	0.00605960i
$681$		0			0
$682$	0.0193123	+	0.210556i	0.000739508	+	0.00806260i
$683$	12.3153	−	21.3308i	0.471233	−	0.816200i	−0.528225	−	0.849104i	$-0.677142\pi$
$683$	12.3153	−	21.3308i	0.471233	−	0.816200i	0.999459	+	0.0329044i	$0.0104757\pi$
$684$		0			0
$685$	−2.31937	−	4.01726i	−0.0886185	−	0.153492i
$686$	7.71854	−	5.45301i	0.294695	−	0.208197i
$687$		0			0
$688$	−6.34255	−	7.30600i	−0.241807	−	0.278539i
$689$	42.1329	−	7.42916i	1.60514	−	0.283029i
$690$		0			0
$691$	−9.45010	+	11.2622i	−0.359499	+	0.428434i	−0.915232	−	0.402926i	$-0.867993\pi$
$691$	−9.45010	+	11.2622i	−0.359499	+	0.428434i	0.555733	+	0.831361i	$0.312438\pi$
$692$	−2.77440	+	0.0232961i	−0.105467	+	0.000885586i
$693$		0			0
$694$	−17.7788	+	17.9287i	−0.674873	+	0.680564i
$695$	2.53938	−	0.924260i	0.0963243	−	0.0350592i
$696$		0			0
$697$	11.9959	−	10.0657i	0.454376	−	0.381267i
$698$	15.1883	+	10.5402i	0.574885	+	0.398952i
$699$		0			0
$700$	−3.67665	−	3.03284i	−0.138964	−	0.114631i
$701$		−	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
$704$	0.329356	+	0.0495560i	0.0124131	+	0.00186771i
$705$		0			0
$706$	−17.3248	+	24.9648i	−0.652029	+	0.939564i
$707$	6.21078	−	5.21147i	0.233581	−	0.195997i
$708$		0			0
$709$	36.8919	−	13.4276i	1.38551	−	0.504283i	0.461663	−	0.887056i	$-0.347253\pi$
$709$	36.8919	−	13.4276i	1.38551	−	0.504283i	0.923842	+	0.382773i	$0.125031\pi$
$710$	1.02615	+	1.01757i	0.0385106	+	0.0381886i
$711$		0			0
$712$	−28.5024	−	7.25370i	−1.06817	−	0.271844i
$713$	15.1631	−	18.0707i	0.567863	−	0.676752i
$714$		0			0
$715$	−0.0535457	+	0.00944156i	−0.00200250	+	0.000353094i
$716$	7.71383	−	21.7604i	0.288279	−	0.813223i
$717$		0			0
$718$	−15.4504	−	21.8694i	−0.576603	−	0.816160i
$719$	−0.482259	−	0.835298i	−0.0179852	−	0.0311514i	0.856893	−	0.515495i	$-0.172392\pi$
$719$	−0.482259	−	0.835298i	−0.0179852	−	0.0311514i	−0.874878	+	0.484343i	$0.839059\pi$
$720$		0			0
$721$	3.85790	−	6.68207i	0.143676	−	0.248853i
$722$	53.8821	−	4.94211i	2.00529	−	0.183926i
$723$		0			0
$724$	−33.7198	+	6.23808i	−1.25319	+	0.231836i
$725$	11.7932	−	32.4016i	0.437989	−	1.20337i
$726$		0			0
$727$	−20.6400	−	3.63939i	−0.765495	−	0.134977i	−0.222751	−	0.974875i	$-0.571504\pi$
$727$	−20.6400	−	3.63939i	−0.765495	−	0.134977i	−0.542744	+	0.839898i	$0.682615\pi$
$728$	−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	0.310681	−	0.950514i	$-0.399443\pi$
$733$	−1.68677	−	0.613933i	−0.0623022	−	0.0226761i	−0.372983	+	0.927838i	$0.621665\pi$
$734$	−14.3645	−	30.4702i	−0.530204	−	1.12467i
$735$		0			0
$736$	−21.9476	−	29.9846i	−0.808998	−	1.10525i
$737$	0.401606	+	0.231867i	0.0147934	+	0.00854095i
$738$		0			0
$739$	−17.1448	+	9.89858i	−0.630683	+	0.364125i	−0.781017	−	0.624510i	$-0.785299\pi$
$739$	−17.1448	+	9.89858i	−0.630683	+	0.364125i	0.150333	+	0.988635i	$0.451965\pi$
$740$	3.80813	−	1.42237i	0.139990	−	0.0522874i
$741$		0			0
$742$	−0.564442	+	6.77930i	−0.0207213	+	0.248876i
$743$	−6.72417	−	38.1347i	−0.246686	−	1.39903i	−0.816544	−	0.577283i	$-0.804113\pi$
$743$	−6.72417	−	38.1347i	−0.246686	−	1.39903i	0.569858	−	0.821743i	$-0.306998\pi$
$744$		0			0
$745$	0.398956	+	0.334764i	0.0146166	+	0.0122648i
$746$	8.05778	+	29.5748i	0.295016	+	1.08281i
$747$		0			0
$748$	0.104578	+	0.177673i	0.00382376	+	0.00649635i
$749$	0.166318	+	0.456954i	0.00607712	+	0.0166967i
$750$		0			0
$751$	−14.8195	−	17.6612i	−0.540770	−	0.644465i	0.424590	−	0.905386i	$-0.360418\pi$
$751$	−14.8195	−	17.6612i	−0.540770	−	0.644465i	−0.965360	+	0.260921i	$0.915974\pi$
$752$	−5.47132	−	28.2470i	−0.199518	−	1.03006i
$753$		0			0
$754$	−38.9538	−	17.9658i	−1.41861	−	0.654274i
$755$	−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	$0.293061\pi$
$758$	−43.2500	−	19.9472i	−1.57091	−	0.724515i
$759$		0			0
$760$	−2.80940	−	5.83187i	−0.101908	−	0.211544i
$761$	−10.2052	−	12.1621i	−0.369940	−	0.440877i	0.548673	−	0.836037i	$-0.315133\pi$
$761$	−10.2052	−	12.1621i	−0.369940	−	0.440877i	−0.918612	+	0.395161i	$0.870689\pi$
$762$		0			0
$763$	1.20654	+	3.31494i	0.0436797	+	0.120009i
$764$	−28.5342	+	16.7952i	−1.03233	+	0.607630i
$765$		0			0
$766$	−0.558912	−	2.05140i	−0.0201943	−	0.0741201i
$767$	14.3993	+	12.0825i	0.519930	+	0.436273i
$768$		0			0
$769$	−3.82683	−	21.7030i	−0.137999	−	0.782631i	−0.972724	−	0.231964i	$-0.925485\pi$
$769$	−3.82683	−	21.7030i	−0.137999	−	0.782631i	0.834725	−	0.550666i	$-0.185626\pi$
$770$	0.000717337	−	0.00861565i	2.58510e−5	−	0.000310487i
$771$		0			0
$772$	−6.16036	−	16.4932i	−0.221716	−	0.593604i
$773$	−18.9410	+	10.9356i	−0.681261	+	0.393326i	−0.800330	−	0.599560i	$-0.795342\pi$
$773$	−18.9410	+	10.9356i	−0.681261	+	0.393326i	0.119069	+	0.992886i	$0.462009\pi$
$774$		0			0
$775$	15.2657	+	8.81366i	0.548360	+	0.316596i
$776$	8.58879	+	3.87409i	0.308320	+	0.139072i
$777$		0			0
$778$	−2.32877	−	4.93980i	−0.0834903	−	0.177101i
$779$	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	$-0.869695\pi$
$787$	1.15642	−	3.17723i	0.0412218	−	0.113256i	0.958596	+	0.284771i	$0.0919174\pi$
$788$	4.54689	+	24.5781i	0.161976	+	0.875559i
$789$		0			0
$790$	1.28955	−	0.118279i	0.0458802	−	0.00420816i
$791$	3.51231	−	6.08351i	0.124884	−	0.216305i
$792$		0			0
$793$	−16.2661	−	28.1737i	−0.577625	−	1.00048i
$794$	16.0009	+	22.6487i	0.567852	+	0.803774i
$795$		0			0
$796$	−8.45708	−	2.99795i	−0.299753	−	0.106260i
$797$	−47.1233	+	8.30912i	−1.66919	+	0.294324i	−0.926776	−	0.375613i	$-0.877432\pi$
$797$	−47.1233	+	8.30912i	−1.66919	+	0.294324i	−0.742418	+	0.669937i	$0.766321\pi$
$798$		0			0
$799$	11.4479	−	13.6431i	0.404999	−	0.482659i
$800$	19.2177	−	20.0419i	0.679447	−	0.708588i
$801$		0			0
$802$	21.7835	+	21.6013i	0.769201	+	0.762769i
$803$	0.0246842	−	0.00898432i	0.000871087	−	0.000317050i
$804$		0			0
$805$	−0.738884	+	0.619997i	−0.0260422	+	0.0218520i
$806$	12.5029	−	18.0165i	0.440395	−	0.634603i
$807$		0			0
$808$	27.5774	+	38.3474i	0.970169	+	1.34906i
$809$			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	$0.922321\pi$
$812$	4.34038	−	5.26177i	0.152318	−	0.184652i
$813$		0			0
$814$	−0.325069	−	0.225588i	−0.0113937	−	0.00790684i
$815$	1.32163	−	1.10898i	0.0462946	−	0.0388458i
$816$		0			0
$817$	17.1990	−	6.25993i	0.601717	−	0.219007i
$818$	10.9513	−	11.0436i	0.382903	−	0.386131i
$819$		0			0
$820$	−0.0321227	−	3.82557i	−0.00112177	−	0.133595i
$821$	17.1467	−	20.4347i	0.598425	−	0.713175i	−0.378777	−	0.925488i	$-0.623655\pi$
$821$	17.1467	−	20.4347i	0.598425	−	0.713175i	0.977202	+	0.212313i	$0.0680997\pi$
$822$		0			0
$823$	−43.4440	+	7.66035i	−1.51436	+	0.267023i	−0.868214	−	0.496190i	$-0.834732\pi$
$823$	−43.4440	+	7.66035i	−1.51436	+	0.267023i	−0.646148	+	0.763212i	$0.723621\pi$
$824$	37.1437	+	25.3172i	1.29396	+	0.881965i
$825$		0			0
$826$	−2.44110	+	1.72460i	−0.0849368	+	0.0600064i
$827$	5.67028	+	9.82121i	0.197175	+	0.341517i	0.947611	−	0.319426i	$-0.103490\pi$
$827$	5.67028	+	9.82121i	0.197175	+	0.341517i	−0.750436	+	0.660943i	$0.770157\pi$
$828$		0			0
$829$	14.5329	−	25.1717i	0.504747	−	0.874248i	−0.495238	−	0.868757i	$-0.664919\pi$
$829$	14.5329	−	25.1717i	0.504747	−	0.874248i	0.999985	−	0.00549015i	$-0.00174758\pi$
$830$	0.224944	+	2.45249i	0.00780793	+	0.0851273i
$831$		0			0
$832$	−22.8640	−	25.8947i	−0.792666	−	0.897736i
$833$	−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	−0.928999	−	0.370083i	$-0.879329\pi$
$839$	2.04353	−	11.5894i	0.0705503	−	0.400111i	0.999549	−	0.0300279i	$-0.00955962\pi$
$840$		0			0
$841$	19.1198	+	6.95904i	0.659304	+	0.239967i
$842$	46.8345	−	22.0791i	1.61402	−	0.760897i
$843$		0			0
$844$	−7.42335	+	44.2704i	−0.255522	+	1.52385i
$845$	1.47865	+	0.853700i	0.0508672	+	0.0293682i
$846$		0			0
$847$	4.62422	−	2.66980i	0.158890	−	0.0917353i
$848$	−39.1399	−	6.22564i	−1.34407	−	0.213789i
$849$		0			0
$850$	17.1283	+	1.42610i	0.587497	+	0.0489148i
$851$	7.66556	+	43.4735i	0.262772	+	1.49025i
$852$		0			0
$853$	−33.4958	−	28.1063i	−1.14687	−	0.962342i	−0.147233	−	0.989102i	$-0.547037\pi$
$853$	−33.4958	−	28.1063i	−1.14687	−	0.962342i	−0.999642	+	0.0267597i	$0.991481\pi$
$854$	4.99090	−	1.35979i	0.170785	−	0.0465311i
$855$		0			0
$856$	−2.72702	+	0.767643i	−0.0932077	+	0.0262375i
$857$	−1.39456	−	3.83152i	−0.0476372	−	0.130882i	0.913593	−	0.406631i	$-0.133296\pi$
$857$	−1.39456	−	3.83152i	−0.0476372	−	0.130882i	−0.961230	+	0.275749i	$0.911074\pi$
$858$		0			0
$859$	25.0149	+	29.8116i	0.853499	+	1.01716i	0.999611	+	0.0278919i	$0.00887943\pi$
$859$	25.0149	+	29.8116i	0.853499	+	1.01716i	−0.146112	+	0.989268i	$0.546676\pi$
$860$	−0.949839	−	1.11286i	−0.0323892	−	0.0379483i
$861$		0			0
$862$	−22.8390	+	49.5202i	−0.777901	+	1.68667i
$863$	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
$866$	−3.88689	+	8.42765i	−0.132082	+	0.286383i
$867$		0			0
$868$	2.26374	+	2.65227i	0.0768362	+	0.0900238i
$869$	−0.0810203	−	0.0965562i	−0.00274843	−	0.00327545i
$870$		0			0
$871$	−16.4501	−	45.1963i	−0.557391	−	1.53142i
$872$	−19.7830	+	5.56881i	−0.669937	+	0.188584i
$873$		0			0
$874$	67.8233	−	18.4787i	2.29416	−	0.625052i
$875$	−1.11455	−	0.935219i	−0.0376787	−	0.0316162i
$876$		0			0
$877$	−2.95518	−	16.7597i	−0.0997895	−	0.565934i	−0.993174	−	0.116641i	$-0.962787\pi$
$877$	−2.95518	−	16.7597i	−0.0997895	−	0.565934i	0.893385	−	0.449293i	$-0.148324\pi$
$878$	−2.57140	−	0.214094i	−0.0867804	−	0.00722531i
$879$		0			0
$880$	0.0497421	+	0.00791203i	0.00167680	+	0.000266714i
$881$	−2.59611	+	1.49886i	−0.0874651	+	0.0504980i	−0.543095	−	0.839672i	$-0.682748\pi$
$881$	−2.59611	+	1.49886i	−0.0874651	+	0.0504980i	0.455630	+	0.890169i	$0.349414\pi$
$882$		0			0
$883$	−17.0858	−	9.86450i	−0.574984	−	0.331967i	0.184154	−	0.982897i	$-0.441046\pi$
$883$	−17.0858	−	9.86450i	−0.574984	−	0.331967i	−0.759137	+	0.650931i	$0.774379\pi$
$884$	3.53613	−	21.0883i	0.118933	−	0.709277i
$885$		0			0
$886$	−2.23187	+	1.05217i	−0.0749812	+	0.0353483i
$887$	−43.7296	−	15.9163i	−1.46830	−	0.534416i	−0.520658	−	0.853765i	$-0.674313\pi$
$887$	−43.7296	−	15.9163i	−1.46830	−	0.534416i	−0.947637	+	0.319349i	$0.896536\pi$
$888$		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
$896$	4.90775	−	2.46661i	0.163957	−	0.0824035i
$897$		0			0
$898$	−1.19346	−	13.0119i	−0.0398263	−	0.434213i
$899$	−12.6135	+	21.8472i	−0.420683	+	0.728645i
$900$		0			0
$901$	−12.2661	−	21.2454i	−0.408642	−	0.707788i
$902$	−0.304132	+	0.214864i	−0.0101265	+	0.00715420i
$903$		0			0
$904$	33.8164	+	23.0493i	1.12472	+	0.766608i
$905$	−5.10700	+	0.900503i	−0.169763	+	0.0299337i
$906$		0			0
$907$	22.3588	−	26.6461i	0.742411	−	0.884771i	−0.254190	−	0.967154i	$-0.581809\pi$
$907$	22.3588	−	26.6461i	0.742411	−	0.884771i	0.996601	+	0.0823838i	$0.0262533\pi$
$908$	−0.329198	−	39.2051i	−0.0109248	−	1.30107i
$909$		0			0
$910$	−0.631379	+	0.636702i	−0.0209300	+	0.0211065i
$911$	28.1223	−	10.2357i	0.931735	−	0.339124i	0.168838	−	0.985644i	$-0.445999\pi$
$911$	28.1223	−	10.2357i	0.931735	−	0.339124i	0.762897	+	0.646520i	$0.223776\pi$
$912$		0			0
$913$	0.183633	−	0.154086i	0.00607735	−	0.00509950i
$914$	32.0467	+	22.2394i	1.06001	+	0.735615i
$915$		0			0
$916$	7.21358	−	8.74490i	0.238344	−	0.288939i
$917$			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	$-0.336058\pi$
$920$	−3.28082	−	4.56211i	−0.108166	−	0.150408i
$921$		0			0
$922$	−16.7184	+	24.0909i	−0.550590	+	0.793393i
$923$	−11.1758	+	9.37762i	−0.367856	+	0.308668i
$924$		0			0
$925$	−30.9974	+	11.2821i	−1.01919	+	0.370954i
$926$	9.62614	+	9.54565i	0.316334	+	0.313689i
$927$		0			0
$928$	28.6825	+	27.5029i	0.941550	+	0.902828i
$929$	35.7471	−	42.6017i	1.17282	−	1.39772i	0.272692	−	0.962101i	$-0.412086\pi$
$929$	35.7471	−	42.6017i	1.17282	−	1.39772i	0.900132	−	0.435617i	$-0.143470\pi$
$930$		0			0
$931$	−50.4082	+	8.88832i	−1.65206	+	0.291303i
$932$	−14.1593	−	5.01933i	−0.463803	−	0.164414i
$933$		0			0
$934$	14.2760	+	20.2071i	0.467125	+	0.661197i
$935$	0.0155887	+	0.0270003i	0.000509803	+	0.000883005i
$936$		0			0
$937$	9.12048	−	15.7971i	0.297953	−	0.516070i	−0.677715	−	0.735325i	$-0.737029\pi$
$937$	9.12048	−	15.7971i	0.297953	−	0.516070i	0.975667	+	0.219255i	$0.0703628\pi$
$938$	7.61576	−	0.698523i	0.248663	−	0.0228076i
$939$		0			0
$940$	−0.791503	−	4.27845i	−0.0258160	−	0.139548i
$941$	5.96053	−	16.3764i	0.194308	−	0.533856i	−0.803830	−	0.594859i	$-0.797208\pi$
$941$	5.96053	−	16.3764i	0.194308	−	0.533856i	0.998138	+	0.0610030i	$0.0194299\pi$
$942$		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	0.582828	+	0.812596i	$0.301946\pi$
$947$	−7.47101	+	42.3702i	−0.242775	+	1.37685i	−0.825603	+	0.564251i	$0.809165\pi$
$948$		0			0
$949$	−2.56016	−	0.931821i	−0.0831063	−	0.0302482i
$950$	22.3991	+	47.5131i	0.726722	+	1.54153i
$951$		0			0
$952$	3.09929	+	1.39798i	0.100449	+	0.0453087i
$953$	−17.5809	−	10.1503i	−0.569502	−	0.328802i	0.187449	−	0.982274i	$-0.439978\pi$
$953$	−17.5809	−	10.1503i	−0.569502	−	0.328802i	−0.756950	+	0.653472i	$0.773312\pi$
$954$		0			0
$955$	−4.33625	+	2.50353i	−0.140318	+	0.0810124i
$956$	4.52886	+	12.1252i	0.146474	+	0.392157i
$957$		0			0
$958$	−3.07394	+	36.9198i	−0.0993143	+	1.19283i
$959$	1.29301	+	7.33301i	0.0417534	+	0.236795i
$960$		0			0
$961$	13.8681	+	11.6367i	0.447359	+	0.375379i
$962$	10.7878	+	39.5948i	0.347811	+	1.27659i
$963$		0			0
$964$	1.19604	−	0.703987i	0.0385217	−	0.0226739i
$965$	−0.910624	−	2.50192i	−0.0293140	−	0.0805396i
$966$		0			0
$967$	30.0283	+	35.7863i	0.965644	+	1.15081i	0.988523	+	0.151071i	$0.0482722\pi$
$967$	30.0283	+	35.7863i	0.965644	+	1.15081i	−0.0228793	+	0.999738i	$0.507283\pi$
$968$	13.5008	+	28.0254i	0.433931	+	0.900771i
$969$		0			0
$970$	1.29387	+	0.596743i	0.0415438	+	0.0191603i
$971$	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
$974$	9.13019	+	4.21090i	0.292550	+	0.134926i
$975$		0			0
$976$	5.73074	+	29.5863i	0.183436	+	0.947035i
$977$	−12.0038	−	14.3055i	−0.384035	−	0.457675i	0.539049	−	0.842275i	$-0.318784\pi$
$977$	−12.0038	−	14.3055i	−0.384035	−	0.457675i	−0.923083	+	0.384600i	$0.874339\pi$
$978$		0			0
$979$	0.148065	+	0.406804i	0.00473217	+	0.0130015i
$980$	2.07554	+	3.52623i	0.0663007	+	0.112641i
$981$		0			0
$982$	−7.34331	−	26.9525i	−0.234335	−	0.860089i
$983$	−20.0449	−	16.8196i	−0.639332	−	0.536463i	0.264481	−	0.964391i	$-0.414799\pi$
$983$	−20.0449	−	16.8196i	−0.639332	−	0.536463i	−0.903813	+	0.427928i	$0.859244\pi$
$984$		0			0
$985$	0.656370	+	3.72246i	0.0209137	+	0.118607i
$986$	−2.04093	+	24.5129i	−0.0649966	+	0.780648i
$987$		0			0
$988$	61.2184	−	22.8656i	1.94762	−	0.727452i
$989$	13.7596	−	7.94413i	0.437531	−	0.252609i
$990$		0			0
$991$	25.5875	+	14.7730i	0.812815	+	0.469279i	0.847932	−	0.530105i	$-0.177847\pi$
$991$	25.5875	+	14.7730i	0.812815	+	0.469279i	−0.0351178	+	0.999383i	$0.511181\pi$
$992$	−16.3926	+	11.9987i	−0.520465	+	0.380961i
$993$		0			0
$994$	−0.989184	−	2.09827i	−0.0313750	−	0.0665530i
$995$	−1.27507	−	0.464087i	−0.0404224	−	0.0147125i
$996$		0			0
$997$	6.87604	−	38.9959i	0.217766	−	1.23501i	−0.658275	−	0.752778i	$-0.728714\pi$
$997$	6.87604	−	38.9959i	0.217766	−	1.23501i	0.876041	−	0.482236i	$-0.160175\pi$
$998$	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.c.755.10		96
3.2	odd	2		972.2.l.b.755.7		96
4.3	odd	2	inner	972.2.l.c.755.8		96
9.2	odd	6		324.2.l.a.143.16		96
9.4	even	3		972.2.l.d.107.12		96
9.5	odd	6		972.2.l.a.107.5		96
9.7	even	3		108.2.l.a.47.1	yes	96
12.11	even	2		972.2.l.b.755.9		96
27.4	even	9		972.2.l.a.863.14		96
27.5	odd	18		108.2.l.a.23.14	yes	96
27.13	even	9		972.2.l.b.215.9		96
27.14	odd	18	inner	972.2.l.c.215.8		96
27.22	even	9		324.2.l.a.179.3		96
27.23	odd	18		972.2.l.d.863.3		96
36.7	odd	6		108.2.l.a.47.14	yes	96
36.11	even	6		324.2.l.a.143.3		96
36.23	even	6		972.2.l.a.107.14		96
36.31	odd	6		972.2.l.d.107.3		96
108.23	even	18		972.2.l.d.863.12		96
108.31	odd	18		972.2.l.a.863.5		96
108.59	even	18		108.2.l.a.23.1	✓	96
108.67	odd	18		972.2.l.b.215.7		96
108.95	even	18	inner	972.2.l.c.215.10		96
108.103	odd	18		324.2.l.a.179.16		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.1	✓	96	108.59	even	18
108.2.l.a.23.14	yes	96	27.5	odd	18
108.2.l.a.47.1	yes	96	9.7	even	3
108.2.l.a.47.14	yes	96	36.7	odd	6
324.2.l.a.143.3		96	36.11	even	6
324.2.l.a.143.16		96	9.2	odd	6
324.2.l.a.179.3		96	27.22	even	9
324.2.l.a.179.16		96	108.103	odd	18
972.2.l.a.107.5		96	9.5	odd	6
972.2.l.a.107.14		96	36.23	even	6
972.2.l.a.863.5		96	108.31	odd	18
972.2.l.a.863.14		96	27.4	even	9
972.2.l.b.215.7		96	108.67	odd	18
972.2.l.b.215.9		96	27.13	even	9
972.2.l.b.755.7		96	3.2	odd	2
972.2.l.b.755.9		96	12.11	even	2
972.2.l.c.215.8		96	27.14	odd	18	inner
972.2.l.c.215.10		96	108.95	even	18	inner
972.2.l.c.755.8		96	4.3	odd	2	inner
972.2.l.c.755.10		96	1.1	even	1	trivial
972.2.l.d.107.3		96	36.31	odd	6
972.2.l.d.107.12		96	9.4	even	3
972.2.l.d.863.3		96	27.23	odd	18
972.2.l.d.863.12		96	108.23	even	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)

\(f(q)\)	\(=\)	\(q+(0.592286 - 1.28421i) q^{2} +(-1.29839 - 1.52124i) q^{4} +(-0.194411 - 0.231690i) q^{5} +(0.166049 + 0.456215i) q^{7} +(-2.72261 + 0.766402i) q^{8} +(-0.412685 + 0.112438i) q^{10} +(0.0318926 + 0.0267611i) q^{11} +(-0.749815 - 4.25241i) q^{13} +(0.684225 + 0.0569684i) q^{14} +(-0.628345 + 3.95034i) q^{16} +(-2.14427 + 1.23800i) q^{17} +(-6.55326 - 3.78353i) q^{19} +(-0.100034 + 0.596570i) q^{20} +(0.0532565 - 0.0251066i) q^{22} +(-6.17265 - 2.24666i) q^{23} +(0.852356 - 4.83395i) q^{25} +(-5.90510 - 1.55572i) q^{26} +(0.478416 - 0.844947i) q^{28} +(6.91801 + 1.21983i) q^{29} +(-1.22825 + 3.37459i) q^{31} +(4.70091 + 3.14666i) q^{32} +(0.319825 + 3.48694i) q^{34} +(0.0734187 - 0.127165i) q^{35} +(-3.36015 - 5.81994i) q^{37} +(-8.74026 + 6.17484i) q^{38} +(0.706873 + 0.481805i) q^{40} +(-6.22846 + 1.09825i) q^{41} +(-1.55474 + 1.85287i) q^{43} +(-0.000699143 - 0.0832628i) q^{44} +(-6.54116 + 6.59631i) q^{46} +(-6.75922 + 2.46015i) q^{47} +(5.18175 - 4.34801i) q^{49} +(-5.70297 - 3.95769i) q^{50} +(-5.49539 + 6.66196i) q^{52} +9.90799i q^{53} -0.0125918i q^{55} +(-0.801731 - 1.11484i) q^{56} +(5.66396 - 8.16169i) q^{58} +(-3.33471 + 2.79816i) q^{59} +(7.07970 - 2.57680i) q^{61} +(3.60621 + 3.57605i) q^{62} +(6.82526 - 4.17323i) q^{64} +(-0.839468 + 1.00044i) q^{65} +(10.9694 - 1.93421i) q^{67} +(4.66740 + 1.65455i) q^{68} +(-0.119822 - 0.169603i) q^{70} +(-1.68932 - 2.92598i) q^{71} +(0.315477 - 0.546421i) q^{73} +(-9.46420 + 0.868063i) q^{74} +(2.75306 + 14.8816i) q^{76} +(-0.00691309 + 0.0189936i) q^{77} +(-2.98154 - 0.525727i) q^{79} +(1.03741 - 0.622407i) q^{80} +(-2.27865 + 8.64913i) q^{82} +(0.999837 - 5.67036i) q^{83} +(0.703701 + 0.256126i) q^{85} +(1.45862 + 3.09404i) q^{86} +(-0.107341 - 0.0484176i) q^{88} +(9.00521 + 5.19916i) q^{89} +(1.81551 - 1.04819i) q^{91} +(4.59682 + 12.3071i) q^{92} +(-0.844035 + 10.1374i) q^{94} +(0.397420 + 2.25388i) q^{95} +(-2.55186 - 2.14126i) q^{97} +(-2.51468 - 9.22972i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} - 12 q^{14} + 3 q^{16} - 18 q^{17} + 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 6 q^{29} - 57 q^{32} - 3 q^{34} - 6 q^{37} + 45 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) \) 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

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Varieties

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Representations

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Database

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