LMFDB - Embedded newform 396.2.j.c.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [396,2,Mod(37,396)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(396, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("396.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,7,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			289.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	396.289
Dual form			396.2.j.c.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.30902 + 1.67760i) q^{5} +(1.30902 - 4.02874i) q^{7} +(-2.19098 - 2.48990i) q^{11} +(1.42705 - 1.03681i) q^{13} +(3.73607 + 2.71441i) q^{17} +(1.88197 + 5.79210i) q^{19} -4.23607 q^{23} +(0.972136 + 2.99193i) q^{25} +(1.38197 - 4.25325i) q^{29} +(6.97214 - 5.06555i) q^{31} +(9.78115 - 7.10642i) q^{35} +(-2.54508 + 7.83297i) q^{37} +(-0.163119 - 0.502029i) q^{41} +0.527864 q^{43} +(-0.427051 - 1.31433i) q^{47} +(-8.85410 - 6.43288i) q^{49} +(-10.9721 + 7.97172i) q^{53} +(-0.881966 - 9.42481i) q^{55} +(-2.73607 + 8.42075i) q^{59} +(0.309017 + 0.224514i) q^{61} +5.03444 q^{65} -6.85410 q^{67} +(-2.92705 - 2.12663i) q^{71} +(-0.381966 + 1.17557i) q^{73} +(-12.8992 + 5.56758i) q^{77} +(-7.89919 + 5.73910i) q^{79} +(5.28115 + 3.83698i) q^{83} +(4.07295 + 12.5352i) q^{85} -1.00000 q^{89} +(-2.30902 - 7.10642i) q^{91} +(-5.37132 + 16.5312i) q^{95} +(-4.92705 + 3.57971i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 7 q^{5} + 3 q^{7} - 11 q^{11} - q^{13} + 6 q^{17} + 12 q^{19} - 8 q^{23} - 14 q^{25} + 10 q^{29} + 10 q^{31} + 19 q^{35} + q^{37} + 15 q^{41} + 20 q^{43} + 5 q^{47} - 22 q^{49} - 26 q^{53} - 8 q^{55}+ \cdots - 13 q^{97}+O(q^{100}) $ 4 * q + 7 * q^5 + 3 * q^7 - 11 * q^11 - q^13 + 6 * q^17 + 12 * q^19 - 8 * q^23 - 14 * q^25 + 10 * q^29 + 10 * q^31 + 19 * q^35 + q^37 + 15 * q^41 + 20 * q^43 + 5 * q^47 - 22 * q^49 - 26 * q^53 - 8 * q^55 - 2 * q^59 - q^61 - 38 * q^65 - 14 * q^67 - 5 * q^71 - 6 * q^73 - 27 * q^77 - 7 * q^79 + q^83 + 23 * q^85 - 4 * q^89 - 7 * q^91 + 21 * q^95 - 13 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.30902	+	1.67760i	1.03262	+	0.750245i	0.968832	−	0.247718i	$-0.0796807\pi$
$5$	2.30902	+	1.67760i	1.03262	+	0.750245i	0.0637916	+	0.997963i	$0.479681\pi$
$6$		0			0
$7$	1.30902	−	4.02874i	0.494762	−	1.52272i	−0.322566	−	0.946547i	$-0.604545\pi$
$7$	1.30902	−	4.02874i	0.494762	−	1.52272i	0.817327	−	0.576173i	$-0.195455\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.19098	−	2.48990i	−0.660606	−	0.750733i
$11$	−2.19098	−	2.48990i	−0.660606	−	0.750733i
$12$		0			0
$13$	1.42705	−	1.03681i	0.395793	−	0.287560i	−0.372032	−	0.928220i	$-0.621339\pi$
$13$	1.42705	−	1.03681i	0.395793	−	0.287560i	0.767825	+	0.640660i	$0.221339\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.73607	+	2.71441i	0.906130	+	0.658342i	0.940033	−	0.341083i	$-0.110794\pi$
$17$	3.73607	+	2.71441i	0.906130	+	0.658342i	−0.0339034	+	0.999425i	$0.510794\pi$
$18$		0			0
$19$	1.88197	+	5.79210i	0.431753	+	1.32880i	0.896378	+	0.443291i	$0.146189\pi$
$19$	1.88197	+	5.79210i	0.431753	+	1.32880i	−0.464625	+	0.885507i	$0.653811\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.23607			−0.883281			−0.441641	−	0.897192i	$-0.645603\pi$
$23$	−4.23607			−0.883281			−0.441641	+	0.897192i	$0.645603\pi$
$24$		0			0
$25$	0.972136	+	2.99193i	0.194427	+	0.598385i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	−0.736881	−	0.676023i	$-0.763702\pi$
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	0.993505	−	0.113787i	$-0.0362980\pi$
$30$		0			0
$31$	6.97214	−	5.06555i	1.25223	−	0.909800i	0.253883	−	0.967235i	$-0.418292\pi$
$31$	6.97214	−	5.06555i	1.25223	−	0.909800i	0.998349	+	0.0574346i	$0.0182921\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.78115	−	7.10642i	1.65332	−	1.20120i
$36$		0			0
$37$	−2.54508	+	7.83297i	−0.418409	+	1.28773i	0.490756	+	0.871297i	$0.336721\pi$
$37$	−2.54508	+	7.83297i	−0.418409	+	1.28773i	−0.909166	+	0.416435i	$0.863279\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.163119	−	0.502029i	−0.0254749	−	0.0784037i	0.937511	−	0.347956i	$-0.113124\pi$
$41$	−0.163119	−	0.502029i	−0.0254749	−	0.0784037i	−0.962986	+	0.269553i	$0.913124\pi$
$42$		0			0
$43$	0.527864			0.0804985			0.0402493	−	0.999190i	$-0.487185\pi$
$43$	0.527864			0.0804985			0.0402493	+	0.999190i	$0.487185\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.427051	−	1.31433i	−0.0622918	−	0.191714i	0.915068	−	0.403301i	$-0.132137\pi$
$47$	−0.427051	−	1.31433i	−0.0622918	−	0.191714i	−0.977359	+	0.211586i	$0.932137\pi$
$48$		0			0
$49$	−8.85410	−	6.43288i	−1.26487	−	0.918983i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.9721	+	7.97172i	−1.50714	+	1.09500i	−0.539712	+	0.841850i	$0.681467\pi$
$53$	−10.9721	+	7.97172i	−1.50714	+	1.09500i	−0.967427	+	0.253151i	$0.918533\pi$
$54$		0			0
$55$	−0.881966	−	9.42481i	−0.118924	−	1.27084i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.73607	+	8.42075i	−0.356206	+	1.09629i	0.599101	+	0.800673i	$0.295525\pi$
$59$	−2.73607	+	8.42075i	−0.356206	+	1.09629i	−0.955307	+	0.295615i	$0.904475\pi$
$60$		0			0
$61$	0.309017	+	0.224514i	0.0395656	+	0.0287461i	0.607392	−	0.794402i	$-0.292216\pi$
$61$	0.309017	+	0.224514i	0.0395656	+	0.0287461i	−0.567827	+	0.823148i	$0.692216\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.03444			0.624446
$66$		0			0
$67$	−6.85410			−0.837362			−0.418681	−	0.908133i	$-0.637507\pi$
$67$	−6.85410			−0.837362			−0.418681	+	0.908133i	$0.637507\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.92705	−	2.12663i	−0.347377	−	0.252384i	0.400391	−	0.916344i	$-0.368874\pi$
$71$	−2.92705	−	2.12663i	−0.347377	−	0.252384i	−0.747768	+	0.663960i	$0.768874\pi$
$72$		0			0
$73$	−0.381966	+	1.17557i	−0.0447057	+	0.137590i	−0.970918	−	0.239412i	$-0.923045\pi$
$73$	−0.381966	+	1.17557i	−0.0447057	+	0.137590i	0.926212	+	0.377003i	$0.123045\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.8992	+	5.56758i	−1.47000	+	0.634485i
$78$		0			0
$79$	−7.89919	+	5.73910i	−0.888728	+	0.645699i	−0.935546	−	0.353205i	$-0.885092\pi$
$79$	−7.89919	+	5.73910i	−0.888728	+	0.645699i	0.0468181	+	0.998903i	$0.485092\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.28115	+	3.83698i	0.579682	+	0.421164i	0.838609	−	0.544733i	$-0.183369\pi$
$83$	5.28115	+	3.83698i	0.579682	+	0.421164i	−0.258928	+	0.965897i	$0.583369\pi$
$84$		0			0
$85$	4.07295	+	12.5352i	0.441773	+	1.35964i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.00000			−0.106000			−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000			−0.106000			−0.0529999	+	0.998595i	$0.516878\pi$
$90$		0			0
$91$	−2.30902	−	7.10642i	−0.242051	−	0.744956i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.37132	+	16.5312i	−0.551086	+	1.69607i
$96$		0			0
$97$	−4.92705	+	3.57971i	−0.500266	+	0.363465i	−0.809119	−	0.587645i	$-0.800055\pi$
$97$	−4.92705	+	3.57971i	−0.500266	+	0.363465i	0.308852	+	0.951110i	$0.400055\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.66312	−	7.02067i	0.961516	−	0.698582i	0.00801387	−	0.999968i	$-0.497449\pi$
$101$	9.66312	−	7.02067i	0.961516	−	0.698582i	0.953502	+	0.301385i	$0.0974491\pi$
$102$		0			0
$103$	1.09017	−	3.35520i	0.107418	−	0.330597i	−0.882873	−	0.469613i	$-0.844394\pi$
$103$	1.09017	−	3.35520i	0.107418	−	0.330597i	0.990290	+	0.139015i	$0.0443936\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.78115	−	14.7149i	−0.462212	−	1.42254i	−0.862456	−	0.506132i	$-0.831075\pi$
$107$	−4.78115	−	14.7149i	−0.462212	−	1.42254i	0.400244	−	0.916408i	$-0.368925\pi$
$108$		0			0
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.39919	−	7.38394i	−0.225697	−	0.694622i	−0.998220	−	0.0596365i	$-0.981006\pi$
$113$	−2.39919	−	7.38394i	−0.225697	−	0.694622i	0.772524	−	0.634986i	$-0.218994\pi$
$114$		0			0
$115$	−9.78115	−	7.10642i	−0.912097	−	0.662677i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	15.8262	−	11.4984i	1.45079	−	1.05406i
$120$		0			0
$121$	−1.39919	+	10.9106i	−0.127199	+	0.991877i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.63525	−	5.03280i	0.146262	−	0.450147i
$126$		0			0
$127$	−1.85410	−	1.34708i	−0.164525	−	0.119534i	0.502476	−	0.864591i	$-0.332422\pi$
$127$	−1.85410	−	1.34708i	−0.164525	−	0.119534i	−0.667001	+	0.745057i	$0.732422\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−11.5623			−1.01020			−0.505102	−	0.863060i	$-0.668545\pi$
$131$	−11.5623			−1.01020			−0.505102	+	0.863060i	$0.668545\pi$
$132$		0			0
$133$	25.7984			2.23700
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.9894	−	12.3435i	−1.45150	−	1.05458i	−0.985478	−	0.169802i	$-0.945687\pi$
$137$	−16.9894	−	12.3435i	−1.45150	−	1.05458i	−0.466020	−	0.884774i	$-0.654313\pi$
$138$		0			0
$139$	−6.42705	+	19.7804i	−0.545135	+	1.67775i	0.175533	+	0.984474i	$0.443835\pi$
$139$	−6.42705	+	19.7804i	−0.545135	+	1.67775i	−0.720668	+	0.693280i	$0.756165\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.70820	−	1.28157i	−0.477344	−	0.107170i
$144$		0			0
$145$	10.3262	−	7.50245i	0.857547	−	0.623045i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.2812	+	11.1024i	1.25188	+	0.909545i	0.998329	−	0.0577773i	$-0.0184013\pi$
$149$	15.2812	+	11.1024i	1.25188	+	0.909545i	0.253551	+	0.967322i	$0.418401\pi$
$150$		0			0
$151$	−1.38197	−	4.25325i	−0.112463	−	0.346125i	0.878947	−	0.476920i	$-0.158247\pi$
$151$	−1.38197	−	4.25325i	−0.112463	−	0.346125i	−0.991409	+	0.130795i	$0.958247\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	24.5967			1.97566
$156$		0			0
$157$	−3.94427	−	12.1392i	−0.314787	−	0.968815i	−0.975842	−	0.218478i	$-0.929891\pi$
$157$	−3.94427	−	12.1392i	−0.314787	−	0.968815i	0.661055	−	0.750338i	$-0.270109\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.54508	+	17.0660i	−0.437014	+	1.34499i
$162$		0			0
$163$	−1.50000	+	1.08981i	−0.117489	+	0.0853608i	−0.644978	−	0.764201i	$-0.723134\pi$
$163$	−1.50000	+	1.08981i	−0.117489	+	0.0853608i	0.527489	+	0.849562i	$0.323134\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.30902	−	0.951057i	0.101295	−	0.0735950i	−0.535985	−	0.844228i	$-0.680060\pi$
$167$	1.30902	−	0.951057i	0.101295	−	0.0735950i	0.637280	+	0.770633i	$0.280060\pi$
$168$		0			0
$169$	−3.05573	+	9.40456i	−0.235056	+	0.723428i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.50000	+	13.8496i	0.342129	+	1.05296i	0.963103	+	0.269133i	$0.0867371\pi$
$173$	4.50000	+	13.8496i	0.342129	+	1.05296i	−0.620974	+	0.783831i	$0.713263\pi$
$174$		0			0
$175$	13.3262			1.00737
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.0172209	+	0.0530006i	0.00128715	+	0.00396145i	0.951698	−	0.307036i	$-0.0993371\pi$
$179$	0.0172209	+	0.0530006i	0.00128715	+	0.00396145i	−0.950411	+	0.310997i	$0.899337\pi$
$180$		0			0
$181$	9.66312	+	7.02067i	0.718254	+	0.521842i	0.885826	−	0.464018i	$-0.153593\pi$
$181$	9.66312	+	7.02067i	0.718254	+	0.521842i	−0.167572	+	0.985860i	$0.553593\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−19.0172	+	13.8168i	−1.39817	+	1.01583i
$186$		0			0
$187$	−1.42705	−	15.2497i	−0.104356	−	1.11517i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.98278	+	9.18005i	−0.215826	+	0.664245i	0.783268	+	0.621685i	$0.213551\pi$
$191$	−2.98278	+	9.18005i	−0.215826	+	0.664245i	−0.999094	+	0.0425604i	$0.986449\pi$
$192$		0			0
$193$	0.263932	+	0.191758i	0.0189982	+	0.0138030i	0.597244	−	0.802060i	$-0.296262\pi$
$193$	0.263932	+	0.191758i	0.0189982	+	0.0138030i	−0.578246	+	0.815863i	$0.696262\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.0902			1.21762			0.608812	−	0.793314i	$-0.291646\pi$
$197$	17.0902			1.21762			0.608812	+	0.793314i	$0.291646\pi$
$198$		0			0
$199$	16.4164			1.16373			0.581864	−	0.813286i	$-0.302324\pi$
$199$	16.4164			1.16373			0.581864	+	0.813286i	$0.302324\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−15.3262	−	11.1352i	−1.07569	−	0.781535i
$204$		0			0
$205$	0.465558	−	1.43284i	0.0325160	−	0.100074i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.2984	−	17.3763i	0.712353	−	1.20194i
$210$		0			0
$211$	19.2082	−	13.9556i	1.32235	−	0.960742i	0.322447	−	0.946587i	$-0.395494\pi$
$211$	19.2082	−	13.9556i	1.32235	−	0.960742i	0.999900	−	0.0141542i	$-0.00450557\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.21885	+	0.885544i	0.0831247	+	0.0603936i
$216$		0			0
$217$	−11.2812	−	34.7198i	−0.765815	−	2.35693i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.14590			0.547952
$222$		0			0
$223$	0.454915	+	1.40008i	0.0304634	+	0.0937566i	0.965132	−	0.261763i	$-0.0843039\pi$
$223$	0.454915	+	1.40008i	0.0304634	+	0.0937566i	−0.934669	+	0.355520i	$0.884304\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.218847	−	0.673542i	0.0145254	−	0.0447046i	−0.943531	−	0.331284i	$-0.892518\pi$
$227$	0.218847	−	0.673542i	0.0145254	−	0.0447046i	0.958057	+	0.286579i	$0.0925182\pi$
$228$		0			0
$229$	5.61803	−	4.08174i	0.371250	−	0.269729i	−0.386479	−	0.922298i	$-0.626309\pi$
$229$	5.61803	−	4.08174i	0.371250	−	0.269729i	0.757729	+	0.652569i	$0.226309\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.8713	−	15.1639i	1.36733	−	0.993420i	0.369385	−	0.929276i	$-0.379568\pi$
$233$	20.8713	−	15.1639i	1.36733	−	0.993420i	0.997941	−	0.0641440i	$-0.0204317\pi$
$234$		0			0
$235$	1.21885	−	3.75123i	0.0795088	−	0.244703i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.33688	+	19.5029i	0.409899	+	1.26154i	0.916735	+	0.399496i	$0.130815\pi$
$239$	6.33688	+	19.5029i	0.409899	+	1.26154i	−0.506836	+	0.862042i	$0.669185\pi$
$240$		0			0
$241$	−10.2918			−0.662953			−0.331476	−	0.943463i	$-0.607547\pi$
$241$	−10.2918			−0.662953			−0.331476	+	0.943463i	$0.607547\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9.65248	−	29.7073i	−0.616674	−	1.89793i
$246$		0			0
$247$	8.69098	+	6.31437i	0.552994	+	0.401774i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	10.4443	−	7.58821i	0.659237	−	0.478963i	−0.207168	−	0.978305i	$-0.566425\pi$
$251$	10.4443	−	7.58821i	0.659237	−	0.478963i	0.866405	+	0.499342i	$0.166425\pi$
$252$		0			0
$253$	9.28115	+	10.5474i	0.583501	+	0.663108i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.73607	+	20.7315i	−0.420184	+	1.29319i	0.487346	+	0.873209i	$0.337965\pi$
$257$	−6.73607	+	20.7315i	−0.420184	+	1.29319i	−0.907531	+	0.419986i	$0.862035\pi$
$258$		0			0
$259$	28.2254	+	20.5070i	1.75384	+	1.27424i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−17.1459			−1.05726			−0.528631	−	0.848852i	$-0.677294\pi$
$263$	−17.1459			−1.05726			−0.528631	+	0.848852i	$0.677294\pi$
$264$		0			0
$265$	−38.7082			−2.37783
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.7984	+	11.4782i	0.963244	+	0.699838i	0.953902	−	0.300119i	$-0.0970263\pi$
$269$	15.7984	+	11.4782i	0.963244	+	0.699838i	0.00934200	+	0.999956i	$0.497026\pi$
$270$		0			0
$271$	−6.97214	+	21.4580i	−0.423527	+	1.30348i	0.480870	+	0.876792i	$0.340321\pi$
$271$	−6.97214	+	21.4580i	−0.423527	+	1.30348i	−0.904398	+	0.426691i	$0.859679\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.31966	−	8.97578i	0.320788	−	0.541260i
$276$		0			0
$277$	14.2082	−	10.3229i	0.853688	−	0.620241i	−0.0724723	−	0.997370i	$-0.523089\pi$
$277$	14.2082	−	10.3229i	0.853688	−	0.620241i	0.926160	+	0.377130i	$0.123089\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−18.7082	−	13.5923i	−1.11604	−	0.810849i	−0.132434	−	0.991192i	$-0.542279\pi$
$281$	−18.7082	−	13.5923i	−1.11604	−	0.810849i	−0.983604	+	0.180343i	$0.942279\pi$
$282$		0			0
$283$	5.79837	+	17.8456i	0.344678	+	1.06081i	0.961756	+	0.273907i	$0.0883160\pi$
$283$	5.79837	+	17.8456i	0.344678	+	1.06081i	−0.617079	+	0.786901i	$0.711684\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.23607			−0.131991
$288$		0			0
$289$	1.33688	+	4.11450i	0.0786401	+	0.242029i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.54508	−	4.75528i	0.0902648	−	0.277807i	−0.895726	−	0.444607i	$-0.853343\pi$
$293$	1.54508	−	4.75528i	0.0902648	−	0.277807i	0.985991	+	0.166800i	$0.0533435\pi$
$294$		0			0
$295$	−20.4443	+	14.8536i	−1.19031	+	0.864812i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.04508	+	4.39201i	−0.349596	+	0.253997i
$300$		0			0
$301$	0.690983	−	2.12663i	0.0398276	−	0.122577i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.336881	+	1.03681i	0.0192898	+	0.0593678i
$306$		0			0
$307$	−16.3262			−0.931788			−0.465894	−	0.884841i	$-0.654267\pi$
$307$	−16.3262			−0.931788			−0.465894	+	0.884841i	$0.654267\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.10739	+	6.48588i	0.119499	+	0.367781i	0.992859	−	0.119295i	$-0.0380635\pi$
$311$	2.10739	+	6.48588i	0.119499	+	0.367781i	−0.873360	+	0.487076i	$0.838064\pi$
$312$		0			0
$313$	0.809017	+	0.587785i	0.0457283	+	0.0332236i	0.610415	−	0.792082i	$-0.291003\pi$
$313$	0.809017	+	0.587785i	0.0457283	+	0.0332236i	−0.564686	+	0.825306i	$0.691003\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.1353	−	10.2699i	0.793915	−	0.576813i	−0.115208	−	0.993341i	$-0.536753\pi$
$317$	14.1353	−	10.2699i	0.793915	−	0.576813i	0.909123	+	0.416528i	$0.136753\pi$
$318$		0			0
$319$	−13.6180	+	5.87785i	−0.762464	+	0.329097i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.69098	+	26.7481i	−0.483579	+	1.48830i
$324$		0			0
$325$	4.48936	+	3.26171i	0.249025	+	0.180927i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.85410			−0.322747
$330$		0			0
$331$	−5.94427			−0.326727			−0.163363	−	0.986566i	$-0.552234\pi$
$331$	−5.94427			−0.326727			−0.163363	+	0.986566i	$0.552234\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−15.8262	−	11.4984i	−0.864680	−	0.628227i
$336$		0			0
$337$	9.76393	−	30.0503i	0.531875	−	1.63694i	−0.218430	−	0.975853i	$-0.570094\pi$
$337$	9.76393	−	30.0503i	0.531875	−	1.63694i	0.750306	−	0.661091i	$-0.229906\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−27.8885	−	6.26137i	−1.51025	−	0.339072i
$342$		0			0
$343$	−13.5172	+	9.82084i	−0.729861	+	0.530275i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.47214	−	4.70228i	−0.347442	−	0.252432i	0.400353	−	0.916361i	$-0.368888\pi$
$347$	−6.47214	−	4.70228i	−0.347442	−	0.252432i	−0.747795	+	0.663929i	$0.768888\pi$
$348$		0			0
$349$	−7.34346	−	22.6008i	−0.393086	−	1.20980i	−0.930442	−	0.366440i	$-0.880577\pi$
$349$	−7.34346	−	22.6008i	−0.393086	−	1.20980i	0.537356	−	0.843356i	$-0.319423\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.52786			0.0813200			0.0406600	−	0.999173i	$-0.487054\pi$
$353$	1.52786			0.0813200			0.0406600	+	0.999173i	$0.487054\pi$
$354$		0			0
$355$	−3.19098	−	9.82084i	−0.169360	−	0.521236i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.79837	−	17.8456i	0.306026	−	0.941853i	−0.673266	−	0.739401i	$-0.735109\pi$
$359$	5.79837	−	17.8456i	0.306026	−	0.941853i	0.979292	−	0.202452i	$-0.0648910\pi$
$360$		0			0
$361$	−14.6353	+	10.6331i	−0.770277	+	0.559639i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.85410	+	2.07363i	−0.149391	+	0.108539i
$366$		0			0
$367$	−2.35410	+	7.24518i	−0.122883	+	0.378195i	−0.993509	−	0.113750i	$-0.963714\pi$
$367$	−2.35410	+	7.24518i	−0.122883	+	0.378195i	0.870626	+	0.491945i	$0.163714\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	17.7533	+	54.6390i	0.921705	+	2.83672i
$372$		0			0
$373$	3.94427			0.204227			0.102113	−	0.994773i	$-0.467440\pi$
$373$	3.94427			0.204227			0.102113	+	0.994773i	$0.467440\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.43769	−	7.50245i	−0.125548	−	0.386396i
$378$		0			0
$379$	−0.572949	−	0.416272i	−0.0294304	−	0.0213824i	0.572973	−	0.819574i	$-0.305790\pi$
$379$	−0.572949	−	0.416272i	−0.0294304	−	0.0213824i	−0.602403	+	0.798192i	$0.705790\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.66312	−	3.38795i	0.238274	−	0.173116i	−0.462240	−	0.886755i	$-0.652954\pi$
$383$	4.66312	−	3.38795i	0.238274	−	0.173116i	0.700514	+	0.713639i	$0.252954\pi$
$384$		0			0
$385$	−39.1246	−	8.78402i	−1.99397	−	0.447675i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.51722	+	4.66953i	−0.0769262	+	0.236754i	−0.982124	−	0.188237i	$-0.939723\pi$
$389$	−1.51722	+	4.66953i	−0.0769262	+	0.236754i	0.905198	+	0.424991i	$0.139723\pi$
$390$		0			0
$391$	−15.8262	−	11.4984i	−0.800367	−	0.581501i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−27.8673			−1.40215
$396$		0			0
$397$	4.81966			0.241892			0.120946	−	0.992659i	$-0.461407\pi$
$397$	4.81966			0.241892			0.120946	+	0.992659i	$0.461407\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.11803	+	2.26538i	0.155707	+	0.113128i	0.662911	−	0.748698i	$-0.269321\pi$
$401$	3.11803	+	2.26538i	0.155707	+	0.113128i	−0.507204	+	0.861826i	$0.669321\pi$
$402$		0			0
$403$	4.69756	−	14.4576i	0.234002	−	0.720185i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	25.0795	−	10.8249i	1.24315	−	0.536570i
$408$		0			0
$409$	20.9443	−	15.2169i	1.03563	−	0.752427i	0.0662003	−	0.997806i	$-0.478912\pi$
$409$	20.9443	−	15.2169i	1.03563	−	0.752427i	0.969427	+	0.245379i	$0.0789124\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	30.3435	+	22.0458i	1.49310	+	1.08480i
$414$		0			0
$415$	5.75735	+	17.7193i	0.282617	+	0.869807i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−11.1459			−0.544513			−0.272256	−	0.962225i	$-0.587770\pi$
$419$	−11.1459			−0.544513			−0.272256	+	0.962225i	$0.587770\pi$
$420$		0			0
$421$	7.50000	+	23.0826i	0.365528	+	1.12498i	0.949650	+	0.313313i	$0.101439\pi$
$421$	7.50000	+	23.0826i	0.365528	+	1.12498i	−0.584122	+	0.811666i	$0.698561\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.48936	+	13.8168i	−0.217766	+	0.670214i
$426$		0			0
$427$	1.30902	−	0.951057i	0.0633478	−	0.0460249i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.88197	+	1.36733i	−0.0906511	+	0.0658619i	−0.632188	−	0.774815i	$-0.717843\pi$
$431$	−1.88197	+	1.36733i	−0.0906511	+	0.0658619i	0.541536	+	0.840677i	$0.317843\pi$
$432$		0			0
$433$	0.909830	−	2.80017i	0.0437236	−	0.134568i	−0.926812	−	0.375526i	$-0.877462\pi$
$433$	0.909830	−	2.80017i	0.0437236	−	0.134568i	0.970535	+	0.240959i	$0.0774619\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.97214	−	24.5357i	−0.381359	−	1.17370i
$438$		0			0
$439$	25.3607			1.21040			0.605200	−	0.796074i	$-0.293093\pi$
$439$	25.3607			1.21040			0.605200	+	0.796074i	$0.293093\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.85410	+	21.0948i	0.325648	+	1.00224i	0.971147	+	0.238481i	$0.0766495\pi$
$443$	6.85410	+	21.0948i	0.325648	+	1.00224i	−0.645499	+	0.763761i	$0.723351\pi$
$444$		0			0
$445$	−2.30902	−	1.67760i	−0.109458	−	0.0795258i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−13.3262	+	9.68208i	−0.628904	+	0.456926i	−0.856020	−	0.516942i	$-0.827070\pi$
$449$	−13.3262	+	9.68208i	−0.628904	+	0.456926i	0.227116	+	0.973868i	$0.427070\pi$
$450$		0			0
$451$	−0.892609	+	1.50609i	−0.0420313	+	0.0709188i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.59017	−	20.2825i	0.308952	−	0.950856i
$456$		0			0
$457$	−6.35410	−	4.61653i	−0.297232	−	0.215952i	0.429166	−	0.903225i	$-0.358807\pi$
$457$	−6.35410	−	4.61653i	−0.297232	−	0.215952i	−0.726399	+	0.687274i	$0.758807\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.562306			0.0261892			0.0130946	−	0.999914i	$-0.495832\pi$
$461$	0.562306			0.0261892			0.0130946	+	0.999914i	$0.495832\pi$
$462$		0			0
$463$	−30.2148			−1.40420			−0.702100	−	0.712078i	$-0.747754\pi$
$463$	−30.2148			−1.40420			−0.702100	+	0.712078i	$0.747754\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−27.3713	−	19.8864i	−1.26659	−	0.920234i	−0.267532	−	0.963549i	$-0.586208\pi$
$467$	−27.3713	−	19.8864i	−1.26659	−	0.920234i	−0.999061	+	0.0433147i	$0.986208\pi$
$468$		0			0
$469$	−8.97214	+	27.6134i	−0.414295	+	1.27507i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.15654	−	1.31433i	−0.0531778	−	0.0604329i
$474$		0			0
$475$	−15.5000	+	11.2614i	−0.711189	+	0.516709i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.88197	−	1.36733i	−0.0859892	−	0.0624748i	0.543960	−	0.839111i	$-0.316924\pi$
$479$	−1.88197	−	1.36733i	−0.0859892	−	0.0624748i	−0.629949	+	0.776636i	$0.716924\pi$
$480$		0			0
$481$	4.48936	+	13.8168i	0.204697	+	0.629993i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−17.3820			−0.789274
$486$		0			0
$487$	−5.51064	−	16.9600i	−0.249711	−	0.768532i	−0.994826	−	0.101595i	$-0.967605\pi$
$487$	−5.51064	−	16.9600i	−0.249711	−	0.768532i	0.745115	−	0.666936i	$-0.232395\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.66312	−	11.2739i	0.165314	−	0.508785i	−0.833745	−	0.552150i	$-0.813808\pi$
$491$	3.66312	−	11.2739i	0.165314	−	0.508785i	0.999059	+	0.0433647i	$0.0138077\pi$
$492$		0			0
$493$	16.7082	−	12.1392i	0.752500	−	0.546723i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.3992	+	9.00854i	−0.556180	+	0.404088i
$498$		0			0
$499$	−5.64590	+	17.3763i	−0.252745	+	0.777869i	0.741520	+	0.670930i	$0.234105\pi$
$499$	−5.64590	+	17.3763i	−0.252745	+	0.777869i	−0.994266	+	0.106939i	$0.965895\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−3.94427	−	12.1392i	−0.175866	−	0.541261i	0.823806	−	0.566872i	$-0.191847\pi$
$503$	−3.94427	−	12.1392i	−0.175866	−	0.541261i	−0.999672	+	0.0256113i	$0.991847\pi$
$504$		0			0
$505$	34.0902			1.51699
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.19098	+	28.2869i	0.407383	+	1.25380i	0.918889	+	0.394517i	$0.129088\pi$
$509$	9.19098	+	28.2869i	0.407383	+	1.25380i	−0.511506	+	0.859280i	$0.670912\pi$
$510$		0			0
$511$	4.23607	+	3.07768i	0.187393	+	0.136149i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.14590	−	5.91834i	0.358951	−	0.260793i
$516$		0			0
$517$	−2.33688	+	3.94298i	−0.102776	+	0.173412i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.0000	−	36.9322i	0.525730	−	1.61803i	−0.237139	−	0.971476i	$-0.576210\pi$
$521$	12.0000	−	36.9322i	0.525730	−	1.61803i	0.762869	−	0.646553i	$-0.223790\pi$
$522$		0			0
$523$	−2.26393	−	1.64484i	−0.0989948	−	0.0719240i	0.537187	−	0.843463i	$-0.319487\pi$
$523$	−2.26393	−	1.64484i	−0.0989948	−	0.0719240i	−0.636182	+	0.771539i	$0.719487\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	39.7984			1.73364
$528$		0			0
$529$	−5.05573			−0.219814
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.753289	−	0.547296i	−0.0326286	−	0.0237060i
$534$		0			0
$535$	13.6459	−	41.9978i	0.589964	−	1.81572i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.38197	+	36.1401i	0.145672	+	1.55667i
$540$		0			0
$541$	−7.54508	+	5.48183i	−0.324389	+	0.235682i	−0.738046	−	0.674751i	$-0.764251\pi$
$541$	−7.54508	+	5.48183i	−0.324389	+	0.235682i	0.413657	+	0.910433i	$0.364251\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−18.4721	−	13.4208i	−0.791259	−	0.574884i
$546$		0			0
$547$	−0.718847	−	2.21238i	−0.0307357	−	0.0945947i	0.934512	−	0.355932i	$-0.115837\pi$
$547$	−0.718847	−	2.21238i	−0.0307357	−	0.0945947i	−0.965248	+	0.261337i	$0.915837\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	27.2361			1.16030
$552$		0			0
$553$	12.7812	+	39.3363i	0.543510	+	1.67275i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.88197	−	5.79210i	0.0797415	−	0.245419i	−0.903236	−	0.429144i	$-0.858815\pi$
$557$	1.88197	−	5.79210i	0.0797415	−	0.245419i	0.982978	+	0.183725i	$0.0588154\pi$
$558$		0			0
$559$	0.753289	−	0.547296i	0.0318607	−	0.0231482i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	22.0795	−	16.0417i	0.930541	−	0.676078i	−0.0155841	−	0.999879i	$-0.504961\pi$
$563$	22.0795	−	16.0417i	0.930541	−	0.676078i	0.946125	+	0.323801i	$0.104961\pi$
$564$		0			0
$565$	6.84752	−	21.0745i	0.288078	−	0.886611i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.9443	−	42.9161i	−0.584574	−	1.79913i	−0.600973	−	0.799269i	$-0.705220\pi$
$569$	−13.9443	−	42.9161i	−0.584574	−	1.79913i	0.0163990	−	0.999866i	$-0.494780\pi$
$570$		0			0
$571$	8.67376			0.362986			0.181493	−	0.983392i	$-0.441907\pi$
$571$	8.67376			0.362986			0.181493	+	0.983392i	$0.441907\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.11803	−	12.6740i	−0.171734	−	0.528543i
$576$		0			0
$577$	−20.0344	−	14.5559i	−0.834045	−	0.605969i	0.0866560	−	0.996238i	$-0.472382\pi$
$577$	−20.0344	−	14.5559i	−0.834045	−	0.605969i	−0.920701	+	0.390269i	$0.872382\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	22.3713	−	16.2537i	0.928119	−	0.674318i
$582$		0			0
$583$	43.8885	+	9.85359i	1.81768	+	0.408094i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.34346	+	28.7562i	−0.385646	+	1.18690i	0.550365	+	0.834924i	$0.314489\pi$
$587$	−9.34346	+	28.7562i	−0.385646	+	1.18690i	−0.936011	+	0.351972i	$0.885511\pi$
$588$		0			0
$589$	42.4615	+	30.8501i	1.74960	+	1.27116i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	36.4508			1.49686			0.748428	−	0.663215i	$-0.230809\pi$
$593$	36.4508			1.49686			0.748428	+	0.663215i	$0.230809\pi$
$594$		0			0
$595$	55.8328			2.28892
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.56231	+	5.49434i	0.308987	+	0.224493i	0.731462	−	0.681882i	$-0.238838\pi$
$599$	7.56231	+	5.49434i	0.308987	+	0.224493i	−0.422474	+	0.906375i	$0.638838\pi$
$600$		0			0
$601$	0.635255	−	1.95511i	0.0259126	−	0.0797507i	−0.937264	−	0.348621i	$-0.886650\pi$
$601$	0.635255	−	1.95511i	0.0259126	−	0.0797507i	0.963177	+	0.268870i	$0.0866502\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−21.5344	+	22.8456i	−0.875500	+	0.928806i
$606$		0			0
$607$	−19.6803	+	14.2986i	−0.798800	+	0.580362i	−0.910562	−	0.413373i	$-0.864351\pi$
$607$	−19.6803	+	14.2986i	−0.798800	+	0.580362i	0.111762	+	0.993735i	$0.464351\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.97214	−	1.43284i	−0.0797841	−	0.0579665i
$612$		0			0
$613$	−7.14590	−	21.9928i	−0.288620	−	0.888281i	−0.985290	−	0.170890i	$-0.945336\pi$
$613$	−7.14590	−	21.9928i	−0.288620	−	0.888281i	0.696670	−	0.717392i	$-0.254664\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.00000			0.281809			0.140905	−	0.990023i	$-0.454999\pi$
$617$	7.00000			0.281809			0.140905	+	0.990023i	$0.454999\pi$
$618$		0			0
$619$	0.454915	+	1.40008i	0.0182846	+	0.0562741i	0.959782	−	0.280745i	$-0.0905814\pi$
$619$	0.454915	+	1.40008i	0.0182846	+	0.0562741i	−0.941498	+	0.337019i	$0.890581\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.30902	+	4.02874i	−0.0524447	+	0.161408i
$624$		0			0
$625$	24.9443	−	18.1231i	0.997771	−	0.724923i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−30.7705	+	22.3561i	−1.22690	+	0.891395i
$630$		0			0
$631$	12.7533	−	39.2506i	0.507700	−	1.56254i	−0.288482	−	0.957485i	$-0.593151\pi$
$631$	12.7533	−	39.2506i	0.507700	−	1.56254i	0.796183	−	0.605056i	$-0.206849\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.02129	−	6.22088i	−0.0802123	−	0.246868i
$636$		0			0
$637$	−19.3050			−0.764890
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.79180	+	20.9030i	0.268260	+	0.825619i	0.990924	+	0.134420i	$0.0429171\pi$
$641$	6.79180	+	20.9030i	0.268260	+	0.825619i	−0.722665	+	0.691199i	$0.757083\pi$
$642$		0			0
$643$	−23.5902	−	17.1393i	−0.930305	−	0.675907i	0.0157621	−	0.999876i	$-0.494983\pi$
$643$	−23.5902	−	17.1393i	−0.930305	−	0.675907i	−0.946068	+	0.323969i	$0.894983\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.9721	+	14.5106i	−0.785186	+	0.570471i	−0.906531	−	0.422140i	$-0.861279\pi$
$647$	−19.9721	+	14.5106i	−0.785186	+	0.570471i	0.121345	+	0.992610i	$0.461279\pi$
$648$		0			0
$649$	26.9615	−	11.6372i	1.05833	−	0.456800i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.60739	−	26.4908i	0.336833	−	1.03667i	−0.628979	−	0.777423i	$-0.716527\pi$
$653$	8.60739	−	26.4908i	0.336833	−	1.03667i	0.965812	−	0.259244i	$-0.0834732\pi$
$654$		0			0
$655$	−26.6976	−	19.3969i	−1.04316	−	0.757900i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.70820			0.144451			0.0722256	−	0.997388i	$-0.476990\pi$
$659$	3.70820			0.144451			0.0722256	+	0.997388i	$0.476990\pi$
$660$		0			0
$661$	2.32624			0.0904802			0.0452401	−	0.998976i	$-0.485595\pi$
$661$	2.32624			0.0904802			0.0452401	+	0.998976i	$0.485595\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	59.5689	+	43.2793i	2.30998	+	1.67830i
$666$		0			0
$667$	−5.85410	+	18.0171i	−0.226672	+	0.697624i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.118034	−	1.26133i	−0.00455665	−	0.0486930i
$672$		0			0
$673$	−21.4615	+	15.5927i	−0.827280	+	0.601054i	−0.918788	−	0.394750i	$-0.870831\pi$
$673$	−21.4615	+	15.5927i	−0.827280	+	0.601054i	0.0915087	+	0.995804i	$0.470831\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.23607	−	3.80423i	−0.201238	−	0.146208i	0.482602	−	0.875840i	$-0.339692\pi$
$677$	−5.23607	−	3.80423i	−0.201238	−	0.146208i	−0.683841	+	0.729631i	$0.739692\pi$
$678$		0			0
$679$	7.97214	+	24.5357i	0.305942	+	0.941594i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.34752			0.242881			0.121441	−	0.992599i	$-0.461249\pi$
$683$	6.34752			0.242881			0.121441	+	0.992599i	$0.461249\pi$
$684$		0			0
$685$	−18.5213	−	57.0027i	−0.707662	−	2.17796i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.39261	+	22.7521i	−0.281636	+	0.866786i
$690$		0			0
$691$	27.9443	−	20.3027i	1.06305	−	0.772351i	0.0883999	−	0.996085i	$-0.471825\pi$
$691$	27.9443	−	20.3027i	1.06305	−	0.772351i	0.974650	+	0.223734i	$0.0718246\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−48.0238	+	34.8913i	−1.82165	+	1.32350i
$696$		0			0
$697$	0.753289	−	2.31838i	0.0285329	−	0.0878151i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.93769	−	9.04129i	−0.110955	−	0.341485i	0.880127	−	0.474739i	$-0.157457\pi$
$701$	−2.93769	−	9.04129i	−0.110955	−	0.341485i	−0.991082	+	0.133254i	$0.957457\pi$
$702$		0			0
$703$	−50.1591			−1.89178
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.6353	−	48.1204i	−0.588024	−	1.80975i
$708$		0			0
$709$	20.8262	+	15.1311i	0.782146	+	0.568262i	0.905622	−	0.424085i	$-0.139404\pi$
$709$	20.8262	+	15.1311i	0.782146	+	0.568262i	−0.123476	+	0.992348i	$0.539404\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−29.5344	+	21.4580i	−1.10607	+	0.803609i
$714$		0			0
$715$	−11.0304	−	12.5352i	−0.412513	−	0.468792i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.0729	−	37.1567i	0.450245	−	1.38571i	−0.426383	−	0.904543i	$-0.640212\pi$
$719$	12.0729	−	37.1567i	0.450245	−	1.38571i	0.876628	−	0.481169i	$-0.159788\pi$
$720$		0			0
$721$	−12.0902	−	8.78402i	−0.450261	−	0.327134i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	14.0689			0.522505
$726$		0			0
$727$	−2.14590			−0.0795870			−0.0397935	−	0.999208i	$-0.512670\pi$
$727$	−2.14590			−0.0795870			−0.0397935	+	0.999208i	$0.512670\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.97214	+	1.43284i	0.0729421	+	0.0529955i
$732$		0			0
$733$	−6.96556	+	21.4378i	−0.257279	+	0.791823i	0.736093	+	0.676880i	$0.236668\pi$
$733$	−6.96556	+	21.4378i	−0.257279	+	0.791823i	−0.993372	+	0.114943i	$0.963332\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15.0172	+	17.0660i	0.553166	+	0.628635i
$738$		0			0
$739$	28.4615	−	20.6785i	1.04697	−	0.760670i	0.0753384	−	0.997158i	$-0.475996\pi$
$739$	28.4615	−	20.6785i	1.04697	−	0.760670i	0.971634	+	0.236488i	$0.0759963\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.04508	+	1.48584i	0.0750269	+	0.0545102i	0.624666	−	0.780892i	$-0.285235\pi$
$743$	2.04508	+	1.48584i	0.0750269	+	0.0545102i	−0.549640	+	0.835402i	$0.685235\pi$
$744$		0			0
$745$	16.6591	+	51.2713i	0.610341	+	1.87843i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−65.5410			−2.39482
$750$		0			0
$751$	11.3197	+	34.8383i	0.413060	+	1.27127i	0.913974	+	0.405772i	$0.132997\pi$
$751$	11.3197	+	34.8383i	0.413060	+	1.27127i	−0.500914	+	0.865497i	$0.667003\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.94427	−	12.1392i	0.143547	−	0.441791i
$756$		0			0
$757$	−13.2812	+	9.64932i	−0.482712	+	0.350711i	−0.802375	−	0.596821i	$-0.796430\pi$
$757$	−13.2812	+	9.64932i	−0.482712	+	0.350711i	0.319663	+	0.947531i	$0.396430\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	41.4615	−	30.1235i	1.50298	−	1.09198i	0.533801	−	0.845610i	$-0.320763\pi$
$761$	41.4615	−	30.1235i	1.50298	−	1.09198i	0.969176	−	0.246368i	$-0.0792370\pi$
$762$		0			0
$763$	−10.4721	+	32.2299i	−0.379117	+	1.16680i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.82624	+	14.8536i	0.174265	+	0.536334i
$768$		0			0
$769$	−13.4377			−0.484576			−0.242288	−	0.970204i	$-0.577898\pi$
$769$	−13.4377			−0.484576			−0.242288	+	0.970204i	$0.577898\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.74671	+	14.6089i	0.170727	+	0.525445i	0.999413	−	0.0342702i	$-0.0109107\pi$
$773$	4.74671	+	14.6089i	0.170727	+	0.525445i	−0.828685	+	0.559715i	$0.810911\pi$
$774$		0			0
$775$	21.9336	+	15.9357i	0.787879	+	0.572428i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.60081	−	1.88960i	0.0931838	−	0.0677020i
$780$		0			0
$781$	1.11803	+	11.9475i	0.0400064	+	0.427514i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	11.2574	−	34.6466i	0.401792	−	1.23659i
$786$		0			0
$787$	−39.8328	−	28.9402i	−1.41989	−	1.03161i	−0.991790	−	0.127875i	$-0.959184\pi$
$787$	−39.8328	−	28.9402i	−1.41989	−	1.03161i	−0.428096	−	0.903733i	$-0.640816\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−32.8885			−1.16938
$792$		0			0
$793$	0.673762			0.0239260
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.8541	+	15.8779i	0.774112	+	0.562425i	0.903206	−	0.429207i	$-0.141207\pi$
$797$	21.8541	+	15.8779i	0.774112	+	0.562425i	−0.129094	+	0.991632i	$0.541207\pi$
$798$		0			0
$799$	1.97214	−	6.06961i	0.0697692	−	0.214727i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.76393	−	1.62460i	0.132826	−	0.0573308i
$804$		0			0
$805$	−41.4336	+	30.1033i	−1.46034	+	1.06100i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.39919	+	1.01657i	0.0491928	+	0.0357407i	0.612110	−	0.790773i	$-0.290321\pi$
$809$	1.39919	+	1.01657i	0.0491928	+	0.0357407i	−0.562917	+	0.826513i	$0.690321\pi$
$810$		0			0
$811$	−8.28115	−	25.4868i	−0.290791	−	0.894961i	−0.984603	−	0.174806i	$-0.944070\pi$
$811$	−8.28115	−	25.4868i	−0.290791	−	0.894961i	0.693812	−	0.720156i	$-0.255930\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.29180			−0.185364
$816$		0			0
$817$	0.993422	+	3.05744i	0.0347554	+	0.106966i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.36475	−	16.5110i	0.187231	−	0.576237i	−0.812749	−	0.582614i	$-0.802030\pi$
$821$	5.36475	−	16.5110i	0.187231	−	0.576237i	0.999980	+	0.00637687i	$0.00202983\pi$
$822$		0			0
$823$	−0.663119	+	0.481784i	−0.0231149	+	0.0167939i	−0.599283	−	0.800537i	$-0.704547\pi$
$823$	−0.663119	+	0.481784i	−0.0231149	+	0.0167939i	0.576168	+	0.817331i	$0.304547\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.708204	+	0.514540i	−0.0246267	+	0.0178923i	−0.600030	−	0.799977i	$-0.704845\pi$
$827$	−0.708204	+	0.514540i	−0.0246267	+	0.0178923i	0.575404	+	0.817869i	$0.304845\pi$
$828$		0			0
$829$	−11.6631	+	35.8954i	−0.405077	+	1.24670i	0.515754	+	0.856737i	$0.327512\pi$
$829$	−11.6631	+	35.8954i	−0.405077	+	1.24670i	−0.920831	+	0.389962i	$0.872488\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15.6180	−	48.0674i	−0.541133	−	1.66544i
$834$		0			0
$835$	4.61803			0.159814
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.89261	+	15.0579i	0.168912	+	0.519857i	0.999303	−	0.0373237i	$-0.0118833\pi$
$839$	4.89261	+	15.0579i	0.168912	+	0.519857i	−0.830392	+	0.557180i	$0.811883\pi$
$840$		0			0
$841$	7.28115	+	5.29007i	0.251074	+	0.182416i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−22.8328	+	16.5890i	−0.785473	+	0.570679i
$846$		0			0
$847$	42.1246	+	19.9192i	1.44742	+	0.684431i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.7812	−	33.1810i	0.369573	−	1.13743i
$852$		0			0
$853$	−44.7877	−	32.5402i	−1.53350	−	1.11415i	−0.954251	−	0.299006i	$-0.903345\pi$
$853$	−44.7877	−	32.5402i	−1.53350	−	1.11415i	−0.579251	−	0.815149i	$-0.696655\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−48.1935			−1.64626			−0.823129	−	0.567854i	$-0.807774\pi$
$857$	−48.1935			−1.64626			−0.823129	+	0.567854i	$0.807774\pi$
$858$		0			0
$859$	31.1803			1.06386			0.531930	−	0.846788i	$-0.321467\pi$
$859$	31.1803			1.06386			0.531930	+	0.846788i	$0.321467\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.5623	+	17.8456i	0.836111	+	0.607470i	0.921281	−	0.388896i	$-0.127144\pi$
$863$	24.5623	+	17.8456i	0.836111	+	0.607470i	−0.0851709	+	0.996366i	$0.527144\pi$
$864$		0			0
$865$	−12.8435	+	39.5281i	−0.436691	+	1.34400i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	31.5967	+	7.09391i	1.07185	+	0.240644i
$870$		0			0
$871$	−9.78115	+	7.10642i	−0.331422	+	0.240792i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.1353	−	13.1760i	−0.613084	−	0.445431i
$876$		0			0
$877$	−10.7812	−	33.1810i	−0.364054	−	1.12044i	−0.950572	−	0.310506i	$-0.899502\pi$
$877$	−10.7812	−	33.1810i	−0.364054	−	1.12044i	0.586518	−	0.809936i	$-0.300498\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−20.4377			−0.688563			−0.344282	−	0.938866i	$-0.611878\pi$
$881$	−20.4377			−0.688563			−0.344282	+	0.938866i	$0.611878\pi$
$882$		0			0
$883$	−0.909830	−	2.80017i	−0.0306182	−	0.0942332i	0.934580	−	0.355754i	$-0.115776\pi$
$883$	−0.909830	−	2.80017i	−0.0306182	−	0.0942332i	−0.965198	+	0.261521i	$0.915776\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.4336	−	44.4221i	0.484634	−	1.49155i	−0.347877	−	0.937540i	$-0.613097\pi$
$887$	14.4336	−	44.4221i	0.484634	−	1.49155i	0.832511	−	0.554009i	$-0.186903\pi$
$888$		0			0
$889$	−7.85410	+	5.70634i	−0.263418	+	0.191384i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.80902	−	4.94704i	0.227855	−	0.165546i
$894$		0			0
$895$	−0.0491503	+	0.151269i	−0.00164291	+	0.00505637i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−11.9098	−	36.6547i	−0.397215	−	1.22250i
$900$		0			0
$901$	−62.6312			−2.08655
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.5344	+	32.4217i	0.350177	+	1.07773i
$906$		0			0
$907$	−32.2533	−	23.4334i	−1.07095	−	0.778093i	−0.0948696	−	0.995490i	$-0.530243\pi$
$907$	−32.2533	−	23.4334i	−1.07095	−	0.778093i	−0.976083	+	0.217397i	$0.930243\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−33.6074	+	24.4172i	−1.11346	+	0.808978i	−0.983205	−	0.182502i	$-0.941580\pi$
$911$	−33.6074	+	24.4172i	−1.11346	+	0.808978i	−0.130257	+	0.991480i	$0.541580\pi$
$912$		0			0
$913$	−2.01722	−	21.5563i	−0.0667603	−	0.713409i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.1353	+	46.5815i	−0.499810	+	1.53826i
$918$		0			0
$919$	−30.6074	−	22.2376i	−1.00964	−	0.733550i	−0.0455101	−	0.998964i	$-0.514491\pi$
$919$	−30.6074	−	22.2376i	−1.00964	−	0.733550i	−0.964135	+	0.265414i	$0.914491\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.38197			−0.210065
$924$		0			0
$925$	−25.9098			−0.851910
$926$		0			0
$927$		0			0
$928$		0			0
$929$	37.5517	+	27.2829i	1.23203	+	0.895122i	0.997041	−	0.0768757i	$-0.0244945\pi$
$929$	37.5517	+	27.2829i	1.23203	+	0.895122i	0.234989	+	0.971998i	$0.424494\pi$
$930$		0			0
$931$	20.5967	−	63.3903i	0.675031	−	2.07753i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	22.2877	−	37.6057i	0.728887	−	1.22984i
$936$		0			0
$937$	−19.6074	+	14.2456i	−0.640546	+	0.465384i	−0.860038	−	0.510231i	$-0.829560\pi$
$937$	−19.6074	+	14.2456i	−0.640546	+	0.465384i	0.219492	+	0.975614i	$0.429560\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.2082	+	10.3229i	0.463174	+	0.336516i	0.794775	−	0.606904i	$-0.207589\pi$
$941$	14.2082	+	10.3229i	0.463174	+	0.336516i	−0.331601	+	0.943420i	$0.607589\pi$
$942$		0			0
$943$	0.690983	+	2.12663i	0.0225015	+	0.0692525i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.7984			−0.708352			−0.354176	−	0.935179i	$-0.615239\pi$
$947$	−21.7984			−0.708352			−0.354176	+	0.935179i	$0.615239\pi$
$948$		0			0
$949$	0.673762	+	2.07363i	0.0218712	+	0.0673128i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−12.1246	+	37.3157i	−0.392755	+	1.20877i	0.537942	+	0.842982i	$0.319202\pi$
$953$	−12.1246	+	37.3157i	−0.392755	+	1.20877i	−0.930696	+	0.365793i	$0.880798\pi$
$954$		0			0
$955$	−22.2877	+	16.1930i	−0.721214	+	0.523993i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−71.9681	+	52.2879i	−2.32397	+	1.68846i
$960$		0			0
$961$	13.3713	−	41.1527i	0.431333	−	1.32751i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.287731	+	0.885544i	0.00926238	+	0.0285067i
$966$		0			0
$967$	48.2705			1.55227			0.776137	−	0.630564i	$-0.217176\pi$
$967$	48.2705			1.55227			0.776137	+	0.630564i	$0.217176\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.0902	+	40.2874i	0.420084	+	1.29288i	0.907624	+	0.419784i	$0.137894\pi$
$971$	13.0902	+	40.2874i	0.420084	+	1.29288i	−0.487541	+	0.873100i	$0.662106\pi$
$972$		0			0
$973$	71.2771	+	51.7858i	2.28504	+	1.66018i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.33688	−	1.69784i	0.0747634	−	0.0543188i	−0.549776	−	0.835312i	$-0.685287\pi$
$977$	2.33688	−	1.69784i	0.0747634	−	0.0543188i	0.624539	+	0.780993i	$0.285287\pi$
$978$		0			0
$979$	2.19098	+	2.48990i	0.0700241	+	0.0795775i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.20163	+	16.0090i	−0.165906	+	0.510606i	−0.999102	−	0.0423716i	$-0.986509\pi$
$983$	−5.20163	+	16.0090i	−0.165906	+	0.510606i	0.833196	+	0.552978i	$0.186509\pi$
$984$		0			0
$985$	39.4615	+	28.6705i	1.25735	+	0.913517i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.23607			−0.0711028
$990$		0			0
$991$	9.72949			0.309067			0.154534	−	0.987988i	$-0.450612\pi$
$991$	9.72949			0.309067			0.154534	+	0.987988i	$0.450612\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	37.9058	+	27.5402i	1.20169	+	0.873081i
$996$		0			0
$997$	−1.31966	+	4.06150i	−0.0417941	+	0.128629i	−0.969776	−	0.243995i	$-0.921542\pi$
$997$	−1.31966	+	4.06150i	−0.0417941	+	0.128629i	0.927982	+	0.372624i	$0.121542\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.j.c.289.1		4
3.2	odd	2		132.2.i.b.25.1	✓	4
11.2	odd	10		4356.2.a.s.1.1		2
11.4	even	5	inner	396.2.j.c.37.1		4
11.9	even	5		4356.2.a.v.1.1		2
12.11	even	2		528.2.y.a.289.1		4
33.2	even	10		1452.2.a.i.1.2		2
33.5	odd	10		1452.2.i.o.493.1		4
33.8	even	10		1452.2.i.p.1237.1		4
33.14	odd	10		1452.2.i.o.1237.1		4
33.17	even	10		1452.2.i.p.493.1		4
33.20	odd	10		1452.2.a.j.1.2		2
33.26	odd	10		132.2.i.b.37.1	yes	4
33.29	even	10		1452.2.i.j.565.1		4
33.32	even	2		1452.2.i.j.1213.1		4
132.35	odd	10		5808.2.a.cf.1.2		2
132.59	even	10		528.2.y.a.433.1		4
132.119	even	10		5808.2.a.cc.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.i.b.25.1	✓	4	3.2	odd	2
132.2.i.b.37.1	yes	4	33.26	odd	10
396.2.j.c.37.1		4	11.4	even	5	inner
396.2.j.c.289.1		4	1.1	even	1	trivial
528.2.y.a.289.1		4	12.11	even	2
528.2.y.a.433.1		4	132.59	even	10
1452.2.a.i.1.2		2	33.2	even	10
1452.2.a.j.1.2		2	33.20	odd	10
1452.2.i.j.565.1		4	33.29	even	10
1452.2.i.j.1213.1		4	33.32	even	2
1452.2.i.o.493.1		4	33.5	odd	10
1452.2.i.o.1237.1		4	33.14	odd	10
1452.2.i.p.493.1		4	33.17	even	10
1452.2.i.p.1237.1		4	33.8	even	10
4356.2.a.s.1.1		2	11.2	odd	10
4356.2.a.v.1.1		2	11.9	even	5
5808.2.a.cc.1.2		2	132.119	even	10
5808.2.a.cf.1.2		2	132.35	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.30902 + 1.67760i) q^{5} +(1.30902 - 4.02874i) q^{7} +(-2.19098 - 2.48990i) q^{11} +(1.42705 - 1.03681i) q^{13} +(3.73607 + 2.71441i) q^{17} +(1.88197 + 5.79210i) q^{19} -4.23607 q^{23} +(0.972136 + 2.99193i) q^{25} +(1.38197 - 4.25325i) q^{29} +(6.97214 - 5.06555i) q^{31} +(9.78115 - 7.10642i) q^{35} +(-2.54508 + 7.83297i) q^{37} +(-0.163119 - 0.502029i) q^{41} +0.527864 q^{43} +(-0.427051 - 1.31433i) q^{47} +(-8.85410 - 6.43288i) q^{49} +(-10.9721 + 7.97172i) q^{53} +(-0.881966 - 9.42481i) q^{55} +(-2.73607 + 8.42075i) q^{59} +(0.309017 + 0.224514i) q^{61} +5.03444 q^{65} -6.85410 q^{67} +(-2.92705 - 2.12663i) q^{71} +(-0.381966 + 1.17557i) q^{73} +(-12.8992 + 5.56758i) q^{77} +(-7.89919 + 5.73910i) q^{79} +(5.28115 + 3.83698i) q^{83} +(4.07295 + 12.5352i) q^{85} -1.00000 q^{89} +(-2.30902 - 7.10642i) q^{91} +(-5.37132 + 16.5312i) q^{95} +(-4.92705 + 3.57971i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 7 q^{5} + 3 q^{7} - 11 q^{11} - q^{13} + 6 q^{17} + 12 q^{19} - 8 q^{23} - 14 q^{25} + 10 q^{29} + 10 q^{31} + 19 q^{35} + q^{37} + 15 q^{41} + 20 q^{43} + 5 q^{47} - 22 q^{49} - 26 q^{53} - 8 q^{55}+ \cdots - 13 q^{97}+O(q^{100}) \) 4 * q + 7 * q^5 + 3 * q^7 - 11 * q^11 - q^13 + 6 * q^17 + 12 * q^19 - 8 * q^23 - 14 * q^25 + 10 * q^29 + 10 * q^31 + 19 * q^35 + q^37 + 15 * q^41 + 20 * q^43 + 5 * q^47 - 22 * q^49 - 26 * q^53 - 8 * q^55 - 2 * q^59 - q^61 - 38 * q^65 - 14 * q^67 - 5 * q^71 - 6 * q^73 - 27 * q^77 - 7 * q^79 + q^83 + 23 * q^85 - 4 * q^89 - 7 * q^91 + 21 * q^95 - 13 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more