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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
795.1.b.a	$795$	$1$	795.b	795.b	$2$	$2$	$2$	$0.397$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-159}) \)	\(\Q(\sqrt{265}) \)		✓			795.1.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-2 i q^{2}-i q^{3}-3 q^{4}-i q^{5}-2 q^{6}+\cdots\)
795.1.b.b	$795$	$1$	795.b	795.b	$2$	$8$	$8$	$0.397$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-159}) \)	None		✓	✓		795.1.b.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{2}-\zeta_{20}^{5}q^{3}+(-1+\cdots)q^{4}+\cdots\)
795.1.x.a	$795$	$1$	795.x	795.x	$26$	$12$	$1$	$0.397$	\(\Q(\zeta_{26})\)	$D_{13}$	\(\Q(\sqrt{-15}) \)	None		✓			795.1.x.a	$4$	$0$	\(-2\)	\(-1\)	\(-1\)	\(0\)		$1$		\(q+(-\zeta_{26}^{7}+\zeta_{26}^{10})q^{2}+\zeta_{26}^{8}q^{3}+\cdots\)
795.1.x.b	$795$	$1$	795.x	795.x	$26$	$12$	$1$	$0.397$	\(\Q(\zeta_{26})\)	$D_{13}$	\(\Q(\sqrt{-15}) \)	None		✓			795.1.x.a	$4$	$0$	\(2\)	\(1\)	\(1\)	\(0\)		$1$		\(q+(\zeta_{26}^{7}-\zeta_{26}^{10})q^{2}-\zeta_{26}^{8}q^{3}+(-\zeta_{26}+\cdots)q^{4}+\cdots\)
795.1.bb.a	$795$	$1$	795.bb	795.ab	$26$	$24$	$2$	$0.397$	\(\Q(\zeta_{52})\)	$D_{26}$	\(\Q(\sqrt{-15}) \)	None		✓	✓	✓	795.1.bb.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(\zeta_{52}^{9}-\zeta_{52}^{11})q^{2}+\zeta_{52}q^{3}+(\zeta_{52}^{18}+\cdots)q^{4}+\cdots\)
795.2.a.a	$795$	$2$	795.a	1.a	$1$	$1$	$1$	$6.348$	\(\Q\)	$_{}$	None	None	✓	✓			795.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
795.2.a.b	$795$	$2$	795.a	1.a	$1$	$1$	$1$	$6.348$	\(\Q\)	$_{}$	None	None	✓	✓			795.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+2q^{7}+q^{9}-2q^{12}+\cdots\)
795.2.a.c	$795$	$2$	795.a	1.a	$1$	$1$	$1$	$6.348$	\(\Q\)	$_{}$	None	None	✓	✓			795.2.a.c	$1$	$1$	\(1\)	\(-1\)	\(-1\)	\(4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
795.2.a.d	$795$	$2$	795.a	1.a	$1$	$1$	$1$	$6.348$	\(\Q\)	$_{}$	None	None	✓	✓			795.2.a.d	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
795.2.a.e	$795$	$2$	795.a	1.a	$1$	$3$	$3$	$6.348$	\(\Q(\zeta_{18})^+\)	$_{}$	None	None	✓	✓	✓	✓	795.2.a.e	$1$	$1$	\(-3\)	\(3\)	\(3\)	\(-9\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
795.2.a.f	$795$	$2$	795.a	1.a	$1$	$3$	$3$	$6.348$	3.3.257.1	$_{}$	None	None	✓	✓	✓		795.2.a.f	$1$	$1$	\(-1\)	\(-3\)	\(-3\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
795.2.a.g	$795$	$2$	795.a	1.a	$1$	$3$	$3$	$6.348$	\(\Q(\zeta_{14})^+\)	$_{}$	None	None	✓	✓	✓	✓	795.2.a.g	$1$	$1$	\(-1\)	\(3\)	\(-3\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
795.2.a.h	$795$	$2$	795.a	1.a	$1$	$3$	$3$	$6.348$	3.3.257.1	$_{}$	None	None	✓	✓	✓		795.2.a.h	$1$	$0$	\(1\)	\(-3\)	\(-3\)	\(-5\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
795.2.a.i	$795$	$2$	795.a	1.a	$1$	$4$	$4$	$6.348$	4.4.2777.1	$_{}$	None	None	✓	✓	✓	✓	795.2.a.i	$1$	$1$	\(-4\)	\(-4\)	\(4\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}-q^{3}+(2+2\beta _{2}-\beta _{3})q^{4}+\cdots\)
795.2.a.j	$795$	$2$	795.a	1.a	$1$	$4$	$4$	$6.348$	4.4.6809.1	$_{}$	None	None	✓	✓	✓	✓	795.2.a.j	$1$	$0$	\(3\)	\(-4\)	\(4\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{2}-q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
795.2.a.k	$795$	$2$	795.a	1.a	$1$	$5$	$5$	$6.348$	5.5.1032140.1	$_{}$	None	None	✓	✓	✓		795.2.a.k	$1$	$0$	\(-1\)	\(5\)	\(-5\)	\(9\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+q^{3}+(3-\beta _{2})q^{4}-q^{5}+\beta _{4}q^{6}+\cdots\)
795.2.a.l	$795$	$2$	795.a	1.a	$1$	$6$	$6$	$6.348$	6.6.66091772.1	$_{}$	None	None	✓	✓	✓	✓	795.2.a.l	$1$	$0$	\(1\)	\(6\)	\(6\)	\(7\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+q^{3}+(1+\beta _{4})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
795.2.c.a	$795$	$2$	795.c	5.b	$2$	$2$	$2$	$6.348$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			795.2.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+(-i+2)q^{5}+\cdots\)
795.2.c.b	$795$	$2$	795.c	5.b	$2$	$2$	$2$	$6.348$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			795.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 q^{4}+(-2 i-1)q^{5}-2 i q^{7}+\cdots\)
795.2.c.c	$795$	$2$	795.c	5.b	$2$	$4$	$4$	$6.348$	\(\Q(\zeta_{8})\)	$_{}$	None	None		✓			795.2.c.c	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}-\beta_1 q^{3}+q^{4}+(-\beta_1-2)q^{5}+\cdots\)
795.2.c.d	$795$	$2$	795.c	5.b	$2$	$14$	$14$	$6.348$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	$_{}$	None	None		✓			795.2.c.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{2}+\beta _{11}q^{3}+(-\beta _{2}+\beta _{6})q^{4}+\cdots\)
795.2.c.e	$795$	$2$	795.c	5.b	$2$	$30$	$30$	$6.348$		$_{}$	None	None		✓	✓		795.2.c.e	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
795.2.e.a	$795$	$2$	795.e	53.b	$2$	$16$	$16$	$6.348$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		✓			795.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-1+\beta _{10}-\beta _{11}+\cdots)q^{4}+\cdots\)
795.2.e.b	$795$	$2$	795.e	53.b	$2$	$20$	$20$	$6.348$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		✓	✓		795.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
795.2.g.a	$795$	$2$	795.g	265.d	$2$	$2$	$2$	$6.348$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			795.2.g.a	$2$	$0$	\(-4\)	\(2\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{2}+q^{3}+2 q^{4}+(-i-2)q^{5}+\cdots\)
795.2.g.b	$795$	$2$	795.g	265.d	$2$	$2$	$2$	$6.348$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			795.2.g.b	$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-q^{3}-q^{4}+(\beta-1)q^{5}+q^{6}+\cdots\)
795.2.g.c	$795$	$2$	795.g	265.d	$2$	$2$	$2$	$6.348$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			795.2.g.b	$2$	$0$	\(2\)	\(2\)	\(2\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{3}-q^{4}+(\beta+1)q^{5}+q^{6}+\cdots\)
795.2.g.d	$795$	$2$	795.g	265.d	$2$	$2$	$2$	$6.348$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			795.2.g.a	$2$	$0$	\(4\)	\(-2\)	\(4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{2}-q^{3}+2 q^{4}+(i+2)q^{5}+\cdots\)
795.2.g.e	$795$	$2$	795.g	265.d	$2$	$24$	$24$	$6.348$		$_{}$	None	None		✓			795.2.g.e	$2$	$0$	\(-2\)	\(24\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
795.2.g.f	$795$	$2$	795.g	265.d	$2$	$24$	$24$	$6.348$		$_{}$	None	None		✓			795.2.g.e	$2$	$0$	\(2\)	\(-24\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
795.2.i.a	$795$	$2$	795.i	265.e	$4$	$54$	$27$	$6.348$		$_{}$	None	None		✓			795.2.i.a	$2$	$0$	\(0\)	\(-54\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
795.2.i.b	$795$	$2$	795.i	265.e	$4$	$54$	$27$	$6.348$		$_{}$	None	None		✓			795.2.i.b	$2$	$0$	\(0\)	\(54\)	\(8\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
795.2.l.a	$795$	$2$	795.l	159.f	$4$	$144$	$72$	$6.348$		$_{}$	None	None		✓	✓	✓	795.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
795.2.m.a	$795$	$2$	795.m	795.m	$4$	$40$	$20$	$6.348$		$_{}$	\(\Q(\sqrt{-159}) \)	None		✓			795.2.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{U}(1)[D_{4}]$
795.2.m.b	$795$	$2$	795.m	795.m	$4$	$168$	$84$	$6.348$		$_{}$	None	None		✓	✓		795.2.m.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
795.2.n.a	$795$	$2$	795.n	15.e	$4$	$4$	$2$	$6.348$	\(\Q(\zeta_{8})\)	$_{}$	None	None		✓			795.2.n.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
795.2.n.b	$795$	$2$	795.n	15.e	$4$	$204$	$102$	$6.348$		$_{}$	None	None		✓	✓		795.2.n.b	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)			$\mathrm{SU}(2)[C_{4}]$
795.2.r.a	$795$	$2$	795.r	795.r	$4$	$8$	$4$	$6.348$	8.0.3317760000.5	$_{}$	\(\Q(\sqrt{-15}) \)	None		✓			795.2.r.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{4}q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}+\beta _{2}q^{5}+\cdots\)
795.2.r.b	$795$	$2$	795.r	795.r	$4$	$200$	$100$	$6.348$		$_{}$	None	None		✓	✓		795.2.r.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
795.2.s.a	$795$	$2$	795.s	265.j	$4$	$54$	$27$	$6.348$		$_{}$	None	None		✓			795.2.i.a	$2$	$0$	\(-6\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
795.2.s.b	$795$	$2$	795.s	265.j	$4$	$54$	$27$	$6.348$		$_{}$	None	None		✓			795.2.i.b	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
795.2.u.a	$795$	$2$	795.u	53.d	$13$	$96$	$8$	$6.348$		$_{}$	None	None		✓			795.2.u.a	$2$	$0$	\(-1\)	\(8\)	\(8\)	\(15\)			$\mathrm{SU}(2)[C_{13}]$
795.2.u.b	$795$	$2$	795.u	53.d	$13$	$96$	$8$	$6.348$		$_{}$	None	None		✓			795.2.u.b	$2$	$0$	\(5\)	\(-8\)	\(-8\)	\(-3\)			$\mathrm{SU}(2)[C_{13}]$
795.2.u.c	$795$	$2$	795.u	53.d	$13$	$120$	$10$	$6.348$		$_{}$	None	None		✓			795.2.u.c	$2$	$0$	\(1\)	\(-10\)	\(10\)	\(7\)			$\mathrm{SU}(2)[C_{13}]$
795.2.u.d	$795$	$2$	795.u	53.d	$13$	$120$	$10$	$6.348$		$_{}$	None	None		✓			795.2.u.d	$2$	$0$	\(3\)	\(10\)	\(-10\)	\(-11\)			$\mathrm{SU}(2)[C_{13}]$
795.2.w.a	$795$	$2$	795.w	265.l	$26$	$336$	$28$	$6.348$		$_{}$	None	None		✓			795.2.w.a	$2$	$0$	\(-4\)	\(28\)	\(2\)	\(0\)			$\mathrm{SU}(2)[C_{26}]$
795.2.w.b	$795$	$2$	795.w	265.l	$26$	$336$	$28$	$6.348$		$_{}$	None	None		✓			795.2.w.a	$2$	$0$	\(4\)	\(-28\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{26}]$
795.2.y.a	$795$	$2$	795.y	53.e	$26$	$192$	$16$	$6.348$		$_{}$	None	None		✓			795.2.y.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)			$\mathrm{SU}(2)[C_{26}]$
795.2.y.b	$795$	$2$	795.y	53.e	$26$	$240$	$20$	$6.348$		$_{}$	None	None		✓	✓		795.2.y.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)			$\mathrm{SU}(2)[C_{26}]$
795.2.ba.a	$795$	$2$	795.ba	265.n	$26$	$624$	$52$	$6.348$		$_{}$	None	None		✓	✓	✓	795.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{26}]$

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