LMFDB - Embedded newform 1728.2.bc.e.1009.4

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			1009.4
Character	$\chi$	$=$	1728.1009
Dual form			1728.2.bc.e.721.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.90072 + 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +O(q^{10})$	$q+(-2.90072 + 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +(-1.36579 + 5.09718i) q^{11} +(-0.541655 - 2.02149i) q^{13} +3.20404 q^{17} +(1.87633 - 1.87633i) q^{19} +(3.61927 + 2.08959i) q^{23} +(3.47994 - 2.00914i) q^{25} +(-7.94194 - 2.12804i) q^{29} +(-1.39155 + 2.41023i) q^{31} +(-2.56298 + 2.56298i) q^{35} +(-5.10207 - 5.10207i) q^{37} +(-9.93271 - 5.73465i) q^{41} +(0.293160 - 1.09409i) q^{43} +(-1.84507 - 3.19576i) q^{47} +(-2.77161 + 4.80057i) q^{49} +(0.613957 + 0.613957i) q^{53} -15.8471i q^{55} +(-11.8105 + 3.16461i) q^{59} +(-7.40505 - 1.98418i) q^{61} +(3.14238 + 5.44277i) q^{65} +(2.64353 + 9.86577i) q^{67} -12.8889i q^{71} +2.87605i q^{73} +(1.64847 + 6.15216i) q^{77} +(0.913281 + 1.58185i) q^{79} +(-2.82747 - 0.757618i) q^{83} +(-9.29402 + 2.49032i) q^{85} +2.11965i q^{89} +(-1.78611 - 1.78611i) q^{91} +(-3.98433 + 6.90107i) q^{95} +(-3.06298 - 5.30524i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

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
$5$	−2.90072	+	0.777246i	−1.29724	+	0.347595i	−0.840406	−	0.541957i	$-0.817684\pi$
$5$	−2.90072	+	0.777246i	−1.29724	+	0.347595i	−0.456835	+	0.889551i	$0.651017\pi$
$6$		0			0
$7$	1.04527	−	0.603486i	0.395074	−	0.228096i	−0.289282	−	0.957244i	$-0.593417\pi$
$7$	1.04527	−	0.603486i	0.395074	−	0.228096i	0.684357	+	0.729148i	$0.260083\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.36579	+	5.09718i	−0.411800	+	1.53686i	0.379360	+	0.925249i	$0.376144\pi$
$11$	−1.36579	+	5.09718i	−0.411800	+	1.53686i	−0.791160	+	0.611609i	$0.790522\pi$
$12$		0			0
$13$	−0.541655	−	2.02149i	−0.150228	−	0.560659i	−0.999467	−	0.0326501i	$-0.989605\pi$
$13$	−0.541655	−	2.02149i	−0.150228	−	0.560659i	0.849239	−	0.528009i	$-0.177061\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.20404			0.777093			0.388547	−	0.921429i	$-0.372977\pi$
$17$	3.20404			0.777093			0.388547	+	0.921429i	$0.372977\pi$
$18$		0			0
$19$	1.87633	−	1.87633i	0.430459	−	0.430459i	−0.458325	−	0.888784i	$-0.651551\pi$
$19$	1.87633	−	1.87633i	0.430459	−	0.430459i	0.888784	+	0.458325i	$0.151551\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.61927	+	2.08959i	0.754670	+	0.435709i	0.827379	−	0.561644i	$-0.189831\pi$
$23$	3.61927	+	2.08959i	0.754670	+	0.435709i	−0.0727090	+	0.997353i	$0.523164\pi$
$24$		0			0
$25$	3.47994	−	2.00914i	0.695988	−	0.401829i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−7.94194	−	2.12804i	−1.47478	−	0.395166i	−0.570214	−	0.821496i	$-0.693140\pi$
$29$	−7.94194	−	2.12804i	−1.47478	−	0.395166i	−0.904568	+	0.426330i	$0.859806\pi$
$30$		0			0
$31$	−1.39155	+	2.41023i	−0.249930	+	0.432891i	−0.963506	−	0.267687i	$-0.913741\pi$
$31$	−1.39155	+	2.41023i	−0.249930	+	0.432891i	0.713576	+	0.700577i	$0.247074\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.56298	+	2.56298i	−0.433222	+	0.433222i
$36$		0			0
$37$	−5.10207	−	5.10207i	−0.838775	−	0.838775i	0.149922	−	0.988698i	$-0.452098\pi$
$37$	−5.10207	−	5.10207i	−0.838775	−	0.838775i	−0.988698	+	0.149922i	$0.952098\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.93271	−	5.73465i	−1.55123	−	0.895602i	−0.998042	−	0.0625444i	$-0.980078\pi$
$41$	−9.93271	−	5.73465i	−1.55123	−	0.895602i	−0.553186	−	0.833058i	$-0.686588\pi$
$42$		0			0
$43$	0.293160	−	1.09409i	0.0447065	−	0.166847i	−0.939963	−	0.341275i	$-0.889141\pi$
$43$	0.293160	−	1.09409i	0.0447065	−	0.166847i	0.984670	+	0.174428i	$0.0558078\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.84507	−	3.19576i	−0.269132	−	0.466150i	0.699506	−	0.714627i	$-0.253403\pi$
$47$	−1.84507	−	3.19576i	−0.269132	−	0.466150i	−0.968638	+	0.248477i	$0.920070\pi$
$48$		0			0
$49$	−2.77161	+	4.80057i	−0.395944	+	0.685795i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.613957	+	0.613957i	0.0843335	+	0.0843335i	0.748015	−	0.663682i	$-0.231007\pi$
$53$	0.613957	+	0.613957i	0.0843335	+	0.0843335i	−0.663682	+	0.748015i	$0.731007\pi$
$54$		0			0
$55$		−	15.8471i		−	2.13682i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−11.8105	+	3.16461i	−1.53759	+	0.411997i	−0.925487	−	0.378779i	$-0.876344\pi$
$59$	−11.8105	+	3.16461i	−1.53759	+	0.411997i	−0.612106	+	0.790776i	$0.709677\pi$
$60$		0			0
$61$	−7.40505	−	1.98418i	−0.948119	−	0.254048i	−0.248555	−	0.968618i	$-0.579956\pi$
$61$	−7.40505	−	1.98418i	−0.948119	−	0.254048i	−0.699564	+	0.714570i	$0.746622\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.14238	+	5.44277i	0.389765	+	0.675092i
$66$		0			0
$67$	2.64353	+	9.86577i	0.322958	+	1.20530i	0.916349	+	0.400381i	$0.131122\pi$
$67$	2.64353	+	9.86577i	0.322958	+	1.20530i	−0.593391	+	0.804915i	$0.702211\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	12.8889i		−	1.52963i	−0.644251	−	0.764814i	$-0.722831\pi$
$71$		−	12.8889i		−	1.52963i	0.644251	−	0.764814i	$-0.277169\pi$
$72$		0			0
$73$			2.87605i			0.336616i	0.985734	+	0.168308i	$0.0538304\pi$
$73$			2.87605i			0.336616i	−0.985734	+	0.168308i	$0.946170\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.64847	+	6.15216i	0.187860	+	0.701104i
$78$		0			0
$79$	0.913281	+	1.58185i	0.102752	+	0.177972i	0.912818	−	0.408367i	$-0.133902\pi$
$79$	0.913281	+	1.58185i	0.102752	+	0.177972i	−0.810065	+	0.586339i	$0.800568\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.82747	−	0.757618i	−0.310355	−	0.0831594i	0.100280	−	0.994959i	$-0.468026\pi$
$83$	−2.82747	−	0.757618i	−0.310355	−	0.0831594i	−0.410635	+	0.911800i	$0.634693\pi$
$84$		0			0
$85$	−9.29402	+	2.49032i	−1.00808	+	0.270114i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			2.11965i			0.224682i	0.993670	+	0.112341i	$0.0358349\pi$
$89$			2.11965i			0.224682i	−0.993670	+	0.112341i	$0.964165\pi$
$90$		0			0
$91$	−1.78611	−	1.78611i	−0.187236	−	0.187236i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.98433	+	6.90107i	−0.408784	+	0.708035i
$96$		0			0
$97$	−3.06298	−	5.30524i	−0.310999	−	0.538666i	0.667580	−	0.744538i	$-0.267330\pi$
$97$	−3.06298	−	5.30524i	−0.310999	−	0.538666i	−0.978579	+	0.205872i	$0.933997\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.38172	−	12.6207i	0.336493	−	1.25581i	−0.565748	−	0.824579i	$-0.691412\pi$
$101$	3.38172	−	12.6207i	0.336493	−	1.25581i	0.902241	−	0.431232i	$-0.141921\pi$
$102$		0			0
$103$	−11.4364	−	6.60279i	−1.12686	−	0.650592i	−0.183715	−	0.982979i	$-0.558813\pi$
$103$	−11.4364	−	6.60279i	−1.12686	−	0.650592i	−0.943143	+	0.332387i	$0.892146\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.92566	+	6.92566i	0.669529	+	0.669529i	0.957607	−	0.288078i	$-0.0930163\pi$
$107$	6.92566	+	6.92566i	0.669529	+	0.669529i	−0.288078	+	0.957607i	$0.593016\pi$
$108$		0			0
$109$	−5.36289	+	5.36289i	−0.513672	+	0.513672i	−0.915650	−	0.401977i	$-0.868323\pi$
$109$	−5.36289	+	5.36289i	−0.513672	+	0.513672i	0.401977	+	0.915650i	$0.368323\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.03493	+	5.25666i	−0.285502	+	0.494505i	−0.972731	−	0.231937i	$-0.925494\pi$
$113$	−3.03493	+	5.25666i	−0.285502	+	0.494505i	0.687228	+	0.726441i	$0.258827\pi$
$114$		0			0
$115$	−12.1226	−	3.24824i	−1.13044	−	0.302900i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.34908	−	1.93359i	0.307010	−	0.177252i
$120$		0			0
$121$	−14.5896	−	8.42332i	−1.32633	−	0.765757i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.08464	−	2.08464i	0.186456	−	0.186456i
$126$		0			0
$127$	−11.7086			−1.03897			−0.519484	−	0.854480i	$-0.673876\pi$
$127$	−11.7086			−1.03897			−0.519484	+	0.854480i	$0.673876\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.31247	−	8.63027i	−0.202042	−	0.754030i	−0.990331	−	0.138725i	$-0.955700\pi$
$131$	−2.31247	−	8.63027i	−0.202042	−	0.754030i	0.788289	−	0.615305i	$-0.210967\pi$
$132$		0			0
$133$	0.828929	−	3.09360i	0.0718772	−	0.268250i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.32169	+	0.763080i	−0.112920	+	0.0651943i	−0.555396	−	0.831586i	$-0.687433\pi$
$137$	−1.32169	+	0.763080i	−0.112920	+	0.0651943i	0.442476	+	0.896780i	$0.354100\pi$
$138$		0			0
$139$	16.8571	−	4.51685i	1.42980	−	0.383114i	0.540852	−	0.841118i	$-0.318102\pi$
$139$	16.8571	−	4.51685i	1.42980	−	0.383114i	0.888950	+	0.458004i	$0.151435\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	11.0437			0.923518
$144$		0			0
$145$	24.6914			2.05051
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.1123	+	4.58523i	−1.40189	+	0.375637i	−0.879025	−	0.476776i	$-0.841805\pi$
$149$	−17.1123	+	4.58523i	−1.40189	+	0.375637i	−0.522870	+	0.852412i	$0.675139\pi$
$150$		0			0
$151$	−4.49848	+	2.59720i	−0.366081	+	0.211357i	−0.671745	−	0.740783i	$-0.734455\pi$
$151$	−4.49848	+	2.59720i	−0.366081	+	0.211357i	0.305664	+	0.952139i	$0.401122\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.16315	−	8.07299i	0.173748	−	0.648438i
$156$		0			0
$157$	2.74719	+	10.2527i	0.219250	+	0.818252i	0.984627	+	0.174670i	$0.0558858\pi$
$157$	2.74719	+	10.2527i	0.219250	+	0.818252i	−0.765377	+	0.643582i	$0.777448\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.04415			0.397534
$162$		0			0
$163$	−2.62311	+	2.62311i	−0.205458	+	0.205458i	−0.802334	−	0.596876i	$-0.796409\pi$
$163$	−2.62311	+	2.62311i	−0.205458	+	0.205458i	0.596876	+	0.802334i	$0.296409\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.07413	−	2.92955i	−0.392648	−	0.226695i	0.290659	−	0.956827i	$-0.406126\pi$
$167$	−5.07413	−	2.92955i	−0.392648	−	0.226695i	−0.683307	+	0.730131i	$0.739459\pi$
$168$		0			0
$169$	7.46532	−	4.31010i	0.574255	−	0.331546i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.719924	−	0.192903i	−0.0547348	−	0.0146662i	0.231348	−	0.972871i	$-0.425686\pi$
$173$	−0.719924	−	0.192903i	−0.0547348	−	0.0146662i	−0.286083	+	0.958205i	$0.592353\pi$
$174$		0			0
$175$	2.42498	−	4.20019i	0.183311	−	0.317505i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.114862	+	0.114862i	−0.00858517	+	0.00858517i	−0.711386	−	0.702801i	$-0.751932\pi$
$179$	−0.114862	+	0.114862i	−0.00858517	+	0.00858517i	0.702801	+	0.711386i	$0.251932\pi$
$180$		0			0
$181$	−7.86110	−	7.86110i	−0.584311	−	0.584311i	0.351774	−	0.936085i	$-0.385578\pi$
$181$	−7.86110	−	7.86110i	−0.584311	−	0.584311i	−0.936085	+	0.351774i	$0.885578\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	18.7652	+	10.8341i	1.37965	+	0.796540i
$186$		0			0
$187$	−4.37603	+	16.3316i	−0.320007	+	1.19428i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.25437	+	3.90468i	0.163120	+	0.282532i	0.935986	−	0.352037i	$-0.114511\pi$
$191$	2.25437	+	3.90468i	0.163120	+	0.282532i	−0.772866	+	0.634569i	$0.781178\pi$
$192$		0			0
$193$	9.64610	−	16.7075i	0.694342	−	1.20264i	−0.276060	−	0.961140i	$-0.589029\pi$
$193$	9.64610	−	16.7075i	0.694342	−	1.20264i	0.970402	−	0.241495i	$-0.0776377\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.03688	+	6.03688i	0.430110	+	0.430110i	0.888666	−	0.458556i	$-0.151633\pi$
$197$	6.03688	+	6.03688i	0.430110	+	0.430110i	−0.458556	+	0.888666i	$0.651633\pi$
$198$		0			0
$199$			8.81333i			0.624760i	0.949957	+	0.312380i	$0.101126\pi$
$199$			8.81333i			0.624760i	−0.949957	+	0.312380i	$0.898874\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.58570	+	2.56848i	−0.672784	+	0.180272i
$204$		0			0
$205$	33.2692	+	8.91447i	2.32362	+	0.622613i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	7.00132	+	12.1266i	0.484292	+	0.838818i
$210$		0			0
$211$	−0.261630	−	0.976416i	−0.0180113	−	0.0672192i	0.956335	−	0.292272i	$-0.0944112\pi$
$211$	−0.261630	−	0.976416i	−0.0180113	−	0.0672192i	−0.974347	+	0.225053i	$0.927745\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			3.40150i			0.231981i
$216$		0			0
$217$			3.35912i			0.228032i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.73548	−	6.47692i	−0.116741	−	0.435685i
$222$		0			0
$223$	4.44475	+	7.69854i	0.297643	+	0.515532i	0.975596	−	0.219573i	$-0.0704663\pi$
$223$	4.44475	+	7.69854i	0.297643	+	0.515532i	−0.677954	+	0.735105i	$0.737133\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−21.7441	−	5.82630i	−1.44320	−	0.386705i	−0.549550	−	0.835461i	$-0.685201\pi$
$227$	−21.7441	−	5.82630i	−1.44320	−	0.386705i	−0.893655	+	0.448756i	$0.851867\pi$
$228$		0			0
$229$	13.3954	−	3.58930i	0.885196	−	0.237187i	0.212548	−	0.977151i	$-0.431824\pi$
$229$	13.3954	−	3.58930i	0.885196	−	0.237187i	0.672647	+	0.739963i	$0.265157\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	6.70075i		−	0.438981i	−0.975615	−	0.219491i	$-0.929561\pi$
$233$		−	6.70075i		−	0.438981i	0.975615	−	0.219491i	$-0.0704395\pi$
$234$		0			0
$235$	7.83593	+	7.83593i	0.511160	+	0.511160i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.04479	−	1.80963i	0.0675819	−	0.117055i	−0.830254	−	0.557385i	$-0.811805\pi$
$239$	1.04479	−	1.80963i	0.0675819	−	0.117055i	0.897836	+	0.440329i	$0.145138\pi$
$240$		0			0
$241$	4.31263	+	7.46970i	0.277801	+	0.481166i	0.970838	−	0.239736i	$-0.0770610\pi$
$241$	4.31263	+	7.46970i	0.277801	+	0.481166i	−0.693037	+	0.720902i	$0.743728\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.30844	−	16.0793i	0.275256	−	1.02727i
$246$		0			0
$247$	−4.80929	−	2.77665i	−0.306008	−	0.176674i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	16.7058	+	16.7058i	1.05446	+	1.05446i	0.998429	+	0.0560334i	$0.0178453\pi$
$251$	16.7058	+	16.7058i	1.05446	+	1.05446i	0.0560334	+	0.998429i	$0.482155\pi$
$252$		0			0
$253$	−15.5941	+	15.5941i	−0.980396	+	0.980396i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.26980	+	12.5917i	−0.453477	+	0.785446i	−0.998599	−	0.0529109i	$-0.983150\pi$
$257$	−7.26980	+	12.5917i	−0.453477	+	0.785446i	0.545122	+	0.838357i	$0.316483\pi$
$258$		0			0
$259$	−8.41207	−	2.25401i	−0.522700	−	0.140057i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.27433	−	4.19984i	0.448555	−	0.258973i	−0.258665	−	0.965967i	$-0.583283\pi$
$263$	7.27433	−	4.19984i	0.448555	−	0.258973i	0.707220	+	0.706994i	$0.249949\pi$
$264$		0			0
$265$	−2.25811	−	1.30372i	−0.138715	−	0.0800871i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.63413	+	3.63413i	−0.221577	+	0.221577i	−0.809162	−	0.587585i	$-0.800079\pi$
$269$	−3.63413	+	3.63413i	−0.221577	+	0.221577i	0.587585	+	0.809162i	$0.300079\pi$
$270$		0			0
$271$	−2.61554			−0.158882			−0.0794412	−	0.996840i	$-0.525314\pi$
$271$	−2.61554			−0.158882			−0.0794412	+	0.996840i	$0.525314\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.48812	+	20.4820i	0.330946	+	1.23511i
$276$		0			0
$277$	−2.76263	+	10.3103i	−0.165990	+	0.619484i	0.831922	+	0.554893i	$0.187241\pi$
$277$	−2.76263	+	10.3103i	−0.165990	+	0.619484i	−0.997912	+	0.0645907i	$0.979426\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.21844	−	3.59022i	0.370961	−	0.214174i	−0.302917	−	0.953017i	$-0.597961\pi$
$281$	6.21844	−	3.59022i	0.370961	−	0.214174i	0.673878	+	0.738842i	$0.264627\pi$
$282$		0			0
$283$	−13.9481	+	3.73738i	−0.829127	+	0.222164i	−0.648333	−	0.761357i	$-0.724533\pi$
$283$	−13.9481	+	3.73738i	−0.829127	+	0.222164i	−0.180794	+	0.983521i	$0.557867\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−13.8431			−0.817134
$288$		0			0
$289$	−6.73414			−0.396126
$290$		0			0
$291$		0			0
$292$		0			0
$293$	24.3455	−	6.52336i	1.42228	−	0.381099i	0.535988	−	0.844226i	$-0.319939\pi$
$293$	24.3455	−	6.52336i	1.42228	−	0.381099i	0.886292	+	0.463127i	$0.153273\pi$
$294$		0			0
$295$	31.7992	−	18.3593i	1.85142	−	1.06892i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.26367	−	8.44814i	0.130911	−	0.488568i
$300$		0			0
$301$	−0.353836	−	1.32053i	−0.0203948	−	0.0761144i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	23.0222			1.31824
$306$		0			0
$307$	−3.57698	+	3.57698i	−0.204149	+	0.204149i	−0.801775	−	0.597626i	$-0.796111\pi$
$307$	−3.57698	+	3.57698i	−0.204149	+	0.204149i	0.597626	+	0.801775i	$0.296111\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.71609	−	2.14548i	−0.210720	−	0.121659i	0.390926	−	0.920422i	$-0.372155\pi$
$311$	−3.71609	−	2.14548i	−0.210720	−	0.121659i	−0.601646	+	0.798763i	$0.705488\pi$
$312$		0			0
$313$	8.68061	−	5.01175i	0.490657	−	0.283281i	−0.234190	−	0.972191i	$-0.575244\pi$
$313$	8.68061	−	5.01175i	0.490657	−	0.283281i	0.724847	+	0.688910i	$0.241910\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−26.6623	−	7.14413i	−1.49750	−	0.401254i	−0.585239	−	0.810861i	$-0.698999\pi$
$317$	−26.6623	−	7.14413i	−1.49750	−	0.401254i	−0.912262	+	0.409606i	$0.865666\pi$
$318$		0			0
$319$	21.6940	−	37.5751i	1.21463	−	2.10380i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.01183	−	6.01183i	0.334507	−	0.334507i
$324$		0			0
$325$	−5.94639	−	5.94639i	−0.329846	−	0.329846i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.85720	−	2.22695i	−0.212654	−	0.122776i
$330$		0			0
$331$	1.23731	−	4.61769i	0.0680085	−	0.253811i	−0.923549	−	0.383481i	$-0.874725\pi$
$331$	1.23731	−	4.61769i	0.0680085	−	0.253811i	0.991557	+	0.129670i	$0.0413918\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−15.3363	−	26.5632i	−0.837909	−	1.45130i
$336$		0			0
$337$	−7.47777	+	12.9519i	−0.407340	+	0.705534i	−0.994591	−	0.103871i	$-0.966877\pi$
$337$	−7.47777	+	12.9519i	−0.407340	+	0.705534i	0.587251	+	0.809405i	$0.300210\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−10.3848	−	10.3848i	−0.562371	−	0.562371i
$342$		0			0
$343$			15.1393i			0.817446i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	29.4830	−	7.89996i	1.58273	−	0.424092i	0.642962	−	0.765898i	$-0.277705\pi$
$347$	29.4830	−	7.89996i	1.58273	−	0.424092i	0.939771	+	0.341806i	$0.111039\pi$
$348$		0			0
$349$	−32.4685	−	8.69992i	−1.73800	−	0.465696i	−0.756000	−	0.654572i	$-0.772849\pi$
$349$	−32.4685	−	8.69992i	−1.73800	−	0.465696i	−0.982001	+	0.188876i	$0.939515\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−16.5277	−	28.6268i	−0.879680	−	1.52365i	−0.851692	−	0.524043i	$-0.824423\pi$
$353$	−16.5277	−	28.6268i	−0.879680	−	1.52365i	−0.0279885	−	0.999608i	$-0.508910\pi$
$354$		0			0
$355$	10.0178	+	37.3870i	0.531691	+	1.98430i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			13.5739i			0.716404i	0.933644	+	0.358202i	$0.116610\pi$
$359$			13.5739i			0.716404i	−0.933644	+	0.358202i	$0.883390\pi$
$360$		0			0
$361$			11.9588i			0.629410i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.23540	−	8.34262i	−0.117006	−	0.436673i
$366$		0			0
$367$	1.88219	+	3.26006i	0.0982497	+	0.170174i	0.910960	−	0.412494i	$-0.135342\pi$
$367$	1.88219	+	3.26006i	0.0982497	+	0.170174i	−0.812711	+	0.582668i	$0.802009\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.01227	+	0.271236i	0.0525542	+	0.0140819i
$372$		0			0
$373$	20.6979	−	5.54598i	1.07170	−	0.287160i	0.320506	−	0.947247i	$-0.396147\pi$
$373$	20.6979	−	5.54598i	1.07170	−	0.287160i	0.751189	+	0.660087i	$0.229480\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			17.2072i			0.886215i
$378$		0			0
$379$	−0.0423205	−	0.0423205i	−0.00217386	−	0.00217386i	0.706019	−	0.708193i	$-0.250489\pi$
$379$	−0.0423205	−	0.0423205i	−0.00217386	−	0.00217386i	−0.708193	+	0.706019i	$0.750489\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.83724	+	11.8424i	−0.349367	+	0.605121i	−0.986137	−	0.165933i	$-0.946937\pi$
$383$	−6.83724	+	11.8424i	−0.349367	+	0.605121i	0.636770	+	0.771053i	$0.280270\pi$
$384$		0			0
$385$	−9.56348	−	16.5644i	−0.487400	−	0.844201i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.68890	+	13.7672i	−0.187035	+	0.698023i	0.807151	+	0.590345i	$0.201008\pi$
$389$	−3.68890	+	13.7672i	−0.187035	+	0.698023i	−0.994186	+	0.107678i	$0.965658\pi$
$390$		0			0
$391$	11.5963	+	6.69511i	0.586449	+	0.338586i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.87866	−	3.87866i	−0.195157	−	0.195157i
$396$		0			0
$397$	16.1526	−	16.1526i	0.810677	−	0.810677i	−0.174058	−	0.984735i	$-0.555688\pi$
$397$	16.1526	−	16.1526i	0.810677	−	0.810677i	0.984735	+	0.174058i	$0.0556881\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.96568	+	3.40466i	−0.0981615	+	0.170021i	−0.910924	−	0.412575i	$-0.864630\pi$
$401$	−1.96568	+	3.40466i	−0.0981615	+	0.170021i	0.812762	+	0.582596i	$0.197963\pi$
$402$		0			0
$403$	5.62599	+	1.50748i	0.280251	+	0.0750929i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	32.9745	−	19.0379i	1.63449	−	0.943671i
$408$		0			0
$409$	17.7471	+	10.2463i	0.877536	+	0.506646i	0.869845	−	0.493325i	$-0.164219\pi$
$409$	17.7471	+	10.2463i	0.877536	+	0.506646i	0.00769067	+	0.999970i	$0.497552\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.4353	+	10.4353i	−0.513489	+	0.513489i
$414$		0			0
$415$	8.79055			0.431511
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.48550	−	5.54398i	−0.0725716	−	0.270841i	0.920100	−	0.391683i	$-0.128107\pi$
$419$	−1.48550	−	5.54398i	−0.0725716	−	0.270841i	−0.992672	+	0.120842i	$0.961440\pi$
$420$		0			0
$421$	−10.0100	+	37.3580i	−0.487859	+	1.82072i	0.0789649	+	0.996877i	$0.474838\pi$
$421$	−10.0100	+	37.3580i	−0.487859	+	1.82072i	−0.566824	+	0.823839i	$0.691828\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	11.1499	−	6.43738i	0.540848	−	0.312259i
$426$		0			0
$427$	−8.93769	+	2.39485i	−0.432525	+	0.115895i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	29.0431			1.39896			0.699479	−	0.714653i	$-0.253415\pi$
$431$	29.0431			1.39896			0.699479	+	0.714653i	$0.253415\pi$
$432$		0			0
$433$	28.4001			1.36482			0.682411	−	0.730969i	$-0.260932\pi$
$433$	28.4001			1.36482			0.682411	+	0.730969i	$0.260932\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.7117	−	2.87019i	0.512409	−	0.137300i
$438$		0			0
$439$	−2.37559	+	1.37154i	−0.113381	+	0.0654603i	−0.555618	−	0.831438i	$-0.687518\pi$
$439$	−2.37559	+	1.37154i	−0.113381	+	0.0654603i	0.442237	+	0.896898i	$0.354185\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.83055	+	6.83170i	−0.0869720	+	0.324584i	−0.995680	−	0.0928477i	$-0.970403\pi$
$443$	−1.83055	+	6.83170i	−0.0869720	+	0.324584i	0.908708	+	0.417432i	$0.137070\pi$
$444$		0			0
$445$	−1.64749	−	6.14850i	−0.0780983	−	0.291467i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.27698			−0.107457			−0.0537287	−	0.998556i	$-0.517111\pi$
$449$	−2.27698			−0.107457			−0.0537287	+	0.998556i	$0.517111\pi$
$450$		0			0
$451$	42.7965	−	42.7965i	2.01521	−	2.01521i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.56927	+	3.79277i	0.307972	+	0.177808i
$456$		0			0
$457$	−21.7536	+	12.5595i	−1.01759	+	0.587507i	−0.913406	−	0.407051i	$-0.866557\pi$
$457$	−21.7536	+	12.5595i	−1.01759	+	0.587507i	−0.104187	+	0.994558i	$0.533224\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	21.4217	+	5.73994i	0.997710	+	0.267336i	0.720486	−	0.693470i	$-0.243919\pi$
$461$	21.4217	+	5.73994i	0.997710	+	0.267336i	0.277224	+	0.960805i	$0.410585\pi$
$462$		0			0
$463$	−19.5447	+	33.8525i	−0.908321	+	1.57326i	−0.0919260	+	0.995766i	$0.529302\pi$
$463$	−19.5447	+	33.8525i	−0.908321	+	1.57326i	−0.816396	+	0.577493i	$0.804031\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.46264	−	4.46264i	0.206506	−	0.206506i	−0.596274	−	0.802781i	$-0.703353\pi$
$467$	4.46264	−	4.46264i	0.206506	−	0.206506i	0.802781	+	0.596274i	$0.203353\pi$
$468$		0			0
$469$	8.71705	+	8.71705i	0.402516	+	0.402516i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.17638	+	2.98858i	0.238010	+	0.137415i
$474$		0			0
$475$	2.75970	−	10.2993i	0.126624	−	0.472565i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.80441	+	4.85738i	0.128137	+	0.221939i	0.922955	−	0.384909i	$-0.125767\pi$
$479$	2.80441	+	4.85738i	0.128137	+	0.221939i	−0.794818	+	0.606848i	$0.792434\pi$
$480$		0			0
$481$	−7.55020	+	13.0773i	−0.344260	+	0.596275i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.0083	+	13.0083i	0.590678	+	0.590678i
$486$		0			0
$487$			34.1026i			1.54534i	0.634810	+	0.772668i	$0.281078\pi$
$487$			34.1026i			1.54534i	−0.634810	+	0.772668i	$0.718922\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−14.5988	+	3.91173i	−0.658833	+	0.176534i	−0.572719	−	0.819751i	$-0.694112\pi$
$491$	−14.5988	+	3.91173i	−0.658833	+	0.176534i	−0.0861138	+	0.996285i	$0.527445\pi$
$492$		0			0
$493$	−25.4463	−	6.81831i	−1.14604	−	0.307081i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.77826	−	13.4723i	−0.348902	−	0.604317i
$498$		0			0
$499$	−2.37206	−	8.85266i	−0.106188	−	0.396300i	0.892289	−	0.451464i	$-0.149098\pi$
$499$	−2.37206	−	8.85266i	−0.106188	−	0.396300i	−0.998477	+	0.0551648i	$0.982432\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			6.41865i			0.286194i	0.989709	+	0.143097i	$0.0457060\pi$
$503$			6.41865i			0.286194i	−0.989709	+	0.143097i	$0.954294\pi$
$504$		0			0
$505$			39.2377i			1.74605i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.23386	+	23.2651i	0.276311	+	1.03121i	0.954958	+	0.296742i	$0.0959001\pi$
$509$	6.23386	+	23.2651i	0.276311	+	1.03121i	−0.678647	+	0.734465i	$0.737433\pi$
$510$		0			0
$511$	1.73566	+	3.00625i	0.0767810	+	0.132989i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	38.3057	+	10.2640i	1.68795	+	0.452285i
$516$		0			0
$517$	18.8094	−	5.03995i	0.827235	−	0.221657i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	15.3122i		−	0.670839i	−0.942069	−	0.335420i	$-0.891122\pi$
$521$		−	15.3122i		−	0.670839i	0.942069	−	0.335420i	$-0.108878\pi$
$522$		0			0
$523$	19.6619	+	19.6619i	0.859756	+	0.859756i	0.991309	−	0.131553i	$-0.0419965\pi$
$523$	19.6619	+	19.6619i	0.859756	+	0.859756i	−0.131553	+	0.991309i	$0.541996\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.45858	+	7.72248i	−0.194219	+	0.336397i
$528$		0			0
$529$	−2.76726	−	4.79304i	−0.120316	−	0.208393i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.21241	+	23.1850i	−0.269089	+	1.00426i
$534$		0			0
$535$	−25.4723	−	14.7065i	−1.10127	−	0.635816i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−20.6839	−	20.6839i	−0.890921	−	0.890921i
$540$		0			0
$541$	12.1084	−	12.1084i	0.520580	−	0.520580i	−0.397167	−	0.917746i	$-0.630007\pi$
$541$	12.1084	−	12.1084i	0.520580	−	0.520580i	0.917746	+	0.397167i	$0.130007\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	11.3880	−	19.7245i	0.487807	−	0.844906i
$546$		0			0
$547$	−36.4729	−	9.77287i	−1.55947	−	0.417858i	−0.626972	−	0.779042i	$-0.715706\pi$
$547$	−36.4729	−	9.77287i	−1.55947	−	0.417858i	−0.932495	+	0.361184i	$0.882373\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−18.8946	+	10.9088i	−0.804936	+	0.464730i
$552$		0			0
$553$	1.90925	+	1.10231i	0.0811895	+	0.0468748i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	29.5565	−	29.5565i	1.25235	−	1.25235i	0.297685	−	0.954664i	$-0.403786\pi$
$557$	29.5565	−	29.5565i	1.25235	−	1.25235i	0.954664	−	0.297685i	$-0.0962144\pi$
$558$		0			0
$559$	−2.37048			−0.100260
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.91061	+	25.7907i	0.291247	+	1.08695i	0.944152	+	0.329510i	$0.106884\pi$
$563$	6.91061	+	25.7907i	0.291247	+	1.08695i	−0.652905	+	0.757440i	$0.726450\pi$
$564$		0			0
$565$	4.71778	−	17.6070i	0.198478	−	0.740731i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.49763	+	5.48346i	−0.398161	+	0.229879i	−0.685690	−	0.727893i	$-0.740500\pi$
$569$	−9.49763	+	5.48346i	−0.398161	+	0.229879i	0.287529	+	0.957772i	$0.407166\pi$
$570$		0			0
$571$	36.2420	−	9.71100i	1.51668	−	0.406393i	0.598032	−	0.801472i	$-0.295950\pi$
$571$	36.2420	−	9.71100i	1.51668	−	0.406393i	0.918647	+	0.395080i	$0.129283\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.7931			0.700322
$576$		0			0
$577$	−29.3500			−1.22186			−0.610929	−	0.791686i	$-0.709204\pi$
$577$	−29.3500			−1.22186			−0.610929	+	0.791686i	$0.709204\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.41268	+	0.914424i	−0.141582	+	0.0379367i
$582$		0			0
$583$	−3.96799	+	2.29092i	−0.164337	+	0.0948802i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.643018	−	2.39978i	0.0265402	−	0.0990494i	−0.951385	−	0.308003i	$-0.900339\pi$
$587$	0.643018	−	2.39978i	0.0265402	−	0.0990494i	0.977925	+	0.208954i	$0.0670059\pi$
$588$		0			0
$589$	1.91139	+	7.13339i	0.0787573	+	0.293926i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	3.31760			0.136238			0.0681188	−	0.997677i	$-0.478300\pi$
$593$	3.31760			0.136238			0.0681188	+	0.997677i	$0.478300\pi$
$594$		0			0
$595$	−8.21187	+	8.21187i	−0.336654	+	0.336654i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	16.9013	+	9.75798i	0.690569	+	0.398700i	0.803825	−	0.594866i	$-0.202795\pi$
$599$	16.9013	+	9.75798i	0.690569	+	0.398700i	−0.113256	+	0.993566i	$0.536128\pi$
$600$		0			0
$601$	−5.79012	+	3.34293i	−0.236184	+	0.136361i	−0.613422	−	0.789756i	$-0.710207\pi$
$601$	−5.79012	+	3.34293i	−0.236184	+	0.136361i	0.377238	+	0.926116i	$0.376874\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	48.8674	+	13.0940i	1.98674	+	0.532346i
$606$		0			0
$607$	4.11486	−	7.12715i	0.167017	−	0.289282i	−0.770353	−	0.637618i	$-0.779920\pi$
$607$	4.11486	−	7.12715i	0.167017	−	0.289282i	0.937370	+	0.348336i	$0.113253\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.46079	+	5.46079i	−0.220920	+	0.220920i
$612$		0			0
$613$	−5.65366	−	5.65366i	−0.228349	−	0.228349i	0.583654	−	0.812003i	$-0.301623\pi$
$613$	−5.65366	−	5.65366i	−0.228349	−	0.228349i	−0.812003	+	0.583654i	$0.801623\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−24.8990	−	14.3754i	−1.00240	−	0.578733i	−0.0934395	−	0.995625i	$-0.529786\pi$
$617$	−24.8990	−	14.3754i	−1.00240	−	0.578733i	−0.908956	+	0.416891i	$0.863120\pi$
$618$		0			0
$619$	5.61764	−	20.9653i	0.225792	−	0.842668i	−0.756293	−	0.654232i	$-0.772992\pi$
$619$	5.61764	−	20.9653i	0.225792	−	0.842668i	0.982086	−	0.188435i	$-0.0603416\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.27918	+	2.21560i	0.0512491	+	0.0887661i
$624$		0			0
$625$	−14.4724	+	25.0669i	−0.578896	+	1.00268i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−16.3472	−	16.3472i	−0.651807	−	0.651807i
$630$		0			0
$631$			13.0320i			0.518796i	0.965770	+	0.259398i	$0.0835242\pi$
$631$			13.0320i			0.518796i	−0.965770	+	0.259398i	$0.916476\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	33.9633	−	9.10043i	1.34779	−	0.361140i
$636$		0			0
$637$	11.2055	+	3.00251i	0.443979	+	0.118964i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6.70219	−	11.6085i	−0.264721	−	0.458510i	0.702770	−	0.711417i	$-0.251946\pi$
$641$	−6.70219	−	11.6085i	−0.264721	−	0.458510i	−0.967490	+	0.252908i	$0.918613\pi$
$642$		0			0
$643$	−2.65048	−	9.89172i	−0.104525	−	0.390091i	0.893766	−	0.448533i	$-0.148053\pi$
$643$	−2.65048	−	9.89172i	−0.104525	−	0.390091i	−0.998291	+	0.0584419i	$0.981387\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			25.5231i			1.00342i	0.865036	+	0.501709i	$0.167295\pi$
$647$			25.5231i			1.00342i	−0.865036	+	0.501709i	$0.832705\pi$
$648$		0			0
$649$		−	64.5223i		−	2.53272i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.44634	−	16.5940i	−0.173999	−	0.649372i	−0.996720	−	0.0809269i	$-0.974212\pi$
$653$	−4.44634	−	16.5940i	−0.173999	−	0.649372i	0.822721	−	0.568445i	$-0.192455\pi$
$654$		0			0
$655$	13.4157	+	23.2366i	0.524194	+	0.907930i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.84828	−	1.29909i	−0.188862	−	0.0506054i	0.163148	−	0.986602i	$-0.447835\pi$
$659$	−4.84828	−	1.29909i	−0.188862	−	0.0506054i	−0.352010	+	0.935996i	$0.614502\pi$
$660$		0			0
$661$	24.2257	−	6.49124i	0.942269	−	0.252480i	0.245190	−	0.969475i	$-0.421150\pi$
$661$	24.2257	−	6.49124i	0.942269	−	0.252480i	0.697079	+	0.716995i	$0.254483\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			9.61796i			0.372969i
$666$		0			0
$667$	−24.2973	−	24.2973i	−0.940795	−	0.940795i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	20.2274	−	35.0349i	0.780871	−	1.35251i
$672$		0			0
$673$	−12.8215	−	22.2075i	−0.494233	−	0.856037i	0.505745	−	0.862683i	$-0.331218\pi$
$673$	−12.8215	−	22.2075i	−0.494233	−	0.856037i	−0.999978	+	0.00664596i	$0.997885\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.01329	−	22.4419i	0.231110	−	0.862513i	−0.748755	−	0.662847i	$-0.769348\pi$
$677$	6.01329	−	22.4419i	0.231110	−	0.862513i	0.979864	−	0.199665i	$-0.0639855\pi$
$678$		0			0
$679$	−6.40328	−	3.69694i	−0.245735	−	0.141875i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−29.4647	−	29.4647i	−1.12744	−	1.12744i	−0.990593	−	0.136843i	$-0.956304\pi$
$683$	−29.4647	−	29.4647i	−1.12744	−	1.12744i	−0.136843	−	0.990593i	$-0.543696\pi$
$684$		0			0
$685$	3.24076	−	3.24076i	0.123823	−	0.123823i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.908553	−	1.57366i	0.0346131	−	0.0599517i
$690$		0			0
$691$	18.9096	+	5.06682i	0.719357	+	0.192751i	0.599885	−	0.800087i	$-0.295213\pi$
$691$	18.9096	+	5.06682i	0.719357	+	0.192751i	0.119472	+	0.992838i	$0.461880\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−45.3871	+	26.2042i	−1.72163	+	0.993984i
$696$		0			0
$697$	−31.8248	−	18.3740i	−1.20545	−	0.695966i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−7.85067	+	7.85067i	−0.296516	+	0.296516i	−0.839647	−	0.543132i	$-0.817238\pi$
$701$	−7.85067	+	7.85067i	−0.296516	+	0.296516i	0.543132	+	0.839647i	$0.317238\pi$
$702$		0			0
$703$	−19.1463			−0.722117
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.08164	−	15.2329i	−0.153506	−	0.572892i
$708$		0			0
$709$	−12.9865	+	48.4664i	−0.487720	+	1.82020i	0.0797675	+	0.996813i	$0.474582\pi$
$709$	−12.9865	+	48.4664i	−0.487720	+	1.82020i	−0.567487	+	0.823382i	$0.692084\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.0728	+	5.81552i	−0.377229	+	0.217793i
$714$		0			0
$715$	−32.0346	+	8.58364i	−1.19803	+	0.321010i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−46.4032			−1.73055			−0.865273	−	0.501301i	$-0.832855\pi$
$719$	−46.4032			−1.73055			−0.865273	+	0.501301i	$0.832855\pi$
$720$		0			0
$721$	−15.9388			−0.593591
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−31.9130	+	8.55107i	−1.18522	+	0.317579i
$726$		0			0
$727$	−13.4929	+	7.79014i	−0.500425	+	0.288920i	−0.728889	−	0.684632i	$-0.759963\pi$
$727$	−13.4929	+	7.79014i	−0.500425	+	0.288920i	0.228464	+	0.973552i	$0.426630\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.939296	−	3.50550i	0.0347411	−	0.129656i
$732$		0			0
$733$	−6.02884	−	22.5000i	−0.222680	−	0.831055i	−0.983321	−	0.181881i	$-0.941781\pi$
$733$	−6.02884	−	22.5000i	−0.222680	−	0.831055i	0.760640	−	0.649174i	$-0.224885\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−53.8981			−1.98536
$738$		0			0
$739$	−17.1341	+	17.1341i	−0.630288	+	0.630288i	−0.948140	−	0.317853i	$-0.897038\pi$
$739$	−17.1341	+	17.1341i	−0.630288	+	0.630288i	0.317853	+	0.948140i	$0.397038\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−34.9775	−	20.1943i	−1.28320	−	0.740855i	−0.305767	−	0.952106i	$-0.598913\pi$
$743$	−34.9775	−	20.1943i	−1.28320	−	0.740855i	−0.977432	+	0.211251i	$0.932246\pi$
$744$		0			0
$745$	46.0742	−	26.6009i	1.68803	−	0.974583i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	11.4187	+	3.05964i	0.417231	+	0.111797i
$750$		0			0
$751$	−2.44188	+	4.22946i	−0.0891056	+	0.154335i	−0.907133	−	0.420843i	$-0.861734\pi$
$751$	−2.44188	+	4.22946i	−0.0891056	+	0.154335i	0.818028	+	0.575179i	$0.195068\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	11.0302	−	11.0302i	0.401429	−	0.401429i
$756$		0			0
$757$	−20.1502	−	20.1502i	−0.732371	−	0.732371i	0.238718	−	0.971089i	$-0.423273\pi$
$757$	−20.1502	−	20.1502i	−0.732371	−	0.732371i	−0.971089	+	0.238718i	$0.923273\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−16.9178	−	9.76748i	−0.613268	−	0.354071i	0.160975	−	0.986958i	$-0.448536\pi$
$761$	−16.9178	−	9.76748i	−0.613268	−	0.354071i	−0.774244	+	0.632888i	$0.781869\pi$
$762$		0			0
$763$	−2.36923	+	8.84210i	−0.0857720	+	0.320105i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.7944	+	22.1606i	0.461980	+	0.800172i
$768$		0			0
$769$	−14.3355	+	24.8299i	−0.516952	+	0.895388i	0.482854	+	0.875701i	$0.339600\pi$
$769$	−14.3355	+	24.8299i	−0.516952	+	0.895388i	−0.999806	+	0.0196866i	$0.993733\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	33.6600	+	33.6600i	1.21067	+	1.21067i	0.970808	+	0.239857i	$0.0771007\pi$
$773$	33.6600	+	33.6600i	1.21067	+	1.21067i	0.239857	+	0.970808i	$0.422899\pi$
$774$		0			0
$775$			11.1833i			0.401716i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−29.3971	+	7.87693i	−1.05326	+	0.282220i
$780$		0			0
$781$	65.6969	+	17.6034i	2.35082	+	0.629901i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.9377	−	27.6049i	−0.568840	−	0.985260i
$786$		0			0
$787$	−7.32646	−	27.3427i	−0.261160	−	0.974662i	−0.964559	−	0.263867i	$-0.915002\pi$
$787$	−7.32646	−	27.3427i	−0.261160	−	0.974662i	0.703399	−	0.710795i	$-0.251665\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			7.32616i			0.260488i
$792$		0			0
$793$			16.0439i			0.569737i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.55450	+	35.6579i	0.338438	+	1.26307i	0.900094	+	0.435696i	$0.143498\pi$
$797$	9.55450	+	35.6579i	0.338438	+	1.26307i	−0.561656	+	0.827371i	$0.689836\pi$
$798$		0			0
$799$	−5.91169	−	10.2393i	−0.209140	−	0.362242i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−14.6598	−	3.92807i	−0.517332	−	0.138619i
$804$		0			0
$805$	−14.6317	+	3.92054i	−0.515698	+	0.138181i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			10.0300i			0.352637i	0.984333	+	0.176318i	$0.0564189\pi$
$809$			10.0300i			0.352637i	−0.984333	+	0.176318i	$0.943581\pi$
$810$		0			0
$811$	−29.2218	−	29.2218i	−1.02612	−	1.02612i	−0.999650	−	0.0264676i	$-0.991574\pi$
$811$	−29.2218	−	29.2218i	−1.02612	−	1.02612i	−0.0264676	−	0.999650i	$-0.508426\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.57011	−	9.64772i	0.195112	−	0.337945i
$816$		0			0
$817$	−1.50280	−	2.60293i	−0.0525765	−	0.0910651i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.55428	+	20.7288i	−0.193846	+	0.723442i	0.798717	+	0.601707i	$0.205512\pi$
$821$	−5.55428	+	20.7288i	−0.193846	+	0.723442i	−0.992563	+	0.121735i	$0.961154\pi$
$822$		0			0
$823$	6.52191	+	3.76543i	0.227340	+	0.131255i	0.609344	−	0.792906i	$-0.291433\pi$
$823$	6.52191	+	3.76543i	0.227340	+	0.131255i	−0.382005	+	0.924160i	$0.624766\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.34158	−	7.34158i	−0.255292	−	0.255292i	0.567844	−	0.823136i	$-0.307778\pi$
$827$	−7.34158	−	7.34158i	−0.255292	−	0.255292i	−0.823136	+	0.567844i	$0.807778\pi$
$828$		0			0
$829$	19.0212	−	19.0212i	0.660632	−	0.660632i	−0.294897	−	0.955529i	$-0.595285\pi$
$829$	19.0212	−	19.0212i	0.660632	−	0.660632i	0.955529	+	0.294897i	$0.0952852\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.88034	+	15.3812i	−0.307686	+	0.532927i
$834$		0			0
$835$	16.9956	+	4.55396i	0.588157	+	0.157596i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−36.1808	+	20.8890i	−1.24910	+	0.721168i	−0.970930	−	0.239364i	$-0.923061\pi$
$839$	−36.1808	+	20.8890i	−1.24910	+	0.721168i	−0.278170	+	0.960532i	$0.589728\pi$
$840$		0			0
$841$	33.4311	+	19.3015i	1.15280	+	0.665568i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.3048	+	18.3048i	−0.629704	+	0.629704i
$846$		0			0
$847$	−20.3334			−0.698665
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−7.80455	−	29.1270i	−0.267537	−	0.998460i
$852$		0			0
$853$	8.76788	−	32.7222i	0.300207	−	1.12039i	−0.636787	−	0.771040i	$-0.719737\pi$
$853$	8.76788	−	32.7222i	0.300207	−	1.12039i	0.936994	−	0.349347i	$-0.113596\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.2530	+	6.49690i	−0.384394	+	0.221930i	−0.679728	−	0.733464i	$-0.737902\pi$
$857$	−11.2530	+	6.49690i	−0.384394	+	0.221930i	0.295334	+	0.955394i	$0.404569\pi$
$858$		0			0
$859$	−31.4765	+	8.43410i	−1.07396	+	0.287768i	−0.752121	−	0.659025i	$-0.770969\pi$
$859$	−31.4765	+	8.43410i	−1.07396	+	0.287768i	−0.321843	+	0.946793i	$0.604302\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−21.7785			−0.741348			−0.370674	−	0.928763i	$-0.620873\pi$
$863$	−21.7785			−0.741348			−0.370674	+	0.928763i	$0.620873\pi$
$864$		0			0
$865$	2.23823			0.0761022
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.31032	+	2.49469i	−0.315831	+	0.0846267i
$870$		0			0
$871$	18.5116	−	10.6877i	0.627243	−	0.362139i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.920957	−	3.43706i	0.0311340	−	0.116194i
$876$		0			0
$877$	−1.27840	−	4.77106i	−0.0431685	−	0.161107i	0.940977	−	0.338471i	$-0.109910\pi$
$877$	−1.27840	−	4.77106i	−0.0431685	−	0.161107i	−0.984145	+	0.177364i	$0.943243\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.82954			0.0616389			0.0308194	−	0.999525i	$-0.490188\pi$
$881$	1.82954			0.0616389			0.0308194	+	0.999525i	$0.490188\pi$
$882$		0			0
$883$	37.7173	−	37.7173i	1.26929	−	1.26929i	0.322834	−	0.946456i	$-0.395365\pi$
$883$	37.7173	−	37.7173i	1.26929	−	1.26929i	0.946456	−	0.322834i	$-0.104635\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.5347	−	13.5877i	−0.790217	−	0.456232i	0.0498220	−	0.998758i	$-0.484135\pi$
$887$	−23.5347	−	13.5877i	−0.790217	−	0.456232i	−0.840039	+	0.542526i	$0.817468\pi$
$888$		0			0
$889$	−12.2386	+	7.06596i	−0.410469	+	0.236985i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.45826	−	2.53433i	−0.316509	−	0.0848082i
$894$		0			0
$895$	0.243906	−	0.422458i	0.00815288	−	0.0141212i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	16.1807	−	16.1807i	0.539655	−	0.539655i
$900$		0			0
$901$	1.96714	+	1.96714i	0.0655350	+	0.0655350i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	28.9128	+	16.6928i	0.961095	+	0.554889i
$906$		0			0
$907$	8.11719	−	30.2938i	0.269527	−	1.00589i	−0.689894	−	0.723911i	$-0.742343\pi$
$907$	8.11719	−	30.2938i	0.269527	−	1.00589i	0.959421	−	0.281978i	$-0.0909905\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	20.6608	+	35.7856i	0.684524	+	1.18563i	0.973586	+	0.228320i	$0.0733232\pi$
$911$	20.6608	+	35.7856i	0.684524	+	1.18563i	−0.289062	+	0.957310i	$0.593343\pi$
$912$		0			0
$913$	7.72343	−	13.3774i	0.255608	−	0.442727i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.62540	−	7.62540i	−0.251813	−	0.251813i
$918$		0			0
$919$		−	2.92729i		−	0.0965624i	−0.998834	−	0.0482812i	$-0.984626\pi$
$919$		−	2.92729i		−	0.0965624i	0.998834	−	0.0482812i	$-0.0153744\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−26.0547	+	6.98133i	−0.857600	+	0.229793i
$924$		0			0
$925$	−28.0057	−	7.50411i	−0.920822	−	0.246734i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.6953	+	47.9696i	0.908652	+	1.57383i	0.815938	+	0.578139i	$0.196221\pi$
$929$	27.6953	+	47.9696i	0.908652	+	1.57383i	0.0927142	+	0.995693i	$0.470446\pi$
$930$		0			0
$931$	3.80699	+	14.2079i	0.124769	+	0.465645i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	50.7746i		−	1.66051i
$936$		0			0
$937$			6.46687i			0.211263i	0.994405	+	0.105632i	$0.0336864\pi$
$937$			6.46687i			0.211263i	−0.994405	+	0.105632i	$0.966314\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.14789	−	30.4083i	−0.265614	−	0.991283i	−0.961874	−	0.273494i	$-0.911821\pi$
$941$	−8.14789	−	30.4083i	−0.265614	−	0.991283i	0.696260	−	0.717790i	$-0.254846\pi$
$942$		0			0
$943$	−23.9661	−	41.5105i	−0.780443	−	1.35177i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.87280	+	0.501815i	0.0608578	+	0.0163068i	0.289120	−	0.957293i	$-0.406638\pi$
$947$	1.87280	+	0.501815i	0.0608578	+	0.0163068i	−0.228262	+	0.973600i	$0.573304\pi$
$948$		0			0
$949$	5.81390	−	1.55783i	0.188727	−	0.0505693i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	10.9796i		−	0.355665i	−0.984061	−	0.177832i	$-0.943092\pi$
$953$		−	10.9796i		−	0.355665i	0.984061	−	0.177832i	$-0.0569085\pi$
$954$		0			0
$955$	−9.57418	−	9.57418i	−0.309813	−	0.309813i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.921016	+	1.59525i	−0.0297412	+	0.0515132i
$960$		0			0
$961$	11.6272	+	20.1389i	0.375070	+	0.649641i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.9948	+	55.9613i	−0.482699	+	1.80146i
$966$		0			0
$967$	6.19539	+	3.57691i	0.199230	+	0.115026i	0.596296	−	0.802764i	$-0.296638\pi$
$967$	6.19539	+	3.57691i	0.199230	+	0.115026i	−0.397066	+	0.917790i	$0.629972\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	40.8697	+	40.8697i	1.31157	+	1.31157i	0.920258	+	0.391312i	$0.127979\pi$
$971$	40.8697	+	40.8697i	1.31157	+	1.31157i	0.391312	+	0.920258i	$0.372021\pi$
$972$		0			0
$973$	14.8944	−	14.8944i	0.477491	−	0.477491i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.1070	−	41.7545i	0.771250	−	1.33584i	−0.165629	−	0.986188i	$-0.552965\pi$
$977$	24.1070	−	41.7545i	0.771250	−	1.33584i	0.936878	−	0.349655i	$-0.113701\pi$
$978$		0			0
$979$	−10.8042	−	2.89498i	−0.345304	−	0.0925240i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.339797	−	0.196182i	0.0108378	−	0.00625722i	−0.494571	−	0.869137i	$-0.664675\pi$
$983$	0.339797	−	0.196182i	0.0108378	−	0.00625722i	0.505409	+	0.862880i	$0.331342\pi$
$984$		0			0
$985$	−22.2034	−	12.8192i	−0.707460	−	0.408452i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.34722	−	3.34722i	0.106435	−	0.106435i
$990$		0			0
$991$	−1.35162			−0.0429357			−0.0214678	−	0.999770i	$-0.506834\pi$
$991$	−1.35162			−0.0429357			−0.0214678	+	0.999770i	$0.506834\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.85012	−	25.5650i	−0.217163	−	0.810465i
$996$		0			0
$997$	−3.67972	+	13.7329i	−0.116538	+	0.434926i	−0.999397	−	0.0347118i	$-0.988949\pi$
$997$	−3.67972	+	13.7329i	−0.116538	+	0.434926i	0.882859	+	0.469637i	$0.155615\pi$
$998$		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.1009.4		72
3.2	odd	2		576.2.bb.e.49.5		72
4.3	odd	2		432.2.y.e.37.9		72
9.2	odd	6		576.2.bb.e.241.5		72
9.7	even	3	inner	1728.2.bc.e.1585.15		72
12.11	even	2		144.2.x.e.85.10	yes	72
16.3	odd	4		432.2.y.e.253.16		72
16.13	even	4	inner	1728.2.bc.e.145.15		72
36.7	odd	6		432.2.y.e.181.16		72
36.11	even	6		144.2.x.e.133.3	yes	72
48.29	odd	4		576.2.bb.e.337.5		72
48.35	even	4		144.2.x.e.13.3	✓	72
144.29	odd	12		576.2.bb.e.529.5		72
144.61	even	12	inner	1728.2.bc.e.721.4		72
144.83	even	12		144.2.x.e.61.10	yes	72
144.115	odd	12		432.2.y.e.397.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.3	✓	72	48.35	even	4
144.2.x.e.61.10	yes	72	144.83	even	12
144.2.x.e.85.10	yes	72	12.11	even	2
144.2.x.e.133.3	yes	72	36.11	even	6
432.2.y.e.37.9		72	4.3	odd	2
432.2.y.e.181.16		72	36.7	odd	6
432.2.y.e.253.16		72	16.3	odd	4
432.2.y.e.397.9		72	144.115	odd	12
576.2.bb.e.49.5		72	3.2	odd	2
576.2.bb.e.241.5		72	9.2	odd	6
576.2.bb.e.337.5		72	48.29	odd	4
576.2.bb.e.529.5		72	144.29	odd	12
1728.2.bc.e.145.15		72	16.13	even	4	inner
1728.2.bc.e.721.4		72	144.61	even	12	inner
1728.2.bc.e.1009.4		72	1.1	even	1	trivial
1728.2.bc.e.1585.15		72	9.7	even	3	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)

\(f(q)\)	\(=\)	\(q+(-2.90072 + 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +O(q^{10})\)	\(q+(-2.90072 + 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +(-1.36579 + 5.09718i) q^{11} +(-0.541655 - 2.02149i) q^{13} +3.20404 q^{17} +(1.87633 - 1.87633i) q^{19} +(3.61927 + 2.08959i) q^{23} +(3.47994 - 2.00914i) q^{25} +(-7.94194 - 2.12804i) q^{29} +(-1.39155 + 2.41023i) q^{31} +(-2.56298 + 2.56298i) q^{35} +(-5.10207 - 5.10207i) q^{37} +(-9.93271 - 5.73465i) q^{41} +(0.293160 - 1.09409i) q^{43} +(-1.84507 - 3.19576i) q^{47} +(-2.77161 + 4.80057i) q^{49} +(0.613957 + 0.613957i) q^{53} -15.8471i q^{55} +(-11.8105 + 3.16461i) q^{59} +(-7.40505 - 1.98418i) q^{61} +(3.14238 + 5.44277i) q^{65} +(2.64353 + 9.86577i) q^{67} -12.8889i q^{71} +2.87605i q^{73} +(1.64847 + 6.15216i) q^{77} +(0.913281 + 1.58185i) q^{79} +(-2.82747 - 0.757618i) q^{83} +(-9.29402 + 2.49032i) q^{85} +2.11965i q^{89} +(-1.78611 - 1.78611i) q^{91} +(-3.98433 + 6.90107i) q^{95} +(-3.06298 - 5.30524i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{5}+O(q^{10}) \) 72 * q - 4 * q^5	\( 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67} + 36 q^{77} - 44 q^{79} + 20 q^{83} - 8 q^{85} + 80 q^{91} + 48 q^{95} + 40 q^{97}+O(q^{100}) \) 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Introduction

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