LMFDB - Embedded newform 130.2.g.c.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.c.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} +(5.00000 - 5.00000i) 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} +(-5.00000 - 5.00000i) 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} +4.00000i q^{29} +(-3.00000 - 1.00000i) q^{30} +(1.00000 - 1.00000i) q^{31} +1.00000 q^{32} -2.00000 q^{33} +(5.00000 - 5.00000i) q^{34} +(4.00000 - 2.00000i) q^{35} +1.00000i q^{36} +8.00000i q^{37} +(-3.00000 - 3.00000i) q^{38} +(5.00000 - 1.00000i) q^{39} +(1.00000 + 2.00000i) q^{40} +(1.00000 - 1.00000i) q^{41} +(2.00000 + 2.00000i) q^{42} +(5.00000 + 5.00000i) q^{43} +(1.00000 + 1.00000i) q^{44} +(-2.00000 + 1.00000i) q^{45} +(-5.00000 - 5.00000i) q^{46} -2.00000i q^{47} +(-1.00000 + 1.00000i) q^{48} +3.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} +10.0000i 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} +4.00000i q^{58} +(3.00000 - 3.00000i) 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} +(1.00000 - 8.00000i) q^{65} -2.00000 q^{66} -12.0000 q^{67} +(5.00000 - 5.00000i) q^{68} +10.0000 q^{69} +(4.00000 - 2.00000i) q^{70} +(1.00000 - 1.00000i) 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} +(5.00000 - 1.00000i) q^{78} +14.0000i q^{79} +(1.00000 + 2.00000i) q^{80} +5.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +6.00000i q^{83} +(2.00000 + 2.00000i) q^{84} +(15.0000 + 5.00000i) q^{85} +(5.00000 + 5.00000i) q^{86} +(-4.00000 - 4.00000i) q^{87} +(1.00000 + 1.00000i) q^{88} +(-7.00000 + 7.00000i) q^{89} +(-2.00000 + 1.00000i) q^{90} +(-4.00000 + 6.00000i) q^{91} +(-5.00000 - 5.00000i) q^{92} +2.00000i q^{93} -2.00000i q^{94} +(3.00000 - 9.00000i) q^{95} +(-1.00000 + 1.00000i) q^{96} -2.00000 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} + 10 q^{17} - 6 q^{19} + 2 q^{20} + 4 q^{21} + 2 q^{22} - 10 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 + 10 * q^17 - 6 * q^19 + 2 * q^20 + 4 * q^21 + 2 * q^22 - 10 * 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 + 10 * q^34 + 8 * q^35 - 6 * q^38 + 10 * q^39 + 2 * q^40 + 2 * q^41 + 4 * q^42 + 10 * q^43 + 2 * q^44 - 4 * q^45 - 10 * 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 + 6 * q^59 - 6 * q^60 + 4 * q^61 + 2 * q^62 + 4 * q^63 + 2 * q^64 + 2 * q^65 - 4 * q^66 - 24 * q^67 + 10 * q^68 + 20 * q^69 + 8 * q^70 + 2 * q^71 - 12 * q^73 - 2 * q^75 - 6 * q^76 + 4 * q^77 + 10 * q^78 + 2 * q^80 + 10 * q^81 + 2 * q^82 + 4 * q^84 + 30 * q^85 + 10 * q^86 - 8 * q^87 + 2 * q^88 - 14 * q^89 - 4 * q^90 - 8 * q^91 - 10 * q^92 + 6 * q^95 - 2 * q^96 - 4 * 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	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	0.356822	+	0.934172i	$0.383860\pi$
$4$	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	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$	−1.00000	+	1.00000i	−0.288675	+	0.288675i
$13$	−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
$17$	5.00000	−	5.00000i	1.21268	−	1.21268i	0.242536	−	0.970143i	$-0.422021\pi$
$17$	5.00000	−	5.00000i	1.21268	−	1.21268i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$			1.00000i			0.235702i
$19$	−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	$0.911786\pi$
$20$	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
$23$	−5.00000	−	5.00000i	−1.04257	−	1.04257i	−0.999053	−	0.0435195i	$-0.986143\pi$
$23$	−5.00000	−	5.00000i	−1.04257	−	1.04257i	−0.0435195	−	0.999053i	$-0.513857\pi$
$24$	−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
$29$			4.00000i			0.742781i	0.928477	+	0.371391i	$0.121119\pi$
$29$			4.00000i			0.742781i	−0.928477	+	0.371391i	$0.878881\pi$
$30$	−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
$34$	5.00000	−	5.00000i	0.857493	−	0.857493i
$35$	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
$39$	5.00000	−	1.00000i	0.800641	−	0.160128i
$40$	1.00000	+	2.00000i	0.158114	+	0.316228i
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	0.780869	+	0.624695i	$0.214777\pi$
$42$	2.00000	+	2.00000i	0.308607	+	0.308607i
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	0.976772	−	0.214280i	$-0.0687403\pi$
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	−0.214280	+	0.976772i	$0.568740\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$	−2.00000	+	1.00000i	−0.298142	+	0.149071i
$46$	−5.00000	−	5.00000i	−0.737210	−	0.737210i
$47$		−	2.00000i		−	0.291730i	−0.989305	−	0.145865i	$-0.953403\pi$
$47$		−	2.00000i		−	0.291730i	0.989305	−	0.145865i	$-0.0465965\pi$
$48$	−1.00000	+	1.00000i	−0.144338	+	0.144338i
$49$	3.00000			0.428571
$50$	−3.00000	+	4.00000i	−0.424264	+	0.565685i
$51$			10.0000i			1.40028i
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	−0.772444	−	0.635083i	$-0.780966\pi$
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	0.635083	+	0.772444i	$0.280966\pi$
$54$	−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
$58$			4.00000i			0.525226i
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	−0.484323	−	0.874889i	$-0.660934\pi$
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	0.874889	+	0.484323i	$0.160934\pi$
$60$	−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
$65$	1.00000	−	8.00000i	0.124035	−	0.992278i
$66$	−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	$0.761888\pi$
$68$	5.00000	−	5.00000i	0.606339	−	0.606339i
$69$	10.0000			1.20386
$70$	4.00000	−	2.00000i	0.478091	−	0.239046i
$71$	1.00000	−	1.00000i	0.118678	−	0.118678i	−0.645273	−	0.763952i	$-0.723257\pi$
$71$	1.00000	−	1.00000i	0.118678	−	0.118678i	0.763952	+	0.645273i	$0.223257\pi$
$72$			1.00000i			0.117851i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$			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
$79$			14.0000i			1.57512i	0.616236	+	0.787562i	$0.288657\pi$
$79$			14.0000i			1.57512i	−0.616236	+	0.787562i	$0.711343\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	5.00000			0.555556
$82$	1.00000	−	1.00000i	0.110432	−	0.110432i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	2.00000	+	2.00000i	0.218218	+	0.218218i
$85$	15.0000	+	5.00000i	1.62698	+	0.542326i
$86$	5.00000	+	5.00000i	0.539164	+	0.539164i
$87$	−4.00000	−	4.00000i	−0.428845	−	0.428845i
$88$	1.00000	+	1.00000i	0.106600	+	0.106600i
$89$	−7.00000	+	7.00000i	−0.741999	+	0.741999i	−0.972962	−	0.230964i	$-0.925812\pi$
$89$	−7.00000	+	7.00000i	−0.741999	+	0.741999i	0.230964	+	0.972962i	$0.425812\pi$
$90$	−2.00000	+	1.00000i	−0.210819	+	0.105409i
$91$	−4.00000	+	6.00000i	−0.419314	+	0.628971i
$92$	−5.00000	−	5.00000i	−0.521286	−	0.521286i
$93$			2.00000i			0.207390i
$94$		−	2.00000i		−	0.206284i
$95$	3.00000	−	9.00000i	0.307794	−	0.923381i
$96$	−1.00000	+	1.00000i	−0.102062	+	0.102062i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	3.00000			0.303046
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$			10.0000i			0.990148i
$103$	−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
$107$	13.0000	+	13.0000i	1.25676	+	1.25676i	0.952632	+	0.304125i	$0.0983642\pi$
$107$	13.0000	+	13.0000i	1.25676	+	1.25676i	0.304125	+	0.952632i	$0.401636\pi$
$108$	−4.00000	−	4.00000i	−0.384900	−	0.384900i
$109$	−13.0000	−	13.0000i	−1.24517	−	1.24517i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$	−13.0000	−	13.0000i	−1.24517	−	1.24517i	−0.287348	−	0.957826i	$-0.592774\pi$
$110$	−1.00000	+	3.00000i	−0.0953463	+	0.286039i
$111$	−8.00000	−	8.00000i	−0.759326	−	0.759326i
$112$		−	2.00000i		−	0.188982i
$113$	9.00000	−	9.00000i	0.846649	−	0.846649i	−0.143065	−	0.989713i	$-0.545696\pi$
$113$	9.00000	−	9.00000i	0.846649	−	0.846649i	0.989713	+	0.143065i	$0.0456957\pi$
$114$	6.00000			0.561951
$115$	5.00000	−	15.0000i	0.466252	−	1.39876i
$116$			4.00000i			0.371391i
$117$	2.00000	−	3.00000i	0.184900	−	0.277350i
$118$	3.00000	−	3.00000i	0.276172	−	0.276172i
$119$	−10.0000	−	10.0000i	−0.916698	−	0.916698i
$120$	−3.00000	−	1.00000i	−0.273861	−	0.0912871i
$121$		−	9.00000i		−	0.818182i
$122$	2.00000			0.181071
$123$			2.00000i			0.180334i
$124$	1.00000	−	1.00000i	0.0898027	−	0.0898027i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	2.00000			0.178174
$127$	−15.0000	+	15.0000i	−1.33103	+	1.33103i	−0.426589	+	0.904445i	$0.640285\pi$
$127$	−15.0000	+	15.0000i	−1.33103	+	1.33103i	−0.904445	+	0.426589i	$0.859715\pi$
$128$	1.00000			0.0883883
$129$	−10.0000			−0.880451
$130$	1.00000	−	8.00000i	0.0877058	−	0.701646i
$131$	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
$136$	5.00000	−	5.00000i	0.428746	−	0.428746i
$137$		−	12.0000i		−	1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$		−	12.0000i		−	1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$	10.0000			0.851257
$139$			14.0000i			1.18746i	0.804663	+	0.593732i	$0.202346\pi$
$139$			14.0000i			1.18746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$	4.00000	−	2.00000i	0.338062	−	0.169031i
$141$	2.00000	+	2.00000i	0.168430	+	0.168430i
$142$	1.00000	−	1.00000i	0.0839181	−	0.0839181i
$143$	−1.00000	−	5.00000i	−0.0836242	−	0.418121i
$144$			1.00000i			0.0833333i
$145$	−8.00000	+	4.00000i	−0.664364	+	0.332182i
$146$	−6.00000			−0.496564
$147$	−3.00000	+	3.00000i	−0.247436	+	0.247436i
$148$			8.00000i			0.657596i
$149$	−13.0000	−	13.0000i	−1.06500	−	1.06500i	−0.997735	−	0.0672664i	$-0.978572\pi$
$149$	−13.0000	−	13.0000i	−1.06500	−	1.06500i	−0.0672664	−	0.997735i	$-0.521428\pi$
$150$	−1.00000	−	7.00000i	−0.0816497	−	0.571548i
$151$	−9.00000	−	9.00000i	−0.732410	−	0.732410i	0.238687	−	0.971097i	$-0.423283\pi$
$151$	−9.00000	−	9.00000i	−0.732410	−	0.732410i	−0.971097	+	0.238687i	$0.923283\pi$
$152$	−3.00000	−	3.00000i	−0.243332	−	0.243332i
$153$	5.00000	+	5.00000i	0.404226	+	0.404226i
$154$	2.00000	−	2.00000i	0.161165	−	0.161165i
$155$	3.00000	+	1.00000i	0.240966	+	0.0803219i
$156$	5.00000	−	1.00000i	0.400320	−	0.0800641i
$157$	3.00000	+	3.00000i	0.239426	+	0.239426i	0.816612	−	0.577186i	$-0.195849\pi$
$157$	3.00000	+	3.00000i	0.239426	+	0.239426i	−0.577186	+	0.816612i	$0.695849\pi$
$158$			14.0000i			1.11378i
$159$		−	2.00000i		−	0.158610i
$160$	1.00000	+	2.00000i	0.0790569	+	0.158114i
$161$	−10.0000	+	10.0000i	−0.788110	+	0.788110i
$162$	5.00000			0.392837
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	1.00000	−	1.00000i	0.0780869	−	0.0780869i
$165$	−2.00000	−	4.00000i	−0.155700	−	0.311400i
$166$			6.00000i			0.465690i
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$	2.00000	+	2.00000i	0.154303	+	0.154303i
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$	15.0000	+	5.00000i	1.15045	+	0.383482i
$171$	3.00000	−	3.00000i	0.229416	−	0.229416i
$172$	5.00000	+	5.00000i	0.381246	+	0.381246i
$173$	15.0000	+	15.0000i	1.14043	+	1.14043i	0.988372	+	0.152057i	$0.0485898\pi$
$173$	15.0000	+	15.0000i	1.14043	+	1.14043i	0.152057	+	0.988372i	$0.451410\pi$
$174$	−4.00000	−	4.00000i	−0.303239	−	0.303239i
$175$	8.00000	+	6.00000i	0.604743	+	0.453557i
$176$	1.00000	+	1.00000i	0.0753778	+	0.0753778i
$177$			6.00000i			0.450988i
$178$	−7.00000	+	7.00000i	−0.524672	+	0.524672i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$	−2.00000	+	1.00000i	−0.149071	+	0.0745356i
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$	−4.00000	+	6.00000i	−0.296500	+	0.444750i
$183$	−2.00000	+	2.00000i	−0.147844	+	0.147844i
$184$	−5.00000	−	5.00000i	−0.368605	−	0.368605i
$185$	−16.0000	+	8.00000i	−1.17634	+	0.588172i
$186$			2.00000i			0.146647i
$187$	10.0000			0.731272
$188$		−	2.00000i		−	0.145865i
$189$	−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	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	−1.00000	+	1.00000i	−0.0721688	+	0.0721688i
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	−2.00000			−0.143592
$195$	7.00000	+	9.00000i	0.501280	+	0.644503i
$196$	3.00000			0.214286
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−1.00000	+	1.00000i	−0.0710669	+	0.0710669i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−3.00000	+	4.00000i	−0.212132	+	0.282843i
$201$	12.0000	−	12.0000i	0.846415	−	0.846415i
$202$		0			0
$203$	8.00000			0.561490
$204$			10.0000i			0.700140i
$205$	3.00000	+	1.00000i	0.209529	+	0.0698430i
$206$	−5.00000	−	5.00000i	−0.348367	−	0.348367i
$207$	5.00000	−	5.00000i	0.347524	−	0.347524i
$208$	−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	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−1.00000	+	1.00000i	−0.0686803	+	0.0686803i
$213$			2.00000i			0.137038i
$214$	13.0000	+	13.0000i	0.888662	+	0.888662i
$215$	−5.00000	+	15.0000i	−0.340997	+	1.02299i
$216$	−4.00000	−	4.00000i	−0.272166	−	0.272166i
$217$	−2.00000	−	2.00000i	−0.135769	−	0.135769i
$218$	−13.0000	−	13.0000i	−0.880471	−	0.880471i
$219$	6.00000	−	6.00000i	0.405442	−	0.405442i
$220$	−1.00000	+	3.00000i	−0.0674200	+	0.202260i
$221$	−25.0000	+	5.00000i	−1.68168	+	0.336336i
$222$	−8.00000	−	8.00000i	−0.536925	−	0.536925i
$223$			6.00000i			0.401790i	0.979613	+	0.200895i	$0.0643850\pi$
$223$			6.00000i			0.401790i	−0.979613	+	0.200895i	$0.935615\pi$
$224$		−	2.00000i		−	0.133631i
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$	9.00000	−	9.00000i	0.598671	−	0.598671i
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$	6.00000			0.397360
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	−0.601002	−	0.799248i	$-0.705232\pi$
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	0.799248	+	0.601002i	$0.205232\pi$
$230$	5.00000	−	15.0000i	0.329690	−	0.989071i
$231$			4.00000i			0.263181i
$232$			4.00000i			0.262613i
$233$	5.00000	+	5.00000i	0.327561	+	0.327561i	0.851658	−	0.524097i	$-0.175597\pi$
$233$	5.00000	+	5.00000i	0.327561	+	0.327561i	−0.524097	+	0.851658i	$0.675597\pi$
$234$	2.00000	−	3.00000i	0.130744	−	0.196116i
$235$	4.00000	−	2.00000i	0.260931	−	0.130466i
$236$	3.00000	−	3.00000i	0.195283	−	0.195283i
$237$	−14.0000	−	14.0000i	−0.909398	−	0.909398i
$238$	−10.0000	−	10.0000i	−0.648204	−	0.648204i
$239$	7.00000	+	7.00000i	0.452792	+	0.452792i	0.896280	−	0.443488i	$-0.146259\pi$
$239$	7.00000	+	7.00000i	0.452792	+	0.452792i	−0.443488	+	0.896280i	$0.646259\pi$
$240$	−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
$246$			2.00000i			0.127515i
$247$	3.00000	+	15.0000i	0.190885	+	0.954427i
$248$	1.00000	−	1.00000i	0.0635001	−	0.0635001i
$249$	−6.00000	−	6.00000i	−0.380235	−	0.380235i
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$			30.0000i			1.89358i	0.321847	+	0.946792i	$0.395696\pi$
$251$			30.0000i			1.89358i	−0.321847	+	0.946792i	$0.604304\pi$
$252$	2.00000			0.125988
$253$		−	10.0000i		−	0.628695i
$254$	−15.0000	+	15.0000i	−0.941184	+	0.941184i
$255$	−20.0000	+	10.0000i	−1.25245	+	0.626224i
$256$	1.00000			0.0625000
$257$	−15.0000	+	15.0000i	−0.935674	+	0.935674i	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$	−15.0000	+	15.0000i	−0.935674	+	0.935674i	0.0623783	+	0.998053i	$0.480131\pi$
$258$	−10.0000			−0.622573
$259$	16.0000			0.994192
$260$	1.00000	−	8.00000i	0.0620174	−	0.496139i
$261$	−4.00000			−0.247594
$262$	12.0000			0.741362
$263$	9.00000	−	9.00000i	0.554964	−	0.554964i	−0.372906	−	0.927869i	$-0.621638\pi$
$263$	9.00000	−	9.00000i	0.554964	−	0.554964i	0.927869	+	0.372906i	$0.121638\pi$
$264$	−2.00000			−0.123091
$265$	−3.00000	−	1.00000i	−0.184289	−	0.0614295i
$266$	−6.00000	+	6.00000i	−0.367884	+	0.367884i
$267$		−	14.0000i		−	0.856786i
$268$	−12.0000			−0.733017
$269$		−	16.0000i		−	0.975537i	−0.872973	−	0.487769i	$-0.837811\pi$
$269$		−	16.0000i		−	0.975537i	0.872973	−	0.487769i	$-0.162189\pi$
$270$	4.00000	−	12.0000i	0.243432	−	0.730297i
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	0.378777	−	0.925488i	$-0.376345\pi$
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	−0.925488	+	0.378777i	$0.876345\pi$
$272$	5.00000	−	5.00000i	0.303170	−	0.303170i
$273$	−2.00000	−	10.0000i	−0.121046	−	0.605228i
$274$		−	12.0000i		−	0.724947i
$275$	−7.00000	+	1.00000i	−0.422116	+	0.0603023i
$276$	10.0000			0.601929
$277$	−5.00000	+	5.00000i	−0.300421	+	0.300421i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−5.00000	+	5.00000i	−0.300421	+	0.300421i	0.540758	+	0.841178i	$0.318138\pi$
$278$			14.0000i			0.839664i
$279$	1.00000	+	1.00000i	0.0598684	+	0.0598684i
$280$	4.00000	−	2.00000i	0.239046	−	0.119523i
$281$	21.0000	+	21.0000i	1.25275	+	1.25275i	0.954480	+	0.298275i	$0.0964112\pi$
$281$	21.0000	+	21.0000i	1.25275	+	1.25275i	0.298275	+	0.954480i	$0.403589\pi$
$282$	2.00000	+	2.00000i	0.119098	+	0.119098i
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	0.103022	−	0.994679i	$-0.467149\pi$
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	−0.994679	+	0.103022i	$0.967149\pi$
$284$	1.00000	−	1.00000i	0.0593391	−	0.0593391i
$285$	6.00000	+	12.0000i	0.355409	+	0.710819i
$286$	−1.00000	−	5.00000i	−0.0591312	−	0.295656i
$287$	−2.00000	−	2.00000i	−0.118056	−	0.118056i
$288$			1.00000i			0.0589256i
$289$		−	33.0000i		−	1.94118i
$290$	−8.00000	+	4.00000i	−0.469776	+	0.234888i
$291$	2.00000	−	2.00000i	0.117242	−	0.117242i
$292$	−6.00000			−0.351123
$293$	−26.0000			−1.51894			−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000			−1.51894			−0.759468	+	0.650545i	$0.774541\pi$
$294$	−3.00000	+	3.00000i	−0.174964	+	0.174964i
$295$	9.00000	+	3.00000i	0.524000	+	0.174667i
$296$			8.00000i			0.464991i
$297$		−	8.00000i		−	0.464207i
$298$	−13.0000	−	13.0000i	−0.753070	−	0.753070i
$299$	5.00000	+	25.0000i	0.289157	+	1.44579i
$300$	−1.00000	−	7.00000i	−0.0577350	−	0.404145i
$301$	10.0000	−	10.0000i	0.576390	−	0.576390i
$302$	−9.00000	−	9.00000i	−0.517892	−	0.517892i
$303$		0			0
$304$	−3.00000	−	3.00000i	−0.172062	−	0.172062i
$305$	2.00000	+	4.00000i	0.114520	+	0.229039i
$306$	5.00000	+	5.00000i	0.285831	+	0.285831i
$307$		−	2.00000i		−	0.114146i	−0.998370	−	0.0570730i	$-0.981823\pi$
$307$		−	2.00000i		−	0.114146i	0.998370	−	0.0570730i	$-0.0181768\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$	10.0000			0.568880
$310$	3.00000	+	1.00000i	0.170389	+	0.0567962i
$311$		−	10.0000i		−	0.567048i	−0.958965	−	0.283524i	$-0.908496\pi$
$311$		−	10.0000i		−	0.567048i	0.958965	−	0.283524i	$-0.0915036\pi$
$312$	5.00000	−	1.00000i	0.283069	−	0.0566139i
$313$	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	$0.132875\pi$
$314$	3.00000	+	3.00000i	0.169300	+	0.169300i
$315$	2.00000	+	4.00000i	0.112687	+	0.225374i
$316$			14.0000i			0.787562i
$317$	−2.00000			−0.112331			−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000			−0.112331			−0.0561656	+	0.998421i	$0.517887\pi$
$318$		−	2.00000i		−	0.112154i
$319$	−4.00000	+	4.00000i	−0.223957	+	0.223957i
$320$	1.00000	+	2.00000i	0.0559017	+	0.111803i
$321$	−26.0000			−1.45118
$322$	−10.0000	+	10.0000i	−0.557278	+	0.557278i
$323$	−30.0000			−1.66924
$324$	5.00000			0.277778
$325$	17.0000	−	6.00000i	0.942990	−	0.332820i
$326$	4.00000			0.221540
$327$	26.0000			1.43780
$328$	1.00000	−	1.00000i	0.0552158	−	0.0552158i
$329$	−4.00000			−0.220527
$330$	−2.00000	−	4.00000i	−0.110096	−	0.220193i
$331$	−9.00000	+	9.00000i	−0.494685	+	0.494685i	−0.909779	−	0.415094i	$-0.863749\pi$
$331$	−9.00000	+	9.00000i	−0.494685	+	0.494685i	0.415094	+	0.909779i	$0.363749\pi$
$332$			6.00000i			0.329293i
$333$	−8.00000			−0.438397
$334$		−	2.00000i		−	0.109435i
$335$	−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
$339$			18.0000i			0.977626i
$340$	15.0000	+	5.00000i	0.813489	+	0.271163i
$341$	2.00000			0.108306
$342$	3.00000	−	3.00000i	0.162221	−	0.162221i
$343$		−	20.0000i		−	1.07990i
$344$	5.00000	+	5.00000i	0.269582	+	0.269582i
$345$	10.0000	+	20.0000i	0.538382	+	1.07676i
$346$	15.0000	+	15.0000i	0.806405	+	0.806405i
$347$	−7.00000	−	7.00000i	−0.375780	−	0.375780i	0.493797	−	0.869577i	$-0.335608\pi$
$347$	−7.00000	−	7.00000i	−0.375780	−	0.375780i	−0.869577	+	0.493797i	$0.835608\pi$
$348$	−4.00000	−	4.00000i	−0.214423	−	0.214423i
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$	8.00000	+	6.00000i	0.427618	+	0.320713i
$351$	4.00000	+	20.0000i	0.213504	+	1.06752i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$			16.0000i			0.851594i	0.904819	+	0.425797i	$0.140006\pi$
$353$			16.0000i			0.851594i	−0.904819	+	0.425797i	$0.859994\pi$
$354$			6.00000i			0.318896i
$355$	3.00000	+	1.00000i	0.159223	+	0.0530745i
$356$	−7.00000	+	7.00000i	−0.370999	+	0.370999i
$357$	20.0000			1.05851
$358$	20.0000			1.05703
$359$	13.0000	−	13.0000i	0.686114	−	0.686114i	−0.275257	−	0.961371i	$-0.588763\pi$
$359$	13.0000	−	13.0000i	0.686114	−	0.686114i	0.961371	+	0.275257i	$0.0887629\pi$
$360$	−2.00000	+	1.00000i	−0.105409	+	0.0527046i
$361$		−	1.00000i		−	0.0526316i
$362$		−	20.0000i		−	1.05118i
$363$	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
$367$	3.00000	+	3.00000i	0.156599	+	0.156599i	0.781058	−	0.624459i	$-0.214680\pi$
$367$	3.00000	+	3.00000i	0.156599	+	0.156599i	−0.624459	+	0.781058i	$0.714680\pi$
$368$	−5.00000	−	5.00000i	−0.260643	−	0.260643i
$369$	1.00000	+	1.00000i	0.0520579	+	0.0520579i
$370$	−16.0000	+	8.00000i	−0.831800	+	0.415900i
$371$	2.00000	+	2.00000i	0.103835	+	0.103835i
$372$			2.00000i			0.103695i
$373$	−1.00000	+	1.00000i	−0.0517780	+	0.0517780i	−0.732522	−	0.680744i	$-0.761657\pi$
$373$	−1.00000	+	1.00000i	−0.0517780	+	0.0517780i	0.680744	+	0.732522i	$0.261657\pi$
$374$	10.0000			0.517088
$375$	13.0000	−	9.00000i	0.671317	−	0.464758i
$376$		−	2.00000i		−	0.103142i
$377$	8.00000	−	12.0000i	0.412021	−	0.618031i
$378$	−8.00000	+	8.00000i	−0.411476	+	0.411476i
$379$	17.0000	+	17.0000i	0.873231	+	0.873231i	0.992823	−	0.119592i	$-0.0381586\pi$
$379$	17.0000	+	17.0000i	0.873231	+	0.873231i	−0.119592	+	0.992823i	$0.538159\pi$
$380$	3.00000	−	9.00000i	0.153897	−	0.461690i
$381$		−	30.0000i		−	1.53695i
$382$	−8.00000			−0.409316
$383$			6.00000i			0.306586i	0.988181	+	0.153293i	$0.0489878\pi$
$383$			6.00000i			0.306586i	−0.988181	+	0.153293i	$0.951012\pi$
$384$	−1.00000	+	1.00000i	−0.0510310	+	0.0510310i
$385$	6.00000	+	2.00000i	0.305788	+	0.101929i
$386$	14.0000			0.712581
$387$	−5.00000	+	5.00000i	−0.254164	+	0.254164i
$388$	−2.00000			−0.101535
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$	7.00000	+	9.00000i	0.354459	+	0.455733i
$391$	−50.0000			−2.52861
$392$	3.00000			0.151523
$393$	−12.0000	+	12.0000i	−0.605320	+	0.605320i
$394$	18.0000			0.906827
$395$	−28.0000	+	14.0000i	−1.40883	+	0.704416i
$396$	−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	$0.935661\pi$
$398$		0			0
$399$		−	12.0000i		−	0.600751i
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	1.00000	+	1.00000i	0.0499376	+	0.0499376i	0.731635	−	0.681697i	$-0.238758\pi$
$401$	1.00000	+	1.00000i	0.0499376	+	0.0499376i	−0.681697	+	0.731635i	$0.738758\pi$
$402$	12.0000	−	12.0000i	0.598506	−	0.598506i
$403$	−5.00000	+	1.00000i	−0.249068	+	0.0498135i
$404$		0			0
$405$	5.00000	+	10.0000i	0.248452	+	0.496904i
$406$	8.00000			0.397033
$407$	−8.00000	+	8.00000i	−0.396545	+	0.396545i
$408$			10.0000i			0.495074i
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	0.629036	−	0.777376i	$-0.283450\pi$
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	−0.777376	+	0.629036i	$0.783450\pi$
$410$	3.00000	+	1.00000i	0.148159	+	0.0493865i
$411$	12.0000	+	12.0000i	0.591916	+	0.591916i
$412$	−5.00000	−	5.00000i	−0.246332	−	0.246332i
$413$	−6.00000	−	6.00000i	−0.295241	−	0.295241i
$414$	5.00000	−	5.00000i	0.245737	−	0.245737i
$415$	−12.0000	+	6.00000i	−0.589057	+	0.294528i
$416$	−3.00000	−	2.00000i	−0.147087	−	0.0980581i
$417$	−14.0000	−	14.0000i	−0.685583	−	0.685583i
$418$		−	6.00000i		−	0.293470i
$419$		−	26.0000i		−	1.27018i	−0.772437	−	0.635092i	$-0.780962\pi$
$419$		−	26.0000i		−	1.27018i	0.772437	−	0.635092i	$-0.219038\pi$
$420$	−2.00000	+	6.00000i	−0.0975900	+	0.292770i
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	−0.891552	−	0.452919i	$-0.850383\pi$
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	0.452919	+	0.891552i	$0.350383\pi$
$422$	12.0000			0.584151
$423$	2.00000			0.0972433
$424$	−1.00000	+	1.00000i	−0.0485643	+	0.0485643i
$425$	5.00000	+	35.0000i	0.242536	+	1.69775i
$426$			2.00000i			0.0969003i
$427$		−	4.00000i		−	0.193574i
$428$	13.0000	+	13.0000i	0.628379	+	0.628379i
$429$	6.00000	+	4.00000i	0.289683	+	0.193122i
$430$	−5.00000	+	15.0000i	−0.241121	+	0.723364i
$431$	21.0000	−	21.0000i	1.01153	−	1.01153i	0.0116017	−	0.999933i	$-0.496307\pi$
$431$	21.0000	−	21.0000i	1.01153	−	1.01153i	0.999933	−	0.0116017i	$-0.00369302\pi$
$432$	−4.00000	−	4.00000i	−0.192450	−	0.192450i
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	0.247925	−	0.968779i	$-0.420251\pi$
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	−0.968779	+	0.247925i	$0.920251\pi$
$434$	−2.00000	−	2.00000i	−0.0960031	−	0.0960031i
$435$	4.00000	−	12.0000i	0.191785	−	0.575356i
$436$	−13.0000	−	13.0000i	−0.622587	−	0.622587i
$437$			30.0000i			1.43509i
$438$	6.00000	−	6.00000i	0.286691	−	0.286691i
$439$	40.0000			1.90910			0.954548	−	0.298057i	$-0.0963387\pi$
$439$	40.0000			1.90910			0.954548	+	0.298057i	$0.0963387\pi$
$440$	−1.00000	+	3.00000i	−0.0476731	+	0.143019i
$441$			3.00000i			0.142857i
$442$	−25.0000	+	5.00000i	−1.18913	+	0.237826i
$443$	19.0000	−	19.0000i	0.902717	−	0.902717i	−0.0929532	−	0.995670i	$-0.529631\pi$
$443$	19.0000	−	19.0000i	0.902717	−	0.902717i	0.995670	+	0.0929532i	$0.0296307\pi$
$444$	−8.00000	−	8.00000i	−0.379663	−	0.379663i
$445$	−21.0000	−	7.00000i	−0.995495	−	0.331832i
$446$			6.00000i			0.284108i
$447$	26.0000			1.22976
$448$		−	2.00000i		−	0.0944911i
$449$	−7.00000	+	7.00000i	−0.330350	+	0.330350i	−0.852720	−	0.522369i	$-0.825048\pi$
$449$	−7.00000	+	7.00000i	−0.330350	+	0.330350i	0.522369	+	0.852720i	$0.325048\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$	2.00000			0.0941763
$452$	9.00000	−	9.00000i	0.423324	−	0.423324i
$453$	18.0000			0.845714
$454$	−12.0000			−0.563188
$455$	−16.0000	−	2.00000i	−0.750092	−	0.0937614i
$456$	6.00000			0.280976
$457$	38.0000			1.77757			0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000			1.77757			0.888783	+	0.458329i	$0.151552\pi$
$458$	3.00000	−	3.00000i	0.140181	−	0.140181i
$459$	−40.0000			−1.86704
$460$	5.00000	−	15.0000i	0.233126	−	0.699379i
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	−0.402916	−	0.915237i	$-0.632003\pi$
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	0.915237	+	0.402916i	$0.132003\pi$
$462$			4.00000i			0.186097i
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$			4.00000i			0.185695i
$465$	−4.00000	+	2.00000i	−0.185496	+	0.0927478i
$466$	5.00000	+	5.00000i	0.231621	+	0.231621i
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	−0.813265	−	0.581893i	$-0.802312\pi$
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	0.581893	+	0.813265i	$0.302312\pi$
$468$	2.00000	−	3.00000i	0.0924500	−	0.138675i
$469$			24.0000i			1.10822i
$470$	4.00000	−	2.00000i	0.184506	−	0.0922531i
$471$	−6.00000			−0.276465
$472$	3.00000	−	3.00000i	0.138086	−	0.138086i
$473$			10.0000i			0.459800i
$474$	−14.0000	−	14.0000i	−0.643041	−	0.643041i
$475$	21.0000	−	3.00000i	0.963546	−	0.137649i
$476$	−10.0000	−	10.0000i	−0.458349	−	0.458349i
$477$	−1.00000	−	1.00000i	−0.0457869	−	0.0457869i
$478$	7.00000	+	7.00000i	0.320173	+	0.320173i
$479$	13.0000	−	13.0000i	0.593985	−	0.593985i	−0.344720	−	0.938705i	$-0.612026\pi$
$479$	13.0000	−	13.0000i	0.593985	−	0.593985i	0.938705	+	0.344720i	$0.112026\pi$
$480$	−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
$483$		−	20.0000i		−	0.910032i
$484$		−	9.00000i		−	0.409091i
$485$	−2.00000	−	4.00000i	−0.0908153	−	0.181631i
$486$	7.00000	−	7.00000i	0.317526	−	0.317526i
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	2.00000			0.0905357
$489$	−4.00000	+	4.00000i	−0.180886	+	0.180886i
$490$	3.00000	+	6.00000i	0.135526	+	0.271052i
$491$		−	10.0000i		−	0.451294i	−0.974209	−	0.225647i	$-0.927550\pi$
$491$		−	10.0000i		−	0.451294i	0.974209	−	0.225647i	$-0.0724495\pi$
$492$			2.00000i			0.0901670i
$493$	20.0000	+	20.0000i	0.900755	+	0.900755i
$494$	3.00000	+	15.0000i	0.134976	+	0.674882i
$495$	−3.00000	−	1.00000i	−0.134840	−	0.0449467i
$496$	1.00000	−	1.00000i	0.0449013	−	0.0449013i
$497$	−2.00000	−	2.00000i	−0.0897123	−	0.0897123i
$498$	−6.00000	−	6.00000i	−0.268866	−	0.268866i
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.999548	−	0.0300737i	$-0.990426\pi$
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.0300737	−	0.999548i	$-0.509574\pi$
$500$	−11.0000	−	2.00000i	−0.491935	−	0.0894427i
$501$	2.00000	+	2.00000i	0.0893534	+	0.0893534i
$502$			30.0000i			1.33897i
$503$	9.00000	−	9.00000i	0.401290	−	0.401290i	−0.477397	−	0.878688i	$-0.658420\pi$
$503$	9.00000	−	9.00000i	0.401290	−	0.401290i	0.878688	+	0.477397i	$0.158420\pi$
$504$	2.00000			0.0890871
$505$		0			0
$506$		−	10.0000i		−	0.444554i
$507$	−17.0000	−	7.00000i	−0.754997	−	0.310881i
$508$	−15.0000	+	15.0000i	−0.665517	+	0.665517i
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	0.357643	−	0.933858i	$-0.383580\pi$
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	−0.933858	+	0.357643i	$0.883580\pi$
$510$	−20.0000	+	10.0000i	−0.885615	+	0.442807i
$511$			12.0000i			0.530849i
$512$	1.00000			0.0441942
$513$			24.0000i			1.05963i
$514$	−15.0000	+	15.0000i	−0.661622	+	0.661622i
$515$	5.00000	−	15.0000i	0.220326	−	0.660979i
$516$	−10.0000			−0.440225
$517$	2.00000	−	2.00000i	0.0879599	−	0.0879599i
$518$	16.0000			0.703000
$519$	−30.0000			−1.31685
$520$	1.00000	−	8.00000i	0.0438529	−	0.350823i
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$	−4.00000			−0.175075
$523$	−21.0000	+	21.0000i	−0.918266	+	0.918266i	−0.996903	−	0.0786374i	$-0.974943\pi$
$523$	−21.0000	+	21.0000i	−0.918266	+	0.918266i	0.0786374	+	0.996903i	$0.474943\pi$
$524$	12.0000			0.524222
$525$	−14.0000	+	2.00000i	−0.611010	+	0.0872872i
$526$	9.00000	−	9.00000i	0.392419	−	0.392419i
$527$		−	10.0000i		−	0.435607i
$528$	−2.00000			−0.0870388
$529$			27.0000i			1.17391i
$530$	−3.00000	−	1.00000i	−0.130312	−	0.0434372i
$531$	3.00000	+	3.00000i	0.130189	+	0.130189i
$532$	−6.00000	+	6.00000i	−0.260133	+	0.260133i
$533$	−5.00000	+	1.00000i	−0.216574	+	0.0433148i
$534$		−	14.0000i		−	0.605839i
$535$	−13.0000	+	39.0000i	−0.562039	+	1.68612i
$536$	−12.0000			−0.518321
$537$	−20.0000	+	20.0000i	−0.863064	+	0.863064i
$538$		−	16.0000i		−	0.689809i
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$	4.00000	−	12.0000i	0.172133	−	0.516398i
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	−9.00000	−	9.00000i	−0.386583	−	0.386583i
$543$	20.0000	+	20.0000i	0.858282	+	0.858282i
$544$	5.00000	−	5.00000i	0.214373	−	0.214373i
$545$	13.0000	−	39.0000i	0.556859	−	1.67058i
$546$	−2.00000	−	10.0000i	−0.0855921	−	0.427960i
$547$	−7.00000	−	7.00000i	−0.299298	−	0.299298i	0.541441	−	0.840739i	$-0.317879\pi$
$547$	−7.00000	−	7.00000i	−0.299298	−	0.299298i	−0.840739	+	0.541441i	$0.817879\pi$
$548$		−	12.0000i		−	0.512615i
$549$			2.00000i			0.0853579i
$550$	−7.00000	+	1.00000i	−0.298481	+	0.0426401i
$551$	12.0000	−	12.0000i	0.511217	−	0.511217i
$552$	10.0000			0.425628
$553$	28.0000			1.19068
$554$	−5.00000	+	5.00000i	−0.212430	+	0.212430i
$555$	8.00000	−	24.0000i	0.339581	−	1.01874i
$556$			14.0000i			0.593732i
$557$			8.00000i			0.338971i	0.985533	+	0.169485i	$0.0542106\pi$
$557$			8.00000i			0.338971i	−0.985533	+	0.169485i	$0.945789\pi$
$558$	1.00000	+	1.00000i	0.0423334	+	0.0423334i
$559$	−5.00000	−	25.0000i	−0.211477	−	1.05739i
$560$	4.00000	−	2.00000i	0.169031	−	0.0845154i
$561$	−10.0000	+	10.0000i	−0.422200	+	0.422200i
$562$	21.0000	+	21.0000i	0.885832	+	0.885832i
$563$	5.00000	+	5.00000i	0.210725	+	0.210725i	0.804575	−	0.593851i	$-0.202393\pi$
$563$	5.00000	+	5.00000i	0.210725	+	0.210725i	−0.593851	+	0.804575i	$0.702393\pi$
$564$	2.00000	+	2.00000i	0.0842152	+	0.0842152i
$565$	27.0000	+	9.00000i	1.13590	+	0.378633i
$566$	−15.0000	−	15.0000i	−0.630497	−	0.630497i
$567$		−	10.0000i		−	0.419961i
$568$	1.00000	−	1.00000i	0.0419591	−	0.0419591i
$569$	−10.0000			−0.419222			−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000			−0.419222			−0.209611	+	0.977785i	$0.567220\pi$
$570$	6.00000	+	12.0000i	0.251312	+	0.502625i
$571$		−	10.0000i		−	0.418487i	−0.977864	−	0.209243i	$-0.932900\pi$
$571$		−	10.0000i		−	0.418487i	0.977864	−	0.209243i	$-0.0671001\pi$
$572$	−1.00000	−	5.00000i	−0.0418121	−	0.209061i
$573$	8.00000	−	8.00000i	0.334205	−	0.334205i
$574$	−2.00000	−	2.00000i	−0.0834784	−	0.0834784i
$575$	35.0000	−	5.00000i	1.45960	−	0.208514i
$576$			1.00000i			0.0416667i
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$		−	33.0000i		−	1.37262i
$579$	−14.0000	+	14.0000i	−0.581820	+	0.581820i
$580$	−8.00000	+	4.00000i	−0.332182	+	0.166091i
$581$	12.0000			0.497844
$582$	2.00000	−	2.00000i	0.0829027	−	0.0829027i
$583$	−2.00000			−0.0828315
$584$	−6.00000			−0.248282
$585$	8.00000	+	1.00000i	0.330759	+	0.0413449i
$586$	−26.0000			−1.07405
$587$	−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
$590$	9.00000	+	3.00000i	0.370524	+	0.123508i
$591$	−18.0000	+	18.0000i	−0.740421	+	0.740421i
$592$			8.00000i			0.328798i
$593$	14.0000			0.574911			0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000			0.574911			0.287456	+	0.957794i	$0.407191\pi$
$594$		−	8.00000i		−	0.328244i
$595$	10.0000	−	30.0000i	0.409960	−	1.22988i
$596$	−13.0000	−	13.0000i	−0.532501	−	0.532501i
$597$		0			0
$598$	5.00000	+	25.0000i	0.204465	+	1.02233i
$599$			14.0000i			0.572024i	0.958226	+	0.286012i	$0.0923298\pi$
$599$			14.0000i			0.572024i	−0.958226	+	0.286012i	$0.907670\pi$
$600$	−1.00000	−	7.00000i	−0.0408248	−	0.285774i
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	10.0000	−	10.0000i	0.407570	−	0.407570i
$603$		−	12.0000i		−	0.488678i
$604$	−9.00000	−	9.00000i	−0.366205	−	0.366205i
$605$	18.0000	−	9.00000i	0.731804	−	0.365902i
$606$		0			0
$607$	3.00000	+	3.00000i	0.121766	+	0.121766i	0.765364	−	0.643598i	$-0.222559\pi$
$607$	3.00000	+	3.00000i	0.121766	+	0.121766i	−0.643598	+	0.765364i	$0.722559\pi$
$608$	−3.00000	−	3.00000i	−0.121666	−	0.121666i
$609$	−8.00000	+	8.00000i	−0.324176	+	0.324176i
$610$	2.00000	+	4.00000i	0.0809776	+	0.161955i
$611$	−4.00000	+	6.00000i	−0.161823	+	0.242734i
$612$	5.00000	+	5.00000i	0.202113	+	0.202113i
$613$		−	4.00000i		−	0.161558i	−0.996732	−	0.0807792i	$-0.974259\pi$
$613$		−	4.00000i		−	0.161558i	0.996732	−	0.0807792i	$-0.0257409\pi$
$614$		−	2.00000i		−	0.0807134i
$615$	−4.00000	+	2.00000i	−0.161296	+	0.0806478i
$616$	2.00000	−	2.00000i	0.0805823	−	0.0805823i
$617$	38.0000			1.52982			0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000			1.52982			0.764911	+	0.644136i	$0.222783\pi$
$618$	10.0000			0.402259
$619$	3.00000	−	3.00000i	0.120580	−	0.120580i	−0.644242	−	0.764822i	$-0.722827\pi$
$619$	3.00000	−	3.00000i	0.120580	−	0.120580i	0.764822	+	0.644242i	$0.222827\pi$
$620$	3.00000	+	1.00000i	0.120483	+	0.0401610i
$621$			40.0000i			1.60514i
$622$		−	10.0000i		−	0.400963i
$623$	14.0000	+	14.0000i	0.560898	+	0.560898i
$624$	5.00000	−	1.00000i	0.200160	−	0.0400320i
$625$	−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
$628$	3.00000	+	3.00000i	0.119713	+	0.119713i
$629$	40.0000	+	40.0000i	1.59490	+	1.59490i
$630$	2.00000	+	4.00000i	0.0796819	+	0.159364i
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	0.891306	−	0.453403i	$-0.149790\pi$
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	−0.453403	+	0.891306i	$0.649790\pi$
$632$			14.0000i			0.556890i
$633$	−12.0000	+	12.0000i	−0.476957	+	0.476957i
$634$	−2.00000			−0.0794301
$635$	−45.0000	−	15.0000i	−1.78577	−	0.595257i
$636$		−	2.00000i		−	0.0793052i
$637$	−9.00000	−	6.00000i	−0.356593	−	0.237729i
$638$	−4.00000	+	4.00000i	−0.158362	+	0.158362i
$639$	1.00000	+	1.00000i	0.0395594	+	0.0395594i
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	−26.0000			−1.02614
$643$			46.0000i			1.81406i	0.421063	+	0.907031i	$0.361657\pi$
$643$			46.0000i			1.81406i	−0.421063	+	0.907031i	$0.638343\pi$
$644$	−10.0000	+	10.0000i	−0.394055	+	0.394055i
$645$	−10.0000	−	20.0000i	−0.393750	−	0.787499i
$646$	−30.0000			−1.18033
$647$	5.00000	−	5.00000i	0.196570	−	0.196570i	−0.601958	−	0.798528i	$-0.705612\pi$
$647$	5.00000	−	5.00000i	0.196570	−	0.196570i	0.798528	+	0.601958i	$0.205612\pi$
$648$	5.00000			0.196419
$649$	6.00000			0.235521
$650$	17.0000	−	6.00000i	0.666795	−	0.235339i
$651$	4.00000			0.156772
$652$	4.00000			0.156652
$653$	−21.0000	+	21.0000i	−0.821794	+	0.821794i	−0.986365	−	0.164572i	$-0.947376\pi$
$653$	−21.0000	+	21.0000i	−0.821794	+	0.821794i	0.164572	+	0.986365i	$0.447376\pi$
$654$	26.0000			1.01668
$655$	12.0000	+	24.0000i	0.468879	+	0.937758i
$656$	1.00000	−	1.00000i	0.0390434	−	0.0390434i
$657$		−	6.00000i		−	0.234082i
$658$	−4.00000			−0.155936
$659$			14.0000i			0.545363i	0.962104	+	0.272681i	$0.0879105\pi$
$659$			14.0000i			0.545363i	−0.962104	+	0.272681i	$0.912090\pi$
$660$	−2.00000	−	4.00000i	−0.0778499	−	0.155700i
$661$	31.0000	+	31.0000i	1.20576	+	1.20576i	0.972387	+	0.233373i	$0.0749763\pi$
$661$	31.0000	+	31.0000i	1.20576	+	1.20576i	0.233373	+	0.972387i	$0.425024\pi$
$662$	−9.00000	+	9.00000i	−0.349795	+	0.349795i
$663$	20.0000	−	30.0000i	0.776736	−	1.16510i
$664$			6.00000i			0.232845i
$665$	−18.0000	−	6.00000i	−0.698010	−	0.232670i
$666$	−8.00000			−0.309994
$667$	20.0000	−	20.0000i	0.774403	−	0.774403i
$668$		−	2.00000i		−	0.0773823i
$669$	−6.00000	−	6.00000i	−0.231973	−	0.231973i
$670$	−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
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	0.796877	−	0.604141i	$-0.206484\pi$
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	−0.604141	+	0.796877i	$0.706484\pi$
$674$	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
$677$	23.0000	+	23.0000i	0.883962	+	0.883962i	0.993935	−	0.109973i	$-0.0350764\pi$
$677$	23.0000	+	23.0000i	0.883962	+	0.883962i	−0.109973	+	0.993935i	$0.535076\pi$
$678$			18.0000i			0.691286i
$679$			4.00000i			0.153506i
$680$	15.0000	+	5.00000i	0.575224	+	0.191741i
$681$	12.0000	−	12.0000i	0.459841	−	0.459841i
$682$	2.00000			0.0765840
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	3.00000	−	3.00000i	0.114708	−	0.114708i
$685$	24.0000	−	12.0000i	0.916993	−	0.458496i
$686$		−	20.0000i		−	0.763604i
$687$			6.00000i			0.228914i
$688$	5.00000	+	5.00000i	0.190623	+	0.190623i
$689$	5.00000	−	1.00000i	0.190485	−	0.0380970i
$690$	10.0000	+	20.0000i	0.380693	+	0.761387i
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	−0.857260	−	0.514884i	$-0.827835\pi$
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	0.514884	+	0.857260i	$0.327835\pi$
$692$	15.0000	+	15.0000i	0.570214	+	0.570214i
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$	−7.00000	−	7.00000i	−0.265716	−	0.265716i
$695$	−28.0000	+	14.0000i	−1.06210	+	0.531050i
$696$	−4.00000	−	4.00000i	−0.151620	−	0.151620i
$697$		−	10.0000i		−	0.378777i
$698$	3.00000	−	3.00000i	0.113552	−	0.113552i
$699$	−10.0000			−0.378235
$700$	8.00000	+	6.00000i	0.302372	+	0.226779i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	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
$705$	−2.00000	+	6.00000i	−0.0753244	+	0.225973i
$706$			16.0000i			0.602168i
$707$		0			0
$708$			6.00000i			0.225494i
$709$	3.00000	−	3.00000i	0.112667	−	0.112667i	−0.648526	−	0.761193i	$-0.724614\pi$
$709$	3.00000	−	3.00000i	0.112667	−	0.112667i	0.761193	+	0.648526i	$0.224614\pi$
$710$	3.00000	+	1.00000i	0.112588	+	0.0375293i
$711$	−14.0000			−0.525041
$712$	−7.00000	+	7.00000i	−0.262336	+	0.262336i
$713$	−10.0000			−0.374503
$714$	20.0000			0.748481
$715$	9.00000	−	7.00000i	0.336581	−	0.261785i
$716$	20.0000			0.747435
$717$	−14.0000			−0.522840
$718$	13.0000	−	13.0000i	0.485156	−	0.485156i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−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
$724$		−	20.0000i		−	0.743294i
$725$	−16.0000	−	12.0000i	−0.594225	−	0.445669i
$726$	9.00000	+	9.00000i	0.334021	+	0.334021i
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.368418	+	0.929660i	$0.620100\pi$
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.929660	+	0.368418i	$0.879900\pi$
$728$	−4.00000	+	6.00000i	−0.148250	+	0.222375i
$729$			29.0000i			1.07407i
$730$	−6.00000	−	12.0000i	−0.222070	−	0.444140i
$731$	50.0000			1.84932
$732$	−2.00000	+	2.00000i	−0.0739221	+	0.0739221i
$733$		−	44.0000i		−	1.62518i	−0.582838	−	0.812589i	$-0.698058\pi$
$733$		−	44.0000i		−	1.62518i	0.582838	−	0.812589i	$-0.301942\pi$
$734$	3.00000	+	3.00000i	0.110732	+	0.110732i
$735$	−9.00000	−	3.00000i	−0.331970	−	0.110657i
$736$	−5.00000	−	5.00000i	−0.184302	−	0.184302i
$737$	−12.0000	−	12.0000i	−0.442026	−	0.442026i
$738$	1.00000	+	1.00000i	0.0368105	+	0.0368105i
$739$	−37.0000	+	37.0000i	−1.36107	+	1.36107i	−0.488507	+	0.872560i	$0.662458\pi$
$739$	−37.0000	+	37.0000i	−1.36107	+	1.36107i	−0.872560	+	0.488507i	$0.837542\pi$
$740$	−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
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$			2.00000i			0.0733236i
$745$	13.0000	−	39.0000i	0.476283	−	1.42885i
$746$	−1.00000	+	1.00000i	−0.0366126	+	0.0366126i
$747$	−6.00000			−0.219529
$748$	10.0000			0.365636
$749$	26.0000	−	26.0000i	0.950019	−	0.950019i
$750$	13.0000	−	9.00000i	0.474693	−	0.328634i
$751$		−	10.0000i		−	0.364905i	−0.983215	−	0.182453i	$-0.941596\pi$
$751$		−	10.0000i		−	0.364905i	0.983215	−	0.182453i	$-0.0584036\pi$
$752$		−	2.00000i		−	0.0729325i
$753$	−30.0000	−	30.0000i	−1.09326	−	1.09326i
$754$	8.00000	−	12.0000i	0.291343	−	0.437014i
$755$	9.00000	−	27.0000i	0.327544	−	0.982631i
$756$	−8.00000	+	8.00000i	−0.290957	+	0.290957i
$757$	−17.0000	−	17.0000i	−0.617876	−	0.617876i	0.327111	−	0.944986i	$-0.393925\pi$
$757$	−17.0000	−	17.0000i	−0.617876	−	0.617876i	−0.944986	+	0.327111i	$0.893925\pi$
$758$	17.0000	+	17.0000i	0.617468	+	0.617468i
$759$	10.0000	+	10.0000i	0.362977	+	0.362977i
$760$	3.00000	−	9.00000i	0.108821	−	0.326464i
$761$	−19.0000	−	19.0000i	−0.688749	−	0.688749i	0.273206	−	0.961956i	$-0.411916\pi$
$761$	−19.0000	−	19.0000i	−0.688749	−	0.688749i	−0.961956	+	0.273206i	$0.911916\pi$
$762$		−	30.0000i		−	1.08679i
$763$	−26.0000	+	26.0000i	−0.941263	+	0.941263i
$764$	−8.00000			−0.289430
$765$	−5.00000	+	15.0000i	−0.180775	+	0.542326i
$766$			6.00000i			0.216789i
$767$	−15.0000	+	3.00000i	−0.541619	+	0.108324i
$768$	−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
$771$		−	30.0000i		−	1.08042i
$772$	14.0000			0.503871
$773$		−	24.0000i		−	0.863220i	−0.902060	−	0.431610i	$-0.857946\pi$
$773$		−	24.0000i		−	0.863220i	0.902060	−	0.431610i	$-0.142054\pi$
$774$	−5.00000	+	5.00000i	−0.179721	+	0.179721i
$775$	1.00000	+	7.00000i	0.0359211	+	0.251447i
$776$	−2.00000			−0.0717958
$777$	−16.0000	+	16.0000i	−0.573997	+	0.573997i
$778$	−10.0000			−0.358517
$779$	−6.00000			−0.214972
$780$	7.00000	+	9.00000i	0.250640	+	0.322252i
$781$	2.00000			0.0715656
$782$	−50.0000			−1.78800
$783$	16.0000	−	16.0000i	0.571793	−	0.571793i
$784$	3.00000			0.107143
$785$	−3.00000	+	9.00000i	−0.107075	+	0.321224i
$786$	−12.0000	+	12.0000i	−0.428026	+	0.428026i
$787$		−	42.0000i		−	1.49714i	−0.663057	−	0.748569i	$-0.730741\pi$
$787$		−	42.0000i		−	1.49714i	0.663057	−	0.748569i	$-0.269259\pi$
$788$	18.0000			0.641223
$789$			18.0000i			0.640817i
$790$	−28.0000	+	14.0000i	−0.996195	+	0.498098i
$791$	−18.0000	−	18.0000i	−0.640006	−	0.640006i
$792$	−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
$796$		0			0
$797$	−5.00000	+	5.00000i	−0.177109	+	0.177109i	−0.790094	−	0.612985i	$-0.789968\pi$
$797$	−5.00000	+	5.00000i	−0.177109	+	0.177109i	0.612985	+	0.790094i	$0.289968\pi$
$798$		−	12.0000i		−	0.424795i
$799$	−10.0000	−	10.0000i	−0.353775	−	0.353775i
$800$	−3.00000	+	4.00000i	−0.106066	+	0.141421i
$801$	−7.00000	−	7.00000i	−0.247333	−	0.247333i
$802$	1.00000	+	1.00000i	0.0353112	+	0.0353112i
$803$	−6.00000	−	6.00000i	−0.211735	−	0.211735i
$804$	12.0000	−	12.0000i	0.423207	−	0.423207i
$805$	−30.0000	−	10.0000i	−1.05736	−	0.352454i
$806$	−5.00000	+	1.00000i	−0.176117	+	0.0352235i
$807$	16.0000	+	16.0000i	0.563227	+	0.563227i
$808$		0			0
$809$		−	36.0000i		−	1.26569i	−0.774277	−	0.632846i	$-0.781886\pi$
$809$		−	36.0000i		−	1.26569i	0.774277	−	0.632846i	$-0.218114\pi$
$810$	5.00000	+	10.0000i	0.175682	+	0.351364i
$811$	11.0000	−	11.0000i	0.386262	−	0.386262i	−0.487090	−	0.873352i	$-0.661942\pi$
$811$	11.0000	−	11.0000i	0.386262	−	0.386262i	0.873352	+	0.487090i	$0.161942\pi$
$812$	8.00000			0.280745
$813$	18.0000			0.631288
$814$	−8.00000	+	8.00000i	−0.280400	+	0.280400i
$815$	4.00000	+	8.00000i	0.140114	+	0.280228i
$816$			10.0000i			0.350070i
$817$		−	30.0000i		−	1.04957i
$818$	−3.00000	−	3.00000i	−0.104893	−	0.104893i
$819$	−6.00000	−	4.00000i	−0.209657	−	0.139771i
$820$	3.00000	+	1.00000i	0.104765	+	0.0349215i
$821$	−29.0000	+	29.0000i	−1.01211	+	1.01211i	−0.0121812	+	0.999926i	$0.503877\pi$
$821$	−29.0000	+	29.0000i	−1.01211	+	1.01211i	−0.999926	+	0.0121812i	$0.996123\pi$
$822$	12.0000	+	12.0000i	0.418548	+	0.418548i
$823$	15.0000	+	15.0000i	0.522867	+	0.522867i	0.918436	−	0.395569i	$-0.129453\pi$
$823$	15.0000	+	15.0000i	0.522867	+	0.522867i	−0.395569	+	0.918436i	$0.629453\pi$
$824$	−5.00000	−	5.00000i	−0.174183	−	0.174183i
$825$	6.00000	−	8.00000i	0.208893	−	0.278524i
$826$	−6.00000	−	6.00000i	−0.208767	−	0.208767i
$827$		−	2.00000i		−	0.0695468i	−0.999395	−	0.0347734i	$-0.988929\pi$
$827$		−	2.00000i		−	0.0695468i	0.999395	−	0.0347734i	$-0.0110710\pi$
$828$	5.00000	−	5.00000i	0.173762	−	0.173762i
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$	−12.0000	+	6.00000i	−0.416526	+	0.208263i
$831$		−	10.0000i		−	0.346896i
$832$	−3.00000	−	2.00000i	−0.104006	−	0.0693375i
$833$	15.0000	−	15.0000i	0.519719	−	0.519719i
$834$	−14.0000	−	14.0000i	−0.484780	−	0.484780i
$835$	4.00000	−	2.00000i	0.138426	−	0.0692129i
$836$		−	6.00000i		−	0.207514i
$837$	−8.00000			−0.276520
$838$		−	26.0000i		−	0.898155i
$839$	13.0000	−	13.0000i	0.448810	−	0.448810i	−0.446149	−	0.894959i	$-0.647205\pi$
$839$	13.0000	−	13.0000i	0.448810	−	0.448810i	0.894959	+	0.446149i	$0.147205\pi$
$840$	−2.00000	+	6.00000i	−0.0690066	+	0.207020i
$841$	13.0000			0.448276
$842$	−9.00000	+	9.00000i	−0.310160	+	0.310160i
$843$	−42.0000			−1.44656
$844$	12.0000			0.413057
$845$	−19.0000	+	22.0000i	−0.653620	+	0.756823i
$846$	2.00000			0.0687614
$847$	−18.0000			−0.618487
$848$	−1.00000	+	1.00000i	−0.0343401	+	0.0343401i
$849$	30.0000			1.02960
$850$	5.00000	+	35.0000i	0.171499	+	1.20049i
$851$	40.0000	−	40.0000i	1.37118	−	1.37118i
$852$			2.00000i			0.0685189i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$		−	4.00000i		−	0.136877i
$855$	9.00000	+	3.00000i	0.307794	+	0.102598i
$856$	13.0000	+	13.0000i	0.444331	+	0.444331i
$857$	5.00000	−	5.00000i	0.170797	−	0.170797i	−0.616533	−	0.787329i	$-0.711463\pi$
$857$	5.00000	−	5.00000i	0.170797	−	0.170797i	0.787329	+	0.616533i	$0.211463\pi$
$858$	6.00000	+	4.00000i	0.204837	+	0.136558i
$859$		−	26.0000i		−	0.887109i	−0.896248	−	0.443554i	$-0.853717\pi$
$859$		−	26.0000i		−	0.887109i	0.896248	−	0.443554i	$-0.146283\pi$
$860$	−5.00000	+	15.0000i	−0.170499	+	0.511496i
$861$	4.00000			0.136320
$862$	21.0000	−	21.0000i	0.715263	−	0.715263i
$863$			46.0000i			1.56586i	0.622111	+	0.782929i	$0.286275\pi$
$863$			46.0000i			1.56586i	−0.622111	+	0.782929i	$0.713725\pi$
$864$	−4.00000	−	4.00000i	−0.136083	−	0.136083i
$865$	−15.0000	+	45.0000i	−0.510015	+	1.53005i
$866$	−15.0000	−	15.0000i	−0.509721	−	0.509721i
$867$	33.0000	+	33.0000i	1.12074	+	1.12074i
$868$	−2.00000	−	2.00000i	−0.0678844	−	0.0678844i
$869$	−14.0000	+	14.0000i	−0.474917	+	0.474917i
$870$	4.00000	−	12.0000i	0.135613	−	0.406838i
$871$	36.0000	+	24.0000i	1.21981	+	0.813209i
$872$	−13.0000	−	13.0000i	−0.440236	−	0.440236i
$873$		−	2.00000i		−	0.0676897i
$874$			30.0000i			1.01477i
$875$	−4.00000	+	22.0000i	−0.135225	+	0.743736i
$876$	6.00000	−	6.00000i	0.202721	−	0.202721i
$877$	18.0000			0.607817			0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000			0.607817			0.303908	+	0.952701i	$0.401708\pi$
$878$	40.0000			1.34993
$879$	26.0000	−	26.0000i	0.876958	−	0.876958i
$880$	−1.00000	+	3.00000i	−0.0337100	+	0.101130i
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$			3.00000i			0.101015i
$883$	5.00000	+	5.00000i	0.168263	+	0.168263i	0.786216	−	0.617952i	$-0.212037\pi$
$883$	5.00000	+	5.00000i	0.168263	+	0.168263i	−0.617952	+	0.786216i	$0.712037\pi$
$884$	−25.0000	+	5.00000i	−0.840841	+	0.168168i
$885$	−12.0000	+	6.00000i	−0.403376	+	0.201688i
$886$	19.0000	−	19.0000i	0.638317	−	0.638317i
$887$	23.0000	+	23.0000i	0.772264	+	0.772264i	0.978502	−	0.206238i	$-0.0661220\pi$
$887$	23.0000	+	23.0000i	0.772264	+	0.772264i	−0.206238	+	0.978502i	$0.566122\pi$
$888$	−8.00000	−	8.00000i	−0.268462	−	0.268462i
$889$	30.0000	+	30.0000i	1.00617	+	1.00617i
$890$	−21.0000	−	7.00000i	−0.703922	−	0.234641i
$891$	5.00000	+	5.00000i	0.167506	+	0.167506i
$892$			6.00000i			0.200895i
$893$	−6.00000	+	6.00000i	−0.200782	+	0.200782i
$894$	26.0000			0.869570
$895$	20.0000	+	40.0000i	0.668526	+	1.33705i
$896$		−	2.00000i		−	0.0668153i
$897$	−30.0000	−	20.0000i	−1.00167	−	0.667781i
$898$	−7.00000	+	7.00000i	−0.233593	+	0.233593i
$899$	4.00000	+	4.00000i	0.133407	+	0.133407i
$900$	−4.00000	−	3.00000i	−0.133333	−	0.100000i
$901$			10.0000i			0.333148i
$902$	2.00000			0.0665927
$903$			20.0000i			0.665558i
$904$	9.00000	−	9.00000i	0.299336	−	0.299336i
$905$	40.0000	−	20.0000i	1.32964	−	0.664822i
$906$	18.0000			0.598010
$907$	35.0000	−	35.0000i	1.16216	−	1.16216i	0.178153	−	0.984003i	$-0.442988\pi$
$907$	35.0000	−	35.0000i	1.16216	−	1.16216i	0.984003	−	0.178153i	$-0.0570122\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$	−16.0000	−	2.00000i	−0.530395	−	0.0662994i
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	6.00000			0.198680
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$	38.0000			1.25693
$915$	−6.00000	−	2.00000i	−0.198354	−	0.0661180i
$916$	3.00000	−	3.00000i	0.0991228	−	0.0991228i
$917$		−	24.0000i		−	0.792550i
$918$	−40.0000			−1.32020
$919$			14.0000i			0.461817i	0.972975	+	0.230909i	$0.0741699\pi$
$919$			14.0000i			0.461817i	−0.972975	+	0.230909i	$0.925830\pi$
$920$	5.00000	−	15.0000i	0.164845	−	0.494535i
$921$	2.00000	+	2.00000i	0.0659022	+	0.0659022i
$922$	11.0000	−	11.0000i	0.362266	−	0.362266i
$923$	−5.00000	+	1.00000i	−0.164577	+	0.0329154i
$924$			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
$928$			4.00000i			0.131306i
$929$	17.0000	+	17.0000i	0.557752	+	0.557752i	0.928667	−	0.370915i	$-0.120956\pi$
$929$	17.0000	+	17.0000i	0.557752	+	0.557752i	−0.370915	+	0.928667i	$0.620956\pi$
$930$	−4.00000	+	2.00000i	−0.131165	+	0.0655826i
$931$	−9.00000	−	9.00000i	−0.294963	−	0.294963i
$932$	5.00000	+	5.00000i	0.163780	+	0.163780i
$933$	10.0000	+	10.0000i	0.327385	+	0.327385i
$934$	−5.00000	+	5.00000i	−0.163605	+	0.163605i
$935$	10.0000	+	20.0000i	0.327035	+	0.654070i
$936$	2.00000	−	3.00000i	0.0653720	−	0.0980581i
$937$	33.0000	+	33.0000i	1.07806	+	1.07806i	0.996683	+	0.0813798i	$0.0259327\pi$
$937$	33.0000	+	33.0000i	1.07806	+	1.07806i	0.0813798	+	0.996683i	$0.474067\pi$
$938$			24.0000i			0.783628i
$939$			18.0000i			0.587408i
$940$	4.00000	−	2.00000i	0.130466	−	0.0652328i
$941$	−29.0000	+	29.0000i	−0.945373	+	0.945373i	−0.998583	−	0.0532103i	$-0.983055\pi$
$941$	−29.0000	+	29.0000i	−0.945373	+	0.945373i	0.0532103	+	0.998583i	$0.483055\pi$
$942$	−6.00000			−0.195491
$943$	−10.0000			−0.325645
$944$	3.00000	−	3.00000i	0.0976417	−	0.0976417i
$945$	−24.0000	−	8.00000i	−0.780720	−	0.260240i
$946$			10.0000i			0.325128i
$947$			38.0000i			1.23483i	0.786636	+	0.617417i	$0.211821\pi$
$947$			38.0000i			1.23483i	−0.786636	+	0.617417i	$0.788179\pi$
$948$	−14.0000	−	14.0000i	−0.454699	−	0.454699i
$949$	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
$952$	−10.0000	−	10.0000i	−0.324102	−	0.324102i
$953$	−35.0000	−	35.0000i	−1.13376	−	1.13376i	−0.989546	−	0.144215i	$-0.953934\pi$
$953$	−35.0000	−	35.0000i	−1.13376	−	1.13376i	−0.144215	−	0.989546i	$-0.546066\pi$
$954$	−1.00000	−	1.00000i	−0.0323762	−	0.0323762i
$955$	−8.00000	−	16.0000i	−0.258874	−	0.517748i
$956$	7.00000	+	7.00000i	0.226396	+	0.226396i
$957$		−	8.00000i		−	0.258603i
$958$	13.0000	−	13.0000i	0.420011	−	0.420011i
$959$	−24.0000			−0.775000
$960$	−3.00000	−	1.00000i	−0.0968246	−	0.0322749i
$961$			29.0000i			0.935484i
$962$	16.0000	−	24.0000i	0.515861	−	0.773791i
$963$	−13.0000	+	13.0000i	−0.418919	+	0.418919i
$964$	1.00000	+	1.00000i	0.0322078	+	0.0322078i
$965$	14.0000	+	28.0000i	0.450676	+	0.901352i
$966$		−	20.0000i		−	0.643489i
$967$	48.0000			1.54358			0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000			1.54358			0.771788	+	0.635880i	$0.219363\pi$
$968$		−	9.00000i		−	0.289271i
$969$	30.0000	−	30.0000i	0.963739	−	0.963739i
$970$	−2.00000	−	4.00000i	−0.0642161	−	0.128432i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	7.00000	−	7.00000i	0.224525	−	0.224525i
$973$	28.0000			0.897639
$974$	−32.0000			−1.02535
$975$	−11.0000	+	23.0000i	−0.352282	+	0.736590i
$976$	2.00000			0.0640184
$977$	−22.0000			−0.703842			−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000			−0.703842			−0.351921	+	0.936030i	$0.614471\pi$
$978$	−4.00000	+	4.00000i	−0.127906	+	0.127906i
$979$	−14.0000			−0.447442
$980$	3.00000	+	6.00000i	0.0958315	+	0.191663i
$981$	13.0000	−	13.0000i	0.415058	−	0.415058i
$982$		−	10.0000i		−	0.319113i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$			2.00000i			0.0637577i
$985$	18.0000	+	36.0000i	0.573528	+	1.14706i
$986$	20.0000	+	20.0000i	0.636930	+	0.636930i
$987$	4.00000	−	4.00000i	0.127321	−	0.127321i
$988$	3.00000	+	15.0000i	0.0954427	+	0.477214i
$989$		−	50.0000i		−	1.58991i
$990$	−3.00000	−	1.00000i	−0.0953463	−	0.0317821i
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	1.00000	−	1.00000i	0.0317500	−	0.0317500i
$993$		−	18.0000i		−	0.571213i
$994$	−2.00000	−	2.00000i	−0.0634361	−	0.0634361i
$995$		0			0
$996$	−6.00000	−	6.00000i	−0.190117	−	0.190117i
$997$	−17.0000	−	17.0000i	−0.538395	−	0.538395i	0.384662	−	0.923057i	$-0.374318\pi$
$997$	−17.0000	−	17.0000i	−0.538395	−	0.538395i	−0.923057	+	0.384662i	$0.874318\pi$
$998$	−23.0000	−	23.0000i	−0.728052	−	0.728052i
$999$	32.0000	−	32.0000i	1.01244	−	1.01244i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.c.57.1	✓	2	1.1	even	1	trivial
130.2.g.c.73.1	yes	2	65.8	even	4	inner
130.2.j.b.47.1	yes	2	13.8	odd	4
130.2.j.b.83.1	yes	2	5.3	odd	4
650.2.g.b.57.1		2	5.4	even	2
650.2.g.b.593.1		2	65.47	even	4
650.2.j.d.307.1		2	65.34	odd	4
650.2.j.d.343.1		2	5.2	odd	4
1040.2.bg.f.577.1		2	4.3	odd	2
1040.2.bg.f.593.1		2	260.203	odd	4
1040.2.cd.e.177.1		2	52.47	even	4
1040.2.cd.e.993.1		2	20.3	even	4
1170.2.m.a.73.1		2	195.8	odd	4
1170.2.m.a.577.1		2	3.2	odd	2
1170.2.w.c.307.1		2	39.8	even	4
1170.2.w.c.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} +(5.00000 - 5.00000i) 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} +(-5.00000 - 5.00000i) 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} +4.00000i q^{29} +(-3.00000 - 1.00000i) q^{30} +(1.00000 - 1.00000i) q^{31} +1.00000 q^{32} -2.00000 q^{33} +(5.00000 - 5.00000i) q^{34} +(4.00000 - 2.00000i) q^{35} +1.00000i q^{36} +8.00000i q^{37} +(-3.00000 - 3.00000i) q^{38} +(5.00000 - 1.00000i) q^{39} +(1.00000 + 2.00000i) q^{40} +(1.00000 - 1.00000i) q^{41} +(2.00000 + 2.00000i) q^{42} +(5.00000 + 5.00000i) q^{43} +(1.00000 + 1.00000i) q^{44} +(-2.00000 + 1.00000i) q^{45} +(-5.00000 - 5.00000i) q^{46} -2.00000i q^{47} +(-1.00000 + 1.00000i) q^{48} +3.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} +10.0000i 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} +4.00000i q^{58} +(3.00000 - 3.00000i) 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} +(1.00000 - 8.00000i) q^{65} -2.00000 q^{66} -12.0000 q^{67} +(5.00000 - 5.00000i) q^{68} +10.0000 q^{69} +(4.00000 - 2.00000i) q^{70} +(1.00000 - 1.00000i) 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} +(5.00000 - 1.00000i) q^{78} +14.0000i q^{79} +(1.00000 + 2.00000i) q^{80} +5.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +6.00000i q^{83} +(2.00000 + 2.00000i) q^{84} +(15.0000 + 5.00000i) q^{85} +(5.00000 + 5.00000i) q^{86} +(-4.00000 - 4.00000i) q^{87} +(1.00000 + 1.00000i) q^{88} +(-7.00000 + 7.00000i) q^{89} +(-2.00000 + 1.00000i) q^{90} +(-4.00000 + 6.00000i) q^{91} +(-5.00000 - 5.00000i) q^{92} +2.00000i q^{93} -2.00000i q^{94} +(3.00000 - 9.00000i) q^{95} +(-1.00000 + 1.00000i) q^{96} -2.00000 q^{97} +3.00000 q^{98} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} - 6 q^{15} + 2 q^{16} + 10 q^{17} - 6 q^{19} + 2 q^{20} + 4 q^{21} + 2 q^{22} - 10 q^{23} - 2 q^{24}+ \cdots - 2 q^{99}+O(q^{100}) \) 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 + 10 * q^17 - 6 * q^19 + 2 * q^20 + 4 * q^21 + 2 * q^22 - 10 * 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 + 10 * q^34 + 8 * q^35 - 6 * q^38 + 10 * q^39 + 2 * q^40 + 2 * q^41 + 4 * q^42 + 10 * q^43 + 2 * q^44 - 4 * q^45 - 10 * 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 + 6 * q^59 - 6 * q^60 + 4 * q^61 + 2 * q^62 + 4 * q^63 + 2 * q^64 + 2 * q^65 - 4 * q^66 - 24 * q^67 + 10 * q^68 + 20 * q^69 + 8 * q^70 + 2 * q^71 - 12 * q^73 - 2 * q^75 - 6 * q^76 + 4 * q^77 + 10 * q^78 + 2 * q^80 + 10 * q^81 + 2 * q^82 + 4 * q^84 + 30 * q^85 + 10 * q^86 - 8 * q^87 + 2 * q^88 - 14 * q^89 - 4 * q^90 - 8 * q^91 - 10 * q^92 + 6 * q^95 - 2 * q^96 - 4 * q^97 + 6 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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