LMFDB - Embedded newform 1274.2.g.g.393.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(295,1274)]

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([0, 4]))

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

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

chi := DirichletCharacter("1274.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: 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			393.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1274.393
Dual form			1274.2.g.g.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} -1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +2.00000 q^{18} +(-2.00000 + 3.46410i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{24} +4.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +5.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} +(1.50000 - 2.59808i) q^{30} +10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(1.00000 + 1.73205i) q^{36} +(-4.00000 - 6.92820i) q^{37} -4.00000 q^{38} +(1.00000 - 3.46410i) q^{39} +3.00000 q^{40} +(-4.00000 + 6.92820i) q^{43} +(-3.00000 + 5.19615i) q^{45} +(1.50000 - 2.59808i) q^{46} -6.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +6.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +12.0000 q^{53} +(2.50000 + 4.33013i) q^{54} -4.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(1.50000 - 2.59808i) q^{59} +3.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(7.50000 + 7.79423i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(3.00000 + 5.19615i) q^{68} +(1.50000 - 2.59808i) q^{69} +(1.50000 - 2.59808i) q^{71} +(-1.00000 + 1.73205i) q^{72} -2.00000 q^{73} +(4.00000 - 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{75} +(-2.00000 - 3.46410i) q^{76} +(3.50000 - 0.866025i) q^{78} -4.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-9.00000 + 15.5885i) q^{85} -8.00000 q^{86} +(3.00000 - 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{89} -6.00000 q^{90} +3.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(6.00000 - 10.3923i) q^{95} +1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} - 6 q^{5} - q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 - 6 * q^5 - q^6 - 2 * q^8 + 2 * q^9	$ 2 q + q^{2} + q^{3} - q^{4} - 6 q^{5} - q^{6} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 2 q^{12} - 5 q^{13} - 3 q^{15} - q^{16} + 6 q^{17} + 4 q^{18} - 4 q^{19} + 3 q^{20} - 3 q^{23} - q^{24} + 8 q^{25} + 2 q^{26} + 10 q^{27} - 6 q^{29} + 3 q^{30} + 20 q^{31} + q^{32} + 12 q^{34} + 2 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} - 8 q^{43} - 6 q^{45} + 3 q^{46} - 12 q^{47} + q^{48} + 4 q^{50} + 12 q^{51} + 7 q^{52} + 24 q^{53} + 5 q^{54} - 8 q^{57} + 6 q^{58} + 3 q^{59} + 6 q^{60} + 11 q^{61} + 10 q^{62} + 2 q^{64} + 15 q^{65} - 2 q^{67} + 6 q^{68} + 3 q^{69} + 3 q^{71} - 2 q^{72} - 4 q^{73} + 8 q^{74} + 4 q^{75} - 4 q^{76} + 7 q^{78} - 8 q^{79} + 3 q^{80} - q^{81} - 18 q^{85} - 16 q^{86} + 6 q^{87} - 6 q^{89} - 12 q^{90} + 6 q^{92} + 10 q^{93} - 6 q^{94} + 12 q^{95} + 2 q^{96} + 2 q^{97}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 - 6 * q^5 - q^6 - 2 * q^8 + 2 * q^9 - 3 * q^10 - 2 * q^12 - 5 * q^13 - 3 * q^15 - q^16 + 6 * q^17 + 4 * q^18 - 4 * q^19 + 3 * q^20 - 3 * q^23 - q^24 + 8 * q^25 + 2 * q^26 + 10 * q^27 - 6 * q^29 + 3 * q^30 + 20 * q^31 + q^32 + 12 * q^34 + 2 * q^36 - 8 * q^37 - 8 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^43 - 6 * q^45 + 3 * q^46 - 12 * q^47 + q^48 + 4 * q^50 + 12 * q^51 + 7 * q^52 + 24 * q^53 + 5 * q^54 - 8 * q^57 + 6 * q^58 + 3 * q^59 + 6 * q^60 + 11 * q^61 + 10 * q^62 + 2 * q^64 + 15 * q^65 - 2 * q^67 + 6 * q^68 + 3 * q^69 + 3 * q^71 - 2 * q^72 - 4 * q^73 + 8 * q^74 + 4 * q^75 - 4 * q^76 + 7 * q^78 - 8 * q^79 + 3 * q^80 - q^81 - 18 * q^85 - 16 * q^86 + 6 * q^87 - 6 * q^89 - 12 * q^90 + 6 * q^92 + 10 * q^93 - 6 * q^94 + 12 * q^95 + 2 * q^96 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−1.00000			−0.288675
$13$	−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	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	2.00000			0.471405
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$		0			0
$22$		0			0
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.00000			0.800000
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$	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	$-0.354747\pi$
$30$	1.50000	−	2.59808i	0.273861	−	0.474342i
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		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	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	−4.00000			−0.648886
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$	3.00000			0.474342
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		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
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$		0			0
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	6.00000			0.840168
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$	2.50000	+	4.33013i	0.340207	+	0.589256i
$55$		0			0
$56$		0			0
$57$	−4.00000			−0.529813
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$	3.00000			0.387298
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$	5.00000	+	8.66025i	0.635001	+	1.09985i
$63$		0			0
$64$	1.00000			0.125000
$65$	7.50000	+	7.79423i	0.930261	+	0.966755i
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	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	$0.109698\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	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
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		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
$86$	−8.00000			−0.862662
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$	3.00000			0.312772
$93$	5.00000	+	8.66025i	0.518476	+	0.898027i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	6.00000	−	10.3923i	0.615587	−	1.06623i
$96$	1.00000			0.102062
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	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	0.861931	+	0.507026i	$0.169255\pi$
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.00813215	+	0.999967i	$0.497411\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$		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
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$	6.00000			0.557086
$117$	−7.00000	+	1.73205i	−0.647150	+	0.160128i
$118$	3.00000			0.276172
$119$		0			0
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	11.0000			0.995893
$123$		0			0
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	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
$129$	−8.00000			−0.704361
$130$	−3.00000	+	10.3923i	−0.263117	+	0.911465i
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$		0			0
$133$		0			0
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	−15.0000			−1.29099
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$	3.00000			0.255377
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$	3.00000			0.251754
$143$		0			0
$144$	−2.00000			−0.166667
$145$	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		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	−2.00000	+	3.46410i	−0.163299	+	0.282843i
$151$	−1.00000			−0.0813788			−0.0406894	−	0.999172i	$-0.512955\pi$
$151$	−1.00000			−0.0813788			−0.0406894	+	0.999172i	$0.512955\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$	−6.00000	−	10.3923i	−0.485071	−	0.840168i
$154$		0			0
$155$	−30.0000			−2.40966
$156$	2.50000	+	2.59808i	0.200160	+	0.208013i
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	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
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	−18.0000			−1.38054
$171$	4.00000	+	6.92820i	0.305888	+	0.529813i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$		0			0
$177$	3.00000			0.225494
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$	−3.00000	−	5.19615i	−0.223607	−	0.387298i
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$		0			0
$183$	11.0000			0.813143
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$	12.0000	+	20.7846i	0.882258	+	1.52811i
$186$	−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
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.00454614	−	0.999990i	$-0.498553\pi$
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.863743	−	0.503932i	$-0.168114\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	2.00000			0.143592
$195$	−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	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$	−4.00000			−0.282843
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	3.00000	−	5.19615i	0.211079	−	0.365600i
$203$		0			0
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$		0			0
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$	−6.00000			−0.417029
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$		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	$0.789367\pi$
$212$	−6.00000	+	10.3923i	−0.412082	+	0.713746i
$213$	3.00000			0.205557
$214$	−9.00000	+	15.5885i	−0.615227	+	1.06561i
$215$	12.0000	−	20.7846i	0.818393	−	1.41750i
$216$	−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
$221$	−21.0000	+	5.19615i	−1.41261	+	0.349531i
$222$	8.00000			0.536925
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	0.968309	−	0.249756i	$-0.0803503\pi$
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	−0.700449	+	0.713702i	$0.747017\pi$
$224$		0			0
$225$	4.00000	−	6.92820i	0.266667	−	0.461880i
$226$	18.0000			1.19734
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$	2.00000	−	3.46410i	0.132453	−	0.229416i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	−4.50000	+	7.79423i	−0.296721	+	0.513936i
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	−3.00000			−0.196537			−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000			−0.196537			−0.0982683	+	0.995160i	$0.531330\pi$
$234$	−5.00000	−	5.19615i	−0.326860	−	0.339683i
$235$	18.0000			1.17419
$236$	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	$0.262332\pi$
$240$	−1.50000	+	2.59808i	−0.0968246	+	0.167705i
$241$	−14.0000	+	24.2487i	−0.901819	+	1.56200i	−0.0766885	+	0.997055i	$0.524435\pi$
$241$	−14.0000	+	24.2487i	−0.901819	+	1.56200i	−0.825131	+	0.564942i	$0.808899\pi$
$242$	11.0000			0.707107
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	5.50000	+	9.52628i	0.352101	+	0.609858i
$245$		0			0
$246$		0			0
$247$	14.0000	−	3.46410i	0.890799	−	0.220416i
$248$	−10.0000			−0.635001
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	−0.814795	−	0.579748i	$-0.803151\pi$
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	0.909475	+	0.415759i	$0.136484\pi$
$252$		0			0
$253$		0			0
$254$	5.50000	−	9.52628i	0.345101	−	0.597732i
$255$	−18.0000			−1.12720
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	−4.00000	−	6.92820i	−0.249029	−	0.431331i
$259$		0			0
$260$	−10.5000	+	2.59808i	−0.651182	+	0.161126i
$261$	−12.0000			−0.742781
$262$	−7.50000	−	12.9904i	−0.463352	−	0.802548i
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	0.896093	+	0.443866i	$0.146393\pi$
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	−0.0636476	+	0.997972i	$0.520273\pi$
$264$		0			0
$265$	−36.0000			−2.21146
$266$		0			0
$267$	3.00000	−	5.19615i	0.183597	−	0.317999i
$268$	2.00000			0.122169
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$	−7.50000	−	12.9904i	−0.456435	−	0.790569i
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	−3.00000			−0.181237
$275$		0			0
$276$	1.50000	+	2.59808i	0.0902894	+	0.156386i
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−16.0000			−0.959616
$279$	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	$0.319597\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	−15.5000	−	26.8468i	−0.921379	−	1.59588i	−0.797283	−	0.603606i	$-0.793730\pi$
$283$	−15.5000	−	26.8468i	−0.921379	−	1.59588i	−0.124096	−	0.992270i	$-0.539603\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$	12.0000			0.710819
$286$		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
$291$	2.00000			0.117242
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$		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
$299$	−3.00000	+	10.3923i	−0.173494	+	0.601003i
$300$	−4.00000			−0.230940
$301$		0			0
$302$	−0.500000	−	0.866025i	−0.0287718	−	0.0498342i
$303$	3.00000	−	5.19615i	0.172345	−	0.298511i
$304$	4.00000			0.229416
$305$	−16.5000	+	28.5788i	−0.944787	+	1.63642i
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$	−15.0000	−	25.9808i	−0.851943	−	1.47561i
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$	−1.00000	+	3.46410i	−0.0566139	+	0.196116i
$313$	−8.00000			−0.452187			−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000			−0.452187			−0.226093	+	0.974106i	$0.572595\pi$
$314$	−1.00000	−	1.73205i	−0.0564333	−	0.0977453i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$	−6.00000	+	10.3923i	−0.336463	+	0.582772i
$319$		0			0
$320$	−3.00000			−0.167705
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$		0			0
$323$	12.0000	+	20.7846i	0.667698	+	1.15649i
$324$	1.00000			0.0555556
$325$	−10.0000	−	10.3923i	−0.554700	−	0.576461i
$326$	−20.0000			−1.10770
$327$	−8.00000	−	13.8564i	−0.442401	−	0.766261i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$		0			0
$333$	−16.0000			−0.876795
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	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	$0.375472\pi$
$338$	−11.5000	+	6.06218i	−0.625518	+	0.329739i
$339$	18.0000			0.977626
$340$	−9.00000	−	15.5885i	−0.488094	−	0.845403i
$341$		0			0
$342$	−4.00000	+	6.92820i	−0.216295	+	0.374634i
$343$		0			0
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$	−4.50000	+	7.79423i	−0.242272	+	0.419627i
$346$	9.00000			0.483843
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	−0.340293	−	0.940319i	$-0.610526\pi$
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	0.984487	−	0.175457i	$-0.0561403\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	14.5000	+	25.1147i	0.776167	+	1.34436i	0.934136	+	0.356917i	$0.116172\pi$
$349$	14.5000	+	25.1147i	0.776167	+	1.34436i	−0.157969	+	0.987444i	$0.550495\pi$
$350$		0			0
$351$	−12.5000	−	12.9904i	−0.667201	−	0.693375i
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	1.50000	+	2.59808i	0.0797241	+	0.138086i
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	6.00000			0.317999
$357$		0			0
$358$	3.00000	−	5.19615i	0.158555	−	0.274625i
$359$	−9.00000			−0.475002			−0.237501	−	0.971387i	$-0.576328\pi$
$359$	−9.00000			−0.475002			−0.237501	+	0.971387i	$0.576328\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	−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
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	0.705509	−	0.708700i	$-0.250718\pi$
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	−0.966507	+	0.256639i	$0.917385\pi$
$368$	−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
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	0.0708063	+	0.997490i	$0.477443\pi$
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	−0.899255	+	0.437425i	$0.855891\pi$
$374$		0			0
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$	6.00000			0.309426
$377$	−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
$382$	24.0000			1.22795
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$	−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
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$	−10.5000	+	2.59808i	−0.531688	+	0.131559i
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−7.50000	−	12.9904i	−0.378325	−	0.655278i
$394$	6.00000	−	10.3923i	0.302276	−	0.523557i
$395$	12.0000			0.603786
$396$		0			0
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	−0.940389	−	0.340099i	$-0.889539\pi$
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	0.764730	+	0.644351i	$0.222873\pi$
$398$	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	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$	2.00000			0.0997509
$403$	−25.0000	−	25.9808i	−1.24534	−	1.29419i
$404$	6.00000			0.298511
$405$	1.50000	+	2.59808i	0.0745356	+	0.129099i
$406$		0			0
$407$		0			0
$408$	−6.00000			−0.297044
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	0.454759	+	0.890614i	$0.349725\pi$
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	−0.998674	+	0.0514740i	$0.983608\pi$
$410$		0			0
$411$	−3.00000			−0.147979
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$		0			0
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$		0			0
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$	−16.0000			−0.783523
$418$		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	$0.281584\pi$
$422$	−2.00000	+	3.46410i	−0.0973585	+	0.168630i
$423$	−6.00000	+	10.3923i	−0.291730	+	0.505291i
$424$	−12.0000			−0.582772
$425$	12.0000	−	20.7846i	0.582086	−	1.00820i
$426$	1.50000	+	2.59808i	0.0726752	+	0.125877i
$427$		0			0
$428$	−18.0000			−0.870063
$429$		0			0
$430$	24.0000			1.15738
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	0.922981	+	0.384846i	$0.125746\pi$
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	−0.128204	+	0.991748i	$0.540921\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	−2.00000	+	3.46410i	−0.0961139	+	0.166474i	−0.910073	−	0.414448i	$-0.863975\pi$
$433$	−2.00000	+	3.46410i	−0.0961139	+	0.166474i	0.813959	+	0.580922i	$0.197308\pi$
$434$		0			0
$435$	−9.00000	+	15.5885i	−0.431517	+	0.747409i
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$	12.0000			0.574038
$438$	1.00000	−	1.73205i	0.0477818	−	0.0827606i
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$		0			0
$441$		0			0
$442$	−15.0000	−	15.5885i	−0.713477	−	0.741467i
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$	4.00000	+	6.92820i	0.189832	+	0.328798i
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		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	$0.234784\pi$
$450$	8.00000			0.377124
$451$		0			0
$452$	9.00000	+	15.5885i	0.423324	+	0.733219i
$453$	−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	−0.975498	−	0.220008i	$-0.929392\pi$
$457$	−14.5000	−	25.1147i	−0.678281	−	1.17482i	0.297217	−	0.954810i	$-0.403942\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$	15.0000	−	25.9808i	0.700140	−	1.21268i
$460$	−9.00000			−0.419627
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	−0.510887	−	0.859648i	$-0.670683\pi$
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	0.999920	+	0.0126168i	$0.00401615\pi$
$462$		0			0
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−15.0000	−	25.9808i	−0.695608	−	1.20483i
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	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
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	−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
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	0.973321	+	0.229447i	$0.0736918\pi$
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	−0.287954	+	0.957644i	$0.592975\pi$
$480$	−3.00000			−0.136931
$481$	−8.00000	+	27.7128i	−0.364769	+	1.26360i
$482$	−28.0000			−1.27537
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−3.00000	+	5.19615i	−0.136223	+	0.235945i
$486$	16.0000			0.725775
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	−0.680335	−	0.732901i	$-0.738166\pi$
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	0.974879	+	0.222737i	$0.0714992\pi$
$488$	−5.50000	+	9.52628i	−0.248973	+	0.431234i
$489$	−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
$493$	−36.0000			−1.62136
$494$	10.0000	+	10.3923i	0.449921	+	0.467572i
$495$		0			0
$496$	−5.00000	−	8.66025i	−0.224507	−	0.388857i
$497$		0			0
$498$		0			0
$499$	−22.0000			−0.984855			−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000			−0.984855			−0.492428	+	0.870353i	$0.663890\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$	3.00000			0.133897
$503$	21.0000	−	36.3731i	0.936344	−	1.62179i	0.164124	−	0.986440i	$-0.447520\pi$
$503$	21.0000	−	36.3731i	0.936344	−	1.62179i	0.772220	−	0.635355i	$-0.219146\pi$
$504$		0			0
$505$	9.00000	+	15.5885i	0.400495	+	0.693677i
$506$		0			0
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$	11.0000			0.488046
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$	−9.00000	−	15.5885i	−0.398527	−	0.690268i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−10.0000	+	17.3205i	−0.441511	+	0.764719i
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	42.0000			1.85074
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$		0			0
$518$		0			0
$519$	9.00000			0.395056
$520$	−7.50000	−	7.79423i	−0.328897	−	0.341800i
$521$	36.0000			1.57719			0.788594	−	0.614914i	$-0.210809\pi$
$521$	36.0000			1.57719			0.788594	+	0.614914i	$0.210809\pi$
$522$	−6.00000	−	10.3923i	−0.262613	−	0.454859i
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	0.854887	−	0.518815i	$-0.173627\pi$
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	−0.876750	+	0.480946i	$0.840293\pi$
$524$	7.50000	−	12.9904i	0.327639	−	0.567487i
$525$		0			0
$526$	−13.5000	+	23.3827i	−0.588628	+	1.01953i
$527$	30.0000	−	51.9615i	1.30682	−	2.26348i
$528$		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
$534$	6.00000			0.259645
$535$	−27.0000	−	46.7654i	−1.16731	−	2.02184i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$	9.00000			0.388018
$539$		0			0
$540$	7.50000	−	12.9904i	0.322749	−	0.559017i
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	−1.00000	+	1.73205i	−0.0429537	+	0.0743980i
$543$	−2.50000	−	4.33013i	−0.107285	−	0.185824i
$544$	−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
$549$	−11.0000	−	19.0526i	−0.469469	−	0.813143i
$550$		0			0
$551$	24.0000			1.02243
$552$	−1.50000	+	2.59808i	−0.0638442	+	0.110581i
$553$		0			0
$554$	−26.0000			−1.10463
$555$	−12.0000	+	20.7846i	−0.509372	+	0.882258i
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−12.0000	−	20.7846i	−0.508456	−	0.880672i	−0.999952	−	0.00979220i	$-0.996883\pi$
$557$	−12.0000	−	20.7846i	−0.508456	−	0.880672i	0.491496	−	0.870880i	$-0.336450\pi$
$558$	20.0000			0.846668
$559$	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	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$	6.00000			0.252646
$565$	−27.0000	+	46.7654i	−1.13590	+	1.96743i
$566$	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	0.759220	+	0.650835i	$0.225581\pi$
$569$	22.5000	+	38.9711i	0.943249	+	1.63376i	0.184030	+	0.982921i	$0.441086\pi$
$570$	6.00000	+	10.3923i	0.251312	+	0.435286i
$571$	8.00000			0.334790			0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000			0.334790			0.167395	+	0.985890i	$0.446465\pi$
$572$		0			0
$573$	24.0000			1.00261
$574$		0			0
$575$	−6.00000	−	10.3923i	−0.250217	−	0.433389i
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	28.0000			1.16566			0.582828	−	0.812596i	$-0.301946\pi$
$577$	28.0000			1.16566			0.582828	+	0.812596i	$0.301946\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	2.50000	−	4.33013i	0.103896	−	0.179954i
$580$	−18.0000			−0.747409
$581$		0			0
$582$	1.00000	+	1.73205i	0.0414513	+	0.0717958i
$583$		0			0
$584$	2.00000			0.0827606
$585$	21.0000	−	5.19615i	0.868243	−	0.214834i
$586$	−6.00000			−0.247858
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	0.895320	−	0.445424i	$-0.146947\pi$
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	−0.833408	+	0.552658i	$0.813614\pi$
$588$		0			0
$589$	−20.0000	+	34.6410i	−0.824086	+	1.42736i
$590$	−9.00000			−0.370524
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	14.0000			0.572982
$598$	−10.5000	+	2.59808i	−0.429377	+	0.106243i
$599$	3.00000			0.122577			0.0612883	−	0.998120i	$-0.480479\pi$
$599$	3.00000			0.122577			0.0612883	+	0.998120i	$0.480479\pi$
$600$	−2.00000	−	3.46410i	−0.0816497	−	0.141421i
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	0.500000	−	0.866025i	0.0203447	−	0.0352381i
$605$	−16.5000	+	28.5788i	−0.670820	+	1.16190i
$606$	6.00000			0.243733
$607$	−5.00000	+	8.66025i	−0.202944	+	0.351509i	−0.949476	−	0.313841i	$-0.898384\pi$
$607$	−5.00000	+	8.66025i	−0.202944	+	0.351509i	0.746532	+	0.665350i	$0.231718\pi$
$608$	2.00000	+	3.46410i	0.0811107	+	0.140488i
$609$		0			0
$610$	−33.0000			−1.33613
$611$	15.0000	+	15.5885i	0.606835	+	0.630641i
$612$	12.0000			0.485071
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	0.998002	−	0.0631797i	$-0.0201241\pi$
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	−0.553716	+	0.832705i	$0.686791\pi$
$614$	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	$0.147433\pi$
$618$	7.00000	−	12.1244i	0.281581	−	0.487713i
$619$	37.0000			1.48716			0.743578	−	0.668649i	$-0.233127\pi$
$619$	37.0000			1.48716			0.743578	+	0.668649i	$0.233127\pi$
$620$	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
$625$	−29.0000			−1.16000
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$		0			0
$628$	1.00000	−	1.73205i	0.0399043	−	0.0691164i
$629$	−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	$0.198398\pi$
$632$	4.00000			0.159111
$633$	−2.00000	+	3.46410i	−0.0794929	+	0.137686i
$634$	−6.00000	−	10.3923i	−0.238290	−	0.412731i
$635$	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
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$	−18.0000			−0.710403
$643$	20.5000	−	35.5070i	0.808441	−	1.40026i	−0.105502	−	0.994419i	$-0.533645\pi$
$643$	20.5000	−	35.5070i	0.808441	−	1.40026i	0.913943	−	0.405842i	$-0.133022\pi$
$644$		0			0
$645$	24.0000			0.944999
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	−18.0000	−	31.1769i	−0.707653	−	1.22569i	−0.965726	−	0.259565i	$-0.916421\pi$
$647$	−18.0000	−	31.1769i	−0.707653	−	1.22569i	0.258073	−	0.966126i	$-0.416913\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$		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	−0.994623	−	0.103558i	$-0.966977\pi$
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$654$	8.00000	−	13.8564i	0.312825	−	0.541828i
$655$	45.0000			1.75830
$656$		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
$661$	11.5000	+	19.9186i	0.447298	+	0.774743i	0.998209	−	0.0598209i	$-0.0190530\pi$
$661$	11.5000	+	19.9186i	0.447298	+	0.774743i	−0.550911	+	0.834564i	$0.685720\pi$
$662$	10.0000			0.388661
$663$	−15.0000	−	15.5885i	−0.582552	−	0.605406i
$664$		0			0
$665$		0			0
$666$	−8.00000	−	13.8564i	−0.309994	−	0.536925i
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$	12.0000			0.464294
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$	−3.00000	+	5.19615i	−0.115900	+	0.200745i
$671$		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
$675$	20.0000			0.769800
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	51.0000			1.96009			0.980045	−	0.198778i	$-0.0636972\pi$
$677$	51.0000			1.96009			0.980045	+	0.198778i	$0.0636972\pi$
$678$	9.00000	+	15.5885i	0.345643	+	0.598671i
$679$		0			0
$680$	9.00000	−	15.5885i	0.345134	−	0.597790i
$681$	−15.0000			−0.574801
$682$		0			0
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$	−8.00000			−0.305888
$685$	4.50000	−	7.79423i	0.171936	−	0.297802i
$686$		0			0
$687$	11.0000	+	19.0526i	0.419676	+	0.726900i
$688$	8.00000			0.304997
$689$	−30.0000	−	31.1769i	−1.14291	−	1.18775i
$690$	−9.00000			−0.342624
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	0.856358	−	0.516382i	$-0.172722\pi$
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	−0.875379	+	0.483437i	$0.839388\pi$
$692$	4.50000	+	7.79423i	0.171064	+	0.296292i
$693$		0			0
$694$	24.0000			0.911028
$695$	24.0000	−	41.5692i	0.910372	−	1.57681i
$696$	−3.00000	+	5.19615i	−0.113715	+	0.196960i
$697$		0			0
$698$	−14.5000	+	25.1147i	−0.548833	+	0.950607i
$699$	−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	$0.572767\pi$
$702$	5.00000	−	17.3205i	0.188713	−	0.653720i
$703$	32.0000			1.20690
$704$		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
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$	−9.00000			−0.337764
$711$	−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
$716$	6.00000			0.224231
$717$	10.5000	+	18.1865i	0.392130	+	0.679189i
$718$	−4.50000	−	7.79423i	−0.167939	−	0.290878i
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$	6.00000			0.223607
$721$		0			0
$722$	−1.50000	+	2.59808i	−0.0558242	+	0.0966904i
$723$	−28.0000			−1.04133
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$	52.0000			1.92857			0.964287	−	0.264861i	$-0.0853260\pi$
$727$	52.0000			1.92857			0.964287	+	0.264861i	$0.0853260\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	3.00000	+	5.19615i	0.111035	+	0.192318i
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$	−5.50000	+	9.52628i	−0.203286	+	0.352101i
$733$	−35.0000			−1.29275			−0.646377	−	0.763018i	$-0.723717\pi$
$733$	−35.0000			−1.29275			−0.646377	+	0.763018i	$0.723717\pi$
$734$	5.00000	−	8.66025i	0.184553	−	0.319656i
$735$		0			0
$736$	−3.00000			−0.110581
$737$		0			0
$738$		0			0
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$	−24.0000			−0.882258
$741$	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
$746$	−32.0000			−1.17160
$747$		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	0.668229	−	0.743955i	$-0.267052\pi$
$751$	−8.50000	−	14.7224i	−0.310169	−	0.537229i	−0.978399	+	0.206726i	$0.933719\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	3.00000			0.109326
$754$	−21.0000	+	5.19615i	−0.764775	+	0.189233i
$755$	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	$0.439408\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$		0			0
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	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
$766$	−6.00000			−0.216789
$767$	−10.5000	+	2.59808i	−0.379133	+	0.0938111i
$768$	−1.00000			−0.0360844
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	0.761680	−	0.647954i	$-0.224375\pi$
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	−0.941984	+	0.335657i	$0.891042\pi$
$770$		0			0
$771$	3.00000	−	5.19615i	0.108042	−	0.187135i
$772$	5.00000			0.179954
$773$	−15.0000	+	25.9808i	−0.539513	+	0.934463i	0.459418	+	0.888220i	$0.348058\pi$
$773$	−15.0000	+	25.9808i	−0.539513	+	0.934463i	−0.998930	+	0.0462427i	$0.985275\pi$
$774$	−8.00000	+	13.8564i	−0.287554	+	0.498058i
$775$	40.0000			1.43684
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$		0			0
$778$	−15.0000	−	25.9808i	−0.537776	−	0.931455i
$779$		0			0
$780$	−7.50000	−	7.79423i	−0.268543	−	0.279078i
$781$		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
$786$	7.50000	−	12.9904i	0.267516	−	0.463352i
$787$	26.5000	−	45.8993i	0.944623	−	1.63614i	0.188119	−	0.982146i	$-0.439761\pi$
$787$	26.5000	−	45.8993i	0.944623	−	1.63614i	0.756504	−	0.653989i	$-0.226906\pi$
$788$	12.0000			0.427482
$789$	−13.5000	+	23.3827i	−0.480613	+	0.832446i
$790$	6.00000	+	10.3923i	0.213470	+	0.369742i
$791$		0			0
$792$		0			0
$793$	−38.5000	+	9.52628i	−1.36718	+	0.338288i
$794$	−7.00000			−0.248421
$795$	−18.0000	−	31.1769i	−0.638394	−	1.10573i
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	−0.967737	−	0.251961i	$-0.918924\pi$
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	0.702074	+	0.712104i	$0.252258\pi$
$798$		0			0
$799$	−18.0000	+	31.1769i	−0.636794	+	1.10296i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	−12.0000			−0.423999
$802$	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
$807$	9.00000			0.316815
$808$	3.00000	+	5.19615i	0.105540	+	0.182800i
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	0.953251	+	0.302180i	$0.0977142\pi$
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	−0.214930	+	0.976629i	$0.568952\pi$
$810$	−1.50000	+	2.59808i	−0.0527046	+	0.0912871i
$811$	19.0000			0.667180			0.333590	−	0.942718i	$-0.391740\pi$
$811$	19.0000			0.667180			0.333590	+	0.942718i	$0.391740\pi$
$812$		0			0
$813$	−1.00000	+	1.73205i	−0.0350715	+	0.0607457i
$814$		0			0
$815$	30.0000	−	51.9615i	1.05085	−	1.82013i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	−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	0.742125	−	0.670262i	$-0.233818\pi$
$821$	−6.00000	−	10.3923i	−0.209401	−	0.362694i	−0.951526	+	0.307568i	$0.900485\pi$
$822$	−1.50000	−	2.59808i	−0.0523185	−	0.0906183i
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	−0.730215	−	0.683217i	$-0.760580\pi$
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	0.956791	+	0.290776i	$0.0939136\pi$
$824$	14.0000			0.487713
$825$		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	$0.362983\pi$
$828$	3.00000	−	5.19615i	0.104257	−	0.180579i
$829$	−12.5000	−	21.6506i	−0.434143	−	0.751958i	0.563082	−	0.826401i	$-0.309615\pi$
$829$	−12.5000	−	21.6506i	−0.434143	−	0.751958i	−0.997225	+	0.0744432i	$0.976282\pi$
$830$		0			0
$831$	−26.0000			−0.901930
$832$	−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
$837$	50.0000			1.72825
$838$		0			0
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.152493	+	0.988304i	$0.548730\pi$
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.779650	+	0.626215i	$0.784603\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$	−4.00000			−0.137686
$845$	1.50000	−	38.9711i	0.0516016	−	1.34065i
$846$	−12.0000			−0.412568
$847$		0			0
$848$	−6.00000	−	10.3923i	−0.206041	−	0.356873i
$849$	15.5000	−	26.8468i	0.531959	−	0.921379i
$850$	24.0000			0.823193
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$	−1.50000	+	2.59808i	−0.0513892	+	0.0890086i
$853$	−17.0000			−0.582069			−0.291034	−	0.956713i	$-0.593999\pi$
$853$	−17.0000			−0.582069			−0.291034	+	0.956713i	$0.593999\pi$
$854$		0			0
$855$	−12.0000	−	20.7846i	−0.410391	−	0.710819i
$856$	−9.00000	−	15.5885i	−0.307614	−	0.532803i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	12.0000	+	20.7846i	0.409197	+	0.708749i
$861$		0			0
$862$	−16.5000	+	28.5788i	−0.561992	+	0.973399i
$863$	−57.0000			−1.94030			−0.970151	−	0.242500i	$-0.922032\pi$
$863$	−57.0000			−1.94030			−0.970151	+	0.242500i	$0.922032\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$	−13.5000	+	23.3827i	−0.459014	+	0.795035i
$866$	−4.00000			−0.135926
$867$	9.50000	−	16.4545i	0.322637	−	0.558824i
$868$		0			0
$869$		0			0
$870$	−18.0000			−0.610257
$871$	−2.00000	+	6.92820i	−0.0677674	+	0.234753i
$872$	16.0000			0.541828
$873$	−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
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−7.00000	+	12.1244i	−0.236239	+	0.409177i
$879$	−6.00000			−0.202375
$880$		0			0
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	0.811054	−	0.584971i	$-0.198894\pi$
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	−0.912127	+	0.409908i	$0.865561\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	6.00000	−	20.7846i	0.201802	−	0.699062i
$885$	−9.00000			−0.302532
$886$	9.00000	+	15.5885i	0.302361	+	0.523704i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$	−4.00000	+	6.92820i	−0.134231	+	0.232495i
$889$		0			0
$890$	−9.00000	+	15.5885i	−0.301681	+	0.522526i
$891$		0			0
$892$	−8.00000			−0.267860
$893$	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
$898$	−9.00000			−0.300334
$899$	−30.0000	−	51.9615i	−1.00056	−	1.73301i
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$	36.0000	−	62.3538i	1.19933	−	2.07731i
$902$		0			0
$903$		0			0
$904$	−9.00000	+	15.5885i	−0.299336	+	0.518464i
$905$	15.0000			0.498617
$906$	0.500000	−	0.866025i	0.0166114	−	0.0287718i
$907$	−7.00000	−	12.1244i	−0.232431	−	0.402583i	0.726092	−	0.687598i	$-0.241335\pi$
$907$	−7.00000	−	12.1244i	−0.232431	−	0.402583i	−0.958523	+	0.285015i	$0.908001\pi$
$908$	−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
$915$	−33.0000			−1.09095
$916$	−11.0000	+	19.0526i	−0.363450	+	0.629514i
$917$		0			0
$918$	30.0000			0.990148
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	−0.802507	−	0.596643i	$-0.796501\pi$
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	0.917961	+	0.396670i	$0.129834\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$	6.50000	+	11.2583i	0.214182	+	0.370975i
$922$	21.0000			0.691598
$923$	−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
$928$	−6.00000			−0.196960
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$	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
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$		0			0
$936$	7.00000	−	1.73205i	0.228802	−	0.0566139i
$937$	−8.00000			−0.261349			−0.130674	−	0.991425i	$-0.541714\pi$
$937$	−8.00000			−0.261349			−0.130674	+	0.991425i	$0.541714\pi$
$938$		0			0
$939$	−4.00000	−	6.92820i	−0.130535	−	0.226093i
$940$	−9.00000	+	15.5885i	−0.293548	+	0.508439i
$941$	−15.0000			−0.488986			−0.244493	−	0.969651i	$-0.578622\pi$
$941$	−15.0000			−0.488986			−0.244493	+	0.969651i	$0.578622\pi$
$942$	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	0.974244	+	0.225497i	$0.0724007\pi$
$947$	21.0000	+	36.3731i	0.682408	+	1.18197i	−0.291835	+	0.956469i	$0.594266\pi$
$948$	4.00000			0.129914
$949$	5.00000	+	5.19615i	0.162307	+	0.168674i
$950$	−16.0000			−0.519109
$951$	−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	$0.0885520\pi$
$954$	24.0000			0.777029
$955$	−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
$961$	69.0000			2.22581
$962$	−28.0000	+	6.92820i	−0.902756	+	0.223374i
$963$	36.0000			1.16008
$964$	−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	$0.582821\pi$
$968$	−5.50000	+	9.52628i	−0.176777	+	0.306186i
$969$	−12.0000	+	20.7846i	−0.385496	+	0.667698i
$970$	−6.00000			−0.192648
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	−0.840953	−	0.541108i	$-0.818005\pi$
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	0.889090	+	0.457732i	$0.151338\pi$
$972$	8.00000	+	13.8564i	0.256600	+	0.444444i
$973$		0			0
$974$	13.0000			0.416547
$975$	4.00000	−	13.8564i	0.128103	−	0.443760i
$976$	−11.0000			−0.352101
$977$	−19.5000	−	33.7750i	−0.623860	−	1.08056i	−0.988760	−	0.149511i	$-0.952230\pi$
$977$	−19.5000	−	33.7750i	−0.623860	−	1.08056i	0.364900	−	0.931047i	$-0.381103\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$		0			0
$980$		0			0
$981$	−16.0000	+	27.7128i	−0.510841	+	0.884802i
$982$	6.00000	−	10.3923i	0.191468	−	0.331632i
$983$	30.0000			0.956851			0.478426	−	0.878128i	$-0.341208\pi$
$983$	30.0000			0.956851			0.478426	+	0.878128i	$0.341208\pi$
$984$		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
$989$	24.0000			0.763156
$990$		0			0
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	0.698853	−	0.715265i	$-0.253694\pi$
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	−0.968864	+	0.247592i	$0.920361\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$	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	−0.443732	−	0.896159i	$-0.646346\pi$
$997$	17.5000	−	30.3109i	0.554231	−	0.959955i	0.997963	−	0.0637961i	$-0.0203207\pi$
$998$	−11.0000	−	19.0526i	−0.348199	−	0.603098i
$999$	−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.g.g.393.1		2
7.2	even	3		1274.2.h.i.263.1		2
7.3	odd	6		1274.2.e.d.471.1		2
7.4	even	3		1274.2.e.i.471.1		2
7.5	odd	6		1274.2.h.j.263.1		2
7.6	odd	2		182.2.g.b.29.1	✓	2
13.9	even	3	inner	1274.2.g.g.295.1		2
21.20	even	2		1638.2.r.c.757.1		2
28.27	even	2		1456.2.s.e.1121.1		2
91.9	even	3		1274.2.e.i.165.1		2
91.41	even	12		2366.2.d.f.337.2		2
91.48	odd	6		182.2.g.b.113.1	yes	2
91.55	odd	6		2366.2.a.f.1.1		1
91.61	odd	6		1274.2.e.d.165.1		2
91.62	odd	6		2366.2.a.n.1.1		1
91.74	even	3		1274.2.h.i.373.1		2
91.76	even	12		2366.2.d.f.337.1		2
91.87	odd	6		1274.2.h.j.373.1		2
273.230	even	6		1638.2.r.c.1387.1		2
364.139	even	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	7.6	odd	2
182.2.g.b.113.1	yes	2	91.48	odd	6
1274.2.e.d.165.1		2	91.61	odd	6
1274.2.e.d.471.1		2	7.3	odd	6
1274.2.e.i.165.1		2	91.9	even	3
1274.2.e.i.471.1		2	7.4	even	3
1274.2.g.g.295.1		2	13.9	even	3	inner
1274.2.g.g.393.1		2	1.1	even	1	trivial
1274.2.h.i.263.1		2	7.2	even	3
1274.2.h.i.373.1		2	91.74	even	3
1274.2.h.j.263.1		2	7.5	odd	6
1274.2.h.j.373.1		2	91.87	odd	6
1456.2.s.e.113.1		2	364.139	even	6
1456.2.s.e.1121.1		2	28.27	even	2
1638.2.r.c.757.1		2	21.20	even	2
1638.2.r.c.1387.1		2	273.230	even	6
2366.2.a.f.1.1		1	91.55	odd	6
2366.2.a.n.1.1		1	91.62	odd	6
2366.2.d.f.337.1		2	91.76	even	12
2366.2.d.f.337.2		2	91.41	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} -1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +2.00000 q^{18} +(-2.00000 + 3.46410i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{24} +4.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +5.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} +(1.50000 - 2.59808i) q^{30} +10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(1.00000 + 1.73205i) q^{36} +(-4.00000 - 6.92820i) q^{37} -4.00000 q^{38} +(1.00000 - 3.46410i) q^{39} +3.00000 q^{40} +(-4.00000 + 6.92820i) q^{43} +(-3.00000 + 5.19615i) q^{45} +(1.50000 - 2.59808i) q^{46} -6.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +6.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +12.0000 q^{53} +(2.50000 + 4.33013i) q^{54} -4.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(1.50000 - 2.59808i) q^{59} +3.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(7.50000 + 7.79423i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(3.00000 + 5.19615i) q^{68} +(1.50000 - 2.59808i) q^{69} +(1.50000 - 2.59808i) q^{71} +(-1.00000 + 1.73205i) q^{72} -2.00000 q^{73} +(4.00000 - 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{75} +(-2.00000 - 3.46410i) q^{76} +(3.50000 - 0.866025i) q^{78} -4.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-9.00000 + 15.5885i) q^{85} -8.00000 q^{86} +(3.00000 - 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{89} -6.00000 q^{90} +3.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(6.00000 - 10.3923i) q^{95} +1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} - 6 q^{5} - q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 - 6 * q^5 - q^6 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} + q^{3} - q^{4} - 6 q^{5} - q^{6} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 2 q^{12} - 5 q^{13} - 3 q^{15} - q^{16} + 6 q^{17} + 4 q^{18} - 4 q^{19} + 3 q^{20} - 3 q^{23} - q^{24} + 8 q^{25} + 2 q^{26} + 10 q^{27} - 6 q^{29} + 3 q^{30} + 20 q^{31} + q^{32} + 12 q^{34} + 2 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} - 8 q^{43} - 6 q^{45} + 3 q^{46} - 12 q^{47} + q^{48} + 4 q^{50} + 12 q^{51} + 7 q^{52} + 24 q^{53} + 5 q^{54} - 8 q^{57} + 6 q^{58} + 3 q^{59} + 6 q^{60} + 11 q^{61} + 10 q^{62} + 2 q^{64} + 15 q^{65} - 2 q^{67} + 6 q^{68} + 3 q^{69} + 3 q^{71} - 2 q^{72} - 4 q^{73} + 8 q^{74} + 4 q^{75} - 4 q^{76} + 7 q^{78} - 8 q^{79} + 3 q^{80} - q^{81} - 18 q^{85} - 16 q^{86} + 6 q^{87} - 6 q^{89} - 12 q^{90} + 6 q^{92} + 10 q^{93} - 6 q^{94} + 12 q^{95} + 2 q^{96} + 2 q^{97}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - 6 * q^5 - q^6 - 2 * q^8 + 2 * q^9 - 3 * q^10 - 2 * q^12 - 5 * q^13 - 3 * q^15 - q^16 + 6 * q^17 + 4 * q^18 - 4 * q^19 + 3 * q^20 - 3 * q^23 - q^24 + 8 * q^25 + 2 * q^26 + 10 * q^27 - 6 * q^29 + 3 * q^30 + 20 * q^31 + q^32 + 12 * q^34 + 2 * q^36 - 8 * q^37 - 8 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^43 - 6 * q^45 + 3 * q^46 - 12 * q^47 + q^48 + 4 * q^50 + 12 * q^51 + 7 * q^52 + 24 * q^53 + 5 * q^54 - 8 * q^57 + 6 * q^58 + 3 * q^59 + 6 * q^60 + 11 * q^61 + 10 * q^62 + 2 * q^64 + 15 * q^65 - 2 * q^67 + 6 * q^68 + 3 * q^69 + 3 * q^71 - 2 * q^72 - 4 * q^73 + 8 * q^74 + 4 * q^75 - 4 * q^76 + 7 * q^78 - 8 * q^79 + 3 * q^80 - q^81 - 18 * q^85 - 16 * q^86 + 6 * q^87 - 6 * q^89 - 12 * q^90 + 6 * q^92 + 10 * q^93 - 6 * q^94 + 12 * q^95 + 2 * q^96 + 2 * q^97

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