LMFDB - Embedded newform 864.2.bk.a.685.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(37,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("864.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bk (of order $24$, degree $8$, not 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			685.30
Character	$\chi$	$=$	864.685
Dual form			864.2.bk.a.613.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.721590 + 1.21627i) q^{2} +(-0.958617 + 1.75529i) q^{4} +(0.00931719 - 0.0707711i) q^{5} +(4.24636 + 1.13781i) q^{7} +(-2.82664 + 0.100666i) q^{8} +O(q^{10})$	\(q+(0.721590 + 1.21627i) q^{2} +(-0.958617 + 1.75529i) q^{4} +(0.00931719 - 0.0707711i) q^{5} +(4.24636 + 1.13781i) q^{7} +(-2.82664 + 0.100666i) q^{8} +(0.0927998 - 0.0397355i) q^{10} +(3.52920 - 4.59934i) q^{11} +(4.11755 - 3.15951i) q^{13} +(1.68025 + 5.98575i) q^{14} +(-2.16211 - 3.36531i) q^{16} +3.33381i q^{17} +(-0.207485 - 0.0859430i) q^{19} +(0.115292 + 0.0841967i) q^{20} +(8.14067 + 0.973616i) q^{22} +(-3.50193 + 0.938339i) q^{23} +(4.82471 + 1.29278i) q^{25} +(6.81399 + 2.72818i) q^{26} +(-6.06783 + 6.36289i) q^{28} +(-3.74015 + 0.492399i) q^{29} +(-1.34451 + 2.32876i) q^{31} +(2.53296 - 5.05807i) q^{32} +(-4.05481 + 2.40564i) q^{34} +(0.120088 - 0.289919i) q^{35} +(-4.86945 + 2.01699i) q^{37} +(-0.0451891 - 0.314373i) q^{38} +(-0.0192121 + 0.200982i) q^{40} +(-6.48519 + 1.73770i) q^{41} +(-1.23067 + 1.60384i) q^{43} +(4.69004 + 10.6038i) q^{44} +(-3.66823 - 3.58219i) q^{46} +(2.50417 - 1.44579i) q^{47} +(10.6748 + 6.16311i) q^{49} +(1.90910 + 6.80099i) q^{50} +(1.59871 + 10.2563i) q^{52} +(-1.65728 - 4.00104i) q^{53} +(-0.292618 - 0.292618i) q^{55} +(-12.1175 - 2.78871i) q^{56} +(-3.29774 - 4.19371i) q^{58} +(-0.511525 + 3.88542i) q^{59} +(9.69374 - 1.27620i) q^{61} +(-3.80259 + 0.0451238i) q^{62} +(7.97973 - 0.569089i) q^{64} +(-0.185238 - 0.320841i) q^{65} +(4.45132 + 5.80107i) q^{67} +(-5.85181 - 3.19585i) q^{68} +(0.439273 - 0.0631427i) q^{70} +(-4.90367 + 4.90367i) q^{71} +(-11.0527 - 11.0527i) q^{73} +(-5.96694 - 4.46711i) q^{74} +(0.349754 - 0.281810i) q^{76} +(20.2195 - 15.5149i) q^{77} +(-10.2828 + 5.93677i) q^{79} +(-0.258311 + 0.121659i) q^{80} +(-6.79316 - 6.63383i) q^{82} +(1.04665 + 7.95008i) q^{83} +(0.235937 + 0.0310617i) q^{85} +(-2.83874 - 0.339510i) q^{86} +(-9.51277 + 13.3559i) q^{88} +(10.0935 - 10.0935i) q^{89} +(21.0795 - 8.73143i) q^{91} +(1.70995 - 7.04642i) q^{92} +(3.56545 + 2.00248i) q^{94} +(-0.00801545 + 0.0138832i) q^{95} +(-3.80827 - 6.59611i) q^{97} +(0.206843 + 17.4307i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.721590	+	1.21627i	0.510241	+	0.860032i
$2$	0.721590	+	1.21627i	0.510241	+	0.860032i
$3$		0			0
$3$		0			0
$4$	−0.958617	+	1.75529i	−0.479309	+	0.877646i
$5$	0.00931719	−	0.0707711i	0.00416677	−	0.0316498i	−0.989235	−	0.146334i	$-0.953252\pi$
$5$	0.00931719	−	0.0707711i	0.00416677	−	0.0316498i	0.993402	+	0.114685i	$0.0365858\pi$
$6$		0			0
$7$	4.24636	+	1.13781i	1.60498	+	0.430052i	0.946540	−	0.322586i	$-0.104552\pi$
$7$	4.24636	+	1.13781i	1.60498	+	0.430052i	0.658435	+	0.752638i	$0.271219\pi$
$8$	−2.82664	+	0.100666i	−0.999366	+	0.0355906i
$9$		0			0
$10$	0.0927998	−	0.0397355i	0.0293459	−	0.0125655i
$11$	3.52920	−	4.59934i	1.06409	−	1.38675i	0.146512	−	0.989209i	$-0.453195\pi$
$11$	3.52920	−	4.59934i	1.06409	−	1.38675i	0.917582	−	0.397546i	$-0.130138\pi$
$12$		0			0
$13$	4.11755	−	3.15951i	1.14200	−	0.876289i	0.148367	−	0.988932i	$-0.452598\pi$
$13$	4.11755	−	3.15951i	1.14200	−	0.876289i	0.993636	+	0.112643i	$0.0359316\pi$
$14$	1.68025	+	5.98575i	0.449066	+	1.59976i
$15$		0			0
$16$	−2.16211	−	3.36531i	−0.540527	−	0.841327i
$17$			3.33381i			0.808568i	0.914634	+	0.404284i	$0.132479\pi$
$17$			3.33381i			0.808568i	−0.914634	+	0.404284i	$0.867521\pi$
$18$		0			0
$19$	−0.207485	−	0.0859430i	−0.0476003	−	0.0197167i	0.358756	−	0.933431i	$-0.383201\pi$
$19$	−0.207485	−	0.0859430i	−0.0476003	−	0.0197167i	−0.406357	+	0.913715i	$0.633201\pi$
$20$	0.115292	+	0.0841967i	0.0257801	+	0.0188270i
$21$		0			0
$22$	8.14067	+	0.973616i	1.73560	+	0.207576i
$23$	−3.50193	+	0.938339i	−0.730202	+	0.195657i	−0.604719	−	0.796439i	$-0.706715\pi$
$23$	−3.50193	+	0.938339i	−0.730202	+	0.195657i	−0.125483	+	0.992096i	$0.540048\pi$
$24$		0			0
$25$	4.82471	+	1.29278i	0.964941	+	0.258555i
$26$	6.81399	+	2.72818i	1.33633	+	0.535040i
$27$		0			0
$28$	−6.06783	+	6.36289i	−1.14671	+	1.20247i
$29$	−3.74015	+	0.492399i	−0.694528	+	0.0914363i	−0.469521	−	0.882921i	$-0.655574\pi$
$29$	−3.74015	+	0.492399i	−0.694528	+	0.0914363i	−0.225006	+	0.974357i	$0.572240\pi$
$30$		0			0
$31$	−1.34451	+	2.32876i	−0.241481	+	0.418258i	−0.961136	−	0.276074i	$-0.910967\pi$
$31$	−1.34451	+	2.32876i	−0.241481	+	0.418258i	0.719655	+	0.694332i	$0.244300\pi$
$32$	2.53296	−	5.05807i	0.447769	−	0.894149i
$33$		0			0
$34$	−4.05481	+	2.40564i	−0.695394	+	0.412564i
$35$	0.120088	−	0.289919i	0.0202986	−	0.0490052i
$36$		0			0
$37$	−4.86945	+	2.01699i	−0.800532	+	0.331591i	−0.745169	−	0.666875i	$-0.767631\pi$
$37$	−4.86945	+	2.01699i	−0.800532	+	0.331591i	−0.0553625	+	0.998466i	$0.517631\pi$
$38$	−0.0451891	−	0.314373i	−0.00733064	−	0.0509980i
$39$		0			0
$40$	−0.0192121	+	0.200982i	−0.00303770	+	0.0317780i
$41$	−6.48519	+	1.73770i	−1.01282	+	0.271383i	−0.726806	−	0.686843i	$-0.758996\pi$
$41$	−6.48519	+	1.73770i	−1.01282	+	0.271383i	−0.286011	+	0.958226i	$0.592329\pi$
$42$		0			0
$43$	−1.23067	+	1.60384i	−0.187675	+	0.244583i	−0.877709	−	0.479194i	$-0.840929\pi$
$43$	−1.23067	+	1.60384i	−0.187675	+	0.244583i	0.690034	+	0.723777i	$0.257596\pi$
$44$	4.69004	+	10.6038i	0.707051	+	1.59858i
$45$		0			0
$46$	−3.66823	−	3.58219i	−0.540850	−	0.528165i
$47$	2.50417	−	1.44579i	0.365271	−	0.210889i	−0.306119	−	0.951993i	$-0.599031\pi$
$47$	2.50417	−	1.44579i	0.365271	−	0.210889i	0.671391	+	0.741104i	$0.265697\pi$
$48$		0			0
$49$	10.6748	+	6.16311i	1.52497	+	0.880445i
$50$	1.90910	+	6.80099i	0.269987	+	0.961806i
$51$		0			0
$52$	1.59871	+	10.2563i	0.221701	+	1.42229i
$53$	−1.65728	−	4.00104i	−0.227646	−	0.549585i	0.768244	−	0.640157i	$-0.221131\pi$
$53$	−1.65728	−	4.00104i	−0.227646	−	0.549585i	−0.995890	+	0.0905717i	$0.971131\pi$
$54$		0			0
$55$	−0.292618	−	0.292618i	−0.0394566	−	0.0394566i
$56$	−12.1175	−	2.78871i	−1.61926	−	0.372657i
$57$		0			0
$58$	−3.29774	−	4.19371i	−0.433014	−	0.550661i
$59$	−0.511525	+	3.88542i	−0.0665949	+	0.505839i	0.925345	+	0.379127i	$0.123776\pi$
$59$	−0.511525	+	3.88542i	−0.0665949	+	0.505839i	−0.991940	+	0.126712i	$0.959558\pi$
$60$		0			0
$61$	9.69374	−	1.27620i	1.24116	−	0.163401i	0.518783	−	0.854906i	$-0.326385\pi$
$61$	9.69374	−	1.27620i	1.24116	−	0.163401i	0.722372	+	0.691504i	$0.243052\pi$
$62$	−3.80259	+	0.0451238i	−0.482929	+	0.00573073i
$63$		0			0
$64$	7.97973	−	0.569089i	0.997467	−	0.0711362i
$65$	−0.185238	−	0.320841i	−0.0229759	−	0.0397954i
$66$		0			0
$67$	4.45132	+	5.80107i	0.543815	+	0.708713i	0.981725	−	0.190306i	$-0.0609479\pi$
$67$	4.45132	+	5.80107i	0.543815	+	0.708713i	−0.437910	+	0.899019i	$0.644281\pi$
$68$	−5.85181	−	3.19585i	−0.709637	−	0.387553i
$69$		0			0
$70$	0.439273	−	0.0631427i	0.0525032	−	0.00754700i
$71$	−4.90367	+	4.90367i	−0.581959	+	0.581959i	−0.935441	−	0.353482i	$-0.884997\pi$
$71$	−4.90367	+	4.90367i	−0.581959	+	0.581959i	0.353482	+	0.935441i	$0.384997\pi$
$72$		0			0
$73$	−11.0527	−	11.0527i	−1.29362	−	1.29362i	−0.932529	−	0.361096i	$-0.882403\pi$
$73$	−11.0527	−	11.0527i	−1.29362	−	1.29362i	−0.361096	−	0.932529i	$-0.617597\pi$
$74$	−5.96694	−	4.46711i	−0.693643	−	0.519291i
$75$		0			0
$76$	0.349754	−	0.281810i	0.0401195	−	0.0323258i
$77$	20.2195	−	15.5149i	2.30422	−	1.76809i
$78$		0			0
$79$	−10.2828	+	5.93677i	−1.15690	+	0.667938i	−0.950560	−	0.310541i	$-0.899490\pi$
$79$	−10.2828	+	5.93677i	−1.15690	+	0.667938i	−0.206343	+	0.978480i	$0.566156\pi$
$80$	−0.258311	+	0.121659i	−0.0288801	+	0.0136019i
$81$		0			0
$82$	−6.79316	−	6.63383i	−0.750179	−	0.732583i
$83$	1.04665	+	7.95008i	0.114884	+	0.872634i	0.947718	+	0.319110i	$0.103384\pi$
$83$	1.04665	+	7.95008i	0.114884	+	0.872634i	−0.832833	+	0.553524i	$0.813283\pi$
$84$		0			0
$85$	0.235937	+	0.0310617i	0.0255910	+	0.00336912i
$86$	−2.83874	−	0.339510i	−0.306109	−	0.0366103i
$87$		0			0
$88$	−9.51277	+	13.3559i	−1.01406	+	1.42375i
$89$	10.0935	−	10.0935i	1.06991	−	1.06991i	0.0725457	−	0.997365i	$-0.476888\pi$
$89$	10.0935	−	10.0935i	1.06991	−	1.06991i	0.997365	−	0.0725457i	$-0.0231123\pi$
$90$		0			0
$91$	21.0795	−	8.73143i	2.20974	−	0.915302i
$92$	1.70995	−	7.04642i	0.178274	−	0.734640i
$93$		0			0
$94$	3.56545	+	2.00248i	0.367748	+	0.206540i
$95$	−0.00801545	+	0.0138832i	−0.000822368	+	0.00142438i
$96$		0			0
$97$	−3.80827	−	6.59611i	−0.386671	−	0.669734i	0.605328	−	0.795976i	$-0.293042\pi$
$97$	−3.80827	−	6.59611i	−0.386671	−	0.669734i	−0.991999	+	0.126242i	$0.959708\pi$
$98$	0.206843	+	17.4307i	0.0208943	+	1.76077i
$99$		0			0
$100$	−6.89425	+	7.22950i	−0.689425	+	0.722950i
$101$	3.91870	+	3.00692i	0.389925	+	0.299200i	0.785056	−	0.619425i	$-0.212634\pi$
$101$	3.91870	+	3.00692i	0.389925	+	0.299200i	−0.395131	+	0.918625i	$0.629301\pi$
$102$		0			0
$103$	1.93673	+	7.22797i	0.190832	+	0.712193i	0.993307	+	0.115508i	$0.0368494\pi$
$103$	1.93673	+	7.22797i	0.190832	+	0.712193i	−0.802475	+	0.596686i	$0.796484\pi$
$104$	−11.3208	+	9.34527i	−1.11009	+	0.916379i
$105$		0			0
$106$	3.67046	−	4.90281i	0.356506	−	0.476203i
$107$	−1.24938	−	3.01627i	−0.120782	−	0.291594i	0.851912	−	0.523685i	$-0.175443\pi$
$107$	−1.24938	−	3.01627i	−0.120782	−	0.291594i	−0.972694	+	0.232091i	$0.925443\pi$
$108$		0			0
$109$	−6.76692	−	2.80295i	−0.648153	−	0.268474i	0.0342907	−	0.999412i	$-0.489083\pi$
$109$	−6.76692	−	2.80295i	−0.648153	−	0.268474i	−0.682444	+	0.730938i	$0.739083\pi$
$110$	0.144752	−	0.567053i	0.0138016	−	0.0540663i
$111$		0			0
$112$	−5.35201	−	16.7504i	−0.505718	−	1.58276i
$113$	−14.3740	−	8.29884i	−1.35219	−	0.780689i	−0.363636	−	0.931541i	$-0.618465\pi$
$113$	−14.3740	−	8.29884i	−1.35219	−	0.780689i	−0.988556	+	0.150852i	$0.951798\pi$
$114$		0			0
$115$	0.0337791	+	0.256578i	0.00314992	+	0.0239260i
$116$	2.72106	−	7.03707i	0.252644	−	0.653376i
$117$		0			0
$118$	−5.09482	+	2.18153i	−0.469017	+	0.200826i
$119$	−3.79324	+	14.1566i	−0.347726	+	1.29773i
$120$		0			0
$121$	−5.85170	−	21.8388i	−0.531973	−	1.98535i
$122$	8.54710	+	10.8693i	0.773819	+	0.984059i
$123$		0			0
$124$	−2.79879	−	4.59240i	−0.251339	−	0.412410i
$125$	0.273027	−	0.659145i	0.0244203	−	0.0589557i
$126$		0			0
$127$	−5.19441			−0.460930			−0.230465	−	0.973081i	$-0.574025\pi$
$127$	−5.19441			−0.460930			−0.230465	+	0.973081i	$0.574025\pi$
$128$	6.45026	+	9.29485i	0.570128	+	0.821556i
$129$		0			0
$130$	0.256563	−	0.456814i	0.0225021	−	0.0400653i
$131$	−2.88532	−	3.76022i	−0.252092	−	0.328532i	0.650115	−	0.759836i	$-0.274721\pi$
$131$	−2.88532	−	3.76022i	−0.252092	−	0.328532i	−0.902207	+	0.431303i	$0.858054\pi$
$132$		0			0
$133$	−0.783269	−	0.601024i	−0.0679181	−	0.0521154i
$134$	−3.84363	+	9.59998i	−0.332039	+	0.829312i
$135$		0			0
$136$	−0.335600	−	9.42346i	−0.0287774	−	0.808055i
$137$	1.70676	−	6.36971i	0.145818	−	0.544201i	−0.853899	−	0.520438i	$-0.825769\pi$
$137$	1.70676	−	6.36971i	0.145818	−	0.544201i	0.999718	−	0.0237631i	$-0.00756473\pi$
$138$		0			0
$139$	−15.7789	−	2.07733i	−1.33835	−	0.176197i	−0.572865	−	0.819650i	$-0.694168\pi$
$139$	−15.7789	−	2.07733i	−1.33835	−	0.176197i	−0.765486	+	0.643453i	$0.777501\pi$
$140$	0.393773	+	0.488711i	0.0332799	+	0.0413036i
$141$		0			0
$142$	−9.50262	−	2.42574i	−0.797442	−	0.203564i
$143$		−	30.0886i		−	2.51613i
$144$		0			0
$145$			0.269282i			0.0223626i
$146$	5.46755	−	21.4186i	0.452498	−	1.77262i
$147$		0			0
$148$	1.12752	−	10.4808i	0.0926820	−	0.861519i
$149$	18.3779	+	2.41949i	1.50557	+	0.198213i	0.837728	−	0.546087i	$-0.183883\pi$
$149$	18.3779	+	2.41949i	1.50557	+	0.198213i	0.667845	+	0.744300i	$0.267217\pi$
$150$		0			0
$151$	−0.442386	+	1.65101i	−0.0360009	+	0.134357i	−0.981587	−	0.191014i	$-0.938822\pi$
$151$	−0.442386	+	1.65101i	−0.0360009	+	0.134357i	0.945586	+	0.325371i	$0.105489\pi$
$152$	0.595135	+	0.222043i	0.0482719	+	0.0180101i
$153$		0			0
$154$	33.4605	+	13.3969i	2.69632	+	1.07955i
$155$	0.152282	+	0.116850i	0.0122316	+	0.00938562i
$156$		0			0
$157$	−6.99114	−	9.11103i	−0.557954	−	0.727139i	0.426166	−	0.904645i	$-0.359864\pi$
$157$	−6.99114	−	9.11103i	−0.557954	−	0.727139i	−0.984120	+	0.177506i	$0.943197\pi$
$158$	−14.6406	−	8.22271i	−1.16475	−	0.654164i
$159$		0			0
$160$	−0.334365	−	0.226387i	−0.0264339	−	0.0178975i
$161$	−15.9381			−1.25610
$162$		0			0
$163$	5.23464	−	12.6375i	0.410009	−	0.989849i	−0.575126	−	0.818065i	$-0.695047\pi$
$163$	5.23464	−	12.6375i	0.410009	−	0.989849i	0.985135	−	0.171784i	$-0.0549531\pi$
$164$	3.16664	−	13.0492i	0.247273	−	1.01897i
$165$		0			0
$166$	−8.91418	+	7.00970i	−0.691874	+	0.544058i
$167$	1.66919	+	6.22951i	0.129166	+	0.482054i	0.999954	−	0.00960509i	$-0.00305744\pi$
$167$	1.66919	+	6.22951i	0.129166	+	0.482054i	−0.870788	+	0.491659i	$0.836391\pi$
$168$		0			0
$169$	3.60708	−	13.4618i	0.277468	−	1.03552i
$170$	0.132470	+	0.309377i	0.0101600	+	0.0237281i
$171$		0			0
$172$	−1.63547	−	3.69765i	−0.124703	−	0.281944i
$173$	0.198906	+	1.51084i	0.0151225	+	0.114867i	0.997341	−	0.0728735i	$-0.0232169\pi$
$173$	0.198906	+	1.51084i	0.0151225	+	0.114867i	−0.982219	+	0.187741i	$0.939884\pi$
$174$		0			0
$175$	19.0165	+	10.9792i	1.43751	+	0.829950i
$176$	−23.1087	−	1.93257i	−1.74189	−	0.145673i
$177$		0			0
$178$	19.5598	+	4.99305i	1.46607	+	0.374245i
$179$	−1.97437	−	0.817809i	−0.147571	−	0.0611259i	0.307676	−	0.951491i	$-0.400449\pi$
$179$	−1.97437	−	0.817809i	−0.147571	−	0.0611259i	−0.455247	+	0.890365i	$0.650449\pi$
$180$		0			0
$181$	5.14739	+	12.4269i	0.382602	+	0.923684i	0.991461	+	0.130405i	$0.0416277\pi$
$181$	5.14739	+	12.4269i	0.382602	+	0.923684i	−0.608858	+	0.793279i	$0.708372\pi$
$182$	25.8305	+	19.3379i	1.91469	+	1.43342i
$183$		0			0
$184$	9.80421	−	3.00486i	0.722776	−	0.221522i
$185$	0.0973750	+	0.363409i	0.00715915	+	0.0267183i
$186$		0			0
$187$	15.3333	+	11.7657i	1.12128	+	0.860392i
$188$	0.137233	+	5.78151i	0.0100088	+	0.421660i
$189$		0			0
$190$	−0.0226695		0.000269010i	−0.00164462		1.95161e-5i
$191$	5.69257	+	9.85982i	0.411900	+	0.713432i	0.995098	−	0.0988986i	$-0.0315320\pi$
$191$	5.69257	+	9.85982i	0.411900	+	0.713432i	−0.583197	+	0.812330i	$0.698199\pi$
$192$		0			0
$193$	−0.741065	+	1.28356i	−0.0533430	+	0.0923929i	−0.891464	−	0.453092i	$-0.850321\pi$
$193$	−0.741065	+	1.28356i	−0.0533430	+	0.0923929i	0.838121	+	0.545485i	$0.183654\pi$
$194$	5.27464	−	9.39156i	0.378697	−	0.674275i
$195$		0			0
$196$	−21.0511	+	12.8294i	−1.50365	+	0.916384i
$197$	15.0674	−	6.24113i	1.07351	−	0.444662i	0.225281	−	0.974294i	$-0.427670\pi$
$197$	15.0674	−	6.24113i	1.07351	−	0.444662i	0.848228	+	0.529632i	$0.177670\pi$
$198$		0			0
$199$	−13.8020	+	13.8020i	−0.978396	+	0.978396i	−0.999772	−	0.0213757i	$-0.993195\pi$
$199$	−13.8020	+	13.8020i	−0.978396	+	0.978396i	0.0213757	+	0.999772i	$0.493195\pi$
$200$	−13.7678	−	3.16853i	−0.973532	−	0.224049i
$201$		0			0
$202$	−0.829533	+	6.93595i	−0.0583658	+	0.488012i
$203$	−16.4423	−	2.16467i	−1.15402	−	0.151930i
$204$		0			0
$205$	0.0625553	+	0.475154i	0.00436905	+	0.0331862i
$206$	−7.39363	+	7.57121i	−0.515139	+	0.527511i
$207$		0			0
$208$	−19.5353	−	7.02563i	−1.35453	−	0.487140i
$209$	−1.12754	+	0.650984i	−0.0779934	+	0.0450295i
$210$		0			0
$211$	5.08758	−	3.90384i	0.350244	−	0.268751i	−0.418624	−	0.908160i	$-0.637487\pi$
$211$	5.08758	−	3.90384i	0.350244	−	0.268751i	0.768867	+	0.639408i	$0.220821\pi$
$212$	8.61170	+	0.926444i	0.591454	+	0.0636285i
$213$		0			0
$214$	2.76705	−	3.69609i	0.189152	−	0.252659i
$215$	0.102039	+	0.102039i	0.00695901	+	0.00695901i
$216$		0			0
$217$	−8.35898	+	8.35898i	−0.567444	+	0.567444i
$218$	−1.47380	−	10.2530i	−0.0998182	−	0.694418i
$219$		0			0
$220$	0.794140	−	0.233122i	0.0535409	−	0.0157171i
$221$	10.5332	+	13.7271i	0.708539	+	0.923386i
$222$		0			0
$223$	1.12503	+	1.94861i	0.0753377	+	0.130489i	0.901233	−	0.433335i	$-0.142663\pi$
$223$	1.12503	+	1.94861i	0.0753377	+	0.130489i	−0.825895	+	0.563823i	$0.809330\pi$
$224$	16.5110	−	18.5964i	1.10319	−	1.24252i
$225$		0			0
$226$	−0.278521	−	23.4710i	−0.0185270	−	1.56127i
$227$	−15.8974	+	2.09293i	−1.05515	+	0.138913i	−0.638085	−	0.769966i	$-0.720273\pi$
$227$	−15.8974	+	2.09293i	−1.05515	+	0.138913i	−0.417061	+	0.908878i	$0.636940\pi$
$228$		0			0
$229$	0.272393	−	2.06903i	0.0180002	−	0.136725i	−0.980085	−	0.198578i	$-0.936368\pi$
$229$	0.272393	−	2.06903i	0.0180002	−	0.136725i	0.998085	+	0.0618528i	$0.0197009\pi$
$230$	−0.287693	+	0.226228i	−0.0189699	+	0.0149171i
$231$		0			0
$232$	10.5225	−	1.76834i	0.690833	−	0.116097i
$233$	6.03707	+	6.03707i	0.395502	+	0.395502i	0.876643	−	0.481141i	$-0.159778\pi$
$233$	6.03707	+	6.03707i	0.395502	+	0.395502i	−0.481141	+	0.876643i	$0.659778\pi$
$234$		0			0
$235$	−0.0789879	−	0.190694i	−0.00515260	−	0.0124395i
$236$	−6.32969	−	4.62251i	−0.412028	−	0.300900i
$237$		0			0
$238$	−19.9554	+	5.60163i	−1.29351	+	0.363100i
$239$	21.6334	+	12.4901i	1.39935	+	0.807915i	0.994324	−	0.106391i	$-0.0339296\pi$
$239$	21.6334	+	12.4901i	1.39935	+	0.807915i	0.405025	+	0.914306i	$0.367263\pi$
$240$		0			0
$241$	−7.15570	+	4.13135i	−0.460939	+	0.266123i	−0.712439	−	0.701734i	$-0.752410\pi$
$241$	−7.15570	+	4.13135i	−0.460939	+	0.266123i	0.251500	+	0.967857i	$0.419076\pi$
$242$	22.3394	−	22.8759i	1.43603	−	1.47052i
$243$		0			0
$244$	−7.05247	+	18.2387i	−0.451488	+	1.16762i
$245$	0.535629	−	0.698046i	0.0342201	−	0.0445965i
$246$		0			0
$247$	−1.12587	+	0.301675i	−0.0716372	+	0.0191951i
$248$	3.56602	−	6.71791i	0.226442	−	0.426588i
$249$		0			0
$250$	0.998711	−	0.143558i	0.0631640	−	0.00907943i
$251$	−4.41255	+	1.82774i	−0.278517	+	0.115366i	−0.517570	−	0.855641i	$-0.673163\pi$
$251$	−4.41255	+	1.82774i	−0.278517	+	0.115366i	0.239052	+	0.971007i	$0.423163\pi$
$252$		0			0
$253$	−8.04326	+	19.4182i	−0.505676	+	1.22081i
$254$	−3.74823	−	6.31780i	−0.235185	−	0.396414i
$255$		0			0
$256$	−6.65059	+	14.5523i	−0.415662	+	0.909519i
$257$	2.68955	−	4.65843i	0.167769	−	0.290585i	−0.769866	−	0.638206i	$-0.779677\pi$
$257$	2.68955	−	4.65843i	0.167769	−	0.290585i	0.937635	+	0.347621i	$0.113010\pi$
$258$		0			0
$259$	−22.9724	+	3.02437i	−1.42744	+	0.187925i
$260$	0.740742	−	0.0175827i	0.0459389	−	0.00109043i
$261$		0			0
$262$	2.49142	−	6.22266i	0.153921	−	0.384437i
$263$	11.0456	+	2.95966i	0.681100	+	0.182500i	0.582750	−	0.812652i	$-0.301977\pi$
$263$	11.0456	+	2.95966i	0.681100	+	0.182500i	0.0983502	+	0.995152i	$0.468643\pi$
$264$		0			0
$265$	−0.298599	+	0.0800094i	−0.0183428	+	0.00491494i
$266$	0.165807	−	1.38636i	0.0101663	−	0.0850031i
$267$		0			0
$268$	−14.4497	+	2.25236i	−0.882655	+	0.137585i
$269$	−21.3465	−	8.84201i	−1.30152	−	0.539107i	−0.379120	−	0.925347i	$-0.623773\pi$
$269$	−21.3465	−	8.84201i	−1.30152	−	0.539107i	−0.922398	+	0.386241i	$0.873773\pi$
$270$		0			0
$271$		−	24.8885i		−	1.51187i	−0.654648	−	0.755934i	$-0.727183\pi$
$271$		−	24.8885i		−	1.51187i	0.654648	−	0.755934i	$-0.272817\pi$
$272$	11.2193	−	7.20805i	0.680270	−	0.437052i
$273$		0			0
$274$	8.97886	−	2.52044i	0.542433	−	0.152265i
$275$	22.9733	−	17.6280i	1.38534	−	1.06301i
$276$		0			0
$277$	−11.3072	+	14.7359i	−0.679387	+	0.885394i	−0.998047	−	0.0624751i	$-0.980101\pi$
$277$	−11.3072	+	14.7359i	−0.679387	+	0.885394i	0.318660	+	0.947869i	$0.396767\pi$
$278$	−8.85931	−	20.6904i	−0.531346	−	1.24093i
$279$		0			0
$280$	−0.310261	+	0.831583i	−0.0185416	+	0.0496966i
$281$	6.80739	+	1.82404i	0.406095	+	0.108813i	0.456084	−	0.889937i	$-0.349252\pi$
$281$	6.80739	+	1.82404i	0.406095	+	0.108813i	−0.0499886	+	0.998750i	$0.515918\pi$
$282$		0			0
$283$	2.26134	−	17.1766i	0.134423	−	1.02104i	−0.782689	−	0.622413i	$-0.786152\pi$
$283$	2.26134	−	17.1766i	0.134423	−	1.02104i	0.917112	−	0.398630i	$-0.130514\pi$
$284$	−3.90664	−	13.3081i	−0.231816	−	0.789692i
$285$		0			0
$286$	36.5958	−	21.7116i	2.16395	−	1.28383i
$287$	−29.5157			−1.74225
$288$		0			0
$289$	5.88571			0.346218
$290$	−0.327519	+	0.194311i	−0.0192326	+	0.0114103i
$291$		0			0
$292$	29.9961	−	8.80545i	1.75539	−	0.515300i
$293$	2.06091	−	15.6542i	0.120400	−	0.914526i	−0.819501	−	0.573078i	$-0.805749\pi$
$293$	2.06091	−	15.6542i	0.120400	−	0.914526i	0.939901	−	0.341448i	$-0.110917\pi$
$294$		0			0
$295$	0.270209	+	0.0724024i	0.0157322	+	0.00421543i
$296$	13.5611	−	6.19148i	0.788223	−	0.359873i
$297$		0			0
$298$	10.3185	+	24.0983i	0.597736	+	1.39598i
$299$	−11.4547	+	14.9280i	−0.662441	+	0.863310i
$300$		0			0
$301$	−7.05074	+	5.41022i	−0.406398	+	0.311840i
$302$	−2.32729	+	0.653290i	−0.133921	+	0.0375926i
$303$		0			0
$304$	0.159380	+	0.884068i	0.00914105	+	0.0507048i
$305$		−	0.697927i		−	0.0399632i
$306$		0			0
$307$	−12.6381	−	5.23488i	−0.721296	−	0.298770i	−0.00832606	−	0.999965i	$-0.502650\pi$
$307$	−12.6381	−	5.23488i	−0.721296	−	0.298770i	−0.712970	+	0.701195i	$0.752650\pi$
$308$	7.85054	+	50.3639i	0.447326	+	2.86975i
$309$		0			0
$310$	−0.0322359	+	0.269533i	−0.00183088	+	0.0153085i
$311$	−3.88664	+	1.04142i	−0.220391	+	0.0590536i	−0.367325	−	0.930093i	$-0.619726\pi$
$311$	−3.88664	+	1.04142i	−0.220391	+	0.0590536i	0.146934	+	0.989146i	$0.453060\pi$
$312$		0			0
$313$	17.6245	+	4.72247i	0.996195	+	0.266930i	0.719850	−	0.694129i	$-0.244210\pi$
$313$	17.6245	+	4.72247i	0.996195	+	0.266930i	0.276344	+	0.961059i	$0.410877\pi$
$314$	6.03672	−	15.0775i	0.340672	−	0.850874i
$315$		0			0
$316$	−0.563515	−	23.7404i	−0.0317002	−	1.33550i
$317$	−15.3008	+	2.01439i	−0.859378	+	0.113139i	−0.547319	−	0.836924i	$-0.684352\pi$
$317$	−15.3008	+	2.01439i	−0.859378	+	0.113139i	−0.312058	+	0.950063i	$0.601018\pi$
$318$		0			0
$319$	−10.9350	+	18.9400i	−0.612243	+	1.06044i
$320$	0.0340736	−	0.570036i	0.00190477	−	0.0318660i
$321$		0			0
$322$	−11.5008	−	19.3850i	−0.640913	−	1.08028i
$323$	0.286518	−	0.691715i	0.0159423	−	0.0384880i
$324$		0			0
$325$	23.9505	−	9.92062i	1.32854	−	0.550297i
$326$	19.1479	−	2.75239i	1.06050	−	0.152441i
$327$		0			0
$328$	18.1563	−	5.56468i	1.00252	−	0.307258i
$329$	12.2787	−	3.29006i	0.676945	−	0.181387i
$330$		0			0
$331$	3.72421	−	4.85348i	0.204701	−	0.266772i	−0.679709	−	0.733481i	$-0.737894\pi$
$331$	3.72421	−	4.85348i	0.204701	−	0.266772i	0.884410	+	0.466710i	$0.154561\pi$
$332$	−14.9580	−	5.78391i	−0.820930	−	0.317433i
$333$		0			0
$334$	−6.37228	+	6.52533i	−0.348676	+	0.357050i
$335$	0.452021	−	0.260975i	0.0246966	−	0.0142586i
$336$		0			0
$337$	−25.6926	−	14.8336i	−1.39957	−	0.808040i	−0.405220	−	0.914219i	$-0.632805\pi$
$337$	−25.6926	−	14.8336i	−1.39957	−	0.808040i	−0.994347	+	0.106179i	$0.966138\pi$
$338$	18.9760	−	5.32672i	1.03216	−	0.289736i
$339$		0			0
$340$	−0.280696	+	0.384363i	−0.0152229	+	0.0208450i
$341$	5.96573	+	14.4025i	0.323062	+	0.779941i
$342$		0			0
$343$	16.5569	+	16.5569i	0.893987	+	0.893987i
$344$	3.31720	−	4.65736i	0.178852	−	0.251108i
$345$		0			0
$346$	−1.69406	+	1.33213i	−0.0910732	+	0.0716157i
$347$	−0.383223	+	2.91087i	−0.0205725	+	0.156264i	−0.998648	−	0.0519885i	$-0.983444\pi$
$347$	−0.383223	+	2.91087i	−0.0205725	+	0.156264i	0.978075	+	0.208252i	$0.0667774\pi$
$348$		0			0
$349$	−11.5650	+	1.52256i	−0.619059	+	0.0815007i	−0.433532	−	0.901138i	$-0.642733\pi$
$349$	−11.5650	+	1.52256i	−0.619059	+	0.0815007i	−0.185528	+	0.982639i	$0.559399\pi$
$350$	0.368478	+	31.0517i	0.0196960	+	1.65978i
$351$		0			0
$352$	−14.3245	−	29.5009i	−0.763497	−	1.57240i
$353$	−1.70426	−	2.95186i	−0.0907084	−	0.157112i	0.817101	−	0.576495i	$-0.195580\pi$
$353$	−1.70426	−	2.95186i	−0.0907084	−	0.157112i	−0.907809	+	0.419383i	$0.862246\pi$
$354$		0			0
$355$	0.301350	+	0.392727i	0.0159940	+	0.0208438i
$356$	8.04126	+	27.3929i	0.426186	+	1.45182i
$357$		0			0
$358$	−0.430006	−	2.99148i	−0.0227265	−	0.158105i
$359$	−18.9345	+	18.9345i	−0.999322	+	0.999322i	−1.00000		0.000677567i	$-0.999784\pi$
$359$	−18.9345	+	18.9345i	−0.999322	+	0.999322i	0.000677567		1.00000i	$0.499784\pi$
$360$		0			0
$361$	−13.3994	−	13.3994i	−0.705230	−	0.705230i
$362$	−11.4001	+	15.2277i	−0.599178	+	0.800351i
$363$		0			0
$364$	−4.88099	+	45.3709i	−0.255833	+	2.37808i
$365$	−0.885194	+	0.679233i	−0.0463332	+	0.0355527i
$366$		0			0
$367$	−12.7127	+	7.33968i	−0.663597	+	0.383128i	−0.793646	−	0.608380i	$-0.791820\pi$
$367$	−12.7127	+	7.33968i	−0.663597	+	0.383128i	0.130049	+	0.991508i	$0.458487\pi$
$368$	10.7293	+	9.75627i	0.559305	+	0.508581i
$369$		0			0
$370$	−0.371737	+	0.380666i	−0.0193257	+	0.0197899i
$371$	−2.48501	−	18.8755i	−0.129015	−	0.979970i
$372$		0			0
$373$	31.9435	+	4.20544i	1.65397	+	0.217749i	0.898981	−	0.437987i	$-0.144308\pi$
$373$	31.9435	+	4.20544i	1.65397	+	0.217749i	0.754990	+	0.655736i	$0.227642\pi$
$374$	−3.24585	+	27.1394i	−0.167839	+	1.40335i
$375$		0			0
$376$	−6.93284	+	4.33879i	−0.357534	+	0.223756i
$377$	−13.8445	+	13.8445i	−0.713028	+	0.713028i
$378$		0			0
$379$	22.0809	−	9.14623i	1.13422	−	0.469810i	0.265008	−	0.964246i	$-0.414625\pi$
$379$	22.0809	−	9.14623i	1.13422	−	0.469810i	0.869214	+	0.494436i	$0.164625\pi$
$380$	−0.0166853	−	0.0273781i	−0.000855937	−	0.00140447i
$381$		0			0
$382$	−7.88449	+	14.0384i	−0.403406	+	0.718269i
$383$	−8.37833	+	14.5117i	−0.428113	+	0.741513i	−0.996705	−	0.0811064i	$-0.974155\pi$
$383$	−8.37833	+	14.5117i	−0.428113	+	0.741513i	0.568593	+	0.822619i	$0.307488\pi$
$384$		0			0
$385$	−0.909620	−	1.57551i	−0.0463585	−	0.0802953i
$386$	−2.09590	+	0.0248712i	−0.106679	+	0.00126591i
$387$		0			0
$388$	15.2288	−	0.361479i	0.773124	−	0.0183513i
$389$	17.0110	+	13.0530i	0.862489	+	0.661811i	0.942216	−	0.335005i	$-0.108738\pi$
$389$	17.0110	+	13.0530i	0.862489	+	0.661811i	−0.0797268	+	0.996817i	$0.525405\pi$
$390$		0			0
$391$	−3.12824	−	11.6748i	−0.158202	−	0.590418i
$392$	−30.7942	−	16.3463i	−1.55534	−	0.825612i
$393$		0			0
$394$	18.4634	+	13.8225i	0.930171	+	0.696367i
$395$	0.324345	+	0.783037i	0.0163195	+	0.0393989i
$396$		0			0
$397$	−3.76660	−	1.56017i	−0.189040	−	0.0783029i	0.286155	−	0.958183i	$-0.407623\pi$
$397$	−3.76660	−	1.56017i	−0.189040	−	0.0783029i	−0.475195	+	0.879880i	$0.657623\pi$
$398$	−26.7463	−	6.82754i	−1.34067	−	0.342234i
$399$		0			0
$400$	−6.08094	−	19.0317i	−0.304047	−	0.951587i
$401$	−8.24914	−	4.76265i	−0.411943	−	0.237835i	0.279681	−	0.960093i	$-0.409771\pi$
$401$	−8.24914	−	4.76265i	−0.411943	−	0.237835i	−0.691624	+	0.722258i	$0.743104\pi$
$402$		0			0
$403$	1.82165	+	13.8368i	0.0907427	+	0.689260i
$404$	−9.03456	+	3.99598i	−0.449486	+	0.198807i
$405$		0			0
$406$	−9.23176	−	21.5602i	−0.458165	−	1.07002i
$407$	−7.90842	+	29.5146i	−0.392006	+	1.46299i
$408$		0			0
$409$	−0.574571	−	2.14433i	−0.0284107	−	0.106030i	0.950265	−	0.311444i	$-0.100813\pi$
$409$	−0.574571	−	2.14433i	−0.0284107	−	0.106030i	−0.978675	+	0.205414i	$0.934146\pi$
$410$	−0.532776	+	0.418950i	−0.0263119	+	0.0206905i
$411$		0			0
$412$	−14.5438	−	3.52933i	−0.716521	−	0.173878i
$413$	−6.59299	+	15.9169i	−0.324420	+	0.783219i
$414$		0			0
$415$	0.572387			0.0280974
$416$	−5.55141	−	28.8298i	−0.272180	−	1.41350i
$417$		0			0
$418$	−1.60539	−	0.901644i	−0.0785222	−	0.0441009i
$419$	−15.5182	−	20.2238i	−0.758116	−	0.987996i	−0.999844	−	0.0176519i	$-0.994381\pi$
$419$	−15.5182	−	20.2238i	−0.758116	−	0.987996i	0.241728	−	0.970344i	$-0.422286\pi$
$420$		0			0
$421$	−10.1301	−	7.77310i	−0.493711	−	0.378837i	0.331687	−	0.943390i	$-0.392382\pi$
$421$	−10.1301	−	7.77310i	−0.493711	−	0.378837i	−0.825397	+	0.564552i	$0.809049\pi$
$422$	8.41927	+	3.37090i	0.409843	+	0.164093i
$423$		0			0
$424$	5.08731	+	11.1426i	0.247061	+	0.541135i
$425$	−4.30987	+	16.0847i	−0.209059	+	0.780220i
$426$		0			0
$427$	42.6152	+	5.61040i	2.06229	+	0.271506i
$428$	6.49211	+	0.698419i	0.313808	+	0.0337594i
$429$		0			0
$430$	−0.0504766	+	0.197737i	−0.00243420	+	0.00953574i
$431$			39.8323i			1.91865i	0.282299	+	0.959327i	$0.408903\pi$
$431$			39.8323i			1.91865i	−0.282299	+	0.959327i	$0.591097\pi$
$432$		0			0
$433$			9.32461i			0.448112i	0.974576	+	0.224056i	$0.0719299\pi$
$433$			9.32461i			0.448112i	−0.974576	+	0.224056i	$0.928070\pi$
$434$	−16.1985	−	4.13501i	−0.777553	−	0.198487i
$435$		0			0
$436$	11.4069	−	9.19097i	0.546290	−	0.440167i
$437$	0.807240	+	0.106275i	0.0386155	+	0.00508383i
$438$		0			0
$439$	−0.133772	+	0.499243i	−0.00638458	+	0.0238276i	−0.969045	−	0.246886i	$-0.920593\pi$
$439$	−0.133772	+	0.499243i	−0.00638458	+	0.0238276i	0.962660	+	0.270713i	$0.0872595\pi$
$440$	0.856582	+	0.797668i	0.0408359	+	0.0380273i
$441$		0			0
$442$	−9.09522	+	22.7165i	−0.432616	+	1.08052i
$443$	−3.54720	−	2.72186i	−0.168533	−	0.129320i	0.521051	−	0.853525i	$-0.325540\pi$
$443$	−3.54720	−	2.72186i	−0.168533	−	0.129320i	−0.689584	+	0.724206i	$0.742207\pi$
$444$		0			0
$445$	−0.620286	−	0.808372i	−0.0294044	−	0.0383205i
$446$	−1.55822	+	2.77444i	−0.0737841	+	0.131374i
$447$		0			0
$448$	34.5324	+	6.66286i	1.63150	+	0.314790i
$449$	−1.59445			−0.0752468			−0.0376234	−	0.999292i	$-0.511979\pi$
$449$	−1.59445			−0.0752468			−0.0376234	+	0.999292i	$0.511979\pi$
$450$		0			0
$451$	−14.8953	+	35.9603i	−0.701390	+	1.69331i
$452$	28.3461	−	17.2752i	1.33329	−	0.812556i
$453$		0			0
$454$	−14.0169	−	17.8252i	−0.657848	−	0.836580i
$455$	−0.421531	−	1.57317i	−0.0197617	−	0.0737515i
$456$		0			0
$457$	4.78858	−	17.8712i	0.224000	−	0.835980i	−0.758802	−	0.651321i	$-0.774215\pi$
$457$	4.78858	−	17.8712i	0.224000	−	0.835980i	0.982803	−	0.184659i	$-0.0591182\pi$
$458$	2.71305	−	1.16169i	0.126773	−	0.0542821i
$459$		0			0
$460$	−0.482750	−	0.186668i	−0.0225084	−	0.00870342i
$461$	−4.70792	−	35.7602i	−0.219270	−	1.66552i	−0.647664	−	0.761926i	$-0.724254\pi$
$461$	−4.70792	−	35.7602i	−0.219270	−	1.66552i	0.428394	−	0.903592i	$-0.359079\pi$
$462$		0			0
$463$	−14.2220	−	8.21109i	−0.660954	−	0.381602i	0.131687	−	0.991291i	$-0.457961\pi$
$463$	−14.2220	−	8.21109i	−0.660954	−	0.381602i	−0.792640	+	0.609690i	$0.791294\pi$
$464$	9.74367	+	11.5221i	0.452338	+	0.534901i
$465$		0			0
$466$	−2.98641	+	11.6990i	−0.138343	+	0.541945i
$467$	4.79173	+	1.98480i	0.221735	+	0.0918455i	0.490785	−	0.871280i	$-0.336710\pi$
$467$	4.79173	+	1.98480i	0.221735	+	0.0918455i	−0.269051	+	0.963126i	$0.586710\pi$
$468$		0			0
$469$	12.3014	+	29.6982i	0.568026	+	1.37134i
$470$	0.174938	−	0.233673i	0.00806928	−	0.0107785i
$471$		0			0
$472$	1.05477	−	11.0342i	0.0485496	−	0.507888i
$473$	3.03333	+	11.3205i	0.139473	+	0.520519i
$474$		0			0
$475$	−0.889948	−	0.682881i	−0.0408336	−	0.0313327i
$476$	−21.2127	−	20.2290i	−0.972281	−	0.927194i
$477$		0			0
$478$	0.419185	+	35.3247i	0.0191731	+	1.61572i
$479$	−8.06725	−	13.9729i	−0.368602	−	0.638437i	0.620745	−	0.784012i	$-0.286830\pi$
$479$	−8.06725	−	13.9729i	−0.368602	−	0.638437i	−0.989347	+	0.145575i	$0.953497\pi$
$480$		0			0
$481$	−13.6775	+	23.6901i	−0.623640	+	1.08018i
$482$	−10.1883	−	5.72212i	−0.464065	−	0.260635i
$483$		0			0
$484$	43.9431	+	10.6636i	1.99741	+	0.484711i
$485$	−0.502296	+	0.208058i	−0.0228081	+	0.00944742i
$486$		0			0
$487$	3.57896	−	3.57896i	0.162178	−	0.162178i	−0.621353	−	0.783531i	$-0.713417\pi$
$487$	3.57896	−	3.57896i	0.162178	−	0.162178i	0.783531	+	0.621353i	$0.213417\pi$
$488$	−27.2722	+	4.58319i	−1.23455	+	0.207471i
$489$		0			0
$490$	1.23552	+	0.147766i	0.0558149	+	0.00667541i
$491$	37.0843	+	4.88224i	1.67359	+	0.220332i	0.906799	−	0.421563i	$-0.138518\pi$
$491$	37.0843	+	4.88224i	1.67359	+	0.220332i	0.766792	+	0.641896i	$0.221852\pi$
$492$		0			0
$493$	−1.64157	−	12.4689i	−0.0739324	−	0.561572i
$494$	−1.17933	−	1.15167i	−0.0530606	−	0.0518161i
$495$		0			0
$496$	10.7440	−	0.510338i	0.482419	−	0.0229148i
$497$	−26.4022	+	15.2433i	−1.18430	+	0.683757i
$498$		0			0
$499$	−22.4174	+	17.2015i	−1.00354	+	0.770043i	−0.973309	−	0.229500i	$-0.926291\pi$
$499$	−22.4174	+	17.2015i	−1.00354	+	0.770043i	−0.0302308	+	0.999543i	$0.509624\pi$
$500$	0.895265	+	1.11111i	0.0400375	+	0.0496904i
$501$		0			0
$502$	−5.40707	−	4.04797i	−0.241329	−	0.180670i
$503$	22.8286	+	22.8286i	1.01788	+	1.01788i	0.999837	+	0.0180392i	$0.00574237\pi$
$503$	22.8286	+	22.8286i	1.01788	+	1.01788i	0.0180392	+	0.999837i	$0.494258\pi$
$504$		0			0
$505$	0.249314	−	0.249314i	0.0110943	−	0.0110943i
$506$	−29.4216	+	4.22917i	−1.30795	+	0.188010i
$507$		0			0
$508$	4.97945	−	9.11772i	0.220927	−	0.404533i
$509$	13.9429	+	18.1708i	0.618009	+	0.805405i	0.992554	−	0.121804i	$-0.0388679\pi$
$509$	13.9429	+	18.1708i	0.618009	+	0.805405i	−0.374546	+	0.927209i	$0.622201\pi$
$510$		0			0
$511$	−34.3580	−	59.5098i	−1.51991	−	2.63256i
$512$	−22.4985	+	2.41189i	−0.994303	+	0.106592i
$513$		0			0
$514$	7.60665	−	0.0902651i	0.335515	−	0.00398143i
$515$	0.529576	−	0.0697200i	0.0233359	−	0.00307223i
$516$		0			0
$517$	2.18807	−	16.6200i	0.0962311	−	0.730948i
$518$	−20.2551	−	25.7582i	−0.889958	−	1.13175i
$519$		0			0
$520$	0.555897	+	0.888253i	0.0243777	+	0.0389525i
$521$	−9.34868	−	9.34868i	−0.409573	−	0.409573i	0.472016	−	0.881590i	$-0.343526\pi$
$521$	−9.34868	−	9.34868i	−0.409573	−	0.409573i	−0.881590	+	0.472016i	$0.843526\pi$
$522$		0			0
$523$	−1.64931	−	3.98178i	−0.0721192	−	0.174111i	0.883709	−	0.468036i	$-0.155038\pi$
$523$	−1.64931	−	3.98178i	−0.0721192	−	0.174111i	−0.955828	+	0.293925i	$0.905038\pi$
$524$	9.36621	−	1.45997i	0.409165	−	0.0637790i
$525$		0			0
$526$	4.37064	+	15.5701i	0.190569	+	0.678887i
$527$	−7.76365	−	4.48235i	−0.338190	−	0.195254i
$528$		0			0
$529$	−8.53557	+	4.92801i	−0.371112	+	0.214261i
$530$	−0.312779	−	0.305443i	−0.0135862	−	0.0132676i
$531$		0			0
$532$	1.80583	−	0.798716i	0.0782926	−	0.0346287i
$533$	−21.2128	+	27.6451i	−0.918829	+	1.19744i
$534$		0			0
$535$	−0.225105	+	0.0603167i	−0.00973214	+	0.00260772i
$536$	−13.1662	−	15.9494i	−0.568694	−	0.688909i
$537$		0			0
$538$	−4.64915	−	32.3434i	−0.200439	−	1.39442i
$539$	66.0199	−	27.3463i	2.84368	−	1.17789i
$540$		0			0
$541$	−4.40167	+	10.6266i	−0.189243	+	0.456872i	−0.989814	−	0.142365i	$-0.954529\pi$
$541$	−4.40167	+	10.6266i	−0.189243	+	0.456872i	0.800572	+	0.599237i	$0.204529\pi$
$542$	30.2711	−	17.9593i	1.30025	−	0.771417i
$543$		0			0
$544$	16.8627	+	8.44442i	0.722980	+	0.362051i
$545$	−0.261416	+	0.452786i	−0.0111978	+	0.0193952i
$546$		0			0
$547$	9.94132	−	1.30880i	0.425060	−	0.0559602i	0.0850381	−	0.996378i	$-0.472899\pi$
$547$	9.94132	−	1.30880i	0.425060	−	0.0559602i	0.340022	+	0.940417i	$0.389565\pi$
$548$	9.54458	+	9.10198i	0.407724	+	0.388817i
$549$		0			0
$550$	38.0177	+	15.2215i	1.62108	+	0.649046i
$551$	0.818342	+	0.219274i	0.0348625	+	0.00934139i
$552$		0			0
$553$	−50.4193	+	13.5098i	−2.14405	+	0.574496i
$554$	−26.0820	−	3.11938i	−1.10812	−	0.132530i
$555$		0			0
$556$	18.7723	−	25.7053i	0.796122	−	1.09015i
$557$	−3.46488	−	1.43520i	−0.146812	−	0.0608114i	0.308068	−	0.951364i	$-0.400318\pi$
$557$	−3.46488	−	1.43520i	−0.146812	−	0.0608114i	−0.454879	+	0.890553i	$0.650318\pi$
$558$		0			0
$559$			10.4922i			0.443773i
$560$	−1.23531	+	0.222701i	−0.0522013	+	0.00941084i
$561$		0			0
$562$	2.69363	+	9.59582i	0.113624	+	0.404775i
$563$	−36.8702	+	28.2915i	−1.55390	+	1.19235i	−0.653787	+	0.756679i	$0.726821\pi$
$563$	−36.8702	+	28.2915i	−1.55390	+	1.19235i	−0.900108	+	0.435667i	$0.856513\pi$
$564$		0			0
$565$	−0.721243	+	0.939942i	−0.0303429	+	0.0395437i
$566$	22.5231	−	9.64406i	0.946717	−	0.405370i
$567$		0			0
$568$	13.3673	−	14.3545i	0.560878	−	0.602302i
$569$	30.0901	+	8.06262i	1.26144	+	0.338002i	0.826746	−	0.562575i	$-0.190189\pi$
$569$	30.0901	+	8.06262i	1.26144	+	0.338002i	0.434696	+	0.900577i	$0.356856\pi$
$570$		0			0
$571$	−2.04914	+	15.5648i	−0.0857538	+	0.651365i	0.893549	+	0.448965i	$0.148207\pi$
$571$	−2.04914	+	15.5648i	−0.0857538	+	0.651365i	−0.979303	+	0.202400i	$0.935126\pi$
$572$	52.8142	+	28.8434i	2.20827	+	1.20600i
$573$		0			0
$574$	−21.2982	−	35.8990i	−0.888969	−	1.49839i
$575$	−18.1088			−0.755191
$576$		0			0
$577$	−38.9155			−1.62007			−0.810037	−	0.586379i	$-0.800553\pi$
$577$	−38.9155			−1.62007			−0.810037	+	0.586379i	$0.800553\pi$
$578$	4.24707	+	7.15861i	0.176655	+	0.297759i
$579$		0			0
$580$	−0.472668	−	0.258138i	−0.0196265	−	0.0107186i
$581$	−4.60123	+	34.9498i	−0.190891	+	1.44996i
$582$		0			0
$583$	−24.2510	−	6.49805i	−1.00438	−	0.269122i
$584$	32.3547	+	30.1294i	1.33885	+	1.24676i
$585$		0			0
$586$	20.5268	−	8.78926i	0.847954	−	0.363081i
$587$	16.3849	−	21.3532i	0.676276	−	0.881341i	−0.321573	−	0.946885i	$-0.604212\pi$
$587$	16.3849	−	21.3532i	0.676276	−	0.881341i	0.997850	+	0.0655441i	$0.0208783\pi$
$588$		0			0
$589$	0.479107	−	0.367631i	0.0197412	−	0.0151480i
$590$	0.106919	+	0.380892i	0.00440181	+	0.0156811i
$591$		0			0
$592$	17.3161	+	12.0262i	0.711685	+	0.494275i
$593$			9.78973i			0.402016i	0.979590	+	0.201008i	$0.0644217\pi$
$593$			9.78973i			0.402016i	−0.979590	+	0.201008i	$0.935578\pi$
$594$		0			0
$595$	0.966533	+	0.400351i	0.0396240	+	0.0164128i
$596$	−21.8643	+	29.9392i	−0.895595	+	1.22636i
$597$		0			0
$598$	−26.4220	−	3.16005i	−1.08048	−	0.129224i
$599$	24.0407	−	6.44169i	0.982277	−	0.263200i	0.268274	−	0.963343i	$-0.413547\pi$
$599$	24.0407	−	6.44169i	0.982277	−	0.263200i	0.714003	+	0.700142i	$0.246880\pi$
$600$		0			0
$601$	42.3097	+	11.3368i	1.72585	+	0.462439i	0.979220	−	0.202803i	$-0.0650051\pi$
$601$	42.3097	+	11.3368i	1.72585	+	0.462439i	0.746627	+	0.665242i	$0.231672\pi$
$602$	−11.6680	−	4.67163i	−0.475553	−	0.190401i
$603$		0			0
$604$	−2.47392	−	2.35920i	−0.100663	−	0.0959946i
$605$	−1.60008	+	0.210654i	−0.0650525	+	0.00856432i
$606$		0			0
$607$	−16.9121	+	29.2926i	−0.686440	+	1.18895i	0.286543	+	0.958068i	$0.407494\pi$
$607$	−16.9121	+	29.2926i	−0.686440	+	1.18895i	−0.972982	+	0.230881i	$0.925839\pi$
$608$	−0.960257	+	0.831783i	−0.0389436	+	0.0337332i
$609$		0			0
$610$	0.848866	−	0.503616i	0.0343696	−	0.0203908i
$611$	5.74309	−	13.8650i	0.232341	−	0.560920i
$612$		0			0
$613$	20.9986	−	8.69791i	0.848126	−	0.351305i	0.0840739	−	0.996460i	$-0.473207\pi$
$613$	20.9986	−	8.69791i	0.848126	−	0.351305i	0.764053	+	0.645154i	$0.223207\pi$
$614$	−2.75252	−	19.1488i	−0.111083	−	0.772782i
$615$		0			0
$616$	−55.5912	+	45.8905i	−2.23983	+	1.84898i
$617$	−30.8991	+	8.27938i	−1.24395	+	0.333315i	−0.819996	−	0.572369i	$-0.806025\pi$
$617$	−30.8991	+	8.27938i	−1.24395	+	0.333315i	−0.423953	+	0.905684i	$0.639358\pi$
$618$		0			0
$619$	−4.86661	+	6.34229i	−0.195605	+	0.254918i	−0.880850	−	0.473395i	$-0.843028\pi$
$619$	−4.86661	+	6.34229i	−0.195605	+	0.254918i	0.685245	+	0.728313i	$0.259695\pi$
$620$	−0.351086	+	0.155285i	−0.0141000	+	0.00623639i
$621$		0			0
$622$	−4.07120	−	3.97571i	−0.163240	−	0.159412i
$623$	54.3453	−	31.3763i	2.17730	−	1.25706i
$624$		0			0
$625$	21.5845	+	12.4618i	0.863379	+	0.498472i
$626$	6.97386	+	24.8438i	0.278731	+	0.992957i
$627$		0			0
$628$	22.6943	−	3.53751i	0.905603	−	0.141162i
$629$	−6.72426	−	16.2338i	−0.268114	−	0.647284i
$630$		0			0
$631$	−3.39677	−	3.39677i	−0.135223	−	0.135223i	0.636255	−	0.771479i	$-0.280482\pi$
$631$	−3.39677	−	3.39677i	−0.135223	−	0.135223i	−0.771479	+	0.636255i	$0.780482\pi$
$632$	28.4680	−	17.8162i	1.13240	−	0.708690i
$633$		0			0
$634$	−13.4909	−	17.1563i	−0.535793	−	0.681364i
$635$	−0.0483973	+	0.367614i	−0.00192059	+	0.0145883i
$636$		0			0
$637$	63.4265	−	8.35026i	2.51305	−	0.330849i
$638$	−30.9267	+	0.366995i	−1.22440	+	0.0145295i
$639$		0			0
$640$	0.717904	−	0.369890i	0.0283777	−	0.0146212i
$641$	6.25032	+	10.8259i	0.246873	+	0.427596i	0.962657	−	0.270726i	$-0.0872637\pi$
$641$	6.25032	+	10.8259i	0.246873	+	0.427596i	−0.715784	+	0.698322i	$0.753930\pi$
$642$		0			0
$643$	8.19989	+	10.6863i	0.323372	+	0.421427i	0.926545	−	0.376184i	$-0.122764\pi$
$643$	8.19989	+	10.6863i	0.323372	+	0.421427i	−0.603173	+	0.797610i	$0.706097\pi$
$644$	15.2785	−	27.9761i	0.602059	−	1.10241i
$645$		0			0
$646$	1.04806	−	0.150652i	0.0412353	−	0.00592732i
$647$	9.85881	−	9.85881i	0.387590	−	0.387590i	−0.486237	−	0.873827i	$-0.661631\pi$
$647$	9.85881	−	9.85881i	0.387590	−	0.387590i	0.873827	+	0.486237i	$0.161631\pi$
$648$		0			0
$649$	16.0651	+	16.0651i	0.630611	+	0.630611i
$650$	29.3486	+	21.9716i	1.15115	+	0.861798i
$651$		0			0
$652$	17.1646	+	21.3029i	0.672217	+	0.834286i
$653$	6.56518	−	5.03764i	0.256915	−	0.197138i	−0.472271	−	0.881454i	$-0.656566\pi$
$653$	6.56518	−	5.03764i	0.256915	−	0.197138i	0.729186	+	0.684315i	$0.239899\pi$
$654$		0			0
$655$	−0.292998	+	0.169162i	−0.0114484	+	0.00660972i
$656$	19.8696	+	18.0676i	0.775777	+	0.705420i
$657$		0			0
$658$	12.8617	+	12.5601i	0.501403	+	0.489643i
$659$	−5.59211	−	42.4763i	−0.217838	−	1.65464i	−0.655272	−	0.755393i	$-0.727446\pi$
$659$	−5.59211	−	42.4763i	−0.217838	−	1.65464i	0.437435	−	0.899250i	$-0.355887\pi$
$660$		0			0
$661$	7.48829	+	0.985853i	0.291261	+	0.0383452i	0.274741	−	0.961518i	$-0.411408\pi$
$661$	7.48829	+	0.985853i	0.291261	+	0.0383452i	0.0165200	+	0.999864i	$0.494741\pi$
$662$	8.59049	+	1.02741i	0.333879	+	0.0399316i
$663$		0			0
$664$	−3.75879	−	22.3666i	−0.145869	−	0.867993i
$665$	−0.0498330	+	0.0498330i	−0.00193244	+	0.00193244i
$666$		0			0
$667$	12.6357	−	5.23387i	0.489255	−	0.202656i
$668$	−12.5347	−	3.04179i	−0.484983	−	0.117690i
$669$		0			0
$670$	0.643589	+	0.361463i	0.0248640	+	0.0139645i
$671$	28.3414	−	49.0888i	1.09411	−	1.89505i
$672$		0			0
$673$	8.66279	+	15.0044i	0.333926	+	0.578377i	0.983278	−	0.182111i	$-0.0582931\pi$
$673$	8.66279	+	15.0044i	0.333926	+	0.578377i	−0.649352	+	0.760488i	$0.724960\pi$
$674$	−0.497839	−	41.9529i	−0.0191760	−	1.61597i
$675$		0			0
$676$	20.1716	+	19.2362i	0.775831	+	0.739854i
$677$	−0.115175	−	0.0883773i	−0.00442655	−	0.00339661i	0.606546	−	0.795049i	$-0.292555\pi$
$677$	−0.115175	−	0.0883773i	−0.00442655	−	0.00339661i	−0.610972	+	0.791652i	$0.709221\pi$
$678$		0			0
$679$	−8.66617	−	32.3426i	−0.332577	−	1.24119i
$680$	−0.670035	−	0.0640494i	−0.0256947	−	0.00245618i
$681$		0			0
$682$	−13.2125	+	17.6487i	−0.505935	+	0.675802i
$683$	3.85043	+	9.29576i	0.147333	+	0.355692i	0.980267	−	0.197680i	$-0.0633407\pi$
$683$	3.85043	+	9.29576i	0.147333	+	0.355692i	−0.832934	+	0.553372i	$0.813341\pi$
$684$		0			0
$685$	−0.434889	−	0.180137i	−0.0166163	−	0.00688268i
$686$	−8.19033	+	32.0848i	−0.312708	+	1.22501i
$687$		0			0
$688$	8.05826	+	0.673909i	0.307218	+	0.0256925i
$689$	−19.4653	−	11.2383i	−0.741567	−	0.428144i
$690$		0			0
$691$	−6.55051	−	49.7561i	−0.249193	−	1.89281i	−0.420029	−	0.907511i	$-0.637980\pi$
$691$	−6.55051	−	49.7561i	−0.249193	−	1.89281i	0.170836	−	0.985299i	$-0.445353\pi$
$692$	−2.84264	−	1.09918i	−0.108061	−	0.0417845i
$693$		0			0
$694$	−3.81693	+	1.63435i	−0.144889	+	0.0620391i
$695$	−0.294030	+	1.09734i	−0.0111532	+	0.0416243i
$696$		0			0
$697$	−5.79317	−	21.6204i	−0.219432	−	0.818931i
$698$	−10.1970	−	12.9675i	−0.385963	−	0.490826i
$699$		0			0
$700$	−37.5013	+	22.8547i	−1.41742	+	0.863828i
$701$	16.2006	−	39.1117i	0.611888	−	1.47723i	−0.249036	−	0.968494i	$-0.580114\pi$
$701$	16.2006	−	39.1117i	0.611888	−	1.47723i	0.860924	−	0.508734i	$-0.169886\pi$
$702$		0			0
$703$	1.18368			0.0446434
$704$	25.5446	−	38.7100i	0.962750	−	1.45894i
$705$		0			0
$706$	2.36048	−	4.20286i	0.0888378	−	0.158177i
$707$	13.2189	+	17.2272i	0.497148	+	0.647896i
$708$		0			0
$709$	24.9914	+	19.1765i	0.938570	+	0.720190i	0.960123	−	0.279578i	$-0.0901945\pi$
$709$	24.9914	+	19.1765i	0.938570	+	0.720190i	−0.0215532	+	0.999768i	$0.506861\pi$
$710$	−0.260210	+	0.649909i	−0.00976551	+	0.0243907i
$711$		0			0
$712$	−27.5146	+	29.5468i	−1.03115	+	1.10731i
$713$	2.52321	−	9.41676i	0.0944951	−	0.352661i
$714$		0			0
$715$	−2.12940	−	0.280341i	−0.0796350	−	0.0104841i
$716$	3.32815	−	2.68162i	0.124379	−	0.100217i
$717$		0			0
$718$	−36.6923	−	9.36647i	−1.36934	−	0.349554i
$719$			0.542286i			0.0202239i	0.999949	+	0.0101119i	$0.00321878\pi$
$719$			0.542286i			0.0202239i	−0.999949	+	0.0101119i	$0.996781\pi$
$720$		0			0
$721$			32.8962i			1.22512i
$722$	6.62838	−	25.9661i	0.246683	−	0.966357i
$723$		0			0
$724$	−26.7472	−	2.87746i	−0.994052	−	0.106940i
$725$	−18.6817	−	2.45949i	−0.693820	−	0.0913431i
$726$		0			0
$727$	−1.52449	+	5.68947i	−0.0565402	+	0.211011i	−0.988417	−	0.151765i	$-0.951504\pi$
$727$	−1.52449	+	5.68947i	−0.0565402	+	0.211011i	0.931876	+	0.362776i	$0.118171\pi$
$728$	−58.7052	+	26.8025i	−2.17576	+	0.993368i
$729$		0			0
$730$	−1.46488	−	0.586506i	−0.0542175	−	0.0217076i
$731$	−5.34690	−	4.10282i	−0.197762	−	0.151748i
$732$		0			0
$733$	−9.27981	−	12.0937i	−0.342758	−	0.446691i	0.589887	−	0.807485i	$-0.299172\pi$
$733$	−9.27981	−	12.0937i	−0.342758	−	0.446691i	−0.932645	+	0.360795i	$0.882505\pi$
$734$	−18.1004	−	10.1658i	−0.668097	−	0.375227i
$735$		0			0
$736$	−4.12407	+	20.0898i	−0.152015	+	0.740519i
$737$	42.3907			1.56148
$738$		0			0
$739$	13.5926	−	32.8155i	0.500013	−	1.20714i	−0.449462	−	0.893299i	$-0.648384\pi$
$739$	13.5926	−	32.8155i	0.500013	−	1.20714i	0.949476	−	0.313840i	$-0.101616\pi$
$740$	−0.731234	−	0.177448i	−0.0268807	−	0.00652312i
$741$		0			0
$742$	21.1646	−	16.6428i	0.776976	−	0.610978i
$743$	−4.91062	−	18.3267i	−0.180153	−	0.672340i	−0.995616	−	0.0935314i	$-0.970184\pi$
$743$	−4.91062	−	18.3267i	−0.180153	−	0.672340i	0.815463	−	0.578809i	$-0.196482\pi$
$744$		0			0
$745$	0.342460	−	1.27808i	0.0125468	−	0.0468252i
$746$	17.9351	+	41.8865i	0.656652	+	1.53357i
$747$		0			0
$748$	−35.3510	+	15.6357i	−1.29256	+	0.571698i
$749$	−1.87338	−	14.2297i	−0.0684518	−	0.519943i
$750$		0			0
$751$	13.4626	+	7.77265i	0.491258	+	0.283628i	0.725096	−	0.688648i	$-0.241795\pi$
$751$	13.4626	+	7.77265i	0.491258	+	0.283628i	−0.233838	+	0.972276i	$0.575129\pi$
$752$	−10.2798	−	5.30137i	−0.374866	−	0.193321i
$753$		0			0
$754$	−26.8287	−	6.84858i	−0.977042	−	0.249410i
$755$	0.112722	+	0.0466909i	0.00410237	+	0.00169926i
$756$		0			0
$757$	−4.07026	−	9.82649i	−0.147936	−	0.357150i	0.832489	−	0.554042i	$-0.186915\pi$
$757$	−4.07026	−	9.82649i	−0.147936	−	0.357150i	−0.980425	+	0.196892i	$0.936915\pi$
$758$	27.0576	+	20.2565i	0.982778	+	0.735750i
$759$		0			0
$760$	0.0212592	−	0.0400495i	0.000771152	−	0.00145275i
$761$	−9.52154	−	35.5349i	−0.345155	−	1.28814i	−0.892431	−	0.451185i	$-0.851002\pi$
$761$	−9.52154	−	35.5349i	−0.345155	−	1.28814i	0.547275	−	0.836953i	$-0.315665\pi$
$762$		0			0
$763$	−25.5456	−	19.6018i	−0.924812	−	0.709633i
$764$	−22.7639	+	0.540336i	−0.823568	+	0.0195487i
$765$		0			0
$766$	−23.6958	+	0.281189i	−0.856165	+	0.0101598i
$767$	10.1698	+	17.6146i	0.367209	+	0.636025i
$768$		0			0
$769$	25.8022	−	44.6908i	0.930452	−	1.61159i	0.147902	−	0.989002i	$-0.452748\pi$
$769$	25.8022	−	44.6908i	0.930452	−	1.61159i	0.782550	−	0.622588i	$-0.213919\pi$
$770$	1.25987	−	2.24321i	0.0454025	−	0.0808397i
$771$		0			0
$772$	−1.54263	−	2.53123i	−0.0555205	−	0.0911010i
$773$	3.72273	−	1.54200i	0.133897	−	0.0554620i	−0.314729	−	0.949182i	$-0.601914\pi$
$773$	3.72273	−	1.54200i	0.133897	−	0.0554620i	0.448626	+	0.893720i	$0.351914\pi$
$774$		0			0
$775$	−9.49745	+	9.49745i	−0.341158	+	0.341158i
$776$	11.4286	+	18.2614i	0.410262	+	0.655548i
$777$		0			0
$778$	−3.60098	+	30.1088i	−0.129101	+	1.07945i
$779$	1.49492	+	0.196810i	0.0535611	+	0.00705146i
$780$		0			0
$781$	5.24763	+	39.8597i	0.187775	+	1.42629i
$782$	11.9423	−	12.2292i	0.427057	−	0.437314i
$783$		0			0
$784$	−2.33934	−	49.2494i	−0.0835478	−	1.75891i
$785$	−0.709935	+	0.409881i	−0.0253387	+	0.0146293i
$786$		0			0
$787$	−14.7433	+	11.3130i	−0.525543	+	0.403263i	−0.837171	−	0.546941i	$-0.815792\pi$
$787$	−14.7433	+	11.3130i	−0.525543	+	0.403263i	0.311628	+	0.950204i	$0.399126\pi$
$788$	−3.48887	+	32.4306i	−0.124286	+	1.15529i
$789$		0			0
$790$	−0.718339	+	0.959521i	−0.0255574	+	0.0341382i
$791$	−51.5948	−	51.5948i	−1.83450	−	1.83450i
$792$		0			0
$793$	35.8823	−	35.8823i	1.27422	−	1.27422i
$794$	−0.820345	−	5.70700i	−0.0291129	−	0.202534i
$795$		0			0
$796$	−10.9957	−	37.4573i	−0.389732	−	1.32764i
$797$	−31.2997	−	40.7906i	−1.10869	−	1.44488i	−0.882207	−	0.470862i	$-0.843943\pi$
$797$	−31.2997	−	40.7906i	−1.10869	−	1.44488i	−0.226486	−	0.974015i	$-0.572724\pi$
$798$		0			0
$799$	4.81997	+	8.34844i	0.170518	+	0.295347i
$800$	18.7598	−	21.1292i	0.663258	−	0.747029i
$801$		0			0
$802$	−0.159841	−	13.4698i	−0.00564420	−	0.475637i
$803$	−89.8426	+	11.8280i	−3.17048	+	0.417401i
$804$		0			0
$805$	−0.148498	+	1.12796i	−0.00523388	+	0.0397553i
$806$	−15.5148	+	12.2001i	−0.546484	+	0.429730i
$807$		0			0
$808$	−11.3794	−	8.10500i	−0.400327	−	0.285133i
$809$	−5.20641	−	5.20641i	−0.183048	−	0.183048i	0.609635	−	0.792682i	$-0.291316\pi$
$809$	−5.20641	−	5.20641i	−0.183048	−	0.183048i	−0.792682	+	0.609635i	$0.791316\pi$
$810$		0			0
$811$	−17.0860	−	41.2492i	−0.599970	−	1.44846i	−0.873611	−	0.486624i	$-0.838228\pi$
$811$	−17.0860	−	41.2492i	−0.599970	−	1.44846i	0.273641	−	0.961832i	$-0.411772\pi$
$812$	19.5615	−	26.7859i	0.686473	−	0.940002i
$813$		0			0
$814$	−41.6043	+	11.6787i	−1.45823	+	0.409338i
$815$	−0.845600	−	0.488208i	−0.0296201	−	0.0171012i
$816$		0			0
$817$	0.393184	−	0.227005i	0.0137558	−	0.00794190i
$818$	2.19347	−	2.24616i	0.0766930	−	0.0785350i
$819$		0			0
$820$	−0.894002	−	0.345688i	−0.0312199	−	0.0120720i
$821$	−11.1729	+	14.5607i	−0.389935	+	0.508173i	−0.946532	−	0.322609i	$-0.895440\pi$
$821$	−11.1729	+	14.5607i	−0.389935	+	0.508173i	0.556597	+	0.830783i	$0.312107\pi$
$822$		0			0
$823$	37.3462	−	10.0069i	1.30181	−	0.348818i	0.459673	−	0.888088i	$-0.347966\pi$
$823$	37.3462	−	10.0069i	1.30181	−	0.348818i	0.842133	+	0.539270i	$0.181300\pi$
$824$	−6.20204	−	20.2359i	−0.216058	−	0.704950i
$825$		0			0
$826$	−24.1166	+	3.46661i	−0.839125	+	0.120619i
$827$	3.76417	−	1.55917i	0.130893	−	0.0542177i	−0.316276	−	0.948667i	$-0.602432\pi$
$827$	3.76417	−	1.55917i	0.130893	−	0.0542177i	0.447169	+	0.894450i	$0.352432\pi$
$828$		0			0
$829$	−19.9219	+	48.0956i	−0.691915	+	1.67043i	0.0489714	+	0.998800i	$0.484406\pi$
$829$	−19.9219	+	48.0956i	−0.691915	+	1.67043i	−0.740886	+	0.671630i	$0.765594\pi$
$830$	0.413029	+	0.696176i	0.0143364	+	0.0241646i
$831$		0			0
$832$	31.0589	−	27.5553i	1.07677	−	0.955307i
$833$	−20.5466	+	35.5878i	−0.711899	+	1.23305i
$834$		0			0
$835$	0.456421	−	0.0600889i	0.0157951	−	0.00207946i
$836$	−0.0617911	−	2.60320i	−0.00213709	−	0.0900336i
$837$		0			0
$838$	13.3997	−	33.4676i	0.462886	−	1.15612i
$839$	27.7669	+	7.44011i	0.958619	+	0.256861i	0.704016	−	0.710184i	$-0.251388\pi$
$839$	27.7669	+	7.44011i	0.958619	+	0.256861i	0.254603	+	0.967046i	$0.418055\pi$
$840$		0			0
$841$	−14.2656	+	3.82246i	−0.491918	+	0.131809i
$842$	2.14440	−	17.9299i	0.0739009	−	0.617905i
$843$		0			0
$844$	1.97534	+	12.6725i	0.0679940	+	0.436205i
$845$	−0.919099	−	0.380703i	−0.0316180	−	0.0130966i
$846$		0			0
$847$		−	99.3938i		−	3.41521i
$848$	−9.88150	+	14.2279i	−0.339332	+	0.488590i
$849$		0			0
$850$	−22.6732	+	6.36456i	−0.777685	+	0.218303i
$851$	15.1598	−	11.6325i	0.519672	−	0.398758i
$852$		0			0
$853$	0.00352105	−	0.00458872i	0.000120558	−	0.000157115i	−0.793293	−	0.608840i	$-0.791635\pi$
$853$	0.00352105	−	0.00458872i	0.000120558	−	0.000157115i	0.793414	+	0.608683i	$0.208302\pi$
$854$	23.9269	+	55.8799i	0.818763	+	1.91217i
$855$		0			0
$856$	3.83517	+	8.40012i	0.131083	+	0.287110i
$857$	44.0847	+	11.8125i	1.50590	+	0.403506i	0.915073	−	0.403289i	$-0.132133\pi$
$857$	44.0847	+	11.8125i	1.50590	+	0.403506i	0.590831	+	0.806795i	$0.298800\pi$
$858$		0			0
$859$	3.31434	−	25.1749i	0.113084	−	0.858957i	−0.837053	−	0.547122i	$-0.815723\pi$
$859$	3.31434	−	25.1749i	0.113084	−	0.858957i	0.950136	−	0.311834i	$-0.100943\pi$
$860$	−0.276925	+	0.0812921i	−0.00944306	+	0.00277204i
$861$		0			0
$862$	−48.4467	+	28.7426i	−1.65010	+	0.978975i
$863$	10.3078			0.350880			0.175440	−	0.984490i	$-0.443865\pi$
$863$	10.3078			0.350880			0.175440	+	0.984490i	$0.443865\pi$
$864$		0			0
$865$	0.108777			0.00369853
$866$	−11.3412	+	6.72854i	−0.385391	+	0.228645i
$867$		0			0
$868$	−6.65940	−	22.6855i	−0.226035	−	0.769996i
$869$	−8.98477	+	68.2461i	−0.304787	+	2.31509i
$870$		0			0
$871$	36.6570	+	9.82222i	1.24208	+	0.332813i
$872$	19.4098	+	7.24172i	0.657298	+	0.245236i
$873$		0			0
$874$	0.453237	+	1.05851i	0.0153310	+	0.0358046i
$875$	1.90935	−	2.48832i	0.0645479	−	0.0841205i
$876$		0			0
$877$	3.56606	−	2.73634i	0.120417	−	0.0923996i	−0.546797	−	0.837265i	$-0.684153\pi$
$877$	3.56606	−	2.73634i	0.120417	−	0.0923996i	0.667215	+	0.744866i	$0.267486\pi$
$878$	−0.703742	+	0.197546i	−0.0237502	+	0.00666687i
$879$		0			0
$880$	−0.352079	+	1.61742i	−0.0118686	+	0.0545233i
$881$			44.6971i			1.50588i	0.658087	+	0.752942i	$0.271366\pi$
$881$			44.6971i			1.50588i	−0.658087	+	0.752942i	$0.728634\pi$
$882$		0			0
$883$	37.7494	+	15.6363i	1.27037	+	0.526205i	0.913077	−	0.407788i	$-0.133700\pi$
$883$	37.7494	+	15.6363i	1.27037	+	0.526205i	0.357293	+	0.933992i	$0.383700\pi$
$884$	−34.1924	+	5.32978i	−1.15002	+	0.179260i
$885$		0			0
$886$	0.750893	−	6.27842i	0.0252267	−	0.210928i
$887$	−27.5228	+	7.37471i	−0.924125	+	0.247619i	−0.689348	−	0.724431i	$-0.742103\pi$
$887$	−27.5228	+	7.37471i	−0.924125	+	0.247619i	−0.234777	+	0.972049i	$0.575436\pi$
$888$		0			0
$889$	−22.0574	−	5.91026i	−0.739781	−	0.198224i
$890$	0.535606	−	1.33775i	0.0179535	−	0.0448414i
$891$		0			0
$892$	−4.49886	+	0.106787i	−0.150633	+	0.00357551i
$893$	−0.643833	+	0.0847622i	−0.0215451	+	0.00283646i
$894$		0			0
$895$	−0.0762727	+	0.132108i	−0.00254952	+	0.00441589i
$896$	16.8144	+	46.8085i	0.561729	+	1.56376i
$897$		0			0
$898$	−1.15054	−	1.93928i	−0.0383940	−	0.0647146i
$899$	3.88199	−	9.37195i	0.129472	−	0.312572i
$900$		0			0
$901$	13.3387	−	5.52507i	0.444377	−	0.184067i
$902$	−54.4857	+	7.83197i	−1.81417	+	0.260776i
$903$		0			0
$904$	41.4655	+	22.0108i	1.37912	+	0.732069i
$905$	0.927424	−	0.248502i	0.0308286	−	0.00826050i
$906$		0			0
$907$	−26.1699	+	34.1053i	−0.868957	+	1.13245i	0.121220	+	0.992626i	$0.461319\pi$
$907$	−26.1699	+	34.1053i	−0.868957	+	1.13245i	−0.990177	+	0.139821i	$0.955347\pi$
$908$	11.5658	−	29.9109i	0.383824	−	0.992627i
$909$		0			0
$910$	1.60923	−	1.64788i	0.0533454	−	0.0546267i
$911$	14.4191	−	8.32490i	0.477728	−	0.275816i	−0.241741	−	0.970341i	$-0.577719\pi$
$911$	14.4191	−	8.32490i	0.477728	−	0.275816i	0.719469	+	0.694525i	$0.244385\pi$
$912$		0			0
$913$	40.2590	+	23.2435i	1.33238	+	0.769249i
$914$	25.1916	−	7.07149i	0.833264	−	0.233904i
$915$		0			0
$916$	3.37064	+	2.46154i	0.111369	+	0.0813315i
$917$	−7.97370	−	19.2502i	−0.263315	−	0.635698i
$918$		0			0
$919$	32.5518	+	32.5518i	1.07379	+	1.07379i	0.997052	+	0.0767339i	$0.0244492\pi$
$919$	32.5518	+	32.5518i	1.07379	+	1.07379i	0.0767339	+	0.997052i	$0.475551\pi$
$920$	−0.121310	−	0.721851i	−0.00399946	−	0.0237987i
$921$		0			0
$922$	40.0968	−	31.5303i	1.32052	−	1.03839i
$923$	−4.69793	+	35.6843i	−0.154634	+	1.17456i
$924$		0			0
$925$	−26.1012	+	3.43628i	−0.858201	+	0.112984i
$926$	−0.275576	−	23.2228i	−0.00905600	−	0.763150i
$927$		0			0
$928$	−6.98306	+	20.1652i	−0.229230	+	0.661954i
$929$	−19.3635	−	33.5385i	−0.635294	−	1.10036i	−0.986453	−	0.164046i	$-0.947545\pi$
$929$	−19.3635	−	33.5385i	−0.635294	−	1.10036i	0.351158	−	0.936316i	$-0.385788\pi$
$930$		0			0
$931$	−1.68519	−	2.19618i	−0.0552298	−	0.0719769i
$932$	−16.3841	+	4.80959i	−0.536678	+	0.157543i
$933$		0			0
$934$	1.04361	+	7.26024i	0.0341481	+	0.237562i
$935$	0.975533	−	0.975533i	0.0319034	−	0.0319034i
$936$		0			0
$937$	12.1807	+	12.1807i	0.397927	+	0.397927i	0.877501	−	0.479574i	$-0.159209\pi$
$937$	12.1807	+	12.1807i	0.397927	+	0.397927i	−0.479574	+	0.877501i	$0.659209\pi$
$938$	−27.2444	+	36.3917i	−0.889562	+	1.18823i
$939$		0			0
$940$	0.410442	+	0.0441553i	0.0133872	+	0.00144019i
$941$	−26.8752	+	20.6221i	−0.876106	+	0.672260i	−0.945603	−	0.325322i	$-0.894527\pi$
$941$	−26.8752	+	20.6221i	−0.876106	+	0.672260i	0.0694971	+	0.997582i	$0.477861\pi$
$942$		0			0
$943$	21.0801	−	12.1706i	0.686463	−	0.396330i
$944$	14.1816	−	6.67925i	0.461572	−	0.217391i
$945$		0			0
$946$	−11.5800	+	11.8581i	−0.376498	+	0.385541i
$947$	−5.76891	−	43.8193i	−0.187465	−	1.42393i	−0.783707	−	0.621130i	$-0.786674\pi$
$947$	−5.76891	−	43.8193i	−0.187465	−	1.42393i	0.596243	−	0.802804i	$-0.296660\pi$
$948$		0			0
$949$	−80.4314	−	10.5890i	−2.61091	−	0.343733i
$950$	0.188390	−	1.57518i	0.00611216	−	0.0511055i
$951$		0			0
$952$	9.29703	−	40.3973i	0.301319	−	1.30928i
$953$	−6.18348	+	6.18348i	−0.200303	+	0.200303i	−0.800130	−	0.599827i	$-0.795236\pi$
$953$	−6.18348	+	6.18348i	−0.200303	+	0.200303i	0.599827	+	0.800130i	$0.295236\pi$
$954$		0			0
$955$	0.750829	−	0.311004i	0.0242963	−	0.0100638i
$956$	−42.6619	+	25.9998i	−1.37978	+	0.840893i
$957$		0			0
$958$	11.1735	−	19.8946i	0.361000	−	0.642766i
$959$	14.4950	−	25.1062i	0.468069	−	0.810720i
$960$		0			0
$961$	11.8846	+	20.5847i	0.383373	+	0.664022i
$962$	−38.6831	+	0.459037i	−1.24719	+	0.0147999i
$963$		0			0
$964$	−0.392145	−	16.5207i	−0.0126301	−	0.532097i
$965$	0.0839344	+	0.0644052i	0.00270194	+	0.00207328i
$966$		0			0
$967$	14.8481	+	55.4138i	0.477482	+	1.78199i	0.611760	+	0.791043i	$0.290462\pi$
$967$	14.8481	+	55.4138i	0.477482	+	1.78199i	−0.134278	+	0.990944i	$0.542872\pi$
$968$	18.7390	+	61.1414i	0.602295	+	1.96516i
$969$		0			0
$970$	−0.615506	−	0.460795i	−0.0197627	−	0.0147952i
$971$	−13.1162	−	31.6653i	−0.420918	−	1.01619i	−0.982077	−	0.188478i	$-0.939644\pi$
$971$	−13.1162	−	31.6653i	−0.420918	−	1.01619i	0.561159	−	0.827708i	$-0.310356\pi$
$972$		0			0
$973$	−64.6394	−	26.7745i	−2.07225	−	0.858352i
$974$	6.93551	+	1.77043i	0.222228	+	0.0567284i
$975$		0			0
$976$	−25.2537	−	29.8631i	−0.808352	−	0.955895i
$977$	−5.00482	−	2.88953i	−0.160118	−	0.0924443i	0.417800	−	0.908539i	$-0.362801\pi$
$977$	−5.00482	−	2.88953i	−0.160118	−	0.0924443i	−0.577918	+	0.816095i	$0.696135\pi$
$978$		0			0
$979$	−10.8015	−	82.0456i	−0.345218	−	2.62219i
$980$	0.711811	+	1.60934i	0.0227380	+	0.0514086i
$981$		0			0
$982$	20.8215	+	48.6274i	0.664442	+	1.55176i
$983$	−4.86554	+	18.1584i	−0.155187	+	0.579164i	0.843903	+	0.536496i	$0.180252\pi$
$983$	−4.86554	+	18.1584i	−0.155187	+	0.579164i	−0.999089	+	0.0426680i	$0.986414\pi$
$984$		0			0
$985$	−0.301305	−	1.12449i	−0.00960038	−	0.0358291i
$986$	13.9810	−	10.9940i	0.445247	−	0.350121i
$987$		0			0
$988$	0.549747	−	2.26542i	0.0174898	−	0.0720725i
$989$	2.80477	−	6.77132i	0.0891865	−	0.215315i
$990$		0			0
$991$	12.3377			0.391919			0.195960	−	0.980612i	$-0.437218\pi$
$991$	12.3377			0.391919			0.195960	+	0.980612i	$0.437218\pi$
$992$	8.37345	+	12.6993i	0.265857	+	0.403203i
$993$		0			0
$994$	−37.5916	−	21.1128i	−1.19233	−	0.669656i
$995$	0.848185	+	1.10538i	0.0268893	+	0.0350428i
$996$		0			0
$997$	18.1364	+	13.9166i	0.574386	+	0.440742i	0.854667	−	0.519176i	$-0.173761\pi$
$997$	18.1364	+	13.9166i	0.574386	+	0.440742i	−0.280282	+	0.959918i	$0.590428\pi$
$998$	−37.0977	−	14.8531i	−1.17431	−	0.470168i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bk.a.685.30		368
3.2	odd	2		288.2.bc.a.13.17	✓	368
9.2	odd	6		288.2.bc.a.205.15	yes	368
9.7	even	3	inner	864.2.bk.a.397.32		368
32.5	even	8	inner	864.2.bk.a.37.32		368
96.5	odd	8		288.2.bc.a.229.15	yes	368
288.101	odd	24		288.2.bc.a.133.17	yes	368
288.133	even	24	inner	864.2.bk.a.613.30		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.17	✓	368	3.2	odd	2
288.2.bc.a.133.17	yes	368	288.101	odd	24
288.2.bc.a.205.15	yes	368	9.2	odd	6
288.2.bc.a.229.15	yes	368	96.5	odd	8
864.2.bk.a.37.32		368	32.5	even	8	inner
864.2.bk.a.397.32		368	9.7	even	3	inner
864.2.bk.a.613.30		368	288.133	even	24	inner
864.2.bk.a.685.30		368	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bk (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.721590 + 1.21627i) q^{2} +(-0.958617 + 1.75529i) q^{4} +(0.00931719 - 0.0707711i) q^{5} +(4.24636 + 1.13781i) q^{7} +(-2.82664 + 0.100666i) q^{8} +O(q^{10})\)	\(q+(0.721590 + 1.21627i) q^{2} +(-0.958617 + 1.75529i) q^{4} +(0.00931719 - 0.0707711i) q^{5} +(4.24636 + 1.13781i) q^{7} +(-2.82664 + 0.100666i) q^{8} +(0.0927998 - 0.0397355i) q^{10} +(3.52920 - 4.59934i) q^{11} +(4.11755 - 3.15951i) q^{13} +(1.68025 + 5.98575i) q^{14} +(-2.16211 - 3.36531i) q^{16} +3.33381i q^{17} +(-0.207485 - 0.0859430i) q^{19} +(0.115292 + 0.0841967i) q^{20} +(8.14067 + 0.973616i) q^{22} +(-3.50193 + 0.938339i) q^{23} +(4.82471 + 1.29278i) q^{25} +(6.81399 + 2.72818i) q^{26} +(-6.06783 + 6.36289i) q^{28} +(-3.74015 + 0.492399i) q^{29} +(-1.34451 + 2.32876i) q^{31} +(2.53296 - 5.05807i) q^{32} +(-4.05481 + 2.40564i) q^{34} +(0.120088 - 0.289919i) q^{35} +(-4.86945 + 2.01699i) q^{37} +(-0.0451891 - 0.314373i) q^{38} +(-0.0192121 + 0.200982i) q^{40} +(-6.48519 + 1.73770i) q^{41} +(-1.23067 + 1.60384i) q^{43} +(4.69004 + 10.6038i) q^{44} +(-3.66823 - 3.58219i) q^{46} +(2.50417 - 1.44579i) q^{47} +(10.6748 + 6.16311i) q^{49} +(1.90910 + 6.80099i) q^{50} +(1.59871 + 10.2563i) q^{52} +(-1.65728 - 4.00104i) q^{53} +(-0.292618 - 0.292618i) q^{55} +(-12.1175 - 2.78871i) q^{56} +(-3.29774 - 4.19371i) q^{58} +(-0.511525 + 3.88542i) q^{59} +(9.69374 - 1.27620i) q^{61} +(-3.80259 + 0.0451238i) q^{62} +(7.97973 - 0.569089i) q^{64} +(-0.185238 - 0.320841i) q^{65} +(4.45132 + 5.80107i) q^{67} +(-5.85181 - 3.19585i) q^{68} +(0.439273 - 0.0631427i) q^{70} +(-4.90367 + 4.90367i) q^{71} +(-11.0527 - 11.0527i) q^{73} +(-5.96694 - 4.46711i) q^{74} +(0.349754 - 0.281810i) q^{76} +(20.2195 - 15.5149i) q^{77} +(-10.2828 + 5.93677i) q^{79} +(-0.258311 + 0.121659i) q^{80} +(-6.79316 - 6.63383i) q^{82} +(1.04665 + 7.95008i) q^{83} +(0.235937 + 0.0310617i) q^{85} +(-2.83874 - 0.339510i) q^{86} +(-9.51277 + 13.3559i) q^{88} +(10.0935 - 10.0935i) q^{89} +(21.0795 - 8.73143i) q^{91} +(1.70995 - 7.04642i) q^{92} +(3.56545 + 2.00248i) q^{94} +(-0.00801545 + 0.0138832i) q^{95} +(-3.80827 - 6.59611i) q^{97} +(0.206843 + 17.4307i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Introduction

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