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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
311.1.b.a	$311$	$1$	311.b	311.b	$2$	$9$	$9$	$0.155$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-311}) \)	None	✓	✓	✓	✓	311.1.b.a	$2$	$0$	\(-1\)	\(-1\)	\(-1\)	\(-1\)		$1$		\(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
311.2.a.a	$311$	$2$	311.a	1.a	$1$	$4$	$4$	$2.483$	4.4.725.1	$_{}$	None	None	✓	✓	✓	✓	311.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(-1\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
311.2.a.b	$311$	$2$	311.a	1.a	$1$	$22$	$22$	$2.483$		$_{}$	None	None	✓	✓	✓	✓	311.2.a.b	$1$	$0$	\(2\)	\(2\)	\(1\)	\(8\)	$-$		$\mathrm{SU}(2)$
311.2.c.a	$311$	$2$	311.c	311.c	$5$	$100$	$25$	$2.483$		$_{}$	None	None		✓	✓	✓	311.2.c.a	$2$	$0$	\(-3\)	\(-1\)	\(-9\)	\(-6\)			$\mathrm{SU}(2)[C_{5}]$
311.2.e.a	$311$	$2$	311.e	311.e	$31$	$750$	$25$	$2.483$		$_{}$	None	None		✓	✓	✓	311.2.e.a	$2$	$0$	\(-29\)	\(-27\)	\(-25\)	\(-27\)			$\mathrm{SU}(2)[C_{31}]$
311.2.g.a	$311$	$2$	311.g	311.g	$155$	$3000$	$25$	$2.483$		$_{}$	None	None		✓	✓	✓	311.2.g.a	$2$	$0$	\(-121\)	\(-123\)	\(-115\)	\(-118\)			$\mathrm{SU}(2)[C_{155}]$
311.3.b.a	$311$	$3$	311.b	311.b	$2$	$19$	$19$	$8.474$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	$_{}$	\(\Q(\sqrt{-311}) \)	None	✓	✓			311.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}-\beta _{14}q^{3}+(4+\beta _{4})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
311.3.b.b	$311$	$3$	311.b	311.b	$2$	$32$	$32$	$8.474$		$_{}$	None	None		✓	✓		311.3.b.b	$2$	$0$	\(-2\)	\(0\)	\(-10\)	\(4\)			$\mathrm{SU}(2)[C_{2}]$
311.3.d.a	$311$	$3$	311.d	311.d	$10$	$204$	$51$	$8.474$		$_{}$	None	None		✓	✓	✓	311.3.d.a	$2$	$0$	\(-3\)	\(-5\)	\(-15\)	\(-14\)			$\mathrm{SU}(2)[C_{10}]$
311.3.f.a	$311$	$3$	311.f	311.f	$62$	$1530$	$51$	$8.474$		$_{}$	None	None		✓	✓	✓	311.3.f.a	$2$	$0$	\(-29\)	\(-31\)	\(-21\)	\(-35\)			$\mathrm{SU}(2)[C_{62}]$
311.3.h.a	$311$	$3$	311.h	311.h	$310$	$6120$	$51$	$8.474$		$_{}$	None	None		✓	✓	✓	311.3.h.a	$2$	$0$	\(-121\)	\(-119\)	\(-109\)	\(-110\)			$\mathrm{SU}(2)[C_{310}]$
311.4.a.a	$311$	$4$	311.a	1.a	$1$	$29$	$29$	$18.350$		$_{}$	None	None	✓	✓	✓	✓	311.4.a.a	$1$	$1$	\(-7\)	\(-11\)	\(-21\)	\(-73\)	$-$		$\mathrm{SU}(2)$
311.4.a.b	$311$	$4$	311.a	1.a	$1$	$48$	$48$	$18.350$		$_{}$	None	None	✓	✓	✓	✓	311.4.a.b	$1$	$0$	\(5\)	\(13\)	\(19\)	\(67\)	$+$		$\mathrm{SU}(2)$
311.6.a.a	$311$	$6$	311.a	1.a	$1$	$55$	$55$	$49.879$		$_{}$	None	None	✓	✓	✓	✓	311.6.a.a	$1$	$1$	\(-13\)	\(-38\)	\(-83\)	\(-432\)	$+$		$\mathrm{SU}(2)$
311.6.a.b	$311$	$6$	311.a	1.a	$1$	$74$	$74$	$49.879$		$_{}$	None	None	✓	✓	✓	✓	311.6.a.b	$1$	$0$	\(11\)	\(34\)	\(117\)	\(548\)	$-$		$\mathrm{SU}(2)$
311.8.a.a	$311$	$8$	311.a	1.a	$1$	$81$	$81$	$97.152$		$_{}$	None	None	✓	✓	✓	✓	311.8.a.a	$1$	$1$	\(-25\)	\(-122\)	\(-431\)	\(-3628\)	$-$		$\mathrm{SU}(2)$
311.8.a.b	$311$	$8$	311.a	1.a	$1$	$100$	$100$	$97.152$		$_{}$	None	None	✓	✓	✓	✓	311.8.a.b	$1$	$0$	\(23\)	\(94\)	\(569\)	\(3232\)	$+$		$\mathrm{SU}(2)$
311.10.a.a	$311$	$10$	311.a	1.a	$1$	$107$	$107$	$160.176$		$_{}$	None	None	✓	✓	✓	✓	311.10.a.a	$1$	$1$	\(-49\)	\(-251\)	\(-3013\)	\(-25917\)	$+$		$\mathrm{SU}(2)$
311.10.a.b	$311$	$10$	311.a	1.a	$1$	$126$	$126$	$160.176$		$_{}$	None	None	✓	✓	✓	✓	311.10.a.b	$1$	$0$	\(47\)	\(397\)	\(1987\)	\(22103\)	$-$		$\mathrm{SU}(2)$

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