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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 13
6760.2.a.a \(1\) \(53.979\) \(\Q\) None \(0\) \(-3\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(q-3q^{3}-q^{5}+3q^{7}+6q^{9}+5q^{11}+\cdots\)
6760.2.a.b \(1\) \(53.979\) \(\Q\) None \(0\) \(-3\) \(1\) \(-3\) \(-\) \(-\) \(+\) \(q-3q^{3}+q^{5}-3q^{7}+6q^{9}-5q^{11}+\cdots\)
6760.2.a.c \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}-3q^{7}-2q^{9}-3q^{11}+\cdots\)
6760.2.a.d \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}+q^{15}+\cdots\)
6760.2.a.e \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots\)
6760.2.a.f \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) \(-\) \(-\) \(+\) \(q-q^{3}+q^{5}-3q^{7}-2q^{9}+5q^{11}+\cdots\)
6760.2.a.g \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(1\) \(3\) \(-\) \(-\) \(+\) \(q-q^{3}+q^{5}+3q^{7}-2q^{9}-q^{11}-q^{15}+\cdots\)
6760.2.a.h \(1\) \(53.979\) \(\Q\) None \(0\) \(-1\) \(1\) \(3\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+3q^{7}-2q^{9}+3q^{11}+\cdots\)
6760.2.a.i \(1\) \(53.979\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(q-q^{5}+4q^{7}-3q^{9}-4q^{11}+2q^{17}+\cdots\)
6760.2.a.j \(1\) \(53.979\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{5}-3q^{9}+4q^{11}-6q^{17}-4q^{19}+\cdots\)
6760.2.a.k \(1\) \(53.979\) \(\Q\) None \(0\) \(2\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{3}-q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots\)
6760.2.a.l \(1\) \(53.979\) \(\Q\) None \(0\) \(2\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(q+2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
6760.2.a.m \(1\) \(53.979\) \(\Q\) None \(0\) \(2\) \(1\) \(-3\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
6760.2.a.n \(2\) \(53.979\) \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(q+(-2+\beta )q^{3}-q^{5}+2q^{7}+(3-4\beta )q^{9}+\cdots\)
6760.2.a.o \(2\) \(53.979\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
6760.2.a.p \(2\) \(53.979\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
6760.2.a.q \(2\) \(53.979\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{3}-q^{5}-q^{7}+(1+\beta )q^{9}+3q^{11}+\cdots\)
6760.2.a.r \(2\) \(53.979\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(2\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-3q^{11}+\cdots\)
6760.2.a.s \(2\) \(53.979\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta q^{3}-q^{5}-2q^{7}+3q^{9}+(2-\beta )q^{11}+\cdots\)
6760.2.a.t \(2\) \(53.979\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{3}+q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots\)
6760.2.a.u \(3\) \(53.979\) 3.3.148.1 None \(0\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
6760.2.a.v \(3\) \(53.979\) 3.3.148.1 None \(0\) \(0\) \(3\) \(2\) \(+\) \(-\) \(-\) \(q-\beta _{2}q^{3}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.w \(3\) \(53.979\) 3.3.1016.1 None \(0\) \(1\) \(-3\) \(9\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}-q^{5}+3q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
6760.2.a.x \(3\) \(53.979\) 3.3.1016.1 None \(0\) \(1\) \(3\) \(-9\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}-3q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
6760.2.a.y \(3\) \(53.979\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-3\) \(-1\) \(+\) \(+\) \(+\) \(q+(1-\beta _{1}-\beta _{2})q^{3}-q^{5}+\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots\)
6760.2.a.z \(3\) \(53.979\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{3}+q^{5}-\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots\)
6760.2.a.ba \(4\) \(53.979\) 4.4.25488.1 None \(0\) \(0\) \(-4\) \(4\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bb \(4\) \(53.979\) 4.4.25488.1 None \(0\) \(0\) \(4\) \(-4\) \(+\) \(-\) \(+\) \(q-\beta _{2}q^{3}+q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
6760.2.a.bc \(4\) \(53.979\) 4.4.34868.1 None \(0\) \(2\) \(-4\) \(-6\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
6760.2.a.bd \(4\) \(53.979\) 4.4.34868.1 None \(0\) \(2\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
6760.2.a.be \(6\) \(53.979\) 6.6.406193977.1 None \(0\) \(-2\) \(-6\) \(-1\) \(+\) \(+\) \(+\) \(q-\beta _{3}q^{3}-q^{5}-\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
6760.2.a.bf \(6\) \(53.979\) 6.6.406193977.1 None \(0\) \(-2\) \(6\) \(1\) \(-\) \(-\) \(-\) \(q-\beta _{3}q^{3}+q^{5}+\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
6760.2.a.bg \(6\) \(53.979\) 6.6.7674048.1 None \(0\) \(0\) \(-6\) \(-4\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
6760.2.a.bh \(6\) \(53.979\) 6.6.2249737.1 None \(0\) \(0\) \(-6\) \(2\) \(-\) \(+\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{3}-q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bi \(6\) \(53.979\) 6.6.2249737.1 None \(0\) \(0\) \(6\) \(-2\) \(+\) \(-\) \(-\) \(q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bj \(6\) \(53.979\) 6.6.7674048.1 None \(0\) \(0\) \(6\) \(4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(\beta _{1}-\beta _{4}+\beta _{5})q^{7}+\cdots\)
6760.2.a.bk \(8\) \(53.979\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(-8\) \(-6\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{5})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.bl \(8\) \(53.979\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(8\) \(6\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(1-\beta _{5})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.bm \(9\) \(53.979\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(1\) \(-9\) \(7\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{8})q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bn \(9\) \(53.979\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(1\) \(9\) \(-7\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}+(-1+\beta _{2}-\beta _{8})q^{7}+\cdots\)
6760.2.a.bo \(12\) \(53.979\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-12\) \(-7\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{10})q^{7}+(2+\cdots)q^{9}+\cdots\)
6760.2.a.bp \(12\) \(53.979\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(12\) \(7\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{10})q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots\)
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