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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 23
5290.2.a.a \(1\) \(42.241\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
5290.2.a.b \(1\) \(42.241\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5290.2.a.c \(1\) \(42.241\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
5290.2.a.d \(1\) \(42.241\) \(\Q\) None \(-1\) \(1\) \(1\) \(4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5290.2.a.e \(2\) \(42.241\) \(\Q(\sqrt{21}) \) None \(-2\) \(-1\) \(2\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.f \(2\) \(42.241\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.g \(2\) \(42.241\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.h \(2\) \(42.241\) \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(-2\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.i \(2\) \(42.241\) \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.j \(2\) \(42.241\) \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(-2\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.k \(2\) \(42.241\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.l \(2\) \(42.241\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.m \(2\) \(42.241\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.n \(2\) \(42.241\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.o \(2\) \(42.241\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(-2\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.p \(3\) \(42.241\) 3.3.1509.1 None \(3\) \(-1\) \(-3\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
5290.2.a.q \(3\) \(42.241\) 3.3.1509.1 None \(3\) \(-1\) \(3\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
5290.2.a.r \(3\) \(42.241\) 3.3.1101.1 None \(3\) \(1\) \(3\) \(-3\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.s \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(-4\) \(-8\) \(+\) \(+\) \(+\) \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.t \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(4\) \(8\) \(+\) \(-\) \(+\) \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.u \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(-4\) \(4\) \(-4\) \(4\) \(+\) \(+\) \(+\) \(q-q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.v \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(-4\) \(4\) \(4\) \(-4\) \(+\) \(-\) \(+\) \(q-q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.w \(4\) \(42.241\) 4.4.13888.1 None \(4\) \(-2\) \(-4\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.x \(4\) \(42.241\) 4.4.13888.1 None \(4\) \(-2\) \(4\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.y \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(-4\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.z \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(4\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.ba \(4\) \(42.241\) 4.4.4752.1 None \(4\) \(2\) \(-4\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
5290.2.a.bb \(4\) \(42.241\) 4.4.4752.1 None \(4\) \(2\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+q^{5}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
5290.2.a.bc \(5\) \(42.241\) \(\Q(\zeta_{22})^+\) None \(5\) \(-4\) \(-5\) \(2\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.bd \(5\) \(42.241\) \(\Q(\zeta_{22})^+\) None \(5\) \(-4\) \(5\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.be \(6\) \(42.241\) 6.6.252973568.1 None \(-6\) \(-2\) \(-6\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bf \(6\) \(42.241\) 6.6.252973568.1 None \(-6\) \(-2\) \(6\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bg \(10\) \(42.241\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-5\) \(-10\) \(5\) \(+\) \(+\) \(+\) \(q-q^{2}+(-1-\beta _{7})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
5290.2.a.bh \(10\) \(42.241\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-5\) \(10\) \(-5\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1-\beta _{7})q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
5290.2.a.bi \(10\) \(42.241\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(-10\) \(7\) \(+\) \(+\) \(-\) \(q-q^{2}+(1+\beta _{7}+\beta _{9})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.bj \(10\) \(42.241\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(10\) \(-7\) \(+\) \(-\) \(+\) \(q-q^{2}+(1+\beta _{7}+\beta _{9})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.bk \(15\) \(42.241\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(5\) \(-15\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bl \(15\) \(42.241\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(5\) \(15\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
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