LMFDB - Embedded newform 80.2.q.b.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.q (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:	$0.638803216170$
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			29.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.29
Dual form			80.2.q.b.69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	0.356822	+	0.934172i	$0.383860\pi$
$4$		−	2.00000i		−	1.00000i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$			2.00000i			0.816497i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$			1.00000i			0.333333i
$10$	1.00000	−	3.00000i	0.316228	−	0.948683i
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	−0.995824	−	0.0912903i	$-0.970901\pi$
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	0.0912903	+	0.995824i	$0.470901\pi$
$12$	2.00000	+	2.00000i	0.577350	+	0.577350i
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	−0.987797	−	0.155747i	$-0.950222\pi$
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	0.155747	+	0.987797i	$0.450222\pi$
$14$		0			0
$15$	−1.00000	+	3.00000i	−0.258199	+	0.774597i
$16$	−4.00000			−1.00000
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$	1.00000	+	1.00000i	0.235702	+	0.235702i
$19$	−1.00000	−	1.00000i	−0.229416	−	0.229416i	0.583033	−	0.812449i	$-0.301866\pi$
$19$	−1.00000	−	1.00000i	−0.229416	−	0.229416i	−0.812449	+	0.583033i	$0.801866\pi$
$20$	−2.00000	−	4.00000i	−0.447214	−	0.894427i
$21$		0			0
$22$			6.00000i			1.27920i
$23$	8.00000			1.66812			0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000			1.66812			0.834058	+	0.551677i	$0.186012\pi$
$24$	4.00000			0.816497
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$			6.00000i			1.17670i
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$		0			0
$29$	3.00000	+	3.00000i	0.557086	+	0.557086i	0.928477	−	0.371391i	$-0.121119\pi$
$29$	3.00000	+	3.00000i	0.557086	+	0.557086i	−0.371391	+	0.928477i	$0.621119\pi$
$30$	2.00000	+	4.00000i	0.365148	+	0.730297i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$		−	6.00000i		−	1.04447i
$34$	−4.00000	−	4.00000i	−0.685994	−	0.685994i
$35$		0			0
$36$	2.00000			0.333333
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$	−2.00000			−0.324443
$39$		−	6.00000i		−	0.960769i
$40$	−6.00000	−	2.00000i	−0.948683	−	0.316228i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	−3.00000	−	3.00000i	−0.457496	−	0.457496i	0.440337	−	0.897833i	$-0.354859\pi$
$43$	−3.00000	−	3.00000i	−0.457496	−	0.457496i	−0.897833	+	0.440337i	$0.854859\pi$
$44$	6.00000	+	6.00000i	0.904534	+	0.904534i
$45$	1.00000	+	2.00000i	0.149071	+	0.298142i
$46$	8.00000	−	8.00000i	1.17954	−	1.17954i
$47$		−	2.00000i		−	0.291730i	−0.989305	−	0.145865i	$-0.953403\pi$
$47$		−	2.00000i		−	0.291730i	0.989305	−	0.145865i	$-0.0465965\pi$
$48$	4.00000	−	4.00000i	0.577350	−	0.577350i
$49$	−7.00000			−1.00000
$50$	−1.00000	−	7.00000i	−0.141421	−	0.989949i
$51$	4.00000	+	4.00000i	0.560112	+	0.560112i
$52$	6.00000	+	6.00000i	0.832050	+	0.832050i
$53$	9.00000	+	9.00000i	1.23625	+	1.23625i	0.961524	+	0.274721i	$0.0885855\pi$
$53$	9.00000	+	9.00000i	1.23625	+	1.23625i	0.274721	+	0.961524i	$0.411414\pi$
$54$	−8.00000			−1.08866
$55$	−3.00000	+	9.00000i	−0.404520	+	1.21356i
$56$		0			0
$57$	2.00000			0.264906
$58$	6.00000			0.787839
$59$	9.00000	−	9.00000i	1.17170	−	1.17170i	0.189896	−	0.981804i	$-0.439185\pi$
$59$	9.00000	−	9.00000i	1.17170	−	1.17170i	0.981804	−	0.189896i	$-0.0608151\pi$
$60$	6.00000	+	2.00000i	0.774597	+	0.258199i
$61$	−5.00000	−	5.00000i	−0.640184	−	0.640184i	0.310416	−	0.950601i	$-0.399532\pi$
$61$	−5.00000	−	5.00000i	−0.640184	−	0.640184i	−0.950601	+	0.310416i	$0.899532\pi$
$62$		0			0
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−3.00000	+	9.00000i	−0.372104	+	1.11631i
$66$	−6.00000	−	6.00000i	−0.738549	−	0.738549i
$67$	3.00000	−	3.00000i	0.366508	−	0.366508i	−0.499694	−	0.866202i	$-0.666554\pi$
$67$	3.00000	−	3.00000i	0.366508	−	0.366508i	0.866202	+	0.499694i	$0.166554\pi$
$68$	−8.00000			−0.970143
$69$	−8.00000	+	8.00000i	−0.963087	+	0.963087i
$70$		0			0
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$	2.00000	−	2.00000i	0.235702	−	0.235702i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	−6.00000			−0.697486
$75$	1.00000	+	7.00000i	0.115470	+	0.808290i
$76$	−2.00000	+	2.00000i	−0.229416	+	0.229416i
$77$		0			0
$78$	−6.00000	−	6.00000i	−0.679366	−	0.679366i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−8.00000	+	4.00000i	−0.894427	+	0.447214i
$81$	5.00000			0.555556
$82$		0			0
$83$	−9.00000	+	9.00000i	−0.987878	+	0.987878i	−0.999927	−	0.0120491i	$-0.996165\pi$
$83$	−9.00000	+	9.00000i	−0.987878	+	0.987878i	0.0120491	+	0.999927i	$0.496165\pi$
$84$		0			0
$85$	−4.00000	−	8.00000i	−0.433861	−	0.867722i
$86$	−6.00000			−0.646997
$87$	−6.00000			−0.643268
$88$	12.0000			1.27920
$89$			12.0000i			1.27200i	0.771690	+	0.635999i	$0.219412\pi$
$89$			12.0000i			1.27200i	−0.771690	+	0.635999i	$0.780588\pi$
$90$	3.00000	+	1.00000i	0.316228	+	0.105409i
$91$		0			0
$92$		−	16.0000i		−	1.66812i
$93$		0			0
$94$	−2.00000	−	2.00000i	−0.206284	−	0.206284i
$95$	−3.00000	−	1.00000i	−0.307794	−	0.102598i
$96$		−	8.00000i		−	0.816497i
$97$			12.0000i			1.21842i	0.793011	+	0.609208i	$0.208512\pi$
$97$			12.0000i			1.21842i	−0.793011	+	0.609208i	$0.791488\pi$
$98$	−7.00000	+	7.00000i	−0.707107	+	0.707107i
$99$	−3.00000	−	3.00000i	−0.301511	−	0.301511i
$100$	−8.00000	−	6.00000i	−0.800000	−	0.600000i
$101$	3.00000	−	3.00000i	0.298511	−	0.298511i	−0.541919	−	0.840431i	$-0.682302\pi$
$101$	3.00000	−	3.00000i	0.298511	−	0.298511i	0.840431	+	0.541919i	$0.182302\pi$
$102$	8.00000			0.792118
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	12.0000			1.17670
$105$		0			0
$106$	18.0000			1.74831
$107$	9.00000	+	9.00000i	0.870063	+	0.870063i	0.992479	−	0.122416i	$-0.0390642\pi$
$107$	9.00000	+	9.00000i	0.870063	+	0.870063i	−0.122416	+	0.992479i	$0.539064\pi$
$108$	−8.00000	+	8.00000i	−0.769800	+	0.769800i
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	0.657592	−	0.753374i	$-0.271575\pi$
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	−0.753374	+	0.657592i	$0.771575\pi$
$110$	6.00000	+	12.0000i	0.572078	+	1.14416i
$111$	6.00000			0.569495
$112$		0			0
$113$		−	8.00000i		−	0.752577i	−0.926503	−	0.376288i	$-0.877200\pi$
$113$		−	8.00000i		−	0.752577i	0.926503	−	0.376288i	$-0.122800\pi$
$114$	2.00000	−	2.00000i	0.187317	−	0.187317i
$115$	16.0000	−	8.00000i	1.49201	−	0.746004i
$116$	6.00000	−	6.00000i	0.557086	−	0.557086i
$117$	−3.00000	−	3.00000i	−0.277350	−	0.277350i
$118$		−	18.0000i		−	1.65703i
$119$		0			0
$120$	8.00000	−	4.00000i	0.730297	−	0.365148i
$121$		−	7.00000i		−	0.636364i
$122$	−10.0000			−0.905357
$123$		0			0
$124$		0			0
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$	6.00000			0.528271
$130$	6.00000	+	12.0000i	0.526235	+	1.05247i
$131$	−9.00000	−	9.00000i	−0.786334	−	0.786334i	0.194557	−	0.980891i	$-0.437673\pi$
$131$	−9.00000	−	9.00000i	−0.786334	−	0.786334i	−0.980891	+	0.194557i	$0.937673\pi$
$132$	−12.0000			−1.04447
$133$		0			0
$134$		−	6.00000i		−	0.518321i
$135$	−12.0000	−	4.00000i	−1.03280	−	0.344265i
$136$	−8.00000	+	8.00000i	−0.685994	+	0.685994i
$137$	−2.00000			−0.170872			−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000			−0.170872			−0.0854358	+	0.996344i	$0.527228\pi$
$138$			16.0000i			1.36201i
$139$	−7.00000	+	7.00000i	−0.593732	+	0.593732i	−0.938638	−	0.344905i	$-0.887911\pi$
$139$	−7.00000	+	7.00000i	−0.593732	+	0.593732i	0.344905	+	0.938638i	$0.387911\pi$
$140$		0			0
$141$	2.00000	+	2.00000i	0.168430	+	0.168430i
$142$	−6.00000	−	6.00000i	−0.503509	−	0.503509i
$143$		−	18.0000i		−	1.50524i
$144$		−	4.00000i		−	0.333333i
$145$	9.00000	+	3.00000i	0.747409	+	0.249136i
$146$	−6.00000	+	6.00000i	−0.496564	+	0.496564i
$147$	7.00000	−	7.00000i	0.577350	−	0.577350i
$148$	−6.00000	+	6.00000i	−0.493197	+	0.493197i
$149$	3.00000	−	3.00000i	0.245770	−	0.245770i	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	3.00000	−	3.00000i	0.245770	−	0.245770i	0.819232	+	0.573462i	$0.194400\pi$
$150$	8.00000	+	6.00000i	0.653197	+	0.489898i
$151$			18.0000i			1.46482i	0.680864	+	0.732410i	$0.261604\pi$
$151$			18.0000i			1.46482i	−0.680864	+	0.732410i	$0.738396\pi$
$152$			4.00000i			0.324443i
$153$	4.00000			0.323381
$154$		0			0
$155$		0			0
$156$	−12.0000			−0.960769
$157$	9.00000	−	9.00000i	0.718278	−	0.718278i	−0.249974	−	0.968252i	$-0.580422\pi$
$157$	9.00000	−	9.00000i	0.718278	−	0.718278i	0.968252	+	0.249974i	$0.0804222\pi$
$158$	8.00000	−	8.00000i	0.636446	−	0.636446i
$159$	−18.0000			−1.42749
$160$	−4.00000	+	12.0000i	−0.316228	+	0.948683i
$161$		0			0
$162$	5.00000	−	5.00000i	0.392837	−	0.392837i
$163$	−9.00000	+	9.00000i	−0.704934	+	0.704934i	−0.965465	−	0.260531i	$-0.916102\pi$
$163$	−9.00000	+	9.00000i	−0.704934	+	0.704934i	0.260531	+	0.965465i	$0.416102\pi$
$164$		0			0
$165$	−6.00000	−	12.0000i	−0.467099	−	0.934199i
$166$			18.0000i			1.39707i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	−12.0000	−	4.00000i	−0.920358	−	0.306786i
$171$	1.00000	−	1.00000i	0.0764719	−	0.0764719i
$172$	−6.00000	+	6.00000i	−0.457496	+	0.457496i
$173$	9.00000	−	9.00000i	0.684257	−	0.684257i	−0.276699	−	0.960957i	$-0.589241\pi$
$173$	9.00000	−	9.00000i	0.684257	−	0.684257i	0.960957	+	0.276699i	$0.0892406\pi$
$174$	−6.00000	+	6.00000i	−0.454859	+	0.454859i
$175$		0			0
$176$	12.0000	−	12.0000i	0.904534	−	0.904534i
$177$			18.0000i			1.35296i
$178$	12.0000	+	12.0000i	0.899438	+	0.899438i
$179$	3.00000	+	3.00000i	0.224231	+	0.224231i	0.810277	−	0.586047i	$-0.199317\pi$
$179$	3.00000	+	3.00000i	0.224231	+	0.224231i	−0.586047	+	0.810277i	$0.699317\pi$
$180$	4.00000	−	2.00000i	0.298142	−	0.149071i
$181$	−1.00000	+	1.00000i	−0.0743294	+	0.0743294i	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−1.00000	+	1.00000i	−0.0743294	+	0.0743294i	0.668965	+	0.743294i	$0.266738\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$	−16.0000	−	16.0000i	−1.17954	−	1.17954i
$185$	−9.00000	−	3.00000i	−0.661693	−	0.220564i
$186$		0			0
$187$	12.0000	+	12.0000i	0.877527	+	0.877527i
$188$	−4.00000			−0.291730
$189$		0			0
$190$	−4.00000	+	2.00000i	−0.290191	+	0.145095i
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$	−8.00000	−	8.00000i	−0.577350	−	0.577350i
$193$		−	12.0000i		−	0.863779i	−0.901927	−	0.431889i	$-0.857847\pi$
$193$		−	12.0000i		−	0.863779i	0.901927	−	0.431889i	$-0.142153\pi$
$194$	12.0000	+	12.0000i	0.861550	+	0.861550i
$195$	−6.00000	−	12.0000i	−0.429669	−	0.859338i
$196$			14.0000i			1.00000i
$197$	5.00000	+	5.00000i	0.356235	+	0.356235i	0.862423	−	0.506188i	$-0.168946\pi$
$197$	5.00000	+	5.00000i	0.356235	+	0.356235i	−0.506188	+	0.862423i	$0.668946\pi$
$198$	−6.00000			−0.426401
$199$			2.00000i			0.141776i	0.997484	+	0.0708881i	$0.0225833\pi$
$199$			2.00000i			0.141776i	−0.997484	+	0.0708881i	$0.977417\pi$
$200$	−14.0000	+	2.00000i	−0.989949	+	0.141421i
$201$			6.00000i			0.423207i
$202$		−	6.00000i		−	0.422159i
$203$		0			0
$204$	8.00000	−	8.00000i	0.560112	−	0.560112i
$205$		0			0
$206$		0			0
$207$			8.00000i			0.556038i
$208$	12.0000	−	12.0000i	0.832050	−	0.832050i
$209$	6.00000			0.415029
$210$		0			0
$211$	11.0000	+	11.0000i	0.757271	+	0.757271i	0.975825	−	0.218554i	$-0.0701339\pi$
$211$	11.0000	+	11.0000i	0.757271	+	0.757271i	−0.218554	+	0.975825i	$0.570134\pi$
$212$	18.0000	−	18.0000i	1.23625	−	1.23625i
$213$	6.00000	+	6.00000i	0.411113	+	0.411113i
$214$	18.0000			1.23045
$215$	−9.00000	−	3.00000i	−0.613795	−	0.204598i
$216$			16.0000i			1.08866i
$217$		0			0
$218$	−2.00000			−0.135457
$219$	6.00000	−	6.00000i	0.405442	−	0.405442i
$220$	18.0000	+	6.00000i	1.21356	+	0.404520i
$221$	12.0000	+	12.0000i	0.807207	+	0.807207i
$222$	6.00000	−	6.00000i	0.402694	−	0.402694i
$223$			6.00000i			0.401790i	0.979613	+	0.200895i	$0.0643850\pi$
$223$			6.00000i			0.401790i	−0.979613	+	0.200895i	$0.935615\pi$
$224$		0			0
$225$	4.00000	+	3.00000i	0.266667	+	0.200000i
$226$	−8.00000	−	8.00000i	−0.532152	−	0.532152i
$227$	−9.00000	+	9.00000i	−0.597351	+	0.597351i	−0.939607	−	0.342256i	$-0.888809\pi$
$227$	−9.00000	+	9.00000i	−0.597351	+	0.597351i	0.342256	+	0.939607i	$0.388809\pi$
$228$		−	4.00000i		−	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	$0.143932\pi$
$230$	8.00000	−	24.0000i	0.527504	−	1.58251i
$231$		0			0
$232$		−	12.0000i		−	0.787839i
$233$	−22.0000			−1.44127			−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000			−1.44127			−0.720634	+	0.693316i	$0.756149\pi$
$234$	−6.00000			−0.392232
$235$	−2.00000	−	4.00000i	−0.130466	−	0.260931i
$236$	−18.0000	−	18.0000i	−1.17170	−	1.17170i
$237$	−8.00000	+	8.00000i	−0.519656	+	0.519656i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	4.00000	−	12.0000i	0.258199	−	0.774597i
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	−7.00000	−	7.00000i	−0.449977	−	0.449977i
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$	−10.0000	+	10.0000i	−0.640184	+	0.640184i
$245$	−14.0000	+	7.00000i	−0.894427	+	0.447214i
$246$		0			0
$247$	6.00000			0.381771
$248$		0			0
$249$		−	18.0000i		−	1.14070i
$250$	−9.00000	−	13.0000i	−0.569210	−	0.822192i
$251$	9.00000	−	9.00000i	0.568075	−	0.568075i	−0.363514	−	0.931589i	$-0.618423\pi$
$251$	9.00000	−	9.00000i	0.568075	−	0.568075i	0.931589	+	0.363514i	$0.118423\pi$
$252$		0			0
$253$	−24.0000	+	24.0000i	−1.50887	+	1.50887i
$254$	6.00000	+	6.00000i	0.376473	+	0.376473i
$255$	12.0000	+	4.00000i	0.751469	+	0.250490i
$256$	16.0000			1.00000
$257$		−	8.00000i		−	0.499026i	−0.968371	−	0.249513i	$-0.919729\pi$
$257$		−	8.00000i		−	0.499026i	0.968371	−	0.249513i	$-0.0802706\pi$
$258$	6.00000	−	6.00000i	0.373544	−	0.373544i
$259$		0			0
$260$	18.0000	+	6.00000i	1.11631	+	0.372104i
$261$	−3.00000	+	3.00000i	−0.185695	+	0.185695i
$262$	−18.0000			−1.11204
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$	−12.0000	+	12.0000i	−0.738549	+	0.738549i
$265$	27.0000	+	9.00000i	1.65860	+	0.552866i
$266$		0			0
$267$	−12.0000	−	12.0000i	−0.734388	−	0.734388i
$268$	−6.00000	−	6.00000i	−0.366508	−	0.366508i
$269$	−9.00000	−	9.00000i	−0.548740	−	0.548740i	0.377337	−	0.926076i	$-0.376840\pi$
$269$	−9.00000	−	9.00000i	−0.548740	−	0.548740i	−0.926076	+	0.377337i	$0.876840\pi$
$270$	−16.0000	+	8.00000i	−0.973729	+	0.486864i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$			16.0000i			0.970143i
$273$		0			0
$274$	−2.00000	+	2.00000i	−0.120824	+	0.120824i
$275$	3.00000	+	21.0000i	0.180907	+	1.26635i
$276$	16.0000	+	16.0000i	0.963087	+	0.963087i
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	0.611213	−	0.791466i	$-0.290682\pi$
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	−0.791466	+	0.611213i	$0.790682\pi$
$278$			14.0000i			0.839664i
$279$		0			0
$280$		0			0
$281$			12.0000i			0.715860i	0.933748	+	0.357930i	$0.116517\pi$
$281$			12.0000i			0.715860i	−0.933748	+	0.357930i	$0.883483\pi$
$282$	4.00000			0.238197
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	0.103022	−	0.994679i	$-0.467149\pi$
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	−0.994679	+	0.103022i	$0.967149\pi$
$284$	−12.0000			−0.712069
$285$	4.00000	−	2.00000i	0.236940	−	0.118470i
$286$	−18.0000	−	18.0000i	−1.06436	−	1.06436i
$287$		0			0
$288$	−4.00000	−	4.00000i	−0.235702	−	0.235702i
$289$	1.00000			0.0588235
$290$	12.0000	−	6.00000i	0.704664	−	0.352332i
$291$	−12.0000	−	12.0000i	−0.703452	−	0.703452i
$292$			12.0000i			0.702247i
$293$	9.00000	+	9.00000i	0.525786	+	0.525786i	0.919313	−	0.393527i	$-0.128745\pi$
$293$	9.00000	+	9.00000i	0.525786	+	0.525786i	−0.393527	+	0.919313i	$0.628745\pi$
$294$		−	14.0000i		−	0.816497i
$295$	9.00000	−	27.0000i	0.524000	−	1.57200i
$296$			12.0000i			0.697486i
$297$	24.0000			1.39262
$298$		−	6.00000i		−	0.347571i
$299$	−24.0000	+	24.0000i	−1.38796	+	1.38796i
$300$	14.0000	−	2.00000i	0.808290	−	0.115470i
$301$		0			0
$302$	18.0000	+	18.0000i	1.03578	+	1.03578i
$303$			6.00000i			0.344691i
$304$	4.00000	+	4.00000i	0.229416	+	0.229416i
$305$	−15.0000	−	5.00000i	−0.858898	−	0.286299i
$306$	4.00000	−	4.00000i	0.228665	−	0.228665i
$307$	3.00000	−	3.00000i	0.171219	−	0.171219i	−0.616296	−	0.787515i	$-0.711367\pi$
$307$	3.00000	−	3.00000i	0.171219	−	0.171219i	0.787515	+	0.616296i	$0.211367\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	6.00000i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$311$		−	6.00000i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$312$	−12.0000	+	12.0000i	−0.679366	+	0.679366i
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		−	18.0000i		−	1.01580i
$315$		0			0
$316$		−	16.0000i		−	0.900070i
$317$	−7.00000	+	7.00000i	−0.393159	+	0.393159i	−0.875812	−	0.482653i	$-0.839673\pi$
$317$	−7.00000	+	7.00000i	−0.393159	+	0.393159i	0.482653	+	0.875812i	$0.339673\pi$
$318$	−18.0000	+	18.0000i	−1.00939	+	1.00939i
$319$	−18.0000			−1.00781
$320$	8.00000	+	16.0000i	0.447214	+	0.894427i
$321$	−18.0000			−1.00466
$322$		0			0
$323$	−4.00000	+	4.00000i	−0.222566	+	0.222566i
$324$		−	10.0000i		−	0.555556i
$325$	3.00000	+	21.0000i	0.166410	+	1.16487i
$326$			18.0000i			0.996928i
$327$	2.00000			0.110600
$328$		0			0
$329$		0			0
$330$	−18.0000	−	6.00000i	−0.990867	−	0.330289i
$331$	5.00000	−	5.00000i	0.274825	−	0.274825i	−0.556214	−	0.831039i	$-0.687747\pi$
$331$	5.00000	−	5.00000i	0.274825	−	0.274825i	0.831039	+	0.556214i	$0.187747\pi$
$332$	18.0000	+	18.0000i	0.987878	+	0.987878i
$333$	3.00000	−	3.00000i	0.164399	−	0.164399i
$334$	−8.00000	+	8.00000i	−0.437741	+	0.437741i
$335$	3.00000	−	9.00000i	0.163908	−	0.491723i
$336$		0			0
$337$		−	24.0000i		−	1.30736i	−0.756770	−	0.653682i	$-0.773224\pi$
$337$		−	24.0000i		−	1.30736i	0.756770	−	0.653682i	$-0.226776\pi$
$338$	−5.00000	−	5.00000i	−0.271964	−	0.271964i
$339$	8.00000	+	8.00000i	0.434500	+	0.434500i
$340$	−16.0000	+	8.00000i	−0.867722	+	0.433861i
$341$		0			0
$342$		−	2.00000i		−	0.108148i
$343$		0			0
$344$			12.0000i			0.646997i
$345$	−8.00000	+	24.0000i	−0.430706	+	1.29212i
$346$		−	18.0000i		−	0.967686i
$347$	−19.0000	−	19.0000i	−1.01997	−	1.01997i	−0.999796	−	0.0201770i	$-0.993577\pi$
$347$	−19.0000	−	19.0000i	−1.01997	−	1.01997i	−0.0201770	−	0.999796i	$-0.506423\pi$
$348$			12.0000i			0.643268i
$349$	−5.00000	−	5.00000i	−0.267644	−	0.267644i	0.560506	−	0.828150i	$-0.310607\pi$
$349$	−5.00000	−	5.00000i	−0.267644	−	0.267644i	−0.828150	+	0.560506i	$0.810607\pi$
$350$		0			0
$351$	24.0000			1.28103
$352$		−	24.0000i		−	1.27920i
$353$		−	16.0000i		−	0.851594i	−0.904819	−	0.425797i	$-0.859994\pi$
$353$		−	16.0000i		−	0.851594i	0.904819	−	0.425797i	$-0.140006\pi$
$354$	18.0000	+	18.0000i	0.956689	+	0.956689i
$355$	−6.00000	−	12.0000i	−0.318447	−	0.636894i
$356$	24.0000			1.27200
$357$		0			0
$358$	6.00000			0.317110
$359$			18.0000i			0.950004i	0.879985	+	0.475002i	$0.157553\pi$
$359$			18.0000i			0.950004i	−0.879985	+	0.475002i	$0.842447\pi$
$360$	2.00000	−	6.00000i	0.105409	−	0.316228i
$361$		−	17.0000i		−	0.894737i
$362$			2.00000i			0.105118i
$363$	7.00000	+	7.00000i	0.367405	+	0.367405i
$364$		0			0
$365$	−12.0000	+	6.00000i	−0.628109	+	0.314054i
$366$	10.0000	−	10.0000i	0.522708	−	0.522708i
$367$		−	18.0000i		−	0.939592i	−0.882775	−	0.469796i	$-0.844327\pi$
$367$		−	18.0000i		−	0.939592i	0.882775	−	0.469796i	$-0.155673\pi$
$368$	−32.0000			−1.66812
$369$		0			0
$370$	−12.0000	+	6.00000i	−0.623850	+	0.311925i
$371$		0			0
$372$		0			0
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	0.625161	−	0.780496i	$-0.285033\pi$
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	−0.780496	+	0.625161i	$0.785033\pi$
$374$	24.0000			1.24101
$375$	9.00000	+	13.0000i	0.464758	+	0.671317i
$376$	−4.00000	+	4.00000i	−0.206284	+	0.206284i
$377$	−18.0000			−0.927047
$378$		0			0
$379$	1.00000	−	1.00000i	0.0513665	−	0.0513665i	−0.680957	−	0.732323i	$-0.738436\pi$
$379$	1.00000	−	1.00000i	0.0513665	−	0.0513665i	0.732323	+	0.680957i	$0.238436\pi$
$380$	−2.00000	+	6.00000i	−0.102598	+	0.307794i
$381$	−6.00000	−	6.00000i	−0.307389	−	0.307389i
$382$	−24.0000	+	24.0000i	−1.22795	+	1.22795i
$383$		−	10.0000i		−	0.510976i	−0.966812	−	0.255488i	$-0.917764\pi$
$383$		−	10.0000i		−	0.510976i	0.966812	−	0.255488i	$-0.0822362\pi$
$384$	−16.0000			−0.816497
$385$		0			0
$386$	−12.0000	−	12.0000i	−0.610784	−	0.610784i
$387$	3.00000	−	3.00000i	0.152499	−	0.152499i
$388$	24.0000			1.21842
$389$	15.0000	−	15.0000i	0.760530	−	0.760530i	−0.215888	−	0.976418i	$-0.569265\pi$
$389$	15.0000	−	15.0000i	0.760530	−	0.760530i	0.976418	+	0.215888i	$0.0692646\pi$
$390$	−18.0000	−	6.00000i	−0.911465	−	0.303822i
$391$		−	32.0000i		−	1.61831i
$392$	14.0000	+	14.0000i	0.707107	+	0.707107i
$393$	18.0000			0.907980
$394$	10.0000			0.503793
$395$	16.0000	−	8.00000i	0.805047	−	0.402524i
$396$	−6.00000	+	6.00000i	−0.301511	+	0.301511i
$397$	9.00000	−	9.00000i	0.451697	−	0.451697i	−0.444220	−	0.895918i	$-0.646519\pi$
$397$	9.00000	−	9.00000i	0.451697	−	0.451697i	0.895918	+	0.444220i	$0.146519\pi$
$398$	2.00000	+	2.00000i	0.100251	+	0.100251i
$399$		0			0
$400$	−12.0000	+	16.0000i	−0.600000	+	0.800000i
$401$	30.0000			1.49813			0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000			1.49813			0.749064	+	0.662497i	$0.230503\pi$
$402$	6.00000	+	6.00000i	0.299253	+	0.299253i
$403$		0			0
$404$	−6.00000	−	6.00000i	−0.298511	−	0.298511i
$405$	10.0000	−	5.00000i	0.496904	−	0.248452i
$406$		0			0
$407$	18.0000			0.892227
$408$		−	16.0000i		−	0.792118i
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$		0			0
$411$	2.00000	−	2.00000i	0.0986527	−	0.0986527i
$412$		0			0
$413$		0			0
$414$	8.00000	+	8.00000i	0.393179	+	0.393179i
$415$	−9.00000	+	27.0000i	−0.441793	+	1.32538i
$416$		−	24.0000i		−	1.17670i
$417$		−	14.0000i		−	0.685583i
$418$	6.00000	−	6.00000i	0.293470	−	0.293470i
$419$	15.0000	+	15.0000i	0.732798	+	0.732798i	0.971173	−	0.238375i	$-0.0766148\pi$
$419$	15.0000	+	15.0000i	0.732798	+	0.732798i	−0.238375	+	0.971173i	$0.576615\pi$
$420$		0			0
$421$	−5.00000	+	5.00000i	−0.243685	+	0.243685i	−0.818373	−	0.574688i	$-0.805124\pi$
$421$	−5.00000	+	5.00000i	−0.243685	+	0.243685i	0.574688	+	0.818373i	$0.305124\pi$
$422$	22.0000			1.07094
$423$	2.00000			0.0972433
$424$		−	36.0000i		−	1.74831i
$425$	−16.0000	−	12.0000i	−0.776114	−	0.582086i
$426$	12.0000			0.581402
$427$		0			0
$428$	18.0000	−	18.0000i	0.870063	−	0.870063i
$429$	18.0000	+	18.0000i	0.869048	+	0.869048i
$430$	−12.0000	+	6.00000i	−0.578691	+	0.289346i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$	16.0000	+	16.0000i	0.769800	+	0.769800i
$433$			36.0000i			1.73005i	0.501729	+	0.865025i	$0.332697\pi$
$433$			36.0000i			1.73005i	−0.501729	+	0.865025i	$0.667303\pi$
$434$		0			0
$435$	−12.0000	+	6.00000i	−0.575356	+	0.287678i
$436$	−2.00000	+	2.00000i	−0.0957826	+	0.0957826i
$437$	−8.00000	−	8.00000i	−0.382692	−	0.382692i
$438$		−	12.0000i		−	0.573382i
$439$			10.0000i			0.477274i	0.971109	+	0.238637i	$0.0767006\pi$
$439$			10.0000i			0.477274i	−0.971109	+	0.238637i	$0.923299\pi$
$440$	24.0000	−	12.0000i	1.14416	−	0.572078i
$441$		−	7.00000i		−	0.333333i
$442$	24.0000			1.14156
$443$	9.00000	+	9.00000i	0.427603	+	0.427603i	0.887811	−	0.460208i	$-0.152225\pi$
$443$	9.00000	+	9.00000i	0.427603	+	0.427603i	−0.460208	+	0.887811i	$0.652225\pi$
$444$		−	12.0000i		−	0.569495i
$445$	12.0000	+	24.0000i	0.568855	+	1.13771i
$446$	6.00000	+	6.00000i	0.284108	+	0.284108i
$447$			6.00000i			0.283790i
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$	7.00000	−	1.00000i	0.329983	−	0.0471405i
$451$		0			0
$452$	−16.0000			−0.752577
$453$	−18.0000	−	18.0000i	−0.845714	−	0.845714i
$454$			18.0000i			0.844782i
$455$		0			0
$456$	−4.00000	−	4.00000i	−0.187317	−	0.187317i
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$		−	14.0000i		−	0.654177i
$459$	−16.0000	+	16.0000i	−0.746816	+	0.746816i
$460$	−16.0000	−	32.0000i	−0.746004	−	1.49201i
$461$	3.00000	+	3.00000i	0.139724	+	0.139724i	0.773509	−	0.633785i	$-0.218500\pi$
$461$	3.00000	+	3.00000i	0.139724	+	0.139724i	−0.633785	+	0.773509i	$0.718500\pi$
$462$		0			0
$463$			30.0000i			1.39422i	0.716965	+	0.697109i	$0.245531\pi$
$463$			30.0000i			1.39422i	−0.716965	+	0.697109i	$0.754469\pi$
$464$	−12.0000	−	12.0000i	−0.557086	−	0.557086i
$465$		0			0
$466$	−22.0000	+	22.0000i	−1.01913	+	1.01913i
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	−0.813265	−	0.581893i	$-0.802312\pi$
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	0.581893	+	0.813265i	$0.302312\pi$
$468$	−6.00000	+	6.00000i	−0.277350	+	0.277350i
$469$		0			0
$470$	−6.00000	−	2.00000i	−0.276759	−	0.0922531i
$471$			18.0000i			0.829396i
$472$	−36.0000			−1.65703
$473$	18.0000			0.827641
$474$			16.0000i			0.734904i
$475$	−7.00000	+	1.00000i	−0.321182	+	0.0458831i
$476$		0			0
$477$	−9.00000	+	9.00000i	−0.412082	+	0.412082i
$478$	24.0000	−	24.0000i	1.09773	−	1.09773i
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$	−8.00000	−	16.0000i	−0.365148	−	0.730297i
$481$	18.0000			0.820729
$482$	−18.0000	+	18.0000i	−0.819878	+	0.819878i
$483$		0			0
$484$	−14.0000			−0.636364
$485$	12.0000	+	24.0000i	0.544892	+	1.08978i
$486$		−	14.0000i		−	0.635053i
$487$	−24.0000			−1.08754			−0.543772	−	0.839233i	$-0.683004\pi$
$487$	−24.0000			−1.08754			−0.543772	+	0.839233i	$0.683004\pi$
$488$			20.0000i			0.905357i
$489$		−	18.0000i		−	0.813988i
$490$	−7.00000	+	21.0000i	−0.316228	+	0.948683i
$491$	−15.0000	+	15.0000i	−0.676941	+	0.676941i	−0.959307	−	0.282366i	$-0.908881\pi$
$491$	−15.0000	+	15.0000i	−0.676941	+	0.676941i	0.282366	+	0.959307i	$0.408881\pi$
$492$		0			0
$493$	12.0000	−	12.0000i	0.540453	−	0.540453i
$494$	6.00000	−	6.00000i	0.269953	−	0.269953i
$495$	−9.00000	−	3.00000i	−0.404520	−	0.134840i
$496$		0			0
$497$		0			0
$498$	−18.0000	−	18.0000i	−0.806599	−	0.806599i
$499$	−29.0000	−	29.0000i	−1.29822	−	1.29822i	−0.929568	−	0.368650i	$-0.879820\pi$
$499$	−29.0000	−	29.0000i	−1.29822	−	1.29822i	−0.368650	−	0.929568i	$-0.620180\pi$
$500$	−22.0000	−	4.00000i	−0.983870	−	0.178885i
$501$	8.00000	−	8.00000i	0.357414	−	0.357414i
$502$		−	18.0000i		−	0.803379i
$503$	−32.0000			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$504$		0			0
$505$	3.00000	−	9.00000i	0.133498	−	0.400495i
$506$			48.0000i			2.13386i
$507$	5.00000	+	5.00000i	0.222058	+	0.222058i
$508$	12.0000			0.532414
$509$	−9.00000	−	9.00000i	−0.398918	−	0.398918i	0.478933	−	0.877851i	$-0.341024\pi$
$509$	−9.00000	−	9.00000i	−0.398918	−	0.398918i	−0.877851	+	0.478933i	$0.841024\pi$
$510$	16.0000	−	8.00000i	0.708492	−	0.354246i
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$			8.00000i			0.353209i
$514$	−8.00000	−	8.00000i	−0.352865	−	0.352865i
$515$		0			0
$516$		−	12.0000i		−	0.528271i
$517$	6.00000	+	6.00000i	0.263880	+	0.263880i
$518$		0			0
$519$			18.0000i			0.790112i
$520$	24.0000	−	12.0000i	1.05247	−	0.526235i
$521$			24.0000i			1.05146i	0.850652	+	0.525730i	$0.176208\pi$
$521$			24.0000i			1.05146i	−0.850652	+	0.525730i	$0.823792\pi$
$522$			6.00000i			0.262613i
$523$	9.00000	+	9.00000i	0.393543	+	0.393543i	0.875948	−	0.482405i	$-0.160237\pi$
$523$	9.00000	+	9.00000i	0.393543	+	0.393543i	−0.482405	+	0.875948i	$0.660237\pi$
$524$	−18.0000	+	18.0000i	−0.786334	+	0.786334i
$525$		0			0
$526$	16.0000	−	16.0000i	0.697633	−	0.697633i
$527$		0			0
$528$			24.0000i			1.04447i
$529$	41.0000			1.78261
$530$	36.0000	−	18.0000i	1.56374	−	0.781870i
$531$	9.00000	+	9.00000i	0.390567	+	0.390567i
$532$		0			0
$533$		0			0
$534$	−24.0000			−1.03858
$535$	27.0000	+	9.00000i	1.16731	+	0.389104i
$536$	−12.0000			−0.518321
$537$	−6.00000			−0.258919
$538$	−18.0000			−0.776035
$539$	21.0000	−	21.0000i	0.904534	−	0.904534i
$540$	−8.00000	+	24.0000i	−0.344265	+	1.03280i
$541$	−1.00000	−	1.00000i	−0.0429934	−	0.0429934i	0.685283	−	0.728277i	$-0.259678\pi$
$541$	−1.00000	−	1.00000i	−0.0429934	−	0.0429934i	−0.728277	+	0.685283i	$0.759678\pi$
$542$	16.0000	−	16.0000i	0.687259	−	0.687259i
$543$		−	2.00000i		−	0.0858282i
$544$	16.0000	+	16.0000i	0.685994	+	0.685994i
$545$	−3.00000	−	1.00000i	−0.128506	−	0.0428353i
$546$		0			0
$547$	3.00000	−	3.00000i	0.128271	−	0.128271i	−0.640057	−	0.768328i	$-0.721089\pi$
$547$	3.00000	−	3.00000i	0.128271	−	0.128271i	0.768328	+	0.640057i	$0.221089\pi$
$548$			4.00000i			0.170872i
$549$	5.00000	−	5.00000i	0.213395	−	0.213395i
$550$	24.0000	+	18.0000i	1.02336	+	0.767523i
$551$		−	6.00000i		−	0.255609i
$552$	32.0000			1.36201
$553$		0			0
$554$	−6.00000			−0.254916
$555$	12.0000	−	6.00000i	0.509372	−	0.254686i
$556$	14.0000	+	14.0000i	0.593732	+	0.593732i
$557$	9.00000	−	9.00000i	0.381342	−	0.381342i	−0.490243	−	0.871586i	$-0.663092\pi$
$557$	9.00000	−	9.00000i	0.381342	−	0.381342i	0.871586	+	0.490243i	$0.163092\pi$
$558$		0			0
$559$	18.0000			0.761319
$560$		0			0
$561$	−24.0000			−1.01328
$562$	12.0000	+	12.0000i	0.506189	+	0.506189i
$563$	19.0000	−	19.0000i	0.800755	−	0.800755i	−0.182459	−	0.983213i	$-0.558406\pi$
$563$	19.0000	−	19.0000i	0.800755	−	0.800755i	0.983213	+	0.182459i	$0.0584057\pi$
$564$	4.00000	−	4.00000i	0.168430	−	0.168430i
$565$	−8.00000	−	16.0000i	−0.336563	−	0.673125i
$566$	−30.0000			−1.26099
$567$		0			0
$568$	−12.0000	+	12.0000i	−0.503509	+	0.503509i
$569$		−	24.0000i		−	1.00613i	−0.864248	−	0.503066i	$-0.832205\pi$
$569$		−	24.0000i		−	1.00613i	0.864248	−	0.503066i	$-0.167795\pi$
$570$	2.00000	−	6.00000i	0.0837708	−	0.251312i
$571$	−11.0000	+	11.0000i	−0.460336	+	0.460336i	−0.898765	−	0.438430i	$-0.855535\pi$
$571$	−11.0000	+	11.0000i	−0.460336	+	0.460336i	0.438430	+	0.898765i	$0.355535\pi$
$572$	−36.0000			−1.50524
$573$	24.0000	−	24.0000i	1.00261	−	1.00261i
$574$		0			0
$575$	24.0000	−	32.0000i	1.00087	−	1.33449i
$576$	−8.00000			−0.333333
$577$			24.0000i			0.999133i	0.866276	+	0.499567i	$0.166507\pi$
$577$			24.0000i			0.999133i	−0.866276	+	0.499567i	$0.833493\pi$
$578$	1.00000	−	1.00000i	0.0415945	−	0.0415945i
$579$	12.0000	+	12.0000i	0.498703	+	0.498703i
$580$	6.00000	−	18.0000i	0.249136	−	0.747409i
$581$		0			0
$582$	−24.0000			−0.994832
$583$	−54.0000			−2.23645
$584$	12.0000	+	12.0000i	0.496564	+	0.496564i
$585$	−9.00000	−	3.00000i	−0.372104	−	0.124035i
$586$	18.0000			0.743573
$587$	9.00000	+	9.00000i	0.371470	+	0.371470i	0.868012	−	0.496543i	$-0.165397\pi$
$587$	9.00000	+	9.00000i	0.371470	+	0.371470i	−0.496543	+	0.868012i	$0.665397\pi$
$588$	−14.0000	−	14.0000i	−0.577350	−	0.577350i
$589$		0			0
$590$	−18.0000	−	36.0000i	−0.741048	−	1.48210i
$591$	−10.0000			−0.411345
$592$	12.0000	+	12.0000i	0.493197	+	0.493197i
$593$			32.0000i			1.31408i	0.753855	+	0.657041i	$0.228192\pi$
$593$			32.0000i			1.31408i	−0.753855	+	0.657041i	$0.771808\pi$
$594$	24.0000	−	24.0000i	0.984732	−	0.984732i
$595$		0			0
$596$	−6.00000	−	6.00000i	−0.245770	−	0.245770i
$597$	−2.00000	−	2.00000i	−0.0818546	−	0.0818546i
$598$			48.0000i			1.96287i
$599$		−	30.0000i		−	1.22577i	−0.790173	−	0.612883i	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$	12.0000	−	16.0000i	0.489898	−	0.653197i
$601$			36.0000i			1.46847i	0.678895	+	0.734235i	$0.262459\pi$
$601$			36.0000i			1.46847i	−0.678895	+	0.734235i	$0.737541\pi$
$602$		0			0
$603$	3.00000	+	3.00000i	0.122169	+	0.122169i
$604$	36.0000			1.46482
$605$	−7.00000	−	14.0000i	−0.284590	−	0.569181i
$606$	6.00000	+	6.00000i	0.243733	+	0.243733i
$607$		−	42.0000i		−	1.70473i	−0.522949	−	0.852364i	$-0.675168\pi$
$607$		−	42.0000i		−	1.70473i	0.522949	−	0.852364i	$-0.324832\pi$
$608$	8.00000			0.324443
$609$		0			0
$610$	−20.0000	+	10.0000i	−0.809776	+	0.404888i
$611$	6.00000	+	6.00000i	0.242734	+	0.242734i
$612$		−	8.00000i		−	0.323381i
$613$	−27.0000	−	27.0000i	−1.09052	−	1.09052i	−0.995473	−	0.0950469i	$-0.969700\pi$
$613$	−27.0000	−	27.0000i	−1.09052	−	1.09052i	−0.0950469	−	0.995473i	$-0.530300\pi$
$614$		−	6.00000i		−	0.242140i
$615$		0			0
$616$		0			0
$617$	10.0000			0.402585			0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000			0.402585			0.201292	+	0.979531i	$0.435486\pi$
$618$		0			0
$619$	13.0000	−	13.0000i	0.522514	−	0.522514i	−0.395816	−	0.918330i	$-0.629538\pi$
$619$	13.0000	−	13.0000i	0.522514	−	0.522514i	0.918330	+	0.395816i	$0.129538\pi$
$620$		0			0
$621$	−32.0000	−	32.0000i	−1.28412	−	1.28412i
$622$	−6.00000	−	6.00000i	−0.240578	−	0.240578i
$623$		0			0
$624$			24.0000i			0.960769i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	6.00000	−	6.00000i	0.239808	−	0.239808i
$627$	−6.00000	+	6.00000i	−0.239617	+	0.239617i
$628$	−18.0000	−	18.0000i	−0.718278	−	0.718278i
$629$	−12.0000	+	12.0000i	−0.478471	+	0.478471i
$630$		0			0
$631$			2.00000i			0.0796187i	0.999207	+	0.0398094i	$0.0126751\pi$
$631$			2.00000i			0.0796187i	−0.999207	+	0.0398094i	$0.987325\pi$
$632$	−16.0000	−	16.0000i	−0.636446	−	0.636446i
$633$	−22.0000			−0.874421
$634$			14.0000i			0.556011i
$635$	6.00000	+	12.0000i	0.238103	+	0.476205i
$636$			36.0000i			1.42749i
$637$	21.0000	−	21.0000i	0.832050	−	0.832050i
$638$	−18.0000	+	18.0000i	−0.712627	+	0.712627i
$639$	6.00000			0.237356
$640$	24.0000	+	8.00000i	0.948683	+	0.316228i
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$	−18.0000	+	18.0000i	−0.710403	+	0.710403i
$643$	27.0000	−	27.0000i	1.06478	−	1.06478i	0.0670247	−	0.997751i	$-0.478649\pi$
$643$	27.0000	−	27.0000i	1.06478	−	1.06478i	0.997751	−	0.0670247i	$-0.0213506\pi$
$644$		0			0
$645$	12.0000	−	6.00000i	0.472500	−	0.236250i
$646$			8.00000i			0.314756i
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	−10.0000	−	10.0000i	−0.392837	−	0.392837i
$649$			54.0000i			2.11969i
$650$	24.0000	+	18.0000i	0.941357	+	0.706018i
$651$		0			0
$652$	18.0000	+	18.0000i	0.704934	+	0.704934i
$653$	9.00000	−	9.00000i	0.352197	−	0.352197i	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	9.00000	−	9.00000i	0.352197	−	0.352197i	0.860927	+	0.508729i	$0.169885\pi$
$654$	2.00000	−	2.00000i	0.0782062	−	0.0782062i
$655$	−27.0000	−	9.00000i	−1.05498	−	0.351659i
$656$		0			0
$657$		−	6.00000i		−	0.234082i
$658$		0			0
$659$	−21.0000	−	21.0000i	−0.818044	−	0.818044i	0.167781	−	0.985824i	$-0.446340\pi$
$659$	−21.0000	−	21.0000i	−0.818044	−	0.818044i	−0.985824	+	0.167781i	$0.946340\pi$
$660$	−24.0000	+	12.0000i	−0.934199	+	0.467099i
$661$	−29.0000	+	29.0000i	−1.12797	+	1.12797i	−0.137462	+	0.990507i	$0.543895\pi$
$661$	−29.0000	+	29.0000i	−1.12797	+	1.12797i	−0.990507	+	0.137462i	$0.956105\pi$
$662$		−	10.0000i		−	0.388661i
$663$	−24.0000			−0.932083
$664$	36.0000			1.39707
$665$		0			0
$666$		−	6.00000i		−	0.232495i
$667$	24.0000	+	24.0000i	0.929284	+	0.929284i
$668$			16.0000i			0.619059i
$669$	−6.00000	−	6.00000i	−0.231973	−	0.231973i
$670$	−6.00000	−	12.0000i	−0.231800	−	0.463600i
$671$	30.0000			1.15814
$672$		0			0
$673$			12.0000i			0.462566i	0.972887	+	0.231283i	$0.0742923\pi$
$673$			12.0000i			0.462566i	−0.972887	+	0.231283i	$0.925708\pi$
$674$	−24.0000	−	24.0000i	−0.924445	−	0.924445i
$675$	−28.0000	+	4.00000i	−1.07772	+	0.153960i
$676$	−10.0000			−0.384615
$677$	9.00000	+	9.00000i	0.345898	+	0.345898i	0.858579	−	0.512681i	$-0.171348\pi$
$677$	9.00000	+	9.00000i	0.345898	+	0.345898i	−0.512681	+	0.858579i	$0.671348\pi$
$678$	16.0000			0.614476
$679$		0			0
$680$	−8.00000	+	24.0000i	−0.306786	+	0.920358i
$681$		−	18.0000i		−	0.689761i
$682$		0			0
$683$	13.0000	+	13.0000i	0.497431	+	0.497431i	0.910637	−	0.413206i	$-0.135591\pi$
$683$	13.0000	+	13.0000i	0.497431	+	0.497431i	−0.413206	+	0.910637i	$0.635591\pi$
$684$	−2.00000	−	2.00000i	−0.0764719	−	0.0764719i
$685$	−4.00000	+	2.00000i	−0.152832	+	0.0764161i
$686$		0			0
$687$			14.0000i			0.534133i
$688$	12.0000	+	12.0000i	0.457496	+	0.457496i
$689$	−54.0000			−2.05724
$690$	16.0000	+	32.0000i	0.609110	+	1.21822i
$691$	−5.00000	−	5.00000i	−0.190209	−	0.190209i	0.605577	−	0.795786i	$-0.292942\pi$
$691$	−5.00000	−	5.00000i	−0.190209	−	0.190209i	−0.795786	+	0.605577i	$0.792942\pi$
$692$	−18.0000	−	18.0000i	−0.684257	−	0.684257i
$693$		0			0
$694$	−38.0000			−1.44246
$695$	−7.00000	+	21.0000i	−0.265525	+	0.796575i
$696$	12.0000	+	12.0000i	0.454859	+	0.454859i
$697$		0			0
$698$	−10.0000			−0.378506
$699$	22.0000	−	22.0000i	0.832116	−	0.832116i
$700$		0			0
$701$	3.00000	+	3.00000i	0.113308	+	0.113308i	0.761488	−	0.648179i	$-0.224469\pi$
$701$	3.00000	+	3.00000i	0.113308	+	0.113308i	−0.648179	+	0.761488i	$0.724469\pi$
$702$	24.0000	−	24.0000i	0.905822	−	0.905822i
$703$			6.00000i			0.226294i
$704$	−24.0000	−	24.0000i	−0.904534	−	0.904534i
$705$	6.00000	+	2.00000i	0.225973	+	0.0753244i
$706$	−16.0000	−	16.0000i	−0.602168	−	0.602168i
$707$		0			0
$708$	36.0000			1.35296
$709$	−13.0000	+	13.0000i	−0.488225	+	0.488225i	−0.907746	−	0.419521i	$-0.862198\pi$
$709$	−13.0000	+	13.0000i	−0.488225	+	0.488225i	0.419521	+	0.907746i	$0.362198\pi$
$710$	−18.0000	−	6.00000i	−0.675528	−	0.225176i
$711$			8.00000i			0.300023i
$712$	24.0000	−	24.0000i	0.899438	−	0.899438i
$713$		0			0
$714$		0			0
$715$	−18.0000	−	36.0000i	−0.673162	−	1.34632i
$716$	6.00000	−	6.00000i	0.224231	−	0.224231i
$717$	−24.0000	+	24.0000i	−0.896296	+	0.896296i
$718$	18.0000	+	18.0000i	0.671754	+	0.671754i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$	−4.00000	−	8.00000i	−0.149071	−	0.298142i
$721$		0			0
$722$	−17.0000	−	17.0000i	−0.632674	−	0.632674i
$723$	18.0000	−	18.0000i	0.669427	−	0.669427i
$724$	2.00000	+	2.00000i	0.0743294	+	0.0743294i
$725$	21.0000	−	3.00000i	0.779920	−	0.111417i
$726$	14.0000			0.519589
$727$	−24.0000			−0.890111			−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000			−0.890111			−0.445055	+	0.895503i	$0.646816\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$	−6.00000	+	18.0000i	−0.222070	+	0.666210i
$731$	−12.0000	+	12.0000i	−0.443836	+	0.443836i
$732$		−	20.0000i		−	0.739221i
$733$	−3.00000	+	3.00000i	−0.110808	+	0.110808i	−0.760337	−	0.649529i	$-0.774966\pi$
$733$	−3.00000	+	3.00000i	−0.110808	+	0.110808i	0.649529	+	0.760337i	$0.274966\pi$
$734$	−18.0000	−	18.0000i	−0.664392	−	0.664392i
$735$	7.00000	−	21.0000i	0.258199	−	0.774597i
$736$	−32.0000	+	32.0000i	−1.17954	+	1.17954i
$737$			18.0000i			0.663039i
$738$		0			0
$739$	19.0000	+	19.0000i	0.698926	+	0.698926i	0.964179	−	0.265253i	$-0.0854554\pi$
$739$	19.0000	+	19.0000i	0.698926	+	0.698926i	−0.265253	+	0.964179i	$0.585455\pi$
$740$	−6.00000	+	18.0000i	−0.220564	+	0.661693i
$741$	−6.00000	+	6.00000i	−0.220416	+	0.220416i
$742$		0			0
$743$	8.00000			0.293492			0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000			0.293492			0.146746	+	0.989174i	$0.453120\pi$
$744$		0			0
$745$	3.00000	−	9.00000i	0.109911	−	0.329734i
$746$	−6.00000			−0.219676
$747$	−9.00000	−	9.00000i	−0.329293	−	0.329293i
$748$	24.0000	−	24.0000i	0.877527	−	0.877527i
$749$		0			0
$750$	22.0000	+	4.00000i	0.803326	+	0.146059i
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$			8.00000i			0.291730i
$753$			18.0000i			0.655956i
$754$	−18.0000	+	18.0000i	−0.655521	+	0.655521i
$755$	18.0000	+	36.0000i	0.655087	+	1.31017i
$756$		0			0
$757$	33.0000	+	33.0000i	1.19941	+	1.19941i	0.974345	+	0.225061i	$0.0722580\pi$
$757$	33.0000	+	33.0000i	1.19941	+	1.19941i	0.225061	+	0.974345i	$0.427742\pi$
$758$		−	2.00000i		−	0.0726433i
$759$		−	48.0000i		−	1.74229i
$760$	4.00000	+	8.00000i	0.145095	+	0.290191i
$761$		−	48.0000i		−	1.74000i	−0.493053	−	0.869999i	$-0.664119\pi$
$761$		−	48.0000i		−	1.74000i	0.493053	−	0.869999i	$-0.335881\pi$
$762$	−12.0000			−0.434714
$763$		0			0
$764$			48.0000i			1.73658i
$765$	8.00000	−	4.00000i	0.289241	−	0.144620i
$766$	−10.0000	−	10.0000i	−0.361315	−	0.361315i
$767$			54.0000i			1.94983i
$768$	−16.0000	+	16.0000i	−0.577350	+	0.577350i
$769$	−18.0000			−0.649097			−0.324548	−	0.945869i	$-0.605212\pi$
$769$	−18.0000			−0.649097			−0.324548	+	0.945869i	$0.605212\pi$
$770$		0			0
$771$	8.00000	+	8.00000i	0.288113	+	0.288113i
$772$	−24.0000			−0.863779
$773$	−23.0000	−	23.0000i	−0.827253	−	0.827253i	0.159883	−	0.987136i	$-0.448888\pi$
$773$	−23.0000	−	23.0000i	−0.827253	−	0.827253i	−0.987136	+	0.159883i	$0.948888\pi$
$774$		−	6.00000i		−	0.215666i
$775$		0			0
$776$	24.0000	−	24.0000i	0.861550	−	0.861550i
$777$		0			0
$778$		−	30.0000i		−	1.07555i
$779$		0			0
$780$	−24.0000	+	12.0000i	−0.859338	+	0.429669i
$781$	18.0000	+	18.0000i	0.644091	+	0.644091i
$782$	−32.0000	−	32.0000i	−1.14432	−	1.14432i
$783$		−	24.0000i		−	0.857690i
$784$	28.0000			1.00000
$785$	9.00000	−	27.0000i	0.321224	−	0.963671i
$786$	18.0000	−	18.0000i	0.642039	−	0.642039i
$787$	−33.0000	+	33.0000i	−1.17632	+	1.17632i	−0.195649	+	0.980674i	$0.562681\pi$
$787$	−33.0000	+	33.0000i	−1.17632	+	1.17632i	−0.980674	+	0.195649i	$0.937319\pi$
$788$	10.0000	−	10.0000i	0.356235	−	0.356235i
$789$	−16.0000	+	16.0000i	−0.569615	+	0.569615i
$790$	8.00000	−	24.0000i	0.284627	−	0.853882i
$791$		0			0
$792$			12.0000i			0.426401i
$793$	30.0000			1.06533
$794$		−	18.0000i		−	0.638796i
$795$	−36.0000	+	18.0000i	−1.27679	+	0.638394i
$796$	4.00000			0.141776
$797$	−19.0000	+	19.0000i	−0.673015	+	0.673015i	−0.958410	−	0.285395i	$-0.907875\pi$
$797$	−19.0000	+	19.0000i	−0.673015	+	0.673015i	0.285395	+	0.958410i	$0.407875\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	4.00000	+	28.0000i	0.141421	+	0.989949i
$801$	−12.0000			−0.423999
$802$	30.0000	−	30.0000i	1.05934	−	1.05934i
$803$	18.0000	−	18.0000i	0.635206	−	0.635206i
$804$	12.0000			0.423207
$805$		0			0
$806$		0			0
$807$	18.0000			0.633630
$808$	−12.0000			−0.422159
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	5.00000	−	15.0000i	0.175682	−	0.527046i
$811$	37.0000	−	37.0000i	1.29925	−	1.29925i	0.370356	−	0.928890i	$-0.379236\pi$
$811$	37.0000	−	37.0000i	1.29925	−	1.29925i	0.928890	−	0.370356i	$-0.120764\pi$
$812$		0			0
$813$	−16.0000	+	16.0000i	−0.561144	+	0.561144i
$814$	18.0000	−	18.0000i	0.630900	−	0.630900i
$815$	−9.00000	+	27.0000i	−0.315256	+	0.945769i
$816$	−16.0000	−	16.0000i	−0.560112	−	0.560112i
$817$			6.00000i			0.209913i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	39.0000	−	39.0000i	1.36111	−	1.36111i	0.488603	−	0.872506i	$-0.337507\pi$
$821$	39.0000	−	39.0000i	1.36111	−	1.36111i	0.872506	−	0.488603i	$-0.162493\pi$
$822$		−	4.00000i		−	0.139516i
$823$	24.0000			0.836587			0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000			0.836587			0.418294	+	0.908312i	$0.362628\pi$
$824$		0			0
$825$	−24.0000	−	18.0000i	−0.835573	−	0.626680i
$826$		0			0
$827$	−31.0000	−	31.0000i	−1.07798	−	1.07798i	−0.996691	−	0.0812847i	$-0.974098\pi$
$827$	−31.0000	−	31.0000i	−1.07798	−	1.07798i	−0.0812847	−	0.996691i	$-0.525902\pi$
$828$	16.0000			0.556038
$829$	35.0000	+	35.0000i	1.21560	+	1.21560i	0.969157	+	0.246443i	$0.0792618\pi$
$829$	35.0000	+	35.0000i	1.21560	+	1.21560i	0.246443	+	0.969157i	$0.420738\pi$
$830$	18.0000	+	36.0000i	0.624789	+	1.24958i
$831$	6.00000			0.208138
$832$	−24.0000	−	24.0000i	−0.832050	−	0.832050i
$833$			28.0000i			0.970143i
$834$	−14.0000	−	14.0000i	−0.484780	−	0.484780i
$835$	−16.0000	+	8.00000i	−0.553703	+	0.276851i
$836$		−	12.0000i		−	0.415029i
$837$		0			0
$838$	30.0000			1.03633
$839$			42.0000i			1.45000i	0.688748	+	0.725001i	$0.258161\pi$
$839$			42.0000i			1.45000i	−0.688748	+	0.725001i	$0.741839\pi$
$840$		0			0
$841$		−	11.0000i		−	0.379310i
$842$			10.0000i			0.344623i
$843$	−12.0000	−	12.0000i	−0.413302	−	0.413302i
$844$	22.0000	−	22.0000i	0.757271	−	0.757271i
$845$	−5.00000	−	10.0000i	−0.172005	−	0.344010i
$846$	2.00000	−	2.00000i	0.0687614	−	0.0687614i
$847$		0			0
$848$	−36.0000	−	36.0000i	−1.23625	−	1.23625i
$849$	30.0000			1.02960
$850$	−28.0000	+	4.00000i	−0.960392	+	0.137199i
$851$	−24.0000	−	24.0000i	−0.822709	−	0.822709i
$852$	12.0000	−	12.0000i	0.411113	−	0.411113i
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	0.402034	−	0.915625i	$-0.368303\pi$
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	−0.915625	+	0.402034i	$0.868303\pi$
$854$		0			0
$855$	1.00000	−	3.00000i	0.0341993	−	0.102598i
$856$		−	36.0000i		−	1.23045i
$857$	38.0000			1.29806			0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000			1.29806			0.649028	+	0.760765i	$0.275176\pi$
$858$	36.0000			1.22902
$859$	−7.00000	+	7.00000i	−0.238837	+	0.238837i	−0.816368	−	0.577531i	$-0.804016\pi$
$859$	−7.00000	+	7.00000i	−0.238837	+	0.238837i	0.577531	+	0.816368i	$0.304016\pi$
$860$	−6.00000	+	18.0000i	−0.204598	+	0.613795i
$861$		0			0
$862$	−24.0000	+	24.0000i	−0.817443	+	0.817443i
$863$			22.0000i			0.748889i	0.927249	+	0.374444i	$0.122167\pi$
$863$			22.0000i			0.748889i	−0.927249	+	0.374444i	$0.877833\pi$
$864$	32.0000			1.08866
$865$	9.00000	−	27.0000i	0.306009	−	0.918028i
$866$	36.0000	+	36.0000i	1.22333	+	1.22333i
$867$	−1.00000	+	1.00000i	−0.0339618	+	0.0339618i
$868$		0			0
$869$	−24.0000	+	24.0000i	−0.814144	+	0.814144i
$870$	−6.00000	+	18.0000i	−0.203419	+	0.610257i
$871$			18.0000i			0.609907i
$872$			4.00000i			0.135457i
$873$	−12.0000			−0.406138
$874$	−16.0000			−0.541208
$875$		0			0
$876$	−12.0000	−	12.0000i	−0.405442	−	0.405442i
$877$	−3.00000	+	3.00000i	−0.101303	+	0.101303i	−0.755942	−	0.654639i	$-0.772821\pi$
$877$	−3.00000	+	3.00000i	−0.101303	+	0.101303i	0.654639	+	0.755942i	$0.272821\pi$
$878$	10.0000	+	10.0000i	0.337484	+	0.337484i
$879$	−18.0000			−0.607125
$880$	12.0000	−	36.0000i	0.404520	−	1.21356i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$	−7.00000	−	7.00000i	−0.235702	−	0.235702i
$883$	−21.0000	+	21.0000i	−0.706706	+	0.706706i	−0.965841	−	0.259135i	$-0.916563\pi$
$883$	−21.0000	+	21.0000i	−0.706706	+	0.706706i	0.259135	+	0.965841i	$0.416563\pi$
$884$	24.0000	−	24.0000i	0.807207	−	0.807207i
$885$	18.0000	+	36.0000i	0.605063	+	1.21013i
$886$	18.0000			0.604722
$887$	8.00000			0.268614			0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000			0.268614			0.134307	+	0.990940i	$0.457119\pi$
$888$	−12.0000	−	12.0000i	−0.402694	−	0.402694i
$889$		0			0
$890$	36.0000	+	12.0000i	1.20672	+	0.402241i
$891$	−15.0000	+	15.0000i	−0.502519	+	0.502519i
$892$	12.0000			0.401790
$893$	−2.00000	+	2.00000i	−0.0669274	+	0.0669274i
$894$	6.00000	+	6.00000i	0.200670	+	0.200670i
$895$	9.00000	+	3.00000i	0.300837	+	0.100279i
$896$		0			0
$897$		−	48.0000i		−	1.60267i
$898$	−18.0000	+	18.0000i	−0.600668	+	0.600668i
$899$		0			0
$900$	6.00000	−	8.00000i	0.200000	−	0.266667i
$901$	36.0000	−	36.0000i	1.19933	−	1.19933i
$902$		0			0
$903$		0			0
$904$	−16.0000	+	16.0000i	−0.532152	+	0.532152i
$905$	−1.00000	+	3.00000i	−0.0332411	+	0.0997234i
$906$	−36.0000			−1.19602
$907$	21.0000	+	21.0000i	0.697294	+	0.697294i	0.963826	−	0.266532i	$-0.0858779\pi$
$907$	21.0000	+	21.0000i	0.697294	+	0.697294i	−0.266532	+	0.963826i	$0.585878\pi$
$908$	18.0000	+	18.0000i	0.597351	+	0.597351i
$909$	3.00000	+	3.00000i	0.0995037	+	0.0995037i
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	−8.00000			−0.264906
$913$		−	54.0000i		−	1.78714i
$914$	−18.0000	+	18.0000i	−0.595387	+	0.595387i
$915$	20.0000	−	10.0000i	0.661180	−	0.330590i
$916$	−14.0000	−	14.0000i	−0.462573	−	0.462573i
$917$		0			0
$918$			32.0000i			1.05616i
$919$		−	54.0000i		−	1.78130i	−0.454694	−	0.890648i	$-0.650251\pi$
$919$		−	54.0000i		−	1.78130i	0.454694	−	0.890648i	$-0.349749\pi$
$920$	−48.0000	−	16.0000i	−1.58251	−	0.527504i
$921$			6.00000i			0.197707i
$922$	6.00000			0.197599
$923$	18.0000	+	18.0000i	0.592477	+	0.592477i
$924$		0			0
$925$	−21.0000	+	3.00000i	−0.690476	+	0.0986394i
$926$	30.0000	+	30.0000i	0.985861	+	0.985861i
$927$		0			0
$928$	−24.0000			−0.787839
$929$	30.0000			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$930$		0			0
$931$	7.00000	+	7.00000i	0.229416	+	0.229416i
$932$			44.0000i			1.44127i
$933$	6.00000	+	6.00000i	0.196431	+	0.196431i
$934$			10.0000i			0.327210i
$935$	36.0000	+	12.0000i	1.17733	+	0.392442i
$936$			12.0000i			0.392232i
$937$	−54.0000			−1.76410			−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000			−1.76410			−0.882052	+	0.471153i	$0.843838\pi$
$938$		0			0
$939$	−6.00000	+	6.00000i	−0.195803	+	0.195803i
$940$	−8.00000	+	4.00000i	−0.260931	+	0.130466i
$941$	27.0000	+	27.0000i	0.880175	+	0.880175i	0.993552	−	0.113377i	$-0.0361668\pi$
$941$	27.0000	+	27.0000i	0.880175	+	0.880175i	−0.113377	+	0.993552i	$0.536167\pi$
$942$	18.0000	+	18.0000i	0.586472	+	0.586472i
$943$		0			0
$944$	−36.0000	+	36.0000i	−1.17170	+	1.17170i
$945$		0			0
$946$	18.0000	−	18.0000i	0.585230	−	0.585230i
$947$	27.0000	−	27.0000i	0.877382	−	0.877382i	−0.115881	−	0.993263i	$-0.536969\pi$
$947$	27.0000	−	27.0000i	0.877382	−	0.877382i	0.993263	+	0.115881i	$0.0369691\pi$
$948$	16.0000	+	16.0000i	0.519656	+	0.519656i
$949$	18.0000	−	18.0000i	0.584305	−	0.584305i
$950$	−6.00000	+	8.00000i	−0.194666	+	0.259554i
$951$		−	14.0000i		−	0.453981i
$952$		0			0
$953$	22.0000			0.712650			0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000			0.712650			0.356325	+	0.934362i	$0.384030\pi$
$954$			18.0000i			0.582772i
$955$	−48.0000	+	24.0000i	−1.55324	+	0.776622i
$956$		−	48.0000i		−	1.55243i
$957$	18.0000	−	18.0000i	0.581857	−	0.581857i
$958$	−24.0000	+	24.0000i	−0.775405	+	0.775405i
$959$		0			0
$960$	−24.0000	−	8.00000i	−0.774597	−	0.258199i
$961$	−31.0000			−1.00000
$962$	18.0000	−	18.0000i	0.580343	−	0.580343i
$963$	−9.00000	+	9.00000i	−0.290021	+	0.290021i
$964$			36.0000i			1.15948i
$965$	−12.0000	−	24.0000i	−0.386294	−	0.772587i
$966$		0			0
$967$	48.0000			1.54358			0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000			1.54358			0.771788	+	0.635880i	$0.219363\pi$
$968$	−14.0000	+	14.0000i	−0.449977	+	0.449977i
$969$		−	8.00000i		−	0.256997i
$970$	36.0000	+	12.0000i	1.15589	+	0.385297i
$971$	9.00000	−	9.00000i	0.288824	−	0.288824i	−0.547791	−	0.836615i	$-0.684531\pi$
$971$	9.00000	−	9.00000i	0.288824	−	0.288824i	0.836615	+	0.547791i	$0.184531\pi$
$972$	−14.0000	−	14.0000i	−0.449050	−	0.449050i
$973$		0			0
$974$	−24.0000	+	24.0000i	−0.769010	+	0.769010i
$975$	−24.0000	−	18.0000i	−0.768615	−	0.576461i
$976$	20.0000	+	20.0000i	0.640184	+	0.640184i
$977$		−	28.0000i		−	0.895799i	−0.894084	−	0.447900i	$-0.852172\pi$
$977$		−	28.0000i		−	0.895799i	0.894084	−	0.447900i	$-0.147828\pi$
$978$	−18.0000	−	18.0000i	−0.575577	−	0.575577i
$979$	−36.0000	−	36.0000i	−1.15056	−	1.15056i
$980$	14.0000	+	28.0000i	0.447214	+	0.894427i
$981$	1.00000	−	1.00000i	0.0319275	−	0.0319275i
$982$			30.0000i			0.957338i
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$		0			0
$985$	15.0000	+	5.00000i	0.477940	+	0.159313i
$986$		−	24.0000i		−	0.764316i
$987$		0			0
$988$		−	12.0000i		−	0.381771i
$989$	−24.0000	−	24.0000i	−0.763156	−	0.763156i
$990$	−12.0000	+	6.00000i	−0.381385	+	0.190693i
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$			10.0000i			0.317340i
$994$		0			0
$995$	2.00000	+	4.00000i	0.0634043	+	0.126809i
$996$	−36.0000			−1.14070
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	0.835112	−	0.550079i	$-0.185403\pi$
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	−0.550079	+	0.835112i	$0.685403\pi$
$998$	−58.0000			−1.83596
$999$			24.0000i			0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.q.b.29.1	yes	2
3.2	odd	2		720.2.bm.a.109.1		2
4.3	odd	2		320.2.q.b.209.1		2
5.2	odd	4		400.2.l.b.301.1		2
5.3	odd	4		400.2.l.a.301.1		2
5.4	even	2		80.2.q.a.29.1	✓	2
8.3	odd	2		640.2.q.a.289.1		2
8.5	even	2		640.2.q.c.289.1		2
15.14	odd	2		720.2.bm.b.109.1		2
16.3	odd	4		640.2.q.d.609.1		2
16.5	even	4		80.2.q.a.69.1	yes	2
16.11	odd	4		320.2.q.a.49.1		2
16.13	even	4		640.2.q.b.609.1		2
20.3	even	4		1600.2.l.c.401.1		2
20.7	even	4		1600.2.l.b.401.1		2
20.19	odd	2		320.2.q.a.209.1		2
40.19	odd	2		640.2.q.d.289.1		2
40.29	even	2		640.2.q.b.289.1		2
48.5	odd	4		720.2.bm.b.469.1		2
80.19	odd	4		640.2.q.a.609.1		2
80.27	even	4		1600.2.l.b.1201.1		2
80.29	even	4		640.2.q.c.609.1		2
80.37	odd	4		400.2.l.b.101.1		2
80.43	even	4		1600.2.l.c.1201.1		2
80.53	odd	4		400.2.l.a.101.1		2
80.59	odd	4		320.2.q.b.49.1		2
80.69	even	4	inner	80.2.q.b.69.1	yes	2
240.149	odd	4		720.2.bm.a.469.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.a.29.1	✓	2	5.4	even	2
80.2.q.a.69.1	yes	2	16.5	even	4
80.2.q.b.29.1	yes	2	1.1	even	1	trivial
80.2.q.b.69.1	yes	2	80.69	even	4	inner
320.2.q.a.49.1		2	16.11	odd	4
320.2.q.a.209.1		2	20.19	odd	2
320.2.q.b.49.1		2	80.59	odd	4
320.2.q.b.209.1		2	4.3	odd	2
400.2.l.a.101.1		2	80.53	odd	4
400.2.l.a.301.1		2	5.3	odd	4
400.2.l.b.101.1		2	80.37	odd	4
400.2.l.b.301.1		2	5.2	odd	4
640.2.q.a.289.1		2	8.3	odd	2
640.2.q.a.609.1		2	80.19	odd	4
640.2.q.b.289.1		2	40.29	even	2
640.2.q.b.609.1		2	16.13	even	4
640.2.q.c.289.1		2	8.5	even	2
640.2.q.c.609.1		2	80.29	even	4
640.2.q.d.289.1		2	40.19	odd	2
640.2.q.d.609.1		2	16.3	odd	4
720.2.bm.a.109.1		2	3.2	odd	2
720.2.bm.a.469.1		2	240.149	odd	4
720.2.bm.b.109.1		2	15.14	odd	2
720.2.bm.b.469.1		2	48.5	odd	4
1600.2.l.b.401.1		2	20.7	even	4
1600.2.l.b.1201.1		2	80.27	even	4
1600.2.l.c.401.1		2	20.3	even	4
1600.2.l.c.1201.1		2	80.43	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

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

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