LMFDB - Embedded newform 972.2.l.c.215.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [96,3,0,3,6,0,0,-9,0,-3,0,0,6,-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			215.4
Character	$\chi$	$=$	972.215
Dual form			972.2.l.c.755.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18930 + 0.765217i) q^{2} +(0.828886 - 1.82015i) q^{4} +(-1.46028 + 1.74029i) q^{5} +(-0.448132 + 1.23123i) q^{7} +(0.407013 + 2.79899i) q^{8} +(0.405013 - 3.18717i) q^{10} +(2.07176 - 1.73841i) q^{11} +(0.789120 - 4.47532i) q^{13} +(-0.409195 - 1.80723i) q^{14} +(-2.62590 - 3.01739i) q^{16} +(4.20783 + 2.42939i) q^{17} +(5.44971 - 3.14639i) q^{19} +(1.95719 + 4.10043i) q^{20} +(-1.13369 + 3.65284i) q^{22} +(-2.38405 + 0.867725i) q^{23} +(-0.0279630 - 0.158586i) q^{25} +(2.48609 + 5.92636i) q^{26} +(1.86958 + 1.83622i) q^{28} +(-4.85038 + 0.855253i) q^{29} +(-0.999738 - 2.74676i) q^{31} +(5.43195 + 1.57922i) q^{32} +(-6.86340 + 0.330619i) q^{34} +(-1.48831 - 2.57783i) q^{35} +(-3.86074 + 6.68701i) q^{37} +(-4.07369 + 7.91222i) q^{38} +(-5.46541 - 3.37898i) q^{40} +(-3.91196 - 0.689785i) q^{41} +(5.46733 + 6.51571i) q^{43} +(-1.44692 - 5.21185i) q^{44} +(2.17137 - 2.85631i) q^{46} +(11.2519 + 4.09536i) q^{47} +(4.04720 + 3.39600i) q^{49} +(0.154609 + 0.167209i) q^{50} +(-7.49167 - 5.14585i) q^{52} -3.84281i q^{53} +6.14402i q^{55} +(-3.62861 - 0.753189i) q^{56} +(5.11412 - 4.72875i) q^{58} +(8.77893 + 7.36639i) q^{59} +(-0.0369509 - 0.0134490i) q^{61} +(3.29086 + 2.50171i) q^{62} +(-7.66868 + 2.27845i) q^{64} +(6.63603 + 7.90851i) q^{65} +(11.7530 + 2.07238i) q^{67} +(7.90967 - 5.64519i) q^{68} +(3.74265 + 1.92694i) q^{70} +(-1.22570 + 2.12297i) q^{71} +(3.09175 + 5.35507i) q^{73} +(-0.525413 - 10.9072i) q^{74} +(-1.20972 - 12.5273i) q^{76} +(1.21197 + 3.32985i) q^{77} +(5.93205 - 1.04598i) q^{79} +(9.08569 - 0.163591i) q^{80} +(5.18035 - 2.17314i) q^{82} +(-1.65768 - 9.40119i) q^{83} +(-10.3725 + 3.77526i) q^{85} +(-11.4882 - 3.56546i) q^{86} +(5.70902 + 5.09126i) q^{88} +(-5.99050 + 3.45862i) q^{89} +(5.15653 + 2.97713i) q^{91} +(-0.396719 + 5.05858i) q^{92} +(-16.5158 + 3.73953i) q^{94} +(-2.48245 + 14.0787i) q^{95} +(-6.70720 + 5.62801i) q^{97} +(-7.41203 - 0.941893i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.18930	+	0.765217i	−0.840965	+	0.541090i
$2$	−1.18930	+	0.765217i	−0.840965	+	0.541090i
$3$		0			0
$3$		0			0
$4$	0.828886	−	1.82015i	0.414443	−	0.910075i
$5$	−1.46028	+	1.74029i	−0.653057	+	0.778282i	−0.986372	−	0.164533i	$-0.947388\pi$
$5$	−1.46028	+	1.74029i	−0.653057	+	0.778282i	0.333315	+	0.942816i	$0.391833\pi$
$6$		0			0
$7$	−0.448132	+	1.23123i	−0.169378	+	0.465363i	−0.995118	−	0.0986879i	$-0.968535\pi$
$7$	−0.448132	+	1.23123i	−0.169378	+	0.465363i	0.825740	+	0.564050i	$0.190758\pi$
$8$	0.407013	+	2.79899i	0.143901	+	0.989592i
$9$		0			0
$10$	0.405013	−	3.18717i	0.128076	−	1.00787i
$11$	2.07176	−	1.73841i	0.624658	−	0.524150i	−0.274606	−	0.961557i	$-0.588547\pi$
$11$	2.07176	−	1.73841i	0.624658	−	0.524150i	0.899264	+	0.437407i	$0.144103\pi$
$12$		0			0
$13$	0.789120	−	4.47532i	0.218862	−	1.24123i	−0.655215	−	0.755443i	$-0.727422\pi$
$13$	0.789120	−	4.47532i	0.218862	−	1.24123i	0.874077	−	0.485788i	$-0.161467\pi$
$14$	−0.409195	−	1.80723i	−0.109362	−	0.483002i
$15$		0			0
$16$	−2.62590	−	3.01739i	−0.656474	−	0.754349i
$17$	4.20783	+	2.42939i	1.02055	+	0.589214i	0.914263	−	0.405122i	$-0.132771\pi$
$17$	4.20783	+	2.42939i	1.02055	+	0.589214i	0.106286	+	0.994336i	$0.466104\pi$
$18$		0			0
$19$	5.44971	−	3.14639i	1.25025	−	0.721832i	0.279090	−	0.960265i	$-0.409967\pi$
$19$	5.44971	−	3.14639i	1.25025	−	0.721832i	0.971159	+	0.238433i	$0.0766339\pi$
$20$	1.95719	+	4.10043i	0.437641	+	0.916884i
$21$		0			0
$22$	−1.13369	+	3.65284i	−0.241703	+	0.778788i
$23$	−2.38405	+	0.867725i	−0.497110	+	0.180933i	−0.578394	−	0.815758i	$-0.696320\pi$
$23$	−2.38405	+	0.867725i	−0.497110	+	0.180933i	0.0812839	+	0.996691i	$0.474098\pi$
$24$		0			0
$25$	−0.0279630	−	0.158586i	−0.00559260	−	0.0317172i
$26$	2.48609	+	5.92636i	0.487562	+	1.16226i
$27$		0			0
$28$	1.86958	+	1.83622i	0.353317	+	0.347013i
$29$	−4.85038	+	0.855253i	−0.900693	+	0.158816i	−0.604775	−	0.796397i	$-0.706737\pi$
$29$	−4.85038	+	0.855253i	−0.900693	+	0.158816i	−0.295918	+	0.955213i	$0.595626\pi$
$30$		0			0
$31$	−0.999738	−	2.74676i	−0.179558	−	0.493332i	0.816961	−	0.576693i	$-0.195657\pi$
$31$	−0.999738	−	2.74676i	−0.179558	−	0.493332i	−0.996519	+	0.0833604i	$0.973435\pi$
$32$	5.43195	+	1.57922i	0.960242	+	0.279169i
$33$		0			0
$34$	−6.86340	+	0.330619i	−1.17706	+	0.0567006i
$35$	−1.48831	−	2.57783i	−0.251570	−	0.435732i
$36$		0			0
$37$	−3.86074	+	6.68701i	−0.634703	+	1.09934i	0.351876	+	0.936047i	$0.385544\pi$
$37$	−3.86074	+	6.68701i	−0.634703	+	1.09934i	−0.986578	+	0.163290i	$0.947789\pi$
$38$	−4.07369	+	7.91222i	−0.660839	+	1.28353i
$39$		0			0
$40$	−5.46541	−	3.37898i	−0.864158	−	0.534264i
$41$	−3.91196	−	0.689785i	−0.610946	−	0.107726i	−0.140390	−	0.990096i	$-0.544836\pi$
$41$	−3.91196	−	0.689785i	−0.610946	−	0.107726i	−0.470556	+	0.882370i	$0.655947\pi$
$42$		0			0
$43$	5.46733	+	6.51571i	0.833760	+	0.993637i	0.999972	+	0.00754644i	$0.00240213\pi$
$43$	5.46733	+	6.51571i	0.833760	+	0.993637i	−0.166211	+	0.986090i	$0.553153\pi$
$44$	−1.44692	−	5.21185i	−0.218131	−	0.785716i
$45$		0			0
$46$	2.17137	−	2.85631i	0.320151	−	0.421140i
$47$	11.2519	+	4.09536i	1.64126	+	0.597370i	0.987259	−	0.159123i	$-0.0508668\pi$
$47$	11.2519	+	4.09536i	1.64126	+	0.597370i	0.654001	+	0.756493i	$0.273089\pi$
$48$		0			0
$49$	4.04720	+	3.39600i	0.578171	+	0.485143i
$50$	0.154609	+	0.167209i	0.0218651	+	0.0236470i
$51$		0			0
$52$	−7.49167	−	5.14585i	−1.03891	−	0.713600i
$53$		−	3.84281i		−	0.527851i	−0.964543	−	0.263925i	$-0.914983\pi$
$53$		−	3.84281i		−	0.527851i	0.964543	−	0.263925i	$-0.0850173\pi$
$54$		0			0
$55$			6.14402i			0.828460i
$56$	−3.62861	−	0.753189i	−0.484893	−	0.100649i
$57$		0			0
$58$	5.11412	−	4.72875i	0.671517	−	0.620915i
$59$	8.77893	+	7.36639i	1.14292	+	0.959023i	0.999530	−	0.0306438i	$-0.00975574\pi$
$59$	8.77893	+	7.36639i	1.14292	+	0.959023i	0.143388	+	0.989666i	$0.454200\pi$
$60$		0			0
$61$	−0.0369509	−	0.0134490i	−0.00473108	−	0.00172197i	0.339654	−	0.940551i	$-0.389690\pi$
$61$	−0.0369509	−	0.0134490i	−0.00473108	−	0.00172197i	−0.344385	+	0.938829i	$0.611912\pi$
$62$	3.29086	+	2.50171i	0.417939	+	0.317718i
$63$		0			0
$64$	−7.66868	+	2.27845i	−0.958585	+	0.284806i
$65$	6.63603	+	7.90851i	0.823098	+	0.980930i
$66$		0			0
$67$	11.7530	+	2.07238i	1.43586	+	0.253181i	0.836795	−	0.547517i	$-0.184427\pi$
$67$	11.7530	+	2.07238i	1.43586	+	0.253181i	0.599068	+	0.800698i	$0.295538\pi$
$68$	7.90967	−	5.64519i	0.959188	−	0.684580i
$69$		0			0
$70$	3.74265	+	1.92694i	0.447332	+	0.230313i
$71$	−1.22570	+	2.12297i	−0.145463	+	0.251950i	−0.929546	−	0.368707i	$-0.879801\pi$
$71$	−1.22570	+	2.12297i	−0.145463	+	0.251950i	0.784082	+	0.620657i	$0.213134\pi$
$72$		0			0
$73$	3.09175	+	5.35507i	0.361862	+	0.626764i	0.988267	−	0.152734i	$-0.0488077\pi$
$73$	3.09175	+	5.35507i	0.361862	+	0.626764i	−0.626405	+	0.779498i	$0.715474\pi$
$74$	−0.525413	−	10.9072i	−0.0610781	−	1.26793i
$75$		0			0
$76$	−1.20972	−	12.5273i	−0.138764	−	1.43698i
$77$	1.21197	+	3.32985i	0.138116	+	0.379472i
$78$		0			0
$79$	5.93205	−	1.04598i	0.667408	−	0.117682i	0.170329	−	0.985387i	$-0.445517\pi$
$79$	5.93205	−	1.04598i	0.667408	−	0.117682i	0.497079	+	0.867705i	$0.334406\pi$
$80$	9.08569	−	0.163591i	1.01581	−	0.0182900i
$81$		0			0
$82$	5.18035	−	2.17314i	0.572074	−	0.239983i
$83$	−1.65768	−	9.40119i	−0.181954	−	1.03191i	−0.929806	−	0.368049i	$-0.880026\pi$
$83$	−1.65768	−	9.40119i	−0.181954	−	1.03191i	0.747852	−	0.663865i	$-0.231085\pi$
$84$		0			0
$85$	−10.3725	+	3.77526i	−1.12505	+	0.409485i
$86$	−11.4882	−	3.56546i	−1.23881	−	0.384474i
$87$		0			0
$88$	5.70902	+	5.09126i	0.608584	+	0.542731i
$89$	−5.99050	+	3.45862i	−0.634991	+	0.366613i	−0.782683	−	0.622421i	$-0.786149\pi$
$89$	−5.99050	+	3.45862i	−0.634991	+	0.366613i	0.147691	+	0.989034i	$0.452816\pi$
$90$		0			0
$91$	5.15653	+	2.97713i	0.540552	+	0.312088i
$92$	−0.396719	+	5.05858i	−0.0413608	+	0.527394i
$93$		0			0
$94$	−16.5158	+	3.73953i	−1.70347	+	0.385703i
$95$	−2.48245	+	14.0787i	−0.254694	+	1.44444i
$96$		0			0
$97$	−6.70720	+	5.62801i	−0.681012	+	0.571437i	−0.916302	−	0.400488i	$-0.868841\pi$
$97$	−6.70720	+	5.62801i	−0.681012	+	0.571437i	0.235290	+	0.971925i	$0.424396\pi$
$98$	−7.41203	−	0.941893i	−0.748728	−	0.0951455i
$99$		0			0
$100$	−0.311829	−	0.0805529i	−0.0311829	−	0.00805529i
$101$	0.753107	−	2.06914i	0.0749369	−	0.205888i	−0.896568	−	0.442905i	$-0.853948\pi$
$101$	0.753107	−	2.06914i	0.0749369	−	0.205888i	0.971505	+	0.237018i	$0.0761700\pi$
$102$		0			0
$103$	1.26442	−	1.50687i	0.124587	−	0.148476i	−0.700145	−	0.714000i	$-0.746882\pi$
$103$	1.26442	−	1.50687i	0.124587	−	0.148476i	0.824732	+	0.565524i	$0.191326\pi$
$104$	12.8476	+	0.387223i	1.25981	+	0.0379703i
$105$		0			0
$106$	2.94059	+	4.57027i	0.285615	+	0.443904i
$107$	−4.06709			−0.393180			−0.196590	−	0.980486i	$-0.562987\pi$
$107$	−4.06709			−0.393180			−0.196590	+	0.980486i	$0.562987\pi$
$108$		0			0
$109$	−1.81021			−0.173387			−0.0866934	−	0.996235i	$-0.527630\pi$
$109$	−1.81021			−0.173387			−0.0866934	+	0.996235i	$0.527630\pi$
$110$	−4.70151	−	7.30711i	−0.448271	−	0.696705i
$111$		0			0
$112$	4.89187	−	1.88090i	0.462238	−	0.177728i
$113$	−2.25644	+	2.68911i	−0.212268	+	0.252971i	−0.861664	−	0.507480i	$-0.830577\pi$
$113$	−2.25644	+	2.68911i	−0.212268	+	0.252971i	0.649396	+	0.760450i	$0.275022\pi$
$114$		0			0
$115$	1.97129	−	5.41607i	0.183824	−	0.505051i
$116$	−2.46372	+	9.53733i	−0.228751	+	0.885519i
$117$		0			0
$118$	−16.0777	−	2.04309i	−1.48007	−	0.188082i
$119$	−4.87681	+	4.09213i	−0.447057	+	0.375125i
$120$		0			0
$121$	−0.640026	+	3.62977i	−0.0581842	+	0.329979i
$122$	0.0542373	−	0.0122805i	0.00491041	−	0.00111182i
$123$		0			0
$124$	−5.82818	−	0.457075i	−0.523386	−	0.0410465i
$125$	−9.52032	−	5.49656i	−0.851523	−	0.491627i
$126$		0			0
$127$	9.71588	−	5.60947i	0.862145	−	0.497760i	−0.00258477	−	0.999997i	$-0.500823\pi$
$127$	9.71588	−	5.60947i	0.862145	−	0.497760i	0.864730	+	0.502237i	$0.167489\pi$
$128$	7.37688	−	8.57798i	0.652030	−	0.758193i
$129$		0			0
$130$	−13.9440	−	4.32762i	−1.22297	−	0.379557i
$131$	4.82128	−	1.75480i	0.421237	−	0.153318i	−0.122700	−	0.992444i	$-0.539155\pi$
$131$	4.82128	−	1.75480i	0.421237	−	0.153318i	0.543937	+	0.839126i	$0.316933\pi$
$132$		0			0
$133$	1.43175	+	8.11986i	0.124149	+	0.704081i
$134$	−15.5638	+	6.52894i	−1.34450	+	0.564015i
$135$		0			0
$136$	−5.08720	+	12.7665i	−0.436224	+	1.09472i
$137$	1.78089	−	0.314019i	0.152152	−	0.0268285i	−0.0970534	−	0.995279i	$-0.530942\pi$
$137$	1.78089	−	0.314019i	0.152152	−	0.0268285i	0.249205	+	0.968451i	$0.419831\pi$
$138$		0			0
$139$	4.44656	+	12.2168i	0.377152	+	1.03622i	0.972531	+	0.232772i	$0.0747796\pi$
$139$	4.44656	+	12.2168i	0.377152	+	1.03622i	−0.595379	+	0.803445i	$0.702998\pi$
$140$	−5.92567	+	0.572222i	−0.500810	+	0.0483616i
$141$		0			0
$142$	−0.166806	−	3.46278i	−0.0139981	−	0.290590i
$143$	−6.14507	−	10.6436i	−0.513877	−	0.890061i
$144$		0			0
$145$	5.59452	−	9.68999i	0.464599	−	0.804710i
$146$	−7.77483	−	4.00295i	−0.643449	−	0.331286i
$147$		0			0
$148$	8.97124	+	12.5699i	0.737431	+	1.03324i
$149$	2.53451	+	0.446902i	0.207635	+	0.0366116i	0.276498	−	0.961014i	$-0.410826\pi$
$149$	2.53451	+	0.446902i	0.207635	+	0.0366116i	−0.0688632	+	0.997626i	$0.521937\pi$
$150$		0			0
$151$	−3.37473	−	4.02185i	−0.274632	−	0.327293i	0.611045	−	0.791596i	$-0.290749\pi$
$151$	−3.37473	−	4.02185i	−0.274632	−	0.327293i	−0.885677	+	0.464303i	$0.846305\pi$
$152$	11.0248	+	13.9731i	0.894231	+	1.13336i
$153$		0			0
$154$	−3.98946	−	3.03279i	−0.321479	−	0.244389i
$155$	6.24006	+	2.27120i	0.501214	+	0.182427i
$156$		0			0
$157$	16.0051	+	13.4298i	1.27734	+	1.07182i	0.993605	+	0.112916i	$0.0360190\pi$
$157$	16.0051	+	13.4298i	1.27734	+	1.07182i	0.283738	+	0.958902i	$0.408425\pi$
$158$	−6.25460	+	5.78329i	−0.497590	+	0.460094i
$159$		0			0
$160$	−10.6805	+	7.14708i	−0.844365	+	0.565027i
$161$		−	3.32418i		−	0.261982i
$162$		0			0
$163$			3.28308i			0.257151i	0.991700	+	0.128575i	$0.0410404\pi$
$163$			3.28308i			0.257151i	−0.991700	+	0.128575i	$0.958960\pi$
$164$	−4.49808	+	6.54861i	−0.351241	+	0.511361i
$165$		0			0
$166$	9.16544	+	9.91238i	0.711376	+	0.769350i
$167$	−14.6697	−	12.3093i	−1.13517	−	0.952523i	−0.135902	−	0.990722i	$-0.543393\pi$
$167$	−14.6697	−	12.3093i	−1.13517	−	0.952523i	−0.999270	+	0.0381993i	$0.987838\pi$
$168$		0			0
$169$	−7.18977	−	2.61686i	−0.553059	−	0.201297i
$170$	9.44710	−	12.4271i	0.724560	−	0.953116i
$171$		0			0
$172$	16.3914	−	4.55058i	1.24983	−	0.346979i
$173$	5.61931	+	6.69683i	0.427228	+	0.509150i	0.936120	−	0.351680i	$-0.114389\pi$
$173$	5.61931	+	6.69683i	0.427228	+	0.509150i	−0.508892	+	0.860830i	$0.669945\pi$
$174$		0			0
$175$	0.207788	+	0.0366386i	0.0157073	+	0.00276962i
$176$	−10.6857	−	1.68642i	−0.805463	−	0.127119i
$177$		0			0
$178$	4.47793	−	8.69737i	0.335635	−	0.651896i
$179$	3.03371	−	5.25454i	0.226750	−	0.392743i	−0.730093	−	0.683348i	$-0.760523\pi$
$179$	3.03371	−	5.25454i	0.226750	−	0.392743i	0.956843	+	0.290605i	$0.0938565\pi$
$180$		0			0
$181$	−8.01419	−	13.8810i	−0.595690	−	1.03177i	−0.993449	−	0.114276i	$-0.963545\pi$
$181$	−8.01419	−	13.8810i	−0.595690	−	1.03177i	0.397759	−	0.917490i	$-0.369788\pi$
$182$	−8.41083	+	0.405161i	−0.623452	+	0.0300325i
$183$		0			0
$184$	−3.39909	−	6.31977i	−0.250585	−	0.465899i
$185$	−5.99958	−	16.4837i	−0.441098	−	1.21191i
$186$		0			0
$187$	12.9409	−	2.28182i	0.946330	−	0.166863i
$188$	16.7807	−	17.0856i	1.22386	−	1.24609i
$189$		0			0
$190$	−7.82087	−	18.6435i	−0.567385	−	1.35254i
$191$	−2.03119	−	11.5195i	−0.146972	−	0.833520i	−0.965763	−	0.259428i	$-0.916466\pi$
$191$	−2.03119	−	11.5195i	−0.146972	−	0.833520i	0.818791	−	0.574092i	$-0.194645\pi$
$192$		0			0
$193$	−16.5117	+	6.00978i	−1.18854	+	0.432593i	−0.859211	−	0.511622i	$-0.829045\pi$
$193$	−16.5117	+	6.00978i	−1.18854	+	0.432593i	−0.329330	+	0.944215i	$0.606823\pi$
$194$	3.67025	−	11.8259i	0.263508	−	0.849048i
$195$		0			0
$196$	9.53590	−	4.55161i	0.681136	−	0.325115i
$197$	19.9607	−	11.5243i	1.42214	−	0.821074i	0.425660	−	0.904883i	$-0.360042\pi$
$197$	19.9607	−	11.5243i	1.42214	−	0.821074i	0.996482	+	0.0838089i	$0.0267085\pi$
$198$		0			0
$199$	2.70763	+	1.56325i	0.191939	+	0.110816i	0.592890	−	0.805284i	$-0.297987\pi$
$199$	2.70763	+	1.56325i	0.191939	+	0.110816i	−0.400951	+	0.916099i	$0.631320\pi$
$200$	0.432499	−	0.142815i	0.0305823	−	0.0100985i
$201$		0			0
$202$	0.687672	+	3.03713i	0.0483844	+	0.213692i
$203$	1.12060	−	6.35522i	0.0786504	−	0.446049i
$204$		0			0
$205$	6.91298	−	5.80068i	0.482824	−	0.405137i
$206$	−0.350690	+	2.75968i	−0.0244337	+	0.192276i
$207$		0			0
$208$	−15.5760	+	9.37064i	−1.08000	+	0.649737i
$209$	5.82075	−	15.9924i	0.402630	−	1.10622i
$210$		0			0
$211$	−8.26193	+	9.84619i	−0.568775	+	0.677839i	−0.971379	−	0.237535i	$-0.923661\pi$
$211$	−8.26193	+	9.84619i	−0.568775	+	0.677839i	0.402604	+	0.915374i	$0.368105\pi$
$212$	−6.99450	−	3.18525i	−0.480384	−	0.218764i
$213$		0			0
$214$	4.83701	−	3.11221i	0.330651	−	0.212746i
$215$	−19.3231			−1.31782
$216$		0			0
$217$	3.82992			0.259992
$218$	2.15289	−	1.38520i	0.145812	−	0.0938179i
$219$		0			0
$220$	11.1830	+	5.09269i	0.753961	+	0.343349i
$221$	14.1928	−	16.9143i	0.954710	−	1.13778i
$222$		0			0
$223$	−3.53622	+	9.71568i	−0.236803	+	0.650610i	0.763187	+	0.646177i	$0.223633\pi$
$223$	−3.53622	+	9.71568i	−0.236803	+	0.650610i	−0.999990	+	0.00443299i	$0.998589\pi$
$224$	−4.37862	+	5.98030i	−0.292559	+	0.399576i
$225$		0			0
$226$	0.625830	−	4.92484i	0.0416296	−	0.327595i
$227$	0.0735740	−	0.0617359i	0.00488328	−	0.00409756i	−0.640343	−	0.768089i	$-0.721208\pi$
$227$	0.0735740	−	0.0617359i	0.00488328	−	0.00409756i	0.645226	+	0.763992i	$0.276763\pi$
$228$		0			0
$229$	4.66642	−	26.4646i	0.308366	−	1.74883i	−0.298856	−	0.954298i	$-0.596605\pi$
$229$	4.66642	−	26.4646i	0.308366	−	1.74883i	0.607222	−	0.794532i	$-0.292284\pi$
$230$	1.80001	+	7.94982i	0.118689	+	0.524195i
$231$		0			0
$232$	−4.36801	−	13.2281i	−0.286774	−	0.868465i
$233$	6.26494	+	3.61706i	0.410430	+	0.236962i	0.690974	−	0.722879i	$-0.257182\pi$
$233$	6.26494	+	3.61706i	0.410430	+	0.236962i	−0.280545	+	0.959841i	$0.590515\pi$
$234$		0			0
$235$	−23.5581	+	13.6013i	−1.53676	+	0.887248i
$236$	20.6847	−	9.87307i	1.34646	−	0.642682i
$237$		0			0
$238$	2.66864	−	8.59861i	0.172982	−	0.557365i
$239$	−11.9878	+	4.36319i	−0.775424	+	0.282231i	−0.699263	−	0.714864i	$-0.746488\pi$
$239$	−11.9878	+	4.36319i	−0.775424	+	0.282231i	−0.0761609	+	0.997096i	$0.524266\pi$
$240$		0			0
$241$	−1.31501	−	7.45780i	−0.0847073	−	0.480399i	−0.997419	−	0.0717956i	$-0.977127\pi$
$241$	−1.31501	−	7.45780i	−0.0847073	−	0.480399i	0.912712	−	0.408603i	$-0.133984\pi$
$242$	−2.01638	−	4.80666i	−0.129618	−	0.308984i
$243$		0			0
$244$	−0.0551074	+	0.0561085i	−0.00352789	+	0.00359198i
$245$	−11.8201	+	2.08420i	−0.755157	+	0.133155i
$246$		0			0
$247$	−9.78063	−	26.8721i	−0.622327	−	1.70983i
$248$	7.28124	−	3.91622i	0.462359	−	0.248680i
$249$		0			0
$250$	15.5286	−	0.748033i	0.982116	−	0.0473098i
$251$	5.95007	+	10.3058i	0.375565	+	0.650498i	0.990411	−	0.138149i	$-0.0441153\pi$
$251$	5.95007	+	10.3058i	0.375565	+	0.650498i	−0.614846	+	0.788647i	$0.710782\pi$
$252$		0			0
$253$	−3.43072	+	5.94217i	−0.215687	+	0.373581i
$254$	−7.26268	+	14.1061i	−0.455701	+	0.885097i
$255$		0			0
$256$	−2.20934	+	15.8467i	−0.138084	+	0.990421i
$257$	5.37613	+	0.947957i	0.335354	+	0.0591320i	0.338790	−	0.940862i	$-0.389982\pi$
$257$	5.37613	+	0.947957i	0.335354	+	0.0591320i	−0.00343564	+	0.999994i	$0.501094\pi$
$258$		0			0
$259$	−6.50314	−	7.75014i	−0.404086	−	0.481570i
$260$	19.8952	−	5.52332i	1.23385	−	0.342542i
$261$		0			0
$262$	−4.39116	+	5.77632i	−0.271287	+	0.356862i
$263$	−19.1400	−	6.96640i	−1.18022	−	0.429566i	−0.323943	−	0.946077i	$-0.605009\pi$
$263$	−19.1400	−	6.96640i	−1.18022	−	0.429566i	−0.856281	+	0.516510i	$0.827231\pi$
$264$		0			0
$265$	6.68762	+	5.61158i	0.410817	+	0.344716i
$266$	−7.91624	−	8.56138i	−0.485376	−	0.524932i
$267$		0			0
$268$	13.5140	−	19.6745i	0.825497	−	1.20181i
$269$			9.12305i			0.556242i	0.960546	+	0.278121i	$0.0897116\pi$
$269$			9.12305i			0.556242i	−0.960546	+	0.278121i	$0.910288\pi$
$270$		0			0
$271$		−	21.2629i		−	1.29163i	−0.763495	−	0.645813i	$-0.776518\pi$
$271$		−	21.2629i		−	1.29163i	0.763495	−	0.645813i	$-0.223482\pi$
$272$	−3.71889	−	19.0760i	−0.225491	−	1.15665i
$273$		0			0
$274$	−1.87773	+	1.73623i	−0.113438	+	0.104890i
$275$	−0.333620	−	0.279940i	−0.0201180	−	0.0168810i
$276$		0			0
$277$	23.9850	+	8.72982i	1.44112	+	0.524524i	0.940096	−	0.340911i	$-0.110735\pi$
$277$	23.9850	+	8.72982i	1.44112	+	0.524524i	0.501022	+	0.865435i	$0.332958\pi$
$278$	−14.6368	−	11.1269i	−0.877858	−	0.667348i
$279$		0			0
$280$	6.60954	−	5.21497i	0.394996	−	0.311654i
$281$	−7.92327	−	9.44259i	−0.472663	−	0.563298i	0.476057	−	0.879414i	$-0.342065\pi$
$281$	−7.92327	−	9.44259i	−0.472663	−	0.563298i	−0.948720	+	0.316116i	$0.897621\pi$
$282$		0			0
$283$	16.4533	+	2.90116i	0.978045	+	0.172456i	0.639749	−	0.768584i	$-0.279038\pi$
$283$	16.4533	+	2.90116i	0.978045	+	0.172456i	0.338296	+	0.941040i	$0.390149\pi$
$284$	2.84816	+	3.99065i	0.169007	+	0.236801i
$285$		0			0
$286$	15.4530	+	7.95613i	0.913755	+	0.470456i
$287$	2.60236	−	4.50743i	0.153613	−	0.266065i
$288$		0			0
$289$	3.30388	+	5.72249i	0.194346	+	0.336617i
$290$	0.761364	+	15.8054i	0.0447089	+	0.928122i
$291$		0			0
$292$	12.3098	−	1.18871i	0.720374	−	0.0695641i
$293$	4.55894	+	12.5256i	0.266336	+	0.731752i	0.998707	+	0.0508459i	$0.0161917\pi$
$293$	4.55894	+	12.5256i	0.266336	+	0.731752i	−0.732370	+	0.680906i	$0.761586\pi$
$294$		0			0
$295$	−25.6394	+	4.52091i	−1.49278	+	0.263218i
$296$	−20.2882	−	8.08448i	−1.17923	−	0.469901i
$297$		0			0
$298$	−3.35627	+	1.40794i	−0.194424	+	0.0815601i
$299$	2.00204	+	11.3541i	0.115781	+	0.656627i
$300$		0			0
$301$	−10.4724	+	3.81166i	−0.603622	+	0.219700i
$302$	7.09117	+	2.20080i	0.408051	+	0.126642i
$303$		0			0
$304$	−23.8043	−	8.18182i	−1.36527	−	0.469260i
$305$	0.0773639	−	0.0446661i	0.00442984	−	0.00255757i
$306$		0			0
$307$	−18.8505	−	10.8833i	−1.07585	−	0.621144i	−0.146078	−	0.989273i	$-0.546665\pi$
$307$	−18.8505	−	10.8833i	−1.07585	−	0.621144i	−0.929775	+	0.368129i	$0.879998\pi$
$308$	7.06541	+	0.554105i	0.402589	+	0.0315730i
$309$		0			0
$310$	−9.15928	+	2.07386i	−0.520212	+	0.117787i
$311$	2.47718	−	14.0488i	0.140468	−	0.796633i	−0.830427	−	0.557128i	$-0.811903\pi$
$311$	2.47718	−	14.0488i	0.140468	−	0.796633i	0.970895	−	0.239506i	$-0.0769854\pi$
$312$		0			0
$313$	16.2981	−	13.6758i	0.921225	−	0.772999i	−0.0529965	−	0.998595i	$-0.516877\pi$
$313$	16.2981	−	13.6758i	0.921225	−	0.772999i	0.974221	+	0.225596i	$0.0724328\pi$
$314$	−29.3116	−	3.72481i	−1.65415	−	0.210203i
$315$		0			0
$316$	3.01315	−	11.6642i	0.169503	−	0.656164i
$317$	−2.30546	+	6.33420i	−0.129488	+	0.355764i	−0.987446	−	0.157954i	$-0.949510\pi$
$317$	−2.30546	+	6.33420i	−0.129488	+	0.355764i	0.857959	+	0.513718i	$0.171732\pi$
$318$		0			0
$319$	−8.56202	+	10.2038i	−0.479381	+	0.571304i
$320$	7.23324	−	16.6729i	0.404350	−	0.932045i
$321$		0			0
$322$	2.54372	+	3.95346i	0.141756	+	0.220318i
$323$	30.5753			1.70125
$324$		0			0
$325$	−0.731790			−0.0405924
$326$	−2.51227	−	3.90458i	−0.139142	−	0.216255i
$327$		0			0
$328$	0.338479	−	11.2303i	0.0186894	−	0.620089i
$329$	−10.0847	+	12.0185i	−0.555987	+	0.662600i
$330$		0			0
$331$	8.27597	−	22.7380i	0.454888	−	1.24980i	−0.474357	−	0.880333i	$-0.657319\pi$
$331$	8.27597	−	22.7380i	0.454888	−	1.24980i	0.929245	−	0.369463i	$-0.120458\pi$
$332$	−18.4856	−	4.77528i	−1.01453	−	0.262077i
$333$		0			0
$334$	26.8660	+	3.41403i	1.47004	+	0.186807i
$335$	−20.7693	+	17.4275i	−1.13475	+	0.952165i
$336$		0			0
$337$	3.79458	−	21.5201i	0.206704	−	1.17228i	−0.688032	−	0.725681i	$-0.741525\pi$
$337$	3.79458	−	21.5201i	0.206704	−	1.17228i	0.894736	−	0.446596i	$-0.147364\pi$
$338$	10.5533	−	2.38949i	0.574023	−	0.129971i
$339$		0			0
$340$	−1.72603	+	22.0087i	−0.0936072	+	1.19359i
$341$	−6.84620	−	3.95266i	−0.370743	−	0.214048i
$342$		0			0
$343$	−13.9379	+	8.04707i	−0.752577	+	0.434501i
$344$	−16.0121	+	17.9550i	−0.863316	+	0.968068i
$345$		0			0
$346$	−11.8076	−	3.66457i	−0.634780	−	0.197009i
$347$	12.1710	−	4.42990i	0.653376	−	0.237809i	0.00600211	−	0.999982i	$-0.498089\pi$
$347$	12.1710	−	4.42990i	0.653376	−	0.237809i	0.647374	+	0.762173i	$0.275867\pi$
$348$		0			0
$349$	−0.671596	−	3.80881i	−0.0359497	−	0.203881i	0.961543	−	0.274656i	$-0.0885639\pi$
$349$	−0.671596	−	3.80881i	−0.0359497	−	0.203881i	−0.997492	+	0.0707748i	$0.977453\pi$
$350$	−0.275159	+	0.115428i	−0.0147079	+	0.00616990i
$351$		0			0
$352$	13.9990	−	6.17120i	0.746149	−	0.328926i
$353$	2.99642	−	0.528350i	0.159483	−	0.0281212i	−0.0933363	−	0.995635i	$-0.529753\pi$
$353$	2.99642	−	0.528350i	0.159483	−	0.0281212i	0.252820	+	0.967513i	$0.418642\pi$
$354$		0			0
$355$	−1.90473	−	5.23319i	−0.101092	−	0.277749i
$356$	1.32976	+	13.7704i	0.0704772	+	0.729830i
$357$		0			0
$358$	0.412862	+	8.57070i	0.0218204	+	0.452975i
$359$	8.27544	+	14.3335i	0.436761	+	0.756492i	0.997438	−	0.0715425i	$-0.0227922\pi$
$359$	8.27544	+	14.3335i	0.436761	+	0.756492i	−0.560676	+	0.828035i	$0.689459\pi$
$360$		0			0
$361$	10.2995	−	17.8393i	0.542082	−	0.938913i
$362$	20.1533	+	10.3761i	1.05923	+	0.545356i
$363$		0			0
$364$	9.69300	−	6.91797i	0.508051	−	0.362600i
$365$	−13.8342	−	2.43935i	−0.724116	−	0.127681i
$366$		0			0
$367$	1.41856	+	1.69058i	0.0740484	+	0.0882474i	0.801797	−	0.597597i	$-0.203878\pi$
$367$	1.41856	+	1.69058i	0.0740484	+	0.0882474i	−0.727748	+	0.685844i	$0.759433\pi$
$368$	8.87855	+	4.91508i	0.462826	+	0.256216i
$369$		0			0
$370$	19.7489	+	15.0132i	1.02670	+	0.780497i
$371$	4.73140	+	1.72209i	0.245642	+	0.0894064i
$372$		0			0
$373$	−8.03381	−	6.74117i	−0.415975	−	0.349044i	0.410655	−	0.911791i	$-0.365300\pi$
$373$	−8.03381	−	6.74117i	−0.415975	−	0.349044i	−0.826629	+	0.562747i	$0.809745\pi$
$374$	−13.6445	+	12.6164i	−0.705542	+	0.652376i
$375$		0			0
$376$	−6.88319	+	33.1608i	−0.354974	+	1.71014i
$377$			22.3819i			1.15273i
$378$		0			0
$379$		−	3.08694i		−	0.158565i	−0.996852	−	0.0792826i	$-0.974737\pi$
$379$		−	3.08694i		−	0.158565i	0.996852	−	0.0792826i	$-0.0252630\pi$
$380$	23.5677	+	16.1881i	1.20900	+	0.830431i
$381$		0			0
$382$	11.2306	+	12.1458i	0.574608	+	0.621436i
$383$	12.3070	+	10.3268i	0.628856	+	0.527673i	0.900573	−	0.434704i	$-0.143147\pi$
$383$	12.3070	+	10.3268i	0.628856	+	0.527673i	−0.271717	+	0.962377i	$0.587592\pi$
$384$		0			0
$385$	−7.56473	−	2.75333i	−0.385534	−	0.140323i
$386$	15.0387	−	19.7825i	0.765449	−	1.00690i
$387$		0			0
$388$	4.68432	+	16.8731i	0.237810	+	0.856601i
$389$	−11.3463	−	13.5220i	−0.575280	−	0.685593i	0.397425	−	0.917635i	$-0.369904\pi$
$389$	−11.3463	−	13.5220i	−0.575280	−	0.685593i	−0.972706	+	0.232042i	$0.925459\pi$
$390$		0			0
$391$	−12.1397	−	2.14056i	−0.613933	−	0.108253i
$392$	−7.85811	+	12.7103i	−0.396894	+	0.641966i
$393$		0			0
$394$	−14.9207	+	28.9802i	−0.751696	+	1.46000i
$395$	−6.84213	+	11.8509i	−0.344265	+	0.596285i
$396$		0			0
$397$	6.73828	+	11.6710i	0.338185	+	0.585753i	0.984091	−	0.177663i	$-0.0568538\pi$
$397$	6.73828	+	11.6710i	0.338185	+	0.585753i	−0.645907	+	0.763416i	$0.723520\pi$
$398$	−4.41642	+	0.212745i	−0.221375	+	0.0106639i
$399$		0			0
$400$	−0.405089	+	0.500806i	−0.0202544	+	0.0250403i
$401$	2.31159	+	6.35103i	0.115435	+	0.317155i	0.983933	−	0.178537i	$-0.0571365\pi$
$401$	2.31159	+	6.35103i	0.115435	+	0.317155i	−0.868498	+	0.495693i	$0.834914\pi$
$402$		0			0
$403$	−13.0815	+	2.30663i	−0.651638	+	0.114901i
$404$	−3.14191	−	3.08585i	−0.156316	−	0.153527i
$405$		0			0
$406$	3.53039	+	8.41578i	0.175210	+	0.417668i
$407$	3.62623	+	20.5654i	0.179746	+	1.01939i
$408$		0			0
$409$	−17.7069	+	6.44479i	−0.875551	+	0.318674i	−0.740413	−	0.672152i	$-0.765370\pi$
$409$	−17.7069	+	6.44479i	−0.875551	+	0.318674i	−0.135138	+	0.990827i	$0.543148\pi$
$410$	−3.78286	+	12.1887i	−0.186822	+	0.601957i
$411$		0			0
$412$	−1.69468	−	3.55045i	−0.0834907	−	0.174918i
$413$	−13.0039	+	7.50779i	−0.639879	+	0.369434i
$414$		0			0
$415$	18.7815	+	10.8435i	0.921947	+	0.532287i
$416$	11.3540	−	23.0635i	0.556674	−	1.13078i
$417$		0			0
$418$	5.31500	+	23.4739i	0.259965	+	1.14815i
$419$	3.31570	−	18.8043i	0.161983	−	0.918649i	−0.790139	−	0.612928i	$-0.789991\pi$
$419$	3.31570	−	18.8043i	0.161983	−	0.918649i	0.952121	−	0.305721i	$-0.0988974\pi$
$420$		0			0
$421$	−17.2688	+	14.4903i	−0.841631	+	0.706212i	−0.957930	−	0.287002i	$-0.907341\pi$
$421$	−17.2688	+	14.4903i	−0.841631	+	0.706212i	0.116299	+	0.993214i	$0.462897\pi$
$422$	2.29148	−	18.0323i	0.111547	−	0.877797i
$423$		0			0
$424$	10.7560	−	1.56408i	0.522357	−	0.0759582i
$425$	0.267604	−	0.735236i	0.0129807	−	0.0356642i
$426$		0			0
$427$	0.0331178	−	0.0394683i	0.00160268	−	0.00191000i
$428$	−3.37115	+	7.40272i	−0.162951	+	0.357824i
$429$		0			0
$430$	22.9810	−	14.7863i	1.10824	−	0.713061i
$431$	10.8059			0.520500			0.260250	−	0.965541i	$-0.416195\pi$
$431$	10.8059			0.520500			0.260250	+	0.965541i	$0.416195\pi$
$432$		0			0
$433$	−37.5914			−1.80653			−0.903264	−	0.429084i	$-0.858836\pi$
$433$	−37.5914			−1.80653			−0.903264	+	0.429084i	$0.858836\pi$
$434$	−4.55493	+	2.93072i	−0.218644	+	0.140679i
$435$		0			0
$436$	−1.50046	+	3.29486i	−0.0718589	+	0.157795i
$437$	−10.2622	+	12.2300i	−0.490908	+	0.585041i
$438$		0			0
$439$	−10.9220	+	30.0080i	−0.521279	+	1.43220i	0.347818	+	0.937562i	$0.386923\pi$
$439$	−10.9220	+	30.0080i	−0.521279	+	1.43220i	−0.869097	+	0.494641i	$0.835300\pi$
$440$	−17.1970	+	2.50070i	−0.819837	+	0.119216i
$441$		0			0
$442$	−3.93642	+	30.9768i	−0.187236	+	1.47342i
$443$	28.7890	−	24.1569i	1.36781	−	1.14773i	0.394324	−	0.918972i	$-0.370979\pi$
$443$	28.7890	−	24.1569i	1.36781	−	1.14773i	0.973484	−	0.228755i	$-0.0734655\pi$
$444$		0			0
$445$	2.72879	−	15.4758i	0.129357	−	0.733621i
$446$	−3.22897	−	14.2609i	−0.152896	−	0.675272i
$447$		0			0
$448$	0.631278	−	10.4630i	0.0298251	−	0.494330i
$449$	−6.99926	−	4.04102i	−0.330315	−	0.190708i	0.325666	−	0.945485i	$-0.394412\pi$
$449$	−6.99926	−	4.04102i	−0.330315	−	0.190708i	−0.655981	+	0.754777i	$0.727745\pi$
$450$		0			0
$451$	−9.30376	+	5.37153i	−0.438097	+	0.252935i
$452$	3.02427	+	6.33602i	0.142250	+	0.298021i
$453$		0			0
$454$	−0.0402605	+	0.129723i	−0.00188952	+	0.00608820i
$455$	−12.7110	+	4.62644i	−0.595903	+	0.216891i
$456$		0			0
$457$	−0.429633	−	2.43657i	−0.0200974	−	0.113978i	0.973109	−	0.230346i	$-0.0739858\pi$
$457$	−0.429633	−	2.43657i	−0.0200974	−	0.113978i	−0.993206	+	0.116368i	$0.962875\pi$
$458$	14.7014	+	35.0453i	0.686950	+	1.63756i
$459$		0			0
$460$	−8.22409	−	8.07735i	−0.383450	−	0.376608i
$461$	8.89827	−	1.56901i	0.414434	−	0.0730759i	0.0374563	−	0.999298i	$-0.488075\pi$
$461$	8.89827	−	1.56901i	0.414434	−	0.0730759i	0.376978	+	0.926222i	$0.376963\pi$
$462$		0			0
$463$	−0.476987	−	1.31051i	−0.0221675	−	0.0609046i	0.928115	−	0.372293i	$-0.121428\pi$
$463$	−0.476987	−	1.31051i	−0.0221675	−	0.0609046i	−0.950283	+	0.311388i	$0.899206\pi$
$464$	15.3172	+	12.3897i	0.711085	+	0.575178i
$465$		0			0
$466$	−10.2188	+	0.492251i	−0.473375	+	0.0228031i
$467$	10.5492	+	18.2717i	0.488158	+	0.845515i	0.999907	−	0.0136203i	$-0.00433561\pi$
$467$	10.5492	+	18.2717i	0.488158	+	0.845515i	−0.511749	+	0.859135i	$0.671002\pi$
$468$		0			0
$469$	−7.81850	+	13.5420i	−0.361025	+	0.625313i
$470$	17.6098	−	34.2030i	0.812278	−	1.57767i
$471$		0			0
$472$	−17.0453	+	27.5703i	−0.784574	+	1.26903i
$473$	22.6539	+	3.99450i	1.04163	+	0.183667i
$474$		0			0
$475$	−0.651364	−	0.776265i	−0.0298866	−	0.0356175i
$476$	3.40597	+	12.2684i	0.156113	+	0.562323i
$477$		0			0
$478$	10.9183	−	14.3624i	0.499392	−	0.656921i
$479$	−13.7237	−	4.99501i	−0.627051	−	0.228228i	0.00889607	−	0.999960i	$-0.497168\pi$
$479$	−13.7237	−	4.99501i	−0.627051	−	0.228228i	−0.635947	+	0.771732i	$0.719390\pi$
$480$		0			0
$481$	26.8799	+	22.5549i	1.22562	+	1.02842i
$482$	7.27078	+	7.86331i	0.331175	+	0.358164i
$483$		0			0
$484$	6.07622	+	4.17361i	0.276192	+	0.189710i
$485$		−	19.8909i		−	0.903201i
$486$		0			0
$487$		−	0.282541i		−	0.0128032i	−0.999980	−	0.00640158i	$-0.997962\pi$
$487$		−	0.282541i		−	0.0128032i	0.999980	−	0.00640158i	$-0.00203770\pi$
$488$	0.0226042	−	0.108899i	0.00102324	−	0.00492963i
$489$		0			0
$490$	12.4628	−	11.5237i	0.563012	−	0.520586i
$491$	−11.8728	−	9.96249i	−0.535814	−	0.449601i	0.334290	−	0.942470i	$-0.391504\pi$
$491$	−11.8728	−	9.96249i	−0.535814	−	0.449601i	−0.870103	+	0.492869i	$0.835948\pi$
$492$		0			0
$493$	−22.4873	−	8.18471i	−1.01278	−	0.368621i
$494$	32.1951	+	24.4747i	1.44853	+	1.10117i
$495$		0			0
$496$	−5.66284	+	10.2293i	−0.254269	+	0.459309i
$497$	−2.06459	−	2.46049i	−0.0926097	−	0.110368i
$498$		0			0
$499$	−40.2749	−	7.10155i	−1.80295	−	0.317909i	−0.831568	−	0.555423i	$-0.812557\pi$
$499$	−40.2749	−	7.10155i	−1.80295	−	0.317909i	−0.971384	+	0.237513i	$0.923668\pi$
$500$	−17.8958	+	12.7724i	−0.800326	+	0.571199i
$501$		0			0
$502$	−14.9626	−	7.70366i	−0.667815	−	0.343831i
$503$	−9.96192	+	17.2546i	−0.444180	+	0.769343i	−0.997995	−	0.0632975i	$-0.979838\pi$
$503$	−9.96192	+	17.2546i	−0.444180	+	0.769343i	0.553815	+	0.832640i	$0.313172\pi$
$504$		0			0
$505$	2.50117	+	4.33215i	0.111301	+	0.192778i
$506$	−0.466890	−	9.69229i	−0.0207558	−	0.430875i
$507$		0			0
$508$	−2.15672	−	22.3340i	−0.0956889	−	0.990910i
$509$	9.68384	+	26.6061i	0.429229	+	1.17930i	0.946282	+	0.323343i	$0.104807\pi$
$509$	9.68384	+	26.6061i	0.429229	+	1.17930i	−0.517053	+	0.855953i	$0.672971\pi$
$510$		0			0
$511$	−7.97886	+	1.40689i	−0.352964	+	0.0622371i
$512$	−9.49862	−	20.5372i	−0.419783	−	0.907624i
$513$		0			0
$514$	−7.11925	+	2.98650i	−0.314017	+	0.131729i
$515$	0.775998	+	4.40091i	0.0341946	+	0.193927i
$516$		0			0
$517$	30.4306	−	11.0758i	1.33834	−	0.487115i
$518$	13.6647	+	4.24096i	0.600395	+	0.186337i
$519$		0			0
$520$	−19.4349	+	21.7930i	−0.852276	+	0.955688i
$521$	−18.4642	+	10.6603i	−0.808931	+	0.467036i	−0.846584	−	0.532255i	$-0.821345\pi$
$521$	−18.4642	+	10.6603i	−0.808931	+	0.467036i	0.0376537	+	0.999291i	$0.488012\pi$
$522$		0			0
$523$	−17.0213	−	9.82725i	−0.744289	−	0.429716i	0.0793376	−	0.996848i	$-0.474719\pi$
$523$	−17.0213	−	9.82725i	−0.744289	−	0.429716i	−0.823627	+	0.567132i	$0.808053\pi$
$524$	0.802286	−	10.2300i	0.0350480	−	0.446899i
$525$		0			0
$526$	28.0941	−	6.36111i	1.22496	−	0.277357i
$527$	2.46622	−	13.9866i	0.107430	−	0.609268i
$528$		0			0
$529$	−12.6883	+	10.6467i	−0.551663	+	0.462900i
$530$	−12.2477	−	1.55639i	−0.532005	−	0.0676053i
$531$		0			0
$532$	15.9661	+	4.12444i	0.692220	+	0.178817i
$533$	−6.17401	+	16.9630i	−0.267426	+	0.734748i
$534$		0			0
$535$	5.93909	−	7.07793i	0.256769	−	0.306005i
$536$	−1.01692	+	33.7401i	−0.0439243	+	1.45735i
$537$		0			0
$538$	−6.98111	−	10.8501i	−0.300977	−	0.467780i
$539$	14.2884			0.615447
$540$		0			0
$541$	41.1619			1.76969			0.884844	−	0.465888i	$-0.154265\pi$
$541$	41.1619			1.76969			0.884844	+	0.465888i	$0.154265\pi$
$542$	16.2707	+	25.2880i	0.698887	+	1.08621i
$543$		0			0
$544$	19.0202	+	19.8414i	0.815483	+	0.850693i
$545$	2.64341	−	3.15030i	0.113231	−	0.134944i
$546$		0			0
$547$	2.48445	−	6.82596i	0.106227	−	0.291857i	−0.875179	−	0.483799i	$-0.839256\pi$
$547$	2.48445	−	6.82596i	0.106227	−	0.291857i	0.981406	+	0.191942i	$0.0614786\pi$
$548$	0.904593	−	3.50178i	0.0386423	−	0.149588i
$549$		0			0
$550$	0.610991	+	0.0776424i	0.0260527	+	0.00331068i
$551$	−23.7422	+	19.9221i	−1.01145	+	0.848709i
$552$		0			0
$553$	−1.37050	+	7.77247i	−0.0582795	+	0.330519i
$554$	−35.2056	+	7.97131i	−1.49574	+	0.338668i
$555$		0			0
$556$	25.9221	+	2.03294i	1.09934	+	0.0862159i
$557$	32.2123	+	18.5978i	1.36488	+	0.788012i	0.990268	−	0.139170i	$-0.0444436\pi$
$557$	32.2123	+	18.5978i	1.36488	+	0.788012i	0.374609	+	0.927183i	$0.377777\pi$
$558$		0			0
$559$	33.4743	−	19.3264i	1.41581	−	0.817419i
$560$	−3.87017	+	11.2599i	−0.163545	+	0.475818i
$561$		0			0
$562$	16.6488	+	5.16708i	0.702288	+	0.217960i
$563$	41.7085	−	15.1806i	1.75780	−	0.639788i	0.757881	−	0.652392i	$-0.226235\pi$
$563$	41.7085	−	15.1806i	1.75780	−	0.639788i	0.999921	+	0.0126049i	$0.00401237\pi$
$564$		0			0
$565$	−1.38482	−	7.85371i	−0.0582599	−	0.330408i
$566$	−21.7879	+	9.13997i	−0.915816	+	0.384181i
$567$		0			0
$568$	−6.44104	−	2.56663i	−0.270260	−	0.107694i
$569$	29.0449	−	5.12140i	1.21763	−	0.214700i	0.472322	−	0.881426i	$-0.343416\pi$
$569$	29.0449	−	5.12140i	1.21763	−	0.214700i	0.745303	+	0.666726i	$0.232305\pi$
$570$		0			0
$571$	−4.48049	−	12.3101i	−0.187503	−	0.515160i	0.809949	−	0.586500i	$-0.199495\pi$
$571$	−4.48049	−	12.3101i	−0.187503	−	0.515160i	−0.997452	+	0.0713402i	$0.977272\pi$
$572$	−24.4665	+	2.36265i	−1.02299	+	0.0987872i
$573$		0			0
$574$	0.354159	+	7.35207i	0.0147823	+	0.306869i
$575$	0.204274	+	0.353814i	0.00851883	+	0.0147550i
$576$		0			0
$577$	2.02124	−	3.50090i	0.0841455	−	0.145744i	−0.820881	−	0.571099i	$-0.806517\pi$
$577$	2.02124	−	3.50090i	0.0841455	−	0.145744i	0.905027	+	0.425355i	$0.139851\pi$
$578$	−8.30827	−	4.27759i	−0.345578	−	0.177924i
$579$		0			0
$580$	−13.0000	−	18.2148i	−0.539796	−	0.756327i
$581$	12.3179	+	2.17198i	0.511033	+	0.0901090i
$582$		0			0
$583$	−6.68038	−	7.96137i	−0.276673	−	0.329726i
$584$	−13.7304	+	10.8334i	−0.568168	+	0.448288i
$585$		0			0
$586$	−15.0068	−	11.4081i	−0.619923	−	0.471266i
$587$	−6.83715	−	2.48852i	−0.282199	−	0.102712i	0.197043	−	0.980395i	$-0.436866\pi$
$587$	−6.83715	−	2.48852i	−0.282199	−	0.102712i	−0.479242	+	0.877683i	$0.659088\pi$
$588$		0			0
$589$	−14.0907	−	11.8235i	−0.580595	−	0.487177i
$590$	27.0335	−	24.9964i	1.11295	−	1.02909i
$591$		0			0
$592$	30.3152	−	5.91000i	1.24595	−	0.242899i
$593$		−	2.93118i		−	0.120369i	−0.998187	−	0.0601846i	$-0.980831\pi$
$593$		−	2.93118i		−	0.120369i	0.998187	−	0.0601846i	$-0.0191689\pi$
$594$		0			0
$595$		−	14.4627i		−	0.592914i
$596$	2.91424	−	4.24275i	0.119372	−	0.173790i
$597$		0			0
$598$	−11.0694	−	11.9715i	−0.452662	−	0.489552i
$599$	−1.03995	−	0.872619i	−0.0424911	−	0.0356543i	0.621295	−	0.783577i	$-0.286607\pi$
$599$	−1.03995	−	0.872619i	−0.0424911	−	0.0356543i	−0.663786	+	0.747923i	$0.731051\pi$
$600$		0			0
$601$	−7.27189	−	2.64675i	−0.296626	−	0.107963i	0.189420	−	0.981896i	$-0.439339\pi$
$601$	−7.27189	−	2.64675i	−0.296626	−	0.107963i	−0.486047	+	0.873933i	$0.661561\pi$
$602$	9.53817	−	12.5469i	0.388747	−	0.511374i
$603$		0			0
$604$	−10.1176	+	2.80887i	−0.411681	+	0.114291i
$605$	−5.38225	−	6.41431i	−0.218819	−	0.260779i
$606$		0			0
$607$	−11.2517	−	1.98398i	−0.456692	−	0.0805271i	−0.0594302	−	0.998232i	$-0.518928\pi$
$607$	−11.2517	−	1.98398i	−0.456692	−	0.0805271i	−0.397262	+	0.917705i	$0.630039\pi$
$608$	34.5714	−	8.48476i	1.40205	−	0.344103i
$609$		0			0
$610$	−0.0578299	+	0.112322i	−0.00234146	+	0.00454777i
$611$	27.2072	−	47.1242i	1.10068	−	1.90644i
$612$		0			0
$613$	−12.0261	−	20.8298i	−0.485729	−	0.841307i	0.514137	−	0.857708i	$-0.328112\pi$
$613$	−12.0261	−	20.8298i	−0.485729	−	0.841307i	−0.999865	+	0.0164015i	$0.994779\pi$
$614$	30.7470	−	1.48112i	1.24085	−	0.0597733i
$615$		0			0
$616$	−8.82693	+	4.74758i	−0.355647	+	0.191285i
$617$	−16.5026	−	45.3406i	−0.664371	−	1.82534i	−0.555909	−	0.831243i	$-0.687630\pi$
$617$	−16.5026	−	45.3406i	−0.664371	−	1.82534i	−0.108462	−	0.994101i	$-0.534593\pi$
$618$		0			0
$619$	4.44121	−	0.783104i	0.178507	−	0.0314756i	−0.0836800	−	0.996493i	$-0.526667\pi$
$619$	4.44121	−	0.783104i	0.178507	−	0.0314756i	0.262187	+	0.965017i	$0.415556\pi$
$620$	9.30621	−	9.47528i	0.373747	−	0.380537i
$621$		0			0
$622$	7.80425	+	18.6038i	0.312922	+	0.745946i
$623$	−1.57383	−	8.92562i	−0.0630541	−	0.357597i
$624$		0			0
$625$	24.2246	−	8.81702i	0.968982	−	0.352681i
$626$	−8.91850	+	28.7362i	−0.356455	+	1.14853i
$627$		0			0
$628$	37.7107	−	17.9998i	1.50482	−	0.718271i
$629$	−32.4907	+	18.7585i	−1.29549	+	0.747951i
$630$		0			0
$631$	9.73065	+	5.61799i	0.387371	+	0.223649i	0.681020	−	0.732264i	$-0.261536\pi$
$631$	9.73065	+	5.61799i	0.387371	+	0.223649i	−0.293649	+	0.955913i	$0.594870\pi$
$632$	5.34211	+	16.1780i	0.212498	+	0.643527i
$633$		0			0
$634$	−2.10515	−	9.29747i	−0.0836061	−	0.369250i
$635$	−4.42578	+	25.0999i	−0.175632	+	0.996058i
$636$		0			0
$637$	18.3919	−	15.4327i	0.728714	−	0.611464i
$638$	2.37471	−	18.6872i	0.0940155	−	0.739835i
$639$		0			0
$640$	4.15589	+	25.3642i	0.164276	+	1.00261i
$641$	−13.8530	+	38.0609i	−0.547163	+	1.50332i	0.290362	+	0.956917i	$0.406224\pi$
$641$	−13.8530	+	38.0609i	−0.547163	+	1.50332i	−0.837524	+	0.546400i	$0.815998\pi$
$642$		0			0
$643$	−20.7380	+	24.7146i	−0.817827	+	0.974648i	−0.999963	−	0.00862524i	$-0.997254\pi$
$643$	−20.7380	+	24.7146i	−0.817827	+	0.974648i	0.182136	+	0.983273i	$0.441699\pi$
$644$	−6.05051	−	2.75537i	−0.238424	−	0.108577i
$645$		0			0
$646$	−36.3633	+	23.3967i	−1.43069	+	0.920531i
$647$	−7.00490			−0.275391			−0.137696	−	0.990475i	$-0.543970\pi$
$647$	−7.00490			−0.275391			−0.137696	+	0.990475i	$0.543970\pi$
$648$		0			0
$649$	30.9936			1.21660
$650$	0.870320	−	0.559978i	0.0341368	−	0.0219641i
$651$		0			0
$652$	5.97570	+	2.72130i	0.234027	+	0.106574i
$653$	22.5667	−	26.8939i	0.883102	−	1.05244i	−0.115150	−	0.993348i	$-0.536735\pi$
$653$	22.5667	−	26.8939i	0.883102	−	1.05244i	0.998253	−	0.0590921i	$-0.0188206\pi$
$654$		0			0
$655$	−3.98654	+	10.9529i	−0.155767	+	0.427967i
$656$	8.19106	+	13.6152i	0.319807	+	0.531586i
$657$		0			0
$658$	2.79702	−	22.0106i	0.109039	−	0.858062i
$659$	6.86177	−	5.75771i	0.267297	−	0.224289i	−0.499281	−	0.866440i	$-0.666402\pi$
$659$	6.86177	−	5.75771i	0.267297	−	0.224289i	0.766578	+	0.642152i	$0.221958\pi$
$660$		0			0
$661$	−6.18560	+	35.0803i	−0.240592	+	1.36447i	0.589919	+	0.807463i	$0.299160\pi$
$661$	−6.18560	+	35.0803i	−0.240592	+	1.36447i	−0.830511	+	0.557003i	$0.811951\pi$
$662$	7.55689	+	33.3753i	0.293707	+	1.29717i
$663$		0			0
$664$	25.6391	−	8.46625i	0.994991	−	0.328554i
$665$	−16.2217	−	9.36560i	−0.629050	−	0.363182i
$666$		0			0
$667$	10.8214	−	6.24776i	0.419008	−	0.241914i
$668$	−34.5643	+	16.4980i	−1.33733	+	0.638326i
$669$		0			0
$670$	11.3652	−	36.6196i	0.439074	−	1.41474i
$671$	−0.0999332	+	0.0363727i	−0.00385788	+	0.00140415i
$672$		0			0
$673$	−0.586335	−	3.32527i	−0.0226015	−	0.128180i	0.971419	−	0.237370i	$-0.0762854\pi$
$673$	−0.586335	−	3.32527i	−0.0226015	−	0.128180i	−0.994021	+	0.109190i	$0.965174\pi$
$674$	11.9547	+	28.4977i	0.460477	+	1.09769i
$675$		0			0
$676$	−10.7226	+	10.9174i	−0.412407	+	0.419900i
$677$	−1.13808	+	0.200675i	−0.0437401	+	0.00771256i	−0.195475	−	0.980709i	$-0.562625\pi$
$677$	−1.13808	+	0.200675i	−0.0437401	+	0.00771256i	0.151735	+	0.988421i	$0.451514\pi$
$678$		0			0
$679$	−3.92368	−	10.7802i	−0.150577	−	0.413707i
$680$	−14.7887	−	27.4958i	−0.567119	−	1.05442i
$681$		0			0
$682$	11.1669	−	0.537922i	0.427601	−	0.0205981i
$683$	−21.5897	−	37.3945i	−0.826107	−	1.43086i	−0.901070	−	0.433673i	$-0.857217\pi$
$683$	−21.5897	−	37.3945i	−0.826107	−	1.43086i	0.0749630	−	0.997186i	$-0.476116\pi$
$684$		0			0
$685$	−2.05411	+	3.55783i	−0.0784836	+	0.135938i
$686$	10.4187	−	20.2359i	0.397787	−	0.772612i
$687$		0			0
$688$	5.30382	−	33.6067i	0.202206	−	1.28124i
$689$	−17.1978	−	3.03244i	−0.655184	−	0.115527i
$690$		0			0
$691$	−8.25397	−	9.83670i	−0.313996	−	0.374206i	0.585846	−	0.810423i	$-0.300762\pi$
$691$	−8.25397	−	9.83670i	−0.313996	−	0.374206i	−0.899842	+	0.436217i	$0.856318\pi$
$692$	16.8470	−	4.67708i	0.640427	−	0.177796i
$693$		0			0
$694$	−11.0852	+	14.5820i	−0.420790	+	0.553525i
$695$	−27.7540	−	10.1016i	−1.05277	−	0.383177i
$696$		0			0
$697$	−14.7851	−	12.4062i	−0.560026	−	0.469918i
$698$	3.71330	+	4.01592i	0.140550	+	0.152005i
$699$		0			0
$700$	0.238920	−	0.347836i	0.00903032	−	0.0131469i
$701$			3.10248i			0.117179i	0.998282	+	0.0585896i	$0.0186603\pi$
$701$			3.10248i			0.117179i	−0.998282	+	0.0585896i	$0.981340\pi$
$702$		0			0
$703$			48.5896i			1.83259i
$704$	−11.9267	+	18.0517i	−0.449506	+	0.680349i
$705$		0			0
$706$	−3.15935	+	2.92128i	−0.118904	+	0.109944i
$707$	2.21011	+	1.85450i	0.0831197	+	0.0697457i
$708$		0			0
$709$	−9.07129	−	3.30168i	−0.340680	−	0.123997i	0.166014	−	0.986123i	$-0.446910\pi$
$709$	−9.07129	−	3.30168i	−0.340680	−	0.123997i	−0.506694	+	0.862126i	$0.669132\pi$
$710$	6.26983	+	4.76633i	0.235302	+	0.178877i
$711$		0			0
$712$	−12.1188	−	15.3596i	−0.454173	−	0.575627i
$713$	4.76686	+	5.68092i	0.178520	+	0.212752i
$714$		0			0
$715$	27.4965	+	4.84837i	1.02831	+	0.181319i
$716$	−7.04946	−	9.87723i	−0.263451	−	0.369129i
$717$		0			0
$718$	−20.8102	−	10.7144i	−0.776631	−	0.399856i
$719$	−20.9190	+	36.2327i	−0.780146	+	1.35125i	0.151711	+	0.988425i	$0.451522\pi$
$719$	−20.9190	+	36.2327i	−0.780146	+	1.35125i	−0.931856	+	0.362827i	$0.881812\pi$
$720$		0			0
$721$	1.28869	+	2.23207i	0.0479931	+	0.0831266i
$722$	1.40168	+	29.0978i	0.0521650	+	1.08291i
$723$		0			0
$724$	−31.9083	+	3.08128i	−1.18586	+	0.114515i
$725$	0.271262	+	0.745287i	0.0100744	+	0.0276793i
$726$		0			0
$727$	−0.483085	+	0.0851808i	−0.0179166	+	0.00315918i	−0.182599	−	0.983187i	$-0.558451\pi$
$727$	−0.483085	+	0.0851808i	−0.0179166	+	0.00315918i	0.164683	+	0.986347i	$0.447340\pi$
$728$	−6.23417	+	15.6448i	−0.231054	+	0.579835i
$729$		0			0
$730$	18.3197	−	7.68506i	0.678043	−	0.284437i
$731$	7.17638	+	40.6993i	0.265428	+	1.50532i
$732$		0			0
$733$	−27.5380	+	10.0230i	−1.01714	+	0.370208i	−0.796170	−	0.605073i	$-0.793144\pi$
$733$	−27.5380	+	10.0230i	−1.01714	+	0.370208i	−0.220969	+	0.975281i	$0.570922\pi$
$734$	−2.98076	−	0.925101i	−0.110022	−	0.0341461i
$735$		0			0
$736$	−14.3204	+	0.948498i	−0.527857	+	0.0349621i
$737$	27.9521	−	16.1381i	1.02963	−	0.594456i
$738$		0			0
$739$	−34.8536	−	20.1228i	−1.28211	−	0.740227i	−0.304877	−	0.952392i	$-0.598616\pi$
$739$	−34.8536	−	20.1228i	−1.28211	−	0.740227i	−0.977234	+	0.212164i	$0.931949\pi$
$740$	−34.9758	−	2.74298i	−1.28574	−	0.100834i
$741$		0			0
$742$	−6.94484	+	1.57246i	−0.254953	+	0.0577269i
$743$	−6.83166	+	38.7443i	−0.250629	+	1.42139i	0.556418	+	0.830902i	$0.312175\pi$
$743$	−6.83166	+	38.7443i	−0.250629	+	1.42139i	−0.807047	+	0.590487i	$0.798936\pi$
$744$		0			0
$745$	−4.47882	+	3.75818i	−0.164091	+	0.137689i
$746$	14.7131	+	1.86969i	0.538685	+	0.0684541i
$747$		0			0
$748$	6.57324	−	25.4457i	0.240341	−	0.930387i
$749$	1.82259	−	5.00754i	0.0665962	−	0.182971i
$750$		0			0
$751$	17.6268	−	21.0068i	0.643211	−	0.766549i	−0.341663	−	0.939823i	$-0.610990\pi$
$751$	17.6268	−	21.0068i	0.643211	−	0.766549i	0.984874	+	0.173273i	$0.0554344\pi$
$752$	−17.1890	−	44.7055i	−0.626820	−	1.63024i
$753$		0			0
$754$	−17.1270	−	26.6189i	−0.623729	−	0.969402i
$755$	11.9272			0.434077
$756$		0			0
$757$	−13.2822			−0.482750			−0.241375	−	0.970432i	$-0.577598\pi$
$757$	−13.2822			−0.482750			−0.241375	+	0.970432i	$0.577598\pi$
$758$	2.36218	+	3.67130i	0.0857981	+	0.133348i
$759$		0			0
$760$	−40.4165	−	1.21815i	−1.46606	−	0.0441868i
$761$	−8.27376	+	9.86029i	−0.299924	+	0.357435i	−0.894867	−	0.446332i	$-0.852730\pi$
$761$	−8.27376	+	9.86029i	−0.299924	+	0.357435i	0.594944	+	0.803767i	$0.297174\pi$
$762$		0			0
$763$	0.811214	−	2.22879i	0.0293679	−	0.0806877i
$764$	−22.6508	−	5.85125i	−0.819477	−	0.211691i
$765$		0			0
$766$	−22.5389	−	2.86416i	−0.814364	−	0.103486i
$767$	39.8946	−	33.4755i	1.44051	−	1.20873i
$768$		0			0
$769$	5.04800	−	28.6286i	0.182036	−	1.03237i	−0.747670	−	0.664071i	$-0.768827\pi$
$769$	5.04800	−	28.6286i	0.182036	−	1.03237i	0.929705	−	0.368304i	$-0.120061\pi$
$770$	11.1037	−	2.51411i	0.400148	−	0.0906021i
$771$		0			0
$772$	−2.74764	+	35.0353i	−0.0988897	+	1.26095i
$773$	4.16046	+	2.40204i	0.149641	+	0.0863954i	0.572951	−	0.819590i	$-0.305798\pi$
$773$	4.16046	+	2.40204i	0.149641	+	0.0863954i	−0.423310	+	0.905985i	$0.639132\pi$
$774$		0			0
$775$	−0.407642	+	0.235352i	−0.0146429	+	0.00845410i
$776$	−18.4826	−	16.4827i	−0.663488	−	0.591694i
$777$		0			0
$778$	23.8415	+	7.39938i	0.854758	+	0.265280i
$779$	−23.4894	+	8.54944i	−0.841595	+	0.306315i
$780$		0			0
$781$	1.15124	+	6.52903i	0.0411948	+	0.233627i
$782$	16.0758	−	6.74375i	0.574870	−	0.241156i
$783$		0			0
$784$	−0.380445	−	21.1295i	−0.0135873	−	0.754626i
$785$	−46.7437	+	8.24217i	−1.66835	+	0.294176i
$786$		0			0
$787$	13.7229	+	37.7035i	0.489170	+	1.34398i	0.901433	+	0.432919i	$0.142516\pi$
$787$	13.7229	+	37.7035i	0.489170	+	1.34398i	−0.412263	+	0.911065i	$0.635261\pi$
$788$	−4.43085	−	45.8839i	−0.157843	−	1.63454i
$789$		0			0
$790$	−0.931154	−	19.3301i	−0.0331290	−	0.687733i
$791$	−2.29975	−	3.98328i	−0.0817696	−	0.141629i
$792$		0			0
$793$	−0.0893474	+	0.154754i	−0.00317282	+	0.00549548i
$794$	−16.9447	−	8.72417i	−0.601347	−	0.309609i
$795$		0			0
$796$	5.08967	−	3.63254i	0.180398	−	0.128752i
$797$	−30.6136	−	5.39800i	−1.08439	−	0.191207i	−0.397234	−	0.917717i	$-0.630030\pi$
$797$	−30.6136	−	5.39800i	−1.08439	−	0.191207i	−0.687156	+	0.726510i	$0.741141\pi$
$798$		0			0
$799$	37.3969	+	44.5679i	1.32301	+	1.57670i
$800$	0.0985482	−	0.905591i	0.00348421	−	0.0320175i
$801$		0			0
$802$	−7.60909	−	5.78444i	−0.268686	−	0.204256i
$803$	15.7147	+	5.71967i	0.554559	+	0.201843i
$804$		0			0
$805$	5.78505	+	4.85423i	0.203896	+	0.171089i
$806$	13.7928	−	12.7535i	0.485832	−	0.449223i
$807$		0			0
$808$	6.09804	+	1.26577i	0.214528	+	0.0445296i
$809$		−	26.7938i		−	0.942021i	−0.882128	−	0.471010i	$-0.843889\pi$
$809$		−	26.7938i		−	0.942021i	0.882128	−	0.471010i	$-0.156111\pi$
$810$		0			0
$811$			22.6335i			0.794769i	0.917652	+	0.397384i	$0.130082\pi$
$811$			22.6335i			0.794769i	−0.917652	+	0.397384i	$0.869918\pi$
$812$	−10.6386	−	7.30740i	−0.373342	−	0.256440i
$813$		0			0
$814$	−20.0497	−	21.6836i	−0.702741	−	0.760011i
$815$	−5.71352	−	4.79422i	−0.200136	−	0.167934i
$816$		0			0
$817$	50.2963	+	18.3064i	1.75965	+	0.640459i
$818$	16.1272	−	21.2144i	0.563876	−	0.741746i
$819$		0			0
$820$	−4.82804	−	17.3908i	−0.168603	−	0.607312i
$821$	8.22523	+	9.80244i	0.287062	+	0.342108i	0.890234	−	0.455504i	$-0.150541\pi$
$821$	8.22523	+	9.80244i	0.287062	+	0.342108i	−0.603171	+	0.797612i	$0.706097\pi$
$822$		0			0
$823$	25.5687	+	4.50845i	0.891269	+	0.157155i	0.600487	−	0.799635i	$-0.294973\pi$
$823$	25.5687	+	4.50845i	0.891269	+	0.157155i	0.290782	+	0.956789i	$0.406085\pi$
$824$	4.73235	+	2.92577i	0.164859	+	0.101924i
$825$		0			0
$826$	9.72046	−	18.8798i	0.338218	−	0.656913i
$827$	9.69134	−	16.7859i	0.337001	−	0.583703i	−0.646866	−	0.762603i	$-0.723921\pi$
$827$	9.69134	−	16.7859i	0.337001	−	0.583703i	0.983867	+	0.178901i	$0.0572542\pi$
$828$		0			0
$829$	−15.3678	−	26.6178i	−0.533745	−	0.924474i	−0.999223	−	0.0394143i	$-0.987451\pi$
$829$	−15.3678	−	26.6178i	−0.533745	−	0.924474i	0.465478	−	0.885060i	$-0.345883\pi$
$830$	−30.6345	+	1.47570i	−1.06334	+	0.0512225i
$831$		0			0
$832$	4.14529	+	36.1178i	0.143712	+	1.25216i
$833$	8.77970	+	24.1220i	0.304199	+	0.835779i
$834$		0			0
$835$	42.8436	−	7.55448i	1.48266	−	0.261434i
$836$	−24.2838	−	23.8505i	−0.839872	−	0.824886i
$837$		0			0
$838$	10.4460	+	24.9012i	0.360850	+	0.860199i
$839$	1.89878	+	10.7685i	0.0655533	+	0.371771i	0.999882	+	0.0153587i	$0.00488902\pi$
$839$	1.89878	+	10.7685i	0.0655533	+	0.371771i	−0.934329	+	0.356412i	$0.884000\pi$
$840$		0			0
$841$	−4.45636	+	1.62198i	−0.153668	+	0.0559304i
$842$	9.44968	−	30.4477i	0.325657	−	1.04930i
$843$		0			0
$844$	11.0733	+	23.1993i	0.381160	+	0.798554i
$845$	15.0532	−	8.69096i	0.517845	−	0.298978i
$846$		0			0
$847$	−4.18228	−	2.41464i	−0.143705	−	0.0829680i
$848$	−11.5953	+	10.0908i	−0.398184	+	0.346520i
$849$		0			0
$850$	0.244353	+	1.07919i	0.00838123	+	0.0370161i
$851$	3.40174	−	19.2923i	0.116610	−	0.661330i
$852$		0			0
$853$	4.92621	−	4.13359i	0.168670	−	0.141531i	−0.554545	−	0.832154i	$-0.687108\pi$
$853$	4.92621	−	4.13359i	0.168670	−	0.141531i	0.723216	+	0.690622i	$0.242663\pi$
$854$	−0.00918534	+	0.0722820i	−0.000314316	+	0.00247344i
$855$		0			0
$856$	−1.65536	−	11.3837i	−0.0565790	−	0.389088i
$857$	−1.08582	+	2.98327i	−0.0370910	+	0.101907i	−0.956856	−	0.290564i	$-0.906157\pi$
$857$	−1.08582	+	2.98327i	−0.0370910	+	0.101907i	0.919765	+	0.392470i	$0.128379\pi$
$858$		0			0
$859$	18.2176	−	21.7108i	0.621575	−	0.740765i	−0.359765	−	0.933043i	$-0.617143\pi$
$859$	18.2176	−	21.7108i	0.621575	−	0.740765i	0.981340	+	0.192278i	$0.0615876\pi$
$860$	−16.0166	+	35.1709i	−0.546162	+	1.19932i
$861$		0			0
$862$	−12.8514	+	8.26882i	−0.437722	+	0.281637i
$863$	−53.5310			−1.82222			−0.911108	−	0.412168i	$-0.864772\pi$
$863$	−53.5310			−1.82222			−0.911108	+	0.412168i	$0.864772\pi$
$864$		0			0
$865$	−19.8602			−0.675267
$866$	44.7076	−	28.7656i	1.51923	−	0.977495i
$867$		0			0
$868$	3.17456	−	6.97102i	0.107752	−	0.236612i
$869$	10.4714	−	12.4793i	0.355218	−	0.423333i
$870$		0			0
$871$	18.5491	−	50.9633i	0.628513	−	1.72682i
$872$	−0.736780	−	5.06676i	−0.0249505	−	0.171582i
$873$		0			0
$874$	2.84626	−	22.3980i	0.0962761	−	0.757624i
$875$	11.0339	−	9.25855i	0.373014	−	0.312996i
$876$		0			0
$877$	−5.19031	+	29.4357i	−0.175264	+	0.993974i	0.762574	+	0.646901i	$0.223935\pi$
$877$	−5.19031	+	29.4357i	−0.175264	+	0.993974i	−0.937838	+	0.347073i	$0.887176\pi$
$878$	−9.97303	−	44.0463i	−0.336574	−	1.48649i
$879$		0			0
$880$	18.5389	−	16.1336i	0.624947	−	0.543862i
$881$	14.9002	+	8.60262i	0.502000	+	0.289830i	0.729539	−	0.683939i	$-0.239735\pi$
$881$	14.9002	+	8.60262i	0.502000	+	0.289830i	−0.227539	+	0.973769i	$0.573068\pi$
$882$		0			0
$883$	−19.9228	+	11.5024i	−0.670455	+	0.387088i	−0.796249	−	0.604969i	$-0.793186\pi$
$883$	−19.9228	+	11.5024i	−0.670455	+	0.387088i	0.125794	+	0.992056i	$0.459852\pi$
$884$	−19.0224	−	39.8530i	−0.639792	−	1.34040i
$885$		0			0
$886$	−15.7536	+	50.7597i	−0.529254	+	1.70530i
$887$	−26.8201	+	9.76172i	−0.900531	+	0.327767i	−0.750466	−	0.660909i	$-0.770171\pi$
$887$	−26.8201	+	9.76172i	−0.900531	+	0.327767i	−0.150066	+	0.988676i	$0.547948\pi$
$888$		0			0
$889$	2.55256	+	14.4763i	0.0856102	+	0.485520i
$890$	8.59695	+	20.4935i	0.288170	+	0.686944i
$891$		0			0
$892$	14.7529	+	14.4896i	0.493963	+	0.485149i
$893$	74.2053	−	13.0844i	2.48318	−	0.437852i
$894$		0			0
$895$	4.71438	+	12.9526i	0.157584	+	0.432959i
$896$	7.25567	+	12.9267i	0.242395	+	0.431852i
$897$		0			0
$898$	11.4165	−	0.549947i	0.380974	−	0.0183520i
$899$	7.19828	+	12.4678i	0.240076	+	0.415824i
$900$		0			0
$901$	9.33569	−	16.1699i	0.311017	−	0.538697i
$902$	6.95461	−	13.5078i	0.231563	−	0.449760i
$903$		0			0
$904$	−8.44520	−	5.22123i	−0.280883	−	0.173656i
$905$	35.8599	+	6.32307i	1.19202	+	0.210186i
$906$		0			0
$907$	−37.4764	−	44.6626i	−1.24438	−	1.48300i	−0.814553	−	0.580089i	$-0.803018\pi$
$907$	−37.4764	−	44.6626i	−1.24438	−	1.48300i	−0.429831	−	0.902909i	$-0.641427\pi$
$908$	−0.0513842	−	0.185088i	−0.00170525	−	0.00614236i
$909$		0			0
$910$	11.5771	−	15.2290i	0.383776	−	0.504835i
$911$	−3.70530	−	1.34862i	−0.122762	−	0.0446817i	0.279909	−	0.960027i	$-0.409696\pi$
$911$	−3.70530	−	1.34862i	−0.122762	−	0.0446817i	−0.402671	+	0.915345i	$0.631918\pi$
$912$		0			0
$913$	−19.7774	−	16.5952i	−0.654537	−	0.549222i
$914$	2.37547	+	2.56906i	0.0785734	+	0.0849768i
$915$		0			0
$916$	−44.3016	−	30.4297i	−1.46377	−	1.00543i
$917$			6.72250i			0.221997i
$918$		0			0
$919$		−	6.45794i		−	0.213028i	−0.994311	−	0.106514i	$-0.966031\pi$
$919$		−	6.45794i		−	0.213028i	0.994311	−	0.106514i	$-0.0339689\pi$
$920$	15.9619	+	3.31320i	0.526247	+	0.109233i
$921$		0			0
$922$	−9.38212	+	8.67513i	−0.308984	+	0.285700i
$923$	8.53374	+	7.16066i	0.280891	+	0.235696i
$924$		0			0
$925$	1.16842	+	0.425272i	0.0384175	+	0.0139828i
$926$	1.57011	+	1.19360i	0.0515970	+	0.0392240i
$927$		0			0
$928$	−27.6976	−	3.01411i	−0.909220	−	0.0989431i
$929$	−36.6277	−	43.6512i	−1.20172	−	1.43215i	−0.872998	−	0.487723i	$-0.837828\pi$
$929$	−36.6277	−	43.6512i	−1.20172	−	1.43215i	−0.328719	−	0.944428i	$-0.606617\pi$
$930$		0			0
$931$	32.7412	+	5.77316i	1.07305	+	0.189208i
$932$	11.7765	−	8.40500i	0.385753	−	0.275315i
$933$		0			0
$934$	−26.5280	−	13.6582i	−0.868023	−	0.446910i
$935$	−14.9262	+	25.8530i	−0.488140	+	0.845483i
$936$		0			0
$937$	9.57464	+	16.5838i	0.312790	+	0.541768i	0.978965	−	0.204027i	$-0.0654031\pi$
$937$	9.57464	+	16.5838i	0.312790	+	0.541768i	−0.666175	+	0.745795i	$0.732070\pi$
$938$	−1.06403	−	22.0884i	−0.0347418	−	0.721213i
$939$		0			0
$940$	5.22938	+	54.1531i	0.170564	+	1.76628i
$941$	−6.39294	−	17.5645i	−0.208404	−	0.572585i	0.790817	−	0.612053i	$-0.209656\pi$
$941$	−6.39294	−	17.5645i	−0.208404	−	0.572585i	−0.999221	+	0.0394679i	$0.987434\pi$
$942$		0			0
$943$	9.92488	−	1.75002i	0.323198	−	0.0569886i
$944$	−0.825237	−	45.8329i	−0.0268592	−	1.49173i
$945$		0			0
$946$	−29.9991	+	12.5845i	−0.975354	+	0.409158i
$947$	−4.94182	−	28.0265i	−0.160588	−	0.910738i	−0.953498	−	0.301400i	$-0.902546\pi$
$947$	−4.94182	−	28.0265i	−0.160588	−	0.910738i	0.792910	−	0.609338i	$-0.208565\pi$
$948$		0			0
$949$	26.4054	−	9.61079i	0.857157	−	0.311980i
$950$	1.36868	+	0.424780i	0.0444059	+	0.0137817i
$951$		0			0
$952$	−13.4388	−	11.9846i	−0.435553	−	0.388423i
$953$	39.0891	−	22.5681i	1.26622	−	0.731052i	0.291949	−	0.956434i	$-0.405696\pi$
$953$	39.0891	−	22.5681i	1.26622	−	0.731052i	0.974270	+	0.225382i	$0.0723630\pi$
$954$		0			0
$955$	23.0134	+	13.2868i	0.744695	+	0.429950i
$956$	−1.99483	+	25.4361i	−0.0645173	+	0.822663i
$957$		0			0
$958$	20.1439	−	4.56101i	0.650820	−	0.147360i
$959$	−0.411444	+	2.33341i	−0.0132862	+	0.0753499i
$960$		0			0
$961$	17.2022	−	14.4343i	0.554909	−	0.465624i
$962$	−49.2278	−	6.25568i	−1.58717	−	0.201691i
$963$		0			0
$964$	−14.6643	−	3.78814i	−0.472305	−	0.122008i
$965$	13.6530	−	37.5112i	0.439504	−	1.20753i
$966$		0			0
$967$	5.89240	−	7.02229i	0.189487	−	0.225822i	−0.662934	−	0.748678i	$-0.730689\pi$
$967$	5.89240	−	7.02229i	0.189487	−	0.225822i	0.852421	+	0.522856i	$0.175133\pi$
$968$	−10.4202	−	0.314062i	−0.334918	−	0.0100943i
$969$		0			0
$970$	15.2209	+	23.6564i	0.488713	+	0.759560i
$971$	−10.7197			−0.344010			−0.172005	−	0.985096i	$-0.555025\pi$
$971$	−10.7197			−0.344010			−0.172005	+	0.985096i	$0.555025\pi$
$972$		0			0
$973$	−17.0344			−0.546098
$974$	0.216205	+	0.336027i	0.00692767	+	0.0107670i
$975$		0			0
$976$	0.0564482	+	0.146811i	0.00180686	+	0.00469931i
$977$	−32.0082	+	38.1459i	−1.02403	+	1.22040i	−0.0488952	+	0.998804i	$0.515570\pi$
$977$	−32.0082	+	38.1459i	−1.02403	+	1.22040i	−0.975139	+	0.221593i	$0.928874\pi$
$978$		0			0
$979$	−6.39836	+	17.5793i	−0.204492	+	0.561838i
$980$	−6.00394	+	23.2419i	−0.191789	+	0.742435i
$981$		0			0
$982$	21.7439	+	2.76313i	0.693875	+	0.0881751i
$983$	−1.39362	+	1.16939i	−0.0444496	+	0.0372976i	−0.664742	−	0.747073i	$-0.731458\pi$
$983$	−1.39362	+	1.16939i	−0.0444496	+	0.0372976i	0.620292	+	0.784371i	$0.287014\pi$
$984$		0			0
$985$	−9.09251	+	51.5662i	−0.289712	+	1.64304i
$986$	33.0073	−	7.47357i	1.05117	−	0.238007i
$987$		0			0
$988$	−57.0182	−	4.47165i	−1.81399	−	0.142262i
$989$	−18.6883	−	10.7897i	−0.594252	−	0.343092i
$990$		0			0
$991$	48.8792	−	28.2204i	1.55270	−	0.896451i	0.554777	−	0.831999i	$-0.312804\pi$
$991$	48.8792	−	28.2204i	1.55270	−	0.896451i	0.997921	−	0.0644516i	$-0.0205298\pi$
$992$	−1.09280	−	16.4991i	−0.0346964	−	0.523845i
$993$		0			0
$994$	4.33824	+	1.34640i	0.137601	+	0.0427054i
$995$	−6.67441	+	2.42928i	−0.211593	+	0.0770135i
$996$		0			0
$997$	2.04998	+	11.6260i	0.0649234	+	0.368199i	0.999909	+	0.0135125i	$0.00430130\pi$
$997$	2.04998	+	11.6260i	0.0649234	+	0.368199i	−0.934985	+	0.354687i	$0.884588\pi$
$998$	53.3333	−	22.3731i	1.68824	−	0.708209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.c.215.4		96
3.2	odd	2		972.2.l.b.215.13		96
4.3	odd	2	inner	972.2.l.c.215.2		96
9.2	odd	6		972.2.l.a.863.2		96
9.4	even	3		108.2.l.a.23.8	✓	96
9.5	odd	6		324.2.l.a.179.9		96
9.7	even	3		972.2.l.d.863.15		96
12.11	even	2		972.2.l.b.215.15		96
27.2	odd	18	inner	972.2.l.c.755.2		96
27.7	even	9		972.2.l.a.107.7		96
27.11	odd	18		108.2.l.a.47.13	yes	96
27.16	even	9		324.2.l.a.143.4		96
27.20	odd	18		972.2.l.d.107.10		96
27.25	even	9		972.2.l.b.755.15		96
36.7	odd	6		972.2.l.d.863.10		96
36.11	even	6		972.2.l.a.863.7		96
36.23	even	6		324.2.l.a.179.4		96
36.31	odd	6		108.2.l.a.23.13	yes	96
108.7	odd	18		972.2.l.a.107.2		96
108.11	even	18		108.2.l.a.47.8	yes	96
108.43	odd	18		324.2.l.a.143.9		96
108.47	even	18		972.2.l.d.107.15		96
108.79	odd	18		972.2.l.b.755.13		96
108.83	even	18	inner	972.2.l.c.755.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.8	✓	96	9.4	even	3
108.2.l.a.23.13	yes	96	36.31	odd	6
108.2.l.a.47.8	yes	96	108.11	even	18
108.2.l.a.47.13	yes	96	27.11	odd	18
324.2.l.a.143.4		96	27.16	even	9
324.2.l.a.143.9		96	108.43	odd	18
324.2.l.a.179.4		96	36.23	even	6
324.2.l.a.179.9		96	9.5	odd	6
972.2.l.a.107.2		96	108.7	odd	18
972.2.l.a.107.7		96	27.7	even	9
972.2.l.a.863.2		96	9.2	odd	6
972.2.l.a.863.7		96	36.11	even	6
972.2.l.b.215.13		96	3.2	odd	2
972.2.l.b.215.15		96	12.11	even	2
972.2.l.b.755.13		96	108.79	odd	18
972.2.l.b.755.15		96	27.25	even	9
972.2.l.c.215.2		96	4.3	odd	2	inner
972.2.l.c.215.4		96	1.1	even	1	trivial
972.2.l.c.755.2		96	27.2	odd	18	inner
972.2.l.c.755.4		96	108.83	even	18	inner
972.2.l.d.107.10		96	27.20	odd	18
972.2.l.d.107.15		96	108.47	even	18
972.2.l.d.863.10		96	36.7	odd	6
972.2.l.d.863.15		96	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.18930 + 0.765217i) q^{2} +(0.828886 - 1.82015i) q^{4} +(-1.46028 + 1.74029i) q^{5} +(-0.448132 + 1.23123i) q^{7} +(0.407013 + 2.79899i) q^{8} +(0.405013 - 3.18717i) q^{10} +(2.07176 - 1.73841i) q^{11} +(0.789120 - 4.47532i) q^{13} +(-0.409195 - 1.80723i) q^{14} +(-2.62590 - 3.01739i) q^{16} +(4.20783 + 2.42939i) q^{17} +(5.44971 - 3.14639i) q^{19} +(1.95719 + 4.10043i) q^{20} +(-1.13369 + 3.65284i) q^{22} +(-2.38405 + 0.867725i) q^{23} +(-0.0279630 - 0.158586i) q^{25} +(2.48609 + 5.92636i) q^{26} +(1.86958 + 1.83622i) q^{28} +(-4.85038 + 0.855253i) q^{29} +(-0.999738 - 2.74676i) q^{31} +(5.43195 + 1.57922i) q^{32} +(-6.86340 + 0.330619i) q^{34} +(-1.48831 - 2.57783i) q^{35} +(-3.86074 + 6.68701i) q^{37} +(-4.07369 + 7.91222i) q^{38} +(-5.46541 - 3.37898i) q^{40} +(-3.91196 - 0.689785i) q^{41} +(5.46733 + 6.51571i) q^{43} +(-1.44692 - 5.21185i) q^{44} +(2.17137 - 2.85631i) q^{46} +(11.2519 + 4.09536i) q^{47} +(4.04720 + 3.39600i) q^{49} +(0.154609 + 0.167209i) q^{50} +(-7.49167 - 5.14585i) q^{52} -3.84281i q^{53} +6.14402i q^{55} +(-3.62861 - 0.753189i) q^{56} +(5.11412 - 4.72875i) q^{58} +(8.77893 + 7.36639i) q^{59} +(-0.0369509 - 0.0134490i) q^{61} +(3.29086 + 2.50171i) q^{62} +(-7.66868 + 2.27845i) q^{64} +(6.63603 + 7.90851i) q^{65} +(11.7530 + 2.07238i) q^{67} +(7.90967 - 5.64519i) q^{68} +(3.74265 + 1.92694i) q^{70} +(-1.22570 + 2.12297i) q^{71} +(3.09175 + 5.35507i) q^{73} +(-0.525413 - 10.9072i) q^{74} +(-1.20972 - 12.5273i) q^{76} +(1.21197 + 3.32985i) q^{77} +(5.93205 - 1.04598i) q^{79} +(9.08569 - 0.163591i) q^{80} +(5.18035 - 2.17314i) q^{82} +(-1.65768 - 9.40119i) q^{83} +(-10.3725 + 3.77526i) q^{85} +(-11.4882 - 3.56546i) q^{86} +(5.70902 + 5.09126i) q^{88} +(-5.99050 + 3.45862i) q^{89} +(5.15653 + 2.97713i) q^{91} +(-0.396719 + 5.05858i) q^{92} +(-16.5158 + 3.73953i) q^{94} +(-2.48245 + 14.0787i) q^{95} +(-6.70720 + 5.62801i) q^{97} +(-7.41203 - 0.941893i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} - 12 q^{14} + 3 q^{16} - 18 q^{17} + 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 6 q^{29} - 57 q^{32} - 3 q^{34} - 6 q^{37} + 45 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) \) 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 - 12 * q^14 + 3 * q^16 - 18 * q^17 + 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 6 * q^29 - 57 * q^32 - 3 * q^34 - 6 * q^37 + 45 * q^38 - 12 * q^40 + 66 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 66 * q^50 - 24 * q^52 - 81 * q^56 - 24 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 - 42 * q^65 + 51 * q^68 - 30 * q^70 - 6 * q^73 - 96 * q^74 - 9 * q^76 + 30 * q^77 - 12 * q^82 + 66 * q^85 + 141 * q^86 - 45 * q^88 - 24 * q^92 - 51 * q^94 + 42 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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