LMFDB - Embedded newform 650.2.j.d.343.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(307,650)] 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("650.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,2,-2,0,-2,4] 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	650.343
Dual form			650.2.j.d.307.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(1.00000 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 + 1.00000i) q^{6} +2.00000 q^{7} -1.00000i q^{8} -1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{12} +(-2.00000 + 3.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(5.00000 + 5.00000i) q^{17} +1.00000 q^{18} +(3.00000 + 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(-5.00000 + 5.00000i) q^{23} +(1.00000 - 1.00000i) q^{24} +(-3.00000 - 2.00000i) q^{26} +(4.00000 - 4.00000i) q^{27} -2.00000 q^{28} -4.00000i q^{29} +(1.00000 - 1.00000i) q^{31} +1.00000i q^{32} +2.00000i q^{33} +(-5.00000 + 5.00000i) q^{34} +1.00000i q^{36} -8.00000 q^{37} +(-3.00000 + 3.00000i) q^{38} +(-5.00000 + 1.00000i) q^{39} +(1.00000 - 1.00000i) q^{41} +(-2.00000 + 2.00000i) q^{42} +(5.00000 - 5.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(-5.00000 - 5.00000i) q^{46} +2.00000 q^{47} +(1.00000 + 1.00000i) q^{48} -3.00000 q^{49} +10.0000i q^{51} +(2.00000 - 3.00000i) q^{52} +(1.00000 + 1.00000i) q^{53} +(4.00000 + 4.00000i) q^{54} -2.00000i q^{56} +6.00000i q^{57} +4.00000 q^{58} +(-3.00000 + 3.00000i) q^{59} +2.00000 q^{61} +(1.00000 + 1.00000i) q^{62} -2.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} -12.0000i q^{67} +(-5.00000 - 5.00000i) q^{68} -10.0000 q^{69} +(1.00000 - 1.00000i) q^{71} -1.00000 q^{72} +6.00000i q^{73} -8.00000i q^{74} +(-3.00000 - 3.00000i) q^{76} +(2.00000 + 2.00000i) q^{77} +(-1.00000 - 5.00000i) q^{78} -14.0000i q^{79} +5.00000 q^{81} +(1.00000 + 1.00000i) q^{82} +6.00000 q^{83} +(-2.00000 - 2.00000i) q^{84} +(5.00000 + 5.00000i) q^{86} +(4.00000 - 4.00000i) q^{87} +(1.00000 - 1.00000i) q^{88} +(7.00000 - 7.00000i) q^{89} +(-4.00000 + 6.00000i) q^{91} +(5.00000 - 5.00000i) q^{92} +2.00000 q^{93} +2.00000i q^{94} +(-1.00000 + 1.00000i) q^{96} -2.00000i q^{97} -3.00000i q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{16} + 10 q^{17} + 2 q^{18} + 6 q^{19} + 4 q^{21} - 2 q^{22} - 10 q^{23} + 2 q^{24} - 6 q^{26} + 8 q^{27} - 4 q^{28} + 2 q^{31}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 2 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^16 + 10 * q^17 + 2 * q^18 + 6 * q^19 + 4 * q^21 - 2 * q^22 - 10 * q^23 + 2 * q^24 - 6 * q^26 + 8 * q^27 - 4 * q^28 + 2 * q^31 - 10 * q^34 - 16 * q^37 - 6 * q^38 - 10 * q^39 + 2 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 10 * q^46 + 4 * q^47 + 2 * q^48 - 6 * q^49 + 4 * q^52 + 2 * q^53 + 8 * q^54 + 8 * q^58 - 6 * q^59 + 4 * q^61 + 2 * q^62 - 2 * q^64 - 4 * q^66 - 10 * q^68 - 20 * q^69 + 2 * q^71 - 2 * q^72 - 6 * q^76 + 4 * q^77 - 2 * q^78 + 10 * q^81 + 2 * q^82 + 12 * q^83 - 4 * q^84 + 10 * q^86 + 8 * q^87 + 2 * q^88 + 14 * q^89 - 8 * q^91 + 10 * q^92 + 4 * q^93 - 2 * q^96 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	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	$0.616140\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.00000	+	1.00000i	−0.408248	+	0.408248i
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$	−1.00000	−	1.00000i	−0.288675	−	0.288675i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$			2.00000i			0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	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	$0.422021\pi$
$18$	1.00000			0.235702
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	0.961844	−	0.273597i	$-0.0882135\pi$
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	−0.273597	+	0.961844i	$0.588214\pi$
$20$		0			0
$21$	2.00000	+	2.00000i	0.436436	+	0.436436i
$22$	−1.00000	+	1.00000i	−0.213201	+	0.213201i
$23$	−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	$0.986143\pi$
$24$	1.00000	−	1.00000i	0.204124	−	0.204124i
$25$		0			0
$26$	−3.00000	−	2.00000i	−0.588348	−	0.392232i
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$	−2.00000			−0.377964
$29$		−	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	$-0.709465\pi$
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	0.791184	+	0.611578i	$0.209465\pi$
$32$			1.00000i			0.176777i
$33$			2.00000i			0.348155i
$34$	−5.00000	+	5.00000i	−0.857493	+	0.857493i
$35$		0			0
$36$			1.00000i			0.166667i
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	−3.00000	+	3.00000i	−0.486664	+	0.486664i
$39$	−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	$0.214777\pi$
$42$	−2.00000	+	2.00000i	−0.308607	+	0.308607i
$43$	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	$0.0687403\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$		0			0
$46$	−5.00000	−	5.00000i	−0.737210	−	0.737210i
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	1.00000	+	1.00000i	0.144338	+	0.144338i
$49$	−3.00000			−0.428571
$50$		0			0
$51$			10.0000i			1.40028i
$52$	2.00000	−	3.00000i	0.277350	−	0.416025i
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$	4.00000	+	4.00000i	0.544331	+	0.544331i
$55$		0			0
$56$		−	2.00000i		−	0.267261i
$57$			6.00000i			0.794719i
$58$	4.00000			0.525226
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	−0.874889	−	0.484323i	$-0.839066\pi$
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	0.484323	+	0.874889i	$0.339066\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	1.00000	+	1.00000i	0.127000	+	0.127000i
$63$		−	2.00000i		−	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−2.00000			−0.246183
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$	−5.00000	−	5.00000i	−0.606339	−	0.606339i
$69$	−10.0000			−1.20386
$70$		0			0
$71$	1.00000	−	1.00000i	0.118678	−	0.118678i	−0.645273	−	0.763952i	$-0.723257\pi$
$71$	1.00000	−	1.00000i	0.118678	−	0.118678i	0.763952	+	0.645273i	$0.223257\pi$
$72$	−1.00000			−0.117851
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$		−	8.00000i		−	0.929981i
$75$		0			0
$76$	−3.00000	−	3.00000i	−0.344124	−	0.344124i
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$	−1.00000	−	5.00000i	−0.113228	−	0.566139i
$79$		−	14.0000i		−	1.57512i	−0.616236	−	0.787562i	$-0.711343\pi$
$79$		−	14.0000i		−	1.57512i	0.616236	−	0.787562i	$-0.288657\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$	1.00000	+	1.00000i	0.110432	+	0.110432i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−2.00000	−	2.00000i	−0.218218	−	0.218218i
$85$		0			0
$86$	5.00000	+	5.00000i	0.539164	+	0.539164i
$87$	4.00000	−	4.00000i	0.428845	−	0.428845i
$88$	1.00000	−	1.00000i	0.106600	−	0.106600i
$89$	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
$92$	5.00000	−	5.00000i	0.521286	−	0.521286i
$93$	2.00000			0.207390
$94$			2.00000i			0.206284i
$95$		0			0
$96$	−1.00000	+	1.00000i	−0.102062	+	0.102062i
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$		−	3.00000i		−	0.303046i
$99$	1.00000	−	1.00000i	0.100504	−	0.100504i
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	−10.0000			−0.990148
$103$	−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	$0.363264\pi$
$104$	3.00000	+	2.00000i	0.294174	+	0.196116i
$105$		0			0
$106$	−1.00000	+	1.00000i	−0.0971286	+	0.0971286i
$107$	−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	$0.901636\pi$
$108$	−4.00000	+	4.00000i	−0.384900	+	0.384900i
$109$	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
$112$	2.00000			0.188982
$113$	−9.00000	−	9.00000i	−0.846649	−	0.846649i	0.143065	−	0.989713i	$-0.454304\pi$
$113$	−9.00000	−	9.00000i	−0.846649	−	0.846649i	−0.989713	+	0.143065i	$0.954304\pi$
$114$	−6.00000			−0.561951
$115$		0			0
$116$			4.00000i			0.371391i
$117$	3.00000	+	2.00000i	0.277350	+	0.184900i
$118$	−3.00000	−	3.00000i	−0.276172	−	0.276172i
$119$	10.0000	+	10.0000i	0.916698	+	0.916698i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$			2.00000i			0.181071i
$123$	2.00000			0.180334
$124$	−1.00000	+	1.00000i	−0.0898027	+	0.0898027i
$125$		0			0
$126$	2.00000			0.178174
$127$	−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	$-0.640285\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	10.0000			0.880451
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		−	2.00000i		−	0.174078i
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$	12.0000			1.03664
$135$		0			0
$136$	5.00000	−	5.00000i	0.428746	−	0.428746i
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$		−	10.0000i		−	0.851257i
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$		0			0
$141$	2.00000	+	2.00000i	0.168430	+	0.168430i
$142$	1.00000	+	1.00000i	0.0839181	+	0.0839181i
$143$	−5.00000	+	1.00000i	−0.418121	+	0.0836242i
$144$		−	1.00000i		−	0.0833333i
$145$		0			0
$146$	−6.00000			−0.496564
$147$	−3.00000	−	3.00000i	−0.247436	−	0.247436i
$148$	8.00000			0.657596
$149$	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	0.238687	−	0.971097i	$-0.423283\pi$
$151$	−9.00000	−	9.00000i	−0.732410	−	0.732410i	−0.971097	+	0.238687i	$0.923283\pi$
$152$	3.00000	−	3.00000i	0.243332	−	0.243332i
$153$	5.00000	−	5.00000i	0.404226	−	0.404226i
$154$	−2.00000	+	2.00000i	−0.161165	+	0.161165i
$155$		0			0
$156$	5.00000	−	1.00000i	0.400320	−	0.0800641i
$157$	−3.00000	+	3.00000i	−0.239426	+	0.239426i	−0.816612	−	0.577186i	$-0.804151\pi$
$157$	−3.00000	+	3.00000i	−0.239426	+	0.239426i	0.577186	+	0.816612i	$0.304151\pi$
$158$	14.0000			1.11378
$159$			2.00000i			0.158610i
$160$		0			0
$161$	−10.0000	+	10.0000i	−0.788110	+	0.788110i
$162$			5.00000i			0.392837i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−1.00000	+	1.00000i	−0.0780869	+	0.0780869i
$165$		0			0
$166$			6.00000i			0.465690i
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$	2.00000	−	2.00000i	0.154303	−	0.154303i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$		0			0
$171$	3.00000	−	3.00000i	0.229416	−	0.229416i
$172$	−5.00000	+	5.00000i	−0.381246	+	0.381246i
$173$	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	$-0.0485898\pi$
$174$	4.00000	+	4.00000i	0.303239	+	0.303239i
$175$		0			0
$176$	1.00000	+	1.00000i	0.0753778	+	0.0753778i
$177$	−6.00000			−0.450988
$178$	7.00000	+	7.00000i	0.524672	+	0.524672i
$179$	−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	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$	−6.00000	−	4.00000i	−0.444750	−	0.296500i
$183$	2.00000	+	2.00000i	0.147844	+	0.147844i
$184$	5.00000	+	5.00000i	0.368605	+	0.368605i
$185$		0			0
$186$			2.00000i			0.146647i
$187$			10.0000i			0.731272i
$188$	−2.00000			−0.145865
$189$	8.00000	−	8.00000i	0.581914	−	0.581914i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	−1.00000	−	1.00000i	−0.0721688	−	0.0721688i
$193$		−	14.0000i		−	1.00774i	−0.863779	−	0.503871i	$-0.831909\pi$
$193$		−	14.0000i		−	1.00774i	0.863779	−	0.503871i	$-0.168091\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$	1.00000	+	1.00000i	0.0710669	+	0.0710669i
$199$		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
$204$		−	10.0000i		−	0.700140i
$205$		0			0
$206$	−5.00000	−	5.00000i	−0.348367	−	0.348367i
$207$	5.00000	+	5.00000i	0.347524	+	0.347524i
$208$	−2.00000	+	3.00000i	−0.138675	+	0.208013i
$209$			6.00000i			0.415029i
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−1.00000	−	1.00000i	−0.0686803	−	0.0686803i
$213$	2.00000			0.137038
$214$	−13.0000	−	13.0000i	−0.888662	−	0.888662i
$215$		0			0
$216$	−4.00000	−	4.00000i	−0.272166	−	0.272166i
$217$	2.00000	−	2.00000i	0.135769	−	0.135769i
$218$	−13.0000	+	13.0000i	−0.880471	+	0.880471i
$219$	−6.00000	+	6.00000i	−0.405442	+	0.405442i
$220$		0			0
$221$	−25.0000	+	5.00000i	−1.68168	+	0.336336i
$222$	8.00000	−	8.00000i	0.536925	−	0.536925i
$223$	6.00000			0.401790			0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000			0.401790			0.200895	+	0.979613i	$0.435615\pi$
$224$			2.00000i			0.133631i
$225$		0			0
$226$	9.00000	−	9.00000i	0.598671	−	0.598671i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	6.00000i		−	0.397360i
$229$	−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
$232$	−4.00000			−0.262613
$233$	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	$0.175597\pi$
$234$	−2.00000	+	3.00000i	−0.130744	+	0.196116i
$235$		0			0
$236$	3.00000	−	3.00000i	0.195283	−	0.195283i
$237$	14.0000	−	14.0000i	0.909398	−	0.909398i
$238$	−10.0000	+	10.0000i	−0.648204	+	0.648204i
$239$	−7.00000	−	7.00000i	−0.452792	−	0.452792i	0.443488	−	0.896280i	$-0.353741\pi$
$239$	−7.00000	−	7.00000i	−0.452792	−	0.452792i	−0.896280	+	0.443488i	$0.853741\pi$
$240$		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	$0.735496\pi$
$242$	9.00000			0.578542
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$	−2.00000			−0.128037
$245$		0			0
$246$			2.00000i			0.127515i
$247$	−15.0000	+	3.00000i	−0.954427	+	0.190885i
$248$	−1.00000	−	1.00000i	−0.0635001	−	0.0635001i
$249$	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	$0.604304\pi$
$252$			2.00000i			0.125988i
$253$	−10.0000			−0.628695
$254$	15.0000	−	15.0000i	0.941184	−	0.941184i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−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	$0.980131\pi$
$258$			10.0000i			0.622573i
$259$	−16.0000			−0.994192
$260$		0			0
$261$	−4.00000			−0.247594
$262$			12.0000i			0.741362i
$263$	−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	$0.878362\pi$
$264$	2.00000			0.123091
$265$		0			0
$266$	−6.00000	+	6.00000i	−0.367884	+	0.367884i
$267$	14.0000			0.856786
$268$			12.0000i			0.733017i
$269$			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	$-0.376345\pi$
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	−0.925488	+	0.378777i	$0.876345\pi$
$272$	5.00000	+	5.00000i	0.303170	+	0.303170i
$273$	−10.0000	+	2.00000i	−0.605228	+	0.121046i
$274$			12.0000i			0.724947i
$275$		0			0
$276$	10.0000			0.601929
$277$	−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	$0.818138\pi$
$278$	14.0000			0.839664
$279$	−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	$0.403589\pi$
$282$	−2.00000	+	2.00000i	−0.119098	+	0.119098i
$283$	−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	$0.467149\pi$
$284$	−1.00000	+	1.00000i	−0.0593391	+	0.0593391i
$285$		0			0
$286$	−1.00000	−	5.00000i	−0.0591312	−	0.295656i
$287$	2.00000	−	2.00000i	0.118056	−	0.118056i
$288$	1.00000			0.0589256
$289$			33.0000i			1.94118i
$290$		0			0
$291$	2.00000	−	2.00000i	0.117242	−	0.117242i
$292$		−	6.00000i		−	0.351123i
$293$			26.0000i			1.51894i	0.650545	+	0.759468i	$0.274541\pi$
$293$			26.0000i			1.51894i	−0.650545	+	0.759468i	$0.725459\pi$
$294$	3.00000	−	3.00000i	0.174964	−	0.174964i
$295$		0			0
$296$			8.00000i			0.464991i
$297$	8.00000			0.464207
$298$	−13.0000	+	13.0000i	−0.753070	+	0.753070i
$299$	−5.00000	−	25.0000i	−0.289157	−	1.44579i
$300$		0			0
$301$	10.0000	−	10.0000i	0.576390	−	0.576390i
$302$	9.00000	−	9.00000i	0.517892	−	0.517892i
$303$		0			0
$304$	3.00000	+	3.00000i	0.172062	+	0.172062i
$305$		0			0
$306$	5.00000	+	5.00000i	0.285831	+	0.285831i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	−2.00000	−	2.00000i	−0.113961	−	0.113961i
$309$	−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	$-0.0915036\pi$
$312$	1.00000	+	5.00000i	0.0566139	+	0.283069i
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	0.405420	−	0.914130i	$-0.367125\pi$
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	−0.914130	+	0.405420i	$0.867125\pi$
$314$	−3.00000	−	3.00000i	−0.169300	−	0.169300i
$315$		0			0
$316$			14.0000i			0.787562i
$317$		−	2.00000i		−	0.112331i	−0.998421	−	0.0561656i	$-0.982113\pi$
$317$		−	2.00000i		−	0.112331i	0.998421	−	0.0561656i	$-0.0178875\pi$
$318$	−2.00000			−0.112154
$319$	4.00000	−	4.00000i	0.223957	−	0.223957i
$320$		0			0
$321$	−26.0000			−1.45118
$322$	−10.0000	−	10.0000i	−0.557278	−	0.557278i
$323$			30.0000i			1.66924i
$324$	−5.00000			−0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$			26.0000i			1.43780i
$328$	−1.00000	−	1.00000i	−0.0552158	−	0.0552158i
$329$	4.00000			0.220527
$330$		0			0
$331$	−9.00000	+	9.00000i	−0.494685	+	0.494685i	−0.909779	−	0.415094i	$-0.863749\pi$
$331$	−9.00000	+	9.00000i	−0.494685	+	0.494685i	0.415094	+	0.909779i	$0.363749\pi$
$332$	−6.00000			−0.329293
$333$			8.00000i			0.438397i
$334$			2.00000i			0.109435i
$335$		0			0
$336$	2.00000	+	2.00000i	0.109109	+	0.109109i
$337$	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	$0.688310\pi$
$338$	12.0000	−	5.00000i	0.652714	−	0.271964i
$339$		−	18.0000i		−	0.977626i
$340$		0			0
$341$	2.00000			0.108306
$342$	3.00000	+	3.00000i	0.162221	+	0.162221i
$343$	−20.0000			−1.07990
$344$	−5.00000	−	5.00000i	−0.269582	−	0.269582i
$345$		0			0
$346$	15.0000	+	15.0000i	0.806405	+	0.806405i
$347$	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	$0.164392\pi$
$348$	−4.00000	+	4.00000i	−0.214423	+	0.214423i
$349$	−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
$352$	−1.00000	+	1.00000i	−0.0533002	+	0.0533002i
$353$	16.0000			0.851594			0.425797	−	0.904819i	$-0.359994\pi$
$353$	16.0000			0.851594			0.425797	+	0.904819i	$0.359994\pi$
$354$		−	6.00000i		−	0.318896i
$355$		0			0
$356$	−7.00000	+	7.00000i	−0.370999	+	0.370999i
$357$			20.0000i			1.05851i
$358$		−	20.0000i		−	1.05703i
$359$	−13.0000	+	13.0000i	−0.686114	+	0.686114i	−0.961371	−	0.275257i	$-0.911237\pi$
$359$	−13.0000	+	13.0000i	−0.686114	+	0.686114i	0.275257	+	0.961371i	$0.411237\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$	20.0000			1.05118
$363$	9.00000	−	9.00000i	0.472377	−	0.472377i
$364$	4.00000	−	6.00000i	0.209657	−	0.314485i
$365$		0			0
$366$	−2.00000	+	2.00000i	−0.104542	+	0.104542i
$367$	−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	$0.285320\pi$
$368$	−5.00000	+	5.00000i	−0.260643	+	0.260643i
$369$	−1.00000	−	1.00000i	−0.0520579	−	0.0520579i
$370$		0			0
$371$	2.00000	+	2.00000i	0.103835	+	0.103835i
$372$	−2.00000			−0.103695
$373$	1.00000	+	1.00000i	0.0517780	+	0.0517780i	0.732522	−	0.680744i	$-0.238343\pi$
$373$	1.00000	+	1.00000i	0.0517780	+	0.0517780i	−0.680744	+	0.732522i	$0.738343\pi$
$374$	−10.0000			−0.517088
$375$		0			0
$376$		−	2.00000i		−	0.103142i
$377$	12.0000	+	8.00000i	0.618031	+	0.412021i
$378$	8.00000	+	8.00000i	0.411476	+	0.411476i
$379$	−17.0000	−	17.0000i	−0.873231	−	0.873231i	0.119592	−	0.992823i	$-0.461841\pi$
$379$	−17.0000	−	17.0000i	−0.873231	−	0.873231i	−0.992823	+	0.119592i	$0.961841\pi$
$380$		0			0
$381$		−	30.0000i		−	1.53695i
$382$		−	8.00000i		−	0.409316i
$383$	6.00000			0.306586			0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000			0.306586			0.153293	+	0.988181i	$0.451012\pi$
$384$	1.00000	−	1.00000i	0.0510310	−	0.0510310i
$385$		0			0
$386$	14.0000			0.712581
$387$	−5.00000	−	5.00000i	−0.254164	−	0.254164i
$388$			2.00000i			0.101535i
$389$	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
$392$			3.00000i			0.151523i
$393$	12.0000	+	12.0000i	0.605320	+	0.605320i
$394$	−18.0000			−0.906827
$395$		0			0
$396$	−1.00000	+	1.00000i	−0.0502519	+	0.0502519i
$397$	−8.00000			−0.401508			−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000			−0.401508			−0.200754	+	0.979642i	$0.564339\pi$
$398$		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	$0.738758\pi$
$402$	12.0000	+	12.0000i	0.598506	+	0.598506i
$403$	1.00000	+	5.00000i	0.0498135	+	0.249068i
$404$		0			0
$405$		0			0
$406$	8.00000			0.397033
$407$	−8.00000	−	8.00000i	−0.396545	−	0.396545i
$408$	10.0000			0.495074
$409$	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
$412$	5.00000	−	5.00000i	0.246332	−	0.246332i
$413$	−6.00000	+	6.00000i	−0.295241	+	0.295241i
$414$	−5.00000	+	5.00000i	−0.245737	+	0.245737i
$415$		0			0
$416$	−3.00000	−	2.00000i	−0.147087	−	0.0980581i
$417$	14.0000	−	14.0000i	0.685583	−	0.685583i
$418$	−6.00000			−0.293470
$419$			26.0000i			1.27018i	0.772437	+	0.635092i	$0.219038\pi$
$419$			26.0000i			1.27018i	−0.772437	+	0.635092i	$0.780962\pi$
$420$		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	$0.350383\pi$
$422$			12.0000i			0.584151i
$423$		−	2.00000i		−	0.0972433i
$424$	1.00000	−	1.00000i	0.0485643	−	0.0485643i
$425$		0			0
$426$			2.00000i			0.0969003i
$427$	4.00000			0.193574
$428$	13.0000	−	13.0000i	0.628379	−	0.628379i
$429$	−6.00000	−	4.00000i	−0.289683	−	0.193122i
$430$		0			0
$431$	21.0000	−	21.0000i	1.01153	−	1.01153i	0.0116017	−	0.999933i	$-0.496307\pi$
$431$	21.0000	−	21.0000i	1.01153	−	1.01153i	0.999933	−	0.0116017i	$-0.00369302\pi$
$432$	4.00000	−	4.00000i	0.192450	−	0.192450i
$433$	−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	$0.420251\pi$
$434$	2.00000	+	2.00000i	0.0960031	+	0.0960031i
$435$		0			0
$436$	−13.0000	−	13.0000i	−0.622587	−	0.622587i
$437$	−30.0000			−1.43509
$438$	−6.00000	−	6.00000i	−0.286691	−	0.286691i
$439$	−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
$442$	−5.00000	−	25.0000i	−0.237826	−	1.18913i
$443$	−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	$0.970369\pi$
$444$	8.00000	+	8.00000i	0.379663	+	0.379663i
$445$		0			0
$446$			6.00000i			0.284108i
$447$			26.0000i			1.22976i
$448$	−2.00000			−0.0944911
$449$	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
$452$	9.00000	+	9.00000i	0.423324	+	0.423324i
$453$		−	18.0000i		−	0.845714i
$454$	12.0000			0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$			38.0000i			1.77757i	0.458329	+	0.888783i	$0.348448\pi$
$457$			38.0000i			1.77757i	−0.458329	+	0.888783i	$0.651552\pi$
$458$	−3.00000	−	3.00000i	−0.140181	−	0.140181i
$459$	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	$0.132003\pi$
$462$	−4.00000			−0.186097
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$		−	4.00000i		−	0.185695i
$465$		0			0
$466$	5.00000	+	5.00000i	0.231621	+	0.231621i
$467$	−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	$0.802312\pi$
$468$	−3.00000	−	2.00000i	−0.138675	−	0.0924500i
$469$		−	24.0000i		−	1.10822i
$470$		0			0
$471$	−6.00000			−0.276465
$472$	3.00000	+	3.00000i	0.138086	+	0.138086i
$473$	10.0000			0.459800
$474$	14.0000	+	14.0000i	0.643041	+	0.643041i
$475$		0			0
$476$	−10.0000	−	10.0000i	−0.458349	−	0.458349i
$477$	1.00000	−	1.00000i	0.0457869	−	0.0457869i
$478$	7.00000	−	7.00000i	0.320173	−	0.320173i
$479$	−13.0000	+	13.0000i	−0.593985	+	0.593985i	−0.938705	−	0.344720i	$-0.887974\pi$
$479$	−13.0000	+	13.0000i	−0.593985	+	0.593985i	0.344720	+	0.938705i	$0.387974\pi$
$480$		0			0
$481$	16.0000	−	24.0000i	0.729537	−	1.09431i
$482$	−1.00000	+	1.00000i	−0.0455488	+	0.0455488i
$483$	−20.0000			−0.910032
$484$			9.00000i			0.409091i
$485$		0			0
$486$	7.00000	−	7.00000i	0.317526	−	0.317526i
$487$		−	32.0000i		−	1.45006i	−0.688718	−	0.725029i	$-0.741826\pi$
$487$		−	32.0000i		−	1.45006i	0.688718	−	0.725029i	$-0.258174\pi$
$488$		−	2.00000i		−	0.0905357i
$489$	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	$-0.0724495\pi$
$492$	−2.00000			−0.0901670
$493$	20.0000	−	20.0000i	0.900755	−	0.900755i
$494$	−3.00000	−	15.0000i	−0.134976	−	0.674882i
$495$		0			0
$496$	1.00000	−	1.00000i	0.0449013	−	0.0449013i
$497$	2.00000	−	2.00000i	0.0897123	−	0.0897123i
$498$	−6.00000	+	6.00000i	−0.268866	+	0.268866i
$499$	23.0000	+	23.0000i	1.02962	+	1.02962i	0.999548	+	0.0300737i	$0.00957421\pi$
$499$	23.0000	+	23.0000i	1.02962	+	1.02962i	0.0300737	+	0.999548i	$0.490426\pi$
$500$		0			0
$501$	2.00000	+	2.00000i	0.0893534	+	0.0893534i
$502$	−30.0000			−1.33897
$503$	−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	$0.841580\pi$
$504$	−2.00000			−0.0890871
$505$		0			0
$506$		−	10.0000i		−	0.444554i
$507$	7.00000	−	17.0000i	0.310881	−	0.754997i
$508$	15.0000	+	15.0000i	0.665517	+	0.665517i
$509$	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
$512$			1.00000i			0.0441942i
$513$	24.0000			1.05963
$514$	15.0000	−	15.0000i	0.661622	−	0.661622i
$515$		0			0
$516$	−10.0000			−0.440225
$517$	2.00000	+	2.00000i	0.0879599	+	0.0879599i
$518$		−	16.0000i		−	0.703000i
$519$	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	$0.339940\pi$
$522$		−	4.00000i		−	0.175075i
$523$	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	$0.525057\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	9.00000	−	9.00000i	0.392419	−	0.392419i
$527$	10.0000			0.435607
$528$			2.00000i			0.0870388i
$529$		−	27.0000i		−	1.17391i
$530$		0			0
$531$	3.00000	+	3.00000i	0.130189	+	0.130189i
$532$	−6.00000	−	6.00000i	−0.260133	−	0.260133i
$533$	1.00000	+	5.00000i	0.0433148	+	0.216574i
$534$			14.0000i			0.605839i
$535$		0			0
$536$	−12.0000			−0.518321
$537$	−20.0000	−	20.0000i	−0.863064	−	0.863064i
$538$	−16.0000			−0.689809
$539$	−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	$0.838217\pi$
$542$	9.00000	−	9.00000i	0.386583	−	0.386583i
$543$	20.0000	−	20.0000i	0.858282	−	0.858282i
$544$	−5.00000	+	5.00000i	−0.214373	+	0.214373i
$545$		0			0
$546$	−2.00000	−	10.0000i	−0.0855921	−	0.427960i
$547$	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	$0.182121\pi$
$548$	−12.0000			−0.512615
$549$		−	2.00000i		−	0.0853579i
$550$		0			0
$551$	12.0000	−	12.0000i	0.511217	−	0.511217i
$552$			10.0000i			0.425628i
$553$		−	28.0000i		−	1.19068i
$554$	5.00000	−	5.00000i	0.212430	−	0.212430i
$555$		0			0
$556$			14.0000i			0.593732i
$557$	−8.00000			−0.338971			−0.169485	−	0.985533i	$-0.554211\pi$
$557$	−8.00000			−0.338971			−0.169485	+	0.985533i	$0.554211\pi$
$558$	1.00000	−	1.00000i	0.0423334	−	0.0423334i
$559$	5.00000	+	25.0000i	0.211477	+	1.05739i
$560$		0			0
$561$	−10.0000	+	10.0000i	−0.422200	+	0.422200i
$562$	−21.0000	+	21.0000i	−0.885832	+	0.885832i
$563$	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	$0.202393\pi$
$564$	−2.00000	−	2.00000i	−0.0842152	−	0.0842152i
$565$		0			0
$566$	−15.0000	−	15.0000i	−0.630497	−	0.630497i
$567$	10.0000			0.419961
$568$	−1.00000	−	1.00000i	−0.0419591	−	0.0419591i
$569$	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	$-0.932900\pi$
$571$		−	10.0000i		−	0.418487i	0.977864	−	0.209243i	$-0.0671001\pi$
$572$	5.00000	−	1.00000i	0.209061	−	0.0418121i
$573$	−8.00000	−	8.00000i	−0.334205	−	0.334205i
$574$	2.00000	+	2.00000i	0.0834784	+	0.0834784i
$575$		0			0
$576$			1.00000i			0.0416667i
$577$		−	22.0000i		−	0.915872i	−0.888985	−	0.457936i	$-0.848589\pi$
$577$		−	22.0000i		−	0.915872i	0.888985	−	0.457936i	$-0.151411\pi$
$578$	−33.0000			−1.37262
$579$	14.0000	−	14.0000i	0.581820	−	0.581820i
$580$		0			0
$581$	12.0000			0.497844
$582$	2.00000	+	2.00000i	0.0829027	+	0.0829027i
$583$			2.00000i			0.0828315i
$584$	6.00000			0.248282
$585$		0			0
$586$	−26.0000			−1.07405
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	3.00000	+	3.00000i	0.123718	+	0.123718i
$589$	6.00000			0.247226
$590$		0			0
$591$	−18.0000	+	18.0000i	−0.740421	+	0.740421i
$592$	−8.00000			−0.328798
$593$		−	14.0000i		−	0.574911i	−0.957794	−	0.287456i	$-0.907191\pi$
$593$		−	14.0000i		−	0.574911i	0.957794	−	0.287456i	$-0.0928094\pi$
$594$			8.00000i			0.328244i
$595$		0			0
$596$	−13.0000	−	13.0000i	−0.532501	−	0.532501i
$597$		0			0
$598$	25.0000	−	5.00000i	1.02233	−	0.204465i
$599$		−	14.0000i		−	0.572024i	−0.958226	−	0.286012i	$-0.907670\pi$
$599$		−	14.0000i		−	0.572024i	0.958226	−	0.286012i	$-0.0923298\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	10.0000	+	10.0000i	0.407570	+	0.407570i
$603$	−12.0000			−0.488678
$604$	9.00000	+	9.00000i	0.366205	+	0.366205i
$605$		0			0
$606$		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	$0.277441\pi$
$608$	−3.00000	+	3.00000i	−0.121666	+	0.121666i
$609$	8.00000	−	8.00000i	0.324176	−	0.324176i
$610$		0			0
$611$	−4.00000	+	6.00000i	−0.161823	+	0.242734i
$612$	−5.00000	+	5.00000i	−0.202113	+	0.202113i
$613$	−4.00000			−0.161558			−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000			−0.161558			−0.0807792	+	0.996732i	$0.525741\pi$
$614$			2.00000i			0.0807134i
$615$		0			0
$616$	2.00000	−	2.00000i	0.0805823	−	0.0805823i
$617$			38.0000i			1.52982i	0.644136	+	0.764911i	$0.277217\pi$
$617$			38.0000i			1.52982i	−0.644136	+	0.764911i	$0.722783\pi$
$618$		−	10.0000i		−	0.402259i
$619$	−3.00000	+	3.00000i	−0.120580	+	0.120580i	−0.764822	−	0.644242i	$-0.777173\pi$
$619$	−3.00000	+	3.00000i	−0.120580	+	0.120580i	0.644242	+	0.764822i	$0.277173\pi$
$620$		0			0
$621$			40.0000i			1.60514i
$622$	10.0000			0.400963
$623$	14.0000	−	14.0000i	0.560898	−	0.560898i
$624$	−5.00000	+	1.00000i	−0.200160	+	0.0400320i
$625$		0			0
$626$	9.00000	−	9.00000i	0.359712	−	0.359712i
$627$	−6.00000	+	6.00000i	−0.239617	+	0.239617i
$628$	3.00000	−	3.00000i	0.119713	−	0.119713i
$629$	−40.0000	−	40.0000i	−1.59490	−	1.59490i
$630$		0			0
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	0.891306	−	0.453403i	$-0.149790\pi$
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	−0.453403	+	0.891306i	$0.649790\pi$
$632$	−14.0000			−0.556890
$633$	12.0000	+	12.0000i	0.476957	+	0.476957i
$634$	2.00000			0.0794301
$635$		0			0
$636$		−	2.00000i		−	0.0793052i
$637$	6.00000	−	9.00000i	0.237729	−	0.356593i
$638$	4.00000	+	4.00000i	0.158362	+	0.158362i
$639$	−1.00000	−	1.00000i	−0.0395594	−	0.0395594i
$640$		0			0
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		−	26.0000i		−	1.02614i
$643$	46.0000			1.81406			0.907031	−	0.421063i	$-0.138343\pi$
$643$	46.0000			1.81406			0.907031	+	0.421063i	$0.138343\pi$
$644$	10.0000	−	10.0000i	0.394055	−	0.394055i
$645$		0			0
$646$	−30.0000			−1.18033
$647$	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	$0.705612\pi$
$648$		−	5.00000i		−	0.196419i
$649$	−6.00000			−0.235521
$650$		0			0
$651$	4.00000			0.156772
$652$			4.00000i			0.156652i
$653$	21.0000	+	21.0000i	0.821794	+	0.821794i	0.986365	−	0.164572i	$-0.0526242\pi$
$653$	21.0000	+	21.0000i	0.821794	+	0.821794i	−0.164572	+	0.986365i	$0.552624\pi$
$654$	−26.0000			−1.01668
$655$		0			0
$656$	1.00000	−	1.00000i	0.0390434	−	0.0390434i
$657$	6.00000			0.234082
$658$			4.00000i			0.155936i
$659$		−	14.0000i		−	0.545363i	−0.962104	−	0.272681i	$-0.912090\pi$
$659$		−	14.0000i		−	0.545363i	0.962104	−	0.272681i	$-0.0879105\pi$
$660$		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	$0.425024\pi$
$662$	−9.00000	−	9.00000i	−0.349795	−	0.349795i
$663$	−30.0000	−	20.0000i	−1.16510	−	0.776736i
$664$		−	6.00000i		−	0.232845i
$665$		0			0
$666$	−8.00000			−0.309994
$667$	20.0000	+	20.0000i	0.774403	+	0.774403i
$668$	−2.00000			−0.0773823
$669$	6.00000	+	6.00000i	0.231973	+	0.231973i
$670$		0			0
$671$	2.00000	+	2.00000i	0.0772091	+	0.0772091i
$672$	−2.00000	+	2.00000i	−0.0771517	+	0.0771517i
$673$	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	$0.206484\pi$
$674$	−5.00000	+	5.00000i	−0.192593	+	0.192593i
$675$		0			0
$676$	5.00000	+	12.0000i	0.192308	+	0.461538i
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	−0.993935	−	0.109973i	$-0.964924\pi$
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	0.109973	+	0.993935i	$0.464924\pi$
$678$	18.0000			0.691286
$679$		−	4.00000i		−	0.153506i
$680$		0			0
$681$	12.0000	−	12.0000i	0.459841	−	0.459841i
$682$			2.00000i			0.0765840i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	−3.00000	+	3.00000i	−0.114708	+	0.114708i
$685$		0			0
$686$		−	20.0000i		−	0.763604i
$687$	−6.00000			−0.228914
$688$	5.00000	−	5.00000i	0.190623	−	0.190623i
$689$	−5.00000	+	1.00000i	−0.190485	+	0.0380970i
$690$		0			0
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	−0.857260	−	0.514884i	$-0.827835\pi$
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	0.514884	+	0.857260i	$0.327835\pi$
$692$	−15.0000	+	15.0000i	−0.570214	+	0.570214i
$693$	2.00000	−	2.00000i	0.0759737	−	0.0759737i
$694$	7.00000	+	7.00000i	0.265716	+	0.265716i
$695$		0			0
$696$	−4.00000	−	4.00000i	−0.151620	−	0.151620i
$697$	10.0000			0.378777
$698$	−3.00000	−	3.00000i	−0.113552	−	0.113552i
$699$	10.0000			0.378235
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−20.0000	+	4.00000i	−0.754851	+	0.150970i
$703$	−24.0000	−	24.0000i	−0.905177	−	0.905177i
$704$	−1.00000	−	1.00000i	−0.0376889	−	0.0376889i
$705$		0			0
$706$			16.0000i			0.602168i
$707$		0			0
$708$	6.00000			0.225494
$709$	−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
$712$	−7.00000	−	7.00000i	−0.262336	−	0.262336i
$713$			10.0000i			0.374503i
$714$	−20.0000			−0.748481
$715$		0			0
$716$	20.0000			0.747435
$717$		−	14.0000i		−	0.522840i
$718$	−13.0000	−	13.0000i	−0.485156	−	0.485156i
$719$		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
$722$	1.00000			0.0372161
$723$			2.00000i			0.0743808i
$724$			20.0000i			0.743294i
$725$		0			0
$726$	9.00000	+	9.00000i	0.334021	+	0.334021i
$727$	−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	$-0.620100\pi$
$728$	6.00000	+	4.00000i	0.222375	+	0.148250i
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	50.0000			1.84932
$732$	−2.00000	−	2.00000i	−0.0739221	−	0.0739221i
$733$	−44.0000			−1.62518			−0.812589	−	0.582838i	$-0.801942\pi$
$733$	−44.0000			−1.62518			−0.812589	+	0.582838i	$0.801942\pi$
$734$	−3.00000	−	3.00000i	−0.110732	−	0.110732i
$735$		0			0
$736$	−5.00000	−	5.00000i	−0.184302	−	0.184302i
$737$	12.0000	−	12.0000i	0.442026	−	0.442026i
$738$	1.00000	−	1.00000i	0.0368105	−	0.0368105i
$739$	37.0000	−	37.0000i	1.36107	−	1.36107i	0.488507	−	0.872560i	$-0.337542\pi$
$739$	37.0000	−	37.0000i	1.36107	−	1.36107i	0.872560	−	0.488507i	$-0.162458\pi$
$740$		0			0
$741$	−18.0000	−	12.0000i	−0.661247	−	0.440831i
$742$	−2.00000	+	2.00000i	−0.0734223	+	0.0734223i
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		−	2.00000i		−	0.0733236i
$745$		0			0
$746$	−1.00000	+	1.00000i	−0.0366126	+	0.0366126i
$747$		−	6.00000i		−	0.219529i
$748$		−	10.0000i		−	0.365636i
$749$	−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	$-0.0584036\pi$
$752$	2.00000			0.0729325
$753$	−30.0000	+	30.0000i	−1.09326	+	1.09326i
$754$	−8.00000	+	12.0000i	−0.291343	+	0.437014i
$755$		0			0
$756$	−8.00000	+	8.00000i	−0.290957	+	0.290957i
$757$	17.0000	−	17.0000i	0.617876	−	0.617876i	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	17.0000	−	17.0000i	0.617876	−	0.617876i	0.944986	+	0.327111i	$0.106075\pi$
$758$	17.0000	−	17.0000i	0.617468	−	0.617468i
$759$	−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	$0.911916\pi$
$762$	30.0000			1.08679
$763$	26.0000	+	26.0000i	0.941263	+	0.941263i
$764$	8.00000			0.289430
$765$		0			0
$766$			6.00000i			0.216789i
$767$	−3.00000	−	15.0000i	−0.108324	−	0.541619i
$768$	1.00000	+	1.00000i	0.0360844	+	0.0360844i
$769$	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
$772$			14.0000i			0.503871i
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$	5.00000	−	5.00000i	0.179721	−	0.179721i
$775$		0			0
$776$	−2.00000			−0.0717958
$777$	−16.0000	−	16.0000i	−0.573997	−	0.573997i
$778$			10.0000i			0.358517i
$779$	6.00000			0.214972
$780$		0			0
$781$	2.00000			0.0715656
$782$		−	50.0000i		−	1.78800i
$783$	−16.0000	−	16.0000i	−0.571793	−	0.571793i
$784$	−3.00000			−0.107143
$785$		0			0
$786$	−12.0000	+	12.0000i	−0.428026	+	0.428026i
$787$	42.0000			1.49714			0.748569	−	0.663057i	$-0.230741\pi$
$787$	42.0000			1.49714			0.748569	+	0.663057i	$0.230741\pi$
$788$		−	18.0000i		−	0.641223i
$789$		−	18.0000i		−	0.640817i
$790$		0			0
$791$	−18.0000	−	18.0000i	−0.640006	−	0.640006i
$792$	−1.00000	−	1.00000i	−0.0355335	−	0.0355335i
$793$	−4.00000	+	6.00000i	−0.142044	+	0.213066i
$794$		−	8.00000i		−	0.283909i
$795$		0			0
$796$		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	$0.789968\pi$
$798$	−12.0000			−0.424795
$799$	10.0000	+	10.0000i	0.353775	+	0.353775i
$800$		0			0
$801$	−7.00000	−	7.00000i	−0.247333	−	0.247333i
$802$	−1.00000	+	1.00000i	−0.0353112	+	0.0353112i
$803$	−6.00000	+	6.00000i	−0.211735	+	0.211735i
$804$	−12.0000	+	12.0000i	−0.423207	+	0.423207i
$805$		0			0
$806$	−5.00000	+	1.00000i	−0.176117	+	0.0352235i
$807$	−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	$-0.661942\pi$
$811$	11.0000	−	11.0000i	0.386262	−	0.386262i	0.873352	+	0.487090i	$0.161942\pi$
$812$			8.00000i			0.280745i
$813$		−	18.0000i		−	0.631288i
$814$	8.00000	−	8.00000i	0.280400	−	0.280400i
$815$		0			0
$816$			10.0000i			0.350070i
$817$	30.0000			1.04957
$818$	−3.00000	+	3.00000i	−0.104893	+	0.104893i
$819$	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	$0.996123\pi$
$822$	−12.0000	+	12.0000i	−0.418548	+	0.418548i
$823$	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	$0.129453\pi$
$824$	5.00000	+	5.00000i	0.174183	+	0.174183i
$825$		0			0
$826$	−6.00000	−	6.00000i	−0.208767	−	0.208767i
$827$	2.00000			0.0695468			0.0347734	−	0.999395i	$-0.488929\pi$
$827$	2.00000			0.0695468			0.0347734	+	0.999395i	$0.488929\pi$
$828$	−5.00000	−	5.00000i	−0.173762	−	0.173762i
$829$	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
$832$	2.00000	−	3.00000i	0.0693375	−	0.104006i
$833$	−15.0000	−	15.0000i	−0.519719	−	0.519719i
$834$	14.0000	+	14.0000i	0.484780	+	0.484780i
$835$		0			0
$836$		−	6.00000i		−	0.207514i
$837$		−	8.00000i		−	0.276520i
$838$	−26.0000			−0.898155
$839$	−13.0000	+	13.0000i	−0.448810	+	0.448810i	−0.894959	−	0.446149i	$-0.852795\pi$
$839$	−13.0000	+	13.0000i	−0.448810	+	0.448810i	0.446149	+	0.894959i	$0.352795\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$	−9.00000	−	9.00000i	−0.310160	−	0.310160i
$843$			42.0000i			1.44656i
$844$	−12.0000			−0.413057
$845$		0			0
$846$	2.00000			0.0687614
$847$		−	18.0000i		−	0.618487i
$848$	1.00000	+	1.00000i	0.0343401	+	0.0343401i
$849$	−30.0000			−1.02960
$850$		0			0
$851$	40.0000	−	40.0000i	1.37118	−	1.37118i
$852$	−2.00000			−0.0685189
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$			4.00000i			0.136877i
$855$		0			0
$856$	13.0000	+	13.0000i	0.444331	+	0.444331i
$857$	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	$0.711463\pi$
$858$	4.00000	−	6.00000i	0.136558	−	0.204837i
$859$			26.0000i			0.887109i	0.896248	+	0.443554i	$0.146283\pi$
$859$			26.0000i			0.887109i	−0.896248	+	0.443554i	$0.853717\pi$
$860$		0			0
$861$	4.00000			0.136320
$862$	21.0000	+	21.0000i	0.715263	+	0.715263i
$863$	46.0000			1.56586			0.782929	−	0.622111i	$-0.213725\pi$
$863$	46.0000			1.56586			0.782929	+	0.622111i	$0.213725\pi$
$864$	4.00000	+	4.00000i	0.136083	+	0.136083i
$865$		0			0
$866$	−15.0000	−	15.0000i	−0.509721	−	0.509721i
$867$	−33.0000	+	33.0000i	−1.12074	+	1.12074i
$868$	−2.00000	+	2.00000i	−0.0678844	+	0.0678844i
$869$	14.0000	−	14.0000i	0.474917	−	0.474917i
$870$		0			0
$871$	36.0000	+	24.0000i	1.21981	+	0.813209i
$872$	13.0000	−	13.0000i	0.440236	−	0.440236i
$873$	−2.00000			−0.0676897
$874$		−	30.0000i		−	1.01477i
$875$		0			0
$876$	6.00000	−	6.00000i	0.202721	−	0.202721i
$877$			18.0000i			0.607817i	0.952701	+	0.303908i	$0.0982917\pi$
$877$			18.0000i			0.607817i	−0.952701	+	0.303908i	$0.901708\pi$
$878$		−	40.0000i		−	1.34993i
$879$	−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	$0.890619\pi$
$882$	−3.00000			−0.101015
$883$	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	$0.212037\pi$
$884$	25.0000	−	5.00000i	0.840841	−	0.168168i
$885$		0			0
$886$	19.0000	−	19.0000i	0.638317	−	0.638317i
$887$	−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	$0.433878\pi$
$888$	−8.00000	+	8.00000i	−0.268462	+	0.268462i
$889$	−30.0000	−	30.0000i	−1.00617	−	1.00617i
$890$		0			0
$891$	5.00000	+	5.00000i	0.167506	+	0.167506i
$892$	−6.00000			−0.200895
$893$	6.00000	+	6.00000i	0.200782	+	0.200782i
$894$	−26.0000			−0.869570
$895$		0			0
$896$		−	2.00000i		−	0.0668153i
$897$	20.0000	−	30.0000i	0.667781	−	1.00167i
$898$	7.00000	+	7.00000i	0.233593	+	0.233593i
$899$	−4.00000	−	4.00000i	−0.133407	−	0.133407i
$900$		0			0
$901$			10.0000i			0.333148i
$902$			2.00000i			0.0665927i
$903$	20.0000			0.665558
$904$	−9.00000	+	9.00000i	−0.299336	+	0.299336i
$905$		0			0
$906$	18.0000			0.598010
$907$	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	$0.442988\pi$
$908$			12.0000i			0.398234i
$909$		0			0
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$			6.00000i			0.198680i
$913$	6.00000	+	6.00000i	0.198571	+	0.198571i
$914$	−38.0000			−1.25693
$915$		0			0
$916$	3.00000	−	3.00000i	0.0991228	−	0.0991228i
$917$	24.0000			0.792550
$918$			40.0000i			1.32020i
$919$		−	14.0000i		−	0.461817i	−0.972975	−	0.230909i	$-0.925830\pi$
$919$		−	14.0000i		−	0.461817i	0.972975	−	0.230909i	$-0.0741699\pi$
$920$		0			0
$921$	2.00000	+	2.00000i	0.0659022	+	0.0659022i
$922$	11.0000	+	11.0000i	0.362266	+	0.362266i
$923$	1.00000	+	5.00000i	0.0329154	+	0.164577i
$924$		−	4.00000i		−	0.131590i
$925$		0			0
$926$	−16.0000			−0.525793
$927$	5.00000	+	5.00000i	0.164222	+	0.164222i
$928$	4.00000			0.131306
$929$	−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
$932$	−5.00000	+	5.00000i	−0.163780	+	0.163780i
$933$	10.0000	−	10.0000i	0.327385	−	0.327385i
$934$	5.00000	−	5.00000i	0.163605	−	0.163605i
$935$		0			0
$936$	2.00000	−	3.00000i	0.0653720	−	0.0980581i
$937$	−33.0000	+	33.0000i	−1.07806	+	1.07806i	−0.0813798	+	0.996683i	$0.525933\pi$
$937$	−33.0000	+	33.0000i	−1.07806	+	1.07806i	−0.996683	+	0.0813798i	$0.974067\pi$
$938$	24.0000			0.783628
$939$		−	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	$0.483055\pi$
$942$		−	6.00000i		−	0.195491i
$943$			10.0000i			0.325645i
$944$	−3.00000	+	3.00000i	−0.0976417	+	0.0976417i
$945$		0			0
$946$			10.0000i			0.325128i
$947$	−38.0000			−1.23483			−0.617417	−	0.786636i	$-0.711821\pi$
$947$	−38.0000			−1.23483			−0.617417	+	0.786636i	$0.711821\pi$
$948$	−14.0000	+	14.0000i	−0.454699	+	0.454699i
$949$	−18.0000	−	12.0000i	−0.584305	−	0.389536i
$950$		0			0
$951$	2.00000	−	2.00000i	0.0648544	−	0.0648544i
$952$	10.0000	−	10.0000i	0.324102	−	0.324102i
$953$	−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	$0.953934\pi$
$954$	1.00000	+	1.00000i	0.0323762	+	0.0323762i
$955$		0			0
$956$	7.00000	+	7.00000i	0.226396	+	0.226396i
$957$	8.00000			0.258603
$958$	−13.0000	−	13.0000i	−0.420011	−	0.420011i
$959$	24.0000			0.775000
$960$		0			0
$961$			29.0000i			0.935484i
$962$	24.0000	+	16.0000i	0.773791	+	0.515861i
$963$	13.0000	+	13.0000i	0.418919	+	0.418919i
$964$	−1.00000	−	1.00000i	−0.0322078	−	0.0322078i
$965$		0			0
$966$		−	20.0000i		−	0.643489i
$967$			48.0000i			1.54358i	0.635880	+	0.771788i	$0.280637\pi$
$967$			48.0000i			1.54358i	−0.635880	+	0.771788i	$0.719363\pi$
$968$	−9.00000			−0.289271
$969$	−30.0000	+	30.0000i	−0.963739	+	0.963739i
$970$		0			0
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	7.00000	+	7.00000i	0.224525	+	0.224525i
$973$		−	28.0000i		−	0.897639i
$974$	32.0000			1.02535
$975$		0			0
$976$	2.00000			0.0640184
$977$		−	22.0000i		−	0.703842i	−0.936030	−	0.351921i	$-0.885529\pi$
$977$		−	22.0000i		−	0.703842i	0.936030	−	0.351921i	$-0.114471\pi$
$978$	4.00000	+	4.00000i	0.127906	+	0.127906i
$979$	14.0000			0.447442
$980$		0			0
$981$	13.0000	−	13.0000i	0.415058	−	0.415058i
$982$	10.0000			0.319113
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$		−	2.00000i		−	0.0637577i
$985$		0			0
$986$	20.0000	+	20.0000i	0.636930	+	0.636930i
$987$	4.00000	+	4.00000i	0.127321	+	0.127321i
$988$	15.0000	−	3.00000i	0.477214	−	0.0954427i
$989$			50.0000i			1.58991i
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	1.00000	+	1.00000i	0.0317500	+	0.0317500i
$993$	−18.0000			−0.571213
$994$	2.00000	+	2.00000i	0.0634361	+	0.0634361i
$995$		0			0
$996$	−6.00000	−	6.00000i	−0.190117	−	0.190117i
$997$	17.0000	−	17.0000i	0.538395	−	0.538395i	−0.384662	−	0.923057i	$-0.625682\pi$
$997$	17.0000	−	17.0000i	0.538395	−	0.538395i	0.923057	+	0.384662i	$0.125682\pi$
$998$	−23.0000	+	23.0000i	−0.728052	+	0.728052i
$999$	−32.0000	+	32.0000i	−1.01244	+	1.01244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.j.d.343.1		2
5.2	odd	4		650.2.g.b.57.1		2
5.3	odd	4		130.2.g.c.57.1	✓	2
5.4	even	2		130.2.j.b.83.1	yes	2
13.8	odd	4		650.2.g.b.593.1		2
15.8	even	4		1170.2.m.a.577.1		2
15.14	odd	2		1170.2.w.c.343.1		2
20.3	even	4		1040.2.bg.f.577.1		2
20.19	odd	2		1040.2.cd.e.993.1		2
65.8	even	4		130.2.j.b.47.1	yes	2
65.34	odd	4		130.2.g.c.73.1	yes	2
65.47	even	4	inner	650.2.j.d.307.1		2
195.8	odd	4		1170.2.w.c.307.1		2
195.164	even	4		1170.2.m.a.73.1		2
260.99	even	4		1040.2.bg.f.593.1		2
260.203	odd	4		1040.2.cd.e.177.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.c.57.1	✓	2	5.3	odd	4
130.2.g.c.73.1	yes	2	65.34	odd	4
130.2.j.b.47.1	yes	2	65.8	even	4
130.2.j.b.83.1	yes	2	5.4	even	2
650.2.g.b.57.1		2	5.2	odd	4
650.2.g.b.593.1		2	13.8	odd	4
650.2.j.d.307.1		2	65.47	even	4	inner
650.2.j.d.343.1		2	1.1	even	1	trivial
1040.2.bg.f.577.1		2	20.3	even	4
1040.2.bg.f.593.1		2	260.99	even	4
1040.2.cd.e.177.1		2	260.203	odd	4
1040.2.cd.e.993.1		2	20.19	odd	2
1170.2.m.a.73.1		2	195.164	even	4
1170.2.m.a.577.1		2	15.8	even	4
1170.2.w.c.307.1		2	195.8	odd	4
1170.2.w.c.343.1		2	15.14	odd	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.00000 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 + 1.00000i) q^{6} +2.00000 q^{7} -1.00000i q^{8} -1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{12} +(-2.00000 + 3.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(5.00000 + 5.00000i) q^{17} +1.00000 q^{18} +(3.00000 + 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(-5.00000 + 5.00000i) q^{23} +(1.00000 - 1.00000i) q^{24} +(-3.00000 - 2.00000i) q^{26} +(4.00000 - 4.00000i) q^{27} -2.00000 q^{28} -4.00000i q^{29} +(1.00000 - 1.00000i) q^{31} +1.00000i q^{32} +2.00000i q^{33} +(-5.00000 + 5.00000i) q^{34} +1.00000i q^{36} -8.00000 q^{37} +(-3.00000 + 3.00000i) q^{38} +(-5.00000 + 1.00000i) q^{39} +(1.00000 - 1.00000i) q^{41} +(-2.00000 + 2.00000i) q^{42} +(5.00000 - 5.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(-5.00000 - 5.00000i) q^{46} +2.00000 q^{47} +(1.00000 + 1.00000i) q^{48} -3.00000 q^{49} +10.0000i q^{51} +(2.00000 - 3.00000i) q^{52} +(1.00000 + 1.00000i) q^{53} +(4.00000 + 4.00000i) q^{54} -2.00000i q^{56} +6.00000i q^{57} +4.00000 q^{58} +(-3.00000 + 3.00000i) q^{59} +2.00000 q^{61} +(1.00000 + 1.00000i) q^{62} -2.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} -12.0000i q^{67} +(-5.00000 - 5.00000i) q^{68} -10.0000 q^{69} +(1.00000 - 1.00000i) q^{71} -1.00000 q^{72} +6.00000i q^{73} -8.00000i q^{74} +(-3.00000 - 3.00000i) q^{76} +(2.00000 + 2.00000i) q^{77} +(-1.00000 - 5.00000i) q^{78} -14.0000i q^{79} +5.00000 q^{81} +(1.00000 + 1.00000i) q^{82} +6.00000 q^{83} +(-2.00000 - 2.00000i) q^{84} +(5.00000 + 5.00000i) q^{86} +(4.00000 - 4.00000i) q^{87} +(1.00000 - 1.00000i) q^{88} +(7.00000 - 7.00000i) q^{89} +(-4.00000 + 6.00000i) q^{91} +(5.00000 - 5.00000i) q^{92} +2.00000 q^{93} +2.00000i q^{94} +(-1.00000 + 1.00000i) q^{96} -2.00000i q^{97} -3.00000i q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{16} + 10 q^{17} + 2 q^{18} + 6 q^{19} + 4 q^{21} - 2 q^{22} - 10 q^{23} + 2 q^{24} - 6 q^{26} + 8 q^{27} - 4 q^{28} + 2 q^{31}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 2 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^16 + 10 * q^17 + 2 * q^18 + 6 * q^19 + 4 * q^21 - 2 * q^22 - 10 * q^23 + 2 * q^24 - 6 * q^26 + 8 * q^27 - 4 * q^28 + 2 * q^31 - 10 * q^34 - 16 * q^37 - 6 * q^38 - 10 * q^39 + 2 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 10 * q^46 + 4 * q^47 + 2 * q^48 - 6 * q^49 + 4 * q^52 + 2 * q^53 + 8 * q^54 + 8 * q^58 - 6 * q^59 + 4 * q^61 + 2 * q^62 - 2 * q^64 - 4 * q^66 - 10 * q^68 - 20 * q^69 + 2 * q^71 - 2 * q^72 - 6 * q^76 + 4 * q^77 - 2 * q^78 + 10 * q^81 + 2 * q^82 + 12 * q^83 - 4 * q^84 + 10 * q^86 + 8 * q^87 + 2 * q^88 + 14 * q^89 - 8 * q^91 + 10 * q^92 + 4 * q^93 - 2 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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