LMFDB - Embedded newform 1728.2.bc.c.721.1

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			721.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1728.721
Dual form			1728.2.bc.c.1009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86603 + 0.500000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +O(q^{10})$	$q+(1.86603 + 0.500000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +(-0.500000 - 1.86603i) q^{11} +(-0.598076 + 2.23205i) q^{13} -4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(-5.59808 + 3.23205i) q^{23} +(-1.09808 - 0.633975i) q^{25} +(0.866025 - 0.232051i) q^{29} +(4.59808 + 7.96410i) q^{31} +(-6.09808 - 6.09808i) q^{35} +(-4.26795 + 4.26795i) q^{37} +(-0.696152 + 0.401924i) q^{41} +(1.69615 + 6.33013i) q^{43} +(-0.598076 + 1.03590i) q^{47} +(6.46410 + 11.1962i) q^{49} +(-5.73205 + 5.73205i) q^{53} -3.73205i q^{55} +(-1.50000 - 0.401924i) q^{59} +(-2.13397 + 0.571797i) q^{61} +(-2.23205 + 3.86603i) q^{65} +(2.23205 - 8.33013i) q^{67} -2.92820i q^{71} +7.46410i q^{73} +(-2.23205 + 8.33013i) q^{77} +(0.866025 - 1.50000i) q^{79} +(-14.1603 + 3.79423i) q^{83} +(-7.46410 - 2.00000i) q^{85} -15.8564i q^{89} +(7.29423 - 7.29423i) q^{91} +(4.09808 + 7.09808i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} - 12 q^{7}+O(q^{10}) $ 4 * q + 4 * q^5 - 12 * q^7	$ 4 q + 4 q^{5} - 12 q^{7} - 2 q^{11} + 8 q^{13} - 16 q^{17} + 12 q^{19} - 12 q^{23} + 6 q^{25} + 8 q^{31} - 14 q^{35} - 24 q^{37} + 18 q^{41} - 14 q^{43} + 8 q^{47} + 12 q^{49} - 16 q^{53} - 6 q^{59} - 12 q^{61} - 2 q^{65} + 2 q^{67} - 2 q^{77} - 22 q^{83} - 16 q^{85} - 2 q^{91} + 6 q^{95} - 2 q^{97}+O(q^{100}) $ 4 * q + 4 * q^5 - 12 * q^7 - 2 * q^11 + 8 * q^13 - 16 * q^17 + 12 * q^19 - 12 * q^23 + 6 * q^25 + 8 * q^31 - 14 * q^35 - 24 * q^37 + 18 * q^41 - 14 * q^43 + 8 * q^47 + 12 * q^49 - 16 * q^53 - 6 * q^59 - 12 * q^61 - 2 * q^65 + 2 * q^67 - 2 * q^77 - 22 * q^83 - 16 * 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

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
$5$	1.86603	+	0.500000i	0.834512	+	0.223607i	0.650681	−	0.759351i	$-0.274483\pi$
$5$	1.86603	+	0.500000i	0.834512	+	0.223607i	0.183831	+	0.982958i	$0.441150\pi$
$6$		0			0
$7$	−3.86603	−	2.23205i	−1.46122	−	0.843636i	−0.462152	−	0.886801i	$-0.652923\pi$
$7$	−3.86603	−	2.23205i	−1.46122	−	0.843636i	−0.999068	+	0.0431647i	$0.986256\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.500000	−	1.86603i	−0.150756	−	0.562628i	−0.999432	−	0.0337145i	$-0.989266\pi$
$11$	−0.500000	−	1.86603i	−0.150756	−	0.562628i	0.848676	−	0.528913i	$-0.177400\pi$
$12$		0			0
$13$	−0.598076	+	2.23205i	−0.165876	+	0.619060i	0.832050	+	0.554700i	$0.187167\pi$
$13$	−0.598076	+	2.23205i	−0.165876	+	0.619060i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$		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	0.961844	−	0.273597i	$-0.0882135\pi$
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	−0.273597	+	0.961844i	$0.588214\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.59808	+	3.23205i	−1.16728	+	0.673929i	−0.953038	−	0.302851i	$-0.902061\pi$
$23$	−5.59808	+	3.23205i	−1.16728	+	0.673929i	−0.214242	+	0.976781i	$0.568728\pi$
$24$		0			0
$25$	−1.09808	−	0.633975i	−0.219615	−	0.126795i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.866025	−	0.232051i	0.160817	−	0.0430908i	−0.177512	−	0.984119i	$-0.556805\pi$
$29$	0.866025	−	0.232051i	0.160817	−	0.0430908i	0.338329	+	0.941028i	$0.390138\pi$
$30$		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	−0.964764	−	0.263117i	$-0.915249\pi$
$37$	−4.26795	+	4.26795i	−0.701647	+	0.701647i	0.263117	+	0.964764i	$0.415249\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.696152	+	0.401924i	−0.108721	+	0.0627700i	−0.553374	−	0.832933i	$-0.686660\pi$
$41$	−0.696152	+	0.401924i	−0.108721	+	0.0627700i	0.444654	+	0.895703i	$0.353327\pi$
$42$		0			0
$43$	1.69615	+	6.33013i	0.258661	+	0.965335i	0.966017	+	0.258478i	$0.0832210\pi$
$43$	1.69615	+	6.33013i	0.258661	+	0.965335i	−0.707356	+	0.706857i	$0.750112\pi$
$44$		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	−0.981060	−	0.193703i	$-0.937950\pi$
$53$	−5.73205	+	5.73205i	−0.787358	+	0.787358i	0.193703	+	0.981060i	$0.437950\pi$
$54$		0			0
$55$		−	3.73205i		−	0.503230i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.50000	−	0.401924i	−0.195283	−	0.0523260i	0.159852	−	0.987141i	$-0.448898\pi$
$59$	−1.50000	−	0.401924i	−0.195283	−	0.0523260i	−0.355135	+	0.934815i	$0.615565\pi$
$60$		0			0
$61$	−2.13397	+	0.571797i	−0.273227	+	0.0732111i	−0.392831	−	0.919611i	$-0.628504\pi$
$61$	−2.13397	+	0.571797i	−0.273227	+	0.0732111i	0.119604	+	0.992822i	$0.461838\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.23205	+	3.86603i	−0.276852	+	0.479521i
$66$		0			0
$67$	2.23205	−	8.33013i	0.272688	−	1.01769i	−0.684686	−	0.728838i	$-0.740061\pi$
$67$	2.23205	−	8.33013i	0.272688	−	1.01769i	0.957375	−	0.288849i	$-0.0932726\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	2.92820i		−	0.347514i	−0.984789	−	0.173757i	$-0.944409\pi$
$71$		−	2.92820i		−	0.347514i	0.984789	−	0.173757i	$-0.0555907\pi$
$72$		0			0
$73$			7.46410i			0.873607i	0.899557	+	0.436804i	$0.143889\pi$
$73$			7.46410i			0.873607i	−0.899557	+	0.436804i	$0.856111\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.23205	+	8.33013i	−0.254366	+	0.949306i
$78$		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
$83$	−14.1603	+	3.79423i	−1.55429	+	0.416471i	−0.930850	−	0.365401i	$-0.880932\pi$
$83$	−14.1603	+	3.79423i	−1.55429	+	0.416471i	−0.623440	+	0.781872i	$0.714265\pi$
$84$		0			0
$85$	−7.46410	−	2.00000i	−0.809595	−	0.216930i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	15.8564i		−	1.68078i	−0.541985	−	0.840388i	$-0.682327\pi$
$89$		−	15.8564i		−	1.68078i	0.541985	−	0.840388i	$-0.317673\pi$
$90$		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
$101$	0.133975	+	0.500000i	0.0133310	+	0.0497519i	0.972271	−	0.233857i	$-0.0751348\pi$
$101$	0.133975	+	0.500000i	0.0133310	+	0.0497519i	−0.958940	+	0.283609i	$0.908468\pi$
$102$		0			0
$103$	−13.7942	+	7.96410i	−1.35919	+	0.784726i	−0.989514	−	0.144436i	$-0.953863\pi$
$103$	−13.7942	+	7.96410i	−1.35919	+	0.784726i	−0.369672	+	0.929162i	$0.620530\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.39230	−	9.39230i	0.907988	−	0.907988i	−0.0881214	−	0.996110i	$-0.528086\pi$
$107$	9.39230	−	9.39230i	0.907988	−	0.907988i	0.996110	+	0.0881214i	$0.0280863\pi$
$108$		0			0
$109$	−1.73205	−	1.73205i	−0.165900	−	0.165900i	0.619274	−	0.785175i	$-0.287427\pi$
$109$	−1.73205	−	1.73205i	−0.165900	−	0.165900i	−0.785175	+	0.619274i	$0.787427\pi$
$110$		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
$115$	−12.0622	+	3.23205i	−1.12480	+	0.301390i
$116$		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
$131$	1.30385	−	4.86603i	0.113918	−	0.425147i	−0.885286	−	0.465047i	$-0.846037\pi$
$131$	1.30385	−	4.86603i	0.113918	−	0.425147i	0.999204	+	0.0399004i	$0.0127041\pi$
$132$		0			0
$133$	−4.90192	−	18.2942i	−0.425051	−	1.58631i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.571797	+	0.330127i	0.0488519	+	0.0282047i	0.524227	−	0.851579i	$-0.324354\pi$
$137$	0.571797	+	0.330127i	0.0488519	+	0.0282047i	−0.475375	+	0.879783i	$0.657688\pi$
$138$		0			0
$139$	−16.1603	−	4.33013i	−1.37069	−	0.367277i	−0.502962	−	0.864308i	$-0.667757\pi$
$139$	−16.1603	−	4.33013i	−1.37069	−	0.367277i	−0.867732	+	0.497032i	$0.834423\pi$
$140$		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
$149$	−16.0622	−	4.30385i	−1.31586	−	0.352585i	−0.468438	−	0.883497i	$-0.655183\pi$
$149$	−16.0622	−	4.30385i	−1.31586	−	0.352585i	−0.847427	+	0.530912i	$0.821850\pi$
$150$		0			0
$151$	6.06218	+	3.50000i	0.493333	+	0.284826i	0.725956	−	0.687741i	$-0.241398\pi$
$151$	6.06218	+	3.50000i	0.493333	+	0.284826i	−0.232623	+	0.972567i	$0.574731\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.59808	+	17.1603i	0.369326	+	1.37834i
$156$		0			0
$157$	−0.866025	+	3.23205i	−0.0691164	+	0.257946i	−0.991835	−	0.127529i	$-0.959296\pi$
$157$	−0.866025	+	3.23205i	−0.0691164	+	0.257946i	0.922719	+	0.385474i	$0.125962\pi$
$158$		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	0.778577	−	0.627549i	$-0.215942\pi$
$163$	1.92820	+	1.92820i	0.151029	+	0.151029i	−0.627549	+	0.778577i	$0.715942\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.2583	+	8.23205i	−1.10334	+	0.637015i	−0.937097	−	0.349069i	$-0.886498\pi$
$167$	−14.2583	+	8.23205i	−1.10334	+	0.637015i	−0.166246	+	0.986084i	$0.553165\pi$
$168$		0			0
$169$	6.63397	+	3.83013i	0.510306	+	0.294625i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.59808	+	2.03590i	−0.577671	+	0.154786i	−0.535812	−	0.844337i	$-0.679995\pi$
$173$	−7.59808	+	2.03590i	−0.577671	+	0.154786i	−0.0418586	+	0.999124i	$0.513328\pi$
$174$		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	0.449956	−	0.893051i	$-0.351440\pi$
$179$	−5.92820	−	5.92820i	−0.443095	−	0.443095i	−0.893051	+	0.449956i	$0.851440\pi$
$180$		0			0
$181$	−7.73205	+	7.73205i	−0.574719	+	0.574719i	−0.933443	−	0.358725i	$-0.883212\pi$
$181$	−7.73205	+	7.73205i	−0.574719	+	0.574719i	0.358725	+	0.933443i	$0.383212\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.0981	+	5.83013i	−0.742425	+	0.428639i
$186$		0			0
$187$	2.00000	+	7.46410i	0.146254	+	0.545829i
$188$		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	−0.821758	−	0.569836i	$-0.807007\pi$
$197$	−3.53590	+	3.53590i	−0.251922	+	0.251922i	0.569836	+	0.821758i	$0.307007\pi$
$198$		0			0
$199$			21.8564i			1.54936i	0.632354	+	0.774680i	$0.282089\pi$
$199$			21.8564i			1.54936i	−0.632354	+	0.774680i	$0.717911\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.86603	−	1.03590i	−0.271342	−	0.0727058i
$204$		0			0
$205$	−1.50000	+	0.401924i	−0.104765	+	0.0280716i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.09808	−	7.09808i	0.283470	−	0.490984i
$210$		0			0
$211$	4.96410	−	18.5263i	0.341743	−	1.27540i	−0.554629	−	0.832098i	$-0.687140\pi$
$211$	4.96410	−	18.5263i	0.341743	−	1.27540i	0.896371	−	0.443304i	$-0.146194\pi$
$212$		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
$221$	2.39230	−	8.92820i	0.160924	−	0.600576i
$222$		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
$227$	19.6244	−	5.25833i	1.30251	−	0.349008i	0.460114	−	0.887860i	$-0.347809\pi$
$227$	19.6244	−	5.25833i	1.30251	−	0.349008i	0.842400	+	0.538852i	$0.181142\pi$
$228$		0			0
$229$	16.5263	+	4.42820i	1.09209	+	0.292624i	0.759539	−	0.650462i	$-0.225425\pi$
$229$	16.5263	+	4.42820i	1.09209	+	0.292624i	0.332549	+	0.943086i	$0.392091\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	9.07180i		−	0.594313i	−0.954829	−	0.297157i	$-0.903962\pi$
$233$		−	9.07180i		−	0.594313i	0.954829	−	0.297157i	$-0.0960383\pi$
$234$		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
$245$	6.46410	+	24.1244i	0.412976	+	1.54125i
$246$		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	−0.989544	−	0.144229i	$-0.953930\pi$
$251$	−13.3923	+	13.3923i	−0.845315	+	0.845315i	0.144229	+	0.989544i	$0.453930\pi$
$252$		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
$259$	26.0263	−	6.97372i	1.61719	−	0.433326i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.59808	−	4.96410i	−0.530180	−	0.306100i	0.210910	−	0.977506i	$-0.432357\pi$
$263$	−8.59808	−	4.96410i	−0.530180	−	0.306100i	−0.741090	+	0.671406i	$0.765691\pi$
$264$		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	0.564923	−	0.825144i	$-0.308906\pi$
$269$	−4.26795	−	4.26795i	−0.260221	−	0.260221i	−0.825144	+	0.564923i	$0.808906\pi$
$270$		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
$275$	−0.633975	+	2.36603i	−0.0382301	+	0.142677i
$276$		0			0
$277$	−1.79423	−	6.69615i	−0.107805	−	0.402333i	0.890844	−	0.454310i	$-0.150114\pi$
$277$	−1.79423	−	6.69615i	−0.107805	−	0.402333i	−0.998648	+	0.0519775i	$0.983448\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.0359	+	5.79423i	0.598692	+	0.345655i	0.768527	−	0.639818i	$-0.220990\pi$
$281$	10.0359	+	5.79423i	0.598692	+	0.345655i	−0.169835	+	0.985472i	$0.554324\pi$
$282$		0			0
$283$	13.1603	+	3.52628i	0.782296	+	0.209616i	0.627797	−	0.778377i	$-0.283957\pi$
$283$	13.1603	+	3.52628i	0.782296	+	0.209616i	0.154499	+	0.987993i	$0.450624\pi$
$284$		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
$293$	−2.13397	−	0.571797i	−0.124668	−	0.0334047i	0.195945	−	0.980615i	$-0.437222\pi$
$293$	−2.13397	−	0.571797i	−0.124668	−	0.0334047i	−0.320614	+	0.947210i	$0.603889\pi$
$294$		0			0
$295$	−2.59808	−	1.50000i	−0.151266	−	0.0873334i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.86603	−	14.4282i	−0.223578	−	0.834405i
$300$		0			0
$301$	7.57180	−	28.2583i	0.436431	−	1.62878i
$302$		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	0.443693	−	0.896179i	$-0.353668\pi$
$307$	−7.92820	−	7.92820i	−0.452486	−	0.452486i	−0.896179	+	0.443693i	$0.853668\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.18653	−	5.30385i	0.520921	−	0.300754i	−0.216391	−	0.976307i	$-0.569428\pi$
$311$	9.18653	−	5.30385i	0.520921	−	0.300754i	0.737311	+	0.675553i	$0.236095\pi$
$312$		0			0
$313$	25.1603	+	14.5263i	1.42214	+	0.821074i	0.996482	−	0.0838094i	$-0.0267087\pi$
$313$	25.1603	+	14.5263i	1.42214	+	0.821074i	0.425660	+	0.904883i	$0.360042\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	33.4545	−	8.96410i	1.87899	−	0.503474i	0.879364	−	0.476150i	$-0.157968\pi$
$317$	33.4545	−	8.96410i	1.87899	−	0.503474i	0.999627	−	0.0273246i	$-0.00869877\pi$
$318$		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
$331$	−1.35641	−	5.06218i	−0.0745548	−	0.278242i	0.918577	−	0.395242i	$-0.129339\pi$
$331$	−1.35641	−	5.06218i	−0.0745548	−	0.278242i	−0.993132	+	0.116999i	$0.962672\pi$
$332$		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
$347$	−1.76795	−	0.473721i	−0.0949085	−	0.0254307i	0.211052	−	0.977475i	$-0.432311\pi$
$347$	−1.76795	−	0.473721i	−0.0949085	−	0.0254307i	−0.305961	+	0.952044i	$0.598978\pi$
$348$		0			0
$349$	−3.86603	+	1.03590i	−0.206944	+	0.0554504i	−0.360802	−	0.932643i	$-0.617497\pi$
$349$	−3.86603	+	1.03590i	−0.206944	+	0.0554504i	0.153858	+	0.988093i	$0.450830\pi$
$350$		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
$355$	1.46410	−	5.46410i	0.0777064	−	0.290004i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	28.9282i		−	1.52677i	−0.645942	−	0.763386i	$-0.723535\pi$
$359$		−	28.9282i		−	1.52677i	0.645942	−	0.763386i	$-0.276465\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.73205	+	13.9282i	−0.195344	+	0.729035i
$366$		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
$371$	34.9545	−	9.36603i	1.81475	−	0.486260i
$372$		0			0
$373$	−1.59808	−	0.428203i	−0.0827452	−	0.0221715i	0.217209	−	0.976125i	$-0.430305\pi$
$373$	−1.59808	−	0.428203i	−0.0827452	−	0.0221715i	−0.299954	+	0.953954i	$0.596971\pi$
$374$		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	−0.182484	−	0.983209i	$-0.558414\pi$
$379$	15.5885	−	15.5885i	0.800725	−	0.800725i	0.983209	+	0.182484i	$0.0584137\pi$
$380$		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
$389$	−2.40192	−	8.96410i	−0.121782	−	0.454498i	0.877922	−	0.478803i	$-0.158929\pi$
$389$	−2.40192	−	8.96410i	−0.121782	−	0.454498i	−0.999705	+	0.0243053i	$0.992263\pi$
$390$		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	0.990845	−	0.135002i	$-0.0431041\pi$
$397$	17.0526	+	17.0526i	0.855843	+	0.855843i	−0.135002	+	0.990845i	$0.543104\pi$
$398$		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
$403$	−20.5263	+	5.50000i	−1.02249	+	0.273975i
$404$		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	−0.899347	−	0.437236i	$-0.855957\pi$
$409$	−19.6244	+	11.3301i	−0.970362	+	0.560239i	−0.0710154	+	0.997475i	$0.522624\pi$
$410$		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
$419$	−4.96410	+	18.5263i	−0.242512	+	0.905068i	0.732105	+	0.681191i	$0.238538\pi$
$419$	−4.96410	+	18.5263i	−0.242512	+	0.905068i	−0.974618	+	0.223876i	$0.928129\pi$
$420$		0			0
$421$	−4.79423	−	17.8923i	−0.233656	−	0.872018i	−0.978750	−	0.205058i	$-0.934262\pi$
$421$	−4.79423	−	17.8923i	−0.233656	−	0.872018i	0.745094	−	0.666960i	$-0.232405\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.39230	+	2.53590i	0.213058	+	0.123009i
$426$		0			0
$427$	9.52628	+	2.55256i	0.461009	+	0.123527i
$428$		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
$437$	−26.4904	−	7.09808i	−1.26721	−	0.339547i
$438$		0			0
$439$	−5.93782	−	3.42820i	−0.283397	−	0.163619i	0.351563	−	0.936164i	$-0.385650\pi$
$439$	−5.93782	−	3.42820i	−0.283397	−	0.163619i	−0.634960	+	0.772545i	$0.718984\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.16025	−	4.33013i	−0.0551253	−	0.205731i	0.932870	−	0.360213i	$-0.117296\pi$
$443$	−1.16025	−	4.33013i	−0.0551253	−	0.205731i	−0.987996	+	0.154482i	$0.950629\pi$
$444$		0			0
$445$	7.92820	−	29.5885i	0.375833	−	1.40263i
$446$		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	0.963747	−	0.266818i	$-0.0859722\pi$
$457$	25.9641	+	14.9904i	1.21455	+	0.701220i	0.250802	+	0.968038i	$0.419306\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.59808	+	1.23205i	−0.214154	+	0.0573823i	−0.364301	−	0.931281i	$-0.618692\pi$
$461$	−4.59808	+	1.23205i	−0.214154	+	0.0573823i	0.150147	+	0.988664i	$0.452025\pi$
$462$		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	0.999967	+	0.00810436i	$0.00257972\pi$
$467$	21.7846	+	21.7846i	1.00807	+	1.00807i	0.00810436	+	0.999967i	$0.497420\pi$
$468$		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
$475$	−1.39230	−	5.19615i	−0.0638833	−	0.238416i
$476$		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	$0.0491254\pi$
$487$			6.78461i			0.307440i	−0.988114	+	0.153720i	$0.950875\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.500000	+	0.133975i	0.0225647	+	0.00604619i	0.270084	−	0.962837i	$-0.412949\pi$
$491$	0.500000	+	0.133975i	0.0225647	+	0.00604619i	−0.247519	+	0.968883i	$0.579615\pi$
$492$		0			0
$493$	−3.46410	+	0.928203i	−0.156015	+	0.0418042i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.53590	+	11.3205i	−0.293175	+	0.507794i
$498$		0			0
$499$	2.50000	−	9.33013i	0.111915	−	0.417674i	−0.887122	−	0.461534i	$-0.847299\pi$
$499$	2.50000	−	9.33013i	0.111915	−	0.417674i	0.999038	+	0.0438606i	$0.0139657\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			13.8564i			0.617827i	0.951090	+	0.308913i	$0.0999653\pi$
$503$			13.8564i			0.617827i	−0.951090	+	0.308913i	$0.900035\pi$
$504$		0			0
$505$			1.00000i			0.0444994i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.25833	+	4.69615i	−0.0557745	+	0.208153i	−0.988190	−	0.153236i	$-0.951031\pi$
$509$	−1.25833	+	4.69615i	−0.0557745	+	0.208153i	0.932415	+	0.361389i	$0.117697\pi$
$510$		0			0
$511$	16.6603	−	28.8564i	0.737006	−	1.27653i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−29.7224	+	7.96410i	−1.30973	+	0.350940i
$516$		0			0
$517$	2.23205	+	0.598076i	0.0981655	+	0.0263034i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			41.8564i			1.83376i	0.399160	+	0.916881i	$0.369302\pi$
$521$			41.8564i			1.83376i	−0.399160	+	0.916881i	$0.630698\pi$
$522$		0			0
$523$	−22.1244	+	22.1244i	−0.967431	+	0.967431i	−0.999486	−	0.0320556i	$-0.989795\pi$
$523$	−22.1244	+	22.1244i	−0.967431	+	0.967431i	0.0320556	+	0.999486i	$0.489795\pi$
$524$		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
$533$	−0.480762	−	1.79423i	−0.0208241	−	0.0777167i
$534$		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	0.306856	−	0.951756i	$-0.400723\pi$
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	−0.951756	+	0.306856i	$0.900723\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.36603	−	4.09808i	−0.101349	−	0.175542i
$546$		0			0
$547$	−21.4282	+	5.74167i	−0.916204	+	0.245496i	−0.685962	−	0.727637i	$-0.740618\pi$
$547$	−21.4282	+	5.74167i	−0.916204	+	0.245496i	−0.230242	+	0.973133i	$0.573952\pi$
$548$		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	0.999868	+	0.0162292i	$0.00516614\pi$
$557$	23.9808	+	23.9808i	1.01610	+	1.01610i	0.0162292	+	0.999868i	$0.494834\pi$
$558$		0			0
$559$	−15.1436			−0.640506
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.64359	+	6.13397i	−0.0692692	+	0.258516i	−0.991873	−	0.127233i	$-0.959390\pi$
$563$	−1.64359	+	6.13397i	−0.0692692	+	0.258516i	0.922604	+	0.385749i	$0.126057\pi$
$564$		0			0
$565$	6.23205	+	23.2583i	0.262184	+	0.978485i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	27.4808	+	15.8660i	1.15205	+	0.665138i	0.949387	−	0.314109i	$-0.101706\pi$
$569$	27.4808	+	15.8660i	1.15205	+	0.665138i	0.202667	+	0.979248i	$0.435039\pi$
$570$		0			0
$571$	−39.5526	−	10.5981i	−1.65522	−	0.443516i	−0.694155	−	0.719826i	$-0.744222\pi$
$571$	−39.5526	−	10.5981i	−1.65522	−	0.443516i	−0.961068	+	0.276310i	$0.910888\pi$
$572$		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
$581$	63.2128	+	16.9378i	2.62251	+	0.702699i
$582$		0			0
$583$	13.5622	+	7.83013i	0.561688	+	0.324291i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.96410	+	14.7942i	0.163616	+	0.610623i	0.998213	+	0.0597617i	$0.0190341\pi$
$587$	3.96410	+	14.7942i	0.163616	+	0.610623i	−0.834597	+	0.550861i	$0.814299\pi$
$588$		0			0
$589$	−10.0981	+	37.6865i	−0.416084	+	1.55285i
$590$		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	−0.968781	−	0.247917i	$-0.920254\pi$
$599$	−30.3109	+	17.5000i	−1.23847	+	0.715031i	−0.269688	+	0.962948i	$0.586921\pi$
$600$		0			0
$601$	−26.7679	−	15.4545i	−1.09189	−	0.630401i	−0.157809	−	0.987470i	$-0.550443\pi$
$601$	−26.7679	−	15.4545i	−1.09189	−	0.630401i	−0.934078	+	0.357068i	$0.883776\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	13.5622	−	3.63397i	0.551381	−	0.147742i
$606$		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	−0.0462032	−	0.998932i	$-0.514712\pi$
$613$	23.5885	−	23.5885i	0.952729	−	0.952729i	0.998932	+	0.0462032i	$0.0147122\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.0885	+	13.3301i	−0.929506	+	0.536651i	−0.886655	−	0.462431i	$-0.846977\pi$
$617$	−23.0885	+	13.3301i	−0.929506	+	0.536651i	−0.0428509	+	0.999081i	$0.513644\pi$
$618$		0			0
$619$	1.91154	+	7.13397i	0.0768314	+	0.286739i	0.993642	−	0.112583i	$-0.0359124\pi$
$619$	1.91154	+	7.13397i	0.0768314	+	0.286739i	−0.916811	+	0.399322i	$0.869246\pi$
$620$		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	$-0.895165\pi$
$631$		−	16.2487i		−	0.646851i	0.946254	−	0.323425i	$-0.104835\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.732051	−	0.196152i	−0.0290506	−	0.00778407i
$636$		0			0
$637$	−28.8564	+	7.73205i	−1.14333	+	0.306355i
$638$		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
$643$	−7.96410	+	29.7224i	−0.314074	+	1.17214i	0.610776	+	0.791804i	$0.290858\pi$
$643$	−7.96410	+	29.7224i	−0.314074	+	1.17214i	−0.924849	+	0.380334i	$0.875809\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			25.6077i			1.00674i	0.864070	+	0.503371i	$0.167907\pi$
$647$			25.6077i			1.00674i	−0.864070	+	0.503371i	$0.832093\pi$
$648$		0			0
$649$			3.00000i			0.117760i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12.6699	−	47.2846i	0.495810	−	1.85039i	−0.0296324	−	0.999561i	$-0.509434\pi$
$653$	12.6699	−	47.2846i	0.495810	−	1.85039i	0.525443	−	0.850829i	$-0.323900\pi$
$654$		0			0
$655$	4.86603	−	8.42820i	0.190131	−	0.329317i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.23205	−	0.330127i	0.0479939	−	0.0128599i	−0.234742	−	0.972058i	$-0.575425\pi$
$659$	1.23205	−	0.330127i	0.0479939	−	0.0128599i	0.282736	+	0.959198i	$0.408758\pi$
$660$		0			0
$661$	19.7942	+	5.30385i	0.769906	+	0.206296i	0.622330	−	0.782755i	$-0.286186\pi$
$661$	19.7942	+	5.30385i	0.769906	+	0.206296i	0.147576	+	0.989051i	$0.452853\pi$
$662$		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
$677$	−2.34936	−	8.76795i	−0.0902934	−	0.336980i	0.905970	−	0.423341i	$-0.139143\pi$
$677$	−2.34936	−	8.76795i	−0.0902934	−	0.336980i	−0.996264	+	0.0863612i	$0.972476\pi$
$678$		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	−0.348382	−	0.937353i	$-0.613269\pi$
$683$	15.3923	−	15.3923i	0.588970	−	0.588970i	0.937353	+	0.348382i	$0.113269\pi$
$684$		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
$691$	1.96410	−	0.526279i	0.0747179	−	0.0200206i	−0.221266	−	0.975213i	$-0.571019\pi$
$691$	1.96410	−	0.526279i	0.0747179	−	0.0200206i	0.295984	+	0.955193i	$0.404352\pi$
$692$		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	0.307486	−	0.951553i	$-0.400512\pi$
$701$	−17.0526	−	17.0526i	−0.644066	−	0.644066i	−0.951553	+	0.307486i	$0.900512\pi$
$702$		0			0
$703$	−25.6077			−0.965813
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.598076	−	2.23205i	0.0224930	−	0.0839449i
$708$		0			0
$709$	10.1147	+	37.7487i	0.379867	+	1.41768i	0.846102	+	0.533022i	$0.178944\pi$
$709$	10.1147	+	37.7487i	0.379867	+	1.41768i	−0.466235	+	0.884661i	$0.654390\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−51.4808	−	29.7224i	−1.92797	−	1.11311i
$714$		0			0
$715$	8.33013	+	2.23205i	0.311529	+	0.0834740i
$716$		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
$725$	−1.09808	−	0.294229i	−0.0407815	−	0.0109274i
$726$		0			0
$727$	−3.06218	−	1.76795i	−0.113570	−	0.0655696i	0.442139	−	0.896947i	$-0.354220\pi$
$727$	−3.06218	−	1.76795i	−0.113570	−	0.0655696i	−0.555709	+	0.831377i	$0.687553\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.78461	−	25.3205i	−0.250938	−	0.936513i
$732$		0			0
$733$	8.47372	−	31.6244i	0.312984	−	1.16807i	−0.612868	−	0.790185i	$-0.709984\pi$
$733$	8.47372	−	31.6244i	0.312984	−	1.16807i	0.925852	−	0.377887i	$-0.123349\pi$
$734$		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	0.999450	−	0.0331677i	$-0.0105595\pi$
$739$	26.2679	+	26.2679i	0.966282	+	0.966282i	−0.0331677	+	0.999450i	$0.510560\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.0372984	−	0.999304i	$-0.488125\pi$
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.884072	+	0.467351i	$0.154791\pi$
$744$		0			0
$745$	−27.8205	−	16.0622i	−1.01926	−	0.588473i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−57.2750	+	15.3468i	−2.09278	+	0.560759i
$750$		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	−0.678644	−	0.734467i	$-0.737432\pi$
$757$	1.53590	−	1.53590i	0.0558232	−	0.0558232i	0.734467	+	0.678644i	$0.237432\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.2846	−	9.40192i	0.590317	−	0.340819i	−0.174906	−	0.984585i	$-0.555962\pi$
$761$	16.2846	−	9.40192i	0.590317	−	0.340819i	0.765223	+	0.643766i	$0.222629\pi$
$762$		0			0
$763$	2.83013	+	10.5622i	0.102457	+	0.382377i
$764$		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	−0.141518	−	0.989936i	$-0.545198\pi$
$773$	23.5885	−	23.5885i	0.848418	−	0.848418i	0.989936	+	0.141518i	$0.0451983\pi$
$774$		0			0
$775$		−	11.6603i		−	0.418849i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.29423	−	0.882686i	−0.118028	−	0.0316255i
$780$		0			0
$781$	−5.46410	+	1.46410i	−0.195521	+	0.0523897i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.23205	+	5.59808i	−0.115357	+	0.199804i
$786$		0			0
$787$	−0.820508	+	3.06218i	−0.0292480	+	0.109155i	−0.979007	−	0.203828i	$-0.934662\pi$
$787$	−0.820508	+	3.06218i	−0.0292480	+	0.109155i	0.949759	+	0.312983i	$0.101328\pi$
$788$		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
$797$	−11.0622	+	41.2846i	−0.391842	+	1.46238i	0.435250	+	0.900310i	$0.356660\pi$
$797$	−11.0622	+	41.2846i	−0.391842	+	1.46238i	−0.827092	+	0.562066i	$0.810007\pi$
$798$		0			0
$799$	2.39230	−	4.14359i	0.0846337	−	0.146590i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	13.9282	−	3.73205i	0.491516	−	0.131701i
$804$		0			0
$805$	53.8468	+	14.4282i	1.89785	+	0.508527i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			36.6410i			1.28823i	0.764929	+	0.644115i	$0.222774\pi$
$809$			36.6410i			1.28823i	−0.764929	+	0.644115i	$0.777226\pi$
$810$		0			0
$811$	18.4641	−	18.4641i	0.648362	−	0.648362i	−0.304235	−	0.952597i	$-0.598401\pi$
$811$	18.4641	−	18.4641i	0.648362	−	0.648362i	0.952597	+	0.304235i	$0.0984007\pi$
$812$		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
$821$	−10.7224	−	40.0167i	−0.374215	−	1.39659i	−0.854488	−	0.519472i	$-0.826129\pi$
$821$	−10.7224	−	40.0167i	−0.374215	−	1.39659i	0.480272	−	0.877119i	$-0.340538\pi$
$822$		0			0
$823$	−36.6506	+	21.1603i	−1.27756	+	0.737600i	−0.976399	−	0.215973i	$-0.930708\pi$
$823$	−36.6506	+	21.1603i	−1.27756	+	0.737600i	−0.301162	+	0.953573i	$0.597374\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−31.3923	+	31.3923i	−1.09162	+	1.09162i	−0.0962613	+	0.995356i	$0.530688\pi$
$827$	−31.3923	+	31.3923i	−1.09162	+	1.09162i	−0.995356	+	0.0962613i	$0.969312\pi$
$828$		0			0
$829$	−14.2679	−	14.2679i	−0.495546	−	0.495546i	0.414502	−	0.910048i	$-0.363956\pi$
$829$	−14.2679	−	14.2679i	−0.495546	−	0.495546i	−0.910048	+	0.414502i	$0.863956\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−25.8564	−	44.7846i	−0.895871	−	1.55169i
$834$		0			0
$835$	−30.7224	+	8.23205i	−1.06319	+	0.284882i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	6.74167	+	3.89230i	0.232748	+	0.134377i	0.611839	−	0.790982i	$-0.290430\pi$
$839$	6.74167	+	3.89230i	0.232748	+	0.134377i	−0.379091	+	0.925359i	$0.623763\pi$
$840$		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
$851$	10.0981	−	37.6865i	0.346158	−	1.29188i
$852$		0			0
$853$	−2.06218	−	7.69615i	−0.0706076	−	0.263511i	0.921594	−	0.388156i	$-0.126888\pi$
$853$	−2.06218	−	7.69615i	−0.0706076	−	0.263511i	−0.992201	+	0.124644i	$0.960221\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.6436	−	8.45448i	−0.500216	−	0.288800i	0.228587	−	0.973523i	$-0.426589\pi$
$857$	−14.6436	−	8.45448i	−0.500216	−	0.288800i	−0.728803	+	0.684724i	$0.759923\pi$
$858$		0			0
$859$	4.50000	+	1.20577i	0.153538	+	0.0411404i	0.334769	−	0.942300i	$-0.391342\pi$
$859$	4.50000	+	1.20577i	0.153538	+	0.0411404i	−0.181231	+	0.983440i	$0.558008\pi$
$860$		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
$869$	−3.23205	−	0.866025i	−0.109640	−	0.0293779i
$870$		0			0
$871$	17.2583	+	9.96410i	0.584776	+	0.337621i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.9904	+	52.2128i	0.472961	+	1.76512i
$876$		0			0
$877$	−13.3827	+	49.9449i	−0.451901	+	1.68652i	0.245140	+	0.969488i	$0.421166\pi$
$877$	−13.3827	+	49.9449i	−0.451901	+	1.68652i	−0.697042	+	0.717031i	$0.745501\pi$
$878$		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	0.755782	−	0.654824i	$-0.227257\pi$
$883$	3.00000	+	3.00000i	0.100958	+	0.100958i	−0.654824	+	0.755782i	$0.727257\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.93782	−	5.16025i	0.300103	−	0.173264i	−0.342386	−	0.939559i	$-0.611235\pi$
$887$	8.93782	−	5.16025i	0.300103	−	0.173264i	0.642489	+	0.766295i	$0.277902\pi$
$888$		0			0
$889$	1.51666	+	0.875644i	0.0508672	+	0.0293682i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.90192	+	1.31347i	−0.164037	+	0.0439535i
$894$		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
$907$	2.42820	+	9.06218i	0.0806272	+	0.300905i	0.994450	−	0.105208i	$-0.0335508\pi$
$907$	2.42820	+	9.06218i	0.0806272	+	0.300905i	−0.913823	+	0.406112i	$0.866884\pi$
$908$		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	$0.205870\pi$
$919$			36.5359i			1.20521i	−0.798040	+	0.602604i	$0.794130\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.53590	+	1.75129i	0.215132	+	0.0576444i
$924$		0			0
$925$	7.39230	−	1.98076i	0.243057	−	0.0651271i
$926$		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
$931$	−14.1962	+	52.9808i	−0.465260	+	1.73637i
$932$		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	$0.100840\pi$
$937$			19.0718i			0.623048i	−0.950238	+	0.311524i	$0.899160\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−9.13397	+	34.0885i	−0.297759	+	1.11125i	0.641242	+	0.767338i	$0.278419\pi$
$941$	−9.13397	+	34.0885i	−0.297759	+	1.11125i	−0.939001	+	0.343913i	$0.888247\pi$
$942$		0			0
$943$	2.59808	−	4.50000i	0.0846050	−	0.146540i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−41.0167	+	10.9904i	−1.33286	+	0.357139i	−0.853782	−	0.520631i	$-0.825697\pi$
$947$	−41.0167	+	10.9904i	−1.33286	+	0.357139i	−0.479081	+	0.877771i	$0.659030\pi$
$948$		0			0
$949$	−16.6603	−	4.46410i	−0.540815	−	0.144911i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			32.5359i			1.05394i	0.849884	+	0.526971i	$0.176672\pi$
$953$			32.5359i			1.05394i	−0.849884	+	0.526971i	$0.823328\pi$
$954$		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
$965$	2.23205	+	8.33013i	0.0718523	+	0.268156i
$966$		0			0
$967$	27.0622	−	15.6244i	0.870261	−	0.502445i	0.00282602	−	0.999996i	$-0.499100\pi$
$967$	27.0622	−	15.6244i	0.870261	−	0.502445i	0.867435	+	0.497551i	$0.165767\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.9808	+	23.9808i	−0.769579	+	0.769579i	−0.978032	−	0.208453i	$-0.933157\pi$
$971$	−23.9808	+	23.9808i	−0.769579	+	0.769579i	0.208453	+	0.978032i	$0.433157\pi$
$972$		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
$979$	−29.5885	+	7.92820i	−0.945651	+	0.253386i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.08142	−	0.624356i	−0.0344918	−	0.0199139i	0.482655	−	0.875811i	$-0.339673\pi$
$983$	−1.08142	−	0.624356i	−0.0344918	−	0.0199139i	−0.517147	+	0.855897i	$0.673006\pi$
$984$		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
$995$	−10.9282	+	40.7846i	−0.346447	+	1.29296i
$996$		0			0
$997$	−1.06218	−	3.96410i	−0.0336395	−	0.125544i	0.947064	−	0.321044i	$-0.104034\pi$
$997$	−1.06218	−	3.96410i	−0.0336395	−	0.125544i	−0.980704	+	0.195500i	$0.937367\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.bc.c.721.1		4
3.2	odd	2		576.2.bb.a.529.1		4
4.3	odd	2		432.2.y.d.397.1		4
9.4	even	3		1728.2.bc.b.145.1		4
9.5	odd	6		576.2.bb.b.337.1		4
12.11	even	2		144.2.x.a.61.1	✓	4
16.5	even	4		1728.2.bc.b.1585.1		4
16.11	odd	4		432.2.y.a.181.1		4
36.23	even	6		144.2.x.d.13.1	yes	4
36.31	odd	6		432.2.y.a.253.1		4
48.5	odd	4		576.2.bb.b.241.1		4
48.11	even	4		144.2.x.d.133.1	yes	4
144.5	odd	12		576.2.bb.a.49.1		4
144.59	even	12		144.2.x.a.85.1	yes	4
144.85	even	12	inner	1728.2.bc.c.1009.1		4
144.139	odd	12		432.2.y.d.37.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.61.1	✓	4	12.11	even	2
144.2.x.a.85.1	yes	4	144.59	even	12
144.2.x.d.13.1	yes	4	36.23	even	6
144.2.x.d.133.1	yes	4	48.11	even	4
432.2.y.a.181.1		4	16.11	odd	4
432.2.y.a.253.1		4	36.31	odd	6
432.2.y.d.37.1		4	144.139	odd	12
432.2.y.d.397.1		4	4.3	odd	2
576.2.bb.a.49.1		4	144.5	odd	12
576.2.bb.a.529.1		4	3.2	odd	2
576.2.bb.b.241.1		4	48.5	odd	4
576.2.bb.b.337.1		4	9.5	odd	6
1728.2.bc.b.145.1		4	9.4	even	3
1728.2.bc.b.1585.1		4	16.5	even	4
1728.2.bc.c.721.1		4	1.1	even	1	trivial
1728.2.bc.c.1009.1		4	144.85	even	12	inner

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)

\(f(q)\)	\(=\)	\(q+(1.86603 + 0.500000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +O(q^{10})\)	\(q+(1.86603 + 0.500000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +(-0.500000 - 1.86603i) q^{11} +(-0.598076 + 2.23205i) q^{13} -4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(-5.59808 + 3.23205i) q^{23} +(-1.09808 - 0.633975i) q^{25} +(0.866025 - 0.232051i) q^{29} +(4.59808 + 7.96410i) q^{31} +(-6.09808 - 6.09808i) q^{35} +(-4.26795 + 4.26795i) q^{37} +(-0.696152 + 0.401924i) q^{41} +(1.69615 + 6.33013i) q^{43} +(-0.598076 + 1.03590i) q^{47} +(6.46410 + 11.1962i) q^{49} +(-5.73205 + 5.73205i) q^{53} -3.73205i q^{55} +(-1.50000 - 0.401924i) q^{59} +(-2.13397 + 0.571797i) q^{61} +(-2.23205 + 3.86603i) q^{65} +(2.23205 - 8.33013i) q^{67} -2.92820i q^{71} +7.46410i q^{73} +(-2.23205 + 8.33013i) q^{77} +(0.866025 - 1.50000i) q^{79} +(-14.1603 + 3.79423i) q^{83} +(-7.46410 - 2.00000i) q^{85} -15.8564i q^{89} +(7.29423 - 7.29423i) q^{91} +(4.09808 + 7.09808i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} - 12 q^{7}+O(q^{10}) \) 4 * q + 4 * q^5 - 12 * q^7	\( 4 q + 4 q^{5} - 12 q^{7} - 2 q^{11} + 8 q^{13} - 16 q^{17} + 12 q^{19} - 12 q^{23} + 6 q^{25} + 8 q^{31} - 14 q^{35} - 24 q^{37} + 18 q^{41} - 14 q^{43} + 8 q^{47} + 12 q^{49} - 16 q^{53} - 6 q^{59} - 12 q^{61} - 2 q^{65} + 2 q^{67} - 2 q^{77} - 22 q^{83} - 16 q^{85} - 2 q^{91} + 6 q^{95} - 2 q^{97}+O(q^{100}) \) 4 * q + 4 * q^5 - 12 * q^7 - 2 * q^11 + 8 * q^13 - 16 * q^17 + 12 * q^19 - 12 * q^23 + 6 * q^25 + 8 * q^31 - 14 * q^35 - 24 * q^37 + 18 * q^41 - 14 * q^43 + 8 * q^47 + 12 * q^49 - 16 * q^53 - 6 * q^59 - 12 * q^61 - 2 * q^65 + 2 * q^67 - 2 * q^77 - 22 * q^83 - 16 * q^85 - 2 * q^91 + 6 * q^95 - 2 * q^97

Introduction

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