LMFDB - Embedded newform 396.2.j.a.181.1

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)

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);

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")

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,-3,0,-7] 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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	396.181
Dual form			396.2.j.a.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 + 0.587785i) q^{5} +(-2.30902 + 1.67760i) q^{7} +(3.23607 + 0.726543i) q^{11} +(1.42705 + 4.39201i) q^{13} +(-1.42705 + 4.39201i) q^{17} +(2.30902 + 1.67760i) q^{19} -6.47214 q^{23} +(3.73607 + 2.71441i) q^{25} +(5.16312 - 3.75123i) q^{29} +(-1.80902 - 5.56758i) q^{31} +(-0.545085 - 1.67760i) q^{35} +(-3.92705 + 2.85317i) q^{37} +(5.16312 + 3.75123i) q^{41} +(2.92705 + 2.12663i) q^{47} +(0.354102 - 1.08981i) q^{49} +(-2.19098 - 6.74315i) q^{53} +(-1.04508 + 1.76336i) q^{55} +(-8.16312 + 5.93085i) q^{59} +(1.42705 - 4.39201i) q^{61} -2.85410 q^{65} -4.94427 q^{67} +(2.66312 - 8.19624i) q^{71} +(9.78115 - 7.10642i) q^{73} +(-8.69098 + 3.75123i) q^{77} +(-4.28115 - 13.1760i) q^{79} +(4.95492 - 15.2497i) q^{83} +(-2.30902 - 1.67760i) q^{85} +8.47214 q^{89} +(-10.6631 - 7.74721i) q^{91} +(-1.42705 + 1.03681i) q^{95} +(1.71885 + 5.29007i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{5} - 7 q^{7} + 4 q^{11} - q^{13} + q^{17} + 7 q^{19} - 8 q^{23} + 6 q^{25} + 5 q^{29} - 5 q^{31} + 9 q^{35} - 9 q^{37} + 5 q^{41} + 5 q^{47} - 12 q^{49} - 11 q^{53} + 7 q^{55} - 17 q^{59} - q^{61}+ \cdots + 27 q^{97}+O(q^{100}) $ 4 * q - 3 * q^5 - 7 * q^7 + 4 * q^11 - q^13 + q^17 + 7 * q^19 - 8 * q^23 + 6 * q^25 + 5 * q^29 - 5 * q^31 + 9 * q^35 - 9 * q^37 + 5 * q^41 + 5 * q^47 - 12 * q^49 - 11 * q^53 + 7 * q^55 - 17 * q^59 - q^61 + 2 * q^65 + 16 * q^67 - 5 * q^71 + 19 * q^73 - 37 * q^77 + 3 * q^79 + 31 * q^83 - 7 * q^85 + 16 * q^89 - 27 * q^91 + q^95 + 27 * q^97

Character values

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

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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
$5$	−0.190983	+	0.587785i	−0.0854102	+	0.262866i	−0.984636	−	0.174619i	$-0.944131\pi$
$5$	−0.190983	+	0.587785i	−0.0854102	+	0.262866i	0.899226	+	0.437485i	$0.144131\pi$
$6$		0			0
$7$	−2.30902	+	1.67760i	−0.872726	+	0.634073i	−0.931317	−	0.364209i	$-0.881339\pi$
$7$	−2.30902	+	1.67760i	−0.872726	+	0.634073i	0.0585908	+	0.998282i	$0.481339\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$12$		0			0
$13$	1.42705	+	4.39201i	0.395793	+	1.21812i	0.928342	+	0.371726i	$0.121234\pi$
$13$	1.42705	+	4.39201i	0.395793	+	1.21812i	−0.532550	+	0.846399i	$0.678766\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.42705	+	4.39201i	−0.346111	+	1.06522i	0.614876	+	0.788624i	$0.289206\pi$
$17$	−1.42705	+	4.39201i	−0.346111	+	1.06522i	−0.960987	+	0.276595i	$0.910794\pi$
$18$		0			0
$19$	2.30902	+	1.67760i	0.529725	+	0.384868i	0.820255	−	0.571998i	$-0.193832\pi$
$19$	2.30902	+	1.67760i	0.529725	+	0.384868i	−0.290530	+	0.956866i	$0.593832\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.47214			−1.34953			−0.674767	−	0.738031i	$-0.735756\pi$
$23$	−6.47214			−1.34953			−0.674767	+	0.738031i	$0.735756\pi$
$24$		0			0
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.16312	−	3.75123i	0.958767	−	0.696585i	0.00590304	−	0.999983i	$-0.498121\pi$
$29$	5.16312	−	3.75123i	0.958767	−	0.696585i	0.952864	+	0.303397i	$0.0981210\pi$
$30$		0			0
$31$	−1.80902	−	5.56758i	−0.324909	−	0.999967i	−0.971482	−	0.237115i	$-0.923798\pi$
$31$	−1.80902	−	5.56758i	−0.324909	−	0.999967i	0.646573	−	0.762852i	$-0.276202\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.545085	−	1.67760i	−0.0921362	−	0.283566i
$36$		0			0
$37$	−3.92705	+	2.85317i	−0.645603	+	0.469058i	−0.861771	−	0.507298i	$-0.830644\pi$
$37$	−3.92705	+	2.85317i	−0.645603	+	0.469058i	0.216167	+	0.976356i	$0.430644\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.16312	+	3.75123i	0.806344	+	0.585843i	0.912768	−	0.408478i	$-0.133940\pi$
$41$	5.16312	+	3.75123i	0.806344	+	0.585843i	−0.106425	+	0.994321i	$0.533940\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.92705	+	2.12663i	0.426954	+	0.310200i	0.780430	−	0.625243i	$-0.215000\pi$
$47$	2.92705	+	2.12663i	0.426954	+	0.310200i	−0.353476	+	0.935444i	$0.615000\pi$
$48$		0			0
$49$	0.354102	−	1.08981i	0.0505860	−	0.155688i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.19098	−	6.74315i	−0.300955	−	0.926243i	−0.981156	−	0.193218i	$-0.938108\pi$
$53$	−2.19098	−	6.74315i	−0.300955	−	0.926243i	0.680201	−	0.733025i	$-0.261892\pi$
$54$		0			0
$55$	−1.04508	+	1.76336i	−0.140919	+	0.237771i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.16312	+	5.93085i	−1.06275	+	0.772131i	−0.974595	−	0.223976i	$-0.928096\pi$
$59$	−8.16312	+	5.93085i	−1.06275	+	0.772131i	−0.0881528	+	0.996107i	$0.528096\pi$
$60$		0			0
$61$	1.42705	−	4.39201i	0.182715	−	0.562339i	−0.817186	−	0.576374i	$-0.804467\pi$
$61$	1.42705	−	4.39201i	0.182715	−	0.562339i	0.999902	+	0.0140341i	$0.00446734\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.85410			−0.354008
$66$		0			0
$67$	−4.94427			−0.604039			−0.302019	−	0.953302i	$-0.597661\pi$
$67$	−4.94427			−0.604039			−0.302019	+	0.953302i	$0.597661\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.66312	−	8.19624i	0.316054	−	0.972714i	−0.659264	−	0.751911i	$-0.729132\pi$
$71$	2.66312	−	8.19624i	0.316054	−	0.972714i	0.975318	−	0.220803i	$-0.0708678\pi$
$72$		0			0
$73$	9.78115	−	7.10642i	1.14480	−	0.831744i	0.157017	−	0.987596i	$-0.449812\pi$
$73$	9.78115	−	7.10642i	1.14480	−	0.831744i	0.987780	+	0.155852i	$0.0498123\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.69098	+	3.75123i	−0.990429	+	0.427492i
$78$		0			0
$79$	−4.28115	−	13.1760i	−0.481667	−	1.48242i	−0.836750	−	0.547585i	$-0.815547\pi$
$79$	−4.28115	−	13.1760i	−0.481667	−	1.48242i	0.355083	−	0.934835i	$-0.384453\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.95492	−	15.2497i	0.543873	−	1.67387i	−0.179783	−	0.983706i	$-0.557540\pi$
$83$	4.95492	−	15.2497i	0.543873	−	1.67387i	0.723655	−	0.690161i	$-0.242460\pi$
$84$		0			0
$85$	−2.30902	−	1.67760i	−0.250448	−	0.181961i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.47214			0.898045			0.449022	−	0.893521i	$-0.351772\pi$
$89$	8.47214			0.898045			0.449022	+	0.893521i	$0.351772\pi$
$90$		0			0
$91$	−10.6631	−	7.74721i	−1.11780	−	0.812128i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.42705	+	1.03681i	−0.146412	+	0.106375i
$96$		0			0
$97$	1.71885	+	5.29007i	0.174522	+	0.537125i	0.999611	−	0.0278780i	$-0.00887501\pi$
$97$	1.71885	+	5.29007i	0.174522	+	0.537125i	−0.825089	+	0.565003i	$0.808875\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.10081	+	6.46564i	0.209039	+	0.643355i	0.999523	+	0.0308731i	$0.00982877\pi$
$101$	2.10081	+	6.46564i	0.209039	+	0.643355i	−0.790485	+	0.612482i	$0.790171\pi$
$102$		0			0
$103$	0.927051	−	0.673542i	0.0913450	−	0.0663661i	−0.541175	−	0.840910i	$-0.682020\pi$
$103$	0.927051	−	0.673542i	0.0913450	−	0.0663661i	0.632520	+	0.774544i	$0.282020\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.92705	+	5.03280i	0.669663	+	0.486539i	0.869912	−	0.493206i	$-0.164175\pi$
$107$	6.92705	+	5.03280i	0.669663	+	0.486539i	−0.200249	+	0.979745i	$0.564175\pi$
$108$		0			0
$109$	−3.52786			−0.337908			−0.168954	−	0.985624i	$-0.554039\pi$
$109$	−3.52786			−0.337908			−0.168954	+	0.985624i	$0.554039\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.07295	−	1.50609i	−0.195007	−	0.141681i	0.485997	−	0.873960i	$-0.338456\pi$
$113$	−2.07295	−	1.50609i	−0.195007	−	0.141681i	−0.681004	+	0.732280i	$0.738456\pi$
$114$		0			0
$115$	1.23607	−	3.80423i	0.115264	−	0.354746i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.07295	−	12.5352i	−0.373367	−	1.14910i
$120$		0			0
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.80902	+	3.49396i	−0.430132	+	0.312509i
$126$		0			0
$127$	−1.42705	+	4.39201i	−0.126630	+	0.389728i	−0.994195	−	0.107597i	$-0.965684\pi$
$127$	−1.42705	+	4.39201i	−0.126630	+	0.389728i	0.867564	+	0.497325i	$0.165684\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−18.4721			−1.61392			−0.806959	−	0.590607i	$-0.798888\pi$
$131$	−18.4721			−1.61392			−0.806959	+	0.590607i	$0.798888\pi$
$132$		0			0
$133$	−8.14590			−0.706339
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.33688	−	10.2699i	0.285089	−	0.877414i	−0.701283	−	0.712883i	$-0.747389\pi$
$137$	3.33688	−	10.2699i	0.285089	−	0.877414i	0.986372	−	0.164531i	$-0.0526110\pi$
$138$		0			0
$139$	6.92705	−	5.03280i	0.587545	−	0.426876i	−0.253891	−	0.967233i	$-0.581711\pi$
$139$	6.92705	−	5.03280i	0.587545	−	0.426876i	0.841436	+	0.540356i	$0.181711\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.42705	+	15.2497i	0.119336	+	1.27524i
$144$		0			0
$145$	1.21885	+	3.75123i	0.101220	+	0.311522i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.42705	+	4.39201i	−0.116909	+	0.359808i	−0.992340	−	0.123534i	$-0.960577\pi$
$149$	−1.42705	+	4.39201i	−0.116909	+	0.359808i	0.875432	+	0.483342i	$0.160577\pi$
$150$		0			0
$151$	11.5451	+	8.38800i	0.939526	+	0.682605i	0.948306	−	0.317356i	$-0.102795\pi$
$151$	11.5451	+	8.38800i	0.939526	+	0.682605i	−0.00878076	+	0.999961i	$0.502795\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.61803			0.290607
$156$		0			0
$157$	2.07295	+	1.50609i	0.165439	+	0.120199i	0.667424	−	0.744678i	$-0.267397\pi$
$157$	2.07295	+	1.50609i	0.165439	+	0.120199i	−0.501985	+	0.864876i	$0.667397\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	14.9443	−	10.8576i	1.17777	−	0.855703i
$162$		0			0
$163$	−1.33688	−	4.11450i	−0.104713	−	0.322272i	0.884950	−	0.465686i	$-0.154192\pi$
$163$	−1.33688	−	4.11450i	−0.104713	−	0.322272i	−0.989663	+	0.143413i	$0.954192\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.10081	+	6.46564i	0.162566	+	0.500326i	0.998849	−	0.0479722i	$-0.0152759\pi$
$167$	2.10081	+	6.46564i	0.162566	+	0.500326i	−0.836283	+	0.548298i	$0.815276\pi$
$168$		0			0
$169$	−6.73607	+	4.89404i	−0.518159	+	0.376465i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	14.3992	+	10.4616i	1.09475	+	0.795382i	0.980195	−	0.198035i	$-0.0634558\pi$
$173$	14.3992	+	10.4616i	1.09475	+	0.795382i	0.114555	+	0.993417i	$0.463456\pi$
$174$		0			0
$175$	−13.1803			−0.996340
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.309017	−	0.224514i	−0.0230970	−	0.0167810i	0.576177	−	0.817325i	$-0.304544\pi$
$179$	−0.309017	−	0.224514i	−0.0230970	−	0.0167810i	−0.599274	+	0.800544i	$0.704544\pi$
$180$		0			0
$181$	0.190983	−	0.587785i	0.0141957	−	0.0436897i	−0.943708	−	0.330780i	$-0.892688\pi$
$181$	0.190983	−	0.587785i	0.0141957	−	0.0436897i	0.957903	+	0.287091i	$0.0926881\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.927051	−	2.85317i	−0.0681581	−	0.209769i
$186$		0			0
$187$	−7.80902	+	13.1760i	−0.571052	+	0.963527i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.45492	+	1.78360i	−0.177631	+	0.129057i	−0.673048	−	0.739599i	$-0.735015\pi$
$191$	−2.45492	+	1.78360i	−0.177631	+	0.129057i	0.495417	+	0.868655i	$0.335015\pi$
$192$		0			0
$193$	−0.753289	+	2.31838i	−0.0542229	+	0.166881i	−0.974501	−	0.224385i	$-0.927963\pi$
$193$	−0.753289	+	2.31838i	−0.0542229	+	0.166881i	0.920278	+	0.391266i	$0.127963\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.9443			−1.06474			−0.532368	−	0.846513i	$-0.678698\pi$
$197$	−14.9443			−1.06474			−0.532368	+	0.846513i	$0.678698\pi$
$198$		0			0
$199$	16.9443			1.20115			0.600574	−	0.799569i	$-0.294939\pi$
$199$	16.9443			1.20115			0.600574	+	0.799569i	$0.294939\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.62868	+	17.3233i	−0.395056	+	1.21586i
$204$		0			0
$205$	−3.19098	+	2.31838i	−0.222868	+	0.161923i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.25329	+	7.10642i	0.432549	+	0.491562i
$210$		0			0
$211$	7.13525	+	21.9601i	0.491211	+	1.51179i	0.822779	+	0.568361i	$0.192422\pi$
$211$	7.13525	+	21.9601i	0.491211	+	1.51179i	−0.331568	+	0.943431i	$0.607578\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	13.5172	+	9.82084i	0.917609	+	0.666682i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−21.3262			−1.43456
$222$		0			0
$223$	15.2533	+	11.0822i	1.02144	+	0.742117i	0.966577	−	0.256378i	$-0.0825290\pi$
$223$	15.2533	+	11.0822i	1.02144	+	0.742117i	0.0548591	+	0.998494i	$0.482529\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.2533	−	12.5352i	1.14514	−	0.831994i	0.157314	−	0.987549i	$-0.449717\pi$
$227$	17.2533	−	12.5352i	1.14514	−	0.831994i	0.987827	+	0.155555i	$0.0497166\pi$
$228$		0			0
$229$	−5.33688	−	16.4252i	−0.352671	−	1.08541i	−0.957348	−	0.288939i	$-0.906698\pi$
$229$	−5.33688	−	16.4252i	−0.352671	−	1.08541i	0.604677	−	0.796471i	$-0.293302\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.42705	−	4.39201i	−0.0934892	−	0.287730i	0.893368	−	0.449326i	$-0.148336\pi$
$233$	−1.42705	−	4.39201i	−0.0934892	−	0.287730i	−0.986857	+	0.161596i	$0.948336\pi$
$234$		0			0
$235$	−1.80902	+	1.31433i	−0.118007	+	0.0857373i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.92705	+	5.03280i	0.448074	+	0.325545i	0.788835	−	0.614605i	$-0.210685\pi$
$239$	6.92705	+	5.03280i	0.448074	+	0.325545i	−0.340761	+	0.940150i	$0.610685\pi$
$240$		0			0
$241$	3.52786			0.227250			0.113625	−	0.993524i	$-0.463754\pi$
$241$	3.52786			0.227250			0.113625	+	0.993524i	$0.463754\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.572949	+	0.416272i	0.0366044	+	0.0265946i
$246$		0			0
$247$	−4.07295	+	12.5352i	−0.259156	+	0.797599i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.371323	−	1.14281i	−0.0234377	−	0.0721338i	0.938654	−	0.344862i	$-0.112074\pi$
$251$	−0.371323	−	1.14281i	−0.0234377	−	0.0721338i	−0.962091	+	0.272728i	$0.912074\pi$
$252$		0			0
$253$	−20.9443	−	4.70228i	−1.31676	−	0.295630i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.0172	+	9.45756i	−0.811992	+	0.589947i	−0.914407	−	0.404795i	$-0.867343\pi$
$257$	−13.0172	+	9.45756i	−0.811992	+	0.589947i	0.102416	+	0.994742i	$0.467343\pi$
$258$		0			0
$259$	4.28115	−	13.1760i	0.266018	−	0.818719i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	29.8885			1.84301			0.921503	−	0.388371i	$-0.126962\pi$
$263$	29.8885			1.84301			0.921503	+	0.388371i	$0.126962\pi$
$264$		0			0
$265$	4.38197			0.269182
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.98936	−	12.2780i	0.243235	−	0.748602i	−0.752686	−	0.658379i	$-0.771242\pi$
$269$	3.98936	−	12.2780i	0.243235	−	0.748602i	0.995922	−	0.0902222i	$-0.0287577\pi$
$270$		0			0
$271$	−11.5451	+	8.38800i	−0.701314	+	0.509534i	−0.880360	−	0.474306i	$-0.842699\pi$
$271$	−11.5451	+	8.38800i	−0.701314	+	0.509534i	0.179046	+	0.983841i	$0.442699\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.1180	+	11.4984i	0.610140	+	0.693382i
$276$		0			0
$277$	−0.753289	−	2.31838i	−0.0452607	−	0.139298i	0.925872	−	0.377836i	$-0.123332\pi$
$277$	−0.753289	−	2.31838i	−0.0452607	−	0.139298i	−0.971133	+	0.238538i	$0.923332\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.60739	+	11.1024i	−0.215199	+	0.662314i	0.783941	+	0.620836i	$0.213207\pi$
$281$	−3.60739	+	11.1024i	−0.215199	+	0.662314i	−0.999139	+	0.0414782i	$0.986793\pi$
$282$		0			0
$283$	−6.92705	−	5.03280i	−0.411770	−	0.299169i	0.362548	−	0.931965i	$-0.381907\pi$
$283$	−6.92705	−	5.03280i	−0.411770	−	0.299169i	−0.774318	+	0.632796i	$0.781907\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.2148			−1.07518
$288$		0			0
$289$	−3.50000	−	2.54290i	−0.205882	−	0.149582i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.16312	−	3.75123i	0.301633	−	0.219149i	−0.426665	−	0.904410i	$-0.640312\pi$
$293$	5.16312	−	3.75123i	0.301633	−	0.219149i	0.728298	+	0.685261i	$0.240312\pi$
$294$		0			0
$295$	−1.92705	−	5.93085i	−0.112197	−	0.345308i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.23607	−	28.4257i	−0.534136	−	1.64390i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.30902	+	1.67760i	0.132214	+	0.0960590i
$306$		0			0
$307$	18.4721			1.05426			0.527130	−	0.849785i	$-0.323268\pi$
$307$	18.4721			1.05426			0.527130	+	0.849785i	$0.323268\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.30902	−	4.58377i	−0.357752	−	0.259922i	0.394362	−	0.918955i	$-0.370966\pi$
$311$	−6.30902	−	4.58377i	−0.357752	−	0.259922i	−0.752114	+	0.659033i	$0.770966\pi$
$312$		0			0
$313$	9.42705	−	29.0135i	0.532848	−	1.63994i	−0.215404	−	0.976525i	$-0.569107\pi$
$313$	9.42705	−	29.0135i	0.532848	−	1.63994i	0.748253	−	0.663414i	$-0.230893\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.71885	−	5.29007i	−0.0965401	−	0.297120i	0.891112	−	0.453784i	$-0.149926\pi$
$317$	−1.71885	−	5.29007i	−0.0965401	−	0.297120i	−0.987652	+	0.156664i	$0.949926\pi$
$318$		0			0
$319$	19.4336	−	8.38800i	1.08807	−	0.469638i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.6631	+	7.74721i	−0.593312	+	0.431066i
$324$		0			0
$325$	−6.59017	+	20.2825i	−0.365557	+	1.12507i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.3262			−0.569304
$330$		0			0
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.944272	−	2.90617i	0.0515911	−	0.158781i
$336$		0			0
$337$	4.07295	−	2.95917i	0.221868	−	0.161196i	−0.471299	−	0.881973i	$-0.656215\pi$
$337$	4.07295	−	2.95917i	0.221868	−	0.161196i	0.693167	+	0.720777i	$0.256215\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.80902	−	19.3314i	−0.0979638	−	1.04685i
$342$		0			0
$343$	−5.16312	−	15.8904i	−0.278782	−	0.858003i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.10081	+	6.46564i	−0.112778	+	0.347094i	−0.991477	−	0.130282i	$-0.958412\pi$
$347$	−2.10081	+	6.46564i	−0.112778	+	0.347094i	0.878699	+	0.477375i	$0.158412\pi$
$348$		0			0
$349$	0.545085	+	0.396027i	0.0291777	+	0.0211989i	0.602279	−	0.798286i	$-0.294260\pi$
$349$	0.545085	+	0.396027i	0.0291777	+	0.0211989i	−0.573101	+	0.819485i	$0.694260\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.94427			−0.156708			−0.0783539	−	0.996926i	$-0.524966\pi$
$353$	−2.94427			−0.156708			−0.0783539	+	0.996926i	$0.524966\pi$
$354$		0			0
$355$	4.30902	+	3.13068i	0.228699	+	0.166159i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.92705	+	5.03280i	−0.365596	+	0.265621i	−0.755382	−	0.655284i	$-0.772549\pi$
$359$	−6.92705	+	5.03280i	−0.365596	+	0.265621i	0.389787	+	0.920905i	$0.372549\pi$
$360$		0			0
$361$	−3.35410	−	10.3229i	−0.176532	−	0.543309i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.30902	+	7.10642i	0.120859	+	0.371967i
$366$		0			0
$367$	−21.7254	+	15.7844i	−1.13406	+	0.823941i	−0.986280	−	0.165079i	$-0.947212\pi$
$367$	−21.7254	+	15.7844i	−1.13406	+	0.823941i	−0.147778	+	0.989021i	$0.547212\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	16.3713	+	11.8945i	0.849957	+	0.617530i
$372$		0			0
$373$	−33.4164			−1.73024			−0.865118	−	0.501568i	$-0.832757\pi$
$373$	−33.4164			−1.73024			−0.865118	+	0.501568i	$0.832757\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	23.8435	+	17.3233i	1.22800	+	0.892195i
$378$		0			0
$379$	3.04508	−	9.37181i	0.156416	−	0.481397i	−0.841886	−	0.539655i	$-0.818555\pi$
$379$	3.04508	−	9.37181i	0.156416	−	0.481397i	0.998302	+	0.0582579i	$0.0185546\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.60739	−	29.5685i	−0.490915	−	1.51088i	−0.823228	−	0.567711i	$-0.807829\pi$
$383$	−9.60739	−	29.5685i	−0.490915	−	1.51088i	0.332313	−	0.943169i	$-0.392171\pi$
$384$		0			0
$385$	−0.545085	−	5.82485i	−0.0277801	−	0.296862i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.78115	+	1.29408i	−0.0903080	+	0.0656126i	−0.632023	−	0.774950i	$-0.717775\pi$
$389$	−1.78115	+	1.29408i	−0.0903080	+	0.0656126i	0.541715	+	0.840562i	$0.317775\pi$
$390$		0			0
$391$	9.23607	−	28.4257i	0.467088	−	1.43755i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.56231			0.430816
$396$		0			0
$397$	−20.8328			−1.04557			−0.522785	−	0.852465i	$-0.675107\pi$
$397$	−20.8328			−1.04557			−0.522785	+	0.852465i	$0.675107\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.0451	−	33.9933i	0.551565	−	1.69754i	−0.153281	−	0.988183i	$-0.548984\pi$
$401$	11.0451	−	33.9933i	0.551565	−	1.69754i	0.704846	−	0.709361i	$-0.251016\pi$
$402$		0			0
$403$	21.8713	−	15.8904i	1.08949	−	0.791560i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−14.7812	+	6.37988i	−0.732675	+	0.316239i
$408$		0			0
$409$	−4.28115	−	13.1760i	−0.211689	−	0.651513i	−0.999372	−	0.0354318i	$-0.988719\pi$
$409$	−4.28115	−	13.1760i	−0.211689	−	0.651513i	0.787683	−	0.616081i	$-0.211281\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.89919	−	27.3889i	0.437900	−	1.34772i
$414$		0			0
$415$	8.01722	+	5.82485i	0.393550	+	0.285931i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	31.4164			1.53479			0.767396	−	0.641173i	$-0.221552\pi$
$419$	31.4164			1.53479			0.767396	+	0.641173i	$0.221552\pi$
$420$		0			0
$421$	−19.6353	−	14.2658i	−0.956964	−	0.695275i	−0.00452016	−	0.999990i	$-0.501439\pi$
$421$	−19.6353	−	14.2658i	−0.956964	−	0.695275i	−0.952444	+	0.304715i	$0.901439\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−17.2533	+	12.5352i	−0.836907	+	0.608049i
$426$		0			0
$427$	4.07295	+	12.5352i	0.197104	+	0.606623i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.98936	+	30.7441i	0.481170	+	1.48089i	0.837452	+	0.546511i	$0.184044\pi$
$431$	9.98936	+	30.7441i	0.481170	+	1.48089i	−0.356281	+	0.934379i	$0.615956\pi$
$432$		0			0
$433$	29.4894	−	21.4253i	1.41717	−	1.02963i	0.424937	−	0.905223i	$-0.360296\pi$
$433$	29.4894	−	21.4253i	1.41717	−	1.02963i	0.992231	−	0.124410i	$-0.0397038\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−14.9443	−	10.8576i	−0.714881	−	0.519392i
$438$		0			0
$439$	11.4164			0.544875			0.272438	−	0.962173i	$-0.412170\pi$
$439$	11.4164			0.544875			0.272438	+	0.962173i	$0.412170\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−24.4894	−	17.7926i	−1.16352	−	0.845350i	−0.173305	−	0.984868i	$-0.555445\pi$
$443$	−24.4894	−	17.7926i	−1.16352	−	0.845350i	−0.990220	+	0.139518i	$0.955445\pi$
$444$		0			0
$445$	−1.61803	+	4.97980i	−0.0767022	+	0.236065i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.71885	−	5.29007i	−0.0811174	−	0.249654i	0.902270	−	0.431171i	$-0.141899\pi$
$449$	−1.71885	−	5.29007i	−0.0811174	−	0.249654i	−0.983388	+	0.181517i	$0.941899\pi$
$450$		0			0
$451$	13.9828	+	15.8904i	0.658423	+	0.748252i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.59017	−	4.78804i	0.308952	−	0.224467i
$456$		0			0
$457$	−4.28115	+	13.1760i	−0.200264	+	0.616349i	0.799611	+	0.600519i	$0.205039\pi$
$457$	−4.28115	+	13.1760i	−0.200264	+	0.616349i	−0.999875	+	0.0158303i	$0.994961\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−37.7771			−1.75945			−0.879727	−	0.475479i	$-0.842275\pi$
$461$	−37.7771			−1.75945			−0.879727	+	0.475479i	$0.842275\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.75329	+	26.9399i	−0.405054	+	1.24663i	0.515796	+	0.856711i	$0.327496\pi$
$467$	−8.75329	+	26.9399i	−0.405054	+	1.24663i	−0.920850	+	0.389916i	$0.872504\pi$
$468$		0			0
$469$	11.4164	−	8.29451i	0.527161	−	0.383005i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	4.07295	+	12.5352i	0.186880	+	0.575157i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.60739	−	11.1024i	0.164826	−	0.507282i	−0.834198	−	0.551466i	$-0.814069\pi$
$479$	3.60739	−	11.1024i	0.164826	−	0.507282i	0.999023	+	0.0441838i	$0.0140687\pi$
$480$		0			0
$481$	−18.1353	−	13.1760i	−0.826896	−	0.600775i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.43769			−0.156098
$486$		0			0
$487$	−8.92705	−	6.48588i	−0.404523	−	0.293903i	0.366858	−	0.930277i	$-0.380434\pi$
$487$	−8.92705	−	6.48588i	−0.404523	−	0.293903i	−0.771381	+	0.636374i	$0.780434\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.92705	+	5.03280i	−0.312613	+	0.227127i	−0.733017	−	0.680210i	$-0.761888\pi$
$491$	−6.92705	+	5.03280i	−0.312613	+	0.227127i	0.420404	+	0.907337i	$0.361888\pi$
$492$		0			0
$493$	9.10739	+	28.0297i	0.410176	+	1.26239i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.60081	+	23.3929i	0.340943	+	1.04931i
$498$		0			0
$499$	−8.30902	+	6.03685i	−0.371963	+	0.270247i	−0.758024	−	0.652226i	$-0.773835\pi$
$499$	−8.30902	+	6.03685i	−0.371963	+	0.270247i	0.386062	+	0.922473i	$0.373835\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.21885	+	0.885544i	0.0543457	+	0.0394845i	0.614626	−	0.788818i	$-0.289307\pi$
$503$	1.21885	+	0.885544i	0.0543457	+	0.0394845i	−0.560281	+	0.828303i	$0.689307\pi$
$504$		0			0
$505$	−4.20163			−0.186970
$506$		0			0
$507$		0			0
$508$		0			0
$509$	25.6353	+	18.6251i	1.13626	+	0.825543i	0.986594	−	0.163193i	$-0.0521793\pi$
$509$	25.6353	+	18.6251i	1.13626	+	0.825543i	0.149669	+	0.988736i	$0.452179\pi$
$510$		0			0
$511$	−10.6631	+	32.8177i	−0.471709	+	1.45177i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.218847	+	0.673542i	0.00964355	+	0.0296798i
$516$		0			0
$517$	7.92705	+	9.00854i	0.348631	+	0.396195i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.8713	−	13.7108i	0.826768	−	0.600682i	−0.0918753	−	0.995771i	$-0.529286\pi$
$521$	18.8713	−	13.7108i	0.826768	−	0.600682i	0.918643	+	0.395089i	$0.129286\pi$
$522$		0			0
$523$	−8.48278	+	26.1073i	−0.370926	+	1.14159i	0.575260	+	0.817970i	$0.304901\pi$
$523$	−8.48278	+	26.1073i	−0.370926	+	1.14159i	−0.946186	+	0.323622i	$0.895099\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	27.0344			1.17764
$528$		0			0
$529$	18.8885			0.821241
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.10739	+	28.0297i	−0.394485	+	1.21410i
$534$		0			0
$535$	−4.28115	+	3.11044i	−0.185090	+	0.134476i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.93769	−	3.26944i	0.0834624	−	0.140825i
$540$		0			0
$541$	−7.80902	−	24.0337i	−0.335736	−	1.03329i	−0.966358	−	0.257199i	$-0.917200\pi$
$541$	−7.80902	−	24.0337i	−0.335736	−	1.03329i	0.630623	−	0.776090i	$-0.282800\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.673762	−	2.07363i	0.0288608	−	0.0888244i
$546$		0			0
$547$	−18.3435	−	13.3273i	−0.784310	−	0.569834i	0.121960	−	0.992535i	$-0.461082\pi$
$547$	−18.3435	−	13.3273i	−0.784310	−	0.569834i	−0.906269	+	0.422701i	$0.861082\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	18.2148			0.775976
$552$		0			0
$553$	31.9894	+	23.2416i	1.36033	+	0.988335i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.69098	−	6.31437i	0.368249	−	0.267548i	−0.388236	−	0.921560i	$-0.626915\pi$
$557$	8.69098	−	6.31437i	0.368249	−	0.267548i	0.756484	+	0.654012i	$0.226915\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.95492	−	15.2497i	−0.208825	−	0.642697i	−0.999535	−	0.0305054i	$-0.990288\pi$
$563$	−4.95492	−	15.2497i	−0.208825	−	0.642697i	0.790710	−	0.612191i	$-0.209712\pi$
$564$		0			0
$565$	1.28115	−	0.930812i	0.0538985	−	0.0391596i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−28.2533	−	20.5272i	−1.18444	−	0.860546i	−0.191774	−	0.981439i	$-0.561424\pi$
$569$	−28.2533	−	20.5272i	−1.18444	−	0.860546i	−0.992665	+	0.120893i	$0.961424\pi$
$570$		0			0
$571$	18.4721			0.773035			0.386517	−	0.922282i	$-0.373678\pi$
$571$	18.4721			0.773035			0.386517	+	0.922282i	$0.373678\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−24.1803	−	17.5680i	−1.00839	−	0.732638i
$576$		0			0
$577$	−7.69756	+	23.6907i	−0.320454	+	0.986255i	0.652998	+	0.757360i	$0.273511\pi$
$577$	−7.69756	+	23.6907i	−0.320454	+	0.986255i	−0.973451	+	0.228895i	$0.926489\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	14.1418	+	43.5241i	0.586702	+	1.80568i
$582$		0			0
$583$	−2.19098	−	23.4131i	−0.0907412	−	0.969673i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.927051	+	0.673542i	−0.0382635	+	0.0278001i	−0.606753	−	0.794891i	$-0.707528\pi$
$587$	−0.927051	+	0.673542i	−0.0382635	+	0.0278001i	0.568489	+	0.822691i	$0.307528\pi$
$588$		0			0
$589$	5.16312	−	15.8904i	0.212743	−	0.654754i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.5836			−0.434616			−0.217308	−	0.976103i	$-0.569728\pi$
$593$	−10.5836			−0.434616			−0.217308	+	0.976103i	$0.569728\pi$
$594$		0			0
$595$	8.14590			0.333949
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.302439	−	0.930812i	0.0123573	−	0.0380320i	−0.944688	−	0.327971i	$-0.893635\pi$
$599$	0.302439	−	0.930812i	0.0123573	−	0.0380320i	0.957045	+	0.289939i	$0.0936351\pi$
$600$		0			0
$601$	−10.8713	+	7.89848i	−0.443451	+	0.322186i	−0.787004	−	0.616947i	$-0.788369\pi$
$601$	−10.8713	+	7.89848i	−0.443451	+	0.322186i	0.343554	+	0.939133i	$0.388369\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.66312	+	4.94704i	−0.189583	+	0.201126i
$606$		0			0
$607$	12.8435	+	39.5281i	0.521300	+	1.60440i	0.771519	+	0.636207i	$0.219497\pi$
$607$	12.8435	+	39.5281i	0.521300	+	1.60440i	−0.250219	+	0.968189i	$0.580503\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.16312	+	15.8904i	−0.208877	+	0.642859i
$612$		0			0
$613$	24.7254	+	17.9641i	0.998651	+	0.725562i	0.961798	−	0.273759i	$-0.0882670\pi$
$613$	24.7254	+	17.9641i	0.998651	+	0.725562i	0.0368521	+	0.999321i	$0.488267\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.4721			0.663143			0.331572	−	0.943430i	$-0.392421\pi$
$617$	16.4721			0.663143			0.331572	+	0.943430i	$0.392421\pi$
$618$		0			0
$619$	−5.39919	−	3.92274i	−0.217012	−	0.157668i	0.473969	−	0.880542i	$-0.342821\pi$
$619$	−5.39919	−	3.92274i	−0.217012	−	0.157668i	−0.690980	+	0.722873i	$0.742821\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−19.5623	+	14.2128i	−0.783747	+	0.569426i
$624$		0			0
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.92705	−	21.3193i	−0.276200	−	0.850055i
$630$		0			0
$631$	13.8713	−	10.0781i	0.552209	−	0.401203i	−0.276390	−	0.961045i	$-0.589138\pi$
$631$	13.8713	−	10.0781i	0.552209	−	0.401203i	0.828599	+	0.559842i	$0.189138\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.30902	−	1.67760i	−0.0916305	−	0.0665735i
$636$		0			0
$637$	5.29180			0.209669
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.8713	+	9.35156i	0.508387	+	0.369365i	0.812211	−	0.583363i	$-0.198264\pi$
$641$	12.8713	+	9.35156i	0.508387	+	0.369365i	−0.303825	+	0.952728i	$0.598264\pi$
$642$		0			0
$643$	6.57295	−	20.2295i	0.259212	−	0.797772i	−0.733759	−	0.679410i	$-0.762236\pi$
$643$	6.57295	−	20.2295i	0.259212	−	0.797772i	0.992971	−	0.118362i	$-0.0377643\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.0451	+	33.9933i	0.434227	+	1.33641i	0.893877	+	0.448313i	$0.147975\pi$
$647$	11.0451	+	33.9933i	0.434227	+	1.33641i	−0.459649	+	0.888100i	$0.652025\pi$
$648$		0			0
$649$	−30.7254	+	13.2618i	−1.20608	+	0.520571i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.8713	−	13.7108i	0.738492	−	0.536546i	−0.153747	−	0.988110i	$-0.549134\pi$
$653$	18.8713	−	13.7108i	0.738492	−	0.536546i	0.892238	+	0.451565i	$0.149134\pi$
$654$		0			0
$655$	3.52786	−	10.8576i	0.137845	−	0.424243i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.36068			0.169868			0.0849340	−	0.996387i	$-0.472932\pi$
$659$	4.36068			0.169868			0.0849340	+	0.996387i	$0.472932\pi$
$660$		0			0
$661$	14.3607			0.558566			0.279283	−	0.960209i	$-0.409903\pi$
$661$	14.3607			0.558566			0.279283	+	0.960209i	$0.409903\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.55573	−	4.78804i	0.0603285	−	0.185672i
$666$		0			0
$667$	−33.4164	+	24.2784i	−1.29389	+	0.940065i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.80902	−	13.1760i	0.301464	−	0.508655i
$672$		0			0
$673$	9.31559	+	28.6705i	0.359090	+	1.10516i	0.953600	+	0.301077i	$0.0973460\pi$
$673$	9.31559	+	28.6705i	0.359090	+	1.10516i	−0.594510	+	0.804088i	$0.702654\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.6631	+	32.8177i	−0.409817	+	1.26129i	0.506989	+	0.861953i	$0.330759\pi$
$677$	−10.6631	+	32.8177i	−0.409817	+	1.26129i	−0.916805	+	0.399334i	$0.869241\pi$
$678$		0			0
$679$	−12.8435	−	9.33132i	−0.492887	−	0.358103i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.9443			−0.648355			−0.324177	−	0.945996i	$-0.605087\pi$
$683$	−16.9443			−0.648355			−0.324177	+	0.945996i	$0.605087\pi$
$684$		0			0
$685$	5.39919	+	3.92274i	0.206292	+	0.149880i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	26.4894	−	19.2456i	1.00916	−	0.733201i
$690$		0			0
$691$	−3.98936	−	12.2780i	−0.151762	−	0.467076i	0.846056	−	0.533094i	$-0.178971\pi$
$691$	−3.98936	−	12.2780i	−0.151762	−	0.467076i	−0.997818	+	0.0660174i	$0.978971\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.63525	+	5.03280i	0.0620288	+	0.190905i
$696$		0			0
$697$	−23.8435	+	17.3233i	−0.903135	+	0.656166i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.63525	+	1.18808i	0.0617627	+	0.0448732i	0.618238	−	0.785991i	$-0.287847\pi$
$701$	1.63525	+	1.18808i	0.0617627	+	0.0448732i	−0.556476	+	0.830864i	$0.687847\pi$
$702$		0			0
$703$	−13.8541			−0.522517
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.6976	−	11.4049i	−0.590368	−	0.428927i
$708$		0			0
$709$	2.37132	−	7.29818i	0.0890569	−	0.274089i	−0.896602	−	0.442836i	$-0.853972\pi$
$709$	2.37132	−	7.29818i	0.0890569	−	0.274089i	0.985659	+	0.168747i	$0.0539722\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	11.7082	+	36.0341i	0.438476	+	1.34949i
$714$		0			0
$715$	−9.23607	−	2.07363i	−0.345409	−	0.0775492i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4.63525	+	3.36771i	−0.172866	+	0.125594i	−0.670854	−	0.741589i	$-0.734072\pi$
$719$	−4.63525	+	3.36771i	−0.172866	+	0.125594i	0.497988	+	0.867184i	$0.334072\pi$
$720$		0			0
$721$	−1.01064	+	3.11044i	−0.0376383	+	0.115839i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	29.4721			1.09457
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−10.8713	+	7.89848i	−0.401541	+	0.291737i	−0.770169	−	0.637840i	$-0.779828\pi$
$733$	−10.8713	+	7.89848i	−0.401541	+	0.291737i	0.368627	+	0.929577i	$0.379828\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.0000	−	3.59222i	−0.589368	−	0.132321i
$738$		0			0
$739$	−11.3369	−	34.8913i	−0.417034	−	1.28350i	−0.910419	−	0.413687i	$-0.864241\pi$
$739$	−11.3369	−	34.8913i	−0.417034	−	1.28350i	0.493385	−	0.869811i	$-0.335759\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.6631	−	32.8177i	0.391192	−	1.20396i	−0.540696	−	0.841218i	$-0.681839\pi$
$743$	10.6631	−	32.8177i	0.391192	−	1.20396i	0.931888	−	0.362747i	$-0.118161\pi$
$744$		0			0
$745$	−2.30902	−	1.67760i	−0.0845958	−	0.0614625i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−24.4377			−0.892934
$750$		0			0
$751$	−14.6353	−	10.6331i	−0.534048	−	0.388009i	0.287822	−	0.957684i	$-0.407069\pi$
$751$	−14.6353	−	10.6331i	−0.534048	−	0.388009i	−0.821870	+	0.569675i	$0.807069\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−7.13525	+	5.18407i	−0.259679	+	0.188667i
$756$		0			0
$757$	−4.86475	−	14.9721i	−0.176812	−	0.544172i	0.822899	−	0.568187i	$-0.192355\pi$
$757$	−4.86475	−	14.9721i	−0.176812	−	0.544172i	−0.999712	+	0.0240152i	$0.992355\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.1910	−	43.6754i	−0.514423	−	1.58323i	−0.784330	−	0.620344i	$-0.786993\pi$
$761$	−14.1910	−	43.6754i	−0.514423	−	1.58323i	0.269907	−	0.962886i	$-0.413007\pi$
$762$		0			0
$763$	8.14590	−	5.91834i	0.294901	−	0.214258i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−37.6976	−	27.3889i	−1.36118	−	0.988955i
$768$		0			0
$769$	10.5836			0.381654			0.190827	−	0.981624i	$-0.438883\pi$
$769$	10.5836			0.381654			0.190827	+	0.981624i	$0.438883\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.2533	−	7.44945i	−0.368785	−	0.267938i	0.387922	−	0.921692i	$-0.373193\pi$
$773$	−10.2533	−	7.44945i	−0.368785	−	0.267938i	−0.756707	+	0.653754i	$0.773193\pi$
$774$		0			0
$775$	8.35410	−	25.7113i	0.300088	−	0.923577i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.62868	+	17.3233i	0.201668	+	0.620671i
$780$		0			0
$781$	14.5729	−	24.5887i	0.521461	−	0.879853i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.28115	+	0.930812i	−0.0457263	+	0.0332221i
$786$		0			0
$787$	9.98936	−	30.7441i	0.356082	−	1.09591i	−0.599297	−	0.800527i	$-0.704553\pi$
$787$	9.98936	−	30.7441i	0.356082	−	1.09591i	0.955379	−	0.295382i	$-0.0954468\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	7.31308			0.260023
$792$		0			0
$793$	21.3262			0.757317
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.33688	−	10.2699i	0.118198	−	0.363777i	−0.874402	−	0.485202i	$-0.838746\pi$
$797$	3.33688	−	10.2699i	0.118198	−	0.363777i	0.992601	+	0.121424i	$0.0387462\pi$
$798$		0			0
$799$	−13.5172	+	9.82084i	−0.478205	+	0.347436i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	36.8156	−	15.8904i	1.29919	−	0.560762i
$804$		0			0
$805$	3.52786	+	10.8576i	0.124341	+	0.382682i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14.1910	+	43.6754i	−0.498928	+	1.53554i	0.311815	+	0.950143i	$0.399063\pi$
$809$	−14.1910	+	43.6754i	−0.498928	+	1.53554i	−0.810744	+	0.585401i	$0.800937\pi$
$810$		0			0
$811$	22.9615	+	16.6825i	0.806287	+	0.585802i	0.912752	−	0.408515i	$-0.133953\pi$
$811$	22.9615	+	16.6825i	0.806287	+	0.585802i	−0.106465	+	0.994316i	$0.533953\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.67376			0.0936578
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.4894	+	11.2537i	−0.540582	+	0.392756i	−0.824301	−	0.566151i	$-0.808432\pi$
$821$	−15.4894	+	11.2537i	−0.540582	+	0.392756i	0.283719	+	0.958907i	$0.408432\pi$
$822$		0			0
$823$	−0.461493	−	1.42033i	−0.0160866	−	0.0495096i	0.942691	−	0.333667i	$-0.108286\pi$
$823$	−0.461493	−	1.42033i	−0.0160866	−	0.0495096i	−0.958778	+	0.284158i	$0.908286\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.95492	−	15.2497i	−0.172299	−	0.530283i	0.827201	−	0.561907i	$-0.189932\pi$
$827$	−4.95492	−	15.2497i	−0.172299	−	0.530283i	−0.999500	+	0.0316241i	$0.989932\pi$
$828$		0			0
$829$	38.7254	−	28.1357i	1.34499	−	0.977192i	0.345745	−	0.938328i	$-0.387626\pi$
$829$	38.7254	−	28.1357i	1.34499	−	0.977192i	0.999245	−	0.0388637i	$-0.0123738\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.28115	+	3.11044i	0.148333	+	0.107770i
$834$		0			0
$835$	−4.20163			−0.145403
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.309017	−	0.224514i	−0.0106685	−	0.00775108i	0.582438	−	0.812875i	$-0.302099\pi$
$839$	−0.309017	−	0.224514i	−0.0106685	−	0.00775108i	−0.593107	+	0.805124i	$0.702099\pi$
$840$		0			0
$841$	3.62461	−	11.1554i	0.124987	−	0.384669i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.59017	−	4.89404i	−0.0547035	−	0.168360i
$846$		0			0
$847$	−30.8500	+	5.82485i	−1.06002	+	0.200144i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	25.4164	−	18.4661i	0.871263	−	0.633010i
$852$		0			0
$853$	−2.10081	+	6.46564i	−0.0719305	+	0.221379i	−0.980558	−	0.196227i	$-0.937131\pi$
$853$	−2.10081	+	6.46564i	−0.0719305	+	0.221379i	0.908628	+	0.417607i	$0.137131\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.9443			0.510487			0.255243	−	0.966877i	$-0.417844\pi$
$857$	14.9443			0.510487			0.255243	+	0.966877i	$0.417844\pi$
$858$		0			0
$859$	−48.9443			−1.66996			−0.834979	−	0.550283i	$-0.814520\pi$
$859$	−48.9443			−1.66996			−0.834979	+	0.550283i	$0.814520\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8.10081	+	24.9317i	−0.275755	+	0.848686i	0.713264	+	0.700896i	$0.247216\pi$
$863$	−8.10081	+	24.9317i	−0.275755	+	0.848686i	−0.989019	+	0.147791i	$0.952784\pi$
$864$		0			0
$865$	−8.89919	+	6.46564i	−0.302581	+	0.219838i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.28115	−	45.7490i	−0.145228	−	1.55193i
$870$		0			0
$871$	−7.05573	−	21.7153i	−0.239074	−	0.735795i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.24265	−	16.1352i	0.177234	−	0.545469i
$876$		0			0
$877$	−35.0517	−	25.4665i	−1.18361	−	0.859943i	−0.191036	−	0.981583i	$-0.561185\pi$
$877$	−35.0517	−	25.4665i	−1.18361	−	0.859943i	−0.992574	+	0.121640i	$0.961185\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	19.8885			0.670062			0.335031	−	0.942207i	$-0.391253\pi$
$881$	19.8885			0.670062			0.335031	+	0.942207i	$0.391253\pi$
$882$		0			0
$883$	−42.0517	−	30.5523i	−1.41515	−	1.02817i	−0.992548	−	0.121853i	$-0.961117\pi$
$883$	−42.0517	−	30.5523i	−1.41515	−	1.02817i	−0.422603	−	0.906315i	$-0.638883\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.8713	+	15.8904i	−0.734367	+	0.533549i	−0.890942	−	0.454117i	$-0.849955\pi$
$887$	−21.8713	+	15.8904i	−0.734367	+	0.533549i	0.156575	+	0.987666i	$0.449955\pi$
$888$		0			0
$889$	−4.07295	−	12.5352i	−0.136602	−	0.420419i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.19098	+	9.82084i	0.106782	+	0.328642i
$894$		0			0
$895$	0.190983	−	0.138757i	0.00638386	−	0.00463814i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.2254	−	21.9601i	−1.00807	−	0.732409i
$900$		0			0
$901$	32.7426			1.09082
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.309017	+	0.224514i	0.0102721	+	0.00746310i
$906$		0			0
$907$	−13.8992	+	42.7773i	−0.461515	+	1.42040i	0.401798	+	0.915728i	$0.368385\pi$
$907$	−13.8992	+	42.7773i	−0.461515	+	1.42040i	−0.863313	+	0.504669i	$0.831615\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.71885	−	17.6008i	−0.189474	−	0.583141i	0.810523	−	0.585707i	$-0.199183\pi$
$911$	−5.71885	−	17.6008i	−0.189474	−	0.583141i	−0.999997	+	0.00256645i	$0.999183\pi$
$912$		0			0
$913$	27.1140	−	45.7490i	0.897341	−	1.51407i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	42.6525	−	30.9888i	1.40851	−	1.02334i
$918$		0			0
$919$	−12.8435	+	39.5281i	−0.423667	+	1.30391i	0.480599	+	0.876941i	$0.340419\pi$
$919$	−12.8435	+	39.5281i	−0.423667	+	1.30391i	−0.904265	+	0.426971i	$0.859581\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	39.7984			1.30998
$924$		0			0
$925$	−22.4164			−0.737047
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.60739	+	29.5685i	−0.315208	+	0.970111i	0.660460	+	0.750861i	$0.270361\pi$
$929$	−9.60739	+	29.5685i	−0.315208	+	0.970111i	−0.975669	+	0.219250i	$0.929639\pi$
$930$		0			0
$931$	2.64590	−	1.92236i	0.0867158	−	0.0630027i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.25329	−	7.10642i	−0.204504	−	0.232405i
$936$		0			0
$937$	−4.28115	−	13.1760i	−0.139859	−	0.430442i	0.856455	−	0.516222i	$-0.172662\pi$
$937$	−4.28115	−	13.1760i	−0.139859	−	0.430442i	−0.996314	+	0.0857795i	$0.972662\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−7.13525	+	21.9601i	−0.232603	+	0.715877i	0.764828	+	0.644235i	$0.222824\pi$
$941$	−7.13525	+	21.9601i	−0.232603	+	0.715877i	−0.997430	+	0.0716425i	$0.977176\pi$
$942$		0			0
$943$	−33.4164	−	24.2784i	−1.08819	−	0.790615i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−47.7771			−1.55255			−0.776273	−	0.630396i	$-0.782892\pi$
$947$	−47.7771			−1.55255			−0.776273	+	0.630396i	$0.782892\pi$
$948$		0			0
$949$	45.1697	+	32.8177i	1.46627	+	1.06531i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−37.4894	+	27.2376i	−1.21440	+	0.882313i	−0.995623	−	0.0934622i	$-0.970207\pi$
$953$	−37.4894	+	27.2376i	−1.21440	+	0.882313i	−0.218777	+	0.975775i	$0.570207\pi$
$954$		0			0
$955$	−0.579527	−	1.78360i	−0.0187530	−	0.0577159i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.52380	+	29.3112i	0.307540	+	0.946509i
$960$		0			0
$961$	−2.64590	+	1.92236i	−0.0853515	+	0.0620115i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.21885	−	0.885544i	−0.0392361	−	0.0285067i
$966$		0			0
$967$	44.0000			1.41494			0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000			1.41494			0.707472	+	0.706741i	$0.249835\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.6353	+	10.6331i	0.469668	+	0.341234i	0.797312	−	0.603568i	$-0.206255\pi$
$971$	14.6353	+	10.6331i	0.469668	+	0.341234i	−0.327644	+	0.944801i	$0.606255\pi$
$972$		0			0
$973$	−7.55166	+	23.2416i	−0.242095	+	0.745092i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.9549	−	33.7158i	−0.350479	−	1.07866i	−0.958585	−	0.284807i	$-0.908070\pi$
$977$	−10.9549	−	33.7158i	−0.350479	−	1.07866i	0.608106	−	0.793856i	$-0.291930\pi$
$978$		0			0
$979$	27.4164	+	6.15537i	0.876232	+	0.196726i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.63525	+	3.36771i	−0.147842	+	0.107413i	−0.659247	−	0.751926i	$-0.729125\pi$
$983$	−4.63525	+	3.36771i	−0.147842	+	0.107413i	0.511406	+	0.859339i	$0.329125\pi$
$984$		0			0
$985$	2.85410	−	8.78402i	0.0909393	−	0.279882i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	24.0000			0.762385			0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000			0.762385			0.381193	+	0.924496i	$0.375513\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.23607	+	9.95959i	−0.102590	+	0.315740i
$996$		0			0
$997$	28.2533	−	20.5272i	0.894791	−	0.650103i	−0.0423320	−	0.999104i	$-0.513479\pi$
$997$	28.2533	−	20.5272i	0.894791	−	0.650103i	0.937123	+	0.349000i	$0.113479\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.j.a.181.1		4
3.2	odd	2		44.2.e.a.5.1	✓	4
11.3	even	5		4356.2.a.t.1.1		2
11.8	odd	10		4356.2.a.u.1.1		2
11.9	even	5	inner	396.2.j.a.361.1		4
12.11	even	2		176.2.m.b.49.1		4
15.2	even	4		1100.2.cb.a.49.2		8
15.8	even	4		1100.2.cb.a.49.1		8
15.14	odd	2		1100.2.n.a.401.1		4
24.5	odd	2		704.2.m.e.577.1		4
24.11	even	2		704.2.m.d.577.1		4
33.2	even	10		484.2.e.c.9.1		4
33.5	odd	10		484.2.e.e.81.1		4
33.8	even	10		484.2.a.c.1.2		2
33.14	odd	10		484.2.a.b.1.2		2
33.17	even	10		484.2.e.d.81.1		4
33.20	odd	10		44.2.e.a.9.1	yes	4
33.26	odd	10		484.2.e.e.245.1		4
33.29	even	10		484.2.e.d.245.1		4
33.32	even	2		484.2.e.c.269.1		4
132.47	even	10		1936.2.a.ba.1.1		2
132.107	odd	10		1936.2.a.z.1.1		2
132.119	even	10		176.2.m.b.97.1		4
165.53	even	20		1100.2.cb.a.449.2		8
165.119	odd	10		1100.2.n.a.801.1		4
165.152	even	20		1100.2.cb.a.449.1		8
264.53	odd	10		704.2.m.e.449.1		4
264.107	odd	10		7744.2.a.bo.1.2		2
264.173	even	10		7744.2.a.db.1.1		2
264.179	even	10		7744.2.a.bp.1.2		2
264.245	odd	10		7744.2.a.da.1.1		2
264.251	even	10		704.2.m.d.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.e.a.5.1	✓	4	3.2	odd	2
44.2.e.a.9.1	yes	4	33.20	odd	10
176.2.m.b.49.1		4	12.11	even	2
176.2.m.b.97.1		4	132.119	even	10
396.2.j.a.181.1		4	1.1	even	1	trivial
396.2.j.a.361.1		4	11.9	even	5	inner
484.2.a.b.1.2		2	33.14	odd	10
484.2.a.c.1.2		2	33.8	even	10
484.2.e.c.9.1		4	33.2	even	10
484.2.e.c.269.1		4	33.32	even	2
484.2.e.d.81.1		4	33.17	even	10
484.2.e.d.245.1		4	33.29	even	10
484.2.e.e.81.1		4	33.5	odd	10
484.2.e.e.245.1		4	33.26	odd	10
704.2.m.d.449.1		4	264.251	even	10
704.2.m.d.577.1		4	24.11	even	2
704.2.m.e.449.1		4	264.53	odd	10
704.2.m.e.577.1		4	24.5	odd	2
1100.2.n.a.401.1		4	15.14	odd	2
1100.2.n.a.801.1		4	165.119	odd	10
1100.2.cb.a.49.1		8	15.8	even	4
1100.2.cb.a.49.2		8	15.2	even	4
1100.2.cb.a.449.1		8	165.152	even	20
1100.2.cb.a.449.2		8	165.53	even	20
1936.2.a.z.1.1		2	132.107	odd	10
1936.2.a.ba.1.1		2	132.47	even	10
4356.2.a.t.1.1		2	11.3	even	5
4356.2.a.u.1.1		2	11.8	odd	10
7744.2.a.bo.1.2		2	264.107	odd	10
7744.2.a.bp.1.2		2	264.179	even	10
7744.2.a.da.1.1		2	264.245	odd	10
7744.2.a.db.1.1		2	264.173	even	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)

\(f(q)\)	\(=\)	\(q+(-0.190983 + 0.587785i) q^{5} +(-2.30902 + 1.67760i) q^{7} +(3.23607 + 0.726543i) q^{11} +(1.42705 + 4.39201i) q^{13} +(-1.42705 + 4.39201i) q^{17} +(2.30902 + 1.67760i) q^{19} -6.47214 q^{23} +(3.73607 + 2.71441i) q^{25} +(5.16312 - 3.75123i) q^{29} +(-1.80902 - 5.56758i) q^{31} +(-0.545085 - 1.67760i) q^{35} +(-3.92705 + 2.85317i) q^{37} +(5.16312 + 3.75123i) q^{41} +(2.92705 + 2.12663i) q^{47} +(0.354102 - 1.08981i) q^{49} +(-2.19098 - 6.74315i) q^{53} +(-1.04508 + 1.76336i) q^{55} +(-8.16312 + 5.93085i) q^{59} +(1.42705 - 4.39201i) q^{61} -2.85410 q^{65} -4.94427 q^{67} +(2.66312 - 8.19624i) q^{71} +(9.78115 - 7.10642i) q^{73} +(-8.69098 + 3.75123i) q^{77} +(-4.28115 - 13.1760i) q^{79} +(4.95492 - 15.2497i) q^{83} +(-2.30902 - 1.67760i) q^{85} +8.47214 q^{89} +(-10.6631 - 7.74721i) q^{91} +(-1.42705 + 1.03681i) q^{95} +(1.71885 + 5.29007i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{5} - 7 q^{7} + 4 q^{11} - q^{13} + q^{17} + 7 q^{19} - 8 q^{23} + 6 q^{25} + 5 q^{29} - 5 q^{31} + 9 q^{35} - 9 q^{37} + 5 q^{41} + 5 q^{47} - 12 q^{49} - 11 q^{53} + 7 q^{55} - 17 q^{59} - q^{61}+ \cdots + 27 q^{97}+O(q^{100}) \) 4 * q - 3 * q^5 - 7 * q^7 + 4 * q^11 - q^13 + q^17 + 7 * q^19 - 8 * q^23 + 6 * q^25 + 5 * q^29 - 5 * q^31 + 9 * q^35 - 9 * q^37 + 5 * q^41 + 5 * q^47 - 12 * q^49 - 11 * q^53 + 7 * q^55 - 17 * q^59 - q^61 + 2 * q^65 + 16 * q^67 - 5 * q^71 + 19 * q^73 - 37 * q^77 + 3 * q^79 + 31 * q^83 - 7 * q^85 + 16 * q^89 - 27 * q^91 + q^95 + 27 * q^97

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