LMFDB - Embedded newform 1728.2.bc.e.1585.12

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			1585.12
Character	$\chi$	$=$	1728.1585
Dual form			1728.2.bc.e.145.12

$q$-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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

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
$5$	0.326078	−	1.21694i	0.145827	−	0.544232i	−0.853891	−	0.520452i	$-0.825763\pi$
$5$	0.326078	−	1.21694i	0.145827	−	0.544232i	0.999717	−	0.0237796i	$-0.00756999\pi$
$6$		0			0
$7$	−0.707732	−	0.408609i	−0.267497	−	0.154440i	0.360252	−	0.932855i	$-0.382691\pi$
$7$	−0.707732	−	0.408609i	−0.267497	−	0.154440i	−0.627750	+	0.778415i	$0.716024\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.85518	+	0.497094i	−0.559357	+	0.149879i	−0.527411	−	0.849610i	$-0.676837\pi$
$11$	−1.85518	+	0.497094i	−0.559357	+	0.149879i	−0.0319463	+	0.999490i	$0.510171\pi$
$12$		0			0
$13$	−0.434170	−	0.116336i	−0.120417	−	0.0322657i	0.198107	−	0.980180i	$-0.436521\pi$
$13$	−0.434170	−	0.116336i	−0.120417	−	0.0322657i	−0.318524	+	0.947915i	$0.603187\pi$
$14$		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	−0.829775	−	0.558098i	$-0.811531\pi$
$19$	−1.18421	+	1.18421i	−0.271677	+	0.271677i	0.558098	+	0.829775i	$0.311531\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.66201	+	1.53691i	−0.555067	+	0.320468i	−0.751163	−	0.660117i	$-0.770507\pi$
$23$	−2.66201	+	1.53691i	−0.555067	+	0.320468i	0.196096	+	0.980585i	$0.437174\pi$
$24$		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	0.751136	+	0.660147i	$0.229506\pi$
$29$	2.31943	+	8.65622i	0.430707	+	1.60742i	−0.320430	+	0.947272i	$0.603827\pi$
$30$		0			0
$31$	4.61440	+	7.99238i	0.828771	+	1.43547i	0.899003	+	0.437943i	$0.144293\pi$
$31$	4.61440	+	7.99238i	0.828771	+	1.43547i	−0.0702316	+	0.997531i	$0.522374\pi$
$32$		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	0.508831	−	0.860866i	$-0.330078\pi$
$37$	−2.14134	−	2.14134i	−0.352035	−	0.352035i	−0.860866	+	0.508831i	$0.830078\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.15868	+	5.28777i	−1.43035	+	0.825810i	−0.997147	−	0.0754884i	$-0.975948\pi$
$41$	−9.15868	+	5.28777i	−1.43035	+	0.825810i	−0.433199	+	0.901299i	$0.642615\pi$
$42$		0			0
$43$	6.19791	−	1.66072i	0.945172	−	0.253258i	0.246860	−	0.969051i	$-0.420601\pi$
$43$	6.19791	−	1.66072i	0.945172	−	0.253258i	0.698312	+	0.715793i	$0.253935\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.140916	+	0.244074i	−0.0205547	+	0.0356018i	−0.876120	−	0.482093i	$-0.839877\pi$
$47$	−0.140916	+	0.244074i	−0.0205547	+	0.0356018i	0.855565	+	0.517695i	$0.173210\pi$
$48$		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	0.291876	−	0.956456i	$-0.405721\pi$
$53$	−4.83822	−	4.83822i	−0.664580	−	0.664580i	−0.956456	+	0.291876i	$0.905721\pi$
$54$		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	−0.721251	−	0.692674i	$-0.756432\pi$
$59$	1.91804	−	7.15823i	0.249708	−	0.931923i	0.970958	−	0.239248i	$-0.0769010\pi$
$60$		0			0
$61$	2.64688	+	9.87829i	0.338898	+	1.26479i	0.899581	+	0.436755i	$0.143872\pi$
$61$	2.64688	+	9.87829i	0.338898	+	1.26479i	−0.560682	+	0.828031i	$0.689461\pi$
$62$		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	0.563376	−	0.826200i	$-0.309502\pi$
$67$	5.22368	+	1.39968i	0.638175	+	0.170998i	0.0747982	+	0.997199i	$0.476169\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			3.27174i			0.388284i	0.980973	+	0.194142i	$0.0621922\pi$
$71$			3.27174i			0.388284i	−0.980973	+	0.194142i	$0.937808\pi$
$72$		0			0
$73$		−	4.92262i		−	0.576150i	−0.957608	−	0.288075i	$-0.906985\pi$
$73$		−	4.92262i		−	0.576150i	0.957608	−	0.288075i	$-0.0930152\pi$
$74$		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	−0.00110666	+	0.999999i	$0.500352\pi$
$79$	−7.70232	+	13.3408i	−0.866578	+	1.50096i	−0.865472	+	0.500958i	$0.832981\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.92711	+	10.9241i	0.321292	+	1.19908i	0.917987	+	0.396610i	$0.129813\pi$
$83$	2.92711	+	10.9241i	0.321292	+	1.19908i	−0.596695	+	0.802468i	$0.703520\pi$
$84$		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	$0.0583850\pi$
$89$			3.44143i			0.364790i	−0.983225	+	0.182395i	$0.941615\pi$
$90$		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	−0.998618	−	0.0525516i	$-0.983265\pi$
$97$	−4.46939	+	7.74121i	−0.453798	+	0.786001i	0.544820	+	0.838553i	$0.316598\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.64577	−	1.78073i	0.661278	−	0.177189i	0.0874556	−	0.996168i	$-0.472126\pi$
$101$	6.64577	−	1.78073i	0.661278	−	0.177189i	0.573823	+	0.818979i	$0.305460\pi$
$102$		0			0
$103$	5.76134	−	3.32631i	0.567681	−	0.327751i	−0.188541	−	0.982065i	$-0.560376\pi$
$103$	5.76134	−	3.32631i	0.567681	−	0.327751i	0.756223	+	0.654314i	$0.227043\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.06262	−	4.06262i	−0.392748	−	0.392748i	0.482918	−	0.875666i	$-0.339577\pi$
$107$	−4.06262	−	4.06262i	−0.392748	−	0.392748i	−0.875666	+	0.482918i	$0.839577\pi$
$108$		0			0
$109$	−7.19802	+	7.19802i	−0.689445	+	0.689445i	−0.962109	−	0.272664i	$-0.912095\pi$
$109$	−7.19802	+	7.19802i	−0.689445	+	0.689445i	0.272664	+	0.962109i	$0.412095\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.45739	−	11.1845i	−0.607460	−	1.05215i	−0.991657	−	0.128901i	$-0.958855\pi$
$113$	−6.45739	−	11.1845i	−0.607460	−	1.05215i	0.384197	−	0.923251i	$-0.374478\pi$
$114$		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	−0.190509	−	0.981685i	$-0.561014\pi$
$131$	−9.68678	−	2.59556i	−0.846338	−	0.226775i	−0.655828	+	0.754910i	$0.727681\pi$
$132$		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	0.597826	−	0.801626i	$-0.296031\pi$
$137$	2.37032	+	1.36850i	0.202510	+	0.116919i	−0.395316	+	0.918545i	$0.629365\pi$
$138$		0			0
$139$	2.26747	−	8.46230i	0.192324	−	0.717763i	−0.800619	−	0.599173i	$-0.795496\pi$
$139$	2.26747	−	8.46230i	0.192324	−	0.717763i	0.992943	−	0.118590i	$-0.0378373\pi$
$140$		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	0.814074	+	0.580761i	$0.197245\pi$
$149$	−2.21323	+	8.25990i	−0.181315	+	0.676678i	−0.995389	+	0.0959167i	$0.969422\pi$
$150$		0			0
$151$	−20.2738	−	11.7051i	−1.64986	−	0.952546i	−0.977126	−	0.212660i	$-0.931787\pi$
$151$	−20.2738	−	11.7051i	−1.64986	−	0.952546i	−0.672732	−	0.739886i	$-0.734879\pi$
$152$		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	0.964854	−	0.262788i	$-0.0846419\pi$
$157$	20.9131	+	5.60365i	1.66905	+	0.447220i	0.704194	+	0.710008i	$0.251309\pi$
$158$		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	−0.759755	−	0.650210i	$-0.774681\pi$
$163$	−1.39858	+	1.39858i	−0.109545	+	0.109545i	0.650210	+	0.759755i	$0.274681\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−20.0385	+	11.5692i	−1.55063	+	0.895254i	−0.552535	+	0.833490i	$0.686339\pi$
$167$	−20.0385	+	11.5692i	−1.55063	+	0.895254i	−0.998091	+	0.0617643i	$0.980327\pi$
$168$		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	0.997858	−	0.0654105i	$-0.0208357\pi$
$173$	1.32822	+	4.95697i	0.100982	+	0.376871i	−0.896876	+	0.442282i	$0.854169\pi$
$174$		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	−0.579612	−	0.814893i	$-0.696796\pi$
$179$	3.14784	−	3.14784i	0.235281	−	0.235281i	0.814893	+	0.579612i	$0.196796\pi$
$180$		0			0
$181$	−2.82816	−	2.82816i	−0.210216	−	0.210216i	0.594143	−	0.804359i	$-0.297491\pi$
$181$	−2.82816	−	2.82816i	−0.210216	−	0.210216i	−0.804359	+	0.594143i	$0.797491\pi$
$182$		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	0.375020	+	0.927017i	$0.377636\pi$
$191$	−8.50375	+	14.7289i	−0.615310	+	1.06575i	−0.990330	+	0.138732i	$0.955697\pi$
$192$		0			0
$193$	−2.70970	−	4.69334i	−0.195049	−	0.337834i	0.751868	−	0.659314i	$-0.229153\pi$
$193$	−2.70970	−	4.69334i	−0.195049	−	0.337834i	−0.946916	+	0.321480i	$0.895820\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.03915	+	8.03915i	0.572766	+	0.572766i	0.932900	−	0.360135i	$-0.117269\pi$
$197$	8.03915	+	8.03915i	0.572766	+	0.572766i	−0.360135	+	0.932900i	$0.617269\pi$
$198$		0			0
$199$			11.2258i			0.795773i	0.917435	+	0.397886i	$0.130256\pi$
$199$			11.2258i			0.795773i	−0.917435	+	0.397886i	$0.869744\pi$
$200$		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	−0.271556	−	0.962423i	$-0.587538\pi$
$211$	−14.3507	−	3.84526i	−0.987942	−	0.264718i	−0.716386	+	0.697704i	$0.754205\pi$
$212$		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	−0.443473	−	0.896288i	$-0.646254\pi$
$223$	8.28003	−	14.3414i	0.554472	−	0.960373i	0.997944	−	0.0640854i	$-0.0204130\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.11338	−	7.88725i	−0.140270	−	0.523495i	−0.999920	−	0.0126123i	$-0.995985\pi$
$227$	−2.11338	−	7.88725i	−0.140270	−	0.523495i	0.859650	−	0.510883i	$-0.170681\pi$
$228$		0			0
$229$	1.16230	−	4.33776i	0.0768068	−	0.286647i	−0.916830	−	0.399278i	$-0.869261\pi$
$229$	1.16230	−	4.33776i	0.0768068	−	0.286647i	0.993637	+	0.112631i	$0.0359277\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	7.33128i		−	0.480288i	−0.970737	−	0.240144i	$-0.922805\pi$
$233$		−	7.33128i		−	0.480288i	0.970737	−	0.240144i	$-0.0771947\pi$
$234$		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	0.954846	−	0.297102i	$-0.0960202\pi$
$239$	3.40305	+	5.89425i	0.220125	+	0.381268i	−0.734721	+	0.678370i	$0.762687\pi$
$240$		0			0
$241$	2.98687	−	5.17340i	0.192401	−	0.333248i	−0.753644	−	0.657282i	$-0.771706\pi$
$241$	2.98687	−	5.17340i	0.192401	−	0.333248i	0.946045	+	0.324034i	$0.105039\pi$
$242$		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	−0.999819	−	0.0190030i	$-0.993951\pi$
$251$	−16.1412	−	16.1412i	−1.01882	−	1.01882i	−0.0190030	−	0.999819i	$-0.506049\pi$
$252$		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	0.871356	−	0.490651i	$-0.163241\pi$
$257$	0.172522	+	0.298817i	0.0107616	+	0.0186397i	−0.860594	+	0.509291i	$0.829908\pi$
$258$		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	0.630361	−	0.776302i	$-0.282907\pi$
$263$	4.43128	+	2.55840i	0.273244	+	0.157758i	−0.357117	+	0.934060i	$0.616240\pi$
$264$		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	−0.0557529	−	0.998445i	$-0.517756\pi$
$269$	15.4613	−	15.4613i	0.942692	−	0.942692i	0.998445	+	0.0557529i	$0.0177559\pi$
$270$		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	0.407757	−	0.913091i	$-0.366311\pi$
$277$	20.2621	−	5.42920i	1.21743	−	0.326209i	0.809673	+	0.586881i	$0.199644\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.9537	+	6.32414i	0.653445	+	0.377266i	0.789775	−	0.613397i	$-0.210197\pi$
$281$	10.9537	+	6.32414i	0.653445	+	0.377266i	−0.136330	+	0.990663i	$0.543531\pi$
$282$		0			0
$283$	−5.69346	+	21.2483i	−0.338441	+	1.26308i	0.561650	+	0.827375i	$0.310167\pi$
$283$	−5.69346	+	21.2483i	−0.338441	+	1.26308i	−0.900090	+	0.435703i	$0.856500\pi$
$284$		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	−0.966794	−	0.255557i	$-0.917741\pi$
$293$	−0.0299075	+	0.111616i	−0.00174721	+	0.00652069i	0.965047	+	0.262078i	$0.0844077\pi$
$294$		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	−0.256428	−	0.966563i	$-0.582546\pi$
$307$	12.4426	−	12.4426i	0.710135	−	0.710135i	0.966563	+	0.256428i	$0.0825456\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.03115	−	1.17269i	0.115176	−	0.0664969i	−0.441305	−	0.897357i	$-0.645484\pi$
$311$	2.03115	−	1.17269i	0.115176	−	0.0664969i	0.556481	+	0.830860i	$0.312151\pi$
$312$		0			0
$313$	−8.62293	−	4.97845i	−0.487397	−	0.281399i	0.236097	−	0.971729i	$-0.424132\pi$
$313$	−8.62293	−	4.97845i	−0.487397	−	0.281399i	−0.723494	+	0.690331i	$0.757465\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.18698	+	4.42985i	0.0666672	+	0.248805i	0.991215	−	0.132261i	$-0.0422236\pi$
$317$	1.18698	+	4.42985i	0.0666672	+	0.248805i	−0.924548	+	0.381066i	$0.875557\pi$
$318$		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	0.233558	−	0.972343i	$-0.424963\pi$
$331$	16.7743	−	4.49465i	0.921997	−	0.247048i	0.688439	+	0.725294i	$0.258296\pi$
$332$		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	−0.913891	−	0.405959i	$-0.866937\pi$
$337$	−14.8424	−	25.7078i	−0.808517	−	1.40039i	0.105375	−	0.994433i	$-0.466396\pi$
$338$		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	−0.978485	−	0.206320i	$-0.933851\pi$
$347$	−0.520318	+	1.94185i	−0.0279321	+	0.104244i	0.950552	+	0.310564i	$0.100518\pi$
$348$		0			0
$349$	−7.13604	−	26.6321i	−0.381984	−	1.42558i	−0.842867	−	0.538122i	$-0.819134\pi$
$349$	−7.13604	−	26.6321i	−0.381984	−	1.42558i	0.460883	−	0.887461i	$-0.347533\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.58657	+	2.74801i	−0.0844444	+	0.146262i	−0.905154	−	0.425083i	$-0.860245\pi$
$353$	−1.58657	+	2.74801i	−0.0844444	+	0.146262i	0.820710	+	0.571345i	$0.193578\pi$
$354$		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	$-0.795556\pi$
$359$		−	22.6997i		−	1.19804i	0.800732	−	0.599022i	$-0.204444\pi$
$360$		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	−0.810897	−	0.585189i	$-0.801020\pi$
$367$	1.94141	−	3.36261i	0.101341	−	0.175527i	0.912237	+	0.409662i	$0.134354\pi$
$368$		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	−0.989560	−	0.144123i	$-0.953964\pi$
$373$	−1.16873	+	4.36176i	−0.0605145	+	0.225843i	0.929045	+	0.369966i	$0.120631\pi$
$374$		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	0.224065	−	0.974574i	$-0.428067\pi$
$379$	−14.6109	−	14.6109i	−0.750509	−	0.750509i	−0.974574	+	0.224065i	$0.928067\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.4164	+	24.9699i	0.736643	+	1.27590i	0.953999	+	0.299811i	$0.0969236\pi$
$383$	14.4164	+	24.9699i	0.736643	+	1.27590i	−0.217355	+	0.976093i	$0.569743\pi$
$384$		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	−0.253988	−	0.967207i	$-0.581742\pi$
$389$	0.190429	−	0.0510254i	0.00965514	−	0.00258709i	0.263643	+	0.964620i	$0.415076\pi$
$390$		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	−0.911791	−	0.410656i	$-0.865300\pi$
$397$	−9.98504	+	9.98504i	−0.501135	+	0.501135i	0.410656	+	0.911791i	$0.365300\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.396741	−	0.687175i	−0.0198123	−	0.0343159i	0.855949	−	0.517060i	$-0.172974\pi$
$401$	−0.396741	−	0.687175i	−0.0198123	−	0.0343159i	−0.875762	+	0.482744i	$0.839640\pi$
$402$		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	−0.494413	−	0.869227i	$-0.664617\pi$
$409$	0.225551	−	0.130222i	0.0111528	−	0.00643907i	0.505566	+	0.862788i	$0.331284\pi$
$410$		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	0.347522	−	0.937672i	$-0.387023\pi$
$419$	3.67732	+	0.985334i	0.179649	+	0.0481367i	−0.167873	+	0.985809i	$0.553690\pi$
$420$		0			0
$421$	0.779608	−	0.208895i	0.0379958	−	0.0101809i	−0.239771	−	0.970829i	$-0.577072\pi$
$421$	0.779608	−	0.208895i	0.0379958	−	0.0101809i	0.277767	+	0.960649i	$0.410406\pi$
$422$		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	0.299892	−	0.953973i	$-0.403049\pi$
$439$	−7.88493	−	4.55237i	−0.376327	−	0.217273i	−0.676219	+	0.736701i	$0.736383\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	27.2979	−	7.31445i	1.29696	−	0.347520i	0.456662	−	0.889640i	$-0.349045\pi$
$443$	27.2979	−	7.31445i	1.29696	−	0.347520i	0.840301	+	0.542120i	$0.182378\pi$
$444$		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	0.605905	−	0.795537i	$-0.292811\pi$
$457$	4.70096	+	2.71410i	0.219902	+	0.126960i	−0.386003	+	0.922497i	$0.626145\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.74777	−	25.1830i	−0.314275	−	1.17289i	−0.924663	−	0.380787i	$-0.875653\pi$
$461$	−6.74777	−	25.1830i	−0.314275	−	1.17289i	0.610388	−	0.792103i	$-0.291014\pi$
$462$		0			0
$463$	9.87708	+	17.1076i	0.459027	+	0.795057i	0.998910	−	0.0466825i	$-0.0148649\pi$
$463$	9.87708	+	17.1076i	0.459027	+	0.795057i	−0.539883	+	0.841740i	$0.681532\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.1348	−	16.1348i	0.746628	−	0.746628i	−0.227217	−	0.973844i	$-0.572963\pi$
$467$	16.1348	−	16.1348i	0.746628	−	0.746628i	0.973844	+	0.227217i	$0.0729625\pi$
$468$		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	−0.488187	−	0.872739i	$-0.662341\pi$
$479$	11.1996	−	19.3982i	0.511721	−	0.886327i	0.999908	−	0.0135877i	$-0.00432523\pi$
$480$		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	$-0.939950\pi$
$487$		−	8.27717i		−	0.375074i	0.982258	−	0.187537i	$-0.0600505\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.31362	+	34.7589i	−0.420318	+	1.56865i	0.353622	+	0.935388i	$0.384950\pi$
$491$	−9.31362	+	34.7589i	−0.420318	+	1.56865i	−0.773940	+	0.633259i	$0.781717\pi$
$492$		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	−0.423911	−	0.905704i	$-0.639343\pi$
$499$	−27.7862	−	7.44528i	−1.24388	−	0.333297i	−0.819969	+	0.572407i	$0.806010\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			15.6106i			0.696044i	0.937486	+	0.348022i	$0.113146\pi$
$503$			15.6106i			0.696044i	−0.937486	+	0.348022i	$0.886854\pi$
$504$		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	0.471915	−	0.881644i	$-0.343563\pi$
$509$	9.92195	+	2.65858i	0.439783	+	0.117839i	−0.0321319	+	0.999484i	$0.510230\pi$
$510$		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	$-0.845661\pi$
$521$		−	21.2775i		−	0.932185i	0.884736	−	0.466092i	$-0.154339\pi$
$522$		0			0
$523$	2.96994	+	2.96994i	0.129867	+	0.129867i	0.769052	−	0.639186i	$-0.220729\pi$
$523$	2.96994	+	2.96994i	0.129867	+	0.129867i	−0.639186	+	0.769052i	$0.720729\pi$
$524$		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	−0.953765	−	0.300552i	$-0.902829\pi$
$541$	−15.1934	+	15.1934i	−0.653214	+	0.653214i	0.300552	+	0.953765i	$0.402829\pi$
$542$		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	0.837943	+	0.545757i	$0.183758\pi$
$547$	9.00771	+	33.6172i	0.385142	+	1.43737i	−0.452802	+	0.891611i	$0.649575\pi$
$548$		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	−0.953279	−	0.302091i	$-0.902315\pi$
$557$	−15.3686	+	15.3686i	−0.651189	+	0.651189i	0.302091	+	0.953279i	$0.402315\pi$
$558$		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	0.567721	−	0.823221i	$-0.307825\pi$
$563$	15.3701	+	4.11840i	0.647772	+	0.173570i	0.0800506	+	0.996791i	$0.474492\pi$
$564$		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	0.999413	+	0.0342597i	$0.0109073\pi$
$569$	36.4673	+	21.0544i	1.52879	+	0.882647i	0.529376	+	0.848387i	$0.322426\pi$
$570$		0			0
$571$	−10.1418	+	37.8497i	−0.424421	+	1.58396i	0.340762	+	0.940150i	$0.389315\pi$
$571$	−10.1418	+	37.8497i	−0.424421	+	1.58396i	−0.765183	+	0.643813i	$0.777352\pi$
$572$		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	−0.834915	−	0.550380i	$-0.814483\pi$
$587$	−31.0793	+	8.32769i	−1.28278	+	0.343720i	−0.447867	+	0.894100i	$0.647816\pi$
$588$		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	0.379961	−	0.925003i	$-0.375937\pi$
$599$	33.5549	−	19.3729i	1.37102	−	0.791557i	0.991056	+	0.133445i	$0.0426041\pi$
$600$		0			0
$601$	21.4630	+	12.3917i	0.875493	+	0.505466i	0.869170	−	0.494514i	$-0.164654\pi$
$601$	21.4630	+	12.3917i	0.875493	+	0.505466i	0.00632336	+	0.999980i	$0.497987\pi$
$602$		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	0.722421	−	0.691454i	$-0.243029\pi$
$607$	−5.85399	−	10.1394i	−0.237606	−	0.411546i	−0.960027	+	0.279908i	$0.909696\pi$
$608$		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	0.00487577	−	0.999988i	$-0.498448\pi$
$613$	−24.6378	−	24.6378i	−0.995112	−	0.995112i	−0.999988	+	0.00487577i	$0.998448\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.72698	−	2.72912i	0.190301	−	0.109870i	−0.401822	−	0.915718i	$-0.631623\pi$
$617$	4.72698	−	2.72912i	0.190301	−	0.109870i	0.592123	+	0.805847i	$0.298290\pi$
$618$		0			0
$619$	−16.5475	+	4.43389i	−0.665101	+	0.178213i	−0.575547	−	0.817769i	$-0.695211\pi$
$619$	−16.5475	+	4.43389i	−0.665101	+	0.178213i	−0.0895538	+	0.995982i	$0.528544\pi$
$620$		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	$0.0320045\pi$
$631$			5.04281i			0.200751i	−0.994950	+	0.100376i	$0.967996\pi$
$632$		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	−0.994261	−	0.106984i	$-0.965881\pi$
$641$	−10.2406	+	17.7373i	−0.404480	+	0.700579i	0.589781	+	0.807563i	$0.299214\pi$
$642$		0			0
$643$	−40.2059	−	10.7731i	−1.58557	−	0.424851i	−0.644922	−	0.764248i	$-0.723110\pi$
$643$	−40.2059	−	10.7731i	−1.58557	−	0.424851i	−0.940643	+	0.339397i	$0.889777\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			9.07428i			0.356747i	0.983963	+	0.178373i	$0.0570835\pi$
$647$			9.07428i			0.356747i	−0.983963	+	0.178373i	$0.942917\pi$
$648$		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	−0.382662	−	0.923888i	$-0.624993\pi$
$653$	−30.0514	−	8.05224i	−1.17600	−	0.315109i	−0.793339	+	0.608780i	$0.791659\pi$
$654$		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	0.999945	−	0.0104620i	$-0.00333022\pi$
$659$	3.30479	+	12.3336i	0.128736	+	0.480450i	−0.871209	+	0.490912i	$0.836664\pi$
$660$		0			0
$661$	−11.4466	+	42.7191i	−0.445219	+	1.66158i	0.270137	+	0.962822i	$0.412931\pi$
$661$	−11.4466	+	42.7191i	−0.445219	+	1.66158i	−0.715357	+	0.698759i	$0.753736\pi$
$662$		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	0.328045	+	0.944662i	$0.393610\pi$
$673$	−16.9683	+	29.3899i	−0.654079	+	1.13290i	−0.982124	+	0.188236i	$0.939723\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	39.9599	−	10.7072i	1.53578	−	0.411512i	0.610882	−	0.791721i	$-0.290815\pi$
$677$	39.9599	−	10.7072i	1.53578	−	0.411512i	0.924900	+	0.380210i	$0.124148\pi$
$678$		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	0.708774	−	0.705436i	$-0.249249\pi$
$683$	0.0872426	+	0.0872426i	0.00333824	+	0.00333824i	−0.705436	+	0.708774i	$0.749249\pi$
$684$		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	−0.999969	−	0.00793395i	$-0.997475\pi$
$691$	−3.62594	−	13.5322i	−0.137937	−	0.514789i	0.862031	−	0.506855i	$-0.169192\pi$
$692$		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	−0.880027	−	0.474924i	$-0.842475\pi$
$701$	−10.7257	+	10.7257i	−0.405103	+	0.405103i	0.474924	+	0.880027i	$0.342475\pi$
$702$		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	0.587468	−	0.809247i	$-0.300125\pi$
$709$	39.9633	−	10.7081i	1.50085	−	0.402153i	0.913386	+	0.407095i	$0.133458\pi$
$710$		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	0.928057	−	0.372439i	$-0.121478\pi$
$727$	28.8380	+	16.6496i	1.06954	+	0.617501i	0.141487	+	0.989940i	$0.454812\pi$
$728$		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	0.855874	−	0.517185i	$-0.173020\pi$
$733$	36.2382	+	9.71001i	1.33849	+	0.358647i	0.482616	+	0.875832i	$0.339687\pi$
$734$		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	−0.531602	−	0.846994i	$-0.678410\pi$
$739$	8.57380	−	8.57380i	0.315392	−	0.315392i	0.846994	+	0.531602i	$0.178410\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.3476	−	5.97418i	0.379616	−	0.219172i	−0.298035	−	0.954555i	$-0.596331\pi$
$743$	10.3476	−	5.97418i	0.379616	−	0.219172i	0.677651	+	0.735383i	$0.262998\pi$
$744$		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	0.551885	−	0.833920i	$-0.313909\pi$
$751$	−12.2293	−	21.1818i	−0.446254	−	0.772934i	−0.998139	+	0.0609863i	$0.980575\pi$
$752$		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	0.804180	−	0.594386i	$-0.202605\pi$
$757$	5.77221	+	5.77221i	0.209794	+	0.209794i	−0.594386	+	0.804180i	$0.702605\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	35.8368	−	20.6904i	1.29908	−	0.750025i	0.318836	−	0.947810i	$-0.396708\pi$
$761$	35.8368	−	20.6904i	1.29908	−	0.750025i	0.980246	+	0.197784i	$0.0633746\pi$
$762$		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	0.963489	+	0.267749i	$0.0862798\pi$
$769$	19.7893	+	34.2761i	0.713622	+	1.23603i	−0.249867	+	0.968280i	$0.580387\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−34.1627	−	34.1627i	−1.22875	−	1.22875i	−0.964439	−	0.264307i	$-0.914857\pi$
$773$	−34.1627	−	34.1627i	−1.22875	−	1.22875i	−0.264307	−	0.964439i	$-0.585143\pi$
$774$		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	0.857174	−	0.515028i	$-0.172218\pi$
$787$	37.6477	+	10.0877i	1.34199	+	0.359586i	0.484820	+	0.874614i	$0.338885\pi$
$788$		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	0.307186	−	0.951649i	$-0.400612\pi$
$797$	2.74952	+	0.736732i	0.0973931	+	0.0260964i	−0.209793	+	0.977746i	$0.567279\pi$
$798$		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	$0.0841722\pi$
$809$			14.8679i			0.522727i	−0.965240	+	0.261364i	$0.915828\pi$
$810$		0			0
$811$	−11.8984	−	11.8984i	−0.417808	−	0.417808i	0.466640	−	0.884447i	$-0.345464\pi$
$811$	−11.8984	−	11.8984i	−0.417808	−	0.417808i	−0.884447	+	0.466640i	$0.845464\pi$
$812$		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	−0.973661	−	0.227999i	$-0.926782\pi$
$821$	−48.7927	+	13.0740i	−1.70288	+	0.456285i	−0.729216	+	0.684283i	$0.760115\pi$
$822$		0			0
$823$	14.3773	−	8.30076i	0.501163	−	0.289346i	−0.228031	−	0.973654i	$-0.573229\pi$
$823$	14.3773	−	8.30076i	0.501163	−	0.289346i	0.729194	+	0.684307i	$0.239895\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	19.8935	+	19.8935i	0.691764	+	0.691764i	0.962620	−	0.270856i	$-0.0873067\pi$
$827$	19.8935	+	19.8935i	0.691764	+	0.691764i	−0.270856	+	0.962620i	$0.587307\pi$
$828$		0			0
$829$	4.51982	−	4.51982i	0.156980	−	0.156980i	−0.624247	−	0.781227i	$-0.714594\pi$
$829$	4.51982	−	4.51982i	0.156980	−	0.156980i	0.781227	+	0.624247i	$0.214594\pi$
$830$		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	0.589346	−	0.807881i	$-0.299386\pi$
$839$	5.34046	+	3.08332i	0.184373	+	0.106448i	−0.404972	+	0.914329i	$0.632719\pi$
$840$		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	−0.717771	−	0.696279i	$-0.754838\pi$
$853$	−28.9503	+	7.75721i	−0.991240	+	0.265602i	−0.273468	+	0.961881i	$0.588171\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.97997	−	1.14314i	−0.0676345	−	0.0390488i	0.465801	−	0.884889i	$-0.345766\pi$
$857$	−1.97997	−	1.14314i	−0.0676345	−	0.0390488i	−0.533436	+	0.845840i	$0.679099\pi$
$858$		0			0
$859$	3.73966	−	13.9566i	0.127595	−	0.476193i	−0.872323	−	0.488929i	$-0.837388\pi$
$859$	3.73966	−	13.9566i	0.127595	−	0.476193i	0.999919	+	0.0127366i	$0.00405431\pi$
$860$		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	0.126546	−	0.991961i	$-0.459611\pi$
$877$	−7.69500	−	2.06187i	−0.259842	−	0.0696244i	−0.386388	+	0.922336i	$0.626277\pi$
$878$		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	−0.987074	−	0.160266i	$-0.948765\pi$
$883$	−24.5689	+	24.5689i	−0.826808	+	0.826808i	0.160266	+	0.987074i	$0.448765\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.4338	−	9.48806i	0.551793	−	0.318578i	−0.198052	−	0.980192i	$-0.563461\pi$
$887$	16.4338	−	9.48806i	0.551793	−	0.318578i	0.749845	+	0.661614i	$0.230128\pi$
$888$		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	−0.567759	−	0.823195i	$-0.692190\pi$
$907$	−19.5111	+	5.22799i	−0.647856	+	0.173593i	−0.0800968	+	0.996787i	$0.525523\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.3761	+	21.4361i	−0.410040	+	0.710209i	−0.994894	−	0.100929i	$-0.967818\pi$
$911$	−12.3761	+	21.4361i	−0.410040	+	0.710209i	0.584854	+	0.811139i	$0.301152\pi$
$912$		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	$0.0154264\pi$
$919$			2.93718i			0.0968887i	−0.998826	+	0.0484444i	$0.984574\pi$
$920$		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	0.354636	+	0.935004i	$0.384605\pi$
$929$	−19.2758	+	33.3867i	−0.632420	+	1.09538i	−0.987056	+	0.160379i	$0.948729\pi$
$930$		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	$0.167877\pi$
$937$			30.8118i			1.00658i	−0.864119	+	0.503288i	$0.832123\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−31.4366	−	8.42341i	−1.02480	−	0.274595i	−0.293001	−	0.956112i	$-0.594654\pi$
$941$	−31.4366	−	8.42341i	−1.02480	−	0.274595i	−0.731802	+	0.681517i	$0.761321\pi$
$942$		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	0.913048	−	0.407853i	$-0.133722\pi$
$947$	−2.51115	−	9.37173i	−0.0816013	−	0.304540i	−0.994649	+	0.103313i	$0.967056\pi$
$948$		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	$0.0666921\pi$
$953$			12.8416i			0.415980i	−0.978131	+	0.207990i	$0.933308\pi$
$954$		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	0.204690	−	0.978827i	$-0.434381\pi$
$967$	35.9080	−	20.7315i	1.15472	−	0.666680i	0.950034	+	0.312147i	$0.101048\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.88730	−	1.88730i	−0.0605663	−	0.0605663i	0.676175	−	0.736741i	$-0.263636\pi$
$971$	−1.88730	−	1.88730i	−0.0605663	−	0.0605663i	−0.736741	+	0.676175i	$0.763636\pi$
$972$		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	0.667853	−	0.744293i	$-0.267213\pi$
$977$	−9.70999	−	16.8182i	−0.310650	−	0.538062i	−0.978503	+	0.206231i	$0.933880\pi$
$978$		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	0.861103	−	0.508431i	$-0.169774\pi$
$983$	26.6919	+	15.4106i	0.851339	+	0.491521i	−0.00976322	+	0.999952i	$0.503108\pi$
$984$		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	−0.332417	−	0.943133i	$-0.607864\pi$
$997$	−4.69625	+	1.25836i	−0.148732	+	0.0398526i	0.183685	+	0.982985i	$0.441197\pi$
$998$		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.1585.12		72
3.2	odd	2		576.2.bb.e.241.6		72
4.3	odd	2		432.2.y.e.181.18		72
9.4	even	3	inner	1728.2.bc.e.1009.7		72
9.5	odd	6		576.2.bb.e.49.13		72
12.11	even	2		144.2.x.e.133.1	yes	72
16.3	odd	4		432.2.y.e.397.6		72
16.13	even	4	inner	1728.2.bc.e.721.7		72
36.23	even	6		144.2.x.e.85.13	yes	72
36.31	odd	6		432.2.y.e.37.6		72
48.29	odd	4		576.2.bb.e.529.13		72
48.35	even	4		144.2.x.e.61.13	yes	72
144.13	even	12	inner	1728.2.bc.e.145.12		72
144.67	odd	12		432.2.y.e.253.18		72
144.77	odd	12		576.2.bb.e.337.6		72
144.131	even	12		144.2.x.e.13.1	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.1	✓	72	144.131	even	12
144.2.x.e.61.13	yes	72	48.35	even	4
144.2.x.e.85.13	yes	72	36.23	even	6
144.2.x.e.133.1	yes	72	12.11	even	2
432.2.y.e.37.6		72	36.31	odd	6
432.2.y.e.181.18		72	4.3	odd	2
432.2.y.e.253.18		72	144.67	odd	12
432.2.y.e.397.6		72	16.3	odd	4
576.2.bb.e.49.13		72	9.5	odd	6
576.2.bb.e.241.6		72	3.2	odd	2
576.2.bb.e.337.6		72	144.77	odd	12
576.2.bb.e.529.13		72	48.29	odd	4
1728.2.bc.e.145.12		72	144.13	even	12	inner
1728.2.bc.e.721.7		72	16.13	even	4	inner
1728.2.bc.e.1009.7		72	9.4	even	3	inner
1728.2.bc.e.1585.12		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)

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

Modular forms

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Database

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