LMFDB - Embedded newform 756.2.j.b.505.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(253,756)]

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, 2, 0]))

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

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

chi := DirichletCharacter("756.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.j (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	756.505
Dual form			756.2.j.b.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119562 + 0.207087i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(0.119562 + 0.207087i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.56238 + 4.43818i) q^{11} +(2.44282 + 4.23109i) q^{13} -3.70370 q^{17} +3.66019 q^{19} +(3.71053 + 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(1.73229 - 3.00041i) q^{29} +(0.358685 + 0.621261i) q^{31} +0.239123 q^{35} +4.60301 q^{37} +(2.80150 + 4.85235i) q^{41} +(-6.24433 + 10.8155i) q^{43} +(2.16991 - 3.75839i) q^{47} +(-0.500000 - 0.866025i) q^{49} +0.942820 q^{53} -1.22545 q^{55} +(3.78947 + 6.56355i) q^{59} +(-2.75404 + 4.77014i) q^{61} +(-0.584135 + 1.01175i) q^{65} +(0.330095 + 0.571741i) q^{67} -13.7414 q^{71} -3.66019 q^{73} +(2.56238 + 4.43818i) q^{77} +(3.11273 - 5.39140i) q^{79} +(4.85185 - 8.40365i) q^{83} +(-0.442820 - 0.766987i) q^{85} +7.48865 q^{89} +4.88564 q^{91} +(0.437618 + 0.757977i) q^{95} +(8.57442 - 14.8513i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q + q^5 + 3 * q^7	$ 6 q + q^{5} + 3 q^{7} + 2 q^{11} - 3 q^{13} - 4 q^{17} + 6 q^{19} + 14 q^{23} + 6 q^{25} + q^{29} + 3 q^{31} + 2 q^{35} - 6 q^{37} - 3 q^{43} + 21 q^{47} - 3 q^{49} - 12 q^{53} + 12 q^{55} + 31 q^{59} - 6 q^{61} + 15 q^{65} - 6 q^{67} - 34 q^{71} - 6 q^{73} - 2 q^{77} + 9 q^{79} + 20 q^{83} + 15 q^{85} - 24 q^{89} - 6 q^{91} + 20 q^{95} + 9 q^{97}+O(q^{100}) $ 6 * q + q^5 + 3 * q^7 + 2 * q^11 - 3 * q^13 - 4 * q^17 + 6 * q^19 + 14 * q^23 + 6 * q^25 + q^29 + 3 * q^31 + 2 * q^35 - 6 * q^37 - 3 * q^43 + 21 * q^47 - 3 * q^49 - 12 * q^53 + 12 * q^55 + 31 * q^59 - 6 * q^61 + 15 * q^65 - 6 * q^67 - 34 * q^71 - 6 * q^73 - 2 * q^77 + 9 * q^79 + 20 * q^83 + 15 * q^85 - 24 * q^89 - 6 * q^91 + 20 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	0.119562	+	0.207087i	0.0534696	+	0.0926120i	0.891521	−	0.452979i	$-0.149639\pi$
$5$	0.119562	+	0.207087i	0.0534696	+	0.0926120i	−0.838052	+	0.545591i	$0.816305\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.56238	+	4.43818i	−0.772587	+	1.33816i	0.163554	+	0.986534i	$0.447704\pi$
$11$	−2.56238	+	4.43818i	−0.772587	+	1.33816i	−0.936141	+	0.351626i	$0.885629\pi$
$12$		0			0
$13$	2.44282	+	4.23109i	0.677516	+	1.17349i	0.975727	+	0.218993i	$0.0702770\pi$
$13$	2.44282	+	4.23109i	0.677516	+	1.17349i	−0.298210	+	0.954500i	$0.596390\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.70370			−0.898278			−0.449139	−	0.893462i	$-0.648269\pi$
$17$	−3.70370			−0.898278			−0.449139	+	0.893462i	$0.648269\pi$
$18$		0			0
$19$	3.66019			0.839705			0.419853	−	0.907592i	$-0.362082\pi$
$19$	3.66019			0.839705			0.419853	+	0.907592i	$0.362082\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.71053	+	6.42683i	0.773700	+	1.34009i	0.935522	+	0.353267i	$0.114929\pi$
$23$	3.71053	+	6.42683i	0.773700	+	1.34009i	−0.161823	+	0.986820i	$0.551737\pi$
$24$		0			0
$25$	2.47141	−	4.28061i	0.494282	−	0.856122i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.73229	−	3.00041i	0.321678	−	0.557162i	−0.659157	−	0.752006i	$-0.729087\pi$
$29$	1.73229	−	3.00041i	0.321678	−	0.557162i	0.980834	+	0.194844i	$0.0624200\pi$
$30$		0			0
$31$	0.358685	+	0.621261i	0.0644217	+	0.111582i	0.896437	−	0.443171i	$-0.146146\pi$
$31$	0.358685	+	0.621261i	0.0644217	+	0.111582i	−0.832016	+	0.554752i	$0.812813\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.239123			0.0404192
$36$		0			0
$37$	4.60301			0.756730			0.378365	−	0.925656i	$-0.376486\pi$
$37$	4.60301			0.756730			0.378365	+	0.925656i	$0.376486\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.80150	+	4.85235i	0.437522	+	0.757810i	0.997498	−	0.0706992i	$-0.0225230\pi$
$41$	2.80150	+	4.85235i	0.437522	+	0.757810i	−0.559976	+	0.828509i	$0.689190\pi$
$42$		0			0
$43$	−6.24433	+	10.8155i	−0.952251	+	1.64935i	−0.211713	+	0.977332i	$0.567904\pi$
$43$	−6.24433	+	10.8155i	−0.952251	+	1.64935i	−0.740538	+	0.672015i	$0.765429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.16991	−	3.75839i	0.316513	−	0.548217i	−0.663245	−	0.748403i	$-0.730821\pi$
$47$	2.16991	−	3.75839i	0.316513	−	0.548217i	0.979758	+	0.200186i	$0.0641545\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.942820			0.129506			0.0647531	−	0.997901i	$-0.479374\pi$
$53$	0.942820			0.129506			0.0647531	+	0.997901i	$0.479374\pi$
$54$		0			0
$55$	−1.22545			−0.165240
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.78947	+	6.56355i	0.493347	+	0.854501i	0.999971	−	0.00766579i	$-0.00244012\pi$
$59$	3.78947	+	6.56355i	0.493347	+	0.854501i	−0.506624	+	0.862167i	$0.669107\pi$
$60$		0			0
$61$	−2.75404	+	4.77014i	−0.352619	+	0.610754i	−0.986707	−	0.162507i	$-0.948042\pi$
$61$	−2.75404	+	4.77014i	−0.352619	+	0.610754i	0.634089	+	0.773260i	$0.281375\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.584135	+	1.01175i	−0.0724530	+	0.125492i
$66$		0			0
$67$	0.330095	+	0.571741i	0.0403275	+	0.0698493i	0.885485	−	0.464669i	$-0.153827\pi$
$67$	0.330095	+	0.571741i	0.0403275	+	0.0698493i	−0.845157	+	0.534518i	$0.820493\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−13.7414			−1.63081			−0.815405	−	0.578891i	$-0.803486\pi$
$71$	−13.7414			−1.63081			−0.815405	+	0.578891i	$0.803486\pi$
$72$		0			0
$73$	−3.66019			−0.428393			−0.214196	−	0.976791i	$-0.568713\pi$
$73$	−3.66019			−0.428393			−0.214196	+	0.976791i	$0.568713\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.56238	+	4.43818i	0.292010	+	0.505777i
$78$		0			0
$79$	3.11273	−	5.39140i	0.350209	−	0.606580i	−0.636077	−	0.771626i	$-0.719444\pi$
$79$	3.11273	−	5.39140i	0.350209	−	0.606580i	0.986286	+	0.165046i	$0.0527772\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.85185	−	8.40365i	0.532560	−	0.922420i	−0.466718	−	0.884406i	$-0.654564\pi$
$83$	4.85185	−	8.40365i	0.532560	−	0.922420i	0.999277	−	0.0380138i	$-0.0121031\pi$
$84$		0			0
$85$	−0.442820	−	0.766987i	−0.0480306	−	0.0831914i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.48865			0.793795			0.396898	−	0.917863i	$-0.370087\pi$
$89$	7.48865			0.793795			0.396898	+	0.917863i	$0.370087\pi$
$90$		0			0
$91$	4.88564			0.512154
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.437618	+	0.757977i	0.0448987	+	0.0777668i
$96$		0			0
$97$	8.57442	−	14.8513i	0.870600	−	1.50792i	0.00922376	−	0.999957i	$-0.497064\pi$
$97$	8.57442	−	14.8513i	0.870600	−	1.50792i	0.861377	−	0.507967i	$-0.169603\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.59097	−	6.21975i	0.357315	−	0.618888i	−0.630196	−	0.776436i	$-0.717026\pi$
$101$	3.59097	−	6.21975i	0.357315	−	0.618888i	0.987511	+	0.157548i	$0.0503589\pi$
$102$		0			0
$103$	6.41423	+	11.1098i	0.632013	+	1.09468i	0.987140	+	0.159860i	$0.0511044\pi$
$103$	6.41423	+	11.1098i	0.632013	+	1.09468i	−0.355127	+	0.934818i	$0.615562\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.56526			−0.731361			−0.365681	−	0.930740i	$-0.619164\pi$
$107$	−7.56526			−0.731361			−0.365681	+	0.930740i	$0.619164\pi$
$108$		0			0
$109$	−6.98057			−0.668617			−0.334309	−	0.942464i	$-0.608503\pi$
$109$	−6.98057			−0.668617			−0.334309	+	0.942464i	$0.608503\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.78495	−	16.9480i	−0.920491	−	1.59434i	−0.798657	−	0.601787i	$-0.794456\pi$
$113$	−9.78495	−	16.9480i	−0.920491	−	1.59434i	−0.121834	−	0.992550i	$-0.538878\pi$
$114$		0			0
$115$	−0.887275	+	1.53681i	−0.0827388	+	0.143308i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.85185	+	3.20750i	−0.169759	+	0.294031i
$120$		0			0
$121$	−7.63160	−	13.2183i	−0.693782	−	1.20167i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.37756			0.212655
$126$		0			0
$127$	−16.8090			−1.49156			−0.745780	−	0.666192i	$-0.767923\pi$
$127$	−16.8090			−1.49156			−0.745780	+	0.666192i	$0.767923\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.44966	+	4.24293i	0.214027	+	0.370706i	0.952971	−	0.303061i	$-0.0980085\pi$
$131$	2.44966	+	4.24293i	0.214027	+	0.370706i	−0.738944	+	0.673767i	$0.764675\pi$
$132$		0			0
$133$	1.83009	−	3.16982i	0.158689	−	0.274858i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.72257	−	4.71563i	0.232605	−	0.402884i	−0.725969	−	0.687727i	$-0.758608\pi$
$137$	2.72257	−	4.71563i	0.232605	−	0.402884i	0.958574	+	0.284844i	$0.0919417\pi$
$138$		0			0
$139$	−2.83009	−	4.90187i	−0.240046	−	0.415771i	0.720681	−	0.693266i	$-0.243829\pi$
$139$	−2.83009	−	4.90187i	−0.240046	−	0.415771i	−0.960727	+	0.277495i	$0.910496\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−25.0377			−2.09376
$144$		0			0
$145$	0.828460			0.0687999
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.14132	+	1.97682i	0.0935002	+	0.161947i	0.908982	−	0.416836i	$-0.136861\pi$
$149$	1.14132	+	1.97682i	0.0935002	+	0.161947i	−0.815481	+	0.578783i	$0.803528\pi$
$150$		0			0
$151$	−5.63160	+	9.75422i	−0.458293	+	0.793787i	−0.998871	−	0.0475071i	$-0.984872\pi$
$151$	−5.63160	+	9.75422i	−0.458293	+	0.793787i	0.540578	+	0.841294i	$0.318206\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.0857699	+	0.148558i	−0.00688921	+	0.0119325i
$156$		0			0
$157$	−2.77292	−	4.80283i	−0.221303	−	0.383308i	0.733901	−	0.679256i	$-0.237698\pi$
$157$	−2.77292	−	4.80283i	−0.221303	−	0.383308i	−0.955204	+	0.295949i	$0.904364\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.42107			0.584862
$162$		0			0
$163$	6.66019			0.521666			0.260833	−	0.965384i	$-0.416003\pi$
$163$	6.66019			0.521666			0.260833	+	0.965384i	$0.416003\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.20370	+	3.81691i	0.170527	+	0.295362i	0.938604	−	0.344996i	$-0.112120\pi$
$167$	2.20370	+	3.81691i	0.170527	+	0.295362i	−0.768077	+	0.640357i	$0.778786\pi$
$168$		0			0
$169$	−5.43474	+	9.41325i	−0.418057	+	0.724096i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.6654	−	21.9371i	0.962932	−	1.66785i	0.247860	−	0.968796i	$-0.420273\pi$
$173$	12.6654	−	21.9371i	0.962932	−	1.66785i	0.715072	−	0.699051i	$-0.246394\pi$
$174$		0			0
$175$	−2.47141	−	4.28061i	−0.186821	−	0.323584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.54583			−0.713489			−0.356744	−	0.934202i	$-0.616113\pi$
$179$	−9.54583			−0.713489			−0.356744	+	0.934202i	$0.616113\pi$
$180$		0			0
$181$	12.3743			0.919774			0.459887	−	0.887978i	$-0.347890\pi$
$181$	12.3743			0.919774			0.459887	+	0.887978i	$0.347890\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.550343	+	0.953223i	0.0404621	+	0.0700823i
$186$		0			0
$187$	9.49028	−	16.4377i	0.693998	−	1.20204i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.58414	−	11.4041i	0.476411	−	0.825169i	−0.523223	−	0.852196i	$-0.675271\pi$
$191$	6.58414	−	11.4041i	0.476411	−	0.825169i	0.999635	+	0.0270270i	$0.00860400\pi$
$192$		0			0
$193$	−5.57442	−	9.65518i	−0.401256	−	0.694995i	0.592622	−	0.805481i	$-0.298093\pi$
$193$	−5.57442	−	9.65518i	−0.401256	−	0.694995i	−0.993878	+	0.110486i	$0.964759\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.144194			0.0102734			0.00513669	−	0.999987i	$-0.498365\pi$
$197$	0.144194			0.0102734			0.00513669	+	0.999987i	$0.498365\pi$
$198$		0			0
$199$	−19.4692			−1.38014			−0.690068	−	0.723744i	$-0.742419\pi$
$199$	−19.4692			−1.38014			−0.690068	+	0.723744i	$0.742419\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.73229	−	3.00041i	−0.121583	−	0.210587i
$204$		0			0
$205$	−0.669905	+	1.16031i	−0.0467882	+	0.0810395i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.37880	+	16.2446i	−0.648745	+	1.12366i
$210$		0			0
$211$	1.61436	+	2.79615i	0.111137	+	0.192495i	0.916229	−	0.400655i	$-0.131217\pi$
$211$	1.61436	+	2.79615i	0.111137	+	0.192495i	−0.805092	+	0.593150i	$0.797884\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.98633			−0.203666
$216$		0			0
$217$	0.717370			0.0486982
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−9.04746	−	15.6707i	−0.608598	−	1.05412i
$222$		0			0
$223$	−10.3856	+	17.9885i	−0.695474	+	1.20460i	0.274547	+	0.961574i	$0.411472\pi$
$223$	−10.3856	+	17.9885i	−0.695474	+	1.20460i	−0.970021	+	0.243022i	$0.921861\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.9714	−	19.0030i	0.728198	−	1.26128i	−0.229446	−	0.973321i	$-0.573691\pi$
$227$	10.9714	−	19.0030i	0.728198	−	1.26128i	0.957644	−	0.287955i	$-0.0929752\pi$
$228$		0			0
$229$	−11.3856	−	19.7205i	−0.752384	−	1.30317i	−0.946664	−	0.322222i	$-0.895570\pi$
$229$	−11.3856	−	19.7205i	−0.752384	−	1.30317i	0.194280	−	0.980946i	$-0.437763\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	25.7817			1.68901			0.844507	−	0.535544i	$-0.179894\pi$
$233$	25.7817			1.68901			0.844507	+	0.535544i	$0.179894\pi$
$234$		0			0
$235$	1.03775			0.0676953
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.6488	−	23.6405i	−0.882870	−	1.52918i	−0.848136	−	0.529779i	$-0.822275\pi$
$239$	−13.6488	−	23.6405i	−0.882870	−	1.52918i	−0.0347345	−	0.999397i	$-0.511059\pi$
$240$		0			0
$241$	−5.01724	+	8.69011i	−0.323189	+	0.559779i	−0.981144	−	0.193277i	$-0.938088\pi$
$241$	−5.01724	+	8.69011i	−0.323189	+	0.559779i	0.657955	+	0.753057i	$0.271422\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.119562	−	0.207087i	0.00763851	−	0.0132303i
$246$		0			0
$247$	8.94119	+	15.4866i	0.568914	+	0.985388i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	28.3171			1.78736			0.893680	−	0.448705i	$-0.148115\pi$
$251$	28.3171			1.78736			0.893680	+	0.448705i	$0.148115\pi$
$252$		0			0
$253$	−38.0312			−2.39100
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.4315	+	24.9960i	0.900210	+	1.55921i	0.827221	+	0.561877i	$0.189921\pi$
$257$	14.4315	+	24.9960i	0.900210	+	1.55921i	0.0729899	+	0.997333i	$0.476746\pi$
$258$		0			0
$259$	2.30150	−	3.98632i	0.143009	−	0.247698i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.604645	+	1.04728i	−0.0372840	+	0.0645778i	−0.884065	−	0.467363i	$-0.845204\pi$
$263$	−0.604645	+	1.04728i	−0.0372840	+	0.0645778i	0.846781	+	0.531941i	$0.178537\pi$
$264$		0			0
$265$	0.112725	+	0.195246i	0.00692465	+	0.0119938i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.01367			−0.549573			−0.274787	−	0.961505i	$-0.588607\pi$
$269$	−9.01367			−0.549573			−0.274787	+	0.961505i	$0.588607\pi$
$270$		0			0
$271$	17.6030			1.06931			0.534653	−	0.845071i	$-0.320442\pi$
$271$	17.6030			1.06931			0.534653	+	0.845071i	$0.320442\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.6654	+	21.9371i	0.763752	+	1.32286i
$276$		0			0
$277$	−0.727085	+	1.25935i	−0.0436863	+	0.0756669i	−0.887042	−	0.461689i	$-0.847244\pi$
$277$	−0.727085	+	1.25935i	−0.0436863	+	0.0756669i	0.843355	+	0.537356i	$0.180577\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.1482	+	17.5771i	−0.605388	+	1.04856i	0.386602	+	0.922247i	$0.373649\pi$
$281$	−10.1482	+	17.5771i	−0.605388	+	1.04856i	−0.991990	+	0.126316i	$0.959685\pi$
$282$		0			0
$283$	2.30150	+	3.98632i	0.136810	+	0.236962i	0.926288	−	0.376817i	$-0.122982\pi$
$283$	2.30150	+	3.98632i	0.136810	+	0.236962i	−0.789477	+	0.613780i	$0.789648\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.60301			0.330735
$288$		0			0
$289$	−3.28263			−0.193096
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.53667	−	6.12569i	−0.206614	−	0.357867i	0.744031	−	0.668145i	$-0.232911\pi$
$293$	−3.53667	−	6.12569i	−0.206614	−	0.357867i	−0.950646	+	0.310278i	$0.899578\pi$
$294$		0			0
$295$	−0.906150	+	1.56950i	−0.0527581	+	0.0913797i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−18.1283	+	31.3992i	−1.04839	+	1.81586i
$300$		0			0
$301$	6.24433	+	10.8155i	0.359917	+	0.623394i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.31711			−0.0754175
$306$		0			0
$307$	15.7518			0.899006			0.449503	−	0.893279i	$-0.351601\pi$
$307$	15.7518			0.899006			0.449503	+	0.893279i	$0.351601\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.81191	−	16.9947i	−0.556382	−	0.963682i	−0.997795	−	0.0663780i	$-0.978856\pi$
$311$	−9.81191	−	16.9947i	−0.556382	−	0.963682i	0.441412	−	0.897304i	$-0.354478\pi$
$312$		0			0
$313$	12.7427	−	22.0710i	0.720259	−	1.24753i	−0.240636	−	0.970615i	$-0.577356\pi$
$313$	12.7427	−	22.0710i	0.720259	−	1.24753i	0.960896	−	0.276911i	$-0.0893106\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.14132	−	7.17297i	0.232599	−	0.402874i	−0.725973	−	0.687723i	$-0.758610\pi$
$317$	4.14132	−	7.17297i	0.232599	−	0.402874i	0.958572	+	0.284849i	$0.0919436\pi$
$318$		0			0
$319$	8.87756	+	15.3764i	0.497048	+	0.860912i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.5562			−0.754289
$324$		0			0
$325$	24.1488			1.33954
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.16991	−	3.75839i	−0.119631	−	0.207207i
$330$		0			0
$331$	5.99028	−	10.3755i	0.329256	−	0.570288i	−0.653109	−	0.757264i	$-0.726535\pi$
$331$	5.99028	−	10.3755i	0.329256	−	0.570288i	0.982364	+	0.186976i	$0.0598688\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.0789334	+	0.136717i	−0.00431259	+	0.00746963i
$336$		0			0
$337$	6.46006	+	11.1892i	0.351902	+	0.609512i	0.986583	−	0.163262i	$-0.0522017\pi$
$337$	6.46006	+	11.1892i	0.351902	+	0.609512i	−0.634681	+	0.772774i	$0.718868\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.67635			−0.199086
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.09329	+	14.0180i	0.434471	+	0.752526i	0.997252	−	0.0740802i	$-0.0236021\pi$
$347$	8.09329	+	14.0180i	0.434471	+	0.752526i	−0.562781	+	0.826606i	$0.690269\pi$
$348$		0			0
$349$	9.05718	−	15.6875i	0.484820	−	0.839732i	−0.515028	−	0.857173i	$-0.672219\pi$
$349$	9.05718	−	15.6875i	0.484820	−	0.839732i	0.999848	+	0.0174409i	$0.00555188\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.84897	+	10.1307i	−0.311309	+	0.539203i	−0.978646	−	0.205553i	$-0.934101\pi$
$353$	−5.84897	+	10.1307i	−0.311309	+	0.539203i	0.667337	+	0.744756i	$0.267434\pi$
$354$		0			0
$355$	−1.64295	−	2.84567i	−0.0871987	−	0.151033i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−35.7245			−1.88547			−0.942734	−	0.333547i	$-0.891755\pi$
$359$	−35.7245			−1.88547			−0.942734	+	0.333547i	$0.891755\pi$
$360$		0			0
$361$	−5.60301			−0.294895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.437618	−	0.757977i	−0.0229060	−	0.0396743i
$366$		0			0
$367$	−8.52696	+	14.7691i	−0.445103	+	0.770942i	−0.998059	−	0.0622687i	$-0.980166\pi$
$367$	−8.52696	+	14.7691i	−0.445103	+	0.770942i	0.552956	+	0.833210i	$0.313500\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.471410	−	0.816506i	0.0244744	−	0.0423909i
$372$		0			0
$373$	12.9617	+	22.4503i	0.671131	+	1.16243i	0.977584	+	0.210547i	$0.0675246\pi$
$373$	12.9617	+	22.4503i	0.671131	+	1.16243i	−0.306453	+	0.951886i	$0.599142\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	16.9267			0.871767
$378$		0			0
$379$	26.8446			1.37892			0.689458	−	0.724326i	$-0.257849\pi$
$379$	26.8446			1.37892			0.689458	+	0.724326i	$0.257849\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.4263	+	21.5229i	0.634953	+	1.09977i	0.986525	+	0.163610i	$0.0523137\pi$
$383$	12.4263	+	21.5229i	0.634953	+	1.09977i	−0.351573	+	0.936161i	$0.614353\pi$
$384$		0			0
$385$	−0.612725	+	1.06127i	−0.0312274	+	0.0540874i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.12640	+	15.8074i	−0.462727	+	0.801466i	−0.999096	−	0.0425174i	$-0.986462\pi$
$389$	−9.12640	+	15.8074i	−0.462727	+	0.801466i	0.536369	+	0.843984i	$0.319796\pi$
$390$		0			0
$391$	−13.7427	−	23.8030i	−0.694998	−	1.20377i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.48865			0.0749021
$396$		0			0
$397$	12.3743			0.621048			0.310524	−	0.950566i	$-0.399496\pi$
$397$	12.3743			0.621048			0.310524	+	0.950566i	$0.399496\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.48113	−	9.49359i	−0.273714	−	0.474087i	0.696096	−	0.717949i	$-0.254919\pi$
$401$	−5.48113	−	9.49359i	−0.273714	−	0.474087i	−0.969810	+	0.243862i	$0.921586\pi$
$402$		0			0
$403$	−1.75241	+	3.03526i	−0.0872935	+	0.151197i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.7947	+	20.4290i	−0.584640	+	1.01263i
$408$		0			0
$409$	6.66019	+	11.5358i	0.329325	+	0.570408i	0.982378	−	0.186904i	$-0.0598454\pi$
$409$	6.66019	+	11.5358i	0.329325	+	0.570408i	−0.653053	+	0.757312i	$0.726512\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.57893			0.372935
$414$		0			0
$415$	2.32038			0.113903
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.35705	+	4.08253i	0.115149	+	0.199445i	0.917839	−	0.396952i	$-0.129932\pi$
$419$	2.35705	+	4.08253i	0.115149	+	0.199445i	−0.802690	+	0.596396i	$0.796599\pi$
$420$		0			0
$421$	−9.65856	+	16.7291i	−0.470729	+	0.815327i	−0.999440	−	0.0334755i	$-0.989342\pi$
$421$	−9.65856	+	16.7291i	−0.470729	+	0.815327i	0.528710	+	0.848802i	$0.322676\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−9.15335	+	15.8541i	−0.444003	+	0.769036i
$426$		0			0
$427$	2.75404	+	4.77014i	0.133277	+	0.230843i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	30.2794			1.45851			0.729253	−	0.684244i	$-0.239868\pi$
$431$	30.2794			1.45851			0.729253	+	0.684244i	$0.239868\pi$
$432$		0			0
$433$	34.2060			1.64384			0.821918	−	0.569606i	$-0.192904\pi$
$433$	34.2060			1.64384			0.821918	+	0.569606i	$0.192904\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.5813	+	23.5234i	0.649680	+	1.12528i
$438$		0			0
$439$	0.311220	−	0.539049i	0.0148537	−	0.0257274i	−0.858503	−	0.512809i	$-0.828605\pi$
$439$	0.311220	−	0.539049i	0.0148537	−	0.0257274i	0.873357	+	0.487081i	$0.161938\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.58934	+	4.48486i	−0.123023	+	0.213082i	−0.920958	−	0.389661i	$-0.872592\pi$
$443$	−2.58934	+	4.48486i	−0.123023	+	0.213082i	0.797935	+	0.602743i	$0.205926\pi$
$444$		0			0
$445$	0.895355	+	1.55080i	0.0424439	+	0.0735150i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	10.4977			0.495416			0.247708	−	0.968835i	$-0.420323\pi$
$449$	10.4977			0.495416			0.247708	+	0.968835i	$0.420323\pi$
$450$		0			0
$451$	−28.7141			−1.35209
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.584135	+	1.01175i	0.0273847	+	0.0474317i
$456$		0			0
$457$	1.60464	−	2.77933i	0.0750621	−	0.130011i	−0.826051	−	0.563595i	$-0.809418\pi$
$457$	1.60464	−	2.77933i	0.0750621	−	0.130011i	0.901113	+	0.433584i	$0.142751\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.1150	+	31.3762i	−0.843702	+	1.46133i	0.0430418	+	0.999073i	$0.486295\pi$
$461$	−18.1150	+	31.3762i	−0.843702	+	1.46133i	−0.886744	+	0.462261i	$0.847038\pi$
$462$		0			0
$463$	−14.5253	−	25.1586i	−0.675049	−	1.16922i	−0.976455	−	0.215723i	$-0.930789\pi$
$463$	−14.5253	−	25.1586i	−0.675049	−	1.16922i	0.301406	−	0.953496i	$-0.402544\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	37.4933			1.73498			0.867491	−	0.497452i	$-0.165731\pi$
$467$	37.4933			1.73498			0.867491	+	0.497452i	$0.165731\pi$
$468$		0			0
$469$	0.660190			0.0304847
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−32.0007	−	55.4268i	−1.47139	−	2.54853i
$474$		0			0
$475$	9.04583	−	15.6678i	0.415051	−	0.718890i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.9549	−	25.9026i	0.683305	−	1.18352i	−0.290661	−	0.956826i	$-0.593875\pi$
$479$	14.9549	−	25.9026i	0.683305	−	1.18352i	0.973966	−	0.226693i	$-0.0727914\pi$
$480$		0			0
$481$	11.2443	+	19.4757i	0.512697	+	0.888017i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.10069			0.186203
$486$		0			0
$487$	21.2632			0.963528			0.481764	−	0.876301i	$-0.339996\pi$
$487$	21.2632			0.963528			0.481764	+	0.876301i	$0.339996\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.6985	−	18.5303i	−0.482816	−	0.836262i	0.516989	−	0.855992i	$-0.327053\pi$
$491$	−10.6985	−	18.5303i	−0.482816	−	0.836262i	−0.999805	+	0.0197296i	$0.993719\pi$
$492$		0			0
$493$	−6.41586	+	11.1126i	−0.288956	+	0.500487i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.87072	+	11.9004i	−0.308194	+	0.533808i
$498$		0			0
$499$	−7.28263	−	12.6139i	−0.326015	−	0.564675i	0.655702	−	0.755020i	$-0.272373\pi$
$499$	−7.28263	−	12.6139i	−0.326015	−	0.564675i	−0.981717	+	0.190345i	$0.939039\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2.92339			−0.130348			−0.0651738	−	0.997874i	$-0.520760\pi$
$503$	−2.92339			−0.130348			−0.0651738	+	0.997874i	$0.520760\pi$
$504$		0			0
$505$	1.71737			0.0764220
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.62025	−	16.6628i	−0.426410	−	0.738564i	0.570141	−	0.821547i	$-0.306889\pi$
$509$	−9.62025	−	16.6628i	−0.426410	−	0.738564i	−0.996551	+	0.0829830i	$0.973555\pi$
$510$		0			0
$511$	−1.83009	+	3.16982i	−0.0809586	+	0.140224i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.53379	+	2.65661i	−0.0675869	+	0.117064i
$516$		0			0
$517$	11.1202	+	19.2608i	0.489068	+	0.847091i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−27.7486			−1.21569			−0.607844	−	0.794057i	$-0.707965\pi$
$521$	−27.7486			−1.21569			−0.607844	+	0.794057i	$0.707965\pi$
$522$		0			0
$523$	−2.73680			−0.119672			−0.0598360	−	0.998208i	$-0.519058\pi$
$523$	−2.73680			−0.119672			−0.0598360	+	0.998208i	$0.519058\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.32846	−	2.30096i	−0.0578686	−	0.100231i
$528$		0			0
$529$	−16.0361	+	27.7754i	−0.697222	+	1.20762i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.6871	+	23.7068i	−0.592856	+	1.02686i
$534$		0			0
$535$	−0.904515	−	1.56667i	−0.0391056	−	0.0677329i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.12476			0.220739
$540$		0			0
$541$	−11.9773			−0.514944			−0.257472	−	0.966286i	$-0.582890\pi$
$541$	−11.9773			−0.514944			−0.257472	+	0.966286i	$0.582890\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.834608	−	1.44558i	−0.0357507	−	0.0619220i
$546$		0			0
$547$	10.7346	−	18.5929i	0.458979	−	0.794975i	−0.539928	−	0.841711i	$-0.681549\pi$
$547$	10.7346	−	18.5929i	0.458979	−	0.794975i	0.998907	+	0.0467363i	$0.0148821\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.34050	−	10.9821i	0.270114	−	0.467852i
$552$		0			0
$553$	−3.11273	−	5.39140i	−0.132367	−	0.229266i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	31.8493			1.34950			0.674748	−	0.738048i	$-0.264252\pi$
$557$	31.8493			1.34950			0.674748	+	0.738048i	$0.264252\pi$
$558$		0			0
$559$	−61.0150			−2.58066
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.7742	+	30.7857i	0.749091	+	1.29746i	0.948259	+	0.317499i	$0.102843\pi$
$563$	17.7742	+	30.7857i	0.749091	+	1.29746i	−0.199167	+	0.979966i	$0.563824\pi$
$564$		0			0
$565$	2.33981	−	4.05267i	0.0984366	−	0.170497i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10.8743	−	18.8348i	0.455874	−	0.789597i	−0.542864	−	0.839821i	$-0.682660\pi$
$569$	10.8743	−	18.8348i	0.455874	−	0.789597i	0.998738	+	0.0502237i	$0.0159934\pi$
$570$		0			0
$571$	4.79987	+	8.31362i	0.200868	+	0.347914i	0.948808	−	0.315852i	$-0.102290\pi$
$571$	4.79987	+	8.31362i	0.200868	+	0.347914i	−0.747940	+	0.663766i	$0.768957\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	36.6810			1.52970
$576$		0			0
$577$	13.0183			0.541960			0.270980	−	0.962585i	$-0.412652\pi$
$577$	13.0183			0.541960			0.270980	+	0.962585i	$0.412652\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.85185	−	8.40365i	−0.201289	−	0.348642i
$582$		0			0
$583$	−2.41586	+	4.18440i	−0.100055	+	0.173300i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.64364	−	14.9712i	0.356761	−	0.617928i	−0.630657	−	0.776062i	$-0.717214\pi$
$587$	8.64364	−	14.9712i	0.356761	−	0.617928i	0.987418	+	0.158134i	$0.0505477\pi$
$588$		0			0
$589$	1.31285	+	2.27393i	0.0540952	+	0.0936957i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.4153			−0.509836			−0.254918	−	0.966963i	$-0.582048\pi$
$593$	−12.4153			−0.509836			−0.254918	+	0.966963i	$0.582048\pi$
$594$		0			0
$595$	−0.885640			−0.0363077
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.94282	−	6.82916i	−0.161099	−	0.279032i	0.774164	−	0.632985i	$-0.218171\pi$
$599$	−3.94282	−	6.82916i	−0.161099	−	0.279032i	−0.935263	+	0.353953i	$0.884837\pi$
$600$		0			0
$601$	−11.1413	+	19.2973i	−0.454464	+	0.787154i	−0.998657	−	0.0518055i	$-0.983502\pi$
$601$	−11.1413	+	19.2973i	−0.454464	+	0.787154i	0.544193	+	0.838960i	$0.316836\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.82489	−	3.16081i	0.0741925	−	0.128505i
$606$		0			0
$607$	−11.0458	−	19.1319i	−0.448336	−	0.776541i	0.549942	−	0.835203i	$-0.314650\pi$
$607$	−11.0458	−	19.1319i	−0.448336	−	0.776541i	−0.998278	+	0.0586617i	$0.981317\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	21.2028			0.857771
$612$		0			0
$613$	−29.5264			−1.19256			−0.596280	−	0.802777i	$-0.703355\pi$
$613$	−29.5264			−1.19256			−0.596280	+	0.802777i	$0.703355\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.01655	−	8.68892i	−0.201959	−	0.349803i	0.747201	−	0.664598i	$-0.231397\pi$
$617$	−5.01655	−	8.68892i	−0.201959	−	0.349803i	−0.949159	+	0.314796i	$0.898064\pi$
$618$		0			0
$619$	19.1283	−	33.1312i	0.768833	−	1.33166i	−0.169364	−	0.985554i	$-0.554171\pi$
$619$	19.1283	−	33.1312i	0.768833	−	1.33166i	0.938196	−	0.346103i	$-0.112495\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.74433	−	6.48536i	0.150013	−	0.259831i
$624$		0			0
$625$	−12.0728	−	20.9107i	−0.482911	−	0.836427i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−17.0482			−0.679754
$630$		0			0
$631$	−23.0377			−0.917118			−0.458559	−	0.888664i	$-0.651634\pi$
$631$	−23.0377			−0.917118			−0.458559	+	0.888664i	$0.651634\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.00972	−	3.48093i	−0.0797531	−	0.138136i
$636$		0			0
$637$	2.44282	−	4.23109i	0.0967881	−	0.167642i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.68646	+	15.0454i	−0.343094	+	0.594257i	−0.985006	−	0.172522i	$-0.944808\pi$
$641$	−8.68646	+	15.0454i	−0.343094	+	0.594257i	0.641911	+	0.766779i	$0.278142\pi$
$642$		0			0
$643$	9.47949	+	16.4190i	0.373835	+	0.647501i	0.990152	−	0.139997i	$-0.0447094\pi$
$643$	9.47949	+	16.4190i	0.373835	+	0.647501i	−0.616317	+	0.787498i	$0.711376\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.0194			−0.747731			−0.373865	−	0.927483i	$-0.621968\pi$
$647$	−19.0194			−0.747731			−0.373865	+	0.927483i	$0.621968\pi$
$648$		0			0
$649$	−38.8402			−1.52461
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.59329	−	6.22377i	−0.140616	−	0.243555i	0.787112	−	0.616810i	$-0.211575\pi$
$653$	−3.59329	−	6.22377i	−0.140616	−	0.243555i	−0.927729	+	0.373255i	$0.878242\pi$
$654$		0			0
$655$	−0.585770	+	1.01458i	−0.0228879	+	0.0396430i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.7261	−	22.0423i	0.495740	−	0.858647i	−0.504248	−	0.863559i	$-0.668230\pi$
$659$	12.7261	−	22.0423i	0.495740	−	0.858647i	0.999988	+	0.00491209i	$0.00156357\pi$
$660$		0			0
$661$	−4.14295	−	7.17580i	−0.161142	−	0.279106i	0.774136	−	0.633019i	$-0.218184\pi$
$661$	−4.14295	−	7.17580i	−0.161142	−	0.279106i	−0.935279	+	0.353912i	$0.884851\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.875237			0.0339402
$666$		0			0
$667$	25.7108			0.995527
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14.1138	−	24.4458i	−0.544857	−	0.943721i
$672$		0			0
$673$	5.91586	−	10.2466i	0.228040	−	0.394977i	−0.729187	−	0.684314i	$-0.760102\pi$
$673$	5.91586	−	10.2466i	0.228040	−	0.394977i	0.957227	+	0.289338i	$0.0934350\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.80314	−	11.7834i	0.261466	−	0.452872i	−0.705166	−	0.709042i	$-0.749127\pi$
$677$	6.80314	−	11.7834i	0.261466	−	0.452872i	0.966632	+	0.256170i	$0.0824608\pi$
$678$		0			0
$679$	−8.57442	−	14.8513i	−0.329056	−	0.569942i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.58142			−0.137039			−0.0685196	−	0.997650i	$-0.521828\pi$
$683$	−3.58142			−0.137039			−0.0685196	+	0.997650i	$0.521828\pi$
$684$		0			0
$685$	1.30206			0.0497492
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.30314	+	3.98916i	0.0877426	+	0.151975i
$690$		0			0
$691$	−5.85868	+	10.1475i	−0.222875	+	0.386031i	−0.955680	−	0.294408i	$-0.904877\pi$
$691$	−5.85868	+	10.1475i	−0.222875	+	0.386031i	0.732805	+	0.680439i	$0.238211\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.676742	−	1.17215i	0.0256703	−	0.0444622i
$696$		0			0
$697$	−10.3759	−	17.9716i	−0.393016	−	0.680724i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.5926			0.400077			0.200039	−	0.979788i	$-0.435893\pi$
$701$	10.5926			0.400077			0.200039	+	0.979788i	$0.435893\pi$
$702$		0			0
$703$	16.8479			0.635430
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.59097	−	6.21975i	−0.135052	−	0.233918i
$708$		0			0
$709$	−19.1488	+	33.1668i	−0.719150	+	1.24560i	0.242187	+	0.970230i	$0.422135\pi$
$709$	−19.1488	+	33.1668i	−0.719150	+	1.24560i	−0.961337	+	0.275374i	$0.911198\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.66182	+	4.61042i	−0.0996861	+	0.172661i
$714$		0			0
$715$	−2.99355	−	5.18499i	−0.111953	−	0.193908i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−41.6752			−1.55422			−0.777112	−	0.629362i	$-0.783316\pi$
$719$	−41.6752			−1.55422			−0.777112	+	0.629362i	$0.783316\pi$
$720$		0			0
$721$	12.8285			0.477757
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.56238	−	14.8305i	−0.317999	−	0.550790i
$726$		0			0
$727$	16.4126	−	28.4274i	0.608709	−	1.05432i	−0.382744	−	0.923854i	$-0.625021\pi$
$727$	16.4126	−	28.4274i	0.608709	−	1.05432i	0.991453	−	0.130461i	$-0.0416458\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	23.1271	−	40.0573i	0.855386	−	1.48157i
$732$		0			0
$733$	−4.64884	−	8.05203i	−0.171709	−	0.297408i	0.767309	−	0.641278i	$-0.221595\pi$
$733$	−4.64884	−	8.05203i	−0.171709	−	0.297408i	−0.939017	+	0.343870i	$0.888262\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.38332			−0.124626
$738$		0			0
$739$	11.3776			0.418530			0.209265	−	0.977859i	$-0.432893\pi$
$739$	11.3776			0.418530			0.209265	+	0.977859i	$0.432893\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.16182	−	2.01234i	−0.0426232	−	0.0738256i	0.843927	−	0.536458i	$-0.180238\pi$
$743$	−1.16182	−	2.01234i	−0.0426232	−	0.0738256i	−0.886550	+	0.462633i	$0.846905\pi$
$744$		0			0
$745$	−0.272915	+	0.472703i	−0.00999883	+	0.0173185i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.78263	+	6.55171i	−0.138214	+	0.239394i
$750$		0			0
$751$	5.56690	+	9.64215i	0.203139	+	0.351847i	0.949538	−	0.313652i	$-0.101552\pi$
$751$	5.56690	+	9.64215i	0.203139	+	0.351847i	−0.746399	+	0.665498i	$0.768219\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.69329			−0.0980190
$756$		0			0
$757$	52.1639			1.89593			0.947964	−	0.318376i	$-0.103138\pi$
$757$	52.1639			1.89593			0.947964	+	0.318376i	$0.103138\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.5127	−	40.7252i	−0.852336	−	1.47629i	−0.879095	−	0.476647i	$-0.841852\pi$
$761$	−23.5127	−	40.7252i	−0.852336	−	1.47629i	0.0267592	−	0.999642i	$-0.491481\pi$
$762$		0			0
$763$	−3.49028	+	6.04535i	−0.126357	+	0.218856i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−18.5140	+	32.0671i	−0.668501	+	1.15788i
$768$		0			0
$769$	3.30314	+	5.72121i	0.119114	+	0.206312i	0.919417	−	0.393284i	$-0.128661\pi$
$769$	3.30314	+	5.72121i	0.119114	+	0.206312i	−0.800303	+	0.599596i	$0.795328\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.0870			−0.686512			−0.343256	−	0.939242i	$-0.611530\pi$
$773$	−19.0870			−0.686512			−0.343256	+	0.939242i	$0.611530\pi$
$774$		0			0
$775$	3.54583			0.127370
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.2540	+	17.7605i	0.367389	+	0.636337i
$780$		0			0
$781$	35.2108	−	60.9869i	1.25994	−	2.18228i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.663069	−	1.14847i	0.0236659	−	0.0409906i
$786$		0			0
$787$	−25.4503	−	44.0813i	−0.907207	−	1.57133i	−0.817927	−	0.575322i	$-0.804877\pi$
$787$	−25.4503	−	44.0813i	−0.907207	−	1.57133i	−0.0892796	−	0.996007i	$-0.528456\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−19.5699			−0.695826
$792$		0			0
$793$	−26.9105			−0.955620
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.38727	+	7.59898i	0.155405	+	0.269170i	0.933207	−	0.359341i	$-0.116998\pi$
$797$	4.38727	+	7.59898i	0.155405	+	0.269170i	−0.777801	+	0.628510i	$0.783665\pi$
$798$		0			0
$799$	−8.03667	+	13.9199i	−0.284317	+	0.492451i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.37880	−	16.2446i	0.330971	−	0.573258i
$804$		0			0
$805$	0.887275	+	1.53681i	0.0312723	+	0.0541653i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.51384			0.334489			0.167244	−	0.985915i	$-0.446513\pi$
$809$	9.51384			0.334489			0.167244	+	0.985915i	$0.446513\pi$
$810$		0			0
$811$	−25.0118			−0.878282			−0.439141	−	0.898418i	$-0.644717\pi$
$811$	−25.0118			−0.878282			−0.439141	+	0.898418i	$0.644717\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.796303	+	1.37924i	0.0278933	+	0.0483126i
$816$		0			0
$817$	−22.8554	+	39.5867i	−0.799610	+	1.38496i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.7970	+	30.8253i	−0.621119	+	1.07581i	0.368158	+	0.929763i	$0.379988\pi$
$821$	−17.7970	+	30.8253i	−0.621119	+	1.07581i	−0.989278	+	0.146047i	$0.953345\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	25.4531			0.885090			0.442545	−	0.896746i	$-0.354076\pi$
$827$	25.4531			0.885090			0.442545	+	0.896746i	$0.354076\pi$
$828$		0			0
$829$	−17.5458			−0.609392			−0.304696	−	0.952450i	$-0.598555\pi$
$829$	−17.5458			−0.609392			−0.304696	+	0.952450i	$0.598555\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.85185	+	3.20750i	0.0641627	+	0.111133i
$834$		0			0
$835$	−0.526955	+	0.912713i	−0.0182360	+	0.0315857i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.0562	−	20.8820i	0.416227	−	0.720927i	−0.579329	−	0.815094i	$-0.696685\pi$
$839$	12.0562	−	20.8820i	0.416227	−	0.720927i	0.995556	+	0.0941668i	$0.0300187\pi$
$840$		0			0
$841$	8.49837	+	14.7196i	0.293047	+	0.507572i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.59915			−0.0894133
$846$		0			0
$847$	−15.2632			−0.524450
$848$		0			0
$849$		0			0
$850$		0			0
$851$	17.0796	+	29.5828i	0.585482	+	1.01408i
$852$		0			0
$853$	−16.2616	+	28.1659i	−0.556785	+	0.964381i	0.440977	+	0.897518i	$0.354632\pi$
$853$	−16.2616	+	28.1659i	−0.556785	+	0.964381i	−0.997762	+	0.0668621i	$0.978701\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.299870	+	0.519390i	−0.0102434	+	0.0177420i	−0.871102	−	0.491103i	$-0.836594\pi$
$857$	−0.299870	+	0.519390i	−0.0102434	+	0.0177420i	0.860858	+	0.508845i	$0.169927\pi$
$858$		0			0
$859$	13.2174	+	22.8932i	0.450971	+	0.781104i	0.998447	−	0.0557171i	$-0.0177445\pi$
$859$	13.2174	+	22.8932i	0.450971	+	0.781104i	−0.547476	+	0.836822i	$0.684411\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19.8454			−0.675545			−0.337773	−	0.941228i	$-0.609674\pi$
$863$	−19.8454			−0.675545			−0.337773	+	0.941228i	$0.609674\pi$
$864$		0			0
$865$	6.05718			0.205950
$866$		0			0
$867$		0			0
$868$		0			0
$869$	15.9520	+	27.6296i	0.541134	+	0.937271i
$870$		0			0
$871$	−1.61273	+	2.79332i	−0.0546451	+	0.0946481i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.18878	−	2.05903i	0.0401881	−	0.0696078i
$876$		0			0
$877$	−10.2352	−	17.7278i	−0.345617	−	0.598626i	0.639849	−	0.768501i	$-0.278997\pi$
$877$	−10.2352	−	17.7278i	−0.345617	−	0.598626i	−0.985466	+	0.169875i	$0.945664\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	31.1683			1.05009			0.525043	−	0.851076i	$-0.324049\pi$
$881$	31.1683			1.05009			0.525043	+	0.851076i	$0.324049\pi$
$882$		0			0
$883$	−2.64187			−0.0889060			−0.0444530	−	0.999011i	$-0.514154\pi$
$883$	−2.64187			−0.0889060			−0.0444530	+	0.999011i	$0.514154\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11.5825	−	20.0615i	−0.388902	−	0.673599i	0.603400	−	0.797439i	$-0.293812\pi$
$887$	−11.5825	−	20.0615i	−0.388902	−	0.673599i	−0.992302	+	0.123840i	$0.960479\pi$
$888$		0			0
$889$	−8.40451	+	14.5570i	−0.281878	+	0.488228i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.94226	−	13.7564i	0.265778	−	0.460341i
$894$		0			0
$895$	−1.14132	−	1.97682i	−0.0381500	−	0.0660777i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.48538			0.0828921
$900$		0			0
$901$	−3.49192			−0.116333
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.47949	+	2.56255i	0.0491799	+	0.0851821i
$906$		0			0
$907$	25.0264	−	43.3470i	0.830988	−	1.43931i	−0.0662676	−	0.997802i	$-0.521109\pi$
$907$	25.0264	−	43.3470i	0.830988	−	1.43931i	0.897256	−	0.441511i	$-0.145558\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.42231	+	9.39172i	−0.179649	+	0.311161i	−0.941760	−	0.336285i	$-0.890830\pi$
$911$	−5.42231	+	9.39172i	−0.179649	+	0.311161i	0.762111	+	0.647446i	$0.224163\pi$
$912$		0			0
$913$	24.8646	+	43.0667i	0.822897	+	1.42530i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.89931			0.161790
$918$		0			0
$919$	11.1910			0.369156			0.184578	−	0.982818i	$-0.440908\pi$
$919$	11.1910			0.369156			0.184578	+	0.982818i	$0.440908\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−33.5679	−	58.1413i	−1.10490	−	1.91374i
$924$		0			0
$925$	11.3759	−	19.7037i	0.374038	−	0.647853i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	20.6478	−	35.7630i	0.677431	−	1.17335i	−0.298321	−	0.954466i	$-0.596427\pi$
$929$	20.6478	−	35.7630i	0.677431	−	1.17335i	0.975752	−	0.218879i	$-0.0702401\pi$
$930$		0			0
$931$	−1.83009	−	3.16982i	−0.0599789	−	0.103887i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.53870			0.148431
$936$		0			0
$937$	−33.5620			−1.09642			−0.548211	−	0.836340i	$-0.684691\pi$
$937$	−33.5620			−1.09642			−0.548211	+	0.836340i	$0.684691\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	25.2112	+	43.6671i	0.821862	+	1.42351i	0.904294	+	0.426911i	$0.140398\pi$
$941$	25.2112	+	43.6671i	0.821862	+	1.42351i	−0.0824315	+	0.996597i	$0.526269\pi$
$942$		0			0
$943$	−20.7902	+	36.0096i	−0.677021	+	1.17263i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.1212	−	17.5304i	0.328895	−	0.569662i	−0.653398	−	0.757014i	$-0.726657\pi$
$947$	10.1212	−	17.5304i	0.328895	−	0.569662i	0.982293	+	0.187352i	$0.0599905\pi$
$948$		0			0
$949$	−8.94119	−	15.4866i	−0.290243	−	0.502716i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	29.3685			0.951340			0.475670	−	0.879624i	$-0.342206\pi$
$953$	29.3685			0.951340			0.475670	+	0.879624i	$0.342206\pi$
$954$		0			0
$955$	3.14884			0.101894
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.72257	−	4.71563i	−0.0879164	−	0.152276i
$960$		0			0
$961$	15.2427	−	26.4011i	0.491700	−	0.851649i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.33297	−	2.30878i	0.0429099	−	0.0743222i
$966$		0			0
$967$	15.2157	+	26.3544i	0.489305	+	0.847501i	0.999924	−	0.0123057i	$-0.00391714\pi$
$967$	15.2157	+	26.3544i	0.489305	+	0.847501i	−0.510619	+	0.859807i	$0.670584\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.18659			−0.230629			−0.115314	−	0.993329i	$-0.536788\pi$
$971$	−7.18659			−0.230629			−0.115314	+	0.993329i	$0.536788\pi$
$972$		0			0
$973$	−5.66019			−0.181457
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.2713	+	24.7186i	0.456579	+	0.790818i	0.998777	−	0.0494328i	$-0.0157414\pi$
$977$	14.2713	+	24.7186i	0.456579	+	0.790818i	−0.542199	+	0.840250i	$0.682408\pi$
$978$		0			0
$979$	−19.1888	+	33.2359i	−0.613276	+	1.06223i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.20821	−	3.82473i	0.0704310	−	0.121990i	−0.828659	−	0.559753i	$-0.810896\pi$
$983$	2.20821	−	3.82473i	0.0704310	−	0.121990i	0.899090	+	0.437763i	$0.144229\pi$
$984$		0			0
$985$	0.0172400	+	0.0298606i	0.000549313	+	0.000951438i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−92.6791			−2.94702
$990$		0			0
$991$	−5.81341			−0.184669			−0.0923345	−	0.995728i	$-0.529433\pi$
$991$	−5.81341			−0.184669			−0.0923345	+	0.995728i	$0.529433\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.32777	−	4.03182i	−0.0737953	−	0.127817i
$996$		0			0
$997$	26.3204	−	45.5882i	0.833575	−	1.44379i	−0.0616108	−	0.998100i	$-0.519624\pi$
$997$	26.3204	−	45.5882i	0.833575	−	1.44379i	0.895186	−	0.445694i	$-0.147043\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.j.b.505.2		6
3.2	odd	2		252.2.j.a.169.1	yes	6
4.3	odd	2		3024.2.r.j.2017.2		6
7.2	even	3		5292.2.i.f.2125.2		6
7.3	odd	6		5292.2.l.f.3313.2		6
7.4	even	3		5292.2.l.e.3313.2		6
7.5	odd	6		5292.2.i.e.2125.2		6
7.6	odd	2		5292.2.j.d.3529.2		6
9.2	odd	6		2268.2.a.i.1.2		3
9.4	even	3	inner	756.2.j.b.253.2		6
9.5	odd	6		252.2.j.a.85.1	✓	6
9.7	even	3		2268.2.a.h.1.2		3
12.11	even	2		1008.2.r.j.673.3		6
21.2	odd	6		1764.2.i.g.1537.2		6
21.5	even	6		1764.2.i.d.1537.2		6
21.11	odd	6		1764.2.l.e.961.3		6
21.17	even	6		1764.2.l.f.961.1		6
21.20	even	2		1764.2.j.e.1177.3		6
36.7	odd	6		9072.2.a.bv.1.2		3
36.11	even	6		9072.2.a.by.1.2		3
36.23	even	6		1008.2.r.j.337.3		6
36.31	odd	6		3024.2.r.j.1009.2		6
63.4	even	3		5292.2.i.f.1549.2		6
63.5	even	6		1764.2.l.f.949.1		6
63.13	odd	6		5292.2.j.d.1765.2		6
63.23	odd	6		1764.2.l.e.949.3		6
63.31	odd	6		5292.2.i.e.1549.2		6
63.32	odd	6		1764.2.i.g.373.2		6
63.40	odd	6		5292.2.l.f.361.2		6
63.41	even	6		1764.2.j.e.589.3		6
63.58	even	3		5292.2.l.e.361.2		6
63.59	even	6		1764.2.i.d.373.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.1	✓	6	9.5	odd	6
252.2.j.a.169.1	yes	6	3.2	odd	2
756.2.j.b.253.2		6	9.4	even	3	inner
756.2.j.b.505.2		6	1.1	even	1	trivial
1008.2.r.j.337.3		6	36.23	even	6
1008.2.r.j.673.3		6	12.11	even	2
1764.2.i.d.373.2		6	63.59	even	6
1764.2.i.d.1537.2		6	21.5	even	6
1764.2.i.g.373.2		6	63.32	odd	6
1764.2.i.g.1537.2		6	21.2	odd	6
1764.2.j.e.589.3		6	63.41	even	6
1764.2.j.e.1177.3		6	21.20	even	2
1764.2.l.e.949.3		6	63.23	odd	6
1764.2.l.e.961.3		6	21.11	odd	6
1764.2.l.f.949.1		6	63.5	even	6
1764.2.l.f.961.1		6	21.17	even	6
2268.2.a.h.1.2		3	9.7	even	3
2268.2.a.i.1.2		3	9.2	odd	6
3024.2.r.j.1009.2		6	36.31	odd	6
3024.2.r.j.2017.2		6	4.3	odd	2
5292.2.i.e.1549.2		6	63.31	odd	6
5292.2.i.e.2125.2		6	7.5	odd	6
5292.2.i.f.1549.2		6	63.4	even	3
5292.2.i.f.2125.2		6	7.2	even	3
5292.2.j.d.1765.2		6	63.13	odd	6
5292.2.j.d.3529.2		6	7.6	odd	2
5292.2.l.e.361.2		6	63.58	even	3
5292.2.l.e.3313.2		6	7.4	even	3
5292.2.l.f.361.2		6	63.40	odd	6
5292.2.l.f.3313.2		6	7.3	odd	6
9072.2.a.bv.1.2		3	36.7	odd	6
9072.2.a.by.1.2		3	36.11	even	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.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.119562 + 0.207087i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(0.119562 + 0.207087i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.56238 + 4.43818i) q^{11} +(2.44282 + 4.23109i) q^{13} -3.70370 q^{17} +3.66019 q^{19} +(3.71053 + 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(1.73229 - 3.00041i) q^{29} +(0.358685 + 0.621261i) q^{31} +0.239123 q^{35} +4.60301 q^{37} +(2.80150 + 4.85235i) q^{41} +(-6.24433 + 10.8155i) q^{43} +(2.16991 - 3.75839i) q^{47} +(-0.500000 - 0.866025i) q^{49} +0.942820 q^{53} -1.22545 q^{55} +(3.78947 + 6.56355i) q^{59} +(-2.75404 + 4.77014i) q^{61} +(-0.584135 + 1.01175i) q^{65} +(0.330095 + 0.571741i) q^{67} -13.7414 q^{71} -3.66019 q^{73} +(2.56238 + 4.43818i) q^{77} +(3.11273 - 5.39140i) q^{79} +(4.85185 - 8.40365i) q^{83} +(-0.442820 - 0.766987i) q^{85} +7.48865 q^{89} +4.88564 q^{91} +(0.437618 + 0.757977i) q^{95} +(8.57442 - 14.8513i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q + q^5 + 3 * q^7	\( 6 q + q^{5} + 3 q^{7} + 2 q^{11} - 3 q^{13} - 4 q^{17} + 6 q^{19} + 14 q^{23} + 6 q^{25} + q^{29} + 3 q^{31} + 2 q^{35} - 6 q^{37} - 3 q^{43} + 21 q^{47} - 3 q^{49} - 12 q^{53} + 12 q^{55} + 31 q^{59} - 6 q^{61} + 15 q^{65} - 6 q^{67} - 34 q^{71} - 6 q^{73} - 2 q^{77} + 9 q^{79} + 20 q^{83} + 15 q^{85} - 24 q^{89} - 6 q^{91} + 20 q^{95} + 9 q^{97}+O(q^{100}) \) 6 * q + q^5 + 3 * q^7 + 2 * q^11 - 3 * q^13 - 4 * q^17 + 6 * q^19 + 14 * q^23 + 6 * q^25 + q^29 + 3 * q^31 + 2 * q^35 - 6 * q^37 - 3 * q^43 + 21 * q^47 - 3 * q^49 - 12 * q^53 + 12 * q^55 + 31 * q^59 - 6 * q^61 + 15 * q^65 - 6 * q^67 - 34 * q^71 - 6 * q^73 - 2 * q^77 + 9 * q^79 + 20 * q^83 + 15 * q^85 - 24 * q^89 - 6 * q^91 + 20 * q^95 + 9 * q^97

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