LMFDB - Embedded newform 288.2.v.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 0.691860i$ of defining polynomial
Character	$\chi$	$=$	288.109
Dual form			288.2.v.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.443806 + 1.34277i) q^{2} +(-1.60607 + 1.19186i) q^{4} +(-0.707107 + 0.292893i) q^{5} +(-2.27133 + 2.27133i) q^{7} +(-2.31318 - 1.62764i) q^{8} +O(q^{10})$	\(q+(0.443806 + 1.34277i) q^{2} +(-1.60607 + 1.19186i) q^{4} +(-0.707107 + 0.292893i) q^{5} +(-2.27133 + 2.27133i) q^{7} +(-2.31318 - 1.62764i) q^{8} +(-0.707107 - 0.819496i) q^{10} +(1.49368 + 3.60607i) q^{11} +(-4.50504 - 1.86605i) q^{13} +(-4.05791 - 2.04185i) q^{14} +(1.15894 - 3.82843i) q^{16} +3.05320i q^{17} +(3.87740 + 1.60607i) q^{19} +(0.786578 - 1.31318i) q^{20} +(-4.17923 + 3.60607i) q^{22} +(-0.271330 - 0.271330i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(0.506316 - 6.87740i) q^{26} +(0.940816 - 6.35503i) q^{28} +(0.931884 - 2.24977i) q^{29} +6.82843 q^{31} +(5.65505 - 0.142883i) q^{32} +(-4.09976 + 1.35503i) q^{34} +(0.940816 - 2.27133i) q^{35} +(3.63349 - 1.50504i) q^{37} +(-0.435776 + 5.91925i) q^{38} +(2.11239 + 0.473398i) q^{40} +(1.54266 + 1.54266i) q^{41} +(0.748956 + 1.80814i) q^{43} +(-6.69690 - 4.01136i) q^{44} +(0.243917 - 0.484753i) q^{46} +7.37109i q^{47} -3.31788i q^{49} +(-5.57648 - 2.80596i) q^{50} +(9.45949 - 2.37236i) q^{52} +(-1.67661 - 4.04770i) q^{53} +(-2.11239 - 2.11239i) q^{55} +(8.95089 - 1.55710i) q^{56} +(3.43450 + 0.252848i) q^{58} +(10.1200 - 4.19186i) q^{59} +(1.35873 - 3.28026i) q^{61} +(3.03049 + 9.16902i) q^{62} +(2.70160 + 7.53003i) q^{64} +3.73210 q^{65} +(-1.99577 + 4.81822i) q^{67} +(-3.63899 - 4.90367i) q^{68} +(3.46742 + 0.255272i) q^{70} +(-6.47085 + 6.47085i) q^{71} +(-2.84106 - 2.84106i) q^{73} +(3.63349 + 4.21100i) q^{74} +(-8.14161 + 2.04185i) q^{76} +(-11.5832 - 4.79793i) q^{77} +9.74996i q^{79} +(0.301825 + 3.04655i) q^{80} +(-1.38680 + 2.75608i) q^{82} +(9.04642 + 3.74715i) q^{83} +(-0.894263 - 2.15894i) q^{85} +(-2.09553 + 1.80814i) q^{86} +(2.41421 - 10.7727i) q^{88} +(-7.58323 + 7.58323i) q^{89} +(14.4708 - 5.99402i) q^{91} +(0.759164 + 0.112389i) q^{92} +(-9.89769 + 3.27133i) q^{94} -3.21215 q^{95} +3.71423 q^{97} +(4.45516 - 1.47250i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8	$ 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} - 4 q^{11} - 8 q^{13} - 12 q^{14} + 4 q^{19} - 4 q^{20} + 4 q^{22} + 8 q^{23} - 8 q^{25} + 20 q^{26} - 16 q^{28} + 32 q^{31} + 24 q^{32} - 16 q^{35} - 8 q^{37} - 8 q^{38} + 16 q^{40} - 8 q^{41} - 12 q^{43} - 20 q^{44} + 12 q^{46} - 16 q^{50} + 12 q^{52} - 8 q^{53} - 16 q^{55} - 8 q^{56} - 12 q^{58} + 20 q^{59} + 24 q^{61} + 24 q^{62} - 8 q^{64} - 36 q^{67} - 16 q^{68} - 8 q^{70} + 24 q^{71} - 32 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{77} - 8 q^{80} - 20 q^{82} - 20 q^{83} + 8 q^{85} - 4 q^{86} + 8 q^{88} + 16 q^{89} + 40 q^{91} + 16 q^{92} - 24 q^{94} + 8 q^{95} + 32 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 - 4 * q^11 - 8 * q^13 - 12 * q^14 + 4 * q^19 - 4 * q^20 + 4 * q^22 + 8 * q^23 - 8 * q^25 + 20 * q^26 - 16 * q^28 + 32 * q^31 + 24 * q^32 - 16 * q^35 - 8 * q^37 - 8 * q^38 + 16 * q^40 - 8 * q^41 - 12 * q^43 - 20 * q^44 + 12 * q^46 - 16 * q^50 + 12 * q^52 - 8 * q^53 - 16 * q^55 - 8 * q^56 - 12 * q^58 + 20 * q^59 + 24 * q^61 + 24 * q^62 - 8 * q^64 - 36 * q^67 - 16 * q^68 - 8 * q^70 + 24 * q^71 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 8 * q^80 - 20 * q^82 - 20 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 + 16 * q^89 + 40 * q^91 + 16 * q^92 - 24 * q^94 + 8 * q^95 + 32 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	0.443806	+	1.34277i	0.313818	+	0.949483i
$2$	0.443806	+	1.34277i	0.313818	+	0.949483i
$3$		0			0
$3$		0			0
$4$	−1.60607	+	1.19186i	−0.803037	+	0.595930i
$5$	−0.707107	+	0.292893i	−0.316228	+	0.130986i	−0.535151	−	0.844756i	$-0.679745\pi$
$5$	−0.707107	+	0.292893i	−0.316228	+	0.130986i	0.218924	+	0.975742i	$0.429745\pi$
$6$		0			0
$7$	−2.27133	+	2.27133i	−0.858482	+	0.858482i	−0.991159	−	0.132677i	$-0.957643\pi$
$7$	−2.27133	+	2.27133i	−0.858482	+	0.858482i	0.132677	+	0.991159i	$0.457643\pi$
$8$	−2.31318	−	1.62764i	−0.817833	−	0.575456i
$9$		0			0
$10$	−0.707107	−	0.819496i	−0.223607	−	0.259147i
$11$	1.49368	+	3.60607i	0.450363	+	1.08727i	0.972184	+	0.234217i	$0.0752527\pi$
$11$	1.49368	+	3.60607i	0.450363	+	1.08727i	−0.521821	+	0.853055i	$0.674747\pi$
$12$		0			0
$13$	−4.50504	−	1.86605i	−1.24947	−	0.517549i	−0.342810	−	0.939405i	$-0.611379\pi$
$13$	−4.50504	−	1.86605i	−1.24947	−	0.517549i	−0.906663	+	0.421856i	$0.861379\pi$
$14$	−4.05791	−	2.04185i	−1.08452	−	0.545707i
$15$		0			0
$16$	1.15894	−	3.82843i	0.289735	−	0.957107i
$17$			3.05320i			0.740511i	0.928930	+	0.370255i	$0.120730\pi$
$17$			3.05320i			0.740511i	−0.928930	+	0.370255i	$0.879270\pi$
$18$		0			0
$19$	3.87740	+	1.60607i	0.889537	+	0.368458i	0.780188	−	0.625545i	$-0.215123\pi$
$19$	3.87740	+	1.60607i	0.889537	+	0.368458i	0.109349	+	0.994003i	$0.465123\pi$
$20$	0.786578	−	1.31318i	0.175884	−	0.293636i
$21$		0			0
$22$	−4.17923	+	3.60607i	−0.891014	+	0.768817i
$23$	−0.271330	−	0.271330i	−0.0565763	−	0.0565763i	0.678253	−	0.734829i	$-0.262738\pi$
$23$	−0.271330	−	0.271330i	−0.0565763	−	0.0565763i	−0.734829	+	0.678253i	$0.762738\pi$
$24$		0			0
$25$	−3.12132	+	3.12132i	−0.624264	+	0.624264i
$26$	0.506316	−	6.87740i	0.0992967	−	1.34877i
$27$		0			0
$28$	0.940816	−	6.35503i	0.177797	−	1.20099i
$29$	0.931884	−	2.24977i	0.173047	−	0.417771i	−0.813432	−	0.581660i	$-0.802404\pi$
$29$	0.931884	−	2.24977i	0.173047	−	0.417771i	0.986479	+	0.163888i	$0.0524036\pi$
$30$		0			0
$31$	6.82843			1.22642			0.613211	−	0.789919i	$-0.289878\pi$
$31$	6.82843			1.22642			0.613211	+	0.789919i	$0.289878\pi$
$32$	5.65505	−	0.142883i	0.999681	−	0.0252584i
$33$		0			0
$34$	−4.09976	+	1.35503i	−0.703103	+	0.232386i
$35$	0.940816	−	2.27133i	0.159027	−	0.383925i
$36$		0			0
$37$	3.63349	−	1.50504i	0.597342	−	0.247427i	−0.0634640	−	0.997984i	$-0.520215\pi$
$37$	3.63349	−	1.50504i	0.597342	−	0.247427i	0.660806	+	0.750557i	$0.270215\pi$
$38$	−0.435776	+	5.91925i	−0.0706923	+	0.960230i
$39$		0			0
$40$	2.11239	+	0.473398i	0.333998	+	0.0748508i
$41$	1.54266	+	1.54266i	0.240923	+	0.240923i	0.817232	−	0.576309i	$-0.195507\pi$
$41$	1.54266	+	1.54266i	0.240923	+	0.240923i	−0.576309	+	0.817232i	$0.695507\pi$
$42$		0			0
$43$	0.748956	+	1.80814i	0.114215	+	0.275739i	0.970642	−	0.240529i	$-0.0773209\pi$
$43$	0.748956	+	1.80814i	0.114215	+	0.275739i	−0.856427	+	0.516268i	$0.827321\pi$
$44$	−6.69690	−	4.01136i	−1.00960	−	0.604735i
$45$		0			0
$46$	0.243917	−	0.484753i	0.0359636	−	0.0714729i
$47$			7.37109i			1.07518i	0.843205	+	0.537592i	$0.180666\pi$
$47$			7.37109i			1.07518i	−0.843205	+	0.537592i	$0.819334\pi$
$48$		0			0
$49$		−	3.31788i		−	0.473983i
$50$	−5.57648	−	2.80596i	−0.788634	−	0.396823i
$51$		0			0
$52$	9.45949	−	2.37236i	1.31180	−	0.328988i
$53$	−1.67661	−	4.04770i	−0.230300	−	0.555994i	0.765912	−	0.642945i	$-0.222288\pi$
$53$	−1.67661	−	4.04770i	−0.230300	−	0.555994i	−0.996213	+	0.0869508i	$0.972288\pi$
$54$		0			0
$55$	−2.11239	−	2.11239i	−0.284834	−	0.284834i
$56$	8.95089	−	1.55710i	1.19611	−	0.208076i
$57$		0			0
$58$	3.43450	+	0.252848i	0.450972	+	0.0332006i
$59$	10.1200	−	4.19186i	1.31752	−	0.545734i	0.390449	−	0.920625i	$-0.372320\pi$
$59$	10.1200	−	4.19186i	1.31752	−	0.545734i	0.927069	+	0.374891i	$0.122320\pi$
$60$		0			0
$61$	1.35873	−	3.28026i	0.173967	−	0.419995i	−0.812713	−	0.582664i	$-0.802010\pi$
$61$	1.35873	−	3.28026i	0.173967	−	0.419995i	0.986681	+	0.162669i	$0.0520104\pi$
$62$	3.03049	+	9.16902i	0.384873	+	1.16447i
$63$		0			0
$64$	2.70160	+	7.53003i	0.337700	+	0.941254i
$65$	3.73210			0.462910
$66$		0			0
$67$	−1.99577	+	4.81822i	−0.243822	+	0.588639i	−0.997656	−	0.0684259i	$-0.978202\pi$
$67$	−1.99577	+	4.81822i	−0.243822	+	0.588639i	0.753834	+	0.657065i	$0.228202\pi$
$68$	−3.63899	−	4.90367i	−0.441292	−	0.594657i
$69$		0			0
$70$	3.46742	+	0.255272i	0.414436	+	0.0305108i
$71$	−6.47085	+	6.47085i	−0.767948	+	0.767948i	−0.977745	−	0.209797i	$-0.932720\pi$
$71$	−6.47085	+	6.47085i	−0.767948	+	0.767948i	0.209797	+	0.977745i	$0.432720\pi$
$72$		0			0
$73$	−2.84106	−	2.84106i	−0.332521	−	0.332521i	0.521022	−	0.853543i	$-0.325551\pi$
$73$	−2.84106	−	2.84106i	−0.332521	−	0.332521i	−0.853543	+	0.521022i	$0.825551\pi$
$74$	3.63349	+	4.21100i	0.422384	+	0.489519i
$75$		0			0
$76$	−8.14161	+	2.04185i	−0.933906	+	0.234216i
$77$	−11.5832	−	4.79793i	−1.32003	−	0.546775i
$78$		0			0
$79$			9.74996i			1.09696i	0.836165	+	0.548478i	$0.184793\pi$
$79$			9.74996i			1.09696i	−0.836165	+	0.548478i	$0.815207\pi$
$80$	0.301825	+	3.04655i	0.0337450	+	0.340615i
$81$		0			0
$82$	−1.38680	+	2.75608i	−0.153146	+	0.304358i
$83$	9.04642	+	3.74715i	0.992974	+	0.411303i	0.819216	−	0.573485i	$-0.194409\pi$
$83$	9.04642	+	3.74715i	0.992974	+	0.411303i	0.173758	+	0.984788i	$0.444409\pi$
$84$		0			0
$85$	−0.894263	−	2.15894i	−0.0969964	−	0.234170i
$86$	−2.09553	+	1.80814i	−0.225967	+	0.194977i
$87$		0			0
$88$	2.41421	−	10.7727i	0.257356	−	1.14837i
$89$	−7.58323	+	7.58323i	−0.803821	+	0.803821i	−0.983691	−	0.179869i	$-0.942433\pi$
$89$	−7.58323	+	7.58323i	−0.803821	+	0.803821i	0.179869	+	0.983691i	$0.442433\pi$
$90$		0			0
$91$	14.4708	−	5.99402i	1.51696	−	0.628344i
$92$	0.759164	+	0.112389i	0.0791483	+	0.0117173i
$93$		0			0
$94$	−9.89769	+	3.27133i	−1.02087	+	0.337412i
$95$	−3.21215			−0.329559
$96$		0			0
$97$	3.71423			0.377123			0.188562	−	0.982061i	$-0.439617\pi$
$97$	3.71423			0.377123			0.188562	+	0.982061i	$0.439617\pi$
$98$	4.45516	−	1.47250i	0.450039	−	0.148744i
$99$		0			0
$100$	1.29289	−	8.73324i	0.129289	−	0.873324i
$101$	9.04770	−	3.74768i	0.900280	−	0.372908i	0.115952	−	0.993255i	$-0.463008\pi$
$101$	9.04770	−	3.74768i	0.900280	−	0.372908i	0.784328	+	0.620347i	$0.213008\pi$
$102$		0			0
$103$	0.450688	−	0.450688i	0.0444076	−	0.0444076i	−0.684554	−	0.728962i	$-0.740003\pi$
$103$	0.450688	−	0.450688i	0.0444076	−	0.0444076i	0.728962	+	0.684554i	$0.240003\pi$
$104$	7.38372	+	11.6491i	0.724033	+	1.14229i
$105$		0			0
$106$	4.69105	−	4.04770i	0.455635	−	0.393147i
$107$	−6.82420	−	16.4751i	−0.659720	−	1.59271i	−0.798236	−	0.602345i	$-0.794233\pi$
$107$	−6.82420	−	16.4751i	−0.659720	−	1.59271i	0.138515	−	0.990360i	$-0.455767\pi$
$108$		0			0
$109$	−7.20664	−	2.98509i	−0.690271	−	0.285920i	0.00984205	−	0.999952i	$-0.496867\pi$
$109$	−7.20664	−	2.98509i	−0.690271	−	0.285920i	−0.700113	+	0.714032i	$0.746867\pi$
$110$	1.89897	−	3.77395i	0.181059	−	0.359832i
$111$		0			0
$112$	6.06328	+	11.3280i	0.572926	+	1.07039i
$113$		−	8.76744i		−	0.824771i	−0.911009	−	0.412386i	$-0.864696\pi$
$113$		−	8.76744i		−	0.824771i	0.911009	−	0.412386i	$-0.135304\pi$
$114$		0			0
$115$	0.271330	+	0.112389i	0.0253017	+	0.0104803i
$116$	1.18473	+	4.72397i	0.110000	+	0.438609i
$117$		0			0
$118$	10.1200	+	11.7285i	0.931626	+	1.07970i
$119$	−6.93484	−	6.93484i	−0.635715	−	0.635715i
$120$		0			0
$121$	−2.99450	+	2.99450i	−0.272227	+	0.272227i
$122$	5.00766	+	0.368664i	0.453372	+	0.0333773i
$123$		0			0
$124$	−10.9670	+	8.13853i	−0.984861	+	0.730861i
$125$	2.75736	−	6.65685i	0.246626	−	0.595407i
$126$		0			0
$127$	−11.4642			−1.01728			−0.508641	−	0.860979i	$-0.669852\pi$
$127$	−11.4642			−1.01728			−0.508641	+	0.860979i	$0.669852\pi$
$128$	−8.91213	+	6.96951i	−0.787728	+	0.616023i
$129$		0			0
$130$	1.65633	+	5.01136i	0.145269	+	0.439525i
$131$	−4.32211	+	10.4345i	−0.377625	+	0.911667i	0.614785	+	0.788694i	$0.289243\pi$
$131$	−4.32211	+	10.4345i	−0.377625	+	0.911667i	−0.992410	+	0.122972i	$0.960757\pi$
$132$		0			0
$133$	−12.4548	+	5.15894i	−1.07997	+	0.447337i
$134$	−7.35550	−	0.541513i	−0.635419	−	0.0467796i
$135$		0			0
$136$	4.96951	−	7.06261i	0.426132	−	0.605614i
$137$	3.42429	+	3.42429i	0.292557	+	0.292557i	0.838090	−	0.545533i	$-0.183673\pi$
$137$	3.42429	+	3.42429i	0.292557	+	0.292557i	−0.545533	+	0.838090i	$0.683673\pi$
$138$		0			0
$139$	−7.35745	−	17.7625i	−0.624051	−	1.50659i	−0.846907	−	0.531741i	$-0.821538\pi$
$139$	−7.35745	−	17.7625i	−0.624051	−	1.50659i	0.222856	−	0.974851i	$-0.428462\pi$
$140$	1.19609	+	4.76924i	0.101088	+	0.403075i
$141$		0			0
$142$	−11.5607	−	5.81707i	−0.970150	−	0.488158i
$143$		−	19.0328i		−	1.59160i
$144$		0			0
$145$			1.86377i			0.154778i
$146$	2.55402	−	5.07577i	0.211372	−	0.420074i
$147$		0			0
$148$	−4.04185	+	6.74781i	−0.332238	+	0.554666i
$149$	0.931884	+	2.24977i	0.0763429	+	0.184308i	0.957443	−	0.288621i	$-0.0931967\pi$
$149$	0.931884	+	2.24977i	0.0763429	+	0.184308i	−0.881101	+	0.472929i	$0.843197\pi$
$150$		0			0
$151$	−4.21395	−	4.21395i	−0.342926	−	0.342926i	0.514540	−	0.857466i	$-0.327963\pi$
$151$	−4.21395	−	4.21395i	−0.342926	−	0.342926i	−0.857466	+	0.514540i	$0.827963\pi$
$152$	−6.35503	−	10.0261i	−0.515461	−	0.813227i
$153$		0			0
$154$	1.30182	−	17.6830i	0.104904	−	1.42494i
$155$	−4.82843	+	2.00000i	−0.387829	+	0.160644i
$156$		0			0
$157$	5.84401	−	14.1087i	0.466403	−	1.12600i	−0.499319	−	0.866418i	$-0.666417\pi$
$157$	5.84401	−	14.1087i	0.466403	−	1.12600i	0.965722	−	0.259578i	$-0.0835835\pi$
$158$	−13.0920	+	4.32709i	−1.04154	+	0.344245i
$159$		0			0
$160$	−3.95687	+	1.75736i	−0.312818	+	0.138931i
$161$	1.23256			0.0971395
$162$		0			0
$163$	−2.72369	+	6.57558i	−0.213336	+	0.515039i	−0.993932	−	0.109997i	$-0.964916\pi$
$163$	−2.72369	+	6.57558i	−0.213336	+	0.515039i	0.780596	+	0.625036i	$0.214916\pi$
$164$	−4.31626	−	0.638991i	−0.337043	−	0.0498968i
$165$		0			0
$166$	−1.01672	+	13.8103i	−0.0789125	+	1.07189i
$167$	−3.26355	+	3.26355i	−0.252541	+	0.252541i	−0.822012	−	0.569471i	$-0.807148\pi$
$167$	−3.26355	+	3.26355i	−0.252541	+	0.252541i	0.569471	+	0.822012i	$0.307148\pi$
$168$		0			0
$169$	7.62086	+	7.62086i	0.586220	+	0.586220i
$170$	2.50209	−	2.15894i	0.191901	−	0.165583i
$171$		0			0
$172$	−3.35793	−	2.01136i	−0.256040	−	0.153364i
$173$	−6.86605	−	2.84401i	−0.522016	−	0.216226i	0.106086	−	0.994357i	$-0.466168\pi$
$173$	−6.86605	−	2.84401i	−0.522016	−	0.216226i	−0.628102	+	0.778131i	$0.716168\pi$
$174$		0			0
$175$		−	14.1791i		−	1.07184i
$176$	15.5367	−	1.53923i	1.17112	−	0.116024i
$177$		0			0
$178$	−13.5480	−	6.81707i	−1.01547	−	0.510961i
$179$	1.79370	+	0.742977i	0.134068	+	0.0555327i	0.448709	−	0.893678i	$-0.351884\pi$
$179$	1.79370	+	0.742977i	0.134068	+	0.0555327i	−0.314641	+	0.949211i	$0.601884\pi$
$180$		0			0
$181$	6.12132	+	14.7782i	0.454994	+	1.09845i	0.970399	+	0.241506i	$0.0776415\pi$
$181$	6.12132	+	14.7782i	0.454994	+	1.09845i	−0.515405	+	0.856947i	$0.672359\pi$
$182$	14.4708	+	16.7709i	1.07265	+	1.24314i
$183$		0			0
$184$	0.186009	+	1.06926i	0.0137128	+	0.0788271i
$185$	−2.12845	+	2.12845i	−0.156487	+	0.156487i
$186$		0			0
$187$	−11.0101	+	4.56052i	−0.805137	+	0.333499i
$188$	−8.78530	−	11.8385i	−0.640734	−	0.863412i
$189$		0			0
$190$	−1.42557	−	4.31318i	−0.103422	−	0.312911i
$191$	6.19266			0.448085			0.224043	−	0.974579i	$-0.428075\pi$
$191$	6.19266			0.448085			0.224043	+	0.974579i	$0.428075\pi$
$192$		0			0
$193$	14.5784			1.04938			0.524688	−	0.851295i	$-0.324182\pi$
$193$	14.5784			1.04938			0.524688	+	0.851295i	$0.324182\pi$
$194$	1.64840	+	4.98737i	0.118348	+	0.358072i
$195$		0			0
$196$	3.95445	+	5.32876i	0.282461	+	0.380626i
$197$	−18.5025	+	7.66398i	−1.31825	+	0.546036i	−0.927280	−	0.374368i	$-0.877860\pi$
$197$	−18.5025	+	7.66398i	−1.31825	+	0.546036i	−0.390968	+	0.920404i	$0.627860\pi$
$198$		0			0
$199$	−12.3777	+	12.3777i	−0.877435	+	0.877435i	−0.993269	−	0.115834i	$-0.963046\pi$
$199$	−12.3777	+	12.3777i	−0.877435	+	0.877435i	0.115834	+	0.993269i	$0.463046\pi$
$200$	12.3005	−	2.13980i	0.869780	−	0.151307i
$201$		0			0
$202$	9.04770	+	10.4858i	0.636594	+	0.737775i
$203$	2.99335	+	7.22658i	0.210092	+	0.507207i
$204$		0			0
$205$	−1.54266	−	0.638991i	−0.107744	−	0.0446291i
$206$	0.805188	+	0.405153i	0.0561001	+	0.0282283i
$207$		0			0
$208$	−12.3651	+	15.0846i	−0.857366	+	1.04593i
$209$			16.3812i			1.13311i
$210$		0			0
$211$	3.54851	+	1.46984i	0.244290	+	0.101188i	0.501469	−	0.865176i	$-0.332793\pi$
$211$	3.54851	+	1.46984i	0.244290	+	0.101188i	−0.257179	+	0.966364i	$0.582793\pi$
$212$	7.51705	+	4.50262i	0.516273	+	0.309241i
$213$		0			0
$214$	19.0936	−	16.4751i	1.30521	−	1.12621i
$215$	−1.05918	−	1.05918i	−0.0722358	−	0.0722358i
$216$		0			0
$217$	−15.5096	+	15.5096i	−1.05286	+	1.05286i
$218$	0.809945	−	11.0017i	0.0548564	−	0.745128i
$219$		0			0
$220$	5.91032	+	0.874980i	0.398474	+	0.0589911i
$221$	5.69743	−	13.7548i	0.383250	−	0.925248i
$222$		0			0
$223$	27.5550			1.84522			0.922611	−	0.385732i	$-0.126051\pi$
$223$	27.5550			1.84522			0.922611	+	0.385732i	$0.126051\pi$
$224$	−12.5200	+	13.1690i	−0.836524	+	0.879892i
$225$		0			0
$226$	11.7727	−	3.89104i	0.783106	−	0.258828i
$227$	6.02694	−	14.5503i	0.400022	−	0.965738i	−0.587638	−	0.809124i	$-0.699942\pi$
$227$	6.02694	−	14.5503i	0.400022	−	0.965738i	0.987660	−	0.156614i	$-0.0500580\pi$
$228$		0			0
$229$	18.2777	−	7.57088i	1.20783	−	0.500298i	0.314306	−	0.949322i	$-0.398228\pi$
$229$	18.2777	−	7.57088i	1.20783	−	0.500298i	0.893520	+	0.449024i	$0.148228\pi$
$230$	−0.0304945	+	0.414214i	−0.00201075	+	0.0273124i
$231$		0			0
$232$	−5.81742	+	3.68735i	−0.381932	+	0.242086i
$233$	6.70939	+	6.70939i	0.439547	+	0.439547i	0.891859	−	0.452313i	$-0.149401\pi$
$233$	6.70939	+	6.70939i	0.439547	+	0.439547i	−0.452313	+	0.891859i	$0.649401\pi$
$234$		0			0
$235$	−2.15894	−	5.21215i	−0.140834	−	0.340003i
$236$	−11.2574	+	18.7941i	−0.732796	+	1.22339i
$237$		0			0
$238$	6.23418	−	12.3896i	0.404102	−	0.803100i
$239$			26.1995i			1.69471i	0.531030	+	0.847353i	$0.321805\pi$
$239$			26.1995i			1.69471i	−0.531030	+	0.847353i	$0.678195\pi$
$240$		0			0
$241$		−	13.6734i		−	0.880781i	−0.897806	−	0.440391i	$-0.854840\pi$
$241$		−	13.6734i		−	0.880781i	0.897806	−	0.440391i	$-0.145160\pi$
$242$	−5.34990	−	2.69195i	−0.343905	−	0.173045i
$243$		0			0
$244$	1.72739	+	6.88775i	0.110585	+	0.440943i
$245$	0.971786	+	2.34610i	0.0620851	+	0.149887i
$246$		0			0
$247$	−14.4708	−	14.4708i	−0.920758	−	0.920758i
$248$	−15.7954	−	11.1142i	−1.00301	−	0.705752i
$249$		0			0
$250$	10.1624	+	0.748155i	0.642725	+	0.0473175i
$251$	13.2054	−	5.46984i	0.833515	−	0.345253i	0.0752219	−	0.997167i	$-0.476033\pi$
$251$	13.2054	−	5.46984i	0.833515	−	0.345253i	0.758293	+	0.651913i	$0.226033\pi$
$252$		0			0
$253$	0.573155	−	1.38372i	0.0360340	−	0.0869937i
$254$	−5.08787	−	15.3938i	−0.319242	−	0.965893i
$255$		0			0
$256$	−13.3137	−	8.87385i	−0.832107	−	0.554615i
$257$	20.0656			1.25166			0.625828	−	0.779961i	$-0.284761\pi$
$257$	20.0656			1.25166			0.625828	+	0.779961i	$0.284761\pi$
$258$		0			0
$259$	−4.83441	+	11.6713i	−0.300395	+	0.725219i
$260$	−5.99402	+	4.44814i	−0.371733	+	0.275862i
$261$		0			0
$262$	−15.9293	−	1.17272i	−0.984117	−	0.0724509i
$263$	−4.74976	+	4.74976i	−0.292883	+	0.292883i	−0.838218	−	0.545335i	$-0.816402\pi$
$263$	−4.74976	+	4.74976i	−0.292883	+	0.292883i	0.545335	+	0.838218i	$0.316402\pi$
$264$		0			0
$265$	2.37109	+	2.37109i	0.145655	+	0.145655i
$266$	−12.4548	−	14.4344i	−0.763652	−	0.885028i
$267$		0			0
$268$	−2.53729	−	10.1171i	−0.154989	−	0.618000i
$269$	22.3818	+	9.27086i	1.36464	+	0.565254i	0.940331	−	0.340262i	$-0.110516\pi$
$269$	22.3818	+	9.27086i	1.36464	+	0.565254i	0.424313	+	0.905516i	$0.360516\pi$
$270$		0			0
$271$		−	0.693146i		−	0.0421056i	−0.999778	−	0.0210528i	$-0.993298\pi$
$271$		−	0.693146i		−	0.0421056i	0.999778	−	0.0210528i	$-0.00670181\pi$
$272$	11.6890	+	3.53849i	0.708748	+	0.214552i
$273$		0			0
$274$	−3.07832	+	6.11776i	−0.185968	+	0.369588i
$275$	−15.9180	−	6.59344i	−0.959890	−	0.397600i
$276$		0			0
$277$	11.1898	+	27.0147i	0.672332	+	1.62315i	0.777637	+	0.628713i	$0.216418\pi$
$277$	11.1898	+	27.0147i	0.672332	+	1.62315i	−0.105305	+	0.994440i	$0.533582\pi$
$278$	20.5857	−	17.7625i	1.23465	−	1.06532i
$279$		0			0
$280$	−5.87318	+	3.72269i	−0.350989	+	0.222473i
$281$	6.97958	−	6.97958i	0.416367	−	0.416367i	−0.467582	−	0.883949i	$-0.654875\pi$
$281$	6.97958	−	6.97958i	0.416367	−	0.416367i	0.883949	+	0.467582i	$0.154875\pi$
$282$		0			0
$283$	14.6079	−	6.05078i	0.868348	−	0.359682i	0.0963814	−	0.995344i	$-0.469273\pi$
$283$	14.6079	−	6.05078i	0.868348	−	0.359682i	0.771967	+	0.635663i	$0.219273\pi$
$284$	2.68031	−	18.1050i	0.159047	−	1.07433i
$285$		0			0
$286$	25.5567	−	8.44686i	1.51120	−	0.499473i
$287$	−7.00778			−0.413656
$288$		0			0
$289$	7.67794			0.451644
$290$	−2.50262	+	0.827151i	−0.146959	+	0.0485720i
$291$		0			0
$292$	7.94909	+	1.17680i	0.465185	+	0.0688673i
$293$	9.85571	−	4.08237i	0.575777	−	0.238495i	−0.0757415	−	0.997127i	$-0.524132\pi$
$293$	9.85571	−	4.08237i	0.575777	−	0.238495i	0.651518	+	0.758633i	$0.274132\pi$
$294$		0			0
$295$	−5.92818	+	5.92818i	−0.345152	+	0.345152i
$296$	−10.8546	−	2.43257i	−0.630909	−	0.141390i
$297$		0			0
$298$	−2.60735	+	2.24977i	−0.151040	+	0.130326i
$299$	0.716038	+	1.72867i	0.0414096	+	0.0999715i
$300$		0			0
$301$	−5.80801	−	2.40576i	−0.334768	−	0.138666i
$302$	3.78820	−	7.52855i	0.217986	−	0.433219i
$303$		0			0
$304$	10.6424	−	12.9830i	0.610385	−	0.744627i
$305$			2.71746i			0.155601i
$306$		0			0
$307$	6.96272	+	2.88406i	0.397384	+	0.164602i	0.572421	−	0.819960i	$-0.306004\pi$
$307$	6.96272	+	2.88406i	0.397384	+	0.164602i	−0.175037	+	0.984562i	$0.556004\pi$
$308$	24.3220	−	6.09976i	1.38587	−	0.347566i
$309$		0			0
$310$	−4.82843	−	5.59587i	−0.274236	−	0.317824i
$311$	−4.65020	−	4.65020i	−0.263689	−	0.263689i	0.562862	−	0.826551i	$-0.309700\pi$
$311$	−4.65020	−	4.65020i	−0.263689	−	0.263689i	−0.826551	+	0.562862i	$0.809700\pi$
$312$		0			0
$313$	−0.325668	+	0.325668i	−0.0184078	+	0.0184078i	−0.716251	−	0.697843i	$-0.754143\pi$
$313$	−0.325668	+	0.325668i	−0.0184078	+	0.0184078i	0.697843	+	0.716251i	$0.254143\pi$
$314$	21.5384	+	1.58566i	1.21548	+	0.0894838i
$315$		0			0
$316$	−11.6206	−	15.6591i	−0.653709	−	0.880896i
$317$	−7.92866	+	19.1415i	−0.445318	+	1.07509i	0.528738	+	0.848785i	$0.322665\pi$
$317$	−7.92866	+	19.1415i	−0.445318	+	1.07509i	−0.974056	+	0.226307i	$0.927335\pi$
$318$		0			0
$319$	9.50477			0.532165
$320$	−4.11582	−	4.53325i	−0.230081	−	0.253417i
$321$		0			0
$322$	0.547018	+	1.65505i	0.0304841	+	0.0922323i
$323$	−4.90367	+	11.8385i	−0.272847	+	0.658712i
$324$		0			0
$325$	19.8862	−	8.23714i	1.10309	−	0.456914i
$326$	−10.0383	−	0.739021i	−0.555970	−	0.0409306i
$327$		0			0
$328$	−1.05756	−	6.07934i	−0.0583941	−	0.335676i
$329$	−16.7422	−	16.7422i	−0.923026	−	0.923026i
$330$		0			0
$331$	−5.91798	−	14.2873i	−0.325281	−	0.785299i	−0.998930	−	0.0462470i	$-0.985274\pi$
$331$	−5.91798	−	14.2873i	−0.325281	−	0.785299i	0.673649	−	0.739052i	$-0.264726\pi$
$332$	−18.9953	+	4.76387i	−1.04250	+	0.261451i
$333$		0			0
$334$	−5.83058	−	2.93382i	−0.319035	−	0.160531i
$335$		−	3.99154i		−	0.218081i
$336$		0			0
$337$			4.44955i			0.242383i	0.992629	+	0.121191i	$0.0386715\pi$
$337$			4.44955i			0.242383i	−0.992629	+	0.121191i	$0.961329\pi$
$338$	−6.85089	+	13.6152i	−0.372639	+	0.740572i
$339$		0			0
$340$	4.00941	+	2.40158i	0.217441	+	0.130244i
$341$	10.1995	+	24.6238i	0.552335	+	1.33345i
$342$		0			0
$343$	−8.36330	−	8.36330i	−0.451576	−	0.451576i
$344$	1.21052	−	5.40158i	0.0652671	−	0.291234i
$345$		0			0
$346$	0.771666	−	10.4817i	0.0414850	−	0.563501i
$347$	−7.87485	+	3.26187i	−0.422744	+	0.175106i	−0.583905	−	0.811822i	$-0.698476\pi$
$347$	−7.87485	+	3.26187i	−0.422744	+	0.175106i	0.161161	+	0.986928i	$0.448476\pi$
$348$		0			0
$349$	−12.9387	+	31.2369i	−0.692595	+	1.67207i	0.0468913	+	0.998900i	$0.485069\pi$
$349$	−12.9387	+	31.2369i	−0.692595	+	1.67207i	−0.739486	+	0.673172i	$0.764931\pi$
$350$	19.0393	−	6.29276i	1.01769	−	0.336362i
$351$		0			0
$352$	8.96211	+	20.1791i	0.477682	+	1.07555i
$353$	−20.7013			−1.10182			−0.550911	−	0.834564i	$-0.685720\pi$
$353$	−20.7013			−1.10182			−0.550911	+	0.834564i	$0.685720\pi$
$354$		0			0
$355$	2.68031	−	6.47085i	0.142256	−	0.343437i
$356$	3.14108	−	21.2174i	0.166477	−	1.12452i
$357$		0			0
$358$	−0.201592	+	2.73827i	−0.0106545	+	0.144722i
$359$	19.9483	−	19.9483i	1.05283	−	1.05283i	0.0543091	−	0.998524i	$-0.482704\pi$
$359$	19.9483	−	19.9483i	1.05283	−	1.05283i	0.998524	−	0.0543091i	$-0.0172956\pi$
$360$		0			0
$361$	−0.980242	−	0.980242i	−0.0515917	−	0.0515917i
$362$	−17.1270	+	14.7782i	−0.900177	+	0.776724i
$363$		0			0
$364$	−16.0972	+	26.8741i	−0.843723	+	1.40858i
$365$	2.84106	+	1.17680i	0.148708	+	0.0615968i
$366$		0			0
$367$			9.14270i			0.477245i	0.971112	+	0.238623i	$0.0766959\pi$
$367$			9.14270i			0.477245i	−0.971112	+	0.238623i	$0.923304\pi$
$368$	−1.35322	+	0.724312i	−0.0705417	+	0.0377574i
$369$		0			0
$370$	−3.80264	−	1.91340i	−0.197690	−	0.0994731i
$371$	13.0018	+	5.38552i	0.675020	+	0.279602i
$372$		0			0
$373$	−3.71974	−	8.98024i	−0.192601	−	0.464979i	0.797848	−	0.602858i	$-0.205972\pi$
$373$	−3.71974	−	8.98024i	−0.192601	−	0.464979i	−0.990449	+	0.137879i	$0.955972\pi$
$374$	−11.0101	−	12.7600i	−0.569318	−	0.659806i
$375$		0			0
$376$	11.9974	−	17.0507i	0.618721	−	0.879320i
$377$	−8.39635	+	8.39635i	−0.432434	+	0.432434i
$378$		0			0
$379$	−7.80216	+	3.23176i	−0.400770	+	0.166004i	−0.573959	−	0.818884i	$-0.694593\pi$
$379$	−7.80216	+	3.23176i	−0.400770	+	0.166004i	0.173189	+	0.984889i	$0.444593\pi$
$380$	5.15894	−	3.82843i	0.264648	−	0.196394i
$381$		0			0
$382$	2.74834	+	8.31533i	0.140617	+	0.425449i
$383$	28.4633			1.45440			0.727202	−	0.686423i	$-0.240820\pi$
$383$	28.4633			1.45440			0.727202	+	0.686423i	$0.240820\pi$
$384$		0			0
$385$	9.59587			0.489051
$386$	6.46997	+	19.5754i	0.329313	+	0.996364i
$387$		0			0
$388$	−5.96533	+	4.42684i	−0.302844	+	0.224739i
$389$	21.0834	−	8.73304i	1.06897	−	0.442783i	0.222344	−	0.974968i	$-0.428629\pi$
$389$	21.0834	−	8.73304i	1.06897	−	0.442783i	0.846628	+	0.532185i	$0.178629\pi$
$390$		0			0
$391$	0.828427	−	0.828427i	0.0418954	−	0.0418954i
$392$	−5.40031	+	7.67486i	−0.272757	+	0.387639i
$393$		0			0
$394$	−18.5025	−	21.4433i	−0.932142	−	1.08030i
$395$	−2.85570	−	6.89426i	−0.143686	−	0.346888i
$396$		0			0
$397$	−6.46808	−	2.67916i	−0.324623	−	0.134463i	0.214420	−	0.976742i	$-0.431214\pi$
$397$	−6.46808	−	2.67916i	−0.324623	−	0.134463i	−0.539043	+	0.842278i	$0.681214\pi$
$398$	−22.1138	−	11.1272i	−1.10846	−	0.557755i
$399$		0			0
$400$	8.33232	+	15.5672i	0.416616	+	0.778359i
$401$		−	24.9871i		−	1.24780i	−0.781505	−	0.623898i	$-0.785548\pi$
$401$		−	24.9871i		−	1.24780i	0.781505	−	0.623898i	$-0.214452\pi$
$402$		0			0
$403$	−30.7623	−	12.7422i	−1.53238	−	0.634733i
$404$	−10.0646	+	16.8026i	−0.500731	+	0.835962i
$405$		0			0
$406$	−8.37519	+	7.22658i	−0.415654	+	0.358649i
$407$	10.8546	+	10.8546i	0.538041	+	0.538041i
$408$		0			0
$409$	9.19951	−	9.19951i	0.454887	−	0.454887i	−0.442086	−	0.896973i	$-0.645761\pi$
$409$	9.19951	−	9.19951i	0.454887	−	0.454887i	0.896973	+	0.442086i	$0.145761\pi$
$410$	0.173378	−	2.35503i	0.00856251	−	0.116307i
$411$		0			0
$412$	−0.186681	+	1.26099i	−0.00919711	+	0.0621247i
$413$	−13.4649	+	32.5071i	−0.662563	+	1.59957i
$414$		0			0
$415$	−7.49430			−0.367881
$416$	−25.7428	−	9.90890i	−1.26215	−	0.485824i
$417$		0			0
$418$	−21.9962	+	7.27005i	−1.07587	+	0.355590i
$419$	−10.4739	+	25.2863i	−0.511685	+	1.23532i	0.431217	+	0.902248i	$0.358084\pi$
$419$	−10.4739	+	25.2863i	−0.511685	+	1.23532i	−0.942902	+	0.333070i	$0.891916\pi$
$420$		0			0
$421$	−16.6841	+	6.91080i	−0.813135	+	0.336812i	−0.750204	−	0.661206i	$-0.770045\pi$
$421$	−16.6841	+	6.91080i	−0.813135	+	0.336812i	−0.0629310	+	0.998018i	$0.520045\pi$
$422$	−0.398813	+	5.41717i	−0.0194139	+	0.263703i
$423$		0			0
$424$	−2.70988	+	12.0920i	−0.131603	+	0.587238i
$425$	−9.53003	−	9.53003i	−0.462274	−	0.462274i
$426$		0			0
$427$	4.36444	+	10.5367i	0.211210	+	0.509906i
$428$	30.5961	+	18.3267i	1.47892	+	0.885854i
$429$		0			0
$430$	0.952171	−	1.89231i	0.0459178	−	0.0912555i
$431$		−	26.5985i		−	1.28121i	−0.767872	−	0.640603i	$-0.778684\pi$
$431$		−	26.5985i		−	1.28121i	0.767872	−	0.640603i	$-0.221316\pi$
$432$		0			0
$433$			9.96788i			0.479026i	0.970893	+	0.239513i	$0.0769878\pi$
$433$			9.96788i			0.479026i	−0.970893	+	0.239513i	$0.923012\pi$
$434$	−27.7091	−	13.9426i	−1.33008	−	0.669267i
$435$		0			0
$436$	15.1322	−	3.79503i	0.724701	−	0.181749i
$437$	−0.616281	−	1.48783i	−0.0294807	−	0.0711727i
$438$		0			0
$439$	17.4631	+	17.4631i	0.833466	+	0.833466i	0.987989	−	0.154523i	$-0.0493840\pi$
$439$	17.4631	+	17.4631i	0.833466	+	0.833466i	−0.154523	+	0.987989i	$0.549384\pi$
$440$	1.44814	+	8.32453i	0.0690371	+	0.396857i
$441$		0			0
$442$	20.9981	+	1.54589i	0.998779	+	0.0735303i
$443$	−34.7377	+	14.3888i	−1.65044	+	0.683634i	−0.997288	−	0.0735956i	$-0.976553\pi$
$443$	−34.7377	+	14.3888i	−1.65044	+	0.683634i	−0.653149	+	0.757229i	$0.726553\pi$
$444$		0			0
$445$	3.14108	−	7.58323i	0.148901	−	0.359480i
$446$	12.2291	+	37.0001i	0.579064	+	1.75201i
$447$		0			0
$448$	−23.2394	−	10.9670i	−1.09796	−	0.518140i
$449$	8.35000			0.394061			0.197030	−	0.980397i	$-0.436870\pi$
$449$	8.35000			0.394061			0.197030	+	0.980397i	$0.436870\pi$
$450$		0			0
$451$	−3.25870	+	7.86720i	−0.153446	+	0.370452i
$452$	10.4496	+	14.0811i	0.491506	+	0.662321i
$453$		0			0
$454$	22.2125	+	1.63529i	1.04249	+	0.0767480i
$455$	−8.47682	+	8.47682i	−0.397400	+	0.397400i
$456$		0			0
$457$	−18.0734	−	18.0734i	−0.845436	−	0.845436i	0.144123	−	0.989560i	$-0.453964\pi$
$457$	−18.0734	−	18.0734i	−0.845436	−	0.845436i	−0.989560	+	0.144123i	$0.953964\pi$
$458$	18.2777	+	21.1828i	0.854061	+	0.989807i
$459$		0			0
$460$	−0.569728	+	0.142883i	−0.0265637	+	0.00666196i
$461$	−26.4451	−	10.9539i	−1.23167	−	0.510175i	−0.330569	−	0.943782i	$-0.607241\pi$
$461$	−26.4451	−	10.9539i	−1.23167	−	0.510175i	−0.901102	+	0.433607i	$0.857241\pi$
$462$		0			0
$463$			4.94169i			0.229660i	0.993385	+	0.114830i	$0.0366323\pi$
$463$			4.94169i			0.229660i	−0.993385	+	0.114830i	$0.963368\pi$
$464$	−7.53307	−	6.17500i	−0.349714	−	0.286667i
$465$		0			0
$466$	−6.03151	+	11.9868i	−0.279404	+	0.555280i
$467$	−20.6806	−	8.56617i	−0.956983	−	0.396395i	−0.151132	−	0.988514i	$-0.548292\pi$
$467$	−20.6806	−	8.56617i	−0.956983	−	0.396395i	−0.805851	+	0.592118i	$0.798292\pi$
$468$		0			0
$469$	−6.41071	−	15.4768i	−0.296019	−	0.714653i
$470$	6.04057	−	5.21215i	0.278631	−	0.240418i
$471$		0			0
$472$	−30.2323	−	6.77522i	−1.39155	−	0.311855i
$473$	−5.40158	+	5.40158i	−0.248365	+	0.248365i
$474$		0			0
$475$	−17.1157	+	7.08955i	−0.785322	+	0.325291i
$476$	19.4032	+	2.87250i	0.889344	+	0.131661i
$477$		0			0
$478$	−35.1800	+	11.6275i	−1.60909	+	0.531829i
$479$	5.50637			0.251592			0.125796	−	0.992056i	$-0.459851\pi$
$479$	5.50637			0.251592			0.125796	+	0.992056i	$0.459851\pi$
$480$		0			0
$481$	−19.1775			−0.874418
$482$	18.3603	−	6.06833i	0.836287	−	0.276405i
$483$		0			0
$484$	1.24036	−	8.37840i	0.0563800	−	0.380836i
$485$	−2.62636	+	1.08787i	−0.119257	+	0.0493978i
$486$		0			0
$487$	24.9561	−	24.9561i	1.13087	−	1.13087i	0.140837	−	0.990033i	$-0.455021\pi$
$487$	24.9561	−	24.9561i	1.13087	−	1.13087i	0.990033	−	0.140837i	$-0.0449794\pi$
$488$	−8.48206	+	5.37632i	−0.383965	+	0.243375i
$489$		0			0
$490$	−2.71899	+	2.34610i	−0.122831	+	0.105986i
$491$	−4.79438	−	11.5746i	−0.216367	−	0.522357i	0.778010	−	0.628252i	$-0.216229\pi$
$491$	−4.79438	−	11.5746i	−0.216367	−	0.522357i	−0.994377	+	0.105895i	$0.966229\pi$
$492$		0			0
$493$	6.86900	+	2.84523i	0.309364	+	0.128143i
$494$	13.0088	−	25.8533i	0.585294	−	1.16319i
$495$		0			0
$496$	7.91375	−	26.1421i	0.355338	−	1.17382i
$497$		−	29.3949i		−	1.31854i
$498$		0			0
$499$	8.71684	+	3.61063i	0.390219	+	0.161634i	0.569162	−	0.822225i	$-0.307268\pi$
$499$	8.71684	+	3.61063i	0.390219	+	0.161634i	−0.178943	+	0.983859i	$0.557268\pi$
$500$	3.50551	+	13.9778i	0.156771	+	0.625105i
$501$		0			0
$502$	13.2054	+	15.3042i	0.589384	+	0.683062i
$503$	−5.07960	−	5.07960i	−0.226488	−	0.226488i	0.584736	−	0.811224i	$-0.301198\pi$
$503$	−5.07960	−	5.07960i	−0.226488	−	0.226488i	−0.811224	+	0.584736i	$0.801198\pi$
$504$		0			0
$505$	−5.30002	+	5.30002i	−0.235848	+	0.235848i
$506$	2.11239	+	0.155514i	0.0939071	+	0.00691346i
$507$		0			0
$508$	18.4123	−	13.6637i	0.816915	−	0.606229i
$509$	13.5628	−	32.7435i	0.601161	−	1.45133i	−0.271227	−	0.962515i	$-0.587429\pi$
$509$	13.5628	−	32.7435i	0.601161	−	1.45133i	0.872388	−	0.488815i	$-0.162571\pi$
$510$		0			0
$511$	12.9060			0.570926
$512$	6.00685	−	21.8155i	0.265468	−	0.964120i
$513$		0			0
$514$	8.90522	+	26.9435i	0.392792	+	1.18843i
$515$	−0.186681	+	0.450688i	−0.00822614	+	0.0198597i
$516$		0			0
$517$	−26.5807	+	11.0101i	−1.16902	+	0.484223i
$518$	−17.8174	−	1.31172i	−0.782852	−	0.0576337i
$519$		0			0
$520$	−8.63301	−	6.07450i	−0.378583	−	0.266384i
$521$	17.4496	+	17.4496i	0.764479	+	0.764479i	0.977129	−	0.212650i	$-0.0682093\pi$
$521$	17.4496	+	17.4496i	0.764479	+	0.764479i	−0.212650	+	0.977129i	$0.568209\pi$
$522$		0			0
$523$	16.6581	+	40.2163i	0.728410	+	1.75854i	0.647825	+	0.761789i	$0.275679\pi$
$523$	16.6581	+	40.2163i	0.728410	+	1.75854i	0.0805847	+	0.996748i	$0.474321\pi$
$524$	−5.49483	−	21.9099i	−0.240043	−	0.957139i
$525$		0			0
$526$	−8.48581	−	4.26987i	−0.369999	−	0.186175i
$527$			20.8486i			0.908179i
$528$		0			0
$529$		−	22.8528i		−	0.993598i
$530$	−2.13153	+	4.23613i	−0.0925877	+	0.184006i
$531$		0			0
$532$	13.8546	−	23.1300i	0.600672	−	1.00281i
$533$	−4.07107	−	9.82843i	−0.176338	−	0.425716i
$534$		0			0
$535$	9.65087	+	9.65087i	0.417244	+	0.417244i
$536$	12.4589	−	7.89702i	0.538142	−	0.341099i
$537$		0			0
$538$	−2.51546	+	34.1681i	−0.108449	+	1.47309i
$539$	11.9645	−	4.95587i	0.515349	−	0.213464i
$540$		0			0
$541$	15.9692	−	38.5531i	0.686571	−	1.65753i	−0.0650071	−	0.997885i	$-0.520707\pi$
$541$	15.9692	−	38.5531i	0.686571	−	1.65753i	0.751578	−	0.659644i	$-0.229293\pi$
$542$	0.930737	−	0.307622i	0.0399786	−	0.0132135i
$543$		0			0
$544$	0.436252	+	17.2660i	0.0187041	+	0.740275i
$545$	5.97018			0.255734
$546$		0			0
$547$	0.383100	−	0.924886i	0.0163802	−	0.0395453i	−0.915478	−	0.402368i	$-0.868187\pi$
$547$	0.383100	−	0.924886i	0.0163802	−	0.0395453i	0.931858	+	0.362823i	$0.118187\pi$
$548$	−9.58094	−	1.41839i	−0.409277	−	0.0605905i
$549$		0			0
$550$	1.78900	−	24.3004i	0.0762833	−	1.03617i
$551$	7.22658	−	7.22658i	0.307863	−	0.307863i
$552$		0			0
$553$	−22.1454	−	22.1454i	−0.941717	−	0.941717i
$554$	−31.3084	+	27.0147i	−1.33017	+	1.14774i
$555$		0			0
$556$	32.9870	+	19.7588i	1.39896	+	0.837958i
$557$	−8.29127	−	3.43436i	−0.351312	−	0.145518i	0.200047	−	0.979786i	$-0.435891\pi$
$557$	−8.29127	−	3.43436i	−0.351312	−	0.145518i	−0.551359	+	0.834268i	$0.685891\pi$
$558$		0			0
$559$		−	9.54333i		−	0.403640i
$560$	−7.60527	−	6.23418i	−0.321381	−	0.263442i
$561$		0			0
$562$	12.4696	+	6.27441i	0.525997	+	0.264670i
$563$	22.7143	+	9.40857i	0.957293	+	0.396524i	0.805967	−	0.591960i	$-0.201646\pi$
$563$	22.7143	+	9.40857i	0.957293	+	0.396524i	0.151326	+	0.988484i	$0.451646\pi$
$564$		0			0
$565$	2.56792	+	6.19951i	0.108033	+	0.260816i
$566$	14.6079	+	16.9297i	0.614015	+	0.711607i
$567$		0			0
$568$	25.5004	−	4.43605i	1.06997	−	0.186132i
$569$	16.6413	−	16.6413i	0.697639	−	0.697639i	−0.266262	−	0.963901i	$-0.585789\pi$
$569$	16.6413	−	16.6413i	0.697639	−	0.697639i	0.963901	+	0.266262i	$0.0857886\pi$
$570$		0			0
$571$	9.37532	−	3.88338i	0.392345	−	0.162515i	−0.177785	−	0.984069i	$-0.556893\pi$
$571$	9.37532	−	3.88338i	0.392345	−	0.162515i	0.570129	+	0.821555i	$0.306893\pi$
$572$	22.6844	+	30.5681i	0.948483	+	1.27811i
$573$		0			0
$574$	−3.11009	−	9.40986i	−0.129813	−	0.392760i
$575$	1.69382			0.0706371
$576$		0			0
$577$	−23.0348			−0.958951			−0.479476	−	0.877555i	$-0.659173\pi$
$577$	−23.0348			−0.958951			−0.479476	+	0.877555i	$0.659173\pi$
$578$	3.40751	+	10.3097i	0.141734	+	0.428828i
$579$		0			0
$580$	−2.22135	−	2.99335i	−0.0922365	−	0.124292i
$581$	−29.0584	+	12.0364i	−1.20555	+	0.499354i
$582$		0			0
$583$	12.0920	−	12.0920i	0.500798	−	0.500798i
$584$	1.94767	+	11.1961i	0.0805952	+	0.463297i
$585$		0			0
$586$	9.85571	+	11.4222i	0.407136	+	0.471847i
$587$	−1.02732	−	2.48018i	−0.0424022	−	0.102368i	0.901260	−	0.433280i	$-0.142644\pi$
$587$	−1.02732	−	2.48018i	−0.0424022	−	0.102368i	−0.943662	+	0.330912i	$0.892644\pi$
$588$		0			0
$589$	26.4766	+	10.9670i	1.09095	+	0.451885i
$590$	−10.5912	−	5.32924i	−0.436031	−	0.219401i
$591$		0			0
$592$	−1.55093	−	15.6548i	−0.0637430	−	0.643408i
$593$		−	13.9339i		−	0.572197i	−0.958200	−	0.286098i	$-0.907642\pi$
$593$		−	13.9339i		−	0.572197i	0.958200	−	0.286098i	$-0.0923584\pi$
$594$		0			0
$595$	6.93484	+	2.87250i	0.284301	+	0.117761i
$596$	−4.17808	−	2.50262i	−0.171141	−	0.102511i
$597$		0			0
$598$	−2.00343	+	1.72867i	−0.0819262	+	0.0706906i
$599$	7.02222	+	7.02222i	0.286920	+	0.286920i	0.835861	−	0.548941i	$-0.184969\pi$
$599$	7.02222	+	7.02222i	0.286920	+	0.286920i	−0.548941	+	0.835861i	$0.684969\pi$
$600$		0			0
$601$	24.0970	−	24.0970i	0.982938	−	0.982938i	−0.0169188	−	0.999857i	$-0.505386\pi$
$601$	24.0970	−	24.0970i	0.982938	−	0.982938i	0.999857	+	0.0169188i	$0.00538568\pi$
$602$	0.652755	−	8.86652i	0.0266043	−	0.361373i
$603$		0			0
$604$	11.7904	+	1.74548i	0.479743	+	0.0710224i
$605$	1.24036	−	2.99450i	0.0504278	−	0.121744i
$606$		0			0
$607$	−27.8275			−1.12948			−0.564742	−	0.825268i	$-0.691024\pi$
$607$	−27.8275			−1.12948			−0.564742	+	0.825268i	$0.691024\pi$
$608$	22.1564	+	8.52841i	0.898560	+	0.345873i
$609$		0			0
$610$	−3.64893	+	1.20602i	−0.147741	+	0.0488305i
$611$	13.7548	−	33.2070i	0.556460	−	1.34341i
$612$		0			0
$613$	−9.98279	+	4.13501i	−0.403201	+	0.167011i	−0.575062	−	0.818110i	$-0.695022\pi$
$613$	−9.98279	+	4.13501i	−0.403201	+	0.167011i	0.171861	+	0.985121i	$0.445022\pi$
$614$	−0.782532	+	10.6293i	−0.0315804	+	0.428964i
$615$		0			0
$616$	18.9848	+	29.9518i	0.764920	+	1.20679i
$617$	−23.2080	−	23.2080i	−0.934318	−	0.934318i	0.0636543	−	0.997972i	$-0.479725\pi$
$617$	−23.2080	−	23.2080i	−0.934318	−	0.934318i	−0.997972	+	0.0636543i	$0.979725\pi$
$618$		0			0
$619$	−11.5644	−	27.9189i	−0.464811	−	1.12215i	−0.966399	−	0.257047i	$-0.917251\pi$
$619$	−11.5644	−	27.9189i	−0.464811	−	1.12215i	0.501588	−	0.865107i	$-0.332749\pi$
$620$	5.37109	−	8.96695i	0.215708	−	0.360122i
$621$		0			0
$622$	4.18038	−	8.30795i	0.167618	−	0.333118i
$623$		−	34.4481i		−	1.38013i
$624$		0			0
$625$		−	16.5563i		−	0.662254i
$626$	−0.581831	−	0.292764i	−0.0232546	−	0.0117012i
$627$		0			0
$628$	7.42967	+	29.6248i	0.296476	+	1.18216i
$629$	4.59519	+	11.0938i	0.183222	+	0.442338i
$630$		0			0
$631$	−1.34980	−	1.34980i	−0.0537346	−	0.0537346i	0.679729	−	0.733463i	$-0.262097\pi$
$631$	−1.34980	−	1.34980i	−0.0537346	−	0.0537346i	−0.733463	+	0.679729i	$0.762097\pi$
$632$	15.8694	−	22.5534i	0.631250	−	0.897127i
$633$		0			0
$634$	−29.2214	−	2.15129i	−1.16053	−	0.0854385i
$635$	8.10641	−	3.35778i	0.321693	−	0.133250i
$636$		0			0
$637$	−6.19133	+	14.9472i	−0.245309	+	0.592229i
$638$	4.21827	+	12.7627i	0.167003	+	0.505282i
$639$		0			0
$640$	4.26050	−	7.53849i	0.168411	−	0.297985i
$641$	−41.5334			−1.64047			−0.820235	−	0.572027i	$-0.806157\pi$
$641$	−41.5334			−1.64047			−0.820235	+	0.572027i	$0.806157\pi$
$642$		0			0
$643$	−1.57282	+	3.79713i	−0.0620261	+	0.149744i	−0.951854	−	0.306553i	$-0.900824\pi$
$643$	−1.57282	+	3.79713i	−0.0620261	+	0.149744i	0.889828	+	0.456297i	$0.150824\pi$
$644$	−1.97958	+	1.46904i	−0.0780066	+	0.0578883i
$645$		0			0
$646$	−18.0727	−	1.33051i	−0.711060	−	0.0523484i
$647$	5.84193	−	5.84193i	0.229670	−	0.229670i	−0.582885	−	0.812555i	$-0.698076\pi$
$647$	5.84193	−	5.84193i	0.229670	−	0.229670i	0.812555	+	0.582885i	$0.198076\pi$
$648$		0			0
$649$	30.2323	+	30.2323i	1.18672	+	1.18672i
$650$	19.8862	+	23.0470i	0.780001	+	0.903976i
$651$		0			0
$652$	−3.46271	−	13.8071i	−0.135610	−	0.540729i
$653$	26.0231	+	10.7791i	1.01836	+	0.421820i	0.828499	−	0.559991i	$-0.189195\pi$
$653$	26.0231	+	10.7791i	1.01836	+	0.421820i	0.189864	+	0.981810i	$0.439195\pi$
$654$		0			0
$655$		−	8.64422i		−	0.337758i
$656$	7.69382	−	4.11811i	0.300393	−	0.160785i
$657$		0			0
$658$	15.0507	−	29.9112i	0.586736	−	1.16606i
$659$	−37.6498	−	15.5951i	−1.46663	−	0.607497i	−0.500541	−	0.865713i	$-0.666866\pi$
$659$	−37.6498	−	15.5951i	−1.46663	−	0.607497i	−0.966087	+	0.258215i	$0.916866\pi$
$660$		0			0
$661$	3.14241	+	7.58644i	0.122226	+	0.295078i	0.973136	−	0.230233i	$-0.0739488\pi$
$661$	3.14241	+	7.58644i	0.122226	+	0.295078i	−0.850910	+	0.525311i	$0.823949\pi$
$662$	16.5581	−	14.2873i	0.643549	−	0.555290i
$663$		0			0
$664$	−14.8270	−	23.3921i	−0.575399	−	0.907790i
$665$	7.29585	−	7.29585i	0.282921	−	0.282921i
$666$		0			0
$667$	−0.863279	+	0.357582i	−0.0334263	+	0.0138456i
$668$	1.35181	−	9.13118i	0.0523029	−	0.353296i
$669$		0			0
$670$	5.35973	−	1.77147i	0.207065	−	0.0684378i
$671$	13.8584			0.534997
$672$		0			0
$673$	−5.24262			−0.202088			−0.101044	−	0.994882i	$-0.532218\pi$
$673$	−5.24262			−0.202088			−0.101044	+	0.994882i	$0.532218\pi$
$674$	−5.97474	+	1.97474i	−0.230138	+	0.0760640i
$675$		0			0
$676$	−21.3226	−	3.15666i	−0.820102	−	0.121410i
$677$	−14.5716	+	6.03574i	−0.560031	+	0.231972i	−0.644699	−	0.764437i	$-0.723017\pi$
$677$	−14.5716	+	6.03574i	−0.560031	+	0.231972i	0.0846677	+	0.996409i	$0.473017\pi$
$678$		0			0
$679$	−8.43625	+	8.43625i	−0.323754	+	0.323754i
$680$	−1.44538	+	6.44955i	−0.0554278	+	0.247329i
$681$		0			0
$682$	−28.5376	+	24.6238i	−1.09276	+	0.942894i
$683$	14.9028	+	35.9785i	0.570240	+	1.37668i	0.901351	+	0.433089i	$0.142576\pi$
$683$	14.9028	+	35.9785i	0.570240	+	1.37668i	−0.331112	+	0.943592i	$0.607424\pi$
$684$		0			0
$685$	−3.42429	−	1.41839i	−0.130835	−	0.0541938i
$686$	7.51833	−	14.9417i	0.287051	−	0.570476i
$687$		0			0
$688$	7.79033	−	0.771795i	0.297004	−	0.0294244i
$689$			21.3637i			0.813892i
$690$		0			0
$691$	14.6714	+	6.07710i	0.558127	+	0.231184i	0.643872	−	0.765133i	$-0.277327\pi$
$691$	14.6714	+	6.07710i	0.558127	+	0.231184i	−0.0857448	+	0.996317i	$0.527327\pi$
$692$	14.4170	−	3.61568i	0.548053	−	0.137447i
$693$		0			0
$694$	−7.87485	−	9.12649i	−0.298925	−	0.346437i
$695$	10.4050	+	10.4050i	0.394685	+	0.394685i
$696$		0			0
$697$	−4.71006	+	4.71006i	−0.178406	+	0.178406i
$698$	−47.6863	−	3.51067i	−1.80495	−	0.132881i
$699$		0			0
$700$	16.8995	+	22.7727i	0.638741	+	0.860726i
$701$	−9.58351	+	23.1366i	−0.361964	+	0.873859i	0.633049	+	0.774112i	$0.281803\pi$
$701$	−9.58351	+	23.1366i	−0.361964	+	0.873859i	−0.995013	+	0.0997466i	$0.968197\pi$
$702$		0			0
$703$	16.5057			0.622524
$704$	−23.1185	+	20.9897i	−0.871311	+	0.791078i
$705$		0			0
$706$	−9.18737	−	27.7972i	−0.345771	−	1.04616i
$707$	−12.0381	+	29.0625i	−0.452739	+	1.09301i
$708$		0			0
$709$	27.4256	−	11.3601i	1.02999	−	0.426636i	0.197282	−	0.980347i	$-0.436789\pi$
$709$	27.4256	−	11.3601i	1.02999	−	0.426636i	0.832709	+	0.553711i	$0.186789\pi$
$710$	9.87841	+	0.727250i	0.370730	+	0.0272932i
$711$		0			0
$712$	29.8841	−	5.19864i	1.11996	−	0.194827i
$713$	−1.85276	−	1.85276i	−0.0693864	−	0.0693864i
$714$		0			0
$715$	5.57457	+	13.4582i	0.208477	+	0.503309i
$716$	−3.76634	+	0.944569i	−0.140755	+	0.0353002i
$717$		0			0
$718$	35.6393	+	17.9329i	1.33005	+	0.669249i
$719$			38.9976i			1.45436i	0.686445	+	0.727182i	$0.259170\pi$
$719$			38.9976i			1.45436i	−0.686445	+	0.727182i	$0.740830\pi$
$720$		0			0
$721$			2.04732i			0.0762462i
$722$	0.881204	−	1.75128i	0.0327950	−	0.0651758i
$723$		0			0
$724$	−27.4448	−	16.4391i	−1.01998	−	0.610953i
$725$	4.11354	+	9.93095i	0.152773	+	0.368826i
$726$		0			0
$727$	34.9474	+	34.9474i	1.29613	+	1.29613i	0.930930	+	0.365198i	$0.118999\pi$
$727$	34.9474	+	34.9474i	1.29613	+	1.29613i	0.365198	+	0.930930i	$0.381001\pi$
$728$	−43.2298	−	9.68802i	−1.60220	−	0.359062i
$729$		0			0
$730$	−0.319303	+	4.33717i	−0.0118179	+	0.160526i
$731$	−5.52062	+	2.28672i	−0.204188	+	0.0845773i
$732$		0			0
$733$	−13.8093	+	33.3387i	−0.510060	+	1.23139i	0.433789	+	0.901015i	$0.357176\pi$
$733$	−13.8093	+	33.3387i	−0.510060	+	1.23139i	−0.943849	+	0.330378i	$0.892824\pi$
$734$	−12.2766	+	4.05758i	−0.453136	+	0.149768i
$735$		0			0
$736$	−1.57316	−	1.49562i	−0.0579873	−	0.0551292i
$737$	−20.3559			−0.749819
$738$		0			0
$739$	6.75096	−	16.2983i	0.248338	−	0.599542i	−0.749725	−	0.661750i	$-0.769814\pi$
$739$	6.75096	−	16.2983i	0.248338	−	0.599542i	0.998063	+	0.0622080i	$0.0198142\pi$
$740$	0.881632	−	5.95525i	0.0324094	−	0.218919i
$741$		0			0
$742$	−1.46126	+	19.8486i	−0.0536444	+	0.728664i
$743$	20.6145	−	20.6145i	0.756272	−	0.756272i	−0.219370	−	0.975642i	$-0.570400\pi$
$743$	20.6145	−	20.6145i	0.756272	−	0.756272i	0.975642	+	0.219370i	$0.0704002\pi$
$744$		0			0
$745$	−1.31788	−	1.31788i	−0.0482835	−	0.0482835i
$746$	10.4076	−	8.98024i	0.381048	−	0.328790i
$747$		0			0
$748$	12.2475	−	20.4470i	0.447812	−	0.747616i
$749$	52.9203	+	21.9203i	1.93367	+	0.800951i
$750$		0			0
$751$			27.0344i			0.986499i	0.869888	+	0.493249i	$0.164191\pi$
$751$			27.0344i			0.986499i	−0.869888	+	0.493249i	$0.835809\pi$
$752$	28.2197	+	8.54266i	1.02907	+	0.311519i
$753$		0			0
$754$	−15.0007	−	7.54804i	−0.546294	−	0.274883i
$755$	4.21395	+	1.74548i	0.153361	+	0.0635244i
$756$		0			0
$757$	−19.5424	−	47.1795i	−0.710280	−	1.71477i	−0.699300	−	0.714828i	$-0.746505\pi$
$757$	−19.5424	−	47.1795i	−0.710280	−	1.71477i	−0.0109802	−	0.999940i	$-0.503495\pi$
$758$	−7.80216	−	9.04225i	−0.283387	−	0.328429i
$759$		0			0
$760$	7.43027	+	5.22820i	0.269524	+	0.189647i
$761$	2.53714	−	2.53714i	0.0919713	−	0.0919713i	−0.659624	−	0.751596i	$-0.729285\pi$
$761$	2.53714	−	2.53714i	0.0919713	−	0.0919713i	0.751596	+	0.659624i	$0.229285\pi$
$762$		0			0
$763$	23.1488	−	9.58854i	0.838042	−	0.347129i
$764$	−9.94587	+	7.38078i	−0.359829	+	0.267027i
$765$		0			0
$766$	12.6322	+	38.2197i	0.456418	+	1.38093i
$767$	−53.4134			−1.92865
$768$		0			0
$769$	−24.0627			−0.867725			−0.433862	−	0.900979i	$-0.642850\pi$
$769$	−24.0627			−0.867725			−0.433862	+	0.900979i	$0.642850\pi$
$770$	4.25870	+	12.8851i	0.153473	+	0.464345i
$771$		0			0
$772$	−23.4140	+	17.3754i	−0.842687	+	0.625354i
$773$	43.4146	−	17.9829i	1.56152	−	0.646801i	0.576163	−	0.817335i	$-0.304549\pi$
$773$	43.4146	−	17.9829i	1.56152	−	0.646801i	0.985352	+	0.170534i	$0.0545492\pi$
$774$		0			0
$775$	−21.3137	+	21.3137i	−0.765611	+	0.765611i
$776$	−8.59169	−	6.04542i	−0.308424	−	0.217018i
$777$		0			0
$778$	21.0834	+	24.4345i	0.755877	+	0.876018i
$779$	3.50389	+	8.45914i	0.125540	+	0.303080i
$780$		0			0
$781$	−32.9997	−	13.6689i	−1.18082	−	0.489113i
$782$	1.48005	+	0.744728i	0.0529265	+	0.0266314i
$783$		0			0
$784$	−12.7023	−	3.84523i	−0.453653	−	0.137330i
$785$			11.6880i			0.417163i
$786$		0			0
$787$	−4.62213	−	1.91455i	−0.164761	−	0.0682463i	0.298778	−	0.954323i	$-0.403421\pi$
$787$	−4.62213	−	1.91455i	−0.164761	−	0.0682463i	−0.463540	+	0.886076i	$0.653421\pi$
$788$	20.5820	−	34.3613i	0.733202	−	1.22407i
$789$		0			0
$790$	7.99005	−	6.89426i	0.284273	−	0.245287i
$791$	19.9137	+	19.9137i	0.708051	+	0.708051i
$792$		0			0
$793$	−12.2423	+	12.2423i	−0.434735	+	0.434735i
$794$	0.726939	−	9.87418i	0.0257981	−	0.350422i
$795$		0			0
$796$	5.12703	−	34.6321i	0.181723	−	1.22750i
$797$	7.78397	−	18.7922i	0.275722	−	0.665653i	−0.723986	−	0.689815i	$-0.757692\pi$
$797$	7.78397	−	18.7922i	0.275722	−	0.665653i	0.999708	+	0.0241622i	$0.00769183\pi$
$798$		0			0
$799$	−22.5054			−0.796185
$800$	−17.2052	+	18.0972i	−0.608297	+	0.639833i
$801$		0			0
$802$	33.5520	−	11.0894i	1.18476	−	0.391581i
$803$	6.00142	−	14.4887i	0.211785	−	0.511295i
$804$		0			0
$805$	−0.871553	+	0.361009i	−0.0307182	+	0.0127239i
$806$	3.45734	−	46.9618i	0.121780	−	1.65416i
$807$		0			0
$808$	−27.0288	−	6.05730i	−0.950870	−	0.213095i
$809$	5.79631	+	5.79631i	0.203787	+	0.203787i	0.801621	−	0.597833i	$-0.203971\pi$
$809$	5.79631	+	5.79631i	0.203787	+	0.203787i	−0.597833	+	0.801621i	$0.703971\pi$
$810$		0			0
$811$	−2.59457	−	6.26386i	−0.0911078	−	0.219954i	0.871757	−	0.489939i	$-0.162981\pi$
$811$	−2.59457	−	6.26386i	−0.0911078	−	0.219954i	−0.962864	+	0.269986i	$0.912981\pi$
$812$	−13.4206	−	8.03877i	−0.470971	−	0.282105i
$813$		0			0
$814$	−9.75789	+	19.3925i	−0.342014	+	0.679708i
$815$		−	5.44739i		−	0.190814i
$816$		0			0
$817$			8.21377i			0.287363i
$818$	16.4356	+	8.27005i	0.574659	+	0.289156i
$819$		0			0
$820$	3.23921	−	0.812369i	0.113118	−	0.0283691i
$821$	−14.5014	−	35.0095i	−0.506103	−	1.22184i	−0.946110	−	0.323847i	$-0.895024\pi$
$821$	−14.5014	−	35.0095i	−0.506103	−	1.22184i	0.440006	−	0.897995i	$-0.354976\pi$
$822$		0			0
$823$	−6.84972	−	6.84972i	−0.238766	−	0.238766i	0.577573	−	0.816339i	$-0.304000\pi$
$823$	−6.84972	−	6.84972i	−0.238766	−	0.238766i	−0.816339	+	0.577573i	$0.804000\pi$
$824$	−1.77608	+	0.308966i	−0.0618726	+	0.0107633i
$825$		0			0
$826$	−49.6254	−	3.65343i	−1.72669	−	0.127119i
$827$	−27.6932	+	11.4709i	−0.962987	+	0.398882i	−0.808097	−	0.589049i	$-0.799502\pi$
$827$	−27.6932	+	11.4709i	−0.962987	+	0.398882i	−0.154890	+	0.987932i	$0.549502\pi$
$828$		0			0
$829$	1.60232	−	3.86834i	0.0556509	−	0.134353i	−0.893609	−	0.448847i	$-0.851835\pi$
$829$	1.60232	−	3.86834i	0.0556509	−	0.134353i	0.949259	+	0.314494i	$0.101835\pi$
$830$	−3.32601	−	10.0631i	−0.115448	−	0.349297i
$831$		0			0
$832$	1.88057	−	38.9644i	0.0651972	−	1.35085i
$833$	10.1302			0.350990
$834$		0			0
$835$	1.35181	−	3.26355i	0.0467811	−	0.112940i
$836$	−19.5240	−	26.3094i	−0.675253	−	0.909928i
$837$		0			0
$838$	−38.6022	−	2.84190i	−1.33349	−	0.0981717i
$839$	−11.4718	+	11.4718i	−0.396050	+	0.396050i	−0.876837	−	0.480787i	$-0.840351\pi$
$839$	−11.4718	+	11.4718i	−0.396050	+	0.396050i	0.480787	+	0.876837i	$0.340351\pi$
$840$		0			0
$841$	16.3131	+	16.3131i	0.562519	+	0.562519i
$842$	−16.6841	−	19.3359i	−0.574973	−	0.666361i
$843$		0			0
$844$	−7.45101	+	1.86865i	−0.256474	+	0.0643217i
$845$	−7.62086	−	3.15666i	−0.262165	−	0.108592i
$846$		0			0
$847$		−	13.6030i		−	0.467404i
$848$	−17.4394	+	1.72774i	−0.598872	+	0.0593308i
$849$		0			0
$850$	8.56718	−	17.0261i	0.293852	−	0.583992i
$851$	−1.39424	−	0.577512i	−0.0477939	−	0.0197969i
$852$		0			0
$853$	−4.85275	−	11.7156i	−0.166155	−	0.401133i	0.818769	−	0.574124i	$-0.194657\pi$
$853$	−4.85275	−	11.7156i	−0.166155	−	0.401133i	−0.984924	+	0.172990i	$0.944657\pi$
$854$	−12.2114	+	10.5367i	−0.417865	+	0.360558i
$855$		0			0
$856$	−11.0298	+	49.2171i	−0.376992	+	1.68221i
$857$	13.5307	−	13.5307i	0.462200	−	0.462200i	−0.437176	−	0.899376i	$-0.644021\pi$
$857$	13.5307	−	13.5307i	0.462200	−	0.462200i	0.899376	+	0.437176i	$0.144021\pi$
$858$		0			0
$859$	−50.3433	+	20.8529i	−1.71769	+	0.711491i	−0.717808	+	0.696241i	$0.754855\pi$
$859$	−50.3433	+	20.8529i	−1.71769	+	0.711491i	−0.999884	+	0.0152507i	$0.995145\pi$
$860$	2.96353	+	0.438728i	0.101055	+	0.0149605i
$861$		0			0
$862$	35.7158	−	11.8046i	1.21648	−	0.402066i
$863$	9.50637			0.323601			0.161800	−	0.986824i	$-0.448270\pi$
$863$	9.50637			0.323601			0.161800	+	0.986824i	$0.448270\pi$
$864$		0			0
$865$	5.68802			0.193399
$866$	−13.3846	+	4.42380i	−0.454827	+	0.150327i
$867$		0			0
$868$	6.42429	−	43.3949i	0.218055	−	1.47292i
$869$	−35.1591	+	14.5634i	−1.19269	+	0.494028i
$870$		0			0
$871$	17.9821	−	17.9821i	0.609299	−	0.609299i
$872$	11.8116	+	18.6348i	0.399992	+	0.631055i
$873$		0			0
$874$	1.72431	−	1.48783i	0.0583257	−	0.0503267i
$875$	8.85704	+	21.3828i	0.299423	+	0.722870i
$876$		0			0
$877$	16.7883	+	6.95392i	0.566899	+	0.234817i	0.647677	−	0.761915i	$-0.275741\pi$
$877$	16.7883	+	6.95392i	0.566899	+	0.234817i	−0.0807782	+	0.996732i	$0.525741\pi$
$878$	−15.6987	+	31.1991i	−0.529806	+	1.05292i
$879$		0			0
$880$	−10.5353	+	5.63899i	−0.355144	+	0.190090i
$881$			46.9687i			1.58242i	0.611547	+	0.791208i	$0.290547\pi$
$881$			46.9687i			1.58242i	−0.611547	+	0.791208i	$0.709453\pi$
$882$		0			0
$883$	11.0237	+	4.56617i	0.370978	+	0.153664i	0.560380	−	0.828236i	$-0.310655\pi$
$883$	11.0237	+	4.56617i	0.370978	+	0.153664i	−0.189403	+	0.981900i	$0.560655\pi$
$884$	7.24331	+	28.8818i	0.243619	+	0.971399i
$885$		0			0
$886$	−34.7377	−	40.2590i	−1.16704	−	1.35253i
$887$	−31.9419	−	31.9419i	−1.07250	−	1.07250i	−0.997157	−	0.0753464i	$-0.975994\pi$
$887$	−31.9419	−	31.9419i	−1.07250	−	1.07250i	−0.0753464	−	0.997157i	$-0.524006\pi$
$888$		0			0
$889$	26.0390	−	26.0390i	0.873319	−	0.873319i
$890$	11.5766	+	0.852270i	0.388048	+	0.0285682i
$891$		0			0
$892$	−44.2554	+	32.8417i	−1.48178	+	1.09962i
$893$	−11.8385	+	28.5807i	−0.396160	+	0.956416i
$894$		0			0
$895$	−1.48595			−0.0496699
$896$	4.41233	−	36.0724i	0.147406	−	1.20510i
$897$		0			0
$898$	3.70578	+	11.2121i	0.123663	+	0.374154i
$899$	6.36330	−	15.3624i	0.212228	−	0.512364i
$900$		0			0
$901$	12.3585	−	5.11904i	0.411720	−	0.170540i
$902$	−12.0101	−	0.884184i	−0.399892	−	0.0294401i
$903$		0			0
$904$	−14.2702	+	20.2807i	−0.474620	+	0.674525i
$905$	−8.65685	−	8.65685i	−0.287764	−	0.287764i
$906$		0			0
$907$	4.99616	+	12.0618i	0.165895	+	0.400505i	0.984863	−	0.173333i	$-0.0554538\pi$
$907$	4.99616	+	12.0618i	0.165895	+	0.400505i	−0.818969	+	0.573838i	$0.805454\pi$
$908$	7.66223	+	30.5521i	0.254280	+	1.01391i
$909$		0			0
$910$	−15.1445	−	7.62038i	−0.502035	−	0.252613i
$911$			13.1188i			0.434645i	0.976100	+	0.217322i	$0.0697323\pi$
$911$			13.1188i			0.434645i	−0.976100	+	0.217322i	$0.930268\pi$
$912$		0			0
$913$			38.2191i			1.26487i
$914$	16.2473	−	32.2895i	0.537414	−	1.06804i
$915$		0			0
$916$	−20.3319	+	33.9438i	−0.671785	+	1.12154i
$917$	−13.8833	−	33.5171i	−0.458465	−	1.10683i
$918$		0			0
$919$	−17.2415	−	17.2415i	−0.568746	−	0.568746i	0.363031	−	0.931777i	$-0.381742\pi$
$919$	−17.2415	−	17.2415i	−0.568746	−	0.568746i	−0.931777	+	0.363031i	$0.881742\pi$
$920$	−0.444708	−	0.701602i	−0.0146616	−	0.0231311i
$921$		0			0
$922$	2.97213	−	40.3712i	0.0978819	−	1.32955i
$923$	41.2263	−	17.0765i	1.35698	−	0.562080i
$924$		0			0
$925$	−6.64357	+	16.0390i	−0.218439	+	0.527359i
$926$	−6.63556	+	2.19315i	−0.218058	+	0.0720714i
$927$		0			0
$928$	4.94840	−	12.8557i	0.162439	−	0.422009i
$929$	45.9966			1.50910			0.754550	−	0.656242i	$-0.227855\pi$
$929$	45.9966			1.50910			0.754550	+	0.656242i	$0.227855\pi$
$930$		0			0
$931$	5.32876	−	12.8648i	0.174643	−	0.421626i
$932$	−18.7724	−	2.77912i	−0.614911	−	0.0910331i
$933$		0			0
$934$	2.32426	−	31.5710i	0.0760522	−	1.03303i
$935$	6.44955	−	6.44955i	0.210923	−	0.210923i
$936$		0			0
$937$	−3.67273	−	3.67273i	−0.119983	−	0.119983i	0.644566	−	0.764549i	$-0.277038\pi$
$937$	−3.67273	−	3.67273i	−0.119983	−	0.119983i	−0.764549	+	0.644566i	$0.777038\pi$
$938$	17.9367	−	15.4768i	0.585655	−	0.505336i
$939$		0			0
$940$	9.67956	+	5.79793i	0.315713	+	0.189108i
$941$	−41.7873	−	17.3089i	−1.36223	−	0.564253i	−0.422558	−	0.906336i	$-0.638868\pi$
$941$	−41.7873	−	17.3089i	−1.36223	−	0.564253i	−0.939670	+	0.342083i	$0.888868\pi$
$942$		0			0
$943$		−	0.837141i		−	0.0272611i
$944$	−4.31969	−	43.6020i	−0.140594	−	1.41912i
$945$		0			0
$946$	−9.65035	−	4.85584i	−0.313760	−	0.157877i
$947$	43.6427	+	18.0774i	1.41820	+	0.587436i	0.954407	−	0.298509i	$-0.0964894\pi$
$947$	43.6427	+	18.0774i	1.41820	+	0.587436i	0.463790	+	0.885945i	$0.346489\pi$
$948$		0			0
$949$	7.49753	+	18.1006i	0.243380	+	0.587571i
$950$	−17.1157	−	19.8361i	−0.555306	−	0.643568i
$951$		0			0
$952$	4.75413	+	27.3289i	0.154082	+	0.885735i
$953$	−6.12750	+	6.12750i	−0.198489	+	0.198489i	−0.799352	−	0.600863i	$-0.794824\pi$
$953$	−6.12750	+	6.12750i	−0.198489	+	0.198489i	0.600863	+	0.799352i	$0.294824\pi$
$954$		0			0
$955$	−4.37887	+	1.81379i	−0.141697	+	0.0586928i
$956$	−31.2261	−	42.0783i	−1.00993	−	1.36091i
$957$		0			0
$958$	2.44376	+	7.39380i	0.0789542	+	0.238883i
$959$	−15.5554			−0.502310
$960$		0			0
$961$	15.6274			0.504110
$962$	−8.51107	−	25.7510i	−0.274408	−	0.830245i
$963$		0			0
$964$	16.2968	+	21.9605i	0.524884	+	0.707300i
$965$	−10.3085	+	4.26991i	−0.331842	+	0.137453i
$966$		0			0
$967$	1.03516	−	1.03516i	0.0332885	−	0.0332885i	−0.690267	−	0.723555i	$-0.742507\pi$
$967$	1.03516	−	1.03516i	0.0332885	−	0.0332885i	0.723555	+	0.690267i	$0.242507\pi$
$968$	11.8008	−	2.05286i	0.379291	−	0.0659814i
$969$		0			0
$970$	−2.62636	−	3.04380i	−0.0843273	−	0.0977305i
$971$	−15.4218	−	37.2315i	−0.494909	−	1.19482i	−0.952194	−	0.305495i	$-0.901178\pi$
$971$	−15.4218	−	37.2315i	−0.494909	−	1.19482i	0.457285	−	0.889320i	$-0.348822\pi$
$972$		0			0
$973$	57.0556	+	23.6332i	1.82912	+	0.757646i
$974$	44.5861	+	22.4347i	1.42863	+	0.718855i
$975$		0			0
$976$	−10.9836	−	9.00343i	−0.351575	−	0.288193i
$977$			28.8457i			0.922857i	0.887177	+	0.461429i	$0.152663\pi$
$977$			28.8457i			0.922857i	−0.887177	+	0.461429i	$0.847337\pi$
$978$		0			0
$979$	−38.6727	−	16.0187i	−1.23598	−	0.511961i
$980$	−4.35698	−	2.60977i	−0.139179	−	0.0833661i
$981$		0			0
$982$	13.4143	−	11.5746i	0.428069	−	0.369362i
$983$	40.9561	+	40.9561i	1.30630	+	1.30630i	0.924067	+	0.382231i	$0.124844\pi$
$983$	40.9561	+	40.9561i	1.30630	+	1.30630i	0.382231	+	0.924067i	$0.375156\pi$
$984$		0			0
$985$	10.8385	−	10.8385i	0.345344	−	0.345344i
$986$	−0.771998	+	10.4862i	−0.0245854	+	0.333950i
$987$		0			0
$988$	40.4885	+	5.99402i	1.28811	+	0.190695i
$989$	0.287389	−	0.693818i	0.00913843	−	0.0220621i
$990$		0			0
$991$	−41.9605			−1.33292			−0.666460	−	0.745541i	$-0.732191\pi$
$991$	−41.9605			−1.33292			−0.666460	+	0.745541i	$0.732191\pi$
$992$	38.6151	−	0.975667i	1.22603	−	0.0309775i
$993$		0			0
$994$	39.4706	−	13.0456i	1.25193	−	0.413781i
$995$	5.12703	−	12.3777i	0.162538	−	0.392401i
$996$		0			0
$997$	−31.4380	+	13.0221i	−0.995652	+	0.412413i	−0.820201	−	0.572076i	$-0.806138\pi$
$997$	−31.4380	+	13.0221i	−0.995652	+	0.412413i	−0.175451	+	0.984488i	$0.556138\pi$
$998$	−0.979674	+	13.3071i	−0.0310111	+	0.421230i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.b.109.1		8
3.2	odd	2		32.2.g.b.13.2	yes	8
4.3	odd	2		1152.2.v.b.145.2		8
12.11	even	2		128.2.g.b.17.1		8
15.2	even	4		800.2.ba.d.749.2		8
15.8	even	4		800.2.ba.c.749.1		8
15.14	odd	2		800.2.y.b.301.1		8
24.5	odd	2		256.2.g.d.33.1		8
24.11	even	2		256.2.g.c.33.2		8
32.5	even	8	inner	288.2.v.b.37.1		8
32.27	odd	8		1152.2.v.b.1009.2		8
48.5	odd	4		512.2.g.h.321.1		8
48.11	even	4		512.2.g.f.321.2		8
48.29	odd	4		512.2.g.e.321.2		8
48.35	even	4		512.2.g.g.321.1		8
96.5	odd	8		32.2.g.b.5.2	✓	8
96.11	even	8		256.2.g.c.225.2		8
96.29	odd	8		512.2.g.e.193.2		8
96.35	even	8		512.2.g.g.193.1		8
96.53	odd	8		256.2.g.d.225.1		8
96.59	even	8		128.2.g.b.113.1		8
96.77	odd	8		512.2.g.h.193.1		8
96.83	even	8		512.2.g.f.193.2		8
192.5	odd	16		4096.2.a.k.1.5		8
192.59	even	16		4096.2.a.q.1.4		8
192.101	odd	16		4096.2.a.k.1.4		8
192.155	even	16		4096.2.a.q.1.5		8
480.197	even	8		800.2.ba.c.549.1		8
480.293	even	8		800.2.ba.d.549.2		8
480.389	odd	8		800.2.y.b.101.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.5.2	✓	8	96.5	odd	8
32.2.g.b.13.2	yes	8	3.2	odd	2
128.2.g.b.17.1		8	12.11	even	2
128.2.g.b.113.1		8	96.59	even	8
256.2.g.c.33.2		8	24.11	even	2
256.2.g.c.225.2		8	96.11	even	8
256.2.g.d.33.1		8	24.5	odd	2
256.2.g.d.225.1		8	96.53	odd	8
288.2.v.b.37.1		8	32.5	even	8	inner
288.2.v.b.109.1		8	1.1	even	1	trivial
512.2.g.e.193.2		8	96.29	odd	8
512.2.g.e.321.2		8	48.29	odd	4
512.2.g.f.193.2		8	96.83	even	8
512.2.g.f.321.2		8	48.11	even	4
512.2.g.g.193.1		8	96.35	even	8
512.2.g.g.321.1		8	48.35	even	4
512.2.g.h.193.1		8	96.77	odd	8
512.2.g.h.321.1		8	48.5	odd	4
800.2.y.b.101.1		8	480.389	odd	8
800.2.y.b.301.1		8	15.14	odd	2
800.2.ba.c.549.1		8	480.197	even	8
800.2.ba.c.749.1		8	15.8	even	4
800.2.ba.d.549.2		8	480.293	even	8
800.2.ba.d.749.2		8	15.2	even	4
1152.2.v.b.145.2		8	4.3	odd	2
1152.2.v.b.1009.2		8	32.27	odd	8
4096.2.a.k.1.4		8	192.101	odd	16
4096.2.a.k.1.5		8	192.5	odd	16
4096.2.a.q.1.4		8	192.59	even	16
4096.2.a.q.1.5		8	192.155	even	16

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.443806 + 1.34277i) q^{2} +(-1.60607 + 1.19186i) q^{4} +(-0.707107 + 0.292893i) q^{5} +(-2.27133 + 2.27133i) q^{7} +(-2.31318 - 1.62764i) q^{8} +O(q^{10})\)	\(q+(0.443806 + 1.34277i) q^{2} +(-1.60607 + 1.19186i) q^{4} +(-0.707107 + 0.292893i) q^{5} +(-2.27133 + 2.27133i) q^{7} +(-2.31318 - 1.62764i) q^{8} +(-0.707107 - 0.819496i) q^{10} +(1.49368 + 3.60607i) q^{11} +(-4.50504 - 1.86605i) q^{13} +(-4.05791 - 2.04185i) q^{14} +(1.15894 - 3.82843i) q^{16} +3.05320i q^{17} +(3.87740 + 1.60607i) q^{19} +(0.786578 - 1.31318i) q^{20} +(-4.17923 + 3.60607i) q^{22} +(-0.271330 - 0.271330i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(0.506316 - 6.87740i) q^{26} +(0.940816 - 6.35503i) q^{28} +(0.931884 - 2.24977i) q^{29} +6.82843 q^{31} +(5.65505 - 0.142883i) q^{32} +(-4.09976 + 1.35503i) q^{34} +(0.940816 - 2.27133i) q^{35} +(3.63349 - 1.50504i) q^{37} +(-0.435776 + 5.91925i) q^{38} +(2.11239 + 0.473398i) q^{40} +(1.54266 + 1.54266i) q^{41} +(0.748956 + 1.80814i) q^{43} +(-6.69690 - 4.01136i) q^{44} +(0.243917 - 0.484753i) q^{46} +7.37109i q^{47} -3.31788i q^{49} +(-5.57648 - 2.80596i) q^{50} +(9.45949 - 2.37236i) q^{52} +(-1.67661 - 4.04770i) q^{53} +(-2.11239 - 2.11239i) q^{55} +(8.95089 - 1.55710i) q^{56} +(3.43450 + 0.252848i) q^{58} +(10.1200 - 4.19186i) q^{59} +(1.35873 - 3.28026i) q^{61} +(3.03049 + 9.16902i) q^{62} +(2.70160 + 7.53003i) q^{64} +3.73210 q^{65} +(-1.99577 + 4.81822i) q^{67} +(-3.63899 - 4.90367i) q^{68} +(3.46742 + 0.255272i) q^{70} +(-6.47085 + 6.47085i) q^{71} +(-2.84106 - 2.84106i) q^{73} +(3.63349 + 4.21100i) q^{74} +(-8.14161 + 2.04185i) q^{76} +(-11.5832 - 4.79793i) q^{77} +9.74996i q^{79} +(0.301825 + 3.04655i) q^{80} +(-1.38680 + 2.75608i) q^{82} +(9.04642 + 3.74715i) q^{83} +(-0.894263 - 2.15894i) q^{85} +(-2.09553 + 1.80814i) q^{86} +(2.41421 - 10.7727i) q^{88} +(-7.58323 + 7.58323i) q^{89} +(14.4708 - 5.99402i) q^{91} +(0.759164 + 0.112389i) q^{92} +(-9.89769 + 3.27133i) q^{94} -3.21215 q^{95} +3.71423 q^{97} +(4.45516 - 1.47250i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8	\( 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} - 4 q^{11} - 8 q^{13} - 12 q^{14} + 4 q^{19} - 4 q^{20} + 4 q^{22} + 8 q^{23} - 8 q^{25} + 20 q^{26} - 16 q^{28} + 32 q^{31} + 24 q^{32} - 16 q^{35} - 8 q^{37} - 8 q^{38} + 16 q^{40} - 8 q^{41} - 12 q^{43} - 20 q^{44} + 12 q^{46} - 16 q^{50} + 12 q^{52} - 8 q^{53} - 16 q^{55} - 8 q^{56} - 12 q^{58} + 20 q^{59} + 24 q^{61} + 24 q^{62} - 8 q^{64} - 36 q^{67} - 16 q^{68} - 8 q^{70} + 24 q^{71} - 32 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{77} - 8 q^{80} - 20 q^{82} - 20 q^{83} + 8 q^{85} - 4 q^{86} + 8 q^{88} + 16 q^{89} + 40 q^{91} + 16 q^{92} - 24 q^{94} + 8 q^{95} + 32 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 - 4 * q^11 - 8 * q^13 - 12 * q^14 + 4 * q^19 - 4 * q^20 + 4 * q^22 + 8 * q^23 - 8 * q^25 + 20 * q^26 - 16 * q^28 + 32 * q^31 + 24 * q^32 - 16 * q^35 - 8 * q^37 - 8 * q^38 + 16 * q^40 - 8 * q^41 - 12 * q^43 - 20 * q^44 + 12 * q^46 - 16 * q^50 + 12 * q^52 - 8 * q^53 - 16 * q^55 - 8 * q^56 - 12 * q^58 + 20 * q^59 + 24 * q^61 + 24 * q^62 - 8 * q^64 - 36 * q^67 - 16 * q^68 - 8 * q^70 + 24 * q^71 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 8 * q^80 - 20 * q^82 - 20 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 + 16 * q^89 + 40 * q^91 + 16 * q^92 - 24 * q^94 + 8 * q^95 + 32 * q^97 + 24 * q^98

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