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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 7
9800.2.a.a \(1\) \(78.253\) \(\Q\) None \(0\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+6q^{9}-5q^{11}-5q^{13}-7q^{17}+\cdots\)
9800.2.a.b \(1\) \(78.253\) \(\Q\) None \(0\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-3q^{3}+6q^{9}-q^{11}-2q^{13}-3q^{17}+\cdots\)
9800.2.a.c \(1\) \(78.253\) \(\Q\) None \(0\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+6q^{9}+q^{11}+4q^{13}+5q^{17}+\cdots\)
9800.2.a.d \(1\) \(78.253\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{3}+q^{9}-4q^{11}-4q^{13}+4q^{19}+\cdots\)
9800.2.a.e \(1\) \(78.253\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{9}-3q^{11}+2q^{13}-4q^{17}+\cdots\)
9800.2.a.f \(1\) \(78.253\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{3}+q^{9}-3q^{11}+2q^{13}-4q^{17}+\cdots\)
9800.2.a.h \(1\) \(78.253\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{3}+q^{9}+q^{11}-4q^{13}-6q^{19}+\cdots\)
9800.2.a.k \(1\) \(78.253\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{3}+q^{9}+4q^{11}+2q^{13}+3q^{17}+\cdots\)
9800.2.a.n \(1\) \(78.253\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{9}-5q^{11}+q^{13}+3q^{17}+\cdots\)
9800.2.a.o \(1\) \(78.253\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{9}-2q^{11}+4q^{13}-6q^{19}+\cdots\)
9800.2.a.r \(1\) \(78.253\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{9}+2q^{11}-4q^{17}-2q^{19}+\cdots\)
9800.2.a.s \(1\) \(78.253\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{9}+3q^{11}-6q^{13}-5q^{17}+\cdots\)
9800.2.a.t \(1\) \(78.253\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{9}+3q^{11}+q^{13}-5q^{17}+\cdots\)
9800.2.a.v \(1\) \(78.253\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{9}+q^{11}-2q^{13}-4q^{17}+2q^{19}+\cdots\)
9800.2.a.w \(1\) \(78.253\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-3q^{9}+q^{11}+2q^{13}+4q^{17}+2q^{19}+\cdots\)
9800.2.a.x \(1\) \(78.253\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{9}+4q^{11}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
9800.2.a.bb \(1\) \(78.253\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{9}-q^{11}-q^{13}-3q^{17}+\cdots\)
9800.2.a.bd \(1\) \(78.253\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{9}+3q^{11}-q^{13}+5q^{17}+\cdots\)
9800.2.a.bg \(1\) \(78.253\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{3}+q^{9}-3q^{11}-2q^{13}+4q^{17}+\cdots\)
9800.2.a.bh \(1\) \(78.253\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{3}+q^{9}-3q^{11}-2q^{13}+4q^{17}+\cdots\)
9800.2.a.bi \(1\) \(78.253\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{3}+q^{9}-q^{11}+3q^{13}+2q^{17}+\cdots\)
9800.2.a.bj \(1\) \(78.253\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{3}+q^{9}-2q^{17}+2q^{19}-8q^{23}+\cdots\)
9800.2.a.bk \(1\) \(78.253\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{3}+q^{9}+q^{11}+4q^{13}-6q^{19}+\cdots\)
9800.2.a.bl \(1\) \(78.253\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{3}+q^{9}+4q^{11}-2q^{13}-3q^{17}+\cdots\)
9800.2.a.bq \(1\) \(78.253\) \(\Q\) None \(0\) \(3\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+6q^{9}+q^{11}-4q^{13}-5q^{17}+\cdots\)
9800.2.a.bs \(2\) \(78.253\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+(-1+\beta )q^{3}-2\beta q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
9800.2.a.bv \(2\) \(78.253\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta q^{3}-q^{9}+6q^{11}-4\beta q^{13}+\beta q^{17}+\cdots\)
9800.2.a.bw \(2\) \(78.253\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+\beta q^{3}+5q^{9}-4q^{11}-\beta q^{13}-2\beta q^{17}+\cdots\)
9800.2.a.bz \(2\) \(78.253\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{3}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots\)
9800.2.a.ca \(2\) \(78.253\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{3}+2\beta q^{9}-q^{11}+(1-\beta )q^{13}+\cdots\)
9800.2.a.cb \(3\) \(78.253\) \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+\cdots\)
9800.2.a.cd \(3\) \(78.253\) 3.3.568.1 None \(0\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(1+2\beta _{1}+\beta _{2})q^{9}+(2-\beta _{2})q^{11}+\cdots\)
9800.2.a.cf \(3\) \(78.253\) 3.3.1944.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
9800.2.a.ch \(3\) \(78.253\) \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+(-2+\cdots)q^{11}+\cdots\)
9800.2.a.cj \(4\) \(78.253\) 4.4.43449.1 None \(0\) \(-3\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots\)
9800.2.a.cm \(4\) \(78.253\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+\beta _{3}q^{9}-q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
9800.2.a.cn \(4\) \(78.253\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{3}+\beta _{3}q^{9}-q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
9800.2.a.co \(4\) \(78.253\) 4.4.13448.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9800.2.a.ct \(4\) \(78.253\) 4.4.43449.1 None \(0\) \(3\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+(1-\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
9800.2.a.cv \(6\) \(78.253\) 6.6.239575536.1 None \(0\) \(-1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
9800.2.a.cw \(6\) \(78.253\) 6.6.239575536.1 None \(0\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
9800.2.a.db \(10\) \(78.253\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{7}q^{3}+(1-\beta _{4}-\beta _{8})q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
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