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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 13
5733.2.a.a \(1\) \(45.778\) \(\Q\) None \(-2\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{2}+2q^{4}+q^{5}-2q^{10}+2q^{11}+\cdots\)
5733.2.a.b \(1\) \(45.778\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{4}+3q^{8}+q^{13}-q^{16}-2q^{17}+\cdots\)
5733.2.a.c \(1\) \(45.778\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{4}+3q^{8}+3q^{11}-q^{13}+\cdots\)
5733.2.a.d \(1\) \(45.778\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{4}+3q^{8}+3q^{11}+q^{13}+\cdots\)
5733.2.a.e \(1\) \(45.778\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
5733.2.a.f \(1\) \(45.778\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{4}-3q^{5}-q^{13}+4q^{16}-6q^{17}+\cdots\)
5733.2.a.g \(1\) \(45.778\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{4}-q^{5}+2q^{11}-q^{13}+4q^{16}+\cdots\)
5733.2.a.h \(1\) \(45.778\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{4}+q^{5}+2q^{11}+q^{13}+4q^{16}+\cdots\)
5733.2.a.i \(1\) \(45.778\) \(\Q\) None \(1\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
5733.2.a.j \(1\) \(45.778\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{4}-3q^{8}+q^{13}-q^{16}+2q^{17}+\cdots\)
5733.2.a.k \(1\) \(45.778\) \(\Q\) None \(1\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
5733.2.a.l \(1\) \(45.778\) \(\Q\) None \(2\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}+6q^{11}+\cdots\)
5733.2.a.m \(1\) \(45.778\) \(\Q\) None \(2\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+2q^{11}+\cdots\)
5733.2.a.n \(2\) \(45.778\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-3+\beta )q^{8}+\cdots\)
5733.2.a.o \(2\) \(45.778\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{4}-\beta q^{5}+2\beta q^{11}-q^{13}+4q^{16}+\cdots\)
5733.2.a.p \(2\) \(45.778\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{4}-\beta q^{5}-2\beta q^{11}+q^{13}+4q^{16}+\cdots\)
5733.2.a.q \(2\) \(45.778\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+2q^{11}+\cdots\)
5733.2.a.r \(2\) \(45.778\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+2q^{11}+\cdots\)
5733.2.a.s \(2\) \(45.778\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+(3-\beta )q^{5}-2\beta q^{8}+(-2+3\beta )q^{10}+\cdots\)
5733.2.a.t \(2\) \(45.778\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}-q^{13}+\cdots\)
5733.2.a.u \(2\) \(45.778\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
5733.2.a.v \(2\) \(45.778\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}+(1+\cdots)q^{8}+\cdots\)
5733.2.a.w \(2\) \(45.778\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
5733.2.a.x \(3\) \(45.778\) 3.3.316.1 None \(-1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
5733.2.a.y \(3\) \(45.778\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{8}+\cdots\)
5733.2.a.z \(3\) \(45.778\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{8}+\cdots\)
5733.2.a.ba \(3\) \(45.778\) \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5733.2.a.bb \(3\) \(45.778\) \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(3\) \(0\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
5733.2.a.bc \(3\) \(45.778\) 3.3.316.1 None \(2\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5733.2.a.bd \(3\) \(45.778\) 3.3.404.1 None \(2\) \(0\) \(-5\) \(0\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
5733.2.a.be \(3\) \(45.778\) 3.3.404.1 None \(2\) \(0\) \(5\) \(0\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
5733.2.a.bf \(4\) \(45.778\) 4.4.17428.1 None \(-1\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
5733.2.a.bg \(4\) \(45.778\) 4.4.7168.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
5733.2.a.bh \(4\) \(45.778\) 4.4.7168.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5733.2.a.bi \(4\) \(45.778\) \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
5733.2.a.bj \(4\) \(45.778\) 4.4.69777.1 None \(1\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
5733.2.a.bk \(4\) \(45.778\) 4.4.69777.1 None \(1\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
5733.2.a.bl \(5\) \(45.778\) 5.5.746052.1 None \(-4\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
5733.2.a.bm \(5\) \(45.778\) 5.5.746052.1 None \(-4\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
5733.2.a.bn \(5\) \(45.778\) 5.5.2196544.1 None \(-2\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
5733.2.a.bo \(5\) \(45.778\) 5.5.2196544.1 None \(-2\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
5733.2.a.bp \(5\) \(45.778\) 5.5.375116.1 None \(0\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5733.2.a.bq \(5\) \(45.778\) 5.5.375116.1 None \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
5733.2.a.br \(6\) \(45.778\) 6.6.4507648.1 None \(0\) \(0\) \(-6\) \(0\) \(-\) \(+\) \(-\) \(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5733.2.a.bs \(6\) \(45.778\) 6.6.46162368.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\beta _{3}q^{8}+\cdots\)
5733.2.a.bt \(6\) \(45.778\) 6.6.46162368.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{3}q^{8}+\cdots\)
5733.2.a.bu \(6\) \(45.778\) 6.6.4507648.1 None \(0\) \(0\) \(6\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
5733.2.a.bv \(6\) \(45.778\) 6.6.199374400.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{4}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(2\beta _{4}+\cdots)q^{8}+\cdots\)
5733.2.a.bw \(10\) \(45.778\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(-6\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots\)
5733.2.a.bx \(10\) \(45.778\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(6\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
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