LMFDB - Embedded newform 1274.2.h.j.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(263,1274)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1274.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

Embedding label			263.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1274.263
Dual form			1274.2.h.j.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{10} +(-0.500000 - 0.866025i) q^{12} +(2.50000 + 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{18} -4.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{23} -1.00000 q^{24} +(-2.00000 + 3.46410i) q^{25} +(3.50000 - 0.866025i) q^{26} -5.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} -3.00000 q^{30} +(5.00000 - 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +(1.00000 + 1.73205i) q^{36} +(-4.00000 + 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(2.50000 + 2.59808i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-4.00000 + 6.92820i) q^{43} +(3.00000 + 5.19615i) q^{45} +(1.50000 + 2.59808i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(1.00000 - 3.46410i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-2.50000 + 4.33013i) q^{54} -4.00000 q^{57} -6.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +(-1.50000 + 2.59808i) q^{60} +11.0000 q^{61} +(-5.00000 - 8.66025i) q^{62} +1.00000 q^{64} +(3.00000 - 10.3923i) q^{65} +2.00000 q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{69} +(1.50000 - 2.59808i) q^{71} +2.00000 q^{72} +(-1.00000 + 1.73205i) q^{73} +(4.00000 + 6.92820i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(2.00000 + 3.46410i) q^{76} +(3.50000 - 0.866025i) q^{78} +(2.00000 + 3.46410i) q^{79} +3.00000 q^{80} +1.00000 q^{81} +(-9.00000 + 15.5885i) q^{85} +(4.00000 + 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{89} +6.00000 q^{90} +3.00000 q^{92} +(5.00000 - 8.66025i) q^{93} -6.00000 q^{94} +(6.00000 + 10.3923i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + q^{6} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + q^6 - 2 * q^8 - 4 * q^9	$ 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + q^{6} - 2 q^{8} - 4 q^{9} - 6 q^{10} - q^{12} + 5 q^{13} - 3 q^{15} - q^{16} - 6 q^{17} - 2 q^{18} - 8 q^{19} - 3 q^{20} - 3 q^{23} - 2 q^{24} - 4 q^{25} + 7 q^{26} - 10 q^{27} - 6 q^{29} - 6 q^{30} + 10 q^{31} + q^{32} - 12 q^{34} + 2 q^{36} - 8 q^{37} - 4 q^{38} + 5 q^{39} + 3 q^{40} - 8 q^{43} + 6 q^{45} + 3 q^{46} - 6 q^{47} - q^{48} + 4 q^{50} - 6 q^{51} + 2 q^{52} - 12 q^{53} - 5 q^{54} - 8 q^{57} - 12 q^{58} - 3 q^{59} - 3 q^{60} + 22 q^{61} - 10 q^{62} + 2 q^{64} + 6 q^{65} + 4 q^{67} - 6 q^{68} - 3 q^{69} + 3 q^{71} + 4 q^{72} - 2 q^{73} + 8 q^{74} - 4 q^{75} + 4 q^{76} + 7 q^{78} + 4 q^{79} + 6 q^{80} + 2 q^{81} - 18 q^{85} + 8 q^{86} - 6 q^{87} + 6 q^{89} + 12 q^{90} + 6 q^{92} + 10 q^{93} - 12 q^{94} + 12 q^{95} + q^{96} - 2 q^{97}+O(q^{100}) $ 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + q^6 - 2 * q^8 - 4 * q^9 - 6 * q^10 - q^12 + 5 * q^13 - 3 * q^15 - q^16 - 6 * q^17 - 2 * q^18 - 8 * q^19 - 3 * q^20 - 3 * q^23 - 2 * q^24 - 4 * q^25 + 7 * q^26 - 10 * q^27 - 6 * q^29 - 6 * q^30 + 10 * q^31 + q^32 - 12 * q^34 + 2 * q^36 - 8 * q^37 - 4 * q^38 + 5 * q^39 + 3 * q^40 - 8 * q^43 + 6 * q^45 + 3 * q^46 - 6 * q^47 - q^48 + 4 * q^50 - 6 * q^51 + 2 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^57 - 12 * q^58 - 3 * q^59 - 3 * q^60 + 22 * q^61 - 10 * q^62 + 2 * q^64 + 6 * q^65 + 4 * q^67 - 6 * q^68 - 3 * q^69 + 3 * q^71 + 4 * q^72 - 2 * q^73 + 8 * q^74 - 4 * q^75 + 4 * q^76 + 7 * q^78 + 4 * q^79 + 6 * q^80 + 2 * q^81 - 18 * q^85 + 8 * q^86 - 6 * q^87 + 6 * q^89 + 12 * q^90 + 6 * q^92 + 10 * q^93 - 12 * q^94 + 12 * q^95 + q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.00000			0.577350			0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000			0.577350			0.288675	+	0.957427i	$0.406785\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.00000			−0.666667
$10$	−3.00000			−0.948683
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$		0			0
$15$	−1.50000	−	2.59808i	−0.387298	−	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	−1.00000	+	1.73205i	−0.235702	+	0.408248i
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	−1.00000			−0.204124
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	3.50000	−	0.866025i	0.686406	−	0.169842i
$27$	−5.00000			−0.962250
$28$		0			0
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	−3.00000			−0.547723
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.830014	−	0.557743i	$-0.188333\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$	3.00000	+	5.19615i	0.447214	+	0.774597i
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$		0			0
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−6.00000			−0.787839
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	11.0000			1.40841			0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000			1.40841			0.704203	+	0.709999i	$0.251305\pi$
$62$	−5.00000	−	8.66025i	−0.635001	−	1.09985i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.00000	−	10.3923i	0.372104	−	1.28901i
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	−1.50000	+	2.59808i	−0.180579	+	0.312772i
$70$		0			0
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	0.941201	+	0.337846i	$0.109698\pi$
$72$	2.00000			0.235702
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$		0			0
$78$	3.50000	−	0.866025i	0.396297	−	0.0980581i
$79$	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	$0.761089\pi$
$80$	3.00000			0.335410
$81$	1.00000			0.111111
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−9.00000	+	15.5885i	−0.976187	+	1.69081i
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	6.00000			0.632456
$91$		0			0
$92$	3.00000			0.312772
$93$	5.00000	−	8.66025i	0.518476	−	0.898027i
$94$	−6.00000			−0.618853
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$		0			0
$100$	4.00000			0.400000
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	−6.00000			−0.594089
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	0.282194	−	0.959357i	$-0.408938\pi$
$104$	−2.50000	−	2.59808i	−0.245145	−	0.254762i
$105$		0			0
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.00813215	−	0.999967i	$-0.497411\pi$
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.861931	−	0.507026i	$-0.169255\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111218\pi$
$110$		0			0
$111$	−4.00000	+	6.92820i	−0.379663	+	0.657596i
$112$		0			0
$113$	9.00000	−	15.5885i	0.846649	−	1.46644i	−0.0375328	−	0.999295i	$-0.511950\pi$
$113$	9.00000	−	15.5885i	0.846649	−	1.46644i	0.884182	−	0.467143i	$-0.154717\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$	9.00000			0.839254
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	−5.00000	−	5.19615i	−0.462250	−	0.480384i
$118$	−3.00000			−0.276172
$119$		0			0
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	−11.0000			−1.00000
$122$	5.50000	−	9.52628i	0.497947	−	0.862469i
$123$		0			0
$124$	−10.0000			−0.898027
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	0.511859	−	0.859069i	$-0.328957\pi$
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	−0.999905	+	0.0137486i	$0.995624\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$	−7.50000	−	7.79423i	−0.657794	−	0.683599i
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$		0			0
$133$		0			0
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	7.50000	+	12.9904i	0.645497	+	1.11803i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	1.50000	+	2.59808i	0.127688	+	0.221163i
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$	−1.50000	−	2.59808i	−0.125877	−	0.218026i
$143$		0			0
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	−9.00000	+	15.5885i	−0.747409	+	1.29455i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$		0			0
$148$	8.00000			0.657596
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	4.00000			0.324443
$153$	6.00000	+	10.3923i	0.485071	+	0.840168i
$154$		0			0
$155$	−30.0000			−2.40966
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$	4.00000			0.318223
$159$	−6.00000	+	10.3923i	−0.475831	+	0.824163i
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$		0			0
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	9.00000	+	15.5885i	0.690268	+	1.19558i
$171$	8.00000			0.611775
$172$	8.00000			0.609994
$173$	9.00000			0.684257			0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000			0.684257			0.342129	+	0.939653i	$0.388852\pi$
$174$	−6.00000			−0.454859
$175$		0			0
$176$		0			0
$177$	−1.50000	−	2.59808i	−0.112747	−	0.195283i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	6.00000			0.448461			0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000			0.448461			0.224231	+	0.974536i	$0.428013\pi$
$180$	3.00000	−	5.19615i	0.223607	−	0.387298i
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		0			0
$183$	11.0000			0.813143
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	24.0000			1.76452
$186$	−5.00000	−	8.66025i	−0.366618	−	0.635001i
$187$		0			0
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$		0			0
$190$	12.0000			0.870572
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$	1.00000			0.0721688
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$	3.00000	−	10.3923i	0.214834	−	0.744208i
$196$		0			0
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	0.569166	−	0.822222i	$-0.307266\pi$
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	−0.996649	+	0.0818013i	$0.973933\pi$
$198$		0			0
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	2.00000			0.141069
$202$	−3.00000	+	5.19615i	−0.211079	+	0.365600i
$203$		0			0
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$		0			0
$206$	−14.0000			−0.975426
$207$	3.00000	−	5.19615i	0.208514	−	0.361158i
$208$	−3.50000	+	0.866025i	−0.242681	+	0.0600481i
$209$		0			0
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	12.0000			0.824163
$213$	1.50000	−	2.59808i	0.102778	−	0.178017i
$214$	−9.00000	−	15.5885i	−0.615227	−	1.06561i
$215$	24.0000			1.63679
$216$	5.00000			0.340207
$217$		0			0
$218$	−8.00000	−	13.8564i	−0.541828	−	0.938474i
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$		0			0
$221$	6.00000	−	20.7846i	0.403604	−	1.39812i
$222$	4.00000	+	6.92820i	0.268462	+	0.464991i
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$	4.00000	−	6.92820i	0.266667	−	0.461880i
$226$	−9.00000	−	15.5885i	−0.598671	−	1.03693i
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	0.999997	−	0.00254715i	$-0.000810783\pi$
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	−0.502204	+	0.864749i	$0.667477\pi$
$228$	2.00000	+	3.46410i	0.132453	+	0.229416i
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	4.50000	−	7.79423i	0.296721	−	0.513936i
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	0.910968	−	0.412477i	$-0.135336\pi$
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	−0.812700	+	0.582683i	$0.802003\pi$
$234$	−7.00000	+	1.73205i	−0.457604	+	0.113228i
$235$	−9.00000	+	15.5885i	−0.587095	+	1.01688i
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	2.00000	+	3.46410i	0.129914	+	0.225018i
$238$		0			0
$239$	21.0000			1.35838			0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000			1.35838			0.679189	+	0.733964i	$0.262332\pi$
$240$	3.00000			0.193649
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.825131	+	0.564942i	$0.191101\pi$
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.0766885	+	0.997055i	$0.475565\pi$
$242$	−5.50000	+	9.52628i	−0.353553	+	0.612372i
$243$	16.0000			1.02640
$244$	−5.50000	−	9.52628i	−0.352101	−	0.609858i
$245$		0			0
$246$		0			0
$247$	−10.0000	−	10.3923i	−0.636285	−	0.661247i
$248$	−5.00000	+	8.66025i	−0.317500	+	0.549927i
$249$		0			0
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	−0.909475	−	0.415759i	$-0.863516\pi$
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	0.814795	+	0.579748i	$0.196849\pi$
$252$		0			0
$253$		0			0
$254$	−11.0000			−0.690201
$255$	−9.00000	+	15.5885i	−0.563602	+	0.976187i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$	4.00000	+	6.92820i	0.249029	+	0.431331i
$259$		0			0
$260$	−10.5000	+	2.59808i	−0.651182	+	0.161126i
$261$	6.00000	+	10.3923i	0.371391	+	0.643268i
$262$	−15.0000			−0.926703
$263$	−27.0000			−1.66489			−0.832446	−	0.554107i	$-0.813060\pi$
$263$	−27.0000			−1.66489			−0.832446	+	0.554107i	$0.813060\pi$
$264$		0			0
$265$	36.0000			2.21146
$266$		0			0
$267$	3.00000	−	5.19615i	0.183597	−	0.317999i
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	0.695606	−	0.718423i	$-0.255136\pi$
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	−0.969976	+	0.243201i	$0.921803\pi$
$270$	15.0000			0.912871
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	−3.00000			−0.181237
$275$		0			0
$276$	3.00000			0.180579
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	0.150210	−	0.988654i	$-0.452005\pi$
$278$	−8.00000	−	13.8564i	−0.479808	−	0.831052i
$279$	−10.0000	+	17.3205i	−0.598684	+	1.03695i
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−6.00000			−0.357295
$283$	−31.0000			−1.84276			−0.921379	−	0.388664i	$-0.872937\pi$
$283$	−31.0000			−1.84276			−0.921379	+	0.388664i	$0.872937\pi$
$284$	−3.00000			−0.178017
$285$	6.00000	+	10.3923i	0.355409	+	0.615587i
$286$		0			0
$287$		0			0
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	9.00000	+	15.5885i	0.528498	+	0.915386i
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$	2.00000			0.117041
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	−0.764990	−	0.644042i	$-0.777256\pi$
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	0.940252	+	0.340480i	$0.110589\pi$
$294$		0			0
$295$	−4.50000	+	7.79423i	−0.262000	+	0.453798i
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$		0			0
$298$		0			0
$299$	−10.5000	+	2.59808i	−0.607231	+	0.150251i
$300$	4.00000			0.230940
$301$		0			0
$302$	−0.500000	−	0.866025i	−0.0287718	−	0.0498342i
$303$	−6.00000			−0.344691
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−16.5000	−	28.5788i	−0.944787	−	1.63642i
$306$	12.0000			0.685994
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$		0			0
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$	−15.0000	+	25.9808i	−0.851943	+	1.47561i
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$	−2.50000	−	2.59808i	−0.141535	−	0.147087i
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$	1.00000	+	1.73205i	0.0564333	+	0.0977453i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$	6.00000	+	10.3923i	0.336463	+	0.582772i
$319$		0			0
$320$	−1.50000	−	2.59808i	−0.0838525	−	0.145237i
$321$	9.00000	−	15.5885i	0.502331	−	0.870063i
$322$		0			0
$323$	12.0000	+	20.7846i	0.667698	+	1.15649i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−14.0000	+	3.46410i	−0.776580	+	0.192154i
$326$	10.0000	−	17.3205i	0.553849	−	0.959294i
$327$	8.00000	−	13.8564i	0.442401	−	0.766261i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−10.0000			−0.549650			−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000			−0.549650			−0.274825	+	0.961494i	$0.588620\pi$
$332$		0			0
$333$	8.00000	−	13.8564i	0.438397	−	0.759326i
$334$	12.0000			0.656611
$335$	−3.00000	−	5.19615i	−0.163908	−	0.283896i
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	11.0000	+	6.92820i	0.598321	+	0.376845i
$339$	9.00000	−	15.5885i	0.488813	−	0.846649i
$340$	18.0000			0.976187
$341$		0			0
$342$	4.00000	−	6.92820i	0.216295	−	0.374634i
$343$		0			0
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$	9.00000			0.484544
$346$	4.50000	−	7.79423i	0.241921	−	0.419020i
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	0.984487	+	0.175457i	$0.0561403\pi$
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	−0.340293	+	0.940319i	$0.610526\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	−14.5000	−	25.1147i	−0.776167	−	1.34436i	−0.934136	−	0.356917i	$-0.883828\pi$
$349$	−14.5000	−	25.1147i	−0.776167	−	1.34436i	0.157969	−	0.987444i	$-0.449505\pi$
$350$		0			0
$351$	−12.5000	−	12.9904i	−0.667201	−	0.693375i
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$	−3.00000			−0.159448
$355$	−9.00000			−0.477670
$356$	−6.00000			−0.317999
$357$		0			0
$358$	3.00000	−	5.19615i	0.158555	−	0.274625i
$359$	4.50000	+	7.79423i	0.237501	+	0.411364i	0.959997	−	0.280012i	$-0.0903384\pi$
$359$	4.50000	+	7.79423i	0.237501	+	0.411364i	−0.722496	+	0.691375i	$0.757005\pi$
$360$	−3.00000	−	5.19615i	−0.158114	−	0.273861i
$361$	−3.00000			−0.157895
$362$	2.50000	−	4.33013i	0.131397	−	0.227586i
$363$	−11.0000			−0.577350
$364$		0			0
$365$	6.00000			0.314054
$366$	5.50000	−	9.52628i	0.287490	−	0.497947i
$367$	−10.0000			−0.521996			−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000			−0.521996			−0.260998	+	0.965339i	$0.584052\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$	12.0000	−	20.7846i	0.623850	−	1.08054i
$371$		0			0
$372$	−10.0000			−0.518476
$373$	32.0000			1.65690			0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000			1.65690			0.828449	+	0.560065i	$0.189224\pi$
$374$		0			0
$375$	−3.00000			−0.154919
$376$	3.00000	+	5.19615i	0.154713	+	0.267971i
$377$	6.00000	−	20.7846i	0.309016	−	1.07046i
$378$		0			0
$379$	14.0000	+	24.2487i	0.719132	+	1.24557i	0.961344	+	0.275349i	$0.0887935\pi$
$379$	14.0000	+	24.2487i	0.719132	+	1.24557i	−0.242213	+	0.970223i	$0.577873\pi$
$380$	6.00000	−	10.3923i	0.307794	−	0.533114i
$381$	−5.50000	−	9.52628i	−0.281774	−	0.488046i
$382$	−12.0000	+	20.7846i	−0.613973	+	1.06343i
$383$	−6.00000			−0.306586			−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000			−0.306586			−0.153293	+	0.988181i	$0.548988\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	2.50000	−	4.33013i	0.127247	−	0.220398i
$387$	8.00000	−	13.8564i	0.406663	−	0.704361i
$388$	2.00000			0.101535
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$	−7.50000	−	7.79423i	−0.379777	−	0.394676i
$391$	18.0000			0.910299
$392$		0			0
$393$	−7.50000	−	12.9904i	−0.378325	−	0.655278i
$394$	−12.0000			−0.604551
$395$	6.00000	−	10.3923i	0.301893	−	0.522894i
$396$		0			0
$397$	−7.00000			−0.351320			−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000			−0.351320			−0.175660	+	0.984451i	$0.556206\pi$
$398$	−14.0000			−0.701757
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$	1.00000	−	1.73205i	0.0498755	−	0.0863868i
$403$	35.0000	−	8.66025i	1.74347	−	0.431398i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	−1.50000	−	2.59808i	−0.0745356	−	0.129099i
$406$		0			0
$407$		0			0
$408$	3.00000	+	5.19615i	0.148522	+	0.257248i
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$		0			0
$411$	−1.50000	−	2.59808i	−0.0739895	−	0.128154i
$412$	−7.00000	+	12.1244i	−0.344865	+	0.597324i
$413$		0			0
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	8.00000	−	13.8564i	0.391762	−	0.678551i
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	4.00000			0.194717
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	24.0000			1.16417
$426$	−1.50000	−	2.59808i	−0.0726752	−	0.125877i
$427$		0			0
$428$	−18.0000			−0.870063
$429$		0			0
$430$	12.0000	−	20.7846i	0.578691	−	1.00232i
$431$	−33.0000			−1.58955			−0.794777	−	0.606902i	$-0.792412\pi$
$431$	−33.0000			−1.58955			−0.794777	+	0.606902i	$0.792412\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	2.00000	−	3.46410i	0.0961139	−	0.166474i	−0.813959	−	0.580922i	$-0.802692\pi$
$433$	2.00000	−	3.46410i	0.0961139	−	0.166474i	0.910073	+	0.414448i	$0.136025\pi$
$434$		0			0
$435$	−9.00000	+	15.5885i	−0.431517	+	0.747409i
$436$	−16.0000			−0.766261
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$		0			0
$441$		0			0
$442$	−15.0000	−	15.5885i	−0.713477	−	0.741467i
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	0.569057	−	0.822298i	$-0.307309\pi$
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	−0.996660	+	0.0816684i	$0.973975\pi$
$444$	8.00000			0.379663
$445$	−18.0000			−0.853282
$446$	−8.00000			−0.378811
$447$		0			0
$448$		0			0
$449$	−4.50000	+	7.79423i	−0.212368	+	0.367832i	−0.952455	−	0.304679i	$-0.901451\pi$
$449$	−4.50000	+	7.79423i	−0.212368	+	0.367832i	0.740087	+	0.672511i	$0.234784\pi$
$450$	−4.00000	−	6.92820i	−0.188562	−	0.326599i
$451$		0			0
$452$	−18.0000			−0.846649
$453$	0.500000	−	0.866025i	0.0234920	−	0.0406894i
$454$	15.0000			0.703985
$455$		0			0
$456$	4.00000			0.187317
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	0.297217	+	0.954810i	$0.403942\pi$
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	−0.975498	+	0.220008i	$0.929392\pi$
$458$	22.0000			1.02799
$459$	15.0000	+	25.9808i	0.700140	+	1.21268i
$460$	−4.50000	−	7.79423i	−0.209814	−	0.363408i
$461$	−10.5000	+	18.1865i	−0.489034	+	0.847031i	−0.999920	−	0.0126168i	$-0.995984\pi$
$461$	−10.5000	+	18.1865i	−0.489034	+	0.847031i	0.510887	+	0.859648i	$0.329317\pi$
$462$		0			0
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	6.00000			0.278543
$465$	−30.0000			−1.39122
$466$	3.00000			0.138972
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$	−2.00000	+	6.92820i	−0.0924500	+	0.320256i
$469$		0			0
$470$	9.00000	+	15.5885i	0.415139	+	0.719042i
$471$	−1.00000	+	1.73205i	−0.0460776	+	0.0798087i
$472$	1.50000	+	2.59808i	0.0690431	+	0.119586i
$473$		0			0
$474$	4.00000			0.183726
$475$	8.00000	−	13.8564i	0.367065	−	0.635776i
$476$		0			0
$477$	12.0000	−	20.7846i	0.549442	−	0.951662i
$478$	10.5000	−	18.1865i	0.480259	−	0.831833i
$479$	30.0000			1.37073			0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000			1.37073			0.685367	+	0.728197i	$0.259642\pi$
$480$	1.50000	−	2.59808i	0.0684653	−	0.118585i
$481$	−28.0000	+	6.92820i	−1.27669	+	0.315899i
$482$	28.0000			1.27537
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	6.00000			0.272446
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	0.974879	−	0.222737i	$-0.0714992\pi$
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	−0.680335	+	0.732901i	$0.738166\pi$
$488$	−11.0000			−0.497947
$489$	20.0000			0.904431
$490$		0			0
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$		0			0
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$	−14.0000	+	3.46410i	−0.629890	+	0.155857i
$495$		0			0
$496$	5.00000	+	8.66025i	0.224507	+	0.388857i
$497$		0			0
$498$		0			0
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	0.999962	−	0.00872186i	$-0.00277629\pi$
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	−0.507534	+	0.861632i	$0.669443\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$	6.00000	+	10.3923i	0.268060	+	0.464294i
$502$	1.50000	+	2.59808i	0.0669483	+	0.115958i
$503$	−21.0000	+	36.3731i	−0.936344	+	1.62179i	−0.164124	+	0.986440i	$0.552480\pi$
$503$	−21.0000	+	36.3731i	−0.936344	+	1.62179i	−0.772220	+	0.635355i	$0.780854\pi$
$504$		0			0
$505$	9.00000	+	15.5885i	0.400495	+	0.693677i
$506$		0			0
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$	−5.50000	+	9.52628i	−0.244023	+	0.422660i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$	9.00000	+	15.5885i	0.398527	+	0.690268i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	20.0000			0.883022
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	−21.0000	+	36.3731i	−0.925371	+	1.60279i
$516$	8.00000			0.352180
$517$		0			0
$518$		0			0
$519$	9.00000			0.395056
$520$	−3.00000	+	10.3923i	−0.131559	+	0.455733i
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	−0.138234	−	0.990400i	$-0.544143\pi$
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	0.926828	−	0.375486i	$-0.122524\pi$
$522$	12.0000			0.525226
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	−0.854887	−	0.518815i	$-0.826373\pi$
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	0.876750	+	0.480946i	$0.159707\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$		0			0
$526$	−13.5000	+	23.3827i	−0.588628	+	1.01953i
$527$	−60.0000			−2.61364
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	18.0000	−	31.1769i	0.781870	−	1.35424i
$531$	3.00000	+	5.19615i	0.130189	+	0.225494i
$532$		0			0
$533$		0			0
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	−54.0000			−2.33462
$536$	−2.00000			−0.0863868
$537$	6.00000			0.258919
$538$	−9.00000			−0.388018
$539$		0			0
$540$	7.50000	−	12.9904i	0.322749	−	0.559017i
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	−0.907975	−	0.419025i	$-0.862372\pi$
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	0.0911008	−	0.995842i	$-0.470961\pi$
$542$	1.00000	+	1.73205i	0.0429537	+	0.0743980i
$543$	5.00000			0.214571
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	−48.0000			−2.05609
$546$		0			0
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$	−22.0000			−0.938937
$550$		0			0
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$	1.50000	−	2.59808i	0.0638442	−	0.110581i
$553$		0			0
$554$	−26.0000			−1.10463
$555$	24.0000			1.01874
$556$	−16.0000			−0.678551
$557$	24.0000			1.01691			0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000			1.01691			0.508456	+	0.861088i	$0.330216\pi$
$558$	10.0000	+	17.3205i	0.423334	+	0.733236i
$559$	−28.0000	+	6.92820i	−1.18427	+	0.293032i
$560$		0			0
$561$		0			0
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	−3.00000	+	5.19615i	−0.126323	+	0.218797i
$565$	−54.0000			−2.27180
$566$	−15.5000	+	26.8468i	−0.651514	+	1.12845i
$567$		0			0
$568$	−1.50000	+	2.59808i	−0.0629386	+	0.109013i
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.184030	−	0.982921i	$-0.441086\pi$
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.759220	−	0.650835i	$-0.225581\pi$
$570$	12.0000			0.502625
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	−0.937503	−	0.347977i	$-0.886869\pi$
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	0.770108	+	0.637913i	$0.220202\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	−6.00000	−	10.3923i	−0.250217	−	0.433389i
$576$	−2.00000			−0.0833333
$577$	14.0000	−	24.2487i	0.582828	−	1.00949i	−0.412315	−	0.911041i	$-0.635280\pi$
$577$	14.0000	−	24.2487i	0.582828	−	1.00949i	0.995142	−	0.0984456i	$-0.0313871\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	5.00000			0.207793
$580$	18.0000			0.747409
$581$		0			0
$582$	1.00000	+	1.73205i	0.0414513	+	0.0717958i
$583$		0			0
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$	−6.00000	+	20.7846i	−0.248069	+	0.859338i
$586$	−3.00000	−	5.19615i	−0.123929	−	0.214651i
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$		0			0
$589$	−20.0000	+	34.6410i	−0.824086	+	1.42736i
$590$	4.50000	+	7.79423i	0.185262	+	0.320883i
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.00000	−	12.1244i	−0.286491	−	0.496217i
$598$	−3.00000	+	10.3923i	−0.122679	+	0.424973i
$599$	−1.50000	+	2.59808i	−0.0612883	+	0.106155i	−0.895042	−	0.445983i	$-0.852854\pi$
$599$	−1.50000	+	2.59808i	−0.0612883	+	0.106155i	0.833753	+	0.552137i	$0.186188\pi$
$600$	2.00000	−	3.46410i	0.0816497	−	0.141421i
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	−1.00000			−0.0406894
$605$	16.5000	+	28.5788i	0.670820	+	1.16190i
$606$	−3.00000	+	5.19615i	−0.121867	+	0.211079i
$607$	−10.0000			−0.405887			−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000			−0.405887			−0.202944	+	0.979190i	$0.565051\pi$
$608$	−2.00000	−	3.46410i	−0.0811107	−	0.140488i
$609$		0			0
$610$	−33.0000			−1.33613
$611$	6.00000	−	20.7846i	0.242734	−	0.840855i
$612$	6.00000	−	10.3923i	0.242536	−	0.420084i
$613$	−22.0000			−0.888572			−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000			−0.888572			−0.444286	+	0.895885i	$0.646543\pi$
$614$	−6.50000	+	11.2583i	−0.262319	+	0.454349i
$615$		0			0
$616$		0			0
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	−0.834251	−	0.551385i	$-0.814100\pi$
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	0.894639	+	0.446790i	$0.147433\pi$
$618$	−14.0000			−0.563163
$619$	18.5000	−	32.0429i	0.743578	−	1.28791i	−0.207279	−	0.978282i	$-0.566461\pi$
$619$	18.5000	−	32.0429i	0.743578	−	1.28791i	0.950856	−	0.309633i	$-0.100206\pi$
$620$	15.0000	+	25.9808i	0.602414	+	1.04341i
$621$	7.50000	−	12.9904i	0.300965	−	0.521286i
$622$	−3.00000	−	5.19615i	−0.120289	−	0.208347i
$623$		0			0
$624$	−3.50000	+	0.866025i	−0.140112	+	0.0346688i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−8.00000			−0.319744
$627$		0			0
$628$	2.00000			0.0798087
$629$	48.0000			1.91389
$630$		0			0
$631$	−2.50000	+	4.33013i	−0.0995234	+	0.172380i	−0.911487	−	0.411328i	$-0.865065\pi$
$631$	−2.50000	+	4.33013i	−0.0995234	+	0.172380i	0.811964	+	0.583707i	$0.198398\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$	12.0000			0.476581
$635$	−16.5000	+	28.5788i	−0.654783	+	1.13412i
$636$	12.0000			0.475831
$637$		0			0
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$	−3.00000			−0.118585
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$	−9.00000	−	15.5885i	−0.355202	−	0.615227i
$643$	−20.5000	+	35.5070i	−0.808441	+	1.40026i	0.105502	+	0.994419i	$0.466355\pi$
$643$	−20.5000	+	35.5070i	−0.808441	+	1.40026i	−0.913943	+	0.405842i	$0.866978\pi$
$644$		0			0
$645$	24.0000			0.944999
$646$	24.0000			0.944267
$647$	−36.0000			−1.41531			−0.707653	−	0.706560i	$-0.750246\pi$
$647$	−36.0000			−1.41531			−0.707653	+	0.706560i	$0.750246\pi$
$648$	−1.00000			−0.0392837
$649$		0			0
$650$	−4.00000	+	13.8564i	−0.156893	+	0.543493i
$651$		0			0
$652$	−10.0000	−	17.3205i	−0.391630	−	0.678323i
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	0.407628	+	0.913148i	$0.366356\pi$
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	−0.994623	+	0.103558i	$0.966977\pi$
$654$	−8.00000	−	13.8564i	−0.312825	−	0.541828i
$655$	−22.5000	+	38.9711i	−0.879148	+	1.52273i
$656$		0			0
$657$	2.00000	−	3.46410i	0.0780274	−	0.135147i
$658$		0			0
$659$	−3.00000	+	5.19615i	−0.116863	+	0.202413i	−0.918523	−	0.395367i	$-0.870617\pi$
$659$	−3.00000	+	5.19615i	−0.116863	+	0.202413i	0.801660	+	0.597781i	$0.203951\pi$
$660$		0			0
$661$	23.0000			0.894596			0.447298	−	0.894385i	$-0.352386\pi$
$661$	23.0000			0.894596			0.447298	+	0.894385i	$0.352386\pi$
$662$	−5.00000	+	8.66025i	−0.194331	+	0.336590i
$663$	6.00000	−	20.7846i	0.233021	−	0.807207i
$664$		0			0
$665$		0			0
$666$	−8.00000	−	13.8564i	−0.309994	−	0.536925i
$667$	18.0000			0.696963
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$	−6.00000			−0.231800
$671$		0			0
$672$		0			0
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$	10.0000	−	17.3205i	0.384900	−	0.666667i
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	25.5000	+	44.1673i	0.980045	+	1.69749i	0.662169	+	0.749355i	$0.269636\pi$
$677$	25.5000	+	44.1673i	0.980045	+	1.69749i	0.317876	+	0.948132i	$0.397030\pi$
$678$	−9.00000	−	15.5885i	−0.345643	−	0.598671i
$679$		0			0
$680$	9.00000	−	15.5885i	0.345134	−	0.597790i
$681$	7.50000	+	12.9904i	0.287401	+	0.497792i
$682$		0			0
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	0.998917	−	0.0465244i	$-0.0148145\pi$
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	−0.539750	+	0.841825i	$0.681481\pi$
$684$	−4.00000	−	6.92820i	−0.152944	−	0.264906i
$685$	−4.50000	+	7.79423i	−0.171936	+	0.297802i
$686$		0			0
$687$	11.0000	+	19.0526i	0.419676	+	0.726900i
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	−42.0000	+	10.3923i	−1.60007	+	0.395915i
$690$	4.50000	−	7.79423i	0.171312	−	0.296721i
$691$	0.500000	−	0.866025i	0.0190209	−	0.0329452i	−0.856358	−	0.516382i	$-0.827278\pi$
$691$	0.500000	−	0.866025i	0.0190209	−	0.0329452i	0.875379	+	0.483437i	$0.160612\pi$
$692$	−4.50000	−	7.79423i	−0.171064	−	0.296292i
$693$		0			0
$694$	24.0000			0.911028
$695$	−48.0000			−1.82074
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$		0			0
$698$	−29.0000			−1.09767
$699$	1.50000	+	2.59808i	0.0567352	+	0.0982683i
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$	−17.5000	+	4.33013i	−0.660495	+	0.163430i
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$		0			0
$705$	−9.00000	+	15.5885i	−0.338960	+	0.587095i
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$		0			0
$708$	−1.50000	+	2.59808i	−0.0563735	+	0.0976417i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	−4.50000	+	7.79423i	−0.168882	+	0.292512i
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$		0			0
$715$		0			0
$716$	−3.00000	−	5.19615i	−0.112115	−	0.194189i
$717$	21.0000			0.784259
$718$	9.00000			0.335877
$719$	−48.0000			−1.79010			−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000			−1.79010			−0.895049	+	0.445968i	$0.852860\pi$
$720$	−6.00000			−0.223607
$721$		0			0
$722$	−1.50000	+	2.59808i	−0.0558242	+	0.0966904i
$723$	14.0000	+	24.2487i	0.520666	+	0.901819i
$724$	−2.50000	−	4.33013i	−0.0929118	−	0.160928i
$725$	24.0000			0.891338
$726$	−5.50000	+	9.52628i	−0.204124	+	0.353553i
$727$	−52.0000			−1.92857			−0.964287	−	0.264861i	$-0.914674\pi$
$727$	−52.0000			−1.92857			−0.964287	+	0.264861i	$0.914674\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$	48.0000			1.77534
$732$	−5.50000	−	9.52628i	−0.203286	−	0.352101i
$733$	−17.5000	−	30.3109i	−0.646377	−	1.11956i	−0.983982	−	0.178270i	$-0.942950\pi$
$733$	−17.5000	−	30.3109i	−0.646377	−	1.11956i	0.337604	−	0.941288i	$-0.390383\pi$
$734$	−5.00000	+	8.66025i	−0.184553	+	0.319656i
$735$		0			0
$736$	−3.00000			−0.110581
$737$		0			0
$738$		0			0
$739$	−16.0000			−0.588570			−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000			−0.588570			−0.294285	+	0.955718i	$0.595081\pi$
$740$	−12.0000	−	20.7846i	−0.441129	−	0.764057i
$741$	−10.0000	−	10.3923i	−0.367359	−	0.381771i
$742$		0			0
$743$	−24.0000	−	41.5692i	−0.880475	−	1.52503i	−0.850814	−	0.525467i	$-0.823891\pi$
$743$	−24.0000	−	41.5692i	−0.880475	−	1.52503i	−0.0296605	−	0.999560i	$-0.509443\pi$
$744$	−5.00000	+	8.66025i	−0.183309	+	0.317500i
$745$		0			0
$746$	16.0000	−	27.7128i	0.585802	−	1.01464i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−1.50000	+	2.59808i	−0.0547723	+	0.0948683i
$751$	−8.50000	+	14.7224i	−0.310169	+	0.537229i	−0.978399	−	0.206726i	$-0.933719\pi$
$751$	−8.50000	+	14.7224i	−0.310169	+	0.537229i	0.668229	+	0.743955i	$0.267052\pi$
$752$	6.00000			0.218797
$753$	−1.50000	+	2.59808i	−0.0546630	+	0.0946792i
$754$	−15.0000	−	15.5885i	−0.546268	−	0.567698i
$755$	−3.00000			−0.109181
$756$		0			0
$757$	26.0000	+	45.0333i	0.944986	+	1.63676i	0.755779	+	0.654827i	$0.227258\pi$
$757$	26.0000	+	45.0333i	0.944986	+	1.63676i	0.189207	+	0.981937i	$0.439408\pi$
$758$	28.0000			1.01701
$759$		0			0
$760$	−6.00000	−	10.3923i	−0.217643	−	0.376969i
$761$	12.0000			0.435000			0.217500	−	0.976060i	$-0.430210\pi$
$761$	12.0000			0.435000			0.217500	+	0.976060i	$0.430210\pi$
$762$	−11.0000			−0.398488
$763$		0			0
$764$	12.0000	+	20.7846i	0.434145	+	0.751961i
$765$	18.0000	−	31.1769i	0.650791	−	1.12720i
$766$	−3.00000	+	5.19615i	−0.108394	+	0.187745i
$767$	3.00000	−	10.3923i	0.108324	−	0.375244i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	0.941984	−	0.335657i	$-0.108958\pi$
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	−0.761680	+	0.647954i	$0.775625\pi$
$770$		0			0
$771$	3.00000	−	5.19615i	0.108042	−	0.187135i
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	0.998930	+	0.0462427i	$0.0147248\pi$
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	−0.459418	+	0.888220i	$0.651942\pi$
$774$	−8.00000	−	13.8564i	−0.287554	−	0.498058i
$775$	20.0000	+	34.6410i	0.718421	+	1.24434i
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$		0			0
$778$	−15.0000	−	25.9808i	−0.537776	−	0.931455i
$779$		0			0
$780$	−10.5000	+	2.59808i	−0.375960	+	0.0930261i
$781$		0			0
$782$	9.00000	−	15.5885i	0.321839	−	0.557442i
$783$	15.0000	+	25.9808i	0.536056	+	0.928477i
$784$		0			0
$785$	6.00000			0.214149
$786$	−15.0000			−0.535032
$787$	−26.5000	−	45.8993i	−0.944623	−	1.63614i	−0.756504	−	0.653989i	$-0.773094\pi$
$787$	−26.5000	−	45.8993i	−0.944623	−	1.63614i	−0.188119	−	0.982146i	$-0.560239\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$	−27.0000			−0.961225
$790$	−6.00000	−	10.3923i	−0.213470	−	0.369742i
$791$		0			0
$792$		0			0
$793$	27.5000	+	28.5788i	0.976554	+	1.01486i
$794$	−3.50000	+	6.06218i	−0.124210	+	0.215139i
$795$	36.0000			1.27679
$796$	−7.00000	+	12.1244i	−0.248108	+	0.429736i
$797$	7.50000	−	12.9904i	0.265664	−	0.460143i	−0.702074	−	0.712104i	$-0.747742\pi$
$797$	7.50000	−	12.9904i	0.265664	−	0.460143i	0.967737	+	0.251961i	$0.0810756\pi$
$798$		0			0
$799$	−18.0000	+	31.1769i	−0.636794	+	1.10296i
$800$	−4.00000			−0.141421
$801$	−6.00000	+	10.3923i	−0.212000	+	0.367194i
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$		0			0
$804$	−1.00000	−	1.73205i	−0.0352673	−	0.0610847i
$805$		0			0
$806$	10.0000	−	34.6410i	0.352235	−	1.22018i
$807$	−4.50000	−	7.79423i	−0.158408	−	0.274370i
$808$	6.00000			0.211079
$809$	−42.0000			−1.47664			−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000			−1.47664			−0.738321	+	0.674450i	$0.764381\pi$
$810$	−3.00000			−0.105409
$811$	−19.0000			−0.667180			−0.333590	−	0.942718i	$-0.608260\pi$
$811$	−19.0000			−0.667180			−0.333590	+	0.942718i	$0.608260\pi$
$812$		0			0
$813$	−1.00000	+	1.73205i	−0.0350715	+	0.0607457i
$814$		0			0
$815$	−30.0000	−	51.9615i	−1.05085	−	1.82013i
$816$	6.00000			0.210042
$817$	16.0000	−	27.7128i	0.559769	−	0.969549i
$818$	22.0000			0.769212
$819$		0			0
$820$		0			0
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	−0.951526	−	0.307568i	$-0.900485\pi$
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	0.742125	+	0.670262i	$0.233818\pi$
$822$	−3.00000			−0.104637
$823$	6.50000	+	11.2583i	0.226576	+	0.392441i	0.956791	−	0.290776i	$-0.0939136\pi$
$823$	6.50000	+	11.2583i	0.226576	+	0.392441i	−0.730215	+	0.683217i	$0.760580\pi$
$824$	7.00000	+	12.1244i	0.243857	+	0.422372i
$825$		0			0
$826$		0			0
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$	−6.00000			−0.208514
$829$	−25.0000			−0.868286			−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000			−0.868286			−0.434143	+	0.900844i	$0.642949\pi$
$830$		0			0
$831$	−13.0000	−	22.5167i	−0.450965	−	0.781094i
$832$	2.50000	+	2.59808i	0.0866719	+	0.0900721i
$833$		0			0
$834$	−8.00000	−	13.8564i	−0.277017	−	0.479808i
$835$	18.0000	−	31.1769i	0.622916	−	1.07892i
$836$		0			0
$837$	−25.0000	+	43.3013i	−0.864126	+	1.49671i
$838$		0			0
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.152493	−	0.988304i	$-0.451270\pi$
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.779650	−	0.626215i	$-0.215397\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	13.0000	−	22.5167i	0.448010	−	0.775975i
$843$	18.0000			0.619953
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	34.5000	−	18.1865i	1.18684	−	0.625636i
$846$	12.0000			0.412568
$847$		0			0
$848$	−6.00000	−	10.3923i	−0.206041	−	0.356873i
$849$	−31.0000			−1.06392
$850$	12.0000	−	20.7846i	0.411597	−	0.712906i
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	−3.00000			−0.102778
$853$	17.0000			0.582069			0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000			0.582069			0.291034	+	0.956713i	$0.406001\pi$
$854$		0			0
$855$	−12.0000	−	20.7846i	−0.410391	−	0.710819i
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	−12.0000	−	20.7846i	−0.409197	−	0.708749i
$861$		0			0
$862$	−16.5000	+	28.5788i	−0.561992	+	0.973399i
$863$	28.5000	+	49.3634i	0.970151	+	1.68035i	0.695087	+	0.718925i	$0.255366\pi$
$863$	28.5000	+	49.3634i	0.970151	+	1.68035i	0.275064	+	0.961426i	$0.411301\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$	−13.5000	−	23.3827i	−0.459014	−	0.795035i
$866$	−2.00000	−	3.46410i	−0.0679628	−	0.117715i
$867$	−9.50000	+	16.4545i	−0.322637	+	0.558824i
$868$		0			0
$869$		0			0
$870$	9.00000	+	15.5885i	0.305129	+	0.528498i
$871$	5.00000	+	5.19615i	0.169419	+	0.176065i
$872$	−8.00000	+	13.8564i	−0.270914	+	0.469237i
$873$	2.00000	−	3.46410i	0.0676897	−	0.117242i
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$		0			0
$876$	2.00000			0.0675737
$877$	−22.0000			−0.742887			−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000			−0.742887			−0.371444	+	0.928456i	$0.621137\pi$
$878$	7.00000	+	12.1244i	0.236239	+	0.409177i
$879$	3.00000	−	5.19615i	0.101187	−	0.175262i
$880$		0			0
$881$	3.00000	+	5.19615i	0.101073	+	0.175063i	0.912127	−	0.409908i	$-0.134439\pi$
$881$	3.00000	+	5.19615i	0.101073	+	0.175063i	−0.811054	+	0.584971i	$0.801106\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−21.0000	+	5.19615i	−0.706306	+	0.174766i
$885$	−4.50000	+	7.79423i	−0.151266	+	0.262000i
$886$	−18.0000			−0.604722
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	−0.948999	−	0.315279i	$-0.897902\pi$
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	0.747539	+	0.664218i	$0.231235\pi$
$888$	4.00000	−	6.92820i	0.134231	−	0.232495i
$889$		0			0
$890$	−9.00000	+	15.5885i	−0.301681	+	0.522526i
$891$		0			0
$892$	−4.00000	+	6.92820i	−0.133930	+	0.231973i
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$		0			0
$895$	−9.00000	−	15.5885i	−0.300837	−	0.521065i
$896$		0			0
$897$	−10.5000	+	2.59808i	−0.350585	+	0.0867472i
$898$	4.50000	+	7.79423i	0.150167	+	0.260097i
$899$	−60.0000			−2.00111
$900$	−8.00000			−0.266667
$901$	72.0000			2.39867
$902$		0			0
$903$		0			0
$904$	−9.00000	+	15.5885i	−0.299336	+	0.518464i
$905$	−7.50000	−	12.9904i	−0.249308	−	0.431815i
$906$	−0.500000	−	0.866025i	−0.0166114	−	0.0287718i
$907$	14.0000			0.464862			0.232431	−	0.972613i	$-0.425332\pi$
$907$	14.0000			0.464862			0.232431	+	0.972613i	$0.425332\pi$
$908$	7.50000	−	12.9904i	0.248896	−	0.431101i
$909$	12.0000			0.398015
$910$		0			0
$911$	21.0000			0.695761			0.347881	−	0.937539i	$-0.386901\pi$
$911$	21.0000			0.695761			0.347881	+	0.937539i	$0.386901\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$		0			0
$914$	14.5000	+	25.1147i	0.479617	+	0.830722i
$915$	−16.5000	−	28.5788i	−0.545473	−	0.944787i
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$		0			0
$918$	30.0000			0.990148
$919$	−7.00000			−0.230909			−0.115454	−	0.993313i	$-0.536832\pi$
$919$	−7.00000			−0.230909			−0.115454	+	0.993313i	$0.536832\pi$
$920$	−9.00000			−0.296721
$921$	−13.0000			−0.428365
$922$	10.5000	+	18.1865i	0.345799	+	0.598942i
$923$	10.5000	−	2.59808i	0.345612	−	0.0855167i
$924$		0			0
$925$	−16.0000	−	27.7128i	−0.526077	−	0.911192i
$926$	−15.5000	+	26.8468i	−0.509362	+	0.882240i
$927$	14.0000	+	24.2487i	0.459820	+	0.796432i
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$	−15.0000	+	25.9808i	−0.491869	+	0.851943i
$931$		0			0
$932$	1.50000	−	2.59808i	0.0491341	−	0.0851028i
$933$	3.00000	−	5.19615i	0.0982156	−	0.170114i
$934$	3.00000			0.0981630
$935$		0			0
$936$	5.00000	+	5.19615i	0.163430	+	0.169842i
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$		0			0
$939$	−4.00000	−	6.92820i	−0.130535	−	0.226093i
$940$	18.0000			0.587095
$941$	−7.50000	+	12.9904i	−0.244493	+	0.423474i	−0.961989	−	0.273088i	$-0.911955\pi$
$941$	−7.50000	+	12.9904i	−0.244493	+	0.423474i	0.717496	+	0.696563i	$0.245288\pi$
$942$	1.00000	+	1.73205i	0.0325818	+	0.0564333i
$943$		0			0
$944$	3.00000			0.0976417
$945$		0			0
$946$		0			0
$947$	21.0000	−	36.3731i	0.682408	−	1.18197i	−0.291835	−	0.956469i	$-0.594266\pi$
$947$	21.0000	−	36.3731i	0.682408	−	1.18197i	0.974244	−	0.225497i	$-0.0724007\pi$
$948$	2.00000	−	3.46410i	0.0649570	−	0.112509i
$949$	−7.00000	+	1.73205i	−0.227230	+	0.0562247i
$950$	−8.00000	−	13.8564i	−0.259554	−	0.449561i
$951$	6.00000	+	10.3923i	0.194563	+	0.336994i
$952$		0			0
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	−0.718604	−	0.695419i	$-0.755219\pi$
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	0.961553	+	0.274620i	$0.0885520\pi$
$954$	−12.0000	−	20.7846i	−0.388514	−	0.672927i
$955$	36.0000	+	62.3538i	1.16493	+	2.01772i
$956$	−10.5000	−	18.1865i	−0.339594	−	0.588195i
$957$		0			0
$958$	15.0000	−	25.9808i	0.484628	−	0.839400i
$959$		0			0
$960$	−1.50000	−	2.59808i	−0.0484123	−	0.0838525i
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	−8.00000	+	27.7128i	−0.257930	+	0.893497i
$963$	−18.0000	+	31.1769i	−0.580042	+	1.00466i
$964$	14.0000	−	24.2487i	0.450910	−	0.780998i
$965$	−7.50000	−	12.9904i	−0.241434	−	0.418175i
$966$		0			0
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	11.0000			0.353553
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$	3.00000	−	5.19615i	0.0963242	−	0.166838i
$971$	3.00000			0.0962746			0.0481373	−	0.998841i	$-0.484672\pi$
$971$	3.00000			0.0962746			0.0481373	+	0.998841i	$0.484672\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$		0			0
$974$	13.0000			0.416547
$975$	−14.0000	+	3.46410i	−0.448359	+	0.110940i
$976$	−5.50000	+	9.52628i	−0.176051	+	0.304929i
$977$	39.0000			1.24772			0.623860	−	0.781536i	$-0.285563\pi$
$977$	39.0000			1.24772			0.623860	+	0.781536i	$0.285563\pi$
$978$	10.0000	−	17.3205i	0.319765	−	0.553849i
$979$		0			0
$980$		0			0
$981$	−16.0000	+	27.7128i	−0.510841	+	0.884802i
$982$	−12.0000			−0.382935
$983$	15.0000	−	25.9808i	0.478426	−	0.828658i	−0.521268	−	0.853393i	$-0.674541\pi$
$983$	15.0000	−	25.9808i	0.478426	−	0.828658i	0.999694	+	0.0247352i	$0.00787426\pi$
$984$		0			0
$985$	−18.0000	+	31.1769i	−0.573528	+	0.993379i
$986$	18.0000	+	31.1769i	0.573237	+	0.992875i
$987$		0			0
$988$	−4.00000	+	13.8564i	−0.127257	+	0.440831i
$989$	−12.0000	−	20.7846i	−0.381578	−	0.660912i
$990$		0			0
$991$	17.0000			0.540023			0.270011	−	0.962857i	$-0.412973\pi$
$991$	17.0000			0.540023			0.270011	+	0.962857i	$0.412973\pi$
$992$	10.0000			0.317500
$993$	−10.0000			−0.317340
$994$		0			0
$995$	−21.0000	+	36.3731i	−0.665745	+	1.15310i
$996$		0			0
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	−0.997963	−	0.0637961i	$-0.979679\pi$
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	0.443732	−	0.896159i	$-0.353654\pi$
$998$	22.0000			0.696398
$999$	20.0000	−	34.6410i	0.632772	−	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.h.j.263.1		2
7.2	even	3		1274.2.e.d.471.1		2
7.3	odd	6		1274.2.g.g.393.1		2
7.4	even	3		182.2.g.b.29.1	✓	2
7.5	odd	6		1274.2.e.i.471.1		2
7.6	odd	2		1274.2.h.i.263.1		2
13.9	even	3		1274.2.e.d.165.1		2
21.11	odd	6		1638.2.r.c.757.1		2
28.11	odd	6		1456.2.s.e.1121.1		2
91.9	even	3	inner	1274.2.h.j.373.1		2
91.11	odd	12		2366.2.d.f.337.1		2
91.48	odd	6		1274.2.e.i.165.1		2
91.61	odd	6		1274.2.h.i.373.1		2
91.67	odd	12		2366.2.d.f.337.2		2
91.74	even	3		182.2.g.b.113.1	yes	2
91.81	even	3		2366.2.a.f.1.1		1
91.87	odd	6		1274.2.g.g.295.1		2
91.88	even	6		2366.2.a.n.1.1		1
273.74	odd	6		1638.2.r.c.1387.1		2
364.347	odd	6		1456.2.s.e.113.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.g.b.29.1	✓	2	7.4	even	3
182.2.g.b.113.1	yes	2	91.74	even	3
1274.2.e.d.165.1		2	13.9	even	3
1274.2.e.d.471.1		2	7.2	even	3
1274.2.e.i.165.1		2	91.48	odd	6
1274.2.e.i.471.1		2	7.5	odd	6
1274.2.g.g.295.1		2	91.87	odd	6
1274.2.g.g.393.1		2	7.3	odd	6
1274.2.h.i.263.1		2	7.6	odd	2
1274.2.h.i.373.1		2	91.61	odd	6
1274.2.h.j.263.1		2	1.1	even	1	trivial
1274.2.h.j.373.1		2	91.9	even	3	inner
1456.2.s.e.113.1		2	364.347	odd	6
1456.2.s.e.1121.1		2	28.11	odd	6
1638.2.r.c.757.1		2	21.11	odd	6
1638.2.r.c.1387.1		2	273.74	odd	6
2366.2.a.f.1.1		1	91.81	even	3
2366.2.a.n.1.1		1	91.88	even	6
2366.2.d.f.337.1		2	91.11	odd	12
2366.2.d.f.337.2		2	91.67	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{10} +(-0.500000 - 0.866025i) q^{12} +(2.50000 + 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{18} -4.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{23} -1.00000 q^{24} +(-2.00000 + 3.46410i) q^{25} +(3.50000 - 0.866025i) q^{26} -5.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} -3.00000 q^{30} +(5.00000 - 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +(1.00000 + 1.73205i) q^{36} +(-4.00000 + 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(2.50000 + 2.59808i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-4.00000 + 6.92820i) q^{43} +(3.00000 + 5.19615i) q^{45} +(1.50000 + 2.59808i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(1.00000 - 3.46410i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-2.50000 + 4.33013i) q^{54} -4.00000 q^{57} -6.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +(-1.50000 + 2.59808i) q^{60} +11.0000 q^{61} +(-5.00000 - 8.66025i) q^{62} +1.00000 q^{64} +(3.00000 - 10.3923i) q^{65} +2.00000 q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{69} +(1.50000 - 2.59808i) q^{71} +2.00000 q^{72} +(-1.00000 + 1.73205i) q^{73} +(4.00000 + 6.92820i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(2.00000 + 3.46410i) q^{76} +(3.50000 - 0.866025i) q^{78} +(2.00000 + 3.46410i) q^{79} +3.00000 q^{80} +1.00000 q^{81} +(-9.00000 + 15.5885i) q^{85} +(4.00000 + 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{89} +6.00000 q^{90} +3.00000 q^{92} +(5.00000 - 8.66025i) q^{93} -6.00000 q^{94} +(6.00000 + 10.3923i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + q^{6} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + q^6 - 2 * q^8 - 4 * q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + q^{6} - 2 q^{8} - 4 q^{9} - 6 q^{10} - q^{12} + 5 q^{13} - 3 q^{15} - q^{16} - 6 q^{17} - 2 q^{18} - 8 q^{19} - 3 q^{20} - 3 q^{23} - 2 q^{24} - 4 q^{25} + 7 q^{26} - 10 q^{27} - 6 q^{29} - 6 q^{30} + 10 q^{31} + q^{32} - 12 q^{34} + 2 q^{36} - 8 q^{37} - 4 q^{38} + 5 q^{39} + 3 q^{40} - 8 q^{43} + 6 q^{45} + 3 q^{46} - 6 q^{47} - q^{48} + 4 q^{50} - 6 q^{51} + 2 q^{52} - 12 q^{53} - 5 q^{54} - 8 q^{57} - 12 q^{58} - 3 q^{59} - 3 q^{60} + 22 q^{61} - 10 q^{62} + 2 q^{64} + 6 q^{65} + 4 q^{67} - 6 q^{68} - 3 q^{69} + 3 q^{71} + 4 q^{72} - 2 q^{73} + 8 q^{74} - 4 q^{75} + 4 q^{76} + 7 q^{78} + 4 q^{79} + 6 q^{80} + 2 q^{81} - 18 q^{85} + 8 q^{86} - 6 q^{87} + 6 q^{89} + 12 q^{90} + 6 q^{92} + 10 q^{93} - 12 q^{94} + 12 q^{95} + q^{96} - 2 q^{97}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + q^6 - 2 * q^8 - 4 * q^9 - 6 * q^10 - q^12 + 5 * q^13 - 3 * q^15 - q^16 - 6 * q^17 - 2 * q^18 - 8 * q^19 - 3 * q^20 - 3 * q^23 - 2 * q^24 - 4 * q^25 + 7 * q^26 - 10 * q^27 - 6 * q^29 - 6 * q^30 + 10 * q^31 + q^32 - 12 * q^34 + 2 * q^36 - 8 * q^37 - 4 * q^38 + 5 * q^39 + 3 * q^40 - 8 * q^43 + 6 * q^45 + 3 * q^46 - 6 * q^47 - q^48 + 4 * q^50 - 6 * q^51 + 2 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^57 - 12 * q^58 - 3 * q^59 - 3 * q^60 + 22 * q^61 - 10 * q^62 + 2 * q^64 + 6 * q^65 + 4 * q^67 - 6 * q^68 - 3 * q^69 + 3 * q^71 + 4 * q^72 - 2 * q^73 + 8 * q^74 - 4 * q^75 + 4 * q^76 + 7 * q^78 + 4 * q^79 + 6 * q^80 + 2 * q^81 - 18 * q^85 + 8 * q^86 - 6 * q^87 + 6 * q^89 + 12 * q^90 + 6 * q^92 + 10 * q^93 - 12 * q^94 + 12 * q^95 + q^96 - 2 * q^97

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