LMFDB - Embedded newform 2592.2.p.a.2159.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2592,2,Mod(431,2592)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2592, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2592.431"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,-12,0,0,0,0,0,12,0,0,0,0,0,16,0,0,0,0,0,-2,0,0,0, 0,0,-12,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(41)] == traces)

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

Self dual:	no
Analytic conductor:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2159.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2592.2159
Dual form			2592.2.p.a.431.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 2.12132i) q^{5} +(-3.00000 + 1.73205i) q^{7} +(2.44949 - 1.41421i) q^{11} +(3.00000 + 1.73205i) q^{13} +1.41421i q^{17} +4.00000 q^{19} +(-2.44949 + 4.24264i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.22474 + 2.12132i) q^{29} +(-3.00000 - 1.73205i) q^{31} -8.48528i q^{35} +(-1.22474 - 0.707107i) q^{41} +(4.00000 + 6.92820i) q^{43} +(2.44949 + 4.24264i) q^{47} +(2.50000 - 4.33013i) q^{49} -7.34847 q^{53} +6.92820i q^{55} +(-9.79796 - 5.65685i) q^{59} +(12.0000 - 6.92820i) q^{61} +(-7.34847 + 4.24264i) q^{65} +(-2.00000 + 3.46410i) q^{67} -14.6969 q^{71} -4.00000 q^{73} +(-4.89898 + 8.48528i) q^{77} +(-3.00000 + 1.73205i) q^{79} +(-12.2474 + 7.07107i) q^{83} +(-3.00000 - 1.73205i) q^{85} -7.07107i q^{89} -12.0000 q^{91} +(-4.89898 + 8.48528i) q^{95} +(-4.00000 - 6.92820i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{7} + 12 q^{13} + 16 q^{19} - 2 q^{25} - 12 q^{31} + 16 q^{43} + 10 q^{49} + 48 q^{61} - 8 q^{67} - 16 q^{73} - 12 q^{79} - 12 q^{85} - 48 q^{91} - 16 q^{97}+O(q^{100}) $ 4 * q - 12 * q^7 + 12 * q^13 + 16 * q^19 - 2 * q^25 - 12 * q^31 + 16 * q^43 + 10 * q^49 + 48 * q^61 - 8 * q^67 - 16 * q^73 - 12 * q^79 - 12 * q^85 - 48 * q^91 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	−1.22474	+	2.12132i	−0.547723	+	0.948683i	0.450708	+	0.892672i	$0.351172\pi$
$5$	−1.22474	+	2.12132i	−0.547723	+	0.948683i	−0.998430	+	0.0560116i	$0.982162\pi$
$6$		0			0
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.188982	+	0.981981i	$0.560519\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.44949	−	1.41421i	0.738549	−	0.426401i	−0.0829925	−	0.996550i	$-0.526448\pi$
$11$	2.44949	−	1.41421i	0.738549	−	0.426401i	0.821541	+	0.570149i	$0.193114\pi$
$12$		0			0
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			1.41421i			0.342997i	0.985184	+	0.171499i	$0.0548609\pi$
$17$			1.41421i			0.342997i	−0.985184	+	0.171499i	$0.945139\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.44949	+	4.24264i	−0.510754	+	0.884652i	0.489168	+	0.872189i	$0.337300\pi$
$23$	−2.44949	+	4.24264i	−0.510754	+	0.884652i	−0.999922	+	0.0124624i	$0.996033\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.22474	+	2.12132i	0.227429	+	0.393919i	0.957046	−	0.289938i	$-0.0936346\pi$
$29$	1.22474	+	2.12132i	0.227429	+	0.393919i	−0.729616	+	0.683857i	$0.760301\pi$
$30$		0			0
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	8.48528i		−	1.43427i
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.22474	−	0.707107i	−0.191273	−	0.110432i	0.401305	−	0.915944i	$-0.368557\pi$
$41$	−1.22474	−	0.707107i	−0.191273	−	0.110432i	−0.592578	+	0.805513i	$0.701890\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.44949	+	4.24264i	0.357295	+	0.618853i	0.987508	−	0.157569i	$-0.0503658\pi$
$47$	2.44949	+	4.24264i	0.357295	+	0.618853i	−0.630213	+	0.776422i	$0.717032\pi$
$48$		0			0
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.34847			−1.00939			−0.504695	−	0.863298i	$-0.668395\pi$
$53$	−7.34847			−1.00939			−0.504695	+	0.863298i	$0.668395\pi$
$54$		0			0
$55$			6.92820i			0.934199i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.79796	−	5.65685i	−1.27559	−	0.736460i	−0.299552	−	0.954080i	$-0.596837\pi$
$59$	−9.79796	−	5.65685i	−1.27559	−	0.736460i	−0.976034	+	0.217620i	$0.930171\pi$
$60$		0			0
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.537400	−	0.843328i	$-0.319407\pi$
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.999043	−	0.0437377i	$-0.0139266\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.34847	+	4.24264i	−0.911465	+	0.526235i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.6969			−1.74421			−0.872103	−	0.489323i	$-0.837244\pi$
$71$	−14.6969			−1.74421			−0.872103	+	0.489323i	$0.837244\pi$
$72$		0			0
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.89898	+	8.48528i	−0.558291	+	0.966988i
$78$		0			0
$79$	−3.00000	+	1.73205i	−0.337526	+	0.194871i	−0.659178	−	0.751987i	$-0.729095\pi$
$79$	−3.00000	+	1.73205i	−0.337526	+	0.194871i	0.321651	+	0.946858i	$0.395762\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−12.2474	+	7.07107i	−1.34433	+	0.776151i	−0.987440	−	0.157995i	$-0.949497\pi$
$83$	−12.2474	+	7.07107i	−1.34433	+	0.776151i	−0.356892	+	0.934146i	$0.616164\pi$
$84$		0			0
$85$	−3.00000	−	1.73205i	−0.325396	−	0.187867i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	7.07107i		−	0.749532i	−0.927119	−	0.374766i	$-0.877723\pi$
$89$		−	7.07107i		−	0.749532i	0.927119	−	0.374766i	$-0.122277\pi$
$90$		0			0
$91$	−12.0000			−1.25794
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.89898	+	8.48528i	−0.502625	+	0.870572i
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.22474	+	2.12132i	0.121867	+	0.211079i	0.920504	−	0.390734i	$-0.127779\pi$
$101$	1.22474	+	2.12132i	0.121867	+	0.211079i	−0.798637	+	0.601813i	$0.794445\pi$
$102$		0			0
$103$	−3.00000	−	1.73205i	−0.295599	−	0.170664i	0.344865	−	0.938652i	$-0.387925\pi$
$103$	−3.00000	−	1.73205i	−0.295599	−	0.170664i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			11.3137i			1.09374i	0.837218	+	0.546869i	$0.184180\pi$
$107$			11.3137i			1.09374i	−0.837218	+	0.546869i	$0.815820\pi$
$108$		0			0
$109$		−	10.3923i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$109$		−	10.3923i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−15.9217	−	9.19239i	−1.49779	−	0.864747i	−0.497789	−	0.867298i	$-0.665855\pi$
$113$	−15.9217	−	9.19239i	−1.49779	−	0.864747i	−0.999997	+	0.00255090i	$0.999188\pi$
$114$		0			0
$115$	−6.00000	−	10.3923i	−0.559503	−	0.969087i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.44949	−	4.24264i	−0.224544	−	0.388922i
$120$		0			0
$121$	−1.50000	+	2.59808i	−0.136364	+	0.236189i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.79796			−0.876356
$126$		0			0
$127$		−	10.3923i		−	0.922168i	−0.887357	−	0.461084i	$-0.847461\pi$
$127$		−	10.3923i		−	0.922168i	0.887357	−	0.461084i	$-0.152539\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.89898	+	2.82843i	0.428026	+	0.247121i	0.698505	−	0.715605i	$-0.253849\pi$
$131$	4.89898	+	2.82843i	0.428026	+	0.247121i	−0.270479	+	0.962726i	$0.587182\pi$
$132$		0			0
$133$	−12.0000	+	6.92820i	−1.04053	+	0.600751i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.57321	−	4.94975i	0.732459	−	0.422885i	−0.0868620	−	0.996220i	$-0.527684\pi$
$137$	8.57321	−	4.94975i	0.732459	−	0.422885i	0.819321	+	0.573335i	$0.194351\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.79796			0.819346
$144$		0			0
$145$	−6.00000			−0.498273
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.57321	+	14.8492i	−0.702345	+	1.21650i	0.265296	+	0.964167i	$0.414530\pi$
$149$	−8.57321	+	14.8492i	−0.702345	+	1.21650i	−0.967641	+	0.252330i	$0.918803\pi$
$150$		0			0
$151$	−3.00000	+	1.73205i	−0.244137	+	0.140952i	−0.617076	−	0.786903i	$-0.711683\pi$
$151$	−3.00000	+	1.73205i	−0.244137	+	0.140952i	0.372940	+	0.927855i	$0.378350\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.34847	−	4.24264i	0.590243	−	0.340777i
$156$		0			0
$157$	12.0000	+	6.92820i	0.957704	+	0.552931i	0.895466	−	0.445130i	$-0.146843\pi$
$157$	12.0000	+	6.92820i	0.957704	+	0.552931i	0.0622385	+	0.998061i	$0.480176\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	16.9706i		−	1.33747i
$162$		0			0
$163$	16.0000			1.25322			0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000			1.25322			0.626608	+	0.779334i	$0.284443\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.79796	+	16.9706i	−0.758189	+	1.31322i	0.185584	+	0.982628i	$0.440582\pi$
$167$	−9.79796	+	16.9706i	−0.758189	+	1.31322i	−0.943773	+	0.330593i	$0.892751\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.22474	+	2.12132i	0.0931156	+	0.161281i	0.908821	−	0.417187i	$-0.136984\pi$
$173$	1.22474	+	2.12132i	0.0931156	+	0.161281i	−0.815705	+	0.578468i	$0.803651\pi$
$174$		0			0
$175$	3.00000	+	1.73205i	0.226779	+	0.130931i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	5.65685i		−	0.422813i	−0.977398	−	0.211407i	$-0.932196\pi$
$179$		−	5.65685i		−	0.422813i	0.977398	−	0.211407i	$-0.0678044\pi$
$180$		0			0
$181$			10.3923i			0.772454i	0.922404	+	0.386227i	$0.126222\pi$
$181$			10.3923i			0.772454i	−0.922404	+	0.386227i	$0.873778\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.00000	+	3.46410i	0.146254	+	0.253320i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.79796	+	16.9706i	0.708955	+	1.22795i	0.965245	+	0.261347i	$0.0841666\pi$
$191$	9.79796	+	16.9706i	0.708955	+	1.22795i	−0.256290	+	0.966600i	$0.582500\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.34847			0.523557			0.261778	−	0.965128i	$-0.415691\pi$
$197$	7.34847			0.523557			0.261778	+	0.965128i	$0.415691\pi$
$198$		0			0
$199$		−	10.3923i		−	0.736691i	−0.929689	−	0.368345i	$-0.879924\pi$
$199$		−	10.3923i		−	0.736691i	0.929689	−	0.368345i	$-0.120076\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.34847	−	4.24264i	−0.515761	−	0.297775i
$204$		0			0
$205$	3.00000	−	1.73205i	0.209529	−	0.120972i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.79796	−	5.65685i	0.677739	−	0.391293i
$210$		0			0
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−19.5959			−1.33643
$216$		0			0
$217$	12.0000			0.814613
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.44949	+	4.24264i	−0.164771	+	0.285391i
$222$		0			0
$223$	15.0000	−	8.66025i	1.00447	−	0.579934i	0.0949052	−	0.995486i	$-0.469745\pi$
$223$	15.0000	−	8.66025i	1.00447	−	0.579934i	0.909569	+	0.415553i	$0.136412\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.44949	−	1.41421i	0.162578	−	0.0938647i	−0.416503	−	0.909134i	$-0.636745\pi$
$227$	2.44949	−	1.41421i	0.162578	−	0.0938647i	0.579082	+	0.815270i	$0.303411\pi$
$228$		0			0
$229$	−15.0000	−	8.66025i	−0.991228	−	0.572286i	−0.0855868	−	0.996331i	$-0.527276\pi$
$229$	−15.0000	−	8.66025i	−0.991228	−	0.572286i	−0.905641	+	0.424045i	$0.860610\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			1.41421i			0.0926482i	0.998926	+	0.0463241i	$0.0147507\pi$
$233$			1.41421i			0.0926482i	−0.998926	+	0.0463241i	$0.985249\pi$
$234$		0			0
$235$	−12.0000			−0.782794
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.89898	−	8.48528i	0.316889	−	0.548867i	−0.662949	−	0.748665i	$-0.730695\pi$
$239$	4.89898	−	8.48528i	0.316889	−	0.548867i	0.979837	+	0.199798i	$0.0640285\pi$
$240$		0			0
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.825131	+	0.564942i	$0.191101\pi$
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.0766885	+	0.997055i	$0.475565\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.12372	+	10.6066i	0.391230	+	0.677631i
$246$		0			0
$247$	12.0000	+	6.92820i	0.763542	+	0.440831i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	14.1421i		−	0.892644i	−0.894873	−	0.446322i	$-0.852734\pi$
$251$		−	14.1421i		−	0.892644i	0.894873	−	0.446322i	$-0.147266\pi$
$252$		0			0
$253$			13.8564i			0.871145i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	20.8207	+	12.0208i	1.29876	+	0.749838i	0.980189	−	0.198062i	$-0.0634648\pi$
$257$	20.8207	+	12.0208i	1.29876	+	0.749838i	0.318568	+	0.947900i	$0.396798\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.89898	−	8.48528i	−0.302084	−	0.523225i	0.674524	−	0.738253i	$-0.264349\pi$
$263$	−4.89898	−	8.48528i	−0.302084	−	0.523225i	−0.976608	+	0.215028i	$0.931016\pi$
$264$		0			0
$265$	9.00000	−	15.5885i	0.552866	−	0.957591i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.34847			−0.448044			−0.224022	−	0.974584i	$-0.571919\pi$
$269$	−7.34847			−0.448044			−0.224022	+	0.974584i	$0.571919\pi$
$270$		0			0
$271$			31.1769i			1.89386i	0.321436	+	0.946931i	$0.395835\pi$
$271$			31.1769i			1.89386i	−0.321436	+	0.946931i	$0.604165\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.44949	−	1.41421i	−0.147710	−	0.0852803i
$276$		0			0
$277$	−15.0000	+	8.66025i	−0.901263	+	0.520344i	−0.877610	−	0.479376i	$-0.840863\pi$
$277$	−15.0000	+	8.66025i	−0.901263	+	0.520344i	−0.0236530	+	0.999720i	$0.507530\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−20.8207	+	12.0208i	−1.24206	+	0.717102i	−0.969513	−	0.245042i	$-0.921198\pi$
$281$	−20.8207	+	12.0208i	−1.24206	+	0.717102i	−0.272544	+	0.962143i	$0.587865\pi$
$282$		0			0
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	−0.999608	−	0.0280052i	$-0.991084\pi$
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	0.524057	+	0.851683i	$0.324418\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.89898			0.289178
$288$		0			0
$289$	15.0000			0.882353
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.4722	−	23.3345i	0.787054	−	1.36322i	−0.140710	−	0.990051i	$-0.544939\pi$
$293$	13.4722	−	23.3345i	0.787054	−	1.36322i	0.927764	−	0.373167i	$-0.121728\pi$
$294$		0			0
$295$	24.0000	−	13.8564i	1.39733	−	0.806751i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−14.6969	+	8.48528i	−0.849946	+	0.490716i
$300$		0			0
$301$	−24.0000	−	13.8564i	−1.38334	−	0.798670i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			33.9411i			1.94346i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.89898	−	8.48528i	0.277796	−	0.481156i	−0.693041	−	0.720898i	$-0.743730\pi$
$311$	4.89898	−	8.48528i	0.277796	−	0.481156i	0.970837	+	0.239742i	$0.0770629\pi$
$312$		0			0
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.12372	−	10.6066i	−0.343943	−	0.595726i	0.641218	−	0.767358i	$-0.278429\pi$
$317$	−6.12372	−	10.6066i	−0.343943	−	0.595726i	−0.985161	+	0.171632i	$0.945096\pi$
$318$		0			0
$319$	6.00000	+	3.46410i	0.335936	+	0.193952i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			5.65685i			0.314756i
$324$		0			0
$325$		−	3.46410i		−	0.192154i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−14.6969	−	8.48528i	−0.810268	−	0.467809i
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.89898	−	8.48528i	−0.267660	−	0.463600i
$336$		0			0
$337$	2.00000	−	3.46410i	0.108947	−	0.188702i	−0.806397	−	0.591375i	$-0.798585\pi$
$337$	2.00000	−	3.46410i	0.108947	−	0.188702i	0.915344	+	0.402673i	$0.131919\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−9.79796			−0.530589
$342$		0			0
$343$		−	6.92820i		−	0.374088i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.2474	+	7.07107i	0.657477	+	0.379595i	0.791315	−	0.611408i	$-0.209397\pi$
$347$	12.2474	+	7.07107i	0.657477	+	0.379595i	−0.133838	+	0.991003i	$0.542730\pi$
$348$		0			0
$349$	−24.0000	+	13.8564i	−1.28469	+	0.741716i	−0.977702	−	0.209997i	$-0.932655\pi$
$349$	−24.0000	+	13.8564i	−1.28469	+	0.741716i	−0.306988	+	0.951713i	$0.599321\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.4722	+	7.77817i	−0.717053	+	0.413990i	−0.813667	−	0.581331i	$-0.802532\pi$
$353$	−13.4722	+	7.77817i	−0.717053	+	0.413990i	0.0966144	+	0.995322i	$0.469199\pi$
$354$		0			0
$355$	18.0000	−	31.1769i	0.955341	−	1.65470i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.6969			0.775675			0.387837	−	0.921728i	$-0.373222\pi$
$359$	14.6969			0.775675			0.387837	+	0.921728i	$0.373222\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.89898	−	8.48528i	0.256424	−	0.444140i
$366$		0			0
$367$	−21.0000	+	12.1244i	−1.09619	+	0.632886i	−0.935218	−	0.354073i	$-0.884797\pi$
$367$	−21.0000	+	12.1244i	−1.09619	+	0.632886i	−0.160973	+	0.986959i	$0.551463\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	22.0454	−	12.7279i	1.14454	−	0.660801i
$372$		0			0
$373$	12.0000	+	6.92820i	0.621336	+	0.358729i	0.777389	−	0.629020i	$-0.216544\pi$
$373$	12.0000	+	6.92820i	0.621336	+	0.358729i	−0.156053	+	0.987749i	$0.549877\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			8.48528i			0.437014i
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.89898	−	8.48528i	0.250326	−	0.433578i	−0.713289	−	0.700870i	$-0.752795\pi$
$383$	4.89898	−	8.48528i	0.250326	−	0.433578i	0.963616	+	0.267292i	$0.0861288\pi$
$384$		0			0
$385$	−12.0000	−	20.7846i	−0.611577	−	1.05928i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−13.4722	−	23.3345i	−0.683067	−	1.18311i	−0.974040	−	0.226376i	$-0.927312\pi$
$389$	−13.4722	−	23.3345i	−0.683067	−	1.18311i	0.290973	−	0.956731i	$-0.406021\pi$
$390$		0			0
$391$	−6.00000	−	3.46410i	−0.303433	−	0.175187i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	8.48528i		−	0.426941i
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.22474	−	0.707107i	−0.0611608	−	0.0353112i	0.469108	−	0.883141i	$-0.344576\pi$
$401$	−1.22474	−	0.707107i	−0.0611608	−	0.0353112i	−0.530269	+	0.847830i	$0.677909\pi$
$402$		0			0
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	0.134107	+	0.990967i	$0.457183\pi$
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	−0.925256	+	0.379344i	$0.876150\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	39.1918			1.92850
$414$		0			0
$415$		−	34.6410i		−	1.70046i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−17.1464	−	9.89949i	−0.837658	−	0.483622i	0.0188096	−	0.999823i	$-0.494012\pi$
$419$	−17.1464	−	9.89949i	−0.837658	−	0.483622i	−0.856467	+	0.516201i	$0.827346\pi$
$420$		0			0
$421$	21.0000	−	12.1244i	1.02348	−	0.590905i	0.108368	−	0.994111i	$-0.465437\pi$
$421$	21.0000	−	12.1244i	1.02348	−	0.590905i	0.915109	+	0.403206i	$0.132104\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.22474	−	0.707107i	0.0594089	−	0.0342997i
$426$		0			0
$427$	−24.0000	+	41.5692i	−1.16144	+	2.01168i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.6969			0.707927			0.353963	−	0.935259i	$-0.384834\pi$
$431$	14.6969			0.707927			0.353963	+	0.935259i	$0.384834\pi$
$432$		0			0
$433$	−22.0000			−1.05725			−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000			−1.05725			−0.528626	+	0.848855i	$0.677293\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.79796	+	16.9706i	−0.468700	+	0.811812i
$438$		0			0
$439$	−3.00000	+	1.73205i	−0.143182	+	0.0826663i	−0.569880	−	0.821728i	$-0.693010\pi$
$439$	−3.00000	+	1.73205i	−0.143182	+	0.0826663i	0.426698	+	0.904394i	$0.359677\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.44949	−	1.41421i	0.116379	−	0.0671913i	−0.440681	−	0.897664i	$-0.645263\pi$
$443$	2.44949	−	1.41421i	0.116379	−	0.0671913i	0.557059	+	0.830473i	$0.311930\pi$
$444$		0			0
$445$	15.0000	+	8.66025i	0.711068	+	0.410535i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	24.0416i		−	1.13459i	−0.823513	−	0.567297i	$-0.807989\pi$
$449$		−	24.0416i		−	1.13459i	0.823513	−	0.567297i	$-0.192011\pi$
$450$		0			0
$451$	−4.00000			−0.188353
$452$		0			0
$453$		0			0
$454$		0			0
$455$	14.6969	−	25.4558i	0.689003	−	1.19339i
$456$		0			0
$457$	−4.00000	−	6.92820i	−0.187112	−	0.324088i	0.757174	−	0.653213i	$-0.226579\pi$
$457$	−4.00000	−	6.92820i	−0.187112	−	0.324088i	−0.944286	+	0.329125i	$0.893246\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	8.57321	+	14.8492i	0.399294	+	0.691598i	0.993639	−	0.112612i	$-0.0359218\pi$
$461$	8.57321	+	14.8492i	0.399294	+	0.691598i	−0.594345	+	0.804210i	$0.702588\pi$
$462$		0			0
$463$	15.0000	+	8.66025i	0.697109	+	0.402476i	0.806270	−	0.591548i	$-0.201483\pi$
$463$	15.0000	+	8.66025i	0.697109	+	0.402476i	−0.109161	+	0.994024i	$0.534816\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			36.7696i			1.70149i	0.525577	+	0.850746i	$0.323849\pi$
$467$			36.7696i			1.70149i	−0.525577	+	0.850746i	$0.676151\pi$
$468$		0			0
$469$		−	13.8564i		−	0.639829i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	19.5959	+	11.3137i	0.901021	+	0.520205i
$474$		0			0
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.2474	−	21.2132i	−0.559600	−	0.969256i	−0.997530	−	0.0702467i	$-0.977621\pi$
$479$	−12.2474	−	21.2132i	−0.559600	−	0.969256i	0.437929	−	0.899009i	$-0.355712\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	19.5959			0.889805
$486$		0			0
$487$		−	10.3923i		−	0.470920i	−0.971884	−	0.235460i	$-0.924340\pi$
$487$		−	10.3923i		−	0.470920i	0.971884	−	0.235460i	$-0.0756597\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	34.2929	+	19.7990i	1.54761	+	0.893516i	0.998323	+	0.0578852i	$0.0184357\pi$
$491$	34.2929	+	19.7990i	1.54761	+	0.893516i	0.549292	+	0.835631i	$0.314898\pi$
$492$		0			0
$493$	−3.00000	+	1.73205i	−0.135113	+	0.0780076i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	44.0908	−	25.4558i	1.97774	−	1.14185i
$498$		0			0
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.6969			0.655304			0.327652	−	0.944798i	$-0.393743\pi$
$503$	14.6969			0.655304			0.327652	+	0.944798i	$0.393743\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$		0			0
$508$		0			0
$509$	20.8207	−	36.0624i	0.922860	−	1.59844i	0.127892	−	0.991788i	$-0.459179\pi$
$509$	20.8207	−	36.0624i	0.922860	−	1.59844i	0.794968	−	0.606652i	$-0.207488\pi$
$510$		0			0
$511$	12.0000	−	6.92820i	0.530849	−	0.306486i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.34847	−	4.24264i	0.323812	−	0.186953i
$516$		0			0
$517$	12.0000	+	6.92820i	0.527759	+	0.304702i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			26.8701i			1.17720i	0.808425	+	0.588599i	$0.200320\pi$
$521$			26.8701i			1.17720i	−0.808425	+	0.588599i	$0.799680\pi$
$522$		0			0
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.44949	−	4.24264i	0.106701	−	0.184812i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.44949	−	4.24264i	−0.106099	−	0.183769i
$534$		0			0
$535$	−24.0000	−	13.8564i	−1.03761	−	0.599065i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	14.1421i		−	0.609145i
$540$		0			0
$541$		−	10.3923i		−	0.446800i	−0.974727	−	0.223400i	$-0.928284\pi$
$541$		−	10.3923i		−	0.446800i	0.974727	−	0.223400i	$-0.0717156\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	22.0454	+	12.7279i	0.944322	+	0.545204i
$546$		0			0
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	0.938779	−	0.344519i	$-0.111958\pi$
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	−0.767752	+	0.640747i	$0.778625\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.89898	+	8.48528i	0.208704	+	0.361485i
$552$		0			0
$553$	6.00000	−	10.3923i	0.255146	−	0.441926i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.34847			−0.311365			−0.155682	−	0.987807i	$-0.549758\pi$
$557$	−7.34847			−0.311365			−0.155682	+	0.987807i	$0.549758\pi$
$558$		0			0
$559$			27.7128i			1.17213i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.2474	+	7.07107i	0.516168	+	0.298010i	0.735366	−	0.677671i	$-0.237010\pi$
$563$	12.2474	+	7.07107i	0.516168	+	0.298010i	−0.219197	+	0.975681i	$0.570344\pi$
$564$		0			0
$565$	39.0000	−	22.5167i	1.64074	−	0.947283i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.57321	−	4.94975i	0.359408	−	0.207504i	−0.309413	−	0.950928i	$-0.600133\pi$
$569$	8.57321	−	4.94975i	0.359408	−	0.207504i	0.668821	+	0.743423i	$0.266799\pi$
$570$		0			0
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	0.0554391	+	0.998462i	$0.482344\pi$
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	−0.892413	+	0.451219i	$0.850989\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.89898			0.204302
$576$		0			0
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	24.4949	−	42.4264i	1.01622	−	1.76014i
$582$		0			0
$583$	−18.0000	+	10.3923i	−0.745484	+	0.430405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.5959	+	11.3137i	−0.808810	+	0.466967i	−0.846542	−	0.532321i	$-0.821320\pi$
$587$	−19.5959	+	11.3137i	−0.808810	+	0.466967i	0.0377324	+	0.999288i	$0.487987\pi$
$588$		0			0
$589$	−12.0000	−	6.92820i	−0.494451	−	0.285472i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	7.07107i		−	0.290374i	−0.989404	−	0.145187i	$-0.953622\pi$
$593$		−	7.07107i		−	0.290374i	0.989404	−	0.145187i	$-0.0463784\pi$
$594$		0			0
$595$	12.0000			0.491952
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.44949	+	4.24264i	−0.100083	+	0.173350i	−0.911719	−	0.410815i	$-0.865244\pi$
$599$	−2.44949	+	4.24264i	−0.100083	+	0.173350i	0.811635	+	0.584164i	$0.198578\pi$
$600$		0			0
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	0.949799	−	0.312861i	$-0.101287\pi$
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	−0.745845	+	0.666120i	$0.767954\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.67423	−	6.36396i	−0.149379	−	0.258732i
$606$		0			0
$607$	−39.0000	−	22.5167i	−1.58296	−	0.913923i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−39.0000	−	22.5167i	−1.58296	−	0.913923i	−0.588537	−	0.808470i	$-0.700296\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			16.9706i			0.686555i
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.8207	+	12.0208i	0.838208	+	0.483940i	0.856655	−	0.515890i	$-0.172539\pi$
$617$	20.8207	+	12.0208i	0.838208	+	0.483940i	−0.0184465	+	0.999830i	$0.505872\pi$
$618$		0			0
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	0.935146	−	0.354262i	$-0.115268\pi$
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	−0.774373	+	0.632730i	$0.781934\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.2474	+	21.2132i	0.490684	+	0.849889i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$			31.1769i			1.24113i	0.784154	+	0.620567i	$0.213097\pi$
$631$			31.1769i			1.24113i	−0.784154	+	0.620567i	$0.786903\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	22.0454	+	12.7279i	0.874845	+	0.505092i
$636$		0			0
$637$	15.0000	−	8.66025i	0.594322	−	0.343132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−13.4722	+	7.77817i	−0.532120	+	0.307219i	−0.741879	−	0.670534i	$-0.766065\pi$
$641$	−13.4722	+	7.77817i	−0.532120	+	0.307219i	0.209760	+	0.977753i	$0.432732\pi$
$642$		0			0
$643$	16.0000	−	27.7128i	0.630978	−	1.09289i	−0.356374	−	0.934344i	$-0.615987\pi$
$643$	16.0000	−	27.7128i	0.630978	−	1.09289i	0.987352	−	0.158543i	$-0.0506797\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.6969			0.577796			0.288898	−	0.957360i	$-0.406711\pi$
$647$	14.6969			0.577796			0.288898	+	0.957360i	$0.406711\pi$
$648$		0			0
$649$	−32.0000			−1.25611
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.57321	+	14.8492i	−0.335496	+	0.581096i	−0.983580	−	0.180473i	$-0.942237\pi$
$653$	−8.57321	+	14.8492i	−0.335496	+	0.581096i	0.648084	+	0.761569i	$0.275570\pi$
$654$		0			0
$655$	−12.0000	+	6.92820i	−0.468879	+	0.270707i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.79796	−	5.65685i	0.381674	−	0.220360i	−0.296872	−	0.954917i	$-0.595944\pi$
$659$	9.79796	−	5.65685i	0.381674	−	0.220360i	0.678546	+	0.734557i	$0.262610\pi$
$660$		0			0
$661$	12.0000	+	6.92820i	0.466746	+	0.269476i	0.714877	−	0.699251i	$-0.246483\pi$
$661$	12.0000	+	6.92820i	0.466746	+	0.269476i	−0.248131	+	0.968727i	$0.579816\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	33.9411i		−	1.31618i
$666$		0			0
$667$	−12.0000			−0.464642
$668$		0			0
$669$		0			0
$670$		0			0
$671$	19.5959	−	33.9411i	0.756492	−	1.31028i
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.57321	+	14.8492i	0.329495	+	0.570703i	0.982412	−	0.186727i	$-0.0597881\pi$
$677$	8.57321	+	14.8492i	0.329495	+	0.570703i	−0.652916	+	0.757430i	$0.726455\pi$
$678$		0			0
$679$	24.0000	+	13.8564i	0.921035	+	0.531760i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			36.7696i			1.40695i	0.710721	+	0.703474i	$0.248369\pi$
$683$			36.7696i			1.40695i	−0.710721	+	0.703474i	$0.751631\pi$
$684$		0			0
$685$			24.2487i			0.926496i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−22.0454	−	12.7279i	−0.839863	−	0.484895i
$690$		0			0
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.89898	−	8.48528i	−0.185829	−	0.321865i
$696$		0			0
$697$	1.00000	−	1.73205i	0.0378777	−	0.0656061i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	7.34847			0.277548			0.138774	−	0.990324i	$-0.455684\pi$
$701$	7.34847			0.277548			0.138774	+	0.990324i	$0.455684\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.34847	−	4.24264i	−0.276368	−	0.159561i
$708$		0			0
$709$	3.00000	−	1.73205i	0.112667	−	0.0650485i	−0.442607	−	0.896716i	$-0.645946\pi$
$709$	3.00000	−	1.73205i	0.112667	−	0.0650485i	0.555275	+	0.831667i	$0.312613\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.6969	−	8.48528i	0.550405	−	0.317776i
$714$		0			0
$715$	−12.0000	+	20.7846i	−0.448775	+	0.777300i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−44.0908			−1.64431			−0.822155	−	0.569264i	$-0.807228\pi$
$719$	−44.0908			−1.64431			−0.822155	+	0.569264i	$0.807228\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.22474	−	2.12132i	0.0454859	−	0.0787839i
$726$		0			0
$727$	−21.0000	+	12.1244i	−0.778847	+	0.449667i	−0.836021	−	0.548697i	$-0.815124\pi$
$727$	−21.0000	+	12.1244i	−0.778847	+	0.449667i	0.0571746	+	0.998364i	$0.481791\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.79796	+	5.65685i	−0.362391	+	0.209226i
$732$		0			0
$733$	−33.0000	−	19.0526i	−1.21888	−	0.703722i	−0.254204	−	0.967151i	$-0.581813\pi$
$733$	−33.0000	−	19.0526i	−1.21888	−	0.703722i	−0.964679	+	0.263428i	$0.915147\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			11.3137i			0.416746i
$738$		0			0
$739$	40.0000			1.47142			0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000			1.47142			0.735712	+	0.677295i	$0.236848\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.5959	−	33.9411i	0.718905	−	1.24518i	−0.242530	−	0.970144i	$-0.577977\pi$
$743$	19.5959	−	33.9411i	0.718905	−	1.24518i	0.961434	−	0.275035i	$-0.0886895\pi$
$744$		0			0
$745$	−21.0000	−	36.3731i	−0.769380	−	1.33261i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−19.5959	−	33.9411i	−0.716019	−	1.24018i
$750$		0			0
$751$	−3.00000	−	1.73205i	−0.109472	−	0.0632034i	0.444265	−	0.895896i	$-0.353465\pi$
$751$	−3.00000	−	1.73205i	−0.109472	−	0.0632034i	−0.553736	+	0.832692i	$0.686798\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	8.48528i		−	0.308811i
$756$		0			0
$757$		−	10.3923i		−	0.377715i	−0.982005	−	0.188857i	$-0.939522\pi$
$757$		−	10.3923i		−	0.377715i	0.982005	−	0.188857i	$-0.0604784\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.9217	−	9.19239i	−0.577161	−	0.333224i	0.182844	−	0.983142i	$-0.441470\pi$
$761$	−15.9217	−	9.19239i	−0.577161	−	0.333224i	−0.760004	+	0.649918i	$0.774803\pi$
$762$		0			0
$763$	18.0000	+	31.1769i	0.651644	+	1.12868i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−19.5959	−	33.9411i	−0.707568	−	1.22554i
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	22.0454			0.792918			0.396459	−	0.918052i	$-0.370239\pi$
$773$	22.0454			0.792918			0.396459	+	0.918052i	$0.370239\pi$
$774$		0			0
$775$			3.46410i			0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.89898	−	2.82843i	−0.175524	−	0.101339i
$780$		0			0
$781$	−36.0000	+	20.7846i	−1.28818	+	0.743732i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−29.3939	+	16.9706i	−1.04911	+	0.605705i
$786$		0			0
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	−0.630905	−	0.775860i	$-0.717316\pi$
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	0.987367	+	0.158450i	$0.0506498\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	63.6867			2.26444
$792$		0			0
$793$	48.0000			1.70453
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.12372	−	10.6066i	0.216913	−	0.375705i	−0.736949	−	0.675948i	$-0.763734\pi$
$797$	6.12372	−	10.6066i	0.216913	−	0.375705i	0.953863	+	0.300243i	$0.0970677\pi$
$798$		0			0
$799$	−6.00000	+	3.46410i	−0.212265	+	0.122551i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.79796	+	5.65685i	−0.345762	+	0.199626i
$804$		0			0
$805$	36.0000	+	20.7846i	1.26883	+	0.732561i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			1.41421i			0.0497211i	0.999691	+	0.0248606i	$0.00791417\pi$
$809$			1.41421i			0.0497211i	−0.999691	+	0.0248606i	$0.992086\pi$
$810$		0			0
$811$	4.00000			0.140459			0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000			0.140459			0.0702295	+	0.997531i	$0.477627\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−19.5959	+	33.9411i	−0.686415	+	1.18891i
$816$		0			0
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.22474	+	2.12132i	0.0427439	+	0.0740346i	0.886606	−	0.462526i	$-0.153057\pi$
$821$	1.22474	+	2.12132i	0.0427439	+	0.0740346i	−0.843862	+	0.536560i	$0.819723\pi$
$822$		0			0
$823$	15.0000	+	8.66025i	0.522867	+	0.301877i	0.738107	−	0.674684i	$-0.235720\pi$
$823$	15.0000	+	8.66025i	0.522867	+	0.301877i	−0.215240	+	0.976561i	$0.569053\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	5.65685i		−	0.196708i	−0.995151	−	0.0983540i	$-0.968642\pi$
$827$		−	5.65685i		−	0.196708i	0.995151	−	0.0983540i	$-0.0313578\pi$
$828$		0			0
$829$		−	10.3923i		−	0.360940i	−0.983581	−	0.180470i	$-0.942238\pi$
$829$		−	10.3923i		−	0.360940i	0.983581	−	0.180470i	$-0.0577618\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.12372	+	3.53553i	0.212174	+	0.122499i
$834$		0			0
$835$	−24.0000	−	41.5692i	−0.830554	−	1.43856i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.44949	+	4.24264i	0.0845658	+	0.146472i	0.905206	−	0.424973i	$-0.139716\pi$
$839$	2.44949	+	4.24264i	0.0845658	+	0.146472i	−0.820640	+	0.571445i	$0.806383\pi$
$840$		0			0
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.44949			0.0842650
$846$		0			0
$847$		−	10.3923i		−	0.357084i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	12.0000	−	6.92820i	0.410872	−	0.237217i	−0.280292	−	0.959915i	$-0.590431\pi$
$853$	12.0000	−	6.92820i	0.410872	−	0.237217i	0.691164	+	0.722698i	$0.257098\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.22474	−	0.707107i	0.0418365	−	0.0241543i	−0.478936	−	0.877850i	$-0.658977\pi$
$857$	1.22474	−	0.707107i	0.0418365	−	0.0241543i	0.520772	+	0.853696i	$0.325644\pi$
$858$		0			0
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−6.00000			−0.204006
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.89898	+	8.48528i	−0.166186	+	0.287843i
$870$		0			0
$871$	−12.0000	+	6.92820i	−0.406604	+	0.234753i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	29.3939	−	16.9706i	0.993694	−	0.573710i
$876$		0			0
$877$	48.0000	+	27.7128i	1.62084	+	0.935795i	0.986694	+	0.162585i	$0.0519833\pi$
$877$	48.0000	+	27.7128i	1.62084	+	0.935795i	0.634150	+	0.773210i	$0.281350\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			43.8406i			1.47703i	0.674238	+	0.738514i	$0.264472\pi$
$881$			43.8406i			1.47703i	−0.674238	+	0.738514i	$0.735528\pi$
$882$		0			0
$883$	40.0000			1.34611			0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000			1.34611			0.673054	+	0.739594i	$0.264982\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.89898	−	8.48528i	0.164492	−	0.284908i	−0.771983	−	0.635643i	$-0.780735\pi$
$887$	4.89898	−	8.48528i	0.164492	−	0.284908i	0.936475	+	0.350735i	$0.114068\pi$
$888$		0			0
$889$	18.0000	+	31.1769i	0.603701	+	1.04564i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.79796	+	16.9706i	0.327876	+	0.567898i
$894$		0			0
$895$	12.0000	+	6.92820i	0.401116	+	0.231584i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	8.48528i		−	0.283000i
$900$		0			0
$901$		−	10.3923i		−	0.346218i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−22.0454	−	12.7279i	−0.732814	−	0.423090i
$906$		0			0
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	0.924762	−	0.380547i	$-0.124264\pi$
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	−0.791944	+	0.610594i	$0.790931\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−19.5959	−	33.9411i	−0.649242	−	1.12452i	−0.983304	−	0.181969i	$-0.941753\pi$
$911$	−19.5959	−	33.9411i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$912$		0			0
$913$	−20.0000	+	34.6410i	−0.661903	+	1.14645i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−19.5959			−0.647114
$918$		0			0
$919$			10.3923i			0.342811i	0.985201	+	0.171405i	$0.0548307\pi$
$919$			10.3923i			0.342811i	−0.985201	+	0.171405i	$0.945169\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−44.0908	−	25.4558i	−1.45127	−	0.837889i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.22474	−	0.707107i	0.0401826	−	0.0231994i	−0.479774	−	0.877392i	$-0.659281\pi$
$929$	1.22474	−	0.707107i	0.0401826	−	0.0231994i	0.519957	+	0.854193i	$0.325948\pi$
$930$		0			0
$931$	10.0000	−	17.3205i	0.327737	−	0.567657i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.79796			−0.320428
$936$		0			0
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.22474	+	2.12132i	−0.0399255	+	0.0691531i	−0.885298	−	0.465025i	$-0.846045\pi$
$941$	−1.22474	+	2.12132i	−0.0399255	+	0.0691531i	0.845372	+	0.534178i	$0.179379\pi$
$942$		0			0
$943$	6.00000	−	3.46410i	0.195387	−	0.112807i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.5959	+	11.3137i	−0.636782	+	0.367646i	−0.783374	−	0.621551i	$-0.786503\pi$
$947$	−19.5959	+	11.3137i	−0.636782	+	0.367646i	0.146592	+	0.989197i	$0.453170\pi$
$948$		0			0
$949$	−12.0000	−	6.92820i	−0.389536	−	0.224899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			26.8701i			0.870407i	0.900332	+	0.435203i	$0.143323\pi$
$953$			26.8701i			0.870407i	−0.900332	+	0.435203i	$0.856677\pi$
$954$		0			0
$955$	−48.0000			−1.55324
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.1464	+	29.6985i	−0.553687	+	0.959014i
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−17.1464	−	29.6985i	−0.551963	−	0.956028i
$966$		0			0
$967$	−39.0000	−	22.5167i	−1.25416	−	0.724087i	−0.282223	−	0.959349i	$-0.591072\pi$
$967$	−39.0000	−	22.5167i	−1.25416	−	0.724087i	−0.971932	+	0.235262i	$0.924405\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	31.1127i		−	0.998454i	−0.866471	−	0.499227i	$-0.833617\pi$
$971$		−	31.1127i		−	0.998454i	0.866471	−	0.499227i	$-0.166383\pi$
$972$		0			0
$973$		−	13.8564i		−	0.444216i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.8207	+	12.0208i	0.666112	+	0.384580i	0.794602	−	0.607131i	$-0.207680\pi$
$977$	20.8207	+	12.0208i	0.666112	+	0.384580i	−0.128490	+	0.991711i	$0.541013\pi$
$978$		0			0
$979$	−10.0000	−	17.3205i	−0.319601	−	0.553566i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24.4949	+	42.4264i	0.781266	+	1.35319i	0.931205	+	0.364497i	$0.118759\pi$
$983$	24.4949	+	42.4264i	0.781266	+	1.35319i	−0.149939	+	0.988695i	$0.547908\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−39.1918			−1.24623
$990$		0			0
$991$		−	51.9615i		−	1.65061i	−0.564686	−	0.825306i	$-0.691003\pi$
$991$		−	51.9615i		−	1.65061i	0.564686	−	0.825306i	$-0.308997\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	22.0454	+	12.7279i	0.698886	+	0.403502i
$996$		0			0
$997$	12.0000	−	6.92820i	0.380044	−	0.219418i	−0.297794	−	0.954630i	$-0.596251\pi$
$997$	12.0000	−	6.92820i	0.380044	−	0.219418i	0.677837	+	0.735212i	$0.262917\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.p.a.2159.1		4
3.2	odd	2	inner	2592.2.p.a.2159.2		4
4.3	odd	2		648.2.l.c.539.2		4
8.3	odd	2		2592.2.p.c.2159.2		4
8.5	even	2		648.2.l.a.539.1		4
9.2	odd	6		2592.2.p.c.431.2		4
9.4	even	3		288.2.f.a.143.3		4
9.5	odd	6		288.2.f.a.143.1		4
9.7	even	3		2592.2.p.c.431.1		4
12.11	even	2		648.2.l.c.539.1		4
24.5	odd	2		648.2.l.a.539.2		4
24.11	even	2		2592.2.p.c.2159.1		4
36.7	odd	6		648.2.l.a.107.1		4
36.11	even	6		648.2.l.a.107.2		4
36.23	even	6		72.2.f.a.35.3	yes	4
36.31	odd	6		72.2.f.a.35.2	yes	4
45.4	even	6		7200.2.b.c.4751.4		4
45.13	odd	12		7200.2.m.c.3599.4		8
45.14	odd	6		7200.2.b.c.4751.3		4
45.22	odd	12		7200.2.m.c.3599.7		8
45.23	even	12		7200.2.m.c.3599.1		8
45.32	even	12		7200.2.m.c.3599.6		8
72.5	odd	6		72.2.f.a.35.1	✓	4
72.11	even	6	inner	2592.2.p.a.431.1		4
72.13	even	6		72.2.f.a.35.4	yes	4
72.29	odd	6		648.2.l.c.107.2		4
72.43	odd	6	inner	2592.2.p.a.431.2		4
72.59	even	6		288.2.f.a.143.4		4
72.61	even	6		648.2.l.c.107.1		4
72.67	odd	6		288.2.f.a.143.2		4
144.5	odd	12		2304.2.c.i.2303.3		8
144.13	even	12		2304.2.c.i.2303.4		8
144.59	even	12		2304.2.c.i.2303.1		8
144.67	odd	12		2304.2.c.i.2303.2		8
144.77	odd	12		2304.2.c.i.2303.8		8
144.85	even	12		2304.2.c.i.2303.7		8
144.131	even	12		2304.2.c.i.2303.6		8
144.139	odd	12		2304.2.c.i.2303.5		8
180.23	odd	12		1800.2.m.c.899.2		8
180.59	even	6		1800.2.b.c.251.2		4
180.67	even	12		1800.2.m.c.899.1		8
180.103	even	12		1800.2.m.c.899.8		8
180.139	odd	6		1800.2.b.c.251.3		4
180.167	odd	12		1800.2.m.c.899.7		8
360.13	odd	12		1800.2.m.c.899.5		8
360.59	even	6		7200.2.b.c.4751.1		4
360.67	even	12		7200.2.m.c.3599.3		8
360.77	even	12		1800.2.m.c.899.6		8
360.139	odd	6		7200.2.b.c.4751.2		4
360.149	odd	6		1800.2.b.c.251.4		4
360.157	odd	12		1800.2.m.c.899.4		8
360.203	odd	12		7200.2.m.c.3599.5		8
360.229	even	6		1800.2.b.c.251.1		4
360.283	even	12		7200.2.m.c.3599.8		8
360.293	even	12		1800.2.m.c.899.3		8
360.347	odd	12		7200.2.m.c.3599.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.f.a.35.1	✓	4	72.5	odd	6
72.2.f.a.35.2	yes	4	36.31	odd	6
72.2.f.a.35.3	yes	4	36.23	even	6
72.2.f.a.35.4	yes	4	72.13	even	6
288.2.f.a.143.1		4	9.5	odd	6
288.2.f.a.143.2		4	72.67	odd	6
288.2.f.a.143.3		4	9.4	even	3
288.2.f.a.143.4		4	72.59	even	6
648.2.l.a.107.1		4	36.7	odd	6
648.2.l.a.107.2		4	36.11	even	6
648.2.l.a.539.1		4	8.5	even	2
648.2.l.a.539.2		4	24.5	odd	2
648.2.l.c.107.1		4	72.61	even	6
648.2.l.c.107.2		4	72.29	odd	6
648.2.l.c.539.1		4	12.11	even	2
648.2.l.c.539.2		4	4.3	odd	2
1800.2.b.c.251.1		4	360.229	even	6
1800.2.b.c.251.2		4	180.59	even	6
1800.2.b.c.251.3		4	180.139	odd	6
1800.2.b.c.251.4		4	360.149	odd	6
1800.2.m.c.899.1		8	180.67	even	12
1800.2.m.c.899.2		8	180.23	odd	12
1800.2.m.c.899.3		8	360.293	even	12
1800.2.m.c.899.4		8	360.157	odd	12
1800.2.m.c.899.5		8	360.13	odd	12
1800.2.m.c.899.6		8	360.77	even	12
1800.2.m.c.899.7		8	180.167	odd	12
1800.2.m.c.899.8		8	180.103	even	12
2304.2.c.i.2303.1		8	144.59	even	12
2304.2.c.i.2303.2		8	144.67	odd	12
2304.2.c.i.2303.3		8	144.5	odd	12
2304.2.c.i.2303.4		8	144.13	even	12
2304.2.c.i.2303.5		8	144.139	odd	12
2304.2.c.i.2303.6		8	144.131	even	12
2304.2.c.i.2303.7		8	144.85	even	12
2304.2.c.i.2303.8		8	144.77	odd	12
2592.2.p.a.431.1		4	72.11	even	6	inner
2592.2.p.a.431.2		4	72.43	odd	6	inner
2592.2.p.a.2159.1		4	1.1	even	1	trivial
2592.2.p.a.2159.2		4	3.2	odd	2	inner
2592.2.p.c.431.1		4	9.7	even	3
2592.2.p.c.431.2		4	9.2	odd	6
2592.2.p.c.2159.1		4	24.11	even	2
2592.2.p.c.2159.2		4	8.3	odd	2
7200.2.b.c.4751.1		4	360.59	even	6
7200.2.b.c.4751.2		4	360.139	odd	6
7200.2.b.c.4751.3		4	45.14	odd	6
7200.2.b.c.4751.4		4	45.4	even	6
7200.2.m.c.3599.1		8	45.23	even	12
7200.2.m.c.3599.2		8	360.347	odd	12
7200.2.m.c.3599.3		8	360.67	even	12
7200.2.m.c.3599.4		8	45.13	odd	12
7200.2.m.c.3599.5		8	360.203	odd	12
7200.2.m.c.3599.6		8	45.32	even	12
7200.2.m.c.3599.7		8	45.22	odd	12
7200.2.m.c.3599.8		8	360.283	even	12

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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 2.12132i) q^{5} +(-3.00000 + 1.73205i) q^{7} +(2.44949 - 1.41421i) q^{11} +(3.00000 + 1.73205i) q^{13} +1.41421i q^{17} +4.00000 q^{19} +(-2.44949 + 4.24264i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.22474 + 2.12132i) q^{29} +(-3.00000 - 1.73205i) q^{31} -8.48528i q^{35} +(-1.22474 - 0.707107i) q^{41} +(4.00000 + 6.92820i) q^{43} +(2.44949 + 4.24264i) q^{47} +(2.50000 - 4.33013i) q^{49} -7.34847 q^{53} +6.92820i q^{55} +(-9.79796 - 5.65685i) q^{59} +(12.0000 - 6.92820i) q^{61} +(-7.34847 + 4.24264i) q^{65} +(-2.00000 + 3.46410i) q^{67} -14.6969 q^{71} -4.00000 q^{73} +(-4.89898 + 8.48528i) q^{77} +(-3.00000 + 1.73205i) q^{79} +(-12.2474 + 7.07107i) q^{83} +(-3.00000 - 1.73205i) q^{85} -7.07107i q^{89} -12.0000 q^{91} +(-4.89898 + 8.48528i) q^{95} +(-4.00000 - 6.92820i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{7} + 12 q^{13} + 16 q^{19} - 2 q^{25} - 12 q^{31} + 16 q^{43} + 10 q^{49} + 48 q^{61} - 8 q^{67} - 16 q^{73} - 12 q^{79} - 12 q^{85} - 48 q^{91} - 16 q^{97}+O(q^{100}) \) 4 * q - 12 * q^7 + 12 * q^13 + 16 * q^19 - 2 * q^25 - 12 * q^31 + 16 * q^43 + 10 * q^49 + 48 * q^61 - 8 * q^67 - 16 * q^73 - 12 * q^79 - 12 * q^85 - 48 * q^91 - 16 * q^97

Introduction

L-functions

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