LMFDB - Embedded newform 1040.2.bg.f.593.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(577,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 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("1040.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.bg (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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1040.593
Dual form			1040.2.bg.f.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{3} +(1.00000 - 2.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{9} +(-1.00000 + 1.00000i) q^{11} +(-3.00000 + 2.00000i) q^{13} +(3.00000 - 1.00000i) q^{15} +(5.00000 + 5.00000i) q^{17} +(3.00000 - 3.00000i) q^{19} +(2.00000 - 2.00000i) q^{21} +(5.00000 - 5.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} -4.00000i q^{29} +(-1.00000 - 1.00000i) q^{31} -2.00000 q^{33} +(-4.00000 - 2.00000i) q^{35} -8.00000i q^{37} +(-5.00000 - 1.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} +(-5.00000 + 5.00000i) q^{43} +(-2.00000 - 1.00000i) q^{45} -2.00000i q^{47} +3.00000 q^{49} +10.0000i q^{51} +(-1.00000 - 1.00000i) q^{53} +(1.00000 + 3.00000i) q^{55} +6.00000 q^{57} +(-3.00000 - 3.00000i) q^{59} +2.00000 q^{61} -2.00000 q^{63} +(1.00000 + 8.00000i) q^{65} +12.0000 q^{67} +10.0000 q^{69} +(-1.00000 - 1.00000i) q^{71} -6.00000 q^{73} +(1.00000 - 7.00000i) q^{75} +(2.00000 + 2.00000i) q^{77} +14.0000i q^{79} +5.00000 q^{81} +6.00000i q^{83} +(15.0000 - 5.00000i) q^{85} +(4.00000 - 4.00000i) q^{87} +(-7.00000 - 7.00000i) q^{89} +(4.00000 + 6.00000i) q^{91} -2.00000i q^{93} +(-3.00000 - 9.00000i) q^{95} -2.00000 q^{97} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 2 q^{5} - 2 q^{11} - 6 q^{13} + 6 q^{15} + 10 q^{17} + 6 q^{19} + 4 q^{21} + 10 q^{23} - 6 q^{25} + 8 q^{27} - 2 q^{31} - 4 q^{33} - 8 q^{35} - 10 q^{39} + 2 q^{41} - 10 q^{43} - 4 q^{45}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^5 - 2 * q^11 - 6 * q^13 + 6 * q^15 + 10 * q^17 + 6 * q^19 + 4 * q^21 + 10 * q^23 - 6 * q^25 + 8 * q^27 - 2 * q^31 - 4 * q^33 - 8 * q^35 - 10 * q^39 + 2 * q^41 - 10 * q^43 - 4 * q^45 + 6 * q^49 - 2 * q^53 + 2 * q^55 + 12 * q^57 - 6 * q^59 + 4 * q^61 - 4 * q^63 + 2 * q^65 + 24 * q^67 + 20 * q^69 - 2 * q^71 - 12 * q^73 + 2 * q^75 + 4 * q^77 + 10 * q^81 + 30 * q^85 + 8 * q^87 - 14 * q^89 + 8 * q^91 - 6 * q^95 - 4 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	0.934172	−	0.356822i	$-0.116140\pi$
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	−0.356822	+	0.934172i	$0.616140\pi$
$4$		0			0
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$		0			0
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		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
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$14$		0			0
$15$	3.00000	−	1.00000i	0.774597	−	0.258199i
$16$		0			0
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$		0			0
$21$	2.00000	−	2.00000i	0.436436	−	0.436436i
$22$		0			0
$23$	5.00000	−	5.00000i	1.04257	−	1.04257i	0.0435195	−	0.999053i	$-0.486143\pi$
$23$	5.00000	−	5.00000i	1.04257	−	1.04257i	0.999053	−	0.0435195i	$-0.0138571\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$		0			0
$29$		−	4.00000i		−	0.742781i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$		−	4.00000i		−	0.742781i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$	−1.00000	−	1.00000i	−0.179605	−	0.179605i	0.611578	−	0.791184i	$-0.290535\pi$
$31$	−1.00000	−	1.00000i	−0.179605	−	0.179605i	−0.791184	+	0.611578i	$0.790535\pi$
$32$		0			0
$33$	−2.00000			−0.348155
$34$		0			0
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		0			0
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$		0			0
$39$	−5.00000	−	1.00000i	−0.800641	−	0.160128i
$40$		0			0
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	−0.976772	−	0.214280i	$-0.931260\pi$
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	0.214280	+	0.976772i	$0.431260\pi$
$44$		0			0
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$		0			0
$47$		−	2.00000i		−	0.291730i	−0.989305	−	0.145865i	$-0.953403\pi$
$47$		−	2.00000i		−	0.291730i	0.989305	−	0.145865i	$-0.0465965\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$			10.0000i			1.40028i
$52$		0			0
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	0.635083	−	0.772444i	$-0.280966\pi$
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	−0.772444	+	0.635083i	$0.780966\pi$
$54$		0			0
$55$	1.00000	+	3.00000i	0.134840	+	0.404520i
$56$		0			0
$57$	6.00000			0.794719
$58$		0			0
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	0.484323	−	0.874889i	$-0.339066\pi$
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	−0.874889	+	0.484323i	$0.839066\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$	−2.00000			−0.251976
$64$		0			0
$65$	1.00000	+	8.00000i	0.124035	+	0.992278i
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$		0			0
$69$	10.0000			1.20386
$70$		0			0
$71$	−1.00000	−	1.00000i	−0.118678	−	0.118678i	0.645273	−	0.763952i	$-0.276743\pi$
$71$	−1.00000	−	1.00000i	−0.118678	−	0.118678i	−0.763952	+	0.645273i	$0.776743\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$		0			0
$75$	1.00000	−	7.00000i	0.115470	−	0.808290i
$76$		0			0
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$			14.0000i			1.57512i	0.616236	+	0.787562i	$0.288657\pi$
$79$			14.0000i			1.57512i	−0.616236	+	0.787562i	$0.711343\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	15.0000	−	5.00000i	1.62698	−	0.542326i
$86$		0			0
$87$	4.00000	−	4.00000i	0.428845	−	0.428845i
$88$		0			0
$89$	−7.00000	−	7.00000i	−0.741999	−	0.741999i	0.230964	−	0.972962i	$-0.425812\pi$
$89$	−7.00000	−	7.00000i	−0.741999	−	0.741999i	−0.972962	+	0.230964i	$0.925812\pi$
$90$		0			0
$91$	4.00000	+	6.00000i	0.419314	+	0.628971i
$92$		0			0
$93$		−	2.00000i		−	0.207390i
$94$		0			0
$95$	−3.00000	−	9.00000i	−0.307794	−	0.923381i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	1.00000	+	1.00000i	0.100504	+	0.100504i
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		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
$105$	−2.00000	−	6.00000i	−0.195180	−	0.585540i
$106$		0			0
$107$	−13.0000	+	13.0000i	−1.25676	+	1.25676i	−0.304125	+	0.952632i	$0.598364\pi$
$107$	−13.0000	+	13.0000i	−1.25676	+	1.25676i	−0.952632	+	0.304125i	$0.901636\pi$
$108$		0			0
$109$	−13.0000	+	13.0000i	−1.24517	+	1.24517i	−0.287348	+	0.957826i	$0.592774\pi$
$109$	−13.0000	+	13.0000i	−1.24517	+	1.24517i	−0.957826	+	0.287348i	$0.907226\pi$
$110$		0			0
$111$	8.00000	−	8.00000i	0.759326	−	0.759326i
$112$		0			0
$113$	9.00000	+	9.00000i	0.846649	+	0.846649i	0.989713	−	0.143065i	$-0.0456957\pi$
$113$	9.00000	+	9.00000i	0.846649	+	0.846649i	−0.143065	+	0.989713i	$0.545696\pi$
$114$		0			0
$115$	−5.00000	−	15.0000i	−0.466252	−	1.39876i
$116$		0			0
$117$	2.00000	+	3.00000i	0.184900	+	0.277350i
$118$		0			0
$119$	10.0000	−	10.0000i	0.916698	−	0.916698i
$120$		0			0
$121$			9.00000i			0.818182i
$122$		0			0
$123$			2.00000i			0.180334i
$124$		0			0
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$		0			0
$127$	15.0000	+	15.0000i	1.33103	+	1.33103i	0.904445	+	0.426589i	$0.140285\pi$
$127$	15.0000	+	15.0000i	1.33103	+	1.33103i	0.426589	+	0.904445i	$0.359715\pi$
$128$		0			0
$129$	−10.0000			−0.880451
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$	−6.00000	−	6.00000i	−0.520266	−	0.520266i
$134$		0			0
$135$	−4.00000	−	12.0000i	−0.344265	−	1.03280i
$136$		0			0
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$		0			0
$139$			14.0000i			1.18746i	0.804663	+	0.593732i	$0.202346\pi$
$139$			14.0000i			1.18746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$		0			0
$141$	2.00000	−	2.00000i	0.168430	−	0.168430i
$142$		0			0
$143$	1.00000	−	5.00000i	0.0836242	−	0.418121i
$144$		0			0
$145$	−8.00000	−	4.00000i	−0.664364	−	0.332182i
$146$		0			0
$147$	3.00000	+	3.00000i	0.247436	+	0.247436i
$148$		0			0
$149$	−13.0000	+	13.0000i	−1.06500	+	1.06500i	−0.0672664	+	0.997735i	$0.521428\pi$
$149$	−13.0000	+	13.0000i	−1.06500	+	1.06500i	−0.997735	+	0.0672664i	$0.978572\pi$
$150$		0			0
$151$	9.00000	−	9.00000i	0.732410	−	0.732410i	−0.238687	−	0.971097i	$-0.576717\pi$
$151$	9.00000	−	9.00000i	0.732410	−	0.732410i	0.971097	+	0.238687i	$0.0767170\pi$
$152$		0			0
$153$	5.00000	−	5.00000i	0.404226	−	0.404226i
$154$		0			0
$155$	−3.00000	+	1.00000i	−0.240966	+	0.0803219i
$156$		0			0
$157$	3.00000	−	3.00000i	0.239426	−	0.239426i	−0.577186	−	0.816612i	$-0.695849\pi$
$157$	3.00000	−	3.00000i	0.239426	−	0.239426i	0.816612	+	0.577186i	$0.195849\pi$
$158$		0			0
$159$		−	2.00000i		−	0.158610i
$160$		0			0
$161$	−10.0000	−	10.0000i	−0.788110	−	0.788110i
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$		0			0
$165$	−2.00000	+	4.00000i	−0.155700	+	0.311400i
$166$		0			0
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$		0			0
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$		0			0
$171$	−3.00000	−	3.00000i	−0.229416	−	0.229416i
$172$		0			0
$173$	15.0000	−	15.0000i	1.14043	−	1.14043i	0.152057	−	0.988372i	$-0.451410\pi$
$173$	15.0000	−	15.0000i	1.14043	−	1.14043i	0.988372	−	0.152057i	$-0.0485898\pi$
$174$		0			0
$175$	−8.00000	+	6.00000i	−0.604743	+	0.453557i
$176$		0			0
$177$		−	6.00000i		−	0.450988i
$178$		0			0
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$		0			0
$181$			20.0000i			1.48659i	0.668965	+	0.743294i	$0.266738\pi$
$181$			20.0000i			1.48659i	−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	2.00000	+	2.00000i	0.147844	+	0.147844i
$184$		0			0
$185$	−16.0000	−	8.00000i	−1.17634	−	0.588172i
$186$		0			0
$187$	−10.0000			−0.731272
$188$		0			0
$189$	−8.00000	−	8.00000i	−0.581914	−	0.581914i
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$		0			0
$195$	−7.00000	+	9.00000i	−0.501280	+	0.644503i
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$	12.0000	+	12.0000i	0.846415	+	0.846415i
$202$		0			0
$203$	−8.00000			−0.561490
$204$		0			0
$205$	3.00000	−	1.00000i	0.209529	−	0.0698430i
$206$		0			0
$207$	−5.00000	−	5.00000i	−0.347524	−	0.347524i
$208$		0			0
$209$			6.00000i			0.415029i
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$		0			0
$213$		−	2.00000i		−	0.137038i
$214$		0			0
$215$	5.00000	+	15.0000i	0.340997	+	1.02299i
$216$		0			0
$217$	−2.00000	+	2.00000i	−0.135769	+	0.135769i
$218$		0			0
$219$	−6.00000	−	6.00000i	−0.405442	−	0.405442i
$220$		0			0
$221$	−25.0000	−	5.00000i	−1.68168	−	0.336336i
$222$		0			0
$223$			6.00000i			0.401790i	0.979613	+	0.200895i	$0.0643850\pi$
$223$			6.00000i			0.401790i	−0.979613	+	0.200895i	$0.935615\pi$
$224$		0			0
$225$	−4.00000	+	3.00000i	−0.266667	+	0.200000i
$226$		0			0
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$		0			0
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	0.799248	−	0.601002i	$-0.205232\pi$
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	−0.601002	+	0.799248i	$0.705232\pi$
$230$		0			0
$231$			4.00000i			0.263181i
$232$		0			0
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	0.851658	+	0.524097i	$0.175597\pi$
$234$		0			0
$235$	−4.00000	−	2.00000i	−0.260931	−	0.130466i
$236$		0			0
$237$	−14.0000	+	14.0000i	−0.909398	+	0.909398i
$238$		0			0
$239$	−7.00000	+	7.00000i	−0.452792	+	0.452792i	−0.896280	−	0.443488i	$-0.853741\pi$
$239$	−7.00000	+	7.00000i	−0.452792	+	0.452792i	0.443488	+	0.896280i	$0.353741\pi$
$240$		0			0
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	−0.674165	−	0.738581i	$-0.735496\pi$
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	0.738581	+	0.674165i	$0.235496\pi$
$242$		0			0
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$		0			0
$245$	3.00000	−	6.00000i	0.191663	−	0.383326i
$246$		0			0
$247$	−3.00000	+	15.0000i	−0.190885	+	0.954427i
$248$		0			0
$249$	−6.00000	+	6.00000i	−0.380235	+	0.380235i
$250$		0			0
$251$			30.0000i			1.89358i	0.321847	+	0.946792i	$0.395696\pi$
$251$			30.0000i			1.89358i	−0.321847	+	0.946792i	$0.604304\pi$
$252$		0			0
$253$			10.0000i			0.628695i
$254$		0			0
$255$	20.0000	+	10.0000i	1.25245	+	0.626224i
$256$		0			0
$257$	−15.0000	−	15.0000i	−0.935674	−	0.935674i	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	−15.0000	−	15.0000i	−0.935674	−	0.935674i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$		0			0
$259$	−16.0000			−0.994192
$260$		0			0
$261$	−4.00000			−0.247594
$262$		0			0
$263$	−9.00000	−	9.00000i	−0.554964	−	0.554964i	0.372906	−	0.927869i	$-0.378362\pi$
$263$	−9.00000	−	9.00000i	−0.554964	−	0.554964i	−0.927869	+	0.372906i	$0.878362\pi$
$264$		0			0
$265$	−3.00000	+	1.00000i	−0.184289	+	0.0614295i
$266$		0			0
$267$		−	14.0000i		−	0.856786i
$268$		0			0
$269$			16.0000i			0.975537i	0.872973	+	0.487769i	$0.162189\pi$
$269$			16.0000i			0.975537i	−0.872973	+	0.487769i	$0.837811\pi$
$270$		0			0
$271$	9.00000	−	9.00000i	0.546711	−	0.546711i	−0.378777	−	0.925488i	$-0.623655\pi$
$271$	9.00000	−	9.00000i	0.546711	−	0.546711i	0.925488	+	0.378777i	$0.123655\pi$
$272$		0			0
$273$	−2.00000	+	10.0000i	−0.121046	+	0.605228i
$274$		0			0
$275$	7.00000	+	1.00000i	0.422116	+	0.0603023i
$276$		0			0
$277$	−5.00000	−	5.00000i	−0.300421	−	0.300421i	0.540758	−	0.841178i	$-0.318138\pi$
$277$	−5.00000	−	5.00000i	−0.300421	−	0.300421i	−0.841178	+	0.540758i	$0.818138\pi$
$278$		0			0
$279$	−1.00000	+	1.00000i	−0.0598684	+	0.0598684i
$280$		0			0
$281$	21.0000	−	21.0000i	1.25275	−	1.25275i	0.298275	−	0.954480i	$-0.403589\pi$
$281$	21.0000	−	21.0000i	1.25275	−	1.25275i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$		0			0
$283$	15.0000	−	15.0000i	0.891657	−	0.891657i	−0.103022	−	0.994679i	$-0.532851\pi$
$283$	15.0000	−	15.0000i	0.891657	−	0.891657i	0.994679	+	0.103022i	$0.0328511\pi$
$284$		0			0
$285$	6.00000	−	12.0000i	0.355409	−	0.710819i
$286$		0			0
$287$	2.00000	−	2.00000i	0.118056	−	0.118056i
$288$		0			0
$289$			33.0000i			1.94118i
$290$		0			0
$291$	−2.00000	−	2.00000i	−0.117242	−	0.117242i
$292$		0			0
$293$	−26.0000			−1.51894			−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000			−1.51894			−0.759468	+	0.650545i	$0.774541\pi$
$294$		0			0
$295$	−9.00000	+	3.00000i	−0.524000	+	0.174667i
$296$		0			0
$297$			8.00000i			0.464207i
$298$		0			0
$299$	−5.00000	+	25.0000i	−0.289157	+	1.44579i
$300$		0			0
$301$	10.0000	+	10.0000i	0.576390	+	0.576390i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.00000	−	4.00000i	0.114520	−	0.229039i
$306$		0			0
$307$		−	2.00000i		−	0.114146i	−0.998370	−	0.0570730i	$-0.981823\pi$
$307$		−	2.00000i		−	0.114146i	0.998370	−	0.0570730i	$-0.0181768\pi$
$308$		0			0
$309$	10.0000			0.568880
$310$		0			0
$311$		−	10.0000i		−	0.567048i	−0.958965	−	0.283524i	$-0.908496\pi$
$311$		−	10.0000i		−	0.567048i	0.958965	−	0.283524i	$-0.0915036\pi$
$312$		0			0
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$		0			0
$315$	−2.00000	+	4.00000i	−0.112687	+	0.225374i
$316$		0			0
$317$	−2.00000			−0.112331			−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000			−0.112331			−0.0561656	+	0.998421i	$0.517887\pi$
$318$		0			0
$319$	4.00000	+	4.00000i	0.223957	+	0.223957i
$320$		0			0
$321$	−26.0000			−1.45118
$322$		0			0
$323$	30.0000			1.66924
$324$		0			0
$325$	17.0000	+	6.00000i	0.942990	+	0.332820i
$326$		0			0
$327$	−26.0000			−1.43780
$328$		0			0
$329$	−4.00000			−0.220527
$330$		0			0
$331$	9.00000	+	9.00000i	0.494685	+	0.494685i	0.909779	−	0.415094i	$-0.136251\pi$
$331$	9.00000	+	9.00000i	0.494685	+	0.494685i	−0.415094	+	0.909779i	$0.636251\pi$
$332$		0			0
$333$	−8.00000			−0.438397
$334$		0			0
$335$	12.0000	−	24.0000i	0.655630	−	1.31126i
$336$		0			0
$337$	5.00000	+	5.00000i	0.272367	+	0.272367i	0.830053	−	0.557685i	$-0.188310\pi$
$337$	5.00000	+	5.00000i	0.272367	+	0.272367i	−0.557685	+	0.830053i	$0.688310\pi$
$338$		0			0
$339$			18.0000i			0.977626i
$340$		0			0
$341$	2.00000			0.108306
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$		0			0
$345$	10.0000	−	20.0000i	0.538382	−	1.07676i
$346$		0			0
$347$	7.00000	−	7.00000i	0.375780	−	0.375780i	−0.493797	−	0.869577i	$-0.664392\pi$
$347$	7.00000	−	7.00000i	0.375780	−	0.375780i	0.869577	+	0.493797i	$0.164392\pi$
$348$		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
$351$	−4.00000	+	20.0000i	−0.213504	+	1.06752i
$352$		0			0
$353$		−	16.0000i		−	0.851594i	−0.904819	−	0.425797i	$-0.859994\pi$
$353$		−	16.0000i		−	0.851594i	0.904819	−	0.425797i	$-0.140006\pi$
$354$		0			0
$355$	−3.00000	+	1.00000i	−0.159223	+	0.0530745i
$356$		0			0
$357$	20.0000			1.05851
$358$		0			0
$359$	−13.0000	−	13.0000i	−0.686114	−	0.686114i	0.275257	−	0.961371i	$-0.411237\pi$
$359$	−13.0000	−	13.0000i	−0.686114	−	0.686114i	−0.961371	+	0.275257i	$0.911237\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$		0			0
$363$	−9.00000	+	9.00000i	−0.472377	+	0.472377i
$364$		0			0
$365$	−6.00000	+	12.0000i	−0.314054	+	0.628109i
$366$		0			0
$367$	−3.00000	+	3.00000i	−0.156599	+	0.156599i	−0.781058	−	0.624459i	$-0.785320\pi$
$367$	−3.00000	+	3.00000i	−0.156599	+	0.156599i	0.624459	+	0.781058i	$0.285320\pi$
$368$		0			0
$369$	1.00000	−	1.00000i	0.0520579	−	0.0520579i
$370$		0			0
$371$	−2.00000	+	2.00000i	−0.103835	+	0.103835i
$372$		0			0
$373$	−1.00000	−	1.00000i	−0.0517780	−	0.0517780i	0.680744	−	0.732522i	$-0.261657\pi$
$373$	−1.00000	−	1.00000i	−0.0517780	−	0.0517780i	−0.732522	+	0.680744i	$0.761657\pi$
$374$		0			0
$375$	−13.0000	−	9.00000i	−0.671317	−	0.464758i
$376$		0			0
$377$	8.00000	+	12.0000i	0.412021	+	0.618031i
$378$		0			0
$379$	−17.0000	+	17.0000i	−0.873231	+	0.873231i	−0.992823	−	0.119592i	$-0.961841\pi$
$379$	−17.0000	+	17.0000i	−0.873231	+	0.873231i	0.119592	+	0.992823i	$0.461841\pi$
$380$		0			0
$381$			30.0000i			1.53695i
$382$		0			0
$383$			6.00000i			0.306586i	0.988181	+	0.153293i	$0.0489878\pi$
$383$			6.00000i			0.306586i	−0.988181	+	0.153293i	$0.951012\pi$
$384$		0			0
$385$	6.00000	−	2.00000i	0.305788	−	0.101929i
$386$		0			0
$387$	5.00000	+	5.00000i	0.254164	+	0.254164i
$388$		0			0
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$		0			0
$391$	50.0000			2.52861
$392$		0			0
$393$	−12.0000	−	12.0000i	−0.605320	−	0.605320i
$394$		0			0
$395$	28.0000	+	14.0000i	1.40883	+	0.704416i
$396$		0			0
$397$		−	8.00000i		−	0.401508i	−0.979642	−	0.200754i	$-0.935661\pi$
$397$		−	8.00000i		−	0.401508i	0.979642	−	0.200754i	$-0.0643393\pi$
$398$		0			0
$399$		−	12.0000i		−	0.600751i
$400$		0			0
$401$	1.00000	−	1.00000i	0.0499376	−	0.0499376i	−0.681697	−	0.731635i	$-0.738758\pi$
$401$	1.00000	−	1.00000i	0.0499376	−	0.0499376i	0.731635	+	0.681697i	$0.238758\pi$
$402$		0			0
$403$	5.00000	+	1.00000i	0.249068	+	0.0498135i
$404$		0			0
$405$	5.00000	−	10.0000i	0.248452	−	0.496904i
$406$		0			0
$407$	8.00000	+	8.00000i	0.396545	+	0.396545i
$408$		0			0
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	−0.777376	−	0.629036i	$-0.783450\pi$
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	0.629036	+	0.777376i	$0.283450\pi$
$410$		0			0
$411$	−12.0000	+	12.0000i	−0.591916	+	0.591916i
$412$		0			0
$413$	−6.00000	+	6.00000i	−0.295241	+	0.295241i
$414$		0			0
$415$	12.0000	+	6.00000i	0.589057	+	0.294528i
$416$		0			0
$417$	−14.0000	+	14.0000i	−0.685583	+	0.685583i
$418$		0			0
$419$		−	26.0000i		−	1.27018i	−0.772437	−	0.635092i	$-0.780962\pi$
$419$		−	26.0000i		−	1.27018i	0.772437	−	0.635092i	$-0.219038\pi$
$420$		0			0
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	0.452919	−	0.891552i	$-0.350383\pi$
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	−0.891552	+	0.452919i	$0.850383\pi$
$422$		0			0
$423$	−2.00000			−0.0972433
$424$		0			0
$425$	5.00000	−	35.0000i	0.242536	−	1.69775i
$426$		0			0
$427$		−	4.00000i		−	0.193574i
$428$		0			0
$429$	6.00000	−	4.00000i	0.289683	−	0.193122i
$430$		0			0
$431$	−21.0000	−	21.0000i	−1.01153	−	1.01153i	−0.999933	−	0.0116017i	$-0.996307\pi$
$431$	−21.0000	−	21.0000i	−1.01153	−	1.01153i	−0.0116017	−	0.999933i	$-0.503693\pi$
$432$		0			0
$433$	−15.0000	+	15.0000i	−0.720854	+	0.720854i	−0.968779	−	0.247925i	$-0.920251\pi$
$433$	−15.0000	+	15.0000i	−0.720854	+	0.720854i	0.247925	+	0.968779i	$0.420251\pi$
$434$		0			0
$435$	−4.00000	−	12.0000i	−0.191785	−	0.575356i
$436$		0			0
$437$		−	30.0000i		−	1.43509i
$438$		0			0
$439$	−40.0000			−1.90910			−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000			−1.90910			−0.954548	+	0.298057i	$0.903661\pi$
$440$		0			0
$441$		−	3.00000i		−	0.142857i
$442$		0			0
$443$	−19.0000	−	19.0000i	−0.902717	−	0.902717i	0.0929532	−	0.995670i	$-0.470369\pi$
$443$	−19.0000	−	19.0000i	−0.902717	−	0.902717i	−0.995670	+	0.0929532i	$0.970369\pi$
$444$		0			0
$445$	−21.0000	+	7.00000i	−0.995495	+	0.331832i
$446$		0			0
$447$	−26.0000			−1.22976
$448$		0			0
$449$	−7.00000	−	7.00000i	−0.330350	−	0.330350i	0.522369	−	0.852720i	$-0.325048\pi$
$449$	−7.00000	−	7.00000i	−0.330350	−	0.330350i	−0.852720	+	0.522369i	$0.825048\pi$
$450$		0			0
$451$	−2.00000			−0.0941763
$452$		0			0
$453$	18.0000			0.845714
$454$		0			0
$455$	16.0000	−	2.00000i	0.750092	−	0.0937614i
$456$		0			0
$457$	38.0000			1.77757			0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000			1.77757			0.888783	+	0.458329i	$0.151552\pi$
$458$		0			0
$459$	40.0000			1.86704
$460$		0			0
$461$	11.0000	+	11.0000i	0.512321	+	0.512321i	0.915237	−	0.402916i	$-0.132003\pi$
$461$	11.0000	+	11.0000i	0.512321	+	0.512321i	−0.402916	+	0.915237i	$0.632003\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$		0			0
$465$	−4.00000	−	2.00000i	−0.185496	−	0.0927478i
$466$		0			0
$467$	5.00000	+	5.00000i	0.231372	+	0.231372i	0.813265	−	0.581893i	$-0.197688\pi$
$467$	5.00000	+	5.00000i	0.231372	+	0.231372i	−0.581893	+	0.813265i	$0.697688\pi$
$468$		0			0
$469$		−	24.0000i		−	1.10822i
$470$		0			0
$471$	6.00000			0.276465
$472$		0			0
$473$		−	10.0000i		−	0.459800i
$474$		0			0
$475$	−21.0000	−	3.00000i	−0.963546	−	0.137649i
$476$		0			0
$477$	−1.00000	+	1.00000i	−0.0457869	+	0.0457869i
$478$		0			0
$479$	−13.0000	−	13.0000i	−0.593985	−	0.593985i	0.344720	−	0.938705i	$-0.387974\pi$
$479$	−13.0000	−	13.0000i	−0.593985	−	0.593985i	−0.938705	+	0.344720i	$0.887974\pi$
$480$		0			0
$481$	16.0000	+	24.0000i	0.729537	+	1.09431i
$482$		0			0
$483$		−	20.0000i		−	0.910032i
$484$		0			0
$485$	−2.00000	+	4.00000i	−0.0908153	+	0.181631i
$486$		0			0
$487$	32.0000			1.45006			0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000			1.45006			0.725029	+	0.688718i	$0.241826\pi$
$488$		0			0
$489$	−4.00000	−	4.00000i	−0.180886	−	0.180886i
$490$		0			0
$491$		−	10.0000i		−	0.451294i	−0.974209	−	0.225647i	$-0.927550\pi$
$491$		−	10.0000i		−	0.451294i	0.974209	−	0.225647i	$-0.0724495\pi$
$492$		0			0
$493$	20.0000	−	20.0000i	0.900755	−	0.900755i
$494$		0			0
$495$	3.00000	−	1.00000i	0.134840	−	0.0449467i
$496$		0			0
$497$	−2.00000	+	2.00000i	−0.0897123	+	0.0897123i
$498$		0			0
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$		0			0
$501$	2.00000	−	2.00000i	0.0893534	−	0.0893534i
$502$		0			0
$503$	−9.00000	−	9.00000i	−0.401290	−	0.401290i	0.477397	−	0.878688i	$-0.341580\pi$
$503$	−9.00000	−	9.00000i	−0.401290	−	0.401290i	−0.878688	+	0.477397i	$0.841580\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	17.0000	−	7.00000i	0.754997	−	0.310881i
$508$		0			0
$509$	−13.0000	+	13.0000i	−0.576215	+	0.576215i	−0.933858	−	0.357643i	$-0.883580\pi$
$509$	−13.0000	+	13.0000i	−0.576215	+	0.576215i	0.357643	+	0.933858i	$0.383580\pi$
$510$		0			0
$511$			12.0000i			0.530849i
$512$		0			0
$513$		−	24.0000i		−	1.05963i
$514$		0			0
$515$	−5.00000	−	15.0000i	−0.220326	−	0.660979i
$516$		0			0
$517$	2.00000	+	2.00000i	0.0879599	+	0.0879599i
$518$		0			0
$519$	30.0000			1.31685
$520$		0			0
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$		0			0
$523$	21.0000	+	21.0000i	0.918266	+	0.918266i	0.996903	−	0.0786374i	$-0.0250569\pi$
$523$	21.0000	+	21.0000i	0.918266	+	0.918266i	−0.0786374	+	0.996903i	$0.525057\pi$
$524$		0			0
$525$	−14.0000	−	2.00000i	−0.611010	−	0.0872872i
$526$		0			0
$527$		−	10.0000i		−	0.435607i
$528$		0			0
$529$		−	27.0000i		−	1.17391i
$530$		0			0
$531$	−3.00000	+	3.00000i	−0.130189	+	0.130189i
$532$		0			0
$533$	−5.00000	−	1.00000i	−0.216574	−	0.0433148i
$534$		0			0
$535$	13.0000	+	39.0000i	0.562039	+	1.68612i
$536$		0			0
$537$	−20.0000	−	20.0000i	−0.863064	−	0.863064i
$538$		0			0
$539$	−3.00000	+	3.00000i	−0.129219	+	0.129219i
$540$		0			0
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$		0			0
$543$	−20.0000	+	20.0000i	−0.858282	+	0.858282i
$544$		0			0
$545$	13.0000	+	39.0000i	0.556859	+	1.67058i
$546$		0			0
$547$	7.00000	−	7.00000i	0.299298	−	0.299298i	−0.541441	−	0.840739i	$-0.682121\pi$
$547$	7.00000	−	7.00000i	0.299298	−	0.299298i	0.840739	+	0.541441i	$0.182121\pi$
$548$		0			0
$549$		−	2.00000i		−	0.0853579i
$550$		0			0
$551$	−12.0000	−	12.0000i	−0.511217	−	0.511217i
$552$		0			0
$553$	28.0000			1.19068
$554$		0			0
$555$	−8.00000	−	24.0000i	−0.339581	−	1.01874i
$556$		0			0
$557$		−	8.00000i		−	0.338971i	−0.985533	−	0.169485i	$-0.945789\pi$
$557$		−	8.00000i		−	0.338971i	0.985533	−	0.169485i	$-0.0542106\pi$
$558$		0			0
$559$	5.00000	−	25.0000i	0.211477	−	1.05739i
$560$		0			0
$561$	−10.0000	−	10.0000i	−0.422200	−	0.422200i
$562$		0			0
$563$	−5.00000	+	5.00000i	−0.210725	+	0.210725i	−0.804575	−	0.593851i	$-0.797607\pi$
$563$	−5.00000	+	5.00000i	−0.210725	+	0.210725i	0.593851	+	0.804575i	$0.297607\pi$
$564$		0			0
$565$	27.0000	−	9.00000i	1.13590	−	0.378633i
$566$		0			0
$567$		−	10.0000i		−	0.419961i
$568$		0			0
$569$	−10.0000			−0.419222			−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000			−0.419222			−0.209611	+	0.977785i	$0.567220\pi$
$570$		0			0
$571$		−	10.0000i		−	0.418487i	−0.977864	−	0.209243i	$-0.932900\pi$
$571$		−	10.0000i		−	0.418487i	0.977864	−	0.209243i	$-0.0671001\pi$
$572$		0			0
$573$	8.00000	+	8.00000i	0.334205	+	0.334205i
$574$		0			0
$575$	−35.0000	−	5.00000i	−1.45960	−	0.208514i
$576$		0			0
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$		0			0
$579$	14.0000	+	14.0000i	0.581820	+	0.581820i
$580$		0			0
$581$	12.0000			0.497844
$582$		0			0
$583$	2.00000			0.0828315
$584$		0			0
$585$	8.00000	−	1.00000i	0.330759	−	0.0413449i
$586$		0			0
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	−6.00000			−0.247226
$590$		0			0
$591$	18.0000	+	18.0000i	0.740421	+	0.740421i
$592$		0			0
$593$	14.0000			0.574911			0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000			0.574911			0.287456	+	0.957794i	$0.407191\pi$
$594$		0			0
$595$	−10.0000	−	30.0000i	−0.409960	−	1.22988i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			14.0000i			0.572024i	0.958226	+	0.286012i	$0.0923298\pi$
$599$			14.0000i			0.572024i	−0.958226	+	0.286012i	$0.907670\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$		0			0
$605$	18.0000	+	9.00000i	0.731804	+	0.365902i
$606$		0			0
$607$	−3.00000	+	3.00000i	−0.121766	+	0.121766i	−0.765364	−	0.643598i	$-0.777441\pi$
$607$	−3.00000	+	3.00000i	−0.121766	+	0.121766i	0.643598	+	0.765364i	$0.277441\pi$
$608$		0			0
$609$	−8.00000	−	8.00000i	−0.324176	−	0.324176i
$610$		0			0
$611$	4.00000	+	6.00000i	0.161823	+	0.242734i
$612$		0			0
$613$			4.00000i			0.161558i	0.996732	+	0.0807792i	$0.0257409\pi$
$613$			4.00000i			0.161558i	−0.996732	+	0.0807792i	$0.974259\pi$
$614$		0			0
$615$	4.00000	+	2.00000i	0.161296	+	0.0806478i
$616$		0			0
$617$	38.0000			1.52982			0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000			1.52982			0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$	−3.00000	−	3.00000i	−0.120580	−	0.120580i	0.644242	−	0.764822i	$-0.277173\pi$
$619$	−3.00000	−	3.00000i	−0.120580	−	0.120580i	−0.764822	+	0.644242i	$0.777173\pi$
$620$		0			0
$621$		−	40.0000i		−	1.60514i
$622$		0			0
$623$	−14.0000	+	14.0000i	−0.560898	+	0.560898i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	−6.00000	+	6.00000i	−0.239617	+	0.239617i
$628$		0			0
$629$	40.0000	−	40.0000i	1.59490	−	1.59490i
$630$		0			0
$631$	−11.0000	+	11.0000i	−0.437903	+	0.437903i	−0.891306	−	0.453403i	$-0.850210\pi$
$631$	−11.0000	+	11.0000i	−0.437903	+	0.437903i	0.453403	+	0.891306i	$0.350210\pi$
$632$		0			0
$633$	−12.0000	−	12.0000i	−0.476957	−	0.476957i
$634$		0			0
$635$	45.0000	−	15.0000i	1.78577	−	0.595257i
$636$		0			0
$637$	−9.00000	+	6.00000i	−0.356593	+	0.237729i
$638$		0			0
$639$	−1.00000	+	1.00000i	−0.0395594	+	0.0395594i
$640$		0			0
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		0			0
$643$			46.0000i			1.81406i	0.421063	+	0.907031i	$0.361657\pi$
$643$			46.0000i			1.81406i	−0.421063	+	0.907031i	$0.638343\pi$
$644$		0			0
$645$	−10.0000	+	20.0000i	−0.393750	+	0.787499i
$646$		0			0
$647$	−5.00000	−	5.00000i	−0.196570	−	0.196570i	0.601958	−	0.798528i	$-0.294388\pi$
$647$	−5.00000	−	5.00000i	−0.196570	−	0.196570i	−0.798528	+	0.601958i	$0.794388\pi$
$648$		0			0
$649$	6.00000			0.235521
$650$		0			0
$651$	−4.00000			−0.156772
$652$		0			0
$653$	−21.0000	−	21.0000i	−0.821794	−	0.821794i	0.164572	−	0.986365i	$-0.447376\pi$
$653$	−21.0000	−	21.0000i	−0.821794	−	0.821794i	−0.986365	+	0.164572i	$0.947376\pi$
$654$		0			0
$655$	−12.0000	+	24.0000i	−0.468879	+	0.937758i
$656$		0			0
$657$			6.00000i			0.234082i
$658$		0			0
$659$			14.0000i			0.545363i	0.962104	+	0.272681i	$0.0879105\pi$
$659$			14.0000i			0.545363i	−0.962104	+	0.272681i	$0.912090\pi$
$660$		0			0
$661$	31.0000	−	31.0000i	1.20576	−	1.20576i	0.233373	−	0.972387i	$-0.425024\pi$
$661$	31.0000	−	31.0000i	1.20576	−	1.20576i	0.972387	−	0.233373i	$-0.0749763\pi$
$662$		0			0
$663$	−20.0000	−	30.0000i	−0.776736	−	1.16510i
$664$		0			0
$665$	−18.0000	+	6.00000i	−0.698010	+	0.232670i
$666$		0			0
$667$	−20.0000	−	20.0000i	−0.774403	−	0.774403i
$668$		0			0
$669$	−6.00000	+	6.00000i	−0.231973	+	0.231973i
$670$		0			0
$671$	−2.00000	+	2.00000i	−0.0772091	+	0.0772091i
$672$		0			0
$673$	5.00000	−	5.00000i	0.192736	−	0.192736i	−0.604141	−	0.796877i	$-0.706484\pi$
$673$	5.00000	−	5.00000i	0.192736	−	0.192736i	0.796877	+	0.604141i	$0.206484\pi$
$674$		0			0
$675$	−28.0000	−	4.00000i	−1.07772	−	0.153960i
$676$		0			0
$677$	23.0000	−	23.0000i	0.883962	−	0.883962i	−0.109973	−	0.993935i	$-0.535076\pi$
$677$	23.0000	−	23.0000i	0.883962	−	0.883962i	0.993935	+	0.109973i	$0.0350764\pi$
$678$		0			0
$679$			4.00000i			0.153506i
$680$		0			0
$681$	12.0000	+	12.0000i	0.459841	+	0.459841i
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	24.0000	+	12.0000i	0.916993	+	0.458496i
$686$		0			0
$687$			6.00000i			0.228914i
$688$		0			0
$689$	5.00000	+	1.00000i	0.190485	+	0.0380970i
$690$		0			0
$691$	9.00000	+	9.00000i	0.342376	+	0.342376i	0.857260	−	0.514884i	$-0.172165\pi$
$691$	9.00000	+	9.00000i	0.342376	+	0.342376i	−0.514884	+	0.857260i	$0.672165\pi$
$692$		0			0
$693$	2.00000	−	2.00000i	0.0759737	−	0.0759737i
$694$		0			0
$695$	28.0000	+	14.0000i	1.06210	+	0.531050i
$696$		0			0
$697$			10.0000i			0.378777i
$698$		0			0
$699$	10.0000			0.378235
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−24.0000	−	24.0000i	−0.905177	−	0.905177i
$704$		0			0
$705$	−2.00000	−	6.00000i	−0.0753244	−	0.225973i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.00000	+	3.00000i	0.112667	+	0.112667i	0.761193	−	0.648526i	$-0.224614\pi$
$709$	3.00000	+	3.00000i	0.112667	+	0.112667i	−0.648526	+	0.761193i	$0.724614\pi$
$710$		0			0
$711$	14.0000			0.525041
$712$		0			0
$713$	−10.0000			−0.374503
$714$		0			0
$715$	−9.00000	−	7.00000i	−0.336581	−	0.261785i
$716$		0			0
$717$	−14.0000			−0.522840
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−10.0000	−	10.0000i	−0.372419	−	0.372419i
$722$		0			0
$723$	2.00000			0.0743808
$724$		0			0
$725$	−16.0000	+	12.0000i	−0.594225	+	0.445669i
$726$		0			0
$727$	35.0000	+	35.0000i	1.29808	+	1.29808i	0.929660	+	0.368418i	$0.120100\pi$
$727$	35.0000	+	35.0000i	1.29808	+	1.29808i	0.368418	+	0.929660i	$0.379900\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	−50.0000			−1.84932
$732$		0			0
$733$			44.0000i			1.62518i	0.582838	+	0.812589i	$0.301942\pi$
$733$			44.0000i			1.62518i	−0.582838	+	0.812589i	$0.698058\pi$
$734$		0			0
$735$	9.00000	−	3.00000i	0.331970	−	0.110657i
$736$		0			0
$737$	−12.0000	+	12.0000i	−0.442026	+	0.442026i
$738$		0			0
$739$	37.0000	+	37.0000i	1.36107	+	1.36107i	0.872560	+	0.488507i	$0.162458\pi$
$739$	37.0000	+	37.0000i	1.36107	+	1.36107i	0.488507	+	0.872560i	$0.337542\pi$
$740$		0			0
$741$	−18.0000	+	12.0000i	−0.661247	+	0.440831i
$742$		0			0
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$		0			0
$745$	13.0000	+	39.0000i	0.476283	+	1.42885i
$746$		0			0
$747$	6.00000			0.219529
$748$		0			0
$749$	26.0000	+	26.0000i	0.950019	+	0.950019i
$750$		0			0
$751$		−	10.0000i		−	0.364905i	−0.983215	−	0.182453i	$-0.941596\pi$
$751$		−	10.0000i		−	0.364905i	0.983215	−	0.182453i	$-0.0584036\pi$
$752$		0			0
$753$	−30.0000	+	30.0000i	−1.09326	+	1.09326i
$754$		0			0
$755$	−9.00000	−	27.0000i	−0.327544	−	0.982631i
$756$		0			0
$757$	−17.0000	+	17.0000i	−0.617876	+	0.617876i	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−17.0000	+	17.0000i	−0.617876	+	0.617876i	0.327111	+	0.944986i	$0.393925\pi$
$758$		0			0
$759$	−10.0000	+	10.0000i	−0.362977	+	0.362977i
$760$		0			0
$761$	−19.0000	+	19.0000i	−0.688749	+	0.688749i	−0.961956	−	0.273206i	$-0.911916\pi$
$761$	−19.0000	+	19.0000i	−0.688749	+	0.688749i	0.273206	+	0.961956i	$0.411916\pi$
$762$		0			0
$763$	26.0000	+	26.0000i	0.941263	+	0.941263i
$764$		0			0
$765$	−5.00000	−	15.0000i	−0.180775	−	0.542326i
$766$		0			0
$767$	15.0000	+	3.00000i	0.541619	+	0.108324i
$768$		0			0
$769$	−23.0000	+	23.0000i	−0.829401	+	0.829401i	−0.987434	−	0.158033i	$-0.949485\pi$
$769$	−23.0000	+	23.0000i	−0.829401	+	0.829401i	0.158033	+	0.987434i	$0.449485\pi$
$770$		0			0
$771$		−	30.0000i		−	1.08042i
$772$		0			0
$773$			24.0000i			0.863220i	0.902060	+	0.431610i	$0.142054\pi$
$773$			24.0000i			0.863220i	−0.902060	+	0.431610i	$0.857946\pi$
$774$		0			0
$775$	−1.00000	+	7.00000i	−0.0359211	+	0.251447i
$776$		0			0
$777$	−16.0000	−	16.0000i	−0.573997	−	0.573997i
$778$		0			0
$779$	6.00000			0.214972
$780$		0			0
$781$	2.00000			0.0715656
$782$		0			0
$783$	−16.0000	−	16.0000i	−0.571793	−	0.571793i
$784$		0			0
$785$	−3.00000	−	9.00000i	−0.107075	−	0.321224i
$786$		0			0
$787$		−	42.0000i		−	1.49714i	−0.663057	−	0.748569i	$-0.730741\pi$
$787$		−	42.0000i		−	1.49714i	0.663057	−	0.748569i	$-0.269259\pi$
$788$		0			0
$789$		−	18.0000i		−	0.640817i
$790$		0			0
$791$	18.0000	−	18.0000i	0.640006	−	0.640006i
$792$		0			0
$793$	−6.00000	+	4.00000i	−0.213066	+	0.142044i
$794$		0			0
$795$	−4.00000	−	2.00000i	−0.141865	−	0.0709327i
$796$		0			0
$797$	−5.00000	−	5.00000i	−0.177109	−	0.177109i	0.612985	−	0.790094i	$-0.289968\pi$
$797$	−5.00000	−	5.00000i	−0.177109	−	0.177109i	−0.790094	+	0.612985i	$0.789968\pi$
$798$		0			0
$799$	10.0000	−	10.0000i	0.353775	−	0.353775i
$800$		0			0
$801$	−7.00000	+	7.00000i	−0.247333	+	0.247333i
$802$		0			0
$803$	6.00000	−	6.00000i	0.211735	−	0.211735i
$804$		0			0
$805$	−30.0000	+	10.0000i	−1.05736	+	0.352454i
$806$		0			0
$807$	−16.0000	+	16.0000i	−0.563227	+	0.563227i
$808$		0			0
$809$			36.0000i			1.26569i	0.774277	+	0.632846i	$0.218114\pi$
$809$			36.0000i			1.26569i	−0.774277	+	0.632846i	$0.781886\pi$
$810$		0			0
$811$	−11.0000	−	11.0000i	−0.386262	−	0.386262i	0.487090	−	0.873352i	$-0.338058\pi$
$811$	−11.0000	−	11.0000i	−0.386262	−	0.386262i	−0.873352	+	0.487090i	$0.838058\pi$
$812$		0			0
$813$	18.0000			0.631288
$814$		0			0
$815$	−4.00000	+	8.00000i	−0.140114	+	0.280228i
$816$		0			0
$817$			30.0000i			1.04957i
$818$		0			0
$819$	6.00000	−	4.00000i	0.209657	−	0.139771i
$820$		0			0
$821$	−29.0000	−	29.0000i	−1.01211	−	1.01211i	−0.999926	−	0.0121812i	$-0.996123\pi$
$821$	−29.0000	−	29.0000i	−1.01211	−	1.01211i	−0.0121812	−	0.999926i	$-0.503877\pi$
$822$		0			0
$823$	−15.0000	+	15.0000i	−0.522867	+	0.522867i	−0.918436	−	0.395569i	$-0.870547\pi$
$823$	−15.0000	+	15.0000i	−0.522867	+	0.522867i	0.395569	+	0.918436i	$0.370547\pi$
$824$		0			0
$825$	6.00000	+	8.00000i	0.208893	+	0.278524i
$826$		0			0
$827$		−	2.00000i		−	0.0695468i	−0.999395	−	0.0347734i	$-0.988929\pi$
$827$		−	2.00000i		−	0.0695468i	0.999395	−	0.0347734i	$-0.0110710\pi$
$828$		0			0
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$		0			0
$831$		−	10.0000i		−	0.346896i
$832$		0			0
$833$	15.0000	+	15.0000i	0.519719	+	0.519719i
$834$		0			0
$835$	−4.00000	−	2.00000i	−0.138426	−	0.0692129i
$836$		0			0
$837$	−8.00000			−0.276520
$838$		0			0
$839$	−13.0000	−	13.0000i	−0.448810	−	0.448810i	0.446149	−	0.894959i	$-0.352795\pi$
$839$	−13.0000	−	13.0000i	−0.448810	−	0.448810i	−0.894959	+	0.446149i	$0.852795\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$		0			0
$843$	42.0000			1.44656
$844$		0			0
$845$	−19.0000	−	22.0000i	−0.653620	−	0.756823i
$846$		0			0
$847$	18.0000			0.618487
$848$		0			0
$849$	30.0000			1.02960
$850$		0			0
$851$	−40.0000	−	40.0000i	−1.37118	−	1.37118i
$852$		0			0
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$		0			0
$855$	−9.00000	+	3.00000i	−0.307794	+	0.102598i
$856$		0			0
$857$	5.00000	+	5.00000i	0.170797	+	0.170797i	0.787329	−	0.616533i	$-0.211463\pi$
$857$	5.00000	+	5.00000i	0.170797	+	0.170797i	−0.616533	+	0.787329i	$0.711463\pi$
$858$		0			0
$859$		−	26.0000i		−	0.887109i	−0.896248	−	0.443554i	$-0.853717\pi$
$859$		−	26.0000i		−	0.887109i	0.896248	−	0.443554i	$-0.146283\pi$
$860$		0			0
$861$	4.00000			0.136320
$862$		0			0
$863$			46.0000i			1.56586i	0.622111	+	0.782929i	$0.286275\pi$
$863$			46.0000i			1.56586i	−0.622111	+	0.782929i	$0.713725\pi$
$864$		0			0
$865$	−15.0000	−	45.0000i	−0.510015	−	1.53005i
$866$		0			0
$867$	−33.0000	+	33.0000i	−1.12074	+	1.12074i
$868$		0			0
$869$	−14.0000	−	14.0000i	−0.474917	−	0.474917i
$870$		0			0
$871$	−36.0000	+	24.0000i	−1.21981	+	0.813209i
$872$		0			0
$873$			2.00000i			0.0676897i
$874$		0			0
$875$	4.00000	+	22.0000i	0.135225	+	0.743736i
$876$		0			0
$877$	18.0000			0.607817			0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000			0.607817			0.303908	+	0.952701i	$0.401708\pi$
$878$		0			0
$879$	−26.0000	−	26.0000i	−0.876958	−	0.876958i
$880$		0			0
$881$		−	20.0000i		−	0.673817i	−0.941537	−	0.336909i	$-0.890619\pi$
$881$		−	20.0000i		−	0.673817i	0.941537	−	0.336909i	$-0.109381\pi$
$882$		0			0
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	−0.786216	−	0.617952i	$-0.787963\pi$
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	0.617952	+	0.786216i	$0.287963\pi$
$884$		0			0
$885$	−12.0000	−	6.00000i	−0.403376	−	0.201688i
$886$		0			0
$887$	−23.0000	+	23.0000i	−0.772264	+	0.772264i	−0.978502	−	0.206238i	$-0.933878\pi$
$887$	−23.0000	+	23.0000i	−0.772264	+	0.772264i	0.206238	+	0.978502i	$0.433878\pi$
$888$		0			0
$889$	30.0000	−	30.0000i	1.00617	−	1.00617i
$890$		0			0
$891$	−5.00000	+	5.00000i	−0.167506	+	0.167506i
$892$		0			0
$893$	−6.00000	−	6.00000i	−0.200782	−	0.200782i
$894$		0			0
$895$	−20.0000	+	40.0000i	−0.668526	+	1.33705i
$896$		0			0
$897$	−30.0000	+	20.0000i	−1.00167	+	0.667781i
$898$		0			0
$899$	−4.00000	+	4.00000i	−0.133407	+	0.133407i
$900$		0			0
$901$		−	10.0000i		−	0.333148i
$902$		0			0
$903$			20.0000i			0.665558i
$904$		0			0
$905$	40.0000	+	20.0000i	1.32964	+	0.664822i
$906$		0			0
$907$	−35.0000	−	35.0000i	−1.16216	−	1.16216i	−0.984003	−	0.178153i	$-0.942988\pi$
$907$	−35.0000	−	35.0000i	−1.16216	−	1.16216i	−0.178153	−	0.984003i	$-0.557012\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	−6.00000	−	6.00000i	−0.198571	−	0.198571i
$914$		0			0
$915$	6.00000	−	2.00000i	0.198354	−	0.0661180i
$916$		0			0
$917$			24.0000i			0.792550i
$918$		0			0
$919$			14.0000i			0.461817i	0.972975	+	0.230909i	$0.0741699\pi$
$919$			14.0000i			0.461817i	−0.972975	+	0.230909i	$0.925830\pi$
$920$		0			0
$921$	2.00000	−	2.00000i	0.0659022	−	0.0659022i
$922$		0			0
$923$	5.00000	+	1.00000i	0.164577	+	0.0329154i
$924$		0			0
$925$	−32.0000	+	24.0000i	−1.05215	+	0.789115i
$926$		0			0
$927$	−5.00000	−	5.00000i	−0.164222	−	0.164222i
$928$		0			0
$929$	17.0000	−	17.0000i	0.557752	−	0.557752i	−0.370915	−	0.928667i	$-0.620956\pi$
$929$	17.0000	−	17.0000i	0.557752	−	0.557752i	0.928667	+	0.370915i	$0.120956\pi$
$930$		0			0
$931$	9.00000	−	9.00000i	0.294963	−	0.294963i
$932$		0			0
$933$	10.0000	−	10.0000i	0.327385	−	0.327385i
$934$		0			0
$935$	−10.0000	+	20.0000i	−0.327035	+	0.654070i
$936$		0			0
$937$	33.0000	−	33.0000i	1.07806	−	1.07806i	0.0813798	−	0.996683i	$-0.474067\pi$
$937$	33.0000	−	33.0000i	1.07806	−	1.07806i	0.996683	−	0.0813798i	$-0.0259327\pi$
$938$		0			0
$939$			18.0000i			0.587408i
$940$		0			0
$941$	−29.0000	−	29.0000i	−0.945373	−	0.945373i	0.0532103	−	0.998583i	$-0.483055\pi$
$941$	−29.0000	−	29.0000i	−0.945373	−	0.945373i	−0.998583	+	0.0532103i	$0.983055\pi$
$942$		0			0
$943$	10.0000			0.325645
$944$		0			0
$945$	−24.0000	+	8.00000i	−0.780720	+	0.260240i
$946$		0			0
$947$			38.0000i			1.23483i	0.786636	+	0.617417i	$0.211821\pi$
$947$			38.0000i			1.23483i	−0.786636	+	0.617417i	$0.788179\pi$
$948$		0			0
$949$	18.0000	−	12.0000i	0.584305	−	0.389536i
$950$		0			0
$951$	−2.00000	−	2.00000i	−0.0648544	−	0.0648544i
$952$		0			0
$953$	−35.0000	+	35.0000i	−1.13376	+	1.13376i	−0.144215	+	0.989546i	$0.546066\pi$
$953$	−35.0000	+	35.0000i	−1.13376	+	1.13376i	−0.989546	+	0.144215i	$0.953934\pi$
$954$		0			0
$955$	8.00000	−	16.0000i	0.258874	−	0.517748i
$956$		0			0
$957$			8.00000i			0.258603i
$958$		0			0
$959$	24.0000			0.775000
$960$		0			0
$961$		−	29.0000i		−	0.935484i
$962$		0			0
$963$	13.0000	+	13.0000i	0.418919	+	0.418919i
$964$		0			0
$965$	14.0000	−	28.0000i	0.450676	−	0.901352i
$966$		0			0
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$		0			0
$969$	30.0000	+	30.0000i	0.963739	+	0.963739i
$970$		0			0
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		0			0
$973$	28.0000			0.897639
$974$		0			0
$975$	11.0000	+	23.0000i	0.352282	+	0.736590i
$976$		0			0
$977$	−22.0000			−0.703842			−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000			−0.703842			−0.351921	+	0.936030i	$0.614471\pi$
$978$		0			0
$979$	14.0000			0.447442
$980$		0			0
$981$	13.0000	+	13.0000i	0.415058	+	0.415058i
$982$		0			0
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	18.0000	−	36.0000i	0.573528	−	1.14706i
$986$		0			0
$987$	−4.00000	−	4.00000i	−0.127321	−	0.127321i
$988$		0			0
$989$			50.0000i			1.58991i
$990$		0			0
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$		0			0
$993$			18.0000i			0.571213i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−17.0000	+	17.0000i	−0.538395	+	0.538395i	−0.923057	−	0.384662i	$-0.874318\pi$
$997$	−17.0000	+	17.0000i	−0.538395	+	0.538395i	0.384662	+	0.923057i	$0.374318\pi$
$998$		0			0
$999$	−32.0000	−	32.0000i	−1.01244	−	1.01244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.bg.f.593.1		2
4.3	odd	2		130.2.g.c.73.1	yes	2
5.2	odd	4		1040.2.cd.e.177.1		2
12.11	even	2		1170.2.m.a.73.1		2
13.5	odd	4		1040.2.cd.e.993.1		2
20.3	even	4		650.2.j.d.307.1		2
20.7	even	4		130.2.j.b.47.1	yes	2
20.19	odd	2		650.2.g.b.593.1		2
52.31	even	4		130.2.j.b.83.1	yes	2
60.47	odd	4		1170.2.w.c.307.1		2
65.57	even	4	inner	1040.2.bg.f.577.1		2
156.83	odd	4		1170.2.w.c.343.1		2
260.83	odd	4		650.2.g.b.57.1		2
260.187	odd	4		130.2.g.c.57.1	✓	2
260.239	even	4		650.2.j.d.343.1		2
780.707	even	4		1170.2.m.a.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.c.57.1	✓	2	260.187	odd	4
130.2.g.c.73.1	yes	2	4.3	odd	2
130.2.j.b.47.1	yes	2	20.7	even	4
130.2.j.b.83.1	yes	2	52.31	even	4
650.2.g.b.57.1		2	260.83	odd	4
650.2.g.b.593.1		2	20.19	odd	2
650.2.j.d.307.1		2	20.3	even	4
650.2.j.d.343.1		2	260.239	even	4
1040.2.bg.f.577.1		2	65.57	even	4	inner
1040.2.bg.f.593.1		2	1.1	even	1	trivial
1040.2.cd.e.177.1		2	5.2	odd	4
1040.2.cd.e.993.1		2	13.5	odd	4
1170.2.m.a.73.1		2	12.11	even	2
1170.2.m.a.577.1		2	780.707	even	4
1170.2.w.c.307.1		2	60.47	odd	4
1170.2.w.c.343.1		2	156.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{3} +(1.00000 - 2.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{9} +(-1.00000 + 1.00000i) q^{11} +(-3.00000 + 2.00000i) q^{13} +(3.00000 - 1.00000i) q^{15} +(5.00000 + 5.00000i) q^{17} +(3.00000 - 3.00000i) q^{19} +(2.00000 - 2.00000i) q^{21} +(5.00000 - 5.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} -4.00000i q^{29} +(-1.00000 - 1.00000i) q^{31} -2.00000 q^{33} +(-4.00000 - 2.00000i) q^{35} -8.00000i q^{37} +(-5.00000 - 1.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} +(-5.00000 + 5.00000i) q^{43} +(-2.00000 - 1.00000i) q^{45} -2.00000i q^{47} +3.00000 q^{49} +10.0000i q^{51} +(-1.00000 - 1.00000i) q^{53} +(1.00000 + 3.00000i) q^{55} +6.00000 q^{57} +(-3.00000 - 3.00000i) q^{59} +2.00000 q^{61} -2.00000 q^{63} +(1.00000 + 8.00000i) q^{65} +12.0000 q^{67} +10.0000 q^{69} +(-1.00000 - 1.00000i) q^{71} -6.00000 q^{73} +(1.00000 - 7.00000i) q^{75} +(2.00000 + 2.00000i) q^{77} +14.0000i q^{79} +5.00000 q^{81} +6.00000i q^{83} +(15.0000 - 5.00000i) q^{85} +(4.00000 - 4.00000i) q^{87} +(-7.00000 - 7.00000i) q^{89} +(4.00000 + 6.00000i) q^{91} -2.00000i q^{93} +(-3.00000 - 9.00000i) q^{95} -2.00000 q^{97} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{5} - 2 q^{11} - 6 q^{13} + 6 q^{15} + 10 q^{17} + 6 q^{19} + 4 q^{21} + 10 q^{23} - 6 q^{25} + 8 q^{27} - 2 q^{31} - 4 q^{33} - 8 q^{35} - 10 q^{39} + 2 q^{41} - 10 q^{43} - 4 q^{45}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^5 - 2 * q^11 - 6 * q^13 + 6 * q^15 + 10 * q^17 + 6 * q^19 + 4 * q^21 + 10 * q^23 - 6 * q^25 + 8 * q^27 - 2 * q^31 - 4 * q^33 - 8 * q^35 - 10 * q^39 + 2 * q^41 - 10 * q^43 - 4 * q^45 + 6 * q^49 - 2 * q^53 + 2 * q^55 + 12 * q^57 - 6 * q^59 + 4 * q^61 - 4 * q^63 + 2 * q^65 + 24 * q^67 + 20 * q^69 - 2 * q^71 - 12 * q^73 + 2 * q^75 + 4 * q^77 + 10 * q^81 + 30 * q^85 + 8 * q^87 - 14 * q^89 + 8 * q^91 - 6 * q^95 - 4 * q^97 + 2 * q^99

Introduction

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