LMFDB - Embedded newform 756.2.i.b.613.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(37,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.37"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			613.3
Root			$1.13119 - 1.31165i$ of defining polynomial
Character	$\chi$	$=$	756.613
Dual form			756.2.i.b.37.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.764702 + 1.32450i) q^{5} +(-1.91978 - 1.82056i) q^{7} +(0.417818 + 0.723682i) q^{11} +(1.81222 + 3.13886i) q^{13} +(-0.301057 + 0.521446i) q^{17} +(0.846884 + 1.46685i) q^{19} +(-3.07202 + 5.32090i) q^{23} +(1.33046 + 2.30443i) q^{25} +(-4.99671 + 8.65455i) q^{29} -3.30841 q^{31} +(3.87940 - 1.15057i) q^{35} +(4.39846 + 7.61835i) q^{37} +(-3.51718 - 6.09194i) q^{41} +(0.846884 - 1.46685i) q^{43} -8.46401 q^{47} +(0.371118 + 6.99016i) q^{49} +(3.99616 - 6.92155i) q^{53} -1.27803 q^{55} -0.130428 q^{59} -4.76685 q^{61} -5.54324 q^{65} -2.24332 q^{67} +9.39130 q^{71} +(-2.25454 + 3.90498i) q^{73} +(0.515388 - 2.14997i) q^{77} +15.7424 q^{79} +(3.16210 - 5.47692i) q^{83} +(-0.460438 - 0.797501i) q^{85} +(0.531180 + 0.920030i) q^{89} +(2.23542 - 9.32519i) q^{91} -2.59046 q^{95} +(-7.76364 + 13.4470i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{5} + 6 q^{7} - 2 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} + 2 q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} - 6 q^{47} - 4 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) $ 14 * q + 2 * q^5 + 6 * q^7 - 2 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 - 11 * q^23 - 9 * q^25 - q^29 + 2 * q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 - 6 * q^47 - 4 * q^49 + 15 * q^53 - 28 * q^55 - 28 * q^59 + 20 * q^61 + 30 * q^65 - 12 * q^67 - 2 * q^71 + 21 * q^73 + 47 * q^77 + 20 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 - 56 * q^95 - 18 * q^97

Character values

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

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

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
$5$	−0.764702	+	1.32450i	−0.341985	+	0.592336i	−0.984801	−	0.173685i	$-0.944433\pi$
$5$	−0.764702	+	1.32450i	−0.341985	+	0.592336i	0.642816	+	0.766021i	$0.277766\pi$
$6$		0			0
$7$	−1.91978	−	1.82056i	−0.725609	−	0.688107i
$7$	−1.91978	−	1.82056i	−0.725609	−	0.688107i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.417818	+	0.723682i	0.125977	+	0.218198i	0.922114	−	0.386917i	$-0.126460\pi$
$11$	0.417818	+	0.723682i	0.125977	+	0.218198i	−0.796137	+	0.605116i	$0.793127\pi$
$12$		0			0
$13$	1.81222	+	3.13886i	0.502620	+	0.870563i	0.999995	+	0.00302796i	$0.000963830\pi$
$13$	1.81222	+	3.13886i	0.502620	+	0.870563i	−0.497375	+	0.867535i	$0.665703\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.301057	+	0.521446i	−0.0730170	+	0.126469i	−0.900222	−	0.435431i	$-0.856596\pi$
$17$	−0.301057	+	0.521446i	−0.0730170	+	0.126469i	0.827205	+	0.561900i	$0.189929\pi$
$18$		0			0
$19$	0.846884	+	1.46685i	0.194289	+	0.336518i	0.946667	−	0.322213i	$-0.104427\pi$
$19$	0.846884	+	1.46685i	0.194289	+	0.336518i	−0.752379	+	0.658731i	$0.771094\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.07202	+	5.32090i	−0.640561	+	1.10948i	0.344746	+	0.938696i	$0.387965\pi$
$23$	−3.07202	+	5.32090i	−0.640561	+	1.10948i	−0.985308	+	0.170789i	$0.945368\pi$
$24$		0			0
$25$	1.33046	+	2.30443i	0.266092	+	0.460885i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.99671	+	8.65455i	−0.927865	+	1.60711i	−0.140977	+	0.990013i	$0.545024\pi$
$29$	−4.99671	+	8.65455i	−0.927865	+	1.60711i	−0.786888	+	0.617096i	$0.788309\pi$
$30$		0			0
$31$	−3.30841			−0.594208			−0.297104	−	0.954845i	$-0.596021\pi$
$31$	−3.30841			−0.594208			−0.297104	+	0.954845i	$0.596021\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.87940	−	1.15057i	0.655738	−	0.194482i
$36$		0			0
$37$	4.39846	+	7.61835i	0.723102	+	1.25245i	0.959751	+	0.280854i	$0.0906177\pi$
$37$	4.39846	+	7.61835i	0.723102	+	1.25245i	−0.236649	+	0.971595i	$0.576049\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.51718	−	6.09194i	−0.549291	−	0.951401i	−0.998323	−	0.0578850i	$-0.981564\pi$
$41$	−3.51718	−	6.09194i	−0.549291	−	0.951401i	0.449032	−	0.893516i	$-0.351769\pi$
$42$		0			0
$43$	0.846884	−	1.46685i	0.129149	−	0.223692i	−0.794198	−	0.607659i	$-0.792109\pi$
$43$	0.846884	−	1.46685i	0.129149	−	0.223692i	0.923347	+	0.383967i	$0.125442\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.46401			−1.23460			−0.617301	−	0.786727i	$-0.711774\pi$
$47$	−8.46401			−1.23460			−0.617301	+	0.786727i	$0.711774\pi$
$48$		0			0
$49$	0.371118	+	6.99016i	0.0530168	+	0.998594i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.99616	−	6.92155i	0.548915	−	0.950748i	−0.449434	−	0.893313i	$-0.648374\pi$
$53$	3.99616	−	6.92155i	0.548915	−	0.950748i	0.998349	−	0.0574350i	$-0.0182922\pi$
$54$		0			0
$55$	−1.27803			−0.172329
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.130428			−0.0169802			−0.00849011	−	0.999964i	$-0.502703\pi$
$59$	−0.130428			−0.0169802			−0.00849011	+	0.999964i	$0.502703\pi$
$60$		0			0
$61$	−4.76685			−0.610333			−0.305166	−	0.952299i	$-0.598712\pi$
$61$	−4.76685			−0.610333			−0.305166	+	0.952299i	$0.598712\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.54324			−0.687554
$66$		0			0
$67$	−2.24332			−0.274066			−0.137033	−	0.990567i	$-0.543757\pi$
$67$	−2.24332			−0.274066			−0.137033	+	0.990567i	$0.543757\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.39130			1.11454			0.557271	−	0.830331i	$-0.311848\pi$
$71$	9.39130			1.11454			0.557271	+	0.830331i	$0.311848\pi$
$72$		0			0
$73$	−2.25454	+	3.90498i	−0.263874	+	0.457044i	−0.967268	−	0.253757i	$-0.918334\pi$
$73$	−2.25454	+	3.90498i	−0.263874	+	0.457044i	0.703394	+	0.710800i	$0.251667\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.515388	−	2.14997i	0.0587339	−	0.245012i
$78$		0			0
$79$	15.7424			1.77116			0.885580	−	0.464488i	$-0.153761\pi$
$79$	15.7424			1.77116			0.885580	+	0.464488i	$0.153761\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.16210	−	5.47692i	0.347085	−	0.601170i	−0.638645	−	0.769502i	$-0.720505\pi$
$83$	3.16210	−	5.47692i	0.347085	−	0.601170i	0.985730	+	0.168332i	$0.0538380\pi$
$84$		0			0
$85$	−0.460438	−	0.797501i	−0.0499415	−	0.0865011i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.531180	+	0.920030i	0.0563049	+	0.0975230i	0.892804	−	0.450445i	$-0.148735\pi$
$89$	0.531180	+	0.920030i	0.0563049	+	0.0975230i	−0.836499	+	0.547968i	$0.815401\pi$
$90$		0			0
$91$	2.23542	−	9.32519i	0.234335	−	0.977545i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.59046			−0.265775
$96$		0			0
$97$	−7.76364	+	13.4470i	−0.788279	+	1.36534i	0.138742	+	0.990329i	$0.455694\pi$
$97$	−7.76364	+	13.4470i	−0.788279	+	1.36534i	−0.927021	+	0.375010i	$0.877639\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.75757	+	16.9006i	0.970914	+	1.68167i	0.692807	+	0.721123i	$0.256374\pi$
$101$	9.75757	+	16.9006i	0.970914	+	1.68167i	0.278107	+	0.960550i	$0.410293\pi$
$102$		0			0
$103$	0.911770	−	1.57923i	0.0898394	−	0.155606i	−0.817604	−	0.575781i	$-0.804698\pi$
$103$	0.911770	−	1.57923i	0.0898394	−	0.155606i	0.907443	+	0.420175i	$0.138031\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.27078	+	9.12926i	0.509546	+	0.882559i	0.999939	+	0.0110578i	$0.00351989\pi$
$107$	5.27078	+	9.12926i	0.509546	+	0.882559i	−0.490393	+	0.871501i	$0.663147\pi$
$108$		0			0
$109$	6.30442	−	10.9196i	0.603854	−	1.04591i	−0.388377	−	0.921501i	$-0.626964\pi$
$109$	6.30442	−	10.9196i	0.603854	−	1.04591i	0.992231	−	0.124406i	$-0.0397025\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.76452	−	13.4485i	−0.730424	−	1.26513i	−0.956702	−	0.291069i	$-0.905989\pi$
$113$	−7.76452	−	13.4485i	−0.730424	−	1.26513i	0.226278	−	0.974063i	$-0.427344\pi$
$114$		0			0
$115$	−4.69837	−	8.13781i	−0.438125	−	0.758855i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.52729	−	0.452969i	0.140006	−	0.0415236i
$120$		0			0
$121$	5.15086	−	8.92154i	0.468260	−	0.811050i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.7166			−1.04797
$126$		0			0
$127$	−10.8966			−0.966919			−0.483460	−	0.875367i	$-0.660620\pi$
$127$	−10.8966			−0.966919			−0.483460	+	0.875367i	$0.660620\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.73088	−	16.8544i	0.850191	−	1.47257i	−0.0308446	−	0.999524i	$-0.509820\pi$
$131$	9.73088	−	16.8544i	0.850191	−	1.47257i	0.881036	−	0.473050i	$-0.156847\pi$
$132$		0			0
$133$	1.04465	−	4.35783i	0.0905827	−	0.377872i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.13833	+	10.6319i	0.524433	+	0.908344i	0.999595	+	0.0284461i	$0.00905590\pi$
$137$	6.13833	+	10.6319i	0.524433	+	0.908344i	−0.475163	+	0.879898i	$0.657611\pi$
$138$		0			0
$139$	−6.44692	−	11.1664i	−0.546821	−	0.947121i	−0.998490	−	0.0549357i	$-0.982505\pi$
$139$	−6.44692	−	11.1664i	−0.546821	−	0.947121i	0.451669	−	0.892185i	$-0.350829\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.51436	+	2.62295i	−0.126637	+	0.219342i
$144$		0			0
$145$	−7.64198	−	13.2363i	−0.634632	−	1.09922i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.03267	+	15.6451i	−0.739986	+	1.28169i	0.212516	+	0.977158i	$0.431834\pi$
$149$	−9.03267	+	15.6451i	−0.739986	+	1.28169i	−0.952501	+	0.304535i	$0.901499\pi$
$150$		0			0
$151$	−4.29891	−	7.44593i	−0.349840	−	0.605941i	0.636381	−	0.771375i	$-0.280431\pi$
$151$	−4.29891	−	7.44593i	−0.349840	−	0.605941i	−0.986221	+	0.165434i	$0.947097\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.52995	−	4.38200i	0.203210	−	0.351971i
$156$		0			0
$157$	3.19366			0.254882			0.127441	−	0.991846i	$-0.459324\pi$
$157$	3.19366			0.254882			0.127441	+	0.991846i	$0.459324\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	15.5846	−	4.62216i	1.22824	−	0.364277i
$162$		0			0
$163$	2.04809	+	3.54740i	0.160419	+	0.277854i	0.935019	−	0.354598i	$-0.115382\pi$
$163$	2.04809	+	3.54740i	0.160419	+	0.277854i	−0.774600	+	0.632451i	$0.782049\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.24859	−	14.2870i	−0.638295	−	1.10556i	−0.985807	−	0.167883i	$-0.946307\pi$
$167$	−8.24859	−	14.2870i	−0.638295	−	1.10556i	0.347512	−	0.937676i	$-0.387027\pi$
$168$		0			0
$169$	−0.0682984	+	0.118296i	−0.00525372	+	0.00909971i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.8213			0.974782			0.487391	−	0.873184i	$-0.337949\pi$
$173$	12.8213			0.974782			0.487391	+	0.873184i	$0.337949\pi$
$174$		0			0
$175$	1.64115	−	6.84618i	0.124060	−	0.517522i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.8750	−	20.5680i	0.887576	−	1.53733i	0.0448441	−	0.998994i	$-0.485721\pi$
$179$	11.8750	−	20.5680i	0.887576	−	1.53733i	0.842732	−	0.538333i	$-0.180946\pi$
$180$		0			0
$181$	−16.0244			−1.19108			−0.595542	−	0.803324i	$-0.703063\pi$
$181$	−16.0244			−1.19108			−0.595542	+	0.803324i	$0.703063\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−13.4540			−0.989161
$186$		0			0
$187$	−0.503148			−0.0367938
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.8095			0.782148			0.391074	−	0.920359i	$-0.372104\pi$
$191$	10.8095			0.782148			0.391074	+	0.920359i	$0.372104\pi$
$192$		0			0
$193$	0.750260			0.0540049			0.0270025	−	0.999635i	$-0.491404\pi$
$193$	0.750260			0.0540049			0.0270025	+	0.999635i	$0.491404\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.3186			−0.735169			−0.367584	−	0.929990i	$-0.619815\pi$
$197$	−10.3186			−0.735169			−0.367584	+	0.929990i	$0.619815\pi$
$198$		0			0
$199$	−2.85430	+	4.94379i	−0.202336	+	0.350456i	−0.949281	−	0.314430i	$-0.898187\pi$
$199$	−2.85430	+	4.94379i	−0.202336	+	0.350456i	0.746945	+	0.664886i	$0.231520\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	25.3487	−	7.51803i	1.77913	−	0.527662i
$204$		0			0
$205$	10.7584			0.751398
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.707687	+	1.22575i	−0.0489517	+	0.0847869i
$210$		0			0
$211$	2.73050	+	4.72937i	0.187976	+	0.325583i	0.944575	−	0.328295i	$-0.106474\pi$
$211$	2.73050	+	4.72937i	0.187976	+	0.325583i	−0.756600	+	0.653878i	$0.773141\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.29523	+	2.24340i	0.0883338	+	0.152999i
$216$		0			0
$217$	6.35143	+	6.02316i	0.431163	+	0.408879i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.18233			−0.146799
$222$		0			0
$223$	−9.00530	+	15.5976i	−0.603040	+	1.04450i	0.389318	+	0.921103i	$0.372711\pi$
$223$	−9.00530	+	15.5976i	−0.603040	+	1.04450i	−0.992358	+	0.123392i	$0.960623\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.08699	−	15.7391i	−0.603125	−	1.04464i	−0.992345	−	0.123498i	$-0.960589\pi$
$227$	−9.08699	−	15.7391i	−0.603125	−	1.04464i	0.389220	−	0.921145i	$-0.372745\pi$
$228$		0			0
$229$	7.71391	−	13.3609i	0.509750	−	0.882912i	−0.490186	−	0.871618i	$-0.663071\pi$
$229$	7.71391	−	13.3609i	0.509750	−	0.882912i	0.999936	−	0.0112949i	$-0.00359534\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.20892	+	5.55801i	0.210223	+	0.364117i	0.951784	−	0.306768i	$-0.0992476\pi$
$233$	3.20892	+	5.55801i	0.210223	+	0.364117i	−0.741561	+	0.670885i	$0.765914\pi$
$234$		0			0
$235$	6.47244	−	11.2106i	0.422216	−	0.731299i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.33317	+	4.04118i	0.150920	+	0.261402i	0.931566	−	0.363572i	$-0.118443\pi$
$239$	2.33317	+	4.04118i	0.150920	+	0.261402i	−0.780646	+	0.624974i	$0.785110\pi$
$240$		0			0
$241$	9.42858	+	16.3308i	0.607348	+	1.05196i	0.991676	+	0.128761i	$0.0411000\pi$
$241$	9.42858	+	16.3308i	0.607348	+	1.05196i	−0.384327	+	0.923197i	$0.625567\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9.54228	−	4.85384i	−0.609634	−	0.310100i
$246$		0			0
$247$	−3.06948	+	5.31650i	−0.195307	+	0.338281i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−15.7016			−0.991074			−0.495537	−	0.868587i	$-0.665029\pi$
$251$	−15.7016			−0.991074			−0.495537	+	0.868587i	$0.665029\pi$
$252$		0			0
$253$	−5.13419			−0.322784
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.60892	−	7.98289i	0.287497	−	0.497959i	−0.685715	−	0.727870i	$-0.740510\pi$
$257$	4.60892	−	7.98289i	0.287497	−	0.497959i	0.973212	+	0.229911i	$0.0738436\pi$
$258$		0			0
$259$	5.42560	−	22.6332i	0.337130	−	1.40636i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.241311	+	0.417962i	0.0148799	+	0.0257727i	0.873369	−	0.487058i	$-0.161930\pi$
$263$	0.241311	+	0.417962i	0.0148799	+	0.0257727i	−0.858490	+	0.512831i	$0.828597\pi$
$264$		0			0
$265$	6.11174	+	10.5859i	0.375442	+	0.650284i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.94288	−	6.82927i	0.240402	−	0.416388i	−0.720427	−	0.693531i	$-0.756054\pi$
$269$	3.94288	−	6.82927i	0.240402	−	0.416388i	0.960829	+	0.277143i	$0.0893875\pi$
$270$		0			0
$271$	12.7947	+	22.1610i	0.777220	+	1.34618i	0.933538	+	0.358478i	$0.116704\pi$
$271$	12.7947	+	22.1610i	0.777220	+	1.34618i	−0.156318	+	0.987707i	$0.549963\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.11178	+	1.92566i	−0.0670429	+	0.116122i
$276$		0			0
$277$	−4.18466	−	7.24804i	−0.251432	−	0.435492i	0.712489	−	0.701684i	$-0.247568\pi$
$277$	−4.18466	−	7.24804i	−0.251432	−	0.435492i	−0.963920	+	0.266191i	$0.914235\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.551848	−	0.955828i	0.0329205	−	0.0570199i	−0.849096	−	0.528239i	$-0.822853\pi$
$281$	0.551848	−	0.955828i	0.0329205	−	0.0570199i	0.882016	+	0.471219i	$0.156186\pi$
$282$		0			0
$283$	2.90738			0.172826			0.0864128	−	0.996259i	$-0.472460\pi$
$283$	2.90738			0.172826			0.0864128	+	0.996259i	$0.472460\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.33852	+	18.0984i	−0.256095	+	1.06832i
$288$		0			0
$289$	8.31873	+	14.4085i	0.489337	+	0.847557i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.4381	+	21.5434i	0.726642	+	1.25858i	0.958295	+	0.285782i	$0.0922532\pi$
$293$	12.4381	+	21.5434i	0.726642	+	1.25858i	−0.231653	+	0.972798i	$0.574413\pi$
$294$		0			0
$295$	0.0997383	−	0.172752i	0.00580699	−	0.0100580i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−22.2688			−1.28784
$300$		0			0
$301$	−4.29631	+	1.27422i	−0.247635	+	0.0734448i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.64522	−	6.31371i	0.208725	−	0.361522i
$306$		0			0
$307$	−23.7968			−1.35816			−0.679078	−	0.734066i	$-0.737620\pi$
$307$	−23.7968			−1.35816			−0.679078	+	0.734066i	$0.737620\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−18.7135			−1.06115			−0.530574	−	0.847639i	$-0.678024\pi$
$311$	−18.7135			−1.06115			−0.530574	+	0.847639i	$0.678024\pi$
$312$		0			0
$313$	−19.3159			−1.09180			−0.545901	−	0.837850i	$-0.683812\pi$
$313$	−19.3159			−1.09180			−0.545901	+	0.837850i	$0.683812\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.79508			0.100822			0.0504110	−	0.998729i	$-0.483947\pi$
$317$	1.79508			0.100822			0.0504110	+	0.998729i	$0.483947\pi$
$318$		0			0
$319$	−8.35085			−0.467558
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.01984			−0.0567455
$324$		0			0
$325$	−4.82218	+	8.35226i	−0.267487	+	0.463300i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	16.2490	+	15.4092i	0.895838	+	0.849539i
$330$		0			0
$331$	−14.1367			−0.777021			−0.388511	−	0.921444i	$-0.627010\pi$
$331$	−14.1367			−0.777021			−0.388511	+	0.921444i	$0.627010\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.71547	−	2.97129i	0.0937264	−	0.162339i
$336$		0			0
$337$	−2.94072	−	5.09348i	−0.160191	−	0.277459i	0.774746	−	0.632273i	$-0.217878\pi$
$337$	−2.94072	−	5.09348i	−0.160191	−	0.277459i	−0.934937	+	0.354813i	$0.884544\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.38231	−	2.39424i	−0.0748565	−	0.129655i
$342$		0			0
$343$	12.0135	−	14.0952i	0.648670	−	0.761070i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.35186			0.340986			0.170493	−	0.985359i	$-0.445464\pi$
$347$	6.35186			0.340986			0.170493	+	0.985359i	$0.445464\pi$
$348$		0			0
$349$	10.4321	−	18.0689i	0.558416	−	0.967205i	−0.439213	−	0.898383i	$-0.644743\pi$
$349$	10.4321	−	18.0689i	0.558416	−	0.967205i	0.997629	−	0.0688222i	$-0.0219241\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.07115	−	1.85528i	−0.0570114	−	0.0987466i	0.836111	−	0.548560i	$-0.184824\pi$
$353$	−1.07115	−	1.85528i	−0.0570114	−	0.0987466i	−0.893123	+	0.449813i	$0.851490\pi$
$354$		0			0
$355$	−7.18155	+	12.4388i	−0.381157	+	0.660183i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.6198	+	18.3940i	0.560492	+	0.970800i	0.997454	+	0.0713198i	$0.0227211\pi$
$359$	10.6198	+	18.3940i	0.560492	+	0.970800i	−0.436962	+	0.899480i	$0.643946\pi$
$360$		0			0
$361$	8.06557	−	13.9700i	0.424504	−	0.735262i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.44811	−	5.97230i	−0.180482	−	0.312605i
$366$		0			0
$367$	16.2053	+	28.0685i	0.845912	+	1.46516i	0.884827	+	0.465919i	$0.154276\pi$
$367$	16.2053	+	28.0685i	0.845912	+	1.46516i	−0.0389156	+	0.999243i	$0.512390\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−20.2729	+	6.01261i	−1.05251	+	0.312159i
$372$		0			0
$373$	−16.8101	+	29.1159i	−0.870393	+	1.50756i	−0.00880173	+	0.999961i	$0.502802\pi$
$373$	−16.8101	+	29.1159i	−0.870393	+	1.50756i	−0.861591	+	0.507603i	$0.830532\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−36.2206			−1.86545
$378$		0			0
$379$	28.2829			1.45279			0.726396	−	0.687276i	$-0.241194\pi$
$379$	28.2829			1.45279			0.726396	+	0.687276i	$0.241194\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.09473	+	8.82434i	−0.260329	+	0.450903i	−0.966329	−	0.257309i	$-0.917164\pi$
$383$	−5.09473	+	8.82434i	−0.260329	+	0.450903i	0.706001	+	0.708211i	$0.250498\pi$
$384$		0			0
$385$	2.45353	+	2.32672i	0.125043	+	0.118581i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	5.22525	+	9.05040i	0.264931	+	0.458873i	0.967545	−	0.252697i	$-0.0813176\pi$
$389$	5.22525	+	9.05040i	0.264931	+	0.458873i	−0.702615	+	0.711570i	$0.747984\pi$
$390$		0			0
$391$	−1.84971	−	3.20379i	−0.0935437	−	0.162022i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−12.0383	+	20.8509i	−0.605710	+	1.04912i
$396$		0			0
$397$	−7.25033	−	12.5579i	−0.363884	−	0.630265i	0.624713	−	0.780855i	$-0.285216\pi$
$397$	−7.25033	−	12.5579i	−0.363884	−	0.630265i	−0.988596	+	0.150590i	$0.951883\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.7071	+	22.0094i	−0.634563	+	1.09909i	0.352045	+	0.935983i	$0.385486\pi$
$401$	−12.7071	+	22.0094i	−0.634563	+	1.09909i	−0.986608	+	0.163112i	$0.947847\pi$
$402$		0			0
$403$	−5.99558	−	10.3846i	−0.298661	−	0.517296i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.67551	+	6.36617i	−0.182188	+	0.315559i
$408$		0			0
$409$	12.3907			0.612680			0.306340	−	0.951922i	$-0.400896\pi$
$409$	12.3907			0.612680			0.306340	+	0.951922i	$0.400896\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.250392	+	0.237451i	0.0123210	+	0.0116842i
$414$		0			0
$415$	4.83613	+	8.37642i	0.237396	+	0.411182i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.3596	+	26.6036i	0.750365	+	1.29967i	0.947646	+	0.319323i	$0.103455\pi$
$419$	15.3596	+	26.6036i	0.750365	+	1.29967i	−0.197281	+	0.980347i	$0.563211\pi$
$420$		0			0
$421$	−2.88912	+	5.00410i	−0.140807	+	0.243885i	−0.927801	−	0.373076i	$-0.878303\pi$
$421$	−2.88912	+	5.00410i	−0.140807	+	0.243885i	0.786994	+	0.616961i	$0.211636\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.60218			−0.0777170
$426$		0			0
$427$	9.15131	+	8.67834i	0.442863	+	0.419975i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.210278	−	0.364212i	0.0101287	−	0.0175435i	−0.860917	−	0.508746i	$-0.830109\pi$
$431$	0.210278	−	0.364212i	0.0101287	−	0.0175435i	0.871045	+	0.491203i	$0.163443\pi$
$432$		0			0
$433$	30.8208			1.48115			0.740576	−	0.671972i	$-0.234553\pi$
$433$	30.8208			1.48115			0.740576	+	0.671972i	$0.234553\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.4066			−0.497815
$438$		0			0
$439$	3.01181			0.143746			0.0718729	−	0.997414i	$-0.477102\pi$
$439$	3.01181			0.143746			0.0718729	+	0.997414i	$0.477102\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.4428			0.876245			0.438122	−	0.898915i	$-0.355644\pi$
$443$	18.4428			0.876245			0.438122	+	0.898915i	$0.355644\pi$
$444$		0			0
$445$	−1.62478			−0.0770218
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.80998			0.321383			0.160691	−	0.987005i	$-0.448628\pi$
$449$	6.80998			0.321383			0.160691	+	0.987005i	$0.448628\pi$
$450$		0			0
$451$	2.93908	−	5.09064i	0.138396	−	0.239709i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.6418	+	10.0918i	0.498896	+	0.473111i
$456$		0			0
$457$	12.3657			0.578441			0.289220	−	0.957263i	$-0.406604\pi$
$457$	12.3657			0.578441			0.289220	+	0.957263i	$0.406604\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	16.3651	−	28.3453i	0.762201	−	1.32017i	−0.179513	−	0.983756i	$-0.557452\pi$
$461$	16.3651	−	28.3453i	0.762201	−	1.32017i	0.941714	−	0.336415i	$-0.109214\pi$
$462$		0			0
$463$	9.61023	+	16.6454i	0.446625	+	0.773577i	0.998164	−	0.0605719i	$-0.0192924\pi$
$463$	9.61023	+	16.6454i	0.446625	+	0.773577i	−0.551539	+	0.834149i	$0.685959\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.50855	−	2.61289i	−0.0698075	−	0.120910i	0.829009	−	0.559235i	$-0.188905\pi$
$467$	−1.50855	−	2.61289i	−0.0698075	−	0.120910i	−0.898816	+	0.438325i	$0.855572\pi$
$468$		0			0
$469$	4.30669	+	4.08411i	0.198864	+	0.188587i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.41537			0.0650790
$474$		0			0
$475$	−2.25349	+	3.90316i	−0.103397	+	0.179089i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.9486	−	22.4276i	−0.591635	−	1.02474i	−0.994012	−	0.109269i	$-0.965149\pi$
$479$	−12.9486	−	22.4276i	−0.591635	−	1.02474i	0.402377	−	0.915474i	$-0.368184\pi$
$480$		0			0
$481$	−15.9420	+	27.6123i	−0.726891	+	1.25901i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−11.8738	−	20.5659i	−0.539159	−	0.933851i
$486$		0			0
$487$	−20.8841	+	36.1724i	−0.946350	+	1.63913i	−0.193326	+	0.981135i	$0.561927\pi$
$487$	−20.8841	+	36.1724i	−0.946350	+	1.63913i	−0.753025	+	0.657992i	$0.771406\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.9879	+	24.2278i	0.631265	+	1.09338i	0.987293	+	0.158908i	$0.0507974\pi$
$491$	13.9879	+	24.2278i	0.631265	+	1.09338i	−0.356028	+	0.934475i	$0.615869\pi$
$492$		0			0
$493$	−3.00858	−	5.21102i	−0.135500	−	0.234693i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.0292	−	17.0974i	−0.808722	−	0.766924i
$498$		0			0
$499$	12.4748	−	21.6070i	0.558450	−	0.967264i	−0.439176	−	0.898401i	$-0.644730\pi$
$499$	12.4748	−	21.6070i	0.558450	−	0.967264i	0.997626	−	0.0688626i	$-0.0219370\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−34.1966			−1.52475			−0.762376	−	0.647135i	$-0.775967\pi$
$503$	−34.1966			−1.52475			−0.762376	+	0.647135i	$0.775967\pi$
$504$		0			0
$505$	−29.8465			−1.32815
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.84342	−	11.8532i	0.303329	−	0.525382i	−0.673559	−	0.739134i	$-0.735235\pi$
$509$	6.84342	−	11.8532i	0.303329	−	0.525382i	0.976888	+	0.213752i	$0.0685685\pi$
$510$		0			0
$511$	11.4375	−	3.39218i	0.505965	−	0.150061i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.39447	+	2.41528i	0.0614475	+	0.106430i
$516$		0			0
$517$	−3.53641	−	6.12525i	−0.155531	−	0.269388i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.3748	−	23.1658i	0.585960	−	1.01491i	−0.408795	−	0.912626i	$-0.634051\pi$
$521$	13.3748	−	23.1658i	0.585960	−	1.01491i	0.994755	−	0.102286i	$-0.0326157\pi$
$522$		0			0
$523$	−10.6131	−	18.3824i	−0.464079	−	0.803808i	0.535081	−	0.844801i	$-0.320281\pi$
$523$	−10.6131	−	18.3824i	−0.464079	−	0.803808i	−0.999159	+	0.0409928i	$0.986948\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.996020	−	1.72516i	0.0433873	−	0.0751490i
$528$		0			0
$529$	−7.37466	−	12.7733i	−0.320637	−	0.555360i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.7478	−	22.0799i	0.552170	−	0.956386i
$534$		0			0
$535$	−16.1223			−0.697029
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.90359	+	3.18918i	−0.211213	+	0.137368i
$540$		0			0
$541$	10.1269	+	17.5402i	0.435388	+	0.754114i	0.997327	−	0.0730646i	$-0.0232779\pi$
$541$	10.1269	+	17.5402i	0.435388	+	0.754114i	−0.561939	+	0.827178i	$0.689945\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.64201	+	16.7005i	0.413019	+	0.715369i
$546$		0			0
$547$	−21.9668	+	38.0476i	−0.939233	+	1.62680i	−0.172327	+	0.985040i	$0.555129\pi$
$547$	−21.9668	+	38.0476i	−0.939233	+	1.62680i	−0.766906	+	0.641760i	$0.778205\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−16.9265			−0.721094
$552$		0			0
$553$	−30.2220	−	28.6600i	−1.28517	−	1.21875i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.45483	−	7.71599i	0.188757	−	0.326937i	−0.756079	−	0.654480i	$-0.772887\pi$
$557$	4.45483	−	7.71599i	0.188757	−	0.326937i	0.944836	+	0.327544i	$0.106221\pi$
$558$		0			0
$559$	6.13897			0.259651
$560$		0			0
$561$		0			0
$562$		0			0
$563$	28.4193			1.19773			0.598865	−	0.800850i	$-0.295619\pi$
$563$	28.4193			1.19773			0.598865	+	0.800850i	$0.295619\pi$
$564$		0			0
$565$	23.7502			0.999177
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.57895			0.359648			0.179824	−	0.983699i	$-0.442447\pi$
$569$	8.57895			0.359648			0.179824	+	0.983699i	$0.442447\pi$
$570$		0			0
$571$	19.3772			0.810912			0.405456	−	0.914115i	$-0.367113\pi$
$571$	19.3772			0.810912			0.405456	+	0.914115i	$0.367113\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.3488			−0.681793
$576$		0			0
$577$	0.584441	−	1.01228i	0.0243306	−	0.0421418i	−0.853604	−	0.520923i	$-0.825588\pi$
$577$	0.584441	−	1.01228i	0.0243306	−	0.0421418i	0.877934	+	0.478781i	$0.158921\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−16.0416	+	4.75769i	−0.665517	+	0.197382i
$582$		0			0
$583$	6.67867			0.276602
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.5863	−	26.9963i	0.643316	−	1.11426i	−0.341372	−	0.939928i	$-0.610892\pi$
$587$	15.5863	−	26.9963i	0.643316	−	1.11426i	0.984688	−	0.174327i	$-0.0557750\pi$
$588$		0			0
$589$	−2.80184	−	4.85293i	−0.115448	−	0.199962i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.1887	+	26.3075i	0.623724	+	1.08032i	0.988786	+	0.149338i	$0.0477143\pi$
$593$	15.1887	+	26.3075i	0.623724	+	1.08032i	−0.365062	+	0.930983i	$0.618952\pi$
$594$		0			0
$595$	−0.567960	+	2.36928i	−0.0232841	+	0.0971311i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.30758			0.298579			0.149290	−	0.988793i	$-0.452301\pi$
$599$	7.30758			0.298579			0.149290	+	0.988793i	$0.452301\pi$
$600$		0			0
$601$	4.61461	−	7.99274i	0.188234	−	0.326031i	−0.756428	−	0.654077i	$-0.773057\pi$
$601$	4.61461	−	7.99274i	0.188234	−	0.326031i	0.944661	+	0.328047i	$0.106390\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.87774	+	13.6446i	0.320276	+	0.554734i
$606$		0			0
$607$	8.53370	−	14.7808i	0.346372	−	0.599934i	−0.639230	−	0.769016i	$-0.720747\pi$
$607$	8.53370	−	14.7808i	0.346372	−	0.599934i	0.985602	+	0.169082i	$0.0540801\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−15.3387	−	26.5673i	−0.620536	−	1.07480i
$612$		0			0
$613$	−0.393059	+	0.680797i	−0.0158755	+	0.0274972i	−0.873854	−	0.486188i	$-0.838387\pi$
$613$	−0.393059	+	0.680797i	−0.0158755	+	0.0274972i	0.857979	+	0.513686i	$0.171720\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.7960	−	41.2159i	−0.957991	−	1.65929i	−0.727370	−	0.686246i	$-0.759257\pi$
$617$	−23.7960	−	41.2159i	−0.957991	−	1.65929i	−0.230621	−	0.973044i	$-0.574076\pi$
$618$		0			0
$619$	−9.48717	−	16.4323i	−0.381321	−	0.660468i	0.609930	−	0.792455i	$-0.291198\pi$
$619$	−9.48717	−	16.4323i	−0.381321	−	0.660468i	−0.991251	+	0.131987i	$0.957864\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.655222	−	2.73330i	0.0262509	−	0.109507i
$624$		0			0
$625$	2.30744	−	3.99660i	0.0922976	−	0.159864i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.29674			−0.211195
$630$		0			0
$631$	0.300343			0.0119565			0.00597823	−	0.999982i	$-0.498097\pi$
$631$	0.300343			0.0119565			0.00597823	+	0.999982i	$0.498097\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.33267	−	14.4326i	0.330672	−	0.572741i
$636$		0			0
$637$	−21.2686	+	13.8326i	−0.842692	+	0.548068i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	14.0548	+	24.3436i	0.555131	+	0.961514i	0.997893	+	0.0648756i	$0.0206651\pi$
$641$	14.0548	+	24.3436i	0.555131	+	0.961514i	−0.442763	+	0.896639i	$0.646002\pi$
$642$		0			0
$643$	−1.55289	−	2.68968i	−0.0612399	−	0.106071i	0.833780	−	0.552097i	$-0.186172\pi$
$643$	−1.55289	−	2.68968i	−0.0612399	−	0.106071i	−0.895020	+	0.446026i	$0.852839\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.3556	+	40.4532i	−0.918205	+	1.59038i	−0.116066	+	0.993242i	$0.537028\pi$
$647$	−23.3556	+	40.4532i	−0.918205	+	1.59038i	−0.802140	+	0.597137i	$0.796305\pi$
$648$		0			0
$649$	−0.0544950	−	0.0943881i	−0.00213912	−	0.00370506i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.998764	+	1.72991i	−0.0390847	+	0.0676966i	−0.884906	−	0.465770i	$-0.845778\pi$
$653$	−0.998764	+	1.72991i	−0.0390847	+	0.0676966i	0.845821	+	0.533466i	$0.179111\pi$
$654$		0			0
$655$	14.8825	+	25.7772i	0.581506	+	1.00720i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.37284	+	14.5022i	−0.326160	+	0.564925i	−0.981746	−	0.190195i	$-0.939088\pi$
$659$	−8.37284	+	14.5022i	−0.326160	+	0.564925i	0.655587	+	0.755120i	$0.272421\pi$
$660$		0			0
$661$	12.5774			0.489205			0.244602	−	0.969624i	$-0.421343\pi$
$661$	12.5774			0.489205			0.244602	+	0.969624i	$0.421343\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.97311	+	4.71608i	0.192849	+	0.182882i
$666$		0			0
$667$	−30.7000	−	53.1740i	−1.18871	−	2.05890i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.99168	−	3.44969i	−0.0768878	−	0.133174i
$672$		0			0
$673$	23.8175	−	41.2531i	0.918096	−	1.59019i	0.115792	−	0.993273i	$-0.463059\pi$
$673$	23.8175	−	41.2531i	0.918096	−	1.59019i	0.802304	−	0.596916i	$-0.203607\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.09327			0.349483			0.174741	−	0.984614i	$-0.444091\pi$
$677$	9.09327			0.349483			0.174741	+	0.984614i	$0.444091\pi$
$678$		0			0
$679$	39.3856	−	11.6812i	1.51148	−	0.448282i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−2.41674	+	4.18592i	−0.0924741	+	0.160170i	−0.908552	−	0.417773i	$-0.862811\pi$
$683$	−2.41674	+	4.18592i	−0.0924741	+	0.160170i	0.816078	+	0.577942i	$0.196144\pi$
$684$		0			0
$685$	−18.7760			−0.717393
$686$		0			0
$687$		0			0
$688$		0			0
$689$	28.9677			1.10358
$690$		0			0
$691$	−10.7846			−0.410264			−0.205132	−	0.978734i	$-0.565762\pi$
$691$	−10.7846			−0.410264			−0.205132	+	0.978734i	$0.565762\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	19.7199			0.748018
$696$		0			0
$697$	4.23548			0.160430
$698$		0			0
$699$		0			0
$700$		0			0
$701$	31.8393			1.20255			0.601276	−	0.799041i	$-0.294659\pi$
$701$	31.8393			1.20255			0.601276	+	0.799041i	$0.294659\pi$
$702$		0			0
$703$	−7.44997	+	12.9037i	−0.280981	+	0.486673i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	12.0362	−	50.2097i	0.452667	−	1.88833i
$708$		0			0
$709$	−27.2064			−1.02176			−0.510879	−	0.859653i	$-0.670680\pi$
$709$	−27.2064			−1.02176			−0.510879	+	0.859653i	$0.670680\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.1635	−	17.6037i	0.380627	−	0.659265i
$714$		0			0
$715$	−2.31607	−	4.01154i	−0.0866160	−	0.150023i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.4549	+	25.0366i	0.539076	+	0.933707i	0.998954	+	0.0457252i	$0.0145598\pi$
$719$	14.4549	+	25.0366i	0.539076	+	0.933707i	−0.459878	+	0.887982i	$0.652107\pi$
$720$		0			0
$721$	−4.62549	+	1.37185i	−0.172262	+	0.0510902i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−26.5917			−0.987591
$726$		0			0
$727$	4.29978	−	7.44744i	0.159470	−	0.276210i	−0.775208	−	0.631706i	$-0.782355\pi$
$727$	4.29978	−	7.44744i	0.159470	−	0.276210i	0.934678	+	0.355496i	$0.115688\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.509920	+	0.883208i	0.0188601	+	0.0326666i
$732$		0			0
$733$	22.7753	−	39.4480i	0.841225	−	1.45705i	−0.0476340	−	0.998865i	$-0.515168\pi$
$733$	22.7753	−	39.4480i	0.841225	−	1.45705i	0.888859	−	0.458180i	$-0.151499\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.937301	−	1.62345i	−0.0345259	−	0.0598007i
$738$		0			0
$739$	6.34491	−	10.9897i	0.233401	−	0.404263i	−0.725405	−	0.688322i	$-0.758348\pi$
$739$	6.34491	−	10.9897i	0.233401	−	0.404263i	0.958807	+	0.284059i	$0.0916811\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.04492	+	8.73806i	0.185080	+	0.320568i	0.943604	−	0.331078i	$-0.107412\pi$
$743$	5.04492	+	8.73806i	0.185080	+	0.320568i	−0.758523	+	0.651646i	$0.774079\pi$
$744$		0			0
$745$	−13.8146	−	23.9276i	−0.506128	−	0.876640i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.50163	−	27.1220i	0.237564	−	0.991015i
$750$		0			0
$751$	−2.50357	+	4.33631i	−0.0913565	+	0.158234i	−0.908082	−	0.418792i	$-0.862454\pi$
$751$	−2.50357	+	4.33631i	−0.0913565	+	0.158234i	0.816726	+	0.577026i	$0.195787\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	13.1495			0.478561
$756$		0			0
$757$	6.83620			0.248466			0.124233	−	0.992253i	$-0.460353\pi$
$757$	6.83620			0.248466			0.124233	+	0.992253i	$0.460353\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.4377	−	23.2747i	0.487115	−	0.843708i	−0.512775	−	0.858523i	$-0.671382\pi$
$761$	13.4377	−	23.2747i	0.487115	−	0.843708i	0.999890	+	0.0148147i	$0.00471582\pi$
$762$		0			0
$763$	−31.9829	+	9.48562i	−1.15786	+	0.343403i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.236364	−	0.409394i	−0.00853460	−	0.0147824i
$768$		0			0
$769$	−2.00631	−	3.47503i	−0.0723493	−	0.125313i	0.827581	−	0.561346i	$-0.189716\pi$
$769$	−2.00631	−	3.47503i	−0.0723493	−	0.125313i	−0.899931	+	0.436033i	$0.856383\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.6861	−	23.7051i	0.492256	−	0.852612i	−0.507704	−	0.861531i	$-0.669506\pi$
$773$	13.6861	−	23.7051i	0.492256	−	0.852612i	0.999960	+	0.00891927i	$0.00283913\pi$
$774$		0			0
$775$	−4.40171	−	7.62399i	−0.158114	−	0.273862i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.95729	−	10.3183i	0.213442	−	0.369693i
$780$		0			0
$781$	3.92385	+	6.79631i	0.140407	+	0.243191i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.44220	+	4.23001i	−0.0871658	+	0.150976i
$786$		0			0
$787$	−12.8727			−0.458863			−0.229432	−	0.973325i	$-0.573687\pi$
$787$	−12.8727			−0.458863			−0.229432	+	0.973325i	$0.573687\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.57771	+	39.9540i	−0.340544	+	1.42060i
$792$		0			0
$793$	−8.63860	−	14.9625i	−0.306766	−	0.531334i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.71139	+	15.0886i	0.308573	+	0.534465i	0.978050	−	0.208368i	$-0.0668152\pi$
$797$	8.71139	+	15.0886i	0.308573	+	0.534465i	−0.669477	+	0.742833i	$0.733482\pi$
$798$		0			0
$799$	2.54815	−	4.41352i	0.0901469	−	0.156139i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.76796			−0.132968
$804$		0			0
$805$	−5.79554	+	24.1765i	−0.204266	+	0.852109i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.04097	−	5.26712i	0.106915	−	0.185182i	−0.807604	−	0.589725i	$-0.799236\pi$
$809$	3.04097	−	5.26712i	0.106915	−	0.185182i	0.914519	+	0.404543i	$0.132569\pi$
$810$		0			0
$811$	14.6219			0.513443			0.256722	−	0.966485i	$-0.417358\pi$
$811$	14.6219			0.513443			0.256722	+	0.966485i	$0.417358\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.26472			−0.219443
$816$		0			0
$817$	2.86885			0.100368
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9.74323			0.340041			0.170021	−	0.985441i	$-0.445617\pi$
$821$	9.74323			0.340041			0.170021	+	0.985441i	$0.445617\pi$
$822$		0			0
$823$	10.7797			0.375755			0.187878	−	0.982192i	$-0.439839\pi$
$823$	10.7797			0.375755			0.187878	+	0.982192i	$0.439839\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13.0521			−0.453867			−0.226933	−	0.973910i	$-0.572870\pi$
$827$	−13.0521			−0.453867			−0.226933	+	0.973910i	$0.572870\pi$
$828$		0			0
$829$	24.5548	−	42.5301i	0.852822	−	1.47713i	−0.0258286	−	0.999666i	$-0.508222\pi$
$829$	24.5548	−	42.5301i	0.852822	−	1.47713i	0.878651	−	0.477465i	$-0.158444\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.75671	−	1.91092i	−0.130162	−	0.0662093i
$834$		0			0
$835$	25.2308			0.873149
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.0830	−	20.9284i	0.417151	−	0.722527i	−0.578500	−	0.815682i	$-0.696362\pi$
$839$	12.0830	−	20.9284i	0.417151	−	0.722527i	0.995652	+	0.0931549i	$0.0296952\pi$
$840$		0			0
$841$	−35.4341	−	61.3737i	−1.22187	−	2.11633i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.104456	−	0.180923i	−0.00359339	−	0.00622393i
$846$		0			0
$847$	−26.1307	+	7.74997i	−0.897862	+	0.266292i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−54.0487			−1.85276
$852$		0			0
$853$	2.72681	−	4.72297i	0.0933641	−	0.161711i	−0.815561	−	0.578672i	$-0.803571\pi$
$853$	2.72681	−	4.72297i	0.0933641	−	0.161711i	0.908925	+	0.416960i	$0.136905\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.4194	+	28.4393i	0.560876	+	0.971466i	0.997420	+	0.0717835i	$0.0228691\pi$
$857$	16.4194	+	28.4393i	0.560876	+	0.971466i	−0.436544	+	0.899683i	$0.643798\pi$
$858$		0			0
$859$	−26.3299	+	45.6048i	−0.898365	+	1.55601i	−0.0687820	+	0.997632i	$0.521911\pi$
$859$	−26.3299	+	45.6048i	−0.898365	+	1.55601i	−0.829583	+	0.558383i	$0.811422\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.4095	−	42.2784i	−0.830908	−	1.43917i	−0.897319	−	0.441382i	$-0.854488\pi$
$863$	−24.4095	−	42.2784i	−0.830908	−	1.43917i	0.0664116	−	0.997792i	$-0.478845\pi$
$864$		0			0
$865$	−9.80445	+	16.9818i	−0.333361	+	0.577398i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.57746	+	11.3925i	0.223125	+	0.386464i
$870$		0			0
$871$	−4.06540	−	7.04148i	−0.137751	−	0.238591i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	22.4934	+	21.3309i	0.760416	+	0.721115i
$876$		0			0
$877$	12.5373	−	21.7152i	0.423353	−	0.733269i	−0.572912	−	0.819617i	$-0.694186\pi$
$877$	12.5373	−	21.7152i	0.423353	−	0.733269i	0.996265	+	0.0863480i	$0.0275197\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	16.2437			0.547263			0.273632	−	0.961835i	$-0.411775\pi$
$881$	16.2437			0.547263			0.273632	+	0.961835i	$0.411775\pi$
$882$		0			0
$883$	29.7137			0.999945			0.499973	−	0.866041i	$-0.333343\pi$
$883$	29.7137			0.999945			0.499973	+	0.866041i	$0.333343\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.87353	+	13.6374i	−0.264367	+	0.457897i	−0.967398	−	0.253262i	$-0.918496\pi$
$887$	−7.87353	+	13.6374i	−0.264367	+	0.457897i	0.703030	+	0.711160i	$0.251830\pi$
$888$		0			0
$889$	20.9191	+	19.8380i	0.701605	+	0.665344i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.16803	−	12.4154i	−0.239869	−	0.415465i
$894$		0			0
$895$	18.1616	+	31.4568i	0.607076	+	1.05149i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	16.5312	−	28.6328i	0.551345	−	0.954957i
$900$		0			0
$901$	2.40614	+	4.16756i	0.0801602	+	0.138842i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.2539	−	21.2244i	0.407333	−	0.705522i
$906$		0			0
$907$	1.29001	+	2.23437i	0.0428342	+	0.0741910i	0.886648	−	0.462446i	$-0.153028\pi$
$907$	1.29001	+	2.23437i	0.0428342	+	0.0741910i	−0.843813	+	0.536637i	$0.819695\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.2170	+	40.2130i	−0.769214	+	1.33232i	0.168776	+	0.985654i	$0.446019\pi$
$911$	−23.2170	+	40.2130i	−0.769214	+	1.33232i	−0.937990	+	0.346663i	$0.887315\pi$
$912$		0			0
$913$	5.28473			0.174899
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−49.3656	+	14.6411i	−1.63020	+	0.483490i
$918$		0			0
$919$	−2.84387	−	4.92572i	−0.0938106	−	0.162485i	0.815301	−	0.579037i	$-0.196571\pi$
$919$	−2.84387	−	4.92572i	−0.0938106	−	0.162485i	−0.909112	+	0.416553i	$0.863238\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	17.0191	+	29.4780i	0.560191	+	0.970279i
$924$		0			0
$925$	−11.7040	+	20.2718i	−0.384824	+	0.666534i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−47.9605			−1.57353			−0.786767	−	0.617251i	$-0.788246\pi$
$929$	−47.9605			−1.57353			−0.786767	+	0.617251i	$0.788246\pi$
$930$		0			0
$931$	−9.93919	+	6.46422i	−0.325744	+	0.211856i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.384758	−	0.666421i	0.0125829	−	0.0217943i
$936$		0			0
$937$	−25.3542			−0.828285			−0.414142	−	0.910212i	$-0.635918\pi$
$937$	−25.3542			−0.828285			−0.414142	+	0.910212i	$0.635918\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2.51303			−0.0819223			−0.0409611	−	0.999161i	$-0.513042\pi$
$941$	−2.51303			−0.0819223			−0.0409611	+	0.999161i	$0.513042\pi$
$942$		0			0
$943$	43.2195			1.40742
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.5307			−0.472186			−0.236093	−	0.971731i	$-0.575867\pi$
$947$	−14.5307			−0.472186			−0.236093	+	0.971731i	$0.575867\pi$
$948$		0			0
$949$	−16.3429			−0.530514
$950$		0			0
$951$		0			0
$952$		0			0
$953$	36.5564			1.18418			0.592089	−	0.805873i	$-0.298303\pi$
$953$	36.5564			1.18418			0.592089	+	0.805873i	$0.298303\pi$
$954$		0			0
$955$	−8.26605	+	14.3172i	−0.267483	+	0.463294i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.57177	−	31.5861i	0.244505	−	1.01997i
$960$		0			0
$961$	−20.0544			−0.646917
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.573726	+	0.993722i	−0.0184689	+	0.0319890i
$966$		0			0
$967$	8.06111	+	13.9623i	0.259228	+	0.448996i	0.966035	−	0.258410i	$-0.0831986\pi$
$967$	8.06111	+	13.9623i	0.259228	+	0.448996i	−0.706807	+	0.707406i	$0.749865\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−8.60100	−	14.8974i	−0.276019	−	0.478079i	0.694373	−	0.719616i	$-0.255682\pi$
$971$	−8.60100	−	14.8974i	−0.276019	−	0.478079i	−0.970392	+	0.241537i	$0.922349\pi$
$972$		0			0
$973$	−7.95242	+	33.1740i	−0.254943	+	1.06351i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−40.2450			−1.28755			−0.643776	−	0.765214i	$-0.722633\pi$
$977$	−40.2450			−1.28755			−0.643776	+	0.765214i	$0.722633\pi$
$978$		0			0
$979$	−0.443873	+	0.768810i	−0.0141862	+	0.0245713i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.2760	+	17.7985i	0.327753	+	0.567685i	0.982066	−	0.188539i	$-0.0603753\pi$
$983$	10.2760	+	17.7985i	0.327753	+	0.567685i	−0.654313	+	0.756224i	$0.727042\pi$
$984$		0			0
$985$	7.89065	−	13.6670i	0.251417	−	0.435467i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.20330	+	9.01237i	0.165455	+	0.286577i
$990$		0			0
$991$	−14.9872	+	25.9586i	−0.476083	+	0.824601i	−0.999625	−	0.0273998i	$-0.991277\pi$
$991$	−14.9872	+	25.9586i	−0.476083	+	0.824601i	0.523541	+	0.852000i	$0.324611\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.36537	−	7.56105i	−0.138392	−	0.239701i
$996$		0			0
$997$	6.01944	+	10.4260i	0.190638	+	0.330194i	0.945462	−	0.325733i	$-0.105611\pi$
$997$	6.01944	+	10.4260i	0.190638	+	0.330194i	−0.754824	+	0.655927i	$0.772278\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.i.b.613.3		14
3.2	odd	2		252.2.i.b.25.4	✓	14
4.3	odd	2		3024.2.q.j.2881.3		14
7.2	even	3		756.2.l.b.289.5		14
7.3	odd	6		5292.2.j.g.3529.5		14
7.4	even	3		5292.2.j.h.3529.3		14
7.5	odd	6		5292.2.l.i.3313.3		14
7.6	odd	2		5292.2.i.i.2125.5		14
9.2	odd	6		2268.2.k.e.1621.5		14
9.4	even	3		756.2.l.b.361.5		14
9.5	odd	6		252.2.l.b.193.5	yes	14
9.7	even	3		2268.2.k.f.1621.3		14
12.11	even	2		1008.2.q.j.529.4		14
21.2	odd	6		252.2.l.b.205.5	yes	14
21.5	even	6		1764.2.l.i.961.3		14
21.11	odd	6		1764.2.j.g.1177.1		14
21.17	even	6		1764.2.j.h.1177.7		14
21.20	even	2		1764.2.i.i.1537.4		14
28.23	odd	6		3024.2.t.j.289.5		14
36.23	even	6		1008.2.t.j.193.3		14
36.31	odd	6		3024.2.t.j.1873.5		14
63.2	odd	6		2268.2.k.e.1297.5		14
63.4	even	3		5292.2.j.h.1765.3		14
63.5	even	6		1764.2.i.i.373.4		14
63.13	odd	6		5292.2.l.i.361.3		14
63.16	even	3		2268.2.k.f.1297.3		14
63.23	odd	6		252.2.i.b.121.4	yes	14
63.31	odd	6		5292.2.j.g.1765.5		14
63.32	odd	6		1764.2.j.g.589.1		14
63.40	odd	6		5292.2.i.i.1549.5		14
63.41	even	6		1764.2.l.i.949.3		14
63.58	even	3	inner	756.2.i.b.37.3		14
63.59	even	6		1764.2.j.h.589.7		14
84.23	even	6		1008.2.t.j.961.3		14
252.23	even	6		1008.2.q.j.625.4		14
252.247	odd	6		3024.2.q.j.2305.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.4	✓	14	3.2	odd	2
252.2.i.b.121.4	yes	14	63.23	odd	6
252.2.l.b.193.5	yes	14	9.5	odd	6
252.2.l.b.205.5	yes	14	21.2	odd	6
756.2.i.b.37.3		14	63.58	even	3	inner
756.2.i.b.613.3		14	1.1	even	1	trivial
756.2.l.b.289.5		14	7.2	even	3
756.2.l.b.361.5		14	9.4	even	3
1008.2.q.j.529.4		14	12.11	even	2
1008.2.q.j.625.4		14	252.23	even	6
1008.2.t.j.193.3		14	36.23	even	6
1008.2.t.j.961.3		14	84.23	even	6
1764.2.i.i.373.4		14	63.5	even	6
1764.2.i.i.1537.4		14	21.20	even	2
1764.2.j.g.589.1		14	63.32	odd	6
1764.2.j.g.1177.1		14	21.11	odd	6
1764.2.j.h.589.7		14	63.59	even	6
1764.2.j.h.1177.7		14	21.17	even	6
1764.2.l.i.949.3		14	63.41	even	6
1764.2.l.i.961.3		14	21.5	even	6
2268.2.k.e.1297.5		14	63.2	odd	6
2268.2.k.e.1621.5		14	9.2	odd	6
2268.2.k.f.1297.3		14	63.16	even	3
2268.2.k.f.1621.3		14	9.7	even	3
3024.2.q.j.2305.3		14	252.247	odd	6
3024.2.q.j.2881.3		14	4.3	odd	2
3024.2.t.j.289.5		14	28.23	odd	6
3024.2.t.j.1873.5		14	36.31	odd	6
5292.2.i.i.1549.5		14	63.40	odd	6
5292.2.i.i.2125.5		14	7.6	odd	2
5292.2.j.g.1765.5		14	63.31	odd	6
5292.2.j.g.3529.5		14	7.3	odd	6
5292.2.j.h.1765.3		14	63.4	even	3
5292.2.j.h.3529.3		14	7.4	even	3
5292.2.l.i.361.3		14	63.13	odd	6
5292.2.l.i.3313.3		14	7.5	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.764702 + 1.32450i) q^{5} +(-1.91978 - 1.82056i) q^{7} +(0.417818 + 0.723682i) q^{11} +(1.81222 + 3.13886i) q^{13} +(-0.301057 + 0.521446i) q^{17} +(0.846884 + 1.46685i) q^{19} +(-3.07202 + 5.32090i) q^{23} +(1.33046 + 2.30443i) q^{25} +(-4.99671 + 8.65455i) q^{29} -3.30841 q^{31} +(3.87940 - 1.15057i) q^{35} +(4.39846 + 7.61835i) q^{37} +(-3.51718 - 6.09194i) q^{41} +(0.846884 - 1.46685i) q^{43} -8.46401 q^{47} +(0.371118 + 6.99016i) q^{49} +(3.99616 - 6.92155i) q^{53} -1.27803 q^{55} -0.130428 q^{59} -4.76685 q^{61} -5.54324 q^{65} -2.24332 q^{67} +9.39130 q^{71} +(-2.25454 + 3.90498i) q^{73} +(0.515388 - 2.14997i) q^{77} +15.7424 q^{79} +(3.16210 - 5.47692i) q^{83} +(-0.460438 - 0.797501i) q^{85} +(0.531180 + 0.920030i) q^{89} +(2.23542 - 9.32519i) q^{91} -2.59046 q^{95} +(-7.76364 + 13.4470i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5} + 6 q^{7} - 2 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} + 2 q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} - 6 q^{47} - 4 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) \) 14 * q + 2 * q^5 + 6 * q^7 - 2 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 - 11 * q^23 - 9 * q^25 - q^29 + 2 * q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 - 6 * q^47 - 4 * q^49 + 15 * q^53 - 28 * q^55 - 28 * q^59 + 20 * q^61 + 30 * q^65 - 12 * q^67 - 2 * q^71 + 21 * q^73 + 47 * q^77 + 20 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 - 56 * q^95 - 18 * q^97

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