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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1600.1.b.a \(1\) \(0.799\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}+2q^{29}-2q^{41}+q^{49}+2q^{61}+\cdots\)
1600.1.m.a \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}-iq^{11}-q^{19}+q^{41}-iq^{49}+\cdots\)
1600.1.m.b \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+iq^{11}+q^{19}+q^{41}-iq^{49}+\cdots\)
1600.1.m.c \(4\) \(0.799\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+2\beta _{2}q^{9}-\beta _{2}q^{11}-\beta _{1}q^{17}+\cdots\)
1600.1.m.d \(4\) \(0.799\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+2\beta _{2}q^{9}+\beta _{2}q^{11}+\beta _{1}q^{17}+\cdots\)
1600.1.p.a \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(-2\) \(q+(-1+i)q^{3}+(-1-i)q^{7}-iq^{9}+\cdots\)
1600.1.p.b \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{9}+(-1+i)q^{13}+(1+i)q^{17}+\cdots\)
1600.1.p.c \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(2\) \(q+(1-i)q^{3}+(1+i)q^{7}-iq^{9}+q^{21}+\cdots\)
1600.1.bd.a \(8\) \(0.799\) \(\Q(\zeta_{20})\) None None \(0\) \(-6\) \(0\) \(0\) \(q+(-1+\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}+\zeta_{20}^{5}q^{7}+\cdots\)
1600.1.bd.b \(8\) \(0.799\) \(\Q(\zeta_{20})\) None None \(0\) \(6\) \(0\) \(0\) \(q+(1-\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}-\zeta_{20}^{5}q^{7}+\cdots\)
1600.1.bf.a \(4\) \(0.799\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}q^{5}+\zeta_{10}^{3}q^{9}+(\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{13}+\cdots\)
1600.1.bh.a \(4\) \(0.799\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
1600.1.bh.b \(8\) \(0.799\) \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{20}^{9}q^{3}-\zeta_{20}^{8}q^{5}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{7}+\cdots\)
1600.1.bw.a \(8\) \(0.799\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{3}q^{5}-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{13}+\cdots\)
1600.2.a.a \(1\) \(12.776\) \(\Q\) None None \(0\) \(-3\) \(0\) \(-2\) \(+\) \(q-3q^{3}-2q^{7}+6q^{9}-q^{11}+4q^{13}+\cdots\)
1600.2.a.b \(1\) \(12.776\) \(\Q\) None None \(0\) \(-3\) \(0\) \(-2\) \(+\) \(q-3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots\)
1600.2.a.c \(1\) \(12.776\) \(\Q\) None None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(q-2q^{3}-2q^{7}+q^{9}+2q^{13}+6q^{17}+\cdots\)
1600.2.a.d \(1\) \(12.776\) \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) \(+\) \(q-2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
1600.2.a.e \(1\) \(12.776\) \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) \(+\) \(q-2q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1600.2.a.f \(1\) \(12.776\) \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) \(-\) \(q-2q^{3}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
1600.2.a.g \(1\) \(12.776\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(q-q^{3}-2q^{7}-2q^{9}-5q^{11}+5q^{17}+\cdots\)
1600.2.a.h \(1\) \(12.776\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(q-q^{3}-2q^{7}-2q^{9}+5q^{11}-5q^{17}+\cdots\)
1600.2.a.i \(1\) \(12.776\) \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) \(-\) \(q-q^{3}+2q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots\)
1600.2.a.j \(1\) \(12.776\) \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) \(-\) \(q-q^{3}+2q^{7}-2q^{9}+3q^{11}+4q^{13}+\cdots\)
1600.2.a.k \(1\) \(12.776\) \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) \(-\) \(q-4q^{7}-3q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
1600.2.a.l \(1\) \(12.776\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-3q^{9}-4q^{13}+8q^{17}-10q^{29}+\cdots\)
1600.2.a.m \(1\) \(12.776\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-3q^{9}+4q^{13}-8q^{17}-10q^{29}+\cdots\)
1600.2.a.n \(1\) \(12.776\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-3q^{9}+6q^{13}-2q^{17}+10q^{29}+\cdots\)
1600.2.a.o \(1\) \(12.776\) \(\Q\) None None \(0\) \(0\) \(0\) \(4\) \(+\) \(q+4q^{7}-3q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
1600.2.a.p \(1\) \(12.776\) \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) \(+\) \(q+q^{3}-2q^{7}-2q^{9}-3q^{11}+4q^{13}+\cdots\)
1600.2.a.q \(1\) \(12.776\) \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) \(+\) \(q+q^{3}-2q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots\)
1600.2.a.r \(1\) \(12.776\) \(\Q\) None None \(0\) \(1\) \(0\) \(2\) \(+\) \(q+q^{3}+2q^{7}-2q^{9}-5q^{11}-5q^{17}+\cdots\)
1600.2.a.s \(1\) \(12.776\) \(\Q\) None None \(0\) \(1\) \(0\) \(2\) \(-\) \(q+q^{3}+2q^{7}-2q^{9}+5q^{11}+5q^{17}+\cdots\)
1600.2.a.t \(1\) \(12.776\) \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) \(+\) \(q+2q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1600.2.a.u \(1\) \(12.776\) \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) \(+\) \(q+2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
1600.2.a.v \(1\) \(12.776\) \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) \(-\) \(q+2q^{3}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
1600.2.a.w \(1\) \(12.776\) \(\Q\) None None \(0\) \(2\) \(0\) \(2\) \(-\) \(q+2q^{3}+2q^{7}+q^{9}+2q^{13}+6q^{17}+\cdots\)
1600.2.a.x \(1\) \(12.776\) \(\Q\) None None \(0\) \(3\) \(0\) \(2\) \(-\) \(q+3q^{3}+2q^{7}+6q^{9}-q^{11}-4q^{13}+\cdots\)
1600.2.a.y \(1\) \(12.776\) \(\Q\) None None \(0\) \(3\) \(0\) \(2\) \(-\) \(q+3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots\)
1600.2.a.z \(2\) \(12.776\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(6\) \(-\) \(q+(-1-\beta )q^{3}+(3-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
1600.2.a.ba \(2\) \(12.776\) \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-\beta q^{3}+2\beta q^{7}+2q^{9}-\beta q^{11}-4q^{13}+\cdots\)
1600.2.a.bb \(2\) \(12.776\) \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta q^{3}+2\beta q^{7}+2q^{9}+\beta q^{11}+4q^{13}+\cdots\)
1600.2.a.bc \(2\) \(12.776\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{3}+\beta q^{7}+5q^{9}+2\beta q^{11}-2q^{13}+\cdots\)
1600.2.a.bd \(2\) \(12.776\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(-6\) \(-\) \(q+(1+\beta )q^{3}+(-3+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
1600.2.c.a \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-2iq^{7}-6q^{9}-q^{11}-4iq^{13}+\cdots\)
1600.2.c.b \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-2iq^{7}-6q^{9}+q^{11}+4iq^{13}+\cdots\)
1600.2.c.c \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}-4q^{11}-3iq^{13}+\cdots\)
1600.2.c.d \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}-q^{9}-iq^{13}+3iq^{17}+\cdots\)
1600.2.c.e \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}-q^{9}+iq^{13}-3iq^{17}+\cdots\)
1600.2.c.f \(2\) \(12.776\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}+4q^{11}+3iq^{13}+\cdots\)
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