LMFDB - Embedded newform 1728.2.bc.b.1585.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(145,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("1728.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.bc (of order $12$, degree $4$, 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:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1585.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1728.1585
Dual form			1728.2.bc.b.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 1.86603i) q^{5} +(3.86603 + 2.23205i) q^{7} +O(q^{10})$	$q+(-0.500000 + 1.86603i) q^{5} +(3.86603 + 2.23205i) q^{7} +(1.86603 - 0.500000i) q^{11} +(2.23205 + 0.598076i) q^{13} -4.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(5.59808 - 3.23205i) q^{23} +(1.09808 + 0.633975i) q^{25} +(-0.232051 - 0.866025i) q^{29} +(4.59808 + 7.96410i) q^{31} +(-6.09808 + 6.09808i) q^{35} +(-4.26795 - 4.26795i) q^{37} +(0.696152 - 0.401924i) q^{41} +(-6.33013 + 1.69615i) q^{43} +(-0.598076 + 1.03590i) q^{47} +(6.46410 + 11.1962i) q^{49} +(-5.73205 - 5.73205i) q^{53} +3.73205i q^{55} +(0.401924 - 1.50000i) q^{59} +(0.571797 + 2.13397i) q^{61} +(-2.23205 + 3.86603i) q^{65} +(-8.33013 - 2.23205i) q^{67} +2.92820i q^{71} -7.46410i q^{73} +(8.33013 + 2.23205i) q^{77} +(0.866025 - 1.50000i) q^{79} +(3.79423 + 14.1603i) q^{83} +(2.00000 - 7.46410i) q^{85} +15.8564i q^{89} +(7.29423 + 7.29423i) q^{91} +(4.09808 + 7.09808i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} + 12 q^{7}+O(q^{10}) $ 4 * q - 2 * q^5 + 12 * q^7	$ 4 q - 2 q^{5} + 12 q^{7} + 4 q^{11} + 2 q^{13} - 16 q^{17} + 12 q^{19} + 12 q^{23} - 6 q^{25} + 6 q^{29} + 8 q^{31} - 14 q^{35} - 24 q^{37} - 18 q^{41} - 8 q^{43} + 8 q^{47} + 12 q^{49} - 16 q^{53} + 12 q^{59} + 30 q^{61} - 2 q^{65} - 16 q^{67} + 16 q^{77} - 16 q^{83} + 8 q^{85} - 2 q^{91} + 6 q^{95} - 2 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 + 12 * q^7 + 4 * q^11 + 2 * q^13 - 16 * q^17 + 12 * q^19 + 12 * q^23 - 6 * q^25 + 6 * q^29 + 8 * q^31 - 14 * q^35 - 24 * q^37 - 18 * q^41 - 8 * q^43 + 8 * q^47 + 12 * q^49 - 16 * q^53 + 12 * q^59 + 30 * q^61 - 2 * q^65 - 16 * q^67 + 16 * q^77 - 16 * q^83 + 8 * q^85 - 2 * q^91 + 6 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$3$		0			0
$4$		0			0
$5$	−0.500000	+	1.86603i	−0.223607	+	0.834512i	0.759351	+	0.650681i	$0.225517\pi$
$5$	−0.500000	+	1.86603i	−0.223607	+	0.834512i	−0.982958	+	0.183831i	$0.941150\pi$
$6$		0			0
$7$	3.86603	+	2.23205i	1.46122	+	0.843636i	0.999068	−	0.0431647i	$-0.0137440\pi$
$7$	3.86603	+	2.23205i	1.46122	+	0.843636i	0.462152	+	0.886801i	$0.347077\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.86603	−	0.500000i	0.562628	−	0.150756i	0.0337145	−	0.999432i	$-0.489266\pi$
$11$	1.86603	−	0.500000i	0.562628	−	0.150756i	0.528913	+	0.848676i	$0.322600\pi$
$12$		0			0
$13$	2.23205	+	0.598076i	0.619060	+	0.165876i	0.554700	−	0.832050i	$-0.312833\pi$
$13$	2.23205	+	0.598076i	0.619060	+	0.165876i	0.0643593	+	0.997927i	$0.479500\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$		0			0
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.59808	−	3.23205i	1.16728	−	0.673929i	0.214242	−	0.976781i	$-0.431272\pi$
$23$	5.59808	−	3.23205i	1.16728	−	0.673929i	0.953038	+	0.302851i	$0.0979386\pi$
$24$		0			0
$25$	1.09808	+	0.633975i	0.219615	+	0.126795i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.232051	−	0.866025i	−0.0430908	−	0.160817i	0.941028	−	0.338329i	$-0.109862\pi$
$29$	−0.232051	−	0.866025i	−0.0430908	−	0.160817i	−0.984119	+	0.177512i	$0.943195\pi$
$30$		0			0
$31$	4.59808	+	7.96410i	0.825839	+	1.43039i	0.901277	+	0.433244i	$0.142631\pi$
$31$	4.59808	+	7.96410i	0.825839	+	1.43039i	−0.0754376	+	0.997151i	$0.524035\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.09808	+	6.09808i	−1.03076	+	1.03076i
$36$		0			0
$37$	−4.26795	−	4.26795i	−0.701647	−	0.701647i	0.263117	−	0.964764i	$-0.415249\pi$
$37$	−4.26795	−	4.26795i	−0.701647	−	0.701647i	−0.964764	+	0.263117i	$0.915249\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.696152	−	0.401924i	0.108721	−	0.0627700i	−0.444654	−	0.895703i	$-0.646673\pi$
$41$	0.696152	−	0.401924i	0.108721	−	0.0627700i	0.553374	+	0.832933i	$0.313340\pi$
$42$		0			0
$43$	−6.33013	+	1.69615i	−0.965335	+	0.258661i	−0.706857	−	0.707356i	$-0.749888\pi$
$43$	−6.33013	+	1.69615i	−0.965335	+	0.258661i	−0.258478	+	0.966017i	$0.583221\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.598076	+	1.03590i	−0.0872384	+	0.151101i	−0.906343	−	0.422543i	$-0.861138\pi$
$47$	−0.598076	+	1.03590i	−0.0872384	+	0.151101i	0.819104	+	0.573644i	$0.194471\pi$
$48$		0			0
$49$	6.46410	+	11.1962i	0.923443	+	1.59945i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.73205	−	5.73205i	−0.787358	−	0.787358i	0.193703	−	0.981060i	$-0.437950\pi$
$53$	−5.73205	−	5.73205i	−0.787358	−	0.787358i	−0.981060	+	0.193703i	$0.937950\pi$
$54$		0			0
$55$			3.73205i			0.503230i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.401924	−	1.50000i	0.0523260	−	0.195283i	−0.934815	−	0.355135i	$-0.884435\pi$
$59$	0.401924	−	1.50000i	0.0523260	−	0.195283i	0.987141	+	0.159852i	$0.0511016\pi$
$60$		0			0
$61$	0.571797	+	2.13397i	0.0732111	+	0.273227i	0.992822	−	0.119604i	$-0.0381624\pi$
$61$	0.571797	+	2.13397i	0.0732111	+	0.273227i	−0.919611	+	0.392831i	$0.871496\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.23205	+	3.86603i	−0.276852	+	0.479521i
$66$		0			0
$67$	−8.33013	−	2.23205i	−1.01769	−	0.272688i	−0.288849	−	0.957375i	$-0.593273\pi$
$67$	−8.33013	−	2.23205i	−1.01769	−	0.272688i	−0.728838	+	0.684686i	$0.759939\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			2.92820i			0.347514i	0.984789	+	0.173757i	$0.0555907\pi$
$71$			2.92820i			0.347514i	−0.984789	+	0.173757i	$0.944409\pi$
$72$		0			0
$73$		−	7.46410i		−	0.873607i	−0.899557	−	0.436804i	$-0.856111\pi$
$73$		−	7.46410i		−	0.873607i	0.899557	−	0.436804i	$-0.143889\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.33013	+	2.23205i	0.949306	+	0.254366i
$78$		0			0
$79$	0.866025	−	1.50000i	0.0974355	−	0.168763i	−0.813187	−	0.582003i	$-0.802269\pi$
$79$	0.866025	−	1.50000i	0.0974355	−	0.168763i	0.910622	+	0.413239i	$0.135603\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.79423	+	14.1603i	0.416471	+	1.55429i	0.781872	+	0.623440i	$0.214265\pi$
$83$	3.79423	+	14.1603i	0.416471	+	1.55429i	−0.365401	+	0.930850i	$0.619068\pi$
$84$		0			0
$85$	2.00000	−	7.46410i	0.216930	−	0.809595i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			15.8564i			1.68078i	0.541985	+	0.840388i	$0.317673\pi$
$89$			15.8564i			1.68078i	−0.541985	+	0.840388i	$0.682327\pi$
$90$		0			0
$91$	7.29423	+	7.29423i	0.764643	+	0.764643i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.09808	+	7.09808i	0.420454	+	0.728247i
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.500000	+	0.133975i	−0.0497519	+	0.0133310i	−0.283609	−	0.958940i	$-0.591532\pi$
$101$	−0.500000	+	0.133975i	−0.0497519	+	0.0133310i	0.233857	+	0.972271i	$0.424865\pi$
$102$		0			0
$103$	13.7942	−	7.96410i	1.35919	−	0.784726i	0.369672	−	0.929162i	$-0.379470\pi$
$103$	13.7942	−	7.96410i	1.35919	−	0.784726i	0.989514	+	0.144436i	$0.0461369\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.39230	+	9.39230i	0.907988	+	0.907988i	0.996110	−	0.0881214i	$-0.0280863\pi$
$107$	9.39230	+	9.39230i	0.907988	+	0.907988i	−0.0881214	+	0.996110i	$0.528086\pi$
$108$		0			0
$109$	−1.73205	+	1.73205i	−0.165900	+	0.165900i	−0.785175	−	0.619274i	$-0.787427\pi$
$109$	−1.73205	+	1.73205i	−0.165900	+	0.165900i	0.619274	+	0.785175i	$0.287427\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.23205	+	10.7942i	0.586262	+	1.01544i	0.994717	+	0.102657i	$0.0327344\pi$
$113$	6.23205	+	10.7942i	0.586262	+	1.01544i	−0.408455	+	0.912779i	$0.633932\pi$
$114$		0			0
$115$	3.23205	+	12.0622i	0.301390	+	1.12480i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−15.4641	−	8.92820i	−1.41759	−	0.818447i
$120$		0			0
$121$	−6.29423	+	3.63397i	−0.572203	+	0.330361i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.56218	+	8.56218i	−0.765824	+	0.765824i
$126$		0			0
$127$	−0.392305			−0.0348114			−0.0174057	−	0.999849i	$-0.505541\pi$
$127$	−0.392305			−0.0348114			−0.0174057	+	0.999849i	$0.505541\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.86603	−	1.30385i	−0.425147	−	0.113918i	0.0399004	−	0.999204i	$-0.487296\pi$
$131$	−4.86603	−	1.30385i	−0.425147	−	0.113918i	−0.465047	+	0.885286i	$0.653963\pi$
$132$		0			0
$133$	18.2942	−	4.90192i	1.58631	−	0.425051i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.571797	−	0.330127i	−0.0488519	−	0.0282047i	0.475375	−	0.879783i	$-0.342312\pi$
$137$	−0.571797	−	0.330127i	−0.0488519	−	0.0282047i	−0.524227	+	0.851579i	$0.675646\pi$
$138$		0			0
$139$	4.33013	−	16.1603i	0.367277	−	1.37069i	−0.497032	−	0.867732i	$-0.665577\pi$
$139$	4.33013	−	16.1603i	0.367277	−	1.37069i	0.864308	−	0.502962i	$-0.167757\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.46410			0.373307
$144$		0			0
$145$	1.73205			0.143839
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.30385	−	16.0622i	0.352585	−	1.31586i	−0.530912	−	0.847427i	$-0.678150\pi$
$149$	4.30385	−	16.0622i	0.352585	−	1.31586i	0.883497	−	0.468438i	$-0.155183\pi$
$150$		0			0
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	0.232623	−	0.972567i	$-0.425269\pi$
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	−0.725956	+	0.687741i	$0.758602\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−17.1603	+	4.59808i	−1.37834	+	0.369326i
$156$		0			0
$157$	3.23205	+	0.866025i	0.257946	+	0.0691164i	0.385474	−	0.922719i	$-0.374038\pi$
$157$	3.23205	+	0.866025i	0.257946	+	0.0691164i	−0.127529	+	0.991835i	$0.540704\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	28.8564			2.27420
$162$		0			0
$163$	1.92820	−	1.92820i	0.151029	−	0.151029i	−0.627549	−	0.778577i	$-0.715942\pi$
$163$	1.92820	−	1.92820i	0.151029	−	0.151029i	0.778577	+	0.627549i	$0.215942\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14.2583	−	8.23205i	1.10334	−	0.637015i	0.166246	−	0.986084i	$-0.446835\pi$
$167$	14.2583	−	8.23205i	1.10334	−	0.637015i	0.937097	+	0.349069i	$0.113502\pi$
$168$		0			0
$169$	−6.63397	−	3.83013i	−0.510306	−	0.294625i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.03590	+	7.59808i	0.154786	+	0.577671i	0.999124	+	0.0418586i	$0.0133279\pi$
$173$	2.03590	+	7.59808i	0.154786	+	0.577671i	−0.844337	+	0.535812i	$0.820005\pi$
$174$		0			0
$175$	2.83013	+	4.90192i	0.213937	+	0.370551i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.92820	+	5.92820i	−0.443095	+	0.443095i	−0.893051	−	0.449956i	$-0.851440\pi$
$179$	−5.92820	+	5.92820i	−0.443095	+	0.443095i	0.449956	+	0.893051i	$0.351440\pi$
$180$		0			0
$181$	−7.73205	−	7.73205i	−0.574719	−	0.574719i	0.358725	−	0.933443i	$-0.383212\pi$
$181$	−7.73205	−	7.73205i	−0.574719	−	0.574719i	−0.933443	+	0.358725i	$0.883212\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.0981	−	5.83013i	0.742425	−	0.428639i
$186$		0			0
$187$	−7.46410	+	2.00000i	−0.545829	+	0.146254i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.40192	−	2.42820i	0.101440	−	0.175699i	−0.810838	−	0.585270i	$-0.800988\pi$
$191$	1.40192	−	2.42820i	0.101440	−	0.175699i	0.912278	+	0.409572i	$0.134322\pi$
$192$		0			0
$193$	2.23205	+	3.86603i	0.160667	+	0.278283i	0.935108	−	0.354363i	$-0.115302\pi$
$193$	2.23205	+	3.86603i	0.160667	+	0.278283i	−0.774441	+	0.632646i	$0.781969\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.53590	−	3.53590i	−0.251922	−	0.251922i	0.569836	−	0.821758i	$-0.307007\pi$
$197$	−3.53590	−	3.53590i	−0.251922	−	0.251922i	−0.821758	+	0.569836i	$0.807007\pi$
$198$		0			0
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.03590	−	3.86603i	0.0727058	−	0.271342i
$204$		0			0
$205$	0.401924	+	1.50000i	0.0280716	+	0.104765i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.09808	−	7.09808i	0.283470	−	0.490984i
$210$		0			0
$211$	−18.5263	−	4.96410i	−1.27540	−	0.341743i	−0.443304	−	0.896371i	$-0.646194\pi$
$211$	−18.5263	−	4.96410i	−1.27540	−	0.341743i	−0.832098	+	0.554629i	$0.812860\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	12.6603i		−	0.863422i
$216$		0			0
$217$			41.0526i			2.78683i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−8.92820	−	2.39230i	−0.600576	−	0.160924i
$222$		0			0
$223$	−7.79423	+	13.5000i	−0.521940	+	0.904027i	0.477734	+	0.878504i	$0.341458\pi$
$223$	−7.79423	+	13.5000i	−0.521940	+	0.904027i	−0.999674	+	0.0255224i	$0.991875\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.25833	−	19.6244i	−0.349008	−	1.30251i	−0.887860	−	0.460114i	$-0.847809\pi$
$227$	−5.25833	−	19.6244i	−0.349008	−	1.30251i	0.538852	−	0.842400i	$-0.318858\pi$
$228$		0			0
$229$	−4.42820	+	16.5263i	−0.292624	+	1.09209i	0.650462	+	0.759539i	$0.274575\pi$
$229$	−4.42820	+	16.5263i	−0.292624	+	1.09209i	−0.943086	+	0.332549i	$0.892091\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			9.07180i			0.594313i	0.954829	+	0.297157i	$0.0960383\pi$
$233$			9.07180i			0.594313i	−0.954829	+	0.297157i	$0.903962\pi$
$234$		0			0
$235$	−1.63397	−	1.63397i	−0.106589	−	0.106589i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.401924	−	0.696152i	−0.0259983	−	0.0450304i	0.852734	−	0.522346i	$-0.174943\pi$
$239$	−0.401924	−	0.696152i	−0.0259983	−	0.0450304i	−0.878732	+	0.477316i	$0.841610\pi$
$240$		0			0
$241$	−2.76795	+	4.79423i	−0.178299	+	0.308823i	−0.941298	−	0.337576i	$-0.890393\pi$
$241$	−2.76795	+	4.79423i	−0.178299	+	0.308823i	0.762999	+	0.646400i	$0.223726\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−24.1244	+	6.46410i	−1.54125	+	0.412976i
$246$		0			0
$247$	8.49038	−	4.90192i	0.540230	−	0.311902i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−13.3923	−	13.3923i	−0.845315	−	0.845315i	0.144229	−	0.989544i	$-0.453930\pi$
$251$	−13.3923	−	13.3923i	−0.845315	−	0.845315i	−0.989544	+	0.144229i	$0.953930\pi$
$252$		0			0
$253$	8.83013	−	8.83013i	0.555145	−	0.555145i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.1603	−	21.0622i	−0.758536	−	1.31382i	−0.943597	−	0.331096i	$-0.892582\pi$
$257$	−12.1603	−	21.0622i	−0.758536	−	1.31382i	0.185061	−	0.982727i	$-0.440752\pi$
$258$		0			0
$259$	−6.97372	−	26.0263i	−0.433326	−	1.61719i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.59808	+	4.96410i	0.530180	+	0.306100i	0.741090	−	0.671406i	$-0.234309\pi$
$263$	8.59808	+	4.96410i	0.530180	+	0.306100i	−0.210910	+	0.977506i	$0.567643\pi$
$264$		0			0
$265$	13.5622	−	7.83013i	0.833118	−	0.481001i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.26795	+	4.26795i	−0.260221	+	0.260221i	−0.825144	−	0.564923i	$-0.808906\pi$
$269$	−4.26795	+	4.26795i	−0.260221	+	0.260221i	0.564923	+	0.825144i	$0.308906\pi$
$270$		0			0
$271$	1.07180			0.0651070			0.0325535	−	0.999470i	$-0.489636\pi$
$271$	1.07180			0.0651070			0.0325535	+	0.999470i	$0.489636\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.36603	+	0.633975i	0.142677	+	0.0382301i
$276$		0			0
$277$	6.69615	−	1.79423i	0.402333	−	0.107805i	−0.0519775	−	0.998648i	$-0.516552\pi$
$277$	6.69615	−	1.79423i	0.402333	−	0.107805i	0.454310	+	0.890844i	$0.349886\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.0359	−	5.79423i	−0.598692	−	0.345655i	0.169835	−	0.985472i	$-0.445676\pi$
$281$	−10.0359	−	5.79423i	−0.598692	−	0.345655i	−0.768527	+	0.639818i	$0.779010\pi$
$282$		0			0
$283$	−3.52628	+	13.1603i	−0.209616	+	0.782296i	0.778377	+	0.627797i	$0.216043\pi$
$283$	−3.52628	+	13.1603i	−0.209616	+	0.782296i	−0.987993	+	0.154499i	$0.950624\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.58846			0.211820
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.571797	−	2.13397i	0.0334047	−	0.124668i	−0.947210	−	0.320614i	$-0.896111\pi$
$293$	0.571797	−	2.13397i	0.0334047	−	0.124668i	0.980615	+	0.195945i	$0.0627776\pi$
$294$		0			0
$295$	2.59808	+	1.50000i	0.151266	+	0.0873334i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	14.4282	−	3.86603i	0.834405	−	0.223578i
$300$		0			0
$301$	−28.2583	−	7.57180i	−1.62878	−	0.436431i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.26795			−0.244382
$306$		0			0
$307$	−7.92820	+	7.92820i	−0.452486	+	0.452486i	−0.896179	−	0.443693i	$-0.853668\pi$
$307$	−7.92820	+	7.92820i	−0.452486	+	0.452486i	0.443693	+	0.896179i	$0.353668\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.18653	+	5.30385i	−0.520921	+	0.300754i	−0.737311	−	0.675553i	$-0.763905\pi$
$311$	−9.18653	+	5.30385i	−0.520921	+	0.300754i	0.216391	+	0.976307i	$0.430572\pi$
$312$		0			0
$313$	−25.1603	−	14.5263i	−1.42214	−	0.821074i	−0.425660	−	0.904883i	$-0.639958\pi$
$313$	−25.1603	−	14.5263i	−1.42214	−	0.821074i	−0.996482	+	0.0838094i	$0.973291\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.96410	−	33.4545i	−0.503474	−	1.87899i	−0.476150	−	0.879364i	$-0.657968\pi$
$317$	−8.96410	−	33.4545i	−0.503474	−	1.87899i	−0.0273246	−	0.999627i	$-0.508699\pi$
$318$		0			0
$319$	−0.866025	−	1.50000i	−0.0484881	−	0.0839839i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−12.0000	+	12.0000i	−0.667698	+	0.667698i
$324$		0			0
$325$	2.07180	+	2.07180i	0.114923	+	0.114923i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−4.62436	+	2.66987i	−0.254949	+	0.147195i
$330$		0			0
$331$	5.06218	−	1.35641i	0.278242	−	0.0745548i	−0.116999	−	0.993132i	$-0.537328\pi$
$331$	5.06218	−	1.35641i	0.278242	−	0.0745548i	0.395242	+	0.918577i	$0.370661\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.33013	−	14.4282i	0.455123	−	0.788297i
$336$		0			0
$337$	−9.69615	−	16.7942i	−0.528183	−	0.914840i	−0.999460	−	0.0328547i	$-0.989540\pi$
$337$	−9.69615	−	16.7942i	−0.528183	−	0.914840i	0.471277	−	0.881985i	$-0.343793\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.5622	+	12.5622i	0.680280	+	0.680280i
$342$		0			0
$343$			26.4641i			1.42893i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.473721	−	1.76795i	0.0254307	−	0.0949085i	−0.952044	−	0.305961i	$-0.901022\pi$
$347$	0.473721	−	1.76795i	0.0254307	−	0.0949085i	0.977475	+	0.211052i	$0.0676890\pi$
$348$		0			0
$349$	1.03590	+	3.86603i	0.0554504	+	0.206944i	0.988093	−	0.153858i	$-0.0491698\pi$
$349$	1.03590	+	3.86603i	0.0554504	+	0.206944i	−0.932643	+	0.360802i	$0.882503\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.7679	−	20.3827i	0.626345	−	1.08486i	−0.361934	−	0.932204i	$-0.617884\pi$
$353$	11.7679	−	20.3827i	0.626345	−	1.08486i	0.988279	−	0.152657i	$-0.0487831\pi$
$354$		0			0
$355$	−5.46410	−	1.46410i	−0.290004	−	0.0777064i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			28.9282i			1.52677i	0.645942	+	0.763386i	$0.276465\pi$
$359$			28.9282i			1.52677i	−0.645942	+	0.763386i	$0.723535\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.9282	+	3.73205i	0.729035	+	0.195344i
$366$		0			0
$367$	17.4545	−	30.2321i	0.911117	−	1.57810i	0.0986270	−	0.995124i	$-0.468555\pi$
$367$	17.4545	−	30.2321i	0.911117	−	1.57810i	0.812490	−	0.582976i	$-0.198112\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.36603	−	34.9545i	−0.486260	−	1.81475i
$372$		0			0
$373$	0.428203	−	1.59808i	0.0221715	−	0.0827452i	−0.953954	−	0.299954i	$-0.903029\pi$
$373$	0.428203	−	1.59808i	0.0221715	−	0.0827452i	0.976125	+	0.217209i	$0.0696953\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	2.07180i		−	0.106703i
$378$		0			0
$379$	15.5885	+	15.5885i	0.800725	+	0.800725i	0.983209	−	0.182484i	$-0.0584137\pi$
$379$	15.5885	+	15.5885i	0.800725	+	0.800725i	−0.182484	+	0.983209i	$0.558414\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.66987	+	6.35641i	0.187522	+	0.324797i	0.944423	−	0.328732i	$-0.106621\pi$
$383$	3.66987	+	6.35641i	0.187522	+	0.324797i	−0.756902	+	0.653529i	$0.773288\pi$
$384$		0			0
$385$	−8.33013	+	14.4282i	−0.424543	+	0.735329i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.96410	−	2.40192i	0.454498	−	0.121782i	−0.0243053	−	0.999705i	$-0.507737\pi$
$389$	8.96410	−	2.40192i	0.454498	−	0.121782i	0.478803	+	0.877922i	$0.341071\pi$
$390$		0			0
$391$	−22.3923	+	12.9282i	−1.13243	+	0.653807i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.36603	+	2.36603i	0.119048	+	0.119048i
$396$		0			0
$397$	17.0526	−	17.0526i	0.855843	−	0.855843i	−0.135002	−	0.990845i	$-0.543104\pi$
$397$	17.0526	−	17.0526i	0.855843	−	0.855843i	0.990845	+	0.135002i	$0.0431041\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.1603	+	27.9904i	0.807005	+	1.39777i	0.914929	+	0.403614i	$0.132246\pi$
$401$	16.1603	+	27.9904i	0.807005	+	1.39777i	−0.107925	+	0.994159i	$0.534421\pi$
$402$		0			0
$403$	5.50000	+	20.5263i	0.273975	+	1.02249i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.0981	−	5.83013i	−0.500543	−	0.288989i
$408$		0			0
$409$	19.6244	−	11.3301i	0.970362	−	0.560239i	0.0710154	−	0.997475i	$-0.477376\pi$
$409$	19.6244	−	11.3301i	0.970362	−	0.560239i	0.899347	+	0.437236i	$0.144043\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.90192	−	4.90192i	0.241208	−	0.241208i
$414$		0			0
$415$	−28.3205			−1.39020
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.5263	+	4.96410i	0.905068	+	0.242512i	0.681191	−	0.732105i	$-0.261462\pi$
$419$	18.5263	+	4.96410i	0.905068	+	0.242512i	0.223876	+	0.974618i	$0.428129\pi$
$420$		0			0
$421$	17.8923	−	4.79423i	0.872018	−	0.233656i	0.205058	−	0.978750i	$-0.434262\pi$
$421$	17.8923	−	4.79423i	0.872018	−	0.233656i	0.666960	+	0.745094i	$0.267595\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.39230	−	2.53590i	−0.213058	−	0.123009i
$426$		0			0
$427$	−2.55256	+	9.52628i	−0.123527	+	0.461009i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3.32051			−0.159943			−0.0799716	−	0.996797i	$-0.525483\pi$
$431$	−3.32051			−0.159943			−0.0799716	+	0.996797i	$0.525483\pi$
$432$		0			0
$433$	3.60770			0.173375			0.0866874	−	0.996236i	$-0.472372\pi$
$433$	3.60770			0.173375			0.0866874	+	0.996236i	$0.472372\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.09808	−	26.4904i	0.339547	−	1.26721i
$438$		0			0
$439$	5.93782	+	3.42820i	0.283397	+	0.163619i	0.634960	−	0.772545i	$-0.281016\pi$
$439$	5.93782	+	3.42820i	0.283397	+	0.163619i	−0.351563	+	0.936164i	$0.614350\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.33013	−	1.16025i	0.205731	−	0.0551253i	−0.154482	−	0.987996i	$-0.549371\pi$
$443$	4.33013	−	1.16025i	0.205731	−	0.0551253i	0.360213	+	0.932870i	$0.382704\pi$
$444$		0			0
$445$	−29.5885	−	7.92820i	−1.40263	−	0.375833i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−35.3205			−1.66688			−0.833439	−	0.552612i	$-0.813631\pi$
$449$	−35.3205			−1.66688			−0.833439	+	0.552612i	$0.813631\pi$
$450$		0			0
$451$	1.09808	−	1.09808i	0.0517064	−	0.0517064i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−17.2583	+	9.96410i	−0.809083	+	0.467124i
$456$		0			0
$457$	−25.9641	−	14.9904i	−1.21455	−	0.701220i	−0.250802	−	0.968038i	$-0.580694\pi$
$457$	−25.9641	−	14.9904i	−1.21455	−	0.701220i	−0.963747	+	0.266818i	$0.914028\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.23205	+	4.59808i	0.0573823	+	0.214154i	0.988664	−	0.150147i	$-0.0479747\pi$
$461$	1.23205	+	4.59808i	0.0573823	+	0.214154i	−0.931281	+	0.364301i	$0.881308\pi$
$462$		0			0
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	0.962891	−	0.269892i	$-0.0869880\pi$
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	−0.715179	+	0.698942i	$0.753655\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	21.7846	−	21.7846i	1.00807	−	1.00807i	0.00810436	−	0.999967i	$-0.497420\pi$
$467$	21.7846	−	21.7846i	1.00807	−	1.00807i	0.999967	−	0.00810436i	$-0.00257972\pi$
$468$		0			0
$469$	−27.2224	−	27.2224i	−1.25702	−	1.25702i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.9641	+	6.33013i	−0.504130	+	0.291060i
$474$		0			0
$475$	5.19615	−	1.39230i	0.238416	−	0.0638833i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.33013	−	16.1603i	0.426304	−	0.738381i	−0.570237	−	0.821480i	$-0.693149\pi$
$479$	9.33013	−	16.1603i	0.426304	−	0.738381i	0.996541	+	0.0830995i	$0.0264819\pi$
$480$		0			0
$481$	−6.97372	−	12.0788i	−0.317974	−	0.550748i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.36603	−	1.36603i	−0.0620280	−	0.0620280i
$486$		0			0
$487$		−	6.78461i		−	0.307440i	−0.988114	−	0.153720i	$-0.950875\pi$
$487$		−	6.78461i		−	0.307440i	0.988114	−	0.153720i	$-0.0491254\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.133975	+	0.500000i	−0.00604619	+	0.0225647i	−0.968883	−	0.247519i	$-0.920385\pi$
$491$	−0.133975	+	0.500000i	−0.00604619	+	0.0225647i	0.962837	+	0.270084i	$0.0870514\pi$
$492$		0			0
$493$	0.928203	+	3.46410i	0.0418042	+	0.156015i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.53590	+	11.3205i	−0.293175	+	0.507794i
$498$		0			0
$499$	−9.33013	−	2.50000i	−0.417674	−	0.111915i	0.0438606	−	0.999038i	$-0.486034\pi$
$499$	−9.33013	−	2.50000i	−0.417674	−	0.111915i	−0.461534	+	0.887122i	$0.652701\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	13.8564i		−	0.617827i	−0.951090	−	0.308913i	$-0.900035\pi$
$503$		−	13.8564i		−	0.617827i	0.951090	−	0.308913i	$-0.0999653\pi$
$504$		0			0
$505$		−	1.00000i		−	0.0444994i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.69615	+	1.25833i	0.208153	+	0.0557745i	0.361389	−	0.932415i	$-0.382303\pi$
$509$	4.69615	+	1.25833i	0.208153	+	0.0557745i	−0.153236	+	0.988190i	$0.548969\pi$
$510$		0			0
$511$	16.6603	−	28.8564i	0.737006	−	1.27653i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.96410	+	29.7224i	0.350940	+	1.30973i
$516$		0			0
$517$	−0.598076	+	2.23205i	−0.0263034	+	0.0981655i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	41.8564i		−	1.83376i	−0.399160	−	0.916881i	$-0.630698\pi$
$521$		−	41.8564i		−	1.83376i	0.399160	−	0.916881i	$-0.369302\pi$
$522$		0			0
$523$	−22.1244	−	22.1244i	−0.967431	−	0.967431i	0.0320556	−	0.999486i	$-0.489795\pi$
$523$	−22.1244	−	22.1244i	−0.967431	−	0.967431i	−0.999486	+	0.0320556i	$0.989795\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−18.3923	−	31.8564i	−0.801181	−	1.38769i
$528$		0			0
$529$	9.39230	−	16.2679i	0.408361	−	0.707302i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.79423	−	0.480762i	0.0777167	−	0.0208241i
$534$		0			0
$535$	−22.2224	+	12.8301i	−0.960760	+	0.554695i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	17.6603	+	17.6603i	0.760681	+	0.760681i
$540$		0			0
$541$	−15.0000	+	15.0000i	−0.644900	+	0.644900i	−0.951756	−	0.306856i	$-0.900723\pi$
$541$	−15.0000	+	15.0000i	−0.644900	+	0.644900i	0.306856	+	0.951756i	$0.400723\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.36603	−	4.09808i	−0.101349	−	0.175542i
$546$		0			0
$547$	5.74167	+	21.4282i	0.245496	+	0.916204i	0.973133	+	0.230242i	$0.0739517\pi$
$547$	5.74167	+	21.4282i	0.245496	+	0.916204i	−0.727637	+	0.685962i	$0.759382\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.29423	−	1.90192i	−0.140339	−	0.0810247i
$552$		0			0
$553$	6.69615	−	3.86603i	0.284749	−	0.164400i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	23.9808	−	23.9808i	1.01610	−	1.01610i	0.0162292	−	0.999868i	$-0.494834\pi$
$557$	23.9808	−	23.9808i	1.01610	−	1.01610i	0.999868	−	0.0162292i	$-0.00516614\pi$
$558$		0			0
$559$	−15.1436			−0.640506
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.13397	+	1.64359i	0.258516	+	0.0692692i	0.385749	−	0.922604i	$-0.373943\pi$
$563$	6.13397	+	1.64359i	0.258516	+	0.0692692i	−0.127233	+	0.991873i	$0.540610\pi$
$564$		0			0
$565$	−23.2583	+	6.23205i	−0.978485	+	0.262184i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−27.4808	−	15.8660i	−1.15205	−	0.665138i	−0.202667	−	0.979248i	$-0.564961\pi$
$569$	−27.4808	−	15.8660i	−1.15205	−	0.665138i	−0.949387	+	0.314109i	$0.898294\pi$
$570$		0			0
$571$	10.5981	−	39.5526i	0.443516	−	1.65522i	−0.276310	−	0.961068i	$-0.589112\pi$
$571$	10.5981	−	39.5526i	0.443516	−	1.65522i	0.719826	−	0.694155i	$-0.244222\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.19615			0.341803
$576$		0			0
$577$	−25.1769			−1.04813			−0.524064	−	0.851679i	$-0.675585\pi$
$577$	−25.1769			−1.04813			−0.524064	+	0.851679i	$0.675585\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−16.9378	+	63.2128i	−0.702699	+	2.62251i
$582$		0			0
$583$	−13.5622	−	7.83013i	−0.561688	−	0.324291i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.7942	+	3.96410i	−0.610623	+	0.163616i	−0.550861	−	0.834597i	$-0.685701\pi$
$587$	−14.7942	+	3.96410i	−0.610623	+	0.163616i	−0.0597617	+	0.998213i	$0.519034\pi$
$588$		0			0
$589$	37.6865	+	10.0981i	1.55285	+	0.416084i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.46410			0.224384			0.112192	−	0.993687i	$-0.464213\pi$
$593$	5.46410			0.224384			0.112192	+	0.993687i	$0.464213\pi$
$594$		0			0
$595$	24.3923	−	24.3923i	0.999987	−	0.999987i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	30.3109	−	17.5000i	1.23847	−	0.715031i	0.269688	−	0.962948i	$-0.413079\pi$
$599$	30.3109	−	17.5000i	1.23847	−	0.715031i	0.968781	+	0.247917i	$0.0797461\pi$
$600$		0			0
$601$	26.7679	+	15.4545i	1.09189	+	0.630401i	0.934078	−	0.357068i	$-0.116224\pi$
$601$	26.7679	+	15.4545i	1.09189	+	0.630401i	0.157809	+	0.987470i	$0.449557\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.63397	−	13.5622i	−0.147742	−	0.551381i
$606$		0			0
$607$	−0.598076	−	1.03590i	−0.0242752	−	0.0420458i	0.853633	−	0.520876i	$-0.174394\pi$
$607$	−0.598076	−	1.03590i	−0.0242752	−	0.0420458i	−0.877908	+	0.478830i	$0.841061\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.95448	+	1.95448i	−0.0790699	+	0.0790699i
$612$		0			0
$613$	23.5885	+	23.5885i	0.952729	+	0.952729i	0.998932	−	0.0462032i	$-0.0147122\pi$
$613$	23.5885	+	23.5885i	0.952729	+	0.952729i	−0.0462032	+	0.998932i	$0.514712\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	23.0885	−	13.3301i	0.929506	−	0.536651i	0.0428509	−	0.999081i	$-0.486356\pi$
$617$	23.0885	−	13.3301i	0.929506	−	0.536651i	0.886655	+	0.462431i	$0.153023\pi$
$618$		0			0
$619$	−7.13397	+	1.91154i	−0.286739	+	0.0768314i	−0.399322	−	0.916811i	$-0.630754\pi$
$619$	−7.13397	+	1.91154i	−0.286739	+	0.0768314i	0.112583	+	0.993642i	$0.464088\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−35.3923	+	61.3013i	−1.41796	+	2.45598i
$624$		0			0
$625$	−8.52628	−	14.7679i	−0.341051	−	0.590718i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	17.0718	+	17.0718i	0.680697	+	0.680697i
$630$		0			0
$631$			16.2487i			0.646851i	0.946254	+	0.323425i	$0.104835\pi$
$631$			16.2487i			0.646851i	−0.946254	+	0.323425i	$0.895165\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.196152	−	0.732051i	0.00778407	−	0.0290506i
$636$		0			0
$637$	7.73205	+	28.8564i	0.306355	+	1.14333i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.23205	+	15.9904i	−0.364644	+	0.631582i	−0.988719	−	0.149782i	$-0.952143\pi$
$641$	−9.23205	+	15.9904i	−0.364644	+	0.631582i	0.624075	+	0.781365i	$0.285476\pi$
$642$		0			0
$643$	29.7224	+	7.96410i	1.17214	+	0.314074i	0.791804	−	0.610776i	$-0.209142\pi$
$643$	29.7224	+	7.96410i	1.17214	+	0.314074i	0.380334	+	0.924849i	$0.375809\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	25.6077i		−	1.00674i	−0.864070	−	0.503371i	$-0.832093\pi$
$647$		−	25.6077i		−	1.00674i	0.864070	−	0.503371i	$-0.167907\pi$
$648$		0			0
$649$		−	3.00000i		−	0.117760i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−47.2846	−	12.6699i	−1.85039	−	0.495810i	−0.850829	−	0.525443i	$-0.823900\pi$
$653$	−47.2846	−	12.6699i	−1.85039	−	0.495810i	−0.999561	+	0.0296324i	$0.990566\pi$
$654$		0			0
$655$	4.86603	−	8.42820i	0.190131	−	0.329317i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.330127	−	1.23205i	−0.0128599	−	0.0479939i	0.959198	−	0.282736i	$-0.0912421\pi$
$659$	−0.330127	−	1.23205i	−0.0128599	−	0.0479939i	−0.972058	+	0.234742i	$0.924575\pi$
$660$		0			0
$661$	−5.30385	+	19.7942i	−0.206296	+	0.769906i	0.782755	+	0.622330i	$0.213814\pi$
$661$	−5.30385	+	19.7942i	−0.206296	+	0.769906i	−0.989051	+	0.147576i	$0.952853\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			36.5885i			1.41884i
$666$		0			0
$667$	−4.09808	−	4.09808i	−0.158678	−	0.158678i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.13397	+	3.69615i	0.0823812	+	0.142688i
$672$		0			0
$673$	21.1603	−	36.6506i	0.815668	−	1.41278i	−0.0931795	−	0.995649i	$-0.529703\pi$
$673$	21.1603	−	36.6506i	0.815668	−	1.41278i	0.908847	−	0.417129i	$-0.136964\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.76795	−	2.34936i	0.336980	−	0.0902934i	−0.0863612	−	0.996264i	$-0.527524\pi$
$677$	8.76795	−	2.34936i	0.336980	−	0.0902934i	0.423341	+	0.905970i	$0.360857\pi$
$678$		0			0
$679$	−3.86603	+	2.23205i	−0.148364	+	0.0856582i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	15.3923	+	15.3923i	0.588970	+	0.588970i	0.937353	−	0.348382i	$-0.113269\pi$
$683$	15.3923	+	15.3923i	0.588970	+	0.588970i	−0.348382	+	0.937353i	$0.613269\pi$
$684$		0			0
$685$	0.901924	−	0.901924i	0.0344607	−	0.0344607i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.36603	−	16.2224i	−0.356817	−	0.618025i
$690$		0			0
$691$	−0.526279	−	1.96410i	−0.0200206	−	0.0747179i	0.955193	−	0.295984i	$-0.0956476\pi$
$691$	−0.526279	−	1.96410i	−0.0200206	−	0.0747179i	−0.975213	+	0.221266i	$0.928981\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	27.9904	+	16.1603i	1.06174	+	0.612993i
$696$		0			0
$697$	−2.78461	+	1.60770i	−0.105475	+	0.0608958i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−17.0526	+	17.0526i	−0.644066	+	0.644066i	−0.951553	−	0.307486i	$-0.900512\pi$
$701$	−17.0526	+	17.0526i	−0.644066	+	0.644066i	0.307486	+	0.951553i	$0.400512\pi$
$702$		0			0
$703$	−25.6077			−0.965813
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.23205	−	0.598076i	−0.0839449	−	0.0224930i
$708$		0			0
$709$	−37.7487	+	10.1147i	−1.41768	+	0.379867i	−0.884661	−	0.466235i	$-0.845610\pi$
$709$	−37.7487	+	10.1147i	−1.41768	+	0.379867i	−0.533022	+	0.846102i	$0.678944\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	51.4808	+	29.7224i	1.92797	+	1.11311i
$714$		0			0
$715$	−2.23205	+	8.33013i	−0.0834740	+	0.311529i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.3205			−0.422184			−0.211092	−	0.977466i	$-0.567702\pi$
$719$	−11.3205			−0.422184			−0.211092	+	0.977466i	$0.567702\pi$
$720$		0			0
$721$	71.1051			2.64809
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.294229	−	1.09808i	0.0109274	−	0.0407815i
$726$		0			0
$727$	3.06218	+	1.76795i	0.113570	+	0.0655696i	0.555709	−	0.831377i	$-0.312447\pi$
$727$	3.06218	+	1.76795i	0.113570	+	0.0655696i	−0.442139	+	0.896947i	$0.645780\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	25.3205	−	6.78461i	0.936513	−	0.250938i
$732$		0			0
$733$	−31.6244	−	8.47372i	−1.16807	−	0.312984i	−0.377887	−	0.925852i	$-0.623349\pi$
$733$	−31.6244	−	8.47372i	−1.16807	−	0.312984i	−0.790185	+	0.612868i	$0.790016\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.6603			−0.613688
$738$		0			0
$739$	26.2679	−	26.2679i	0.966282	−	0.966282i	−0.0331677	−	0.999450i	$-0.510560\pi$
$739$	26.2679	−	26.2679i	0.966282	−	0.966282i	0.999450	+	0.0331677i	$0.0105595\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.1147	+	14.5000i	−0.921370	+	0.531953i	−0.884072	−	0.467351i	$-0.845209\pi$
$743$	−25.1147	+	14.5000i	−0.921370	+	0.531953i	−0.0372984	+	0.999304i	$0.511875\pi$
$744$		0			0
$745$	27.8205	+	16.0622i	1.01926	+	0.588473i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.3468	+	57.2750i	0.560759	+	2.09278i
$750$		0			0
$751$	24.7224	+	42.8205i	0.902134	+	1.56254i	0.824718	+	0.565544i	$0.191334\pi$
$751$	24.7224	+	42.8205i	0.902134	+	1.56254i	0.0774160	+	0.996999i	$0.475333\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	9.56218	−	9.56218i	0.348003	−	0.348003i
$756$		0			0
$757$	1.53590	+	1.53590i	0.0558232	+	0.0558232i	0.734467	−	0.678644i	$-0.237432\pi$
$757$	1.53590	+	1.53590i	0.0558232	+	0.0558232i	−0.678644	+	0.734467i	$0.737432\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−16.2846	+	9.40192i	−0.590317	+	0.340819i	−0.765223	−	0.643766i	$-0.777371\pi$
$761$	−16.2846	+	9.40192i	−0.590317	+	0.340819i	0.174906	+	0.984585i	$0.444038\pi$
$762$		0			0
$763$	−10.5622	+	2.83013i	−0.382377	+	0.102457i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.79423	−	3.10770i	0.0647858	−	0.112212i
$768$		0			0
$769$	−3.50000	−	6.06218i	−0.126213	−	0.218608i	0.795993	−	0.605305i	$-0.206949\pi$
$769$	−3.50000	−	6.06218i	−0.126213	−	0.218608i	−0.922207	+	0.386698i	$0.873616\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	23.5885	+	23.5885i	0.848418	+	0.848418i	0.989936	−	0.141518i	$-0.0451983\pi$
$773$	23.5885	+	23.5885i	0.848418	+	0.848418i	−0.141518	+	0.989936i	$0.545198\pi$
$774$		0			0
$775$			11.6603i			0.418849i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.882686	−	3.29423i	0.0316255	−	0.118028i
$780$		0			0
$781$	1.46410	+	5.46410i	0.0523897	+	0.195521i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.23205	+	5.59808i	−0.115357	+	0.199804i
$786$		0			0
$787$	3.06218	+	0.820508i	0.109155	+	0.0292480i	0.312983	−	0.949759i	$-0.398672\pi$
$787$	3.06218	+	0.820508i	0.109155	+	0.0292480i	−0.203828	+	0.979007i	$0.565338\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			55.6410i			1.97837i
$792$		0			0
$793$			5.10512i			0.181288i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	41.2846	+	11.0622i	1.46238	+	0.391842i	0.900310	−	0.435250i	$-0.143340\pi$
$797$	41.2846	+	11.0622i	1.46238	+	0.391842i	0.562066	+	0.827092i	$0.310007\pi$
$798$		0			0
$799$	2.39230	−	4.14359i	0.0846337	−	0.146590i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.73205	−	13.9282i	−0.131701	−	0.491516i
$804$		0			0
$805$	−14.4282	+	53.8468i	−0.508527	+	1.89785i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	36.6410i		−	1.28823i	−0.764929	−	0.644115i	$-0.777226\pi$
$809$		−	36.6410i		−	1.28823i	0.764929	−	0.644115i	$-0.222774\pi$
$810$		0			0
$811$	18.4641	+	18.4641i	0.648362	+	0.648362i	0.952597	−	0.304235i	$-0.0984007\pi$
$811$	18.4641	+	18.4641i	0.648362	+	0.648362i	−0.304235	+	0.952597i	$0.598401\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.63397	+	4.56218i	0.0922641	+	0.159806i
$816$		0			0
$817$	−13.9019	+	24.0788i	−0.486367	+	0.842412i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	40.0167	−	10.7224i	1.39659	−	0.374215i	0.519472	−	0.854488i	$-0.326129\pi$
$821$	40.0167	−	10.7224i	1.39659	−	0.374215i	0.877119	+	0.480272i	$0.159462\pi$
$822$		0			0
$823$	36.6506	−	21.1603i	1.27756	−	0.737600i	0.301162	−	0.953573i	$-0.402626\pi$
$823$	36.6506	−	21.1603i	1.27756	−	0.737600i	0.976399	+	0.215973i	$0.0692923\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−31.3923	−	31.3923i	−1.09162	−	1.09162i	−0.995356	−	0.0962613i	$-0.969312\pi$
$827$	−31.3923	−	31.3923i	−1.09162	−	1.09162i	−0.0962613	−	0.995356i	$-0.530688\pi$
$828$		0			0
$829$	−14.2679	+	14.2679i	−0.495546	+	0.495546i	−0.910048	−	0.414502i	$-0.863956\pi$
$829$	−14.2679	+	14.2679i	−0.495546	+	0.495546i	0.414502	+	0.910048i	$0.363956\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−25.8564	−	44.7846i	−0.895871	−	1.55169i
$834$		0			0
$835$	8.23205	+	30.7224i	0.284882	+	1.06319i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−6.74167	−	3.89230i	−0.232748	−	0.134377i	0.379091	−	0.925359i	$-0.376237\pi$
$839$	−6.74167	−	3.89230i	−0.232748	−	0.134377i	−0.611839	+	0.790982i	$0.709570\pi$
$840$		0			0
$841$	24.4186	−	14.0981i	0.842020	−	0.486141i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.4641	−	10.4641i	0.359976	−	0.359976i
$846$		0			0
$847$	−32.4449			−1.11482
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−37.6865	−	10.0981i	−1.29188	−	0.346158i
$852$		0			0
$853$	7.69615	−	2.06218i	0.263511	−	0.0706076i	−0.124644	−	0.992201i	$-0.539779\pi$
$853$	7.69615	−	2.06218i	0.263511	−	0.0706076i	0.388156	+	0.921594i	$0.373112\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.6436	+	8.45448i	0.500216	+	0.288800i	0.728803	−	0.684724i	$-0.240077\pi$
$857$	14.6436	+	8.45448i	0.500216	+	0.288800i	−0.228587	+	0.973523i	$0.573411\pi$
$858$		0			0
$859$	−1.20577	+	4.50000i	−0.0411404	+	0.153538i	−0.983440	−	0.181231i	$-0.941992\pi$
$859$	−1.20577	+	4.50000i	−0.0411404	+	0.153538i	0.942300	+	0.334769i	$0.108658\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.5359			−0.903292			−0.451646	−	0.892197i	$-0.649163\pi$
$863$	−26.5359			−0.903292			−0.451646	+	0.892197i	$0.649163\pi$
$864$		0			0
$865$	−15.1962			−0.516685
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.866025	−	3.23205i	0.0293779	−	0.109640i
$870$		0			0
$871$	−17.2583	−	9.96410i	−0.584776	−	0.337621i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−52.2128	+	13.9904i	−1.76512	+	0.472961i
$876$		0			0
$877$	49.9449	+	13.3827i	1.68652	+	0.451901i	0.969488	−	0.245140i	$-0.0788341\pi$
$877$	49.9449	+	13.3827i	1.68652	+	0.451901i	0.717031	+	0.697042i	$0.245501\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−31.3205			−1.05521			−0.527607	−	0.849488i	$-0.676911\pi$
$881$	−31.3205			−1.05521			−0.527607	+	0.849488i	$0.676911\pi$
$882$		0			0
$883$	3.00000	−	3.00000i	0.100958	−	0.100958i	−0.654824	−	0.755782i	$-0.727257\pi$
$883$	3.00000	−	3.00000i	0.100958	−	0.100958i	0.755782	+	0.654824i	$0.227257\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.93782	+	5.16025i	−0.300103	+	0.173264i	−0.642489	−	0.766295i	$-0.722098\pi$
$887$	−8.93782	+	5.16025i	−0.300103	+	0.173264i	0.342386	+	0.939559i	$0.388765\pi$
$888$		0			0
$889$	−1.51666	−	0.875644i	−0.0508672	−	0.0293682i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.31347	+	4.90192i	0.0439535	+	0.164037i
$894$		0			0
$895$	−8.09808	−	14.0263i	−0.270689	−	0.468847i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.83013	−	5.83013i	0.194446	−	0.194446i
$900$		0			0
$901$	22.9282	+	22.9282i	0.763849	+	0.763849i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	18.2942	−	10.5622i	0.608121	−	0.351099i
$906$		0			0
$907$	−9.06218	+	2.42820i	−0.300905	+	0.0806272i	−0.406112	−	0.913823i	$-0.633116\pi$
$907$	−9.06218	+	2.42820i	−0.300905	+	0.0806272i	0.105208	+	0.994450i	$0.466449\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.13397	+	7.16025i	−0.136965	+	0.237230i	−0.926346	−	0.376673i	$-0.877068\pi$
$911$	−4.13397	+	7.16025i	−0.136965	+	0.237230i	0.789382	+	0.613903i	$0.210401\pi$
$912$		0			0
$913$	14.1603	+	24.5263i	0.468636	+	0.811701i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.9019	−	15.9019i	−0.525128	−	0.525128i
$918$		0			0
$919$		−	36.5359i		−	1.20521i	−0.798040	−	0.602604i	$-0.794130\pi$
$919$		−	36.5359i		−	1.20521i	0.798040	−	0.602604i	$-0.205870\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.75129	+	6.53590i	−0.0576444	+	0.215132i
$924$		0			0
$925$	−1.98076	−	7.39230i	−0.0651271	−	0.243057i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.35641	+	16.2058i	−0.306974	+	0.531694i	−0.977699	−	0.210012i	$-0.932650\pi$
$929$	−9.35641	+	16.2058i	−0.306974	+	0.531694i	0.670725	+	0.741706i	$0.265983\pi$
$930$		0			0
$931$	52.9808	+	14.1962i	1.73637	+	0.465260i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	14.9282i		−	0.488204i
$936$		0			0
$937$		−	19.0718i		−	0.623048i	−0.950238	−	0.311524i	$-0.899160\pi$
$937$		−	19.0718i		−	0.623048i	0.950238	−	0.311524i	$-0.100840\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	34.0885	+	9.13397i	1.11125	+	0.297759i	0.767338	−	0.641242i	$-0.221581\pi$
$941$	34.0885	+	9.13397i	1.11125	+	0.297759i	0.343913	+	0.939001i	$0.388247\pi$
$942$		0			0
$943$	2.59808	−	4.50000i	0.0846050	−	0.146540i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.9904	+	41.0167i	0.357139	+	1.33286i	0.877771	+	0.479081i	$0.159030\pi$
$947$	10.9904	+	41.0167i	0.357139	+	1.33286i	−0.520631	+	0.853782i	$0.674303\pi$
$948$		0			0
$949$	4.46410	−	16.6603i	0.144911	−	0.540815i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	32.5359i		−	1.05394i	−0.849884	−	0.526971i	$-0.823328\pi$
$953$		−	32.5359i		−	1.05394i	0.849884	−	0.526971i	$-0.176672\pi$
$954$		0			0
$955$	3.83013	+	3.83013i	0.123940	+	0.123940i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.47372	−	2.55256i	−0.0475889	−	0.0824264i
$960$		0			0
$961$	−26.7846	+	46.3923i	−0.864020	+	1.49653i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.33013	+	2.23205i	−0.268156	+	0.0718523i
$966$		0			0
$967$	−27.0622	+	15.6244i	−0.870261	+	0.502445i	−0.867435	−	0.497551i	$-0.834233\pi$
$967$	−27.0622	+	15.6244i	−0.870261	+	0.502445i	−0.00282602	+	0.999996i	$0.500900\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.9808	−	23.9808i	−0.769579	−	0.769579i	0.208453	−	0.978032i	$-0.433157\pi$
$971$	−23.9808	−	23.9808i	−0.769579	−	0.769579i	−0.978032	+	0.208453i	$0.933157\pi$
$972$		0			0
$973$	52.8109	−	52.8109i	1.69304	−	1.69304i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.2846	+	42.0622i	0.776933	+	1.34569i	0.933701	+	0.358053i	$0.116559\pi$
$977$	24.2846	+	42.0622i	0.776933	+	1.34569i	−0.156768	+	0.987635i	$0.550107\pi$
$978$		0			0
$979$	7.92820	+	29.5885i	0.253386	+	0.945651i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.08142	+	0.624356i	0.0344918	+	0.0199139i	0.517147	−	0.855897i	$-0.326994\pi$
$983$	1.08142	+	0.624356i	0.0344918	+	0.0199139i	−0.482655	+	0.875811i	$0.660327\pi$
$984$		0			0
$985$	8.36603	−	4.83013i	0.266564	−	0.153901i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−29.9545	+	29.9545i	−0.952497	+	0.952497i
$990$		0			0
$991$	44.3923			1.41017			0.705084	−	0.709124i	$-0.250909\pi$
$991$	44.3923			1.41017			0.705084	+	0.709124i	$0.250909\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	40.7846	+	10.9282i	1.29296	+	0.346447i
$996$		0			0
$997$	3.96410	−	1.06218i	0.125544	−	0.0336395i	−0.195500	−	0.980704i	$-0.562633\pi$
$997$	3.96410	−	1.06218i	0.125544	−	0.0336395i	0.321044	+	0.947064i	$0.395966\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.bc.b.1585.1		4
3.2	odd	2		576.2.bb.b.241.1		4
4.3	odd	2		432.2.y.a.181.1		4
9.4	even	3		1728.2.bc.c.1009.1		4
9.5	odd	6		576.2.bb.a.49.1		4
12.11	even	2		144.2.x.d.133.1	yes	4
16.3	odd	4		432.2.y.d.397.1		4
16.13	even	4		1728.2.bc.c.721.1		4
36.23	even	6		144.2.x.a.85.1	yes	4
36.31	odd	6		432.2.y.d.37.1		4
48.29	odd	4		576.2.bb.a.529.1		4
48.35	even	4		144.2.x.a.61.1	✓	4
144.13	even	12	inner	1728.2.bc.b.145.1		4
144.67	odd	12		432.2.y.a.253.1		4
144.77	odd	12		576.2.bb.b.337.1		4
144.131	even	12		144.2.x.d.13.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.61.1	✓	4	48.35	even	4
144.2.x.a.85.1	yes	4	36.23	even	6
144.2.x.d.13.1	yes	4	144.131	even	12
144.2.x.d.133.1	yes	4	12.11	even	2
432.2.y.a.181.1		4	4.3	odd	2
432.2.y.a.253.1		4	144.67	odd	12
432.2.y.d.37.1		4	36.31	odd	6
432.2.y.d.397.1		4	16.3	odd	4
576.2.bb.a.49.1		4	9.5	odd	6
576.2.bb.a.529.1		4	48.29	odd	4
576.2.bb.b.241.1		4	3.2	odd	2
576.2.bb.b.337.1		4	144.77	odd	12
1728.2.bc.b.145.1		4	144.13	even	12	inner
1728.2.bc.b.1585.1		4	1.1	even	1	trivial
1728.2.bc.c.721.1		4	16.13	even	4
1728.2.bc.c.1009.1		4	9.4	even	3

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.86603i) q^{5} +(3.86603 + 2.23205i) q^{7} +O(q^{10})\)	\(q+(-0.500000 + 1.86603i) q^{5} +(3.86603 + 2.23205i) q^{7} +(1.86603 - 0.500000i) q^{11} +(2.23205 + 0.598076i) q^{13} -4.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(5.59808 - 3.23205i) q^{23} +(1.09808 + 0.633975i) q^{25} +(-0.232051 - 0.866025i) q^{29} +(4.59808 + 7.96410i) q^{31} +(-6.09808 + 6.09808i) q^{35} +(-4.26795 - 4.26795i) q^{37} +(0.696152 - 0.401924i) q^{41} +(-6.33013 + 1.69615i) q^{43} +(-0.598076 + 1.03590i) q^{47} +(6.46410 + 11.1962i) q^{49} +(-5.73205 - 5.73205i) q^{53} +3.73205i q^{55} +(0.401924 - 1.50000i) q^{59} +(0.571797 + 2.13397i) q^{61} +(-2.23205 + 3.86603i) q^{65} +(-8.33013 - 2.23205i) q^{67} +2.92820i q^{71} -7.46410i q^{73} +(8.33013 + 2.23205i) q^{77} +(0.866025 - 1.50000i) q^{79} +(3.79423 + 14.1603i) q^{83} +(2.00000 - 7.46410i) q^{85} +15.8564i q^{89} +(7.29423 + 7.29423i) q^{91} +(4.09808 + 7.09808i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} + 12 q^{7}+O(q^{10}) \) 4 * q - 2 * q^5 + 12 * q^7	\( 4 q - 2 q^{5} + 12 q^{7} + 4 q^{11} + 2 q^{13} - 16 q^{17} + 12 q^{19} + 12 q^{23} - 6 q^{25} + 6 q^{29} + 8 q^{31} - 14 q^{35} - 24 q^{37} - 18 q^{41} - 8 q^{43} + 8 q^{47} + 12 q^{49} - 16 q^{53} + 12 q^{59} + 30 q^{61} - 2 q^{65} - 16 q^{67} + 16 q^{77} - 16 q^{83} + 8 q^{85} - 2 q^{91} + 6 q^{95} - 2 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 + 12 * q^7 + 4 * q^11 + 2 * q^13 - 16 * q^17 + 12 * q^19 + 12 * q^23 - 6 * q^25 + 6 * q^29 + 8 * q^31 - 14 * q^35 - 24 * q^37 - 18 * q^41 - 8 * q^43 + 8 * q^47 + 12 * q^49 - 16 * q^53 + 12 * q^59 + 30 * q^61 - 2 * q^65 - 16 * q^67 + 16 * q^77 - 16 * q^83 + 8 * q^85 - 2 * q^91 + 6 * q^95 - 2 * q^97

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