LMFDB - Embedded newform 676.2.h.d.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(361,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("676.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.h (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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	676.361
Dual form			676.2.h.d.485.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{3} +3.00000i q^{5} +(3.46410 + 2.00000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-5.19615 + 3.00000i) q^{15} +(1.50000 - 2.59808i) q^{17} +(1.73205 + 1.00000i) q^{19} +8.00000i q^{21} +(-3.00000 - 5.19615i) q^{23} -4.00000 q^{25} +4.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} -2.00000i q^{31} +(-6.00000 + 10.3923i) q^{35} +(-6.06218 + 3.50000i) q^{37} +(-2.59808 + 1.50000i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(-2.59808 - 1.50000i) q^{45} -6.00000i q^{47} +(4.50000 + 7.79423i) q^{49} +6.00000 q^{51} +9.00000 q^{53} +4.00000i q^{57} +(-2.50000 + 4.33013i) q^{61} +(-3.46410 + 2.00000i) q^{63} +(-1.73205 + 1.00000i) q^{67} +(6.00000 - 10.3923i) q^{69} +(-5.19615 - 3.00000i) q^{71} -1.00000i q^{73} +(-4.00000 - 6.92820i) q^{75} -4.00000 q^{79} +(5.50000 + 9.52628i) q^{81} -12.0000i q^{83} +(7.79423 + 4.50000i) q^{85} +(9.00000 - 15.5885i) q^{87} +(5.19615 - 3.00000i) q^{89} +(3.46410 - 2.00000i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(12.1244 + 7.00000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 2 q^{9} + 6 q^{17} - 12 q^{23} - 16 q^{25} + 16 q^{27} - 18 q^{29} - 24 q^{35} - 8 q^{43} + 18 q^{49} + 24 q^{51} + 36 q^{53} - 10 q^{61} + 24 q^{69} - 16 q^{75} - 16 q^{79} + 22 q^{81}+ \cdots - 12 q^{95}+O(q^{100}) $ 4 * q + 4 * q^3 - 2 * q^9 + 6 * q^17 - 12 * q^23 - 16 * q^25 + 16 * q^27 - 18 * q^29 - 24 * q^35 - 8 * q^43 + 18 * q^49 + 24 * q^51 + 36 * q^53 - 10 * q^61 + 24 * q^69 - 16 * q^75 - 16 * q^79 + 22 * q^81 + 36 * q^87 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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	0.995782	+	0.0917517i	$0.0292466\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	−0.418432	+	0.908248i	$0.637420\pi$
$4$		0			0
$5$			3.00000i			1.34164i	0.741620	+	0.670820i	$0.234058\pi$
$5$			3.00000i			1.34164i	−0.741620	+	0.670820i	$0.765942\pi$
$6$		0			0
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.981981	−	0.188982i	$-0.0605189\pi$
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.327327	+	0.944911i	$0.393852\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−5.19615	+	3.00000i	−1.34164	+	0.774597i
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	0.685344	−	0.728219i	$-0.259652\pi$
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	−0.287984	+	0.957635i	$0.592985\pi$
$20$		0			0
$21$			8.00000i			1.74574i
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.00000	+	10.3923i	−1.01419	+	1.75662i
$36$		0			0
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.907245	−	0.420602i	$-0.861819\pi$
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.0893706	+	0.995998i	$0.528486\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	−0.688963	−	0.724797i	$-0.741934\pi$
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	0.283211	+	0.959058i	$0.408600\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$		0			0
$45$	−2.59808	−	1.50000i	−0.387298	−	0.223607i
$46$		0			0
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$		0			0
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$		0			0
$51$	6.00000			0.840168
$52$		0			0
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			4.00000i			0.529813i
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$		0			0
$63$	−3.46410	+	2.00000i	−0.436436	+	0.251976i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.73205	+	1.00000i	−0.211604	+	0.122169i	−0.602056	−	0.798454i	$-0.705652\pi$
$67$	−1.73205	+	1.00000i	−0.211604	+	0.122169i	0.390453	+	0.920623i	$0.372318\pi$
$68$		0			0
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$		0			0
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	0.158901	−	0.987294i	$-0.449205\pi$
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	−0.775571	+	0.631260i	$0.782538\pi$
$72$		0			0
$73$		−	1.00000i		−	0.117041i	−0.998286	−	0.0585206i	$-0.981362\pi$
$73$		−	1.00000i		−	0.117041i	0.998286	−	0.0585206i	$-0.0186383\pi$
$74$		0			0
$75$	−4.00000	−	6.92820i	−0.461880	−	0.800000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$		0			0
$85$	7.79423	+	4.50000i	0.845403	+	0.488094i
$86$		0			0
$87$	9.00000	−	15.5885i	0.964901	−	1.67126i
$88$		0			0
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	−0.198650	−	0.980071i	$-0.563656\pi$
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	0.749441	+	0.662071i	$0.230322\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	12.1244	+	7.00000i	1.23104	+	0.710742i	0.967247	−	0.253837i	$-0.0816925\pi$
$97$	12.1244	+	7.00000i	1.23104	+	0.710742i	0.263795	+	0.964579i	$0.415026\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	−2.00000			−0.197066			−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000			−0.197066			−0.0985329	+	0.995134i	$0.531415\pi$
$104$		0			0
$105$	−24.0000			−2.34216
$106$		0			0
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$		0			0
$109$			10.0000i			0.957826i	0.877862	+	0.478913i	$0.158969\pi$
$109$			10.0000i			0.957826i	−0.877862	+	0.478913i	$0.841031\pi$
$110$		0			0
$111$	−12.1244	−	7.00000i	−1.15079	−	0.664411i
$112$		0			0
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$		0			0
$115$	15.5885	−	9.00000i	1.45363	−	0.839254i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.3923	−	6.00000i	0.952661	−	0.550019i
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$		0			0
$123$	−5.19615	−	3.00000i	−0.468521	−	0.270501i
$124$		0			0
$125$			3.00000i			0.268328i
$126$		0			0
$127$	−5.00000	−	8.66025i	−0.443678	−	0.768473i	0.554281	−	0.832330i	$-0.312993\pi$
$127$	−5.00000	−	8.66025i	−0.443678	−	0.768473i	−0.997959	+	0.0638564i	$0.979660\pi$
$128$		0			0
$129$	−8.00000			−0.704361
$130$		0			0
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$		0			0
$135$			12.0000i			1.03280i
$136$		0			0
$137$	−12.9904	−	7.50000i	−1.10984	−	0.640768i	−0.171054	−	0.985262i	$-0.554717\pi$
$137$	−12.9904	−	7.50000i	−1.10984	−	0.640768i	−0.938789	+	0.344493i	$0.888051\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$	10.3923	−	6.00000i	0.875190	−	0.505291i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	23.3827	−	13.5000i	1.94183	−	1.12111i
$146$		0			0
$147$	−9.00000	+	15.5885i	−0.742307	+	1.28571i
$148$		0			0
$149$	7.79423	+	4.50000i	0.638528	+	0.368654i	0.784047	−	0.620701i	$-0.213152\pi$
$149$	7.79423	+	4.50000i	0.638528	+	0.368654i	−0.145519	+	0.989355i	$0.546485\pi$
$150$		0			0
$151$		−	10.0000i		−	0.813788i	−0.913475	−	0.406894i	$-0.866612\pi$
$151$		−	10.0000i		−	0.813788i	0.913475	−	0.406894i	$-0.133388\pi$
$152$		0			0
$153$	1.50000	+	2.59808i	0.121268	+	0.210042i
$154$		0			0
$155$	6.00000			0.481932
$156$		0			0
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$		0			0
$159$	9.00000	+	15.5885i	0.713746	+	1.23625i
$160$		0			0
$161$		−	24.0000i		−	1.89146i
$162$		0			0
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	0.203497	−	0.979076i	$-0.434769\pi$
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	−0.746156	+	0.665771i	$0.768103\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−20.7846	+	12.0000i	−1.60836	+	0.928588i	−0.618624	+	0.785687i	$0.712310\pi$
$167$	−20.7846	+	12.0000i	−1.60836	+	0.928588i	−0.989737	+	0.142901i	$0.954357\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−1.73205	+	1.00000i	−0.132453	+	0.0764719i
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	−13.8564	−	8.00000i	−1.04745	−	0.604743i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.831408	+	0.555663i	$0.187536\pi$
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.0655145	+	0.997852i	$0.479131\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$	−10.0000			−0.739221
$184$		0			0
$185$	−10.5000	−	18.1865i	−0.771975	−	1.33710i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	13.8564	+	8.00000i	1.00791	+	0.581914i
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	−0.116289	−	0.993215i	$-0.537100\pi$
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	0.802005	+	0.597317i	$0.203766\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	−0.673550	−	0.739141i	$-0.735232\pi$
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	0.303340	+	0.952882i	$0.401898\pi$
$198$		0			0
$199$	13.0000	−	22.5167i	0.921546	−	1.59616i	0.124521	−	0.992217i	$-0.460261\pi$
$199$	13.0000	−	22.5167i	0.921546	−	1.59616i	0.797025	−	0.603947i	$-0.206406\pi$
$200$		0			0
$201$	−3.46410	−	2.00000i	−0.244339	−	0.141069i
$202$		0			0
$203$		−	36.0000i		−	2.52670i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.00000	−	1.73205i	−0.0688428	−	0.119239i	0.829549	−	0.558433i	$-0.188597\pi$
$211$	−1.00000	−	1.73205i	−0.0688428	−	0.119239i	−0.898392	+	0.439194i	$0.855264\pi$
$212$		0			0
$213$		−	12.0000i		−	0.822226i
$214$		0			0
$215$	−10.3923	−	6.00000i	−0.708749	−	0.409197i
$216$		0			0
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$		0			0
$219$	1.73205	−	1.00000i	0.117041	−	0.0675737i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−22.5167	+	13.0000i	−1.50783	+	0.870544i	−0.507869	+	0.861435i	$0.669566\pi$
$223$	−22.5167	+	13.0000i	−1.50783	+	0.870544i	−0.999959	+	0.00910984i	$0.997100\pi$
$224$		0			0
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$		0			0
$227$	5.19615	+	3.00000i	0.344881	+	0.199117i	0.662428	−	0.749125i	$-0.269526\pi$
$227$	5.19615	+	3.00000i	0.344881	+	0.199117i	−0.317547	+	0.948242i	$0.602859\pi$
$228$		0			0
$229$			14.0000i			0.925146i	0.886581	+	0.462573i	$0.153074\pi$
$229$			14.0000i			0.925146i	−0.886581	+	0.462573i	$0.846926\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	18.0000			1.17419
$236$		0			0
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$		0			0
$239$		−	24.0000i		−	1.55243i	−0.630468	−	0.776215i	$-0.717137\pi$
$239$		−	24.0000i		−	1.55243i	0.630468	−	0.776215i	$-0.282863\pi$
$240$		0			0
$241$	0.866025	+	0.500000i	0.0557856	+	0.0322078i	0.527633	−	0.849472i	$-0.323079\pi$
$241$	0.866025	+	0.500000i	0.0557856	+	0.0322078i	−0.471848	+	0.881680i	$0.656413\pi$
$242$		0			0
$243$	−5.00000	+	8.66025i	−0.320750	+	0.555556i
$244$		0			0
$245$	−23.3827	+	13.5000i	−1.49387	+	0.862483i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	20.7846	−	12.0000i	1.31717	−	0.760469i
$250$		0			0
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	−0.945036	−	0.326965i	$-0.893974\pi$
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	0.755678	+	0.654943i	$0.227307\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$			18.0000i			1.12720i
$256$		0			0
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$		0			0
$259$	−28.0000			−1.73984
$260$		0			0
$261$	9.00000			0.557086
$262$		0			0
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$			27.0000i			1.65860i
$266$		0			0
$267$	10.3923	+	6.00000i	0.635999	+	0.367194i
$268$		0			0
$269$	−15.0000	+	25.9808i	−0.914566	+	1.58408i	−0.107031	+	0.994256i	$0.534134\pi$
$269$	−15.0000	+	25.9808i	−0.914566	+	1.58408i	−0.807535	+	0.589819i	$0.799199\pi$
$270$		0			0
$271$	6.92820	−	4.00000i	0.420858	−	0.242983i	−0.274586	−	0.961563i	$-0.588541\pi$
$271$	6.92820	−	4.00000i	0.420858	−	0.242983i	0.695444	+	0.718580i	$0.255208\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	0.425684	+	0.904872i	$0.360033\pi$
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	−0.996484	+	0.0837823i	$0.973300\pi$
$278$		0			0
$279$	1.73205	+	1.00000i	0.103695	+	0.0598684i
$280$		0			0
$281$			3.00000i			0.178965i	0.995988	+	0.0894825i	$0.0285213\pi$
$281$			3.00000i			0.178965i	−0.995988	+	0.0894825i	$0.971479\pi$
$282$		0			0
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	0.524057	−	0.851683i	$-0.324418\pi$
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	−0.999608	+	0.0280052i	$0.991084\pi$
$284$		0			0
$285$	−12.0000			−0.710819
$286$		0			0
$287$	−12.0000			−0.708338
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$			28.0000i			1.64139i
$292$		0			0
$293$	−7.79423	−	4.50000i	−0.455344	−	0.262893i	0.254741	−	0.967009i	$-0.418010\pi$
$293$	−7.79423	−	4.50000i	−0.455344	−	0.262893i	−0.710084	+	0.704117i	$0.751343\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−13.8564	+	8.00000i	−0.798670	+	0.461112i
$302$		0			0
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$		0			0
$305$	−12.9904	−	7.50000i	−0.743827	−	0.429449i
$306$		0			0
$307$			26.0000i			1.48390i	0.670456	+	0.741949i	$0.266098\pi$
$307$			26.0000i			1.48390i	−0.670456	+	0.741949i	$0.733902\pi$
$308$		0			0
$309$	−2.00000	−	3.46410i	−0.113776	−	0.197066i
$310$		0			0
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$	−6.00000	−	10.3923i	−0.338062	−	0.585540i
$316$		0			0
$317$			15.0000i			0.842484i	0.906948	+	0.421242i	$0.138406\pi$
$317$			15.0000i			0.842484i	−0.906948	+	0.421242i	$0.861594\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$	5.19615	−	3.00000i	0.289122	−	0.166924i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−17.3205	+	10.0000i	−0.957826	+	0.553001i
$328$		0			0
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	27.7128	+	16.0000i	1.52323	+	0.879440i	0.999622	+	0.0274825i	$0.00874905\pi$
$331$	27.7128	+	16.0000i	1.52323	+	0.879440i	0.523612	+	0.851957i	$0.324584\pi$
$332$		0			0
$333$		−	7.00000i		−	0.383598i
$334$		0			0
$335$	−3.00000	−	5.19615i	−0.163908	−	0.283896i
$336$		0			0
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$		0			0
$339$	18.0000			0.977626
$340$		0			0
$341$		0			0
$342$		0			0
$343$			8.00000i			0.431959i
$344$		0			0
$345$	31.1769	+	18.0000i	1.67851	+	0.969087i
$346$		0			0
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$		0			0
$349$	12.1244	−	7.00000i	0.649002	−	0.374701i	−0.139072	−	0.990282i	$-0.544412\pi$
$349$	12.1244	−	7.00000i	0.649002	−	0.374701i	0.788074	+	0.615581i	$0.211079\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−23.3827	+	13.5000i	−1.24453	+	0.718532i	−0.970014	−	0.243049i	$-0.921853\pi$
$353$	−23.3827	+	13.5000i	−1.24453	+	0.718532i	−0.274521	+	0.961581i	$0.588519\pi$
$354$		0			0
$355$	9.00000	−	15.5885i	0.477670	−	0.827349i
$356$		0			0
$357$	20.7846	+	12.0000i	1.10004	+	0.635107i
$358$		0			0
$359$			36.0000i			1.90001i	0.312239	+	0.950004i	$0.398921\pi$
$359$			36.0000i			1.90001i	−0.312239	+	0.950004i	$0.601079\pi$
$360$		0			0
$361$	−7.50000	−	12.9904i	−0.394737	−	0.683704i
$362$		0			0
$363$	−22.0000			−1.15470
$364$		0			0
$365$	3.00000			0.157027
$366$		0			0
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	0.996129	+	0.0879086i	$0.0280183\pi$
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	−0.421933	+	0.906627i	$0.638648\pi$
$368$		0			0
$369$		−	3.00000i		−	0.156174i
$370$		0			0
$371$	31.1769	+	18.0000i	1.61862	+	0.934513i
$372$		0			0
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	−0.761074	−	0.648665i	$-0.775328\pi$
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	0.942297	+	0.334777i	$0.108661\pi$
$374$		0			0
$375$	−5.19615	+	3.00000i	−0.268328	+	0.154919i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	8.66025	−	5.00000i	0.444847	−	0.256833i	−0.260804	−	0.965392i	$-0.583988\pi$
$379$	8.66025	−	5.00000i	0.444847	−	0.256833i	0.705652	+	0.708559i	$0.250654\pi$
$380$		0			0
$381$	10.0000	−	17.3205i	0.512316	−	0.887357i
$382$		0			0
$383$	−31.1769	−	18.0000i	−1.59307	−	0.919757i	−0.992777	−	0.119974i	$-0.961719\pi$
$383$	−31.1769	−	18.0000i	−1.59307	−	0.919757i	−0.600289	−	0.799783i	$-0.704948\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.00000	−	3.46410i	−0.101666	−	0.176090i
$388$		0			0
$389$	−21.0000			−1.06474			−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000			−1.06474			−0.532371	+	0.846511i	$0.678699\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$		0			0
$395$		−	12.0000i		−	0.603786i
$396$		0			0
$397$	8.66025	+	5.00000i	0.434646	+	0.250943i	0.701324	−	0.712843i	$-0.252593\pi$
$397$	8.66025	+	5.00000i	0.434646	+	0.250943i	−0.266678	+	0.963786i	$0.585926\pi$
$398$		0			0
$399$	−8.00000	+	13.8564i	−0.400501	+	0.693688i
$400$		0			0
$401$	−28.5788	+	16.5000i	−1.42716	+	0.823971i	−0.996896	−	0.0787327i	$-0.974913\pi$
$401$	−28.5788	+	16.5000i	−1.42716	+	0.823971i	−0.430263	+	0.902703i	$0.641579\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−28.5788	+	16.5000i	−1.42009	+	0.819892i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−21.6506	−	12.5000i	−1.07056	−	0.618085i	−0.142222	−	0.989835i	$-0.545425\pi$
$409$	−21.6506	−	12.5000i	−1.07056	−	0.618085i	−0.928333	+	0.371750i	$0.878758\pi$
$410$		0			0
$411$		−	30.0000i		−	1.47979i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	36.0000			1.76717
$416$		0			0
$417$	32.0000			1.56705
$418$		0			0
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	−0.955683	−	0.294398i	$-0.904881\pi$
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	0.222885	−	0.974845i	$-0.428453\pi$
$420$		0			0
$421$		−	5.00000i		−	0.243685i	−0.992549	−	0.121843i	$-0.961120\pi$
$421$		−	5.00000i		−	0.243685i	0.992549	−	0.121843i	$-0.0388803\pi$
$422$		0			0
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$		0			0
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	−17.3205	+	10.0000i	−0.838198	+	0.483934i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.3923	−	6.00000i	0.500580	−	0.289010i	−0.228373	−	0.973574i	$-0.573341\pi$
$431$	10.3923	−	6.00000i	0.500580	−	0.289010i	0.728953	+	0.684564i	$0.240007\pi$
$432$		0			0
$433$	−0.500000	+	0.866025i	−0.0240285	+	0.0416185i	−0.877790	−	0.479046i	$-0.840983\pi$
$433$	−0.500000	+	0.866025i	−0.0240285	+	0.0416185i	0.853761	+	0.520665i	$0.174316\pi$
$434$		0			0
$435$	46.7654	+	27.0000i	2.24223	+	1.29455i
$436$		0			0
$437$		−	12.0000i		−	0.574038i
$438$		0			0
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	0.940963	+	0.338508i	$0.109922\pi$
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	−0.177325	+	0.984152i	$0.556744\pi$
$440$		0			0
$441$	−9.00000			−0.428571
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$		0			0
$447$			18.0000i			0.851371i
$448$		0			0
$449$	−25.9808	−	15.0000i	−1.22611	−	0.707894i	−0.259895	−	0.965637i	$-0.583688\pi$
$449$	−25.9808	−	15.0000i	−1.22611	−	0.707894i	−0.966213	+	0.257743i	$0.917021\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	17.3205	−	10.0000i	0.813788	−	0.469841i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.9186	+	11.5000i	−0.931752	+	0.537947i	−0.887365	−	0.461067i	$-0.847467\pi$
$457$	−19.9186	+	11.5000i	−0.931752	+	0.537947i	−0.0443868	+	0.999014i	$0.514133\pi$
$458$		0			0
$459$	6.00000	−	10.3923i	0.280056	−	0.485071i
$460$		0			0
$461$	−33.7750	−	19.5000i	−1.57306	−	0.908206i	−0.995791	−	0.0916500i	$-0.970786\pi$
$461$	−33.7750	−	19.5000i	−1.57306	−	0.908206i	−0.577267	−	0.816556i	$-0.695881\pi$
$462$		0			0
$463$			20.0000i			0.929479i	0.885448	+	0.464739i	$0.153852\pi$
$463$			20.0000i			0.929479i	−0.885448	+	0.464739i	$0.846148\pi$
$464$		0			0
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$		0			0
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−8.00000			−0.369406
$470$		0			0
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−6.92820	−	4.00000i	−0.317888	−	0.183533i
$476$		0			0
$477$	−4.50000	+	7.79423i	−0.206041	+	0.356873i
$478$		0			0
$479$	15.5885	−	9.00000i	0.712255	−	0.411220i	−0.0996406	−	0.995023i	$-0.531769\pi$
$479$	15.5885	−	9.00000i	0.712255	−	0.411220i	0.811895	+	0.583803i	$0.198436\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	41.5692	−	24.0000i	1.89146	−	1.09204i
$484$		0			0
$485$	−21.0000	+	36.3731i	−0.953561	+	1.65162i
$486$		0			0
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	0.152042	−	0.988374i	$-0.451415\pi$
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	−0.779936	+	0.625859i	$0.784748\pi$
$488$		0			0
$489$		−	16.0000i		−	0.723545i
$490$		0			0
$491$	−12.0000	−	20.7846i	−0.541552	−	0.937996i	−0.998815	−	0.0486647i	$-0.984503\pi$
$491$	−12.0000	−	20.7846i	−0.541552	−	0.937996i	0.457263	−	0.889332i	$-0.348830\pi$
$492$		0			0
$493$	−27.0000			−1.21602
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$		−	14.0000i		−	0.626726i	−0.949633	−	0.313363i	$-0.898544\pi$
$499$		−	14.0000i		−	0.626726i	0.949633	−	0.313363i	$-0.101456\pi$
$500$		0			0
$501$	−41.5692	−	24.0000i	−1.85718	−	1.07224i
$502$		0			0
$503$	−6.00000	+	10.3923i	−0.267527	+	0.463370i	−0.968223	−	0.250090i	$-0.919540\pi$
$503$	−6.00000	+	10.3923i	−0.267527	+	0.463370i	0.700696	+	0.713460i	$0.252873\pi$
$504$		0			0
$505$	−23.3827	+	13.5000i	−1.04052	+	0.600742i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.9904	−	7.50000i	0.575789	−	0.332432i	−0.183669	−	0.982988i	$-0.558798\pi$
$509$	12.9904	−	7.50000i	0.575789	−	0.332432i	0.759458	+	0.650556i	$0.225464\pi$
$510$		0			0
$511$	2.00000	−	3.46410i	0.0884748	−	0.153243i
$512$		0			0
$513$	6.92820	+	4.00000i	0.305888	+	0.176604i
$514$		0			0
$515$		−	6.00000i		−	0.264392i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	−9.00000			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$522$		0			0
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$		0			0
$525$		−	32.0000i		−	1.39659i
$526$		0			0
$527$	−5.19615	−	3.00000i	−0.226348	−	0.130682i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	15.5885	−	9.00000i	0.673948	−	0.389104i
$536$		0			0
$537$	−24.0000	+	41.5692i	−1.03568	+	1.79384i
$538$		0			0
$539$		0			0
$540$		0			0
$541$		−	19.0000i		−	0.816874i	−0.912787	−	0.408437i	$-0.866074\pi$
$541$		−	19.0000i		−	0.816874i	0.912787	−	0.408437i	$-0.133926\pi$
$542$		0			0
$543$	7.00000	+	12.1244i	0.300399	+	0.520306i
$544$		0			0
$545$	−30.0000			−1.28506
$546$		0			0
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$		0			0
$549$	−2.50000	−	4.33013i	−0.106697	−	0.184805i
$550$		0			0
$551$		−	18.0000i		−	0.766826i
$552$		0			0
$553$	−13.8564	−	8.00000i	−0.589234	−	0.340195i
$554$		0			0
$555$	21.0000	−	36.3731i	0.891400	−	1.54395i
$556$		0			0
$557$	−2.59808	+	1.50000i	−0.110084	+	0.0635570i	−0.554031	−	0.832496i	$-0.686911\pi$
$557$	−2.59808	+	1.50000i	−0.110084	+	0.0635570i	0.443947	+	0.896053i	$0.353578\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$		0			0
$565$	23.3827	+	13.5000i	0.983717	+	0.567949i
$566$		0			0
$567$			44.0000i			1.84783i
$568$		0			0
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$	12.0000	+	20.7846i	0.500435	+	0.866778i
$576$		0			0
$577$		−	11.0000i		−	0.457936i	−0.973434	−	0.228968i	$-0.926465\pi$
$577$		−	11.0000i		−	0.457936i	0.973434	−	0.228968i	$-0.0735351\pi$
$578$		0			0
$579$	19.0526	+	11.0000i	0.791797	+	0.457144i
$580$		0			0
$581$	24.0000	−	41.5692i	0.995688	−	1.72458i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$		0			0
$589$	2.00000	−	3.46410i	0.0824086	−	0.142736i
$590$		0			0
$591$	−10.3923	−	6.00000i	−0.427482	−	0.246807i
$592$		0			0
$593$		−	9.00000i		−	0.369586i	−0.982777	−	0.184793i	$-0.940839\pi$
$593$		−	9.00000i		−	0.369586i	0.982777	−	0.184793i	$-0.0591614\pi$
$594$		0			0
$595$	18.0000	+	31.1769i	0.737928	+	1.27813i
$596$		0			0
$597$	52.0000			2.12822
$598$		0			0
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$		0			0
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	0.876043	−	0.482233i	$-0.160174\pi$
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	−0.855648	+	0.517559i	$0.826841\pi$
$602$		0			0
$603$		−	2.00000i		−	0.0814463i
$604$		0			0
$605$	−28.5788	−	16.5000i	−1.16190	−	0.670820i
$606$		0			0
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	−0.551678	−	0.834058i	$-0.686012\pi$
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	0.998154	+	0.0607380i	$0.0193454\pi$
$608$		0			0
$609$	62.3538	−	36.0000i	2.52670	−	1.45879i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	16.4545	−	9.50000i	0.664590	−	0.383701i	−0.129433	−	0.991588i	$-0.541316\pi$
$613$	16.4545	−	9.50000i	0.664590	−	0.383701i	0.794024	+	0.607887i	$0.207983\pi$
$614$		0			0
$615$	9.00000	−	15.5885i	0.362915	−	0.628587i
$616$		0			0
$617$	23.3827	+	13.5000i	0.941351	+	0.543490i	0.890384	−	0.455211i	$-0.150436\pi$
$617$	23.3827	+	13.5000i	0.941351	+	0.543490i	0.0509678	+	0.998700i	$0.483769\pi$
$618$		0			0
$619$		−	40.0000i		−	1.60774i	−0.594808	−	0.803868i	$-0.702772\pi$
$619$		−	40.0000i		−	1.60774i	0.594808	−	0.803868i	$-0.297228\pi$
$620$		0			0
$621$	−12.0000	−	20.7846i	−0.481543	−	0.834058i
$622$		0			0
$623$	24.0000			0.961540
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$		0			0
$628$		0			0
$629$			21.0000i			0.837325i
$630$		0			0
$631$	24.2487	+	14.0000i	0.965326	+	0.557331i	0.897808	−	0.440387i	$-0.145159\pi$
$631$	24.2487	+	14.0000i	0.965326	+	0.557331i	0.0675178	+	0.997718i	$0.478492\pi$
$632$		0			0
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$		0			0
$635$	25.9808	−	15.0000i	1.03102	−	0.595257i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	5.19615	−	3.00000i	0.205557	−	0.118678i
$640$		0			0
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	−0.679039	−	0.734103i	$-0.737603\pi$
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	0.975271	+	0.221013i	$0.0709364\pi$
$642$		0			0
$643$	−13.8564	−	8.00000i	−0.546443	−	0.315489i	0.201243	−	0.979541i	$-0.435502\pi$
$643$	−13.8564	−	8.00000i	−0.546443	−	0.315489i	−0.747686	+	0.664052i	$0.768835\pi$
$644$		0			0
$645$		−	24.0000i		−	0.944999i
$646$		0			0
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	16.0000			0.627089
$652$		0			0
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	0.904345	+	0.426801i	$0.140360\pi$
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	−0.0825519	+	0.996587i	$0.526307\pi$
$654$		0			0
$655$			18.0000i			0.703318i
$656$		0			0
$657$	0.866025	+	0.500000i	0.0337869	+	0.0195069i
$658$		0			0
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	−6.06218	+	3.50000i	−0.235791	+	0.136134i	−0.613241	−	0.789896i	$-0.710135\pi$
$661$	−6.06218	+	3.50000i	−0.235791	+	0.136134i	0.377450	+	0.926030i	$0.376801\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−20.7846	+	12.0000i	−0.805993	+	0.465340i
$666$		0			0
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$		0			0
$669$	−45.0333	−	26.0000i	−1.74109	−	1.00522i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	0.713123	−	0.701039i	$-0.247280\pi$
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	−0.963679	+	0.267063i	$0.913947\pi$
$674$		0			0
$675$	−16.0000			−0.615840
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	28.0000	+	48.4974i	1.07454	+	1.86116i
$680$		0			0
$681$			12.0000i			0.459841i
$682$		0			0
$683$	5.19615	+	3.00000i	0.198825	+	0.114792i	0.596107	−	0.802905i	$-0.296713\pi$
$683$	5.19615	+	3.00000i	0.198825	+	0.114792i	−0.397282	+	0.917697i	$0.630047\pi$
$684$		0			0
$685$	22.5000	−	38.9711i	0.859681	−	1.48901i
$686$		0			0
$687$	−24.2487	+	14.0000i	−0.925146	+	0.534133i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	34.6410	−	20.0000i	1.31781	−	0.760836i	0.334431	−	0.942420i	$-0.391456\pi$
$691$	34.6410	−	20.0000i	1.31781	−	0.760836i	0.983375	+	0.181584i	$0.0581226\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	41.5692	+	24.0000i	1.57681	+	0.910372i
$696$		0			0
$697$			9.00000i			0.340899i
$698$		0			0
$699$	18.0000	+	31.1769i	0.680823	+	1.17922i
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$		0			0
$705$	18.0000	+	31.1769i	0.677919	+	1.17419i
$706$		0			0
$707$			36.0000i			1.35392i
$708$		0			0
$709$	26.8468	+	15.5000i	1.00825	+	0.582115i	0.910679	−	0.413114i	$-0.135559\pi$
$709$	26.8468	+	15.5000i	1.00825	+	0.582115i	0.0975728	+	0.995228i	$0.468892\pi$
$710$		0			0
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$		0			0
$713$	−10.3923	+	6.00000i	−0.389195	+	0.224702i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	41.5692	−	24.0000i	1.55243	−	0.896296i
$718$		0			0
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	−0.732185	−	0.681106i	$-0.761499\pi$
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	0.955947	+	0.293538i	$0.0948328\pi$
$720$		0			0
$721$	−6.92820	−	4.00000i	−0.258020	−	0.148968i
$722$		0			0
$723$			2.00000i			0.0743808i
$724$		0			0
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$		0			0
$733$		−	29.0000i		−	1.07114i	−0.844491	−	0.535570i	$-0.820097\pi$
$733$		−	29.0000i		−	1.07114i	0.844491	−	0.535570i	$-0.179903\pi$
$734$		0			0
$735$	−46.7654	−	27.0000i	−1.72497	−	0.995910i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	17.3205	−	10.0000i	0.637145	−	0.367856i	−0.146369	−	0.989230i	$-0.546759\pi$
$739$	17.3205	−	10.0000i	0.637145	−	0.367856i	0.783514	+	0.621374i	$0.213425\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	20.7846	−	12.0000i	0.762513	−	0.440237i	−0.0676840	−	0.997707i	$-0.521561\pi$
$743$	20.7846	−	12.0000i	0.762513	−	0.440237i	0.830197	+	0.557470i	$0.188228\pi$
$744$		0			0
$745$	−13.5000	+	23.3827i	−0.494602	+	0.856675i
$746$		0			0
$747$	10.3923	+	6.00000i	0.380235	+	0.219529i
$748$		0			0
$749$		−	24.0000i		−	0.876941i
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$		0			0
$753$	−12.0000			−0.437304
$754$		0			0
$755$	30.0000			1.09181
$756$		0			0
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	−0.971652	−	0.236414i	$-0.924028\pi$
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	0.281086	−	0.959683i	$-0.409305\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	15.5885	+	9.00000i	0.565081	+	0.326250i	0.755182	−	0.655515i	$-0.227548\pi$
$761$	15.5885	+	9.00000i	0.565081	+	0.326250i	−0.190101	+	0.981764i	$0.560882\pi$
$762$		0			0
$763$	−20.0000	+	34.6410i	−0.724049	+	1.25409i
$764$		0			0
$765$	−7.79423	+	4.50000i	−0.281801	+	0.162698i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−12.1244	+	7.00000i	−0.437215	+	0.252426i	−0.702416	−	0.711767i	$-0.747895\pi$
$769$	−12.1244	+	7.00000i	−0.437215	+	0.252426i	0.265200	+	0.964193i	$0.414562\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$		0			0
$773$	−5.19615	−	3.00000i	−0.186893	−	0.107903i	0.403634	−	0.914920i	$-0.367747\pi$
$773$	−5.19615	−	3.00000i	−0.186893	−	0.107903i	−0.590527	+	0.807018i	$0.701080\pi$
$774$		0			0
$775$			8.00000i			0.287368i
$776$		0			0
$777$	−28.0000	−	48.4974i	−1.00449	−	1.73984i
$778$		0			0
$779$	−6.00000			−0.214972
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−18.0000	−	31.1769i	−0.643268	−	1.11417i
$784$		0			0
$785$		−	21.0000i		−	0.749522i
$786$		0			0
$787$	−32.9090	−	19.0000i	−1.17308	−	0.677277i	−0.218675	−	0.975798i	$-0.570173\pi$
$787$	−32.9090	−	19.0000i	−1.17308	−	0.677277i	−0.954403	+	0.298521i	$0.903507\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	31.1769	−	18.0000i	1.10852	−	0.640006i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−46.7654	+	27.0000i	−1.65860	+	0.957591i
$796$		0			0
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	−0.980237	−	0.197826i	$-0.936612\pi$
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	0.661441	+	0.749997i	$0.269945\pi$
$798$		0			0
$799$	−15.5885	−	9.00000i	−0.551480	−	0.318397i
$800$		0			0
$801$			6.00000i			0.212000i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	72.0000			2.53767
$806$		0			0
$807$	−60.0000			−2.11210
$808$		0			0
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	0.703533	−	0.710663i	$-0.251605\pi$
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	−0.967219	+	0.253946i	$0.918272\pi$
$810$		0			0
$811$			10.0000i			0.351147i	0.984466	+	0.175574i	$0.0561780\pi$
$811$			10.0000i			0.351147i	−0.984466	+	0.175574i	$0.943822\pi$
$812$		0			0
$813$	13.8564	+	8.00000i	0.485965	+	0.280572i
$814$		0			0
$815$	12.0000	−	20.7846i	0.420342	−	0.728053i
$816$		0			0
$817$	−6.92820	+	4.00000i	−0.242387	+	0.139942i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.5885	−	9.00000i	0.544041	−	0.314102i	−0.202674	−	0.979246i	$-0.564963\pi$
$821$	15.5885	−	9.00000i	0.544041	−	0.314102i	0.746715	+	0.665144i	$0.231630\pi$
$822$		0			0
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$	−9.50000	−	16.4545i	−0.329949	−	0.571488i	0.652553	−	0.757743i	$-0.273698\pi$
$829$	−9.50000	−	16.4545i	−0.329949	−	0.571488i	−0.982501	+	0.186256i	$0.940365\pi$
$830$		0			0
$831$	−38.0000			−1.31821
$832$		0			0
$833$	27.0000			0.935495
$834$		0			0
$835$	−36.0000	−	62.3538i	−1.24583	−	2.15784i
$836$		0			0
$837$		−	8.00000i		−	0.276520i
$838$		0			0
$839$	−36.3731	−	21.0000i	−1.25574	−	0.725001i	−0.283495	−	0.958974i	$-0.591494\pi$
$839$	−36.3731	−	21.0000i	−1.25574	−	0.725001i	−0.972243	+	0.233973i	$0.924827\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	−5.19615	+	3.00000i	−0.178965	+	0.103325i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−38.1051	+	22.0000i	−1.30931	+	0.755929i
$848$		0			0
$849$	16.0000	−	27.7128i	0.549119	−	0.951101i
$850$		0			0
$851$	36.3731	+	21.0000i	1.24685	+	0.719871i
$852$		0			0
$853$			5.00000i			0.171197i	0.996330	+	0.0855984i	$0.0272802\pi$
$853$			5.00000i			0.171197i	−0.996330	+	0.0855984i	$0.972720\pi$
$854$		0			0
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$		0			0
$857$	−3.00000			−0.102478			−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000			−0.102478			−0.0512390	+	0.998686i	$0.516317\pi$
$858$		0			0
$859$	2.00000			0.0682391			0.0341196	−	0.999418i	$-0.489137\pi$
$859$	2.00000			0.0682391			0.0341196	+	0.999418i	$0.489137\pi$
$860$		0			0
$861$	−12.0000	−	20.7846i	−0.408959	−	0.708338i
$862$		0			0
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$		0			0
$865$	15.5885	+	9.00000i	0.530023	+	0.306009i
$866$		0			0
$867$	−8.00000	+	13.8564i	−0.271694	+	0.470588i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−12.1244	+	7.00000i	−0.410347	+	0.236914i
$874$		0			0
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$		0			0
$877$	4.33013	+	2.50000i	0.146218	+	0.0844190i	0.571324	−	0.820724i	$-0.306430\pi$
$877$	4.33013	+	2.50000i	0.146218	+	0.0844190i	−0.425106	+	0.905143i	$0.639763\pi$
$878$		0			0
$879$		−	18.0000i		−	0.607125i
$880$		0			0
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	0.872772	+	0.488127i	$0.162320\pi$
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	−0.0136556	+	0.999907i	$0.504347\pi$
$882$		0			0
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$		0			0
$885$		0			0
$886$		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
$889$		−	40.0000i		−	1.34156i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$		0			0
$895$	−62.3538	+	36.0000i	−2.08426	+	1.20335i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−15.5885	+	9.00000i	−0.519904	+	0.300167i
$900$		0			0
$901$	13.5000	−	23.3827i	0.449750	−	0.778990i
$902$		0			0
$903$	−27.7128	−	16.0000i	−0.922225	−	0.532447i
$904$		0			0
$905$			21.0000i			0.698064i
$906$		0			0
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	0.924762	−	0.380547i	$-0.124264\pi$
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	−0.791944	+	0.610594i	$0.790931\pi$
$908$		0			0
$909$	−9.00000			−0.298511
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		−	30.0000i		−	0.991769i
$916$		0			0
$917$	20.7846	+	12.0000i	0.686368	+	0.396275i
$918$		0			0
$919$	−19.0000	+	32.9090i	−0.626752	+	1.08557i	0.361447	+	0.932393i	$0.382283\pi$
$919$	−19.0000	+	32.9090i	−0.626752	+	1.08557i	−0.988199	+	0.153174i	$0.951051\pi$
$920$		0			0
$921$	−45.0333	+	26.0000i	−1.48390	+	0.856729i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	24.2487	−	14.0000i	0.797293	−	0.460317i
$926$		0			0
$927$	1.00000	−	1.73205i	0.0328443	−	0.0568880i
$928$		0			0
$929$	−18.1865	−	10.5000i	−0.596681	−	0.344494i	0.171054	−	0.985262i	$-0.445283\pi$
$929$	−18.1865	−	10.5000i	−0.596681	−	0.344494i	−0.767735	+	0.640768i	$0.778616\pi$
$930$		0			0
$931$			18.0000i			0.589926i
$932$		0			0
$933$	−6.00000	−	10.3923i	−0.196431	−	0.340229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	47.0000			1.53542			0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000			1.53542			0.767712	+	0.640796i	$0.221395\pi$
$938$		0			0
$939$	14.0000	+	24.2487i	0.456873	+	0.791327i
$940$		0			0
$941$			30.0000i			0.977972i	0.872292	+	0.488986i	$0.162633\pi$
$941$			30.0000i			0.977972i	−0.872292	+	0.488986i	$0.837367\pi$
$942$		0			0
$943$	15.5885	+	9.00000i	0.507630	+	0.293080i
$944$		0			0
$945$	−24.0000	+	41.5692i	−0.780720	+	1.35225i
$946$		0			0
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	−0.731417	−	0.681930i	$-0.761141\pi$
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	0.224860	+	0.974391i	$0.427807\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−25.9808	+	15.0000i	−0.842484	+	0.486408i
$952$		0			0
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$		0			0
$955$	−15.5885	−	9.00000i	−0.504431	−	0.291233i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−30.0000	−	51.9615i	−0.968751	−	1.67793i
$960$		0			0
$961$	27.0000			0.870968
$962$		0			0
$963$	6.00000			0.193347
$964$		0			0
$965$	16.5000	+	28.5788i	0.531154	+	0.919985i
$966$		0			0
$967$			58.0000i			1.86515i	0.360971	+	0.932577i	$0.382445\pi$
$967$			58.0000i			1.86515i	−0.360971	+	0.932577i	$0.617555\pi$
$968$		0			0
$969$	10.3923	+	6.00000i	0.333849	+	0.192748i
$970$		0			0
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	−0.999771	−	0.0213768i	$-0.993195\pi$
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	0.518399	+	0.855139i	$0.326528\pi$
$972$		0			0
$973$	55.4256	−	32.0000i	1.77686	−	1.02587i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−33.7750	+	19.5000i	−1.08056	+	0.623860i	−0.931047	−	0.364900i	$-0.881103\pi$
$977$	−33.7750	+	19.5000i	−1.08056	+	0.623860i	−0.149511	+	0.988760i	$0.547770\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−8.66025	−	5.00000i	−0.276501	−	0.159638i
$982$		0			0
$983$		−	6.00000i		−	0.191370i	−0.995412	−	0.0956851i	$-0.969496\pi$
$983$		−	6.00000i		−	0.191370i	0.995412	−	0.0956851i	$-0.0305042\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$	48.0000			1.52786
$988$		0			0
$989$	24.0000			0.763156
$990$		0			0
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$		0			0
$993$			64.0000i			2.03098i
$994$		0			0
$995$	67.5500	+	39.0000i	2.14148	+	1.23638i
$996$		0			0
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	−0.902895	−	0.429862i	$-0.858562\pi$
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	0.823719	+	0.566999i	$0.191896\pi$
$998$		0			0
$999$	−24.2487	+	14.0000i	−0.767195	+	0.442940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.h.d.361.2		4
13.2	odd	12		676.2.a.b.1.1		1
13.3	even	3		676.2.d.a.337.2		2
13.4	even	6	inner	676.2.h.d.485.1		4
13.5	odd	4		676.2.e.d.653.1		2
13.6	odd	12		676.2.e.d.529.1		2
13.7	odd	12		52.2.e.b.9.1	✓	2
13.8	odd	4		52.2.e.b.29.1	yes	2
13.9	even	3	inner	676.2.h.d.485.2		4
13.10	even	6		676.2.d.a.337.1		2
13.11	odd	12		676.2.a.a.1.1		1
13.12	even	2	inner	676.2.h.d.361.1		4
39.2	even	12		6084.2.a.c.1.1		1
39.8	even	4		468.2.l.d.289.1		2
39.11	even	12		6084.2.a.o.1.1		1
39.20	even	12		468.2.l.d.217.1		2
39.23	odd	6		6084.2.b.k.4393.2		2
39.29	odd	6		6084.2.b.k.4393.1		2
52.3	odd	6		2704.2.f.i.337.2		2
52.7	even	12		208.2.i.a.113.1		2
52.11	even	12		2704.2.a.l.1.1		1
52.15	even	12		2704.2.a.m.1.1		1
52.23	odd	6		2704.2.f.i.337.1		2
52.47	even	4		208.2.i.a.81.1		2
65.7	even	12		1300.2.bb.d.1049.1		4
65.8	even	4		1300.2.bb.d.549.1		4
65.33	even	12		1300.2.bb.d.1049.2		4
65.34	odd	4		1300.2.i.b.601.1		2
65.47	even	4		1300.2.bb.d.549.2		4
65.59	odd	12		1300.2.i.b.1101.1		2
91.20	even	12		2548.2.k.a.1569.1		2
91.33	even	12		2548.2.i.b.165.1		2
91.34	even	4		2548.2.k.a.393.1		2
91.46	odd	12		2548.2.l.b.373.1		2
91.47	even	12		2548.2.l.g.1537.1		2
91.59	even	12		2548.2.l.g.373.1		2
91.60	odd	12		2548.2.i.g.1745.1		2
91.72	odd	12		2548.2.i.g.165.1		2
91.73	even	12		2548.2.i.b.1745.1		2
91.86	odd	12		2548.2.l.b.1537.1		2
104.21	odd	4		832.2.i.c.705.1		2
104.59	even	12		832.2.i.i.321.1		2
104.85	odd	12		832.2.i.c.321.1		2
104.99	even	4		832.2.i.i.705.1		2
156.47	odd	4		1872.2.t.m.289.1		2
156.59	odd	12		1872.2.t.m.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.e.b.9.1	✓	2	13.7	odd	12
52.2.e.b.29.1	yes	2	13.8	odd	4
208.2.i.a.81.1		2	52.47	even	4
208.2.i.a.113.1		2	52.7	even	12
468.2.l.d.217.1		2	39.20	even	12
468.2.l.d.289.1		2	39.8	even	4
676.2.a.a.1.1		1	13.11	odd	12
676.2.a.b.1.1		1	13.2	odd	12
676.2.d.a.337.1		2	13.10	even	6
676.2.d.a.337.2		2	13.3	even	3
676.2.e.d.529.1		2	13.6	odd	12
676.2.e.d.653.1		2	13.5	odd	4
676.2.h.d.361.1		4	13.12	even	2	inner
676.2.h.d.361.2		4	1.1	even	1	trivial
676.2.h.d.485.1		4	13.4	even	6	inner
676.2.h.d.485.2		4	13.9	even	3	inner
832.2.i.c.321.1		2	104.85	odd	12
832.2.i.c.705.1		2	104.21	odd	4
832.2.i.i.321.1		2	104.59	even	12
832.2.i.i.705.1		2	104.99	even	4
1300.2.i.b.601.1		2	65.34	odd	4
1300.2.i.b.1101.1		2	65.59	odd	12
1300.2.bb.d.549.1		4	65.8	even	4
1300.2.bb.d.549.2		4	65.47	even	4
1300.2.bb.d.1049.1		4	65.7	even	12
1300.2.bb.d.1049.2		4	65.33	even	12
1872.2.t.m.289.1		2	156.47	odd	4
1872.2.t.m.1153.1		2	156.59	odd	12
2548.2.i.b.165.1		2	91.33	even	12
2548.2.i.b.1745.1		2	91.73	even	12
2548.2.i.g.165.1		2	91.72	odd	12
2548.2.i.g.1745.1		2	91.60	odd	12
2548.2.k.a.393.1		2	91.34	even	4
2548.2.k.a.1569.1		2	91.20	even	12
2548.2.l.b.373.1		2	91.46	odd	12
2548.2.l.b.1537.1		2	91.86	odd	12
2548.2.l.g.373.1		2	91.59	even	12
2548.2.l.g.1537.1		2	91.47	even	12
2704.2.a.l.1.1		1	52.11	even	12
2704.2.a.m.1.1		1	52.15	even	12
2704.2.f.i.337.1		2	52.23	odd	6
2704.2.f.i.337.2		2	52.3	odd	6
6084.2.a.c.1.1		1	39.2	even	12
6084.2.a.o.1.1		1	39.11	even	12
6084.2.b.k.4393.1		2	39.29	odd	6
6084.2.b.k.4393.2		2	39.23	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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{3} +3.00000i q^{5} +(3.46410 + 2.00000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-5.19615 + 3.00000i) q^{15} +(1.50000 - 2.59808i) q^{17} +(1.73205 + 1.00000i) q^{19} +8.00000i q^{21} +(-3.00000 - 5.19615i) q^{23} -4.00000 q^{25} +4.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} -2.00000i q^{31} +(-6.00000 + 10.3923i) q^{35} +(-6.06218 + 3.50000i) q^{37} +(-2.59808 + 1.50000i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(-2.59808 - 1.50000i) q^{45} -6.00000i q^{47} +(4.50000 + 7.79423i) q^{49} +6.00000 q^{51} +9.00000 q^{53} +4.00000i q^{57} +(-2.50000 + 4.33013i) q^{61} +(-3.46410 + 2.00000i) q^{63} +(-1.73205 + 1.00000i) q^{67} +(6.00000 - 10.3923i) q^{69} +(-5.19615 - 3.00000i) q^{71} -1.00000i q^{73} +(-4.00000 - 6.92820i) q^{75} -4.00000 q^{79} +(5.50000 + 9.52628i) q^{81} -12.0000i q^{83} +(7.79423 + 4.50000i) q^{85} +(9.00000 - 15.5885i) q^{87} +(5.19615 - 3.00000i) q^{89} +(3.46410 - 2.00000i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(12.1244 + 7.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 2 q^{9} + 6 q^{17} - 12 q^{23} - 16 q^{25} + 16 q^{27} - 18 q^{29} - 24 q^{35} - 8 q^{43} + 18 q^{49} + 24 q^{51} + 36 q^{53} - 10 q^{61} + 24 q^{69} - 16 q^{75} - 16 q^{79} + 22 q^{81}+ \cdots - 12 q^{95}+O(q^{100}) \) 4 * q + 4 * q^3 - 2 * q^9 + 6 * q^17 - 12 * q^23 - 16 * q^25 + 16 * q^27 - 18 * q^29 - 24 * q^35 - 8 * q^43 + 18 * q^49 + 24 * q^51 + 36 * q^53 - 10 * q^61 + 24 * q^69 - 16 * q^75 - 16 * q^79 + 22 * q^81 + 36 * q^87 - 12 * q^95

Introduction

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