LMFDB - Embedded newform 784.2.p.c.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:	$0$
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:	$\Z[a_1, a_2, a_3]$
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.c.607.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(1.50000 + 0.866025i) q^{11} -1.73205i q^{15} +(4.50000 + 2.59808i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-7.50000 + 4.33013i) q^{23} +(-1.00000 + 1.73205i) q^{25} -5.00000 q^{27} -6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-1.50000 + 0.866025i) q^{33} +(2.50000 + 4.33013i) q^{37} +6.92820i q^{41} -3.46410i q^{43} +(-3.00000 - 1.73205i) q^{45} +(-1.50000 - 2.59808i) q^{47} +(-4.50000 + 2.59808i) q^{51} +(4.50000 - 7.79423i) q^{53} -3.00000 q^{55} +7.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(-7.50000 + 4.33013i) q^{61} +(-4.50000 - 2.59808i) q^{67} -8.66025i q^{69} +3.46410i q^{71} +(-1.50000 - 0.866025i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(4.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} -9.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +(10.5000 - 6.06218i) q^{89} +(-2.50000 - 4.33013i) q^{93} +(10.5000 + 6.06218i) q^{95} +6.92820i q^{97} +3.46410i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 3 q^{5} + 2 q^{9}+O(q^{10}) $ 2 * q - q^3 - 3 * q^5 + 2 * q^9	$ 2 q - q^{3} - 3 q^{5} + 2 q^{9} + 3 q^{11} + 9 q^{17} - 7 q^{19} - 15 q^{23} - 2 q^{25} - 10 q^{27} - 12 q^{29} - 5 q^{31} - 3 q^{33} + 5 q^{37} - 6 q^{45} - 3 q^{47} - 9 q^{51} + 9 q^{53} - 6 q^{55} + 14 q^{57} - 9 q^{59} - 15 q^{61} - 9 q^{67} - 3 q^{73} - 2 q^{75} + 9 q^{79} - q^{81} + 24 q^{83} - 18 q^{85} + 6 q^{87} + 21 q^{89} - 5 q^{93} + 21 q^{95}+O(q^{100}) $ 2 * q - q^3 - 3 * q^5 + 2 * q^9 + 3 * q^11 + 9 * q^17 - 7 * q^19 - 15 * q^23 - 2 * q^25 - 10 * q^27 - 12 * q^29 - 5 * q^31 - 3 * q^33 + 5 * q^37 - 6 * q^45 - 3 * q^47 - 9 * q^51 + 9 * q^53 - 6 * q^55 + 14 * q^57 - 9 * q^59 - 15 * q^61 - 9 * q^67 - 3 * q^73 - 2 * q^75 + 9 * q^79 - q^81 + 24 * q^83 - 18 * q^85 + 6 * q^87 + 21 * q^89 - 5 * q^93 + 21 * q^95

Display 100 coefficients 10 coefficients

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$		0			0
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$		−	1.73205i		−	0.447214i
$16$		0			0
$17$	4.50000	+	2.59808i	1.09141	+	0.630126i	0.933952	−	0.357400i	$-0.116337\pi$
$17$	4.50000	+	2.59808i	1.09141	+	0.630126i	0.157459	+	0.987526i	$0.449670\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.50000	+	4.33013i	−1.56386	+	0.902894i	−0.566997	+	0.823720i	$0.691895\pi$
$23$	−7.50000	+	4.33013i	−1.56386	+	0.902894i	−0.996861	+	0.0791743i	$0.974772\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$		0			0
$33$	−1.50000	+	0.866025i	−0.261116	+	0.150756i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	0.994999	−	0.0998840i	$-0.0318472\pi$
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	−0.584002	+	0.811752i	$0.698514\pi$
$38$		0			0
$39$		0			0
$40$		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
$43$		−	3.46410i		−	0.528271i	−0.964486	−	0.264135i	$-0.914913\pi$
$43$		−	3.46410i		−	0.528271i	0.964486	−	0.264135i	$-0.0850865\pi$
$44$		0			0
$45$	−3.00000	−	1.73205i	−0.447214	−	0.258199i
$46$		0			0
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	0.735643	−	0.677369i	$-0.236880\pi$
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	−0.954441	+	0.298401i	$0.903547\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$		0			0
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	7.00000			0.927173
$58$		0			0
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	0.408919	+	0.912571i	$0.365906\pi$
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	−0.994769	+	0.102151i	$0.967427\pi$
$60$		0			0
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.50000	−	2.59808i	−0.549762	−	0.317406i	0.199264	−	0.979946i	$-0.436145\pi$
$67$	−4.50000	−	2.59808i	−0.549762	−	0.317406i	−0.749026	+	0.662540i	$0.769478\pi$
$68$		0			0
$69$		−	8.66025i		−	1.04257i
$70$		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
$73$	−1.50000	−	0.866025i	−0.175562	−	0.101361i	0.409644	−	0.912245i	$-0.365653\pi$
$73$	−1.50000	−	0.866025i	−0.175562	−	0.101361i	−0.585206	+	0.810885i	$0.698986\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.50000	−	2.59808i	0.506290	−	0.292306i	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	4.50000	−	2.59808i	0.506290	−	0.292306i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−9.00000			−0.976187
$86$		0			0
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$	10.5000	−	6.06218i	1.11300	−	0.642590i	0.173394	−	0.984853i	$-0.444527\pi$
$89$	10.5000	−	6.06218i	1.11300	−	0.642590i	0.939604	+	0.342263i	$0.111193\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$		0			0
$95$	10.5000	+	6.06218i	1.07728	+	0.621966i
$96$		0			0
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	4.50000	+	2.59808i	0.447767	+	0.258518i	0.706887	−	0.707327i	$-0.250099\pi$
$101$	4.50000	+	2.59808i	0.447767	+	0.258518i	−0.259120	+	0.965845i	$0.583432\pi$
$102$		0			0
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.50000	−	2.59808i	0.435031	−	0.251166i	−0.266456	−	0.963847i	$-0.585853\pi$
$107$	4.50000	−	2.59808i	0.435031	−	0.251166i	0.701488	+	0.712681i	$0.252519\pi$
$108$		0			0
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$		0			0
$111$	−5.00000			−0.474579
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	7.50000	−	12.9904i	0.699379	−	1.21136i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$	−6.00000	−	3.46410i	−0.541002	−	0.312348i
$124$		0			0
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$			3.46410i			0.307389i	0.988118	+	0.153695i	$0.0491172\pi$
$127$			3.46410i			0.307389i	−0.988118	+	0.153695i	$0.950883\pi$
$128$		0			0
$129$	3.00000	+	1.73205i	0.264135	+	0.152499i
$130$		0			0
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.803365	+	0.595487i	$0.203041\pi$
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.114024	+	0.993478i	$0.463626\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	7.50000	−	4.33013i	0.645497	−	0.372678i
$136$		0			0
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	3.00000			0.252646
$142$		0			0
$143$		0			0
$144$		0			0
$145$	9.00000	−	5.19615i	0.747409	−	0.431517i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$		0			0
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	0.00768132	−	0.999970i	$-0.497555\pi$
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	−0.862159	+	0.506637i	$0.830888\pi$
$152$		0			0
$153$			10.3923i			0.840168i
$154$		0			0
$155$		−	8.66025i		−	0.695608i
$156$		0			0
$157$	−13.5000	−	7.79423i	−1.07742	−	0.622047i	−0.147219	−	0.989104i	$-0.547032\pi$
$157$	−13.5000	−	7.79423i	−1.07742	−	0.622047i	−0.930199	+	0.367057i	$0.880365\pi$
$158$		0			0
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	10.5000	−	6.06218i	0.822423	−	0.474826i	−0.0288280	−	0.999584i	$-0.509178\pi$
$163$	10.5000	−	6.06218i	0.822423	−	0.474826i	0.851251	+	0.524758i	$0.175844\pi$
$164$		0			0
$165$	1.50000	−	2.59808i	0.116775	−	0.202260i
$166$		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
$169$	13.0000			1.00000
$170$		0			0
$171$	7.00000	−	12.1244i	0.535303	−	0.927173i
$172$		0			0
$173$	−7.50000	+	4.33013i	−0.570214	+	0.329213i	−0.757235	−	0.653143i	$-0.773450\pi$
$173$	−7.50000	+	4.33013i	−0.570214	+	0.329213i	0.187021	+	0.982356i	$0.440117\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.50000	−	7.79423i	−0.338241	−	0.585850i
$178$		0			0
$179$	13.5000	+	7.79423i	1.00904	+	0.582568i	0.910910	−	0.412606i	$-0.135381\pi$
$179$	13.5000	+	7.79423i	1.00904	+	0.582568i	0.0981277	+	0.995174i	$0.468715\pi$
$180$		0			0
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$		0			0
$183$		−	8.66025i		−	0.640184i
$184$		0			0
$185$	−7.50000	−	4.33013i	−0.551411	−	0.318357i
$186$		0			0
$187$	4.50000	+	7.79423i	0.329073	+	0.569970i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.5000	−	6.06218i	0.759753	−	0.438644i	−0.0694538	−	0.997585i	$-0.522126\pi$
$191$	10.5000	−	6.06218i	0.759753	−	0.438644i	0.829207	+	0.558941i	$0.188792\pi$
$192$		0			0
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	−0.761911	−	0.647682i	$-0.775738\pi$
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	0.941865	+	0.335993i	$0.109072\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$		0			0
$201$	4.50000	−	2.59808i	0.317406	−	0.183254i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$		0			0
$207$	−15.0000	−	8.66025i	−1.04257	−	0.601929i
$208$		0			0
$209$		−	12.1244i		−	0.838659i
$210$		0			0
$211$			24.2487i			1.66935i	0.550743	+	0.834675i	$0.314345\pi$
$211$			24.2487i			1.66935i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$	−3.00000	−	1.73205i	−0.205557	−	0.118678i
$214$		0			0
$215$	3.00000	+	5.19615i	0.204598	+	0.354375i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.50000	−	0.866025i	0.101361	−	0.0585206i
$220$		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
$225$	−4.00000			−0.266667
$226$		0			0
$227$	−10.5000	+	18.1865i	−0.696909	+	1.20708i	0.272623	+	0.962121i	$0.412109\pi$
$227$	−10.5000	+	18.1865i	−0.696909	+	1.20708i	−0.969533	+	0.244962i	$0.921225\pi$
$228$		0			0
$229$	10.5000	−	6.06218i	0.693860	−	0.400600i	−0.111197	−	0.993798i	$-0.535468\pi$
$229$	10.5000	−	6.06218i	0.693860	−	0.400600i	0.805056	+	0.593198i	$0.202135\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$		0			0
$235$	4.50000	+	2.59808i	0.293548	+	0.169480i
$236$		0			0
$237$			5.19615i			0.337526i
$238$		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
$241$	10.5000	+	6.06218i	0.676364	+	0.390499i	0.798484	−	0.602016i	$-0.205636\pi$
$241$	10.5000	+	6.06218i	0.676364	+	0.390499i	−0.122119	+	0.992515i	$0.538969\pi$
$242$		0			0
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−15.0000			−0.943042
$254$		0			0
$255$	4.50000	−	7.79423i	0.281801	−	0.488094i
$256$		0			0
$257$	16.5000	−	9.52628i	1.02924	−	0.594233i	0.112474	−	0.993655i	$-0.464122\pi$
$257$	16.5000	−	9.52628i	1.02924	−	0.594233i	0.916767	+	0.399422i	$0.130789\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$		0			0
$263$	7.50000	+	4.33013i	0.462470	+	0.267007i	0.713082	−	0.701080i	$-0.247299\pi$
$263$	7.50000	+	4.33013i	0.462470	+	0.267007i	−0.250612	+	0.968088i	$0.580632\pi$
$264$		0			0
$265$			15.5885i			0.957591i
$266$		0			0
$267$			12.1244i			0.741999i
$268$		0			0
$269$	−1.50000	−	0.866025i	−0.0914566	−	0.0528025i	0.453574	−	0.891219i	$-0.350149\pi$
$269$	−1.50000	−	0.866025i	−0.0914566	−	0.0528025i	−0.545031	+	0.838416i	$0.683482\pi$
$270$		0			0
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.00000	+	1.73205i	−0.180907	+	0.104447i
$276$		0			0
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	−0.489207	−	0.872167i	$-0.662714\pi$
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	0.999923	−	0.0124177i	$-0.00395278\pi$
$278$		0			0
$279$	−10.0000			−0.598684
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	5.50000	−	9.52628i	0.326941	−	0.566279i	−0.654962	−	0.755662i	$-0.727315\pi$
$283$	5.50000	−	9.52628i	0.326941	−	0.566279i	0.981903	+	0.189383i	$0.0606488\pi$
$284$		0			0
$285$	−10.5000	+	6.06218i	−0.621966	+	0.359092i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.00000	+	8.66025i	0.294118	+	0.509427i
$290$		0			0
$291$	−6.00000	−	3.46410i	−0.351726	−	0.203069i
$292$		0			0
$293$		−	20.7846i		−	1.21425i	−0.794606	−	0.607125i	$-0.792323\pi$
$293$		−	20.7846i		−	1.21425i	0.794606	−	0.607125i	$-0.207677\pi$
$294$		0			0
$295$		−	15.5885i		−	0.907595i
$296$		0			0
$297$	−7.50000	−	4.33013i	−0.435194	−	0.251259i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4.50000	+	2.59808i	−0.258518	+	0.149256i
$304$		0			0
$305$	7.50000	−	12.9904i	0.429449	−	0.743827i
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−1.00000			−0.0568880
$310$		0			0
$311$	−16.5000	+	28.5788i	−0.935629	+	1.62056i	−0.162121	+	0.986771i	$0.551833\pi$
$311$	−16.5000	+	28.5788i	−0.935629	+	1.62056i	−0.773508	+	0.633786i	$0.781500\pi$
$312$		0			0
$313$	−25.5000	+	14.7224i	−1.44135	+	0.832161i	−0.997940	−	0.0641600i	$-0.979563\pi$
$313$	−25.5000	+	14.7224i	−1.44135	+	0.832161i	−0.443406	+	0.896321i	$0.646230\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	0.994266	+	0.106932i	$0.0341026\pi$
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	−0.404528	+	0.914526i	$0.632564\pi$
$318$		0			0
$319$	−9.00000	−	5.19615i	−0.503903	−	0.290929i
$320$		0			0
$321$			5.19615i			0.290021i
$322$		0			0
$323$		−	36.3731i		−	2.02385i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−5.50000	−	9.52628i	−0.304151	−	0.526804i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−25.5000	+	14.7224i	−1.40161	+	0.809218i	−0.994558	−	0.104188i	$-0.966776\pi$
$331$	−25.5000	+	14.7224i	−1.40161	+	0.809218i	−0.407049	+	0.913406i	$0.633442\pi$
$332$		0			0
$333$	−5.00000	+	8.66025i	−0.273998	+	0.474579i
$334$		0			0
$335$	9.00000			0.491723
$336$		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
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	−7.50000	+	4.33013i	−0.406148	+	0.234490i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	7.50000	+	12.9904i	0.403786	+	0.699379i
$346$		0			0
$347$	7.50000	+	4.33013i	0.402621	+	0.232453i	0.687614	−	0.726076i	$-0.258658\pi$
$347$	7.50000	+	4.33013i	0.402621	+	0.232453i	−0.284993	+	0.958530i	$0.591991\pi$
$348$		0			0
$349$			27.7128i			1.48343i	0.670714	+	0.741716i	$0.265988\pi$
$349$			27.7128i			1.48343i	−0.670714	+	0.741716i	$0.734012\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	16.5000	+	9.52628i	0.878206	+	0.507033i	0.870067	−	0.492934i	$-0.164076\pi$
$353$	16.5000	+	9.52628i	0.878206	+	0.507033i	0.00813978	+	0.999967i	$0.497409\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.5000	+	7.79423i	−0.712503	+	0.411364i	−0.811987	−	0.583675i	$-0.801614\pi$
$359$	−13.5000	+	7.79423i	−0.712503	+	0.411364i	0.0994843	+	0.995039i	$0.468281\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$	8.00000			0.419891
$364$		0			0
$365$	3.00000			0.157027
$366$		0			0
$367$	−0.500000	+	0.866025i	−0.0260998	+	0.0452062i	−0.878780	−	0.477227i	$-0.841642\pi$
$367$	−0.500000	+	0.866025i	−0.0260998	+	0.0452062i	0.852680	+	0.522433i	$0.174975\pi$
$368$		0			0
$369$	−12.0000	+	6.92820i	−0.624695	+	0.360668i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	−0.647225	+	0.762299i	$0.724071\pi$
$374$		0			0
$375$	10.5000	+	6.06218i	0.542218	+	0.313050i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	10.3923i		−	0.533817i	−0.963722	−	0.266908i	$-0.913998\pi$
$379$		−	10.3923i		−	0.533817i	0.963722	−	0.266908i	$-0.0860021\pi$
$380$		0			0
$381$	−3.00000	−	1.73205i	−0.153695	−	0.0887357i
$382$		0			0
$383$	−13.5000	−	23.3827i	−0.689818	−	1.19480i	−0.971897	−	0.235408i	$-0.924357\pi$
$383$	−13.5000	−	23.3827i	−0.689818	−	1.19480i	0.282079	−	0.959391i	$-0.408976\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.00000	−	3.46410i	0.304997	−	0.176090i
$388$		0			0
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	−0.466915	−	0.884302i	$-0.654634\pi$
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	0.999286	−	0.0377914i	$-0.0120322\pi$
$390$		0			0
$391$	−45.0000			−2.27575
$392$		0			0
$393$	−21.0000			−1.05931
$394$		0			0
$395$	−4.50000	+	7.79423i	−0.226420	+	0.392170i
$396$		0			0
$397$	10.5000	−	6.06218i	0.526980	−	0.304252i	−0.212806	−	0.977095i	$-0.568260\pi$
$397$	10.5000	−	6.06218i	0.526980	−	0.304252i	0.739786	+	0.672843i	$0.234927\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		−	1.73205i		−	0.0860663i
$406$		0			0
$407$			8.66025i			0.429273i
$408$		0			0
$409$	4.50000	+	2.59808i	0.222511	+	0.128467i	0.607112	−	0.794616i	$-0.292328\pi$
$409$	4.50000	+	2.59808i	0.222511	+	0.128467i	−0.384602	+	0.923083i	$0.625661\pi$
$410$		0			0
$411$	−1.50000	−	2.59808i	−0.0739895	−	0.128154i
$412$		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
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	−9.00000	+	5.19615i	−0.436564	+	0.252050i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	25.5000	+	14.7224i	1.22829	+	0.709155i	0.966672	−	0.256017i	$-0.0824102\pi$
$431$	25.5000	+	14.7224i	1.22829	+	0.709155i	0.261619	+	0.965171i	$0.415743\pi$
$432$		0			0
$433$		−	34.6410i		−	1.66474i	−0.554220	−	0.832370i	$-0.686983\pi$
$433$		−	34.6410i		−	1.66474i	0.554220	−	0.832370i	$-0.313017\pi$
$434$		0			0
$435$			10.3923i			0.498273i
$436$		0			0
$437$	52.5000	+	30.3109i	2.51142	+	1.44997i
$438$		0			0
$439$	−9.50000	−	16.4545i	−0.453410	−	0.785330i	0.545185	−	0.838316i	$-0.316459\pi$
$439$	−9.50000	−	16.4545i	−0.453410	−	0.785330i	−0.998595	+	0.0529862i	$0.983126\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.5000	+	11.2583i	−0.926473	+	0.534899i	−0.885694	−	0.464269i	$-0.846317\pi$
$443$	−19.5000	+	11.2583i	−0.926473	+	0.534899i	−0.0407786	+	0.999168i	$0.512984\pi$
$444$		0			0
$445$	−10.5000	+	18.1865i	−0.497748	+	0.862124i
$446$		0			0
$447$	−9.00000			−0.425685
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$		0			0
$453$	10.5000	−	6.06218i	0.493333	−	0.284826i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$		0			0
$459$	−22.5000	−	12.9904i	−1.05021	−	0.606339i
$460$		0			0
$461$			27.7128i			1.29071i	0.763881	+	0.645357i	$0.223291\pi$
$461$			27.7128i			1.29071i	−0.763881	+	0.645357i	$0.776709\pi$
$462$		0			0
$463$			3.46410i			0.160990i	0.996755	+	0.0804952i	$0.0256502\pi$
$463$			3.46410i			0.160990i	−0.996755	+	0.0804952i	$0.974350\pi$
$464$		0			0
$465$	7.50000	+	4.33013i	0.347804	+	0.200805i
$466$		0			0
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	0.829231	−	0.558906i	$-0.188779\pi$
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	−0.898642	+	0.438682i	$0.855446\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	13.5000	−	7.79423i	0.622047	−	0.359139i
$472$		0			0
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	14.0000			0.642364
$476$		0			0
$477$	18.0000			0.824163
$478$		0			0
$479$	−4.50000	+	7.79423i	−0.205610	+	0.356127i	−0.950327	−	0.311253i	$-0.899251\pi$
$479$	−4.50000	+	7.79423i	−0.205610	+	0.356127i	0.744717	+	0.667381i	$0.232585\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.00000	−	10.3923i	−0.272446	−	0.471890i
$486$		0			0
$487$	7.50000	+	4.33013i	0.339857	+	0.196217i	0.660209	−	0.751082i	$-0.270468\pi$
$487$	7.50000	+	4.33013i	0.339857	+	0.196217i	−0.320352	+	0.947299i	$0.603801\pi$
$488$		0			0
$489$			12.1244i			0.548282i
$490$		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
$493$	−27.0000	−	15.5885i	−1.21602	−	0.702069i
$494$		0			0
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.5000	−	6.06218i	0.470045	−	0.271380i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	10.5000	−	6.06218i	0.470045	−	0.271380i	0.716258	+	0.697835i	$0.245853\pi$
$500$		0			0
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	−9.00000			−0.400495
$506$		0			0
$507$	−6.50000	+	11.2583i	−0.288675	+	0.500000i
$508$		0			0
$509$	−13.5000	+	7.79423i	−0.598377	+	0.345473i	−0.768403	−	0.639966i	$-0.778948\pi$
$509$	−13.5000	+	7.79423i	−0.598377	+	0.345473i	0.170026	+	0.985440i	$0.445615\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	17.5000	+	30.3109i	0.772644	+	1.33826i
$514$		0			0
$515$	−1.50000	−	0.866025i	−0.0660979	−	0.0381616i
$516$		0			0
$517$		−	5.19615i		−	0.228527i
$518$		0			0
$519$		−	8.66025i		−	0.380143i
$520$		0			0
$521$	−25.5000	−	14.7224i	−1.11718	−	0.645001i	−0.176497	−	0.984301i	$-0.556477\pi$
$521$	−25.5000	−	14.7224i	−1.11718	−	0.645001i	−0.940678	+	0.339300i	$0.889810\pi$
$522$		0			0
$523$	−11.5000	−	19.9186i	−0.502860	−	0.870979i	−0.999995	−	0.00330547i	$-0.998948\pi$
$523$	−11.5000	−	19.9186i	−0.502860	−	0.870979i	0.497135	−	0.867673i	$-0.334385\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−22.5000	+	12.9904i	−0.980115	+	0.565870i
$528$		0			0
$529$	26.0000	−	45.0333i	1.13043	−	1.95797i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−4.50000	+	7.79423i	−0.194552	+	0.336974i
$536$		0			0
$537$	−13.5000	+	7.79423i	−0.582568	+	0.336346i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−3.50000	−	6.06218i	−0.150477	−	0.260633i	0.780926	−	0.624623i	$-0.214748\pi$
$541$	−3.50000	−	6.06218i	−0.150477	−	0.260633i	−0.931403	+	0.363990i	$0.881414\pi$
$542$		0			0
$543$	6.00000	+	3.46410i	0.257485	+	0.148659i
$544$		0			0
$545$		−	19.0526i		−	0.816122i
$546$		0			0
$547$		−	24.2487i		−	1.03680i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$		−	24.2487i		−	1.03680i	0.855138	−	0.518400i	$-0.173472\pi$
$548$		0			0
$549$	−15.0000	−	8.66025i	−0.640184	−	0.369611i
$550$		0			0
$551$	21.0000	+	36.3731i	0.894630	+	1.54954i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	7.50000	−	4.33013i	0.318357	−	0.183804i
$556$		0			0
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	−0.896053	−	0.443947i	$-0.853578\pi$
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	0.832496	+	0.554031i	$0.186911\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−9.00000			−0.379980
$562$		0			0
$563$	7.50000	−	12.9904i	0.316087	−	0.547479i	−0.663581	−	0.748105i	$-0.730964\pi$
$563$	7.50000	−	12.9904i	0.316087	−	0.547479i	0.979668	+	0.200625i	$0.0642974\pi$
$564$		0			0
$565$	−9.00000	+	5.19615i	−0.378633	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$		0			0
$571$	−10.5000	−	6.06218i	−0.439411	−	0.253694i	0.263937	−	0.964540i	$-0.414979\pi$
$571$	−10.5000	−	6.06218i	−0.439411	−	0.253694i	−0.703348	+	0.710846i	$0.748312\pi$
$572$		0			0
$573$			12.1244i			0.506502i
$574$		0			0
$575$		−	17.3205i		−	0.722315i
$576$		0			0
$577$	−13.5000	−	7.79423i	−0.562012	−	0.324478i	0.191940	−	0.981407i	$-0.438522\pi$
$577$	−13.5000	−	7.79423i	−0.562012	−	0.324478i	−0.753953	+	0.656929i	$0.771855\pi$
$578$		0			0
$579$	2.50000	+	4.33013i	0.103896	+	0.179954i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	13.5000	−	7.79423i	0.559113	−	0.322804i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	35.0000			1.44215
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$		0			0
$593$	16.5000	−	9.52628i	0.677574	−	0.391197i	−0.121367	−	0.992608i	$-0.538728\pi$
$593$	16.5000	−	9.52628i	0.677574	−	0.391197i	0.798940	+	0.601410i	$0.205394\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.50000	+	9.52628i	0.225100	+	0.389885i
$598$		0			0
$599$	−28.5000	−	16.4545i	−1.16448	−	0.672312i	−0.212105	−	0.977247i	$-0.568032\pi$
$599$	−28.5000	−	16.4545i	−1.16448	−	0.672312i	−0.952373	+	0.304935i	$0.901365\pi$
$600$		0			0
$601$		−	6.92820i		−	0.282607i	−0.989966	−	0.141304i	$-0.954871\pi$
$601$		−	6.92820i		−	0.282607i	0.989966	−	0.141304i	$-0.0451294\pi$
$602$		0			0
$603$		−	10.3923i		−	0.423207i
$604$		0			0
$605$	12.0000	+	6.92820i	0.487869	+	0.281672i
$606$		0			0
$607$	14.5000	+	25.1147i	0.588537	+	1.01938i	0.994424	+	0.105453i	$0.0336291\pi$
$607$	14.5000	+	25.1147i	0.588537	+	1.01938i	−0.405887	+	0.913923i	$0.633038\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	−0.955458	−	0.295126i	$-0.904638\pi$
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	0.733316	+	0.679888i	$0.237972\pi$
$614$		0			0
$615$	12.0000			0.483887
$616$		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
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	−0.787075	−	0.616858i	$-0.788405\pi$
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	0.927752	+	0.373198i	$0.121739\pi$
$620$		0			0
$621$	37.5000	−	21.6506i	1.50482	−	0.868810i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$	10.5000	+	6.06218i	0.419330	+	0.242100i
$628$		0			0
$629$			25.9808i			1.03592i
$630$		0			0
$631$			45.0333i			1.79275i	0.443298	+	0.896374i	$0.353808\pi$
$631$			45.0333i			1.79275i	−0.443298	+	0.896374i	$0.646192\pi$
$632$		0			0
$633$	−21.0000	−	12.1244i	−0.834675	−	0.481900i
$634$		0			0
$635$	−3.00000	−	5.19615i	−0.119051	−	0.206203i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−6.00000	+	3.46410i	−0.237356	+	0.137038i
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$		0			0
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	−6.00000			−0.236250
$646$		0			0
$647$	7.50000	−	12.9904i	0.294855	−	0.510705i	−0.680096	−	0.733123i	$-0.738062\pi$
$647$	7.50000	−	12.9904i	0.294855	−	0.510705i	0.974951	+	0.222419i	$0.0713952\pi$
$648$		0			0
$649$	−13.5000	+	7.79423i	−0.529921	+	0.305950i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	0.835182	−	0.549973i	$-0.185362\pi$
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	−0.893882	+	0.448303i	$0.852029\pi$
$654$		0			0
$655$	−31.5000	−	18.1865i	−1.23081	−	0.710607i
$656$		0			0
$657$		−	3.46410i		−	0.135147i
$658$		0			0
$659$			24.2487i			0.944596i	0.881439	+	0.472298i	$0.156575\pi$
$659$			24.2487i			0.944596i	−0.881439	+	0.472298i	$0.843425\pi$
$660$		0			0
$661$	34.5000	+	19.9186i	1.34189	+	0.774743i	0.987085	−	0.160196i	$-0.0512125\pi$
$661$	34.5000	+	19.9186i	1.34189	+	0.774743i	0.354809	+	0.934939i	$0.384546\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	45.0000	−	25.9808i	1.74241	−	1.00598i
$668$		0			0
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$		0			0
$671$	−15.0000			−0.579069
$672$		0			0
$673$	−50.0000			−1.92736			−0.963679	−	0.267063i	$-0.913947\pi$
$673$	−50.0000			−1.92736			−0.963679	+	0.267063i	$0.913947\pi$
$674$		0			0
$675$	5.00000	−	8.66025i	0.192450	−	0.333333i
$676$		0			0
$677$	34.5000	−	19.9186i	1.32594	−	0.765533i	0.341273	−	0.939964i	$-0.389142\pi$
$677$	34.5000	−	19.9186i	1.32594	−	0.765533i	0.984669	+	0.174431i	$0.0558085\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−10.5000	−	18.1865i	−0.402361	−	0.696909i
$682$		0			0
$683$	37.5000	+	21.6506i	1.43490	+	0.828439i	0.997489	−	0.0708242i	$-0.0225629\pi$
$683$	37.5000	+	21.6506i	1.43490	+	0.828439i	0.437409	+	0.899263i	$0.355896\pi$
$684$		0			0
$685$		−	5.19615i		−	0.198535i
$686$		0			0
$687$			12.1244i			0.462573i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	0.962768	−	0.270330i	$-0.0871327\pi$
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	−0.715496	+	0.698617i	$0.753799\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.00000	−	3.46410i	0.227593	−	0.131401i
$696$		0			0
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$		0			0
$699$	3.00000			0.113470
$700$		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
$703$	17.5000	−	30.3109i	0.660025	−	1.14320i
$704$		0			0
$705$	−4.50000	+	2.59808i	−0.169480	+	0.0978492i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	−0.981331	−	0.192328i	$-0.938396\pi$
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	0.324104	−	0.946021i	$-0.394937\pi$
$710$		0			0
$711$	9.00000	+	5.19615i	0.337526	+	0.194871i
$712$		0			0
$713$		−	43.3013i		−	1.62165i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$		0			0
$719$	16.5000	+	28.5788i	0.615346	+	1.06581i	0.990324	+	0.138777i	$0.0443171\pi$
$719$	16.5000	+	28.5788i	0.615346	+	1.06581i	−0.374978	+	0.927034i	$0.622350\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−10.5000	+	6.06218i	−0.390499	+	0.225455i
$724$		0			0
$725$	6.00000	−	10.3923i	0.222834	−	0.385961i
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	9.00000	−	15.5885i	0.332877	−	0.576560i
$732$		0			0
$733$	16.5000	−	9.52628i	0.609441	−	0.351861i	−0.163305	−	0.986576i	$-0.552216\pi$
$733$	16.5000	−	9.52628i	0.609441	−	0.351861i	0.772747	+	0.634714i	$0.218882\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.50000	−	7.79423i	−0.165760	−	0.287104i
$738$		0			0
$739$	1.50000	+	0.866025i	0.0551784	+	0.0318573i	0.527335	−	0.849657i	$-0.323191\pi$
$739$	1.50000	+	0.866025i	0.0551784	+	0.0318573i	−0.472157	+	0.881514i	$0.656524\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	38.1051i		−	1.39794i	−0.715150	−	0.698971i	$-0.753642\pi$
$743$		−	38.1051i		−	1.39794i	0.715150	−	0.698971i	$-0.246358\pi$
$744$		0			0
$745$	−13.5000	−	7.79423i	−0.494602	−	0.285558i
$746$		0			0
$747$	12.0000	+	20.7846i	0.439057	+	0.760469i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	34.5000	−	19.9186i	1.25892	−	0.726839i	0.286058	−	0.958212i	$-0.407655\pi$
$751$	34.5000	−	19.9186i	1.25892	−	0.726839i	0.972865	+	0.231373i	$0.0743217\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	21.0000			0.764268
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$		0			0
$759$	7.50000	−	12.9904i	0.272233	−	0.471521i
$760$		0			0
$761$	4.50000	−	2.59808i	0.163125	−	0.0941802i	−0.416215	−	0.909266i	$-0.636644\pi$
$761$	4.50000	−	2.59808i	0.163125	−	0.0941802i	0.579340	+	0.815086i	$0.303310\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−9.00000	−	15.5885i	−0.325396	−	0.563602i
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	6.92820i		−	0.249837i	−0.992167	−	0.124919i	$-0.960133\pi$
$769$		−	6.92820i		−	0.249837i	0.992167	−	0.124919i	$-0.0398670\pi$
$770$		0			0
$771$			19.0526i			0.686161i
$772$		0			0
$773$	−7.50000	−	4.33013i	−0.269756	−	0.155744i	0.359021	−	0.933330i	$-0.383111\pi$
$773$	−7.50000	−	4.33013i	−0.269756	−	0.155744i	−0.628777	+	0.777586i	$0.716444\pi$
$774$		0			0
$775$	−5.00000	−	8.66025i	−0.179605	−	0.311086i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	42.0000	−	24.2487i	1.50481	−	0.868800i
$780$		0			0
$781$	−3.00000	+	5.19615i	−0.107348	+	0.185933i
$782$		0			0
$783$	30.0000			1.07211
$784$		0			0
$785$	27.0000			0.963671
$786$		0			0
$787$	3.50000	−	6.06218i	0.124762	−	0.216093i	−0.796878	−	0.604140i	$-0.793517\pi$
$787$	3.50000	−	6.06218i	0.124762	−	0.216093i	0.921640	+	0.388047i	$0.126850\pi$
$788$		0			0
$789$	−7.50000	+	4.33013i	−0.267007	+	0.154157i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−13.5000	−	7.79423i	−0.478796	−	0.276433i
$796$		0			0
$797$			13.8564i			0.490819i	0.969419	+	0.245410i	$0.0789224\pi$
$797$			13.8564i			0.490819i	−0.969419	+	0.245410i	$0.921078\pi$
$798$		0			0
$799$		−	15.5885i		−	0.551480i
$800$		0			0
$801$	21.0000	+	12.1244i	0.741999	+	0.428393i
$802$		0			0
$803$	−1.50000	−	2.59808i	−0.0529339	−	0.0916841i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.50000	−	0.866025i	0.0528025	−	0.0304855i
$808$		0			0
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	−0.967219	−	0.253946i	$-0.918272\pi$
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	0.703533	+	0.710663i	$0.251605\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$	−1.00000			−0.0350715
$814$		0			0
$815$	−10.5000	+	18.1865i	−0.367799	+	0.637046i
$816$		0			0
$817$	−21.0000	+	12.1244i	−0.734697	+	0.424178i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	28.5000	+	49.3634i	0.994657	+	1.72280i	0.586734	+	0.809780i	$0.300414\pi$
$821$	28.5000	+	49.3634i	0.994657	+	1.72280i	0.407923	+	0.913016i	$0.366253\pi$
$822$		0			0
$823$	19.5000	+	11.2583i	0.679727	+	0.392441i	0.799752	−	0.600330i	$-0.204964\pi$
$823$	19.5000	+	11.2583i	0.679727	+	0.392441i	−0.120025	+	0.992771i	$0.538297\pi$
$824$		0			0
$825$		−	3.46410i		−	0.120605i
$826$		0			0
$827$			38.1051i			1.32504i	0.749042	+	0.662522i	$0.230514\pi$
$827$			38.1051i			1.32504i	−0.749042	+	0.662522i	$0.769486\pi$
$828$		0			0
$829$	−7.50000	−	4.33013i	−0.260486	−	0.150392i	0.364070	−	0.931371i	$-0.381387\pi$
$829$	−7.50000	−	4.33013i	−0.260486	−	0.150392i	−0.624556	+	0.780980i	$0.714720\pi$
$830$		0			0
$831$	8.50000	+	14.7224i	0.294862	+	0.510716i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.0000	+	10.3923i	−0.622916	+	0.359641i
$836$		0			0
$837$	12.5000	−	21.6506i	0.432063	−	0.748355i
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−3.00000	+	5.19615i	−0.103325	+	0.178965i
$844$		0			0
$845$	−19.5000	+	11.2583i	−0.670820	+	0.387298i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	5.50000	+	9.52628i	0.188760	+	0.326941i
$850$		0			0
$851$	−37.5000	−	21.6506i	−1.28548	−	0.742174i
$852$		0			0
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$		0			0
$855$			24.2487i			0.829288i
$856$		0			0
$857$	−37.5000	−	21.6506i	−1.28098	−	0.739572i	−0.303949	−	0.952688i	$-0.598305\pi$
$857$	−37.5000	−	21.6506i	−1.28098	−	0.739572i	−0.977027	+	0.213117i	$0.931639\pi$
$858$		0			0
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	0.968657	+	0.248402i	$0.0799054\pi$
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	−0.269206	+	0.963083i	$0.586761\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	40.5000	−	23.3827i	1.37864	−	0.795956i	0.386641	−	0.922230i	$-0.373635\pi$
$863$	40.5000	−	23.3827i	1.37864	−	0.795956i	0.991995	+	0.126275i	$0.0403020\pi$
$864$		0			0
$865$	7.50000	−	12.9904i	0.255008	−	0.441686i
$866$		0			0
$867$	−10.0000			−0.339618
$868$		0			0
$869$	9.00000			0.305304
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−12.0000	+	6.92820i	−0.406138	+	0.234484i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.5000	−	40.7032i	−0.793539	−	1.37445i	−0.923763	−	0.382965i	$-0.874903\pi$
$877$	−23.5000	−	40.7032i	−0.793539	−	1.37445i	0.130224	−	0.991485i	$-0.458430\pi$
$878$		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
$883$		−	45.0333i		−	1.51549i	−0.652550	−	0.757746i	$-0.726301\pi$
$883$		−	45.0333i		−	1.51549i	0.652550	−	0.757746i	$-0.273699\pi$
$884$		0			0
$885$	13.5000	+	7.79423i	0.453798	+	0.262000i
$886$		0			0
$887$	−1.50000	−	2.59808i	−0.0503651	−	0.0872349i	0.839744	−	0.542983i	$-0.182705\pi$
$887$	−1.50000	−	2.59808i	−0.0503651	−	0.0872349i	−0.890109	+	0.455748i	$0.849372\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.50000	+	0.866025i	−0.0502519	+	0.0290129i
$892$		0			0
$893$	−10.5000	+	18.1865i	−0.351369	+	0.608589i
$894$		0			0
$895$	−27.0000			−0.902510
$896$		0			0
$897$		0			0
$898$		0			0
$899$	15.0000	−	25.9808i	0.500278	−	0.866507i
$900$		0			0
$901$	40.5000	−	23.3827i	1.34925	−	0.778990i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.00000	+	10.3923i	0.199447	+	0.345452i
$906$		0			0
$907$	−4.50000	−	2.59808i	−0.149420	−	0.0862677i	0.423426	−	0.905931i	$-0.360827\pi$
$907$	−4.50000	−	2.59808i	−0.149420	−	0.0862677i	−0.572846	+	0.819663i	$0.694161\pi$
$908$		0			0
$909$			10.3923i			0.344691i
$910$		0			0
$911$		−	10.3923i		−	0.344312i	−0.985070	−	0.172156i	$-0.944927\pi$
$911$		−	10.3923i		−	0.344312i	0.985070	−	0.172156i	$-0.0550734\pi$
$912$		0			0
$913$	18.0000	+	10.3923i	0.595713	+	0.343935i
$914$		0			0
$915$	7.50000	+	12.9904i	0.247942	+	0.429449i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−37.5000	+	21.6506i	−1.23701	+	0.714189i	−0.968482	−	0.249083i	$-0.919871\pi$
$919$	−37.5000	+	21.6506i	−1.23701	+	0.714189i	−0.268529	+	0.963272i	$0.586537\pi$
$920$		0			0
$921$	10.0000	−	17.3205i	0.329511	−	0.570730i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−10.0000			−0.328798
$926$		0			0
$927$	−1.00000	+	1.73205i	−0.0328443	+	0.0568880i
$928$		0			0
$929$	22.5000	−	12.9904i	0.738201	−	0.426201i	−0.0832138	−	0.996532i	$-0.526518\pi$
$929$	22.5000	−	12.9904i	0.738201	−	0.426201i	0.821415	+	0.570331i	$0.193185\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−16.5000	−	28.5788i	−0.540186	−	0.935629i
$934$		0			0
$935$	−13.5000	−	7.79423i	−0.441497	−	0.254899i
$936$		0			0
$937$			41.5692i			1.35801i	0.734135	+	0.679004i	$0.237588\pi$
$937$			41.5692i			1.35801i	−0.734135	+	0.679004i	$0.762412\pi$
$938$		0			0
$939$		−	29.4449i		−	0.960897i
$940$		0			0
$941$	−25.5000	−	14.7224i	−0.831276	−	0.479938i	0.0230132	−	0.999735i	$-0.492674\pi$
$941$	−25.5000	−	14.7224i	−0.831276	−	0.479938i	−0.854289	+	0.519798i	$0.826007\pi$
$942$		0			0
$943$	−30.0000	−	51.9615i	−0.976934	−	1.69210i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.5000	+	14.7224i	−0.828639	+	0.478415i	−0.853386	−	0.521279i	$-0.825455\pi$
$947$	−25.5000	+	14.7224i	−0.828639	+	0.478415i	0.0247477	+	0.999694i	$0.492122\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−21.0000			−0.680972
$952$		0			0
$953$	−18.0000			−0.583077			−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000			−0.583077			−0.291539	+	0.956559i	$0.594167\pi$
$954$		0			0
$955$	−10.5000	+	18.1865i	−0.339772	+	0.588502i
$956$		0			0
$957$	9.00000	−	5.19615i	0.290929	−	0.167968i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$	9.00000	+	5.19615i	0.290021	+	0.167444i
$964$		0			0
$965$			8.66025i			0.278783i
$966$		0			0
$967$			31.1769i			1.00258i	0.865279	+	0.501291i	$0.167141\pi$
$967$			31.1769i			1.00258i	−0.865279	+	0.501291i	$0.832859\pi$
$968$		0			0
$969$	31.5000	+	18.1865i	1.01193	+	0.584236i
$970$		0			0
$971$	−1.50000	−	2.59808i	−0.0481373	−	0.0833762i	0.840953	−	0.541108i	$-0.181995\pi$
$971$	−1.50000	−	2.59808i	−0.0481373	−	0.0833762i	−0.889090	+	0.457732i	$0.848662\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.5000	+	23.3827i	−0.431903	+	0.748078i	−0.997037	−	0.0769208i	$-0.975491\pi$
$977$	−13.5000	+	23.3827i	−0.431903	+	0.748078i	0.565134	+	0.824999i	$0.308824\pi$
$978$		0			0
$979$	21.0000			0.671163
$980$		0			0
$981$	−22.0000			−0.702406
$982$		0			0
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	−0.841112	−	0.540860i	$-0.818099\pi$
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	0.888955	+	0.457995i	$0.151432\pi$
$984$		0			0
$985$	9.00000	−	5.19615i	0.286764	−	0.165563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	15.0000	+	25.9808i	0.476972	+	0.826140i
$990$		0			0
$991$	−4.50000	−	2.59808i	−0.142947	−	0.0825306i	0.426821	−	0.904336i	$-0.359634\pi$
$991$	−4.50000	−	2.59808i	−0.142947	−	0.0825306i	−0.569768	+	0.821806i	$0.692967\pi$
$992$		0			0
$993$		−	29.4449i		−	0.934405i
$994$		0			0
$995$			19.0526i			0.604007i
$996$		0			0
$997$	−1.50000	−	0.866025i	−0.0475055	−	0.0274273i	0.476059	−	0.879413i	$-0.342065\pi$
$997$	−1.50000	−	0.866025i	−0.0475055	−	0.0274273i	−0.523565	+	0.851986i	$0.675398\pi$
$998$		0			0
$999$	−12.5000	−	21.6506i	−0.395482	−	0.684996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.p.c.31.1		2
4.3	odd	2		784.2.p.d.31.1		2
7.2	even	3		112.2.p.a.47.1	yes	2
7.3	odd	6		784.2.f.a.783.2		2
7.4	even	3		784.2.f.b.783.1		2
7.5	odd	6		784.2.p.d.607.1		2
7.6	odd	2		112.2.p.b.31.1	yes	2
21.2	odd	6		1008.2.cs.f.271.1		2
21.11	odd	6		7056.2.b.m.1567.2		2
21.17	even	6		7056.2.b.b.1567.1		2
21.20	even	2		1008.2.cs.c.703.1		2
28.3	even	6		784.2.f.b.783.2		2
28.11	odd	6		784.2.f.a.783.1		2
28.19	even	6	inner	784.2.p.c.607.1		2
28.23	odd	6		112.2.p.b.47.1	yes	2
28.27	even	2		112.2.p.a.31.1	✓	2
56.3	even	6		3136.2.f.a.3135.1		2
56.11	odd	6		3136.2.f.b.3135.2		2
56.13	odd	2		448.2.p.a.255.1		2
56.27	even	2		448.2.p.b.255.1		2
56.37	even	6		448.2.p.b.383.1		2
56.45	odd	6		3136.2.f.b.3135.1		2
56.51	odd	6		448.2.p.a.383.1		2
56.53	even	6		3136.2.f.a.3135.2		2
84.11	even	6		7056.2.b.b.1567.2		2
84.23	even	6		1008.2.cs.c.271.1		2
84.59	odd	6		7056.2.b.m.1567.1		2
84.83	odd	2		1008.2.cs.f.703.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.p.a.31.1	✓	2	28.27	even	2
112.2.p.a.47.1	yes	2	7.2	even	3
112.2.p.b.31.1	yes	2	7.6	odd	2
112.2.p.b.47.1	yes	2	28.23	odd	6
448.2.p.a.255.1		2	56.13	odd	2
448.2.p.a.383.1		2	56.51	odd	6
448.2.p.b.255.1		2	56.27	even	2
448.2.p.b.383.1		2	56.37	even	6
784.2.f.a.783.1		2	28.11	odd	6
784.2.f.a.783.2		2	7.3	odd	6
784.2.f.b.783.1		2	7.4	even	3
784.2.f.b.783.2		2	28.3	even	6
784.2.p.c.31.1		2	1.1	even	1	trivial
784.2.p.c.607.1		2	28.19	even	6	inner
784.2.p.d.31.1		2	4.3	odd	2
784.2.p.d.607.1		2	7.5	odd	6
1008.2.cs.c.271.1		2	84.23	even	6
1008.2.cs.c.703.1		2	21.20	even	2
1008.2.cs.f.271.1		2	21.2	odd	6
1008.2.cs.f.703.1		2	84.83	odd	2
3136.2.f.a.3135.1		2	56.3	even	6
3136.2.f.a.3135.2		2	56.53	even	6
3136.2.f.b.3135.1		2	56.45	odd	6
3136.2.f.b.3135.2		2	56.11	odd	6
7056.2.b.b.1567.1		2	21.17	even	6
7056.2.b.b.1567.2		2	84.11	even	6
7056.2.b.m.1567.1		2	84.59	odd	6
7056.2.b.m.1567.2		2	21.11	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(1.50000 + 0.866025i) q^{11} -1.73205i q^{15} +(4.50000 + 2.59808i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-7.50000 + 4.33013i) q^{23} +(-1.00000 + 1.73205i) q^{25} -5.00000 q^{27} -6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-1.50000 + 0.866025i) q^{33} +(2.50000 + 4.33013i) q^{37} +6.92820i q^{41} -3.46410i q^{43} +(-3.00000 - 1.73205i) q^{45} +(-1.50000 - 2.59808i) q^{47} +(-4.50000 + 2.59808i) q^{51} +(4.50000 - 7.79423i) q^{53} -3.00000 q^{55} +7.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(-7.50000 + 4.33013i) q^{61} +(-4.50000 - 2.59808i) q^{67} -8.66025i q^{69} +3.46410i q^{71} +(-1.50000 - 0.866025i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(4.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} -9.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +(10.5000 - 6.06218i) q^{89} +(-2.50000 - 4.33013i) q^{93} +(10.5000 + 6.06218i) q^{95} +6.92820i q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 3 q^{5} + 2 q^{9}+O(q^{10}) \) 2 * q - q^3 - 3 * q^5 + 2 * q^9	\( 2 q - q^{3} - 3 q^{5} + 2 q^{9} + 3 q^{11} + 9 q^{17} - 7 q^{19} - 15 q^{23} - 2 q^{25} - 10 q^{27} - 12 q^{29} - 5 q^{31} - 3 q^{33} + 5 q^{37} - 6 q^{45} - 3 q^{47} - 9 q^{51} + 9 q^{53} - 6 q^{55} + 14 q^{57} - 9 q^{59} - 15 q^{61} - 9 q^{67} - 3 q^{73} - 2 q^{75} + 9 q^{79} - q^{81} + 24 q^{83} - 18 q^{85} + 6 q^{87} + 21 q^{89} - 5 q^{93} + 21 q^{95}+O(q^{100}) \) 2 * q - q^3 - 3 * q^5 + 2 * q^9 + 3 * q^11 + 9 * q^17 - 7 * q^19 - 15 * q^23 - 2 * q^25 - 10 * q^27 - 12 * q^29 - 5 * q^31 - 3 * q^33 + 5 * q^37 - 6 * q^45 - 3 * q^47 - 9 * q^51 + 9 * q^53 - 6 * q^55 + 14 * q^57 - 9 * q^59 - 15 * q^61 - 9 * q^67 - 3 * q^73 - 2 * q^75 + 9 * q^79 - q^81 + 24 * q^83 - 18 * q^85 + 6 * q^87 + 21 * q^89 - 5 * q^93 + 21 * q^95

Introduction

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