LMFDB - Embedded newform 560.2.bb.b.309.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (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:	$4.47162251319$
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			309.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	560.309
Dual form			560.2.bb.b.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.00000 + 1.00000i) q^{3} +2.00000i q^{4} +(2.00000 - 1.00000i) q^{5} +2.00000i q^{6} -1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(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} -1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +(3.00000 + 1.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(-2.00000 + 2.00000i) q^{12} +(3.00000 + 3.00000i) q^{13} +(-1.00000 - 1.00000i) q^{14} +(3.00000 + 1.00000i) q^{15} -4.00000 q^{16} +(1.00000 - 1.00000i) q^{18} +(-3.00000 + 3.00000i) q^{19} +(2.00000 + 4.00000i) q^{20} +(-1.00000 - 1.00000i) q^{21} +2.00000i q^{22} -4.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +6.00000i q^{26} +(4.00000 - 4.00000i) q^{27} -2.00000i q^{28} +(-1.00000 + 1.00000i) q^{29} +(2.00000 + 4.00000i) q^{30} -8.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +2.00000i q^{33} +(-2.00000 + 1.00000i) q^{35} +2.00000 q^{36} +(5.00000 - 5.00000i) q^{37} -6.00000 q^{38} +6.00000i q^{39} +(-2.00000 + 6.00000i) q^{40} -12.0000i q^{41} -2.00000i q^{42} +(1.00000 - 1.00000i) q^{43} +(-2.00000 + 2.00000i) q^{44} +(-1.00000 - 2.00000i) q^{45} -10.0000i q^{47} +(-4.00000 - 4.00000i) q^{48} +1.00000 q^{49} +(7.00000 - 1.00000i) q^{50} +(-6.00000 + 6.00000i) q^{52} +(-3.00000 + 3.00000i) q^{53} +8.00000 q^{54} +(3.00000 + 1.00000i) q^{55} +(2.00000 - 2.00000i) q^{56} -6.00000 q^{57} -2.00000 q^{58} +(-1.00000 - 1.00000i) q^{59} +(-2.00000 + 6.00000i) q^{60} +(-7.00000 + 7.00000i) q^{61} +(-8.00000 - 8.00000i) q^{62} +1.00000i q^{63} -8.00000i q^{64} +(9.00000 + 3.00000i) q^{65} +(-2.00000 + 2.00000i) q^{66} +(3.00000 + 3.00000i) q^{67} +(-3.00000 - 1.00000i) q^{70} +6.00000i q^{71} +(2.00000 + 2.00000i) q^{72} +10.0000 q^{73} +10.0000 q^{74} +(7.00000 - 1.00000i) q^{75} +(-6.00000 - 6.00000i) q^{76} +(-1.00000 - 1.00000i) q^{77} +(-6.00000 + 6.00000i) q^{78} -8.00000 q^{79} +(-8.00000 + 4.00000i) q^{80} +5.00000 q^{81} +(12.0000 - 12.0000i) q^{82} +(5.00000 + 5.00000i) q^{83} +(2.00000 - 2.00000i) q^{84} +2.00000 q^{86} -2.00000 q^{87} -4.00000 q^{88} +(1.00000 - 3.00000i) q^{90} +(-3.00000 - 3.00000i) q^{91} +(-8.00000 - 8.00000i) q^{93} +(10.0000 - 10.0000i) q^{94} +(-3.00000 + 9.00000i) q^{95} -8.00000i q^{96} -8.00000i q^{97} +(1.00000 + 1.00000i) q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 2 * q^7 - 4 * q^8	$ 2 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 2 q^{7} - 4 q^{8} + 6 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 2 q^{18} - 6 q^{19} + 4 q^{20} - 2 q^{21} - 8 q^{24} + 6 q^{25} + 8 q^{27} - 2 q^{29} + 4 q^{30} - 16 q^{31} - 8 q^{32} - 4 q^{35} + 4 q^{36} + 10 q^{37} - 12 q^{38} - 4 q^{40} + 2 q^{43} - 4 q^{44} - 2 q^{45} - 8 q^{48} + 2 q^{49} + 14 q^{50} - 12 q^{52} - 6 q^{53} + 16 q^{54} + 6 q^{55} + 4 q^{56} - 12 q^{57} - 4 q^{58} - 2 q^{59} - 4 q^{60} - 14 q^{61} - 16 q^{62} + 18 q^{65} - 4 q^{66} + 6 q^{67} - 6 q^{70} + 4 q^{72} + 20 q^{73} + 20 q^{74} + 14 q^{75} - 12 q^{76} - 2 q^{77} - 12 q^{78} - 16 q^{79} - 16 q^{80} + 10 q^{81} + 24 q^{82} + 10 q^{83} + 4 q^{84} + 4 q^{86} - 4 q^{87} - 8 q^{88} + 2 q^{90} - 6 q^{91} - 16 q^{93} + 20 q^{94} - 6 q^{95} + 2 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 2 * q^7 - 4 * q^8 + 6 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 2 * q^18 - 6 * q^19 + 4 * q^20 - 2 * q^21 - 8 * q^24 + 6 * q^25 + 8 * q^27 - 2 * q^29 + 4 * q^30 - 16 * q^31 - 8 * q^32 - 4 * q^35 + 4 * q^36 + 10 * q^37 - 12 * q^38 - 4 * q^40 + 2 * q^43 - 4 * q^44 - 2 * q^45 - 8 * q^48 + 2 * q^49 + 14 * q^50 - 12 * q^52 - 6 * q^53 + 16 * q^54 + 6 * q^55 + 4 * q^56 - 12 * q^57 - 4 * q^58 - 2 * q^59 - 4 * q^60 - 14 * q^61 - 16 * q^62 + 18 * q^65 - 4 * q^66 + 6 * q^67 - 6 * q^70 + 4 * q^72 + 20 * q^73 + 20 * q^74 + 14 * q^75 - 12 * q^76 - 2 * q^77 - 12 * q^78 - 16 * q^79 - 16 * q^80 + 10 * q^81 + 24 * q^82 + 10 * q^83 + 4 * q^84 + 4 * q^86 - 4 * q^87 - 8 * q^88 + 2 * q^90 - 6 * q^91 - 16 * q^93 + 20 * q^94 - 6 * q^95 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	0.934172	−	0.356822i	$-0.116140\pi$
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	−0.356822	+	0.934172i	$0.616140\pi$
$4$			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
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		−	1.00000i		−	0.333333i
$10$	3.00000	+	1.00000i	0.948683	+	0.316228i
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$	−2.00000	+	2.00000i	−0.577350	+	0.577350i
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	0.987797	−	0.155747i	$-0.0497784\pi$
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	−0.155747	+	0.987797i	$0.549778\pi$
$14$	−1.00000	−	1.00000i	−0.267261	−	0.267261i
$15$	3.00000	+	1.00000i	0.774597	+	0.258199i
$16$	−4.00000			−1.00000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	1.00000	−	1.00000i	0.235702	−	0.235702i
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	−0.961844	−	0.273597i	$-0.911786\pi$
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	0.273597	+	0.961844i	$0.411786\pi$
$20$	2.00000	+	4.00000i	0.447214	+	0.894427i
$21$	−1.00000	−	1.00000i	−0.218218	−	0.218218i
$22$			2.00000i			0.426401i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−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
$28$		−	2.00000i		−	0.377964i
$29$	−1.00000	+	1.00000i	−0.185695	+	0.185695i	−0.793832	−	0.608137i	$-0.791917\pi$
$29$	−1.00000	+	1.00000i	−0.185695	+	0.185695i	0.608137	+	0.793832i	$0.291917\pi$
$30$	2.00000	+	4.00000i	0.365148	+	0.730297i
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$			2.00000i			0.348155i
$34$		0			0
$35$	−2.00000	+	1.00000i	−0.338062	+	0.169031i
$36$	2.00000			0.333333
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	0.986394	+	0.164399i	$0.0525685\pi$
$38$	−6.00000			−0.973329
$39$			6.00000i			0.960769i
$40$	−2.00000	+	6.00000i	−0.316228	+	0.948683i
$41$		−	12.0000i		−	1.87409i	−0.349215	−	0.937043i	$-0.613552\pi$
$41$		−	12.0000i		−	1.87409i	0.349215	−	0.937043i	$-0.386448\pi$
$42$		−	2.00000i		−	0.308607i
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	−0.626734	−	0.779233i	$-0.715609\pi$
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	0.779233	+	0.626734i	$0.215609\pi$
$44$	−2.00000	+	2.00000i	−0.301511	+	0.301511i
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$		0			0
$47$		−	10.0000i		−	1.45865i	−0.684167	−	0.729325i	$-0.739834\pi$
$47$		−	10.0000i		−	1.45865i	0.684167	−	0.729325i	$-0.260166\pi$
$48$	−4.00000	−	4.00000i	−0.577350	−	0.577350i
$49$	1.00000			0.142857
$50$	7.00000	−	1.00000i	0.989949	−	0.141421i
$51$		0			0
$52$	−6.00000	+	6.00000i	−0.832050	+	0.832050i
$53$	−3.00000	+	3.00000i	−0.412082	+	0.412082i	−0.882463	−	0.470381i	$-0.844116\pi$
$53$	−3.00000	+	3.00000i	−0.412082	+	0.412082i	0.470381	+	0.882463i	$0.344116\pi$
$54$	8.00000			1.08866
$55$	3.00000	+	1.00000i	0.404520	+	0.134840i
$56$	2.00000	−	2.00000i	0.267261	−	0.267261i
$57$	−6.00000			−0.794719
$58$	−2.00000			−0.262613
$59$	−1.00000	−	1.00000i	−0.130189	−	0.130189i	0.639010	−	0.769199i	$-0.279344\pi$
$59$	−1.00000	−	1.00000i	−0.130189	−	0.130189i	−0.769199	+	0.639010i	$0.779344\pi$
$60$	−2.00000	+	6.00000i	−0.258199	+	0.774597i
$61$	−7.00000	+	7.00000i	−0.896258	+	0.896258i	−0.995103	−	0.0988447i	$-0.968485\pi$
$61$	−7.00000	+	7.00000i	−0.896258	+	0.896258i	0.0988447	+	0.995103i	$0.468485\pi$
$62$	−8.00000	−	8.00000i	−1.01600	−	1.01600i
$63$			1.00000i			0.125988i
$64$		−	8.00000i		−	1.00000i
$65$	9.00000	+	3.00000i	1.11631	+	0.372104i
$66$	−2.00000	+	2.00000i	−0.246183	+	0.246183i
$67$	3.00000	+	3.00000i	0.366508	+	0.366508i	0.866202	−	0.499694i	$-0.166554\pi$
$67$	3.00000	+	3.00000i	0.366508	+	0.366508i	−0.499694	+	0.866202i	$0.666554\pi$
$68$		0			0
$69$		0			0
$70$	−3.00000	−	1.00000i	−0.358569	−	0.119523i
$71$			6.00000i			0.712069i	0.934473	+	0.356034i	$0.115871\pi$
$71$			6.00000i			0.712069i	−0.934473	+	0.356034i	$0.884129\pi$
$72$	2.00000	+	2.00000i	0.235702	+	0.235702i
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$	10.0000			1.16248
$75$	7.00000	−	1.00000i	0.808290	−	0.115470i
$76$	−6.00000	−	6.00000i	−0.688247	−	0.688247i
$77$	−1.00000	−	1.00000i	−0.113961	−	0.113961i
$78$	−6.00000	+	6.00000i	−0.679366	+	0.679366i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	−8.00000	+	4.00000i	−0.894427	+	0.447214i
$81$	5.00000			0.555556
$82$	12.0000	−	12.0000i	1.32518	−	1.32518i
$83$	5.00000	+	5.00000i	0.548821	+	0.548821i	0.926100	−	0.377279i	$-0.123140\pi$
$83$	5.00000	+	5.00000i	0.548821	+	0.548821i	−0.377279	+	0.926100i	$0.623140\pi$
$84$	2.00000	−	2.00000i	0.218218	−	0.218218i
$85$		0			0
$86$	2.00000			0.215666
$87$	−2.00000			−0.214423
$88$	−4.00000			−0.426401
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	1.00000	−	3.00000i	0.105409	−	0.316228i
$91$	−3.00000	−	3.00000i	−0.314485	−	0.314485i
$92$		0			0
$93$	−8.00000	−	8.00000i	−0.829561	−	0.829561i
$94$	10.0000	−	10.0000i	1.03142	−	1.03142i
$95$	−3.00000	+	9.00000i	−0.307794	+	0.923381i
$96$		−	8.00000i		−	0.816497i
$97$		−	8.00000i		−	0.812277i	−0.913812	−	0.406138i	$-0.866875\pi$
$97$		−	8.00000i		−	0.812277i	0.913812	−	0.406138i	$-0.133125\pi$
$98$	1.00000	+	1.00000i	0.101015	+	0.101015i
$99$	1.00000	−	1.00000i	0.100504	−	0.100504i
$100$	8.00000	+	6.00000i	0.800000	+	0.600000i
$101$	−7.00000	−	7.00000i	−0.696526	−	0.696526i	0.267133	−	0.963660i	$-0.413924\pi$
$101$	−7.00000	−	7.00000i	−0.696526	−	0.696526i	−0.963660	+	0.267133i	$0.913924\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−12.0000			−1.17670
$105$	−3.00000	−	1.00000i	−0.292770	−	0.0975900i
$106$	−6.00000			−0.582772
$107$	9.00000	−	9.00000i	0.870063	−	0.870063i	−0.122416	−	0.992479i	$-0.539064\pi$
$107$	9.00000	−	9.00000i	0.870063	−	0.870063i	0.992479	+	0.122416i	$0.0390642\pi$
$108$	8.00000	+	8.00000i	0.769800	+	0.769800i
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	−0.548683	−	0.836031i	$-0.684871\pi$
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	0.836031	+	0.548683i	$0.184871\pi$
$110$	2.00000	+	4.00000i	0.190693	+	0.381385i
$111$	10.0000			0.949158
$112$	4.00000			0.377964
$113$			16.0000i			1.50515i	0.658505	+	0.752577i	$0.271189\pi$
$113$			16.0000i			1.50515i	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−6.00000	−	6.00000i	−0.561951	−	0.561951i
$115$		0			0
$116$	−2.00000	−	2.00000i	−0.185695	−	0.185695i
$117$	3.00000	−	3.00000i	0.277350	−	0.277350i
$118$		−	2.00000i		−	0.184115i
$119$		0			0
$120$	−8.00000	+	4.00000i	−0.730297	+	0.365148i
$121$		−	9.00000i		−	0.818182i
$122$	−14.0000			−1.26750
$123$	12.0000	−	12.0000i	1.08200	−	1.08200i
$124$		−	16.0000i		−	1.43684i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	−1.00000	+	1.00000i	−0.0890871	+	0.0890871i
$127$			18.0000i			1.59724i	0.601834	+	0.798621i	$0.294437\pi$
$127$			18.0000i			1.59724i	−0.601834	+	0.798621i	$0.705563\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	2.00000			0.176090
$130$	6.00000	+	12.0000i	0.526235	+	1.05247i
$131$	5.00000	−	5.00000i	0.436852	−	0.436852i	−0.454099	−	0.890951i	$-0.650039\pi$
$131$	5.00000	−	5.00000i	0.436852	−	0.436852i	0.890951	+	0.454099i	$0.150039\pi$
$132$	−4.00000			−0.348155
$133$	3.00000	−	3.00000i	0.260133	−	0.260133i
$134$			6.00000i			0.518321i
$135$	4.00000	−	12.0000i	0.344265	−	1.03280i
$136$		0			0
$137$	−10.0000			−0.854358			−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000			−0.854358			−0.427179	+	0.904167i	$0.640493\pi$
$138$		0			0
$139$	3.00000	+	3.00000i	0.254457	+	0.254457i	0.822795	−	0.568338i	$-0.192414\pi$
$139$	3.00000	+	3.00000i	0.254457	+	0.254457i	−0.568338	+	0.822795i	$0.692414\pi$
$140$	−2.00000	−	4.00000i	−0.169031	−	0.338062i
$141$	10.0000	−	10.0000i	0.842152	−	0.842152i
$142$	−6.00000	+	6.00000i	−0.503509	+	0.503509i
$143$			6.00000i			0.501745i
$144$			4.00000i			0.333333i
$145$	−1.00000	+	3.00000i	−0.0830455	+	0.249136i
$146$	10.0000	+	10.0000i	0.827606	+	0.827606i
$147$	1.00000	+	1.00000i	0.0824786	+	0.0824786i
$148$	10.0000	+	10.0000i	0.821995	+	0.821995i
$149$	11.0000	+	11.0000i	0.901155	+	0.901155i	0.995536	−	0.0943810i	$-0.0300872\pi$
$149$	11.0000	+	11.0000i	0.901155	+	0.901155i	−0.0943810	+	0.995536i	$0.530087\pi$
$150$	8.00000	+	6.00000i	0.653197	+	0.489898i
$151$			14.0000i			1.13930i	0.821886	+	0.569652i	$0.192922\pi$
$151$			14.0000i			1.13930i	−0.821886	+	0.569652i	$0.807078\pi$
$152$		−	12.0000i		−	0.973329i
$153$		0			0
$154$		−	2.00000i		−	0.161165i
$155$	−16.0000	+	8.00000i	−1.28515	+	0.642575i
$156$	−12.0000			−0.960769
$157$	−17.0000	−	17.0000i	−1.35675	−	1.35675i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−17.0000	−	17.0000i	−1.35675	−	1.35675i	−0.478852	−	0.877896i	$-0.658947\pi$
$158$	−8.00000	−	8.00000i	−0.636446	−	0.636446i
$159$	−6.00000			−0.475831
$160$	−12.0000	−	4.00000i	−0.948683	−	0.316228i
$161$		0			0
$162$	5.00000	+	5.00000i	0.392837	+	0.392837i
$163$	−5.00000	−	5.00000i	−0.391630	−	0.391630i	0.483638	−	0.875268i	$-0.339315\pi$
$163$	−5.00000	−	5.00000i	−0.391630	−	0.391630i	−0.875268	+	0.483638i	$0.839315\pi$
$164$	24.0000			1.87409
$165$	2.00000	+	4.00000i	0.155700	+	0.311400i
$166$			10.0000i			0.776151i
$167$	−24.0000			−1.85718			−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000			−1.85718			−0.928588	+	0.371113i	$0.878976\pi$
$168$	4.00000			0.308607
$169$			5.00000i			0.384615i
$170$		0			0
$171$	3.00000	+	3.00000i	0.229416	+	0.229416i
$172$	2.00000	+	2.00000i	0.152499	+	0.152499i
$173$	7.00000	+	7.00000i	0.532200	+	0.532200i	0.921227	−	0.389026i	$-0.127189\pi$
$173$	7.00000	+	7.00000i	0.532200	+	0.532200i	−0.389026	+	0.921227i	$0.627189\pi$
$174$	−2.00000	−	2.00000i	−0.151620	−	0.151620i
$175$	−3.00000	+	4.00000i	−0.226779	+	0.302372i
$176$	−4.00000	−	4.00000i	−0.301511	−	0.301511i
$177$		−	2.00000i		−	0.150329i
$178$		0			0
$179$	−13.0000	+	13.0000i	−0.971666	+	0.971666i	−0.999609	−	0.0279439i	$-0.991104\pi$
$179$	−13.0000	+	13.0000i	−0.971666	+	0.971666i	0.0279439	+	0.999609i	$0.491104\pi$
$180$	4.00000	−	2.00000i	0.298142	−	0.149071i
$181$	−15.0000	−	15.0000i	−1.11494	−	1.11494i	−0.992472	−	0.122469i	$-0.960919\pi$
$181$	−15.0000	−	15.0000i	−1.11494	−	1.11494i	−0.122469	−	0.992472i	$-0.539081\pi$
$182$		−	6.00000i		−	0.444750i
$183$	−14.0000			−1.03491
$184$		0			0
$185$	5.00000	−	15.0000i	0.367607	−	1.10282i
$186$		−	16.0000i		−	1.17318i
$187$		0			0
$188$	20.0000			1.45865
$189$	−4.00000	+	4.00000i	−0.290957	+	0.290957i
$190$	−12.0000	+	6.00000i	−0.870572	+	0.435286i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$	8.00000	−	8.00000i	0.577350	−	0.577350i
$193$			20.0000i			1.43963i	0.694165	+	0.719816i	$0.255774\pi$
$193$			20.0000i			1.43963i	−0.694165	+	0.719816i	$0.744226\pi$
$194$	8.00000	−	8.00000i	0.574367	−	0.574367i
$195$	6.00000	+	12.0000i	0.429669	+	0.859338i
$196$			2.00000i			0.142857i
$197$	1.00000	−	1.00000i	0.0712470	−	0.0712470i	−0.670585	−	0.741832i	$-0.733957\pi$
$197$	1.00000	−	1.00000i	0.0712470	−	0.0712470i	0.741832	+	0.670585i	$0.233957\pi$
$198$	2.00000			0.142134
$199$			10.0000i			0.708881i	0.935079	+	0.354441i	$0.115329\pi$
$199$			10.0000i			0.708881i	−0.935079	+	0.354441i	$0.884671\pi$
$200$	2.00000	+	14.0000i	0.141421	+	0.989949i
$201$			6.00000i			0.423207i
$202$		−	14.0000i		−	0.985037i
$203$	1.00000	−	1.00000i	0.0701862	−	0.0701862i
$204$		0			0
$205$	−12.0000	−	24.0000i	−0.838116	−	1.67623i
$206$		0			0
$207$		0			0
$208$	−12.0000	−	12.0000i	−0.832050	−	0.832050i
$209$	−6.00000			−0.415029
$210$	−2.00000	−	4.00000i	−0.138013	−	0.276026i
$211$	11.0000	−	11.0000i	0.757271	−	0.757271i	−0.218554	−	0.975825i	$-0.570134\pi$
$211$	11.0000	−	11.0000i	0.757271	−	0.757271i	0.975825	+	0.218554i	$0.0701339\pi$
$212$	−6.00000	−	6.00000i	−0.412082	−	0.412082i
$213$	−6.00000	+	6.00000i	−0.411113	+	0.411113i
$214$	18.0000			1.23045
$215$	1.00000	−	3.00000i	0.0681994	−	0.204598i
$216$			16.0000i			1.08866i
$217$	8.00000			0.543075
$218$	6.00000			0.406371
$219$	10.0000	+	10.0000i	0.675737	+	0.675737i
$220$	−2.00000	+	6.00000i	−0.134840	+	0.404520i
$221$		0			0
$222$	10.0000	+	10.0000i	0.671156	+	0.671156i
$223$		−	2.00000i		−	0.133930i	−0.997755	−	0.0669650i	$-0.978668\pi$
$223$		−	2.00000i		−	0.133930i	0.997755	−	0.0669650i	$-0.0213316\pi$
$224$	4.00000	+	4.00000i	0.267261	+	0.267261i
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$	−16.0000	+	16.0000i	−1.06430	+	1.06430i
$227$	13.0000	+	13.0000i	0.862840	+	0.862840i	0.991667	−	0.128827i	$-0.0411211\pi$
$227$	13.0000	+	13.0000i	0.862840	+	0.862840i	−0.128827	+	0.991667i	$0.541121\pi$
$228$		−	12.0000i		−	0.794719i
$229$	−7.00000	−	7.00000i	−0.462573	−	0.462573i	0.436925	−	0.899498i	$-0.356068\pi$
$229$	−7.00000	−	7.00000i	−0.462573	−	0.462573i	−0.899498	+	0.436925i	$0.856068\pi$
$230$		0			0
$231$		−	2.00000i		−	0.131590i
$232$		−	4.00000i		−	0.262613i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$	6.00000			0.392232
$235$	−10.0000	−	20.0000i	−0.652328	−	1.30466i
$236$	2.00000	−	2.00000i	0.130189	−	0.130189i
$237$	−8.00000	−	8.00000i	−0.519656	−	0.519656i
$238$		0			0
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$	−12.0000	−	4.00000i	−0.774597	−	0.258199i
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$	9.00000	−	9.00000i	0.578542	−	0.578542i
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$	−14.0000	−	14.0000i	−0.896258	−	0.896258i
$245$	2.00000	−	1.00000i	0.127775	−	0.0638877i
$246$	24.0000			1.53018
$247$	−18.0000			−1.14531
$248$	16.0000	−	16.0000i	1.01600	−	1.01600i
$249$			10.0000i			0.633724i
$250$	13.0000	−	9.00000i	0.822192	−	0.569210i
$251$	11.0000	+	11.0000i	0.694314	+	0.694314i	0.963178	−	0.268864i	$-0.0866483\pi$
$251$	11.0000	+	11.0000i	0.694314	+	0.694314i	−0.268864	+	0.963178i	$0.586648\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$	−18.0000	+	18.0000i	−1.12942	+	1.12942i
$255$		0			0
$256$	16.0000			1.00000
$257$			4.00000i			0.249513i	0.992187	+	0.124757i	$0.0398150\pi$
$257$			4.00000i			0.249513i	−0.992187	+	0.124757i	$0.960185\pi$
$258$	2.00000	+	2.00000i	0.124515	+	0.124515i
$259$	−5.00000	+	5.00000i	−0.310685	+	0.310685i
$260$	−6.00000	+	18.0000i	−0.372104	+	1.11631i
$261$	1.00000	+	1.00000i	0.0618984	+	0.0618984i
$262$	10.0000			0.617802
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$	−4.00000	−	4.00000i	−0.246183	−	0.246183i
$265$	−3.00000	+	9.00000i	−0.184289	+	0.552866i
$266$	6.00000			0.367884
$267$		0			0
$268$	−6.00000	+	6.00000i	−0.366508	+	0.366508i
$269$	−7.00000	+	7.00000i	−0.426798	+	0.426798i	−0.887536	−	0.460738i	$-0.847585\pi$
$269$	−7.00000	+	7.00000i	−0.426798	+	0.426798i	0.460738	+	0.887536i	$0.347585\pi$
$270$	16.0000	−	8.00000i	0.973729	−	0.486864i
$271$	−24.0000			−1.45790			−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000			−1.45790			−0.728948	+	0.684569i	$0.759990\pi$
$272$		0			0
$273$		−	6.00000i		−	0.363137i
$274$	−10.0000	−	10.0000i	−0.604122	−	0.604122i
$275$	7.00000	−	1.00000i	0.422116	−	0.0603023i
$276$		0			0
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	−0.995545	−	0.0942828i	$-0.969944\pi$
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	0.0942828	+	0.995545i	$0.469944\pi$
$278$			6.00000i			0.359856i
$279$			8.00000i			0.478947i
$280$	2.00000	−	6.00000i	0.119523	−	0.358569i
$281$			28.0000i			1.67034i	0.549992	+	0.835170i	$0.314631\pi$
$281$			28.0000i			1.67034i	−0.549992	+	0.835170i	$0.685369\pi$
$282$	20.0000			1.19098
$283$	−9.00000	+	9.00000i	−0.534994	+	0.534994i	−0.922055	−	0.387060i	$-0.873491\pi$
$283$	−9.00000	+	9.00000i	−0.534994	+	0.534994i	0.387060	+	0.922055i	$0.373491\pi$
$284$	−12.0000			−0.712069
$285$	−12.0000	+	6.00000i	−0.710819	+	0.355409i
$286$	−6.00000	+	6.00000i	−0.354787	+	0.354787i
$287$			12.0000i			0.708338i
$288$	−4.00000	+	4.00000i	−0.235702	+	0.235702i
$289$	17.0000			1.00000
$290$	−4.00000	+	2.00000i	−0.234888	+	0.117444i
$291$	8.00000	−	8.00000i	0.468968	−	0.468968i
$292$			20.0000i			1.17041i
$293$	11.0000	−	11.0000i	0.642627	−	0.642627i	−0.308574	−	0.951200i	$-0.599852\pi$
$293$	11.0000	−	11.0000i	0.642627	−	0.642627i	0.951200	+	0.308574i	$0.0998516\pi$
$294$			2.00000i			0.116642i
$295$	−3.00000	−	1.00000i	−0.174667	−	0.0582223i
$296$			20.0000i			1.16248i
$297$	8.00000			0.464207
$298$			22.0000i			1.27443i
$299$		0			0
$300$	2.00000	+	14.0000i	0.115470	+	0.808290i
$301$	−1.00000	+	1.00000i	−0.0576390	+	0.0576390i
$302$	−14.0000	+	14.0000i	−0.805609	+	0.805609i
$303$		−	14.0000i		−	0.804279i
$304$	12.0000	−	12.0000i	0.688247	−	0.688247i
$305$	−7.00000	+	21.0000i	−0.400819	+	1.20246i
$306$		0			0
$307$	−15.0000	−	15.0000i	−0.856095	−	0.856095i	0.134780	−	0.990876i	$-0.456967\pi$
$307$	−15.0000	−	15.0000i	−0.856095	−	0.856095i	−0.990876	+	0.134780i	$0.956967\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$		0			0
$310$	−24.0000	−	8.00000i	−1.36311	−	0.454369i
$311$			26.0000i			1.47432i	0.675716	+	0.737162i	$0.263835\pi$
$311$			26.0000i			1.47432i	−0.675716	+	0.737162i	$0.736165\pi$
$312$	−12.0000	−	12.0000i	−0.679366	−	0.679366i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		−	34.0000i		−	1.91873i
$315$	1.00000	+	2.00000i	0.0563436	+	0.112687i
$316$		−	16.0000i		−	0.900070i
$317$	13.0000	+	13.0000i	0.730153	+	0.730153i	0.970650	−	0.240497i	$-0.0773105\pi$
$317$	13.0000	+	13.0000i	0.730153	+	0.730153i	−0.240497	+	0.970650i	$0.577310\pi$
$318$	−6.00000	−	6.00000i	−0.336463	−	0.336463i
$319$	−2.00000			−0.111979
$320$	−8.00000	−	16.0000i	−0.447214	−	0.894427i
$321$	18.0000			1.00466
$322$		0			0
$323$		0			0
$324$			10.0000i			0.555556i
$325$	21.0000	−	3.00000i	1.16487	−	0.166410i
$326$		−	10.0000i		−	0.553849i
$327$	6.00000			0.331801
$328$	24.0000	+	24.0000i	1.32518	+	1.32518i
$329$			10.0000i			0.551318i
$330$	−2.00000	+	6.00000i	−0.110096	+	0.330289i
$331$	−15.0000	−	15.0000i	−0.824475	−	0.824475i	0.162272	−	0.986746i	$-0.448118\pi$
$331$	−15.0000	−	15.0000i	−0.824475	−	0.824475i	−0.986746	+	0.162272i	$0.948118\pi$
$332$	−10.0000	+	10.0000i	−0.548821	+	0.548821i
$333$	−5.00000	−	5.00000i	−0.273998	−	0.273998i
$334$	−24.0000	−	24.0000i	−1.31322	−	1.31322i
$335$	9.00000	+	3.00000i	0.491723	+	0.163908i
$336$	4.00000	+	4.00000i	0.218218	+	0.218218i
$337$		−	8.00000i		−	0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$		−	8.00000i		−	0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$	−5.00000	+	5.00000i	−0.271964	+	0.271964i
$339$	−16.0000	+	16.0000i	−0.869001	+	0.869001i
$340$		0			0
$341$	−8.00000	−	8.00000i	−0.433224	−	0.433224i
$342$			6.00000i			0.324443i
$343$	−1.00000			−0.0539949
$344$			4.00000i			0.215666i
$345$		0			0
$346$			14.0000i			0.752645i
$347$	17.0000	−	17.0000i	0.912608	−	0.912608i	−0.0838690	−	0.996477i	$-0.526728\pi$
$347$	17.0000	−	17.0000i	0.912608	−	0.912608i	0.996477	+	0.0838690i	$0.0267277\pi$
$348$		−	4.00000i		−	0.214423i
$349$	−11.0000	+	11.0000i	−0.588817	+	0.588817i	−0.937311	−	0.348494i	$-0.886693\pi$
$349$	−11.0000	+	11.0000i	−0.588817	+	0.588817i	0.348494	+	0.937311i	$0.386693\pi$
$350$	−7.00000	+	1.00000i	−0.374166	+	0.0534522i
$351$	24.0000			1.28103
$352$		−	8.00000i		−	0.426401i
$353$			36.0000i			1.91609i	0.286623	+	0.958043i	$0.407467\pi$
$353$			36.0000i			1.91609i	−0.286623	+	0.958043i	$0.592533\pi$
$354$	2.00000	−	2.00000i	0.106299	−	0.106299i
$355$	6.00000	+	12.0000i	0.318447	+	0.636894i
$356$		0			0
$357$		0			0
$358$	−26.0000			−1.37414
$359$			6.00000i			0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$			6.00000i			0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$	6.00000	+	2.00000i	0.316228	+	0.105409i
$361$			1.00000i			0.0526316i
$362$		−	30.0000i		−	1.57676i
$363$	9.00000	−	9.00000i	0.472377	−	0.472377i
$364$	6.00000	−	6.00000i	0.314485	−	0.314485i
$365$	20.0000	−	10.0000i	1.04685	−	0.523424i
$366$	−14.0000	−	14.0000i	−0.731792	−	0.731792i
$367$			6.00000i			0.313197i	0.987662	+	0.156599i	$0.0500529\pi$
$367$			6.00000i			0.313197i	−0.987662	+	0.156599i	$0.949947\pi$
$368$		0			0
$369$	−12.0000			−0.624695
$370$	20.0000	−	10.0000i	1.03975	−	0.519875i
$371$	3.00000	−	3.00000i	0.155752	−	0.155752i
$372$	16.0000	−	16.0000i	0.829561	−	0.829561i
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	−0.979263	−	0.202593i	$-0.935063\pi$
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	0.202593	+	0.979263i	$0.435063\pi$
$374$		0			0
$375$	13.0000	−	9.00000i	0.671317	−	0.464758i
$376$	20.0000	+	20.0000i	1.03142	+	1.03142i
$377$	−6.00000			−0.309016
$378$	−8.00000			−0.411476
$379$	−19.0000	−	19.0000i	−0.975964	−	0.975964i	0.0237534	−	0.999718i	$-0.492438\pi$
$379$	−19.0000	−	19.0000i	−0.975964	−	0.975964i	−0.999718	+	0.0237534i	$0.992438\pi$
$380$	−18.0000	−	6.00000i	−0.923381	−	0.307794i
$381$	−18.0000	+	18.0000i	−0.922168	+	0.922168i
$382$	16.0000	+	16.0000i	0.818631	+	0.818631i
$383$		−	34.0000i		−	1.73732i	−0.495410	−	0.868659i	$-0.664982\pi$
$383$		−	34.0000i		−	1.73732i	0.495410	−	0.868659i	$-0.335018\pi$
$384$	16.0000			0.816497
$385$	−3.00000	−	1.00000i	−0.152894	−	0.0509647i
$386$	−20.0000	+	20.0000i	−1.01797	+	1.01797i
$387$	−1.00000	−	1.00000i	−0.0508329	−	0.0508329i
$388$	16.0000			0.812277
$389$	11.0000	+	11.0000i	0.557722	+	0.557722i	0.928658	−	0.370936i	$-0.120963\pi$
$389$	11.0000	+	11.0000i	0.557722	+	0.557722i	−0.370936	+	0.928658i	$0.620963\pi$
$390$	−6.00000	+	18.0000i	−0.303822	+	0.911465i
$391$		0			0
$392$	−2.00000	+	2.00000i	−0.101015	+	0.101015i
$393$	10.0000			0.504433
$394$	2.00000			0.100759
$395$	−16.0000	+	8.00000i	−0.805047	+	0.402524i
$396$	2.00000	+	2.00000i	0.100504	+	0.100504i
$397$	15.0000	+	15.0000i	0.752828	+	0.752828i	0.975006	−	0.222178i	$-0.0713165\pi$
$397$	15.0000	+	15.0000i	0.752828	+	0.752828i	−0.222178	+	0.975006i	$0.571317\pi$
$398$	−10.0000	+	10.0000i	−0.501255	+	0.501255i
$399$	6.00000			0.300376
$400$	−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
$403$	−24.0000	−	24.0000i	−1.19553	−	1.19553i
$404$	14.0000	−	14.0000i	0.696526	−	0.696526i
$405$	10.0000	−	5.00000i	0.496904	−	0.248452i
$406$	2.00000			0.0992583
$407$	10.0000			0.495682
$408$		0			0
$409$			12.0000i			0.593362i	0.954977	+	0.296681i	$0.0958798\pi$
$409$			12.0000i			0.593362i	−0.954977	+	0.296681i	$0.904120\pi$
$410$	12.0000	−	36.0000i	0.592638	−	1.77791i
$411$	−10.0000	−	10.0000i	−0.493264	−	0.493264i
$412$		0			0
$413$	1.00000	+	1.00000i	0.0492068	+	0.0492068i
$414$		0			0
$415$	15.0000	+	5.00000i	0.736321	+	0.245440i
$416$		−	24.0000i		−	1.17670i
$417$			6.00000i			0.293821i
$418$	−6.00000	−	6.00000i	−0.293470	−	0.293470i
$419$	9.00000	−	9.00000i	0.439679	−	0.439679i	−0.452225	−	0.891904i	$-0.649370\pi$
$419$	9.00000	−	9.00000i	0.439679	−	0.439679i	0.891904	+	0.452225i	$0.149370\pi$
$420$	2.00000	−	6.00000i	0.0975900	−	0.292770i
$421$	19.0000	+	19.0000i	0.926003	+	0.926003i	0.997445	−	0.0714415i	$-0.0227599\pi$
$421$	19.0000	+	19.0000i	0.926003	+	0.926003i	−0.0714415	+	0.997445i	$0.522760\pi$
$422$	22.0000			1.07094
$423$	−10.0000			−0.486217
$424$		−	12.0000i		−	0.582772i
$425$		0			0
$426$	−12.0000			−0.581402
$427$	7.00000	−	7.00000i	0.338754	−	0.338754i
$428$	18.0000	+	18.0000i	0.870063	+	0.870063i
$429$	−6.00000	+	6.00000i	−0.289683	+	0.289683i
$430$	4.00000	−	2.00000i	0.192897	−	0.0964486i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−16.0000	+	16.0000i	−0.769800	+	0.769800i
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	8.00000	+	8.00000i	0.384012	+	0.384012i
$435$	−4.00000	+	2.00000i	−0.191785	+	0.0958927i
$436$	6.00000	+	6.00000i	0.287348	+	0.287348i
$437$		0			0
$438$			20.0000i			0.955637i
$439$		−	38.0000i		−	1.81364i	−0.421517	−	0.906821i	$-0.638502\pi$
$439$		−	38.0000i		−	1.81364i	0.421517	−	0.906821i	$-0.361498\pi$
$440$	−8.00000	+	4.00000i	−0.381385	+	0.190693i
$441$		−	1.00000i		−	0.0476190i
$442$		0			0
$443$	1.00000	−	1.00000i	0.0475114	−	0.0475114i	−0.682952	−	0.730463i	$-0.739304\pi$
$443$	1.00000	−	1.00000i	0.0475114	−	0.0475114i	0.730463	+	0.682952i	$0.239304\pi$
$444$			20.0000i			0.949158i
$445$		0			0
$446$	2.00000	−	2.00000i	0.0947027	−	0.0947027i
$447$			22.0000i			1.04056i
$448$			8.00000i			0.377964i
$449$	−34.0000			−1.60456			−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000			−1.60456			−0.802280	+	0.596948i	$0.796380\pi$
$450$	−1.00000	−	7.00000i	−0.0471405	−	0.329983i
$451$	12.0000	−	12.0000i	0.565058	−	0.565058i
$452$	−32.0000			−1.50515
$453$	−14.0000	+	14.0000i	−0.657777	+	0.657777i
$454$			26.0000i			1.22024i
$455$	−9.00000	−	3.00000i	−0.421927	−	0.140642i
$456$	12.0000	−	12.0000i	0.561951	−	0.561951i
$457$	30.0000			1.40334			0.701670	−	0.712502i	$-0.252438\pi$
$457$	30.0000			1.40334			0.701670	+	0.712502i	$0.252438\pi$
$458$		−	14.0000i		−	0.654177i
$459$		0			0
$460$		0			0
$461$	5.00000	−	5.00000i	0.232873	−	0.232873i	−0.581018	−	0.813891i	$-0.697345\pi$
$461$	5.00000	−	5.00000i	0.232873	−	0.232873i	0.813891	+	0.581018i	$0.197345\pi$
$462$	2.00000	−	2.00000i	0.0930484	−	0.0930484i
$463$		−	22.0000i		−	1.02243i	−0.859454	−	0.511213i	$-0.829196\pi$
$463$		−	22.0000i		−	1.02243i	0.859454	−	0.511213i	$-0.170804\pi$
$464$	4.00000	−	4.00000i	0.185695	−	0.185695i
$465$	−24.0000	−	8.00000i	−1.11297	−	0.370991i
$466$	10.0000	+	10.0000i	0.463241	+	0.463241i
$467$	17.0000	+	17.0000i	0.786666	+	0.786666i	0.980946	−	0.194280i	$-0.0622370\pi$
$467$	17.0000	+	17.0000i	0.786666	+	0.786666i	−0.194280	+	0.980946i	$0.562237\pi$
$468$	6.00000	+	6.00000i	0.277350	+	0.277350i
$469$	−3.00000	−	3.00000i	−0.138527	−	0.138527i
$470$	10.0000	−	30.0000i	0.461266	−	1.38380i
$471$		−	34.0000i		−	1.56664i
$472$	4.00000			0.184115
$473$	2.00000			0.0919601
$474$		−	16.0000i		−	0.734904i
$475$	3.00000	+	21.0000i	0.137649	+	0.963546i
$476$		0			0
$477$	3.00000	+	3.00000i	0.137361	+	0.137361i
$478$	8.00000	+	8.00000i	0.365911	+	0.365911i
$479$	16.0000			0.731059			0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000			0.731059			0.365529	+	0.930800i	$0.380888\pi$
$480$	−8.00000	−	16.0000i	−0.365148	−	0.730297i
$481$	30.0000			1.36788
$482$	−10.0000	−	10.0000i	−0.455488	−	0.455488i
$483$		0			0
$484$	18.0000			0.818182
$485$	−8.00000	−	16.0000i	−0.363261	−	0.726523i
$486$		−	14.0000i		−	0.635053i
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$		−	28.0000i		−	1.26750i
$489$		−	10.0000i		−	0.452216i
$490$	3.00000	+	1.00000i	0.135526	+	0.0451754i
$491$	−15.0000	−	15.0000i	−0.676941	−	0.676941i	0.282366	−	0.959307i	$-0.408881\pi$
$491$	−15.0000	−	15.0000i	−0.676941	−	0.676941i	−0.959307	+	0.282366i	$0.908881\pi$
$492$	24.0000	+	24.0000i	1.08200	+	1.08200i
$493$		0			0
$494$	−18.0000	−	18.0000i	−0.809858	−	0.809858i
$495$	1.00000	−	3.00000i	0.0449467	−	0.134840i
$496$	32.0000			1.43684
$497$		−	6.00000i		−	0.269137i
$498$	−10.0000	+	10.0000i	−0.448111	+	0.448111i
$499$	19.0000	−	19.0000i	0.850557	−	0.850557i	−0.139645	−	0.990202i	$-0.544596\pi$
$499$	19.0000	−	19.0000i	0.850557	−	0.850557i	0.990202	+	0.139645i	$0.0445961\pi$
$500$	22.0000	+	4.00000i	0.983870	+	0.178885i
$501$	−24.0000	−	24.0000i	−1.07224	−	1.07224i
$502$			22.0000i			0.981908i
$503$	16.0000			0.713405			0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000			0.713405			0.356702	+	0.934218i	$0.383901\pi$
$504$	−2.00000	−	2.00000i	−0.0890871	−	0.0890871i
$505$	−21.0000	−	7.00000i	−0.934488	−	0.311496i
$506$		0			0
$507$	−5.00000	+	5.00000i	−0.222058	+	0.222058i
$508$	−36.0000			−1.59724
$509$	−7.00000	+	7.00000i	−0.310270	+	0.310270i	−0.845014	−	0.534744i	$-0.820408\pi$
$509$	−7.00000	+	7.00000i	−0.310270	+	0.310270i	0.534744	+	0.845014i	$0.320408\pi$
$510$		0			0
$511$	−10.0000			−0.442374
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$			24.0000i			1.05963i
$514$	−4.00000	+	4.00000i	−0.176432	+	0.176432i
$515$		0			0
$516$			4.00000i			0.176090i
$517$	10.0000	−	10.0000i	0.439799	−	0.439799i
$518$	−10.0000			−0.439375
$519$			14.0000i			0.614532i
$520$	−24.0000	+	12.0000i	−1.05247	+	0.526235i
$521$			4.00000i			0.175243i	0.996154	+	0.0876216i	$0.0279266\pi$
$521$			4.00000i			0.175243i	−0.996154	+	0.0876216i	$0.972073\pi$
$522$			2.00000i			0.0875376i
$523$	−9.00000	+	9.00000i	−0.393543	+	0.393543i	−0.875948	−	0.482405i	$-0.839763\pi$
$523$	−9.00000	+	9.00000i	−0.393543	+	0.393543i	0.482405	+	0.875948i	$0.339763\pi$
$524$	10.0000	+	10.0000i	0.436852	+	0.436852i
$525$	−7.00000	+	1.00000i	−0.305505	+	0.0436436i
$526$	−16.0000	−	16.0000i	−0.697633	−	0.697633i
$527$		0			0
$528$		−	8.00000i		−	0.348155i
$529$	−23.0000			−1.00000
$530$	−12.0000	+	6.00000i	−0.521247	+	0.260623i
$531$	−1.00000	+	1.00000i	−0.0433963	+	0.0433963i
$532$	6.00000	+	6.00000i	0.260133	+	0.260133i
$533$	36.0000	−	36.0000i	1.55933	−	1.55933i
$534$		0			0
$535$	9.00000	−	27.0000i	0.389104	−	1.16731i
$536$	−12.0000			−0.518321
$537$	−26.0000			−1.12198
$538$	−14.0000			−0.603583
$539$	1.00000	+	1.00000i	0.0430730	+	0.0430730i
$540$	24.0000	+	8.00000i	1.03280	+	0.344265i
$541$	−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	$0.338217\pi$
$542$	−24.0000	−	24.0000i	−1.03089	−	1.03089i
$543$		−	30.0000i		−	1.28742i
$544$		0			0
$545$	3.00000	−	9.00000i	0.128506	−	0.385518i
$546$	6.00000	−	6.00000i	0.256776	−	0.256776i
$547$	15.0000	+	15.0000i	0.641354	+	0.641354i	0.950888	−	0.309535i	$-0.100173\pi$
$547$	15.0000	+	15.0000i	0.641354	+	0.641354i	−0.309535	+	0.950888i	$0.600173\pi$
$548$		−	20.0000i		−	0.854358i
$549$	7.00000	+	7.00000i	0.298753	+	0.298753i
$550$	8.00000	+	6.00000i	0.341121	+	0.255841i
$551$		−	6.00000i		−	0.255609i
$552$		0			0
$553$	8.00000			0.340195
$554$	−30.0000			−1.27458
$555$	20.0000	−	10.0000i	0.848953	−	0.424476i
$556$	−6.00000	+	6.00000i	−0.254457	+	0.254457i
$557$	5.00000	+	5.00000i	0.211857	+	0.211857i	0.805056	−	0.593199i	$-0.202135\pi$
$557$	5.00000	+	5.00000i	0.211857	+	0.211857i	−0.593199	+	0.805056i	$0.702135\pi$
$558$	−8.00000	+	8.00000i	−0.338667	+	0.338667i
$559$	6.00000			0.253773
$560$	8.00000	−	4.00000i	0.338062	−	0.169031i
$561$		0			0
$562$	−28.0000	+	28.0000i	−1.18111	+	1.18111i
$563$	−3.00000	−	3.00000i	−0.126435	−	0.126435i	0.641058	−	0.767493i	$-0.278496\pi$
$563$	−3.00000	−	3.00000i	−0.126435	−	0.126435i	−0.767493	+	0.641058i	$0.778496\pi$
$564$	20.0000	+	20.0000i	0.842152	+	0.842152i
$565$	16.0000	+	32.0000i	0.673125	+	1.34625i
$566$	−18.0000			−0.756596
$567$	−5.00000			−0.209980
$568$	−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	$-0.167795\pi$
$570$	−18.0000	−	6.00000i	−0.753937	−	0.251312i
$571$	−23.0000	−	23.0000i	−0.962520	−	0.962520i	0.0368025	−	0.999323i	$-0.488283\pi$
$571$	−23.0000	−	23.0000i	−0.962520	−	0.962520i	−0.999323	+	0.0368025i	$0.988283\pi$
$572$	−12.0000			−0.501745
$573$	16.0000	+	16.0000i	0.668410	+	0.668410i
$574$	−12.0000	+	12.0000i	−0.500870	+	0.500870i
$575$		0			0
$576$	−8.00000			−0.333333
$577$		−	28.0000i		−	1.16566i	−0.812596	−	0.582828i	$-0.801946\pi$
$577$		−	28.0000i		−	1.16566i	0.812596	−	0.582828i	$-0.198054\pi$
$578$	17.0000	+	17.0000i	0.707107	+	0.707107i
$579$	−20.0000	+	20.0000i	−0.831172	+	0.831172i
$580$	−6.00000	−	2.00000i	−0.249136	−	0.0830455i
$581$	−5.00000	−	5.00000i	−0.207435	−	0.207435i
$582$	16.0000			0.663221
$583$	−6.00000			−0.248495
$584$	−20.0000	+	20.0000i	−0.827606	+	0.827606i
$585$	3.00000	−	9.00000i	0.124035	−	0.372104i
$586$	22.0000			0.908812
$587$	−21.0000	+	21.0000i	−0.866763	+	0.866763i	−0.992113	−	0.125350i	$-0.959995\pi$
$587$	−21.0000	+	21.0000i	−0.866763	+	0.866763i	0.125350	+	0.992113i	$0.459995\pi$
$588$	−2.00000	+	2.00000i	−0.0824786	+	0.0824786i
$589$	24.0000	−	24.0000i	0.988903	−	0.988903i
$590$	−2.00000	−	4.00000i	−0.0823387	−	0.164677i
$591$	2.00000			0.0822690
$592$	−20.0000	+	20.0000i	−0.821995	+	0.821995i
$593$			4.00000i			0.164260i	0.996622	+	0.0821302i	$0.0261723\pi$
$593$			4.00000i			0.164260i	−0.996622	+	0.0821302i	$0.973828\pi$
$594$	8.00000	+	8.00000i	0.328244	+	0.328244i
$595$		0			0
$596$	−22.0000	+	22.0000i	−0.901155	+	0.901155i
$597$	−10.0000	+	10.0000i	−0.409273	+	0.409273i
$598$		0			0
$599$		−	18.0000i		−	0.735460i	−0.929933	−	0.367730i	$-0.880135\pi$
$599$		−	18.0000i		−	0.735460i	0.929933	−	0.367730i	$-0.119865\pi$
$600$	−12.0000	+	16.0000i	−0.489898	+	0.653197i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$	−2.00000			−0.0815139
$603$	3.00000	−	3.00000i	0.122169	−	0.122169i
$604$	−28.0000			−1.13930
$605$	−9.00000	−	18.0000i	−0.365902	−	0.731804i
$606$	14.0000	−	14.0000i	0.568711	−	0.568711i
$607$			14.0000i			0.568242i	0.958788	+	0.284121i	$0.0917018\pi$
$607$			14.0000i			0.568242i	−0.958788	+	0.284121i	$0.908298\pi$
$608$	24.0000			0.973329
$609$	2.00000			0.0810441
$610$	−28.0000	+	14.0000i	−1.13369	+	0.566843i
$611$	30.0000	−	30.0000i	1.21367	−	1.21367i
$612$		0			0
$613$	−3.00000	+	3.00000i	−0.121169	+	0.121169i	−0.765091	−	0.643922i	$-0.777306\pi$
$613$	−3.00000	+	3.00000i	−0.121169	+	0.121169i	0.643922	+	0.765091i	$0.277306\pi$
$614$		−	30.0000i		−	1.21070i
$615$	12.0000	−	36.0000i	0.483887	−	1.45166i
$616$	4.00000			0.161165
$617$	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	$-0.370462\pi$
$619$	−13.0000	−	13.0000i	−0.522514	−	0.522514i	−0.918330	+	0.395816i	$0.870462\pi$
$620$	−16.0000	−	32.0000i	−0.642575	−	1.28515i
$621$		0			0
$622$	−26.0000	+	26.0000i	−1.04251	+	1.04251i
$623$		0			0
$624$		−	24.0000i		−	0.960769i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−10.0000	−	10.0000i	−0.399680	−	0.399680i
$627$	−6.00000	−	6.00000i	−0.239617	−	0.239617i
$628$	34.0000	−	34.0000i	1.35675	−	1.35675i
$629$		0			0
$630$	−1.00000	+	3.00000i	−0.0398410	+	0.119523i
$631$			46.0000i			1.83123i	0.402055	+	0.915616i	$0.368296\pi$
$631$			46.0000i			1.83123i	−0.402055	+	0.915616i	$0.631704\pi$
$632$	16.0000	−	16.0000i	0.636446	−	0.636446i
$633$	22.0000			0.874421
$634$			26.0000i			1.03259i
$635$	18.0000	+	36.0000i	0.714308	+	1.42862i
$636$		−	12.0000i		−	0.475831i
$637$	3.00000	+	3.00000i	0.118864	+	0.118864i
$638$	−2.00000	−	2.00000i	−0.0791808	−	0.0791808i
$639$	6.00000			0.237356
$640$	8.00000	−	24.0000i	0.316228	−	0.948683i
$641$	−2.00000			−0.0789953			−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000			−0.0789953			−0.0394976	+	0.999220i	$0.512576\pi$
$642$	18.0000	+	18.0000i	0.710403	+	0.710403i
$643$	−19.0000	−	19.0000i	−0.749287	−	0.749287i	0.225058	−	0.974345i	$-0.427743\pi$
$643$	−19.0000	−	19.0000i	−0.749287	−	0.749287i	−0.974345	+	0.225058i	$0.927743\pi$
$644$		0			0
$645$	4.00000	−	2.00000i	0.157500	−	0.0787499i
$646$		0			0
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$	−10.0000	+	10.0000i	−0.392837	+	0.392837i
$649$		−	2.00000i		−	0.0785069i
$650$	24.0000	+	18.0000i	0.941357	+	0.706018i
$651$	8.00000	+	8.00000i	0.313545	+	0.313545i
$652$	10.0000	−	10.0000i	0.391630	−	0.391630i
$653$	9.00000	+	9.00000i	0.352197	+	0.352197i	0.860927	−	0.508729i	$-0.169885\pi$
$653$	9.00000	+	9.00000i	0.352197	+	0.352197i	−0.508729	+	0.860927i	$0.669885\pi$
$654$	6.00000	+	6.00000i	0.234619	+	0.234619i
$655$	5.00000	−	15.0000i	0.195366	−	0.586098i
$656$			48.0000i			1.87409i
$657$		−	10.0000i		−	0.390137i
$658$	−10.0000	+	10.0000i	−0.389841	+	0.389841i
$659$	23.0000	−	23.0000i	0.895953	−	0.895953i	−0.0991224	−	0.995075i	$-0.531604\pi$
$659$	23.0000	−	23.0000i	0.895953	−	0.895953i	0.995075	+	0.0991224i	$0.0316036\pi$
$660$	−8.00000	+	4.00000i	−0.311400	+	0.155700i
$661$	1.00000	+	1.00000i	0.0388955	+	0.0388955i	0.726287	−	0.687392i	$-0.241244\pi$
$661$	1.00000	+	1.00000i	0.0388955	+	0.0388955i	−0.687392	+	0.726287i	$0.741244\pi$
$662$		−	30.0000i		−	1.16598i
$663$		0			0
$664$	−20.0000			−0.776151
$665$	3.00000	−	9.00000i	0.116335	−	0.349005i
$666$		−	10.0000i		−	0.387492i
$667$		0			0
$668$		−	48.0000i		−	1.85718i
$669$	2.00000	−	2.00000i	0.0773245	−	0.0773245i
$670$	6.00000	+	12.0000i	0.231800	+	0.463600i
$671$	−14.0000			−0.540464
$672$			8.00000i			0.308607i
$673$		−	44.0000i		−	1.69608i	−0.529936	−	0.848038i	$-0.677784\pi$
$673$		−	44.0000i		−	1.69608i	0.529936	−	0.848038i	$-0.322216\pi$
$674$	8.00000	−	8.00000i	0.308148	−	0.308148i
$675$	−4.00000	−	28.0000i	−0.153960	−	1.07772i
$676$	−10.0000			−0.384615
$677$	7.00000	−	7.00000i	0.269032	−	0.269032i	−0.559678	−	0.828710i	$-0.689075\pi$
$677$	7.00000	−	7.00000i	0.269032	−	0.269032i	0.828710	+	0.559678i	$0.189075\pi$
$678$	−32.0000			−1.22895
$679$			8.00000i			0.307012i
$680$		0			0
$681$			26.0000i			0.996322i
$682$		−	16.0000i		−	0.612672i
$683$	29.0000	−	29.0000i	1.10965	−	1.10965i	0.116459	−	0.993196i	$-0.462846\pi$
$683$	29.0000	−	29.0000i	1.10965	−	1.10965i	0.993196	−	0.116459i	$-0.0371542\pi$
$684$	−6.00000	+	6.00000i	−0.229416	+	0.229416i
$685$	−20.0000	+	10.0000i	−0.764161	+	0.382080i
$686$	−1.00000	−	1.00000i	−0.0381802	−	0.0381802i
$687$		−	14.0000i		−	0.534133i
$688$	−4.00000	+	4.00000i	−0.152499	+	0.152499i
$689$	−18.0000			−0.685745
$690$		0			0
$691$	1.00000	−	1.00000i	0.0380418	−	0.0380418i	−0.687830	−	0.725872i	$-0.741437\pi$
$691$	1.00000	−	1.00000i	0.0380418	−	0.0380418i	0.725872	+	0.687830i	$0.241437\pi$
$692$	−14.0000	+	14.0000i	−0.532200	+	0.532200i
$693$	−1.00000	+	1.00000i	−0.0379869	+	0.0379869i
$694$	34.0000			1.29062
$695$	9.00000	+	3.00000i	0.341389	+	0.113796i
$696$	4.00000	−	4.00000i	0.151620	−	0.151620i
$697$		0			0
$698$	−22.0000			−0.832712
$699$	10.0000	+	10.0000i	0.378235	+	0.378235i
$700$	−8.00000	−	6.00000i	−0.302372	−	0.226779i
$701$	−9.00000	+	9.00000i	−0.339925	+	0.339925i	−0.856339	−	0.516414i	$-0.827267\pi$
$701$	−9.00000	+	9.00000i	−0.339925	+	0.339925i	0.516414	+	0.856339i	$0.327267\pi$
$702$	24.0000	+	24.0000i	0.905822	+	0.905822i
$703$			30.0000i			1.13147i
$704$	8.00000	−	8.00000i	0.301511	−	0.301511i
$705$	10.0000	−	30.0000i	0.376622	−	1.12987i
$706$	−36.0000	+	36.0000i	−1.35488	+	1.35488i
$707$	7.00000	+	7.00000i	0.263262	+	0.263262i
$708$	4.00000			0.150329
$709$	31.0000	+	31.0000i	1.16423	+	1.16423i	0.983540	+	0.180689i	$0.0578328\pi$
$709$	31.0000	+	31.0000i	1.16423	+	1.16423i	0.180689	+	0.983540i	$0.442167\pi$
$710$	−6.00000	+	18.0000i	−0.225176	+	0.675528i
$711$			8.00000i			0.300023i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	6.00000	+	12.0000i	0.224387	+	0.448775i
$716$	−26.0000	−	26.0000i	−0.971666	−	0.971666i
$717$	8.00000	+	8.00000i	0.298765	+	0.298765i
$718$	−6.00000	+	6.00000i	−0.223918	+	0.223918i
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$	4.00000	+	8.00000i	0.149071	+	0.298142i
$721$		0			0
$722$	−1.00000	+	1.00000i	−0.0372161	+	0.0372161i
$723$	−10.0000	−	10.0000i	−0.371904	−	0.371904i
$724$	30.0000	−	30.0000i	1.11494	−	1.11494i
$725$	1.00000	+	7.00000i	0.0371391	+	0.259973i
$726$	18.0000			0.668043
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	12.0000			0.444750
$729$		−	29.0000i		−	1.07407i
$730$	30.0000	+	10.0000i	1.11035	+	0.370117i
$731$		0			0
$732$		−	28.0000i		−	1.03491i
$733$	31.0000	+	31.0000i	1.14501	+	1.14501i	0.987520	+	0.157491i	$0.0503404\pi$
$733$	31.0000	+	31.0000i	1.14501	+	1.14501i	0.157491	+	0.987520i	$0.449660\pi$
$734$	−6.00000	+	6.00000i	−0.221464	+	0.221464i
$735$	3.00000	+	1.00000i	0.110657	+	0.0368856i
$736$		0			0
$737$			6.00000i			0.221013i
$738$	−12.0000	−	12.0000i	−0.441726	−	0.441726i
$739$	−9.00000	+	9.00000i	−0.331070	+	0.331070i	−0.852993	−	0.521923i	$-0.825215\pi$
$739$	−9.00000	+	9.00000i	−0.331070	+	0.331070i	0.521923	+	0.852993i	$0.325215\pi$
$740$	30.0000	+	10.0000i	1.10282	+	0.367607i
$741$	−18.0000	−	18.0000i	−0.661247	−	0.661247i
$742$	6.00000			0.220267
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$	32.0000			1.17318
$745$	33.0000	+	11.0000i	1.20903	+	0.403009i
$746$	−30.0000			−1.09838
$747$	5.00000	−	5.00000i	0.182940	−	0.182940i
$748$		0			0
$749$	−9.00000	+	9.00000i	−0.328853	+	0.328853i
$750$	22.0000	+	4.00000i	0.803326	+	0.146059i
$751$	−40.0000			−1.45962			−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000			−1.45962			−0.729810	+	0.683650i	$0.760392\pi$
$752$			40.0000i			1.45865i
$753$			22.0000i			0.801725i
$754$	−6.00000	−	6.00000i	−0.218507	−	0.218507i
$755$	14.0000	+	28.0000i	0.509512	+	1.01902i
$756$	−8.00000	−	8.00000i	−0.290957	−	0.290957i
$757$	9.00000	−	9.00000i	0.327111	−	0.327111i	−0.524376	−	0.851487i	$-0.675701\pi$
$757$	9.00000	−	9.00000i	0.327111	−	0.327111i	0.851487	+	0.524376i	$0.175701\pi$
$758$		−	38.0000i		−	1.38022i
$759$		0			0
$760$	−12.0000	−	24.0000i	−0.435286	−	0.870572i
$761$			12.0000i			0.435000i	0.976060	+	0.217500i	$0.0697902\pi$
$761$			12.0000i			0.435000i	−0.976060	+	0.217500i	$0.930210\pi$
$762$	−36.0000			−1.30414
$763$	−3.00000	+	3.00000i	−0.108607	+	0.108607i
$764$			32.0000i			1.15772i
$765$		0			0
$766$	34.0000	−	34.0000i	1.22847	−	1.22847i
$767$		−	6.00000i		−	0.216647i
$768$	16.0000	+	16.0000i	0.577350	+	0.577350i
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$	−2.00000	−	4.00000i	−0.0720750	−	0.144150i
$771$	−4.00000	+	4.00000i	−0.144056	+	0.144056i
$772$	−40.0000			−1.43963
$773$	3.00000	−	3.00000i	0.107903	−	0.107903i	−0.651094	−	0.758997i	$-0.725690\pi$
$773$	3.00000	−	3.00000i	0.107903	−	0.107903i	0.758997	+	0.651094i	$0.225690\pi$
$774$		−	2.00000i		−	0.0718885i
$775$	−24.0000	+	32.0000i	−0.862105	+	1.14947i
$776$	16.0000	+	16.0000i	0.574367	+	0.574367i
$777$	−10.0000			−0.358748
$778$			22.0000i			0.788738i
$779$	36.0000	+	36.0000i	1.28983	+	1.28983i
$780$	−24.0000	+	12.0000i	−0.859338	+	0.429669i
$781$	−6.00000	+	6.00000i	−0.214697	+	0.214697i
$782$		0			0
$783$			8.00000i			0.285897i
$784$	−4.00000			−0.142857
$785$	−51.0000	−	17.0000i	−1.82027	−	0.606756i
$786$	10.0000	+	10.0000i	0.356688	+	0.356688i
$787$	13.0000	+	13.0000i	0.463400	+	0.463400i	0.899768	−	0.436368i	$-0.143735\pi$
$787$	13.0000	+	13.0000i	0.463400	+	0.463400i	−0.436368	+	0.899768i	$0.643735\pi$
$788$	2.00000	+	2.00000i	0.0712470	+	0.0712470i
$789$	−16.0000	−	16.0000i	−0.569615	−	0.569615i
$790$	−24.0000	−	8.00000i	−0.853882	−	0.284627i
$791$		−	16.0000i		−	0.568895i
$792$			4.00000i			0.142134i
$793$	−42.0000			−1.49146
$794$			30.0000i			1.06466i
$795$	−12.0000	+	6.00000i	−0.425596	+	0.212798i
$796$	−20.0000			−0.708881
$797$	11.0000	+	11.0000i	0.389640	+	0.389640i	0.874559	−	0.484919i	$-0.161151\pi$
$797$	11.0000	+	11.0000i	0.389640	+	0.389640i	−0.484919	+	0.874559i	$0.661151\pi$
$798$	6.00000	+	6.00000i	0.212398	+	0.212398i
$799$		0			0
$800$	−28.0000	+	4.00000i	−0.989949	+	0.141421i
$801$		0			0
$802$	30.0000	+	30.0000i	1.05934	+	1.05934i
$803$	10.0000	+	10.0000i	0.352892	+	0.352892i
$804$	−12.0000			−0.423207
$805$		0			0
$806$		−	48.0000i		−	1.69073i
$807$	−14.0000			−0.492823
$808$	28.0000			0.985037
$809$			56.0000i			1.96886i	0.175791	+	0.984428i	$0.443752\pi$
$809$			56.0000i			1.96886i	−0.175791	+	0.984428i	$0.556248\pi$
$810$	15.0000	+	5.00000i	0.527046	+	0.175682i
$811$	11.0000	+	11.0000i	0.386262	+	0.386262i	0.873352	−	0.487090i	$-0.161942\pi$
$811$	11.0000	+	11.0000i	0.386262	+	0.386262i	−0.487090	+	0.873352i	$0.661942\pi$
$812$	2.00000	+	2.00000i	0.0701862	+	0.0701862i
$813$	−24.0000	−	24.0000i	−0.841717	−	0.841717i
$814$	10.0000	+	10.0000i	0.350500	+	0.350500i
$815$	−15.0000	−	5.00000i	−0.525427	−	0.175142i
$816$		0			0
$817$			6.00000i			0.209913i
$818$	−12.0000	+	12.0000i	−0.419570	+	0.419570i
$819$	−3.00000	+	3.00000i	−0.104828	+	0.104828i
$820$	48.0000	−	24.0000i	1.67623	−	0.838116i
$821$	−25.0000	−	25.0000i	−0.872506	−	0.872506i	0.120239	−	0.992745i	$-0.461634\pi$
$821$	−25.0000	−	25.0000i	−0.872506	−	0.872506i	−0.992745	+	0.120239i	$0.961634\pi$
$822$		−	20.0000i		−	0.697580i
$823$	56.0000			1.95204			0.976019	−	0.217687i	$-0.0698512\pi$
$823$	56.0000			1.95204			0.976019	+	0.217687i	$0.0698512\pi$
$824$		0			0
$825$	8.00000	+	6.00000i	0.278524	+	0.208893i
$826$			2.00000i			0.0695889i
$827$	−31.0000	+	31.0000i	−1.07798	+	1.07798i	−0.0812847	+	0.996691i	$0.525902\pi$
$827$	−31.0000	+	31.0000i	−1.07798	+	1.07798i	−0.996691	+	0.0812847i	$0.974098\pi$
$828$		0			0
$829$	9.00000	−	9.00000i	0.312583	−	0.312583i	−0.533327	−	0.845909i	$-0.679058\pi$
$829$	9.00000	−	9.00000i	0.312583	−	0.312583i	0.845909	+	0.533327i	$0.179058\pi$
$830$	10.0000	+	20.0000i	0.347105	+	0.694210i
$831$	−30.0000			−1.04069
$832$	24.0000	−	24.0000i	0.832050	−	0.832050i
$833$		0			0
$834$	−6.00000	+	6.00000i	−0.207763	+	0.207763i
$835$	−48.0000	+	24.0000i	−1.66111	+	0.830554i
$836$		−	12.0000i		−	0.415029i
$837$	−32.0000	+	32.0000i	−1.10608	+	1.10608i
$838$	18.0000			0.621800
$839$		−	46.0000i		−	1.58810i	−0.607855	−	0.794048i	$-0.707970\pi$
$839$		−	46.0000i		−	1.58810i	0.607855	−	0.794048i	$-0.292030\pi$
$840$	8.00000	−	4.00000i	0.276026	−	0.138013i
$841$			27.0000i			0.931034i
$842$			38.0000i			1.30957i
$843$	−28.0000	+	28.0000i	−0.964371	+	0.964371i
$844$	22.0000	+	22.0000i	0.757271	+	0.757271i
$845$	5.00000	+	10.0000i	0.172005	+	0.344010i
$846$	−10.0000	−	10.0000i	−0.343807	−	0.343807i
$847$			9.00000i			0.309244i
$848$	12.0000	−	12.0000i	0.412082	−	0.412082i
$849$	−18.0000			−0.617758
$850$		0			0
$851$		0			0
$852$	−12.0000	−	12.0000i	−0.411113	−	0.411113i
$853$	7.00000	−	7.00000i	0.239675	−	0.239675i	−0.577040	−	0.816716i	$-0.695792\pi$
$853$	7.00000	−	7.00000i	0.239675	−	0.239675i	0.816716	+	0.577040i	$0.195792\pi$
$854$	14.0000			0.479070
$855$	9.00000	+	3.00000i	0.307794	+	0.102598i
$856$			36.0000i			1.23045i
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$	−12.0000			−0.409673
$859$	11.0000	+	11.0000i	0.375315	+	0.375315i	0.869409	−	0.494094i	$-0.164500\pi$
$859$	11.0000	+	11.0000i	0.375315	+	0.375315i	−0.494094	+	0.869409i	$0.664500\pi$
$860$	6.00000	+	2.00000i	0.204598	+	0.0681994i
$861$	−12.0000	+	12.0000i	−0.408959	+	0.408959i
$862$		0			0
$863$			26.0000i			0.885050i	0.896756	+	0.442525i	$0.145917\pi$
$863$			26.0000i			0.885050i	−0.896756	+	0.442525i	$0.854083\pi$
$864$	−32.0000			−1.08866
$865$	21.0000	+	7.00000i	0.714021	+	0.238007i
$866$	16.0000	−	16.0000i	0.543702	−	0.543702i
$867$	17.0000	+	17.0000i	0.577350	+	0.577350i
$868$			16.0000i			0.543075i
$869$	−8.00000	−	8.00000i	−0.271381	−	0.271381i
$870$	−6.00000	−	2.00000i	−0.203419	−	0.0678064i
$871$			18.0000i			0.609907i
$872$			12.0000i			0.406371i
$873$	−8.00000			−0.270759
$874$		0			0
$875$	−2.00000	+	11.0000i	−0.0676123	+	0.371868i
$876$	−20.0000	+	20.0000i	−0.675737	+	0.675737i
$877$	5.00000	+	5.00000i	0.168838	+	0.168838i	0.786468	−	0.617630i	$-0.211907\pi$
$877$	5.00000	+	5.00000i	0.168838	+	0.168838i	−0.617630	+	0.786468i	$0.711907\pi$
$878$	38.0000	−	38.0000i	1.28244	−	1.28244i
$879$	22.0000			0.742042
$880$	−12.0000	−	4.00000i	−0.404520	−	0.134840i
$881$	−14.0000			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$882$	1.00000	−	1.00000i	0.0336718	−	0.0336718i
$883$	−21.0000	−	21.0000i	−0.706706	−	0.706706i	0.259135	−	0.965841i	$-0.416563\pi$
$883$	−21.0000	−	21.0000i	−0.706706	−	0.706706i	−0.965841	+	0.259135i	$0.916563\pi$
$884$		0			0
$885$	−2.00000	−	4.00000i	−0.0672293	−	0.134459i
$886$	2.00000			0.0671913
$887$	48.0000			1.61168			0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000			1.61168			0.805841	+	0.592132i	$0.201714\pi$
$888$	−20.0000	+	20.0000i	−0.671156	+	0.671156i
$889$		−	18.0000i		−	0.603701i
$890$		0			0
$891$	5.00000	+	5.00000i	0.167506	+	0.167506i
$892$	4.00000			0.133930
$893$	30.0000	+	30.0000i	1.00391	+	1.00391i
$894$	−22.0000	+	22.0000i	−0.735790	+	0.735790i
$895$	−13.0000	+	39.0000i	−0.434542	+	1.30363i
$896$	−8.00000	+	8.00000i	−0.267261	+	0.267261i
$897$		0			0
$898$	−34.0000	−	34.0000i	−1.13459	−	1.13459i
$899$	8.00000	−	8.00000i	0.266815	−	0.266815i
$900$	6.00000	−	8.00000i	0.200000	−	0.266667i
$901$		0			0
$902$	24.0000			0.799113
$903$	−2.00000			−0.0665558
$904$	−32.0000	−	32.0000i	−1.06430	−	1.06430i
$905$	−45.0000	−	15.0000i	−1.49585	−	0.498617i
$906$	−28.0000			−0.930238
$907$	13.0000	−	13.0000i	0.431658	−	0.431658i	−0.457534	−	0.889192i	$-0.651267\pi$
$907$	13.0000	−	13.0000i	0.431658	−	0.431658i	0.889192	+	0.457534i	$0.151267\pi$
$908$	−26.0000	+	26.0000i	−0.862840	+	0.862840i
$909$	−7.00000	+	7.00000i	−0.232175	+	0.232175i
$910$	−6.00000	−	12.0000i	−0.198898	−	0.397796i
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$	24.0000			0.794719
$913$			10.0000i			0.330952i
$914$	30.0000	+	30.0000i	0.992312	+	0.992312i
$915$	−28.0000	+	14.0000i	−0.925651	+	0.462826i
$916$	14.0000	−	14.0000i	0.462573	−	0.462573i
$917$	−5.00000	+	5.00000i	−0.165115	+	0.165115i
$918$		0			0
$919$		−	10.0000i		−	0.329870i	−0.986304	−	0.164935i	$-0.947259\pi$
$919$		−	10.0000i		−	0.329870i	0.986304	−	0.164935i	$-0.0527414\pi$
$920$		0			0
$921$		−	30.0000i		−	0.988534i
$922$	10.0000			0.329332
$923$	−18.0000	+	18.0000i	−0.592477	+	0.592477i
$924$	4.00000			0.131590
$925$	−5.00000	−	35.0000i	−0.164399	−	1.15079i
$926$	22.0000	−	22.0000i	0.722965	−	0.722965i
$927$		0			0
$928$	8.00000			0.262613
$929$	30.0000			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$930$	−16.0000	−	32.0000i	−0.524661	−	1.04932i
$931$	−3.00000	+	3.00000i	−0.0983210	+	0.0983210i
$932$			20.0000i			0.655122i
$933$	−26.0000	+	26.0000i	−0.851202	+	0.851202i
$934$			34.0000i			1.11251i
$935$		0			0
$936$			12.0000i			0.392232i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		−	6.00000i		−	0.195907i
$939$	−10.0000	−	10.0000i	−0.326338	−	0.326338i
$940$	40.0000	−	20.0000i	1.30466	−	0.652328i
$941$	41.0000	−	41.0000i	1.33656	−	1.33656i	0.437195	−	0.899367i	$-0.355972\pi$
$941$	41.0000	−	41.0000i	1.33656	−	1.33656i	0.899367	−	0.437195i	$-0.144028\pi$
$942$	34.0000	−	34.0000i	1.10778	−	1.10778i
$943$		0			0
$944$	4.00000	+	4.00000i	0.130189	+	0.130189i
$945$	−4.00000	+	12.0000i	−0.130120	+	0.390360i
$946$	2.00000	+	2.00000i	0.0650256	+	0.0650256i
$947$	−1.00000	−	1.00000i	−0.0324956	−	0.0324956i	0.690672	−	0.723168i	$-0.257315\pi$
$947$	−1.00000	−	1.00000i	−0.0324956	−	0.0324956i	−0.723168	+	0.690672i	$0.757315\pi$
$948$	16.0000	−	16.0000i	0.519656	−	0.519656i
$949$	30.0000	+	30.0000i	0.973841	+	0.973841i
$950$	−18.0000	+	24.0000i	−0.583997	+	0.778663i
$951$			26.0000i			0.843108i
$952$		0			0
$953$	14.0000			0.453504			0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000			0.453504			0.226752	+	0.973952i	$0.427189\pi$
$954$			6.00000i			0.194257i
$955$	32.0000	−	16.0000i	1.03550	−	0.517748i
$956$			16.0000i			0.517477i
$957$	−2.00000	−	2.00000i	−0.0646508	−	0.0646508i
$958$	16.0000	+	16.0000i	0.516937	+	0.516937i
$959$	10.0000			0.322917
$960$	8.00000	−	24.0000i	0.258199	−	0.774597i
$961$	33.0000			1.06452
$962$	30.0000	+	30.0000i	0.967239	+	0.967239i
$963$	−9.00000	−	9.00000i	−0.290021	−	0.290021i
$964$		−	20.0000i		−	0.644157i
$965$	20.0000	+	40.0000i	0.643823	+	1.28765i
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	18.0000	+	18.0000i	0.578542	+	0.578542i
$969$		0			0
$970$	8.00000	−	24.0000i	0.256865	−	0.770594i
$971$	31.0000	+	31.0000i	0.994837	+	0.994837i	0.999987	−	0.00514940i	$-0.00163911\pi$
$971$	31.0000	+	31.0000i	0.994837	+	0.994837i	−0.00514940	+	0.999987i	$0.501639\pi$
$972$	14.0000	−	14.0000i	0.449050	−	0.449050i
$973$	−3.00000	−	3.00000i	−0.0961756	−	0.0961756i
$974$	8.00000	+	8.00000i	0.256337	+	0.256337i
$975$	24.0000	+	18.0000i	0.768615	+	0.576461i
$976$	28.0000	−	28.0000i	0.896258	−	0.896258i
$977$			12.0000i			0.383914i	0.981403	+	0.191957i	$0.0614834\pi$
$977$			12.0000i			0.383914i	−0.981403	+	0.191957i	$0.938517\pi$
$978$	10.0000	−	10.0000i	0.319765	−	0.319765i
$979$		0			0
$980$	2.00000	+	4.00000i	0.0638877	+	0.127775i
$981$	−3.00000	−	3.00000i	−0.0957826	−	0.0957826i
$982$		−	30.0000i		−	0.957338i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$			48.0000i			1.53018i
$985$	1.00000	−	3.00000i	0.0318626	−	0.0955879i
$986$		0			0
$987$	−10.0000	+	10.0000i	−0.318304	+	0.318304i
$988$		−	36.0000i		−	1.14531i
$989$		0			0
$990$	4.00000	−	2.00000i	0.127128	−	0.0635642i
$991$	−24.0000			−0.762385			−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000			−0.762385			−0.381193	+	0.924496i	$0.624487\pi$
$992$	32.0000	+	32.0000i	1.01600	+	1.01600i
$993$		−	30.0000i		−	0.952021i
$994$	6.00000	−	6.00000i	0.190308	−	0.190308i
$995$	10.0000	+	20.0000i	0.317021	+	0.634043i
$996$	−20.0000			−0.633724
$997$	27.0000	−	27.0000i	0.855099	−	0.855099i	−0.135657	−	0.990756i	$-0.543315\pi$
$997$	27.0000	−	27.0000i	0.855099	−	0.855099i	0.990756	+	0.135657i	$0.0433146\pi$
$998$	38.0000			1.20287
$999$		−	40.0000i		−	1.26554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.b.309.1	yes	2
5.4	even	2		560.2.bb.a.309.1	yes	2
16.13	even	4		560.2.bb.a.29.1	✓	2
80.29	even	4	inner	560.2.bb.b.29.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.a.29.1	✓	2	16.13	even	4
560.2.bb.a.309.1	yes	2	5.4	even	2
560.2.bb.b.29.1	yes	2	80.29	even	4	inner
560.2.bb.b.309.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.00000 + 1.00000i) q^{3} +2.00000i q^{4} +(2.00000 - 1.00000i) q^{5} +2.00000i q^{6} -1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(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} -1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +(3.00000 + 1.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(-2.00000 + 2.00000i) q^{12} +(3.00000 + 3.00000i) q^{13} +(-1.00000 - 1.00000i) q^{14} +(3.00000 + 1.00000i) q^{15} -4.00000 q^{16} +(1.00000 - 1.00000i) q^{18} +(-3.00000 + 3.00000i) q^{19} +(2.00000 + 4.00000i) q^{20} +(-1.00000 - 1.00000i) q^{21} +2.00000i q^{22} -4.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +6.00000i q^{26} +(4.00000 - 4.00000i) q^{27} -2.00000i q^{28} +(-1.00000 + 1.00000i) q^{29} +(2.00000 + 4.00000i) q^{30} -8.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +2.00000i q^{33} +(-2.00000 + 1.00000i) q^{35} +2.00000 q^{36} +(5.00000 - 5.00000i) q^{37} -6.00000 q^{38} +6.00000i q^{39} +(-2.00000 + 6.00000i) q^{40} -12.0000i q^{41} -2.00000i q^{42} +(1.00000 - 1.00000i) q^{43} +(-2.00000 + 2.00000i) q^{44} +(-1.00000 - 2.00000i) q^{45} -10.0000i q^{47} +(-4.00000 - 4.00000i) q^{48} +1.00000 q^{49} +(7.00000 - 1.00000i) q^{50} +(-6.00000 + 6.00000i) q^{52} +(-3.00000 + 3.00000i) q^{53} +8.00000 q^{54} +(3.00000 + 1.00000i) q^{55} +(2.00000 - 2.00000i) q^{56} -6.00000 q^{57} -2.00000 q^{58} +(-1.00000 - 1.00000i) q^{59} +(-2.00000 + 6.00000i) q^{60} +(-7.00000 + 7.00000i) q^{61} +(-8.00000 - 8.00000i) q^{62} +1.00000i q^{63} -8.00000i q^{64} +(9.00000 + 3.00000i) q^{65} +(-2.00000 + 2.00000i) q^{66} +(3.00000 + 3.00000i) q^{67} +(-3.00000 - 1.00000i) q^{70} +6.00000i q^{71} +(2.00000 + 2.00000i) q^{72} +10.0000 q^{73} +10.0000 q^{74} +(7.00000 - 1.00000i) q^{75} +(-6.00000 - 6.00000i) q^{76} +(-1.00000 - 1.00000i) q^{77} +(-6.00000 + 6.00000i) q^{78} -8.00000 q^{79} +(-8.00000 + 4.00000i) q^{80} +5.00000 q^{81} +(12.0000 - 12.0000i) q^{82} +(5.00000 + 5.00000i) q^{83} +(2.00000 - 2.00000i) q^{84} +2.00000 q^{86} -2.00000 q^{87} -4.00000 q^{88} +(1.00000 - 3.00000i) q^{90} +(-3.00000 - 3.00000i) q^{91} +(-8.00000 - 8.00000i) q^{93} +(10.0000 - 10.0000i) q^{94} +(-3.00000 + 9.00000i) q^{95} -8.00000i q^{96} -8.00000i q^{97} +(1.00000 + 1.00000i) q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 2 * q^7 - 4 * q^8	\( 2 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 2 q^{7} - 4 q^{8} + 6 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 2 q^{18} - 6 q^{19} + 4 q^{20} - 2 q^{21} - 8 q^{24} + 6 q^{25} + 8 q^{27} - 2 q^{29} + 4 q^{30} - 16 q^{31} - 8 q^{32} - 4 q^{35} + 4 q^{36} + 10 q^{37} - 12 q^{38} - 4 q^{40} + 2 q^{43} - 4 q^{44} - 2 q^{45} - 8 q^{48} + 2 q^{49} + 14 q^{50} - 12 q^{52} - 6 q^{53} + 16 q^{54} + 6 q^{55} + 4 q^{56} - 12 q^{57} - 4 q^{58} - 2 q^{59} - 4 q^{60} - 14 q^{61} - 16 q^{62} + 18 q^{65} - 4 q^{66} + 6 q^{67} - 6 q^{70} + 4 q^{72} + 20 q^{73} + 20 q^{74} + 14 q^{75} - 12 q^{76} - 2 q^{77} - 12 q^{78} - 16 q^{79} - 16 q^{80} + 10 q^{81} + 24 q^{82} + 10 q^{83} + 4 q^{84} + 4 q^{86} - 4 q^{87} - 8 q^{88} + 2 q^{90} - 6 q^{91} - 16 q^{93} + 20 q^{94} - 6 q^{95} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 2 * q^7 - 4 * q^8 + 6 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 2 * q^18 - 6 * q^19 + 4 * q^20 - 2 * q^21 - 8 * q^24 + 6 * q^25 + 8 * q^27 - 2 * q^29 + 4 * q^30 - 16 * q^31 - 8 * q^32 - 4 * q^35 + 4 * q^36 + 10 * q^37 - 12 * q^38 - 4 * q^40 + 2 * q^43 - 4 * q^44 - 2 * q^45 - 8 * q^48 + 2 * q^49 + 14 * q^50 - 12 * q^52 - 6 * q^53 + 16 * q^54 + 6 * q^55 + 4 * q^56 - 12 * q^57 - 4 * q^58 - 2 * q^59 - 4 * q^60 - 14 * q^61 - 16 * q^62 + 18 * q^65 - 4 * q^66 + 6 * q^67 - 6 * q^70 + 4 * q^72 + 20 * q^73 + 20 * q^74 + 14 * q^75 - 12 * q^76 - 2 * q^77 - 12 * q^78 - 16 * q^79 - 16 * q^80 + 10 * q^81 + 24 * q^82 + 10 * q^83 + 4 * q^84 + 4 * q^86 - 4 * q^87 - 8 * q^88 + 2 * q^90 - 6 * q^91 - 16 * q^93 + 20 * q^94 - 6 * q^95 + 2 * q^98 + 2 * q^99

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