LMFDB - Embedded newform 315.2.bs.e.52.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(52,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3, 2]))

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

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

chi := DirichletCharacter("315.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bs (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			52.11
Character	$\chi$	$=$	315.52
Dual form			315.2.bs.e.103.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03040 - 1.03040i) q^{2} +(-0.767189 + 1.55288i) q^{3} +0.123432i q^{4} +(-0.154472 - 2.23073i) q^{5} +(2.39058 - 0.809568i) q^{6} +(2.47377 + 0.938328i) q^{7} +(-1.93361 + 1.93361i) q^{8} +(-1.82284 - 2.38270i) q^{9} +O(q^{10})$	\(q+(-1.03040 - 1.03040i) q^{2} +(-0.767189 + 1.55288i) q^{3} +0.123432i q^{4} +(-0.154472 - 2.23073i) q^{5} +(2.39058 - 0.809568i) q^{6} +(2.47377 + 0.938328i) q^{7} +(-1.93361 + 1.93361i) q^{8} +(-1.82284 - 2.38270i) q^{9} +(-2.13936 + 2.45770i) q^{10} +(-0.793669 - 1.37468i) q^{11} +(-0.191675 - 0.0946957i) q^{12} +(0.320320 - 1.19545i) q^{13} +(-1.58211 - 3.51581i) q^{14} +(3.58255 + 1.47151i) q^{15} +4.23163 q^{16} +(-0.0629387 - 0.234890i) q^{17} +(-0.576871 + 4.33337i) q^{18} +(-2.23848 - 3.87716i) q^{19} +(0.275343 - 0.0190667i) q^{20} +(-3.35496 + 3.12158i) q^{21} +(-0.598667 + 2.23425i) q^{22} +(-2.03197 - 7.58343i) q^{23} +(-1.51921 - 4.48609i) q^{24} +(-4.95228 + 0.689167i) q^{25} +(-1.56185 + 0.901732i) q^{26} +(5.09850 - 1.00267i) q^{27} +(-0.115820 + 0.305343i) q^{28} +(-5.88800 - 3.39944i) q^{29} +(-2.17520 - 5.20768i) q^{30} -7.73765i q^{31} +(-0.493037 - 0.493037i) q^{32} +(2.74359 - 0.177834i) q^{33} +(-0.177178 + 0.306882i) q^{34} +(1.71103 - 5.66325i) q^{35} +(0.294101 - 0.224997i) q^{36} +(-1.42497 + 5.31806i) q^{37} +(-1.68849 + 6.30154i) q^{38} +(1.61064 + 1.41455i) q^{39} +(4.61204 + 4.01466i) q^{40} +(0.131166 - 0.0757285i) q^{41} +(6.67340 + 0.240467i) q^{42} +(0.420219 + 1.56828i) q^{43} +(0.169679 - 0.0979643i) q^{44} +(-5.03357 + 4.43432i) q^{45} +(-5.72019 + 9.90767i) q^{46} +(5.60899 - 5.60899i) q^{47} +(-3.24646 + 6.57119i) q^{48} +(5.23908 + 4.64242i) q^{49} +(5.81292 + 4.39269i) q^{50} +(0.413041 + 0.0824693i) q^{51} +(0.147557 + 0.0395378i) q^{52} +(2.14503 + 8.00536i) q^{53} +(-6.28662 - 4.22032i) q^{54} +(-2.94393 + 1.98281i) q^{55} +(-6.59766 + 2.96894i) q^{56} +(7.73809 - 0.501567i) q^{57} +(2.56420 + 9.56974i) q^{58} -2.96041 q^{59} +(-0.181632 + 0.442201i) q^{60} -3.47447i q^{61} +(-7.97285 + 7.97285i) q^{62} +(-2.27354 - 7.60467i) q^{63} -7.44721i q^{64} +(-2.71620 - 0.529883i) q^{65} +(-3.01023 - 2.64375i) q^{66} +(4.64244 + 4.64244i) q^{67} +(0.0289930 - 0.00776866i) q^{68} +(13.3350 + 2.66252i) q^{69} +(-7.59842 + 4.07235i) q^{70} +14.3282 q^{71} +(8.13187 + 1.08254i) q^{72} +(-3.56691 + 0.955752i) q^{73} +(6.94800 - 4.01143i) q^{74} +(2.72914 - 8.21899i) q^{75} +(0.478566 - 0.276300i) q^{76} +(-0.673459 - 4.14535i) q^{77} +(-0.202047 - 3.11715i) q^{78} +8.45600i q^{79} +(-0.653666 - 9.43960i) q^{80} +(-2.35449 + 8.68656i) q^{81} +(-0.213183 - 0.0571222i) q^{82} +(-5.01411 + 1.34353i) q^{83} +(-0.385303 - 0.414109i) q^{84} +(-0.514254 + 0.176683i) q^{85} +(1.18296 - 2.04894i) q^{86} +(9.79611 - 6.53532i) q^{87} +(4.19273 + 1.12344i) q^{88} +(4.50127 + 7.79642i) q^{89} +(9.75567 + 0.617458i) q^{90} +(1.91412 - 2.65671i) q^{91} +(0.936038 - 0.250811i) q^{92} +(12.0156 + 5.93624i) q^{93} -11.5590 q^{94} +(-8.30311 + 5.59235i) q^{95} +(1.14388 - 0.387373i) q^{96} +(-3.82688 - 14.2821i) q^{97} +(-0.614799 - 10.1819i) q^{98} +(-1.82870 + 4.39689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8}+O(q^{10}) $ 160 * q + 4 * q^2 - 18 * q^3 - 6 * q^5 + 24 * q^6 - 16 * q^8	$ 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8} - 24 q^{10} - 16 q^{11} - 30 q^{12} + 16 q^{15} - 152 q^{16} - 6 q^{17} + 58 q^{18} + 60 q^{20} - 36 q^{21} + 8 q^{22} + 8 q^{23} + 2 q^{25} - 36 q^{26} - 36 q^{27} + 22 q^{28} - 26 q^{30} + 12 q^{32} - 6 q^{33} - 36 q^{35} - 32 q^{36} - 4 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 28 q^{42} - 4 q^{43} - 54 q^{45} - 16 q^{46} - 18 q^{48} - 44 q^{50} + 80 q^{51} + 54 q^{52} + 8 q^{53} + 148 q^{56} - 4 q^{57} + 28 q^{58} + 104 q^{60} - 60 q^{63} - 124 q^{65} + 36 q^{66} - 24 q^{67} + 42 q^{68} - 34 q^{70} - 40 q^{71} + 70 q^{72} + 36 q^{73} - 60 q^{75} + 96 q^{76} + 58 q^{77} - 62 q^{78} + 36 q^{80} + 8 q^{81} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 16 q^{86} + 102 q^{87} + 46 q^{88} + 18 q^{90} - 48 q^{91} - 26 q^{92} + 82 q^{93} + 188 q^{95} - 48 q^{96} + 48 q^{97} + 102 q^{98}+O(q^{100}) $ 160 * q + 4 * q^2 - 18 * q^3 - 6 * q^5 + 24 * q^6 - 16 * q^8 - 24 * q^10 - 16 * q^11 - 30 * q^12 + 16 * q^15 - 152 * q^16 - 6 * q^17 + 58 * q^18 + 60 * q^20 - 36 * q^21 + 8 * q^22 + 8 * q^23 + 2 * q^25 - 36 * q^26 - 36 * q^27 + 22 * q^28 - 26 * q^30 + 12 * q^32 - 6 * q^33 - 36 * q^35 - 32 * q^36 - 4 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 28 * q^42 - 4 * q^43 - 54 * q^45 - 16 * q^46 - 18 * q^48 - 44 * q^50 + 80 * q^51 + 54 * q^52 + 8 * q^53 + 148 * q^56 - 4 * q^57 + 28 * q^58 + 104 * q^60 - 60 * q^63 - 124 * q^65 + 36 * q^66 - 24 * q^67 + 42 * q^68 - 34 * q^70 - 40 * q^71 + 70 * q^72 + 36 * q^73 - 60 * q^75 + 96 * q^76 + 58 * q^77 - 62 * q^78 + 36 * q^80 + 8 * q^81 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 16 * q^86 + 102 * q^87 + 46 * q^88 + 18 * q^90 - 48 * q^91 - 26 * q^92 + 82 * q^93 + 188 * q^95 - 48 * q^96 + 48 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.03040	−	1.03040i	−0.728600	−	0.728600i	0.241741	−	0.970341i	$-0.422282\pi$
$2$	−1.03040	−	1.03040i	−0.728600	−	0.728600i	−0.970341	+	0.241741i	$0.922282\pi$
$3$	−0.767189	+	1.55288i	−0.442937	+	0.896553i
$3$	−0.767189	+	1.55288i	−0.442937	+	0.896553i
$4$			0.123432i			0.0617160i
$5$	−0.154472	−	2.23073i	−0.0690818	−	0.997611i
$5$	−0.154472	−	2.23073i	−0.0690818	−	0.997611i
$6$	2.39058	−	0.809568i	0.975952	−	0.330505i
$7$	2.47377	+	0.938328i	0.934997	+	0.354655i
$7$	2.47377	+	0.938328i	0.934997	+	0.354655i
$8$	−1.93361	+	1.93361i	−0.683634	+	0.683634i
$9$	−1.82284	−	2.38270i	−0.607614	−	0.794232i
$10$	−2.13936	+	2.45770i	−0.676526	+	0.777192i
$11$	−0.793669	−	1.37468i	−0.239300	−	0.414480i	0.721213	−	0.692713i	$-0.243585\pi$
$11$	−0.793669	−	1.37468i	−0.239300	−	0.414480i	−0.960514	+	0.278233i	$0.910251\pi$
$12$	−0.191675	−	0.0946957i	−0.0553317	−	0.0273363i
$13$	0.320320	−	1.19545i	0.0888409	−	0.331559i	−0.907173	−	0.420758i	$-0.861764\pi$
$13$	0.320320	−	1.19545i	0.0888409	−	0.331559i	0.996014	+	0.0891994i	$0.0284308\pi$
$14$	−1.58211	−	3.51581i	−0.422838	−	0.939641i
$15$	3.58255	+	1.47151i	0.925010	+	0.379943i
$16$	4.23163			1.05791
$17$	−0.0629387	−	0.234890i	−0.0152649	−	0.0569693i	0.957873	−	0.287191i	$-0.0927215\pi$
$17$	−0.0629387	−	0.234890i	−0.0152649	−	0.0569693i	−0.973138	+	0.230222i	$0.926055\pi$
$18$	−0.576871	+	4.33337i	−0.135970	+	1.02139i
$19$	−2.23848	−	3.87716i	−0.513543	−	0.889482i	−0.999877	−	0.0157093i	$-0.994999\pi$
$19$	−2.23848	−	3.87716i	−0.513543	−	0.889482i	0.486334	−	0.873773i	$-0.338334\pi$
$20$	0.275343	−	0.0190667i	0.0615686	−	0.00426345i
$21$	−3.35496	+	3.12158i	−0.732111	+	0.681185i
$22$	−0.598667	+	2.23425i	−0.127636	+	0.476345i
$23$	−2.03197	−	7.58343i	−0.423696	−	1.58125i	−0.766755	−	0.641940i	$-0.778130\pi$
$23$	−2.03197	−	7.58343i	−0.423696	−	1.58125i	0.343059	−	0.939314i	$-0.388537\pi$
$24$	−1.51921	−	4.48609i	−0.310107	−	0.915720i
$25$	−4.95228	+	0.689167i	−0.990455	+	0.137833i
$26$	−1.56185	+	0.901732i	−0.306303	+	0.176844i
$27$	5.09850	−	1.00267i	0.981206	−	0.192964i
$28$	−0.115820	+	0.305343i	−0.0218879	+	0.0577043i
$29$	−5.88800	−	3.39944i	−1.09337	−	0.631260i	−0.158901	−	0.987294i	$-0.550795\pi$
$29$	−5.88800	−	3.39944i	−1.09337	−	0.631260i	−0.934473	+	0.356035i	$0.884128\pi$
$30$	−2.17520	−	5.20768i	−0.397136	−	0.950789i
$31$		−	7.73765i		−	1.38972i	−0.719143	−	0.694862i	$-0.755466\pi$
$31$		−	7.73765i		−	1.38972i	0.719143	−	0.694862i	$-0.244534\pi$
$32$	−0.493037	−	0.493037i	−0.0871575	−	0.0871575i
$33$	2.74359	−	0.177834i	0.477598	−	0.0309569i
$34$	−0.177178	+	0.306882i	−0.0303858	+	0.0526298i
$35$	1.71103	−	5.66325i	0.289216	−	0.957264i
$36$	0.294101	−	0.224997i	0.0490169	−	0.0374996i
$37$	−1.42497	+	5.31806i	−0.234264	+	0.874284i	0.744216	+	0.667939i	$0.232823\pi$
$37$	−1.42497	+	5.31806i	−0.234264	+	0.874284i	−0.978479	+	0.206345i	$0.933843\pi$
$38$	−1.68849	+	6.30154i	−0.273910	+	1.02224i
$39$	1.61064	+	1.41455i	0.257909	+	0.226510i
$40$	4.61204	+	4.01466i	0.729227	+	0.634774i
$41$	0.131166	−	0.0757285i	0.0204846	−	0.0118268i	−0.489723	−	0.871878i	$-0.662902\pi$
$41$	0.131166	−	0.0757285i	0.0204846	−	0.0118268i	0.510207	+	0.860051i	$0.329569\pi$
$42$	6.67340	+	0.240467i	1.02973	+	0.0371048i
$43$	0.420219	+	1.56828i	0.0640828	+	0.239160i	0.990537	−	0.137248i	$-0.0438257\pi$
$43$	0.420219	+	1.56828i	0.0640828	+	0.239160i	−0.926454	+	0.376408i	$0.877159\pi$
$44$	0.169679	−	0.0979643i	0.0255801	−	0.0147687i
$45$	−5.03357	+	4.43432i	−0.750360	+	0.661030i
$46$	−5.72019	+	9.90767i	−0.843397	+	1.46081i
$47$	5.60899	−	5.60899i	0.818155	−	0.818155i	−0.167685	−	0.985841i	$-0.553629\pi$
$47$	5.60899	−	5.60899i	0.818155	−	0.818155i	0.985841	+	0.167685i	$0.0536293\pi$
$48$	−3.24646	+	6.57119i	−0.468586	+	0.948470i
$49$	5.23908	+	4.64242i	0.748440	+	0.663202i
$50$	5.81292	+	4.39269i	0.822071	+	0.621220i
$51$	0.413041	+	0.0824693i	0.0578374	+	0.0115480i
$52$	0.147557	+	0.0395378i	0.0204625	+	0.00548291i
$53$	2.14503	+	8.00536i	0.294643	+	1.09962i	0.941501	+	0.337011i	$0.109416\pi$
$53$	2.14503	+	8.00536i	0.294643	+	1.09962i	−0.646858	+	0.762610i	$0.723917\pi$
$54$	−6.28662	−	4.22032i	−0.855500	−	0.574313i
$55$	−2.94393	+	1.98281i	−0.396959	+	0.267362i
$56$	−6.59766	+	2.96894i	−0.881650	+	0.396742i
$57$	7.73809	−	0.501567i	1.02494	−	0.0664341i
$58$	2.56420	+	9.56974i	0.336696	+	1.25657i
$59$	−2.96041			−0.385413			−0.192706	−	0.981256i	$-0.561726\pi$
$59$	−2.96041			−0.385413			−0.192706	+	0.981256i	$0.561726\pi$
$60$	−0.181632	+	0.442201i	−0.0234486	+	0.0570880i
$61$		−	3.47447i		−	0.444860i	−0.974949	−	0.222430i	$-0.928601\pi$
$61$		−	3.47447i		−	0.444860i	0.974949	−	0.222430i	$-0.0713989\pi$
$62$	−7.97285	+	7.97285i	−1.01255	+	1.01255i
$63$	−2.27354	−	7.60467i	−0.286440	−	0.958098i
$64$		−	7.44721i		−	0.930901i
$65$	−2.71620	−	0.529883i	−0.336904	−	0.0657240i
$66$	−3.01023	−	2.64375i	−0.370533	−	0.325423i
$67$	4.64244	+	4.64244i	0.567165	+	0.567165i	0.931333	−	0.364168i	$-0.118647\pi$
$67$	4.64244	+	4.64244i	0.567165	+	0.567165i	−0.364168	+	0.931333i	$0.618647\pi$
$68$	0.0289930	−	0.00776866i	0.00351592	−	0.000942088i
$69$	13.3350	+	2.66252i	1.60535	+	0.320529i
$70$	−7.59842	+	4.07235i	−0.908185	+	0.486740i
$71$	14.3282			1.70045			0.850225	−	0.526419i	$-0.176466\pi$
$71$	14.3282			1.70045			0.850225	+	0.526419i	$0.176466\pi$
$72$	8.13187	+	1.08254i	0.958350	+	0.127578i
$73$	−3.56691	+	0.955752i	−0.417476	+	0.111862i	−0.461441	−	0.887171i	$-0.652667\pi$
$73$	−3.56691	+	0.955752i	−0.417476	+	0.111862i	0.0439655	+	0.999033i	$0.486001\pi$
$74$	6.94800	−	4.01143i	0.807688	−	0.466319i
$75$	2.72914	−	8.21899i	0.315134	−	0.949047i
$76$	0.478566	−	0.276300i	0.0548953	−	0.0316938i
$77$	−0.673459	−	4.14535i	−0.0767477	−	0.472407i
$78$	−0.202047	−	3.11715i	−0.0228773	−	0.352948i
$79$			8.45600i			0.951375i	0.879614	+	0.475687i	$0.157801\pi$
$79$			8.45600i			0.951375i	−0.879614	+	0.475687i	$0.842199\pi$
$80$	−0.653666	−	9.43960i	−0.0730821	−	1.05538i
$81$	−2.35449	+	8.68656i	−0.261610	+	0.965174i
$82$	−0.213183	−	0.0571222i	−0.0235421	−	0.00630809i
$83$	−5.01411	+	1.34353i	−0.550370	+	0.147471i	−0.523278	−	0.852162i	$-0.675291\pi$
$83$	−5.01411	+	1.34353i	−0.550370	+	0.147471i	−0.0270914	+	0.999633i	$0.508625\pi$
$84$	−0.385303	−	0.414109i	−0.0420400	−	0.0451830i
$85$	−0.514254	+	0.176683i	−0.0557787	+	0.0191640i
$86$	1.18296	−	2.04894i	0.127562	−	0.220943i
$87$	9.79611	−	6.53532i	1.05025	−	0.700660i
$88$	4.19273	+	1.12344i	0.446946	+	0.119759i
$89$	4.50127	+	7.79642i	0.477133	+	0.826419i	0.999657	−	0.0262061i	$-0.00834260\pi$
$89$	4.50127	+	7.79642i	0.477133	+	0.826419i	−0.522523	+	0.852625i	$0.675009\pi$
$90$	9.75567	+	0.617458i	1.02834	+	0.0650858i
$91$	1.91412	−	2.65671i	0.200655	−	0.278499i
$92$	0.936038	−	0.250811i	0.0975887	−	0.0261488i
$93$	12.0156	+	5.93624i	1.24596	+	0.615559i
$94$	−11.5590			−1.19222
$95$	−8.30311	+	5.59235i	−0.851881	+	0.573763i
$96$	1.14388	−	0.387373i	0.116747	−	0.0395361i
$97$	−3.82688	−	14.2821i	−0.388561	−	1.45013i	−0.832476	−	0.554061i	$-0.813077\pi$
$97$	−3.82688	−	14.2821i	−0.388561	−	1.45013i	0.443915	−	0.896069i	$-0.353589\pi$
$98$	−0.614799	−	10.1819i	−0.0621041	−	1.02852i
$99$	−1.82870	+	4.39689i	−0.183791	+	0.441904i
$100$	−0.0850654	−	0.611270i	−0.00850654	−	0.0611270i
$101$	12.1371	−	7.00734i	1.20768	−	0.697256i	0.245431	−	0.969414i	$-0.421071\pi$
$101$	12.1371	−	7.00734i	1.20768	−	0.697256i	0.962253	+	0.272158i	$0.0877373\pi$
$102$	−0.340620	−	0.510572i	−0.0337264	−	0.0505542i
$103$	14.3980	−	3.85793i	1.41868	−	0.380133i	0.533662	−	0.845698i	$-0.320815\pi$
$103$	14.3980	−	3.85793i	1.41868	−	0.380133i	0.885014	+	0.465565i	$0.154149\pi$
$104$	1.69216	+	2.93091i	0.165930	+	0.287399i
$105$	7.48164	+	7.00179i	0.730133	+	0.683305i
$106$	6.03846	−	10.4589i	0.586507	−	1.01586i
$107$	−3.92014	+	14.6302i	−0.378974	+	1.41435i	0.468476	+	0.883476i	$0.344803\pi$
$107$	−3.92014	+	14.6302i	−0.378974	+	1.41435i	−0.847450	+	0.530875i	$0.821863\pi$
$108$	0.123762	+	0.629318i	0.0119090	+	0.0605561i
$109$	4.28062	+	2.47141i	0.410009	+	0.236719i	0.690793	−	0.723052i	$-0.257261\pi$
$109$	4.28062	+	2.47141i	0.410009	+	0.236719i	−0.280785	+	0.959771i	$0.590595\pi$
$110$	5.07649	+	0.990332i	0.484024	+	0.0944245i
$111$	−7.16507	−	6.29276i	−0.680078	−	0.597282i
$112$	10.4681	+	3.97066i	0.989140	+	0.375192i
$113$	−7.86317	−	2.10693i	−0.739705	−	0.198203i	−0.130758	−	0.991414i	$-0.541741\pi$
$113$	−7.86317	−	2.10693i	−0.739705	−	0.198203i	−0.608947	+	0.793211i	$0.708408\pi$
$114$	−8.49011	−	7.45649i	−0.795172	−	0.698364i
$115$	−16.6027	+	5.70420i	−1.54821	+	0.531919i
$116$	0.419600	−	0.726768i	0.0389589	−	0.0674787i
$117$	−3.43229	+	1.41589i	−0.317315	+	0.130899i
$118$	3.05039	+	3.05039i	0.280812	+	0.280812i
$119$	0.0647084	−	0.640122i	0.00593181	−	0.0586799i
$120$	−9.77257	+	4.08192i	−0.892110	+	0.372626i
$121$	4.24018	−	7.34420i	0.385471	−	0.667655i
$122$	−3.58008	+	3.58008i	−0.324125	+	0.324125i
$123$	0.0169682	+	0.261782i	0.00152997	+	0.0236041i
$124$	0.955075			0.0857682
$125$	2.30233	+	10.9407i	0.205927	+	0.978567i
$126$	−5.49317	+	10.1785i	−0.489371	+	0.906770i
$127$	−12.6824	−	12.6824i	−1.12538	−	1.12538i	−0.990919	−	0.134461i	$-0.957070\pi$
$127$	−12.6824	−	12.6824i	−1.12538	−	1.12538i	−0.134461	−	0.990919i	$-0.542930\pi$
$128$	−8.65965	+	8.65965i	−0.765412	+	0.765412i
$129$	−2.75773	−	0.550618i	−0.242805	−	0.0484792i
$130$	2.25278	+	3.34476i	0.197582	+	0.293355i
$131$	4.12979	+	2.38433i	0.360821	+	0.208320i	0.669441	−	0.742865i	$-0.266534\pi$
$131$	4.12979	+	2.38433i	0.360821	+	0.208320i	−0.308620	+	0.951185i	$0.599867\pi$
$132$	0.0219504	+	0.338647i	0.00191054	+	0.0294755i
$133$	−1.89944	−	11.6916i	−0.164702	−	1.01379i
$134$		−	9.56711i		−	0.826472i
$135$	−3.02426	−	11.2185i	−0.260286	−	0.965531i
$136$	0.575885	+	0.332487i	0.0493817	+	0.0285106i
$137$	−4.51431	+	16.8476i	−0.385683	+	1.43939i	0.451403	+	0.892320i	$0.350924\pi$
$137$	−4.51431	+	16.8476i	−0.385683	+	1.43939i	−0.837087	+	0.547070i	$0.815743\pi$
$138$	−10.9969	−	16.4838i	−0.936119	−	1.40319i
$139$	−11.3357	−	19.6341i	−0.961485	−	1.66534i	−0.718776	−	0.695242i	$-0.755297\pi$
$139$	−11.3357	−	19.6341i	−0.961485	−	1.66534i	−0.242709	−	0.970099i	$-0.578036\pi$
$140$	0.699027	+	0.211196i	0.0590785	+	0.0178493i
$141$	4.40691	+	13.0132i	0.371129	+	1.09591i
$142$	−14.7638	−	14.7638i	−1.23895	−	1.23895i
$143$	−1.89759	+	0.508457i	−0.158684	+	0.0425193i
$144$	−7.71360	−	10.0827i	−0.642800	−	0.840224i
$145$	−6.67369	+	13.6596i	−0.554219	+	1.13437i
$146$	4.66014	+	2.69053i	0.385676	+	0.222670i
$147$	−11.2285	+	4.57403i	−0.926108	+	0.377260i
$148$	−0.656420	−	0.175887i	−0.0539574	−	0.0144578i
$149$	0.447172	+	0.258175i	0.0366338	+	0.0211505i	0.518205	−	0.855256i	$-0.326600\pi$
$149$	0.447172	+	0.258175i	0.0366338	+	0.0211505i	−0.481571	+	0.876407i	$0.659934\pi$
$150$	−11.2809	+	5.65672i	−0.921082	+	0.461869i
$151$	−0.863556	−	1.49572i	−0.0702752	−	0.121720i	0.828747	−	0.559624i	$-0.189054\pi$
$151$	−0.863556	−	1.49572i	−0.0702752	−	0.121720i	−0.899022	+	0.437904i	$0.855721\pi$
$152$	11.8253	+	3.16857i	0.959156	+	0.257005i
$153$	−0.444945	+	0.578132i	−0.0359717	+	0.0467392i
$154$	−3.57743	+	4.96529i	−0.288277	+	0.400114i
$155$	−17.2606	+	1.19525i	−1.38640	+	0.0960046i
$156$	−0.174601	+	0.198805i	−0.0139793	+	0.0159171i
$157$	−8.01038	+	8.01038i	−0.639298	+	0.639298i	−0.950382	−	0.311084i	$-0.899308\pi$
$157$	−8.01038	+	8.01038i	−0.639298	+	0.639298i	0.311084	+	0.950382i	$0.399308\pi$
$158$	8.71303	−	8.71303i	0.693172	−	0.693172i
$159$	−14.0770	−	2.81066i	−1.11638	−	0.222900i
$160$	−1.02367	+	1.17599i	−0.0809283	+	0.0929703i
$161$	2.08911	−	20.6663i	0.164645	−	1.62873i
$162$	11.3767	−	6.52455i	0.893834	−	0.512617i
$163$	0.591440	+	0.158476i	0.0463251	+	0.0124128i	0.281907	−	0.959442i	$-0.409033\pi$
$163$	0.591440	+	0.158476i	0.0463251	+	0.0124128i	−0.235582	+	0.971854i	$0.575700\pi$
$164$	0.00934733	+	0.0161901i	0.000729904	+	0.00126423i
$165$	−0.820506	−	6.09274i	−0.0638763	−	0.474319i
$166$	6.55088	+	3.78215i	0.508447	+	0.293552i
$167$	6.26508	+	1.67872i	0.484807	+	0.129904i	0.492940	−	0.870063i	$-0.335922\pi$
$167$	6.26508	+	1.67872i	0.484807	+	0.129904i	−0.00813329	+	0.999967i	$0.502589\pi$
$168$	0.451252	−	12.5231i	0.0348149	−	0.966177i
$169$	9.93183	+	5.73415i	0.763987	+	0.441088i
$170$	0.711939	+	0.347832i	0.0546032	+	0.0266775i
$171$	−5.15770	+	12.4011i	−0.394420	+	0.948335i
$172$	−0.193576	+	0.0518685i	−0.0147600	+	0.00395494i
$173$	5.64287	+	5.64287i	0.429020	+	0.429020i	0.888294	−	0.459275i	$-0.151891\pi$
$173$	5.64287	+	5.64287i	0.429020	+	0.429020i	−0.459275	+	0.888294i	$0.651891\pi$
$174$	−16.8278	−	3.35991i	−1.27572	−	0.254714i
$175$	−12.8975	−	2.94202i	−0.974956	−	0.222396i
$176$	−3.35851	−	5.81712i	−0.253157	−	0.438482i
$177$	2.27119	−	4.59715i	0.170713	−	0.345543i
$178$	3.39531	−	12.6715i	0.254490	−	0.949768i
$179$	13.7994	+	7.96712i	1.03142	+	0.595490i	0.917391	−	0.397987i	$-0.130291\pi$
$179$	13.7994	+	7.96712i	1.03142	+	0.595490i	0.114028	+	0.993477i	$0.463625\pi$
$180$	−0.547338	−	0.621304i	−0.0407961	−	0.0463092i
$181$			6.89770i			0.512702i	0.966584	+	0.256351i	$0.0825203\pi$
$181$			6.89770i			0.512702i	−0.966584	+	0.256351i	$0.917480\pi$
$182$	−4.70977	+	0.765154i	−0.349111	+	0.0567170i
$183$	5.39542	+	2.66557i	0.398841	+	0.197045i
$184$	18.5924	+	10.7343i	1.37065	+	0.791346i
$185$	12.0833	+	2.35723i	0.888379	+	0.173307i
$186$	−6.26416	−	18.4975i	−0.459310	−	1.35630i
$187$	−0.272946	+	0.272946i	−0.0199598	+	0.0199598i
$188$	0.692329	+	0.692329i	0.0504933	+	0.0504933i
$189$	13.5533	+	2.30369i	0.985860	+	0.167568i
$190$	14.3178	+	2.79315i	1.03872	+	0.202637i
$191$	10.8201			0.782915			0.391458	−	0.920196i	$-0.371971\pi$
$191$	10.8201			0.782915			0.391458	+	0.920196i	$0.371971\pi$
$192$	11.5646	+	5.71342i	0.834602	+	0.412330i
$193$	2.93159	−	2.93159i	0.211020	−	0.211020i	−0.593681	−	0.804701i	$-0.702326\pi$
$193$	2.93159	−	2.93159i	0.211020	−	0.211020i	0.804701	+	0.593681i	$0.202326\pi$
$194$	−10.7730	+	18.6594i	−0.773459	+	1.33967i
$195$	2.90668	−	3.81141i	0.208152	−	0.272941i
$196$	−0.573023	+	0.646671i	−0.0409302	+	0.0461908i
$197$	−8.75322	−	8.75322i	−0.623641	−	0.623641i	0.322819	−	0.946461i	$-0.395369\pi$
$197$	−8.75322	−	8.75322i	−0.623641	−	0.623641i	−0.946461	+	0.322819i	$0.895369\pi$
$198$	6.41482	−	2.64625i	0.455882	−	0.188061i
$199$	−2.96168	+	5.12978i	−0.209948	+	0.363641i	−0.951698	−	0.307036i	$-0.900663\pi$
$199$	−2.96168	+	5.12978i	−0.209948	+	0.363641i	0.741750	+	0.670677i	$0.233996\pi$
$200$	8.24318	−	10.9083i	0.582881	−	0.771336i
$201$	−10.7708	+	3.64751i	−0.759711	+	0.257275i
$202$	−19.7263	−	5.28565i	−1.38794	−	0.371897i
$203$	−11.3758	−	13.9343i	−0.798422	−	0.977996i
$204$	−0.0101794	+	0.0509826i	−0.000712698	+	0.00356949i
$205$	−0.189191	−	0.280897i	−0.0132137	−	0.0196187i
$206$	−18.8108	−	10.8604i	−1.31061	−	0.756682i
$207$	−14.3650	+	18.6650i	−0.998439	+	1.29731i
$208$	1.35548	−	5.05871i	0.0939854	−	0.350758i
$209$	−3.55323	+	6.15437i	−0.245782	+	0.425707i
$210$	−0.494435	−	14.9237i	−0.0341192	−	1.02983i
$211$	−3.67279	−	6.36146i	−0.252845	−	0.437941i	0.711463	−	0.702724i	$-0.248033\pi$
$211$	−3.67279	−	6.36146i	−0.252845	−	0.437941i	−0.964308	+	0.264783i	$0.914700\pi$
$212$	−0.988118	+	0.264766i	−0.0678643	+	0.0181842i
$213$	−10.9925	+	22.2500i	−0.753192	+	1.52454i
$214$	19.1142	−	11.0356i	1.30662	−	0.754376i
$215$	3.43349	−	1.17965i	0.234162	−	0.0804514i
$216$	−7.91972	+	11.7973i	−0.538869	+	0.802702i
$217$	7.26046	−	19.1412i	0.492872	−	1.29939i
$218$	−1.86419	−	6.95727i	−0.126259	−	0.471206i
$219$	1.25233	−	6.27221i	0.0846248	−	0.423837i
$220$	−0.244742	−	0.363375i	−0.0165005	−	0.0244987i
$221$	−0.300961			−0.0202448
$222$	0.898823	+	13.8669i	0.0603250	+	0.930685i
$223$	13.9680	−	3.74273i	0.935370	−	0.250632i	0.241227	−	0.970469i	$-0.422450\pi$
$223$	13.9680	−	3.74273i	0.935370	−	0.250632i	0.694143	+	0.719837i	$0.255784\pi$
$224$	−0.757030	−	1.68229i	−0.0505812	−	0.112403i
$225$	10.6693	+	10.5435i	0.711287	+	0.702902i
$226$	5.93121	+	10.2731i	0.394538	+	0.683360i
$227$	7.50355	+	2.01057i	0.498028	+	0.133446i	0.499085	−	0.866553i	$-0.333670\pi$
$227$	7.50355	+	2.01057i	0.498028	+	0.133446i	−0.00105657	+	0.999999i	$0.500336\pi$
$228$	0.0619094	+	0.955129i	0.00410005	+	0.0632549i
$229$	−8.44633	+	14.6295i	−0.558149	+	0.966742i	0.439502	+	0.898242i	$0.355155\pi$
$229$	−8.44633	+	14.6295i	−0.558149	+	0.966742i	−0.997651	+	0.0685008i	$0.978178\pi$
$230$	22.9849	+	11.2297i	1.51558	+	0.740467i
$231$	6.95389	+	2.13447i	0.457532	+	0.140438i
$232$	17.9583	−	4.81190i	1.17902	−	0.315917i
$233$	−7.47923	−	2.00405i	−0.489981	−	0.131290i	0.00536536	−	0.999986i	$-0.498292\pi$
$233$	−7.47923	−	2.00405i	−0.489981	−	0.131290i	−0.495346	+	0.868696i	$0.664959\pi$
$234$	4.99555	+	2.07769i	0.326569	+	0.135823i
$235$	−13.3785	−	11.6457i	−0.872720	−	0.759681i
$236$		−	0.365410i		−	0.0237861i
$237$	−13.1311	−	6.48735i	−0.852958	−	0.421399i
$238$	−0.726255	+	0.592904i	−0.0470761	+	0.0384323i
$239$	19.3368	−	11.1641i	1.25079	−	0.722147i	0.279528	−	0.960138i	$-0.409822\pi$
$239$	19.3368	−	11.1641i	1.25079	−	0.722147i	0.971267	+	0.237991i	$0.0764888\pi$
$240$	15.1600	+	6.22690i	0.978575	+	0.401944i
$241$	12.5043	−	7.21938i	0.805475	−	0.465041i	−0.0399069	−	0.999203i	$-0.512706\pi$
$241$	12.5043	−	7.21938i	0.805475	−	0.465041i	0.845382	+	0.534162i	$0.179373\pi$
$242$	−11.9365	+	3.19838i	−0.767307	+	0.205599i
$243$	−11.6828	−	10.3205i	−0.749453	−	0.662058i
$244$	0.428861			0.0274550
$245$	9.54667	−	12.4041i	0.609915	−	0.792467i
$246$	0.252255	−	0.287223i	0.0160832	−	0.0183127i
$247$	−5.35199	+	1.43406i	−0.340539	+	0.0912472i
$248$	14.9616	+	14.9616i	0.950062	+	0.950062i
$249$	1.76044	−	8.81702i	0.111563	−	0.558756i
$250$	8.90096	−	13.6456i	0.562946	−	0.863022i
$251$		−	15.4984i		−	0.978249i	−0.872214	−	0.489124i	$-0.837316\pi$
$251$		−	15.4984i		−	0.978249i	0.872214	−	0.489124i	$-0.162684\pi$
$252$	0.938660	−	0.280628i	0.0591300	−	0.0176779i
$253$	−8.81203	+	8.81203i	−0.554008	+	0.554008i
$254$			26.1358i			1.63990i
$255$	0.120163	−	0.934122i	0.00752492	−	0.0584970i
$256$	2.95132			0.184457
$257$	−2.06401	−	7.70299i	−0.128749	−	0.480499i	0.871196	−	0.490935i	$-0.163345\pi$
$257$	−2.06401	−	7.70299i	−0.128749	−	0.480499i	−0.999946	+	0.0104359i	$0.996678\pi$
$258$	2.27420	+	3.40891i	0.141585	+	0.212229i
$259$	−8.51514	+	11.8186i	−0.529105	+	0.734371i
$260$	0.0654046	−	0.335267i	0.00405622	−	0.0207924i
$261$	2.63307	+	20.2260i	0.162983	+	1.25196i
$262$	−1.79851	−	6.71212i	−0.111112	−	0.414676i
$263$	−15.5052	−	4.15460i	−0.956091	−	0.256184i	−0.253146	−	0.967428i	$-0.581465\pi$
$263$	−15.5052	−	4.15460i	−0.956091	−	0.256184i	−0.702945	+	0.711244i	$0.748132\pi$
$264$	−4.96117	+	5.64890i	−0.305339	+	0.347666i
$265$	17.5264	−	6.02157i	1.07664	−	0.369902i
$266$	−10.0899	+	14.0042i	−0.618649	+	0.858652i
$267$	−15.5602	+	1.00858i	−0.952268	+	0.0617240i
$268$	−0.573026	+	0.573026i	−0.0350032	+	0.0350032i
$269$	6.81093	−	11.7969i	0.415270	−	0.719269i	−0.580187	−	0.814483i	$-0.697020\pi$
$269$	6.81093	−	11.7969i	0.415270	−	0.719269i	0.995457	+	0.0952149i	$0.0303538\pi$
$270$	−8.44328	+	14.6756i	−0.513842	+	0.893131i
$271$	8.78837	−	5.07397i	0.533856	−	0.308222i	−0.208729	−	0.977973i	$-0.566933\pi$
$271$	8.78837	−	5.07397i	0.533856	−	0.308222i	0.742585	+	0.669752i	$0.233599\pi$
$272$	−0.266333	−	0.993969i	−0.0161488	−	0.0602682i
$273$	2.65704	+	5.01059i	0.160811	+	0.303255i
$274$	22.0113	−	12.7082i	1.32975	−	0.767731i
$275$	4.87785	+	6.26080i	0.294146	+	0.377541i
$276$	−0.328640	+	1.64597i	−0.0197818	+	0.0990757i
$277$	4.00044	−	14.9298i	0.240363	−	0.897047i	−0.735294	−	0.677748i	$-0.762956\pi$
$277$	4.00044	−	14.9298i	0.240363	−	0.897047i	0.975658	−	0.219300i	$-0.0703772\pi$
$278$	−8.55058	+	31.9112i	−0.512829	+	1.91391i
$279$	−18.4365	+	14.1045i	−1.10376	+	0.844416i
$280$	7.64205	+	14.2590i	0.456700	+	0.852136i
$281$	−5.68128	+	9.84027i	−0.338917	+	0.587021i	−0.984229	−	0.176897i	$-0.943394\pi$
$281$	−5.68128	+	9.84027i	−0.338917	+	0.587021i	0.645312	+	0.763919i	$0.276727\pi$
$282$	8.86790	−	17.9496i	0.528076	−	1.06888i
$283$	−0.718184	−	0.718184i	−0.0426916	−	0.0426916i	0.685439	−	0.728130i	$-0.259610\pi$
$283$	−0.718184	−	0.718184i	−0.0426916	−	0.0426916i	−0.728130	+	0.685439i	$0.759610\pi$
$284$			1.76857i			0.104945i
$285$	−2.31417	−	17.1841i	−0.137080	−	1.01790i
$286$	2.47918	+	1.43135i	0.146597	+	0.0846377i
$287$	0.395532	−	0.0642586i	0.0233475	−	0.00379306i
$288$	−0.276029	+	2.07349i	−0.0162651	+	0.122181i
$289$	14.6712	−	8.47043i	0.863013	−	0.498261i
$290$	20.9514	−	7.19829i	1.23031	−	0.422698i
$291$	25.1143	+	5.01441i	1.47223	+	0.293950i
$292$	−0.117970	−	0.440272i	−0.00690370	−	0.0257649i
$293$	−2.82889	+	10.5576i	−0.165266	+	0.616779i	0.832741	+	0.553663i	$0.186771\pi$
$293$	−2.82889	+	10.5576i	−0.165266	+	0.616779i	−0.998006	+	0.0631162i	$0.979896\pi$
$294$	16.2828	+	6.85670i	0.949633	+	0.399891i
$295$	0.457299	+	6.60386i	0.0266250	+	0.384492i
$296$	−7.52771	−	13.0384i	−0.437540	−	0.757841i
$297$	−5.42487	−	6.21299i	−0.314783	−	0.360514i
$298$	−0.194742	−	0.726787i	−0.0112811	−	0.0421016i
$299$	−9.71650			−0.561920
$300$	1.01449	+	0.336863i	0.0585714	+	0.0194488i
$301$	−0.432035	+	4.27387i	−0.0249021	+	0.246342i
$302$	−0.651383	+	2.43099i	−0.0374829	+	0.139888i
$303$	1.57010	+	24.2233i	0.0902001	+	1.39159i
$304$	−9.47242	−	16.4067i	−0.543281	−	0.940990i
$305$	−7.75059	+	0.536707i	−0.443797	+	0.0307317i
$306$	1.05418	−	0.137235i	0.0602632	−	0.00784523i
$307$	7.71847	−	7.71847i	0.440516	−	0.440516i	−0.451669	−	0.892185i	$-0.649171\pi$
$307$	7.71847	−	7.71847i	0.440516	−	0.440516i	0.892185	+	0.451669i	$0.149171\pi$
$308$	0.511670	−	0.0831264i	0.0291551	−	0.00473657i
$309$	−5.05509	+	25.3180i	−0.287574	+	1.44029i
$310$	19.0168	+	16.5537i	1.08008	+	0.940185i
$311$			19.1915i			1.08825i	0.839004	+	0.544125i	$0.183138\pi$
$311$			19.1915i			1.08825i	−0.839004	+	0.544125i	$0.816862\pi$
$312$	−5.84954	+	0.379155i	−0.331165	+	0.0214654i
$313$	7.17958	+	7.17958i	0.405814	+	0.405814i	0.880276	−	0.474462i	$-0.157357\pi$
$313$	7.17958	+	7.17958i	0.405814	+	0.405814i	−0.474462	+	0.880276i	$0.657357\pi$
$314$	16.5077			0.931585
$315$	−16.6127	+	6.24636i	−0.936022	+	0.351942i
$316$	−1.04374			−0.0587151
$317$	−17.0449	−	17.0449i	−0.957337	−	0.957337i	0.0417895	−	0.999126i	$-0.486694\pi$
$317$	−17.0449	−	17.0449i	−0.957337	−	0.957337i	−0.999126	+	0.0417895i	$0.986694\pi$
$318$	11.6088	+	17.4009i	0.650987	+	0.975797i
$319$			10.7921i			0.604243i
$320$	−16.6127	+	1.15038i	−0.928677	+	0.0643083i
$321$	−19.7113	−	17.3116i	−1.10018	−	0.966238i
$322$	−23.4471	+	19.1419i	−1.30666	+	1.06674i
$323$	−0.769822	+	0.769822i	−0.0428340	+	0.0428340i
$324$	−1.07220	−	0.290619i	−0.0595667	−	0.0161455i
$325$	−0.762449	+	6.14096i	−0.0422930	+	0.340639i
$326$	−0.446124	−	0.772710i	−0.0247085	−	0.0427965i
$327$	−7.12184	+	4.75122i	−0.393839	+	0.262743i
$328$	−0.107194	+	0.400052i	−0.00591878	+	0.0220892i
$329$	19.1384	−	8.61228i	1.05514	−	0.474810i
$330$	−5.43248	+	7.12338i	−0.299048	+	0.392129i
$331$	−26.5604			−1.45989			−0.729945	−	0.683506i	$-0.760454\pi$
$331$	−26.5604			−1.45989			−0.729945	+	0.683506i	$0.760454\pi$
$332$	−0.165834	−	0.618902i	−0.00910133	−	0.0339666i
$333$	15.2688	−	6.29872i	0.836727	−	0.345168i
$334$	−4.72576	−	8.18526i	−0.258582	−	0.447878i
$335$	9.63889	−	11.0731i	0.526629	−	0.604990i
$336$	−14.1969	+	13.2094i	−0.774506	+	0.720631i
$337$	−8.20766	+	30.6314i	−0.447100	+	1.66860i	0.263233	+	0.964732i	$0.415211\pi$
$337$	−8.20766	+	30.6314i	−0.447100	+	1.66860i	−0.710332	+	0.703866i	$0.751455\pi$
$338$	−4.32528	−	16.1422i	−0.235264	−	0.878018i
$339$	9.30433	−	10.5941i	0.505342	−	0.575393i
$340$	−0.0218083	−	0.0634754i	−0.00118272	−	0.00344244i
$341$	−10.6368	+	6.14114i	−0.576013	+	0.332561i
$342$	18.0925	−	7.46355i	0.978331	−	0.403583i
$343$	8.60417	+	16.4003i	0.464582	+	0.885530i
$344$	−3.84498	−	2.21990i	−0.207307	−	0.119689i
$345$	3.87947	−	30.1581i	0.208863	−	1.62366i
$346$		−	11.6288i		−	0.625168i
$347$	17.1797	+	17.1797i	0.922255	+	0.922255i	0.997189	−	0.0749337i	$-0.0238745\pi$
$347$	17.1797	+	17.1797i	0.922255	+	0.922255i	−0.0749337	+	0.997189i	$0.523875\pi$
$348$	0.806668	+	1.20915i	0.0432419	+	0.0648175i
$349$	−17.8421	+	30.9035i	−0.955068	+	1.65423i	−0.220855	+	0.975307i	$0.570885\pi$
$349$	−17.8421	+	30.9035i	−0.955068	+	1.65423i	−0.734213	+	0.678919i	$0.762449\pi$
$350$	10.2580	+	16.3209i	0.548316	+	0.872391i
$351$	0.434507	−	6.41618i	0.0231923	−	0.342470i
$352$	−0.286458	+	1.06907i	−0.0152682	+	0.0569819i
$353$	6.55165	−	24.4511i	0.348709	−	1.30140i	−0.539509	−	0.841980i	$-0.681390\pi$
$353$	6.55165	−	24.4511i	0.348709	−	1.30140i	0.888218	−	0.459421i	$-0.151943\pi$
$354$	−7.07711	+	2.39665i	−0.376144	+	0.127381i
$355$	−2.21331	−	31.9624i	−0.117470	−	1.69639i
$356$	−0.962328	+	0.555601i	−0.0510033	+	0.0294468i
$357$	0.944386	+	0.591579i	0.0499822	+	0.0313097i
$358$	−6.00961	−	22.4282i	−0.317618	−	1.18537i
$359$	−22.9894	+	13.2729i	−1.21333	+	0.700518i	−0.963484	−	0.267766i	$-0.913714\pi$
$359$	−22.9894	+	13.2729i	−1.21333	+	0.700518i	−0.249849	+	0.968285i	$0.580381\pi$
$360$	1.15870	−	18.3072i	0.0610689	−	0.964873i
$361$	−0.521602	+	0.903441i	−0.0274527	+	0.0475495i
$362$	7.10737	−	7.10737i	0.373555	−	0.373555i
$363$	8.15162	+	12.2189i	0.427849	+	0.641324i
$364$	0.327923	+	0.236264i	0.0171878	+	0.0123836i
$365$	2.68301	+	7.80917i	0.140435	+	0.408751i
$366$	−2.81282	−	8.30601i	−0.147029	−	0.434162i
$367$	7.14790	+	1.91527i	0.373117	+	0.0999764i	0.440504	−	0.897750i	$-0.354800\pi$
$367$	7.14790	+	1.91527i	0.373117	+	0.0999764i	−0.0673873	+	0.997727i	$0.521466\pi$
$368$	−8.59855	−	32.0902i	−0.448231	−	1.67282i
$369$	−0.419533	−	0.174487i	−0.0218400	−	0.00908342i
$370$	−10.0217	−	14.8794i	−0.521001	−	0.773544i
$371$	−2.20534	+	21.8162i	−0.114496	+	1.13264i
$372$	−0.732722	+	1.48311i	−0.0379899	+	0.0768958i
$373$	0.811695	+	3.02929i	0.0420280	+	0.156851i	0.983751	−	0.179539i	$-0.0574607\pi$
$373$	0.811695	+	3.02929i	0.0420280	+	0.156851i	−0.941723	+	0.336390i	$0.890794\pi$
$374$	0.562484			0.0290854
$375$	−18.7559	−	4.81836i	−0.968550	−	0.248819i
$376$			21.6912i			1.11864i
$377$	−5.94991	+	5.94991i	−0.306436	+	0.306436i
$378$	−11.5916	−	16.3390i	−0.596208	−	0.840388i
$379$			2.65661i			0.136461i	0.997670	+	0.0682305i	$0.0217353\pi$
$379$			2.65661i			0.136461i	−0.997670	+	0.0682305i	$0.978265\pi$
$380$	−0.690276	−	1.02487i	−0.0354104	−	0.0525747i
$381$	29.4239	−	9.96438i	1.50743	−	0.510491i
$382$	−11.1490	−	11.1490i	−0.570432	−	0.570432i
$383$	6.11098	−	1.63743i	0.312257	−	0.0836689i	−0.0992873	−	0.995059i	$-0.531656\pi$
$383$	6.11098	−	1.63743i	0.312257	−	0.0836689i	0.411544	+	0.911390i	$0.364990\pi$
$384$	−6.80377	−	20.0909i	−0.347204	−	1.02526i
$385$	−9.14312	+	2.14264i	−0.465976	+	0.109199i
$386$	−6.04139			−0.307499
$387$	2.97074	−	3.85998i	0.151011	−	0.196214i
$388$	1.76287	−	0.472360i	0.0894963	−	0.0239805i
$389$	27.6506	−	15.9641i	1.40194	−	0.809411i	0.407350	−	0.913272i	$-0.366453\pi$
$389$	27.6506	−	15.9641i	1.40194	−	0.809411i	0.994592	+	0.103861i	$0.0331196\pi$
$390$	−6.92229	+	0.932222i	−0.350524	+	0.0472049i
$391$	−1.65338	+	0.954582i	−0.0836153	+	0.0482753i
$392$	−19.1069	+	1.15371i	−0.965046	+	0.0582713i
$393$	−6.87090	+	4.58381i	−0.346591	+	0.231223i
$394$			18.0386i			0.908770i
$395$	18.8630	−	1.30621i	0.949102	−	0.0657226i
$396$	−0.542717	−	0.225720i	−0.0272726	−	0.0113429i
$397$	−7.91481	−	2.12077i	−0.397233	−	0.106438i	0.0546721	−	0.998504i	$-0.482589\pi$
$397$	−7.91481	−	2.12077i	−0.397233	−	0.106438i	−0.451905	+	0.892066i	$0.649255\pi$
$398$	8.33742	−	2.23400i	0.417917	−	0.111980i
$399$	19.6129	+	6.02011i	0.981873	+	0.301382i
$400$	−20.9562	+	2.91630i	−1.04781	+	0.145815i
$401$	2.26353	−	3.92055i	0.113035	−	0.195783i	−0.803957	−	0.594687i	$-0.797276\pi$
$401$	2.26353	−	3.92055i	0.113035	−	0.195783i	0.916993	+	0.398904i	$0.130609\pi$
$402$	14.8565	+	7.33978i	0.740976	+	0.366075i
$403$	−9.24999	−	2.47853i	−0.460775	−	0.123464i
$404$	0.864930	+	1.49810i	0.0430319	+	0.0745334i
$405$	19.7410	+	3.91039i	0.980940	+	0.194309i
$406$	−2.63630	+	26.0794i	−0.130838	+	1.29430i
$407$	8.44157	−	2.26191i	0.418433	−	0.112119i
$408$	−0.958124	+	0.639197i	−0.0474342	+	0.0316450i
$409$	−24.4909			−1.21100			−0.605498	−	0.795847i	$-0.707026\pi$
$409$	−24.4909			−1.21100			−0.605498	+	0.795847i	$0.707026\pi$
$410$	−0.0944933	+	0.484377i	−0.00466669	+	0.0239217i
$411$	−22.6989	−	19.9355i	−1.11966	−	0.983344i
$412$	0.476192	+	1.77717i	0.0234603	+	0.0875551i
$413$	−7.32337	−	2.77784i	−0.360360	−	0.136688i
$414$	34.0340	−	4.43064i	1.67268	−	0.217754i
$415$	3.77157	+	10.9776i	0.185139	+	0.538867i
$416$	−0.747332	+	0.431472i	−0.0366410	+	0.0211547i
$417$	39.1859	−	2.53995i	1.91894	−	0.124382i
$418$	10.0027	−	2.68021i	0.489247	−	0.131093i
$419$	−11.2791	−	19.5359i	−0.551018	−	0.954392i	−0.998201	−	0.0599492i	$-0.980906\pi$
$419$	−11.2791	−	19.5359i	−0.551018	−	0.954392i	0.447183	−	0.894442i	$-0.352427\pi$
$420$	−0.864246	+	0.923474i	−0.0421709	+	0.0450609i
$421$	−17.0914	+	29.6031i	−0.832982	+	1.44277i	0.0626805	+	0.998034i	$0.480035\pi$
$421$	−17.0914	+	29.6031i	−0.832982	+	1.44277i	−0.895663	+	0.444734i	$0.853298\pi$
$422$	−2.77039	+	10.3393i	−0.134861	+	0.503307i
$423$	−23.5888	−	3.14021i	−1.14693	−	0.152682i
$424$	−19.6269	−	11.3316i	−0.953166	−	0.550310i
$425$	0.473569	+	1.11987i	0.0229715	+	0.0543215i
$426$	34.2529	−	11.5997i	1.65956	−	0.562007i
$427$	3.26019	−	8.59504i	0.157772	−	0.415943i
$428$	−1.80583	−	0.483871i	−0.0872882	−	0.0233888i
$429$	0.666237	−	3.33680i	0.0321662	−	0.161102i
$430$	−4.75336	−	2.32235i	−0.229227	−	0.111994i
$431$	−0.650289	+	1.12633i	−0.0313233	+	0.0542536i	−0.881262	−	0.472628i	$-0.843305\pi$
$431$	−0.650289	+	1.12633i	−0.0313233	+	0.0542536i	0.849939	+	0.526881i	$0.176639\pi$
$432$	21.5749	−	4.24293i	1.03802	−	0.204138i
$433$	9.72464	+	9.72464i	0.467336	+	0.467336i	0.901051	−	0.433714i	$-0.142797\pi$
$433$	9.72464	+	9.72464i	0.467336	+	0.467336i	−0.433714	+	0.901051i	$0.642797\pi$
$434$	−27.2041	+	12.2418i	−1.30584	+	0.587627i
$435$	−16.0917	−	20.8429i	−0.771539	−	0.999341i
$436$	−0.305052	+	0.528365i	−0.0146093	+	0.0253041i
$437$	−24.8537	+	24.8537i	−1.18891	+	1.18891i
$438$	−7.75326	+	5.17247i	−0.370465	+	0.247150i
$439$	35.9086			1.71382			0.856912	−	0.515463i	$-0.172380\pi$
$439$	35.9086			1.71382			0.856912	+	0.515463i	$0.172380\pi$
$440$	1.85843	−	9.52637i	0.0885970	−	0.454152i
$441$	1.51145	−	20.9455i	0.0719738	−	0.997407i
$442$	0.310109	+	0.310109i	0.0147504	+	0.0147504i
$443$	6.61758	−	6.61758i	0.314411	−	0.314411i	−0.532205	−	0.846616i	$-0.678636\pi$
$443$	6.61758	−	6.61758i	0.314411	−	0.314411i	0.846616	+	0.532205i	$0.178636\pi$
$444$	0.776728	−	0.884399i	0.0368619	−	0.0419717i
$445$	16.6964	−	11.2454i	0.791483	−	0.533084i
$446$	−18.2491	−	10.5361i	−0.864120	−	0.498900i
$447$	−0.743979	+	0.496334i	−0.0351890	+	0.0234758i
$448$	6.98793	−	18.4227i	0.330149	−	0.870390i
$449$		−	8.36495i		−	0.394766i	−0.980326	−	0.197383i	$-0.936756\pi$
$449$		−	8.36495i		−	0.394766i	0.980326	−	0.197383i	$-0.0632443\pi$
$450$	−0.129594	−	21.8576i	−0.00610914	−	1.03038i
$451$	−0.208204	−	0.120207i	−0.00980396	−	0.00566032i
$452$	0.260063	−	0.970567i	0.0122323	−	0.0456516i
$453$	2.98518	−	0.193493i	0.140256	−	0.00909111i
$454$	−5.65995	−	9.80331i	−0.265634	−	0.460092i
$455$	−6.22206	−	3.85950i	−0.291695	−	0.180936i
$456$	−13.9926	+	15.9323i	−0.655264	+	0.746097i
$457$	10.7352	+	10.7352i	0.502173	+	0.502173i	0.912113	−	0.409940i	$-0.134450\pi$
$457$	10.7352	+	10.7352i	0.502173	+	0.502173i	−0.409940	+	0.912113i	$0.634450\pi$
$458$	23.7772	−	6.37108i	1.11104	−	0.297701i
$459$	−0.556410	−	1.13448i	−0.0259710	−	0.0529530i
$460$	−0.704081	−	2.04930i	−0.0328279	−	0.0955492i
$461$	−16.7586	−	9.67556i	−0.780524	−	0.450636i	0.0560919	−	0.998426i	$-0.482136\pi$
$461$	−16.7586	−	9.67556i	−0.780524	−	0.450636i	−0.836616	+	0.547790i	$0.815469\pi$
$462$	−4.96591	−	9.36461i	−0.231035	−	0.435681i
$463$	−29.1128	−	7.80075i	−1.35299	−	0.362532i	−0.491750	−	0.870736i	$-0.663643\pi$
$463$	−29.1128	−	7.80075i	−1.35299	−	0.362532i	−0.861236	+	0.508205i	$0.830309\pi$
$464$	−24.9158	−	14.3852i	−1.15669	−	0.667814i
$465$	11.3861	−	27.7205i	0.528016	−	1.28551i
$466$	5.64160	+	9.77154i	0.261342	+	0.452658i
$467$	33.4095	+	8.95206i	1.54601	+	0.414252i	0.928202	−	0.372078i	$-0.121355\pi$
$467$	33.4095	+	8.95206i	1.54601	+	0.414252i	0.617807	+	0.786330i	$0.288021\pi$
$468$	−0.174767	−	0.423655i	−0.00807860	−	0.0195835i
$469$	7.12820	+	15.8405i	0.329150	+	0.731445i
$470$	1.78553	+	25.7849i	0.0823604	+	1.18937i
$471$	−6.29365	−	18.5846i	−0.289996	−	0.856333i
$472$	5.72427	−	5.72427i	0.263481	−	0.263481i
$473$	1.82236	−	1.82236i	0.0837922	−	0.0837922i
$474$	6.84571	+	20.2148i	0.314434	+	0.928496i
$475$	13.7576	+	17.6581i	0.631242	+	0.810209i
$476$	0.0790116	+	0.00798710i	0.00362149	+	0.000366088i
$477$	15.1643	−	19.7035i	0.694325	−	0.902160i
$478$	−31.4280	−	8.42112i	−1.43749	−	0.385173i
$479$	6.65500	+	11.5268i	0.304075	+	0.526673i	0.977055	−	0.212988i	$-0.0683194\pi$
$479$	6.65500	+	11.5268i	0.304075	+	0.526673i	−0.672980	+	0.739660i	$0.734986\pi$
$480$	−1.04082	−	2.49184i	−0.0475067	−	0.113736i
$481$	5.90104	+	3.40697i	0.269064	+	0.155344i
$482$	−20.3232	−	5.44560i	−0.925698	−	0.248040i
$483$	30.4895	+	19.0991i	1.38732	+	0.869038i
$484$	0.906510	+	0.523374i	0.0412050	+	0.0237897i
$485$	−31.2684	+	10.7429i	−1.41982	+	0.487810i
$486$	1.40377	+	22.6721i	0.0636763	+	1.02843i
$487$	30.0177	−	8.04323i	1.36023	−	0.364474i	0.496332	−	0.868133i	$-0.334680\pi$
$487$	30.0177	−	8.04323i	1.36023	−	0.364474i	0.863902	+	0.503659i	$0.168013\pi$
$488$	6.71826	+	6.71826i	0.304121	+	0.304121i
$489$	−0.699839	+	0.796851i	−0.0316478	+	0.0360349i
$490$	−22.6180	+	2.94426i	−1.02178	+	0.133008i
$491$	−10.5617	−	18.2934i	−0.476643	−	0.825570i	0.522999	−	0.852333i	$-0.324813\pi$
$491$	−10.5617	−	18.2934i	−0.476643	−	0.825570i	−0.999642	+	0.0267636i	$0.991480\pi$
$492$	−0.0323123	+	0.00209442i	−0.00145675	+	9.44235e-5i
$493$	−0.427912	+	1.59699i	−0.0192722	+	0.0719249i
$494$	6.99232	+	4.03702i	0.314600	+	0.181634i
$495$	10.0907	+	3.40013i	0.453545	+	0.152825i
$496$		−	32.7429i		−	1.47020i
$497$	35.4448	+	13.4446i	1.58992	+	0.603073i
$498$	−10.8990	+	7.27107i	−0.488395	+	0.325825i
$499$	−4.78320	−	2.76158i	−0.214125	−	0.123625i	0.389102	−	0.921195i	$-0.372785\pi$
$499$	−4.78320	−	2.76158i	−0.214125	−	0.123625i	−0.603227	+	0.797569i	$0.706119\pi$
$500$	−1.35044	+	0.284181i	−0.0603933	+	0.0127090i
$501$	−7.41335	+	8.44099i	−0.331204	+	0.377116i
$502$	−15.9695	+	15.9695i	−0.712752	+	0.712752i
$503$	14.5679	+	14.5679i	0.649552	+	0.649552i	0.952885	−	0.303333i	$-0.0980995\pi$
$503$	14.5679	+	14.5679i	0.649552	+	0.649552i	−0.303333	+	0.952885i	$0.598099\pi$
$504$	19.1006	+	10.3083i	0.850808	+	0.459169i
$505$	−17.5063	−	25.9920i	−0.779019	−	1.15663i
$506$	18.1598			0.807300
$507$	−16.5240	+	11.0237i	−0.733857	+	0.489581i
$508$	1.56541	−	1.56541i	0.0694540	−	0.0694540i
$509$	10.1148	−	17.5193i	0.448330	−	0.776530i	−0.549948	−	0.835199i	$-0.685352\pi$
$509$	10.1148	−	17.5193i	0.448330	−	0.776530i	0.998277	+	0.0586691i	$0.0186857\pi$
$510$	−1.08633	+	0.838699i	−0.0481035	+	0.0371382i
$511$	−9.72054	−	0.982626i	−0.430011	−	0.0434688i
$512$	14.2783	+	14.2783i	0.631017	+	0.631017i
$513$	−15.3004	−	17.5232i	−0.675529	−	0.773670i
$514$	−5.81038	+	10.0639i	−0.256285	+	0.443898i
$515$	−10.8301	−	31.5220i	−0.477230	−	1.38903i
$516$	0.0679640	−	0.340392i	0.00299195	−	0.0149849i
$517$	−12.1622	−	3.25886i	−0.534894	−	0.143324i
$518$	20.9518	−	3.40385i	0.920568	−	0.149557i
$519$	−13.0918	+	4.43353i	−0.574668	+	0.194610i
$520$	6.27666	−	4.22749i	0.275250	−	0.185388i
$521$	2.53885	+	1.46581i	0.111229	+	0.0642182i	0.554583	−	0.832129i	$-0.312878\pi$
$521$	2.53885	+	1.46581i	0.111229	+	0.0642182i	−0.443353	+	0.896347i	$0.646211\pi$
$522$	18.1276	−	23.5539i	0.793425	−	1.03092i
$523$	9.79334	−	36.5492i	0.428233	−	1.59819i	−0.328528	−	0.944494i	$-0.606553\pi$
$523$	9.79334	−	36.5492i	0.428233	−	1.59819i	0.756761	−	0.653692i	$-0.226781\pi$
$524$	−0.294303	+	0.509748i	−0.0128567	+	0.0222684i
$525$	14.4634	−	17.7711i	0.631233	−	0.775593i
$526$	11.6956	+	20.2574i	0.509952	+	0.883263i
$527$	−1.81750	+	0.486998i	−0.0791716	+	0.0212140i
$528$	11.6099	−	0.752527i	0.505255	−	0.0327495i
$529$	−33.4608	+	19.3186i	−1.45482	+	0.839940i
$530$	−24.2638	−	11.8545i	−1.05395	−	0.514929i
$531$	5.39636	+	7.05376i	0.234182	+	0.306107i
$532$	1.44312	−	0.234452i	0.0625674	−	0.0101648i
$533$	−0.0485148	−	0.181060i	−0.00210141	−	0.00784256i
$534$	17.0724	+	14.9939i	0.738795	+	0.648850i
$535$	33.2414	+	6.48482i	1.43715	+	0.280363i
$536$	−17.9533			−0.775466
$537$	−22.9587	+	15.3165i	−0.990742	+	0.660958i
$538$	−19.1734	+	5.13750i	−0.826625	+	0.221493i
$539$	2.22372	−	10.8866i	0.0957824	−	0.468918i
$540$	1.38472	−	0.373290i	0.0595888	−	0.0160638i
$541$	−2.50955	−	4.34666i	−0.107894	−	0.186878i	0.807023	−	0.590520i	$-0.201077\pi$
$541$	−2.50955	−	4.34666i	−0.107894	−	0.186878i	−0.914917	+	0.403642i	$0.867744\pi$
$542$	−14.2837	−	3.82731i	−0.613538	−	0.164397i
$543$	−10.7113	−	5.29184i	−0.459665	−	0.227095i
$544$	−0.0847786	+	0.146841i	−0.00363485	+	0.00629575i
$545$	4.85182	−	9.93065i	0.207829	−	0.425382i
$546$	2.42509	−	7.90070i	0.103784	−	0.338119i
$547$	7.92855	−	2.12445i	0.339000	−	0.0908349i	−0.0853028	−	0.996355i	$-0.527186\pi$
$547$	7.92855	−	2.12445i	0.339000	−	0.0908349i	0.424303	+	0.905520i	$0.360519\pi$
$548$	−2.07954	−	0.557210i	−0.0888334	−	0.0238029i
$549$	−8.27861	+	6.33341i	−0.353322	+	0.270303i
$550$	1.42499	−	11.4772i	0.0607617	−	0.489391i
$551$			30.4383i			1.29672i
$552$	−30.9330	+	20.6364i	−1.31659	+	0.878345i
$553$	−7.93451	+	20.9182i	−0.337409	+	0.889533i
$554$	−19.5057	+	11.2616i	−0.828717	+	0.478460i
$555$	−12.9306	+	16.9554i	−0.548874	+	0.719715i
$556$	2.42348	−	1.39919i	0.102778	−	0.0593390i
$557$	−36.4391	+	9.76383i	−1.54397	+	0.413707i	−0.927547	−	0.373706i	$-0.878087\pi$
$557$	−36.4391	+	9.76383i	−1.54397	+	0.413707i	−0.616427	+	0.787412i	$0.711420\pi$
$558$	33.5301	+	4.46363i	1.41944	+	0.188960i
$559$	2.00941			0.0849889
$560$	7.24043	−	23.9648i	0.305964	−	1.01270i
$561$	−0.214450	−	0.633251i	−0.00905408	−	0.0267359i
$562$	15.9933	−	4.28540i	0.674639	−	0.180769i
$563$	0.477376	+	0.477376i	0.0201190	+	0.0201190i	0.717095	−	0.696976i	$-0.245471\pi$
$563$	0.477376	+	0.477376i	0.0201190	+	0.0201190i	−0.696976	+	0.717095i	$0.745471\pi$
$564$	−1.60625	+	0.543954i	−0.0676353	+	0.0229046i
$565$	−3.48535	+	17.8660i	−0.146630	+	0.751630i
$566$			1.48003i			0.0622102i
$567$	−13.9753	+	19.2793i	−0.586908	+	0.809654i
$568$	−27.7052	+	27.7052i	−1.16249	+	1.16249i
$569$		−	23.5050i		−	0.985381i	−0.870205	−	0.492691i	$-0.836013\pi$
$569$		−	23.5050i		−	0.985381i	0.870205	−	0.492691i	$-0.163987\pi$
$570$	−15.3219	+	20.0909i	−0.641764	+	0.841516i
$571$	−23.7639			−0.994489			−0.497245	−	0.867610i	$-0.665655\pi$
$571$	−23.7639			−0.994489			−0.497245	+	0.867610i	$0.665655\pi$
$572$	−0.0627599	−	0.234223i	−0.00262412	−	0.00979336i
$573$	−8.30106	+	16.8023i	−0.346782	+	0.701925i
$574$	−0.473766	−	0.341343i	−0.0197746	−	0.0142474i
$575$	15.2891	+	36.1549i	0.637601	+	1.50776i
$576$	−17.7444	+	13.5751i	−0.739352	+	0.565629i
$577$	2.62661	+	9.80265i	0.109347	+	0.408090i	0.998802	−	0.0489336i	$-0.0155823\pi$
$577$	2.62661	+	9.80265i	0.109347	+	0.408090i	−0.889455	+	0.457023i	$0.848916\pi$
$578$	−23.8451	−	6.38927i	−0.991824	−	0.265758i
$579$	2.30331	+	6.80147i	0.0957223	+	0.282660i
$580$	−1.68604	−	0.823747i	−0.0700089	−	0.0342042i
$581$	−13.6644	−	1.38130i	−0.566895	−	0.0573061i
$582$	−20.7108	−	31.0445i	−0.858492	−	1.28684i
$583$	9.30233	−	9.30233i	0.385263	−	0.385263i
$584$	5.04896	−	8.74506i	0.208928	−	0.361873i
$585$	3.68866	+	7.43779i	0.152507	+	0.307515i
$586$	13.7933	−	7.96359i	0.569798	−	0.328973i
$587$	−3.39769	−	12.6804i	−0.140238	−	0.523374i	−0.999921	−	0.0125473i	$-0.996006\pi$
$587$	−3.39769	−	12.6804i	−0.140238	−	0.523374i	0.859684	−	0.510827i	$-0.170661\pi$
$588$	−0.564582	−	1.38595i	−0.0232830	−	0.0571557i
$589$	−30.0002	+	17.3206i	−1.23613	+	0.713683i
$590$	6.33340	−	7.27579i	0.260742	−	0.299540i
$591$	20.3080	−	6.87729i	0.835361	−	0.282894i
$592$	−6.02995	+	22.5041i	−0.247829	+	0.924911i
$593$	3.71556	−	13.8667i	0.152580	−	0.569436i	−0.846720	−	0.532038i	$-0.821426\pi$
$593$	3.71556	−	13.8667i	0.152580	−	0.569436i	0.999300	−	0.0373982i	$-0.0119070\pi$
$594$	−0.812078	+	11.9916i	−0.0333200	+	0.492021i
$595$	−1.43793	−	0.0454661i	−0.0589495	−	0.00186393i
$596$	−0.0318671	+	0.0551954i	−0.00130533	+	0.00226089i
$597$	−5.69375	−	8.53464i	−0.233030	−	0.349299i
$598$	10.0118	+	10.0118i	0.409415	+	0.409415i
$599$		−	10.1553i		−	0.414933i	−0.978242	−	0.207467i	$-0.933478\pi$
$599$		−	10.1553i		−	0.414933i	0.978242	−	0.207467i	$-0.0665218\pi$
$600$	10.6152	+	21.1694i	0.433365	+	0.864237i
$601$	38.1532	+	22.0278i	1.55630	+	0.898532i	0.997606	+	0.0691610i	$0.0220322\pi$
$601$	38.1532	+	22.0278i	1.55630	+	0.898532i	0.558698	+	0.829371i	$0.311301\pi$
$602$	4.84894	−	3.95861i	0.197628	−	0.161341i
$603$	2.59909	−	19.5240i	0.105843	−	0.795078i
$604$	0.184620	−	0.106591i	0.00751209	−	0.00433711i
$605$	−17.0379	−	8.32421i	−0.692689	−	0.338427i
$606$	23.3418	−	26.5774i	0.948195	−	1.07963i
$607$	−10.6834	−	39.8710i	−0.433626	−	1.61832i	−0.744332	−	0.667809i	$-0.767232\pi$
$607$	−10.6834	−	39.8710i	−0.433626	−	1.61832i	0.310706	−	0.950506i	$-0.399434\pi$
$608$	−0.807931	+	3.01524i	−0.0327659	+	0.122284i
$609$	30.3656	−	6.97491i	1.23048	−	0.282638i
$610$	8.53920	+	7.43316i	0.345742	+	0.300960i
$611$	−4.90860	−	8.50195i	−0.198581	−	0.343952i
$612$	−0.0713601	−	0.0549205i	−0.00288456	−	0.00222003i
$613$	−0.766262	−	2.85973i	−0.0309490	−	0.115503i	0.948723	−	0.316108i	$-0.102376\pi$
$613$	−0.766262	−	2.85973i	−0.0309490	−	0.115503i	−0.979672	+	0.200604i	$0.935709\pi$
$614$	−15.9062			−0.641920
$615$	0.581343	−	0.0782892i	0.0234420	−	0.00315692i
$616$	9.31770	+	6.71328i	0.375421	+	0.270486i
$617$	9.17604	−	34.2455i	0.369414	−	1.37867i	−0.491924	−	0.870638i	$-0.663706\pi$
$617$	9.17604	−	34.2455i	0.369414	−	1.37867i	0.861338	−	0.508032i	$-0.169627\pi$
$618$	31.2964	−	20.8789i	1.25892	−	0.839871i
$619$	−8.50373	−	14.7289i	−0.341794	−	0.592004i	0.642972	−	0.765889i	$-0.277701\pi$
$619$	−8.50373	−	14.7289i	−0.341794	−	0.592004i	−0.984766	+	0.173886i	$0.944368\pi$
$620$	−0.147532	−	2.13051i	−0.00592502	−	0.0855633i
$621$	−17.9637	−	36.6267i	−0.720858	−	1.46978i
$622$	19.7748	−	19.7748i	0.792899	−	0.792899i
$623$	3.81950	+	23.5102i	0.153025	+	0.941917i
$624$	6.81563	+	5.98587i	0.272844	+	0.239626i
$625$	24.0501	−	6.82590i	0.962004	−	0.273036i
$626$		−	14.7956i		−	0.591352i
$627$	−6.83098	−	10.2393i	−0.272803	−	0.408918i
$628$	−0.988738	−	0.988738i	−0.0394549	−	0.0394549i
$629$	1.33885			0.0533834
$630$	23.5539	+	10.6815i	0.938411	+	0.425560i
$631$	19.5886			0.779812			0.389906	−	0.920855i	$-0.372508\pi$
$631$	19.5886			0.779812			0.389906	+	0.920855i	$0.372508\pi$
$632$	−16.3506	−	16.3506i	−0.650392	−	0.650392i
$633$	12.6963	−	0.822946i	0.504632	−	0.0327092i
$634$			35.1260i			1.39503i
$635$	−26.3319	+	30.2500i	−1.04495	+	1.20043i
$636$	0.346925	−	1.73755i	0.0137565	−	0.0688983i
$637$	7.22797	−	4.77601i	0.286383	−	0.189232i
$638$	11.1202	−	11.1202i	0.440251	−	0.440251i
$639$	−26.1181	−	34.1399i	−1.03322	−	1.35055i
$640$	20.6550	+	17.9796i	0.816460	+	0.710708i
$641$	8.47407	+	14.6775i	0.334706	+	0.579727i	0.983428	−	0.181298i	$-0.0580298\pi$
$641$	8.47407	+	14.6775i	0.334706	+	0.579727i	−0.648723	+	0.761025i	$0.724696\pi$
$642$	2.47269	+	38.1483i	0.0975893	+	1.50559i
$643$	−4.18364	+	15.6136i	−0.164987	+	0.615739i	0.833055	+	0.553190i	$0.186590\pi$
$643$	−4.18364	+	15.6136i	−0.164987	+	0.615739i	−0.998042	+	0.0625489i	$0.980077\pi$
$644$	2.55089	+	0.257863i	0.100519	+	0.0101612i
$645$	−0.802288	+	6.23680i	−0.0315900	+	0.245574i
$646$	1.58644			0.0624178
$647$	−11.6268	−	43.3917i	−0.457095	−	1.70590i	−0.681855	−	0.731488i	$-0.738826\pi$
$647$	−11.6268	−	43.3917i	−0.457095	−	1.70590i	0.224760	−	0.974414i	$-0.427840\pi$
$648$	−12.2438	−	21.3491i	−0.480980	−	0.838670i
$649$	2.34959	+	4.06960i	0.0922293	+	0.159746i
$650$	7.11325	−	5.54200i	0.279004	−	0.217375i
$651$	24.1537	+	25.9595i	0.946659	+	1.01743i
$652$	−0.0195610	+	0.0730026i	−0.000766068	+	0.00285900i
$653$	2.82687	+	10.5500i	0.110624	+	0.412854i	0.998922	−	0.0464124i	$-0.0147788\pi$
$653$	2.82687	+	10.5500i	0.110624	+	0.412854i	−0.888298	+	0.459267i	$0.848112\pi$
$654$	12.2340	+	2.44268i	0.478386	+	0.0955162i
$655$	4.68086	−	9.58073i	0.182896	−	0.374350i
$656$	0.555044	−	0.320455i	0.0216708	−	0.0125117i
$657$	8.77919	+	6.75669i	0.342509	+	0.263604i
$658$	−28.5942	−	10.8461i	−1.11472	−	0.422825i
$659$	22.7922	+	13.1591i	0.887857	+	0.512605i	0.873241	−	0.487289i	$-0.162014\pi$
$659$	22.7922	+	13.1591i	0.887857	+	0.512605i	0.0146161	+	0.999893i	$0.495347\pi$
$660$	0.752039	−	0.101277i	0.0292731	−	0.00394219i
$661$		−	2.39828i		−	0.0932822i	−0.998912	−	0.0466411i	$-0.985148\pi$
$661$		−	2.39828i		−	0.0932822i	0.998912	−	0.0466411i	$-0.0148517\pi$
$662$	27.3677	+	27.3677i	1.06368	+	1.06368i
$663$	0.230894	−	0.467354i	0.00896717	−	0.0181505i
$664$	7.09746	−	12.2932i	0.275435	−	0.477067i
$665$	−25.7874	+	6.04315i	−0.999994	+	0.234343i
$666$	−22.2231	−	9.24276i	−0.861128	−	0.358150i
$667$	−13.8151	+	51.5588i	−0.534924	+	1.99636i
$668$	−0.207208	+	0.773312i	−0.00801713	+	0.0299203i
$669$	−4.90414	+	24.5620i	−0.189605	+	0.949622i
$670$	−21.3416	+	1.47785i	−0.824498	+	0.0570942i
$671$	−4.77627	+	2.75758i	−0.184386	+	0.106455i
$672$	3.19317	+	0.115062i	0.123179	+	0.00443860i
$673$	−0.660582	−	2.46532i	−0.0254635	−	0.0950313i	0.952025	−	0.306021i	$-0.0989979\pi$
$673$	−0.660582	−	2.46532i	−0.0254635	−	0.0950313i	−0.977488	+	0.210990i	$0.932331\pi$
$674$	40.0196	−	23.1053i	1.54150	−	0.889984i
$675$	−24.5582	+	8.47922i	−0.945244	+	0.326365i
$676$	−0.707778	+	1.22591i	−0.0272222	+	0.0471503i
$677$	−8.10700	+	8.10700i	−0.311577	+	0.311577i	−0.845520	−	0.533943i	$-0.820710\pi$
$677$	−8.10700	+	8.10700i	−0.311577	+	0.311577i	0.533943	+	0.845520i	$0.320710\pi$
$678$	−20.5033	+	1.32898i	−0.787423	+	0.0510391i
$679$	3.93449	−	38.9216i	0.150992	−	1.49367i
$680$	0.652730	−	1.33600i	0.0250311	−	0.0512333i
$681$	−8.87880	+	10.1096i	−0.340236	+	0.387400i
$682$	17.2879	+	4.63227i	0.661987	+	0.177379i
$683$	9.30327	+	34.7203i	0.355980	+	1.32854i	0.879247	+	0.476366i	$0.158046\pi$
$683$	9.30327	+	34.7203i	0.355980	+	1.32854i	−0.523267	+	0.852169i	$0.675287\pi$
$684$	−1.53069	−	0.636626i	−0.0585275	−	0.0243420i
$685$	38.2798	+	7.46771i	1.46259	+	0.285326i
$686$	8.03305	−	25.7645i	0.306703	−	0.983692i
$687$	−16.2378	−	24.3397i	−0.619511	−	0.928616i
$688$	1.77821	+	6.63638i	0.0677937	+	0.253010i
$689$	10.2571			0.390765
$690$	−35.0721	+	27.0774i	−1.33517	+	1.03082i
$691$		−	29.6002i		−	1.12604i	−0.826442	−	0.563022i	$-0.809639\pi$
$691$		−	29.6002i		−	1.12604i	0.826442	−	0.563022i	$-0.190361\pi$
$692$	−0.696512	+	0.696512i	−0.0264774	+	0.0264774i
$693$	−8.64951	+	9.16098i	−0.328568	+	0.347997i
$694$		−	35.4038i		−	1.34391i
$695$	−42.0472	+	28.3198i	−1.59494	+	1.07423i
$696$	−6.30509	+	31.5786i	−0.238994	+	1.19698i
$697$	−0.0260433	−	0.0260433i	−0.000986461	−	0.000986461i
$698$	50.2273	−	13.4584i	1.90113	−	0.509407i
$699$	8.85003	−	10.0768i	0.334739	−	0.381141i
$700$	0.363140	−	1.59196i	0.0137254	−	0.0601705i
$701$	23.4566			0.885945			0.442972	−	0.896535i	$-0.353924\pi$
$701$	23.4566			0.885945			0.442972	+	0.896535i	$0.353924\pi$
$702$	−7.05892	+	6.16349i	−0.266422	+	0.232626i
$703$	23.8088	−	6.37954i	0.897965	−	0.240609i
$704$	−10.2375	+	5.91062i	−0.385840	+	0.222765i
$705$	28.3482	−	11.8408i	1.06765	−	0.445949i
$706$	−31.9451	+	18.4435i	−1.20227	+	0.694131i
$707$	36.5995	−	5.94600i	1.37647	−	0.223622i
$708$	0.567435	+	0.280338i	0.0213255	+	0.0105357i
$709$		−	14.1419i		−	0.531111i	−0.964096	−	0.265556i	$-0.914445\pi$
$709$		−	14.1419i		−	0.531111i	0.964096	−	0.265556i	$-0.0855554\pi$
$710$	−30.6533	+	35.2145i	−1.15040	+	1.32158i
$711$	20.1481	−	15.4140i	0.755612	−	0.578069i
$712$	−23.7789	−	6.37154i	−0.891152	−	0.238783i
$713$	−58.6779	+	15.7227i	−2.19751	+	0.588820i
$714$	−0.363532	−	1.58265i	−0.0136048	−	0.0592293i
$715$	1.42735	+	4.15445i	0.0533799	+	0.155368i
$716$	−0.983398	+	1.70329i	−0.0367513	+	0.0636551i
$717$	2.50149	+	38.5927i	0.0934200	+	1.44127i
$718$	37.3645	+	10.0118i	1.39443	+	0.373637i
$719$	−9.68860	−	16.7812i	−0.361324	−	0.625831i	0.626855	−	0.779136i	$-0.284342\pi$
$719$	−9.68860	−	16.7812i	−0.361324	−	0.625831i	−0.988179	+	0.153304i	$0.951008\pi$
$720$	−21.3002	+	18.7644i	−0.793811	+	0.699308i
$721$	39.2373	+	3.96641i	1.46127	+	0.147717i
$722$	1.46836	−	0.393445i	0.0546466	−	0.0146425i
$723$	1.61762	+	24.9563i	0.0601598	+	0.928135i
$724$	−0.851398			−0.0316420
$725$	31.5018	+	12.7771i	1.16995	+	0.474531i
$726$	4.19087	−	20.9897i	0.155538	−	0.778999i
$727$	13.1895	+	49.2238i	0.489170	+	1.82561i	0.560499	+	0.828155i	$0.310610\pi$
$727$	13.1895	+	49.2238i	0.489170	+	1.82561i	−0.0713282	+	0.997453i	$0.522724\pi$
$728$	1.43586	+	8.83820i	0.0532166	+	0.327565i
$729$	24.9893	−	10.2242i	0.925530	−	0.378675i
$730$	5.28198	−	10.8111i	0.195495	−	0.400137i
$731$	0.341926	−	0.197411i	0.0126466	−	0.00730151i
$732$	−0.329017	+	0.665968i	−0.0121608	+	0.0246149i
$733$	18.4812	−	4.95201i	0.682617	−	0.182907i	0.0991856	−	0.995069i	$-0.468376\pi$
$733$	18.4812	−	4.95201i	0.682617	−	0.182907i	0.583432	+	0.812162i	$0.301710\pi$
$734$	−5.39167	−	9.33865i	−0.199010	−	0.344696i
$735$	11.9379	+	24.3411i	0.440335	+	0.897833i
$736$	−2.73707	+	4.74075i	−0.100890	+	0.174746i
$737$	2.69729	−	10.0664i	0.0993559	−	0.370801i
$738$	0.252494	+	0.612075i	0.00929444	+	0.0225308i
$739$	−1.41281	−	0.815684i	−0.0519709	−	0.0300054i	0.473789	−	0.880638i	$-0.342886\pi$
$739$	−1.41281	−	0.815684i	−0.0519709	−	0.0300054i	−0.525760	+	0.850633i	$0.676219\pi$
$740$	−0.290958	+	1.49146i	−0.0106958	+	0.0548272i
$741$	1.87907	−	9.41117i	0.0690293	−	0.345728i
$742$	24.7517	−	20.2069i	0.908662	−	0.741819i
$743$	−43.7636	−	11.7264i	−1.60553	−	0.430201i	−0.658824	−	0.752297i	$-0.728946\pi$
$743$	−43.7636	−	11.7264i	−1.60553	−	0.430201i	−0.946707	+	0.322097i	$0.895612\pi$
$744$	−34.7118	+	11.7551i	−1.27260	+	0.430964i
$745$	0.506842	−	1.03740i	0.0185693	−	0.0380074i
$746$	2.28500	−	3.95773i	0.0836598	−	0.144903i
$747$	12.3411	+	9.49806i	0.451539	+	0.347516i
$748$	−0.0336903	−	0.0336903i	−0.00123184	−	0.00123184i
$749$	−23.4254	+	32.5133i	−0.855946	+	1.18801i
$750$	14.3612	+	24.2908i	0.524396	+	0.886975i
$751$	2.94999	−	5.10953i	0.107647	−	0.186450i	−0.807170	−	0.590319i	$-0.799002\pi$
$751$	2.94999	−	5.10953i	0.107647	−	0.186450i	0.914816	+	0.403870i	$0.132335\pi$
$752$	23.7352	−	23.7352i	0.865532	−	0.865532i
$753$	24.0670	+	11.8902i	0.877052	+	0.433302i
$754$	12.2615			0.446538
$755$	−3.20315	+	2.15740i	−0.116575	+	0.0785160i
$756$	−0.284349	+	1.67292i	−0.0103417	+	0.0608434i
$757$	−4.53833	−	4.53833i	−0.164948	−	0.164948i	0.619806	−	0.784755i	$-0.287211\pi$
$757$	−4.53833	−	4.53833i	−0.164948	−	0.164948i	−0.784755	+	0.619806i	$0.787211\pi$
$758$	2.73736	−	2.73736i	0.0994255	−	0.0994255i
$759$	−6.92350	−	20.4445i	−0.251307	−	0.742088i
$760$	5.24154	−	26.8684i	0.190131	−	0.974618i
$761$	−2.20928	−	1.27553i	−0.0800862	−	0.0462378i	0.459422	−	0.888218i	$-0.348057\pi$
$761$	−2.20928	−	1.27553i	−0.0800862	−	0.0462378i	−0.539508	+	0.841980i	$0.681390\pi$
$762$	−40.5856	−	20.0511i	−1.47026	−	0.726373i
$763$	8.27026	+	10.1303i	0.299404	+	0.366743i
$764$			1.33555i			0.0483184i
$765$	1.35839	+	0.903246i	0.0491126	+	0.0326569i
$766$	−7.98394	−	4.60953i	−0.288471	−	0.166549i
$767$	−0.948279	+	3.53903i	−0.0342404	+	0.127787i
$768$	−2.26422	+	4.58303i	−0.0817029	+	0.165376i
$769$	3.13614	+	5.43196i	0.113092	+	0.195881i	0.917015	−	0.398852i	$-0.130591\pi$
$769$	3.13614	+	5.43196i	0.113092	+	0.195881i	−0.803923	+	0.594733i	$0.797258\pi$
$770$	11.6288	+	7.21326i	0.419073	+	0.259948i
$771$	13.5453	+	2.70450i	0.487821	+	0.0974000i
$772$	0.361852	+	0.361852i	0.0130233	+	0.0130233i
$773$	28.1593	−	7.54526i	1.01282	−	0.271384i	0.286013	−	0.958226i	$-0.407670\pi$
$773$	28.1593	−	7.54526i	1.01282	−	0.271384i	0.726807	+	0.686842i	$0.241003\pi$
$774$	−7.03835	+	0.916272i	−0.252988	+	0.0329347i
$775$	5.33254	+	38.3190i	0.191550	+	1.37646i
$776$	35.0157	+	20.2163i	1.25699	+	0.725724i
$777$	−11.8201	−	22.2900i	−0.424042	−	0.799650i
$778$	−44.9404	−	12.0417i	−1.61119	−	0.431718i
$779$	−0.587224	−	0.339034i	−0.0210395	−	0.0121472i
$780$	0.470450	+	0.358778i	0.0168448	+	0.0128463i
$781$	−11.3719	−	19.6967i	−0.406918	−	0.704803i
$782$	2.68724	+	0.720043i	0.0960955	+	0.0257487i
$783$	−33.4284	−	11.4283i	−1.19464	−	0.408414i
$784$	22.1698	+	19.6450i	0.791780	+	0.701607i
$785$	19.1063	+	16.6316i	0.681934	+	0.593607i
$786$	11.8029	+	2.35661i	0.420995	+	0.0840573i
$787$	12.9961	−	12.9961i	0.463262	−	0.463262i	−0.436461	−	0.899723i	$-0.643768\pi$
$787$	12.9961	−	12.9961i	0.463262	−	0.463262i	0.899723	+	0.436461i	$0.143768\pi$
$788$	1.08043	−	1.08043i	0.0384887	−	0.0384887i
$789$	18.3470	−	20.8903i	0.653170	−	0.743713i
$790$	−20.7823	−	18.0905i	−0.739401	−	0.643630i
$791$	−17.4747	−	12.5903i	−0.621328	−	0.447659i
$792$	−4.96588	−	12.0379i	−0.176455	−	0.427746i
$793$	−4.15356	−	1.11294i	−0.147497	−	0.0395218i
$794$	5.97016	+	10.3406i	0.211873	+	0.366975i
$795$	−4.09532	+	31.8360i	−0.145246	+	1.12911i
$796$	−0.633180	−	0.365567i	−0.0224425	−	0.0129572i
$797$	−7.61511	−	2.04046i	−0.269741	−	0.0722769i	0.121413	−	0.992602i	$-0.461257\pi$
$797$	−7.61511	−	2.04046i	−0.269741	−	0.0722769i	−0.391154	+	0.920325i	$0.627924\pi$
$798$	−14.0060	−	26.4121i	−0.495805	−	0.934980i
$799$	−1.67052	−	0.964476i	−0.0590988	−	0.0341207i
$800$	2.78144	+	2.10187i	0.0983388	+	0.0743124i
$801$	10.3714	−	24.9368i	0.366455	−	0.881099i
$802$	−6.37205	+	1.70739i	−0.225005	+	0.0602899i
$803$	4.14480	+	4.14480i	0.146267	+	0.146267i
$804$	−0.450219	−	1.32946i	−0.0158780	−	0.0468864i
$805$	−46.4236	−	1.46787i	−1.63622	−	0.0517357i
$806$	6.97729	+	12.0850i	0.245764	+	0.425677i
$807$	13.0938	+	19.6270i	0.460924	+	0.690902i
$808$	−9.91888	+	37.0178i	−0.348945	+	1.30228i
$809$	11.1011	+	6.40922i	0.390293	+	0.225336i	0.682287	−	0.731084i	$-0.260985\pi$
$809$	11.1011	+	6.40922i	0.390293	+	0.225336i	−0.291994	+	0.956420i	$0.594319\pi$
$810$	−16.3119	−	24.3703i	−0.573140	−	0.856287i
$811$		−	22.8117i		−	0.801028i	−0.916291	−	0.400514i	$-0.868832\pi$
$811$		−	22.8117i		−	0.801028i	0.916291	−	0.400514i	$-0.131168\pi$
$812$	1.71994	−	1.40413i	0.0603581	−	0.0492755i
$813$	1.13690	+	17.5399i	0.0398729	+	0.615152i
$814$	−11.0288	−	6.36749i	−0.386560	−	0.223180i
$815$	0.262156	−	1.34382i	0.00918291	−	0.0470720i
$816$	1.74784	+	0.348980i	0.0611866	+	0.0122167i
$817$	5.13983	−	5.13983i	0.179820	−	0.179820i
$818$	25.2353	+	25.2353i	0.882332	+	0.882332i
$819$	−9.81928	+	0.281982i	−0.343113	+	0.00985325i
$820$	0.0346717	−	0.0233522i	0.00121079	−	0.000815496i
$821$	6.31763			0.220487			0.110243	−	0.993905i	$-0.464837\pi$
$821$	6.31763			0.220487			0.110243	+	0.993905i	$0.464837\pi$
$822$	2.84747	+	43.9303i	0.0993169	+	1.53225i
$823$	7.74974	−	7.74974i	0.270139	−	0.270139i	−0.559017	−	0.829156i	$-0.688821\pi$
$823$	7.74974	−	7.74974i	0.270139	−	0.270139i	0.829156	+	0.559017i	$0.188821\pi$
$824$	−20.3803	+	35.2998i	−0.709983	+	1.22973i
$825$	−13.4645	+	2.77148i	−0.468773	+	0.0964905i
$826$	4.68370	+	10.4082i	0.162967	+	0.362149i
$827$	−0.738803	−	0.738803i	−0.0256907	−	0.0256907i	0.694145	−	0.719835i	$-0.255783\pi$
$827$	−0.738803	−	0.738803i	−0.0256907	−	0.0256907i	−0.719835	+	0.694145i	$0.755783\pi$
$828$	−2.30386	−	1.77311i	−0.0800645	−	0.0616197i
$829$	−4.48578	+	7.76960i	−0.155798	+	0.269849i	−0.933349	−	0.358970i	$-0.883128\pi$
$829$	−4.48578	+	7.76960i	−0.155798	+	0.269849i	0.777552	+	0.628819i	$0.216461\pi$
$830$	7.42502	−	15.1975i	0.257726	−	0.527511i
$831$	20.1151	+	17.6662i	0.697785	+	0.612833i
$832$	−8.90278	−	2.38549i	−0.308648	−	0.0827021i
$833$	0.760719	−	1.52280i	0.0263573	−	0.0527618i
$834$	−42.9942	−	37.7599i	−1.48877	−	1.30752i
$835$	2.77700	−	14.2350i	0.0961019	−	0.492622i
$836$	−0.759647	−	0.438582i	−0.0262729	−	0.0151687i
$837$	−7.75831	−	39.4504i	−0.268167	−	1.36360i
$838$	−8.50782	+	31.7516i	−0.293898	+	1.09684i
$839$	19.6423	−	34.0214i	0.678126	−	1.17455i	−0.297418	−	0.954747i	$-0.596126\pi$
$839$	19.6423	−	34.0214i	0.678126	−	1.17455i	0.975545	−	0.219802i	$-0.0705410\pi$
$840$	−28.0053	+	0.927840i	−0.966274	+	0.0320135i
$841$	8.61235	+	14.9170i	0.296978	+	0.514381i
$842$	48.1138	−	12.8921i	1.65811	−	0.444290i
$843$	−10.9221	−	16.3717i	−0.376177	−	0.563870i
$844$	0.785208	−	0.453340i	0.0270280	−	0.0156046i
$845$	11.2571	−	23.0410i	0.387257	−	0.792633i
$846$	21.0702	+	27.5415i	0.724408	+	0.946896i
$847$	17.3805	−	14.1892i	0.597201	−	0.487547i
$848$	9.07697	+	33.8757i	0.311704	+	1.16330i
$849$	1.66623	−	0.564268i	0.0571850	−	0.0193656i
$850$	0.665944	−	1.64187i	0.0228417	−	0.0563157i
$851$	43.2246			1.48172
$852$	−2.74636	−	1.35682i	−0.0940888	−	0.0464840i
$853$	−40.2469	+	10.7841i	−1.37803	+	0.369242i	−0.870405	−	0.492337i	$-0.836143\pi$
$853$	−40.2469	+	10.7841i	−1.37803	+	0.369242i	−0.507624	+	0.861579i	$0.669476\pi$
$854$	−12.2156	+	5.49701i	−0.418009	+	0.188104i
$855$	28.4601	+	9.58981i	0.973316	+	0.327965i
$856$	−20.7090	−	35.8690i	−0.707819	−	1.22598i
$857$	−17.6167	−	4.72039i	−0.601776	−	0.161245i	−0.0549464	−	0.998489i	$-0.517499\pi$
$857$	−17.6167	−	4.72039i	−0.601776	−	0.161245i	−0.546830	+	0.837244i	$0.684165\pi$
$858$	−4.12471	+	2.75173i	−0.140815	+	0.0939427i
$859$	7.54666	−	13.0712i	0.257489	−	0.445984i	−0.708080	−	0.706132i	$-0.750438\pi$
$859$	7.54666	−	13.0712i	0.257489	−	0.445984i	0.965569	+	0.260149i	$0.0837716\pi$
$860$	0.145607	+	0.423803i	0.00496514	+	0.0144516i
$861$	−0.203662	+	0.663510i	−0.00694079	+	0.0226124i
$862$	1.83062	−	0.490514i	0.0623513	−	0.0167070i
$863$	21.7388	+	5.82489i	0.739997	+	0.198282i	0.609077	−	0.793111i	$-0.291540\pi$
$863$	21.7388	+	5.82489i	0.739997	+	0.198282i	0.130921	+	0.991393i	$0.458207\pi$
$864$	−3.00810	−	2.01939i	−0.102338	−	0.0687012i
$865$	11.7160	−	13.4594i	0.398357	−	0.457632i
$866$		−	20.0405i		−	0.681003i
$867$	1.89793	+	29.2810i	0.0644572	+	0.994435i
$868$	2.36264	+	0.896173i	0.0801931	+	0.0304181i
$869$	11.6243	−	6.71127i	0.394326	−	0.227664i
$870$	−4.89561	+	38.0573i	−0.165977	+	1.29026i
$871$	7.03688	−	4.06275i	0.238436	−	0.137661i
$872$	−13.0558	+	3.49829i	−0.442125	+	0.118467i
$873$	−27.0542	+	35.1524i	−0.915644	+	1.18973i
$874$	51.2182			1.73248
$875$	−4.57055	+	29.2252i	−0.154513	+	0.987991i
$876$	0.774193	+	0.154578i	0.0261575	+	0.00522271i
$877$	−17.1425	+	4.59333i	−0.578862	+	0.155106i	−0.536358	−	0.843991i	$-0.680200\pi$
$877$	−17.1425	+	4.59333i	−0.578862	+	0.155106i	−0.0425042	+	0.999096i	$0.513534\pi$
$878$	−37.0001	−	37.0001i	−1.24869	−	1.24869i
$879$	−14.2243	−	12.4926i	−0.479773	−	0.421363i
$880$	−12.4576	+	8.39050i	−0.419946	+	0.282844i
$881$		−	17.8940i		−	0.602864i	−0.953488	−	0.301432i	$-0.902535\pi$
$881$		−	17.8940i		−	0.602864i	0.953488	−	0.301432i	$-0.0974646\pi$
$882$	−23.1396	+	20.0248i	−0.779151	+	0.674270i
$883$	26.7263	−	26.7263i	0.899411	−	0.899411i	−0.0959726	−	0.995384i	$-0.530596\pi$
$883$	26.7263	−	26.7263i	0.899411	−	0.899411i	0.995384	+	0.0959726i	$0.0305961\pi$
$884$		−	0.0371482i		−	0.00124943i
$885$	−10.6058	−	4.35628i	−0.356510	−	0.146435i
$886$	−13.6375			−0.458160
$887$	5.10380	+	19.0476i	0.171369	+	0.639557i	0.997142	+	0.0755541i	$0.0240725\pi$
$887$	5.10380	+	19.0476i	0.171369	+	0.639557i	−0.825773	+	0.564003i	$0.809261\pi$
$888$	26.0222	−	1.68670i	0.873247	−	0.0566020i
$889$	−19.4731	−	43.2736i	−0.653106	−	1.45135i
$890$	−28.7911	−	5.61663i	−0.965080	−	0.188270i
$891$	13.8099	−	3.65761i	0.462649	−	0.122534i
$892$	0.461973	+	1.72411i	0.0154680	+	0.0577273i
$893$	−34.3026	−	9.19135i	−1.14789	−	0.307577i
$894$	1.27801	+	0.255173i	0.0427432	+	0.00853425i
$895$	15.6408	−	32.0135i	0.522815	−	1.07009i
$896$	−29.5476	+	13.2964i	−0.987115	+	0.444201i
$897$	7.45439	−	15.0885i	0.248895	−	0.503791i
$898$	−8.61921	+	8.61921i	−0.287627	+	0.287627i
$899$	−26.3037	+	45.5593i	−0.877276	+	1.51949i
$900$	−1.30141	+	1.31693i	−0.0433803	+	0.0438978i
$901$	1.74538	−	1.00769i	0.0581470	−	0.0335712i
$902$	0.0906723	+	0.338394i	0.00301906	+	0.0112673i
$903$	−6.30533	−	3.94976i	−0.209828	−	0.131440i
$904$	19.2783	−	11.1303i	0.641185	−	0.370189i
$905$	15.3869	−	1.06550i	0.511477	−	0.0354184i
$906$	−3.27530	−	2.87655i	−0.108814	−	0.0955668i
$907$	13.7810	−	51.4315i	0.457592	−	1.70776i	−0.222763	−	0.974873i	$-0.571508\pi$
$907$	13.7810	−	51.4315i	0.457592	−	1.70776i	0.680354	−	0.732883i	$-0.261826\pi$
$908$	−0.248169	+	0.926179i	−0.00823577	+	0.0307363i
$909$	−38.8203	−	16.1457i	−1.28759	−	0.535518i
$910$	2.43437	+	10.3880i	0.0806987	+	0.344359i
$911$	23.9942	−	41.5591i	0.794962	−	1.37692i	−0.127901	−	0.991787i	$-0.540824\pi$
$911$	23.9942	−	41.5591i	0.794962	−	1.37692i	0.922863	−	0.385128i	$-0.125843\pi$
$912$	32.7447	−	2.12244i	1.08429	−	0.0702811i
$913$	5.82645	+	5.82645i	0.192827	+	0.192827i
$914$		−	22.1231i		−	0.731766i
$915$	5.11273	−	12.4475i	0.169022	−	0.411500i
$916$	−1.80575	−	1.04255i	−0.0596635	−	0.0344467i
$917$	7.97885	+	9.77339i	0.263485	+	0.322746i
$918$	−0.595642	+	1.74229i	−0.0196591	+	0.0575041i
$919$	21.0188	−	12.1352i	0.693346	−	0.400304i	−0.111518	−	0.993762i	$-0.535571\pi$
$919$	21.0188	−	12.1352i	0.693346	−	0.400304i	0.804864	+	0.593459i	$0.202238\pi$
$920$	21.0734	−	43.1327i	0.694768	−	1.42204i
$921$	6.06430	+	17.9073i	0.199825	+	0.590067i
$922$	7.29830	+	27.2376i	0.240357	+	0.897023i
$923$	4.58963	−	17.1287i	0.151069	−	0.563799i
$924$	−0.263462	+	0.858333i	−0.00866727	+	0.0282371i
$925$	3.39181	−	27.3186i	0.111522	−	0.898229i
$926$	21.9598	+	38.0356i	0.721645	+	1.24993i
$927$	−35.4376	−	27.2736i	−1.16392	−	0.895784i
$928$	1.22695	+	4.57905i	0.0402767	+	0.150315i
$929$	−28.7023			−0.941690			−0.470845	−	0.882216i	$-0.656051\pi$
$929$	−28.7023			−0.941690			−0.470845	+	0.882216i	$0.656051\pi$
$930$	−40.2953	+	16.8310i	−1.32133	+	0.551909i
$931$	6.27183	−	30.7047i	0.205551	−	1.00631i
$932$	0.247365	−	0.923177i	0.00810270	−	0.0302397i
$933$	−29.8020	−	14.7235i	−0.975673	−	0.482026i
$934$	−25.2009	−	43.6492i	−0.824598	−	1.42825i
$935$	0.651029	+	0.566705i	0.0212909	+	0.0185332i
$936$	3.89892	−	9.37449i	0.127440	−	0.306415i
$937$	−11.7115	+	11.7115i	−0.382597	+	0.382597i	−0.872037	−	0.489440i	$-0.837201\pi$
$937$	−11.7115	+	11.7115i	−0.382597	+	0.382597i	0.489440	+	0.872037i	$0.337201\pi$
$938$	8.97709	−	23.6668i	0.293112	−	0.772750i
$939$	−16.6571	+	5.64090i	−0.543584	+	0.184084i
$940$	1.43745	−	1.65134i	0.0468845	−	0.0538608i
$941$			33.3128i			1.08597i	0.839743	+	0.542984i	$0.182706\pi$
$941$			33.3128i			1.08597i	−0.839743	+	0.542984i	$0.817294\pi$
$942$	−12.6645	+	25.6344i	−0.412633	+	0.835215i
$943$	−0.840807	−	0.840807i	−0.0273804	−	0.0273804i
$944$	−12.5274			−0.407731
$945$	3.04529	−	30.5896i	0.0990632	−	0.995081i
$946$	−3.75551			−0.122102
$947$	−0.785591	−	0.785591i	−0.0255283	−	0.0255283i	0.694227	−	0.719756i	$-0.255746\pi$
$947$	−0.785591	−	0.785591i	−0.0255283	−	0.0255283i	−0.719756	+	0.694227i	$0.755746\pi$
$948$	0.800747	−	1.62080i	0.0260071	−	0.0526412i
$949$			4.57022i			0.148356i
$950$	4.01907	−	32.3706i	0.130396	−	1.05024i
$951$	39.5453	−	13.3919i	1.28234	−	0.434264i
$952$	1.11262	+	1.36287i	0.0360604	+	0.0441708i
$953$	−17.5696	+	17.5696i	−0.569134	+	0.569134i	−0.931886	−	0.362751i	$-0.881837\pi$
$953$	−17.5696	+	17.5696i	−0.569134	+	0.569134i	0.362751	+	0.931886i	$0.381837\pi$
$954$	−35.9276	+	4.67715i	−1.16320	+	0.151428i
$955$	−1.67140	−	24.1367i	−0.0540852	−	0.781045i
$956$	1.37801	+	2.38678i	0.0445680	+	0.0771941i
$957$	−16.7588	−	8.27959i	−0.541735	−	0.267641i
$958$	5.01988	−	18.7344i	0.162185	−	0.605283i
$959$	−26.9760	+	37.4413i	−0.871099	+	1.20904i
$960$	10.9587	−	26.6800i	0.353689	−	0.861093i
$961$	−28.8713			−0.931331
$962$	−2.56988	−	9.59093i	−0.0828563	−	0.309224i
$963$	42.0050	−	17.3280i	1.35359	−	0.558387i
$964$	0.891103	+	1.54344i	0.0287005	+	0.0497107i
$965$	−6.99242	−	6.08672i	−0.225094	−	0.195939i
$966$	−11.7366	−	51.0958i	−0.377619	−	1.64398i
$967$	−14.3506	+	53.5573i	−0.461486	+	1.72229i	0.206800	+	0.978383i	$0.433695\pi$
$967$	−14.3506	+	53.5573i	−0.461486	+	1.72229i	−0.668286	+	0.743905i	$0.732972\pi$
$968$	6.00197	+	22.3997i	0.192911	+	0.719952i
$969$	−0.604839	−	1.78604i	−0.0194302	−	0.0573757i
$970$	43.2882	+	21.1493i	1.38990	+	0.679064i
$971$	−5.38635	+	3.10981i	−0.172856	+	0.0997985i	−0.583932	−	0.811803i	$-0.698486\pi$
$971$	−5.38635	+	3.10981i	−0.172856	+	0.0997985i	0.411076	+	0.911601i	$0.365153\pi$
$972$	1.27388	−	1.44203i	0.0408596	−	0.0462533i
$973$	−9.61881	−	59.2068i	−0.308365	−	1.89808i
$974$	−39.2179	−	22.6425i	−1.25662	−	0.725511i
$975$	−8.95120	−	5.89526i	−0.286668	−	0.188800i
$976$		−	14.7027i		−	0.470621i
$977$	−13.2881	−	13.2881i	−0.425123	−	0.425123i	0.461840	−	0.886963i	$-0.347189\pi$
$977$	−13.2881	−	13.2881i	−0.425123	−	0.425123i	−0.886963	+	0.461840i	$0.847189\pi$
$978$	1.54218	−	0.0999611i	0.0493136	−	0.00319640i
$979$	7.14503	−	12.3756i	0.228356	−	0.395525i
$980$	1.53106	+	1.17837i	0.0489079	+	0.0376415i
$981$	−1.91426	−	14.7044i	−0.0611176	−	0.469476i
$982$	−7.96672	+	29.7322i	−0.254228	+	0.948792i
$983$	−6.26266	+	23.3726i	−0.199748	+	0.745469i	0.791239	+	0.611507i	$0.209437\pi$
$983$	−6.26266	+	23.3726i	−0.199748	+	0.745469i	−0.990987	+	0.133962i	$0.957230\pi$
$984$	−0.538994	−	0.473374i	−0.0171825	−	0.0150906i
$985$	−18.1739	+	20.8782i	−0.579069	+	0.665234i
$986$	2.08645	−	1.20461i	0.0664462	−	0.0383627i
$987$	−1.30899	+	36.3268i	−0.0416655	+	1.15630i
$988$	−0.177009	−	0.660608i	−0.00563142	−	0.0210167i
$989$	11.0391	−	6.37340i	0.351022	−	0.202662i
$990$	−6.89398	−	13.9009i	−0.219105	−	0.441801i
$991$	−24.9276	+	43.1759i	−0.791852	+	1.37153i	0.132966	+	0.991121i	$0.457550\pi$
$991$	−24.9276	+	43.1759i	−0.791852	+	1.37153i	−0.924819	+	0.380408i	$0.875784\pi$
$992$	−3.81495	+	3.81495i	−0.121125	+	0.121125i
$993$	20.3768	−	41.2450i	0.646639	−	1.30887i
$994$	−22.6689	−	50.3754i	−0.719014	−	1.59781i
$995$	11.9006	+	5.81430i	0.377276	+	0.184326i
$996$	1.08830	+	0.217294i	0.0344842	+	0.00688524i
$997$	−0.410231	−	0.109921i	−0.0129922	−	0.00348124i	0.252317	−	0.967645i	$-0.418807\pi$
$997$	−0.410231	−	0.109921i	−0.0129922	−	0.00348124i	−0.265309	+	0.964163i	$0.585474\pi$
$998$	2.08307	+	7.77411i	0.0659383	+	0.246085i
$999$	−1.93294	+	28.5429i	−0.0611556	+	0.903057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bs.e.52.11	✓	160
3.2	odd	2		945.2.bv.e.262.30		160
5.3	odd	4	inner	315.2.bs.e.178.11	yes	160
7.5	odd	6		315.2.cg.e.187.11	yes	160
9.4	even	3		315.2.cg.e.157.30	yes	160
9.5	odd	6		945.2.cj.e.577.11		160
15.8	even	4		945.2.bv.e.73.30		160
21.5	even	6		945.2.cj.e.397.30		160
35.33	even	12		315.2.cg.e.313.30	yes	160
45.13	odd	12		315.2.cg.e.283.11	yes	160
45.23	even	12		945.2.cj.e.388.30		160
63.5	even	6		945.2.bv.e.712.30		160
63.40	odd	6	inner	315.2.bs.e.292.11	yes	160
105.68	odd	12		945.2.cj.e.208.11		160
315.68	odd	12		945.2.bv.e.523.30		160
315.103	even	12	inner	315.2.bs.e.103.11	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.11	✓	160	1.1	even	1	trivial
315.2.bs.e.103.11	yes	160	315.103	even	12	inner
315.2.bs.e.178.11	yes	160	5.3	odd	4	inner
315.2.bs.e.292.11	yes	160	63.40	odd	6	inner
315.2.cg.e.157.30	yes	160	9.4	even	3
315.2.cg.e.187.11	yes	160	7.5	odd	6
315.2.cg.e.283.11	yes	160	45.13	odd	12
315.2.cg.e.313.30	yes	160	35.33	even	12
945.2.bv.e.73.30		160	15.8	even	4
945.2.bv.e.262.30		160	3.2	odd	2
945.2.bv.e.523.30		160	315.68	odd	12
945.2.bv.e.712.30		160	63.5	even	6
945.2.cj.e.208.11		160	105.68	odd	12
945.2.cj.e.388.30		160	45.23	even	12
945.2.cj.e.397.30		160	21.5	even	6
945.2.cj.e.577.11		160	9.5	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03040 - 1.03040i) q^{2} +(-0.767189 + 1.55288i) q^{3} +0.123432i q^{4} +(-0.154472 - 2.23073i) q^{5} +(2.39058 - 0.809568i) q^{6} +(2.47377 + 0.938328i) q^{7} +(-1.93361 + 1.93361i) q^{8} +(-1.82284 - 2.38270i) q^{9} +O(q^{10})\)	\(q+(-1.03040 - 1.03040i) q^{2} +(-0.767189 + 1.55288i) q^{3} +0.123432i q^{4} +(-0.154472 - 2.23073i) q^{5} +(2.39058 - 0.809568i) q^{6} +(2.47377 + 0.938328i) q^{7} +(-1.93361 + 1.93361i) q^{8} +(-1.82284 - 2.38270i) q^{9} +(-2.13936 + 2.45770i) q^{10} +(-0.793669 - 1.37468i) q^{11} +(-0.191675 - 0.0946957i) q^{12} +(0.320320 - 1.19545i) q^{13} +(-1.58211 - 3.51581i) q^{14} +(3.58255 + 1.47151i) q^{15} +4.23163 q^{16} +(-0.0629387 - 0.234890i) q^{17} +(-0.576871 + 4.33337i) q^{18} +(-2.23848 - 3.87716i) q^{19} +(0.275343 - 0.0190667i) q^{20} +(-3.35496 + 3.12158i) q^{21} +(-0.598667 + 2.23425i) q^{22} +(-2.03197 - 7.58343i) q^{23} +(-1.51921 - 4.48609i) q^{24} +(-4.95228 + 0.689167i) q^{25} +(-1.56185 + 0.901732i) q^{26} +(5.09850 - 1.00267i) q^{27} +(-0.115820 + 0.305343i) q^{28} +(-5.88800 - 3.39944i) q^{29} +(-2.17520 - 5.20768i) q^{30} -7.73765i q^{31} +(-0.493037 - 0.493037i) q^{32} +(2.74359 - 0.177834i) q^{33} +(-0.177178 + 0.306882i) q^{34} +(1.71103 - 5.66325i) q^{35} +(0.294101 - 0.224997i) q^{36} +(-1.42497 + 5.31806i) q^{37} +(-1.68849 + 6.30154i) q^{38} +(1.61064 + 1.41455i) q^{39} +(4.61204 + 4.01466i) q^{40} +(0.131166 - 0.0757285i) q^{41} +(6.67340 + 0.240467i) q^{42} +(0.420219 + 1.56828i) q^{43} +(0.169679 - 0.0979643i) q^{44} +(-5.03357 + 4.43432i) q^{45} +(-5.72019 + 9.90767i) q^{46} +(5.60899 - 5.60899i) q^{47} +(-3.24646 + 6.57119i) q^{48} +(5.23908 + 4.64242i) q^{49} +(5.81292 + 4.39269i) q^{50} +(0.413041 + 0.0824693i) q^{51} +(0.147557 + 0.0395378i) q^{52} +(2.14503 + 8.00536i) q^{53} +(-6.28662 - 4.22032i) q^{54} +(-2.94393 + 1.98281i) q^{55} +(-6.59766 + 2.96894i) q^{56} +(7.73809 - 0.501567i) q^{57} +(2.56420 + 9.56974i) q^{58} -2.96041 q^{59} +(-0.181632 + 0.442201i) q^{60} -3.47447i q^{61} +(-7.97285 + 7.97285i) q^{62} +(-2.27354 - 7.60467i) q^{63} -7.44721i q^{64} +(-2.71620 - 0.529883i) q^{65} +(-3.01023 - 2.64375i) q^{66} +(4.64244 + 4.64244i) q^{67} +(0.0289930 - 0.00776866i) q^{68} +(13.3350 + 2.66252i) q^{69} +(-7.59842 + 4.07235i) q^{70} +14.3282 q^{71} +(8.13187 + 1.08254i) q^{72} +(-3.56691 + 0.955752i) q^{73} +(6.94800 - 4.01143i) q^{74} +(2.72914 - 8.21899i) q^{75} +(0.478566 - 0.276300i) q^{76} +(-0.673459 - 4.14535i) q^{77} +(-0.202047 - 3.11715i) q^{78} +8.45600i q^{79} +(-0.653666 - 9.43960i) q^{80} +(-2.35449 + 8.68656i) q^{81} +(-0.213183 - 0.0571222i) q^{82} +(-5.01411 + 1.34353i) q^{83} +(-0.385303 - 0.414109i) q^{84} +(-0.514254 + 0.176683i) q^{85} +(1.18296 - 2.04894i) q^{86} +(9.79611 - 6.53532i) q^{87} +(4.19273 + 1.12344i) q^{88} +(4.50127 + 7.79642i) q^{89} +(9.75567 + 0.617458i) q^{90} +(1.91412 - 2.65671i) q^{91} +(0.936038 - 0.250811i) q^{92} +(12.0156 + 5.93624i) q^{93} -11.5590 q^{94} +(-8.30311 + 5.59235i) q^{95} +(1.14388 - 0.387373i) q^{96} +(-3.82688 - 14.2821i) q^{97} +(-0.614799 - 10.1819i) q^{98} +(-1.82870 + 4.39689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8}+O(q^{10}) \) 160 * q + 4 * q^2 - 18 * q^3 - 6 * q^5 + 24 * q^6 - 16 * q^8	\( 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8} - 24 q^{10} - 16 q^{11} - 30 q^{12} + 16 q^{15} - 152 q^{16} - 6 q^{17} + 58 q^{18} + 60 q^{20} - 36 q^{21} + 8 q^{22} + 8 q^{23} + 2 q^{25} - 36 q^{26} - 36 q^{27} + 22 q^{28} - 26 q^{30} + 12 q^{32} - 6 q^{33} - 36 q^{35} - 32 q^{36} - 4 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 28 q^{42} - 4 q^{43} - 54 q^{45} - 16 q^{46} - 18 q^{48} - 44 q^{50} + 80 q^{51} + 54 q^{52} + 8 q^{53} + 148 q^{56} - 4 q^{57} + 28 q^{58} + 104 q^{60} - 60 q^{63} - 124 q^{65} + 36 q^{66} - 24 q^{67} + 42 q^{68} - 34 q^{70} - 40 q^{71} + 70 q^{72} + 36 q^{73} - 60 q^{75} + 96 q^{76} + 58 q^{77} - 62 q^{78} + 36 q^{80} + 8 q^{81} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 16 q^{86} + 102 q^{87} + 46 q^{88} + 18 q^{90} - 48 q^{91} - 26 q^{92} + 82 q^{93} + 188 q^{95} - 48 q^{96} + 48 q^{97} + 102 q^{98}+O(q^{100}) \) 160 * q + 4 * q^2 - 18 * q^3 - 6 * q^5 + 24 * q^6 - 16 * q^8 - 24 * q^10 - 16 * q^11 - 30 * q^12 + 16 * q^15 - 152 * q^16 - 6 * q^17 + 58 * q^18 + 60 * q^20 - 36 * q^21 + 8 * q^22 + 8 * q^23 + 2 * q^25 - 36 * q^26 - 36 * q^27 + 22 * q^28 - 26 * q^30 + 12 * q^32 - 6 * q^33 - 36 * q^35 - 32 * q^36 - 4 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 28 * q^42 - 4 * q^43 - 54 * q^45 - 16 * q^46 - 18 * q^48 - 44 * q^50 + 80 * q^51 + 54 * q^52 + 8 * q^53 + 148 * q^56 - 4 * q^57 + 28 * q^58 + 104 * q^60 - 60 * q^63 - 124 * q^65 + 36 * q^66 - 24 * q^67 + 42 * q^68 - 34 * q^70 - 40 * q^71 + 70 * q^72 + 36 * q^73 - 60 * q^75 + 96 * q^76 + 58 * q^77 - 62 * q^78 + 36 * q^80 + 8 * q^81 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 16 * q^86 + 102 * q^87 + 46 * q^88 + 18 * q^90 - 48 * q^91 - 26 * q^92 + 82 * q^93 + 188 * q^95 - 48 * q^96 + 48 * q^97 + 102 * q^98

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