LMFDB - Embedded newform 156.2.k.d.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(31,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("156.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.k (of order $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			151.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	156.151
Dual form			156.2.k.d.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +(2.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +(2.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +4.00000 q^{10} +(-1.00000 - 1.00000i) q^{11} -2.00000 q^{12} +(-3.00000 + 2.00000i) q^{13} +(2.00000 - 2.00000i) q^{15} -4.00000 q^{16} +2.00000i q^{17} +(-1.00000 + 1.00000i) q^{18} +(-2.00000 + 2.00000i) q^{19} +(4.00000 - 4.00000i) q^{20} -2.00000 q^{22} +6.00000 q^{23} +(-2.00000 + 2.00000i) q^{24} +3.00000i q^{25} +(-1.00000 + 5.00000i) q^{26} +1.00000i q^{27} +10.0000 q^{29} -4.00000i q^{30} +(-6.00000 + 6.00000i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-1.00000 + 1.00000i) q^{33} +(2.00000 + 2.00000i) q^{34} +2.00000i q^{36} +(3.00000 - 3.00000i) q^{37} +4.00000i q^{38} +(2.00000 + 3.00000i) q^{39} -8.00000i q^{40} +(-4.00000 - 4.00000i) q^{41} -4.00000 q^{43} +(-2.00000 + 2.00000i) q^{44} +(-2.00000 - 2.00000i) q^{45} +(6.00000 - 6.00000i) q^{46} +(-5.00000 - 5.00000i) q^{47} +4.00000i q^{48} -7.00000i q^{49} +(3.00000 + 3.00000i) q^{50} +2.00000 q^{51} +(4.00000 + 6.00000i) q^{52} -6.00000 q^{53} +(1.00000 + 1.00000i) q^{54} -4.00000i q^{55} +(2.00000 + 2.00000i) q^{57} +(10.0000 - 10.0000i) q^{58} +(7.00000 + 7.00000i) q^{59} +(-4.00000 - 4.00000i) q^{60} -8.00000 q^{61} +12.0000i q^{62} +8.00000i q^{64} +(-10.0000 - 2.00000i) q^{65} +2.00000i q^{66} +(-8.00000 + 8.00000i) q^{67} +4.00000 q^{68} -6.00000i q^{69} +(9.00000 - 9.00000i) q^{71} +(2.00000 + 2.00000i) q^{72} +(5.00000 - 5.00000i) q^{73} -6.00000i q^{74} +3.00000 q^{75} +(4.00000 + 4.00000i) q^{76} +(5.00000 + 1.00000i) q^{78} -16.0000i q^{79} +(-8.00000 - 8.00000i) q^{80} +1.00000 q^{81} -8.00000 q^{82} +(-5.00000 + 5.00000i) q^{83} +(-4.00000 + 4.00000i) q^{85} +(-4.00000 + 4.00000i) q^{86} -10.0000i q^{87} +4.00000i q^{88} +(2.00000 - 2.00000i) q^{89} -4.00000 q^{90} -12.0000i q^{92} +(6.00000 + 6.00000i) q^{93} -10.0000 q^{94} -8.00000 q^{95} +(4.00000 + 4.00000i) q^{96} +(5.00000 + 5.00000i) q^{97} +(-7.00000 - 7.00000i) q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 4 q^{5} - 2 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 4 * q^5 - 2 * q^6 - 4 * q^8 - 2 * q^9	$ 2 q + 2 q^{2} + 4 q^{5} - 2 q^{6} - 4 q^{8} - 2 q^{9} + 8 q^{10} - 2 q^{11} - 4 q^{12} - 6 q^{13} + 4 q^{15} - 8 q^{16} - 2 q^{18} - 4 q^{19} + 8 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{24} - 2 q^{26} + 20 q^{29} - 12 q^{31} - 8 q^{32} - 2 q^{33} + 4 q^{34} + 6 q^{37} + 4 q^{39} - 8 q^{41} - 8 q^{43} - 4 q^{44} - 4 q^{45} + 12 q^{46} - 10 q^{47} + 6 q^{50} + 4 q^{51} + 8 q^{52} - 12 q^{53} + 2 q^{54} + 4 q^{57} + 20 q^{58} + 14 q^{59} - 8 q^{60} - 16 q^{61} - 20 q^{65} - 16 q^{67} + 8 q^{68} + 18 q^{71} + 4 q^{72} + 10 q^{73} + 6 q^{75} + 8 q^{76} + 10 q^{78} - 16 q^{80} + 2 q^{81} - 16 q^{82} - 10 q^{83} - 8 q^{85} - 8 q^{86} + 4 q^{89} - 8 q^{90} + 12 q^{93} - 20 q^{94} - 16 q^{95} + 8 q^{96} + 10 q^{97} - 14 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 4 * q^5 - 2 * q^6 - 4 * q^8 - 2 * q^9 + 8 * q^10 - 2 * q^11 - 4 * q^12 - 6 * q^13 + 4 * q^15 - 8 * q^16 - 2 * q^18 - 4 * q^19 + 8 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^24 - 2 * q^26 + 20 * q^29 - 12 * q^31 - 8 * q^32 - 2 * q^33 + 4 * q^34 + 6 * q^37 + 4 * q^39 - 8 * q^41 - 8 * q^43 - 4 * q^44 - 4 * q^45 + 12 * q^46 - 10 * q^47 + 6 * q^50 + 4 * q^51 + 8 * q^52 - 12 * q^53 + 2 * q^54 + 4 * q^57 + 20 * q^58 + 14 * q^59 - 8 * q^60 - 16 * q^61 - 20 * q^65 - 16 * q^67 + 8 * q^68 + 18 * q^71 + 4 * q^72 + 10 * q^73 + 6 * q^75 + 8 * q^76 + 10 * q^78 - 16 * q^80 + 2 * q^81 - 16 * q^82 - 10 * q^83 - 8 * q^85 - 8 * q^86 + 4 * q^89 - 8 * q^90 + 12 * q^93 - 20 * q^94 - 16 * q^95 + 8 * q^96 + 10 * q^97 - 14 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		−	2.00000i		−	1.00000i
$5$	2.00000	+	2.00000i	0.894427	+	0.894427i	0.994936	−	0.100509i	$-0.0320471\pi$
$5$	2.00000	+	2.00000i	0.894427	+	0.894427i	−0.100509	+	0.994936i	$0.532047\pi$
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−1.00000			−0.333333
$10$	4.00000			1.26491
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$	−2.00000			−0.577350
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$14$		0			0
$15$	2.00000	−	2.00000i	0.516398	−	0.516398i
$16$	−4.00000			−1.00000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	−1.00000	+	1.00000i	−0.235702	+	0.235702i
$19$	−2.00000	+	2.00000i	−0.458831	+	0.458831i	−0.898272	−	0.439440i	$-0.855177\pi$
$19$	−2.00000	+	2.00000i	−0.458831	+	0.458831i	0.439440	+	0.898272i	$0.355177\pi$
$20$	4.00000	−	4.00000i	0.894427	−	0.894427i
$21$		0			0
$22$	−2.00000			−0.426401
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	−2.00000	+	2.00000i	−0.408248	+	0.408248i
$25$			3.00000i			0.600000i
$26$	−1.00000	+	5.00000i	−0.196116	+	0.980581i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$		−	4.00000i		−	0.730297i
$31$	−6.00000	+	6.00000i	−1.07763	+	1.07763i	−0.0809104	+	0.996721i	$0.525783\pi$
$31$	−6.00000	+	6.00000i	−1.07763	+	1.07763i	−0.996721	+	0.0809104i	$0.974217\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$	−1.00000	+	1.00000i	−0.174078	+	0.174078i
$34$	2.00000	+	2.00000i	0.342997	+	0.342997i
$35$		0			0
$36$			2.00000i			0.333333i
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$			4.00000i			0.648886i
$39$	2.00000	+	3.00000i	0.320256	+	0.480384i
$40$		−	8.00000i		−	1.26491i
$41$	−4.00000	−	4.00000i	−0.624695	−	0.624695i	0.322033	−	0.946728i	$-0.395634\pi$
$41$	−4.00000	−	4.00000i	−0.624695	−	0.624695i	−0.946728	+	0.322033i	$0.895634\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−2.00000	+	2.00000i	−0.301511	+	0.301511i
$45$	−2.00000	−	2.00000i	−0.298142	−	0.298142i
$46$	6.00000	−	6.00000i	0.884652	−	0.884652i
$47$	−5.00000	−	5.00000i	−0.729325	−	0.729325i	0.241160	−	0.970485i	$-0.422472\pi$
$47$	−5.00000	−	5.00000i	−0.729325	−	0.729325i	−0.970485	+	0.241160i	$0.922472\pi$
$48$			4.00000i			0.577350i
$49$		−	7.00000i		−	1.00000i
$50$	3.00000	+	3.00000i	0.424264	+	0.424264i
$51$	2.00000			0.280056
$52$	4.00000	+	6.00000i	0.554700	+	0.832050i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	+	1.00000i	0.136083	+	0.136083i
$55$		−	4.00000i		−	0.539360i
$56$		0			0
$57$	2.00000	+	2.00000i	0.264906	+	0.264906i
$58$	10.0000	−	10.0000i	1.31306	−	1.31306i
$59$	7.00000	+	7.00000i	0.911322	+	0.911322i	0.996376	−	0.0850540i	$-0.0271063\pi$
$59$	7.00000	+	7.00000i	0.911322	+	0.911322i	−0.0850540	+	0.996376i	$0.527106\pi$
$60$	−4.00000	−	4.00000i	−0.516398	−	0.516398i
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$			12.0000i			1.52400i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−10.0000	−	2.00000i	−1.24035	−	0.248069i
$66$			2.00000i			0.246183i
$67$	−8.00000	+	8.00000i	−0.977356	+	0.977356i	−0.999749	−	0.0223937i	$-0.992871\pi$
$67$	−8.00000	+	8.00000i	−0.977356	+	0.977356i	0.0223937	+	0.999749i	$0.492871\pi$
$68$	4.00000			0.485071
$69$		−	6.00000i		−	0.722315i
$70$		0			0
$71$	9.00000	−	9.00000i	1.06810	−	1.06810i	0.0705987	−	0.997505i	$-0.477509\pi$
$71$	9.00000	−	9.00000i	1.06810	−	1.06810i	0.997505	−	0.0705987i	$-0.0224910\pi$
$72$	2.00000	+	2.00000i	0.235702	+	0.235702i
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	0.936329	+	0.351123i	$0.114200\pi$
$74$		−	6.00000i		−	0.697486i
$75$	3.00000			0.346410
$76$	4.00000	+	4.00000i	0.458831	+	0.458831i
$77$		0			0
$78$	5.00000	+	1.00000i	0.566139	+	0.113228i
$79$		−	16.0000i		−	1.80014i	−0.435745	−	0.900070i	$-0.643515\pi$
$79$		−	16.0000i		−	1.80014i	0.435745	−	0.900070i	$-0.356485\pi$
$80$	−8.00000	−	8.00000i	−0.894427	−	0.894427i
$81$	1.00000			0.111111
$82$	−8.00000			−0.883452
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	−0.926100	−	0.377279i	$-0.876860\pi$
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	0.377279	+	0.926100i	$0.376860\pi$
$84$		0			0
$85$	−4.00000	+	4.00000i	−0.433861	+	0.433861i
$86$	−4.00000	+	4.00000i	−0.431331	+	0.431331i
$87$		−	10.0000i		−	1.07211i
$88$			4.00000i			0.426401i
$89$	2.00000	−	2.00000i	0.212000	−	0.212000i	−0.593117	−	0.805116i	$-0.702103\pi$
$89$	2.00000	−	2.00000i	0.212000	−	0.212000i	0.805116	+	0.593117i	$0.202103\pi$
$90$	−4.00000			−0.421637
$91$		0			0
$92$		−	12.0000i		−	1.25109i
$93$	6.00000	+	6.00000i	0.622171	+	0.622171i
$94$	−10.0000			−1.03142
$95$	−8.00000			−0.820783
$96$	4.00000	+	4.00000i	0.408248	+	0.408248i
$97$	5.00000	+	5.00000i	0.507673	+	0.507673i	0.913812	−	0.406138i	$-0.133125\pi$
$97$	5.00000	+	5.00000i	0.507673	+	0.507673i	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−7.00000	−	7.00000i	−0.707107	−	0.707107i
$99$	1.00000	+	1.00000i	0.100504	+	0.100504i
$100$	6.00000			0.600000
$101$		−	10.0000i		−	0.995037i	−0.867453	−	0.497519i	$-0.834245\pi$
$101$		−	10.0000i		−	0.995037i	0.867453	−	0.497519i	$-0.165755\pi$
$102$	2.00000	−	2.00000i	0.198030	−	0.198030i
$103$	16.0000			1.57653			0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000			1.57653			0.788263	+	0.615338i	$0.210980\pi$
$104$	10.0000	+	2.00000i	0.980581	+	0.196116i
$105$		0			0
$106$	−6.00000	+	6.00000i	−0.582772	+	0.582772i
$107$		−	2.00000i		−	0.193347i	−0.995316	−	0.0966736i	$-0.969180\pi$
$107$		−	2.00000i		−	0.193347i	0.995316	−	0.0966736i	$-0.0308203\pi$
$108$	2.00000			0.192450
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	0.836031	−	0.548683i	$-0.184871\pi$
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	−0.548683	+	0.836031i	$0.684871\pi$
$110$	−4.00000	−	4.00000i	−0.381385	−	0.381385i
$111$	−3.00000	−	3.00000i	−0.284747	−	0.284747i
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	4.00000			0.374634
$115$	12.0000	+	12.0000i	1.11901	+	1.11901i
$116$		−	20.0000i		−	1.85695i
$117$	3.00000	−	2.00000i	0.277350	−	0.184900i
$118$	14.0000			1.28880
$119$		0			0
$120$	−8.00000			−0.730297
$121$		−	9.00000i		−	0.818182i
$122$	−8.00000	+	8.00000i	−0.724286	+	0.724286i
$123$	−4.00000	+	4.00000i	−0.360668	+	0.360668i
$124$	12.0000	+	12.0000i	1.07763	+	1.07763i
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$			4.00000i			0.352180i
$130$	−12.0000	+	8.00000i	−1.05247	+	0.701646i
$131$			10.0000i			0.873704i	0.899533	+	0.436852i	$0.143907\pi$
$131$			10.0000i			0.873704i	−0.899533	+	0.436852i	$0.856093\pi$
$132$	2.00000	+	2.00000i	0.174078	+	0.174078i
$133$		0			0
$134$			16.0000i			1.38219i
$135$	−2.00000	+	2.00000i	−0.172133	+	0.172133i
$136$	4.00000	−	4.00000i	0.342997	−	0.342997i
$137$	−12.0000	+	12.0000i	−1.02523	+	1.02523i	−0.0255558	+	0.999673i	$0.508136\pi$
$137$	−12.0000	+	12.0000i	−1.02523	+	1.02523i	−0.999673	+	0.0255558i	$0.991864\pi$
$138$	−6.00000	−	6.00000i	−0.510754	−	0.510754i
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$		0			0
$141$	−5.00000	+	5.00000i	−0.421076	+	0.421076i
$142$		−	18.0000i		−	1.51053i
$143$	5.00000	+	1.00000i	0.418121	+	0.0836242i
$144$	4.00000			0.333333
$145$	20.0000	+	20.0000i	1.66091	+	1.66091i
$146$		−	10.0000i		−	0.827606i
$147$	−7.00000			−0.577350
$148$	−6.00000	−	6.00000i	−0.493197	−	0.493197i
$149$	8.00000	+	8.00000i	0.655386	+	0.655386i	0.954285	−	0.298899i	$-0.0966194\pi$
$149$	8.00000	+	8.00000i	0.655386	+	0.655386i	−0.298899	+	0.954285i	$0.596619\pi$
$150$	3.00000	−	3.00000i	0.244949	−	0.244949i
$151$	−6.00000	−	6.00000i	−0.488273	−	0.488273i	0.419488	−	0.907761i	$-0.362210\pi$
$151$	−6.00000	−	6.00000i	−0.488273	−	0.488273i	−0.907761	+	0.419488i	$0.862210\pi$
$152$	8.00000			0.648886
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	−24.0000			−1.92773
$156$	6.00000	−	4.00000i	0.480384	−	0.320256i
$157$	−12.0000			−0.957704			−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000			−0.957704			−0.478852	+	0.877896i	$0.658947\pi$
$158$	−16.0000	−	16.0000i	−1.27289	−	1.27289i
$159$			6.00000i			0.475831i
$160$	−16.0000			−1.26491
$161$		0			0
$162$	1.00000	−	1.00000i	0.0785674	−	0.0785674i
$163$	6.00000	+	6.00000i	0.469956	+	0.469956i	0.901900	−	0.431944i	$-0.142172\pi$
$163$	6.00000	+	6.00000i	0.469956	+	0.469956i	−0.431944	+	0.901900i	$0.642172\pi$
$164$	−8.00000	+	8.00000i	−0.624695	+	0.624695i
$165$	−4.00000			−0.311400
$166$			10.0000i			0.776151i
$167$	−5.00000	−	5.00000i	−0.386912	−	0.386912i	0.486673	−	0.873584i	$-0.338210\pi$
$167$	−5.00000	−	5.00000i	−0.386912	−	0.386912i	−0.873584	+	0.486673i	$0.838210\pi$
$168$		0			0
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$			8.00000i			0.613572i
$171$	2.00000	−	2.00000i	0.152944	−	0.152944i
$172$			8.00000i			0.609994i
$173$			14.0000i			1.06440i	0.846619	+	0.532200i	$0.178635\pi$
$173$			14.0000i			1.06440i	−0.846619	+	0.532200i	$0.821365\pi$
$174$	−10.0000	−	10.0000i	−0.758098	−	0.758098i
$175$		0			0
$176$	4.00000	+	4.00000i	0.301511	+	0.301511i
$177$	7.00000	−	7.00000i	0.526152	−	0.526152i
$178$		−	4.00000i		−	0.299813i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$	−4.00000	+	4.00000i	−0.298142	+	0.298142i
$181$			10.0000i			0.743294i	0.928374	+	0.371647i	$0.121207\pi$
$181$			10.0000i			0.743294i	−0.928374	+	0.371647i	$0.878793\pi$
$182$		0			0
$183$			8.00000i			0.591377i
$184$	−12.0000	−	12.0000i	−0.884652	−	0.884652i
$185$	12.0000			0.882258
$186$	12.0000			0.879883
$187$	2.00000	−	2.00000i	0.146254	−	0.146254i
$188$	−10.0000	+	10.0000i	−0.729325	+	0.729325i
$189$		0			0
$190$	−8.00000	+	8.00000i	−0.580381	+	0.580381i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	8.00000			0.577350
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$	10.0000			0.717958
$195$	−2.00000	+	10.0000i	−0.143223	+	0.716115i
$196$	−14.0000			−1.00000
$197$	10.0000	+	10.0000i	0.712470	+	0.712470i	0.967051	−	0.254581i	$-0.0819375\pi$
$197$	10.0000	+	10.0000i	0.712470	+	0.712470i	−0.254581	+	0.967051i	$0.581938\pi$
$198$	2.00000			0.142134
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	6.00000	−	6.00000i	0.424264	−	0.424264i
$201$	8.00000	+	8.00000i	0.564276	+	0.564276i
$202$	−10.0000	−	10.0000i	−0.703598	−	0.703598i
$203$		0			0
$204$		−	4.00000i		−	0.280056i
$205$		−	16.0000i		−	1.11749i
$206$	16.0000	−	16.0000i	1.11477	−	1.11477i
$207$	−6.00000			−0.417029
$208$	12.0000	−	8.00000i	0.832050	−	0.554700i
$209$	4.00000			0.276686
$210$		0			0
$211$		−	20.0000i		−	1.37686i	−0.725304	−	0.688428i	$-0.758301\pi$
$211$		−	20.0000i		−	1.37686i	0.725304	−	0.688428i	$-0.241699\pi$
$212$			12.0000i			0.824163i
$213$	−9.00000	−	9.00000i	−0.616670	−	0.616670i
$214$	−2.00000	−	2.00000i	−0.136717	−	0.136717i
$215$	−8.00000	−	8.00000i	−0.545595	−	0.545595i
$216$	2.00000	−	2.00000i	0.136083	−	0.136083i
$217$		0			0
$218$	6.00000			0.406371
$219$	−5.00000	−	5.00000i	−0.337869	−	0.337869i
$220$	−8.00000			−0.539360
$221$	−4.00000	−	6.00000i	−0.269069	−	0.403604i
$222$	−6.00000			−0.402694
$223$	10.0000	−	10.0000i	0.669650	−	0.669650i	−0.287985	−	0.957635i	$-0.592985\pi$
$223$	10.0000	−	10.0000i	0.669650	−	0.669650i	0.957635	+	0.287985i	$0.0929854\pi$
$224$		0			0
$225$		−	3.00000i		−	0.200000i
$226$	−6.00000	+	6.00000i	−0.399114	+	0.399114i
$227$	−3.00000	+	3.00000i	−0.199117	+	0.199117i	−0.799621	−	0.600504i	$-0.794966\pi$
$227$	−3.00000	+	3.00000i	−0.199117	+	0.199117i	0.600504	+	0.799621i	$0.294966\pi$
$228$	4.00000	−	4.00000i	0.264906	−	0.264906i
$229$	7.00000	−	7.00000i	0.462573	−	0.462573i	−0.436925	−	0.899498i	$-0.643932\pi$
$229$	7.00000	−	7.00000i	0.462573	−	0.462573i	0.899498	+	0.436925i	$0.143932\pi$
$230$	24.0000			1.58251
$231$		0			0
$232$	−20.0000	−	20.0000i	−1.31306	−	1.31306i
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$	1.00000	−	5.00000i	0.0653720	−	0.326860i
$235$		−	20.0000i		−	1.30466i
$236$	14.0000	−	14.0000i	0.911322	−	0.911322i
$237$	−16.0000			−1.03931
$238$		0			0
$239$	3.00000	−	3.00000i	0.194054	−	0.194054i	−0.603391	−	0.797445i	$-0.706184\pi$
$239$	3.00000	−	3.00000i	0.194054	−	0.194054i	0.797445	+	0.603391i	$0.206184\pi$
$240$	−8.00000	+	8.00000i	−0.516398	+	0.516398i
$241$	−9.00000	+	9.00000i	−0.579741	+	0.579741i	−0.934832	−	0.355091i	$-0.884450\pi$
$241$	−9.00000	+	9.00000i	−0.579741	+	0.579741i	0.355091	+	0.934832i	$0.384450\pi$
$242$	−9.00000	−	9.00000i	−0.578542	−	0.578542i
$243$		−	1.00000i		−	0.0641500i
$244$			16.0000i			1.02430i
$245$	14.0000	−	14.0000i	0.894427	−	0.894427i
$246$			8.00000i			0.510061i
$247$	2.00000	−	10.0000i	0.127257	−	0.636285i
$248$	24.0000			1.52400
$249$	5.00000	+	5.00000i	0.316862	+	0.316862i
$250$		−	8.00000i		−	0.505964i
$251$	−2.00000			−0.126239			−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000			−0.126239			−0.0631194	+	0.998006i	$0.520105\pi$
$252$		0			0
$253$	−6.00000	−	6.00000i	−0.377217	−	0.377217i
$254$	−8.00000	+	8.00000i	−0.501965	+	0.501965i
$255$	4.00000	+	4.00000i	0.250490	+	0.250490i
$256$	16.0000			1.00000
$257$		−	18.0000i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$		−	18.0000i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$	4.00000	+	4.00000i	0.249029	+	0.249029i
$259$		0			0
$260$	−4.00000	+	20.0000i	−0.248069	+	1.24035i
$261$	−10.0000			−0.618984
$262$	10.0000	+	10.0000i	0.617802	+	0.617802i
$263$			26.0000i			1.60323i	0.597841	+	0.801614i	$0.296025\pi$
$263$			26.0000i			1.60323i	−0.597841	+	0.801614i	$0.703975\pi$
$264$	4.00000			0.246183
$265$	−12.0000	−	12.0000i	−0.737154	−	0.737154i
$266$		0			0
$267$	−2.00000	−	2.00000i	−0.122398	−	0.122398i
$268$	16.0000	+	16.0000i	0.977356	+	0.977356i
$269$	10.0000			0.609711			0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000			0.609711			0.304855	+	0.952399i	$0.401392\pi$
$270$			4.00000i			0.243432i
$271$	4.00000	+	4.00000i	0.242983	+	0.242983i	0.818083	−	0.575100i	$-0.195037\pi$
$271$	4.00000	+	4.00000i	0.242983	+	0.242983i	−0.575100	+	0.818083i	$0.695037\pi$
$272$		−	8.00000i		−	0.485071i
$273$		0			0
$274$			24.0000i			1.44989i
$275$	3.00000	−	3.00000i	0.180907	−	0.180907i
$276$	−12.0000			−0.722315
$277$		−	8.00000i		−	0.480673i	−0.970690	−	0.240337i	$-0.922742\pi$
$277$		−	8.00000i		−	0.480673i	0.970690	−	0.240337i	$-0.0772579\pi$
$278$	4.00000	+	4.00000i	0.239904	+	0.239904i
$279$	6.00000	−	6.00000i	0.359211	−	0.359211i
$280$		0			0
$281$	−4.00000	+	4.00000i	−0.238620	+	0.238620i	−0.816279	−	0.577659i	$-0.803967\pi$
$281$	−4.00000	+	4.00000i	−0.238620	+	0.238620i	0.577659	+	0.816279i	$0.303967\pi$
$282$			10.0000i			0.595491i
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$	−18.0000	−	18.0000i	−1.06810	−	1.06810i
$285$			8.00000i			0.473879i
$286$	6.00000	−	4.00000i	0.354787	−	0.236525i
$287$		0			0
$288$	4.00000	−	4.00000i	0.235702	−	0.235702i
$289$	13.0000			0.764706
$290$	40.0000			2.34888
$291$	5.00000	−	5.00000i	0.293105	−	0.293105i
$292$	−10.0000	−	10.0000i	−0.585206	−	0.585206i
$293$	−20.0000	+	20.0000i	−1.16841	+	1.16841i	−0.185831	+	0.982582i	$0.559498\pi$
$293$	−20.0000	+	20.0000i	−1.16841	+	1.16841i	−0.982582	+	0.185831i	$0.940502\pi$
$294$	−7.00000	+	7.00000i	−0.408248	+	0.408248i
$295$			28.0000i			1.63022i
$296$	−12.0000			−0.697486
$297$	1.00000	−	1.00000i	0.0580259	−	0.0580259i
$298$	16.0000			0.926855
$299$	−18.0000	+	12.0000i	−1.04097	+	0.693978i
$300$		−	6.00000i		−	0.346410i
$301$		0			0
$302$	−12.0000			−0.690522
$303$	−10.0000			−0.574485
$304$	8.00000	−	8.00000i	0.458831	−	0.458831i
$305$	−16.0000	−	16.0000i	−0.916157	−	0.916157i
$306$	−2.00000	−	2.00000i	−0.114332	−	0.114332i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		−	16.0000i		−	0.910208i
$310$	−24.0000	+	24.0000i	−1.36311	+	1.36311i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	2.00000	−	10.0000i	0.113228	−	0.566139i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−12.0000	+	12.0000i	−0.677199	+	0.677199i
$315$		0			0
$316$	−32.0000			−1.80014
$317$	10.0000	+	10.0000i	0.561656	+	0.561656i	0.929778	−	0.368122i	$-0.119999\pi$
$317$	10.0000	+	10.0000i	0.561656	+	0.561656i	−0.368122	+	0.929778i	$0.619999\pi$
$318$	6.00000	+	6.00000i	0.336463	+	0.336463i
$319$	−10.0000	−	10.0000i	−0.559893	−	0.559893i
$320$	−16.0000	+	16.0000i	−0.894427	+	0.894427i
$321$	−2.00000			−0.111629
$322$		0			0
$323$	−4.00000	−	4.00000i	−0.222566	−	0.222566i
$324$		−	2.00000i		−	0.111111i
$325$	−6.00000	−	9.00000i	−0.332820	−	0.499230i
$326$	12.0000			0.664619
$327$	3.00000	−	3.00000i	0.165900	−	0.165900i
$328$			16.0000i			0.883452i
$329$		0			0
$330$	−4.00000	+	4.00000i	−0.220193	+	0.220193i
$331$	−16.0000	+	16.0000i	−0.879440	+	0.879440i	−0.993477	−	0.114037i	$-0.963622\pi$
$331$	−16.0000	+	16.0000i	−0.879440	+	0.879440i	0.114037	+	0.993477i	$0.463622\pi$
$332$	10.0000	+	10.0000i	0.548821	+	0.548821i
$333$	−3.00000	+	3.00000i	−0.164399	+	0.164399i
$334$	−10.0000			−0.547176
$335$	−32.0000			−1.74835
$336$		0			0
$337$		−	8.00000i		−	0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$		−	8.00000i		−	0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$	−7.00000	−	17.0000i	−0.380750	−	0.924678i
$339$			6.00000i			0.325875i
$340$	8.00000	+	8.00000i	0.433861	+	0.433861i
$341$	12.0000			0.649836
$342$		−	4.00000i		−	0.216295i
$343$		0			0
$344$	8.00000	+	8.00000i	0.431331	+	0.431331i
$345$	12.0000	−	12.0000i	0.646058	−	0.646058i
$346$	14.0000	+	14.0000i	0.752645	+	0.752645i
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$	−20.0000			−1.07211
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	−0.782826	−	0.622240i	$-0.786223\pi$
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	0.622240	+	0.782826i	$0.286223\pi$
$350$		0			0
$351$	−2.00000	−	3.00000i	−0.106752	−	0.160128i
$352$	8.00000			0.426401
$353$	−16.0000	−	16.0000i	−0.851594	−	0.851594i	0.138735	−	0.990329i	$-0.455696\pi$
$353$	−16.0000	−	16.0000i	−0.851594	−	0.851594i	−0.990329	+	0.138735i	$0.955696\pi$
$354$		−	14.0000i		−	0.744092i
$355$	36.0000			1.91068
$356$	−4.00000	−	4.00000i	−0.212000	−	0.212000i
$357$		0			0
$358$	20.0000	−	20.0000i	1.05703	−	1.05703i
$359$	17.0000	+	17.0000i	0.897226	+	0.897226i	0.995190	−	0.0979643i	$-0.0312331\pi$
$359$	17.0000	+	17.0000i	0.897226	+	0.897226i	−0.0979643	+	0.995190i	$0.531233\pi$
$360$			8.00000i			0.421637i
$361$			11.0000i			0.578947i
$362$	10.0000	+	10.0000i	0.525588	+	0.525588i
$363$	−9.00000			−0.472377
$364$		0			0
$365$	20.0000			1.04685
$366$	8.00000	+	8.00000i	0.418167	+	0.418167i
$367$			28.0000i			1.46159i	0.682598	+	0.730794i	$0.260850\pi$
$367$			28.0000i			1.46159i	−0.682598	+	0.730794i	$0.739150\pi$
$368$	−24.0000			−1.25109
$369$	4.00000	+	4.00000i	0.208232	+	0.208232i
$370$	12.0000	−	12.0000i	0.623850	−	0.623850i
$371$		0			0
$372$	12.0000	−	12.0000i	0.622171	−	0.622171i
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		−	4.00000i		−	0.206835i
$375$	−4.00000	−	4.00000i	−0.206559	−	0.206559i
$376$			20.0000i			1.03142i
$377$	−30.0000	+	20.0000i	−1.54508	+	1.03005i
$378$		0			0
$379$	−22.0000	+	22.0000i	−1.13006	+	1.13006i	−0.139898	+	0.990166i	$0.544678\pi$
$379$	−22.0000	+	22.0000i	−1.13006	+	1.13006i	−0.990166	+	0.139898i	$0.955322\pi$
$380$			16.0000i			0.820783i
$381$			8.00000i			0.409852i
$382$		0			0
$383$	5.00000	−	5.00000i	0.255488	−	0.255488i	−0.567728	−	0.823216i	$-0.692177\pi$
$383$	5.00000	−	5.00000i	0.255488	−	0.255488i	0.823216	+	0.567728i	$0.192177\pi$
$384$	8.00000	−	8.00000i	0.408248	−	0.408248i
$385$		0			0
$386$			30.0000i			1.52696i
$387$	4.00000			0.203331
$388$	10.0000	−	10.0000i	0.507673	−	0.507673i
$389$		−	14.0000i		−	0.709828i	−0.934899	−	0.354914i	$-0.884510\pi$
$389$		−	14.0000i		−	0.709828i	0.934899	−	0.354914i	$-0.115490\pi$
$390$	8.00000	+	12.0000i	0.405096	+	0.607644i
$391$			12.0000i			0.606866i
$392$	−14.0000	+	14.0000i	−0.707107	+	0.707107i
$393$	10.0000			0.504433
$394$	20.0000			1.00759
$395$	32.0000	−	32.0000i	1.61009	−	1.61009i
$396$	2.00000	−	2.00000i	0.100504	−	0.100504i
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	0.953583	+	0.301131i	$0.0973643\pi$
$398$	20.0000	−	20.0000i	1.00251	−	1.00251i
$399$		0			0
$400$		−	12.0000i		−	0.600000i
$401$	6.00000	−	6.00000i	0.299626	−	0.299626i	−0.541241	−	0.840867i	$-0.682046\pi$
$401$	6.00000	−	6.00000i	0.299626	−	0.299626i	0.840867	+	0.541241i	$0.182046\pi$
$402$	16.0000			0.798007
$403$	6.00000	−	30.0000i	0.298881	−	1.49441i
$404$	−20.0000			−0.995037
$405$	2.00000	+	2.00000i	0.0993808	+	0.0993808i
$406$		0			0
$407$	−6.00000			−0.297409
$408$	−4.00000	−	4.00000i	−0.198030	−	0.198030i
$409$	13.0000	+	13.0000i	0.642809	+	0.642809i	0.951245	−	0.308436i	$-0.0998057\pi$
$409$	13.0000	+	13.0000i	0.642809	+	0.642809i	−0.308436	+	0.951245i	$0.599806\pi$
$410$	−16.0000	−	16.0000i	−0.790184	−	0.790184i
$411$	12.0000	+	12.0000i	0.591916	+	0.591916i
$412$		−	32.0000i		−	1.57653i
$413$		0			0
$414$	−6.00000	+	6.00000i	−0.294884	+	0.294884i
$415$	−20.0000			−0.981761
$416$	4.00000	−	20.0000i	0.196116	−	0.980581i
$417$	4.00000			0.195881
$418$	4.00000	−	4.00000i	0.195646	−	0.195646i
$419$		−	26.0000i		−	1.27018i	−0.772437	−	0.635092i	$-0.780962\pi$
$419$		−	26.0000i		−	1.27018i	0.772437	−	0.635092i	$-0.219038\pi$
$420$		0			0
$421$	21.0000	+	21.0000i	1.02348	+	1.02348i	0.999718	+	0.0237597i	$0.00756365\pi$
$421$	21.0000	+	21.0000i	1.02348	+	1.02348i	0.0237597	+	0.999718i	$0.492436\pi$
$422$	−20.0000	−	20.0000i	−0.973585	−	0.973585i
$423$	5.00000	+	5.00000i	0.243108	+	0.243108i
$424$	12.0000	+	12.0000i	0.582772	+	0.582772i
$425$	−6.00000			−0.291043
$426$	−18.0000			−0.872103
$427$		0			0
$428$	−4.00000			−0.193347
$429$	1.00000	−	5.00000i	0.0482805	−	0.241402i
$430$	−16.0000			−0.771589
$431$	9.00000	−	9.00000i	0.433515	−	0.433515i	−0.456307	−	0.889822i	$-0.650828\pi$
$431$	9.00000	−	9.00000i	0.433515	−	0.433515i	0.889822	+	0.456307i	$0.150828\pi$
$432$		−	4.00000i		−	0.192450i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$		0			0
$435$	20.0000	−	20.0000i	0.958927	−	0.958927i
$436$	6.00000	−	6.00000i	0.287348	−	0.287348i
$437$	−12.0000	+	12.0000i	−0.574038	+	0.574038i
$438$	−10.0000			−0.477818
$439$	−20.0000			−0.954548			−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000			−0.954548			−0.477274	+	0.878755i	$0.658375\pi$
$440$	−8.00000	+	8.00000i	−0.381385	+	0.381385i
$441$			7.00000i			0.333333i
$442$	−10.0000	−	2.00000i	−0.475651	−	0.0951303i
$443$			6.00000i			0.285069i	0.989790	+	0.142534i	$0.0455251\pi$
$443$			6.00000i			0.285069i	−0.989790	+	0.142534i	$0.954475\pi$
$444$	−6.00000	+	6.00000i	−0.284747	+	0.284747i
$445$	8.00000			0.379236
$446$		−	20.0000i		−	0.947027i
$447$	8.00000	−	8.00000i	0.378387	−	0.378387i
$448$		0			0
$449$	2.00000	−	2.00000i	0.0943858	−	0.0943858i	−0.658337	−	0.752723i	$-0.728740\pi$
$449$	2.00000	−	2.00000i	0.0943858	−	0.0943858i	0.752723	+	0.658337i	$0.228740\pi$
$450$	−3.00000	−	3.00000i	−0.141421	−	0.141421i
$451$			8.00000i			0.376705i
$452$			12.0000i			0.564433i
$453$	−6.00000	+	6.00000i	−0.281905	+	0.281905i
$454$			6.00000i			0.281594i
$455$		0			0
$456$		−	8.00000i		−	0.374634i
$457$	−5.00000	−	5.00000i	−0.233890	−	0.233890i	0.580424	−	0.814314i	$-0.302887\pi$
$457$	−5.00000	−	5.00000i	−0.233890	−	0.233890i	−0.814314	+	0.580424i	$0.802887\pi$
$458$		−	14.0000i		−	0.654177i
$459$	−2.00000			−0.0933520
$460$	24.0000	−	24.0000i	1.11901	−	1.11901i
$461$	6.00000	+	6.00000i	0.279448	+	0.279448i	0.832889	−	0.553441i	$-0.186685\pi$
$461$	6.00000	+	6.00000i	0.279448	+	0.279448i	−0.553441	+	0.832889i	$0.686685\pi$
$462$		0			0
$463$	−24.0000	−	24.0000i	−1.11537	−	1.11537i	−0.992411	−	0.122963i	$-0.960760\pi$
$463$	−24.0000	−	24.0000i	−1.11537	−	1.11537i	−0.122963	−	0.992411i	$-0.539240\pi$
$464$	−40.0000			−1.85695
$465$			24.0000i			1.11297i
$466$	−6.00000	−	6.00000i	−0.277945	−	0.277945i
$467$	22.0000			1.01804			0.509019	−	0.860755i	$-0.330008\pi$
$467$	22.0000			1.01804			0.509019	+	0.860755i	$0.330008\pi$
$468$	−4.00000	−	6.00000i	−0.184900	−	0.277350i
$469$		0			0
$470$	−20.0000	−	20.0000i	−0.922531	−	0.922531i
$471$			12.0000i			0.552931i
$472$		−	28.0000i		−	1.28880i
$473$	4.00000	+	4.00000i	0.183920	+	0.183920i
$474$	−16.0000	+	16.0000i	−0.734904	+	0.734904i
$475$	−6.00000	−	6.00000i	−0.275299	−	0.275299i
$476$		0			0
$477$	6.00000			0.274721
$478$		−	6.00000i		−	0.274434i
$479$	7.00000	+	7.00000i	0.319838	+	0.319838i	0.848705	−	0.528867i	$-0.177383\pi$
$479$	7.00000	+	7.00000i	0.319838	+	0.319838i	−0.528867	+	0.848705i	$0.677383\pi$
$480$			16.0000i			0.730297i
$481$	−3.00000	+	15.0000i	−0.136788	+	0.683941i
$482$			18.0000i			0.819878i
$483$		0			0
$484$	−18.0000			−0.818182
$485$			20.0000i			0.908153i
$486$	−1.00000	−	1.00000i	−0.0453609	−	0.0453609i
$487$	−18.0000	+	18.0000i	−0.815658	+	0.815658i	−0.985476	−	0.169818i	$-0.945682\pi$
$487$	−18.0000	+	18.0000i	−0.815658	+	0.815658i	0.169818	+	0.985476i	$0.445682\pi$
$488$	16.0000	+	16.0000i	0.724286	+	0.724286i
$489$	6.00000	−	6.00000i	0.271329	−	0.271329i
$490$		−	28.0000i		−	1.26491i
$491$	−22.0000			−0.992846			−0.496423	−	0.868081i	$-0.665354\pi$
$491$	−22.0000			−0.992846			−0.496423	+	0.868081i	$0.665354\pi$
$492$	8.00000	+	8.00000i	0.360668	+	0.360668i
$493$			20.0000i			0.900755i
$494$	−8.00000	−	12.0000i	−0.359937	−	0.539906i
$495$			4.00000i			0.179787i
$496$	24.0000	−	24.0000i	1.07763	−	1.07763i
$497$		0			0
$498$	10.0000			0.448111
$499$	8.00000	−	8.00000i	0.358129	−	0.358129i	−0.504994	−	0.863123i	$-0.668505\pi$
$499$	8.00000	−	8.00000i	0.358129	−	0.358129i	0.863123	+	0.504994i	$0.168505\pi$
$500$	−8.00000	−	8.00000i	−0.357771	−	0.357771i
$501$	−5.00000	+	5.00000i	−0.223384	+	0.223384i
$502$	−2.00000	+	2.00000i	−0.0892644	+	0.0892644i
$503$		−	14.0000i		−	0.624229i	−0.950044	−	0.312115i	$-0.898963\pi$
$503$		−	14.0000i		−	0.624229i	0.950044	−	0.312115i	$-0.101037\pi$
$504$		0			0
$505$	20.0000	−	20.0000i	0.889988	−	0.889988i
$506$	−12.0000			−0.533465
$507$	−12.0000	−	5.00000i	−0.532939	−	0.222058i
$508$			16.0000i			0.709885i
$509$	−22.0000	−	22.0000i	−0.975133	−	0.975133i	0.0245654	−	0.999698i	$-0.492180\pi$
$509$	−22.0000	−	22.0000i	−0.975133	−	0.975133i	−0.999698	+	0.0245654i	$0.992180\pi$
$510$	8.00000			0.354246
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	−2.00000	−	2.00000i	−0.0883022	−	0.0883022i
$514$	−18.0000	−	18.0000i	−0.793946	−	0.793946i
$515$	32.0000	+	32.0000i	1.41009	+	1.41009i
$516$	8.00000			0.352180
$517$			10.0000i			0.439799i
$518$		0			0
$519$	14.0000			0.614532
$520$	16.0000	+	24.0000i	0.701646	+	1.05247i
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$	−10.0000	+	10.0000i	−0.437688	+	0.437688i
$523$		−	24.0000i		−	1.04945i	−0.851273	−	0.524723i	$-0.824169\pi$
$523$		−	24.0000i		−	1.04945i	0.851273	−	0.524723i	$-0.175831\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	26.0000	+	26.0000i	1.13365	+	1.13365i
$527$	−12.0000	−	12.0000i	−0.522728	−	0.522728i
$528$	4.00000	−	4.00000i	0.174078	−	0.174078i
$529$	13.0000			0.565217
$530$	−24.0000			−1.04249
$531$	−7.00000	−	7.00000i	−0.303774	−	0.303774i
$532$		0			0
$533$	20.0000	+	4.00000i	0.866296	+	0.173259i
$534$	−4.00000			−0.173097
$535$	4.00000	−	4.00000i	0.172935	−	0.172935i
$536$	32.0000			1.38219
$537$		−	20.0000i		−	0.863064i
$538$	10.0000	−	10.0000i	0.431131	−	0.431131i
$539$	−7.00000	+	7.00000i	−0.301511	+	0.301511i
$540$	4.00000	+	4.00000i	0.172133	+	0.172133i
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$	8.00000			0.343629
$543$	10.0000			0.429141
$544$	−8.00000	−	8.00000i	−0.342997	−	0.342997i
$545$			12.0000i			0.514024i
$546$		0			0
$547$			28.0000i			1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$	24.0000	+	24.0000i	1.02523	+	1.02523i
$549$	8.00000			0.341432
$550$		−	6.00000i		−	0.255841i
$551$	−20.0000	+	20.0000i	−0.852029	+	0.852029i
$552$	−12.0000	+	12.0000i	−0.510754	+	0.510754i
$553$		0			0
$554$	−8.00000	−	8.00000i	−0.339887	−	0.339887i
$555$		−	12.0000i		−	0.509372i
$556$	8.00000			0.339276
$557$	8.00000	−	8.00000i	0.338971	−	0.338971i	−0.517009	−	0.855980i	$-0.672955\pi$
$557$	8.00000	−	8.00000i	0.338971	−	0.338971i	0.855980	+	0.517009i	$0.172955\pi$
$558$		−	12.0000i		−	0.508001i
$559$	12.0000	−	8.00000i	0.507546	−	0.338364i
$560$		0			0
$561$	−2.00000	−	2.00000i	−0.0844401	−	0.0844401i
$562$			8.00000i			0.337460i
$563$	−4.00000			−0.168580			−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000			−0.168580			−0.0842900	+	0.996441i	$0.526862\pi$
$564$	10.0000	+	10.0000i	0.421076	+	0.421076i
$565$	−12.0000	−	12.0000i	−0.504844	−	0.504844i
$566$	−4.00000	+	4.00000i	−0.168133	+	0.168133i
$567$		0			0
$568$	−36.0000			−1.51053
$569$			26.0000i			1.08998i	0.838444	+	0.544988i	$0.183466\pi$
$569$			26.0000i			1.08998i	−0.838444	+	0.544988i	$0.816534\pi$
$570$	8.00000	+	8.00000i	0.335083	+	0.335083i
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$	2.00000	−	10.0000i	0.0836242	−	0.418121i
$573$		0			0
$574$		0			0
$575$			18.0000i			0.750652i
$576$		−	8.00000i		−	0.333333i
$577$	−15.0000	−	15.0000i	−0.624458	−	0.624458i	0.322210	−	0.946668i	$-0.395574\pi$
$577$	−15.0000	−	15.0000i	−0.624458	−	0.624458i	−0.946668	+	0.322210i	$0.895574\pi$
$578$	13.0000	−	13.0000i	0.540729	−	0.540729i
$579$	15.0000	+	15.0000i	0.623379	+	0.623379i
$580$	40.0000	−	40.0000i	1.66091	−	1.66091i
$581$		0			0
$582$		−	10.0000i		−	0.414513i
$583$	6.00000	+	6.00000i	0.248495	+	0.248495i
$584$	−20.0000			−0.827606
$585$	10.0000	+	2.00000i	0.413449	+	0.0826898i
$586$			40.0000i			1.65238i
$587$	−3.00000	+	3.00000i	−0.123823	+	0.123823i	−0.766303	−	0.642480i	$-0.777906\pi$
$587$	−3.00000	+	3.00000i	−0.123823	+	0.123823i	0.642480	+	0.766303i	$0.277906\pi$
$588$			14.0000i			0.577350i
$589$		−	24.0000i		−	0.988903i
$590$	28.0000	+	28.0000i	1.15274	+	1.15274i
$591$	10.0000	−	10.0000i	0.411345	−	0.411345i
$592$	−12.0000	+	12.0000i	−0.493197	+	0.493197i
$593$	10.0000	−	10.0000i	0.410651	−	0.410651i	−0.471314	−	0.881965i	$-0.656220\pi$
$593$	10.0000	−	10.0000i	0.410651	−	0.410651i	0.881965	+	0.471314i	$0.156220\pi$
$594$		−	2.00000i		−	0.0820610i
$595$		0			0
$596$	16.0000	−	16.0000i	0.655386	−	0.655386i
$597$		−	20.0000i		−	0.818546i
$598$	−6.00000	+	30.0000i	−0.245358	+	1.22679i
$599$			14.0000i			0.572024i	0.958226	+	0.286012i	$0.0923298\pi$
$599$			14.0000i			0.572024i	−0.958226	+	0.286012i	$0.907670\pi$
$600$	−6.00000	−	6.00000i	−0.244949	−	0.244949i
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$		0			0
$603$	8.00000	−	8.00000i	0.325785	−	0.325785i
$604$	−12.0000	+	12.0000i	−0.488273	+	0.488273i
$605$	18.0000	−	18.0000i	0.731804	−	0.731804i
$606$	−10.0000	+	10.0000i	−0.406222	+	0.406222i
$607$			28.0000i			1.13648i	0.822861	+	0.568242i	$0.192376\pi$
$607$			28.0000i			1.13648i	−0.822861	+	0.568242i	$0.807624\pi$
$608$		−	16.0000i		−	0.648886i
$609$		0			0
$610$	−32.0000			−1.29564
$611$	25.0000	+	5.00000i	1.01139	+	0.202278i
$612$	−4.00000			−0.161690
$613$	−11.0000	−	11.0000i	−0.444286	−	0.444286i	0.449164	−	0.893449i	$-0.351722\pi$
$613$	−11.0000	−	11.0000i	−0.444286	−	0.444286i	−0.893449	+	0.449164i	$0.851722\pi$
$614$		0			0
$615$	−16.0000			−0.645182
$616$		0			0
$617$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$617$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$618$	−16.0000	−	16.0000i	−0.643614	−	0.643614i
$619$	−28.0000	−	28.0000i	−1.12542	−	1.12542i	−0.990913	−	0.134502i	$-0.957057\pi$
$619$	−28.0000	−	28.0000i	−1.12542	−	1.12542i	−0.134502	−	0.990913i	$-0.542943\pi$
$620$			48.0000i			1.92773i
$621$			6.00000i			0.240772i
$622$	18.0000	−	18.0000i	0.721734	−	0.721734i
$623$		0			0
$624$	−8.00000	−	12.0000i	−0.320256	−	0.480384i
$625$	31.0000			1.24000
$626$	−6.00000	+	6.00000i	−0.239808	+	0.239808i
$627$		−	4.00000i		−	0.159745i
$628$			24.0000i			0.957704i
$629$	6.00000	+	6.00000i	0.239236	+	0.239236i
$630$		0			0
$631$	14.0000	+	14.0000i	0.557331	+	0.557331i	0.928547	−	0.371216i	$-0.121059\pi$
$631$	14.0000	+	14.0000i	0.557331	+	0.557331i	−0.371216	+	0.928547i	$0.621059\pi$
$632$	−32.0000	+	32.0000i	−1.27289	+	1.27289i
$633$	−20.0000			−0.794929
$634$	20.0000			0.794301
$635$	−16.0000	−	16.0000i	−0.634941	−	0.634941i
$636$	12.0000			0.475831
$637$	14.0000	+	21.0000i	0.554700	+	0.832050i
$638$	−20.0000			−0.791808
$639$	−9.00000	+	9.00000i	−0.356034	+	0.356034i
$640$			32.0000i			1.26491i
$641$		−	30.0000i		−	1.18493i	−0.805597	−	0.592464i	$-0.798155\pi$
$641$		−	30.0000i		−	1.18493i	0.805597	−	0.592464i	$-0.201845\pi$
$642$	−2.00000	+	2.00000i	−0.0789337	+	0.0789337i
$643$	−20.0000	+	20.0000i	−0.788723	+	0.788723i	−0.981285	−	0.192562i	$-0.938320\pi$
$643$	−20.0000	+	20.0000i	−0.788723	+	0.788723i	0.192562	+	0.981285i	$0.438320\pi$
$644$		0			0
$645$	−8.00000	+	8.00000i	−0.315000	+	0.315000i
$646$	−8.00000			−0.314756
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	−2.00000	−	2.00000i	−0.0785674	−	0.0785674i
$649$		−	14.0000i		−	0.549548i
$650$	−15.0000	−	3.00000i	−0.588348	−	0.117670i
$651$		0			0
$652$	12.0000	−	12.0000i	0.469956	−	0.469956i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$		−	6.00000i		−	0.234619i
$655$	−20.0000	+	20.0000i	−0.781465	+	0.781465i
$656$	16.0000	+	16.0000i	0.624695	+	0.624695i
$657$	−5.00000	+	5.00000i	−0.195069	+	0.195069i
$658$		0			0
$659$		−	36.0000i		−	1.40236i	−0.712984	−	0.701180i	$-0.752657\pi$
$659$		−	36.0000i		−	1.40236i	0.712984	−	0.701180i	$-0.247343\pi$
$660$			8.00000i			0.311400i
$661$	−9.00000	+	9.00000i	−0.350059	+	0.350059i	−0.860132	−	0.510072i	$-0.829619\pi$
$661$	−9.00000	+	9.00000i	−0.350059	+	0.350059i	0.510072	+	0.860132i	$0.329619\pi$
$662$			32.0000i			1.24372i
$663$	−6.00000	+	4.00000i	−0.233021	+	0.155347i
$664$	20.0000			0.776151
$665$		0			0
$666$			6.00000i			0.232495i
$667$	60.0000			2.32321
$668$	−10.0000	+	10.0000i	−0.386912	+	0.386912i
$669$	−10.0000	−	10.0000i	−0.386622	−	0.386622i
$670$	−32.0000	+	32.0000i	−1.23627	+	1.23627i
$671$	8.00000	+	8.00000i	0.308837	+	0.308837i
$672$		0			0
$673$		−	6.00000i		−	0.231283i	−0.993291	−	0.115642i	$-0.963108\pi$
$673$		−	6.00000i		−	0.231283i	0.993291	−	0.115642i	$-0.0368924\pi$
$674$	−8.00000	−	8.00000i	−0.308148	−	0.308148i
$675$	−3.00000			−0.115470
$676$	−24.0000	−	10.0000i	−0.923077	−	0.384615i
$677$	−2.00000			−0.0768662			−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000			−0.0768662			−0.0384331	+	0.999261i	$0.512237\pi$
$678$	6.00000	+	6.00000i	0.230429	+	0.230429i
$679$		0			0
$680$	16.0000			0.613572
$681$	3.00000	+	3.00000i	0.114960	+	0.114960i
$682$	12.0000	−	12.0000i	0.459504	−	0.459504i
$683$	−19.0000	−	19.0000i	−0.727015	−	0.727015i	0.243009	−	0.970024i	$-0.421865\pi$
$683$	−19.0000	−	19.0000i	−0.727015	−	0.727015i	−0.970024	+	0.243009i	$0.921865\pi$
$684$	−4.00000	−	4.00000i	−0.152944	−	0.152944i
$685$	−48.0000			−1.83399
$686$		0			0
$687$	−7.00000	−	7.00000i	−0.267067	−	0.267067i
$688$	16.0000			0.609994
$689$	18.0000	−	12.0000i	0.685745	−	0.457164i
$690$		−	24.0000i		−	0.913664i
$691$	24.0000	−	24.0000i	0.913003	−	0.913003i	−0.0835044	−	0.996507i	$-0.526611\pi$
$691$	24.0000	−	24.0000i	0.913003	−	0.913003i	0.996507	+	0.0835044i	$0.0266113\pi$
$692$	28.0000			1.06440
$693$		0			0
$694$	−12.0000	−	12.0000i	−0.455514	−	0.455514i
$695$	−8.00000	+	8.00000i	−0.303457	+	0.303457i
$696$	−20.0000	+	20.0000i	−0.758098	+	0.758098i
$697$	8.00000	−	8.00000i	0.303022	−	0.303022i
$698$			6.00000i			0.227103i
$699$	−6.00000			−0.226941
$700$		0			0
$701$		−	30.0000i		−	1.13308i	−0.824033	−	0.566542i	$-0.808281\pi$
$701$		−	30.0000i		−	1.13308i	0.824033	−	0.566542i	$-0.191719\pi$
$702$	−5.00000	−	1.00000i	−0.188713	−	0.0377426i
$703$			12.0000i			0.452589i
$704$	8.00000	−	8.00000i	0.301511	−	0.301511i
$705$	−20.0000			−0.753244
$706$	−32.0000			−1.20434
$707$		0			0
$708$	−14.0000	−	14.0000i	−0.526152	−	0.526152i
$709$	37.0000	−	37.0000i	1.38956	−	1.38956i	0.563337	−	0.826227i	$-0.309517\pi$
$709$	37.0000	−	37.0000i	1.38956	−	1.38956i	0.826227	−	0.563337i	$-0.190483\pi$
$710$	36.0000	−	36.0000i	1.35106	−	1.35106i
$711$			16.0000i			0.600047i
$712$	−8.00000			−0.299813
$713$	−36.0000	+	36.0000i	−1.34821	+	1.34821i
$714$		0			0
$715$	8.00000	+	12.0000i	0.299183	+	0.448775i
$716$		−	40.0000i		−	1.49487i
$717$	−3.00000	−	3.00000i	−0.112037	−	0.112037i
$718$	34.0000			1.26887
$719$	−30.0000			−1.11881			−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000			−1.11881			−0.559406	+	0.828894i	$0.688971\pi$
$720$	8.00000	+	8.00000i	0.298142	+	0.298142i
$721$		0			0
$722$	11.0000	+	11.0000i	0.409378	+	0.409378i
$723$	9.00000	+	9.00000i	0.334714	+	0.334714i
$724$	20.0000			0.743294
$725$			30.0000i			1.11417i
$726$	−9.00000	+	9.00000i	−0.334021	+	0.334021i
$727$	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
$729$	−1.00000			−0.0370370
$730$	20.0000	−	20.0000i	0.740233	−	0.740233i
$731$		−	8.00000i		−	0.295891i
$732$	16.0000			0.591377
$733$	−11.0000	−	11.0000i	−0.406294	−	0.406294i	0.474150	−	0.880444i	$-0.342755\pi$
$733$	−11.0000	−	11.0000i	−0.406294	−	0.406294i	−0.880444	+	0.474150i	$0.842755\pi$
$734$	28.0000	+	28.0000i	1.03350	+	1.03350i
$735$	−14.0000	−	14.0000i	−0.516398	−	0.516398i
$736$	−24.0000	+	24.0000i	−0.884652	+	0.884652i
$737$	16.0000			0.589368
$738$	8.00000			0.294484
$739$	−28.0000	−	28.0000i	−1.03000	−	1.03000i	−0.999536	−	0.0304607i	$-0.990303\pi$
$739$	−28.0000	−	28.0000i	−1.03000	−	1.03000i	−0.0304607	−	0.999536i	$-0.509697\pi$
$740$		−	24.0000i		−	0.882258i
$741$	−10.0000	−	2.00000i	−0.367359	−	0.0734718i
$742$		0			0
$743$	15.0000	−	15.0000i	0.550297	−	0.550297i	−0.376230	−	0.926526i	$-0.622780\pi$
$743$	15.0000	−	15.0000i	0.550297	−	0.550297i	0.926526	+	0.376230i	$0.122780\pi$
$744$		−	24.0000i		−	0.879883i
$745$			32.0000i			1.17239i
$746$	−6.00000	+	6.00000i	−0.219676	+	0.219676i
$747$	5.00000	−	5.00000i	0.182940	−	0.182940i
$748$	−4.00000	−	4.00000i	−0.146254	−	0.146254i
$749$		0			0
$750$	−8.00000			−0.292119
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$	20.0000	+	20.0000i	0.729325	+	0.729325i
$753$			2.00000i			0.0728841i
$754$	−10.0000	+	50.0000i	−0.364179	+	1.82089i
$755$		−	24.0000i		−	0.873449i
$756$		0			0
$757$	−52.0000			−1.88997			−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−52.0000			−1.88997			−0.944986	+	0.327111i	$0.893925\pi$
$758$			44.0000i			1.59815i
$759$	−6.00000	+	6.00000i	−0.217786	+	0.217786i
$760$	16.0000	+	16.0000i	0.580381	+	0.580381i
$761$	36.0000	−	36.0000i	1.30500	−	1.30500i	0.380021	−	0.924978i	$-0.375917\pi$
$761$	36.0000	−	36.0000i	1.30500	−	1.30500i	0.924978	−	0.380021i	$-0.124083\pi$
$762$	8.00000	+	8.00000i	0.289809	+	0.289809i
$763$		0			0
$764$		0			0
$765$	4.00000	−	4.00000i	0.144620	−	0.144620i
$766$		−	10.0000i		−	0.361315i
$767$	−35.0000	−	7.00000i	−1.26378	−	0.252755i
$768$		−	16.0000i		−	0.577350i
$769$	−7.00000	−	7.00000i	−0.252426	−	0.252426i	0.569538	−	0.821965i	$-0.307122\pi$
$769$	−7.00000	−	7.00000i	−0.252426	−	0.252426i	−0.821965	+	0.569538i	$0.807122\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	30.0000	+	30.0000i	1.07972	+	1.07972i
$773$	4.00000	+	4.00000i	0.143870	+	0.143870i	0.775373	−	0.631503i	$-0.217562\pi$
$773$	4.00000	+	4.00000i	0.143870	+	0.143870i	−0.631503	+	0.775373i	$0.717562\pi$
$774$	4.00000	−	4.00000i	0.143777	−	0.143777i
$775$	−18.0000	−	18.0000i	−0.646579	−	0.646579i
$776$		−	20.0000i		−	0.717958i
$777$		0			0
$778$	−14.0000	−	14.0000i	−0.501924	−	0.501924i
$779$	16.0000			0.573259
$780$	20.0000	+	4.00000i	0.716115	+	0.143223i
$781$	−18.0000			−0.644091
$782$	12.0000	+	12.0000i	0.429119	+	0.429119i
$783$			10.0000i			0.357371i
$784$			28.0000i			1.00000i
$785$	−24.0000	−	24.0000i	−0.856597	−	0.856597i
$786$	10.0000	−	10.0000i	0.356688	−	0.356688i
$787$	20.0000	+	20.0000i	0.712923	+	0.712923i	0.967146	−	0.254223i	$-0.0818196\pi$
$787$	20.0000	+	20.0000i	0.712923	+	0.712923i	−0.254223	+	0.967146i	$0.581820\pi$
$788$	20.0000	−	20.0000i	0.712470	−	0.712470i
$789$	26.0000			0.925625
$790$		−	64.0000i		−	2.27702i
$791$		0			0
$792$		−	4.00000i		−	0.142134i
$793$	24.0000	−	16.0000i	0.852265	−	0.568177i
$794$		−	26.0000i		−	0.922705i
$795$	−12.0000	+	12.0000i	−0.425596	+	0.425596i
$796$		−	40.0000i		−	1.41776i
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		0			0
$799$	10.0000	−	10.0000i	0.353775	−	0.353775i
$800$	−12.0000	−	12.0000i	−0.424264	−	0.424264i
$801$	−2.00000	+	2.00000i	−0.0706665	+	0.0706665i
$802$		−	12.0000i		−	0.423735i
$803$	−10.0000			−0.352892
$804$	16.0000	−	16.0000i	0.564276	−	0.564276i
$805$		0			0
$806$	−24.0000	−	36.0000i	−0.845364	−	1.26805i
$807$		−	10.0000i		−	0.352017i
$808$	−20.0000	+	20.0000i	−0.703598	+	0.703598i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$	4.00000			0.140546
$811$	−6.00000	+	6.00000i	−0.210688	+	0.210688i	−0.804560	−	0.593871i	$-0.797599\pi$
$811$	−6.00000	+	6.00000i	−0.210688	+	0.210688i	0.593871	+	0.804560i	$0.297599\pi$
$812$		0			0
$813$	4.00000	−	4.00000i	0.140286	−	0.140286i
$814$	−6.00000	+	6.00000i	−0.210300	+	0.210300i
$815$			24.0000i			0.840683i
$816$	−8.00000			−0.280056
$817$	8.00000	−	8.00000i	0.279885	−	0.279885i
$818$	26.0000			0.909069
$819$		0			0
$820$	−32.0000			−1.11749
$821$	16.0000	+	16.0000i	0.558404	+	0.558404i	0.928853	−	0.370449i	$-0.120796\pi$
$821$	16.0000	+	16.0000i	0.558404	+	0.558404i	−0.370449	+	0.928853i	$0.620796\pi$
$822$	24.0000			0.837096
$823$	−4.00000			−0.139431			−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000			−0.139431			−0.0697156	+	0.997567i	$0.522209\pi$
$824$	−32.0000	−	32.0000i	−1.11477	−	1.11477i
$825$	−3.00000	−	3.00000i	−0.104447	−	0.104447i
$826$		0			0
$827$	−5.00000	−	5.00000i	−0.173867	−	0.173867i	0.614809	−	0.788676i	$-0.289233\pi$
$827$	−5.00000	−	5.00000i	−0.173867	−	0.173867i	−0.788676	+	0.614809i	$0.789233\pi$
$828$			12.0000i			0.417029i
$829$			26.0000i			0.903017i	0.892267	+	0.451509i	$0.149114\pi$
$829$			26.0000i			0.903017i	−0.892267	+	0.451509i	$0.850886\pi$
$830$	−20.0000	+	20.0000i	−0.694210	+	0.694210i
$831$	−8.00000			−0.277517
$832$	−16.0000	−	24.0000i	−0.554700	−	0.832050i
$833$	14.0000			0.485071
$834$	4.00000	−	4.00000i	0.138509	−	0.138509i
$835$		−	20.0000i		−	0.692129i
$836$		−	8.00000i		−	0.276686i
$837$	−6.00000	−	6.00000i	−0.207390	−	0.207390i
$838$	−26.0000	−	26.0000i	−0.898155	−	0.898155i
$839$	27.0000	+	27.0000i	0.932144	+	0.932144i	0.997840	−	0.0656962i	$-0.0209268\pi$
$839$	27.0000	+	27.0000i	0.932144	+	0.932144i	−0.0656962	+	0.997840i	$0.520927\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$	42.0000			1.44742
$843$	4.00000	+	4.00000i	0.137767	+	0.137767i
$844$	−40.0000			−1.37686
$845$	34.0000	−	14.0000i	1.16964	−	0.481615i
$846$	10.0000			0.343807
$847$		0			0
$848$	24.0000			0.824163
$849$			4.00000i			0.137280i
$850$	−6.00000	+	6.00000i	−0.205798	+	0.205798i
$851$	18.0000	−	18.0000i	0.617032	−	0.617032i
$852$	−18.0000	+	18.0000i	−0.616670	+	0.616670i
$853$	−15.0000	+	15.0000i	−0.513590	+	0.513590i	−0.915625	−	0.402034i	$-0.868303\pi$
$853$	−15.0000	+	15.0000i	−0.513590	+	0.513590i	0.402034	+	0.915625i	$0.368303\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$	−4.00000	+	4.00000i	−0.136717	+	0.136717i
$857$			42.0000i			1.43469i	0.696717	+	0.717346i	$0.254643\pi$
$857$			42.0000i			1.43469i	−0.696717	+	0.717346i	$0.745357\pi$
$858$	−4.00000	−	6.00000i	−0.136558	−	0.204837i
$859$		−	56.0000i		−	1.91070i	−0.295484	−	0.955348i	$-0.595481\pi$
$859$		−	56.0000i		−	1.91070i	0.295484	−	0.955348i	$-0.404519\pi$
$860$	−16.0000	+	16.0000i	−0.545595	+	0.545595i
$861$		0			0
$862$		−	18.0000i		−	0.613082i
$863$	−5.00000	+	5.00000i	−0.170202	+	0.170202i	−0.787068	−	0.616866i	$-0.788402\pi$
$863$	−5.00000	+	5.00000i	−0.170202	+	0.170202i	0.616866	+	0.787068i	$0.288402\pi$
$864$	−4.00000	−	4.00000i	−0.136083	−	0.136083i
$865$	−28.0000	+	28.0000i	−0.952029	+	0.952029i
$866$	14.0000	+	14.0000i	0.475739	+	0.475739i
$867$		−	13.0000i		−	0.441503i
$868$		0			0
$869$	−16.0000	+	16.0000i	−0.542763	+	0.542763i
$870$		−	40.0000i		−	1.35613i
$871$	8.00000	−	40.0000i	0.271070	−	1.35535i
$872$		−	12.0000i		−	0.406371i
$873$	−5.00000	−	5.00000i	−0.169224	−	0.169224i
$874$			24.0000i			0.811812i
$875$		0			0
$876$	−10.0000	+	10.0000i	−0.337869	+	0.337869i
$877$	15.0000	+	15.0000i	0.506514	+	0.506514i	0.913455	−	0.406941i	$-0.133404\pi$
$877$	15.0000	+	15.0000i	0.506514	+	0.506514i	−0.406941	+	0.913455i	$0.633404\pi$
$878$	−20.0000	+	20.0000i	−0.674967	+	0.674967i
$879$	20.0000	+	20.0000i	0.674583	+	0.674583i
$880$			16.0000i			0.539360i
$881$			30.0000i			1.01073i	0.862907	+	0.505363i	$0.168641\pi$
$881$			30.0000i			1.01073i	−0.862907	+	0.505363i	$0.831359\pi$
$882$	7.00000	+	7.00000i	0.235702	+	0.235702i
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−12.0000	+	8.00000i	−0.403604	+	0.269069i
$885$	28.0000			0.941210
$886$	6.00000	+	6.00000i	0.201574	+	0.201574i
$887$			8.00000i			0.268614i	0.990940	+	0.134307i	$0.0428808\pi$
$887$			8.00000i			0.268614i	−0.990940	+	0.134307i	$0.957119\pi$
$888$			12.0000i			0.402694i
$889$		0			0
$890$	8.00000	−	8.00000i	0.268161	−	0.268161i
$891$	−1.00000	−	1.00000i	−0.0335013	−	0.0335013i
$892$	−20.0000	−	20.0000i	−0.669650	−	0.669650i
$893$	20.0000			0.669274
$894$		−	16.0000i		−	0.535120i
$895$	40.0000	+	40.0000i	1.33705	+	1.33705i
$896$		0			0
$897$	12.0000	+	18.0000i	0.400668	+	0.601003i
$898$		−	4.00000i		−	0.133482i
$899$	−60.0000	+	60.0000i	−2.00111	+	2.00111i
$900$	−6.00000			−0.200000
$901$		−	12.0000i		−	0.399778i
$902$	8.00000	+	8.00000i	0.266371	+	0.266371i
$903$		0			0
$904$	12.0000	+	12.0000i	0.399114	+	0.399114i
$905$	−20.0000	+	20.0000i	−0.664822	+	0.664822i
$906$			12.0000i			0.398673i
$907$	32.0000			1.06254			0.531271	−	0.847202i	$-0.321714\pi$
$907$	32.0000			1.06254			0.531271	+	0.847202i	$0.321714\pi$
$908$	6.00000	+	6.00000i	0.199117	+	0.199117i
$909$			10.0000i			0.331679i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	−8.00000	−	8.00000i	−0.264906	−	0.264906i
$913$	10.0000			0.330952
$914$	−10.0000			−0.330771
$915$	−16.0000	+	16.0000i	−0.528944	+	0.528944i
$916$	−14.0000	−	14.0000i	−0.462573	−	0.462573i
$917$		0			0
$918$	−2.00000	+	2.00000i	−0.0660098	+	0.0660098i
$919$		−	16.0000i		−	0.527791i	−0.964551	−	0.263896i	$-0.914993\pi$
$919$		−	16.0000i		−	0.527791i	0.964551	−	0.263896i	$-0.0850075\pi$
$920$		−	48.0000i		−	1.58251i
$921$		0			0
$922$	12.0000			0.395199
$923$	−9.00000	+	45.0000i	−0.296239	+	1.48119i
$924$		0			0
$925$	9.00000	+	9.00000i	0.295918	+	0.295918i
$926$	−48.0000			−1.57738
$927$	−16.0000			−0.525509
$928$	−40.0000	+	40.0000i	−1.31306	+	1.31306i
$929$	−12.0000	−	12.0000i	−0.393707	−	0.393707i	0.482299	−	0.876007i	$-0.339802\pi$
$929$	−12.0000	−	12.0000i	−0.393707	−	0.393707i	−0.876007	+	0.482299i	$0.839802\pi$
$930$	24.0000	+	24.0000i	0.786991	+	0.786991i
$931$	14.0000	+	14.0000i	0.458831	+	0.458831i
$932$	−12.0000			−0.393073
$933$		−	18.0000i		−	0.589294i
$934$	22.0000	−	22.0000i	0.719862	−	0.719862i
$935$	8.00000			0.261628
$936$	−10.0000	−	2.00000i	−0.326860	−	0.0653720i
$937$	28.0000			0.914720			0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000			0.914720			0.457360	+	0.889282i	$0.348795\pi$
$938$		0			0
$939$			6.00000i			0.195803i
$940$	−40.0000			−1.30466
$941$	−24.0000	−	24.0000i	−0.782378	−	0.782378i	0.197854	−	0.980232i	$-0.436603\pi$
$941$	−24.0000	−	24.0000i	−0.782378	−	0.782378i	−0.980232	+	0.197854i	$0.936603\pi$
$942$	12.0000	+	12.0000i	0.390981	+	0.390981i
$943$	−24.0000	−	24.0000i	−0.781548	−	0.781548i
$944$	−28.0000	−	28.0000i	−0.911322	−	0.911322i
$945$		0			0
$946$	8.00000			0.260102
$947$	−5.00000	−	5.00000i	−0.162478	−	0.162478i	0.621185	−	0.783664i	$-0.286651\pi$
$947$	−5.00000	−	5.00000i	−0.162478	−	0.162478i	−0.783664	+	0.621185i	$0.786651\pi$
$948$			32.0000i			1.03931i
$949$	−5.00000	+	25.0000i	−0.162307	+	0.811534i
$950$	−12.0000			−0.389331
$951$	10.0000	−	10.0000i	0.324272	−	0.324272i
$952$		0			0
$953$			14.0000i			0.453504i	0.973952	+	0.226752i	$0.0728108\pi$
$953$			14.0000i			0.453504i	−0.973952	+	0.226752i	$0.927189\pi$
$954$	6.00000	−	6.00000i	0.194257	−	0.194257i
$955$		0			0
$956$	−6.00000	−	6.00000i	−0.194054	−	0.194054i
$957$	−10.0000	+	10.0000i	−0.323254	+	0.323254i
$958$	14.0000			0.452319
$959$		0			0
$960$	16.0000	+	16.0000i	0.516398	+	0.516398i
$961$		−	41.0000i		−	1.32258i
$962$	12.0000	+	18.0000i	0.386896	+	0.580343i
$963$			2.00000i			0.0644491i
$964$	18.0000	+	18.0000i	0.579741	+	0.579741i
$965$	−60.0000			−1.93147
$966$		0			0
$967$	2.00000	−	2.00000i	0.0643157	−	0.0643157i	−0.674217	−	0.738533i	$-0.735519\pi$
$967$	2.00000	−	2.00000i	0.0643157	−	0.0643157i	0.738533	+	0.674217i	$0.235519\pi$
$968$	−18.0000	+	18.0000i	−0.578542	+	0.578542i
$969$	−4.00000	+	4.00000i	−0.128499	+	0.128499i
$970$	20.0000	+	20.0000i	0.642161	+	0.642161i
$971$			20.0000i			0.641831i	0.947108	+	0.320915i	$0.103990\pi$
$971$			20.0000i			0.641831i	−0.947108	+	0.320915i	$0.896010\pi$
$972$	−2.00000			−0.0641500
$973$		0			0
$974$			36.0000i			1.15351i
$975$	−9.00000	+	6.00000i	−0.288231	+	0.192154i
$976$	32.0000			1.02430
$977$	10.0000	+	10.0000i	0.319928	+	0.319928i	0.848740	−	0.528811i	$-0.177362\pi$
$977$	10.0000	+	10.0000i	0.319928	+	0.319928i	−0.528811	+	0.848740i	$0.677362\pi$
$978$		−	12.0000i		−	0.383718i
$979$	−4.00000			−0.127841
$980$	−28.0000	−	28.0000i	−0.894427	−	0.894427i
$981$	−3.00000	−	3.00000i	−0.0957826	−	0.0957826i
$982$	−22.0000	+	22.0000i	−0.702048	+	0.702048i
$983$	−29.0000	−	29.0000i	−0.924956	−	0.924956i	0.0724180	−	0.997374i	$-0.476928\pi$
$983$	−29.0000	−	29.0000i	−0.924956	−	0.924956i	−0.997374	+	0.0724180i	$0.976928\pi$
$984$	16.0000			0.510061
$985$			40.0000i			1.27451i
$986$	20.0000	+	20.0000i	0.636930	+	0.636930i
$987$		0			0
$988$	−20.0000	−	4.00000i	−0.636285	−	0.127257i
$989$	−24.0000			−0.763156
$990$	4.00000	+	4.00000i	0.127128	+	0.127128i
$991$		−	40.0000i		−	1.27064i	−0.772248	−	0.635321i	$-0.780868\pi$
$991$		−	40.0000i		−	1.27064i	0.772248	−	0.635321i	$-0.219132\pi$
$992$		−	48.0000i		−	1.52400i
$993$	16.0000	+	16.0000i	0.507745	+	0.507745i
$994$		0			0
$995$	40.0000	+	40.0000i	1.26809	+	1.26809i
$996$	10.0000	−	10.0000i	0.316862	−	0.316862i
$997$	38.0000			1.20347			0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000			1.20347			0.601736	+	0.798695i	$0.294476\pi$
$998$		−	16.0000i		−	0.506471i
$999$	3.00000	+	3.00000i	0.0949158	+	0.0949158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.k.d.151.1	yes	2
3.2	odd	2		468.2.n.b.307.1		2
4.3	odd	2		156.2.k.c.151.1	yes	2
12.11	even	2		468.2.n.d.307.1		2
13.5	odd	4		156.2.k.c.31.1	✓	2
39.5	even	4		468.2.n.d.343.1		2
52.31	even	4	inner	156.2.k.d.31.1	yes	2
156.83	odd	4		468.2.n.b.343.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.k.c.31.1	✓	2	13.5	odd	4
156.2.k.c.151.1	yes	2	4.3	odd	2
156.2.k.d.31.1	yes	2	52.31	even	4	inner
156.2.k.d.151.1	yes	2	1.1	even	1	trivial
468.2.n.b.307.1		2	3.2	odd	2
468.2.n.b.343.1		2	156.83	odd	4
468.2.n.d.307.1		2	12.11	even	2
468.2.n.d.343.1		2	39.5	even	4

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +(2.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +(2.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +4.00000 q^{10} +(-1.00000 - 1.00000i) q^{11} -2.00000 q^{12} +(-3.00000 + 2.00000i) q^{13} +(2.00000 - 2.00000i) q^{15} -4.00000 q^{16} +2.00000i q^{17} +(-1.00000 + 1.00000i) q^{18} +(-2.00000 + 2.00000i) q^{19} +(4.00000 - 4.00000i) q^{20} -2.00000 q^{22} +6.00000 q^{23} +(-2.00000 + 2.00000i) q^{24} +3.00000i q^{25} +(-1.00000 + 5.00000i) q^{26} +1.00000i q^{27} +10.0000 q^{29} -4.00000i q^{30} +(-6.00000 + 6.00000i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-1.00000 + 1.00000i) q^{33} +(2.00000 + 2.00000i) q^{34} +2.00000i q^{36} +(3.00000 - 3.00000i) q^{37} +4.00000i q^{38} +(2.00000 + 3.00000i) q^{39} -8.00000i q^{40} +(-4.00000 - 4.00000i) q^{41} -4.00000 q^{43} +(-2.00000 + 2.00000i) q^{44} +(-2.00000 - 2.00000i) q^{45} +(6.00000 - 6.00000i) q^{46} +(-5.00000 - 5.00000i) q^{47} +4.00000i q^{48} -7.00000i q^{49} +(3.00000 + 3.00000i) q^{50} +2.00000 q^{51} +(4.00000 + 6.00000i) q^{52} -6.00000 q^{53} +(1.00000 + 1.00000i) q^{54} -4.00000i q^{55} +(2.00000 + 2.00000i) q^{57} +(10.0000 - 10.0000i) q^{58} +(7.00000 + 7.00000i) q^{59} +(-4.00000 - 4.00000i) q^{60} -8.00000 q^{61} +12.0000i q^{62} +8.00000i q^{64} +(-10.0000 - 2.00000i) q^{65} +2.00000i q^{66} +(-8.00000 + 8.00000i) q^{67} +4.00000 q^{68} -6.00000i q^{69} +(9.00000 - 9.00000i) q^{71} +(2.00000 + 2.00000i) q^{72} +(5.00000 - 5.00000i) q^{73} -6.00000i q^{74} +3.00000 q^{75} +(4.00000 + 4.00000i) q^{76} +(5.00000 + 1.00000i) q^{78} -16.0000i q^{79} +(-8.00000 - 8.00000i) q^{80} +1.00000 q^{81} -8.00000 q^{82} +(-5.00000 + 5.00000i) q^{83} +(-4.00000 + 4.00000i) q^{85} +(-4.00000 + 4.00000i) q^{86} -10.0000i q^{87} +4.00000i q^{88} +(2.00000 - 2.00000i) q^{89} -4.00000 q^{90} -12.0000i q^{92} +(6.00000 + 6.00000i) q^{93} -10.0000 q^{94} -8.00000 q^{95} +(4.00000 + 4.00000i) q^{96} +(5.00000 + 5.00000i) q^{97} +(-7.00000 - 7.00000i) q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 4 q^{5} - 2 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 4 * q^5 - 2 * q^6 - 4 * q^8 - 2 * q^9	\( 2 q + 2 q^{2} + 4 q^{5} - 2 q^{6} - 4 q^{8} - 2 q^{9} + 8 q^{10} - 2 q^{11} - 4 q^{12} - 6 q^{13} + 4 q^{15} - 8 q^{16} - 2 q^{18} - 4 q^{19} + 8 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{24} - 2 q^{26} + 20 q^{29} - 12 q^{31} - 8 q^{32} - 2 q^{33} + 4 q^{34} + 6 q^{37} + 4 q^{39} - 8 q^{41} - 8 q^{43} - 4 q^{44} - 4 q^{45} + 12 q^{46} - 10 q^{47} + 6 q^{50} + 4 q^{51} + 8 q^{52} - 12 q^{53} + 2 q^{54} + 4 q^{57} + 20 q^{58} + 14 q^{59} - 8 q^{60} - 16 q^{61} - 20 q^{65} - 16 q^{67} + 8 q^{68} + 18 q^{71} + 4 q^{72} + 10 q^{73} + 6 q^{75} + 8 q^{76} + 10 q^{78} - 16 q^{80} + 2 q^{81} - 16 q^{82} - 10 q^{83} - 8 q^{85} - 8 q^{86} + 4 q^{89} - 8 q^{90} + 12 q^{93} - 20 q^{94} - 16 q^{95} + 8 q^{96} + 10 q^{97} - 14 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 4 * q^5 - 2 * q^6 - 4 * q^8 - 2 * q^9 + 8 * q^10 - 2 * q^11 - 4 * q^12 - 6 * q^13 + 4 * q^15 - 8 * q^16 - 2 * q^18 - 4 * q^19 + 8 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^24 - 2 * q^26 + 20 * q^29 - 12 * q^31 - 8 * q^32 - 2 * q^33 + 4 * q^34 + 6 * q^37 + 4 * q^39 - 8 * q^41 - 8 * q^43 - 4 * q^44 - 4 * q^45 + 12 * q^46 - 10 * q^47 + 6 * q^50 + 4 * q^51 + 8 * q^52 - 12 * q^53 + 2 * q^54 + 4 * q^57 + 20 * q^58 + 14 * q^59 - 8 * q^60 - 16 * q^61 - 20 * q^65 - 16 * q^67 + 8 * q^68 + 18 * q^71 + 4 * q^72 + 10 * q^73 + 6 * q^75 + 8 * q^76 + 10 * q^78 - 16 * q^80 + 2 * q^81 - 16 * q^82 - 10 * q^83 - 8 * q^85 - 8 * q^86 + 4 * q^89 - 8 * q^90 + 12 * q^93 - 20 * q^94 - 16 * q^95 + 8 * q^96 + 10 * q^97 - 14 * q^98 + 2 * q^99

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