LMFDB - Embedded newform 864.2.bn.a.35.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (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			35.40
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31275 - 0.526004i) q^{2} +(1.44664 - 1.38103i) q^{4} +(-1.23257 - 0.945783i) q^{5} +(-4.39511 + 1.17766i) q^{7} +(1.17266 - 2.57388i) q^{8} +O(q^{10})$	\(q+(1.31275 - 0.526004i) q^{2} +(1.44664 - 1.38103i) q^{4} +(-1.23257 - 0.945783i) q^{5} +(-4.39511 + 1.17766i) q^{7} +(1.17266 - 2.57388i) q^{8} +(-2.11554 - 0.593244i) q^{10} +(0.647702 - 4.91978i) q^{11} +(-1.11076 + 0.146234i) q^{13} +(-5.15023 + 3.85782i) q^{14} +(0.185536 - 3.99569i) q^{16} -4.08402 q^{17} +(2.37867 + 0.985278i) q^{19} +(-3.08923 + 0.334001i) q^{20} +(-1.73755 - 6.79916i) q^{22} +(-1.43586 + 5.35870i) q^{23} +(-0.669376 - 2.49815i) q^{25} +(-1.38123 + 0.776232i) q^{26} +(-4.73175 + 7.77341i) q^{28} +(-5.76810 - 7.51713i) q^{29} +(0.512694 - 0.296004i) q^{31} +(-1.85819 - 5.34295i) q^{32} +(-5.36130 + 2.14821i) q^{34} +(6.53108 + 2.70526i) q^{35} +(-1.95073 - 4.70947i) q^{37} +(3.64087 + 0.0422366i) q^{38} +(-3.87971 + 2.06341i) q^{40} +(4.67789 + 1.25344i) q^{41} +(-2.65553 - 0.349608i) q^{43} +(-5.85736 - 8.01165i) q^{44} +(0.933768 + 7.78992i) q^{46} +(2.20325 + 1.27205i) q^{47} +(11.8679 - 6.85192i) q^{49} +(-2.19276 - 2.92735i) q^{50} +(-1.40491 + 1.74553i) q^{52} +(2.74153 + 6.61863i) q^{53} +(-5.45138 + 5.45138i) q^{55} +(-2.12278 + 12.6935i) q^{56} +(-11.5261 - 6.83409i) q^{58} +(0.387332 - 0.504781i) q^{59} +(9.82581 - 7.53961i) q^{61} +(0.517341 - 0.658259i) q^{62} +(-5.24975 - 6.03656i) q^{64} +(1.50739 + 0.870292i) q^{65} +(9.52916 - 1.25454i) q^{67} +(-5.90810 + 5.64013i) q^{68} +(9.99667 + 0.115968i) q^{70} +(1.64564 - 1.64564i) q^{71} +(-0.361810 - 0.361810i) q^{73} +(-5.03802 - 5.15628i) q^{74} +(4.80178 - 1.85966i) q^{76} +(2.94714 + 22.3857i) q^{77} +(-3.24123 + 5.61397i) q^{79} +(-4.00774 + 4.74949i) q^{80} +(6.80022 - 0.815134i) q^{82} +(7.37393 + 9.60989i) q^{83} +(5.03383 + 3.86259i) q^{85} +(-3.66996 + 0.937872i) q^{86} +(-11.9034 - 7.43633i) q^{88} +(-2.45638 - 2.45638i) q^{89} +(4.70968 - 1.95082i) q^{91} +(5.32333 + 9.73507i) q^{92} +(3.56142 + 0.510966i) q^{94} +(-2.00002 - 3.46413i) q^{95} +(8.51749 - 14.7527i) q^{97} +(11.9755 - 15.2374i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.31275	−	0.526004i	0.928256	−	0.371941i
$2$	1.31275	−	0.526004i	0.928256	−	0.371941i
$3$		0			0
$3$		0			0
$4$	1.44664	−	1.38103i	0.723320	−	0.690513i
$5$	−1.23257	−	0.945783i	−0.551221	−	0.422967i	0.295236	−	0.955425i	$-0.404602\pi$
$5$	−1.23257	−	0.945783i	−0.551221	−	0.422967i	−0.846457	+	0.532458i	$0.821269\pi$
$6$		0			0
$7$	−4.39511	+	1.17766i	−1.66119	+	0.445116i	−0.962716	−	0.270516i	$-0.912806\pi$
$7$	−4.39511	+	1.17766i	−1.66119	+	0.445116i	−0.698478	+	0.715631i	$0.746139\pi$
$8$	1.17266	−	2.57388i	0.414597	−	0.910005i
$9$		0			0
$10$	−2.11554	−	0.593244i	−0.668993	−	0.187600i
$11$	0.647702	−	4.91978i	0.195289	−	1.48337i	−0.560280	−	0.828303i	$-0.689307\pi$
$11$	0.647702	−	4.91978i	0.195289	−	1.48337i	0.755570	−	0.655068i	$-0.227360\pi$
$12$		0			0
$13$	−1.11076	+	0.146234i	−0.308069	+	0.0405580i	−0.282976	−	0.959127i	$-0.591322\pi$
$13$	−1.11076	+	0.146234i	−0.308069	+	0.0405580i	−0.0250932	+	0.999685i	$0.507988\pi$
$14$	−5.15023	+	3.85782i	−1.37646	+	1.03105i
$15$		0			0
$16$	0.185536	−	3.99569i	0.0463840	−	0.998924i
$17$	−4.08402			−0.990519			−0.495260	−	0.868745i	$-0.664927\pi$
$17$	−4.08402			−0.990519			−0.495260	+	0.868745i	$0.664927\pi$
$18$		0			0
$19$	2.37867	+	0.985278i	0.545705	+	0.226038i	0.638466	−	0.769650i	$-0.279569\pi$
$19$	2.37867	+	0.985278i	0.545705	+	0.226038i	−0.0927611	+	0.995688i	$0.529569\pi$
$20$	−3.08923	+	0.334001i	−0.690773	+	0.0746848i
$21$		0			0
$22$	−1.73755	−	6.79916i	−0.370447	−	1.44958i
$23$	−1.43586	+	5.35870i	−0.299397	+	1.11737i	0.638264	+	0.769817i	$0.279653\pi$
$23$	−1.43586	+	5.35870i	−0.299397	+	1.11737i	−0.937662	+	0.347549i	$0.887014\pi$
$24$		0			0
$25$	−0.669376	−	2.49815i	−0.133875	−	0.499629i
$26$	−1.38123	+	0.776232i	−0.270882	+	0.152232i
$27$		0			0
$28$	−4.73175	+	7.77341i	−0.894217	+	1.46904i
$29$	−5.76810	−	7.51713i	−1.07111	−	1.39590i	−0.912752	−	0.408514i	$-0.866047\pi$
$29$	−5.76810	−	7.51713i	−1.07111	−	1.39590i	−0.158356	−	0.987382i	$-0.550619\pi$
$30$		0			0
$31$	0.512694	−	0.296004i	0.0920825	−	0.0531639i	−0.453252	−	0.891383i	$-0.649736\pi$
$31$	0.512694	−	0.296004i	0.0920825	−	0.0531639i	0.545334	+	0.838219i	$0.316403\pi$
$32$	−1.85819	−	5.34295i	−0.328484	−	0.944509i
$33$		0			0
$34$	−5.36130	+	2.14821i	−0.919456	+	0.368415i
$35$	6.53108	+	2.70526i	1.10395	+	0.457273i
$36$		0			0
$37$	−1.95073	−	4.70947i	−0.320698	−	0.774233i	−0.999214	−	0.0396471i	$-0.987377\pi$
$37$	−1.95073	−	4.70947i	−0.320698	−	0.774233i	0.678516	−	0.734586i	$-0.262623\pi$
$38$	3.64087	+	0.0422366i	0.590627	+	0.00685168i
$39$		0			0
$40$	−3.87971	+	2.06341i	−0.613437	+	0.326253i
$41$	4.67789	+	1.25344i	0.730563	+	0.195754i	0.604880	−	0.796317i	$-0.293221\pi$
$41$	4.67789	+	1.25344i	0.730563	+	0.195754i	0.125683	+	0.992070i	$0.459888\pi$
$42$		0			0
$43$	−2.65553	−	0.349608i	−0.404965	−	0.0533147i	−0.0747075	−	0.997205i	$-0.523802\pi$
$43$	−2.65553	−	0.349608i	−0.404965	−	0.0533147i	−0.330258	+	0.943891i	$0.607136\pi$
$44$	−5.85736	−	8.01165i	−0.883030	−	1.20780i
$45$		0			0
$46$	0.933768	+	7.78992i	0.137677	+	1.14856i
$47$	2.20325	+	1.27205i	0.321377	+	0.185547i	0.652006	−	0.758214i	$-0.273928\pi$
$47$	2.20325	+	1.27205i	0.321377	+	0.185547i	−0.330629	+	0.943761i	$0.607261\pi$
$48$		0			0
$49$	11.8679	−	6.85192i	1.69541	−	0.978846i
$50$	−2.19276	−	2.92735i	−0.310103	−	0.413990i
$51$		0			0
$52$	−1.40491	+	1.74553i	−0.194827	+	0.242062i
$53$	2.74153	+	6.61863i	0.376578	+	0.909139i	0.992602	+	0.121412i	$0.0387423\pi$
$53$	2.74153	+	6.61863i	0.376578	+	0.909139i	−0.616024	+	0.787727i	$0.711258\pi$
$54$		0			0
$55$	−5.45138	+	5.45138i	−0.735064	+	0.735064i
$56$	−2.12278	+	12.6935i	−0.283668	+	1.69624i
$57$		0			0
$58$	−11.5261	−	6.83409i	−1.51345	−	0.897360i
$59$	0.387332	−	0.504781i	0.0504264	−	0.0657170i	−0.767459	−	0.641098i	$-0.778479\pi$
$59$	0.387332	−	0.504781i	0.0504264	−	0.0657170i	0.817886	+	0.575381i	$0.195146\pi$
$60$		0			0
$61$	9.82581	−	7.53961i	1.25807	−	0.965348i	0.258066	−	0.966127i	$-0.416915\pi$
$61$	9.82581	−	7.53961i	1.25807	−	0.965348i	1.00000		0.000779171i	$0.000248018\pi$
$62$	0.517341	−	0.658259i	0.0657024	−	0.0835990i
$63$		0			0
$64$	−5.24975	−	6.03656i	−0.656219	−	0.754570i
$65$	1.50739	+	0.870292i	0.186969	+	0.107946i
$66$		0			0
$67$	9.52916	−	1.25454i	1.16417	−	0.153266i	0.476424	−	0.879216i	$-0.341933\pi$
$67$	9.52916	−	1.25454i	1.16417	−	0.153266i	0.687748	+	0.725949i	$0.258599\pi$
$68$	−5.90810	+	5.64013i	−0.716463	+	0.683966i
$69$		0			0
$70$	9.99667	+	0.115968i	1.19483	+	0.0138609i
$71$	1.64564	−	1.64564i	0.195301	−	0.195301i	−0.602681	−	0.797982i	$-0.705901\pi$
$71$	1.64564	−	1.64564i	0.195301	−	0.195301i	0.797982	+	0.602681i	$0.205901\pi$
$72$		0			0
$73$	−0.361810	−	0.361810i	−0.0423466	−	0.0423466i	0.685616	−	0.727963i	$-0.259533\pi$
$73$	−0.361810	−	0.361810i	−0.0423466	−	0.0423466i	−0.727963	+	0.685616i	$0.759533\pi$
$74$	−5.03802	−	5.15628i	−0.585658	−	0.599406i
$75$		0			0
$76$	4.80178	−	1.85966i	0.550802	−	0.213318i
$77$	2.94714	+	22.3857i	0.335858	+	2.55109i
$78$		0			0
$79$	−3.24123	+	5.61397i	−0.364667	+	0.631622i	−0.988723	−	0.149758i	$-0.952150\pi$
$79$	−3.24123	+	5.61397i	−0.364667	+	0.631622i	0.624056	+	0.781380i	$0.285484\pi$
$80$	−4.00774	+	4.74949i	−0.448079	+	0.531009i
$81$		0			0
$82$	6.80022	−	0.815134i	0.750959	−	0.0900165i
$83$	7.37393	+	9.60989i	0.809394	+	1.05482i	0.997358	+	0.0726465i	$0.0231445\pi$
$83$	7.37393	+	9.60989i	0.809394	+	1.05482i	−0.187964	+	0.982176i	$0.560189\pi$
$84$		0			0
$85$	5.03383	+	3.86259i	0.545995	+	0.418957i
$86$	−3.66996	+	0.937872i	−0.395741	+	0.101133i
$87$		0			0
$88$	−11.9034	−	7.43633i	−1.26891	−	0.792715i
$89$	−2.45638	−	2.45638i	−0.260376	−	0.260376i	0.564831	−	0.825207i	$-0.308941\pi$
$89$	−2.45638	−	2.45638i	−0.260376	−	0.260376i	−0.825207	+	0.564831i	$0.808941\pi$
$90$		0			0
$91$	4.70968	−	1.95082i	0.493709	−	0.204501i
$92$	5.32333	+	9.73507i	0.554996	+	1.01495i
$93$		0			0
$94$	3.56142	+	0.510966i	0.367333	+	0.0527021i
$95$	−2.00002	−	3.46413i	−0.205197	−	0.355412i
$96$		0			0
$97$	8.51749	−	14.7527i	0.864820	−	1.49791i	−0.00240483	−	0.999997i	$-0.500765\pi$
$97$	8.51749	−	14.7527i	0.864820	−	1.49791i	0.867225	−	0.497916i	$-0.165901\pi$
$98$	11.9755	−	15.2374i	1.20970	−	1.53921i
$99$		0			0
$100$	−4.41835	−	2.68949i	−0.441835	−	0.268949i
$101$	0.526559	−	3.99961i	0.0523945	−	0.397976i	−0.945073	−	0.326858i	$-0.894010\pi$
$101$	0.526559	−	3.99961i	0.0523945	−	0.397976i	0.997468	−	0.0711178i	$-0.0226566\pi$
$102$		0			0
$103$	−4.11044	+	15.3404i	−0.405013	+	1.51153i	0.399018	+	0.916943i	$0.369351\pi$
$103$	−4.11044	+	15.3404i	−0.405013	+	1.51153i	−0.804031	+	0.594587i	$0.797316\pi$
$104$	−0.926148	+	3.03044i	−0.0908163	+	0.297160i
$105$		0			0
$106$	7.08038	+	7.24658i	0.687707	+	0.703850i
$107$	−2.60587	+	1.07939i	−0.251919	+	0.104348i	−0.505070	−	0.863079i	$-0.668533\pi$
$107$	−2.60587	+	1.07939i	−0.251919	+	0.104348i	0.253150	+	0.967427i	$0.418533\pi$
$108$		0			0
$109$	−0.946606	+	2.28531i	−0.0906684	+	0.218893i	−0.962708	−	0.270542i	$-0.912797\pi$
$109$	−0.946606	+	2.28531i	−0.0906684	+	0.218893i	0.872040	+	0.489435i	$0.162797\pi$
$110$	−4.28887	+	10.0238i	−0.408928	+	0.955729i
$111$		0			0
$112$	3.89014	+	17.7800i	0.367584	+	1.68005i
$113$	−8.13956	−	14.0981i	−0.765705	−	1.32624i	−0.939873	−	0.341525i	$-0.889057\pi$
$113$	−8.13956	−	14.0981i	−0.765705	−	1.32624i	0.174167	−	0.984716i	$-0.444277\pi$
$114$		0			0
$115$	6.83796	−	5.24695i	0.637643	−	0.489281i
$116$	−18.7257	−	2.90869i	−1.73864	−	0.270065i
$117$		0			0
$118$	0.242955	−	0.866392i	0.0223658	−	0.0797578i
$119$	17.9497	−	4.80960i	1.64544	−	0.440896i
$120$		0			0
$121$	−13.1596	−	3.52610i	−1.19633	−	0.320554i
$122$	8.93300	−	15.0661i	0.808756	−	1.36402i
$123$		0			0
$124$	0.332894	−	1.13625i	0.0298948	−	0.102039i
$125$	−4.51037	+	10.8890i	−0.403420	+	0.973942i
$126$		0			0
$127$		−	21.9679i		−	1.94934i	−0.223651	−	0.974669i	$-0.571798\pi$
$127$		−	21.9679i		−	1.94934i	0.223651	−	0.974669i	$-0.428202\pi$
$128$	−10.0669	−	5.16313i	−0.889795	−	0.456360i
$129$		0			0
$130$	2.43661	+	0.349586i	0.213705	+	0.0306607i
$131$	−0.425820	−	3.23442i	−0.0372040	−	0.282593i	−0.999927	−	0.0121025i	$-0.996148\pi$
$131$	−0.425820	−	3.23442i	−0.0372040	−	0.282593i	0.962723	−	0.270490i	$-0.0871858\pi$
$132$		0			0
$133$	−11.6148	−	1.52912i	−1.00713	−	0.132592i
$134$	11.8495	−	6.65927i	1.02364	−	0.575274i
$135$		0			0
$136$	−4.78915	+	10.5118i	−0.410666	+	0.901378i
$137$	0.899631	+	3.35747i	0.0768606	+	0.286848i	0.993649	−	0.112526i	$-0.0358942\pi$
$137$	0.899631	+	3.35747i	0.0768606	+	0.286848i	−0.916788	+	0.399374i	$0.869228\pi$
$138$		0			0
$139$	9.94055	−	12.9548i	0.843146	−	1.09881i	−0.150759	−	0.988571i	$-0.548172\pi$
$139$	9.94055	−	12.9548i	0.843146	−	1.09881i	0.993905	−	0.110239i	$-0.0351617\pi$
$140$	13.1842	−	5.10605i	1.11427	−	0.431540i
$141$		0			0
$142$	1.29471	−	3.02593i	0.108649	−	0.253930i
$143$			5.55941i			0.464901i
$144$		0			0
$145$			14.7207i			1.22249i
$146$	−0.665280	−	0.284654i	−0.0550590	−	0.0235581i
$147$		0			0
$148$	−9.32590	−	4.11891i	−0.766585	−	0.338572i
$149$	6.06859	−	7.90874i	0.497158	−	0.647910i	−0.475619	−	0.879651i	$-0.657776\pi$
$149$	6.06859	−	7.90874i	0.497158	−	0.647910i	0.972777	+	0.231742i	$0.0744425\pi$
$150$		0			0
$151$	1.15942	+	4.32703i	0.0943526	+	0.352129i	0.996921	−	0.0784188i	$-0.0249871\pi$
$151$	1.15942	+	4.32703i	0.0943526	+	0.352129i	−0.902568	+	0.430548i	$0.858320\pi$
$152$	5.32536	−	4.96703i	0.431944	−	0.402880i
$153$		0			0
$154$	15.6439	+	27.8368i	1.26062	+	2.24315i
$155$	−0.911885	−	0.120052i	−0.0732444	−	0.00964281i
$156$		0			0
$157$	1.01101	+	7.67935i	0.0806870	+	0.612879i	0.983242	+	0.182305i	$0.0583557\pi$
$157$	1.01101	+	7.67935i	0.0806870	+	0.612879i	−0.902555	+	0.430574i	$0.858311\pi$
$158$	−1.30196	+	9.07466i	−0.103579	+	0.721941i
$159$		0			0
$160$	−2.76293	+	8.34299i	−0.218429	+	0.659572i
$161$		−	25.2430i		−	1.98943i
$162$		0			0
$163$	−4.51520	+	10.9007i	−0.353658	+	0.853806i	0.642504	+	0.766282i	$0.277895\pi$
$163$	−4.51520	+	10.9007i	−0.353658	+	0.853806i	−0.996162	+	0.0875240i	$0.972105\pi$
$164$	8.49825	−	4.64701i	0.663602	−	0.362871i
$165$		0			0
$166$	14.7350	+	8.73670i	1.14366	+	0.678099i
$167$	−0.875847	−	0.234682i	−0.0677751	−	0.0181603i	0.224772	−	0.974411i	$-0.427836\pi$
$167$	−0.875847	−	0.234682i	−0.0677751	−	0.0181603i	−0.292547	+	0.956251i	$0.594503\pi$
$168$		0			0
$169$	−11.3446	+	3.03979i	−0.872664	+	0.233830i
$170$	8.63991	+	2.42282i	0.662651	+	0.185822i
$171$		0			0
$172$	−4.32442	+	3.16160i	−0.329734	+	0.241070i
$173$	0.836588	−	0.641936i	0.0636046	−	0.0488055i	−0.576470	−	0.817118i	$-0.695570\pi$
$173$	0.836588	−	0.641936i	0.0636046	−	0.0488055i	0.640074	+	0.768313i	$0.278904\pi$
$174$		0			0
$175$	5.88396	+	10.1913i	0.444785	+	0.770391i
$176$	−19.5378	−	3.50082i	−1.47272	−	0.263884i
$177$		0			0
$178$	−4.51669	−	1.93256i	−0.338540	−	0.144851i
$179$	−8.10504	+	19.5673i	−0.605799	+	1.46253i	0.261730	+	0.965141i	$0.415707\pi$
$179$	−8.10504	+	19.5673i	−0.605799	+	1.46253i	−0.867529	+	0.497387i	$0.834293\pi$
$180$		0			0
$181$	4.74472	−	1.96533i	0.352672	−	0.146082i	−0.199312	−	0.979936i	$-0.563871\pi$
$181$	4.74472	−	1.96533i	0.352672	−	0.146082i	0.551984	+	0.833854i	$0.313871\pi$
$182$	5.15652	−	5.03825i	0.382226	−	0.373460i
$183$		0			0
$184$	12.1089	+	9.97965i	0.892680	+	0.735710i
$185$	−2.04973	+	7.64971i	−0.150699	+	0.562418i
$186$		0			0
$187$	−2.64523	+	20.0925i	−0.193438	+	1.46931i
$188$	4.94404	−	1.20255i	0.360581	−	0.0877050i
$189$		0			0
$190$	−4.44767	−	3.49553i	−0.322668	−	0.253592i
$191$	2.81155	−	4.86975i	0.203437	−	0.352363i	−0.746197	−	0.665725i	$-0.768122\pi$
$191$	2.81155	−	4.86975i	0.203437	−	0.352363i	0.949634	+	0.313363i	$0.101456\pi$
$192$		0			0
$193$	0.551350	+	0.954966i	0.0396870	+	0.0687399i	0.885187	−	0.465236i	$-0.154031\pi$
$193$	0.551350	+	0.954966i	0.0396870	+	0.0687399i	−0.845500	+	0.533976i	$0.820697\pi$
$194$	3.42137	−	23.8469i	0.245640	−	1.71211i
$195$		0			0
$196$	7.70587	−	26.3021i	0.550419	−	1.87872i
$197$	−7.02701	+	2.91068i	−0.500653	+	0.207377i	−0.618695	−	0.785631i	$-0.712338\pi$
$197$	−7.02701	+	2.91068i	−0.500653	+	0.207377i	0.118042	+	0.993009i	$0.462338\pi$
$198$		0			0
$199$	1.84792	+	1.84792i	0.130996	+	0.130996i	0.769565	−	0.638569i	$-0.220473\pi$
$199$	1.84792	+	1.84792i	0.130996	+	0.130996i	−0.638569	+	0.769565i	$0.720473\pi$
$200$	−7.21489	−	1.20657i	−0.510170	−	0.0853175i
$201$		0			0
$202$	−1.41257	−	5.52747i	−0.0993879	−	0.388911i
$203$	34.2040	+	26.2457i	2.40065	+	1.84209i
$204$		0			0
$205$	−4.58034	−	5.96921i	−0.319905	−	0.416908i
$206$	2.67310	+	22.3002i	0.186243	+	1.55373i
$207$		0			0
$208$	0.378221	+	4.46538i	0.0262249	+	0.309619i
$209$	6.38803	−	11.0644i	0.441869	−	0.765340i
$210$		0			0
$211$	0.141909	+	1.07790i	0.00976940	+	0.0742060i	0.995635	−	0.0933318i	$-0.0297517\pi$
$211$	0.141909	+	1.07790i	0.00976940	+	0.0742060i	−0.985866	+	0.167538i	$0.946418\pi$
$212$	13.1065	+	5.78866i	0.900159	+	0.397567i
$213$		0			0
$214$	−2.85311	+	2.78767i	−0.195034	+	0.190561i
$215$	2.94247	+	2.94247i	0.200675	+	0.200675i
$216$		0			0
$217$	−1.90475	+	1.90475i	−0.129303	+	0.129303i
$218$	−0.0405788	+	3.49796i	−0.00274834	+	0.236912i
$219$		0			0
$220$	−0.357690	+	15.4147i	−0.0241155	+	1.03926i
$221$	4.53635	−	0.597222i	0.305148	−	0.0401735i
$222$		0			0
$223$	−5.00046	−	2.88701i	−0.334855	−	0.193329i	0.323139	−	0.946351i	$-0.395262\pi$
$223$	−5.00046	−	2.88701i	−0.334855	−	0.193329i	−0.657995	+	0.753023i	$0.728595\pi$
$224$	14.4591	+	21.2945i	0.966092	+	1.42280i
$225$		0			0
$226$	−18.1009	−	14.2259i	−1.20405	−	0.946294i
$227$	−4.88016	+	3.74468i	−0.323908	+	0.248543i	−0.757896	−	0.652375i	$-0.773773\pi$
$227$	−4.88016	+	3.74468i	−0.323908	+	0.248543i	0.433988	+	0.900918i	$0.357106\pi$
$228$		0			0
$229$	9.03017	−	11.7684i	0.596731	−	0.777675i	−0.393166	−	0.919468i	$-0.628620\pi$
$229$	9.03017	−	11.7684i	0.596731	−	0.777675i	0.989896	+	0.141793i	$0.0452868\pi$
$230$	6.21664	−	10.4847i	0.409913	−	0.691344i
$231$		0			0
$232$	−26.1122	+	6.03140i	−1.71435	+	0.395981i
$233$	14.8047	−	14.8047i	0.969888	−	0.969888i	−0.0296721	−	0.999560i	$-0.509446\pi$
$233$	14.8047	−	14.8047i	0.969888	−	0.969888i	0.999560	+	0.0296721i	$0.00944630\pi$
$234$		0			0
$235$	−1.51258	−	3.65168i	−0.0986695	−	0.238209i
$236$	−0.136785	−	1.26515i	−0.00890398	−	0.0823545i
$237$		0			0
$238$	21.0336	−	15.7554i	1.36341	−	1.02127i
$239$	−5.86397	+	3.38557i	−0.379309	+	0.218994i	−0.677518	−	0.735507i	$-0.736944\pi$
$239$	−5.86397	+	3.38557i	−0.379309	+	0.218994i	0.298209	+	0.954501i	$0.403611\pi$
$240$		0			0
$241$	−25.0688	−	14.4735i	−1.61482	−	0.932318i	−0.988231	−	0.152970i	$-0.951116\pi$
$241$	−25.0688	−	14.4735i	−1.61482	−	0.932318i	−0.626592	−	0.779348i	$-0.715551\pi$
$242$	−19.1300	+	2.29309i	−1.22972	+	0.147406i
$243$		0			0
$244$	3.80202	−	24.4768i	0.243399	−	1.56697i
$245$	−21.1084	−	2.77897i	−1.34857	−	0.177542i
$246$		0			0
$247$	−2.78621	−	0.746563i	−0.177282	−	0.0475027i
$248$	−0.160666	−	1.66673i	−0.0102023	−	0.105837i
$249$		0			0
$250$	−0.193349	+	16.6670i	−0.0122285	+	1.05412i
$251$	1.10999	+	2.67976i	0.0700622	+	0.169145i	0.955032	−	0.296504i	$-0.0958208\pi$
$251$	1.10999	+	2.67976i	0.0700622	+	0.169145i	−0.884969	+	0.465649i	$0.845821\pi$
$252$		0			0
$253$	25.4337	+	10.5350i	1.59900	+	0.662327i
$254$	−11.5552	−	28.8385i	−0.725039	−	1.80949i
$255$		0			0
$256$	−15.9312	−	1.48269i	−0.995697	−	0.0926682i
$257$	19.8010	−	11.4321i	1.23515	−	0.713115i	0.267052	−	0.963682i	$-0.413950\pi$
$257$	19.8010	−	11.4321i	1.23515	−	0.713115i	0.968099	+	0.250567i	$0.0806170\pi$
$258$		0			0
$259$	14.1198	+	18.4013i	0.877364	+	1.14340i
$260$	3.38255	−	0.822745i	0.209777	−	0.0510245i
$261$		0			0
$262$	−2.26031	−	4.02201i	−0.139643	−	0.248481i
$263$	−0.158349	−	0.590968i	−0.00976425	−	0.0364407i	0.960872	−	0.276993i	$-0.0893380\pi$
$263$	−0.158349	−	0.590968i	−0.00976425	−	0.0364407i	−0.970636	+	0.240553i	$0.922671\pi$
$264$		0			0
$265$	2.88067	−	10.7508i	0.176958	−	0.660417i
$266$	−16.0517	+	4.10209i	−0.984196	+	0.251515i
$267$		0			0
$268$	12.0527	−	14.9749i	0.736237	−	0.914737i
$269$	−1.42907	−	0.591941i	−0.0871321	−	0.0360913i	0.338692	−	0.940897i	$-0.390016\pi$
$269$	−1.42907	−	0.591941i	−0.0871321	−	0.0360913i	−0.425824	+	0.904806i	$0.640016\pi$
$270$		0			0
$271$	12.8060			0.777912			0.388956	−	0.921256i	$-0.372836\pi$
$271$	12.8060			0.777912			0.388956	+	0.921256i	$0.372836\pi$
$272$	−0.757732	+	16.3185i	−0.0459443	+	0.989453i
$273$		0			0
$274$	2.94703	+	3.93432i	0.178037	+	0.237681i
$275$	−12.7239	+	1.67513i	−0.767280	+	0.101014i
$276$		0			0
$277$	−1.37192	+	10.4208i	−0.0824309	+	0.626125i	0.899505	+	0.436911i	$0.143927\pi$
$277$	−1.37192	+	10.4208i	−0.0824309	+	0.626125i	−0.981936	+	0.189214i	$0.939406\pi$
$278$	6.23523	−	22.2352i	0.373964	−	1.33358i
$279$		0			0
$280$	14.6217	−	13.6379i	0.873816	−	0.815020i
$281$	−7.83178	+	2.09852i	−0.467205	+	0.125187i	−0.484738	−	0.874659i	$-0.661085\pi$
$281$	−7.83178	+	2.09852i	−0.467205	+	0.125187i	0.0175337	+	0.999846i	$0.494419\pi$
$282$		0			0
$283$	−9.18149	−	7.04520i	−0.545783	−	0.418794i	0.298723	−	0.954340i	$-0.403439\pi$
$283$	−9.18149	−	7.04520i	−0.545783	−	0.418794i	−0.844506	+	0.535546i	$0.820106\pi$
$284$	0.107978	−	4.65332i	0.00640731	−	0.276124i
$285$		0			0
$286$	2.92427	+	7.29813i	0.172916	+	0.431547i
$287$	−22.0359			−1.30074
$288$		0			0
$289$	−0.320814			−0.0188714
$290$	7.74316	+	19.3247i	0.454694	+	1.13478i
$291$		0			0
$292$	−1.02308	−	0.0237400i	−0.0598711	−	0.00138928i
$293$	2.29923	+	1.76426i	0.134322	+	0.103069i	0.673737	−	0.738971i	$-0.264688\pi$
$293$	2.29923	+	1.76426i	0.134322	+	0.103069i	−0.539415	+	0.842040i	$0.681355\pi$
$294$		0			0
$295$	−0.954827	+	0.255845i	−0.0555922	+	0.0148959i
$296$	−14.4092	−	0.501649i	−0.837516	−	0.0291577i
$297$		0			0
$298$	3.80653	−	13.5743i	0.220507	−	0.786340i
$299$	0.811268	−	6.16219i	0.0469168	−	0.356369i
$300$		0			0
$301$	12.0831	−	1.59077i	0.696457	−	0.0916903i
$302$	3.79807	+	5.07046i	0.218554	+	0.291772i
$303$		0			0
$304$	4.37820	−	9.32165i	0.251107	−	0.534633i
$305$	−19.2418			−1.10178
$306$		0			0
$307$	−25.8180	−	10.6941i	−1.47351	−	0.610347i	−0.505852	−	0.862620i	$-0.668822\pi$
$307$	−25.8180	−	10.6941i	−1.47351	−	0.610347i	−0.967656	+	0.252273i	$0.918822\pi$
$308$	35.1787	+	28.3141i	2.00450	+	1.61334i
$309$		0			0
$310$	−1.26023	+	0.322056i	−0.0715761	+	0.0182916i
$311$	8.69628	−	32.4549i	0.493121	−	1.84035i	−0.0471908	−	0.998886i	$-0.515027\pi$
$311$	8.69628	−	32.4549i	0.493121	−	1.84035i	0.540311	−	0.841465i	$-0.318306\pi$
$312$		0			0
$313$	3.01691	+	11.2593i	0.170526	+	0.636412i	0.997271	+	0.0738342i	$0.0235236\pi$
$313$	3.01691	+	11.2593i	0.170526	+	0.636412i	−0.826745	+	0.562578i	$0.809810\pi$
$314$	5.36657	+	9.54930i	0.302853	+	0.538898i
$315$		0			0
$316$	3.06415	+	12.5976i	0.172372	+	0.708672i
$317$	−15.9632	−	20.8036i	−0.896582	−	1.16845i	−0.985033	−	0.172368i	$-0.944858\pi$
$317$	−15.9632	−	20.8036i	−0.896582	−	1.16845i	0.0884501	−	0.996081i	$-0.471809\pi$
$318$		0			0
$319$	−40.7187	+	23.5089i	−2.27981	+	1.31625i
$320$	0.761401	+	12.4056i	0.0425636	+	0.693494i
$321$		0			0
$322$	−13.2779	−	33.1378i	−0.739950	−	1.84670i
$323$	−9.71454	−	4.02389i	−0.540531	−	0.223895i
$324$		0			0
$325$	1.10883	+	2.67695i	0.0615068	+	0.148491i
$326$	−0.193556	+	16.6849i	−0.0107201	+	0.924091i
$327$		0			0
$328$	8.71176	−	10.5705i	0.481026	−	0.583658i
$329$	−11.1816	−	2.99609i	−0.616460	−	0.165180i
$330$		0			0
$331$	33.4239	+	4.40034i	1.83714	+	0.241864i	0.967689	−	0.252149i	$-0.0811372\pi$
$331$	33.4239	+	4.40034i	1.83714	+	0.241864i	0.869454	+	0.494013i	$0.164471\pi$
$332$	23.9389	+	3.71847i	1.31382	+	0.204078i
$333$		0			0
$334$	−1.27321	+	0.152619i	−0.0696672	+	0.00835092i
$335$	−12.9319	−	7.46621i	−0.706543	−	0.407923i
$336$		0			0
$337$	−2.73282	+	1.57779i	−0.148866	+	0.0859478i	−0.572583	−	0.819847i	$-0.694058\pi$
$337$	−2.73282	+	1.57779i	−0.148866	+	0.0859478i	0.423717	+	0.905795i	$0.360725\pi$
$338$	−13.2938	+	9.95781i	−0.723086	+	0.541633i
$339$		0			0
$340$	12.6165	−	1.36406i	0.684224	−	0.0739768i
$341$	−1.12420	−	2.71407i	−0.0608790	−	0.146975i
$342$		0			0
$343$	−21.5692	+	21.5692i	−1.16463	+	1.16463i
$344$	−4.01388	+	6.42507i	−0.216414	+	0.346416i
$345$		0			0
$346$	0.760572	−	1.28275i	0.0408886	−	0.0689612i
$347$	15.6447	−	20.3886i	0.839853	−	1.09452i	−0.154458	−	0.987999i	$-0.549363\pi$
$347$	15.6447	−	20.3886i	0.839853	−	1.09452i	0.994311	−	0.106518i	$-0.0339703\pi$
$348$		0			0
$349$	−9.63369	+	7.39219i	−0.515680	+	0.395695i	−0.833554	−	0.552438i	$-0.813698\pi$
$349$	−9.63369	+	7.39219i	−0.515680	+	0.395695i	0.317874	+	0.948133i	$0.397031\pi$
$350$	13.0849	+	10.2837i	0.699415	+	0.549687i
$351$		0			0
$352$	−27.4897	+	5.68124i	−1.46521	+	0.302811i
$353$	3.33343	+	1.92456i	0.177421	+	0.102434i	0.586080	−	0.810253i	$-0.300670\pi$
$353$	3.33343	+	1.92456i	0.177421	+	0.102434i	−0.408660	+	0.912687i	$0.634004\pi$
$354$		0			0
$355$	−3.58478	+	0.471945i	−0.190260	+	0.0250483i
$356$	−6.94583	−	0.161174i	−0.368128	−	0.00854223i
$357$		0			0
$358$	−0.347444	+	29.9503i	−0.0183630	+	1.58292i
$359$	−14.3336	+	14.3336i	−0.756497	+	0.756497i	−0.975683	−	0.219186i	$-0.929660\pi$
$359$	−14.3336	+	14.3336i	−0.756497	+	0.756497i	0.219186	+	0.975683i	$0.429660\pi$
$360$		0			0
$361$	−8.74772	−	8.74772i	−0.460406	−	0.460406i
$362$	5.19487	−	5.07573i	0.273036	−	0.266774i
$363$		0			0
$364$	4.11909	−	9.32632i	0.215899	−	0.488832i
$365$	0.103762	+	0.788149i	0.00543114	+	0.0412536i
$366$		0			0
$367$	4.67472	−	8.09686i	0.244019	−	0.422652i	−0.717837	−	0.696212i	$-0.754868\pi$
$367$	4.67472	−	8.09686i	0.244019	−	0.422652i	0.961855	+	0.273559i	$0.0882009\pi$
$368$	21.1453	+	6.73149i	1.10228	+	0.350903i
$369$		0			0
$370$	1.33298	+	11.1203i	0.0692984	+	0.578119i
$371$	−19.8438	−	25.8610i	−1.03024	−	1.34264i
$372$		0			0
$373$	−4.50562	−	3.45728i	−0.233292	−	0.179011i	0.485500	−	0.874237i	$-0.338638\pi$
$373$	−4.50562	−	3.45728i	−0.233292	−	0.179011i	−0.718791	+	0.695226i	$0.755304\pi$
$374$	7.09619	+	27.7679i	0.366935	+	1.43584i
$375$		0			0
$376$	5.85776	−	4.17924i	0.302091	−	0.215528i
$377$	7.50622	+	7.50622i	0.386590	+	0.386590i
$378$		0			0
$379$	21.3058	−	8.82516i	1.09441	−	0.453318i	0.238865	−	0.971053i	$-0.423225\pi$
$379$	21.3058	−	8.82516i	1.09441	−	0.453318i	0.855541	+	0.517735i	$0.173225\pi$
$380$	−7.67736	−	2.24928i	−0.393840	−	0.115385i
$381$		0			0
$382$	1.12937	−	7.87167i	0.0577834	−	0.402750i
$383$	−11.6397	−	20.1606i	−0.594762	−	1.03016i	−0.993580	−	0.113128i	$-0.963913\pi$
$383$	−11.6397	−	20.1606i	−0.594762	−	1.03016i	0.398818	−	0.917030i	$-0.369420\pi$
$384$		0			0
$385$	17.5395	−	30.3793i	0.893896	−	1.54827i
$386$	1.22610	+	0.963622i	0.0624069	+	0.0490471i
$387$		0			0
$388$	−8.05215	−	33.1048i	−0.408786	−	1.68064i
$389$	−0.359571	+	2.73121i	−0.0182310	+	0.138478i	−0.998140	−	0.0609685i	$-0.980581\pi$
$389$	−0.359571	+	2.73121i	−0.0182310	+	0.138478i	0.979909	+	0.199447i	$0.0639144\pi$
$390$		0			0
$391$	5.86407	−	21.8850i	0.296559	−	1.10677i
$392$	−3.71911	−	38.5815i	−0.187843	−	1.94866i
$393$		0			0
$394$	−7.69369	+	7.51724i	−0.387603	+	0.378713i
$395$	9.30464	−	3.85411i	0.468167	−	0.193921i
$396$		0			0
$397$	−7.43673	+	17.9539i	−0.373239	+	0.901078i	0.619958	+	0.784635i	$0.287149\pi$
$397$	−7.43673	+	17.9539i	−0.373239	+	0.901078i	−0.993197	+	0.116444i	$0.962851\pi$
$398$	3.39788	+	1.45385i	0.170321	+	0.0728751i
$399$		0			0
$400$	−10.1060	+	2.21113i	−0.505301	+	0.110556i
$401$	10.3222	+	17.8787i	0.515468	+	0.892817i	0.999839	+	0.0179544i	$0.00571538\pi$
$401$	10.3222	+	17.8787i	0.515468	+	0.892817i	−0.484370	+	0.874863i	$0.660951\pi$
$402$		0			0
$403$	−0.526193	+	0.403762i	−0.0262115	+	0.0201128i
$404$	−4.76182	−	6.51319i	−0.236909	−	0.324043i
$405$		0			0
$406$	58.7068	+	16.4626i	2.91357	+	0.817027i
$407$	−24.4331	+	6.54683i	−1.21110	+	0.324514i
$408$		0			0
$409$	−18.4213	−	4.93596i	−0.910873	−	0.244068i	−0.227193	−	0.973850i	$-0.572955\pi$
$409$	−18.4213	−	4.93596i	−0.910873	−	0.244068i	−0.683680	+	0.729782i	$0.739622\pi$
$410$	−9.15268	−	5.42682i	−0.452018	−	0.268012i
$411$		0			0
$412$	15.2391	+	27.8686i	0.750777	+	1.37299i
$413$	−1.10790	+	2.67472i	−0.0545164	+	0.131614i
$414$		0			0
$415$		−	18.8190i		−	0.923787i
$416$	2.84532	+	5.66300i	0.139503	+	0.277651i
$417$		0			0
$418$	2.56599	−	17.8849i	0.125507	−	0.874781i
$419$	3.80400	+	28.8942i	0.185837	+	1.41158i	0.789214	+	0.614119i	$0.210488\pi$
$419$	3.80400	+	28.8942i	0.185837	+	1.41158i	−0.603376	+	0.797457i	$0.706178\pi$
$420$		0			0
$421$	−26.5497	−	3.49534i	−1.29395	−	0.170352i	−0.548072	−	0.836431i	$-0.684638\pi$
$421$	−26.5497	−	3.49534i	−1.29395	−	0.170352i	−0.745881	+	0.666079i	$0.767971\pi$
$422$	0.753273	+	1.34038i	0.0366687	+	0.0652485i
$423$		0			0
$424$	20.2505	+	0.705011i	0.983450	+	0.0342383i
$425$	2.73374	+	10.2025i	0.132606	+	0.494892i
$426$		0			0
$427$	−34.3063	+	44.7089i	−1.66020	+	2.16361i
$428$	−2.27910	+	5.16027i	−0.110164	+	0.249431i
$429$		0			0
$430$	5.41049	+	2.31499i	0.260917	+	0.111639i
$431$		−	0.846314i		−	0.0407655i	−0.999792	−	0.0203828i	$-0.993512\pi$
$431$		−	0.846314i		−	0.0407655i	0.999792	−	0.0203828i	$-0.00648848\pi$
$432$		0			0
$433$			35.1194i			1.68773i	0.536554	+	0.843866i	$0.319726\pi$
$433$			35.1194i			1.68773i	−0.536554	+	0.843866i	$0.680274\pi$
$434$	−1.49856	+	3.50237i	−0.0719332	+	0.168119i
$435$		0			0
$436$	1.78667	+	4.61331i	0.0855661	+	0.220937i
$437$	−8.69525	+	11.3319i	−0.415950	+	0.542077i
$438$		0			0
$439$	1.64799	+	6.15039i	0.0786544	+	0.293542i	0.994037	−	0.109043i	$-0.0347785\pi$
$439$	1.64799	+	6.15039i	0.0786544	+	0.293542i	−0.915383	+	0.402585i	$0.868112\pi$
$440$	7.63863	+	20.4238i	0.364157	+	0.973668i
$441$		0			0
$442$	5.64097	−	3.17014i	0.268314	−	0.150788i
$443$	19.9204	+	2.62257i	0.946447	+	0.124602i	0.587922	−	0.808918i	$-0.299946\pi$
$443$	19.9204	+	2.62257i	0.946447	+	0.124602i	0.358525	+	0.933520i	$0.383280\pi$
$444$		0			0
$445$	0.704455	+	5.35086i	0.0333944	+	0.253655i
$446$	−8.08294	−	1.15968i	−0.382738	−	0.0549124i
$447$		0			0
$448$	30.1823	+	20.3489i	1.42598	+	0.961394i
$449$		−	2.52101i		−	0.118974i	−0.998229	−	0.0594870i	$-0.981054\pi$
$449$		−	2.52101i		−	0.118974i	0.998229	−	0.0594870i	$-0.0189465\pi$
$450$		0			0
$451$	9.19651	−	22.2023i	0.433047	−	1.04547i
$452$	−31.2449	−	9.15398i	−1.46964	−	0.430567i
$453$		0			0
$454$	−4.43673	+	7.48282i	−0.208226	+	0.351186i
$455$	−7.65005	−	2.04983i	−0.358640	−	0.0960973i
$456$		0			0
$457$	21.2878	−	5.70405i	0.995801	−	0.266824i	0.276116	−	0.961124i	$-0.410953\pi$
$457$	21.2878	−	5.70405i	0.995801	−	0.266824i	0.719686	+	0.694300i	$0.244286\pi$
$458$	5.66419	−	20.1988i	0.264670	−	0.943830i
$459$		0			0
$460$	2.64589	−	17.0339i	0.123365	−	0.794208i
$461$	−0.552658	+	0.424069i	−0.0257398	+	0.0197509i	−0.621551	−	0.783374i	$-0.713497\pi$
$461$	−0.552658	+	0.424069i	−0.0257398	+	0.0197509i	0.595811	+	0.803124i	$0.296831\pi$
$462$		0			0
$463$	−7.41183	−	12.8377i	−0.344457	−	0.596617i	0.640798	−	0.767710i	$-0.278604\pi$
$463$	−7.41183	−	12.8377i	−0.344457	−	0.596617i	−0.985255	+	0.171092i	$0.945270\pi$
$464$	−31.1063	+	21.6528i	−1.44408	+	1.00521i
$465$		0			0
$466$	11.6476	−	27.2222i	0.539564	−	1.26105i
$467$	−0.222565	+	0.537320i	−0.0102991	+	0.0248642i	−0.928945	−	0.370217i	$-0.879283\pi$
$467$	−0.222565	+	0.537320i	−0.0102991	+	0.0248642i	0.918646	+	0.395081i	$0.129283\pi$
$468$		0			0
$469$	−40.4042	+	16.7360i	−1.86569	+	0.772796i
$470$	−3.90644	−	3.99813i	−0.180190	−	0.184420i
$471$		0			0
$472$	−0.845041	−	1.58888i	−0.0388962	−	0.0731343i
$473$	−3.43999	+	12.8382i	−0.158171	+	0.590302i
$474$		0			0
$475$	0.869143	−	6.60179i	0.0398790	−	0.302911i
$476$	19.3245	−	31.7467i	0.885739	−	1.45511i
$477$		0			0
$478$	−5.91713	+	7.52888i	−0.270643	+	0.344363i
$479$	−18.1501	+	31.4369i	−0.829300	+	1.43639i	0.0692877	+	0.997597i	$0.477927\pi$
$479$	−18.1501	+	31.4369i	−0.829300	+	1.43639i	−0.898588	+	0.438793i	$0.855406\pi$
$480$		0			0
$481$	2.85547	+	4.94582i	0.130198	+	0.225510i
$482$	−40.5222	−	5.81382i	−1.84574	−	0.264812i
$483$		0			0
$484$	−23.9068	+	13.0727i	−1.08667	+	0.594215i
$485$	−24.4513	+	10.1280i	−1.11027	+	0.459891i
$486$		0			0
$487$	5.14815	+	5.14815i	0.233285	+	0.233285i	0.814062	−	0.580777i	$-0.197251\pi$
$487$	5.14815	+	5.14815i	0.233285	+	0.233285i	−0.580777	+	0.814062i	$0.697251\pi$
$488$	−7.88378	−	34.1319i	−0.356882	−	1.54508i
$489$		0			0
$490$	−29.1719	+	7.45499i	−1.31785	+	0.336782i
$491$	17.1385	+	13.1508i	0.773449	+	0.593488i	0.918263	−	0.395971i	$-0.129592\pi$
$491$	17.1385	+	13.1508i	0.773449	+	0.593488i	−0.144814	+	0.989459i	$0.546259\pi$
$492$		0			0
$493$	23.5570	+	30.7001i	1.06095	+	1.38266i
$494$	−4.05030	+	0.485505i	−0.182232	+	0.0218439i
$495$		0			0
$496$	−1.08762	−	2.10349i	−0.0488355	−	0.0944494i
$497$	−5.29475	+	9.17077i	−0.237502	+	0.411365i
$498$		0			0
$499$	−4.42483	−	33.6099i	−0.198083	−	1.50459i	−0.744810	−	0.667277i	$-0.767460\pi$
$499$	−4.42483	−	33.6099i	−0.198083	−	1.50459i	0.546727	−	0.837311i	$-0.315873\pi$
$500$	8.51310	+	21.9814i	0.380718	+	0.983038i
$501$		0			0
$502$	2.86671	+	2.93401i	0.127948	+	0.130951i
$503$	8.18706	+	8.18706i	0.365043	+	0.365043i	0.865666	−	0.500623i	$-0.166896\pi$
$503$	8.18706	+	8.18706i	0.365043	+	0.365043i	−0.500623	+	0.865666i	$0.666896\pi$
$504$		0			0
$505$	−4.43178	+	4.43178i	−0.197212	+	0.197212i
$506$	38.9295	+	0.451609i	1.73063	+	0.0200765i
$507$		0			0
$508$	−30.3383	−	31.7797i	−1.34604	−	1.41000i
$509$	20.5911	−	2.71087i	0.912683	−	0.120157i	0.340464	−	0.940258i	$-0.389416\pi$
$509$	20.5911	−	2.71087i	0.912683	−	0.120157i	0.572219	+	0.820101i	$0.306083\pi$
$510$		0			0
$511$	2.01628	+	1.16410i	0.0891951	+	0.0514968i
$512$	−21.6936	+	6.43344i	−0.958729	+	0.284321i
$513$		0			0
$514$	19.9805	−	25.4229i	0.881301	−	1.12136i
$515$	19.5750	−	15.0204i	0.862579	−	0.661880i
$516$		0			0
$517$	7.68525	−	10.0156i	0.337997	−	0.440486i
$518$	28.2150	+	16.7293i	1.23970	+	0.735044i
$519$		0			0
$520$	4.00768	−	2.85929i	0.175748	−	0.125388i
$521$	−20.7314	+	20.7314i	−0.908261	+	0.908261i	−0.996132	−	0.0878707i	$-0.971994\pi$
$521$	−20.7314	+	20.7314i	−0.908261	+	0.908261i	0.0878707	+	0.996132i	$0.471994\pi$
$522$		0			0
$523$	−5.99966	−	14.4845i	−0.262347	−	0.633361i	0.736736	−	0.676181i	$-0.236366\pi$
$523$	−5.99966	−	14.4845i	−0.262347	−	0.633361i	−0.999083	+	0.0428191i	$0.986366\pi$
$524$	−5.08283	−	4.09098i	−0.222044	−	0.178715i
$525$		0			0
$526$	−0.518725	−	0.692503i	−0.0226175	−	0.0301946i
$527$	−2.09385	+	1.20888i	−0.0912095	+	0.0526598i
$528$		0			0
$529$	−6.73541	−	3.88869i	−0.292844	−	0.169073i
$530$	−1.87336	−	15.6284i	−0.0813734	−	0.678854i
$531$		0			0
$532$	−18.9143	+	13.8283i	−0.820037	+	0.599533i
$533$	−5.37930	−	0.708198i	−0.233003	−	0.0306755i
$534$		0			0
$535$	4.23278	+	1.13417i	0.182999	+	0.0490345i
$536$	7.94540	−	25.9981i	0.343189	−	1.12295i
$537$		0			0
$538$	−2.18738	−	0.0253751i	−0.0943047	−	0.00109400i
$539$	−26.0231	−	62.8254i	−1.12090	−	2.70608i
$540$		0			0
$541$	−4.63048	−	1.91801i	−0.199080	−	0.0824617i	0.280916	−	0.959732i	$-0.409362\pi$
$541$	−4.63048	−	1.91801i	−0.199080	−	0.0824617i	−0.479996	+	0.877271i	$0.659362\pi$
$542$	16.8112	−	6.73603i	0.722102	−	0.289337i
$543$		0			0
$544$	7.58887	+	21.8207i	0.325370	+	0.935555i
$545$	3.32816	−	1.92152i	0.142563	−	0.0823087i
$546$		0			0
$547$	−19.8489	−	25.8676i	−0.848679	−	1.10602i	−0.993189	−	0.116517i	$-0.962827\pi$
$547$	−19.8489	−	25.8676i	−0.848679	−	1.10602i	0.144510	−	0.989503i	$-0.453840\pi$
$548$	5.93819	+	3.61463i	0.253667	+	0.154410i
$549$		0			0
$550$	−15.8222	+	8.89185i	−0.674661	+	0.379150i
$551$	−6.31395	−	23.5640i	−0.268983	−	1.00386i
$552$		0			0
$553$	7.63417	−	28.4911i	0.324638	−	1.21156i
$554$	3.68038	+	14.4016i	0.156364	+	0.611864i
$555$		0			0
$556$	−3.51048	−	32.4691i	−0.148878	−	1.37699i
$557$	29.0633	+	12.0384i	1.23145	+	0.510083i	0.901033	−	0.433751i	$-0.142810\pi$
$557$	29.0633	+	12.0384i	1.23145	+	0.510083i	0.330418	+	0.943835i	$0.392810\pi$
$558$		0			0
$559$	3.00078			0.126920
$560$	12.0212	−	25.5943i	0.507986	−	1.08156i
$561$		0			0
$562$	−9.17736	+	6.87438i	−0.387124	+	0.289978i
$563$	−0.314743	+	0.0414367i	−0.0132648	+	0.00174635i	−0.137156	−	0.990550i	$-0.543796\pi$
$563$	−0.314743	+	0.0414367i	−0.0132648	+	0.00174635i	0.123891	+	0.992296i	$0.460463\pi$
$564$		0			0
$565$	−3.30121	+	25.0752i	−0.138883	+	1.05492i
$566$	−15.7588	−	4.41911i	−0.662393	−	0.185749i
$567$		0			0
$568$	−2.30591	−	6.16546i	−0.0967540	−	0.258697i
$569$	42.7781	−	11.4624i	1.79335	−	0.480527i	0.800444	−	0.599408i	$-0.204597\pi$
$569$	42.7781	−	11.4624i	1.79335	−	0.480527i	0.992909	+	0.118881i	$0.0379306\pi$
$570$		0			0
$571$	−5.09120	−	3.90662i	−0.213060	−	0.163487i	0.496718	−	0.867912i	$-0.334538\pi$
$571$	−5.09120	−	3.90662i	−0.213060	−	0.163487i	−0.709778	+	0.704425i	$0.751205\pi$
$572$	7.67768	+	8.04246i	0.321020	+	0.336272i
$573$		0			0
$574$	−28.9277	+	11.5910i	−1.20742	+	0.483798i
$575$	14.3480			0.598351
$576$		0			0
$577$	6.71403			0.279509			0.139754	−	0.990186i	$-0.455369\pi$
$577$	6.71403			0.279509			0.139754	+	0.990186i	$0.455369\pi$
$578$	−0.421149	+	0.168749i	−0.0175175	+	0.00701904i
$579$		0			0
$580$	20.3297	+	21.2956i	0.844145	+	0.884252i
$581$	−43.7264	−	33.5525i	−1.81408	−	1.39199i
$582$		0			0
$583$	34.3380	−	9.20083i	1.42213	−	0.381059i
$584$	−1.35553	+	0.506978i	−0.0560924	+	0.0209789i
$585$		0			0
$586$	3.94633	+	1.10663i	0.163021	+	0.0457147i
$587$	−1.37700	+	10.4594i	−0.0568349	+	0.431704i	0.939245	+	0.343247i	$0.111527\pi$
$587$	−1.37700	+	10.4594i	−0.0568349	+	0.431704i	−0.996080	+	0.0884568i	$0.971806\pi$
$588$		0			0
$589$	1.51118	−	0.198950i	0.0622670	−	0.00819760i
$590$	−1.11888	+	0.838104i	−0.0460634	+	0.0345042i
$591$		0			0
$592$	−19.1795	+	6.92073i	−0.788274	+	0.284440i
$593$	−13.6954			−0.562403			−0.281202	−	0.959649i	$-0.590733\pi$
$593$	−13.6954			−0.562403			−0.281202	+	0.959649i	$0.590733\pi$
$594$		0			0
$595$	−26.6730	−	11.0483i	−1.09349	−	0.452938i
$596$	−2.14311	−	19.8220i	−0.0877851	−	0.811940i
$597$		0			0
$598$	−2.17634	−	8.51617i	−0.0889972	−	0.348252i
$599$	−10.5998	+	39.5590i	−0.433096	+	1.61634i	0.312485	+	0.949923i	$0.398839\pi$
$599$	−10.5998	+	39.5590i	−0.433096	+	1.61634i	−0.745581	+	0.666415i	$0.767828\pi$
$600$		0			0
$601$	−6.05516	−	22.5982i	−0.246995	−	0.921798i	−0.972370	−	0.233444i	$-0.925000\pi$
$601$	−6.05516	−	22.5982i	−0.246995	−	0.921798i	0.725375	−	0.688354i	$-0.241666\pi$
$602$	15.0253	−	8.44403i	0.612387	−	0.344153i
$603$		0			0
$604$	7.65301	+	4.65846i	0.311397	+	0.189550i
$605$	12.8852	+	16.7923i	0.523856	+	0.682703i
$606$		0			0
$607$	16.3379	−	9.43267i	0.663133	−	0.382860i	−0.130337	−	0.991470i	$-0.541606\pi$
$607$	16.3379	−	9.43267i	0.663133	−	0.382860i	0.793470	+	0.608610i	$0.208272\pi$
$608$	0.844277	−	14.5400i	0.0342399	−	0.589674i
$609$		0			0
$610$	−25.2597	+	10.1213i	−1.02274	+	0.409798i
$611$	−2.63329	−	1.09075i	−0.106532	−	0.0441269i
$612$		0			0
$613$	−9.88791	−	23.8715i	−0.399369	−	0.964162i	−0.987816	−	0.155626i	$-0.950260\pi$
$613$	−9.88791	−	23.8715i	−0.399369	−	0.964162i	0.588447	−	0.808536i	$-0.299740\pi$
$614$	−39.5178	−	0.458433i	−1.59481	−	0.0185009i
$615$		0			0
$616$	61.0743	+	18.6652i	2.46075	+	0.752042i
$617$	−1.01203	−	0.271173i	−0.0407428	−	0.0109170i	0.238390	−	0.971169i	$-0.423380\pi$
$617$	−1.01203	−	0.271173i	−0.0407428	−	0.0109170i	−0.279133	+	0.960252i	$0.590047\pi$
$618$		0			0
$619$	8.02100	+	1.05599i	0.322391	+	0.0424436i	0.289985	−	0.957031i	$-0.406350\pi$
$619$	8.02100	+	1.05599i	0.322391	+	0.0424436i	0.0324062	+	0.999475i	$0.489683\pi$
$620$	−1.48496	+	1.08567i	−0.0596376	+	0.0436014i
$621$		0			0
$622$	−5.65536	−	47.1796i	−0.226759	−	1.89173i
$623$	13.6889	+	7.90327i	0.548433	+	0.316638i
$624$		0			0
$625$	4.65908	−	2.68992i	0.186363	−	0.107597i
$626$	9.88288	+	13.1937i	0.394999	+	0.527328i
$627$		0			0
$628$	12.0679	+	9.71303i	0.481563	+	0.387592i
$629$	7.96680	+	19.2336i	0.317657	+	0.766892i
$630$		0			0
$631$	−2.84039	+	2.84039i	−0.113074	+	0.113074i	−0.761380	−	0.648306i	$-0.775478\pi$
$631$	−2.84039	+	2.84039i	−0.113074	+	0.113074i	0.648306	+	0.761380i	$0.275478\pi$
$632$	10.6489	+	14.9258i	0.423589	+	0.593717i
$633$		0			0
$634$	−31.8985	−	18.9133i	−1.26685	−	0.751145i
$635$	−20.7769	+	27.0770i	−0.824506	+	1.07452i
$636$		0			0
$637$	−12.1804	+	9.34632i	−0.482603	+	0.370315i
$638$	−41.0878	+	52.2796i	−1.62668	+	2.06977i
$639$		0			0
$640$	7.52492	+	15.8850i	0.297449	+	0.627909i
$641$	18.8927	+	10.9077i	0.746215	+	0.430828i	0.824325	−	0.566117i	$-0.191555\pi$
$641$	18.8927	+	10.9077i	0.746215	+	0.430828i	−0.0781094	+	0.996945i	$0.524888\pi$
$642$		0			0
$643$	−3.20671	+	0.422172i	−0.126460	+	0.0166488i	−0.193491	−	0.981102i	$-0.561981\pi$
$643$	−3.20671	+	0.422172i	−0.126460	+	0.0166488i	0.0670303	+	0.997751i	$0.478648\pi$
$644$	−34.8613	−	36.5176i	−1.37373	−	1.43899i
$645$		0			0
$646$	−14.8694	−	0.172495i	−0.585028	−	0.00678672i
$647$	16.3835	−	16.3835i	0.644101	−	0.644101i	−0.307460	−	0.951561i	$-0.599479\pi$
$647$	16.3835	−	16.3835i	0.644101	−	0.644101i	0.951561	+	0.307460i	$0.0994790\pi$
$648$		0			0
$649$	−2.23254	−	2.23254i	−0.0876349	−	0.0876349i
$650$	2.86370	+	2.93093i	0.112324	+	0.114960i
$651$		0			0
$652$	8.52222	+	22.0050i	0.333756	+	0.861781i
$653$	−3.15272	−	23.9473i	−0.123375	−	0.937129i	−0.935421	−	0.353535i	$-0.884979\pi$
$653$	−3.15272	−	23.9473i	−0.123375	−	0.937129i	0.812046	−	0.583594i	$-0.198354\pi$
$654$		0			0
$655$	−2.53421	+	4.38938i	−0.0990197	+	0.171507i
$656$	5.87627	−	18.4589i	0.229430	−	0.720697i
$657$		0			0
$658$	−16.2546	+	1.94842i	−0.633670	+	0.0759572i
$659$	4.31241	+	5.62005i	0.167988	+	0.218926i	0.869759	−	0.493476i	$-0.164274\pi$
$659$	4.31241	+	5.62005i	0.167988	+	0.218926i	−0.701772	+	0.712402i	$0.747607\pi$
$660$		0			0
$661$	30.6268	+	23.5008i	1.19125	+	0.914075i	0.997751	−	0.0670263i	$-0.0213511\pi$
$661$	30.6268	+	23.5008i	1.19125	+	0.914075i	0.193495	+	0.981101i	$0.438018\pi$
$662$	46.1919	−	11.8045i	1.79530	−	0.458796i
$663$		0			0
$664$	33.3818	−	7.71053i	1.29547	−	0.299227i
$665$	12.8699	+	12.8699i	0.499072	+	0.499072i
$666$		0			0
$667$	48.5642	−	20.1160i	1.88041	−	0.778893i
$668$	−1.59114	+	0.870066i	−0.0615630	+	0.0336639i
$669$		0			0
$670$	−20.9036	−	2.99909i	−0.807576	−	0.115865i
$671$	−30.7291	−	53.2243i	−1.18628	−	2.05470i
$672$		0			0
$673$	−4.86626	+	8.42860i	−0.187580	+	0.324899i	−0.944443	−	0.328675i	$-0.893398\pi$
$673$	−4.86626	+	8.42860i	−0.187580	+	0.324899i	0.756863	+	0.653574i	$0.226731\pi$
$674$	−2.75759	+	3.50872i	−0.106218	+	0.135151i
$675$		0			0
$676$	−12.2136	+	20.0647i	−0.469753	+	0.771720i
$677$	−3.48507	+	26.4718i	−0.133942	+	1.01739i	0.784023	+	0.620732i	$0.213164\pi$
$677$	−3.48507	+	26.4718i	−0.133942	+	1.01739i	−0.917965	+	0.396661i	$0.870169\pi$
$678$		0			0
$679$	−20.0615	+	74.8706i	−0.769890	+	2.87327i
$680$	15.8448	−	8.42699i	0.607621	−	0.323160i
$681$		0			0
$682$	−2.90341	−	2.97156i	−0.111177	−	0.113787i
$683$	13.9691	−	5.78620i	0.534513	−	0.221403i	−0.0990653	−	0.995081i	$-0.531585\pi$
$683$	13.9691	−	5.78620i	0.534513	−	0.221403i	0.633579	+	0.773678i	$0.281585\pi$
$684$		0			0
$685$	2.06658	−	4.98916i	0.0789599	−	0.190626i
$686$	−16.9696	+	39.6606i	−0.647901	+	1.51425i
$687$		0			0
$688$	−1.88962	+	10.5458i	−0.0720412	+	0.402056i
$689$	−4.01304	−	6.95080i	−0.152885	−	0.264804i
$690$		0			0
$691$	−26.7099	+	20.4952i	−1.01609	+	0.779676i	−0.975611	−	0.219504i	$-0.929556\pi$
$691$	−26.7099	+	20.4952i	−1.01609	+	0.779676i	−0.0404818	+	0.999180i	$0.512889\pi$
$692$	0.323711	−	2.08400i	0.0123056	−	0.0792218i
$693$		0			0
$694$	9.81318	−	34.9944i	0.372503	−	1.32837i
$695$	−24.5048	+	6.56604i	−0.929520	+	0.249064i
$696$		0			0
$697$	−19.1046	−	5.11905i	−0.723637	−	0.193898i
$698$	−8.75834	+	14.7715i	−0.331508	+	0.559109i
$699$		0			0
$700$	22.5864	+	6.61727i	0.853687	+	0.250109i
$701$	8.97900	−	21.6772i	0.339132	−	0.818737i	−0.658667	−	0.752434i	$-0.728880\pi$
$701$	8.97900	−	21.6772i	0.339132	−	0.818737i	0.997800	−	0.0663032i	$-0.0211205\pi$
$702$		0			0
$703$		−	13.1243i		−	0.494993i
$704$	−33.0989	+	21.9178i	−1.24746	+	0.826057i
$705$		0			0
$706$	5.38829	+	0.773071i	0.202791	+	0.0290949i
$707$	2.39592	+	18.1988i	0.0901078	+	0.684437i
$708$		0			0
$709$	29.6997	+	3.91003i	1.11539	+	0.146844i	0.665615	−	0.746295i	$-0.268169\pi$
$709$	29.6997	+	3.91003i	1.11539	+	0.146844i	0.449779	+	0.893140i	$0.351503\pi$
$710$	−4.45769	+	2.50516i	−0.167294	+	0.0940168i
$711$		0			0
$712$	−9.20294	+	3.44195i	−0.344895	+	0.128993i
$713$	0.850040	+	3.17239i	0.0318343	+	0.118807i
$714$		0			0
$715$	5.25799	−	6.85235i	0.196638	−	0.256263i
$716$	15.2979	+	39.5001i	0.571708	+	1.47619i
$717$		0			0
$718$	−11.2769	+	26.3560i	−0.420851	+	0.983595i
$719$		−	40.2309i		−	1.50036i	−0.661234	−	0.750180i	$-0.729967\pi$
$719$		−	40.2309i		−	1.50036i	0.661234	−	0.750180i	$-0.270033\pi$
$720$		0			0
$721$		−	72.2632i		−	2.69122i
$722$	−16.0849	−	6.88226i	−0.598619	−	0.256131i
$723$		0			0
$724$	4.14973	−	9.39570i	0.154224	−	0.349188i
$725$	−14.9179	+	19.4413i	−0.554035	+	0.722033i
$726$		0			0
$727$	3.89504	+	14.5365i	0.144459	+	0.539129i	0.999779	+	0.0210282i	$0.00669397\pi$
$727$	3.89504	+	14.5365i	0.144459	+	0.539129i	−0.855320	+	0.518100i	$0.826639\pi$
$728$	0.501671	−	14.4098i	0.0185932	−	0.534063i
$729$		0			0
$730$	0.550783	+	0.980065i	0.0203854	+	0.0362738i
$731$	10.8452	+	1.42780i	0.401126	+	0.0528092i
$732$		0			0
$733$	0.172177	+	1.30781i	0.00635950	+	0.0483052i	0.994330	−	0.106335i	$-0.0339115\pi$
$733$	0.172177	+	1.30781i	0.00635950	+	0.0483052i	−0.987971	+	0.154640i	$0.950578\pi$
$734$	1.87778	−	13.0881i	0.0693101	−	0.483090i
$735$		0			0
$736$	31.2994	−	2.28574i	1.15371	−	0.0842535i
$737$		−	47.6940i		−	1.75683i
$738$		0			0
$739$	−11.4907	+	27.7409i	−0.422691	+	1.02047i	0.558860	+	0.829262i	$0.311239\pi$
$739$	−11.4907	+	27.7409i	−0.422691	+	1.02047i	−0.981550	+	0.191204i	$0.938761\pi$
$740$	7.59922	+	13.8971i	0.279353	+	0.510868i
$741$		0			0
$742$	−39.6530	−	23.5112i	−1.45571	−	0.863122i
$743$	−5.46342	−	1.46392i	−0.200433	−	0.0537060i	0.157206	−	0.987566i	$-0.449751\pi$
$743$	−5.46342	−	1.46392i	−0.200433	−	0.0537060i	−0.357639	+	0.933860i	$0.616418\pi$
$744$		0			0
$745$	−14.9599	+	4.00849i	−0.548089	+	0.146860i
$746$	−7.73330	−	2.16858i	−0.283136	−	0.0793975i
$747$		0			0
$748$	23.9215	+	32.7197i	0.874658	+	1.19635i
$749$	10.1819	−	7.81287i	0.372040	−	0.285476i
$750$		0			0
$751$	−26.9412	−	46.6635i	−0.983099	−	1.70278i	−0.650098	−	0.759850i	$-0.725272\pi$
$751$	−26.9412	−	46.6635i	−0.983099	−	1.70278i	−0.333001	−	0.942927i	$-0.608061\pi$
$752$	5.49149	−	8.56751i	0.200254	−	0.312425i
$753$		0			0
$754$	13.8021	+	5.90551i	0.502643	+	0.215066i
$755$	2.66336	−	6.42992i	0.0969296	−	0.234009i
$756$		0			0
$757$	34.5808	−	14.3238i	1.25686	−	0.520609i	0.347916	−	0.937526i	$-0.386889\pi$
$757$	34.5808	−	14.3238i	1.25686	−	0.520609i	0.908945	+	0.416917i	$0.136889\pi$
$758$	23.3272	−	22.7922i	0.847283	−	0.827850i
$759$		0			0
$760$	−11.2616	+	1.08557i	−0.408501	+	0.0393779i
$761$	5.54843	−	20.7070i	0.201130	−	0.750629i	−0.789464	−	0.613797i	$-0.789641\pi$
$761$	5.54843	−	20.7070i	0.201130	−	0.750629i	0.990594	−	0.136832i	$-0.0436920\pi$
$762$		0			0
$763$	1.46910	−	11.1590i	0.0531852	−	0.403981i
$764$	−2.65795	−	10.9276i	−0.0961612	−	0.395347i
$765$		0			0
$766$	−25.8846	−	20.3433i	−0.935250	−	0.735035i
$767$	−0.356416	+	0.617331i	−0.0128695	+	0.0222905i
$768$		0			0
$769$	23.0680	+	39.9550i	0.831854	+	1.44081i	0.896566	+	0.442910i	$0.146054\pi$
$769$	23.0680	+	39.9550i	0.831854	+	1.44081i	−0.0647118	+	0.997904i	$0.520613\pi$
$770$	7.04540	−	49.1064i	0.253899	−	1.76967i
$771$		0			0
$772$	2.11644	+	0.620064i	0.0761722	+	0.0223166i
$773$	−3.48172	+	1.44218i	−0.125229	+	0.0518715i	−0.444418	−	0.895820i	$-0.646589\pi$
$773$	−3.48172	+	1.44218i	−0.125229	+	0.0518715i	0.319189	+	0.947691i	$0.396589\pi$
$774$		0			0
$775$	−1.08265	−	1.08265i	−0.0388898	−	0.0388898i
$776$	−27.9837	−	39.2229i	−1.00456	−	1.40802i
$777$		0			0
$778$	0.964601	+	3.77455i	0.0345826	+	0.135324i
$779$	9.89218	+	7.59054i	0.354424	+	0.271959i
$780$		0			0
$781$	−7.03031	−	9.16208i	−0.251564	−	0.327845i
$782$	−3.81352	−	31.8142i	−0.136371	−	1.13767i
$783$		0			0
$784$	−25.1763	−	48.6917i	−0.899153	−	1.73899i
$785$	6.01686	−	10.4215i	0.214751	−	0.371960i
$786$		0			0
$787$	0.488356	+	3.70943i	0.0174080	+	0.132227i	0.997942	−	0.0641222i	$-0.0204247\pi$
$787$	0.488356	+	3.70943i	0.0174080	+	0.132227i	−0.980534	+	0.196349i	$0.937091\pi$
$788$	−6.14582	+	13.9152i	−0.218936	+	0.495708i
$789$		0			0
$790$	10.1874	−	9.95376i	0.362452	−	0.354139i
$791$	52.3771	+	52.3771i	1.86232	+	1.86232i
$792$		0			0
$793$	−9.81155	+	9.81155i	−0.348418	+	0.348418i
$794$	−0.318795	+	27.4807i	−0.0113136	+	0.975255i
$795$		0			0
$796$	5.22531	+	0.121251i	0.185206	+	0.00429762i
$797$	29.0768	−	3.82803i	1.02995	−	0.135596i	0.403439	−	0.915006i	$-0.367815\pi$
$797$	29.0768	−	3.82803i	1.02995	−	0.135596i	0.626514	+	0.779410i	$0.284481\pi$
$798$		0			0
$799$	−8.99811	−	5.19506i	−0.318330	−	0.183788i
$800$	−12.1037	+	8.21847i	−0.427929	+	0.290567i
$801$		0			0
$802$	22.9548	+	18.0407i	0.810562	+	0.637040i
$803$	−2.01437	+	1.54568i	−0.0710856	+	0.0545459i
$804$		0			0
$805$	−23.8744	+	31.1137i	−0.841462	+	1.09662i
$806$	−0.478381	+	0.806819i	−0.0168503	+	0.0284190i
$807$		0			0
$808$	−9.67706	−	6.04547i	−0.340438	−	0.212679i
$809$	−14.3467	+	14.3467i	−0.504404	+	0.504404i	−0.912803	−	0.408400i	$-0.866087\pi$
$809$	−14.3467	+	14.3467i	−0.504404	+	0.504404i	0.408400	+	0.912803i	$0.366087\pi$
$810$		0			0
$811$	13.2334	+	31.9483i	0.464688	+	1.12186i	0.966451	+	0.256851i	$0.0826848\pi$
$811$	13.2334	+	31.9483i	0.464688	+	1.12186i	−0.501763	+	0.865005i	$0.667315\pi$
$812$	85.7269	−	9.26860i	3.00842	−	0.325264i
$813$		0			0
$814$	−28.6309	+	21.4463i	−1.00351	+	0.751691i
$815$	15.8750	−	9.16541i	0.556075	−	0.321050i
$816$		0			0
$817$	−5.97219	−	3.44804i	−0.208940	−	0.120632i
$818$	−26.7789	+	3.20995i	−0.936303	+	0.112233i
$819$		0			0
$820$	−14.8697	−	2.30974i	−0.519274	−	0.0806596i
$821$	27.9809	+	3.68375i	0.976540	+	0.128564i	0.601870	−	0.798594i	$-0.294423\pi$
$821$	27.9809	+	3.68375i	0.976540	+	0.128564i	0.374670	+	0.927158i	$0.377756\pi$
$822$		0			0
$823$	−20.7098	−	5.54918i	−0.721899	−	0.193432i	−0.120880	−	0.992667i	$-0.538572\pi$
$823$	−20.7098	−	5.54918i	−0.721899	−	0.193432i	−0.601019	+	0.799235i	$0.705238\pi$
$824$	34.6642	+	28.5687i	1.20758	+	0.995239i
$825$		0			0
$826$	−0.0474932	+	4.09400i	−0.00165250	+	0.142449i
$827$	−1.83537	−	4.43098i	−0.0638222	−	0.154080i	0.888751	−	0.458391i	$-0.151574\pi$
$827$	−1.83537	−	4.43098i	−0.0638222	−	0.154080i	−0.952573	+	0.304310i	$0.901574\pi$
$828$		0			0
$829$	31.7765	+	13.1623i	1.10364	+	0.457144i	0.858744	−	0.512405i	$-0.171245\pi$
$829$	31.7765	+	13.1623i	1.10364	+	0.457144i	0.244899	+	0.969549i	$0.421245\pi$
$830$	−9.89885	−	24.7047i	−0.343594	−	0.857511i
$831$		0			0
$832$	6.71396	+	5.93747i	0.232765	+	0.205845i
$833$	−48.4686	+	27.9834i	−1.67934	+	0.969566i
$834$		0			0
$835$	0.857582	+	1.11762i	0.0296779	+	0.0386769i
$836$	−6.03903	−	24.8282i	−0.208864	−	0.858702i
$837$		0			0
$838$	20.1922	+	35.9301i	0.697527	+	1.24118i
$839$	1.62295	+	6.05695i	0.0560306	+	0.209109i	0.988266	−	0.152744i	$-0.0488109\pi$
$839$	1.62295	+	6.05695i	0.0560306	+	0.209109i	−0.932235	+	0.361853i	$0.882144\pi$
$840$		0			0
$841$	−15.7305	+	58.7072i	−0.542432	+	2.02439i
$842$	−36.6918	+	9.37673i	−1.26448	+	0.323144i
$843$		0			0
$844$	1.69390	+	1.36336i	0.0583066	+	0.0469288i
$845$	16.8580	+	6.98282i	0.579933	+	0.240216i
$846$		0			0
$847$	61.9903			2.13001
$848$	26.9547	−	9.72631i	0.925628	−	0.334003i
$849$		0			0
$850$	8.95527	+	11.9554i	0.307163	+	0.410066i
$851$	28.0376	−	3.69122i	0.961118	−	0.126534i
$852$		0			0
$853$	6.08693	−	46.2348i	0.208412	−	1.58305i	−0.492829	−	0.870126i	$-0.664037\pi$
$853$	6.08693	−	46.2348i	0.208412	−	1.58305i	0.701242	−	0.712924i	$-0.252629\pi$
$854$	−21.5187	+	76.7370i	−0.736355	+	2.62589i
$855$		0			0
$856$	−0.277575	+	7.97297i	−0.00948733	+	0.272510i
$857$	9.74444	−	2.61101i	0.332864	−	0.0891906i	−0.0885163	−	0.996075i	$-0.528213\pi$
$857$	9.74444	−	2.61101i	0.332864	−	0.0891906i	0.421380	+	0.906884i	$0.361546\pi$
$858$		0			0
$859$	14.2715	+	10.9509i	0.486937	+	0.373640i	0.822855	−	0.568251i	$-0.192380\pi$
$859$	14.2715	+	10.9509i	0.486937	+	0.373640i	−0.335918	+	0.941891i	$0.609047\pi$
$860$	8.32033	+	0.193069i	0.283721	+	0.00658360i
$861$		0			0
$862$	−0.445164	−	1.11100i	−0.0151624	−	0.0378408i
$863$	0.213637			0.00727230			0.00363615	−	0.999993i	$-0.498843\pi$
$863$	0.213637			0.00727230			0.00363615	+	0.999993i	$0.498843\pi$
$864$		0			0
$865$	−1.63828			−0.0557033
$866$	18.4729	+	46.1031i	0.627736	+	1.56665i
$867$		0			0
$868$	−0.124979	+	5.38600i	−0.00424207	+	0.182813i
$869$	25.5202	+	19.5823i	0.865713	+	0.664285i
$870$		0			0
$871$	−10.4011	+	2.78698i	−0.352429	+	0.0944331i
$872$	4.77208	+	5.11634i	0.161603	+	0.173261i
$873$		0			0
$874$	−5.45411	+	19.4497i	−0.184488	+	0.657896i
$875$	6.99996	−	53.1700i	0.236642	−	1.79747i
$876$		0			0
$877$	32.0647	−	4.22140i	1.08275	−	0.142546i	0.432025	−	0.901862i	$-0.357799\pi$
$877$	32.0647	−	4.22140i	1.08275	−	0.142546i	0.650723	+	0.759315i	$0.274466\pi$
$878$	5.39853	+	7.20709i	0.182192	+	0.243228i
$879$		0			0
$880$	20.7706	+	22.7935i	0.700178	+	0.768369i
$881$	40.2583			1.35634			0.678168	−	0.734907i	$-0.262774\pi$
$881$	40.2583			1.35634			0.678168	+	0.734907i	$0.262774\pi$
$882$		0			0
$883$	25.3073	+	10.4826i	0.851660	+	0.352769i	0.765440	−	0.643507i	$-0.222521\pi$
$883$	25.3073	+	10.4826i	0.851660	+	0.352769i	0.0862196	+	0.996276i	$0.472521\pi$
$884$	5.73769	−	7.12879i	0.192979	−	0.239767i
$885$		0			0
$886$	27.5300	−	7.03542i	0.924890	−	0.236359i
$887$	0.474768	−	1.77186i	0.0159411	−	0.0594931i	−0.957497	−	0.288443i	$-0.906862\pi$
$887$	0.474768	−	1.77186i	0.0159411	−	0.0594931i	0.973438	+	0.228950i	$0.0735291\pi$
$888$		0			0
$889$	25.8709	+	96.5514i	0.867681	+	3.23823i
$890$	3.73935	+	6.65382i	0.125343	+	0.223036i
$891$		0			0
$892$	−11.2209	+	2.72929i	−0.375704	+	0.0913833i
$893$	3.98749	+	5.19660i	0.133436	+	0.173898i
$894$		0			0
$895$	28.4964	−	16.4524i	0.952530	−	0.549944i
$896$	50.3254	+	10.8371i	1.68126	+	0.362041i
$897$		0			0
$898$	−1.32606	−	3.30947i	−0.0442513	−	0.110438i
$899$	−5.18237	−	2.14661i	−0.172842	−	0.0715933i
$900$		0			0
$901$	−11.1964	−	27.0306i	−0.373008	−	0.900520i
$902$	0.394233	−	33.9836i	0.0131265	−	1.13153i
$903$		0			0
$904$	−45.8319	+	4.41801i	−1.52435	+	0.146941i
$905$	−7.70696	−	2.06507i	−0.256188	−	0.0686454i
$906$		0			0
$907$	56.6006	+	7.45161i	1.87939	+	0.247427i	0.981315	−	0.192410i	$-0.0616303\pi$
$907$	56.6006	+	7.45161i	1.87939	+	0.247427i	0.898078	+	0.439836i	$0.144964\pi$
$908$	−1.88834	+	12.1568i	−0.0626667	+	0.403438i
$909$		0			0
$910$	−11.1208	+	1.33304i	−0.368652	+	0.0441899i
$911$	3.88028	+	2.24028i	0.128559	+	0.0742237i	0.562900	−	0.826525i	$-0.309685\pi$
$911$	3.88028	+	2.24028i	0.128559	+	0.0742237i	−0.434341	+	0.900748i	$0.643019\pi$
$912$		0			0
$913$	52.0547	−	30.0538i	1.72276	−	0.994635i
$914$	24.9453	−	18.6855i	0.825116	−	0.618060i
$915$		0			0
$916$	−3.18898	−	29.4955i	−0.105367	−	0.974558i
$917$	5.68059	+	13.7142i	0.187590	+	0.452881i
$918$		0			0
$919$	12.8420	−	12.8420i	0.423620	−	0.423620i	−0.462828	−	0.886448i	$-0.653165\pi$
$919$	12.8420	−	12.8420i	0.423620	−	0.423620i	0.886448	+	0.462828i	$0.153165\pi$
$920$	−5.48646	−	23.7530i	−0.180883	−	0.783113i
$921$		0			0
$922$	−0.502441	+	0.847398i	−0.0165470	+	0.0279076i
$923$	−1.58726	+	2.06856i	−0.0522453	+	0.0680874i
$924$		0			0
$925$	−10.4592	+	8.02561i	−0.343896	+	0.263881i
$926$	−16.4826	−	12.9540i	−0.541651	−	0.425696i
$927$		0			0
$928$	−29.4455	+	44.7869i	−0.966594	+	1.47020i
$929$	37.2662	+	21.5156i	1.22266	+	0.705905i	0.965485	−	0.260459i	$-0.0838739\pi$
$929$	37.2662	+	21.5156i	1.22266	+	0.705905i	0.257178	+	0.966364i	$0.417207\pi$
$930$		0			0
$931$	34.9809	−	4.60532i	1.14645	−	0.150933i
$932$	0.971403	−	41.8627i	0.0318194	−	1.37126i
$933$		0			0
$934$	−0.00954085	+	0.822438i	−0.000312186	+	0.0269110i
$935$	22.2635	−	22.2635i	0.728096	−	0.728096i
$936$		0			0
$937$	30.0408	+	30.0408i	0.981392	+	0.981392i	0.999830	−	0.0184383i	$-0.00586941\pi$
$937$	30.0408	+	30.0408i	0.981392	+	0.981392i	−0.0184383	+	0.999830i	$0.505869\pi$
$938$	−44.2376	+	43.2230i	−1.44441	+	1.41128i
$939$		0			0
$940$	−7.23122	−	3.19376i	−0.235856	−	0.104169i
$941$	2.79738	+	21.2482i	0.0911920	+	0.692672i	0.974582	+	0.224033i	$0.0719222\pi$
$941$	2.79738	+	21.2482i	0.0911920	+	0.692672i	−0.883390	+	0.468639i	$0.844744\pi$
$942$		0			0
$943$	−13.4336	+	23.2676i	−0.437458	+	0.757699i
$944$	−1.94509	−	1.64132i	−0.0633072	−	0.0534203i
$945$		0			0
$946$	2.23709	+	18.6629i	0.0727342	+	0.606782i
$947$	7.88938	+	10.2816i	0.256370	+	0.334108i	0.903751	−	0.428058i	$-0.140802\pi$
$947$	7.88938	+	10.2816i	0.256370	+	0.334108i	−0.647381	+	0.762167i	$0.724136\pi$
$948$		0			0
$949$	0.454792	+	0.348974i	0.0147632	+	0.0113282i
$950$	−2.33160	−	9.12370i	−0.0756471	−	0.296012i
$951$		0			0
$952$	8.66945	−	51.8404i	0.280979	−	1.68016i
$953$	17.4567	+	17.4567i	0.565477	+	0.565477i	0.930858	−	0.365381i	$-0.119061\pi$
$953$	17.4567	+	17.4567i	0.565477	+	0.565477i	−0.365381	+	0.930858i	$0.619061\pi$
$954$		0			0
$955$	−8.07116	+	3.34318i	−0.261176	+	0.108183i
$956$	−3.80751	+	12.9960i	−0.123144	+	0.420320i
$957$		0			0
$958$	−7.29068	+	50.8160i	−0.235551	+	1.64179i
$959$	−7.90794	−	13.6970i	−0.255361	−	0.442298i
$960$		0			0
$961$	−15.3248	+	26.5433i	−0.494347	+	0.856234i
$962$	6.35005	+	4.99065i	0.204734	+	0.160905i
$963$		0			0
$964$	−56.2537	+	13.6827i	−1.81181	+	0.440691i
$965$	0.223614	−	1.69852i	0.00719839	−	0.0546772i
$966$		0			0
$967$	11.5775	−	43.2077i	0.372306	−	1.38947i	−0.484935	−	0.874550i	$-0.661157\pi$
$967$	11.5775	−	43.2077i	0.372306	−	1.38947i	0.857241	−	0.514915i	$-0.172177\pi$
$968$	−24.5074	+	29.7363i	−0.787699	+	0.955762i
$969$		0			0
$970$	−26.7711	+	26.1571i	−0.859568	+	0.839853i
$971$	−35.1496	+	14.5595i	−1.12801	+	0.467235i	−0.867103	−	0.498130i	$-0.834020\pi$
$971$	−35.1496	+	14.5595i	−1.12801	+	0.467235i	−0.260903	+	0.965365i	$0.584020\pi$
$972$		0			0
$973$	−28.4334	+	68.6443i	−0.911532	+	2.20063i
$974$	9.46620	+	4.05030i	0.303317	+	0.129780i
$975$		0			0
$976$	−28.3029	−	40.6598i	−0.905955	−	1.30149i
$977$	−3.00365	−	5.20247i	−0.0960952	−	0.166442i	0.813970	−	0.580907i	$-0.197302\pi$
$977$	−3.00365	−	5.20247i	−0.0960952	−	0.166442i	−0.910065	+	0.414465i	$0.863969\pi$
$978$		0			0
$979$	−13.6759	+	10.4939i	−0.437083	+	0.335386i
$980$	−34.3741	+	25.1311i	−1.09804	+	0.802782i
$981$		0			0
$982$	29.4160	+	8.24887i	0.938701	+	0.263232i
$983$	−27.9412	+	7.48681i	−0.891184	+	0.238792i	−0.675226	−	0.737611i	$-0.735954\pi$
$983$	−27.9412	+	7.48681i	−0.891184	+	0.238792i	−0.215958	+	0.976403i	$0.569287\pi$
$984$		0			0
$985$	11.4141	+	3.05841i	0.363685	+	0.0974490i
$986$	47.0729	+	27.9105i	1.49911	+	0.888853i
$987$		0			0
$988$	−5.06167	+	2.76782i	−0.161033	+	0.0880561i
$989$	5.68642	−	13.7282i	0.180818	−	0.436532i
$990$		0			0
$991$		−	36.4148i		−	1.15675i	−0.815770	−	0.578377i	$-0.803686\pi$
$991$		−	36.4148i		−	1.15675i	0.815770	−	0.578377i	$-0.196314\pi$
$992$	−2.53422	−	2.18927i	−0.0804614	−	0.0695093i
$993$		0			0
$994$	−2.12684	+	14.8240i	−0.0674591	+	0.470189i
$995$	−0.529958	−	4.02543i	−0.0168008	−	0.127615i
$996$		0			0
$997$	38.7999	+	5.10810i	1.22880	+	0.161775i	0.716844	−	0.697234i	$-0.245586\pi$
$997$	38.7999	+	5.10810i	1.22880	+	0.161775i	0.511960	+	0.859009i	$0.328919\pi$
$998$	−23.4877	−	41.7941i	−0.743489	−	1.32297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.40		368
3.2	odd	2		288.2.bf.a.227.7	yes	368
9.4	even	3		288.2.bf.a.131.23	yes	368
9.5	odd	6	inner	864.2.bn.a.611.24		368
32.11	odd	8	inner	864.2.bn.a.683.24		368
96.11	even	8		288.2.bf.a.11.23	✓	368
288.139	odd	24		288.2.bf.a.203.7	yes	368
288.203	even	24	inner	864.2.bn.a.395.40		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.23	✓	368	96.11	even	8
288.2.bf.a.131.23	yes	368	9.4	even	3
288.2.bf.a.203.7	yes	368	288.139	odd	24
288.2.bf.a.227.7	yes	368	3.2	odd	2
864.2.bn.a.35.40		368	1.1	even	1	trivial
864.2.bn.a.395.40		368	288.203	even	24	inner
864.2.bn.a.611.24		368	9.5	odd	6	inner
864.2.bn.a.683.24		368	32.11	odd	8	inner

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.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.31275 - 0.526004i) q^{2} +(1.44664 - 1.38103i) q^{4} +(-1.23257 - 0.945783i) q^{5} +(-4.39511 + 1.17766i) q^{7} +(1.17266 - 2.57388i) q^{8} +O(q^{10})\)	\(q+(1.31275 - 0.526004i) q^{2} +(1.44664 - 1.38103i) q^{4} +(-1.23257 - 0.945783i) q^{5} +(-4.39511 + 1.17766i) q^{7} +(1.17266 - 2.57388i) q^{8} +(-2.11554 - 0.593244i) q^{10} +(0.647702 - 4.91978i) q^{11} +(-1.11076 + 0.146234i) q^{13} +(-5.15023 + 3.85782i) q^{14} +(0.185536 - 3.99569i) q^{16} -4.08402 q^{17} +(2.37867 + 0.985278i) q^{19} +(-3.08923 + 0.334001i) q^{20} +(-1.73755 - 6.79916i) q^{22} +(-1.43586 + 5.35870i) q^{23} +(-0.669376 - 2.49815i) q^{25} +(-1.38123 + 0.776232i) q^{26} +(-4.73175 + 7.77341i) q^{28} +(-5.76810 - 7.51713i) q^{29} +(0.512694 - 0.296004i) q^{31} +(-1.85819 - 5.34295i) q^{32} +(-5.36130 + 2.14821i) q^{34} +(6.53108 + 2.70526i) q^{35} +(-1.95073 - 4.70947i) q^{37} +(3.64087 + 0.0422366i) q^{38} +(-3.87971 + 2.06341i) q^{40} +(4.67789 + 1.25344i) q^{41} +(-2.65553 - 0.349608i) q^{43} +(-5.85736 - 8.01165i) q^{44} +(0.933768 + 7.78992i) q^{46} +(2.20325 + 1.27205i) q^{47} +(11.8679 - 6.85192i) q^{49} +(-2.19276 - 2.92735i) q^{50} +(-1.40491 + 1.74553i) q^{52} +(2.74153 + 6.61863i) q^{53} +(-5.45138 + 5.45138i) q^{55} +(-2.12278 + 12.6935i) q^{56} +(-11.5261 - 6.83409i) q^{58} +(0.387332 - 0.504781i) q^{59} +(9.82581 - 7.53961i) q^{61} +(0.517341 - 0.658259i) q^{62} +(-5.24975 - 6.03656i) q^{64} +(1.50739 + 0.870292i) q^{65} +(9.52916 - 1.25454i) q^{67} +(-5.90810 + 5.64013i) q^{68} +(9.99667 + 0.115968i) q^{70} +(1.64564 - 1.64564i) q^{71} +(-0.361810 - 0.361810i) q^{73} +(-5.03802 - 5.15628i) q^{74} +(4.80178 - 1.85966i) q^{76} +(2.94714 + 22.3857i) q^{77} +(-3.24123 + 5.61397i) q^{79} +(-4.00774 + 4.74949i) q^{80} +(6.80022 - 0.815134i) q^{82} +(7.37393 + 9.60989i) q^{83} +(5.03383 + 3.86259i) q^{85} +(-3.66996 + 0.937872i) q^{86} +(-11.9034 - 7.43633i) q^{88} +(-2.45638 - 2.45638i) q^{89} +(4.70968 - 1.95082i) q^{91} +(5.32333 + 9.73507i) q^{92} +(3.56142 + 0.510966i) q^{94} +(-2.00002 - 3.46413i) q^{95} +(8.51749 - 14.7527i) q^{97} +(11.9755 - 15.2374i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

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