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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3800.1.b.a \(2\) \(1.896\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-38}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}-iq^{7}+iq^{8}+\cdots\)
3800.1.b.b \(2\) \(1.896\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-38}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
3800.1.b.c \(6\) \(1.896\) 6.0.419904.1 \(\Q(\sqrt{-38}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{4}q^{6}+\beta _{1}q^{7}+\cdots\)
3800.1.b.d \(6\) \(1.896\) 6.0.419904.1 \(\Q(\sqrt{-38}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{5})q^{3}-q^{4}-\beta _{2}q^{6}+\cdots\)
3800.1.o.a \(1\) \(1.896\) \(\Q\) \(\Q(\sqrt{-38}) \) None \(-1\) \(1\) \(0\) \(1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
3800.1.o.b \(1\) \(1.896\) \(\Q\) \(\Q(\sqrt{-38}) \) None \(1\) \(-1\) \(0\) \(1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
3800.1.o.c \(3\) \(1.896\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-38}) \) None \(-3\) \(0\) \(0\) \(0\) \(q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots\)
3800.1.o.d \(3\) \(1.896\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-38}) \) None \(-3\) \(0\) \(0\) \(0\) \(q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots\)
3800.1.o.e \(3\) \(1.896\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-38}) \) None \(3\) \(0\) \(0\) \(0\) \(q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots\)
3800.1.o.f \(3\) \(1.896\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-38}) \) None \(3\) \(0\) \(0\) \(0\) \(q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots\)
3800.1.o.g \(8\) \(1.896\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)
3800.1.y.a \(2\) \(1.896\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-95}) \) None \(-2\) \(-2\) \(0\) \(0\) \(q-q^{2}+(-1-i)q^{3}+q^{4}+(1+i)q^{6}+\cdots\)
3800.1.y.b \(2\) \(1.896\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-95}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}+(-1-i)q^{3}-q^{4}+(1-i+\cdots)q^{6}+\cdots\)
3800.1.y.c \(2\) \(1.896\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-95}) \) None \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+(1+i)q^{3}-q^{4}+(1-i)q^{6}+\cdots\)
3800.1.y.d \(2\) \(1.896\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-95}) \) None \(2\) \(2\) \(0\) \(0\) \(q+q^{2}+(1+i)q^{3}+q^{4}+(1+i)q^{6}+\cdots\)
3800.1.y.e \(4\) \(1.896\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{190}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-2q^{6}+\cdots\)
3800.1.y.f \(4\) \(1.896\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{38}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}+\zeta_{8}^{2}q^{9}+\cdots\)
3800.1.y.g \(8\) \(1.896\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{6}q^{4}+\cdots\)
3800.1.bd.a \(2\) \(1.896\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-2\zeta_{6}q^{6}+\cdots\)
3800.1.bd.b \(2\) \(1.896\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.c \(2\) \(1.896\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.d \(2\) \(1.896\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.e \(2\) \(1.896\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(2\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-2\zeta_{6}q^{6}+\cdots\)
3800.1.bd.f \(4\) \(1.896\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{7}+\cdots\)
3800.1.bn.a \(4\) \(1.896\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
3800.1.bn.b \(4\) \(1.896\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
3800.1.bn.c \(4\) \(1.896\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
3800.1.cj.a \(4\) \(1.896\) \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{4})q^{3}-\zeta_{12}^{5}q^{9}+q^{11}+\cdots\)
3800.1.cj.b \(4\) \(1.896\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{9}-q^{11}+(-\zeta_{12}^{2}-\zeta_{12}^{5}+\cdots)q^{13}+\cdots\)
3800.1.cj.c \(4\) \(1.896\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{9}-q^{11}+(\zeta_{12}^{2}+\zeta_{12}^{5}+\cdots)q^{13}+\cdots\)
3800.1.ck.a \(8\) \(1.896\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{8}q^{6}+\cdots\)
3800.1.ck.b \(8\) \(1.896\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{8}q^{6}+\cdots\)
3800.1.ck.c \(8\) \(1.896\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
3800.1.ck.d \(8\) \(1.896\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{2}q^{4}-2\zeta_{24}^{8}q^{6}+\cdots\)
3800.1.cq.a \(12\) \(1.896\) \(\Q(\zeta_{36})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}q^{2}+(-\zeta_{36}^{11}-\zeta_{36}^{15})q^{3}+\cdots\)
3800.1.cq.b \(12\) \(1.896\) \(\Q(\zeta_{36})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}q^{2}+(\zeta_{36}^{3}-\zeta_{36}^{5})q^{3}+\zeta_{36}^{2}q^{4}+\cdots\)
3800.1.cq.c \(12\) \(1.896\) \(\Q(\zeta_{36})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}q^{2}+(-\zeta_{36}^{9}-\zeta_{36}^{17})q^{3}+\cdots\)
3800.1.cv.a \(6\) \(1.896\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-6\) \(0\) \(0\) \(q+\zeta_{18}^{5}q^{2}+(-1-\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots\)
3800.1.cv.b \(6\) \(1.896\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-3\) \(0\) \(0\) \(q-\zeta_{18}^{5}q^{2}+(-\zeta_{18}-\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots\)
3800.1.cv.c \(6\) \(1.896\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(3\) \(0\) \(0\) \(q+\zeta_{18}^{5}q^{2}+(-\zeta_{18}^{6}+\zeta_{18}^{7})q^{3}+\cdots\)
3800.1.cv.d \(6\) \(1.896\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(3\) \(0\) \(0\) \(q+\zeta_{18}^{5}q^{2}+(\zeta_{18}+\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots\)
3800.1.cv.e \(6\) \(1.896\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(6\) \(0\) \(0\) \(q-\zeta_{18}^{5}q^{2}+(1+\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots\)
3800.1.cv.f \(12\) \(1.896\) \(\Q(\zeta_{36})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(-\zeta_{36}^{13}-\zeta_{36}^{17}+\cdots)q^{7}+\cdots\)
3800.1.eb.a \(24\) \(1.896\) \(\Q(\zeta_{72})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{72}^{31}q^{2}+(\zeta_{72}^{5}-\zeta_{72}^{9})q^{3}-\zeta_{72}^{26}q^{4}+\cdots\)
3800.1.eb.b \(24\) \(1.896\) \(\Q(\zeta_{72})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{72}^{13}q^{2}+\zeta_{72}^{26}q^{4}+(-\zeta_{72}^{5}+\cdots)q^{7}+\cdots\)
3800.1.eb.c \(24\) \(1.896\) \(\Q(\zeta_{72})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{72}^{31}q^{2}+(\zeta_{72}^{17}+\zeta_{72}^{33})q^{3}+\cdots\)
3800.1.eb.d \(24\) \(1.896\) \(\Q(\zeta_{72})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{72}^{31}q^{2}+(\zeta_{72}^{21}+\zeta_{72}^{29})q^{3}+\cdots\)
3800.2.a.a \(1\) \(30.343\) \(\Q\) None None \(0\) \(-3\) \(0\) \(1\) \(-\) \(q-3q^{3}+q^{7}+6q^{9}+4q^{11}-q^{13}+\cdots\)
3800.2.a.b \(1\) \(30.343\) \(\Q\) None None \(0\) \(-2\) \(0\) \(-4\) \(-\) \(q-2q^{3}-4q^{7}+q^{9}-4q^{11}-6q^{17}+\cdots\)
3800.2.a.c \(1\) \(30.343\) \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) \(-\) \(q-2q^{3}+2q^{7}+q^{9}+4q^{11}+8q^{17}+\cdots\)
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