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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3332.1.g.a \(1\) \(1.663\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}-q^{9}+2q^{13}+q^{16}+\cdots\)
3332.1.g.b \(1\) \(1.663\) \(\Q\) \(\Q(\sqrt{-17}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots\)
3332.1.g.c \(1\) \(1.663\) \(\Q\) \(\Q(\sqrt{-17}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{11}+\cdots\)
3332.1.g.d \(1\) \(1.663\) \(\Q\) \(\Q(\sqrt{-17}) \) None \(1\) \(1\) \(0\) \(0\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-q^{11}+\cdots\)
3332.1.g.e \(1\) \(1.663\) \(\Q\) \(\Q(\sqrt{-17}) \) None \(1\) \(1\) \(0\) \(0\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{11}+\cdots\)
3332.1.g.f \(2\) \(1.663\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-17}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+2q^{9}+\cdots\)
3332.1.g.g \(2\) \(1.663\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-17}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+2q^{9}+\cdots\)
3332.1.g.h \(2\) \(1.663\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-119}) \) \(\Q(\sqrt{119}) \) \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-iq^{5}+q^{8}-q^{9}-2iq^{10}+\cdots\)
3332.1.g.i \(8\) \(1.663\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-119}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{6}q^{2}+(\zeta_{20}-\zeta_{20}^{9})q^{3}-\zeta_{20}^{2}q^{4}+\cdots\)
3332.1.m.a \(2\) \(1.663\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{2}-q^{4}+(-1-i)q^{5}+iq^{8}+\cdots\)
3332.1.m.b \(2\) \(1.663\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-q^{4}+(1+i)q^{5}-iq^{8}+iq^{9}+\cdots\)
3332.1.m.c \(2\) \(1.663\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-q^{4}+(1+i)q^{5}+iq^{8}+iq^{9}+\cdots\)
3332.1.o.a \(2\) \(1.663\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-17}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}+q^{8}+\cdots\)
3332.1.o.b \(2\) \(1.663\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-17}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{8}+\cdots\)
3332.1.o.c \(2\) \(1.663\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}^{2}q^{9}+\cdots\)
3332.1.o.d \(2\) \(1.663\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}^{2}q^{9}+\cdots\)
3332.1.o.e \(4\) \(1.663\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-119}) \) \(\Q(\sqrt{119}) \) \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
3332.1.o.f \(4\) \(1.663\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-17}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots\)
3332.1.o.g \(16\) \(1.663\) \(\Q(\zeta_{60})\) \(\Q(\sqrt{-119}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{60}^{4}q^{2}+(-\zeta_{60}^{11}-\zeta_{60}^{29})q^{3}+\cdots\)
3332.1.w.a \(4\) \(1.663\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{5}+\cdots\)
3332.1.w.b \(4\) \(1.663\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\)
3332.1.w.c \(4\) \(1.663\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\)
3332.1.w.d \(4\) \(1.663\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{3})q^{5}-\zeta_{8}^{3}q^{8}+\cdots\)
3332.1.bc.a \(4\) \(1.663\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3332.1.bc.b \(4\) \(1.663\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3332.1.bc.c \(4\) \(1.663\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3332.1.bc.d \(4\) \(1.663\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3332.1.be.a \(6\) \(1.663\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-17}) \) None \(-1\) \(-5\) \(0\) \(1\) \(q+\zeta_{14}^{4}q^{2}+(-1+\zeta_{14}^{3})q^{3}-\zeta_{14}q^{4}+\cdots\)
3332.1.be.b \(6\) \(1.663\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-17}) \) None \(-1\) \(5\) \(0\) \(-1\) \(q+\zeta_{14}^{4}q^{2}+(1-\zeta_{14}^{3})q^{3}-\zeta_{14}q^{4}+\cdots\)
3332.1.be.c \(12\) \(1.663\) \(\Q(\zeta_{28})\) \(\Q(\sqrt{-17}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{28}^{8}q^{2}+(\zeta_{28}^{7}+\zeta_{28}^{13})q^{3}-\zeta_{28}^{2}q^{4}+\cdots\)
3332.1.bn.a \(8\) \(1.663\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(-\zeta_{16}^{2}+\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
3332.1.bn.b \(8\) \(1.663\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(-\zeta_{16}+\zeta_{16}^{6}+\cdots)q^{5}+\cdots\)
3332.1.bn.c \(8\) \(1.663\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
3332.1.bn.d \(8\) \(1.663\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(\zeta_{16}-\zeta_{16}^{6}+\cdots)q^{5}+\cdots\)
3332.1.bp.a \(8\) \(1.663\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
3332.1.bp.b \(8\) \(1.663\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{7}-\zeta_{24}^{10}+\cdots)q^{5}+\cdots\)
3332.1.bp.c \(8\) \(1.663\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}^{7}+\zeta_{24}^{10}+\cdots)q^{5}+\cdots\)
3332.1.bp.d \(8\) \(1.663\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
3332.1.cc.a \(12\) \(1.663\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-17}) \) None \(1\) \(-13\) \(0\) \(2\) \(q-\zeta_{42}^{17}q^{2}+(-1+\zeta_{42}^{11})q^{3}-\zeta_{42}^{13}q^{4}+\cdots\)
3332.1.cc.b \(12\) \(1.663\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-17}) \) None \(1\) \(13\) \(0\) \(-2\) \(q-\zeta_{42}^{17}q^{2}+(1-\zeta_{42}^{11})q^{3}-\zeta_{42}^{13}q^{4}+\cdots\)
3332.1.cc.c \(24\) \(1.663\) \(\Q(\zeta_{84})\) \(\Q(\sqrt{-17}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{84}^{40}q^{2}+(\zeta_{84}^{21}-\zeta_{84}^{37})q^{3}+\cdots\)
3332.1.ce.a \(16\) \(1.663\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}q^{2}+\zeta_{48}^{2}q^{4}+(\zeta_{48}^{13}-\zeta_{48}^{22}+\cdots)q^{5}+\cdots\)
3332.1.ce.b \(16\) \(1.663\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}q^{2}+\zeta_{48}^{2}q^{4}+(-\zeta_{48}-\zeta_{48}^{10}+\cdots)q^{5}+\cdots\)
3332.1.ce.c \(16\) \(1.663\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}q^{2}+\zeta_{48}^{2}q^{4}+(-\zeta_{48}^{13}+\zeta_{48}^{22}+\cdots)q^{5}+\cdots\)
3332.1.ce.d \(16\) \(1.663\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}q^{2}+\zeta_{48}^{2}q^{4}+(\zeta_{48}+\zeta_{48}^{10}+\cdots)q^{5}+\cdots\)
3332.2.a.a \(1\) \(26.606\) \(\Q\) None None \(0\) \(-3\) \(4\) \(0\) \(-\) \(q-3q^{3}+4q^{5}+6q^{9}+q^{11}+3q^{13}+\cdots\)
3332.2.a.b \(1\) \(26.606\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(-\) \(q-q^{3}-2q^{9}-5q^{11}-5q^{13}-q^{17}+\cdots\)
3332.2.a.c \(1\) \(26.606\) \(\Q\) None None \(0\) \(-1\) \(4\) \(0\) \(-\) \(q-q^{3}+4q^{5}-2q^{9}-3q^{11}+5q^{13}+\cdots\)
3332.2.a.d \(1\) \(26.606\) \(\Q\) None None \(0\) \(1\) \(-4\) \(0\) \(-\) \(q+q^{3}-4q^{5}-2q^{9}-3q^{11}-5q^{13}+\cdots\)
3332.2.a.e \(1\) \(26.606\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(-\) \(q+q^{3}-2q^{9}-5q^{11}+5q^{13}+q^{17}+\cdots\)
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