LMFDB - Embedded newform 1078.2.e.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1078.67
Dual form			1078.2.e.a.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.00000 - 1.73205i) q^{12} -2.00000 q^{13} +4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +2.00000 q^{20} +1.00000 q^{22} +(-1.00000 + 1.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} -4.00000 q^{27} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-1.00000 - 1.73205i) q^{40} -8.00000 q^{41} +12.0000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-1.00000 + 1.73205i) q^{45} +(6.00000 + 10.3923i) q^{47} +2.00000 q^{48} -1.00000 q^{50} +(1.00000 - 1.73205i) q^{52} +(1.00000 - 1.73205i) q^{53} +(2.00000 + 3.46410i) q^{54} +2.00000 q^{55} +4.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-2.00000 + 3.46410i) q^{60} +(-5.00000 - 8.66025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-1.00000 + 1.73205i) q^{66} +(6.00000 - 10.3923i) q^{67} +4.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(6.00000 - 10.3923i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{75} +2.00000 q^{76} -4.00000 q^{78} +(-1.00000 + 1.73205i) q^{80} +(5.50000 - 9.52628i) q^{81} +(4.00000 + 6.92820i) q^{82} +18.0000 q^{83} +(-6.00000 - 10.3923i) q^{86} +(-6.00000 + 10.3923i) q^{87} +(-0.500000 + 0.866025i) q^{88} +2.00000 q^{90} +(4.00000 + 6.92820i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{96} +12.0000 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^5 + 4 * q^6 + 2 * q^8 - q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{8} - q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 4 q^{13} + 8 q^{15} - q^{16} - q^{18} - 2 q^{19} + 4 q^{20} + 2 q^{22} - 2 q^{24} + q^{25} + 2 q^{26} - 8 q^{27} + 12 q^{29} - 4 q^{30} + 4 q^{31} - q^{32} - 2 q^{33} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 4 q^{39} - 2 q^{40} - 16 q^{41} + 24 q^{43} - q^{44} - 2 q^{45} + 12 q^{47} + 4 q^{48} - 2 q^{50} + 2 q^{52} + 2 q^{53} + 4 q^{54} + 4 q^{55} + 8 q^{57} - 6 q^{58} + 10 q^{59} - 4 q^{60} - 10 q^{61} - 8 q^{62} + 2 q^{64} + 4 q^{65} - 2 q^{66} + 12 q^{67} + 8 q^{71} - q^{72} + 12 q^{73} - 2 q^{74} + 2 q^{75} + 4 q^{76} - 8 q^{78} - 2 q^{80} + 11 q^{81} + 8 q^{82} + 36 q^{83} - 12 q^{86} - 12 q^{87} - q^{88} + 4 q^{90} + 8 q^{93} + 12 q^{94} - 4 q^{95} - 2 q^{96} + 24 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^5 + 4 * q^6 + 2 * q^8 - q^9 - 2 * q^10 - q^11 - 2 * q^12 - 4 * q^13 + 8 * q^15 - q^16 - q^18 - 2 * q^19 + 4 * q^20 + 2 * q^22 - 2 * q^24 + q^25 + 2 * q^26 - 8 * q^27 + 12 * q^29 - 4 * q^30 + 4 * q^31 - q^32 - 2 * q^33 + 2 * q^36 - 2 * q^37 - 2 * q^38 + 4 * q^39 - 2 * q^40 - 16 * q^41 + 24 * q^43 - q^44 - 2 * q^45 + 12 * q^47 + 4 * q^48 - 2 * q^50 + 2 * q^52 + 2 * q^53 + 4 * q^54 + 4 * q^55 + 8 * q^57 - 6 * q^58 + 10 * q^59 - 4 * q^60 - 10 * q^61 - 8 * q^62 + 2 * q^64 + 4 * q^65 - 2 * q^66 + 12 * q^67 + 8 * q^71 - q^72 + 12 * q^73 - 2 * q^74 + 2 * q^75 + 4 * q^76 - 8 * q^78 - 2 * q^80 + 11 * q^81 + 8 * q^82 + 36 * q^83 - 12 * q^86 - 12 * q^87 - q^88 + 4 * q^90 + 8 * q^93 + 12 * q^94 - 4 * q^95 - 2 * q^96 + 24 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$	2.00000			0.816497
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	4.00000			1.03280
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	1.00000			0.213201
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−2.00000	−	3.46410i	−0.365148	−	0.632456i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	−8.00000			−1.24939			−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000			−1.24939			−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$		0			0
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.856560	+	0.516047i	$0.172597\pi$
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.0186297	+	0.999826i	$0.494070\pi$
$48$	2.00000			0.288675
$49$		0			0
$50$	−1.00000			−0.141421
$51$		0			0
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	2.00000			0.269680
$56$		0			0
$57$	4.00000			0.529813
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$	−2.00000	+	3.46410i	−0.258199	+	0.447214i
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000	+	3.46410i	0.248069	+	0.429669i
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	6.00000	−	10.3923i	0.702247	−	1.21633i	−0.265429	−	0.964130i	$-0.585514\pi$
$73$	6.00000	−	10.3923i	0.702247	−	1.21633i	0.967676	−	0.252197i	$-0.0811531\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$	2.00000			0.229416
$77$		0			0
$78$	−4.00000			−0.452911
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	4.00000	+	6.92820i	0.441726	+	0.765092i
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$		0			0
$85$		0			0
$86$	−6.00000	−	10.3923i	−0.646997	−	1.12063i
$87$	−6.00000	+	10.3923i	−0.643268	+	1.11417i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$		0			0
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$	−1.00000	−	1.73205i	−0.102062	−	0.176777i
$97$	12.0000			1.21842			0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000			1.21842			0.609208	+	0.793011i	$0.291488\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	6.00000	+	10.3923i	0.591198	+	1.02398i	0.994071	+	0.108729i	$0.0346780\pi$
$103$	6.00000	+	10.3923i	0.591198	+	1.02398i	−0.402874	+	0.915255i	$0.631989\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	−1.00000	−	1.73205i	−0.0953463	−	0.165145i
$111$	4.00000			0.379663
$112$		0			0
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$	−10.0000			−0.920575
$119$		0			0
$120$	4.00000			0.365148
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$	8.00000	−	13.8564i	0.721336	−	1.24939i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−12.0000	+	20.7846i	−1.05654	+	1.82998i
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	−1.00000	−	1.73205i	−0.0873704	−	0.151330i	0.819028	−	0.573753i	$-0.194513\pi$
$131$	−1.00000	−	1.73205i	−0.0873704	−	0.151330i	−0.906399	+	0.422423i	$0.861180\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$	−12.0000			−1.03664
$135$	4.00000	+	6.92820i	0.344265	+	0.596285i
$136$		0			0
$137$	−11.0000	+	19.0526i	−0.939793	+	1.62777i	−0.173939	+	0.984757i	$0.555649\pi$
$137$	−11.0000	+	19.0526i	−0.939793	+	1.62777i	−0.765855	+	0.643013i	$0.777684\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	−24.0000			−2.02116
$142$	−2.00000	−	3.46410i	−0.167836	−	0.290701i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−6.00000	−	10.3923i	−0.498273	−	0.863034i
$146$	−12.0000			−0.993127
$147$		0			0
$148$	2.00000			0.164399
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	0.996207	+	0.0870170i	$0.0277334\pi$
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	−0.422744	+	0.906249i	$0.638933\pi$
$150$	1.00000	−	1.73205i	0.0816497	−	0.141421i
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$		0			0
$155$	−8.00000			−0.642575
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$	2.00000	+	3.46410i	0.158610	+	0.274721i
$160$	2.00000			0.158114
$161$		0			0
$162$	−11.0000			−0.864242
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	0.529454	−	0.848339i	$-0.322397\pi$
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	−0.999410	+	0.0343508i	$0.989064\pi$
$164$	4.00000	−	6.92820i	0.312348	−	0.541002i
$165$	−2.00000	+	3.46410i	−0.155700	+	0.269680i
$166$	−9.00000	−	15.5885i	−0.698535	−	1.20990i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	−6.00000	+	10.3923i	−0.457496	+	0.792406i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	12.0000			0.909718
$175$		0			0
$176$	1.00000			0.0753778
$177$	10.0000	+	17.3205i	0.751646	+	1.30189i
$178$		0			0
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	20.0000			1.47844
$184$		0			0
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$		0			0
$188$	−12.0000			−0.875190
$189$		0			0
$190$	4.00000			0.290191
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$	−6.00000	−	10.3923i	−0.430775	−	0.746124i
$195$	−8.00000			−0.572892
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	12.0000	+	20.7846i	0.846415	+	1.46603i
$202$	−6.00000			−0.422159
$203$		0			0
$204$		0			0
$205$	8.00000	+	13.8564i	0.558744	+	0.967773i
$206$	6.00000	−	10.3923i	0.418040	−	0.724066i
$207$		0			0
$208$	1.00000	+	1.73205i	0.0693375	+	0.120096i
$209$	2.00000			0.138343
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	1.00000	+	1.73205i	0.0686803	+	0.118958i
$213$	−4.00000	+	6.92820i	−0.274075	+	0.474713i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−12.0000	−	20.7846i	−0.818393	−	1.41750i
$216$	−4.00000			−0.272166
$217$		0			0
$218$	−10.0000			−0.677285
$219$	12.0000	+	20.7846i	0.810885	+	1.40449i
$220$	−1.00000	+	1.73205i	−0.0674200	+	0.116775i
$221$		0			0
$222$	−2.00000	−	3.46410i	−0.134231	−	0.232495i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$	5.00000	+	8.66025i	0.332595	+	0.576072i
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	−0.749125	−	0.662428i	$-0.769526\pi$
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	0.948242	+	0.317547i	$0.102859\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	−15.0000	−	25.9808i	−0.991228	−	1.71686i	−0.610071	−	0.792347i	$-0.708859\pi$
$229$	−15.0000	−	25.9808i	−0.991228	−	1.71686i	−0.381157	−	0.924510i	$-0.624474\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	5.00000	+	8.66025i	0.327561	+	0.567352i	0.982027	−	0.188739i	$-0.0604400\pi$
$233$	5.00000	+	8.66025i	0.327561	+	0.567352i	−0.654466	+	0.756091i	$0.727107\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$	12.0000	−	20.7846i	0.782794	−	1.35584i
$236$	5.00000	+	8.66025i	0.325472	+	0.563735i
$237$		0			0
$238$		0			0
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	−2.00000	−	3.46410i	−0.129099	−	0.223607i
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	−0.707953	−	0.706260i	$-0.750381\pi$
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	0.965615	+	0.259975i	$0.0837143\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	10.0000			0.640184
$245$		0			0
$246$	−16.0000			−1.02012
$247$	2.00000	+	3.46410i	0.127257	+	0.220416i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	−18.0000	+	31.1769i	−1.14070	+	1.97576i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$		0			0
$254$	−2.00000	−	3.46410i	−0.125491	−	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.00000	+	13.8564i	0.499026	+	0.864339i	0.999999	−	0.00112398i	$-0.000357774\pi$
$257$	8.00000	+	13.8564i	0.499026	+	0.864339i	−0.500973	+	0.865463i	$0.667024\pi$
$258$	24.0000			1.49417
$259$		0			0
$260$	−4.00000			−0.248069
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$	−1.00000	+	1.73205i	−0.0617802	+	0.107006i
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$	−1.00000	−	1.73205i	−0.0615457	−	0.106600i
$265$	−4.00000			−0.245718
$266$		0			0
$267$		0			0
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$	4.00000	−	6.92820i	0.243432	−	0.421637i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$		0			0
$273$		0			0
$274$	22.0000			1.32907
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$		0			0
$277$	7.00000	−	12.1244i	0.420589	−	0.728482i	−0.575408	−	0.817867i	$-0.695157\pi$
$277$	7.00000	−	12.1244i	0.420589	−	0.728482i	0.995997	+	0.0893846i	$0.0284900\pi$
$278$	−7.00000	−	12.1244i	−0.419832	−	0.727171i
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	12.0000	+	20.7846i	0.714590	+	1.23771i
$283$	−1.00000	+	1.73205i	−0.0594438	+	0.102960i	−0.894216	−	0.447636i	$-0.852266\pi$
$283$	−1.00000	+	1.73205i	−0.0594438	+	0.102960i	0.834772	+	0.550596i	$0.185599\pi$
$284$	−2.00000	+	3.46410i	−0.118678	+	0.205557i
$285$	−4.00000	−	6.92820i	−0.236940	−	0.410391i
$286$	−2.00000			−0.118262
$287$		0			0
$288$	1.00000			0.0589256
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−6.00000	+	10.3923i	−0.352332	+	0.610257i
$291$	−12.0000	+	20.7846i	−0.703452	+	1.21842i
$292$	6.00000	+	10.3923i	0.351123	+	0.608164i
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$		0			0
$295$	−20.0000			−1.16445
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$	7.00000	−	12.1244i	0.405499	−	0.702345i
$299$		0			0
$300$	−2.00000			−0.115470
$301$		0			0
$302$	−4.00000			−0.230174
$303$	6.00000	+	10.3923i	0.344691	+	0.597022i
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	−10.0000	+	17.3205i	−0.572598	+	0.991769i
$306$		0			0
$307$	−14.0000			−0.799022			−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000			−0.799022			−0.399511	+	0.916728i	$0.630820\pi$
$308$		0			0
$309$	−24.0000			−1.36531
$310$	4.00000	+	6.92820i	0.227185	+	0.393496i
$311$	8.00000	−	13.8564i	0.453638	−	0.785725i	−0.544970	−	0.838455i	$-0.683459\pi$
$311$	8.00000	−	13.8564i	0.453638	−	0.785725i	0.998609	+	0.0527306i	$0.0167924\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	−2.00000	−	3.46410i	−0.113047	−	0.195803i	0.803951	−	0.594696i	$-0.202728\pi$
$313$	−2.00000	−	3.46410i	−0.113047	−	0.195803i	−0.916997	+	0.398894i	$0.869394\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$		0			0
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	−0.887788	−	0.460252i	$-0.847759\pi$
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	0.0453045	−	0.998973i	$-0.485574\pi$
$318$	2.00000	−	3.46410i	0.112154	−	0.194257i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	−1.00000	−	1.73205i	−0.0559017	−	0.0968246i
$321$	24.0000			1.33955
$322$		0			0
$323$		0			0
$324$	5.50000	+	9.52628i	0.305556	+	0.529238i
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	10.0000	+	17.3205i	0.553001	+	0.957826i
$328$	−8.00000			−0.441726
$329$		0			0
$330$	4.00000			0.220193
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$	−9.00000	+	15.5885i	−0.493939	+	0.855528i
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$	6.00000	+	10.3923i	0.328305	+	0.568642i
$335$	−24.0000			−1.31126
$336$		0			0
$337$	34.0000			1.85210			0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000			1.85210			0.926049	+	0.377403i	$0.123183\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$	10.0000	−	17.3205i	0.543125	−	0.940721i
$340$		0			0
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$	2.00000			0.108148
$343$		0			0
$344$	12.0000			0.646997
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	0.462244	+	0.886753i	$0.347044\pi$
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	−0.999072	+	0.0430610i	$0.986289\pi$
$348$	−6.00000	−	10.3923i	−0.321634	−	0.557086i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$	10.0000	−	17.3205i	0.531494	−	0.920575i
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$		0			0
$357$		0			0
$358$	12.0000			0.634220
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$	−1.00000	+	1.73205i	−0.0527046	+	0.0912871i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	9.00000	+	15.5885i	0.473029	+	0.819311i
$363$	2.00000			0.104973
$364$		0			0
$365$	−24.0000			−1.25622
$366$	−10.0000	−	17.3205i	−0.522708	−	0.905357i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$		0			0
$369$	4.00000	+	6.92820i	0.208232	+	0.360668i
$370$	4.00000			0.207950
$371$		0			0
$372$	−8.00000			−0.414781
$373$	15.0000	+	25.9808i	0.776671	+	1.34523i	0.933851	+	0.357663i	$0.116426\pi$
$373$	15.0000	+	25.9808i	0.776671	+	1.34523i	−0.157180	+	0.987570i	$0.550240\pi$
$374$		0			0
$375$	12.0000	−	20.7846i	0.619677	−	1.07331i
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$	−12.0000			−0.618031
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$	2.00000			0.102062
$385$		0			0
$386$	−2.00000			−0.101797
$387$	−6.00000	−	10.3923i	−0.304997	−	0.528271i
$388$	−6.00000	+	10.3923i	−0.304604	+	0.527589i
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	−0.964490	−	0.264120i	$-0.914918\pi$
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	0.710980	+	0.703213i	$0.248252\pi$
$390$	4.00000	+	6.92820i	0.202548	+	0.350823i
$391$		0			0
$392$		0			0
$393$	4.00000			0.201773
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$		0			0
$396$	−0.500000	+	0.866025i	−0.0251259	+	0.0435194i
$397$	17.0000	+	29.4449i	0.853206	+	1.47780i	0.878300	+	0.478110i	$0.158678\pi$
$397$	17.0000	+	29.4449i	0.853206	+	1.47780i	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	12.0000	−	20.7846i	0.598506	−	1.03664i
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	−22.0000			−1.09319
$406$		0			0
$407$	2.00000			0.0991363
$408$		0			0
$409$	8.00000	−	13.8564i	0.395575	−	0.685155i	−0.597600	−	0.801795i	$-0.703879\pi$
$409$	8.00000	−	13.8564i	0.395575	−	0.685155i	0.993174	+	0.116639i	$0.0372122\pi$
$410$	8.00000	−	13.8564i	0.395092	−	0.684319i
$411$	−22.0000	−	38.1051i	−1.08518	−	1.87959i
$412$	−12.0000			−0.591198
$413$		0			0
$414$		0			0
$415$	−18.0000	−	31.1769i	−0.883585	−	1.53041i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	−14.0000	+	24.2487i	−0.685583	+	1.18746i
$418$	−1.00000	−	1.73205i	−0.0489116	−	0.0847174i
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$		0			0
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	2.00000	+	3.46410i	0.0973585	+	0.168630i
$423$	6.00000	−	10.3923i	0.291730	−	0.505291i
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$		0			0
$426$	8.00000			0.387601
$427$		0			0
$428$	12.0000			0.580042
$429$	2.00000	+	3.46410i	0.0965609	+	0.167248i
$430$	−12.0000	+	20.7846i	−0.578691	+	1.00232i
$431$	18.0000	−	31.1769i	0.867029	−	1.50174i	0.00201168	−	0.999998i	$-0.499360\pi$
$431$	18.0000	−	31.1769i	0.867029	−	1.50174i	0.865018	−	0.501741i	$-0.167307\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$		0			0
$435$	24.0000			1.15071
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$		0			0
$438$	12.0000	−	20.7846i	0.573382	−	0.993127i
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	0.609503	−	0.792784i	$-0.291369\pi$
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	−0.991322	+	0.131453i	$0.958036\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$		0			0
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$	−28.0000			−1.32435
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	0.500000	+	0.866025i	0.0235702	+	0.0408248i
$451$	4.00000	−	6.92820i	0.188353	−	0.326236i
$452$	5.00000	−	8.66025i	0.235180	−	0.407344i
$453$	4.00000	+	6.92820i	0.187936	+	0.325515i
$454$	−6.00000			−0.281594
$455$		0			0
$456$	4.00000			0.187317
$457$	−3.00000	−	5.19615i	−0.140334	−	0.243066i	0.787288	−	0.616585i	$-0.211484\pi$
$457$	−3.00000	−	5.19615i	−0.140334	−	0.243066i	−0.927622	+	0.373519i	$0.878151\pi$
$458$	−15.0000	+	25.9808i	−0.700904	+	1.21400i
$459$		0			0
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	8.00000	−	13.8564i	0.370991	−	0.642575i
$466$	5.00000	−	8.66025i	0.231621	−	0.401179i
$467$	−11.0000	−	19.0526i	−0.509019	−	0.881647i	−0.999945	−	0.0104461i	$-0.996675\pi$
$467$	−11.0000	−	19.0526i	−0.509019	−	0.881647i	0.490926	−	0.871201i	$-0.336658\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$	−24.0000			−1.10704
$471$	−14.0000	−	24.2487i	−0.645086	−	1.11732i
$472$	5.00000	−	8.66025i	0.230144	−	0.398621i
$473$	−6.00000	+	10.3923i	−0.275880	+	0.477839i
$474$		0			0
$475$	−2.00000			−0.0917663
$476$		0			0
$477$	−2.00000			−0.0915737
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$	−2.00000	+	3.46410i	−0.0912871	+	0.158114i
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	−8.00000			−0.364390
$483$		0			0
$484$	1.00000			0.0454545
$485$	−12.0000	−	20.7846i	−0.544892	−	0.943781i
$486$	5.00000	−	8.66025i	0.226805	−	0.392837i
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	−0.942309	−	0.334744i	$-0.891350\pi$
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	0.761052	+	0.648691i	$0.224683\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$	24.0000			1.08532
$490$		0			0
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$	8.00000	+	13.8564i	0.360668	+	0.624695i
$493$		0			0
$494$	2.00000	−	3.46410i	0.0899843	−	0.155857i
$495$	−1.00000	−	1.73205i	−0.0449467	−	0.0778499i
$496$	−4.00000			−0.179605
$497$		0			0
$498$	36.0000			1.61320
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	0.550572	−	0.834788i	$-0.314410\pi$
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	−0.998233	+	0.0594153i	$0.981076\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$	−9.00000	−	15.5885i	−0.401690	−	0.695747i
$503$	8.00000			0.356702			0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000			0.356702			0.178351	+	0.983967i	$0.442924\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$		0			0
$507$	9.00000	−	15.5885i	0.399704	−	0.692308i
$508$	−2.00000	+	3.46410i	−0.0887357	+	0.153695i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$	4.00000	+	6.92820i	0.176604	+	0.305888i
$514$	8.00000	−	13.8564i	0.352865	−	0.611180i
$515$	12.0000	−	20.7846i	0.528783	−	0.915879i
$516$	−12.0000	−	20.7846i	−0.528271	−	0.914991i
$517$	−12.0000			−0.527759
$518$		0			0
$519$	12.0000			0.526742
$520$	2.00000	+	3.46410i	0.0877058	+	0.151911i
$521$	−2.00000	+	3.46410i	−0.0876216	+	0.151765i	−0.906505	−	0.422194i	$-0.861260\pi$
$521$	−2.00000	+	3.46410i	−0.0876216	+	0.151765i	0.818884	+	0.573959i	$0.194593\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	−0.950958	−	0.309320i	$-0.899899\pi$
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	0.207600	−	0.978214i	$-0.433435\pi$
$524$	2.00000			0.0873704
$525$		0			0
$526$	16.0000			0.697633
$527$		0			0
$528$	−1.00000	+	1.73205i	−0.0435194	+	0.0753778i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	2.00000	+	3.46410i	0.0868744	+	0.150471i
$531$	−10.0000			−0.433963
$532$		0			0
$533$	16.0000			0.693037
$534$		0			0
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	−12.0000	−	20.7846i	−0.517838	−	0.896922i
$538$	6.00000			0.258678
$539$		0			0
$540$	−8.00000			−0.344265
$541$	−17.0000	−	29.4449i	−0.730887	−	1.26593i	−0.956504	−	0.291718i	$-0.905773\pi$
$541$	−17.0000	−	29.4449i	−0.730887	−	1.26593i	0.225617	−	0.974216i	$-0.427560\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$	18.0000	−	31.1769i	0.772454	−	1.33793i
$544$		0			0
$545$	−20.0000			−0.856706
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−11.0000	−	19.0526i	−0.469897	−	0.813885i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$	0.500000	−	0.866025i	0.0213201	−	0.0369274i
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$	−14.0000			−0.594803
$555$	−4.00000	−	6.92820i	−0.169791	−	0.294086i
$556$	−7.00000	+	12.1244i	−0.296866	+	0.514187i
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	0.240561	+	0.970634i	$0.422669\pi$
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	−0.960874	+	0.276985i	$0.910665\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	−24.0000			−1.01509
$560$		0			0
$561$		0			0
$562$	5.00000	+	8.66025i	0.210912	+	0.365311i
$563$	−11.0000	+	19.0526i	−0.463595	+	0.802970i	−0.999137	−	0.0415389i	$-0.986774\pi$
$563$	−11.0000	+	19.0526i	−0.463595	+	0.802970i	0.535542	+	0.844508i	$0.320107\pi$
$564$	12.0000	−	20.7846i	0.505291	−	0.875190i
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$	2.00000			0.0840663
$567$		0			0
$568$	4.00000			0.167836
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$	−4.00000	+	6.92820i	−0.167542	+	0.290191i
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	1.00000	+	1.73205i	0.0418121	+	0.0724207i
$573$	24.0000			1.00261
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−16.0000	+	27.7128i	−0.666089	+	1.15370i	0.312900	+	0.949786i	$0.398699\pi$
$577$	−16.0000	+	27.7128i	−0.666089	+	1.15370i	−0.978989	+	0.203913i	$0.934634\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$	2.00000	+	3.46410i	0.0831172	+	0.143963i
$580$	12.0000			0.498273
$581$		0			0
$582$	24.0000			0.994832
$583$	1.00000	+	1.73205i	0.0414158	+	0.0717342i
$584$	6.00000	−	10.3923i	0.248282	−	0.430037i
$585$	2.00000	−	3.46410i	0.0826898	−	0.143223i
$586$	−13.0000	−	22.5167i	−0.537025	−	0.930155i
$587$	42.0000			1.73353			0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000			1.73353			0.866763	+	0.498721i	$0.166197\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$	10.0000	+	17.3205i	0.411693	+	0.713074i
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	10.0000	+	17.3205i	0.410651	+	0.711268i	0.994961	−	0.100262i	$-0.0319682\pi$
$593$	10.0000	+	17.3205i	0.410651	+	0.711268i	−0.584310	+	0.811530i	$0.698635\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−14.0000			−0.573462
$597$	4.00000	+	6.92820i	0.163709	+	0.283552i
$598$		0			0
$599$	−14.0000	+	24.2487i	−0.572024	+	0.990775i	0.424333	+	0.905506i	$0.360508\pi$
$599$	−14.0000	+	24.2487i	−0.572024	+	0.990775i	−0.996358	+	0.0852695i	$0.972825\pi$
$600$	1.00000	+	1.73205i	0.0408248	+	0.0707107i
$601$	−4.00000			−0.163163			−0.0815817	−	0.996667i	$-0.525997\pi$
$601$	−4.00000			−0.163163			−0.0815817	+	0.996667i	$0.525997\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$	2.00000	+	3.46410i	0.0813788	+	0.140952i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	6.00000	−	10.3923i	0.243733	−	0.422159i
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	0.983262	+	0.182199i	$0.0583216\pi$
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	−0.333842	+	0.942629i	$0.608345\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$	20.0000			0.809776
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$		0			0
$613$	21.0000	−	36.3731i	0.848182	−	1.46909i	−0.0346469	−	0.999400i	$-0.511031\pi$
$613$	21.0000	−	36.3731i	0.848182	−	1.46909i	0.882829	−	0.469695i	$-0.155636\pi$
$614$	7.00000	+	12.1244i	0.282497	+	0.489299i
$615$	−32.0000			−1.29036
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	12.0000	+	20.7846i	0.482711	+	0.836080i
$619$	−7.00000	+	12.1244i	−0.281354	+	0.487319i	−0.971718	−	0.236143i	$-0.924117\pi$
$619$	−7.00000	+	12.1244i	−0.281354	+	0.487319i	0.690365	+	0.723462i	$0.257450\pi$
$620$	4.00000	−	6.92820i	0.160644	−	0.278243i
$621$		0			0
$622$	−16.0000			−0.641542
$623$		0			0
$624$	−4.00000			−0.160128
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−2.00000	+	3.46410i	−0.0799361	+	0.138453i
$627$	−2.00000	+	3.46410i	−0.0798723	+	0.138343i
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$		0			0
$630$		0			0
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$		0			0
$633$	4.00000	−	6.92820i	0.158986	−	0.275371i
$634$	−15.0000	+	25.9808i	−0.595726	+	1.03183i
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$	−4.00000			−0.158610
$637$		0			0
$638$	6.00000			0.237542
$639$	−2.00000	−	3.46410i	−0.0791188	−	0.137038i
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$	−12.0000	−	20.7846i	−0.473602	−	0.820303i
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$		0			0
$645$	48.0000			1.89000
$646$		0			0
$647$	−22.0000	+	38.1051i	−0.864909	+	1.49807i	0.00222801	+	0.999998i	$0.499291\pi$
$647$	−22.0000	+	38.1051i	−0.864909	+	1.49807i	−0.867137	+	0.498069i	$0.834043\pi$
$648$	5.50000	−	9.52628i	0.216060	−	0.374228i
$649$	5.00000	+	8.66025i	0.196267	+	0.339945i
$650$	2.00000			0.0784465
$651$		0			0
$652$	12.0000			0.469956
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	10.0000	−	17.3205i	0.391031	−	0.677285i
$655$	−2.00000	+	3.46410i	−0.0781465	+	0.135354i
$656$	4.00000	+	6.92820i	0.156174	+	0.270501i
$657$	−12.0000			−0.468165
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	−2.00000	−	3.46410i	−0.0778499	−	0.134840i
$661$	3.00000	−	5.19615i	0.116686	−	0.202107i	−0.801766	−	0.597638i	$-0.796106\pi$
$661$	3.00000	−	5.19615i	0.116686	−	0.202107i	0.918453	+	0.395531i	$0.129439\pi$
$662$	−6.00000	+	10.3923i	−0.233197	+	0.403908i
$663$		0			0
$664$	18.0000			0.698535
$665$		0			0
$666$	2.00000			0.0774984
$667$		0			0
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$	12.0000	+	20.7846i	0.463600	+	0.802980i
$671$	10.0000			0.386046
$672$		0			0
$673$	6.00000			0.231283			0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000			0.231283			0.115642	+	0.993291i	$0.463108\pi$
$674$	−17.0000	−	29.4449i	−0.654816	−	1.13417i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$678$	−20.0000			−0.768095
$679$		0			0
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	−2.00000	+	3.46410i	−0.0765279	+	0.132550i	−0.901750	−	0.432259i	$-0.857717\pi$
$683$	−2.00000	+	3.46410i	−0.0765279	+	0.132550i	0.825222	+	0.564809i	$0.191050\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$	44.0000			1.68115
$686$		0			0
$687$	60.0000			2.28914
$688$	−6.00000	−	10.3923i	−0.228748	−	0.396203i
$689$	−2.00000	+	3.46410i	−0.0761939	+	0.131972i
$690$		0			0
$691$	25.0000	+	43.3013i	0.951045	+	1.64726i	0.743170	+	0.669102i	$0.233321\pi$
$691$	25.0000	+	43.3013i	0.951045	+	1.64726i	0.207875	+	0.978155i	$0.433345\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	20.0000			0.759190
$695$	−14.0000	−	24.2487i	−0.531050	−	0.919806i
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$		0			0
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$	−20.0000			−0.756469
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$	−4.00000	−	6.92820i	−0.150970	−	0.261488i
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	24.0000	+	41.5692i	0.903892	+	1.56559i
$706$	−24.0000			−0.903252
$707$		0			0
$708$	−20.0000			−0.751646
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	0.967009	−	0.254743i	$-0.0819909\pi$
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	−0.704118	+	0.710083i	$0.748658\pi$
$710$	−4.00000	+	6.92820i	−0.150117	+	0.260011i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−4.00000			−0.149592
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	4.00000	−	6.92820i	0.149383	−	0.258738i
$718$	−10.0000	+	17.3205i	−0.373197	+	0.646396i
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	−0.999669	−	0.0257237i	$-0.991811\pi$
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	0.477557	−	0.878601i	$-0.341522\pi$
$720$	2.00000			0.0745356
$721$		0			0
$722$	−15.0000			−0.558242
$723$	8.00000	+	13.8564i	0.297523	+	0.515325i
$724$	9.00000	−	15.5885i	0.334482	−	0.579340i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	−12.0000			−0.445055			−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000			−0.445055			−0.222528	+	0.974926i	$0.571431\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	12.0000	+	20.7846i	0.444140	+	0.769273i
$731$		0			0
$732$	−10.0000	+	17.3205i	−0.369611	+	0.640184i
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$		0			0
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$	4.00000	−	6.92820i	0.147242	−	0.255031i
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	−0.826893	−	0.562360i	$-0.809894\pi$
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	0.900464	+	0.434930i	$0.143227\pi$
$740$	−2.00000	−	3.46410i	−0.0735215	−	0.127343i
$741$	−8.00000			−0.293887
$742$		0			0
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$	14.0000	−	24.2487i	0.512920	−	0.888404i
$746$	15.0000	−	25.9808i	0.549189	−	0.951223i
$747$	−9.00000	−	15.5885i	−0.329293	−	0.570352i
$748$		0			0
$749$		0			0
$750$	−24.0000			−0.876356
$751$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$751$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$	−18.0000	+	31.1769i	−0.655956	+	1.13615i
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−30.0000			−1.09037			−0.545184	−	0.838316i	$-0.683540\pi$
$757$	−30.0000			−1.09037			−0.545184	+	0.838316i	$0.683540\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$		0			0
$760$	−2.00000	+	3.46410i	−0.0725476	+	0.125656i
$761$	4.00000	+	6.92820i	0.145000	+	0.251147i	0.929373	−	0.369142i	$-0.120348\pi$
$761$	4.00000	+	6.92820i	0.145000	+	0.251147i	−0.784373	+	0.620289i	$0.787015\pi$
$762$	8.00000			0.289809
$763$		0			0
$764$	12.0000			0.434145
$765$		0			0
$766$	6.00000	−	10.3923i	0.216789	−	0.375489i
$767$	−10.0000	+	17.3205i	−0.361079	+	0.625407i
$768$	−1.00000	−	1.73205i	−0.0360844	−	0.0625000i
$769$	40.0000			1.44244			0.721218	−	0.692708i	$-0.243582\pi$
$769$	40.0000			1.44244			0.721218	+	0.692708i	$0.243582\pi$
$770$		0			0
$771$	−32.0000			−1.15245
$772$	1.00000	+	1.73205i	0.0359908	+	0.0623379i
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	−0.712241	−	0.701935i	$-0.752320\pi$
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$774$	−6.00000	+	10.3923i	−0.215666	+	0.373544i
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$	12.0000			0.430775
$777$		0			0
$778$	10.0000			0.358517
$779$	8.00000	+	13.8564i	0.286630	+	0.496457i
$780$	4.00000	−	6.92820i	0.143223	−	0.248069i
$781$	−2.00000	+	3.46410i	−0.0715656	+	0.123955i
$782$		0			0
$783$	−24.0000			−0.857690
$784$		0			0
$785$	28.0000			0.999363
$786$	−2.00000	−	3.46410i	−0.0713376	−	0.123560i
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	−0.713871	−	0.700278i	$-0.753059\pi$
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	0.963394	+	0.268091i	$0.0863928\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$	−16.0000	−	27.7128i	−0.569615	−	0.986602i
$790$		0			0
$791$		0			0
$792$	1.00000			0.0355335
$793$	10.0000	+	17.3205i	0.355110	+	0.615069i
$794$	17.0000	−	29.4449i	0.603307	−	1.04496i
$795$	4.00000	−	6.92820i	0.141865	−	0.245718i
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	6.00000	+	10.3923i	0.211735	+	0.366736i
$804$	−24.0000			−0.846415
$805$		0			0
$806$	8.00000			0.281788
$807$	−6.00000	−	10.3923i	−0.211210	−	0.365826i
$808$	3.00000	−	5.19615i	0.105540	−	0.182800i
$809$	−19.0000	+	32.9090i	−0.668004	+	1.15702i	0.310457	+	0.950587i	$0.399518\pi$
$809$	−19.0000	+	32.9090i	−0.668004	+	1.15702i	−0.978461	+	0.206430i	$0.933815\pi$
$810$	11.0000	+	19.0526i	0.386501	+	0.669439i
$811$	50.0000			1.75574			0.877869	−	0.478901i	$-0.158965\pi$
$811$	50.0000			1.75574			0.877869	+	0.478901i	$0.158965\pi$
$812$		0			0
$813$	−32.0000			−1.12229
$814$	−1.00000	−	1.73205i	−0.0350500	−	0.0607083i
$815$	−12.0000	+	20.7846i	−0.420342	+	0.728053i
$816$		0			0
$817$	−12.0000	−	20.7846i	−0.419827	−	0.727161i
$818$	−16.0000			−0.559427
$819$		0			0
$820$	−16.0000			−0.558744
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$	−22.0000	+	38.1051i	−0.767338	+	1.32907i
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	−0.637419	−	0.770517i	$-0.719998\pi$
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	0.985997	+	0.166762i	$0.0533313\pi$
$824$	6.00000	+	10.3923i	0.209020	+	0.362033i
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$	−18.0000	+	31.1769i	−0.624789	+	1.08217i
$831$	14.0000	+	24.2487i	0.485655	+	0.841178i
$832$	−2.00000			−0.0693375
$833$		0			0
$834$	28.0000			0.969561
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	−1.00000	+	1.73205i	−0.0345857	+	0.0599042i
$837$	−8.00000	+	13.8564i	−0.276520	+	0.478947i
$838$	−9.00000	−	15.5885i	−0.310900	−	0.538494i
$839$	36.0000			1.24286			0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000			1.24286			0.621429	+	0.783470i	$0.286552\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	17.0000	+	29.4449i	0.585859	+	1.01474i
$843$	10.0000	−	17.3205i	0.344418	−	0.596550i
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	9.00000	+	15.5885i	0.309609	+	0.536259i
$846$	−12.0000			−0.412568
$847$		0			0
$848$	−2.00000			−0.0686803
$849$	−2.00000	−	3.46410i	−0.0686398	−	0.118888i
$850$		0			0
$851$		0			0
$852$	−4.00000	−	6.92820i	−0.137038	−	0.237356i
$853$	−42.0000			−1.43805			−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000			−1.43805			−0.719026	+	0.694983i	$0.755412\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	24.0000	−	41.5692i	0.819824	−	1.41998i	−0.0859870	−	0.996296i	$-0.527404\pi$
$857$	24.0000	−	41.5692i	0.819824	−	1.41998i	0.905811	−	0.423681i	$-0.139262\pi$
$858$	2.00000	−	3.46410i	0.0682789	−	0.118262i
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	−0.995475	−	0.0950262i	$-0.969707\pi$
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	0.415442	−	0.909620i	$-0.363627\pi$
$860$	24.0000			0.818393
$861$		0			0
$862$	−36.0000			−1.22616
$863$	26.0000	+	45.0333i	0.885050	+	1.53295i	0.845656	+	0.533728i	$0.179210\pi$
$863$	26.0000	+	45.0333i	0.885050	+	1.53295i	0.0393943	+	0.999224i	$0.487457\pi$
$864$	2.00000	−	3.46410i	0.0680414	−	0.117851i
$865$	−6.00000	+	10.3923i	−0.204006	+	0.353349i
$866$	2.00000	+	3.46410i	0.0679628	+	0.117715i
$867$	−34.0000			−1.15470
$868$		0			0
$869$		0			0
$870$	−12.0000	−	20.7846i	−0.406838	−	0.704664i
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$	−6.00000	−	10.3923i	−0.203069	−	0.351726i
$874$		0			0
$875$		0			0
$876$	−24.0000			−0.810885
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	0.882415	−	0.470471i	$-0.155916\pi$
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	−0.848648	+	0.528958i	$0.822583\pi$
$878$	−8.00000	+	13.8564i	−0.269987	+	0.467631i
$879$	−26.0000	+	45.0333i	−0.876958	+	1.51894i
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	−24.0000			−0.808581			−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000			−0.808581			−0.404290	+	0.914631i	$0.632481\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$	20.0000	−	34.6410i	0.672293	−	1.16445i
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	10.0000	+	17.3205i	0.335767	+	0.581566i	0.983632	−	0.180190i	$-0.0576711\pi$
$887$	10.0000	+	17.3205i	0.335767	+	0.581566i	−0.647865	+	0.761755i	$0.724338\pi$
$888$	4.00000			0.134231
$889$		0			0
$890$		0			0
$891$	5.50000	+	9.52628i	0.184257	+	0.319142i
$892$	4.00000	−	6.92820i	0.133930	−	0.231973i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$	14.0000	+	24.2487i	0.468230	+	0.810998i
$895$	24.0000			0.802232
$896$		0			0
$897$		0			0
$898$	15.0000	+	25.9808i	0.500556	+	0.866989i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$		0			0
$902$	−8.00000			−0.266371
$903$		0			0
$904$	−10.0000			−0.332595
$905$	18.0000	+	31.1769i	0.598340	+	1.03636i
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−2.00000	+	3.46410i	−0.0664089	+	0.115024i	−0.897318	−	0.441384i	$-0.854488\pi$
$907$	−2.00000	+	3.46410i	−0.0664089	+	0.115024i	0.830909	+	0.556408i	$0.187821\pi$
$908$	3.00000	+	5.19615i	0.0995585	+	0.172440i
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−32.0000			−1.06021			−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000			−1.06021			−0.530104	+	0.847933i	$0.677847\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−9.00000	+	15.5885i	−0.297857	+	0.515903i
$914$	−3.00000	+	5.19615i	−0.0992312	+	0.171873i
$915$	−20.0000	−	34.6410i	−0.661180	−	1.14520i
$916$	30.0000			0.991228
$917$		0			0
$918$		0			0
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	0.924427	−	0.381358i	$-0.124544\pi$
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	−0.792480	+	0.609898i	$0.791210\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$	−3.00000	−	5.19615i	−0.0987997	−	0.171126i
$923$	−8.00000			−0.263323
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	−2.00000	−	3.46410i	−0.0657241	−	0.113837i
$927$	6.00000	−	10.3923i	0.197066	−	0.341328i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	−2.00000	−	3.46410i	−0.0656179	−	0.113653i	0.831350	−	0.555749i	$-0.187569\pi$
$929$	−2.00000	−	3.46410i	−0.0656179	−	0.113653i	−0.896968	+	0.442096i	$0.854235\pi$
$930$	−16.0000			−0.524661
$931$		0			0
$932$	−10.0000			−0.327561
$933$	16.0000	+	27.7128i	0.523816	+	0.907277i
$934$	−11.0000	+	19.0526i	−0.359931	+	0.623419i
$935$		0			0
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$	20.0000			0.653372			0.326686	−	0.945133i	$-0.394068\pi$
$937$	20.0000			0.653372			0.326686	+	0.945133i	$0.394068\pi$
$938$		0			0
$939$	8.00000			0.261070
$940$	12.0000	+	20.7846i	0.391397	+	0.677919i
$941$	−21.0000	+	36.3731i	−0.684580	+	1.18573i	0.288988	+	0.957333i	$0.406681\pi$
$941$	−21.0000	+	36.3731i	−0.684580	+	1.18573i	−0.973568	+	0.228395i	$0.926652\pi$
$942$	−14.0000	+	24.2487i	−0.456145	+	0.790066i
$943$		0			0
$944$	−10.0000			−0.325472
$945$		0			0
$946$	12.0000			0.390154
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$	−12.0000	+	20.7846i	−0.389536	+	0.674697i
$950$	1.00000	+	1.73205i	0.0324443	+	0.0561951i
$951$	60.0000			1.94563
$952$		0			0
$953$	34.0000			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$	1.00000	+	1.73205i	0.0323762	+	0.0560772i
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$	2.00000	−	3.46410i	0.0646846	−	0.112037i
$957$	−6.00000	−	10.3923i	−0.193952	−	0.335936i
$958$	36.0000			1.16311
$959$		0			0
$960$	4.00000			0.129099
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	4.00000	+	6.92820i	0.128831	+	0.223142i
$965$	−4.00000			−0.128765
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$		0			0
$970$	−12.0000	+	20.7846i	−0.385297	+	0.667354i
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	0.813865	−	0.581054i	$-0.197359\pi$
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	−0.910140	+	0.414301i	$0.864026\pi$
$972$	−10.0000			−0.320750
$973$		0			0
$974$	8.00000			0.256337
$975$	−2.00000	−	3.46410i	−0.0640513	−	0.110940i
$976$	−5.00000	+	8.66025i	−0.160046	+	0.277208i
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	−0.849586	−	0.527451i	$-0.823148\pi$
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	0.881579	+	0.472037i	$0.156481\pi$
$978$	−12.0000	−	20.7846i	−0.383718	−	0.664619i
$979$		0			0
$980$		0			0
$981$	−10.0000			−0.319275
$982$	−14.0000	−	24.2487i	−0.446758	−	0.773807i
$983$	22.0000	−	38.1051i	0.701691	−	1.21536i	−0.266181	−	0.963923i	$-0.585762\pi$
$983$	22.0000	−	38.1051i	0.701691	−	1.21536i	0.967872	−	0.251442i	$-0.0809046\pi$
$984$	8.00000	−	13.8564i	0.255031	−	0.441726i
$985$	6.00000	+	10.3923i	0.191176	+	0.331126i
$986$		0			0
$987$		0			0
$988$	−4.00000			−0.127257
$989$		0			0
$990$	−1.00000	+	1.73205i	−0.0317821	+	0.0550482i
$991$	26.0000	−	45.0333i	0.825917	−	1.43053i	−0.0752991	−	0.997161i	$-0.523991\pi$
$991$	26.0000	−	45.0333i	0.825917	−	1.43053i	0.901216	−	0.433370i	$-0.142676\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	24.0000			0.761617
$994$		0			0
$995$	−8.00000			−0.253617
$996$	−18.0000	−	31.1769i	−0.570352	−	0.987878i
$997$	31.0000	−	53.6936i	0.981780	−	1.70049i	0.326326	−	0.945257i	$-0.394189\pi$
$997$	31.0000	−	53.6936i	0.981780	−	1.70049i	0.655454	−	0.755235i	$-0.272477\pi$
$998$	−10.0000	+	17.3205i	−0.316544	+	0.548271i
$999$	4.00000	+	6.92820i	0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.a.67.1		2
7.2	even	3	inner	1078.2.e.a.177.1		2
7.3	odd	6		1078.2.a.h.1.1	✓	1
7.4	even	3		1078.2.a.l.1.1	yes	1
7.5	odd	6		1078.2.e.e.177.1		2
7.6	odd	2		1078.2.e.e.67.1		2
21.11	odd	6		9702.2.a.e.1.1		1
21.17	even	6		9702.2.a.t.1.1		1
28.3	even	6		8624.2.a.y.1.1		1
28.11	odd	6		8624.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.a.h.1.1	✓	1	7.3	odd	6
1078.2.a.l.1.1	yes	1	7.4	even	3
1078.2.e.a.67.1		2	1.1	even	1	trivial
1078.2.e.a.177.1		2	7.2	even	3	inner
1078.2.e.e.67.1		2	7.6	odd	2
1078.2.e.e.177.1		2	7.5	odd	6
8624.2.a.g.1.1		1	28.11	odd	6
8624.2.a.y.1.1		1	28.3	even	6
9702.2.a.e.1.1		1	21.11	odd	6
9702.2.a.t.1.1		1	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.00000 - 1.73205i) q^{12} -2.00000 q^{13} +4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +2.00000 q^{20} +1.00000 q^{22} +(-1.00000 + 1.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} -4.00000 q^{27} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-1.00000 - 1.73205i) q^{40} -8.00000 q^{41} +12.0000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-1.00000 + 1.73205i) q^{45} +(6.00000 + 10.3923i) q^{47} +2.00000 q^{48} -1.00000 q^{50} +(1.00000 - 1.73205i) q^{52} +(1.00000 - 1.73205i) q^{53} +(2.00000 + 3.46410i) q^{54} +2.00000 q^{55} +4.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-2.00000 + 3.46410i) q^{60} +(-5.00000 - 8.66025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-1.00000 + 1.73205i) q^{66} +(6.00000 - 10.3923i) q^{67} +4.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(6.00000 - 10.3923i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{75} +2.00000 q^{76} -4.00000 q^{78} +(-1.00000 + 1.73205i) q^{80} +(5.50000 - 9.52628i) q^{81} +(4.00000 + 6.92820i) q^{82} +18.0000 q^{83} +(-6.00000 - 10.3923i) q^{86} +(-6.00000 + 10.3923i) q^{87} +(-0.500000 + 0.866025i) q^{88} +2.00000 q^{90} +(4.00000 + 6.92820i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{96} +12.0000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^5 + 4 * q^6 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{8} - q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 4 q^{13} + 8 q^{15} - q^{16} - q^{18} - 2 q^{19} + 4 q^{20} + 2 q^{22} - 2 q^{24} + q^{25} + 2 q^{26} - 8 q^{27} + 12 q^{29} - 4 q^{30} + 4 q^{31} - q^{32} - 2 q^{33} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 4 q^{39} - 2 q^{40} - 16 q^{41} + 24 q^{43} - q^{44} - 2 q^{45} + 12 q^{47} + 4 q^{48} - 2 q^{50} + 2 q^{52} + 2 q^{53} + 4 q^{54} + 4 q^{55} + 8 q^{57} - 6 q^{58} + 10 q^{59} - 4 q^{60} - 10 q^{61} - 8 q^{62} + 2 q^{64} + 4 q^{65} - 2 q^{66} + 12 q^{67} + 8 q^{71} - q^{72} + 12 q^{73} - 2 q^{74} + 2 q^{75} + 4 q^{76} - 8 q^{78} - 2 q^{80} + 11 q^{81} + 8 q^{82} + 36 q^{83} - 12 q^{86} - 12 q^{87} - q^{88} + 4 q^{90} + 8 q^{93} + 12 q^{94} - 4 q^{95} - 2 q^{96} + 24 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^5 + 4 * q^6 + 2 * q^8 - q^9 - 2 * q^10 - q^11 - 2 * q^12 - 4 * q^13 + 8 * q^15 - q^16 - q^18 - 2 * q^19 + 4 * q^20 + 2 * q^22 - 2 * q^24 + q^25 + 2 * q^26 - 8 * q^27 + 12 * q^29 - 4 * q^30 + 4 * q^31 - q^32 - 2 * q^33 + 2 * q^36 - 2 * q^37 - 2 * q^38 + 4 * q^39 - 2 * q^40 - 16 * q^41 + 24 * q^43 - q^44 - 2 * q^45 + 12 * q^47 + 4 * q^48 - 2 * q^50 + 2 * q^52 + 2 * q^53 + 4 * q^54 + 4 * q^55 + 8 * q^57 - 6 * q^58 + 10 * q^59 - 4 * q^60 - 10 * q^61 - 8 * q^62 + 2 * q^64 + 4 * q^65 - 2 * q^66 + 12 * q^67 + 8 * q^71 - q^72 + 12 * q^73 - 2 * q^74 + 2 * q^75 + 4 * q^76 - 8 * q^78 - 2 * q^80 + 11 * q^81 + 8 * q^82 + 36 * q^83 - 12 * q^86 - 12 * q^87 - q^88 + 4 * q^90 + 8 * q^93 + 12 * q^94 - 4 * q^95 - 2 * q^96 + 24 * q^97 + 2 * q^99

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