LMFDB - Embedded newform 1728.2.bc.c.145.1

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			145.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1728.145
Dual form			1728.2.bc.c.1585.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133975 + 0.500000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +O(q^{10})$	$q+(0.133975 + 0.500000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-0.500000 - 0.133975i) q^{11} +(4.59808 - 1.23205i) q^{13} -4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(-0.401924 - 0.232051i) q^{23} +(4.09808 - 2.36603i) q^{25} +(-0.866025 + 3.23205i) q^{29} +(-0.598076 + 1.03590i) q^{31} +(-0.901924 - 0.901924i) q^{35} +(-7.73205 + 7.73205i) q^{37} +(9.69615 + 5.59808i) q^{41} +(-8.69615 - 2.33013i) q^{43} +(4.59808 + 7.96410i) q^{47} +(-0.464102 + 0.803848i) q^{49} +(-2.26795 + 2.26795i) q^{53} -0.267949i q^{55} +(-1.50000 - 5.59808i) q^{59} +(-3.86603 + 14.4282i) q^{61} +(1.23205 + 2.13397i) q^{65} +(-1.23205 + 0.330127i) q^{67} +10.9282i q^{71} +0.535898i q^{73} +(1.23205 - 0.330127i) q^{77} +(-0.866025 - 1.50000i) q^{79} +(3.16025 - 11.7942i) q^{83} +(-0.535898 - 2.00000i) q^{85} +11.8564i q^{89} +(-8.29423 + 8.29423i) q^{91} +(-1.09808 + 1.90192i) q^{95} +(-0.500000 - 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

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
$5$	0.133975	+	0.500000i	0.0599153	+	0.223607i	0.989391	−	0.145276i	$-0.0464070\pi$
$5$	0.133975	+	0.500000i	0.0599153	+	0.223607i	−0.929476	+	0.368883i	$0.879740\pi$
$6$		0			0
$7$	−2.13397	+	1.23205i	−0.806567	+	0.465671i	−0.845762	−	0.533560i	$-0.820854\pi$
$7$	−2.13397	+	1.23205i	−0.806567	+	0.465671i	0.0391956	+	0.999232i	$0.487520\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.500000	−	0.133975i	−0.150756	−	0.0403949i	0.182652	−	0.983178i	$-0.441532\pi$
$11$	−0.500000	−	0.133975i	−0.150756	−	0.0403949i	−0.333408	+	0.942783i	$0.608199\pi$
$12$		0			0
$13$	4.59808	−	1.23205i	1.27528	−	0.341709i	0.443227	−	0.896410i	$-0.353834\pi$
$13$	4.59808	−	1.23205i	1.27528	−	0.341709i	0.832050	+	0.554700i	$0.187167\pi$
$14$		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
$23$	−0.401924	−	0.232051i	−0.0838069	−	0.0483859i	0.457511	−	0.889204i	$-0.348741\pi$
$23$	−0.401924	−	0.232051i	−0.0838069	−	0.0483859i	−0.541318	+	0.840818i	$0.682074\pi$
$24$		0			0
$25$	4.09808	−	2.36603i	0.819615	−	0.473205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.866025	+	3.23205i	−0.160817	+	0.600177i	0.837720	+	0.546100i	$0.183888\pi$
$29$	−0.866025	+	3.23205i	−0.160817	+	0.600177i	−0.998537	+	0.0540766i	$0.982778\pi$
$30$		0			0
$31$	−0.598076	+	1.03590i	−0.107418	+	0.186053i	−0.914723	−	0.404081i	$-0.867592\pi$
$31$	−0.598076	+	1.03590i	−0.107418	+	0.186053i	0.807306	+	0.590133i	$0.200925\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.901924	−	0.901924i	−0.152453	−	0.152453i
$36$		0			0
$37$	−7.73205	+	7.73205i	−1.27114	+	1.27114i	−0.325651	+	0.945490i	$0.605584\pi$
$37$	−7.73205	+	7.73205i	−1.27114	+	1.27114i	−0.945490	+	0.325651i	$0.894416\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	9.69615	+	5.59808i	1.51428	+	0.874273i	0.999860	+	0.0167371i	$0.00532782\pi$
$41$	9.69615	+	5.59808i	1.51428	+	0.874273i	0.514425	+	0.857536i	$0.328006\pi$
$42$		0			0
$43$	−8.69615	−	2.33013i	−1.32615	−	0.355341i	−0.474872	−	0.880055i	$-0.657506\pi$
$43$	−8.69615	−	2.33013i	−1.32615	−	0.355341i	−0.851279	+	0.524714i	$0.824172\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.59808	+	7.96410i	0.670698	+	1.16168i	0.977706	+	0.209977i	$0.0673388\pi$
$47$	4.59808	+	7.96410i	0.670698	+	1.16168i	−0.307008	+	0.951707i	$0.599328\pi$
$48$		0			0
$49$	−0.464102	+	0.803848i	−0.0663002	+	0.114835i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.26795	+	2.26795i	−0.311527	+	0.311527i	−0.845501	−	0.533974i	$-0.820698\pi$
$53$	−2.26795	+	2.26795i	−0.311527	+	0.311527i	0.533974	+	0.845501i	$0.320698\pi$
$54$		0			0
$55$		−	0.267949i		−	0.0361303i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.50000	−	5.59808i	−0.195283	−	0.728807i	−0.992193	−	0.124709i	$-0.960200\pi$
$59$	−1.50000	−	5.59808i	−0.195283	−	0.728807i	0.796910	−	0.604098i	$-0.206467\pi$
$60$		0			0
$61$	−3.86603	+	14.4282i	−0.494994	+	1.84734i	0.0350707	+	0.999385i	$0.488834\pi$
$61$	−3.86603	+	14.4282i	−0.494994	+	1.84734i	−0.530065	+	0.847957i	$0.677832\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.23205	+	2.13397i	0.152817	+	0.264687i
$66$		0			0
$67$	−1.23205	+	0.330127i	−0.150519	+	0.0403314i	−0.333292	−	0.942824i	$-0.608159\pi$
$67$	−1.23205	+	0.330127i	−0.150519	+	0.0403314i	0.182773	+	0.983155i	$0.441493\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			10.9282i			1.29694i	0.761241	+	0.648470i	$0.224591\pi$
$71$			10.9282i			1.29694i	−0.761241	+	0.648470i	$0.775409\pi$
$72$		0			0
$73$			0.535898i			0.0627222i	0.999508	+	0.0313611i	$0.00998418\pi$
$73$			0.535898i			0.0627222i	−0.999508	+	0.0313611i	$0.990016\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.23205	−	0.330127i	0.140405	−	0.0376215i
$78$		0			0
$79$	−0.866025	−	1.50000i	−0.0974355	−	0.168763i	0.813187	−	0.582003i	$-0.197731\pi$
$79$	−0.866025	−	1.50000i	−0.0974355	−	0.168763i	−0.910622	+	0.413239i	$0.864397\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.16025	−	11.7942i	0.346883	−	1.29458i	−0.543514	−	0.839400i	$-0.682907\pi$
$83$	3.16025	−	11.7942i	0.346883	−	1.29458i	0.890397	−	0.455185i	$-0.150427\pi$
$84$		0			0
$85$	−0.535898	−	2.00000i	−0.0581263	−	0.216930i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			11.8564i			1.25678i	0.777900	+	0.628388i	$0.216285\pi$
$89$			11.8564i			1.25678i	−0.777900	+	0.628388i	$0.783715\pi$
$90$		0			0
$91$	−8.29423	+	8.29423i	−0.869471	+	0.869471i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.09808	+	1.90192i	−0.112660	+	0.195133i
$96$		0			0
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	0.839525	−	0.543321i	$-0.182833\pi$
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	−0.890292	+	0.455389i	$0.849500\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.86603	+	0.500000i	0.185676	+	0.0497519i	0.350459	−	0.936578i	$-0.386026\pi$
$101$	1.86603	+	0.500000i	0.185676	+	0.0497519i	−0.164783	+	0.986330i	$0.552692\pi$
$102$		0			0
$103$	1.79423	+	1.03590i	0.176791	+	0.102070i	0.585784	−	0.810467i	$-0.300787\pi$
$103$	1.79423	+	1.03590i	0.176791	+	0.102070i	−0.408993	+	0.912537i	$0.634120\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.3923	+	11.3923i	−1.10134	+	1.10134i	−0.107086	+	0.994250i	$0.534152\pi$
$107$	−11.3923	+	11.3923i	−1.10134	+	1.10134i	−0.994250	+	0.107086i	$0.965848\pi$
$108$		0			0
$109$	1.73205	+	1.73205i	0.165900	+	0.165900i	0.785175	−	0.619274i	$-0.212573\pi$
$109$	1.73205	+	1.73205i	0.165900	+	0.165900i	−0.619274	+	0.785175i	$0.712573\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.76795	−	4.79423i	0.260387	−	0.451003i	−0.705958	−	0.708254i	$-0.749483\pi$
$113$	2.76795	−	4.79423i	0.260387	−	0.451003i	0.966345	+	0.257251i	$0.0828166\pi$
$114$		0			0
$115$	0.0621778	−	0.232051i	0.00579811	−	0.0216388i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.53590	−	4.92820i	0.782485	−	0.451768i
$120$		0			0
$121$	−9.29423	−	5.36603i	−0.844930	−	0.487820i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.56218	+	3.56218i	0.318611	+	0.318611i
$126$		0			0
$127$	20.3923			1.80952			0.904762	−	0.425917i	$-0.140048\pi$
$127$	20.3923			1.80952			0.904762	+	0.425917i	$0.140048\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	11.6962	−	3.13397i	1.02190	−	0.273817i	0.291305	−	0.956630i	$-0.405911\pi$
$131$	11.6962	−	3.13397i	1.02190	−	0.273817i	0.730593	+	0.682814i	$0.239244\pi$
$132$		0			0
$133$	−10.0981	−	2.70577i	−0.875614	−	0.234620i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.4282	−	8.33013i	1.23268	−	0.711691i	0.265096	−	0.964222i	$-0.414596\pi$
$137$	14.4282	−	8.33013i	1.23268	−	0.711691i	0.967589	+	0.252531i	$0.0812631\pi$
$138$		0			0
$139$	1.16025	+	4.33013i	0.0984115	+	0.367277i	0.997515	−	0.0704603i	$-0.0224468\pi$
$139$	1.16025	+	4.33013i	0.0984115	+	0.367277i	−0.899103	+	0.437737i	$0.855780\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.46410			−0.206059
$144$		0			0
$145$	−1.73205			−0.143839
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.93782	−	14.6962i	−0.322599	−	1.20396i	−0.916704	−	0.399568i	$-0.869160\pi$
$149$	−3.93782	−	14.6962i	−0.322599	−	1.20396i	0.594105	−	0.804388i	$-0.297507\pi$
$150$		0			0
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	−0.725956	−	0.687741i	$-0.758602\pi$
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	0.232623	+	0.972567i	$0.425269\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.598076	−	0.160254i	−0.0480386	−	0.0128719i
$156$		0			0
$157$	0.866025	−	0.232051i	0.0691164	−	0.0185197i	−0.224095	−	0.974567i	$-0.571943\pi$
$157$	0.866025	−	0.232051i	0.0691164	−	0.0185197i	0.293212	+	0.956048i	$0.405276\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.14359			0.0901278
$162$		0			0
$163$	−11.9282	−	11.9282i	−0.934289	−	0.934289i	0.0636813	−	0.997970i	$-0.479716\pi$
$163$	−11.9282	−	11.9282i	−0.934289	−	0.934289i	−0.997970	+	0.0636813i	$0.979716\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.25833	+	4.76795i	0.639049	+	0.368955i	0.784248	−	0.620447i	$-0.213049\pi$
$167$	8.25833	+	4.76795i	0.639049	+	0.368955i	−0.145199	+	0.989402i	$0.546382\pi$
$168$		0			0
$169$	8.36603	−	4.83013i	0.643540	−	0.371548i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.40192	+	8.96410i	−0.182615	+	0.681528i	0.812514	+	0.582942i	$0.198099\pi$
$173$	−2.40192	+	8.96410i	−0.182615	+	0.681528i	−0.995129	+	0.0985859i	$0.968568\pi$
$174$		0			0
$175$	−5.83013	+	10.0981i	−0.440716	+	0.763343i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.92820	+	7.92820i	0.592582	+	0.592582i	0.938328	−	0.345746i	$-0.112374\pi$
$179$	7.92820	+	7.92820i	0.592582	+	0.592582i	−0.345746	+	0.938328i	$0.612374\pi$
$180$		0			0
$181$	−4.26795	+	4.26795i	−0.317234	+	0.317234i	−0.847704	−	0.530470i	$-0.822016\pi$
$181$	−4.26795	+	4.26795i	−0.317234	+	0.317234i	0.530470	+	0.847704i	$0.322016\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.90192	−	2.83013i	−0.360397	−	0.208075i
$186$		0			0
$187$	2.00000	+	0.535898i	0.146254	+	0.0391888i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.59808	+	11.4282i	0.477420	+	0.826916i	0.999665	−	0.0258797i	$-0.00823869\pi$
$191$	6.59808	+	11.4282i	0.477420	+	0.826916i	−0.522245	+	0.852795i	$0.674905\pi$
$192$		0			0
$193$	−1.23205	+	2.13397i	−0.0886850	+	0.153607i	−0.906956	−	0.421226i	$-0.861600\pi$
$193$	−1.23205	+	2.13397i	−0.0886850	+	0.153607i	0.818271	+	0.574833i	$0.194933\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.4641	+	10.4641i	−0.745536	+	0.745536i	−0.973637	−	0.228101i	$-0.926748\pi$
$197$	−10.4641	+	10.4641i	−0.745536	+	0.745536i	0.228101	+	0.973637i	$0.426748\pi$
$198$		0			0
$199$		−	5.85641i		−	0.415150i	−0.978219	−	0.207575i	$-0.933443\pi$
$199$		−	5.85641i		−	0.415150i	0.978219	−	0.207575i	$-0.0665570\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.13397	−	7.96410i	−0.149776	−	0.558970i
$204$		0			0
$205$	−1.50000	+	5.59808i	−0.104765	+	0.390987i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.09808	−	1.90192i	−0.0759555	−	0.131559i
$210$		0			0
$211$	−1.96410	+	0.526279i	−0.135214	+	0.0362306i	−0.325791	−	0.945442i	$-0.605631\pi$
$211$	−1.96410	+	0.526279i	−0.135214	+	0.0362306i	0.190577	+	0.981672i	$0.438964\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	4.66025i		−	0.317827i
$216$		0			0
$217$		−	2.94744i		−	0.200085i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−18.3923	+	4.92820i	−1.23720	+	0.331507i
$222$		0			0
$223$	7.79423	+	13.5000i	0.521940	+	0.904027i	0.999674	+	0.0255224i	$0.00812491\pi$
$223$	7.79423	+	13.5000i	0.521940	+	0.904027i	−0.477734	+	0.878504i	$0.658542\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.62436	+	17.2583i	−0.306929	+	1.14548i	0.624343	+	0.781151i	$0.285367\pi$
$227$	−4.62436	+	17.2583i	−0.306929	+	1.14548i	−0.931272	+	0.364325i	$0.881300\pi$
$228$		0			0
$229$	−2.52628	−	9.42820i	−0.166941	−	0.623033i	−0.997785	−	0.0665269i	$-0.978808\pi$
$229$	−2.52628	−	9.42820i	−0.166941	−	0.623033i	0.830843	−	0.556506i	$-0.187858\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	22.9282i		−	1.50208i	−0.660259	−	0.751038i	$-0.729553\pi$
$233$		−	22.9282i		−	1.50208i	0.660259	−	0.751038i	$-0.270447\pi$
$234$		0			0
$235$	−3.36603	+	3.36603i	−0.219575	+	0.219575i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.59808	+	9.69615i	−0.362109	+	0.627192i	−0.988308	−	0.152472i	$-0.951277\pi$
$239$	−5.59808	+	9.69615i	−0.362109	+	0.627192i	0.626198	+	0.779664i	$0.284610\pi$
$240$		0			0
$241$	−6.23205	−	10.7942i	−0.401442	−	0.695317i	0.592458	−	0.805601i	$-0.298157\pi$
$241$	−6.23205	−	10.7942i	−0.401442	−	0.695317i	−0.993900	+	0.110284i	$0.964824\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.464102	−	0.124356i	−0.0296504	−	0.00794479i
$246$		0			0
$247$	17.4904	+	10.0981i	1.11289	+	0.642525i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.39230	−	7.39230i	0.466598	−	0.466598i	−0.434212	−	0.900811i	$-0.642973\pi$
$251$	7.39230	−	7.39230i	0.466598	−	0.466598i	0.900811	+	0.434212i	$0.142973\pi$
$252$		0			0
$253$	0.169873	+	0.169873i	0.0106798	+	0.0106798i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.16025	−	8.93782i	0.321888	−	0.557526i	−0.658990	−	0.752152i	$-0.729016\pi$
$257$	5.16025	−	8.93782i	0.321888	−	0.557526i	0.980878	+	0.194626i	$0.0623493\pi$
$258$		0			0
$259$	6.97372	−	26.0263i	0.433326	−	1.61719i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.40192	+	1.96410i	−0.209772	+	0.121112i	−0.601205	−	0.799095i	$-0.705313\pi$
$263$	−3.40192	+	1.96410i	−0.209772	+	0.121112i	0.391434	+	0.920206i	$0.371979\pi$
$264$		0			0
$265$	−1.43782	−	0.830127i	−0.0883247	−	0.0509943i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.73205	−	7.73205i	−0.471431	−	0.471431i	0.430946	−	0.902378i	$-0.358180\pi$
$269$	−7.73205	−	7.73205i	−0.471431	−	0.471431i	−0.902378	+	0.430946i	$0.858180\pi$
$270$		0			0
$271$	14.9282			0.906824			0.453412	−	0.891301i	$-0.350207\pi$
$271$	14.9282			0.906824			0.453412	+	0.891301i	$0.350207\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.36603	+	0.633975i	−0.142677	+	0.0382301i
$276$		0			0
$277$	13.7942	+	3.69615i	0.828815	+	0.222080i	0.648197	−	0.761473i	$-0.275523\pi$
$277$	13.7942	+	3.69615i	0.828815	+	0.222080i	0.180618	+	0.983553i	$0.442190\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.9641	−	9.79423i	1.01199	−	0.584275i	0.100219	−	0.994965i	$-0.468046\pi$
$281$	16.9641	−	9.79423i	1.01199	−	0.584275i	0.911775	+	0.410691i	$0.134712\pi$
$282$		0			0
$283$	−4.16025	−	15.5263i	−0.247301	−	0.922942i	−0.972213	−	0.234099i	$-0.924786\pi$
$283$	−4.16025	−	15.5263i	−0.247301	−	0.922942i	0.724911	−	0.688842i	$-0.241881\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−27.5885			−1.62850
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.86603	−	14.4282i	−0.225856	−	0.842905i	−0.982060	−	0.188569i	$-0.939615\pi$
$293$	−3.86603	−	14.4282i	−0.225856	−	0.842905i	0.756204	−	0.654336i	$-0.227052\pi$
$294$		0			0
$295$	2.59808	−	1.50000i	0.151266	−	0.0873334i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.13397	−	0.571797i	−0.123411	−	0.0330679i
$300$		0			0
$301$	21.4282	−	5.74167i	1.23510	−	0.330944i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.73205			−0.442736
$306$		0			0
$307$	5.92820	+	5.92820i	0.338340	+	0.338340i	0.855742	−	0.517402i	$-0.173101\pi$
$307$	5.92820	+	5.92820i	0.338340	+	0.338340i	−0.517402	+	0.855742i	$0.673101\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−27.1865	−	15.6962i	−1.54161	−	0.890047i	−0.998738	−	0.0502299i	$-0.984005\pi$
$311$	−27.1865	−	15.6962i	−1.54161	−	0.890047i	−0.542869	−	0.839817i	$-0.682662\pi$
$312$		0			0
$313$	7.83975	−	4.52628i	0.443129	−	0.255840i	−0.261795	−	0.965123i	$-0.584314\pi$
$313$	7.83975	−	4.52628i	0.443129	−	0.255840i	0.704924	+	0.709283i	$0.250981\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.545517	−	2.03590i	0.0306393	−	0.114347i	−0.948913	−	0.315539i	$-0.897815\pi$
$317$	0.545517	−	2.03590i	0.0306393	−	0.114347i	0.979552	+	0.201192i	$0.0644814\pi$
$318$		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
$325$	15.9282	−	15.9282i	0.883538	−	0.883538i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−19.6244	−	11.3301i	−1.08193	−	0.624650i
$330$		0			0
$331$	26.3564	+	7.06218i	1.44868	+	0.388172i	0.895564	−	0.444933i	$-0.146772\pi$
$331$	26.3564	+	7.06218i	1.44868	+	0.388172i	0.553115	+	0.833105i	$0.313439\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.330127	−	0.571797i	−0.0180368	−	0.0312406i
$336$		0			0
$337$	0.696152	−	1.20577i	0.0379218	−	0.0656826i	−0.846442	−	0.532482i	$-0.821260\pi$
$337$	0.696152	−	1.20577i	0.0379218	−	0.0656826i	0.884363	+	0.466799i	$0.154593\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.437822	−	0.437822i	0.0237094	−	0.0237094i
$342$		0			0
$343$		−	19.5359i		−	1.05484i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.23205	−	19.5263i	−0.280871	−	1.04823i	−0.951804	−	0.306707i	$-0.900773\pi$
$347$	−5.23205	−	19.5263i	−0.280871	−	1.04823i	0.670933	−	0.741518i	$-0.265894\pi$
$348$		0			0
$349$	−2.13397	+	7.96410i	−0.114229	+	0.426309i	−0.999228	−	0.0392843i	$-0.987492\pi$
$349$	−2.13397	+	7.96410i	−0.114229	+	0.426309i	0.884999	+	0.465593i	$0.154159\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.2321	+	26.3827i	0.810720	+	1.40421i	0.912361	+	0.409387i	$0.134258\pi$
$353$	15.2321	+	26.3827i	0.810720	+	1.40421i	−0.101640	+	0.994821i	$0.532409\pi$
$354$		0			0
$355$	−5.46410	+	1.46410i	−0.290004	+	0.0777064i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	15.0718i		−	0.795459i	−0.917503	−	0.397730i	$-0.869798\pi$
$359$		−	15.0718i		−	0.795459i	0.917503	−	0.397730i	$-0.130202\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.267949	+	0.0717968i	−0.0140251	+	0.00375801i
$366$		0			0
$367$	−15.4545	−	26.7679i	−0.806717	−	1.39728i	−0.915125	−	0.403169i	$-0.867909\pi$
$367$	−15.4545	−	26.7679i	−0.806717	−	1.39728i	0.108408	−	0.994106i	$-0.465425\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.04552	−	7.63397i	0.106198	−	0.396336i
$372$		0			0
$373$	3.59808	+	13.4282i	0.186301	+	0.695286i	0.994348	+	0.106168i	$0.0338581\pi$
$373$	3.59808	+	13.4282i	0.186301	+	0.695286i	−0.808047	+	0.589118i	$0.799475\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			15.9282i			0.820344i
$378$		0			0
$379$	−15.5885	+	15.5885i	−0.800725	+	0.800725i	−0.983209	−	0.182484i	$-0.941586\pi$
$379$	−15.5885	+	15.5885i	−0.800725	+	0.800725i	0.182484	+	0.983209i	$0.441586\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.3301	−	21.3564i	0.630040	−	1.09126i	−0.357503	−	0.933912i	$-0.616372\pi$
$383$	12.3301	−	21.3564i	0.630040	−	1.09126i	0.987543	−	0.157349i	$-0.0502949\pi$
$384$		0			0
$385$	0.330127	+	0.571797i	0.0168248	+	0.0291415i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.59808	−	2.03590i	−0.385238	−	0.103224i	0.0610019	−	0.998138i	$-0.480570\pi$
$389$	−7.59808	−	2.03590i	−0.385238	−	0.103224i	−0.446240	+	0.894914i	$0.647237\pi$
$390$		0			0
$391$	1.60770	+	0.928203i	0.0813046	+	0.0469413i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.633975	−	0.633975i	0.0318987	−	0.0318987i
$396$		0			0
$397$	−21.0526	−	21.0526i	−1.05660	−	1.05660i	−0.998299	−	0.0582984i	$-0.981433\pi$
$397$	−21.0526	−	21.0526i	−1.05660	−	1.05660i	−0.0582984	−	0.998299i	$-0.518567\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.16025	+	2.00962i	−0.0579403	+	0.100356i	−0.893541	−	0.448982i	$-0.851787\pi$
$401$	−1.16025	+	2.00962i	−0.0579403	+	0.100356i	0.835600	+	0.549338i	$0.185120\pi$
$402$		0			0
$403$	−1.47372	+	5.50000i	−0.0734112	+	0.273975i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.90192	−	2.83013i	0.242979	−	0.140284i
$408$		0			0
$409$	4.62436	+	2.66987i	0.228660	+	0.132017i	0.609954	−	0.792437i	$-0.291188\pi$
$409$	4.62436	+	2.66987i	0.228660	+	0.132017i	−0.381294	+	0.924454i	$0.624521\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.0981	+	10.0981i	0.496894	+	0.496894i
$414$		0			0
$415$	6.32051			0.310262
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.96410	−	0.526279i	0.0959526	−	0.0257104i	−0.210523	−	0.977589i	$-0.567517\pi$
$419$	1.96410	−	0.526279i	0.0959526	−	0.0257104i	0.306476	+	0.951878i	$0.400850\pi$
$420$		0			0
$421$	10.7942	+	2.89230i	0.526079	+	0.140962i	0.512077	−	0.858940i	$-0.328876\pi$
$421$	10.7942	+	2.89230i	0.526079	+	0.140962i	0.0140017	+	0.999902i	$0.495543\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−16.3923	+	9.46410i	−0.795144	+	0.459076i
$426$		0			0
$427$	−9.52628	−	35.5526i	−0.461009	−	1.72051i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	31.3205			1.50866			0.754328	−	0.656498i	$-0.227963\pi$
$431$	31.3205			1.50866			0.754328	+	0.656498i	$0.227963\pi$
$432$		0			0
$433$	24.3923			1.17222			0.586110	−	0.810232i	$-0.300659\pi$
$433$	24.3923			1.17222			0.586110	+	0.810232i	$0.300659\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.509619	−	1.90192i	−0.0243784	−	0.0909814i
$438$		0			0
$439$	−18.0622	+	10.4282i	−0.862061	+	0.497711i	−0.864702	−	0.502286i	$-0.832493\pi$
$439$	−18.0622	+	10.4282i	−0.862061	+	0.497711i	0.00264111	+	0.999997i	$0.499159\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.1603	+	4.33013i	0.767797	+	0.205731i	0.621398	−	0.783495i	$-0.286565\pi$
$443$	16.1603	+	4.33013i	0.767797	+	0.205731i	0.146399	+	0.989226i	$0.453232\pi$
$444$		0			0
$445$	−5.92820	+	1.58846i	−0.281024	+	0.0753001i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.679492			−0.0320672			−0.0160336	−	0.999871i	$-0.505104\pi$
$449$	−0.679492			−0.0320672			−0.0160336	+	0.999871i	$0.505104\pi$
$450$		0			0
$451$	−4.09808	−	4.09808i	−0.192971	−	0.192971i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.25833	−	3.03590i	−0.246514	−	0.142325i
$456$		0			0
$457$	19.0359	−	10.9904i	0.890462	−	0.514108i	0.0163683	−	0.999866i	$-0.494790\pi$
$457$	19.0359	−	10.9904i	0.890462	−	0.514108i	0.874094	+	0.485758i	$0.161456\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.598076	−	2.23205i	0.0278552	−	0.103957i	−0.950599	−	0.310423i	$-0.899529\pi$
$461$	0.598076	−	2.23205i	0.0278552	−	0.103957i	0.978454	+	0.206466i	$0.0661961\pi$
$462$		0			0
$463$	−3.33013	+	5.76795i	−0.154764	+	0.268059i	−0.932973	−	0.359946i	$-0.882795\pi$
$463$	−3.33013	+	5.76795i	−0.154764	+	0.268059i	0.778209	+	0.628005i	$0.216128\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.7846	−	19.7846i	−0.915523	−	0.915523i	0.0811771	−	0.996700i	$-0.474132\pi$
$467$	−19.7846	−	19.7846i	−0.915523	−	0.915523i	−0.996700	+	0.0811771i	$0.974132\pi$
$468$		0			0
$469$	2.22243	−	2.22243i	0.102622	−	0.102622i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.03590	+	2.33013i	0.185571	+	0.107139i
$474$		0			0
$475$	19.3923	+	5.19615i	0.889780	+	0.238416i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.669873	+	1.16025i	0.0306073	+	0.0530134i	0.880923	−	0.473259i	$-0.156923\pi$
$479$	0.669873	+	1.16025i	0.0306073	+	0.0530134i	−0.850316	+	0.526272i	$0.823589\pi$
$480$		0			0
$481$	−26.0263	+	45.0788i	−1.18670	+	2.05542i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.366025	−	0.366025i	0.0166204	−	0.0166204i
$486$		0			0
$487$		−	34.7846i		−	1.57624i	−0.615521	−	0.788121i	$-0.711054\pi$
$487$		−	34.7846i		−	1.57624i	0.615521	−	0.788121i	$-0.288946\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.500000	+	1.86603i	0.0225647	+	0.0842125i	0.976290	−	0.216467i	$-0.0694533\pi$
$491$	0.500000	+	1.86603i	0.0225647	+	0.0842125i	−0.953725	+	0.300679i	$0.902787\pi$
$492$		0			0
$493$	3.46410	−	12.9282i	0.156015	−	0.582257i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.4641	−	23.3205i	−0.603947	−	1.04607i
$498$		0			0
$499$	2.50000	−	0.669873i	0.111915	−	0.0299876i	−0.202427	−	0.979297i	$-0.564883\pi$
$499$	2.50000	−	0.669873i	0.111915	−	0.0299876i	0.314342	+	0.949310i	$0.398216\pi$
$500$		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
$509$	21.2583	−	5.69615i	0.942259	−	0.252478i	0.245185	−	0.969476i	$-0.421151\pi$
$509$	21.2583	−	5.69615i	0.942259	−	0.252478i	0.697074	+	0.716999i	$0.254485\pi$
$510$		0			0
$511$	−0.660254	−	1.14359i	−0.0292079	−	0.0505896i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.277568	+	1.03590i	−0.0122311	+	0.0456471i
$516$		0			0
$517$	−1.23205	−	4.59808i	−0.0541855	−	0.202223i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			14.1436i			0.619642i	0.950795	+	0.309821i	$0.100269\pi$
$521$			14.1436i			0.619642i	−0.950795	+	0.309821i	$0.899731\pi$
$522$		0			0
$523$	2.12436	−	2.12436i	0.0928916	−	0.0928916i	−0.659134	−	0.752026i	$-0.729077\pi$
$523$	2.12436	−	2.12436i	0.0928916	−	0.0928916i	0.752026	+	0.659134i	$0.229077\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.39230	−	4.14359i	0.104210	−	0.180498i
$528$		0			0
$529$	−11.3923	−	19.7321i	−0.495318	−	0.857915i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	51.4808	+	13.7942i	2.22988	+	0.597494i
$534$		0			0
$535$	−7.22243	−	4.16987i	−0.312253	−	0.180279i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.339746	−	0.339746i	0.0146339	−	0.0146339i
$540$		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
$545$	−0.633975	+	1.09808i	−0.0271565	+	0.0470364i
$546$		0			0
$547$	−7.57180	+	28.2583i	−0.323747	+	1.20824i	0.591819	+	0.806071i	$0.298410\pi$
$547$	−7.57180	+	28.2583i	−0.323747	+	1.20824i	−0.915566	+	0.402168i	$0.868257\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.2942	+	7.09808i	−0.523752	+	0.302388i
$552$		0			0
$553$	3.69615	+	2.13397i	0.157176	+	0.0907458i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−27.9808	−	27.9808i	−1.18558	−	1.18558i	−0.978276	−	0.207307i	$-0.933530\pi$
$557$	−27.9808	−	27.9808i	−1.18558	−	1.18558i	−0.207307	−	0.978276i	$-0.566470\pi$
$558$		0			0
$559$	−42.8564			−1.81263
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−29.3564	+	7.86603i	−1.23723	+	0.331513i	−0.817389	−	0.576086i	$-0.804579\pi$
$563$	−29.3564	+	7.86603i	−1.23723	+	0.331513i	−0.419836	+	0.907600i	$0.637912\pi$
$564$		0			0
$565$	2.76795	+	0.741670i	0.116448	+	0.0312023i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−24.4808	+	14.1340i	−1.02629	+	0.592527i	−0.915919	−	0.401364i	$-0.868536\pi$
$569$	−24.4808	+	14.1340i	−1.02629	+	0.592527i	−0.110368	+	0.993891i	$0.535203\pi$
$570$		0			0
$571$	−1.44744	−	5.40192i	−0.0605735	−	0.226063i	0.929003	−	0.370073i	$-0.120667\pi$
$571$	−1.44744	−	5.40192i	−0.0605735	−	0.226063i	−0.989576	+	0.144009i	$0.954001\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.19615			−0.0915859
$576$		0			0
$577$	37.1769			1.54770			0.773848	−	0.633372i	$-0.218330\pi$
$577$	37.1769			1.54770			0.773848	+	0.633372i	$0.218330\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	7.78719	+	29.0622i	0.323067	+	1.20570i
$582$		0			0
$583$	1.43782	−	0.830127i	0.0595485	−	0.0343803i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.96410	−	0.794229i	−0.122342	−	0.0327813i	0.197129	−	0.980378i	$-0.436838\pi$
$587$	−2.96410	−	0.794229i	−0.122342	−	0.0327813i	−0.319470	+	0.947596i	$0.603505\pi$
$588$		0			0
$589$	−4.90192	+	1.31347i	−0.201980	+	0.0541204i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.46410			−0.0601234			−0.0300617	−	0.999548i	$-0.509570\pi$
$593$	−1.46410			−0.0601234			−0.0300617	+	0.999548i	$0.509570\pi$
$594$		0			0
$595$	3.60770	+	3.60770i	0.147901	+	0.147901i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	30.3109	+	17.5000i	1.23847	+	0.715031i	0.968781	−	0.247917i	$-0.0797461\pi$
$599$	30.3109	+	17.5000i	1.23847	+	0.715031i	0.269688	+	0.962948i	$0.413079\pi$
$600$		0			0
$601$	−30.2321	+	17.4545i	−1.23319	+	0.711983i	−0.967694	−	0.252128i	$-0.918869\pi$
$601$	−30.2321	+	17.4545i	−1.23319	+	0.711983i	−0.265497	+	0.964112i	$0.585536\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.43782	−	5.36603i	0.0584558	−	0.218160i
$606$		0			0
$607$	4.59808	−	7.96410i	0.186630	−	0.323253i	−0.757494	−	0.652842i	$-0.773577\pi$
$607$	4.59808	−	7.96410i	0.186630	−	0.323253i	0.944125	+	0.329589i	$0.106910\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	30.9545	+	30.9545i	1.25228	+	1.25228i
$612$		0			0
$613$	−7.58846	+	7.58846i	−0.306495	+	0.306495i	−0.843548	−	0.537053i	$-0.819537\pi$
$613$	−7.58846	+	7.58846i	−0.306495	+	0.306495i	0.537053	+	0.843548i	$0.319537\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.08846	+	4.66987i	0.325629	+	0.188002i	0.653899	−	0.756582i	$-0.273132\pi$
$617$	8.08846	+	4.66987i	0.325629	+	0.188002i	−0.328270	+	0.944584i	$0.606466\pi$
$618$		0			0
$619$	33.0885	+	8.86603i	1.32994	+	0.356356i	0.852692	−	0.522414i	$-0.174969\pi$
$619$	33.0885	+	8.86603i	1.32994	+	0.356356i	0.477246	+	0.878770i	$0.341635\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−14.6077	−	25.3013i	−0.585245	−	1.01367i
$624$		0			0
$625$	10.5263	−	18.2321i	0.421051	−	0.729282i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	30.9282	−	30.9282i	1.23319	−	1.23319i
$630$		0			0
$631$			32.2487i			1.28380i	0.766788	+	0.641900i	$0.221854\pi$
$631$			32.2487i			1.28380i	−0.766788	+	0.641900i	$0.778146\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.73205	+	10.1962i	0.108418	+	0.404622i
$636$		0			0
$637$	−1.14359	+	4.26795i	−0.0453108	+	0.169102i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.76795	−	9.99038i	−0.227820	−	0.394596i	0.729342	−	0.684150i	$-0.239827\pi$
$641$	−5.76795	−	9.99038i	−0.227820	−	0.394596i	−0.957162	+	0.289553i	$0.906493\pi$
$642$		0			0
$643$	−1.03590	+	0.277568i	−0.0408518	+	0.0109462i	−0.279187	−	0.960237i	$-0.590065\pi$
$643$	−1.03590	+	0.277568i	−0.0408518	+	0.0109462i	0.238335	+	0.971183i	$0.423398\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			46.3923i			1.82387i	0.410335	+	0.911935i	$0.365412\pi$
$647$			46.3923i			1.82387i	−0.410335	+	0.911935i	$0.634588\pi$
$648$		0			0
$649$			3.00000i			0.117760i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	21.3301	−	5.71539i	0.834712	−	0.223661i	0.183944	−	0.982937i	$-0.441114\pi$
$653$	21.3301	−	5.71539i	0.834712	−	0.223661i	0.650768	+	0.759276i	$0.274447\pi$
$654$		0			0
$655$	3.13397	+	5.42820i	0.122455	+	0.212097i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.23205	+	8.33013i	−0.0869484	+	0.324496i	−0.995676	−	0.0928939i	$-0.970388\pi$
$659$	−2.23205	+	8.33013i	−0.0869484	+	0.324496i	0.908728	+	0.417390i	$0.137055\pi$
$660$		0			0
$661$	4.20577	+	15.6962i	0.163586	+	0.610510i	0.998216	+	0.0596998i	$0.0190143\pi$
$661$	4.20577	+	15.6962i	0.163586	+	0.610510i	−0.834631	+	0.550810i	$0.814319\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	5.41154i		−	0.209851i
$666$		0			0
$667$	1.09808	−	1.09808i	0.0425177	−	0.0425177i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.86603	−	6.69615i	0.149246	−	0.258502i
$672$		0			0
$673$	3.83975	+	6.65064i	0.148011	+	0.256363i	0.930492	−	0.366311i	$-0.119379\pi$
$673$	3.83975	+	6.65064i	0.148011	+	0.256363i	−0.782481	+	0.622674i	$0.786046\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−45.6506	−	12.2321i	−1.75450	−	0.470116i	−0.768920	−	0.639345i	$-0.779205\pi$
$677$	−45.6506	−	12.2321i	−1.75450	−	0.470116i	−0.985577	+	0.169229i	$0.945872\pi$
$678$		0			0
$679$	2.13397	+	1.23205i	0.0818944	+	0.0472818i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.39230	+	5.39230i	−0.206331	+	0.206331i	−0.802706	−	0.596375i	$-0.796607\pi$
$683$	−5.39230	+	5.39230i	−0.206331	+	0.206331i	0.596375	+	0.802706i	$0.296607\pi$
$684$		0			0
$685$	6.09808	+	6.09808i	0.232996	+	0.232996i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.63397	+	13.2224i	−0.290831	+	0.503735i
$690$		0			0
$691$	−4.96410	+	18.5263i	−0.188843	+	0.704773i	0.804932	+	0.593367i	$0.202202\pi$
$691$	−4.96410	+	18.5263i	−0.188843	+	0.704773i	−0.993775	+	0.111405i	$0.964465\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.00962	+	1.16025i	−0.0762292	+	0.0440109i
$696$		0			0
$697$	−38.7846	−	22.3923i	−1.46907	−	0.848169i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	21.0526	+	21.0526i	0.795144	+	0.795144i	0.982325	−	0.187181i	$-0.0599352\pi$
$701$	21.0526	+	21.0526i	0.795144	+	0.795144i	−0.187181	+	0.982325i	$0.559935\pi$
$702$		0			0
$703$	−46.3923			−1.74972
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.59808	+	1.23205i	−0.172928	+	0.0463360i
$708$		0			0
$709$	−40.1147	−	10.7487i	−1.50654	−	0.403676i	−0.591256	−	0.806484i	$-0.701368\pi$
$709$	−40.1147	−	10.7487i	−1.50654	−	0.403676i	−0.915285	+	0.402808i	$0.868034\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.480762	−	0.277568i	0.0180047	−	0.0103950i
$714$		0			0
$715$	−0.330127	−	1.23205i	−0.0123461	−	0.0460761i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	23.3205			0.869708			0.434854	−	0.900501i	$-0.356800\pi$
$719$	23.3205			0.869708			0.434854	+	0.900501i	$0.356800\pi$
$720$		0			0
$721$	−5.10512			−0.190125
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.09808	+	15.2942i	0.152199	+	0.568013i
$726$		0			0
$727$	9.06218	−	5.23205i	0.336098	−	0.194046i	−0.322447	−	0.946587i	$-0.604506\pi$
$727$	9.06218	−	5.23205i	0.336098	−	0.194046i	0.658545	+	0.752541i	$0.271172\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	34.7846	+	9.32051i	1.28656	+	0.344731i
$732$		0			0
$733$	27.5263	−	7.37564i	1.01671	−	0.272426i	0.288277	−	0.957547i	$-0.406917\pi$
$733$	27.5263	−	7.37564i	1.01671	−	0.272426i	0.728429	+	0.685121i	$0.240251\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.660254			0.0243208
$738$		0			0
$739$	29.7321	+	29.7321i	1.09371	+	1.09371i	0.995129	+	0.0985823i	$0.0314308\pi$
$739$	29.7321	+	29.7321i	1.09371	+	1.09371i	0.0985823	+	0.995129i	$0.468569\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.1147	−	14.5000i	−0.921370	−	0.531953i	−0.0372984	−	0.999304i	$-0.511875\pi$
$743$	−25.1147	−	14.5000i	−0.921370	−	0.531953i	−0.884072	+	0.467351i	$0.845209\pi$
$744$		0			0
$745$	6.82051	−	3.93782i	0.249884	−	0.144271i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.2750	−	38.3468i	0.375440	−	1.40116i
$750$		0			0
$751$	−4.72243	+	8.17949i	−0.172324	+	0.298474i	−0.939232	−	0.343283i	$-0.888461\pi$
$751$	−4.72243	+	8.17949i	−0.172324	+	0.298474i	0.766908	+	0.641757i	$0.221794\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.56218	−	2.56218i	−0.0932472	−	0.0932472i
$756$		0			0
$757$	8.46410	−	8.46410i	0.307633	−	0.307633i	−0.536358	−	0.843991i	$-0.680200\pi$
$757$	8.46410	−	8.46410i	0.307633	−	0.307633i	0.843991	+	0.536358i	$0.180200\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−25.2846	−	14.5981i	−0.916566	−	0.529180i	−0.0340283	−	0.999421i	$-0.510834\pi$
$761$	−25.2846	−	14.5981i	−0.916566	−	0.529180i	−0.882538	+	0.470241i	$0.844167\pi$
$762$		0			0
$763$	−5.83013	−	1.56218i	−0.211065	−	0.0565546i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.7942	−	23.8923i	−0.498081	−	0.862701i
$768$		0			0
$769$	−3.50000	+	6.06218i	−0.126213	+	0.218608i	−0.922207	−	0.386698i	$-0.873616\pi$
$769$	−3.50000	+	6.06218i	−0.126213	+	0.218608i	0.795993	+	0.605305i	$0.206949\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.58846	+	7.58846i	−0.272938	+	0.272938i	−0.830282	−	0.557344i	$-0.811821\pi$
$773$	−7.58846	+	7.58846i	−0.272938	+	0.272938i	0.557344	+	0.830282i	$0.311821\pi$
$774$		0			0
$775$			5.66025i			0.203322i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.2942	+	45.8827i	0.440486	+	1.64392i
$780$		0			0
$781$	1.46410	−	5.46410i	0.0523897	−	0.195521i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.232051	+	0.401924i	0.00828225	+	0.0143453i
$786$		0			0
$787$	33.8205	−	9.06218i	1.20557	−	0.323032i	0.400548	−	0.916276i	$-0.368820\pi$
$787$	33.8205	−	9.06218i	1.20557	−	0.323032i	0.805023	+	0.593244i	$0.202153\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			13.6410i			0.485019i
$792$		0			0
$793$			71.1051i			2.52502i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.06218	−	0.284610i	0.0376243	−	0.0100814i	−0.239958	−	0.970783i	$-0.577134\pi$
$797$	1.06218	−	0.284610i	0.0376243	−	0.0100814i	0.277582	+	0.960702i	$0.410467\pi$
$798$		0			0
$799$	−18.3923	−	31.8564i	−0.650673	−	1.12700i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.0717968	−	0.267949i	0.00253365	−	0.00945572i
$804$		0			0
$805$	0.153212	+	0.571797i	0.00540003	+	0.0201532i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	32.6410i		−	1.14760i	−0.818997	−	0.573799i	$-0.805469\pi$
$809$		−	32.6410i		−	1.14760i	0.818997	−	0.573799i	$-0.194531\pi$
$810$		0			0
$811$	11.5359	−	11.5359i	0.405080	−	0.405080i	−0.474939	−	0.880019i	$-0.657530\pi$
$811$	11.5359	−	11.5359i	0.405080	−	0.405080i	0.880019	+	0.474939i	$0.157530\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4.36603	−	7.56218i	0.152935	−	0.264892i
$816$		0			0
$817$	−19.0981	−	33.0788i	−0.668157	−	1.15728i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18.7224	+	5.01666i	0.653417	+	0.175083i	0.570273	−	0.821455i	$-0.306837\pi$
$821$	18.7224	+	5.01666i	0.653417	+	0.175083i	0.0831439	+	0.996538i	$0.473504\pi$
$822$		0			0
$823$	6.65064	+	3.83975i	0.231827	+	0.133845i	0.611414	−	0.791311i	$-0.290601\pi$
$823$	6.65064	+	3.83975i	0.231827	+	0.133845i	−0.379588	+	0.925156i	$0.623934\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.6077	+	10.6077i	−0.368866	+	0.368866i	−0.867063	−	0.498198i	$-0.833995\pi$
$827$	−10.6077	+	10.6077i	−0.368866	+	0.368866i	0.498198	+	0.867063i	$0.333995\pi$
$828$		0			0
$829$	−17.7321	−	17.7321i	−0.615860	−	0.615860i	0.328607	−	0.944467i	$-0.393421\pi$
$829$	−17.7321	−	17.7321i	−0.615860	−	0.615860i	−0.944467	+	0.328607i	$0.893421\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.85641	−	3.21539i	0.0643207	−	0.111407i
$834$		0			0
$835$	−1.27757	+	4.76795i	−0.0442121	+	0.165002i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	29.2583	−	16.8923i	1.01011	−	0.583187i	0.0988859	−	0.995099i	$-0.468472\pi$
$839$	29.2583	−	16.8923i	1.01011	−	0.583187i	0.911224	+	0.411912i	$0.135139\pi$
$840$		0			0
$841$	15.4186	+	8.90192i	0.531675	+	0.306963i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.53590	+	3.53590i	0.121639	+	0.121639i
$846$		0			0
$847$	26.4449			0.908656
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.90192	−	1.31347i	0.168036	−	0.0450251i
$852$		0			0
$853$	10.0622	+	2.69615i	0.344522	+	0.0923145i	0.426931	−	0.904284i	$-0.359595\pi$
$853$	10.0622	+	2.69615i	0.344522	+	0.0923145i	−0.0824088	+	0.996599i	$0.526261\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−42.3564	+	24.4545i	−1.44687	+	0.835349i	−0.998293	−	0.0583966i	$-0.981401\pi$
$857$	−42.3564	+	24.4545i	−1.44687	+	0.835349i	−0.448574	+	0.893746i	$0.648068\pi$
$858$		0			0
$859$	4.50000	+	16.7942i	0.153538	+	0.573012i	0.999226	+	0.0393342i	$0.0125237\pi$
$859$	4.50000	+	16.7942i	0.153538	+	0.573012i	−0.845688	+	0.533677i	$0.820810\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−33.4641			−1.13913			−0.569566	−	0.821946i	$-0.692889\pi$
$863$	−33.4641			−1.13913			−0.569566	+	0.821946i	$0.692889\pi$
$864$		0			0
$865$	−4.80385			−0.163336
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.232051	+	0.866025i	0.00787178	+	0.0293779i
$870$		0			0
$871$	−5.25833	+	3.03590i	−0.178172	+	0.102867i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−11.9904	−	3.21281i	−0.405349	−	0.108613i
$876$		0			0
$877$	33.3827	−	8.94486i	1.12725	−	0.302047i	0.353438	−	0.935458i	$-0.385013\pi$
$877$	33.3827	−	8.94486i	1.12725	−	0.302047i	0.773815	+	0.633411i	$0.218346\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	3.32051			0.111871			0.0559354	−	0.998434i	$-0.482186\pi$
$881$	3.32051			0.111871			0.0559354	+	0.998434i	$0.482186\pi$
$882$		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
$887$	21.0622	+	12.1603i	0.707199	+	0.408301i	0.810023	−	0.586398i	$-0.199455\pi$
$887$	21.0622	+	12.1603i	0.707199	+	0.408301i	−0.102824	+	0.994700i	$0.532788\pi$
$888$		0			0
$889$	−43.5167	+	25.1244i	−1.45950	+	0.842644i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−10.0981	+	37.6865i	−0.337919	+	1.26113i
$894$		0			0
$895$	−2.90192	+	5.02628i	−0.0970006	+	0.168010i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.83013	−	2.83013i	−0.0943900	−	0.0943900i
$900$		0			0
$901$	9.07180	−	9.07180i	0.302225	−	0.302225i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.70577	−	1.56218i	−0.0899429	−	0.0519285i
$906$		0			0
$907$	−11.4282	−	3.06218i	−0.379467	−	0.101678i	0.0640432	−	0.997947i	$-0.479600\pi$
$907$	−11.4282	−	3.06218i	−0.379467	−	0.101678i	−0.443510	+	0.896269i	$0.646267\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.86603	−	10.1603i	−0.194350	−	0.336624i	0.752337	−	0.658778i	$-0.228926\pi$
$911$	−5.86603	−	10.1603i	−0.194350	−	0.336624i	−0.946687	+	0.322154i	$0.895593\pi$
$912$		0			0
$913$	−3.16025	+	5.47372i	−0.104589	+	0.181154i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.0981	+	21.0981i	−0.696720	+	0.696720i
$918$		0			0
$919$			43.4641i			1.43375i	0.697203	+	0.716874i	$0.254428\pi$
$919$			43.4641i			1.43375i	−0.697203	+	0.716874i	$0.745572\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13.4641	+	50.2487i	0.443176	+	1.65396i
$924$		0			0
$925$	−13.3923	+	49.9808i	−0.440336	+	1.64336i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.3564	+	31.7942i	0.602254	+	1.04313i	0.992479	+	0.122415i	$0.0390640\pi$
$929$	18.3564	+	31.7942i	0.602254	+	1.04313i	−0.390225	+	0.920720i	$0.627603\pi$
$930$		0			0
$931$	−3.80385	+	1.01924i	−0.124666	+	0.0334042i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			1.07180i			0.0350515i
$936$		0			0
$937$			32.9282i			1.07572i	0.843035	+	0.537859i	$0.180767\pi$
$937$			32.9282i			1.07572i	−0.843035	+	0.537859i	$0.819233\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.8660	+	2.91154i	−0.354222	+	0.0949136i	−0.431542	−	0.902093i	$-0.642030\pi$
$941$	−10.8660	+	2.91154i	−0.354222	+	0.0949136i	0.0773199	+	0.997006i	$0.475364\pi$
$942$		0			0
$943$	−2.59808	−	4.50000i	−0.0846050	−	0.146540i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.01666	−	14.9904i	0.130524	−	0.487122i	−0.869452	−	0.494017i	$-0.835528\pi$
$947$	4.01666	−	14.9904i	0.130524	−	0.487122i	0.999976	+	0.00689497i	$0.00219475\pi$
$948$		0			0
$949$	0.660254	+	2.46410i	0.0214328	+	0.0799881i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			39.4641i			1.27837i	0.769054	+	0.639184i	$0.220728\pi$
$953$			39.4641i			1.27837i	−0.769054	+	0.639184i	$0.779272\pi$
$954$		0			0
$955$	−4.83013	+	4.83013i	−0.156299	+	0.156299i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−20.5263	+	35.5526i	−0.662828	+	1.14805i
$960$		0			0
$961$	14.7846	+	25.6077i	0.476923	+	0.826055i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.23205	−	0.330127i	−0.0396611	−	0.0106272i
$966$		0			0
$967$	14.9378	+	8.62436i	0.480368	+	0.277341i	0.720570	−	0.693382i	$-0.243880\pi$
$967$	14.9378	+	8.62436i	0.480368	+	0.277341i	−0.240202	+	0.970723i	$0.577214\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	27.9808	−	27.9808i	0.897945	−	0.897945i	−0.0973088	−	0.995254i	$-0.531023\pi$
$971$	27.9808	−	27.9808i	0.897945	−	0.897945i	0.995254	+	0.0973088i	$0.0310235\pi$
$972$		0			0
$973$	−7.81089	−	7.81089i	−0.250406	−	0.250406i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.2846	+	29.9378i	−0.552984	+	0.957796i	0.445074	+	0.895494i	$0.353177\pi$
$977$	−17.2846	+	29.9378i	−0.552984	+	0.957796i	−0.998057	+	0.0623018i	$0.980156\pi$
$978$		0			0
$979$	1.58846	−	5.92820i	0.0507673	−	0.189466i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−40.9186	+	23.6244i	−1.30510	+	0.753500i	−0.981274	−	0.192617i	$-0.938303\pi$
$983$	−40.9186	+	23.6244i	−1.30510	+	0.753500i	−0.323826	+	0.946117i	$0.604969\pi$
$984$		0			0
$985$	−6.63397	−	3.83013i	−0.211376	−	0.122038i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.95448	+	2.95448i	0.0939471	+	0.0939471i
$990$		0			0
$991$	23.6077			0.749923			0.374962	−	0.927040i	$-0.377656\pi$
$991$	23.6077			0.749923			0.374962	+	0.927040i	$0.377656\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.92820	−	0.784610i	0.0928303	−	0.0248738i
$996$		0			0
$997$	11.0622	+	2.96410i	0.350343	+	0.0938740i	0.429699	−	0.902972i	$-0.358620\pi$
$997$	11.0622	+	2.96410i	0.350343	+	0.0938740i	−0.0793561	+	0.996846i	$0.525286\pi$
$998$		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.145.1		4
3.2	odd	2		576.2.bb.a.337.1		4
4.3	odd	2		432.2.y.d.253.1		4
9.2	odd	6		576.2.bb.b.529.1		4
9.7	even	3		1728.2.bc.b.721.1		4
12.11	even	2		144.2.x.a.13.1	✓	4
16.5	even	4		1728.2.bc.b.1009.1		4
16.11	odd	4		432.2.y.a.37.1		4
36.7	odd	6		432.2.y.a.397.1		4
36.11	even	6		144.2.x.d.61.1	yes	4
48.5	odd	4		576.2.bb.b.49.1		4
48.11	even	4		144.2.x.d.85.1	yes	4
144.11	even	12		144.2.x.a.133.1	yes	4
144.43	odd	12		432.2.y.d.181.1		4
144.101	odd	12		576.2.bb.a.241.1		4
144.133	even	12	inner	1728.2.bc.c.1585.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.13.1	✓	4	12.11	even	2
144.2.x.a.133.1	yes	4	144.11	even	12
144.2.x.d.61.1	yes	4	36.11	even	6
144.2.x.d.85.1	yes	4	48.11	even	4
432.2.y.a.37.1		4	16.11	odd	4
432.2.y.a.397.1		4	36.7	odd	6
432.2.y.d.181.1		4	144.43	odd	12
432.2.y.d.253.1		4	4.3	odd	2
576.2.bb.a.241.1		4	144.101	odd	12
576.2.bb.a.337.1		4	3.2	odd	2
576.2.bb.b.49.1		4	48.5	odd	4
576.2.bb.b.529.1		4	9.2	odd	6
1728.2.bc.b.721.1		4	9.7	even	3
1728.2.bc.b.1009.1		4	16.5	even	4
1728.2.bc.c.145.1		4	1.1	even	1	trivial
1728.2.bc.c.1585.1		4	144.133	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)

\(f(q)\)	\(=\)	\(q+(0.133975 + 0.500000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +O(q^{10})\)	\(q+(0.133975 + 0.500000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-0.500000 - 0.133975i) q^{11} +(4.59808 - 1.23205i) q^{13} -4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(-0.401924 - 0.232051i) q^{23} +(4.09808 - 2.36603i) q^{25} +(-0.866025 + 3.23205i) q^{29} +(-0.598076 + 1.03590i) q^{31} +(-0.901924 - 0.901924i) q^{35} +(-7.73205 + 7.73205i) q^{37} +(9.69615 + 5.59808i) q^{41} +(-8.69615 - 2.33013i) q^{43} +(4.59808 + 7.96410i) q^{47} +(-0.464102 + 0.803848i) q^{49} +(-2.26795 + 2.26795i) q^{53} -0.267949i q^{55} +(-1.50000 - 5.59808i) q^{59} +(-3.86603 + 14.4282i) q^{61} +(1.23205 + 2.13397i) q^{65} +(-1.23205 + 0.330127i) q^{67} +10.9282i q^{71} +0.535898i q^{73} +(1.23205 - 0.330127i) q^{77} +(-0.866025 - 1.50000i) q^{79} +(3.16025 - 11.7942i) q^{83} +(-0.535898 - 2.00000i) q^{85} +11.8564i q^{89} +(-8.29423 + 8.29423i) q^{91} +(-1.09808 + 1.90192i) q^{95} +(-0.500000 - 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} - 12 q^{7}+O(q^{10}) \) 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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