LMFDB - Embedded newform 185.2.k.b.117.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(68,185)]

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, 1]))

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

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

chi := DirichletCharacter("185.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.k (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			117.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	185.117
Dual form			185.2.k.b.68.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	0.934172	−	0.356822i	$-0.116140\pi$
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	−0.356822	+	0.934172i	$0.616140\pi$
$4$	−1.00000			−0.500000
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$	−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	$-0.546115\pi$
$8$	3.00000			1.06066
$9$		−	1.00000i		−	0.333333i
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	−1.00000	−	1.00000i	−0.288675	−	0.288675i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	3.00000	+	3.00000i	0.801784	+	0.801784i
$15$	1.00000	−	3.00000i	0.258199	−	0.774597i
$16$	−1.00000			−0.250000
$17$			4.00000i			0.970143i	0.874475	+	0.485071i	$0.161206\pi$
$17$			4.00000i			0.970143i	−0.874475	+	0.485071i	$0.838794\pi$
$18$			1.00000i			0.235702i
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$	1.00000	+	2.00000i	0.223607	+	0.447214i
$21$		−	6.00000i		−	1.30931i
$22$			2.00000i			0.426401i
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$	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	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−7.00000	−	7.00000i	−1.29987	−	1.29987i	−0.371391	−	0.928477i	$-0.621119\pi$
$30$	−1.00000	+	3.00000i	−0.182574	+	0.547723i
$31$	3.00000	−	3.00000i	0.538816	−	0.538816i	−0.384365	−	0.923181i	$-0.625580\pi$
$31$	3.00000	−	3.00000i	0.538816	−	0.538816i	0.923181	+	0.384365i	$0.125580\pi$
$32$	−5.00000			−0.883883
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$		−	4.00000i		−	0.685994i
$35$	−3.00000	+	9.00000i	−0.507093	+	1.52128i
$36$			1.00000i			0.166667i
$37$	−1.00000	+	6.00000i	−0.164399	+	0.986394i
$37$	−1.00000	+	6.00000i	−0.164399	+	0.986394i
$38$	−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			$\pi$
$42$			6.00000i			0.925820i
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$			2.00000i			0.301511i
$45$	−2.00000	+	1.00000i	−0.298142	+	0.149071i
$46$	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
$50$	3.00000	−	4.00000i	0.424264	−	0.565685i
$51$	−4.00000	+	4.00000i	−0.560112	+	0.560112i
$52$	−2.00000			−0.277350
$53$	−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
$55$	−4.00000	+	2.00000i	−0.539360	+	0.269680i
$56$	−9.00000	−	9.00000i	−1.20268	−	1.20268i
$57$	6.00000			0.794719
$58$	7.00000	+	7.00000i	0.919145	+	0.919145i
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	−0.0850540	−	0.996376i	$-0.527106\pi$
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	0.996376	+	0.0850540i	$0.0271063\pi$
$60$	−1.00000	+	3.00000i	−0.129099	+	0.387298i
$61$	1.00000	−	1.00000i	0.128037	−	0.128037i	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	1.00000	−	1.00000i	0.128037	−	0.128037i	0.768221	+	0.640184i	$0.221142\pi$
$62$	−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	−0.499694	−	0.866202i	$-0.666554\pi$
$67$	3.00000	−	3.00000i	0.366508	−	0.366508i	0.866202	+	0.499694i	$0.166554\pi$
$68$		−	4.00000i		−	0.485071i
$69$	−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	$0.342552\pi$
$72$		−	3.00000i		−	0.353553i
$73$	1.00000	+	1.00000i	0.117041	+	0.117041i	0.763202	−	0.646160i	$-0.223626\pi$
$73$	1.00000	+	1.00000i	0.117041	+	0.117041i	−0.646160	+	0.763202i	$0.723626\pi$
$74$	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	$-0.673290\pi$
$79$	3.00000	−	3.00000i	0.337526	−	0.337526i	0.855436	+	0.517909i	$0.173290\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	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
$87$		−	14.0000i		−	1.50096i
$88$		−	6.00000i		−	0.639602i
$89$	5.00000	+	5.00000i	0.529999	+	0.529999i	0.920572	−	0.390573i	$-0.127723\pi$
$89$	5.00000	+	5.00000i	0.529999	+	0.529999i	−0.390573	+	0.920572i	$0.627723\pi$
$90$	2.00000	−	1.00000i	0.210819	−	0.105409i
$91$	−6.00000	−	6.00000i	−0.628971	−	0.628971i
$92$	8.00000			0.834058
$93$	6.00000			0.622171
$94$	−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
$97$		−	8.00000i		−	0.812277i	−0.913812	−	0.406138i	$-0.866875\pi$
$97$		−	8.00000i		−	0.812277i	0.913812	−	0.406138i	$-0.133125\pi$
$98$		−	11.0000i		−	1.11117i
$99$	−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
$103$		−	14.0000i		−	1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$		−	14.0000i		−	1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$	6.00000			0.588348
$105$	−12.0000	+	6.00000i	−1.17108	+	0.585540i
$106$	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	$-0.815129\pi$
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	0.548683	+	0.836031i	$0.315129\pi$
$110$	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
$113$		−	4.00000i		−	0.376288i	−0.982141	−	0.188144i	$-0.939753\pi$
$113$		−	4.00000i		−	0.376288i	0.982141	−	0.188144i	$-0.0602472\pi$
$114$	−6.00000			−0.561951
$115$	8.00000	+	16.0000i	0.746004	+	1.49201i
$116$	7.00000	+	7.00000i	0.649934	+	0.649934i
$117$		−	2.00000i		−	0.184900i
$118$	−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
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$	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	$0.558988\pi$
$128$	3.00000			0.265165
$129$	12.0000	+	12.0000i	1.05654	+	1.05654i
$130$	2.00000	+	4.00000i	0.175412	+	0.350823i
$131$	−5.00000	+	5.00000i	−0.436852	+	0.436852i	−0.890951	−	0.454099i	$-0.849961\pi$
$131$	−5.00000	+	5.00000i	−0.436852	+	0.436852i	0.454099	+	0.890951i	$0.349961\pi$
$132$	−2.00000	+	2.00000i	−0.174078	+	0.174078i
$133$	−18.0000			−1.56080
$134$	−3.00000	+	3.00000i	−0.259161	+	0.259161i
$135$	−12.0000	−	4.00000i	−1.03280	−	0.344265i
$136$			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	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	3.00000	−	9.00000i	0.253546	−	0.760639i
$141$			10.0000i			0.842152i
$142$	−8.00000			−0.671345
$143$		−	4.00000i		−	0.334497i
$144$			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
$148$	1.00000	−	6.00000i	0.0821995	−	0.493197i
$149$			16.0000i			1.31077i	0.755295	+	0.655386i	$0.227494\pi$
$149$			16.0000i			1.31077i	−0.755295	+	0.655386i	$0.772506\pi$
$150$	7.00000	−	1.00000i	0.571548	−	0.0816497i
$151$			2.00000i			0.162758i	0.996683	+	0.0813788i	$0.0259324\pi$
$151$			2.00000i			0.162758i	−0.996683	+	0.0813788i	$0.974068\pi$
$152$	9.00000	−	9.00000i	0.729996	−	0.729996i
$153$	4.00000			0.323381
$154$	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
$162$	−5.00000			−0.392837
$163$		−	10.0000i		−	0.783260i	−0.920123	−	0.391630i	$-0.871911\pi$
$163$		−	10.0000i		−	0.783260i	0.920123	−	0.391630i	$-0.128089\pi$
$164$		0			0
$165$	−6.00000	−	2.00000i	−0.467099	−	0.155700i
$166$	5.00000	−	5.00000i	0.388075	−	0.388075i
$167$		−	6.00000i		−	0.464294i	−0.972681	−	0.232147i	$-0.925425\pi$
$167$		−	6.00000i		−	0.464294i	0.972681	−	0.232147i	$-0.0745750\pi$
$168$		−	18.0000i		−	1.38873i
$169$	−9.00000			−0.692308
$170$	−8.00000	+	4.00000i	−0.613572	+	0.306786i
$171$	−3.00000	−	3.00000i	−0.229416	−	0.229416i
$172$	−12.0000			−0.914991
$173$	1.00000	+	1.00000i	0.0760286	+	0.0760286i	0.744099	−	0.668070i	$-0.232879\pi$
$173$	1.00000	+	1.00000i	0.0760286	+	0.0760286i	−0.668070	+	0.744099i	$0.732879\pi$
$174$			14.0000i			1.06134i
$175$	21.0000	−	3.00000i	1.58745	−	0.226779i
$176$			2.00000i			0.150756i
$177$	14.0000			1.05230
$178$	−5.00000	−	5.00000i	−0.374766	−	0.374766i
$179$	−7.00000	−	7.00000i	−0.523205	−	0.523205i	0.395333	−	0.918538i	$-0.370629\pi$
$179$	−7.00000	−	7.00000i	−0.523205	−	0.523205i	−0.918538	+	0.395333i	$0.870629\pi$
$180$	2.00000	−	1.00000i	0.149071	−	0.0745356i
$181$	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
$183$	2.00000			0.147844
$184$	−24.0000			−1.76930
$185$	13.0000	−	4.00000i	0.955779	−	0.294086i
$186$	−6.00000			−0.439941
$187$	8.00000			0.585018
$188$	−5.00000	−	5.00000i	−0.364662	−	0.364662i
$189$	−24.0000			−1.74574
$190$	9.00000	+	3.00000i	0.652929	+	0.217643i
$191$	−11.0000	−	11.0000i	−0.795932	−	0.795932i	0.186519	−	0.982451i	$-0.440279\pi$
$191$	−11.0000	−	11.0000i	−0.795932	−	0.795932i	−0.982451	+	0.186519i	$0.940279\pi$
$192$	7.00000	+	7.00000i	0.505181	+	0.505181i
$193$	2.00000			0.143963			0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000			0.143963			0.0719816	+	0.997406i	$0.477068\pi$
$194$			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	$0.733957\pi$
$198$	2.00000			0.142134
$199$	−15.0000	−	15.0000i	−1.06332	−	1.06332i	−0.997855	−	0.0654671i	$-0.979146\pi$
$199$	−15.0000	−	15.0000i	−1.06332	−	1.06332i	−0.0654671	−	0.997855i	$-0.520854\pi$
$200$	−9.00000	+	12.0000i	−0.636396	+	0.848528i
$201$	6.00000			0.423207
$202$		0			0
$203$			42.0000i			2.94782i
$204$	4.00000	−	4.00000i	0.280056	−	0.280056i
$205$		0			0
$206$			14.0000i			0.975426i
$207$			8.00000i			0.556038i
$208$	−2.00000			−0.138675
$209$	−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
$217$	−18.0000			−1.22192
$218$	3.00000	−	3.00000i	0.203186	−	0.203186i
$219$			2.00000i			0.135147i
$220$	4.00000	−	2.00000i	0.269680	−	0.134840i
$221$			8.00000i			0.538138i
$222$	7.00000	−	5.00000i	0.469809	−	0.335578i
$223$	−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
$227$		−	2.00000i		−	0.132745i	−0.997795	−	0.0663723i	$-0.978857\pi$
$227$		−	2.00000i		−	0.132745i	0.997795	−	0.0663723i	$-0.0211425\pi$
$228$	−6.00000			−0.397360
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$	−8.00000	−	16.0000i	−0.527504	−	1.05501i
$231$	−12.0000			−0.789542
$232$	−21.0000	−	21.0000i	−1.37872	−	1.37872i
$233$	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	$0.735249\pi$
$234$			2.00000i			0.130744i
$235$	5.00000	−	15.0000i	0.326164	−	0.978492i
$236$	−7.00000	+	7.00000i	−0.455661	+	0.455661i
$237$	6.00000			0.389742
$238$	−12.0000	+	12.0000i	−0.777844	+	0.777844i
$239$	7.00000	−	7.00000i	0.452792	−	0.452792i	−0.443488	−	0.896280i	$-0.646259\pi$
$239$	7.00000	−	7.00000i	0.452792	−	0.452792i	0.896280	+	0.443488i	$0.146259\pi$
$240$	−1.00000	+	3.00000i	−0.0645497	+	0.193649i
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	0.738581	−	0.674165i	$-0.235496\pi$
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	−0.674165	+	0.738581i	$0.735496\pi$
$242$	−7.00000			−0.449977
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$	−1.00000	+	1.00000i	−0.0640184	+	0.0640184i
$245$	22.0000	−	11.0000i	1.40553	−	0.702764i
$246$		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	−0.847073	−	0.531476i	$-0.821638\pi$
$251$	−5.00000	+	5.00000i	−0.315597	+	0.315597i	0.531476	+	0.847073i	$0.321638\pi$
$252$	3.00000	−	3.00000i	0.188982	−	0.188982i
$253$			16.0000i			1.00591i
$254$	−9.00000	−	9.00000i	−0.564710	−	0.564710i
$255$	12.0000	+	4.00000i	0.751469	+	0.250490i
$256$	−17.0000			−1.06250
$257$			28.0000i			1.74659i	0.487190	+	0.873296i	$0.338022\pi$
$257$			28.0000i			1.74659i	−0.487190	+	0.873296i	$0.661978\pi$
$258$	−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	0.457547	−	0.889185i	$-0.348728\pi$
$263$	−7.00000	−	7.00000i	−0.431638	−	0.431638i	−0.889185	+	0.457547i	$0.848728\pi$
$264$	6.00000	−	6.00000i	0.369274	−	0.369274i
$265$	9.00000	+	3.00000i	0.552866	+	0.184289i
$266$	18.0000			1.10365
$267$			10.0000i			0.611990i
$268$	−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	$0.578126\pi$
$272$		−	4.00000i		−	0.242536i
$273$		−	12.0000i		−	0.726273i
$274$	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
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$	−4.00000			−0.239904
$279$	−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	0.922616	−	0.385721i	$-0.126047\pi$
$281$	9.00000	+	9.00000i	0.536895	+	0.536895i	−0.385721	+	0.922616i	$0.626047\pi$
$282$		−	10.0000i		−	0.595491i
$283$			22.0000i			1.30776i	0.756596	+	0.653882i	$0.226861\pi$
$283$			22.0000i			1.30776i	−0.756596	+	0.653882i	$0.773139\pi$
$284$	−8.00000			−0.474713
$285$	−6.00000	−	12.0000i	−0.355409	−	0.710819i
$286$			4.00000i			0.236525i
$287$		0			0
$288$			5.00000i			0.294628i
$289$	1.00000			0.0588235
$290$	7.00000	−	21.0000i	0.411054	−	1.23316i
$291$	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
$298$		−	16.0000i		−	0.926855i
$299$	−16.0000			−0.925304
$300$	7.00000	−	1.00000i	0.404145	−	0.0577350i
$301$	−36.0000	−	36.0000i	−2.07501	−	2.07501i
$302$		−	2.00000i		−	0.115087i
$303$		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	−0.915645	−	0.401988i	$-0.868319\pi$
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	0.401988	+	0.915645i	$0.368319\pi$
$308$	6.00000	−	6.00000i	0.341882	−	0.341882i
$309$	14.0000	−	14.0000i	0.796432	−	0.796432i
$310$	9.00000	+	3.00000i	0.511166	+	0.170389i
$311$	3.00000	−	3.00000i	0.170114	−	0.170114i	−0.616915	−	0.787030i	$-0.711618\pi$
$311$	3.00000	−	3.00000i	0.170114	−	0.170114i	0.787030	+	0.616915i	$0.211618\pi$
$312$	6.00000	+	6.00000i	0.339683	+	0.339683i
$313$	−30.0000			−1.69570			−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−30.0000			−1.69570			−0.847850	+	0.530236i	$0.822103\pi$
$314$	3.00000	+	3.00000i	0.169300	+	0.169300i
$315$	9.00000	+	3.00000i	0.507093	+	0.169031i
$316$	−3.00000	+	3.00000i	−0.168763	+	0.168763i
$317$	17.0000	−	17.0000i	0.954815	−	0.954815i	−0.0442073	−	0.999022i	$-0.514076\pi$
$317$	17.0000	−	17.0000i	0.954815	−	0.954815i	0.999022	+	0.0442073i	$0.0140762\pi$
$318$	6.00000			0.336463
$319$	−14.0000	+	14.0000i	−0.783850	+	0.783850i
$320$	−7.00000	−	14.0000i	−0.391312	−	0.782624i
$321$		−	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
$325$	−6.00000	+	8.00000i	−0.332820	+	0.443760i
$326$			10.0000i			0.553849i
$327$	−6.00000			−0.331801
$328$		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	0.488057	−	0.872812i	$-0.337706\pi$
$331$	−7.00000	−	7.00000i	−0.384755	−	0.384755i	−0.872812	+	0.488057i	$0.837706\pi$
$332$	5.00000	−	5.00000i	0.274411	−	0.274411i
$333$	6.00000	+	1.00000i	0.328798	+	0.0547997i
$334$			6.00000i			0.328305i
$335$	−9.00000	−	3.00000i	−0.491723	−	0.163908i
$336$			6.00000i			0.327327i
$337$	−15.0000	+	15.0000i	−0.817102	+	0.817102i	−0.985687	−	0.168585i	$-0.946080\pi$
$337$	−15.0000	+	15.0000i	−0.817102	+	0.817102i	0.168585	+	0.985687i	$0.446080\pi$
$338$	9.00000			0.489535
$339$	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
$347$	4.00000			0.214731			0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000			0.214731			0.107366	+	0.994220i	$0.465758\pi$
$348$			14.0000i			0.750479i
$349$			32.0000i			1.71292i	0.516213	+	0.856460i	$0.327341\pi$
$349$			32.0000i			1.71292i	−0.516213	+	0.856460i	$0.672659\pi$
$350$	−21.0000	+	3.00000i	−1.12250	+	0.160357i
$351$	8.00000	−	8.00000i	0.427008	−	0.427008i
$352$			10.0000i			0.533002i
$353$		−	32.0000i		−	1.70319i	−0.524202	−	0.851594i	$-0.675636\pi$
$353$		−	32.0000i		−	1.70319i	0.524202	−	0.851594i	$-0.324364\pi$
$354$	−14.0000			−0.744092
$355$	−8.00000	−	16.0000i	−0.424596	−	0.849192i
$356$	−5.00000	−	5.00000i	−0.264999	−	0.264999i
$357$	24.0000			1.27021
$358$	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
$362$	−10.0000			−0.525588
$363$	7.00000	+	7.00000i	0.367405	+	0.367405i
$364$	6.00000	+	6.00000i	0.314485	+	0.314485i
$365$	1.00000	−	3.00000i	0.0523424	−	0.157027i
$366$	−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	$0.534086\pi$
$368$	8.00000			0.417029
$369$		0			0
$370$	−13.0000	+	4.00000i	−0.675838	+	0.207950i
$371$	18.0000			0.934513
$372$	−6.00000			−0.311086
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	0.625161	−	0.780496i	$-0.285033\pi$
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	−0.780496	+	0.625161i	$0.785033\pi$
$374$	−8.00000			−0.413670
$375$	9.00000	+	13.0000i	0.464758	+	0.671317i
$376$	15.0000	+	15.0000i	0.773566	+	0.773566i
$377$	−14.0000	−	14.0000i	−0.721037	−	0.721037i
$378$	24.0000			1.23443
$379$			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
$383$	8.00000			0.408781			0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000			0.408781			0.204390	+	0.978889i	$0.434479\pi$
$384$	3.00000	+	3.00000i	0.153093	+	0.153093i
$385$	18.0000	+	6.00000i	0.917365	+	0.305788i
$386$	−2.00000			−0.101797
$387$		−	12.0000i		−	0.609994i
$388$			8.00000i			0.406138i
$389$	5.00000	−	5.00000i	0.253510	−	0.253510i	−0.568898	−	0.822408i	$-0.692630\pi$
$389$	5.00000	−	5.00000i	0.253510	−	0.253510i	0.822408	+	0.568898i	$0.192630\pi$
$390$	−2.00000	+	6.00000i	−0.101274	+	0.303822i
$391$		−	32.0000i		−	1.61831i
$392$			33.0000i			1.66675i
$393$	−10.0000			−0.504433
$394$	−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	−0.570414	−	0.821357i	$-0.693217\pi$
$397$	5.00000	−	5.00000i	0.250943	−	0.250943i	0.821357	+	0.570414i	$0.193217\pi$
$398$	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	−0.681697	−	0.731635i	$-0.738758\pi$
$401$	1.00000	−	1.00000i	0.0499376	−	0.0499376i	0.731635	+	0.681697i	$0.238758\pi$
$402$	−6.00000			−0.299253
$403$	6.00000	−	6.00000i	0.298881	−	0.298881i
$404$		0			0
$405$	−5.00000	−	10.0000i	−0.248452	−	0.496904i
$406$		−	42.0000i		−	2.08443i
$407$	12.0000	+	2.00000i	0.594818	+	0.0991363i
$408$	−12.0000	+	12.0000i	−0.594089	+	0.594089i
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	0.629036	−	0.777376i	$-0.283450\pi$
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	−0.777376	+	0.629036i	$0.783450\pi$
$410$		0			0
$411$		−	14.0000i		−	0.690569i
$412$			14.0000i			0.689730i
$413$	−42.0000			−2.06668
$414$		−	8.00000i		−	0.393179i
$415$	15.0000	+	5.00000i	0.736321	+	0.245440i
$416$	−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	$0.819412\pi$
$420$	12.0000	−	6.00000i	0.585540	−	0.292770i
$421$	−27.0000	+	27.0000i	−1.31590	+	1.31590i	−0.398909	+	0.916991i	$0.630611\pi$
$421$	−27.0000	+	27.0000i	−1.31590	+	1.31590i	−0.916991	+	0.398909i	$0.869389\pi$
$422$	−20.0000			−0.973585
$423$	5.00000	−	5.00000i	0.243108	−	0.243108i
$424$	−9.00000	+	9.00000i	−0.437079	+	0.437079i
$425$	−16.0000	−	12.0000i	−0.776114	−	0.582086i
$426$	−8.00000	−	8.00000i	−0.387601	−	0.387601i
$427$	−6.00000			−0.290360
$428$	3.00000	+	3.00000i	0.145010	+	0.145010i
$429$	4.00000	−	4.00000i	0.193122	−	0.193122i
$430$	12.0000	+	24.0000i	0.578691	+	1.15738i
$431$	11.0000	−	11.0000i	0.529851	−	0.529851i	−0.390677	−	0.920528i	$-0.627759\pi$
$431$	11.0000	−	11.0000i	0.529851	−	0.529851i	0.920528	+	0.390677i	$0.127759\pi$
$432$	−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
$438$		−	2.00000i		−	0.0955637i
$439$	17.0000	+	17.0000i	0.811366	+	0.811366i	0.984839	−	0.173473i	$-0.0554989\pi$
$439$	17.0000	+	17.0000i	0.811366	+	0.811366i	−0.173473	+	0.984839i	$0.555499\pi$
$440$	−12.0000	+	6.00000i	−0.572078	+	0.286039i
$441$	11.0000			0.523810
$442$		−	8.00000i		−	0.380521i
$443$	−11.0000	−	11.0000i	−0.522626	−	0.522626i	0.395738	−	0.918364i	$-0.370489\pi$
$443$	−11.0000	−	11.0000i	−0.522626	−	0.522626i	−0.918364	+	0.395738i	$0.870489\pi$
$444$	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	$-0.696640\pi$
$449$	5.00000	−	5.00000i	0.235965	−	0.235965i	0.815177	+	0.579212i	$0.196640\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$		0			0
$452$			4.00000i			0.188144i
$453$	−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
$457$		−	32.0000i		−	1.49690i	−0.663193	−	0.748448i	$-0.730799\pi$
$457$		−	32.0000i		−	1.49690i	0.663193	−	0.748448i	$-0.269201\pi$
$458$		−	4.00000i		−	0.186908i
$459$	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	0.999765	−	0.0216971i	$-0.00690694\pi$
$461$	21.0000	+	21.0000i	0.978068	+	0.978068i	−0.0216971	+	0.999765i	$0.506907\pi$
$462$	12.0000			0.558291
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$	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
$467$			38.0000i			1.75843i	0.476425	+	0.879215i	$0.341932\pi$
$467$			38.0000i			1.75843i	−0.476425	+	0.879215i	$0.658068\pi$
$468$			2.00000i			0.0924500i
$469$	−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
$473$		−	24.0000i		−	1.10352i
$474$	−6.00000			−0.275589
$475$	3.00000	+	21.0000i	0.137649	+	0.963546i
$476$	−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	0.0522635	−	0.998633i	$-0.483356\pi$
$479$	23.0000	−	23.0000i	1.05090	−	1.05090i	0.998633	−	0.0522635i	$-0.0166436\pi$
$480$	−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
$483$			48.0000i			2.18408i
$484$	−7.00000			−0.318182
$485$	−16.0000	+	8.00000i	−0.726523	+	0.363261i
$486$	7.00000	+	7.00000i	0.317526	+	0.317526i
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$	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
$495$	2.00000	+	4.00000i	0.0898933	+	0.179787i
$496$	−3.00000	+	3.00000i	−0.134704	+	0.134704i
$497$	−24.0000	−	24.0000i	−1.07655	−	1.07655i
$498$	10.0000			0.448111
$499$	−27.0000	−	27.0000i	−1.20869	−	1.20869i	−0.971453	−	0.237233i	$-0.923759\pi$
$499$	−27.0000	−	27.0000i	−1.20869	−	1.20869i	−0.237233	−	0.971453i	$-0.576241\pi$
$500$	−11.0000	−	2.00000i	−0.491935	−	0.0894427i
$501$	6.00000	−	6.00000i	0.268060	−	0.268060i
$502$	5.00000	−	5.00000i	0.223161	−	0.223161i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−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	$-0.268490\pi$
$509$	30.0000			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$510$	−12.0000	−	4.00000i	−0.531369	−	0.177123i
$511$		−	6.00000i		−	0.265424i
$512$	11.0000			0.486136
$513$		−	24.0000i		−	1.05963i
$514$		−	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
$518$	−21.0000	+	15.0000i	−0.922687	+	0.659062i
$519$			2.00000i			0.0877903i
$520$	−6.00000	−	12.0000i	−0.263117	−	0.526235i
$521$		−	44.0000i		−	1.92767i	−0.266491	−	0.963837i	$-0.585864\pi$
$521$		−	44.0000i		−	1.92767i	0.266491	−	0.963837i	$-0.414136\pi$
$522$	7.00000	−	7.00000i	0.306382	−	0.306382i
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$	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
$532$	18.0000			0.780399
$533$		0			0
$534$		−	10.0000i		−	0.432742i
$535$	−3.00000	+	9.00000i	−0.129701	+	0.389104i
$536$	9.00000	−	9.00000i	0.388741	−	0.388741i
$537$		−	14.0000i		−	0.604145i
$538$			16.0000i			0.689809i
$539$	22.0000			0.947607
$540$	12.0000	+	4.00000i	0.516398	+	0.172133i
$541$	1.00000	+	1.00000i	0.0429934	+	0.0429934i	0.728277	−	0.685283i	$-0.240322\pi$
$541$	1.00000	+	1.00000i	0.0429934	+	0.0429934i	−0.685283	+	0.728277i	$0.740322\pi$
$542$	8.00000			0.343629
$543$	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
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	7.00000	+	7.00000i	0.299025	+	0.299025i
$549$	−1.00000	−	1.00000i	−0.0426790	−	0.0426790i
$550$	−8.00000	−	6.00000i	−0.341121	−	0.255841i
$551$	−42.0000			−1.78926
$552$	−24.0000	−	24.0000i	−1.02151	−	1.02151i
$553$	−18.0000			−0.765438
$554$	−26.0000			−1.10463
$555$	17.0000	+	9.00000i	0.721610	+	0.382029i
$556$	−4.00000			−0.169638
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$	3.00000	+	3.00000i	0.127000	+	0.127000i
$559$	24.0000			1.01509
$560$	3.00000	−	9.00000i	0.126773	−	0.380319i
$561$	8.00000	+	8.00000i	0.337760	+	0.337760i
$562$	−9.00000	−	9.00000i	−0.379642	−	0.379642i
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		−	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
$568$	24.0000			1.00702
$569$	25.0000	+	25.0000i	1.04805	+	1.04805i	0.998786	+	0.0492690i	$0.0156892\pi$
$569$	25.0000	+	25.0000i	1.04805	+	1.04805i	0.0492690	+	0.998786i	$0.484311\pi$
$570$	6.00000	+	12.0000i	0.251312	+	0.502625i
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$			4.00000i			0.167248i
$573$		−	22.0000i		−	0.919063i
$574$		0			0
$575$	24.0000	−	32.0000i	1.00087	−	1.33449i
$576$		−	7.00000i		−	0.291667i
$577$			12.0000i			0.499567i	0.968302	+	0.249783i	$0.0803594\pi$
$577$			12.0000i			0.499567i	−0.968302	+	0.249783i	$0.919641\pi$
$578$	−1.00000			−0.0415945
$579$	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
$587$	−36.0000			−1.48588			−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000			−1.48588			−0.742940	+	0.669359i	$0.766569\pi$
$588$	11.0000	−	11.0000i	0.453632	−	0.453632i
$589$		−	18.0000i		−	0.741677i
$590$	21.0000	+	7.00000i	0.864556	+	0.288185i
$591$			2.00000i			0.0822690i
$592$	1.00000	−	6.00000i	0.0410997	−	0.246598i
$593$	−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
$597$		−	30.0000i		−	1.22782i
$598$	16.0000			0.654289
$599$		−	6.00000i		−	0.245153i	−0.992459	−	0.122577i	$-0.960884\pi$
$599$		−	6.00000i		−	0.245153i	0.992459	−	0.122577i	$-0.0391157\pi$
$600$	−21.0000	+	3.00000i	−0.857321	+	0.122474i
$601$	−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
$605$	−7.00000	−	14.0000i	−0.284590	−	0.569181i
$606$		0			0
$607$	−32.0000			−1.29884			−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000			−1.29884			−0.649420	+	0.760430i	$0.724988\pi$
$608$	−15.0000	+	15.0000i	−0.608330	+	0.608330i
$609$	−42.0000	+	42.0000i	−1.70193	+	1.70193i
$610$	3.00000	+	1.00000i	0.121466	+	0.0404888i
$611$	10.0000	+	10.0000i	0.404557	+	0.404557i
$612$	−4.00000			−0.161690
$613$	21.0000	+	21.0000i	0.848182	+	0.848182i	0.989906	−	0.141724i	$-0.0452646\pi$
$613$	21.0000	+	21.0000i	0.848182	+	0.848182i	−0.141724	+	0.989906i	$0.545265\pi$
$614$	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	−0.276593	−	0.960987i	$-0.589205\pi$
$617$	17.0000	−	17.0000i	0.684394	−	0.684394i	0.960987	+	0.276593i	$0.0892054\pi$
$618$	−14.0000	+	14.0000i	−0.563163	+	0.563163i
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$	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
$623$		−	30.0000i		−	1.20192i
$624$	−2.00000	−	2.00000i	−0.0800641	−	0.0800641i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	30.0000			1.19904
$627$		−	12.0000i		−	0.479234i
$628$	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	−0.0810911	−	0.996707i	$-0.525840\pi$
$631$	23.0000	−	23.0000i	0.915616	−	0.915616i	0.996707	+	0.0810911i	$0.0258405\pi$
$632$	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
$635$	9.00000	−	27.0000i	0.357154	−	1.07146i
$636$	6.00000			0.237915
$637$			22.0000i			0.871672i
$638$	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	$0.615682\pi$
$642$			6.00000i			0.236801i
$643$		−	10.0000i		−	0.394362i	−0.980367	−	0.197181i	$-0.936821\pi$
$643$		−	10.0000i		−	0.394362i	0.980367	−	0.197181i	$-0.0631786\pi$
$644$	−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
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$	15.0000			0.589256
$649$	−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
$652$			10.0000i			0.391630i
$653$			36.0000i			1.40879i	0.709809	+	0.704394i	$0.248781\pi$
$653$			36.0000i			1.40879i	−0.709809	+	0.704394i	$0.751219\pi$
$654$	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
$658$			30.0000i			1.16952i
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$	6.00000	+	2.00000i	0.233550	+	0.0778499i
$661$	33.0000	−	33.0000i	1.28355	−	1.28355i	0.344919	−	0.938633i	$-0.387906\pi$
$661$	33.0000	−	33.0000i	1.28355	−	1.28355i	0.938633	−	0.344919i	$-0.112094\pi$
$662$	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
$668$			6.00000i			0.232147i
$669$	−2.00000			−0.0773245
$670$	9.00000	+	3.00000i	0.347700	+	0.115900i
$671$	−2.00000	−	2.00000i	−0.0772091	−	0.0772091i
$672$			30.0000i			1.15728i
$673$	−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	−0.993935	−	0.109973i	$-0.964924\pi$
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	0.109973	+	0.993935i	$0.464924\pi$
$678$	−4.00000	+	4.00000i	−0.153619	+	0.153619i
$679$	−24.0000	+	24.0000i	−0.921035	+	0.921035i
$680$	24.0000	−	12.0000i	0.920358	−	0.460179i
$681$	2.00000	−	2.00000i	0.0766402	−	0.0766402i
$682$	6.00000	+	6.00000i	0.229752	+	0.229752i
$683$	4.00000			0.153056			0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$	3.00000	+	3.00000i	0.114708	+	0.114708i
$685$	−7.00000	+	21.0000i	−0.267456	+	0.802369i
$686$	−12.0000	+	12.0000i	−0.458162	+	0.458162i
$687$	−4.00000	+	4.00000i	−0.152610	+	0.152610i
$688$	−12.0000			−0.457496
$689$	−6.00000	+	6.00000i	−0.228582	+	0.228582i
$690$	8.00000	−	24.0000i	0.304555	−	0.913664i
$691$			46.0000i			1.74992i	0.484193	+	0.874961i	$0.339113\pi$
$691$			46.0000i			1.74992i	−0.484193	+	0.874961i	$0.660887\pi$
$692$	−1.00000	−	1.00000i	−0.0380143	−	0.0380143i
$693$	6.00000	+	6.00000i	0.227921	+	0.227921i
$694$	−4.00000			−0.151838
$695$	−4.00000	−	8.00000i	−0.151729	−	0.303457i
$696$		−	42.0000i		−	1.59201i
$697$		0			0
$698$		−	32.0000i		−	1.21122i
$699$			2.00000i			0.0756469i
$700$	−21.0000	+	3.00000i	−0.793725	+	0.113389i
$701$	9.00000	+	9.00000i	0.339925	+	0.339925i	0.856339	−	0.516414i	$-0.172733\pi$
$701$	9.00000	+	9.00000i	0.339925	+	0.339925i	−0.516414	+	0.856339i	$0.672733\pi$
$702$	−8.00000	+	8.00000i	−0.301941	+	0.301941i
$703$	15.0000	+	21.0000i	0.565736	+	0.792030i
$704$		−	14.0000i		−	0.527645i
$705$	20.0000	−	10.0000i	0.753244	−	0.376622i
$706$			32.0000i			1.20434i
$707$		0			0
$708$	−14.0000			−0.526152
$709$	−15.0000	+	15.0000i	−0.563337	+	0.563337i	−0.930254	−	0.366917i	$-0.880413\pi$
$709$	−15.0000	+	15.0000i	−0.563337	+	0.563337i	0.366917	+	0.930254i	$0.380413\pi$
$710$	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
$717$	14.0000			0.522840
$718$		−	34.0000i		−	1.26887i
$719$			26.0000i			0.969636i	0.874615	+	0.484818i	$0.161114\pi$
$719$			26.0000i			0.969636i	−0.874615	+	0.484818i	$0.838886\pi$
$720$	2.00000	−	1.00000i	0.0745356	−	0.0372678i
$721$	−42.0000	+	42.0000i	−1.56416	+	1.56416i
$722$		−	1.00000i		−	0.0372161i
$723$			2.00000i			0.0743808i
$724$	−10.0000			−0.371647
$725$	49.0000	−	7.00000i	1.81981	−	0.259973i
$726$	−7.00000	−	7.00000i	−0.259794	−	0.259794i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−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
$732$	−2.00000			−0.0739221
$733$	−3.00000	−	3.00000i	−0.110808	−	0.110808i	0.649529	−	0.760337i	$-0.274966\pi$
$733$	−3.00000	−	3.00000i	−0.110808	−	0.110808i	−0.760337	+	0.649529i	$0.774966\pi$
$734$	−17.0000	−	17.0000i	−0.627481	−	0.627481i
$735$	33.0000	+	11.0000i	1.21722	+	0.405741i
$736$	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	$-0.199856\pi$
$739$	44.0000			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$740$	−13.0000	+	4.00000i	−0.477890	+	0.147043i
$741$	12.0000			0.440831
$742$	−18.0000			−0.660801
$743$	5.00000	+	5.00000i	0.183432	+	0.183432i	0.792850	−	0.609417i	$-0.208597\pi$
$743$	5.00000	+	5.00000i	0.183432	+	0.183432i	−0.609417	+	0.792850i	$0.708597\pi$
$744$	18.0000			0.659912
$745$	32.0000	−	16.0000i	1.17239	−	0.586195i
$746$	3.00000	+	3.00000i	0.109838	+	0.109838i
$747$	5.00000	+	5.00000i	0.182940	+	0.182940i
$748$	−8.00000			−0.292509
$749$			18.0000i			0.657706i
$750$	−9.00000	−	13.0000i	−0.328634	−	0.474693i
$751$		−	22.0000i		−	0.802791i	−0.915905	−	0.401396i	$-0.868525\pi$
$751$		−	22.0000i		−	0.802791i	0.915905	−	0.401396i	$-0.131475\pi$
$752$	−5.00000	−	5.00000i	−0.182331	−	0.182331i
$753$	−10.0000			−0.364420
$754$	14.0000	+	14.0000i	0.509850	+	0.509850i
$755$	4.00000	−	2.00000i	0.145575	−	0.0727875i
$756$	24.0000			0.872872
$757$		−	36.0000i		−	1.30844i	−0.756303	−	0.654221i	$-0.772997\pi$
$757$		−	36.0000i		−	1.30844i	0.756303	−	0.654221i	$-0.227003\pi$
$758$		−	14.0000i		−	0.508503i
$759$	−16.0000	+	16.0000i	−0.580763	+	0.580763i
$760$	−27.0000	−	9.00000i	−0.979393	−	0.326464i
$761$			8.00000i			0.290000i	0.989432	+	0.145000i	$0.0463182\pi$
$761$			8.00000i			0.290000i	−0.989432	+	0.145000i	$0.953682\pi$
$762$		−	18.0000i		−	0.652071i
$763$	18.0000			0.651644
$764$	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	$-0.374931\pi$
$769$	−15.0000	−	15.0000i	−0.540914	−	0.540914i	−0.923797	+	0.382883i	$0.874931\pi$
$770$	−18.0000	−	6.00000i	−0.648675	−	0.216225i
$771$	−28.0000	+	28.0000i	−1.00840	+	1.00840i
$772$	−2.00000			−0.0719816
$773$	−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
$775$	3.00000	+	21.0000i	0.107763	+	0.754342i
$776$		−	24.0000i		−	0.861550i
$777$	36.0000	+	6.00000i	1.29149	+	0.215249i
$778$	−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
$782$			32.0000i			1.14432i
$783$	−56.0000			−2.00128
$784$		−	11.0000i		−	0.392857i
$785$	−3.00000	+	9.00000i	−0.107075	+	0.321224i
$786$	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
$790$	9.00000	+	3.00000i	0.320206	+	0.106735i
$791$	−12.0000	+	12.0000i	−0.426671	+	0.426671i
$792$	−6.00000			−0.213201
$793$	2.00000	−	2.00000i	0.0710221	−	0.0710221i
$794$	−5.00000	+	5.00000i	−0.177443	+	0.177443i
$795$	6.00000	+	12.0000i	0.212798	+	0.425596i
$796$	15.0000	+	15.0000i	0.531661	+	0.531661i
$797$	−46.0000			−1.62940			−0.814702	−	0.579880i	$-0.803099\pi$
$797$	−46.0000			−1.62940			−0.814702	+	0.579880i	$0.803099\pi$
$798$	18.0000	+	18.0000i	0.637193	+	0.637193i
$799$	−20.0000	+	20.0000i	−0.707549	+	0.707549i
$800$	15.0000	−	20.0000i	0.530330	−	0.707107i
$801$	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	$-0.0365180\pi$
$809$	25.0000	+	25.0000i	0.878953	+	0.878953i	−0.114473	+	0.993426i	$0.536518\pi$
$810$	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	$0.385792\pi$
$812$		−	42.0000i		−	1.47391i
$813$	−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	$0.601703\pi$
$822$			14.0000i			0.488306i
$823$	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
$827$			38.0000i			1.32139i	0.750655	+	0.660695i	$0.229738\pi$
$827$			38.0000i			1.32139i	−0.750655	+	0.660695i	$0.770262\pi$
$828$		−	8.00000i		−	0.278019i
$829$	21.0000	+	21.0000i	0.729360	+	0.729360i	0.970492	−	0.241132i	$-0.0775187\pi$
$829$	21.0000	+	21.0000i	0.729360	+	0.729360i	−0.241132	+	0.970492i	$0.577519\pi$
$830$	−15.0000	−	5.00000i	−0.520658	−	0.173553i
$831$	26.0000	+	26.0000i	0.901930	+	0.901930i
$832$	14.0000			0.485363
$833$	−44.0000			−1.52451
$834$	−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
$837$		−	24.0000i		−	0.829561i
$838$		−	22.0000i		−	0.759977i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$	−36.0000	+	18.0000i	−1.24212	+	0.621059i
$841$			69.0000i			2.37931i
$842$	27.0000	−	27.0000i	0.930481	−	0.930481i
$843$			18.0000i			0.619953i
$844$	−20.0000			−0.688428
$845$	9.00000	+	18.0000i	0.309609	+	0.619219i
$846$	−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
$853$		−	44.0000i		−	1.50653i	−0.657716	−	0.753266i	$-0.728477\pi$
$853$		−	44.0000i		−	1.50653i	0.657716	−	0.753266i	$-0.271523\pi$
$854$	6.00000			0.205316
$855$	−3.00000	+	9.00000i	−0.102598	+	0.307794i
$856$	−9.00000	−	9.00000i	−0.307614	−	0.307614i
$857$		−	32.0000i		−	1.09310i	−0.837427	−	0.546550i	$-0.815941\pi$
$857$		−	32.0000i		−	1.09310i	0.837427	−	0.546550i	$-0.184059\pi$
$858$	−4.00000	+	4.00000i	−0.136558	+	0.136558i
$859$	7.00000	−	7.00000i	0.238837	−	0.238837i	−0.577531	−	0.816368i	$-0.695984\pi$
$859$	7.00000	−	7.00000i	0.238837	−	0.238837i	0.816368	+	0.577531i	$0.195984\pi$
$860$	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
$865$	1.00000	−	3.00000i	0.0340010	−	0.102003i
$866$	−5.00000	+	5.00000i	−0.169907	+	0.169907i
$867$	1.00000	+	1.00000i	0.0339618	+	0.0339618i
$868$	18.0000			0.610960
$869$	−6.00000	−	6.00000i	−0.203536	−	0.203536i
$870$	28.0000	−	14.0000i	0.949289	−	0.474644i
$871$	6.00000	−	6.00000i	0.203302	−	0.203302i
$872$	−9.00000	+	9.00000i	−0.304778	+	0.304778i
$873$	−8.00000			−0.270759
$874$	24.0000	−	24.0000i	0.811812	−	0.811812i
$875$	−27.0000	−	39.0000i	−0.912767	−	1.31844i
$876$		−	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
$880$	4.00000	−	2.00000i	0.134840	−	0.0674200i
$881$			12.0000i			0.404290i	0.979356	+	0.202145i	$0.0647913\pi$
$881$			12.0000i			0.404290i	−0.979356	+	0.202145i	$0.935209\pi$
$882$	−11.0000			−0.370389
$883$		−	2.00000i		−	0.0673054i	−0.999434	−	0.0336527i	$-0.989286\pi$
$883$		−	2.00000i		−	0.0673054i	0.999434	−	0.0336527i	$-0.0107140\pi$
$884$		−	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	−0.786048	−	0.618165i	$-0.787876\pi$
$887$	−5.00000	+	5.00000i	−0.167884	+	0.167884i	0.618165	+	0.786048i	$0.287876\pi$
$888$	−21.0000	+	15.0000i	−0.704714	+	0.503367i
$889$		−	54.0000i		−	1.81110i
$890$	−5.00000	+	15.0000i	−0.167600	+	0.502801i
$891$		−	10.0000i		−	0.335013i
$892$	1.00000	−	1.00000i	0.0334825	−	0.0334825i
$893$	30.0000			1.00391
$894$	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
$903$		−	72.0000i		−	2.39601i
$904$		−	12.0000i		−	0.399114i
$905$	−10.0000	−	20.0000i	−0.332411	−	0.664822i
$906$	2.00000	−	2.00000i	0.0664455	−	0.0664455i
$907$			14.0000i			0.464862i	0.972613	+	0.232431i	$0.0746680\pi$
$907$			14.0000i			0.464862i	−0.972613	+	0.232431i	$0.925332\pi$
$908$			2.00000i			0.0663723i
$909$		0			0
$910$	6.00000	−	18.0000i	0.198898	−	0.596694i
$911$	−11.0000	−	11.0000i	−0.364446	−	0.364446i	0.501001	−	0.865447i	$-0.332965\pi$
$911$	−11.0000	−	11.0000i	−0.364446	−	0.364446i	−0.865447	+	0.501001i	$0.832965\pi$
$912$	−6.00000			−0.198680
$913$	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
$917$	30.0000			0.990687
$918$	−16.0000	−	16.0000i	−0.528079	−	0.528079i
$919$	−3.00000	−	3.00000i	−0.0989609	−	0.0989609i	0.655893	−	0.754854i	$-0.272292\pi$
$919$	−3.00000	−	3.00000i	−0.0989609	−	0.0989609i	−0.754854	+	0.655893i	$0.772292\pi$
$920$	24.0000	+	48.0000i	0.791257	+	1.58251i
$921$	−18.0000			−0.593120
$922$	−21.0000	−	21.0000i	−0.691598	−	0.691598i
$923$	16.0000			0.526646
$924$	12.0000			0.394771
$925$	−21.0000	−	22.0000i	−0.690476	−	0.723356i
$926$	−40.0000			−1.31448
$927$	−14.0000			−0.459820
$928$	35.0000	+	35.0000i	1.14893	+	1.14893i
$929$	34.0000			1.11550			0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000			1.11550			0.557752	+	0.830008i	$0.311664\pi$
$930$	6.00000	+	12.0000i	0.196748	+	0.393496i
$931$	33.0000	+	33.0000i	1.08153	+	1.08153i
$932$	−1.00000	−	1.00000i	−0.0327561	−	0.0327561i
$933$	6.00000			0.196431
$934$		−	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	$-0.549723\pi$
$938$	18.0000			0.587721
$939$	−30.0000	−	30.0000i	−0.979013	−	0.979013i
$940$	−5.00000	+	15.0000i	−0.163082	+	0.489246i
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$			6.00000i			0.195491i
$943$		0			0
$944$	−7.00000	+	7.00000i	−0.227831	+	0.227831i
$945$	24.0000	+	48.0000i	0.780720	+	1.56144i
$946$			24.0000i			0.780307i
$947$		−	18.0000i		−	0.584921i	−0.956278	−	0.292461i	$-0.905526\pi$
$947$		−	18.0000i		−	0.584921i	0.956278	−	0.292461i	$-0.0944741\pi$
$948$	−6.00000			−0.194871
$949$	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	0.584582	−	0.811334i	$-0.301258\pi$
$953$	−7.00000	−	7.00000i	−0.226752	−	0.226752i	−0.811334	+	0.584582i	$0.801258\pi$
$954$	−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
$957$	−28.0000			−0.905111
$958$	−23.0000	+	23.0000i	−0.743096	+	0.743096i
$959$			42.0000i			1.35625i
$960$	7.00000	−	21.0000i	0.225924	−	0.677772i
$961$			13.0000i			0.419355i
$962$	2.00000	−	12.0000i	0.0644826	−	0.386896i
$963$	−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
$967$			2.00000i			0.0643157i	0.999483	+	0.0321578i	$0.0102379\pi$
$967$			2.00000i			0.0643157i	−0.999483	+	0.0321578i	$0.989762\pi$
$968$	21.0000			0.674966
$969$			24.0000i			0.770991i
$970$	16.0000	−	8.00000i	0.513729	−	0.256865i
$971$	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
$975$	−14.0000	+	2.00000i	−0.448359	+	0.0640513i
$976$	−1.00000	+	1.00000i	−0.0320092	+	0.0320092i
$977$	18.0000			0.575871			0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000			0.575871			0.287936	+	0.957650i	$0.407031\pi$
$978$	−10.0000	+	10.0000i	−0.319765	+	0.319765i
$979$	10.0000	−	10.0000i	0.319601	−	0.319601i
$980$	−22.0000	+	11.0000i	−0.702764	+	0.351382i
$981$	3.00000	+	3.00000i	0.0957826	+	0.0957826i
$982$	4.00000			0.127645
$983$	−15.0000	−	15.0000i	−0.478426	−	0.478426i	0.426202	−	0.904628i	$-0.359851\pi$
$983$	−15.0000	−	15.0000i	−0.478426	−	0.478426i	−0.904628	+	0.426202i	$0.859851\pi$
$984$		0			0
$985$	1.00000	−	3.00000i	0.0318626	−	0.0955879i
$986$	−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	0.278415	−	0.960461i	$-0.410191\pi$
$991$	39.0000	−	39.0000i	1.23888	−	1.23888i	0.960461	−	0.278415i	$-0.0898090\pi$
$992$	−15.0000	+	15.0000i	−0.476250	+	0.476250i
$993$		−	14.0000i		−	0.444277i
$994$	24.0000	+	24.0000i	0.761234	+	0.761234i
$995$	−15.0000	+	45.0000i	−0.475532	+	1.42660i
$996$	10.0000			0.316862
$997$			28.0000i			0.886769i	0.896332	+	0.443384i	$0.146222\pi$
$997$			28.0000i			0.886769i	−0.896332	+	0.443384i	$0.853778\pi$
$998$	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.k.b.117.1	yes	2
5.2	odd	4		925.2.f.b.43.1		2
5.3	odd	4		185.2.f.a.43.1	✓	2
5.4	even	2		925.2.k.a.857.1		2
37.31	odd	4		185.2.f.a.142.1	yes	2
185.68	even	4	inner	185.2.k.b.68.1	yes	2
185.142	even	4		925.2.k.a.68.1		2
185.179	odd	4		925.2.f.b.882.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.f.a.43.1	✓	2	5.3	odd	4
185.2.f.a.142.1	yes	2	37.31	odd	4
185.2.k.b.68.1	yes	2	185.68	even	4	inner
185.2.k.b.117.1	yes	2	1.1	even	1	trivial
925.2.f.b.43.1		2	5.2	odd	4
925.2.f.b.882.1		2	185.179	odd	4
925.2.k.a.68.1		2	185.142	even	4
925.2.k.a.857.1		2	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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