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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 13 19
6422.2.a.a $1$ $51.280$ \(\Q\) None \(-1\) \(-1\) \(1\) \(3\) $+$ $+$ $-$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
6422.2.a.b $1$ $51.280$ \(\Q\) None \(-1\) \(-1\) \(4\) \(-3\) $+$ $+$ $-$ \(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}-3q^{7}+\cdots\)
6422.2.a.c $1$ $51.280$ \(\Q\) None \(-1\) \(1\) \(3\) \(-1\) $+$ $-$ $-$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
6422.2.a.d $1$ $51.280$ \(\Q\) None \(-1\) \(2\) \(-3\) \(0\) $+$ $+$ $-$ \(q-q^{2}+2q^{3}+q^{4}-3q^{5}-2q^{6}-q^{8}+\cdots\)
6422.2.a.e $1$ $51.280$ \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) $-$ $+$ $-$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
6422.2.a.f $1$ $51.280$ \(\Q\) None \(1\) \(0\) \(-2\) \(-4\) $-$ $+$ $+$ \(q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots\)
6422.2.a.g $1$ $51.280$ \(\Q\) None \(1\) \(1\) \(-3\) \(1\) $-$ $-$ $+$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
6422.2.a.h $1$ $51.280$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $+$ $+$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
6422.2.a.i $1$ $51.280$ \(\Q\) None \(1\) \(2\) \(3\) \(0\) $-$ $+$ $+$ \(q+q^{2}+2q^{3}+q^{4}+3q^{5}+2q^{6}+q^{8}+\cdots\)
6422.2.a.j $1$ $51.280$ \(\Q\) None \(1\) \(3\) \(3\) \(-3\) $-$ $+$ $+$ \(q+q^{2}+3q^{3}+q^{4}+3q^{5}+3q^{6}-3q^{7}+\cdots\)
6422.2.a.k $3$ $51.280$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(-5\) \(2\) $+$ $-$ $-$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
6422.2.a.l $3$ $51.280$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(3\) \(2\) $+$ $+$ $-$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
6422.2.a.m $3$ $51.280$ 3.3.169.1 None \(-3\) \(-2\) \(-2\) \(1\) $+$ $+$ $+$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
6422.2.a.n $3$ $51.280$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-1\) \(7\) \(4\) $+$ $-$ $+$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(3-\beta _{1}+\beta _{2})q^{5}+\cdots\)
6422.2.a.o $3$ $51.280$ 3.3.1129.1 None \(-3\) \(0\) \(0\) \(-4\) $+$ $+$ $-$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
6422.2.a.p $3$ $51.280$ 3.3.1129.1 None \(-3\) \(0\) \(2\) \(3\) $+$ $+$ $-$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
6422.2.a.q $3$ $51.280$ \(\Q(\zeta_{14})^+\) None \(-3\) \(5\) \(-5\) \(2\) $+$ $+$ $-$ \(q-q^{2}+(2-\beta _{1})q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
6422.2.a.r $3$ $51.280$ \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(-3\) \(-2\) $-$ $-$ $+$ \(q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
6422.2.a.s $3$ $51.280$ \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(-3\) \(6\) $-$ $+$ $+$ \(q+q^{2}+(-1-2\beta _{1}+\beta _{2})q^{3}+q^{4}+\cdots\)
6422.2.a.t $3$ $51.280$ \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(5\) \(-2\) $-$ $-$ $+$ \(q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(2+\cdots)q^{5}+\cdots\)
6422.2.a.u $3$ $51.280$ 3.3.169.1 None \(3\) \(-2\) \(2\) \(-1\) $-$ $+$ $-$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
6422.2.a.v $3$ $51.280$ \(\Q(\zeta_{14})^+\) None \(3\) \(-1\) \(-7\) \(-4\) $-$ $+$ $-$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-3+\beta _{1}-\beta _{2})q^{5}+\cdots\)
6422.2.a.w $3$ $51.280$ 3.3.361.1 None \(3\) \(-1\) \(-1\) \(-2\) $-$ $+$ $-$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
6422.2.a.x $3$ $51.280$ 3.3.1129.1 None \(3\) \(0\) \(-2\) \(-3\) $-$ $+$ $+$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
6422.2.a.y $3$ $51.280$ 3.3.1129.1 None \(3\) \(0\) \(0\) \(4\) $-$ $+$ $+$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
6422.2.a.z $4$ $51.280$ 4.4.10273.1 None \(-4\) \(-2\) \(-1\) \(1\) $+$ $+$ $+$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
6422.2.a.ba $4$ $51.280$ 4.4.16609.1 None \(-4\) \(2\) \(-2\) \(-7\) $+$ $+$ $+$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
6422.2.a.bb $4$ $51.280$ 4.4.10273.1 None \(4\) \(-2\) \(1\) \(-1\) $-$ $+$ $-$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
6422.2.a.bc $6$ $51.280$ 6.6.316645497.1 None \(-6\) \(2\) \(-2\) \(-1\) $+$ $+$ $-$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
6422.2.a.bd $6$ $51.280$ 6.6.316645497.1 None \(6\) \(2\) \(2\) \(1\) $-$ $+$ $+$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
6422.2.a.be $7$ $51.280$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(2\) \(-2\) \(-1\) $+$ $-$ $+$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
6422.2.a.bf $7$ $51.280$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(2\) \(2\) \(1\) $-$ $-$ $-$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
6422.2.a.bg $8$ $51.280$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-4\) \(2\) \(2\) $+$ $-$ $-$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
6422.2.a.bh $8$ $51.280$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-4\) \(-2\) \(-2\) $-$ $-$ $+$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)
6422.2.a.bi $9$ $51.280$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-5\) \(-1\) \(13\) $+$ $-$ $+$ \(q-q^{2}+(-1+\beta _{7})q^{3}+q^{4}+\beta _{4}q^{5}+\cdots\)
6422.2.a.bj $9$ $51.280$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(1\) \(-1\) \(13\) $+$ $+$ $-$ \(q-q^{2}+\beta _{6}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
6422.2.a.bk $9$ $51.280$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-5\) \(1\) \(-13\) $-$ $+$ $-$ \(q+q^{2}+(-1+\beta _{7})q^{3}+q^{4}-\beta _{4}q^{5}+\cdots\)
6422.2.a.bl $9$ $51.280$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(1\) \(1\) \(-13\) $-$ $-$ $+$ \(q+q^{2}+\beta _{6}q^{3}+q^{4}+(1-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
6422.2.a.bm $14$ $51.280$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(4\) \(2\) \(-2\) $+$ $-$ $+$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
6422.2.a.bn $14$ $51.280$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(4\) \(-2\) \(2\) $-$ $-$ $-$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots\)
6422.2.a.bo $15$ $51.280$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(0\) \(-1\) \(-18\) $+$ $-$ $-$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{10}q^{5}-\beta _{1}q^{6}+\cdots\)
6422.2.a.bp $15$ $51.280$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(4\) \(-3\) \(-10\) $+$ $+$ $+$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{13}q^{5}-\beta _{1}q^{6}+\cdots\)
6422.2.a.bq $15$ $51.280$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(0\) \(1\) \(18\) $-$ $+$ $+$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{10}q^{5}+\beta _{1}q^{6}+\cdots\)
6422.2.a.br $15$ $51.280$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(4\) \(3\) \(10\) $-$ $-$ $-$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{13}q^{5}+\beta _{1}q^{6}+\cdots\)
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