LMFDB - Embedded newform 640.2.s.a.287.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(223,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("640.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.s (of order $4$, degree $2$, not 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:	$5.11042572936$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	640.287
Dual form			640.2.s.a.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{3} +(2.00000 - 1.00000i) q^{5} +(3.00000 + 3.00000i) q^{7} +1.00000 q^{9} +(-1.00000 + 1.00000i) q^{11} -2.00000i q^{13} +(-4.00000 + 2.00000i) q^{15} +(1.00000 + 1.00000i) q^{17} +(-3.00000 + 3.00000i) q^{19} +(-6.00000 - 6.00000i) q^{21} +(1.00000 - 1.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +4.00000 q^{27} +(7.00000 + 7.00000i) q^{29} +2.00000i q^{31} +(2.00000 - 2.00000i) q^{33} +(9.00000 + 3.00000i) q^{35} +6.00000i q^{37} +4.00000i q^{39} +4.00000i q^{41} -4.00000i q^{43} +(2.00000 - 1.00000i) q^{45} +(7.00000 - 7.00000i) q^{47} +11.0000i q^{49} +(-2.00000 - 2.00000i) q^{51} +8.00000 q^{53} +(-1.00000 + 3.00000i) q^{55} +(6.00000 - 6.00000i) q^{57} +(3.00000 + 3.00000i) q^{59} +(1.00000 - 1.00000i) q^{61} +(3.00000 + 3.00000i) q^{63} +(-2.00000 - 4.00000i) q^{65} +4.00000i q^{67} +(-2.00000 + 2.00000i) q^{69} +(3.00000 + 3.00000i) q^{73} +(-6.00000 + 8.00000i) q^{75} -6.00000 q^{77} -8.00000 q^{79} -11.0000 q^{81} -2.00000 q^{83} +(3.00000 + 1.00000i) q^{85} +(-14.0000 - 14.0000i) q^{87} -6.00000 q^{89} +(6.00000 - 6.00000i) q^{91} -4.00000i q^{93} +(-3.00000 + 9.00000i) q^{95} +(-11.0000 - 11.0000i) q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{3} + 4 q^{5} + 6 q^{7} + 2 q^{9} - 2 q^{11} - 8 q^{15} + 2 q^{17} - 6 q^{19} - 12 q^{21} + 2 q^{23} + 6 q^{25} + 8 q^{27} + 14 q^{29} + 4 q^{33} + 18 q^{35} + 4 q^{45} + 14 q^{47} - 4 q^{51}+ \cdots - 2 q^{99}+O(q^{100}) $ 2 * q - 4 * q^3 + 4 * q^5 + 6 * q^7 + 2 * q^9 - 2 * q^11 - 8 * q^15 + 2 * q^17 - 6 * q^19 - 12 * q^21 + 2 * q^23 + 6 * q^25 + 8 * q^27 + 14 * q^29 + 4 * q^33 + 18 * q^35 + 4 * q^45 + 14 * q^47 - 4 * q^51 + 16 * q^53 - 2 * q^55 + 12 * q^57 + 6 * q^59 + 2 * q^61 + 6 * q^63 - 4 * q^65 - 4 * q^69 + 6 * q^73 - 12 * q^75 - 12 * q^77 - 16 * q^79 - 22 * q^81 - 4 * q^83 + 6 * q^85 - 28 * q^87 - 12 * q^89 + 12 * q^91 - 6 * q^95 - 22 * q^97 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.00000			−1.15470			−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000			−1.15470			−0.577350	+	0.816497i	$0.695913\pi$
$4$		0			0
$5$	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	0.989524	+	0.144370i	$0.0461154\pi$
$7$	3.00000	+	3.00000i	1.13389	+	1.13389i	0.144370	+	0.989524i	$0.453885\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	−0.841605	−	0.540094i	$-0.818389\pi$
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	0.540094	+	0.841605i	$0.318389\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		0			0
$15$	−4.00000	+	2.00000i	−1.03280	+	0.516398i
$16$		0			0
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$		0			0
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	−0.961844	−	0.273597i	$-0.911786\pi$
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	0.273597	+	0.961844i	$0.411786\pi$
$20$		0			0
$21$	−6.00000	−	6.00000i	−1.30931	−	1.30931i
$22$		0			0
$23$	1.00000	−	1.00000i	0.208514	−	0.208514i	−0.595121	−	0.803636i	$-0.702896\pi$
$23$	1.00000	−	1.00000i	0.208514	−	0.208514i	0.803636	+	0.595121i	$0.202896\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	7.00000	+	7.00000i	1.29987	+	1.29987i	0.928477	+	0.371391i	$0.121119\pi$
$29$	7.00000	+	7.00000i	1.29987	+	1.29987i	0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$			2.00000i			0.359211i	0.983739	+	0.179605i	$0.0574821\pi$
$31$			2.00000i			0.359211i	−0.983739	+	0.179605i	$0.942518\pi$
$32$		0			0
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$		0			0
$35$	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	$0.835828\pi$
$38$		0			0
$39$			4.00000i			0.640513i
$40$		0			0
$41$			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	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$	2.00000	−	1.00000i	0.298142	−	0.149071i
$46$		0			0
$47$	7.00000	−	7.00000i	1.02105	−	1.02105i	0.0212814	−	0.999774i	$-0.493225\pi$
$47$	7.00000	−	7.00000i	1.02105	−	1.02105i	0.999774	−	0.0212814i	$-0.00677460\pi$
$48$		0			0
$49$			11.0000i			1.57143i
$50$		0			0
$51$	−2.00000	−	2.00000i	−0.280056	−	0.280056i
$52$		0			0
$53$	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
$56$		0			0
$57$	6.00000	−	6.00000i	0.794719	−	0.794719i
$58$		0			0
$59$	3.00000	+	3.00000i	0.390567	+	0.390567i	0.874889	−	0.484323i	$-0.160934\pi$
$59$	3.00000	+	3.00000i	0.390567	+	0.390567i	−0.484323	+	0.874889i	$0.660934\pi$
$60$		0			0
$61$	1.00000	−	1.00000i	0.128037	−	0.128037i	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	1.00000	−	1.00000i	0.128037	−	0.128037i	0.768221	+	0.640184i	$0.221142\pi$
$62$		0			0
$63$	3.00000	+	3.00000i	0.377964	+	0.377964i
$64$		0			0
$65$	−2.00000	−	4.00000i	−0.248069	−	0.496139i
$66$		0			0
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$		0			0
$69$	−2.00000	+	2.00000i	−0.240772	+	0.240772i
$70$		0			0
$71$		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	0.860527	−	0.509404i	$-0.170134\pi$
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	−0.509404	+	0.860527i	$0.670134\pi$
$74$		0			0
$75$	−6.00000	+	8.00000i	−0.692820	+	0.923760i
$76$		0			0
$77$	−6.00000			−0.683763
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	−11.0000			−1.22222
$82$		0			0
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$		0			0
$85$	3.00000	+	1.00000i	0.325396	+	0.108465i
$86$		0			0
$87$	−14.0000	−	14.0000i	−1.50096	−	1.50096i
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	6.00000	−	6.00000i	0.628971	−	0.628971i
$92$		0			0
$93$		−	4.00000i		−	0.414781i
$94$		0			0
$95$	−3.00000	+	9.00000i	−0.307794	+	0.923381i
$96$		0			0
$97$	−11.0000	−	11.0000i	−1.11688	−	1.11688i	−0.992196	−	0.124684i	$-0.960208\pi$
$97$	−11.0000	−	11.0000i	−1.11688	−	1.11688i	−0.124684	−	0.992196i	$-0.539792\pi$
$98$		0			0
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$		0			0
$101$	5.00000	+	5.00000i	0.497519	+	0.497519i	0.910665	−	0.413146i	$-0.135570\pi$
$101$	5.00000	+	5.00000i	0.497519	+	0.497519i	−0.413146	+	0.910665i	$0.635570\pi$
$102$		0			0
$103$	5.00000	−	5.00000i	0.492665	−	0.492665i	−0.416480	−	0.909145i	$-0.636736\pi$
$103$	5.00000	−	5.00000i	0.492665	−	0.492665i	0.909145	+	0.416480i	$0.136736\pi$
$104$		0			0
$105$	−18.0000	−	6.00000i	−1.75662	−	0.585540i
$106$		0			0
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$		0			0
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	0.425871	−	0.904784i	$-0.359968\pi$
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	−0.904784	+	0.425871i	$0.859968\pi$
$110$		0			0
$111$		−	12.0000i		−	1.13899i
$112$		0			0
$113$	13.0000	−	13.0000i	1.22294	−	1.22294i	0.256354	−	0.966583i	$-0.417479\pi$
$113$	13.0000	−	13.0000i	1.22294	−	1.22294i	0.966583	−	0.256354i	$-0.0825214\pi$
$114$		0			0
$115$	1.00000	−	3.00000i	0.0932505	−	0.279751i
$116$		0			0
$117$		−	2.00000i		−	0.184900i
$118$		0			0
$119$			6.00000i			0.550019i
$120$		0			0
$121$			9.00000i			0.818182i
$122$		0			0
$123$		−	8.00000i		−	0.721336i
$124$		0			0
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	−0.324676	−	0.945825i	$-0.605255\pi$
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	0.945825	+	0.324676i	$0.105255\pi$
$128$		0			0
$129$			8.00000i			0.704361i
$130$		0			0
$131$	−7.00000	−	7.00000i	−0.611593	−	0.611593i	0.331768	−	0.943361i	$-0.392355\pi$
$131$	−7.00000	−	7.00000i	−0.611593	−	0.611593i	−0.943361	+	0.331768i	$0.892355\pi$
$132$		0			0
$133$	−18.0000			−1.56080
$134$		0			0
$135$	8.00000	−	4.00000i	0.688530	−	0.344265i
$136$		0			0
$137$	−9.00000	+	9.00000i	−0.768922	+	0.768922i	−0.977917	−	0.208995i	$-0.932981\pi$
$137$	−9.00000	+	9.00000i	−0.768922	+	0.768922i	0.208995	+	0.977917i	$0.432981\pi$
$138$		0			0
$139$	−9.00000	−	9.00000i	−0.763370	−	0.763370i	0.213560	−	0.976930i	$-0.431494\pi$
$139$	−9.00000	−	9.00000i	−0.763370	−	0.763370i	−0.976930	+	0.213560i	$0.931494\pi$
$140$		0			0
$141$	−14.0000	+	14.0000i	−1.17901	+	1.17901i
$142$		0			0
$143$	2.00000	+	2.00000i	0.167248	+	0.167248i
$144$		0			0
$145$	21.0000	+	7.00000i	1.74396	+	0.581318i
$146$		0			0
$147$		−	22.0000i		−	1.81453i
$148$		0			0
$149$	−1.00000	+	1.00000i	−0.0819232	+	0.0819232i	−0.746881	−	0.664958i	$-0.768450\pi$
$149$	−1.00000	+	1.00000i	−0.0819232	+	0.0819232i	0.664958	+	0.746881i	$0.268450\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$		0			0
$155$	2.00000	+	4.00000i	0.160644	+	0.321288i
$156$		0			0
$157$	−20.0000			−1.59617			−0.798087	−	0.602542i	$-0.794154\pi$
$157$	−20.0000			−1.59617			−0.798087	+	0.602542i	$0.794154\pi$
$158$		0			0
$159$	−16.0000			−1.26888
$160$		0			0
$161$	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	$0.315282\pi$
$164$		0			0
$165$	2.00000	−	6.00000i	0.155700	−	0.467099i
$166$		0			0
$167$	3.00000	+	3.00000i	0.232147	+	0.232147i	0.813588	−	0.581441i	$-0.197511\pi$
$167$	3.00000	+	3.00000i	0.232147	+	0.232147i	−0.581441	+	0.813588i	$0.697511\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	−3.00000	+	3.00000i	−0.229416	+	0.229416i
$172$		0			0
$173$		−	6.00000i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$		−	6.00000i		−	0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$		0			0
$175$	21.0000	−	3.00000i	1.58745	−	0.226779i
$176$		0			0
$177$	−6.00000	−	6.00000i	−0.450988	−	0.450988i
$178$		0			0
$179$	5.00000	−	5.00000i	0.373718	−	0.373718i	−0.495112	−	0.868829i	$-0.664873\pi$
$179$	5.00000	−	5.00000i	0.373718	−	0.373718i	0.868829	+	0.495112i	$0.164873\pi$
$180$		0			0
$181$	−3.00000	−	3.00000i	−0.222988	−	0.222988i	0.586767	−	0.809756i	$-0.300400\pi$
$181$	−3.00000	−	3.00000i	−0.222988	−	0.222988i	−0.809756	+	0.586767i	$0.800400\pi$
$182$		0			0
$183$	−2.00000	+	2.00000i	−0.147844	+	0.147844i
$184$		0			0
$185$	6.00000	+	12.0000i	0.441129	+	0.882258i
$186$		0			0
$187$	−2.00000			−0.146254
$188$		0			0
$189$	12.0000	+	12.0000i	0.872872	+	0.872872i
$190$		0			0
$191$			18.0000i			1.30243i	0.758891	+	0.651217i	$0.225741\pi$
$191$			18.0000i			1.30243i	−0.758891	+	0.651217i	$0.774259\pi$
$192$		0			0
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$		0			0
$195$	4.00000	+	8.00000i	0.286446	+	0.572892i
$196$		0			0
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$		0			0
$199$		−	10.0000i		−	0.708881i	−0.935079	−	0.354441i	$-0.884671\pi$
$199$		−	10.0000i		−	0.708881i	0.935079	−	0.354441i	$-0.115329\pi$
$200$		0			0
$201$		−	8.00000i		−	0.564276i
$202$		0			0
$203$			42.0000i			2.94782i
$204$		0			0
$205$	4.00000	+	8.00000i	0.279372	+	0.558744i
$206$		0			0
$207$	1.00000	−	1.00000i	0.0695048	−	0.0695048i
$208$		0			0
$209$		−	6.00000i		−	0.415029i
$210$		0			0
$211$	−19.0000	−	19.0000i	−1.30801	−	1.30801i	−0.922847	−	0.385167i	$-0.874144\pi$
$211$	−19.0000	−	19.0000i	−1.30801	−	1.30801i	−0.385167	−	0.922847i	$-0.625856\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.00000	−	8.00000i	−0.272798	−	0.545595i
$216$		0			0
$217$	−6.00000	+	6.00000i	−0.407307	+	0.407307i
$218$		0			0
$219$	−6.00000	−	6.00000i	−0.405442	−	0.405442i
$220$		0			0
$221$	2.00000	−	2.00000i	0.134535	−	0.134535i
$222$		0			0
$223$	9.00000	+	9.00000i	0.602685	+	0.602685i	0.941024	−	0.338340i	$-0.109865\pi$
$223$	9.00000	+	9.00000i	0.602685	+	0.602685i	−0.338340	+	0.941024i	$0.609865\pi$
$224$		0			0
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$		0			0
$227$			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	$-0.764879\pi$
$229$	−1.00000	+	1.00000i	−0.0660819	+	0.0660819i	0.673293	+	0.739375i	$0.264879\pi$
$230$		0			0
$231$	12.0000			0.789542
$232$		0			0
$233$	−9.00000	−	9.00000i	−0.589610	−	0.589610i	0.347916	−	0.937526i	$-0.386889\pi$
$233$	−9.00000	−	9.00000i	−0.589610	−	0.589610i	−0.937526	+	0.347916i	$0.886889\pi$
$234$		0			0
$235$	7.00000	−	21.0000i	0.456630	−	1.36989i
$236$		0			0
$237$	16.0000			1.03931
$238$		0			0
$239$		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	$0.648900\pi$
$242$		0			0
$243$	10.0000			0.641500
$244$		0			0
$245$	11.0000	+	22.0000i	0.702764	+	1.40553i
$246$		0			0
$247$	6.00000	+	6.00000i	0.381771	+	0.381771i
$248$		0			0
$249$	4.00000			0.253490
$250$		0			0
$251$	11.0000	−	11.0000i	0.694314	−	0.694314i	−0.268864	−	0.963178i	$-0.586648\pi$
$251$	11.0000	−	11.0000i	0.694314	−	0.694314i	0.963178	+	0.268864i	$0.0866483\pi$
$252$		0			0
$253$			2.00000i			0.125739i
$254$		0			0
$255$	−6.00000	−	2.00000i	−0.375735	−	0.125245i
$256$		0			0
$257$	13.0000	+	13.0000i	0.810918	+	0.810918i	0.984771	−	0.173854i	$-0.0556220\pi$
$257$	13.0000	+	13.0000i	0.810918	+	0.810918i	−0.173854	+	0.984771i	$0.555622\pi$
$258$		0			0
$259$	−18.0000	+	18.0000i	−1.11847	+	1.11847i
$260$		0			0
$261$	7.00000	+	7.00000i	0.433289	+	0.433289i
$262$		0			0
$263$	−7.00000	+	7.00000i	−0.431638	+	0.431638i	−0.889185	−	0.457547i	$-0.848728\pi$
$263$	−7.00000	+	7.00000i	−0.431638	+	0.431638i	0.457547	+	0.889185i	$0.348728\pi$
$264$		0			0
$265$	16.0000	−	8.00000i	0.982872	−	0.491436i
$266$		0			0
$267$	12.0000			0.734388
$268$		0			0
$269$	−1.00000	−	1.00000i	−0.0609711	−	0.0609711i	0.675964	−	0.736935i	$-0.263728\pi$
$269$	−1.00000	−	1.00000i	−0.0609711	−	0.0609711i	−0.736935	+	0.675964i	$0.763728\pi$
$270$		0			0
$271$		−	30.0000i		−	1.82237i	−0.411997	−	0.911185i	$-0.635169\pi$
$271$		−	30.0000i		−	1.82237i	0.411997	−	0.911185i	$-0.364831\pi$
$272$		0			0
$273$	−12.0000	+	12.0000i	−0.726273	+	0.726273i
$274$		0			0
$275$	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	$-0.181862\pi$
$278$		0			0
$279$			2.00000i			0.119737i
$280$		0			0
$281$		−	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	$-0.883914\pi$
$283$		−	12.0000i		−	0.713326i	0.934233	−	0.356663i	$-0.116086\pi$
$284$		0			0
$285$	6.00000	−	18.0000i	0.355409	−	1.06623i
$286$		0			0
$287$	−12.0000	+	12.0000i	−0.708338	+	0.708338i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$	22.0000	+	22.0000i	1.28966	+	1.28966i
$292$		0			0
$293$	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
$296$		0			0
$297$	−4.00000	+	4.00000i	−0.232104	+	0.232104i
$298$		0			0
$299$	−2.00000	−	2.00000i	−0.115663	−	0.115663i
$300$		0			0
$301$	12.0000	−	12.0000i	0.691669	−	0.691669i
$302$		0			0
$303$	−10.0000	−	10.0000i	−0.574485	−	0.574485i
$304$		0			0
$305$	1.00000	−	3.00000i	0.0572598	−	0.171780i
$306$		0			0
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	−10.0000	+	10.0000i	−0.568880	+	0.568880i
$310$		0			0
$311$	−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	0.236764	−	0.971567i	$-0.423913\pi$
$313$	−13.0000	−	13.0000i	−0.734803	−	0.734803i	−0.971567	+	0.236764i	$0.923913\pi$
$314$		0			0
$315$	9.00000	+	3.00000i	0.507093	+	0.169031i
$316$		0			0
$317$	−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
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$	−6.00000			−0.333849
$324$		0			0
$325$	−8.00000	−	6.00000i	−0.443760	−	0.332820i
$326$		0			0
$327$	10.0000	+	10.0000i	0.553001	+	0.553001i
$328$		0			0
$329$	42.0000			2.31553
$330$		0			0
$331$	−21.0000	+	21.0000i	−1.15426	+	1.15426i	−0.168576	+	0.985689i	$0.553917\pi$
$331$	−21.0000	+	21.0000i	−1.15426	+	1.15426i	−0.985689	+	0.168576i	$0.946083\pi$
$332$		0			0
$333$			6.00000i			0.328798i
$334$		0			0
$335$	4.00000	+	8.00000i	0.218543	+	0.437087i
$336$		0			0
$337$	−11.0000	−	11.0000i	−0.599208	−	0.599208i	0.340894	−	0.940102i	$-0.389270\pi$
$337$	−11.0000	−	11.0000i	−0.599208	−	0.599208i	−0.940102	+	0.340894i	$0.889270\pi$
$338$		0			0
$339$	−26.0000	+	26.0000i	−1.41213	+	1.41213i
$340$		0			0
$341$	−2.00000	−	2.00000i	−0.108306	−	0.108306i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$	−2.00000	+	6.00000i	−0.107676	+	0.323029i
$346$		0			0
$347$	2.00000			0.107366			0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000			0.107366			0.0536828	+	0.998558i	$0.482904\pi$
$348$		0			0
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	0.782826	−	0.622240i	$-0.213777\pi$
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	−0.622240	+	0.782826i	$0.713777\pi$
$350$		0			0
$351$		−	8.00000i		−	0.427008i
$352$		0			0
$353$	13.0000	−	13.0000i	0.691920	−	0.691920i	−0.270734	−	0.962654i	$-0.587266\pi$
$353$	13.0000	−	13.0000i	0.691920	−	0.691920i	0.962654	+	0.270734i	$0.0872664\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	12.0000i		−	0.635107i
$358$		0			0
$359$			14.0000i			0.738892i	0.929252	+	0.369446i	$0.120452\pi$
$359$			14.0000i			0.738892i	−0.929252	+	0.369446i	$0.879548\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$		0			0
$363$		−	18.0000i		−	0.944755i
$364$		0			0
$365$	9.00000	+	3.00000i	0.471082	+	0.157027i
$366$		0			0
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.101339	+	0.994852i	$0.532313\pi$
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.994852	+	0.101339i	$0.967687\pi$
$368$		0			0
$369$			4.00000i			0.208232i
$370$		0			0
$371$	24.0000	+	24.0000i	1.24602	+	1.24602i
$372$		0			0
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$	−4.00000	+	22.0000i	−0.206559	+	1.13608i
$376$		0			0
$377$	14.0000	−	14.0000i	0.721037	−	0.721037i
$378$		0			0
$379$	15.0000	+	15.0000i	0.770498	+	0.770498i	0.978194	−	0.207695i	$-0.0665963\pi$
$379$	15.0000	+	15.0000i	0.770498	+	0.770498i	−0.207695	+	0.978194i	$0.566596\pi$
$380$		0			0
$381$	−14.0000	+	14.0000i	−0.717242	+	0.717242i
$382$		0			0
$383$	5.00000	+	5.00000i	0.255488	+	0.255488i	0.823216	−	0.567728i	$-0.192177\pi$
$383$	5.00000	+	5.00000i	0.255488	+	0.255488i	−0.567728	+	0.823216i	$0.692177\pi$
$384$		0			0
$385$	−12.0000	+	6.00000i	−0.611577	+	0.305788i
$386$		0			0
$387$		−	4.00000i		−	0.203331i
$388$		0			0
$389$	23.0000	−	23.0000i	1.16615	−	1.16615i	0.183041	−	0.983105i	$-0.441406\pi$
$389$	23.0000	−	23.0000i	1.16615	−	1.16615i	0.983105	−	0.183041i	$-0.0585941\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$		0			0
$393$	14.0000	+	14.0000i	0.706207	+	0.706207i
$394$		0			0
$395$	−16.0000	+	8.00000i	−0.805047	+	0.402524i
$396$		0			0
$397$	32.0000			1.60603			0.803017	−	0.595956i	$-0.203227\pi$
$397$	32.0000			1.60603			0.803017	+	0.595956i	$0.203227\pi$
$398$		0			0
$399$	36.0000			1.80225
$400$		0			0
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$		0			0
$403$	4.00000			0.199254
$404$		0			0
$405$	−22.0000	+	11.0000i	−1.09319	+	0.546594i
$406$		0			0
$407$	−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	$0.888700\pi$
$410$		0			0
$411$	18.0000	−	18.0000i	0.887875	−	0.887875i
$412$		0			0
$413$			18.0000i			0.885722i
$414$		0			0
$415$	−4.00000	+	2.00000i	−0.196352	+	0.0981761i
$416$		0			0
$417$	18.0000	+	18.0000i	0.881464	+	0.881464i
$418$		0			0
$419$	17.0000	−	17.0000i	0.830504	−	0.830504i	−0.157081	−	0.987586i	$-0.550208\pi$
$419$	17.0000	−	17.0000i	0.830504	−	0.830504i	0.987586	+	0.157081i	$0.0502085\pi$
$420$		0			0
$421$	5.00000	+	5.00000i	0.243685	+	0.243685i	0.818373	−	0.574688i	$-0.194876\pi$
$421$	5.00000	+	5.00000i	0.243685	+	0.243685i	−0.574688	+	0.818373i	$0.694876\pi$
$422$		0			0
$423$	7.00000	−	7.00000i	0.340352	−	0.340352i
$424$		0			0
$425$	7.00000	−	1.00000i	0.339550	−	0.0485071i
$426$		0			0
$427$	6.00000			0.290360
$428$		0			0
$429$	−4.00000	−	4.00000i	−0.193122	−	0.193122i
$430$		0			0
$431$			2.00000i			0.0963366i	0.998839	+	0.0481683i	$0.0153384\pi$
$431$			2.00000i			0.0963366i	−0.998839	+	0.0481683i	$0.984662\pi$
$432$		0			0
$433$	5.00000	−	5.00000i	0.240285	−	0.240285i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$	5.00000	−	5.00000i	0.240285	−	0.240285i	0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$	−42.0000	−	14.0000i	−2.01375	−	0.671249i
$436$		0			0
$437$			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	$-0.213053\pi$
$440$		0			0
$441$			11.0000i			0.523810i
$442$		0			0
$443$			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
$446$		0			0
$447$	2.00000	−	2.00000i	0.0945968	−	0.0945968i
$448$		0			0
$449$			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
$452$		0			0
$453$	16.0000			0.751746
$454$		0			0
$455$	6.00000	−	18.0000i	0.281284	−	0.843853i
$456$		0			0
$457$	7.00000	−	7.00000i	0.327446	−	0.327446i	−0.524168	−	0.851615i	$-0.675624\pi$
$457$	7.00000	−	7.00000i	0.327446	−	0.327446i	0.851615	+	0.524168i	$0.175624\pi$
$458$		0			0
$459$	4.00000	+	4.00000i	0.186704	+	0.186704i
$460$		0			0
$461$	21.0000	−	21.0000i	0.978068	−	0.978068i	−0.0216971	−	0.999765i	$-0.506907\pi$
$461$	21.0000	−	21.0000i	0.978068	−	0.978068i	0.999765	+	0.0216971i	$0.00690694\pi$
$462$		0			0
$463$	−19.0000	−	19.0000i	−0.883005	−	0.883005i	0.110834	−	0.993839i	$-0.464648\pi$
$463$	−19.0000	−	19.0000i	−0.883005	−	0.883005i	−0.993839	+	0.110834i	$0.964648\pi$
$464$		0			0
$465$	−4.00000	−	8.00000i	−0.185496	−	0.370991i
$466$		0			0
$467$		−	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
$470$		0			0
$471$	40.0000			1.84310
$472$		0			0
$473$	4.00000	+	4.00000i	0.183920	+	0.183920i
$474$		0			0
$475$	3.00000	+	21.0000i	0.137649	+	0.963546i
$476$		0			0
$477$	8.00000			0.366295
$478$		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
$482$		0			0
$483$	−12.0000			−0.546019
$484$		0			0
$485$	−33.0000	−	11.0000i	−1.49845	−	0.499484i
$486$		0			0
$487$	15.0000	+	15.0000i	0.679715	+	0.679715i	0.959936	−	0.280221i	$-0.0904077\pi$
$487$	15.0000	+	15.0000i	0.679715	+	0.679715i	−0.280221	+	0.959936i	$0.590408\pi$
$488$		0			0
$489$	−28.0000			−1.26620
$490$		0			0
$491$	−9.00000	+	9.00000i	−0.406164	+	0.406164i	−0.880399	−	0.474234i	$-0.842725\pi$
$491$	−9.00000	+	9.00000i	−0.406164	+	0.406164i	0.474234	+	0.880399i	$0.342725\pi$
$492$		0			0
$493$			14.0000i			0.630528i
$494$		0			0
$495$	−1.00000	+	3.00000i	−0.0449467	+	0.134840i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	29.0000	−	29.0000i	1.29822	−	1.29822i	0.368650	−	0.929568i	$-0.379820\pi$
$499$	29.0000	−	29.0000i	1.29822	−	1.29822i	0.929568	−	0.368650i	$-0.120180\pi$
$500$		0			0
$501$	−6.00000	−	6.00000i	−0.268060	−	0.268060i
$502$		0			0
$503$	29.0000	−	29.0000i	1.29305	−	1.29305i	0.360153	−	0.932893i	$-0.382725\pi$
$503$	29.0000	−	29.0000i	1.29305	−	1.29305i	0.932893	−	0.360153i	$-0.117275\pi$
$504$		0			0
$505$	15.0000	+	5.00000i	0.667491	+	0.222497i
$506$		0			0
$507$	−18.0000			−0.799408
$508$		0			0
$509$	−17.0000	−	17.0000i	−0.753512	−	0.753512i	0.221621	−	0.975133i	$-0.428865\pi$
$509$	−17.0000	−	17.0000i	−0.753512	−	0.753512i	−0.975133	+	0.221621i	$0.928865\pi$
$510$		0			0
$511$			18.0000i			0.796273i
$512$		0			0
$513$	−12.0000	+	12.0000i	−0.529813	+	0.529813i
$514$		0			0
$515$	5.00000	−	15.0000i	0.220326	−	0.660979i
$516$		0			0
$517$			14.0000i			0.615719i
$518$		0			0
$519$			12.0000i			0.526742i
$520$		0			0
$521$			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	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$		0			0
$525$	−42.0000	+	6.00000i	−1.83303	+	0.261861i
$526$		0			0
$527$	−2.00000	+	2.00000i	−0.0871214	+	0.0871214i
$528$		0			0
$529$			21.0000i			0.913043i
$530$		0			0
$531$	3.00000	+	3.00000i	0.130189	+	0.130189i
$532$		0			0
$533$	8.00000			0.346518
$534$		0			0
$535$	−12.0000	+	6.00000i	−0.518805	+	0.259403i
$536$		0			0
$537$	−10.0000	+	10.0000i	−0.431532	+	0.431532i
$538$		0			0
$539$	−11.0000	−	11.0000i	−0.473804	−	0.473804i
$540$		0			0
$541$	−15.0000	+	15.0000i	−0.644900	+	0.644900i	−0.951756	−	0.306856i	$-0.900723\pi$
$541$	−15.0000	+	15.0000i	−0.644900	+	0.644900i	0.306856	+	0.951756i	$0.400723\pi$
$542$		0			0
$543$	6.00000	+	6.00000i	0.257485	+	0.257485i
$544$		0			0
$545$	−15.0000	−	5.00000i	−0.642529	−	0.214176i
$546$		0			0
$547$			28.0000i			1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$		0			0
$549$	1.00000	−	1.00000i	0.0426790	−	0.0426790i
$550$		0			0
$551$	−42.0000			−1.78926
$552$		0			0
$553$	−24.0000	−	24.0000i	−1.02058	−	1.02058i
$554$		0			0
$555$	−12.0000	−	24.0000i	−0.509372	−	1.01874i
$556$		0			0
$557$	−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
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	−18.0000			−0.758610			−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000			−0.758610			−0.379305	+	0.925272i	$0.623837\pi$
$564$		0			0
$565$	13.0000	−	39.0000i	0.546914	−	1.64074i
$566$		0			0
$567$	−33.0000	−	33.0000i	−1.38587	−	1.38587i
$568$		0			0
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$	−25.0000	+	25.0000i	−1.04622	+	1.04622i	−0.0473385	+	0.998879i	$0.515074\pi$
$571$	−25.0000	+	25.0000i	−1.04622	+	1.04622i	−0.998879	+	0.0473385i	$0.984926\pi$
$572$		0			0
$573$		−	36.0000i		−	1.50392i
$574$		0			0
$575$	−1.00000	−	7.00000i	−0.0417029	−	0.291920i
$576$		0			0
$577$	9.00000	+	9.00000i	0.374675	+	0.374675i	0.869177	−	0.494502i	$-0.164649\pi$
$577$	9.00000	+	9.00000i	0.374675	+	0.374675i	−0.494502	+	0.869177i	$0.664649\pi$
$578$		0			0
$579$	30.0000	−	30.0000i	1.24676	−	1.24676i
$580$		0			0
$581$	−6.00000	−	6.00000i	−0.248922	−	0.248922i
$582$		0			0
$583$	−8.00000	+	8.00000i	−0.331326	+	0.331326i
$584$		0			0
$585$	−2.00000	−	4.00000i	−0.0826898	−	0.165380i
$586$		0			0
$587$	2.00000			0.0825488			0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000			0.0825488			0.0412744	+	0.999148i	$0.486858\pi$
$588$		0			0
$589$	−6.00000	−	6.00000i	−0.247226	−	0.247226i
$590$		0			0
$591$			12.0000i			0.493614i
$592$		0			0
$593$	17.0000	−	17.0000i	0.698106	−	0.698106i	−0.265896	−	0.964002i	$-0.585668\pi$
$593$	17.0000	−	17.0000i	0.698106	−	0.698106i	0.964002	+	0.265896i	$0.0856676\pi$
$594$		0			0
$595$	6.00000	+	12.0000i	0.245976	+	0.491952i
$596$		0			0
$597$			20.0000i			0.818546i
$598$		0			0
$599$			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
$601$		−	16.0000i		−	0.652654i	−0.945257	−	0.326327i	$-0.894189\pi$
$601$		−	16.0000i		−	0.652654i	0.945257	−	0.326327i	$-0.105811\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$		0			0
$605$	9.00000	+	18.0000i	0.365902	+	0.731804i
$606$		0			0
$607$	23.0000	−	23.0000i	0.933541	−	0.933541i	−0.0643840	−	0.997925i	$-0.520508\pi$
$607$	23.0000	−	23.0000i	0.933541	−	0.933541i	0.997925	+	0.0643840i	$0.0205082\pi$
$608$		0			0
$609$		−	84.0000i		−	3.40385i
$610$		0			0
$611$	−14.0000	−	14.0000i	−0.566379	−	0.566379i
$612$		0			0
$613$	−8.00000			−0.323117			−0.161558	−	0.986863i	$-0.551652\pi$
$613$	−8.00000			−0.323117			−0.161558	+	0.986863i	$0.551652\pi$
$614$		0			0
$615$	−8.00000	−	16.0000i	−0.322591	−	0.645182i
$616$		0			0
$617$	−25.0000	+	25.0000i	−1.00646	+	1.00646i	−0.00648312	+	0.999979i	$0.502064\pi$
$617$	−25.0000	+	25.0000i	−1.00646	+	1.00646i	−0.999979	+	0.00648312i	$0.997936\pi$
$618$		0			0
$619$	7.00000	+	7.00000i	0.281354	+	0.281354i	0.833649	−	0.552295i	$-0.186248\pi$
$619$	7.00000	+	7.00000i	0.281354	+	0.281354i	−0.552295	+	0.833649i	$0.686248\pi$
$620$		0			0
$621$	4.00000	−	4.00000i	0.160514	−	0.160514i
$622$		0			0
$623$	−18.0000	−	18.0000i	−0.721155	−	0.721155i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$			12.0000i			0.479234i
$628$		0			0
$629$	−6.00000	+	6.00000i	−0.239236	+	0.239236i
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$		0			0
$633$	38.0000	+	38.0000i	1.51036	+	1.51036i
$634$		0			0
$635$	7.00000	−	21.0000i	0.277787	−	0.833360i
$636$		0			0
$637$	22.0000			0.871672
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−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
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$		0			0
$645$	8.00000	+	16.0000i	0.315000	+	0.629999i
$646$		0			0
$647$	15.0000	+	15.0000i	0.589711	+	0.589711i	0.937553	−	0.347842i	$-0.113086\pi$
$647$	15.0000	+	15.0000i	0.589711	+	0.589711i	−0.347842	+	0.937553i	$0.613086\pi$
$648$		0			0
$649$	−6.00000			−0.235521
$650$		0			0
$651$	12.0000	−	12.0000i	0.470317	−	0.470317i
$652$		0			0
$653$		−	2.00000i		−	0.0782660i	−0.999234	−	0.0391330i	$-0.987540\pi$
$653$		−	2.00000i		−	0.0782660i	0.999234	−	0.0391330i	$-0.0124596\pi$
$654$		0			0
$655$	−21.0000	−	7.00000i	−0.820538	−	0.273513i
$656$		0			0
$657$	3.00000	+	3.00000i	0.117041	+	0.117041i
$658$		0			0
$659$	−11.0000	+	11.0000i	−0.428499	+	0.428499i	−0.888117	−	0.459618i	$-0.847986\pi$
$659$	−11.0000	+	11.0000i	−0.428499	+	0.428499i	0.459618	+	0.888117i	$0.347986\pi$
$660$		0			0
$661$	25.0000	+	25.0000i	0.972387	+	0.972387i	0.999629	−	0.0272416i	$-0.00867234\pi$
$661$	25.0000	+	25.0000i	0.972387	+	0.972387i	−0.0272416	+	0.999629i	$0.508672\pi$
$662$		0			0
$663$	−4.00000	+	4.00000i	−0.155347	+	0.155347i
$664$		0			0
$665$	−36.0000	+	18.0000i	−1.39602	+	0.698010i
$666$		0			0
$667$	14.0000			0.542082
$668$		0			0
$669$	−18.0000	−	18.0000i	−0.695920	−	0.695920i
$670$		0			0
$671$			2.00000i			0.0772091i
$672$		0			0
$673$	1.00000	−	1.00000i	0.0385472	−	0.0385472i	−0.687570	−	0.726118i	$-0.741323\pi$
$673$	1.00000	−	1.00000i	0.0385472	−	0.0385472i	0.726118	+	0.687570i	$0.241323\pi$
$674$		0			0
$675$	12.0000	−	16.0000i	0.461880	−	0.615840i
$676$		0			0
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$		0			0
$679$		−	66.0000i		−	2.53285i
$680$		0			0
$681$		−	24.0000i		−	0.919682i
$682$		0			0
$683$			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
$686$		0			0
$687$	2.00000	−	2.00000i	0.0763048	−	0.0763048i
$688$		0			0
$689$		−	16.0000i		−	0.609551i
$690$		0			0
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	0.982919	−	0.184041i	$-0.0589179\pi$
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	−0.184041	+	0.982919i	$0.558918\pi$
$692$		0			0
$693$	−6.00000			−0.227921
$694$		0			0
$695$	−27.0000	−	9.00000i	−1.02417	−	0.341389i
$696$		0			0
$697$	−4.00000	+	4.00000i	−0.151511	+	0.151511i
$698$		0			0
$699$	18.0000	+	18.0000i	0.680823	+	0.680823i
$700$		0			0
$701$	13.0000	−	13.0000i	0.491003	−	0.491003i	−0.417619	−	0.908622i	$-0.637135\pi$
$701$	13.0000	−	13.0000i	0.491003	−	0.491003i	0.908622	+	0.417619i	$0.137135\pi$
$702$		0			0
$703$	−18.0000	−	18.0000i	−0.678883	−	0.678883i
$704$		0			0
$705$	−14.0000	+	42.0000i	−0.527271	+	1.58181i
$706$		0			0
$707$			30.0000i			1.12827i
$708$		0			0
$709$	−1.00000	+	1.00000i	−0.0375558	+	0.0375558i	−0.725635	−	0.688080i	$-0.758454\pi$
$709$	−1.00000	+	1.00000i	−0.0375558	+	0.0375558i	0.688080	+	0.725635i	$0.258454\pi$
$710$		0			0
$711$	−8.00000			−0.300023
$712$		0			0
$713$	2.00000	+	2.00000i	0.0749006	+	0.0749006i
$714$		0			0
$715$	6.00000	+	2.00000i	0.224387	+	0.0747958i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	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
$722$		0			0
$723$	28.0000			1.04133
$724$		0			0
$725$	49.0000	−	7.00000i	1.81981	−	0.259973i
$726$		0			0
$727$	7.00000	+	7.00000i	0.259616	+	0.259616i	0.824898	−	0.565282i	$-0.191233\pi$
$727$	7.00000	+	7.00000i	0.259616	+	0.259616i	−0.565282	+	0.824898i	$0.691233\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	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	$-0.186914\pi$
$734$		0			0
$735$	−22.0000	−	44.0000i	−0.811482	−	1.62296i
$736$		0			0
$737$	−4.00000	−	4.00000i	−0.147342	−	0.147342i
$738$		0			0
$739$	21.0000	−	21.0000i	0.772497	−	0.772497i	−0.206045	−	0.978543i	$-0.566059\pi$
$739$	21.0000	−	21.0000i	0.772497	−	0.772497i	0.978543	+	0.206045i	$0.0660593\pi$
$740$		0			0
$741$	−12.0000	−	12.0000i	−0.440831	−	0.440831i
$742$		0			0
$743$	−31.0000	+	31.0000i	−1.13728	+	1.13728i	−0.148344	+	0.988936i	$0.547394\pi$
$743$	−31.0000	+	31.0000i	−1.13728	+	1.13728i	−0.988936	+	0.148344i	$0.952606\pi$
$744$		0			0
$745$	−1.00000	+	3.00000i	−0.0366372	+	0.109911i
$746$		0			0
$747$	−2.00000			−0.0731762
$748$		0			0
$749$	−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	$0.634333\pi$
$752$		0			0
$753$	−22.0000	+	22.0000i	−0.801725	+	0.801725i
$754$		0			0
$755$	−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	$-0.0115717\pi$
$758$		0			0
$759$		−	4.00000i		−	0.145191i
$760$		0			0
$761$		−	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
$764$		0			0
$765$	3.00000	+	1.00000i	0.108465	+	0.0361551i
$766$		0			0
$767$	6.00000	−	6.00000i	0.216647	−	0.216647i
$768$		0			0
$769$			4.00000i			0.144244i	0.997396	+	0.0721218i	$0.0229770\pi$
$769$			4.00000i			0.144244i	−0.997396	+	0.0721218i	$0.977023\pi$
$770$		0			0
$771$	−26.0000	−	26.0000i	−0.936367	−	0.936367i
$772$		0			0
$773$	−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
$776$		0			0
$777$	36.0000	−	36.0000i	1.29149	−	1.29149i
$778$		0			0
$779$	−12.0000	−	12.0000i	−0.429945	−	0.429945i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	28.0000	+	28.0000i	1.00064	+	1.00064i
$784$		0			0
$785$	−40.0000	+	20.0000i	−1.42766	+	0.713831i
$786$		0			0
$787$		−	4.00000i		−	0.142585i	−0.997455	−	0.0712923i	$-0.977288\pi$
$787$		−	4.00000i		−	0.142585i	0.997455	−	0.0712923i	$-0.0227123\pi$
$788$		0			0
$789$	14.0000	−	14.0000i	0.498413	−	0.498413i
$790$		0			0
$791$	78.0000			2.77336
$792$		0			0
$793$	−2.00000	−	2.00000i	−0.0710221	−	0.0710221i
$794$		0			0
$795$	−32.0000	+	16.0000i	−1.13492	+	0.567462i
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	14.0000			0.495284
$800$		0			0
$801$	−6.00000			−0.212000
$802$		0			0
$803$	−6.00000			−0.211735
$804$		0			0
$805$	12.0000	−	6.00000i	0.422944	−	0.211472i
$806$		0			0
$807$	2.00000	+	2.00000i	0.0704033	+	0.0704033i
$808$		0			0
$809$	−26.0000			−0.914111			−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000			−0.914111			−0.457056	+	0.889438i	$0.651096\pi$
$810$		0			0
$811$	−9.00000	+	9.00000i	−0.316033	+	0.316033i	−0.847241	−	0.531208i	$-0.821738\pi$
$811$	−9.00000	+	9.00000i	−0.316033	+	0.316033i	0.531208	+	0.847241i	$0.321738\pi$
$812$		0			0
$813$			60.0000i			2.10429i
$814$		0			0
$815$	28.0000	−	14.0000i	0.980797	−	0.490399i
$816$		0			0
$817$	12.0000	+	12.0000i	0.419827	+	0.419827i
$818$		0			0
$819$	6.00000	−	6.00000i	0.209657	−	0.209657i
$820$		0			0
$821$	−15.0000	−	15.0000i	−0.523504	−	0.523504i	0.395124	−	0.918628i	$-0.370702\pi$
$821$	−15.0000	−	15.0000i	−0.523504	−	0.523504i	−0.918628	+	0.395124i	$0.870702\pi$
$822$		0			0
$823$	21.0000	−	21.0000i	0.732014	−	0.732014i	−0.239004	−	0.971018i	$-0.576821\pi$
$823$	21.0000	−	21.0000i	0.732014	−	0.732014i	0.971018	+	0.239004i	$0.0768211\pi$
$824$		0			0
$825$	−2.00000	−	14.0000i	−0.0696311	−	0.487417i
$826$		0			0
$827$	−54.0000			−1.87776			−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000			−1.87776			−0.938882	+	0.344239i	$0.888137\pi$
$828$		0			0
$829$	27.0000	+	27.0000i	0.937749	+	0.937749i	0.998173	−	0.0604240i	$-0.0192453\pi$
$829$	27.0000	+	27.0000i	0.937749	+	0.937749i	−0.0604240	+	0.998173i	$0.519245\pi$
$830$		0			0
$831$			36.0000i			1.24883i
$832$		0			0
$833$	−11.0000	+	11.0000i	−0.381127	+	0.381127i
$834$		0			0
$835$	9.00000	+	3.00000i	0.311458	+	0.103819i
$836$		0			0
$837$			8.00000i			0.276520i
$838$		0			0
$839$		−	18.0000i		−	0.621429i	−0.950503	−	0.310715i	$-0.899432\pi$
$839$		−	18.0000i		−	0.621429i	0.950503	−	0.310715i	$-0.100568\pi$
$840$		0			0
$841$			69.0000i			2.37931i
$842$		0			0
$843$			32.0000i			1.10214i
$844$		0			0
$845$	18.0000	−	9.00000i	0.619219	−	0.309609i
$846$		0			0
$847$	−27.0000	+	27.0000i	−0.927731	+	0.927731i
$848$		0			0
$849$			24.0000i			0.823678i
$850$		0			0
$851$	6.00000	+	6.00000i	0.205677	+	0.205677i
$852$		0			0
$853$	−16.0000			−0.547830			−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000			−0.547830			−0.273915	+	0.961754i	$0.588319\pi$
$854$		0			0
$855$	−3.00000	+	9.00000i	−0.102598	+	0.307794i
$856$		0			0
$857$	27.0000	−	27.0000i	0.922302	−	0.922302i	−0.0748894	−	0.997192i	$-0.523860\pi$
$857$	27.0000	−	27.0000i	0.922302	−	0.922302i	0.997192	+	0.0748894i	$0.0238604\pi$
$858$		0			0
$859$	19.0000	+	19.0000i	0.648272	+	0.648272i	0.952575	−	0.304303i	$-0.0984237\pi$
$859$	19.0000	+	19.0000i	0.648272	+	0.648272i	−0.304303	+	0.952575i	$0.598424\pi$
$860$		0			0
$861$	24.0000	−	24.0000i	0.817918	−	0.817918i
$862$		0			0
$863$	5.00000	+	5.00000i	0.170202	+	0.170202i	0.787068	−	0.616866i	$-0.211598\pi$
$863$	5.00000	+	5.00000i	0.170202	+	0.170202i	−0.616866	+	0.787068i	$0.711598\pi$
$864$		0			0
$865$	−6.00000	−	12.0000i	−0.204006	−	0.408012i
$866$		0			0
$867$			30.0000i			1.01885i
$868$		0			0
$869$	8.00000	−	8.00000i	0.271381	−	0.271381i
$870$		0			0
$871$	8.00000			0.271070
$872$		0			0
$873$	−11.0000	−	11.0000i	−0.372294	−	0.372294i
$874$		0			0
$875$	39.0000	−	27.0000i	1.31844	−	0.912767i
$876$		0			0
$877$	−4.00000			−0.135070			−0.0675352	−	0.997717i	$-0.521513\pi$
$877$	−4.00000			−0.135070			−0.0675352	+	0.997717i	$0.521513\pi$
$878$		0			0
$879$	−24.0000			−0.809500
$880$		0			0
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$		0			0
$883$	6.00000			0.201916			0.100958	−	0.994891i	$-0.467809\pi$
$883$	6.00000			0.201916			0.100958	+	0.994891i	$0.467809\pi$
$884$		0			0
$885$	−18.0000	−	6.00000i	−0.605063	−	0.201688i
$886$		0			0
$887$	23.0000	+	23.0000i	0.772264	+	0.772264i	0.978502	−	0.206238i	$-0.0661220\pi$
$887$	23.0000	+	23.0000i	0.772264	+	0.772264i	−0.206238	+	0.978502i	$0.566122\pi$
$888$		0			0
$889$	42.0000			1.40863
$890$		0			0
$891$	11.0000	−	11.0000i	0.368514	−	0.368514i
$892$		0			0
$893$			42.0000i			1.40548i
$894$		0			0
$895$	5.00000	−	15.0000i	0.167132	−	0.501395i
$896$		0			0
$897$	4.00000	+	4.00000i	0.133556	+	0.133556i
$898$		0			0
$899$	−14.0000	+	14.0000i	−0.466926	+	0.466926i
$900$		0			0
$901$	8.00000	+	8.00000i	0.266519	+	0.266519i
$902$		0			0
$903$	−24.0000	+	24.0000i	−0.798670	+	0.798670i
$904$		0			0
$905$	−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	$0.188277\pi$
$908$		0			0
$909$	5.00000	+	5.00000i	0.165840	+	0.165840i
$910$		0			0
$911$		−	38.0000i		−	1.25900i	−0.777002	−	0.629498i	$-0.783261\pi$
$911$		−	38.0000i		−	1.25900i	0.777002	−	0.629498i	$-0.216739\pi$
$912$		0			0
$913$	2.00000	−	2.00000i	0.0661903	−	0.0661903i
$914$		0			0
$915$	−2.00000	+	6.00000i	−0.0661180	+	0.198354i
$916$		0			0
$917$		−	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	$0.725835\pi$
$920$		0			0
$921$			8.00000i			0.263609i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	24.0000	+	18.0000i	0.789115	+	0.591836i
$926$		0			0
$927$	5.00000	−	5.00000i	0.164222	−	0.164222i
$928$		0			0
$929$		−	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
$932$		0			0
$933$	32.0000			1.04763
$934$		0			0
$935$	−4.00000	+	2.00000i	−0.130814	+	0.0654070i
$936$		0			0
$937$	3.00000	−	3.00000i	0.0980057	−	0.0980057i	−0.656404	−	0.754410i	$-0.727923\pi$
$937$	3.00000	−	3.00000i	0.0980057	−	0.0980057i	0.754410	+	0.656404i	$0.227923\pi$
$938$		0			0
$939$	26.0000	+	26.0000i	0.848478	+	0.848478i
$940$		0			0
$941$	1.00000	−	1.00000i	0.0325991	−	0.0325991i	−0.690619	−	0.723218i	$-0.742662\pi$
$941$	1.00000	−	1.00000i	0.0325991	−	0.0325991i	0.723218	+	0.690619i	$0.242662\pi$
$942$		0			0
$943$	4.00000	+	4.00000i	0.130258	+	0.130258i
$944$		0			0
$945$	36.0000	+	12.0000i	1.17108	+	0.390360i
$946$		0			0
$947$			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
$950$		0			0
$951$	16.0000			0.518836
$952$		0			0
$953$	31.0000	+	31.0000i	1.00419	+	1.00419i	0.999991	+	0.00419731i	$0.00133605\pi$
$953$	31.0000	+	31.0000i	1.00419	+	1.00419i	0.00419731	+	0.999991i	$0.498664\pi$
$954$		0			0
$955$	18.0000	+	36.0000i	0.582466	+	1.16493i
$956$		0			0
$957$	28.0000			0.905111
$958$		0			0
$959$	−54.0000			−1.74375
$960$		0			0
$961$	27.0000			0.870968
$962$		0			0
$963$	−6.00000			−0.193347
$964$		0			0
$965$	−15.0000	+	45.0000i	−0.482867	+	1.44860i
$966$		0			0
$967$	−33.0000	−	33.0000i	−1.06121	−	1.06121i	−0.998000	−	0.0632081i	$-0.979867\pi$
$967$	−33.0000	−	33.0000i	−1.06121	−	1.06121i	−0.0632081	−	0.998000i	$-0.520133\pi$
$968$		0			0
$969$	12.0000			0.385496
$970$		0			0
$971$	31.0000	−	31.0000i	0.994837	−	0.994837i	−0.00514940	−	0.999987i	$-0.501639\pi$
$971$	31.0000	−	31.0000i	0.994837	−	0.994837i	0.999987	+	0.00514940i	$0.00163911\pi$
$972$		0			0
$973$		−	54.0000i		−	1.73116i
$974$		0			0
$975$	16.0000	+	12.0000i	0.512410	+	0.384308i
$976$		0			0
$977$	17.0000	+	17.0000i	0.543878	+	0.543878i	0.924663	−	0.380785i	$-0.124346\pi$
$977$	17.0000	+	17.0000i	0.543878	+	0.543878i	−0.380785	+	0.924663i	$0.624346\pi$
$978$		0			0
$979$	6.00000	−	6.00000i	0.191761	−	0.191761i
$980$		0			0
$981$	−5.00000	−	5.00000i	−0.159638	−	0.159638i
$982$		0			0
$983$	5.00000	−	5.00000i	0.159475	−	0.159475i	−0.622859	−	0.782334i	$-0.714029\pi$
$983$	5.00000	−	5.00000i	0.159475	−	0.159475i	0.782334	+	0.622859i	$0.214029\pi$
$984$		0			0
$985$	−6.00000	−	12.0000i	−0.191176	−	0.382352i
$986$		0			0
$987$	−84.0000			−2.67375
$988$		0			0
$989$	−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	$0.949228\pi$
$992$		0			0
$993$	42.0000	−	42.0000i	1.33283	−	1.33283i
$994$		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	$-0.113266\pi$
$998$		0			0
$999$			24.0000i			0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.s.a.287.1		2
4.3	odd	2		640.2.s.b.287.1		2
5.3	odd	4		640.2.j.b.543.1		2
8.3	odd	2		80.2.s.a.27.1	yes	2
8.5	even	2		320.2.s.a.207.1		2
16.3	odd	4		640.2.j.b.607.1		2
16.5	even	4		80.2.j.a.67.1	yes	2
16.11	odd	4		320.2.j.a.47.1		2
16.13	even	4		640.2.j.a.607.1		2
20.3	even	4		640.2.j.a.543.1		2
24.11	even	2		720.2.z.d.667.1		2
40.3	even	4		80.2.j.a.43.1	✓	2
40.13	odd	4		320.2.j.a.143.1		2
40.19	odd	2		400.2.s.a.107.1		2
40.27	even	4		400.2.j.a.43.1		2
40.29	even	2		1600.2.s.a.207.1		2
40.37	odd	4		1600.2.j.a.143.1		2
48.5	odd	4		720.2.bd.a.307.1		2
80.3	even	4	inner	640.2.s.a.223.1		2
80.13	odd	4		640.2.s.b.223.1		2
80.27	even	4		1600.2.s.a.943.1		2
80.37	odd	4		400.2.s.a.243.1		2
80.43	even	4		320.2.s.a.303.1		2
80.53	odd	4		80.2.s.a.3.1	yes	2
80.59	odd	4		1600.2.j.a.1007.1		2
80.69	even	4		400.2.j.a.307.1		2
120.83	odd	4		720.2.bd.a.523.1		2
240.53	even	4		720.2.z.d.163.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.a.43.1	✓	2	40.3	even	4
80.2.j.a.67.1	yes	2	16.5	even	4
80.2.s.a.3.1	yes	2	80.53	odd	4
80.2.s.a.27.1	yes	2	8.3	odd	2
320.2.j.a.47.1		2	16.11	odd	4
320.2.j.a.143.1		2	40.13	odd	4
320.2.s.a.207.1		2	8.5	even	2
320.2.s.a.303.1		2	80.43	even	4
400.2.j.a.43.1		2	40.27	even	4
400.2.j.a.307.1		2	80.69	even	4
400.2.s.a.107.1		2	40.19	odd	2
400.2.s.a.243.1		2	80.37	odd	4
640.2.j.a.543.1		2	20.3	even	4
640.2.j.a.607.1		2	16.13	even	4
640.2.j.b.543.1		2	5.3	odd	4
640.2.j.b.607.1		2	16.3	odd	4
640.2.s.a.223.1		2	80.3	even	4	inner
640.2.s.a.287.1		2	1.1	even	1	trivial
640.2.s.b.223.1		2	80.13	odd	4
640.2.s.b.287.1		2	4.3	odd	2
720.2.z.d.163.1		2	240.53	even	4
720.2.z.d.667.1		2	24.11	even	2
720.2.bd.a.307.1		2	48.5	odd	4
720.2.bd.a.523.1		2	120.83	odd	4
1600.2.j.a.143.1		2	40.37	odd	4
1600.2.j.a.1007.1		2	80.59	odd	4
1600.2.s.a.207.1		2	40.29	even	2
1600.2.s.a.943.1		2	80.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{3} +(2.00000 - 1.00000i) q^{5} +(3.00000 + 3.00000i) q^{7} +1.00000 q^{9} +(-1.00000 + 1.00000i) q^{11} -2.00000i q^{13} +(-4.00000 + 2.00000i) q^{15} +(1.00000 + 1.00000i) q^{17} +(-3.00000 + 3.00000i) q^{19} +(-6.00000 - 6.00000i) q^{21} +(1.00000 - 1.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +4.00000 q^{27} +(7.00000 + 7.00000i) q^{29} +2.00000i q^{31} +(2.00000 - 2.00000i) q^{33} +(9.00000 + 3.00000i) q^{35} +6.00000i q^{37} +4.00000i q^{39} +4.00000i q^{41} -4.00000i q^{43} +(2.00000 - 1.00000i) q^{45} +(7.00000 - 7.00000i) q^{47} +11.0000i q^{49} +(-2.00000 - 2.00000i) q^{51} +8.00000 q^{53} +(-1.00000 + 3.00000i) q^{55} +(6.00000 - 6.00000i) q^{57} +(3.00000 + 3.00000i) q^{59} +(1.00000 - 1.00000i) q^{61} +(3.00000 + 3.00000i) q^{63} +(-2.00000 - 4.00000i) q^{65} +4.00000i q^{67} +(-2.00000 + 2.00000i) q^{69} +(3.00000 + 3.00000i) q^{73} +(-6.00000 + 8.00000i) q^{75} -6.00000 q^{77} -8.00000 q^{79} -11.0000 q^{81} -2.00000 q^{83} +(3.00000 + 1.00000i) q^{85} +(-14.0000 - 14.0000i) q^{87} -6.00000 q^{89} +(6.00000 - 6.00000i) q^{91} -4.00000i q^{93} +(-3.00000 + 9.00000i) q^{95} +(-11.0000 - 11.0000i) q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} + 4 q^{5} + 6 q^{7} + 2 q^{9} - 2 q^{11} - 8 q^{15} + 2 q^{17} - 6 q^{19} - 12 q^{21} + 2 q^{23} + 6 q^{25} + 8 q^{27} + 14 q^{29} + 4 q^{33} + 18 q^{35} + 4 q^{45} + 14 q^{47} - 4 q^{51}+ \cdots - 2 q^{99}+O(q^{100}) \) 2 * q - 4 * q^3 + 4 * q^5 + 6 * q^7 + 2 * q^9 - 2 * q^11 - 8 * q^15 + 2 * q^17 - 6 * q^19 - 12 * q^21 + 2 * q^23 + 6 * q^25 + 8 * q^27 + 14 * q^29 + 4 * q^33 + 18 * q^35 + 4 * q^45 + 14 * q^47 - 4 * q^51 + 16 * q^53 - 2 * q^55 + 12 * q^57 + 6 * q^59 + 2 * q^61 + 6 * q^63 - 4 * q^65 - 4 * q^69 + 6 * q^73 - 12 * q^75 - 12 * q^77 - 16 * q^79 - 22 * q^81 - 4 * q^83 + 6 * q^85 - 28 * q^87 - 12 * q^89 + 12 * q^91 - 6 * q^95 - 22 * q^97 - 2 * q^99

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