LMFDB - Embedded newform 756.2.w.a.341.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(341,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("756.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

Embedding label			341.3
Root			$-1.61108 + 0.635951i$ of defining polynomial
Character	$\chi$	$=$	756.341
Dual form			756.2.w.a.521.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09150 - 1.89054i) q^{5} +(-1.25859 + 2.32722i) q^{7} +(1.26889 + 0.732592i) q^{11} +(2.92752 + 1.69021i) q^{13} +(-1.32136 - 2.28866i) q^{17} +(6.87816 + 3.97111i) q^{19} +(3.47245 - 2.00482i) q^{23} +(0.117249 - 0.203081i) q^{25} +(6.71261 - 3.87553i) q^{29} -0.706968i q^{31} +(5.77345 - 0.160752i) q^{35} +(1.41738 - 2.45498i) q^{37} +(-3.74173 + 6.48086i) q^{41} +(-1.27112 - 2.20164i) q^{43} +12.5508 q^{47} +(-3.83190 - 5.85803i) q^{49} +(2.41675 - 1.39531i) q^{53} -3.19850i q^{55} -13.4330 q^{59} +7.79493i q^{61} -7.37945i q^{65} +5.84058 q^{67} +11.6854i q^{71} +(-3.95924 + 2.28587i) q^{73} +(-3.30191 + 2.03094i) q^{77} +9.38377 q^{79} +(-1.70847 - 2.95917i) q^{83} +(-2.88452 + 4.99614i) q^{85} +(-4.61937 + 8.00099i) q^{89} +(-7.61803 + 4.68571i) q^{91} -17.3379i q^{95} +(6.38394 - 3.68577i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - q^{7} + 6 q^{11} - 3 q^{13} - 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + 15 q^{35} + q^{37} + 6 q^{41} - 2 q^{43} + 36 q^{47} - 5 q^{49} + 30 q^{59} + 14 q^{67} - 3 q^{77} + 2 q^{79} + 6 q^{85}+ \cdots - 3 q^{97}+O(q^{100})$ 16 * q - q^7 + 6 * q^11 - 3 * q^13 - 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + 15 * q^35 + q^37 + 6 * q^41 - 2 * q^43 + 36 * q^47 - 5 * q^49 + 30 * q^59 + 14 * q^67 - 3 * q^77 + 2 * q^79 + 6 * q^85 - 21 * q^89 + 9 * q^91 - 3 * q^97

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.09150	−	1.89054i	−0.488134	−	0.845473i	0.511773	−	0.859121i	$-0.328989\pi$
$5$	−1.09150	−	1.89054i	−0.488134	−	0.845473i	−0.999907	+	0.0136476i	$0.995656\pi$
$6$		0			0
$7$	−1.25859	+	2.32722i	−0.475703	+	0.879606i
$7$	−1.25859	+	2.32722i	−0.475703	+	0.879606i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.26889	+	0.732592i	0.382584	+	0.220885i	0.678942	−	0.734192i	$-0.262439\pi$
$11$	1.26889	+	0.732592i	0.382584	+	0.220885i	−0.296358	+	0.955077i	$0.595772\pi$
$12$		0			0
$13$	2.92752	+	1.69021i	0.811948	+	0.468779i	0.847632	−	0.530585i	$-0.178028\pi$
$13$	2.92752	+	1.69021i	0.811948	+	0.468779i	−0.0356837	+	0.999363i	$0.511361\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.32136	−	2.28866i	−0.320476	−	0.555081i	0.660110	−	0.751169i	$-0.270509\pi$
$17$	−1.32136	−	2.28866i	−0.320476	−	0.555081i	−0.980586	+	0.196088i	$0.937176\pi$
$18$		0			0
$19$	6.87816	+	3.97111i	1.57796	+	0.911034i	0.995144	+	0.0984279i	$0.0313814\pi$
$19$	6.87816	+	3.97111i	1.57796	+	0.911034i	0.582813	+	0.812606i	$0.301952\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.47245	−	2.00482i	0.724056	−	0.418034i	−0.0921879	−	0.995742i	$-0.529386\pi$
$23$	3.47245	−	2.00482i	0.724056	−	0.418034i	0.816244	+	0.577708i	$0.196053\pi$
$24$		0			0
$25$	0.117249	−	0.203081i	0.0234498	−	0.0406163i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.71261	−	3.87553i	1.24650	−	0.719667i	0.276091	−	0.961132i	$-0.410961\pi$
$29$	6.71261	−	3.87553i	1.24650	−	0.719667i	0.970410	+	0.241464i	$0.0776276\pi$
$30$		0			0
$31$		−	0.706968i		−	0.126975i	−0.997983	−	0.0634876i	$-0.979778\pi$
$31$		−	0.706968i		−	0.126975i	0.997983	−	0.0634876i	$-0.0202223\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.77345	−	0.160752i	0.975890	−	0.0271721i
$36$		0			0
$37$	1.41738	−	2.45498i	0.233016	−	0.403596i	−0.725678	−	0.688034i	$-0.758474\pi$
$37$	1.41738	−	2.45498i	0.233016	−	0.403596i	0.958694	+	0.284438i	$0.0918071\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.74173	+	6.48086i	−0.584360	+	1.01214i	0.410595	+	0.911818i	$0.365321\pi$
$41$	−3.74173	+	6.48086i	−0.584360	+	1.01214i	−0.994955	+	0.100323i	$0.968012\pi$
$42$		0			0
$43$	−1.27112	−	2.20164i	−0.193844	−	0.335748i	0.752677	−	0.658390i	$-0.228762\pi$
$43$	−1.27112	−	2.20164i	−0.193844	−	0.335748i	−0.946521	+	0.322642i	$0.895429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12.5508			1.83072			0.915358	−	0.402640i	$-0.131907\pi$
$47$	12.5508			1.83072			0.915358	+	0.402640i	$0.131907\pi$
$48$		0			0
$49$	−3.83190	−	5.85803i	−0.547414	−	0.836862i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.41675	−	1.39531i	0.331966	−	0.191661i	−0.324748	−	0.945801i	$-0.605279\pi$
$53$	2.41675	−	1.39531i	0.331966	−	0.191661i	0.656714	+	0.754140i	$0.271946\pi$
$54$		0			0
$55$		−	3.19850i		−	0.431286i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−13.4330			−1.74883			−0.874414	−	0.485180i	$-0.838754\pi$
$59$	−13.4330			−1.74883			−0.874414	+	0.485180i	$0.838754\pi$
$60$		0			0
$61$			7.79493i			0.998039i	0.866591	+	0.499020i	$0.166306\pi$
$61$			7.79493i			0.998039i	−0.866591	+	0.499020i	$0.833694\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	7.37945i		−	0.915308i
$66$		0			0
$67$	5.84058			0.713541			0.356770	−	0.934192i	$-0.383878\pi$
$67$	5.84058			0.713541			0.356770	+	0.934192i	$0.383878\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			11.6854i			1.38680i	0.720554	+	0.693398i	$0.243887\pi$
$71$			11.6854i			1.38680i	−0.720554	+	0.693398i	$0.756113\pi$
$72$		0			0
$73$	−3.95924	+	2.28587i	−0.463394	+	0.267541i	−0.713470	−	0.700685i	$-0.752878\pi$
$73$	−3.95924	+	2.28587i	−0.463394	+	0.267541i	0.250076	+	0.968226i	$0.419544\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.30191	+	2.03094i	−0.376288	+	0.231448i
$78$		0			0
$79$	9.38377			1.05576			0.527879	−	0.849320i	$-0.322988\pi$
$79$	9.38377			1.05576			0.527879	+	0.849320i	$0.322988\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.70847	−	2.95917i	−0.187529	−	0.324811i	0.756896	−	0.653535i	$-0.226715\pi$
$83$	−1.70847	−	2.95917i	−0.187529	−	0.324811i	−0.944426	+	0.328724i	$0.893381\pi$
$84$		0			0
$85$	−2.88452	+	4.99614i	−0.312871	+	0.541908i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.61937	+	8.00099i	−0.489653	+	0.848103i	−0.999929	−	0.0119070i	$-0.996210\pi$
$89$	−4.61937	+	8.00099i	−0.489653	+	0.848103i	0.510276	+	0.860010i	$0.329543\pi$
$90$		0			0
$91$	−7.61803	+	4.68571i	−0.798586	+	0.491196i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	17.3379i		−	1.77883i
$96$		0			0
$97$	6.38394	−	3.68577i	0.648191	−	0.374233i	−0.139572	−	0.990212i	$-0.544573\pi$
$97$	6.38394	−	3.68577i	0.648191	−	0.374233i	0.787763	+	0.615979i	$0.211239\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.96357	+	6.86510i	−0.394390	+	0.683103i	−0.993023	−	0.117920i	$-0.962377\pi$
$101$	−3.96357	+	6.86510i	−0.394390	+	0.683103i	0.598633	+	0.801023i	$0.295711\pi$
$102$		0			0
$103$	−3.26825	+	1.88693i	−0.322031	+	0.185924i	−0.652297	−	0.757963i	$-0.726195\pi$
$103$	−3.26825	+	1.88693i	−0.322031	+	0.185924i	0.330267	+	0.943888i	$0.392861\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.88241	+	3.97356i	0.665347	+	0.384138i	0.794311	−	0.607511i	$-0.207832\pi$
$107$	6.88241	+	3.97356i	0.665347	+	0.384138i	−0.128964	+	0.991649i	$0.541165\pi$
$108$		0			0
$109$	0.505142	+	0.874932i	0.0483838	+	0.0838033i	0.889203	−	0.457513i	$-0.151260\pi$
$109$	0.505142	+	0.874932i	0.0483838	+	0.0838033i	−0.840819	+	0.541316i	$0.817926\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	10.5557	+	6.09431i	0.992992	+	0.573304i	0.906167	−	0.422919i	$-0.138995\pi$
$113$	10.5557	+	6.09431i	0.992992	+	0.573304i	0.0868250	+	0.996224i	$0.472328\pi$
$114$		0			0
$115$	−7.58037	−	4.37653i	−0.706873	−	0.408113i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.98925	−	0.194605i	0.640703	−	0.0178394i
$120$		0			0
$121$	−4.42662	−	7.66713i	−0.402420	−	0.697012i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.4269			−1.02206
$126$		0			0
$127$	6.79350			0.602826			0.301413	−	0.953494i	$-0.402542\pi$
$127$	6.79350			0.602826			0.301413	+	0.953494i	$0.402542\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.86790	−	11.8956i	−0.600051	−	1.03932i	−0.992813	−	0.119679i	$-0.961813\pi$
$131$	−6.86790	−	11.8956i	−0.600051	−	1.03932i	0.392761	−	0.919640i	$-0.371520\pi$
$132$		0			0
$133$	−17.8984	+	11.0090i	−1.55199	+	0.954600i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−17.4028	−	10.0475i	−1.48682	−	0.858416i	−0.486933	−	0.873439i	$-0.661884\pi$
$137$	−17.4028	−	10.0475i	−1.48682	−	0.858416i	−0.999887	+	0.0150235i	$0.995218\pi$
$138$		0			0
$139$	8.51403	+	4.91558i	0.722151	+	0.416934i	0.815544	−	0.578695i	$-0.196438\pi$
$139$	8.51403	+	4.91558i	0.722151	+	0.416934i	−0.0933930	+	0.995629i	$0.529771\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.47646	+	4.28936i	0.207092	+	0.358694i
$144$		0			0
$145$	−14.6536	−	8.46029i	−1.21692	−	0.702589i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.3512	+	10.0177i	−1.42146	+	0.820682i	−0.996424	−	0.0844939i	$-0.973073\pi$
$149$	−17.3512	+	10.0177i	−1.42146	+	0.820682i	−0.425038	+	0.905175i	$0.639739\pi$
$150$		0			0
$151$	11.1168	−	19.2549i	0.904675	−	1.56694i	0.0833218	−	0.996523i	$-0.473447\pi$
$151$	11.1168	−	19.2549i	0.904675	−	1.56694i	0.821353	−	0.570420i	$-0.193220\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.33655	+	0.771657i	−0.107354	+	0.0619810i
$156$		0			0
$157$		−	8.02869i		−	0.640759i	−0.947289	−	0.320380i	$-0.896189\pi$
$157$		−	8.02869i		−	0.640759i	0.947289	−	0.320380i	$-0.103811\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.295263	+	10.6044i	0.0232700	+	0.835744i
$162$		0			0
$163$	−6.22604	+	10.7838i	−0.487661	+	0.844654i	−0.999899	−	0.0141893i	$-0.995483\pi$
$163$	−6.22604	+	10.7838i	−0.487661	+	0.844654i	0.512238	+	0.858844i	$0.328817\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.85984	−	17.0777i	0.762978	−	1.32152i	−0.178332	−	0.983970i	$-0.557070\pi$
$167$	9.85984	−	17.0777i	0.762978	−	1.32152i	0.941309	−	0.337546i	$-0.109597\pi$
$168$		0			0
$169$	−0.786412	−	1.36211i	−0.0604933	−	0.104777i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.82747			−0.138940			−0.0694699	−	0.997584i	$-0.522131\pi$
$173$	−1.82747			−0.138940			−0.0694699	+	0.997584i	$0.522131\pi$
$174$		0			0
$175$	0.325046	+	0.528460i	0.0245712	+	0.0399479i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.1182	+	6.99645i	−0.905757	+	0.522939i	−0.879064	−	0.476705i	$-0.841831\pi$
$179$	−12.1182	+	6.99645i	−0.905757	+	0.522939i	−0.0266934	+	0.999644i	$0.508498\pi$
$180$		0			0
$181$		−	16.3594i		−	1.21599i	−0.793942	−	0.607994i	$-0.791975\pi$
$181$		−	16.3594i		−	1.21599i	0.793942	−	0.607994i	$-0.208025\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.18830			−0.454973
$186$		0			0
$187$		−	3.87206i		−	0.283153i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	13.6631i		−	0.988624i	−0.869285	−	0.494312i	$-0.835420\pi$
$191$		−	13.6631i		−	0.988624i	0.869285	−	0.494312i	$-0.164580\pi$
$192$		0			0
$193$	−4.37769			−0.315113			−0.157557	−	0.987510i	$-0.550362\pi$
$193$	−4.37769			−0.315113			−0.157557	+	0.987510i	$0.550362\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.00603i		−	0.0716767i	−0.999358	−	0.0358384i	$-0.988590\pi$
$197$		−	1.00603i		−	0.0716767i	0.999358	−	0.0358384i	$-0.0114101\pi$
$198$		0			0
$199$	−5.67639	+	3.27726i	−0.402388	+	0.232319i	−0.687514	−	0.726171i	$-0.741298\pi$
$199$	−5.67639	+	3.27726i	−0.402388	+	0.232319i	0.285126	+	0.958490i	$0.407965\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.570774	+	20.4994i	0.0400605	+	1.43878i
$204$		0			0
$205$	16.3364			1.14098
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.81840	+	10.0778i	0.402467	+	0.697094i
$210$		0			0
$211$	−9.11202	+	15.7825i	−0.627297	+	1.08651i	0.360794	+	0.932645i	$0.382506\pi$
$211$	−9.11202	+	15.7825i	−0.627297	+	1.08651i	−0.988092	+	0.153866i	$0.950828\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.77486	+	4.80620i	−0.189244	+	0.327780i
$216$		0			0
$217$	1.64527	+	0.889784i	0.111688	+	0.0604024i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	8.93345i		−	0.600929i
$222$		0			0
$223$	−8.71705	+	5.03279i	−0.583737	+	0.337021i	−0.762617	−	0.646850i	$-0.776086\pi$
$223$	−8.71705	+	5.03279i	−0.583737	+	0.337021i	0.178880	+	0.983871i	$0.442753\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.94372	+	17.2230i	−0.659988	+	1.14313i	0.320630	+	0.947204i	$0.396105\pi$
$227$	−9.94372	+	17.2230i	−0.659988	+	1.14313i	−0.980618	+	0.195928i	$0.937228\pi$
$228$		0			0
$229$	−15.3854	+	8.88275i	−1.01669	+	0.586988i	−0.913145	−	0.407636i	$-0.866353\pi$
$229$	−15.3854	+	8.88275i	−1.01669	+	0.586988i	−0.103549	+	0.994624i	$0.533020\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.9077	+	8.02962i	0.911124	+	0.526038i	0.880793	−	0.473502i	$-0.157010\pi$
$233$	13.9077	+	8.02962i	0.911124	+	0.526038i	0.0303317	+	0.999540i	$0.490344\pi$
$234$		0			0
$235$	−13.6992	−	23.7277i	−0.893636	−	1.54782i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.11117	+	4.10564i	0.459983	+	0.265572i	0.712037	−	0.702142i	$-0.247773\pi$
$239$	7.11117	+	4.10564i	0.459983	+	0.265572i	−0.252054	+	0.967713i	$0.581106\pi$
$240$		0			0
$241$	−24.6614	−	14.2382i	−1.58858	−	0.917166i	−0.993542	−	0.113468i	$-0.963804\pi$
$241$	−24.6614	−	14.2382i	−1.58858	−	0.917166i	−0.595037	−	0.803698i	$-0.702863\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.89230	+	13.6384i	−0.440333	+	0.871325i
$246$		0			0
$247$	13.4240	+	23.2510i	0.854147	+	1.47943i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.656343			−0.0414280			−0.0207140	−	0.999785i	$-0.506594\pi$
$251$	−0.656343			−0.0414280			−0.0207140	+	0.999785i	$0.506594\pi$
$252$		0			0
$253$	5.87486			0.369349
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.82042	+	6.61716i	0.238311	+	0.412767i	0.960230	−	0.279211i	$-0.0900728\pi$
$257$	3.82042	+	6.61716i	0.238311	+	0.412767i	−0.721918	+	0.691978i	$0.756739\pi$
$258$		0			0
$259$	3.92937	+	6.38837i	0.244159	+	0.396954i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.73888	+	3.31334i	0.353874	+	0.204310i	0.666390	−	0.745603i	$-0.267838\pi$
$263$	5.73888	+	3.31334i	0.353874	+	0.204310i	−0.312516	+	0.949913i	$0.601172\pi$
$264$		0			0
$265$	−5.27577	−	3.04597i	−0.324088	−	0.187112i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.38347	−	7.59239i	−0.267265	−	0.462916i	0.700890	−	0.713270i	$-0.252786\pi$
$269$	−4.38347	−	7.59239i	−0.267265	−	0.462916i	−0.968154	+	0.250354i	$0.919453\pi$
$270$		0			0
$271$	14.2608	+	8.23346i	0.866280	+	0.500147i	0.866110	−	0.499853i	$-0.166613\pi$
$271$	14.2608	+	8.23346i	0.866280	+	0.500147i	0.000169619		1.00000i	$0.499946\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.297551	−	0.171791i	0.0179430	−	0.0103594i
$276$		0			0
$277$	8.88732	−	15.3933i	0.533987	−	0.924893i	−0.465225	−	0.885193i	$-0.654026\pi$
$277$	8.88732	−	15.3933i	0.533987	−	0.924893i	0.999212	−	0.0397001i	$-0.0126402\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.0252	−	8.09748i	0.836676	−	0.483055i	−0.0194568	−	0.999811i	$-0.506194\pi$
$281$	14.0252	−	8.09748i	0.836676	−	0.483055i	0.856133	+	0.516755i	$0.172860\pi$
$282$		0			0
$283$		−	28.3729i		−	1.68660i	−0.537447	−	0.843298i	$-0.680611\pi$
$283$		−	28.3729i		−	1.68660i	0.537447	−	0.843298i	$-0.319389\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.3731	−	16.8646i	−0.612304	−	0.995484i
$288$		0			0
$289$	5.00804	−	8.67417i	0.294590	−	0.510246i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.38260	−	7.59088i	0.256034	−	0.443464i	−0.709142	−	0.705066i	$-0.750917\pi$
$293$	4.38260	−	7.59088i	0.256034	−	0.443464i	0.965176	+	0.261602i	$0.0842507\pi$
$294$		0			0
$295$	14.6621	+	25.3956i	0.853663	+	1.47859i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	13.5542			0.783861
$300$		0			0
$301$	6.72353	−	0.187206i	0.387538	−	0.0107904i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	14.7366	−	8.50818i	0.843816	−	0.487177i
$306$		0			0
$307$			12.8497i			0.733372i	0.930345	+	0.366686i	$0.119508\pi$
$307$			12.8497i			0.733372i	−0.930345	+	0.366686i	$0.880492\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.59343			0.373879			0.186939	−	0.982371i	$-0.440143\pi$
$311$	6.59343			0.373879			0.186939	+	0.982371i	$0.440143\pi$
$312$		0			0
$313$		−	3.41458i		−	0.193004i	−0.995333	−	0.0965018i	$-0.969235\pi$
$313$		−	3.41458i		−	0.193004i	0.995333	−	0.0965018i	$-0.0307654\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	32.1010i		−	1.80297i	−0.432810	−	0.901485i	$-0.642478\pi$
$317$		−	32.1010i		−	1.80297i	0.432810	−	0.901485i	$-0.357522\pi$
$318$		0			0
$319$	11.3567			0.635854
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	20.9890i		−	1.16786i
$324$		0			0
$325$	0.686498	−	0.396350i	0.0380801	−	0.0219855i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−15.7963	+	29.2084i	−0.870877	+	1.61031i
$330$		0			0
$331$	−28.8833			−1.58757			−0.793784	−	0.608199i	$-0.791892\pi$
$331$	−28.8833			−1.58757			−0.793784	+	0.608199i	$0.791892\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.37501	−	11.0418i	−0.348304	−	0.603280i
$336$		0			0
$337$	4.82568	−	8.35833i	0.262872	−	0.455307i	−0.704132	−	0.710069i	$-0.748664\pi$
$337$	4.82568	−	8.35833i	0.262872	−	0.455307i	0.967004	+	0.254762i	$0.0819971\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.517919	−	0.897063i	0.0280469	−	0.0485787i
$342$		0			0
$343$	18.4557	−	1.54481i	0.996515	−	0.0834117i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	12.3273i		−	0.661766i	−0.943672	−	0.330883i	$-0.892653\pi$
$347$		−	12.3273i		−	0.661766i	0.943672	−	0.330883i	$-0.107347\pi$
$348$		0			0
$349$	−10.2211	+	5.90115i	−0.547123	+	0.315881i	−0.747961	−	0.663743i	$-0.768967\pi$
$349$	−10.2211	+	5.90115i	−0.547123	+	0.315881i	0.200838	+	0.979624i	$0.435634\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.59855	+	11.4290i	−0.351205	+	0.608305i	−0.986461	−	0.163997i	$-0.947561\pi$
$353$	−6.59855	+	11.4290i	−0.351205	+	0.608305i	0.635256	+	0.772302i	$0.280895\pi$
$354$		0			0
$355$	22.0916	−	12.7546i	1.17250	−	0.676943i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.22483	+	3.01656i	0.275756	+	0.159208i	0.631501	−	0.775375i	$-0.282439\pi$
$359$	5.22483	+	3.01656i	0.275756	+	0.159208i	−0.355745	+	0.934583i	$0.615773\pi$
$360$		0			0
$361$	22.0394	+	38.1733i	1.15997	+	2.00912i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.64304	+	4.99006i	0.452397	+	0.261192i
$366$		0			0
$367$	14.8755	+	8.58836i	0.776494	+	0.448309i	0.835186	−	0.549967i	$-0.185360\pi$
$367$	14.8755	+	8.58836i	0.776494	+	0.448309i	−0.0586924	+	0.998276i	$0.518693\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.205496	+	7.38043i	0.0106688	+	0.383173i
$372$		0			0
$373$	−2.35902	−	4.08595i	−0.122146	−	0.211562i	0.798468	−	0.602037i	$-0.205644\pi$
$373$	−2.35902	−	4.08595i	−0.122146	−	0.211562i	−0.920614	+	0.390475i	$0.872311\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	26.2017			1.34946
$378$		0			0
$379$	9.34015			0.479771			0.239886	−	0.970801i	$-0.422890\pi$
$379$	9.34015			0.479771			0.239886	+	0.970801i	$0.422890\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.85036	−	4.93696i	−0.145646	−	0.252267i	0.783968	−	0.620802i	$-0.213193\pi$
$383$	−2.85036	−	4.93696i	−0.145646	−	0.252267i	−0.929614	+	0.368535i	$0.879860\pi$
$384$		0			0
$385$	7.44361	+	4.02560i	0.379362	+	0.205164i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.63671	−	3.83171i	−0.336495	−	0.194275i	0.322226	−	0.946663i	$-0.395569\pi$
$389$	−6.63671	−	3.83171i	−0.336495	−	0.194275i	−0.658721	+	0.752387i	$0.728902\pi$
$390$		0			0
$391$	−9.17668	−	5.29816i	−0.464085	−	0.267939i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−10.2424	−	17.7404i	−0.515351	−	0.892615i
$396$		0			0
$397$	−1.12810	−	0.651310i	−0.0566178	−	0.0326883i	0.471424	−	0.881907i	$-0.343740\pi$
$397$	−1.12810	−	0.651310i	−0.0566178	−	0.0326883i	−0.528042	+	0.849218i	$0.677074\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.18778	−	4.72722i	0.408878	−	0.236066i	−0.281429	−	0.959582i	$-0.590809\pi$
$401$	8.18778	−	4.72722i	0.408878	−	0.236066i	0.690308	+	0.723516i	$0.257475\pi$
$402$		0			0
$403$	1.19492	−	2.06966i	0.0595233	−	0.103097i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.59700	−	2.07673i	0.178296	−	0.102940i
$408$		0			0
$409$			19.0736i			0.943126i	0.881832	+	0.471563i	$0.156310\pi$
$409$			19.0736i			0.943126i	−0.881832	+	0.471563i	$0.843690\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.9067	−	31.2615i	0.831922	−	1.53828i
$414$		0			0
$415$	−3.72961	+	6.45987i	−0.183079	+	0.317102i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.20003	−	7.27466i	0.205185	−	0.355390i	−0.745007	−	0.667057i	$-0.767554\pi$
$419$	4.20003	−	7.27466i	0.205185	−	0.355390i	0.950192	+	0.311666i	$0.100887\pi$
$420$		0			0
$421$	19.7178	+	34.1522i	0.960985	+	1.66448i	0.720035	+	0.693938i	$0.244126\pi$
$421$	19.7178	+	34.1522i	0.960985	+	1.66448i	0.240951	+	0.970537i	$0.422541\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.619711			−0.0300604
$426$		0			0
$427$	−18.1405	−	9.81063i	−0.877881	−	0.474770i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.3340	+	5.96634i	−0.497772	+	0.287389i	−0.727793	−	0.685797i	$-0.759454\pi$
$431$	−10.3340	+	5.96634i	−0.497772	+	0.287389i	0.230021	+	0.973186i	$0.426120\pi$
$432$		0			0
$433$			12.2121i			0.586875i	0.955978	+	0.293437i	$0.0947992\pi$
$433$			12.2121i			0.586875i	−0.955978	+	0.293437i	$0.905201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	31.8454			1.52337
$438$		0			0
$439$			16.7015i			0.797120i	0.917142	+	0.398560i	$0.130490\pi$
$439$			16.7015i			0.797120i	−0.917142	+	0.398560i	$0.869510\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			30.2997i			1.43958i	0.694190	+	0.719791i	$0.255763\pi$
$443$			30.2997i			1.43958i	−0.694190	+	0.719791i	$0.744237\pi$
$444$		0			0
$445$	20.1682			0.956065
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	30.1253i		−	1.42170i	−0.703343	−	0.710851i	$-0.748310\pi$
$449$		−	30.1253i		−	1.42170i	0.703343	−	0.710851i	$-0.251690\pi$
$450$		0			0
$451$	−9.49566	+	5.48232i	−0.447133	+	0.258152i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	17.1736	+	9.28770i	0.805110	+	0.435414i
$456$		0			0
$457$	25.2318			1.18029			0.590146	−	0.807297i	$-0.299070\pi$
$457$	25.2318			1.18029			0.590146	+	0.807297i	$0.299070\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.3174	+	21.3344i	0.573680	+	0.993643i	0.996184	+	0.0872820i	$0.0278181\pi$
$461$	12.3174	+	21.3344i	0.573680	+	0.993643i	−0.422503	+	0.906361i	$0.638849\pi$
$462$		0			0
$463$	−6.33215	+	10.9676i	−0.294280	+	0.509708i	−0.974817	−	0.223006i	$-0.928413\pi$
$463$	−6.33215	+	10.9676i	−0.294280	+	0.509708i	0.680537	+	0.732713i	$0.261746\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.4723	+	18.1385i	−0.484599	+	0.839350i	−0.999843	−	0.0176932i	$-0.994368\pi$
$467$	−10.4723	+	18.1385i	−0.484599	+	0.839350i	0.515245	+	0.857043i	$0.327701\pi$
$468$		0			0
$469$	−7.35090	+	13.5923i	−0.339433	+	0.627635i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	3.72485i		−	0.171269i
$474$		0			0
$475$	1.61291	−	0.931217i	0.0740056	−	0.0427271i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.8852	+	27.5141i	−0.725816	+	1.25715i	0.232822	+	0.972519i	$0.425204\pi$
$479$	−15.8852	+	27.5141i	−0.725816	+	1.25715i	−0.958637	+	0.284630i	$0.908129\pi$
$480$		0			0
$481$	8.29884	−	4.79134i	0.378394	−	0.218466i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−13.9362	−	8.04605i	−0.632809	−	0.365352i
$486$		0			0
$487$	−17.7821	−	30.7995i	−0.805784	−	1.39566i	−0.915761	−	0.401724i	$-0.868411\pi$
$487$	−17.7821	−	30.7995i	−0.805784	−	1.39566i	0.109977	−	0.993934i	$-0.464922\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.75734	−	1.59195i	−0.124437	−	0.0718437i	0.436490	−	0.899709i	$-0.356222\pi$
$491$	−2.75734	−	1.59195i	−0.124437	−	0.0718437i	−0.560926	+	0.827866i	$0.689555\pi$
$492$		0			0
$493$	−17.7395	−	10.2419i	−0.798947	−	0.461272i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−27.1944	−	14.7071i	−1.21983	−	0.659703i
$498$		0			0
$499$	−16.0214	−	27.7498i	−0.717215	−	1.24225i	−0.962099	−	0.272700i	$-0.912083\pi$
$499$	−16.0214	−	27.7498i	−0.717215	−	1.24225i	0.244884	−	0.969552i	$-0.421250\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−11.6608			−0.519930			−0.259965	−	0.965618i	$-0.583711\pi$
$503$	−11.6608			−0.519930			−0.259965	+	0.965618i	$0.583711\pi$
$504$		0			0
$505$	17.3050			0.770061
$506$		0			0
$507$		0			0
$508$		0			0
$509$	13.4427	+	23.2834i	0.595836	+	1.03202i	0.993428	+	0.114457i	$0.0365127\pi$
$509$	13.4427	+	23.2834i	0.595836	+	1.03202i	−0.397592	+	0.917562i	$0.630154\pi$
$510$		0			0
$511$	−0.336655	−	12.0910i	−0.0148927	−	0.534875i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.13461	+	4.11917i	0.314388	+	0.181512i
$516$		0			0
$517$	15.9255	+	9.19459i	0.700402	+	0.404378i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.0385	−	29.5116i	−0.746471	−	1.29293i	−0.949504	−	0.313754i	$-0.898413\pi$
$521$	−17.0385	−	29.5116i	−0.746471	−	1.29293i	0.203033	−	0.979172i	$-0.434920\pi$
$522$		0			0
$523$	4.71003	+	2.71933i	0.205955	+	0.118908i	0.599430	−	0.800427i	$-0.295394\pi$
$523$	4.71003	+	2.71933i	0.205955	+	0.118908i	−0.393475	+	0.919335i	$0.628727\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.61801	+	0.934157i	−0.0704815	+	0.0406925i
$528$		0			0
$529$	−3.46140	+	5.99532i	−0.150496	+	0.260666i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−21.9080	+	12.6486i	−0.948940	+	0.547871i
$534$		0			0
$535$		−	17.3486i		−	0.750045i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.570698	−	10.2404i	−0.0245817	−	0.441085i
$540$		0			0
$541$	11.8329	−	20.4952i	0.508737	−	0.881158i	−0.491212	−	0.871040i	$-0.663446\pi$
$541$	11.8329	−	20.4952i	0.508737	−	0.881158i	0.999949	−	0.0101183i	$-0.00322080\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.10273	−	1.90998i	0.0472356	−	0.0818145i
$546$		0			0
$547$	−12.0824	−	20.9273i	−0.516606	−	0.894788i	−0.999814	−	0.0192822i	$-0.993862\pi$
$547$	−12.0824	−	20.9273i	−0.516606	−	0.894788i	0.483208	−	0.875505i	$-0.339471\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	61.5605			2.62257
$552$		0			0
$553$	−11.8103	+	21.8381i	−0.502226	+	0.928650i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.36315	−	4.25111i	0.311987	−	0.180126i	−0.335829	−	0.941923i	$-0.609016\pi$
$557$	7.36315	−	4.25111i	0.311987	−	0.180126i	0.647815	+	0.761798i	$0.275683\pi$
$558$		0			0
$559$		−	8.59381i		−	0.363480i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.947553			−0.0399346			−0.0199673	−	0.999801i	$-0.506356\pi$
$563$	−0.947553			−0.0399346			−0.0199673	+	0.999801i	$0.506356\pi$
$564$		0			0
$565$		−	26.6078i		−	1.11940i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	18.2280i		−	0.764158i	−0.924130	−	0.382079i	$-0.875208\pi$
$569$		−	18.2280i		−	0.764158i	0.924130	−	0.382079i	$-0.124792\pi$
$570$		0			0
$571$	−12.2424			−0.512330			−0.256165	−	0.966633i	$-0.582459\pi$
$571$	−12.2424			−0.512330			−0.256165	+	0.966633i	$0.582459\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	0.940253i		−	0.0392112i
$576$		0			0
$577$	−10.2500	+	5.91784i	−0.426713	+	0.246363i	−0.697945	−	0.716151i	$-0.745902\pi$
$577$	−10.2500	+	5.91784i	−0.426713	+	0.246363i	0.271232	+	0.962514i	$0.412569\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9.03690	−	0.251618i	0.374914	−	0.0104389i
$582$		0			0
$583$	4.08878			0.169340
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.57681	−	6.19521i	−0.147631	−	0.255704i	0.782721	−	0.622373i	$-0.213831\pi$
$587$	−3.57681	−	6.19521i	−0.147631	−	0.255704i	−0.930351	+	0.366669i	$0.880498\pi$
$588$		0			0
$589$	2.80745	−	4.86264i	0.115679	−	0.200362i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−13.4811	+	23.3500i	−0.553603	+	0.958869i	0.444408	+	0.895825i	$0.353414\pi$
$593$	−13.4811	+	23.3500i	−0.553603	+	0.958869i	−0.998011	+	0.0630442i	$0.979919\pi$
$594$		0			0
$595$	−7.99668	−	13.0010i	−0.327832	−	0.532990i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			35.2441i			1.44004i	0.693955	+	0.720018i	$0.255867\pi$
$599$			35.2441i			1.44004i	−0.693955	+	0.720018i	$0.744133\pi$
$600$		0			0
$601$	3.39266	−	1.95875i	0.138389	−	0.0798991i	−0.429207	−	0.903206i	$-0.641207\pi$
$601$	3.39266	−	1.95875i	0.138389	−	0.0798991i	0.567596	+	0.823307i	$0.307874\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9.66332	+	16.7374i	−0.392870	+	0.680470i
$606$		0			0
$607$	−12.5377	+	7.23862i	−0.508888	+	0.293807i	−0.732376	−	0.680900i	$-0.761589\pi$
$607$	−12.5377	+	7.23862i	−0.508888	+	0.293807i	0.223488	+	0.974707i	$0.428256\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	36.7426	+	21.2134i	1.48645	+	0.858201i
$612$		0			0
$613$	−6.51761	−	11.2888i	−0.263244	−	0.455952i	0.703858	−	0.710341i	$-0.251459\pi$
$613$	−6.51761	−	11.2888i	−0.263244	−	0.455952i	−0.967102	+	0.254389i	$0.918126\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.14491	+	1.81571i	0.126609	+	0.0730979i	0.561967	−	0.827160i	$-0.310045\pi$
$617$	3.14491	+	1.81571i	0.126609	+	0.0730979i	−0.435358	+	0.900258i	$0.643378\pi$
$618$		0			0
$619$	−14.2737	−	8.24091i	−0.573708	−	0.331230i	0.184921	−	0.982753i	$-0.440797\pi$
$619$	−14.2737	−	8.24091i	−0.573708	−	0.331230i	−0.758629	+	0.651523i	$0.774130\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12.8062	−	20.8203i	−0.513068	−	0.834147i
$624$		0			0
$625$	11.8863	+	20.5876i	0.475450	+	0.823504i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.49147			−0.298704
$630$		0			0
$631$	−34.8383			−1.38689			−0.693446	−	0.720508i	$-0.743909\pi$
$631$	−34.8383			−1.38689			−0.693446	+	0.720508i	$0.743909\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−7.41512	−	12.8434i	−0.294260	−	0.509673i
$636$		0			0
$637$	−1.31669	−	23.6262i	−0.0521692	−	0.936105i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.25538	−	4.18889i	−0.286570	−	0.165451i	0.349824	−	0.936815i	$-0.386241\pi$
$641$	−7.25538	−	4.18889i	−0.286570	−	0.165451i	−0.636394	+	0.771364i	$0.719575\pi$
$642$		0			0
$643$	−18.0021	−	10.3935i	−0.709934	−	0.409881i	0.101103	−	0.994876i	$-0.467763\pi$
$643$	−18.0021	−	10.3935i	−0.709934	−	0.409881i	−0.811037	+	0.584995i	$0.801096\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.74770	−	8.22325i	−0.186651	−	0.323289i	0.757480	−	0.652858i	$-0.226430\pi$
$647$	−4.74770	−	8.22325i	−0.186651	−	0.323289i	−0.944132	+	0.329568i	$0.893097\pi$
$648$		0			0
$649$	−17.0450	−	9.84091i	−0.669073	−	0.386290i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.64747	−	3.83792i	0.260136	−	0.150189i	−0.364261	−	0.931297i	$-0.618678\pi$
$653$	6.64747	−	3.83792i	0.260136	−	0.150189i	0.624396	+	0.781108i	$0.285345\pi$
$654$		0			0
$655$	−14.9927	+	25.9680i	−0.585811	+	1.01465i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−38.0493	+	21.9678i	−1.48219	+	0.855743i	−0.999796	−	0.0202102i	$-0.993566\pi$
$659$	−38.0493	+	21.9678i	−1.48219	+	0.855743i	−0.482395	+	0.875954i	$0.660233\pi$
$660$		0			0
$661$			25.5938i			0.995484i	0.867325	+	0.497742i	$0.165837\pi$
$661$			25.5938i			0.995484i	−0.867325	+	0.497742i	$0.834163\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	40.3490	+	21.8213i	1.56467	+	0.846193i
$666$		0			0
$667$	15.5395	−	26.9151i	0.601691	−	1.04216i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−5.71051	+	9.89089i	−0.220452	+	0.381834i
$672$		0			0
$673$	−7.64671	−	13.2445i	−0.294759	−	0.510538i	0.680170	−	0.733055i	$-0.261906\pi$
$673$	−7.64671	−	13.2445i	−0.294759	−	0.510538i	−0.974929	+	0.222517i	$0.928573\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−45.2918			−1.74070			−0.870352	−	0.492430i	$-0.836109\pi$
$677$	−45.2918			−1.74070			−0.870352	+	0.492430i	$0.836109\pi$
$678$		0			0
$679$	0.542827	+	19.4957i	0.0208318	+	0.748177i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−24.0891	+	13.9079i	−0.921744	+	0.532169i	−0.884191	−	0.467126i	$-0.845290\pi$
$683$	−24.0891	+	13.9079i	−0.921744	+	0.532169i	−0.0375529	+	0.999295i	$0.511956\pi$
$684$		0			0
$685$			43.8674i			1.67609i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.43345			0.359386
$690$		0			0
$691$			16.2946i			0.619875i	0.950757	+	0.309938i	$0.100308\pi$
$691$			16.2946i			0.619875i	−0.950757	+	0.309938i	$0.899692\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	21.4614i		−	0.814079i
$696$		0			0
$697$	19.7766			0.749093
$698$		0			0
$699$		0			0
$700$		0			0
$701$			0.393403i			0.0148586i	0.999972	+	0.00742932i	$0.00236485\pi$
$701$			0.393403i			0.0148586i	−0.999972	+	0.00742932i	$0.997635\pi$
$702$		0			0
$703$	19.4980	−	11.2572i	0.735379	−	0.424572i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.9881	−	17.8644i	−0.413250	−	0.671862i
$708$		0			0
$709$	−32.6366			−1.22569			−0.612846	−	0.790202i	$-0.709975\pi$
$709$	−32.6366			−1.22569			−0.612846	+	0.790202i	$0.709975\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.41734	−	2.45491i	−0.0530799	−	0.0919372i
$714$		0			0
$715$	5.40612	−	9.36368i	0.202178	−	0.350182i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.106604	+	0.184643i	−0.00397565	+	0.00688602i	−0.868006	−	0.496553i	$-0.834599\pi$
$719$	−0.106604	+	0.184643i	−0.00397565	+	0.00688602i	0.864031	+	0.503439i	$0.167932\pi$
$720$		0			0
$721$	−0.277900	−	9.98081i	−0.0103495	−	0.371705i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	1.81761i		−	0.0675042i
$726$		0			0
$727$	31.8208	−	18.3717i	1.18017	−	0.681370i	0.224114	−	0.974563i	$-0.428051\pi$
$727$	31.8208	−	18.3717i	1.18017	−	0.681370i	0.956053	+	0.293193i	$0.0947180\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.35920	+	5.81831i	−0.124245	+	0.215198i
$732$		0			0
$733$	9.41829	−	5.43765i	0.347873	−	0.200844i	−0.315875	−	0.948801i	$-0.602298\pi$
$733$	9.41829	−	5.43765i	0.347873	−	0.200844i	0.663748	+	0.747956i	$0.268965\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.41104	+	4.27877i	0.272989	+	0.157610i
$738$		0			0
$739$	6.91282	+	11.9734i	0.254292	+	0.440447i	0.964703	−	0.263340i	$-0.0848242\pi$
$739$	6.91282	+	11.9734i	0.254292	+	0.440447i	−0.710411	+	0.703787i	$0.751491\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	15.8751	+	9.16552i	0.582403	+	0.336250i	0.762088	−	0.647474i	$-0.224175\pi$
$743$	15.8751	+	9.16552i	0.582403	+	0.336250i	−0.179685	+	0.983724i	$0.557508\pi$
$744$		0			0
$745$	37.8776	+	21.8687i	1.38773	+	0.801206i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−17.9095	+	11.0158i	−0.654398	+	0.402508i
$750$		0			0
$751$	9.97084	+	17.2700i	0.363841	+	0.630191i	0.988589	−	0.150635i	$-0.0481318\pi$
$751$	9.97084	+	17.2700i	0.363841	+	0.630191i	−0.624748	+	0.780826i	$0.714798\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−48.5362			−1.76641
$756$		0			0
$757$	−46.9292			−1.70567			−0.852836	−	0.522178i	$-0.825119\pi$
$757$	−46.9292			−1.70567			−0.852836	+	0.522178i	$0.825119\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−26.7769	−	46.3789i	−0.970661	−	1.68123i	−0.693568	−	0.720391i	$-0.743962\pi$
$761$	−26.7769	−	46.3789i	−0.970661	−	1.68123i	−0.277093	−	0.960843i	$-0.589371\pi$
$762$		0			0
$763$	−2.67193	+	0.0743955i	−0.0967302	+	0.00269330i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−39.3254	−	22.7045i	−1.41996	−	0.819813i
$768$		0			0
$769$	−34.7306	−	20.0517i	−1.25242	−	0.723085i	−0.280830	−	0.959758i	$-0.590610\pi$
$769$	−34.7306	−	20.0517i	−1.25242	−	0.723085i	−0.971589	+	0.236673i	$0.923943\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.82375	+	13.5511i	0.281401	+	0.487400i	0.971730	−	0.236095i	$-0.0758677\pi$
$773$	7.82375	+	13.5511i	0.281401	+	0.487400i	−0.690329	+	0.723495i	$0.742534\pi$
$774$		0			0
$775$	−0.143572	−	0.0828913i	−0.00515726	−	0.00297755i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−51.4724	+	29.7176i	−1.84419	+	1.06474i
$780$		0			0
$781$	−8.56060	+	14.8274i	−0.306322	+	0.530566i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.1785	+	8.76333i	−0.541745	+	0.312777i
$786$		0			0
$787$			46.1788i			1.64610i	0.567972	+	0.823048i	$0.307728\pi$
$787$			46.1788i			1.64610i	−0.567972	+	0.823048i	$0.692272\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−27.4680	+	16.8951i	−0.976651	+	0.600720i
$792$		0			0
$793$	−13.1750	+	22.8198i	−0.467859	+	0.810356i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.9388	−	29.3388i	0.600002	−	1.03923i	−0.392818	−	0.919616i	$-0.628500\pi$
$797$	16.9388	−	29.3388i	0.600002	−	1.03923i	0.992820	−	0.119618i	$-0.0381669\pi$
$798$		0			0
$799$	−16.5840	−	28.7244i	−0.586701	−	1.01620i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.69844			−0.236383
$804$		0			0
$805$	19.7257	−	12.1329i	0.695240	−	0.427629i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	33.7873	−	19.5071i	1.18790	−	0.685834i	0.230070	−	0.973174i	$-0.426104\pi$
$809$	33.7873	−	19.5071i	1.18790	−	0.685834i	0.957829	+	0.287340i	$0.0927711\pi$
$810$		0			0
$811$		−	7.73397i		−	0.271577i	−0.990738	−	0.135788i	$-0.956643\pi$
$811$		−	7.73397i		−	0.271577i	0.990738	−	0.135788i	$-0.0433567\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	27.1829			0.952177
$816$		0			0
$817$		−	20.1910i		−	0.706394i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	0.512269i		−	0.0178783i	−0.999960	−	0.00893915i	$-0.997155\pi$
$821$		−	0.512269i		−	0.0178783i	0.999960	−	0.00893915i	$-0.00284546\pi$
$822$		0			0
$823$	−48.3506			−1.68540			−0.842698	−	0.538387i	$-0.819034\pi$
$823$	−48.3506			−1.68540			−0.842698	+	0.538387i	$0.819034\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			17.3086i			0.601879i	0.953643	+	0.300940i	$0.0973003\pi$
$827$			17.3086i			0.601879i	−0.953643	+	0.300940i	$0.902700\pi$
$828$		0			0
$829$	33.0205	−	19.0644i	1.14685	−	0.662134i	0.198733	−	0.980054i	$-0.436317\pi$
$829$	33.0205	−	19.0644i	1.14685	−	0.662134i	0.948118	+	0.317919i	$0.102984\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.34372	+	16.5104i	−0.289093	+	0.572053i
$834$		0			0
$835$	−43.0481			−1.48974
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.2026	+	26.3317i	0.524852	+	0.909071i	0.999581	+	0.0289389i	$0.00921281\pi$
$839$	15.2026	+	26.3317i	0.524852	+	0.909071i	−0.474729	+	0.880132i	$0.657454\pi$
$840$		0			0
$841$	15.5394	−	26.9151i	0.535842	−	0.928106i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.71674	+	2.97348i	−0.0590577	+	0.102291i
$846$		0			0
$847$	23.4144	−	0.651937i	0.804528	−	0.0224008i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	11.3664i		−	0.389635i
$852$		0			0
$853$	27.7143	−	16.0008i	0.948919	−	0.547858i	0.0561738	−	0.998421i	$-0.482110\pi$
$853$	27.7143	−	16.0008i	0.948919	−	0.547858i	0.892745	+	0.450563i	$0.148777\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22.5774	−	39.1053i	0.771230	−	1.33581i	−0.165659	−	0.986183i	$-0.552975\pi$
$857$	22.5774	−	39.1053i	0.771230	−	1.33581i	0.936889	−	0.349627i	$-0.113692\pi$
$858$		0			0
$859$	−15.7911	+	9.11701i	−0.538786	+	0.311068i	−0.744587	−	0.667526i	$-0.767353\pi$
$859$	−15.7911	+	9.11701i	−0.538786	+	0.311068i	0.205801	+	0.978594i	$0.434020\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.61966	+	3.82186i	0.225336	+	0.130098i	0.608419	−	0.793616i	$-0.291804\pi$
$863$	6.61966	+	3.82186i	0.225336	+	0.130098i	−0.383083	+	0.923714i	$0.625138\pi$
$864$		0			0
$865$	1.99468	+	3.45489i	0.0678213	+	0.117470i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.9069	+	6.87448i	0.403915	+	0.233201i
$870$		0			0
$871$	17.0984	+	9.87179i	0.579358	+	0.334493i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	14.3818	−	26.5930i	0.486194	−	0.899006i
$876$		0			0
$877$	−8.01581	−	13.8838i	−0.270675	−	0.468822i	0.698360	−	0.715747i	$-0.253913\pi$
$877$	−8.01581	−	13.8838i	−0.270675	−	0.468822i	−0.969035	+	0.246924i	$0.920580\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−24.7532			−0.833958			−0.416979	−	0.908916i	$-0.636911\pi$
$881$	−24.7532			−0.833958			−0.416979	+	0.908916i	$0.636911\pi$
$882$		0			0
$883$	−11.6958			−0.393595			−0.196798	−	0.980444i	$-0.563054\pi$
$883$	−11.6958			−0.393595			−0.196798	+	0.980444i	$0.563054\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−27.5429	−	47.7058i	−0.924801	−	1.60180i	−0.791880	−	0.610676i	$-0.790898\pi$
$887$	−27.5429	−	47.7058i	−0.924801	−	1.60180i	−0.132921	−	0.991127i	$-0.542436\pi$
$888$		0			0
$889$	−8.55024	+	15.8100i	−0.286766	+	0.530249i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	86.3261	+	49.8404i	2.88879	+	1.66785i
$894$		0			0
$895$	26.4541	+	15.2733i	0.884262	+	0.510529i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.73987	−	4.74560i	−0.0913799	−	0.158275i
$900$		0			0
$901$	−6.38677	−	3.68741i	−0.212774	−	0.122845i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−30.9281	+	17.8563i	−1.02808	+	0.593565i
$906$		0			0
$907$	12.9383	−	22.4098i	0.429610	−	0.744107i	−0.567228	−	0.823560i	$-0.691984\pi$
$907$	12.9383	−	22.4098i	0.429610	−	0.744107i	0.996839	+	0.0794540i	$0.0253177\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.86306	−	2.23034i	0.127989	−	0.0738944i	−0.434639	−	0.900605i	$-0.643124\pi$
$911$	3.86306	−	2.23034i	0.127989	−	0.0738944i	0.562627	+	0.826711i	$0.309791\pi$
$912$		0			0
$913$		−	5.00646i		−	0.165690i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	36.3274	−	1.01148i	1.19964	−	0.0334020i
$918$		0			0
$919$	−21.2352	+	36.7805i	−0.700485	+	1.21328i	0.267811	+	0.963471i	$0.413700\pi$
$919$	−21.2352	+	36.7805i	−0.700485	+	1.21328i	−0.968296	+	0.249804i	$0.919634\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−19.7507	+	34.2091i	−0.650101	+	1.12601i
$924$		0			0
$925$	−0.332373	−	0.575688i	−0.0109284	−	0.0189285i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15.4502			0.506903			0.253452	−	0.967348i	$-0.418434\pi$
$929$	15.4502			0.506903			0.253452	+	0.967348i	$0.418434\pi$
$930$		0			0
$931$	−3.09354	−	55.5093i	−0.101387	−	1.81925i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.32027	+	4.22636i	−0.239398	+	0.138217i
$936$		0			0
$937$		−	46.1410i		−	1.50736i	−0.657241	−	0.753680i	$-0.728277\pi$
$937$		−	46.1410i		−	1.50736i	0.657241	−	0.753680i	$-0.271723\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	41.0104			1.33690			0.668451	−	0.743756i	$-0.266958\pi$
$941$	41.0104			1.33690			0.668451	+	0.743756i	$0.266958\pi$
$942$		0			0
$943$			30.0060i			0.977128i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	9.82254i		−	0.319190i	−0.987183	−	0.159595i	$-0.948981\pi$
$947$		−	9.82254i		−	0.319190i	0.987183	−	0.159595i	$-0.0510188\pi$
$948$		0			0
$949$	−15.4544			−0.501670
$950$		0			0
$951$		0			0
$952$		0			0
$953$			17.0826i			0.553359i	0.960962	+	0.276679i	$0.0892340\pi$
$953$			17.0826i			0.553359i	−0.960962	+	0.276679i	$0.910766\pi$
$954$		0			0
$955$	−25.8305	+	14.9132i	−0.835855	+	0.482581i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	45.2857	−	27.8544i	1.46235	−	0.899466i
$960$		0			0
$961$	30.5002			0.983877
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.77826	+	8.27619i	0.153818	+	0.266420i
$966$		0			0
$967$	21.3240	−	36.9343i	0.685735	−	1.18773i	−0.287471	−	0.957789i	$-0.592814\pi$
$967$	21.3240	−	36.9343i	0.685735	−	1.18773i	0.973205	−	0.229938i	$-0.0738523\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−11.7562	+	20.3623i	−0.377275	+	0.653459i	−0.990665	−	0.136321i	$-0.956472\pi$
$971$	−11.7562	+	20.3623i	−0.377275	+	0.653459i	0.613390	+	0.789780i	$0.289805\pi$
$972$		0			0
$973$	−22.1553	+	13.6273i	−0.710267	+	0.436872i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			34.8654i			1.11544i	0.830028	+	0.557722i	$0.188325\pi$
$977$			34.8654i			1.11544i	−0.830028	+	0.557722i	$0.811675\pi$
$978$		0			0
$979$	−11.7229	+	6.76824i	−0.374666	+	0.216314i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.1804	−	22.8292i	0.420390	−	0.728137i	−0.575587	−	0.817740i	$-0.695227\pi$
$983$	13.1804	−	22.8292i	0.420390	−	0.728137i	0.995978	+	0.0896033i	$0.0285599\pi$
$984$		0			0
$985$	−1.90194	+	1.09808i	−0.0606008	+	0.0349879i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.82780	−	5.09673i	−0.280708	−	0.162067i
$990$		0			0
$991$	0.0805213	+	0.139467i	0.00255784	+	0.00443031i	0.867301	−	0.497783i	$-0.165852\pi$
$991$	0.0805213	+	0.139467i	0.00255784	+	0.00443031i	−0.864744	+	0.502214i	$0.832519\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.3916	+	7.15427i	0.392839	+	0.226806i
$996$		0			0
$997$	14.5820	+	8.41890i	0.461816	+	0.266629i	0.712807	−	0.701360i	$-0.247423\pi$
$997$	14.5820	+	8.41890i	0.461816	+	0.266629i	−0.250992	+	0.967989i	$0.580757\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.w.a.341.3		16
3.2	odd	2		252.2.w.a.5.2	✓	16
4.3	odd	2		3024.2.ca.d.2609.3		16
7.2	even	3		5292.2.x.a.881.3		16
7.3	odd	6		756.2.bm.a.17.3		16
7.4	even	3		5292.2.bm.a.2285.6		16
7.5	odd	6		5292.2.x.b.881.6		16
7.6	odd	2		5292.2.w.b.1097.6		16
9.2	odd	6		756.2.bm.a.89.3		16
9.4	even	3		2268.2.t.a.2105.3		16
9.5	odd	6		2268.2.t.b.2105.6		16
9.7	even	3		252.2.bm.a.173.4	yes	16
12.11	even	2		1008.2.ca.d.257.7		16
21.2	odd	6		1764.2.x.a.293.7		16
21.5	even	6		1764.2.x.b.293.2		16
21.11	odd	6		1764.2.bm.a.1697.5		16
21.17	even	6		252.2.bm.a.185.4	yes	16
21.20	even	2		1764.2.w.b.509.7		16
28.3	even	6		3024.2.df.d.17.3		16
36.7	odd	6		1008.2.df.d.929.5		16
36.11	even	6		3024.2.df.d.1601.3		16
63.2	odd	6		5292.2.x.b.4409.6		16
63.11	odd	6		5292.2.w.b.521.6		16
63.16	even	3		1764.2.x.b.1469.2		16
63.20	even	6		5292.2.bm.a.4625.6		16
63.25	even	3		1764.2.w.b.1109.7		16
63.31	odd	6		2268.2.t.b.1781.6		16
63.34	odd	6		1764.2.bm.a.1685.5		16
63.38	even	6	inner	756.2.w.a.521.3		16
63.47	even	6		5292.2.x.a.4409.3		16
63.52	odd	6		252.2.w.a.101.2	yes	16
63.59	even	6		2268.2.t.a.1781.3		16
63.61	odd	6		1764.2.x.a.1469.7		16
84.59	odd	6		1008.2.df.d.689.5		16
252.115	even	6		1008.2.ca.d.353.7		16
252.227	odd	6		3024.2.ca.d.2033.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.2	✓	16	3.2	odd	2
252.2.w.a.101.2	yes	16	63.52	odd	6
252.2.bm.a.173.4	yes	16	9.7	even	3
252.2.bm.a.185.4	yes	16	21.17	even	6
756.2.w.a.341.3		16	1.1	even	1	trivial
756.2.w.a.521.3		16	63.38	even	6	inner
756.2.bm.a.17.3		16	7.3	odd	6
756.2.bm.a.89.3		16	9.2	odd	6
1008.2.ca.d.257.7		16	12.11	even	2
1008.2.ca.d.353.7		16	252.115	even	6
1008.2.df.d.689.5		16	84.59	odd	6
1008.2.df.d.929.5		16	36.7	odd	6
1764.2.w.b.509.7		16	21.20	even	2
1764.2.w.b.1109.7		16	63.25	even	3
1764.2.x.a.293.7		16	21.2	odd	6
1764.2.x.a.1469.7		16	63.61	odd	6
1764.2.x.b.293.2		16	21.5	even	6
1764.2.x.b.1469.2		16	63.16	even	3
1764.2.bm.a.1685.5		16	63.34	odd	6
1764.2.bm.a.1697.5		16	21.11	odd	6
2268.2.t.a.1781.3		16	63.59	even	6
2268.2.t.a.2105.3		16	9.4	even	3
2268.2.t.b.1781.6		16	63.31	odd	6
2268.2.t.b.2105.6		16	9.5	odd	6
3024.2.ca.d.2033.3		16	252.227	odd	6
3024.2.ca.d.2609.3		16	4.3	odd	2
3024.2.df.d.17.3		16	28.3	even	6
3024.2.df.d.1601.3		16	36.11	even	6
5292.2.w.b.521.6		16	63.11	odd	6
5292.2.w.b.1097.6		16	7.6	odd	2
5292.2.x.a.881.3		16	7.2	even	3
5292.2.x.a.4409.3		16	63.47	even	6
5292.2.x.b.881.6		16	7.5	odd	6
5292.2.x.b.4409.6		16	63.2	odd	6
5292.2.bm.a.2285.6		16	7.4	even	3
5292.2.bm.a.4625.6		16	63.20	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	756.2.w.a.341.3

Level	$756$
Weight	$2$
Character	756.341
Analytic conductor	$6.037$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$