LMFDB - Embedded newform 784.2.p.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(31,784)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$1$
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.a.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	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$		0			0
$5$	−3.00000	+	1.73205i	−1.34164	+	0.774597i	−0.987048	−	0.160424i	$-0.948714\pi$
$5$	−3.00000	+	1.73205i	−1.34164	+	0.774597i	−0.354593	+	0.935021i	$0.615380\pi$
$6$		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	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$		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	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		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	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		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	$-0.818045\pi$
$41$		−	6.92820i		−	1.08200i	0.841021	−	0.541002i	$-0.181955\pi$
$42$		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	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	−0.295495	−	0.955344i	$-0.595484\pi$
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	0.679605	+	0.733578i	$0.262151\pi$
$62$		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	0.105937	−	0.994373i	$-0.466216\pi$
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	−0.808184	+	0.588930i	$0.799549\pi$
$74$		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	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		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	−0.783072	−	0.621932i	$-0.786348\pi$
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	0.147073	+	0.989126i	$0.453015\pi$
$90$		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	$0.248359\pi$
$97$			13.8564i			1.40690i	−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	−9.00000	−	5.19615i	−0.895533	−	0.517036i	−0.0197851	−	0.999804i	$-0.506298\pi$
$101$	−9.00000	−	5.19615i	−0.895533	−	0.517036i	−0.875748	+	0.482768i	$0.839632\pi$
$102$		0			0
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	0.750510	−	0.660859i	$-0.229808\pi$
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	−0.947576	+	0.319531i	$0.896475\pi$
$104$		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	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$		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	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		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	0.814119	−	0.580699i	$-0.197221\pi$
$157$	9.00000	+	5.19615i	0.718278	+	0.414698i	−0.0958404	+	0.995397i	$0.530554\pi$
$158$		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	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		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	−0.381603	−	0.924326i	$-0.624628\pi$
$173$	3.00000	−	1.73205i	0.228086	−	0.131685i	0.609689	+	0.792641i	$0.291294\pi$
$174$		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	$-0.777394\pi$
$181$		−	17.3205i		−	1.28742i	0.765268	−	0.643712i	$-0.222606\pi$
$182$		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	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$		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	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$	−7.00000			−0.466667
$226$		0			0
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	−0.749125	−	0.662428i	$-0.769526\pi$
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	0.948242	+	0.317547i	$0.102859\pi$
$228$		0			0
$229$	9.00000	−	5.19615i	0.594737	−	0.343371i	−0.172231	−	0.985057i	$-0.555098\pi$
$229$	9.00000	−	5.19615i	0.594737	−	0.343371i	0.766968	+	0.641685i	$0.221764\pi$
$230$		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	$-0.982234\pi$
$241$	−24.0000	−	13.8564i	−1.54598	−	0.892570i	−0.547533	−	0.836784i	$-0.684433\pi$
$242$		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	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$		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	0.497085	−	0.867702i	$-0.334404\pi$
$257$	24.0000	−	13.8564i	1.49708	−	0.864339i	0.999994	+	0.00336324i	$0.00107055\pi$
$258$		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	0.405747	−	0.913985i	$-0.367011\pi$
$269$	−3.00000	−	1.73205i	−0.182913	−	0.105605i	−0.588661	+	0.808380i	$0.700345\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		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	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$		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	$0.0981761\pi$
$293$			10.3923i			0.607125i	−0.952812	+	0.303562i	$0.901824\pi$
$294$		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	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	6.00000	−	3.46410i	0.339140	−	0.195803i	−0.320752	−	0.947163i	$-0.603935\pi$
$313$	6.00000	−	3.46410i	0.339140	−	0.195803i	0.659892	+	0.751361i	$0.270602\pi$
$314$		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	$0.0295544\pi$
$349$			3.46410i			0.185429i	−0.995693	+	0.0927146i	$0.970446\pi$
$350$		0			0
$351$		−	13.8564i		−	0.739600i
$352$		0			0
$353$	24.0000	+	13.8564i	1.27739	+	0.737502i	0.976368	−	0.216115i	$-0.0693385\pi$
$353$	24.0000	+	13.8564i	1.27739	+	0.737502i	0.301023	+	0.953617i	$0.402672\pi$
$354$		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	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$		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	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$		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	−0.708547	−	0.705664i	$-0.750649\pi$
$397$	−9.00000	+	5.19615i	−0.451697	+	0.260787i	0.256850	+	0.966451i	$0.417315\pi$
$398$		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	0.344270	−	0.938871i	$-0.388126\pi$
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	−0.640951	+	0.767582i	$0.721460\pi$
$410$		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	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$		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	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		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	$-0.652533\pi$
$461$		−	38.1051i		−	1.77473i	0.461065	−	0.887366i	$-0.347467\pi$
$462$		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	$0.0775384\pi$
$467$	15.0000	+	25.9808i	0.694117	+	1.20225i	−0.276360	+	0.961054i	$0.589128\pi$
$468$		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	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		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	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$		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	0.236924	−	0.971528i	$-0.423861\pi$
$509$	27.0000	−	15.5885i	1.19675	−	0.690946i	0.959830	+	0.280582i	$0.0905275\pi$
$510$		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	0.982809	−	0.184625i	$-0.0591070\pi$
$521$	30.0000	+	17.3205i	1.31432	+	0.758825i	0.331515	+	0.943450i	$0.392440\pi$
$522$		0			0
$523$	1.00000	+	1.73205i	0.0437269	+	0.0757373i	0.887061	−	0.461653i	$-0.152744\pi$
$523$	1.00000	+	1.73205i	0.0437269	+	0.0757373i	−0.843334	+	0.537390i	$0.819410\pi$
$524$		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	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$		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	0.907992	−	0.418988i	$-0.137615\pi$
$577$	24.0000	+	13.8564i	0.999133	+	0.576850i	0.0911414	+	0.995838i	$0.470948\pi$
$578$		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	$-0.621146\pi$
$587$	−18.0000			−0.742940			−0.371470	+	0.928445i	$0.621146\pi$
$588$		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	−0.725727	−	0.687982i	$-0.758497\pi$
$593$	−12.0000	+	6.92820i	−0.492781	+	0.284507i	0.232946	+	0.972490i	$0.425163\pi$
$594$		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	$0.139343\pi$
$601$			20.7846i			0.847822i	−0.905704	+	0.423911i	$0.860657\pi$
$602$		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	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$		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	$-0.658328\pi$
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	0.999657	−	0.0261952i	$-0.00833914\pi$
$620$		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	$-0.328656\pi$
$643$	26.0000			1.02534			0.512670	+	0.858586i	$0.328656\pi$
$644$		0			0
$645$	−72.0000			−2.83500
$646$		0			0
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	−0.723645	−	0.690172i	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$		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	0.557207	−	0.830373i	$-0.311873\pi$
$661$	3.00000	+	1.73205i	0.116686	+	0.0673690i	−0.440521	+	0.897742i	$0.645206\pi$
$662$		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	−0.556541	−	0.830820i	$-0.687872\pi$
$677$	−3.00000	+	1.73205i	−0.115299	+	0.0665681i	0.441241	+	0.897389i	$0.354538\pi$
$678$		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	0.755110	−	0.655598i	$-0.227583\pi$
$691$	−5.00000	−	8.66025i	−0.190209	−	0.329452i	−0.945319	+	0.326146i	$0.894250\pi$
$692$		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	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$		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	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		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	$0.742569\pi$
$733$	−45.0000	+	25.9808i	−1.66211	+	0.959621i	−0.971704	+	0.236202i	$0.924097\pi$
$734$		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	−0.789413	−	0.613862i	$-0.789615\pi$
$761$	−18.0000	+	10.3923i	−0.652499	+	0.376721i	0.136914	+	0.990583i	$0.456282\pi$
$762$		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	$0.0803772\pi$
$769$			13.8564i			0.499675i	−0.968288	+	0.249837i	$0.919623\pi$
$770$		0			0
$771$			55.4256i			1.99611i
$772$		0			0
$773$	3.00000	+	1.73205i	0.107903	+	0.0622975i	0.552980	−	0.833194i	$-0.313491\pi$
$773$	3.00000	+	1.73205i	0.107903	+	0.0622975i	−0.445078	+	0.895492i	$0.646824\pi$
$774$		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	$0.373887\pi$
$787$	−17.0000	+	29.4449i	−0.605985	+	1.04960i	−0.991895	+	0.127060i	$0.959446\pi$
$788$		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	$0.0992455\pi$
$797$			17.3205i			0.613524i	−0.951786	+	0.306762i	$0.900754\pi$
$798$		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	$-0.373766\pi$
$811$	22.0000			0.772524			0.386262	+	0.922389i	$0.373766\pi$
$812$		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	0.446997	−	0.894535i	$-0.352493\pi$
$829$	−3.00000	−	1.73205i	−0.104194	−	0.0601566i	−0.551192	+	0.834379i	$0.685827\pi$
$830$		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	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$		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	$-0.981112\pi$
$853$		−	3.46410i		−	0.118609i	0.998240	−	0.0593043i	$-0.0188882\pi$
$854$		0			0
$855$		−	6.92820i		−	0.236940i
$856$		0			0
$857$	−30.0000	−	17.3205i	−1.02478	−	0.591657i	−0.109295	−	0.994009i	$-0.534859\pi$
$857$	−30.0000	−	17.3205i	−1.02478	−	0.591657i	−0.915485	+	0.402352i	$0.868193\pi$
$858$		0			0
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	−0.960381	+	0.278691i	$0.910099\pi$
$860$		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	$0.0749907\pi$
$881$			13.8564i			0.466834i	−0.972377	+	0.233417i	$0.925009\pi$
$882$		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	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$		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	0.224848	−	0.974394i	$-0.427811\pi$
$929$	36.0000	−	20.7846i	1.18112	−	0.681921i	0.956274	+	0.292473i	$0.0944781\pi$
$930$		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	$-0.708951\pi$
$937$		−	48.4974i		−	1.58434i	0.610299	−	0.792171i	$-0.291049\pi$
$938$		0			0
$939$			13.8564i			0.452187i
$940$		0			0
$941$	21.0000	+	12.1244i	0.684580	+	0.395243i	0.801579	−	0.597889i	$-0.203994\pi$
$941$	21.0000	+	12.1244i	0.684580	+	0.395243i	−0.116998	+	0.993132i	$0.537327\pi$
$942$		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	0.973529	−	0.228562i	$-0.0734025\pi$
$971$	9.00000	+	15.5885i	0.288824	+	0.500257i	−0.684706	+	0.728820i	$0.740069\pi$
$972$		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	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		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	−0.428430	−	0.903575i	$-0.640933\pi$
$997$	−45.0000	−	25.9808i	−1.42516	−	0.822819i	−0.996734	+	0.0807558i	$0.974267\pi$
$998$		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.a.31.1		2
4.3	odd	2		784.2.p.e.31.1		2
7.2	even	3		784.2.p.b.607.1		2
7.3	odd	6		112.2.f.a.111.2	yes	2
7.4	even	3		112.2.f.b.111.1	yes	2
7.5	odd	6		784.2.p.e.607.1		2
7.6	odd	2		784.2.p.f.31.1		2
21.11	odd	6		1008.2.b.b.559.2		2
21.17	even	6		1008.2.b.g.559.1		2
28.3	even	6		112.2.f.b.111.2	yes	2
28.11	odd	6		112.2.f.a.111.1	✓	2
28.19	even	6	inner	784.2.p.a.607.1		2
28.23	odd	6		784.2.p.f.607.1		2
28.27	even	2		784.2.p.b.31.1		2
35.3	even	12		2800.2.e.c.2799.2		4
35.4	even	6		2800.2.k.b.2351.1		2
35.17	even	12		2800.2.e.c.2799.3		4
35.18	odd	12		2800.2.e.b.2799.4		4
35.24	odd	6		2800.2.k.e.2351.1		2
35.32	odd	12		2800.2.e.b.2799.1		4
56.3	even	6		448.2.f.a.447.1		2
56.11	odd	6		448.2.f.c.447.2		2
56.45	odd	6		448.2.f.c.447.1		2
56.53	even	6		448.2.f.a.447.2		2
84.11	even	6		1008.2.b.g.559.2		2
84.59	odd	6		1008.2.b.b.559.1		2
112.3	even	12		1792.2.e.c.895.4		4
112.11	odd	12		1792.2.e.a.895.4		4
112.45	odd	12		1792.2.e.a.895.2		4
112.53	even	12		1792.2.e.c.895.2		4
112.59	even	12		1792.2.e.c.895.1		4
112.67	odd	12		1792.2.e.a.895.1		4
112.101	odd	12		1792.2.e.a.895.3		4
112.109	even	12		1792.2.e.c.895.3		4
140.3	odd	12		2800.2.e.b.2799.3		4
140.39	odd	6		2800.2.k.e.2351.2		2
140.59	even	6		2800.2.k.b.2351.2		2
140.67	even	12		2800.2.e.c.2799.4		4
140.87	odd	12		2800.2.e.b.2799.2		4
140.123	even	12		2800.2.e.c.2799.1		4
168.11	even	6		4032.2.b.h.3583.1		2
168.53	odd	6		4032.2.b.b.3583.1		2
168.59	odd	6		4032.2.b.b.3583.2		2
168.101	even	6		4032.2.b.h.3583.2		2

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