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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1001.1.r.a 1001.r 1001.r $4$ $0.500$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
1001.1.y.a 1001.y 1001.y $2$ $0.500$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-143}) \) None \(-1\) \(1\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots\)
1001.1.y.b 1001.y 1001.y $2$ $0.500$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-143}) \) None \(1\) \(1\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots\)
1001.1.y.c 1001.y 1001.y $8$ $0.500$ \(\Q(\zeta_{15})\) $D_{15}$ \(\Q(\sqrt{-143}) \) None \(-1\) \(-1\) \(0\) \(1\) \(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
1001.1.y.d 1001.y 1001.y $8$ $0.500$ \(\Q(\zeta_{15})\) $D_{15}$ \(\Q(\sqrt{-143}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
1001.1.bo.a 1001.bo 1001.ao $4$ $0.500$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1003.1.b.a 1003.b 1003.b $1$ $0.501$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1003}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots\)
1003.1.b.b 1003.b 1003.b $2$ $0.501$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
1003.1.f.a 1003.f 1003.f $2$ $0.501$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-59}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots\)
1003.1.f.b 1003.f 1003.f $4$ $0.501$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-59}) \) None \(0\) \(2\) \(2\) \(2\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
1003.1.h.a 1003.h 1003.h $4$ $0.501$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
1003.1.h.b 1003.h 1003.h $8$ $0.501$ \(\Q(\zeta_{24})\) $D_{24}$ \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1004.1.d.a 1004.d 251.b $1$ $0.501$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-251}) \) None \(0\) \(2\) \(-1\) \(-1\) \(q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots\)
1004.1.d.b 1004.d 251.b $6$ $0.501$ \(\Q(\zeta_{21})^+\) $D_{21}$ \(\Q(\sqrt{-251}) \) None \(0\) \(-2\) \(1\) \(1\) \(q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1005.1.p.a 1005.p 1005.p $4$ $0.502$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{3}q^{5}+\cdots\)
1005.1.p.b 1005.p 1005.p $4$ $0.502$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)
1007.1.d.a 1007.d 1007.d $1$ $0.503$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1007}) \) None \(-1\) \(-1\) \(0\) \(2\) \(q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}-q^{11}+\cdots\)
1007.1.d.b 1007.d 1007.d $1$ $0.503$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1007}) \) None \(1\) \(1\) \(0\) \(2\) \(q+q^{2}+q^{3}+q^{6}+2q^{7}-q^{8}-q^{11}+\cdots\)
1007.1.d.c 1007.d 1007.d $2$ $0.503$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-1007}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1007.1.d.d 1007.d 1007.d $2$ $0.503$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-1007}) \) None \(1\) \(1\) \(0\) \(-1\) \(q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1007.1.d.e 1007.d 1007.d $4$ $0.503$ \(\Q(\zeta_{15})^+\) $D_{15}$ \(\Q(\sqrt{-1007}) \) None \(-1\) \(-1\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1007.1.d.f 1007.d 1007.d $4$ $0.503$ \(\Q(\zeta_{15})^+\) $D_{15}$ \(\Q(\sqrt{-1007}) \) None \(1\) \(1\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1008.1.f.a 1008.f 7.b $1$ $0.503$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots\)
1008.1.u.a 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots\)
1008.1.u.b 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots\)
1008.1.u.c 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots\)
1008.1.y.a 1008.y 336.v $4$ $0.503$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
1008.1.y.b 1008.y 336.v $4$ $0.503$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{8}+\cdots\)
1008.1.bw.a 1008.bw 252.u $4$ $0.503$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1008.1.cd.a 1008.cd 28.g $2$ $0.503$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots\)
1008.1.cd.b 1008.cd 28.g $2$ $0.503$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots\)
1008.1.cg.a 1008.cg 7.d $2$ $0.503$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1008.1.dc.a 1008.dc 21.h $4$ $0.503$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
1008.1.dd.a 1008.dd 252.al $4$ $0.503$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)
1008.1.dt.a 1008.dt 112.u $8$ $0.503$ \(\Q(\zeta_{24})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots\)
1008.1.ed.a 1008.ed 336.at $8$ $0.503$ \(\Q(\zeta_{24})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\)
1011.1.c.a 1011.c 1011.c $1$ $0.505$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1011}) \) \(\Q(\sqrt{337}) \) \(0\) \(-1\) \(0\) \(2\) \(q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots\)
1011.1.c.b 1011.c 1011.c $1$ $0.505$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1011}) \) None \(0\) \(1\) \(-1\) \(-1\) \(q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
1011.1.c.c 1011.c 1011.c $1$ $0.505$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-1011}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
1011.1.c.d 1011.c 1011.c $2$ $0.505$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-1011}) \) None \(0\) \(-2\) \(0\) \(-2\) \(q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots\)
1011.1.f.a 1011.f 1011.f $2$ $0.505$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots\)
1011.1.f.b 1011.f 1011.f $4$ $0.505$ \(\Q(\zeta_{8})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
1011.1.l.a 1011.l 1011.l $4$ $0.505$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{3}+q^{4}+(-1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
1011.1.q.a 1011.q 1011.q $6$ $0.505$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-2\) \(q-\zeta_{14}^{6}q^{3}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots\)
1011.1.r.a 1011.r 1011.r $6$ $0.505$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\)
1011.1.y.a 1011.y 1011.y $12$ $0.505$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots\)
1011.1.bf.a 1011.bf 1011.af $24$ $0.505$ \(\Q(\zeta_{56})\) $D_{56}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{56}^{15}q^{3}+\zeta_{56}^{8}q^{4}+(\zeta_{56}^{6}-\zeta_{56}^{16}+\cdots)q^{7}+\cdots\)
1012.1.r.a 1012.r 253.k $20$ $0.505$ \(\Q(\zeta_{33})\) $D_{33}$ \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(2\) \(0\) \(q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots\)
1015.1.f.a 1015.f 1015.f $1$ $0.507$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \) \(\Q(\sqrt{29}) \) \(0\) \(0\) \(-1\) \(-1\) \(q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots\)
1015.1.f.b 1015.f 1015.f $1$ $0.507$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \) \(\Q(\sqrt{29}) \) \(0\) \(0\) \(1\) \(1\) \(q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots\)
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