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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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