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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 31
7440.2.a.a \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7440.2.a.b \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
7440.2.a.c \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
7440.2.a.d \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}-2q^{17}+\cdots\)
7440.2.a.e \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{15}+2q^{17}+\cdots\)
7440.2.a.f \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots\)
7440.2.a.g \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7440.2.a.h \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
7440.2.a.i \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}+6q^{17}+\cdots\)
7440.2.a.j \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
7440.2.a.k \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
7440.2.a.l \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.m \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.n \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.o \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7440.2.a.p \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-3q^{7}+q^{9}-5q^{11}-6q^{13}+\cdots\)
7440.2.a.q \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
7440.2.a.r \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+q^{9}+6q^{11}-2q^{13}+\cdots\)
7440.2.a.s \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-6q^{13}+\cdots\)
7440.2.a.t \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
7440.2.a.u \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
7440.2.a.v \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.w \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
7440.2.a.x \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.y \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.z \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}-4q^{17}+\cdots\)
7440.2.a.ba \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots\)
7440.2.a.bb \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7440.2.a.bc \(2\) \(59.409\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(-1+\beta )q^{7}+q^{9}+4q^{11}+\cdots\)
7440.2.a.bd \(2\) \(59.409\) \(\Q(\sqrt{65}) \) None \(0\) \(-2\) \(-2\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
7440.2.a.be \(2\) \(59.409\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}-2\beta q^{11}+\cdots\)
7440.2.a.bf \(2\) \(59.409\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-6\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(-3+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7440.2.a.bg \(2\) \(59.409\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
7440.2.a.bh \(2\) \(59.409\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(2+\beta )q^{7}+q^{9}-2\beta q^{11}+\cdots\)
7440.2.a.bi \(2\) \(59.409\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{13}+\cdots\)
7440.2.a.bj \(2\) \(59.409\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{13}+\cdots\)
7440.2.a.bk \(2\) \(59.409\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(6\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(3+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7440.2.a.bl \(2\) \(59.409\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+2q^{13}+\cdots\)
7440.2.a.bm \(3\) \(59.409\) 3.3.148.1 None \(0\) \(-3\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
7440.2.a.bn \(3\) \(59.409\) 3.3.404.1 None \(0\) \(-3\) \(-3\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(1-\beta _{2})q^{7}+q^{9}-2\beta _{2}q^{11}+\cdots\)
7440.2.a.bo \(3\) \(59.409\) 3.3.148.1 None \(0\) \(-3\) \(-3\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(1-\beta _{1})q^{7}+q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.bp \(3\) \(59.409\) 3.3.148.1 None \(0\) \(-3\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}-2q^{11}+\cdots\)
7440.2.a.bq \(3\) \(59.409\) 3.3.7636.1 None \(0\) \(-3\) \(3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}-2q^{11}+\cdots\)
7440.2.a.br \(3\) \(59.409\) 3.3.148.1 None \(0\) \(-3\) \(3\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(2\beta _{1}+\beta _{2})q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
7440.2.a.bs \(3\) \(59.409\) 3.3.564.1 None \(0\) \(3\) \(-3\) \(-8\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+(-3+\beta _{1})q^{7}+q^{9}-2\beta _{1}q^{11}+\cdots\)
7440.2.a.bt \(3\) \(59.409\) 3.3.564.1 None \(0\) \(3\) \(-3\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
7440.2.a.bu \(3\) \(59.409\) 3.3.404.1 None \(0\) \(3\) \(-3\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(1+\beta _{1})q^{7}+q^{9}-4q^{11}+\cdots\)
7440.2.a.bv \(3\) \(59.409\) 3.3.316.1 None \(0\) \(3\) \(3\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.bw \(3\) \(59.409\) 3.3.568.1 None \(0\) \(3\) \(3\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
7440.2.a.bx \(4\) \(59.409\) 4.4.78292.1 None \(0\) \(4\) \(-4\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
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