LMFDB - Embedded newform 1040.2.cd.e.993.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(177,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.177"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [2,0,2,0,-4,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
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			993.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1040.993
Dual form			1040.2.cd.e.177.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{3} +(-2.00000 - 1.00000i) q^{5} +2.00000 q^{7} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +(2.00000 - 3.00000i) q^{13} +(-1.00000 - 3.00000i) q^{15} +(-5.00000 - 5.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +(-5.00000 + 5.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} -4.00000i q^{29} +(-1.00000 + 1.00000i) q^{31} -2.00000i q^{33} +(-4.00000 - 2.00000i) q^{35} +8.00000 q^{37} +(5.00000 - 1.00000i) q^{39} +(1.00000 - 1.00000i) q^{41} +(5.00000 - 5.00000i) q^{43} +(-1.00000 + 2.00000i) q^{45} +2.00000 q^{47} -3.00000 q^{49} -10.0000i q^{51} +(-1.00000 - 1.00000i) q^{53} +(1.00000 + 3.00000i) q^{55} -6.00000i q^{57} +(3.00000 - 3.00000i) q^{59} +2.00000 q^{61} -2.00000i q^{63} +(-7.00000 + 4.00000i) q^{65} -12.0000i q^{67} -10.0000 q^{69} +(-1.00000 + 1.00000i) q^{71} -6.00000i q^{73} +(-1.00000 + 7.00000i) q^{75} +(-2.00000 - 2.00000i) q^{77} +14.0000i q^{79} +5.00000 q^{81} +6.00000 q^{83} +(5.00000 + 15.0000i) q^{85} +(4.00000 - 4.00000i) q^{87} +(7.00000 - 7.00000i) q^{89} +(4.00000 - 6.00000i) q^{91} -2.00000 q^{93} +(3.00000 + 9.00000i) q^{95} +2.00000i q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 4 q^{5} + 4 q^{7} - 2 q^{11} + 4 q^{13} - 2 q^{15} - 10 q^{17} - 6 q^{19} + 4 q^{21} - 10 q^{23} + 6 q^{25} + 8 q^{27} - 2 q^{31} - 8 q^{35} + 16 q^{37} + 10 q^{39} + 2 q^{41} + 10 q^{43}+ \cdots - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 4 * q^5 + 4 * q^7 - 2 * q^11 + 4 * q^13 - 2 * q^15 - 10 * q^17 - 6 * q^19 + 4 * q^21 - 10 * q^23 + 6 * q^25 + 8 * q^27 - 2 * q^31 - 8 * q^35 + 16 * q^37 + 10 * q^39 + 2 * q^41 + 10 * q^43 - 2 * q^45 + 4 * q^47 - 6 * q^49 - 2 * q^53 + 2 * q^55 + 6 * q^59 + 4 * q^61 - 14 * q^65 - 20 * q^69 - 2 * q^71 - 2 * q^75 - 4 * q^77 + 10 * q^81 + 12 * q^83 + 10 * q^85 + 8 * q^87 + 14 * q^89 + 8 * q^91 - 4 * q^93 + 6 * q^95 - 2 * q^99

Character values

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

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

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
$3$	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
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$		0			0
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$		0			0
$15$	−1.00000	−	3.00000i	−0.258199	−	0.774597i
$16$		0			0
$17$	−5.00000	−	5.00000i	−1.21268	−	1.21268i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−5.00000	−	5.00000i	−1.21268	−	1.21268i	−0.242536	−	0.970143i	$-0.577979\pi$
$18$		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
$21$	2.00000	+	2.00000i	0.436436	+	0.436436i
$22$		0			0
$23$	−5.00000	+	5.00000i	−1.04257	+	1.04257i	−0.0435195	+	0.999053i	$0.513857\pi$
$23$	−5.00000	+	5.00000i	−1.04257	+	1.04257i	−0.999053	+	0.0435195i	$0.986143\pi$
$24$		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	−0.791184	−	0.611578i	$-0.790535\pi$
$31$	−1.00000	+	1.00000i	−0.179605	+	0.179605i	0.611578	+	0.791184i	$0.290535\pi$
$32$		0			0
$33$		−	2.00000i		−	0.348155i
$34$		0			0
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$		0			0
$39$	5.00000	−	1.00000i	0.800641	−	0.160128i
$40$		0			0
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	5.00000	−	5.00000i	0.762493	−	0.762493i	−0.214280	−	0.976772i	$-0.568740\pi$
$43$	5.00000	−	5.00000i	0.762493	−	0.762493i	0.976772	+	0.214280i	$0.0687403\pi$
$44$		0			0
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$		0			0
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$		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
$57$		−	6.00000i		−	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
$61$	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
$63$		−	2.00000i		−	0.251976i
$64$		0			0
$65$	−7.00000	+	4.00000i	−0.868243	+	0.496139i
$66$		0			0
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$		0			0
$69$	−10.0000			−1.20386
$70$		0			0
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	−0.763952	−	0.645273i	$-0.776743\pi$
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	0.645273	+	0.763952i	$0.276743\pi$
$72$		0			0
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$		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
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$	5.00000	+	15.0000i	0.542326	+	1.62698i
$86$		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	$-0.574188\pi$
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	0.972962	+	0.230964i	$0.0741879\pi$
$90$		0			0
$91$	4.00000	−	6.00000i	0.419314	−	0.628971i
$92$		0			0
$93$	−2.00000			−0.207390
$94$		0			0
$95$	3.00000	+	9.00000i	0.307794	+	0.923381i
$96$		0			0
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$		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	−0.909145	−	0.416480i	$-0.863264\pi$
$103$	−5.00000	+	5.00000i	−0.492665	+	0.492665i	0.416480	+	0.909145i	$0.363264\pi$
$104$		0			0
$105$	−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	0.957826	+	0.287348i	$0.0927736\pi$
$109$	13.0000	+	13.0000i	1.24517	+	1.24517i	0.287348	+	0.957826i	$0.407226\pi$
$110$		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
$115$	15.0000	−	5.00000i	1.39876	−	0.466252i
$116$		0			0
$117$	−3.00000	−	2.00000i	−0.277350	−	0.184900i
$118$		0			0
$119$	−10.0000	−	10.0000i	−0.916698	−	0.916698i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		0			0
$123$	2.00000			0.180334
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	−15.0000	−	15.0000i	−1.33103	−	1.33103i	−0.904445	−	0.426589i	$-0.859715\pi$
$127$	−15.0000	−	15.0000i	−1.33103	−	1.33103i	−0.426589	−	0.904445i	$-0.640285\pi$
$128$		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
$135$	−12.0000	+	4.00000i	−1.03280	+	0.344265i
$136$		0			0
$137$	−12.0000			−1.02523			−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000			−1.02523			−0.512615	+	0.858619i	$0.671323\pi$
$138$		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
$143$	−5.00000	+	1.00000i	−0.418121	+	0.0836242i
$144$		0			0
$145$	−4.00000	+	8.00000i	−0.332182	+	0.664364i
$146$		0			0
$147$	−3.00000	−	3.00000i	−0.247436	−	0.247436i
$148$		0			0
$149$	13.0000	+	13.0000i	1.06500	+	1.06500i	0.997735	+	0.0672664i	$0.0214278\pi$
$149$	13.0000	+	13.0000i	1.06500	+	1.06500i	0.0672664	+	0.997735i	$0.478572\pi$
$150$		0			0
$151$	9.00000	+	9.00000i	0.732410	+	0.732410i	0.971097	−	0.238687i	$-0.0767170\pi$
$151$	9.00000	+	9.00000i	0.732410	+	0.732410i	−0.238687	+	0.971097i	$0.576717\pi$
$152$		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
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$		0			0
$165$	−2.00000	+	4.00000i	−0.155700	+	0.311400i
$166$		0			0
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$		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	$0.548590\pi$
$173$	−15.0000	+	15.0000i	−1.14043	+	1.14043i	−0.988372	+	0.152057i	$0.951410\pi$
$174$		0			0
$175$	6.00000	+	8.00000i	0.453557	+	0.604743i
$176$		0			0
$177$	6.00000			0.450988
$178$		0			0
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$		0			0
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$		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
$187$			10.0000i			0.731272i
$188$		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
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$		0			0
$195$	−11.0000	−	3.00000i	−0.787726	−	0.214834i
$196$		0			0
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		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
$203$		−	8.00000i		−	0.561490i
$204$		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
$213$	−2.00000			−0.137038
$214$		0			0
$215$	−15.0000	+	5.00000i	−1.02299	+	0.340997i
$216$		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
$223$	6.00000			0.401790			0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000			0.401790			0.200895	+	0.979613i	$0.435615\pi$
$224$		0			0
$225$	4.00000	−	3.00000i	0.266667	−	0.200000i
$226$		0			0
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		0			0
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	−0.799248	−	0.601002i	$-0.794768\pi$
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	0.601002	+	0.799248i	$0.294768\pi$
$230$		0			0
$231$		−	4.00000i		−	0.263181i
$232$		0			0
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	0.524097	+	0.851658i	$0.324403\pi$
$234$		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	$-0.146259\pi$
$239$	7.00000	+	7.00000i	0.452792	+	0.452792i	−0.443488	+	0.896280i	$0.646259\pi$
$240$		0			0
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	0.738581	−	0.674165i	$-0.235496\pi$
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	−0.674165	+	0.738581i	$0.735496\pi$
$242$		0			0
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$		0			0
$245$	6.00000	+	3.00000i	0.383326	+	0.191663i
$246$		0			0
$247$	−15.0000	+	3.00000i	−0.954427	+	0.190885i
$248$		0			0
$249$	6.00000	+	6.00000i	0.380235	+	0.380235i
$250$		0			0
$251$		−	30.0000i		−	1.89358i	−0.321847	−	0.946792i	$-0.604304\pi$
$251$		−	30.0000i		−	1.89358i	0.321847	−	0.946792i	$-0.395696\pi$
$252$		0			0
$253$	10.0000			0.628695
$254$		0			0
$255$	−10.0000	+	20.0000i	−0.626224	+	1.25245i
$256$		0			0
$257$	15.0000	+	15.0000i	0.935674	+	0.935674i	0.998053	−	0.0623783i	$-0.0198685\pi$
$257$	15.0000	+	15.0000i	0.935674	+	0.935674i	−0.0623783	+	0.998053i	$0.519869\pi$
$258$		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
$265$	1.00000	+	3.00000i	0.0614295	+	0.184289i
$266$		0			0
$267$	14.0000			0.856786
$268$		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	0.925488	−	0.378777i	$-0.123655\pi$
$271$	9.00000	+	9.00000i	0.546711	+	0.546711i	−0.378777	+	0.925488i	$0.623655\pi$
$272$		0			0
$273$	10.0000	−	2.00000i	0.605228	−	0.121046i
$274$		0			0
$275$	1.00000	−	7.00000i	0.0603023	−	0.422116i
$276$		0			0
$277$	5.00000	+	5.00000i	0.300421	+	0.300421i	0.841178	−	0.540758i	$-0.181862\pi$
$277$	5.00000	+	5.00000i	0.300421	+	0.300421i	−0.540758	+	0.841178i	$0.681862\pi$
$278$		0			0
$279$	1.00000	+	1.00000i	0.0598684	+	0.0598684i
$280$		0			0
$281$	21.0000	+	21.0000i	1.25275	+	1.25275i	0.954480	+	0.298275i	$0.0964112\pi$
$281$	21.0000	+	21.0000i	1.25275	+	1.25275i	0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	−0.994679	−	0.103022i	$-0.967149\pi$
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	0.103022	+	0.994679i	$0.467149\pi$
$284$		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
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$		0			0
$295$	−9.00000	+	3.00000i	−0.524000	+	0.174667i
$296$		0			0
$297$	−8.00000			−0.464207
$298$		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
$305$	−4.00000	−	2.00000i	−0.229039	−	0.114520i
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$		0			0
$309$	−10.0000			−0.568880
$310$		0			0
$311$			10.0000i			0.567048i	0.958965	+	0.283524i	$0.0915036\pi$
$311$			10.0000i			0.567048i	−0.958965	+	0.283524i	$0.908496\pi$
$312$		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
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		0			0
$319$	−4.00000	+	4.00000i	−0.223957	+	0.223957i
$320$		0			0
$321$	−26.0000			−1.45118
$322$		0			0
$323$			30.0000i			1.66924i
$324$		0			0
$325$	18.0000	−	1.00000i	0.998460	−	0.0554700i
$326$		0			0
$327$			26.0000i			1.43780i
$328$		0			0
$329$	4.00000			0.220527
$330$		0			0
$331$	9.00000	−	9.00000i	0.494685	−	0.494685i	−0.415094	−	0.909779i	$-0.636251\pi$
$331$	9.00000	−	9.00000i	0.494685	−	0.494685i	0.909779	+	0.415094i	$0.136251\pi$
$332$		0			0
$333$		−	8.00000i		−	0.438397i
$334$		0			0
$335$	−12.0000	+	24.0000i	−0.655630	+	1.31126i
$336$		0			0
$337$	−5.00000	−	5.00000i	−0.272367	−	0.272367i	0.557685	−	0.830053i	$-0.311690\pi$
$337$	−5.00000	−	5.00000i	−0.272367	−	0.272367i	−0.830053	+	0.557685i	$0.811690\pi$
$338$		0			0
$339$			18.0000i			0.977626i
$340$		0			0
$341$	2.00000			0.108306
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$	20.0000	+	10.0000i	1.07676	+	0.538382i
$346$		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	$-0.786223\pi$
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	0.622240	+	0.782826i	$0.286223\pi$
$350$		0			0
$351$	−4.00000	−	20.0000i	−0.213504	−	1.06752i
$352$		0			0
$353$	−16.0000			−0.851594			−0.425797	−	0.904819i	$-0.640006\pi$
$353$	−16.0000			−0.851594			−0.425797	+	0.904819i	$0.640006\pi$
$354$		0			0
$355$	3.00000	−	1.00000i	0.159223	−	0.0530745i
$356$		0			0
$357$		−	20.0000i		−	1.05851i
$358$		0			0
$359$	13.0000	−	13.0000i	0.686114	−	0.686114i	−0.275257	−	0.961371i	$-0.588763\pi$
$359$	13.0000	−	13.0000i	0.686114	−	0.686114i	0.961371	+	0.275257i	$0.0887629\pi$
$360$		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
$375$	9.00000	−	13.0000i	0.464758	−	0.671317i
$376$		0			0
$377$	−12.0000	−	8.00000i	−0.618031	−	0.412021i
$378$		0			0
$379$	17.0000	+	17.0000i	0.873231	+	0.873231i	0.992823	−	0.119592i	$-0.0381586\pi$
$379$	17.0000	+	17.0000i	0.873231	+	0.873231i	−0.119592	+	0.992823i	$0.538159\pi$
$380$		0			0
$381$		−	30.0000i		−	1.53695i
$382$		0			0
$383$	6.00000			0.306586			0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000			0.306586			0.153293	+	0.988181i	$0.451012\pi$
$384$		0			0
$385$	2.00000	+	6.00000i	0.101929	+	0.305788i
$386$		0			0
$387$	−5.00000	−	5.00000i	−0.254164	−	0.254164i
$388$		0			0
$389$	10.0000			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$390$		0			0
$391$	50.0000			2.52861
$392$		0			0
$393$	−12.0000	−	12.0000i	−0.605320	−	0.605320i
$394$		0			0
$395$	14.0000	−	28.0000i	0.704416	−	1.40883i
$396$		0			0
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$		0			0
$399$		−	12.0000i		−	0.600751i
$400$		0			0
$401$	1.00000	+	1.00000i	0.0499376	+	0.0499376i	0.731635	−	0.681697i	$-0.238758\pi$
$401$	1.00000	+	1.00000i	0.0499376	+	0.0499376i	−0.681697	+	0.731635i	$0.738758\pi$
$402$		0			0
$403$	1.00000	+	5.00000i	0.0498135	+	0.249068i
$404$		0			0
$405$	−10.0000	−	5.00000i	−0.496904	−	0.248452i
$406$		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	$-0.216550\pi$
$409$	3.00000	+	3.00000i	0.148340	+	0.148340i	−0.629036	+	0.777376i	$0.716550\pi$
$410$		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	−0.891552	−	0.452919i	$-0.850383\pi$
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	0.452919	+	0.891552i	$0.350383\pi$
$422$		0			0
$423$		−	2.00000i		−	0.0972433i
$424$		0			0
$425$	5.00000	−	35.0000i	0.242536	−	1.69775i
$426$		0			0
$427$	4.00000			0.193574
$428$		0			0
$429$	−6.00000	−	4.00000i	−0.289683	−	0.193122i
$430$		0			0
$431$	−21.0000	+	21.0000i	−1.01153	+	1.01153i	−0.0116017	+	0.999933i	$0.503693\pi$
$431$	−21.0000	+	21.0000i	−1.01153	+	1.01153i	−0.999933	+	0.0116017i	$0.996307\pi$
$432$		0			0
$433$	15.0000	−	15.0000i	0.720854	−	0.720854i	−0.247925	−	0.968779i	$-0.579749\pi$
$433$	15.0000	−	15.0000i	0.720854	−	0.720854i	0.968779	+	0.247925i	$0.0797487\pi$
$434$		0			0
$435$	−12.0000	+	4.00000i	−0.575356	+	0.191785i
$436$		0			0
$437$	30.0000			1.43509
$438$		0			0
$439$	40.0000			1.90910			0.954548	−	0.298057i	$-0.0963387\pi$
$439$	40.0000			1.90910			0.954548	+	0.298057i	$0.0963387\pi$
$440$		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
$447$			26.0000i			1.22976i
$448$		0			0
$449$	7.00000	−	7.00000i	0.330350	−	0.330350i	−0.522369	−	0.852720i	$-0.674952\pi$
$449$	7.00000	−	7.00000i	0.330350	−	0.330350i	0.852720	+	0.522369i	$0.174952\pi$
$450$		0			0
$451$	−2.00000			−0.0941763
$452$		0			0
$453$			18.0000i			0.845714i
$454$		0			0
$455$	−14.0000	+	8.00000i	−0.656330	+	0.375046i
$456$		0			0
$457$		−	38.0000i		−	1.77757i	−0.458329	−	0.888783i	$-0.651552\pi$
$457$		−	38.0000i		−	1.77757i	0.458329	−	0.888783i	$-0.348448\pi$
$458$		0			0
$459$	−40.0000			−1.86704
$460$		0			0
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	−0.402916	−	0.915237i	$-0.632003\pi$
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	0.915237	+	0.402916i	$0.132003\pi$
$462$		0			0
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$		0			0
$465$	4.00000	+	2.00000i	0.185496	+	0.0927478i
$466$		0			0
$467$	−5.00000	−	5.00000i	−0.231372	−	0.231372i	0.581893	−	0.813265i	$-0.302312\pi$
$467$	−5.00000	−	5.00000i	−0.231372	−	0.231372i	−0.813265	+	0.581893i	$0.802312\pi$
$468$		0			0
$469$		−	24.0000i		−	1.10822i
$470$		0			0
$471$	6.00000			0.276465
$472$		0			0
$473$	−10.0000			−0.459800
$474$		0			0
$475$	3.00000	−	21.0000i	0.137649	−	0.963546i
$476$		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	$-0.612026\pi$
$479$	13.0000	−	13.0000i	0.593985	−	0.593985i	0.938705	+	0.344720i	$0.112026\pi$
$480$		0			0
$481$	16.0000	−	24.0000i	0.729537	−	1.09431i
$482$		0			0
$483$	−20.0000			−0.910032
$484$		0			0
$485$	2.00000	−	4.00000i	0.0908153	−	0.181631i
$486$		0			0
$487$		−	32.0000i		−	1.45006i	−0.688718	−	0.725029i	$-0.741826\pi$
$487$		−	32.0000i		−	1.45006i	0.688718	−	0.725029i	$-0.258174\pi$
$488$		0			0
$489$	4.00000	−	4.00000i	0.180886	−	0.180886i
$490$		0			0
$491$			10.0000i			0.451294i	0.974209	+	0.225647i	$0.0724495\pi$
$491$			10.0000i			0.451294i	−0.974209	+	0.225647i	$0.927550\pi$
$492$		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	−0.999548	−	0.0300737i	$-0.990426\pi$
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.0300737	−	0.999548i	$-0.509574\pi$
$500$		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
$507$	7.00000	−	17.0000i	0.310881	−	0.754997i
$508$		0			0
$509$	13.0000	+	13.0000i	0.576215	+	0.576215i	0.933858	−	0.357643i	$-0.116420\pi$
$509$	13.0000	+	13.0000i	0.576215	+	0.576215i	−0.357643	+	0.933858i	$0.616420\pi$
$510$		0			0
$511$		−	12.0000i		−	0.530849i
$512$		0			0
$513$	−24.0000			−1.05963
$514$		0			0
$515$	15.0000	−	5.00000i	0.660979	−	0.220326i
$516$		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
$525$	−2.00000	+	14.0000i	−0.0872872	+	0.611010i
$526$		0			0
$527$	10.0000			0.435607
$528$		0			0
$529$		−	27.0000i		−	1.17391i
$530$		0			0
$531$	−3.00000	−	3.00000i	−0.130189	−	0.130189i
$532$		0			0
$533$	−1.00000	−	5.00000i	−0.0433148	−	0.216574i
$534$		0			0
$535$	39.0000	−	13.0000i	1.68612	−	0.562039i
$536$		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	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$		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
$553$			28.0000i			1.19068i
$554$		0			0
$555$	−8.00000	−	24.0000i	−0.339581	−	1.01874i
$556$		0			0
$557$	8.00000			0.338971			0.169485	−	0.985533i	$-0.445789\pi$
$557$	8.00000			0.338971			0.169485	+	0.985533i	$0.445789\pi$
$558$		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	−0.593851	−	0.804575i	$-0.702393\pi$
$563$	5.00000	−	5.00000i	0.210725	−	0.210725i	0.804575	+	0.593851i	$0.202393\pi$
$564$		0			0
$565$	−9.00000	−	27.0000i	−0.378633	−	1.13590i
$566$		0			0
$567$	10.0000			0.419961
$568$		0			0
$569$	10.0000			0.419222			0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000			0.419222			0.209611	+	0.977785i	$0.432780\pi$
$570$		0			0
$571$			10.0000i			0.418487i	0.977864	+	0.209243i	$0.0671001\pi$
$571$			10.0000i			0.418487i	−0.977864	+	0.209243i	$0.932900\pi$
$572$		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
$577$			22.0000i			0.915872i	0.888985	+	0.457936i	$0.151411\pi$
$577$			22.0000i			0.915872i	−0.888985	+	0.457936i	$0.848589\pi$
$578$		0			0
$579$	−14.0000	+	14.0000i	−0.581820	+	0.581820i
$580$		0			0
$581$	12.0000			0.497844
$582$		0			0
$583$			2.00000i			0.0828315i
$584$		0			0
$585$	4.00000	+	7.00000i	0.165380	+	0.289414i
$586$		0			0
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$		0			0
$591$	18.0000	−	18.0000i	0.740421	−	0.740421i
$592$		0			0
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$		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
$603$	−12.0000			−0.488678
$604$		0			0
$605$	−9.00000	+	18.0000i	−0.365902	+	0.731804i
$606$		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
$613$	4.00000			0.161558			0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000			0.161558			0.0807792	+	0.996732i	$0.474259\pi$
$614$		0			0
$615$	−4.00000	−	2.00000i	−0.161296	−	0.0806478i
$616$		0			0
$617$		−	38.0000i		−	1.52982i	−0.644136	−	0.764911i	$-0.722783\pi$
$617$		−	38.0000i		−	1.52982i	0.644136	−	0.764911i	$-0.277217\pi$
$618$		0			0
$619$	3.00000	−	3.00000i	0.120580	−	0.120580i	−0.644242	−	0.764822i	$-0.722827\pi$
$619$	3.00000	−	3.00000i	0.120580	−	0.120580i	0.764822	+	0.644242i	$0.222827\pi$
$620$		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	0.453403	−	0.891306i	$-0.350210\pi$
$631$	−11.0000	−	11.0000i	−0.437903	−	0.437903i	−0.891306	+	0.453403i	$0.850210\pi$
$632$		0			0
$633$	−12.0000	−	12.0000i	−0.476957	−	0.476957i
$634$		0			0
$635$	15.0000	+	45.0000i	0.595257	+	1.78577i
$636$		0			0
$637$	−6.00000	+	9.00000i	−0.237729	+	0.356593i
$638$		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
$643$	46.0000			1.81406			0.907031	−	0.421063i	$-0.138343\pi$
$643$	46.0000			1.81406			0.907031	+	0.421063i	$0.138343\pi$
$644$		0			0
$645$	−20.0000	−	10.0000i	−0.787499	−	0.393750i
$646$		0			0
$647$	5.00000	+	5.00000i	0.196570	+	0.196570i	0.798528	−	0.601958i	$-0.205612\pi$
$647$	5.00000	+	5.00000i	0.196570	+	0.196570i	−0.601958	+	0.798528i	$0.705612\pi$
$648$		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
$655$	24.0000	+	12.0000i	0.937758	+	0.468879i
$656$		0			0
$657$	−6.00000			−0.234082
$658$		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	0.972387	+	0.233373i	$0.0749763\pi$
$661$	31.0000	+	31.0000i	1.20576	+	1.20576i	0.233373	+	0.972387i	$0.425024\pi$
$662$		0			0
$663$	−30.0000	−	20.0000i	−1.16510	−	0.776736i
$664$		0			0
$665$	6.00000	+	18.0000i	0.232670	+	0.698010i
$666$		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	−0.796877	−	0.604141i	$-0.793516\pi$
$673$	−5.00000	+	5.00000i	−0.192736	+	0.192736i	0.604141	+	0.796877i	$0.293516\pi$
$674$		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
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$		0			0
$685$	24.0000	+	12.0000i	0.916993	+	0.458496i
$686$		0			0
$687$	−6.00000			−0.228914
$688$		0			0
$689$	−5.00000	+	1.00000i	−0.190485	+	0.0380970i
$690$		0			0
$691$	9.00000	−	9.00000i	0.342376	−	0.342376i	−0.514884	−	0.857260i	$-0.672165\pi$
$691$	9.00000	−	9.00000i	0.342376	−	0.342376i	0.857260	+	0.514884i	$0.172165\pi$
$692$		0			0
$693$	−2.00000	+	2.00000i	−0.0759737	+	0.0759737i
$694$		0			0
$695$	14.0000	−	28.0000i	0.531050	−	1.06210i
$696$		0			0
$697$	−10.0000			−0.378777
$698$		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	$-0.775386\pi$
$709$	−3.00000	+	3.00000i	−0.112667	+	0.112667i	0.648526	+	0.761193i	$0.275386\pi$
$710$		0			0
$711$	14.0000			0.525041
$712$		0			0
$713$		−	10.0000i		−	0.374503i
$714$		0			0
$715$	11.0000	+	3.00000i	0.411377	+	0.112194i
$716$		0			0
$717$			14.0000i			0.522840i
$718$		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
$723$			2.00000i			0.0743808i
$724$		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	$-0.879900\pi$
$727$	−35.0000	−	35.0000i	−1.29808	−	1.29808i	−0.368418	−	0.929660i	$-0.620100\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	−50.0000			−1.84932
$732$		0			0
$733$	44.0000			1.62518			0.812589	−	0.582838i	$-0.198058\pi$
$733$	44.0000			1.62518			0.812589	+	0.582838i	$0.198058\pi$
$734$		0			0
$735$	3.00000	+	9.00000i	0.110657	+	0.331970i
$736$		0			0
$737$	−12.0000	+	12.0000i	−0.442026	+	0.442026i
$738$		0			0
$739$	−37.0000	+	37.0000i	−1.36107	+	1.36107i	−0.488507	+	0.872560i	$0.662458\pi$
$739$	−37.0000	+	37.0000i	−1.36107	+	1.36107i	−0.872560	+	0.488507i	$0.837542\pi$
$740$		0			0
$741$	−18.0000	−	12.0000i	−0.661247	−	0.440831i
$742$		0			0
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	−13.0000	−	39.0000i	−0.476283	−	1.42885i
$746$		0			0
$747$		−	6.00000i		−	0.219529i
$748$		0			0
$749$	−26.0000	+	26.0000i	−0.950019	+	0.950019i
$750$		0			0
$751$			10.0000i			0.364905i	0.983215	+	0.182453i	$0.0584036\pi$
$751$			10.0000i			0.364905i	−0.983215	+	0.182453i	$0.941596\pi$
$752$		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	0.273206	−	0.961956i	$-0.411916\pi$
$761$	−19.0000	−	19.0000i	−0.688749	−	0.688749i	−0.961956	+	0.273206i	$0.911916\pi$
$762$		0			0
$763$	26.0000	+	26.0000i	0.941263	+	0.941263i
$764$		0			0
$765$	15.0000	−	5.00000i	0.542326	−	0.180775i
$766$		0			0
$767$	−3.00000	−	15.0000i	−0.108324	−	0.541619i
$768$		0			0
$769$	23.0000	+	23.0000i	0.829401	+	0.829401i	0.987434	−	0.158033i	$-0.0505151\pi$
$769$	23.0000	+	23.0000i	0.829401	+	0.829401i	−0.158033	+	0.987434i	$0.550515\pi$
$770$		0			0
$771$			30.0000i			1.08042i
$772$		0			0
$773$	24.0000			0.863220			0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000			0.863220			0.431610	+	0.902060i	$0.357946\pi$
$774$		0			0
$775$	−7.00000	−	1.00000i	−0.251447	−	0.0359211i
$776$		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
$785$	−9.00000	+	3.00000i	−0.321224	+	0.107075i
$786$		0			0
$787$	42.0000			1.49714			0.748569	−	0.663057i	$-0.230741\pi$
$787$	42.0000			1.49714			0.748569	+	0.663057i	$0.230741\pi$
$788$		0			0
$789$		−	18.0000i		−	0.640817i
$790$		0			0
$791$	18.0000	+	18.0000i	0.640006	+	0.640006i
$792$		0			0
$793$	4.00000	−	6.00000i	0.142044	−	0.213066i
$794$		0			0
$795$	−2.00000	+	4.00000i	−0.0709327	+	0.141865i
$796$		0			0
$797$	5.00000	+	5.00000i	0.177109	+	0.177109i	0.790094	−	0.612985i	$-0.210032\pi$
$797$	5.00000	+	5.00000i	0.177109	+	0.177109i	−0.612985	+	0.790094i	$0.710032\pi$
$798$		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	−0.873352	−	0.487090i	$-0.838058\pi$
$811$	−11.0000	+	11.0000i	−0.386262	+	0.386262i	0.487090	+	0.873352i	$0.338058\pi$
$812$		0			0
$813$			18.0000i			0.631288i
$814$		0			0
$815$	−4.00000	+	8.00000i	−0.140114	+	0.280228i
$816$		0			0
$817$	−30.0000			−1.04957
$818$		0			0
$819$	−6.00000	−	4.00000i	−0.209657	−	0.139771i
$820$		0			0
$821$	−29.0000	+	29.0000i	−1.01211	+	1.01211i	−0.0121812	+	0.999926i	$0.503877\pi$
$821$	−29.0000	+	29.0000i	−1.01211	+	1.01211i	−0.999926	+	0.0121812i	$0.996123\pi$
$822$		0			0
$823$	15.0000	−	15.0000i	0.522867	−	0.522867i	−0.395569	−	0.918436i	$-0.629453\pi$
$823$	15.0000	−	15.0000i	0.522867	−	0.522867i	0.918436	+	0.395569i	$0.129453\pi$
$824$		0			0
$825$	8.00000	−	6.00000i	0.278524	−	0.208893i
$826$		0			0
$827$	2.00000			0.0695468			0.0347734	−	0.999395i	$-0.488929\pi$
$827$	2.00000			0.0695468			0.0347734	+	0.999395i	$0.488929\pi$
$828$		0			0
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$		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
$837$			8.00000i			0.276520i
$838$		0			0
$839$	13.0000	−	13.0000i	0.448810	−	0.448810i	−0.446149	−	0.894959i	$-0.647205\pi$
$839$	13.0000	−	13.0000i	0.448810	−	0.448810i	0.894959	+	0.446149i	$0.147205\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$		0			0
$843$			42.0000i			1.44656i
$844$		0			0
$845$	−2.00000	+	29.0000i	−0.0688021	+	0.997630i
$846$		0			0
$847$		−	18.0000i		−	0.618487i
$848$		0			0
$849$	−30.0000			−1.02960
$850$		0			0
$851$	−40.0000	+	40.0000i	−1.37118	+	1.37118i
$852$		0			0
$853$		−	26.0000i		−	0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$		−	26.0000i		−	0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$		0			0
$855$	9.00000	−	3.00000i	0.307794	−	0.102598i
$856$		0			0
$857$	−5.00000	−	5.00000i	−0.170797	−	0.170797i	0.616533	−	0.787329i	$-0.288537\pi$
$857$	−5.00000	−	5.00000i	−0.170797	−	0.170797i	−0.787329	+	0.616533i	$0.788537\pi$
$858$		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
$863$	46.0000			1.56586			0.782929	−	0.622111i	$-0.213725\pi$
$863$	46.0000			1.56586			0.782929	+	0.622111i	$0.213725\pi$
$864$		0			0
$865$	45.0000	−	15.0000i	1.53005	−	0.510015i
$866$		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
$873$	2.00000			0.0676897
$874$		0			0
$875$	−4.00000	−	22.0000i	−0.135225	−	0.743736i
$876$		0			0
$877$		−	18.0000i		−	0.607817i	−0.952701	−	0.303908i	$-0.901708\pi$
$877$		−	18.0000i		−	0.607817i	0.952701	−	0.303908i	$-0.0982917\pi$
$878$		0			0
$879$	26.0000	−	26.0000i	0.876958	−	0.876958i
$880$		0			0
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$		0			0
$883$	5.00000	−	5.00000i	0.168263	−	0.168263i	−0.617952	−	0.786216i	$-0.712037\pi$
$883$	5.00000	−	5.00000i	0.168263	−	0.168263i	0.786216	+	0.617952i	$0.212037\pi$
$884$		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
$895$	−40.0000	−	20.0000i	−1.33705	−	0.668526i
$896$		0			0
$897$	−20.0000	+	30.0000i	−0.667781	+	1.00167i
$898$		0			0
$899$	4.00000	+	4.00000i	0.133407	+	0.133407i
$900$		0			0
$901$			10.0000i			0.333148i
$902$		0			0
$903$	20.0000			0.665558
$904$		0			0
$905$	−20.0000	+	40.0000i	−0.664822	+	1.32964i
$906$		0			0
$907$	35.0000	+	35.0000i	1.16216	+	1.16216i	0.984003	+	0.178153i	$0.0570122\pi$
$907$	35.0000	+	35.0000i	1.16216	+	1.16216i	0.178153	+	0.984003i	$0.442988\pi$
$908$		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
$915$	−2.00000	−	6.00000i	−0.0661180	−	0.198354i
$916$		0			0
$917$	−24.0000			−0.792550
$918$		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
$923$	1.00000	+	5.00000i	0.0329154	+	0.164577i
$924$		0			0
$925$	24.0000	+	32.0000i	0.789115	+	1.05215i
$926$		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	$-0.379044\pi$
$929$	−17.0000	−	17.0000i	−0.557752	−	0.557752i	−0.928667	+	0.370915i	$0.879044\pi$
$930$		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	−0.998583	−	0.0532103i	$-0.983055\pi$
$941$	−29.0000	+	29.0000i	−0.945373	+	0.945373i	0.0532103	+	0.998583i	$0.483055\pi$
$942$		0			0
$943$			10.0000i			0.325645i
$944$		0			0
$945$	−24.0000	+	8.00000i	−0.780720	+	0.260240i
$946$		0			0
$947$	−38.0000			−1.23483			−0.617417	−	0.786636i	$-0.711821\pi$
$947$	−38.0000			−1.23483			−0.617417	+	0.786636i	$0.711821\pi$
$948$		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	$-0.453934\pi$
$953$	35.0000	−	35.0000i	1.13376	−	1.13376i	0.989546	−	0.144215i	$-0.0460656\pi$
$954$		0			0
$955$	−16.0000	−	8.00000i	−0.517748	−	0.258874i
$956$		0			0
$957$	−8.00000			−0.258603
$958$		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
$967$			48.0000i			1.54358i	0.635880	+	0.771788i	$0.280637\pi$
$967$			48.0000i			1.54358i	−0.635880	+	0.771788i	$0.719363\pi$
$968$		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
$973$			28.0000i			0.897639i
$974$		0			0
$975$	19.0000	+	17.0000i	0.608487	+	0.544436i
$976$		0			0
$977$			22.0000i			0.703842i	0.936030	+	0.351921i	$0.114471\pi$
$977$			22.0000i			0.703842i	−0.936030	+	0.351921i	$0.885529\pi$
$978$		0			0
$979$	−14.0000			−0.447442
$980$		0			0
$981$	13.0000	−	13.0000i	0.415058	−	0.415058i
$982$		0			0
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$		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
$993$	18.0000			0.571213
$994$		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.cd.e.993.1		2
4.3	odd	2		130.2.j.b.83.1	yes	2
5.2	odd	4		1040.2.bg.f.577.1		2
12.11	even	2		1170.2.w.c.343.1		2
13.8	odd	4		1040.2.bg.f.593.1		2
20.3	even	4		650.2.g.b.57.1		2
20.7	even	4		130.2.g.c.57.1	✓	2
20.19	odd	2		650.2.j.d.343.1		2
52.47	even	4		130.2.g.c.73.1	yes	2
60.47	odd	4		1170.2.m.a.577.1		2
65.47	even	4	inner	1040.2.cd.e.177.1		2
156.47	odd	4		1170.2.m.a.73.1		2
260.47	odd	4		130.2.j.b.47.1	yes	2
260.99	even	4		650.2.g.b.593.1		2
260.203	odd	4		650.2.j.d.307.1		2
780.47	even	4		1170.2.w.c.307.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.c.57.1	✓	2	20.7	even	4
130.2.g.c.73.1	yes	2	52.47	even	4
130.2.j.b.47.1	yes	2	260.47	odd	4
130.2.j.b.83.1	yes	2	4.3	odd	2
650.2.g.b.57.1		2	20.3	even	4
650.2.g.b.593.1		2	260.99	even	4
650.2.j.d.307.1		2	260.203	odd	4
650.2.j.d.343.1		2	20.19	odd	2
1040.2.bg.f.577.1		2	5.2	odd	4
1040.2.bg.f.593.1		2	13.8	odd	4
1040.2.cd.e.177.1		2	65.47	even	4	inner
1040.2.cd.e.993.1		2	1.1	even	1	trivial
1170.2.m.a.73.1		2	156.47	odd	4
1170.2.m.a.577.1		2	60.47	odd	4
1170.2.w.c.307.1		2	780.47	even	4
1170.2.w.c.343.1		2	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{3} +(-2.00000 - 1.00000i) q^{5} +2.00000 q^{7} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +(2.00000 - 3.00000i) q^{13} +(-1.00000 - 3.00000i) q^{15} +(-5.00000 - 5.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +(-5.00000 + 5.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} -4.00000i q^{29} +(-1.00000 + 1.00000i) q^{31} -2.00000i q^{33} +(-4.00000 - 2.00000i) q^{35} +8.00000 q^{37} +(5.00000 - 1.00000i) q^{39} +(1.00000 - 1.00000i) q^{41} +(5.00000 - 5.00000i) q^{43} +(-1.00000 + 2.00000i) q^{45} +2.00000 q^{47} -3.00000 q^{49} -10.0000i q^{51} +(-1.00000 - 1.00000i) q^{53} +(1.00000 + 3.00000i) q^{55} -6.00000i q^{57} +(3.00000 - 3.00000i) q^{59} +2.00000 q^{61} -2.00000i q^{63} +(-7.00000 + 4.00000i) q^{65} -12.0000i q^{67} -10.0000 q^{69} +(-1.00000 + 1.00000i) q^{71} -6.00000i q^{73} +(-1.00000 + 7.00000i) q^{75} +(-2.00000 - 2.00000i) q^{77} +14.0000i q^{79} +5.00000 q^{81} +6.00000 q^{83} +(5.00000 + 15.0000i) q^{85} +(4.00000 - 4.00000i) q^{87} +(7.00000 - 7.00000i) q^{89} +(4.00000 - 6.00000i) q^{91} -2.00000 q^{93} +(3.00000 + 9.00000i) q^{95} +2.00000i q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 4 q^{5} + 4 q^{7} - 2 q^{11} + 4 q^{13} - 2 q^{15} - 10 q^{17} - 6 q^{19} + 4 q^{21} - 10 q^{23} + 6 q^{25} + 8 q^{27} - 2 q^{31} - 8 q^{35} + 16 q^{37} + 10 q^{39} + 2 q^{41} + 10 q^{43}+ \cdots - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 4 * q^5 + 4 * q^7 - 2 * q^11 + 4 * q^13 - 2 * q^15 - 10 * q^17 - 6 * q^19 + 4 * q^21 - 10 * q^23 + 6 * q^25 + 8 * q^27 - 2 * q^31 - 8 * q^35 + 16 * q^37 + 10 * q^39 + 2 * q^41 + 10 * q^43 - 2 * q^45 + 4 * q^47 - 6 * q^49 - 2 * q^53 + 2 * q^55 + 6 * q^59 + 4 * q^61 - 14 * q^65 - 20 * q^69 - 2 * q^71 - 2 * q^75 - 4 * q^77 + 10 * q^81 + 12 * q^83 + 10 * q^85 + 8 * q^87 + 14 * q^89 + 8 * q^91 - 4 * q^93 + 6 * q^95 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more