LMFDB - Embedded newform 1152.2.w.a.1007.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(143,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.w (of order $8$, degree $4$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			1007.5
Character	$\chi$	$=$	1152.1007
Dual form			1152.2.w.a.143.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0963530 - 0.232617i) q^{5} +(-0.617536 - 0.617536i) q^{7} +O(q^{10})$	$q+(-0.0963530 - 0.232617i) q^{5} +(-0.617536 - 0.617536i) q^{7} +(-0.505112 - 1.21945i) q^{11} +(3.41575 + 1.41485i) q^{13} +2.76109 q^{17} +(-0.189895 + 0.458448i) q^{19} +(-4.46959 - 4.46959i) q^{23} +(3.49071 - 3.49071i) q^{25} +(-0.0101033 - 0.00418494i) q^{29} +4.03370i q^{31} +(-0.0841477 + 0.203151i) q^{35} +(6.30586 - 2.61197i) q^{37} +(5.34633 - 5.34633i) q^{41} +(10.1719 - 4.21336i) q^{43} -11.5870i q^{47} -6.23730i q^{49} +(-9.04956 + 3.74845i) q^{53} +(-0.234995 + 0.234995i) q^{55} +(-0.939369 + 0.389099i) q^{59} +(-2.97084 + 7.17223i) q^{61} -0.930884i q^{65} +(7.40244 + 3.06619i) q^{67} +(1.20890 - 1.20890i) q^{71} +(3.73875 + 3.73875i) q^{73} +(-0.441128 + 1.06498i) q^{77} +7.22016 q^{79} +(11.2970 + 4.67935i) q^{83} +(-0.266039 - 0.642275i) q^{85} +(-3.70197 - 3.70197i) q^{89} +(-1.23563 - 2.98307i) q^{91} +0.124940 q^{95} -14.0257 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) $ 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.0963530	−	0.232617i	−0.0430904	−	0.104029i	0.900869	−	0.434091i	$-0.142930\pi$
$5$	−0.0963530	−	0.232617i	−0.0430904	−	0.104029i	−0.943959	+	0.330062i	$0.892930\pi$
$6$		0			0
$7$	−0.617536	−	0.617536i	−0.233407	−	0.233407i	0.580706	−	0.814113i	$-0.302776\pi$
$7$	−0.617536	−	0.617536i	−0.233407	−	0.233407i	−0.814113	+	0.580706i	$0.802776\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.505112	−	1.21945i	−0.152297	−	0.367677i	0.829256	−	0.558869i	$-0.188765\pi$
$11$	−0.505112	−	1.21945i	−0.152297	−	0.367677i	−0.981553	+	0.191192i	$0.938765\pi$
$12$		0			0
$13$	3.41575	+	1.41485i	0.947358	+	0.392408i	0.802237	−	0.597006i	$-0.203643\pi$
$13$	3.41575	+	1.41485i	0.947358	+	0.392408i	0.145121	+	0.989414i	$0.453643\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.76109			0.669662			0.334831	−	0.942278i	$-0.391321\pi$
$17$	2.76109			0.669662			0.334831	+	0.942278i	$0.391321\pi$
$18$		0			0
$19$	−0.189895	+	0.458448i	−0.0435650	+	0.105175i	−0.944164	−	0.329475i	$-0.893128\pi$
$19$	−0.189895	+	0.458448i	−0.0435650	+	0.105175i	0.900599	+	0.434651i	$0.143128\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.46959	−	4.46959i	−0.931975	−	0.931975i	0.0658547	−	0.997829i	$-0.479023\pi$
$23$	−4.46959	−	4.46959i	−0.931975	−	0.931975i	−0.997829	+	0.0658547i	$0.979023\pi$
$24$		0			0
$25$	3.49071	−	3.49071i	0.698141	−	0.698141i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.0101033	−	0.00418494i	−0.00187614	−	0.000777123i	0.381745	−	0.924268i	$-0.375323\pi$
$29$	−0.0101033	−	0.00418494i	−0.00187614	−	0.000777123i	−0.383621	+	0.923490i	$0.625323\pi$
$30$		0			0
$31$			4.03370i			0.724474i	0.932086	+	0.362237i	$0.117987\pi$
$31$			4.03370i			0.724474i	−0.932086	+	0.362237i	$0.882013\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0841477	+	0.203151i	−0.0142236	+	0.0343387i
$36$		0			0
$37$	6.30586	−	2.61197i	1.03668	−	0.429406i	0.201559	−	0.979476i	$-0.435399\pi$
$37$	6.30586	−	2.61197i	1.03668	−	0.429406i	0.835118	+	0.550071i	$0.185399\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.34633	−	5.34633i	0.834957	−	0.834957i	−0.153233	−	0.988190i	$-0.548969\pi$
$41$	5.34633	−	5.34633i	0.834957	−	0.834957i	0.988190	+	0.153233i	$0.0489686\pi$
$42$		0			0
$43$	10.1719	−	4.21336i	1.55121	−	0.642531i	0.567673	−	0.823254i	$-0.307844\pi$
$43$	10.1719	−	4.21336i	1.55121	−	0.642531i	0.983534	+	0.180724i	$0.0578440\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	11.5870i		−	1.69013i	−0.534660	−	0.845067i	$-0.679560\pi$
$47$		−	11.5870i		−	1.69013i	0.534660	−	0.845067i	$-0.320440\pi$
$48$		0			0
$49$		−	6.23730i		−	0.891043i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.04956	+	3.74845i	−1.24305	+	0.514889i	−0.904667	−	0.426119i	$-0.859881\pi$
$53$	−9.04956	+	3.74845i	−1.24305	+	0.514889i	−0.338385	+	0.941008i	$0.609881\pi$
$54$		0			0
$55$	−0.234995	+	0.234995i	−0.0316867	+	0.0316867i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.939369	+	0.389099i	−0.122295	+	0.0506564i	−0.442992	−	0.896526i	$-0.646083\pi$
$59$	−0.939369	+	0.389099i	−0.122295	+	0.0506564i	0.320697	+	0.947182i	$0.396083\pi$
$60$		0			0
$61$	−2.97084	+	7.17223i	−0.380377	+	0.918311i	0.611516	+	0.791232i	$0.290560\pi$
$61$	−2.97084	+	7.17223i	−0.380377	+	0.918311i	−0.991893	+	0.127078i	$0.959440\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	0.930884i		−	0.115462i
$66$		0			0
$67$	7.40244	+	3.06619i	0.904352	+	0.374595i	0.785892	−	0.618364i	$-0.212204\pi$
$67$	7.40244	+	3.06619i	0.904352	+	0.374595i	0.118460	+	0.992959i	$0.462204\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.20890	−	1.20890i	0.143470	−	0.143470i	−0.631724	−	0.775194i	$-0.717652\pi$
$71$	1.20890	−	1.20890i	0.143470	−	0.143470i	0.775194	+	0.631724i	$0.217652\pi$
$72$		0			0
$73$	3.73875	+	3.73875i	0.437588	+	0.437588i	0.891199	−	0.453612i	$-0.149865\pi$
$73$	3.73875	+	3.73875i	0.437588	+	0.437588i	−0.453612	+	0.891199i	$0.649865\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.441128	+	1.06498i	−0.0502712	+	0.121366i
$78$		0			0
$79$	7.22016			0.812331			0.406166	−	0.913800i	$-0.366866\pi$
$79$	7.22016			0.812331			0.406166	+	0.913800i	$0.366866\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	11.2970	+	4.67935i	1.24000	+	0.513626i	0.903715	−	0.428134i	$-0.140829\pi$
$83$	11.2970	+	4.67935i	1.24000	+	0.513626i	0.336287	+	0.941760i	$0.390829\pi$
$84$		0			0
$85$	−0.266039	−	0.642275i	−0.0288560	−	0.0696645i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.70197	−	3.70197i	−0.392408	−	0.392408i	0.483137	−	0.875545i	$-0.339497\pi$
$89$	−3.70197	−	3.70197i	−0.392408	−	0.392408i	−0.875545	+	0.483137i	$0.839497\pi$
$90$		0			0
$91$	−1.23563	−	2.98307i	−0.129529	−	0.312710i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.124940			0.0128185
$96$		0			0
$97$	−14.0257			−1.42409			−0.712046	−	0.702133i	$-0.752231\pi$
$97$	−14.0257			−1.42409			−0.712046	+	0.702133i	$0.752231\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.26734	−	10.3023i	−0.424616	−	1.02511i	−0.980968	−	0.194168i	$-0.937799\pi$
$101$	−4.26734	−	10.3023i	−0.424616	−	1.02511i	0.556352	−	0.830947i	$-0.312201\pi$
$102$		0			0
$103$	−8.34273	−	8.34273i	−0.822034	−	0.822034i	0.164366	−	0.986399i	$-0.447442\pi$
$103$	−8.34273	−	8.34273i	−0.822034	−	0.822034i	−0.986399	+	0.164366i	$0.947442\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.28476	+	3.10168i	0.124202	+	0.299850i	0.973735	−	0.227686i	$-0.0731159\pi$
$107$	1.28476	+	3.10168i	0.124202	+	0.299850i	−0.849533	+	0.527536i	$0.823116\pi$
$108$		0			0
$109$	8.00684	+	3.31654i	0.766916	+	0.317667i	0.731623	−	0.681710i	$-0.238763\pi$
$109$	8.00684	+	3.31654i	0.766916	+	0.317667i	0.0352935	+	0.999377i	$0.488763\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.12115			0.481757			0.240879	−	0.970555i	$-0.422564\pi$
$113$	5.12115			0.481757			0.240879	+	0.970555i	$0.422564\pi$
$114$		0			0
$115$	−0.609043	+	1.47036i	−0.0567936	+	0.137112i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.70507	−	1.70507i	−0.156304	−	0.156304i
$120$		0			0
$121$	6.54626	−	6.54626i	0.595114	−	0.595114i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.31142	−	0.957421i	−0.206740	−	0.0856344i
$126$		0			0
$127$			8.28564i			0.735232i	0.929978	+	0.367616i	$0.119826\pi$
$127$			8.28564i			0.735232i	−0.929978	+	0.367616i	$0.880174\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.82244	+	18.8850i	−0.683450	+	1.64999i	0.0741279	+	0.997249i	$0.476383\pi$
$131$	−7.82244	+	18.8850i	−0.683450	+	1.64999i	−0.757578	+	0.652745i	$0.773617\pi$
$132$		0			0
$133$	0.400375	−	0.165841i	0.0347169	−	0.0143802i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.3963	−	13.3963i	1.14452	−	1.14452i	0.156906	−	0.987613i	$-0.449848\pi$
$137$	13.3963	−	13.3963i	1.14452	−	1.14452i	0.987613	−	0.156906i	$-0.0501521\pi$
$138$		0			0
$139$	18.0954	−	7.49538i	1.53484	−	0.635750i	0.554340	−	0.832290i	$-0.312971\pi$
$139$	18.0954	−	7.49538i	1.53484	−	0.635750i	0.980496	+	0.196540i	$0.0629706\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	4.87998i		−	0.408085i
$144$		0			0
$145$			0.00275343i			0.000228660i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−14.0938	+	5.83786i	−1.15461	+	0.478256i	−0.876078	−	0.482170i	$-0.839849\pi$
$149$	−14.0938	+	5.83786i	−1.15461	+	0.478256i	−0.278535	+	0.960426i	$0.589849\pi$
$150$		0			0
$151$	−3.91247	+	3.91247i	−0.318392	+	0.318392i	−0.848149	−	0.529757i	$-0.822283\pi$
$151$	−3.91247	+	3.91247i	−0.318392	+	0.318392i	0.529757	+	0.848149i	$0.322283\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.938306	−	0.388659i	0.0753665	−	0.0312178i
$156$		0			0
$157$	−7.38756	+	17.8351i	−0.589591	+	1.42340i	0.294303	+	0.955712i	$0.404912\pi$
$157$	−7.38756	+	17.8351i	−0.589591	+	1.42340i	−0.883894	+	0.467687i	$0.845088\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			5.52027i			0.435058i
$162$		0			0
$163$	−17.9611	−	7.43971i	−1.40682	−	0.582723i	−0.455307	−	0.890335i	$-0.650470\pi$
$163$	−17.9611	−	7.43971i	−1.40682	−	0.582723i	−0.951512	+	0.307611i	$0.900470\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.9383	+	13.9383i	−1.07858	+	1.07858i	−0.0819391	+	0.996637i	$0.526111\pi$
$167$	−13.9383	+	13.9383i	−1.07858	+	1.07858i	−0.996637	+	0.0819391i	$0.973889\pi$
$168$		0			0
$169$	0.473139	+	0.473139i	0.0363953	+	0.0363953i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.06460	+	2.57018i	−0.0809402	+	0.195407i	−0.959169	−	0.282834i	$-0.908725\pi$
$173$	−1.06460	+	2.57018i	−0.0809402	+	0.195407i	0.878229	+	0.478241i	$0.158725\pi$
$174$		0			0
$175$	−4.31128			−0.325902
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.3931	+	5.96183i	1.07579	+	0.445608i	0.849031	−	0.528342i	$-0.177186\pi$
$179$	14.3931	+	5.96183i	1.07579	+	0.445608i	0.226761	+	0.973950i	$0.427186\pi$
$180$		0			0
$181$	−2.56470	−	6.19174i	−0.190633	−	0.460229i	0.799446	−	0.600737i	$-0.205126\pi$
$181$	−2.56470	−	6.19174i	−0.190633	−	0.460229i	−0.990079	+	0.140509i	$0.955126\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.21518	−	1.21518i	−0.0893415	−	0.0893415i
$186$		0			0
$187$	−1.39466	−	3.36700i	−0.101988	−	0.246220i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	15.0419			1.08840			0.544198	−	0.838957i	$-0.316834\pi$
$191$	15.0419			1.08840			0.544198	+	0.838957i	$0.316834\pi$
$192$		0			0
$193$	−19.6537			−1.41470			−0.707352	−	0.706861i	$-0.750111\pi$
$193$	−19.6537			−1.41470			−0.707352	+	0.706861i	$0.750111\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.28693	+	7.93534i	0.234184	+	0.565370i	0.996661	−	0.0816448i	$-0.0260173\pi$
$197$	3.28693	+	7.93534i	0.234184	+	0.565370i	−0.762478	+	0.647015i	$0.776017\pi$
$198$		0			0
$199$	−14.6374	−	14.6374i	−1.03761	−	1.03761i	−0.999264	−	0.0383500i	$-0.987790\pi$
$199$	−14.6374	−	14.6374i	−1.03761	−	1.03761i	−0.0383500	−	0.999264i	$-0.512210\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.00365482	+	0.00882352i	0.000256518	+	0.000619290i
$204$		0			0
$205$	−1.75878	−	0.728511i	−0.122839	−	0.0508814i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.654971			0.0453053
$210$		0			0
$211$	−6.76173	+	16.3243i	−0.465497	+	1.12381i	0.500612	+	0.865672i	$0.333109\pi$
$211$	−6.76173	+	16.3243i	−0.465497	+	1.12381i	−0.966108	+	0.258137i	$0.916891\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.96019	−	1.96019i	−0.133684	−	0.133684i
$216$		0			0
$217$	2.49096	−	2.49096i	0.169097	−	0.169097i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.43118	+	3.90652i	0.634410	+	0.262781i
$222$		0			0
$223$			15.8618i			1.06219i	0.847313	+	0.531093i	$0.178219\pi$
$223$			15.8618i			1.06219i	−0.847313	+	0.531093i	$0.821781\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.50806	−	6.05500i	0.166466	−	0.401884i	−0.818530	−	0.574464i	$-0.805210\pi$
$227$	2.50806	−	6.05500i	0.166466	−	0.401884i	0.984995	+	0.172580i	$0.0552104\pi$
$228$		0			0
$229$	−7.60466	+	3.14995i	−0.502530	+	0.208155i	−0.619524	−	0.784978i	$-0.712674\pi$
$229$	−7.60466	+	3.14995i	−0.502530	+	0.208155i	0.116994	+	0.993133i	$0.462674\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.99464	+	5.99464i	−0.392722	+	0.392722i	−0.875656	−	0.482935i	$-0.839571\pi$
$233$	−5.99464	+	5.99464i	−0.392722	+	0.392722i	0.482935	+	0.875656i	$0.339571\pi$
$234$		0			0
$235$	−2.69532	+	1.11644i	−0.175824	+	0.0728285i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	1.11236i		−	0.0719527i	−0.999353	−	0.0359763i	$-0.988546\pi$
$239$		−	1.11236i		−	0.0719527i	0.999353	−	0.0359763i	$-0.0114541\pi$
$240$		0			0
$241$		−	0.709331i		−	0.0456920i	−0.999739	−	0.0228460i	$-0.992727\pi$
$241$		−	0.709331i		−	0.0456920i	0.999739	−	0.0228460i	$-0.00727274\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.45090	+	0.600982i	−0.0926946	+	0.0383953i
$246$		0			0
$247$	−1.29727	+	1.29727i	−0.0825432	+	0.0825432i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.3657	+	4.29361i	−0.654276	+	0.271010i	−0.685028	−	0.728517i	$-0.740210\pi$
$251$	−10.3657	+	4.29361i	−0.654276	+	0.271010i	0.0307514	+	0.999527i	$0.490210\pi$
$252$		0			0
$253$	−3.19279	+	7.70808i	−0.200729	+	0.484603i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			29.1264i			1.81686i	0.418042	+	0.908428i	$0.362716\pi$
$257$			29.1264i			1.81686i	−0.418042	+	0.908428i	$0.637284\pi$
$258$		0			0
$259$	−5.50708	−	2.28111i	−0.342194	−	0.141741i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.87052	−	1.87052i	0.115341	−	0.115341i	−0.647080	−	0.762422i	$-0.724010\pi$
$263$	1.87052	−	1.87052i	0.115341	−	0.115341i	0.762422	+	0.647080i	$0.224010\pi$
$264$		0			0
$265$	1.74390	+	1.74390i	0.107127	+	0.107127i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.63828	+	3.95517i	−0.0998879	+	0.241151i	−0.965922	−	0.258835i	$-0.916661\pi$
$269$	−1.63828	+	3.95517i	−0.0998879	+	0.241151i	0.866034	+	0.499986i	$0.166661\pi$
$270$		0			0
$271$	−0.865193			−0.0525567			−0.0262784	−	0.999655i	$-0.508366\pi$
$271$	−0.865193			−0.0525567			−0.0262784	+	0.999655i	$0.508366\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.01993	−	2.49354i	−0.363016	−	0.150366i
$276$		0			0
$277$	−10.8442	−	26.1801i	−0.651563	−	1.57301i	−0.810510	−	0.585724i	$-0.800810\pi$
$277$	−10.8442	−	26.1801i	−0.651563	−	1.57301i	0.158948	−	0.987287i	$-0.449190\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.20552	+	3.20552i	0.191225	+	0.191225i	0.796225	−	0.605000i	$-0.206827\pi$
$281$	3.20552	+	3.20552i	0.191225	+	0.191225i	−0.605000	+	0.796225i	$0.706827\pi$
$282$		0			0
$283$	0.808604	+	1.95214i	0.0480665	+	0.116043i	0.946089	−	0.323907i	$-0.104996\pi$
$283$	0.808604	+	1.95214i	0.0480665	+	0.116043i	−0.898023	+	0.439949i	$0.854996\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.60311			−0.389769
$288$		0			0
$289$	−9.37639			−0.551552
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.84084	+	6.85839i	0.165964	+	0.400671i	0.984879	−	0.173242i	$-0.0554244\pi$
$293$	2.84084	+	6.85839i	0.165964	+	0.400671i	−0.818916	+	0.573914i	$0.805424\pi$
$294$		0			0
$295$	0.181022	+	0.181022i	0.0105395	+	0.0105395i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.94320	−	21.5908i	−0.517199	−	1.24863i
$300$		0			0
$301$	−8.88344	−	3.67964i	−0.512033	−	0.212091i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.95463			0.111922
$306$		0			0
$307$	−5.75328	+	13.8897i	−0.328357	+	0.792724i	0.670357	+	0.742038i	$0.266141\pi$
$307$	−5.75328	+	13.8897i	−0.328357	+	0.792724i	−0.998715	+	0.0506860i	$0.983859\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.92757	+	9.92757i	0.562941	+	0.562941i	0.930142	−	0.367201i	$-0.119684\pi$
$311$	9.92757	+	9.92757i	0.562941	+	0.562941i	−0.367201	+	0.930142i	$0.619684\pi$
$312$		0			0
$313$	−6.07029	+	6.07029i	−0.343113	+	0.343113i	−0.857536	−	0.514423i	$-0.828006\pi$
$313$	−6.07029	+	6.07029i	−0.343113	+	0.343113i	0.514423	+	0.857536i	$0.328006\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	28.8754	+	11.9606i	1.62180	+	0.671773i	0.994278	−	0.106823i	$-0.0340678\pi$
$317$	28.8754	+	11.9606i	1.62180	+	0.671773i	0.627525	+	0.778596i	$0.284068\pi$
$318$		0			0
$319$			0.0144343i			0.000808168i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.524318	+	1.26581i	−0.0291738	+	0.0704318i
$324$		0			0
$325$	16.8622	−	6.98455i	0.935346	−	0.387433i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.15538	+	7.15538i	−0.394489	+	0.394489i
$330$		0			0
$331$	−13.5735	+	5.62233i	−0.746067	+	0.309031i	−0.723136	−	0.690706i	$-0.757300\pi$
$331$	−13.5735	+	5.62233i	−0.746067	+	0.309031i	−0.0229312	+	0.999737i	$0.507300\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	2.01737i		−	0.110221i
$336$		0			0
$337$		−	7.22397i		−	0.393515i	−0.980452	−	0.196757i	$-0.936959\pi$
$337$		−	7.22397i		−	0.393515i	0.980452	−	0.196757i	$-0.0630411\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.91889	−	2.03747i	0.266373	−	0.110335i
$342$		0			0
$343$	−8.17451	+	8.17451i	−0.441382	+	0.441382i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.78836	+	2.81183i	−0.364418	+	0.150947i	−0.557376	−	0.830260i	$-0.688192\pi$
$347$	−6.78836	+	2.81183i	−0.364418	+	0.150947i	0.192958	+	0.981207i	$0.438192\pi$
$348$		0			0
$349$	0.0989263	−	0.238829i	0.00529540	−	0.0127842i	−0.921210	−	0.389066i	$-0.872798\pi$
$349$	0.0989263	−	0.238829i	0.00529540	−	0.0127842i	0.926505	+	0.376282i	$0.122798\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			1.04908i			0.0558369i	0.999610	+	0.0279184i	$0.00888787\pi$
$353$			1.04908i			0.0558369i	−0.999610	+	0.0279184i	$0.991112\pi$
$354$		0			0
$355$	−0.397691	−	0.164729i	−0.0211072	−	0.00874290i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.9586	+	10.9586i	−0.578375	+	0.578375i	−0.934455	−	0.356080i	$-0.884113\pi$
$359$	−10.9586	+	10.9586i	−0.578375	+	0.578375i	0.356080	+	0.934455i	$0.384113\pi$
$360$		0			0
$361$	13.2609	+	13.2609i	0.697943	+	0.697943i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.509456	−	1.22994i	0.0266662	−	0.0643778i
$366$		0			0
$367$	14.0919			0.735589			0.367795	−	0.929907i	$-0.380113\pi$
$367$	14.0919			0.735589			0.367795	+	0.929907i	$0.380113\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.90323	+	3.27363i	0.410315	+	0.169958i
$372$		0			0
$373$	0.973904	+	2.35121i	0.0504268	+	0.121741i	0.947086	−	0.320981i	$-0.104013\pi$
$373$	0.973904	+	2.35121i	0.0504268	+	0.121741i	−0.896659	+	0.442723i	$0.854013\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.0285894	−	0.0285894i	−0.00147243	−	0.00147243i
$378$		0			0
$379$	−7.22577	−	17.4446i	−0.371163	−	0.896067i	−0.993554	−	0.113360i	$-0.963839\pi$
$379$	−7.22577	−	17.4446i	−0.371163	−	0.896067i	0.622391	−	0.782707i	$-0.286161\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.91841			0.251319			0.125660	−	0.992073i	$-0.459895\pi$
$383$	4.91841			0.251319			0.125660	+	0.992073i	$0.459895\pi$
$384$		0			0
$385$	0.290236			0.0147918
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.57039	−	15.8623i	−0.333132	−	0.804252i	−0.998340	−	0.0575939i	$-0.981657\pi$
$389$	−6.57039	−	15.8623i	−0.333132	−	0.804252i	0.665208	−	0.746658i	$-0.268343\pi$
$390$		0			0
$391$	−12.3409	−	12.3409i	−0.624108	−	0.624108i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.695683	−	1.67953i	−0.0350036	−	0.0845062i
$396$		0			0
$397$	1.49381	+	0.618757i	0.0749723	+	0.0310545i	0.419854	−	0.907591i	$-0.362081\pi$
$397$	1.49381	+	0.618757i	0.0749723	+	0.0310545i	−0.344882	+	0.938646i	$0.612081\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−29.8271			−1.48949			−0.744747	−	0.667347i	$-0.767430\pi$
$401$	−29.8271			−1.48949			−0.744747	+	0.667347i	$0.767430\pi$
$402$		0			0
$403$	−5.70708	+	13.7781i	−0.284290	+	0.686336i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.37033	−	6.37033i	−0.315765	−	0.315765i
$408$		0			0
$409$	9.09883	−	9.09883i	0.449908	−	0.449908i	−0.445416	−	0.895324i	$-0.646944\pi$
$409$	9.09883	−	9.09883i	0.449908	−	0.449908i	0.895324	+	0.445416i	$0.146944\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.820377	+	0.339811i	0.0403681	+	0.0167210i
$414$		0			0
$415$		−	3.07873i		−	0.151129i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.94681	−	9.52845i	0.192814	−	0.465495i	−0.797674	−	0.603088i	$-0.793937\pi$
$419$	3.94681	−	9.52845i	0.192814	−	0.465495i	0.990489	+	0.137593i	$0.0439366\pi$
$420$		0			0
$421$	2.91334	−	1.20674i	0.141987	−	0.0588131i	−0.310558	−	0.950554i	$-0.600516\pi$
$421$	2.91334	−	1.20674i	0.141987	−	0.0588131i	0.452546	+	0.891741i	$0.350516\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.63815	−	9.63815i	0.467519	−	0.467519i
$426$		0			0
$427$	6.26371	−	2.59451i	0.303122	−	0.125557i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			23.1792i			1.11650i	0.829672	+	0.558252i	$0.188528\pi$
$431$			23.1792i			1.11650i	−0.829672	+	0.558252i	$0.811472\pi$
$432$		0			0
$433$			25.2987i			1.21578i	0.794023	+	0.607888i	$0.207983\pi$
$433$			25.2987i			1.21578i	−0.794023	+	0.607888i	$0.792017\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.89783	−	1.20032i	0.138622	−	0.0574191i
$438$		0			0
$439$	28.3833	−	28.3833i	1.35466	−	1.35466i	0.474297	−	0.880365i	$-0.342702\pi$
$439$	28.3833	−	28.3833i	1.35466	−	1.35466i	0.880365	−	0.474297i	$-0.157298\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	19.8722	−	8.23132i	0.944155	−	0.391082i	0.143124	−	0.989705i	$-0.454285\pi$
$443$	19.8722	−	8.23132i	0.944155	−	0.391082i	0.801031	+	0.598623i	$0.204285\pi$
$444$		0			0
$445$	−0.504444	+	1.21784i	−0.0239130	+	0.0577310i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	12.5843i		−	0.593889i	−0.954895	−	0.296944i	$-0.904032\pi$
$449$		−	12.5843i		−	0.593889i	0.954895	−	0.296944i	$-0.0959676\pi$
$450$		0			0
$451$	−9.22007	−	3.81908i	−0.434156	−	0.179833i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.574855	+	0.574855i	−0.0269496	+	0.0269496i
$456$		0			0
$457$	8.93449	+	8.93449i	0.417938	+	0.417938i	0.884492	−	0.466554i	$-0.154505\pi$
$457$	8.93449	+	8.93449i	0.417938	+	0.417938i	−0.466554	+	0.884492i	$0.654505\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.9213	−	31.1949i	0.601807	−	1.45289i	−0.269913	−	0.962885i	$-0.586995\pi$
$461$	12.9213	−	31.1949i	0.601807	−	1.45289i	0.871720	−	0.490005i	$-0.163005\pi$
$462$		0			0
$463$	1.78637			0.0830196			0.0415098	−	0.999138i	$-0.486783\pi$
$463$	1.78637			0.0830196			0.0415098	+	0.999138i	$0.486783\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−37.9374	−	15.7142i	−1.75553	−	0.727166i	−0.997157	−	0.0753479i	$-0.975993\pi$
$467$	−37.9374	−	15.7142i	−1.75553	−	0.727166i	−0.758376	−	0.651818i	$-0.774007\pi$
$468$		0			0
$469$	−2.67779	−	6.46476i	−0.123649	−	0.298515i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.2759	−	10.2759i	−0.472488	−	0.472488i
$474$		0			0
$475$	0.937438	+	2.26318i	0.0430126	+	0.103842i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	30.3196			1.38534			0.692669	−	0.721256i	$-0.256435\pi$
$479$	30.3196			1.38534			0.692669	+	0.721256i	$0.256435\pi$
$480$		0			0
$481$	25.2348			1.15061
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.35142	+	3.26260i	0.0613646	+	0.148147i
$486$		0			0
$487$	23.2907	+	23.2907i	1.05540	+	1.05540i	0.998373	+	0.0570287i	$0.0181627\pi$
$487$	23.2907	+	23.2907i	1.05540	+	1.05540i	0.0570287	+	0.998373i	$0.481837\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.68275	−	11.3052i	−0.211330	−	0.510195i	0.782298	−	0.622904i	$-0.214047\pi$
$491$	−4.68275	−	11.3052i	−0.211330	−	0.510195i	−0.993628	+	0.112709i	$0.964047\pi$
$492$		0			0
$493$	−0.0278962	−	0.0115550i	−0.00125638	−	0.000520410i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.49308			−0.0669736
$498$		0			0
$499$	8.69892	−	21.0011i	0.389417	−	0.940136i	−0.600646	−	0.799515i	$-0.705090\pi$
$499$	8.69892	−	21.0011i	0.389417	−	0.940136i	0.990063	−	0.140621i	$-0.0449100\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	27.4548	+	27.4548i	1.22415	+	1.22415i	0.966144	+	0.258004i	$0.0830649\pi$
$503$	27.4548	+	27.4548i	1.22415	+	1.22415i	0.258004	+	0.966144i	$0.416935\pi$
$504$		0			0
$505$	−1.98531	+	1.98531i	−0.0883451	+	0.0883451i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.5641	−	6.86109i	−0.734193	−	0.304113i	−0.0159191	−	0.999873i	$-0.505067\pi$
$509$	−16.5641	−	6.86109i	−0.734193	−	0.304113i	−0.718274	+	0.695761i	$0.755067\pi$
$510$		0			0
$511$		−	4.61763i		−	0.204272i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.13681	+	2.74451i	−0.0500939	+	0.120937i
$516$		0			0
$517$	−14.1297	+	5.85272i	−0.621424	+	0.257402i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−24.2903	+	24.2903i	−1.06418	+	1.06418i	−0.0663854	+	0.997794i	$0.521147\pi$
$521$	−24.2903	+	24.2903i	−1.06418	+	1.06418i	−0.997794	+	0.0663854i	$0.978853\pi$
$522$		0			0
$523$	−3.09598	+	1.28240i	−0.135378	+	0.0560753i	−0.449344	−	0.893359i	$-0.648342\pi$
$523$	−3.09598	+	1.28240i	−0.135378	+	0.0560753i	0.313966	+	0.949434i	$0.398342\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			11.1374i			0.485153i
$528$		0			0
$529$			16.9545i			0.737153i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	25.8260	−	10.6975i	1.11865	−	0.463359i
$534$		0			0
$535$	0.597711	−	0.597711i	0.0258413	−	0.0258413i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.60606	+	3.15053i	−0.327616	+	0.135703i
$540$		0			0
$541$	12.7340	−	30.7426i	0.547477	−	1.32173i	−0.371872	−	0.928284i	$-0.621284\pi$
$541$	12.7340	−	30.7426i	0.547477	−	1.32173i	0.919349	−	0.393443i	$-0.128716\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	2.18208i		−	0.0934701i
$546$		0			0
$547$	−1.08569	−	0.449709i	−0.0464209	−	0.0192282i	0.359352	−	0.933202i	$-0.382998\pi$
$547$	−1.08569	−	0.449709i	−0.0464209	−	0.0192282i	−0.405773	+	0.913974i	$0.632998\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.00383715	−	0.00383715i	0.000163468	−	0.000163468i
$552$		0			0
$553$	−4.45871	−	4.45871i	−0.189604	−	0.189604i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.36569	−	22.6108i	0.396837	−	0.958049i	−0.591574	−	0.806250i	$-0.701493\pi$
$557$	9.36569	−	22.6108i	0.396837	−	0.958049i	0.988411	−	0.151799i	$-0.0485066\pi$
$558$		0			0
$559$	40.7060			1.72168
$560$		0			0
$561$		0			0
$562$		0			0
$563$	25.1131	+	10.4022i	1.05839	+	0.438400i	0.842880	−	0.538101i	$-0.180858\pi$
$563$	25.1131	+	10.4022i	1.05839	+	0.438400i	0.215511	+	0.976501i	$0.430858\pi$
$564$		0			0
$565$	−0.493438	−	1.19126i	−0.0207591	−	0.0501169i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−21.7622	−	21.7622i	−0.912319	−	0.912319i	0.0841358	−	0.996454i	$-0.473187\pi$
$569$	−21.7622	−	21.7622i	−0.912319	−	0.912319i	−0.996454	+	0.0841358i	$0.973187\pi$
$570$		0			0
$571$	12.7421	+	30.7622i	0.533241	+	1.28736i	0.929365	+	0.369161i	$0.120355\pi$
$571$	12.7421	+	30.7622i	0.533241	+	1.28736i	−0.396124	+	0.918197i	$0.629645\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−31.2041			−1.30130
$576$		0			0
$577$	9.17163			0.381820			0.190910	−	0.981608i	$-0.438856\pi$
$577$	9.17163			0.381820			0.190910	+	0.981608i	$0.438856\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.08661	−	9.86595i	−0.169541	−	0.409308i
$582$		0			0
$583$	9.14208	+	9.14208i	0.378626	+	0.378626i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.6350	−	25.6751i	−0.438953	−	1.05973i	−0.976311	−	0.216371i	$-0.930578\pi$
$587$	−10.6350	−	25.6751i	−0.438953	−	1.05973i	0.537359	−	0.843354i	$-0.319422\pi$
$588$		0			0
$589$	−1.84924	−	0.765981i	−0.0761966	−	0.0315617i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	10.8973			0.447497			0.223748	−	0.974647i	$-0.428171\pi$
$593$	10.8973			0.447497			0.223748	+	0.974647i	$0.428171\pi$
$594$		0			0
$595$	−0.232339	+	0.560917i	−0.00952498	+	0.0229953i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.15470	−	7.15470i	−0.292333	−	0.292333i	0.545668	−	0.838001i	$-0.316276\pi$
$599$	−7.15470	−	7.15470i	−0.292333	−	0.292333i	−0.838001	+	0.545668i	$0.816276\pi$
$600$		0			0
$601$	−16.0354	+	16.0354i	−0.654098	+	0.654098i	−0.953977	−	0.299879i	$-0.903054\pi$
$601$	−16.0354	+	16.0354i	−0.654098	+	0.654098i	0.299879	+	0.953977i	$0.403054\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.15352	−	0.892017i	−0.0875530	−	0.0362657i
$606$		0			0
$607$		−	26.1378i		−	1.06090i	−0.847716	−	0.530450i	$-0.822023\pi$
$607$		−	26.1378i		−	1.06090i	0.847716	−	0.530450i	$-0.177977\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.3938	−	39.5782i	0.663223	−	1.60116i
$612$		0			0
$613$	−0.264513	+	0.109565i	−0.0106836	+	0.00442529i	−0.388019	−	0.921651i	$-0.626840\pi$
$613$	−0.264513	+	0.109565i	−0.0106836	+	0.00442529i	0.377335	+	0.926077i	$0.376840\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.11322	+	9.11322i	−0.366884	+	0.366884i	−0.866340	−	0.499455i	$-0.833533\pi$
$617$	−9.11322	+	9.11322i	−0.366884	+	0.366884i	0.499455	+	0.866340i	$0.333533\pi$
$618$		0			0
$619$	4.31772	−	1.78846i	0.173544	−	0.0718842i	−0.294220	−	0.955738i	$-0.595060\pi$
$619$	4.31772	−	1.78846i	0.173544	−	0.0718842i	0.467764	+	0.883854i	$0.345060\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			4.57221i			0.183182i
$624$		0			0
$625$		−	24.0531i		−	0.962124i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	17.4110	−	7.21189i	0.694223	−	0.287557i
$630$		0			0
$631$	24.3839	−	24.3839i	0.970707	−	0.970707i	−0.0288764	−	0.999583i	$-0.509193\pi$
$631$	24.3839	−	24.3839i	0.970707	−	0.970707i	0.999583	+	0.0288764i	$0.00919293\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.92738	−	0.798346i	0.0764856	−	0.0316814i
$636$		0			0
$637$	8.82483	−	21.3050i	0.349653	−	0.844136i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	8.45729i		−	0.334043i	−0.985953	−	0.167022i	$-0.946585\pi$
$641$		−	8.45729i		−	0.334043i	0.985953	−	0.167022i	$-0.0534149\pi$
$642$		0			0
$643$	34.7117	+	14.3781i	1.36890	+	0.567015i	0.941489	−	0.337044i	$-0.109427\pi$
$643$	34.7117	+	14.3781i	1.36890	+	0.567015i	0.427407	+	0.904059i	$0.359427\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	26.4083	−	26.4083i	1.03822	−	1.03822i	0.0389780	−	0.999240i	$-0.487590\pi$
$647$	26.4083	−	26.4083i	1.03822	−	1.03822i	0.999240	−	0.0389780i	$-0.0124102\pi$
$648$		0			0
$649$	0.948973	+	0.948973i	0.0372504	+	0.0372504i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.3223	+	27.3345i	−0.443076	+	1.06968i	0.531788	+	0.846878i	$0.321520\pi$
$653$	−11.3223	+	27.3345i	−0.443076	+	1.06968i	−0.974864	+	0.222802i	$0.928480\pi$
$654$		0			0
$655$	5.14669			0.201098
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−35.5774	−	14.7366i	−1.38590	−	0.574058i	−0.439847	−	0.898073i	$-0.644967\pi$
$659$	−35.5774	−	14.7366i	−1.38590	−	0.574058i	−0.946052	+	0.324015i	$0.894967\pi$
$660$		0			0
$661$	11.9242	+	28.7874i	0.463796	+	1.11970i	0.966827	+	0.255434i	$0.0822182\pi$
$661$	11.9242	+	28.7874i	0.463796	+	1.11970i	−0.503031	+	0.864268i	$0.667782\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.0771547	−	0.0771547i	−0.00299193	−	0.00299193i
$666$		0			0
$667$	0.0264528	+	0.0638627i	0.00102426	+	0.00247278i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.2468			0.395572
$672$		0			0
$673$	4.89312			0.188616			0.0943080	−	0.995543i	$-0.469936\pi$
$673$	4.89312			0.188616			0.0943080	+	0.995543i	$0.469936\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.36496	−	8.12372i	−0.129326	−	0.312220i	0.845932	−	0.533291i	$-0.179045\pi$
$677$	−3.36496	−	8.12372i	−0.129326	−	0.312220i	−0.975258	+	0.221071i	$0.929045\pi$
$678$		0			0
$679$	8.66136	+	8.66136i	0.332392	+	0.332392i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	13.0545	+	31.5165i	0.499518	+	1.20594i	0.949744	+	0.313029i	$0.101344\pi$
$683$	13.0545	+	31.5165i	0.499518	+	1.20594i	−0.450225	+	0.892915i	$0.648656\pi$
$684$		0			0
$685$	−4.40696	−	1.82542i	−0.168381	−	0.0697459i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−36.2145			−1.37966
$690$		0			0
$691$	13.7784	−	33.2640i	0.524155	−	1.26542i	−0.411146	−	0.911569i	$-0.634871\pi$
$691$	13.7784	−	33.2640i	0.524155	−	1.26542i	0.935301	−	0.353853i	$-0.115129\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.48710	−	3.48710i	−0.132273	−	0.132273i
$696$		0			0
$697$	14.7617	−	14.7617i	0.559139	−	0.559139i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.9772	−	8.27483i	−0.754529	−	0.312536i	−0.0279411	−	0.999610i	$-0.508895\pi$
$701$	−19.9772	−	8.27483i	−0.754529	−	0.312536i	−0.726588	+	0.687073i	$0.758895\pi$
$702$		0			0
$703$			3.38691i			0.127740i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.72679	+	8.99726i	−0.140160	+	0.338377i
$708$		0			0
$709$	16.4355	−	6.80779i	0.617246	−	0.255672i	−0.0520769	−	0.998643i	$-0.516584\pi$
$709$	16.4355	−	6.80779i	0.617246	−	0.255672i	0.669323	+	0.742971i	$0.266584\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	18.0290	−	18.0290i	0.675191	−	0.675191i
$714$		0			0
$715$	−1.13516	+	0.470201i	−0.0424528	+	0.0175845i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	13.9143i		−	0.518917i	−0.965754	−	0.259458i	$-0.916456\pi$
$719$		−	13.9143i		−	0.518917i	0.965754	−	0.259458i	$-0.0835440\pi$
$720$		0			0
$721$			10.3039i			0.383736i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.0498762	+	0.0206594i	−0.00185235	+	0.000767270i
$726$		0			0
$727$	−21.4548	+	21.4548i	−0.795713	+	0.795713i	−0.982416	−	0.186703i	$-0.940220\pi$
$727$	−21.4548	+	21.4548i	−0.795713	+	0.795713i	0.186703	+	0.982416i	$0.440220\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	28.0856	−	11.6334i	1.03878	−	0.430279i
$732$		0			0
$733$	−6.82805	+	16.4844i	−0.252200	+	0.608864i	−0.998381	−	0.0568787i	$-0.981885\pi$
$733$	−6.82805	+	16.4844i	−0.252200	+	0.608864i	0.746181	+	0.665743i	$0.231885\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	10.5757i		−	0.389559i
$738$		0			0
$739$	−6.45405	−	2.67336i	−0.237416	−	0.0983410i	0.260803	−	0.965392i	$-0.416013\pi$
$739$	−6.45405	−	2.67336i	−0.237416	−	0.0983410i	−0.498219	+	0.867051i	$0.666013\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.5864	+	15.5864i	−0.571811	+	0.571811i	−0.932634	−	0.360823i	$-0.882496\pi$
$743$	−15.5864	+	15.5864i	−0.571811	+	0.571811i	0.360823	+	0.932634i	$0.382496\pi$
$744$		0			0
$745$	2.71597	+	2.71597i	0.0995053	+	0.0995053i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.12201	−	2.70878i	0.0409975	−	0.0989767i
$750$		0			0
$751$	−42.0270			−1.53359			−0.766793	−	0.641894i	$-0.778149\pi$
$751$	−42.0270			−1.53359			−0.766793	+	0.641894i	$0.778149\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.28708	+	0.533128i	0.0468418	+	0.0194025i
$756$		0			0
$757$	−7.05779	−	17.0390i	−0.256520	−	0.619294i	0.742184	−	0.670196i	$-0.233790\pi$
$757$	−7.05779	−	17.0390i	−0.256520	−	0.619294i	−0.998704	+	0.0509027i	$0.983790\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.7062	+	26.7062i	0.968098	+	0.968098i	0.999507	−	0.0314086i	$-0.00999931\pi$
$761$	26.7062	+	26.7062i	0.968098	+	0.968098i	−0.0314086	+	0.999507i	$0.509999\pi$
$762$		0			0
$763$	−2.89643	−	6.99260i	−0.104858	−	0.253149i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.75916			−0.135735
$768$		0			0
$769$	44.3834			1.60051			0.800253	−	0.599662i	$-0.204698\pi$
$769$	44.3834			1.60051			0.800253	+	0.599662i	$0.204698\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	14.1152	+	34.0770i	0.507687	+	1.22566i	0.945212	+	0.326458i	$0.105855\pi$
$773$	14.1152	+	34.0770i	0.507687	+	1.22566i	−0.437525	+	0.899206i	$0.644145\pi$
$774$		0			0
$775$	14.0805	+	14.0805i	0.505785	+	0.505785i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.43577	+	3.46626i	0.0514418	+	0.124191i
$780$		0			0
$781$	−2.08482	−	0.863560i	−0.0746006	−	0.0309006i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.86056			0.173481
$786$		0			0
$787$	−5.82978	+	14.0743i	−0.207809	+	0.501696i	−0.993078	−	0.117460i	$-0.962525\pi$
$787$	−5.82978	+	14.0743i	−0.207809	+	0.501696i	0.785269	+	0.619155i	$0.212525\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.16250	−	3.16250i	−0.112445	−	0.112445i
$792$		0			0
$793$	−20.2953	+	20.2953i	−0.720705	+	0.720705i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.7102	+	7.33581i	0.627328	+	0.259848i	0.673617	−	0.739080i	$-0.264740\pi$
$797$	17.7102	+	7.33581i	0.627328	+	0.259848i	−0.0462892	+	0.998928i	$0.514740\pi$
$798$		0			0
$799$		−	31.9927i		−	1.13182i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.67073	−	6.44770i	0.0942479	−	0.227535i
$804$		0			0
$805$	1.28411	−	0.531894i	0.0452588	−	0.0187468i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.6456	+	15.6456i	−0.550069	+	0.550069i	−0.926461	−	0.376391i	$-0.877165\pi$
$809$	−15.6456	+	15.6456i	−0.550069	+	0.550069i	0.376391	+	0.926461i	$0.377165\pi$
$810$		0			0
$811$	−44.2382	+	18.3241i	−1.55341	+	0.643445i	−0.983929	−	0.178558i	$-0.942857\pi$
$811$	−44.2382	+	18.3241i	−1.55341	+	0.643445i	−0.569484	+	0.822003i	$0.692857\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			4.89488i			0.171460i
$816$		0			0
$817$			5.46340i			0.191140i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9.06690	−	3.75563i	0.316437	−	0.131072i	−0.218812	−	0.975767i	$-0.570218\pi$
$821$	9.06690	−	3.75563i	0.316437	−	0.131072i	0.535248	+	0.844695i	$0.320218\pi$
$822$		0			0
$823$	−21.6440	+	21.6440i	−0.754461	+	0.754461i	−0.975308	−	0.220847i	$-0.929118\pi$
$823$	−21.6440	+	21.6440i	−0.754461	+	0.754461i	0.220847	+	0.975308i	$0.429118\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−38.2211	+	15.8317i	−1.32908	+	0.550522i	−0.930392	−	0.366566i	$-0.880533\pi$
$827$	−38.2211	+	15.8317i	−1.32908	+	0.550522i	−0.398685	+	0.917088i	$0.630533\pi$
$828$		0			0
$829$	14.2172	−	34.3234i	0.493784	−	1.19210i	−0.458996	−	0.888438i	$-0.651791\pi$
$829$	14.2172	−	34.3234i	0.493784	−	1.19210i	0.952780	−	0.303661i	$-0.0982091\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		−	17.2217i		−	0.596698i
$834$		0			0
$835$	4.58527	+	1.89928i	0.158680	+	0.0657273i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	25.0743	−	25.0743i	0.865660	−	0.865660i	−0.126329	−	0.991988i	$-0.540319\pi$
$839$	25.0743	−	25.0743i	0.865660	−	0.865660i	0.991988	+	0.126329i	$0.0403194\pi$
$840$		0			0
$841$	−20.5060	−	20.5060i	−0.707104	−	0.707104i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.0644717	−	0.155648i	0.00221789	−	0.00535447i
$846$		0			0
$847$	−8.08510			−0.277807
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−39.8591	−	16.5102i	−1.36635	−	0.565961i
$852$		0			0
$853$	19.6749	+	47.4993i	0.673655	+	1.62635i	0.775351	+	0.631531i	$0.217573\pi$
$853$	19.6749	+	47.4993i	0.673655	+	1.62635i	−0.101696	+	0.994816i	$0.532427\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0148	+	21.0148i	0.717851	+	0.717851i	0.968165	−	0.250314i	$-0.0805339\pi$
$857$	21.0148	+	21.0148i	0.717851	+	0.717851i	−0.250314	+	0.968165i	$0.580534\pi$
$858$		0			0
$859$	−0.592319	−	1.42998i	−0.0202097	−	0.0487905i	0.913453	−	0.406945i	$-0.133406\pi$
$859$	−0.592319	−	1.42998i	−0.0202097	−	0.0487905i	−0.933662	+	0.358155i	$0.883406\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−46.0354			−1.56706			−0.783531	−	0.621352i	$-0.786584\pi$
$863$	−46.0354			−1.56706			−0.783531	+	0.621352i	$0.786584\pi$
$864$		0			0
$865$	0.700443			0.0238158
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.64699	−	8.80461i	−0.123716	−	0.298676i
$870$		0			0
$871$	20.9467	+	20.9467i	0.709750	+	0.709750i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.836143	+	2.01863i	0.0282668	+	0.0682421i
$876$		0			0
$877$	5.47725	+	2.26875i	0.184954	+	0.0766103i	0.473238	−	0.880934i	$-0.343085\pi$
$877$	5.47725	+	2.26875i	0.184954	+	0.0766103i	−0.288285	+	0.957545i	$0.593085\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	27.4957			0.926355			0.463178	−	0.886265i	$-0.346709\pi$
$881$	27.4957			0.926355			0.463178	+	0.886265i	$0.346709\pi$
$882$		0			0
$883$	10.6048	−	25.6023i	0.356880	−	0.861585i	−0.638855	−	0.769327i	$-0.720592\pi$
$883$	10.6048	−	25.6023i	0.356880	−	0.861585i	0.995735	−	0.0922578i	$-0.0294084\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.2715	+	10.2715i	0.344883	+	0.344883i	0.858199	−	0.513316i	$-0.171583\pi$
$887$	10.2715	+	10.2715i	0.344883	+	0.344883i	−0.513316	+	0.858199i	$0.671583\pi$
$888$		0			0
$889$	5.11668	−	5.11668i	0.171608	−	0.171608i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.31202	+	2.20031i	0.177760	+	0.0736306i
$894$		0			0
$895$		−	3.92252i		−	0.131115i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.0168808	−	0.0407538i	0.000563006	−	0.00135922i
$900$		0			0
$901$	−24.9866	+	10.3498i	−0.832425	+	0.344802i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.19319	+	1.19319i	−0.0396628	+	0.0396628i
$906$		0			0
$907$	−39.7977	+	16.4847i	−1.32146	+	0.547367i	−0.928207	−	0.372064i	$-0.878650\pi$
$907$	−39.7977	+	16.4847i	−1.32146	+	0.547367i	−0.393253	+	0.919430i	$0.628650\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			12.4103i			0.411171i	0.978639	+	0.205585i	$0.0659098\pi$
$911$			12.4103i			0.411171i	−0.978639	+	0.205585i	$0.934090\pi$
$912$		0			0
$913$		−	16.1396i		−	0.534144i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	16.4928	−	6.83156i	0.544641	−	0.225598i
$918$		0			0
$919$	1.07058	−	1.07058i	0.0353151	−	0.0353151i	−0.689229	−	0.724544i	$-0.742050\pi$
$919$	1.07058	−	1.07058i	0.0353151	−	0.0353151i	0.724544	+	0.689229i	$0.242050\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.83970	−	2.41888i	0.192216	−	0.0796185i
$924$		0			0
$925$	12.8943	−	31.1295i	0.423961	−	1.02353i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			7.00180i			0.229722i	0.993382	+	0.114861i	$0.0366422\pi$
$929$			7.00180i			0.229722i	−0.993382	+	0.114861i	$0.963358\pi$
$930$		0			0
$931$	2.85947	+	1.18443i	0.0937155	+	0.0388182i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.648842	+	0.648842i	−0.0212194	+	0.0212194i
$936$		0			0
$937$	−18.5015	−	18.5015i	−0.604417	−	0.604417i	0.337065	−	0.941481i	$-0.390566\pi$
$937$	−18.5015	−	18.5015i	−0.604417	−	0.604417i	−0.941481	+	0.337065i	$0.890566\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−14.8709	+	35.9014i	−0.484776	+	1.17035i	0.472540	+	0.881309i	$0.343337\pi$
$941$	−14.8709	+	35.9014i	−0.484776	+	1.17035i	−0.957316	+	0.289044i	$0.906663\pi$
$942$		0			0
$943$	−47.7918			−1.55632
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.6795	+	11.0510i	0.866969	+	0.359110i	0.771429	−	0.636315i	$-0.219542\pi$
$947$	26.6795	+	11.0510i	0.866969	+	0.359110i	0.0955398	+	0.995426i	$0.469542\pi$
$948$		0			0
$949$	7.48086	+	18.0604i	0.242839	+	0.586265i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	12.5517	+	12.5517i	0.406591	+	0.406591i	0.880548	−	0.473957i	$-0.157175\pi$
$953$	12.5517	+	12.5517i	0.406591	+	0.406591i	−0.473957	+	0.880548i	$0.657175\pi$
$954$		0			0
$955$	−1.44933	−	3.49900i	−0.0468993	−	0.113225i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.5454			−0.534277
$960$		0			0
$961$	14.7293			0.475137
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.89369	+	4.57178i	0.0609601	+	0.147171i
$966$		0			0
$967$	−33.7248	−	33.7248i	−1.08452	−	1.08452i	−0.996082	−	0.0884351i	$-0.971813\pi$
$967$	−33.7248	−	33.7248i	−1.08452	−	1.08452i	−0.0884351	−	0.996082i	$-0.528187\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	18.5211	+	44.7139i	0.594371	+	1.43494i	0.879243	+	0.476373i	$0.158049\pi$
$971$	18.5211	+	44.7139i	0.594371	+	1.43494i	−0.284873	+	0.958565i	$0.591951\pi$
$972$		0			0
$973$	−15.8033	−	6.54593i	−0.506629	−	0.209853i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	40.3998			1.29250			0.646252	−	0.763124i	$-0.276336\pi$
$977$	40.3998			1.29250			0.646252	+	0.763124i	$0.276336\pi$
$978$		0			0
$979$	−2.64445	+	6.38428i	−0.0845171	+	0.204042i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−39.1712	−	39.1712i	−1.24937	−	1.24937i	−0.955999	−	0.293369i	$-0.905224\pi$
$983$	−39.1712	−	39.1712i	−1.24937	−	1.24937i	−0.293369	−	0.955999i	$-0.594776\pi$
$984$		0			0
$985$	1.52919	−	1.52919i	0.0487240	−	0.0487240i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−64.2964	−	26.6325i	−2.04451	−	0.846863i
$990$		0			0
$991$			16.6218i			0.528007i	0.964522	+	0.264004i	$0.0850431\pi$
$991$			16.6218i			0.528007i	−0.964522	+	0.264004i	$0.914957\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.99454	+	4.81524i	−0.0632311	+	0.152653i
$996$		0			0
$997$	−17.9978	+	7.45495i	−0.569997	+	0.236101i	−0.649019	−	0.760772i	$-0.724820\pi$
$997$	−17.9978	+	7.45495i	−0.569997	+	0.236101i	0.0790217	+	0.996873i	$0.474820\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.a.1007.5		32
3.2	odd	2		1152.2.w.b.1007.4		32
4.3	odd	2		288.2.w.b.179.2	yes	32
12.11	even	2		288.2.w.a.179.7	✓	32
32.5	even	8		288.2.w.a.251.7	yes	32
32.27	odd	8		1152.2.w.b.143.4		32
96.5	odd	8		288.2.w.b.251.2	yes	32
96.59	even	8	inner	1152.2.w.a.143.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.7	✓	32	12.11	even	2
288.2.w.a.251.7	yes	32	32.5	even	8
288.2.w.b.179.2	yes	32	4.3	odd	2
288.2.w.b.251.2	yes	32	96.5	odd	8
1152.2.w.a.143.5		32	96.59	even	8	inner
1152.2.w.a.1007.5		32	1.1	even	1	trivial
1152.2.w.b.143.4		32	32.27	odd	8
1152.2.w.b.1007.4		32	3.2	odd	2

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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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.w (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0963530 - 0.232617i) q^{5} +(-0.617536 - 0.617536i) q^{7} +O(q^{10})\)	\(q+(-0.0963530 - 0.232617i) q^{5} +(-0.617536 - 0.617536i) q^{7} +(-0.505112 - 1.21945i) q^{11} +(3.41575 + 1.41485i) q^{13} +2.76109 q^{17} +(-0.189895 + 0.458448i) q^{19} +(-4.46959 - 4.46959i) q^{23} +(3.49071 - 3.49071i) q^{25} +(-0.0101033 - 0.00418494i) q^{29} +4.03370i q^{31} +(-0.0841477 + 0.203151i) q^{35} +(6.30586 - 2.61197i) q^{37} +(5.34633 - 5.34633i) q^{41} +(10.1719 - 4.21336i) q^{43} -11.5870i q^{47} -6.23730i q^{49} +(-9.04956 + 3.74845i) q^{53} +(-0.234995 + 0.234995i) q^{55} +(-0.939369 + 0.389099i) q^{59} +(-2.97084 + 7.17223i) q^{61} -0.930884i q^{65} +(7.40244 + 3.06619i) q^{67} +(1.20890 - 1.20890i) q^{71} +(3.73875 + 3.73875i) q^{73} +(-0.441128 + 1.06498i) q^{77} +7.22016 q^{79} +(11.2970 + 4.67935i) q^{83} +(-0.266039 - 0.642275i) q^{85} +(-3.70197 - 3.70197i) q^{89} +(-1.23563 - 2.98307i) q^{91} +0.124940 q^{95} -14.0257 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) \) 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

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