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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 13
4225.2.a.a \(1\) \(33.737\) \(\Q\) None \(-2\) \(-1\) \(0\) \(2\) \(+\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots\)
4225.2.a.b \(1\) \(33.737\) \(\Q\) None \(-2\) \(1\) \(0\) \(-2\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots\)
4225.2.a.c \(1\) \(33.737\) \(\Q\) None \(-2\) \(1\) \(0\) \(2\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+2q^{7}+\cdots\)
4225.2.a.d \(1\) \(33.737\) \(\Q\) None \(-1\) \(-2\) \(0\) \(-5\) \(-\) \(-\) \(q-q^{2}-2q^{3}-q^{4}+2q^{6}-5q^{7}+3q^{8}+\cdots\)
4225.2.a.e \(1\) \(33.737\) \(\Q\) None \(-1\) \(-2\) \(0\) \(0\) \(-\) \(-\) \(q-q^{2}-2q^{3}-q^{4}+2q^{6}+3q^{8}+q^{9}+\cdots\)
4225.2.a.f \(1\) \(33.737\) \(\Q\) None \(-1\) \(2\) \(0\) \(-5\) \(+\) \(-\) \(q-q^{2}+2q^{3}-q^{4}-2q^{6}-5q^{7}+3q^{8}+\cdots\)
4225.2.a.g \(1\) \(33.737\) \(\Q\) None \(-1\) \(2\) \(0\) \(-4\) \(+\) \(+\) \(q-q^{2}+2q^{3}-q^{4}-2q^{6}-4q^{7}+3q^{8}+\cdots\)
4225.2.a.h \(1\) \(33.737\) \(\Q\) None \(-1\) \(2\) \(0\) \(0\) \(-\) \(-\) \(q-q^{2}+2q^{3}-q^{4}-2q^{6}+3q^{8}+q^{9}+\cdots\)
4225.2.a.i \(1\) \(33.737\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(q-q^{3}-2q^{4}-4q^{7}-2q^{9}+6q^{11}+\cdots\)
4225.2.a.j \(1\) \(33.737\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(-\) \(+\) \(q+q^{3}-2q^{4}+4q^{7}-2q^{9}+6q^{11}+\cdots\)
4225.2.a.k \(1\) \(33.737\) \(\Q\) None \(1\) \(-2\) \(0\) \(0\) \(-\) \(-\) \(q+q^{2}-2q^{3}-q^{4}-2q^{6}-3q^{8}+q^{9}+\cdots\)
4225.2.a.l \(1\) \(33.737\) \(\Q\) None \(1\) \(-2\) \(0\) \(5\) \(-\) \(-\) \(q+q^{2}-2q^{3}-q^{4}-2q^{6}+5q^{7}-3q^{8}+\cdots\)
4225.2.a.m \(1\) \(33.737\) \(\Q\) None \(1\) \(2\) \(0\) \(0\) \(-\) \(-\) \(q+q^{2}+2q^{3}-q^{4}+2q^{6}-3q^{8}+q^{9}+\cdots\)
4225.2.a.n \(1\) \(33.737\) \(\Q\) None \(1\) \(2\) \(0\) \(5\) \(+\) \(-\) \(q+q^{2}+2q^{3}-q^{4}+2q^{6}+5q^{7}-3q^{8}+\cdots\)
4225.2.a.o \(1\) \(33.737\) \(\Q\) None \(2\) \(-1\) \(0\) \(-2\) \(+\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots\)
4225.2.a.p \(1\) \(33.737\) \(\Q\) None \(2\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+2q^{7}+\cdots\)
4225.2.a.q \(1\) \(33.737\) \(\Q\) None \(2\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-2q^{7}+\cdots\)
4225.2.a.r \(2\) \(33.737\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(4\) \(+\) \(+\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
4225.2.a.s \(2\) \(33.737\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q+(-1+\beta )q^{2}+2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
4225.2.a.t \(2\) \(33.737\) \(\Q(\sqrt{13}) \) None \(-1\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
4225.2.a.u \(2\) \(33.737\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
4225.2.a.v \(2\) \(33.737\) \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(0\) \(0\) \(+\) \(-\) \(q+\beta q^{2}-2q^{3}+q^{4}-2\beta q^{6}-\beta q^{8}+\cdots\)
4225.2.a.w \(2\) \(33.737\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(4\) \(+\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}+(3-\beta )q^{6}+\cdots\)
4225.2.a.x \(2\) \(33.737\) \(\Q(\sqrt{13}) \) None \(1\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-\beta q^{6}+q^{7}+\cdots\)
4225.2.a.y \(2\) \(33.737\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(4\) \(+\) \(+\) \(q+\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
4225.2.a.z \(2\) \(33.737\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(+\) \(q+(1+\beta )q^{2}+2\beta q^{3}+(1+2\beta )q^{4}+(4+\cdots)q^{6}+\cdots\)
4225.2.a.ba \(3\) \(33.737\) 3.3.148.1 None \(-3\) \(4\) \(0\) \(-2\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{2}+(1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
4225.2.a.bb \(3\) \(33.737\) \(\Q(\zeta_{14})^+\) None \(-2\) \(2\) \(0\) \(-3\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
4225.2.a.bc \(3\) \(33.737\) 3.3.564.1 None \(-1\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
4225.2.a.bd \(3\) \(33.737\) \(\Q(\zeta_{14})^+\) None \(-1\) \(5\) \(0\) \(-5\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
4225.2.a.be \(3\) \(33.737\) 3.3.564.1 None \(1\) \(2\) \(0\) \(2\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
4225.2.a.bf \(3\) \(33.737\) \(\Q(\zeta_{14})^+\) None \(1\) \(5\) \(0\) \(5\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
4225.2.a.bg \(3\) \(33.737\) \(\Q(\zeta_{14})^+\) None \(2\) \(2\) \(0\) \(3\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
4225.2.a.bh \(3\) \(33.737\) 3.3.148.1 None \(3\) \(-4\) \(0\) \(2\) \(-\) \(+\) \(q+(1+\beta _{2})q^{2}+(-1-\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
4225.2.a.bi \(4\) \(33.737\) 4.4.4752.1 None \(-2\) \(2\) \(0\) \(-10\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
4225.2.a.bj \(4\) \(33.737\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(-4\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
4225.2.a.bk \(4\) \(33.737\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(4\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{3}q^{2}+q^{3}-\beta _{2}q^{4}+\beta _{3}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
4225.2.a.bl \(4\) \(33.737\) 4.4.4752.1 None \(2\) \(2\) \(0\) \(10\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
4225.2.a.bm \(5\) \(33.737\) 5.5.1068321.1 None \(0\) \(-3\) \(0\) \(-2\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4225.2.a.bn \(5\) \(33.737\) 5.5.1068321.1 None \(0\) \(-3\) \(0\) \(2\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4225.2.a.bo \(5\) \(33.737\) 5.5.1068321.1 None \(0\) \(3\) \(0\) \(2\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4225.2.a.bp \(5\) \(33.737\) 5.5.1068321.1 None \(0\) \(3\) \(0\) \(-2\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4225.2.a.bq \(6\) \(33.737\) 6.6.199374400.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
4225.2.a.br \(6\) \(33.737\) 6.6.199374400.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4225.2.a.bs \(9\) \(33.737\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(-7\) \(0\) \(-7\) \(+\) \(+\) \(q+(-\beta _{1}-\beta _{6})q^{2}+(-1+\beta _{4})q^{3}+(2+\cdots)q^{4}+\cdots\)
4225.2.a.bt \(9\) \(33.737\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(-7\) \(0\) \(7\) \(+\) \(-\) \(q+(\beta _{1}+\beta _{6})q^{2}+(-1+\beta _{4})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots\)
4225.2.a.bu \(10\) \(33.737\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(-1-\beta _{7})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4225.2.a.bv \(10\) \(33.737\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(6\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{7})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4225.2.a.bw \(12\) \(33.737\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(-1\) \(0\) \(-12\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+\beta _{7}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
4225.2.a.bx \(12\) \(33.737\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(1\) \(0\) \(-12\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}-\beta _{7}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
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