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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
625.2.a.a 625.a 1.a $2$ $4.991$ \(\Q(\sqrt{5}) \) None 625.2.a.a \(-1\) \(-3\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
625.2.a.b 625.a 1.a $2$ $4.991$ \(\Q(\sqrt{5}) \) None 25.2.d.a \(-1\) \(2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
625.2.a.c 625.a 1.a $2$ $4.991$ \(\Q(\sqrt{5}) \) None 25.2.d.a \(1\) \(-2\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
625.2.a.d 625.a 1.a $2$ $4.991$ \(\Q(\sqrt{5}) \) None 625.2.a.a \(1\) \(3\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
625.2.a.e 625.a 1.a $8$ $4.991$ 8.8.6152203125.1 None 625.2.a.e \(-5\) \(-5\) \(0\) \(-10\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(\beta _{3}-\beta _{5}+\beta _{7})q^{3}+\cdots\)
625.2.a.f 625.a 1.a $8$ $4.991$ 8.8.\(\cdots\).2 None 25.2.e.a \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
625.2.a.g 625.a 1.a $8$ $4.991$ 8.8.6152203125.1 None 625.2.a.e \(5\) \(5\) \(0\) \(10\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{3}+\beta _{5}-\beta _{7})q^{3}+\cdots\)
625.2.b.a 625.b 5.b $4$ $4.991$ \(\Q(i, \sqrt{5})\) None 25.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
625.2.b.b 625.b 5.b $4$ $4.991$ \(\Q(i, \sqrt{5})\) None 625.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
625.2.b.c 625.b 5.b $8$ $4.991$ 8.0.58140625.2 None 25.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{5}+\beta _{6})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
625.2.b.d 625.b 5.b $16$ $4.991$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 625.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{2}-\beta _{10}q^{3}+(-1-\beta _{12})q^{4}+\cdots\)
625.2.d.a 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 125.2.a.a \(-3\) \(-4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.b 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 25.2.d.a \(-3\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
625.2.d.c 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 625.2.a.a \(-3\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{2}+(1-\zeta_{10}-2\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.d 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 125.2.a.a \(-2\) \(-1\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\cdots)q^{3}+\cdots\)
625.2.d.e 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 625.2.a.a \(-2\) \(4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.f 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 625.2.a.a \(2\) \(-4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.g 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 125.2.a.a \(2\) \(1\) \(0\) \(12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}-2\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.h 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 25.2.d.a \(3\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
625.2.d.i 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 625.2.a.a \(3\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.j 625.d 25.d $4$ $4.991$ \(\Q(\zeta_{10})\) None 125.2.a.a \(3\) \(4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10}+\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.k 625.d 25.d $8$ $4.991$ 8.0.484000000.9 None 125.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}-\beta _{6})q^{2}+(-\beta _{1}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
625.2.d.l 625.d 25.d $8$ $4.991$ 8.0.484000000.9 None 125.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
625.2.d.m 625.d 25.d $16$ $4.991$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 625.2.a.e \(-5\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6})q^{2}+(\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
625.2.d.n 625.d 25.d $16$ $4.991$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 625.2.a.e \(0\) \(-5\) \(0\) \(20\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{5}-\beta _{6}+\beta _{7}-\beta _{8}-\beta _{12})q^{2}+\cdots\)
625.2.d.o 625.d 25.d $16$ $4.991$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 25.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{11}-\beta _{13})q^{2}+(-\beta _{6}+\beta _{11}+\cdots)q^{3}+\cdots\)
625.2.d.p 625.d 25.d $16$ $4.991$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 625.2.a.e \(0\) \(5\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{5}+\beta _{6}-\beta _{7}+\beta _{8}+\beta _{12})q^{2}+(1+\cdots)q^{3}+\cdots\)
625.2.d.q 625.d 25.d $16$ $4.991$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 625.2.a.e \(5\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(\beta _{5}-\beta _{15})q^{3}+\cdots\)
625.2.e.a 625.e 25.e $8$ $4.991$ 8.0.58140625.2 None 25.2.e.a \(0\) \(-5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{1}+\beta _{5}+\beta _{7})q^{2}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
625.2.e.b 625.e 25.e $8$ $4.991$ 8.0.484000000.6 None 125.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(1+\beta _{2}-3\beta _{3}+\cdots)q^{4}+\cdots\)
625.2.e.c 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None 25.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}q^{3}+(-1+\cdots)q^{4}+\cdots\)
625.2.e.d 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None 125.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(\zeta_{20}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{3}+\cdots\)
625.2.e.e 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None 625.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(2\zeta_{20}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots\)
625.2.e.f 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None 625.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(\zeta_{20}+\cdots)q^{3}+\cdots\)
625.2.e.g 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None 125.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(2\zeta_{20}+\cdots)q^{3}+\cdots\)
625.2.e.h 625.e 25.e $8$ $4.991$ 8.0.484000000.6 None 125.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{1}-\beta _{6})q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\cdots\)
625.2.e.i 625.e 25.e $8$ $4.991$ 8.0.58140625.2 None 25.2.e.a \(0\) \(5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\beta _{4}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{3}+\cdots\)
625.2.e.j 625.e 25.e $32$ $4.991$ None 625.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
625.2.e.k 625.e 25.e $32$ $4.991$ None 625.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
625.2.g.a 625.g 125.g $220$ $4.991$ None 125.2.g.a \(20\) \(20\) \(0\) \(15\) $\mathrm{SU}(2)[C_{25}]$
625.2.g.b 625.g 125.g $480$ $4.991$ None 125.2.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{25}]$
625.2.h.a 625.h 125.h $240$ $4.991$ None 125.2.h.a \(20\) \(20\) \(0\) \(25\) $\mathrm{SU}(2)[C_{50}]$
625.2.h.b 625.h 125.h $440$ $4.991$ None 125.2.g.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{50}]$
625.2.j.a 625.j 625.j $6100$ $4.991$ None 625.2.j.a \(-100\) \(-100\) \(-100\) \(-100\) $\mathrm{SU}(2)[C_{125}]$
625.2.k.a 625.k 625.k $6200$ $4.991$ None 625.2.k.a \(-100\) \(-100\) \(-100\) \(-100\) $\mathrm{SU}(2)[C_{250}]$
625.4.a.a 625.a 1.a $10$ $36.876$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 625.4.a.a \(-3\) \(-1\) \(0\) \(-38\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(5+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
625.4.a.b 625.a 1.a $10$ $36.876$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 625.4.a.a \(3\) \(1\) \(0\) \(38\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(5+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
625.4.a.c 625.a 1.a $14$ $36.876$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 25.4.d.a \(-3\) \(-1\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots\)
625.4.a.d 625.a 1.a $14$ $36.876$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 25.4.d.a \(3\) \(1\) \(0\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots\)
625.4.a.e 625.a 1.a $20$ $36.876$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 625.4.a.e \(-9\) \(-23\) \(0\) \(-64\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{8})q^{3}+(3+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
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