LMFDB - Embedded newform 130.2.g.b.57.1

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			57.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	130.57
Dual form			130.2.g.b.73.1

$q$-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 $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	0.934172	+	0.356822i	$0.116140\pi$
$4$	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	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	−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	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$	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	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$		−	1.00000i		−	0.235702i
$19$	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	$0.588214\pi$
$20$	−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	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$	−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	$0.266494\pi$
$29$			8.00000i			1.48556i	−0.669534	+	0.742781i	$0.733506\pi$
$30$	3.00000	+	1.00000i	0.547723	+	0.182574i
$31$	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	$0.209465\pi$
$32$	−1.00000			−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	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	−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	−0.0980332	+	0.995183i	$0.531255\pi$
$41$	−7.00000	+	7.00000i	−1.09322	+	1.09322i	−0.995183	+	0.0980332i	$0.968745\pi$
$42$	2.00000	+	2.00000i	0.308607	+	0.308607i
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	0.626734	−	0.779233i	$-0.284391\pi$
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	−0.779233	+	0.626734i	$0.784391\pi$
$44$	−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	$-0.739834\pi$
$47$		−	10.0000i		−	1.45865i	0.684167	−	0.729325i	$-0.260166\pi$
$48$	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	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$	−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	0.189896	−	0.981804i	$-0.439185\pi$
$59$	9.00000	−	9.00000i	1.17170	−	1.17170i	0.981804	−	0.189896i	$-0.0608151\pi$
$60$	−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	−0.345155	−	0.938546i	$-0.612174\pi$
$71$	5.00000	−	5.00000i	0.593391	−	0.593391i	0.938546	+	0.345155i	$0.112174\pi$
$72$		−	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	$-0.809823\pi$
$79$		−	10.0000i		−	1.12509i	0.826767	−	0.562544i	$-0.190177\pi$
$80$	−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	$0.450388\pi$
$83$			18.0000i			1.97576i	−0.155230	+	0.987878i	$0.549612\pi$
$84$	−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	−0.182858	+	0.983139i	$0.558535\pi$
$89$	−11.0000	+	11.0000i	−1.16600	+	1.16600i	−0.983139	+	0.182858i	$0.941465\pi$
$90$	−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	$-0.796350\pi$
$101$		−	12.0000i		−	1.19404i	0.802225	−	0.597022i	$-0.203650\pi$
$102$			2.00000i			0.198030i
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$104$	−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	0.657116	−	0.753790i	$-0.271776\pi$
$107$	−1.00000	−	1.00000i	−0.0966736	−	0.0966736i	−0.753790	+	0.657116i	$0.771776\pi$
$108$	4.00000	+	4.00000i	0.384900	+	0.384900i
$109$	5.00000	+	5.00000i	0.478913	+	0.478913i	0.904784	−	0.425871i	$-0.140032\pi$
$109$	5.00000	+	5.00000i	0.478913	+	0.478913i	−0.425871	+	0.904784i	$0.640032\pi$
$110$	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	−0.833992	−	0.551776i	$-0.813950\pi$
$113$	−3.00000	+	3.00000i	−0.282216	+	0.282216i	0.551776	+	0.833992i	$0.313950\pi$
$114$	−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	−0.827570	−	0.561363i	$-0.810277\pi$
$127$	−3.00000	+	3.00000i	−0.266207	+	0.266207i	0.561363	+	0.827570i	$0.310277\pi$
$128$	−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	$0.0270312\pi$
$139$			2.00000i			0.169638i	−0.996396	+	0.0848189i	$0.972969\pi$
$140$	−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	0.746881	−	0.664958i	$-0.231550\pi$
$149$	1.00000	+	1.00000i	0.0819232	+	0.0819232i	−0.664958	+	0.746881i	$0.731550\pi$
$150$	−1.00000	−	7.00000i	−0.0816497	−	0.571548i
$151$	3.00000	+	3.00000i	0.244137	+	0.244137i	0.818559	−	0.574422i	$-0.194773\pi$
$151$	3.00000	+	3.00000i	0.244137	+	0.244137i	−0.574422	+	0.818559i	$0.694773\pi$
$152$	−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	−0.975022	−	0.222108i	$-0.928706\pi$
$157$	−15.0000	−	15.0000i	−1.19713	−	1.19713i	−0.222108	−	0.975022i	$-0.571294\pi$
$158$			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	$0.182210\pi$
$167$			14.0000i			1.08335i	−0.840587	+	0.541676i	$0.817790\pi$
$168$	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	0.960957	−	0.276699i	$-0.0892406\pi$
$173$	9.00000	+	9.00000i	0.684257	+	0.684257i	−0.276699	+	0.960957i	$0.589241\pi$
$174$	−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	$0.202704\pi$
$181$			16.0000i			1.18927i	−0.803996	+	0.594635i	$0.797296\pi$
$182$	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	$-0.794098\pi$
$223$		−	18.0000i		−	1.20537i	0.797980	−	0.602685i	$-0.205902\pi$
$224$			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	−0.999962	−	0.00873396i	$-0.997220\pi$
$229$	−15.0000	+	15.0000i	−0.991228	+	0.991228i	0.00873396	+	0.999962i	$0.497220\pi$
$230$	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	0.739104	−	0.673592i	$-0.235249\pi$
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	−0.673592	+	0.739104i	$0.735249\pi$
$234$	−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	0.674024	−	0.738709i	$-0.264564\pi$
$239$	−1.00000	−	1.00000i	−0.0646846	−	0.0646846i	−0.738709	+	0.674024i	$0.764564\pi$
$240$	−3.00000	−	1.00000i	−0.193649	−	0.0645497i
$241$	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	$0.735496\pi$
$242$			9.00000i			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	$0.192312\pi$
$251$			18.0000i			1.13615i	−0.822977	+	0.568075i	$0.807688\pi$
$252$	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	0.388492	−	0.921452i	$-0.372996\pi$
$257$	21.0000	−	21.0000i	1.30994	−	1.30994i	0.921452	−	0.388492i	$-0.127004\pi$
$258$	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	−0.793525	−	0.608537i	$-0.791757\pi$
$263$	−3.00000	+	3.00000i	−0.184988	+	0.184988i	0.608537	+	0.793525i	$0.291757\pi$
$264$	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	$0.0389122\pi$
$269$			4.00000i			0.243884i	−0.992537	+	0.121942i	$0.961088\pi$
$270$	−4.00000	+	12.0000i	−0.243432	+	0.730297i
$271$	3.00000	+	3.00000i	0.182237	+	0.182237i	0.792330	−	0.610093i	$-0.208868\pi$
$271$	3.00000	+	3.00000i	0.182237	+	0.182237i	−0.610093	+	0.792330i	$0.708868\pi$
$272$	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	−0.955598	−	0.294672i	$-0.904789\pi$
$277$	−11.0000	+	11.0000i	−0.660926	+	0.660926i	0.294672	+	0.955598i	$0.404789\pi$
$278$		−	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	0.922616	−	0.385721i	$-0.126047\pi$
$281$	9.00000	+	9.00000i	0.536895	+	0.536895i	−0.385721	+	0.922616i	$0.626047\pi$
$282$	10.0000	+	10.0000i	0.595491	+	0.595491i
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	0.994679	−	0.103022i	$-0.0328511\pi$
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	−0.103022	+	0.994679i	$0.532851\pi$
$284$	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	$0.0921148\pi$
$307$			10.0000i			0.570730i	−0.958419	+	0.285365i	$0.907885\pi$
$308$	−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	$-0.981941\pi$
$311$		−	2.00000i		−	0.113410i	0.998391	−	0.0567048i	$-0.0180594\pi$
$312$	−1.00000	+	5.00000i	−0.0566139	+	0.283069i
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$	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	0.168576	−	0.985689i	$-0.446083\pi$
$331$	21.0000	−	21.0000i	1.15426	−	1.15426i	0.985689	−	0.168576i	$-0.0539168\pi$
$332$			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	−0.557685	−	0.830053i	$-0.688310\pi$
$337$	5.00000	−	5.00000i	0.272367	−	0.272367i	0.830053	+	0.557685i	$0.188310\pi$
$338$	−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	0.560047	−	0.828461i	$-0.310783\pi$
$347$	−5.00000	−	5.00000i	−0.268414	−	0.268414i	−0.828461	+	0.560047i	$0.810783\pi$
$348$	8.00000	+	8.00000i	0.428845	+	0.428845i
$349$	21.0000	−	21.0000i	1.12410	−	1.12410i	0.132986	−	0.991118i	$-0.457543\pi$
$349$	21.0000	−	21.0000i	1.12410	−	1.12410i	0.991118	−	0.132986i	$-0.0424566\pi$
$350$	−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	$-0.966052\pi$
$353$		−	4.00000i		−	0.212899i	0.994318	−	0.106449i	$-0.0339482\pi$
$354$			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	−0.562742	−	0.826632i	$-0.690254\pi$
$359$	5.00000	−	5.00000i	0.263890	−	0.263890i	0.826632	+	0.562742i	$0.190254\pi$
$360$	−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	−0.994852	−	0.101339i	$-0.967687\pi$
$367$	−21.0000	−	21.0000i	−1.09619	−	1.09619i	−0.101339	−	0.994852i	$-0.532313\pi$
$368$	−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	−0.565712	−	0.824603i	$-0.691399\pi$
$373$	5.00000	−	5.00000i	0.258890	−	0.258890i	0.824603	+	0.565712i	$0.191399\pi$
$374$	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	0.979374	+	0.202057i	$0.0647626\pi$
$379$	23.0000	+	23.0000i	1.18143	+	1.18143i	0.202057	+	0.979374i	$0.435237\pi$
$380$	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	$-0.847893\pi$
$383$		−	18.0000i		−	0.919757i	0.887982	−	0.459879i	$-0.152107\pi$
$384$	−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	$0.0643393\pi$
$397$			8.00000i			0.401508i	−0.979642	+	0.200754i	$0.935661\pi$
$398$	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	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	−19.0000	−	19.0000i	−0.948815	−	0.948815i	−0.998752	+	0.0499376i	$0.984098\pi$
$402$	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	0.893695	−	0.448674i	$-0.148104\pi$
$409$	9.00000	+	9.00000i	0.445021	+	0.445021i	−0.448674	+	0.893695i	$0.648104\pi$
$410$	−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	$-0.819412\pi$
$419$		−	22.0000i		−	1.07477i	0.843337	−	0.537385i	$-0.180588\pi$
$420$	−2.00000	+	6.00000i	−0.0975900	+	0.292770i
$421$	9.00000	−	9.00000i	0.438633	−	0.438633i	−0.452919	−	0.891552i	$-0.649617\pi$
$421$	9.00000	−	9.00000i	0.438633	−	0.438633i	0.891552	+	0.452919i	$0.149617\pi$
$422$	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	−0.969119	−	0.246594i	$-0.920689\pi$
$431$	−15.0000	+	15.0000i	−0.722525	+	0.722525i	0.246594	+	0.969119i	$0.420689\pi$
$432$	4.00000	+	4.00000i	0.192450	+	0.192450i
$433$	9.00000	+	9.00000i	0.432512	+	0.432512i	0.889482	−	0.456970i	$-0.151065\pi$
$433$	9.00000	+	9.00000i	0.432512	+	0.432512i	−0.456970	+	0.889482i	$0.651065\pi$
$434$	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	−0.176590	−	0.984284i	$-0.556507\pi$
$443$	17.0000	−	17.0000i	0.807694	−	0.807694i	0.984284	+	0.176590i	$0.0565067\pi$
$444$	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	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	13.0000	−	13.0000i	0.613508	−	0.613508i	0.943858	+	0.330350i	$0.107167\pi$
$450$	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	−0.915237	−	0.402916i	$-0.867997\pi$
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	0.402916	+	0.915237i	$0.367997\pi$
$462$		−	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	−0.850269	−	0.526348i	$-0.823561\pi$
$467$	−7.00000	+	7.00000i	−0.323921	+	0.323921i	0.526348	+	0.850269i	$0.323561\pi$
$468$	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	−0.992266	−	0.124133i	$-0.960385\pi$
$479$	−19.0000	+	19.0000i	−0.868132	+	0.868132i	0.124133	+	0.992266i	$0.460385\pi$
$480$	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	$-0.672042\pi$
$491$		−	38.0000i		−	1.71492i	0.514554	−	0.857458i	$-0.327958\pi$
$492$			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	0.990202	−	0.139645i	$-0.0445961\pi$
$499$	19.0000	+	19.0000i	0.850557	+	0.850557i	−0.139645	+	0.990202i	$0.544596\pi$
$500$	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	−0.957442	−	0.288625i	$-0.906802\pi$
$503$	−15.0000	+	15.0000i	−0.668817	+	0.668817i	0.288625	+	0.957442i	$0.406802\pi$
$504$	−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	0.728922	−	0.684597i	$-0.240022\pi$
$509$	1.00000	+	1.00000i	0.0443242	+	0.0443242i	−0.684597	+	0.728922i	$0.740022\pi$
$510$	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	−0.954408	−	0.298504i	$-0.903512\pi$
$523$	−15.0000	+	15.0000i	−0.655904	+	0.655904i	0.298504	+	0.954408i	$0.403512\pi$
$524$	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	−0.984296	−	0.176524i	$-0.943515\pi$
$541$	−27.0000	−	27.0000i	−1.16082	−	1.16082i	−0.176524	−	0.984296i	$-0.556485\pi$
$542$	−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	0.999865	−	0.0164556i	$-0.00523822\pi$
$547$	23.0000	+	23.0000i	0.983409	+	0.983409i	−0.0164556	+	0.999865i	$0.505238\pi$
$548$		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	$-0.762872\pi$
$557$		−	32.0000i		−	1.35588i	0.735116	−	0.677942i	$-0.237128\pi$
$558$	−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	0.923928	+	0.382566i	$0.124960\pi$
$563$	31.0000	+	31.0000i	1.30649	+	1.30649i	0.382566	+	0.923928i	$0.375040\pi$
$564$	−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	$-0.847729\pi$
$571$		−	22.0000i		−	0.920671i	0.887745	−	0.460336i	$-0.152271\pi$
$572$	−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	$-0.821754\pi$
$599$		−	26.0000i		−	1.06233i	0.847268	−	0.531166i	$-0.178246\pi$
$600$	−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	0.500461	−	0.865759i	$-0.333164\pi$
$607$	−9.00000	−	9.00000i	−0.365299	−	0.365299i	−0.865759	+	0.500461i	$0.833164\pi$
$608$	−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	$-0.974259\pi$
$613$		−	4.00000i		−	0.161558i	0.996732	−	0.0807792i	$-0.0257409\pi$
$614$		−	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	−0.502713	−	0.864453i	$-0.667665\pi$
$619$	9.00000	−	9.00000i	0.361741	−	0.361741i	0.864453	+	0.502713i	$0.167665\pi$
$620$	−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	0.996707	−	0.0810911i	$-0.0258405\pi$
$631$	23.0000	+	23.0000i	0.915616	+	0.915616i	−0.0810911	+	0.996707i	$0.525840\pi$
$632$			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	$-0.842820\pi$
$641$		−	24.0000i		−	0.947943i	0.880540	−	0.473972i	$-0.157180\pi$
$642$	2.00000			0.0789337
$643$			10.0000i			0.394362i	0.980367	+	0.197181i	$0.0631786\pi$
$643$			10.0000i			0.394362i	−0.980367	+	0.197181i	$0.936821\pi$
$644$	−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	−0.403775	−	0.914858i	$-0.632302\pi$
$647$	13.0000	−	13.0000i	0.511083	−	0.511083i	0.914858	+	0.403775i	$0.132302\pi$
$648$	−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	−0.936817	−	0.349821i	$-0.886242\pi$
$653$	−15.0000	+	15.0000i	−0.586995	+	0.586995i	0.349821	+	0.936817i	$0.386242\pi$
$654$	−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	$-0.734762\pi$
$659$		−	38.0000i		−	1.48027i	0.672458	−	0.740135i	$-0.265238\pi$
$660$	2.00000	+	4.00000i	0.0778499	+	0.155700i
$661$	13.0000	+	13.0000i	0.505641	+	0.505641i	0.913186	−	0.407544i	$-0.133615\pi$
$661$	13.0000	+	13.0000i	0.505641	+	0.505641i	−0.407544	+	0.913186i	$0.633615\pi$
$662$	−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	0.954265	−	0.298963i	$-0.0966407\pi$
$673$	17.0000	+	17.0000i	0.655302	+	0.655302i	−0.298963	+	0.954265i	$0.596641\pi$
$674$	−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	0.911323	−	0.411692i	$-0.135062\pi$
$677$	13.0000	+	13.0000i	0.499631	+	0.499631i	−0.411692	+	0.911323i	$0.635062\pi$
$678$		−	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	−0.184041	−	0.982919i	$-0.558918\pi$
$691$	21.0000	−	21.0000i	0.798878	−	0.798878i	0.982919	+	0.184041i	$0.0589179\pi$
$692$	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	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$	−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	0.279070	−	0.960271i	$-0.409974\pi$
$709$	33.0000	−	33.0000i	1.23934	−	1.23934i	0.960271	−	0.279070i	$-0.0900263\pi$
$710$	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	−0.688320	−	0.725408i	$-0.741651\pi$
$727$	1.00000	−	1.00000i	0.0370879	−	0.0370879i	0.725408	+	0.688320i	$0.241651\pi$
$728$	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	$-0.879577\pi$
$733$		−	20.0000i		−	0.738717i	0.929287	−	0.369358i	$-0.120423\pi$
$734$	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	−0.609137	−	0.793065i	$-0.708484\pi$
$739$	5.00000	−	5.00000i	0.183928	−	0.183928i	0.793065	+	0.609137i	$0.208484\pi$
$740$	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	$-0.892891\pi$
$743$		−	18.0000i		−	0.660356i	0.943919	−	0.330178i	$-0.107109\pi$
$744$			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	$0.243853\pi$
$751$			38.0000i			1.38664i	−0.720630	+	0.693320i	$0.756147\pi$
$752$		−	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	0.996163	−	0.0875221i	$-0.0278948\pi$
$757$	25.0000	+	25.0000i	0.908640	+	0.908640i	−0.0875221	+	0.996163i	$0.527895\pi$
$758$	−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	0.724999	−	0.688749i	$-0.241840\pi$
$761$	1.00000	+	1.00000i	0.0362500	+	0.0362500i	−0.688749	+	0.724999i	$0.741840\pi$
$762$		−	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	0.158033	−	0.987434i	$-0.449485\pi$
$769$	−23.0000	−	23.0000i	−0.829401	−	0.829401i	−0.987434	+	0.158033i	$0.949485\pi$
$770$	−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	$-0.857946\pi$
$773$		−	24.0000i		−	0.863220i	0.902060	−	0.431610i	$-0.142054\pi$
$774$	−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	$-0.820428\pi$
$787$		−	30.0000i		−	1.06938i	0.845047	−	0.534692i	$-0.179572\pi$
$788$	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	−0.612985	−	0.790094i	$-0.710032\pi$
$797$	5.00000	−	5.00000i	0.177109	−	0.177109i	0.790094	+	0.612985i	$0.210032\pi$
$798$			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	$0.0676553\pi$
$809$			12.0000i			0.421898i	−0.977497	+	0.210949i	$0.932345\pi$
$810$	5.00000	+	10.0000i	0.175682	+	0.351364i
$811$	5.00000	−	5.00000i	0.175574	−	0.175574i	−0.613849	−	0.789423i	$-0.710380\pi$
$811$	5.00000	−	5.00000i	0.175574	−	0.175574i	0.789423	+	0.613849i	$0.210380\pi$
$812$	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	−0.956111	−	0.293006i	$-0.905344\pi$
$821$	−19.0000	+	19.0000i	−0.663105	+	0.663105i	0.293006	+	0.956111i	$0.405344\pi$
$822$		0			0
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	0.757458	−	0.652884i	$-0.226441\pi$
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	−0.652884	+	0.757458i	$0.726441\pi$
$824$	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	$0.149309\pi$
$827$			26.0000i			0.904109i	−0.891990	+	0.452054i	$0.850691\pi$
$828$	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	−0.817539	−	0.575873i	$-0.804662\pi$
$839$	−7.00000	+	7.00000i	−0.241667	+	0.241667i	0.575873	+	0.817539i	$0.304662\pi$
$840$	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	−0.869567	−	0.493814i	$-0.835602\pi$
$857$	−11.0000	+	11.0000i	−0.375753	+	0.375753i	0.493814	+	0.869567i	$0.335602\pi$
$858$	6.00000	−	4.00000i	0.204837	−	0.136558i
$859$			34.0000i			1.16007i	0.814593	+	0.580033i	$0.196960\pi$
$859$			34.0000i			1.16007i	−0.814593	+	0.580033i	$0.803040\pi$
$860$	−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	$-0.803565\pi$
$863$		−	34.0000i		−	1.15737i	0.815550	−	0.578687i	$-0.196435\pi$
$864$	−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	$-0.890619\pi$
$881$		−	20.0000i		−	0.673817i	0.941537	−	0.336909i	$-0.109381\pi$
$882$		−	3.00000i		−	0.101015i
$883$	−25.0000	−	25.0000i	−0.841317	−	0.841317i	0.147713	−	0.989030i	$-0.452809\pi$
$883$	−25.0000	−	25.0000i	−0.841317	−	0.841317i	−0.989030	+	0.147713i	$0.952809\pi$
$884$	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	0.950051	−	0.312094i	$-0.101030\pi$
$887$	19.0000	+	19.0000i	0.637958	+	0.637958i	−0.312094	+	0.950051i	$0.601030\pi$
$888$	−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	−0.813707	−	0.581276i	$-0.802554\pi$
$907$	−7.00000	+	7.00000i	−0.232431	+	0.232431i	0.581276	+	0.813707i	$0.302554\pi$
$908$	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	$0.0741699\pi$
$919$			14.0000i			0.461817i	−0.972975	+	0.230909i	$0.925830\pi$
$920$	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	0.887440	−	0.460924i	$-0.152482\pi$
$929$	13.0000	+	13.0000i	0.426516	+	0.426516i	−0.460924	+	0.887440i	$0.652482\pi$
$930$	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	0.838665	−	0.544648i	$-0.183337\pi$
$937$	9.00000	+	9.00000i	0.294017	+	0.294017i	−0.544648	+	0.838665i	$0.683337\pi$
$938$		−	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	−0.373462	−	0.927646i	$-0.621829\pi$
$941$	17.0000	−	17.0000i	0.554184	−	0.554184i	0.927646	+	0.373462i	$0.121829\pi$
$942$	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	$0.0519487\pi$
$947$			10.0000i			0.324956i	−0.986712	+	0.162478i	$0.948051\pi$
$948$	−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	0.783437	−	0.621471i	$-0.213465\pi$
$953$	5.00000	+	5.00000i	0.161966	+	0.161966i	−0.621471	+	0.783437i	$0.713465\pi$
$954$	−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	0.882335	−	0.470621i	$-0.155970\pi$
$997$	13.0000	+	13.0000i	0.411714	+	0.411714i	−0.470621	+	0.882335i	$0.655970\pi$
$998$	−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.57.1	✓	2
3.2	odd	2		1170.2.m.b.577.1		2
4.3	odd	2		1040.2.bg.b.577.1		2
5.2	odd	4		650.2.j.a.343.1		2
5.3	odd	4		130.2.j.c.83.1	yes	2
5.4	even	2		650.2.g.c.57.1		2
13.8	odd	4		130.2.j.c.47.1	yes	2
15.8	even	4		1170.2.w.a.343.1		2
20.3	even	4		1040.2.cd.c.993.1		2
39.8	even	4		1170.2.w.a.307.1		2
52.47	even	4		1040.2.cd.c.177.1		2
65.8	even	4	inner	130.2.g.b.73.1	yes	2
65.34	odd	4		650.2.j.a.307.1		2
65.47	even	4		650.2.g.c.593.1		2
195.8	odd	4		1170.2.m.b.73.1		2
260.203	odd	4		1040.2.bg.b.593.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.b.57.1	✓	2	1.1	even	1	trivial
130.2.g.b.73.1	yes	2	65.8	even	4	inner
130.2.j.c.47.1	yes	2	13.8	odd	4
130.2.j.c.83.1	yes	2	5.3	odd	4
650.2.g.c.57.1		2	5.4	even	2
650.2.g.c.593.1		2	65.47	even	4
650.2.j.a.307.1		2	65.34	odd	4
650.2.j.a.343.1		2	5.2	odd	4
1040.2.bg.b.577.1		2	4.3	odd	2
1040.2.bg.b.593.1		2	260.203	odd	4
1040.2.cd.c.177.1		2	52.47	even	4
1040.2.cd.c.993.1		2	20.3	even	4
1170.2.m.b.73.1		2	195.8	odd	4
1170.2.m.b.577.1		2	3.2	odd	2
1170.2.w.a.307.1		2	39.8	even	4
1170.2.w.a.343.1		2	15.8	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

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Database

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