LMFDB - Embedded newform 185.2.f.a.142.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(43,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("185.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			142.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	185.142
Dual form			185.2.f.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	−0.934172	+	0.356822i	$0.883860\pi$
$4$	1.00000			0.500000
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$	−1.00000	+	1.00000i	−0.408248	+	0.408248i
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.144370	−	0.989524i	$-0.546115\pi$
$8$		−	3.00000i		−	1.06066i
$9$		−	1.00000i		−	0.333333i
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	−1.00000	−	1.00000i	−0.288675	−	0.288675i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−3.00000	+	3.00000i	−0.801784	+	0.801784i
$15$	3.00000	+	1.00000i	0.774597	+	0.258199i
$16$	−1.00000			−0.250000
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	−1.00000			−0.235702
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$	−2.00000	+	1.00000i	−0.447214	+	0.223607i
$21$			6.00000i			1.30931i
$22$	2.00000			0.426401
$23$			8.00000i			1.66812i	0.551677	+	0.834058i	$0.313988\pi$
$23$			8.00000i			1.66812i	−0.551677	+	0.834058i	$0.686012\pi$
$24$	−3.00000	+	3.00000i	−0.612372	+	0.612372i
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	−2.00000			−0.392232
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$	−3.00000	−	3.00000i	−0.566947	−	0.566947i
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.371391	−	0.928477i	$-0.378881\pi$
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.928477	−	0.371391i	$-0.121119\pi$
$30$	1.00000	−	3.00000i	0.182574	−	0.547723i
$31$	3.00000	+	3.00000i	0.538816	+	0.538816i	0.923181	−	0.384365i	$-0.125580\pi$
$31$	3.00000	+	3.00000i	0.538816	+	0.538816i	−0.384365	+	0.923181i	$0.625580\pi$
$32$		−	5.00000i		−	0.883883i
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$		−	4.00000i		−	0.685994i
$35$	9.00000	+	3.00000i	1.52128	+	0.507093i
$36$		−	1.00000i		−	0.166667i
$37$	6.00000	−	1.00000i	0.986394	−	0.164399i
$37$	6.00000	−	1.00000i	0.986394	−	0.164399i
$38$	−3.00000	+	3.00000i	−0.486664	+	0.486664i
$39$	−2.00000	+	2.00000i	−0.320256	+	0.320256i
$40$	3.00000	+	6.00000i	0.474342	+	0.948683i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	6.00000			0.925820
$43$		−	12.0000i		−	1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$		−	12.0000i		−	1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$			2.00000i			0.301511i
$45$	1.00000	+	2.00000i	0.149071	+	0.298142i
$46$	8.00000			1.17954
$47$	5.00000	+	5.00000i	0.729325	+	0.729325i	0.970485	−	0.241160i	$-0.0775280\pi$
$47$	5.00000	+	5.00000i	0.729325	+	0.729325i	−0.241160	+	0.970485i	$0.577528\pi$
$48$	1.00000	+	1.00000i	0.144338	+	0.144338i
$49$			11.0000i			1.57143i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	−4.00000	−	4.00000i	−0.560112	−	0.560112i
$52$		−	2.00000i		−	0.277350i
$53$	−3.00000	+	3.00000i	−0.412082	+	0.412082i	−0.882463	−	0.470381i	$-0.844116\pi$
$53$	−3.00000	+	3.00000i	−0.412082	+	0.412082i	0.470381	+	0.882463i	$0.344116\pi$
$54$	4.00000	+	4.00000i	0.544331	+	0.544331i
$55$	−2.00000	−	4.00000i	−0.269680	−	0.539360i
$56$	−9.00000	+	9.00000i	−1.20268	+	1.20268i
$57$			6.00000i			0.794719i
$58$	−7.00000	−	7.00000i	−0.919145	−	0.919145i
$59$	−7.00000	−	7.00000i	−0.911322	−	0.911322i	0.0850540	−	0.996376i	$-0.472894\pi$
$59$	−7.00000	−	7.00000i	−0.911322	−	0.911322i	−0.996376	+	0.0850540i	$0.972894\pi$
$60$	3.00000	+	1.00000i	0.387298	+	0.129099i
$61$	1.00000	+	1.00000i	0.128037	+	0.128037i	0.768221	−	0.640184i	$-0.221142\pi$
$61$	1.00000	+	1.00000i	0.128037	+	0.128037i	−0.640184	+	0.768221i	$0.721142\pi$
$62$	3.00000	−	3.00000i	0.381000	−	0.381000i
$63$	−3.00000	+	3.00000i	−0.377964	+	0.377964i
$64$	−7.00000			−0.875000
$65$	2.00000	+	4.00000i	0.248069	+	0.496139i
$66$	−2.00000	−	2.00000i	−0.246183	−	0.246183i
$67$	−3.00000	+	3.00000i	−0.366508	+	0.366508i	−0.866202	−	0.499694i	$-0.833446\pi$
$67$	−3.00000	+	3.00000i	−0.366508	+	0.366508i	0.499694	+	0.866202i	$0.333446\pi$
$68$	4.00000			0.485071
$69$	8.00000	−	8.00000i	0.963087	−	0.963087i
$70$	3.00000	−	9.00000i	0.358569	−	1.07571i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	−3.00000			−0.353553
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	0.646160	−	0.763202i	$-0.276374\pi$
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	−0.763202	+	0.646160i	$0.776374\pi$
$74$	−1.00000	−	6.00000i	−0.116248	−	0.697486i
$75$	−7.00000	+	1.00000i	−0.808290	+	0.115470i
$76$	−3.00000	−	3.00000i	−0.344124	−	0.344124i
$77$	6.00000	−	6.00000i	0.683763	−	0.683763i
$78$	2.00000	+	2.00000i	0.226455	+	0.226455i
$79$	−3.00000	−	3.00000i	−0.337526	−	0.337526i	0.517909	−	0.855436i	$-0.326710\pi$
$79$	−3.00000	−	3.00000i	−0.337526	−	0.337526i	−0.855436	+	0.517909i	$0.826710\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$	5.00000			0.555556
$82$		0			0
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	−0.926100	−	0.377279i	$-0.876860\pi$
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	0.377279	+	0.926100i	$0.376860\pi$
$84$			6.00000i			0.654654i
$85$	−8.00000	+	4.00000i	−0.867722	+	0.433861i
$86$	−12.0000			−1.29399
$87$	−14.0000			−1.50096
$88$	6.00000			0.639602
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	−0.920572	−	0.390573i	$-0.872277\pi$
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	0.390573	+	0.920572i	$0.372277\pi$
$90$	2.00000	−	1.00000i	0.210819	−	0.105409i
$91$	−6.00000	+	6.00000i	−0.628971	+	0.628971i
$92$			8.00000i			0.834058i
$93$		−	6.00000i		−	0.622171i
$94$	5.00000	−	5.00000i	0.515711	−	0.515711i
$95$	9.00000	+	3.00000i	0.923381	+	0.307794i
$96$	−5.00000	+	5.00000i	−0.510310	+	0.510310i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	11.0000			1.11117
$99$	2.00000			0.201008
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	−4.00000	+	4.00000i	−0.396059	+	0.396059i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	−6.00000			−0.588348
$105$	−6.00000	−	12.0000i	−0.585540	−	1.17108i
$106$	3.00000	+	3.00000i	0.291386	+	0.291386i
$107$	−3.00000	−	3.00000i	−0.290021	−	0.290021i	0.547068	−	0.837088i	$-0.315744\pi$
$107$	−3.00000	−	3.00000i	−0.290021	−	0.290021i	−0.837088	+	0.547068i	$0.815744\pi$
$108$	−4.00000	+	4.00000i	−0.384900	+	0.384900i
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	0.836031	−	0.548683i	$-0.184871\pi$
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	−0.548683	+	0.836031i	$0.684871\pi$
$110$	−4.00000	+	2.00000i	−0.381385	+	0.190693i
$111$	−7.00000	−	5.00000i	−0.664411	−	0.474579i
$112$	3.00000	+	3.00000i	0.283473	+	0.283473i
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$	6.00000			0.561951
$115$	−8.00000	−	16.0000i	−0.746004	−	1.49201i
$116$	7.00000	−	7.00000i	0.649934	−	0.649934i
$117$	−2.00000			−0.184900
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	−12.0000	−	12.0000i	−1.10004	−	1.10004i
$120$	3.00000	−	9.00000i	0.273861	−	0.821584i
$121$	7.00000			0.636364
$122$	1.00000	−	1.00000i	0.0905357	−	0.0905357i
$123$		0			0
$124$	3.00000	+	3.00000i	0.269408	+	0.269408i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	3.00000	+	3.00000i	0.267261	+	0.267261i
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	0.982878	−	0.184257i	$-0.0589879\pi$
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	−0.184257	+	0.982878i	$0.558988\pi$
$128$		−	3.00000i		−	0.265165i
$129$	−12.0000	+	12.0000i	−1.05654	+	1.05654i
$130$	4.00000	−	2.00000i	0.350823	−	0.175412i
$131$	−5.00000	−	5.00000i	−0.436852	−	0.436852i	0.454099	−	0.890951i	$-0.349961\pi$
$131$	−5.00000	−	5.00000i	−0.436852	−	0.436852i	−0.890951	+	0.454099i	$0.849961\pi$
$132$	2.00000	−	2.00000i	0.174078	−	0.174078i
$133$			18.0000i			1.56080i
$134$	3.00000	+	3.00000i	0.259161	+	0.259161i
$135$	4.00000	−	12.0000i	0.344265	−	1.03280i
$136$		−	12.0000i		−	1.02899i
$137$	−7.00000	−	7.00000i	−0.598050	−	0.598050i	0.341743	−	0.939793i	$-0.388983\pi$
$137$	−7.00000	−	7.00000i	−0.598050	−	0.598050i	−0.939793	+	0.341743i	$0.888983\pi$
$138$	−8.00000	−	8.00000i	−0.681005	−	0.681005i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	9.00000	+	3.00000i	0.760639	+	0.253546i
$141$		−	10.0000i		−	0.842152i
$142$		−	8.00000i		−	0.671345i
$143$	4.00000			0.334497
$144$			1.00000i			0.0833333i
$145$	−7.00000	+	21.0000i	−0.581318	+	1.74396i
$146$	−1.00000	+	1.00000i	−0.0827606	+	0.0827606i
$147$	11.0000	−	11.0000i	0.907265	−	0.907265i
$148$	6.00000	−	1.00000i	0.493197	−	0.0821995i
$149$			16.0000i			1.31077i	0.755295	+	0.655386i	$0.227494\pi$
$149$			16.0000i			1.31077i	−0.755295	+	0.655386i	$0.772506\pi$
$150$	1.00000	+	7.00000i	0.0816497	+	0.571548i
$151$		−	2.00000i		−	0.162758i	−0.996683	−	0.0813788i	$-0.974068\pi$
$151$		−	2.00000i		−	0.162758i	0.996683	−	0.0813788i	$-0.0259324\pi$
$152$	−9.00000	+	9.00000i	−0.729996	+	0.729996i
$153$		−	4.00000i		−	0.323381i
$154$	−6.00000	−	6.00000i	−0.483494	−	0.483494i
$155$	−9.00000	−	3.00000i	−0.722897	−	0.240966i
$156$	−2.00000	+	2.00000i	−0.160128	+	0.160128i
$157$	−3.00000	−	3.00000i	−0.239426	−	0.239426i	0.577186	−	0.816612i	$-0.304151\pi$
$157$	−3.00000	−	3.00000i	−0.239426	−	0.239426i	−0.816612	+	0.577186i	$0.804151\pi$
$158$	−3.00000	+	3.00000i	−0.238667	+	0.238667i
$159$	6.00000			0.475831
$160$	5.00000	+	10.0000i	0.395285	+	0.790569i
$161$	24.0000	−	24.0000i	1.89146	−	1.89146i
$162$		−	5.00000i		−	0.392837i
$163$	10.0000			0.783260			0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000			0.783260			0.391630	+	0.920123i	$0.371911\pi$
$164$		0			0
$165$	−2.00000	+	6.00000i	−0.155700	+	0.467099i
$166$	5.00000	+	5.00000i	0.388075	+	0.388075i
$167$	−6.00000			−0.464294			−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000			−0.464294			−0.232147	+	0.972681i	$0.574575\pi$
$168$	18.0000			1.38873
$169$	9.00000			0.692308
$170$	4.00000	+	8.00000i	0.306786	+	0.613572i
$171$	−3.00000	+	3.00000i	−0.229416	+	0.229416i
$172$		−	12.0000i		−	0.914991i
$173$	−1.00000	−	1.00000i	−0.0760286	−	0.0760286i	0.668070	−	0.744099i	$-0.267121\pi$
$173$	−1.00000	−	1.00000i	−0.0760286	−	0.0760286i	−0.744099	+	0.668070i	$0.767121\pi$
$174$			14.0000i			1.06134i
$175$	−21.0000	+	3.00000i	−1.58745	+	0.226779i
$176$		−	2.00000i		−	0.150756i
$177$			14.0000i			1.05230i
$178$	5.00000	+	5.00000i	0.374766	+	0.374766i
$179$	7.00000	−	7.00000i	0.523205	−	0.523205i	−0.395333	−	0.918538i	$-0.629371\pi$
$179$	7.00000	−	7.00000i	0.523205	−	0.523205i	0.918538	+	0.395333i	$0.129371\pi$
$180$	1.00000	+	2.00000i	0.0745356	+	0.149071i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$	6.00000	+	6.00000i	0.444750	+	0.444750i
$183$		−	2.00000i		−	0.147844i
$184$	24.0000			1.76930
$185$	−11.0000	+	8.00000i	−0.808736	+	0.588172i
$186$	−6.00000			−0.439941
$187$			8.00000i			0.585018i
$188$	5.00000	+	5.00000i	0.364662	+	0.364662i
$189$	24.0000			1.74574
$190$	3.00000	−	9.00000i	0.217643	−	0.652929i
$191$	−11.0000	+	11.0000i	−0.795932	+	0.795932i	−0.982451	−	0.186519i	$-0.940279\pi$
$191$	−11.0000	+	11.0000i	−0.795932	+	0.795932i	0.186519	+	0.982451i	$0.440279\pi$
$192$	7.00000	+	7.00000i	0.505181	+	0.505181i
$193$		−	2.00000i		−	0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$		−	2.00000i		−	0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$			8.00000i			0.574367i
$195$	2.00000	−	6.00000i	0.143223	−	0.429669i
$196$			11.0000i			0.785714i
$197$	1.00000	+	1.00000i	0.0712470	+	0.0712470i	0.741832	−	0.670585i	$-0.233957\pi$
$197$	1.00000	+	1.00000i	0.0712470	+	0.0712470i	−0.670585	+	0.741832i	$0.733957\pi$
$198$		−	2.00000i		−	0.142134i
$199$	15.0000	−	15.0000i	1.06332	−	1.06332i	0.0654671	−	0.997855i	$-0.479146\pi$
$199$	15.0000	−	15.0000i	1.06332	−	1.06332i	0.997855	−	0.0654671i	$-0.0208537\pi$
$200$	−12.0000	−	9.00000i	−0.848528	−	0.636396i
$201$	6.00000			0.423207
$202$		0			0
$203$	−42.0000			−2.94782
$204$	−4.00000	−	4.00000i	−0.280056	−	0.280056i
$205$		0			0
$206$		−	14.0000i		−	0.975426i
$207$	8.00000			0.556038
$208$			2.00000i			0.138675i
$209$	6.00000	−	6.00000i	0.415029	−	0.415029i
$210$	−12.0000	+	6.00000i	−0.828079	+	0.414039i
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−3.00000	+	3.00000i	−0.206041	+	0.206041i
$213$	−8.00000	−	8.00000i	−0.548151	−	0.548151i
$214$	−3.00000	+	3.00000i	−0.205076	+	0.205076i
$215$	12.0000	+	24.0000i	0.818393	+	1.63679i
$216$	12.0000	+	12.0000i	0.816497	+	0.816497i
$217$		−	18.0000i		−	1.22192i
$218$	3.00000	−	3.00000i	0.203186	−	0.203186i
$219$			2.00000i			0.135147i
$220$	−2.00000	−	4.00000i	−0.134840	−	0.269680i
$221$		−	8.00000i		−	0.538138i
$222$	−5.00000	+	7.00000i	−0.335578	+	0.469809i
$223$	−1.00000	+	1.00000i	−0.0669650	+	0.0669650i	−0.739796	−	0.672831i	$-0.765078\pi$
$223$	−1.00000	+	1.00000i	−0.0669650	+	0.0669650i	0.672831	+	0.739796i	$0.265078\pi$
$224$	−15.0000	+	15.0000i	−1.00223	+	1.00223i
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$		−	4.00000i		−	0.266076i
$227$	−2.00000			−0.132745			−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000			−0.132745			−0.0663723	+	0.997795i	$0.521143\pi$
$228$			6.00000i			0.397360i
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$	−16.0000	+	8.00000i	−1.05501	+	0.527504i
$231$	−12.0000			−0.789542
$232$	−21.0000	−	21.0000i	−1.37872	−	1.37872i
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	0.673592	−	0.739104i	$-0.264751\pi$
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	−0.739104	+	0.673592i	$0.764751\pi$
$234$			2.00000i			0.130744i
$235$	−15.0000	−	5.00000i	−0.978492	−	0.326164i
$236$	−7.00000	−	7.00000i	−0.455661	−	0.455661i
$237$			6.00000i			0.389742i
$238$	−12.0000	+	12.0000i	−0.777844	+	0.777844i
$239$	−7.00000	−	7.00000i	−0.452792	−	0.452792i	0.443488	−	0.896280i	$-0.353741\pi$
$239$	−7.00000	−	7.00000i	−0.452792	−	0.452792i	−0.896280	+	0.443488i	$0.853741\pi$
$240$	−3.00000	−	1.00000i	−0.193649	−	0.0645497i
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	−0.674165	−	0.738581i	$-0.735496\pi$
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	0.738581	+	0.674165i	$0.235496\pi$
$242$		−	7.00000i		−	0.449977i
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$	1.00000	+	1.00000i	0.0640184	+	0.0640184i
$245$	−11.0000	−	22.0000i	−0.702764	−	1.40553i
$246$		0			0
$247$	−6.00000	+	6.00000i	−0.381771	+	0.381771i
$248$	9.00000	−	9.00000i	0.571501	−	0.571501i
$249$	10.0000			0.633724
$250$	11.0000	+	2.00000i	0.695701	+	0.126491i
$251$	−5.00000	−	5.00000i	−0.315597	−	0.315597i	0.531476	−	0.847073i	$-0.321638\pi$
$251$	−5.00000	−	5.00000i	−0.315597	−	0.315597i	−0.847073	+	0.531476i	$0.821638\pi$
$252$	−3.00000	+	3.00000i	−0.188982	+	0.188982i
$253$	−16.0000			−1.00591
$254$	9.00000	−	9.00000i	0.564710	−	0.564710i
$255$	12.0000	+	4.00000i	0.751469	+	0.250490i
$256$	−17.0000			−1.06250
$257$	28.0000			1.74659			0.873296	−	0.487190i	$-0.161978\pi$
$257$	28.0000			1.74659			0.873296	+	0.487190i	$0.161978\pi$
$258$	12.0000	+	12.0000i	0.747087	+	0.747087i
$259$	−21.0000	−	15.0000i	−1.30488	−	0.932055i
$260$	2.00000	+	4.00000i	0.124035	+	0.248069i
$261$	−7.00000	−	7.00000i	−0.433289	−	0.433289i
$262$	−5.00000	+	5.00000i	−0.308901	+	0.308901i
$263$	7.00000	+	7.00000i	0.431638	+	0.431638i	0.889185	−	0.457547i	$-0.151272\pi$
$263$	7.00000	+	7.00000i	0.431638	+	0.431638i	−0.457547	+	0.889185i	$0.651272\pi$
$264$	−6.00000	−	6.00000i	−0.369274	−	0.369274i
$265$	3.00000	−	9.00000i	0.184289	−	0.552866i
$266$	18.0000			1.10365
$267$	10.0000			0.611990
$268$	−3.00000	+	3.00000i	−0.183254	+	0.183254i
$269$		−	16.0000i		−	0.975537i	−0.872973	−	0.487769i	$-0.837811\pi$
$269$		−	16.0000i		−	0.975537i	0.872973	−	0.487769i	$-0.162189\pi$
$270$	−12.0000	−	4.00000i	−0.730297	−	0.243432i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	−4.00000			−0.242536
$273$	12.0000			0.726273
$274$	−7.00000	+	7.00000i	−0.422885	+	0.422885i
$275$	8.00000	+	6.00000i	0.482418	+	0.361814i
$276$	8.00000	−	8.00000i	0.481543	−	0.481543i
$277$			26.0000i			1.56219i	0.624413	+	0.781094i	$0.285338\pi$
$277$			26.0000i			1.56219i	−0.624413	+	0.781094i	$0.714662\pi$
$278$			4.00000i			0.239904i
$279$	3.00000	−	3.00000i	0.179605	−	0.179605i
$280$	9.00000	−	27.0000i	0.537853	−	1.61356i
$281$	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			−0.595491
$283$	−22.0000			−1.30776			−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000			−1.30776			−0.653882	+	0.756596i	$0.726861\pi$
$284$	8.00000			0.474713
$285$	−6.00000	−	12.0000i	−0.355409	−	0.710819i
$286$		−	4.00000i		−	0.236525i
$287$		0			0
$288$	−5.00000			−0.294628
$289$	−1.00000			−0.0588235
$290$	21.0000	+	7.00000i	1.23316	+	0.411054i
$291$	8.00000	+	8.00000i	0.468968	+	0.468968i
$292$	−1.00000	−	1.00000i	−0.0585206	−	0.0585206i
$293$	1.00000	−	1.00000i	0.0584206	−	0.0584206i	−0.677293	−	0.735714i	$-0.736847\pi$
$293$	1.00000	−	1.00000i	0.0584206	−	0.0584206i	0.735714	+	0.677293i	$0.236847\pi$
$294$	−11.0000	−	11.0000i	−0.641533	−	0.641533i
$295$	21.0000	+	7.00000i	1.22267	+	0.407556i
$296$	−3.00000	−	18.0000i	−0.174371	−	1.04623i
$297$	−8.00000	−	8.00000i	−0.464207	−	0.464207i
$298$	16.0000			0.926855
$299$	16.0000			0.925304
$300$	−7.00000	+	1.00000i	−0.404145	+	0.0577350i
$301$	−36.0000	+	36.0000i	−2.07501	+	2.07501i
$302$	−2.00000			−0.115087
$303$		0			0
$304$	3.00000	+	3.00000i	0.172062	+	0.172062i
$305$	−3.00000	−	1.00000i	−0.171780	−	0.0572598i
$306$	−4.00000			−0.228665
$307$	9.00000	−	9.00000i	0.513657	−	0.513657i	−0.401988	−	0.915645i	$-0.631681\pi$
$307$	9.00000	−	9.00000i	0.513657	−	0.513657i	0.915645	+	0.401988i	$0.131681\pi$
$308$	6.00000	−	6.00000i	0.341882	−	0.341882i
$309$	−14.0000	−	14.0000i	−0.796432	−	0.796432i
$310$	−3.00000	+	9.00000i	−0.170389	+	0.511166i
$311$	3.00000	+	3.00000i	0.170114	+	0.170114i	0.787030	−	0.616915i	$-0.211618\pi$
$311$	3.00000	+	3.00000i	0.170114	+	0.170114i	−0.616915	+	0.787030i	$0.711618\pi$
$312$	6.00000	+	6.00000i	0.339683	+	0.339683i
$313$			30.0000i			1.69570i	0.530236	+	0.847850i	$0.322103\pi$
$313$			30.0000i			1.69570i	−0.530236	+	0.847850i	$0.677897\pi$
$314$	−3.00000	+	3.00000i	−0.169300	+	0.169300i
$315$	3.00000	−	9.00000i	0.169031	−	0.507093i
$316$	−3.00000	−	3.00000i	−0.168763	−	0.168763i
$317$	−17.0000	+	17.0000i	−0.954815	+	0.954815i	−0.999022	−	0.0442073i	$-0.985924\pi$
$317$	−17.0000	+	17.0000i	−0.954815	+	0.954815i	0.0442073	+	0.999022i	$0.485924\pi$
$318$		−	6.00000i		−	0.336463i
$319$	14.0000	+	14.0000i	0.783850	+	0.783850i
$320$	14.0000	−	7.00000i	0.782624	−	0.391312i
$321$			6.00000i			0.334887i
$322$	−24.0000	−	24.0000i	−1.33747	−	1.33747i
$323$	−12.0000	−	12.0000i	−0.667698	−	0.667698i
$324$	5.00000			0.277778
$325$	−8.00000	−	6.00000i	−0.443760	−	0.332820i
$326$		−	10.0000i		−	0.553849i
$327$		−	6.00000i		−	0.331801i
$328$		0			0
$329$		−	30.0000i		−	1.65395i
$330$	6.00000	+	2.00000i	0.330289	+	0.110096i
$331$	−7.00000	+	7.00000i	−0.384755	+	0.384755i	−0.872812	−	0.488057i	$-0.837706\pi$
$331$	−7.00000	+	7.00000i	−0.384755	+	0.384755i	0.488057	+	0.872812i	$0.337706\pi$
$332$	−5.00000	+	5.00000i	−0.274411	+	0.274411i
$333$	−1.00000	−	6.00000i	−0.0547997	−	0.328798i
$334$			6.00000i			0.328305i
$335$	3.00000	−	9.00000i	0.163908	−	0.491723i
$336$		−	6.00000i		−	0.327327i
$337$	15.0000	−	15.0000i	0.817102	−	0.817102i	−0.168585	−	0.985687i	$-0.553920\pi$
$337$	15.0000	−	15.0000i	0.817102	−	0.817102i	0.985687	+	0.168585i	$0.0539198\pi$
$338$		−	9.00000i		−	0.489535i
$339$	−4.00000	−	4.00000i	−0.217250	−	0.217250i
$340$	−8.00000	+	4.00000i	−0.433861	+	0.216930i
$341$	−6.00000	+	6.00000i	−0.324918	+	0.324918i
$342$	3.00000	+	3.00000i	0.162221	+	0.162221i
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	−36.0000			−1.94099
$345$	−8.00000	+	24.0000i	−0.430706	+	1.29212i
$346$	−1.00000	+	1.00000i	−0.0537603	+	0.0537603i
$347$			4.00000i			0.214731i	0.994220	+	0.107366i	$0.0342415\pi$
$347$			4.00000i			0.214731i	−0.994220	+	0.107366i	$0.965758\pi$
$348$	−14.0000			−0.750479
$349$			32.0000i			1.71292i	0.516213	+	0.856460i	$0.327341\pi$
$349$			32.0000i			1.71292i	−0.516213	+	0.856460i	$0.672659\pi$
$350$	3.00000	+	21.0000i	0.160357	+	1.12250i
$351$	8.00000	+	8.00000i	0.427008	+	0.427008i
$352$	10.0000			0.533002
$353$	32.0000			1.70319			0.851594	−	0.524202i	$-0.175636\pi$
$353$	32.0000			1.70319			0.851594	+	0.524202i	$0.175636\pi$
$354$	14.0000			0.744092
$355$	−16.0000	+	8.00000i	−0.849192	+	0.424596i
$356$	−5.00000	+	5.00000i	−0.264999	+	0.264999i
$357$			24.0000i			1.27021i
$358$	−7.00000	−	7.00000i	−0.369961	−	0.369961i
$359$			34.0000i			1.79445i	0.441572	+	0.897226i	$0.354421\pi$
$359$			34.0000i			1.79445i	−0.441572	+	0.897226i	$0.645579\pi$
$360$	6.00000	−	3.00000i	0.316228	−	0.158114i
$361$		−	1.00000i		−	0.0526316i
$362$		−	10.0000i		−	0.525588i
$363$	−7.00000	−	7.00000i	−0.367405	−	0.367405i
$364$	−6.00000	+	6.00000i	−0.314485	+	0.314485i
$365$	3.00000	+	1.00000i	0.157027	+	0.0523424i
$366$	−2.00000			−0.104542
$367$	17.0000	+	17.0000i	0.887393	+	0.887393i	0.994272	−	0.106879i	$-0.0340858\pi$
$367$	17.0000	+	17.0000i	0.887393	+	0.887393i	−0.106879	+	0.994272i	$0.534086\pi$
$368$		−	8.00000i		−	0.417029i
$369$		0			0
$370$	8.00000	+	11.0000i	0.415900	+	0.571863i
$371$	18.0000			0.934513
$372$		−	6.00000i		−	0.311086i
$373$	3.00000	+	3.00000i	0.155334	+	0.155334i	0.780496	−	0.625161i	$-0.214967\pi$
$373$	3.00000	+	3.00000i	0.155334	+	0.155334i	−0.625161	+	0.780496i	$0.714967\pi$
$374$	8.00000			0.413670
$375$	13.0000	−	9.00000i	0.671317	−	0.464758i
$376$	15.0000	−	15.0000i	0.773566	−	0.773566i
$377$	−14.0000	−	14.0000i	−0.721037	−	0.721037i
$378$		−	24.0000i		−	1.23443i
$379$			14.0000i			0.719132i	0.933120	+	0.359566i	$0.117075\pi$
$379$			14.0000i			0.719132i	−0.933120	+	0.359566i	$0.882925\pi$
$380$	9.00000	+	3.00000i	0.461690	+	0.153897i
$381$		−	18.0000i		−	0.922168i
$382$	11.0000	+	11.0000i	0.562809	+	0.562809i
$383$		−	8.00000i		−	0.408781i	−0.978889	−	0.204390i	$-0.934479\pi$
$383$		−	8.00000i		−	0.408781i	0.978889	−	0.204390i	$-0.0655212\pi$
$384$	−3.00000	+	3.00000i	−0.153093	+	0.153093i
$385$	−6.00000	+	18.0000i	−0.305788	+	0.917365i
$386$	−2.00000			−0.101797
$387$	−12.0000			−0.609994
$388$	−8.00000			−0.406138
$389$	−5.00000	−	5.00000i	−0.253510	−	0.253510i	0.568898	−	0.822408i	$-0.307370\pi$
$389$	−5.00000	−	5.00000i	−0.253510	−	0.253510i	−0.822408	+	0.568898i	$0.807370\pi$
$390$	−6.00000	−	2.00000i	−0.303822	−	0.101274i
$391$			32.0000i			1.61831i
$392$	33.0000			1.66675
$393$			10.0000i			0.504433i
$394$	1.00000	−	1.00000i	0.0503793	−	0.0503793i
$395$	9.00000	+	3.00000i	0.452839	+	0.150946i
$396$	2.00000			0.100504
$397$	−5.00000	+	5.00000i	−0.250943	+	0.250943i	−0.821357	−	0.570414i	$-0.806783\pi$
$397$	−5.00000	+	5.00000i	−0.250943	+	0.250943i	0.570414	+	0.821357i	$0.306783\pi$
$398$	−15.0000	−	15.0000i	−0.751882	−	0.751882i
$399$	18.0000	−	18.0000i	0.901127	−	0.901127i
$400$	−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	$0.738758\pi$
$402$		−	6.00000i		−	0.299253i
$403$	6.00000	−	6.00000i	0.298881	−	0.298881i
$404$		0			0
$405$	−10.0000	+	5.00000i	−0.496904	+	0.248452i
$406$			42.0000i			2.08443i
$407$	2.00000	+	12.0000i	0.0991363	+	0.594818i
$408$	−12.0000	+	12.0000i	−0.594089	+	0.594089i
$409$	3.00000	−	3.00000i	0.148340	−	0.148340i	−0.629036	−	0.777376i	$-0.716550\pi$
$409$	3.00000	−	3.00000i	0.148340	−	0.148340i	0.777376	+	0.629036i	$0.216550\pi$
$410$		0			0
$411$			14.0000i			0.690569i
$412$	14.0000			0.689730
$413$			42.0000i			2.06668i
$414$		−	8.00000i		−	0.393179i
$415$	5.00000	−	15.0000i	0.245440	−	0.736321i
$416$	−10.0000			−0.490290
$417$	4.00000	+	4.00000i	0.195881	+	0.195881i
$418$	−6.00000	−	6.00000i	−0.293470	−	0.293470i
$419$			22.0000i			1.07477i	0.843337	+	0.537385i	$0.180588\pi$
$419$			22.0000i			1.07477i	−0.843337	+	0.537385i	$0.819412\pi$
$420$	−6.00000	−	12.0000i	−0.292770	−	0.585540i
$421$	−27.0000	−	27.0000i	−1.31590	−	1.31590i	−0.916991	−	0.398909i	$-0.869389\pi$
$421$	−27.0000	−	27.0000i	−1.31590	−	1.31590i	−0.398909	−	0.916991i	$-0.630611\pi$
$422$		−	20.0000i		−	0.973585i
$423$	5.00000	−	5.00000i	0.243108	−	0.243108i
$424$	9.00000	+	9.00000i	0.437079	+	0.437079i
$425$	12.0000	−	16.0000i	0.582086	−	0.776114i
$426$	−8.00000	+	8.00000i	−0.387601	+	0.387601i
$427$		−	6.00000i		−	0.290360i
$428$	−3.00000	−	3.00000i	−0.145010	−	0.145010i
$429$	−4.00000	−	4.00000i	−0.193122	−	0.193122i
$430$	24.0000	−	12.0000i	1.15738	−	0.578691i
$431$	11.0000	+	11.0000i	0.529851	+	0.529851i	0.920528	−	0.390677i	$-0.127759\pi$
$431$	11.0000	+	11.0000i	0.529851	+	0.529851i	−0.390677	+	0.920528i	$0.627759\pi$
$432$	4.00000	−	4.00000i	0.192450	−	0.192450i
$433$	5.00000	−	5.00000i	0.240285	−	0.240285i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$	5.00000	−	5.00000i	0.240285	−	0.240285i	0.816968	+	0.576683i	$0.195653\pi$
$434$	−18.0000			−0.864028
$435$	28.0000	−	14.0000i	1.34250	−	0.671249i
$436$	3.00000	+	3.00000i	0.143674	+	0.143674i
$437$	24.0000	−	24.0000i	1.14808	−	1.14808i
$438$	2.00000			0.0955637
$439$	−17.0000	+	17.0000i	−0.811366	+	0.811366i	−0.984839	−	0.173473i	$-0.944501\pi$
$439$	−17.0000	+	17.0000i	−0.811366	+	0.811366i	0.173473	+	0.984839i	$0.444501\pi$
$440$	−12.0000	+	6.00000i	−0.572078	+	0.286039i
$441$	11.0000			0.523810
$442$	−8.00000			−0.380521
$443$	11.0000	+	11.0000i	0.522626	+	0.522626i	0.918364	−	0.395738i	$-0.129511\pi$
$443$	11.0000	+	11.0000i	0.522626	+	0.522626i	−0.395738	+	0.918364i	$0.629511\pi$
$444$	−7.00000	−	5.00000i	−0.332205	−	0.237289i
$445$	5.00000	−	15.0000i	0.237023	−	0.711068i
$446$	1.00000	+	1.00000i	0.0473514	+	0.0473514i
$447$	16.0000	−	16.0000i	0.756774	−	0.756774i
$448$	21.0000	+	21.0000i	0.992157	+	0.992157i
$449$	−5.00000	−	5.00000i	−0.235965	−	0.235965i	0.579212	−	0.815177i	$-0.303360\pi$
$449$	−5.00000	−	5.00000i	−0.235965	−	0.235965i	−0.815177	+	0.579212i	$0.803360\pi$
$450$	−3.00000	+	4.00000i	−0.141421	+	0.188562i
$451$		0			0
$452$	4.00000			0.188144
$453$	−2.00000	+	2.00000i	−0.0939682	+	0.0939682i
$454$			2.00000i			0.0938647i
$455$	6.00000	−	18.0000i	0.281284	−	0.843853i
$456$	18.0000			0.842927
$457$	−32.0000			−1.49690			−0.748448	−	0.663193i	$-0.769201\pi$
$457$	−32.0000			−1.49690			−0.748448	+	0.663193i	$0.769201\pi$
$458$	4.00000			0.186908
$459$	−16.0000	+	16.0000i	−0.746816	+	0.746816i
$460$	−8.00000	−	16.0000i	−0.373002	−	0.746004i
$461$	21.0000	−	21.0000i	0.978068	−	0.978068i	−0.0216971	−	0.999765i	$-0.506907\pi$
$461$	21.0000	−	21.0000i	0.978068	−	0.978068i	0.999765	+	0.0216971i	$0.00690694\pi$
$462$			12.0000i			0.558291i
$463$		−	40.0000i		−	1.85896i	−0.368875	−	0.929479i	$-0.620257\pi$
$463$		−	40.0000i		−	1.85896i	0.368875	−	0.929479i	$-0.379743\pi$
$464$	−7.00000	+	7.00000i	−0.324967	+	0.324967i
$465$	6.00000	+	12.0000i	0.278243	+	0.556487i
$466$	−1.00000	+	1.00000i	−0.0463241	+	0.0463241i
$467$	38.0000			1.75843			0.879215	−	0.476425i	$-0.158068\pi$
$467$	38.0000			1.75843			0.879215	+	0.476425i	$0.158068\pi$
$468$	−2.00000			−0.0924500
$469$	18.0000			0.831163
$470$	−5.00000	+	15.0000i	−0.230633	+	0.691898i
$471$			6.00000i			0.276465i
$472$	−21.0000	+	21.0000i	−0.966603	+	0.966603i
$473$	24.0000			1.10352
$474$	6.00000			0.275589
$475$	−21.0000	+	3.00000i	−0.963546	+	0.137649i
$476$	−12.0000	−	12.0000i	−0.550019	−	0.550019i
$477$	3.00000	+	3.00000i	0.137361	+	0.137361i
$478$	−7.00000	+	7.00000i	−0.320173	+	0.320173i
$479$	−23.0000	−	23.0000i	−1.05090	−	1.05090i	−0.998633	−	0.0522635i	$-0.983356\pi$
$479$	−23.0000	−	23.0000i	−1.05090	−	1.05090i	−0.0522635	−	0.998633i	$-0.516644\pi$
$480$	5.00000	−	15.0000i	0.228218	−	0.684653i
$481$	−2.00000	−	12.0000i	−0.0911922	−	0.547153i
$482$	−1.00000	−	1.00000i	−0.0455488	−	0.0455488i
$483$	−48.0000			−2.18408
$484$	7.00000			0.318182
$485$	16.0000	−	8.00000i	0.726523	−	0.363261i
$486$	7.00000	−	7.00000i	0.317526	−	0.317526i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	3.00000	−	3.00000i	0.135804	−	0.135804i
$489$	−10.0000	−	10.0000i	−0.452216	−	0.452216i
$490$	−22.0000	+	11.0000i	−0.993859	+	0.496929i
$491$	−4.00000			−0.180517			−0.0902587	−	0.995918i	$-0.528769\pi$
$491$	−4.00000			−0.180517			−0.0902587	+	0.995918i	$0.528769\pi$
$492$		0			0
$493$	28.0000	−	28.0000i	1.26106	−	1.26106i
$494$	6.00000	+	6.00000i	0.269953	+	0.269953i
$495$	−4.00000	+	2.00000i	−0.179787	+	0.0898933i
$496$	−3.00000	−	3.00000i	−0.134704	−	0.134704i
$497$	−24.0000	−	24.0000i	−1.07655	−	1.07655i
$498$		−	10.0000i		−	0.448111i
$499$	27.0000	−	27.0000i	1.20869	−	1.20869i	0.237233	−	0.971453i	$-0.423759\pi$
$499$	27.0000	−	27.0000i	1.20869	−	1.20869i	0.971453	−	0.237233i	$-0.0762406\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$	6.00000	+	6.00000i	0.268060	+	0.268060i
$502$	−5.00000	+	5.00000i	−0.223161	+	0.223161i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	9.00000	+	9.00000i	0.400892	+	0.400892i
$505$		0			0
$506$			16.0000i			0.711287i
$507$	−9.00000	−	9.00000i	−0.399704	−	0.399704i
$508$	9.00000	+	9.00000i	0.399310	+	0.399310i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$	4.00000	−	12.0000i	0.177123	−	0.531369i
$511$			6.00000i			0.265424i
$512$			11.0000i			0.486136i
$513$	24.0000			1.05963
$514$		−	28.0000i		−	1.23503i
$515$	−28.0000	+	14.0000i	−1.23383	+	0.616914i
$516$	−12.0000	+	12.0000i	−0.528271	+	0.528271i
$517$	−10.0000	+	10.0000i	−0.439799	+	0.439799i
$518$	−15.0000	+	21.0000i	−0.659062	+	0.922687i
$519$			2.00000i			0.0877903i
$520$	12.0000	−	6.00000i	0.526235	−	0.263117i
$521$			44.0000i			1.92767i	0.266491	+	0.963837i	$0.414136\pi$
$521$			44.0000i			1.92767i	−0.266491	+	0.963837i	$0.585864\pi$
$522$	−7.00000	+	7.00000i	−0.306382	+	0.306382i
$523$			4.00000i			0.174908i	0.996169	+	0.0874539i	$0.0278730\pi$
$523$			4.00000i			0.174908i	−0.996169	+	0.0874539i	$0.972127\pi$
$524$	−5.00000	−	5.00000i	−0.218426	−	0.218426i
$525$	24.0000	+	18.0000i	1.04745	+	0.785584i
$526$	7.00000	−	7.00000i	0.305215	−	0.305215i
$527$	12.0000	+	12.0000i	0.522728	+	0.522728i
$528$	−2.00000	+	2.00000i	−0.0870388	+	0.0870388i
$529$	−41.0000			−1.78261
$530$	−9.00000	−	3.00000i	−0.390935	−	0.130312i
$531$	−7.00000	+	7.00000i	−0.303774	+	0.303774i
$532$			18.0000i			0.780399i
$533$		0			0
$534$		−	10.0000i		−	0.432742i
$535$	9.00000	+	3.00000i	0.389104	+	0.129701i
$536$	9.00000	+	9.00000i	0.388741	+	0.388741i
$537$	−14.0000			−0.604145
$538$	−16.0000			−0.689809
$539$	−22.0000			−0.947607
$540$	4.00000	−	12.0000i	0.172133	−	0.516398i
$541$	1.00000	−	1.00000i	0.0429934	−	0.0429934i	−0.685283	−	0.728277i	$-0.740322\pi$
$541$	1.00000	−	1.00000i	0.0429934	−	0.0429934i	0.728277	+	0.685283i	$0.240322\pi$
$542$			8.00000i			0.343629i
$543$	−10.0000	−	10.0000i	−0.429141	−	0.429141i
$544$		−	20.0000i		−	0.857493i
$545$	−9.00000	−	3.00000i	−0.385518	−	0.128506i
$546$		−	12.0000i		−	0.513553i
$547$			20.0000i			0.855138i	0.903983	+	0.427569i	$0.140630\pi$
$547$			20.0000i			0.855138i	−0.903983	+	0.427569i	$0.859370\pi$
$548$	−7.00000	−	7.00000i	−0.299025	−	0.299025i
$549$	1.00000	−	1.00000i	0.0426790	−	0.0426790i
$550$	6.00000	−	8.00000i	0.255841	−	0.341121i
$551$	−42.0000			−1.78926
$552$	−24.0000	−	24.0000i	−1.02151	−	1.02151i
$553$			18.0000i			0.765438i
$554$	26.0000			1.10463
$555$	19.0000	+	3.00000i	0.806505	+	0.127343i
$556$	−4.00000			−0.169638
$557$		−	14.0000i		−	0.593199i	−0.955002	−	0.296600i	$-0.904147\pi$
$557$		−	14.0000i		−	0.593199i	0.955002	−	0.296600i	$-0.0958526\pi$
$558$	−3.00000	−	3.00000i	−0.127000	−	0.127000i
$559$	−24.0000			−1.01509
$560$	−9.00000	−	3.00000i	−0.380319	−	0.126773i
$561$	8.00000	−	8.00000i	0.337760	−	0.337760i
$562$	−9.00000	−	9.00000i	−0.379642	−	0.379642i
$563$			12.0000i			0.505740i	0.967500	+	0.252870i	$0.0813744\pi$
$563$			12.0000i			0.505740i	−0.967500	+	0.252870i	$0.918626\pi$
$564$		−	10.0000i		−	0.421076i
$565$	−8.00000	+	4.00000i	−0.336563	+	0.168281i
$566$			22.0000i			0.924729i
$567$	−15.0000	−	15.0000i	−0.629941	−	0.629941i
$568$		−	24.0000i		−	1.00702i
$569$	−25.0000	+	25.0000i	−1.04805	+	1.04805i	−0.0492690	+	0.998786i	$0.515689\pi$
$569$	−25.0000	+	25.0000i	−1.04805	+	1.04805i	−0.998786	+	0.0492690i	$0.984311\pi$
$570$	−12.0000	+	6.00000i	−0.502625	+	0.251312i
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$	4.00000			0.167248
$573$	22.0000			0.919063
$574$		0			0
$575$	32.0000	+	24.0000i	1.33449	+	1.00087i
$576$			7.00000i			0.291667i
$577$	12.0000			0.499567			0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000			0.499567			0.249783	+	0.968302i	$0.419641\pi$
$578$			1.00000i			0.0415945i
$579$	−2.00000	+	2.00000i	−0.0831172	+	0.0831172i
$580$	−7.00000	+	21.0000i	−0.290659	+	0.871978i
$581$	30.0000			1.24461
$582$	8.00000	−	8.00000i	0.331611	−	0.331611i
$583$	−6.00000	−	6.00000i	−0.248495	−	0.248495i
$584$	−3.00000	+	3.00000i	−0.124141	+	0.124141i
$585$	4.00000	−	2.00000i	0.165380	−	0.0826898i
$586$	−1.00000	−	1.00000i	−0.0413096	−	0.0413096i
$587$		−	36.0000i		−	1.48588i	−0.669359	−	0.742940i	$-0.733431\pi$
$587$		−	36.0000i		−	1.48588i	0.669359	−	0.742940i	$-0.266569\pi$
$588$	11.0000	−	11.0000i	0.453632	−	0.453632i
$589$		−	18.0000i		−	0.741677i
$590$	7.00000	−	21.0000i	0.288185	−	0.864556i
$591$		−	2.00000i		−	0.0822690i
$592$	−6.00000	+	1.00000i	−0.246598	+	0.0410997i
$593$	−3.00000	+	3.00000i	−0.123195	+	0.123195i	−0.766016	−	0.642821i	$-0.777764\pi$
$593$	−3.00000	+	3.00000i	−0.123195	+	0.123195i	0.642821	+	0.766016i	$0.277764\pi$
$594$	−8.00000	+	8.00000i	−0.328244	+	0.328244i
$595$	36.0000	+	12.0000i	1.47586	+	0.491952i
$596$			16.0000i			0.655386i
$597$	−30.0000			−1.22782
$598$		−	16.0000i		−	0.654289i
$599$		−	6.00000i		−	0.245153i	−0.992459	−	0.122577i	$-0.960884\pi$
$599$		−	6.00000i		−	0.245153i	0.992459	−	0.122577i	$-0.0391157\pi$
$600$	3.00000	+	21.0000i	0.122474	+	0.857321i
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	36.0000	+	36.0000i	1.46725	+	1.46725i
$603$	3.00000	+	3.00000i	0.122169	+	0.122169i
$604$		−	2.00000i		−	0.0813788i
$605$	−14.0000	+	7.00000i	−0.569181	+	0.284590i
$606$		0			0
$607$		−	32.0000i		−	1.29884i	−0.760430	−	0.649420i	$-0.775012\pi$
$607$		−	32.0000i		−	1.29884i	0.760430	−	0.649420i	$-0.224988\pi$
$608$	−15.0000	+	15.0000i	−0.608330	+	0.608330i
$609$	42.0000	+	42.0000i	1.70193	+	1.70193i
$610$	−1.00000	+	3.00000i	−0.0404888	+	0.121466i
$611$	10.0000	−	10.0000i	0.404557	−	0.404557i
$612$		−	4.00000i		−	0.161690i
$613$	−21.0000	−	21.0000i	−0.848182	−	0.848182i	0.141724	−	0.989906i	$-0.454735\pi$
$613$	−21.0000	−	21.0000i	−0.848182	−	0.848182i	−0.989906	+	0.141724i	$0.954735\pi$
$614$	−9.00000	−	9.00000i	−0.363210	−	0.363210i
$615$		0			0
$616$	−18.0000	−	18.0000i	−0.725241	−	0.725241i
$617$	−17.0000	+	17.0000i	−0.684394	+	0.684394i	−0.960987	−	0.276593i	$-0.910795\pi$
$617$	−17.0000	+	17.0000i	−0.684394	+	0.684394i	0.276593	+	0.960987i	$0.410795\pi$
$618$	−14.0000	+	14.0000i	−0.563163	+	0.563163i
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$	−9.00000	−	3.00000i	−0.361449	−	0.120483i
$621$	−32.0000	−	32.0000i	−1.28412	−	1.28412i
$622$	3.00000	−	3.00000i	0.120289	−	0.120289i
$623$	30.0000			1.20192
$624$	2.00000	−	2.00000i	0.0800641	−	0.0800641i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	30.0000			1.19904
$627$	−12.0000			−0.479234
$628$	−3.00000	−	3.00000i	−0.119713	−	0.119713i
$629$	24.0000	−	4.00000i	0.956943	−	0.159490i
$630$	−9.00000	−	3.00000i	−0.358569	−	0.119523i
$631$	23.0000	+	23.0000i	0.915616	+	0.915616i	0.996707	−	0.0810911i	$-0.0258405\pi$
$631$	23.0000	+	23.0000i	0.915616	+	0.915616i	−0.0810911	+	0.996707i	$0.525840\pi$
$632$	−9.00000	+	9.00000i	−0.358001	+	0.358001i
$633$	−20.0000	−	20.0000i	−0.794929	−	0.794929i
$634$	17.0000	+	17.0000i	0.675156	+	0.675156i
$635$	−27.0000	−	9.00000i	−1.07146	−	0.357154i
$636$	6.00000			0.237915
$637$	22.0000			0.871672
$638$	14.0000	−	14.0000i	0.554265	−	0.554265i
$639$		−	8.00000i		−	0.316475i
$640$	3.00000	+	6.00000i	0.118585	+	0.237171i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	6.00000			0.236801
$643$	10.0000			0.394362			0.197181	−	0.980367i	$-0.436821\pi$
$643$	10.0000			0.394362			0.197181	+	0.980367i	$0.436821\pi$
$644$	24.0000	−	24.0000i	0.945732	−	0.945732i
$645$	12.0000	−	36.0000i	0.472500	−	1.41750i
$646$	−12.0000	+	12.0000i	−0.472134	+	0.472134i
$647$		−	24.0000i		−	0.943537i	−0.881722	−	0.471769i	$-0.843616\pi$
$647$		−	24.0000i		−	0.943537i	0.881722	−	0.471769i	$-0.156384\pi$
$648$		−	15.0000i		−	0.589256i
$649$	14.0000	−	14.0000i	0.549548	−	0.549548i
$650$	−6.00000	+	8.00000i	−0.235339	+	0.313786i
$651$	−18.0000	+	18.0000i	−0.705476	+	0.705476i
$652$	10.0000			0.391630
$653$	−36.0000			−1.40879			−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000			−1.40879			−0.704394	+	0.709809i	$0.748781\pi$
$654$	−6.00000			−0.234619
$655$	15.0000	+	5.00000i	0.586098	+	0.195366i
$656$		0			0
$657$	−1.00000	+	1.00000i	−0.0390137	+	0.0390137i
$658$	−30.0000			−1.16952
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$	−2.00000	+	6.00000i	−0.0778499	+	0.233550i
$661$	33.0000	+	33.0000i	1.28355	+	1.28355i	0.938633	+	0.344919i	$0.112094\pi$
$661$	33.0000	+	33.0000i	1.28355	+	1.28355i	0.344919	+	0.938633i	$0.387906\pi$
$662$	7.00000	+	7.00000i	0.272063	+	0.272063i
$663$	−8.00000	+	8.00000i	−0.310694	+	0.310694i
$664$	15.0000	+	15.0000i	0.582113	+	0.582113i
$665$	−18.0000	−	36.0000i	−0.698010	−	1.39602i
$666$	−6.00000	+	1.00000i	−0.232495	+	0.0387492i
$667$	56.0000	+	56.0000i	2.16833	+	2.16833i
$668$	−6.00000			−0.232147
$669$	2.00000			0.0773245
$670$	−9.00000	−	3.00000i	−0.347700	−	0.115900i
$671$	−2.00000	+	2.00000i	−0.0772091	+	0.0772091i
$672$	30.0000			1.15728
$673$	−15.0000	+	15.0000i	−0.578208	+	0.578208i	−0.934409	−	0.356202i	$-0.884072\pi$
$673$	−15.0000	+	15.0000i	−0.578208	+	0.578208i	0.356202	+	0.934409i	$0.384072\pi$
$674$	−15.0000	−	15.0000i	−0.577778	−	0.577778i
$675$	4.00000	+	28.0000i	0.153960	+	1.07772i
$676$	9.00000			0.346154
$677$	23.0000	−	23.0000i	0.883962	−	0.883962i	−0.109973	−	0.993935i	$-0.535076\pi$
$677$	23.0000	−	23.0000i	0.883962	−	0.883962i	0.993935	+	0.109973i	$0.0350764\pi$
$678$	−4.00000	+	4.00000i	−0.153619	+	0.153619i
$679$	24.0000	+	24.0000i	0.921035	+	0.921035i
$680$	12.0000	+	24.0000i	0.460179	+	0.920358i
$681$	2.00000	+	2.00000i	0.0766402	+	0.0766402i
$682$	6.00000	+	6.00000i	0.229752	+	0.229752i
$683$		−	4.00000i		−	0.153056i	−0.997067	−	0.0765279i	$-0.975617\pi$
$683$		−	4.00000i		−	0.153056i	0.997067	−	0.0765279i	$-0.0243834\pi$
$684$	−3.00000	+	3.00000i	−0.114708	+	0.114708i
$685$	21.0000	+	7.00000i	0.802369	+	0.267456i
$686$	−12.0000	−	12.0000i	−0.458162	−	0.458162i
$687$	4.00000	−	4.00000i	0.152610	−	0.152610i
$688$			12.0000i			0.457496i
$689$	6.00000	+	6.00000i	0.228582	+	0.228582i
$690$	24.0000	+	8.00000i	0.913664	+	0.304555i
$691$		−	46.0000i		−	1.74992i	−0.484193	−	0.874961i	$-0.660887\pi$
$691$		−	46.0000i		−	1.74992i	0.484193	−	0.874961i	$-0.339113\pi$
$692$	−1.00000	−	1.00000i	−0.0380143	−	0.0380143i
$693$	−6.00000	−	6.00000i	−0.227921	−	0.227921i
$694$	4.00000			0.151838
$695$	8.00000	−	4.00000i	0.303457	−	0.151729i
$696$			42.0000i			1.59201i
$697$		0			0
$698$	32.0000			1.21122
$699$			2.00000i			0.0756469i
$700$	−21.0000	+	3.00000i	−0.793725	+	0.113389i
$701$	9.00000	−	9.00000i	0.339925	−	0.339925i	−0.516414	−	0.856339i	$-0.672733\pi$
$701$	9.00000	−	9.00000i	0.339925	−	0.339925i	0.856339	+	0.516414i	$0.172733\pi$
$702$	8.00000	−	8.00000i	0.301941	−	0.301941i
$703$	−21.0000	−	15.0000i	−0.792030	−	0.565736i
$704$		−	14.0000i		−	0.527645i
$705$	10.0000	+	20.0000i	0.376622	+	0.753244i
$706$		−	32.0000i		−	1.20434i
$707$		0			0
$708$			14.0000i			0.526152i
$709$	15.0000	+	15.0000i	0.563337	+	0.563337i	0.930254	−	0.366917i	$-0.119587\pi$
$709$	15.0000	+	15.0000i	0.563337	+	0.563337i	−0.366917	+	0.930254i	$0.619587\pi$
$710$	8.00000	+	16.0000i	0.300235	+	0.600469i
$711$	−3.00000	+	3.00000i	−0.112509	+	0.112509i
$712$	15.0000	+	15.0000i	0.562149	+	0.562149i
$713$	−24.0000	+	24.0000i	−0.898807	+	0.898807i
$714$	24.0000			0.898177
$715$	−8.00000	+	4.00000i	−0.299183	+	0.149592i
$716$	7.00000	−	7.00000i	0.261602	−	0.261602i
$717$			14.0000i			0.522840i
$718$	34.0000			1.26887
$719$			26.0000i			0.969636i	0.874615	+	0.484818i	$0.161114\pi$
$719$			26.0000i			0.969636i	−0.874615	+	0.484818i	$0.838886\pi$
$720$	−1.00000	−	2.00000i	−0.0372678	−	0.0745356i
$721$	−42.0000	−	42.0000i	−1.56416	−	1.56416i
$722$	−1.00000			−0.0372161
$723$	−2.00000			−0.0743808
$724$	10.0000			0.371647
$725$	−7.00000	−	49.0000i	−0.259973	−	1.81981i
$726$	−7.00000	+	7.00000i	−0.259794	+	0.259794i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	18.0000	+	18.0000i	0.667124	+	0.667124i
$729$		−	29.0000i		−	1.07407i
$730$	1.00000	−	3.00000i	0.0370117	−	0.111035i
$731$		−	48.0000i		−	1.77534i
$732$		−	2.00000i		−	0.0739221i
$733$	3.00000	+	3.00000i	0.110808	+	0.110808i	0.760337	−	0.649529i	$-0.225034\pi$
$733$	3.00000	+	3.00000i	0.110808	+	0.110808i	−0.649529	+	0.760337i	$0.725034\pi$
$734$	17.0000	−	17.0000i	0.627481	−	0.627481i
$735$	−11.0000	+	33.0000i	−0.405741	+	1.21722i
$736$	40.0000			1.47442
$737$	−6.00000	−	6.00000i	−0.221013	−	0.221013i
$738$		0			0
$739$	−44.0000			−1.61857			−0.809283	−	0.587419i	$-0.800144\pi$
$739$	−44.0000			−1.61857			−0.809283	+	0.587419i	$0.800144\pi$
$740$	−11.0000	+	8.00000i	−0.404368	+	0.294086i
$741$	12.0000			0.440831
$742$		−	18.0000i		−	0.660801i
$743$	−5.00000	−	5.00000i	−0.183432	−	0.183432i	0.609417	−	0.792850i	$-0.291403\pi$
$743$	−5.00000	−	5.00000i	−0.183432	−	0.183432i	−0.792850	+	0.609417i	$0.791403\pi$
$744$	−18.0000			−0.659912
$745$	−16.0000	−	32.0000i	−0.586195	−	1.17239i
$746$	3.00000	−	3.00000i	0.109838	−	0.109838i
$747$	5.00000	+	5.00000i	0.182940	+	0.182940i
$748$			8.00000i			0.292509i
$749$			18.0000i			0.657706i
$750$	−9.00000	−	13.0000i	−0.328634	−	0.474693i
$751$			22.0000i			0.802791i	0.915905	+	0.401396i	$0.131475\pi$
$751$			22.0000i			0.802791i	−0.915905	+	0.401396i	$0.868525\pi$
$752$	−5.00000	−	5.00000i	−0.182331	−	0.182331i
$753$			10.0000i			0.364420i
$754$	−14.0000	+	14.0000i	−0.509850	+	0.509850i
$755$	2.00000	+	4.00000i	0.0727875	+	0.145575i
$756$	24.0000			0.872872
$757$	−36.0000			−1.30844			−0.654221	−	0.756303i	$-0.727003\pi$
$757$	−36.0000			−1.30844			−0.654221	+	0.756303i	$0.727003\pi$
$758$	14.0000			0.508503
$759$	16.0000	+	16.0000i	0.580763	+	0.580763i
$760$	9.00000	−	27.0000i	0.326464	−	0.979393i
$761$		−	8.00000i		−	0.290000i	−0.989432	−	0.145000i	$-0.953682\pi$
$761$		−	8.00000i		−	0.290000i	0.989432	−	0.145000i	$-0.0463182\pi$
$762$	−18.0000			−0.652071
$763$		−	18.0000i		−	0.651644i
$764$	−11.0000	+	11.0000i	−0.397966	+	0.397966i
$765$	4.00000	+	8.00000i	0.144620	+	0.289241i
$766$	−8.00000			−0.289052
$767$	−14.0000	+	14.0000i	−0.505511	+	0.505511i
$768$	17.0000	+	17.0000i	0.613435	+	0.613435i
$769$	15.0000	−	15.0000i	0.540914	−	0.540914i	−0.382883	−	0.923797i	$-0.625069\pi$
$769$	15.0000	−	15.0000i	0.540914	−	0.540914i	0.923797	+	0.382883i	$0.125069\pi$
$770$	18.0000	+	6.00000i	0.648675	+	0.216225i
$771$	−28.0000	−	28.0000i	−1.00840	−	1.00840i
$772$		−	2.00000i		−	0.0719816i
$773$	−11.0000	+	11.0000i	−0.395643	+	0.395643i	−0.876693	−	0.481050i	$-0.840255\pi$
$773$	−11.0000	+	11.0000i	−0.395643	+	0.395643i	0.481050	+	0.876693i	$0.340255\pi$
$774$			12.0000i			0.431331i
$775$	21.0000	−	3.00000i	0.754342	−	0.107763i
$776$			24.0000i			0.861550i
$777$	6.00000	+	36.0000i	0.215249	+	1.29149i
$778$	−5.00000	+	5.00000i	−0.179259	+	0.179259i
$779$		0			0
$780$	2.00000	−	6.00000i	0.0716115	−	0.214834i
$781$			16.0000i			0.572525i
$782$	32.0000			1.14432
$783$			56.0000i			2.00128i
$784$		−	11.0000i		−	0.392857i
$785$	9.00000	+	3.00000i	0.321224	+	0.107075i
$786$	10.0000			0.356688
$787$	−27.0000	−	27.0000i	−0.962446	−	0.962446i	0.0368739	−	0.999320i	$-0.488260\pi$
$787$	−27.0000	−	27.0000i	−0.962446	−	0.962446i	−0.999320	+	0.0368739i	$0.988260\pi$
$788$	1.00000	+	1.00000i	0.0356235	+	0.0356235i
$789$		−	14.0000i		−	0.498413i
$790$	3.00000	−	9.00000i	0.106735	−	0.320206i
$791$	−12.0000	−	12.0000i	−0.426671	−	0.426671i
$792$		−	6.00000i		−	0.213201i
$793$	2.00000	−	2.00000i	0.0710221	−	0.0710221i
$794$	5.00000	+	5.00000i	0.177443	+	0.177443i
$795$	−12.0000	+	6.00000i	−0.425596	+	0.212798i
$796$	15.0000	−	15.0000i	0.531661	−	0.531661i
$797$		−	46.0000i		−	1.62940i	−0.579880	−	0.814702i	$-0.696901\pi$
$797$		−	46.0000i		−	1.62940i	0.579880	−	0.814702i	$-0.303099\pi$
$798$	−18.0000	−	18.0000i	−0.637193	−	0.637193i
$799$	20.0000	+	20.0000i	0.707549	+	0.707549i
$800$	−20.0000	−	15.0000i	−0.707107	−	0.530330i
$801$	5.00000	+	5.00000i	0.176666	+	0.176666i
$802$	1.00000	−	1.00000i	0.0353112	−	0.0353112i
$803$	2.00000	−	2.00000i	0.0705785	−	0.0705785i
$804$	6.00000			0.211604
$805$	−24.0000	+	72.0000i	−0.845889	+	2.53767i
$806$	−6.00000	−	6.00000i	−0.211341	−	0.211341i
$807$	−16.0000	+	16.0000i	−0.563227	+	0.563227i
$808$		0			0
$809$	−25.0000	+	25.0000i	−0.878953	+	0.878953i	−0.993426	−	0.114473i	$-0.963482\pi$
$809$	−25.0000	+	25.0000i	−0.878953	+	0.878953i	0.114473	+	0.993426i	$0.463482\pi$
$810$	5.00000	+	10.0000i	0.175682	+	0.351364i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−42.0000			−1.47391
$813$	8.00000	+	8.00000i	0.280572	+	0.280572i
$814$	12.0000	−	2.00000i	0.420600	−	0.0701000i
$815$	−20.0000	+	10.0000i	−0.700569	+	0.350285i
$816$	4.00000	+	4.00000i	0.140028	+	0.140028i
$817$	−36.0000	+	36.0000i	−1.25948	+	1.25948i
$818$	−3.00000	−	3.00000i	−0.104893	−	0.104893i
$819$	6.00000	+	6.00000i	0.209657	+	0.209657i
$820$		0			0
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$	14.0000			0.488306
$823$	11.0000	−	11.0000i	0.383436	−	0.383436i	−0.488903	−	0.872338i	$-0.662603\pi$
$823$	11.0000	−	11.0000i	0.383436	−	0.383436i	0.872338	+	0.488903i	$0.162603\pi$
$824$		−	42.0000i		−	1.46314i
$825$	−2.00000	−	14.0000i	−0.0696311	−	0.487417i
$826$	42.0000			1.46137
$827$	38.0000			1.32139			0.660695	−	0.750655i	$-0.270262\pi$
$827$	38.0000			1.32139			0.660695	+	0.750655i	$0.270262\pi$
$828$	8.00000			0.278019
$829$	−21.0000	+	21.0000i	−0.729360	+	0.729360i	−0.970492	−	0.241132i	$-0.922481\pi$
$829$	−21.0000	+	21.0000i	−0.729360	+	0.729360i	0.241132	+	0.970492i	$0.422481\pi$
$830$	−15.0000	−	5.00000i	−0.520658	−	0.173553i
$831$	26.0000	−	26.0000i	0.901930	−	0.901930i
$832$			14.0000i			0.485363i
$833$			44.0000i			1.52451i
$834$	4.00000	−	4.00000i	0.138509	−	0.138509i
$835$	12.0000	−	6.00000i	0.415277	−	0.207639i
$836$	6.00000	−	6.00000i	0.207514	−	0.207514i
$837$	−24.0000			−0.829561
$838$	22.0000			0.759977
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$	−36.0000	+	18.0000i	−1.24212	+	0.621059i
$841$		−	69.0000i		−	2.37931i
$842$	−27.0000	+	27.0000i	−0.930481	+	0.930481i
$843$	−18.0000			−0.619953
$844$	20.0000			0.688428
$845$	−18.0000	+	9.00000i	−0.619219	+	0.309609i
$846$	−5.00000	−	5.00000i	−0.171904	−	0.171904i
$847$	−21.0000	−	21.0000i	−0.721569	−	0.721569i
$848$	3.00000	−	3.00000i	0.103020	−	0.103020i
$849$	22.0000	+	22.0000i	0.755038	+	0.755038i
$850$	−16.0000	−	12.0000i	−0.548795	−	0.411597i
$851$	8.00000	+	48.0000i	0.274236	+	1.64542i
$852$	−8.00000	−	8.00000i	−0.274075	−	0.274075i
$853$	44.0000			1.50653			0.753266	−	0.657716i	$-0.228477\pi$
$853$	44.0000			1.50653			0.753266	+	0.657716i	$0.228477\pi$
$854$	−6.00000			−0.205316
$855$	3.00000	−	9.00000i	0.102598	−	0.307794i
$856$	−9.00000	+	9.00000i	−0.307614	+	0.307614i
$857$	−32.0000			−1.09310			−0.546550	−	0.837427i	$-0.684059\pi$
$857$	−32.0000			−1.09310			−0.546550	+	0.837427i	$0.684059\pi$
$858$	−4.00000	+	4.00000i	−0.136558	+	0.136558i
$859$	−7.00000	−	7.00000i	−0.238837	−	0.238837i	0.577531	−	0.816368i	$-0.304016\pi$
$859$	−7.00000	−	7.00000i	−0.238837	−	0.238837i	−0.816368	+	0.577531i	$0.804016\pi$
$860$	12.0000	+	24.0000i	0.409197	+	0.818393i
$861$		0			0
$862$	11.0000	−	11.0000i	0.374661	−	0.374661i
$863$	15.0000	−	15.0000i	0.510606	−	0.510606i	−0.404106	−	0.914712i	$-0.632417\pi$
$863$	15.0000	−	15.0000i	0.510606	−	0.510606i	0.914712	+	0.404106i	$0.132417\pi$
$864$	20.0000	+	20.0000i	0.680414	+	0.680414i
$865$	3.00000	+	1.00000i	0.102003	+	0.0340010i
$866$	−5.00000	−	5.00000i	−0.169907	−	0.169907i
$867$	1.00000	+	1.00000i	0.0339618	+	0.0339618i
$868$		−	18.0000i		−	0.610960i
$869$	6.00000	−	6.00000i	0.203536	−	0.203536i
$870$	−14.0000	−	28.0000i	−0.474644	−	0.949289i
$871$	6.00000	+	6.00000i	0.203302	+	0.203302i
$872$	9.00000	−	9.00000i	0.304778	−	0.304778i
$873$			8.00000i			0.270759i
$874$	−24.0000	−	24.0000i	−0.811812	−	0.811812i
$875$	39.0000	−	27.0000i	1.31844	−	0.912767i
$876$			2.00000i			0.0675737i
$877$	37.0000	+	37.0000i	1.24940	+	1.24940i	0.955985	+	0.293417i	$0.0947923\pi$
$877$	37.0000	+	37.0000i	1.24940	+	1.24940i	0.293417	+	0.955985i	$0.405208\pi$
$878$	17.0000	+	17.0000i	0.573722	+	0.573722i
$879$	−2.00000			−0.0674583
$880$	2.00000	+	4.00000i	0.0674200	+	0.134840i
$881$		−	12.0000i		−	0.404290i	−0.979356	−	0.202145i	$-0.935209\pi$
$881$		−	12.0000i		−	0.404290i	0.979356	−	0.202145i	$-0.0647913\pi$
$882$		−	11.0000i		−	0.370389i
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$		−	8.00000i		−	0.269069i
$885$	−14.0000	−	28.0000i	−0.470605	−	0.941210i
$886$	11.0000	−	11.0000i	0.369552	−	0.369552i
$887$	5.00000	−	5.00000i	0.167884	−	0.167884i	−0.618165	−	0.786048i	$-0.712124\pi$
$887$	5.00000	−	5.00000i	0.167884	−	0.167884i	0.786048	+	0.618165i	$0.212124\pi$
$888$	−15.0000	+	21.0000i	−0.503367	+	0.704714i
$889$		−	54.0000i		−	1.81110i
$890$	−15.0000	−	5.00000i	−0.502801	−	0.167600i
$891$			10.0000i			0.335013i
$892$	−1.00000	+	1.00000i	−0.0334825	+	0.0334825i
$893$		−	30.0000i		−	1.00391i
$894$	−16.0000	−	16.0000i	−0.535120	−	0.535120i
$895$	−7.00000	+	21.0000i	−0.233984	+	0.701953i
$896$	−9.00000	+	9.00000i	−0.300669	+	0.300669i
$897$	−16.0000	−	16.0000i	−0.534224	−	0.534224i
$898$	−5.00000	+	5.00000i	−0.166852	+	0.166852i
$899$	42.0000			1.40078
$900$	−4.00000	−	3.00000i	−0.133333	−	0.100000i
$901$	−12.0000	+	12.0000i	−0.399778	+	0.399778i
$902$		0			0
$903$	72.0000			2.39601
$904$		−	12.0000i		−	0.399114i
$905$	−20.0000	+	10.0000i	−0.664822	+	0.332411i
$906$	2.00000	+	2.00000i	0.0664455	+	0.0664455i
$907$	14.0000			0.464862			0.232431	−	0.972613i	$-0.425332\pi$
$907$	14.0000			0.464862			0.232431	+	0.972613i	$0.425332\pi$
$908$	−2.00000			−0.0663723
$909$		0			0
$910$	−18.0000	−	6.00000i	−0.596694	−	0.198898i
$911$	−11.0000	+	11.0000i	−0.364446	+	0.364446i	−0.865447	−	0.501001i	$-0.832965\pi$
$911$	−11.0000	+	11.0000i	−0.364446	+	0.364446i	0.501001	+	0.865447i	$0.332965\pi$
$912$		−	6.00000i		−	0.198680i
$913$	−10.0000	−	10.0000i	−0.330952	−	0.330952i
$914$			32.0000i			1.05847i
$915$	2.00000	+	4.00000i	0.0661180	+	0.132236i
$916$			4.00000i			0.132164i
$917$			30.0000i			0.990687i
$918$	16.0000	+	16.0000i	0.528079	+	0.528079i
$919$	3.00000	−	3.00000i	0.0989609	−	0.0989609i	−0.655893	−	0.754854i	$-0.727708\pi$
$919$	3.00000	−	3.00000i	0.0989609	−	0.0989609i	0.754854	+	0.655893i	$0.227708\pi$
$920$	−48.0000	+	24.0000i	−1.58251	+	0.791257i
$921$	−18.0000			−0.593120
$922$	−21.0000	−	21.0000i	−0.691598	−	0.691598i
$923$		−	16.0000i		−	0.526646i
$924$	−12.0000			−0.394771
$925$	14.0000	−	27.0000i	0.460317	−	0.887755i
$926$	−40.0000			−1.31448
$927$		−	14.0000i		−	0.459820i
$928$	−35.0000	−	35.0000i	−1.14893	−	1.14893i
$929$	−34.0000			−1.11550			−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000			−1.11550			−0.557752	+	0.830008i	$0.688336\pi$
$930$	12.0000	−	6.00000i	0.393496	−	0.196748i
$931$	33.0000	−	33.0000i	1.08153	−	1.08153i
$932$	−1.00000	−	1.00000i	−0.0327561	−	0.0327561i
$933$		−	6.00000i		−	0.196431i
$934$		−	38.0000i		−	1.24340i
$935$	−8.00000	−	16.0000i	−0.261628	−	0.523256i
$936$			6.00000i			0.196116i
$937$	−35.0000	−	35.0000i	−1.14340	−	1.14340i	−0.987824	−	0.155576i	$-0.950277\pi$
$937$	−35.0000	−	35.0000i	−1.14340	−	1.14340i	−0.155576	−	0.987824i	$-0.549723\pi$
$938$		−	18.0000i		−	0.587721i
$939$	30.0000	−	30.0000i	0.979013	−	0.979013i
$940$	−15.0000	−	5.00000i	−0.489246	−	0.163082i
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$	6.00000			0.195491
$943$		0			0
$944$	7.00000	+	7.00000i	0.227831	+	0.227831i
$945$	−48.0000	+	24.0000i	−1.56144	+	0.780720i
$946$		−	24.0000i		−	0.780307i
$947$	−18.0000			−0.584921			−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000			−0.584921			−0.292461	+	0.956278i	$0.594474\pi$
$948$			6.00000i			0.194871i
$949$	−2.00000	+	2.00000i	−0.0649227	+	0.0649227i
$950$	3.00000	+	21.0000i	0.0973329	+	0.681330i
$951$	34.0000			1.10253
$952$	−36.0000	+	36.0000i	−1.16677	+	1.16677i
$953$	7.00000	+	7.00000i	0.226752	+	0.226752i	0.811334	−	0.584582i	$-0.198742\pi$
$953$	7.00000	+	7.00000i	0.226752	+	0.226752i	−0.584582	+	0.811334i	$0.698742\pi$
$954$	3.00000	−	3.00000i	0.0971286	−	0.0971286i
$955$	11.0000	−	33.0000i	0.355952	−	1.06785i
$956$	−7.00000	−	7.00000i	−0.226396	−	0.226396i
$957$		−	28.0000i		−	0.905111i
$958$	−23.0000	+	23.0000i	−0.743096	+	0.743096i
$959$			42.0000i			1.35625i
$960$	−21.0000	−	7.00000i	−0.677772	−	0.225924i
$961$		−	13.0000i		−	0.419355i
$962$	−12.0000	+	2.00000i	−0.386896	+	0.0644826i
$963$	−3.00000	+	3.00000i	−0.0966736	+	0.0966736i
$964$	1.00000	−	1.00000i	0.0322078	−	0.0322078i
$965$	2.00000	+	4.00000i	0.0643823	+	0.128765i
$966$			48.0000i			1.54437i
$967$	2.00000			0.0643157			0.0321578	−	0.999483i	$-0.489762\pi$
$967$	2.00000			0.0643157			0.0321578	+	0.999483i	$0.489762\pi$
$968$		−	21.0000i		−	0.674966i
$969$			24.0000i			0.770991i
$970$	−8.00000	−	16.0000i	−0.256865	−	0.513729i
$971$	36.0000			1.15529			0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000			1.15529			0.577647	+	0.816286i	$0.303971\pi$
$972$	7.00000	+	7.00000i	0.224525	+	0.224525i
$973$	12.0000	+	12.0000i	0.384702	+	0.384702i
$974$		−	2.00000i		−	0.0640841i
$975$	2.00000	+	14.0000i	0.0640513	+	0.448359i
$976$	−1.00000	−	1.00000i	−0.0320092	−	0.0320092i
$977$			18.0000i			0.575871i	0.957650	+	0.287936i	$0.0929689\pi$
$977$			18.0000i			0.575871i	−0.957650	+	0.287936i	$0.907031\pi$
$978$	−10.0000	+	10.0000i	−0.319765	+	0.319765i
$979$	−10.0000	−	10.0000i	−0.319601	−	0.319601i
$980$	−11.0000	−	22.0000i	−0.351382	−	0.702764i
$981$	3.00000	−	3.00000i	0.0957826	−	0.0957826i
$982$			4.00000i			0.127645i
$983$	15.0000	+	15.0000i	0.478426	+	0.478426i	0.904628	−	0.426202i	$-0.140149\pi$
$983$	15.0000	+	15.0000i	0.478426	+	0.478426i	−0.426202	+	0.904628i	$0.640149\pi$
$984$		0			0
$985$	−3.00000	−	1.00000i	−0.0955879	−	0.0318626i
$986$	−28.0000	−	28.0000i	−0.891702	−	0.891702i
$987$	−30.0000	+	30.0000i	−0.954911	+	0.954911i
$988$	−6.00000	+	6.00000i	−0.190885	+	0.190885i
$989$	96.0000			3.05262
$990$	2.00000	+	4.00000i	0.0635642	+	0.127128i
$991$	39.0000	+	39.0000i	1.23888	+	1.23888i	0.960461	+	0.278415i	$0.0898090\pi$
$991$	39.0000	+	39.0000i	1.23888	+	1.23888i	0.278415	+	0.960461i	$0.410191\pi$
$992$	15.0000	−	15.0000i	0.476250	−	0.476250i
$993$	14.0000			0.444277
$994$	−24.0000	+	24.0000i	−0.761234	+	0.761234i
$995$	−15.0000	+	45.0000i	−0.475532	+	1.42660i
$996$	10.0000			0.316862
$997$	28.0000			0.886769			0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000			0.886769			0.443384	+	0.896332i	$0.353778\pi$
$998$	−27.0000	−	27.0000i	−0.854670	−	0.854670i
$999$	−20.0000	+	28.0000i	−0.632772	+	0.885881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.f.a.142.1	yes	2
5.2	odd	4		925.2.k.a.68.1		2
5.3	odd	4		185.2.k.b.68.1	yes	2
5.4	even	2		925.2.f.b.882.1		2
37.6	odd	4		185.2.k.b.117.1	yes	2
185.43	even	4	inner	185.2.f.a.43.1	✓	2
185.117	even	4		925.2.f.b.43.1		2
185.154	odd	4		925.2.k.a.857.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.f.a.43.1	✓	2	185.43	even	4	inner
185.2.f.a.142.1	yes	2	1.1	even	1	trivial
185.2.k.b.68.1	yes	2	5.3	odd	4
185.2.k.b.117.1	yes	2	37.6	odd	4
925.2.f.b.43.1		2	185.117	even	4
925.2.f.b.882.1		2	5.4	even	2
925.2.k.a.68.1		2	5.2	odd	4
925.2.k.a.857.1		2	185.154	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.f (of order \(4\), degree \(2\), minimal)

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

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