LMFDB - Embedded newform 338.2.c.f.315.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,2,Mod(191,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.69894358832$
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 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	338.315
Dual form			338.2.c.f.191.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{10} -1.00000 q^{12} -3.00000 q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +2.00000 q^{18} +(-3.00000 + 5.19615i) q^{19} +(-1.50000 + 2.59808i) q^{20} -3.00000 q^{21} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +4.00000 q^{25} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{28} +(-1.50000 + 2.59808i) q^{30} +(0.500000 - 0.866025i) q^{32} +3.00000 q^{34} +(-4.50000 + 7.79423i) q^{35} +(1.00000 + 1.73205i) q^{36} +(-1.50000 - 2.59808i) q^{37} -6.00000 q^{38} -3.00000 q^{40} +(-1.50000 - 2.59808i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{45} +(3.00000 - 5.19615i) q^{46} +3.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} +3.00000 q^{51} -6.00000 q^{53} +(2.50000 + 4.33013i) q^{54} +(1.50000 - 2.59808i) q^{56} -6.00000 q^{57} +(3.00000 - 5.19615i) q^{59} -3.00000 q^{60} +(4.00000 - 6.92820i) q^{61} +(3.00000 + 5.19615i) q^{63} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.00000 - 5.19615i) q^{69} -9.00000 q^{70} +(7.50000 - 12.9904i) q^{71} +(-1.00000 + 1.73205i) q^{72} +6.00000 q^{73} +(1.50000 - 2.59808i) q^{74} +(2.00000 + 3.46410i) q^{75} +(-3.00000 - 5.19615i) q^{76} +10.0000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{83} +(1.50000 - 2.59808i) q^{84} +(4.50000 - 7.79423i) q^{85} -1.00000 q^{86} +(3.00000 + 5.19615i) q^{89} +6.00000 q^{90} +6.00000 q^{92} +(1.50000 + 2.59808i) q^{94} +(-9.00000 + 15.5885i) q^{95} +1.00000 q^{96} +(-6.00000 + 10.3923i) q^{97} +(1.00000 - 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 6 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 3 q^{10} - 2 q^{12} - 6 q^{14} + 3 q^{15} - q^{16} + 3 q^{17} + 4 q^{18} - 6 q^{19} - 3 q^{20} - 6 q^{21} - 6 q^{23} - q^{24}+ \cdots + 2 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 6 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9 + 3 * q^10 - 2 * q^12 - 6 * q^14 + 3 * q^15 - q^16 + 3 * q^17 + 4 * q^18 - 6 * q^19 - 3 * q^20 - 6 * q^21 - 6 * q^23 - q^24 + 8 * q^25 + 10 * q^27 - 3 * q^28 - 3 * q^30 + q^32 + 6 * q^34 - 9 * q^35 + 2 * q^36 - 3 * q^37 - 12 * q^38 - 6 * q^40 - 3 * q^42 - q^43 + 6 * q^45 + 6 * q^46 + 6 * q^47 + q^48 - 2 * q^49 + 4 * q^50 + 6 * q^51 - 12 * q^53 + 5 * q^54 + 3 * q^56 - 12 * q^57 + 6 * q^59 - 6 * q^60 + 8 * q^61 + 6 * q^63 + 2 * q^64 - 12 * q^67 + 3 * q^68 + 6 * q^69 - 18 * q^70 + 15 * q^71 - 2 * q^72 + 12 * q^73 + 3 * q^74 + 4 * q^75 - 6 * q^76 + 20 * q^79 - 3 * q^80 - q^81 - 12 * q^83 + 3 * q^84 + 9 * q^85 - 2 * q^86 + 6 * q^89 + 12 * q^90 + 12 * q^92 + 3 * q^94 - 18 * q^95 + 2 * q^96 - 12 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−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	$0.265942\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−3.00000			−0.801784
$15$	1.50000	+	2.59808i	0.387298	+	0.670820i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	2.00000			0.471405
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$	−3.00000			−0.654654
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.00000			0.800000
$26$		0			0
$27$	5.00000			0.962250
$28$	−1.50000	−	2.59808i	−0.283473	−	0.490990i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	−4.50000	+	7.79423i	−0.760639	+	1.31747i
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	−6.00000			−0.973329
$39$		0			0
$40$	−3.00000			−0.474342
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	−1.50000	−	2.59808i	−0.231455	−	0.400892i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$	3.00000	−	5.19615i	0.447214	−	0.774597i
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	3.00000			0.420084
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	2.50000	+	4.33013i	0.340207	+	0.589256i
$55$		0			0
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	−6.00000			−0.794719
$58$		0			0
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$	−3.00000			−0.387298
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$		0			0
$63$	3.00000	+	5.19615i	0.377964	+	0.654654i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	−9.00000			−1.07571
$71$	7.50000	−	12.9904i	0.890086	−	1.54167i	0.0503155	−	0.998733i	$-0.483977\pi$
$71$	7.50000	−	12.9904i	0.890086	−	1.54167i	0.839771	−	0.542941i	$-0.182689\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	−3.00000	−	5.19615i	−0.344124	−	0.596040i
$77$		0			0
$78$		0			0
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	1.50000	−	2.59808i	0.163663	−	0.283473i
$85$	4.50000	−	7.79423i	0.488094	−	0.845403i
$86$	−1.00000			−0.107833
$87$		0			0
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	6.00000			0.632456
$91$		0			0
$92$	6.00000			0.625543
$93$		0			0
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	−9.00000	+	15.5885i	−0.923381	+	1.59934i
$96$	1.00000			0.102062
$97$	−6.00000	+	10.3923i	−0.609208	+	1.05518i	0.382164	+	0.924095i	$0.375179\pi$
$97$	−6.00000	+	10.3923i	−0.609208	+	1.05518i	−0.991371	+	0.131084i	$0.958154\pi$
$98$	1.00000	−	1.73205i	0.101015	−	0.174964i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$		0			0
$105$	−9.00000			−0.878310
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	−9.00000			−0.862044			−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000			−0.862044			−0.431022	+	0.902342i	$0.641847\pi$
$110$		0			0
$111$	1.50000	−	2.59808i	0.142374	−	0.246598i
$112$	3.00000			0.283473
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	−3.00000	−	5.19615i	−0.280976	−	0.486664i
$115$	−9.00000	−	15.5885i	−0.839254	−	1.45363i
$116$		0			0
$117$		0			0
$118$	6.00000			0.552345
$119$	4.50000	+	7.79423i	0.412514	+	0.714496i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	8.00000			0.724286
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$	−3.00000	+	5.19615i	−0.267261	+	0.462910i
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	−0.906977	+	0.421180i	$0.861616\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.00000			−0.0880451
$130$		0			0
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$		0			0
$133$	−9.00000	−	15.5885i	−0.780399	−	1.35169i
$134$	6.00000	−	10.3923i	0.518321	−	0.897758i
$135$	15.0000			1.29099
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$	6.00000			0.510754
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$	−4.50000	−	7.79423i	−0.380319	−	0.658733i
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	15.0000			1.25877
$143$		0			0
$144$	−2.00000			−0.166667
$145$		0			0
$146$	3.00000	+	5.19615i	0.248282	+	0.430037i
$147$	1.00000	−	1.73205i	0.0824786	−	0.142857i
$148$	3.00000			0.246598
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	−2.00000	+	3.46410i	−0.163299	+	0.282843i
$151$	−15.0000			−1.22068			−0.610341	−	0.792139i	$-0.708968\pi$
$151$	−15.0000			−1.22068			−0.610341	+	0.792139i	$0.708968\pi$
$152$	3.00000	−	5.19615i	0.243332	−	0.421464i
$153$	−3.00000	−	5.19615i	−0.242536	−	0.420084i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	5.00000	+	8.66025i	0.397779	+	0.688973i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$	18.0000			1.41860
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−3.00000	+	5.19615i	−0.234978	+	0.406994i	−0.959266	−	0.282503i	$-0.908835\pi$
$163$	−3.00000	+	5.19615i	−0.234978	+	0.406994i	0.724288	+	0.689497i	$0.242169\pi$
$164$		0			0
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$	3.00000			0.231455
$169$		0			0
$170$	9.00000			0.690268
$171$	6.00000	+	10.3923i	0.458831	+	0.794719i
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	−6.00000	+	10.3923i	−0.453557	+	0.785584i
$176$		0			0
$177$	6.00000			0.450988
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	0.997446	+	0.0714220i	$0.0227537\pi$
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	−0.436870	+	0.899525i	$0.643913\pi$
$180$	3.00000	+	5.19615i	0.223607	+	0.387298i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−4.50000	−	7.79423i	−0.330847	−	0.573043i
$186$		0			0
$187$		0			0
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$	−7.50000	+	12.9904i	−0.545545	+	0.944911i
$190$	−18.0000			−1.30586
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	0.737620	−	0.675216i	$-0.235950\pi$
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	−0.953564	+	0.301189i	$0.902616\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	2.00000			0.142857
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	0.914501	−	0.404584i	$-0.132584\pi$
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	−0.807630	+	0.589689i	$0.799250\pi$
$198$		0			0
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$	−4.00000			−0.282843
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$		0			0
$204$	−1.50000	+	2.59808i	−0.105021	+	0.181902i
$205$		0			0
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$	−12.0000			−0.834058
$208$		0			0
$209$		0			0
$210$	−4.50000	−	7.79423i	−0.310530	−	0.537853i
$211$	11.5000	+	19.9186i	0.791693	+	1.37125i	0.924918	+	0.380166i	$0.124133\pi$
$211$	11.5000	+	19.9186i	0.791693	+	1.37125i	−0.133226	+	0.991086i	$0.542533\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	15.0000			1.02778
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$	−5.00000			−0.340207
$217$		0			0
$218$	−4.50000	−	7.79423i	−0.304778	−	0.527892i
$219$	3.00000	+	5.19615i	0.202721	+	0.351123i
$220$		0			0
$221$		0			0
$222$	3.00000			0.201347
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	0.675098	−	0.737728i	$-0.264101\pi$
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	−0.976440	+	0.215788i	$0.930768\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$	4.00000	−	6.92820i	0.266667	−	0.461880i
$226$	6.00000			0.399114
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$	3.00000	−	5.19615i	0.198680	−	0.344124i
$229$	9.00000			0.594737			0.297368	−	0.954763i	$-0.403891\pi$
$229$	9.00000			0.594737			0.297368	+	0.954763i	$0.403891\pi$
$230$	9.00000	−	15.5885i	0.593442	−	1.02787i
$231$		0			0
$232$		0			0
$233$	21.0000			1.37576			0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000			1.37576			0.687878	+	0.725826i	$0.258542\pi$
$234$		0			0
$235$	9.00000			0.587095
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	5.00000	+	8.66025i	0.324785	+	0.562544i
$238$	−4.50000	+	7.79423i	−0.291692	+	0.505225i
$239$	−9.00000			−0.582162			−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−9.00000			−0.582162			−0.291081	+	0.956698i	$0.594015\pi$
$240$	1.50000	−	2.59808i	0.0968246	−	0.167705i
$241$	15.0000	−	25.9808i	0.966235	−	1.67357i	0.259975	−	0.965615i	$-0.416286\pi$
$241$	15.0000	−	25.9808i	0.966235	−	1.67357i	0.706260	−	0.707953i	$-0.250381\pi$
$242$	11.0000			0.707107
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	4.00000	+	6.92820i	0.256074	+	0.443533i
$245$	−3.00000	−	5.19615i	−0.191663	−	0.331970i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$	−6.00000			−0.377964
$253$		0			0
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$	9.00000			0.563602
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	−0.500000	−	0.866025i	−0.0311286	−	0.0539164i
$259$	9.00000			0.559233
$260$		0			0
$261$		0			0
$262$	−1.50000	−	2.59808i	−0.0926703	−	0.160510i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$	−18.0000			−1.10573
$266$	9.00000	−	15.5885i	0.551825	−	0.955790i
$267$	−3.00000	+	5.19615i	−0.183597	+	0.317999i
$268$	12.0000			0.733017
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	7.50000	+	12.9904i	0.456435	+	0.790569i
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	0.543130	−	0.839649i	$-0.317239\pi$
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	−0.998722	+	0.0505395i	$0.983906\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	−18.0000			−1.08742
$275$		0			0
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	4.00000	−	6.92820i	0.240337	−	0.416275i	−0.720473	−	0.693482i	$-0.756075\pi$
$277$	4.00000	−	6.92820i	0.240337	−	0.416275i	0.960810	+	0.277207i	$0.0894088\pi$
$278$	−5.00000			−0.299880
$279$		0			0
$280$	4.50000	−	7.79423i	0.268926	−	0.465794i
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$	−1.50000	+	2.59808i	−0.0893237	+	0.154713i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	7.50000	+	12.9904i	0.445043	+	0.770837i
$285$	−18.0000			−1.06623
$286$		0			0
$287$		0			0
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−12.0000			−0.703452
$292$	−3.00000	+	5.19615i	−0.175562	+	0.304082i
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$	2.00000			0.116642
$295$	9.00000	−	15.5885i	0.524000	−	0.907595i
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$		0			0
$298$	−6.00000			−0.347571
$299$		0			0
$300$	−4.00000			−0.230940
$301$	−1.50000	−	2.59808i	−0.0864586	−	0.149751i
$302$	−7.50000	−	12.9904i	−0.431577	−	0.747512i
$303$	−6.00000	+	10.3923i	−0.344691	+	0.597022i
$304$	6.00000			0.344124
$305$	12.0000	−	20.7846i	0.687118	−	1.19012i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$		0			0
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$		0			0
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$		0			0
$313$	19.0000			1.07394			0.536972	−	0.843600i	$-0.319568\pi$
$313$	19.0000			1.07394			0.536972	+	0.843600i	$0.319568\pi$
$314$	−11.0000	−	19.0526i	−0.620766	−	1.07520i
$315$	9.00000	+	15.5885i	0.507093	+	0.878310i
$316$	−5.00000	+	8.66025i	−0.281272	+	0.487177i
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	3.00000	−	5.19615i	0.168232	−	0.291386i
$319$		0			0
$320$	3.00000			0.167705
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$	9.00000	+	15.5885i	0.501550	+	0.868711i
$323$	9.00000	+	15.5885i	0.500773	+	0.867365i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−6.00000			−0.332309
$327$	−4.50000	−	7.79423i	−0.248851	−	0.431022i
$328$		0			0
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	15.0000	−	25.9808i	0.824475	−	1.42803i	−0.0778456	−	0.996965i	$-0.524804\pi$
$331$	15.0000	−	25.9808i	0.824475	−	1.42803i	0.902320	−	0.431066i	$-0.141863\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	−6.00000			−0.328798
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−18.0000	−	31.1769i	−0.983445	−	1.70338i
$336$	1.50000	+	2.59808i	0.0818317	+	0.141737i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$		0			0
$339$	6.00000			0.325875
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$		0			0
$342$	−6.00000	+	10.3923i	−0.324443	+	0.561951i
$343$	−15.0000			−0.809924
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$	9.00000	−	15.5885i	0.484544	−	0.839254i
$346$	−6.00000			−0.322562
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.0409337	+	0.999162i	$0.513033\pi$
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.844833	+	0.535031i	$0.820300\pi$
$348$		0			0
$349$	10.5000	+	18.1865i	0.562052	+	0.973503i	0.997317	+	0.0732005i	$0.0233213\pi$
$349$	10.5000	+	18.1865i	0.562052	+	0.973503i	−0.435265	+	0.900302i	$0.643345\pi$
$350$	−12.0000			−0.641427
$351$		0			0
$352$		0			0
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	0.934751	−	0.355303i	$-0.115622\pi$
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	−0.775077	+	0.631867i	$0.782289\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$	22.5000	−	38.9711i	1.19418	−	2.06837i
$356$	−6.00000			−0.317999
$357$	−4.50000	+	7.79423i	−0.238165	+	0.412514i
$358$	−7.50000	+	12.9904i	−0.396387	+	0.686563i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	−3.00000	+	5.19615i	−0.158114	+	0.273861i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$	11.0000			0.577350
$364$		0			0
$365$	18.0000			0.942163
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$		0			0
$370$	4.50000	−	7.79423i	0.233944	−	0.405203i
$371$	9.00000	−	15.5885i	0.467257	−	0.809312i
$372$		0			0
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	−0.913147	−	0.407630i	$-0.866355\pi$
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	0.809591	+	0.586994i	$0.199689\pi$
$374$		0			0
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$	−3.00000			−0.154713
$377$		0			0
$378$	−15.0000			−0.771517
$379$	−3.00000	−	5.19615i	−0.154100	−	0.266908i	0.778631	−	0.627482i	$-0.215914\pi$
$379$	−3.00000	−	5.19615i	−0.154100	−	0.266908i	−0.932731	+	0.360573i	$0.882581\pi$
$380$	−9.00000	−	15.5885i	−0.461690	−	0.799671i
$381$	1.00000	−	1.73205i	0.0512316	−	0.0887357i
$382$	−12.0000			−0.613973
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	−0.957790	−	0.287469i	$-0.907186\pi$
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	0.727851	+	0.685736i	$0.240519\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	3.00000	−	5.19615i	0.152696	−	0.264477i
$387$	1.00000	+	1.73205i	0.0508329	+	0.0880451i
$388$	−6.00000	−	10.3923i	−0.304604	−	0.527589i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$	1.00000	+	1.73205i	0.0505076	+	0.0874818i
$393$	−1.50000	−	2.59808i	−0.0756650	−	0.131056i
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$	30.0000			1.50946
$396$		0			0
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	−0.998492	−	0.0549046i	$-0.982515\pi$
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	0.546795	+	0.837267i	$0.315848\pi$
$398$	−20.0000			−1.00251
$399$	9.00000	−	15.5885i	0.450564	−	0.780399i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$	12.0000			0.598506
$403$		0			0
$404$	−12.0000			−0.597022
$405$	−1.50000	−	2.59808i	−0.0745356	−	0.129099i
$406$		0			0
$407$		0			0
$408$	−3.00000			−0.148522
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$		0			0
$411$	−18.0000			−0.887875
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$	9.00000	+	15.5885i	0.442861	+	0.767058i
$414$	−6.00000	−	10.3923i	−0.294884	−	0.510754i
$415$	−18.0000			−0.883585
$416$		0			0
$417$	−5.00000			−0.244851
$418$		0			0
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	0.622601	−	0.782540i	$-0.286076\pi$
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	−0.989000	+	0.147918i	$0.952743\pi$
$420$	4.50000	−	7.79423i	0.219578	−	0.380319i
$421$	15.0000			0.731055			0.365528	−	0.930800i	$-0.380889\pi$
$421$	15.0000			0.731055			0.365528	+	0.930800i	$0.380889\pi$
$422$	−11.5000	+	19.9186i	−0.559811	+	0.969622i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	6.00000			0.291386
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	7.50000	+	12.9904i	0.363376	+	0.629386i
$427$	12.0000	+	20.7846i	0.580721	+	1.00584i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−3.00000			−0.144673
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	0.626907	−	0.779094i	$-0.284321\pi$
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	−0.988169	+	0.153370i	$0.950987\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	−5.50000	+	9.52628i	−0.264313	+	0.457804i	−0.967383	−	0.253317i	$-0.918479\pi$
$433$	−5.50000	+	9.52628i	−0.264313	+	0.457804i	0.703070	+	0.711120i	$0.251812\pi$
$434$		0			0
$435$		0			0
$436$	4.50000	−	7.79423i	0.215511	−	0.373276i
$437$	36.0000			1.72211
$438$	−3.00000	+	5.19615i	−0.143346	+	0.248282i
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$	−4.00000			−0.190476
$442$		0			0
$443$	−21.0000			−0.997740			−0.498870	−	0.866677i	$-0.666252\pi$
$443$	−21.0000			−0.997740			−0.498870	+	0.866677i	$0.666252\pi$
$444$	1.50000	+	2.59808i	0.0711868	+	0.123299i
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$	−6.00000			−0.283790
$448$	−1.50000	+	2.59808i	−0.0708683	+	0.122748i
$449$	−12.0000	+	20.7846i	−0.566315	+	0.980886i	0.430611	+	0.902538i	$0.358298\pi$
$449$	−12.0000	+	20.7846i	−0.566315	+	0.980886i	−0.996926	+	0.0783487i	$0.975035\pi$
$450$	8.00000			0.377124
$451$		0			0
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−7.50000	−	12.9904i	−0.352381	−	0.610341i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	4.50000	+	7.79423i	0.210271	+	0.364200i
$459$	7.50000	−	12.9904i	0.350070	−	0.606339i
$460$	18.0000			0.839254
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	−0.986127	−	0.165992i	$-0.946917\pi$
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	0.636817	+	0.771015i	$0.280251\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$		0			0
$465$		0			0
$466$	10.5000	+	18.1865i	0.486403	+	0.842475i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	36.0000			1.66233
$470$	4.50000	+	7.79423i	0.207570	+	0.359521i
$471$	−11.0000	−	19.0526i	−0.506853	−	0.877896i
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$		0			0
$474$	−5.00000	+	8.66025i	−0.229658	+	0.397779i
$475$	−12.0000	+	20.7846i	−0.550598	+	0.953663i
$476$	−9.00000			−0.412514
$477$	−6.00000	+	10.3923i	−0.274721	+	0.475831i
$478$	−4.50000	−	7.79423i	−0.205825	−	0.356500i
$479$	−19.5000	−	33.7750i	−0.890978	−	1.54322i	−0.838705	−	0.544586i	$-0.816687\pi$
$479$	−19.5000	−	33.7750i	−0.890978	−	1.54322i	−0.0522726	−	0.998633i	$-0.516646\pi$
$480$	3.00000			0.136931
$481$		0			0
$482$	30.0000			1.36646
$483$	9.00000	+	15.5885i	0.409514	+	0.709299i
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−18.0000	+	31.1769i	−0.817338	+	1.41567i
$486$	16.0000			0.725775
$487$	−6.00000	+	10.3923i	−0.271886	+	0.470920i	−0.969345	−	0.245705i	$-0.920981\pi$
$487$	−6.00000	+	10.3923i	−0.271886	+	0.470920i	0.697459	+	0.716625i	$0.254314\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	−6.00000			−0.271329
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	13.5000	+	23.3827i	0.609246	+	1.05525i	0.991365	+	0.131132i	$0.0418613\pi$
$491$	13.5000	+	23.3827i	0.609246	+	1.05525i	−0.382118	+	0.924113i	$0.624805\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.5000	+	38.9711i	1.00926	+	1.74809i
$498$	3.00000	−	5.19615i	0.134433	−	0.232845i
$499$	36.0000			1.61158			0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000			1.61158			0.805791	+	0.592200i	$0.201741\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$	12.0000			0.535586
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	−0.791361	−	0.611349i	$-0.790627\pi$
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	0.925124	+	0.379664i	$0.123960\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$	18.0000	+	31.1769i	0.800989	+	1.38735i
$506$		0			0
$507$		0			0
$508$	2.00000			0.0887357
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$	4.50000	+	7.79423i	0.199263	+	0.345134i
$511$	−9.00000	+	15.5885i	−0.398137	+	0.689593i
$512$	−1.00000			−0.0441942
$513$	−15.0000	+	25.9808i	−0.662266	+	1.14708i
$514$	−1.50000	+	2.59808i	−0.0661622	+	0.114596i
$515$	−42.0000			−1.85074
$516$	0.500000	−	0.866025i	0.0220113	−	0.0381246i
$517$		0			0
$518$	4.50000	+	7.79423i	0.197719	+	0.342459i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		0			0
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	0.986216	−	0.165460i	$-0.0529109\pi$
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	−0.636401	+	0.771358i	$0.719578\pi$
$524$	1.50000	−	2.59808i	0.0655278	−	0.113497i
$525$	−12.0000			−0.523723
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$		0			0
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−9.00000	−	15.5885i	−0.390935	−	0.677119i
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$	18.0000			0.780399
$533$		0			0
$534$	−6.00000			−0.259645
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	−7.50000	+	12.9904i	−0.323649	+	0.560576i
$538$		0			0
$539$		0			0
$540$	−7.50000	+	12.9904i	−0.322749	+	0.559017i
$541$	−15.0000			−0.644900			−0.322450	−	0.946586i	$-0.604506\pi$
$541$	−15.0000			−0.644900			−0.322450	+	0.946586i	$0.604506\pi$
$542$	7.50000	−	12.9904i	0.322153	−	0.557985i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	−27.0000			−1.15655
$546$		0			0
$547$	−37.0000			−1.58201			−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000			−1.58201			−0.791003	+	0.611812i	$0.790441\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$	−8.00000	−	13.8564i	−0.341432	−	0.591377i
$550$		0			0
$551$		0			0
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	−15.0000	+	25.9808i	−0.637865	+	1.10481i
$554$	8.00000			0.339887
$555$	4.50000	−	7.79423i	0.191014	−	0.330847i
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	13.5000	+	23.3827i	0.572013	+	0.990756i	0.996359	+	0.0852559i	$0.0271708\pi$
$557$	13.5000	+	23.3827i	0.572013	+	0.990756i	−0.424346	+	0.905500i	$0.639496\pi$
$558$		0			0
$559$		0			0
$560$	9.00000			0.380319
$561$		0			0
$562$	−15.0000	−	25.9808i	−0.632737	−	1.09593i
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	−0.0824933	−	0.996592i	$-0.526288\pi$
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	0.904320	−	0.426855i	$-0.140378\pi$
$564$	−3.00000			−0.126323
$565$	9.00000	−	15.5885i	0.378633	−	0.655811i
$566$	−2.00000	+	3.46410i	−0.0840663	+	0.145607i
$567$	3.00000			0.125988
$568$	−7.50000	+	12.9904i	−0.314693	+	0.545064i
$569$	22.5000	+	38.9711i	0.943249	+	1.63376i	0.759220	+	0.650835i	$0.225581\pi$
$569$	22.5000	+	38.9711i	0.943249	+	1.63376i	0.184030	+	0.982921i	$0.441086\pi$
$570$	−9.00000	−	15.5885i	−0.376969	−	0.652929i
$571$	23.0000			0.962520			0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000			0.962520			0.481260	+	0.876578i	$0.340179\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$	−12.0000	−	20.7846i	−0.500435	−	0.866778i
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	42.0000			1.74848			0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000			1.74848			0.874241	+	0.485491i	$0.161359\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	3.00000	−	5.19615i	0.124676	−	0.215945i
$580$		0			0
$581$	9.00000	−	15.5885i	0.373383	−	0.646718i
$582$	−6.00000	−	10.3923i	−0.248708	−	0.430775i
$583$		0			0
$584$	−6.00000			−0.248282
$585$		0			0
$586$	9.00000			0.371787
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	0.989792	−	0.142520i	$-0.0455206\pi$
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	−0.618322	+	0.785925i	$0.712187\pi$
$588$	1.00000	+	1.73205i	0.0412393	+	0.0714286i
$589$		0			0
$590$	18.0000			0.741048
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	−1.50000	+	2.59808i	−0.0616496	+	0.106780i
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$	13.5000	+	23.3827i	0.553446	+	0.958597i
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$	−20.0000			−0.818546
$598$		0			0
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$	−2.00000	−	3.46410i	−0.0816497	−	0.141421i
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	−0.945558	−	0.325455i	$-0.894483\pi$
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	0.190927	−	0.981604i	$-0.438851\pi$
$602$	1.50000	−	2.59808i	0.0611354	−	0.105890i
$603$	−24.0000			−0.977356
$604$	7.50000	−	12.9904i	0.305171	−	0.528571i
$605$	16.5000	−	28.5788i	0.670820	−	1.16190i
$606$	−12.0000			−0.487467
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	−0.551678	−	0.834058i	$-0.686012\pi$
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	0.998154	+	0.0607380i	$0.0193454\pi$
$608$	3.00000	+	5.19615i	0.121666	+	0.210732i
$609$		0			0
$610$	24.0000			0.971732
$611$		0			0
$612$	6.00000			0.242536
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	0.920229	−	0.391381i	$-0.128002\pi$
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	−0.799060	+	0.601251i	$0.794669\pi$
$614$	9.00000	+	15.5885i	0.363210	+	0.629099i
$615$		0			0
$616$		0			0
$617$	−6.00000	+	10.3923i	−0.241551	+	0.418378i	−0.961156	−	0.276005i	$-0.910989\pi$
$617$	−6.00000	+	10.3923i	−0.241551	+	0.418378i	0.719605	+	0.694383i	$0.244323\pi$
$618$	7.00000	−	12.1244i	0.281581	−	0.487713i
$619$	24.0000			0.964641			0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000			0.964641			0.482321	+	0.875995i	$0.339794\pi$
$620$		0			0
$621$	−15.0000	−	25.9808i	−0.601929	−	1.04257i
$622$	9.00000	+	15.5885i	0.360867	+	0.625040i
$623$	−18.0000			−0.721155
$624$		0			0
$625$	−29.0000			−1.16000
$626$	9.50000	+	16.4545i	0.379696	+	0.657653i
$627$		0			0
$628$	11.0000	−	19.0526i	0.438948	−	0.760280i
$629$	−9.00000			−0.358854
$630$	−9.00000	+	15.5885i	−0.358569	+	0.621059i
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	−0.677239	−	0.735763i	$-0.736824\pi$
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	0.975809	+	0.218624i	$0.0701569\pi$
$632$	−10.0000			−0.397779
$633$	−11.5000	+	19.9186i	−0.457084	+	0.791693i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	−3.00000	−	5.19615i	−0.119051	−	0.206203i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$	−15.0000	−	25.9808i	−0.593391	−	1.02778i
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$	−12.0000			−0.473602
$643$	18.0000	−	31.1769i	0.709851	−	1.22950i	−0.255062	−	0.966925i	$-0.582096\pi$
$643$	18.0000	−	31.1769i	0.709851	−	1.22950i	0.964912	−	0.262573i	$-0.0845709\pi$
$644$	−9.00000	+	15.5885i	−0.354650	+	0.614271i
$645$	−3.00000			−0.118125
$646$	−9.00000	+	15.5885i	−0.354100	+	0.613320i
$647$	−21.0000	−	36.3731i	−0.825595	−	1.42997i	−0.901464	−	0.432855i	$-0.857506\pi$
$647$	−21.0000	−	36.3731i	−0.825595	−	1.42997i	0.0758684	−	0.997118i	$-0.475827\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−3.00000	−	5.19615i	−0.117489	−	0.203497i
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$	4.50000	−	7.79423i	0.175964	−	0.304778i
$655$	−9.00000			−0.351659
$656$		0			0
$657$	6.00000	−	10.3923i	0.234082	−	0.405442i
$658$	−9.00000			−0.350857
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	−0.995069	−	0.0991864i	$-0.968376\pi$
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	0.411636	−	0.911348i	$-0.364957\pi$
$662$	30.0000			1.16598
$663$		0			0
$664$	6.00000			0.232845
$665$	−27.0000	−	46.7654i	−1.04702	−	1.81348i
$666$	−3.00000	−	5.19615i	−0.116248	−	0.201347i
$667$		0			0
$668$	−12.0000			−0.464294
$669$	4.50000	−	7.79423i	0.173980	−	0.301342i
$670$	18.0000	−	31.1769i	0.695401	−	1.20447i
$671$		0			0
$672$	−1.50000	+	2.59808i	−0.0578638	+	0.100223i
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	0.856228	−	0.516599i	$-0.172802\pi$
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	−0.875501	+	0.483216i	$0.839469\pi$
$674$	−6.50000	−	11.2583i	−0.250371	−	0.433655i
$675$	20.0000			0.769800
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	3.00000	+	5.19615i	0.115214	+	0.199557i
$679$	−18.0000	−	31.1769i	−0.690777	−	1.19646i
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$	−12.0000			−0.459841
$682$		0			0
$683$	−3.00000	+	5.19615i	−0.114792	+	0.198825i	−0.917697	−	0.397282i	$-0.869953\pi$
$683$	−3.00000	+	5.19615i	−0.114792	+	0.198825i	0.802905	+	0.596107i	$0.203287\pi$
$684$	−12.0000			−0.458831
$685$	−27.0000	+	46.7654i	−1.03162	+	1.78681i
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	4.50000	+	7.79423i	0.171686	+	0.297368i
$688$	1.00000			0.0381246
$689$		0			0
$690$	18.0000			0.685248
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$		0			0
$694$	−33.0000			−1.25266
$695$	−7.50000	+	12.9904i	−0.284491	+	0.492753i
$696$		0			0
$697$		0			0
$698$	−10.5000	+	18.1865i	−0.397431	+	0.688370i
$699$	10.5000	+	18.1865i	0.397146	+	0.687878i
$700$	−6.00000	−	10.3923i	−0.226779	−	0.392792i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	18.0000			0.678883
$704$		0			0
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$	−36.0000			−1.35392
$708$	−3.00000	+	5.19615i	−0.112747	+	0.195283i
$709$	3.00000	−	5.19615i	0.112667	−	0.195146i	−0.804178	−	0.594389i	$-0.797394\pi$
$709$	3.00000	−	5.19615i	0.112667	−	0.195146i	0.916845	+	0.399244i	$0.130727\pi$
$710$	45.0000			1.68882
$711$	10.0000	−	17.3205i	0.375029	−	0.649570i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$		0			0
$714$	−9.00000			−0.336817
$715$		0			0
$716$	−15.0000			−0.560576
$717$	−4.50000	−	7.79423i	−0.168056	−	0.291081i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	−6.00000			−0.223607
$721$	21.0000	−	36.3731i	0.782081	−	1.35460i
$722$	8.50000	−	14.7224i	0.316337	−	0.547912i
$723$	30.0000			1.11571
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$		0			0
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	9.00000	+	15.5885i	0.333105	+	0.576955i
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$	−4.00000	+	6.92820i	−0.147844	+	0.256074i
$733$	9.00000			0.332423			0.166211	−	0.986090i	$-0.446847\pi$
$733$	9.00000			0.332423			0.166211	+	0.986090i	$0.446847\pi$
$734$	4.00000	−	6.92820i	0.147643	−	0.255725i
$735$	3.00000	−	5.19615i	0.110657	−	0.191663i
$736$	−6.00000			−0.221163
$737$		0			0
$738$		0			0
$739$	18.0000	+	31.1769i	0.662141	+	1.14686i	0.980052	+	0.198741i	$0.0636852\pi$
$739$	18.0000	+	31.1769i	0.662141	+	1.14686i	−0.317911	+	0.948120i	$0.602981\pi$
$740$	9.00000			0.330847
$741$		0			0
$742$	18.0000			0.660801
$743$	−19.5000	−	33.7750i	−0.715386	−	1.23908i	−0.962811	−	0.270177i	$-0.912918\pi$
$743$	−19.5000	−	33.7750i	−0.715386	−	1.23908i	0.247425	−	0.968907i	$-0.420416\pi$
$744$		0			0
$745$	−9.00000	+	15.5885i	−0.329734	+	0.571117i
$746$	−4.00000			−0.146450
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$		0			0
$749$	−36.0000			−1.31541
$750$	1.50000	−	2.59808i	0.0547723	−	0.0948683i
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	12.0000			0.437304
$754$		0			0
$755$	−45.0000			−1.63772
$756$	−7.50000	−	12.9904i	−0.272772	−	0.472456i
$757$	1.00000	+	1.73205i	0.0363456	+	0.0629525i	0.883626	−	0.468193i	$-0.155095\pi$
$757$	1.00000	+	1.73205i	0.0363456	+	0.0629525i	−0.847280	+	0.531146i	$0.821762\pi$
$758$	3.00000	−	5.19615i	0.108965	−	0.188733i
$759$		0			0
$760$	9.00000	−	15.5885i	0.326464	−	0.565453i
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$	2.00000			0.0724524
$763$	13.5000	−	23.3827i	0.488733	−	0.846510i
$764$	−6.00000	−	10.3923i	−0.217072	−	0.375980i
$765$	−9.00000	−	15.5885i	−0.325396	−	0.563602i
$766$	−9.00000			−0.325183
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	12.0000	+	20.7846i	0.432731	+	0.749512i	0.997107	−	0.0760054i	$-0.0242166\pi$
$769$	12.0000	+	20.7846i	0.432731	+	0.749512i	−0.564376	+	0.825518i	$0.690883\pi$
$770$		0			0
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$	6.00000			0.215945
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	−0.613062	−	0.790034i	$-0.710063\pi$
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	0.990721	+	0.135910i	$0.0433959\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$		0			0
$776$	6.00000	−	10.3923i	0.215387	−	0.373062i
$777$	4.50000	+	7.79423i	0.161437	+	0.279616i
$778$	15.0000	+	25.9808i	0.537776	+	0.931455i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−9.00000	−	15.5885i	−0.321839	−	0.557442i
$783$		0			0
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	−66.0000			−2.35564
$786$	1.50000	−	2.59808i	0.0535032	−	0.0926703i
$787$	6.00000	−	10.3923i	0.213877	−	0.370446i	−0.739048	−	0.673653i	$-0.764724\pi$
$787$	6.00000	−	10.3923i	0.213877	−	0.370446i	0.952925	+	0.303207i	$0.0980575\pi$
$788$	−3.00000			−0.106871
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$	15.0000	+	25.9808i	0.533676	+	0.924354i
$791$	9.00000	+	15.5885i	0.320003	+	0.554262i
$792$		0			0
$793$		0			0
$794$	−18.0000			−0.638796
$795$	−9.00000	−	15.5885i	−0.319197	−	0.552866i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	−0.661441	−	0.749997i	$-0.730055\pi$
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	0.980237	+	0.197826i	$0.0633881\pi$
$798$	18.0000			0.637193
$799$	4.50000	−	7.79423i	0.159199	−	0.275740i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	12.0000			0.423999
$802$	15.0000	−	25.9808i	0.529668	−	0.917413i
$803$		0			0
$804$	6.00000	+	10.3923i	0.211604	+	0.366508i
$805$	54.0000			1.90325
$806$		0			0
$807$		0			0
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	0.703533	−	0.710663i	$-0.251605\pi$
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	−0.967219	+	0.253946i	$0.918272\pi$
$810$	1.50000	−	2.59808i	0.0527046	−	0.0912871i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	7.50000	−	12.9904i	0.263036	−	0.455593i
$814$		0			0
$815$	−9.00000	+	15.5885i	−0.315256	+	0.546040i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−3.00000	−	5.19615i	−0.104957	−	0.181790i
$818$	−6.00000			−0.209785
$819$		0			0
$820$		0			0
$821$	22.5000	+	38.9711i	0.785255	+	1.36010i	0.928846	+	0.370465i	$0.120802\pi$
$821$	22.5000	+	38.9711i	0.785255	+	1.36010i	−0.143591	+	0.989637i	$0.545865\pi$
$822$	−9.00000	−	15.5885i	−0.313911	−	0.543710i
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	−0.717847	−	0.696201i	$-0.754872\pi$
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	0.961851	+	0.273573i	$0.0882054\pi$
$824$	14.0000			0.487713
$825$		0			0
$826$	−9.00000	+	15.5885i	−0.313150	+	0.542392i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	6.00000	−	10.3923i	0.208514	−	0.361158i
$829$	−10.0000	−	17.3205i	−0.347314	−	0.601566i	0.638457	−	0.769657i	$-0.279573\pi$
$829$	−10.0000	−	17.3205i	−0.347314	−	0.601566i	−0.985771	+	0.168091i	$0.946240\pi$
$830$	−9.00000	−	15.5885i	−0.312395	−	0.541083i
$831$	8.00000			0.277517
$832$		0			0
$833$	−6.00000			−0.207888
$834$	−2.50000	−	4.33013i	−0.0865679	−	0.149940i
$835$	18.0000	+	31.1769i	0.622916	+	1.07892i
$836$		0			0
$837$		0			0
$838$	7.50000	−	12.9904i	0.259083	−	0.448745i
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	−0.995353	−	0.0962912i	$-0.969302\pi$
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	0.581067	+	0.813856i	$0.302635\pi$
$840$	9.00000			0.310530
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	7.50000	+	12.9904i	0.258467	+	0.447678i
$843$	−15.0000	−	25.9808i	−0.516627	−	0.894825i
$844$	−23.0000			−0.791693
$845$		0			0
$846$	6.00000			0.206284
$847$	16.5000	+	28.5788i	0.566947	+	0.981981i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$	12.0000			0.411597
$851$	−9.00000	+	15.5885i	−0.308516	+	0.534365i
$852$	−7.50000	+	12.9904i	−0.256946	+	0.445043i
$853$	−39.0000			−1.33533			−0.667667	−	0.744460i	$-0.732707\pi$
$853$	−39.0000			−1.33533			−0.667667	+	0.744460i	$0.732707\pi$
$854$	−12.0000	+	20.7846i	−0.410632	+	0.711235i
$855$	18.0000	+	31.1769i	0.615587	+	1.06623i
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$	−1.50000	−	2.59808i	−0.0511496	−	0.0885937i
$861$		0			0
$862$	7.50000	−	12.9904i	0.255451	−	0.442454i
$863$	39.0000			1.32758			0.663788	−	0.747921i	$-0.268948\pi$
$863$	39.0000			1.32758			0.663788	+	0.747921i	$0.268948\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$	−9.00000	+	15.5885i	−0.306009	+	0.530023i
$866$	−11.0000			−0.373795
$867$	−4.00000	+	6.92820i	−0.135847	+	0.235294i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	9.00000			0.304778
$873$	12.0000	+	20.7846i	0.406138	+	0.703452i
$874$	18.0000	+	31.1769i	0.608859	+	1.05457i
$875$	4.50000	−	7.79423i	0.152128	−	0.263493i
$876$	−6.00000			−0.202721
$877$	1.50000	−	2.59808i	0.0506514	−	0.0877308i	−0.839588	−	0.543224i	$-0.817204\pi$
$877$	1.50000	−	2.59808i	0.0506514	−	0.0877308i	0.890239	+	0.455493i	$0.150537\pi$
$878$	5.00000	−	8.66025i	0.168742	−	0.292269i
$879$	9.00000			0.303562
$880$		0			0
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	−0.997833	−	0.0657979i	$-0.979041\pi$
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	0.441934	−	0.897048i	$-0.354293\pi$
$882$	−2.00000	−	3.46410i	−0.0673435	−	0.116642i
$883$	11.0000			0.370179			0.185090	−	0.982722i	$-0.440742\pi$
$883$	11.0000			0.370179			0.185090	+	0.982722i	$0.440742\pi$
$884$		0			0
$885$	18.0000			0.605063
$886$	−10.5000	−	18.1865i	−0.352754	−	0.610989i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$	−1.50000	+	2.59808i	−0.0503367	+	0.0871857i
$889$	6.00000			0.201234
$890$	−9.00000	+	15.5885i	−0.301681	+	0.522526i
$891$		0			0
$892$	9.00000			0.301342
$893$	−9.00000	+	15.5885i	−0.301174	+	0.521648i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	22.5000	+	38.9711i	0.752092	+	1.30266i
$896$	−3.00000			−0.100223
$897$		0			0
$898$	−24.0000			−0.800890
$899$		0			0
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$		0			0
$903$	1.50000	−	2.59808i	0.0499169	−	0.0864586i
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	−6.00000			−0.199447
$906$	7.50000	−	12.9904i	0.249171	−	0.431577i
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$	−6.00000	−	10.3923i	−0.199117	−	0.344881i
$909$	24.0000			0.796030
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	3.00000	+	5.19615i	0.0993399	+	0.172062i
$913$		0			0
$914$	−9.00000	+	15.5885i	−0.297694	+	0.515620i
$915$	24.0000			0.793416
$916$	−4.50000	+	7.79423i	−0.148684	+	0.257529i
$917$	4.50000	−	7.79423i	0.148603	−	0.257388i
$918$	15.0000			0.495074
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	−0.652616	−	0.757689i	$-0.726329\pi$
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	0.982486	+	0.186338i	$0.0596619\pi$
$920$	9.00000	+	15.5885i	0.296721	+	0.513936i
$921$	9.00000	+	15.5885i	0.296560	+	0.513657i
$922$	−15.0000			−0.493999
$923$		0			0
$924$		0			0
$925$	−6.00000	−	10.3923i	−0.197279	−	0.341697i
$926$	−12.0000	−	20.7846i	−0.394344	−	0.683025i
$927$	−14.0000	+	24.2487i	−0.459820	+	0.796432i
$928$		0			0
$929$	−18.0000	+	31.1769i	−0.590561	+	1.02288i	0.403596	+	0.914937i	$0.367760\pi$
$929$	−18.0000	+	31.1769i	−0.590561	+	1.02288i	−0.994157	+	0.107944i	$0.965573\pi$
$930$		0			0
$931$	12.0000			0.393284
$932$	−10.5000	+	18.1865i	−0.343939	+	0.595720i
$933$	9.00000	+	15.5885i	0.294647	+	0.510343i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	18.0000	+	31.1769i	0.587721	+	1.01796i
$939$	9.50000	+	16.4545i	0.310021	+	0.536972i
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$	45.0000			1.46696			0.733479	−	0.679712i	$-0.237895\pi$
$941$	45.0000			1.46696			0.733479	+	0.679712i	$0.237895\pi$
$942$	11.0000	−	19.0526i	0.358399	−	0.620766i
$943$		0			0
$944$	−6.00000			−0.195283
$945$	−22.5000	+	38.9711i	−0.731925	+	1.26773i
$946$		0			0
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	−0.932002	−	0.362454i	$-0.881939\pi$
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	0.152106	−	0.988364i	$-0.451394\pi$
$948$	−10.0000			−0.324785
$949$		0			0
$950$	−24.0000			−0.778663
$951$	−9.00000	−	15.5885i	−0.291845	−	0.505490i
$952$	−4.50000	−	7.79423i	−0.145846	−	0.252612i
$953$	4.50000	−	7.79423i	0.145769	−	0.252480i	−0.783890	−	0.620899i	$-0.786768\pi$
$953$	4.50000	−	7.79423i	0.145769	−	0.252480i	0.929660	+	0.368419i	$0.120101\pi$
$954$	−12.0000			−0.388514
$955$	−18.0000	+	31.1769i	−0.582466	+	1.00886i
$956$	4.50000	−	7.79423i	0.145540	−	0.252083i
$957$		0			0
$958$	19.5000	−	33.7750i	0.630016	−	1.09122i
$959$	−27.0000	−	46.7654i	−0.871875	−	1.51013i
$960$	1.50000	+	2.59808i	0.0484123	+	0.0838525i
$961$	−31.0000			−1.00000
$962$		0			0
$963$	24.0000			0.773389
$964$	15.0000	+	25.9808i	0.483117	+	0.836784i
$965$	−9.00000	−	15.5885i	−0.289720	−	0.501810i
$966$	−9.00000	+	15.5885i	−0.289570	+	0.501550i
$967$	−3.00000			−0.0964735			−0.0482367	−	0.998836i	$-0.515360\pi$
$967$	−3.00000			−0.0964735			−0.0482367	+	0.998836i	$0.515360\pi$
$968$	−5.50000	+	9.52628i	−0.176777	+	0.306186i
$969$	−9.00000	+	15.5885i	−0.289122	+	0.500773i
$970$	−36.0000			−1.15589
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	−0.997150	−	0.0754473i	$-0.975962\pi$
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	0.563914	+	0.825833i	$0.309295\pi$
$972$	8.00000	+	13.8564i	0.256600	+	0.444444i
$973$	−7.50000	−	12.9904i	−0.240439	−	0.416452i
$974$	−12.0000			−0.384505
$975$		0			0
$976$	−8.00000			−0.256074
$977$	−6.00000	−	10.3923i	−0.191957	−	0.332479i	0.753942	−	0.656941i	$-0.228150\pi$
$977$	−6.00000	−	10.3923i	−0.191957	−	0.332479i	−0.945899	+	0.324462i	$0.894817\pi$
$978$	−3.00000	−	5.19615i	−0.0959294	−	0.166155i
$979$		0			0
$980$	6.00000			0.191663
$981$	−9.00000	+	15.5885i	−0.287348	+	0.497701i
$982$	−13.5000	+	23.3827i	−0.430802	+	0.746171i
$983$	−9.00000			−0.287055			−0.143528	−	0.989646i	$-0.545845\pi$
$983$	−9.00000			−0.287055			−0.143528	+	0.989646i	$0.545845\pi$
$984$		0			0
$985$	4.50000	+	7.79423i	0.143382	+	0.248345i
$986$		0			0
$987$	−9.00000			−0.286473
$988$		0			0
$989$	6.00000			0.190789
$990$		0			0
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$		0			0
$993$	30.0000			0.952021
$994$	−22.5000	+	38.9711i	−0.713657	+	1.23609i
$995$	−30.0000	+	51.9615i	−0.951064	+	1.64729i
$996$	6.00000			0.190117
$997$	−4.00000	+	6.92820i	−0.126681	+	0.219418i	−0.922389	−	0.386263i	$-0.873766\pi$
$997$	−4.00000	+	6.92820i	−0.126681	+	0.219418i	0.795708	+	0.605681i	$0.207099\pi$
$998$	18.0000	+	31.1769i	0.569780	+	0.986888i
$999$	−7.50000	−	12.9904i	−0.237289	−	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.c.f.315.1		2
13.2	odd	12		26.2.b.a.25.2	yes	2
13.3	even	3		338.2.a.b.1.1		1
13.4	even	6		338.2.c.b.191.1		2
13.5	odd	4		338.2.e.c.23.2		4
13.6	odd	12		338.2.e.c.147.1		4
13.7	odd	12		338.2.e.c.147.2		4
13.8	odd	4		338.2.e.c.23.1		4
13.9	even	3	inner	338.2.c.f.191.1		2
13.10	even	6		338.2.a.d.1.1		1
13.11	odd	12		26.2.b.a.25.1	✓	2
13.12	even	2		338.2.c.b.315.1		2
39.2	even	12		234.2.b.b.181.1		2
39.11	even	12		234.2.b.b.181.2		2
39.23	odd	6		3042.2.a.g.1.1		1
39.29	odd	6		3042.2.a.j.1.1		1
52.3	odd	6		2704.2.a.k.1.1		1
52.11	even	12		208.2.f.a.129.2		2
52.15	even	12		208.2.f.a.129.1		2
52.23	odd	6		2704.2.a.j.1.1		1
65.2	even	12		650.2.c.a.649.2		2
65.24	odd	12		650.2.d.b.51.2		2
65.28	even	12		650.2.c.d.649.1		2
65.29	even	6		8450.2.a.u.1.1		1
65.37	even	12		650.2.c.d.649.2		2
65.49	even	6		8450.2.a.h.1.1		1
65.54	odd	12		650.2.d.b.51.1		2
65.63	even	12		650.2.c.a.649.1		2
91.2	odd	12		1274.2.n.d.753.2		4
91.11	odd	12		1274.2.n.d.961.2		4
91.24	even	12		1274.2.n.c.961.2		4
91.37	odd	12		1274.2.n.d.753.1		4
91.41	even	12		1274.2.d.c.883.2		2
91.54	even	12		1274.2.n.c.753.2		4
91.67	odd	12		1274.2.n.d.961.1		4
91.76	even	12		1274.2.d.c.883.1		2
91.80	even	12		1274.2.n.c.961.1		4
91.89	even	12		1274.2.n.c.753.1		4
104.11	even	12		832.2.f.b.129.1		2
104.37	odd	12		832.2.f.d.129.1		2
104.67	even	12		832.2.f.b.129.2		2
104.93	odd	12		832.2.f.d.129.2		2
156.11	odd	12		1872.2.c.f.1585.1		2
156.119	odd	12		1872.2.c.f.1585.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.b.a.25.1	✓	2	13.11	odd	12
26.2.b.a.25.2	yes	2	13.2	odd	12
208.2.f.a.129.1		2	52.15	even	12
208.2.f.a.129.2		2	52.11	even	12
234.2.b.b.181.1		2	39.2	even	12
234.2.b.b.181.2		2	39.11	even	12
338.2.a.b.1.1		1	13.3	even	3
338.2.a.d.1.1		1	13.10	even	6
338.2.c.b.191.1		2	13.4	even	6
338.2.c.b.315.1		2	13.12	even	2
338.2.c.f.191.1		2	13.9	even	3	inner
338.2.c.f.315.1		2	1.1	even	1	trivial
338.2.e.c.23.1		4	13.8	odd	4
338.2.e.c.23.2		4	13.5	odd	4
338.2.e.c.147.1		4	13.6	odd	12
338.2.e.c.147.2		4	13.7	odd	12
650.2.c.a.649.1		2	65.63	even	12
650.2.c.a.649.2		2	65.2	even	12
650.2.c.d.649.1		2	65.28	even	12
650.2.c.d.649.2		2	65.37	even	12
650.2.d.b.51.1		2	65.54	odd	12
650.2.d.b.51.2		2	65.24	odd	12
832.2.f.b.129.1		2	104.11	even	12
832.2.f.b.129.2		2	104.67	even	12
832.2.f.d.129.1		2	104.37	odd	12
832.2.f.d.129.2		2	104.93	odd	12
1274.2.d.c.883.1		2	91.76	even	12
1274.2.d.c.883.2		2	91.41	even	12
1274.2.n.c.753.1		4	91.89	even	12
1274.2.n.c.753.2		4	91.54	even	12
1274.2.n.c.961.1		4	91.80	even	12
1274.2.n.c.961.2		4	91.24	even	12
1274.2.n.d.753.1		4	91.37	odd	12
1274.2.n.d.753.2		4	91.2	odd	12
1274.2.n.d.961.1		4	91.67	odd	12
1274.2.n.d.961.2		4	91.11	odd	12
1872.2.c.f.1585.1		2	156.11	odd	12
1872.2.c.f.1585.2		2	156.119	odd	12
2704.2.a.j.1.1		1	52.23	odd	6
2704.2.a.k.1.1		1	52.3	odd	6
3042.2.a.g.1.1		1	39.23	odd	6
3042.2.a.j.1.1		1	39.29	odd	6
8450.2.a.h.1.1		1	65.49	even	6
8450.2.a.u.1.1		1	65.29	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{10} -1.00000 q^{12} -3.00000 q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +2.00000 q^{18} +(-3.00000 + 5.19615i) q^{19} +(-1.50000 + 2.59808i) q^{20} -3.00000 q^{21} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +4.00000 q^{25} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{28} +(-1.50000 + 2.59808i) q^{30} +(0.500000 - 0.866025i) q^{32} +3.00000 q^{34} +(-4.50000 + 7.79423i) q^{35} +(1.00000 + 1.73205i) q^{36} +(-1.50000 - 2.59808i) q^{37} -6.00000 q^{38} -3.00000 q^{40} +(-1.50000 - 2.59808i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{45} +(3.00000 - 5.19615i) q^{46} +3.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} +3.00000 q^{51} -6.00000 q^{53} +(2.50000 + 4.33013i) q^{54} +(1.50000 - 2.59808i) q^{56} -6.00000 q^{57} +(3.00000 - 5.19615i) q^{59} -3.00000 q^{60} +(4.00000 - 6.92820i) q^{61} +(3.00000 + 5.19615i) q^{63} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.00000 - 5.19615i) q^{69} -9.00000 q^{70} +(7.50000 - 12.9904i) q^{71} +(-1.00000 + 1.73205i) q^{72} +6.00000 q^{73} +(1.50000 - 2.59808i) q^{74} +(2.00000 + 3.46410i) q^{75} +(-3.00000 - 5.19615i) q^{76} +10.0000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{83} +(1.50000 - 2.59808i) q^{84} +(4.50000 - 7.79423i) q^{85} -1.00000 q^{86} +(3.00000 + 5.19615i) q^{89} +6.00000 q^{90} +6.00000 q^{92} +(1.50000 + 2.59808i) q^{94} +(-9.00000 + 15.5885i) q^{95} +1.00000 q^{96} +(-6.00000 + 10.3923i) q^{97} +(1.00000 - 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 6 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 3 q^{10} - 2 q^{12} - 6 q^{14} + 3 q^{15} - q^{16} + 3 q^{17} + 4 q^{18} - 6 q^{19} - 3 q^{20} - 6 q^{21} - 6 q^{23} - q^{24}+ \cdots + 2 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 6 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9 + 3 * q^10 - 2 * q^12 - 6 * q^14 + 3 * q^15 - q^16 + 3 * q^17 + 4 * q^18 - 6 * q^19 - 3 * q^20 - 6 * q^21 - 6 * q^23 - q^24 + 8 * q^25 + 10 * q^27 - 3 * q^28 - 3 * q^30 + q^32 + 6 * q^34 - 9 * q^35 + 2 * q^36 - 3 * q^37 - 12 * q^38 - 6 * q^40 - 3 * q^42 - q^43 + 6 * q^45 + 6 * q^46 + 6 * q^47 + q^48 - 2 * q^49 + 4 * q^50 + 6 * q^51 - 12 * q^53 + 5 * q^54 + 3 * q^56 - 12 * q^57 + 6 * q^59 - 6 * q^60 + 8 * q^61 + 6 * q^63 + 2 * q^64 - 12 * q^67 + 3 * q^68 + 6 * q^69 - 18 * q^70 + 15 * q^71 - 2 * q^72 + 12 * q^73 + 3 * q^74 + 4 * q^75 - 6 * q^76 + 20 * q^79 - 3 * q^80 - q^81 - 12 * q^83 + 3 * q^84 + 9 * q^85 - 2 * q^86 + 6 * q^89 + 12 * q^90 + 12 * q^92 + 3 * q^94 - 18 * q^95 + 2 * q^96 - 12 * q^97 + 2 * q^98

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