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