LMFDB - Embedded newform 1274.2.n.b.753.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(753,1274)] 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("1274.753"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,2,0,0,0,0,4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			753.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1274.753
Dual form			1274.2.n.b.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.73205 - 1.00000i) q^{5} -1.00000i q^{6} +1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(4.33013 + 2.50000i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.00000 - 2.00000i) q^{13} +2.00000i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.73205 - 1.00000i) q^{18} +(3.46410 - 2.00000i) q^{19} -2.00000i q^{20} -5.00000 q^{22} +(-4.50000 - 7.79423i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.59808 + 3.23205i) q^{26} -5.00000 q^{27} +(-1.00000 - 1.73205i) q^{30} +(4.33013 + 2.50000i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.33013 + 2.50000i) q^{33} -2.00000i q^{34} +2.00000 q^{36} +(-2.59808 + 1.50000i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(0.232051 + 3.59808i) q^{39} +(1.00000 + 1.73205i) q^{40} -5.00000i q^{41} +4.00000 q^{43} +(4.33013 - 2.50000i) q^{44} +(3.46410 + 2.00000i) q^{45} +(7.79423 + 4.50000i) q^{46} +(11.2583 - 6.50000i) q^{47} +1.00000 q^{48} -1.00000i q^{50} +(-1.00000 - 1.73205i) q^{51} +(-0.232051 - 3.59808i) q^{52} +(-7.00000 + 12.1244i) q^{53} +(4.33013 - 2.50000i) q^{54} +10.0000 q^{55} +4.00000i q^{57} +(5.19615 + 3.00000i) q^{59} +(1.73205 + 1.00000i) q^{60} +(-6.50000 - 11.2583i) q^{61} -5.00000 q^{62} -1.00000 q^{64} +(3.19615 - 6.46410i) q^{65} +(2.50000 - 4.33013i) q^{66} +(2.59808 + 1.50000i) q^{67} +(1.00000 + 1.73205i) q^{68} +9.00000 q^{69} +(-1.73205 + 1.00000i) q^{72} +(-0.866025 - 0.500000i) q^{73} +(1.50000 - 2.59808i) q^{74} +(-0.500000 - 0.866025i) q^{75} -4.00000i q^{76} +(-2.00000 - 3.00000i) q^{78} +(7.50000 + 12.9904i) q^{79} +(-1.73205 - 1.00000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.50000 + 4.33013i) q^{82} +6.00000i q^{83} +4.00000i q^{85} +(-3.46410 + 2.00000i) q^{86} +(-2.50000 + 4.33013i) q^{88} +(-5.19615 + 3.00000i) q^{89} -4.00000 q^{90} -9.00000 q^{92} +(-4.33013 + 2.50000i) q^{93} +(-6.50000 + 11.2583i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-0.866025 + 0.500000i) q^{96} -7.00000i q^{97} +10.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} + 4 q^{9} - 4 q^{10} + 2 q^{12} + 12 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{22} - 18 q^{23} - 2 q^{25} + 4 q^{26} - 20 q^{27} - 4 q^{30} + 8 q^{36} - 8 q^{38} - 6 q^{39} + 4 q^{40}+ \cdots + 16 q^{95}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 + 4 * q^9 - 4 * q^10 + 2 * q^12 + 12 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^22 - 18 * q^23 - 2 * q^25 + 4 * q^26 - 20 * q^27 - 4 * q^30 + 8 * q^36 - 8 * q^38 - 6 * q^39 + 4 * q^40 + 16 * q^43 + 4 * q^48 - 4 * q^51 + 6 * q^52 - 28 * q^53 + 40 * q^55 - 26 * q^61 - 20 * q^62 - 4 * q^64 - 8 * q^65 + 10 * q^66 + 4 * q^68 + 36 * q^69 + 6 * q^74 - 2 * q^75 - 8 * q^78 + 30 * q^79 - 2 * q^81 + 10 * q^82 - 10 * q^88 - 16 * q^90 - 36 * q^92 - 26 * q^94 + 16 * q^95

Character values

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

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

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.73205	−	1.00000i	0.774597	−	0.447214i	−0.0599153	−	0.998203i	$-0.519083\pi$
$5$	1.73205	−	1.00000i	0.774597	−	0.447214i	0.834512	+	0.550990i	$0.185750\pi$
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	4.33013	+	2.50000i	1.30558	+	0.753778i	0.981356	−	0.192201i	$-0.0615626\pi$
$11$	4.33013	+	2.50000i	1.30558	+	0.753778i	0.324227	+	0.945979i	$0.394896\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$14$		0			0
$15$			2.00000i			0.516398i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	−1.73205	−	1.00000i	−0.408248	−	0.235702i
$19$	3.46410	−	2.00000i	0.794719	−	0.458831i	−0.0469020	−	0.998899i	$-0.514935\pi$
$19$	3.46410	−	2.00000i	0.794719	−	0.458831i	0.841621	+	0.540068i	$0.181602\pi$
$20$		−	2.00000i		−	0.447214i
$21$		0			0
$22$	−5.00000			−1.06600
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.768613	−	0.639713i	$-0.779053\pi$
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.169701	−	0.985496i	$-0.554280\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.59808	+	3.23205i	−0.313409	+	0.633857i
$27$	−5.00000			−0.962250
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−1.00000	−	1.73205i	−0.182574	−	0.316228i
$31$	4.33013	+	2.50000i	0.777714	+	0.449013i	0.835619	−	0.549309i	$-0.185109\pi$
$31$	4.33013	+	2.50000i	0.777714	+	0.449013i	−0.0579057	+	0.998322i	$0.518442\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.33013	+	2.50000i	−0.753778	+	0.435194i
$34$		−	2.00000i		−	0.342997i
$35$		0			0
$36$	2.00000			0.333333
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	−0.698119	−	0.715981i	$-0.745980\pi$
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	0.270998	+	0.962580i	$0.412646\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$	0.232051	+	3.59808i	0.0371579	+	0.576153i
$40$	1.00000	+	1.73205i	0.158114	+	0.273861i
$41$		−	5.00000i		−	0.780869i	−0.920631	−	0.390434i	$-0.872325\pi$
$41$		−	5.00000i		−	0.780869i	0.920631	−	0.390434i	$-0.127675\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	4.33013	−	2.50000i	0.652791	−	0.376889i
$45$	3.46410	+	2.00000i	0.516398	+	0.298142i
$46$	7.79423	+	4.50000i	1.14920	+	0.663489i
$47$	11.2583	−	6.50000i	1.64220	−	0.948122i	0.662145	−	0.749375i	$-0.269646\pi$
$47$	11.2583	−	6.50000i	1.64220	−	0.948122i	0.980051	−	0.198747i	$-0.0636872\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	−0.232051	−	3.59808i	−0.0321797	−	0.498963i
$53$	−7.00000	+	12.1244i	−0.961524	+	1.66541i	−0.242846	+	0.970065i	$0.578081\pi$
$53$	−7.00000	+	12.1244i	−0.961524	+	1.66541i	−0.718677	+	0.695344i	$0.755252\pi$
$54$	4.33013	−	2.50000i	0.589256	−	0.340207i
$55$	10.0000			1.34840
$56$		0			0
$57$			4.00000i			0.529813i
$58$		0			0
$59$	5.19615	+	3.00000i	0.676481	+	0.390567i	0.798528	−	0.601958i	$-0.205612\pi$
$59$	5.19615	+	3.00000i	0.676481	+	0.390567i	−0.122047	+	0.992524i	$0.538946\pi$
$60$	1.73205	+	1.00000i	0.223607	+	0.129099i
$61$	−6.50000	−	11.2583i	−0.832240	−	1.44148i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−6.50000	−	11.2583i	−0.832240	−	1.44148i	0.0640184	−	0.997949i	$-0.479608\pi$
$62$	−5.00000			−0.635001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.19615	−	6.46410i	0.396434	−	0.801773i
$66$	2.50000	−	4.33013i	0.307729	−	0.533002i
$67$	2.59808	+	1.50000i	0.317406	+	0.183254i	0.650236	−	0.759733i	$-0.274670\pi$
$67$	2.59808	+	1.50000i	0.317406	+	0.183254i	−0.332830	+	0.942987i	$0.608004\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$	9.00000			1.08347
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−1.73205	+	1.00000i	−0.204124	+	0.117851i
$73$	−0.866025	−	0.500000i	−0.101361	−	0.0585206i	0.448463	−	0.893801i	$-0.351972\pi$
$73$	−0.866025	−	0.500000i	−0.101361	−	0.0585206i	−0.549823	+	0.835281i	$0.685305\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		−	4.00000i		−	0.458831i
$77$		0			0
$78$	−2.00000	−	3.00000i	−0.226455	−	0.339683i
$79$	7.50000	+	12.9904i	0.843816	+	1.46153i	0.886646	+	0.462450i	$0.153029\pi$
$79$	7.50000	+	12.9904i	0.843816	+	1.46153i	−0.0428296	+	0.999082i	$0.513637\pi$
$80$	−1.73205	−	1.00000i	−0.193649	−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.50000	+	4.33013i	0.276079	+	0.478183i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$			4.00000i			0.433861i
$86$	−3.46410	+	2.00000i	−0.373544	+	0.215666i
$87$		0			0
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	−5.19615	+	3.00000i	−0.550791	+	0.317999i	−0.749441	−	0.662071i	$-0.769678\pi$
$89$	−5.19615	+	3.00000i	−0.550791	+	0.317999i	0.198650	+	0.980071i	$0.436344\pi$
$90$	−4.00000			−0.421637
$91$		0			0
$92$	−9.00000			−0.938315
$93$	−4.33013	+	2.50000i	−0.449013	+	0.259238i
$94$	−6.50000	+	11.2583i	−0.670424	+	1.16121i
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$		−	7.00000i		−	0.710742i	−0.934725	−	0.355371i	$-0.884354\pi$
$97$		−	7.00000i		−	0.710742i	0.934725	−	0.355371i	$-0.115646\pi$
$98$		0			0
$99$			10.0000i			1.00504i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	−0.637678	−	0.770303i	$-0.720105\pi$
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	0.985941	+	0.167094i	$0.0534383\pi$
$102$	1.73205	+	1.00000i	0.171499	+	0.0990148i
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	2.00000	+	3.00000i	0.196116	+	0.294174i
$105$		0			0
$106$		−	14.0000i		−	1.35980i
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	12.1244	+	7.00000i	1.16130	+	0.670478i	0.951616	−	0.307290i	$-0.0994222\pi$
$109$	12.1244	+	7.00000i	1.16130	+	0.670478i	0.209687	+	0.977769i	$0.432756\pi$
$110$	−8.66025	+	5.00000i	−0.825723	+	0.476731i
$111$		−	3.00000i		−	0.284747i
$112$		0			0
$113$	−11.0000			−1.03479			−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000			−1.03479			−0.517396	+	0.855746i	$0.673099\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$	−15.5885	−	9.00000i	−1.45363	−	0.839254i
$116$		0			0
$117$	6.46410	+	3.19615i	0.597606	+	0.295484i
$118$	−6.00000			−0.552345
$119$		0			0
$120$	−2.00000			−0.182574
$121$	7.00000	+	12.1244i	0.636364	+	1.10221i
$122$	11.2583	+	6.50000i	1.01928	+	0.588482i
$123$	4.33013	+	2.50000i	0.390434	+	0.225417i
$124$	4.33013	−	2.50000i	0.388857	−	0.224507i
$125$			12.0000i			1.07331i
$126$		0			0
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$	0.464102	+	7.19615i	0.0407044	+	0.631144i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$			5.00000i			0.435194i
$133$		0			0
$134$	−3.00000			−0.259161
$135$	−8.66025	+	5.00000i	−0.745356	+	0.430331i
$136$	−1.73205	−	1.00000i	−0.148522	−	0.0857493i
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.0146279	−	0.999893i	$-0.504656\pi$
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.873247	+	0.487278i	$0.837990\pi$
$138$	−7.79423	+	4.50000i	−0.663489	+	0.383065i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$			13.0000i			1.09480i
$142$		0			0
$143$	17.9904	−	1.16025i	1.50443	−	0.0970253i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$		0			0
$146$	1.00000			0.0827606
$147$		0			0
$148$			3.00000i			0.246598i
$149$	−7.79423	+	4.50000i	−0.638528	+	0.368654i	−0.784047	−	0.620701i	$-0.786848\pi$
$149$	−7.79423	+	4.50000i	−0.638528	+	0.368654i	0.145519	+	0.989355i	$0.453515\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$	−8.66025	−	5.00000i	−0.704761	−	0.406894i	0.104357	−	0.994540i	$-0.466722\pi$
$151$	−8.66025	−	5.00000i	−0.704761	−	0.406894i	−0.809118	+	0.587646i	$0.800055\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	−4.00000			−0.323381
$154$		0			0
$155$	10.0000			0.803219
$156$	3.23205	+	1.59808i	0.258771	+	0.127948i
$157$	1.50000	−	2.59808i	0.119713	−	0.207349i	−0.799941	−	0.600079i	$-0.795136\pi$
$157$	1.50000	−	2.59808i	0.119713	−	0.207349i	0.919654	+	0.392730i	$0.128469\pi$
$158$	−12.9904	−	7.50000i	−1.03346	−	0.596668i
$159$	−7.00000	−	12.1244i	−0.555136	−	0.961524i
$160$	2.00000			0.158114
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	−0.358162	−	0.933659i	$-0.616597\pi$
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	0.629492	+	0.777007i	$0.283263\pi$
$164$	−4.33013	−	2.50000i	−0.338126	−	0.195217i
$165$	−5.00000	+	8.66025i	−0.389249	+	0.674200i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$			8.00000i			0.619059i	0.950890	+	0.309529i	$0.100171\pi$
$167$			8.00000i			0.619059i	−0.950890	+	0.309529i	$0.899829\pi$
$168$		0			0
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$	−2.00000	−	3.46410i	−0.153393	−	0.265684i
$171$	6.92820	+	4.00000i	0.529813	+	0.305888i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		0			0
$175$		0			0
$176$		−	5.00000i		−	0.376889i
$177$	−5.19615	+	3.00000i	−0.390567	+	0.225494i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	3.46410	−	2.00000i	0.258199	−	0.149071i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	13.0000			0.960988
$184$	7.79423	−	4.50000i	0.574598	−	0.331744i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$	2.50000	−	4.33013i	0.183309	−	0.317500i
$187$	−8.66025	+	5.00000i	−0.633300	+	0.365636i
$188$		−	13.0000i		−	0.948122i
$189$		0			0
$190$			8.00000i			0.580381i
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−20.7846	−	12.0000i	−1.49611	−	0.863779i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	−20.7846	−	12.0000i	−1.49611	−	0.863779i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	3.50000	+	6.06218i	0.251285	+	0.435239i
$195$	4.00000	+	6.00000i	0.286446	+	0.429669i
$196$		0			0
$197$			7.00000i			0.498729i	0.968410	+	0.249365i	$0.0802218\pi$
$197$			7.00000i			0.498729i	−0.968410	+	0.249365i	$0.919778\pi$
$198$	−5.00000	−	8.66025i	−0.355335	−	0.615457i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−2.59808	+	1.50000i	−0.183254	+	0.105802i
$202$			7.00000i			0.492518i
$203$		0			0
$204$	−2.00000			−0.140028
$205$	−5.00000	−	8.66025i	−0.349215	−	0.604858i
$206$	−3.46410	−	2.00000i	−0.241355	−	0.139347i
$207$	9.00000	−	15.5885i	0.625543	−	1.08347i
$208$	−3.23205	−	1.59808i	−0.224102	−	0.110807i
$209$	20.0000			1.38343
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	7.00000	+	12.1244i	0.480762	+	0.832704i
$213$		0			0
$214$	−1.73205	−	1.00000i	−0.118401	−	0.0683586i
$215$	6.92820	−	4.00000i	0.472500	−	0.272798i
$216$		−	5.00000i		−	0.340207i
$217$		0			0
$218$	−14.0000			−0.948200
$219$	0.866025	−	0.500000i	0.0585206	−	0.0337869i
$220$	5.00000	−	8.66025i	0.337100	−	0.583874i
$221$	0.464102	+	7.19615i	0.0312189	+	0.484066i
$222$	1.50000	+	2.59808i	0.100673	+	0.174371i
$223$		−	19.0000i		−	1.27233i	−0.771551	−	0.636167i	$-0.780519\pi$
$223$		−	19.0000i		−	1.27233i	0.771551	−	0.636167i	$-0.219481\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$	9.52628	−	5.50000i	0.633679	−	0.365855i
$227$	−15.5885	−	9.00000i	−1.03464	−	0.597351i	−0.116331	−	0.993210i	$-0.537113\pi$
$227$	−15.5885	−	9.00000i	−1.03464	−	0.597351i	−0.918311	+	0.395860i	$0.870447\pi$
$228$	3.46410	+	2.00000i	0.229416	+	0.132453i
$229$	3.46410	−	2.00000i	0.228914	−	0.132164i	−0.381157	−	0.924510i	$-0.624474\pi$
$229$	3.46410	−	2.00000i	0.228914	−	0.132164i	0.610071	+	0.792347i	$0.291141\pi$
$230$	18.0000			1.18688
$231$		0			0
$232$		0			0
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	0.680135	−	0.733087i	$-0.261921\pi$
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	−0.974939	+	0.222470i	$0.928588\pi$
$234$	−7.19615	+	0.464102i	−0.470427	+	0.0303393i
$235$	13.0000	−	22.5167i	0.848026	−	1.46882i
$236$	5.19615	−	3.00000i	0.338241	−	0.195283i
$237$	−15.0000			−0.974355
$238$		0			0
$239$		−	14.0000i		−	0.905585i	−0.891616	−	0.452792i	$-0.850428\pi$
$239$		−	14.0000i		−	0.905585i	0.891616	−	0.452792i	$-0.149572\pi$
$240$	1.73205	−	1.00000i	0.111803	−	0.0645497i
$241$	8.66025	+	5.00000i	0.557856	+	0.322078i	0.752285	−	0.658838i	$-0.228952\pi$
$241$	8.66025	+	5.00000i	0.557856	+	0.322078i	−0.194429	+	0.980917i	$0.562285\pi$
$242$	−12.1244	−	7.00000i	−0.779383	−	0.449977i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−13.0000			−0.832240
$245$		0			0
$246$	−5.00000			−0.318788
$247$	6.39230	−	12.9282i	0.406733	−	0.822602i
$248$	−2.50000	+	4.33013i	−0.158750	+	0.274963i
$249$	−5.19615	−	3.00000i	−0.329293	−	0.190117i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−17.0000			−1.07303			−0.536515	−	0.843891i	$-0.680260\pi$
$251$	−17.0000			−1.07303			−0.536515	+	0.843891i	$0.680260\pi$
$252$		0			0
$253$		−	45.0000i		−	2.82913i
$254$	−11.2583	+	6.50000i	−0.706410	+	0.407846i
$255$	−3.46410	−	2.00000i	−0.216930	−	0.125245i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.0000	−	19.0526i	−0.686161	−	1.18847i	−0.973070	−	0.230508i	$-0.925961\pi$
$257$	−11.0000	−	19.0526i	−0.686161	−	1.18847i	0.286909	−	0.957958i	$-0.407372\pi$
$258$		−	4.00000i		−	0.249029i
$259$		0			0
$260$	−4.00000	−	6.00000i	−0.248069	−	0.372104i
$261$		0			0
$262$	−10.3923	−	6.00000i	−0.642039	−	0.370681i
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	−0.921077	−	0.389380i	$-0.872689\pi$
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	0.797752	+	0.602986i	$0.206023\pi$
$264$	−2.50000	−	4.33013i	−0.153864	−	0.266501i
$265$			28.0000i			1.72003i
$266$		0			0
$267$		−	6.00000i		−	0.367194i
$268$	2.59808	−	1.50000i	0.158703	−	0.0916271i
$269$	−2.50000	+	4.33013i	−0.152428	+	0.264013i	−0.932119	−	0.362151i	$-0.882042\pi$
$269$	−2.50000	+	4.33013i	−0.152428	+	0.264013i	0.779692	+	0.626164i	$0.215376\pi$
$270$	5.00000	−	8.66025i	0.304290	−	0.527046i
$271$	−4.33013	+	2.50000i	−0.263036	+	0.151864i	−0.625719	−	0.780049i	$-0.715194\pi$
$271$	−4.33013	+	2.50000i	−0.263036	+	0.151864i	0.362682	+	0.931913i	$0.381861\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	12.0000			0.724947
$275$	−4.33013	+	2.50000i	−0.261116	+	0.150756i
$276$	4.50000	−	7.79423i	0.270868	−	0.469157i
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$		0			0
$279$			10.0000i			0.598684i
$280$		0			0
$281$			20.0000i			1.19310i	0.802576	+	0.596550i	$0.203462\pi$
$281$			20.0000i			1.19310i	−0.802576	+	0.596550i	$0.796538\pi$
$282$	−6.50000	−	11.2583i	−0.387069	−	0.670424i
$283$	−5.50000	+	9.52628i	−0.326941	+	0.566279i	−0.981903	−	0.189383i	$-0.939351\pi$
$283$	−5.50000	+	9.52628i	−0.326941	+	0.566279i	0.654962	+	0.755662i	$0.272685\pi$
$284$		0			0
$285$	4.00000	+	6.92820i	0.236940	+	0.410391i
$286$	−15.0000	+	10.0000i	−0.886969	+	0.591312i
$287$		0			0
$288$			2.00000i			0.117851i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	6.06218	+	3.50000i	0.355371	+	0.205174i
$292$	−0.866025	+	0.500000i	−0.0506803	+	0.0292603i
$293$			26.0000i			1.51894i	0.650545	+	0.759468i	$0.274541\pi$
$293$			26.0000i			1.51894i	−0.650545	+	0.759468i	$0.725459\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$	−21.6506	−	12.5000i	−1.25630	−	0.725324i
$298$	4.50000	−	7.79423i	0.260678	−	0.451508i
$299$	−29.0885	−	14.3827i	−1.68223	−	0.831772i
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	10.0000			0.575435
$303$	3.50000	+	6.06218i	0.201070	+	0.348263i
$304$	−3.46410	−	2.00000i	−0.198680	−	0.114708i
$305$	−22.5167	−	13.0000i	−1.28930	−	0.744378i
$306$	3.46410	−	2.00000i	0.198030	−	0.114332i
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$	−8.66025	+	5.00000i	−0.491869	+	0.283981i
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	0.129689	+	0.991555i	$0.458602\pi$
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	−0.923556	+	0.383464i	$0.874731\pi$
$312$	−3.59808	+	0.232051i	−0.203701	+	0.0131373i
$313$	2.00000	+	3.46410i	0.113047	+	0.195803i	0.916997	−	0.398894i	$-0.130606\pi$
$313$	2.00000	+	3.46410i	0.113047	+	0.195803i	−0.803951	+	0.594696i	$0.797272\pi$
$314$			3.00000i			0.169300i
$315$		0			0
$316$	15.0000			0.843816
$317$	23.3827	−	13.5000i	1.31330	−	0.758236i	0.330661	−	0.943750i	$-0.392728\pi$
$317$	23.3827	−	13.5000i	1.31330	−	0.758236i	0.982642	+	0.185514i	$0.0593950\pi$
$318$	12.1244	+	7.00000i	0.679900	+	0.392541i
$319$		0			0
$320$	−1.73205	+	1.00000i	−0.0968246	+	0.0559017i
$321$	−2.00000			−0.111629
$322$		0			0
$323$			8.00000i			0.445132i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	0.232051	+	3.59808i	0.0128719	+	0.199585i
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$	−12.1244	+	7.00000i	−0.670478	+	0.387101i
$328$	5.00000			0.276079
$329$		0			0
$330$		−	10.0000i		−	0.550482i
$331$	21.6506	−	12.5000i	1.19003	−	0.687062i	0.231714	−	0.972784i	$-0.425567\pi$
$331$	21.6506	−	12.5000i	1.19003	−	0.687062i	0.958313	+	0.285722i	$0.0922333\pi$
$332$	5.19615	+	3.00000i	0.285176	+	0.164646i
$333$	−5.19615	−	3.00000i	−0.284747	−	0.164399i
$334$	−4.00000	−	6.92820i	−0.218870	−	0.379094i
$335$	6.00000			0.327815
$336$		0			0
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$	1.66987	+	12.8923i	0.0908291	+	0.701249i
$339$	5.50000	−	9.52628i	0.298719	−	0.517396i
$340$	3.46410	+	2.00000i	0.187867	+	0.108465i
$341$	12.5000	+	21.6506i	0.676913	+	1.17245i
$342$	−8.00000			−0.432590
$343$		0			0
$344$			4.00000i			0.215666i
$345$	15.5885	−	9.00000i	0.839254	−	0.484544i
$346$	−12.1244	−	7.00000i	−0.651809	−	0.376322i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$		−	26.0000i		−	1.39175i	−0.718164	−	0.695874i	$-0.755017\pi$
$349$		−	26.0000i		−	1.39175i	0.718164	−	0.695874i	$-0.244983\pi$
$350$		0			0
$351$	−15.0000	+	10.0000i	−0.800641	+	0.533761i
$352$	2.50000	+	4.33013i	0.133250	+	0.230797i
$353$	−26.8468	−	15.5000i	−1.42891	−	0.824982i	−0.431875	−	0.901933i	$-0.642148\pi$
$353$	−26.8468	−	15.5000i	−1.42891	−	0.824982i	−0.997035	+	0.0769515i	$0.975481\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$		0			0
$356$			6.00000i			0.317999i
$357$		0			0
$358$		0			0
$359$	−20.7846	+	12.0000i	−1.09697	+	0.633336i	−0.935423	−	0.353529i	$-0.884981\pi$
$359$	−20.7846	+	12.0000i	−1.09697	+	0.633336i	−0.161546	+	0.986865i	$0.551648\pi$
$360$	−2.00000	+	3.46410i	−0.105409	+	0.182574i
$361$	−1.50000	+	2.59808i	−0.0789474	+	0.136741i
$362$	6.06218	−	3.50000i	0.318621	−	0.183956i
$363$	−14.0000			−0.734809
$364$		0			0
$365$	−2.00000			−0.104685
$366$	−11.2583	+	6.50000i	−0.588482	+	0.339760i
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$	−4.50000	+	7.79423i	−0.234579	+	0.406302i
$369$	8.66025	−	5.00000i	0.450835	−	0.260290i
$370$		−	6.00000i		−	0.311925i
$371$		0			0
$372$			5.00000i			0.259238i
$373$	−17.0000	−	29.4449i	−0.880227	−	1.52460i	−0.851089	−	0.525022i	$-0.824057\pi$
$373$	−17.0000	−	29.4449i	−0.880227	−	1.52460i	−0.0291379	−	0.999575i	$-0.509276\pi$
$374$	5.00000	−	8.66025i	0.258544	−	0.447811i
$375$	−10.3923	−	6.00000i	−0.536656	−	0.309839i
$376$	6.50000	+	11.2583i	0.335212	+	0.580604i
$377$		0			0
$378$		0			0
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$	−4.00000	−	6.92820i	−0.205196	−	0.355409i
$381$	−6.50000	+	11.2583i	−0.333005	+	0.576782i
$382$	−6.92820	−	4.00000i	−0.354478	−	0.204658i
$383$	0.866025	−	0.500000i	0.0442518	−	0.0255488i	−0.477711	−	0.878517i	$-0.658533\pi$
$383$	0.866025	−	0.500000i	0.0442518	−	0.0255488i	0.521963	+	0.852968i	$0.325200\pi$
$384$			1.00000i			0.0510310i
$385$		0			0
$386$	24.0000			1.22157
$387$	4.00000	+	6.92820i	0.203331	+	0.352180i
$388$	−6.06218	−	3.50000i	−0.307760	−	0.177686i
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	−0.710980	−	0.703213i	$-0.751748\pi$
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	0.964490	+	0.264120i	$0.0850816\pi$
$390$	−6.46410	−	3.19615i	−0.327323	−	0.161843i
$391$	18.0000			0.910299
$392$		0			0
$393$	−12.0000			−0.605320
$394$	−3.50000	−	6.06218i	−0.176327	−	0.305408i
$395$	25.9808	+	15.0000i	1.30723	+	0.754732i
$396$	8.66025	+	5.00000i	0.435194	+	0.251259i
$397$	−19.0526	+	11.0000i	−0.956221	+	0.552074i	−0.895008	−	0.446051i	$-0.852830\pi$
$397$	−19.0526	+	11.0000i	−0.956221	+	0.552074i	−0.0612128	+	0.998125i	$0.519497\pi$
$398$			20.0000i			1.00251i
$399$		0			0
$400$	1.00000			0.0500000
$401$	17.3205	−	10.0000i	0.864945	−	0.499376i	−0.000720188	−	1.00000i	$-0.500229\pi$
$401$	17.3205	−	10.0000i	0.864945	−	0.499376i	0.865665	+	0.500624i	$0.166896\pi$
$402$	1.50000	−	2.59808i	0.0748132	−	0.129580i
$403$	17.9904	−	1.16025i	0.896165	−	0.0577964i
$404$	−3.50000	−	6.06218i	−0.174132	−	0.301605i
$405$			2.00000i			0.0993808i
$406$		0			0
$407$	−15.0000			−0.743522
$408$	1.73205	−	1.00000i	0.0857493	−	0.0495074i
$409$	5.19615	+	3.00000i	0.256933	+	0.148340i	0.622935	−	0.782274i	$-0.285940\pi$
$409$	5.19615	+	3.00000i	0.256933	+	0.148340i	−0.366002	+	0.930614i	$0.619274\pi$
$410$	8.66025	+	5.00000i	0.427699	+	0.246932i
$411$	10.3923	−	6.00000i	0.512615	−	0.295958i
$412$	4.00000			0.197066
$413$		0			0
$414$			18.0000i			0.884652i
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	3.59808	−	0.232051i	0.176410	−	0.0113772i
$417$		0			0
$418$	−17.3205	+	10.0000i	−0.847174	+	0.489116i
$419$	−35.0000			−1.70986			−0.854931	−	0.518742i	$-0.826401\pi$
$419$	−35.0000			−1.70986			−0.854931	+	0.518742i	$0.826401\pi$
$420$		0			0
$421$		−	35.0000i		−	1.70580i	−0.522078	−	0.852898i	$-0.674843\pi$
$421$		−	35.0000i		−	1.70580i	0.522078	−	0.852898i	$-0.325157\pi$
$422$	6.92820	−	4.00000i	0.337260	−	0.194717i
$423$	22.5167	+	13.0000i	1.09480	+	0.632082i
$424$	−12.1244	−	7.00000i	−0.588811	−	0.339950i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$		0			0
$428$	2.00000			0.0966736
$429$	−7.99038	+	16.1603i	−0.385779	+	0.780224i
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$		0			0
$436$	12.1244	−	7.00000i	0.580651	−	0.335239i
$437$	−31.1769	−	18.0000i	−1.49139	−	0.861057i
$438$	−0.500000	+	0.866025i	−0.0238909	+	0.0413803i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$			10.0000i			0.476731i
$441$		0			0
$442$	−4.00000	−	6.00000i	−0.190261	−	0.285391i
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$	−2.59808	−	1.50000i	−0.123299	−	0.0711868i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	9.50000	+	16.4545i	0.449838	+	0.779142i
$447$		−	9.00000i		−	0.425685i
$448$		0			0
$449$			6.00000i			0.283158i	0.989927	+	0.141579i	$0.0452178\pi$
$449$			6.00000i			0.283158i	−0.989927	+	0.141579i	$0.954782\pi$
$450$	1.73205	−	1.00000i	0.0816497	−	0.0471405i
$451$	12.5000	−	21.6506i	0.588602	−	1.01949i
$452$	−5.50000	+	9.52628i	−0.258698	+	0.448078i
$453$	8.66025	−	5.00000i	0.406894	−	0.234920i
$454$	18.0000			0.844782
$455$		0			0
$456$	−4.00000			−0.187317
$457$	−6.92820	+	4.00000i	−0.324088	+	0.187112i	−0.653213	−	0.757174i	$-0.726579\pi$
$457$	−6.92820	+	4.00000i	−0.324088	+	0.187112i	0.329125	+	0.944286i	$0.393246\pi$
$458$	−2.00000	+	3.46410i	−0.0934539	+	0.161867i
$459$	5.00000	−	8.66025i	0.233380	−	0.404226i
$460$	−15.5885	+	9.00000i	−0.726816	+	0.419627i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$			14.0000i			0.650635i	0.945605	+	0.325318i	$0.105471\pi$
$463$			14.0000i			0.650635i	−0.945605	+	0.325318i	$0.894529\pi$
$464$		0			0
$465$	−5.00000	+	8.66025i	−0.231869	+	0.401610i
$466$	7.79423	+	4.50000i	0.361061	+	0.208458i
$467$	4.00000	+	6.92820i	0.185098	+	0.320599i	0.943610	−	0.331061i	$-0.107406\pi$
$467$	4.00000	+	6.92820i	0.185098	+	0.320599i	−0.758512	+	0.651660i	$0.774073\pi$
$468$	6.00000	−	4.00000i	0.277350	−	0.184900i
$469$		0			0
$470$			26.0000i			1.19929i
$471$	1.50000	+	2.59808i	0.0691164	+	0.119713i
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	17.3205	+	10.0000i	0.796398	+	0.459800i
$474$	12.9904	−	7.50000i	0.596668	−	0.344486i
$475$			4.00000i			0.183533i
$476$		0			0
$477$	−28.0000			−1.28203
$478$	7.00000	+	12.1244i	0.320173	+	0.554555i
$479$	−20.7846	−	12.0000i	−0.949673	−	0.548294i	−0.0566937	−	0.998392i	$-0.518056\pi$
$479$	−20.7846	−	12.0000i	−0.949673	−	0.548294i	−0.892979	+	0.450098i	$0.851389\pi$
$480$	−1.00000	+	1.73205i	−0.0456435	+	0.0790569i
$481$	−4.79423	+	9.69615i	−0.218598	+	0.442106i
$482$	−10.0000			−0.455488
$483$		0			0
$484$	14.0000			0.636364
$485$	−7.00000	−	12.1244i	−0.317854	−	0.550539i
$486$	13.8564	+	8.00000i	0.628539	+	0.362887i
$487$	24.2487	+	14.0000i	1.09881	+	0.634401i	0.935909	−	0.352241i	$-0.114580\pi$
$487$	24.2487	+	14.0000i	1.09881	+	0.634401i	0.162905	+	0.986642i	$0.447914\pi$
$488$	11.2583	−	6.50000i	0.509641	−	0.294241i
$489$			4.00000i			0.180886i
$490$		0			0
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	4.33013	−	2.50000i	0.195217	−	0.112709i
$493$		0			0
$494$	0.928203	+	14.3923i	0.0417618	+	0.647540i
$495$	10.0000	+	17.3205i	0.449467	+	0.778499i
$496$		−	5.00000i		−	0.224507i
$497$		0			0
$498$	6.00000			0.268866
$499$	9.52628	−	5.50000i	0.426455	−	0.246214i	−0.271380	−	0.962472i	$-0.587480\pi$
$499$	9.52628	−	5.50000i	0.426455	−	0.246214i	0.697835	+	0.716258i	$0.254147\pi$
$500$	10.3923	+	6.00000i	0.464758	+	0.268328i
$501$	−6.92820	−	4.00000i	−0.309529	−	0.178707i
$502$	14.7224	−	8.50000i	0.657094	−	0.379374i
$503$	−34.0000			−1.51599			−0.757993	−	0.652263i	$-0.773820\pi$
$503$	−34.0000			−1.51599			−0.757993	+	0.652263i	$0.773820\pi$
$504$		0			0
$505$		−	14.0000i		−	0.622992i
$506$	22.5000	+	38.9711i	1.00025	+	1.73248i
$507$	7.89230	+	10.3301i	0.350510	+	0.458777i
$508$	6.50000	−	11.2583i	0.288391	−	0.499508i
$509$	29.4449	−	17.0000i	1.30512	−	0.753512i	0.323843	−	0.946111i	$-0.395025\pi$
$509$	29.4449	−	17.0000i	1.30512	−	0.753512i	0.981278	+	0.192599i	$0.0616917\pi$
$510$	4.00000			0.177123
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−17.3205	+	10.0000i	−0.764719	+	0.441511i
$514$	19.0526	+	11.0000i	0.840372	+	0.485189i
$515$	6.92820	+	4.00000i	0.305293	+	0.176261i
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$	65.0000			2.85870
$518$		0			0
$519$	−14.0000			−0.614532
$520$	6.46410	+	3.19615i	0.283470	+	0.140161i
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	0.377320	+	0.926083i	$0.376846\pi$
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	−0.990671	+	0.136272i	$0.956488\pi$
$522$		0			0
$523$	−10.5000	−	18.1865i	−0.459133	−	0.795242i	0.539782	−	0.841805i	$-0.318507\pi$
$523$	−10.5000	−	18.1865i	−0.459133	−	0.795242i	−0.998915	+	0.0465630i	$0.985173\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$		−	4.00000i		−	0.174408i
$527$	−8.66025	+	5.00000i	−0.377247	+	0.217803i
$528$	4.33013	+	2.50000i	0.188445	+	0.108799i
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$	−14.0000	−	24.2487i	−0.608121	−	1.05330i
$531$			12.0000i			0.520756i
$532$		0			0
$533$	−10.0000	−	15.0000i	−0.433148	−	0.649722i
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$	3.46410	+	2.00000i	0.149766	+	0.0864675i
$536$	−1.50000	+	2.59808i	−0.0647901	+	0.112220i
$537$		0			0
$538$		−	5.00000i		−	0.215565i
$539$		0			0
$540$			10.0000i			0.430331i
$541$	−8.66025	+	5.00000i	−0.372333	+	0.214967i	−0.674477	−	0.738296i	$-0.735631\pi$
$541$	−8.66025	+	5.00000i	−0.372333	+	0.214967i	0.302144	+	0.953262i	$0.402298\pi$
$542$	2.50000	−	4.33013i	0.107384	−	0.185995i
$543$	3.50000	−	6.06218i	0.150199	−	0.260153i
$544$	−1.73205	+	1.00000i	−0.0742611	+	0.0428746i
$545$	28.0000			1.19939
$546$		0			0
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$	−10.3923	+	6.00000i	−0.443937	+	0.256307i
$549$	13.0000	−	22.5167i	0.554826	−	0.960988i
$550$	2.50000	−	4.33013i	0.106600	−	0.184637i
$551$		0			0
$552$			9.00000i			0.383065i
$553$		0			0
$554$			2.00000i			0.0849719i
$555$	−3.00000	−	5.19615i	−0.127343	−	0.220564i
$556$		0			0
$557$	−32.0429	−	18.5000i	−1.35770	−	0.783870i	−0.368389	−	0.929672i	$-0.620091\pi$
$557$	−32.0429	−	18.5000i	−1.35770	−	0.783870i	−0.989314	+	0.145802i	$0.953424\pi$
$558$	−5.00000	−	8.66025i	−0.211667	−	0.366618i
$559$	12.0000	−	8.00000i	0.507546	−	0.338364i
$560$		0			0
$561$		−	10.0000i		−	0.422200i
$562$	−10.0000	−	17.3205i	−0.421825	−	0.730622i
$563$	−15.5000	+	26.8468i	−0.653247	+	1.13146i	0.329083	+	0.944301i	$0.393260\pi$
$563$	−15.5000	+	26.8468i	−0.653247	+	1.13146i	−0.982330	+	0.187156i	$0.940073\pi$
$564$	11.2583	+	6.50000i	0.474061	+	0.273699i
$565$	−19.0526	+	11.0000i	−0.801547	+	0.462773i
$566$		−	11.0000i		−	0.462364i
$567$		0			0
$568$		0			0
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$	−6.92820	−	4.00000i	−0.290191	−	0.167542i
$571$	−1.00000	+	1.73205i	−0.0418487	+	0.0724841i	−0.886191	−	0.463320i	$-0.846658\pi$
$571$	−1.00000	+	1.73205i	−0.0418487	+	0.0724841i	0.844342	+	0.535804i	$0.179991\pi$
$572$	7.99038	−	16.1603i	0.334095	−	0.675694i
$573$	−8.00000			−0.334205
$574$		0			0
$575$	9.00000			0.375326
$576$	−1.00000	−	1.73205i	−0.0416667	−	0.0721688i
$577$	36.3731	+	21.0000i	1.51423	+	0.874241i	0.999861	+	0.0166728i	$0.00530737\pi$
$577$	36.3731	+	21.0000i	1.51423	+	0.874241i	0.514370	+	0.857569i	$0.328026\pi$
$578$	−11.2583	−	6.50000i	−0.468285	−	0.270364i
$579$	20.7846	−	12.0000i	0.863779	−	0.498703i
$580$		0			0
$581$		0			0
$582$	−7.00000			−0.290159
$583$	−60.6218	+	35.0000i	−2.51070	+	1.44955i
$584$	0.500000	−	0.866025i	0.0206901	−	0.0358364i
$585$	14.3923	−	0.928203i	0.595049	−	0.0383765i
$586$	−13.0000	−	22.5167i	−0.537025	−	0.930155i
$587$		−	2.00000i		−	0.0825488i	−0.999148	−	0.0412744i	$-0.986858\pi$
$587$		−	2.00000i		−	0.0825488i	0.999148	−	0.0412744i	$-0.0131418\pi$
$588$		0			0
$589$	20.0000			0.824086
$590$	−10.3923	+	6.00000i	−0.427844	+	0.247016i
$591$	−6.06218	−	3.50000i	−0.249365	−	0.143971i
$592$	2.59808	+	1.50000i	0.106780	+	0.0616496i
$593$	−12.1244	+	7.00000i	−0.497888	+	0.287456i	−0.727841	−	0.685746i	$-0.759476\pi$
$593$	−12.1244	+	7.00000i	−0.497888	+	0.287456i	0.229953	+	0.973202i	$0.426143\pi$
$594$	25.0000			1.02576
$595$		0			0
$596$			9.00000i			0.368654i
$597$	10.0000	+	17.3205i	0.409273	+	0.708881i
$598$	32.3827	−	2.08846i	1.32423	−	0.0854034i
$599$	7.50000	−	12.9904i	0.306442	−	0.530773i	−0.671140	−	0.741331i	$-0.734195\pi$
$599$	7.50000	−	12.9904i	0.306442	−	0.530773i	0.977581	+	0.210558i	$0.0675282\pi$
$600$	0.866025	−	0.500000i	0.0353553	−	0.0204124i
$601$	28.0000			1.14214			0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000			1.14214			0.571072	+	0.820900i	$0.306528\pi$
$602$		0			0
$603$			6.00000i			0.244339i
$604$	−8.66025	+	5.00000i	−0.352381	+	0.203447i
$605$	24.2487	+	14.0000i	0.985850	+	0.569181i
$606$	−6.06218	−	3.50000i	−0.246259	−	0.142178i
$607$	−1.00000	−	1.73205i	−0.0405887	−	0.0703018i	0.845017	−	0.534739i	$-0.179590\pi$
$607$	−1.00000	−	1.73205i	−0.0405887	−	0.0703018i	−0.885606	+	0.464437i	$0.846257\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$	26.0000			1.05271
$611$	20.7750	−	42.0167i	0.840466	−	1.69981i
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	9.52628	+	5.50000i	0.384763	+	0.222143i	0.679888	−	0.733316i	$-0.262028\pi$
$613$	9.52628	+	5.50000i	0.384763	+	0.222143i	−0.295126	+	0.955458i	$0.595362\pi$
$614$	11.0000	+	19.0526i	0.443924	+	0.768899i
$615$	10.0000			0.403239
$616$		0			0
$617$			32.0000i			1.28827i	0.764911	+	0.644136i	$0.222783\pi$
$617$			32.0000i			1.28827i	−0.764911	+	0.644136i	$0.777217\pi$
$618$	3.46410	−	2.00000i	0.139347	−	0.0804518i
$619$	−20.7846	−	12.0000i	−0.835404	−	0.482321i	0.0202954	−	0.999794i	$-0.493539\pi$
$619$	−20.7846	−	12.0000i	−0.835404	−	0.482321i	−0.855699	+	0.517473i	$0.826873\pi$
$620$	5.00000	−	8.66025i	0.200805	−	0.347804i
$621$	22.5000	+	38.9711i	0.902894	+	1.56386i
$622$		−	28.0000i		−	1.12270i
$623$		0			0
$624$	3.00000	−	2.00000i	0.120096	−	0.0800641i
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−3.46410	−	2.00000i	−0.138453	−	0.0799361i
$627$	−10.0000	+	17.3205i	−0.399362	+	0.691714i
$628$	−1.50000	−	2.59808i	−0.0598565	−	0.103675i
$629$		−	6.00000i		−	0.239236i
$630$		0			0
$631$		−	40.0000i		−	1.59237i	−0.605050	−	0.796187i	$-0.706847\pi$
$631$		−	40.0000i		−	1.59237i	0.605050	−	0.796187i	$-0.293153\pi$
$632$	−12.9904	+	7.50000i	−0.516730	+	0.298334i
$633$	4.00000	−	6.92820i	0.158986	−	0.275371i
$634$	−13.5000	+	23.3827i	−0.536153	+	0.928645i
$635$	22.5167	−	13.0000i	0.893546	−	0.515889i
$636$	−14.0000			−0.555136
$637$		0			0
$638$		0			0
$639$		0			0
$640$	1.00000	−	1.73205i	0.0395285	−	0.0684653i
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	0.225876	+	0.974156i	$0.427476\pi$
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	−0.956582	+	0.291464i	$0.905858\pi$
$642$	1.73205	−	1.00000i	0.0683586	−	0.0394669i
$643$		−	14.0000i		−	0.552106i	−0.961142	−	0.276053i	$-0.910973\pi$
$643$		−	14.0000i		−	0.552106i	0.961142	−	0.276053i	$-0.0890266\pi$
$644$		0			0
$645$			8.00000i			0.315000i
$646$	−4.00000	−	6.92820i	−0.157378	−	0.272587i
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	−0.633090	−	0.774078i	$-0.718214\pi$
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	0.986916	+	0.161233i	$0.0515470\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	15.0000	+	25.9808i	0.588802	+	1.01983i
$650$	−2.00000	−	3.00000i	−0.0784465	−	0.117670i
$651$		0			0
$652$		−	4.00000i		−	0.156652i
$653$	8.00000	+	13.8564i	0.313064	+	0.542243i	0.979024	−	0.203744i	$-0.0653112\pi$
$653$	8.00000	+	13.8564i	0.313064	+	0.542243i	−0.665960	+	0.745988i	$0.731978\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$	20.7846	+	12.0000i	0.812122	+	0.468879i
$656$	−4.33013	+	2.50000i	−0.169063	+	0.0976086i
$657$		−	2.00000i		−	0.0780274i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	5.00000	+	8.66025i	0.194625	+	0.337100i
$661$	−34.6410	−	20.0000i	−1.34738	−	0.777910i	−0.359502	−	0.933144i	$-0.617053\pi$
$661$	−34.6410	−	20.0000i	−1.34738	−	0.777910i	−0.987878	+	0.155235i	$0.950387\pi$
$662$	−12.5000	+	21.6506i	−0.485826	+	0.841476i
$663$	−6.46410	−	3.19615i	−0.251045	−	0.124128i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	6.00000			0.232495
$667$		0			0
$668$	6.92820	+	4.00000i	0.268060	+	0.154765i
$669$	16.4545	+	9.50000i	0.636167	+	0.367291i
$670$	−5.19615	+	3.00000i	−0.200745	+	0.115900i
$671$		−	65.0000i		−	2.50930i
$672$		0			0
$673$	−31.0000			−1.19496			−0.597481	−	0.801883i	$-0.703832\pi$
$673$	−31.0000			−1.19496			−0.597481	+	0.801883i	$0.703832\pi$
$674$	−19.9186	+	11.5000i	−0.767235	+	0.442963i
$675$	2.50000	−	4.33013i	0.0962250	−	0.166667i
$676$	−7.89230	−	10.3301i	−0.303550	−	0.397313i
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	0.790897	−	0.611950i	$-0.209615\pi$
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	−0.925412	+	0.378962i	$0.876281\pi$
$678$			11.0000i			0.422452i
$679$		0			0
$680$	−4.00000			−0.153393
$681$	15.5885	−	9.00000i	0.597351	−	0.344881i
$682$	−21.6506	−	12.5000i	−0.829046	−	0.478650i
$683$	35.5070	+	20.5000i	1.35864	+	0.784411i	0.989440	−	0.144940i	$-0.0462988\pi$
$683$	35.5070	+	20.5000i	1.35864	+	0.784411i	0.369199	+	0.929350i	$0.379632\pi$
$684$	6.92820	−	4.00000i	0.264906	−	0.152944i
$685$	−24.0000			−0.916993
$686$		0			0
$687$			4.00000i			0.152610i
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	3.24871	+	50.3731i	0.123766	+	1.91906i
$690$	−9.00000	+	15.5885i	−0.342624	+	0.593442i
$691$	8.66025	−	5.00000i	0.329452	−	0.190209i	−0.326146	−	0.945319i	$-0.605750\pi$
$691$	8.66025	−	5.00000i	0.329452	−	0.190209i	0.655598	+	0.755110i	$0.272417\pi$
$692$	14.0000			0.532200
$693$		0			0
$694$			12.0000i			0.455514i
$695$		0			0
$696$		0			0
$697$	8.66025	+	5.00000i	0.328031	+	0.189389i
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$	9.00000			0.340411
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	7.99038	−	16.1603i	0.301577	−	0.609929i
$703$	−6.00000	+	10.3923i	−0.226294	+	0.391953i
$704$	−4.33013	−	2.50000i	−0.163198	−	0.0942223i
$705$	13.0000	+	22.5167i	0.489608	+	0.848026i
$706$	31.0000			1.16670
$707$		0			0
$708$			6.00000i			0.225494i
$709$	26.8468	−	15.5000i	1.00825	−	0.582115i	0.0975728	−	0.995228i	$-0.468892\pi$
$709$	26.8468	−	15.5000i	1.00825	−	0.582115i	0.910679	+	0.413114i	$0.135559\pi$
$710$		0			0
$711$	−15.0000	+	25.9808i	−0.562544	+	0.974355i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$		−	45.0000i		−	1.68526i
$714$		0			0
$715$	30.0000	−	20.0000i	1.12194	−	0.747958i
$716$		0			0
$717$	12.1244	+	7.00000i	0.452792	+	0.261420i
$718$	12.0000	−	20.7846i	0.447836	−	0.775675i
$719$	20.0000	+	34.6410i	0.745874	+	1.29189i	0.949785	+	0.312903i	$0.101301\pi$
$719$	20.0000	+	34.6410i	0.745874	+	1.29189i	−0.203911	+	0.978989i	$0.565365\pi$
$720$		−	4.00000i		−	0.149071i
$721$		0			0
$722$		−	3.00000i		−	0.111648i
$723$	−8.66025	+	5.00000i	−0.322078	+	0.185952i
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$		0			0
$726$	12.1244	−	7.00000i	0.449977	−	0.259794i
$727$	−38.0000			−1.40934			−0.704671	−	0.709534i	$-0.748905\pi$
$727$	−38.0000			−1.40934			−0.704671	+	0.709534i	$0.748905\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	1.73205	−	1.00000i	0.0641061	−	0.0370117i
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$	6.50000	−	11.2583i	0.240247	−	0.416120i
$733$	−38.1051	+	22.0000i	−1.40744	+	0.812589i	−0.995141	−	0.0984580i	$-0.968609\pi$
$733$	−38.1051	+	22.0000i	−1.40744	+	0.812589i	−0.412303	+	0.911047i	$0.635276\pi$
$734$			28.0000i			1.03350i
$735$		0			0
$736$		−	9.00000i		−	0.331744i
$737$	7.50000	+	12.9904i	0.276266	+	0.478507i
$738$	−5.00000	+	8.66025i	−0.184053	+	0.318788i
$739$	3.46410	+	2.00000i	0.127429	+	0.0735712i	0.562360	−	0.826893i	$-0.309894\pi$
$739$	3.46410	+	2.00000i	0.127429	+	0.0735712i	−0.434930	+	0.900464i	$0.643227\pi$
$740$	3.00000	+	5.19615i	0.110282	+	0.191014i
$741$	8.00000	+	12.0000i	0.293887	+	0.440831i
$742$		0			0
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$	−2.50000	−	4.33013i	−0.0916544	−	0.158750i
$745$	−9.00000	+	15.5885i	−0.329734	+	0.571117i
$746$	29.4449	+	17.0000i	1.07805	+	0.622414i
$747$	−10.3923	+	6.00000i	−0.380235	+	0.219529i
$748$			10.0000i			0.365636i
$749$		0			0
$750$	12.0000			0.438178
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	0.929270	+	0.369402i	$0.120437\pi$
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	−0.144724	+	0.989472i	$0.546229\pi$
$752$	−11.2583	−	6.50000i	−0.410549	−	0.237031i
$753$	8.50000	−	14.7224i	0.309757	−	0.536515i
$754$		0			0
$755$	−20.0000			−0.727875
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$	38.9711	+	22.5000i	1.41456	+	0.816698i
$760$	6.92820	+	4.00000i	0.251312	+	0.145095i
$761$	−12.9904	+	7.50000i	−0.470901	+	0.271875i	−0.716617	−	0.697467i	$-0.754310\pi$
$761$	−12.9904	+	7.50000i	−0.470901	+	0.271875i	0.245716	+	0.969342i	$0.420977\pi$
$762$		−	13.0000i		−	0.470940i
$763$		0			0
$764$	8.00000			0.289430
$765$	−6.92820	+	4.00000i	−0.250490	+	0.144620i
$766$	−0.500000	+	0.866025i	−0.0180657	+	0.0312908i
$767$	21.5885	−	1.39230i	0.779514	−	0.0502732i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	1.00000i		−	0.0360609i	−0.999837	−	0.0180305i	$-0.994260\pi$
$769$		−	1.00000i		−	0.0360609i	0.999837	−	0.0180305i	$-0.00573959\pi$
$770$		0			0
$771$	22.0000			0.792311
$772$	−20.7846	+	12.0000i	−0.748054	+	0.431889i
$773$	29.4449	+	17.0000i	1.05906	+	0.611448i	0.925172	−	0.379549i	$-0.123921\pi$
$773$	29.4449	+	17.0000i	1.05906	+	0.611448i	0.133887	+	0.990997i	$0.457254\pi$
$774$	−6.92820	−	4.00000i	−0.249029	−	0.143777i
$775$	−4.33013	+	2.50000i	−0.155543	+	0.0898027i
$776$	7.00000			0.251285
$777$		0			0
$778$			10.0000i			0.358517i
$779$	−10.0000	−	17.3205i	−0.358287	−	0.620572i
$780$	7.19615	−	0.464102i	0.257664	−	0.0166175i
$781$		0			0
$782$	−15.5885	+	9.00000i	−0.557442	+	0.321839i
$783$		0			0
$784$		0			0
$785$		−	6.00000i		−	0.214149i
$786$	10.3923	−	6.00000i	0.370681	−	0.214013i
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	0.00110111	−	0.999999i	$-0.499650\pi$
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	−0.865474	+	0.500953i	$0.832983\pi$
$788$	6.06218	+	3.50000i	0.215956	+	0.124682i
$789$	−2.00000	−	3.46410i	−0.0712019	−	0.123325i
$790$	−30.0000			−1.06735
$791$		0			0
$792$	−10.0000			−0.355335
$793$	−42.0167	−	20.7750i	−1.49206	−	0.737742i
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$	−24.2487	−	14.0000i	−0.860013	−	0.496529i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	37.0000			1.31061			0.655304	−	0.755366i	$-0.272541\pi$
$797$	37.0000			1.31061			0.655304	+	0.755366i	$0.272541\pi$
$798$		0			0
$799$			26.0000i			0.919814i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−10.3923	−	6.00000i	−0.367194	−	0.212000i
$802$	−10.0000	+	17.3205i	−0.353112	+	0.611608i
$803$	−2.50000	−	4.33013i	−0.0882231	−	0.152807i
$804$			3.00000i			0.105802i
$805$		0			0
$806$	−15.0000	+	10.0000i	−0.528352	+	0.352235i
$807$	−2.50000	−	4.33013i	−0.0880042	−	0.152428i
$808$	6.06218	+	3.50000i	0.213267	+	0.123130i
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	−0.764644	−	0.644453i	$-0.777085\pi$
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	0.940435	+	0.339975i	$0.110418\pi$
$810$	−1.00000	−	1.73205i	−0.0351364	−	0.0608581i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$		−	5.00000i		−	0.175358i
$814$	12.9904	−	7.50000i	0.455313	−	0.262875i
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$	−1.00000	+	1.73205i	−0.0350070	+	0.0606339i
$817$	13.8564	−	8.00000i	0.484774	−	0.279885i
$818$	−6.00000			−0.209785
$819$		0			0
$820$	−10.0000			−0.349215
$821$	25.9808	−	15.0000i	0.906735	−	0.523504i	0.0273557	−	0.999626i	$-0.491291\pi$
$821$	25.9808	−	15.0000i	0.906735	−	0.523504i	0.879379	+	0.476122i	$0.157958\pi$
$822$	−6.00000	+	10.3923i	−0.209274	+	0.362473i
$823$	5.50000	−	9.52628i	0.191718	−	0.332065i	−0.754102	−	0.656758i	$-0.771927\pi$
$823$	5.50000	−	9.52628i	0.191718	−	0.332065i	0.945820	+	0.324692i	$0.105261\pi$
$824$	−3.46410	+	2.00000i	−0.120678	+	0.0696733i
$825$		−	5.00000i		−	0.174078i
$826$		0			0
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	−9.00000	−	15.5885i	−0.312772	−	0.541736i
$829$	5.00000	−	8.66025i	0.173657	−	0.300783i	−0.766039	−	0.642795i	$-0.777775\pi$
$829$	5.00000	−	8.66025i	0.173657	−	0.300783i	0.939696	+	0.342012i	$0.111108\pi$
$830$	−10.3923	−	6.00000i	−0.360722	−	0.208263i
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$	−3.00000	+	2.00000i	−0.104006	+	0.0693375i
$833$		0			0
$834$		0			0
$835$	8.00000	+	13.8564i	0.276851	+	0.479521i
$836$	10.0000	−	17.3205i	0.345857	−	0.599042i
$837$	−21.6506	−	12.5000i	−0.748355	−	0.432063i
$838$	30.3109	−	17.5000i	1.04707	−	0.604527i
$839$		−	1.00000i		−	0.0345238i	−0.999851	−	0.0172619i	$-0.994505\pi$
$839$		−	1.00000i		−	0.0345238i	0.999851	−	0.0172619i	$-0.00549491\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	17.5000	+	30.3109i	0.603090	+	1.04458i
$843$	−17.3205	−	10.0000i	−0.596550	−	0.344418i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	−3.33975	−	25.7846i	−0.114891	−	0.887018i
$846$	−26.0000			−0.893898
$847$		0			0
$848$	14.0000			0.480762
$849$	−5.50000	−	9.52628i	−0.188760	−	0.326941i
$850$	1.73205	+	1.00000i	0.0594089	+	0.0342997i
$851$	23.3827	+	13.5000i	0.801548	+	0.462774i
$852$		0			0
$853$			56.0000i			1.91740i	0.284413	+	0.958702i	$0.408201\pi$
$853$			56.0000i			1.91740i	−0.284413	+	0.958702i	$0.591799\pi$
$854$		0			0
$855$	16.0000			0.547188
$856$	−1.73205	+	1.00000i	−0.0592003	+	0.0341793i
$857$	4.00000	−	6.92820i	0.136637	−	0.236663i	−0.789584	−	0.613642i	$-0.789704\pi$
$857$	4.00000	−	6.92820i	0.136637	−	0.236663i	0.926222	+	0.376979i	$0.123037\pi$
$858$	−1.16025	−	17.9904i	−0.0396104	−	0.614181i
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	−0.993248	−	0.116011i	$-0.962989\pi$
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	0.396156	−	0.918183i	$-0.370344\pi$
$860$		−	8.00000i		−	0.272798i
$861$		0			0
$862$		0			0
$863$	−5.19615	+	3.00000i	−0.176879	+	0.102121i	−0.585826	−	0.810437i	$-0.699230\pi$
$863$	−5.19615	+	3.00000i	−0.176879	+	0.102121i	0.408946	+	0.912558i	$0.365896\pi$
$864$	−4.33013	−	2.50000i	−0.147314	−	0.0850517i
$865$	24.2487	+	14.0000i	0.824481	+	0.476014i
$866$	29.4449	−	17.0000i	1.00058	−	0.577684i
$867$	−13.0000			−0.441503
$868$		0			0
$869$			75.0000i			2.54420i
$870$		0			0
$871$	10.7942	−	0.696152i	0.365748	−	0.0235882i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$	12.1244	−	7.00000i	0.410347	−	0.236914i
$874$	36.0000			1.21772
$875$		0			0
$876$		−	1.00000i		−	0.0337869i
$877$	14.7224	−	8.50000i	0.497141	−	0.287025i	−0.230391	−	0.973098i	$-0.574001\pi$
$877$	14.7224	−	8.50000i	0.497141	−	0.287025i	0.727532	+	0.686074i	$0.240667\pi$
$878$		0			0
$879$	−22.5167	−	13.0000i	−0.759468	−	0.438479i
$880$	−5.00000	−	8.66025i	−0.168550	−	0.291937i
$881$	8.00000			0.269527			0.134763	−	0.990878i	$-0.456973\pi$
$881$	8.00000			0.269527			0.134763	+	0.990878i	$0.456973\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	6.46410	+	3.19615i	0.217411	+	0.107498i
$885$	−6.00000	+	10.3923i	−0.201688	+	0.349334i
$886$	20.7846	+	12.0000i	0.698273	+	0.403148i
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$	3.00000			0.100673
$889$		0			0
$890$		−	12.0000i		−	0.402241i
$891$	−4.33013	+	2.50000i	−0.145065	+	0.0837532i
$892$	−16.4545	−	9.50000i	−0.550937	−	0.318084i
$893$	26.0000	−	45.0333i	0.870057	−	1.50698i
$894$	4.50000	+	7.79423i	0.150503	+	0.260678i
$895$		0			0
$896$		0			0
$897$	27.0000	−	18.0000i	0.901504	−	0.601003i
$898$	−3.00000	−	5.19615i	−0.100111	−	0.173398i
$899$		0			0
$900$	−1.00000	+	1.73205i	−0.0333333	+	0.0577350i
$901$	−14.0000	−	24.2487i	−0.466408	−	0.807842i
$902$			25.0000i			0.832409i
$903$		0			0
$904$		−	11.0000i		−	0.365855i
$905$	−12.1244	+	7.00000i	−0.403027	+	0.232688i
$906$	−5.00000	+	8.66025i	−0.166114	+	0.287718i
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$	−15.5885	+	9.00000i	−0.517321	+	0.298675i
$909$	14.0000			0.464351
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$	3.46410	−	2.00000i	0.114708	−	0.0662266i
$913$	−15.0000	+	25.9808i	−0.496428	+	0.859838i
$914$	4.00000	−	6.92820i	0.132308	−	0.229165i
$915$	22.5167	−	13.0000i	0.744378	−	0.429767i
$916$		−	4.00000i		−	0.132164i
$917$		0			0
$918$			10.0000i			0.330049i
$919$	17.5000	+	30.3109i	0.577272	+	0.999864i	0.995791	+	0.0916559i	$0.0292160\pi$
$919$	17.5000	+	30.3109i	0.577272	+	0.999864i	−0.418519	+	0.908208i	$0.637451\pi$
$920$	9.00000	−	15.5885i	0.296721	−	0.513936i
$921$	19.0526	+	11.0000i	0.627803	+	0.362462i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		−	3.00000i		−	0.0986394i
$926$	−7.00000	−	12.1244i	−0.230034	−	0.398431i
$927$	−4.00000	+	6.92820i	−0.131377	+	0.227552i
$928$		0			0
$929$	−0.866025	+	0.500000i	−0.0284134	+	0.0164045i	−0.514139	−	0.857707i	$-0.671889\pi$
$929$	−0.866025	+	0.500000i	−0.0284134	+	0.0164045i	0.485726	+	0.874111i	$0.338555\pi$
$930$		−	10.0000i		−	0.327913i
$931$		0			0
$932$	−9.00000			−0.294805
$933$	−14.0000	−	24.2487i	−0.458339	−	0.793867i
$934$	−6.92820	−	4.00000i	−0.226698	−	0.130884i
$935$	−10.0000	+	17.3205i	−0.327035	+	0.566441i
$936$	−3.19615	+	6.46410i	−0.104470	+	0.211286i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$	−4.00000			−0.130535
$940$	−13.0000	−	22.5167i	−0.424013	−	0.734412i
$941$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$941$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$942$	−2.59808	−	1.50000i	−0.0846499	−	0.0488726i
$943$	−38.9711	+	22.5000i	−1.26908	+	0.732701i
$944$		−	6.00000i		−	0.195283i
$945$		0			0
$946$	−20.0000			−0.650256
$947$	−6.92820	+	4.00000i	−0.225136	+	0.129983i	−0.608326	−	0.793687i	$-0.708159\pi$
$947$	−6.92820	+	4.00000i	−0.225136	+	0.129983i	0.383190	+	0.923670i	$0.374825\pi$
$948$	−7.50000	+	12.9904i	−0.243589	+	0.421908i
$949$	−3.59808	+	0.232051i	−0.116798	+	0.00753269i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$			27.0000i			0.875535i
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	24.2487	−	14.0000i	0.785081	−	0.453267i
$955$	13.8564	+	8.00000i	0.448383	+	0.258874i
$956$	−12.1244	−	7.00000i	−0.392130	−	0.226396i
$957$		0			0
$958$	24.0000			0.775405
$959$		0			0
$960$		−	2.00000i		−	0.0645497i
$961$	−3.00000	−	5.19615i	−0.0967742	−	0.167618i
$962$	−0.696152	−	10.7942i	−0.0224449	−	0.348020i
$963$	−2.00000	+	3.46410i	−0.0644491	+	0.111629i
$964$	8.66025	−	5.00000i	0.278928	−	0.161039i
$965$	−48.0000			−1.54517
$966$		0			0
$967$		−	48.0000i		−	1.54358i	−0.635880	−	0.771788i	$-0.719363\pi$
$967$		−	48.0000i		−	1.54358i	0.635880	−	0.771788i	$-0.280637\pi$
$968$	−12.1244	+	7.00000i	−0.389692	+	0.224989i
$969$	−6.92820	−	4.00000i	−0.222566	−	0.128499i
$970$	12.1244	+	7.00000i	0.389290	+	0.224756i
$971$	−21.5000	−	37.2391i	−0.689968	−	1.19506i	−0.971848	−	0.235610i	$-0.924291\pi$
$971$	−21.5000	−	37.2391i	−0.689968	−	1.19506i	0.281880	−	0.959450i	$-0.409042\pi$
$972$	−16.0000			−0.513200
$973$		0			0
$974$	−28.0000			−0.897178
$975$	−3.23205	−	1.59808i	−0.103508	−	0.0511794i
$976$	−6.50000	+	11.2583i	−0.208060	+	0.360370i
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	0.728184	−	0.685381i	$-0.240364\pi$
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	−0.229465	+	0.973317i	$0.573698\pi$
$978$	−2.00000	−	3.46410i	−0.0639529	−	0.110770i
$979$	−30.0000			−0.958804
$980$		0			0
$981$			28.0000i			0.893971i
$982$	15.5885	−	9.00000i	0.497448	−	0.287202i
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.0878058	−	0.996138i	$-0.527985\pi$
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.906583	+	0.422027i	$0.861319\pi$
$984$	−2.50000	+	4.33013i	−0.0796971	+	0.138039i
$985$	7.00000	+	12.1244i	0.223039	+	0.386314i
$986$		0			0
$987$		0			0
$988$	−8.00000	−	12.0000i	−0.254514	−	0.381771i
$989$	−18.0000	−	31.1769i	−0.572367	−	0.991368i
$990$	−17.3205	−	10.0000i	−0.550482	−	0.317821i
$991$	1.50000	−	2.59808i	0.0476491	−	0.0825306i	−0.841217	−	0.540697i	$-0.818160\pi$
$991$	1.50000	−	2.59808i	0.0476491	−	0.0825306i	0.888866	+	0.458167i	$0.151494\pi$
$992$	2.50000	+	4.33013i	0.0793751	+	0.137482i
$993$			25.0000i			0.793351i
$994$		0			0
$995$		−	40.0000i		−	1.26809i
$996$	−5.19615	+	3.00000i	−0.164646	+	0.0950586i
$997$	−8.50000	+	14.7224i	−0.269198	+	0.466264i	−0.968655	−	0.248410i	$-0.920092\pi$
$997$	−8.50000	+	14.7224i	−0.269198	+	0.466264i	0.699457	+	0.714675i	$0.253425\pi$
$998$	−5.50000	+	9.52628i	−0.174099	+	0.301549i
$999$	12.9904	−	7.50000i	0.410997	−	0.237289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.n.b.753.1		4
7.2	even	3	inner	1274.2.n.b.961.2		4
7.3	odd	6		182.2.d.a.155.1	✓	2
7.4	even	3		1274.2.d.d.883.1		2
7.5	odd	6		1274.2.n.e.961.2		4
7.6	odd	2		1274.2.n.e.753.1		4
13.12	even	2	inner	1274.2.n.b.753.2		4
21.17	even	6		1638.2.c.a.883.2		2
28.3	even	6		1456.2.k.a.337.1		2
91.12	odd	6		1274.2.n.e.961.1		4
91.25	even	6		1274.2.d.d.883.2		2
91.31	even	12		2366.2.a.c.1.1		1
91.38	odd	6		182.2.d.a.155.2	yes	2
91.51	even	6	inner	1274.2.n.b.961.1		4
91.73	even	12		2366.2.a.l.1.1		1
91.90	odd	2		1274.2.n.e.753.2		4
273.38	even	6		1638.2.c.a.883.1		2
364.311	even	6		1456.2.k.a.337.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.d.a.155.1	✓	2	7.3	odd	6
182.2.d.a.155.2	yes	2	91.38	odd	6
1274.2.d.d.883.1		2	7.4	even	3
1274.2.d.d.883.2		2	91.25	even	6
1274.2.n.b.753.1		4	1.1	even	1	trivial
1274.2.n.b.753.2		4	13.12	even	2	inner
1274.2.n.b.961.1		4	91.51	even	6	inner
1274.2.n.b.961.2		4	7.2	even	3	inner
1274.2.n.e.753.1		4	7.6	odd	2
1274.2.n.e.753.2		4	91.90	odd	2
1274.2.n.e.961.1		4	91.12	odd	6
1274.2.n.e.961.2		4	7.5	odd	6
1456.2.k.a.337.1		2	28.3	even	6
1456.2.k.a.337.2		2	364.311	even	6
1638.2.c.a.883.1		2	273.38	even	6
1638.2.c.a.883.2		2	21.17	even	6
2366.2.a.c.1.1		1	91.31	even	12
2366.2.a.l.1.1		1	91.73	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.73205 - 1.00000i) q^{5} -1.00000i q^{6} +1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(4.33013 + 2.50000i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.00000 - 2.00000i) q^{13} +2.00000i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.73205 - 1.00000i) q^{18} +(3.46410 - 2.00000i) q^{19} -2.00000i q^{20} -5.00000 q^{22} +(-4.50000 - 7.79423i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.59808 + 3.23205i) q^{26} -5.00000 q^{27} +(-1.00000 - 1.73205i) q^{30} +(4.33013 + 2.50000i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.33013 + 2.50000i) q^{33} -2.00000i q^{34} +2.00000 q^{36} +(-2.59808 + 1.50000i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(0.232051 + 3.59808i) q^{39} +(1.00000 + 1.73205i) q^{40} -5.00000i q^{41} +4.00000 q^{43} +(4.33013 - 2.50000i) q^{44} +(3.46410 + 2.00000i) q^{45} +(7.79423 + 4.50000i) q^{46} +(11.2583 - 6.50000i) q^{47} +1.00000 q^{48} -1.00000i q^{50} +(-1.00000 - 1.73205i) q^{51} +(-0.232051 - 3.59808i) q^{52} +(-7.00000 + 12.1244i) q^{53} +(4.33013 - 2.50000i) q^{54} +10.0000 q^{55} +4.00000i q^{57} +(5.19615 + 3.00000i) q^{59} +(1.73205 + 1.00000i) q^{60} +(-6.50000 - 11.2583i) q^{61} -5.00000 q^{62} -1.00000 q^{64} +(3.19615 - 6.46410i) q^{65} +(2.50000 - 4.33013i) q^{66} +(2.59808 + 1.50000i) q^{67} +(1.00000 + 1.73205i) q^{68} +9.00000 q^{69} +(-1.73205 + 1.00000i) q^{72} +(-0.866025 - 0.500000i) q^{73} +(1.50000 - 2.59808i) q^{74} +(-0.500000 - 0.866025i) q^{75} -4.00000i q^{76} +(-2.00000 - 3.00000i) q^{78} +(7.50000 + 12.9904i) q^{79} +(-1.73205 - 1.00000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.50000 + 4.33013i) q^{82} +6.00000i q^{83} +4.00000i q^{85} +(-3.46410 + 2.00000i) q^{86} +(-2.50000 + 4.33013i) q^{88} +(-5.19615 + 3.00000i) q^{89} -4.00000 q^{90} -9.00000 q^{92} +(-4.33013 + 2.50000i) q^{93} +(-6.50000 + 11.2583i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-0.866025 + 0.500000i) q^{96} -7.00000i q^{97} +10.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} + 4 q^{9} - 4 q^{10} + 2 q^{12} + 12 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{22} - 18 q^{23} - 2 q^{25} + 4 q^{26} - 20 q^{27} - 4 q^{30} + 8 q^{36} - 8 q^{38} - 6 q^{39} + 4 q^{40}+ \cdots + 16 q^{95}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 + 4 * q^9 - 4 * q^10 + 2 * q^12 + 12 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^22 - 18 * q^23 - 2 * q^25 + 4 * q^26 - 20 * q^27 - 4 * q^30 + 8 * q^36 - 8 * q^38 - 6 * q^39 + 4 * q^40 + 16 * q^43 + 4 * q^48 - 4 * q^51 + 6 * q^52 - 28 * q^53 + 40 * q^55 - 26 * q^61 - 20 * q^62 - 4 * q^64 - 8 * q^65 + 10 * q^66 + 4 * q^68 + 36 * q^69 + 6 * q^74 - 2 * q^75 - 8 * q^78 + 30 * q^79 - 2 * q^81 + 10 * q^82 - 10 * q^88 - 16 * q^90 - 36 * q^92 - 26 * q^94 + 16 * q^95

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