LMFDB - Embedded newform 784.2.p.f.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(31,784)] 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("784.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,2,0,6,0,0,0,-1,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	784.31
Dual form			784.2.p.f.607.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{3} +(3.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} -3.46410i q^{13} -6.92820i q^{15} +(1.00000 + 1.73205i) q^{19} +(-3.00000 + 1.73205i) q^{23} +(3.50000 - 6.06218i) q^{25} +4.00000 q^{27} +6.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(-6.00000 + 3.46410i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-6.00000 - 3.46410i) q^{39} +6.92820i q^{41} -10.3923i q^{43} +(-3.00000 - 1.73205i) q^{45} +(-3.00000 + 5.19615i) q^{53} -12.0000 q^{55} +4.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-3.00000 + 1.73205i) q^{61} +(-6.00000 - 10.3923i) q^{65} +(-3.00000 - 1.73205i) q^{67} +6.92820i q^{69} +3.46410i q^{71} +(6.00000 + 3.46410i) q^{73} +(-7.00000 - 12.1244i) q^{75} +(3.00000 - 1.73205i) q^{79} +(5.50000 - 9.52628i) q^{81} +6.00000 q^{83} +(6.00000 - 10.3923i) q^{87} +(6.00000 - 3.46410i) q^{89} +(8.00000 + 13.8564i) q^{93} +(6.00000 + 3.46410i) q^{95} -13.8564i q^{97} +3.46410i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 6 q^{5} - q^{9} - 6 q^{11} + 2 q^{19} - 6 q^{23} + 7 q^{25} + 8 q^{27} + 12 q^{29} - 8 q^{31} - 12 q^{33} + 2 q^{37} - 12 q^{39} - 6 q^{45} - 6 q^{53} - 24 q^{55} + 8 q^{57} + 6 q^{59}+ \cdots + 12 q^{95}+O(q^{100}) $ 2 * q + 2 * q^3 + 6 * q^5 - q^9 - 6 * q^11 + 2 * q^19 - 6 * q^23 + 7 * q^25 + 8 * q^27 + 12 * q^29 - 8 * q^31 - 12 * q^33 + 2 * q^37 - 12 * q^39 - 6 * q^45 - 6 * q^53 - 24 * q^55 + 8 * q^57 + 6 * q^59 - 6 * q^61 - 12 * q^65 - 6 * q^67 + 12 * q^73 - 14 * q^75 + 6 * q^79 + 11 * q^81 + 12 * q^83 + 12 * q^87 + 12 * q^89 + 16 * q^93 + 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$		0			0
$5$	3.00000	−	1.73205i	1.34164	−	0.774597i	0.354593	−	0.935021i	$-0.384620\pi$
$5$	3.00000	−	1.73205i	1.34164	−	0.774597i	0.987048	+	0.160424i	$0.0512862\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$		0			0
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$		0			0
$15$		−	6.92820i		−	1.78885i
$16$		0			0
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000	+	1.73205i	−0.625543	+	0.361158i	−0.779024	−	0.626994i	$-0.784285\pi$
$23$	−3.00000	+	1.73205i	−0.625543	+	0.361158i	0.153481	+	0.988152i	$0.450952\pi$
$24$		0			0
$25$	3.50000	−	6.06218i	0.700000	−	1.21244i
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$		0			0
$33$	−6.00000	+	3.46410i	−1.04447	+	0.603023i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	−6.00000	−	3.46410i	−0.960769	−	0.554700i
$40$		0			0
$41$			6.92820i			1.08200i	0.841021	+	0.541002i	$0.181955\pi$
$41$			6.92820i			1.08200i	−0.841021	+	0.541002i	$0.818045\pi$
$42$		0			0
$43$		−	10.3923i		−	1.58481i	−0.609994	−	0.792406i	$-0.708828\pi$
$43$		−	10.3923i		−	1.58481i	0.609994	−	0.792406i	$-0.291172\pi$
$44$		0			0
$45$	−3.00000	−	1.73205i	−0.447214	−	0.258199i
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$	−12.0000			−1.61808
$56$		0			0
$57$	4.00000			0.529813
$58$		0			0
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	−3.00000	+	1.73205i	−0.384111	+	0.221766i	−0.679605	−	0.733578i	$-0.737849\pi$
$61$	−3.00000	+	1.73205i	−0.384111	+	0.221766i	0.295495	+	0.955344i	$0.404516\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.00000	−	10.3923i	−0.744208	−	1.28901i
$66$		0			0
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	0.305424	−	0.952217i	$-0.401202\pi$
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	−0.671932	+	0.740613i	$0.734535\pi$
$68$		0			0
$69$			6.92820i			0.834058i
$70$		0			0
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$		0			0
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	0.808184	−	0.588930i	$-0.200451\pi$
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	−0.105937	+	0.994373i	$0.533784\pi$
$74$		0			0
$75$	−7.00000	−	12.1244i	−0.808290	−	1.40000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.00000	−	1.73205i	0.337526	−	0.194871i	−0.321651	−	0.946858i	$-0.604238\pi$
$79$	3.00000	−	1.73205i	0.337526	−	0.194871i	0.659178	+	0.751987i	$0.270905\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.00000	−	10.3923i	0.643268	−	1.11417i
$88$		0			0
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	−0.147073	−	0.989126i	$-0.546985\pi$
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	0.783072	+	0.621932i	$0.213652\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	8.00000	+	13.8564i	0.829561	+	1.43684i
$94$		0			0
$95$	6.00000	+	3.46410i	0.615587	+	0.355409i
$96$		0			0
$97$		−	13.8564i		−	1.40690i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$		−	13.8564i		−	1.40690i	0.710742	−	0.703452i	$-0.248359\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	9.00000	+	5.19615i	0.895533	+	0.517036i	0.875748	−	0.482768i	$-0.160368\pi$
$101$	9.00000	+	5.19615i	0.895533	+	0.517036i	0.0197851	+	0.999804i	$0.493702\pi$
$102$		0			0
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000	+	5.19615i	−0.870063	+	0.502331i	−0.867369	−	0.497665i	$-0.834191\pi$
$107$	−9.00000	+	5.19615i	−0.870063	+	0.502331i	−0.00269372	+	0.999996i	$0.500857\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	−6.00000	+	10.3923i	−0.559503	+	0.969087i
$116$		0			0
$117$	−3.00000	+	1.73205i	−0.277350	+	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		0			0
$123$	12.0000	+	6.92820i	1.08200	+	0.624695i
$124$		0			0
$125$		−	6.92820i		−	0.619677i
$126$		0			0
$127$			10.3923i			0.922168i	0.887357	+	0.461084i	$0.152539\pi$
$127$			10.3923i			0.922168i	−0.887357	+	0.461084i	$0.847461\pi$
$128$		0			0
$129$	−18.0000	−	10.3923i	−1.58481	−	0.914991i
$130$		0			0
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	12.0000	−	6.92820i	1.03280	−	0.596285i
$136$		0			0
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.00000	+	10.3923i	−0.501745	+	0.869048i
$144$		0			0
$145$	18.0000	−	10.3923i	1.49482	−	0.863034i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	3.00000	+	1.73205i	0.244137	+	0.140952i	0.617076	−	0.786903i	$-0.288317\pi$
$151$	3.00000	+	1.73205i	0.244137	+	0.140952i	−0.372940	+	0.927855i	$0.621650\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			27.7128i			2.22595i
$156$		0			0
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	0.0958404	−	0.995397i	$-0.469446\pi$
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	−0.814119	+	0.580699i	$0.802779\pi$
$158$		0			0
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	15.0000	−	8.66025i	1.17489	−	0.678323i	0.220064	−	0.975486i	$-0.429374\pi$
$163$	15.0000	−	8.66025i	1.17489	−	0.678323i	0.954827	+	0.297162i	$0.0960402\pi$
$164$		0			0
$165$	−12.0000	+	20.7846i	−0.934199	+	1.61808i
$166$		0			0
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$		0			0
$173$	−3.00000	+	1.73205i	−0.228086	+	0.131685i	−0.609689	−	0.792641i	$-0.708706\pi$
$173$	−3.00000	+	1.73205i	−0.228086	+	0.131685i	0.381603	+	0.924326i	$0.375372\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$		0			0
$179$	9.00000	+	5.19615i	0.672692	+	0.388379i	0.797096	−	0.603853i	$-0.206369\pi$
$179$	9.00000	+	5.19615i	0.672692	+	0.388379i	−0.124404	+	0.992232i	$0.539702\pi$
$180$		0			0
$181$			17.3205i			1.28742i	0.765268	+	0.643712i	$0.222606\pi$
$181$			17.3205i			1.28742i	−0.765268	+	0.643712i	$0.777394\pi$
$182$		0			0
$183$			6.92820i			0.512148i
$184$		0			0
$185$	6.00000	+	3.46410i	0.441129	+	0.254686i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−21.0000	+	12.1244i	−1.51951	+	0.877288i	−0.519771	+	0.854306i	$0.673983\pi$
$191$	−21.0000	+	12.1244i	−1.51951	+	0.877288i	−0.999736	+	0.0229818i	$0.992684\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$		0			0
$195$	−24.0000			−1.71868
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$		0			0
$201$	−6.00000	+	3.46410i	−0.423207	+	0.244339i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	12.0000	+	20.7846i	0.838116	+	1.45166i
$206$		0			0
$207$	3.00000	+	1.73205i	0.208514	+	0.120386i
$208$		0			0
$209$		−	6.92820i		−	0.479234i
$210$		0			0
$211$			3.46410i			0.238479i	0.992866	+	0.119239i	$0.0380456\pi$
$211$			3.46410i			0.238479i	−0.992866	+	0.119239i	$0.961954\pi$
$212$		0			0
$213$	6.00000	+	3.46410i	0.411113	+	0.237356i
$214$		0			0
$215$	−18.0000	−	31.1769i	−1.22759	−	2.12625i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	12.0000	−	6.92820i	0.810885	−	0.468165i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$	−7.00000			−0.466667
$226$		0			0
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	−9.00000	+	5.19615i	−0.594737	+	0.343371i	−0.766968	−	0.641685i	$-0.778236\pi$
$229$	−9.00000	+	5.19615i	−0.594737	+	0.343371i	0.172231	+	0.985057i	$0.444902\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	6.92820i		−	0.450035i
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$	24.0000	+	13.8564i	1.54598	+	0.892570i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$	24.0000	+	13.8564i	1.54598	+	0.892570i	0.547533	+	0.836784i	$0.315567\pi$
$242$		0			0
$243$	−5.00000	−	8.66025i	−0.320750	−	0.555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.00000	−	3.46410i	0.381771	−	0.220416i
$248$		0			0
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$		0			0
$251$	−30.0000			−1.89358			−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000			−1.89358			−0.946792	+	0.321847i	$0.895696\pi$
$252$		0			0
$253$	12.0000			0.754434
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−24.0000	+	13.8564i	−1.49708	+	0.864339i	−0.999994	−	0.00336324i	$-0.998929\pi$
$257$	−24.0000	+	13.8564i	−1.49708	+	0.864339i	−0.497085	+	0.867702i	$0.665596\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	21.0000	+	12.1244i	1.29492	+	0.747620i	0.979521	−	0.201341i	$-0.0645299\pi$
$263$	21.0000	+	12.1244i	1.29492	+	0.747620i	0.315394	+	0.948961i	$0.397863\pi$
$264$		0			0
$265$			20.7846i			1.27679i
$266$		0			0
$267$		−	13.8564i		−	0.847998i
$268$		0			0
$269$	3.00000	+	1.73205i	0.182913	+	0.105605i	0.588661	−	0.808380i	$-0.299655\pi$
$269$	3.00000	+	1.73205i	0.182913	+	0.105605i	−0.405747	+	0.913985i	$0.632989\pi$
$270$		0			0
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	0.718580	−	0.695444i	$-0.244792\pi$
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	−0.961563	+	0.274586i	$0.911459\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−21.0000	+	12.1244i	−1.26635	+	0.731126i
$276$		0			0
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$		0			0
$279$	8.00000			0.478947
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$		0			0
$285$	12.0000	−	6.92820i	0.710819	−	0.410391i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$	−24.0000	−	13.8564i	−1.40690	−	0.812277i
$292$		0			0
$293$		−	10.3923i		−	0.607125i	−0.952812	−	0.303562i	$-0.901824\pi$
$293$		−	10.3923i		−	0.607125i	0.952812	−	0.303562i	$-0.0981761\pi$
$294$		0			0
$295$		−	20.7846i		−	1.21013i
$296$		0			0
$297$	−12.0000	−	6.92820i	−0.696311	−	0.402015i
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	18.0000	−	10.3923i	1.03407	−	0.597022i
$304$		0			0
$305$	−6.00000	+	10.3923i	−0.343559	+	0.595062i
$306$		0			0
$307$	22.0000			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$		0			0
$313$	−6.00000	+	3.46410i	−0.339140	+	0.195803i	−0.659892	−	0.751361i	$-0.729398\pi$
$313$	−6.00000	+	3.46410i	−0.339140	+	0.195803i	0.320752	+	0.947163i	$0.396065\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	−18.0000	−	10.3923i	−1.00781	−	0.581857i
$320$		0			0
$321$			20.7846i			1.16008i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−21.0000	−	12.1244i	−1.16487	−	0.672538i
$326$		0			0
$327$	14.0000	+	24.2487i	0.774202	+	1.34096i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3.00000	−	1.73205i	0.164895	−	0.0952021i	−0.415282	−	0.909693i	$-0.636317\pi$
$331$	3.00000	−	1.73205i	0.164895	−	0.0952021i	0.580176	+	0.814491i	$0.302984\pi$
$332$		0			0
$333$	1.00000	−	1.73205i	0.0547997	−	0.0949158i
$334$		0			0
$335$	−12.0000			−0.655630
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	−18.0000	+	31.1769i	−0.977626	+	1.69330i
$340$		0			0
$341$	24.0000	−	13.8564i	1.29967	−	0.750366i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	12.0000	+	20.7846i	0.646058	+	1.11901i
$346$		0			0
$347$	−15.0000	−	8.66025i	−0.805242	−	0.464907i	0.0400587	−	0.999197i	$-0.487246\pi$
$347$	−15.0000	−	8.66025i	−0.805242	−	0.464907i	−0.845301	+	0.534291i	$0.820579\pi$
$348$		0			0
$349$		−	3.46410i		−	0.185429i	−0.995693	−	0.0927146i	$-0.970446\pi$
$349$		−	3.46410i		−	0.185429i	0.995693	−	0.0927146i	$-0.0295544\pi$
$350$		0			0
$351$		−	13.8564i		−	0.739600i
$352$		0			0
$353$	−24.0000	−	13.8564i	−1.27739	−	0.737502i	−0.301023	−	0.953617i	$-0.597328\pi$
$353$	−24.0000	−	13.8564i	−1.27739	−	0.737502i	−0.976368	+	0.216115i	$0.930661\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−27.0000	+	15.5885i	−1.42501	+	0.822727i	−0.996721	−	0.0809166i	$-0.974215\pi$
$359$	−27.0000	+	15.5885i	−1.42501	+	0.822727i	−0.428285	+	0.903644i	$0.640882\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	2.00000			0.104973
$364$		0			0
$365$	24.0000			1.25622
$366$		0			0
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$		0			0
$369$	6.00000	−	3.46410i	0.312348	−	0.180334i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$	−12.0000	−	6.92820i	−0.619677	−	0.357771i
$376$		0			0
$377$		−	20.7846i		−	1.07046i
$378$		0			0
$379$		−	24.2487i		−	1.24557i	−0.782392	−	0.622786i	$-0.786001\pi$
$379$		−	24.2487i		−	1.24557i	0.782392	−	0.622786i	$-0.213999\pi$
$380$		0			0
$381$	18.0000	+	10.3923i	0.922168	+	0.532414i
$382$		0			0
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.00000	+	5.19615i	−0.457496	+	0.264135i
$388$		0			0
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	36.0000			1.81596
$394$		0			0
$395$	6.00000	−	10.3923i	0.301893	−	0.522894i
$396$		0			0
$397$	9.00000	−	5.19615i	0.451697	−	0.260787i	−0.256850	−	0.966451i	$-0.582685\pi$
$397$	9.00000	−	5.19615i	0.451697	−	0.260787i	0.708547	+	0.705664i	$0.249351\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$		0			0
$403$	24.0000	+	13.8564i	1.19553	+	0.690237i
$404$		0			0
$405$		−	38.1051i		−	1.89346i
$406$		0			0
$407$		−	6.92820i		−	0.343418i
$408$		0			0
$409$	6.00000	+	3.46410i	0.296681	+	0.171289i	0.640951	−	0.767582i	$-0.278540\pi$
$409$	6.00000	+	3.46410i	0.296681	+	0.171289i	−0.344270	+	0.938871i	$0.611874\pi$
$410$		0			0
$411$	−6.00000	−	10.3923i	−0.295958	−	0.512615i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	18.0000	−	10.3923i	0.883585	−	0.510138i
$416$		0			0
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$		0			0
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	12.0000	+	20.7846i	0.579365	+	1.00349i
$430$		0			0
$431$	−33.0000	−	19.0526i	−1.58955	−	0.917729i	−0.993380	−	0.114874i	$-0.963353\pi$
$431$	−33.0000	−	19.0526i	−1.58955	−	0.917729i	−0.596174	−	0.802855i	$-0.703313\pi$
$432$		0			0
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		−	41.5692i		−	1.99309i
$436$		0			0
$437$	−6.00000	−	3.46410i	−0.287019	−	0.165710i
$438$		0			0
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.00000	−	1.73205i	0.142534	−	0.0822922i	−0.427037	−	0.904234i	$-0.640443\pi$
$443$	3.00000	−	1.73205i	0.142534	−	0.0822922i	0.569571	+	0.821942i	$0.307109\pi$
$444$		0			0
$445$	12.0000	−	20.7846i	0.568855	−	0.985285i
$446$		0			0
$447$	−12.0000			−0.567581
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	12.0000	−	20.7846i	0.565058	−	0.978709i
$452$		0			0
$453$	6.00000	−	3.46410i	0.281905	−	0.162758i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.0000	+	29.4449i	0.795226	+	1.37737i	0.922695	+	0.385530i	$0.125981\pi$
$457$	17.0000	+	29.4449i	0.795226	+	1.37737i	−0.127469	+	0.991843i	$0.540685\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			38.1051i			1.77473i	0.461065	+	0.887366i	$0.347467\pi$
$461$			38.1051i			1.77473i	−0.461065	+	0.887366i	$0.652533\pi$
$462$		0			0
$463$		−	24.2487i		−	1.12693i	−0.826139	−	0.563467i	$-0.809467\pi$
$463$		−	24.2487i		−	1.12693i	0.826139	−	0.563467i	$-0.190533\pi$
$464$		0			0
$465$	48.0000	+	27.7128i	2.22595	+	1.28515i
$466$		0			0
$467$	−15.0000	−	25.9808i	−0.694117	−	1.20225i	−0.970477	−	0.241192i	$-0.922462\pi$
$467$	−15.0000	−	25.9808i	−0.694117	−	1.20225i	0.276360	−	0.961054i	$-0.410872\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−18.0000	+	10.3923i	−0.829396	+	0.478852i
$472$		0			0
$473$	−18.0000	+	31.1769i	−0.827641	+	1.43352i
$474$		0			0
$475$	14.0000			0.642364
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$	6.00000	−	3.46410i	0.273576	−	0.157949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−24.0000	−	41.5692i	−1.08978	−	1.88756i
$486$		0			0
$487$	−21.0000	−	12.1244i	−0.951601	−	0.549407i	−0.0580230	−	0.998315i	$-0.518480\pi$
$487$	−21.0000	−	12.1244i	−0.951601	−	0.549407i	−0.893578	+	0.448908i	$0.851813\pi$
$488$		0			0
$489$		−	34.6410i		−	1.56652i
$490$		0			0
$491$			17.3205i			0.781664i	0.920462	+	0.390832i	$0.127813\pi$
$491$			17.3205i			0.781664i	−0.920462	+	0.390832i	$0.872187\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	6.00000	+	10.3923i	0.269680	+	0.467099i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−9.00000	+	5.19615i	−0.402895	+	0.232612i	−0.687733	−	0.725964i	$-0.741394\pi$
$499$	−9.00000	+	5.19615i	−0.402895	+	0.232612i	0.284837	+	0.958576i	$0.408060\pi$
$500$		0			0
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$		0			0
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$		0			0
$507$	1.00000	−	1.73205i	0.0444116	−	0.0769231i
$508$		0			0
$509$	−27.0000	+	15.5885i	−1.19675	+	0.690946i	−0.959830	−	0.280582i	$-0.909473\pi$
$509$	−27.0000	+	15.5885i	−1.19675	+	0.690946i	−0.236924	+	0.971528i	$0.576139\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	4.00000	+	6.92820i	0.176604	+	0.305888i
$514$		0			0
$515$	12.0000	+	6.92820i	0.528783	+	0.305293i
$516$		0			0
$517$		0			0
$518$		0			0
$519$			6.92820i			0.304114i
$520$		0			0
$521$	−30.0000	−	17.3205i	−1.31432	−	0.758825i	−0.331515	−	0.943450i	$-0.607560\pi$
$521$	−30.0000	−	17.3205i	−1.31432	−	0.758825i	−0.982809	+	0.184625i	$0.940893\pi$
$522$		0			0
$523$	−1.00000	−	1.73205i	−0.0437269	−	0.0757373i	0.843334	−	0.537390i	$-0.180590\pi$
$523$	−1.00000	−	1.73205i	−0.0437269	−	0.0757373i	−0.887061	+	0.461653i	$0.847256\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−5.50000	+	9.52628i	−0.239130	+	0.414186i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	24.0000			1.03956
$534$		0			0
$535$	−18.0000	+	31.1769i	−0.778208	+	1.34790i
$536$		0			0
$537$	18.0000	−	10.3923i	0.776757	−	0.448461i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	0.886721	−	0.462304i	$-0.152977\pi$
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	−0.843728	+	0.536771i	$0.819644\pi$
$542$		0			0
$543$	30.0000	+	17.3205i	1.28742	+	0.743294i
$544$		0			0
$545$			48.4974i			2.07740i
$546$		0			0
$547$			17.3205i			0.740571i	0.928918	+	0.370286i	$0.120740\pi$
$547$			17.3205i			0.740571i	−0.928918	+	0.370286i	$0.879260\pi$
$548$		0			0
$549$	3.00000	+	1.73205i	0.128037	+	0.0739221i
$550$		0			0
$551$	6.00000	+	10.3923i	0.255609	+	0.442727i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	12.0000	−	6.92820i	0.509372	−	0.294086i
$556$		0			0
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	−0.609912	−	0.792469i	$-0.708795\pi$
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	0.991254	+	0.131965i	$0.0421286\pi$
$558$		0			0
$559$	−36.0000			−1.52264
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	−0.611656	−	0.791123i	$-0.709497\pi$
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	0.990961	+	0.134148i	$0.0428299\pi$
$564$		0			0
$565$	−54.0000	+	31.1769i	−2.27180	+	1.31162i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	−39.0000	−	22.5167i	−1.63210	−	0.942293i	−0.983444	−	0.181210i	$-0.941999\pi$
$571$	−39.0000	−	22.5167i	−1.63210	−	0.942293i	−0.648655	−	0.761083i	$-0.724668\pi$
$572$		0			0
$573$			48.4974i			2.02601i
$574$		0			0
$575$			24.2487i			1.01124i
$576$		0			0
$577$	−24.0000	−	13.8564i	−0.999133	−	0.576850i	−0.0911414	−	0.995838i	$-0.529052\pi$
$577$	−24.0000	−	13.8564i	−0.999133	−	0.576850i	−0.907992	+	0.418988i	$0.862385\pi$
$578$		0			0
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	18.0000	−	10.3923i	0.745484	−	0.430405i
$584$		0			0
$585$	−6.00000	+	10.3923i	−0.248069	+	0.429669i
$586$		0			0
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$		0			0
$589$	−16.0000			−0.659269
$590$		0			0
$591$	−18.0000	+	31.1769i	−0.740421	+	1.28245i
$592$		0			0
$593$	12.0000	−	6.92820i	0.492781	−	0.284507i	−0.232946	−	0.972490i	$-0.574837\pi$
$593$	12.0000	−	6.92820i	0.492781	−	0.284507i	0.725727	+	0.687982i	$0.241503\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−20.0000	−	34.6410i	−0.818546	−	1.41776i
$598$		0			0
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	0.863354	−	0.504598i	$-0.168359\pi$
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	−0.00531761	+	0.999986i	$0.501693\pi$
$600$		0			0
$601$		−	20.7846i		−	0.847822i	−0.905704	−	0.423911i	$-0.860657\pi$
$601$		−	20.7846i		−	0.847822i	0.905704	−	0.423911i	$-0.139343\pi$
$602$		0			0
$603$			3.46410i			0.141069i
$604$		0			0
$605$	3.00000	+	1.73205i	0.121967	+	0.0704179i
$606$		0			0
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	0.171564	+	0.985173i	$0.445118\pi$
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	−0.938967	+	0.344008i	$0.888215\pi$
$614$		0			0
$615$	48.0000			1.93555
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$		0			0
$619$	−13.0000	+	22.5167i	−0.522514	+	0.905021i	0.477143	+	0.878826i	$0.341672\pi$
$619$	−13.0000	+	22.5167i	−0.522514	+	0.905021i	−0.999657	+	0.0261952i	$0.991661\pi$
$620$		0			0
$621$	−12.0000	+	6.92820i	−0.481543	+	0.278019i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$	−12.0000	−	6.92820i	−0.479234	−	0.276686i
$628$		0			0
$629$		0			0
$630$		0			0
$631$			3.46410i			0.137904i	0.997620	+	0.0689519i	$0.0219655\pi$
$631$			3.46410i			0.137904i	−0.997620	+	0.0689519i	$0.978035\pi$
$632$		0			0
$633$	6.00000	+	3.46410i	0.238479	+	0.137686i
$634$		0			0
$635$	18.0000	+	31.1769i	0.714308	+	1.23722i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	3.00000	−	1.73205i	0.118678	−	0.0685189i
$640$		0			0
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$		0			0
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$		0			0
$645$	−72.0000			−2.83500
$646$		0			0
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$		0			0
$649$	−18.0000	+	10.3923i	−0.706562	+	0.407934i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		0			0
$655$	54.0000	+	31.1769i	2.10995	+	1.21818i
$656$		0			0
$657$		−	6.92820i		−	0.270295i
$658$		0			0
$659$			3.46410i			0.134942i	0.997721	+	0.0674711i	$0.0214931\pi$
$659$			3.46410i			0.134942i	−0.997721	+	0.0674711i	$0.978507\pi$
$660$		0			0
$661$	−3.00000	−	1.73205i	−0.116686	−	0.0673690i	0.440521	−	0.897742i	$-0.354794\pi$
$661$	−3.00000	−	1.73205i	−0.116686	−	0.0673690i	−0.557207	+	0.830373i	$0.688127\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−18.0000	+	10.3923i	−0.696963	+	0.402392i
$668$		0			0
$669$	16.0000	−	27.7128i	0.618596	−	1.07144i
$670$		0			0
$671$	12.0000			0.463255
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$		0			0
$675$	14.0000	−	24.2487i	0.538860	−	0.933333i
$676$		0			0
$677$	3.00000	−	1.73205i	0.115299	−	0.0665681i	−0.441241	−	0.897389i	$-0.645462\pi$
$677$	3.00000	−	1.73205i	0.115299	−	0.0665681i	0.556541	+	0.830820i	$0.312128\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$		0			0
$683$	33.0000	+	19.0526i	1.26271	+	0.729026i	0.973598	−	0.228269i	$-0.0733067\pi$
$683$	33.0000	+	19.0526i	1.26271	+	0.729026i	0.289112	+	0.957295i	$0.406640\pi$
$684$		0			0
$685$		−	20.7846i		−	0.794139i
$686$		0			0
$687$			20.7846i			0.792982i
$688$		0			0
$689$	18.0000	+	10.3923i	0.685745	+	0.395915i
$690$		0			0
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	0.945319	−	0.326146i	$-0.105750\pi$
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	−0.755110	+	0.655598i	$0.772417\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.00000	−	3.46410i	0.227593	−	0.131401i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	12.0000			0.453882
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$	−3.00000	−	1.73205i	−0.112509	−	0.0649570i
$712$		0			0
$713$		−	27.7128i		−	1.03785i
$714$		0			0
$715$			41.5692i			1.55460i
$716$		0			0
$717$	18.0000	+	10.3923i	0.672222	+	0.388108i
$718$		0			0
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.833744	−	0.552151i	$-0.813807\pi$
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.0613050	−	0.998119i	$-0.519526\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	48.0000	−	27.7128i	1.78514	−	1.03065i
$724$		0			0
$725$	21.0000	−	36.3731i	0.779920	−	1.35086i
$726$		0			0
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$		0			0
$733$	45.0000	−	25.9808i	1.66211	−	0.959621i	0.690409	−	0.723419i	$-0.257431\pi$
$733$	45.0000	−	25.9808i	1.66211	−	0.959621i	0.971704	−	0.236202i	$-0.0759027\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$		0			0
$739$	9.00000	+	5.19615i	0.331070	+	0.191144i	0.656316	−	0.754486i	$-0.272114\pi$
$739$	9.00000	+	5.19615i	0.331070	+	0.191144i	−0.325246	+	0.945629i	$0.605447\pi$
$740$		0			0
$741$		−	13.8564i		−	0.509028i
$742$		0			0
$743$			24.2487i			0.889599i	0.895630	+	0.444799i	$0.146725\pi$
$743$			24.2487i			0.889599i	−0.895630	+	0.444799i	$0.853275\pi$
$744$		0			0
$745$	−18.0000	−	10.3923i	−0.659469	−	0.380745i
$746$		0			0
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−39.0000	+	22.5167i	−1.42313	+	0.821645i	−0.996565	−	0.0828123i	$-0.973610\pi$
$751$	−39.0000	+	22.5167i	−1.42313	+	0.821645i	−0.426565	+	0.904457i	$0.640276\pi$
$752$		0			0
$753$	−30.0000	+	51.9615i	−1.09326	+	1.89358i
$754$		0			0
$755$	12.0000			0.436725
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$	12.0000	−	20.7846i	0.435572	−	0.754434i
$760$		0			0
$761$	18.0000	−	10.3923i	0.652499	−	0.376721i	−0.136914	−	0.990583i	$-0.543718\pi$
$761$	18.0000	−	10.3923i	0.652499	−	0.376721i	0.789413	+	0.613862i	$0.210385\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−18.0000	−	10.3923i	−0.649942	−	0.375244i
$768$		0			0
$769$		−	13.8564i		−	0.499675i	−0.968288	−	0.249837i	$-0.919623\pi$
$769$		−	13.8564i		−	0.499675i	0.968288	−	0.249837i	$-0.0803772\pi$
$770$		0			0
$771$			55.4256i			1.99611i
$772$		0			0
$773$	−3.00000	−	1.73205i	−0.107903	−	0.0622975i	0.445078	−	0.895492i	$-0.353176\pi$
$773$	−3.00000	−	1.73205i	−0.107903	−	0.0622975i	−0.552980	+	0.833194i	$0.686509\pi$
$774$		0			0
$775$	28.0000	+	48.4974i	1.00579	+	1.74208i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.0000	+	6.92820i	−0.429945	+	0.248229i
$780$		0			0
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$		0			0
$783$	24.0000			0.857690
$784$		0			0
$785$	−36.0000			−1.28490
$786$		0			0
$787$	17.0000	−	29.4449i	0.605985	−	1.04960i	−0.385911	−	0.922536i	$-0.626113\pi$
$787$	17.0000	−	29.4449i	0.605985	−	1.04960i	0.991895	−	0.127060i	$-0.0405540\pi$
$788$		0			0
$789$	42.0000	−	24.2487i	1.49524	−	0.863277i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.00000	+	10.3923i	0.213066	+	0.369042i
$794$		0			0
$795$	36.0000	+	20.7846i	1.27679	+	0.737154i
$796$		0			0
$797$		−	17.3205i		−	0.613524i	−0.951786	−	0.306762i	$-0.900754\pi$
$797$		−	17.3205i		−	0.613524i	0.951786	−	0.306762i	$-0.0992455\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−6.00000	−	3.46410i	−0.212000	−	0.122398i
$802$		0			0
$803$	−12.0000	−	20.7846i	−0.423471	−	0.733473i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.00000	−	3.46410i	0.211210	−	0.121942i
$808$		0			0
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$		0			0
$811$	−22.0000			−0.772524			−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000			−0.772524			−0.386262	+	0.922389i	$0.626234\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$		0			0
$815$	30.0000	−	51.9615i	1.05085	−	1.82013i
$816$		0			0
$817$	18.0000	−	10.3923i	0.629740	−	0.363581i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		0			0
$823$	−3.00000	−	1.73205i	−0.104573	−	0.0603755i	0.446801	−	0.894633i	$-0.352563\pi$
$823$	−3.00000	−	1.73205i	−0.104573	−	0.0603755i	−0.551375	+	0.834258i	$0.685896\pi$
$824$		0			0
$825$			48.4974i			1.68846i
$826$		0			0
$827$		−	24.2487i		−	0.843210i	−0.906780	−	0.421605i	$-0.861467\pi$
$827$		−	24.2487i		−	0.843210i	0.906780	−	0.421605i	$-0.138533\pi$
$828$		0			0
$829$	3.00000	+	1.73205i	0.104194	+	0.0601566i	0.551192	−	0.834379i	$-0.314173\pi$
$829$	3.00000	+	1.73205i	0.104194	+	0.0601566i	−0.446997	+	0.894535i	$0.647507\pi$
$830$		0			0
$831$	−2.00000	−	3.46410i	−0.0693792	−	0.120168i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	36.0000	−	20.7846i	1.24583	−	0.719281i
$836$		0			0
$837$	−16.0000	+	27.7128i	−0.553041	+	0.957895i
$838$		0			0
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−6.00000	+	10.3923i	−0.206651	+	0.357930i
$844$		0			0
$845$	3.00000	−	1.73205i	0.103203	−	0.0595844i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$		0			0
$851$	−6.00000	−	3.46410i	−0.205677	−	0.118748i
$852$		0			0
$853$			3.46410i			0.118609i	0.998240	+	0.0593043i	$0.0188882\pi$
$853$			3.46410i			0.118609i	−0.998240	+	0.0593043i	$0.981112\pi$
$854$		0			0
$855$		−	6.92820i		−	0.236940i
$856$		0			0
$857$	30.0000	+	17.3205i	1.02478	+	0.591657i	0.915485	−	0.402352i	$-0.131807\pi$
$857$	30.0000	+	17.3205i	1.02478	+	0.591657i	0.109295	+	0.994009i	$0.465141\pi$
$858$		0			0
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	0.960381	−	0.278691i	$-0.0899005\pi$
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	−0.721544	+	0.692369i	$0.756567\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.0000	−	15.5885i	0.919091	−	0.530637i	0.0357458	−	0.999361i	$-0.488619\pi$
$863$	27.0000	−	15.5885i	0.919091	−	0.530637i	0.883345	+	0.468724i	$0.155286\pi$
$864$		0			0
$865$	−6.00000	+	10.3923i	−0.204006	+	0.353349i
$866$		0			0
$867$	−34.0000			−1.15470
$868$		0			0
$869$	−12.0000			−0.407072
$870$		0			0
$871$	−6.00000	+	10.3923i	−0.203302	+	0.352130i
$872$		0			0
$873$	−12.0000	+	6.92820i	−0.406138	+	0.234484i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	0.343495	−	0.939155i	$-0.388389\pi$
$878$		0			0
$879$	−18.0000	−	10.3923i	−0.607125	−	0.350524i
$880$		0			0
$881$		−	13.8564i		−	0.466834i	−0.972377	−	0.233417i	$-0.925009\pi$
$881$		−	13.8564i		−	0.466834i	0.972377	−	0.233417i	$-0.0749907\pi$
$882$		0			0
$883$			3.46410i			0.116576i	0.998300	+	0.0582882i	$0.0185642\pi$
$883$			3.46410i			0.116576i	−0.998300	+	0.0582882i	$0.981436\pi$
$884$		0			0
$885$	−36.0000	−	20.7846i	−1.21013	−	0.698667i
$886$		0			0
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−33.0000	+	19.0526i	−1.10554	+	0.638285i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	36.0000			1.20335
$896$		0			0
$897$	24.0000			0.801337
$898$		0			0
$899$	−24.0000	+	41.5692i	−0.800445	+	1.38641i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	30.0000	+	51.9615i	0.997234	+	1.72726i
$906$		0			0
$907$	21.0000	+	12.1244i	0.697294	+	0.402583i	0.806339	−	0.591454i	$-0.201446\pi$
$907$	21.0000	+	12.1244i	0.697294	+	0.402583i	−0.109045	+	0.994037i	$0.534779\pi$
$908$		0			0
$909$		−	10.3923i		−	0.344691i
$910$		0			0
$911$			10.3923i			0.344312i	0.985070	+	0.172156i	$0.0550734\pi$
$911$			10.3923i			0.344312i	−0.985070	+	0.172156i	$0.944927\pi$
$912$		0			0
$913$	−18.0000	−	10.3923i	−0.595713	−	0.343935i
$914$		0			0
$915$	12.0000	+	20.7846i	0.396708	+	0.687118i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	27.0000	−	15.5885i	0.890648	−	0.514216i	0.0164935	−	0.999864i	$-0.494750\pi$
$919$	27.0000	−	15.5885i	0.890648	−	0.514216i	0.874154	+	0.485648i	$0.161416\pi$
$920$		0			0
$921$	22.0000	−	38.1051i	0.724925	−	1.25561i
$922$		0			0
$923$	12.0000			0.394985
$924$		0			0
$925$	14.0000			0.460317
$926$		0			0
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$		0			0
$929$	−36.0000	+	20.7846i	−1.18112	+	0.681921i	−0.956274	−	0.292473i	$-0.905522\pi$
$929$	−36.0000	+	20.7846i	−1.18112	+	0.681921i	−0.224848	+	0.974394i	$0.572189\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			48.4974i			1.58434i	0.610299	+	0.792171i	$0.291049\pi$
$937$			48.4974i			1.58434i	−0.610299	+	0.792171i	$0.708951\pi$
$938$		0			0
$939$			13.8564i			0.452187i
$940$		0			0
$941$	−21.0000	−	12.1244i	−0.684580	−	0.395243i	0.116998	−	0.993132i	$-0.462673\pi$
$941$	−21.0000	−	12.1244i	−0.684580	−	0.395243i	−0.801579	+	0.597889i	$0.796006\pi$
$942$		0			0
$943$	−12.0000	−	20.7846i	−0.390774	−	0.676840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.0000	+	12.1244i	−0.682408	+	0.393989i	−0.800762	−	0.598983i	$-0.795572\pi$
$947$	−21.0000	+	12.1244i	−0.682408	+	0.393989i	0.118354	+	0.992972i	$0.462238\pi$
$948$		0			0
$949$	12.0000	−	20.7846i	0.389536	−	0.674697i
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$	−42.0000	+	72.7461i	−1.35909	+	2.35401i
$956$		0			0
$957$	−36.0000	+	20.7846i	−1.16371	+	0.671871i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$	9.00000	+	5.19615i	0.290021	+	0.167444i
$964$		0			0
$965$		−	6.92820i		−	0.223027i
$966$		0			0
$967$			24.2487i			0.779786i	0.920860	+	0.389893i	$0.127488\pi$
$967$			24.2487i			0.779786i	−0.920860	+	0.389893i	$0.872512\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.00000	−	15.5885i	−0.288824	−	0.500257i	0.684706	−	0.728820i	$-0.259931\pi$
$971$	−9.00000	−	15.5885i	−0.288824	−	0.500257i	−0.973529	+	0.228562i	$0.926597\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−42.0000	+	24.2487i	−1.34508	+	0.776580i
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$		0			0
$979$	−24.0000			−0.767043
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	−54.0000	+	31.1769i	−1.72058	+	0.993379i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18.0000	+	31.1769i	0.572367	+	0.991368i
$990$		0			0
$991$	−3.00000	−	1.73205i	−0.0952981	−	0.0550204i	0.451594	−	0.892224i	$-0.350856\pi$
$991$	−3.00000	−	1.73205i	−0.0952981	−	0.0550204i	−0.546892	+	0.837203i	$0.684189\pi$
$992$		0			0
$993$		−	6.92820i		−	0.219860i
$994$		0			0
$995$		−	69.2820i		−	2.19639i
$996$		0			0
$997$	45.0000	+	25.9808i	1.42516	+	0.822819i	0.996734	−	0.0807558i	$-0.0257334\pi$
$997$	45.0000	+	25.9808i	1.42516	+	0.822819i	0.428430	+	0.903575i	$0.359067\pi$
$998$		0			0
$999$	4.00000	+	6.92820i	0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.p.f.31.1		2
4.3	odd	2		784.2.p.b.31.1		2
7.2	even	3		784.2.p.e.607.1		2
7.3	odd	6		112.2.f.b.111.1	yes	2
7.4	even	3		112.2.f.a.111.2	yes	2
7.5	odd	6		784.2.p.b.607.1		2
7.6	odd	2		784.2.p.a.31.1		2
21.11	odd	6		1008.2.b.g.559.1		2
21.17	even	6		1008.2.b.b.559.2		2
28.3	even	6		112.2.f.a.111.1	✓	2
28.11	odd	6		112.2.f.b.111.2	yes	2
28.19	even	6	inner	784.2.p.f.607.1		2
28.23	odd	6		784.2.p.a.607.1		2
28.27	even	2		784.2.p.e.31.1		2
35.3	even	12		2800.2.e.b.2799.4		4
35.4	even	6		2800.2.k.e.2351.1		2
35.17	even	12		2800.2.e.b.2799.1		4
35.18	odd	12		2800.2.e.c.2799.2		4
35.24	odd	6		2800.2.k.b.2351.1		2
35.32	odd	12		2800.2.e.c.2799.3		4
56.3	even	6		448.2.f.c.447.2		2
56.11	odd	6		448.2.f.a.447.1		2
56.45	odd	6		448.2.f.a.447.2		2
56.53	even	6		448.2.f.c.447.1		2
84.11	even	6		1008.2.b.b.559.1		2
84.59	odd	6		1008.2.b.g.559.2		2
112.3	even	12		1792.2.e.a.895.1		4
112.11	odd	12		1792.2.e.c.895.1		4
112.45	odd	12		1792.2.e.c.895.3		4
112.53	even	12		1792.2.e.a.895.3		4
112.59	even	12		1792.2.e.a.895.4		4
112.67	odd	12		1792.2.e.c.895.4		4
112.101	odd	12		1792.2.e.c.895.2		4
112.109	even	12		1792.2.e.a.895.2		4
140.3	odd	12		2800.2.e.c.2799.1		4
140.39	odd	6		2800.2.k.b.2351.2		2
140.59	even	6		2800.2.k.e.2351.2		2
140.67	even	12		2800.2.e.b.2799.2		4
140.87	odd	12		2800.2.e.c.2799.4		4
140.123	even	12		2800.2.e.b.2799.3		4
168.11	even	6		4032.2.b.b.3583.2		2
168.53	odd	6		4032.2.b.h.3583.2		2
168.59	odd	6		4032.2.b.h.3583.1		2
168.101	even	6		4032.2.b.b.3583.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.f.a.111.1	✓	2	28.3	even	6
112.2.f.a.111.2	yes	2	7.4	even	3
112.2.f.b.111.1	yes	2	7.3	odd	6
112.2.f.b.111.2	yes	2	28.11	odd	6
448.2.f.a.447.1		2	56.11	odd	6
448.2.f.a.447.2		2	56.45	odd	6
448.2.f.c.447.1		2	56.53	even	6
448.2.f.c.447.2		2	56.3	even	6
784.2.p.a.31.1		2	7.6	odd	2
784.2.p.a.607.1		2	28.23	odd	6
784.2.p.b.31.1		2	4.3	odd	2
784.2.p.b.607.1		2	7.5	odd	6
784.2.p.e.31.1		2	28.27	even	2
784.2.p.e.607.1		2	7.2	even	3
784.2.p.f.31.1		2	1.1	even	1	trivial
784.2.p.f.607.1		2	28.19	even	6	inner
1008.2.b.b.559.1		2	84.11	even	6
1008.2.b.b.559.2		2	21.17	even	6
1008.2.b.g.559.1		2	21.11	odd	6
1008.2.b.g.559.2		2	84.59	odd	6
1792.2.e.a.895.1		4	112.3	even	12
1792.2.e.a.895.2		4	112.109	even	12
1792.2.e.a.895.3		4	112.53	even	12
1792.2.e.a.895.4		4	112.59	even	12
1792.2.e.c.895.1		4	112.11	odd	12
1792.2.e.c.895.2		4	112.101	odd	12
1792.2.e.c.895.3		4	112.45	odd	12
1792.2.e.c.895.4		4	112.67	odd	12
2800.2.e.b.2799.1		4	35.17	even	12
2800.2.e.b.2799.2		4	140.67	even	12
2800.2.e.b.2799.3		4	140.123	even	12
2800.2.e.b.2799.4		4	35.3	even	12
2800.2.e.c.2799.1		4	140.3	odd	12
2800.2.e.c.2799.2		4	35.18	odd	12
2800.2.e.c.2799.3		4	35.32	odd	12
2800.2.e.c.2799.4		4	140.87	odd	12
2800.2.k.b.2351.1		2	35.24	odd	6
2800.2.k.b.2351.2		2	140.39	odd	6
2800.2.k.e.2351.1		2	35.4	even	6
2800.2.k.e.2351.2		2	140.59	even	6
4032.2.b.b.3583.1		2	168.101	even	6
4032.2.b.b.3583.2		2	168.11	even	6
4032.2.b.h.3583.1		2	168.59	odd	6
4032.2.b.h.3583.2		2	168.53	odd	6

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{3} +(3.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} -3.46410i q^{13} -6.92820i q^{15} +(1.00000 + 1.73205i) q^{19} +(-3.00000 + 1.73205i) q^{23} +(3.50000 - 6.06218i) q^{25} +4.00000 q^{27} +6.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(-6.00000 + 3.46410i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-6.00000 - 3.46410i) q^{39} +6.92820i q^{41} -10.3923i q^{43} +(-3.00000 - 1.73205i) q^{45} +(-3.00000 + 5.19615i) q^{53} -12.0000 q^{55} +4.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-3.00000 + 1.73205i) q^{61} +(-6.00000 - 10.3923i) q^{65} +(-3.00000 - 1.73205i) q^{67} +6.92820i q^{69} +3.46410i q^{71} +(6.00000 + 3.46410i) q^{73} +(-7.00000 - 12.1244i) q^{75} +(3.00000 - 1.73205i) q^{79} +(5.50000 - 9.52628i) q^{81} +6.00000 q^{83} +(6.00000 - 10.3923i) q^{87} +(6.00000 - 3.46410i) q^{89} +(8.00000 + 13.8564i) q^{93} +(6.00000 + 3.46410i) q^{95} -13.8564i q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 6 q^{5} - q^{9} - 6 q^{11} + 2 q^{19} - 6 q^{23} + 7 q^{25} + 8 q^{27} + 12 q^{29} - 8 q^{31} - 12 q^{33} + 2 q^{37} - 12 q^{39} - 6 q^{45} - 6 q^{53} - 24 q^{55} + 8 q^{57} + 6 q^{59}+ \cdots + 12 q^{95}+O(q^{100}) \) 2 * q + 2 * q^3 + 6 * q^5 - q^9 - 6 * q^11 + 2 * q^19 - 6 * q^23 + 7 * q^25 + 8 * q^27 + 12 * q^29 - 8 * q^31 - 12 * q^33 + 2 * q^37 - 12 * q^39 - 6 * q^45 - 6 * q^53 - 24 * q^55 + 8 * q^57 + 6 * q^59 - 6 * q^61 - 12 * q^65 - 6 * q^67 + 12 * q^73 - 14 * q^75 + 6 * q^79 + 11 * q^81 + 12 * q^83 + 12 * q^87 + 12 * q^89 + 16 * q^93 + 12 * q^95

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