LMFDB - Embedded newform 1152.2.w.a.143.5

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			143.5
Character	$\chi$	$=$	1152.143
Dual form			1152.2.w.a.1007.5

$q$-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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

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

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	−0.943959	−	0.330062i	$-0.892930\pi$
$5$	−0.0963530	+	0.232617i	−0.0430904	+	0.104029i	0.900869	+	0.434091i	$0.142930\pi$
$6$		0			0
$7$	−0.617536	+	0.617536i	−0.233407	+	0.233407i	−0.814113	−	0.580706i	$-0.802776\pi$
$7$	−0.617536	+	0.617536i	−0.233407	+	0.233407i	0.580706	+	0.814113i	$0.302776\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.505112	+	1.21945i	−0.152297	+	0.367677i	−0.981553	−	0.191192i	$-0.938765\pi$
$11$	−0.505112	+	1.21945i	−0.152297	+	0.367677i	0.829256	+	0.558869i	$0.188765\pi$
$12$		0			0
$13$	3.41575	−	1.41485i	0.947358	−	0.392408i	0.145121	−	0.989414i	$-0.453643\pi$
$13$	3.41575	−	1.41485i	0.947358	−	0.392408i	0.802237	+	0.597006i	$0.203643\pi$
$14$		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	0.900599	−	0.434651i	$-0.143128\pi$
$19$	−0.189895	−	0.458448i	−0.0435650	−	0.105175i	−0.944164	+	0.329475i	$0.893128\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.46959	+	4.46959i	−0.931975	+	0.931975i	−0.997829	−	0.0658547i	$-0.979023\pi$
$23$	−4.46959	+	4.46959i	−0.931975	+	0.931975i	0.0658547	+	0.997829i	$0.479023\pi$
$24$		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	−0.383621	−	0.923490i	$-0.625323\pi$
$29$	−0.0101033	+	0.00418494i	−0.00187614	+	0.000777123i	0.381745	+	0.924268i	$0.375323\pi$
$30$		0			0
$31$		−	4.03370i		−	0.724474i	−0.932086	−	0.362237i	$-0.882013\pi$
$31$		−	4.03370i		−	0.724474i	0.932086	−	0.362237i	$-0.117987\pi$
$32$		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	0.835118	−	0.550071i	$-0.185399\pi$
$37$	6.30586	+	2.61197i	1.03668	+	0.429406i	0.201559	+	0.979476i	$0.435399\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.34633	+	5.34633i	0.834957	+	0.834957i	0.988190	−	0.153233i	$-0.0489686\pi$
$41$	5.34633	+	5.34633i	0.834957	+	0.834957i	−0.153233	+	0.988190i	$0.548969\pi$
$42$		0			0
$43$	10.1719	+	4.21336i	1.55121	+	0.642531i	0.983534	−	0.180724i	$-0.0578440\pi$
$43$	10.1719	+	4.21336i	1.55121	+	0.642531i	0.567673	+	0.823254i	$0.307844\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			11.5870i			1.69013i	0.534660	+	0.845067i	$0.320440\pi$
$47$			11.5870i			1.69013i	−0.534660	+	0.845067i	$0.679560\pi$
$48$		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	−0.338385	−	0.941008i	$-0.609881\pi$
$53$	−9.04956	−	3.74845i	−1.24305	−	0.514889i	−0.904667	+	0.426119i	$0.859881\pi$
$54$		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	0.320697	−	0.947182i	$-0.396083\pi$
$59$	−0.939369	−	0.389099i	−0.122295	−	0.0506564i	−0.442992	+	0.896526i	$0.646083\pi$
$60$		0			0
$61$	−2.97084	−	7.17223i	−0.380377	−	0.918311i	−0.991893	−	0.127078i	$-0.959440\pi$
$61$	−2.97084	−	7.17223i	−0.380377	−	0.918311i	0.611516	−	0.791232i	$-0.290560\pi$
$62$		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	0.118460	−	0.992959i	$-0.462204\pi$
$67$	7.40244	−	3.06619i	0.904352	−	0.374595i	0.785892	+	0.618364i	$0.212204\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.20890	+	1.20890i	0.143470	+	0.143470i	0.775194	−	0.631724i	$-0.217652\pi$
$71$	1.20890	+	1.20890i	0.143470	+	0.143470i	−0.631724	+	0.775194i	$0.717652\pi$
$72$		0			0
$73$	3.73875	−	3.73875i	0.437588	−	0.437588i	−0.453612	−	0.891199i	$-0.649865\pi$
$73$	3.73875	−	3.73875i	0.437588	−	0.437588i	0.891199	+	0.453612i	$0.149865\pi$
$74$		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	0.336287	−	0.941760i	$-0.390829\pi$
$83$	11.2970	−	4.67935i	1.24000	−	0.513626i	0.903715	+	0.428134i	$0.140829\pi$
$84$		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	−0.875545	−	0.483137i	$-0.839497\pi$
$89$	−3.70197	+	3.70197i	−0.392408	+	0.392408i	0.483137	+	0.875545i	$0.339497\pi$
$90$		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	0.556352	+	0.830947i	$0.312201\pi$
$101$	−4.26734	+	10.3023i	−0.424616	+	1.02511i	−0.980968	+	0.194168i	$0.937799\pi$
$102$		0			0
$103$	−8.34273	+	8.34273i	−0.822034	+	0.822034i	−0.986399	−	0.164366i	$-0.947442\pi$
$103$	−8.34273	+	8.34273i	−0.822034	+	0.822034i	0.164366	+	0.986399i	$0.447442\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.28476	−	3.10168i	0.124202	−	0.299850i	−0.849533	−	0.527536i	$-0.823116\pi$
$107$	1.28476	−	3.10168i	0.124202	−	0.299850i	0.973735	+	0.227686i	$0.0731159\pi$
$108$		0			0
$109$	8.00684	−	3.31654i	0.766916	−	0.317667i	0.0352935	−	0.999377i	$-0.488763\pi$
$109$	8.00684	−	3.31654i	0.766916	−	0.317667i	0.731623	+	0.681710i	$0.238763\pi$
$110$		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	$-0.880174\pi$
$127$		−	8.28564i		−	0.735232i	0.929978	−	0.367616i	$-0.119826\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.82244	−	18.8850i	−0.683450	−	1.64999i	−0.757578	−	0.652745i	$-0.773617\pi$
$131$	−7.82244	−	18.8850i	−0.683450	−	1.64999i	0.0741279	−	0.997249i	$-0.476383\pi$
$132$		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	0.987613	+	0.156906i	$0.0501521\pi$
$137$	13.3963	+	13.3963i	1.14452	+	1.14452i	0.156906	+	0.987613i	$0.449848\pi$
$138$		0			0
$139$	18.0954	+	7.49538i	1.53484	+	0.635750i	0.980496	−	0.196540i	$-0.0629706\pi$
$139$	18.0954	+	7.49538i	1.53484	+	0.635750i	0.554340	+	0.832290i	$0.312971\pi$
$140$		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	−0.278535	−	0.960426i	$-0.589849\pi$
$149$	−14.0938	−	5.83786i	−1.15461	−	0.478256i	−0.876078	+	0.482170i	$0.839849\pi$
$150$		0			0
$151$	−3.91247	−	3.91247i	−0.318392	−	0.318392i	0.529757	−	0.848149i	$-0.322283\pi$
$151$	−3.91247	−	3.91247i	−0.318392	−	0.318392i	−0.848149	+	0.529757i	$0.822283\pi$
$152$		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	−0.883894	−	0.467687i	$-0.845088\pi$
$157$	−7.38756	−	17.8351i	−0.589591	−	1.42340i	0.294303	−	0.955712i	$-0.404912\pi$
$158$		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	−0.951512	−	0.307611i	$-0.900470\pi$
$163$	−17.9611	+	7.43971i	−1.40682	+	0.582723i	−0.455307	+	0.890335i	$0.650470\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.9383	−	13.9383i	−1.07858	−	1.07858i	−0.996637	−	0.0819391i	$-0.973889\pi$
$167$	−13.9383	−	13.9383i	−1.07858	−	1.07858i	−0.0819391	−	0.996637i	$-0.526111\pi$
$168$		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	0.878229	−	0.478241i	$-0.158725\pi$
$173$	−1.06460	−	2.57018i	−0.0809402	−	0.195407i	−0.959169	+	0.282834i	$0.908725\pi$
$174$		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	0.226761	−	0.973950i	$-0.427186\pi$
$179$	14.3931	−	5.96183i	1.07579	−	0.445608i	0.849031	+	0.528342i	$0.177186\pi$
$180$		0			0
$181$	−2.56470	+	6.19174i	−0.190633	+	0.460229i	−0.990079	−	0.140509i	$-0.955126\pi$
$181$	−2.56470	+	6.19174i	−0.190633	+	0.460229i	0.799446	+	0.600737i	$0.205126\pi$
$182$		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	−0.762478	−	0.647015i	$-0.776017\pi$
$197$	3.28693	−	7.93534i	0.234184	−	0.565370i	0.996661	+	0.0816448i	$0.0260173\pi$
$198$		0			0
$199$	−14.6374	+	14.6374i	−1.03761	+	1.03761i	−0.0383500	+	0.999264i	$0.512210\pi$
$199$	−14.6374	+	14.6374i	−1.03761	+	1.03761i	−0.999264	+	0.0383500i	$0.987790\pi$
$200$		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	−0.966108	−	0.258137i	$-0.916891\pi$
$211$	−6.76173	−	16.3243i	−0.465497	−	1.12381i	0.500612	−	0.865672i	$-0.333109\pi$
$212$		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	$-0.821781\pi$
$223$		−	15.8618i		−	1.06219i	0.847313	−	0.531093i	$-0.178219\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.50806	+	6.05500i	0.166466	+	0.401884i	0.984995	−	0.172580i	$-0.0552104\pi$
$227$	2.50806	+	6.05500i	0.166466	+	0.401884i	−0.818530	+	0.574464i	$0.805210\pi$
$228$		0			0
$229$	−7.60466	−	3.14995i	−0.502530	−	0.208155i	0.116994	−	0.993133i	$-0.462674\pi$
$229$	−7.60466	−	3.14995i	−0.502530	−	0.208155i	−0.619524	+	0.784978i	$0.712674\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.99464	−	5.99464i	−0.392722	−	0.392722i	0.482935	−	0.875656i	$-0.339571\pi$
$233$	−5.99464	−	5.99464i	−0.392722	−	0.392722i	−0.875656	+	0.482935i	$0.839571\pi$
$234$		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	$0.0114541\pi$
$239$			1.11236i			0.0719527i	−0.999353	+	0.0359763i	$0.988546\pi$
$240$		0			0
$241$			0.709331i			0.0456920i	0.999739	+	0.0228460i	$0.00727274\pi$
$241$			0.709331i			0.0456920i	−0.999739	+	0.0228460i	$0.992727\pi$
$242$		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	0.0307514	−	0.999527i	$-0.490210\pi$
$251$	−10.3657	−	4.29361i	−0.654276	−	0.271010i	−0.685028	+	0.728517i	$0.740210\pi$
$252$		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	$-0.637284\pi$
$257$		−	29.1264i		−	1.81686i	0.418042	−	0.908428i	$-0.362716\pi$
$258$		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	0.762422	−	0.647080i	$-0.224010\pi$
$263$	1.87052	+	1.87052i	0.115341	+	0.115341i	−0.647080	+	0.762422i	$0.724010\pi$
$264$		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	0.866034	−	0.499986i	$-0.166661\pi$
$269$	−1.63828	−	3.95517i	−0.0998879	−	0.241151i	−0.965922	+	0.258835i	$0.916661\pi$
$270$		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	0.158948	+	0.987287i	$0.449190\pi$
$277$	−10.8442	+	26.1801i	−0.651563	+	1.57301i	−0.810510	+	0.585724i	$0.800810\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.20552	−	3.20552i	0.191225	−	0.191225i	−0.605000	−	0.796225i	$-0.706827\pi$
$281$	3.20552	−	3.20552i	0.191225	−	0.191225i	0.796225	+	0.605000i	$0.206827\pi$
$282$		0			0
$283$	0.808604	−	1.95214i	0.0480665	−	0.116043i	−0.898023	−	0.439949i	$-0.854996\pi$
$283$	0.808604	−	1.95214i	0.0480665	−	0.116043i	0.946089	+	0.323907i	$0.104996\pi$
$284$		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	−0.818916	−	0.573914i	$-0.805424\pi$
$293$	2.84084	−	6.85839i	0.165964	−	0.400671i	0.984879	+	0.173242i	$0.0554244\pi$
$294$		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	−0.998715	−	0.0506860i	$-0.983859\pi$
$307$	−5.75328	−	13.8897i	−0.328357	−	0.792724i	0.670357	−	0.742038i	$-0.266141\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.92757	−	9.92757i	0.562941	−	0.562941i	−0.367201	−	0.930142i	$-0.619684\pi$
$311$	9.92757	−	9.92757i	0.562941	−	0.562941i	0.930142	+	0.367201i	$0.119684\pi$
$312$		0			0
$313$	−6.07029	−	6.07029i	−0.343113	−	0.343113i	0.514423	−	0.857536i	$-0.328006\pi$
$313$	−6.07029	−	6.07029i	−0.343113	−	0.343113i	−0.857536	+	0.514423i	$0.828006\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	28.8754	−	11.9606i	1.62180	−	0.671773i	0.627525	−	0.778596i	$-0.284068\pi$
$317$	28.8754	−	11.9606i	1.62180	−	0.671773i	0.994278	+	0.106823i	$0.0340678\pi$
$318$		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	−0.0229312	−	0.999737i	$-0.507300\pi$
$331$	−13.5735	−	5.62233i	−0.746067	−	0.309031i	−0.723136	+	0.690706i	$0.757300\pi$
$332$		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	$0.0630411\pi$
$337$			7.22397i			0.393515i	−0.980452	+	0.196757i	$0.936959\pi$
$338$		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	0.192958	−	0.981207i	$-0.438192\pi$
$347$	−6.78836	−	2.81183i	−0.364418	−	0.150947i	−0.557376	+	0.830260i	$0.688192\pi$
$348$		0			0
$349$	0.0989263	+	0.238829i	0.00529540	+	0.0127842i	0.926505	−	0.376282i	$-0.122798\pi$
$349$	0.0989263	+	0.238829i	0.00529540	+	0.0127842i	−0.921210	+	0.389066i	$0.872798\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	1.04908i		−	0.0558369i	−0.999610	−	0.0279184i	$-0.991112\pi$
$353$		−	1.04908i		−	0.0558369i	0.999610	−	0.0279184i	$-0.00888787\pi$
$354$		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	0.356080	−	0.934455i	$-0.384113\pi$
$359$	−10.9586	−	10.9586i	−0.578375	−	0.578375i	−0.934455	+	0.356080i	$0.884113\pi$
$360$		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	−0.896659	−	0.442723i	$-0.854013\pi$
$373$	0.973904	−	2.35121i	0.0504268	−	0.121741i	0.947086	+	0.320981i	$0.104013\pi$
$374$		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	0.622391	+	0.782707i	$0.286161\pi$
$379$	−7.22577	+	17.4446i	−0.371163	+	0.896067i	−0.993554	+	0.113360i	$0.963839\pi$
$380$		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	0.665208	+	0.746658i	$0.268343\pi$
$389$	−6.57039	+	15.8623i	−0.333132	+	0.804252i	−0.998340	+	0.0575939i	$0.981657\pi$
$390$		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	−0.344882	−	0.938646i	$-0.612081\pi$
$397$	1.49381	−	0.618757i	0.0749723	−	0.0310545i	0.419854	+	0.907591i	$0.362081\pi$
$398$		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	0.895324	−	0.445416i	$-0.146944\pi$
$409$	9.09883	+	9.09883i	0.449908	+	0.449908i	−0.445416	+	0.895324i	$0.646944\pi$
$410$		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	0.990489	−	0.137593i	$-0.0439366\pi$
$419$	3.94681	+	9.52845i	0.192814	+	0.465495i	−0.797674	+	0.603088i	$0.793937\pi$
$420$		0			0
$421$	2.91334	+	1.20674i	0.141987	+	0.0588131i	0.452546	−	0.891741i	$-0.350516\pi$
$421$	2.91334	+	1.20674i	0.141987	+	0.0588131i	−0.310558	+	0.950554i	$0.600516\pi$
$422$		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	$-0.811472\pi$
$431$		−	23.1792i		−	1.11650i	0.829672	−	0.558252i	$-0.188528\pi$
$432$		0			0
$433$		−	25.2987i		−	1.21578i	−0.794023	−	0.607888i	$-0.792017\pi$
$433$		−	25.2987i		−	1.21578i	0.794023	−	0.607888i	$-0.207983\pi$
$434$		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	0.880365	+	0.474297i	$0.157298\pi$
$439$	28.3833	+	28.3833i	1.35466	+	1.35466i	0.474297	+	0.880365i	$0.342702\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	19.8722	+	8.23132i	0.944155	+	0.391082i	0.801031	−	0.598623i	$-0.204285\pi$
$443$	19.8722	+	8.23132i	0.944155	+	0.391082i	0.143124	+	0.989705i	$0.454285\pi$
$444$		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	$0.0959676\pi$
$449$			12.5843i			0.593889i	−0.954895	+	0.296944i	$0.904032\pi$
$450$		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	−0.466554	−	0.884492i	$-0.654505\pi$
$457$	8.93449	−	8.93449i	0.417938	−	0.417938i	0.884492	+	0.466554i	$0.154505\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.9213	+	31.1949i	0.601807	+	1.45289i	0.871720	+	0.490005i	$0.163005\pi$
$461$	12.9213	+	31.1949i	0.601807	+	1.45289i	−0.269913	+	0.962885i	$0.586995\pi$
$462$		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	−0.758376	+	0.651818i	$0.774007\pi$
$467$	−37.9374	+	15.7142i	−1.75553	+	0.727166i	−0.997157	+	0.0753479i	$0.975993\pi$
$468$		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	0.0570287	−	0.998373i	$-0.481837\pi$
$487$	23.2907	−	23.2907i	1.05540	−	1.05540i	0.998373	−	0.0570287i	$-0.0181627\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.68275	+	11.3052i	−0.211330	+	0.510195i	−0.993628	−	0.112709i	$-0.964047\pi$
$491$	−4.68275	+	11.3052i	−0.211330	+	0.510195i	0.782298	+	0.622904i	$0.214047\pi$
$492$		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	0.990063	+	0.140621i	$0.0449100\pi$
$499$	8.69892	+	21.0011i	0.389417	+	0.940136i	−0.600646	+	0.799515i	$0.705090\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	27.4548	−	27.4548i	1.22415	−	1.22415i	0.258004	−	0.966144i	$-0.416935\pi$
$503$	27.4548	−	27.4548i	1.22415	−	1.22415i	0.966144	−	0.258004i	$-0.0830649\pi$
$504$		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	−0.718274	−	0.695761i	$-0.755067\pi$
$509$	−16.5641	+	6.86109i	−0.734193	+	0.304113i	−0.0159191	+	0.999873i	$0.505067\pi$
$510$		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	−0.997794	−	0.0663854i	$-0.978853\pi$
$521$	−24.2903	−	24.2903i	−1.06418	−	1.06418i	−0.0663854	−	0.997794i	$-0.521147\pi$
$522$		0			0
$523$	−3.09598	−	1.28240i	−0.135378	−	0.0560753i	0.313966	−	0.949434i	$-0.398342\pi$
$523$	−3.09598	−	1.28240i	−0.135378	−	0.0560753i	−0.449344	+	0.893359i	$0.648342\pi$
$524$		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	0.919349	+	0.393443i	$0.128716\pi$
$541$	12.7340	+	30.7426i	0.547477	+	1.32173i	−0.371872	+	0.928284i	$0.621284\pi$
$542$		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	−0.405773	−	0.913974i	$-0.632998\pi$
$547$	−1.08569	+	0.449709i	−0.0464209	+	0.0192282i	0.359352	+	0.933202i	$0.382998\pi$
$548$		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	0.988411	+	0.151799i	$0.0485066\pi$
$557$	9.36569	+	22.6108i	0.396837	+	0.958049i	−0.591574	+	0.806250i	$0.701493\pi$
$558$		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	0.215511	−	0.976501i	$-0.430858\pi$
$563$	25.1131	−	10.4022i	1.05839	−	0.438400i	0.842880	+	0.538101i	$0.180858\pi$
$564$		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	−0.996454	−	0.0841358i	$-0.973187\pi$
$569$	−21.7622	+	21.7622i	−0.912319	+	0.912319i	0.0841358	+	0.996454i	$0.473187\pi$
$570$		0			0
$571$	12.7421	−	30.7622i	0.533241	−	1.28736i	−0.396124	−	0.918197i	$-0.629645\pi$
$571$	12.7421	−	30.7622i	0.533241	−	1.28736i	0.929365	−	0.369161i	$-0.120355\pi$
$572$		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	0.537359	+	0.843354i	$0.319422\pi$
$587$	−10.6350	+	25.6751i	−0.438953	+	1.05973i	−0.976311	+	0.216371i	$0.930578\pi$
$588$		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	−0.838001	−	0.545668i	$-0.816276\pi$
$599$	−7.15470	+	7.15470i	−0.292333	+	0.292333i	0.545668	+	0.838001i	$0.316276\pi$
$600$		0			0
$601$	−16.0354	−	16.0354i	−0.654098	−	0.654098i	0.299879	−	0.953977i	$-0.403054\pi$
$601$	−16.0354	−	16.0354i	−0.654098	−	0.654098i	−0.953977	+	0.299879i	$0.903054\pi$
$602$		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	$0.177977\pi$
$607$			26.1378i			1.06090i	−0.847716	+	0.530450i	$0.822023\pi$
$608$		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	0.377335	−	0.926077i	$-0.376840\pi$
$613$	−0.264513	−	0.109565i	−0.0106836	−	0.00442529i	−0.388019	+	0.921651i	$0.626840\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.11322	−	9.11322i	−0.366884	−	0.366884i	0.499455	−	0.866340i	$-0.333533\pi$
$617$	−9.11322	−	9.11322i	−0.366884	−	0.366884i	−0.866340	+	0.499455i	$0.833533\pi$
$618$		0			0
$619$	4.31772	+	1.78846i	0.173544	+	0.0718842i	0.467764	−	0.883854i	$-0.345060\pi$
$619$	4.31772	+	1.78846i	0.173544	+	0.0718842i	−0.294220	+	0.955738i	$0.595060\pi$
$620$		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	0.999583	−	0.0288764i	$-0.00919293\pi$
$631$	24.3839	+	24.3839i	0.970707	+	0.970707i	−0.0288764	+	0.999583i	$0.509193\pi$
$632$		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	$0.0534149\pi$
$641$			8.45729i			0.334043i	−0.985953	+	0.167022i	$0.946585\pi$
$642$		0			0
$643$	34.7117	−	14.3781i	1.36890	−	0.567015i	0.427407	−	0.904059i	$-0.359427\pi$
$643$	34.7117	−	14.3781i	1.36890	−	0.567015i	0.941489	+	0.337044i	$0.109427\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	26.4083	+	26.4083i	1.03822	+	1.03822i	0.999240	+	0.0389780i	$0.0124102\pi$
$647$	26.4083	+	26.4083i	1.03822	+	1.03822i	0.0389780	+	0.999240i	$0.487590\pi$
$648$		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	−0.974864	−	0.222802i	$-0.928480\pi$
$653$	−11.3223	−	27.3345i	−0.443076	−	1.06968i	0.531788	−	0.846878i	$-0.321520\pi$
$654$		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	−0.946052	−	0.324015i	$-0.894967\pi$
$659$	−35.5774	+	14.7366i	−1.38590	+	0.574058i	−0.439847	+	0.898073i	$0.644967\pi$
$660$		0			0
$661$	11.9242	−	28.7874i	0.463796	−	1.11970i	−0.503031	−	0.864268i	$-0.667782\pi$
$661$	11.9242	−	28.7874i	0.463796	−	1.11970i	0.966827	−	0.255434i	$-0.0822182\pi$
$662$		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	−0.975258	−	0.221071i	$-0.929045\pi$
$677$	−3.36496	+	8.12372i	−0.129326	+	0.312220i	0.845932	+	0.533291i	$0.179045\pi$
$678$		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	−0.450225	−	0.892915i	$-0.648656\pi$
$683$	13.0545	−	31.5165i	0.499518	−	1.20594i	0.949744	−	0.313029i	$-0.101344\pi$
$684$		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	0.935301	+	0.353853i	$0.115129\pi$
$691$	13.7784	+	33.2640i	0.524155	+	1.26542i	−0.411146	+	0.911569i	$0.634871\pi$
$692$		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	−0.726588	−	0.687073i	$-0.758895\pi$
$701$	−19.9772	+	8.27483i	−0.754529	+	0.312536i	−0.0279411	+	0.999610i	$0.508895\pi$
$702$		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	0.669323	−	0.742971i	$-0.266584\pi$
$709$	16.4355	+	6.80779i	0.617246	+	0.255672i	−0.0520769	+	0.998643i	$0.516584\pi$
$710$		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	$0.0835440\pi$
$719$			13.9143i			0.518917i	−0.965754	+	0.259458i	$0.916456\pi$
$720$		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	0.186703	−	0.982416i	$-0.440220\pi$
$727$	−21.4548	−	21.4548i	−0.795713	−	0.795713i	−0.982416	+	0.186703i	$0.940220\pi$
$728$		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	0.746181	−	0.665743i	$-0.231885\pi$
$733$	−6.82805	−	16.4844i	−0.252200	−	0.608864i	−0.998381	+	0.0568787i	$0.981885\pi$
$734$		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	−0.498219	−	0.867051i	$-0.666013\pi$
$739$	−6.45405	+	2.67336i	−0.237416	+	0.0983410i	0.260803	+	0.965392i	$0.416013\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.5864	−	15.5864i	−0.571811	−	0.571811i	0.360823	−	0.932634i	$-0.382496\pi$
$743$	−15.5864	−	15.5864i	−0.571811	−	0.571811i	−0.932634	+	0.360823i	$0.882496\pi$
$744$		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	−0.998704	−	0.0509027i	$-0.983790\pi$
$757$	−7.05779	+	17.0390i	−0.256520	+	0.619294i	0.742184	+	0.670196i	$0.233790\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.7062	−	26.7062i	0.968098	−	0.968098i	−0.0314086	−	0.999507i	$-0.509999\pi$
$761$	26.7062	−	26.7062i	0.968098	−	0.968098i	0.999507	+	0.0314086i	$0.00999931\pi$
$762$		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	−0.437525	−	0.899206i	$-0.644145\pi$
$773$	14.1152	−	34.0770i	0.507687	−	1.22566i	0.945212	−	0.326458i	$-0.105855\pi$
$774$		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	0.785269	−	0.619155i	$-0.212525\pi$
$787$	−5.82978	−	14.0743i	−0.207809	−	0.501696i	−0.993078	+	0.117460i	$0.962525\pi$
$788$		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	−0.0462892	−	0.998928i	$-0.514740\pi$
$797$	17.7102	−	7.33581i	0.627328	−	0.259848i	0.673617	+	0.739080i	$0.264740\pi$
$798$		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	0.376391	−	0.926461i	$-0.377165\pi$
$809$	−15.6456	−	15.6456i	−0.550069	−	0.550069i	−0.926461	+	0.376391i	$0.877165\pi$
$810$		0			0
$811$	−44.2382	−	18.3241i	−1.55341	−	0.643445i	−0.569484	−	0.822003i	$-0.692857\pi$
$811$	−44.2382	−	18.3241i	−1.55341	−	0.643445i	−0.983929	+	0.178558i	$0.942857\pi$
$812$		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	0.535248	−	0.844695i	$-0.320218\pi$
$821$	9.06690	+	3.75563i	0.316437	+	0.131072i	−0.218812	+	0.975767i	$0.570218\pi$
$822$		0			0
$823$	−21.6440	−	21.6440i	−0.754461	−	0.754461i	0.220847	−	0.975308i	$-0.429118\pi$
$823$	−21.6440	−	21.6440i	−0.754461	−	0.754461i	−0.975308	+	0.220847i	$0.929118\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−38.2211	−	15.8317i	−1.32908	−	0.550522i	−0.398685	−	0.917088i	$-0.630533\pi$
$827$	−38.2211	−	15.8317i	−1.32908	−	0.550522i	−0.930392	+	0.366566i	$0.880533\pi$
$828$		0			0
$829$	14.2172	+	34.3234i	0.493784	+	1.19210i	0.952780	+	0.303661i	$0.0982091\pi$
$829$	14.2172	+	34.3234i	0.493784	+	1.19210i	−0.458996	+	0.888438i	$0.651791\pi$
$830$		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	0.991988	−	0.126329i	$-0.0403194\pi$
$839$	25.0743	+	25.0743i	0.865660	+	0.865660i	−0.126329	+	0.991988i	$0.540319\pi$
$840$		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	−0.101696	−	0.994816i	$-0.532427\pi$
$853$	19.6749	−	47.4993i	0.673655	−	1.62635i	0.775351	−	0.631531i	$-0.217573\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0148	−	21.0148i	0.717851	−	0.717851i	−0.250314	−	0.968165i	$-0.580534\pi$
$857$	21.0148	−	21.0148i	0.717851	−	0.717851i	0.968165	+	0.250314i	$0.0805339\pi$
$858$		0			0
$859$	−0.592319	+	1.42998i	−0.0202097	+	0.0487905i	−0.933662	−	0.358155i	$-0.883406\pi$
$859$	−0.592319	+	1.42998i	−0.0202097	+	0.0487905i	0.913453	+	0.406945i	$0.133406\pi$
$860$		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	−0.288285	−	0.957545i	$-0.593085\pi$
$877$	5.47725	−	2.26875i	0.184954	−	0.0766103i	0.473238	+	0.880934i	$0.343085\pi$
$878$		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	0.995735	+	0.0922578i	$0.0294084\pi$
$883$	10.6048	+	25.6023i	0.356880	+	0.861585i	−0.638855	+	0.769327i	$0.720592\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.2715	−	10.2715i	0.344883	−	0.344883i	−0.513316	−	0.858199i	$-0.671583\pi$
$887$	10.2715	−	10.2715i	0.344883	−	0.344883i	0.858199	+	0.513316i	$0.171583\pi$
$888$		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	−0.393253	−	0.919430i	$-0.628650\pi$
$907$	−39.7977	−	16.4847i	−1.32146	−	0.547367i	−0.928207	+	0.372064i	$0.878650\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	12.4103i		−	0.411171i	−0.978639	−	0.205585i	$-0.934090\pi$
$911$		−	12.4103i		−	0.411171i	0.978639	−	0.205585i	$-0.0659098\pi$
$912$		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	0.724544	−	0.689229i	$-0.242050\pi$
$919$	1.07058	+	1.07058i	0.0353151	+	0.0353151i	−0.689229	+	0.724544i	$0.742050\pi$
$920$		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	$-0.963358\pi$
$929$		−	7.00180i		−	0.229722i	0.993382	−	0.114861i	$-0.0366422\pi$
$930$		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	−0.941481	−	0.337065i	$-0.890566\pi$
$937$	−18.5015	+	18.5015i	−0.604417	+	0.604417i	0.337065	+	0.941481i	$0.390566\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−14.8709	−	35.9014i	−0.484776	−	1.17035i	−0.957316	−	0.289044i	$-0.906663\pi$
$941$	−14.8709	−	35.9014i	−0.484776	−	1.17035i	0.472540	−	0.881309i	$-0.343337\pi$
$942$		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	0.0955398	−	0.995426i	$-0.469542\pi$
$947$	26.6795	−	11.0510i	0.866969	−	0.359110i	0.771429	+	0.636315i	$0.219542\pi$
$948$		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	−0.473957	−	0.880548i	$-0.657175\pi$
$953$	12.5517	−	12.5517i	0.406591	−	0.406591i	0.880548	+	0.473957i	$0.157175\pi$
$954$		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	−0.0884351	+	0.996082i	$0.528187\pi$
$967$	−33.7248	+	33.7248i	−1.08452	+	1.08452i	−0.996082	+	0.0884351i	$0.971813\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	18.5211	−	44.7139i	0.594371	−	1.43494i	−0.284873	−	0.958565i	$-0.591951\pi$
$971$	18.5211	−	44.7139i	0.594371	−	1.43494i	0.879243	−	0.476373i	$-0.158049\pi$
$972$		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	−0.293369	+	0.955999i	$0.594776\pi$
$983$	−39.1712	+	39.1712i	−1.24937	+	1.24937i	−0.955999	+	0.293369i	$0.905224\pi$
$984$		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	$-0.914957\pi$
$991$		−	16.6218i		−	0.528007i	0.964522	−	0.264004i	$-0.0850431\pi$
$992$		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	0.0790217	−	0.996873i	$-0.474820\pi$
$997$	−17.9978	−	7.45495i	−0.569997	−	0.236101i	−0.649019	+	0.760772i	$0.724820\pi$
$998$		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.143.5		32
3.2	odd	2		1152.2.w.b.143.4		32
4.3	odd	2		288.2.w.b.251.2	yes	32
12.11	even	2		288.2.w.a.251.7	yes	32
32.13	even	8		288.2.w.a.179.7	✓	32
32.19	odd	8		1152.2.w.b.1007.4		32
96.77	odd	8		288.2.w.b.179.2	yes	32
96.83	even	8	inner	1152.2.w.a.1007.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.7	✓	32	32.13	even	8
288.2.w.a.251.7	yes	32	12.11	even	2
288.2.w.b.179.2	yes	32	96.77	odd	8
288.2.w.b.251.2	yes	32	4.3	odd	2
1152.2.w.a.143.5		32	1.1	even	1	trivial
1152.2.w.a.1007.5		32	96.83	even	8	inner
1152.2.w.b.143.4		32	3.2	odd	2
1152.2.w.b.1007.4		32	32.19	odd	8

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more