LMFDB - Embedded newform 972.2.l.b.215.3

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			215.3
Character	$\chi$	$=$	972.215
Dual form			972.2.l.b.755.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24786 - 0.665466i) q^{2} +(1.11431 + 1.66082i) q^{4} +(2.16884 - 2.58472i) q^{5} +(-0.918599 + 2.52383i) q^{7} +(-0.285283 - 2.81400i) q^{8} +(-4.42645 + 1.78208i) q^{10} +(-2.23543 + 1.87575i) q^{11} +(-0.102135 + 0.579238i) q^{13} +(2.82581 - 2.53809i) q^{14} +(-1.51663 + 3.70133i) q^{16} +(6.36286 + 3.67360i) q^{17} +(2.82795 - 1.63272i) q^{19} +(6.70951 + 0.721869i) q^{20} +(4.03775 - 0.853067i) q^{22} +(0.447833 - 0.162998i) q^{23} +(-1.10868 - 6.28766i) q^{25} +(0.512914 - 0.654840i) q^{26} +(-5.21523 + 1.28670i) q^{28} +(4.30473 - 0.759041i) q^{29} +(1.98883 + 5.46427i) q^{31} +(4.35565 - 3.60947i) q^{32} +(-5.49530 - 8.81841i) q^{34} +(4.53111 + 7.84811i) q^{35} +(-1.59532 + 2.76318i) q^{37} +(-4.61540 + 0.155497i) q^{38} +(-7.89215 - 5.36574i) q^{40} +(-3.16373 - 0.557851i) q^{41} +(1.17032 + 1.39474i) q^{43} +(-5.60623 - 1.62248i) q^{44} +(-0.667302 - 0.0946193i) q^{46} +(-1.15406 - 0.420044i) q^{47} +(-0.163586 - 0.137265i) q^{49} +(-2.80074 + 8.58391i) q^{50} +(-1.07582 + 0.475822i) q^{52} -7.37157i q^{53} +9.84615i q^{55} +(7.36413 + 1.86494i) q^{56} +(-5.87682 - 1.91748i) q^{58} +(3.17067 + 2.66051i) q^{59} +(-0.517322 - 0.188290i) q^{61} +(1.15450 - 8.14214i) q^{62} +(-7.83723 + 1.60557i) q^{64} +(1.27565 + 1.52027i) q^{65} +(9.97683 + 1.75918i) q^{67} +(0.989012 + 14.6611i) q^{68} +(-0.431535 - 12.8086i) q^{70} +(0.616505 - 1.06782i) q^{71} +(1.18077 + 2.04515i) q^{73} +(3.82954 - 2.38643i) q^{74} +(5.86285 + 2.87736i) q^{76} +(-2.68060 - 7.36490i) q^{77} +(9.60516 - 1.69365i) q^{79} +(6.27757 + 11.9477i) q^{80} +(3.57666 + 2.80148i) q^{82} +(-3.12278 - 17.7102i) q^{83} +(23.2953 - 8.47878i) q^{85} +(-0.532249 - 2.51925i) q^{86} +(5.91608 + 5.75538i) q^{88} +(4.81205 - 2.77824i) q^{89} +(-1.36808 - 0.789860i) q^{91} +(0.769734 + 0.562139i) q^{92} +(1.16058 + 1.29215i) q^{94} +(1.91325 - 10.8506i) q^{95} +(8.11117 - 6.80608i) q^{97} +(0.112787 + 0.280148i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.24786	−	0.665466i	−0.882370	−	0.470556i
$2$	−1.24786	−	0.665466i	−0.882370	−	0.470556i
$3$		0			0
$3$		0			0
$4$	1.11431	+	1.66082i	0.557154	+	0.830409i
$5$	2.16884	−	2.58472i	0.969935	−	1.15592i	−0.0178097	−	0.999841i	$-0.505669\pi$
$5$	2.16884	−	2.58472i	0.969935	−	1.15592i	0.987744	−	0.156082i	$-0.0498863\pi$
$6$		0			0
$7$	−0.918599	+	2.52383i	−0.347198	+	0.953918i	0.636050	+	0.771647i	$0.280567\pi$
$7$	−0.918599	+	2.52383i	−0.347198	+	0.953918i	−0.983248	+	0.182271i	$0.941655\pi$
$8$	−0.285283	−	2.81400i	−0.100863	−	0.994900i
$9$		0			0
$10$	−4.42645	+	1.78208i	−1.39977	+	0.563544i
$11$	−2.23543	+	1.87575i	−0.674007	+	0.565559i	−0.914248	−	0.405154i	$-0.867218\pi$
$11$	−2.23543	+	1.87575i	−0.674007	+	0.565559i	0.240242	+	0.970713i	$0.422773\pi$
$12$		0			0
$13$	−0.102135	+	0.579238i	−0.0283272	+	0.160652i	−0.995690	−	0.0927437i	$-0.970436\pi$
$13$	−0.102135	+	0.579238i	−0.0283272	+	0.160652i	0.967363	+	0.253395i	$0.0815474\pi$
$14$	2.82581	−	2.53809i	0.755229	−	0.678333i
$15$		0			0
$16$	−1.51663	+	3.70133i	−0.379158	+	0.925332i
$17$	6.36286	+	3.67360i	1.54322	+	0.890979i	0.998633	+	0.0522747i	$0.0166472\pi$
$17$	6.36286	+	3.67360i	1.54322	+	0.890979i	0.544588	+	0.838704i	$0.316686\pi$
$18$		0			0
$19$	2.82795	−	1.63272i	0.648776	−	0.374571i	−0.139211	−	0.990263i	$-0.544457\pi$
$19$	2.82795	−	1.63272i	0.648776	−	0.374571i	0.787987	+	0.615692i	$0.211123\pi$
$20$	6.70951	+	0.721869i	1.50029	+	0.161415i
$21$		0			0
$22$	4.03775	−	0.853067i	0.860850	−	0.181874i
$23$	0.447833	−	0.162998i	0.0933796	−	0.0339874i	−0.294908	−	0.955526i	$-0.595289\pi$
$23$	0.447833	−	0.162998i	0.0933796	−	0.0339874i	0.388288	+	0.921538i	$0.373067\pi$
$24$		0			0
$25$	−1.10868	−	6.28766i	−0.221737	−	1.25753i
$26$	0.512914	−	0.654840i	0.100591	−	0.128425i
$27$		0			0
$28$	−5.21523	+	1.28670i	−0.985585	+	0.243164i
$29$	4.30473	−	0.759041i	0.799369	−	0.140950i	0.240981	−	0.970530i	$-0.422531\pi$
$29$	4.30473	−	0.759041i	0.799369	−	0.140950i	0.558388	+	0.829580i	$0.311420\pi$
$30$		0			0
$31$	1.98883	+	5.46427i	0.357204	+	0.981411i	0.979995	+	0.199022i	$0.0637767\pi$
$31$	1.98883	+	5.46427i	0.357204	+	0.981411i	−0.622790	+	0.782389i	$0.714001\pi$
$32$	4.35565	−	3.60947i	0.769978	−	0.638070i
$33$		0			0
$34$	−5.49530	−	8.81841i	−0.942436	−	1.51234i
$35$	4.53111	+	7.84811i	0.765897	+	1.32657i
$36$		0			0
$37$	−1.59532	+	2.76318i	−0.262269	+	0.454264i	−0.966845	−	0.255365i	$-0.917804\pi$
$37$	−1.59532	+	2.76318i	−0.262269	+	0.454264i	0.704575	+	0.709629i	$0.251138\pi$
$38$	−4.61540	+	0.155497i	−0.748717	+	0.0252249i
$39$		0			0
$40$	−7.89215	−	5.36574i	−1.24786	−	0.848399i
$41$	−3.16373	−	0.557851i	−0.494092	−	0.0871217i	−0.0789502	−	0.996879i	$-0.525157\pi$
$41$	−3.16373	−	0.557851i	−0.494092	−	0.0871217i	−0.415141	+	0.909757i	$0.636268\pi$
$42$		0			0
$43$	1.17032	+	1.39474i	0.178473	+	0.212695i	0.847863	−	0.530216i	$-0.177889\pi$
$43$	1.17032	+	1.39474i	0.178473	+	0.212695i	−0.669390	+	0.742911i	$0.733445\pi$
$44$	−5.60623	−	1.62248i	−0.845171	−	0.244598i
$45$		0			0
$46$	−0.667302	−	0.0946193i	−0.0983884	−	0.0139509i
$47$	−1.15406	−	0.420044i	−0.168337	−	0.0612697i	0.256477	−	0.966550i	$-0.417438\pi$
$47$	−1.15406	−	0.420044i	−0.168337	−	0.0612697i	−0.424814	+	0.905281i	$0.639660\pi$
$48$		0			0
$49$	−0.163586	−	0.137265i	−0.0233694	−	0.0196093i
$50$	−2.80074	+	8.58391i	−0.396085	+	1.21395i
$51$		0			0
$52$	−1.07582	+	0.475822i	−0.149189	+	0.0659846i
$53$		−	7.37157i		−	1.01256i	−0.862368	−	0.506282i	$-0.831020\pi$
$53$		−	7.37157i		−	1.01256i	0.862368	−	0.506282i	$-0.168980\pi$
$54$		0			0
$55$			9.84615i			1.32765i
$56$	7.36413	+	1.86494i	0.984073	+	0.249213i
$57$		0			0
$58$	−5.87682	−	1.91748i	−0.771664	−	0.251777i
$59$	3.17067	+	2.66051i	0.412786	+	0.346369i	0.825411	−	0.564532i	$-0.190943\pi$
$59$	3.17067	+	2.66051i	0.412786	+	0.346369i	−0.412625	+	0.910901i	$0.635388\pi$
$60$		0			0
$61$	−0.517322	−	0.188290i	−0.0662363	−	0.0241080i	0.308690	−	0.951163i	$-0.400110\pi$
$61$	−0.517322	−	0.188290i	−0.0662363	−	0.0241080i	−0.374926	+	0.927055i	$0.622332\pi$
$62$	1.15450	−	8.14214i	0.146622	−	1.03405i
$63$		0			0
$64$	−7.83723	+	1.60557i	−0.979653	+	0.200697i
$65$	1.27565	+	1.52027i	0.158225	+	0.188566i
$66$		0			0
$67$	9.97683	+	1.75918i	1.21886	+	0.214919i	0.745836	−	0.666129i	$-0.232050\pi$
$67$	9.97683	+	1.75918i	1.21886	+	0.214919i	0.473027	+	0.881048i	$0.343161\pi$
$68$	0.989012	+	14.6611i	0.119935	+	1.77792i
$69$		0			0
$70$	−0.431535	−	12.8086i	−0.0515782	−	1.53093i
$71$	0.616505	−	1.06782i	0.0731657	−	0.126727i	−0.827121	−	0.562023i	$-0.810023\pi$
$71$	0.616505	−	1.06782i	0.0731657	−	0.126727i	0.900287	+	0.435297i	$0.143356\pi$
$72$		0			0
$73$	1.18077	+	2.04515i	0.138198	+	0.239366i	0.926815	−	0.375519i	$-0.122536\pi$
$73$	1.18077	+	2.04515i	0.138198	+	0.239366i	−0.788616	+	0.614885i	$0.789202\pi$
$74$	3.82954	−	2.38643i	0.445175	−	0.277416i
$75$		0			0
$76$	5.86285	+	2.87736i	0.672515	+	0.330055i
$77$	−2.68060	−	7.36490i	−0.305483	−	0.839308i
$78$		0			0
$79$	9.60516	−	1.69365i	1.08066	−	0.190550i	0.395156	−	0.918614i	$-0.370691\pi$
$79$	9.60516	−	1.69365i	1.08066	−	0.190550i	0.685509	+	0.728064i	$0.259580\pi$
$80$	6.27757	+	11.9477i	0.701854	+	1.33579i
$81$		0			0
$82$	3.57666	+	2.80148i	0.394976	+	0.309371i
$83$	−3.12278	−	17.7102i	−0.342769	−	1.94394i	−0.329874	−	0.944025i	$-0.607006\pi$
$83$	−3.12278	−	17.7102i	−0.342769	−	1.94394i	−0.0128957	−	0.999917i	$-0.504105\pi$
$84$		0			0
$85$	23.2953	−	8.47878i	2.52673	−	0.919653i
$86$	−0.532249	−	2.51925i	−0.0573938	−	0.271657i
$87$		0			0
$88$	5.91608	+	5.75538i	0.630657	+	0.613526i
$89$	4.81205	−	2.77824i	0.510076	−	0.294493i	−0.222789	−	0.974867i	$-0.571516\pi$
$89$	4.81205	−	2.77824i	0.510076	−	0.294493i	0.732865	+	0.680374i	$0.238183\pi$
$90$		0			0
$91$	−1.36808	−	0.789860i	−0.143413	−	0.0827998i
$92$	0.769734	+	0.562139i	0.0802503	+	0.0586070i
$93$		0			0
$94$	1.16058	+	1.29215i	0.119705	+	0.133275i
$95$	1.91325	−	10.8506i	0.196295	−	1.11324i
$96$		0			0
$97$	8.11117	−	6.80608i	0.823564	−	0.691052i	−0.130240	−	0.991483i	$-0.541575\pi$
$97$	8.11117	−	6.80608i	0.823564	−	0.691052i	0.953804	+	0.300430i	$0.0971302\pi$
$98$	0.112787	+	0.280148i	0.0113932	+	0.0282992i
$99$		0			0
$100$	9.20724	−	8.84771i	0.920724	−	0.884771i
$101$	−2.92521	+	8.03695i	−0.291069	+	0.799707i	0.704841	+	0.709365i	$0.251018\pi$
$101$	−2.92521	+	8.03695i	−0.291069	+	0.799707i	−0.995911	+	0.0903418i	$0.971204\pi$
$102$		0			0
$103$	−10.9002	+	12.9904i	−1.07403	+	1.27998i	−0.116024	+	0.993246i	$0.537015\pi$
$103$	−10.9002	+	12.9904i	−1.07403	+	1.27998i	−0.958009	+	0.286737i	$0.907430\pi$
$104$	1.65912	+	0.122162i	0.162690	+	0.0119790i
$105$		0			0
$106$	−4.90553	+	9.19869i	−0.476468	+	0.893456i
$107$	−3.73466			−0.361043			−0.180522	−	0.983571i	$-0.557779\pi$
$107$	−3.73466			−0.361043			−0.180522	+	0.983571i	$0.557779\pi$
$108$		0			0
$109$	10.6061			1.01588			0.507940	−	0.861393i	$-0.330407\pi$
$109$	10.6061			1.01588			0.507940	+	0.861393i	$0.330407\pi$
$110$	6.55228	−	12.2866i	0.624736	−	1.17148i
$111$		0			0
$112$	−7.94835	−	7.22776i	−0.751048	−	0.682959i
$113$	−3.75393	+	4.47376i	−0.353140	+	0.420856i	−0.913146	−	0.407632i	$-0.866354\pi$
$113$	−3.75393	+	4.47376i	−0.353140	+	0.420856i	0.560006	+	0.828489i	$0.310799\pi$
$114$		0			0
$115$	0.549974	−	1.51104i	0.0512853	−	0.140905i
$116$	6.05743	+	6.30357i	0.562418	+	0.585272i
$117$		0			0
$118$	−2.18607	−	5.42992i	−0.201244	−	0.499864i
$119$	−15.1165	+	12.6842i	−1.38572	+	1.16276i
$120$		0			0
$121$	−0.431419	+	2.44670i	−0.0392199	+	0.222427i
$122$	0.520245	+	0.579220i	0.0471008	+	0.0524401i
$123$		0			0
$124$	−6.85898	+	9.39196i	−0.615955	+	0.843423i
$125$	−4.04606	−	2.33599i	−0.361890	−	0.208937i
$126$		0			0
$127$	1.06513	−	0.614951i	0.0945147	−	0.0545681i	−0.451998	−	0.892019i	$-0.649288\pi$
$127$	1.06513	−	0.614951i	0.0945147	−	0.0545681i	0.546512	+	0.837451i	$0.315955\pi$
$128$	10.8482	+	3.21188i	0.958856	+	0.283893i
$129$		0			0
$130$	−0.580152	−	2.74598i	−0.0508827	−	0.240839i
$131$	16.5863	−	6.03692i	1.44915	−	0.527448i	0.506797	−	0.862065i	$-0.330829\pi$
$131$	16.5863	−	6.03692i	1.44915	−	0.527448i	0.942354	+	0.334617i	$0.108607\pi$
$132$		0			0
$133$	1.52295	+	8.63707i	0.132056	+	0.748929i
$134$	−11.2790	−	8.83446i	−0.974358	−	0.763181i
$135$		0			0
$136$	8.52231	−	18.9531i	0.730782	−	1.62522i
$137$	−10.2214	+	1.80231i	−0.873275	+	0.153982i	−0.592285	−	0.805729i	$-0.701774\pi$
$137$	−10.2214	+	1.80231i	−0.873275	+	0.153982i	−0.280990	+	0.959711i	$0.590663\pi$
$138$		0			0
$139$	−7.46408	−	20.5074i	−0.633095	−	1.73941i	−0.672401	−	0.740187i	$-0.734737\pi$
$139$	−7.46408	−	20.5074i	−0.633095	−	1.73941i	0.0393065	−	0.999227i	$-0.487485\pi$
$140$	−7.98523	+	16.2706i	−0.674875	+	1.37511i
$141$		0			0
$142$	−1.47991	+	0.922224i	−0.124191	+	0.0773913i
$143$	−0.858188	−	1.48642i	−0.0717653	−	0.124301i
$144$		0			0
$145$	7.37437	−	12.7728i	0.612408	−	1.06072i
$146$	−0.112454	−	3.33782i	−0.00930676	−	0.276240i
$147$		0			0
$148$	−6.36682	+	0.429495i	−0.523349	+	0.0353043i
$149$	3.67763	+	0.648465i	0.301283	+	0.0531243i	0.322246	−	0.946656i	$-0.395562\pi$
$149$	3.67763	+	0.648465i	0.301283	+	0.0531243i	−0.0209631	+	0.999780i	$0.506673\pi$
$150$		0			0
$151$	9.38343	+	11.1827i	0.763612	+	0.910038i	0.998071	−	0.0620885i	$-0.0197761\pi$
$151$	9.38343	+	11.1827i	0.763612	+	0.910038i	−0.234458	+	0.972126i	$0.575332\pi$
$152$	−5.40123	−	7.49207i	−0.438098	−	0.607687i
$153$		0			0
$154$	−1.55607	+	10.9742i	−0.125392	+	0.884327i
$155$	18.4371	+	6.71054i	1.48090	+	0.539004i
$156$		0			0
$157$	−12.7715	−	10.7165i	−1.01928	−	0.855274i	−0.0297390	−	0.999558i	$-0.509468\pi$
$157$	−12.7715	−	10.7165i	−1.01928	−	0.855274i	−0.989536	+	0.144284i	$0.953912\pi$
$158$	−13.1130	−	4.27848i	−1.04321	−	0.340377i
$159$		0			0
$160$	0.117234	−	19.0865i	0.00926813	−	1.50892i
$161$			1.27998i			0.100877i
$162$		0			0
$163$			2.78256i			0.217947i	0.994045	+	0.108973i	$0.0347563\pi$
$163$			2.78256i			0.217947i	−0.994045	+	0.108973i	$0.965244\pi$
$164$	−2.59888	−	5.87600i	−0.202939	−	0.458838i
$165$		0			0
$166$	−7.88872	+	24.1779i	−0.612284	+	1.87657i
$167$	−10.8578	−	9.11076i	−0.840200	−	0.705012i	0.117408	−	0.993084i	$-0.462541\pi$
$167$	−10.8578	−	9.11076i	−0.840200	−	0.705012i	−0.957609	+	0.288072i	$0.906986\pi$
$168$		0			0
$169$	11.8909	+	4.32794i	0.914686	+	0.332919i
$170$	−34.7116	−	4.92188i	−2.66226	−	0.377491i
$171$		0			0
$172$	−1.01230	+	3.49786i	−0.0771873	+	0.266709i
$173$	0.792993	+	0.945052i	0.0602901	+	0.0718509i	0.795347	−	0.606155i	$-0.207289\pi$
$173$	0.792993	+	0.945052i	0.0602901	+	0.0718509i	−0.735057	+	0.678006i	$0.762844\pi$
$174$		0			0
$175$	16.8874	+	2.97771i	1.27657	+	0.225094i
$176$	−3.55243	−	11.1189i	−0.267775	−	0.838116i
$177$		0			0
$178$	−7.85358	+	0.264594i	−0.588651	+	0.0198322i
$179$	−8.60015	+	14.8959i	−0.642805	+	1.11337i	0.341998	+	0.939701i	$0.388896\pi$
$179$	−8.60015	+	14.8959i	−0.642805	+	1.11337i	−0.984804	+	0.173671i	$0.944437\pi$
$180$		0			0
$181$	−10.8176	−	18.7366i	−0.804065	−	1.39268i	−0.916920	−	0.399071i	$-0.869333\pi$
$181$	−10.8176	−	18.7366i	−0.804065	−	1.39268i	0.112855	−	0.993611i	$-0.464000\pi$
$182$	1.18154	+	1.89604i	0.0875819	+	0.140544i
$183$		0			0
$184$	−0.586436	−	1.21370i	−0.0432326	−	0.0894754i
$185$	3.68205	+	10.1164i	0.270710	+	0.743769i
$186$		0			0
$187$	−21.1145	+	3.72305i	−1.54404	+	0.272256i
$188$	−0.588364	−	2.38474i	−0.0429109	−	0.173925i
$189$		0			0
$190$	−9.60815	+	12.2668i	−0.697048	+	0.889925i
$191$	0.828636	+	4.69943i	0.0599580	+	0.340039i	0.999999	−	0.00102135i	$-0.000325107\pi$
$191$	0.828636	+	4.69943i	0.0599580	+	0.340039i	−0.940041	+	0.341060i	$0.889214\pi$
$192$		0			0
$193$	−8.51361	+	3.09870i	−0.612823	+	0.223049i	−0.629738	−	0.776808i	$-0.716838\pi$
$193$	−8.51361	+	3.09870i	−0.612823	+	0.223049i	0.0169149	+	0.999857i	$0.494616\pi$
$194$	−14.6508	+	3.09532i	−1.05187	+	0.222231i
$195$		0			0
$196$	0.0456867	−	0.424642i	0.00326334	−	0.0303315i
$197$	−1.80241	+	1.04062i	−0.128416	+	0.0741411i	−0.562832	−	0.826571i	$-0.690288\pi$
$197$	−1.80241	+	1.04062i	−0.128416	+	0.0741411i	0.434416	+	0.900712i	$0.356955\pi$
$198$		0			0
$199$	9.74989	+	5.62910i	0.691151	+	0.399036i	0.804043	−	0.594571i	$-0.202678\pi$
$199$	9.74989	+	5.62910i	0.691151	+	0.399036i	−0.112892	+	0.993607i	$0.536011\pi$
$200$	−17.3772	+	4.91360i	−1.22875	+	0.347444i
$201$		0			0
$202$	8.99858	−	8.08236i	0.633138	−	0.568673i
$203$	−2.03863	+	11.5617i	−0.143084	+	0.811470i
$204$		0			0
$205$	−8.30351	+	6.96748i	−0.579943	+	0.486630i
$206$	22.2467	−	8.95646i	1.55000	−	0.624026i
$207$		0			0
$208$	−1.98905	−	1.25653i	−0.137916	−	0.0871245i
$209$	−3.25911	+	8.95433i	−0.225437	+	0.619384i
$210$		0			0
$211$	3.53807	−	4.21651i	0.243571	−	0.290277i	−0.630384	−	0.776283i	$-0.717103\pi$
$211$	3.53807	−	4.21651i	0.243571	−	0.290277i	0.873955	+	0.486007i	$0.161547\pi$
$212$	12.2428	−	8.21421i	0.840842	−	0.564154i
$213$		0			0
$214$	4.66034	+	2.48529i	0.318574	+	0.169891i
$215$	6.14325			0.418966
$216$		0			0
$217$	−15.6178			−1.06021
$218$	−13.2349	−	7.05800i	−0.896382	−	0.478028i
$219$		0			0
$220$	−16.3527	+	10.9717i	−1.10250	+	0.739709i
$221$	−2.77776	+	3.31041i	−0.186852	+	0.222682i
$222$		0			0
$223$	−1.86824	+	5.13294i	−0.125106	+	0.343727i	−0.986396	−	0.164388i	$-0.947435\pi$
$223$	−1.86824	+	5.13294i	−0.125106	+	0.343727i	0.861289	+	0.508115i	$0.169657\pi$
$224$	5.10859	+	14.3086i	0.341332	+	0.956033i
$225$		0			0
$226$	7.66152	−	3.08451i	0.509637	−	0.205179i
$227$	−1.13729	+	0.954298i	−0.0754845	+	0.0633390i	−0.679749	−	0.733445i	$-0.737911\pi$
$227$	−1.13729	+	0.954298i	−0.0754845	+	0.0633390i	0.604265	+	0.796784i	$0.293467\pi$
$228$		0			0
$229$	−4.52439	+	25.6591i	−0.298980	+	1.69560i	0.351591	+	0.936154i	$0.385641\pi$
$229$	−4.52439	+	25.6591i	−0.298980	+	1.69560i	−0.650570	+	0.759446i	$0.725470\pi$
$230$	−1.69184	+	1.51958i	−0.111556	+	0.100198i
$231$		0			0
$232$	−3.36401	−	11.8970i	−0.220858	−	0.781076i
$233$	−5.81401	−	3.35672i	−0.380889	−	0.219906i	0.297316	−	0.954779i	$-0.403908\pi$
$233$	−5.81401	−	3.35672i	−0.380889	−	0.219906i	−0.678205	+	0.734873i	$0.737242\pi$
$234$		0			0
$235$	−3.58867	+	2.07192i	−0.234099	+	0.135157i
$236$	−0.885514	+	8.23053i	−0.0576420	+	0.535762i
$237$		0			0
$238$	27.3041	−	5.76863i	1.76987	−	0.373925i
$239$	−19.2606	+	7.01030i	−1.24587	+	0.453458i	−0.879003	−	0.476816i	$-0.841791\pi$
$239$	−19.2606	+	7.01030i	−1.24587	+	0.453458i	−0.366864	+	0.930275i	$0.619568\pi$
$240$		0			0
$241$	2.19302	+	12.4372i	0.141265	+	0.801151i	0.970291	+	0.241941i	$0.0777842\pi$
$241$	2.19302	+	12.4372i	0.141265	+	0.801151i	−0.829026	+	0.559210i	$0.811105\pi$
$242$	2.16654	−	2.76604i	0.139271	−	0.177808i
$243$		0			0
$244$	−0.263741	−	1.06899i	−0.0168843	−	0.0684351i
$245$	−0.709583	+	0.125119i	−0.0453336	+	0.00799353i
$246$		0			0
$247$	0.656898	+	1.80481i	0.0417974	+	0.114837i
$248$	14.8091	−	7.15544i	0.940378	−	0.454371i
$249$		0			0
$250$	3.49439	+	5.60750i	0.221004	+	0.354650i
$251$	−6.38939	−	11.0668i	−0.403295	−	0.698527i	0.590827	−	0.806799i	$-0.298802\pi$
$251$	−6.38939	−	11.0668i	−0.403295	−	0.698527i	−0.994121	+	0.108272i	$0.965468\pi$
$252$		0			0
$253$	−0.695355	+	1.20439i	−0.0437166	+	0.0757194i
$254$	−1.73836	+	0.0585668i	−0.109074	+	0.00367481i
$255$		0			0
$256$	−11.3997	−	11.2271i	−0.712478	−	0.701694i
$257$	−9.79078	−	1.72638i	−0.610732	−	0.107689i	−0.140277	−	0.990112i	$-0.544799\pi$
$257$	−9.79078	−	1.72638i	−0.610732	−	0.107689i	−0.470455	+	0.882424i	$0.655910\pi$
$258$		0			0
$259$	−5.50833	−	6.56458i	−0.342271	−	0.407903i
$260$	−1.10341	+	3.81268i	−0.0684307	+	0.236452i
$261$		0			0
$262$	−24.7147	−	3.50440i	−1.52688	−	0.216502i
$263$	−18.3733	−	6.68733i	−1.13295	−	0.412359i	−0.293585	−	0.955933i	$-0.594848\pi$
$263$	−18.3733	−	6.68733i	−1.13295	−	0.412359i	−0.839361	+	0.543574i	$0.817071\pi$
$264$		0			0
$265$	−19.0535	−	15.9878i	−1.17045	−	0.982120i
$266$	3.84726	−	11.7913i	0.235890	−	0.722973i
$267$		0			0
$268$	8.19558	+	18.5300i	0.500625	+	1.13190i
$269$			30.3293i			1.84921i	0.380930	+	0.924604i	$0.375604\pi$
$269$			30.3293i			1.84921i	−0.380930	+	0.924604i	$0.624396\pi$
$270$		0			0
$271$		−	19.1257i		−	1.16181i	−0.813973	−	0.580903i	$-0.802699\pi$
$271$		−	19.1257i		−	1.16181i	0.813973	−	0.580903i	$-0.197301\pi$
$272$	−23.2473	+	17.9795i	−1.40958	+	1.09017i
$273$		0			0
$274$	13.9543	+	4.55298i	0.843009	+	0.275056i
$275$	14.2724	+	11.9760i	0.860660	+	0.722179i
$276$		0			0
$277$	−9.24931	−	3.36647i	−0.555737	−	0.202272i	0.0488566	−	0.998806i	$-0.484442\pi$
$277$	−9.24931	−	3.36647i	−0.555737	−	0.202272i	−0.604594	+	0.796534i	$0.706664\pi$
$278$	−4.33285	+	30.5574i	−0.259867	+	1.83271i
$279$		0			0
$280$	20.7920	−	14.9895i	1.24256	−	0.895793i
$281$	−14.8986	−	17.7554i	−0.888775	−	1.05920i	−0.997874	−	0.0651694i	$-0.979241\pi$
$281$	−14.8986	−	17.7554i	−0.888775	−	1.05920i	0.109100	−	0.994031i	$-0.465203\pi$
$282$		0			0
$283$	−17.1795	−	3.02921i	−1.02121	−	0.180068i	−0.362123	−	0.932130i	$-0.617948\pi$
$283$	−17.1795	−	3.02921i	−1.02121	−	0.180068i	−0.659092	+	0.752063i	$0.729059\pi$
$284$	2.46043	−	0.165977i	0.146000	−	0.00984889i
$285$		0			0
$286$	0.0817322	+	2.42594i	0.00483293	+	0.143449i
$287$	4.31412	−	7.47228i	0.254655	−	0.441075i
$288$		0			0
$289$	18.4907	+	32.0268i	1.08769	+	1.88393i
$290$	−17.7020	+	11.0312i	−1.03950	+	0.647777i
$291$		0			0
$292$	−2.08088	+	4.23996i	−0.121774	+	0.248125i
$293$	−6.50696	−	17.8777i	−0.380141	−	1.04443i	−0.971297	−	0.237871i	$-0.923550\pi$
$293$	−6.50696	−	17.8777i	−0.380141	−	1.04443i	0.591156	−	0.806557i	$-0.298672\pi$
$294$		0			0
$295$	13.7534	−	2.42509i	0.800751	−	0.141194i
$296$	8.23071	+	3.70095i	0.478400	+	0.215114i
$297$		0			0
$298$	−4.15763	−	3.25653i	−0.240845	−	0.188646i
$299$	0.0486750	+	0.276050i	0.00281495	+	0.0159644i
$300$		0			0
$301$	−4.59514	+	1.67249i	−0.264859	+	0.0964009i
$302$	−4.26747	−	20.1988i	−0.245565	−	1.16231i
$303$		0			0
$304$	1.75426	+	12.9434i	0.100614	+	0.742354i
$305$	−1.60867	+	0.928763i	−0.0921119	+	0.0531808i
$306$		0			0
$307$	14.3110	+	8.26248i	0.816773	+	0.471564i	0.849303	−	0.527906i	$-0.177023\pi$
$307$	14.3110	+	8.26248i	0.816773	+	0.471564i	−0.0325291	+	0.999471i	$0.510356\pi$
$308$	9.24474	−	12.6588i	0.526768	−	0.721300i
$309$		0			0
$310$	−18.5412	−	20.6431i	−1.05307	−	1.17245i
$311$	−0.361337	+	2.04924i	−0.0204895	+	0.116202i	−0.993337	−	0.115245i	$-0.963235\pi$
$311$	−0.361337	+	2.04924i	−0.0204895	+	0.116202i	0.972848	+	0.231447i	$0.0743459\pi$
$312$		0			0
$313$	−0.116592	+	0.0978326i	−0.00659019	+	0.00552982i	−0.646077	−	0.763272i	$-0.723591\pi$
$313$	−0.116592	+	0.0978326i	−0.00659019	+	0.00552982i	0.639487	+	0.768802i	$0.279147\pi$
$314$	8.80552	+	21.8717i	0.496924	+	1.23429i
$315$		0			0
$316$	13.5160	+	14.0652i	0.760332	+	0.791228i
$317$	2.29569	−	6.30735i	0.128939	−	0.354256i	−0.858378	−	0.513017i	$-0.828528\pi$
$317$	2.29569	−	6.30735i	0.128939	−	0.354256i	0.987317	+	0.158761i	$0.0507500\pi$
$318$		0			0
$319$	−8.19915	+	9.77137i	−0.459064	+	0.547092i
$320$	−12.8477	+	23.7393i	−0.718210	+	1.32707i
$321$		0			0
$322$	0.851787	−	1.59724i	0.0474682	−	0.0890108i
$323$	23.9918			1.33494
$324$		0			0
$325$	3.75529			0.208306
$326$	1.85170	−	3.47224i	0.102556	−	0.192310i
$327$		0			0
$328$	−0.667237	+	9.06189i	−0.0368420	+	0.500359i
$329$	2.12024	−	2.52680i	0.116893	−	0.139307i
$330$		0			0
$331$	4.51800	−	12.4131i	0.248332	−	0.682285i	−0.751416	−	0.659828i	$-0.770629\pi$
$331$	4.51800	−	12.4131i	0.248332	−	0.682285i	0.999748	−	0.0224569i	$-0.00714885\pi$
$332$	25.9336	−	24.9209i	1.42329	−	1.36771i
$333$		0			0
$334$	7.48609	+	18.5944i	0.409620	+	1.01744i
$335$	26.1851	−	21.9719i	1.43065	−	1.20046i
$336$		0			0
$337$	−3.35965	+	19.0535i	−0.183012	+	1.03791i	0.745472	+	0.666537i	$0.232224\pi$
$337$	−3.35965	+	19.0535i	−0.183012	+	1.03791i	−0.928483	+	0.371374i	$0.878887\pi$
$338$	−11.9581	−	13.3137i	−0.650435	−	0.724168i
$339$		0			0
$340$	40.0398	+	29.2412i	2.17146	+	1.58583i
$341$	−14.6955	−	8.48443i	−0.795804	−	0.459458i
$342$		0			0
$343$	−15.7851	+	9.11354i	−0.852316	+	0.492085i
$344$	3.59092	−	3.69119i	0.193609	−	0.199015i
$345$		0			0
$346$	−0.360643	−	1.70700i	−0.0193883	−	0.0917690i
$347$	−12.0164	+	4.37362i	−0.645075	+	0.234788i	−0.643779	−	0.765211i	$-0.722635\pi$
$347$	−12.0164	+	4.37362i	−0.645075	+	0.234788i	−0.00129537	+	0.999999i	$0.500412\pi$
$348$		0			0
$349$	−2.10360	−	11.9301i	−0.112603	−	0.638603i	−0.987909	−	0.155034i	$-0.950451\pi$
$349$	−2.10360	−	11.9301i	−0.112603	−	0.638603i	0.875306	−	0.483569i	$-0.160660\pi$
$350$	−19.0916	−	14.9538i	−1.02049	−	0.799313i
$351$		0			0
$352$	−2.96630	+	16.2388i	−0.158104	+	0.865532i
$353$	19.6660	−	3.46765i	1.04672	−	0.184564i	0.376261	−	0.926514i	$-0.377210\pi$
$353$	19.6660	−	3.46765i	1.04672	−	0.184564i	0.670456	+	0.741949i	$0.266099\pi$
$354$		0			0
$355$	−1.42291	−	3.90942i	−0.0755204	−	0.207491i
$356$	9.97625	+	4.89612i	0.528740	+	0.259494i
$357$		0			0
$358$	20.6445	−	12.8649i	1.09110	−	0.679930i
$359$	−10.5259	−	18.2314i	−0.555535	−	0.962214i	−0.997862	−	0.0653605i	$-0.979180\pi$
$359$	−10.5259	−	18.2314i	−0.555535	−	0.962214i	0.442327	−	0.896854i	$-0.354153\pi$
$360$		0			0
$361$	−4.16848	+	7.22001i	−0.219393	+	0.380001i
$362$	1.03025	+	30.5794i	0.0541486	+	1.60722i
$363$		0			0
$364$	−0.212647	−	3.15228i	−0.0111457	−	0.165224i
$365$	7.84703	+	1.38364i	0.410732	+	0.0724232i
$366$		0			0
$367$	−17.8938	−	21.3251i	−0.934051	−	1.11316i	−0.993375	−	0.114920i	$-0.963339\pi$
$367$	−17.8938	−	21.3251i	−0.934051	−	1.11316i	0.0593238	−	0.998239i	$-0.481106\pi$
$368$	−0.0758892	+	1.90478i	−0.00395600	+	0.0992937i
$369$		0			0
$370$	2.13741	−	15.0741i	0.111119	−	0.783664i
$371$	18.6046	+	6.77152i	0.965903	+	0.351560i
$372$		0			0
$373$	4.57301	+	3.83721i	0.236781	+	0.198683i	0.753455	−	0.657499i	$-0.228386\pi$
$373$	4.57301	+	3.83721i	0.236781	+	0.198683i	−0.516674	+	0.856182i	$0.672830\pi$
$374$	28.8254	+	9.40512i	1.49053	+	0.486327i
$375$		0			0
$376$	−0.852771	+	3.36736i	−0.0439783	+	0.173659i
$377$			2.57099i			0.132413i
$378$		0			0
$379$		−	14.2394i		−	0.731429i	−0.930727	−	0.365715i	$-0.880825\pi$
$379$		−	14.2394i		−	0.731429i	0.930727	−	0.365715i	$-0.119175\pi$
$380$	20.1527	−	8.91332i	1.03381	−	0.457244i
$381$		0			0
$382$	2.09329	−	6.41566i	0.107102	−	0.328254i
$383$	−12.2570	−	10.2848i	−0.626302	−	0.525530i	0.273475	−	0.961879i	$-0.411827\pi$
$383$	−12.2570	−	10.2848i	−0.626302	−	0.525530i	−0.899777	+	0.436349i	$0.856271\pi$
$384$		0			0
$385$	−24.8500	−	9.04467i	−1.26647	−	0.460959i
$386$	12.6859	+	1.79878i	0.645694	+	0.0915554i
$387$		0			0
$388$	20.3420	+	5.88710i	1.03271	+	0.298872i
$389$	11.4416	+	13.6355i	0.580111	+	0.691350i	0.973673	−	0.227948i	$-0.0732018\pi$
$389$	11.4416	+	13.6355i	0.580111	+	0.691350i	−0.393562	+	0.919298i	$0.628757\pi$
$390$		0			0
$391$	3.44829	+	0.608026i	0.174387	+	0.0307492i
$392$	−0.339595	+	0.499490i	−0.0171522	+	0.0252281i
$393$		0			0
$394$	2.94165	−	0.0991068i	0.148198	−	0.00499293i
$395$	16.4544	−	28.4999i	0.827913	−	1.43399i
$396$		0			0
$397$	−9.34449	−	16.1851i	−0.468987	−	0.812309i	0.530385	−	0.847757i	$-0.322047\pi$
$397$	−9.34449	−	16.1851i	−0.468987	−	0.812309i	−0.999372	+	0.0354484i	$0.988714\pi$
$398$	−8.42052	−	13.5126i	−0.422083	−	0.677323i
$399$		0			0
$400$	24.9541	+	5.43246i	1.24771	+	0.271623i
$401$	10.5675	+	29.0339i	0.527714	+	1.44988i	0.861755	+	0.507324i	$0.169365\pi$
$401$	10.5675	+	29.0339i	0.527714	+	1.44988i	−0.334042	+	0.942558i	$0.608413\pi$
$402$		0			0
$403$	−3.36824	+	0.593912i	−0.167784	+	0.0295849i
$404$	−16.6075	+	4.09740i	−0.826254	+	0.203853i
$405$		0			0
$406$	10.2378	−	13.0707i	0.508095	−	0.648688i
$407$	−1.61680	−	9.16930i	−0.0801416	−	0.454506i
$408$		0			0
$409$	23.1303	−	8.41873i	1.14372	−	0.416279i	0.300463	−	0.953793i	$-0.402859\pi$
$409$	23.1303	−	8.41873i	1.14372	−	0.416279i	0.843255	+	0.537514i	$0.180636\pi$
$410$	14.9982	−	3.16872i	0.740710	−	0.156492i
$411$		0			0
$412$	−33.7209	−	3.62800i	−1.66131	−	0.178739i
$413$	−9.62725	+	5.55829i	−0.473726	+	0.273506i
$414$		0			0
$415$	−52.5486	−	30.3390i	−2.57951	−	1.48928i
$416$	1.64588	+	2.89161i	0.0806958	+	0.141773i
$417$		0			0
$418$	10.0257	−	9.00492i	0.490374	−	0.440445i
$419$	1.38270	−	7.84169i	0.0675494	−	0.383091i	−0.932226	−	0.361878i	$-0.882136\pi$
$419$	1.38270	−	7.84169i	0.0675494	−	0.383091i	0.999775	−	0.0212138i	$-0.00675307\pi$
$420$		0			0
$421$	−3.14899	+	2.64231i	−0.153472	+	0.128778i	−0.716291	−	0.697802i	$-0.754161\pi$
$421$	−3.14899	+	2.64231i	−0.153472	+	0.128778i	0.562818	+	0.826581i	$0.309717\pi$
$422$	−7.22096	+	2.90715i	−0.351511	+	0.141518i
$423$		0			0
$424$	−20.7436	+	2.10298i	−1.00740	+	0.102130i
$425$	16.0439	−	44.0803i	0.778245	−	2.13821i
$426$		0			0
$427$	0.950423	−	1.13267i	0.0459942	−	0.0548138i
$428$	−4.16157	−	6.20259i	−0.201157	−	0.299814i
$429$		0			0
$430$	−7.66591	−	4.08812i	−0.369683	−	0.197147i
$431$	−34.6402			−1.66856			−0.834281	−	0.551340i	$-0.814117\pi$
$431$	−34.6402			−1.66856			−0.834281	+	0.551340i	$0.814117\pi$
$432$		0			0
$433$	−8.55521			−0.411137			−0.205569	−	0.978643i	$-0.565904\pi$
$433$	−8.55521			−0.411137			−0.205569	+	0.978643i	$0.565904\pi$
$434$	19.4889	+	10.3931i	0.935495	+	0.498886i
$435$		0			0
$436$	11.8185	+	17.6148i	0.566002	+	0.843596i
$437$	1.00032	−	1.19213i	0.0478517	−	0.0570275i
$438$		0			0
$439$	2.74002	−	7.52815i	0.130774	−	0.359299i	−0.856973	−	0.515361i	$-0.827658\pi$
$439$	2.74002	−	7.52815i	0.130774	−	0.359299i	0.987747	+	0.156062i	$0.0498800\pi$
$440$	27.7071	−	2.80894i	1.32088	−	0.133911i
$441$		0			0
$442$	5.66922	−	2.28242i	0.269657	−	0.108564i
$443$	−6.08399	+	5.10508i	−0.289059	+	0.242549i	−0.775773	−	0.631012i	$-0.782640\pi$
$443$	−6.08399	+	5.10508i	−0.289059	+	0.242549i	0.486714	+	0.873561i	$0.338195\pi$
$444$		0			0
$445$	3.25559	−	18.4634i	0.154330	−	0.875247i
$446$	5.74710	−	5.16194i	0.272133	−	0.244425i
$447$		0			0
$448$	3.14708	−	21.2547i	0.148685	−	1.00419i
$449$	−0.748371	−	0.432072i	−0.0353178	−	0.0203907i	0.482237	−	0.876041i	$-0.339824\pi$
$449$	−0.748371	−	0.432072i	−0.0353178	−	0.0203907i	−0.517555	+	0.855650i	$0.673158\pi$
$450$		0			0
$451$	8.11868	−	4.68732i	0.382294	−	0.220717i
$452$	−11.6131	−	1.24945i	−0.546237	−	0.0587690i
$453$		0			0
$454$	2.05423	−	0.434003i	0.0964098	−	0.0203688i
$455$	−5.00871	+	1.82302i	−0.234812	+	0.0854645i
$456$		0			0
$457$	−5.09989	−	28.9229i	−0.238563	−	1.35296i	−0.834979	−	0.550282i	$-0.814520\pi$
$457$	−5.09989	−	28.9229i	−0.238563	−	1.35296i	0.596416	−	0.802676i	$-0.296591\pi$
$458$	22.7211	−	29.0081i	1.06169	−	1.35546i
$459$		0			0
$460$	3.12240	−	0.770359i	0.145583	−	0.0359182i
$461$	−5.66042	+	0.998086i	−0.263632	+	0.0464855i	−0.303902	−	0.952703i	$-0.598289\pi$
$461$	−5.66042	+	0.998086i	−0.263632	+	0.0464855i	0.0402695	+	0.999189i	$0.487178\pi$
$462$		0			0
$463$	−9.40923	−	25.8516i	−0.437284	−	1.20143i	−0.941252	−	0.337706i	$-0.890349\pi$
$463$	−9.40923	−	25.8516i	−0.437284	−	1.20143i	0.503968	−	0.863722i	$-0.331873\pi$
$464$	−3.71924	+	17.0844i	−0.172661	+	0.793124i
$465$		0			0
$466$	5.02129	+	8.05775i	0.232607	+	0.373268i
$467$	8.41790	+	14.5802i	0.389534	+	0.674692i	0.992387	−	0.123160i	$-0.0393028\pi$
$467$	8.41790	+	14.5802i	0.389534	+	0.674692i	−0.602853	+	0.797852i	$0.705969\pi$
$468$		0			0
$469$	−13.6046	+	23.5638i	−0.628202	+	1.08808i
$470$	5.85695	−	0.197326i	0.270161	−	0.00910197i
$471$		0			0
$472$	6.58214	−	9.68127i	0.302968	−	0.445617i
$473$	−5.23234	−	0.922603i	−0.240583	−	0.0424213i
$474$		0			0
$475$	−13.4013	−	15.9710i	−0.614892	−	0.732800i
$476$	−37.9106	−	10.9716i	−1.73763	−	0.502880i
$477$		0			0
$478$	28.6997	+	4.06944i	1.31269	+	0.186132i
$479$	−2.07561	−	0.755461i	−0.0948371	−	0.0345179i	0.294166	−	0.955754i	$-0.404958\pi$
$479$	−2.07561	−	0.755461i	−0.0948371	−	0.0345179i	−0.389003	+	0.921237i	$0.627180\pi$
$480$		0			0
$481$	−1.43760	−	1.20629i	−0.0655489	−	0.0550021i
$482$	5.53997	−	16.9793i	0.252339	−	0.773385i
$483$		0			0
$484$	−4.54425	+	2.00987i	−0.206557	+	0.0913576i
$485$		−	35.7264i		−	1.62225i
$486$		0			0
$487$		−	40.4859i		−	1.83459i	−0.398206	−	0.917296i	$-0.630367\pi$
$487$		−	40.4859i		−	1.83459i	0.398206	−	0.917296i	$-0.369633\pi$
$488$	−0.382265	+	1.50946i	−0.0173043	+	0.0683301i
$489$		0			0
$490$	0.968722	+	0.316073i	0.0437624	+	0.0142787i
$491$	12.1210	+	10.1707i	0.547012	+	0.458998i	0.873928	−	0.486056i	$-0.161565\pi$
$491$	12.1210	+	10.1707i	0.547012	+	0.458998i	−0.326916	+	0.945054i	$0.606009\pi$
$492$		0			0
$493$	30.1788	+	10.9842i	1.35919	+	0.494703i
$494$	0.381326	−	2.68930i	0.0171566	−	0.120997i
$495$		0			0
$496$	−23.2414	−	0.925968i	−1.04357	−	0.0415772i
$497$	2.12867	+	2.53685i	0.0954840	+	0.113793i
$498$		0			0
$499$	32.9473	+	5.80950i	1.47492	+	0.260069i	0.852548	−	0.522649i	$-0.175056\pi$
$499$	32.9473	+	5.80950i	1.47492	+	0.260069i	0.622377	+	0.782718i	$0.286167\pi$
$500$	−0.628899	−	9.32278i	−0.0281252	−	0.416927i
$501$		0			0
$502$	0.608514	+	18.0617i	0.0271593	+	0.806132i
$503$	−12.0161	+	20.8125i	−0.535772	+	0.927984i	0.463354	+	0.886173i	$0.346646\pi$
$503$	−12.0161	+	20.8125i	−0.535772	+	0.927984i	−0.999126	+	0.0418106i	$0.986687\pi$
$504$		0			0
$505$	14.4290	+	24.9917i	0.642081	+	1.11212i
$506$	1.66919	−	1.04018i	0.0742045	−	0.0462414i
$507$		0			0
$508$	2.20820	+	1.08374i	0.0979731	+	0.0480830i
$509$	8.48989	+	23.3258i	0.376308	+	1.03390i	0.972874	+	0.231334i	$0.0743090\pi$
$509$	8.48989	+	23.3258i	0.376308	+	1.03390i	−0.596567	+	0.802564i	$0.703469\pi$
$510$		0			0
$511$	−6.24625	+	1.10138i	−0.276318	+	0.0487223i
$512$	6.75391	+	21.5959i	0.298484	+	0.954415i
$513$		0			0
$514$	11.0687	+	8.66972i	0.488218	+	0.382405i
$515$	9.93571	+	56.3482i	0.437820	+	2.48300i
$516$		0			0
$517$	3.36772	−	1.22575i	0.148112	−	0.0539084i
$518$	2.50512	+	11.8573i	0.110069	+	0.520979i
$519$		0			0
$520$	3.91411	−	4.02340i	0.171645	−	0.176438i
$521$	13.6964	−	7.90761i	0.600049	−	0.346439i	−0.169012	−	0.985614i	$-0.554058\pi$
$521$	13.6964	−	7.90761i	0.600049	−	0.346439i	0.769061	+	0.639175i	$0.220724\pi$
$522$		0			0
$523$	27.0410	+	15.6122i	1.18242	+	0.682672i	0.956574	−	0.291491i	$-0.0941512\pi$
$523$	27.0410	+	15.6122i	1.18242	+	0.682672i	0.225849	+	0.974162i	$0.427485\pi$
$524$	28.5085	+	20.8198i	1.24540	+	0.909518i
$525$		0			0
$526$	18.4771	+	20.5717i	0.805640	+	0.896967i
$527$	−7.41887	+	42.0745i	−0.323171	+	1.83280i
$528$		0			0
$529$	−17.4450	+	14.6381i	−0.758480	+	0.636440i
$530$	13.1367	+	32.6299i	0.570624	+	1.41735i
$531$		0			0
$532$	−12.6476	+	12.1537i	−0.548342	+	0.526930i
$533$	0.646257	−	1.77558i	0.0279925	−	0.0769088i
$534$		0			0
$535$	−8.09988	+	9.65307i	−0.350189	+	0.417338i
$536$	2.10413	−	28.5767i	0.0908847	−	1.23433i
$537$		0			0
$538$	20.1831	−	37.8467i	0.870156	−	1.63169i
$539$	0.623158			0.0268413
$540$		0			0
$541$	−14.4554			−0.621486			−0.310743	−	0.950494i	$-0.600578\pi$
$541$	−14.4554			−0.621486			−0.310743	+	0.950494i	$0.600578\pi$
$542$	−12.7275	+	23.8663i	−0.546695	+	1.02514i
$543$		0			0
$544$	40.9742	−	6.96563i	1.75675	−	0.298649i
$545$	23.0029	−	27.4138i	0.985337	−	1.17428i
$546$		0			0
$547$	−12.2384	+	33.6246i	−0.523274	+	1.43768i	0.343581	+	0.939123i	$0.388360\pi$
$547$	−12.2384	+	33.6246i	−0.523274	+	1.43768i	−0.866855	+	0.498561i	$0.833862\pi$
$548$	−14.3831	−	14.9676i	−0.614417	−	0.639384i
$549$		0			0
$550$	−9.84037	−	24.4422i	−0.419595	−	1.04222i
$551$	10.9343	−	9.17494i	0.465815	−	0.390865i
$552$		0			0
$553$	−4.54881	+	25.7976i	−0.193435	+	1.09702i
$554$	9.30157	+	10.3560i	0.395186	+	0.439984i
$555$		0			0
$556$	25.7417	−	35.2480i	1.09169	−	1.49485i
$557$	25.5879	+	14.7732i	1.08419	+	0.625960i	0.932025	−	0.362394i	$-0.118041\pi$
$557$	25.5879	+	14.7732i	1.08419	+	0.625960i	0.152170	+	0.988354i	$0.451374\pi$
$558$		0			0
$559$	−0.927416	+	0.535444i	−0.0392255	+	0.0226469i
$560$	−35.9204	+	4.86842i	−1.51792	+	0.205728i
$561$		0			0
$562$	6.77569	+	32.0708i	0.285815	+	1.35282i
$563$	10.8554	−	3.95105i	0.457501	−	0.166517i	−0.102981	−	0.994683i	$-0.532838\pi$
$563$	10.8554	−	3.95105i	0.457501	−	0.166517i	0.560482	+	0.828167i	$0.310616\pi$
$564$		0			0
$565$	3.42176	+	19.4058i	0.143954	+	0.816406i
$566$	19.4218	+	15.2124i	0.816358	+	0.639425i
$567$		0			0
$568$	−3.18072	−	1.43022i	−0.133460	−	0.0600106i
$569$	12.5805	−	2.21828i	0.527402	−	0.0929951i	0.0963937	−	0.995343i	$-0.469269\pi$
$569$	12.5805	−	2.21828i	0.527402	−	0.0929951i	0.431008	+	0.902348i	$0.358158\pi$
$570$		0			0
$571$	−13.2433	−	36.3857i	−0.554215	−	1.52269i	−0.827902	−	0.560873i	$-0.810465\pi$
$571$	−13.2433	−	36.3857i	−0.554215	−	1.52269i	0.273687	−	0.961819i	$-0.411757\pi$
$572$	1.51239	−	3.08163i	0.0632364	−	0.128849i
$573$		0			0
$574$	−10.3560	+	6.45345i	−0.432250	+	0.269362i
$575$	−1.52138	−	2.63511i	−0.0634459	−	0.109892i
$576$		0			0
$577$	10.5964	−	18.3535i	0.441134	−	0.764067i	−0.556640	−	0.830754i	$-0.687910\pi$
$577$	10.5964	−	18.3535i	0.441134	−	0.764067i	0.997774	+	0.0666873i	$0.0212430\pi$
$578$	−1.76102	−	52.2698i	−0.0732487	−	2.17414i
$579$		0			0
$580$	29.4306	−	1.98534i	1.22204	−	0.0824367i
$581$	47.5660	+	8.38717i	1.97337	+	0.347958i
$582$		0			0
$583$	13.8272	+	16.4786i	0.572664	+	0.682475i
$584$	5.41820	−	3.90612i	0.224207	−	0.161637i
$585$		0			0
$586$	−3.77725	+	26.6391i	−0.156037	+	1.10045i
$587$	14.2660	+	5.19242i	0.588823	+	0.214314i	0.619212	−	0.785224i	$-0.287452\pi$
$587$	14.2660	+	5.19242i	0.588823	+	0.214314i	−0.0303888	+	0.999538i	$0.509675\pi$
$588$		0			0
$589$	14.5459	+	12.2055i	0.599354	+	0.502917i
$590$	−18.7761	−	6.12622i	−0.772999	−	0.252213i
$591$		0			0
$592$	−7.80791	−	10.0955i	−0.320903	−	0.414924i
$593$		−	25.8789i		−	1.06272i	−0.847147	−	0.531359i	$-0.821681\pi$
$593$		−	25.8789i		−	1.06272i	0.847147	−	0.531359i	$-0.178319\pi$
$594$		0			0
$595$			66.5819i			2.72959i
$596$	3.02103	+	6.83046i	0.123746	+	0.279787i
$597$		0			0
$598$	0.122962	−	0.376863i	0.00502830	−	0.0154111i
$599$	−0.119950	−	0.100650i	−0.00490101	−	0.00411244i	0.640334	−	0.768097i	$-0.278796\pi$
$599$	−0.119950	−	0.100650i	−0.00490101	−	0.00411244i	−0.645235	+	0.763984i	$0.723240\pi$
$600$		0			0
$601$	−4.19563	−	1.52708i	−0.171143	−	0.0622910i	0.255028	−	0.966934i	$-0.417915\pi$
$601$	−4.19563	−	1.52708i	−0.171143	−	0.0622910i	−0.426171	+	0.904643i	$0.640138\pi$
$602$	6.84707	+	0.970872i	0.279066	+	0.0395698i
$603$		0			0
$604$	−8.11645	+	28.0452i	−0.330253	+	1.14114i
$605$	5.38835	+	6.42159i	0.219068	+	0.261075i
$606$		0			0
$607$	−37.0248	−	6.52847i	−1.50279	−	0.264983i	−0.639147	−	0.769085i	$-0.720712\pi$
$607$	−37.0248	−	6.52847i	−1.50279	−	0.264983i	−0.863644	+	0.504102i	$0.831823\pi$
$608$	6.42432	−	17.3189i	0.260540	−	0.702376i
$609$		0			0
$610$	2.62545	−	0.0884537i	0.106301	−	0.00358139i
$611$	0.361176	−	0.625575i	0.0146116	−	0.0253081i
$612$		0			0
$613$	−9.84356	−	17.0495i	−0.397577	−	0.688624i	0.595849	−	0.803096i	$-0.296816\pi$
$613$	−9.84356	−	17.0495i	−0.397577	−	0.688624i	−0.993426	+	0.114472i	$0.963482\pi$
$614$	−12.3598	−	19.8339i	−0.498799	−	0.800432i
$615$		0			0
$616$	−19.9601	+	9.64431i	−0.804216	+	0.388580i
$617$	−7.89362	−	21.6875i	−0.317785	−	0.873107i	−0.991024	−	0.133682i	$-0.957320\pi$
$617$	−7.89362	−	21.6875i	−0.317785	−	0.873107i	0.673239	−	0.739425i	$-0.264902\pi$
$618$		0			0
$619$	2.06484	−	0.364086i	0.0829927	−	0.0146339i	−0.131998	−	0.991250i	$-0.542139\pi$
$619$	2.06484	−	0.364086i	0.0829927	−	0.0146339i	0.214990	+	0.976616i	$0.431028\pi$
$620$	9.39959	+	38.0982i	0.377497	+	1.53006i
$621$		0			0
$622$	1.81460	−	2.31671i	0.0727588	−	0.0928916i
$623$	2.59146	+	14.6969i	0.103825	+	0.588818i
$624$		0			0
$625$	15.1849	−	5.52686i	0.607397	−	0.221074i
$626$	0.210595	−	0.0444931i	0.00841708	−	0.00177830i
$627$		0			0
$628$	3.56686	−	33.1527i	0.142333	−	1.32293i
$629$	−20.3016	+	11.7211i	−0.809479	+	0.467353i
$630$		0			0
$631$	−4.15935	−	2.40140i	−0.165581	−	0.0955982i	0.414920	−	0.909858i	$-0.363810\pi$
$631$	−4.15935	−	2.40140i	−0.165581	−	0.0955982i	−0.580500	+	0.814260i	$0.697143\pi$
$632$	−7.50612	−	26.5458i	−0.298577	−	1.05593i
$633$		0			0
$634$	−7.06202	+	6.34298i	−0.280469	+	0.251912i
$635$	0.720611	−	4.08679i	0.0285966	−	0.162179i
$636$		0			0
$637$	0.0962169	−	0.0807356i	0.00381225	−	0.00319886i
$638$	16.7339	−	6.73704i	0.662502	−	0.266722i
$639$		0			0
$640$	31.8299	−	21.0736i	1.25819	−	0.833006i
$641$	−9.68895	+	26.6202i	−0.382690	+	1.05143i	0.587528	+	0.809204i	$0.300101\pi$
$641$	−9.68895	+	26.6202i	−0.382690	+	1.05143i	−0.970219	+	0.242230i	$0.922121\pi$
$642$		0			0
$643$	2.41104	−	2.87336i	0.0950820	−	0.113314i	−0.716405	−	0.697684i	$-0.754214\pi$
$643$	2.41104	−	2.87336i	0.0950820	−	0.113314i	0.811487	+	0.584370i	$0.198658\pi$
$644$	−2.12582	+	1.42630i	−0.0837691	+	0.0562040i
$645$		0			0
$646$	−29.9384	−	15.9657i	−1.17791	−	0.628163i
$647$	−44.7799			−1.76048			−0.880239	−	0.474530i	$-0.842618\pi$
$647$	−44.7799			−1.76048			−0.880239	+	0.474530i	$0.842618\pi$
$648$		0			0
$649$	−12.0782			−0.474112
$650$	−4.68607	−	2.49902i	−0.183803	−	0.0980195i
$651$		0			0
$652$	−4.62132	+	3.10063i	−0.180985	+	0.121430i
$653$	−21.7078	+	25.8703i	−0.849490	+	1.01238i	0.150228	+	0.988651i	$0.451999\pi$
$653$	−21.7078	+	25.8703i	−0.849490	+	1.01238i	−0.999718	+	0.0237317i	$0.992445\pi$
$654$		0			0
$655$	20.3693	−	55.9641i	0.795893	−	2.18670i
$656$	6.86300	−	10.8639i	0.267955	−	0.424166i
$657$		0			0
$658$	−4.32727	+	1.74215i	−0.168694	+	0.0679160i
$659$	24.1988	−	20.3052i	0.942653	−	0.790980i	−0.0353922	−	0.999374i	$-0.511268\pi$
$659$	24.1988	−	20.3052i	0.942653	−	0.790980i	0.978045	+	0.208394i	$0.0668236\pi$
$660$		0			0
$661$	−0.839971	+	4.76371i	−0.0326711	+	0.185287i	−0.996776	−	0.0802346i	$-0.974433\pi$
$661$	−0.839971	+	4.76371i	−0.0326711	+	0.185287i	0.964105	+	0.265522i	$0.0855442\pi$
$662$	−13.8983	+	12.4832i	−0.540174	+	0.485174i
$663$		0			0
$664$	−48.9456	+	13.8399i	−1.89946	+	0.537093i
$665$	25.6275	+	14.7960i	0.993791	+	0.573765i
$666$		0			0
$667$	1.80408	−	1.04159i	0.0698542	−	0.0403304i
$668$	3.03239	−	28.1850i	0.117327	−	1.09051i
$669$		0			0
$670$	−47.2970	+	9.99257i	−1.82724	+	0.386047i
$671$	1.50962	−	0.549457i	0.0582782	−	0.0212115i
$672$		0			0
$673$	3.86976	+	21.9465i	0.149168	+	0.845975i	0.963925	+	0.266172i	$0.0857591\pi$
$673$	3.86976	+	21.9465i	0.149168	+	0.845975i	−0.814757	+	0.579802i	$0.803130\pi$
$674$	16.8719	−	21.5404i	0.649880	−	0.829705i
$675$		0			0
$676$	6.06223	+	24.5713i	0.233163	+	0.945050i
$677$	−0.870609	+	0.153512i	−0.0334602	+	0.00589994i	−0.190353	−	0.981716i	$-0.560963\pi$
$677$	−0.870609	+	0.153512i	−0.0334602	+	0.00589994i	0.156893	+	0.987616i	$0.449852\pi$
$678$		0			0
$679$	9.72648	+	26.7233i	0.373268	+	1.02555i
$680$	−30.5050	−	63.1341i	−1.16982	−	2.42108i
$681$		0			0
$682$	12.6918	+	20.3667i	0.485993	+	0.779882i
$683$	13.1484	+	22.7737i	0.503110	+	0.871412i	0.999994	+	0.00359510i	$0.00114436\pi$
$683$	13.1484	+	22.7737i	0.503110	+	0.871412i	−0.496883	+	0.867817i	$0.665522\pi$
$684$		0			0
$685$	−17.5101	+	30.3285i	−0.669028	+	1.15879i
$686$	25.7624	−	0.867958i	0.983612	−	0.0331388i
$687$		0			0
$688$	−6.93732	+	2.21645i	−0.264483	+	0.0845012i
$689$	4.26990	+	0.752898i	0.162670	+	0.0286831i
$690$		0			0
$691$	17.5236	+	20.8838i	0.666629	+	0.794457i	0.988321	−	0.152387i	$-0.0486960\pi$
$691$	17.5236	+	20.8838i	0.666629	+	0.794457i	−0.321692	+	0.946844i	$0.604252\pi$
$692$	−0.685920	+	2.37010i	−0.0260748	+	0.0900975i
$693$		0			0
$694$	17.9053	+	2.53886i	0.679676	+	0.0963737i
$695$	−69.1943	−	25.1847i	−2.62469	−	0.955309i
$696$		0			0
$697$	−18.0811	−	15.1718i	−0.684869	−	0.574673i
$698$	−5.31408	+	16.2870i	−0.201141	+	0.616470i
$699$		0			0
$700$	13.8724	+	31.3650i	0.524326	+	1.18549i
$701$		−	0.940626i		−	0.0355270i	−0.999842	−	0.0177635i	$-0.994345\pi$
$701$		−	0.940626i		−	0.0355270i	0.999842	−	0.0177635i	$-0.00565459\pi$
$702$		0			0
$703$			10.4188i			0.392954i
$704$	14.5079	−	18.2898i	0.546787	−	0.689322i
$705$		0			0
$706$	−26.8480	−	8.75994i	−1.01044	−	0.329685i
$707$	−17.5968	−	14.7655i	−0.661796	−	0.555313i
$708$		0			0
$709$	−33.6283	−	12.2397i	−1.26294	−	0.459671i	−0.378183	−	0.925731i	$-0.623451\pi$
$709$	−33.6283	−	12.2397i	−1.26294	−	0.459671i	−0.884753	+	0.466060i	$0.845673\pi$
$710$	−0.825993	+	5.82531i	−0.0309990	+	0.218620i
$711$		0			0
$712$	−9.19076	−	12.7485i	−0.344438	−	0.477772i
$713$	1.78133	+	2.12290i	0.0667112	+	0.0795034i
$714$		0			0
$715$	−5.70327	−	1.00564i	−0.213290	−	0.0376088i
$716$	−34.3226	+	2.31535i	−1.28270	+	0.0865286i
$717$		0			0
$718$	1.00247	+	29.7548i	0.0374117	+	1.11044i
$719$	16.5947	−	28.7429i	0.618879	−	1.07193i	−0.370812	−	0.928708i	$-0.620921\pi$
$719$	16.5947	−	28.7429i	0.618879	−	1.07193i	0.989691	−	0.143221i	$-0.0457461\pi$
$720$		0			0
$721$	−22.7726	−	39.4434i	−0.848097	−	1.46895i
$722$	10.0063	−	6.23558i	0.372398	−	0.232064i
$723$		0			0
$724$	19.0640	−	38.8444i	0.708507	−	1.44364i
$725$	−9.54517	−	26.2252i	−0.354499	−	0.973978i
$726$		0			0
$727$	31.7731	−	5.60245i	1.17840	−	0.207783i	0.450058	−	0.892999i	$-0.351403\pi$
$727$	31.7731	−	5.60245i	1.17840	−	0.207783i	0.728340	+	0.685216i	$0.240292\pi$
$728$	−1.83238	+	4.07511i	−0.0679125	+	0.151034i
$729$		0			0
$730$	−8.87122	−	6.94853i	−0.328339	−	0.257177i
$731$	2.32290	+	13.1738i	0.0859155	+	0.487251i
$732$		0			0
$733$	−41.2520	+	15.0145i	−1.52368	+	0.554573i	−0.962064	−	0.272825i	$-0.912042\pi$
$733$	−41.2520	+	15.0145i	−1.52368	+	0.554573i	−0.561615	+	0.827399i	$0.689820\pi$
$734$	8.13790	+	38.5184i	0.300375	+	1.42174i
$735$		0			0
$736$	1.36227	−	2.32640i	0.0502139	−	0.0857523i
$737$	−25.6023	+	14.7815i	−0.943071	+	0.544482i
$738$		0			0
$739$	−14.8213	−	8.55709i	−0.545211	−	0.314778i	0.201977	−	0.979390i	$-0.435263\pi$
$739$	−14.8213	−	8.55709i	−0.545211	−	0.314778i	−0.747188	+	0.664613i	$0.768597\pi$
$740$	−12.6985	+	17.3880i	−0.466805	+	0.639194i
$741$		0			0
$742$	−18.7097	−	20.8307i	−0.686855	−	0.764717i
$743$	7.59713	−	43.0854i	0.278711	−	1.58065i	−0.448208	−	0.893929i	$-0.647938\pi$
$743$	7.59713	−	43.0854i	0.278711	−	1.58065i	0.726920	−	0.686722i	$-0.240951\pi$
$744$		0			0
$745$	9.65229	−	8.09923i	0.353632	−	0.296733i
$746$	−3.15294	−	7.83148i	−0.115437	−	0.286731i
$747$		0			0
$748$	−29.7113	−	30.9186i	−1.08635	−	1.13050i
$749$	3.43066	−	9.42566i	0.125354	−	0.344406i
$750$		0			0
$751$	3.83442	−	4.56968i	0.139920	−	0.166750i	−0.691534	−	0.722344i	$-0.743065\pi$
$751$	3.83442	−	4.56968i	0.139920	−	0.166750i	0.831454	+	0.555594i	$0.187509\pi$
$752$	3.30501	−	3.63451i	0.120521	−	0.132537i
$753$		0			0
$754$	1.71091	−	3.20824i	0.0623076	−	0.116837i
$755$	49.2554			1.79259
$756$		0			0
$757$	33.2521			1.20857			0.604284	−	0.796769i	$-0.293459\pi$
$757$	33.2521			1.20857			0.604284	+	0.796769i	$0.293459\pi$
$758$	−9.47585	+	17.7688i	−0.344178	+	0.645392i
$759$		0			0
$760$	−31.0793	−	2.28840i	−1.12737	−	0.0830091i
$761$	−3.22885	+	3.84799i	−0.117046	+	0.139489i	−0.821386	−	0.570373i	$-0.806799\pi$
$761$	−3.22885	+	3.84799i	−0.117046	+	0.139489i	0.704340	+	0.709863i	$0.251243\pi$
$762$		0			0
$763$	−9.74275	+	26.7680i	−0.352711	+	0.969066i
$764$	−6.88154	+	6.61283i	−0.248965	+	0.239244i
$765$		0			0
$766$	8.45078	+	20.9906i	0.305339	+	0.758422i
$767$	−1.86491	+	1.56484i	−0.0673378	+	0.0565031i
$768$		0			0
$769$	8.98596	−	50.9619i	0.324042	−	1.83773i	−0.192280	−	0.981340i	$-0.561588\pi$
$769$	8.98596	−	50.9619i	0.324042	−	1.83773i	0.516322	−	0.856394i	$-0.327301\pi$
$770$	24.9904	+	27.8233i	0.900592	+	1.00268i
$771$		0			0
$772$	−14.6332	−	10.6866i	−0.526659	−	0.384621i
$773$	−8.36174	−	4.82765i	−0.300751	−	0.173639i	0.342029	−	0.939689i	$-0.388886\pi$
$773$	−8.36174	−	4.82765i	−0.300751	−	0.173639i	−0.642780	+	0.766051i	$0.722219\pi$
$774$		0			0
$775$	32.1524	−	18.5632i	1.15495	−	0.666811i
$776$	−21.4663	−	20.8832i	−0.770595	−	0.749663i
$777$		0			0
$778$	−5.20349	−	24.6292i	−0.186554	−	0.883001i
$779$	−9.85768	+	3.58790i	−0.353188	+	0.128550i
$780$		0			0
$781$	0.624804	+	3.54344i	0.0223572	+	0.126794i
$782$	−3.89836	−	3.05345i	−0.139405	−	0.109191i
$783$		0			0
$784$	0.756161	−	0.397305i	0.0270058	−	0.0141894i
$785$	−55.3986	+	9.76827i	−1.97726	+	0.348644i
$786$		0			0
$787$	13.7527	+	37.7851i	0.490229	+	1.34689i	0.900471	+	0.434917i	$0.143222\pi$
$787$	13.7527	+	37.7851i	0.490229	+	1.34689i	−0.410242	+	0.911977i	$0.634556\pi$
$788$	−3.73672	−	1.83390i	−0.133115	−	0.0653299i
$789$		0			0
$790$	−39.4986	+	24.6140i	−1.40530	+	0.875728i
$791$	−7.84266	−	13.5839i	−0.278853	−	0.482987i
$792$		0			0
$793$	0.161901	−	0.280422i	0.00574929	−	0.00995806i
$794$	0.889953	+	26.4152i	0.0315832	+	0.937441i
$795$		0			0
$796$	1.51548	+	22.4654i	0.0537146	+	0.796263i
$797$	−4.52678	−	0.798193i	−0.160347	−	0.0282735i	0.0928984	−	0.995676i	$-0.470387\pi$
$797$	−4.52678	−	0.798193i	−0.160347	−	0.0282735i	−0.253245	+	0.967402i	$0.581498\pi$
$798$		0			0
$799$	−5.80006	−	6.91224i	−0.205191	−	0.244538i
$800$	−27.5242	−	23.3851i	−0.973126	−	0.826788i
$801$		0			0
$802$	6.13435	−	43.2625i	0.216611	−	1.52765i
$803$	−6.47569	−	2.35696i	−0.228522	−	0.0831753i
$804$		0			0
$805$	3.30840	+	2.77608i	0.116606	+	0.0978440i
$806$	4.59832	+	1.50033i	0.161969	+	0.0528470i
$807$		0			0
$808$	23.4505	+	5.93875i	0.824987	+	0.208925i
$809$			17.3051i			0.608415i	0.952606	+	0.304208i	$0.0983917\pi$
$809$			17.3051i			0.608415i	−0.952606	+	0.304208i	$0.901608\pi$
$810$		0			0
$811$			4.64157i			0.162987i	0.996674	+	0.0814937i	$0.0259691\pi$
$811$			4.64157i			0.162987i	−0.996674	+	0.0814937i	$0.974031\pi$
$812$	−21.4735	+	9.49747i	−0.753572	+	0.333296i
$813$		0			0
$814$	−4.08433	+	12.5179i	−0.143156	+	0.438753i
$815$	7.19214	+	6.03492i	0.251930	+	0.211394i
$816$		0			0
$817$	5.58682	+	2.03344i	0.195458	+	0.0711409i
$818$	−34.4657	−	4.88702i	−1.20507	−	0.170871i
$819$		0			0
$820$	−20.8244	−	6.02670i	−0.727219	−	0.210462i
$821$	−22.5753	−	26.9043i	−0.787885	−	0.938965i	0.211376	−	0.977405i	$-0.432206\pi$
$821$	−22.5753	−	26.9043i	−0.787885	−	0.938965i	−0.999261	+	0.0384400i	$0.987761\pi$
$822$		0			0
$823$	−0.203632	−	0.0359058i	−0.00709815	−	0.00125160i	0.170098	−	0.985427i	$-0.445592\pi$
$823$	−0.203632	−	0.0359058i	−0.00709815	−	0.00125160i	−0.177196	+	0.984176i	$0.556703\pi$
$824$	39.6647	+	26.9674i	1.38179	+	0.939454i
$825$		0			0
$826$	15.7123	−	0.529362i	0.546701	−	0.0184189i
$827$	6.40289	−	11.0901i	0.222650	−	0.385642i	−0.732962	−	0.680270i	$-0.761863\pi$
$827$	6.40289	−	11.0901i	0.222650	−	0.385642i	0.955612	+	0.294628i	$0.0951959\pi$
$828$		0			0
$829$	14.0149	+	24.2745i	0.486757	+	0.843088i	0.999884	−	0.0152250i	$-0.00484646\pi$
$829$	14.0149	+	24.2745i	0.486757	+	0.843088i	−0.513127	+	0.858313i	$0.671513\pi$
$830$	45.3838	+	72.8281i	1.57529	+	2.52790i
$831$		0			0
$832$	−0.129551	−	4.70361i	−0.00449138	−	0.163068i
$833$	−0.536618	−	1.47435i	−0.0185927	−	0.0510830i
$834$		0			0
$835$	−47.0976	+	8.30457i	−1.62988	+	0.287392i
$836$	−18.5032	+	4.56510i	−0.639945	+	0.157887i
$837$		0			0
$838$	−6.94380	+	8.86519i	−0.239869	+	0.306243i
$839$	−5.80061	−	32.8969i	−0.200259	−	1.13573i	−0.904727	−	0.425991i	$-0.859926\pi$
$839$	−5.80061	−	32.8969i	−0.200259	−	1.13573i	0.704468	−	0.709736i	$-0.251186\pi$
$840$		0			0
$841$	−9.29650	+	3.38365i	−0.320569	+	0.116678i
$842$	5.68787	−	1.20169i	0.196017	−	0.0414130i
$843$		0			0
$844$	10.9454	+	1.17760i	0.376755	+	0.0405346i
$845$	36.9760	−	21.3481i	1.27201	−	0.734397i
$846$		0			0
$847$	−5.77875	−	3.33636i	−0.198560	−	0.114639i
$848$	27.2846	+	11.1800i	0.936957	+	0.383922i
$849$		0			0
$850$	−49.3546	+	44.3294i	−1.69285	+	1.52049i
$851$	−0.264046	+	1.49748i	−0.00905136	+	0.0513328i
$852$		0			0
$853$	31.0106	−	26.0210i	1.06178	−	0.890941i	0.0674988	−	0.997719i	$-0.478498\pi$
$853$	31.0106	−	26.0210i	1.06178	−	0.890941i	0.994283	+	0.106779i	$0.0340537\pi$
$854$	−1.93975	+	0.780939i	−0.0663768	+	0.0267232i
$855$		0			0
$856$	1.06543	+	10.5094i	0.0364158	+	0.359202i
$857$	−5.22146	+	14.3458i	−0.178362	+	0.490045i	−0.996367	−	0.0851662i	$-0.972858\pi$
$857$	−5.22146	+	14.3458i	−0.178362	+	0.490045i	0.818005	+	0.575211i	$0.195080\pi$
$858$		0			0
$859$	16.2814	−	19.4034i	0.555515	−	0.662037i	−0.413076	−	0.910696i	$-0.635546\pi$
$859$	16.2814	−	19.4034i	0.555515	−	0.662037i	0.968591	+	0.248660i	$0.0799902\pi$
$860$	6.84547	+	10.2028i	0.233429	+	0.347913i
$861$		0			0
$862$	43.2262	+	23.0519i	1.47229	+	0.785151i
$863$	25.0571			0.852954			0.426477	−	0.904498i	$-0.359755\pi$
$863$	25.0571			0.852954			0.426477	+	0.904498i	$0.359755\pi$
$864$		0			0
$865$	4.16257			0.141532
$866$	10.6757	+	5.69321i	0.362775	+	0.193463i
$867$		0			0
$868$	−17.4031	−	25.9384i	−0.590699	−	0.880405i
$869$	−18.2948	+	21.8029i	−0.620608	+	0.739612i
$870$		0			0
$871$	−2.03797	+	5.59928i	−0.0690541	+	0.189725i
$872$	−3.02574	−	29.8456i	−0.102464	−	1.01070i
$873$		0			0
$874$	−2.04158	+	0.821937i	−0.0690576	+	0.0278024i
$875$	9.61235	−	8.06572i	0.324957	−	0.272671i
$876$		0			0
$877$	5.23679	−	29.6993i	0.176834	−	1.00287i	−0.759172	−	0.650890i	$-0.774396\pi$
$877$	5.23679	−	29.6993i	0.176834	−	1.00287i	0.936006	−	0.351985i	$-0.114493\pi$
$878$	−8.42889	+	7.57068i	−0.284461	+	0.255498i
$879$		0			0
$880$	−36.4438	−	14.9330i	−1.22852	−	0.503391i
$881$	−33.7727	−	19.4987i	−1.13783	−	0.656927i	−0.191938	−	0.981407i	$-0.561477\pi$
$881$	−33.7727	−	19.4987i	−1.13783	−	0.656927i	−0.945892	+	0.324480i	$0.894811\pi$
$882$		0			0
$883$	−7.27427	+	4.19980i	−0.244799	+	0.141335i	−0.617380	−	0.786665i	$-0.711806\pi$
$883$	−7.27427	+	4.19980i	−0.244799	+	0.141335i	0.372582	+	0.927999i	$0.378473\pi$
$884$	−8.59327	−	0.924540i	−0.289023	−	0.0310956i
$885$		0			0
$886$	10.9892	−	2.32173i	0.369190	−	0.0779999i
$887$	22.3828	−	8.14666i	0.751540	−	0.273538i	0.0622862	−	0.998058i	$-0.480161\pi$
$887$	22.3828	−	8.14666i	0.751540	−	0.273538i	0.689254	+	0.724520i	$0.257939\pi$
$888$		0			0
$889$	0.573608	+	3.25309i	0.0192382	+	0.109105i
$890$	−16.3493	+	20.8732i	−0.548029	+	0.699671i
$891$		0			0
$892$	−10.6067	+	2.61688i	−0.355138	+	0.0876195i
$893$	−3.94944	+	0.696393i	−0.132163	+	0.0233039i
$894$		0			0
$895$	19.8494	+	54.5358i	0.663493	+	1.82293i
$896$	−18.0714	+	24.4286i	−0.603723	+	0.816103i
$897$		0			0
$898$	0.646333	+	1.03718i	0.0215684	+	0.0346112i
$899$	12.7090	+	22.0126i	0.423868	+	0.734162i
$900$		0			0
$901$	27.0802	−	46.9043i	0.902173	−	1.56261i
$902$	−13.2502	+	0.446412i	−0.441184	+	0.0148639i
$903$		0			0
$904$	13.6601	+	9.28729i	0.454329	+	0.308891i
$905$	−71.8906	−	12.6762i	−2.38972	−	0.421373i
$906$		0			0
$907$	8.72657	+	10.3999i	0.289761	+	0.345324i	0.891213	−	0.453585i	$-0.149855\pi$
$907$	8.72657	+	10.3999i	0.289761	+	0.345324i	−0.601452	+	0.798909i	$0.705411\pi$
$908$	−2.85221	−	0.825446i	−0.0946538	−	0.0273934i
$909$		0			0
$910$	7.46333	+	1.05825i	0.247407	+	0.0350807i
$911$	3.61785	+	1.31679i	0.119865	+	0.0436272i	0.401256	−	0.915966i	$-0.368574\pi$
$911$	3.61785	+	1.31679i	0.119865	+	0.0436272i	−0.281391	+	0.959593i	$0.590796\pi$
$912$		0			0
$913$	40.2005	+	33.7322i	1.33044	+	1.11637i
$914$	−12.8833	+	39.4856i	−0.426141	+	1.30607i
$915$		0			0
$916$	−47.6566	+	21.0780i	−1.57462	+	0.696435i
$917$			47.4065i			1.56550i
$918$		0			0
$919$			7.14983i			0.235851i	0.993022	+	0.117926i	$0.0376244\pi$
$919$			7.14983i			0.235851i	−0.993022	+	0.117926i	$0.962376\pi$
$920$	−4.40897	−	1.11655i	−0.145359	−	0.0368117i
$921$		0			0
$922$	7.72761	+	2.52135i	0.254495	+	0.0830363i
$923$	0.555554	+	0.466165i	0.0182863	+	0.0153440i
$924$		0			0
$925$	19.1426	+	6.96735i	0.629406	+	0.229085i
$926$	−5.46200	+	38.5208i	−0.179493	+	1.26587i
$927$		0			0
$928$	16.0102	−	18.8439i	0.525560	−	0.618582i
$929$	16.0658	+	19.1465i	0.527102	+	0.628175i	0.962245	−	0.272186i	$-0.0877466\pi$
$929$	16.0658	+	19.1465i	0.527102	+	0.628175i	−0.435143	+	0.900361i	$0.643302\pi$
$930$		0			0
$931$	−0.686727	−	0.121088i	−0.0225066	−	0.00396851i
$932$	−0.903702	−	13.3964i	−0.0296017	−	0.438815i
$933$		0			0
$934$	−0.801706	−	23.7959i	−0.0262326	−	0.778626i
$935$	−36.1708	+	62.6497i	−1.18291	+	2.04886i
$936$		0			0
$937$	−1.71158	−	2.96455i	−0.0559150	−	0.0968475i	0.836713	−	0.547642i	$-0.184474\pi$
$937$	−1.71158	−	2.96455i	−0.0559150	−	0.0968475i	−0.892628	+	0.450794i	$0.851141\pi$
$938$	32.6576	−	20.3510i	1.06631	−	0.664483i
$939$		0			0
$940$	−7.43997	−	3.65137i	−0.242665	−	0.119095i
$941$	−12.4624	−	34.2402i	−0.406263	−	1.11620i	−0.959139	−	0.282936i	$-0.908692\pi$
$941$	−12.4624	−	34.2402i	−0.406263	−	1.11620i	0.552876	−	0.833264i	$-0.313530\pi$
$942$		0			0
$943$	−1.50775	+	0.265857i	−0.0490991	+	0.00865750i
$944$	−14.6562	+	7.70068i	−0.477017	+	0.250636i
$945$		0			0
$946$	5.91527	+	4.63323i	0.192322	+	0.150639i
$947$	−1.21337	−	6.88137i	−0.0394292	−	0.223614i	0.958726	−	0.284333i	$-0.0917720\pi$
$947$	−1.21337	−	6.88137i	−0.0394292	−	0.223614i	−0.998155	+	0.0607182i	$0.980661\pi$
$948$		0			0
$949$	−1.30522	+	0.475063i	−0.0423694	+	0.0154212i
$950$	6.09473	+	28.8477i	0.197739	+	0.935942i
$951$		0			0
$952$	40.0059	+	38.9192i	1.29660	+	1.26138i
$953$	−6.10328	+	3.52373i	−0.197705	+	0.114145i	−0.595584	−	0.803293i	$-0.703079\pi$
$953$	−6.10328	+	3.52373i	−0.197705	+	0.114145i	0.397880	+	0.917438i	$0.369746\pi$
$954$		0			0
$955$	13.9439	+	8.05052i	0.451214	+	0.260509i
$956$	−33.1051	−	24.1768i	−1.07070	−	0.781933i
$957$		0			0
$958$	2.08734	+	2.32396i	0.0674388	+	0.0750837i
$959$	4.84066	−	27.4527i	0.156313	−	0.886495i
$960$		0			0
$961$	−2.15538	+	1.80858i	−0.0695284	+	0.0583413i
$962$	0.991178	+	2.46195i	0.0319569	+	0.0793766i
$963$		0			0
$964$	−18.2122	+	17.5011i	−0.586577	+	0.563672i
$965$	−10.4554	+	28.7259i	−0.336570	+	0.924720i
$966$		0			0
$967$	16.9709	−	20.2251i	0.545746	−	0.650395i	−0.420720	−	0.907191i	$-0.638222\pi$
$967$	16.9709	−	20.2251i	0.545746	−	0.650395i	0.966466	+	0.256796i	$0.0826669\pi$
$968$	7.00809	+	0.516013i	0.225249	+	0.0165853i
$969$		0			0
$970$	−23.7747	+	44.5816i	−0.763360	+	1.43143i
$971$	−34.6797			−1.11292			−0.556462	−	0.830873i	$-0.687841\pi$
$971$	−34.6797			−1.11292			−0.556462	+	0.830873i	$0.687841\pi$
$972$		0			0
$973$	58.6137			1.87907
$974$	−26.9420	+	50.5207i	−0.863278	+	1.61879i
$975$		0			0
$976$	1.48151	−	1.62921i	0.0474220	−	0.0521498i
$977$	28.9842	−	34.5421i	0.927288	−	1.10510i	−0.0669346	−	0.997757i	$-0.521322\pi$
$977$	28.9842	−	34.5421i	0.927288	−	1.10510i	0.994222	−	0.107341i	$-0.0342337\pi$
$978$		0			0
$979$	−5.54571	+	15.2367i	−0.177242	+	0.486968i
$980$	−0.998493	−	1.03907i	−0.0318957	−	0.0331918i
$981$		0			0
$982$	−8.35702	−	20.7577i	−0.266683	−	0.662406i
$983$	−30.4016	+	25.5100i	−0.969662	+	0.813643i	−0.982498	−	0.186275i	$-0.940359\pi$
$983$	−30.4016	+	25.5100i	−0.969662	+	0.813643i	0.0128359	+	0.999918i	$0.495914\pi$
$984$		0			0
$985$	−1.21942	+	6.91566i	−0.0388539	+	0.220351i
$986$	−30.3493	−	33.7897i	−0.966520	−	1.07608i
$987$		0			0
$988$	−2.26548	+	3.10211i	−0.0720745	+	0.0986912i
$989$	0.751448	+	0.433849i	0.0238947	+	0.0137956i
$990$		0			0
$991$	−16.9550	+	9.78895i	−0.538592	+	0.310956i	−0.744508	−	0.667613i	$-0.767316\pi$
$991$	−16.9550	+	9.78895i	−0.538592	+	0.310956i	0.205916	+	0.978570i	$0.433983\pi$
$992$	28.3858	+	16.6218i	0.901249	+	0.527743i
$993$		0			0
$994$	−0.968094	−	4.58220i	−0.0307061	−	0.145338i
$995$	35.6956	−	12.9921i	1.13163	−	0.411879i
$996$		0			0
$997$	−6.52118	−	36.9834i	−0.206528	−	1.17128i	−0.895018	−	0.446031i	$-0.852837\pi$
$997$	−6.52118	−	36.9834i	−0.206528	−	1.17128i	0.688490	−	0.725246i	$-0.258274\pi$
$998$	−37.2476	−	29.1748i	−1.17905	−	0.923512i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.b.215.3		96
3.2	odd	2		972.2.l.c.215.14		96
4.3	odd	2	inner	972.2.l.b.215.5		96
9.2	odd	6		972.2.l.d.863.8		96
9.4	even	3		324.2.l.a.179.13		96
9.5	odd	6		108.2.l.a.23.4	✓	96
9.7	even	3		972.2.l.a.863.9		96
12.11	even	2		972.2.l.c.215.12		96
27.2	odd	18	inner	972.2.l.b.755.5		96
27.7	even	9		972.2.l.d.107.2		96
27.11	odd	18		324.2.l.a.143.7		96
27.16	even	9		108.2.l.a.47.10	yes	96
27.20	odd	18		972.2.l.a.107.15		96
27.25	even	9		972.2.l.c.755.12		96
36.7	odd	6		972.2.l.a.863.15		96
36.11	even	6		972.2.l.d.863.2		96
36.23	even	6		108.2.l.a.23.10	yes	96
36.31	odd	6		324.2.l.a.179.7		96
108.7	odd	18		972.2.l.d.107.8		96
108.11	even	18		324.2.l.a.143.13		96
108.43	odd	18		108.2.l.a.47.4	yes	96
108.47	even	18		972.2.l.a.107.9		96
108.79	odd	18		972.2.l.c.755.14		96
108.83	even	18	inner	972.2.l.b.755.3		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.4	✓	96	9.5	odd	6
108.2.l.a.23.10	yes	96	36.23	even	6
108.2.l.a.47.4	yes	96	108.43	odd	18
108.2.l.a.47.10	yes	96	27.16	even	9
324.2.l.a.143.7		96	27.11	odd	18
324.2.l.a.143.13		96	108.11	even	18
324.2.l.a.179.7		96	36.31	odd	6
324.2.l.a.179.13		96	9.4	even	3
972.2.l.a.107.9		96	108.47	even	18
972.2.l.a.107.15		96	27.20	odd	18
972.2.l.a.863.9		96	9.7	even	3
972.2.l.a.863.15		96	36.7	odd	6
972.2.l.b.215.3		96	1.1	even	1	trivial
972.2.l.b.215.5		96	4.3	odd	2	inner
972.2.l.b.755.3		96	108.83	even	18	inner
972.2.l.b.755.5		96	27.2	odd	18	inner
972.2.l.c.215.12		96	12.11	even	2
972.2.l.c.215.14		96	3.2	odd	2
972.2.l.c.755.12		96	27.25	even	9
972.2.l.c.755.14		96	108.79	odd	18
972.2.l.d.107.2		96	27.7	even	9
972.2.l.d.107.8		96	108.7	odd	18
972.2.l.d.863.2		96	36.11	even	6
972.2.l.d.863.8		96	9.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.24786 - 0.665466i) q^{2} +(1.11431 + 1.66082i) q^{4} +(2.16884 - 2.58472i) q^{5} +(-0.918599 + 2.52383i) q^{7} +(-0.285283 - 2.81400i) q^{8} +(-4.42645 + 1.78208i) q^{10} +(-2.23543 + 1.87575i) q^{11} +(-0.102135 + 0.579238i) q^{13} +(2.82581 - 2.53809i) q^{14} +(-1.51663 + 3.70133i) q^{16} +(6.36286 + 3.67360i) q^{17} +(2.82795 - 1.63272i) q^{19} +(6.70951 + 0.721869i) q^{20} +(4.03775 - 0.853067i) q^{22} +(0.447833 - 0.162998i) q^{23} +(-1.10868 - 6.28766i) q^{25} +(0.512914 - 0.654840i) q^{26} +(-5.21523 + 1.28670i) q^{28} +(4.30473 - 0.759041i) q^{29} +(1.98883 + 5.46427i) q^{31} +(4.35565 - 3.60947i) q^{32} +(-5.49530 - 8.81841i) q^{34} +(4.53111 + 7.84811i) q^{35} +(-1.59532 + 2.76318i) q^{37} +(-4.61540 + 0.155497i) q^{38} +(-7.89215 - 5.36574i) q^{40} +(-3.16373 - 0.557851i) q^{41} +(1.17032 + 1.39474i) q^{43} +(-5.60623 - 1.62248i) q^{44} +(-0.667302 - 0.0946193i) q^{46} +(-1.15406 - 0.420044i) q^{47} +(-0.163586 - 0.137265i) q^{49} +(-2.80074 + 8.58391i) q^{50} +(-1.07582 + 0.475822i) q^{52} -7.37157i q^{53} +9.84615i q^{55} +(7.36413 + 1.86494i) q^{56} +(-5.87682 - 1.91748i) q^{58} +(3.17067 + 2.66051i) q^{59} +(-0.517322 - 0.188290i) q^{61} +(1.15450 - 8.14214i) q^{62} +(-7.83723 + 1.60557i) q^{64} +(1.27565 + 1.52027i) q^{65} +(9.97683 + 1.75918i) q^{67} +(0.989012 + 14.6611i) q^{68} +(-0.431535 - 12.8086i) q^{70} +(0.616505 - 1.06782i) q^{71} +(1.18077 + 2.04515i) q^{73} +(3.82954 - 2.38643i) q^{74} +(5.86285 + 2.87736i) q^{76} +(-2.68060 - 7.36490i) q^{77} +(9.60516 - 1.69365i) q^{79} +(6.27757 + 11.9477i) q^{80} +(3.57666 + 2.80148i) q^{82} +(-3.12278 - 17.7102i) q^{83} +(23.2953 - 8.47878i) q^{85} +(-0.532249 - 2.51925i) q^{86} +(5.91608 + 5.75538i) q^{88} +(4.81205 - 2.77824i) q^{89} +(-1.36808 - 0.789860i) q^{91} +(0.769734 + 0.562139i) q^{92} +(1.16058 + 1.29215i) q^{94} +(1.91325 - 10.8506i) q^{95} +(8.11117 - 6.80608i) q^{97} +(0.112787 + 0.280148i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 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

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