LMFDB - Embedded newform 1274.2.g.c.295.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(295,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.295"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,-2,-1,6,2,0,-2,-1,3,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1274.295
Dual form			1274.2.g.c.393.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(1.00000 + 1.73205i) q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(3.00000 - 5.19615i) q^{11} +2.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} -1.00000 q^{18} +(-2.00000 - 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(3.00000 - 5.19615i) q^{23} +(1.00000 - 1.73205i) q^{24} +4.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} -4.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +(3.00000 + 5.19615i) q^{30} +10.0000 q^{31} +(0.500000 + 0.866025i) q^{32} +(6.00000 + 10.3923i) q^{33} -3.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{37} -4.00000 q^{38} +(7.00000 - 1.73205i) q^{39} -3.00000 q^{40} +(-1.50000 + 2.59808i) q^{41} +(5.00000 + 8.66025i) q^{43} -6.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(-1.00000 - 1.73205i) q^{48} +(2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} -9.00000 q^{53} +(-2.00000 + 3.46410i) q^{54} +(9.00000 - 15.5885i) q^{55} +8.00000 q^{57} +(1.50000 + 2.59808i) q^{58} +(-3.00000 - 5.19615i) q^{59} +6.00000 q^{60} +(-3.50000 - 6.06218i) q^{61} +(5.00000 - 8.66025i) q^{62} +1.00000 q^{64} +(-7.50000 - 7.79423i) q^{65} +12.0000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{69} +(0.500000 + 0.866025i) q^{72} +7.00000 q^{73} +(-0.500000 - 0.866025i) q^{74} +(-4.00000 + 6.92820i) q^{75} +(-2.00000 + 3.46410i) q^{76} +(2.00000 - 6.92820i) q^{78} +14.0000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(5.50000 - 9.52628i) q^{81} +(1.50000 + 2.59808i) q^{82} +18.0000 q^{83} +(-4.50000 - 7.79423i) q^{85} +10.0000 q^{86} +(-3.00000 - 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-3.00000 + 5.19615i) q^{89} -3.00000 q^{90} -6.00000 q^{92} +(-10.0000 + 17.3205i) q^{93} +(-6.00000 - 10.3923i) q^{95} -2.00000 q^{96} +(1.00000 + 1.73205i) q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} + 6 q^{5} + 2 q^{6} - 2 q^{8} - q^{9} + 3 q^{10} + 6 q^{11} + 4 q^{12} - 5 q^{13} - 6 q^{15} - q^{16} - 3 q^{17} - 2 q^{18} - 4 q^{19} - 3 q^{20} - 6 q^{22} + 6 q^{23}+ \cdots - 12 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 + 6 * q^5 + 2 * q^6 - 2 * q^8 - q^9 + 3 * q^10 + 6 * q^11 + 4 * q^12 - 5 * q^13 - 6 * q^15 - q^16 - 3 * q^17 - 2 * q^18 - 4 * q^19 - 3 * q^20 - 6 * q^22 + 6 * q^23 + 2 * q^24 + 8 * q^25 - 7 * q^26 - 8 * q^27 - 3 * q^29 + 6 * q^30 + 20 * q^31 + q^32 + 12 * q^33 - 6 * q^34 - q^36 + q^37 - 8 * q^38 + 14 * q^39 - 6 * q^40 - 3 * q^41 + 10 * q^43 - 12 * q^44 - 3 * q^45 - 6 * q^46 - 2 * q^48 + 4 * q^50 + 12 * q^51 - 2 * q^52 - 18 * q^53 - 4 * q^54 + 18 * q^55 + 16 * q^57 + 3 * q^58 - 6 * q^59 + 12 * q^60 - 7 * q^61 + 10 * q^62 + 2 * q^64 - 15 * q^65 + 24 * q^66 - 2 * q^67 - 3 * q^68 + 12 * q^69 + q^72 + 14 * q^73 - q^74 - 8 * q^75 - 4 * q^76 + 4 * q^78 + 28 * q^79 - 3 * q^80 + 11 * q^81 + 3 * q^82 + 36 * q^83 - 9 * q^85 + 20 * q^86 - 6 * q^87 - 6 * q^88 - 6 * q^89 - 6 * q^90 - 12 * q^92 - 20 * q^93 - 12 * q^95 - 4 * q^96 + 2 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$	1.00000	+	1.73205i	0.408248	+	0.707107i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	2.00000			0.577350
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$		0			0
$15$	−3.00000	+	5.19615i	−0.774597	+	1.34164i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	−1.00000			−0.235702
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	1.00000	−	1.73205i	0.204124	−	0.353553i
$25$	4.00000			0.800000
$26$	−3.50000	+	0.866025i	−0.686406	+	0.169842i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$	3.00000	+	5.19615i	0.547723	+	0.948683i
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	6.00000	+	10.3923i	1.04447	+	1.80907i
$34$	−3.00000			−0.514496
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−4.00000			−0.648886
$39$	7.00000	−	1.73205i	1.12090	−	0.277350i
$40$	−3.00000			−0.474342
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	−6.00000			−0.904534
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−1.00000	−	1.73205i	−0.144338	−	0.250000i
$49$		0			0
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$	6.00000			0.840168
$52$	−1.00000	+	3.46410i	−0.138675	+	0.480384i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	−2.00000	+	3.46410i	−0.272166	+	0.471405i
$55$	9.00000	−	15.5885i	1.21356	−	2.10195i
$56$		0			0
$57$	8.00000			1.05963
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	6.00000			0.774597
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$	5.00000	−	8.66025i	0.635001	−	1.09985i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.50000	−	7.79423i	−0.930261	−	0.966755i
$66$	12.0000			1.47710
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	6.00000	+	10.3923i	0.722315	+	1.25109i
$70$		0			0
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	7.00000			0.819288			0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000			0.819288			0.409644	+	0.912245i	$0.365653\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	−4.00000	+	6.92820i	−0.461880	+	0.800000i
$76$	−2.00000	+	3.46410i	−0.229416	+	0.397360i
$77$		0			0
$78$	2.00000	−	6.92820i	0.226455	−	0.784465i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$		0			0
$85$	−4.50000	−	7.79423i	−0.488094	−	0.845403i
$86$	10.0000			1.07833
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	−3.00000			−0.316228
$91$		0			0
$92$	−6.00000			−0.625543
$93$	−10.0000	+	17.3205i	−1.03695	+	1.79605i
$94$		0			0
$95$	−6.00000	−	10.3923i	−0.615587	−	1.06623i
$96$	−2.00000			−0.204124
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$		0			0
$106$	−4.50000	+	7.79423i	−0.437079	+	0.757042i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	−9.00000	−	15.5885i	−0.858116	−	1.48630i
$111$	1.00000	+	1.73205i	0.0949158	+	0.164399i
$112$		0			0
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	0.786806	−	0.617200i	$-0.211733\pi$
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	−0.927914	+	0.372794i	$0.878400\pi$
$114$	4.00000	−	6.92820i	0.374634	−	0.648886i
$115$	9.00000	−	15.5885i	0.839254	−	1.45363i
$116$	3.00000			0.278543
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$	−6.00000			−0.552345
$119$		0			0
$120$	3.00000	−	5.19615i	0.273861	−	0.474342i
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	−7.00000			−0.633750
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$	−5.00000	−	8.66025i	−0.449013	−	0.777714i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.0443678	+	0.999015i	$0.514127\pi$
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.842989	+	0.537931i	$0.819206\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−20.0000			−1.76090
$130$	−10.5000	+	2.59808i	−0.920911	+	0.227866i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	6.00000	−	10.3923i	0.522233	−	0.904534i
$133$		0			0
$134$	1.00000	+	1.73205i	0.0863868	+	0.149626i
$135$	−12.0000			−1.03280
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	12.0000			1.02151
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	0.905314	−	0.424743i	$-0.139635\pi$
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	−0.820495	+	0.571654i	$0.806302\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−21.0000	+	5.19615i	−1.75611	+	0.434524i
$144$	1.00000			0.0833333
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	3.50000	−	6.06218i	0.289662	−	0.501709i
$147$		0			0
$148$	−1.00000			−0.0821995
$149$	10.5000	+	18.1865i	0.860194	+	1.48990i	0.871742	+	0.489966i	$0.162991\pi$
$149$	10.5000	+	18.1865i	0.860194	+	1.48990i	−0.0115483	+	0.999933i	$0.503676\pi$
$150$	4.00000	+	6.92820i	0.326599	+	0.565685i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	−1.50000	+	2.59808i	−0.121268	+	0.210042i
$154$		0			0
$155$	30.0000			2.40966
$156$	−5.00000	−	5.19615i	−0.400320	−	0.416025i
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$	7.00000	−	12.1244i	0.556890	−	0.964562i
$159$	9.00000	−	15.5885i	0.713746	−	1.23625i
$160$	1.50000	+	2.59808i	0.118585	+	0.205396i
$161$		0			0
$162$	−5.50000	−	9.52628i	−0.432121	−	0.748455i
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	0.824202	−	0.566296i	$-0.191624\pi$
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	−0.902528	+	0.430632i	$0.858291\pi$
$164$	3.00000			0.234261
$165$	18.0000	+	31.1769i	1.40130	+	2.42712i
$166$	9.00000	−	15.5885i	0.698535	−	1.20990i
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	−9.00000			−0.690268
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	−6.00000			−0.454859
$175$		0			0
$176$	3.00000	+	5.19615i	0.226134	+	0.391675i
$177$	12.0000			0.901975
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$	10.0000	+	17.3205i	0.733236	+	1.27000i
$187$	−18.0000			−1.31629
$188$		0			0
$189$		0			0
$190$	−12.0000			−0.870572
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	0.0719816	+	0.997406i	$0.477068\pi$
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	2.00000			0.143592
$195$	21.0000	−	5.19615i	1.50384	−	0.372104i
$196$		0			0
$197$	−9.00000	+	15.5885i	−0.641223	+	1.11063i	0.343937	+	0.938993i	$0.388239\pi$
$197$	−9.00000	+	15.5885i	−0.641223	+	1.11063i	−0.985160	+	0.171639i	$0.945094\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	−4.00000			−0.282843
$201$	−2.00000	−	3.46410i	−0.141069	−	0.244339i
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$		0			0
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	2.00000	−	3.46410i	0.139347	−	0.241355i
$207$	−6.00000			−0.417029
$208$	3.50000	−	0.866025i	0.242681	−	0.0600481i
$209$	−24.0000			−1.66011
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$		0			0
$214$		0			0
$215$	15.0000	+	25.9808i	1.02299	+	1.77187i
$216$	4.00000			0.272166
$217$		0			0
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$	−18.0000			−1.21356
$221$	−3.00000	+	10.3923i	−0.201802	+	0.699062i
$222$	2.00000			0.134231
$223$	−14.0000	+	24.2487i	−0.937509	+	1.62381i	−0.167412	+	0.985887i	$0.553541\pi$
$223$	−14.0000	+	24.2487i	−0.937509	+	1.62381i	−0.770097	+	0.637927i	$0.779792\pi$
$224$		0			0
$225$	−2.00000	−	3.46410i	−0.133333	−	0.230940i
$226$	−3.00000			−0.199557
$227$	−3.00000	−	5.19615i	−0.199117	−	0.344881i	0.749125	−	0.662428i	$-0.230474\pi$
$227$	−3.00000	−	5.19615i	−0.199117	−	0.344881i	−0.948242	+	0.317547i	$0.897141\pi$
$228$	−4.00000	−	6.92820i	−0.264906	−	0.458831i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$	−9.00000	−	15.5885i	−0.593442	−	1.02787i
$231$		0			0
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	2.50000	+	2.59808i	0.163430	+	0.169842i
$235$		0			0
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$	−14.0000	+	24.2487i	−0.909398	+	1.57512i
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	−3.00000	−	5.19615i	−0.193649	−	0.335410i
$241$	8.50000	+	14.7224i	0.547533	+	0.948355i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$	8.50000	+	14.7224i	0.547533	+	0.948355i	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−25.0000			−1.60706
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	−3.50000	+	6.06218i	−0.224065	+	0.388091i
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−4.00000	+	13.8564i	−0.254514	+	0.881662i
$248$	−10.0000			−0.635001
$249$	−18.0000	+	31.1769i	−1.14070	+	1.97576i
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$		0			0
$253$	−18.0000	−	31.1769i	−1.13165	−	1.96008i
$254$	10.0000	+	17.3205i	0.627456	+	1.08679i
$255$	18.0000			1.12720
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$258$	−10.0000	+	17.3205i	−0.622573	+	1.07833i
$259$		0			0
$260$	−3.00000	+	10.3923i	−0.186052	+	0.644503i
$261$	3.00000			0.185695
$262$		0			0
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	−0.758585	−	0.651575i	$-0.774109\pi$
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	0.943572	+	0.331166i	$0.107442\pi$
$264$	−6.00000	−	10.3923i	−0.369274	−	0.639602i
$265$	−27.0000			−1.65860
$266$		0			0
$267$	−6.00000	−	10.3923i	−0.367194	−	0.635999i
$268$	2.00000			0.122169
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$	−6.00000	+	10.3923i	−0.365148	+	0.632456i
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	−3.00000			−0.181237
$275$	12.0000	−	20.7846i	0.723627	−	1.25336i
$276$	6.00000	−	10.3923i	0.361158	−	0.625543i
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	2.00000			0.119952
$279$	−5.00000	−	8.66025i	−0.299342	−	0.518476i
$280$		0			0
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$		0			0
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	0.328291	+	0.944577i	$0.393527\pi$
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	−0.982173	+	0.187980i	$0.939806\pi$
$284$		0			0
$285$	24.0000			1.42164
$286$	−6.00000	+	20.7846i	−0.354787	+	1.22902i
$287$		0			0
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$	−4.00000			−0.234484
$292$	−3.50000	−	6.06218i	−0.204822	−	0.354762i
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	0.818878	−	0.573967i	$-0.194596\pi$
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	−0.906509	+	0.422186i	$0.861263\pi$
$294$		0			0
$295$	−9.00000	−	15.5885i	−0.524000	−	0.907595i
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$	−12.0000	+	20.7846i	−0.696311	+	1.20605i
$298$	21.0000			1.21650
$299$	−21.0000	+	5.19615i	−1.21446	+	0.300501i
$300$	8.00000			0.461880
$301$		0			0
$302$	4.00000	−	6.92820i	0.230174	−	0.398673i
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$	4.00000			0.229416
$305$	−10.5000	−	18.1865i	−0.601228	−	1.04136i
$306$	1.50000	+	2.59808i	0.0857493	+	0.148522i
$307$	22.0000			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$308$		0			0
$309$	−4.00000	+	6.92820i	−0.227552	+	0.394132i
$310$	15.0000	−	25.9808i	0.851943	−	1.47561i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	−7.00000	+	1.73205i	−0.396297	+	0.0980581i
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$	3.50000	−	6.06218i	0.197516	−	0.342108i
$315$		0			0
$316$	−7.00000	−	12.1244i	−0.393781	−	0.682048i
$317$	−9.00000			−0.505490			−0.252745	−	0.967533i	$-0.581333\pi$
$317$	−9.00000			−0.505490			−0.252745	+	0.967533i	$0.581333\pi$
$318$	−9.00000	−	15.5885i	−0.504695	−	0.874157i
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$	3.00000			0.167705
$321$		0			0
$322$		0			0
$323$	−6.00000	+	10.3923i	−0.333849	+	0.578243i
$324$	−11.0000			−0.611111
$325$	−10.0000	−	10.3923i	−0.554700	−	0.576461i
$326$	−2.00000			−0.110770
$327$	−2.00000	+	3.46410i	−0.110600	+	0.191565i
$328$	1.50000	−	2.59808i	0.0828236	−	0.143455i
$329$		0			0
$330$	36.0000			1.98173
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	0.970091	−	0.242742i	$-0.0780468\pi$
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	−0.695266	+	0.718752i	$0.744713\pi$
$332$	−9.00000	−	15.5885i	−0.493939	−	0.855528i
$333$	−1.00000			−0.0547997
$334$	3.00000	+	5.19615i	0.164153	+	0.284321i
$335$	−3.00000	+	5.19615i	−0.163908	+	0.283896i
$336$		0			0
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	11.0000	+	6.92820i	0.598321	+	0.376845i
$339$	6.00000			0.325875
$340$	−4.50000	+	7.79423i	−0.244047	+	0.422701i
$341$	30.0000	−	51.9615i	1.62459	−	2.81387i
$342$	2.00000	+	3.46410i	0.108148	+	0.187317i
$343$		0			0
$344$	−5.00000	−	8.66025i	−0.269582	−	0.466930i
$345$	18.0000	+	31.1769i	0.969087	+	1.67851i
$346$	6.00000			0.322562
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	0.935245	−	0.354001i	$-0.115179\pi$
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	−0.774197	+	0.632945i	$0.781846\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	−0.838019	−	0.545640i	$-0.816286\pi$
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	0.891548	+	0.452926i	$0.149620\pi$
$350$		0			0
$351$	10.0000	+	10.3923i	0.533761	+	0.554700i
$352$	6.00000			0.319801
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$	6.00000	−	10.3923i	0.318896	−	0.552345i
$355$		0			0
$356$	6.00000			0.317999
$357$		0			0
$358$		0			0
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−2.50000	+	4.33013i	−0.131397	+	0.227586i
$363$	50.0000			2.62432
$364$		0			0
$365$	21.0000			1.09919
$366$	7.00000	−	12.1244i	0.365896	−	0.633750i
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	−0.966507	−	0.256639i	$-0.917385\pi$
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	0.705509	+	0.708700i	$0.250718\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	3.00000			0.156174
$370$	−1.50000	−	2.59808i	−0.0779813	−	0.135068i
$371$		0			0
$372$	20.0000			1.03695
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	−0.647225	+	0.762299i	$0.724071\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$	3.00000	−	5.19615i	0.154919	−	0.268328i
$376$		0			0
$377$	10.5000	−	2.59808i	0.540778	−	0.133808i
$378$		0			0
$379$	−13.0000	+	22.5167i	−0.667765	+	1.15660i	0.310763	+	0.950488i	$0.399416\pi$
$379$	−13.0000	+	22.5167i	−0.667765	+	1.15660i	−0.978528	+	0.206116i	$0.933918\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$	−20.0000	−	34.6410i	−1.02463	−	1.77471i
$382$	−18.0000			−0.920960
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$	1.00000	+	1.73205i	0.0510310	+	0.0883883i
$385$		0			0
$386$	11.5000	+	19.9186i	0.585335	+	1.01383i
$387$	5.00000	−	8.66025i	0.254164	−	0.440225i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	−33.0000			−1.67317			−0.836583	−	0.547840i	$-0.815450\pi$
$389$	−33.0000			−1.67317			−0.836583	+	0.547840i	$0.815450\pi$
$390$	6.00000	−	20.7846i	0.303822	−	1.05247i
$391$	−18.0000			−0.910299
$392$		0			0
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	42.0000			2.11325
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	0.0250943	−	0.999685i	$-0.492011\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$	−4.00000			−0.199502
$403$	−25.0000	−	25.9808i	−1.24534	−	1.29419i
$404$	3.00000			0.149256
$405$	16.5000	−	28.5788i	0.819892	−	1.42009i
$406$		0			0
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$	−6.00000			−0.297044
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$	4.50000	+	7.79423i	0.222239	+	0.384930i
$411$	6.00000			0.295958
$412$	−2.00000	−	3.46410i	−0.0985329	−	0.170664i
$413$		0			0
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	54.0000			2.65076
$416$	1.00000	−	3.46410i	0.0490290	−	0.169842i
$417$	−4.00000			−0.195881
$418$	−12.0000	+	20.7846i	−0.586939	+	1.01661i
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	−0.783394	−	0.621525i	$-0.786513\pi$
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	0.929954	+	0.367677i	$0.119847\pi$
$420$		0			0
$421$	35.0000			1.70580			0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000			1.70580			0.852898	+	0.522078i	$0.174843\pi$
$422$	−11.0000	−	19.0526i	−0.535472	−	0.927464i
$423$		0			0
$424$	9.00000			0.437079
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	12.0000	−	41.5692i	0.579365	−	2.00698i
$430$	30.0000			1.44673
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	2.50000	+	4.33013i	0.120142	+	0.208093i	0.919824	−	0.392332i	$-0.128332\pi$
$433$	2.50000	+	4.33013i	0.120142	+	0.208093i	−0.799681	+	0.600425i	$0.794998\pi$
$434$		0			0
$435$	−9.00000	−	15.5885i	−0.431517	−	0.747409i
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−24.0000			−1.14808
$438$	7.00000	+	12.1244i	0.334473	+	0.579324i
$439$	−11.0000	+	19.0526i	−0.525001	+	0.909329i	0.474575	+	0.880215i	$0.342602\pi$
$439$	−11.0000	+	19.0526i	−0.525001	+	0.909329i	−0.999576	+	0.0291138i	$0.990731\pi$
$440$	−9.00000	+	15.5885i	−0.429058	+	0.743151i
$441$		0			0
$442$	7.50000	+	7.79423i	0.356739	+	0.370734i
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$	1.00000	−	1.73205i	0.0474579	−	0.0821995i
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	14.0000	+	24.2487i	0.662919	+	1.14821i
$447$	−42.0000			−1.98653
$448$		0			0
$449$	−15.0000	−	25.9808i	−0.707894	−	1.22611i	−0.965637	−	0.259895i	$-0.916312\pi$
$449$	−15.0000	−	25.9808i	−0.707894	−	1.22611i	0.257743	−	0.966213i	$-0.417021\pi$
$450$	−4.00000			−0.188562
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	−1.50000	+	2.59808i	−0.0705541	+	0.122203i
$453$	−8.00000	+	13.8564i	−0.375873	+	0.651031i
$454$	−6.00000			−0.281594
$455$		0			0
$456$	−8.00000			−0.374634
$457$	12.5000	−	21.6506i	0.584725	−	1.01277i	−0.410184	−	0.912003i	$-0.634536\pi$
$457$	12.5000	−	21.6506i	0.584725	−	1.01277i	0.994910	−	0.100771i	$-0.0321310\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$	6.00000	+	10.3923i	0.280056	+	0.485071i
$460$	−18.0000			−0.839254
$461$	16.5000	+	28.5788i	0.768482	+	1.33105i	0.938386	+	0.345589i	$0.112321\pi$
$461$	16.5000	+	28.5788i	0.768482	+	1.33105i	−0.169904	+	0.985461i	$0.554346\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$	−30.0000	+	51.9615i	−1.39122	+	2.40966i
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$	3.50000	−	0.866025i	0.161788	−	0.0400320i
$469$		0			0
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	60.0000			2.75880
$474$	14.0000	+	24.2487i	0.643041	+	1.11378i
$475$	−8.00000	−	13.8564i	−0.367065	−	0.635776i
$476$		0			0
$477$	4.50000	+	7.79423i	0.206041	+	0.356873i
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.235833	−	0.971794i	$-0.424218\pi$
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.723681	−	0.690134i	$-0.242449\pi$
$480$	−6.00000			−0.273861
$481$	−3.50000	+	0.866025i	−0.159586	+	0.0394874i
$482$	17.0000			0.774329
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$	10.0000			0.453609
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$	3.50000	+	6.06218i	0.158438	+	0.274422i
$489$	4.00000			0.180886
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$	−3.00000	+	5.19615i	−0.135250	+	0.234261i
$493$	9.00000			0.405340
$494$	10.0000	+	10.3923i	0.449921	+	0.467572i
$495$	−18.0000			−0.809040
$496$	−5.00000	+	8.66025i	−0.224507	+	0.388857i
$497$		0			0
$498$	18.0000	+	31.1769i	0.806599	+	1.39707i
$499$	−22.0000			−0.984855			−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000			−0.984855			−0.492428	+	0.870353i	$0.663890\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	−12.0000			−0.535586
$503$	−9.00000	−	15.5885i	−0.401290	−	0.695055i	0.592592	−	0.805503i	$-0.298105\pi$
$503$	−9.00000	−	15.5885i	−0.401290	−	0.695055i	−0.993882	+	0.110448i	$0.964771\pi$
$504$		0			0
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$	−36.0000			−1.60040
$507$	−22.0000	−	13.8564i	−0.977054	−	0.615385i
$508$	20.0000			0.887357
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	−0.533815	−	0.845601i	$-0.679242\pi$
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	0.999220	+	0.0394971i	$0.0125756\pi$
$510$	9.00000	−	15.5885i	0.398527	−	0.690268i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	8.00000	+	13.8564i	0.353209	+	0.611775i
$514$	−10.5000	−	18.1865i	−0.463135	−	0.802174i
$515$	12.0000			0.528783
$516$	10.0000	+	17.3205i	0.440225	+	0.762493i
$517$		0			0
$518$		0			0
$519$	−12.0000			−0.526742
$520$	7.50000	+	7.79423i	0.328897	+	0.341800i
$521$	39.0000			1.70862			0.854311	−	0.519763i	$-0.173980\pi$
$521$	39.0000			1.70862			0.854311	+	0.519763i	$0.173980\pi$
$522$	1.50000	−	2.59808i	0.0656532	−	0.113715i
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	0.378695	+	0.925521i	$0.376373\pi$
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	−0.990873	+	0.134801i	$0.956961\pi$
$524$		0			0
$525$		0			0
$526$	−3.00000	−	5.19615i	−0.130806	−	0.226563i
$527$	−15.0000	−	25.9808i	−0.653410	−	1.13174i
$528$	−12.0000			−0.522233
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−13.5000	+	23.3827i	−0.586403	+	1.01568i
$531$	−3.00000	+	5.19615i	−0.130189	+	0.225494i
$532$		0			0
$533$	10.5000	−	2.59808i	0.454805	−	0.112535i
$534$	−12.0000			−0.519291
$535$		0			0
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$		0			0
$538$	18.0000			0.776035
$539$		0			0
$540$	6.00000	+	10.3923i	0.258199	+	0.447214i
$541$	−25.0000			−1.07483			−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000			−1.07483			−0.537417	+	0.843317i	$0.680600\pi$
$542$	−1.00000	−	1.73205i	−0.0429537	−	0.0743980i
$543$	5.00000	−	8.66025i	0.214571	−	0.371647i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	6.00000			0.257012
$546$		0			0
$547$	−34.0000			−1.45374			−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000			−1.45374			−0.726868	+	0.686778i	$0.759025\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$	−3.50000	+	6.06218i	−0.149376	+	0.258727i
$550$	−12.0000	−	20.7846i	−0.511682	−	0.886259i
$551$	12.0000			0.511217
$552$	−6.00000	−	10.3923i	−0.255377	−	0.442326i
$553$		0			0
$554$	1.00000			0.0424859
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	1.00000	−	1.73205i	0.0424094	−	0.0734553i
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	−0.754802	−	0.655953i	$-0.772267\pi$
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	0.945473	+	0.325701i	$0.105600\pi$
$558$	−10.0000			−0.423334
$559$	10.0000	−	34.6410i	0.422955	−	1.46516i
$560$		0			0
$561$	18.0000	−	31.1769i	0.759961	−	1.31629i
$562$	13.5000	−	23.3827i	0.569463	−	0.986339i
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$		0			0
$565$	−4.50000	−	7.79423i	−0.189316	−	0.327906i
$566$	11.0000	+	19.0526i	0.462364	+	0.800839i
$567$		0			0
$568$		0			0
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$	12.0000	−	20.7846i	0.502625	−	0.870572i
$571$	8.00000			0.334790			0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000			0.334790			0.167395	+	0.985890i	$0.446465\pi$
$572$	15.0000	+	15.5885i	0.627182	+	0.651786i
$573$	36.0000			1.50392
$574$		0			0
$575$	12.0000	−	20.7846i	0.500435	−	0.866778i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	19.0000			0.790980			0.395490	−	0.918470i	$-0.370575\pi$
$577$	19.0000			0.790980			0.395490	+	0.918470i	$0.370575\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−23.0000	−	39.8372i	−0.955847	−	1.65558i
$580$	9.00000			0.373705
$581$		0			0
$582$	−2.00000	+	3.46410i	−0.0829027	+	0.143592i
$583$	−27.0000	+	46.7654i	−1.11823	+	1.93682i
$584$	−7.00000			−0.289662
$585$	−3.00000	+	10.3923i	−0.124035	+	0.429669i
$586$	−3.00000			−0.123929
$587$	−18.0000	+	31.1769i	−0.742940	+	1.28681i	0.208212	+	0.978084i	$0.433236\pi$
$587$	−18.0000	+	31.1769i	−0.742940	+	1.28681i	−0.951151	+	0.308725i	$0.900098\pi$
$588$		0			0
$589$	−20.0000	−	34.6410i	−0.824086	−	1.42736i
$590$	−18.0000			−0.741048
$591$	−18.0000	−	31.1769i	−0.740421	−	1.28245i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	15.0000			0.615976			0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000			0.615976			0.307988	+	0.951390i	$0.400344\pi$
$594$	12.0000	+	20.7846i	0.492366	+	0.852803i
$595$		0			0
$596$	10.5000	−	18.1865i	0.430097	−	0.744949i
$597$	8.00000			0.327418
$598$	−6.00000	+	20.7846i	−0.245358	+	0.849946i
$599$	36.0000			1.47092			0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000			1.47092			0.735460	+	0.677568i	$0.236966\pi$
$600$	4.00000	−	6.92820i	0.163299	−	0.282843i
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	−37.5000	−	64.9519i	−1.52459	−	2.64067i
$606$	−6.00000			−0.243733
$607$	22.0000	+	38.1051i	0.892952	+	1.54664i	0.836318	+	0.548244i	$0.184703\pi$
$607$	22.0000	+	38.1051i	0.892952	+	1.54664i	0.0566340	+	0.998395i	$0.481963\pi$
$608$	2.00000	−	3.46410i	0.0811107	−	0.140488i
$609$		0			0
$610$	−21.0000			−0.850265
$611$		0			0
$612$	3.00000			0.121268
$613$	6.50000	−	11.2583i	0.262533	−	0.454720i	−0.704382	−	0.709821i	$-0.748776\pi$
$613$	6.50000	−	11.2583i	0.262533	−	0.454720i	0.966914	+	0.255102i	$0.0821090\pi$
$614$	11.0000	−	19.0526i	0.443924	−	0.768899i
$615$	−9.00000	−	15.5885i	−0.362915	−	0.628587i
$616$		0			0
$617$	22.5000	+	38.9711i	0.905816	+	1.56892i	0.819818	+	0.572624i	$0.194074\pi$
$617$	22.5000	+	38.9711i	0.905816	+	1.56892i	0.0859976	+	0.996295i	$0.472592\pi$
$618$	4.00000	+	6.92820i	0.160904	+	0.278693i
$619$	−26.0000			−1.04503			−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000			−1.04503			−0.522514	+	0.852631i	$0.675006\pi$
$620$	−15.0000	−	25.9808i	−0.602414	−	1.04341i
$621$	−12.0000	+	20.7846i	−0.481543	+	0.834058i
$622$	9.00000	−	15.5885i	0.360867	−	0.625040i
$623$		0			0
$624$	−2.00000	+	6.92820i	−0.0800641	+	0.277350i
$625$	−29.0000			−1.16000
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$	24.0000	−	41.5692i	0.958468	−	1.66011i
$628$	−3.50000	−	6.06218i	−0.139665	−	0.241907i
$629$	−3.00000			−0.119618
$630$		0			0
$631$	2.00000	+	3.46410i	0.0796187	+	0.137904i	0.903085	−	0.429461i	$-0.141296\pi$
$631$	2.00000	+	3.46410i	0.0796187	+	0.137904i	−0.823467	+	0.567365i	$0.807963\pi$
$632$	−14.0000			−0.556890
$633$	22.0000	+	38.1051i	0.874421	+	1.51454i
$634$	−4.50000	+	7.79423i	−0.178718	+	0.309548i
$635$	−30.0000	+	51.9615i	−1.19051	+	2.06203i
$636$	−18.0000			−0.713746
$637$		0			0
$638$	18.0000			0.712627
$639$		0			0
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$		0			0
$643$	−20.0000	−	34.6410i	−0.788723	−	1.36611i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−20.0000	−	34.6410i	−0.788723	−	1.36611i	0.138027	−	0.990429i	$-0.455924\pi$
$644$		0			0
$645$	−60.0000			−2.36250
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	−0.999478	−	0.0322975i	$-0.989718\pi$
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	0.527710	+	0.849425i	$0.323051\pi$
$648$	−5.50000	+	9.52628i	−0.216060	+	0.374228i
$649$	−36.0000			−1.41312
$650$	−14.0000	+	3.46410i	−0.549125	+	0.135873i
$651$		0			0
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$	2.00000	+	3.46410i	0.0782062	+	0.135457i
$655$		0			0
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$	−3.50000	−	6.06218i	−0.136548	−	0.236508i
$658$		0			0
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$	18.0000	−	31.1769i	0.700649	−	1.21356i
$661$	2.50000	−	4.33013i	0.0972387	−	0.168422i	−0.813302	−	0.581842i	$-0.802332\pi$
$661$	2.50000	−	4.33013i	0.0972387	−	0.168422i	0.910541	+	0.413419i	$0.135666\pi$
$662$	10.0000			0.388661
$663$	−15.0000	−	15.5885i	−0.582552	−	0.605406i
$664$	−18.0000			−0.698535
$665$		0			0
$666$	−0.500000	+	0.866025i	−0.0193746	+	0.0335578i
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	6.00000			0.232147
$669$	−28.0000	−	48.4974i	−1.08254	−	1.87502i
$670$	3.00000	+	5.19615i	0.115900	+	0.200745i
$671$	−42.0000			−1.62139
$672$		0			0
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	0.302017	+	0.953302i	$0.402340\pi$
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	−0.976593	+	0.215096i	$0.930993\pi$
$674$	−6.50000	+	11.2583i	−0.250371	+	0.433655i
$675$	−16.0000			−0.615840
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$	3.00000	−	5.19615i	0.115214	−	0.199557i
$679$		0			0
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$	12.0000			0.459841
$682$	−30.0000	−	51.9615i	−1.14876	−	1.98971i
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	0.998917	−	0.0465244i	$-0.0148145\pi$
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	−0.539750	+	0.841825i	$0.681481\pi$
$684$	4.00000			0.152944
$685$	−4.50000	−	7.79423i	−0.171936	−	0.297802i
$686$		0			0
$687$	14.0000	−	24.2487i	0.534133	−	0.925146i
$688$	−10.0000			−0.381246
$689$	22.5000	+	23.3827i	0.857182	+	0.890809i
$690$	36.0000			1.37050
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$		0			0
$694$	6.00000			0.227757
$695$	3.00000	+	5.19615i	0.113796	+	0.197101i
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$	9.00000			0.340899
$698$	−1.00000	−	1.73205i	−0.0378506	−	0.0655591i
$699$	18.0000	−	31.1769i	0.680823	−	1.17922i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	14.0000	−	3.46410i	0.528396	−	0.130744i
$703$	−4.00000			−0.150863
$704$	3.00000	−	5.19615i	0.113067	−	0.195837i
$705$		0			0
$706$	1.50000	+	2.59808i	0.0564532	+	0.0977799i
$707$		0			0
$708$	−6.00000	−	10.3923i	−0.225494	−	0.390567i
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$		0			0
$711$	−7.00000	−	12.1244i	−0.262521	−	0.454699i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	30.0000	−	51.9615i	1.12351	−	1.94597i
$714$		0			0
$715$	−63.0000	+	15.5885i	−2.35607	+	0.582975i
$716$		0			0
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$	3.00000			0.111803
$721$		0			0
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$	−34.0000			−1.26447
$724$	2.50000	+	4.33013i	0.0929118	+	0.160928i
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$	25.0000	−	43.3013i	0.927837	−	1.60706i
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	10.5000	−	18.1865i	0.388622	−	0.673114i
$731$	15.0000	−	25.9808i	0.554795	−	0.960933i
$732$	−7.00000	−	12.1244i	−0.258727	−	0.448129i
$733$	−17.0000			−0.627909			−0.313955	−	0.949438i	$-0.601654\pi$
$733$	−17.0000			−0.627909			−0.313955	+	0.949438i	$0.601654\pi$
$734$	5.00000	+	8.66025i	0.184553	+	0.319656i
$735$		0			0
$736$	6.00000			0.221163
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$	1.50000	−	2.59808i	0.0552158	−	0.0956365i
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$	−3.00000			−0.110282
$741$	−20.0000	−	20.7846i	−0.734718	−	0.763542i
$742$		0			0
$743$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$743$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$744$	10.0000	−	17.3205i	0.366618	−	0.635001i
$745$	31.5000	+	54.5596i	1.15407	+	1.99891i
$746$	13.0000			0.475964
$747$	−9.00000	−	15.5885i	−0.329293	−	0.570352i
$748$	9.00000	+	15.5885i	0.329073	+	0.569970i
$749$		0			0
$750$	−3.00000	−	5.19615i	−0.109545	−	0.189737i
$751$	23.0000	−	39.8372i	0.839282	−	1.45368i	−0.0512140	−	0.998688i	$-0.516309\pi$
$751$	23.0000	−	39.8372i	0.839282	−	1.45368i	0.890496	−	0.454991i	$-0.150358\pi$
$752$		0			0
$753$	24.0000			0.874609
$754$	3.00000	−	10.3923i	0.109254	−	0.378465i
$755$	24.0000			0.873449
$756$		0			0
$757$	−1.00000	+	1.73205i	−0.0363456	+	0.0629525i	−0.883626	−	0.468193i	$-0.844905\pi$
$757$	−1.00000	+	1.73205i	−0.0363456	+	0.0629525i	0.847280	+	0.531146i	$0.178238\pi$
$758$	13.0000	+	22.5167i	0.472181	+	0.817842i
$759$	72.0000			2.61343
$760$	6.00000	+	10.3923i	0.217643	+	0.376969i
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$	−40.0000			−1.44905
$763$		0			0
$764$	−9.00000	+	15.5885i	−0.325609	+	0.563971i
$765$	−4.50000	+	7.79423i	−0.162698	+	0.281801i
$766$	−18.0000			−0.650366
$767$	−6.00000	+	20.7846i	−0.216647	+	0.750489i
$768$	2.00000			0.0721688
$769$	−23.0000	+	39.8372i	−0.829401	+	1.43657i	0.0691074	+	0.997609i	$0.477985\pi$
$769$	−23.0000	+	39.8372i	−0.829401	+	1.43657i	−0.898509	+	0.438956i	$0.855348\pi$
$770$		0			0
$771$	21.0000	+	36.3731i	0.756297	+	1.30994i
$772$	23.0000			0.827788
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	0.914920	−	0.403634i	$-0.132253\pi$
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	−0.807018	+	0.590527i	$0.798920\pi$
$774$	−5.00000	−	8.66025i	−0.179721	−	0.311286i
$775$	40.0000			1.43684
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$		0			0
$778$	−16.5000	+	28.5788i	−0.591554	+	1.02460i
$779$	12.0000			0.429945
$780$	−15.0000	−	15.5885i	−0.537086	−	0.558156i
$781$		0			0
$782$	−9.00000	+	15.5885i	−0.321839	+	0.557442i
$783$	6.00000	−	10.3923i	0.214423	−	0.371391i
$784$		0			0
$785$	21.0000			0.749522
$786$		0			0
$787$	−5.00000	−	8.66025i	−0.178231	−	0.308705i	0.763044	−	0.646347i	$-0.223704\pi$
$787$	−5.00000	−	8.66025i	−0.178231	−	0.308705i	−0.941275	+	0.337642i	$0.890371\pi$
$788$	18.0000			0.641223
$789$	6.00000	+	10.3923i	0.213606	+	0.369976i
$790$	21.0000	−	36.3731i	0.747146	−	1.29410i
$791$		0			0
$792$	6.00000			0.213201
$793$	−7.00000	+	24.2487i	−0.248577	+	0.861097i
$794$	−34.0000			−1.20661
$795$	27.0000	−	46.7654i	0.957591	−	1.65860i
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	3.00000	+	5.19615i	0.106265	+	0.184057i	0.914255	−	0.405140i	$-0.132777\pi$
$797$	3.00000	+	5.19615i	0.106265	+	0.184057i	−0.807989	+	0.589197i	$0.799444\pi$
$798$		0			0
$799$		0			0
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	6.00000			0.212000
$802$	7.50000	+	12.9904i	0.264834	+	0.458706i
$803$	21.0000	−	36.3731i	0.741074	−	1.28358i
$804$	−2.00000	+	3.46410i	−0.0705346	+	0.122169i
$805$		0			0
$806$	−35.0000	+	8.66025i	−1.23282	+	0.305044i
$807$	−36.0000			−1.26726
$808$	1.50000	−	2.59808i	0.0527698	−	0.0914000i
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.0646355	+	0.997909i	$0.520588\pi$
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.831897	+	0.554930i	$0.812745\pi$
$810$	−16.5000	−	28.5788i	−0.579751	−	1.00416i
$811$	−26.0000			−0.912983			−0.456492	−	0.889728i	$-0.650894\pi$
$811$	−26.0000			−0.912983			−0.456492	+	0.889728i	$0.650894\pi$
$812$		0			0
$813$	2.00000	+	3.46410i	0.0701431	+	0.121491i
$814$	−6.00000			−0.210300
$815$	−3.00000	−	5.19615i	−0.105085	−	0.182013i
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	20.0000	−	34.6410i	0.699711	−	1.21194i
$818$	5.00000			0.174821
$819$		0			0
$820$	9.00000			0.314294
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$	3.00000	−	5.19615i	0.104637	−	0.181237i
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	−4.00000			−0.139347
$825$	24.0000	+	41.5692i	0.835573	+	1.44725i
$826$		0			0
$827$	42.0000			1.46048			0.730242	−	0.683189i	$-0.239408\pi$
$827$	42.0000			1.46048			0.730242	+	0.683189i	$0.239408\pi$
$828$	3.00000	+	5.19615i	0.104257	+	0.180579i
$829$	−3.50000	+	6.06218i	−0.121560	+	0.210548i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−3.50000	+	6.06218i	−0.121560	+	0.210548i	0.798823	+	0.601566i	$0.205456\pi$
$830$	27.0000	−	46.7654i	0.937184	−	1.62325i
$831$	−2.00000			−0.0693792
$832$	−2.50000	−	2.59808i	−0.0866719	−	0.0900721i
$833$		0			0
$834$	−2.00000	+	3.46410i	−0.0692543	+	0.119952i
$835$	−9.00000	+	15.5885i	−0.311458	+	0.539461i
$836$	12.0000	+	20.7846i	0.415029	+	0.718851i
$837$	−40.0000			−1.38260
$838$	−3.00000	−	5.19615i	−0.103633	−	0.179498i
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	0.950813	−	0.309764i	$-0.100250\pi$
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	−0.743670	+	0.668546i	$0.766917\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	17.5000	−	30.3109i	0.603090	−	1.04458i
$843$	−27.0000	+	46.7654i	−0.929929	+	1.61068i
$844$	−22.0000			−0.757271
$845$	−1.50000	+	38.9711i	−0.0516016	+	1.34065i
$846$		0			0
$847$		0			0
$848$	4.50000	−	7.79423i	0.154531	−	0.267655i
$849$	−22.0000	−	38.1051i	−0.755038	−	1.30776i
$850$	−12.0000			−0.411597
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$		0			0
$853$	19.0000			0.650548			0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000			0.650548			0.325274	+	0.945620i	$0.394544\pi$
$854$		0			0
$855$	−6.00000	+	10.3923i	−0.205196	+	0.355409i
$856$		0			0
$857$	−33.0000			−1.12726			−0.563629	−	0.826028i	$-0.690595\pi$
$857$	−33.0000			−1.12726			−0.563629	+	0.826028i	$0.690595\pi$
$858$	−30.0000	−	31.1769i	−1.02418	−	1.06436i
$859$	−14.0000			−0.477674			−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000			−0.477674			−0.238837	+	0.971060i	$0.576766\pi$
$860$	15.0000	−	25.9808i	0.511496	−	0.885937i
$861$		0			0
$862$	−6.00000	−	10.3923i	−0.204361	−	0.353963i
$863$	54.0000			1.83818			0.919091	−	0.394046i	$-0.128925\pi$
$863$	54.0000			1.83818			0.919091	+	0.394046i	$0.128925\pi$
$864$	−2.00000	−	3.46410i	−0.0680414	−	0.117851i
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	5.00000			0.169907
$867$	8.00000	+	13.8564i	0.271694	+	0.470588i
$868$		0			0
$869$	42.0000	−	72.7461i	1.42475	−	2.46774i
$870$	−18.0000			−0.610257
$871$	7.00000	−	1.73205i	0.237186	−	0.0586883i
$872$	−2.00000			−0.0677285
$873$	1.00000	−	1.73205i	0.0338449	−	0.0586210i
$874$	−12.0000	+	20.7846i	−0.405906	+	0.703050i
$875$		0			0
$876$	14.0000			0.473016
$877$	24.5000	+	42.4352i	0.827306	+	1.43294i	0.900144	+	0.435593i	$0.143461\pi$
$877$	24.5000	+	42.4352i	0.827306	+	1.43294i	−0.0728377	+	0.997344i	$0.523206\pi$
$878$	11.0000	+	19.0526i	0.371232	+	0.642993i
$879$	6.00000			0.202375
$880$	9.00000	+	15.5885i	0.303390	+	0.525487i
$881$	22.5000	−	38.9711i	0.758044	−	1.31297i	−0.185802	−	0.982587i	$-0.559488\pi$
$881$	22.5000	−	38.9711i	0.758044	−	1.31297i	0.943847	−	0.330384i	$-0.107178\pi$
$882$		0			0
$883$	38.0000			1.27880			0.639401	−	0.768874i	$-0.279182\pi$
$883$	38.0000			1.27880			0.639401	+	0.768874i	$0.279182\pi$
$884$	10.5000	−	2.59808i	0.353153	−	0.0873828i
$885$	36.0000			1.21013
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$	−1.00000	−	1.73205i	−0.0335578	−	0.0581238i
$889$		0			0
$890$	9.00000	+	15.5885i	0.301681	+	0.522526i
$891$	−33.0000	−	57.1577i	−1.10554	−	1.91485i
$892$	28.0000			0.937509
$893$		0			0
$894$	−21.0000	+	36.3731i	−0.702345	+	1.21650i
$895$		0			0
$896$		0			0
$897$	12.0000	−	41.5692i	0.400668	−	1.38796i
$898$	−30.0000			−1.00111
$899$	−15.0000	+	25.9808i	−0.500278	+	0.866507i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	13.5000	+	23.3827i	0.449750	+	0.778990i
$902$	18.0000			0.599334
$903$		0			0
$904$	1.50000	+	2.59808i	0.0498893	+	0.0864107i
$905$	−15.0000			−0.498617
$906$	8.00000	+	13.8564i	0.265782	+	0.460348i
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	−0.958523	−	0.285015i	$-0.908001\pi$
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	0.726092	+	0.687598i	$0.241335\pi$
$908$	−3.00000	+	5.19615i	−0.0995585	+	0.172440i
$909$	3.00000			0.0995037
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−4.00000	+	6.92820i	−0.132453	+	0.229416i
$913$	54.0000	−	93.5307i	1.78714	−	3.09542i
$914$	−12.5000	−	21.6506i	−0.413463	−	0.716139i
$915$	42.0000			1.38848
$916$	7.00000	+	12.1244i	0.231287	+	0.400600i
$917$		0			0
$918$	12.0000			0.396059
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$	−22.0000	+	38.1051i	−0.724925	+	1.25561i
$922$	33.0000			1.08680
$923$		0			0
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	−11.0000	+	19.0526i	−0.361482	+	0.626106i
$927$	−2.00000	−	3.46410i	−0.0656886	−	0.113776i
$928$	−3.00000			−0.0984798
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	0.998827	+	0.0484211i	$0.0154190\pi$
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	−0.457480	+	0.889220i	$0.651248\pi$
$930$	30.0000	+	51.9615i	0.983739	+	1.70389i
$931$		0			0
$932$	9.00000	+	15.5885i	0.294805	+	0.510617i
$933$	−18.0000	+	31.1769i	−0.589294	+	1.02069i
$934$	9.00000	−	15.5885i	0.294489	−	0.510070i
$935$	−54.0000			−1.76599
$936$	1.00000	−	3.46410i	0.0326860	−	0.113228i
$937$	19.0000			0.620703			0.310351	−	0.950622i	$-0.399553\pi$
$937$	19.0000			0.620703			0.310351	+	0.950622i	$0.399553\pi$
$938$		0			0
$939$	−10.0000	+	17.3205i	−0.326338	+	0.565233i
$940$		0			0
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$	7.00000	+	12.1244i	0.228072	+	0.395033i
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$	6.00000			0.195283
$945$		0			0
$946$	30.0000	−	51.9615i	0.975384	−	1.68941i
$947$	21.0000	−	36.3731i	0.682408	−	1.18197i	−0.291835	−	0.956469i	$-0.594266\pi$
$947$	21.0000	−	36.3731i	0.682408	−	1.18197i	0.974244	−	0.225497i	$-0.0724007\pi$
$948$	28.0000			0.909398
$949$	−17.5000	−	18.1865i	−0.568074	−	0.590360i
$950$	−16.0000			−0.519109
$951$	9.00000	−	15.5885i	0.291845	−	0.505490i
$952$		0			0
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	0.813337	−	0.581793i	$-0.197649\pi$
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	−0.910516	+	0.413473i	$0.864315\pi$
$954$	9.00000			0.291386
$955$	−27.0000	−	46.7654i	−0.873699	−	1.51329i
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	−36.0000			−1.16371
$958$	−21.0000	−	36.3731i	−0.678479	−	1.17516i
$959$		0			0
$960$	−3.00000	+	5.19615i	−0.0968246	+	0.167705i
$961$	69.0000			2.22581
$962$	−1.00000	+	3.46410i	−0.0322413	+	0.111687i
$963$		0			0
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$	−34.5000	+	59.7558i	−1.11059	+	1.92361i
$966$		0			0
$967$	−34.0000			−1.09337			−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000			−1.09337			−0.546683	+	0.837340i	$0.684110\pi$
$968$	12.5000	+	21.6506i	0.401765	+	0.695878i
$969$	−12.0000	−	20.7846i	−0.385496	−	0.667698i
$970$	6.00000			0.192648
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$	5.00000	−	8.66025i	0.160375	−	0.277778i
$973$		0			0
$974$	−32.0000			−1.02535
$975$	28.0000	−	6.92820i	0.896718	−	0.221880i
$976$	7.00000			0.224065
$977$	−25.5000	+	44.1673i	−0.815817	+	1.41304i	0.0929223	+	0.995673i	$0.470379\pi$
$977$	−25.5000	+	44.1673i	−0.815817	+	1.41304i	−0.908740	+	0.417364i	$0.862954\pi$
$978$	2.00000	−	3.46410i	0.0639529	−	0.110770i
$979$	18.0000	+	31.1769i	0.575282	+	0.996419i
$980$		0			0
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$		0			0
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$	−27.0000	+	46.7654i	−0.860292	+	1.49007i
$986$	4.50000	−	7.79423i	0.143309	−	0.248219i
$987$		0			0
$988$	14.0000	−	3.46410i	0.445399	−	0.110208i
$989$	60.0000			1.90789
$990$	−9.00000	+	15.5885i	−0.286039	+	0.495434i
$991$	5.00000	−	8.66025i	0.158830	−	0.275102i	−0.775617	−	0.631204i	$-0.782561\pi$
$991$	5.00000	−	8.66025i	0.158830	−	0.275102i	0.934447	+	0.356102i	$0.115894\pi$
$992$	5.00000	+	8.66025i	0.158750	+	0.274963i
$993$	−20.0000			−0.634681
$994$		0			0
$995$	−6.00000	−	10.3923i	−0.190213	−	0.329458i
$996$	36.0000			1.14070
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	0.890511	+	0.454961i	$0.150347\pi$
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	−0.0512480	+	0.998686i	$0.516320\pi$
$998$	−11.0000	+	19.0526i	−0.348199	+	0.603098i
$999$	−2.00000	+	3.46410i	−0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.g.c.295.1		2
7.2	even	3		1274.2.e.b.165.1		2
7.3	odd	6		1274.2.h.e.373.1		2
7.4	even	3		1274.2.h.l.373.1		2
7.5	odd	6		1274.2.e.k.165.1		2
7.6	odd	2		182.2.g.c.113.1	yes	2
13.3	even	3	inner	1274.2.g.c.393.1		2
21.20	even	2		1638.2.r.m.1387.1		2
28.27	even	2		1456.2.s.a.113.1		2
91.3	odd	6		1274.2.e.k.471.1		2
91.6	even	12		2366.2.d.a.337.2		2
91.16	even	3		1274.2.h.l.263.1		2
91.20	even	12		2366.2.d.a.337.1		2
91.48	odd	6		2366.2.a.a.1.1		1
91.55	odd	6		182.2.g.c.29.1	✓	2
91.68	odd	6		1274.2.h.e.263.1		2
91.69	odd	6		2366.2.a.k.1.1		1
91.81	even	3		1274.2.e.b.471.1		2
273.146	even	6		1638.2.r.m.757.1		2
364.55	even	6		1456.2.s.a.1121.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.g.c.29.1	✓	2	91.55	odd	6
182.2.g.c.113.1	yes	2	7.6	odd	2
1274.2.e.b.165.1		2	7.2	even	3
1274.2.e.b.471.1		2	91.81	even	3
1274.2.e.k.165.1		2	7.5	odd	6
1274.2.e.k.471.1		2	91.3	odd	6
1274.2.g.c.295.1		2	1.1	even	1	trivial
1274.2.g.c.393.1		2	13.3	even	3	inner
1274.2.h.e.263.1		2	91.68	odd	6
1274.2.h.e.373.1		2	7.3	odd	6
1274.2.h.l.263.1		2	91.16	even	3
1274.2.h.l.373.1		2	7.4	even	3
1456.2.s.a.113.1		2	28.27	even	2
1456.2.s.a.1121.1		2	364.55	even	6
1638.2.r.m.757.1		2	273.146	even	6
1638.2.r.m.1387.1		2	21.20	even	2
2366.2.a.a.1.1		1	91.48	odd	6
2366.2.a.k.1.1		1	91.69	odd	6
2366.2.d.a.337.1		2	91.20	even	12
2366.2.d.a.337.2		2	91.6	even	12

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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(1.00000 + 1.73205i) q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(3.00000 - 5.19615i) q^{11} +2.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} -1.00000 q^{18} +(-2.00000 - 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(3.00000 - 5.19615i) q^{23} +(1.00000 - 1.73205i) q^{24} +4.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} -4.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +(3.00000 + 5.19615i) q^{30} +10.0000 q^{31} +(0.500000 + 0.866025i) q^{32} +(6.00000 + 10.3923i) q^{33} -3.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{37} -4.00000 q^{38} +(7.00000 - 1.73205i) q^{39} -3.00000 q^{40} +(-1.50000 + 2.59808i) q^{41} +(5.00000 + 8.66025i) q^{43} -6.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(-1.00000 - 1.73205i) q^{48} +(2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} -9.00000 q^{53} +(-2.00000 + 3.46410i) q^{54} +(9.00000 - 15.5885i) q^{55} +8.00000 q^{57} +(1.50000 + 2.59808i) q^{58} +(-3.00000 - 5.19615i) q^{59} +6.00000 q^{60} +(-3.50000 - 6.06218i) q^{61} +(5.00000 - 8.66025i) q^{62} +1.00000 q^{64} +(-7.50000 - 7.79423i) q^{65} +12.0000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{69} +(0.500000 + 0.866025i) q^{72} +7.00000 q^{73} +(-0.500000 - 0.866025i) q^{74} +(-4.00000 + 6.92820i) q^{75} +(-2.00000 + 3.46410i) q^{76} +(2.00000 - 6.92820i) q^{78} +14.0000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(5.50000 - 9.52628i) q^{81} +(1.50000 + 2.59808i) q^{82} +18.0000 q^{83} +(-4.50000 - 7.79423i) q^{85} +10.0000 q^{86} +(-3.00000 - 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-3.00000 + 5.19615i) q^{89} -3.00000 q^{90} -6.00000 q^{92} +(-10.0000 + 17.3205i) q^{93} +(-6.00000 - 10.3923i) q^{95} -2.00000 q^{96} +(1.00000 + 1.73205i) q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} + 6 q^{5} + 2 q^{6} - 2 q^{8} - q^{9} + 3 q^{10} + 6 q^{11} + 4 q^{12} - 5 q^{13} - 6 q^{15} - q^{16} - 3 q^{17} - 2 q^{18} - 4 q^{19} - 3 q^{20} - 6 q^{22} + 6 q^{23}+ \cdots - 12 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 + 6 * q^5 + 2 * q^6 - 2 * q^8 - q^9 + 3 * q^10 + 6 * q^11 + 4 * q^12 - 5 * q^13 - 6 * q^15 - q^16 - 3 * q^17 - 2 * q^18 - 4 * q^19 - 3 * q^20 - 6 * q^22 + 6 * q^23 + 2 * q^24 + 8 * q^25 - 7 * q^26 - 8 * q^27 - 3 * q^29 + 6 * q^30 + 20 * q^31 + q^32 + 12 * q^33 - 6 * q^34 - q^36 + q^37 - 8 * q^38 + 14 * q^39 - 6 * q^40 - 3 * q^41 + 10 * q^43 - 12 * q^44 - 3 * q^45 - 6 * q^46 - 2 * q^48 + 4 * q^50 + 12 * q^51 - 2 * q^52 - 18 * q^53 - 4 * q^54 + 18 * q^55 + 16 * q^57 + 3 * q^58 - 6 * q^59 + 12 * q^60 - 7 * q^61 + 10 * q^62 + 2 * q^64 - 15 * q^65 + 24 * q^66 - 2 * q^67 - 3 * q^68 + 12 * q^69 + q^72 + 14 * q^73 - q^74 - 8 * q^75 - 4 * q^76 + 4 * q^78 + 28 * q^79 - 3 * q^80 + 11 * q^81 + 3 * q^82 + 36 * q^83 - 9 * q^85 + 20 * q^86 - 6 * q^87 - 6 * q^88 - 6 * q^89 - 6 * q^90 - 12 * q^92 - 20 * q^93 - 12 * q^95 - 4 * q^96 + 2 * q^97 - 12 * q^99

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