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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
10000.2.a.a $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(0\) \(-6\) $-$ $+$ \(q+(-1-\beta )q^{3}-3q^{7}+(-1+3\beta )q^{9}+\cdots\)
10000.2.a.b $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(0\) \(-1\) $-$ $-$ \(q+(-1-\beta )q^{3}+(1-3\beta )q^{7}+(-1+3\beta )q^{9}+\cdots\)
10000.2.a.c $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(1\) $-$ $+$ \(q-q^{3}+\beta q^{7}-2q^{9}+(4-2\beta )q^{11}+\cdots\)
10000.2.a.d $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(1\) $-$ $+$ \(q-q^{3}+(1-\beta )q^{7}-2q^{9}+3q^{11}+(3+\cdots)q^{13}+\cdots\)
10000.2.a.e $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(0\) \(1\) $-$ $-$ \(q-\beta q^{3}+\beta q^{7}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
10000.2.a.f $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(-3\) $+$ $+$ \(q+(1-2\beta )q^{3}+(-1-\beta )q^{7}+2q^{9}+\cdots\)
10000.2.a.g $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(-3\) $+$ $+$ \(q+(1-2\beta )q^{3}+(-2+\beta )q^{7}+2q^{9}+\cdots\)
10000.2.a.h $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(3\) $+$ $-$ \(q+(1-2\beta )q^{3}+(2-\beta )q^{7}+2q^{9}+(-5+\cdots)q^{11}+\cdots\)
10000.2.a.i $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(3\) $+$ $+$ \(q+(1-2\beta )q^{3}+(1+\beta )q^{7}+2q^{9}+(2+\cdots)q^{11}+\cdots\)
10000.2.a.j $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ \(q+\beta q^{3}-\beta q^{7}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
10000.2.a.k $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-1\) $-$ $-$ \(q+q^{3}-\beta q^{7}-2q^{9}+3q^{11}+(1-4\beta )q^{13}+\cdots\)
10000.2.a.l $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-1\) $-$ $+$ \(q+q^{3}+(-1+\beta )q^{7}-2q^{9}+(2+2\beta )q^{11}+\cdots\)
10000.2.a.m $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(0\) \(1\) $-$ $+$ \(q+(1+\beta )q^{3}+(-1+3\beta )q^{7}+(-1+3\beta )q^{9}+\cdots\)
10000.2.a.n $2$ $79.850$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(0\) \(6\) $-$ $+$ \(q+(1+\beta )q^{3}+3q^{7}+(-1+3\beta )q^{9}+\cdots\)
10000.2.a.o $4$ $79.850$ \(\Q(\zeta_{20})^+\) None \(0\) \(-4\) \(0\) \(-8\) $-$ $-$ \(q+(-1+\beta _{1})q^{3}+(-2-\beta _{1}-\beta _{3})q^{7}+\cdots\)
10000.2.a.p $4$ $79.850$ 4.4.7625.1 None \(0\) \(-3\) \(0\) \(2\) $+$ $+$ \(q+(-1+\beta _{1})q^{3}-\beta _{2}q^{7}+(3-\beta _{1}+\beta _{3})q^{9}+\cdots\)
10000.2.a.q $4$ $79.850$ 4.4.7625.1 None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ \(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{7}+(-2-\beta _{2}+\cdots)q^{9}+\cdots\)
10000.2.a.r $4$ $79.850$ 4.4.108625.1 None \(0\) \(-2\) \(0\) \(3\) $+$ $+$ \(q+(-1-\beta _{2})q^{3}+(\beta _{1}-\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
10000.2.a.s $4$ $79.850$ \(\Q(\zeta_{15})^+\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ \(q+(\beta _{2}+\beta _{3})q^{3}+(2\beta _{2}+2\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
10000.2.a.t $4$ $79.850$ 4.4.7625.1 None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(2+\beta _{1}+\beta _{3})q^{9}+\cdots\)
10000.2.a.u $4$ $79.850$ 4.4.18625.1 None \(0\) \(-1\) \(0\) \(3\) $-$ $+$ \(q+(\beta _{1}-\beta _{2})q^{3}+(2-2\beta _{2}-\beta _{3})q^{7}+\cdots\)
10000.2.a.v $4$ $79.850$ 4.4.18625.1 None \(0\) \(1\) \(0\) \(-3\) $-$ $-$ \(q+(-\beta _{1}+\beta _{2})q^{3}+(-2+2\beta _{2}+\beta _{3})q^{7}+\cdots\)
10000.2.a.w $4$ $79.850$ \(\Q(\zeta_{15})^+\) None \(0\) \(1\) \(0\) \(2\) $-$ $-$ \(q+(-\beta _{2}-\beta _{3})q^{3}+(-2\beta _{2}-2\beta _{3})q^{7}+\cdots\)
10000.2.a.x $4$ $79.850$ 4.4.7625.1 None \(0\) \(1\) \(0\) \(2\) $-$ $+$ \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(2+\beta _{1}+\beta _{3})q^{9}+\cdots\)
10000.2.a.y $4$ $79.850$ 4.4.108625.1 None \(0\) \(2\) \(0\) \(-3\) $+$ $-$ \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
10000.2.a.z $4$ $79.850$ 4.4.7625.1 None \(0\) \(2\) \(0\) \(2\) $+$ $+$ \(q-\beta _{2}q^{3}+(1+\beta _{3})q^{7}+(-2-\beta _{2})q^{9}+\cdots\)
10000.2.a.ba $4$ $79.850$ 4.4.7625.1 None \(0\) \(3\) \(0\) \(-2\) $+$ $-$ \(q+(1-\beta _{1})q^{3}+\beta _{2}q^{7}+(3-\beta _{1}+\beta _{3})q^{9}+\cdots\)
10000.2.a.bb $4$ $79.850$ \(\Q(\zeta_{20})^+\) None \(0\) \(4\) \(0\) \(8\) $-$ $-$ \(q+(1+\beta _{1})q^{3}+(2-\beta _{1}-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
10000.2.a.bc $6$ $79.850$ 6.6.103238125.1 None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ \(q-\beta _{1}q^{3}+(1-\beta _{3}+\beta _{4})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
10000.2.a.bd $6$ $79.850$ 6.6.103238125.1 None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ \(q+\beta _{1}q^{3}+(-1+\beta _{3}-\beta _{4})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
10000.2.a.be $8$ $79.850$ 8.8.6152203125.1 None \(0\) \(-5\) \(0\) \(-10\) $-$ $-$ \(q+(-1+\beta _{5})q^{3}+(-1+\beta _{1}+\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
10000.2.a.bf $8$ $79.850$ 8.8.\(\cdots\).1 None \(0\) \(-5\) \(0\) \(0\) $-$ $+$ \(q+(-1+\beta _{1})q^{3}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{7}+\cdots\)
10000.2.a.bg $8$ $79.850$ 8.8.3266578125.1 None \(0\) \(-3\) \(0\) \(-2\) $+$ $+$ \(q+(-1+\beta _{1}-\beta _{3})q^{3}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
10000.2.a.bh $8$ $79.850$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-2\) \(0\) \(-3\) $+$ $+$ \(q-\beta _{1}q^{3}+\beta _{2}q^{7}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots\)
10000.2.a.bi $8$ $79.850$ 8.8.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{6})q^{7}+\beta _{2}q^{9}+\cdots\)
10000.2.a.bj $8$ $79.850$ 8.8.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ \(q+(\beta _{5}-\beta _{6})q^{3}+(-\beta _{1}-\beta _{6}+\beta _{7})q^{7}+\cdots\)
10000.2.a.bk $8$ $79.850$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2\) \(0\) \(3\) $+$ $+$ \(q+\beta _{1}q^{3}-\beta _{2}q^{7}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots\)
10000.2.a.bl $8$ $79.850$ 8.8.3266578125.1 None \(0\) \(3\) \(0\) \(2\) $+$ $-$ \(q+(1-\beta _{1}+\beta _{3})q^{3}+(-\beta _{4}+\beta _{5})q^{7}+\cdots\)
10000.2.a.bm $8$ $79.850$ 8.8.\(\cdots\).1 None \(0\) \(5\) \(0\) \(0\) $-$ $-$ \(q+(1-\beta _{1})q^{3}+(\beta _{2}+\beta _{4}+\beta _{7})q^{7}+(2+\cdots)q^{9}+\cdots\)
10000.2.a.bn $8$ $79.850$ 8.8.6152203125.1 None \(0\) \(5\) \(0\) \(10\) $-$ $+$ \(q+(1-\beta _{5})q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{5}-\beta _{7})q^{7}+\cdots\)
10000.2.a.bo $12$ $79.850$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $+$ $+$ \(q-\beta _{6}q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{5})q^{7}+(2+\cdots)q^{9}+\cdots\)
10000.2.a.bp $12$ $79.850$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) $+$ $-$ \(q+\beta _{6}q^{3}+(-1-\beta _{1}+\beta _{2}-\beta _{5})q^{7}+\cdots\)
10000.2.a.bq $16$ $79.850$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(-8\) $+$ $-$ \(q-\beta _{1}q^{3}+(-1+\beta _{8})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
10000.2.a.br $16$ $79.850$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(0\) \(8\) $+$ $-$ \(q+\beta _{1}q^{3}+(1-\beta _{8})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
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