LMFDB - Embedded newform 720.2.z.d.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.74922894553$
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			163.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	720.163
Dual form			720.2.z.d.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.00000 + 3.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} -2.00000i q^{13} -6.00000 q^{14} -4.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(-2.00000 + 4.00000i) q^{20} +2.00000i q^{22} +(1.00000 + 1.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(2.00000 - 2.00000i) q^{26} +(-6.00000 - 6.00000i) q^{28} +(7.00000 - 7.00000i) q^{29} +2.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} -2.00000 q^{34} +(-9.00000 + 3.00000i) q^{35} +6.00000i q^{37} -6.00000i q^{38} +(-6.00000 + 2.00000i) q^{40} +4.00000i q^{41} +4.00000i q^{43} +(-2.00000 + 2.00000i) q^{44} +2.00000i q^{46} +(7.00000 + 7.00000i) q^{47} -11.0000i q^{49} +(-1.00000 + 7.00000i) q^{50} +4.00000 q^{52} +8.00000 q^{53} +(1.00000 + 3.00000i) q^{55} -12.0000i q^{56} +14.0000 q^{58} +(-3.00000 + 3.00000i) q^{59} +(-1.00000 - 1.00000i) q^{61} +(-2.00000 + 2.00000i) q^{62} -8.00000i q^{64} +(2.00000 - 4.00000i) q^{65} -4.00000i q^{67} +(-2.00000 - 2.00000i) q^{68} +(-12.0000 - 6.00000i) q^{70} +(3.00000 - 3.00000i) q^{73} +(-6.00000 + 6.00000i) q^{74} +(6.00000 - 6.00000i) q^{76} -6.00000 q^{77} +8.00000 q^{79} +(-8.00000 - 4.00000i) q^{80} +(-4.00000 + 4.00000i) q^{82} +2.00000 q^{83} +(-3.00000 + 1.00000i) q^{85} +(-4.00000 + 4.00000i) q^{86} -4.00000 q^{88} +6.00000 q^{89} +(6.00000 + 6.00000i) q^{91} +(-2.00000 + 2.00000i) q^{92} +14.0000i q^{94} +(-3.00000 - 9.00000i) q^{95} +(-11.0000 + 11.0000i) q^{97} +(11.0000 - 11.0000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 4 q^{5} - 6 q^{7} - 4 q^{8} + 2 q^{10} + 2 q^{11} - 12 q^{14} - 8 q^{16} - 2 q^{17} - 6 q^{19} - 4 q^{20} + 2 q^{23} + 6 q^{25} + 4 q^{26} - 12 q^{28} + 14 q^{29} - 8 q^{32} - 4 q^{34} - 18 q^{35}+ \cdots + 22 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 4 * q^5 - 6 * q^7 - 4 * q^8 + 2 * q^10 + 2 * q^11 - 12 * q^14 - 8 * q^16 - 2 * q^17 - 6 * q^19 - 4 * q^20 + 2 * q^23 + 6 * q^25 + 4 * q^26 - 12 * q^28 + 14 * q^29 - 8 * q^32 - 4 * q^34 - 18 * q^35 - 12 * q^40 - 4 * q^44 + 14 * q^47 - 2 * q^50 + 8 * q^52 + 16 * q^53 + 2 * q^55 + 28 * q^58 - 6 * q^59 - 2 * q^61 - 4 * q^62 + 4 * q^65 - 4 * q^68 - 24 * q^70 + 6 * q^73 - 12 * q^74 + 12 * q^76 - 12 * q^77 + 16 * q^79 - 16 * q^80 - 8 * q^82 + 4 * q^83 - 6 * q^85 - 8 * q^86 - 8 * q^88 + 12 * q^89 + 12 * q^91 - 4 * q^92 - 6 * q^95 - 22 * q^97 + 22 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$		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
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.144370	+	0.989524i	$0.546115\pi$
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.989524	+	0.144370i	$0.953885\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	1.00000	+	3.00000i	0.316228	+	0.948683i
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−6.00000			−1.60357
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$		0			0
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$	−2.00000	+	4.00000i	−0.447214	+	0.894427i
$21$		0			0
$22$			2.00000i			0.426401i
$23$	1.00000	+	1.00000i	0.208514	+	0.208514i	0.803636	−	0.595121i	$-0.202896\pi$
$23$	1.00000	+	1.00000i	0.208514	+	0.208514i	−0.595121	+	0.803636i	$0.702896\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	2.00000	−	2.00000i	0.392232	−	0.392232i
$27$		0			0
$28$	−6.00000	−	6.00000i	−1.13389	−	1.13389i
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.371391	−	0.928477i	$-0.378881\pi$
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$			2.00000i			0.359211i	0.983739	+	0.179605i	$0.0574821\pi$
$31$			2.00000i			0.359211i	−0.983739	+	0.179605i	$0.942518\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	−9.00000	+	3.00000i	−1.52128	+	0.507093i
$36$		0			0
$37$			6.00000i			0.986394i	0.869918	+	0.493197i	$0.164172\pi$
$37$			6.00000i			0.986394i	−0.869918	+	0.493197i	$0.835828\pi$
$38$		−	6.00000i		−	0.973329i
$39$		0			0
$40$	−6.00000	+	2.00000i	−0.948683	+	0.316228i
$41$			4.00000i			0.624695i	0.949968	+	0.312348i	$0.101115\pi$
$41$			4.00000i			0.624695i	−0.949968	+	0.312348i	$0.898885\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−2.00000	+	2.00000i	−0.301511	+	0.301511i
$45$		0			0
$46$			2.00000i			0.294884i
$47$	7.00000	+	7.00000i	1.02105	+	1.02105i	0.999774	+	0.0212814i	$0.00677460\pi$
$47$	7.00000	+	7.00000i	1.02105	+	1.02105i	0.0212814	+	0.999774i	$0.493225\pi$
$48$		0			0
$49$		−	11.0000i		−	1.57143i
$50$	−1.00000	+	7.00000i	−0.141421	+	0.989949i
$51$		0			0
$52$	4.00000			0.554700
$53$	8.00000			1.09888			0.549442	−	0.835532i	$-0.314840\pi$
$53$	8.00000			1.09888			0.549442	+	0.835532i	$0.314840\pi$
$54$		0			0
$55$	1.00000	+	3.00000i	0.134840	+	0.404520i
$56$		−	12.0000i		−	1.60357i
$57$		0			0
$58$	14.0000			1.83829
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	−0.874889	−	0.484323i	$-0.839066\pi$
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	0.484323	+	0.874889i	$0.339066\pi$
$60$		0			0
$61$	−1.00000	−	1.00000i	−0.128037	−	0.128037i	0.640184	−	0.768221i	$-0.278858\pi$
$61$	−1.00000	−	1.00000i	−0.128037	−	0.128037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$	−2.00000	+	2.00000i	−0.254000	+	0.254000i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	2.00000	−	4.00000i	0.248069	−	0.496139i
$66$		0			0
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	−2.00000	−	2.00000i	−0.242536	−	0.242536i
$69$		0			0
$70$	−12.0000	−	6.00000i	−1.43427	−	0.717137i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	3.00000	−	3.00000i	0.351123	−	0.351123i	−0.509404	−	0.860527i	$-0.670134\pi$
$73$	3.00000	−	3.00000i	0.351123	−	0.351123i	0.860527	+	0.509404i	$0.170134\pi$
$74$	−6.00000	+	6.00000i	−0.697486	+	0.697486i
$75$		0			0
$76$	6.00000	−	6.00000i	0.688247	−	0.688247i
$77$	−6.00000			−0.683763
$78$		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
$82$	−4.00000	+	4.00000i	−0.441726	+	0.441726i
$83$	2.00000			0.219529			0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000			0.219529			0.109764	+	0.993958i	$0.464990\pi$
$84$		0			0
$85$	−3.00000	+	1.00000i	−0.325396	+	0.108465i
$86$	−4.00000	+	4.00000i	−0.431331	+	0.431331i
$87$		0			0
$88$	−4.00000			−0.426401
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	6.00000	+	6.00000i	0.628971	+	0.628971i
$92$	−2.00000	+	2.00000i	−0.208514	+	0.208514i
$93$		0			0
$94$			14.0000i			1.44399i
$95$	−3.00000	−	9.00000i	−0.307794	−	0.923381i
$96$		0			0
$97$	−11.0000	+	11.0000i	−1.11688	+	1.11688i	−0.124684	+	0.992196i	$0.539792\pi$
$97$	−11.0000	+	11.0000i	−1.11688	+	1.11688i	−0.992196	+	0.124684i	$0.960208\pi$
$98$	11.0000	−	11.0000i	1.11117	−	1.11117i
$99$		0			0
$100$	−8.00000	+	6.00000i	−0.800000	+	0.600000i
$101$	5.00000	−	5.00000i	0.497519	−	0.497519i	−0.413146	−	0.910665i	$-0.635570\pi$
$101$	5.00000	−	5.00000i	0.497519	−	0.497519i	0.910665	+	0.413146i	$0.135570\pi$
$102$		0			0
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$104$	4.00000	+	4.00000i	0.392232	+	0.392232i
$105$		0			0
$106$	8.00000	+	8.00000i	0.777029	+	0.777029i
$107$	6.00000			0.580042			0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000			0.580042			0.290021	+	0.957020i	$0.406338\pi$
$108$		0			0
$109$	5.00000	−	5.00000i	0.478913	−	0.478913i	−0.425871	−	0.904784i	$-0.640032\pi$
$109$	5.00000	−	5.00000i	0.478913	−	0.478913i	0.904784	+	0.425871i	$0.140032\pi$
$110$	−2.00000	+	4.00000i	−0.190693	+	0.381385i
$111$		0			0
$112$	12.0000	−	12.0000i	1.13389	−	1.13389i
$113$	−13.0000	−	13.0000i	−1.22294	−	1.22294i	−0.966583	−	0.256354i	$-0.917479\pi$
$113$	−13.0000	−	13.0000i	−1.22294	−	1.22294i	−0.256354	−	0.966583i	$-0.582521\pi$
$114$		0			0
$115$	1.00000	+	3.00000i	0.0932505	+	0.279751i
$116$	14.0000	+	14.0000i	1.29987	+	1.29987i
$117$		0			0
$118$	−6.00000			−0.552345
$119$		−	6.00000i		−	0.550019i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		−	2.00000i		−	0.181071i
$123$		0			0
$124$	−4.00000			−0.359211
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	0.324676	−	0.945825i	$-0.394745\pi$
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	−0.945825	+	0.324676i	$0.894745\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$		0			0
$130$	6.00000	−	2.00000i	0.526235	−	0.175412i
$131$	7.00000	−	7.00000i	0.611593	−	0.611593i	−0.331768	−	0.943361i	$-0.607645\pi$
$131$	7.00000	−	7.00000i	0.611593	−	0.611593i	0.943361	+	0.331768i	$0.107645\pi$
$132$		0			0
$133$	18.0000			1.56080
$134$	4.00000	−	4.00000i	0.345547	−	0.345547i
$135$		0			0
$136$		−	4.00000i		−	0.342997i
$137$	9.00000	+	9.00000i	0.768922	+	0.768922i	0.977917	−	0.208995i	$-0.0670192\pi$
$137$	9.00000	+	9.00000i	0.768922	+	0.768922i	−0.208995	+	0.977917i	$0.567019\pi$
$138$		0			0
$139$	−9.00000	+	9.00000i	−0.763370	+	0.763370i	−0.976930	−	0.213560i	$-0.931494\pi$
$139$	−9.00000	+	9.00000i	−0.763370	+	0.763370i	0.213560	+	0.976930i	$0.431494\pi$
$140$	−6.00000	−	18.0000i	−0.507093	−	1.52128i
$141$		0			0
$142$		0			0
$143$	2.00000	−	2.00000i	0.167248	−	0.167248i
$144$		0			0
$145$	21.0000	−	7.00000i	1.74396	−	0.581318i
$146$	6.00000			0.496564
$147$		0			0
$148$	−12.0000			−0.986394
$149$	−1.00000	−	1.00000i	−0.0819232	−	0.0819232i	0.664958	−	0.746881i	$-0.268450\pi$
$149$	−1.00000	−	1.00000i	−0.0819232	−	0.0819232i	−0.746881	+	0.664958i	$0.768450\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	12.0000			0.973329
$153$		0			0
$154$	−6.00000	−	6.00000i	−0.483494	−	0.483494i
$155$	−2.00000	+	4.00000i	−0.160644	+	0.321288i
$156$		0			0
$157$	20.0000			1.59617			0.798087	−	0.602542i	$-0.205846\pi$
$157$	20.0000			1.59617			0.798087	+	0.602542i	$0.205846\pi$
$158$	8.00000	+	8.00000i	0.636446	+	0.636446i
$159$		0			0
$160$	−4.00000	−	12.0000i	−0.316228	−	0.948683i
$161$	−6.00000			−0.472866
$162$		0			0
$163$	14.0000			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$164$	−8.00000			−0.624695
$165$		0			0
$166$	2.00000	+	2.00000i	0.155230	+	0.155230i
$167$	3.00000	−	3.00000i	0.232147	−	0.232147i	−0.581441	−	0.813588i	$-0.697511\pi$
$167$	3.00000	−	3.00000i	0.232147	−	0.232147i	0.813588	+	0.581441i	$0.197511\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−4.00000	−	2.00000i	−0.306786	−	0.153393i
$171$		0			0
$172$	−8.00000			−0.609994
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$		0			0
$175$	−21.0000	−	3.00000i	−1.58745	−	0.226779i
$176$	−4.00000	−	4.00000i	−0.301511	−	0.301511i
$177$		0			0
$178$	6.00000	+	6.00000i	0.449719	+	0.449719i
$179$	−5.00000	−	5.00000i	−0.373718	−	0.373718i	0.495112	−	0.868829i	$-0.335127\pi$
$179$	−5.00000	−	5.00000i	−0.373718	−	0.373718i	−0.868829	+	0.495112i	$0.835127\pi$
$180$		0			0
$181$	3.00000	−	3.00000i	0.222988	−	0.222988i	−0.586767	−	0.809756i	$-0.699600\pi$
$181$	3.00000	−	3.00000i	0.222988	−	0.222988i	0.809756	+	0.586767i	$0.199600\pi$
$182$			12.0000i			0.889499i
$183$		0			0
$184$	−4.00000			−0.294884
$185$	−6.00000	+	12.0000i	−0.441129	+	0.882258i
$186$		0			0
$187$	−2.00000			−0.146254
$188$	−14.0000	+	14.0000i	−1.02105	+	1.02105i
$189$		0			0
$190$	6.00000	−	12.0000i	0.435286	−	0.870572i
$191$		−	18.0000i		−	1.30243i	−0.758891	−	0.651217i	$-0.774259\pi$
$191$		−	18.0000i		−	1.30243i	0.758891	−	0.651217i	$-0.225741\pi$
$192$		0			0
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.996534	−	0.0831899i	$-0.973489\pi$
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.0831899	−	0.996534i	$-0.526511\pi$
$194$	−22.0000			−1.57951
$195$		0			0
$196$	22.0000			1.57143
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		0			0
$199$		−	10.0000i		−	0.708881i	−0.935079	−	0.354441i	$-0.884671\pi$
$199$		−	10.0000i		−	0.708881i	0.935079	−	0.354441i	$-0.115329\pi$
$200$	−14.0000	−	2.00000i	−0.989949	−	0.141421i
$201$		0			0
$202$	10.0000			0.703598
$203$			42.0000i			2.94782i
$204$		0			0
$205$	−4.00000	+	8.00000i	−0.279372	+	0.558744i
$206$		−	10.0000i		−	0.696733i
$207$		0			0
$208$			8.00000i			0.554700i
$209$		−	6.00000i		−	0.415029i
$210$		0			0
$211$	−19.0000	+	19.0000i	−1.30801	+	1.30801i	−0.385167	+	0.922847i	$0.625856\pi$
$211$	−19.0000	+	19.0000i	−1.30801	+	1.30801i	−0.922847	+	0.385167i	$0.874144\pi$
$212$			16.0000i			1.09888i
$213$		0			0
$214$	6.00000	+	6.00000i	0.410152	+	0.410152i
$215$	−4.00000	+	8.00000i	−0.272798	+	0.545595i
$216$		0			0
$217$	−6.00000	−	6.00000i	−0.407307	−	0.407307i
$218$	10.0000			0.677285
$219$		0			0
$220$	−6.00000	+	2.00000i	−0.404520	+	0.134840i
$221$	2.00000	+	2.00000i	0.134535	+	0.134535i
$222$		0			0
$223$	−9.00000	+	9.00000i	−0.602685	+	0.602685i	−0.941024	−	0.338340i	$-0.890135\pi$
$223$	−9.00000	+	9.00000i	−0.602685	+	0.602685i	0.338340	+	0.941024i	$0.390135\pi$
$224$	24.0000			1.60357
$225$		0			0
$226$		−	26.0000i		−	1.72949i
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$		0			0
$229$	1.00000	+	1.00000i	0.0660819	+	0.0660819i	0.739375	−	0.673293i	$-0.235121\pi$
$229$	1.00000	+	1.00000i	0.0660819	+	0.0660819i	−0.673293	+	0.739375i	$0.735121\pi$
$230$	−2.00000	+	4.00000i	−0.131876	+	0.263752i
$231$		0			0
$232$			28.0000i			1.83829i
$233$	9.00000	−	9.00000i	0.589610	−	0.589610i	−0.347916	−	0.937526i	$-0.613111\pi$
$233$	9.00000	−	9.00000i	0.589610	−	0.589610i	0.937526	+	0.347916i	$0.113111\pi$
$234$		0			0
$235$	7.00000	+	21.0000i	0.456630	+	1.36989i
$236$	−6.00000	−	6.00000i	−0.390567	−	0.390567i
$237$		0			0
$238$	6.00000	−	6.00000i	0.388922	−	0.388922i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$	9.00000	−	9.00000i	0.578542	−	0.578542i
$243$		0			0
$244$	2.00000	−	2.00000i	0.128037	−	0.128037i
$245$	11.0000	−	22.0000i	0.702764	−	1.40553i
$246$		0			0
$247$	−6.00000	+	6.00000i	−0.381771	+	0.381771i
$248$	−4.00000	−	4.00000i	−0.254000	−	0.254000i
$249$		0			0
$250$	−9.00000	+	13.0000i	−0.569210	+	0.822192i
$251$	−11.0000	−	11.0000i	−0.694314	−	0.694314i	0.268864	−	0.963178i	$-0.413352\pi$
$251$	−11.0000	−	11.0000i	−0.694314	−	0.694314i	−0.963178	+	0.268864i	$0.913352\pi$
$252$		0			0
$253$			2.00000i			0.125739i
$254$		−	14.0000i		−	0.878438i
$255$		0			0
$256$	16.0000			1.00000
$257$	−13.0000	+	13.0000i	−0.810918	+	0.810918i	−0.984771	−	0.173854i	$-0.944378\pi$
$257$	−13.0000	+	13.0000i	−0.810918	+	0.810918i	0.173854	+	0.984771i	$0.444378\pi$
$258$		0			0
$259$	−18.0000	−	18.0000i	−1.11847	−	1.11847i
$260$	8.00000	+	4.00000i	0.496139	+	0.248069i
$261$		0			0
$262$	14.0000			0.864923
$263$	−7.00000	−	7.00000i	−0.431638	−	0.431638i	0.457547	−	0.889185i	$-0.348728\pi$
$263$	−7.00000	−	7.00000i	−0.431638	−	0.431638i	−0.889185	+	0.457547i	$0.848728\pi$
$264$		0			0
$265$	16.0000	+	8.00000i	0.982872	+	0.491436i
$266$	18.0000	+	18.0000i	1.10365	+	1.10365i
$267$		0			0
$268$	8.00000			0.488678
$269$	−1.00000	+	1.00000i	−0.0609711	+	0.0609711i	−0.736935	−	0.675964i	$-0.763728\pi$
$269$	−1.00000	+	1.00000i	−0.0609711	+	0.0609711i	0.675964	+	0.736935i	$0.263728\pi$
$270$		0			0
$271$		−	30.0000i		−	1.82237i	−0.411997	−	0.911185i	$-0.635169\pi$
$271$		−	30.0000i		−	1.82237i	0.411997	−	0.911185i	$-0.364831\pi$
$272$	4.00000	−	4.00000i	0.242536	−	0.242536i
$273$		0			0
$274$			18.0000i			1.08742i
$275$	−1.00000	+	7.00000i	−0.0603023	+	0.422116i
$276$		0			0
$277$		−	18.0000i		−	1.08152i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$		−	18.0000i		−	1.08152i	0.841178	−	0.540758i	$-0.181862\pi$
$278$	−18.0000			−1.07957
$279$		0			0
$280$	12.0000	−	24.0000i	0.717137	−	1.43427i
$281$		−	16.0000i		−	0.954480i	−0.878773	−	0.477240i	$-0.841637\pi$
$281$		−	16.0000i		−	0.954480i	0.878773	−	0.477240i	$-0.158363\pi$
$282$		0			0
$283$			12.0000i			0.713326i	0.934233	+	0.356663i	$0.116086\pi$
$283$			12.0000i			0.713326i	−0.934233	+	0.356663i	$0.883914\pi$
$284$		0			0
$285$		0			0
$286$	4.00000			0.236525
$287$	−12.0000	−	12.0000i	−0.708338	−	0.708338i
$288$		0			0
$289$			15.0000i			0.882353i
$290$	28.0000	+	14.0000i	1.64422	+	0.822108i
$291$		0			0
$292$	6.00000	+	6.00000i	0.351123	+	0.351123i
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$	−9.00000	+	3.00000i	−0.524000	+	0.174667i
$296$	−12.0000	−	12.0000i	−0.697486	−	0.697486i
$297$		0			0
$298$		−	2.00000i		−	0.115857i
$299$	2.00000	−	2.00000i	0.115663	−	0.115663i
$300$		0			0
$301$	−12.0000	−	12.0000i	−0.691669	−	0.691669i
$302$	8.00000	+	8.00000i	0.460348	+	0.460348i
$303$		0			0
$304$	12.0000	+	12.0000i	0.688247	+	0.688247i
$305$	−1.00000	−	3.00000i	−0.0572598	−	0.171780i
$306$		0			0
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$		−	12.0000i		−	0.683763i
$309$		0			0
$310$	−6.00000	+	2.00000i	−0.340777	+	0.113592i
$311$	−16.0000			−0.907277			−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000			−0.907277			−0.453638	+	0.891186i	$0.649874\pi$
$312$		0			0
$313$	−13.0000	+	13.0000i	−0.734803	+	0.734803i	−0.971567	−	0.236764i	$-0.923913\pi$
$313$	−13.0000	+	13.0000i	−0.734803	+	0.734803i	0.236764	+	0.971567i	$0.423913\pi$
$314$	20.0000	+	20.0000i	1.12867	+	1.12867i
$315$		0			0
$316$			16.0000i			0.900070i
$317$	−8.00000			−0.449325			−0.224662	−	0.974437i	$-0.572128\pi$
$317$	−8.00000			−0.449325			−0.224662	+	0.974437i	$0.572128\pi$
$318$		0			0
$319$	14.0000			0.783850
$320$	8.00000	−	16.0000i	0.447214	−	0.894427i
$321$		0			0
$322$	−6.00000	−	6.00000i	−0.334367	−	0.334367i
$323$	6.00000			0.333849
$324$		0			0
$325$	8.00000	−	6.00000i	0.443760	−	0.332820i
$326$	14.0000	+	14.0000i	0.775388	+	0.775388i
$327$		0			0
$328$	−8.00000	−	8.00000i	−0.441726	−	0.441726i
$329$	−42.0000			−2.31553
$330$		0			0
$331$	−21.0000	−	21.0000i	−1.15426	−	1.15426i	−0.985689	−	0.168576i	$-0.946083\pi$
$331$	−21.0000	−	21.0000i	−1.15426	−	1.15426i	−0.168576	−	0.985689i	$-0.553917\pi$
$332$			4.00000i			0.219529i
$333$		0			0
$334$	6.00000			0.328305
$335$	4.00000	−	8.00000i	0.218543	−	0.437087i
$336$		0			0
$337$	−11.0000	+	11.0000i	−0.599208	+	0.599208i	−0.940102	−	0.340894i	$-0.889270\pi$
$337$	−11.0000	+	11.0000i	−0.599208	+	0.599208i	0.340894	+	0.940102i	$0.389270\pi$
$338$	9.00000	+	9.00000i	0.489535	+	0.489535i
$339$		0			0
$340$	−2.00000	−	6.00000i	−0.108465	−	0.325396i
$341$	−2.00000	+	2.00000i	−0.108306	+	0.108306i
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−8.00000	−	8.00000i	−0.431331	−	0.431331i
$345$		0			0
$346$	−6.00000	+	6.00000i	−0.322562	+	0.322562i
$347$	−2.00000			−0.107366			−0.0536828	−	0.998558i	$-0.517096\pi$
$347$	−2.00000			−0.107366			−0.0536828	+	0.998558i	$0.517096\pi$
$348$		0			0
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	−0.782826	−	0.622240i	$-0.786223\pi$
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	0.622240	+	0.782826i	$0.286223\pi$
$350$	−18.0000	−	24.0000i	−0.962140	−	1.28285i
$351$		0			0
$352$		−	8.00000i		−	0.426401i
$353$	−13.0000	−	13.0000i	−0.691920	−	0.691920i	0.270734	−	0.962654i	$-0.412734\pi$
$353$	−13.0000	−	13.0000i	−0.691920	−	0.691920i	−0.962654	+	0.270734i	$0.912734\pi$
$354$		0			0
$355$		0			0
$356$			12.0000i			0.635999i
$357$		0			0
$358$		−	10.0000i		−	0.528516i
$359$		−	14.0000i		−	0.738892i	−0.929252	−	0.369446i	$-0.879548\pi$
$359$		−	14.0000i		−	0.738892i	0.929252	−	0.369446i	$-0.120452\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$	6.00000			0.315353
$363$		0			0
$364$	−12.0000	+	12.0000i	−0.628971	+	0.628971i
$365$	9.00000	−	3.00000i	0.471082	−	0.157027i
$366$		0			0
$367$	21.0000	+	21.0000i	1.09619	+	1.09619i	0.994852	+	0.101339i	$0.0323127\pi$
$367$	21.0000	+	21.0000i	1.09619	+	1.09619i	0.101339	+	0.994852i	$0.467687\pi$
$368$	−4.00000	−	4.00000i	−0.208514	−	0.208514i
$369$		0			0
$370$	−18.0000	+	6.00000i	−0.935775	+	0.311925i
$371$	−24.0000	+	24.0000i	−1.24602	+	1.24602i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$	−2.00000	−	2.00000i	−0.103418	−	0.103418i
$375$		0			0
$376$	−28.0000			−1.44399
$377$	−14.0000	−	14.0000i	−0.721037	−	0.721037i
$378$		0			0
$379$	15.0000	−	15.0000i	0.770498	−	0.770498i	−0.207695	−	0.978194i	$-0.566596\pi$
$379$	15.0000	−	15.0000i	0.770498	−	0.770498i	0.978194	+	0.207695i	$0.0665963\pi$
$380$	18.0000	−	6.00000i	0.923381	−	0.307794i
$381$		0			0
$382$	18.0000	−	18.0000i	0.920960	−	0.920960i
$383$	5.00000	−	5.00000i	0.255488	−	0.255488i	−0.567728	−	0.823216i	$-0.692177\pi$
$383$	5.00000	−	5.00000i	0.255488	−	0.255488i	0.823216	+	0.567728i	$0.192177\pi$
$384$		0			0
$385$	−12.0000	−	6.00000i	−0.611577	−	0.305788i
$386$		−	30.0000i		−	1.52696i
$387$		0			0
$388$	−22.0000	−	22.0000i	−1.11688	−	1.11688i
$389$	23.0000	+	23.0000i	1.16615	+	1.16615i	0.983105	+	0.183041i	$0.0585941\pi$
$389$	23.0000	+	23.0000i	1.16615	+	1.16615i	0.183041	+	0.983105i	$0.441406\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$	22.0000	+	22.0000i	1.11117	+	1.11117i
$393$		0			0
$394$	−6.00000	+	6.00000i	−0.302276	+	0.302276i
$395$	16.0000	+	8.00000i	0.805047	+	0.402524i
$396$		0			0
$397$	−32.0000			−1.60603			−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000			−1.60603			−0.803017	+	0.595956i	$0.796773\pi$
$398$	10.0000	−	10.0000i	0.501255	−	0.501255i
$399$		0			0
$400$	−12.0000	−	16.0000i	−0.600000	−	0.800000i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$		0			0
$403$	4.00000			0.199254
$404$	10.0000	+	10.0000i	0.497519	+	0.497519i
$405$		0			0
$406$	−42.0000	+	42.0000i	−2.08443	+	2.08443i
$407$	−6.00000	+	6.00000i	−0.297409	+	0.297409i
$408$		0			0
$409$	−38.0000			−1.87898			−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−38.0000			−1.87898			−0.939490	+	0.342578i	$0.888700\pi$
$410$	−12.0000	+	4.00000i	−0.592638	+	0.197546i
$411$		0			0
$412$	10.0000	−	10.0000i	0.492665	−	0.492665i
$413$		−	18.0000i		−	0.885722i
$414$		0			0
$415$	4.00000	+	2.00000i	0.196352	+	0.0981761i
$416$	−8.00000	+	8.00000i	−0.392232	+	0.392232i
$417$		0			0
$418$	6.00000	−	6.00000i	0.293470	−	0.293470i
$419$	−17.0000	−	17.0000i	−0.830504	−	0.830504i	0.157081	−	0.987586i	$-0.449792\pi$
$419$	−17.0000	−	17.0000i	−0.830504	−	0.830504i	−0.987586	+	0.157081i	$0.949792\pi$
$420$		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	$0.305124\pi$
$422$	−38.0000			−1.84981
$423$		0			0
$424$	−16.0000	+	16.0000i	−0.777029	+	0.777029i
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$		0			0
$427$	6.00000			0.290360
$428$			12.0000i			0.580042i
$429$		0			0
$430$	−12.0000	+	4.00000i	−0.578691	+	0.192897i
$431$		−	2.00000i		−	0.0963366i	−0.998839	−	0.0481683i	$-0.984662\pi$
$431$		−	2.00000i		−	0.0963366i	0.998839	−	0.0481683i	$-0.0153384\pi$
$432$		0			0
$433$	5.00000	+	5.00000i	0.240285	+	0.240285i	0.816968	−	0.576683i	$-0.195653\pi$
$433$	5.00000	+	5.00000i	0.240285	+	0.240285i	−0.576683	+	0.816968i	$0.695653\pi$
$434$		−	12.0000i		−	0.576018i
$435$		0			0
$436$	10.0000	+	10.0000i	0.478913	+	0.478913i
$437$		−	6.00000i		−	0.287019i
$438$		0			0
$439$		−	26.0000i		−	1.24091i	−0.784241	−	0.620456i	$-0.786947\pi$
$439$		−	26.0000i		−	1.24091i	0.784241	−	0.620456i	$-0.213053\pi$
$440$	−8.00000	−	4.00000i	−0.381385	−	0.190693i
$441$		0			0
$442$			4.00000i			0.190261i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$		0			0
$445$	12.0000	+	6.00000i	0.568855	+	0.284427i
$446$	−18.0000			−0.852325
$447$		0			0
$448$	24.0000	+	24.0000i	1.13389	+	1.13389i
$449$			24.0000i			1.13263i	0.824189	+	0.566315i	$0.191631\pi$
$449$			24.0000i			1.13263i	−0.824189	+	0.566315i	$0.808369\pi$
$450$		0			0
$451$	−4.00000	+	4.00000i	−0.188353	+	0.188353i
$452$	26.0000	−	26.0000i	1.22294	−	1.22294i
$453$		0			0
$454$	−12.0000	+	12.0000i	−0.563188	+	0.563188i
$455$	6.00000	+	18.0000i	0.281284	+	0.843853i
$456$		0			0
$457$	7.00000	+	7.00000i	0.327446	+	0.327446i	0.851615	−	0.524168i	$-0.175624\pi$
$457$	7.00000	+	7.00000i	0.327446	+	0.327446i	−0.524168	+	0.851615i	$0.675624\pi$
$458$			2.00000i			0.0934539i
$459$		0			0
$460$	−6.00000	+	2.00000i	−0.279751	+	0.0932505i
$461$	21.0000	+	21.0000i	0.978068	+	0.978068i	0.999765	−	0.0216971i	$-0.00690694\pi$
$461$	21.0000	+	21.0000i	0.978068	+	0.978068i	−0.0216971	+	0.999765i	$0.506907\pi$
$462$		0			0
$463$	19.0000	−	19.0000i	0.883005	−	0.883005i	−0.110834	−	0.993839i	$-0.535352\pi$
$463$	19.0000	−	19.0000i	0.883005	−	0.883005i	0.993839	+	0.110834i	$0.0353522\pi$
$464$	−28.0000	+	28.0000i	−1.29987	+	1.29987i
$465$		0			0
$466$	18.0000			0.833834
$467$		−	28.0000i		−	1.29569i	−0.761774	−	0.647843i	$-0.775671\pi$
$467$		−	28.0000i		−	1.29569i	0.761774	−	0.647843i	$-0.224329\pi$
$468$		0			0
$469$	12.0000	+	12.0000i	0.554109	+	0.554109i
$470$	−14.0000	+	28.0000i	−0.645772	+	1.29154i
$471$		0			0
$472$		−	12.0000i		−	0.552345i
$473$	−4.00000	+	4.00000i	−0.183920	+	0.183920i
$474$		0			0
$475$	3.00000	−	21.0000i	0.137649	−	0.963546i
$476$	12.0000			0.550019
$477$		0			0
$478$		0			0
$479$	32.0000			1.46212			0.731059	−	0.682315i	$-0.239027\pi$
$479$	32.0000			1.46212			0.731059	+	0.682315i	$0.239027\pi$
$480$		0			0
$481$	12.0000			0.547153
$482$	−14.0000	−	14.0000i	−0.637683	−	0.637683i
$483$		0			0
$484$	18.0000			0.818182
$485$	−33.0000	+	11.0000i	−1.49845	+	0.499484i
$486$		0			0
$487$	−15.0000	+	15.0000i	−0.679715	+	0.679715i	−0.959936	−	0.280221i	$-0.909592\pi$
$487$	−15.0000	+	15.0000i	−0.679715	+	0.679715i	0.280221	+	0.959936i	$0.409592\pi$
$488$	4.00000			0.181071
$489$		0			0
$490$	33.0000	−	11.0000i	1.49079	−	0.496929i
$491$	9.00000	+	9.00000i	0.406164	+	0.406164i	0.880399	−	0.474234i	$-0.157275\pi$
$491$	9.00000	+	9.00000i	0.406164	+	0.406164i	−0.474234	+	0.880399i	$0.657275\pi$
$492$		0			0
$493$			14.0000i			0.630528i
$494$	−12.0000			−0.539906
$495$		0			0
$496$		−	8.00000i		−	0.359211i
$497$		0			0
$498$		0			0
$499$	29.0000	+	29.0000i	1.29822	+	1.29822i	0.929568	+	0.368650i	$0.120180\pi$
$499$	29.0000	+	29.0000i	1.29822	+	1.29822i	0.368650	+	0.929568i	$0.379820\pi$
$500$	−22.0000	+	4.00000i	−0.983870	+	0.178885i
$501$		0			0
$502$		−	22.0000i		−	0.981908i
$503$	29.0000	+	29.0000i	1.29305	+	1.29305i	0.932893	+	0.360153i	$0.117275\pi$
$503$	29.0000	+	29.0000i	1.29305	+	1.29305i	0.360153	+	0.932893i	$0.382725\pi$
$504$		0			0
$505$	15.0000	−	5.00000i	0.667491	−	0.222497i
$506$	−2.00000	+	2.00000i	−0.0889108	+	0.0889108i
$507$		0			0
$508$	14.0000	−	14.0000i	0.621150	−	0.621150i
$509$	−17.0000	+	17.0000i	−0.753512	+	0.753512i	−0.975133	−	0.221621i	$-0.928865\pi$
$509$	−17.0000	+	17.0000i	−0.753512	+	0.753512i	0.221621	+	0.975133i	$0.428865\pi$
$510$		0			0
$511$			18.0000i			0.796273i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	−26.0000			−1.14681
$515$	−5.00000	−	15.0000i	−0.220326	−	0.660979i
$516$		0			0
$517$			14.0000i			0.615719i
$518$		−	36.0000i		−	1.58175i
$519$		0			0
$520$	4.00000	+	12.0000i	0.175412	+	0.526235i
$521$			16.0000i			0.700973i	0.936568	+	0.350486i	$0.113984\pi$
$521$			16.0000i			0.700973i	−0.936568	+	0.350486i	$0.886016\pi$
$522$		0			0
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	14.0000	+	14.0000i	0.611593	+	0.611593i
$525$		0			0
$526$		−	14.0000i		−	0.610429i
$527$	−2.00000	−	2.00000i	−0.0871214	−	0.0871214i
$528$		0			0
$529$		−	21.0000i		−	0.913043i
$530$	8.00000	+	24.0000i	0.347498	+	1.04249i
$531$		0			0
$532$			36.0000i			1.56080i
$533$	8.00000			0.346518
$534$		0			0
$535$	12.0000	+	6.00000i	0.518805	+	0.259403i
$536$	8.00000	+	8.00000i	0.345547	+	0.345547i
$537$		0			0
$538$	−2.00000			−0.0862261
$539$	11.0000	−	11.0000i	0.473804	−	0.473804i
$540$		0			0
$541$	15.0000	+	15.0000i	0.644900	+	0.644900i	0.951756	−	0.306856i	$-0.0992769\pi$
$541$	15.0000	+	15.0000i	0.644900	+	0.644900i	−0.306856	+	0.951756i	$0.599277\pi$
$542$	30.0000	−	30.0000i	1.28861	−	1.28861i
$543$		0			0
$544$	8.00000			0.342997
$545$	15.0000	−	5.00000i	0.642529	−	0.214176i
$546$		0			0
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$	−18.0000	+	18.0000i	−0.768922	+	0.768922i
$549$		0			0
$550$	−8.00000	+	6.00000i	−0.341121	+	0.255841i
$551$	−42.0000			−1.78926
$552$		0			0
$553$	−24.0000	+	24.0000i	−1.02058	+	1.02058i
$554$	18.0000	−	18.0000i	0.764747	−	0.764747i
$555$		0			0
$556$	−18.0000	−	18.0000i	−0.763370	−	0.763370i
$557$	−28.0000			−1.18640			−0.593199	−	0.805056i	$-0.702135\pi$
$557$	−28.0000			−1.18640			−0.593199	+	0.805056i	$0.702135\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	36.0000	−	12.0000i	1.52128	−	0.507093i
$561$		0			0
$562$	16.0000	−	16.0000i	0.674919	−	0.674919i
$563$	18.0000			0.758610			0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000			0.758610			0.379305	+	0.925272i	$0.376163\pi$
$564$		0			0
$565$	−13.0000	−	39.0000i	−0.546914	−	1.64074i
$566$	−12.0000	+	12.0000i	−0.504398	+	0.504398i
$567$		0			0
$568$		0			0
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$	−25.0000	−	25.0000i	−1.04622	−	1.04622i	−0.998879	−	0.0473385i	$-0.984926\pi$
$571$	−25.0000	−	25.0000i	−1.04622	−	1.04622i	−0.0473385	−	0.998879i	$-0.515074\pi$
$572$	4.00000	+	4.00000i	0.167248	+	0.167248i
$573$		0			0
$574$		−	24.0000i		−	1.00174i
$575$	−1.00000	+	7.00000i	−0.0417029	+	0.291920i
$576$		0			0
$577$	9.00000	−	9.00000i	0.374675	−	0.374675i	−0.494502	−	0.869177i	$-0.664649\pi$
$577$	9.00000	−	9.00000i	0.374675	−	0.374675i	0.869177	+	0.494502i	$0.164649\pi$
$578$	−15.0000	+	15.0000i	−0.623918	+	0.623918i
$579$		0			0
$580$	14.0000	+	42.0000i	0.581318	+	1.74396i
$581$	−6.00000	+	6.00000i	−0.248922	+	0.248922i
$582$		0			0
$583$	8.00000	+	8.00000i	0.331326	+	0.331326i
$584$			12.0000i			0.496564i
$585$		0			0
$586$	12.0000	+	12.0000i	0.495715	+	0.495715i
$587$	−2.00000			−0.0825488			−0.0412744	−	0.999148i	$-0.513142\pi$
$587$	−2.00000			−0.0825488			−0.0412744	+	0.999148i	$0.513142\pi$
$588$		0			0
$589$	6.00000	−	6.00000i	0.247226	−	0.247226i
$590$	−12.0000	−	6.00000i	−0.494032	−	0.247016i
$591$		0			0
$592$		−	24.0000i		−	0.986394i
$593$	−17.0000	−	17.0000i	−0.698106	−	0.698106i	0.265896	−	0.964002i	$-0.414332\pi$
$593$	−17.0000	−	17.0000i	−0.698106	−	0.698106i	−0.964002	+	0.265896i	$0.914332\pi$
$594$		0			0
$595$	6.00000	−	12.0000i	0.245976	−	0.491952i
$596$	2.00000	−	2.00000i	0.0819232	−	0.0819232i
$597$		0			0
$598$	4.00000			0.163572
$599$		−	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
$601$			16.0000i			0.652654i	0.945257	+	0.326327i	$0.105811\pi$
$601$			16.0000i			0.652654i	−0.945257	+	0.326327i	$0.894189\pi$
$602$		−	24.0000i		−	0.978167i
$603$		0			0
$604$			16.0000i			0.651031i
$605$	9.00000	−	18.0000i	0.365902	−	0.731804i
$606$		0			0
$607$	−23.0000	−	23.0000i	−0.933541	−	0.933541i	0.0643840	−	0.997925i	$-0.479492\pi$
$607$	−23.0000	−	23.0000i	−0.933541	−	0.933541i	−0.997925	+	0.0643840i	$0.979492\pi$
$608$			24.0000i			0.973329i
$609$		0			0
$610$	2.00000	−	4.00000i	0.0809776	−	0.161955i
$611$	14.0000	−	14.0000i	0.566379	−	0.566379i
$612$		0			0
$613$	8.00000			0.323117			0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000			0.323117			0.161558	+	0.986863i	$0.448348\pi$
$614$	−4.00000	+	4.00000i	−0.161427	+	0.161427i
$615$		0			0
$616$	12.0000	−	12.0000i	0.483494	−	0.483494i
$617$	25.0000	+	25.0000i	1.00646	+	1.00646i	0.999979	+	0.00648312i	$0.00206366\pi$
$617$	25.0000	+	25.0000i	1.00646	+	1.00646i	0.00648312	+	0.999979i	$0.497936\pi$
$618$		0			0
$619$	7.00000	−	7.00000i	0.281354	−	0.281354i	−0.552295	−	0.833649i	$-0.686248\pi$
$619$	7.00000	−	7.00000i	0.281354	−	0.281354i	0.833649	+	0.552295i	$0.186248\pi$
$620$	−8.00000	−	4.00000i	−0.321288	−	0.160644i
$621$		0			0
$622$	−16.0000	−	16.0000i	−0.641542	−	0.641542i
$623$	−18.0000	+	18.0000i	−0.721155	+	0.721155i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−26.0000			−1.03917
$627$		0			0
$628$			40.0000i			1.59617i
$629$	−6.00000	−	6.00000i	−0.239236	−	0.239236i
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$	−16.0000	+	16.0000i	−0.636446	+	0.636446i
$633$		0			0
$634$	−8.00000	−	8.00000i	−0.317721	−	0.317721i
$635$	−7.00000	−	21.0000i	−0.277787	−	0.833360i
$636$		0			0
$637$	−22.0000			−0.871672
$638$	14.0000	+	14.0000i	0.554265	+	0.554265i
$639$		0			0
$640$	24.0000	−	8.00000i	0.948683	−	0.316228i
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$		−	12.0000i		−	0.472866i
$645$		0			0
$646$	6.00000	+	6.00000i	0.236067	+	0.236067i
$647$	15.0000	−	15.0000i	0.589711	−	0.589711i	−0.347842	−	0.937553i	$-0.613086\pi$
$647$	15.0000	−	15.0000i	0.589711	−	0.589711i	0.937553	+	0.347842i	$0.113086\pi$
$648$		0			0
$649$	−6.00000			−0.235521
$650$	14.0000	+	2.00000i	0.549125	+	0.0784465i
$651$		0			0
$652$			28.0000i			1.09656i
$653$			2.00000i			0.0782660i	0.999234	+	0.0391330i	$0.0124596\pi$
$653$			2.00000i			0.0782660i	−0.999234	+	0.0391330i	$0.987540\pi$
$654$		0			0
$655$	21.0000	−	7.00000i	0.820538	−	0.273513i
$656$		−	16.0000i		−	0.624695i
$657$		0			0
$658$	−42.0000	−	42.0000i	−1.63733	−	1.63733i
$659$	11.0000	+	11.0000i	0.428499	+	0.428499i	0.888117	−	0.459618i	$-0.152014\pi$
$659$	11.0000	+	11.0000i	0.428499	+	0.428499i	−0.459618	+	0.888117i	$0.652014\pi$
$660$		0			0
$661$	−25.0000	+	25.0000i	−0.972387	+	0.972387i	−0.999629	−	0.0272416i	$-0.991328\pi$
$661$	−25.0000	+	25.0000i	−0.972387	+	0.972387i	0.0272416	+	0.999629i	$0.491328\pi$
$662$		−	42.0000i		−	1.63238i
$663$		0			0
$664$	−4.00000	+	4.00000i	−0.155230	+	0.155230i
$665$	36.0000	+	18.0000i	1.39602	+	0.698010i
$666$		0			0
$667$	14.0000			0.542082
$668$	6.00000	+	6.00000i	0.232147	+	0.232147i
$669$		0			0
$670$	12.0000	−	4.00000i	0.463600	−	0.154533i
$671$		−	2.00000i		−	0.0772091i
$672$		0			0
$673$	1.00000	+	1.00000i	0.0385472	+	0.0385472i	0.726118	−	0.687570i	$-0.241323\pi$
$673$	1.00000	+	1.00000i	0.0385472	+	0.0385472i	−0.687570	+	0.726118i	$0.741323\pi$
$674$	−22.0000			−0.847408
$675$		0			0
$676$			18.0000i			0.692308i
$677$		−	42.0000i		−	1.61419i	−0.590421	−	0.807096i	$-0.701038\pi$
$677$		−	42.0000i		−	1.61419i	0.590421	−	0.807096i	$-0.298962\pi$
$678$		0			0
$679$		−	66.0000i		−	2.53285i
$680$	4.00000	−	8.00000i	0.153393	−	0.306786i
$681$		0			0
$682$	−4.00000			−0.153168
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	9.00000	+	27.0000i	0.343872	+	1.03162i
$686$			24.0000i			0.916324i
$687$		0			0
$688$		−	16.0000i		−	0.609994i
$689$		−	16.0000i		−	0.609551i
$690$		0			0
$691$	21.0000	−	21.0000i	0.798878	−	0.798878i	−0.184041	−	0.982919i	$-0.558918\pi$
$691$	21.0000	−	21.0000i	0.798878	−	0.798878i	0.982919	+	0.184041i	$0.0589179\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	−2.00000	−	2.00000i	−0.0759190	−	0.0759190i
$695$	−27.0000	+	9.00000i	−1.02417	+	0.341389i
$696$		0			0
$697$	−4.00000	−	4.00000i	−0.151511	−	0.151511i
$698$	−6.00000			−0.227103
$699$		0			0
$700$	6.00000	−	42.0000i	0.226779	−	1.58745i
$701$	13.0000	+	13.0000i	0.491003	+	0.491003i	0.908622	−	0.417619i	$-0.137135\pi$
$701$	13.0000	+	13.0000i	0.491003	+	0.491003i	−0.417619	+	0.908622i	$0.637135\pi$
$702$		0			0
$703$	18.0000	−	18.0000i	0.678883	−	0.678883i
$704$	8.00000	−	8.00000i	0.301511	−	0.301511i
$705$		0			0
$706$		−	26.0000i		−	0.978523i
$707$			30.0000i			1.12827i
$708$		0			0
$709$	1.00000	+	1.00000i	0.0375558	+	0.0375558i	0.725635	−	0.688080i	$-0.241546\pi$
$709$	1.00000	+	1.00000i	0.0375558	+	0.0375558i	−0.688080	+	0.725635i	$0.741546\pi$
$710$		0			0
$711$		0			0
$712$	−12.0000	+	12.0000i	−0.449719	+	0.449719i
$713$	−2.00000	+	2.00000i	−0.0749006	+	0.0749006i
$714$		0			0
$715$	6.00000	−	2.00000i	0.224387	−	0.0747958i
$716$	10.0000	−	10.0000i	0.373718	−	0.373718i
$717$		0			0
$718$	14.0000	−	14.0000i	0.522475	−	0.522475i
$719$	32.0000			1.19340			0.596699	−	0.802465i	$-0.296479\pi$
$719$	32.0000			1.19340			0.596699	+	0.802465i	$0.296479\pi$
$720$		0			0
$721$	30.0000			1.11726
$722$	1.00000	−	1.00000i	0.0372161	−	0.0372161i
$723$		0			0
$724$	6.00000	+	6.00000i	0.222988	+	0.222988i
$725$	49.0000	+	7.00000i	1.81981	+	0.259973i
$726$		0			0
$727$	−7.00000	+	7.00000i	−0.259616	+	0.259616i	−0.824898	−	0.565282i	$-0.808767\pi$
$727$	−7.00000	+	7.00000i	−0.259616	+	0.259616i	0.565282	+	0.824898i	$0.308767\pi$
$728$	−24.0000			−0.889499
$729$		0			0
$730$	12.0000	+	6.00000i	0.444140	+	0.222070i
$731$	−4.00000	−	4.00000i	−0.147945	−	0.147945i
$732$		0			0
$733$		−	30.0000i		−	1.10808i	−0.832492	−	0.554038i	$-0.813086\pi$
$733$		−	30.0000i		−	1.10808i	0.832492	−	0.554038i	$-0.186914\pi$
$734$			42.0000i			1.55025i
$735$		0			0
$736$		−	8.00000i		−	0.294884i
$737$	4.00000	−	4.00000i	0.147342	−	0.147342i
$738$		0			0
$739$	21.0000	+	21.0000i	0.772497	+	0.772497i	0.978543	−	0.206045i	$-0.0660593\pi$
$739$	21.0000	+	21.0000i	0.772497	+	0.772497i	−0.206045	+	0.978543i	$0.566059\pi$
$740$	−24.0000	−	12.0000i	−0.882258	−	0.441129i
$741$		0			0
$742$	−48.0000			−1.76214
$743$	−31.0000	−	31.0000i	−1.13728	−	1.13728i	−0.988936	−	0.148344i	$-0.952606\pi$
$743$	−31.0000	−	31.0000i	−1.13728	−	1.13728i	−0.148344	−	0.988936i	$-0.547394\pi$
$744$		0			0
$745$	−1.00000	−	3.00000i	−0.0366372	−	0.109911i
$746$	−4.00000	−	4.00000i	−0.146450	−	0.146450i
$747$		0			0
$748$		−	4.00000i		−	0.146254i
$749$	−18.0000	+	18.0000i	−0.657706	+	0.657706i
$750$		0			0
$751$			50.0000i			1.82453i	0.409605	+	0.912263i	$0.365667\pi$
$751$			50.0000i			1.82453i	−0.409605	+	0.912263i	$0.634333\pi$
$752$	−28.0000	−	28.0000i	−1.02105	−	1.02105i
$753$		0			0
$754$		−	28.0000i		−	1.01970i
$755$	16.0000	+	8.00000i	0.582300	+	0.291150i
$756$		0			0
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$	30.0000			1.08965
$759$		0			0
$760$	24.0000	+	12.0000i	0.870572	+	0.435286i
$761$		−	40.0000i		−	1.45000i	−0.688749	−	0.724999i	$-0.741840\pi$
$761$		−	40.0000i		−	1.45000i	0.688749	−	0.724999i	$-0.258160\pi$
$762$		0			0
$763$			30.0000i			1.08607i
$764$	36.0000			1.30243
$765$		0			0
$766$	10.0000			0.361315
$767$	6.00000	+	6.00000i	0.216647	+	0.216647i
$768$		0			0
$769$		−	4.00000i		−	0.144244i	−0.997396	−	0.0721218i	$-0.977023\pi$
$769$		−	4.00000i		−	0.144244i	0.997396	−	0.0721218i	$-0.0229770\pi$
$770$	−6.00000	−	18.0000i	−0.216225	−	0.648675i
$771$		0			0
$772$	30.0000	−	30.0000i	1.07972	−	1.07972i
$773$	−48.0000			−1.72644			−0.863220	−	0.504828i	$-0.831556\pi$
$773$	−48.0000			−1.72644			−0.863220	+	0.504828i	$0.831556\pi$
$774$		0			0
$775$	−8.00000	+	6.00000i	−0.287368	+	0.215526i
$776$		−	44.0000i		−	1.57951i
$777$		0			0
$778$			46.0000i			1.64918i
$779$	12.0000	−	12.0000i	0.429945	−	0.429945i
$780$		0			0
$781$		0			0
$782$	−2.00000	−	2.00000i	−0.0715199	−	0.0715199i
$783$		0			0
$784$			44.0000i			1.57143i
$785$	40.0000	+	20.0000i	1.42766	+	0.713831i
$786$		0			0
$787$			4.00000i			0.142585i	0.997455	+	0.0712923i	$0.0227123\pi$
$787$			4.00000i			0.142585i	−0.997455	+	0.0712923i	$0.977288\pi$
$788$	−12.0000			−0.427482
$789$		0			0
$790$	8.00000	+	24.0000i	0.284627	+	0.853882i
$791$	78.0000			2.77336
$792$		0			0
$793$	−2.00000	+	2.00000i	−0.0710221	+	0.0710221i
$794$	−32.0000	−	32.0000i	−1.13564	−	1.13564i
$795$		0			0
$796$	20.0000			0.708881
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	−14.0000			−0.495284
$800$	4.00000	−	28.0000i	0.141421	−	0.989949i
$801$		0			0
$802$	2.00000	+	2.00000i	0.0706225	+	0.0706225i
$803$	6.00000			0.211735
$804$		0			0
$805$	−12.0000	−	6.00000i	−0.422944	−	0.211472i
$806$	4.00000	+	4.00000i	0.140894	+	0.140894i
$807$		0			0
$808$			20.0000i			0.703598i
$809$	26.0000			0.914111			0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000			0.914111			0.457056	+	0.889438i	$0.348904\pi$
$810$		0			0
$811$	−9.00000	−	9.00000i	−0.316033	−	0.316033i	0.531208	−	0.847241i	$-0.321738\pi$
$811$	−9.00000	−	9.00000i	−0.316033	−	0.316033i	−0.847241	+	0.531208i	$0.821738\pi$
$812$	−84.0000			−2.94782
$813$		0			0
$814$	−12.0000			−0.420600
$815$	28.0000	+	14.0000i	0.980797	+	0.490399i
$816$		0			0
$817$	12.0000	−	12.0000i	0.419827	−	0.419827i
$818$	−38.0000	−	38.0000i	−1.32864	−	1.32864i
$819$		0			0
$820$	−16.0000	−	8.00000i	−0.558744	−	0.279372i
$821$	−15.0000	+	15.0000i	−0.523504	+	0.523504i	−0.918628	−	0.395124i	$-0.870702\pi$
$821$	−15.0000	+	15.0000i	−0.523504	+	0.523504i	0.395124	+	0.918628i	$0.370702\pi$
$822$		0			0
$823$	−21.0000	−	21.0000i	−0.732014	−	0.732014i	0.239004	−	0.971018i	$-0.423179\pi$
$823$	−21.0000	−	21.0000i	−0.732014	−	0.732014i	−0.971018	+	0.239004i	$0.923179\pi$
$824$	20.0000			0.696733
$825$		0			0
$826$	18.0000	−	18.0000i	0.626300	−	0.626300i
$827$	54.0000			1.87776			0.938882	−	0.344239i	$-0.111863\pi$
$827$	54.0000			1.87776			0.938882	+	0.344239i	$0.111863\pi$
$828$		0			0
$829$	−27.0000	+	27.0000i	−0.937749	+	0.937749i	−0.998173	−	0.0604240i	$-0.980755\pi$
$829$	−27.0000	+	27.0000i	−0.937749	+	0.937749i	0.0604240	+	0.998173i	$0.480755\pi$
$830$	2.00000	+	6.00000i	0.0694210	+	0.208263i
$831$		0			0
$832$	−16.0000			−0.554700
$833$	11.0000	+	11.0000i	0.381127	+	0.381127i
$834$		0			0
$835$	9.00000	−	3.00000i	0.311458	−	0.103819i
$836$	12.0000			0.415029
$837$		0			0
$838$		−	34.0000i		−	1.17451i
$839$			18.0000i			0.621429i	0.950503	+	0.310715i	$0.100568\pi$
$839$			18.0000i			0.621429i	−0.950503	+	0.310715i	$0.899432\pi$
$840$		0			0
$841$		−	69.0000i		−	2.37931i
$842$	−10.0000			−0.344623
$843$		0			0
$844$	−38.0000	−	38.0000i	−1.30801	−	1.30801i
$845$	18.0000	+	9.00000i	0.619219	+	0.309609i
$846$		0			0
$847$	27.0000	+	27.0000i	0.927731	+	0.927731i
$848$	−32.0000			−1.09888
$849$		0			0
$850$	−6.00000	−	8.00000i	−0.205798	−	0.274398i
$851$	−6.00000	+	6.00000i	−0.205677	+	0.205677i
$852$		0			0
$853$	16.0000			0.547830			0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000			0.547830			0.273915	+	0.961754i	$0.411681\pi$
$854$	6.00000	+	6.00000i	0.205316	+	0.205316i
$855$		0			0
$856$	−12.0000	+	12.0000i	−0.410152	+	0.410152i
$857$	−27.0000	−	27.0000i	−0.922302	−	0.922302i	0.0748894	−	0.997192i	$-0.476140\pi$
$857$	−27.0000	−	27.0000i	−0.922302	−	0.922302i	−0.997192	+	0.0748894i	$0.976140\pi$
$858$		0			0
$859$	19.0000	−	19.0000i	0.648272	−	0.648272i	−0.304303	−	0.952575i	$-0.598424\pi$
$859$	19.0000	−	19.0000i	0.648272	−	0.648272i	0.952575	+	0.304303i	$0.0984237\pi$
$860$	−16.0000	−	8.00000i	−0.545595	−	0.272798i
$861$		0			0
$862$	2.00000	−	2.00000i	0.0681203	−	0.0681203i
$863$	5.00000	−	5.00000i	0.170202	−	0.170202i	−0.616866	−	0.787068i	$-0.711598\pi$
$863$	5.00000	−	5.00000i	0.170202	−	0.170202i	0.787068	+	0.616866i	$0.211598\pi$
$864$		0			0
$865$	−6.00000	+	12.0000i	−0.204006	+	0.408012i
$866$			10.0000i			0.339814i
$867$		0			0
$868$	12.0000	−	12.0000i	0.407307	−	0.407307i
$869$	8.00000	+	8.00000i	0.271381	+	0.271381i
$870$		0			0
$871$	−8.00000			−0.271070
$872$			20.0000i			0.677285i
$873$		0			0
$874$	6.00000	−	6.00000i	0.202953	−	0.202953i
$875$	−39.0000	−	27.0000i	−1.31844	−	0.912767i
$876$		0			0
$877$	4.00000			0.135070			0.0675352	−	0.997717i	$-0.478487\pi$
$877$	4.00000			0.135070			0.0675352	+	0.997717i	$0.478487\pi$
$878$	26.0000	−	26.0000i	0.877457	−	0.877457i
$879$		0			0
$880$	−4.00000	−	12.0000i	−0.134840	−	0.404520i
$881$	−46.0000			−1.54978			−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000			−1.54978			−0.774890	+	0.632096i	$0.782195\pi$
$882$		0			0
$883$	6.00000			0.201916			0.100958	−	0.994891i	$-0.467809\pi$
$883$	6.00000			0.201916			0.100958	+	0.994891i	$0.467809\pi$
$884$	−4.00000	+	4.00000i	−0.134535	+	0.134535i
$885$		0			0
$886$	−4.00000	+	4.00000i	−0.134383	+	0.134383i
$887$	23.0000	−	23.0000i	0.772264	−	0.772264i	−0.206238	−	0.978502i	$-0.566122\pi$
$887$	23.0000	−	23.0000i	0.772264	−	0.772264i	0.978502	+	0.206238i	$0.0661220\pi$
$888$		0			0
$889$	42.0000			1.40863
$890$	6.00000	+	18.0000i	0.201120	+	0.603361i
$891$		0			0
$892$	−18.0000	−	18.0000i	−0.602685	−	0.602685i
$893$		−	42.0000i		−	1.40548i
$894$		0			0
$895$	−5.00000	−	15.0000i	−0.167132	−	0.501395i
$896$			48.0000i			1.60357i
$897$		0			0
$898$	−24.0000	+	24.0000i	−0.800890	+	0.800890i
$899$	14.0000	+	14.0000i	0.466926	+	0.466926i
$900$		0			0
$901$	−8.00000	+	8.00000i	−0.266519	+	0.266519i
$902$	−8.00000			−0.266371
$903$		0			0
$904$	52.0000			1.72949
$905$	9.00000	−	3.00000i	0.299170	−	0.0997234i
$906$		0			0
$907$	50.0000			1.66022			0.830111	−	0.557598i	$-0.188277\pi$
$907$	50.0000			1.66022			0.830111	+	0.557598i	$0.188277\pi$
$908$	−24.0000			−0.796468
$909$		0			0
$910$	−12.0000	+	24.0000i	−0.397796	+	0.795592i
$911$			38.0000i			1.25900i	0.777002	+	0.629498i	$0.216739\pi$
$911$			38.0000i			1.25900i	−0.777002	+	0.629498i	$0.783261\pi$
$912$		0			0
$913$	2.00000	+	2.00000i	0.0661903	+	0.0661903i
$914$			14.0000i			0.463079i
$915$		0			0
$916$	−2.00000	+	2.00000i	−0.0660819	+	0.0660819i
$917$			42.0000i			1.38696i
$918$		0			0
$919$			46.0000i			1.51740i	0.651440	+	0.758700i	$0.274165\pi$
$919$			46.0000i			1.51740i	−0.651440	+	0.758700i	$0.725835\pi$
$920$	−8.00000	−	4.00000i	−0.263752	−	0.131876i
$921$		0			0
$922$			42.0000i			1.38320i
$923$		0			0
$924$		0			0
$925$	−24.0000	+	18.0000i	−0.789115	+	0.591836i
$926$	38.0000			1.24876
$927$		0			0
$928$	−56.0000			−1.83829
$929$		−	16.0000i		−	0.524943i	−0.964940	−	0.262471i	$-0.915462\pi$
$929$		−	16.0000i		−	0.524943i	0.964940	−	0.262471i	$-0.0845376\pi$
$930$		0			0
$931$	−33.0000	+	33.0000i	−1.08153	+	1.08153i
$932$	18.0000	+	18.0000i	0.589610	+	0.589610i
$933$		0			0
$934$	28.0000	−	28.0000i	0.916188	−	0.916188i
$935$	−4.00000	−	2.00000i	−0.130814	−	0.0654070i
$936$		0			0
$937$	3.00000	+	3.00000i	0.0980057	+	0.0980057i	0.754410	−	0.656404i	$-0.227923\pi$
$937$	3.00000	+	3.00000i	0.0980057	+	0.0980057i	−0.656404	+	0.754410i	$0.727923\pi$
$938$			24.0000i			0.783628i
$939$		0			0
$940$	−42.0000	+	14.0000i	−1.36989	+	0.456630i
$941$	1.00000	+	1.00000i	0.0325991	+	0.0325991i	0.723218	−	0.690619i	$-0.242662\pi$
$941$	1.00000	+	1.00000i	0.0325991	+	0.0325991i	−0.690619	+	0.723218i	$0.742662\pi$
$942$		0			0
$943$	−4.00000	+	4.00000i	−0.130258	+	0.130258i
$944$	12.0000	−	12.0000i	0.390567	−	0.390567i
$945$		0			0
$946$	−8.00000			−0.260102
$947$			28.0000i			0.909878i	0.890523	+	0.454939i	$0.150339\pi$
$947$			28.0000i			0.909878i	−0.890523	+	0.454939i	$0.849661\pi$
$948$		0			0
$949$	−6.00000	−	6.00000i	−0.194768	−	0.194768i
$950$	24.0000	−	18.0000i	0.778663	−	0.583997i
$951$		0			0
$952$	12.0000	+	12.0000i	0.388922	+	0.388922i
$953$	−31.0000	+	31.0000i	−1.00419	+	1.00419i	−0.00419731	+	0.999991i	$0.501336\pi$
$953$	−31.0000	+	31.0000i	−1.00419	+	1.00419i	−0.999991	+	0.00419731i	$0.998664\pi$
$954$		0			0
$955$	18.0000	−	36.0000i	0.582466	−	1.16493i
$956$		0			0
$957$		0			0
$958$	32.0000	+	32.0000i	1.03387	+	1.03387i
$959$	−54.0000			−1.74375
$960$		0			0
$961$	27.0000			0.870968
$962$	12.0000	+	12.0000i	0.386896	+	0.386896i
$963$		0			0
$964$		−	28.0000i		−	0.901819i
$965$	−15.0000	−	45.0000i	−0.482867	−	1.44860i
$966$		0			0
$967$	33.0000	−	33.0000i	1.06121	−	1.06121i	0.0632081	−	0.998000i	$-0.479867\pi$
$967$	33.0000	−	33.0000i	1.06121	−	1.06121i	0.998000	−	0.0632081i	$-0.0201332\pi$
$968$	18.0000	+	18.0000i	0.578542	+	0.578542i
$969$		0			0
$970$	−44.0000	−	22.0000i	−1.41275	−	0.706377i
$971$	−31.0000	−	31.0000i	−0.994837	−	0.994837i	0.00514940	−	0.999987i	$-0.498361\pi$
$971$	−31.0000	−	31.0000i	−0.994837	−	0.994837i	−0.999987	+	0.00514940i	$0.998361\pi$
$972$		0			0
$973$		−	54.0000i		−	1.73116i
$974$	−30.0000			−0.961262
$975$		0			0
$976$	4.00000	+	4.00000i	0.128037	+	0.128037i
$977$	−17.0000	+	17.0000i	−0.543878	+	0.543878i	−0.924663	−	0.380785i	$-0.875654\pi$
$977$	−17.0000	+	17.0000i	−0.543878	+	0.543878i	0.380785	+	0.924663i	$0.375654\pi$
$978$		0			0
$979$	6.00000	+	6.00000i	0.191761	+	0.191761i
$980$	44.0000	+	22.0000i	1.40553	+	0.702764i
$981$		0			0
$982$			18.0000i			0.574403i
$983$	5.00000	+	5.00000i	0.159475	+	0.159475i	0.782334	−	0.622859i	$-0.214029\pi$
$983$	5.00000	+	5.00000i	0.159475	+	0.159475i	−0.622859	+	0.782334i	$0.714029\pi$
$984$		0			0
$985$	−6.00000	+	12.0000i	−0.191176	+	0.382352i
$986$	−14.0000	+	14.0000i	−0.445851	+	0.445851i
$987$		0			0
$988$	−12.0000	−	12.0000i	−0.381771	−	0.381771i
$989$	−4.00000	+	4.00000i	−0.127193	+	0.127193i
$990$		0			0
$991$			10.0000i			0.317660i	0.987306	+	0.158830i	$0.0507723\pi$
$991$			10.0000i			0.317660i	−0.987306	+	0.158830i	$0.949228\pi$
$992$	8.00000	−	8.00000i	0.254000	−	0.254000i
$993$		0			0
$994$		0			0
$995$	10.0000	−	20.0000i	0.317021	−	0.634043i
$996$		0			0
$997$		−	22.0000i		−	0.696747i	−0.937356	−	0.348373i	$-0.886734\pi$
$997$		−	22.0000i		−	0.696747i	0.937356	−	0.348373i	$-0.113266\pi$
$998$			58.0000i			1.83596i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.d.163.1		2
3.2	odd	2		80.2.s.a.3.1	yes	2
5.2	odd	4		720.2.bd.a.307.1		2
12.11	even	2		320.2.s.a.303.1		2
15.2	even	4		80.2.j.a.67.1	yes	2
15.8	even	4		400.2.j.a.307.1		2
15.14	odd	2		400.2.s.a.243.1		2
16.11	odd	4		720.2.bd.a.523.1		2
24.5	odd	2		640.2.s.b.223.1		2
24.11	even	2		640.2.s.a.223.1		2
48.5	odd	4		320.2.j.a.143.1		2
48.11	even	4		80.2.j.a.43.1	✓	2
48.29	odd	4		640.2.j.b.543.1		2
48.35	even	4		640.2.j.a.543.1		2
60.23	odd	4		1600.2.j.a.1007.1		2
60.47	odd	4		320.2.j.a.47.1		2
60.59	even	2		1600.2.s.a.943.1		2
80.27	even	4	inner	720.2.z.d.667.1		2
120.77	even	4		640.2.j.a.607.1		2
120.107	odd	4		640.2.j.b.607.1		2
240.53	even	4		1600.2.s.a.207.1		2
240.59	even	4		400.2.j.a.43.1		2
240.77	even	4		640.2.s.a.287.1		2
240.107	odd	4		80.2.s.a.27.1	yes	2
240.149	odd	4		1600.2.j.a.143.1		2
240.197	even	4		320.2.s.a.207.1		2
240.203	odd	4		400.2.s.a.107.1		2
240.227	odd	4		640.2.s.b.287.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.a.43.1	✓	2	48.11	even	4
80.2.j.a.67.1	yes	2	15.2	even	4
80.2.s.a.3.1	yes	2	3.2	odd	2
80.2.s.a.27.1	yes	2	240.107	odd	4
320.2.j.a.47.1		2	60.47	odd	4
320.2.j.a.143.1		2	48.5	odd	4
320.2.s.a.207.1		2	240.197	even	4
320.2.s.a.303.1		2	12.11	even	2
400.2.j.a.43.1		2	240.59	even	4
400.2.j.a.307.1		2	15.8	even	4
400.2.s.a.107.1		2	240.203	odd	4
400.2.s.a.243.1		2	15.14	odd	2
640.2.j.a.543.1		2	48.35	even	4
640.2.j.a.607.1		2	120.77	even	4
640.2.j.b.543.1		2	48.29	odd	4
640.2.j.b.607.1		2	120.107	odd	4
640.2.s.a.223.1		2	24.11	even	2
640.2.s.a.287.1		2	240.77	even	4
640.2.s.b.223.1		2	24.5	odd	2
640.2.s.b.287.1		2	240.227	odd	4
720.2.z.d.163.1		2	1.1	even	1	trivial
720.2.z.d.667.1		2	80.27	even	4	inner
720.2.bd.a.307.1		2	5.2	odd	4
720.2.bd.a.523.1		2	16.11	odd	4
1600.2.j.a.143.1		2	240.149	odd	4
1600.2.j.a.1007.1		2	60.23	odd	4
1600.2.s.a.207.1		2	240.53	even	4
1600.2.s.a.943.1		2	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.00000 + 3.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} -2.00000i q^{13} -6.00000 q^{14} -4.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(-2.00000 + 4.00000i) q^{20} +2.00000i q^{22} +(1.00000 + 1.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(2.00000 - 2.00000i) q^{26} +(-6.00000 - 6.00000i) q^{28} +(7.00000 - 7.00000i) q^{29} +2.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} -2.00000 q^{34} +(-9.00000 + 3.00000i) q^{35} +6.00000i q^{37} -6.00000i q^{38} +(-6.00000 + 2.00000i) q^{40} +4.00000i q^{41} +4.00000i q^{43} +(-2.00000 + 2.00000i) q^{44} +2.00000i q^{46} +(7.00000 + 7.00000i) q^{47} -11.0000i q^{49} +(-1.00000 + 7.00000i) q^{50} +4.00000 q^{52} +8.00000 q^{53} +(1.00000 + 3.00000i) q^{55} -12.0000i q^{56} +14.0000 q^{58} +(-3.00000 + 3.00000i) q^{59} +(-1.00000 - 1.00000i) q^{61} +(-2.00000 + 2.00000i) q^{62} -8.00000i q^{64} +(2.00000 - 4.00000i) q^{65} -4.00000i q^{67} +(-2.00000 - 2.00000i) q^{68} +(-12.0000 - 6.00000i) q^{70} +(3.00000 - 3.00000i) q^{73} +(-6.00000 + 6.00000i) q^{74} +(6.00000 - 6.00000i) q^{76} -6.00000 q^{77} +8.00000 q^{79} +(-8.00000 - 4.00000i) q^{80} +(-4.00000 + 4.00000i) q^{82} +2.00000 q^{83} +(-3.00000 + 1.00000i) q^{85} +(-4.00000 + 4.00000i) q^{86} -4.00000 q^{88} +6.00000 q^{89} +(6.00000 + 6.00000i) q^{91} +(-2.00000 + 2.00000i) q^{92} +14.0000i q^{94} +(-3.00000 - 9.00000i) q^{95} +(-11.0000 + 11.0000i) q^{97} +(11.0000 - 11.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 4 q^{5} - 6 q^{7} - 4 q^{8} + 2 q^{10} + 2 q^{11} - 12 q^{14} - 8 q^{16} - 2 q^{17} - 6 q^{19} - 4 q^{20} + 2 q^{23} + 6 q^{25} + 4 q^{26} - 12 q^{28} + 14 q^{29} - 8 q^{32} - 4 q^{34} - 18 q^{35}+ \cdots + 22 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 4 * q^5 - 6 * q^7 - 4 * q^8 + 2 * q^10 + 2 * q^11 - 12 * q^14 - 8 * q^16 - 2 * q^17 - 6 * q^19 - 4 * q^20 + 2 * q^23 + 6 * q^25 + 4 * q^26 - 12 * q^28 + 14 * q^29 - 8 * q^32 - 4 * q^34 - 18 * q^35 - 12 * q^40 - 4 * q^44 + 14 * q^47 - 2 * q^50 + 8 * q^52 + 16 * q^53 + 2 * q^55 + 28 * q^58 - 6 * q^59 - 2 * q^61 - 4 * q^62 + 4 * q^65 - 4 * q^68 - 24 * q^70 + 6 * q^73 - 12 * q^74 + 12 * q^76 - 12 * q^77 + 16 * q^79 - 16 * q^80 - 8 * q^82 + 4 * q^83 - 6 * q^85 - 8 * q^86 - 8 * q^88 + 12 * q^89 + 12 * q^91 - 4 * q^92 - 6 * q^95 - 22 * q^97 + 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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