LMFDB - Embedded newform 1728.2.bc.e.1585.14

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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1585.14
Character	$\chi$	$=$	1728.1585
Dual form			1728.2.bc.e.145.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.733432 - 2.73721i) q^{5} +(-1.14487 - 0.660988i) q^{7} +O(q^{10})$	$q+(0.733432 - 2.73721i) q^{5} +(-1.14487 - 0.660988i) q^{7} +(1.28367 - 0.343957i) q^{11} +(3.36696 + 0.902174i) q^{13} +7.60772 q^{17} +(-4.32297 + 4.32297i) q^{19} +(3.46087 - 1.99814i) q^{23} +(-2.62424 - 1.51511i) q^{25} +(-0.950303 - 3.54658i) q^{29} +(-0.569129 - 0.985760i) q^{31} +(-2.64894 + 2.64894i) q^{35} +(2.26014 + 2.26014i) q^{37} +(-1.42311 + 0.821634i) q^{41} +(6.17424 - 1.65438i) q^{43} +(4.58731 - 7.94546i) q^{47} +(-2.62619 - 4.54869i) q^{49} +(-7.72215 - 7.72215i) q^{53} -3.76593i q^{55} +(1.28879 - 4.80982i) q^{59} +(-2.66068 - 9.92979i) q^{61} +(4.93887 - 8.55438i) q^{65} +(-13.9276 - 3.73189i) q^{67} +7.87498i q^{71} +0.577222i q^{73} +(-1.69698 - 0.454704i) q^{77} +(-0.716890 + 1.24169i) q^{79} +(-0.885341 - 3.30414i) q^{83} +(5.57975 - 20.8239i) q^{85} +16.2114i q^{89} +(-3.25839 - 3.25839i) q^{91} +(8.66225 + 15.0035i) q^{95} +(-0.648931 + 1.12398i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{5}+O(q^{10}) $ 72 * q - 4 * q^5	$ 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67} + 36 q^{77} - 44 q^{79} + 20 q^{83} - 8 q^{85} + 80 q^{91} + 48 q^{95} + 40 q^{97}+O(q^{100}) $ 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.733432	−	2.73721i	0.328001	−	1.22412i	−0.583260	−	0.812286i	$-0.698223\pi$
$5$	0.733432	−	2.73721i	0.328001	−	1.22412i	0.911261	−	0.411830i	$-0.135110\pi$
$6$		0			0
$7$	−1.14487	−	0.660988i	−0.432718	−	0.249830i	0.267786	−	0.963479i	$-0.413708\pi$
$7$	−1.14487	−	0.660988i	−0.432718	−	0.249830i	−0.700504	+	0.713648i	$0.747041\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.28367	−	0.343957i	0.387040	−	0.103707i	−0.0600515	−	0.998195i	$-0.519126\pi$
$11$	1.28367	−	0.343957i	0.387040	−	0.103707i	0.447092	+	0.894488i	$0.352460\pi$
$12$		0			0
$13$	3.36696	+	0.902174i	0.933827	+	0.250218i	0.693486	−	0.720470i	$-0.256074\pi$
$13$	3.36696	+	0.902174i	0.933827	+	0.250218i	0.240341	+	0.970689i	$0.422741\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.60772			1.84514			0.922572	−	0.385825i	$-0.126083\pi$
$17$	7.60772			1.84514			0.922572	+	0.385825i	$0.126083\pi$
$18$		0			0
$19$	−4.32297	+	4.32297i	−0.991757	+	0.991757i	−0.999966	−	0.00820954i	$-0.997387\pi$
$19$	−4.32297	+	4.32297i	−0.991757	+	0.991757i	0.00820954	+	0.999966i	$0.497387\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.46087	−	1.99814i	0.721642	−	0.416640i	−0.0937148	−	0.995599i	$-0.529874\pi$
$23$	3.46087	−	1.99814i	0.721642	−	0.416640i	0.815357	+	0.578959i	$0.196541\pi$
$24$		0			0
$25$	−2.62424	−	1.51511i	−0.524849	−	0.303021i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.950303	−	3.54658i	−0.176467	−	0.658583i	−0.996297	−	0.0859765i	$-0.972599\pi$
$29$	−0.950303	−	3.54658i	−0.176467	−	0.658583i	0.819830	−	0.572606i	$-0.194068\pi$
$30$		0			0
$31$	−0.569129	−	0.985760i	−0.102219	−	0.177048i	0.810380	−	0.585905i	$-0.199261\pi$
$31$	−0.569129	−	0.985760i	−0.102219	−	0.177048i	−0.912598	+	0.408857i	$0.865927\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.64894	+	2.64894i	−0.447753	+	0.447753i
$36$		0			0
$37$	2.26014	+	2.26014i	0.371565	+	0.371565i	0.868047	−	0.496482i	$-0.165375\pi$
$37$	2.26014	+	2.26014i	0.371565	+	0.371565i	−0.496482	+	0.868047i	$0.665375\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.42311	+	0.821634i	−0.222253	+	0.128318i	−0.606993	−	0.794707i	$-0.707624\pi$
$41$	−1.42311	+	0.821634i	−0.222253	+	0.128318i	0.384740	+	0.923025i	$0.374291\pi$
$42$		0			0
$43$	6.17424	−	1.65438i	0.941563	−	0.252291i	0.244784	−	0.969578i	$-0.421283\pi$
$43$	6.17424	−	1.65438i	0.941563	−	0.252291i	0.696778	+	0.717287i	$0.254616\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.58731	−	7.94546i	0.669129	−	1.15896i	−0.309020	−	0.951056i	$-0.600001\pi$
$47$	4.58731	−	7.94546i	0.669129	−	1.15896i	0.978148	−	0.207909i	$-0.0666658\pi$
$48$		0			0
$49$	−2.62619	−	4.54869i	−0.375170	−	0.649813i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.72215	−	7.72215i	−1.06072	−	1.06072i	−0.998033	−	0.0626852i	$-0.980034\pi$
$53$	−7.72215	−	7.72215i	−1.06072	−	1.06072i	−0.0626852	−	0.998033i	$-0.519966\pi$
$54$		0			0
$55$		−	3.76593i		−	0.507798i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.28879	−	4.80982i	0.167786	−	0.626185i	−0.829883	−	0.557938i	$-0.811593\pi$
$59$	1.28879	−	4.80982i	0.167786	−	0.626185i	0.997668	−	0.0682473i	$-0.0217407\pi$
$60$		0			0
$61$	−2.66068	−	9.92979i	−0.340665	−	1.27138i	−0.897596	−	0.440820i	$-0.854688\pi$
$61$	−2.66068	−	9.92979i	−0.340665	−	1.27138i	0.556931	−	0.830559i	$-0.311979\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.93887	−	8.55438i	0.612592	−	1.06104i
$66$		0			0
$67$	−13.9276	−	3.73189i	−1.70153	−	0.455923i	−0.728205	−	0.685359i	$-0.759645\pi$
$67$	−13.9276	−	3.73189i	−1.70153	−	0.455923i	−0.973324	+	0.229436i	$0.926312\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.87498i			0.934588i	0.884102	+	0.467294i	$0.154771\pi$
$71$			7.87498i			0.934588i	−0.884102	+	0.467294i	$0.845229\pi$
$72$		0			0
$73$			0.577222i			0.0675588i	0.999429	+	0.0337794i	$0.0107544\pi$
$73$			0.577222i			0.0675588i	−0.999429	+	0.0337794i	$0.989246\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.69698	−	0.454704i	−0.193389	−	0.0518183i
$78$		0			0
$79$	−0.716890	+	1.24169i	−0.0806564	+	0.139701i	−0.903532	−	0.428521i	$-0.859035\pi$
$79$	−0.716890	+	1.24169i	−0.0806564	+	0.139701i	0.822876	+	0.568221i	$0.192368\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.885341	−	3.30414i	−0.0971788	−	0.362676i	0.900162	−	0.435555i	$-0.143448\pi$
$83$	−0.885341	−	3.30414i	−0.0971788	−	0.362676i	−0.997341	+	0.0728790i	$0.976781\pi$
$84$		0			0
$85$	5.57975	−	20.8239i	0.605208	−	2.25867i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			16.2114i			1.71841i	0.511635	+	0.859203i	$0.329040\pi$
$89$			16.2114i			1.71841i	−0.511635	+	0.859203i	$0.670960\pi$
$90$		0			0
$91$	−3.25839	−	3.25839i	−0.341572	−	0.341572i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.66225	+	15.0035i	0.888728	+	1.53932i
$96$		0			0
$97$	−0.648931	+	1.12398i	−0.0658889	+	0.114123i	−0.897088	−	0.441852i	$-0.854322\pi$
$97$	−0.648931	+	1.12398i	−0.0658889	+	0.114123i	0.831199	+	0.555975i	$0.187655\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.73900	−	2.60956i	0.969067	−	0.259661i	0.260633	−	0.965438i	$-0.416069\pi$
$101$	9.73900	−	2.60956i	0.969067	−	0.259661i	0.708434	+	0.705777i	$0.249402\pi$
$102$		0			0
$103$	8.04850	−	4.64680i	0.793042	−	0.457863i	−0.0479901	−	0.998848i	$-0.515282\pi$
$103$	8.04850	−	4.64680i	0.793042	−	0.457863i	0.841033	+	0.540985i	$0.181948\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.89502	+	1.89502i	0.183199	+	0.183199i	0.792748	−	0.609549i	$-0.208650\pi$
$107$	1.89502	+	1.89502i	0.183199	+	0.183199i	−0.609549	+	0.792748i	$0.708650\pi$
$108$		0			0
$109$	−8.63272	+	8.63272i	−0.826864	+	0.826864i	−0.987082	−	0.160217i	$-0.948780\pi$
$109$	−8.63272	+	8.63272i	−0.826864	+	0.826864i	0.160217	+	0.987082i	$0.448780\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.70180	+	2.94761i	0.160092	+	0.277288i	0.934902	−	0.354907i	$-0.115488\pi$
$113$	1.70180	+	2.94761i	0.160092	+	0.277288i	−0.774809	+	0.632195i	$0.782154\pi$
$114$		0			0
$115$	−2.93099	−	10.9386i	−0.273317	−	1.02003i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.70982	−	5.02862i	−0.798428	−	0.460972i
$120$		0			0
$121$	−7.99679	+	4.61695i	−0.726981	+	0.419722i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.94700	−	3.94700i	0.353031	−	0.353031i
$126$		0			0
$127$	5.24504			0.465422			0.232711	−	0.972546i	$-0.425240\pi$
$127$	5.24504			0.465422			0.232711	+	0.972546i	$0.425240\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.27080	−	1.68026i	−0.547883	−	0.146805i	−0.0257490	−	0.999668i	$-0.508197\pi$
$131$	−6.27080	−	1.68026i	−0.547883	−	0.146805i	−0.522134	+	0.852864i	$0.674864\pi$
$132$		0			0
$133$	7.80665	−	2.09178i	0.676922	−	0.181381i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.16622	−	3.56007i	−0.526816	−	0.304157i	0.212903	−	0.977073i	$-0.431708\pi$
$137$	−6.16622	−	3.56007i	−0.526816	−	0.304157i	−0.739719	+	0.672916i	$0.765042\pi$
$138$		0			0
$139$	1.09091	−	4.07133i	0.0925298	−	0.345326i	−0.904104	−	0.427313i	$-0.859460\pi$
$139$	1.09091	−	4.07133i	0.0925298	−	0.345326i	0.996633	+	0.0819876i	$0.0261268\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.63236			0.387378
$144$		0			0
$145$	−10.4047			−0.864063
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.25338	+	8.40971i	−0.184604	+	0.688950i	0.810111	+	0.586276i	$0.199407\pi$
$149$	−2.25338	+	8.40971i	−0.184604	+	0.688950i	−0.994715	+	0.102674i	$0.967260\pi$
$150$		0			0
$151$	17.8103	+	10.2828i	1.44938	+	0.836803i	0.998445	−	0.0557515i	$-0.0177554\pi$
$151$	17.8103	+	10.2828i	1.44938	+	0.836803i	0.450940	+	0.892554i	$0.351089\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.11564	+	0.834834i	−0.250255	+	0.0670555i
$156$		0			0
$157$	8.90879	+	2.38710i	0.710999	+	0.190512i	0.596152	−	0.802872i	$-0.296696\pi$
$157$	8.90879	+	2.38710i	0.710999	+	0.190512i	0.114847	+	0.993383i	$0.463362\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.28298			−0.416357
$162$		0			0
$163$	10.4053	−	10.4053i	0.815004	−	0.815004i	−0.170375	−	0.985379i	$-0.554498\pi$
$163$	10.4053	−	10.4053i	0.815004	−	0.815004i	0.985379	+	0.170375i	$0.0544981\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.95392	−	3.43750i	0.460728	−	0.266001i	−0.251622	−	0.967826i	$-0.580964\pi$
$167$	5.95392	−	3.43750i	0.460728	−	0.266001i	0.712350	+	0.701824i	$0.247631\pi$
$168$		0			0
$169$	−0.735830	−	0.424832i	−0.0566023	−	0.0326794i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.823927	−	3.07494i	−0.0626420	−	0.233783i	0.927506	−	0.373808i	$-0.121948\pi$
$173$	−0.823927	−	3.07494i	−0.0626420	−	0.233783i	−0.990148	+	0.140025i	$0.955282\pi$
$174$		0			0
$175$	2.00294	+	3.46919i	0.151408	+	0.262246i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.73648	+	3.73648i	−0.279278	+	0.279278i	−0.832821	−	0.553543i	$-0.813275\pi$
$179$	−3.73648	+	3.73648i	−0.279278	+	0.279278i	0.553543	+	0.832821i	$0.313275\pi$
$180$		0			0
$181$	0.169132	+	0.169132i	0.0125715	+	0.0125715i	0.713365	−	0.700793i	$-0.247170\pi$
$181$	0.169132	+	0.169132i	0.0125715	+	0.0125715i	−0.700793	+	0.713365i	$0.747170\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.84414	−	4.52882i	0.576713	−	0.332965i
$186$		0			0
$187$	9.76578	−	2.61673i	0.714145	−	0.191354i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0451	−	19.1306i	0.799194	−	1.38424i	−0.120947	−	0.992659i	$-0.538593\pi$
$191$	11.0451	−	19.1306i	0.799194	−	1.38424i	0.920142	−	0.391586i	$-0.128073\pi$
$192$		0			0
$193$	7.90683	+	13.6950i	0.569146	+	0.985790i	0.996651	+	0.0817767i	$0.0260594\pi$
$193$	7.90683	+	13.6950i	0.569146	+	0.985790i	−0.427505	+	0.904013i	$0.640607\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.19611	−	1.19611i	−0.0852196	−	0.0852196i	0.663212	−	0.748432i	$-0.269193\pi$
$197$	−1.19611	−	1.19611i	−0.0852196	−	0.0852196i	−0.748432	+	0.663212i	$0.769193\pi$
$198$		0			0
$199$		−	6.39170i		−	0.453095i	−0.974000	−	0.226548i	$-0.927256\pi$
$199$		−	6.39170i		−	0.453095i	0.974000	−	0.226548i	$-0.0727439\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.25628	+	4.68849i	−0.0881734	+	0.329068i
$204$		0			0
$205$	1.20523	+	4.49796i	0.0841766	+	0.314151i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.06233	+	7.03617i	−0.280997	+	0.486702i
$210$		0			0
$211$	2.01376	+	0.539586i	0.138633	+	0.0371466i	0.327468	−	0.944862i	$-0.393805\pi$
$211$	2.01376	+	0.539586i	0.138633	+	0.0371466i	−0.188835	+	0.982009i	$0.560471\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	18.1135i		−	1.23533i
$216$		0			0
$217$			1.50475i			0.102149i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	25.6149	+	6.86349i	1.72304	+	0.461688i
$222$		0			0
$223$	−13.6496	+	23.6417i	−0.914042	+	1.58317i	−0.105745	+	0.994393i	$0.533723\pi$
$223$	−13.6496	+	23.6417i	−0.914042	+	1.58317i	−0.808297	+	0.588775i	$0.799611\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.752368	−	2.80787i	−0.0499364	−	0.186365i	0.936452	−	0.350794i	$-0.114088\pi$
$227$	−0.752368	−	2.80787i	−0.0499364	−	0.186365i	−0.986389	+	0.164429i	$0.947422\pi$
$228$		0			0
$229$	1.73787	−	6.48583i	0.114842	−	0.428596i	−0.884433	−	0.466667i	$-0.845455\pi$
$229$	1.73787	−	6.48583i	0.114842	−	0.428596i	0.999275	+	0.0380710i	$0.0121213\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			11.8159i			0.774086i	0.922062	+	0.387043i	$0.126503\pi$
$233$			11.8159i			0.774086i	−0.922062	+	0.387043i	$0.873497\pi$
$234$		0			0
$235$	−18.3839	−	18.3839i	−1.19923	−	1.19923i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.75364	−	3.03739i	−0.113433	−	0.196472i	0.803719	−	0.595009i	$-0.202852\pi$
$239$	−1.75364	−	3.03739i	−0.113433	−	0.196472i	−0.917152	+	0.398537i	$0.869518\pi$
$240$		0			0
$241$	−4.35635	+	7.54543i	−0.280617	+	0.486044i	−0.971537	−	0.236888i	$-0.923873\pi$
$241$	−4.35635	+	7.54543i	−0.280617	+	0.486044i	0.690920	+	0.722932i	$0.257206\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−14.3768	+	3.85226i	−0.918502	+	0.246112i
$246$		0			0
$247$	−18.4553	+	10.6552i	−1.17428	+	0.677973i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.70213	−	9.70213i	−0.612393	−	0.612393i	0.331176	−	0.943569i	$-0.392555\pi$
$251$	−9.70213	−	9.70213i	−0.612393	−	0.612393i	−0.943569	+	0.331176i	$0.892555\pi$
$252$		0			0
$253$	3.75533	−	3.75533i	0.236096	−	0.236096i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.26857	+	16.0536i	0.578158	+	1.00140i	0.995691	+	0.0927366i	$0.0295615\pi$
$257$	9.26857	+	16.0536i	0.578158	+	1.00140i	−0.417533	+	0.908662i	$0.637105\pi$
$258$		0			0
$259$	−1.09363	−	4.08149i	−0.0679550	−	0.253611i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.42692	−	1.97853i	−0.211313	−	0.122002i	0.390608	−	0.920557i	$-0.372265\pi$
$263$	−3.42692	−	1.97853i	−0.211313	−	0.122002i	−0.601922	+	0.798555i	$0.705598\pi$
$264$		0			0
$265$	−26.8008	+	15.4734i	−1.64636	+	0.950525i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−17.6742	+	17.6742i	−1.07762	+	1.07762i	−0.0808951	+	0.996723i	$0.525778\pi$
$269$	−17.6742	+	17.6742i	−1.07762	+	1.07762i	−0.996723	+	0.0808951i	$0.974222\pi$
$270$		0			0
$271$	26.9563			1.63748			0.818738	−	0.574167i	$-0.194674\pi$
$271$	26.9563			1.63748			0.818738	+	0.574167i	$0.194674\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.88979	−	1.04226i	−0.234563	−	0.0628509i
$276$		0			0
$277$	−9.24514	+	2.47723i	−0.555487	+	0.148842i	−0.525632	−	0.850712i	$-0.676171\pi$
$277$	−9.24514	+	2.47723i	−0.555487	+	0.148842i	−0.0298548	+	0.999554i	$0.509504\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.51476	+	4.91600i	0.507948	+	0.293264i	0.731990	−	0.681316i	$-0.238592\pi$
$281$	8.51476	+	4.91600i	0.507948	+	0.293264i	−0.224042	+	0.974580i	$0.571925\pi$
$282$		0			0
$283$	−8.06496	+	30.0988i	−0.479412	+	1.78919i	0.124591	+	0.992208i	$0.460238\pi$
$283$	−8.06496	+	30.0988i	−0.479412	+	1.78919i	−0.604003	+	0.796982i	$0.706428\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.17236			0.128231
$288$		0			0
$289$	40.8774			2.40456
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.20472	−	30.6204i	0.479325	−	1.78886i	−0.125035	−	0.992152i	$-0.539904\pi$
$293$	8.20472	−	30.6204i	0.479325	−	1.78886i	0.604360	−	0.796711i	$-0.293429\pi$
$294$		0			0
$295$	−12.2202	−	7.05535i	−0.711489	−	0.410778i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	13.4553	−	3.60533i	0.778139	−	0.208502i
$300$		0			0
$301$	−8.16220	−	2.18706i	−0.470462	−	0.126060i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−29.1313			−1.66805
$306$		0			0
$307$	−17.2513	+	17.2513i	−0.984581	+	0.984581i	−0.999883	−	0.0153018i	$-0.995129\pi$
$307$	−17.2513	+	17.2513i	−0.984581	+	0.984581i	0.0153018	+	0.999883i	$0.495129\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.53625	−	4.92841i	0.484046	−	0.279464i	−0.238055	−	0.971252i	$-0.576510\pi$
$311$	8.53625	−	4.92841i	0.484046	−	0.279464i	0.722101	+	0.691787i	$0.243176\pi$
$312$		0			0
$313$	8.45774	+	4.88308i	0.478060	+	0.276008i	0.719608	−	0.694381i	$-0.244322\pi$
$313$	8.45774	+	4.88308i	0.478060	+	0.276008i	−0.241548	+	0.970389i	$0.577655\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.43237	−	12.8098i	−0.192781	−	0.719469i	−0.992830	−	0.119534i	$-0.961860\pi$
$317$	−3.43237	−	12.8098i	−0.192781	−	0.719469i	0.800049	−	0.599935i	$-0.204807\pi$
$318$		0			0
$319$	−2.43974	−	4.22576i	−0.136599	−	0.236597i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−32.8879	+	32.8879i	−1.82993	+	1.82993i
$324$		0			0
$325$	−7.46883	−	7.46883i	−0.414296	−	0.414296i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.5037	+	6.06432i	−0.579089	+	0.334337i
$330$		0			0
$331$	1.02314	−	0.274151i	0.0562371	−	0.0150687i	−0.230591	−	0.973051i	$-0.574066\pi$
$331$	1.02314	−	0.274151i	0.0562371	−	0.0150687i	0.286828	+	0.957982i	$0.407399\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−20.4299	+	35.3857i	−1.11621	+	1.93332i
$336$		0			0
$337$	−2.50387	−	4.33683i	−0.136395	−	0.236242i	0.789735	−	0.613448i	$-0.210218\pi$
$337$	−2.50387	−	4.33683i	−0.136395	−	0.236242i	−0.926129	+	0.377206i	$0.876885\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.06963	−	1.06963i	−0.0579238	−	0.0579238i
$342$		0			0
$343$			16.1974i			0.874575i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.57745	+	5.88711i	−0.0846817	+	0.316036i	−0.995254	−	0.0973140i	$-0.968975\pi$
$347$	−1.57745	+	5.88711i	−0.0846817	+	0.316036i	0.910572	+	0.413350i	$0.135642\pi$
$348$		0			0
$349$	1.45289	+	5.42227i	0.0777715	+	0.290247i	0.993847	−	0.110758i	$-0.0353277\pi$
$349$	1.45289	+	5.42227i	0.0777715	+	0.290247i	−0.916076	+	0.401005i	$0.868661\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.06146	−	8.76671i	0.269395	−	0.466605i	−0.699311	−	0.714817i	$-0.746510\pi$
$353$	5.06146	−	8.76671i	0.269395	−	0.466605i	0.968706	+	0.248212i	$0.0798431\pi$
$354$		0			0
$355$	21.5554	+	5.77576i	1.14404	+	0.306546i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	5.28081i		−	0.278710i	−0.990242	−	0.139355i	$-0.955497\pi$
$359$		−	5.28081i		−	0.278710i	0.990242	−	0.139355i	$-0.0445030\pi$
$360$		0			0
$361$		−	18.3761i		−	0.967163i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.57998	+	0.423353i	0.0826997	+	0.0221593i
$366$		0			0
$367$	−5.01941	+	8.69388i	−0.262011	+	0.453817i	−0.966776	−	0.255624i	$-0.917719\pi$
$367$	−5.01941	+	8.69388i	−0.262011	+	0.453817i	0.704765	+	0.709441i	$0.251052\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.73657	+	13.9451i	0.193993	+	0.723992i
$372$		0			0
$373$	−6.74869	+	25.1865i	−0.349434	+	1.30411i	0.537912	+	0.843001i	$0.319213\pi$
$373$	−6.74869	+	25.1865i	−0.349434	+	1.30411i	−0.887346	+	0.461105i	$0.847453\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	12.7985i		−	0.659157i
$378$		0			0
$379$	11.3259	+	11.3259i	0.581771	+	0.581771i	0.935390	−	0.353619i	$-0.115049\pi$
$379$	11.3259	+	11.3259i	0.581771	+	0.581771i	−0.353619	+	0.935390i	$0.615049\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.50076	+	4.33145i	0.127783	+	0.221327i	0.922817	−	0.385238i	$-0.125881\pi$
$383$	2.50076	+	4.33145i	0.127783	+	0.221327i	−0.795034	+	0.606564i	$0.792547\pi$
$384$		0			0
$385$	−2.48924	+	4.31148i	−0.126863	+	0.219733i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.9035	+	3.45749i	−0.654235	+	0.175302i	−0.570643	−	0.821198i	$-0.693306\pi$
$389$	−12.9035	+	3.45749i	−0.654235	+	0.175302i	−0.0835921	+	0.996500i	$0.526639\pi$
$390$		0			0
$391$	26.3294	−	15.2013i	1.33153	−	0.768761i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.87297	+	2.87297i	0.144555	+	0.144555i
$396$		0			0
$397$	−18.7165	+	18.7165i	−0.939356	+	0.939356i	−0.998263	−	0.0589078i	$-0.981238\pi$
$397$	−18.7165	+	18.7165i	−0.939356	+	0.939356i	0.0589078	+	0.998263i	$0.481238\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.66124	−	11.5376i	−0.332647	−	0.576161i	0.650383	−	0.759606i	$-0.274608\pi$
$401$	−6.66124	−	11.5376i	−0.332647	−	0.576161i	−0.983030	+	0.183445i	$0.941275\pi$
$402$		0			0
$403$	−1.02691	−	3.83247i	−0.0511538	−	0.190909i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.67866	+	2.12388i	0.182345	+	0.105277i
$408$		0			0
$409$	10.6037	−	6.12206i	0.524320	−	0.302717i	−0.214380	−	0.976750i	$-0.568773\pi$
$409$	10.6037	−	6.12206i	0.524320	−	0.302717i	0.738701	+	0.674034i	$0.235440\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.65472	+	4.65472i	−0.229044	+	0.229044i
$414$		0			0
$415$	−9.69344			−0.475832
$416$		0			0
$417$		0			0
$418$		0			0
$419$	32.0424	+	8.58573i	1.56537	+	0.419440i	0.934360	−	0.356332i	$-0.115973\pi$
$419$	32.0424	+	8.58573i	1.56537	+	0.419440i	0.631013	+	0.775772i	$0.282639\pi$
$420$		0			0
$421$	−24.7035	+	6.61930i	−1.20398	+	0.322605i	−0.804396	−	0.594093i	$-0.797511\pi$
$421$	−24.7035	+	6.61930i	−1.20398	+	0.322605i	−0.399581	+	0.916698i	$0.630844\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−19.9645	−	11.5265i	−0.968421	−	0.559118i
$426$		0			0
$427$	−3.51736	+	13.1269i	−0.170217	+	0.635258i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.3041			−0.496332			−0.248166	−	0.968717i	$-0.579828\pi$
$431$	−10.3041			−0.496332			−0.248166	+	0.968717i	$0.579828\pi$
$432$		0			0
$433$	−11.7692			−0.565591			−0.282795	−	0.959180i	$-0.591262\pi$
$433$	−11.7692			−0.565591			−0.282795	+	0.959180i	$0.591262\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.32337	+	23.5991i	−0.302488	+	1.12890i
$438$		0			0
$439$	−23.9893	−	13.8502i	−1.14494	−	0.661034i	−0.197294	−	0.980344i	$-0.563215\pi$
$439$	−23.9893	−	13.8502i	−1.14494	−	0.661034i	−0.947650	+	0.319310i	$0.896549\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−24.2836	+	6.50677i	−1.15375	+	0.309146i	−0.784466	−	0.620172i	$-0.787063\pi$
$443$	−24.2836	+	6.50677i	−1.15375	+	0.309146i	−0.369282	+	0.929317i	$0.620396\pi$
$444$		0			0
$445$	44.3739	+	11.8900i	2.10353	+	0.563638i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.0988			0.948522			0.474261	−	0.880384i	$-0.342715\pi$
$449$	20.0988			0.948522			0.474261	+	0.880384i	$0.342715\pi$
$450$		0			0
$451$	−1.54419	+	1.54419i	−0.0727133	+	0.0727133i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−11.3087	+	6.52907i	−0.530159	+	0.306088i
$456$		0			0
$457$	20.8270	+	12.0245i	0.974244	+	0.562480i	0.900527	−	0.434799i	$-0.143181\pi$
$457$	20.8270	+	12.0245i	0.974244	+	0.562480i	0.0737167	+	0.997279i	$0.476514\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.04759	−	3.90967i	−0.0487913	−	0.182092i	0.937230	−	0.348713i	$-0.113381\pi$
$461$	−1.04759	−	3.90967i	−0.0487913	−	0.182092i	−0.986021	+	0.166621i	$0.946714\pi$
$462$		0			0
$463$	−5.16489	−	8.94585i	−0.240033	−	0.415749i	0.720691	−	0.693257i	$-0.243825\pi$
$463$	−5.16489	−	8.94585i	−0.240033	−	0.415749i	−0.960723	+	0.277508i	$0.910492\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.8966	−	11.8966i	0.550509	−	0.550509i	−0.376079	−	0.926588i	$-0.622728\pi$
$467$	11.8966	−	11.8966i	0.550509	−	0.550509i	0.926588	+	0.376079i	$0.122728\pi$
$468$		0			0
$469$	13.4785	+	13.4785i	0.622380	+	0.622380i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	7.35663	−	4.24735i	0.338258	−	0.195293i
$474$		0			0
$475$	17.8943	−	4.79476i	0.821046	−	0.219999i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.47878	+	12.9536i	−0.341714	+	0.591866i	−0.984751	−	0.173969i	$-0.944341\pi$
$479$	−7.47878	+	12.9536i	−0.341714	+	0.591866i	0.643037	+	0.765835i	$0.277674\pi$
$480$		0			0
$481$	5.57077	+	9.64886i	0.254005	+	0.439950i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.60062	+	2.60062i	0.118088	+	0.118088i
$486$		0			0
$487$			27.0362i			1.22513i	0.790420	+	0.612565i	$0.209862\pi$
$487$			27.0362i			1.22513i	−0.790420	+	0.612565i	$0.790138\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.45189	+	5.41853i	−0.0655229	+	0.244535i	−0.990918	−	0.134470i	$-0.957067\pi$
$491$	−1.45189	+	5.41853i	−0.0655229	+	0.244535i	0.925395	+	0.379005i	$0.123734\pi$
$492$		0			0
$493$	−7.22964	−	26.9814i	−0.325607	−	1.21518i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.20527	−	9.01579i	0.233488	−	0.404413i
$498$		0			0
$499$	21.2035	+	5.68146i	0.949198	+	0.254337i	0.700022	−	0.714121i	$-0.253174\pi$
$499$	21.2035	+	5.68146i	0.949198	+	0.254337i	0.249176	+	0.968458i	$0.419840\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			23.1955i			1.03423i	0.855915	+	0.517117i	$0.172995\pi$
$503$			23.1955i			1.03423i	−0.855915	+	0.517117i	$0.827005\pi$
$504$		0			0
$505$		−	28.5716i		−	1.27142i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.5788	−	3.37049i	−0.557547	−	0.149394i	−0.0309681	−	0.999520i	$-0.509859\pi$
$509$	−12.5788	−	3.37049i	−0.557547	−	0.149394i	−0.526579	+	0.850126i	$0.676526\pi$
$510$		0			0
$511$	0.381537	−	0.660842i	0.0168782	−	0.0292339i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.81623	−	25.4385i	−0.300359	−	1.12095i
$516$		0			0
$517$	3.15568	−	11.7772i	0.138787	−	0.517959i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	21.4547i		−	0.939949i	−0.882680	−	0.469974i	$-0.844263\pi$
$521$		−	21.4547i		−	0.939949i	0.882680	−	0.469974i	$-0.155737\pi$
$522$		0			0
$523$	−2.07495	−	2.07495i	−0.0907314	−	0.0907314i	0.660284	−	0.751016i	$-0.270436\pi$
$523$	−2.07495	−	2.07495i	−0.0907314	−	0.0907314i	−0.751016	+	0.660284i	$0.770436\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.32977	−	7.49939i	−0.188608	−	0.326678i
$528$		0			0
$529$	−3.51490	+	6.08799i	−0.152822	+	0.264695i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.53282	+	1.48251i	−0.239653	+	0.0642148i
$534$		0			0
$535$	6.57693	−	3.79719i	0.284346	−	0.164167i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.93571	−	4.93571i	−0.212596	−	0.212596i
$540$		0			0
$541$	22.7947	−	22.7947i	0.980022	−	0.980022i	−0.0197819	−	0.999804i	$-0.506297\pi$
$541$	22.7947	−	22.7947i	0.980022	−	0.980022i	0.999804	+	0.0197819i	$0.00629719\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.2980	+	29.9610i	0.740965	+	1.28339i
$546$		0			0
$547$	3.58528	+	13.3804i	0.153295	+	0.572106i	0.999245	+	0.0388438i	$0.0123675\pi$
$547$	3.58528	+	13.3804i	0.153295	+	0.572106i	−0.845950	+	0.533262i	$0.820966\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	19.4399	+	11.2236i	0.828166	+	0.478142i
$552$		0			0
$553$	1.64148	−	0.947711i	0.0698030	−	0.0403008i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.62660	−	8.62660i	0.365521	−	0.365521i	−0.500320	−	0.865841i	$-0.666784\pi$
$557$	8.62660	−	8.62660i	0.365521	−	0.365521i	0.865841	+	0.500320i	$0.166784\pi$
$558$		0			0
$559$	22.2810			0.942384
$560$		0			0
$561$		0			0
$562$		0			0
$563$	20.3923	+	5.46409i	0.859432	+	0.230284i	0.661513	−	0.749934i	$-0.269915\pi$
$563$	20.3923	+	5.46409i	0.859432	+	0.230284i	0.197920	+	0.980218i	$0.436582\pi$
$564$		0			0
$565$	9.31636	−	2.49631i	0.391942	−	0.105021i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.4776	+	12.4001i	0.900389	+	0.519840i	0.877326	−	0.479894i	$-0.159325\pi$
$569$	21.4776	+	12.4001i	0.900389	+	0.519840i	0.0230625	+	0.999734i	$0.492658\pi$
$570$		0			0
$571$	4.74438	−	17.7063i	0.198546	−	0.740985i	−0.792774	−	0.609516i	$-0.791364\pi$
$571$	4.74438	−	17.7063i	0.198546	−	0.740985i	0.991320	−	0.131469i	$-0.0419694\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.1096			−0.505004
$576$		0			0
$577$	−23.4462			−0.976078			−0.488039	−	0.872822i	$-0.662288\pi$
$577$	−23.4462			−0.976078			−0.488039	+	0.872822i	$0.662288\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.17040	+	4.36800i	−0.0485564	+	0.181215i
$582$		0			0
$583$	−12.5688	−	7.25657i	−0.520545	−	0.300537i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.1657	+	4.33159i	−0.667230	+	0.178784i	−0.576507	−	0.817092i	$-0.695585\pi$
$587$	−16.1657	+	4.33159i	−0.667230	+	0.178784i	−0.0907235	+	0.995876i	$0.528918\pi$
$588$		0			0
$589$	6.72173	+	1.80108i	0.276964	+	0.0742123i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.18675			−0.254059			−0.127030	−	0.991899i	$-0.540544\pi$
$593$	−6.18675			−0.254059			−0.127030	+	0.991899i	$0.540544\pi$
$594$		0			0
$595$	−20.1524	+	20.1524i	−0.826168	+	0.826168i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.98730	+	4.61147i	−0.326352	+	0.188420i	−0.654220	−	0.756304i	$-0.727003\pi$
$599$	−7.98730	+	4.61147i	−0.326352	+	0.188420i	0.327868	+	0.944723i	$0.393670\pi$
$600$		0			0
$601$	15.0097	+	8.66586i	0.612259	+	0.353488i	0.773849	−	0.633370i	$-0.218329\pi$
$601$	15.0097	+	8.66586i	0.612259	+	0.353488i	−0.161590	+	0.986858i	$0.551662\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.77243	+	25.2751i	0.275339	+	1.02758i
$606$		0			0
$607$	−11.8418	−	20.5106i	−0.480643	−	0.832498i	0.519110	−	0.854707i	$-0.326263\pi$
$607$	−11.8418	−	20.5106i	−0.480643	−	0.832498i	−0.999753	+	0.0222090i	$0.992930\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	22.6135	−	22.6135i	0.914844	−	0.914844i
$612$		0			0
$613$	15.4110	+	15.4110i	0.622445	+	0.622445i	0.946156	−	0.323711i	$-0.104930\pi$
$613$	15.4110	+	15.4110i	0.622445	+	0.622445i	−0.323711	+	0.946156i	$0.604930\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.9979	+	6.92700i	−0.483018	+	0.278870i	−0.721673	−	0.692234i	$-0.756627\pi$
$617$	−11.9979	+	6.92700i	−0.483018	+	0.278870i	0.238655	+	0.971104i	$0.423293\pi$
$618$		0			0
$619$	−38.6333	+	10.3518i	−1.55280	+	0.416072i	−0.930376	−	0.366606i	$-0.880520\pi$
$619$	−38.6333	+	10.3518i	−1.55280	+	0.416072i	−0.622427	+	0.782678i	$0.713853\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.7156	−	18.5599i	0.429310	−	0.743586i
$624$		0			0
$625$	−15.4844	−	26.8198i	−0.619377	−	1.07279i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	17.1945	+	17.1945i	0.685591	+	0.685591i
$630$		0			0
$631$		−	16.7956i		−	0.668624i	−0.942462	−	0.334312i	$-0.891496\pi$
$631$		−	16.7956i		−	0.668624i	0.942462	−	0.334312i	$-0.108504\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.84688	−	14.3567i	0.152659	−	0.569730i
$636$		0			0
$637$	−4.73856	−	17.6845i	−0.187749	−	0.700687i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−20.0246	+	34.6837i	−0.790925	+	1.36992i	0.134470	+	0.990918i	$0.457067\pi$
$641$	−20.0246	+	34.6837i	−0.790925	+	1.36992i	−0.925395	+	0.379005i	$0.876266\pi$
$642$		0			0
$643$	−1.07859	−	0.289008i	−0.0425356	−	0.0113974i	0.237489	−	0.971390i	$-0.423676\pi$
$643$	−1.07859	−	0.289008i	−0.0425356	−	0.0113974i	−0.280024	+	0.959993i	$0.590342\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			31.9272i			1.25519i	0.778541	+	0.627594i	$0.215960\pi$
$647$			31.9272i			1.25519i	−0.778541	+	0.627594i	$0.784040\pi$
$648$		0			0
$649$		−	6.61750i		−	0.259759i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.5651	−	3.36682i	−0.491712	−	0.131754i	0.00443888	−	0.999990i	$-0.498587\pi$
$653$	−12.5651	−	3.36682i	−0.491712	−	0.131754i	−0.496151	+	0.868236i	$0.665254\pi$
$654$		0			0
$655$	−9.19841	+	15.9321i	−0.359412	+	0.622519i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.15007	−	15.4883i	−0.161664	−	0.603337i	−0.998442	−	0.0557954i	$-0.982231\pi$
$659$	−4.15007	−	15.4883i	−0.161664	−	0.603337i	0.836779	−	0.547541i	$-0.184436\pi$
$660$		0			0
$661$	−5.89283	+	21.9923i	−0.229204	+	0.855403i	0.751472	+	0.659765i	$0.229344\pi$
$661$	−5.89283	+	21.9923i	−0.229204	+	0.855403i	−0.980676	+	0.195637i	$0.937322\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	22.9026i		−	0.888124i
$666$		0			0
$667$	−10.3754	−	10.3754i	−0.401738	−	0.401738i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.83085	−	11.8314i	−0.263702	−	0.456745i
$672$		0			0
$673$	16.3212	−	28.2692i	0.629136	−	1.08970i	−0.358589	−	0.933496i	$-0.616742\pi$
$673$	16.3212	−	28.2692i	0.629136	−	1.08970i	0.987725	−	0.156201i	$-0.0499246\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.3681	−	3.84993i	0.552212	−	0.147965i	0.0280861	−	0.999606i	$-0.491059\pi$
$677$	14.3681	−	3.84993i	0.552212	−	0.147965i	0.524126	+	0.851641i	$0.324392\pi$
$678$		0			0
$679$	1.48588	−	0.857871i	0.0570227	−	0.0329221i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	21.4912	+	21.4912i	0.822338	+	0.822338i	0.986443	−	0.164105i	$-0.0524736\pi$
$683$	21.4912	+	21.4912i	0.822338	+	0.822338i	−0.164105	+	0.986443i	$0.552474\pi$
$684$		0			0
$685$	−14.2671	+	14.2671i	−0.545120	+	0.545120i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−19.0334	−	32.9669i	−0.725116	−	1.25594i
$690$		0			0
$691$	−2.36807	−	8.83775i	−0.0900855	−	0.336204i	0.906143	−	0.422971i	$-0.139013\pi$
$691$	−2.36807	−	8.83775i	−0.0900855	−	0.336204i	−0.996229	+	0.0867676i	$0.972346\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.3440	−	5.97209i	−0.392369	−	0.226534i
$696$		0			0
$697$	−10.8266	+	6.25077i	−0.410088	+	0.236765i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	4.05144	−	4.05144i	0.153021	−	0.153021i	−0.626445	−	0.779466i	$-0.715491\pi$
$701$	4.05144	−	4.05144i	0.153021	−	0.153021i	0.779466	+	0.626445i	$0.215491\pi$
$702$		0			0
$703$	−19.5411			−0.737005
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−12.8747	−	3.44978i	−0.484204	−	0.129742i
$708$		0			0
$709$	3.76098	−	1.00775i	0.141247	−	0.0378469i	−0.187503	−	0.982264i	$-0.560039\pi$
$709$	3.76098	−	1.00775i	0.141247	−	0.0378469i	0.328750	+	0.944417i	$0.393373\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.93936	−	2.27439i	−0.147530	−	0.0851767i
$714$		0			0
$715$	3.39752	−	12.6797i	0.127060	−	0.474195i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−37.0063			−1.38010			−0.690050	−	0.723761i	$-0.742412\pi$
$719$	−37.0063			−1.38010			−0.690050	+	0.723761i	$0.742412\pi$
$720$		0			0
$721$	−12.2859			−0.457552
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.87962	+	10.7469i	−0.106946	+	0.399129i
$726$		0			0
$727$	28.4066	+	16.4006i	1.05354	+	0.608264i	0.923640	−	0.383262i	$-0.125199\pi$
$727$	28.4066	+	16.4006i	1.05354	+	0.608264i	0.129905	+	0.991526i	$0.458533\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	46.9719	−	12.5861i	1.73732	−	0.465513i
$732$		0			0
$733$	−40.9566	−	10.9743i	−1.51277	−	0.405345i	−0.595413	−	0.803419i	$-0.703012\pi$
$733$	−40.9566	−	10.9743i	−1.51277	−	0.405345i	−0.917353	+	0.398075i	$0.869678\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−19.1620			−0.705842
$738$		0			0
$739$	15.3761	−	15.3761i	0.565620	−	0.565620i	−0.365278	−	0.930898i	$-0.619026\pi$
$739$	15.3761	−	15.3761i	0.565620	−	0.565620i	0.930898	+	0.365278i	$0.119026\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−40.4824	+	23.3725i	−1.48516	+	0.857456i	−0.999857	−	0.0168926i	$-0.994623\pi$
$743$	−40.4824	+	23.3725i	−1.48516	+	0.857456i	−0.485299	+	0.874348i	$0.661289\pi$
$744$		0			0
$745$	21.3664	+	12.3359i	0.782805	+	0.451952i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.916958	−	3.42213i	−0.0335049	−	0.125042i
$750$		0			0
$751$	−25.7074	−	44.5265i	−0.938077	−	1.62480i	−0.769054	−	0.639184i	$-0.779272\pi$
$751$	−25.7074	−	44.5265i	−0.938077	−	1.62480i	−0.169023	−	0.985612i	$-0.554061\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	41.2088	−	41.2088i	1.49974	−	1.49974i
$756$		0			0
$757$	25.4143	+	25.4143i	0.923698	+	0.923698i	0.997289	−	0.0735910i	$-0.0234459\pi$
$757$	25.4143	+	25.4143i	0.923698	+	0.923698i	−0.0735910	+	0.997289i	$0.523446\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	20.2336	−	11.6819i	0.733467	−	0.423467i	−0.0862220	−	0.996276i	$-0.527479\pi$
$761$	20.2336	−	11.6819i	0.733467	−	0.423467i	0.819689	+	0.572808i	$0.194146\pi$
$762$		0			0
$763$	15.5894	−	4.17717i	0.564375	−	0.151224i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.67859	−	15.0318i	0.313366	−	0.542765i
$768$		0			0
$769$	−12.7645	−	22.1087i	−0.460299	−	0.797261i	0.538677	−	0.842513i	$-0.318924\pi$
$769$	−12.7645	−	22.1087i	−0.460299	−	0.797261i	−0.998976	+	0.0452513i	$0.985591\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	19.2256	+	19.2256i	0.691496	+	0.691496i	0.962561	−	0.271065i	$-0.0873758\pi$
$773$	19.2256	+	19.2256i	0.691496	+	0.691496i	−0.271065	+	0.962561i	$0.587376\pi$
$774$		0			0
$775$			3.44916i			0.123898i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.60017	−	9.70397i	0.0931608	−	0.347681i
$780$		0			0
$781$	2.70866	+	10.1088i	0.0969234	+	0.361723i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	13.0680	−	22.6344i	0.466416	−	0.807857i
$786$		0			0
$787$	19.2671	+	5.16260i	0.686797	+	0.184027i	0.585309	−	0.810810i	$-0.300973\pi$
$787$	19.2671	+	5.16260i	0.686797	+	0.184027i	0.101488	+	0.994837i	$0.467640\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	4.49949i		−	0.159983i
$792$		0			0
$793$		−	35.8336i		−	1.27249i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.2772	−	3.02171i	−0.399458	−	0.107035i	0.0534965	−	0.998568i	$-0.482963\pi$
$797$	−11.2772	−	3.02171i	−0.399458	−	0.107035i	−0.452955	+	0.891534i	$0.649630\pi$
$798$		0			0
$799$	34.8990	−	60.4469i	1.23464	−	2.13846i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.198540	+	0.740961i	0.00700632	+	0.0261479i
$804$		0			0
$805$	−3.87471	+	14.4606i	−0.136565	+	0.509669i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			13.1110i			0.460958i	0.973077	+	0.230479i	$0.0740292\pi$
$809$			13.1110i			0.460958i	−0.973077	+	0.230479i	$0.925971\pi$
$810$		0			0
$811$	34.1945	+	34.1945i	1.20073	+	1.20073i	0.973944	+	0.226789i	$0.0728227\pi$
$811$	34.1945	+	34.1945i	1.20073	+	1.20073i	0.226789	+	0.973944i	$0.427177\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−20.8498	−	36.1129i	−0.730337	−	1.26498i
$816$		0			0
$817$	−19.5392	+	33.8429i	−0.683590	+	1.18401i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	23.8714	−	6.39631i	0.833116	−	0.223233i	0.183044	−	0.983105i	$-0.441405\pi$
$821$	23.8714	−	6.39631i	0.833116	−	0.223233i	0.650073	+	0.759872i	$0.274738\pi$
$822$		0			0
$823$	−16.2152	+	9.36184i	−0.565226	+	0.326333i	−0.755240	−	0.655448i	$-0.772480\pi$
$823$	−16.2152	+	9.36184i	−0.565226	+	0.326333i	0.190014	+	0.981781i	$0.439147\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.1212	−	24.1212i	−0.838775	−	0.838775i	0.149923	−	0.988698i	$-0.452098\pi$
$827$	−24.1212	−	24.1212i	−0.838775	−	0.838775i	−0.988698	+	0.149923i	$0.952098\pi$
$828$		0			0
$829$	−20.8683	+	20.8683i	−0.724787	+	0.724787i	−0.969576	−	0.244789i	$-0.921281\pi$
$829$	−20.8683	+	20.8683i	−0.724787	+	0.724787i	0.244789	+	0.969576i	$0.421281\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−19.9793	−	34.6052i	−0.692242	−	1.19900i
$834$		0			0
$835$	−5.04234	−	18.8183i	−0.174497	−	0.651233i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.01977	+	2.89816i	0.173302	+	0.100056i	0.584142	−	0.811652i	$-0.301431\pi$
$839$	5.01977	+	2.89816i	0.173302	+	0.100056i	−0.410840	+	0.911707i	$0.634765\pi$
$840$		0			0
$841$	13.4396	−	7.75936i	0.463435	−	0.267564i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.70253	+	1.70253i	−0.0585689	+	0.0585689i
$846$		0			0
$847$	12.2070			0.419437
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.3381	+	3.30600i	0.422946	+	0.113328i
$852$		0			0
$853$	1.72171	−	0.461332i	0.0589504	−	0.0157957i	−0.229223	−	0.973374i	$-0.573619\pi$
$853$	1.72171	−	0.461332i	0.0589504	−	0.0157957i	0.288174	+	0.957578i	$0.406952\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.6918	+	7.32760i	0.433543	+	0.250306i	0.700855	−	0.713304i	$-0.252802\pi$
$857$	12.6918	+	7.32760i	0.433543	+	0.250306i	−0.267312	+	0.963610i	$0.586135\pi$
$858$		0			0
$859$	−13.7688	+	51.3859i	−0.469786	+	1.75327i	0.170727	+	0.985318i	$0.445388\pi$
$859$	−13.7688	+	51.3859i	−0.469786	+	1.75327i	−0.640513	+	0.767947i	$0.721278\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	23.9467			0.815157			0.407578	−	0.913170i	$-0.366373\pi$
$863$	23.9467			0.815157			0.407578	+	0.913170i	$0.366373\pi$
$864$		0			0
$865$	−9.02103			−0.306724
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.493159	+	1.84049i	−0.0167293	+	0.0624345i
$870$		0			0
$871$	−43.5269	−	25.1303i	−1.47485	−	0.851507i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.12771	+	1.90986i	−0.240961	+	0.0645652i
$876$		0			0
$877$	−39.7266	−	10.6447i	−1.34147	−	0.359446i	−0.484492	−	0.874796i	$-0.660996\pi$
$877$	−39.7266	−	10.6447i	−1.34147	−	0.359446i	−0.856980	+	0.515349i	$0.827662\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	41.2335			1.38919			0.694597	−	0.719399i	$-0.255583\pi$
$881$	41.2335			1.38919			0.694597	+	0.719399i	$0.255583\pi$
$882$		0			0
$883$	11.9719	−	11.9719i	0.402885	−	0.402885i	−0.476364	−	0.879248i	$-0.658045\pi$
$883$	11.9719	−	11.9719i	0.402885	−	0.402885i	0.879248	+	0.476364i	$0.158045\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.7452	−	15.4413i	0.898016	−	0.518470i	0.0214599	−	0.999770i	$-0.493169\pi$
$887$	26.7452	−	15.4413i	0.898016	−	0.518470i	0.876556	+	0.481300i	$0.159835\pi$
$888$		0			0
$889$	−6.00486	−	3.46691i	−0.201397	−	0.116276i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	14.5172	+	54.1788i	0.485798	+	1.81302i
$894$		0			0
$895$	7.48706	+	12.9680i	0.250265	+	0.433471i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.95523	+	2.95523i	−0.0985624	+	0.0985624i
$900$		0			0
$901$	−58.7480	−	58.7480i	−1.95718	−	1.95718i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.586997	−	0.338903i	0.0195125	−	0.0112655i
$906$		0			0
$907$	26.7351	−	7.16365i	0.887725	−	0.237865i	0.213988	−	0.976836i	$-0.431355\pi$
$907$	26.7351	−	7.16365i	0.887725	−	0.237865i	0.673737	+	0.738971i	$0.264688\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.83009	+	8.36596i	−0.160028	+	0.277177i	−0.934878	−	0.354968i	$-0.884492\pi$
$911$	−4.83009	+	8.36596i	−0.160028	+	0.277177i	0.774850	+	0.632145i	$0.217825\pi$
$912$		0			0
$913$	−2.27297	−	3.93689i	−0.0752242	−	0.130292i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.06859	+	6.06859i	0.200403	+	0.200403i
$918$		0			0
$919$		−	12.5574i		−	0.414229i	−0.978317	−	0.207115i	$-0.933593\pi$
$919$		−	12.5574i		−	0.414229i	0.978317	−	0.207115i	$-0.0664073\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−7.10460	+	26.5147i	−0.233851	+	0.872743i
$924$		0			0
$925$	−2.50681	−	9.35553i	−0.0824233	−	0.307608i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.50031	+	7.79477i	−0.147650	+	0.255738i	−0.930359	−	0.366651i	$-0.880504\pi$
$929$	−4.50031	+	7.79477i	−0.147650	+	0.255738i	0.782708	+	0.622389i	$0.213838\pi$
$930$		0			0
$931$	31.0168	+	8.31092i	1.01653	+	0.272379i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	28.6501i		−	0.936960i
$936$		0			0
$937$			59.2265i			1.93485i	0.253166	+	0.967423i	$0.418528\pi$
$937$			59.2265i			1.93485i	−0.253166	+	0.967423i	$0.581472\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.0262	−	2.95446i	−0.359443	−	0.0963126i	0.0745778	−	0.997215i	$-0.476239\pi$
$941$	−11.0262	−	2.95446i	−0.359443	−	0.0963126i	−0.434021	+	0.900903i	$0.642906\pi$
$942$		0			0
$943$	−3.28347	+	5.68714i	−0.106925	+	0.185199i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.22949	−	8.32058i	−0.0724488	−	0.270382i	0.920194	−	0.391463i	$-0.128031\pi$
$947$	−2.22949	−	8.32058i	−0.0724488	−	0.270382i	−0.992643	+	0.121080i	$0.961364\pi$
$948$		0			0
$949$	−0.520755	+	1.94348i	−0.0169044	+	0.0630882i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	43.5260i		−	1.40995i	−0.709234	−	0.704973i	$-0.750959\pi$
$953$		−	43.5260i		−	1.40995i	0.709234	−	0.704973i	$-0.249041\pi$
$954$		0			0
$955$	−44.2637	−	44.2637i	−1.43234	−	1.43234i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.70633	+	8.15160i	0.151975	+	0.263229i
$960$		0			0
$961$	14.8522	−	25.7247i	0.479103	−	0.829830i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	43.2852	−	11.5982i	1.39340	−	0.373361i
$966$		0			0
$967$	−26.2267	+	15.1420i	−0.843393	+	0.486933i	−0.858416	−	0.512954i	$-0.828551\pi$
$967$	−26.2267	+	15.1420i	−0.843393	+	0.486933i	0.0150229	+	0.999887i	$0.495218\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.06755	+	9.06755i	0.290992	+	0.290992i	0.837472	−	0.546480i	$-0.184033\pi$
$971$	9.06755	+	9.06755i	0.290992	+	0.290992i	−0.546480	+	0.837472i	$0.684033\pi$
$972$		0			0
$973$	−3.94005	+	3.94005i	−0.126312	+	0.126312i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.4475	−	18.0956i	−0.334246	−	0.578931i	0.649094	−	0.760708i	$-0.275148\pi$
$977$	−10.4475	−	18.0956i	−0.334246	−	0.578931i	−0.983340	+	0.181778i	$0.941815\pi$
$978$		0			0
$979$	5.57603	+	20.8100i	0.178211	+	0.665092i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.14158	+	0.659092i	0.0364108	+	0.0210218i	0.518095	−	0.855323i	$-0.326641\pi$
$983$	1.14158	+	0.659092i	0.0364108	+	0.0210218i	−0.481684	+	0.876345i	$0.659975\pi$
$984$		0			0
$985$	−4.15128	+	2.39674i	−0.132271	+	0.0763665i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18.0626	−	18.0626i	0.574357	−	0.574357i
$990$		0			0
$991$	−2.51185			−0.0797914			−0.0398957	−	0.999204i	$-0.512703\pi$
$991$	−2.51185			−0.0797914			−0.0398957	+	0.999204i	$0.512703\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−17.4954	−	4.68788i	−0.554641	−	0.148616i
$996$		0			0
$997$	−44.4227	+	11.9030i	−1.40688	+	0.376973i	−0.880811	−	0.473468i	$-0.843002\pi$
$997$	−44.4227	+	11.9030i	−1.40688	+	0.376973i	−0.526071	+	0.850441i	$0.676335\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.bc.e.1585.14		72
3.2	odd	2		576.2.bb.e.241.11		72
4.3	odd	2		432.2.y.e.181.12		72
9.4	even	3	inner	1728.2.bc.e.1009.5		72
9.5	odd	6		576.2.bb.e.49.18		72
12.11	even	2		144.2.x.e.133.7	yes	72
16.3	odd	4		432.2.y.e.397.2		72
16.13	even	4	inner	1728.2.bc.e.721.5		72
36.23	even	6		144.2.x.e.85.17	yes	72
36.31	odd	6		432.2.y.e.37.2		72
48.29	odd	4		576.2.bb.e.529.18		72
48.35	even	4		144.2.x.e.61.17	yes	72
144.13	even	12	inner	1728.2.bc.e.145.14		72
144.67	odd	12		432.2.y.e.253.12		72
144.77	odd	12		576.2.bb.e.337.11		72
144.131	even	12		144.2.x.e.13.7	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.7	✓	72	144.131	even	12
144.2.x.e.61.17	yes	72	48.35	even	4
144.2.x.e.85.17	yes	72	36.23	even	6
144.2.x.e.133.7	yes	72	12.11	even	2
432.2.y.e.37.2		72	36.31	odd	6
432.2.y.e.181.12		72	4.3	odd	2
432.2.y.e.253.12		72	144.67	odd	12
432.2.y.e.397.2		72	16.3	odd	4
576.2.bb.e.49.18		72	9.5	odd	6
576.2.bb.e.241.11		72	3.2	odd	2
576.2.bb.e.337.11		72	144.77	odd	12
576.2.bb.e.529.18		72	48.29	odd	4
1728.2.bc.e.145.14		72	144.13	even	12	inner
1728.2.bc.e.721.5		72	16.13	even	4	inner
1728.2.bc.e.1009.5		72	9.4	even	3	inner
1728.2.bc.e.1585.14		72	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.733432 - 2.73721i) q^{5} +(-1.14487 - 0.660988i) q^{7} +O(q^{10})\)	\(q+(0.733432 - 2.73721i) q^{5} +(-1.14487 - 0.660988i) q^{7} +(1.28367 - 0.343957i) q^{11} +(3.36696 + 0.902174i) q^{13} +7.60772 q^{17} +(-4.32297 + 4.32297i) q^{19} +(3.46087 - 1.99814i) q^{23} +(-2.62424 - 1.51511i) q^{25} +(-0.950303 - 3.54658i) q^{29} +(-0.569129 - 0.985760i) q^{31} +(-2.64894 + 2.64894i) q^{35} +(2.26014 + 2.26014i) q^{37} +(-1.42311 + 0.821634i) q^{41} +(6.17424 - 1.65438i) q^{43} +(4.58731 - 7.94546i) q^{47} +(-2.62619 - 4.54869i) q^{49} +(-7.72215 - 7.72215i) q^{53} -3.76593i q^{55} +(1.28879 - 4.80982i) q^{59} +(-2.66068 - 9.92979i) q^{61} +(4.93887 - 8.55438i) q^{65} +(-13.9276 - 3.73189i) q^{67} +7.87498i q^{71} +0.577222i q^{73} +(-1.69698 - 0.454704i) q^{77} +(-0.716890 + 1.24169i) q^{79} +(-0.885341 - 3.30414i) q^{83} +(5.57975 - 20.8239i) q^{85} +16.2114i q^{89} +(-3.25839 - 3.25839i) q^{91} +(8.66225 + 15.0035i) q^{95} +(-0.648931 + 1.12398i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{5}+O(q^{10}) \) 72 * q - 4 * q^5	\( 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67} + 36 q^{77} - 44 q^{79} + 20 q^{83} - 8 q^{85} + 80 q^{91} + 48 q^{95} + 40 q^{97}+O(q^{100}) \) 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Introduction

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Database

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