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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
980.1.f.a \(1\) \(0.489\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
980.1.f.b \(1\) \(0.489\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(-1\) \(1\) \(1\) \(0\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
980.1.f.c \(1\) \(0.489\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(1\) \(-1\) \(1\) \(0\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
980.1.f.d \(1\) \(0.489\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
980.1.f.e \(4\) \(0.489\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{8}+\cdots\)
980.1.j.a \(8\) \(0.489\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{4}+\zeta_{16}^{5}q^{5}+\cdots\)
980.1.l.a \(4\) \(0.489\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}-q^{11}-\zeta_{8}q^{13}+\cdots\)
980.1.n.a \(2\) \(0.489\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+q^{13}+\cdots\)
980.1.n.b \(2\) \(0.489\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-q^{13}+\cdots\)
980.1.p.a \(2\) \(0.489\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
980.1.p.b \(2\) \(0.489\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
980.1.p.c \(8\) \(0.489\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots\)
980.1.w.a \(8\) \(0.489\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{11}+\cdots\)
980.1.y.a \(16\) \(0.489\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{2}q^{2}+\zeta_{48}^{4}q^{4}+\zeta_{48}^{5}q^{5}+\cdots\)
980.1.ba.a \(6\) \(0.489\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(5\) \(-1\) \(-1\) \(q-\zeta_{14}q^{2}+(1+\zeta_{14}^{6})q^{3}+\zeta_{14}^{2}q^{4}+\cdots\)
980.1.ba.b \(6\) \(0.489\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-5}) \) None \(1\) \(-5\) \(-1\) \(1\) \(q+\zeta_{14}q^{2}+(-1-\zeta_{14}^{6})q^{3}+\zeta_{14}^{2}q^{4}+\cdots\)
980.1.bq.a \(12\) \(0.489\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(8\) \(1\) \(-1\) \(q-\zeta_{42}^{4}q^{2}+(\zeta_{42}^{3}+\zeta_{42}^{7})q^{3}+\zeta_{42}^{8}q^{4}+\cdots\)
980.1.bq.b \(12\) \(0.489\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-5}) \) None \(1\) \(-8\) \(1\) \(1\) \(q+\zeta_{42}^{4}q^{2}+(-\zeta_{42}^{3}-\zeta_{42}^{7})q^{3}+\cdots\)
980.2.a.a \(1\) \(7.825\) \(\Q\) None None \(0\) \(-3\) \(-1\) \(0\) \(-\) \(q-3q^{3}-q^{5}+6q^{9}-2q^{11}-6q^{13}+\cdots\)
980.2.a.b \(1\) \(7.825\) \(\Q\) None None \(0\) \(-3\) \(1\) \(0\) \(-\) \(q-3q^{3}+q^{5}+6q^{9}-5q^{11}+3q^{13}+\cdots\)
980.2.a.c \(1\) \(7.825\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(q-q^{3}-q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots\)
980.2.a.d \(1\) \(7.825\) \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) \(-\) \(q-q^{3}+q^{5}-2q^{9}-q^{11}+5q^{13}+\cdots\)
980.2.a.e \(1\) \(7.825\) \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) \(-\) \(q-q^{3}+q^{5}-2q^{9}+6q^{11}-2q^{13}+\cdots\)
980.2.a.f \(1\) \(7.825\) \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) \(+\) \(q+q^{3}-q^{5}-2q^{9}-q^{11}-5q^{13}+\cdots\)
980.2.a.g \(1\) \(7.825\) \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) \(-\) \(q+q^{3}-q^{5}-2q^{9}+6q^{11}+2q^{13}+\cdots\)
980.2.a.h \(1\) \(7.825\) \(\Q\) None None \(0\) \(2\) \(1\) \(0\) \(-\) \(q+2q^{3}+q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
980.2.a.i \(1\) \(7.825\) \(\Q\) None None \(0\) \(3\) \(1\) \(0\) \(-\) \(q+3q^{3}+q^{5}+6q^{9}-2q^{11}+6q^{13}+\cdots\)
980.2.a.j \(2\) \(7.825\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(2\) \(0\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-1+\cdots)q^{11}+\cdots\)
980.2.a.k \(2\) \(7.825\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(0\) \(-\) \(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-1+2\beta )q^{11}+\cdots\)
980.2.c.a \(8\) \(7.825\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}-2q^{4}-\zeta_{16}^{4}q^{5}+2\zeta_{16}^{2}q^{8}+\cdots\)
980.2.c.b \(8\) \(7.825\) 8.0.3317760000.3 \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{6}q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots\)
980.2.c.c \(16\) \(7.825\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(-\beta _{8}-\beta _{10}-\beta _{12})q^{3}+\cdots\)
980.2.c.d \(32\) \(7.825\) None None \(0\) \(0\) \(0\) \(0\)
980.2.c.e \(48\) \(7.825\) None None \(0\) \(0\) \(0\) \(0\)
980.2.e.a \(2\) \(7.825\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+3q^{9}+2iq^{13}-2iq^{17}+\cdots\)
980.2.e.b \(2\) \(7.825\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) \(q+3iq^{3}+(2+i)q^{5}-6q^{9}+3q^{11}+\cdots\)
980.2.e.c \(4\) \(7.825\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(0\) \(-1\) \(0\) \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots\)
980.2.e.d \(4\) \(7.825\) \(\Q(\sqrt{-5}, \sqrt{-21})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-4+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
980.2.e.e \(4\) \(7.825\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{11}-\beta _{2}q^{13}+\cdots\)
980.2.e.f \(4\) \(7.825\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(0\) \(1\) \(0\) \(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots\)
980.2.g.a \(32\) \(7.825\) None None \(-4\) \(0\) \(0\) \(0\)
980.2.g.b \(48\) \(7.825\) None None \(8\) \(0\) \(0\) \(0\)
980.2.i.a \(2\) \(7.825\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-1\) \(0\) \(q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
980.2.i.b \(2\) \(7.825\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(1\) \(0\) \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
980.2.i.c \(2\) \(7.825\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-1\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
980.2.i.d \(2\) \(7.825\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
980.2.i.e \(2\) \(7.825\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
980.2.i.f \(2\) \(7.825\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
980.2.i.g \(2\) \(7.825\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
980.2.i.h \(2\) \(7.825\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
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