LMFDB - Embedded newform 792.2.r.g.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [792,2,Mod(289,792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(792, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("792.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$792 = 2^{3} \cdot 3^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	792.r (of order $5$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121$ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			289.1
Root			$0.581882 + 1.79085i$ of defining polynomial
Character	$\chi$	$=$	792.289
Dual form			792.2.r.g.433.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.132489 - 0.0962586i) q^{5} +(1.08188 - 3.32969i) q^{7} +(0.605270 - 3.26093i) q^{11} +(-2.17926 + 1.58333i) q^{13} +(-6.12970 - 4.45349i) q^{17} +(1.42705 + 4.39201i) q^{19} +0.706114 q^{23} +(-1.53680 - 4.72978i) q^{25} +(0.317950 - 0.978551i) q^{29} +(-4.36856 + 3.17394i) q^{31} +(-0.463848 + 0.337006i) q^{35} +(3.58293 - 11.0271i) q^{37} +(0.0867577 + 0.267013i) q^{41} +4.31175 q^{43} +(-1.80113 - 5.54330i) q^{47} +(-4.25326 - 3.09017i) q^{49} +(7.98659 - 5.80260i) q^{53} +(-0.394084 + 0.373773i) q^{55} +(0.954915 - 2.93893i) q^{59} +(-5.60801 - 4.07446i) q^{61} +0.441137 q^{65} +1.91665 q^{67} +(9.84407 + 7.15214i) q^{71} +(-3.51550 + 10.8196i) q^{73} +(-10.2031 - 5.54330i) q^{77} +(1.39747 - 1.01532i) q^{79} +(3.81006 + 2.76817i) q^{83} +(0.383429 + 1.18007i) q^{85} -6.31175 q^{89} +(2.91429 + 8.96925i) q^{91} +(0.233701 - 0.719257i) q^{95} +(-5.66755 + 4.11771i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 3 q^{5} + 7 q^{7} - 7 q^{11} + 7 q^{13} - q^{17} - 2 q^{19} + 4 q^{23} - 33 q^{25} - 17 q^{29} - 13 q^{31} - 11 q^{35} + q^{37} - 9 q^{41} + 6 q^{43} + q^{47} + 3 q^{49} + 33 q^{53} + 13 q^{55}+ \cdots + 8 q^{97}+O(q^{100})$ 8 * q + 3 * q^5 + 7 * q^7 - 7 * q^11 + 7 * q^13 - q^17 - 2 * q^19 + 4 * q^23 - 33 * q^25 - 17 * q^29 - 13 * q^31 - 11 * q^35 + q^37 - 9 * q^41 + 6 * q^43 + q^47 + 3 * q^49 + 33 * q^53 + 13 * q^55 + 30 * q^59 - 9 * q^61 + 10 * q^65 - 10 * q^67 + 25 * q^71 - 7 * q^73 + 7 * q^77 - q^79 + 39 * q^85 - 22 * q^89 + 7 * q^91 - 7 * q^95 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$ .

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.132489	−	0.0962586i	−0.0592507	−	0.0430481i	0.557766	−	0.829998i	$-0.311659\pi$
$5$	−0.132489	−	0.0962586i	−0.0592507	−	0.0430481i	−0.617016	+	0.786950i	$0.711659\pi$
$6$		0			0
$7$	1.08188	−	3.32969i	0.408913	−	1.25851i	−0.508670	−	0.860962i	$-0.669863\pi$
$7$	1.08188	−	3.32969i	0.408913	−	1.25851i	0.917583	−	0.397544i	$-0.130137\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.605270	−	3.26093i	0.182496	−	0.983207i
$11$	0.605270	−	3.26093i	0.182496	−	0.983207i
$12$		0			0
$13$	−2.17926	+	1.58333i	−0.604419	+	0.439136i	−0.847445	−	0.530884i	$-0.821860\pi$
$13$	−2.17926	+	1.58333i	−0.604419	+	0.439136i	0.243025	+	0.970020i	$0.421860\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.12970	−	4.45349i	−1.48667	−	1.08013i	−0.975330	−	0.220753i	$-0.929149\pi$
$17$	−6.12970	−	4.45349i	−1.48667	−	1.08013i	−0.511342	−	0.859378i	$-0.670851\pi$
$18$		0			0
$19$	1.42705	+	4.39201i	0.327388	+	1.00760i	0.970351	+	0.241699i	$0.0777048\pi$
$19$	1.42705	+	4.39201i	0.327388	+	1.00760i	−0.642963	+	0.765897i	$0.722295\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.706114			0.147235			0.0736174	−	0.997287i	$-0.476546\pi$
$23$	0.706114			0.147235			0.0736174	+	0.997287i	$0.476546\pi$
$24$		0			0
$25$	−1.53680	−	4.72978i	−0.307359	−	0.945955i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.317950	−	0.978551i	0.0590419	−	0.181712i	−0.917186	−	0.398460i	$-0.869545\pi$
$29$	0.317950	−	0.978551i	0.0590419	−	0.181712i	0.976228	+	0.216748i	$0.0695448\pi$
$30$		0			0
$31$	−4.36856	+	3.17394i	−0.784616	+	0.570057i	−0.906361	−	0.422505i	$-0.861151\pi$
$31$	−4.36856	+	3.17394i	−0.784616	+	0.570057i	0.121745	+	0.992561i	$0.461151\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.463848	+	0.337006i	−0.0784047	+	0.0569643i
$36$		0			0
$37$	3.58293	−	11.0271i	0.589030	−	1.81285i	0.00658248	−	0.999978i	$-0.497905\pi$
$37$	3.58293	−	11.0271i	0.589030	−	1.81285i	0.582447	−	0.812869i	$-0.302095\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.0867577	+	0.267013i	0.0135493	+	0.0417004i	0.957603	−	0.288093i	$-0.0930211\pi$
$41$	0.0867577	+	0.267013i	0.0135493	+	0.0417004i	−0.944053	+	0.329793i	$0.893021\pi$
$42$		0			0
$43$	4.31175			0.657536			0.328768	−	0.944411i	$-0.393367\pi$
$43$	4.31175			0.657536			0.328768	+	0.944411i	$0.393367\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.80113	−	5.54330i	−0.262722	−	0.808574i	−0.992210	−	0.124580i	$-0.960242\pi$
$47$	−1.80113	−	5.54330i	−0.262722	−	0.808574i	0.729488	−	0.683994i	$-0.239758\pi$
$48$		0			0
$49$	−4.25326	−	3.09017i	−0.607608	−	0.441453i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.98659	−	5.80260i	1.09704	−	0.797048i	0.116468	−	0.993194i	$-0.462843\pi$
$53$	7.98659	−	5.80260i	1.09704	−	0.797048i	0.980575	+	0.196146i	$0.0628428\pi$
$54$		0			0
$55$	−0.394084	+	0.373773i	−0.0531382	+	0.0503996i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.954915	−	2.93893i	0.124319	−	0.382616i	−0.869457	−	0.494008i	$-0.835531\pi$
$59$	0.954915	−	2.93893i	0.124319	−	0.382616i	0.993776	+	0.111393i	$0.0355312\pi$
$60$		0			0
$61$	−5.60801	−	4.07446i	−0.718032	−	0.521681i	0.167723	−	0.985834i	$-0.446359\pi$
$61$	−5.60801	−	4.07446i	−0.718032	−	0.521681i	−0.885755	+	0.464154i	$0.846359\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.441137			0.0547163
$66$		0			0
$67$	1.91665			0.234157			0.117078	−	0.993123i	$-0.462647\pi$
$67$	1.91665			0.234157			0.117078	+	0.993123i	$0.462647\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.84407	+	7.15214i	1.16828	+	0.848803i	0.990802	−	0.135323i	$-0.0432071\pi$
$71$	9.84407	+	7.15214i	1.16828	+	0.848803i	0.177475	+	0.984125i	$0.443207\pi$
$72$		0			0
$73$	−3.51550	+	10.8196i	−0.411458	+	1.26634i	0.503923	+	0.863749i	$0.331890\pi$
$73$	−3.51550	+	10.8196i	−0.411458	+	1.26634i	−0.915381	+	0.402589i	$0.868110\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.2031	−	5.54330i	−1.16275	−	0.631718i
$78$		0			0
$79$	1.39747	−	1.01532i	0.157227	−	0.114232i	−0.506390	−	0.862305i	$-0.669020\pi$
$79$	1.39747	−	1.01532i	0.157227	−	0.114232i	0.663617	+	0.748072i	$0.269020\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.81006	+	2.76817i	0.418209	+	0.303846i	0.776917	−	0.629603i	$-0.216783\pi$
$83$	3.81006	+	2.76817i	0.418209	+	0.303846i	−0.358708	+	0.933450i	$0.616783\pi$
$84$		0			0
$85$	0.383429	+	1.18007i	0.0415887	+	0.127997i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.31175			−0.669044			−0.334522	−	0.942388i	$-0.608575\pi$
$89$	−6.31175			−0.669044			−0.334522	+	0.942388i	$0.608575\pi$
$90$		0			0
$91$	2.91429	+	8.96925i	0.305500	+	0.940233i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.233701	−	0.719257i	0.0239772	−	0.0737942i
$96$		0			0
$97$	−5.66755	+	4.11771i	−0.575452	+	0.418090i	−0.837082	−	0.547078i	$-0.815740\pi$
$97$	−5.66755	+	4.11771i	−0.575452	+	0.418090i	0.261630	+	0.965168i	$0.415740\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.25495	−	2.36486i	0.323880	−	0.235312i	−0.413950	−	0.910300i	$-0.635851\pi$
$101$	3.25495	−	2.36486i	0.323880	−	0.235312i	0.737829	+	0.674988i	$0.235851\pi$
$102$		0			0
$103$	4.65523	−	14.3273i	0.458694	−	1.41171i	−0.408050	−	0.912960i	$-0.633791\pi$
$103$	4.65523	−	14.3273i	0.458694	−	1.41171i	0.866744	−	0.498754i	$-0.166209\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.160353	+	0.493515i	0.0155019	+	0.0477099i	0.958508	−	0.285065i	$-0.0920151\pi$
$107$	0.160353	+	0.493515i	0.0155019	+	0.0477099i	−0.943006	+	0.332775i	$0.892015\pi$
$108$		0			0
$109$	−0.285032			−0.0273011			−0.0136506	−	0.999907i	$-0.504345\pi$
$109$	−0.285032			−0.0273011			−0.0136506	+	0.999907i	$0.504345\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.57504	+	11.0028i	0.336311	+	1.03506i	0.966072	+	0.258271i	$0.0831528\pi$
$113$	3.57504	+	11.0028i	0.336311	+	1.03506i	−0.629761	+	0.776789i	$0.716847\pi$
$114$		0			0
$115$	−0.0935520	−	0.0679695i	−0.00872377	−	0.00633819i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−21.4604	+	15.5919i	−1.96727	+	1.42930i
$120$		0			0
$121$	−10.2673	−	3.94749i	−0.933390	−	0.358862i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.504704	+	1.55332i	−0.0451421	+	0.138933i
$126$		0			0
$127$	13.8495	+	10.0623i	1.22895	+	0.892883i	0.996811	−	0.0797996i	$-0.0254280\pi$
$127$	13.8495	+	10.0623i	1.22895	+	0.892883i	0.232138	+	0.972683i	$0.425428\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.02344			−0.438900			−0.219450	−	0.975624i	$-0.570426\pi$
$131$	−5.02344			−0.438900			−0.219450	+	0.975624i	$0.570426\pi$
$132$		0			0
$133$	16.1679			1.40194
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.43148	+	1.76657i	0.207735	+	0.150928i	0.686788	−	0.726857i	$-0.259020\pi$
$137$	2.43148	+	1.76657i	0.207735	+	0.150928i	−0.479053	+	0.877786i	$0.659020\pi$
$138$		0			0
$139$	−1.65652	+	5.09825i	−0.140504	+	0.432428i	−0.996406	−	0.0847114i	$-0.973003\pi$
$139$	−1.65652	+	5.09825i	−0.140504	+	0.432428i	0.855901	+	0.517140i	$0.173003\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.84407	+	8.06477i	0.321458	+	0.674410i
$144$		0			0
$145$	−0.136319	+	0.0990413i	−0.0113207	+	0.00822493i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.70922	+	3.42145i	0.385794	+	0.280296i	0.763730	−	0.645536i	$-0.223366\pi$
$149$	4.70922	+	3.42145i	0.385794	+	0.280296i	−0.377936	+	0.925832i	$0.623366\pi$
$150$		0			0
$151$	1.12657	+	3.46722i	0.0916788	+	0.282158i	0.986374	−	0.164519i	$-0.0526072\pi$
$151$	1.12657	+	3.46722i	0.0916788	+	0.282158i	−0.894695	+	0.446677i	$0.852607\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.884303			0.0710289
$156$		0			0
$157$	0.0448569	+	0.138055i	0.00357997	+	0.0110180i	0.952831	−	0.303503i	$-0.0981562\pi$
$157$	0.0448569	+	0.138055i	0.00357997	+	0.0110180i	−0.949251	+	0.314521i	$0.898156\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.763932	−	2.35114i	0.0602063	−	0.185296i
$162$		0			0
$163$	11.6809	−	8.48668i	0.914919	−	0.664728i	−0.0273349	−	0.999626i	$-0.508702\pi$
$163$	11.6809	−	8.48668i	0.914919	−	0.664728i	0.942254	+	0.334899i	$0.108702\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14.1091	−	10.2508i	1.09179	−	0.793233i	0.112090	−	0.993698i	$-0.464245\pi$
$167$	14.1091	−	10.2508i	1.09179	−	0.793233i	0.979701	+	0.200465i	$0.0642454\pi$
$168$		0			0
$169$	−1.77496	+	5.46275i	−0.136535	+	0.420212i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.63736	+	17.3500i	0.428601	+	1.31910i	0.899504	+	0.436913i	$0.143928\pi$
$173$	5.63736	+	17.3500i	0.428601	+	1.31910i	−0.470903	+	0.882185i	$0.656072\pi$
$174$		0			0
$175$	−17.4113			−1.31617
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.82688	+	8.70025i	0.211291	+	0.650288i	0.999396	+	0.0347466i	$0.0110624\pi$
$179$	2.82688	+	8.70025i	0.211291	+	0.650288i	−0.788105	+	0.615541i	$0.788938\pi$
$180$		0			0
$181$	13.4621	+	9.78079i	1.00063	+	0.727001i	0.962223	−	0.272261i	$-0.0877716\pi$
$181$	13.4621	+	9.78079i	1.00063	+	0.727001i	0.0384073	+	0.999262i	$0.487772\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.53615	+	1.11608i	−0.112940	+	0.0820558i
$186$		0			0
$187$	−18.2326	+	17.2930i	−1.33330	+	1.26459i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.37239	−	7.30146i	0.171660	−	0.528315i	−0.827805	−	0.561015i	$-0.810411\pi$
$191$	2.37239	−	7.30146i	0.171660	−	0.528315i	0.999465	+	0.0327007i	$0.0104108\pi$
$192$		0			0
$193$	−15.9130	−	11.5615i	−1.14544	−	0.832213i	−0.157574	−	0.987507i	$-0.550367\pi$
$193$	−15.9130	−	11.5615i	−1.14544	−	0.832213i	−0.987868	+	0.155294i	$0.950367\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−22.7460			−1.62059			−0.810294	−	0.586024i	$-0.800692\pi$
$197$	−22.7460			−1.62059			−0.810294	+	0.586024i	$0.800692\pi$
$198$		0			0
$199$	6.85748			0.486114			0.243057	−	0.970012i	$-0.421850\pi$
$199$	6.85748			0.486114			0.243057	+	0.970012i	$0.421850\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.91429	−	2.11735i	−0.204543	−	0.148609i
$204$		0			0
$205$	0.0142079	−	0.0437273i	0.000992320	−	0.00305405i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	15.1858	−	1.99516i	1.05042	−	0.138008i
$210$		0			0
$211$	9.30563	−	6.76094i	0.640626	−	0.465442i	−0.219439	−	0.975626i	$-0.570423\pi$
$211$	9.30563	−	6.76094i	0.640626	−	0.465442i	0.860065	+	0.510184i	$0.170423\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.571258	−	0.415043i	−0.0389595	−	0.0283057i
$216$		0			0
$217$	5.84198	+	17.9798i	0.396580	+	1.22055i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	20.4096			1.37290
$222$		0			0
$223$	5.02745	+	15.4729i	0.336663	+	1.03614i	0.965897	+	0.258926i	$0.0833685\pi$
$223$	5.02745	+	15.4729i	0.336663	+	1.03614i	−0.629235	+	0.777215i	$0.716632\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.91835	+	5.90406i	−0.127325	+	0.391866i	−0.994318	−	0.106455i	$-0.966050\pi$
$227$	−1.91835	+	5.90406i	−0.127325	+	0.391866i	0.866992	+	0.498321i	$0.166050\pi$
$228$		0			0
$229$	16.6982	−	12.1319i	1.10345	−	0.801701i	0.121827	−	0.992551i	$-0.461125\pi$
$229$	16.6982	−	12.1319i	1.10345	−	0.801701i	0.981619	+	0.190850i	$0.0611246\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.31111	+	6.03837i	−0.544479	+	0.395587i	−0.825746	−	0.564043i	$-0.809245\pi$
$233$	−8.31111	+	6.03837i	−0.544479	+	0.395587i	0.281267	+	0.959630i	$0.409245\pi$
$234$		0			0
$235$	−0.294962	+	0.907799i	−0.0192412	+	0.0592182i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.19330	+	19.0610i	0.400611	+	1.23295i	0.924505	+	0.381171i	$0.124479\pi$
$239$	6.19330	+	19.0610i	0.400611	+	1.23295i	−0.523893	+	0.851784i	$0.675521\pi$
$240$		0			0
$241$	−6.87625			−0.442938			−0.221469	−	0.975167i	$-0.571085\pi$
$241$	−6.87625			−0.442938			−0.221469	+	0.975167i	$0.571085\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.266052	+	0.818825i	0.0169975	+	0.0523128i
$246$		0			0
$247$	−10.0639	−	7.31186i	−0.640352	−	0.465243i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.20817	−	3.05742i	0.265618	−	0.192982i	−0.447002	−	0.894533i	$-0.647508\pi$
$251$	4.20817	−	3.05742i	0.265618	−	0.192982i	0.712620	+	0.701550i	$0.247508\pi$
$252$		0			0
$253$	0.427390	−	2.30259i	0.0268698	−	0.144762i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.74683	+	17.6869i	−0.358478	+	1.10328i	0.595488	+	0.803364i	$0.296959\pi$
$257$	−5.74683	+	17.6869i	−0.358478	+	1.10328i	−0.953965	+	0.299916i	$0.903041\pi$
$258$		0			0
$259$	−32.8406	−	23.8601i	−2.04062	−	1.48259i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.27857			−0.0788397			−0.0394199	−	0.999223i	$-0.512551\pi$
$263$	−1.27857			−0.0788397			−0.0394199	+	0.999223i	$0.512551\pi$
$264$		0			0
$265$	−1.61668			−0.0993120
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.17926	+	1.58333i	0.132872	+	0.0965372i	0.652236	−	0.758016i	$-0.273831\pi$
$269$	2.17926	+	1.58333i	0.132872	+	0.0965372i	−0.519364	+	0.854553i	$0.673831\pi$
$270$		0			0
$271$	−3.20991	+	9.87910i	−0.194988	+	0.600112i	0.804988	+	0.593291i	$0.202171\pi$
$271$	−3.20991	+	9.87910i	−0.194988	+	0.600112i	−0.999977	+	0.00682189i	$0.997829\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−16.3536	+	2.14859i	−0.986161	+	0.129565i
$276$		0			0
$277$	5.91429	−	4.29698i	0.355355	−	0.258181i	−0.395757	−	0.918355i	$-0.629518\pi$
$277$	5.91429	−	4.29698i	0.355355	−	0.258181i	0.751112	+	0.660175i	$0.229518\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.5472	−	9.84260i	−0.808157	−	0.587160i	0.105139	−	0.994458i	$-0.466471\pi$
$281$	−13.5472	−	9.84260i	−0.808157	−	0.587160i	−0.913296	+	0.407297i	$0.866471\pi$
$282$		0			0
$283$	−6.32816	−	19.4761i	−0.376170	−	1.15773i	−0.942686	−	0.333681i	$-0.891709\pi$
$283$	−6.32816	−	19.4761i	−0.376170	−	1.15773i	0.566516	−	0.824051i	$-0.308291\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.982932			0.0580206
$288$		0			0
$289$	12.4864	+	38.4292i	0.734494	+	2.26054i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.76665	−	17.7479i	0.336891	−	1.03684i	−0.628892	−	0.777493i	$-0.716491\pi$
$293$	5.76665	−	17.7479i	0.336891	−	1.03684i	0.965783	−	0.259352i	$-0.0835089\pi$
$294$		0			0
$295$	−0.409412	+	0.297455i	−0.0238369	+	0.0173185i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.53881	+	1.11801i	−0.0889916	+	0.0646562i
$300$		0			0
$301$	4.66481	−	14.3568i	0.268875	−	0.827513i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.350795	+	1.07964i	0.0200865	+	0.0618199i
$306$		0			0
$307$	−16.2802			−0.929160			−0.464580	−	0.885531i	$-0.653795\pi$
$307$	−16.2802			−0.929160			−0.464580	+	0.885531i	$0.653795\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.22987	−	9.94052i	−0.183149	−	0.563675i	0.816762	−	0.576974i	$-0.195767\pi$
$311$	−3.22987	−	9.94052i	−0.183149	−	0.563675i	−0.999912	+	0.0132990i	$0.995767\pi$
$312$		0			0
$313$	−6.81457	−	4.95107i	−0.385182	−	0.279851i	0.378296	−	0.925685i	$-0.376510\pi$
$313$	−6.81457	−	4.95107i	−0.385182	−	0.279851i	−0.763478	+	0.645833i	$0.776510\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.3685	−	12.6189i	0.975510	−	0.708749i	0.0188092	−	0.999823i	$-0.494012\pi$
$317$	17.3685	−	12.6189i	0.975510	−	0.708749i	0.956701	+	0.291074i	$0.0940125\pi$
$318$		0			0
$319$	−2.99854	−	1.62910i	−0.167886	−	0.0912121i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	10.8124	−	33.2771i	0.601617	−	1.85159i
$324$		0			0
$325$	10.8379	+	7.87418i	0.601177	+	0.436781i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−20.4061			−1.12502
$330$		0			0
$331$	21.5452			1.18423			0.592117	−	0.805852i	$-0.298292\pi$
$331$	21.5452			1.18423			0.592117	+	0.805852i	$0.298292\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.253935	−	0.184494i	−0.0138739	−	0.0100800i
$336$		0			0
$337$	3.46278	−	10.6574i	0.188630	−	0.580543i	−0.811362	−	0.584544i	$-0.801273\pi$
$337$	3.46278	−	10.6574i	0.188630	−	0.580543i	0.999992	+	0.00400074i	$0.00127348\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	7.70584	+	16.1666i	0.417294	+	0.875473i
$342$		0			0
$343$	4.93598	−	3.58620i	0.266518	−	0.193637i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.1421	+	7.36867i	0.544456	+	0.395571i	0.825737	−	0.564055i	$-0.190759\pi$
$347$	10.1421	+	7.36867i	0.544456	+	0.395571i	−0.281281	+	0.959625i	$0.590759\pi$
$348$		0			0
$349$	4.96963	+	15.2949i	0.266018	+	0.818719i	0.991457	+	0.130433i	$0.0416368\pi$
$349$	4.96963	+	15.2949i	0.266018	+	0.818719i	−0.725439	+	0.688286i	$0.758363\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	16.9450			0.901892			0.450946	−	0.892551i	$-0.351087\pi$
$353$	16.9450			0.901892			0.450946	+	0.892551i	$0.351087\pi$
$354$		0			0
$355$	−0.615773	−	1.89515i	−0.0326818	−	0.100584i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.62469	−	23.4664i	0.402416	−	1.23851i	−0.520618	−	0.853789i	$-0.674299\pi$
$359$	7.62469	−	23.4664i	0.402416	−	1.23851i	0.923034	−	0.384718i	$-0.125701\pi$
$360$		0			0
$361$	−1.88197	+	1.36733i	−0.0990508	+	0.0719646i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.50724	−	1.09508i	0.0788927	−	0.0573189i
$366$		0			0
$367$	9.56377	−	29.4343i	0.499225	−	1.53646i	−0.311043	−	0.950396i	$-0.600678\pi$
$367$	9.56377	−	29.4343i	0.499225	−	1.53646i	0.810268	−	0.586060i	$-0.199322\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−10.6803	−	32.8706i	−0.554494	−	1.70656i
$372$		0			0
$373$	−16.6908			−0.864217			−0.432108	−	0.901822i	$-0.642230\pi$
$373$	−16.6908			−0.864217			−0.432108	+	0.901822i	$0.642230\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.856469	+	2.63594i	0.0441104	+	0.135758i
$378$		0			0
$379$	13.4370	+	9.76252i	0.690210	+	0.501467i	0.876729	−	0.480985i	$-0.159721\pi$
$379$	13.4370	+	9.76252i	0.690210	+	0.501467i	−0.186519	+	0.982451i	$0.559721\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.20817	−	1.60433i	0.112832	−	0.0819775i	−0.529938	−	0.848036i	$-0.677785\pi$
$383$	2.20817	−	1.60433i	0.112832	−	0.0819775i	0.642771	+	0.766059i	$0.277785\pi$
$384$		0			0
$385$	0.818197	+	1.71656i	0.0416992	+	0.0874838i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.71908	−	14.5238i	0.239267	−	0.736387i	−0.757260	−	0.653113i	$-0.773462\pi$
$389$	4.71908	−	14.5238i	0.239267	−	0.736387i	0.996527	−	0.0832735i	$-0.0265375\pi$
$390$		0			0
$391$	−4.32827	−	3.14467i	−0.218890	−	0.159033i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.282881			−0.0142333
$396$		0			0
$397$	21.4810			1.07810			0.539050	−	0.842274i	$-0.318783\pi$
$397$	21.4810			1.07810			0.539050	+	0.842274i	$0.318783\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−28.9448	−	21.0296i	−1.44544	−	1.05017i	−0.986871	−	0.161509i	$-0.948364\pi$
$401$	−28.9448	−	21.0296i	−1.44544	−	1.05017i	−0.458564	−	0.888661i	$-0.651636\pi$
$402$		0			0
$403$	4.49485	−	13.8337i	0.223904	−	0.689107i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−33.7900	−	18.3581i	−1.67491	−	0.909975i
$408$		0			0
$409$	−8.54327	+	6.20705i	−0.422437	+	0.306919i	−0.778618	−	0.627499i	$-0.784079\pi$
$409$	−8.54327	+	6.20705i	−0.422437	+	0.306919i	0.356180	+	0.934417i	$0.384079\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.75261	−	6.35915i	−0.430688	−	0.312913i
$414$		0			0
$415$	−0.238329	−	0.733502i	−0.0116991	−	0.0360062i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−29.9952			−1.46536			−0.732680	−	0.680573i	$-0.761731\pi$
$419$	−29.9952			−1.46536			−0.732680	+	0.680573i	$0.761731\pi$
$420$		0			0
$421$	−6.55267	−	20.1670i	−0.319357	−	0.982881i	−0.973924	−	0.226876i	$-0.927149\pi$
$421$	−6.55267	−	20.1670i	−0.319357	−	0.982881i	0.654566	−	0.756005i	$-0.272851\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.6439	+	35.8362i	−0.564812	+	1.73831i
$426$		0			0
$427$	−19.6339	+	14.2649i	−0.950150	+	0.690325i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.8875	+	7.91021i	−0.524431	+	0.381021i	−0.818270	−	0.574833i	$-0.805067\pi$
$431$	−10.8875	+	7.91021i	−0.524431	+	0.381021i	0.293840	+	0.955855i	$0.405067\pi$
$432$		0			0
$433$	9.24458	−	28.4519i	0.444266	−	1.36731i	−0.439020	−	0.898477i	$-0.644674\pi$
$433$	9.24458	−	28.4519i	0.444266	−	1.36731i	0.883286	−	0.468834i	$-0.155326\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.00766	+	3.10126i	0.0482029	+	0.148353i
$438$		0			0
$439$	−33.1644			−1.58285			−0.791425	−	0.611266i	$-0.790661\pi$
$439$	−33.1644			−1.58285			−0.791425	+	0.611266i	$0.790661\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.59675	+	26.4581i	0.408444	+	1.25706i	0.917985	+	0.396615i	$0.129815\pi$
$443$	8.59675	+	26.4581i	0.408444	+	1.25706i	−0.509541	+	0.860447i	$0.670185\pi$
$444$		0			0
$445$	0.836235	+	0.607560i	0.0396413	+	0.0288011i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−5.90249	+	4.28841i	−0.278556	+	0.202383i	−0.718287	−	0.695747i	$-0.755074\pi$
$449$	−5.90249	+	4.28841i	−0.278556	+	0.202383i	0.439731	+	0.898129i	$0.355074\pi$
$450$		0			0
$451$	0.923221	−	0.121296i	0.0434728	−	0.00571159i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.477258	−	1.46885i	0.0223742	−	0.0688607i
$456$		0			0
$457$	13.0495	+	9.48103i	0.610430	+	0.443504i	0.849566	−	0.527483i	$-0.176864\pi$
$457$	13.0495	+	9.48103i	0.610430	+	0.443504i	−0.239135	+	0.970986i	$0.576864\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.4253			0.671851			0.335926	−	0.941888i	$-0.390951\pi$
$461$	14.4253			0.671851			0.335926	+	0.941888i	$0.390951\pi$
$462$		0			0
$463$	−19.7906			−0.919748			−0.459874	−	0.887984i	$-0.652105\pi$
$463$	−19.7906			−0.919748			−0.459874	+	0.887984i	$0.652105\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	30.5957	+	22.2291i	1.41580	+	1.02864i	0.992447	+	0.122673i	$0.0391465\pi$
$467$	30.5957	+	22.2291i	1.41580	+	1.02864i	0.423352	+	0.905965i	$0.360853\pi$
$468$		0			0
$469$	2.07359	−	6.38187i	0.0957497	−	0.294687i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.60978	−	14.0603i	0.119998	−	0.646494i
$474$		0			0
$475$	18.5801	−	13.4993i	0.852515	−	0.619389i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−31.0120	−	22.5316i	−1.41698	−	1.02949i	−0.992262	−	0.124165i	$-0.960375\pi$
$479$	−31.0120	−	22.5316i	−1.41698	−	1.02949i	−0.424714	−	0.905328i	$-0.639625\pi$
$480$		0			0
$481$	9.65140	+	29.7040i	0.440066	+	1.35438i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.14725			0.0520940
$486$		0			0
$487$	−3.54083	−	10.8975i	−0.160450	−	0.493815i	0.838222	−	0.545329i	$-0.183595\pi$
$487$	−3.54083	−	10.8975i	−0.160450	−	0.493815i	−0.998672	+	0.0515142i	$0.983595\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.56701	+	23.2889i	−0.341494	+	1.05101i	0.621939	+	0.783065i	$0.286345\pi$
$491$	−7.56701	+	23.2889i	−0.341494	+	1.05101i	−0.963434	+	0.267946i	$0.913655\pi$
$492$		0			0
$493$	−6.30691	+	4.58224i	−0.284049	+	0.206374i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	34.4645	−	25.0400i	1.54595	−	1.12320i
$498$		0			0
$499$	4.69978	−	14.4644i	0.210391	−	0.647516i	−0.789058	−	0.614319i	$-0.789431\pi$
$499$	4.69978	−	14.4644i	0.210391	−	0.647516i	0.999449	−	0.0331977i	$-0.0105691\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−8.23196	−	25.3354i	−0.367045	−	1.12965i	−0.948691	−	0.316206i	$-0.897591\pi$
$503$	−8.23196	−	25.3354i	−0.367045	−	1.12965i	0.581646	−	0.813442i	$-0.302409\pi$
$504$		0			0
$505$	−0.658882			−0.0293198
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.72544	−	14.5434i	−0.209452	−	0.644626i	−0.999501	−	0.0315827i	$-0.989945\pi$
$509$	−4.72544	−	14.5434i	−0.209452	−	0.644626i	0.790050	−	0.613043i	$-0.210055\pi$
$510$		0			0
$511$	32.2226	+	23.4111i	1.42544	+	1.03564i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.99589	+	1.45010i	−0.0879496	+	0.0638991i
$516$		0			0
$517$	−19.1665	+	2.51815i	−0.842941	+	0.110748i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.7044	−	32.9446i	0.468967	−	1.44333i	−0.384958	−	0.922934i	$-0.625784\pi$
$521$	10.7044	−	32.9446i	0.468967	−	1.44333i	0.853925	−	0.520397i	$-0.174216\pi$
$522$		0			0
$523$	13.5192	+	9.82230i	0.591155	+	0.429499i	0.842728	−	0.538339i	$-0.180948\pi$
$523$	13.5192	+	9.82230i	0.591155	+	0.429499i	−0.251574	+	0.967838i	$0.580948\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	40.9131			1.78220
$528$		0			0
$529$	−22.5014			−0.978322
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.611837	−	0.444525i	−0.0265016	−	0.0192545i
$534$		0			0
$535$	0.0262601	−	0.0808204i	0.00113532	−	0.00349417i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12.6512	+	11.9992i	−0.544926	+	0.516841i
$540$		0			0
$541$	10.4552	−	7.59614i	0.449504	−	0.326583i	−0.339896	−	0.940463i	$-0.610392\pi$
$541$	10.4552	−	7.59614i	0.449504	−	0.326583i	0.789400	+	0.613880i	$0.210392\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.0377635	+	0.0274368i	0.00161761	+	0.00117526i
$546$		0			0
$547$	1.61370	+	4.96645i	0.0689968	+	0.212350i	0.979610	−	0.200910i	$-0.0643899\pi$
$547$	1.61370	+	4.96645i	0.0689968	+	0.212350i	−0.910613	+	0.413260i	$0.864390\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.75154			0.202422
$552$		0			0
$553$	−1.86880	−	5.75159i	−0.0794696	−	0.244582i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.64711	−	11.2247i	0.154533	−	0.475604i	−0.843580	−	0.537003i	$-0.819556\pi$
$557$	3.64711	−	11.2247i	0.154533	−	0.475604i	0.998113	+	0.0613991i	$0.0195562\pi$
$558$		0			0
$559$	−9.39645	+	6.82692i	−0.397428	+	0.288748i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	29.8190	−	21.6648i	1.25672	−	0.913061i	0.258128	−	0.966111i	$-0.416894\pi$
$563$	29.8190	−	21.6648i	1.25672	−	0.913061i	0.998592	+	0.0530501i	$0.0168943\pi$
$564$		0			0
$565$	0.585466	−	1.80188i	0.0246307	−	0.0758056i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.33266	+	25.6453i	0.349323	+	1.07511i	0.959228	+	0.282632i	$0.0912076\pi$
$569$	8.33266	+	25.6453i	0.349323	+	1.07511i	−0.609905	+	0.792475i	$0.708792\pi$
$570$		0			0
$571$	−14.3565			−0.600801			−0.300400	−	0.953813i	$-0.597120\pi$
$571$	−14.3565			−0.600801			−0.300400	+	0.953813i	$0.597120\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.08515	−	3.33976i	−0.0452540	−	0.139278i
$576$		0			0
$577$	−8.57084	−	6.22708i	−0.356809	−	0.259237i	0.394911	−	0.918719i	$-0.370775\pi$
$577$	−8.57084	−	6.22708i	−0.356809	−	0.259237i	−0.751720	+	0.659483i	$0.770775\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	13.3392	−	9.69150i	0.553403	−	0.402071i
$582$		0			0
$583$	−14.0878	−	29.5558i	−0.583457	−	1.22408i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.17859	+	19.0157i	−0.255018	+	0.784864i	0.738809	+	0.673915i	$0.235389\pi$
$587$	−6.17859	+	19.0157i	−0.255018	+	0.784864i	−0.993826	+	0.110948i	$0.964611\pi$
$588$		0			0
$589$	−20.1741	−	14.6574i	−0.831261	−	0.603947i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.8414			−0.527334			−0.263667	−	0.964614i	$-0.584932\pi$
$593$	−12.8414			−0.527334			−0.263667	+	0.964614i	$0.584932\pi$
$594$		0			0
$595$	4.34410			0.178091
$596$		0			0
$597$		0			0
$598$		0			0
$599$	14.8097	+	10.7599i	0.605108	+	0.439636i	0.847688	−	0.530495i	$-0.177994\pi$
$599$	14.8097	+	10.7599i	0.605108	+	0.439636i	−0.242581	+	0.970131i	$0.577994\pi$
$600$		0			0
$601$	4.98290	−	15.3358i	0.203257	−	0.625560i	−0.796524	−	0.604607i	$-0.793330\pi$
$601$	4.98290	−	15.3358i	0.203257	−	0.625560i	0.999780	−	0.0209527i	$-0.00666995\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.980320	+	1.51131i	0.0398557	+	0.0614436i
$606$		0			0
$607$	8.08900	−	5.87700i	0.328322	−	0.238540i	−0.411396	−	0.911457i	$-0.634959\pi$
$607$	8.08900	−	5.87700i	0.328322	−	0.238540i	0.739718	+	0.672917i	$0.234959\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.7020	+	9.22855i	0.513868	+	0.373347i
$612$		0			0
$613$	12.3469	+	37.9997i	0.498685	+	1.53479i	0.811134	+	0.584860i	$0.198851\pi$
$613$	12.3469	+	37.9997i	0.498685	+	1.53479i	−0.312449	+	0.949934i	$0.601149\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	28.5485			1.14932			0.574660	−	0.818392i	$-0.305134\pi$
$617$	28.5485			1.14932			0.574660	+	0.818392i	$0.305134\pi$
$618$		0			0
$619$	4.02429	+	12.3855i	0.161750	+	0.497815i	0.998782	−	0.0493385i	$-0.0157113\pi$
$619$	4.02429	+	12.3855i	0.161750	+	0.497815i	−0.837032	+	0.547154i	$0.815711\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.82857	+	21.0162i	−0.273581	+	0.841996i
$624$		0			0
$625$	−19.9006	+	14.4586i	−0.796022	+	0.578344i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−71.0714	+	51.6364i	−2.83380	+	2.05888i
$630$		0			0
$631$	−6.00401	+	18.4784i	−0.239016	+	0.735615i	0.757547	+	0.652780i	$0.226397\pi$
$631$	−6.00401	+	18.4784i	−0.239016	+	0.735615i	−0.996563	+	0.0828350i	$0.973603\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.866325	−	2.66628i	−0.0343791	−	0.105808i
$636$		0			0
$637$	14.1617			0.561108
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.50108	+	13.8529i	0.177782	+	0.547156i	0.999750	−	0.0223779i	$-0.00712370\pi$
$641$	4.50108	+	13.8529i	0.177782	+	0.547156i	−0.821968	+	0.569534i	$0.807124\pi$
$642$		0			0
$643$	2.92158	+	2.12265i	0.115216	+	0.0837092i	0.643901	−	0.765109i	$-0.277315\pi$
$643$	2.92158	+	2.12265i	0.115216	+	0.0837092i	−0.528685	+	0.848818i	$0.677315\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.38652	+	3.91354i	−0.211766	+	0.153857i	−0.688612	−	0.725130i	$-0.741780\pi$
$647$	−5.38652	+	3.91354i	−0.211766	+	0.153857i	0.476846	+	0.878987i	$0.341780\pi$
$648$		0			0
$649$	−9.00564	−	4.89275i	−0.353502	−	0.192057i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.814815	+	2.50774i	−0.0318862	+	0.0981356i	−0.965733	−	0.259538i	$-0.916430\pi$
$653$	−0.814815	+	2.50774i	−0.0318862	+	0.0981356i	0.933847	+	0.357673i	$0.116430\pi$
$654$		0			0
$655$	0.665548	+	0.483549i	0.0260051	+	0.0188938i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−18.2059			−0.709200			−0.354600	−	0.935018i	$-0.615383\pi$
$659$	−18.2059			−0.709200			−0.354600	+	0.935018i	$0.615383\pi$
$660$		0			0
$661$	37.6750			1.46539			0.732693	−	0.680559i	$-0.238263\pi$
$661$	37.6750			1.46539			0.732693	+	0.680559i	$0.238263\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.14207	−	1.55630i	−0.0830658	−	0.0603509i
$666$		0			0
$667$	0.224509	−	0.690968i	0.00869303	−	0.0267544i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−16.6809	+	15.8212i	−0.643958	+	0.610769i
$672$		0			0
$673$	−13.9996	+	10.1713i	−0.539644	+	0.392074i	−0.823953	−	0.566658i	$-0.808236\pi$
$673$	−13.9996	+	10.1713i	−0.539644	+	0.392074i	0.284309	+	0.958733i	$0.408236\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.77933	+	5.65202i	0.298984	+	0.217225i	0.727155	−	0.686473i	$-0.240842\pi$
$677$	7.77933	+	5.65202i	0.298984	+	0.217225i	−0.428171	+	0.903698i	$0.640842\pi$
$678$		0			0
$679$	7.57910	+	23.3261i	0.290859	+	0.895172i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	33.2554			1.27248			0.636241	−	0.771491i	$-0.280489\pi$
$683$	33.2554			1.27248			0.636241	+	0.771491i	$0.280489\pi$
$684$		0			0
$685$	−0.152095	−	0.468101i	−0.00581126	−	0.0178852i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.21748	+	25.2908i	−0.313061	+	0.963502i
$690$		0			0
$691$	−13.7945	+	10.0223i	−0.524768	+	0.381266i	−0.818397	−	0.574653i	$-0.805137\pi$
$691$	−13.7945	+	10.0223i	−0.524768	+	0.381266i	0.293629	+	0.955919i	$0.405137\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.710221	−	0.516006i	0.0269402	−	0.0195732i
$696$		0			0
$697$	0.657340	−	2.02308i	0.0248985	−	0.0766297i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	11.3166	+	34.8289i	0.427422	+	1.31547i	0.900656	+	0.434533i	$0.143087\pi$
$701$	11.3166	+	34.8289i	0.427422	+	1.31547i	−0.473234	+	0.880937i	$0.656913\pi$
$702$		0			0
$703$	53.5442			2.01946
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.35278	−	13.3965i	−0.163703	−	0.503826i
$708$		0			0
$709$	−15.8194	−	11.4935i	−0.594112	−	0.431647i	0.249672	−	0.968330i	$-0.419677\pi$
$709$	−15.8194	−	11.4935i	−0.594112	−	0.431647i	−0.843784	+	0.536683i	$0.819677\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.08470	+	2.24116i	−0.115523	+	0.0839323i
$714$		0			0
$715$	0.267007	−	1.43851i	0.00998549	−	0.0537974i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.09209	+	3.36110i	−0.0407280	+	0.125348i	−0.969353	−	0.245671i	$-0.920992\pi$
$719$	−1.09209	+	3.36110i	−0.0407280	+	0.125348i	0.928625	+	0.371019i	$0.120992\pi$
$720$		0			0
$721$	−42.6692	−	31.0010i	−1.58908	−	1.15454i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.11695			−0.190039
$726$		0			0
$727$	5.02836			0.186491			0.0932457	−	0.995643i	$-0.470276\pi$
$727$	5.02836			0.186491			0.0932457	+	0.995643i	$0.470276\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−26.4298	−	19.2024i	−0.977540	−	0.710225i
$732$		0			0
$733$	−3.52505	+	10.8490i	−0.130201	+	0.400716i	−0.994813	−	0.101724i	$-0.967564\pi$
$733$	−3.52505	+	10.8490i	−0.130201	+	0.400716i	0.864612	+	0.502440i	$0.167564\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.16009	−	6.25007i	0.0427326	−	0.230224i
$738$		0			0
$739$	−3.65966	+	2.65890i	−0.134623	+	0.0978091i	−0.653059	−	0.757307i	$-0.726514\pi$
$739$	−3.65966	+	2.65890i	−0.134623	+	0.0978091i	0.518436	+	0.855116i	$0.326514\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.5365	+	14.1941i	0.716725	+	0.520731i	0.885336	−	0.464952i	$-0.153928\pi$
$743$	19.5365	+	14.1941i	0.716725	+	0.520731i	−0.168611	+	0.985683i	$0.553928\pi$
$744$		0			0
$745$	−0.294574	−	0.906605i	−0.0107924	−	0.0332155i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.81673			0.0663820
$750$		0			0
$751$	4.56162	+	14.0392i	0.166456	+	0.512298i	0.999141	−	0.0414489i	$-0.0131974\pi$
$751$	4.56162	+	14.0392i	0.166456	+	0.512298i	−0.832685	+	0.553747i	$0.813197\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.184492	−	0.567809i	0.00671436	−	0.0206647i
$756$		0			0
$757$	−10.2060	+	7.41508i	−0.370943	+	0.269506i	−0.757602	−	0.652717i	$-0.773629\pi$
$757$	−10.2060	+	7.41508i	−0.370943	+	0.269506i	0.386659	+	0.922223i	$0.373629\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−20.0141	+	14.5411i	−0.725509	+	0.527113i	−0.888140	−	0.459574i	$-0.848002\pi$
$761$	−20.0141	+	14.5411i	−0.725509	+	0.527113i	0.162630	+	0.986687i	$0.448002\pi$
$762$		0			0
$763$	−0.308371	+	0.949069i	−0.0111638	+	0.0343586i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.57227	+	7.91664i	0.0928794	+	0.285853i
$768$		0			0
$769$	−5.37741			−0.193914			−0.0969571	−	0.995289i	$-0.530911\pi$
$769$	−5.37741			−0.193914			−0.0969571	+	0.995289i	$0.530911\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−5.02699	−	15.4715i	−0.180808	−	0.556471i	0.819043	−	0.573733i	$-0.194505\pi$
$773$	−5.02699	−	15.4715i	−0.180808	−	0.556471i	−0.999851	+	0.0172619i	$0.994505\pi$
$774$		0			0
$775$	21.7256	+	15.7846i	0.780407	+	0.566999i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.04892	+	0.762081i	−0.0375813	+	0.0273044i
$780$		0			0
$781$	29.2809	−	27.7718i	1.04775	−	0.993754i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.00734599	−	0.0226086i	0.000262190	−	0.000806937i
$786$		0			0
$787$	15.0196	+	10.9124i	0.535392	+	0.388985i	0.822371	−	0.568952i	$-0.192651\pi$
$787$	15.0196	+	10.9124i	0.535392	+	0.388985i	−0.286979	+	0.957937i	$0.592651\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	40.5038			1.44015
$792$		0			0
$793$	18.6725			0.663081
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.0278	−	18.9103i	−0.921952	−	0.669837i	0.0220572	−	0.999757i	$-0.492978\pi$
$797$	−26.0278	−	18.9103i	−0.921952	−	0.669837i	−0.944009	+	0.329919i	$0.892978\pi$
$798$		0			0
$799$	−13.6467	+	42.0001i	−0.482784	+	1.48586i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	33.1541	+	18.0126i	1.16998	+	0.635650i
$804$		0			0
$805$	−0.327530	+	0.237964i	−0.0115439	+	0.00838714i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−23.4124	−	17.0101i	−0.823138	−	0.598045i	0.0944717	−	0.995528i	$-0.469884\pi$
$809$	−23.4124	−	17.0101i	−0.823138	−	0.598045i	−0.917610	+	0.397483i	$0.869884\pi$
$810$		0			0
$811$	3.10198	+	9.54691i	0.108925	+	0.335237i	0.990632	−	0.136561i	$-0.0436050\pi$
$811$	3.10198	+	9.54691i	0.108925	+	0.335237i	−0.881706	+	0.471799i	$0.843605\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.36450			−0.0828249
$816$		0			0
$817$	6.15309	+	18.9373i	0.215269	+	0.662531i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9.27874	−	28.5570i	0.323830	−	0.996647i	−0.648136	−	0.761525i	$-0.724451\pi$
$821$	9.27874	−	28.5570i	0.323830	−	0.996647i	0.971966	−	0.235122i	$-0.0755489\pi$
$822$		0			0
$823$	24.7215	−	17.9612i	0.861738	−	0.626089i	−0.0666193	−	0.997778i	$-0.521221\pi$
$823$	24.7215	−	17.9612i	0.861738	−	0.626089i	0.928357	+	0.371689i	$0.121221\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.75466	+	3.45446i	−0.165336	+	0.120123i	−0.667376	−	0.744721i	$-0.732583\pi$
$827$	−4.75466	+	3.45446i	−0.165336	+	0.120123i	0.502041	+	0.864844i	$0.332583\pi$
$828$		0			0
$829$	−3.23670	+	9.96152i	−0.112415	+	0.345978i	−0.991399	−	0.130873i	$-0.958222\pi$
$829$	−3.23670	+	9.96152i	−0.112415	+	0.345978i	0.878984	+	0.476851i	$0.158222\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.3092	+	37.8837i	0.426487	+	1.31259i
$834$		0			0
$835$	−2.85602			−0.0988366
$836$		0			0
$837$		0			0
$838$		0			0
$839$	10.3026	+	31.7082i	0.355686	+	1.09469i	0.955610	+	0.294633i	$0.0951974\pi$
$839$	10.3026	+	31.7082i	0.355686	+	1.09469i	−0.599924	+	0.800057i	$0.704803\pi$
$840$		0			0
$841$	22.6050	+	16.4235i	0.779484	+	0.566328i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.760998	−	0.552897i	0.0261791	−	0.0190203i
$846$		0			0
$847$	−24.2519	+	29.9162i	−0.833306	+	1.02793i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.52995	−	7.78640i	0.0867257	−	0.266914i
$852$		0			0
$853$	22.4071	+	16.2797i	0.767205	+	0.557407i	0.901112	−	0.433587i	$-0.142752\pi$
$853$	22.4071	+	16.2797i	0.767205	+	0.557407i	−0.133907	+	0.990994i	$0.542752\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.13818			0.0730387			0.0365194	−	0.999333i	$-0.488373\pi$
$857$	2.13818			0.0730387			0.0365194	+	0.999333i	$0.488373\pi$
$858$		0			0
$859$	−6.06982			−0.207099			−0.103550	−	0.994624i	$-0.533020\pi$
$859$	−6.06982			−0.207099			−0.103550	+	0.994624i	$0.533020\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.1070	+	17.5148i	0.820613	+	0.596210i	0.916888	−	0.399145i	$-0.130693\pi$
$863$	24.1070	+	17.5148i	0.820613	+	0.596210i	−0.0962753	+	0.995355i	$0.530693\pi$
$864$		0			0
$865$	0.923202	−	2.84132i	0.0313898	−	0.0966079i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.46503	−	5.17158i	−0.0836206	−	0.175434i
$870$		0			0
$871$	−4.17690	+	3.03469i	−0.141529	+	0.102827i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.62604	+	3.36102i	0.156389	+	0.113623i
$876$		0			0
$877$	−11.4515	−	35.2440i	−0.386688	−	1.19010i	−0.935248	−	0.353993i	$-0.884824\pi$
$877$	−11.4515	−	35.2440i	−0.386688	−	1.19010i	0.548560	−	0.836111i	$-0.315176\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	10.6956			0.360345			0.180172	−	0.983635i	$-0.442334\pi$
$881$	10.6956			0.360345			0.180172	+	0.983635i	$0.442334\pi$
$882$		0			0
$883$	−4.97395	−	15.3082i	−0.167387	−	0.515163i	0.831818	−	0.555049i	$-0.187301\pi$
$883$	−4.97395	−	15.3082i	−0.167387	−	0.515163i	−0.999204	+	0.0398858i	$0.987301\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.12229	+	24.9978i	−0.272720	+	0.839345i	0.717094	+	0.696977i	$0.245472\pi$
$887$	−8.12229	+	24.9978i	−0.272720	+	0.839345i	−0.989814	+	0.142369i	$0.954528\pi$
$888$		0			0
$889$	48.4879	−	35.2285i	1.62623	−	1.18153i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	21.7760	−	15.8212i	0.728704	−	0.529435i
$894$		0			0
$895$	0.462944	−	1.42480i	0.0154745	−	0.0476257i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.71688	+	5.28401i	0.0572611	+	0.176232i
$900$		0			0
$901$	−74.7972			−2.49186
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.842090	−	2.59169i	−0.0279920	−	0.0861506i
$906$		0			0
$907$	5.33332	+	3.87489i	0.177090	+	0.128663i	0.672799	−	0.739825i	$-0.265092\pi$
$907$	5.33332	+	3.87489i	0.177090	+	0.128663i	−0.495709	+	0.868489i	$0.665092\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−35.7326	+	25.9613i	−1.18387	+	0.860135i	−0.992603	−	0.121402i	$-0.961261\pi$
$911$	−35.7326	+	25.9613i	−1.18387	+	0.860135i	−0.191271	+	0.981537i	$0.561261\pi$
$912$		0			0
$913$	11.3329	−	10.7488i	0.375065	−	0.355735i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.43477	+	16.7265i	−0.179472	+	0.552358i
$918$		0			0
$919$	−25.4641	−	18.5008i	−0.839983	−	0.610284i	0.0823828	−	0.996601i	$-0.473747\pi$
$919$	−25.4641	−	18.5008i	−0.839983	−	0.610284i	−0.922366	+	0.386317i	$0.873747\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−32.7770			−1.07887
$924$		0			0
$925$	−57.6620			−1.89592
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−26.2675	−	19.0845i	−0.861810	−	0.626142i	0.0665666	−	0.997782i	$-0.478796\pi$
$929$	−26.2675	−	19.0845i	−0.861810	−	0.626142i	−0.928377	+	0.371640i	$0.878796\pi$
$930$		0			0
$931$	7.50246	−	23.0902i	0.245883	−	0.756751i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.08021	−	0.536071i	0.133437	−	0.0175314i
$936$		0			0
$937$	23.4691	−	17.0513i	0.766701	−	0.557041i	−0.134257	−	0.990947i	$-0.542865\pi$
$937$	23.4691	−	17.0513i	0.766701	−	0.557041i	0.900958	+	0.433905i	$0.142865\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.76511	+	3.46205i	0.155338	+	0.112860i	0.662739	−	0.748850i	$-0.269394\pi$
$941$	4.76511	+	3.46205i	0.155338	+	0.112860i	−0.507401	+	0.861710i	$0.669394\pi$
$942$		0			0
$943$	0.0612608	+	0.188541i	0.00199493	+	0.00613975i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−52.2319			−1.69731			−0.848655	−	0.528947i	$-0.822587\pi$
$947$	−52.2319			−1.69731			−0.848655	+	0.528947i	$0.822587\pi$
$948$		0			0
$949$	−9.46977	−	29.1450i	−0.307402	−	0.946085i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	11.8723	−	36.5391i	0.384581	−	1.18362i	−0.552203	−	0.833710i	$-0.686213\pi$
$953$	11.8723	−	36.5391i	0.384581	−	1.18362i	0.936784	−	0.349909i	$-0.113787\pi$
$954$		0			0
$955$	−1.01714	+	0.738997i	−0.0329139	+	0.0239134i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	8.51271	−	6.18485i	0.274890	−	0.199719i
$960$		0			0
$961$	−0.569149	+	1.75166i	−0.0183596	+	0.0565052i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.995400	+	3.06352i	0.0320430	+	0.0986183i
$966$		0			0
$967$	50.8436			1.63502			0.817509	−	0.575915i	$-0.195354\pi$
$967$	50.8436			1.63502			0.817509	+	0.575915i	$0.195354\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.44121	+	7.51327i	0.0783422	+	0.241112i	0.982556	−	0.185968i	$-0.0595421\pi$
$971$	2.44121	+	7.51327i	0.0783422	+	0.241112i	−0.904214	+	0.427080i	$0.859542\pi$
$972$		0			0
$973$	15.1834	+	11.0314i	0.486759	+	0.353651i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.9596	+	9.41571i	−0.414615	+	0.301235i	−0.775467	−	0.631388i	$-0.782486\pi$
$977$	−12.9596	+	9.41571i	−0.414615	+	0.301235i	0.360853	+	0.932623i	$0.382486\pi$
$978$		0			0
$979$	−3.82032	+	20.5822i	−0.122098	+	0.657809i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.0716	−	55.6186i	0.576394	−	1.77396i	−0.0549895	−	0.998487i	$-0.517513\pi$
$983$	18.0716	−	55.6186i	0.576394	−	1.77396i	0.631383	−	0.775471i	$-0.282487\pi$
$984$		0			0
$985$	3.01359	+	2.18950i	0.0960209	+	0.0697633i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.04459			0.0968123
$990$		0			0
$991$	−17.1741			−0.545552			−0.272776	−	0.962078i	$-0.587942\pi$
$991$	−17.1741			−0.545552			−0.272776	+	0.962078i	$0.587942\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.908538	−	0.660092i	−0.0288026	−	0.0209263i
$996$		0			0
$997$	−12.8382	+	39.5118i	−0.406588	+	1.25135i	0.512973	+	0.858405i	$0.328544\pi$
$997$	−12.8382	+	39.5118i	−0.406588	+	1.25135i	−0.919562	+	0.392946i	$0.871456\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.r.g.289.1		8
3.2	odd	2		88.2.i.b.25.1	✓	8
11.2	odd	10		8712.2.a.cd.1.3		4
11.4	even	5	inner	792.2.r.g.433.1		8
11.9	even	5		8712.2.a.ce.1.3		4
12.11	even	2		176.2.m.d.113.2		8
24.5	odd	2		704.2.m.l.641.2		8
24.11	even	2		704.2.m.i.641.1		8
33.2	even	10		968.2.a.m.1.1		4
33.5	odd	10		968.2.i.s.9.2		8
33.8	even	10		968.2.i.t.753.2		8
33.14	odd	10		968.2.i.s.753.2		8
33.17	even	10		968.2.i.t.9.2		8
33.20	odd	10		968.2.a.n.1.1		4
33.26	odd	10		88.2.i.b.81.1	yes	8
33.29	even	10		968.2.i.p.81.1		8
33.32	even	2		968.2.i.p.729.1		8
132.35	odd	10		1936.2.a.bc.1.4		4
132.59	even	10		176.2.m.d.81.2		8
132.119	even	10		1936.2.a.bb.1.4		4
264.35	odd	10		7744.2.a.ds.1.1		4
264.53	odd	10		7744.2.a.di.1.4		4
264.59	even	10		704.2.m.i.257.1		8
264.101	even	10		7744.2.a.dh.1.4		4
264.125	odd	10		704.2.m.l.257.2		8
264.251	even	10		7744.2.a.dr.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.b.25.1	✓	8	3.2	odd	2
88.2.i.b.81.1	yes	8	33.26	odd	10
176.2.m.d.81.2		8	132.59	even	10
176.2.m.d.113.2		8	12.11	even	2
704.2.m.i.257.1		8	264.59	even	10
704.2.m.i.641.1		8	24.11	even	2
704.2.m.l.257.2		8	264.125	odd	10
704.2.m.l.641.2		8	24.5	odd	2
792.2.r.g.289.1		8	1.1	even	1	trivial
792.2.r.g.433.1		8	11.4	even	5	inner
968.2.a.m.1.1		4	33.2	even	10
968.2.a.n.1.1		4	33.20	odd	10
968.2.i.p.81.1		8	33.29	even	10
968.2.i.p.729.1		8	33.32	even	2
968.2.i.s.9.2		8	33.5	odd	10
968.2.i.s.753.2		8	33.14	odd	10
968.2.i.t.9.2		8	33.17	even	10
968.2.i.t.753.2		8	33.8	even	10
1936.2.a.bb.1.4		4	132.119	even	10
1936.2.a.bc.1.4		4	132.35	odd	10
7744.2.a.dh.1.4		4	264.101	even	10
7744.2.a.di.1.4		4	264.53	odd	10
7744.2.a.dr.1.1		4	264.251	even	10
7744.2.a.ds.1.1		4	264.35	odd	10
8712.2.a.cd.1.3		4	11.2	odd	10
8712.2.a.ce.1.3		4	11.9	even	5

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	792.2.r.g.289.1

Level	$792$
Weight	$2$
Character	792.289
Analytic conductor	$6.324$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$