LMFDB - Embedded newform 720.2.bm.b.109.1

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,-2,0,0] 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:	$0$
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:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.b.469.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-1.00000 + 2.00000i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(1.00000 + 3.00000i) q^{10} +(3.00000 - 3.00000i) q^{11} +(3.00000 - 3.00000i) q^{13} -4.00000 q^{16} -4.00000i q^{17} +(-1.00000 - 1.00000i) q^{19} +(4.00000 + 2.00000i) q^{20} -6.00000i q^{22} +8.00000 q^{23} +(-3.00000 - 4.00000i) q^{25} -6.00000i q^{26} +(-3.00000 - 3.00000i) q^{29} +(-4.00000 + 4.00000i) q^{32} +(-4.00000 - 4.00000i) q^{34} +(3.00000 + 3.00000i) q^{37} -2.00000 q^{38} +(6.00000 - 2.00000i) q^{40} +(3.00000 + 3.00000i) q^{43} +(-6.00000 - 6.00000i) q^{44} +(8.00000 - 8.00000i) q^{46} -2.00000i q^{47} -7.00000 q^{49} +(-7.00000 - 1.00000i) q^{50} +(-6.00000 - 6.00000i) q^{52} +(9.00000 + 9.00000i) q^{53} +(3.00000 + 9.00000i) q^{55} -6.00000 q^{58} +(-9.00000 + 9.00000i) q^{59} +(-5.00000 - 5.00000i) q^{61} +8.00000i q^{64} +(3.00000 + 9.00000i) q^{65} +(-3.00000 + 3.00000i) q^{67} -8.00000 q^{68} +6.00000i q^{71} +6.00000 q^{73} +6.00000 q^{74} +(-2.00000 + 2.00000i) q^{76} +8.00000 q^{79} +(4.00000 - 8.00000i) q^{80} +(-9.00000 + 9.00000i) q^{83} +(8.00000 + 4.00000i) q^{85} +6.00000 q^{86} -12.0000 q^{88} -12.0000i q^{89} -16.0000i q^{92} +(-2.00000 - 2.00000i) q^{94} +(3.00000 - 1.00000i) q^{95} -12.0000i q^{97} +(-7.00000 + 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{5} - 4 q^{8} + 2 q^{10} + 6 q^{11} + 6 q^{13} - 8 q^{16} - 2 q^{19} + 8 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 - 2 * q^5 - 4 * q^8 + 2 * q^10 + 6 * q^11 + 6 * q^13 - 8 * q^16 - 2 * q^19 + 8 * 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 - 14 * 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 + 8 * q^80 - 18 * q^83 + 16 * 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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$1$

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
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		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	−0.0912903	−	0.995824i	$-0.529099\pi$
$11$	3.00000	−	3.00000i	0.904534	−	0.904534i	0.995824	+	0.0912903i	$0.0290991\pi$
$12$		0			0
$13$	3.00000	−	3.00000i	0.832050	−	0.832050i	−0.155747	−	0.987797i	$-0.549778\pi$
$13$	3.00000	−	3.00000i	0.832050	−	0.832050i	0.987797	+	0.155747i	$0.0497784\pi$
$14$		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	0.583033	−	0.812449i	$-0.301866\pi$
$19$	−1.00000	−	1.00000i	−0.229416	−	0.229416i	−0.812449	+	0.583033i	$0.801866\pi$
$20$	4.00000	+	2.00000i	0.894427	+	0.447214i
$21$		0			0
$22$		−	6.00000i		−	1.27920i
$23$	8.00000			1.66812			0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000			1.66812			0.834058	+	0.551677i	$0.186012\pi$
$24$		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	0.371391	−	0.928477i	$-0.378881\pi$
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	−0.928477	+	0.371391i	$0.878881\pi$
$30$		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	$-0.136609\pi$
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	−0.416115	+	0.909312i	$0.636609\pi$
$38$	−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	$-0.145141\pi$
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	−0.440337	+	0.897833i	$0.645141\pi$
$44$	−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
$50$	−7.00000	−	1.00000i	−0.989949	−	0.141421i
$51$		0			0
$52$	−6.00000	−	6.00000i	−0.832050	−	0.832050i
$53$	9.00000	+	9.00000i	1.23625	+	1.23625i	0.961524	+	0.274721i	$0.0885855\pi$
$53$	9.00000	+	9.00000i	1.23625	+	1.23625i	0.274721	+	0.961524i	$0.411414\pi$
$54$		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	−0.189896	+	0.981804i	$0.560815\pi$
$59$	−9.00000	+	9.00000i	−1.17170	+	1.17170i	−0.981804	+	0.189896i	$0.939185\pi$
$60$		0			0
$61$	−5.00000	−	5.00000i	−0.640184	−	0.640184i	0.310416	−	0.950601i	$-0.399532\pi$
$61$	−5.00000	−	5.00000i	−0.640184	−	0.640184i	−0.950601	+	0.310416i	$0.899532\pi$
$62$		0			0
$63$		0			0
$64$			8.00000i			1.00000i
$65$	3.00000	+	9.00000i	0.372104	+	1.11631i
$66$		0			0
$67$	−3.00000	+	3.00000i	−0.366508	+	0.366508i	−0.866202	−	0.499694i	$-0.833446\pi$
$67$	−3.00000	+	3.00000i	−0.366508	+	0.366508i	0.499694	+	0.866202i	$0.333446\pi$
$68$	−8.00000			−0.970143
$69$		0			0
$70$		0			0
$71$			6.00000i			0.712069i	0.934473	+	0.356034i	$0.115871\pi$
$71$			6.00000i			0.712069i	−0.934473	+	0.356034i	$0.884129\pi$
$72$		0			0
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	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	$0.351411\pi$
$80$	4.00000	−	8.00000i	0.447214	−	0.894427i
$81$		0			0
$82$		0			0
$83$	−9.00000	+	9.00000i	−0.987878	+	0.987878i	−0.999927	−	0.0120491i	$-0.996165\pi$
$83$	−9.00000	+	9.00000i	−0.987878	+	0.987878i	0.0120491	+	0.999927i	$0.496165\pi$
$84$		0			0
$85$	8.00000	+	4.00000i	0.867722	+	0.433861i
$86$	6.00000			0.646997
$87$		0			0
$88$	−12.0000			−1.27920
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$		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	−0.840431	−	0.541919i	$-0.817698\pi$
$101$	−3.00000	+	3.00000i	−0.298511	+	0.298511i	0.541919	+	0.840431i	$0.317698\pi$
$102$		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	$-0.0390642\pi$
$107$	9.00000	+	9.00000i	0.870063	+	0.870063i	−0.122416	+	0.992479i	$0.539064\pi$
$108$		0			0
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	0.657592	−	0.753374i	$-0.271575\pi$
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	−0.753374	+	0.657592i	$0.771575\pi$
$110$	12.0000	+	6.00000i	1.14416	+	0.572078i
$111$		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
$115$	−8.00000	+	16.0000i	−0.746004	+	1.49201i
$116$	−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
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		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
$130$	12.0000	+	6.00000i	1.05247	+	0.526235i
$131$	9.00000	+	9.00000i	0.786334	+	0.786334i	0.980891	−	0.194557i	$-0.0623271\pi$
$131$	9.00000	+	9.00000i	0.786334	+	0.786334i	−0.194557	+	0.980891i	$0.562327\pi$
$132$		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	$-0.527228\pi$
$137$	−2.00000			−0.170872			−0.0854358	+	0.996344i	$0.527228\pi$
$138$		0			0
$139$	−7.00000	+	7.00000i	−0.593732	+	0.593732i	−0.938638	−	0.344905i	$-0.887911\pi$
$139$	−7.00000	+	7.00000i	−0.593732	+	0.593732i	0.344905	+	0.938638i	$0.387911\pi$
$140$		0			0
$141$		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	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−3.00000	+	3.00000i	−0.245770	+	0.245770i	0.573462	+	0.819232i	$0.305600\pi$
$150$		0			0
$151$			18.0000i			1.46482i	0.680864	+	0.732410i	$0.261604\pi$
$151$			18.0000i			1.46482i	−0.680864	+	0.732410i	$0.738396\pi$
$152$			4.00000i			0.324443i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.00000	+	9.00000i	−0.718278	+	0.718278i	−0.968252	−	0.249974i	$-0.919578\pi$
$157$	−9.00000	+	9.00000i	−0.718278	+	0.718278i	0.249974	+	0.968252i	$0.419578\pi$
$158$	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	$-0.583898\pi$
$163$	9.00000	−	9.00000i	0.704934	−	0.704934i	0.965465	+	0.260531i	$0.0838976\pi$
$164$		0			0
$165$		0			0
$166$			18.0000i			1.39707i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	12.0000	−	4.00000i	0.920358	−	0.306786i
$171$		0			0
$172$	6.00000	−	6.00000i	0.457496	−	0.457496i
$173$	9.00000	−	9.00000i	0.684257	−	0.684257i	−0.276699	−	0.960957i	$-0.589241\pi$
$173$	9.00000	−	9.00000i	0.684257	−	0.684257i	0.960957	+	0.276699i	$0.0892406\pi$
$174$		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	0.586047	−	0.810277i	$-0.300683\pi$
$179$	−3.00000	−	3.00000i	−0.224231	−	0.224231i	−0.810277	+	0.586047i	$0.800683\pi$
$180$		0			0
$181$	−1.00000	+	1.00000i	−0.0743294	+	0.0743294i	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−1.00000	+	1.00000i	−0.0743294	+	0.0743294i	0.668965	+	0.743294i	$0.266738\pi$
$182$		0			0
$183$		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
$190$	2.00000	−	4.00000i	0.145095	−	0.290191i
$191$	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	$-0.168946\pi$
$197$	5.00000	+	5.00000i	0.356235	+	0.356235i	−0.506188	+	0.862423i	$0.668946\pi$
$198$		0			0
$199$			2.00000i			0.141776i	0.997484	+	0.0708881i	$0.0225833\pi$
$199$			2.00000i			0.141776i	−0.997484	+	0.0708881i	$0.977417\pi$
$200$	−2.00000	+	14.0000i	−0.141421	+	0.989949i
$201$		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	0.975825	−	0.218554i	$-0.0701339\pi$
$211$	11.0000	+	11.0000i	0.757271	+	0.757271i	−0.218554	+	0.975825i	$0.570134\pi$
$212$	18.0000	−	18.0000i	1.23625	−	1.23625i
$213$		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	$-0.888809\pi$
$227$	−9.00000	+	9.00000i	−0.597351	+	0.597351i	0.342256	+	0.939607i	$0.388809\pi$
$228$		0			0
$229$	7.00000	−	7.00000i	0.462573	−	0.462573i	−0.436925	−	0.899498i	$-0.643932\pi$
$229$	7.00000	−	7.00000i	0.462573	−	0.462573i	0.899498	+	0.436925i	$0.143932\pi$
$230$	8.00000	+	24.0000i	0.527504	+	1.58251i
$231$		0			0
$232$			12.0000i			0.787839i
$233$	−22.0000			−1.44127			−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000			−1.44127			−0.720634	+	0.693316i	$0.756149\pi$
$234$		0			0
$235$	4.00000	+	2.00000i	0.260931	+	0.130466i
$236$	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
$245$	7.00000	−	14.0000i	0.447214	−	0.894427i
$246$		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	−0.931589	−	0.363514i	$-0.881577\pi$
$251$	−9.00000	+	9.00000i	−0.568075	+	0.568075i	0.363514	+	0.931589i	$0.381577\pi$
$252$		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	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		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	0.926076	−	0.377337i	$-0.123160\pi$
$269$	9.00000	+	9.00000i	0.548740	+	0.548740i	−0.377337	+	0.926076i	$0.623160\pi$
$270$		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
$275$	−21.0000	−	3.00000i	−1.26635	−	0.180907i
$276$		0			0
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	0.791466	−	0.611213i	$-0.209318\pi$
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	−0.611213	+	0.791466i	$0.709318\pi$
$278$			14.0000i			0.839664i
$279$		0			0
$280$		0			0
$281$		−	12.0000i		−	0.715860i	−0.933748	−	0.357930i	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$		0			0
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	0.994679	−	0.103022i	$-0.0328511\pi$
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	−0.103022	+	0.994679i	$0.532851\pi$
$284$	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
$290$	6.00000	−	12.0000i	0.352332	−	0.704664i
$291$		0			0
$292$		−	12.0000i		−	0.702247i
$293$	9.00000	+	9.00000i	0.525786	+	0.525786i	0.919313	−	0.393527i	$-0.128745\pi$
$293$	9.00000	+	9.00000i	0.525786	+	0.525786i	−0.393527	+	0.919313i	$0.628745\pi$
$294$		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	$-0.788633\pi$
$307$	−3.00000	+	3.00000i	−0.171219	+	0.171219i	0.616296	+	0.787515i	$0.288633\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			6.00000i			0.340229i	0.985424	+	0.170114i	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$			18.0000i			1.01580i
$315$		0			0
$316$		−	16.0000i		−	0.900070i
$317$	−7.00000	+	7.00000i	−0.393159	+	0.393159i	−0.875812	−	0.482653i	$-0.839673\pi$
$317$	−7.00000	+	7.00000i	−0.393159	+	0.393159i	0.482653	+	0.875812i	$0.339673\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$	−16.0000	−	8.00000i	−0.894427	−	0.447214i
$321$		0			0
$322$		0			0
$323$	−4.00000	+	4.00000i	−0.222566	+	0.222566i
$324$		0			0
$325$	−21.0000	−	3.00000i	−1.16487	−	0.166410i
$326$		−	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	−0.556214	−	0.831039i	$-0.687747\pi$
$331$	5.00000	−	5.00000i	0.274825	−	0.274825i	0.831039	+	0.556214i	$0.187747\pi$
$332$	18.0000	+	18.0000i	0.987878	+	0.987878i
$333$		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
$340$	8.00000	−	16.0000i	0.433861	−	0.867722i
$341$		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	−0.999796	−	0.0201770i	$-0.993577\pi$
$347$	−19.0000	−	19.0000i	−1.01997	−	1.01997i	−0.0201770	−	0.999796i	$-0.506423\pi$
$348$		0			0
$349$	−5.00000	−	5.00000i	−0.267644	−	0.267644i	0.560506	−	0.828150i	$-0.310607\pi$
$349$	−5.00000	−	5.00000i	−0.267644	−	0.267644i	−0.828150	+	0.560506i	$0.810607\pi$
$350$		0			0
$351$		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
$355$	−12.0000	−	6.00000i	−0.636894	−	0.318447i
$356$	−24.0000			−1.27200
$357$		0			0
$358$	−6.00000			−0.317110
$359$		−	18.0000i		−	0.950004i	−0.879985	−	0.475002i	$-0.842447\pi$
$359$		−	18.0000i		−	0.950004i	0.879985	−	0.475002i	$-0.157553\pi$
$360$		0			0
$361$		−	17.0000i		−	0.894737i
$362$			2.00000i			0.105118i
$363$		0			0
$364$		0			0
$365$	−6.00000	+	12.0000i	−0.314054	+	0.628109i
$366$		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
$370$	−6.00000	+	12.0000i	−0.311925	+	0.623850i
$371$		0			0
$372$		0			0
$373$	3.00000	+	3.00000i	0.155334	+	0.155334i	0.780496	−	0.625161i	$-0.214967\pi$
$373$	3.00000	+	3.00000i	0.155334	+	0.155334i	−0.625161	+	0.780496i	$0.714967\pi$
$374$	−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	−0.680957	−	0.732323i	$-0.738436\pi$
$379$	1.00000	−	1.00000i	0.0513665	−	0.0513665i	0.732323	+	0.680957i	$0.238436\pi$
$380$	−2.00000	−	6.00000i	−0.102598	−	0.307794i
$381$		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	−0.976418	−	0.215888i	$-0.930735\pi$
$389$	−15.0000	+	15.0000i	−0.760530	+	0.760530i	0.215888	+	0.976418i	$0.430735\pi$
$390$		0			0
$391$		−	32.0000i		−	1.61831i
$392$	14.0000	+	14.0000i	0.707107	+	0.707107i
$393$		0			0
$394$	10.0000			0.503793
$395$	−8.00000	+	16.0000i	−0.402524	+	0.805047i
$396$		0			0
$397$	−9.00000	+	9.00000i	−0.451697	+	0.451697i	−0.895918	−	0.444220i	$-0.853481\pi$
$397$	−9.00000	+	9.00000i	−0.451697	+	0.451697i	0.444220	+	0.895918i	$0.353481\pi$
$398$	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	0.238375	−	0.971173i	$-0.423385\pi$
$419$	−15.0000	−	15.0000i	−0.732798	−	0.732798i	−0.971173	+	0.238375i	$0.923385\pi$
$420$		0			0
$421$	−5.00000	+	5.00000i	−0.243685	+	0.243685i	−0.818373	−	0.574688i	$-0.805124\pi$
$421$	−5.00000	+	5.00000i	−0.243685	+	0.243685i	0.574688	+	0.818373i	$0.305124\pi$
$422$	22.0000			1.07094
$423$		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
$430$	−6.00000	+	12.0000i	−0.289346	+	0.578691i
$431$	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	$0.0767006\pi$
$439$			10.0000i			0.477274i	−0.971109	+	0.238637i	$0.923299\pi$
$440$	12.0000	−	24.0000i	0.572078	−	1.14416i
$441$		0			0
$442$	−24.0000			−1.14156
$443$	9.00000	+	9.00000i	0.427603	+	0.427603i	0.887811	−	0.460208i	$-0.152225\pi$
$443$	9.00000	+	9.00000i	0.427603	+	0.427603i	−0.460208	+	0.887811i	$0.652225\pi$
$444$		0			0
$445$	24.0000	+	12.0000i	1.13771	+	0.568855i
$446$	−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	$-0.361678\pi$
$457$	18.0000			0.842004			0.421002	+	0.907060i	$0.361678\pi$
$458$		−	14.0000i		−	0.654177i
$459$		0			0
$460$	32.0000	+	16.0000i	1.49201	+	0.746004i
$461$	−3.00000	−	3.00000i	−0.139724	−	0.139724i	0.633785	−	0.773509i	$-0.281500\pi$
$461$	−3.00000	−	3.00000i	−0.139724	−	0.139724i	−0.773509	+	0.633785i	$0.781500\pi$
$462$		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	$-0.802312\pi$
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	0.581893	+	0.813265i	$0.302312\pi$
$468$		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
$475$	−1.00000	+	7.00000i	−0.0458831	+	0.321182i
$476$		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
$485$	24.0000	+	12.0000i	1.08978	+	0.544892i
$486$		0			0
$487$	24.0000			1.08754			0.543772	−	0.839233i	$-0.316996\pi$
$487$	24.0000			1.08754			0.543772	+	0.839233i	$0.316996\pi$
$488$			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	−0.282366	−	0.959307i	$-0.591119\pi$
$491$	15.0000	−	15.0000i	0.676941	−	0.676941i	0.959307	+	0.282366i	$0.0911193\pi$
$492$		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	−0.929568	−	0.368650i	$-0.879820\pi$
$499$	−29.0000	−	29.0000i	−1.29822	−	1.29822i	−0.368650	−	0.929568i	$-0.620180\pi$
$500$	−4.00000	−	22.0000i	−0.178885	−	0.983870i
$501$		0			0
$502$			18.0000i			0.803379i
$503$	−32.0000			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$504$		0			0
$505$	−3.00000	−	9.00000i	−0.133498	−	0.400495i
$506$		−	48.0000i		−	2.13386i
$507$		0			0
$508$	−12.0000			−0.532414
$509$	9.00000	+	9.00000i	0.398918	+	0.398918i	0.877851	−	0.478933i	$-0.158976\pi$
$509$	9.00000	+	9.00000i	0.398918	+	0.398918i	−0.478933	+	0.877851i	$0.658976\pi$
$510$		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
$520$	12.0000	−	24.0000i	0.526235	−	1.05247i
$521$		−	24.0000i		−	1.05146i	−0.850652	−	0.525730i	$-0.823792\pi$
$521$		−	24.0000i		−	1.05146i	0.850652	−	0.525730i	$-0.176208\pi$
$522$		0			0
$523$	−9.00000	−	9.00000i	−0.393543	−	0.393543i	0.482405	−	0.875948i	$-0.339763\pi$
$523$	−9.00000	−	9.00000i	−0.393543	−	0.393543i	−0.875948	+	0.482405i	$0.839763\pi$
$524$	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
$530$	−18.0000	+	36.0000i	−0.781870	+	1.56374i
$531$		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	0.685283	−	0.728277i	$-0.259678\pi$
$541$	−1.00000	−	1.00000i	−0.0429934	−	0.0429934i	−0.728277	+	0.685283i	$0.759678\pi$
$542$	16.0000	−	16.0000i	0.687259	−	0.687259i
$543$		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	$-0.778911\pi$
$547$	−3.00000	+	3.00000i	−0.128271	+	0.128271i	0.640057	+	0.768328i	$0.278911\pi$
$548$			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	$-0.663092\pi$
$557$	9.00000	−	9.00000i	0.381342	−	0.381342i	0.871586	+	0.490243i	$0.163092\pi$
$558$		0			0
$559$	18.0000			0.761319
$560$		0			0
$561$		0			0
$562$	−12.0000	−	12.0000i	−0.506189	−	0.506189i
$563$	19.0000	−	19.0000i	0.800755	−	0.800755i	−0.182459	−	0.983213i	$-0.558406\pi$
$563$	19.0000	−	19.0000i	0.800755	−	0.800755i	0.983213	+	0.182459i	$0.0584057\pi$
$564$		0			0
$565$	16.0000	+	8.00000i	0.673125	+	0.336563i
$566$	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	$0.167795\pi$
$569$			24.0000i			1.00613i	−0.864248	+	0.503066i	$0.832205\pi$
$570$		0			0
$571$	−11.0000	+	11.0000i	−0.460336	+	0.460336i	−0.898765	−	0.438430i	$-0.855535\pi$
$571$	−11.0000	+	11.0000i	−0.460336	+	0.460336i	0.438430	+	0.898765i	$0.355535\pi$
$572$	−36.0000			−1.50524
$573$		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	$-0.165397\pi$
$587$	9.00000	+	9.00000i	0.371470	+	0.371470i	−0.496543	+	0.868012i	$0.665397\pi$
$588$		0			0
$589$		0			0
$590$	−36.0000	−	18.0000i	−1.48210	−	0.741048i
$591$		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	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$		0			0
$601$			36.0000i			1.46847i	0.678895	+	0.734235i	$0.262459\pi$
$601$			36.0000i			1.46847i	−0.678895	+	0.734235i	$0.737541\pi$
$602$		0			0
$603$		0			0
$604$	36.0000			1.46482
$605$	14.0000	+	7.00000i	0.569181	+	0.284590i
$606$		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
$610$	10.0000	−	20.0000i	0.404888	−	0.809776i
$611$	−6.00000	−	6.00000i	−0.242734	−	0.242734i
$612$		0			0
$613$	27.0000	+	27.0000i	1.09052	+	1.09052i	0.995473	+	0.0950469i	$0.0303001\pi$
$613$	27.0000	+	27.0000i	1.09052	+	1.09052i	0.0950469	+	0.995473i	$0.469700\pi$
$614$			6.00000i			0.242140i
$615$		0			0
$616$		0			0
$617$	10.0000			0.402585			0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000			0.402585			0.201292	+	0.979531i	$0.435486\pi$
$618$		0			0
$619$	13.0000	−	13.0000i	0.522514	−	0.522514i	−0.395816	−	0.918330i	$-0.629538\pi$
$619$	13.0000	−	13.0000i	0.522514	−	0.522514i	0.918330	+	0.395816i	$0.129538\pi$
$620$		0			0
$621$		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	$0.0126751\pi$
$631$			2.00000i			0.0796187i	−0.999207	+	0.0398094i	$0.987325\pi$
$632$	−16.0000	−	16.0000i	−0.636446	−	0.636446i
$633$		0			0
$634$			14.0000i			0.556011i
$635$	12.0000	+	6.00000i	0.476205	+	0.238103i
$636$		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	−0.0670247	+	0.997751i	$0.521351\pi$
$643$	−27.0000	+	27.0000i	−1.06478	+	1.06478i	−0.997751	+	0.0670247i	$0.978649\pi$
$644$		0			0
$645$		0			0
$646$			8.00000i			0.314756i
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$		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	$-0.669885\pi$
$653$	9.00000	−	9.00000i	0.352197	−	0.352197i	0.860927	+	0.508729i	$0.169885\pi$
$654$		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	0.985824	−	0.167781i	$-0.0536600\pi$
$659$	21.0000	+	21.0000i	0.818044	+	0.818044i	−0.167781	+	0.985824i	$0.553660\pi$
$660$		0			0
$661$	−29.0000	+	29.0000i	−1.12797	+	1.12797i	−0.137462	+	0.990507i	$0.543895\pi$
$661$	−29.0000	+	29.0000i	−1.12797	+	1.12797i	−0.990507	+	0.137462i	$0.956105\pi$
$662$		−	10.0000i		−	0.388661i
$663$		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
$670$	−12.0000	−	6.00000i	−0.463600	−	0.231800i
$671$	−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	$-0.171348\pi$
$677$	9.00000	+	9.00000i	0.345898	+	0.345898i	−0.512681	+	0.858579i	$0.671348\pi$
$678$		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	$-0.135591\pi$
$683$	13.0000	+	13.0000i	0.497431	+	0.497431i	−0.413206	+	0.910637i	$0.635591\pi$
$684$		0			0
$685$	2.00000	−	4.00000i	0.0764161	−	0.152832i
$686$		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	0.605577	−	0.795786i	$-0.292942\pi$
$691$	−5.00000	−	5.00000i	−0.190209	−	0.190209i	−0.795786	+	0.605577i	$0.792942\pi$
$692$	−18.0000	−	18.0000i	−0.684257	−	0.684257i
$693$		0			0
$694$	−38.0000			−1.44246
$695$	−7.00000	−	21.0000i	−0.265525	−	0.796575i
$696$		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	0.648179	−	0.761488i	$-0.275531\pi$
$701$	−3.00000	−	3.00000i	−0.113308	−	0.113308i	−0.761488	+	0.648179i	$0.775531\pi$
$702$		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	−0.907746	−	0.419521i	$-0.862198\pi$
$709$	−13.0000	+	13.0000i	−0.488225	+	0.488225i	0.419521	+	0.907746i	$0.362198\pi$
$710$	−18.0000	+	6.00000i	−0.675528	+	0.225176i
$711$		0			0
$712$	−24.0000	+	24.0000i	−0.899438	+	0.899438i
$713$		0			0
$714$		0			0
$715$	36.0000	+	18.0000i	1.34632	+	0.673162i
$716$	−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
$725$	−3.00000	+	21.0000i	−0.111417	+	0.779920i
$726$		0			0
$727$	24.0000			0.890111			0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000			0.890111			0.445055	+	0.895503i	$0.353184\pi$
$728$		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	$-0.725034\pi$
$733$	3.00000	−	3.00000i	0.110808	−	0.110808i	0.760337	+	0.649529i	$0.225034\pi$
$734$	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	0.964179	−	0.265253i	$-0.0854554\pi$
$739$	19.0000	+	19.0000i	0.698926	+	0.698926i	−0.265253	+	0.964179i	$0.585455\pi$
$740$	6.00000	+	18.0000i	0.220564	+	0.661693i
$741$		0			0
$742$		0			0
$743$	8.00000			0.293492			0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000			0.293492			0.146746	+	0.989174i	$0.453120\pi$
$744$		0			0
$745$	−3.00000	−	9.00000i	−0.109911	−	0.329734i
$746$	6.00000			0.219676
$747$		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
$755$	−36.0000	−	18.0000i	−1.31017	−	0.655087i
$756$		0			0
$757$	−33.0000	−	33.0000i	−1.19941	−	1.19941i	−0.974345	−	0.225061i	$-0.927742\pi$
$757$	−33.0000	−	33.0000i	−1.19941	−	1.19941i	−0.225061	−	0.974345i	$-0.572258\pi$
$758$		−	2.00000i		−	0.0726433i
$759$		0			0
$760$	−8.00000	−	4.00000i	−0.290191	−	0.145095i
$761$			48.0000i			1.74000i	0.493053	+	0.869999i	$0.335881\pi$
$761$			48.0000i			1.74000i	−0.493053	+	0.869999i	$0.664119\pi$
$762$		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	$-0.448888\pi$
$773$	−23.0000	−	23.0000i	−0.827253	−	0.827253i	−0.987136	+	0.159883i	$0.948888\pi$
$774$		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	0.195649	−	0.980674i	$-0.437319\pi$
$787$	33.0000	−	33.0000i	1.17632	−	1.17632i	0.980674	−	0.195649i	$-0.0626813\pi$
$788$	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	$-0.907875\pi$
$797$	−19.0000	+	19.0000i	−0.673015	+	0.673015i	0.285395	+	0.958410i	$0.407875\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	28.0000	+	4.00000i	0.989949	+	0.141421i
$801$		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	0.370356	−	0.928890i	$-0.379236\pi$
$811$	37.0000	−	37.0000i	1.29925	−	1.29925i	0.928890	−	0.370356i	$-0.120764\pi$
$812$		0			0
$813$		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	−0.488603	+	0.872506i	$0.662493\pi$
$821$	−39.0000	+	39.0000i	−1.36111	+	1.36111i	−0.872506	+	0.488603i	$0.837507\pi$
$822$		0			0
$823$	−24.0000			−0.836587			−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000			−0.836587			−0.418294	+	0.908312i	$0.637372\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−31.0000	−	31.0000i	−1.07798	−	1.07798i	−0.996691	−	0.0812847i	$-0.974098\pi$
$827$	−31.0000	−	31.0000i	−1.07798	−	1.07798i	−0.0812847	−	0.996691i	$-0.525902\pi$
$828$		0			0
$829$	35.0000	+	35.0000i	1.21560	+	1.21560i	0.969157	+	0.246443i	$0.0792618\pi$
$829$	35.0000	+	35.0000i	1.21560	+	1.21560i	0.246443	+	0.969157i	$0.420738\pi$
$830$	−36.0000	−	18.0000i	−1.24958	−	0.624789i
$831$		0			0
$832$	24.0000	+	24.0000i	0.832050	+	0.832050i
$833$			28.0000i			0.970143i
$834$		0			0
$835$	8.00000	−	16.0000i	0.276851	−	0.553703i
$836$			12.0000i			0.415029i
$837$		0			0
$838$	−30.0000			−1.03633
$839$		−	42.0000i		−	1.45000i	−0.688748	−	0.725001i	$-0.741839\pi$
$839$		−	42.0000i		−	1.45000i	0.688748	−	0.725001i	$-0.258161\pi$
$840$		0			0
$841$		−	11.0000i		−	0.379310i
$842$			10.0000i			0.344623i
$843$		0			0
$844$	22.0000	−	22.0000i	0.757271	−	0.757271i
$845$	10.0000	+	5.00000i	0.344010	+	0.172005i
$846$		0			0
$847$		0			0
$848$	−36.0000	−	36.0000i	−1.23625	−	1.23625i
$849$		0			0
$850$	−4.00000	+	28.0000i	−0.137199	+	0.960392i
$851$	24.0000	+	24.0000i	0.822709	+	0.822709i
$852$		0			0
$853$	15.0000	+	15.0000i	0.513590	+	0.513590i	0.915625	−	0.402034i	$-0.131697\pi$
$853$	15.0000	+	15.0000i	0.513590	+	0.513590i	−0.402034	+	0.915625i	$0.631697\pi$
$854$		0			0
$855$		0			0
$856$		−	36.0000i		−	1.23045i
$857$	38.0000			1.29806			0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000			1.29806			0.649028	+	0.760765i	$0.275176\pi$
$858$		0			0
$859$	−7.00000	+	7.00000i	−0.238837	+	0.238837i	−0.816368	−	0.577531i	$-0.804016\pi$
$859$	−7.00000	+	7.00000i	−0.238837	+	0.238837i	0.577531	+	0.816368i	$0.304016\pi$
$860$	6.00000	+	18.0000i	0.204598	+	0.613795i
$861$		0			0
$862$	24.0000	−	24.0000i	0.817443	−	0.817443i
$863$			22.0000i			0.748889i	0.927249	+	0.374444i	$0.122167\pi$
$863$			22.0000i			0.748889i	−0.927249	+	0.374444i	$0.877833\pi$
$864$		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	$-0.727179\pi$
$877$	3.00000	−	3.00000i	0.101303	−	0.101303i	0.755942	+	0.654639i	$0.227179\pi$
$878$	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	$-0.583437\pi$
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	0.965841	+	0.259135i	$0.0834374\pi$
$884$	−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	$-0.457119\pi$
$887$	8.00000			0.268614			0.134307	+	0.990940i	$0.457119\pi$
$888$		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	$-0.414122\pi$
$907$	−21.0000	−	21.0000i	−0.697294	−	0.697294i	−0.963826	+	0.266532i	$0.914122\pi$
$908$	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	$-0.650251\pi$
$919$		−	54.0000i		−	1.78130i	0.454694	−	0.890648i	$-0.349749\pi$
$920$	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
$925$	3.00000	−	21.0000i	0.0986394	−	0.690476i
$926$	−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	$-0.156162\pi$
$937$	54.0000			1.76410			0.882052	+	0.471153i	$0.156162\pi$
$938$		0			0
$939$		0			0
$940$	4.00000	−	8.00000i	0.130466	−	0.260931i
$941$	−27.0000	−	27.0000i	−0.880175	−	0.880175i	0.113377	−	0.993552i	$-0.463833\pi$
$941$	−27.0000	−	27.0000i	−0.880175	−	0.880175i	−0.993552	+	0.113377i	$0.963833\pi$
$942$		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	$-0.536969\pi$
$947$	27.0000	−	27.0000i	0.877382	−	0.877382i	0.993263	+	0.115881i	$0.0369691\pi$
$948$		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	$-0.384030\pi$
$953$	22.0000			0.712650			0.356325	+	0.934362i	$0.384030\pi$
$954$		0			0
$955$	−24.0000	+	48.0000i	−0.776622	+	1.55324i
$956$			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
$965$	−24.0000	−	12.0000i	−0.772587	−	0.386294i
$966$		0			0
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$	−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	−0.836615	−	0.547791i	$-0.815469\pi$
$971$	−9.00000	+	9.00000i	−0.288824	+	0.288824i	0.547791	+	0.836615i	$0.315469\pi$
$972$		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
$980$	−28.0000	−	14.0000i	−0.894427	−	0.447214i
$981$		0			0
$982$		−	30.0000i		−	0.957338i
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$		0			0
$985$	−15.0000	+	5.00000i	−0.477940	+	0.159313i
$986$			24.0000i			0.764316i
$987$		0			0
$988$			12.0000i			0.381771i
$989$	24.0000	+	24.0000i	0.763156	+	0.763156i
$990$		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
$995$	−4.00000	−	2.00000i	−0.126809	−	0.0634043i
$996$		0			0
$997$	−9.00000	−	9.00000i	−0.285033	−	0.285033i	0.550079	−	0.835112i	$-0.314597\pi$
$997$	−9.00000	−	9.00000i	−0.285033	−	0.285033i	−0.835112	+	0.550079i	$0.814597\pi$
$998$	−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.b.109.1		2
3.2	odd	2		80.2.q.a.29.1	✓	2
5.4	even	2		720.2.bm.a.109.1		2
12.11	even	2		320.2.q.a.209.1		2
15.2	even	4		400.2.l.a.301.1		2
15.8	even	4		400.2.l.b.301.1		2
15.14	odd	2		80.2.q.b.29.1	yes	2
16.5	even	4		720.2.bm.a.469.1		2
24.5	odd	2		640.2.q.b.289.1		2
24.11	even	2		640.2.q.d.289.1		2
48.5	odd	4		80.2.q.b.69.1	yes	2
48.11	even	4		320.2.q.b.49.1		2
48.29	odd	4		640.2.q.c.609.1		2
48.35	even	4		640.2.q.a.609.1		2
60.23	odd	4		1600.2.l.b.401.1		2
60.47	odd	4		1600.2.l.c.401.1		2
60.59	even	2		320.2.q.b.209.1		2
80.69	even	4	inner	720.2.bm.b.469.1		2
120.29	odd	2		640.2.q.c.289.1		2
120.59	even	2		640.2.q.a.289.1		2
240.29	odd	4		640.2.q.b.609.1		2
240.53	even	4		400.2.l.b.101.1		2
240.59	even	4		320.2.q.a.49.1		2
240.107	odd	4		1600.2.l.c.1201.1		2
240.149	odd	4		80.2.q.a.69.1	yes	2
240.179	even	4		640.2.q.d.609.1		2
240.197	even	4		400.2.l.a.101.1		2
240.203	odd	4		1600.2.l.b.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.a.29.1	✓	2	3.2	odd	2
80.2.q.a.69.1	yes	2	240.149	odd	4
80.2.q.b.29.1	yes	2	15.14	odd	2
80.2.q.b.69.1	yes	2	48.5	odd	4
320.2.q.a.49.1		2	240.59	even	4
320.2.q.a.209.1		2	12.11	even	2
320.2.q.b.49.1		2	48.11	even	4
320.2.q.b.209.1		2	60.59	even	2
400.2.l.a.101.1		2	240.197	even	4
400.2.l.a.301.1		2	15.2	even	4
400.2.l.b.101.1		2	240.53	even	4
400.2.l.b.301.1		2	15.8	even	4
640.2.q.a.289.1		2	120.59	even	2
640.2.q.a.609.1		2	48.35	even	4
640.2.q.b.289.1		2	24.5	odd	2
640.2.q.b.609.1		2	240.29	odd	4
640.2.q.c.289.1		2	120.29	odd	2
640.2.q.c.609.1		2	48.29	odd	4
640.2.q.d.289.1		2	24.11	even	2
640.2.q.d.609.1		2	240.179	even	4
720.2.bm.a.109.1		2	5.4	even	2
720.2.bm.a.469.1		2	16.5	even	4
720.2.bm.b.109.1		2	1.1	even	1	trivial
720.2.bm.b.469.1		2	80.69	even	4	inner
1600.2.l.b.401.1		2	60.23	odd	4
1600.2.l.b.1201.1		2	240.203	odd	4
1600.2.l.c.401.1		2	60.47	odd	4
1600.2.l.c.1201.1		2	240.107	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)

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

Introduction

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