LMFDB - Embedded newform 38.2.c.a.7.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [38,2,Mod(7,38)] 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("38.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.303431527681$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.2.c.a.11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -4.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +3.00000 q^{11} +1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +2.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} -2.00000 q^{26} -5.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(-3.00000 + 5.19615i) q^{34} +(1.00000 + 1.73205i) q^{36} -10.0000 q^{37} +(-4.00000 - 1.73205i) q^{38} +2.00000 q^{39} +(-4.50000 - 7.79423i) q^{41} +(-2.00000 + 3.46410i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-1.50000 + 2.59808i) q^{44} +6.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} +9.00000 q^{49} +5.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-2.50000 - 4.33013i) q^{54} +4.00000 q^{56} +(4.00000 + 1.73205i) q^{57} +(4.50000 + 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-4.00000 + 6.92820i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(3.50000 - 6.06218i) q^{67} -6.00000 q^{68} -6.00000 q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(0.500000 + 0.866025i) q^{73} +(-5.00000 - 8.66025i) q^{74} -5.00000 q^{75} +(-0.500000 - 4.33013i) q^{76} -12.0000 q^{77} +(1.00000 + 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +3.00000 q^{83} -4.00000 q^{84} +(-2.00000 + 3.46410i) q^{86} -3.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-1.00000 - 1.73205i) q^{93} -1.00000 q^{96} +(-8.50000 - 14.7224i) q^{97} +(4.50000 + 7.79423i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 8 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 4 q^{18} - 7 q^{19} + 4 q^{21} + 3 q^{22} + 6 q^{23} + q^{24} + 5 q^{25}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^6 - 8 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 4 * q^18 - 7 * q^19 + 4 * q^21 + 3 * q^22 + 6 * q^23 + q^24 + 5 * q^25 - 4 * q^26 - 10 * q^27 + 4 * q^28 + 4 * q^31 + q^32 - 3 * q^33 - 6 * q^34 + 2 * q^36 - 20 * q^37 - 8 * q^38 + 4 * q^39 - 9 * q^41 - 4 * q^42 + 4 * q^43 - 3 * q^44 + 12 * q^46 - q^48 + 18 * q^49 + 10 * q^50 + 6 * q^51 - 2 * q^52 - 6 * q^53 - 5 * q^54 + 8 * q^56 + 8 * q^57 + 9 * q^59 + 4 * q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 + 3 * q^66 + 7 * q^67 - 12 * q^68 - 12 * q^69 + 6 * q^71 - 2 * q^72 + q^73 - 10 * q^74 - 10 * q^75 - q^76 - 24 * q^77 + 2 * q^78 + 4 * q^79 - q^81 + 9 * q^82 + 6 * q^83 - 8 * q^84 - 4 * q^86 - 6 * q^88 - 6 * q^89 + 8 * q^91 + 6 * q^92 - 2 * q^93 - 2 * q^96 - 17 * q^97 + 9 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−4.00000			−1.51186			−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000			−1.51186			−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$	1.00000			0.288675
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	2.00000			0.471405
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$20$		0			0
$21$	2.00000	+	3.46410i	0.436436	+	0.755929i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	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	$-0.0484560\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	−2.00000			−0.392232
$27$	−5.00000			−0.962250
$28$	2.00000	−	3.46410i	0.377964	−	0.654654i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$		0			0
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$	−4.00000	−	1.73205i	−0.648886	−	0.280976i
$39$	2.00000			0.320256
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	−2.00000	+	3.46410i	−0.308607	+	0.534522i
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	6.00000			0.884652
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	9.00000			1.28571
$50$	5.00000			0.707107
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$		0			0
$56$	4.00000			0.534522
$57$	4.00000	+	1.73205i	0.529813	+	0.229416i
$58$		0			0
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	1.00000	+	1.73205i	0.127000	+	0.219971i
$63$	−4.00000	+	6.92820i	−0.503953	+	0.872872i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.50000	−	2.59808i	0.184637	−	0.319801i
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	−6.00000			−0.727607
$69$	−6.00000			−0.722315
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	0.893801	−	0.448463i	$-0.148028\pi$
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	−0.835281	+	0.549823i	$0.814695\pi$
$74$	−5.00000	−	8.66025i	−0.581238	−	1.00673i
$75$	−5.00000			−0.577350
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$	−12.0000			−1.36753
$78$	1.00000	+	1.73205i	0.113228	+	0.196116i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	3.00000			0.329293			0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000			0.329293			0.164646	+	0.986353i	$0.447352\pi$
$84$	−4.00000			−0.436436
$85$		0			0
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$		0			0
$88$	−3.00000			−0.319801
$89$	−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	$0.269678\pi$
$90$		0			0
$91$	4.00000	−	6.92820i	0.419314	−	0.726273i
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$	−1.00000	−	1.73205i	−0.103695	−	0.179605i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	−0.868976	−	0.494854i	$-0.835222\pi$
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	0.00593185	−	0.999982i	$-0.498112\pi$
$98$	4.50000	+	7.79423i	0.454569	+	0.787336i
$99$	3.00000	−	5.19615i	0.301511	−	0.522233i
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	6.00000			0.594089
$103$	2.00000			0.197066			0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000			0.197066			0.0985329	+	0.995134i	$0.468585\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	−6.00000			−0.582772
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$	5.00000	+	8.66025i	0.474579	+	0.821995i
$112$	2.00000	+	3.46410i	0.188982	+	0.327327i
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$	0.500000	+	4.33013i	0.0468293	+	0.405554i
$115$		0			0
$116$		0			0
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$	−4.50000	+	7.79423i	−0.414259	+	0.717517i
$119$	−12.0000	−	20.7846i	−1.10004	−	1.90532i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	4.00000			0.362143
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$	−8.00000			−0.712697
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$	3.00000			0.261116
$133$	14.0000	−	10.3923i	1.21395	−	0.901127i
$134$	7.00000			0.604708
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$	−3.00000	−	5.19615i	−0.255377	−	0.442326i
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	−0.999268	−	0.0382553i	$-0.987820\pi$
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	0.532764	+	0.846264i	$0.321153\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−3.00000	+	5.19615i	−0.250873	+	0.434524i
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−0.500000	+	0.866025i	−0.0413803	+	0.0716728i
$147$	−4.50000	−	7.79423i	−0.371154	−	0.642857i
$148$	5.00000	−	8.66025i	0.410997	−	0.711868i
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	−2.50000	−	4.33013i	−0.204124	−	0.353553i
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	3.50000	−	2.59808i	0.283887	−	0.210732i
$153$	12.0000			0.970143
$154$	−6.00000	−	10.3923i	−0.483494	−	0.837436i
$155$		0			0
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	8.00000	+	13.8564i	0.638470	+	1.10586i	0.985769	+	0.168107i	$0.0537655\pi$
$157$	8.00000	+	13.8564i	0.638470	+	1.10586i	−0.347299	+	0.937754i	$0.612901\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$	6.00000			0.475831
$160$		0			0
$161$	−12.0000	+	20.7846i	−0.945732	+	1.63806i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−19.0000			−1.48819			−0.744097	−	0.668071i	$-0.767120\pi$
$163$	−19.0000			−1.48819			−0.744097	+	0.668071i	$0.767120\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$	1.50000	+	2.59808i	0.116423	+	0.201650i
$167$	12.0000	−	20.7846i	0.928588	−	1.60836i	0.142901	−	0.989737i	$-0.454357\pi$
$167$	12.0000	−	20.7846i	0.928588	−	1.60836i	0.785687	−	0.618624i	$-0.212310\pi$
$168$	−2.00000	−	3.46410i	−0.154303	−	0.267261i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	1.00000	+	8.66025i	0.0764719	+	0.662266i
$172$	−4.00000			−0.304997
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−10.0000	+	17.3205i	−0.755929	+	1.30931i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	4.50000	−	7.79423i	0.338241	−	0.585850i
$178$	−6.00000			−0.449719
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$	8.00000			0.592999
$183$	−4.00000			−0.295689
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$		0			0
$186$	1.00000	−	1.73205i	0.0733236	−	0.127000i
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$		0			0
$189$	20.0000			1.45479
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	8.50000	−	14.7224i	0.610264	−	1.05701i
$195$		0			0
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	6.00000			0.426401
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$	−7.00000			−0.493742
$202$		0			0
$203$		0			0
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$		0			0
$206$	1.00000	+	1.73205i	0.0696733	+	0.120678i
$207$	−6.00000	−	10.3923i	−0.417029	−	0.722315i
$208$	2.00000			0.138675
$209$	−10.5000	+	7.79423i	−0.726300	+	0.539138i
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$		0			0
$215$		0			0
$216$	5.00000			0.340207
$217$	−8.00000			−0.543075
$218$	−8.00000	+	13.8564i	−0.541828	+	0.938474i
$219$	0.500000	−	0.866025i	0.0337869	−	0.0585206i
$220$		0			0
$221$	−12.0000			−0.807207
$222$	−5.00000	+	8.66025i	−0.335578	+	0.581238i
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	0.530607	−	0.847618i	$-0.321964\pi$
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	−0.999362	+	0.0357107i	$0.988630\pi$
$224$	−2.00000	+	3.46410i	−0.133631	+	0.231455i
$225$	−5.00000	−	8.66025i	−0.333333	−	0.577350i
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$	−3.50000	+	2.59808i	−0.231793	+	0.172062i
$229$	−16.0000			−1.05731			−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000			−1.05731			−0.528655	+	0.848837i	$0.677303\pi$
$230$		0			0
$231$	6.00000	+	10.3923i	0.394771	+	0.683763i
$232$		0			0
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$		0			0
$236$	−9.00000			−0.585850
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$	12.0000	−	20.7846i	0.777844	−	1.34727i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	2.00000	+	3.46410i	0.128037	+	0.221766i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	−1.00000	−	8.66025i	−0.0636285	−	0.551039i
$248$	−2.00000			−0.127000
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$		0			0
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	−0.814795	−	0.579748i	$-0.803151\pi$
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	0.909475	+	0.415759i	$0.136484\pi$
$252$	−4.00000	−	6.92820i	−0.251976	−	0.436436i
$253$	9.00000	−	15.5885i	0.565825	−	0.980038i
$254$	−2.00000			−0.125491
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$	4.00000			0.249029
$259$	40.0000			2.48548
$260$		0			0
$261$		0			0
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$		0			0
$266$	16.0000	+	6.92820i	0.981023	+	0.424795i
$267$	6.00000			0.367194
$268$	3.50000	+	6.06218i	0.213797	+	0.370306i
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	3.00000	−	5.19615i	0.181902	−	0.315063i
$273$	−8.00000			−0.484182
$274$	−9.00000			−0.543710
$275$	7.50000	−	12.9904i	0.452267	−	0.783349i
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$	−11.0000			−0.659736
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$		0			0
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$		0			0
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	0.782104	−	0.623148i	$-0.214146\pi$
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	−0.930714	+	0.365748i	$0.880813\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−6.00000			−0.354787
$287$	18.0000	+	31.1769i	1.06251	+	1.84032i
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−8.50000	+	14.7224i	−0.498279	+	0.863044i
$292$	−1.00000			−0.0585206
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$	4.50000	−	7.79423i	0.262445	−	0.454569i
$295$		0			0
$296$	10.0000			0.581238
$297$	−15.0000			−0.870388
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$	2.50000	−	4.33013i	0.144338	−	0.250000i
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$		0			0
$304$	4.00000	+	1.73205i	0.229416	+	0.0993399i
$305$		0			0
$306$	6.00000	+	10.3923i	0.342997	+	0.594089i
$307$	3.50000	+	6.06218i	0.199756	+	0.345987i	0.948449	−	0.316929i	$-0.102652\pi$
$307$	3.50000	+	6.06218i	0.199756	+	0.345987i	−0.748694	+	0.662916i	$0.769319\pi$
$308$	6.00000	−	10.3923i	0.341882	−	0.592157i
$309$	−1.00000	−	1.73205i	−0.0568880	−	0.0985329i
$310$		0			0
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$	−2.00000			−0.113228
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$	−8.00000	+	13.8564i	−0.451466	+	0.781962i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	3.00000	+	5.19615i	0.168232	+	0.291386i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−24.0000			−1.33747
$323$	−24.0000	−	10.3923i	−1.33540	−	0.578243i
$324$	1.00000			0.0555556
$325$	5.00000	+	8.66025i	0.277350	+	0.480384i
$326$	−9.50000	−	16.4545i	−0.526156	−	0.911330i
$327$	8.00000	−	13.8564i	0.442401	−	0.766261i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	−1.50000	+	2.59808i	−0.0823232	+	0.142588i
$333$	−10.0000	+	17.3205i	−0.547997	+	0.949158i
$334$	24.0000			1.31322
$335$		0			0
$336$	2.00000	−	3.46410i	0.109109	−	0.188982i
$337$	−5.50000	−	9.52628i	−0.299604	−	0.518930i	0.676441	−	0.736497i	$-0.263521\pi$
$337$	−5.50000	−	9.52628i	−0.299604	−	0.518930i	−0.976045	+	0.217567i	$0.930188\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−7.50000	−	12.9904i	−0.407344	−	0.705541i
$340$		0			0
$341$	6.00000			0.324918
$342$	−7.00000	+	5.19615i	−0.378517	+	0.280976i
$343$	−8.00000			−0.431959
$344$	−2.00000	−	3.46410i	−0.107833	−	0.186772i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	0.961162	−	0.275983i	$-0.0890035\pi$
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	−0.719590	+	0.694399i	$0.755670\pi$
$348$		0			0
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$	−20.0000			−1.06904
$351$	5.00000	−	8.66025i	0.266880	−	0.462250i
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	3.00000			0.159674			0.0798369	−	0.996808i	$-0.474560\pi$
$353$	3.00000			0.159674			0.0798369	+	0.996808i	$0.474560\pi$
$354$	9.00000			0.478345
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	−12.0000	+	20.7846i	−0.635107	+	1.10004i
$358$	4.50000	+	7.79423i	0.237832	+	0.411938i
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	−2.00000			−0.105118
$363$	1.00000	+	1.73205i	0.0524864	+	0.0909091i
$364$	4.00000	+	6.92820i	0.209657	+	0.363137i
$365$		0			0
$366$	−2.00000	−	3.46410i	−0.104542	−	0.181071i
$367$	11.0000	−	19.0526i	0.574195	−	0.994535i	−0.421933	−	0.906627i	$-0.638648\pi$
$367$	11.0000	−	19.0526i	0.574195	−	0.994535i	0.996129	−	0.0879086i	$-0.0280183\pi$
$368$	−6.00000			−0.312772
$369$	−18.0000			−0.937043
$370$		0			0
$371$	12.0000	−	20.7846i	0.623009	−	1.07908i
$372$	2.00000			0.103695
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	10.0000	+	17.3205i	0.514344	+	0.890871i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	1.00000	−	1.73205i	0.0508987	−	0.0881591i
$387$	8.00000			0.406663
$388$	17.0000			0.863044
$389$	18.0000	−	31.1769i	0.912636	−	1.58073i	0.102311	−	0.994753i	$-0.467376\pi$
$389$	18.0000	−	31.1769i	0.912636	−	1.58073i	0.810326	−	0.585980i	$-0.199290\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$	−9.00000			−0.454569
$393$	−4.50000	+	7.79423i	−0.226995	+	0.393167i
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$		0			0
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	5.00000	+	8.66025i	0.250943	+	0.434646i	0.963786	−	0.266678i	$-0.0859261\pi$
$397$	5.00000	+	8.66025i	0.250943	+	0.434646i	−0.712843	+	0.701324i	$0.752593\pi$
$398$	10.0000			0.501255
$399$	−16.0000	−	6.92820i	−0.801002	−	0.346844i
$400$	−5.00000			−0.250000
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	−3.50000	−	6.06218i	−0.174564	−	0.302354i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−30.0000			−1.48704
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$	−1.00000	+	1.73205i	−0.0492665	+	0.0853320i
$413$	−18.0000	−	31.1769i	−0.885722	−	1.53412i
$414$	6.00000	−	10.3923i	0.294884	−	0.510754i
$415$		0			0
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	11.0000			0.538672
$418$	−12.0000	−	5.19615i	−0.586939	−	0.254152i
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$		0			0
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	30.0000			1.45521
$426$	6.00000			0.290701
$427$	−8.00000	+	13.8564i	−0.387147	+	0.670559i
$428$		0			0
$429$	6.00000			0.289683
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	−13.0000	+	22.5167i	−0.624740	+	1.08208i	0.363851	+	0.931457i	$0.381462\pi$
$433$	−13.0000	+	22.5167i	−0.624740	+	1.08208i	−0.988591	+	0.150624i	$0.951872\pi$
$434$	−4.00000	−	6.92820i	−0.192006	−	0.332564i
$435$		0			0
$436$	−16.0000			−0.766261
$437$	3.00000	+	25.9808i	0.143509	+	1.24283i
$438$	1.00000			0.0477818
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	0.649218	−	0.760602i	$-0.275096\pi$
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	−0.983310	+	0.181938i	$0.941763\pi$
$440$		0			0
$441$	9.00000	−	15.5885i	0.428571	−	0.742307i
$442$	−6.00000	−	10.3923i	−0.285391	−	0.494312i
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	−0.952901	−	0.303281i	$-0.901918\pi$
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	0.739100	+	0.673596i	$0.235251\pi$
$444$	−10.0000			−0.474579
$445$		0			0
$446$	7.00000	−	12.1244i	0.331460	−	0.574105i
$447$	−9.00000	+	15.5885i	−0.425685	+	0.737309i
$448$	−4.00000			−0.188982
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	5.00000	−	8.66025i	0.235702	−	0.408248i
$451$	−13.5000	−	23.3827i	−0.635690	−	1.10105i
$452$	−7.50000	+	12.9904i	−0.352770	+	0.611016i
$453$	5.00000	+	8.66025i	0.234920	+	0.406894i
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$		0			0
$456$	−4.00000	−	1.73205i	−0.187317	−	0.0811107i
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$	−8.00000	−	13.8564i	−0.373815	−	0.647467i
$459$	−15.0000	−	25.9808i	−0.700140	−	1.21268i
$460$		0			0
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$	−6.00000	+	10.3923i	−0.279145	+	0.483494i
$463$	−34.0000			−1.58011			−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000			−1.58011			−0.790057	+	0.613033i	$0.789949\pi$
$464$		0			0
$465$		0			0
$466$	1.50000	−	2.59808i	0.0694862	−	0.120354i
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$	−4.00000			−0.184900
$469$	−14.0000	+	24.2487i	−0.646460	+	1.11970i
$470$		0			0
$471$	8.00000	−	13.8564i	0.368621	−	0.638470i
$472$	−4.50000	−	7.79423i	−0.207129	−	0.358758i
$473$	6.00000	+	10.3923i	0.275880	+	0.477839i
$474$	4.00000			0.183726
$475$	2.50000	+	21.6506i	0.114708	+	0.993399i
$476$	24.0000			1.10004
$477$	6.00000	+	10.3923i	0.274721	+	0.475831i
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$		0			0
$481$	10.0000	−	17.3205i	0.455961	−	0.789747i
$482$	−5.00000			−0.227744
$483$	24.0000			1.09204
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$	−16.0000			−0.725775
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−2.00000	+	3.46410i	−0.0905357	+	0.156813i
$489$	9.50000	+	16.4545i	0.429605	+	0.744097i
$490$		0			0
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$	−4.50000	−	7.79423i	−0.202876	−	0.351391i
$493$		0			0
$494$	7.00000	−	5.19615i	0.314945	−	0.233786i
$495$		0			0
$496$	−1.00000	−	1.73205i	−0.0449013	−	0.0777714i
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$	1.50000	−	2.59808i	0.0672166	−	0.116423i
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	0.997532	+	0.0702185i	$0.0223697\pi$
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	−0.437955	+	0.898997i	$0.644297\pi$
$500$		0			0
$501$	−24.0000			−1.07224
$502$	3.00000			0.133897
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$504$	4.00000	−	6.92820i	0.178174	−	0.308607i
$505$		0			0
$506$	18.0000			0.800198
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$	−1.00000			−0.0441942
$513$	17.5000	−	12.9904i	0.772644	−	0.573539i
$514$	−3.00000			−0.132324
$515$		0			0
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$		0			0
$518$	20.0000	+	34.6410i	0.878750	+	1.52204i
$519$	−3.00000	+	5.19615i	−0.131685	+	0.228086i
$520$		0			0
$521$	9.00000			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$522$		0			0
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	−0.378695	−	0.925521i	$-0.623627\pi$
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	0.990873	−	0.134801i	$-0.0430394\pi$
$524$	9.00000			0.393167
$525$	20.0000			0.872872
$526$	−6.00000	+	10.3923i	−0.261612	+	0.453126i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$	−1.50000	+	2.59808i	−0.0652791	+	0.113067i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	18.0000			0.781133
$532$	2.00000	+	17.3205i	0.0867110	+	0.750939i
$533$	18.0000			0.779667
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$		0			0
$536$	−3.50000	+	6.06218i	−0.151177	+	0.261846i
$537$	−4.50000	−	7.79423i	−0.194189	−	0.336346i
$538$	6.00000	−	10.3923i	0.258678	−	0.448044i
$539$	27.0000			1.16297
$540$		0			0
$541$	−22.0000	+	38.1051i	−0.945854	+	1.63827i	−0.191821	+	0.981430i	$0.561439\pi$
$541$	−22.0000	+	38.1051i	−0.945854	+	1.63827i	−0.754032	+	0.656837i	$0.771894\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	2.00000			0.0858282
$544$	6.00000			0.257248
$545$		0			0
$546$	−4.00000	−	6.92820i	−0.171184	−	0.296500i
$547$	2.00000	−	3.46410i	0.0855138	−	0.148114i	−0.820096	−	0.572226i	$-0.806080\pi$
$547$	2.00000	−	3.46410i	0.0855138	−	0.148114i	0.905610	+	0.424111i	$0.139413\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$	15.0000			0.639602
$551$		0			0
$552$	6.00000			0.255377
$553$	−8.00000	−	13.8564i	−0.340195	−	0.589234i
$554$	4.00000	+	6.92820i	0.169944	+	0.294351i
$555$		0			0
$556$	−5.50000	−	9.52628i	−0.233252	−	0.404004i
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	0.491496	+	0.870880i	$0.336450\pi$
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	−0.999952	+	0.00979220i	$0.996883\pi$
$558$	4.00000			0.169334
$559$	−8.00000			−0.338364
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$	−27.0000			−1.13893
$563$	−21.0000			−0.885044			−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000			−0.885044			−0.442522	+	0.896758i	$0.645916\pi$
$564$		0			0
$565$		0			0
$566$	2.50000	−	4.33013i	0.105083	−	0.182009i
$567$	2.00000	+	3.46410i	0.0839921	+	0.145479i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$	−6.00000	−	10.3923i	−0.250654	−	0.434145i
$574$	−18.0000	+	31.1769i	−0.751305	+	1.30130i
$575$	−15.0000	−	25.9808i	−0.625543	−	1.08347i
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$	−19.0000			−0.790296
$579$	−1.00000	+	1.73205i	−0.0415586	+	0.0719816i
$580$		0			0
$581$	−12.0000			−0.497844
$582$	−17.0000			−0.704673
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$	−0.500000	−	0.866025i	−0.0206901	−	0.0358364i
$585$		0			0
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$	9.00000			0.371154
$589$	−7.00000	+	5.19615i	−0.288430	+	0.214104i
$590$		0			0
$591$	−9.00000	−	15.5885i	−0.370211	−	0.641223i
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	10.5000	−	18.1865i	0.431183	−	0.746831i	−0.565792	−	0.824548i	$-0.691430\pi$
$593$	10.5000	−	18.1865i	0.431183	−	0.746831i	0.996976	+	0.0777165i	$0.0247629\pi$
$594$	−7.50000	−	12.9904i	−0.307729	−	0.533002i
$595$		0			0
$596$	18.0000			0.737309
$597$	−10.0000			−0.409273
$598$	−6.00000	+	10.3923i	−0.245358	+	0.424973i
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	−0.798206	−	0.602384i	$-0.794218\pi$
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$600$	5.00000			0.204124
$601$	−13.0000			−0.530281			−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000			−0.530281			−0.265141	+	0.964210i	$0.585418\pi$
$602$	8.00000	−	13.8564i	0.326056	−	0.564745i
$603$	−7.00000	−	12.1244i	−0.285062	−	0.493742i
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$		0			0
$606$		0			0
$607$	20.0000			0.811775			0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000			0.811775			0.405887	+	0.913923i	$0.366962\pi$
$608$	0.500000	+	4.33013i	0.0202777	+	0.175610i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−6.00000	+	10.3923i	−0.242536	+	0.420084i
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	−3.50000	+	6.06218i	−0.141249	+	0.244650i
$615$		0			0
$616$	12.0000			0.483494
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	−0.894639	−	0.446790i	$-0.852567\pi$
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	0.834251	+	0.551385i	$0.185900\pi$
$618$	1.00000	−	1.73205i	0.0402259	−	0.0696733i
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$		0			0
$621$	−15.0000	+	25.9808i	−0.601929	+	1.04257i
$622$	−15.0000	−	25.9808i	−0.601445	−	1.04173i
$623$	12.0000	−	20.7846i	0.480770	−	0.832718i
$624$	−1.00000	−	1.73205i	−0.0400320	−	0.0693375i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	19.0000			0.759393
$627$	12.0000	+	5.19615i	0.479234	+	0.207514i
$628$	−16.0000			−0.638470
$629$	−30.0000	−	51.9615i	−1.19618	−	2.07184i
$630$		0			0
$631$	14.0000	−	24.2487i	0.557331	−	0.965326i	−0.440387	−	0.897808i	$-0.645159\pi$
$631$	14.0000	−	24.2487i	0.557331	−	0.965326i	0.997718	−	0.0675178i	$-0.0215080\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$	18.0000			0.714871
$635$		0			0
$636$	−3.00000	+	5.19615i	−0.118958	+	0.206041i
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$		0			0
$639$	12.0000			0.474713
$640$		0			0
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$		0			0
$643$	21.5000	+	37.2391i	0.847877	+	1.46857i	0.883099	+	0.469187i	$0.155453\pi$
$643$	21.5000	+	37.2391i	0.847877	+	1.46857i	−0.0352216	+	0.999380i	$0.511214\pi$
$644$	−12.0000	−	20.7846i	−0.472866	−	0.819028i
$645$		0			0
$646$	−3.00000	−	25.9808i	−0.118033	−	1.02220i
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	13.5000	+	23.3827i	0.529921	+	0.917851i
$650$	−5.00000	+	8.66025i	−0.196116	+	0.339683i
$651$	4.00000	+	6.92820i	0.156772	+	0.271538i
$652$	9.50000	−	16.4545i	0.372049	−	0.644407i
$653$	−12.0000			−0.469596			−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000			−0.469596			−0.234798	+	0.972044i	$0.575443\pi$
$654$	16.0000			0.625650
$655$		0			0
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$	2.00000			0.0780274
$658$		0			0
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$	2.50000	+	4.33013i	0.0971653	+	0.168295i
$663$	6.00000	+	10.3923i	0.233021	+	0.403604i
$664$	−3.00000			−0.116423
$665$		0			0
$666$	−20.0000			−0.774984
$667$		0			0
$668$	12.0000	+	20.7846i	0.464294	+	0.804181i
$669$	−7.00000	+	12.1244i	−0.270636	+	0.468755i
$670$		0			0
$671$	6.00000	−	10.3923i	0.231627	−	0.401190i
$672$	4.00000			0.154303
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	5.50000	−	9.52628i	0.211852	−	0.366939i
$675$	−12.5000	+	21.6506i	−0.481125	+	0.833333i
$676$	−9.00000			−0.346154
$677$	−42.0000			−1.61419			−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000			−1.61419			−0.807096	+	0.590421i	$0.798962\pi$
$678$	7.50000	−	12.9904i	0.288036	−	0.498893i
$679$	34.0000	+	58.8897i	1.30480	+	2.25998i
$680$		0			0
$681$	−1.50000	−	2.59808i	−0.0574801	−	0.0995585i
$682$	3.00000	+	5.19615i	0.114876	+	0.198971i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	−8.00000	−	3.46410i	−0.305888	−	0.132453i
$685$		0			0
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$	8.00000	+	13.8564i	0.305219	+	0.528655i
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	44.0000			1.67384			0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000			1.67384			0.836919	+	0.547326i	$0.184354\pi$
$692$	6.00000			0.228086
$693$	−12.0000	+	20.7846i	−0.455842	+	0.789542i
$694$	−4.50000	+	7.79423i	−0.170818	+	0.295865i
$695$		0			0
$696$		0			0
$697$	27.0000	−	46.7654i	1.02270	−	1.77136i
$698$	−2.00000	−	3.46410i	−0.0757011	−	0.131118i
$699$	−1.50000	+	2.59808i	−0.0567352	+	0.0982683i
$700$	−10.0000	−	17.3205i	−0.377964	−	0.654654i
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	0.998585	−	0.0531839i	$-0.0169370\pi$
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	−0.545351	+	0.838208i	$0.683604\pi$
$702$	10.0000			0.377426
$703$	35.0000	−	25.9808i	1.32005	−	0.979883i
$704$	3.00000			0.113067
$705$		0			0
$706$	1.50000	+	2.59808i	0.0564532	+	0.0977799i
$707$		0			0
$708$	4.50000	+	7.79423i	0.169120	+	0.292925i
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$	−24.0000			−0.898177
$715$		0			0
$716$	−4.50000	+	7.79423i	−0.168173	+	0.291284i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	−0.997546	−	0.0700124i	$-0.977696\pi$
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	0.438141	−	0.898906i	$-0.355637\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	18.5000	−	4.33013i	0.688499	−	0.161151i
$723$	5.00000			0.185952
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$		0			0
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	−16.0000	−	27.7128i	−0.593407	−	1.02781i	−0.993770	−	0.111454i	$-0.964449\pi$
$727$	−16.0000	−	27.7128i	−0.593407	−	1.02781i	0.400362	−	0.916357i	$-0.368884\pi$
$728$	−4.00000	+	6.92820i	−0.148250	+	0.256776i
$729$	13.0000			0.481481
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	2.00000	−	3.46410i	0.0739221	−	0.128037i
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$	22.0000			0.812035
$735$		0			0
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	10.5000	−	18.1865i	0.386772	−	0.669910i
$738$	−9.00000	−	15.5885i	−0.331295	−	0.573819i
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	−0.984589	−	0.174883i	$-0.944045\pi$
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	0.340841	−	0.940121i	$-0.389288\pi$
$740$		0			0
$741$	−7.00000	+	5.19615i	−0.257151	+	0.190885i
$742$	24.0000			0.881068
$743$	9.00000	+	15.5885i	0.330178	+	0.571885i	0.982547	−	0.186017i	$-0.0595579\pi$
$743$	9.00000	+	15.5885i	0.330178	+	0.571885i	−0.652369	+	0.757902i	$0.726225\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$		0			0
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	−18.0000			−0.658145
$749$		0			0
$750$		0			0
$751$	−19.0000	+	32.9090i	−0.693320	+	1.20087i	0.277424	+	0.960748i	$0.410519\pi$
$751$	−19.0000	+	32.9090i	−0.693320	+	1.20087i	−0.970744	+	0.240118i	$0.922814\pi$
$752$		0			0
$753$	−3.00000			−0.109326
$754$		0			0
$755$		0			0
$756$	−10.0000	+	17.3205i	−0.363696	+	0.629941i
$757$	5.00000	+	8.66025i	0.181728	+	0.314762i	0.942469	−	0.334293i	$-0.108498\pi$
$757$	5.00000	+	8.66025i	0.181728	+	0.314762i	−0.760741	+	0.649056i	$0.775164\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$	−18.0000			−0.653359
$760$		0			0
$761$	−39.0000			−1.41375			−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000			−1.41375			−0.706874	+	0.707339i	$0.749895\pi$
$762$	1.00000	+	1.73205i	0.0362262	+	0.0627456i
$763$	−32.0000	−	55.4256i	−1.15848	−	2.00654i
$764$	−6.00000	+	10.3923i	−0.217072	+	0.375980i
$765$		0			0
$766$	−18.0000	+	31.1769i	−0.650366	+	1.12647i
$767$	−18.0000			−0.649942
$768$	1.00000			0.0360844
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$	2.00000			0.0719816
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	−0.00558380	−	0.999984i	$-0.501777\pi$
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	0.868804	−	0.495156i	$-0.164889\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$	5.00000	−	8.66025i	0.179605	−	0.311086i
$776$	8.50000	+	14.7224i	0.305132	+	0.528505i
$777$	−20.0000	−	34.6410i	−0.717496	−	1.24274i
$778$	36.0000			1.29066
$779$	36.0000	+	15.5885i	1.28983	+	0.558514i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	18.0000	+	31.1769i	0.643679	+	1.11488i
$783$		0			0
$784$	−4.50000	−	7.79423i	−0.160714	−	0.278365i
$785$		0			0
$786$	−9.00000			−0.321019
$787$	−7.00000			−0.249523			−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000			−0.249523			−0.124762	+	0.992187i	$0.539817\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$	6.00000	−	10.3923i	0.213606	−	0.369976i
$790$		0			0
$791$	−60.0000			−2.13335
$792$	−3.00000	+	5.19615i	−0.106600	+	0.184637i
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$	−5.00000	+	8.66025i	−0.177443	+	0.307341i
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$	−2.00000	−	17.3205i	−0.0707992	−	0.613139i
$799$		0			0
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	−13.5000	+	23.3827i	−0.476702	+	0.825671i
$803$	1.50000	+	2.59808i	0.0529339	+	0.0916841i
$804$	3.50000	−	6.06218i	0.123435	−	0.213797i
$805$		0			0
$806$	−4.00000			−0.140894
$807$	−6.00000	+	10.3923i	−0.211210	+	0.365826i
$808$		0			0
$809$	45.0000			1.58212			0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000			1.58212			0.791058	+	0.611741i	$0.209531\pi$
$810$		0			0
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	−0.690693	−	0.723148i	$-0.742694\pi$
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	0.971611	+	0.236584i	$0.0760278\pi$
$812$		0			0
$813$	8.00000	−	13.8564i	0.280572	−	0.485965i
$814$	−15.0000	−	25.9808i	−0.525750	−	0.910625i
$815$		0			0
$816$	−6.00000			−0.210042
$817$	−16.0000	−	6.92820i	−0.559769	−	0.242387i
$818$	−5.00000			−0.174821
$819$	−8.00000	−	13.8564i	−0.279543	−	0.484182i
$820$		0			0
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$	4.50000	+	7.79423i	0.156956	+	0.271855i
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	−2.00000			−0.0696733
$825$	−15.0000			−0.522233
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$	19.5000	−	33.7750i	0.678081	−	1.17447i	−0.297477	−	0.954729i	$-0.596145\pi$
$827$	19.5000	−	33.7750i	0.678081	−	1.17447i	0.975558	−	0.219742i	$-0.0705217\pi$
$828$	12.0000			0.417029
$829$	44.0000			1.52818			0.764092	−	0.645108i	$-0.223188\pi$
$829$	44.0000			1.52818			0.764092	+	0.645108i	$0.223188\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	27.0000	+	46.7654i	0.935495	+	1.62032i
$834$	5.50000	+	9.52628i	0.190449	+	0.329868i
$835$		0			0
$836$	−1.50000	−	12.9904i	−0.0518786	−	0.449282i
$837$	−10.0000			−0.345651
$838$	−6.00000	−	10.3923i	−0.207267	−	0.358996i
$839$	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
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−5.00000	+	8.66025i	−0.172311	+	0.298452i
$843$	27.0000			0.929929
$844$	20.0000			0.688428
$845$		0			0
$846$		0			0
$847$	8.00000			0.274883
$848$	6.00000			0.206041
$849$	−2.50000	+	4.33013i	−0.0857998	+	0.148610i
$850$	15.0000	+	25.9808i	0.514496	+	0.891133i
$851$	−30.0000	+	51.9615i	−1.02839	+	1.78122i
$852$	3.00000	+	5.19615i	0.102778	+	0.178017i
$853$	11.0000	+	19.0526i	0.376633	+	0.652347i	0.990570	−	0.137008i	$-0.0437485\pi$
$853$	11.0000	+	19.0526i	0.376633	+	0.652347i	−0.613937	+	0.789355i	$0.710415\pi$
$854$	−16.0000			−0.547509
$855$		0			0
$856$		0			0
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	0.890507	−	0.454969i	$-0.150350\pi$
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	−0.839268	+	0.543718i	$0.817016\pi$
$858$	3.00000	+	5.19615i	0.102418	+	0.177394i
$859$	21.5000	−	37.2391i	0.733571	−	1.27058i	−0.221777	−	0.975097i	$-0.571186\pi$
$859$	21.5000	−	37.2391i	0.733571	−	1.27058i	0.955348	−	0.295484i	$-0.0954809\pi$
$860$		0			0
$861$	18.0000	−	31.1769i	0.613438	−	1.06251i
$862$	30.0000			1.02180
$863$	18.0000			0.612727			0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000			0.612727			0.306364	+	0.951915i	$0.400888\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$		0			0
$866$	−26.0000			−0.883516
$867$	19.0000			0.645274
$868$	4.00000	−	6.92820i	0.135769	−	0.235159i
$869$	6.00000	+	10.3923i	0.203536	+	0.352535i
$870$		0			0
$871$	7.00000	+	12.1244i	0.237186	+	0.410818i
$872$	−8.00000	−	13.8564i	−0.270914	−	0.469237i
$873$	−34.0000			−1.15073
$874$	−21.0000	+	15.5885i	−0.710336	+	0.527287i
$875$		0			0
$876$	0.500000	+	0.866025i	0.0168934	+	0.0292603i
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	0.646319	−	0.763067i	$-0.276307\pi$
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	−0.983995	+	0.178195i	$0.942974\pi$
$878$	7.00000	−	12.1244i	0.236239	−	0.409177i
$879$	−12.0000	−	20.7846i	−0.404750	−	0.701047i
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$	18.0000			0.606092
$883$	9.50000	−	16.4545i	0.319700	−	0.553737i	−0.660725	−	0.750628i	$-0.729751\pi$
$883$	9.50000	−	16.4545i	0.319700	−	0.553737i	0.980425	+	0.196891i	$0.0630844\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	−9.00000			−0.302361
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$	−5.00000	−	8.66025i	−0.167789	−	0.290619i
$889$	4.00000	−	6.92820i	0.134156	−	0.232364i
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$	14.0000			0.468755
$893$		0			0
$894$	−18.0000			−0.602010
$895$		0			0
$896$	−2.00000	−	3.46410i	−0.0668153	−	0.115728i
$897$	6.00000	−	10.3923i	0.200334	−	0.346989i
$898$	4.50000	+	7.79423i	0.150167	+	0.260097i
$899$		0			0
$900$	10.0000			0.333333
$901$	−36.0000			−1.19933
$902$	13.5000	−	23.3827i	0.449501	−	0.778558i
$903$	−8.00000	+	13.8564i	−0.266223	+	0.461112i
$904$	−15.0000			−0.498893
$905$		0			0
$906$	−5.00000	+	8.66025i	−0.166114	+	0.287718i
$907$	−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	$0.924410\pi$
$908$	−1.50000	+	2.59808i	−0.0497792	+	0.0862202i
$909$		0			0
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	−0.500000	−	4.33013i	−0.0165567	−	0.143385i
$913$	9.00000			0.297857
$914$	2.50000	+	4.33013i	0.0826927	+	0.143228i
$915$		0			0
$916$	8.00000	−	13.8564i	0.264327	−	0.457829i
$917$	18.0000	+	31.1769i	0.594412	+	1.02955i
$918$	15.0000	−	25.9808i	0.495074	−	0.857493i
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$		0			0
$921$	3.50000	−	6.06218i	0.115329	−	0.199756i
$922$	3.00000	−	5.19615i	0.0987997	−	0.171126i
$923$	−12.0000			−0.394985
$924$	−12.0000			−0.394771
$925$	−25.0000	+	43.3013i	−0.821995	+	1.42374i
$926$	−17.0000	−	29.4449i	−0.558655	−	0.967618i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$		0			0
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	0.889583	−	0.456774i	$-0.150995\pi$
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	−0.840369	+	0.542014i	$0.817662\pi$
$930$		0			0
$931$	−31.5000	+	23.3827i	−1.03237	+	0.766337i
$932$	3.00000			0.0982683
$933$	15.0000	+	25.9808i	0.491078	+	0.850572i
$934$	−13.5000	−	23.3827i	−0.441733	−	0.765105i
$935$		0			0
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	−17.5000	+	30.3109i	−0.571700	+	0.990214i	0.424691	+	0.905338i	$0.360383\pi$
$937$	−17.5000	+	30.3109i	−0.571700	+	0.990214i	−0.996392	+	0.0848755i	$0.972951\pi$
$938$	−28.0000			−0.914232
$939$	−19.0000			−0.620042
$940$		0			0
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	−0.288988	−	0.957333i	$-0.593319\pi$
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	0.973568	−	0.228395i	$-0.0733479\pi$
$942$	16.0000			0.521308
$943$	−54.0000			−1.75848
$944$	4.50000	−	7.79423i	0.146463	−	0.253681i
$945$		0			0
$946$	−6.00000	+	10.3923i	−0.195077	+	0.337883i
$947$	−30.0000	−	51.9615i	−0.974869	−	1.68852i	−0.680367	−	0.732872i	$-0.738179\pi$
$947$	−30.0000	−	51.9615i	−0.974869	−	1.68852i	−0.294502	−	0.955651i	$-0.595154\pi$
$948$	2.00000	+	3.46410i	0.0649570	+	0.112509i
$949$	−2.00000			−0.0649227
$950$	−17.5000	+	12.9904i	−0.567775	+	0.421464i
$951$	−18.0000			−0.583690
$952$	12.0000	+	20.7846i	0.388922	+	0.673633i
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	0.961553	−	0.274620i	$-0.0885520\pi$
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	−0.718604	+	0.695419i	$0.755219\pi$
$954$	−6.00000	+	10.3923i	−0.194257	+	0.336463i
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$	−36.0000			−1.16311
$959$	18.0000	−	31.1769i	0.581250	−	1.00676i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	20.0000			0.644826
$963$		0			0
$964$	−2.50000	−	4.33013i	−0.0805196	−	0.139464i
$965$		0			0
$966$	12.0000	+	20.7846i	0.386094	+	0.668734i
$967$	17.0000	+	29.4449i	0.546683	+	0.946883i	0.998499	+	0.0547717i	$0.0174431\pi$
$967$	17.0000	+	29.4449i	0.546683	+	0.946883i	−0.451816	+	0.892111i	$0.649224\pi$
$968$	2.00000			0.0642824
$969$	3.00000	+	25.9808i	0.0963739	+	0.834622i
$970$		0			0
$971$	−10.5000	−	18.1865i	−0.336961	−	0.583634i	0.646899	−	0.762576i	$-0.276066\pi$
$971$	−10.5000	−	18.1865i	−0.336961	−	0.583634i	−0.983860	+	0.178942i	$0.942732\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	22.0000	−	38.1051i	0.705288	−	1.22159i
$974$	1.00000	+	1.73205i	0.0320421	+	0.0554985i
$975$	5.00000	−	8.66025i	0.160128	−	0.277350i
$976$	−4.00000			−0.128037
$977$	33.0000			1.05576			0.527882	−	0.849318i	$-0.322986\pi$
$977$	33.0000			1.05576			0.527882	+	0.849318i	$0.322986\pi$
$978$	−9.50000	+	16.4545i	−0.303777	+	0.526156i
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$		0			0
$981$	32.0000			1.02168
$982$		0			0
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	0.608712	−	0.793391i	$-0.291686\pi$
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	8.00000	+	3.46410i	0.254514	+	0.110208i
$989$	24.0000			0.763156
$990$		0			0
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	−2.50000	−	4.33013i	−0.0793351	−	0.137412i
$994$	12.0000	−	20.7846i	0.380617	−	0.659248i
$995$		0			0
$996$	3.00000			0.0950586
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	−0.832616	−	0.553851i	$-0.813158\pi$
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	0.895957	+	0.444141i	$0.146491\pi$
$998$	−12.5000	+	21.6506i	−0.395681	+	0.685339i
$999$	50.0000			1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.2.c.a.7.1	✓	2
3.2	odd	2		342.2.g.b.235.1		2
4.3	odd	2		304.2.i.c.273.1		2
5.2	odd	4		950.2.j.e.349.1		4
5.3	odd	4		950.2.j.e.349.2		4
5.4	even	2		950.2.e.d.501.1		2
8.3	odd	2		1216.2.i.d.577.1		2
8.5	even	2		1216.2.i.h.577.1		2
12.11	even	2		2736.2.s.m.577.1		2
19.2	odd	18		722.2.e.i.389.1		6
19.3	odd	18		722.2.e.i.595.1		6
19.4	even	9		722.2.e.j.245.1		6
19.5	even	9		722.2.e.j.99.1		6
19.6	even	9		722.2.e.j.423.1		6
19.7	even	3		722.2.a.c.1.1		1
19.8	odd	6		722.2.c.b.429.1		2
19.9	even	9		722.2.e.j.415.1		6
19.10	odd	18		722.2.e.i.415.1		6
19.11	even	3	inner	38.2.c.a.11.1	yes	2
19.12	odd	6		722.2.a.d.1.1		1
19.13	odd	18		722.2.e.i.423.1		6
19.14	odd	18		722.2.e.i.99.1		6
19.15	odd	18		722.2.e.i.245.1		6
19.16	even	9		722.2.e.j.595.1		6
19.17	even	9		722.2.e.j.389.1		6
19.18	odd	2		722.2.c.b.653.1		2
57.11	odd	6		342.2.g.b.163.1		2
57.26	odd	6		6498.2.a.s.1.1		1
57.50	even	6		6498.2.a.e.1.1		1
76.7	odd	6		5776.2.a.g.1.1		1
76.11	odd	6		304.2.i.c.49.1		2
76.31	even	6		5776.2.a.n.1.1		1
95.49	even	6		950.2.e.d.201.1		2
95.68	odd	12		950.2.j.e.49.1		4
95.87	odd	12		950.2.j.e.49.2		4
152.11	odd	6		1216.2.i.d.961.1		2
152.125	even	6		1216.2.i.h.961.1		2
228.11	even	6		2736.2.s.m.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.a.7.1	✓	2	1.1	even	1	trivial
38.2.c.a.11.1	yes	2	19.11	even	3	inner
304.2.i.c.49.1		2	76.11	odd	6
304.2.i.c.273.1		2	4.3	odd	2
342.2.g.b.163.1		2	57.11	odd	6
342.2.g.b.235.1		2	3.2	odd	2
722.2.a.c.1.1		1	19.7	even	3
722.2.a.d.1.1		1	19.12	odd	6
722.2.c.b.429.1		2	19.8	odd	6
722.2.c.b.653.1		2	19.18	odd	2
722.2.e.i.99.1		6	19.14	odd	18
722.2.e.i.245.1		6	19.15	odd	18
722.2.e.i.389.1		6	19.2	odd	18
722.2.e.i.415.1		6	19.10	odd	18
722.2.e.i.423.1		6	19.13	odd	18
722.2.e.i.595.1		6	19.3	odd	18
722.2.e.j.99.1		6	19.5	even	9
722.2.e.j.245.1		6	19.4	even	9
722.2.e.j.389.1		6	19.17	even	9
722.2.e.j.415.1		6	19.9	even	9
722.2.e.j.423.1		6	19.6	even	9
722.2.e.j.595.1		6	19.16	even	9
950.2.e.d.201.1		2	95.49	even	6
950.2.e.d.501.1		2	5.4	even	2
950.2.j.e.49.1		4	95.68	odd	12
950.2.j.e.49.2		4	95.87	odd	12
950.2.j.e.349.1		4	5.2	odd	4
950.2.j.e.349.2		4	5.3	odd	4
1216.2.i.d.577.1		2	8.3	odd	2
1216.2.i.d.961.1		2	152.11	odd	6
1216.2.i.h.577.1		2	8.5	even	2
1216.2.i.h.961.1		2	152.125	even	6
2736.2.s.m.577.1		2	12.11	even	2
2736.2.s.m.1873.1		2	228.11	even	6
5776.2.a.g.1.1		1	76.7	odd	6
5776.2.a.n.1.1		1	76.31	even	6
6498.2.a.e.1.1		1	57.50	even	6
6498.2.a.s.1.1		1	57.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -4.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +3.00000 q^{11} +1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +2.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} -2.00000 q^{26} -5.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(-3.00000 + 5.19615i) q^{34} +(1.00000 + 1.73205i) q^{36} -10.0000 q^{37} +(-4.00000 - 1.73205i) q^{38} +2.00000 q^{39} +(-4.50000 - 7.79423i) q^{41} +(-2.00000 + 3.46410i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-1.50000 + 2.59808i) q^{44} +6.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} +9.00000 q^{49} +5.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-2.50000 - 4.33013i) q^{54} +4.00000 q^{56} +(4.00000 + 1.73205i) q^{57} +(4.50000 + 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-4.00000 + 6.92820i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(3.50000 - 6.06218i) q^{67} -6.00000 q^{68} -6.00000 q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(0.500000 + 0.866025i) q^{73} +(-5.00000 - 8.66025i) q^{74} -5.00000 q^{75} +(-0.500000 - 4.33013i) q^{76} -12.0000 q^{77} +(1.00000 + 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +3.00000 q^{83} -4.00000 q^{84} +(-2.00000 + 3.46410i) q^{86} -3.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-1.00000 - 1.73205i) q^{93} -1.00000 q^{96} +(-8.50000 - 14.7224i) q^{97} +(4.50000 + 7.79423i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - 8 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 4 q^{18} - 7 q^{19} + 4 q^{21} + 3 q^{22} + 6 q^{23} + q^{24} + 5 q^{25}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^6 - 8 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 4 * q^18 - 7 * q^19 + 4 * q^21 + 3 * q^22 + 6 * q^23 + q^24 + 5 * q^25 - 4 * q^26 - 10 * q^27 + 4 * q^28 + 4 * q^31 + q^32 - 3 * q^33 - 6 * q^34 + 2 * q^36 - 20 * q^37 - 8 * q^38 + 4 * q^39 - 9 * q^41 - 4 * q^42 + 4 * q^43 - 3 * q^44 + 12 * q^46 - q^48 + 18 * q^49 + 10 * q^50 + 6 * q^51 - 2 * q^52 - 6 * q^53 - 5 * q^54 + 8 * q^56 + 8 * q^57 + 9 * q^59 + 4 * q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 + 3 * q^66 + 7 * q^67 - 12 * q^68 - 12 * q^69 + 6 * q^71 - 2 * q^72 + q^73 - 10 * q^74 - 10 * q^75 - q^76 - 24 * q^77 + 2 * q^78 + 4 * q^79 - q^81 + 9 * q^82 + 6 * q^83 - 8 * q^84 - 4 * q^86 - 6 * q^88 - 6 * q^89 + 8 * q^91 + 6 * q^92 - 2 * q^93 - 2 * q^96 - 17 * q^97 + 9 * q^98 + 6 * q^99

Introduction

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