LMFDB - Embedded newform 650.2.j.a.307.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(307,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.307"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [2,0,-2,-2,0,-2,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

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

Embedding invariants

Embedding label			307.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	650.307
Dual form			650.2.j.a.343.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−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
$5$		0			0
$5$		0			0
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	−0.841605	−	0.540094i	$-0.818389\pi$
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	0.540094	+	0.841605i	$0.318389\pi$
$12$	1.00000	−	1.00000i	0.288675	−	0.288675i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$			2.00000i			0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$	−1.00000			−0.235702
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	−0.961844	−	0.273597i	$-0.911786\pi$
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	0.273597	+	0.961844i	$0.411786\pi$
$20$		0			0
$21$	−2.00000	+	2.00000i	−0.436436	+	0.436436i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$	1.00000	+	1.00000i	0.204124	+	0.204124i
$25$		0			0
$26$	−3.00000	−	2.00000i	−0.588348	−	0.392232i
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$	−2.00000			−0.377964
$29$			8.00000i			1.48556i	0.669534	+	0.742781i	$0.266494\pi$
$29$			8.00000i			1.48556i	−0.669534	+	0.742781i	$0.733506\pi$
$30$		0			0
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	0.791184	−	0.611578i	$-0.209465\pi$
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	−0.611578	+	0.791184i	$0.709465\pi$
$32$			1.00000i			0.176777i
$33$		−	2.00000i		−	0.348155i
$34$	1.00000	+	1.00000i	0.171499	+	0.171499i
$35$		0			0
$36$		−	1.00000i		−	0.166667i
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	−3.00000	−	3.00000i	−0.486664	−	0.486664i
$39$	−1.00000	−	5.00000i	−0.160128	−	0.800641i
$40$		0			0
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.995183	−	0.0980332i	$-0.968745\pi$
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.0980332	−	0.995183i	$-0.531255\pi$
$42$	−2.00000	−	2.00000i	−0.308607	−	0.308607i
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	0.626734	−	0.779233i	$-0.284391\pi$
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	−0.779233	+	0.626734i	$0.784391\pi$
$44$	1.00000	−	1.00000i	0.150756	−	0.150756i
$45$		0			0
$46$	1.00000	−	1.00000i	0.147442	−	0.147442i
$47$	10.0000			1.45865			0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000			1.45865			0.729325	+	0.684167i	$0.239834\pi$
$48$	−1.00000	+	1.00000i	−0.144338	+	0.144338i
$49$	−3.00000			−0.428571
$50$		0			0
$51$			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	$-0.780966\pi$
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	0.635083	+	0.772444i	$0.280966\pi$
$54$	4.00000	−	4.00000i	0.544331	−	0.544331i
$55$		0			0
$56$		−	2.00000i		−	0.267261i
$57$		−	6.00000i		−	0.794719i
$58$	−8.00000			−1.05045
$59$	−9.00000	−	9.00000i	−1.17170	−	1.17170i	−0.981804	−	0.189896i	$-0.939185\pi$
$59$	−9.00000	−	9.00000i	−1.17170	−	1.17170i	−0.189896	−	0.981804i	$-0.560815\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	−1.00000	+	1.00000i	−0.127000	+	0.127000i
$63$			2.00000i			0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.00000			0.246183
$67$			12.0000i			1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$			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
$70$		0			0
$71$	5.00000	+	5.00000i	0.593391	+	0.593391i	0.938546	−	0.345155i	$-0.112174\pi$
$71$	5.00000	+	5.00000i	0.593391	+	0.593391i	−0.345155	+	0.938546i	$0.612174\pi$
$72$	1.00000			0.117851
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$		−	8.00000i		−	0.929981i
$75$		0			0
$76$	3.00000	−	3.00000i	0.344124	−	0.344124i
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$	5.00000	−	1.00000i	0.566139	−	0.113228i
$79$		−	10.0000i		−	1.12509i	−0.826767	−	0.562544i	$-0.809823\pi$
$79$		−	10.0000i		−	1.12509i	0.826767	−	0.562544i	$-0.190177\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$	7.00000	−	7.00000i	0.773021	−	0.773021i
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$	2.00000	−	2.00000i	0.218218	−	0.218218i
$85$		0			0
$86$	1.00000	−	1.00000i	0.107833	−	0.107833i
$87$	−8.00000	−	8.00000i	−0.857690	−	0.857690i
$88$	1.00000	+	1.00000i	0.106600	+	0.106600i
$89$	11.0000	+	11.0000i	1.16600	+	1.16600i	0.983139	+	0.182858i	$0.0585350\pi$
$89$	11.0000	+	11.0000i	1.16600	+	1.16600i	0.182858	+	0.983139i	$0.441465\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	−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
$100$		0			0
$101$			12.0000i			1.19404i	0.802225	+	0.597022i	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$	−2.00000			−0.198030
$103$	−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
$105$		0			0
$106$	−1.00000	−	1.00000i	−0.0971286	−	0.0971286i
$107$	1.00000	+	1.00000i	0.0966736	+	0.0966736i	0.753790	−	0.657116i	$-0.228224\pi$
$107$	1.00000	+	1.00000i	0.0966736	+	0.0966736i	−0.657116	+	0.753790i	$0.728224\pi$
$108$	4.00000	+	4.00000i	0.384900	+	0.384900i
$109$	−5.00000	+	5.00000i	−0.478913	+	0.478913i	−0.904784	−	0.425871i	$-0.859968\pi$
$109$	−5.00000	+	5.00000i	−0.478913	+	0.478913i	0.425871	+	0.904784i	$0.359968\pi$
$110$		0			0
$111$	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	$-0.686050\pi$
$113$	3.00000	−	3.00000i	0.282216	−	0.282216i	0.833992	+	0.551776i	$0.186050\pi$
$114$	6.00000			0.561951
$115$		0			0
$116$		−	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
$120$		0			0
$121$			9.00000i			0.818182i
$122$			2.00000i			0.181071i
$123$	14.0000			1.26234
$124$	−1.00000	−	1.00000i	−0.0898027	−	0.0898027i
$125$		0			0
$126$	−2.00000			−0.178174
$127$	−3.00000	+	3.00000i	−0.266207	+	0.266207i	−0.827570	−	0.561363i	$-0.810277\pi$
$127$	−3.00000	+	3.00000i	−0.266207	+	0.266207i	0.561363	+	0.827570i	$0.310277\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.00000			0.176090
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$			2.00000i			0.174078i
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	−12.0000			−1.03664
$135$		0			0
$136$	−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	$0.0270312\pi$
$139$			2.00000i			0.169638i	−0.996396	+	0.0848189i	$0.972969\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	−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	−0.746881	−	0.664958i	$-0.768450\pi$
$149$	−1.00000	+	1.00000i	−0.0819232	+	0.0819232i	0.664958	+	0.746881i	$0.268450\pi$
$150$		0			0
$151$	3.00000	−	3.00000i	0.244137	−	0.244137i	−0.574422	−	0.818559i	$-0.694773\pi$
$151$	3.00000	−	3.00000i	0.244137	−	0.244137i	0.818559	+	0.574422i	$0.194773\pi$
$152$	3.00000	+	3.00000i	0.243332	+	0.243332i
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$	−2.00000	−	2.00000i	−0.161165	−	0.161165i
$155$		0			0
$156$	1.00000	+	5.00000i	0.0800641	+	0.400320i
$157$	15.0000	+	15.0000i	1.19713	+	1.19713i	0.975022	+	0.222108i	$0.0712939\pi$
$157$	15.0000	+	15.0000i	1.19713	+	1.19713i	0.222108	+	0.975022i	$0.428706\pi$
$158$	10.0000			0.795557
$159$		−	2.00000i		−	0.158610i
$160$		0			0
$161$	−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
$165$		0			0
$166$			18.0000i			1.39707i
$167$	−14.0000			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$168$	2.00000	+	2.00000i	0.154303	+	0.154303i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$		0			0
$171$	−3.00000	−	3.00000i	−0.229416	−	0.229416i
$172$	1.00000	+	1.00000i	0.0762493	+	0.0762493i
$173$	9.00000	+	9.00000i	0.684257	+	0.684257i	0.960957	−	0.276699i	$-0.0892406\pi$
$173$	9.00000	+	9.00000i	0.684257	+	0.684257i	−0.276699	+	0.960957i	$0.589241\pi$
$174$	8.00000	−	8.00000i	0.606478	−	0.606478i
$175$		0			0
$176$	−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	$0.231285\pi$
$180$		0			0
$181$		−	16.0000i		−	1.18927i	−0.803996	−	0.594635i	$-0.797296\pi$
$181$		−	16.0000i		−	1.18927i	0.803996	−	0.594635i	$-0.202704\pi$
$182$	−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
$185$		0			0
$186$		−	2.00000i		−	0.146647i
$187$			2.00000i			0.146254i
$188$	−10.0000			−0.729325
$189$	−8.00000	−	8.00000i	−0.581914	−	0.581914i
$190$		0			0
$191$	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
$195$		0			0
$196$	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	$0.176204\pi$
$200$		0			0
$201$	−12.0000	−	12.0000i	−0.846415	−	0.846415i
$202$	−12.0000			−0.844317
$203$			16.0000i			1.12298i
$204$		−	2.00000i		−	0.140028i
$205$		0			0
$206$	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
$210$		0			0
$211$	−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
$215$		0			0
$216$	−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
$220$		0			0
$221$	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	$-0.705902\pi$
$223$	−18.0000			−1.20537			−0.602685	+	0.797980i	$0.705902\pi$
$224$			2.00000i			0.133631i
$225$		0			0
$226$	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	0.999962	−	0.00873396i	$-0.00278014\pi$
$229$	15.0000	+	15.0000i	0.991228	+	0.991228i	−0.00873396	+	0.999962i	$0.502780\pi$
$230$		0			0
$231$		−	4.00000i		−	0.263181i
$232$	8.00000			0.525226
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	0.739104	−	0.673592i	$-0.235249\pi$
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	−0.673592	+	0.739104i	$0.735249\pi$
$234$	2.00000	−	3.00000i	0.130744	−	0.196116i
$235$		0			0
$236$	9.00000	+	9.00000i	0.585850	+	0.585850i
$237$	10.0000	+	10.0000i	0.649570	+	0.649570i
$238$	2.00000	+	2.00000i	0.129641	+	0.129641i
$239$	1.00000	−	1.00000i	0.0646846	−	0.0646846i	−0.674024	−	0.738709i	$-0.735436\pi$
$239$	1.00000	−	1.00000i	0.0646846	−	0.0646846i	0.738709	+	0.674024i	$0.235436\pi$
$240$		0			0
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	−0.674165	−	0.738581i	$-0.735496\pi$
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	0.738581	+	0.674165i	$0.235496\pi$
$242$	−9.00000			−0.578542
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$	−2.00000			−0.128037
$245$		0			0
$246$			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
$250$		0			0
$251$		−	18.0000i		−	1.13615i	−0.822977	−	0.568075i	$-0.807688\pi$
$251$		−	18.0000i		−	1.13615i	0.822977	−	0.568075i	$-0.192312\pi$
$252$		−	2.00000i		−	0.125988i
$253$	2.00000			0.125739
$254$	−3.00000	−	3.00000i	−0.188237	−	0.188237i
$255$		0			0
$256$	1.00000			0.0625000
$257$	21.0000	−	21.0000i	1.30994	−	1.30994i	0.388492	−	0.921452i	$-0.372996\pi$
$257$	21.0000	−	21.0000i	1.30994	−	1.30994i	0.921452	−	0.388492i	$-0.127004\pi$
$258$			2.00000i			0.124515i
$259$	−16.0000			−0.994192
$260$		0			0
$261$	−8.00000			−0.495188
$262$			12.0000i			0.741362i
$263$	3.00000	−	3.00000i	0.184988	−	0.184988i	−0.608537	−	0.793525i	$-0.708243\pi$
$263$	3.00000	−	3.00000i	0.184988	−	0.184988i	0.793525	+	0.608537i	$0.208243\pi$
$264$	−2.00000			−0.123091
$265$		0			0
$266$	−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	$0.0389122\pi$
$269$			4.00000i			0.243884i	−0.992537	+	0.121942i	$0.961088\pi$
$270$		0			0
$271$	3.00000	−	3.00000i	0.182237	−	0.182237i	−0.610093	−	0.792330i	$-0.708868\pi$
$271$	3.00000	−	3.00000i	0.182237	−	0.182237i	0.792330	+	0.610093i	$0.208868\pi$
$272$	1.00000	−	1.00000i	0.0606339	−	0.0606339i
$273$	−2.00000	−	10.0000i	−0.121046	−	0.605228i
$274$		0			0
$275$		0			0
$276$	−2.00000			−0.120386
$277$	−11.0000	+	11.0000i	−0.660926	+	0.660926i	−0.955598	−	0.294672i	$-0.904789\pi$
$277$	−11.0000	+	11.0000i	−0.660926	+	0.660926i	0.294672	+	0.955598i	$0.404789\pi$
$278$	−2.00000			−0.119952
$279$	−1.00000	+	1.00000i	−0.0598684	+	0.0598684i
$280$		0			0
$281$	9.00000	−	9.00000i	0.536895	−	0.536895i	−0.385721	−	0.922616i	$-0.626047\pi$
$281$	9.00000	−	9.00000i	0.536895	−	0.536895i	0.922616	+	0.385721i	$0.126047\pi$
$282$	−10.0000	−	10.0000i	−0.595491	−	0.595491i
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	0.994679	−	0.103022i	$-0.0328511\pi$
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	−0.103022	+	0.994679i	$0.532851\pi$
$284$	−5.00000	−	5.00000i	−0.296695	−	0.296695i
$285$		0			0
$286$	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
$290$		0			0
$291$	−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
$295$		0			0
$296$			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
$300$		0			0
$301$	−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
$305$		0			0
$306$	−1.00000	+	1.00000i	−0.0571662	+	0.0571662i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$	10.0000			0.568880
$310$		0			0
$311$			2.00000i			0.113410i	0.998391	+	0.0567048i	$0.0180594\pi$
$311$			2.00000i			0.113410i	−0.998391	+	0.0567048i	$0.981941\pi$
$312$	−5.00000	+	1.00000i	−0.283069	+	0.0566139i
$313$	−9.00000	+	9.00000i	−0.508710	+	0.508710i	−0.914130	−	0.405420i	$-0.867125\pi$
$313$	−9.00000	+	9.00000i	−0.508710	+	0.508710i	0.405420	+	0.914130i	$0.367125\pi$
$314$	−15.0000	+	15.0000i	−0.846499	+	0.846499i
$315$		0			0
$316$			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
$320$		0			0
$321$	−2.00000			−0.111629
$322$	2.00000	−	2.00000i	0.111456	−	0.111456i
$323$			6.00000i			0.333849i
$324$	−5.00000			−0.277778
$325$		0			0
$326$	20.0000			1.10770
$327$		−	10.0000i		−	0.553001i
$328$	−7.00000	+	7.00000i	−0.386510	+	0.386510i
$329$	20.0000			1.10264
$330$		0			0
$331$	21.0000	+	21.0000i	1.15426	+	1.15426i	0.985689	+	0.168576i	$0.0539168\pi$
$331$	21.0000	+	21.0000i	1.15426	+	1.15426i	0.168576	+	0.985689i	$0.446083\pi$
$332$	−18.0000			−0.987878
$333$		−	8.00000i		−	0.438397i
$334$		−	14.0000i		−	0.766046i
$335$		0			0
$336$	−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	$0.188310\pi$
$338$	12.0000	−	5.00000i	0.652714	−	0.271964i
$339$			6.00000i			0.325875i
$340$		0			0
$341$	−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
$345$		0			0
$346$	−9.00000	+	9.00000i	−0.483843	+	0.483843i
$347$	5.00000	+	5.00000i	0.268414	+	0.268414i	0.828461	−	0.560047i	$-0.189217\pi$
$347$	5.00000	+	5.00000i	0.268414	+	0.268414i	−0.560047	+	0.828461i	$0.689217\pi$
$348$	8.00000	+	8.00000i	0.428845	+	0.428845i
$349$	−21.0000	−	21.0000i	−1.12410	−	1.12410i	−0.991118	−	0.132986i	$-0.957543\pi$
$349$	−21.0000	−	21.0000i	−1.12410	−	1.12410i	−0.132986	−	0.991118i	$-0.542457\pi$
$350$		0			0
$351$	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	$-0.533948\pi$
$353$	−4.00000			−0.212899			−0.106449	+	0.994318i	$0.533948\pi$
$354$			18.0000i			0.956689i
$355$		0			0
$356$	−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	0.562742	−	0.826632i	$-0.309746\pi$
$359$	−5.00000	−	5.00000i	−0.263890	−	0.263890i	−0.826632	+	0.562742i	$0.809746\pi$
$360$		0			0
$361$			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
$365$		0			0
$366$	−2.00000	−	2.00000i	−0.104542	−	0.104542i
$367$	21.0000	+	21.0000i	1.09619	+	1.09619i	0.994852	+	0.101339i	$0.0323127\pi$
$367$	21.0000	+	21.0000i	1.09619	+	1.09619i	0.101339	+	0.994852i	$0.467687\pi$
$368$	−1.00000	−	1.00000i	−0.0521286	−	0.0521286i
$369$	7.00000	−	7.00000i	0.364405	−	0.364405i
$370$		0			0
$371$	−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	$-0.808601\pi$
$373$	−5.00000	+	5.00000i	−0.258890	+	0.258890i	0.565712	+	0.824603i	$0.308601\pi$
$374$	−2.00000			−0.103418
$375$		0			0
$376$		−	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	−0.202057	+	0.979374i	$0.564763\pi$
$379$	−23.0000	+	23.0000i	−1.18143	+	1.18143i	−0.979374	+	0.202057i	$0.935237\pi$
$380$		0			0
$381$		−	6.00000i		−	0.307389i
$382$			8.00000i			0.409316i
$383$	−18.0000			−0.919757			−0.459879	−	0.887982i	$-0.652107\pi$
$383$	−18.0000			−0.919757			−0.459879	+	0.887982i	$0.652107\pi$
$384$	1.00000	+	1.00000i	0.0510310	+	0.0510310i
$385$		0			0
$386$	−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	$0.483854\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$			3.00000i			0.151523i
$393$	−12.0000	+	12.0000i	−0.605320	+	0.605320i
$394$	6.00000			0.302276
$395$		0			0
$396$	1.00000	+	1.00000i	0.0502519	+	0.0502519i
$397$	−8.00000			−0.401508			−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000			−0.401508			−0.200754	+	0.979642i	$0.564339\pi$
$398$			24.0000i			1.20301i
$399$		−	12.0000i		−	0.600751i
$400$		0			0
$401$	−19.0000	+	19.0000i	−0.948815	+	0.948815i	−0.998752	−	0.0499376i	$-0.984098\pi$
$401$	−19.0000	+	19.0000i	−0.948815	+	0.948815i	0.0499376	+	0.998752i	$0.484098\pi$
$402$	12.0000	−	12.0000i	0.598506	−	0.598506i
$403$	−5.00000	+	1.00000i	−0.249068	+	0.0498135i
$404$		−	12.0000i		−	0.597022i
$405$		0			0
$406$	−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	−0.893695	−	0.448674i	$-0.851896\pi$
$409$	−9.00000	+	9.00000i	−0.445021	+	0.445021i	0.448674	+	0.893695i	$0.351896\pi$
$410$		0			0
$411$		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
$415$		0			0
$416$	−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	$-0.819412\pi$
$419$		−	22.0000i		−	1.07477i	0.843337	−	0.537385i	$-0.180588\pi$
$420$		0			0
$421$	9.00000	+	9.00000i	0.438633	+	0.438633i	0.891552	−	0.452919i	$-0.149617\pi$
$421$	9.00000	+	9.00000i	0.438633	+	0.438633i	−0.452919	+	0.891552i	$0.649617\pi$
$422$		−	12.0000i		−	0.584151i
$423$			10.0000i			0.486217i
$424$	1.00000	+	1.00000i	0.0485643	+	0.0485643i
$425$		0			0
$426$		−	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
$430$		0			0
$431$	−15.0000	−	15.0000i	−0.722525	−	0.722525i	0.246594	−	0.969119i	$-0.420689\pi$
$431$	−15.0000	−	15.0000i	−0.722525	−	0.722525i	−0.969119	+	0.246594i	$0.920689\pi$
$432$	−4.00000	−	4.00000i	−0.192450	−	0.192450i
$433$	9.00000	+	9.00000i	0.432512	+	0.432512i	0.889482	−	0.456970i	$-0.151065\pi$
$433$	9.00000	+	9.00000i	0.432512	+	0.432512i	−0.456970	+	0.889482i	$0.651065\pi$
$434$	−2.00000	+	2.00000i	−0.0960031	+	0.0960031i
$435$		0			0
$436$	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	$0.223411\pi$
$440$		0			0
$441$		−	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	$-0.943493\pi$
$443$	−17.0000	+	17.0000i	−0.807694	+	0.807694i	0.176590	+	0.984284i	$0.443493\pi$
$444$	−8.00000	+	8.00000i	−0.379663	+	0.379663i
$445$		0			0
$446$		−	18.0000i		−	0.852325i
$447$		−	2.00000i		−	0.0945968i
$448$	−2.00000			−0.0944911
$449$	−13.0000	−	13.0000i	−0.613508	−	0.613508i	0.330350	−	0.943858i	$-0.392833\pi$
$449$	−13.0000	−	13.0000i	−0.613508	−	0.613508i	−0.943858	+	0.330350i	$0.892833\pi$
$450$		0			0
$451$	14.0000			0.659234
$452$	−3.00000	+	3.00000i	−0.141108	+	0.141108i
$453$			6.00000i			0.281905i
$454$	12.0000			0.563188
$455$		0			0
$456$	−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
$460$		0			0
$461$	−11.0000	−	11.0000i	−0.512321	−	0.512321i	0.402916	−	0.915237i	$-0.367997\pi$
$461$	−11.0000	−	11.0000i	−0.512321	−	0.512321i	−0.915237	+	0.402916i	$0.867997\pi$
$462$	4.00000			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
$465$		0			0
$466$	−1.00000	+	1.00000i	−0.0463241	+	0.0463241i
$467$	−7.00000	+	7.00000i	−0.323921	+	0.323921i	−0.850269	−	0.526348i	$-0.823561\pi$
$467$	−7.00000	+	7.00000i	−0.323921	+	0.323921i	0.526348	+	0.850269i	$0.323561\pi$
$468$	3.00000	+	2.00000i	0.138675	+	0.0924500i
$469$			24.0000i			1.10822i
$470$		0			0
$471$	−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
$475$		0			0
$476$	−2.00000	+	2.00000i	−0.0916698	+	0.0916698i
$477$	−1.00000	−	1.00000i	−0.0457869	−	0.0457869i
$478$	1.00000	+	1.00000i	0.0457389	+	0.0457389i
$479$	19.0000	+	19.0000i	0.868132	+	0.868132i	0.992266	−	0.124133i	$-0.0396151\pi$
$479$	19.0000	+	19.0000i	0.868132	+	0.868132i	−0.124133	+	0.992266i	$0.539615\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	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
$490$		0			0
$491$			38.0000i			1.71492i	0.514554	+	0.857458i	$0.327958\pi$
$491$			38.0000i			1.71492i	−0.514554	+	0.857458i	$0.672042\pi$
$492$	−14.0000			−0.631169
$493$	8.00000	+	8.00000i	0.360302	+	0.360302i
$494$	15.0000	−	3.00000i	0.674882	−	0.134976i
$495$		0			0
$496$	1.00000	+	1.00000i	0.0449013	+	0.0449013i
$497$	10.0000	+	10.0000i	0.448561	+	0.448561i
$498$	−18.0000	−	18.0000i	−0.806599	−	0.806599i
$499$	−19.0000	+	19.0000i	−0.850557	+	0.850557i	−0.990202	−	0.139645i	$-0.955404\pi$
$499$	−19.0000	+	19.0000i	−0.850557	+	0.850557i	0.139645	+	0.990202i	$0.455404\pi$
$500$		0			0
$501$	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	$-0.593198\pi$
$503$	15.0000	−	15.0000i	0.668817	−	0.668817i	0.957442	+	0.288625i	$0.0931982\pi$
$504$	2.00000			0.0890871
$505$		0			0
$506$			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	−0.728922	−	0.684597i	$-0.759978\pi$
$509$	−1.00000	+	1.00000i	−0.0443242	+	0.0443242i	0.684597	+	0.728922i	$0.259978\pi$
$510$		0			0
$511$			12.0000i			0.530849i
$512$			1.00000i			0.0441942i
$513$	24.0000			1.05963
$514$	21.0000	+	21.0000i	0.926270	+	0.926270i
$515$		0			0
$516$	−2.00000			−0.0880451
$517$	−10.0000	+	10.0000i	−0.439799	+	0.439799i
$518$		−	16.0000i		−	0.703000i
$519$	−18.0000			−0.790112
$520$		0			0
$521$	−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	$-0.596488\pi$
$523$	15.0000	−	15.0000i	0.655904	−	0.655904i	0.954408	+	0.298504i	$0.0964877\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	3.00000	+	3.00000i	0.130806	+	0.130806i
$527$	2.00000			0.0871214
$528$		−	2.00000i		−	0.0870388i
$529$		−	21.0000i		−	0.913043i
$530$		0			0
$531$	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
$535$		0			0
$536$	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
$540$		0			0
$541$	−27.0000	+	27.0000i	−1.16082	+	1.16082i	−0.176524	+	0.984296i	$0.556485\pi$
$541$	−27.0000	+	27.0000i	−1.16082	+	1.16082i	−0.984296	+	0.176524i	$0.943515\pi$
$542$	3.00000	+	3.00000i	0.128861	+	0.128861i
$543$	16.0000	+	16.0000i	0.686626	+	0.686626i
$544$	1.00000	+	1.00000i	0.0428746	+	0.0428746i
$545$		0			0
$546$	10.0000	−	2.00000i	0.427960	−	0.0855921i
$547$	−23.0000	−	23.0000i	−0.983409	−	0.983409i	0.0164556	−	0.999865i	$-0.494762\pi$
$547$	−23.0000	−	23.0000i	−0.983409	−	0.983409i	−0.999865	+	0.0164556i	$0.994762\pi$
$548$		0			0
$549$			2.00000i			0.0853579i
$550$		0			0
$551$	−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
$555$		0			0
$556$		−	2.00000i		−	0.0848189i
$557$	32.0000			1.35588			0.677942	−	0.735116i	$-0.262872\pi$
$557$	32.0000			1.35588			0.677942	+	0.735116i	$0.262872\pi$
$558$	−1.00000	−	1.00000i	−0.0423334	−	0.0423334i
$559$	5.00000	−	1.00000i	0.211477	−	0.0422955i
$560$		0			0
$561$	−2.00000	−	2.00000i	−0.0844401	−	0.0844401i
$562$	9.00000	+	9.00000i	0.379642	+	0.379642i
$563$	31.0000	+	31.0000i	1.30649	+	1.30649i	0.923928	+	0.382566i	$0.124960\pi$
$563$	31.0000	+	31.0000i	1.30649	+	1.30649i	0.382566	+	0.923928i	$0.375040\pi$
$564$	10.0000	−	10.0000i	0.421076	−	0.421076i
$565$		0			0
$566$	−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	$0.316534\pi$
$570$		0			0
$571$			22.0000i			0.920671i	0.887745	+	0.460336i	$0.152271\pi$
$571$			22.0000i			0.920671i	−0.887745	+	0.460336i	$0.847729\pi$
$572$	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
$575$		0			0
$576$		−	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
$580$		0			0
$581$	36.0000			1.49353
$582$	14.0000	−	14.0000i	0.580319	−	0.580319i
$583$		−	2.00000i		−	0.0828315i
$584$	6.00000			0.248282
$585$		0			0
$586$	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
$590$		0			0
$591$	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
$595$		0			0
$596$	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	$-0.821754\pi$
$599$		−	26.0000i		−	1.06233i	0.847268	−	0.531166i	$-0.178246\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	12.0000	−	12.0000i	0.487467	−	0.487467i
$607$	9.00000	+	9.00000i	0.365299	+	0.365299i	0.865759	−	0.500461i	$-0.166836\pi$
$607$	9.00000	+	9.00000i	0.365299	+	0.365299i	−0.500461	+	0.865759i	$0.666836\pi$
$608$	−3.00000	−	3.00000i	−0.121666	−	0.121666i
$609$	−16.0000	−	16.0000i	−0.648353	−	0.648353i
$610$		0			0
$611$	−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	$-0.525741\pi$
$613$	−4.00000			−0.161558			−0.0807792	+	0.996732i	$0.525741\pi$
$614$		−	10.0000i		−	0.403567i
$615$		0			0
$616$	2.00000	+	2.00000i	0.0805823	+	0.0805823i
$617$			38.0000i			1.52982i	0.644136	+	0.764911i	$0.277217\pi$
$617$			38.0000i			1.52982i	−0.644136	+	0.764911i	$0.722783\pi$
$618$			10.0000i			0.402259i
$619$	−9.00000	−	9.00000i	−0.361741	−	0.361741i	0.502713	−	0.864453i	$-0.332335\pi$
$619$	−9.00000	−	9.00000i	−0.361741	−	0.361741i	−0.864453	+	0.502713i	$0.832335\pi$
$620$		0			0
$621$			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
$625$		0			0
$626$	−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
$630$		0			0
$631$	23.0000	−	23.0000i	0.915616	−	0.915616i	−0.0810911	−	0.996707i	$-0.525840\pi$
$631$	23.0000	−	23.0000i	0.915616	−	0.915616i	0.996707	+	0.0810911i	$0.0258405\pi$
$632$	−10.0000			−0.397779
$633$	12.0000	−	12.0000i	0.476957	−	0.476957i
$634$	2.00000			0.0794301
$635$		0			0
$636$			2.00000i			0.0793052i
$637$	6.00000	−	9.00000i	0.237729	−	0.356593i
$638$	8.00000	−	8.00000i	0.316723	−	0.316723i
$639$	−5.00000	+	5.00000i	−0.197797	+	0.197797i
$640$		0			0
$641$			24.0000i			0.947943i	0.880540	+	0.473972i	$0.157180\pi$
$641$			24.0000i			0.947943i	−0.880540	+	0.473972i	$0.842820\pi$
$642$		−	2.00000i		−	0.0789337i
$643$	10.0000			0.394362			0.197181	−	0.980367i	$-0.436821\pi$
$643$	10.0000			0.394362			0.197181	+	0.980367i	$0.436821\pi$
$644$	2.00000	+	2.00000i	0.0788110	+	0.0788110i
$645$		0			0
$646$	−6.00000			−0.236067
$647$	13.0000	−	13.0000i	0.511083	−	0.511083i	−0.403775	−	0.914858i	$-0.632302\pi$
$647$	13.0000	−	13.0000i	0.511083	−	0.511083i	0.914858	+	0.403775i	$0.132302\pi$
$648$		−	5.00000i		−	0.196419i
$649$	18.0000			0.706562
$650$		0			0
$651$	−4.00000			−0.156772
$652$			20.0000i			0.783260i
$653$	15.0000	−	15.0000i	0.586995	−	0.586995i	−0.349821	−	0.936817i	$-0.613758\pi$
$653$	15.0000	−	15.0000i	0.586995	−	0.586995i	0.936817	+	0.349821i	$0.113758\pi$
$654$	10.0000			0.391031
$655$		0			0
$656$	−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	$-0.734762\pi$
$659$		−	38.0000i		−	1.48027i	0.672458	−	0.740135i	$-0.265238\pi$
$660$		0			0
$661$	13.0000	−	13.0000i	0.505641	−	0.505641i	−0.407544	−	0.913186i	$-0.633615\pi$
$661$	13.0000	−	13.0000i	0.505641	−	0.505641i	0.913186	+	0.407544i	$0.133615\pi$
$662$	−21.0000	+	21.0000i	−0.816188	+	0.816188i
$663$	−6.00000	−	4.00000i	−0.233021	−	0.155347i
$664$		−	18.0000i		−	0.698535i
$665$		0			0
$666$	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
$670$		0			0
$671$	−2.00000	+	2.00000i	−0.0772091	+	0.0772091i
$672$	−2.00000	−	2.00000i	−0.0771517	−	0.0771517i
$673$	17.0000	+	17.0000i	0.655302	+	0.655302i	0.954265	−	0.298963i	$-0.0966407\pi$
$673$	17.0000	+	17.0000i	0.655302	+	0.655302i	−0.298963	+	0.954265i	$0.596641\pi$
$674$	5.00000	+	5.00000i	0.192593	+	0.192593i
$675$		0			0
$676$	5.00000	+	12.0000i	0.192308	+	0.461538i
$677$	−13.0000	−	13.0000i	−0.499631	−	0.499631i	0.411692	−	0.911323i	$-0.364938\pi$
$677$	−13.0000	−	13.0000i	−0.499631	−	0.499631i	−0.911323	+	0.411692i	$0.864938\pi$
$678$	−6.00000			−0.230429
$679$			28.0000i			1.07454i
$680$		0			0
$681$	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
$690$		0			0
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	0.982919	−	0.184041i	$-0.0589179\pi$
$691$	21.0000	+	21.0000i	0.798878	+	0.798878i	−0.184041	+	0.982919i	$0.558918\pi$
$692$	−9.00000	−	9.00000i	−0.342129	−	0.342129i
$693$	−2.00000	−	2.00000i	−0.0759737	−	0.0759737i
$694$	−5.00000	+	5.00000i	−0.189797	+	0.189797i
$695$		0			0
$696$	−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
$700$		0			0
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$	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
$705$		0			0
$706$		−	4.00000i		−	0.150542i
$707$			24.0000i			0.902613i
$708$	−18.0000			−0.676481
$709$	−33.0000	−	33.0000i	−1.23934	−	1.23934i	−0.960271	−	0.279070i	$-0.909974\pi$
$709$	−33.0000	−	33.0000i	−1.23934	−	1.23934i	−0.279070	−	0.960271i	$-0.590026\pi$
$710$		0			0
$711$	10.0000			0.375029
$712$	11.0000	−	11.0000i	0.412242	−	0.412242i
$713$		−	2.00000i		−	0.0749006i
$714$	−4.00000			−0.149696
$715$		0			0
$716$	−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	$0.647694\pi$
$720$		0			0
$721$	−10.0000	−	10.0000i	−0.372419	−	0.372419i
$722$	−1.00000			−0.0372161
$723$			2.00000i			0.0743808i
$724$			16.0000i			0.594635i
$725$		0			0
$726$	9.00000	−	9.00000i	0.334021	−	0.334021i
$727$	1.00000	−	1.00000i	0.0370879	−	0.0370879i	−0.688320	−	0.725408i	$-0.741651\pi$
$727$	1.00000	−	1.00000i	0.0370879	−	0.0370879i	0.725408	+	0.688320i	$0.241651\pi$
$728$	6.00000	+	4.00000i	0.222375	+	0.148250i
$729$			29.0000i			1.07407i
$730$		0			0
$731$	−2.00000			−0.0739727
$732$	2.00000	−	2.00000i	0.0739221	−	0.0739221i
$733$	−20.0000			−0.738717			−0.369358	−	0.929287i	$-0.620423\pi$
$733$	−20.0000			−0.738717			−0.369358	+	0.929287i	$0.620423\pi$
$734$	−21.0000	+	21.0000i	−0.775124	+	0.775124i
$735$		0			0
$736$	1.00000	−	1.00000i	0.0368605	−	0.0368605i
$737$	−12.0000	−	12.0000i	−0.442026	−	0.442026i
$738$	7.00000	+	7.00000i	0.257674	+	0.257674i
$739$	−5.00000	−	5.00000i	−0.183928	−	0.183928i	0.609137	−	0.793065i	$-0.291516\pi$
$739$	−5.00000	−	5.00000i	−0.183928	−	0.183928i	−0.793065	+	0.609137i	$0.791516\pi$
$740$		0			0
$741$	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	$-0.607109\pi$
$743$	−18.0000			−0.660356			−0.330178	+	0.943919i	$0.607109\pi$
$744$			2.00000i			0.0733236i
$745$		0			0
$746$	−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
$750$		0			0
$751$		−	38.0000i		−	1.38664i	−0.720630	−	0.693320i	$-0.756147\pi$
$751$		−	38.0000i		−	1.38664i	0.720630	−	0.693320i	$-0.243853\pi$
$752$	10.0000			0.364662
$753$	18.0000	+	18.0000i	0.655956	+	0.655956i
$754$	16.0000	−	24.0000i	0.582686	−	0.874028i
$755$		0			0
$756$	8.00000	+	8.00000i	0.290957	+	0.290957i
$757$	−25.0000	−	25.0000i	−0.908640	−	0.908640i	0.0875221	−	0.996163i	$-0.472105\pi$
$757$	−25.0000	−	25.0000i	−0.908640	−	0.908640i	−0.996163	+	0.0875221i	$0.972105\pi$
$758$	−23.0000	−	23.0000i	−0.835398	−	0.835398i
$759$	−2.00000	+	2.00000i	−0.0725954	+	0.0725954i
$760$		0			0
$761$	1.00000	−	1.00000i	0.0362500	−	0.0362500i	−0.688749	−	0.724999i	$-0.741840\pi$
$761$	1.00000	−	1.00000i	0.0362500	−	0.0362500i	0.724999	+	0.688749i	$0.241840\pi$
$762$	6.00000			0.217357
$763$	−10.0000	+	10.0000i	−0.362024	+	0.362024i
$764$	−8.00000			−0.289430
$765$		0			0
$766$		−	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	−0.158033	−	0.987434i	$-0.550515\pi$
$769$	23.0000	−	23.0000i	0.829401	−	0.829401i	0.987434	+	0.158033i	$0.0505151\pi$
$770$		0			0
$771$			42.0000i			1.51259i
$772$		−	2.00000i		−	0.0719816i
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$	1.00000	+	1.00000i	0.0359443	+	0.0359443i
$775$		0			0
$776$	14.0000			0.502571
$777$	16.0000	−	16.0000i	0.573997	−	0.573997i
$778$			2.00000i			0.0717035i
$779$	42.0000			1.50481
$780$		0			0
$781$	−10.0000			−0.357828
$782$		−	2.00000i		−	0.0715199i
$783$	32.0000	−	32.0000i	1.14359	−	1.14359i
$784$	−3.00000			−0.107143
$785$		0			0
$786$	−12.0000	−	12.0000i	−0.428026	−	0.428026i
$787$	30.0000			1.06938			0.534692	−	0.845047i	$-0.320428\pi$
$787$	30.0000			1.06938			0.534692	+	0.845047i	$0.320428\pi$
$788$			6.00000i			0.213741i
$789$			6.00000i			0.213606i
$790$		0			0
$791$	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
$795$		0			0
$796$	−24.0000			−0.850657
$797$	5.00000	−	5.00000i	0.177109	−	0.177109i	−0.612985	−	0.790094i	$-0.710032\pi$
$797$	5.00000	−	5.00000i	0.177109	−	0.177109i	0.790094	+	0.612985i	$0.210032\pi$
$798$	12.0000			0.424795
$799$	10.0000	−	10.0000i	0.353775	−	0.353775i
$800$		0			0
$801$	−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
$805$		0			0
$806$	−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	$0.0676553\pi$
$809$			12.0000i			0.421898i	−0.977497	+	0.210949i	$0.932345\pi$
$810$		0			0
$811$	5.00000	+	5.00000i	0.175574	+	0.175574i	0.789423	−	0.613849i	$-0.210380\pi$
$811$	5.00000	+	5.00000i	0.175574	+	0.175574i	−0.613849	+	0.789423i	$0.710380\pi$
$812$		−	16.0000i		−	0.561490i
$813$			6.00000i			0.210429i
$814$	8.00000	+	8.00000i	0.280400	+	0.280400i
$815$		0			0
$816$			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
$820$		0			0
$821$	−19.0000	−	19.0000i	−0.663105	−	0.663105i	0.293006	−	0.956111i	$-0.405344\pi$
$821$	−19.0000	−	19.0000i	−0.663105	−	0.663105i	−0.956111	+	0.293006i	$0.905344\pi$
$822$		0			0
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	0.757458	−	0.652884i	$-0.226441\pi$
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	−0.652884	+	0.757458i	$0.726441\pi$
$824$	−5.00000	+	5.00000i	−0.174183	+	0.174183i
$825$		0			0
$826$	18.0000	−	18.0000i	0.626300	−	0.626300i
$827$	−26.0000			−0.904109			−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000			−0.904109			−0.452054	+	0.891990i	$0.649309\pi$
$828$	−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	$0.601194\pi$
$830$		0			0
$831$		−	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
$835$		0			0
$836$			6.00000i			0.207514i
$837$		−	8.00000i		−	0.276520i
$838$	22.0000			0.759977
$839$	7.00000	+	7.00000i	0.241667	+	0.241667i	0.817539	−	0.575873i	$-0.195338\pi$
$839$	7.00000	+	7.00000i	0.241667	+	0.241667i	−0.575873	+	0.817539i	$0.695338\pi$
$840$		0			0
$841$	−35.0000			−1.20690
$842$	−9.00000	+	9.00000i	−0.310160	+	0.310160i
$843$			18.0000i			0.619953i
$844$	12.0000			0.413057
$845$		0			0
$846$	−10.0000			−0.343807
$847$			18.0000i			0.618487i
$848$	−1.00000	+	1.00000i	−0.0343401	+	0.0343401i
$849$	−30.0000			−1.02960
$850$		0			0
$851$	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
$855$		0			0
$856$	1.00000	−	1.00000i	0.0341793	−	0.0341793i
$857$	−11.0000	+	11.0000i	−0.375753	+	0.375753i	−0.869567	−	0.493814i	$-0.835602\pi$
$857$	−11.0000	+	11.0000i	−0.375753	+	0.375753i	0.493814	+	0.869567i	$0.335602\pi$
$858$	−4.00000	+	6.00000i	−0.136558	+	0.204837i
$859$			34.0000i			1.16007i	0.814593	+	0.580033i	$0.196960\pi$
$859$			34.0000i			1.16007i	−0.814593	+	0.580033i	$0.803040\pi$
$860$		0			0
$861$	28.0000			0.954237
$862$	15.0000	−	15.0000i	0.510902	−	0.510902i
$863$	−34.0000			−1.15737			−0.578687	−	0.815550i	$-0.696435\pi$
$863$	−34.0000			−1.15737			−0.578687	+	0.815550i	$0.696435\pi$
$864$	4.00000	−	4.00000i	0.136083	−	0.136083i
$865$		0			0
$866$	−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
$870$		0			0
$871$	−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
$875$		0			0
$876$	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
$880$		0			0
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$	3.00000			0.101015
$883$	−25.0000	−	25.0000i	−0.841317	−	0.841317i	0.147713	−	0.989030i	$-0.452809\pi$
$883$	−25.0000	−	25.0000i	−0.841317	−	0.841317i	−0.989030	+	0.147713i	$0.952809\pi$
$884$	−1.00000	−	5.00000i	−0.0336336	−	0.168168i
$885$		0			0
$886$	−17.0000	−	17.0000i	−0.571126	−	0.571126i
$887$	−19.0000	−	19.0000i	−0.637958	−	0.637958i	0.312094	−	0.950051i	$-0.398970\pi$
$887$	−19.0000	−	19.0000i	−0.637958	−	0.637958i	−0.950051	+	0.312094i	$0.898970\pi$
$888$	−8.00000	−	8.00000i	−0.268462	−	0.268462i
$889$	−6.00000	+	6.00000i	−0.201234	+	0.201234i
$890$		0			0
$891$	−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
$895$		0			0
$896$		−	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
$900$		0			0
$901$			2.00000i			0.0666297i
$902$			14.0000i			0.466149i
$903$	4.00000			0.133112
$904$	−3.00000	−	3.00000i	−0.0997785	−	0.0997785i
$905$		0			0
$906$	−6.00000			−0.199337
$907$	−7.00000	+	7.00000i	−0.232431	+	0.232431i	−0.813707	−	0.581276i	$-0.802554\pi$
$907$	−7.00000	+	7.00000i	−0.232431	+	0.232431i	0.581276	+	0.813707i	$0.302554\pi$
$908$			12.0000i			0.398234i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	−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
$915$		0			0
$916$	−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	$0.0741699\pi$
$919$			14.0000i			0.461817i	−0.972975	+	0.230909i	$0.925830\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	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	−0.887440	−	0.460924i	$-0.847518\pi$
$929$	−13.0000	+	13.0000i	−0.426516	+	0.426516i	0.460924	+	0.887440i	$0.347518\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$	−2.00000	+	3.00000i	−0.0653720	+	0.0980581i
$937$	−9.00000	−	9.00000i	−0.294017	−	0.294017i	0.544648	−	0.838665i	$-0.316663\pi$
$937$	−9.00000	−	9.00000i	−0.294017	−	0.294017i	−0.838665	+	0.544648i	$0.816663\pi$
$938$	−24.0000			−0.783628
$939$		−	18.0000i		−	0.587408i
$940$		0			0
$941$	17.0000	+	17.0000i	0.554184	+	0.554184i	0.927646	−	0.373462i	$-0.121829\pi$
$941$	17.0000	+	17.0000i	0.554184	+	0.554184i	−0.373462	+	0.927646i	$0.621829\pi$
$942$		−	30.0000i		−	0.977453i
$943$			14.0000i			0.455903i
$944$	−9.00000	−	9.00000i	−0.292925	−	0.292925i
$945$		0			0
$946$			2.00000i			0.0650256i
$947$	−10.0000			−0.324956			−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000			−0.324956			−0.162478	+	0.986712i	$0.551949\pi$
$948$	−10.0000	−	10.0000i	−0.324785	−	0.324785i
$949$	−18.0000	−	12.0000i	−0.584305	−	0.389536i
$950$		0			0
$951$	2.00000	+	2.00000i	0.0648544	+	0.0648544i
$952$	−2.00000	−	2.00000i	−0.0648204	−	0.0648204i
$953$	5.00000	+	5.00000i	0.161966	+	0.161966i	0.783437	−	0.621471i	$-0.213465\pi$
$953$	5.00000	+	5.00000i	0.161966	+	0.161966i	−0.621471	+	0.783437i	$0.713465\pi$
$954$	1.00000	−	1.00000i	0.0323762	−	0.0323762i
$955$		0			0
$956$	−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
$960$		0			0
$961$		−	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
$965$		0			0
$966$			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
$970$		0			0
$971$	−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
$975$		0			0
$976$	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
$980$		0			0
$981$	−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
$985$		0			0
$986$	−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
$990$		0			0
$991$	−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
$995$		0			0
$996$	18.0000	−	18.0000i	0.570352	−	0.570352i
$997$	−13.0000	−	13.0000i	−0.411714	−	0.411714i	0.470621	−	0.882335i	$-0.344030\pi$
$997$	−13.0000	−	13.0000i	−0.411714	−	0.411714i	−0.882335	+	0.470621i	$0.844030\pi$
$998$	−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	650.2.j.a.307.1		2
5.2	odd	4		130.2.g.b.73.1	yes	2
5.3	odd	4		650.2.g.c.593.1		2
5.4	even	2		130.2.j.c.47.1	yes	2
13.5	odd	4		650.2.g.c.57.1		2
15.2	even	4		1170.2.m.b.73.1		2
15.14	odd	2		1170.2.w.a.307.1		2
20.7	even	4		1040.2.bg.b.593.1		2
20.19	odd	2		1040.2.cd.c.177.1		2
65.18	even	4	inner	650.2.j.a.343.1		2
65.44	odd	4		130.2.g.b.57.1	✓	2
65.57	even	4		130.2.j.c.83.1	yes	2
195.44	even	4		1170.2.m.b.577.1		2
195.122	odd	4		1170.2.w.a.343.1		2
260.187	odd	4		1040.2.cd.c.993.1		2
260.239	even	4		1040.2.bg.b.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.b.57.1	✓	2	65.44	odd	4
130.2.g.b.73.1	yes	2	5.2	odd	4
130.2.j.c.47.1	yes	2	5.4	even	2
130.2.j.c.83.1	yes	2	65.57	even	4
650.2.g.c.57.1		2	13.5	odd	4
650.2.g.c.593.1		2	5.3	odd	4
650.2.j.a.307.1		2	1.1	even	1	trivial
650.2.j.a.343.1		2	65.18	even	4	inner
1040.2.bg.b.577.1		2	260.239	even	4
1040.2.bg.b.593.1		2	20.7	even	4
1040.2.cd.c.177.1		2	20.19	odd	2
1040.2.cd.c.993.1		2	260.187	odd	4
1170.2.m.b.73.1		2	15.2	even	4
1170.2.m.b.577.1		2	195.44	even	4
1170.2.w.a.307.1		2	15.14	odd	2
1170.2.w.a.343.1		2	195.122	odd	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.j (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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