LMFDB - Embedded newform 720.2.bm.a.469.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(109,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("720.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bm (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,0,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$1$
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:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			469.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	720.469
Dual form			720.2.bm.a.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(2.00000 - 2.00000i) q^{8} +(1.00000 + 3.00000i) q^{10} +(3.00000 + 3.00000i) q^{11} +(-3.00000 - 3.00000i) q^{13} -4.00000 q^{16} -4.00000i q^{17} +(-1.00000 + 1.00000i) q^{19} +(2.00000 - 4.00000i) q^{20} -6.00000i q^{22} -8.00000 q^{23} +(3.00000 + 4.00000i) q^{25} +6.00000i q^{26} +(-3.00000 + 3.00000i) q^{29} +(4.00000 + 4.00000i) q^{32} +(-4.00000 + 4.00000i) q^{34} +(-3.00000 + 3.00000i) q^{37} +2.00000 q^{38} +(-6.00000 + 2.00000i) q^{40} +(-3.00000 + 3.00000i) q^{43} +(-6.00000 + 6.00000i) q^{44} +(8.00000 + 8.00000i) q^{46} -2.00000i q^{47} -7.00000 q^{49} +(1.00000 - 7.00000i) q^{50} +(6.00000 - 6.00000i) q^{52} +(-9.00000 + 9.00000i) q^{53} +(-3.00000 - 9.00000i) q^{55} +6.00000 q^{58} +(-9.00000 - 9.00000i) q^{59} +(-5.00000 + 5.00000i) q^{61} -8.00000i q^{64} +(3.00000 + 9.00000i) q^{65} +(3.00000 + 3.00000i) q^{67} +8.00000 q^{68} -6.00000i q^{71} -6.00000 q^{73} +6.00000 q^{74} +(-2.00000 - 2.00000i) q^{76} +8.00000 q^{79} +(8.00000 + 4.00000i) q^{80} +(9.00000 + 9.00000i) q^{83} +(-4.00000 + 8.00000i) q^{85} +6.00000 q^{86} +12.0000 q^{88} +12.0000i q^{89} -16.0000i q^{92} +(-2.00000 + 2.00000i) q^{94} +(3.00000 - 1.00000i) q^{95} -12.0000i q^{97} +(7.00000 + 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 2 q^{10} + 6 q^{11} - 6 q^{13} - 8 q^{16} - 2 q^{19} + 4 q^{20} - 16 q^{23} + 6 q^{25} - 6 q^{29} + 8 q^{32} - 8 q^{34} - 6 q^{37} + 4 q^{38} - 12 q^{40} - 6 q^{43} - 12 q^{44}+ \cdots + 14 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 2 * q^10 + 6 * q^11 - 6 * q^13 - 8 * q^16 - 2 * q^19 + 4 * q^20 - 16 * q^23 + 6 * q^25 - 6 * q^29 + 8 * q^32 - 8 * q^34 - 6 * q^37 + 4 * q^38 - 12 * q^40 - 6 * q^43 - 12 * q^44 + 16 * q^46 - 14 * q^49 + 2 * q^50 + 12 * q^52 - 18 * q^53 - 6 * q^55 + 12 * q^58 - 18 * q^59 - 10 * q^61 + 6 * q^65 + 6 * q^67 + 16 * q^68 - 12 * q^73 + 12 * q^74 - 4 * q^76 + 16 * q^79 + 16 * q^80 + 18 * q^83 - 8 * q^85 + 12 * q^86 + 24 * q^88 - 4 * q^94 + 6 * q^95 + 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	1.00000	+	3.00000i	0.316228	+	0.948683i
$11$	3.00000	+	3.00000i	0.904534	+	0.904534i	0.995824	−	0.0912903i	$-0.0290991\pi$
$11$	3.00000	+	3.00000i	0.904534	+	0.904534i	−0.0912903	+	0.995824i	$0.529099\pi$
$12$		0			0
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$		0			0
$15$		0			0
$16$	−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	$-0.161206\pi$
$18$		0			0
$19$	−1.00000	+	1.00000i	−0.229416	+	0.229416i	−0.812449	−	0.583033i	$-0.801866\pi$
$19$	−1.00000	+	1.00000i	−0.229416	+	0.229416i	0.583033	+	0.812449i	$0.301866\pi$
$20$	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	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$			6.00000i			1.17670i
$27$		0			0
$28$		0			0
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$		0			0
$34$	−4.00000	+	4.00000i	−0.685994	+	0.685994i
$35$		0			0
$36$		0			0
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	−0.909312	−	0.416115i	$-0.863391\pi$
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	0.416115	+	0.909312i	$0.363391\pi$
$38$	2.00000			0.324443
$39$		0			0
$40$	−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	−0.897833	−	0.440337i	$-0.854859\pi$
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	0.440337	+	0.897833i	$0.354859\pi$
$44$	−6.00000	+	6.00000i	−0.904534	+	0.904534i
$45$		0			0
$46$	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	$-0.0465965\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$	1.00000	−	7.00000i	0.141421	−	0.989949i
$51$		0			0
$52$	6.00000	−	6.00000i	0.832050	−	0.832050i
$53$	−9.00000	+	9.00000i	−1.23625	+	1.23625i	−0.274721	+	0.961524i	$0.588586\pi$
$53$	−9.00000	+	9.00000i	−1.23625	+	1.23625i	−0.961524	+	0.274721i	$0.911414\pi$
$54$		0			0
$55$	−3.00000	−	9.00000i	−0.404520	−	1.21356i
$56$		0			0
$57$		0			0
$58$	6.00000			0.787839
$59$	−9.00000	−	9.00000i	−1.17170	−	1.17170i	−0.981804	−	0.189896i	$-0.939185\pi$
$59$	−9.00000	−	9.00000i	−1.17170	−	1.17170i	−0.189896	−	0.981804i	$-0.560815\pi$
$60$		0			0
$61$	−5.00000	+	5.00000i	−0.640184	+	0.640184i	−0.950601	−	0.310416i	$-0.899532\pi$
$61$	−5.00000	+	5.00000i	−0.640184	+	0.640184i	0.310416	+	0.950601i	$0.399532\pi$
$62$		0			0
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	3.00000	+	9.00000i	0.372104	+	1.11631i
$66$		0			0
$67$	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	$0.666554\pi$
$68$	8.00000			0.970143
$69$		0			0
$70$		0			0
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	−2.00000	−	2.00000i	−0.229416	−	0.229416i
$77$		0			0
$78$		0			0
$79$	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
$81$		0			0
$82$		0			0
$83$	9.00000	+	9.00000i	0.987878	+	0.987878i	0.999927	−	0.0120491i	$-0.00383543\pi$
$83$	9.00000	+	9.00000i	0.987878	+	0.987878i	−0.0120491	+	0.999927i	$0.503835\pi$
$84$		0			0
$85$	−4.00000	+	8.00000i	−0.433861	+	0.867722i
$86$	6.00000			0.646997
$87$		0			0
$88$	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	$0.780588\pi$
$90$		0			0
$91$		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
$96$		0			0
$97$		−	12.0000i		−	1.21842i	−0.793011	−	0.609208i	$-0.791488\pi$
$97$		−	12.0000i		−	1.21842i	0.793011	−	0.609208i	$-0.208512\pi$
$98$	7.00000	+	7.00000i	0.707107	+	0.707107i
$99$		0			0
$100$	−8.00000	+	6.00000i	−0.800000	+	0.600000i
$101$	−3.00000	−	3.00000i	−0.298511	−	0.298511i	0.541919	−	0.840431i	$-0.317698\pi$
$101$	−3.00000	−	3.00000i	−0.298511	−	0.298511i	−0.840431	+	0.541919i	$0.817698\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−12.0000			−1.17670
$105$		0			0
$106$	18.0000			1.74831
$107$	−9.00000	+	9.00000i	−0.870063	+	0.870063i	−0.992479	−	0.122416i	$-0.960936\pi$
$107$	−9.00000	+	9.00000i	−0.870063	+	0.870063i	0.122416	+	0.992479i	$0.460936\pi$
$108$		0			0
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	−0.753374	−	0.657592i	$-0.771575\pi$
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	0.657592	+	0.753374i	$0.271575\pi$
$110$	−6.00000	+	12.0000i	−0.572078	+	1.14416i
$111$		0			0
$112$		0			0
$113$		−	8.00000i		−	0.752577i	−0.926503	−	0.376288i	$-0.877200\pi$
$113$		−	8.00000i		−	0.752577i	0.926503	−	0.376288i	$-0.122800\pi$
$114$		0			0
$115$	16.0000	+	8.00000i	1.49201	+	0.746004i
$116$	−6.00000	−	6.00000i	−0.557086	−	0.557086i
$117$		0			0
$118$			18.0000i			1.65703i
$119$		0			0
$120$		0			0
$121$			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	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$		0			0
$130$	6.00000	−	12.0000i	0.526235	−	1.05247i
$131$	9.00000	−	9.00000i	0.786334	−	0.786334i	−0.194557	−	0.980891i	$-0.562327\pi$
$131$	9.00000	−	9.00000i	0.786334	−	0.786334i	0.980891	+	0.194557i	$0.0623271\pi$
$132$		0			0
$133$		0			0
$134$		−	6.00000i		−	0.518321i
$135$		0			0
$136$	−8.00000	−	8.00000i	−0.685994	−	0.685994i
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$		0			0
$139$	−7.00000	−	7.00000i	−0.593732	−	0.593732i	0.344905	−	0.938638i	$-0.387911\pi$
$139$	−7.00000	−	7.00000i	−0.593732	−	0.593732i	−0.938638	+	0.344905i	$0.887911\pi$
$140$		0			0
$141$		0			0
$142$	−6.00000	+	6.00000i	−0.503509	+	0.503509i
$143$		−	18.0000i		−	1.50524i
$144$		0			0
$145$	9.00000	−	3.00000i	0.747409	−	0.249136i
$146$	6.00000	+	6.00000i	0.496564	+	0.496564i
$147$		0			0
$148$	−6.00000	−	6.00000i	−0.493197	−	0.493197i
$149$	−3.00000	−	3.00000i	−0.245770	−	0.245770i	0.573462	−	0.819232i	$-0.305600\pi$
$149$	−3.00000	−	3.00000i	−0.245770	−	0.245770i	−0.819232	+	0.573462i	$0.805600\pi$
$150$		0			0
$151$		−	18.0000i		−	1.46482i	−0.680864	−	0.732410i	$-0.738396\pi$
$151$		−	18.0000i		−	1.46482i	0.680864	−	0.732410i	$-0.261604\pi$
$152$			4.00000i			0.324443i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.00000	+	9.00000i	0.718278	+	0.718278i	0.968252	−	0.249974i	$-0.0804222\pi$
$157$	9.00000	+	9.00000i	0.718278	+	0.718278i	−0.249974	+	0.968252i	$0.580422\pi$
$158$	−8.00000	−	8.00000i	−0.636446	−	0.636446i
$159$		0			0
$160$	−4.00000	−	12.0000i	−0.316228	−	0.948683i
$161$		0			0
$162$		0			0
$163$	−9.00000	−	9.00000i	−0.704934	−	0.704934i	0.260531	−	0.965465i	$-0.416102\pi$
$163$	−9.00000	−	9.00000i	−0.704934	−	0.704934i	−0.965465	+	0.260531i	$0.916102\pi$
$164$		0			0
$165$		0			0
$166$		−	18.0000i		−	1.39707i
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	12.0000	−	4.00000i	0.920358	−	0.306786i
$171$		0			0
$172$	−6.00000	−	6.00000i	−0.457496	−	0.457496i
$173$	−9.00000	−	9.00000i	−0.684257	−	0.684257i	0.276699	−	0.960957i	$-0.410759\pi$
$173$	−9.00000	−	9.00000i	−0.684257	−	0.684257i	−0.960957	+	0.276699i	$0.910759\pi$
$174$		0			0
$175$		0			0
$176$	−12.0000	−	12.0000i	−0.904534	−	0.904534i
$177$		0			0
$178$	12.0000	−	12.0000i	0.899438	−	0.899438i
$179$	−3.00000	+	3.00000i	−0.224231	+	0.224231i	−0.810277	−	0.586047i	$-0.800683\pi$
$179$	−3.00000	+	3.00000i	−0.224231	+	0.224231i	0.586047	+	0.810277i	$0.300683\pi$
$180$		0			0
$181$	−1.00000	−	1.00000i	−0.0743294	−	0.0743294i	0.668965	−	0.743294i	$-0.266738\pi$
$181$	−1.00000	−	1.00000i	−0.0743294	−	0.0743294i	−0.743294	+	0.668965i	$0.766738\pi$
$182$		0			0
$183$		0			0
$184$	−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	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$		0			0
$193$			12.0000i			0.863779i	0.901927	+	0.431889i	$0.142153\pi$
$193$			12.0000i			0.863779i	−0.901927	+	0.431889i	$0.857847\pi$
$194$	−12.0000	+	12.0000i	−0.861550	+	0.861550i
$195$		0			0
$196$		−	14.0000i		−	1.00000i
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	−0.862423	−	0.506188i	$-0.831054\pi$
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	0.506188	+	0.862423i	$0.331054\pi$
$198$		0			0
$199$		−	2.00000i		−	0.141776i	−0.997484	−	0.0708881i	$-0.977417\pi$
$199$		−	2.00000i		−	0.141776i	0.997484	−	0.0708881i	$-0.0225833\pi$
$200$	14.0000	+	2.00000i	0.989949	+	0.141421i
$201$		0			0
$202$			6.00000i			0.422159i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	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	−0.218554	−	0.975825i	$-0.570134\pi$
$211$	11.0000	−	11.0000i	0.757271	−	0.757271i	0.975825	+	0.218554i	$0.0701339\pi$
$212$	−18.0000	−	18.0000i	−1.23625	−	1.23625i
$213$		0			0
$214$	18.0000			1.23045
$215$	9.00000	−	3.00000i	0.613795	−	0.204598i
$216$		0			0
$217$		0			0
$218$	2.00000			0.135457
$219$		0			0
$220$	18.0000	−	6.00000i	1.21356	−	0.404520i
$221$	−12.0000	+	12.0000i	−0.807207	+	0.807207i
$222$		0			0
$223$		−	6.00000i		−	0.401790i	−0.979613	−	0.200895i	$-0.935615\pi$
$223$		−	6.00000i		−	0.401790i	0.979613	−	0.200895i	$-0.0643850\pi$
$224$		0			0
$225$		0			0
$226$	−8.00000	+	8.00000i	−0.532152	+	0.532152i
$227$	9.00000	+	9.00000i	0.597351	+	0.597351i	0.939607	−	0.342256i	$-0.111191\pi$
$227$	9.00000	+	9.00000i	0.597351	+	0.597351i	−0.342256	+	0.939607i	$0.611191\pi$
$228$		0			0
$229$	7.00000	+	7.00000i	0.462573	+	0.462573i	0.899498	−	0.436925i	$-0.143932\pi$
$229$	7.00000	+	7.00000i	0.462573	+	0.462573i	−0.436925	+	0.899498i	$0.643932\pi$
$230$	−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	$-0.243851\pi$
$233$	22.0000			1.44127			0.720634	+	0.693316i	$0.243851\pi$
$234$		0			0
$235$	−2.00000	+	4.00000i	−0.130466	+	0.260931i
$236$	18.0000	−	18.0000i	1.17170	−	1.17170i
$237$		0			0
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−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
$249$		0			0
$250$	−9.00000	+	13.0000i	−0.569210	+	0.822192i
$251$	−9.00000	−	9.00000i	−0.568075	−	0.568075i	0.363514	−	0.931589i	$-0.381577\pi$
$251$	−9.00000	−	9.00000i	−0.568075	−	0.568075i	−0.931589	+	0.363514i	$0.881577\pi$
$252$		0			0
$253$	−24.0000	−	24.0000i	−1.50887	−	1.50887i
$254$	−6.00000	+	6.00000i	−0.376473	+	0.376473i
$255$		0			0
$256$	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	$-0.0802706\pi$
$258$		0			0
$259$		0			0
$260$	−18.0000	+	6.00000i	−1.11631	+	0.372104i
$261$		0			0
$262$	−18.0000			−1.11204
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$		0			0
$265$	27.0000	−	9.00000i	1.65860	−	0.552866i
$266$		0			0
$267$		0			0
$268$	−6.00000	+	6.00000i	−0.366508	+	0.366508i
$269$	9.00000	−	9.00000i	0.548740	−	0.548740i	−0.377337	−	0.926076i	$-0.623160\pi$
$269$	9.00000	−	9.00000i	0.548740	−	0.548740i	0.926076	+	0.377337i	$0.123160\pi$
$270$		0			0
$271$	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
$276$		0			0
$277$	−3.00000	+	3.00000i	−0.180253	+	0.180253i	−0.791466	−	0.611213i	$-0.790682\pi$
$277$	−3.00000	+	3.00000i	−0.180253	+	0.180253i	0.611213	+	0.791466i	$0.290682\pi$
$278$			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	$0.883483\pi$
$282$		0			0
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	−0.994679	−	0.103022i	$-0.967149\pi$
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	0.103022	+	0.994679i	$0.467149\pi$
$284$	12.0000			0.712069
$285$		0			0
$286$	−18.0000	+	18.0000i	−1.06436	+	1.06436i
$287$		0			0
$288$		0			0
$289$	1.00000			0.0588235
$290$	−12.0000	−	6.00000i	−0.704664	−	0.352332i
$291$		0			0
$292$		−	12.0000i		−	0.702247i
$293$	−9.00000	+	9.00000i	−0.525786	+	0.525786i	−0.919313	−	0.393527i	$-0.871255\pi$
$293$	−9.00000	+	9.00000i	−0.525786	+	0.525786i	0.393527	+	0.919313i	$0.371255\pi$
$294$		0			0
$295$	9.00000	+	27.0000i	0.524000	+	1.57200i
$296$			12.0000i			0.697486i
$297$		0			0
$298$			6.00000i			0.347571i
$299$	24.0000	+	24.0000i	1.38796	+	1.38796i
$300$		0			0
$301$		0			0
$302$	−18.0000	+	18.0000i	−1.03578	+	1.03578i
$303$		0			0
$304$	4.00000	−	4.00000i	0.229416	−	0.229416i
$305$	15.0000	−	5.00000i	0.858898	−	0.286299i
$306$		0			0
$307$	3.00000	+	3.00000i	0.171219	+	0.171219i	0.787515	−	0.616296i	$-0.211367\pi$
$307$	3.00000	+	3.00000i	0.171219	+	0.171219i	−0.616296	+	0.787515i	$0.711367\pi$
$308$		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	$-0.0544137\pi$
$312$		0			0
$313$	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	$-0.160327\pi$
$317$	7.00000	+	7.00000i	0.393159	+	0.393159i	−0.482653	+	0.875812i	$0.660327\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$	−8.00000	+	16.0000i	−0.447214	+	0.894427i
$321$		0			0
$322$		0			0
$323$	4.00000	+	4.00000i	0.222566	+	0.222566i
$324$		0			0
$325$	3.00000	−	21.0000i	0.166410	−	1.16487i
$326$			18.0000i			0.996928i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	5.00000	+	5.00000i	0.274825	+	0.274825i	0.831039	−	0.556214i	$-0.187747\pi$
$331$	5.00000	+	5.00000i	0.274825	+	0.274825i	−0.556214	+	0.831039i	$0.687747\pi$
$332$	−18.0000	+	18.0000i	−0.987878	+	0.987878i
$333$		0			0
$334$	−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	$0.226776\pi$
$337$			24.0000i			1.30736i	−0.756770	+	0.653682i	$0.773224\pi$
$338$	5.00000	−	5.00000i	0.271964	−	0.271964i
$339$		0			0
$340$	−16.0000	−	8.00000i	−0.867722	−	0.433861i
$341$		0			0
$342$		0			0
$343$		0			0
$344$			12.0000i			0.646997i
$345$		0			0
$346$			18.0000i			0.967686i
$347$	19.0000	−	19.0000i	1.01997	−	1.01997i	0.0201770	−	0.999796i	$-0.493577\pi$
$347$	19.0000	−	19.0000i	1.01997	−	1.01997i	0.999796	−	0.0201770i	$-0.00642298\pi$
$348$		0			0
$349$	−5.00000	+	5.00000i	−0.267644	+	0.267644i	−0.828150	−	0.560506i	$-0.810607\pi$
$349$	−5.00000	+	5.00000i	−0.267644	+	0.267644i	0.560506	+	0.828150i	$0.310607\pi$
$350$		0			0
$351$		0			0
$352$			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	$-0.140006\pi$
$354$		0			0
$355$	−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	$0.842447\pi$
$360$		0			0
$361$			17.0000i			0.894737i
$362$			2.00000i			0.105118i
$363$		0			0
$364$		0			0
$365$	12.0000	+	6.00000i	0.628109	+	0.314054i
$366$		0			0
$367$			18.0000i			0.939592i	0.882775	+	0.469796i	$0.155673\pi$
$367$			18.0000i			0.939592i	−0.882775	+	0.469796i	$0.844327\pi$
$368$	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	−0.780496	−	0.625161i	$-0.785033\pi$
$373$	−3.00000	+	3.00000i	−0.155334	+	0.155334i	0.625161	+	0.780496i	$0.285033\pi$
$374$	−24.0000			−1.24101
$375$		0			0
$376$	−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	0.732323	−	0.680957i	$-0.238436\pi$
$379$	1.00000	+	1.00000i	0.0513665	+	0.0513665i	−0.680957	+	0.732323i	$0.738436\pi$
$380$	2.00000	+	6.00000i	0.102598	+	0.307794i
$381$		0			0
$382$	−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	$-0.0822362\pi$
$384$		0			0
$385$		0			0
$386$	12.0000	−	12.0000i	0.610784	−	0.610784i
$387$		0			0
$388$	24.0000			1.21842
$389$	−15.0000	−	15.0000i	−0.760530	−	0.760530i	0.215888	−	0.976418i	$-0.430735\pi$
$389$	−15.0000	−	15.0000i	−0.760530	−	0.760530i	−0.976418	+	0.215888i	$0.930735\pi$
$390$		0			0
$391$			32.0000i			1.61831i
$392$	−14.0000	+	14.0000i	−0.707107	+	0.707107i
$393$		0			0
$394$	10.0000			0.503793
$395$	−16.0000	−	8.00000i	−0.805047	−	0.402524i
$396$		0			0
$397$	9.00000	+	9.00000i	0.451697	+	0.451697i	0.895918	−	0.444220i	$-0.146519\pi$
$397$	9.00000	+	9.00000i	0.451697	+	0.451697i	−0.444220	+	0.895918i	$0.646519\pi$
$398$	−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	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$		0			0
$403$		0			0
$404$	6.00000	−	6.00000i	0.298511	−	0.298511i
$405$		0			0
$406$		0			0
$407$	−18.0000			−0.892227
$408$		0			0
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−9.00000	−	27.0000i	−0.441793	−	1.32538i
$416$		−	24.0000i		−	1.17670i
$417$		0			0
$418$	6.00000	+	6.00000i	0.293470	+	0.293470i
$419$	−15.0000	+	15.0000i	−0.732798	+	0.732798i	−0.971173	−	0.238375i	$-0.923385\pi$
$419$	−15.0000	+	15.0000i	−0.732798	+	0.732798i	0.238375	+	0.971173i	$0.423385\pi$
$420$		0			0
$421$	−5.00000	−	5.00000i	−0.243685	−	0.243685i	0.574688	−	0.818373i	$-0.305124\pi$
$421$	−5.00000	−	5.00000i	−0.243685	−	0.243685i	−0.818373	+	0.574688i	$0.805124\pi$
$422$	−22.0000			−1.07094
$423$		0			0
$424$			36.0000i			1.74831i
$425$	16.0000	−	12.0000i	0.776114	−	0.582086i
$426$		0			0
$427$		0			0
$428$	−18.0000	−	18.0000i	−0.870063	−	0.870063i
$429$		0			0
$430$	−12.0000	−	6.00000i	−0.578691	−	0.289346i
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$		0			0
$433$		−	36.0000i		−	1.73005i	−0.501729	−	0.865025i	$-0.667303\pi$
$433$		−	36.0000i		−	1.73005i	0.501729	−	0.865025i	$-0.332697\pi$
$434$		0			0
$435$		0			0
$436$	−2.00000	−	2.00000i	−0.0957826	−	0.0957826i
$437$	8.00000	−	8.00000i	0.382692	−	0.382692i
$438$		0			0
$439$		−	10.0000i		−	0.477274i	−0.971109	−	0.238637i	$-0.923299\pi$
$439$		−	10.0000i		−	0.477274i	0.971109	−	0.238637i	$-0.0767006\pi$
$440$	−24.0000	−	12.0000i	−1.14416	−	0.572078i
$441$		0			0
$442$	24.0000			1.14156
$443$	−9.00000	+	9.00000i	−0.427603	+	0.427603i	−0.887811	−	0.460208i	$-0.847775\pi$
$443$	−9.00000	+	9.00000i	−0.427603	+	0.427603i	0.460208	+	0.887811i	$0.347775\pi$
$444$		0			0
$445$	12.0000	−	24.0000i	0.568855	−	1.13771i
$446$	−6.00000	+	6.00000i	−0.284108	+	0.284108i
$447$		0			0
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$		0			0
$452$	16.0000			0.752577
$453$		0			0
$454$		−	18.0000i		−	0.844782i
$455$		0			0
$456$		0			0
$457$	−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
$459$		0			0
$460$	−16.0000	+	32.0000i	−0.746004	+	1.49201i
$461$	−3.00000	+	3.00000i	−0.139724	+	0.139724i	−0.773509	−	0.633785i	$-0.781500\pi$
$461$	−3.00000	+	3.00000i	−0.139724	+	0.139724i	0.633785	+	0.773509i	$0.281500\pi$
$462$		0			0
$463$		−	30.0000i		−	1.39422i	−0.716965	−	0.697109i	$-0.754469\pi$
$463$		−	30.0000i		−	1.39422i	0.716965	−	0.697109i	$-0.245531\pi$
$464$	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	$-0.197688\pi$
$467$	5.00000	+	5.00000i	0.231372	+	0.231372i	−0.581893	+	0.813265i	$0.697688\pi$
$468$		0			0
$469$		0			0
$470$	6.00000	−	2.00000i	0.276759	−	0.0922531i
$471$		0			0
$472$	−36.0000			−1.65703
$473$	−18.0000			−0.827641
$474$		0			0
$475$	−7.00000	−	1.00000i	−0.321182	−	0.0458831i
$476$		0			0
$477$		0			0
$478$	24.0000	+	24.0000i	1.09773	+	1.09773i
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$		0			0
$481$	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
$486$		0			0
$487$	−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
$489$		0			0
$490$	−7.00000	−	21.0000i	−0.316228	−	0.948683i
$491$	15.0000	+	15.0000i	0.676941	+	0.676941i	0.959307	−	0.282366i	$-0.0911193\pi$
$491$	15.0000	+	15.0000i	0.676941	+	0.676941i	−0.282366	+	0.959307i	$0.591119\pi$
$492$		0			0
$493$	12.0000	+	12.0000i	0.540453	+	0.540453i
$494$	−6.00000	−	6.00000i	−0.269953	−	0.269953i
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−29.0000	+	29.0000i	−1.29822	+	1.29822i	−0.368650	+	0.929568i	$0.620180\pi$
$499$	−29.0000	+	29.0000i	−1.29822	+	1.29822i	−0.929568	+	0.368650i	$0.879820\pi$
$500$	22.0000	−	4.00000i	0.983870	−	0.178885i
$501$		0			0
$502$			18.0000i			0.803379i
$503$	32.0000			1.42681			0.713405	−	0.700752i	$-0.247152\pi$
$503$	32.0000			1.42681			0.713405	+	0.700752i	$0.247152\pi$
$504$		0			0
$505$	3.00000	+	9.00000i	0.133498	+	0.400495i
$506$			48.0000i			2.13386i
$507$		0			0
$508$	12.0000			0.532414
$509$	9.00000	−	9.00000i	0.398918	−	0.398918i	−0.478933	−	0.877851i	$-0.658976\pi$
$509$	9.00000	−	9.00000i	0.398918	−	0.398918i	0.877851	+	0.478933i	$0.158976\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	−8.00000	+	8.00000i	−0.352865	+	0.352865i
$515$		0			0
$516$		0			0
$517$	6.00000	−	6.00000i	0.263880	−	0.263880i
$518$		0			0
$519$		0			0
$520$	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	$0.823792\pi$
$522$		0			0
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	−0.482405	−	0.875948i	$-0.660237\pi$
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	0.875948	+	0.482405i	$0.160237\pi$
$524$	18.0000	+	18.0000i	0.786334	+	0.786334i
$525$		0			0
$526$	16.0000	+	16.0000i	0.697633	+	0.697633i
$527$		0			0
$528$		0			0
$529$	41.0000			1.78261
$530$	−36.0000	−	18.0000i	−1.56374	−	0.781870i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	27.0000	−	9.00000i	1.16731	−	0.389104i
$536$	12.0000			0.518321
$537$		0			0
$538$	−18.0000			−0.776035
$539$	−21.0000	−	21.0000i	−0.904534	−	0.904534i
$540$		0			0
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	−0.728277	−	0.685283i	$-0.759678\pi$
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	0.685283	+	0.728277i	$0.259678\pi$
$542$	−16.0000	−	16.0000i	−0.687259	−	0.687259i
$543$		0			0
$544$	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	0.768328	−	0.640057i	$-0.221089\pi$
$547$	3.00000	+	3.00000i	0.128271	+	0.128271i	−0.640057	+	0.768328i	$0.721089\pi$
$548$			4.00000i			0.170872i
$549$		0			0
$550$	24.0000	−	18.0000i	1.02336	−	0.767523i
$551$		−	6.00000i		−	0.255609i
$552$		0			0
$553$		0			0
$554$	6.00000			0.254916
$555$		0			0
$556$	14.0000	−	14.0000i	0.593732	−	0.593732i
$557$	−9.00000	−	9.00000i	−0.381342	−	0.381342i	0.490243	−	0.871586i	$-0.336908\pi$
$557$	−9.00000	−	9.00000i	−0.381342	−	0.381342i	−0.871586	+	0.490243i	$0.836908\pi$
$558$		0			0
$559$	18.0000			0.761319
$560$		0			0
$561$		0			0
$562$	12.0000	−	12.0000i	0.506189	−	0.506189i
$563$	−19.0000	−	19.0000i	−0.800755	−	0.800755i	0.182459	−	0.983213i	$-0.441594\pi$
$563$	−19.0000	−	19.0000i	−0.800755	−	0.800755i	−0.983213	+	0.182459i	$0.941594\pi$
$564$		0			0
$565$	−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	$-0.167795\pi$
$570$		0			0
$571$	−11.0000	−	11.0000i	−0.460336	−	0.460336i	0.438430	−	0.898765i	$-0.355535\pi$
$571$	−11.0000	−	11.0000i	−0.460336	−	0.460336i	−0.898765	+	0.438430i	$0.855535\pi$
$572$	36.0000			1.50524
$573$		0			0
$574$		0			0
$575$	−24.0000	−	32.0000i	−1.00087	−	1.33449i
$576$		0			0
$577$		−	24.0000i		−	0.999133i	−0.866276	−	0.499567i	$-0.833493\pi$
$577$		−	24.0000i		−	0.999133i	0.866276	−	0.499567i	$-0.166507\pi$
$578$	−1.00000	−	1.00000i	−0.0415945	−	0.0415945i
$579$		0			0
$580$	6.00000	+	18.0000i	0.249136	+	0.747409i
$581$		0			0
$582$		0			0
$583$	−54.0000			−2.23645
$584$	−12.0000	+	12.0000i	−0.496564	+	0.496564i
$585$		0			0
$586$	18.0000			0.743573
$587$	−9.00000	+	9.00000i	−0.371470	+	0.371470i	−0.868012	−	0.496543i	$-0.834603\pi$
$587$	−9.00000	+	9.00000i	−0.371470	+	0.371470i	0.496543	+	0.868012i	$0.334603\pi$
$588$		0			0
$589$		0			0
$590$	18.0000	−	36.0000i	0.741048	−	1.48210i
$591$		0			0
$592$	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	$0.771808\pi$
$594$		0			0
$595$		0			0
$596$	6.00000	−	6.00000i	0.245770	−	0.245770i
$597$		0			0
$598$		−	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	$-0.209990\pi$
$600$		0			0
$601$		−	36.0000i		−	1.46847i	−0.678895	−	0.734235i	$-0.737541\pi$
$601$		−	36.0000i		−	1.46847i	0.678895	−	0.734235i	$-0.262459\pi$
$602$		0			0
$603$		0			0
$604$	36.0000			1.46482
$605$	7.00000	−	14.0000i	0.284590	−	0.569181i
$606$		0			0
$607$			42.0000i			1.70473i	0.522949	+	0.852364i	$0.324832\pi$
$607$			42.0000i			1.70473i	−0.522949	+	0.852364i	$0.675168\pi$
$608$	−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
$612$		0			0
$613$	−27.0000	+	27.0000i	−1.09052	+	1.09052i	−0.0950469	+	0.995473i	$0.530300\pi$
$613$	−27.0000	+	27.0000i	−1.09052	+	1.09052i	−0.995473	+	0.0950469i	$0.969700\pi$
$614$		−	6.00000i		−	0.242140i
$615$		0			0
$616$		0			0
$617$	−10.0000			−0.402585			−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000			−0.402585			−0.201292	+	0.979531i	$0.564514\pi$
$618$		0			0
$619$	13.0000	+	13.0000i	0.522514	+	0.522514i	0.918330	−	0.395816i	$-0.129538\pi$
$619$	13.0000	+	13.0000i	0.522514	+	0.522514i	−0.395816	+	0.918330i	$0.629538\pi$
$620$		0			0
$621$		0			0
$622$	−6.00000	+	6.00000i	−0.240578	+	0.240578i
$623$		0			0
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−6.00000	−	6.00000i	−0.239808	−	0.239808i
$627$		0			0
$628$	−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	$-0.987325\pi$
$631$		−	2.00000i		−	0.0796187i	0.999207	−	0.0398094i	$-0.0126751\pi$
$632$	16.0000	−	16.0000i	0.636446	−	0.636446i
$633$		0			0
$634$		−	14.0000i		−	0.556011i
$635$	−6.00000	+	12.0000i	−0.238103	+	0.476205i
$636$		0			0
$637$	21.0000	+	21.0000i	0.832050	+	0.832050i
$638$	18.0000	+	18.0000i	0.712627	+	0.712627i
$639$		0			0
$640$	24.0000	−	8.00000i	0.948683	−	0.316228i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$		0			0
$643$	27.0000	+	27.0000i	1.06478	+	1.06478i	0.997751	+	0.0670247i	$0.0213506\pi$
$643$	27.0000	+	27.0000i	1.06478	+	1.06478i	0.0670247	+	0.997751i	$0.478649\pi$
$644$		0			0
$645$		0			0
$646$		−	8.00000i		−	0.314756i
$647$	−32.0000			−1.25805			−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000			−1.25805			−0.629025	+	0.777385i	$0.716546\pi$
$648$		0			0
$649$		−	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	$-0.330115\pi$
$653$	−9.00000	−	9.00000i	−0.352197	−	0.352197i	−0.860927	+	0.508729i	$0.830115\pi$
$654$		0			0
$655$	−27.0000	+	9.00000i	−1.05498	+	0.351659i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.0000	−	21.0000i	0.818044	−	0.818044i	−0.167781	−	0.985824i	$-0.553660\pi$
$659$	21.0000	−	21.0000i	0.818044	−	0.818044i	0.985824	+	0.167781i	$0.0536600\pi$
$660$		0			0
$661$	−29.0000	−	29.0000i	−1.12797	−	1.12797i	−0.990507	−	0.137462i	$-0.956105\pi$
$661$	−29.0000	−	29.0000i	−1.12797	−	1.12797i	−0.137462	−	0.990507i	$-0.543895\pi$
$662$		−	10.0000i		−	0.388661i
$663$		0			0
$664$	36.0000			1.39707
$665$		0			0
$666$		0			0
$667$	24.0000	−	24.0000i	0.929284	−	0.929284i
$668$			16.0000i			0.619059i
$669$		0			0
$670$	−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	$-0.925708\pi$
$673$		−	12.0000i		−	0.462566i	0.972887	−	0.231283i	$-0.0742923\pi$
$674$	24.0000	−	24.0000i	0.924445	−	0.924445i
$675$		0			0
$676$	−10.0000			−0.384615
$677$	−9.00000	+	9.00000i	−0.345898	+	0.345898i	−0.858579	−	0.512681i	$-0.828652\pi$
$677$	−9.00000	+	9.00000i	−0.345898	+	0.345898i	0.512681	+	0.858579i	$0.328652\pi$
$678$		0			0
$679$		0			0
$680$	8.00000	+	24.0000i	0.306786	+	0.920358i
$681$		0			0
$682$		0			0
$683$	−13.0000	+	13.0000i	−0.497431	+	0.497431i	−0.910637	−	0.413206i	$-0.864409\pi$
$683$	−13.0000	+	13.0000i	−0.497431	+	0.497431i	0.413206	+	0.910637i	$0.364409\pi$
$684$		0			0
$685$	−4.00000	−	2.00000i	−0.152832	−	0.0764161i
$686$		0			0
$687$		0			0
$688$	12.0000	−	12.0000i	0.457496	−	0.457496i
$689$	54.0000			2.05724
$690$		0			0
$691$	−5.00000	+	5.00000i	−0.190209	+	0.190209i	−0.795786	−	0.605577i	$-0.792942\pi$
$691$	−5.00000	+	5.00000i	−0.190209	+	0.190209i	0.605577	+	0.795786i	$0.292942\pi$
$692$	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
$696$		0			0
$697$		0			0
$698$	10.0000			0.378506
$699$		0			0
$700$		0			0
$701$	−3.00000	+	3.00000i	−0.113308	+	0.113308i	−0.761488	−	0.648179i	$-0.775531\pi$
$701$	−3.00000	+	3.00000i	−0.113308	+	0.113308i	0.648179	+	0.761488i	$0.275531\pi$
$702$		0			0
$703$		−	6.00000i		−	0.226294i
$704$	24.0000	−	24.0000i	0.904534	−	0.904534i
$705$		0			0
$706$	−16.0000	+	16.0000i	−0.602168	+	0.602168i
$707$		0			0
$708$		0			0
$709$	−13.0000	−	13.0000i	−0.488225	−	0.488225i	0.419521	−	0.907746i	$-0.362198\pi$
$709$	−13.0000	−	13.0000i	−0.488225	−	0.488225i	−0.907746	+	0.419521i	$0.862198\pi$
$710$	18.0000	−	6.00000i	0.675528	−	0.225176i
$711$		0			0
$712$	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
$717$		0			0
$718$	18.0000	−	18.0000i	0.671754	−	0.671754i
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$		0			0
$722$	17.0000	−	17.0000i	0.632674	−	0.632674i
$723$		0			0
$724$	2.00000	−	2.00000i	0.0743294	−	0.0743294i
$725$	−21.0000	−	3.00000i	−0.779920	−	0.111417i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−6.00000	−	18.0000i	−0.222070	−	0.666210i
$731$	12.0000	+	12.0000i	0.443836	+	0.443836i
$732$		0			0
$733$	−3.00000	−	3.00000i	−0.110808	−	0.110808i	0.649529	−	0.760337i	$-0.274966\pi$
$733$	−3.00000	−	3.00000i	−0.110808	−	0.110808i	−0.760337	+	0.649529i	$0.774966\pi$
$734$	18.0000	−	18.0000i	0.664392	−	0.664392i
$735$		0			0
$736$	−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	−0.265253	−	0.964179i	$-0.585455\pi$
$739$	19.0000	−	19.0000i	0.698926	−	0.698926i	0.964179	+	0.265253i	$0.0854554\pi$
$740$	6.00000	+	18.0000i	0.220564	+	0.661693i
$741$		0			0
$742$		0			0
$743$	−8.00000			−0.293492			−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000			−0.293492			−0.146746	+	0.989174i	$0.546880\pi$
$744$		0			0
$745$	3.00000	+	9.00000i	0.109911	+	0.329734i
$746$	6.00000			0.219676
$747$		0			0
$748$	24.0000	+	24.0000i	0.877527	+	0.877527i
$749$		0			0
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$			8.00000i			0.291730i
$753$		0			0
$754$	−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	0.225061	−	0.974345i	$-0.427742\pi$
$757$	33.0000	−	33.0000i	1.19941	−	1.19941i	0.974345	−	0.225061i	$-0.0722580\pi$
$758$		−	2.00000i		−	0.0726433i
$759$		0			0
$760$	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	$-0.335881\pi$
$762$		0			0
$763$		0			0
$764$			48.0000i			1.73658i
$765$		0			0
$766$	−10.0000	+	10.0000i	−0.361315	+	0.361315i
$767$			54.0000i			1.94983i
$768$		0			0
$769$	−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
$771$		0			0
$772$	−24.0000			−0.863779
$773$	23.0000	−	23.0000i	0.827253	−	0.827253i	−0.159883	−	0.987136i	$-0.551112\pi$
$773$	23.0000	−	23.0000i	0.827253	−	0.827253i	0.987136	+	0.159883i	$0.0511118\pi$
$774$		0			0
$775$		0			0
$776$	−24.0000	−	24.0000i	−0.861550	−	0.861550i
$777$		0			0
$778$			30.0000i			1.07555i
$779$		0			0
$780$		0			0
$781$	18.0000	−	18.0000i	0.644091	−	0.644091i
$782$	32.0000	−	32.0000i	1.14432	−	1.14432i
$783$		0			0
$784$	28.0000			1.00000
$785$	−9.00000	−	27.0000i	−0.321224	−	0.963671i
$786$		0			0
$787$	−33.0000	−	33.0000i	−1.17632	−	1.17632i	−0.980674	−	0.195649i	$-0.937319\pi$
$787$	−33.0000	−	33.0000i	−1.17632	−	1.17632i	−0.195649	−	0.980674i	$-0.562681\pi$
$788$	−10.0000	−	10.0000i	−0.356235	−	0.356235i
$789$		0			0
$790$	8.00000	+	24.0000i	0.284627	+	0.853882i
$791$		0			0
$792$		0			0
$793$	30.0000			1.06533
$794$		−	18.0000i		−	0.638796i
$795$		0			0
$796$	4.00000			0.141776
$797$	19.0000	+	19.0000i	0.673015	+	0.673015i	0.958410	−	0.285395i	$-0.0921249\pi$
$797$	19.0000	+	19.0000i	0.673015	+	0.673015i	−0.285395	+	0.958410i	$0.592125\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	−4.00000	+	28.0000i	−0.141421	+	0.989949i
$801$		0			0
$802$	30.0000	+	30.0000i	1.05934	+	1.05934i
$803$	−18.0000	−	18.0000i	−0.635206	−	0.635206i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−12.0000			−0.422159
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		0			0
$811$	37.0000	+	37.0000i	1.29925	+	1.29925i	0.928890	+	0.370356i	$0.120764\pi$
$811$	37.0000	+	37.0000i	1.29925	+	1.29925i	0.370356	+	0.928890i	$0.379236\pi$
$812$		0			0
$813$		0			0
$814$	18.0000	+	18.0000i	0.630900	+	0.630900i
$815$	9.00000	+	27.0000i	0.315256	+	0.945769i
$816$		0			0
$817$		−	6.00000i		−	0.209913i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−39.0000	−	39.0000i	−1.36111	−	1.36111i	−0.872506	−	0.488603i	$-0.837507\pi$
$821$	−39.0000	−	39.0000i	−1.36111	−	1.36111i	−0.488603	−	0.872506i	$-0.662493\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$		0			0
$827$	31.0000	−	31.0000i	1.07798	−	1.07798i	0.0812847	−	0.996691i	$-0.474098\pi$
$827$	31.0000	−	31.0000i	1.07798	−	1.07798i	0.996691	−	0.0812847i	$-0.0259023\pi$
$828$		0			0
$829$	35.0000	−	35.0000i	1.21560	−	1.21560i	0.246443	−	0.969157i	$-0.420738\pi$
$829$	35.0000	−	35.0000i	1.21560	−	1.21560i	0.969157	−	0.246443i	$-0.0792618\pi$
$830$	−18.0000	+	36.0000i	−0.624789	+	1.24958i
$831$		0			0
$832$	−24.0000	+	24.0000i	−0.832050	+	0.832050i
$833$			28.0000i			0.970143i
$834$		0			0
$835$	−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
$843$		0			0
$844$	22.0000	+	22.0000i	0.757271	+	0.757271i
$845$	5.00000	−	10.0000i	0.172005	−	0.344010i
$846$		0			0
$847$		0			0
$848$	36.0000	−	36.0000i	1.23625	−	1.23625i
$849$		0			0
$850$	−28.0000	−	4.00000i	−0.960392	−	0.137199i
$851$	24.0000	−	24.0000i	0.822709	−	0.822709i
$852$		0			0
$853$	−15.0000	+	15.0000i	−0.513590	+	0.513590i	−0.915625	−	0.402034i	$-0.868303\pi$
$853$	−15.0000	+	15.0000i	−0.513590	+	0.513590i	0.402034	+	0.915625i	$0.368303\pi$
$854$		0			0
$855$		0			0
$856$			36.0000i			1.23045i
$857$	−38.0000			−1.29806			−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000			−1.29806			−0.649028	+	0.760765i	$0.724824\pi$
$858$		0			0
$859$	−7.00000	−	7.00000i	−0.238837	−	0.238837i	0.577531	−	0.816368i	$-0.304016\pi$
$859$	−7.00000	−	7.00000i	−0.238837	−	0.238837i	−0.816368	+	0.577531i	$0.804016\pi$
$860$	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	$0.877833\pi$
$864$		0			0
$865$	9.00000	+	27.0000i	0.306009	+	0.918028i
$866$	−36.0000	+	36.0000i	−1.22333	+	1.22333i
$867$		0			0
$868$		0			0
$869$	24.0000	+	24.0000i	0.814144	+	0.814144i
$870$		0			0
$871$		−	18.0000i		−	0.609907i
$872$			4.00000i			0.135457i
$873$		0			0
$874$	−16.0000			−0.541208
$875$		0			0
$876$		0			0
$877$	−3.00000	−	3.00000i	−0.101303	−	0.101303i	0.654639	−	0.755942i	$-0.272821\pi$
$877$	−3.00000	−	3.00000i	−0.101303	−	0.101303i	−0.755942	+	0.654639i	$0.772821\pi$
$878$	−10.0000	+	10.0000i	−0.337484	+	0.337484i
$879$		0			0
$880$	12.0000	+	36.0000i	0.404520	+	1.21356i
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		0			0
$883$	−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	$0.916563\pi$
$884$	−24.0000	−	24.0000i	−0.807207	−	0.807207i
$885$		0			0
$886$	18.0000			0.604722
$887$	−8.00000			−0.268614			−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000			−0.268614			−0.134307	+	0.990940i	$0.542881\pi$
$888$		0			0
$889$		0			0
$890$	−36.0000	+	12.0000i	−1.20672	+	0.402241i
$891$		0			0
$892$	12.0000			0.401790
$893$	2.00000	+	2.00000i	0.0669274	+	0.0669274i
$894$		0			0
$895$	9.00000	−	3.00000i	0.300837	−	0.100279i
$896$		0			0
$897$		0			0
$898$	−18.0000	−	18.0000i	−0.600668	−	0.600668i
$899$		0			0
$900$		0			0
$901$	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
$906$		0			0
$907$	21.0000	−	21.0000i	0.697294	−	0.697294i	−0.266532	−	0.963826i	$-0.585878\pi$
$907$	21.0000	−	21.0000i	0.697294	−	0.697294i	0.963826	+	0.266532i	$0.0858779\pi$
$908$	−18.0000	+	18.0000i	−0.597351	+	0.597351i
$909$		0			0
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$			54.0000i			1.78714i
$914$	18.0000	+	18.0000i	0.595387	+	0.595387i
$915$		0			0
$916$	−14.0000	+	14.0000i	−0.462573	+	0.462573i
$917$		0			0
$918$		0			0
$919$			54.0000i			1.78130i	0.454694	+	0.890648i	$0.349749\pi$
$919$			54.0000i			1.78130i	−0.454694	+	0.890648i	$0.650251\pi$
$920$	48.0000	−	16.0000i	1.58251	−	0.527504i
$921$		0			0
$922$	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	$-0.663783\pi$
$929$	−30.0000			−0.984268			−0.492134	+	0.870519i	$0.663783\pi$
$930$		0			0
$931$	7.00000	−	7.00000i	0.229416	−	0.229416i
$932$			44.0000i			1.44127i
$933$		0			0
$934$		−	10.0000i		−	0.327210i
$935$	−36.0000	+	12.0000i	−1.17733	+	0.392442i
$936$		0			0
$937$	−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
$939$		0			0
$940$	−8.00000	−	4.00000i	−0.260931	−	0.130466i
$941$	−27.0000	+	27.0000i	−0.880175	+	0.880175i	−0.993552	−	0.113377i	$-0.963833\pi$
$941$	−27.0000	+	27.0000i	−0.880175	+	0.880175i	0.113377	+	0.993552i	$0.463833\pi$
$942$		0			0
$943$		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	$-0.463031\pi$
$947$	−27.0000	−	27.0000i	−0.877382	−	0.877382i	−0.993263	+	0.115881i	$0.963031\pi$
$948$		0			0
$949$	18.0000	+	18.0000i	0.584305	+	0.584305i
$950$	6.00000	+	8.00000i	0.194666	+	0.259554i
$951$		0			0
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$		0			0
$955$	−48.0000	−	24.0000i	−1.55324	−	0.776622i
$956$		−	48.0000i		−	1.55243i
$957$		0			0
$958$	−24.0000	−	24.0000i	−0.775405	−	0.775405i
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−18.0000	−	18.0000i	−0.580343	−	0.580343i
$963$		0			0
$964$		−	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
$969$		0			0
$970$	36.0000	−	12.0000i	1.15589	−	0.385297i
$971$	−9.00000	−	9.00000i	−0.288824	−	0.288824i	0.547791	−	0.836615i	$-0.315469\pi$
$971$	−9.00000	−	9.00000i	−0.288824	−	0.288824i	−0.836615	+	0.547791i	$0.815469\pi$
$972$		0			0
$973$		0			0
$974$	24.0000	+	24.0000i	0.769010	+	0.769010i
$975$		0			0
$976$	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	$-0.147828\pi$
$978$		0			0
$979$	−36.0000	+	36.0000i	−1.15056	+	1.15056i
$980$	−14.0000	+	28.0000i	−0.447214	+	0.894427i
$981$		0			0
$982$		−	30.0000i		−	0.957338i
$983$	16.0000			0.510321			0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000			0.510321			0.255160	+	0.966899i	$0.417872\pi$
$984$		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
$990$		0			0
$991$	−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
$993$		0			0
$994$		0			0
$995$	−2.00000	+	4.00000i	−0.0634043	+	0.126809i
$996$		0			0
$997$	9.00000	−	9.00000i	0.285033	−	0.285033i	−0.550079	−	0.835112i	$-0.685403\pi$
$997$	9.00000	−	9.00000i	0.285033	−	0.285033i	0.835112	+	0.550079i	$0.185403\pi$
$998$	58.0000			1.83596
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.a.469.1		2
3.2	odd	2		80.2.q.b.69.1	yes	2
5.4	even	2		720.2.bm.b.469.1		2
12.11	even	2		320.2.q.b.49.1		2
15.2	even	4		400.2.l.a.101.1		2
15.8	even	4		400.2.l.b.101.1		2
15.14	odd	2		80.2.q.a.69.1	yes	2
16.13	even	4		720.2.bm.b.109.1		2
24.5	odd	2		640.2.q.c.609.1		2
24.11	even	2		640.2.q.a.609.1		2
48.5	odd	4		640.2.q.b.289.1		2
48.11	even	4		640.2.q.d.289.1		2
48.29	odd	4		80.2.q.a.29.1	✓	2
48.35	even	4		320.2.q.a.209.1		2
60.23	odd	4		1600.2.l.b.1201.1		2
60.47	odd	4		1600.2.l.c.1201.1		2
60.59	even	2		320.2.q.a.49.1		2
80.29	even	4	inner	720.2.bm.a.109.1		2
120.29	odd	2		640.2.q.b.609.1		2
120.59	even	2		640.2.q.d.609.1		2
240.29	odd	4		80.2.q.b.29.1	yes	2
240.59	even	4		640.2.q.a.289.1		2
240.77	even	4		400.2.l.a.301.1		2
240.83	odd	4		1600.2.l.b.401.1		2
240.149	odd	4		640.2.q.c.289.1		2
240.173	even	4		400.2.l.b.301.1		2
240.179	even	4		320.2.q.b.209.1		2
240.227	odd	4		1600.2.l.c.401.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.a.29.1	✓	2	48.29	odd	4
80.2.q.a.69.1	yes	2	15.14	odd	2
80.2.q.b.29.1	yes	2	240.29	odd	4
80.2.q.b.69.1	yes	2	3.2	odd	2
320.2.q.a.49.1		2	60.59	even	2
320.2.q.a.209.1		2	48.35	even	4
320.2.q.b.49.1		2	12.11	even	2
320.2.q.b.209.1		2	240.179	even	4
400.2.l.a.101.1		2	15.2	even	4
400.2.l.a.301.1		2	240.77	even	4
400.2.l.b.101.1		2	15.8	even	4
400.2.l.b.301.1		2	240.173	even	4
640.2.q.a.289.1		2	240.59	even	4
640.2.q.a.609.1		2	24.11	even	2
640.2.q.b.289.1		2	48.5	odd	4
640.2.q.b.609.1		2	120.29	odd	2
640.2.q.c.289.1		2	240.149	odd	4
640.2.q.c.609.1		2	24.5	odd	2
640.2.q.d.289.1		2	48.11	even	4
640.2.q.d.609.1		2	120.59	even	2
720.2.bm.a.109.1		2	80.29	even	4	inner
720.2.bm.a.469.1		2	1.1	even	1	trivial
720.2.bm.b.109.1		2	16.13	even	4
720.2.bm.b.469.1		2	5.4	even	2
1600.2.l.b.401.1		2	240.83	odd	4
1600.2.l.b.1201.1		2	60.23	odd	4
1600.2.l.c.401.1		2	240.227	odd	4
1600.2.l.c.1201.1		2	60.47	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(2.00000 - 2.00000i) q^{8} +(1.00000 + 3.00000i) q^{10} +(3.00000 + 3.00000i) q^{11} +(-3.00000 - 3.00000i) q^{13} -4.00000 q^{16} -4.00000i q^{17} +(-1.00000 + 1.00000i) q^{19} +(2.00000 - 4.00000i) q^{20} -6.00000i q^{22} -8.00000 q^{23} +(3.00000 + 4.00000i) q^{25} +6.00000i q^{26} +(-3.00000 + 3.00000i) q^{29} +(4.00000 + 4.00000i) q^{32} +(-4.00000 + 4.00000i) q^{34} +(-3.00000 + 3.00000i) q^{37} +2.00000 q^{38} +(-6.00000 + 2.00000i) q^{40} +(-3.00000 + 3.00000i) q^{43} +(-6.00000 + 6.00000i) q^{44} +(8.00000 + 8.00000i) q^{46} -2.00000i q^{47} -7.00000 q^{49} +(1.00000 - 7.00000i) q^{50} +(6.00000 - 6.00000i) q^{52} +(-9.00000 + 9.00000i) q^{53} +(-3.00000 - 9.00000i) q^{55} +6.00000 q^{58} +(-9.00000 - 9.00000i) q^{59} +(-5.00000 + 5.00000i) q^{61} -8.00000i q^{64} +(3.00000 + 9.00000i) q^{65} +(3.00000 + 3.00000i) q^{67} +8.00000 q^{68} -6.00000i q^{71} -6.00000 q^{73} +6.00000 q^{74} +(-2.00000 - 2.00000i) q^{76} +8.00000 q^{79} +(8.00000 + 4.00000i) q^{80} +(9.00000 + 9.00000i) q^{83} +(-4.00000 + 8.00000i) q^{85} +6.00000 q^{86} +12.0000 q^{88} +12.0000i q^{89} -16.0000i q^{92} +(-2.00000 + 2.00000i) q^{94} +(3.00000 - 1.00000i) q^{95} -12.0000i q^{97} +(7.00000 + 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 2 q^{10} + 6 q^{11} - 6 q^{13} - 8 q^{16} - 2 q^{19} + 4 q^{20} - 16 q^{23} + 6 q^{25} - 6 q^{29} + 8 q^{32} - 8 q^{34} - 6 q^{37} + 4 q^{38} - 12 q^{40} - 6 q^{43} - 12 q^{44}+ \cdots + 14 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 2 * q^10 + 6 * q^11 - 6 * q^13 - 8 * q^16 - 2 * q^19 + 4 * q^20 - 16 * q^23 + 6 * q^25 - 6 * q^29 + 8 * q^32 - 8 * q^34 - 6 * q^37 + 4 * q^38 - 12 * q^40 - 6 * q^43 - 12 * q^44 + 16 * q^46 - 14 * q^49 + 2 * q^50 + 12 * q^52 - 18 * q^53 - 6 * q^55 + 12 * q^58 - 18 * q^59 - 10 * q^61 + 6 * q^65 + 6 * q^67 + 16 * q^68 - 12 * q^73 + 12 * q^74 - 4 * q^76 + 16 * q^79 + 16 * q^80 + 18 * q^83 - 8 * q^85 + 12 * q^86 + 24 * q^88 - 4 * q^94 + 6 * q^95 + 14 * q^98

Introduction

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