LMFDB - Embedded newform 130.2.g.b.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,2,Mod(57,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.57"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.03805522628$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	130.73
Dual form			130.2.g.b.57.1

$q$-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 q^{2} +(1.00000 + 1.00000i) q^{3} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +2.00000i q^{7} -1.00000 q^{8} -1.00000i q^{9} +(1.00000 - 2.00000i) q^{10} +(-1.00000 + 1.00000i) q^{11} +(1.00000 + 1.00000i) q^{12} +(3.00000 + 2.00000i) q^{13} -2.00000i q^{14} +(-3.00000 + 1.00000i) q^{15} +1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +1.00000i q^{18} +(3.00000 - 3.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(-2.00000 + 2.00000i) q^{21} +(1.00000 - 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-1.00000 - 1.00000i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +(4.00000 - 4.00000i) q^{27} +2.00000i q^{28} -8.00000i q^{29} +(3.00000 - 1.00000i) q^{30} +(1.00000 + 1.00000i) q^{31} -1.00000 q^{32} -2.00000 q^{33} +(-1.00000 - 1.00000i) q^{34} +(-4.00000 - 2.00000i) q^{35} -1.00000i q^{36} -8.00000i q^{37} +(-3.00000 + 3.00000i) q^{38} +(1.00000 + 5.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +(-7.00000 - 7.00000i) q^{41} +(2.00000 - 2.00000i) q^{42} +(-1.00000 + 1.00000i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(2.00000 + 1.00000i) q^{45} +(1.00000 - 1.00000i) q^{46} +10.0000i q^{47} +(1.00000 + 1.00000i) q^{48} +3.00000 q^{49} +(3.00000 + 4.00000i) q^{50} +2.00000i q^{51} +(3.00000 + 2.00000i) q^{52} +(1.00000 + 1.00000i) q^{53} +(-4.00000 + 4.00000i) q^{54} +(-1.00000 - 3.00000i) q^{55} -2.00000i q^{56} +6.00000 q^{57} +8.00000i q^{58} +(9.00000 + 9.00000i) q^{59} +(-3.00000 + 1.00000i) q^{60} +2.00000 q^{61} +(-1.00000 - 1.00000i) q^{62} +2.00000 q^{63} +1.00000 q^{64} +(-7.00000 + 4.00000i) q^{65} +2.00000 q^{66} -12.0000 q^{67} +(1.00000 + 1.00000i) q^{68} -2.00000 q^{69} +(4.00000 + 2.00000i) q^{70} +(5.00000 + 5.00000i) q^{71} +1.00000i q^{72} +6.00000 q^{73} +8.00000i q^{74} +(1.00000 - 7.00000i) q^{75} +(3.00000 - 3.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +(-1.00000 - 5.00000i) q^{78} +10.0000i q^{79} +(-1.00000 + 2.00000i) q^{80} +5.00000 q^{81} +(7.00000 + 7.00000i) q^{82} -18.0000i q^{83} +(-2.00000 + 2.00000i) q^{84} +(-3.00000 + 1.00000i) q^{85} +(1.00000 - 1.00000i) q^{86} +(8.00000 - 8.00000i) q^{87} +(1.00000 - 1.00000i) q^{88} +(-11.0000 - 11.0000i) q^{89} +(-2.00000 - 1.00000i) q^{90} +(-4.00000 + 6.00000i) q^{91} +(-1.00000 + 1.00000i) q^{92} +2.00000i q^{93} -10.0000i q^{94} +(3.00000 + 9.00000i) q^{95} +(-1.00000 - 1.00000i) q^{96} -14.0000 q^{97} -3.00000 q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 6 q^{15} + 2 q^{16} + 2 q^{17} + 6 q^{19} - 2 q^{20} - 4 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 6 * q^15 + 2 * q^16 + 2 * q^17 + 6 * q^19 - 2 * q^20 - 4 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 - 6 * q^25 - 6 * q^26 + 8 * q^27 + 6 * q^30 + 2 * q^31 - 2 * q^32 - 4 * q^33 - 2 * q^34 - 8 * q^35 - 6 * q^38 + 2 * q^39 + 2 * q^40 - 14 * q^41 + 4 * q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 + 2 * q^46 + 2 * q^48 + 6 * q^49 + 6 * q^50 + 6 * q^52 + 2 * q^53 - 8 * q^54 - 2 * q^55 + 12 * q^57 + 18 * q^59 - 6 * q^60 + 4 * q^61 - 2 * q^62 + 4 * q^63 + 2 * q^64 - 14 * q^65 + 4 * q^66 - 24 * q^67 + 2 * q^68 - 4 * q^69 + 8 * q^70 + 10 * q^71 + 12 * q^73 + 2 * q^75 + 6 * q^76 - 4 * q^77 - 2 * q^78 - 2 * q^80 + 10 * q^81 + 14 * q^82 - 4 * q^84 - 6 * q^85 + 2 * q^86 + 16 * q^87 + 2 * q^88 - 22 * q^89 - 4 * q^90 - 8 * q^91 - 2 * q^92 + 6 * q^95 - 2 * q^96 - 28 * q^97 - 6 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	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
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	−0.841605	−	0.540094i	$-0.818389\pi$
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	0.540094	+	0.841605i	$0.318389\pi$
$12$	1.00000	+	1.00000i	0.288675	+	0.288675i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$		−	2.00000i		−	0.534522i
$15$	−3.00000	+	1.00000i	−0.774597	+	0.258199i
$16$	1.00000			0.250000
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$			1.00000i			0.235702i
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$	−2.00000	+	2.00000i	−0.436436	+	0.436436i
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$	−1.00000	−	1.00000i	−0.204124	−	0.204124i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	−3.00000	−	2.00000i	−0.588348	−	0.392232i
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$			2.00000i			0.377964i
$29$		−	8.00000i		−	1.48556i	−0.669534	−	0.742781i	$-0.733506\pi$
$29$		−	8.00000i		−	1.48556i	0.669534	−	0.742781i	$-0.266494\pi$
$30$	3.00000	−	1.00000i	0.547723	−	0.182574i
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	0.791184	−	0.611578i	$-0.209465\pi$
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	−0.611578	+	0.791184i	$0.709465\pi$
$32$	−1.00000			−0.176777
$33$	−2.00000			−0.348155
$34$	−1.00000	−	1.00000i	−0.171499	−	0.171499i
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		−	1.00000i		−	0.166667i
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$	−3.00000	+	3.00000i	−0.486664	+	0.486664i
$39$	1.00000	+	5.00000i	0.160128	+	0.800641i
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.995183	−	0.0980332i	$-0.968745\pi$
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.0980332	−	0.995183i	$-0.531255\pi$
$42$	2.00000	−	2.00000i	0.308607	−	0.308607i
$43$	−1.00000	+	1.00000i	−0.152499	+	0.152499i	−0.779233	−	0.626734i	$-0.784391\pi$
$43$	−1.00000	+	1.00000i	−0.152499	+	0.152499i	0.626734	+	0.779233i	$0.284391\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$	2.00000	+	1.00000i	0.298142	+	0.149071i
$46$	1.00000	−	1.00000i	0.147442	−	0.147442i
$47$			10.0000i			1.45865i	0.684167	+	0.729325i	$0.260166\pi$
$47$			10.0000i			1.45865i	−0.684167	+	0.729325i	$0.739834\pi$
$48$	1.00000	+	1.00000i	0.144338	+	0.144338i
$49$	3.00000			0.428571
$50$	3.00000	+	4.00000i	0.424264	+	0.565685i
$51$			2.00000i			0.280056i
$52$	3.00000	+	2.00000i	0.416025	+	0.277350i
$53$	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
$55$	−1.00000	−	3.00000i	−0.134840	−	0.404520i
$56$		−	2.00000i		−	0.267261i
$57$	6.00000			0.794719
$58$			8.00000i			1.05045i
$59$	9.00000	+	9.00000i	1.17170	+	1.17170i	0.981804	+	0.189896i	$0.0608151\pi$
$59$	9.00000	+	9.00000i	1.17170	+	1.17170i	0.189896	+	0.981804i	$0.439185\pi$
$60$	−3.00000	+	1.00000i	−0.387298	+	0.129099i
$61$	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
$63$	2.00000			0.251976
$64$	1.00000			0.125000
$65$	−7.00000	+	4.00000i	−0.868243	+	0.496139i
$66$	2.00000			0.246183
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	1.00000	+	1.00000i	0.121268	+	0.121268i
$69$	−2.00000			−0.240772
$70$	4.00000	+	2.00000i	0.478091	+	0.239046i
$71$	5.00000	+	5.00000i	0.593391	+	0.593391i	0.938546	−	0.345155i	$-0.112174\pi$
$71$	5.00000	+	5.00000i	0.593391	+	0.593391i	−0.345155	+	0.938546i	$0.612174\pi$
$72$			1.00000i			0.117851i
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$			8.00000i			0.929981i
$75$	1.00000	−	7.00000i	0.115470	−	0.808290i
$76$	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
$79$			10.0000i			1.12509i	0.826767	+	0.562544i	$0.190177\pi$
$79$			10.0000i			1.12509i	−0.826767	+	0.562544i	$0.809823\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$	5.00000			0.555556
$82$	7.00000	+	7.00000i	0.773021	+	0.773021i
$83$		−	18.0000i		−	1.97576i	−0.155230	−	0.987878i	$-0.549612\pi$
$83$		−	18.0000i		−	1.97576i	0.155230	−	0.987878i	$-0.450388\pi$
$84$	−2.00000	+	2.00000i	−0.218218	+	0.218218i
$85$	−3.00000	+	1.00000i	−0.325396	+	0.108465i
$86$	1.00000	−	1.00000i	0.107833	−	0.107833i
$87$	8.00000	−	8.00000i	0.857690	−	0.857690i
$88$	1.00000	−	1.00000i	0.106600	−	0.106600i
$89$	−11.0000	−	11.0000i	−1.16600	−	1.16600i	−0.983139	−	0.182858i	$-0.941465\pi$
$89$	−11.0000	−	11.0000i	−1.16600	−	1.16600i	−0.182858	−	0.983139i	$-0.558535\pi$
$90$	−2.00000	−	1.00000i	−0.210819	−	0.105409i
$91$	−4.00000	+	6.00000i	−0.419314	+	0.628971i
$92$	−1.00000	+	1.00000i	−0.104257	+	0.104257i
$93$			2.00000i			0.207390i
$94$		−	10.0000i		−	1.03142i
$95$	3.00000	+	9.00000i	0.307794	+	0.923381i
$96$	−1.00000	−	1.00000i	−0.102062	−	0.102062i
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$	−3.00000			−0.303046
$99$	1.00000	+	1.00000i	0.100504	+	0.100504i
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$			12.0000i			1.19404i	0.802225	+	0.597022i	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$		−	2.00000i		−	0.198030i
$103$	−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
$105$	−2.00000	−	6.00000i	−0.195180	−	0.585540i
$106$	−1.00000	−	1.00000i	−0.0971286	−	0.0971286i
$107$	−1.00000	+	1.00000i	−0.0966736	+	0.0966736i	−0.753790	−	0.657116i	$-0.771776\pi$
$107$	−1.00000	+	1.00000i	−0.0966736	+	0.0966736i	0.657116	+	0.753790i	$0.271776\pi$
$108$	4.00000	−	4.00000i	0.384900	−	0.384900i
$109$	5.00000	−	5.00000i	0.478913	−	0.478913i	−0.425871	−	0.904784i	$-0.640032\pi$
$109$	5.00000	−	5.00000i	0.478913	−	0.478913i	0.904784	+	0.425871i	$0.140032\pi$
$110$	1.00000	+	3.00000i	0.0953463	+	0.286039i
$111$	8.00000	−	8.00000i	0.759326	−	0.759326i
$112$			2.00000i			0.188982i
$113$	−3.00000	−	3.00000i	−0.282216	−	0.282216i	0.551776	−	0.833992i	$-0.313950\pi$
$113$	−3.00000	−	3.00000i	−0.282216	−	0.282216i	−0.833992	+	0.551776i	$0.813950\pi$
$114$	−6.00000			−0.561951
$115$	−1.00000	−	3.00000i	−0.0932505	−	0.279751i
$116$		−	8.00000i		−	0.742781i
$117$	2.00000	−	3.00000i	0.184900	−	0.277350i
$118$	−9.00000	−	9.00000i	−0.828517	−	0.828517i
$119$	−2.00000	+	2.00000i	−0.183340	+	0.183340i
$120$	3.00000	−	1.00000i	0.273861	−	0.0912871i
$121$			9.00000i			0.818182i
$122$	−2.00000			−0.181071
$123$		−	14.0000i		−	1.26234i
$124$	1.00000	+	1.00000i	0.0898027	+	0.0898027i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	−2.00000			−0.178174
$127$	−3.00000	−	3.00000i	−0.266207	−	0.266207i	0.561363	−	0.827570i	$-0.310277\pi$
$127$	−3.00000	−	3.00000i	−0.266207	−	0.266207i	−0.827570	+	0.561363i	$0.810277\pi$
$128$	−1.00000			−0.0883883
$129$	−2.00000			−0.176090
$130$	7.00000	−	4.00000i	0.613941	−	0.350823i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	−2.00000			−0.174078
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$	12.0000			1.03664
$135$	4.00000	+	12.0000i	0.344265	+	1.03280i
$136$	−1.00000	−	1.00000i	−0.0857493	−	0.0857493i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	2.00000			0.170251
$139$		−	2.00000i		−	0.169638i	−0.996396	−	0.0848189i	$-0.972969\pi$
$139$		−	2.00000i		−	0.169638i	0.996396	−	0.0848189i	$-0.0270312\pi$
$140$	−4.00000	−	2.00000i	−0.338062	−	0.169031i
$141$	−10.0000	+	10.0000i	−0.842152	+	0.842152i
$142$	−5.00000	−	5.00000i	−0.419591	−	0.419591i
$143$	−5.00000	+	1.00000i	−0.418121	+	0.0836242i
$144$		−	1.00000i		−	0.0833333i
$145$	16.0000	+	8.00000i	1.32873	+	0.664364i
$146$	−6.00000			−0.496564
$147$	3.00000	+	3.00000i	0.247436	+	0.247436i
$148$		−	8.00000i		−	0.657596i
$149$	1.00000	−	1.00000i	0.0819232	−	0.0819232i	−0.664958	−	0.746881i	$-0.731550\pi$
$149$	1.00000	−	1.00000i	0.0819232	−	0.0819232i	0.746881	+	0.664958i	$0.231550\pi$
$150$	−1.00000	+	7.00000i	−0.0816497	+	0.571548i
$151$	3.00000	−	3.00000i	0.244137	−	0.244137i	−0.574422	−	0.818559i	$-0.694773\pi$
$151$	3.00000	−	3.00000i	0.244137	−	0.244137i	0.818559	+	0.574422i	$0.194773\pi$
$152$	−3.00000	+	3.00000i	−0.243332	+	0.243332i
$153$	1.00000	−	1.00000i	0.0808452	−	0.0808452i
$154$	2.00000	+	2.00000i	0.161165	+	0.161165i
$155$	−3.00000	+	1.00000i	−0.240966	+	0.0803219i
$156$	1.00000	+	5.00000i	0.0800641	+	0.400320i
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.222108	+	0.975022i	$0.571294\pi$
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.975022	+	0.222108i	$0.928706\pi$
$158$		−	10.0000i		−	0.795557i
$159$			2.00000i			0.158610i
$160$	1.00000	−	2.00000i	0.0790569	−	0.158114i
$161$	−2.00000	−	2.00000i	−0.157622	−	0.157622i
$162$	−5.00000			−0.392837
$163$	−20.0000			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$164$	−7.00000	−	7.00000i	−0.546608	−	0.546608i
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$			18.0000i			1.39707i
$167$		−	14.0000i		−	1.08335i	−0.840587	−	0.541676i	$-0.817790\pi$
$167$		−	14.0000i		−	1.08335i	0.840587	−	0.541676i	$-0.182210\pi$
$168$	2.00000	−	2.00000i	0.154303	−	0.154303i
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$	3.00000	−	1.00000i	0.230089	−	0.0766965i
$171$	−3.00000	−	3.00000i	−0.229416	−	0.229416i
$172$	−1.00000	+	1.00000i	−0.0762493	+	0.0762493i
$173$	9.00000	−	9.00000i	0.684257	−	0.684257i	−0.276699	−	0.960957i	$-0.589241\pi$
$173$	9.00000	−	9.00000i	0.684257	−	0.684257i	0.960957	+	0.276699i	$0.0892406\pi$
$174$	−8.00000	+	8.00000i	−0.606478	+	0.606478i
$175$	8.00000	−	6.00000i	0.604743	−	0.453557i
$176$	−1.00000	+	1.00000i	−0.0753778	+	0.0753778i
$177$			18.0000i			1.35296i
$178$	11.0000	+	11.0000i	0.824485	+	0.824485i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$	2.00000	+	1.00000i	0.149071	+	0.0745356i
$181$		−	16.0000i		−	1.18927i	−0.803996	−	0.594635i	$-0.797296\pi$
$181$		−	16.0000i		−	1.18927i	0.803996	−	0.594635i	$-0.202704\pi$
$182$	4.00000	−	6.00000i	0.296500	−	0.444750i
$183$	2.00000	+	2.00000i	0.147844	+	0.147844i
$184$	1.00000	−	1.00000i	0.0737210	−	0.0737210i
$185$	16.0000	+	8.00000i	1.17634	+	0.588172i
$186$		−	2.00000i		−	0.146647i
$187$	−2.00000			−0.146254
$188$			10.0000i			0.729325i
$189$	8.00000	+	8.00000i	0.581914	+	0.581914i
$190$	−3.00000	−	9.00000i	−0.217643	−	0.652929i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$	1.00000	+	1.00000i	0.0721688	+	0.0721688i
$193$	2.00000			0.143963			0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000			0.143963			0.0719816	+	0.997406i	$0.477068\pi$
$194$	14.0000			1.00514
$195$	−11.0000	−	3.00000i	−0.787726	−	0.214834i
$196$	3.00000			0.214286
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	−1.00000	−	1.00000i	−0.0710669	−	0.0710669i
$199$	−24.0000			−1.70131			−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000			−1.70131			−0.850657	+	0.525720i	$0.823796\pi$
$200$	3.00000	+	4.00000i	0.212132	+	0.282843i
$201$	−12.0000	−	12.0000i	−0.846415	−	0.846415i
$202$		−	12.0000i		−	0.844317i
$203$	16.0000			1.12298
$204$			2.00000i			0.140028i
$205$	21.0000	−	7.00000i	1.46670	−	0.488901i
$206$	5.00000	−	5.00000i	0.348367	−	0.348367i
$207$	1.00000	+	1.00000i	0.0695048	+	0.0695048i
$208$	3.00000	+	2.00000i	0.208013	+	0.138675i
$209$			6.00000i			0.415029i
$210$	2.00000	+	6.00000i	0.138013	+	0.414039i
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	1.00000	+	1.00000i	0.0686803	+	0.0686803i
$213$			10.0000i			0.685189i
$214$	1.00000	−	1.00000i	0.0683586	−	0.0683586i
$215$	−1.00000	−	3.00000i	−0.0681994	−	0.204598i
$216$	−4.00000	+	4.00000i	−0.272166	+	0.272166i
$217$	−2.00000	+	2.00000i	−0.135769	+	0.135769i
$218$	−5.00000	+	5.00000i	−0.338643	+	0.338643i
$219$	6.00000	+	6.00000i	0.405442	+	0.405442i
$220$	−1.00000	−	3.00000i	−0.0674200	−	0.202260i
$221$	1.00000	+	5.00000i	0.0672673	+	0.336336i
$222$	−8.00000	+	8.00000i	−0.536925	+	0.536925i
$223$			18.0000i			1.20537i	0.797980	+	0.602685i	$0.205902\pi$
$223$			18.0000i			1.20537i	−0.797980	+	0.602685i	$0.794098\pi$
$224$		−	2.00000i		−	0.133631i
$225$	−4.00000	+	3.00000i	−0.266667	+	0.200000i
$226$	3.00000	+	3.00000i	0.199557	+	0.199557i
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$	6.00000			0.397360
$229$	−15.0000	−	15.0000i	−0.991228	−	0.991228i	0.00873396	−	0.999962i	$-0.497220\pi$
$229$	−15.0000	−	15.0000i	−0.991228	−	0.991228i	−0.999962	+	0.00873396i	$0.997220\pi$
$230$	1.00000	+	3.00000i	0.0659380	+	0.197814i
$231$		−	4.00000i		−	0.263181i
$232$			8.00000i			0.525226i
$233$	1.00000	−	1.00000i	0.0655122	−	0.0655122i	−0.673592	−	0.739104i	$-0.735249\pi$
$233$	1.00000	−	1.00000i	0.0655122	−	0.0655122i	0.739104	+	0.673592i	$0.235249\pi$
$234$	−2.00000	+	3.00000i	−0.130744	+	0.196116i
$235$	−20.0000	−	10.0000i	−1.30466	−	0.652328i
$236$	9.00000	+	9.00000i	0.585850	+	0.585850i
$237$	−10.0000	+	10.0000i	−0.649570	+	0.649570i
$238$	2.00000	−	2.00000i	0.129641	−	0.129641i
$239$	−1.00000	+	1.00000i	−0.0646846	+	0.0646846i	−0.738709	−	0.674024i	$-0.764564\pi$
$239$	−1.00000	+	1.00000i	−0.0646846	+	0.0646846i	0.674024	+	0.738709i	$0.264564\pi$
$240$	−3.00000	+	1.00000i	−0.193649	+	0.0645497i
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	−0.674165	−	0.738581i	$-0.735496\pi$
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	0.738581	+	0.674165i	$0.235496\pi$
$242$		−	9.00000i		−	0.578542i
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$	2.00000			0.128037
$245$	−3.00000	+	6.00000i	−0.191663	+	0.383326i
$246$			14.0000i			0.892607i
$247$	15.0000	−	3.00000i	0.954427	−	0.190885i
$248$	−1.00000	−	1.00000i	−0.0635001	−	0.0635001i
$249$	18.0000	−	18.0000i	1.14070	−	1.14070i
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$		−	18.0000i		−	1.13615i	−0.822977	−	0.568075i	$-0.807688\pi$
$251$		−	18.0000i		−	1.13615i	0.822977	−	0.568075i	$-0.192312\pi$
$252$	2.00000			0.125988
$253$		−	2.00000i		−	0.125739i
$254$	3.00000	+	3.00000i	0.188237	+	0.188237i
$255$	−4.00000	−	2.00000i	−0.250490	−	0.125245i
$256$	1.00000			0.0625000
$257$	21.0000	+	21.0000i	1.30994	+	1.30994i	0.921452	+	0.388492i	$0.127004\pi$
$257$	21.0000	+	21.0000i	1.30994	+	1.30994i	0.388492	+	0.921452i	$0.372996\pi$
$258$	2.00000			0.124515
$259$	16.0000			0.994192
$260$	−7.00000	+	4.00000i	−0.434122	+	0.248069i
$261$	−8.00000			−0.495188
$262$	−12.0000			−0.741362
$263$	−3.00000	−	3.00000i	−0.184988	−	0.184988i	0.608537	−	0.793525i	$-0.291757\pi$
$263$	−3.00000	−	3.00000i	−0.184988	−	0.184988i	−0.793525	+	0.608537i	$0.791757\pi$
$264$	2.00000			0.123091
$265$	−3.00000	+	1.00000i	−0.184289	+	0.0614295i
$266$	−6.00000	−	6.00000i	−0.367884	−	0.367884i
$267$		−	22.0000i		−	1.34638i
$268$	−12.0000			−0.733017
$269$		−	4.00000i		−	0.243884i	−0.992537	−	0.121942i	$-0.961088\pi$
$269$		−	4.00000i		−	0.243884i	0.992537	−	0.121942i	$-0.0389122\pi$
$270$	−4.00000	−	12.0000i	−0.243432	−	0.730297i
$271$	3.00000	−	3.00000i	0.182237	−	0.182237i	−0.610093	−	0.792330i	$-0.708868\pi$
$271$	3.00000	−	3.00000i	0.182237	−	0.182237i	0.792330	+	0.610093i	$0.208868\pi$
$272$	1.00000	+	1.00000i	0.0606339	+	0.0606339i
$273$	−10.0000	+	2.00000i	−0.605228	+	0.121046i
$274$		0			0
$275$	7.00000	+	1.00000i	0.422116	+	0.0603023i
$276$	−2.00000			−0.120386
$277$	−11.0000	−	11.0000i	−0.660926	−	0.660926i	0.294672	−	0.955598i	$-0.404789\pi$
$277$	−11.0000	−	11.0000i	−0.660926	−	0.660926i	−0.955598	+	0.294672i	$0.904789\pi$
$278$			2.00000i			0.119952i
$279$	1.00000	−	1.00000i	0.0598684	−	0.0598684i
$280$	4.00000	+	2.00000i	0.239046	+	0.119523i
$281$	9.00000	−	9.00000i	0.536895	−	0.536895i	−0.385721	−	0.922616i	$-0.626047\pi$
$281$	9.00000	−	9.00000i	0.536895	−	0.536895i	0.922616	+	0.385721i	$0.126047\pi$
$282$	10.0000	−	10.0000i	0.595491	−	0.595491i
$283$	15.0000	−	15.0000i	0.891657	−	0.891657i	−0.103022	−	0.994679i	$-0.532851\pi$
$283$	15.0000	−	15.0000i	0.891657	−	0.891657i	0.994679	+	0.103022i	$0.0328511\pi$
$284$	5.00000	+	5.00000i	0.296695	+	0.296695i
$285$	−6.00000	+	12.0000i	−0.355409	+	0.710819i
$286$	5.00000	−	1.00000i	0.295656	−	0.0591312i
$287$	14.0000	−	14.0000i	0.826394	−	0.826394i
$288$			1.00000i			0.0589256i
$289$		−	15.0000i		−	0.882353i
$290$	−16.0000	−	8.00000i	−0.939552	−	0.469776i
$291$	−14.0000	−	14.0000i	−0.820695	−	0.820695i
$292$	6.00000			0.351123
$293$	−22.0000			−1.28525			−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000			−1.28525			−0.642627	+	0.766179i	$0.722155\pi$
$294$	−3.00000	−	3.00000i	−0.174964	−	0.174964i
$295$	−27.0000	+	9.00000i	−1.57200	+	0.524000i
$296$			8.00000i			0.464991i
$297$			8.00000i			0.464207i
$298$	−1.00000	+	1.00000i	−0.0579284	+	0.0579284i
$299$	−5.00000	+	1.00000i	−0.289157	+	0.0578315i
$300$	1.00000	−	7.00000i	0.0577350	−	0.404145i
$301$	−2.00000	−	2.00000i	−0.115278	−	0.115278i
$302$	−3.00000	+	3.00000i	−0.172631	+	0.172631i
$303$	−12.0000	+	12.0000i	−0.689382	+	0.689382i
$304$	3.00000	−	3.00000i	0.172062	−	0.172062i
$305$	−2.00000	+	4.00000i	−0.114520	+	0.229039i
$306$	−1.00000	+	1.00000i	−0.0571662	+	0.0571662i
$307$		−	10.0000i		−	0.570730i	−0.958419	−	0.285365i	$-0.907885\pi$
$307$		−	10.0000i		−	0.570730i	0.958419	−	0.285365i	$-0.0921148\pi$
$308$	−2.00000	−	2.00000i	−0.113961	−	0.113961i
$309$	−10.0000			−0.568880
$310$	3.00000	−	1.00000i	0.170389	−	0.0567962i
$311$			2.00000i			0.113410i	0.998391	+	0.0567048i	$0.0180594\pi$
$311$			2.00000i			0.113410i	−0.998391	+	0.0567048i	$0.981941\pi$
$312$	−1.00000	−	5.00000i	−0.0566139	−	0.283069i
$313$	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	$0.632875\pi$
$314$	15.0000	−	15.0000i	0.846499	−	0.846499i
$315$	−2.00000	+	4.00000i	−0.112687	+	0.225374i
$316$			10.0000i			0.562544i
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$		−	2.00000i		−	0.112154i
$319$	8.00000	+	8.00000i	0.447914	+	0.447914i
$320$	−1.00000	+	2.00000i	−0.0559017	+	0.111803i
$321$	−2.00000			−0.111629
$322$	2.00000	+	2.00000i	0.111456	+	0.111456i
$323$	6.00000			0.333849
$324$	5.00000			0.277778
$325$	−1.00000	−	18.0000i	−0.0554700	−	0.998460i
$326$	20.0000			1.10770
$327$	10.0000			0.553001
$328$	7.00000	+	7.00000i	0.386510	+	0.386510i
$329$	−20.0000			−1.10264
$330$	−2.00000	+	4.00000i	−0.110096	+	0.220193i
$331$	21.0000	+	21.0000i	1.15426	+	1.15426i	0.985689	+	0.168576i	$0.0539168\pi$
$331$	21.0000	+	21.0000i	1.15426	+	1.15426i	0.168576	+	0.985689i	$0.446083\pi$
$332$		−	18.0000i		−	0.987878i
$333$	−8.00000			−0.438397
$334$			14.0000i			0.766046i
$335$	12.0000	−	24.0000i	0.655630	−	1.31126i
$336$	−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	$0.688310\pi$
$338$	−5.00000	−	12.0000i	−0.271964	−	0.652714i
$339$		−	6.00000i		−	0.325875i
$340$	−3.00000	+	1.00000i	−0.162698	+	0.0542326i
$341$	−2.00000			−0.108306
$342$	3.00000	+	3.00000i	0.162221	+	0.162221i
$343$			20.0000i			1.07990i
$344$	1.00000	−	1.00000i	0.0539164	−	0.0539164i
$345$	2.00000	−	4.00000i	0.107676	−	0.215353i
$346$	−9.00000	+	9.00000i	−0.483843	+	0.483843i
$347$	−5.00000	+	5.00000i	−0.268414	+	0.268414i	−0.828461	−	0.560047i	$-0.810783\pi$
$347$	−5.00000	+	5.00000i	−0.268414	+	0.268414i	0.560047	+	0.828461i	$0.310783\pi$
$348$	8.00000	−	8.00000i	0.428845	−	0.428845i
$349$	21.0000	+	21.0000i	1.12410	+	1.12410i	0.991118	+	0.132986i	$0.0424566\pi$
$349$	21.0000	+	21.0000i	1.12410	+	1.12410i	0.132986	+	0.991118i	$0.457543\pi$
$350$	−8.00000	+	6.00000i	−0.427618	+	0.320713i
$351$	20.0000	−	4.00000i	1.06752	−	0.213504i
$352$	1.00000	−	1.00000i	0.0533002	−	0.0533002i
$353$			4.00000i			0.212899i	0.994318	+	0.106449i	$0.0339482\pi$
$353$			4.00000i			0.212899i	−0.994318	+	0.106449i	$0.966052\pi$
$354$		−	18.0000i		−	0.956689i
$355$	−15.0000	+	5.00000i	−0.796117	+	0.265372i
$356$	−11.0000	−	11.0000i	−0.582999	−	0.582999i
$357$	−4.00000			−0.211702
$358$	20.0000			1.05703
$359$	5.00000	+	5.00000i	0.263890	+	0.263890i	0.826632	−	0.562742i	$-0.190254\pi$
$359$	5.00000	+	5.00000i	0.263890	+	0.263890i	−0.562742	+	0.826632i	$0.690254\pi$
$360$	−2.00000	−	1.00000i	−0.105409	−	0.0527046i
$361$			1.00000i			0.0526316i
$362$			16.0000i			0.840941i
$363$	−9.00000	+	9.00000i	−0.472377	+	0.472377i
$364$	−4.00000	+	6.00000i	−0.209657	+	0.314485i
$365$	−6.00000	+	12.0000i	−0.314054	+	0.628109i
$366$	−2.00000	−	2.00000i	−0.104542	−	0.104542i
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.101339	+	0.994852i	$0.532313\pi$
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.994852	+	0.101339i	$0.967687\pi$
$368$	−1.00000	+	1.00000i	−0.0521286	+	0.0521286i
$369$	−7.00000	+	7.00000i	−0.364405	+	0.364405i
$370$	−16.0000	−	8.00000i	−0.831800	−	0.415900i
$371$	−2.00000	+	2.00000i	−0.103835	+	0.103835i
$372$			2.00000i			0.103695i
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	0.824603	−	0.565712i	$-0.191399\pi$
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	−0.565712	+	0.824603i	$0.691399\pi$
$374$	2.00000			0.103418
$375$	13.0000	+	9.00000i	0.671317	+	0.464758i
$376$		−	10.0000i		−	0.515711i
$377$	16.0000	−	24.0000i	0.824042	−	1.23606i
$378$	−8.00000	−	8.00000i	−0.411476	−	0.411476i
$379$	23.0000	−	23.0000i	1.18143	−	1.18143i	0.202057	−	0.979374i	$-0.435237\pi$
$379$	23.0000	−	23.0000i	1.18143	−	1.18143i	0.979374	−	0.202057i	$-0.0647626\pi$
$380$	3.00000	+	9.00000i	0.153897	+	0.461690i
$381$		−	6.00000i		−	0.307389i
$382$	−8.00000			−0.409316
$383$			18.0000i			0.919757i	0.887982	+	0.459879i	$0.152107\pi$
$383$			18.0000i			0.919757i	−0.887982	+	0.459879i	$0.847893\pi$
$384$	−1.00000	−	1.00000i	−0.0510310	−	0.0510310i
$385$	6.00000	−	2.00000i	0.305788	−	0.101929i
$386$	−2.00000			−0.101797
$387$	1.00000	+	1.00000i	0.0508329	+	0.0508329i
$388$	−14.0000			−0.710742
$389$	−2.00000			−0.101404			−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000			−0.101404			−0.0507020	+	0.998714i	$0.516146\pi$
$390$	11.0000	+	3.00000i	0.557007	+	0.151911i
$391$	−2.00000			−0.101144
$392$	−3.00000			−0.151523
$393$	12.0000	+	12.0000i	0.605320	+	0.605320i
$394$	−6.00000			−0.302276
$395$	−20.0000	−	10.0000i	−1.00631	−	0.503155i
$396$	1.00000	+	1.00000i	0.0502519	+	0.0502519i
$397$		−	8.00000i		−	0.401508i	−0.979642	−	0.200754i	$-0.935661\pi$
$397$		−	8.00000i		−	0.401508i	0.979642	−	0.200754i	$-0.0643393\pi$
$398$	24.0000			1.20301
$399$			12.0000i			0.600751i
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	−19.0000	+	19.0000i	−0.948815	+	0.948815i	−0.998752	−	0.0499376i	$-0.984098\pi$
$401$	−19.0000	+	19.0000i	−0.948815	+	0.948815i	0.0499376	+	0.998752i	$0.484098\pi$
$402$	12.0000	+	12.0000i	0.598506	+	0.598506i
$403$	1.00000	+	5.00000i	0.0498135	+	0.249068i
$404$			12.0000i			0.597022i
$405$	−5.00000	+	10.0000i	−0.248452	+	0.496904i
$406$	−16.0000			−0.794067
$407$	8.00000	+	8.00000i	0.396545	+	0.396545i
$408$		−	2.00000i		−	0.0990148i
$409$	9.00000	−	9.00000i	0.445021	−	0.445021i	−0.448674	−	0.893695i	$-0.648104\pi$
$409$	9.00000	−	9.00000i	0.445021	−	0.445021i	0.893695	+	0.448674i	$0.148104\pi$
$410$	−21.0000	+	7.00000i	−1.03712	+	0.345705i
$411$		0			0
$412$	−5.00000	+	5.00000i	−0.246332	+	0.246332i
$413$	−18.0000	+	18.0000i	−0.885722	+	0.885722i
$414$	−1.00000	−	1.00000i	−0.0491473	−	0.0491473i
$415$	36.0000	+	18.0000i	1.76717	+	0.883585i
$416$	−3.00000	−	2.00000i	−0.147087	−	0.0980581i
$417$	2.00000	−	2.00000i	0.0979404	−	0.0979404i
$418$		−	6.00000i		−	0.293470i
$419$			22.0000i			1.07477i	0.843337	+	0.537385i	$0.180588\pi$
$419$			22.0000i			1.07477i	−0.843337	+	0.537385i	$0.819412\pi$
$420$	−2.00000	−	6.00000i	−0.0975900	−	0.292770i
$421$	9.00000	+	9.00000i	0.438633	+	0.438633i	0.891552	−	0.452919i	$-0.149617\pi$
$421$	9.00000	+	9.00000i	0.438633	+	0.438633i	−0.452919	+	0.891552i	$0.649617\pi$
$422$	12.0000			0.584151
$423$	10.0000			0.486217
$424$	−1.00000	−	1.00000i	−0.0485643	−	0.0485643i
$425$	1.00000	−	7.00000i	0.0485071	−	0.339550i
$426$		−	10.0000i		−	0.484502i
$427$			4.00000i			0.193574i
$428$	−1.00000	+	1.00000i	−0.0483368	+	0.0483368i
$429$	−6.00000	−	4.00000i	−0.289683	−	0.193122i
$430$	1.00000	+	3.00000i	0.0482243	+	0.144673i
$431$	−15.0000	−	15.0000i	−0.722525	−	0.722525i	0.246594	−	0.969119i	$-0.420689\pi$
$431$	−15.0000	−	15.0000i	−0.722525	−	0.722525i	−0.969119	+	0.246594i	$0.920689\pi$
$432$	4.00000	−	4.00000i	0.192450	−	0.192450i
$433$	9.00000	−	9.00000i	0.432512	−	0.432512i	−0.456970	−	0.889482i	$-0.651065\pi$
$433$	9.00000	−	9.00000i	0.432512	−	0.432512i	0.889482	+	0.456970i	$0.151065\pi$
$434$	2.00000	−	2.00000i	0.0960031	−	0.0960031i
$435$	8.00000	+	24.0000i	0.383571	+	1.15071i
$436$	5.00000	−	5.00000i	0.239457	−	0.239457i
$437$			6.00000i			0.287019i
$438$	−6.00000	−	6.00000i	−0.286691	−	0.286691i
$439$	−32.0000			−1.52728			−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000			−1.52728			−0.763638	+	0.645644i	$0.776589\pi$
$440$	1.00000	+	3.00000i	0.0476731	+	0.143019i
$441$		−	3.00000i		−	0.142857i
$442$	−1.00000	−	5.00000i	−0.0475651	−	0.237826i
$443$	17.0000	+	17.0000i	0.807694	+	0.807694i	0.984284	−	0.176590i	$-0.0565067\pi$
$443$	17.0000	+	17.0000i	0.807694	+	0.807694i	−0.176590	+	0.984284i	$0.556507\pi$
$444$	8.00000	−	8.00000i	0.379663	−	0.379663i
$445$	33.0000	−	11.0000i	1.56435	−	0.521450i
$446$		−	18.0000i		−	0.852325i
$447$	2.00000			0.0945968
$448$			2.00000i			0.0944911i
$449$	13.0000	+	13.0000i	0.613508	+	0.613508i	0.943858	−	0.330350i	$-0.107167\pi$
$449$	13.0000	+	13.0000i	0.613508	+	0.613508i	−0.330350	+	0.943858i	$0.607167\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	14.0000			0.659234
$452$	−3.00000	−	3.00000i	−0.141108	−	0.141108i
$453$	6.00000			0.281905
$454$	−12.0000			−0.563188
$455$	−8.00000	−	14.0000i	−0.375046	−	0.656330i
$456$	−6.00000			−0.280976
$457$	2.00000			0.0935561			0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000			0.0935561			0.0467780	+	0.998905i	$0.485105\pi$
$458$	15.0000	+	15.0000i	0.700904	+	0.700904i
$459$	8.00000			0.373408
$460$	−1.00000	−	3.00000i	−0.0466252	−	0.139876i
$461$	−11.0000	−	11.0000i	−0.512321	−	0.512321i	0.402916	−	0.915237i	$-0.367997\pi$
$461$	−11.0000	−	11.0000i	−0.512321	−	0.512321i	−0.915237	+	0.402916i	$0.867997\pi$
$462$			4.00000i			0.186097i
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		−	8.00000i		−	0.371391i
$465$	−4.00000	−	2.00000i	−0.185496	−	0.0927478i
$466$	−1.00000	+	1.00000i	−0.0463241	+	0.0463241i
$467$	−7.00000	−	7.00000i	−0.323921	−	0.323921i	0.526348	−	0.850269i	$-0.323561\pi$
$467$	−7.00000	−	7.00000i	−0.323921	−	0.323921i	−0.850269	+	0.526348i	$0.823561\pi$
$468$	2.00000	−	3.00000i	0.0924500	−	0.138675i
$469$		−	24.0000i		−	1.10822i
$470$	20.0000	+	10.0000i	0.922531	+	0.461266i
$471$	−30.0000			−1.38233
$472$	−9.00000	−	9.00000i	−0.414259	−	0.414259i
$473$		−	2.00000i		−	0.0919601i
$474$	10.0000	−	10.0000i	0.459315	−	0.459315i
$475$	−21.0000	−	3.00000i	−0.963546	−	0.137649i
$476$	−2.00000	+	2.00000i	−0.0916698	+	0.0916698i
$477$	1.00000	−	1.00000i	0.0457869	−	0.0457869i
$478$	1.00000	−	1.00000i	0.0457389	−	0.0457389i
$479$	−19.0000	−	19.0000i	−0.868132	−	0.868132i	0.124133	−	0.992266i	$-0.460385\pi$
$479$	−19.0000	−	19.0000i	−0.868132	−	0.868132i	−0.992266	+	0.124133i	$0.960385\pi$
$480$	3.00000	−	1.00000i	0.136931	−	0.0456435i
$481$	16.0000	−	24.0000i	0.729537	−	1.09431i
$482$	−1.00000	+	1.00000i	−0.0455488	+	0.0455488i
$483$		−	4.00000i		−	0.182006i
$484$			9.00000i			0.409091i
$485$	14.0000	−	28.0000i	0.635707	−	1.27141i
$486$	7.00000	+	7.00000i	0.317526	+	0.317526i
$487$	−8.00000			−0.362515			−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000			−0.362515			−0.181257	+	0.983436i	$0.558017\pi$
$488$	−2.00000			−0.0905357
$489$	−20.0000	−	20.0000i	−0.904431	−	0.904431i
$490$	3.00000	−	6.00000i	0.135526	−	0.271052i
$491$			38.0000i			1.71492i	0.514554	+	0.857458i	$0.327958\pi$
$491$			38.0000i			1.71492i	−0.514554	+	0.857458i	$0.672042\pi$
$492$		−	14.0000i		−	0.631169i
$493$	8.00000	−	8.00000i	0.360302	−	0.360302i
$494$	−15.0000	+	3.00000i	−0.674882	+	0.134976i
$495$	−3.00000	+	1.00000i	−0.134840	+	0.0449467i
$496$	1.00000	+	1.00000i	0.0449013	+	0.0449013i
$497$	−10.0000	+	10.0000i	−0.448561	+	0.448561i
$498$	−18.0000	+	18.0000i	−0.806599	+	0.806599i
$499$	19.0000	−	19.0000i	0.850557	−	0.850557i	−0.139645	−	0.990202i	$-0.544596\pi$
$499$	19.0000	−	19.0000i	0.850557	−	0.850557i	0.990202	+	0.139645i	$0.0445961\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$	14.0000	−	14.0000i	0.625474	−	0.625474i
$502$			18.0000i			0.803379i
$503$	−15.0000	−	15.0000i	−0.668817	−	0.668817i	0.288625	−	0.957442i	$-0.406802\pi$
$503$	−15.0000	−	15.0000i	−0.668817	−	0.668817i	−0.957442	+	0.288625i	$0.906802\pi$
$504$	−2.00000			−0.0890871
$505$	−24.0000	−	12.0000i	−1.06799	−	0.533993i
$506$			2.00000i			0.0889108i
$507$	−7.00000	+	17.0000i	−0.310881	+	0.754997i
$508$	−3.00000	−	3.00000i	−0.133103	−	0.133103i
$509$	1.00000	−	1.00000i	0.0443242	−	0.0443242i	−0.684597	−	0.728922i	$-0.740022\pi$
$509$	1.00000	−	1.00000i	0.0443242	−	0.0443242i	0.728922	+	0.684597i	$0.240022\pi$
$510$	4.00000	+	2.00000i	0.177123	+	0.0885615i
$511$			12.0000i			0.530849i
$512$	−1.00000			−0.0441942
$513$		−	24.0000i		−	1.05963i
$514$	−21.0000	−	21.0000i	−0.926270	−	0.926270i
$515$	−5.00000	−	15.0000i	−0.220326	−	0.660979i
$516$	−2.00000			−0.0880451
$517$	−10.0000	−	10.0000i	−0.439799	−	0.439799i
$518$	−16.0000			−0.703000
$519$	18.0000			0.790112
$520$	7.00000	−	4.00000i	0.306970	−	0.175412i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$	8.00000			0.350150
$523$	−15.0000	−	15.0000i	−0.655904	−	0.655904i	0.298504	−	0.954408i	$-0.403512\pi$
$523$	−15.0000	−	15.0000i	−0.655904	−	0.655904i	−0.954408	+	0.298504i	$0.903512\pi$
$524$	12.0000			0.524222
$525$	14.0000	+	2.00000i	0.611010	+	0.0872872i
$526$	3.00000	+	3.00000i	0.130806	+	0.130806i
$527$			2.00000i			0.0871214i
$528$	−2.00000			−0.0870388
$529$			21.0000i			0.913043i
$530$	3.00000	−	1.00000i	0.130312	−	0.0434372i
$531$	9.00000	−	9.00000i	0.390567	−	0.390567i
$532$	6.00000	+	6.00000i	0.260133	+	0.260133i
$533$	−7.00000	−	35.0000i	−0.303204	−	1.51602i
$534$			22.0000i			0.952033i
$535$	−1.00000	−	3.00000i	−0.0432338	−	0.129701i
$536$	12.0000			0.518321
$537$	−20.0000	−	20.0000i	−0.863064	−	0.863064i
$538$			4.00000i			0.172452i
$539$	−3.00000	+	3.00000i	−0.129219	+	0.129219i
$540$	4.00000	+	12.0000i	0.172133	+	0.516398i
$541$	−27.0000	+	27.0000i	−1.16082	+	1.16082i	−0.176524	+	0.984296i	$0.556485\pi$
$541$	−27.0000	+	27.0000i	−1.16082	+	1.16082i	−0.984296	+	0.176524i	$0.943515\pi$
$542$	−3.00000	+	3.00000i	−0.128861	+	0.128861i
$543$	16.0000	−	16.0000i	0.686626	−	0.686626i
$544$	−1.00000	−	1.00000i	−0.0428746	−	0.0428746i
$545$	5.00000	+	15.0000i	0.214176	+	0.642529i
$546$	10.0000	−	2.00000i	0.427960	−	0.0855921i
$547$	23.0000	−	23.0000i	0.983409	−	0.983409i	−0.0164556	−	0.999865i	$-0.505238\pi$
$547$	23.0000	−	23.0000i	0.983409	−	0.983409i	0.999865	+	0.0164556i	$0.00523822\pi$
$548$		0			0
$549$		−	2.00000i		−	0.0853579i
$550$	−7.00000	−	1.00000i	−0.298481	−	0.0426401i
$551$	−24.0000	−	24.0000i	−1.02243	−	1.02243i
$552$	2.00000			0.0851257
$553$	−20.0000			−0.850487
$554$	11.0000	+	11.0000i	0.467345	+	0.467345i
$555$	8.00000	+	24.0000i	0.339581	+	1.01874i
$556$		−	2.00000i		−	0.0848189i
$557$			32.0000i			1.35588i	0.735116	+	0.677942i	$0.237128\pi$
$557$			32.0000i			1.35588i	−0.735116	+	0.677942i	$0.762872\pi$
$558$	−1.00000	+	1.00000i	−0.0423334	+	0.0423334i
$559$	−5.00000	+	1.00000i	−0.211477	+	0.0422955i
$560$	−4.00000	−	2.00000i	−0.169031	−	0.0845154i
$561$	−2.00000	−	2.00000i	−0.0844401	−	0.0844401i
$562$	−9.00000	+	9.00000i	−0.379642	+	0.379642i
$563$	31.0000	−	31.0000i	1.30649	−	1.30649i	0.382566	−	0.923928i	$-0.375040\pi$
$563$	31.0000	−	31.0000i	1.30649	−	1.30649i	0.923928	−	0.382566i	$-0.124960\pi$
$564$	−10.0000	+	10.0000i	−0.421076	+	0.421076i
$565$	9.00000	−	3.00000i	0.378633	−	0.126211i
$566$	−15.0000	+	15.0000i	−0.630497	+	0.630497i
$567$			10.0000i			0.419961i
$568$	−5.00000	−	5.00000i	−0.209795	−	0.209795i
$569$	−26.0000			−1.08998			−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000			−1.08998			−0.544988	+	0.838444i	$0.683466\pi$
$570$	6.00000	−	12.0000i	0.251312	−	0.502625i
$571$			22.0000i			0.920671i	0.887745	+	0.460336i	$0.152271\pi$
$571$			22.0000i			0.920671i	−0.887745	+	0.460336i	$0.847729\pi$
$572$	−5.00000	+	1.00000i	−0.209061	+	0.0418121i
$573$	8.00000	+	8.00000i	0.334205	+	0.334205i
$574$	−14.0000	+	14.0000i	−0.584349	+	0.584349i
$575$	7.00000	+	1.00000i	0.291920	+	0.0417029i
$576$		−	1.00000i		−	0.0416667i
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$			15.0000i			0.623918i
$579$	2.00000	+	2.00000i	0.0831172	+	0.0831172i
$580$	16.0000	+	8.00000i	0.664364	+	0.332182i
$581$	36.0000			1.49353
$582$	14.0000	+	14.0000i	0.580319	+	0.580319i
$583$	−2.00000			−0.0828315
$584$	−6.00000			−0.248282
$585$	4.00000	+	7.00000i	0.165380	+	0.289414i
$586$	22.0000			0.908812
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	3.00000	+	3.00000i	0.123718	+	0.123718i
$589$	6.00000			0.247226
$590$	27.0000	−	9.00000i	1.11157	−	0.370524i
$591$	6.00000	+	6.00000i	0.246807	+	0.246807i
$592$		−	8.00000i		−	0.328798i
$593$	10.0000			0.410651			0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000			0.410651			0.205325	+	0.978694i	$0.434175\pi$
$594$		−	8.00000i		−	0.328244i
$595$	−2.00000	−	6.00000i	−0.0819920	−	0.245976i
$596$	1.00000	−	1.00000i	0.0409616	−	0.0409616i
$597$	−24.0000	−	24.0000i	−0.982255	−	0.982255i
$598$	5.00000	−	1.00000i	0.204465	−	0.0408930i
$599$			26.0000i			1.06233i	0.847268	+	0.531166i	$0.178246\pi$
$599$			26.0000i			1.06233i	−0.847268	+	0.531166i	$0.821754\pi$
$600$	−1.00000	+	7.00000i	−0.0408248	+	0.285774i
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	2.00000	+	2.00000i	0.0815139	+	0.0815139i
$603$			12.0000i			0.488678i
$604$	3.00000	−	3.00000i	0.122068	−	0.122068i
$605$	−18.0000	−	9.00000i	−0.731804	−	0.365902i
$606$	12.0000	−	12.0000i	0.487467	−	0.487467i
$607$	−9.00000	+	9.00000i	−0.365299	+	0.365299i	−0.865759	−	0.500461i	$-0.833164\pi$
$607$	−9.00000	+	9.00000i	−0.365299	+	0.365299i	0.500461	+	0.865759i	$0.333164\pi$
$608$	−3.00000	+	3.00000i	−0.121666	+	0.121666i
$609$	16.0000	+	16.0000i	0.648353	+	0.648353i
$610$	2.00000	−	4.00000i	0.0809776	−	0.161955i
$611$	−20.0000	+	30.0000i	−0.809113	+	1.21367i
$612$	1.00000	−	1.00000i	0.0404226	−	0.0404226i
$613$			4.00000i			0.161558i	0.996732	+	0.0807792i	$0.0257409\pi$
$613$			4.00000i			0.161558i	−0.996732	+	0.0807792i	$0.974259\pi$
$614$			10.0000i			0.403567i
$615$	28.0000	+	14.0000i	1.12907	+	0.564534i
$616$	2.00000	+	2.00000i	0.0805823	+	0.0805823i
$617$	−38.0000			−1.52982			−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−38.0000			−1.52982			−0.764911	+	0.644136i	$0.777217\pi$
$618$	10.0000			0.402259
$619$	9.00000	+	9.00000i	0.361741	+	0.361741i	0.864453	−	0.502713i	$-0.167665\pi$
$619$	9.00000	+	9.00000i	0.361741	+	0.361741i	−0.502713	+	0.864453i	$0.667665\pi$
$620$	−3.00000	+	1.00000i	−0.120483	+	0.0401610i
$621$			8.00000i			0.321029i
$622$		−	2.00000i		−	0.0801927i
$623$	22.0000	−	22.0000i	0.881411	−	0.881411i
$624$	1.00000	+	5.00000i	0.0400320	+	0.200160i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−9.00000	−	9.00000i	−0.359712	−	0.359712i
$627$	−6.00000	+	6.00000i	−0.239617	+	0.239617i
$628$	−15.0000	+	15.0000i	−0.598565	+	0.598565i
$629$	8.00000	−	8.00000i	0.318981	−	0.318981i
$630$	2.00000	−	4.00000i	0.0796819	−	0.159364i
$631$	23.0000	−	23.0000i	0.915616	−	0.915616i	−0.0810911	−	0.996707i	$-0.525840\pi$
$631$	23.0000	−	23.0000i	0.915616	−	0.915616i	0.996707	+	0.0810911i	$0.0258405\pi$
$632$		−	10.0000i		−	0.397779i
$633$	−12.0000	−	12.0000i	−0.476957	−	0.476957i
$634$	−2.00000			−0.0794301
$635$	9.00000	−	3.00000i	0.357154	−	0.119051i
$636$			2.00000i			0.0793052i
$637$	9.00000	+	6.00000i	0.356593	+	0.237729i
$638$	−8.00000	−	8.00000i	−0.316723	−	0.316723i
$639$	5.00000	−	5.00000i	0.197797	−	0.197797i
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$			24.0000i			0.947943i	0.880540	+	0.473972i	$0.157180\pi$
$641$			24.0000i			0.947943i	−0.880540	+	0.473972i	$0.842820\pi$
$642$	2.00000			0.0789337
$643$		−	10.0000i		−	0.394362i	−0.980367	−	0.197181i	$-0.936821\pi$
$643$		−	10.0000i		−	0.394362i	0.980367	−	0.197181i	$-0.0631786\pi$
$644$	−2.00000	−	2.00000i	−0.0788110	−	0.0788110i
$645$	2.00000	−	4.00000i	0.0787499	−	0.157500i
$646$	−6.00000			−0.236067
$647$	13.0000	+	13.0000i	0.511083	+	0.511083i	0.914858	−	0.403775i	$-0.132302\pi$
$647$	13.0000	+	13.0000i	0.511083	+	0.511083i	−0.403775	+	0.914858i	$0.632302\pi$
$648$	−5.00000			−0.196419
$649$	−18.0000			−0.706562
$650$	1.00000	+	18.0000i	0.0392232	+	0.706018i
$651$	−4.00000			−0.156772
$652$	−20.0000			−0.783260
$653$	−15.0000	−	15.0000i	−0.586995	−	0.586995i	0.349821	−	0.936817i	$-0.386242\pi$
$653$	−15.0000	−	15.0000i	−0.586995	−	0.586995i	−0.936817	+	0.349821i	$0.886242\pi$
$654$	−10.0000			−0.391031
$655$	−12.0000	+	24.0000i	−0.468879	+	0.937758i
$656$	−7.00000	−	7.00000i	−0.273304	−	0.273304i
$657$		−	6.00000i		−	0.234082i
$658$	20.0000			0.779681
$659$			38.0000i			1.48027i	0.672458	+	0.740135i	$0.265238\pi$
$659$			38.0000i			1.48027i	−0.672458	+	0.740135i	$0.734762\pi$
$660$	2.00000	−	4.00000i	0.0778499	−	0.155700i
$661$	13.0000	−	13.0000i	0.505641	−	0.505641i	−0.407544	−	0.913186i	$-0.633615\pi$
$661$	13.0000	−	13.0000i	0.505641	−	0.505641i	0.913186	+	0.407544i	$0.133615\pi$
$662$	−21.0000	−	21.0000i	−0.816188	−	0.816188i
$663$	−4.00000	+	6.00000i	−0.155347	+	0.233021i
$664$			18.0000i			0.698535i
$665$	−18.0000	+	6.00000i	−0.698010	+	0.232670i
$666$	8.00000			0.309994
$667$	8.00000	+	8.00000i	0.309761	+	0.309761i
$668$		−	14.0000i		−	0.541676i
$669$	−18.0000	+	18.0000i	−0.695920	+	0.695920i
$670$	−12.0000	+	24.0000i	−0.463600	+	0.927201i
$671$	−2.00000	+	2.00000i	−0.0772091	+	0.0772091i
$672$	2.00000	−	2.00000i	0.0771517	−	0.0771517i
$673$	17.0000	−	17.0000i	0.655302	−	0.655302i	−0.298963	−	0.954265i	$-0.596641\pi$
$673$	17.0000	−	17.0000i	0.655302	−	0.655302i	0.954265	+	0.298963i	$0.0966407\pi$
$674$	−5.00000	−	5.00000i	−0.192593	−	0.192593i
$675$	−28.0000	−	4.00000i	−1.07772	−	0.153960i
$676$	5.00000	+	12.0000i	0.192308	+	0.461538i
$677$	13.0000	−	13.0000i	0.499631	−	0.499631i	−0.411692	−	0.911323i	$-0.635062\pi$
$677$	13.0000	−	13.0000i	0.499631	−	0.499631i	0.911323	+	0.411692i	$0.135062\pi$
$678$			6.00000i			0.230429i
$679$		−	28.0000i		−	1.07454i
$680$	3.00000	−	1.00000i	0.115045	−	0.0383482i
$681$	12.0000	+	12.0000i	0.459841	+	0.459841i
$682$	2.00000			0.0765840
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−3.00000	−	3.00000i	−0.114708	−	0.114708i
$685$		0			0
$686$		−	20.0000i		−	0.763604i
$687$		−	30.0000i		−	1.14457i
$688$	−1.00000	+	1.00000i	−0.0381246	+	0.0381246i
$689$	1.00000	+	5.00000i	0.0380970	+	0.190485i
$690$	−2.00000	+	4.00000i	−0.0761387	+	0.152277i
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	0.982919	−	0.184041i	$-0.0589179\pi$
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	−0.184041	+	0.982919i	$0.558918\pi$
$692$	9.00000	−	9.00000i	0.342129	−	0.342129i
$693$	−2.00000	+	2.00000i	−0.0759737	+	0.0759737i
$694$	5.00000	−	5.00000i	0.189797	−	0.189797i
$695$	4.00000	+	2.00000i	0.151729	+	0.0758643i
$696$	−8.00000	+	8.00000i	−0.303239	+	0.303239i
$697$		−	14.0000i		−	0.530288i
$698$	−21.0000	−	21.0000i	−0.794862	−	0.794862i
$699$	2.00000			0.0756469
$700$	8.00000	−	6.00000i	0.302372	−	0.226779i
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$	−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
$705$	−10.0000	−	30.0000i	−0.376622	−	1.12987i
$706$		−	4.00000i		−	0.150542i
$707$	−24.0000			−0.902613
$708$			18.0000i			0.676481i
$709$	33.0000	+	33.0000i	1.23934	+	1.23934i	0.960271	+	0.279070i	$0.0900263\pi$
$709$	33.0000	+	33.0000i	1.23934	+	1.23934i	0.279070	+	0.960271i	$0.409974\pi$
$710$	15.0000	−	5.00000i	0.562940	−	0.187647i
$711$	10.0000			0.375029
$712$	11.0000	+	11.0000i	0.412242	+	0.412242i
$713$	−2.00000			−0.0749006
$714$	4.00000			0.149696
$715$	3.00000	−	11.0000i	0.112194	−	0.411377i
$716$	−20.0000			−0.747435
$717$	−2.00000			−0.0746914
$718$	−5.00000	−	5.00000i	−0.186598	−	0.186598i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$	2.00000	+	1.00000i	0.0745356	+	0.0372678i
$721$	−10.0000	−	10.0000i	−0.372419	−	0.372419i
$722$		−	1.00000i		−	0.0372161i
$723$	2.00000			0.0743808
$724$		−	16.0000i		−	0.594635i
$725$	−32.0000	+	24.0000i	−1.18845	+	0.891338i
$726$	9.00000	−	9.00000i	0.334021	−	0.334021i
$727$	1.00000	+	1.00000i	0.0370879	+	0.0370879i	0.725408	−	0.688320i	$-0.241651\pi$
$727$	1.00000	+	1.00000i	0.0370879	+	0.0370879i	−0.688320	+	0.725408i	$0.741651\pi$
$728$	4.00000	−	6.00000i	0.148250	−	0.222375i
$729$		−	29.0000i		−	1.07407i
$730$	6.00000	−	12.0000i	0.222070	−	0.444140i
$731$	−2.00000			−0.0739727
$732$	2.00000	+	2.00000i	0.0739221	+	0.0739221i
$733$			20.0000i			0.738717i	0.929287	+	0.369358i	$0.120423\pi$
$733$			20.0000i			0.738717i	−0.929287	+	0.369358i	$0.879577\pi$
$734$	21.0000	−	21.0000i	0.775124	−	0.775124i
$735$	−9.00000	+	3.00000i	−0.331970	+	0.110657i
$736$	1.00000	−	1.00000i	0.0368605	−	0.0368605i
$737$	12.0000	−	12.0000i	0.442026	−	0.442026i
$738$	7.00000	−	7.00000i	0.257674	−	0.257674i
$739$	5.00000	+	5.00000i	0.183928	+	0.183928i	0.793065	−	0.609137i	$-0.208484\pi$
$739$	5.00000	+	5.00000i	0.183928	+	0.183928i	−0.609137	+	0.793065i	$0.708484\pi$
$740$	16.0000	+	8.00000i	0.588172	+	0.294086i
$741$	18.0000	+	12.0000i	0.661247	+	0.440831i
$742$	2.00000	−	2.00000i	0.0734223	−	0.0734223i
$743$			18.0000i			0.660356i	0.943919	+	0.330178i	$0.107109\pi$
$743$			18.0000i			0.660356i	−0.943919	+	0.330178i	$0.892891\pi$
$744$		−	2.00000i		−	0.0733236i
$745$	1.00000	+	3.00000i	0.0366372	+	0.109911i
$746$	−5.00000	−	5.00000i	−0.183063	−	0.183063i
$747$	−18.0000			−0.658586
$748$	−2.00000			−0.0731272
$749$	−2.00000	−	2.00000i	−0.0730784	−	0.0730784i
$750$	−13.0000	−	9.00000i	−0.474693	−	0.328634i
$751$		−	38.0000i		−	1.38664i	−0.720630	−	0.693320i	$-0.756147\pi$
$751$		−	38.0000i		−	1.38664i	0.720630	−	0.693320i	$-0.243853\pi$
$752$			10.0000i			0.364662i
$753$	18.0000	−	18.0000i	0.655956	−	0.655956i
$754$	−16.0000	+	24.0000i	−0.582686	+	0.874028i
$755$	3.00000	+	9.00000i	0.109181	+	0.327544i
$756$	8.00000	+	8.00000i	0.290957	+	0.290957i
$757$	25.0000	−	25.0000i	0.908640	−	0.908640i	−0.0875221	−	0.996163i	$-0.527895\pi$
$757$	25.0000	−	25.0000i	0.908640	−	0.908640i	0.996163	+	0.0875221i	$0.0278948\pi$
$758$	−23.0000	+	23.0000i	−0.835398	+	0.835398i
$759$	2.00000	−	2.00000i	0.0725954	−	0.0725954i
$760$	−3.00000	−	9.00000i	−0.108821	−	0.326464i
$761$	1.00000	−	1.00000i	0.0362500	−	0.0362500i	−0.688749	−	0.724999i	$-0.741840\pi$
$761$	1.00000	−	1.00000i	0.0362500	−	0.0362500i	0.724999	+	0.688749i	$0.241840\pi$
$762$			6.00000i			0.217357i
$763$	10.0000	+	10.0000i	0.362024	+	0.362024i
$764$	8.00000			0.289430
$765$	1.00000	+	3.00000i	0.0361551	+	0.108465i
$766$		−	18.0000i		−	0.650366i
$767$	9.00000	+	45.0000i	0.324971	+	1.62486i
$768$	1.00000	+	1.00000i	0.0360844	+	0.0360844i
$769$	−23.0000	+	23.0000i	−0.829401	+	0.829401i	−0.987434	−	0.158033i	$-0.949485\pi$
$769$	−23.0000	+	23.0000i	−0.829401	+	0.829401i	0.158033	+	0.987434i	$0.449485\pi$
$770$	−6.00000	+	2.00000i	−0.216225	+	0.0720750i
$771$			42.0000i			1.51259i
$772$	2.00000			0.0719816
$773$			24.0000i			0.863220i	0.902060	+	0.431610i	$0.142054\pi$
$773$			24.0000i			0.863220i	−0.902060	+	0.431610i	$0.857946\pi$
$774$	−1.00000	−	1.00000i	−0.0359443	−	0.0359443i
$775$	1.00000	−	7.00000i	0.0359211	−	0.251447i
$776$	14.0000			0.502571
$777$	16.0000	+	16.0000i	0.573997	+	0.573997i
$778$	2.00000			0.0717035
$779$	−42.0000			−1.50481
$780$	−11.0000	−	3.00000i	−0.393863	−	0.107417i
$781$	−10.0000			−0.357828
$782$	2.00000			0.0715199
$783$	−32.0000	−	32.0000i	−1.14359	−	1.14359i
$784$	3.00000			0.107143
$785$	−15.0000	−	45.0000i	−0.535373	−	1.60612i
$786$	−12.0000	−	12.0000i	−0.428026	−	0.428026i
$787$			30.0000i			1.06938i	0.845047	+	0.534692i	$0.179572\pi$
$787$			30.0000i			1.06938i	−0.845047	+	0.534692i	$0.820428\pi$
$788$	6.00000			0.213741
$789$		−	6.00000i		−	0.213606i
$790$	20.0000	+	10.0000i	0.711568	+	0.355784i
$791$	6.00000	−	6.00000i	0.213335	−	0.213335i
$792$	−1.00000	−	1.00000i	−0.0355335	−	0.0355335i
$793$	6.00000	+	4.00000i	0.213066	+	0.142044i
$794$			8.00000i			0.283909i
$795$	−4.00000	−	2.00000i	−0.141865	−	0.0709327i
$796$	−24.0000			−0.850657
$797$	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	$0.710032\pi$
$798$		−	12.0000i		−	0.424795i
$799$	−10.0000	+	10.0000i	−0.353775	+	0.353775i
$800$	3.00000	+	4.00000i	0.106066	+	0.141421i
$801$	−11.0000	+	11.0000i	−0.388666	+	0.388666i
$802$	19.0000	−	19.0000i	0.670913	−	0.670913i
$803$	−6.00000	+	6.00000i	−0.211735	+	0.211735i
$804$	−12.0000	−	12.0000i	−0.423207	−	0.423207i
$805$	6.00000	−	2.00000i	0.211472	−	0.0704907i
$806$	−1.00000	−	5.00000i	−0.0352235	−	0.176117i
$807$	4.00000	−	4.00000i	0.140807	−	0.140807i
$808$		−	12.0000i		−	0.422159i
$809$		−	12.0000i		−	0.421898i	−0.977497	−	0.210949i	$-0.932345\pi$
$809$		−	12.0000i		−	0.421898i	0.977497	−	0.210949i	$-0.0676553\pi$
$810$	5.00000	−	10.0000i	0.175682	−	0.351364i
$811$	5.00000	+	5.00000i	0.175574	+	0.175574i	0.789423	−	0.613849i	$-0.210380\pi$
$811$	5.00000	+	5.00000i	0.175574	+	0.175574i	−0.613849	+	0.789423i	$0.710380\pi$
$812$	16.0000			0.561490
$813$	6.00000			0.210429
$814$	−8.00000	−	8.00000i	−0.280400	−	0.280400i
$815$	20.0000	−	40.0000i	0.700569	−	1.40114i
$816$			2.00000i			0.0700140i
$817$			6.00000i			0.209913i
$818$	−9.00000	+	9.00000i	−0.314678	+	0.314678i
$819$	6.00000	+	4.00000i	0.209657	+	0.139771i
$820$	21.0000	−	7.00000i	0.733352	−	0.244451i
$821$	−19.0000	−	19.0000i	−0.663105	−	0.663105i	0.293006	−	0.956111i	$-0.405344\pi$
$821$	−19.0000	−	19.0000i	−0.663105	−	0.663105i	−0.956111	+	0.293006i	$0.905344\pi$
$822$		0			0
$823$	3.00000	−	3.00000i	0.104573	−	0.104573i	−0.652884	−	0.757458i	$-0.726441\pi$
$823$	3.00000	−	3.00000i	0.104573	−	0.104573i	0.757458	+	0.652884i	$0.226441\pi$
$824$	5.00000	−	5.00000i	0.174183	−	0.174183i
$825$	6.00000	+	8.00000i	0.208893	+	0.278524i
$826$	18.0000	−	18.0000i	0.626300	−	0.626300i
$827$		−	26.0000i		−	0.904109i	−0.891990	−	0.452054i	$-0.850691\pi$
$827$		−	26.0000i		−	0.904109i	0.891990	−	0.452054i	$-0.149309\pi$
$828$	1.00000	+	1.00000i	0.0347524	+	0.0347524i
$829$	18.0000			0.625166			0.312583	−	0.949890i	$-0.398806\pi$
$829$	18.0000			0.625166			0.312583	+	0.949890i	$0.398806\pi$
$830$	−36.0000	−	18.0000i	−1.24958	−	0.624789i
$831$		−	22.0000i		−	0.763172i
$832$	3.00000	+	2.00000i	0.104006	+	0.0693375i
$833$	3.00000	+	3.00000i	0.103944	+	0.103944i
$834$	−2.00000	+	2.00000i	−0.0692543	+	0.0692543i
$835$	28.0000	+	14.0000i	0.968980	+	0.484490i
$836$			6.00000i			0.207514i
$837$	8.00000			0.276520
$838$		−	22.0000i		−	0.759977i
$839$	−7.00000	−	7.00000i	−0.241667	−	0.241667i	0.575873	−	0.817539i	$-0.304662\pi$
$839$	−7.00000	−	7.00000i	−0.241667	−	0.241667i	−0.817539	+	0.575873i	$0.804662\pi$
$840$	2.00000	+	6.00000i	0.0690066	+	0.207020i
$841$	−35.0000			−1.20690
$842$	−9.00000	−	9.00000i	−0.310160	−	0.310160i
$843$	18.0000			0.619953
$844$	−12.0000			−0.413057
$845$	−29.0000	−	2.00000i	−0.997630	−	0.0688021i
$846$	−10.0000			−0.343807
$847$	−18.0000			−0.618487
$848$	1.00000	+	1.00000i	0.0343401	+	0.0343401i
$849$	30.0000			1.02960
$850$	−1.00000	+	7.00000i	−0.0342997	+	0.240098i
$851$	8.00000	+	8.00000i	0.274236	+	0.274236i
$852$			10.0000i			0.342594i
$853$	−38.0000			−1.30110			−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000			−1.30110			−0.650548	+	0.759465i	$0.725461\pi$
$854$		−	4.00000i		−	0.136877i
$855$	9.00000	−	3.00000i	0.307794	−	0.102598i
$856$	1.00000	−	1.00000i	0.0341793	−	0.0341793i
$857$	−11.0000	−	11.0000i	−0.375753	−	0.375753i	0.493814	−	0.869567i	$-0.335602\pi$
$857$	−11.0000	−	11.0000i	−0.375753	−	0.375753i	−0.869567	+	0.493814i	$0.835602\pi$
$858$	6.00000	+	4.00000i	0.204837	+	0.136558i
$859$		−	34.0000i		−	1.16007i	−0.814593	−	0.580033i	$-0.803040\pi$
$859$		−	34.0000i		−	1.16007i	0.814593	−	0.580033i	$-0.196960\pi$
$860$	−1.00000	−	3.00000i	−0.0340997	−	0.102299i
$861$	28.0000			0.954237
$862$	15.0000	+	15.0000i	0.510902	+	0.510902i
$863$			34.0000i			1.15737i	0.815550	+	0.578687i	$0.196435\pi$
$863$			34.0000i			1.15737i	−0.815550	+	0.578687i	$0.803565\pi$
$864$	−4.00000	+	4.00000i	−0.136083	+	0.136083i
$865$	9.00000	+	27.0000i	0.306009	+	0.918028i
$866$	−9.00000	+	9.00000i	−0.305832	+	0.305832i
$867$	15.0000	−	15.0000i	0.509427	−	0.509427i
$868$	−2.00000	+	2.00000i	−0.0678844	+	0.0678844i
$869$	−10.0000	−	10.0000i	−0.339227	−	0.339227i
$870$	−8.00000	−	24.0000i	−0.271225	−	0.813676i
$871$	−36.0000	−	24.0000i	−1.21981	−	0.813209i
$872$	−5.00000	+	5.00000i	−0.169321	+	0.169321i
$873$			14.0000i			0.473828i
$874$		−	6.00000i		−	0.202953i
$875$	4.00000	+	22.0000i	0.135225	+	0.743736i
$876$	6.00000	+	6.00000i	0.202721	+	0.202721i
$877$	6.00000			0.202606			0.101303	−	0.994856i	$-0.467699\pi$
$877$	6.00000			0.202606			0.101303	+	0.994856i	$0.467699\pi$
$878$	32.0000			1.07995
$879$	−22.0000	−	22.0000i	−0.742042	−	0.742042i
$880$	−1.00000	−	3.00000i	−0.0337100	−	0.101130i
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$			3.00000i			0.101015i
$883$	−25.0000	+	25.0000i	−0.841317	+	0.841317i	−0.989030	−	0.147713i	$-0.952809\pi$
$883$	−25.0000	+	25.0000i	−0.841317	+	0.841317i	0.147713	+	0.989030i	$0.452809\pi$
$884$	1.00000	+	5.00000i	0.0336336	+	0.168168i
$885$	−36.0000	−	18.0000i	−1.21013	−	0.605063i
$886$	−17.0000	−	17.0000i	−0.571126	−	0.571126i
$887$	19.0000	−	19.0000i	0.637958	−	0.637958i	−0.312094	−	0.950051i	$-0.601030\pi$
$887$	19.0000	−	19.0000i	0.637958	−	0.637958i	0.950051	+	0.312094i	$0.101030\pi$
$888$	−8.00000	+	8.00000i	−0.268462	+	0.268462i
$889$	6.00000	−	6.00000i	0.201234	−	0.201234i
$890$	−33.0000	+	11.0000i	−1.10616	+	0.368721i
$891$	−5.00000	+	5.00000i	−0.167506	+	0.167506i
$892$			18.0000i			0.602685i
$893$	30.0000	+	30.0000i	1.00391	+	1.00391i
$894$	−2.00000			−0.0668900
$895$	20.0000	−	40.0000i	0.668526	−	1.33705i
$896$		−	2.00000i		−	0.0668153i
$897$	−6.00000	−	4.00000i	−0.200334	−	0.133556i
$898$	−13.0000	−	13.0000i	−0.433816	−	0.433816i
$899$	8.00000	−	8.00000i	0.266815	−	0.266815i
$900$	−4.00000	+	3.00000i	−0.133333	+	0.100000i
$901$			2.00000i			0.0666297i
$902$	−14.0000			−0.466149
$903$		−	4.00000i		−	0.133112i
$904$	3.00000	+	3.00000i	0.0997785	+	0.0997785i
$905$	32.0000	+	16.0000i	1.06372	+	0.531858i
$906$	−6.00000			−0.199337
$907$	−7.00000	−	7.00000i	−0.232431	−	0.232431i	0.581276	−	0.813707i	$-0.302554\pi$
$907$	−7.00000	−	7.00000i	−0.232431	−	0.232431i	−0.813707	+	0.581276i	$0.802554\pi$
$908$	12.0000			0.398234
$909$	12.0000			0.398015
$910$	8.00000	+	14.0000i	0.265197	+	0.464095i
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	6.00000			0.198680
$913$	18.0000	+	18.0000i	0.595713	+	0.595713i
$914$	−2.00000			−0.0661541
$915$	−6.00000	+	2.00000i	−0.198354	+	0.0661180i
$916$	−15.0000	−	15.0000i	−0.495614	−	0.495614i
$917$			24.0000i			0.792550i
$918$	−8.00000			−0.264039
$919$		−	14.0000i		−	0.461817i	−0.972975	−	0.230909i	$-0.925830\pi$
$919$		−	14.0000i		−	0.461817i	0.972975	−	0.230909i	$-0.0741699\pi$
$920$	1.00000	+	3.00000i	0.0329690	+	0.0989071i
$921$	10.0000	−	10.0000i	0.329511	−	0.329511i
$922$	11.0000	+	11.0000i	0.362266	+	0.362266i
$923$	5.00000	+	25.0000i	0.164577	+	0.822885i
$924$		−	4.00000i		−	0.131590i
$925$	−32.0000	+	24.0000i	−1.05215	+	0.789115i
$926$	16.0000			0.525793
$927$	5.00000	+	5.00000i	0.164222	+	0.164222i
$928$			8.00000i			0.262613i
$929$	13.0000	−	13.0000i	0.426516	−	0.426516i	−0.460924	−	0.887440i	$-0.652482\pi$
$929$	13.0000	−	13.0000i	0.426516	−	0.426516i	0.887440	+	0.460924i	$0.152482\pi$
$930$	4.00000	+	2.00000i	0.131165	+	0.0655826i
$931$	9.00000	−	9.00000i	0.294963	−	0.294963i
$932$	1.00000	−	1.00000i	0.0327561	−	0.0327561i
$933$	−2.00000	+	2.00000i	−0.0654771	+	0.0654771i
$934$	7.00000	+	7.00000i	0.229047	+	0.229047i
$935$	2.00000	−	4.00000i	0.0654070	−	0.130814i
$936$	−2.00000	+	3.00000i	−0.0653720	+	0.0980581i
$937$	9.00000	−	9.00000i	0.294017	−	0.294017i	−0.544648	−	0.838665i	$-0.683337\pi$
$937$	9.00000	−	9.00000i	0.294017	−	0.294017i	0.838665	+	0.544648i	$0.183337\pi$
$938$			24.0000i			0.783628i
$939$			18.0000i			0.587408i
$940$	−20.0000	−	10.0000i	−0.652328	−	0.326164i
$941$	17.0000	+	17.0000i	0.554184	+	0.554184i	0.927646	−	0.373462i	$-0.121829\pi$
$941$	17.0000	+	17.0000i	0.554184	+	0.554184i	−0.373462	+	0.927646i	$0.621829\pi$
$942$	30.0000			0.977453
$943$	14.0000			0.455903
$944$	9.00000	+	9.00000i	0.292925	+	0.292925i
$945$	−24.0000	+	8.00000i	−0.780720	+	0.260240i
$946$			2.00000i			0.0650256i
$947$		−	10.0000i		−	0.324956i	−0.986712	−	0.162478i	$-0.948051\pi$
$947$		−	10.0000i		−	0.324956i	0.986712	−	0.162478i	$-0.0519487\pi$
$948$	−10.0000	+	10.0000i	−0.324785	+	0.324785i
$949$	18.0000	+	12.0000i	0.584305	+	0.389536i
$950$	21.0000	+	3.00000i	0.681330	+	0.0973329i
$951$	2.00000	+	2.00000i	0.0648544	+	0.0648544i
$952$	2.00000	−	2.00000i	0.0648204	−	0.0648204i
$953$	5.00000	−	5.00000i	0.161966	−	0.161966i	−0.621471	−	0.783437i	$-0.713465\pi$
$953$	5.00000	−	5.00000i	0.161966	−	0.161966i	0.783437	+	0.621471i	$0.213465\pi$
$954$	−1.00000	+	1.00000i	−0.0323762	+	0.0323762i
$955$	−8.00000	+	16.0000i	−0.258874	+	0.517748i
$956$	−1.00000	+	1.00000i	−0.0323423	+	0.0323423i
$957$			16.0000i			0.517207i
$958$	19.0000	+	19.0000i	0.613862	+	0.613862i
$959$		0			0
$960$	−3.00000	+	1.00000i	−0.0968246	+	0.0322749i
$961$		−	29.0000i		−	0.935484i
$962$	−16.0000	+	24.0000i	−0.515861	+	0.773791i
$963$	1.00000	+	1.00000i	0.0322245	+	0.0322245i
$964$	1.00000	−	1.00000i	0.0322078	−	0.0322078i
$965$	−2.00000	+	4.00000i	−0.0643823	+	0.128765i
$966$			4.00000i			0.128698i
$967$	−24.0000			−0.771788			−0.385894	−	0.922543i	$-0.626107\pi$
$967$	−24.0000			−0.771788			−0.385894	+	0.922543i	$0.626107\pi$
$968$		−	9.00000i		−	0.289271i
$969$	6.00000	+	6.00000i	0.192748	+	0.192748i
$970$	−14.0000	+	28.0000i	−0.449513	+	0.899026i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$	−7.00000	−	7.00000i	−0.224525	−	0.224525i
$973$	4.00000			0.128234
$974$	8.00000			0.256337
$975$	17.0000	−	19.0000i	0.544436	−	0.608487i
$976$	2.00000			0.0640184
$977$	−2.00000			−0.0639857			−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000			−0.0639857			−0.0319928	+	0.999488i	$0.510185\pi$
$978$	20.0000	+	20.0000i	0.639529	+	0.639529i
$979$	22.0000			0.703123
$980$	−3.00000	+	6.00000i	−0.0958315	+	0.191663i
$981$	−5.00000	−	5.00000i	−0.159638	−	0.159638i
$982$		−	38.0000i		−	1.21263i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$			14.0000i			0.446304i
$985$	−6.00000	+	12.0000i	−0.191176	+	0.382352i
$986$	−8.00000	+	8.00000i	−0.254772	+	0.254772i
$987$	−20.0000	−	20.0000i	−0.636607	−	0.636607i
$988$	15.0000	−	3.00000i	0.477214	−	0.0954427i
$989$		−	2.00000i		−	0.0635963i
$990$	3.00000	−	1.00000i	0.0953463	−	0.0317821i
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$	−1.00000	−	1.00000i	−0.0317500	−	0.0317500i
$993$			42.0000i			1.33283i
$994$	10.0000	−	10.0000i	0.317181	−	0.317181i
$995$	24.0000	−	48.0000i	0.760851	−	1.52170i
$996$	18.0000	−	18.0000i	0.570352	−	0.570352i
$997$	13.0000	−	13.0000i	0.411714	−	0.411714i	−0.470621	−	0.882335i	$-0.655970\pi$
$997$	13.0000	−	13.0000i	0.411714	−	0.411714i	0.882335	+	0.470621i	$0.155970\pi$
$998$	−19.0000	+	19.0000i	−0.601434	+	0.601434i
$999$	−32.0000	−	32.0000i	−1.01244	−	1.01244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.g.b.73.1	yes	2
3.2	odd	2		1170.2.m.b.73.1		2
4.3	odd	2		1040.2.bg.b.593.1		2
5.2	odd	4		130.2.j.c.47.1	yes	2
5.3	odd	4		650.2.j.a.307.1		2
5.4	even	2		650.2.g.c.593.1		2
13.5	odd	4		130.2.j.c.83.1	yes	2
15.2	even	4		1170.2.w.a.307.1		2
20.7	even	4		1040.2.cd.c.177.1		2
39.5	even	4		1170.2.w.a.343.1		2
52.31	even	4		1040.2.cd.c.993.1		2
65.18	even	4		650.2.g.c.57.1		2
65.44	odd	4		650.2.j.a.343.1		2
65.57	even	4	inner	130.2.g.b.57.1	✓	2
195.122	odd	4		1170.2.m.b.577.1		2
260.187	odd	4		1040.2.bg.b.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.b.57.1	✓	2	65.57	even	4	inner
130.2.g.b.73.1	yes	2	1.1	even	1	trivial
130.2.j.c.47.1	yes	2	5.2	odd	4
130.2.j.c.83.1	yes	2	13.5	odd	4
650.2.g.c.57.1		2	65.18	even	4
650.2.g.c.593.1		2	5.4	even	2
650.2.j.a.307.1		2	5.3	odd	4
650.2.j.a.343.1		2	65.44	odd	4
1040.2.bg.b.577.1		2	260.187	odd	4
1040.2.bg.b.593.1		2	4.3	odd	2
1040.2.cd.c.177.1		2	20.7	even	4
1040.2.cd.c.993.1		2	52.31	even	4
1170.2.m.b.73.1		2	3.2	odd	2
1170.2.m.b.577.1		2	195.122	odd	4
1170.2.w.a.307.1		2	15.2	even	4
1170.2.w.a.343.1		2	39.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.00000 + 1.00000i) q^{3} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +2.00000i q^{7} -1.00000 q^{8} -1.00000i q^{9} +(1.00000 - 2.00000i) q^{10} +(-1.00000 + 1.00000i) q^{11} +(1.00000 + 1.00000i) q^{12} +(3.00000 + 2.00000i) q^{13} -2.00000i q^{14} +(-3.00000 + 1.00000i) q^{15} +1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +1.00000i q^{18} +(3.00000 - 3.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(-2.00000 + 2.00000i) q^{21} +(1.00000 - 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-1.00000 - 1.00000i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +(4.00000 - 4.00000i) q^{27} +2.00000i q^{28} -8.00000i q^{29} +(3.00000 - 1.00000i) q^{30} +(1.00000 + 1.00000i) q^{31} -1.00000 q^{32} -2.00000 q^{33} +(-1.00000 - 1.00000i) q^{34} +(-4.00000 - 2.00000i) q^{35} -1.00000i q^{36} -8.00000i q^{37} +(-3.00000 + 3.00000i) q^{38} +(1.00000 + 5.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +(-7.00000 - 7.00000i) q^{41} +(2.00000 - 2.00000i) q^{42} +(-1.00000 + 1.00000i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(2.00000 + 1.00000i) q^{45} +(1.00000 - 1.00000i) q^{46} +10.0000i q^{47} +(1.00000 + 1.00000i) q^{48} +3.00000 q^{49} +(3.00000 + 4.00000i) q^{50} +2.00000i q^{51} +(3.00000 + 2.00000i) q^{52} +(1.00000 + 1.00000i) q^{53} +(-4.00000 + 4.00000i) q^{54} +(-1.00000 - 3.00000i) q^{55} -2.00000i q^{56} +6.00000 q^{57} +8.00000i q^{58} +(9.00000 + 9.00000i) q^{59} +(-3.00000 + 1.00000i) q^{60} +2.00000 q^{61} +(-1.00000 - 1.00000i) q^{62} +2.00000 q^{63} +1.00000 q^{64} +(-7.00000 + 4.00000i) q^{65} +2.00000 q^{66} -12.0000 q^{67} +(1.00000 + 1.00000i) q^{68} -2.00000 q^{69} +(4.00000 + 2.00000i) q^{70} +(5.00000 + 5.00000i) q^{71} +1.00000i q^{72} +6.00000 q^{73} +8.00000i q^{74} +(1.00000 - 7.00000i) q^{75} +(3.00000 - 3.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +(-1.00000 - 5.00000i) q^{78} +10.0000i q^{79} +(-1.00000 + 2.00000i) q^{80} +5.00000 q^{81} +(7.00000 + 7.00000i) q^{82} -18.0000i q^{83} +(-2.00000 + 2.00000i) q^{84} +(-3.00000 + 1.00000i) q^{85} +(1.00000 - 1.00000i) q^{86} +(8.00000 - 8.00000i) q^{87} +(1.00000 - 1.00000i) q^{88} +(-11.0000 - 11.0000i) q^{89} +(-2.00000 - 1.00000i) q^{90} +(-4.00000 + 6.00000i) q^{91} +(-1.00000 + 1.00000i) q^{92} +2.00000i q^{93} -10.0000i q^{94} +(3.00000 + 9.00000i) q^{95} +(-1.00000 - 1.00000i) q^{96} -14.0000 q^{97} -3.00000 q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 6 q^{15} + 2 q^{16} + 2 q^{17} + 6 q^{19} - 2 q^{20} - 4 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 6 * q^15 + 2 * q^16 + 2 * q^17 + 6 * q^19 - 2 * q^20 - 4 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 - 6 * q^25 - 6 * q^26 + 8 * q^27 + 6 * q^30 + 2 * q^31 - 2 * q^32 - 4 * q^33 - 2 * q^34 - 8 * q^35 - 6 * q^38 + 2 * q^39 + 2 * q^40 - 14 * q^41 + 4 * q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 + 2 * q^46 + 2 * q^48 + 6 * q^49 + 6 * q^50 + 6 * q^52 + 2 * q^53 - 8 * q^54 - 2 * q^55 + 12 * q^57 + 18 * q^59 - 6 * q^60 + 4 * q^61 - 2 * q^62 + 4 * q^63 + 2 * q^64 - 14 * q^65 + 4 * q^66 - 24 * q^67 + 2 * q^68 - 4 * q^69 + 8 * q^70 + 10 * q^71 + 12 * q^73 + 2 * q^75 + 6 * q^76 - 4 * q^77 - 2 * q^78 - 2 * q^80 + 10 * q^81 + 14 * q^82 - 4 * q^84 - 6 * q^85 + 2 * q^86 + 16 * q^87 + 2 * q^88 - 22 * q^89 - 4 * q^90 - 8 * q^91 - 2 * q^92 + 6 * q^95 - 2 * q^96 - 28 * q^97 - 6 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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