LMFDB - Embedded newform 756.2.bm.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(17,756)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bm (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$-0.811340 - 1.53027i$ of defining polynomial
Character	$\chi$	$=$	756.17
Dual form			756.2.bm.a.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74332 q^{5} +(1.70417 - 2.02381i) q^{7} +O(q^{10})$	$q-2.74332 q^{5} +(1.70417 - 2.02381i) q^{7} -0.418355i q^{11} +(-1.32512 - 0.765056i) q^{13} +(-1.95291 + 3.38253i) q^{17} +(-5.11994 + 2.95600i) q^{19} -8.92450i q^{23} +2.52579 q^{25} +(-6.00378 + 3.46629i) q^{29} +(-3.05626 + 1.76453i) q^{31} +(-4.67507 + 5.55196i) q^{35} +(-4.54861 - 7.87842i) q^{37} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(0.885373 - 1.53351i) q^{47} +(-1.19164 - 6.89783i) q^{49} +(-3.39526 - 1.96025i) q^{53} +1.14768i q^{55} +(2.02728 + 3.51135i) q^{59} +(-1.61459 - 0.932184i) q^{61} +(3.63521 + 2.09879i) q^{65} +(6.38441 + 11.0581i) q^{67} +8.51021i q^{71} +(1.65059 + 0.952971i) q^{73} +(-0.846673 - 0.712947i) q^{77} +(0.433633 - 0.751074i) q^{79} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(-4.88864 - 8.46738i) q^{89} +(-3.80655 + 1.37800i) q^{91} +(14.0456 - 8.10924i) q^{95} +(-0.200411 + 0.115707i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} + 6 q^{31} - 15 q^{35} + q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 13 q^{49} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 45 q^{77} - q^{79} + 6 q^{85} + 21 q^{89} + 9 q^{91} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 16 * q - q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 + 6 * q^31 - 15 * q^35 + q^37 - 6 * q^41 - 2 * q^43 + 18 * q^47 + 13 * q^49 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 45 * q^77 - q^79 + 6 * q^85 + 21 * q^89 + 9 * q^91 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	−2.74332			−1.22685			−0.613425	−	0.789753i	$-0.710209\pi$
$5$	−2.74332			−1.22685			−0.613425	+	0.789753i	$0.710209\pi$
$6$		0			0
$7$	1.70417	−	2.02381i	0.644114	−	0.764929i
$7$	1.70417	−	2.02381i	0.644114	−	0.764929i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	0.418355i		−	0.126139i	−0.998009	−	0.0630695i	$-0.979911\pi$
$11$		−	0.418355i		−	0.126139i	0.998009	−	0.0630695i	$-0.0200890\pi$
$12$		0			0
$13$	−1.32512	−	0.765056i	−0.367521	−	0.212188i	0.304854	−	0.952399i	$-0.401392\pi$
$13$	−1.32512	−	0.765056i	−0.367521	−	0.212188i	−0.672375	+	0.740211i	$0.734726\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.95291	+	3.38253i	−0.473649	+	0.820385i	−0.999545	−	0.0301645i	$-0.990397\pi$
$17$	−1.95291	+	3.38253i	−0.473649	+	0.820385i	0.525896	+	0.850549i	$0.323730\pi$
$18$		0			0
$19$	−5.11994	+	2.95600i	−1.17459	+	0.678152i	−0.954758	−	0.297385i	$-0.903886\pi$
$19$	−5.11994	+	2.95600i	−1.17459	+	0.678152i	−0.219836	+	0.975537i	$0.570552\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	8.92450i		−	1.86089i	−0.366436	−	0.930443i	$-0.619422\pi$
$23$		−	8.92450i		−	1.86089i	0.366436	−	0.930443i	$-0.380578\pi$
$24$		0			0
$25$	2.52579			0.505159
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.00378	+	3.46629i	−1.11487	+	0.643673i	−0.940088	−	0.340933i	$-0.889257\pi$
$29$	−6.00378	+	3.46629i	−1.11487	+	0.643673i	−0.174787	+	0.984606i	$0.555924\pi$
$30$		0			0
$31$	−3.05626	+	1.76453i	−0.548921	+	0.316920i	−0.748687	−	0.662924i	$-0.769315\pi$
$31$	−3.05626	+	1.76453i	−0.548921	+	0.316920i	0.199766	+	0.979844i	$0.435982\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.67507	+	5.55196i	−0.790231	+	0.938453i
$36$		0			0
$37$	−4.54861	−	7.87842i	−0.747787	−	1.29520i	−0.948881	−	0.315633i	$-0.897783\pi$
$37$	−4.54861	−	7.87842i	−0.747787	−	1.29520i	0.201095	−	0.979572i	$-0.435550\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.06236	−	1.84006i	0.165913	−	0.287370i	−0.771066	−	0.636755i	$-0.780276\pi$
$41$	1.06236	−	1.84006i	0.165913	−	0.287370i	0.936979	+	0.349385i	$0.113610\pi$
$42$		0			0
$43$	−5.77846	−	10.0086i	−0.881208	−	1.52630i	−0.850000	−	0.526783i	$-0.823398\pi$
$43$	−5.77846	−	10.0086i	−0.881208	−	1.52630i	−0.0312079	−	0.999513i	$-0.509935\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.885373	−	1.53351i	0.129145	−	0.223686i	−0.794201	−	0.607656i	$-0.792110\pi$
$47$	0.885373	−	1.53351i	0.129145	−	0.223686i	0.923346	+	0.383970i	$0.125443\pi$
$48$		0			0
$49$	−1.19164	−	6.89783i	−0.170234	−	0.985404i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.39526	−	1.96025i	−0.466374	−	0.269261i	0.248346	−	0.968671i	$-0.420113\pi$
$53$	−3.39526	−	1.96025i	−0.466374	−	0.269261i	−0.714721	+	0.699410i	$0.753446\pi$
$54$		0			0
$55$			1.14768i			0.154753i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.02728	+	3.51135i	0.263929	+	0.457139i	0.967283	−	0.253702i	$-0.0816481\pi$
$59$	2.02728	+	3.51135i	0.263929	+	0.457139i	−0.703353	+	0.710840i	$0.748315\pi$
$60$		0			0
$61$	−1.61459	−	0.932184i	−0.206727	−	0.119354i	0.393062	−	0.919512i	$-0.371416\pi$
$61$	−1.61459	−	0.932184i	−0.206727	−	0.119354i	−0.599789	+	0.800158i	$0.704749\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.63521	+	2.09879i	0.450893	+	0.260323i
$66$		0			0
$67$	6.38441	+	11.0581i	0.779979	+	1.35096i	0.931953	+	0.362579i	$0.118104\pi$
$67$	6.38441	+	11.0581i	0.779979	+	1.35096i	−0.151974	+	0.988385i	$0.548563\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			8.51021i			1.00998i	0.863126	+	0.504988i	$0.168503\pi$
$71$			8.51021i			1.00998i	−0.863126	+	0.504988i	$0.831497\pi$
$72$		0			0
$73$	1.65059	+	0.952971i	0.193187	+	0.111537i	0.593474	−	0.804853i	$-0.297756\pi$
$73$	1.65059	+	0.952971i	0.193187	+	0.111537i	−0.400286	+	0.916390i	$0.631089\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.846673	−	0.712947i	−0.0964874	−	0.0812479i
$78$		0			0
$79$	0.433633	−	0.751074i	0.0487875	−	0.0845024i	−0.840600	−	0.541656i	$-0.817798\pi$
$79$	0.433633	−	0.751074i	0.0487875	−	0.0845024i	0.889388	+	0.457153i	$0.151131\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.45880	+	5.99082i	0.379653	+	0.657578i	0.991012	−	0.133775i	$-0.0427100\pi$
$83$	3.45880	+	5.99082i	0.379653	+	0.657578i	−0.611359	+	0.791354i	$0.709377\pi$
$84$		0			0
$85$	5.35744	−	9.27936i	0.581096	−	1.00649i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.88864	−	8.46738i	−0.518195	−	0.897540i	−0.999777	−	0.0211389i	$-0.993271\pi$
$89$	−4.88864	−	8.46738i	−0.518195	−	0.897540i	0.481581	−	0.876401i	$-0.340063\pi$
$90$		0			0
$91$	−3.80655	+	1.37800i	−0.399035	+	0.144454i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	14.0456	−	8.10924i	1.44105	−	0.831990i
$96$		0			0
$97$	−0.200411	+	0.115707i	−0.0203486	+	0.0117483i	−0.510140	−	0.860091i	$-0.670406\pi$
$97$	−0.200411	+	0.115707i	−0.0203486	+	0.0117483i	0.489791	+	0.871840i	$0.337073\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	14.2806			1.42097			0.710487	−	0.703710i	$-0.248475\pi$
$101$	14.2806			1.42097			0.710487	+	0.703710i	$0.248475\pi$
$102$		0			0
$103$			10.7458i			1.05882i	0.848366	+	0.529410i	$0.177587\pi$
$103$			10.7458i			1.05882i	−0.848366	+	0.529410i	$0.822413\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.50534	+	3.17851i	−0.532221	+	0.307278i	−0.741920	−	0.670488i	$-0.766085\pi$
$107$	−5.50534	+	3.17851i	−0.532221	+	0.307278i	0.209699	+	0.977766i	$0.432751\pi$
$108$		0			0
$109$	2.58036	−	4.46932i	0.247154	−	0.428083i	−0.715581	−	0.698530i	$-0.753838\pi$
$109$	2.58036	−	4.46932i	0.247154	−	0.428083i	0.962735	+	0.270447i	$0.0871714\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.19186	−	5.30692i	−0.864697	−	0.499233i	0.000885276	−	1.00000i	$-0.499718\pi$
$113$	−9.19186	−	5.30692i	−0.864697	−	0.499233i	−0.865582	+	0.500766i	$0.833052\pi$
$114$		0			0
$115$			24.4827i			2.28303i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.51754	+	9.71671i	0.322452	+	0.890730i
$120$		0			0
$121$	10.8250			0.984089
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.78753			0.607096
$126$		0			0
$127$	10.2909			0.913169			0.456584	−	0.889680i	$-0.349073\pi$
$127$	10.2909			0.913169			0.456584	+	0.889680i	$0.349073\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−19.6610			−1.71779			−0.858893	−	0.512155i	$-0.828847\pi$
$131$	−19.6610			−1.71779			−0.858893	+	0.512155i	$0.828847\pi$
$132$		0			0
$133$	−2.74284	+	15.3993i	−0.237834	+	1.33529i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	5.38565i		−	0.460127i	−0.973176	−	0.230063i	$-0.926107\pi$
$137$		−	5.38565i		−	0.460127i	0.973176	−	0.230063i	$-0.0738933\pi$
$138$		0			0
$139$	−14.7839	−	8.53549i	−1.25395	−	0.723971i	−0.282062	−	0.959396i	$-0.591018\pi$
$139$	−14.7839	−	8.53549i	−1.25395	−	0.723971i	−0.971892	+	0.235425i	$0.924352\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.320065	+	0.554369i	−0.0267652	+	0.0463587i
$144$		0			0
$145$	16.4703	−	9.50912i	1.36778	−	0.789690i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	10.7521i		−	0.880849i	−0.897790	−	0.440425i	$-0.854828\pi$
$149$		−	10.7521i		−	0.880849i	0.897790	−	0.440425i	$-0.145172\pi$
$150$		0			0
$151$	7.56447			0.615588			0.307794	−	0.951453i	$-0.400409\pi$
$151$	7.56447			0.615588			0.307794	+	0.951453i	$0.400409\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.38430	−	4.84068i	0.673443	−	0.388812i
$156$		0			0
$157$	−10.6317	+	6.13820i	−0.848500	+	0.489882i	−0.860144	−	0.510051i	$-0.829627\pi$
$157$	−10.6317	+	6.13820i	−0.848500	+	0.489882i	0.0116445	+	0.999932i	$0.496293\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−18.0615	−	15.2088i	−1.42345	−	1.19862i
$162$		0			0
$163$	5.91745	+	10.2493i	0.463490	+	0.802789i	0.999132	−	0.0416566i	$-0.0132635\pi$
$163$	5.91745	+	10.2493i	0.463490	+	0.802789i	−0.535642	+	0.844445i	$0.679930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.78854	−	11.7581i	0.525313	−	0.909869i	−0.474252	−	0.880389i	$-0.657282\pi$
$167$	6.78854	−	11.7581i	0.525313	−	0.909869i	0.999565	−	0.0294798i	$-0.00938508\pi$
$168$		0			0
$169$	−5.32938	−	9.23075i	−0.409952	−	0.710058i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.31085	−	14.3948i	0.631862	−	1.09442i	−0.355308	−	0.934749i	$-0.615624\pi$
$173$	8.31085	−	14.3948i	0.631862	−	1.09442i	0.987171	−	0.159668i	$-0.0510425\pi$
$174$		0			0
$175$	4.30437	−	5.11173i	0.325380	−	0.386411i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.8080	+	8.54942i	1.10680	+	0.639014i	0.938000	−	0.346636i	$-0.112676\pi$
$179$	14.8080	+	8.54942i	1.10680	+	0.639014i	0.168805	+	0.985650i	$0.446009\pi$
$180$		0			0
$181$			18.2171i			1.35407i	0.735952	+	0.677034i	$0.236735\pi$
$181$			18.2171i			1.35407i	−0.735952	+	0.677034i	$0.763265\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.4783	+	21.6130i	0.917422	+	1.58902i
$186$		0			0
$187$	1.41510	+	0.817009i	0.103482	+	0.0597456i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.1860	+	10.4997i	1.31589	+	0.759730i	0.983065	−	0.183258i	$-0.0586644\pi$
$191$	18.1860	+	10.4997i	1.31589	+	0.759730i	0.332826	+	0.942988i	$0.391998\pi$
$192$		0			0
$193$	3.48741	+	6.04038i	0.251030	+	0.434796i	0.963810	−	0.266592i	$-0.0858975\pi$
$193$	3.48741	+	6.04038i	0.251030	+	0.434796i	−0.712780	+	0.701388i	$0.752564\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	16.0756i		−	1.14534i	−0.819786	−	0.572670i	$-0.805908\pi$
$197$		−	16.0756i		−	1.14534i	0.819786	−	0.572670i	$-0.194092\pi$
$198$		0			0
$199$	−5.44956	−	3.14630i	−0.386309	−	0.223036i	0.294251	−	0.955728i	$-0.404930\pi$
$199$	−5.44956	−	3.14630i	−0.386309	−	0.223036i	−0.680560	+	0.732693i	$0.738263\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.21633	+	18.0577i	−0.225742	+	1.26740i
$204$		0			0
$205$	−2.91440	+	5.04788i	−0.203550	+	0.352559i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.23666	+	2.14195i	0.0855414	+	0.148162i
$210$		0			0
$211$	−1.29814	+	2.24844i	−0.0893674	+	0.154789i	−0.907244	−	0.420605i	$-0.861818\pi$
$211$	−1.29814	+	2.24844i	−0.0893674	+	0.154789i	0.817876	+	0.575394i	$0.195151\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	15.8522	+	27.4568i	1.08111	+	1.87254i
$216$		0			0
$217$	−1.63729	+	9.19236i	−0.111147	+	0.624018i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.17565	−	2.98816i	0.348152	−	0.201006i
$222$		0			0
$223$	20.7215	−	11.9636i	1.38762	−	0.801141i	0.394571	−	0.918866i	$-0.370893\pi$
$223$	20.7215	−	11.9636i	1.38762	−	0.801141i	0.993046	+	0.117725i	$0.0375600\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.73218			0.247713			0.123857	−	0.992300i	$-0.460474\pi$
$227$	3.73218			0.247713			0.123857	+	0.992300i	$0.460474\pi$
$228$		0			0
$229$		−	21.0681i		−	1.39222i	−0.717935	−	0.696111i	$-0.754912\pi$
$229$		−	21.0681i		−	1.39222i	0.717935	−	0.696111i	$-0.245088\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.0542	+	6.38215i	−0.724186	+	0.418109i	−0.816291	−	0.577640i	$-0.803974\pi$
$233$	−11.0542	+	6.38215i	−0.724186	+	0.418109i	0.0921057	+	0.995749i	$0.470640\pi$
$234$		0			0
$235$	−2.42886	+	4.20691i	−0.158441	+	0.274429i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.0521	−	6.38091i	−0.714899	−	0.412747i	0.0979736	−	0.995189i	$-0.468764\pi$
$239$	−11.0521	−	6.38091i	−0.714899	−	0.412747i	−0.812872	+	0.582442i	$0.802097\pi$
$240$		0			0
$241$		−	3.04192i		−	0.195947i	−0.995189	−	0.0979737i	$-0.968764\pi$
$241$		−	3.04192i		−	0.195947i	0.995189	−	0.0979737i	$-0.0312361\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.26904	+	18.9229i	0.208851	+	1.20894i
$246$		0			0
$247$	9.04601			0.575584
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.32067			−0.398957			−0.199478	−	0.979902i	$-0.563925\pi$
$251$	−6.32067			−0.398957			−0.199478	+	0.979902i	$0.563925\pi$
$252$		0			0
$253$	−3.73361			−0.234730
$254$		0			0
$255$		0			0
$256$		0			0
$257$	24.5076			1.52874			0.764372	−	0.644776i	$-0.223049\pi$
$257$	24.5076			1.52874			0.764372	+	0.644776i	$0.223049\pi$
$258$		0			0
$259$	−23.6960	−	4.22061i	−1.47240	−	0.262256i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	24.3830i		−	1.50352i	−0.659438	−	0.751759i	$-0.729206\pi$
$263$		−	24.3830i		−	1.50352i	0.659438	−	0.751759i	$-0.270794\pi$
$264$		0			0
$265$	9.31427	+	5.37760i	0.572171	+	0.330343i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.94525	−	8.56542i	0.301517	−	0.522243i	−0.674963	−	0.737852i	$-0.735840\pi$
$269$	4.94525	−	8.56542i	0.301517	−	0.522243i	0.976480	+	0.215609i	$0.0691737\pi$
$270$		0			0
$271$	−5.10505	+	2.94740i	−0.310110	+	0.179042i	−0.646976	−	0.762511i	$-0.723966\pi$
$271$	−5.10505	+	2.94740i	−0.310110	+	0.179042i	0.336866	+	0.941553i	$0.390633\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	1.05668i		−	0.0637202i
$276$		0			0
$277$	23.2939			1.39959			0.699796	−	0.714343i	$-0.253274\pi$
$277$	23.2939			1.39959			0.699796	+	0.714343i	$0.253274\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−21.7962	+	12.5840i	−1.30025	+	0.750700i	−0.980447	−	0.196784i	$-0.936950\pi$
$281$	−21.7962	+	12.5840i	−1.30025	+	0.750700i	−0.319803	+	0.947484i	$0.603617\pi$
$282$		0			0
$283$	−8.62942	+	4.98220i	−0.512966	+	0.296161i	−0.734052	−	0.679093i	$-0.762373\pi$
$283$	−8.62942	+	4.98220i	−0.512966	+	0.296161i	0.221086	+	0.975254i	$0.429040\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.91350	−	5.28579i	−0.112951	−	0.312011i
$288$		0			0
$289$	0.872317	+	1.51090i	0.0513128	+	0.0888764i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.79065	+	11.7618i	−0.396714	+	0.687129i	−0.993318	−	0.115406i	$-0.963183\pi$
$293$	−6.79065	+	11.7618i	−0.396714	+	0.687129i	0.596604	+	0.802536i	$0.296516\pi$
$294$		0			0
$295$	−5.56147	−	9.63275i	−0.323801	−	0.560841i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.82774	+	11.8260i	−0.394858	+	0.683915i
$300$		0			0
$301$	−30.1030	−	5.36177i	−1.73511	−	0.309048i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.42933	+	2.55728i	0.253623	+	0.146429i
$306$		0			0
$307$		−	16.9849i		−	0.969381i	−0.874686	−	0.484691i	$-0.838932\pi$
$307$		−	16.9849i		−	0.969381i	0.874686	−	0.484691i	$-0.161068\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.00148940	−	0.00257972i	−8.44563e−5	−	0.000146283i	0.865983	−	0.500073i	$-0.166694\pi$
$311$	−0.00148940	−	0.00257972i	−8.44563e−5	−	0.000146283i	−0.866068	+	0.499927i	$0.833360\pi$
$312$		0			0
$313$	−10.6154	−	6.12878i	−0.600015	−	0.346419i	0.169032	−	0.985611i	$-0.445936\pi$
$313$	−10.6154	−	6.12878i	−0.600015	−	0.346419i	−0.769048	+	0.639191i	$0.779269\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.0008	−	11.5475i	−1.12336	−	0.648571i	−0.181102	−	0.983464i	$-0.557966\pi$
$317$	−20.0008	−	11.5475i	−1.12336	−	0.648571i	−0.942256	+	0.334894i	$0.891300\pi$
$318$		0			0
$319$	1.45014	+	2.51172i	0.0811922	+	0.140629i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	23.0911i		−	1.28482i
$324$		0			0
$325$	−3.34697	−	1.93237i	−0.185656	−	0.107189i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.59472	−	4.40519i	−0.0879196	−	0.242866i
$330$		0			0
$331$	1.73106	−	2.99829i	0.0951479	−	0.164801i	−0.814522	−	0.580132i	$-0.803001\pi$
$331$	1.73106	−	2.99829i	0.0951479	−	0.164801i	0.909670	+	0.415331i	$0.136334\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−17.5145	−	30.3359i	−0.956917	−	1.65743i
$336$		0			0
$337$	−9.13018	+	15.8139i	−0.497352	+	0.861440i	−0.999995	−	0.00305455i	$-0.999028\pi$
$337$	−9.13018	+	15.8139i	−0.497352	+	0.861440i	0.502643	+	0.864494i	$0.332361\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.738202	+	1.27860i	0.0399759	+	0.0692403i
$342$		0			0
$343$	−15.9907	−	9.34339i	−0.863414	−	0.504496i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.62386	−	2.66959i	0.248222	−	0.143311i	−0.370728	−	0.928741i	$-0.620892\pi$
$347$	4.62386	−	2.66959i	0.248222	−	0.143311i	0.618950	+	0.785431i	$0.287558\pi$
$348$		0			0
$349$	0.0136817	−	0.00789914i	0.000732365	−	0.000422831i	−0.499634	−	0.866237i	$-0.666532\pi$
$349$	0.0136817	−	0.00789914i	0.000732365	−	0.000422831i	0.500366	+	0.865814i	$0.333199\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−34.3085			−1.82606			−0.913029	−	0.407894i	$-0.866263\pi$
$353$	−34.3085			−1.82606			−0.913029	+	0.407894i	$0.866263\pi$
$354$		0			0
$355$		−	23.3462i		−	1.23909i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.42754	+	3.13359i	−0.286454	+	0.165385i	−0.636342	−	0.771407i	$-0.719553\pi$
$359$	−5.42754	+	3.13359i	−0.286454	+	0.165385i	0.349887	+	0.936792i	$0.386220\pi$
$360$		0			0
$361$	7.97583	−	13.8145i	0.419781	−	0.727081i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.52811	−	2.61430i	−0.237012	−	0.136839i
$366$		0			0
$367$			19.0397i			0.993863i	0.867790	+	0.496931i	$0.165540\pi$
$367$			19.0397i			0.993863i	−0.867790	+	0.496931i	$0.834460\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.75326	+	3.53077i	−0.506364	+	0.183308i
$372$		0			0
$373$	10.8380			0.561172			0.280586	−	0.959829i	$-0.409471\pi$
$373$	10.8380			0.561172			0.280586	+	0.959829i	$0.409471\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.6076			0.546320
$378$		0			0
$379$	0.700312			0.0359726			0.0179863	−	0.999838i	$-0.494274\pi$
$379$	0.700312			0.0359726			0.0179863	+	0.999838i	$0.494274\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−38.0470			−1.94411			−0.972056	−	0.234749i	$-0.924573\pi$
$383$	−38.0470			−1.94411			−0.972056	+	0.234749i	$0.924573\pi$
$384$		0			0
$385$	2.32269	+	1.95584i	0.118375	+	0.0996789i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			19.2787i			0.977468i	0.872433	+	0.488734i	$0.162541\pi$
$389$			19.2787i			0.977468i	−0.872433	+	0.488734i	$0.837459\pi$
$390$		0			0
$391$	30.1874	+	17.4287i	1.52664	+	0.881407i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.18959	+	2.06044i	−0.0598549	+	0.103672i
$396$		0			0
$397$	−17.3610	+	10.0234i	−0.871325	+	0.503059i	−0.867788	−	0.496934i	$-0.834459\pi$
$397$	−17.3610	+	10.0234i	−0.871325	+	0.503059i	−0.00353639	+	0.999994i	$0.501126\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	30.5109i		−	1.52364i	−0.647789	−	0.761820i	$-0.724306\pi$
$401$		−	30.5109i		−	1.52364i	0.647789	−	0.761820i	$-0.275694\pi$
$402$		0			0
$403$	5.39987			0.268987
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.29598	+	1.90294i	−0.163376	+	0.0943250i
$408$		0			0
$409$	−0.150631	+	0.0869667i	−0.00744821	+	0.00430023i	−0.503719	−	0.863867i	$-0.668035\pi$
$409$	−0.150631	+	0.0869667i	−0.00744821	+	0.00430023i	0.496271	+	0.868168i	$0.334702\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.5611	+	1.88109i	0.519680	+	0.0925624i
$414$		0			0
$415$	−9.48860	−	16.4347i	−0.465777	−	0.806749i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.0690	+	24.3682i	−0.687316	+	1.19047i	0.285387	+	0.958412i	$0.407878\pi$
$419$	−14.0690	+	24.3682i	−0.687316	+	1.19047i	−0.972703	+	0.232054i	$0.925455\pi$
$420$		0			0
$421$	−1.56130	−	2.70424i	−0.0760929	−	0.131797i	0.825468	−	0.564449i	$-0.190911\pi$
$421$	−1.56130	−	2.70424i	−0.0760929	−	0.131797i	−0.901561	+	0.432652i	$0.857578\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.93264	+	8.54358i	−0.239268	+	0.414424i
$426$		0			0
$427$	−4.63809	+	1.67903i	−0.224453	+	0.0812540i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.58876	+	4.95872i	0.413706	+	0.238853i	0.692381	−	0.721532i	$-0.256562\pi$
$431$	8.58876	+	4.95872i	0.413706	+	0.238853i	−0.278675	+	0.960385i	$0.589895\pi$
$432$		0			0
$433$		−	17.1274i		−	0.823092i	−0.911389	−	0.411546i	$-0.864989\pi$
$433$		−	17.1274i		−	0.823092i	0.911389	−	0.411546i	$-0.135011\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	26.3808	+	45.6929i	1.26196	+	2.18579i
$438$		0			0
$439$	−18.5795	−	10.7269i	−0.886750	−	0.511965i	−0.0138721	−	0.999904i	$-0.504416\pi$
$439$	−18.5795	−	10.7269i	−0.886750	−	0.511965i	−0.872878	+	0.487938i	$0.837749\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.84340	+	3.37369i	0.277628	+	0.160289i	0.632349	−	0.774683i	$-0.282091\pi$
$443$	5.84340	+	3.37369i	0.277628	+	0.160289i	−0.354721	+	0.934972i	$0.615424\pi$
$444$		0			0
$445$	13.4111	+	23.2287i	0.635747	+	1.10115i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	5.81624i		−	0.274485i	−0.990537	−	0.137243i	$-0.956176\pi$
$449$		−	5.81624i		−	0.274485i	0.990537	−	0.137243i	$-0.0438240\pi$
$450$		0			0
$451$	−0.769801	−	0.444445i	−0.0362485	−	0.0209281i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.4426	−	3.78030i	0.489555	−	0.177223i
$456$		0			0
$457$	16.6949	−	28.9164i	0.780954	−	1.35265i	−0.150432	−	0.988620i	$-0.548066\pi$
$457$	16.6949	−	28.9164i	0.780954	−	1.35265i	0.931386	−	0.364032i	$-0.118600\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.5154	−	32.0696i	−0.862347	−	1.49363i	−0.869657	−	0.493656i	$-0.835660\pi$
$461$	−18.5154	−	32.0696i	−0.862347	−	1.49363i	0.00730959	−	0.999973i	$-0.497673\pi$
$462$		0			0
$463$	10.5618	−	18.2935i	0.490848	−	0.850173i	−0.509097	−	0.860709i	$-0.670020\pi$
$463$	10.5618	−	18.2935i	0.490848	−	0.850173i	0.999944	+	0.0105362i	$0.00335383\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.30470	+	16.1162i	0.430570	+	0.745770i	0.996922	−	0.0783937i	$-0.0249791\pi$
$467$	9.30470	+	16.1162i	0.430570	+	0.745770i	−0.566352	+	0.824163i	$0.691646\pi$
$468$		0			0
$469$	33.2596	+	5.92402i	1.53579	+	0.273546i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.18715	+	2.41745i	−0.192525	+	0.111155i
$474$		0			0
$475$	−12.9319	+	7.46624i	−0.593356	+	0.342574i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.3341			−0.654940			−0.327470	−	0.944862i	$-0.606196\pi$
$479$	−14.3341			−0.654940			−0.327470	+	0.944862i	$0.606196\pi$
$480$		0			0
$481$			13.9198i			0.634687i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.549791	−	0.317422i	0.0249647	−	0.0144134i
$486$		0			0
$487$	−5.64829	+	9.78313i	−0.255949	+	0.443316i	−0.965153	−	0.261687i	$-0.915721\pi$
$487$	−5.64829	+	9.78313i	−0.255949	+	0.443316i	0.709204	+	0.705003i	$0.249054\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.84097	+	5.10434i	0.398988	+	0.230356i	0.686047	−	0.727557i	$-0.259344\pi$
$491$	8.84097	+	5.10434i	0.398988	+	0.230356i	−0.287059	+	0.957913i	$0.592678\pi$
$492$		0			0
$493$		−	27.0773i		−	1.21950i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	17.2231	+	14.5028i	0.772561	+	0.650540i
$498$		0			0
$499$	−19.1334			−0.856531			−0.428265	−	0.903653i	$-0.640875\pi$
$499$	−19.1334			−0.856531			−0.428265	+	0.903653i	$0.640875\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.268917			0.0119904			0.00599520	−	0.999982i	$-0.498092\pi$
$503$	0.268917			0.0119904			0.00599520	+	0.999982i	$0.498092\pi$
$504$		0			0
$505$	−39.1763			−1.74332
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−21.8877			−0.970157			−0.485079	−	0.874471i	$-0.661209\pi$
$509$	−21.8877			−0.970157			−0.485079	+	0.874471i	$0.661209\pi$
$510$		0			0
$511$	4.74152	−	1.71647i	0.209753	−	0.0759323i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	29.4793i		−	1.29901i
$516$		0			0
$517$	−0.641553	−	0.370401i	−0.0282155	−	0.0162902i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.856074	−	1.48276i	0.0375053	−	0.0649610i	−0.846663	−	0.532129i	$-0.821392\pi$
$521$	0.856074	−	1.48276i	0.0375053	−	0.0649610i	0.884169	+	0.467168i	$0.154726\pi$
$522$		0			0
$523$	7.16320	−	4.13568i	0.313225	−	0.180841i	−0.335144	−	0.942167i	$-0.608785\pi$
$523$	7.16320	−	4.13568i	0.313225	−	0.180841i	0.648369	+	0.761326i	$0.275452\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	13.7839i		−	0.600435i
$528$		0			0
$529$	−56.6466			−2.46290
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.81550	+	1.62553i	−0.121953	+	0.0704096i
$534$		0			0
$535$	15.1029	−	8.71966i	0.652955	−	0.376984i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−2.88574	+	0.498528i	−0.124298	+	0.0214731i
$540$		0			0
$541$	−10.1997	−	17.6664i	−0.438518	−	0.759536i	0.559057	−	0.829129i	$-0.311163\pi$
$541$	−10.1997	−	17.6664i	−0.438518	−	0.759536i	−0.997575	+	0.0695932i	$0.977830\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.07875	+	12.2608i	−0.303220	+	0.525193i
$546$		0			0
$547$	18.9630	+	32.8449i	0.810801	+	1.40435i	0.912304	+	0.409513i	$0.134301\pi$
$547$	18.9630	+	32.8449i	0.810801	+	1.40435i	−0.101503	+	0.994835i	$0.532365\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	20.4927	−	35.4943i	0.873017	−	1.51211i
$552$		0			0
$553$	−0.781051	−	2.15755i	−0.0332137	−	0.0917482i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.5919	+	8.42463i	0.618278	+	0.356963i	0.776198	−	0.630489i	$-0.217146\pi$
$557$	14.5919	+	8.42463i	0.618278	+	0.356963i	−0.157920	+	0.987452i	$0.550479\pi$
$558$		0			0
$559$			17.6834i			0.747928i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.28035	+	14.3420i	0.348975	+	0.604443i	0.986068	−	0.166345i	$-0.0531965\pi$
$563$	8.28035	+	14.3420i	0.348975	+	0.604443i	−0.637093	+	0.770787i	$0.719863\pi$
$564$		0			0
$565$	25.2162	+	14.5586i	1.06085	+	0.612484i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.49856	+	3.17460i	0.230512	+	0.133086i	0.610808	−	0.791779i	$-0.290845\pi$
$569$	5.49856	+	3.17460i	0.230512	+	0.133086i	−0.380296	+	0.924865i	$0.624178\pi$
$570$		0			0
$571$	−22.8703	−	39.6125i	−0.957092	−	1.65773i	−0.729507	−	0.683973i	$-0.760250\pi$
$571$	−22.8703	−	39.6125i	−0.957092	−	1.65773i	−0.227585	−	0.973758i	$-0.573083\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	22.5414i		−	0.940043i
$576$		0			0
$577$	15.3719	+	8.87497i	0.639940	+	0.369470i	0.784592	−	0.620013i	$-0.212873\pi$
$577$	15.3719	+	8.87497i	0.639940	+	0.369470i	−0.144651	+	0.989483i	$0.546206\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.0187	+	3.20939i	0.747541	+	0.133148i
$582$		0			0
$583$	−0.820082	+	1.42042i	−0.0339643	+	0.0588280i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.41148	+	7.64091i	0.182081	+	0.315374i	0.942589	−	0.333955i	$-0.108383\pi$
$587$	4.41148	+	7.64091i	0.182081	+	0.315374i	−0.760508	+	0.649329i	$0.775050\pi$
$588$		0			0
$589$	10.4319	−	18.0686i	0.429839	−	0.744503i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.24849	+	7.35860i	0.174465	+	0.302181i	0.939976	−	0.341241i	$-0.110847\pi$
$593$	4.24849	+	7.35860i	0.174465	+	0.302181i	−0.765511	+	0.643422i	$0.777514\pi$
$594$		0			0
$595$	−9.64972	−	26.6560i	−0.395600	−	1.09279i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.21158	−	1.85421i	0.131222	−	0.0757609i	−0.432952	−	0.901417i	$-0.642528\pi$
$599$	3.21158	−	1.85421i	0.131222	−	0.0757609i	0.564174	+	0.825656i	$0.309195\pi$
$600$		0			0
$601$	−6.14043	+	3.54518i	−0.250473	+	0.144611i	−0.619981	−	0.784617i	$-0.712860\pi$
$601$	−6.14043	+	3.54518i	−0.250473	+	0.144611i	0.369508	+	0.929228i	$0.379526\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−29.6964			−1.20733
$606$		0			0
$607$			33.9940i			1.37977i	0.723918	+	0.689886i	$0.242339\pi$
$607$			33.9940i			1.37977i	−0.723918	+	0.689886i	$0.757661\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.34644	+	1.35472i	−0.0949270	+	0.0548061i
$612$		0			0
$613$	−11.6761	+	20.2237i	−0.471595	+	0.816827i	−0.999472	−	0.0324944i	$-0.989655\pi$
$613$	−11.6761	+	20.2237i	−0.471595	+	0.816827i	0.527877	+	0.849321i	$0.322988\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.0817	+	22.5638i	1.57337	+	0.908386i	0.995752	+	0.0920787i	$0.0293511\pi$
$617$	39.0817	+	22.5638i	1.57337	+	0.908386i	0.577618	+	0.816307i	$0.303982\pi$
$618$		0			0
$619$		−	9.21352i		−	0.370323i	−0.982708	−	0.185161i	$-0.940719\pi$
$619$		−	9.21352i		−	0.370323i	0.982708	−	0.185161i	$-0.0592808\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−25.4674	−	4.53612i	−1.02033	−	0.181736i
$624$		0			0
$625$	−31.2493			−1.24997
$626$		0			0
$627$		0			0
$628$		0			0
$629$	35.5320			1.41675
$630$		0			0
$631$	17.6136			0.701188			0.350594	−	0.936528i	$-0.385980\pi$
$631$	17.6136			0.701188			0.350594	+	0.936528i	$0.385980\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−28.2312			−1.12032
$636$		0			0
$637$	−3.69817	+	10.0521i	−0.146527	+	0.398278i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			19.1402i			0.755991i	0.925807	+	0.377996i	$0.123387\pi$
$641$			19.1402i			0.755991i	−0.925807	+	0.377996i	$0.876613\pi$
$642$		0			0
$643$	2.01129	+	1.16122i	0.0793177	+	0.0457941i	0.539134	−	0.842220i	$-0.318752\pi$
$643$	2.01129	+	1.16122i	0.0793177	+	0.0457941i	−0.459817	+	0.888014i	$0.652085\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.9310	−	22.3971i	0.508370	−	0.880522i	−0.491583	−	0.870831i	$-0.663582\pi$
$647$	12.9310	−	22.3971i	0.508370	−	0.880522i	0.999953	−	0.00969167i	$-0.00308500\pi$
$648$		0			0
$649$	1.46899	−	0.848123i	0.0576630	−	0.0332918i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			23.2257i			0.908891i	0.890774	+	0.454446i	$0.150163\pi$
$653$			23.2257i			0.908891i	−0.890774	+	0.454446i	$0.849837\pi$
$654$		0			0
$655$	53.9363			2.10746
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.7002	+	7.90981i	−0.533684	+	0.308122i	−0.742515	−	0.669829i	$-0.766367\pi$
$659$	−13.7002	+	7.90981i	−0.533684	+	0.308122i	0.208832	+	0.977952i	$0.433034\pi$
$660$		0			0
$661$	−15.8006	+	9.12248i	−0.614572	+	0.354823i	−0.774753	−	0.632264i	$-0.782126\pi$
$661$	−15.8006	+	9.12248i	−0.614572	+	0.354823i	0.160181	+	0.987088i	$0.448792\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.52447	−	42.2452i	0.291787	−	1.63820i
$666$		0			0
$667$	30.9349	+	53.5807i	1.19780	+	2.07465i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.389984	+	0.675472i	−0.0150552	+	0.0260763i
$672$		0			0
$673$	14.4184	+	24.9733i	0.555787	+	0.962651i	0.997842	+	0.0656633i	$0.0209163\pi$
$673$	14.4184	+	24.9733i	0.555787	+	0.962651i	−0.442055	+	0.896988i	$0.645750\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.7668	−	29.0409i	0.644400	−	1.11613i	−0.340040	−	0.940411i	$-0.610441\pi$
$677$	16.7668	−	29.0409i	0.644400	−	1.11613i	0.984440	−	0.175722i	$-0.0562261\pi$
$678$		0			0
$679$	−0.107364	+	0.602779i	−0.00412023	+	0.0231325i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−19.0943	−	11.0241i	−0.730621	−	0.421824i	0.0880282	−	0.996118i	$-0.471943\pi$
$683$	−19.0943	−	11.0241i	−0.730621	−	0.421824i	−0.818649	+	0.574294i	$0.805277\pi$
$684$		0			0
$685$			14.7745i			0.564506i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.99941	+	5.19512i	0.114268	+	0.197918i
$690$		0			0
$691$	−22.8662	−	13.2018i	−0.869869	−	0.502219i	−0.00256453	−	0.999997i	$-0.500816\pi$
$691$	−22.8662	−	13.2018i	−0.869869	−	0.502219i	−0.867305	+	0.497777i	$0.834150\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	40.5569	+	23.4156i	1.53841	+	0.888203i
$696$		0			0
$697$	4.14938	+	7.18694i	0.157169	+	0.272225i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			20.5140i			0.774804i	0.921911	+	0.387402i	$0.126627\pi$
$701$			20.5140i			0.774804i	−0.921911	+	0.387402i	$0.873373\pi$
$702$		0			0
$703$	46.5772	+	26.8913i	1.75669	+	1.01423i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	24.3365	−	28.9013i	0.915270	−	1.08695i
$708$		0			0
$709$	3.13054	−	5.42226i	0.117570	−	0.203637i	−0.801234	−	0.598351i	$-0.795823\pi$
$709$	3.13054	−	5.42226i	0.117570	−	0.203637i	0.918804	+	0.394714i	$0.129156\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.7476	+	27.2756i	0.589751	+	1.02148i
$714$		0			0
$715$	0.878041	−	1.52081i	0.0328369	−	0.0568751i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.6111	−	20.1111i	−0.433023	−	0.750017i	0.564109	−	0.825700i	$-0.309220\pi$
$719$	−11.6111	−	20.1111i	−0.433023	−	0.750017i	−0.997132	+	0.0756828i	$0.975886\pi$
$720$		0			0
$721$	21.7476	+	18.3127i	0.809922	+	0.682001i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.1643	+	8.75512i	−0.563189	+	0.325157i
$726$		0			0
$727$	−2.50999	+	1.44914i	−0.0930903	+	0.0537457i	−0.545822	−	0.837901i	$-0.683783\pi$
$727$	−2.50999	+	1.44914i	−0.0930903	+	0.0537457i	0.452732	+	0.891647i	$0.350449\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	45.1392			1.66953
$732$		0			0
$733$		−	11.8891i		−	0.439135i	−0.975597	−	0.219568i	$-0.929535\pi$
$733$		−	11.8891i		−	0.439135i	0.975597	−	0.219568i	$-0.0704647\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.62622	−	2.67095i	0.170409	−	0.0983858i
$738$		0			0
$739$	17.2254	−	29.8354i	0.633648	−	1.09751i	−0.353151	−	0.935566i	$-0.614890\pi$
$739$	17.2254	−	29.8354i	0.633648	−	1.09751i	0.986800	−	0.161945i	$-0.0517767\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.44069	+	1.40913i	0.0895401	+	0.0516960i	0.544101	−	0.839019i	$-0.316871\pi$
$743$	2.44069	+	1.40913i	0.0895401	+	0.0516960i	−0.454561	+	0.890715i	$0.650204\pi$
$744$		0			0
$745$			29.4965i			1.08067i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.94930	+	16.5585i	−0.107765	+	0.605034i
$750$		0			0
$751$	7.72089			0.281739			0.140870	−	0.990028i	$-0.455010\pi$
$751$	7.72089			0.281739			0.140870	+	0.990028i	$0.455010\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−20.7517			−0.755233
$756$		0			0
$757$	1.17924			0.0428603			0.0214302	−	0.999770i	$-0.493178\pi$
$757$	1.17924			0.0428603			0.0214302	+	0.999770i	$0.493178\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.13289			0.113567			0.0567835	−	0.998387i	$-0.481916\pi$
$761$	3.13289			0.113567			0.0567835	+	0.998387i	$0.481916\pi$
$762$		0			0
$763$	−4.64770	−	12.8386i	−0.168258	−	0.464790i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	6.20393i		−	0.224011i
$768$		0			0
$769$	−5.53497	−	3.19562i	−0.199596	−	0.115237i	0.396871	−	0.917874i	$-0.370096\pi$
$769$	−5.53497	−	3.19562i	−0.199596	−	0.115237i	−0.596467	+	0.802637i	$0.703429\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	23.9779	−	41.5309i	0.862425	−	1.49376i	−0.00715621	−	0.999974i	$-0.502278\pi$
$773$	23.9779	−	41.5309i	0.862425	−	1.49376i	0.869581	−	0.493790i	$-0.164389\pi$
$774$		0			0
$775$	−7.71948	+	4.45685i	−0.277292	+	0.160095i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			12.5613i			0.450057i
$780$		0			0
$781$	3.56029			0.127397
$782$		0			0
$783$		0			0
$784$		0			0
$785$	29.1661	−	16.8390i	1.04098	−	0.601011i
$786$		0			0
$787$	5.23136	−	3.02033i	0.186478	−	0.107663i	−0.403855	−	0.914823i	$-0.632330\pi$
$787$	5.23136	−	3.02033i	0.186478	−	0.107663i	0.590333	+	0.807160i	$0.298997\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−26.4047	+	9.55872i	−0.938842	+	0.339869i
$792$		0			0
$793$	1.42635	+	2.47050i	0.0506510	+	0.0877301i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.782501	−	1.35533i	0.0277176	−	0.0480083i	−0.851834	−	0.523812i	$-0.824509\pi$
$797$	0.782501	−	1.35533i	0.0277176	−	0.0480083i	0.879551	+	0.475804i	$0.157843\pi$
$798$		0			0
$799$	3.45810	+	5.98961i	0.122339	+	0.211897i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.398681	−	0.690535i	0.0140691	−	0.0243685i
$804$		0			0
$805$	49.5485	+	41.7226i	1.74635	+	1.47053i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.3445	−	8.85918i	−0.539485	−	0.311472i	0.205385	−	0.978681i	$-0.434155\pi$
$809$	−15.3445	−	8.85918i	−0.539485	−	0.311472i	−0.744870	+	0.667209i	$0.767489\pi$
$810$		0			0
$811$		−	27.5261i		−	0.966571i	−0.875463	−	0.483285i	$-0.839443\pi$
$811$		−	27.5261i		−	0.966571i	0.875463	−	0.483285i	$-0.160557\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−16.2334	−	28.1171i	−0.568633	−	0.984901i
$816$		0			0
$817$	59.1707	+	34.1622i	2.07012	+	1.19519i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23.0343	−	13.2989i	−0.803903	−	0.464134i	0.0409311	−	0.999162i	$-0.486968\pi$
$821$	−23.0343	−	13.2989i	−0.803903	−	0.464134i	−0.844834	+	0.535028i	$0.820301\pi$
$822$		0			0
$823$	−12.0797	−	20.9227i	−0.421073	−	0.729319i	0.574972	−	0.818173i	$-0.305013\pi$
$823$	−12.0797	−	20.9227i	−0.421073	−	0.729319i	−0.996045	+	0.0888537i	$0.971680\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			9.64923i			0.335537i	0.985826	+	0.167768i	$0.0536561\pi$
$827$			9.64923i			0.335537i	−0.985826	+	0.167768i	$0.946344\pi$
$828$		0			0
$829$	−25.1481	−	14.5193i	−0.873430	−	0.504275i	−0.00494329	−	0.999988i	$-0.501574\pi$
$829$	−25.1481	−	14.5193i	−0.873430	−	0.504275i	−0.868486	+	0.495713i	$0.834907\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	25.6593	+	9.44005i	0.889041	+	0.327078i
$834$		0			0
$835$	−18.6231	+	32.2562i	−0.644480	+	1.11627i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	6.84383	+	11.8539i	0.236275	+	0.409241i	0.959642	−	0.281223i	$-0.0907400\pi$
$839$	6.84383	+	11.8539i	0.236275	+	0.409241i	−0.723367	+	0.690463i	$0.757407\pi$
$840$		0			0
$841$	9.53027	−	16.5069i	0.328630	−	0.569204i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	14.6202	+	25.3229i	0.502949	+	0.871134i
$846$		0			0
$847$	18.4476	−	21.9077i	0.633866	−	0.752759i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−70.3110	+	40.5941i	−2.41023	+	1.39155i
$852$		0			0
$853$	−40.5184	+	23.3933i	−1.38732	+	0.800972i	−0.993013	−	0.118006i	$-0.962350\pi$
$853$	−40.5184	+	23.3933i	−1.38732	+	0.800972i	−0.394310	+	0.918977i	$0.629017\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−31.7960			−1.08613			−0.543065	−	0.839691i	$-0.682736\pi$
$857$	−31.7960			−1.08613			−0.543065	+	0.839691i	$0.682736\pi$
$858$		0			0
$859$		−	25.2885i		−	0.862832i	−0.902153	−	0.431416i	$-0.858014\pi$
$859$		−	25.2885i		−	0.862832i	0.902153	−	0.431416i	$-0.141986\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.9513	−	9.20946i	0.542987	−	0.313494i	−0.203302	−	0.979116i	$-0.565167\pi$
$863$	15.9513	−	9.20946i	0.542987	−	0.313494i	0.746289	+	0.665622i	$0.231834\pi$
$864$		0			0
$865$	−22.7993	+	39.4896i	−0.775200	+	1.34269i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.314216	−	0.181413i	−0.0106590	−	0.00615400i
$870$		0			0
$871$		−	19.5377i		−	0.662010i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.5671	−	13.7367i	0.391039	−	0.464385i
$876$		0			0
$877$	−8.89389			−0.300325			−0.150163	−	0.988661i	$-0.547980\pi$
$877$	−8.89389			−0.300325			−0.150163	+	0.988661i	$0.547980\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13.1721			0.443780			0.221890	−	0.975072i	$-0.428777\pi$
$881$	13.1721			0.443780			0.221890	+	0.975072i	$0.428777\pi$
$882$		0			0
$883$	12.6729			0.426477			0.213239	−	0.977000i	$-0.431599\pi$
$883$	12.6729			0.426477			0.213239	+	0.977000i	$0.431599\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	33.3983			1.12141			0.560703	−	0.828017i	$-0.310531\pi$
$887$	33.3983			1.12141			0.560703	+	0.828017i	$0.310531\pi$
$888$		0			0
$889$	17.5374	−	20.8268i	0.588185	−	0.698510i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			10.4686i			0.350320i
$894$		0			0
$895$	−40.6231	−	23.4538i	−1.35788	−	0.783974i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.2328	−	21.1877i	0.407985	−	0.706651i
$900$		0			0
$901$	13.2612	−	7.65638i	0.441796	−	0.255071i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	49.9753i		−	1.66124i
$906$		0			0
$907$	−29.3127			−0.973311			−0.486655	−	0.873594i	$-0.661783\pi$
$907$	−29.3127			−0.973311			−0.486655	+	0.873594i	$0.661783\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.72555	+	0.996246i	−0.0571700	+	0.0330071i	−0.528313	−	0.849050i	$-0.677175\pi$
$911$	−1.72555	+	0.996246i	−0.0571700	+	0.0330071i	0.471143	+	0.882057i	$0.343842\pi$
$912$		0			0
$913$	2.50629	−	1.44701i	0.0829462	−	0.0478890i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−33.5055	+	39.7901i	−1.10645	+	1.31398i
$918$		0			0
$919$	−0.897678	−	1.55482i	−0.0296117	−	0.0512889i	0.850840	−	0.525425i	$-0.176094\pi$
$919$	−0.897678	−	1.55482i	−0.0296117	−	0.0512889i	−0.880451	+	0.474136i	$0.842760\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.51079	−	11.2770i	0.214305	−	0.371188i
$924$		0			0
$925$	−11.4889	−	19.8993i	−0.377751	−	0.654284i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.4178	−	21.5083i	0.407415	−	0.705664i	−0.587184	−	0.809453i	$-0.699763\pi$
$929$	12.4178	−	21.5083i	0.407415	−	0.705664i	0.994599	+	0.103789i	$0.0330968\pi$
$930$		0			0
$931$	26.4911	+	31.7940i	0.868209	+	1.04200i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.88207	−	2.24132i	−0.126957	−	0.0732988i
$936$		0			0
$937$		−	27.9046i		−	0.911605i	−0.890081	−	0.455802i	$-0.849352\pi$
$937$		−	27.9046i		−	0.911605i	0.890081	−	0.455802i	$-0.150648\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−26.2537	−	45.4728i	−0.855847	−	1.48237i	−0.875857	−	0.482571i	$-0.839703\pi$
$941$	−26.2537	−	45.4728i	−0.855847	−	1.48237i	0.0200094	−	0.999800i	$-0.493630\pi$
$942$		0			0
$943$	−16.4216	−	9.48104i	−0.534762	−	0.308745i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	37.3591	+	21.5693i	1.21401	+	0.700907i	0.963630	−	0.267241i	$-0.0861121\pi$
$947$	37.3591	+	21.5693i	1.21401	+	0.700907i	0.250377	+	0.968148i	$0.419445\pi$
$948$		0			0
$949$	−1.45815	−	2.52559i	−0.0473336	−	0.0819843i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			59.9829i			1.94304i	0.236965	+	0.971518i	$0.423847\pi$
$953$			59.9829i			1.94304i	−0.236965	+	0.971518i	$0.576153\pi$
$954$		0			0
$955$	−49.8899	−	28.8040i	−1.61440	−	0.932074i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−10.8995	−	9.17803i	−0.351964	−	0.296374i
$960$		0			0
$961$	−9.27285	+	16.0610i	−0.299124	+	0.518098i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.56709	−	16.5707i	−0.307975	−	0.533429i
$966$		0			0
$967$	−26.6398	+	46.1414i	−0.856677	+	1.48381i	0.0184029	+	0.999831i	$0.494142\pi$
$967$	−26.6398	+	46.1414i	−0.856677	+	1.48381i	−0.875080	+	0.483978i	$0.839191\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	28.1556	+	48.7669i	0.903555	+	1.56500i	0.822845	+	0.568266i	$0.192385\pi$
$971$	28.1556	+	48.7669i	0.903555	+	1.56500i	0.0807100	+	0.996738i	$0.474281\pi$
$972$		0			0
$973$	−42.4685	+	15.3740i	−1.36148	+	0.492867i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.5755	−	13.0340i	0.722254	−	0.416994i	−0.0933275	−	0.995635i	$-0.529750\pi$
$977$	22.5755	−	13.0340i	0.722254	−	0.416994i	0.815582	+	0.578642i	$0.196417\pi$
$978$		0			0
$979$	−3.54237	+	2.04519i	−0.113215	+	0.0653646i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−38.0505			−1.21362			−0.606811	−	0.794846i	$-0.707551\pi$
$983$	−38.0505			−1.21362			−0.606811	+	0.794846i	$0.707551\pi$
$984$		0			0
$985$			44.1005i			1.40516i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−89.3217	+	51.5699i	−2.84026	+	1.63983i
$990$		0			0
$991$	−5.68758	+	9.85118i	−0.180672	+	0.312933i	−0.942110	−	0.335305i	$-0.891161\pi$
$991$	−5.68758	+	9.85118i	−0.180672	+	0.312933i	0.761438	+	0.648238i	$0.224494\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	14.9499	+	8.63131i	0.473943	+	0.273631i
$996$		0			0
$997$		−	50.9904i		−	1.61488i	−0.589948	−	0.807441i	$-0.700852\pi$
$997$		−	50.9904i		−	1.61488i	0.589948	−	0.807441i	$-0.299148\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bm.a.17.2		16
3.2	odd	2		252.2.bm.a.185.5	yes	16
4.3	odd	2		3024.2.df.d.17.2		16
7.2	even	3		5292.2.w.b.1097.7		16
7.3	odd	6		5292.2.x.a.881.2		16
7.4	even	3		5292.2.x.b.881.7		16
7.5	odd	6		756.2.w.a.341.2		16
7.6	odd	2		5292.2.bm.a.2285.7		16
9.2	odd	6		756.2.w.a.521.2		16
9.4	even	3		2268.2.t.b.1781.7		16
9.5	odd	6		2268.2.t.a.1781.2		16
9.7	even	3		252.2.w.a.101.7	yes	16
12.11	even	2		1008.2.df.d.689.4		16
21.2	odd	6		1764.2.w.b.509.2		16
21.5	even	6		252.2.w.a.5.7	✓	16
21.11	odd	6		1764.2.x.b.293.7		16
21.17	even	6		1764.2.x.a.293.2		16
21.20	even	2		1764.2.bm.a.1697.4		16
28.19	even	6		3024.2.ca.d.2609.2		16
36.7	odd	6		1008.2.ca.d.353.2		16
36.11	even	6		3024.2.ca.d.2033.2		16
63.2	odd	6		5292.2.bm.a.4625.7		16
63.5	even	6		2268.2.t.b.2105.7		16
63.11	odd	6		5292.2.x.a.4409.2		16
63.16	even	3		1764.2.bm.a.1685.4		16
63.20	even	6		5292.2.w.b.521.7		16
63.25	even	3		1764.2.x.a.1469.2		16
63.34	odd	6		1764.2.w.b.1109.2		16
63.38	even	6		5292.2.x.b.4409.7		16
63.40	odd	6		2268.2.t.a.2105.2		16
63.47	even	6	inner	756.2.bm.a.89.2		16
63.52	odd	6		1764.2.x.b.1469.7		16
63.61	odd	6		252.2.bm.a.173.5	yes	16
84.47	odd	6		1008.2.ca.d.257.2		16
252.47	odd	6		3024.2.df.d.1601.2		16
252.187	even	6		1008.2.df.d.929.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	21.5	even	6
252.2.w.a.101.7	yes	16	9.7	even	3
252.2.bm.a.173.5	yes	16	63.61	odd	6
252.2.bm.a.185.5	yes	16	3.2	odd	2
756.2.w.a.341.2		16	7.5	odd	6
756.2.w.a.521.2		16	9.2	odd	6
756.2.bm.a.17.2		16	1.1	even	1	trivial
756.2.bm.a.89.2		16	63.47	even	6	inner
1008.2.ca.d.257.2		16	84.47	odd	6
1008.2.ca.d.353.2		16	36.7	odd	6
1008.2.df.d.689.4		16	12.11	even	2
1008.2.df.d.929.4		16	252.187	even	6
1764.2.w.b.509.2		16	21.2	odd	6
1764.2.w.b.1109.2		16	63.34	odd	6
1764.2.x.a.293.2		16	21.17	even	6
1764.2.x.a.1469.2		16	63.25	even	3
1764.2.x.b.293.7		16	21.11	odd	6
1764.2.x.b.1469.7		16	63.52	odd	6
1764.2.bm.a.1685.4		16	63.16	even	3
1764.2.bm.a.1697.4		16	21.20	even	2
2268.2.t.a.1781.2		16	9.5	odd	6
2268.2.t.a.2105.2		16	63.40	odd	6
2268.2.t.b.1781.7		16	9.4	even	3
2268.2.t.b.2105.7		16	63.5	even	6
3024.2.ca.d.2033.2		16	36.11	even	6
3024.2.ca.d.2609.2		16	28.19	even	6
3024.2.df.d.17.2		16	4.3	odd	2
3024.2.df.d.1601.2		16	252.47	odd	6
5292.2.w.b.521.7		16	63.20	even	6
5292.2.w.b.1097.7		16	7.2	even	3
5292.2.x.a.881.2		16	7.3	odd	6
5292.2.x.a.4409.2		16	63.11	odd	6
5292.2.x.b.881.7		16	7.4	even	3
5292.2.x.b.4409.7		16	63.38	even	6
5292.2.bm.a.2285.7		16	7.6	odd	2
5292.2.bm.a.4625.7		16	63.2	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.74332 q^{5} +(1.70417 - 2.02381i) q^{7} +O(q^{10})\)	\(q-2.74332 q^{5} +(1.70417 - 2.02381i) q^{7} -0.418355i q^{11} +(-1.32512 - 0.765056i) q^{13} +(-1.95291 + 3.38253i) q^{17} +(-5.11994 + 2.95600i) q^{19} -8.92450i q^{23} +2.52579 q^{25} +(-6.00378 + 3.46629i) q^{29} +(-3.05626 + 1.76453i) q^{31} +(-4.67507 + 5.55196i) q^{35} +(-4.54861 - 7.87842i) q^{37} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(0.885373 - 1.53351i) q^{47} +(-1.19164 - 6.89783i) q^{49} +(-3.39526 - 1.96025i) q^{53} +1.14768i q^{55} +(2.02728 + 3.51135i) q^{59} +(-1.61459 - 0.932184i) q^{61} +(3.63521 + 2.09879i) q^{65} +(6.38441 + 11.0581i) q^{67} +8.51021i q^{71} +(1.65059 + 0.952971i) q^{73} +(-0.846673 - 0.712947i) q^{77} +(0.433633 - 0.751074i) q^{79} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(-4.88864 - 8.46738i) q^{89} +(-3.80655 + 1.37800i) q^{91} +(14.0456 - 8.10924i) q^{95} +(-0.200411 + 0.115707i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} + 6 q^{31} - 15 q^{35} + q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 13 q^{49} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 45 q^{77} - q^{79} + 6 q^{85} + 21 q^{89} + 9 q^{91} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 16 * q - q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 + 6 * q^31 - 15 * q^35 + q^37 - 6 * q^41 - 2 * q^43 + 18 * q^47 + 13 * q^49 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 45 * q^77 - q^79 + 6 * q^85 + 21 * q^89 + 9 * q^91 - 6 * q^95 + 3 * q^97

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