LMFDB - Embedded newform 640.2.j.a.607.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(543,640)]

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, 1, 3]))

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

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

chi := DirichletCharacter("640.543");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$640 = 2^{7} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	640.j (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			607.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	640.607
Dual form			640.2.j.a.543.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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

)

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

$2$		0			0
$2$		0			0
$3$		−	2.00000i		−	1.15470i	−0.816497	−	0.577350i	$-0.804087\pi$
$3$		−	2.00000i		−	1.15470i	0.816497	−	0.577350i	$-0.195913\pi$
$4$		0			0
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		0			0
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.144370	−	0.989524i	$-0.546115\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		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	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$		0			0
$21$	−6.00000	+	6.00000i	−1.30931	+	1.30931i
$22$		0			0
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$		−	4.00000i		−	0.769800i
$28$		0			0
$29$	−7.00000	+	7.00000i	−1.29987	+	1.29987i	−0.371391	+	0.928477i	$0.621119\pi$
$29$	−7.00000	+	7.00000i	−1.29987	+	1.29987i	−0.928477	+	0.371391i	$0.878881\pi$
$30$		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
$35$	−3.00000	+	9.00000i	−0.507093	+	1.52128i
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$		−	4.00000i		−	0.640513i
$40$		0			0
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	1.00000	+	2.00000i	0.149071	+	0.298142i
$46$		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
$53$		−	8.00000i		−	1.09888i	−0.835532	−	0.549442i	$-0.814840\pi$
$53$		−	8.00000i		−	1.09888i	0.835532	−	0.549442i	$-0.185160\pi$
$54$		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	−0.484323	−	0.874889i	$-0.660934\pi$
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	0.874889	+	0.484323i	$0.160934\pi$
$60$		0			0
$61$	1.00000	+	1.00000i	0.128037	+	0.128037i	0.768221	−	0.640184i	$-0.221142\pi$
$61$	1.00000	+	1.00000i	0.128037	+	0.128037i	−0.640184	+	0.768221i	$0.721142\pi$
$62$		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
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		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	0.509404	−	0.860527i	$-0.329866\pi$
$73$	−3.00000	−	3.00000i	−0.351123	−	0.351123i	−0.860527	+	0.509404i	$0.829866\pi$
$74$		0			0
$75$	8.00000	+	6.00000i	0.923760	+	0.692820i
$76$		0			0
$77$		−	6.00000i		−	0.683763i
$78$		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
$83$		−	2.00000i		−	0.219529i	−0.993958	−	0.109764i	$-0.964990\pi$
$83$		−	2.00000i		−	0.219529i	0.993958	−	0.109764i	$-0.0350096\pi$
$84$		0			0
$85$	1.00000	−	3.00000i	0.108465	−	0.325396i
$86$		0			0
$87$	14.0000	+	14.0000i	1.50096	+	1.50096i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	−6.00000	−	6.00000i	−0.628971	−	0.628971i
$92$		0			0
$93$	4.00000			0.414781
$94$		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	−0.413146	−	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	−0.909145	−	0.416480i	$-0.863264\pi$
$103$	−5.00000	+	5.00000i	−0.492665	+	0.492665i	0.416480	+	0.909145i	$0.363264\pi$
$104$		0			0
$105$	18.0000	+	6.00000i	1.75662	+	0.585540i
$106$		0			0
$107$			6.00000i			0.580042i	0.957020	+	0.290021i	$0.0936623\pi$
$107$			6.00000i			0.580042i	−0.957020	+	0.290021i	$0.906338\pi$
$108$		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	$0.140032\pi$
$110$		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
$115$	3.00000	+	1.00000i	0.279751	+	0.0932505i
$116$		0			0
$117$	−2.00000			−0.184900
$118$		0			0
$119$		−	6.00000i		−	0.550019i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		0			0
$123$	−8.00000			−0.721336
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		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	$-0.607645\pi$
$131$	7.00000	−	7.00000i	0.611593	−	0.611593i	0.943361	+	0.331768i	$0.107645\pi$
$132$		0			0
$133$			18.0000i			1.56080i
$134$		0			0
$135$	−8.00000	+	4.00000i	−0.688530	+	0.344265i
$136$		0			0
$137$	9.00000	−	9.00000i	0.768922	−	0.768922i	−0.208995	−	0.977917i	$-0.567019\pi$
$137$	9.00000	−	9.00000i	0.768922	−	0.768922i	0.977917	+	0.208995i	$0.0670192\pi$
$138$		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	$0.431494\pi$
$140$		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
$147$	22.0000			1.81453
$148$		0			0
$149$	1.00000	+	1.00000i	0.0819232	+	0.0819232i	0.746881	−	0.664958i	$-0.231550\pi$
$149$	1.00000	+	1.00000i	0.0819232	+	0.0819232i	−0.664958	+	0.746881i	$0.731550\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$		0			0
$153$	−1.00000	−	1.00000i	−0.0808452	−	0.0808452i
$154$		0			0
$155$	4.00000	−	2.00000i	0.321288	−	0.160644i
$156$		0			0
$157$		−	20.0000i		−	1.59617i	−0.602542	−	0.798087i	$-0.705846\pi$
$157$		−	20.0000i		−	1.59617i	0.602542	−	0.798087i	$-0.294154\pi$
$158$		0			0
$159$	−16.0000			−1.26888
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$			14.0000i			1.09656i	0.836293	+	0.548282i	$0.184718\pi$
$163$			14.0000i			1.09656i	−0.836293	+	0.548282i	$0.815282\pi$
$164$		0			0
$165$	−6.00000	−	2.00000i	−0.467099	−	0.155700i
$166$		0			0
$167$	−3.00000	−	3.00000i	−0.232147	−	0.232147i	0.581441	−	0.813588i	$-0.302489\pi$
$167$	−3.00000	−	3.00000i	−0.232147	−	0.232147i	−0.813588	+	0.581441i	$0.802489\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	3.00000	+	3.00000i	0.229416	+	0.229416i
$172$		0			0
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		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	0.868829	−	0.495112i	$-0.164873\pi$
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	−0.495112	+	0.868829i	$0.664873\pi$
$180$		0			0
$181$	−3.00000	+	3.00000i	−0.222988	+	0.222988i	−0.809756	−	0.586767i	$-0.800400\pi$
$181$	−3.00000	+	3.00000i	−0.222988	+	0.222988i	0.586767	+	0.809756i	$0.300400\pi$
$182$		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
$187$			2.00000i			0.146254i
$188$		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
$195$	−8.00000	+	4.00000i	−0.572892	+	0.286446i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$			10.0000i			0.708881i	0.935079	+	0.354441i	$0.115329\pi$
$199$			10.0000i			0.708881i	−0.935079	+	0.354441i	$0.884671\pi$
$200$		0			0
$201$			8.00000i			0.564276i
$202$		0			0
$203$	42.0000			2.94782
$204$		0			0
$205$	−8.00000	+	4.00000i	−0.558744	+	0.279372i
$206$		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	0.385167	−	0.922847i	$-0.374144\pi$
$211$	19.0000	−	19.0000i	1.30801	−	1.30801i	0.922847	−	0.385167i	$-0.125856\pi$
$212$		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
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$		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	$0.735121\pi$
$230$		0			0
$231$	−12.0000			−0.789542
$232$		0			0
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	0.937526	−	0.347916i	$-0.113111\pi$
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	−0.347916	+	0.937526i	$0.613111\pi$
$234$		0			0
$235$	−21.0000	−	7.00000i	−1.36989	−	0.456630i
$236$		0			0
$237$			16.0000i			1.03931i
$238$		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
$243$			10.0000i			0.641500i
$244$		0			0
$245$	22.0000	−	11.0000i	1.40553	−	0.702764i
$246$		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	$-0.413352\pi$
$251$	−11.0000	−	11.0000i	−0.694314	−	0.694314i	−0.963178	+	0.268864i	$0.913352\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$		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	−0.457547	−	0.889185i	$-0.651272\pi$
$263$	7.00000	−	7.00000i	0.431638	−	0.431638i	0.889185	+	0.457547i	$0.151272\pi$
$264$		0			0
$265$	−16.0000	+	8.00000i	−0.982872	+	0.491436i
$266$		0			0
$267$		−	12.0000i		−	0.734388i
$268$		0			0
$269$	1.00000	−	1.00000i	0.0609711	−	0.0609711i	−0.675964	−	0.736935i	$-0.736272\pi$
$269$	1.00000	−	1.00000i	0.0609711	−	0.0609711i	0.736935	+	0.675964i	$0.236272\pi$
$270$		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
$275$	−7.00000	+	1.00000i	−0.422116	+	0.0603023i
$276$		0			0
$277$	−18.0000			−1.08152			−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000			−1.08152			−0.540758	+	0.841178i	$0.681862\pi$
$278$		0			0
$279$		−	2.00000i		−	0.119737i
$280$		0			0
$281$			16.0000i			0.954480i	0.878773	+	0.477240i	$0.158363\pi$
$281$			16.0000i			0.954480i	−0.878773	+	0.477240i	$0.841637\pi$
$282$		0			0
$283$	−12.0000			−0.713326			−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000			−0.713326			−0.356663	+	0.934233i	$0.616086\pi$
$284$		0			0
$285$	18.0000	+	6.00000i	1.06623	+	0.355409i
$286$		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
$293$		−	12.0000i		−	0.701047i	−0.936554	−	0.350524i	$-0.886004\pi$
$293$		−	12.0000i		−	0.701047i	0.936554	−	0.350524i	$-0.113996\pi$
$294$		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
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	10.0000	+	10.0000i	0.568880	+	0.568880i
$310$		0			0
$311$	16.0000			0.907277			0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000			0.907277			0.453638	+	0.891186i	$0.350126\pi$
$312$		0			0
$313$	13.0000	+	13.0000i	0.734803	+	0.734803i	0.971567	−	0.236764i	$-0.0760868\pi$
$313$	13.0000	+	13.0000i	0.734803	+	0.734803i	−0.236764	+	0.971567i	$0.576087\pi$
$314$		0			0
$315$	3.00000	−	9.00000i	0.169031	−	0.507093i
$316$		0			0
$317$		−	8.00000i		−	0.449325i	−0.974437	−	0.224662i	$-0.927872\pi$
$317$		−	8.00000i		−	0.449325i	0.974437	−	0.224662i	$-0.0721279\pi$
$318$		0			0
$319$	−14.0000			−0.783850
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$		−	6.00000i		−	0.333849i
$324$		0			0
$325$	−6.00000	+	8.00000i	−0.332820	+	0.443760i
$326$		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	0.985689	+	0.168576i	$0.0539168\pi$
$331$	21.0000	+	21.0000i	1.15426	+	1.15426i	0.168576	+	0.985689i	$0.446083\pi$
$332$		0			0
$333$	−6.00000			−0.328798
$334$		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
$347$		−	2.00000i		−	0.107366i	−0.998558	−	0.0536828i	$-0.982904\pi$
$347$		−	2.00000i		−	0.107366i	0.998558	−	0.0536828i	$-0.0170960\pi$
$348$		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	$0.286223\pi$
$350$		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
$357$	−12.0000			−0.635107
$358$		0			0
$359$		−	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
$362$		0			0
$363$	−18.0000			−0.944755
$364$		0			0
$365$	−3.00000	+	9.00000i	−0.157027	+	0.471082i
$366$		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
$373$		−	4.00000i		−	0.207112i	−0.994624	−	0.103556i	$-0.966978\pi$
$373$		−	4.00000i		−	0.207112i	0.994624	−	0.103556i	$-0.0330221\pi$
$374$		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	−0.207695	−	0.978194i	$-0.566596\pi$
$379$	15.0000	−	15.0000i	0.770498	−	0.770498i	0.978194	+	0.207695i	$0.0665963\pi$
$380$		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
$387$	4.00000			0.203331
$388$		0			0
$389$	−23.0000	−	23.0000i	−1.16615	−	1.16615i	−0.983105	−	0.183041i	$-0.941406\pi$
$389$	−23.0000	−	23.0000i	−1.16615	−	1.16615i	−0.183041	−	0.983105i	$-0.558594\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$		0			0
$393$	−14.0000	−	14.0000i	−0.706207	−	0.706207i
$394$		0			0
$395$	8.00000	+	16.0000i	0.402524	+	0.805047i
$396$		0			0
$397$			32.0000i			1.60603i	0.595956	+	0.803017i	$0.296773\pi$
$397$			32.0000i			1.60603i	−0.595956	+	0.803017i	$0.703227\pi$
$398$		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
$403$			4.00000i			0.199254i
$404$		0			0
$405$	11.0000	+	22.0000i	0.546594	+	1.09319i
$406$		0			0
$407$	6.00000	+	6.00000i	0.297409	+	0.297409i
$408$		0			0
$409$	38.0000			1.87898			0.939490	−	0.342578i	$-0.111300\pi$
$409$	38.0000			1.87898			0.939490	+	0.342578i	$0.111300\pi$
$410$		0			0
$411$	−18.0000	−	18.0000i	−0.887875	−	0.887875i
$412$		0			0
$413$	−18.0000			−0.885722
$414$		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	0.987586	−	0.157081i	$-0.0502085\pi$
$419$	17.0000	+	17.0000i	0.830504	+	0.830504i	−0.157081	+	0.987586i	$0.550208\pi$
$420$		0			0
$421$	5.00000	−	5.00000i	0.243685	−	0.243685i	−0.574688	−	0.818373i	$-0.694876\pi$
$421$	5.00000	−	5.00000i	0.243685	−	0.243685i	0.818373	+	0.574688i	$0.194876\pi$
$422$		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
$427$		−	6.00000i		−	0.290360i
$428$		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
$435$	14.0000	−	42.0000i	0.671249	−	2.01375i
$436$		0			0
$437$	6.00000			0.287019
$438$		0			0
$439$			26.0000i			1.24091i	0.784241	+	0.620456i	$0.213053\pi$
$439$			26.0000i			1.24091i	−0.784241	+	0.620456i	$0.786947\pi$
$440$		0			0
$441$		−	11.0000i		−	0.523810i
$442$		0			0
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$		0			0
$445$	−6.00000	−	12.0000i	−0.284427	−	0.568855i
$446$		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
$453$		−	16.0000i		−	0.751746i
$454$		0			0
$455$	−6.00000	+	18.0000i	−0.281284	+	0.843853i
$456$		0			0
$457$	−7.00000	+	7.00000i	−0.327446	+	0.327446i	−0.851615	−	0.524168i	$-0.824376\pi$
$457$	−7.00000	+	7.00000i	−0.327446	+	0.327446i	0.524168	+	0.851615i	$0.324376\pi$
$458$		0			0
$459$	4.00000	−	4.00000i	0.186704	−	0.186704i
$460$		0			0
$461$	21.0000	+	21.0000i	0.978068	+	0.978068i	0.999765	−	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	$-0.464648\pi$
$463$	−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
$467$	28.0000			1.29569			0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000			1.29569			0.647843	+	0.761774i	$0.275671\pi$
$468$		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
$475$	21.0000	−	3.00000i	0.963546	−	0.137649i
$476$		0			0
$477$			8.00000i			0.366295i
$478$		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
$483$		−	12.0000i		−	0.546019i
$484$		0			0
$485$	−11.0000	+	33.0000i	−0.499484	+	1.49845i
$486$		0			0
$487$	−15.0000	−	15.0000i	−0.679715	−	0.679715i	0.280221	−	0.959936i	$-0.409592\pi$
$487$	−15.0000	−	15.0000i	−0.679715	−	0.679715i	−0.959936	+	0.280221i	$0.909592\pi$
$488$		0			0
$489$	28.0000			1.26620
$490$		0			0
$491$	9.00000	+	9.00000i	0.406164	+	0.406164i	0.880399	−	0.474234i	$-0.157275\pi$
$491$	9.00000	+	9.00000i	0.406164	+	0.406164i	−0.474234	+	0.880399i	$0.657275\pi$
$492$		0			0
$493$	−14.0000			−0.630528
$494$		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	0.929568	+	0.368650i	$0.120180\pi$
$499$	29.0000	+	29.0000i	1.29822	+	1.29822i	0.368650	+	0.929568i	$0.379820\pi$
$500$		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	$0.617275\pi$
$503$	−29.0000	+	29.0000i	−1.29305	+	1.29305i	−0.932893	+	0.360153i	$0.882725\pi$
$504$		0			0
$505$	−15.0000	−	5.00000i	−0.667491	−	0.222497i
$506$		0			0
$507$			18.0000i			0.799408i
$508$		0			0
$509$	17.0000	−	17.0000i	0.753512	−	0.753512i	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	17.0000	−	17.0000i	0.753512	−	0.753512i	0.975133	+	0.221621i	$0.0711348\pi$
$510$		0			0
$511$			18.0000i			0.796273i
$512$		0			0
$513$	−12.0000	+	12.0000i	−0.529813	+	0.529813i
$514$		0			0
$515$	15.0000	+	5.00000i	0.660979	+	0.220326i
$516$		0			0
$517$	14.0000			0.615719
$518$		0			0
$519$		−	12.0000i		−	0.526742i
$520$		0			0
$521$		−	16.0000i		−	0.700973i	−0.936568	−	0.350486i	$-0.886016\pi$
$521$		−	16.0000i		−	0.700973i	0.936568	−	0.350486i	$-0.113984\pi$
$522$		0			0
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$		0			0
$525$	−6.00000	−	42.0000i	−0.261861	−	1.83303i
$526$		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
$533$		−	8.00000i		−	0.346518i
$534$		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	0.306856	−	0.951756i	$-0.400723\pi$
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	−0.951756	+	0.306856i	$0.900723\pi$
$542$		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
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		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
$555$	−24.0000	+	12.0000i	−1.01874	+	0.509372i
$556$		0			0
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$		−	18.0000i		−	0.758610i	−0.925272	−	0.379305i	$-0.876163\pi$
$563$		−	18.0000i		−	0.758610i	0.925272	−	0.379305i	$-0.123837\pi$
$564$		0			0
$565$	−39.0000	−	13.0000i	−1.64074	−	0.546914i
$566$		0			0
$567$	33.0000	+	33.0000i	1.38587	+	1.38587i
$568$		0			0
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	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	$0.0150740\pi$
$571$	25.0000	+	25.0000i	1.04622	+	1.04622i	0.0473385	+	0.998879i	$0.484926\pi$
$572$		0			0
$573$	36.0000			1.50392
$574$		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
$587$		−	2.00000i		−	0.0825488i	−0.999148	−	0.0412744i	$-0.986858\pi$
$587$		−	2.00000i		−	0.0825488i	0.999148	−	0.0412744i	$-0.0131418\pi$
$588$		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
$595$	−12.0000	+	6.00000i	−0.491952	+	0.245976i
$596$		0			0
$597$	20.0000			0.818546
$598$		0			0
$599$		−	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	$0.894189\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$		0			0
$605$	−18.0000	+	9.00000i	−0.731804	+	0.365902i
$606$		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
$613$			8.00000i			0.323117i	0.986863	+	0.161558i	$0.0516520\pi$
$613$			8.00000i			0.323117i	−0.986863	+	0.161558i	$0.948348\pi$
$614$		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	$-0.497936\pi$
$617$	25.0000	−	25.0000i	1.00646	−	1.00646i	0.999979	−	0.00648312i	$-0.00206366\pi$
$618$		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	$0.186248\pi$
$620$		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
$627$	−12.0000			−0.479234
$628$		0			0
$629$	6.00000	+	6.00000i	0.239236	+	0.239236i
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	−38.0000	−	38.0000i	−1.51036	−	1.51036i
$634$		0			0
$635$	−21.0000	−	7.00000i	−0.833360	−	0.277787i
$636$		0			0
$637$			22.0000i			0.871672i
$638$		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
$643$		−	26.0000i		−	1.02534i	−0.858586	−	0.512670i	$-0.828656\pi$
$643$		−	26.0000i		−	1.02534i	0.858586	−	0.512670i	$-0.171344\pi$
$644$		0			0
$645$	16.0000	−	8.00000i	0.629999	−	0.315000i
$646$		0			0
$647$	−15.0000	−	15.0000i	−0.589711	−	0.589711i	0.347842	−	0.937553i	$-0.386914\pi$
$647$	−15.0000	−	15.0000i	−0.589711	−	0.589711i	−0.937553	+	0.347842i	$0.886914\pi$
$648$		0			0
$649$	6.00000			0.235521
$650$		0			0
$651$	−12.0000	−	12.0000i	−0.470317	−	0.470317i
$652$		0			0
$653$	2.00000			0.0782660			0.0391330	−	0.999234i	$-0.487540\pi$
$653$	2.00000			0.0782660			0.0391330	+	0.999234i	$0.487540\pi$
$654$		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	0.459618	−	0.888117i	$-0.347986\pi$
$659$	−11.0000	−	11.0000i	−0.428499	−	0.428499i	−0.888117	+	0.459618i	$0.847986\pi$
$660$		0			0
$661$	25.0000	−	25.0000i	0.972387	−	0.972387i	−0.0272416	−	0.999629i	$-0.508672\pi$
$661$	25.0000	−	25.0000i	0.972387	−	0.972387i	0.999629	+	0.0272416i	$0.00867234\pi$
$662$		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
$667$		−	14.0000i		−	0.542082i
$668$		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
$675$	16.0000	+	12.0000i	0.615840	+	0.461880i
$676$		0			0
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$		0			0
$679$			66.0000i			2.53285i
$680$		0			0
$681$			24.0000i			0.919682i
$682$		0			0
$683$	4.00000			0.153056			0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$		0			0
$685$	−27.0000	−	9.00000i	−1.03162	−	0.343872i
$686$		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	$-0.941082\pi$
$691$	−21.0000	+	21.0000i	−0.798878	+	0.798878i	0.184041	+	0.982919i	$0.441082\pi$
$692$		0			0
$693$			6.00000i			0.227921i
$694$		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	0.908622	−	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
$704$		0			0
$705$	−14.0000	+	42.0000i	−0.527271	+	1.58181i
$706$		0			0
$707$	−30.0000			−1.12827
$708$		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
$711$	8.00000			0.300023
$712$		0			0
$713$	−2.00000	−	2.00000i	−0.0749006	−	0.0749006i
$714$		0			0
$715$	2.00000	−	6.00000i	0.0747958	−	0.224387i
$716$		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
$723$			28.0000i			1.04133i
$724$		0			0
$725$	−7.00000	−	49.0000i	−0.259973	−	1.81981i
$726$		0			0
$727$	−7.00000	−	7.00000i	−0.259616	−	0.259616i	0.565282	−	0.824898i	$-0.308767\pi$
$727$	−7.00000	−	7.00000i	−0.259616	−	0.259616i	−0.824898	+	0.565282i	$0.808767\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−4.00000	−	4.00000i	−0.147945	−	0.147945i
$732$		0			0
$733$	30.0000			1.10808			0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000			1.10808			0.554038	+	0.832492i	$0.313086\pi$
$734$		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	0.978543	−	0.206045i	$-0.0660593\pi$
$739$	21.0000	+	21.0000i	0.772497	+	0.772497i	−0.206045	+	0.978543i	$0.566059\pi$
$740$		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	$-0.452606\pi$
$743$	31.0000	−	31.0000i	1.13728	−	1.13728i	0.988936	−	0.148344i	$-0.0473942\pi$
$744$		0			0
$745$	1.00000	−	3.00000i	0.0366372	−	0.109911i
$746$		0			0
$747$			2.00000i			0.0731762i
$748$		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
$755$	−8.00000	−	16.0000i	−0.291150	−	0.582300i
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$		0			0
$759$			4.00000i			0.145191i
$760$		0			0
$761$			40.0000i			1.45000i	0.688749	+	0.724999i	$0.258160\pi$
$761$			40.0000i			1.45000i	−0.688749	+	0.724999i	$0.741840\pi$
$762$		0			0
$763$	−30.0000			−1.08607
$764$		0			0
$765$	−1.00000	+	3.00000i	−0.0361551	+	0.108465i
$766$		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
$773$			48.0000i			1.72644i	0.504828	+	0.863220i	$0.331556\pi$
$773$			48.0000i			1.72644i	−0.504828	+	0.863220i	$0.668444\pi$
$774$		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
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$		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
$795$	16.0000	+	32.0000i	0.567462	+	1.13492i
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$	14.0000			0.495284
$800$		0			0
$801$	−6.00000			−0.212000
$802$		0			0
$803$		−	6.00000i		−	0.211735i
$804$		0			0
$805$	−6.00000	−	12.0000i	−0.211472	−	0.422944i
$806$		0			0
$807$	−2.00000	−	2.00000i	−0.0704033	−	0.0704033i
$808$		0			0
$809$	26.0000			0.914111			0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000			0.914111			0.457056	+	0.889438i	$0.348904\pi$
$810$		0			0
$811$	9.00000	+	9.00000i	0.316033	+	0.316033i	0.847241	−	0.531208i	$-0.178262\pi$
$811$	9.00000	+	9.00000i	0.316033	+	0.316033i	−0.531208	+	0.847241i	$0.678262\pi$
$812$		0			0
$813$	−60.0000			−2.10429
$814$		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	−0.918628	−	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	−0.971018	−	0.239004i	$-0.923179\pi$
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	0.239004	+	0.971018i	$0.423179\pi$
$824$		0			0
$825$	2.00000	+	14.0000i	0.0696311	+	0.487417i
$826$		0			0
$827$			54.0000i			1.87776i	0.344239	+	0.938882i	$0.388137\pi$
$827$			54.0000i			1.87776i	−0.344239	+	0.938882i	$0.611863\pi$
$828$		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	$0.480755\pi$
$830$		0			0
$831$			36.0000i			1.24883i
$832$		0			0
$833$	−11.0000	+	11.0000i	−0.381127	+	0.381127i
$834$		0			0
$835$	−3.00000	+	9.00000i	−0.103819	+	0.311458i
$836$		0			0
$837$	8.00000			0.276520
$838$		0			0
$839$			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
$842$		0			0
$843$	32.0000			1.10214
$844$		0			0
$845$	9.00000	+	18.0000i	0.309609	+	0.619219i
$846$		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
$853$			16.0000i			0.547830i	0.961754	+	0.273915i	$0.0883186\pi$
$853$			16.0000i			0.547830i	−0.961754	+	0.273915i	$0.911681\pi$
$854$		0			0
$855$	3.00000	−	9.00000i	0.102598	−	0.307794i
$856$		0			0
$857$	−27.0000	+	27.0000i	−0.922302	+	0.922302i	−0.997192	−	0.0748894i	$-0.976140\pi$
$857$	−27.0000	+	27.0000i	−0.922302	+	0.922302i	0.0748894	+	0.997192i	$0.476140\pi$
$858$		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	$0.0984237\pi$
$860$		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
$867$	−30.0000			−1.01885
$868$		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
$875$	−27.0000	−	39.0000i	−0.912767	−	1.31844i
$876$		0			0
$877$		−	4.00000i		−	0.135070i	−0.997717	−	0.0675352i	$-0.978487\pi$
$877$		−	4.00000i		−	0.135070i	0.997717	−	0.0675352i	$-0.0215135\pi$
$878$		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
$883$			6.00000i			0.201916i	0.994891	+	0.100958i	$0.0321908\pi$
$883$			6.00000i			0.201916i	−0.994891	+	0.100958i	$0.967809\pi$
$884$		0			0
$885$	−6.00000	+	18.0000i	−0.201688	+	0.605063i
$886$		0			0
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	0.206238	−	0.978502i	$-0.433878\pi$
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	−0.978502	+	0.206238i	$0.933878\pi$
$888$		0			0
$889$	−42.0000			−1.40863
$890$		0			0
$891$	−11.0000	−	11.0000i	−0.368514	−	0.368514i
$892$		0			0
$893$	−42.0000			−1.40548
$894$		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
$907$		−	50.0000i		−	1.66022i	−0.557598	−	0.830111i	$-0.688277\pi$
$907$		−	50.0000i		−	1.66022i	0.557598	−	0.830111i	$-0.311723\pi$
$908$		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
$915$	−6.00000	−	2.00000i	−0.198354	−	0.0661180i
$916$		0			0
$917$	−42.0000			−1.38696
$918$		0			0
$919$		−	46.0000i		−	1.51740i	−0.651440	−	0.758700i	$-0.725835\pi$
$919$		−	46.0000i		−	1.51740i	0.651440	−	0.758700i	$-0.274165\pi$
$920$		0			0
$921$		−	8.00000i		−	0.263609i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−18.0000	+	24.0000i	−0.591836	+	0.789115i
$926$		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
$933$		−	32.0000i		−	1.04763i
$934$		0			0
$935$	4.00000	−	2.00000i	0.130814	−	0.0654070i
$936$		0			0
$937$	−3.00000	+	3.00000i	−0.0980057	+	0.0980057i	−0.754410	−	0.656404i	$-0.772077\pi$
$937$	−3.00000	+	3.00000i	−0.0980057	+	0.0980057i	0.656404	+	0.754410i	$0.272077\pi$
$938$		0			0
$939$	26.0000	−	26.0000i	0.848478	−	0.848478i
$940$		0			0
$941$	1.00000	+	1.00000i	0.0325991	+	0.0325991i	0.723218	−	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
$944$		0			0
$945$	36.0000	+	12.0000i	1.17108	+	0.390360i
$946$		0			0
$947$	−28.0000			−0.909878			−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000			−0.909878			−0.454939	+	0.890523i	$0.650339\pi$
$948$		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	$-0.998664\pi$
$953$	−31.0000	−	31.0000i	−1.00419	−	1.00419i	−0.00419731	−	0.999991i	$-0.501336\pi$
$954$		0			0
$955$	36.0000	−	18.0000i	1.16493	−	0.582466i
$956$		0			0
$957$			28.0000i			0.905111i
$958$		0			0
$959$	−54.0000			−1.74375
$960$		0			0
$961$	27.0000			0.870968
$962$		0			0
$963$		−	6.00000i		−	0.193347i
$964$		0			0
$965$	45.0000	+	15.0000i	1.44860	+	0.482867i
$966$		0			0
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.998000	+	0.0632081i	$0.0201332\pi$
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.0632081	+	0.998000i	$0.479867\pi$
$968$		0			0
$969$	−12.0000			−0.385496
$970$		0			0
$971$	−31.0000	−	31.0000i	−0.994837	−	0.994837i	0.00514940	−	0.999987i	$-0.498361\pi$
$971$	−31.0000	−	31.0000i	−0.994837	−	0.994837i	−0.999987	+	0.00514940i	$0.998361\pi$
$972$		0			0
$973$	54.0000			1.73116
$974$		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	−0.782334	−	0.622859i	$-0.785971\pi$
$983$	−5.00000	+	5.00000i	−0.159475	+	0.159475i	0.622859	+	0.782334i	$0.285971\pi$
$984$		0			0
$985$	6.00000	+	12.0000i	0.191176	+	0.382352i
$986$		0			0
$987$			84.0000i			2.67375i
$988$		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
$995$	20.0000	−	10.0000i	0.634043	−	0.317021i
$996$		0			0
$997$	−22.0000			−0.696747			−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000			−0.696747			−0.348373	+	0.937356i	$0.613266\pi$
$998$		0			0
$999$		−	24.0000i		−	0.759326i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.a.43.1	✓	2	80.3	even	4
80.2.j.a.67.1	yes	2	8.5	even	2
80.2.s.a.3.1	yes	2	40.13	odd	4
80.2.s.a.27.1	yes	2	16.3	odd	4
320.2.j.a.47.1		2	8.3	odd	2
320.2.j.a.143.1		2	80.13	odd	4
320.2.s.a.207.1		2	16.13	even	4
320.2.s.a.303.1		2	40.3	even	4
400.2.j.a.43.1		2	80.67	even	4
400.2.j.a.307.1		2	40.29	even	2
400.2.s.a.107.1		2	80.19	odd	4
400.2.s.a.243.1		2	40.37	odd	4
640.2.j.a.543.1		2	80.43	even	4	inner
640.2.j.a.607.1		2	1.1	even	1	trivial
640.2.j.b.543.1		2	80.53	odd	4
640.2.j.b.607.1		2	4.3	odd	2
640.2.s.a.223.1		2	20.3	even	4
640.2.s.a.287.1		2	16.5	even	4
640.2.s.b.223.1		2	5.3	odd	4
640.2.s.b.287.1		2	16.11	odd	4
720.2.z.d.163.1		2	120.53	even	4
720.2.z.d.667.1		2	48.35	even	4
720.2.bd.a.307.1		2	24.5	odd	2
720.2.bd.a.523.1		2	240.83	odd	4
1600.2.j.a.143.1		2	80.77	odd	4
1600.2.j.a.1007.1		2	40.19	odd	2
1600.2.s.a.207.1		2	80.29	even	4
1600.2.s.a.943.1		2	40.27	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	640.2.j.a.607.1

Level	$640$
Weight	$2$
Character	640.607
Analytic conductor	$5.110$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$