LMFDB - Embedded newform 1728.2.bc.e.145.12

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			145.12
Character	$\chi$	$=$	1728.145
Dual form			1728.2.bc.e.1585.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.326078 + 1.21694i) q^{5} +(-0.707732 + 0.408609i) q^{7} +O(q^{10})$	$q+(0.326078 + 1.21694i) q^{5} +(-0.707732 + 0.408609i) q^{7} +(-1.85518 - 0.497094i) q^{11} +(-0.434170 + 0.116336i) q^{13} -6.62002 q^{17} +(-1.18421 - 1.18421i) q^{19} +(-2.66201 - 1.53691i) q^{23} +(2.95551 - 1.70637i) q^{25} +(2.31943 - 8.65622i) q^{29} +(4.61440 - 7.99238i) q^{31} +(-0.728028 - 0.728028i) q^{35} +(-2.14134 + 2.14134i) q^{37} +(-9.15868 - 5.28777i) q^{41} +(6.19791 + 1.66072i) q^{43} +(-0.140916 - 0.244074i) q^{47} +(-3.16608 + 5.48381i) q^{49} +(-4.83822 + 4.83822i) q^{53} -2.41973i q^{55} +(1.91804 + 7.15823i) q^{59} +(2.64688 - 9.87829i) q^{61} +(-0.283147 - 0.490424i) q^{65} +(5.22368 - 1.39968i) q^{67} -3.27174i q^{71} +4.92262i q^{73} +(1.51609 - 0.406234i) q^{77} +(-7.70232 - 13.3408i) q^{79} +(2.92711 - 10.9241i) q^{83} +(-2.15864 - 8.05616i) q^{85} -3.44143i q^{89} +(0.259740 - 0.259740i) q^{91} +(1.05497 - 1.82726i) q^{95} +(-4.46939 - 7.74121i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

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
$5$	0.326078	+	1.21694i	0.145827	+	0.544232i	0.999717	+	0.0237796i	$0.00756999\pi$
$5$	0.326078	+	1.21694i	0.145827	+	0.544232i	−0.853891	+	0.520452i	$0.825763\pi$
$6$		0			0
$7$	−0.707732	+	0.408609i	−0.267497	+	0.154440i	−0.627750	−	0.778415i	$-0.716024\pi$
$7$	−0.707732	+	0.408609i	−0.267497	+	0.154440i	0.360252	+	0.932855i	$0.382691\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.85518	−	0.497094i	−0.559357	−	0.149879i	−0.0319463	−	0.999490i	$-0.510171\pi$
$11$	−1.85518	−	0.497094i	−0.559357	−	0.149879i	−0.527411	+	0.849610i	$0.676837\pi$
$12$		0			0
$13$	−0.434170	+	0.116336i	−0.120417	+	0.0322657i	−0.318524	−	0.947915i	$-0.603187\pi$
$13$	−0.434170	+	0.116336i	−0.120417	+	0.0322657i	0.198107	+	0.980180i	$0.436521\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.62002			−1.60559			−0.802795	−	0.596255i	$-0.796655\pi$
$17$	−6.62002			−1.60559			−0.802795	+	0.596255i	$0.796655\pi$
$18$		0			0
$19$	−1.18421	−	1.18421i	−0.271677	−	0.271677i	0.558098	−	0.829775i	$-0.311531\pi$
$19$	−1.18421	−	1.18421i	−0.271677	−	0.271677i	−0.829775	+	0.558098i	$0.811531\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.66201	−	1.53691i	−0.555067	−	0.320468i	0.196096	−	0.980585i	$-0.437174\pi$
$23$	−2.66201	−	1.53691i	−0.555067	−	0.320468i	−0.751163	+	0.660117i	$0.770507\pi$
$24$		0			0
$25$	2.95551	−	1.70637i	0.591102	−	0.341273i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.31943	−	8.65622i	0.430707	−	1.60742i	−0.320430	−	0.947272i	$-0.603827\pi$
$29$	2.31943	−	8.65622i	0.430707	−	1.60742i	0.751136	−	0.660147i	$-0.229506\pi$
$30$		0			0
$31$	4.61440	−	7.99238i	0.828771	−	1.43547i	−0.0702316	−	0.997531i	$-0.522374\pi$
$31$	4.61440	−	7.99238i	0.828771	−	1.43547i	0.899003	−	0.437943i	$-0.144293\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.728028	−	0.728028i	−0.123059	−	0.123059i
$36$		0			0
$37$	−2.14134	+	2.14134i	−0.352035	+	0.352035i	−0.860866	−	0.508831i	$-0.830078\pi$
$37$	−2.14134	+	2.14134i	−0.352035	+	0.352035i	0.508831	+	0.860866i	$0.330078\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.15868	−	5.28777i	−1.43035	−	0.825810i	−0.433199	−	0.901299i	$-0.642615\pi$
$41$	−9.15868	−	5.28777i	−1.43035	−	0.825810i	−0.997147	+	0.0754884i	$0.975948\pi$
$42$		0			0
$43$	6.19791	+	1.66072i	0.945172	+	0.253258i	0.698312	−	0.715793i	$-0.253935\pi$
$43$	6.19791	+	1.66072i	0.945172	+	0.253258i	0.246860	+	0.969051i	$0.420601\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.140916	−	0.244074i	−0.0205547	−	0.0356018i	0.855565	−	0.517695i	$-0.173210\pi$
$47$	−0.140916	−	0.244074i	−0.0205547	−	0.0356018i	−0.876120	+	0.482093i	$0.839877\pi$
$48$		0			0
$49$	−3.16608	+	5.48381i	−0.452297	+	0.783401i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.83822	+	4.83822i	−0.664580	+	0.664580i	−0.956456	−	0.291876i	$-0.905721\pi$
$53$	−4.83822	+	4.83822i	−0.664580	+	0.664580i	0.291876	+	0.956456i	$0.405721\pi$
$54$		0			0
$55$		−	2.41973i		−	0.326277i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.91804	+	7.15823i	0.249708	+	0.931923i	0.970958	+	0.239248i	$0.0769010\pi$
$59$	1.91804	+	7.15823i	0.249708	+	0.931923i	−0.721251	+	0.692674i	$0.756432\pi$
$60$		0			0
$61$	2.64688	−	9.87829i	0.338898	−	1.26479i	−0.560682	−	0.828031i	$-0.689461\pi$
$61$	2.64688	−	9.87829i	0.338898	−	1.26479i	0.899581	−	0.436755i	$-0.143872\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.283147	−	0.490424i	−0.0351200	−	0.0608296i
$66$		0			0
$67$	5.22368	−	1.39968i	0.638175	−	0.170998i	0.0747982	−	0.997199i	$-0.476169\pi$
$67$	5.22368	−	1.39968i	0.638175	−	0.170998i	0.563376	+	0.826200i	$0.309502\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.27174i		−	0.388284i	−0.980973	−	0.194142i	$-0.937808\pi$
$71$		−	3.27174i		−	0.388284i	0.980973	−	0.194142i	$-0.0621922\pi$
$72$		0			0
$73$			4.92262i			0.576150i	0.957608	+	0.288075i	$0.0930152\pi$
$73$			4.92262i			0.576150i	−0.957608	+	0.288075i	$0.906985\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.51609	−	0.406234i	0.172774	−	0.0462947i
$78$		0			0
$79$	−7.70232	−	13.3408i	−0.866578	−	1.50096i	−0.865472	−	0.500958i	$-0.832981\pi$
$79$	−7.70232	−	13.3408i	−0.866578	−	1.50096i	−0.00110666	−	0.999999i	$-0.500352\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.92711	−	10.9241i	0.321292	−	1.19908i	−0.596695	−	0.802468i	$-0.703520\pi$
$83$	2.92711	−	10.9241i	0.321292	−	1.19908i	0.917987	−	0.396610i	$-0.129813\pi$
$84$		0			0
$85$	−2.15864	−	8.05616i	−0.234138	−	0.873813i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	3.44143i		−	0.364790i	−0.983225	−	0.182395i	$-0.941615\pi$
$89$		−	3.44143i		−	0.364790i	0.983225	−	0.182395i	$-0.0583850\pi$
$90$		0			0
$91$	0.259740	−	0.259740i	0.0272282	−	0.0272282i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.05497	−	1.82726i	0.108238	−	0.187473i
$96$		0			0
$97$	−4.46939	−	7.74121i	−0.453798	−	0.786001i	0.544820	−	0.838553i	$-0.316598\pi$
$97$	−4.46939	−	7.74121i	−0.453798	−	0.786001i	−0.998618	+	0.0525516i	$0.983265\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.64577	+	1.78073i	0.661278	+	0.177189i	0.573823	−	0.818979i	$-0.305460\pi$
$101$	6.64577	+	1.78073i	0.661278	+	0.177189i	0.0874556	+	0.996168i	$0.472126\pi$
$102$		0			0
$103$	5.76134	+	3.32631i	0.567681	+	0.327751i	0.756223	−	0.654314i	$-0.227043\pi$
$103$	5.76134	+	3.32631i	0.567681	+	0.327751i	−0.188541	+	0.982065i	$0.560376\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.06262	+	4.06262i	−0.392748	+	0.392748i	−0.875666	−	0.482918i	$-0.839577\pi$
$107$	−4.06262	+	4.06262i	−0.392748	+	0.392748i	0.482918	+	0.875666i	$0.339577\pi$
$108$		0			0
$109$	−7.19802	−	7.19802i	−0.689445	−	0.689445i	0.272664	−	0.962109i	$-0.412095\pi$
$109$	−7.19802	−	7.19802i	−0.689445	−	0.689445i	−0.962109	+	0.272664i	$0.912095\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.45739	+	11.1845i	−0.607460	+	1.05215i	0.384197	+	0.923251i	$0.374478\pi$
$113$	−6.45739	+	11.1845i	−0.607460	+	1.05215i	−0.991657	+	0.128901i	$0.958855\pi$
$114$		0			0
$115$	1.00231	−	3.74066i	0.0934655	−	0.348818i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.68520	−	2.70500i	0.429491	−	0.247967i
$120$		0			0
$121$	−6.33169	−	3.65560i	−0.575608	−	0.332328i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7.49458	+	7.49458i	0.670336	+	0.670336i
$126$		0			0
$127$	−14.6917			−1.30368			−0.651838	−	0.758358i	$-0.726002\pi$
$127$	−14.6917			−1.30368			−0.651838	+	0.758358i	$0.726002\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.68678	+	2.59556i	−0.846338	+	0.226775i	−0.655828	−	0.754910i	$-0.727681\pi$
$131$	−9.68678	+	2.59556i	−0.846338	+	0.226775i	−0.190509	+	0.981685i	$0.561014\pi$
$132$		0			0
$133$	1.32198	+	0.354225i	0.114631	+	0.0307152i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.37032	−	1.36850i	0.202510	−	0.116919i	−0.395316	−	0.918545i	$-0.629365\pi$
$137$	2.37032	−	1.36850i	0.202510	−	0.116919i	0.597826	+	0.801626i	$0.296031\pi$
$138$		0			0
$139$	2.26747	+	8.46230i	0.192324	+	0.717763i	0.992943	+	0.118590i	$0.0378373\pi$
$139$	2.26747	+	8.46230i	0.192324	+	0.717763i	−0.800619	+	0.599173i	$0.795496\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.863293			0.0721922
$144$		0			0
$145$	11.2904			0.937617
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.21323	−	8.25990i	−0.181315	−	0.676678i	−0.995389	−	0.0959167i	$-0.969422\pi$
$149$	−2.21323	−	8.25990i	−0.181315	−	0.676678i	0.814074	−	0.580761i	$-0.197245\pi$
$150$		0			0
$151$	−20.2738	+	11.7051i	−1.64986	+	0.952546i	−0.672732	+	0.739886i	$0.734879\pi$
$151$	−20.2738	+	11.7051i	−1.64986	+	0.952546i	−0.977126	+	0.212660i	$0.931787\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.2309	+	3.00931i	0.902087	+	0.241714i
$156$		0			0
$157$	20.9131	−	5.60365i	1.66905	−	0.447220i	0.704194	−	0.710008i	$-0.251309\pi$
$157$	20.9131	−	5.60365i	1.66905	−	0.447220i	0.964854	+	0.262788i	$0.0846419\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.51198			0.197972
$162$		0			0
$163$	−1.39858	−	1.39858i	−0.109545	−	0.109545i	0.650210	−	0.759755i	$-0.274681\pi$
$163$	−1.39858	−	1.39858i	−0.109545	−	0.109545i	−0.759755	+	0.650210i	$0.774681\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−20.0385	−	11.5692i	−1.55063	−	0.895254i	−0.998091	−	0.0617643i	$-0.980327\pi$
$167$	−20.0385	−	11.5692i	−1.55063	−	0.895254i	−0.552535	−	0.833490i	$-0.686339\pi$
$168$		0			0
$169$	−11.0834	+	6.39898i	−0.852566	+	0.492229i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.32822	−	4.95697i	0.100982	−	0.376871i	−0.896876	−	0.442282i	$-0.854169\pi$
$173$	1.32822	−	4.95697i	0.100982	−	0.376871i	0.997858	+	0.0654105i	$0.0208357\pi$
$174$		0			0
$175$	−1.39447	+	2.41530i	−0.105412	+	0.182579i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.14784	+	3.14784i	0.235281	+	0.235281i	0.814893	−	0.579612i	$-0.196796\pi$
$179$	3.14784	+	3.14784i	0.235281	+	0.235281i	−0.579612	+	0.814893i	$0.696796\pi$
$180$		0			0
$181$	−2.82816	+	2.82816i	−0.210216	+	0.210216i	−0.804359	−	0.594143i	$-0.797491\pi$
$181$	−2.82816	+	2.82816i	−0.210216	+	0.210216i	0.594143	+	0.804359i	$0.297491\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.30413	−	1.90764i	−0.242924	−	0.140253i
$186$		0			0
$187$	12.2813	+	3.29077i	0.898099	+	0.240645i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.50375	−	14.7289i	−0.615310	−	1.06575i	−0.990330	−	0.138732i	$-0.955697\pi$
$191$	−8.50375	−	14.7289i	−0.615310	−	1.06575i	0.375020	−	0.927017i	$-0.377636\pi$
$192$		0			0
$193$	−2.70970	+	4.69334i	−0.195049	+	0.337834i	−0.946916	−	0.321480i	$-0.895820\pi$
$193$	−2.70970	+	4.69334i	−0.195049	+	0.337834i	0.751868	+	0.659314i	$0.229153\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.03915	−	8.03915i	0.572766	−	0.572766i	−0.360135	−	0.932900i	$-0.617269\pi$
$197$	8.03915	−	8.03915i	0.572766	−	0.572766i	0.932900	+	0.360135i	$0.117269\pi$
$198$		0			0
$199$		−	11.2258i		−	0.795773i	−0.917435	−	0.397886i	$-0.869744\pi$
$199$		−	11.2258i		−	0.795773i	0.917435	−	0.397886i	$-0.130256\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.89548	+	7.07402i	0.133036	+	0.496499i
$204$		0			0
$205$	3.44845	−	12.8698i	0.240850	−	0.898865i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.60826	+	2.78559i	0.111246	+	0.192683i
$210$		0			0
$211$	−14.3507	+	3.84526i	−0.987942	+	0.264718i	−0.716386	−	0.697704i	$-0.754205\pi$
$211$	−14.3507	+	3.84526i	−0.987942	+	0.264718i	−0.271556	+	0.962423i	$0.587538\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			8.08400i			0.551324i
$216$		0			0
$217$			7.54195i			0.511981i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.87421	−	0.770143i	0.193340	−	0.0518054i
$222$		0			0
$223$	8.28003	+	14.3414i	0.554472	+	0.960373i	0.997944	+	0.0640854i	$0.0204130\pi$
$223$	8.28003	+	14.3414i	0.554472	+	0.960373i	−0.443473	+	0.896288i	$0.646254\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.11338	+	7.88725i	−0.140270	+	0.523495i	0.859650	+	0.510883i	$0.170681\pi$
$227$	−2.11338	+	7.88725i	−0.140270	+	0.523495i	−0.999920	+	0.0126123i	$0.995985\pi$
$228$		0			0
$229$	1.16230	+	4.33776i	0.0768068	+	0.286647i	0.993637	−	0.112631i	$-0.0359277\pi$
$229$	1.16230	+	4.33776i	0.0768068	+	0.286647i	−0.916830	+	0.399278i	$0.869261\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			7.33128i			0.480288i	0.970737	+	0.240144i	$0.0771947\pi$
$233$			7.33128i			0.480288i	−0.970737	+	0.240144i	$0.922805\pi$
$234$		0			0
$235$	0.251073	−	0.251073i	0.0163782	−	0.0163782i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.40305	−	5.89425i	0.220125	−	0.381268i	−0.734721	−	0.678370i	$-0.762687\pi$
$239$	3.40305	−	5.89425i	0.220125	−	0.381268i	0.954846	+	0.297102i	$0.0960202\pi$
$240$		0			0
$241$	2.98687	+	5.17340i	0.192401	+	0.333248i	0.946045	−	0.324034i	$-0.105039\pi$
$241$	2.98687	+	5.17340i	0.192401	+	0.333248i	−0.753644	+	0.657282i	$0.771706\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.70585	−	2.06478i	−0.492309	−	0.131914i
$246$		0			0
$247$	0.651915	+	0.376383i	0.0414804	+	0.0239487i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−16.1412	+	16.1412i	−1.01882	+	1.01882i	−0.0190030	+	0.999819i	$0.506049\pi$
$251$	−16.1412	+	16.1412i	−1.01882	+	1.01882i	−0.999819	+	0.0190030i	$0.993951\pi$
$252$		0			0
$253$	4.17451	+	4.17451i	0.262449	+	0.262449i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.172522	−	0.298817i	0.0107616	−	0.0186397i	−0.860594	−	0.509291i	$-0.829908\pi$
$257$	0.172522	−	0.298817i	0.0107616	−	0.0186397i	0.871356	+	0.490651i	$0.163241\pi$
$258$		0			0
$259$	0.640524	−	2.39047i	0.0398002	−	0.148536i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.43128	−	2.55840i	0.273244	−	0.157758i	−0.357117	−	0.934060i	$-0.616240\pi$
$263$	4.43128	−	2.55840i	0.273244	−	0.157758i	0.630361	+	0.776302i	$0.282907\pi$
$264$		0			0
$265$	−7.46546	−	4.31018i	−0.458599	−	0.264772i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.4613	+	15.4613i	0.942692	+	0.942692i	0.998445	−	0.0557529i	$-0.0177559\pi$
$269$	15.4613	+	15.4613i	0.942692	+	0.942692i	−0.0557529	+	0.998445i	$0.517756\pi$
$270$		0			0
$271$	12.4048			0.753538			0.376769	−	0.926307i	$-0.377035\pi$
$271$	12.4048			0.753538			0.376769	+	0.926307i	$0.377035\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.33123	+	1.69645i	−0.381787	+	0.102300i
$276$		0			0
$277$	20.2621	+	5.42920i	1.21743	+	0.326209i	0.809673	−	0.586881i	$-0.199644\pi$
$277$	20.2621	+	5.42920i	1.21743	+	0.326209i	0.407757	+	0.913091i	$0.366311\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.9537	−	6.32414i	0.653445	−	0.377266i	−0.136330	−	0.990663i	$-0.543531\pi$
$281$	10.9537	−	6.32414i	0.653445	−	0.377266i	0.789775	+	0.613397i	$0.210197\pi$
$282$		0			0
$283$	−5.69346	−	21.2483i	−0.338441	−	1.26308i	−0.900090	−	0.435703i	$-0.856500\pi$
$283$	−5.69346	−	21.2483i	−0.338441	−	1.26308i	0.561650	−	0.827375i	$-0.310167\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.64252			0.510152
$288$		0			0
$289$	26.8246			1.57792
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.0299075	−	0.111616i	−0.00174721	−	0.00652069i	0.965047	−	0.262078i	$-0.0844077\pi$
$293$	−0.0299075	−	0.111616i	−0.00174721	−	0.00652069i	−0.966794	+	0.255557i	$0.917741\pi$
$294$		0			0
$295$	−8.08571	+	4.66828i	−0.470768	+	0.271798i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.33456	+	0.357595i	0.0771797	+	0.0206802i
$300$		0			0
$301$	−5.06504	+	1.35717i	−0.291944	+	0.0782262i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.8844			0.737757
$306$		0			0
$307$	12.4426	+	12.4426i	0.710135	+	0.710135i	0.966563	−	0.256428i	$-0.0825456\pi$
$307$	12.4426	+	12.4426i	0.710135	+	0.710135i	−0.256428	+	0.966563i	$0.582546\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.03115	+	1.17269i	0.115176	+	0.0664969i	0.556481	−	0.830860i	$-0.312151\pi$
$311$	2.03115	+	1.17269i	0.115176	+	0.0664969i	−0.441305	+	0.897357i	$0.645484\pi$
$312$		0			0
$313$	−8.62293	+	4.97845i	−0.487397	+	0.281399i	−0.723494	−	0.690331i	$-0.757465\pi$
$313$	−8.62293	+	4.97845i	−0.487397	+	0.281399i	0.236097	+	0.971729i	$0.424132\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.18698	−	4.42985i	0.0666672	−	0.248805i	−0.924548	−	0.381066i	$-0.875557\pi$
$317$	1.18698	−	4.42985i	0.0666672	−	0.248805i	0.991215	+	0.132261i	$0.0422236\pi$
$318$		0			0
$319$	−8.60590	+	14.9059i	−0.481838	+	0.834568i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	7.83950	+	7.83950i	0.436202	+	0.436202i
$324$		0			0
$325$	−1.08468	+	1.08468i	−0.0601674	+	0.0601674i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.199461	+	0.115159i	0.0109967	+	0.00634892i
$330$		0			0
$331$	16.7743	+	4.49465i	0.921997	+	0.247048i	0.688439	−	0.725294i	$-0.258296\pi$
$331$	16.7743	+	4.49465i	0.921997	+	0.247048i	0.233558	+	0.972343i	$0.424963\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.40666	+	5.90050i	0.186126	+	0.322379i
$336$		0			0
$337$	−14.8424	+	25.7078i	−0.808517	+	1.40039i	0.105375	+	0.994433i	$0.466396\pi$
$337$	−14.8424	+	25.7078i	−0.808517	+	1.40039i	−0.913891	+	0.405959i	$0.866937\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.5335	+	12.5335i	−0.678727	+	0.678727i
$342$		0			0
$343$		−	10.8953i		−	0.588290i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.520318	−	1.94185i	−0.0279321	−	0.104244i	0.950552	−	0.310564i	$-0.100518\pi$
$347$	−0.520318	−	1.94185i	−0.0279321	−	0.104244i	−0.978485	+	0.206320i	$0.933851\pi$
$348$		0			0
$349$	−7.13604	+	26.6321i	−0.381984	+	1.42558i	0.460883	+	0.887461i	$0.347533\pi$
$349$	−7.13604	+	26.6321i	−0.381984	+	1.42558i	−0.842867	+	0.538122i	$0.819134\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.58657	−	2.74801i	−0.0844444	−	0.146262i	0.820710	−	0.571345i	$-0.193578\pi$
$353$	−1.58657	−	2.74801i	−0.0844444	−	0.146262i	−0.905154	+	0.425083i	$0.860245\pi$
$354$		0			0
$355$	3.98150	−	1.06684i	0.211316	−	0.0566220i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			22.6997i			1.19804i	0.800732	+	0.599022i	$0.204444\pi$
$359$			22.6997i			1.19804i	−0.800732	+	0.599022i	$0.795556\pi$
$360$		0			0
$361$		−	16.1953i		−	0.852383i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.99054	+	1.60516i	−0.313559	+	0.0840179i
$366$		0			0
$367$	1.94141	+	3.36261i	0.101341	+	0.175527i	0.912237	−	0.409662i	$-0.134354\pi$
$367$	1.94141	+	3.36261i	0.101341	+	0.175527i	−0.810897	+	0.585189i	$0.801020\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.44722	−	5.40110i	0.0751359	−	0.280411i
$372$		0			0
$373$	−1.16873	−	4.36176i	−0.0605145	−	0.225843i	0.929045	−	0.369966i	$-0.120631\pi$
$373$	−1.16873	−	4.36176i	−0.0605145	−	0.225843i	−0.989560	+	0.144123i	$0.953964\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			4.02810i			0.207458i
$378$		0			0
$379$	−14.6109	+	14.6109i	−0.750509	+	0.750509i	−0.974574	−	0.224065i	$-0.928067\pi$
$379$	−14.6109	+	14.6109i	−0.750509	+	0.750509i	0.224065	+	0.974574i	$0.428067\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.4164	−	24.9699i	0.736643	−	1.27590i	−0.217355	−	0.976093i	$-0.569743\pi$
$383$	14.4164	−	24.9699i	0.736643	−	1.27590i	0.953999	−	0.299811i	$-0.0969236\pi$
$384$		0			0
$385$	0.988724	+	1.71252i	0.0503901	+	0.0872781i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.190429	+	0.0510254i	0.00965514	+	0.00258709i	0.263643	−	0.964620i	$-0.415076\pi$
$389$	0.190429	+	0.0510254i	0.00965514	+	0.00258709i	−0.253988	+	0.967207i	$0.581742\pi$
$390$		0			0
$391$	17.6225	+	10.1744i	0.891210	+	0.514540i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	13.7234	−	13.7234i	0.690499	−	0.690499i
$396$		0			0
$397$	−9.98504	−	9.98504i	−0.501135	−	0.501135i	0.410656	−	0.911791i	$-0.365300\pi$
$397$	−9.98504	−	9.98504i	−0.501135	−	0.501135i	−0.911791	+	0.410656i	$0.865300\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.396741	+	0.687175i	−0.0198123	+	0.0343159i	−0.875762	−	0.482744i	$-0.839640\pi$
$401$	−0.396741	+	0.687175i	−0.0198123	+	0.0343159i	0.855949	+	0.517060i	$0.172974\pi$
$402$		0			0
$403$	−1.07364	+	4.00687i	−0.0534817	+	0.199596i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.03702	−	2.90813i	0.249676	−	0.144150i
$408$		0			0
$409$	0.225551	+	0.130222i	0.0111528	+	0.00643907i	0.505566	−	0.862788i	$-0.331284\pi$
$409$	0.225551	+	0.130222i	0.0111528	+	0.00643907i	−0.494413	+	0.869227i	$0.664617\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.28238	−	4.28238i	−0.210722	−	0.210722i
$414$		0			0
$415$	14.2485			0.699429
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.67732	−	0.985334i	0.179649	−	0.0481367i	−0.167873	−	0.985809i	$-0.553690\pi$
$419$	3.67732	−	0.985334i	0.179649	−	0.0481367i	0.347522	+	0.937672i	$0.387023\pi$
$420$		0			0
$421$	0.779608	+	0.208895i	0.0379958	+	0.0101809i	0.277767	−	0.960649i	$-0.410406\pi$
$421$	0.779608	+	0.208895i	0.0379958	+	0.0101809i	−0.239771	+	0.970829i	$0.577072\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−19.5655	+	11.2962i	−0.949068	+	0.547945i
$426$		0			0
$427$	2.16308	+	8.07272i	0.104679	+	0.390666i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	25.6515			1.23559			0.617796	−	0.786339i	$-0.288026\pi$
$431$	25.6515			1.23559			0.617796	+	0.786339i	$0.288026\pi$
$432$		0			0
$433$	−23.0987			−1.11005			−0.555026	−	0.831833i	$-0.687292\pi$
$433$	−23.0987			−1.11005			−0.555026	+	0.831833i	$0.687292\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.33235	+	4.97241i	0.0637351	+	0.237863i
$438$		0			0
$439$	−7.88493	+	4.55237i	−0.376327	+	0.217273i	−0.676219	−	0.736701i	$-0.736383\pi$
$439$	−7.88493	+	4.55237i	−0.376327	+	0.217273i	0.299892	+	0.953973i	$0.403049\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	27.2979	+	7.31445i	1.29696	+	0.347520i	0.840301	−	0.542120i	$-0.182378\pi$
$443$	27.2979	+	7.31445i	1.29696	+	0.347520i	0.456662	+	0.889640i	$0.349045\pi$
$444$		0			0
$445$	4.18801	−	1.12217i	0.198531	−	0.0531961i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−5.90915			−0.278870			−0.139435	−	0.990231i	$-0.544529\pi$
$449$	−5.90915			−0.278870			−0.139435	+	0.990231i	$0.544529\pi$
$450$		0			0
$451$	14.3625	+	14.3625i	0.676302	+	0.676302i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.400784	+	0.231393i	0.0187890	+	0.0108478i
$456$		0			0
$457$	4.70096	−	2.71410i	0.219902	−	0.126960i	−0.386003	−	0.922497i	$-0.626145\pi$
$457$	4.70096	−	2.71410i	0.219902	−	0.126960i	0.605905	+	0.795537i	$0.292811\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.74777	+	25.1830i	−0.314275	+	1.17289i	0.610388	+	0.792103i	$0.291014\pi$
$461$	−6.74777	+	25.1830i	−0.314275	+	1.17289i	−0.924663	+	0.380787i	$0.875653\pi$
$462$		0			0
$463$	9.87708	−	17.1076i	0.459027	−	0.795057i	−0.539883	−	0.841740i	$-0.681532\pi$
$463$	9.87708	−	17.1076i	0.459027	−	0.795057i	0.998910	+	0.0466825i	$0.0148649\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.1348	+	16.1348i	0.746628	+	0.746628i	0.973844	−	0.227217i	$-0.0729625\pi$
$467$	16.1348	+	16.1348i	0.746628	+	0.746628i	−0.227217	+	0.973844i	$0.572963\pi$
$468$		0			0
$469$	−3.12504	+	3.12504i	−0.144301	+	0.144301i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.6727	−	6.16188i	−0.490731	−	0.283324i
$474$		0			0
$475$	−5.52065	−	1.47925i	−0.253305	−	0.0678728i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.1996	+	19.3982i	0.511721	+	0.886327i	0.999908	+	0.0135877i	$0.00432523\pi$
$479$	11.1996	+	19.3982i	0.511721	+	0.886327i	−0.488187	+	0.872739i	$0.662341\pi$
$480$		0			0
$481$	0.680593	−	1.17882i	0.0310324	−	0.0537496i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.96322	−	7.96322i	0.361591	−	0.361591i
$486$		0			0
$487$			8.27717i			0.375074i	0.982258	+	0.187537i	$0.0600505\pi$
$487$			8.27717i			0.375074i	−0.982258	+	0.187537i	$0.939950\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.31362	−	34.7589i	−0.420318	−	1.56865i	−0.773940	−	0.633259i	$-0.781717\pi$
$491$	−9.31362	−	34.7589i	−0.420318	−	1.56865i	0.353622	−	0.935388i	$-0.384950\pi$
$492$		0			0
$493$	−15.3546	+	57.3043i	−0.691538	+	2.58086i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.33686	+	2.31551i	0.0599664	+	0.103865i
$498$		0			0
$499$	−27.7862	+	7.44528i	−1.24388	+	0.333297i	−0.819969	−	0.572407i	$-0.806010\pi$
$499$	−27.7862	+	7.44528i	−1.24388	+	0.333297i	−0.423911	+	0.905704i	$0.639343\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	15.6106i		−	0.696044i	−0.937486	−	0.348022i	$-0.886854\pi$
$503$		−	15.6106i		−	0.696044i	0.937486	−	0.348022i	$-0.113146\pi$
$504$		0			0
$505$			8.66815i			0.385728i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.92195	−	2.65858i	0.439783	−	0.117839i	−0.0321319	−	0.999484i	$-0.510230\pi$
$509$	9.92195	−	2.65858i	0.439783	−	0.117839i	0.471915	+	0.881644i	$0.343563\pi$
$510$		0			0
$511$	−2.01143	−	3.48390i	−0.0889804	−	0.154119i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.16927	+	8.09583i	−0.0955896	+	0.356745i
$516$		0			0
$517$	0.140097	+	0.522849i	0.00616145	+	0.0229949i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			21.2775i			0.932185i	0.884736	+	0.466092i	$0.154339\pi$
$521$			21.2775i			0.932185i	−0.884736	+	0.466092i	$0.845661\pi$
$522$		0			0
$523$	2.96994	−	2.96994i	0.129867	−	0.129867i	−0.639186	−	0.769052i	$-0.720729\pi$
$523$	2.96994	−	2.96994i	0.129867	−	0.129867i	0.769052	+	0.639186i	$0.220729\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−30.5474	+	52.9097i	−1.33067	+	2.30478i
$528$		0			0
$529$	−6.77581	−	11.7360i	−0.294600	−	0.510263i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.59158	+	1.23031i	0.198883	+	0.0532906i
$534$		0			0
$535$	−6.26869	−	3.61923i	−0.271019	−	0.156473i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	8.59960	−	8.59960i	0.370411	−	0.370411i
$540$		0			0
$541$	−15.1934	−	15.1934i	−0.653214	−	0.653214i	0.300552	−	0.953765i	$-0.402829\pi$
$541$	−15.1934	−	15.1934i	−0.653214	−	0.653214i	−0.953765	+	0.300552i	$0.902829\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.41244	−	11.1067i	0.274679	−	0.475757i
$546$		0			0
$547$	9.00771	−	33.6172i	0.385142	−	1.43737i	−0.452802	−	0.891611i	$-0.649575\pi$
$547$	9.00771	−	33.6172i	0.385142	−	1.43737i	0.837943	−	0.545757i	$-0.183758\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.9975	+	7.50410i	−0.553712	+	0.319686i
$552$		0			0
$553$	10.9023	+	6.29447i	0.463615	+	0.267668i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.3686	−	15.3686i	−0.651189	−	0.651189i	0.302091	−	0.953279i	$-0.402315\pi$
$557$	−15.3686	−	15.3686i	−0.651189	−	0.651189i	−0.953279	+	0.302091i	$0.902315\pi$
$558$		0			0
$559$	−2.88415			−0.121986
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.3701	−	4.11840i	0.647772	−	0.173570i	0.0800506	−	0.996791i	$-0.474492\pi$
$563$	15.3701	−	4.11840i	0.647772	−	0.173570i	0.567721	+	0.823221i	$0.307825\pi$
$564$		0			0
$565$	−15.7165	−	4.21123i	−0.661199	−	0.177168i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	36.4673	−	21.0544i	1.52879	−	0.882647i	0.529376	−	0.848387i	$-0.322426\pi$
$569$	36.4673	−	21.0544i	1.52879	−	0.882647i	0.999413	−	0.0342597i	$-0.0109073\pi$
$570$		0			0
$571$	−10.1418	−	37.8497i	−0.424421	−	1.58396i	−0.765183	−	0.643813i	$-0.777352\pi$
$571$	−10.1418	−	37.8497i	−0.424421	−	1.58396i	0.340762	−	0.940150i	$-0.389315\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−10.4901			−0.437469
$576$		0			0
$577$	13.5220			0.562927			0.281463	−	0.959572i	$-0.409180\pi$
$577$	13.5220			0.562927			0.281463	+	0.959572i	$0.409180\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.39209	+	8.92739i	0.0992405	+	0.370371i
$582$		0			0
$583$	11.3808	−	6.57071i	0.471345	−	0.272131i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−31.0793	−	8.32769i	−1.28278	−	0.343720i	−0.447867	−	0.894100i	$-0.647816\pi$
$587$	−31.0793	−	8.32769i	−1.28278	−	0.343720i	−0.834915	+	0.550380i	$0.814483\pi$
$588$		0			0
$589$	−14.9291	+	4.00024i	−0.615143	+	0.164827i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	24.2071			0.994066			0.497033	−	0.867732i	$-0.334423\pi$
$593$	24.2071			0.994066			0.497033	+	0.867732i	$0.334423\pi$
$594$		0			0
$595$	4.81956	+	4.81956i	0.197583	+	0.197583i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	33.5549	+	19.3729i	1.37102	+	0.791557i	0.991056	−	0.133445i	$-0.0426041\pi$
$599$	33.5549	+	19.3729i	1.37102	+	0.791557i	0.379961	+	0.925003i	$0.375937\pi$
$600$		0			0
$601$	21.4630	−	12.3917i	0.875493	−	0.505466i	0.00632336	−	0.999980i	$-0.497987\pi$
$601$	21.4630	−	12.3917i	0.875493	−	0.505466i	0.869170	+	0.494514i	$0.164654\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.38402	−	8.89730i	0.0969244	−	0.361727i
$606$		0			0
$607$	−5.85399	+	10.1394i	−0.237606	+	0.411546i	−0.960027	−	0.279908i	$-0.909696\pi$
$607$	−5.85399	+	10.1394i	−0.237606	+	0.411546i	0.722421	+	0.691454i	$0.243029\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0895759	+	0.0895759i	0.00362385	+	0.00362385i
$612$		0			0
$613$	−24.6378	+	24.6378i	−0.995112	+	0.995112i	−0.999988	−	0.00487577i	$-0.998448\pi$
$613$	−24.6378	+	24.6378i	−0.995112	+	0.995112i	0.00487577	+	0.999988i	$0.498448\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.72698	+	2.72912i	0.190301	+	0.109870i	0.592123	−	0.805847i	$-0.298290\pi$
$617$	4.72698	+	2.72912i	0.190301	+	0.109870i	−0.401822	+	0.915718i	$0.631623\pi$
$618$		0			0
$619$	−16.5475	−	4.43389i	−0.665101	−	0.178213i	−0.0895538	−	0.995982i	$-0.528544\pi$
$619$	−16.5475	−	4.43389i	−0.665101	−	0.178213i	−0.575547	+	0.817769i	$0.695211\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.40620	+	2.43561i	0.0563381	+	0.0975805i
$624$		0			0
$625$	1.85520	−	3.21329i	0.0742078	−	0.128532i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	14.1757	−	14.1757i	0.565223	−	0.565223i
$630$		0			0
$631$		−	5.04281i		−	0.200751i	−0.994950	−	0.100376i	$-0.967996\pi$
$631$		−	5.04281i		−	0.200751i	0.994950	−	0.100376i	$-0.0320045\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.79063	−	17.8789i	−0.190111	−	0.709502i
$636$		0			0
$637$	0.736654	−	2.74923i	0.0291873	−	0.108929i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.2406	−	17.7373i	−0.404480	−	0.700579i	0.589781	−	0.807563i	$-0.299214\pi$
$641$	−10.2406	−	17.7373i	−0.404480	−	0.700579i	−0.994261	+	0.106984i	$0.965881\pi$
$642$		0			0
$643$	−40.2059	+	10.7731i	−1.58557	+	0.424851i	−0.940643	−	0.339397i	$-0.889777\pi$
$643$	−40.2059	+	10.7731i	−1.58557	+	0.424851i	−0.644922	+	0.764248i	$0.723110\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	9.07428i		−	0.356747i	−0.983963	−	0.178373i	$-0.942917\pi$
$647$		−	9.07428i		−	0.356747i	0.983963	−	0.178373i	$-0.0570835\pi$
$648$		0			0
$649$		−	14.2332i		−	0.558704i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−30.0514	+	8.05224i	−1.17600	+	0.315109i	−0.793339	−	0.608780i	$-0.791659\pi$
$653$	−30.0514	+	8.05224i	−1.17600	+	0.315109i	−0.382662	+	0.923888i	$0.624993\pi$
$654$		0			0
$655$	−6.31729	−	10.9419i	−0.246837	−	0.427534i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.30479	−	12.3336i	0.128736	−	0.480450i	−0.871209	−	0.490912i	$-0.836664\pi$
$659$	3.30479	−	12.3336i	0.128736	−	0.480450i	0.999945	+	0.0104620i	$0.00333022\pi$
$660$		0			0
$661$	−11.4466	−	42.7191i	−0.445219	−	1.66158i	−0.715357	−	0.698759i	$-0.753736\pi$
$661$	−11.4466	−	42.7191i	−0.445219	−	1.66158i	0.270137	−	0.962822i	$-0.412931\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			1.72428i			0.0668647i
$666$		0			0
$667$	−19.4782	+	19.4782i	−0.754198	+	0.754198i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.82087	+	17.0102i	−0.379131	+	0.656673i
$672$		0			0
$673$	−16.9683	−	29.3899i	−0.654079	−	1.13290i	−0.982124	−	0.188236i	$-0.939723\pi$
$673$	−16.9683	−	29.3899i	−0.654079	−	1.13290i	0.328045	−	0.944662i	$-0.393610\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	39.9599	+	10.7072i	1.53578	+	0.411512i	0.924900	−	0.380210i	$-0.124148\pi$
$677$	39.9599	+	10.7072i	1.53578	+	0.411512i	0.610882	+	0.791721i	$0.290815\pi$
$678$		0			0
$679$	6.32626	+	3.65247i	0.242780	+	0.140169i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.0872426	−	0.0872426i	0.00333824	−	0.00333824i	−0.705436	−	0.708774i	$-0.749249\pi$
$683$	0.0872426	−	0.0872426i	0.00333824	−	0.00333824i	0.708774	+	0.705436i	$0.249249\pi$
$684$		0			0
$685$	2.43830	+	2.43830i	0.0931625	+	0.0931625i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.53775	−	2.66347i	0.0585837	−	0.101470i
$690$		0			0
$691$	−3.62594	+	13.5322i	−0.137937	+	0.514789i	0.862031	+	0.506855i	$0.169192\pi$
$691$	−3.62594	+	13.5322i	−0.137937	+	0.514789i	−0.999969	+	0.00793395i	$0.997475\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.55874	+	5.51874i	−0.362584	+	0.209338i
$696$		0			0
$697$	60.6306	+	35.0051i	2.29655	+	1.32591i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−10.7257	−	10.7257i	−0.405103	−	0.405103i	0.474924	−	0.880027i	$-0.342475\pi$
$701$	−10.7257	−	10.7257i	−0.405103	−	0.405103i	−0.880027	+	0.474924i	$0.842475\pi$
$702$		0			0
$703$	5.07161			0.191279
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.43104	+	1.45524i	−0.204255	+	0.0547300i
$708$		0			0
$709$	39.9633	+	10.7081i	1.50085	+	0.402153i	0.913386	−	0.407095i	$-0.133458\pi$
$709$	39.9633	+	10.7081i	1.50085	+	0.402153i	0.587468	+	0.809247i	$0.300125\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−24.5671	+	14.1839i	−0.920047	+	0.531189i
$714$		0			0
$715$	0.281501	+	1.05057i	0.0105275	+	0.0392893i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−34.2734			−1.27818			−0.639091	−	0.769131i	$-0.720689\pi$
$719$	−34.2734			−1.27818			−0.639091	+	0.769131i	$0.720689\pi$
$720$		0			0
$721$	−5.43664			−0.202471
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.91558	−	29.5413i	−0.293977	−	1.09714i
$726$		0			0
$727$	28.8380	−	16.6496i	1.06954	−	0.617501i	0.141487	−	0.989940i	$-0.454812\pi$
$727$	28.8380	−	16.6496i	1.06954	−	0.617501i	0.928057	+	0.372439i	$0.121478\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−41.0302	−	10.9940i	−1.51756	−	0.406629i
$732$		0			0
$733$	36.2382	−	9.71001i	1.33849	−	0.358647i	0.482616	−	0.875832i	$-0.339687\pi$
$733$	36.2382	−	9.71001i	1.33849	−	0.358647i	0.855874	+	0.517185i	$0.173020\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.3866			−0.382597
$738$		0			0
$739$	8.57380	+	8.57380i	0.315392	+	0.315392i	0.846994	−	0.531602i	$-0.178410\pi$
$739$	8.57380	+	8.57380i	0.315392	+	0.315392i	−0.531602	+	0.846994i	$0.678410\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.3476	+	5.97418i	0.379616	+	0.219172i	0.677651	−	0.735383i	$-0.262998\pi$
$743$	10.3476	+	5.97418i	0.379616	+	0.219172i	−0.298035	+	0.954555i	$0.596331\pi$
$744$		0			0
$745$	9.33012	−	5.38674i	0.341829	−	0.197355i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.21522	−	4.53526i	0.0444032	−	0.165715i
$750$		0			0
$751$	−12.2293	+	21.1818i	−0.446254	+	0.772934i	−0.998139	−	0.0609863i	$-0.980575\pi$
$751$	−12.2293	+	21.1818i	−0.446254	+	0.772934i	0.551885	+	0.833920i	$0.313909\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−20.8552	−	20.8552i	−0.758999	−	0.758999i
$756$		0			0
$757$	5.77221	−	5.77221i	0.209794	−	0.209794i	−0.594386	−	0.804180i	$-0.702605\pi$
$757$	5.77221	−	5.77221i	0.209794	−	0.209794i	0.804180	+	0.594386i	$0.202605\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	35.8368	+	20.6904i	1.29908	+	0.750025i	0.980246	−	0.197784i	$-0.0633746\pi$
$761$	35.8368	+	20.6904i	1.29908	+	0.750025i	0.318836	+	0.947810i	$0.396708\pi$
$762$		0			0
$763$	8.03544	+	2.15309i	0.290902	+	0.0779471i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.66551	−	2.88475i	−0.0601382	−	0.104162i
$768$		0			0
$769$	19.7893	−	34.2761i	0.713622	−	1.23603i	−0.249867	−	0.968280i	$-0.580387\pi$
$769$	19.7893	−	34.2761i	0.713622	−	1.23603i	0.963489	−	0.267749i	$-0.0862798\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−34.1627	+	34.1627i	−1.22875	+	1.22875i	−0.264307	+	0.964439i	$0.585143\pi$
$773$	−34.1627	+	34.1627i	−1.22875	+	1.22875i	−0.964439	+	0.264307i	$0.914857\pi$
$774$		0			0
$775$		−	31.4954i		−	1.13135i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.58398	+	17.1076i	0.164238	+	0.612945i
$780$		0			0
$781$	−1.62636	+	6.06965i	−0.0581957	+	0.217189i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	13.6386	+	23.6228i	0.486783	+	0.843132i
$786$		0			0
$787$	37.6477	−	10.0877i	1.34199	−	0.359586i	0.484820	−	0.874614i	$-0.338885\pi$
$787$	37.6477	−	10.0877i	1.34199	−	0.359586i	0.857174	+	0.515028i	$0.172218\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	10.5542i		−	0.375264i
$792$		0			0
$793$			4.59678i			0.163237i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.74952	−	0.736732i	0.0973931	−	0.0260964i	−0.209793	−	0.977746i	$-0.567279\pi$
$797$	2.74952	−	0.736732i	0.0973931	−	0.0260964i	0.307186	+	0.951649i	$0.400612\pi$
$798$		0			0
$799$	0.932866	+	1.61577i	0.0330024	+	0.0571619i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.44701	−	9.13235i	0.0863529	−	0.322274i
$804$		0			0
$805$	0.819102	+	3.05693i	0.0288696	+	0.107743i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	14.8679i		−	0.522727i	−0.965240	−	0.261364i	$-0.915828\pi$
$809$		−	14.8679i		−	0.522727i	0.965240	−	0.261364i	$-0.0841722\pi$
$810$		0			0
$811$	−11.8984	+	11.8984i	−0.417808	+	0.417808i	−0.884447	−	0.466640i	$-0.845464\pi$
$811$	−11.8984	+	11.8984i	−0.417808	+	0.417808i	0.466640	+	0.884447i	$0.345464\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.24594	−	2.15803i	0.0436433	−	0.0755925i
$816$		0			0
$817$	−5.37299	−	9.30628i	−0.187977	−	0.325586i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−48.7927	−	13.0740i	−1.70288	−	0.456285i	−0.729216	−	0.684283i	$-0.760115\pi$
$821$	−48.7927	−	13.0740i	−1.70288	−	0.456285i	−0.973661	+	0.227999i	$0.926782\pi$
$822$		0			0
$823$	14.3773	+	8.30076i	0.501163	+	0.289346i	0.729194	−	0.684307i	$-0.239895\pi$
$823$	14.3773	+	8.30076i	0.501163	+	0.289346i	−0.228031	+	0.973654i	$0.573229\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	19.8935	−	19.8935i	0.691764	−	0.691764i	−0.270856	−	0.962620i	$-0.587307\pi$
$827$	19.8935	−	19.8935i	0.691764	−	0.691764i	0.962620	+	0.270856i	$0.0873067\pi$
$828$		0			0
$829$	4.51982	+	4.51982i	0.156980	+	0.156980i	0.781227	−	0.624247i	$-0.214594\pi$
$829$	4.51982	+	4.51982i	0.156980	+	0.156980i	−0.624247	+	0.781227i	$0.714594\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	20.9595	−	36.3029i	0.726203	−	1.25782i
$834$		0			0
$835$	7.54494	−	28.1581i	0.261104	−	0.974452i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.34046	−	3.08332i	0.184373	−	0.106448i	−0.404972	−	0.914329i	$-0.632719\pi$
$839$	5.34046	−	3.08332i	0.184373	−	0.106448i	0.589346	+	0.807881i	$0.299386\pi$
$840$		0			0
$841$	−44.4356	−	25.6549i	−1.53226	−	0.884653i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−11.4012	−	11.4012i	−0.392214	−	0.392214i
$846$		0			0
$847$	5.97485			0.205298
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8.99133	−	2.40922i	0.308219	−	0.0825869i
$852$		0			0
$853$	−28.9503	−	7.75721i	−0.991240	−	0.265602i	−0.273468	−	0.961881i	$-0.588171\pi$
$853$	−28.9503	−	7.75721i	−0.991240	−	0.265602i	−0.717771	+	0.696279i	$0.754838\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.97997	+	1.14314i	−0.0676345	+	0.0390488i	−0.533436	−	0.845840i	$-0.679099\pi$
$857$	−1.97997	+	1.14314i	−0.0676345	+	0.0390488i	0.465801	+	0.884889i	$0.345766\pi$
$858$		0			0
$859$	3.73966	+	13.9566i	0.127595	+	0.476193i	0.999919	−	0.0127366i	$-0.00405431\pi$
$859$	3.73966	+	13.9566i	0.127595	+	0.476193i	−0.872323	+	0.488929i	$0.837388\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−47.8654			−1.62936			−0.814678	−	0.579913i	$-0.803087\pi$
$863$	−47.8654			−1.62936			−0.814678	+	0.579913i	$0.803087\pi$
$864$		0			0
$865$	6.46544			0.219831
$866$		0			0
$867$		0			0
$868$		0			0
$869$	7.65754	+	28.5783i	0.259764	+	0.969454i
$870$		0			0
$871$	−2.10513	+	1.21540i	−0.0713298	+	0.0411823i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.36650	−	2.24180i	−0.282839	−	0.0757866i
$876$		0			0
$877$	−7.69500	+	2.06187i	−0.259842	+	0.0696244i	−0.386388	−	0.922336i	$-0.626277\pi$
$877$	−7.69500	+	2.06187i	−0.259842	+	0.0696244i	0.126546	+	0.991961i	$0.459611\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−11.0782			−0.373234			−0.186617	−	0.982433i	$-0.559752\pi$
$881$	−11.0782			−0.373234			−0.186617	+	0.982433i	$0.559752\pi$
$882$		0			0
$883$	−24.5689	−	24.5689i	−0.826808	−	0.826808i	0.160266	−	0.987074i	$-0.448765\pi$
$883$	−24.5689	−	24.5689i	−0.826808	−	0.826808i	−0.987074	+	0.160266i	$0.948765\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.4338	+	9.48806i	0.551793	+	0.318578i	0.749845	−	0.661614i	$-0.230128\pi$
$887$	16.4338	+	9.48806i	0.551793	+	0.318578i	−0.198052	+	0.980192i	$0.563461\pi$
$888$		0			0
$889$	10.3978	−	6.00315i	0.348730	−	0.201339i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.122160	+	0.455909i	−0.00408795	+	0.0152564i
$894$		0			0
$895$	−2.80429	+	4.85718i	−0.0937371	+	0.162357i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−58.4810	−	58.4810i	−1.95045	−	1.95045i
$900$		0			0
$901$	32.0291	−	32.0291i	1.06704	−	1.06704i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.36391	−	2.51950i	−0.145061	−	0.0837511i
$906$		0			0
$907$	−19.5111	−	5.22799i	−0.647856	−	0.173593i	−0.0800968	−	0.996787i	$-0.525523\pi$
$907$	−19.5111	−	5.22799i	−0.647856	−	0.173593i	−0.567759	+	0.823195i	$0.692190\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.3761	−	21.4361i	−0.410040	−	0.710209i	0.584854	−	0.811139i	$-0.301152\pi$
$911$	−12.3761	−	21.4361i	−0.410040	−	0.710209i	−0.994894	+	0.100929i	$0.967818\pi$
$912$		0			0
$913$	−10.8606	+	18.8112i	−0.359434	+	0.622558i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.79507	−	5.79507i	0.191370	−	0.191370i
$918$		0			0
$919$		−	2.93718i		−	0.0968887i	−0.998826	−	0.0484444i	$-0.984574\pi$
$919$		−	2.93718i		−	0.0968887i	0.998826	−	0.0484444i	$-0.0154264\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.380619	+	1.42049i	0.0125282	+	0.0467560i
$924$		0			0
$925$	−2.67485	+	9.98268i	−0.0879486	+	0.328229i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.2758	−	33.3867i	−0.632420	−	1.09538i	−0.987056	−	0.160379i	$-0.948729\pi$
$929$	−19.2758	−	33.3867i	−0.632420	−	1.09538i	0.354636	−	0.935004i	$-0.384605\pi$
$930$		0			0
$931$	10.2433	−	2.74468i	0.335710	−	0.0899533i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			16.0187i			0.523866i
$936$		0			0
$937$		−	30.8118i		−	1.00658i	−0.864119	−	0.503288i	$-0.832123\pi$
$937$		−	30.8118i		−	1.00658i	0.864119	−	0.503288i	$-0.167877\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−31.4366	+	8.42341i	−1.02480	+	0.274595i	−0.731802	−	0.681517i	$-0.761321\pi$
$941$	−31.4366	+	8.42341i	−1.02480	+	0.274595i	−0.293001	+	0.956112i	$0.594654\pi$
$942$		0			0
$943$	16.2536	+	28.1521i	0.529292	+	0.916760i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.51115	+	9.37173i	−0.0816013	+	0.304540i	−0.994649	−	0.103313i	$-0.967056\pi$
$947$	−2.51115	+	9.37173i	−0.0816013	+	0.304540i	0.913048	+	0.407853i	$0.133722\pi$
$948$		0			0
$949$	−0.572676	−	2.13726i	−0.0185898	−	0.0693783i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	12.8416i		−	0.415980i	−0.978131	−	0.207990i	$-0.933308\pi$
$953$		−	12.8416i		−	0.415980i	0.978131	−	0.207990i	$-0.0666921\pi$
$954$		0			0
$955$	15.1513	−	15.1513i	0.490286	−	0.490286i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.11837	+	1.93707i	−0.0361139	+	0.0625512i
$960$		0			0
$961$	−27.0854	−	46.9133i	−0.873723	−	1.51333i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.59508	−	1.76715i	−0.212303	−	0.0568865i
$966$		0			0
$967$	35.9080	+	20.7315i	1.15472	+	0.666680i	0.950034	−	0.312147i	$-0.101048\pi$
$967$	35.9080	+	20.7315i	1.15472	+	0.666680i	0.204690	+	0.978827i	$0.434381\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.88730	+	1.88730i	−0.0605663	+	0.0605663i	−0.736741	−	0.676175i	$-0.763636\pi$
$971$	−1.88730	+	1.88730i	−0.0605663	+	0.0605663i	0.676175	+	0.736741i	$0.263636\pi$
$972$		0			0
$973$	−5.06253	−	5.06253i	−0.162297	−	0.162297i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.70999	+	16.8182i	−0.310650	+	0.538062i	−0.978503	−	0.206231i	$-0.933880\pi$
$977$	−9.70999	+	16.8182i	−0.310650	+	0.538062i	0.667853	+	0.744293i	$0.267213\pi$
$978$		0			0
$979$	−1.71071	+	6.38446i	−0.0546746	+	0.204048i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	26.6919	−	15.4106i	0.851339	−	0.491521i	−0.00976322	−	0.999952i	$-0.503108\pi$
$983$	26.6919	−	15.4106i	0.851339	−	0.491521i	0.861103	+	0.508431i	$0.169774\pi$
$984$		0			0
$985$	12.4046	+	7.16177i	0.395242	+	0.228193i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−13.9465	−	13.9465i	−0.443473	−	0.443473i
$990$		0			0
$991$	−19.7024			−0.625869			−0.312934	−	0.949775i	$-0.601312\pi$
$991$	−19.7024			−0.625869			−0.312934	+	0.949775i	$0.601312\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	13.6611	−	3.66047i	0.433085	−	0.116045i
$996$		0			0
$997$	−4.69625	−	1.25836i	−0.148732	−	0.0398526i	0.183685	−	0.982985i	$-0.441197\pi$
$997$	−4.69625	−	1.25836i	−0.148732	−	0.0398526i	−0.332417	+	0.943133i	$0.607864\pi$
$998$		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.145.12		72
3.2	odd	2		576.2.bb.e.337.6		72
4.3	odd	2		432.2.y.e.253.18		72
9.2	odd	6		576.2.bb.e.529.13		72
9.7	even	3	inner	1728.2.bc.e.721.7		72
12.11	even	2		144.2.x.e.13.1	✓	72
16.5	even	4	inner	1728.2.bc.e.1009.7		72
16.11	odd	4		432.2.y.e.37.6		72
36.7	odd	6		432.2.y.e.397.6		72
36.11	even	6		144.2.x.e.61.13	yes	72
48.5	odd	4		576.2.bb.e.49.13		72
48.11	even	4		144.2.x.e.85.13	yes	72
144.11	even	12		144.2.x.e.133.1	yes	72
144.43	odd	12		432.2.y.e.181.18		72
144.101	odd	12		576.2.bb.e.241.6		72
144.133	even	12	inner	1728.2.bc.e.1585.12		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.1	✓	72	12.11	even	2
144.2.x.e.61.13	yes	72	36.11	even	6
144.2.x.e.85.13	yes	72	48.11	even	4
144.2.x.e.133.1	yes	72	144.11	even	12
432.2.y.e.37.6		72	16.11	odd	4
432.2.y.e.181.18		72	144.43	odd	12
432.2.y.e.253.18		72	4.3	odd	2
432.2.y.e.397.6		72	36.7	odd	6
576.2.bb.e.49.13		72	48.5	odd	4
576.2.bb.e.241.6		72	144.101	odd	12
576.2.bb.e.337.6		72	3.2	odd	2
576.2.bb.e.529.13		72	9.2	odd	6
1728.2.bc.e.145.12		72	1.1	even	1	trivial
1728.2.bc.e.721.7		72	9.7	even	3	inner
1728.2.bc.e.1009.7		72	16.5	even	4	inner
1728.2.bc.e.1585.12		72	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)

\(f(q)\)	\(=\)	\(q+(0.326078 + 1.21694i) q^{5} +(-0.707732 + 0.408609i) q^{7} +O(q^{10})\)	\(q+(0.326078 + 1.21694i) q^{5} +(-0.707732 + 0.408609i) q^{7} +(-1.85518 - 0.497094i) q^{11} +(-0.434170 + 0.116336i) q^{13} -6.62002 q^{17} +(-1.18421 - 1.18421i) q^{19} +(-2.66201 - 1.53691i) q^{23} +(2.95551 - 1.70637i) q^{25} +(2.31943 - 8.65622i) q^{29} +(4.61440 - 7.99238i) q^{31} +(-0.728028 - 0.728028i) q^{35} +(-2.14134 + 2.14134i) q^{37} +(-9.15868 - 5.28777i) q^{41} +(6.19791 + 1.66072i) q^{43} +(-0.140916 - 0.244074i) q^{47} +(-3.16608 + 5.48381i) q^{49} +(-4.83822 + 4.83822i) q^{53} -2.41973i q^{55} +(1.91804 + 7.15823i) q^{59} +(2.64688 - 9.87829i) q^{61} +(-0.283147 - 0.490424i) q^{65} +(5.22368 - 1.39968i) q^{67} -3.27174i q^{71} +4.92262i q^{73} +(1.51609 - 0.406234i) q^{77} +(-7.70232 - 13.3408i) q^{79} +(2.92711 - 10.9241i) q^{83} +(-2.15864 - 8.05616i) q^{85} -3.44143i q^{89} +(0.259740 - 0.259740i) q^{91} +(1.05497 - 1.82726i) q^{95} +(-4.46939 - 7.74121i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{5}+O(q^{10}) \) 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

L-functions

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