LMFDB - Embedded newform 130.2.j.c.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(47,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("130.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.03805522628$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	130.83
Dual form			130.2.j.c.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	0.934172	−	0.356822i	$-0.116140\pi$
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	−0.356822	+	0.934172i	$0.616140\pi$
$4$	−1.00000			−0.500000
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	−1.00000	+	1.00000i	−0.408248	+	0.408248i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	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
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$		−	2.00000i		−	0.534522i
$15$	1.00000	+	3.00000i	0.258199	+	0.774597i
$16$	1.00000			0.250000
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	0.575363	−	0.817898i	$-0.304861\pi$
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	−0.817898	+	0.575363i	$0.804861\pi$
$18$	1.00000			0.235702
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	−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	$-0.702896\pi$
$23$	1.00000	−	1.00000i	0.208514	−	0.208514i	0.803636	+	0.595121i	$0.202896\pi$
$24$	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
$28$	2.00000			0.377964
$29$		−	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	−0.611578	−	0.791184i	$-0.709465\pi$
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	0.791184	+	0.611578i	$0.209465\pi$
$32$			1.00000i			0.176777i
$33$		−	2.00000i		−	0.348155i
$34$	1.00000	−	1.00000i	0.171499	−	0.171499i
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$			1.00000i			0.166667i
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	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	$-0.715609\pi$
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	0.779233	+	0.626734i	$0.215609\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$	1.00000	−	2.00000i	0.149071	−	0.298142i
$46$	1.00000	+	1.00000i	0.147442	+	0.147442i
$47$	−10.0000			−1.45865			−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000			−1.45865			−0.729325	+	0.684167i	$0.760166\pi$
$48$	1.00000	+	1.00000i	0.144338	+	0.144338i
$49$	−3.00000			−0.428571
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$		−	2.00000i		−	0.280056i
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$	4.00000	+	4.00000i	0.544331	+	0.544331i
$55$	−1.00000	−	3.00000i	−0.134840	−	0.404520i
$56$			2.00000i			0.267261i
$57$		−	6.00000i		−	0.794719i
$58$	8.00000			1.05045
$59$	−9.00000	+	9.00000i	−1.17170	+	1.17170i	−0.189896	+	0.981804i	$0.560815\pi$
$59$	−9.00000	+	9.00000i	−1.17170	+	1.17170i	−0.981804	+	0.189896i	$0.939185\pi$
$60$	−1.00000	−	3.00000i	−0.129099	−	0.387298i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	1.00000	+	1.00000i	0.127000	+	0.127000i
$63$			2.00000i			0.251976i
$64$	−1.00000			−0.125000
$65$	1.00000	+	8.00000i	0.124035	+	0.992278i
$66$	2.00000			0.246183
$67$			12.0000i			1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$			12.0000i			1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$	1.00000	+	1.00000i	0.121268	+	0.121268i
$69$	2.00000			0.240772
$70$	2.00000	−	4.00000i	0.239046	−	0.478091i
$71$	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	$0.112174\pi$
$72$	−1.00000			−0.117851
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$			8.00000i			0.929981i
$75$	−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
$78$	−5.00000	−	1.00000i	−0.566139	−	0.113228i
$79$			10.0000i			1.12509i	0.826767	+	0.562544i	$0.190177\pi$
$79$			10.0000i			1.12509i	−0.826767	+	0.562544i	$0.809823\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	5.00000			0.555556
$82$	−7.00000	−	7.00000i	−0.773021	−	0.773021i
$83$	−18.0000			−1.97576			−0.987878	−	0.155230i	$-0.950388\pi$
$83$	−18.0000			−1.97576			−0.987878	+	0.155230i	$0.950388\pi$
$84$	2.00000	+	2.00000i	0.218218	+	0.218218i
$85$	−1.00000	−	3.00000i	−0.108465	−	0.325396i
$86$	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	$-0.441465\pi$
$89$	11.0000	−	11.0000i	1.16600	−	1.16600i	0.983139	−	0.182858i	$-0.0585350\pi$
$90$	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
$93$	2.00000			0.207390
$94$		−	10.0000i		−	1.03142i
$95$	−3.00000	−	9.00000i	−0.307794	−	0.923381i
$96$	−1.00000	+	1.00000i	−0.102062	+	0.102062i
$97$			14.0000i			1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$			14.0000i			1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$		−	3.00000i		−	0.303046i
$99$	−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	$-0.203650\pi$
$102$	2.00000			0.198030
$103$	5.00000	−	5.00000i	0.492665	−	0.492665i	−0.416480	−	0.909145i	$-0.636736\pi$
$103$	5.00000	−	5.00000i	0.492665	−	0.492665i	0.909145	+	0.416480i	$0.136736\pi$
$104$	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	$-0.359968\pi$
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	−0.904784	+	0.425871i	$0.859968\pi$
$110$	3.00000	−	1.00000i	0.286039	−	0.0953463i
$111$	8.00000	+	8.00000i	0.759326	+	0.759326i
$112$	−2.00000			−0.188982
$113$	−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
$115$	3.00000	−	1.00000i	0.279751	−	0.0932505i
$116$			8.00000i			0.742781i
$117$	3.00000	−	2.00000i	0.277350	−	0.184900i
$118$	−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
$122$			2.00000i			0.181071i
$123$	−14.0000			−1.26234
$124$	−1.00000	+	1.00000i	−0.0898027	+	0.0898027i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−2.00000			−0.178174
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	0.827570	−	0.561363i	$-0.189723\pi$
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	−0.561363	+	0.827570i	$0.689723\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.00000			0.176090
$130$	−8.00000	+	1.00000i	−0.701646	+	0.0877058i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$			2.00000i			0.174078i
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$	−12.0000			−1.03664
$135$	12.0000	−	4.00000i	1.03280	−	0.344265i
$136$	−1.00000	+	1.00000i	−0.0857493	+	0.0857493i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$			2.00000i			0.170251i
$139$		−	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
$143$	1.00000	−	5.00000i	0.0836242	−	0.418121i
$144$		−	1.00000i		−	0.0833333i
$145$	8.00000	−	16.0000i	0.664364	−	1.32873i
$146$	−6.00000			−0.496564
$147$	−3.00000	−	3.00000i	−0.247436	−	0.247436i
$148$	−8.00000			−0.657596
$149$	−1.00000	−	1.00000i	−0.0819232	−	0.0819232i	0.664958	−	0.746881i	$-0.268450\pi$
$149$	−1.00000	−	1.00000i	−0.0819232	−	0.0819232i	−0.746881	+	0.664958i	$0.768450\pi$
$150$	−7.00000	−	1.00000i	−0.571548	−	0.0816497i
$151$	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	−0.222108	+	0.975022i	$0.571294\pi$
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.975022	+	0.222108i	$0.928706\pi$
$158$	−10.0000			−0.795557
$159$			2.00000i			0.158610i
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	−2.00000	+	2.00000i	−0.157622	+	0.157622i
$162$			5.00000i			0.392837i
$163$		−	20.0000i		−	1.56652i	−0.621694	−	0.783260i	$-0.713555\pi$
$163$		−	20.0000i		−	1.56652i	0.621694	−	0.783260i	$-0.286445\pi$
$164$	7.00000	−	7.00000i	0.546608	−	0.546608i
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$		−	18.0000i		−	1.39707i
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$	−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	$-0.910759\pi$
$173$	−9.00000	+	9.00000i	−0.684257	+	0.684257i	0.276699	+	0.960957i	$0.410759\pi$
$174$	8.00000	+	8.00000i	0.606478	+	0.606478i
$175$	−6.00000	−	8.00000i	−0.453557	−	0.604743i
$176$	−1.00000	−	1.00000i	−0.0753778	−	0.0753778i
$177$	−18.0000			−1.35296
$178$	11.0000	+	11.0000i	0.824485	+	0.824485i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$	−1.00000	+	2.00000i	−0.0745356	+	0.149071i
$181$			16.0000i			1.18927i	0.803996	+	0.594635i	$0.202704\pi$
$181$			16.0000i			1.18927i	−0.803996	+	0.594635i	$0.797296\pi$
$182$	6.00000	−	4.00000i	0.444750	−	0.296500i
$183$	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
$187$			2.00000i			0.146254i
$188$	10.0000			0.729325
$189$	−8.00000	+	8.00000i	−0.581914	+	0.581914i
$190$	9.00000	−	3.00000i	0.652929	−	0.217643i
$191$	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
$193$			2.00000i			0.143963i	0.997406	+	0.0719816i	$0.0229323\pi$
$193$			2.00000i			0.143963i	−0.997406	+	0.0719816i	$0.977068\pi$
$194$	−14.0000			−1.00514
$195$	−7.00000	+	9.00000i	−0.501280	+	0.644503i
$196$	3.00000			0.214286
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$	−1.00000	−	1.00000i	−0.0710669	−	0.0710669i
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$	−12.0000	+	12.0000i	−0.846415	+	0.846415i
$202$	12.0000			0.844317
$203$			16.0000i			1.12298i
$204$			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
$208$	2.00000	+	3.00000i	0.138675	+	0.208013i
$209$			6.00000i			0.415029i
$210$	6.00000	−	2.00000i	0.414039	−	0.138013i
$211$	−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
$213$	10.0000			0.685189
$214$	−1.00000	−	1.00000i	−0.0683586	−	0.0683586i
$215$	3.00000	−	1.00000i	0.204598	−	0.0681994i
$216$	−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
$223$	18.0000			1.20537			0.602685	−	0.797980i	$-0.294098\pi$
$223$	18.0000			1.20537			0.602685	+	0.797980i	$0.294098\pi$
$224$		−	2.00000i		−	0.133631i
$225$	4.00000	−	3.00000i	0.266667	−	0.200000i
$226$	3.00000	−	3.00000i	0.199557	−	0.199557i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$			6.00000i			0.397360i
$229$	15.0000	−	15.0000i	0.991228	−	0.991228i	−0.00873396	−	0.999962i	$-0.502780\pi$
$229$	15.0000	−	15.0000i	0.991228	−	0.991228i	0.999962	+	0.00873396i	$0.00278014\pi$
$230$	1.00000	+	3.00000i	0.0659380	+	0.197814i
$231$			4.00000i			0.263181i
$232$	−8.00000			−0.525226
$233$	−1.00000	+	1.00000i	−0.0655122	+	0.0655122i	−0.739104	−	0.673592i	$-0.764751\pi$
$233$	−1.00000	+	1.00000i	−0.0655122	+	0.0655122i	0.673592	+	0.739104i	$0.264751\pi$
$234$	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	$-0.235436\pi$
$239$	1.00000	+	1.00000i	0.0646846	+	0.0646846i	−0.674024	+	0.738709i	$0.735436\pi$
$240$	1.00000	+	3.00000i	0.0645497	+	0.193649i
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	0.738581	−	0.674165i	$-0.235496\pi$
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	−0.674165	+	0.738581i	$0.735496\pi$
$242$	9.00000			0.578542
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$	−2.00000			−0.128037
$245$	−6.00000	−	3.00000i	−0.383326	−	0.191663i
$246$		−	14.0000i		−	0.892607i
$247$	3.00000	−	15.0000i	0.190885	−	0.954427i
$248$	−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	$0.807688\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−2.00000			−0.125739
$254$	−3.00000	+	3.00000i	−0.188237	+	0.188237i
$255$	2.00000	−	4.00000i	0.125245	−	0.250490i
$256$	1.00000			0.0625000
$257$	−21.0000	−	21.0000i	−1.30994	−	1.30994i	−0.921452	−	0.388492i	$-0.872996\pi$
$257$	−21.0000	−	21.0000i	−1.30994	−	1.30994i	−0.388492	−	0.921452i	$-0.627004\pi$
$258$			2.00000i			0.124515i
$259$	−16.0000			−0.994192
$260$	−1.00000	−	8.00000i	−0.0620174	−	0.496139i
$261$	−8.00000			−0.495188
$262$			12.0000i			0.741362i
$263$	−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
$265$	1.00000	+	3.00000i	0.0614295	+	0.184289i
$266$	−6.00000	+	6.00000i	−0.367884	+	0.367884i
$267$	22.0000			1.34638
$268$		−	12.0000i		−	0.733017i
$269$		−	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	0.792330	−	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
$273$	2.00000	−	10.0000i	0.121046	−	0.605228i
$274$		0			0
$275$	1.00000	−	7.00000i	0.0603023	−	0.422116i
$276$	−2.00000			−0.120386
$277$	11.0000	+	11.0000i	0.660926	+	0.660926i	0.955598	−	0.294672i	$-0.0952105\pi$
$277$	11.0000	+	11.0000i	0.660926	+	0.660926i	−0.294672	+	0.955598i	$0.595211\pi$
$278$	2.00000			0.119952
$279$	−1.00000	−	1.00000i	−0.0598684	−	0.0598684i
$280$	−2.00000	+	4.00000i	−0.119523	+	0.239046i
$281$	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	$-0.967149\pi$
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	0.103022	+	0.994679i	$0.467149\pi$
$284$	−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
$288$	1.00000			0.0589256
$289$		−	15.0000i		−	0.882353i
$290$	16.0000	+	8.00000i	0.939552	+	0.469776i
$291$	−14.0000	+	14.0000i	−0.820695	+	0.820695i
$292$		−	6.00000i		−	0.351123i
$293$		−	22.0000i		−	1.28525i	−0.766179	−	0.642627i	$-0.777845\pi$
$293$		−	22.0000i		−	1.28525i	0.766179	−	0.642627i	$-0.222155\pi$
$294$	3.00000	−	3.00000i	0.174964	−	0.174964i
$295$	−27.0000	+	9.00000i	−1.57200	+	0.524000i
$296$		−	8.00000i		−	0.464991i
$297$	−8.00000			−0.464207
$298$	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
$305$	4.00000	+	2.00000i	0.229039	+	0.114520i
$306$	−1.00000	−	1.00000i	−0.0571662	−	0.0571662i
$307$	10.0000			0.570730			0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000			0.570730			0.285365	+	0.958419i	$0.407885\pi$
$308$	−2.00000	−	2.00000i	−0.113961	−	0.113961i
$309$	10.0000			0.568880
$310$	1.00000	+	3.00000i	0.0567962	+	0.170389i
$311$		−	2.00000i		−	0.113410i	−0.998391	−	0.0567048i	$-0.981941\pi$
$311$		−	2.00000i		−	0.113410i	0.998391	−	0.0567048i	$-0.0180594\pi$
$312$	5.00000	+	1.00000i	0.283069	+	0.0566139i
$313$	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
$317$		−	2.00000i		−	0.112331i	−0.998421	−	0.0561656i	$-0.982113\pi$
$317$		−	2.00000i		−	0.112331i	0.998421	−	0.0561656i	$-0.0178875\pi$
$318$	−2.00000			−0.112154
$319$	−8.00000	+	8.00000i	−0.447914	+	0.447914i
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$	−2.00000			−0.111629
$322$	−2.00000	−	2.00000i	−0.111456	−	0.111456i
$323$			6.00000i			0.333849i
$324$	−5.00000			−0.277778
$325$	−6.00000	+	17.0000i	−0.332820	+	0.942990i
$326$	20.0000			1.10770
$327$		−	10.0000i		−	0.553001i
$328$	7.00000	+	7.00000i	0.386510	+	0.386510i
$329$	20.0000			1.10264
$330$	4.00000	+	2.00000i	0.220193	+	0.110096i
$331$	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	$-0.0539168\pi$
$332$	18.0000			0.987878
$333$		−	8.00000i		−	0.438397i
$334$			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	$-0.311690\pi$
$337$	−5.00000	−	5.00000i	−0.272367	−	0.272367i	−0.830053	+	0.557685i	$0.811690\pi$
$338$	−12.0000	−	5.00000i	−0.652714	−	0.271964i
$339$		−	6.00000i		−	0.325875i
$340$	1.00000	+	3.00000i	0.0542326	+	0.162698i
$341$	−2.00000			−0.108306
$342$	−3.00000	−	3.00000i	−0.162221	−	0.162221i
$343$	20.0000			1.07990
$344$	−1.00000	−	1.00000i	−0.0539164	−	0.0539164i
$345$	4.00000	+	2.00000i	0.215353	+	0.107676i
$346$	−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	−0.132986	+	0.991118i	$0.542457\pi$
$349$	−21.0000	+	21.0000i	−1.12410	+	1.12410i	−0.991118	+	0.132986i	$0.957543\pi$
$350$	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
$353$	4.00000			0.212899			0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000			0.212899			0.106449	+	0.994318i	$0.466052\pi$
$354$		−	18.0000i		−	0.956689i
$355$	15.0000	−	5.00000i	0.796117	−	0.265372i
$356$	−11.0000	+	11.0000i	−0.582999	+	0.582999i
$357$			4.00000i			0.211702i
$358$			20.0000i			1.05703i
$359$	−5.00000	+	5.00000i	−0.263890	+	0.263890i	−0.826632	−	0.562742i	$-0.809746\pi$
$359$	−5.00000	+	5.00000i	−0.263890	+	0.263890i	0.562742	+	0.826632i	$0.309746\pi$
$360$	−2.00000	−	1.00000i	−0.105409	−	0.0527046i
$361$		−	1.00000i		−	0.0526316i
$362$	−16.0000			−0.840941
$363$	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
$370$	−8.00000	+	16.0000i	−0.415900	+	0.831800i
$371$	−2.00000	−	2.00000i	−0.103835	−	0.103835i
$372$	−2.00000			−0.103695
$373$	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
$375$	−9.00000	+	13.0000i	−0.464758	+	0.671317i
$376$			10.0000i			0.515711i
$377$	24.0000	−	16.0000i	1.23606	−	0.824042i
$378$	−8.00000	−	8.00000i	−0.411476	−	0.411476i
$379$	−23.0000	−	23.0000i	−1.18143	−	1.18143i	−0.979374	−	0.202057i	$-0.935237\pi$
$379$	−23.0000	−	23.0000i	−1.18143	−	1.18143i	−0.202057	−	0.979374i	$-0.564763\pi$
$380$	3.00000	+	9.00000i	0.153897	+	0.461690i
$381$			6.00000i			0.307389i
$382$			8.00000i			0.409316i
$383$	18.0000			0.919757			0.459879	−	0.887982i	$-0.347893\pi$
$383$	18.0000			0.919757			0.459879	+	0.887982i	$0.347893\pi$
$384$	1.00000	−	1.00000i	0.0510310	−	0.0510310i
$385$	2.00000	+	6.00000i	0.101929	+	0.305788i
$386$	−2.00000			−0.101797
$387$	−1.00000	−	1.00000i	−0.0508329	−	0.0508329i
$388$		−	14.0000i		−	0.710742i
$389$	2.00000			0.101404			0.0507020	−	0.998714i	$-0.483854\pi$
$389$	2.00000			0.101404			0.0507020	+	0.998714i	$0.483854\pi$
$390$	−9.00000	−	7.00000i	−0.455733	−	0.354459i
$391$	−2.00000			−0.101144
$392$			3.00000i			0.151523i
$393$	12.0000	+	12.0000i	0.605320	+	0.605320i
$394$	6.00000			0.302276
$395$	−10.0000	+	20.0000i	−0.503155	+	1.00631i
$396$	1.00000	−	1.00000i	0.0502519	−	0.0502519i
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$			24.0000i			1.20301i
$399$			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
$403$	5.00000	+	1.00000i	0.249068	+	0.0498135i
$404$			12.0000i			0.597022i
$405$	10.0000	+	5.00000i	0.496904	+	0.248452i
$406$	−16.0000			−0.794067
$407$	−8.00000	−	8.00000i	−0.396545	−	0.396545i
$408$	−2.00000			−0.0990148
$409$	−9.00000	−	9.00000i	−0.445021	−	0.445021i	0.448674	−	0.893695i	$-0.351896\pi$
$409$	−9.00000	−	9.00000i	−0.445021	−	0.445021i	−0.893695	+	0.448674i	$0.851896\pi$
$410$	−7.00000	−	21.0000i	−0.345705	−	1.03712i
$411$		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
$418$	−6.00000			−0.293470
$419$			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	−0.452919	−	0.891552i	$-0.649617\pi$
$421$	9.00000	−	9.00000i	0.438633	−	0.438633i	0.891552	+	0.452919i	$0.149617\pi$
$422$		−	12.0000i		−	0.584151i
$423$			10.0000i			0.486217i
$424$	1.00000	−	1.00000i	0.0485643	−	0.0485643i
$425$	1.00000	−	7.00000i	0.0485071	−	0.339550i
$426$			10.0000i			0.484502i
$427$	−4.00000			−0.193574
$428$	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	$-0.848935\pi$
$433$	−9.00000	+	9.00000i	−0.432512	+	0.432512i	0.456970	+	0.889482i	$0.348935\pi$
$434$	−2.00000	−	2.00000i	−0.0960031	−	0.0960031i
$435$	24.0000	−	8.00000i	1.15071	−	0.383571i
$436$	5.00000	+	5.00000i	0.239457	+	0.239457i
$437$	−6.00000			−0.287019
$438$	−6.00000	−	6.00000i	−0.286691	−	0.286691i
$439$	32.0000			1.52728			0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000			1.52728			0.763638	+	0.645644i	$0.223411\pi$
$440$	−3.00000	+	1.00000i	−0.143019	+	0.0476731i
$441$			3.00000i			0.142857i
$442$	5.00000	+	1.00000i	0.237826	+	0.0475651i
$443$	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
$447$		−	2.00000i		−	0.0945968i
$448$	2.00000			0.0944911
$449$	−13.0000	+	13.0000i	−0.613508	+	0.613508i	−0.943858	−	0.330350i	$-0.892833\pi$
$449$	−13.0000	+	13.0000i	−0.613508	+	0.613508i	0.330350	+	0.943858i	$0.392833\pi$
$450$	3.00000	+	4.00000i	0.141421	+	0.188562i
$451$	14.0000			0.659234
$452$	3.00000	+	3.00000i	0.141108	+	0.141108i
$453$			6.00000i			0.281905i
$454$	12.0000			0.563188
$455$	−2.00000	−	16.0000i	−0.0937614	−	0.750092i
$456$	−6.00000			−0.280976
$457$		−	2.00000i		−	0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$		−	2.00000i		−	0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$	15.0000	+	15.0000i	0.700904	+	0.700904i
$459$	−8.00000			−0.373408
$460$	−3.00000	+	1.00000i	−0.139876	+	0.0466252i
$461$	−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	$0.367997\pi$
$462$	−4.00000			−0.186097
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$		−	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	$-0.176439\pi$
$467$	7.00000	+	7.00000i	0.323921	+	0.323921i	−0.526348	+	0.850269i	$0.676439\pi$
$468$	−3.00000	+	2.00000i	−0.138675	+	0.0924500i
$469$		−	24.0000i		−	1.10822i
$470$	10.0000	−	20.0000i	0.461266	−	0.922531i
$471$	−30.0000			−1.38233
$472$	9.00000	+	9.00000i	0.414259	+	0.414259i
$473$	−2.00000			−0.0919601
$474$	−10.0000	−	10.0000i	−0.459315	−	0.459315i
$475$	3.00000	−	21.0000i	0.137649	−	0.963546i
$476$	−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	$-0.539615\pi$
$479$	19.0000	−	19.0000i	0.868132	−	0.868132i	0.992266	+	0.124133i	$0.0396151\pi$
$480$	−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
$483$	−4.00000			−0.182006
$484$			9.00000i			0.409091i
$485$	−14.0000	+	28.0000i	−0.635707	+	1.27141i
$486$	7.00000	−	7.00000i	0.317526	−	0.317526i
$487$			8.00000i			0.362515i	0.983436	+	0.181257i	$0.0580167\pi$
$487$			8.00000i			0.362515i	−0.983436	+	0.181257i	$0.941983\pi$
$488$		−	2.00000i		−	0.0905357i
$489$	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	$-0.327958\pi$
$492$	14.0000			0.631169
$493$	−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	$-0.455404\pi$
$499$	−19.0000	−	19.0000i	−0.850557	−	0.850557i	−0.990202	+	0.139645i	$0.955404\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	14.0000	+	14.0000i	0.625474	+	0.625474i
$502$	−18.0000			−0.803379
$503$	−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
$505$	12.0000	−	24.0000i	0.533993	−	1.06799i
$506$		−	2.00000i		−	0.0889108i
$507$	−17.0000	+	7.00000i	−0.754997	+	0.310881i
$508$	−3.00000	−	3.00000i	−0.133103	−	0.133103i
$509$	−1.00000	−	1.00000i	−0.0443242	−	0.0443242i	0.684597	−	0.728922i	$-0.259978\pi$
$509$	−1.00000	−	1.00000i	−0.0443242	−	0.0443242i	−0.728922	+	0.684597i	$0.759978\pi$
$510$	4.00000	+	2.00000i	0.177123	+	0.0885615i
$511$		−	12.0000i		−	0.530849i
$512$			1.00000i			0.0441942i
$513$	−24.0000			−1.05963
$514$	21.0000	−	21.0000i	0.926270	−	0.926270i
$515$	15.0000	−	5.00000i	0.660979	−	0.220326i
$516$	−2.00000			−0.0880451
$517$	10.0000	+	10.0000i	0.439799	+	0.439799i
$518$		−	16.0000i		−	0.703000i
$519$	−18.0000			−0.790112
$520$	8.00000	−	1.00000i	0.350823	−	0.0438529i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		−	8.00000i		−	0.350150i
$523$	−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
$525$	2.00000	−	14.0000i	0.0872872	−	0.611010i
$526$	3.00000	−	3.00000i	0.130806	−	0.130806i
$527$	−2.00000			−0.0871214
$528$		−	2.00000i		−	0.0870388i
$529$			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
$533$	−35.0000	−	7.00000i	−1.51602	−	0.303204i
$534$			22.0000i			0.952033i
$535$	−3.00000	+	1.00000i	−0.129701	+	0.0432338i
$536$	12.0000			0.518321
$537$	20.0000	+	20.0000i	0.863064	+	0.863064i
$538$	4.00000			0.172452
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$	−12.0000	+	4.00000i	−0.516398	+	0.172133i
$541$	−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	−0.0164556	−	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
$552$		−	2.00000i		−	0.0851257i
$553$		−	20.0000i		−	0.850487i
$554$	−11.0000	+	11.0000i	−0.467345	+	0.467345i
$555$	8.00000	+	24.0000i	0.339581	+	1.01874i
$556$			2.00000i			0.0848189i
$557$	−32.0000			−1.35588			−0.677942	−	0.735116i	$-0.737128\pi$
$557$	−32.0000			−1.35588			−0.677942	+	0.735116i	$0.737128\pi$
$558$	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	$0.624960\pi$
$563$	−31.0000	+	31.0000i	−1.30649	+	1.30649i	−0.923928	+	0.382566i	$0.875040\pi$
$564$	10.0000	+	10.0000i	0.421076	+	0.421076i
$565$	−3.00000	−	9.00000i	−0.126211	−	0.378633i
$566$	−15.0000	−	15.0000i	−0.630497	−	0.630497i
$567$	−10.0000			−0.419961
$568$	−5.00000	−	5.00000i	−0.209795	−	0.209795i
$569$	26.0000			1.08998			0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000			1.08998			0.544988	+	0.838444i	$0.316534\pi$
$570$	12.0000	+	6.00000i	0.502625	+	0.251312i
$571$		−	22.0000i		−	0.920671i	−0.887745	−	0.460336i	$-0.847729\pi$
$571$		−	22.0000i		−	0.920671i	0.887745	−	0.460336i	$-0.152271\pi$
$572$	−1.00000	+	5.00000i	−0.0418121	+	0.209061i
$573$	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
$577$		−	14.0000i		−	0.582828i	−0.956597	−	0.291414i	$-0.905874\pi$
$577$		−	14.0000i		−	0.582828i	0.956597	−	0.291414i	$-0.0941257\pi$
$578$	15.0000			0.623918
$579$	−2.00000	+	2.00000i	−0.0831172	+	0.0831172i
$580$	−8.00000	+	16.0000i	−0.332182	+	0.664364i
$581$	36.0000			1.49353
$582$	−14.0000	−	14.0000i	−0.580319	−	0.580319i
$583$		−	2.00000i		−	0.0828315i
$584$	6.00000			0.248282
$585$	8.00000	−	1.00000i	0.330759	−	0.0413449i
$586$	22.0000			0.908812
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$	3.00000	+	3.00000i	0.123718	+	0.123718i
$589$	−6.00000			−0.247226
$590$	−9.00000	−	27.0000i	−0.370524	−	1.11157i
$591$	6.00000	−	6.00000i	0.246807	−	0.246807i
$592$	8.00000			0.328798
$593$			10.0000i			0.410651i	0.978694	+	0.205325i	$0.0658253\pi$
$593$			10.0000i			0.410651i	−0.978694	+	0.205325i	$0.934175\pi$
$594$		−	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
$598$	−1.00000	+	5.00000i	−0.0408930	+	0.204465i
$599$			26.0000i			1.06233i	0.847268	+	0.531166i	$0.178246\pi$
$599$			26.0000i			1.06233i	−0.847268	+	0.531166i	$0.821754\pi$
$600$	7.00000	+	1.00000i	0.285774	+	0.0408248i
$601$	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
$603$	12.0000			0.488678
$604$	−3.00000	−	3.00000i	−0.122068	−	0.122068i
$605$	9.00000	−	18.0000i	0.365902	−	0.731804i
$606$	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
$613$	4.00000			0.161558			0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000			0.161558			0.0807792	+	0.996732i	$0.474259\pi$
$614$			10.0000i			0.403567i
$615$	−28.0000	−	14.0000i	−1.12907	−	0.564534i
$616$	2.00000	−	2.00000i	0.0805823	−	0.0805823i
$617$			38.0000i			1.52982i	0.644136	+	0.764911i	$0.277217\pi$
$617$			38.0000i			1.52982i	−0.644136	+	0.764911i	$0.722783\pi$
$618$			10.0000i			0.402259i
$619$	−9.00000	+	9.00000i	−0.361741	+	0.361741i	−0.864453	−	0.502713i	$-0.832335\pi$
$619$	−9.00000	+	9.00000i	−0.361741	+	0.361741i	0.502713	+	0.864453i	$0.332335\pi$
$620$	−3.00000	+	1.00000i	−0.120483	+	0.0401610i
$621$		−	8.00000i		−	0.321029i
$622$	2.00000			0.0801927
$623$	−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
$630$	−4.00000	−	2.00000i	−0.159364	−	0.0796819i
$631$	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	$0.525840\pi$
$632$	10.0000			0.397779
$633$	−12.0000	−	12.0000i	−0.476957	−	0.476957i
$634$	2.00000			0.0794301
$635$	3.00000	+	9.00000i	0.119051	+	0.357154i
$636$		−	2.00000i		−	0.0793052i
$637$	−6.00000	−	9.00000i	−0.237729	−	0.356593i
$638$	−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	$-0.157180\pi$
$642$		−	2.00000i		−	0.0789337i
$643$	−10.0000			−0.394362			−0.197181	−	0.980367i	$-0.563179\pi$
$643$	−10.0000			−0.394362			−0.197181	+	0.980367i	$0.563179\pi$
$644$	2.00000	−	2.00000i	0.0788110	−	0.0788110i
$645$	4.00000	+	2.00000i	0.157500	+	0.0787499i
$646$	−6.00000			−0.236067
$647$	−13.0000	−	13.0000i	−0.511083	−	0.511083i	0.403775	−	0.914858i	$-0.367698\pi$
$647$	−13.0000	−	13.0000i	−0.511083	−	0.511083i	−0.914858	+	0.403775i	$0.867698\pi$
$648$		−	5.00000i		−	0.196419i
$649$	18.0000			0.706562
$650$	−17.0000	−	6.00000i	−0.666795	−	0.235339i
$651$	−4.00000			−0.156772
$652$			20.0000i			0.783260i
$653$	−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
$655$	24.0000	+	12.0000i	0.937758	+	0.468879i
$656$	−7.00000	+	7.00000i	−0.273304	+	0.273304i
$657$	6.00000			0.234082
$658$			20.0000i			0.779681i
$659$			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	0.913186	−	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
$663$	6.00000	−	4.00000i	0.233021	−	0.155347i
$664$			18.0000i			0.698535i
$665$	6.00000	+	18.0000i	0.232670	+	0.698010i
$666$	8.00000			0.309994
$667$	−8.00000	−	8.00000i	−0.309761	−	0.309761i
$668$	−14.0000			−0.541676
$669$	18.0000	+	18.0000i	0.695920	+	0.695920i
$670$	−24.0000	−	12.0000i	−0.927201	−	0.463600i
$671$	−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	$-0.903359\pi$
$673$	−17.0000	+	17.0000i	−0.655302	+	0.655302i	0.298963	+	0.954265i	$0.403359\pi$
$674$	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	$0.135062\pi$
$678$	6.00000			0.230429
$679$		−	28.0000i		−	1.07454i
$680$	−3.00000	+	1.00000i	−0.115045	+	0.0383482i
$681$	12.0000	−	12.0000i	0.459841	−	0.459841i
$682$		−	2.00000i		−	0.0765840i
$683$			12.0000i			0.459167i	0.973289	+	0.229584i	$0.0737364\pi$
$683$			12.0000i			0.459167i	−0.973289	+	0.229584i	$0.926264\pi$
$684$	3.00000	−	3.00000i	0.114708	−	0.114708i
$685$		0			0
$686$			20.0000i			0.763604i
$687$	30.0000			1.14457
$688$	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
$695$	2.00000	−	4.00000i	0.0758643	−	0.151729i
$696$	−8.00000	−	8.00000i	−0.303239	−	0.303239i
$697$	14.0000			0.530288
$698$	−21.0000	−	21.0000i	−0.794862	−	0.794862i
$699$	−2.00000			−0.0756469
$700$	6.00000	+	8.00000i	0.226779	+	0.302372i
$701$		−	12.0000i		−	0.453234i	−0.973984	−	0.226617i	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$	−4.00000	+	20.0000i	−0.150970	+	0.754851i
$703$	−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
$707$			24.0000i			0.902613i
$708$	18.0000			0.676481
$709$	−33.0000	+	33.0000i	−1.23934	+	1.23934i	−0.279070	+	0.960271i	$0.590026\pi$
$709$	−33.0000	+	33.0000i	−1.23934	+	1.23934i	−0.960271	+	0.279070i	$0.909974\pi$
$710$	5.00000	+	15.0000i	0.187647	+	0.562940i
$711$	10.0000			0.375029
$712$	−11.0000	−	11.0000i	−0.412242	−	0.412242i
$713$		−	2.00000i		−	0.0749006i
$714$	−4.00000			−0.149696
$715$	7.00000	−	9.00000i	0.261785	−	0.336581i
$716$	−20.0000			−0.747435
$717$			2.00000i			0.0746914i
$718$	−5.00000	−	5.00000i	−0.186598	−	0.186598i
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$	1.00000	−	2.00000i	0.0372678	−	0.0745356i
$721$	−10.0000	+	10.0000i	−0.372419	+	0.372419i
$722$	1.00000			0.0372161
$723$			2.00000i			0.0743808i
$724$		−	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	$-0.258349\pi$
$727$	−1.00000	−	1.00000i	−0.0370879	−	0.0370879i	−0.725408	+	0.688320i	$0.758349\pi$
$728$	−6.00000	+	4.00000i	−0.222375	+	0.148250i
$729$		−	29.0000i		−	1.07407i
$730$	−12.0000	−	6.00000i	−0.444140	−	0.222070i
$731$	−2.00000			−0.0739727
$732$	−2.00000	−	2.00000i	−0.0739221	−	0.0739221i
$733$	20.0000			0.738717			0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000			0.738717			0.369358	+	0.929287i	$0.379577\pi$
$734$	−21.0000	−	21.0000i	−0.775124	−	0.775124i
$735$	−3.00000	−	9.00000i	−0.110657	−	0.331970i
$736$	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	$-0.791516\pi$
$739$	−5.00000	+	5.00000i	−0.183928	+	0.183928i	0.609137	+	0.793065i	$0.291516\pi$
$740$	−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
$743$	18.0000			0.660356			0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000			0.660356			0.330178	+	0.943919i	$0.392891\pi$
$744$		−	2.00000i		−	0.0733236i
$745$	−1.00000	−	3.00000i	−0.0366372	−	0.109911i
$746$	−5.00000	+	5.00000i	−0.183063	+	0.183063i
$747$			18.0000i			0.658586i
$748$		−	2.00000i		−	0.0731272i
$749$	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	$0.756147\pi$
$752$	−10.0000			−0.364662
$753$	−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
$760$	−9.00000	+	3.00000i	−0.326464	+	0.108821i
$761$	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	$0.741840\pi$
$762$	−6.00000			−0.217357
$763$	10.0000	+	10.0000i	0.362024	+	0.362024i
$764$	−8.00000			−0.289430
$765$	−3.00000	+	1.00000i	−0.108465	+	0.0361551i
$766$			18.0000i			0.650366i
$767$	−45.0000	−	9.00000i	−1.62486	−	0.324971i
$768$	1.00000	+	1.00000i	0.0360844	+	0.0360844i
$769$	23.0000	+	23.0000i	0.829401	+	0.829401i	0.987434	−	0.158033i	$-0.0505151\pi$
$769$	23.0000	+	23.0000i	0.829401	+	0.829401i	−0.158033	+	0.987434i	$0.550515\pi$
$770$	−6.00000	+	2.00000i	−0.216225	+	0.0720750i
$771$		−	42.0000i		−	1.51259i
$772$		−	2.00000i		−	0.0719816i
$773$	24.0000			0.863220			0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000			0.863220			0.431610	+	0.902060i	$0.357946\pi$
$774$	1.00000	−	1.00000i	0.0359443	−	0.0359443i
$775$	7.00000	+	1.00000i	0.251447	+	0.0359211i
$776$	14.0000			0.502571
$777$	−16.0000	−	16.0000i	−0.573997	−	0.573997i
$778$			2.00000i			0.0717035i
$779$	42.0000			1.50481
$780$	7.00000	−	9.00000i	0.250640	−	0.322252i
$781$	−10.0000			−0.357828
$782$		−	2.00000i		−	0.0715199i
$783$	−32.0000	−	32.0000i	−1.14359	−	1.14359i
$784$	−3.00000			−0.107143
$785$	−45.0000	+	15.0000i	−1.60612	+	0.535373i
$786$	−12.0000	+	12.0000i	−0.428026	+	0.428026i
$787$	−30.0000			−1.06938			−0.534692	−	0.845047i	$-0.679572\pi$
$787$	−30.0000			−1.06938			−0.534692	+	0.845047i	$0.679572\pi$
$788$			6.00000i			0.213741i
$789$		−	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
$793$	4.00000	+	6.00000i	0.142044	+	0.213066i
$794$			8.00000i			0.283909i
$795$	−2.00000	+	4.00000i	−0.0709327	+	0.141865i
$796$	−24.0000			−0.850657
$797$	−5.00000	−	5.00000i	−0.177109	−	0.177109i	0.612985	−	0.790094i	$-0.289968\pi$
$797$	−5.00000	−	5.00000i	−0.177109	−	0.177109i	−0.790094	+	0.612985i	$0.789968\pi$
$798$	−12.0000			−0.424795
$799$	10.0000	+	10.0000i	0.353775	+	0.353775i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	−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
$808$	−12.0000			−0.422159
$809$		−	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	−0.613849	−	0.789423i	$-0.710380\pi$
$811$	5.00000	−	5.00000i	0.175574	−	0.175574i	0.789423	+	0.613849i	$0.210380\pi$
$812$		−	16.0000i		−	0.561490i
$813$			6.00000i			0.210429i
$814$	8.00000	−	8.00000i	0.280400	−	0.280400i
$815$	20.0000	−	40.0000i	0.700569	−	1.40114i
$816$		−	2.00000i		−	0.0700140i
$817$	−6.00000			−0.209913
$818$	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	$-0.773559\pi$
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	0.652884	+	0.757458i	$0.273559\pi$
$824$	−5.00000	−	5.00000i	−0.174183	−	0.174183i
$825$	8.00000	−	6.00000i	0.278524	−	0.208893i
$826$	18.0000	+	18.0000i	0.626300	+	0.626300i
$827$	26.0000			0.904109			0.452054	−	0.891990i	$-0.350691\pi$
$827$	26.0000			0.904109			0.452054	+	0.891990i	$0.350691\pi$
$828$	1.00000	+	1.00000i	0.0347524	+	0.0347524i
$829$	−18.0000			−0.625166			−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000			−0.625166			−0.312583	+	0.949890i	$0.601194\pi$
$830$	18.0000	−	36.0000i	0.624789	−	1.24958i
$831$			22.0000i			0.763172i
$832$	−2.00000	−	3.00000i	−0.0693375	−	0.104006i
$833$	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
$837$		−	8.00000i		−	0.276520i
$838$	−22.0000			−0.759977
$839$	7.00000	−	7.00000i	0.241667	−	0.241667i	−0.575873	−	0.817539i	$-0.695338\pi$
$839$	7.00000	−	7.00000i	0.241667	−	0.241667i	0.817539	+	0.575873i	$0.195338\pi$
$840$	−6.00000	+	2.00000i	−0.207020	+	0.0690066i
$841$	−35.0000			−1.20690
$842$	9.00000	+	9.00000i	0.310160	+	0.310160i
$843$			18.0000i			0.619953i
$844$	12.0000			0.413057
$845$	−22.0000	+	19.0000i	−0.756823	+	0.653620i
$846$	−10.0000			−0.343807
$847$			18.0000i			0.618487i
$848$	1.00000	+	1.00000i	0.0343401	+	0.0343401i
$849$	−30.0000			−1.02960
$850$	7.00000	+	1.00000i	0.240098	+	0.0342997i
$851$	8.00000	−	8.00000i	0.274236	−	0.274236i
$852$	−10.0000			−0.342594
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$		−	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	$-0.164398\pi$
$857$	11.0000	+	11.0000i	0.375753	+	0.375753i	−0.493814	+	0.869567i	$0.664398\pi$
$858$	4.00000	+	6.00000i	0.136558	+	0.204837i
$859$		−	34.0000i		−	1.16007i	−0.814593	−	0.580033i	$-0.803040\pi$
$859$		−	34.0000i		−	1.16007i	0.814593	−	0.580033i	$-0.196960\pi$
$860$	−3.00000	+	1.00000i	−0.102299	+	0.0340997i
$861$	28.0000			0.954237
$862$	−15.0000	−	15.0000i	−0.510902	−	0.510902i
$863$	34.0000			1.15737			0.578687	−	0.815550i	$-0.303565\pi$
$863$	34.0000			1.15737			0.578687	+	0.815550i	$0.303565\pi$
$864$	4.00000	+	4.00000i	0.136083	+	0.136083i
$865$	−27.0000	+	9.00000i	−0.918028	+	0.306009i
$866$	−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
$873$	14.0000			0.473828
$874$		−	6.00000i		−	0.202953i
$875$	−4.00000	−	22.0000i	−0.135225	−	0.743736i
$876$	6.00000	−	6.00000i	0.202721	−	0.202721i
$877$		−	6.00000i		−	0.202606i	−0.994856	−	0.101303i	$-0.967699\pi$
$877$		−	6.00000i		−	0.202606i	0.994856	−	0.101303i	$-0.0323011\pi$
$878$			32.0000i			1.07995i
$879$	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	$-0.109381\pi$
$882$	−3.00000			−0.101015
$883$	25.0000	−	25.0000i	0.841317	−	0.841317i	−0.147713	−	0.989030i	$-0.547191\pi$
$883$	25.0000	−	25.0000i	0.841317	−	0.841317i	0.989030	+	0.147713i	$0.0471913\pi$
$884$	−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
$890$	11.0000	+	33.0000i	0.368721	+	1.10616i
$891$	−5.00000	−	5.00000i	−0.167506	−	0.167506i
$892$	−18.0000			−0.602685
$893$	30.0000	+	30.0000i	1.00391	+	1.00391i
$894$	2.00000			0.0668900
$895$	40.0000	+	20.0000i	1.33705	+	0.668526i
$896$			2.00000i			0.0668153i
$897$	4.00000	+	6.00000i	0.133556	+	0.200334i
$898$	−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
$902$			14.0000i			0.466149i
$903$	−4.00000			−0.133112
$904$	−3.00000	+	3.00000i	−0.0997785	+	0.0997785i
$905$	−16.0000	+	32.0000i	−0.531858	+	1.06372i
$906$	−6.00000			−0.199337
$907$	7.00000	+	7.00000i	0.232431	+	0.232431i	0.813707	−	0.581276i	$-0.197446\pi$
$907$	7.00000	+	7.00000i	0.232431	+	0.232431i	−0.581276	+	0.813707i	$0.697446\pi$
$908$			12.0000i			0.398234i
$909$	−12.0000			−0.398015
$910$	16.0000	−	2.00000i	0.530395	−	0.0662994i
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		−	6.00000i		−	0.198680i
$913$	18.0000	+	18.0000i	0.595713	+	0.595713i
$914$	2.00000			0.0661541
$915$	2.00000	+	6.00000i	0.0661180	+	0.198354i
$916$	−15.0000	+	15.0000i	−0.495614	+	0.495614i
$917$	−24.0000			−0.792550
$918$		−	8.00000i		−	0.264039i
$919$		−	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
$923$	25.0000	+	5.00000i	0.822885	+	0.164577i
$924$		−	4.00000i		−	0.131590i
$925$	24.0000	+	32.0000i	0.789115	+	1.05215i
$926$	16.0000			0.525793
$927$	−5.00000	−	5.00000i	−0.164222	−	0.164222i
$928$	8.00000			0.262613
$929$	−13.0000	−	13.0000i	−0.426516	−	0.426516i	0.460924	−	0.887440i	$-0.347518\pi$
$929$	−13.0000	−	13.0000i	−0.426516	−	0.426516i	−0.887440	+	0.460924i	$0.847518\pi$
$930$	−2.00000	+	4.00000i	−0.0655826	+	0.131165i
$931$	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	$0.183337\pi$
$938$	24.0000			0.783628
$939$			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	$0.121829\pi$
$942$		−	30.0000i		−	0.977453i
$943$			14.0000i			0.455903i
$944$	−9.00000	+	9.00000i	−0.292925	+	0.292925i
$945$	−24.0000	+	8.00000i	−0.780720	+	0.260240i
$946$		−	2.00000i		−	0.0650256i
$947$	10.0000			0.324956			0.162478	−	0.986712i	$-0.448051\pi$
$947$	10.0000			0.324956			0.162478	+	0.986712i	$0.448051\pi$
$948$	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	$-0.786535\pi$
$953$	−5.00000	+	5.00000i	−0.161966	+	0.161966i	0.621471	+	0.783437i	$0.286535\pi$
$954$	1.00000	+	1.00000i	0.0323762	+	0.0323762i
$955$	16.0000	+	8.00000i	0.517748	+	0.258874i
$956$	−1.00000	−	1.00000i	−0.0323423	−	0.0323423i
$957$	−16.0000			−0.517207
$958$	19.0000	+	19.0000i	0.613862	+	0.613862i
$959$		0			0
$960$	−1.00000	−	3.00000i	−0.0322749	−	0.0968246i
$961$			29.0000i			0.935484i
$962$	−24.0000	+	16.0000i	−0.773791	+	0.515861i
$963$	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
$967$			24.0000i			0.771788i	0.922543	+	0.385894i	$0.126107\pi$
$967$			24.0000i			0.771788i	−0.922543	+	0.385894i	$0.873893\pi$
$968$	−9.00000			−0.289271
$969$	−6.00000	+	6.00000i	−0.192748	+	0.192748i
$970$	−28.0000	−	14.0000i	−0.899026	−	0.449513i
$971$	−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
$973$			4.00000i			0.128234i
$974$	−8.00000			−0.256337
$975$	−23.0000	+	11.0000i	−0.736590	+	0.352282i
$976$	2.00000			0.0640184
$977$			2.00000i			0.0639857i	0.999488	+	0.0319928i	$0.0101854\pi$
$977$			2.00000i			0.0639857i	−0.999488	+	0.0319928i	$0.989815\pi$
$978$	20.0000	+	20.0000i	0.639529	+	0.639529i
$979$	−22.0000			−0.703123
$980$	6.00000	+	3.00000i	0.191663	+	0.0958315i
$981$	−5.00000	+	5.00000i	−0.159638	+	0.159638i
$982$	38.0000			1.21263
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$			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
$988$	−3.00000	+	15.0000i	−0.0954427	+	0.477214i
$989$		−	2.00000i		−	0.0635963i
$990$	−1.00000	−	3.00000i	−0.0317821	−	0.0953463i
$991$	−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
$993$	42.0000			1.33283
$994$	−10.0000	−	10.0000i	−0.317181	−	0.317181i
$995$	48.0000	+	24.0000i	1.52170	+	0.760851i
$996$	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.j.c.83.1	yes	2
3.2	odd	2		1170.2.w.a.343.1		2
4.3	odd	2		1040.2.cd.c.993.1		2
5.2	odd	4		130.2.g.b.57.1	✓	2
5.3	odd	4		650.2.g.c.57.1		2
5.4	even	2		650.2.j.a.343.1		2
13.8	odd	4		130.2.g.b.73.1	yes	2
15.2	even	4		1170.2.m.b.577.1		2
20.7	even	4		1040.2.bg.b.577.1		2
39.8	even	4		1170.2.m.b.73.1		2
52.47	even	4		1040.2.bg.b.593.1		2
65.8	even	4		650.2.j.a.307.1		2
65.34	odd	4		650.2.g.c.593.1		2
65.47	even	4	inner	130.2.j.c.47.1	yes	2
195.47	odd	4		1170.2.w.a.307.1		2
260.47	odd	4		1040.2.cd.c.177.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.b.57.1	✓	2	5.2	odd	4
130.2.g.b.73.1	yes	2	13.8	odd	4
130.2.j.c.47.1	yes	2	65.47	even	4	inner
130.2.j.c.83.1	yes	2	1.1	even	1	trivial
650.2.g.c.57.1		2	5.3	odd	4
650.2.g.c.593.1		2	65.34	odd	4
650.2.j.a.307.1		2	65.8	even	4
650.2.j.a.343.1		2	5.4	even	2
1040.2.bg.b.577.1		2	20.7	even	4
1040.2.bg.b.593.1		2	52.47	even	4
1040.2.cd.c.177.1		2	260.47	odd	4
1040.2.cd.c.993.1		2	4.3	odd	2
1170.2.m.b.73.1		2	39.8	even	4
1170.2.m.b.577.1		2	15.2	even	4
1170.2.w.a.307.1		2	195.47	odd	4
1170.2.w.a.343.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more