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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
300.1.l.a 300.l 60.l $4$ $0.150$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\)
363.1.h.a 363.h 33.h $4$ $0.181$ \(\Q(\zeta_{10})\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{33}) \) \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{3}q^{9}-q^{12}+\cdots\)
525.1.k.a 525.k 105.k $4$ $0.262$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{105}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
525.1.be.a 525.be 105.w $8$ $0.262$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+\cdots\)
600.1.q.a 600.q 120.q $4$ $0.299$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{30}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots\)
600.1.q.b 600.q 120.q $8$ $0.299$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{6}q^{4}-\zeta_{24}^{4}q^{6}+\cdots\)
605.1.h.a 605.h 55.h $4$ $0.302$ \(\Q(\zeta_{10})\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots\)
605.1.l.a 605.l 55.k $8$ $0.302$ \(\Q(\zeta_{20})\) $D_{4}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{20}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
700.1.j.a 700.j 140.j $4$ $0.349$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{35}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\)
700.1.j.b 700.j 140.j $8$ $0.349$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\)
700.1.bf.a 700.bf 140.x $8$ $0.349$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
867.1.g.a 867.g 51.g $8$ $0.433$ \(\Q(\zeta_{16})\) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{7}q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{5}q^{7}+\cdots\)
900.1.bd.a 900.bd 180.v $8$ $0.449$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
961.1.h.a 961.h 31.h $8$ $0.480$ \(\Q(\zeta_{15})\) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(2\) \(0\) \(4\) \(-1\) \(q+\zeta_{30}^{3}q^{2}-\zeta_{30}^{10}q^{5}+\zeta_{30}^{11}q^{7}+\cdots\)
980.1.p.c 980.p 140.p $8$ $0.489$ \(\Q(\zeta_{24})\) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots\)
980.1.y.a 980.y 140.x $16$ $0.489$ \(\Q(\zeta_{48})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{2}q^{2}+\zeta_{48}^{4}q^{4}+\zeta_{48}^{5}q^{5}+\cdots\)
1089.1.k.a 1089.k 11.d $8$ $0.543$ 8.0.64000000.1 $D_{4}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{4}-\beta _{7}q^{7}-\beta _{1}q^{13}+\beta _{4}q^{16}+\cdots\)
1089.1.r.a 1089.r 99.n $8$ $0.543$ \(\Q(\zeta_{15})\) $D_{6}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-3\) \(0\) \(q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{11}+\cdots)q^{5}+\cdots\)
1089.1.s.a 1089.s 99.o $8$ $0.543$ \(\Q(\zeta_{15})\) $D_{3}$ \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-1\) \(0\) \(q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots\)
1089.1.s.b 1089.s 99.o $16$ $0.543$ 16.0.\(\cdots\).1 $S_{4}$ None None \(0\) \(-2\) \(-2\) \(0\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots\)
1156.1.g.a 1156.g 68.g $4$ $0.577$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\)
1156.1.g.b 1156.g 68.g $8$ $0.577$ \(\Q(\zeta_{16})\) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(-\zeta_{16}^{3}-\zeta_{16}^{7}+\cdots)q^{5}+\cdots\)
1176.1.s.c 1176.s 168.s $8$ $0.587$ \(\Q(\zeta_{24})\) $D_{4}$ \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)
1176.1.be.a 1176.be 168.ae $16$ $0.587$ \(\Q(\zeta_{48})\) $D_{8}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{4}q^{2}+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+\cdots\)
1200.1.bj.a 1200.bj 60.l $4$ $0.599$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}-2q^{21}+\cdots\)
1200.1.bj.b 1200.bj 60.l $8$ $0.599$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{3}+\zeta_{24}^{9}q^{7}+\zeta_{24}^{6}q^{9}+\cdots\)
1225.1.q.a 1225.q 35.l $4$ $0.611$ \(\Q(\zeta_{12})\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{4}-\zeta_{12}^{5}q^{9}+\zeta_{12}^{4}q^{11}+\cdots\)
1225.1.q.b 1225.q 35.l $8$ $0.611$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
1400.1.y.a 1400.y 280.y $4$ $0.699$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{70}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\)
1400.1.y.b 1400.y 280.y $8$ $0.699$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\)
1400.1.cf.a 1400.cf 280.ap $8$ $0.699$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{3}q^{7}+\cdots\)
1425.1.j.e 1425.j 285.j $4$ $0.711$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{285}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{9}+\zeta_{8}q^{12}+\cdots\)
1425.1.j.f 1425.j 285.j $4$ $0.711$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{57}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}-3\zeta_{8}^{2}q^{4}+2q^{6}+\cdots\)
1425.1.j.g 1425.j 285.j $8$ $0.711$ \(\Q(\zeta_{24})\) $D_{6}$ None \(\Q(\sqrt{57}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{9}q^{2}-\zeta_{24}^{3}q^{3}-q^{6}+(-\zeta_{24}^{7}+\cdots)q^{7}+\cdots\)
1425.1.be.a 1425.be 285.w $8$ $0.711$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
1425.1.be.b 1425.be 285.w $8$ $0.711$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}+\zeta_{24}q^{3}-\zeta_{24}^{8}q^{6}-\zeta_{24}^{9}q^{8}+\cdots\)
1425.1.cd.a 1425.cd 285.aj $24$ $0.711$ \(\Q(\zeta_{72})\) $D_{18}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{72}^{3}+\zeta_{72}^{35})q^{2}+\zeta_{72}^{13}q^{3}+\cdots\)
1425.1.cd.b 1425.cd 285.aj $24$ $0.711$ \(\Q(\zeta_{72})\) $D_{18}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{72}^{31}q^{3}+\zeta_{72}^{2}q^{4}+(\zeta_{72}^{5}+\zeta_{72}^{25}+\cdots)q^{7}+\cdots\)
1452.1.m.c 1452.m 33.h $8$ $0.725$ \(\Q(\zeta_{15})\) $D_{6}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{30}q^{3}+(\zeta_{30}^{8}+\zeta_{30}^{13})q^{5}+\zeta_{30}^{2}q^{9}+\cdots\)
1452.1.m.d 1452.m 33.h $8$ $0.725$ 8.0.324000000.3 $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{3}-\beta _{7}q^{7}+\beta _{6}q^{9}+\cdots\)
1500.1.l.a 1500.l 60.l $16$ $0.749$ \(\Q(\zeta_{40})\) $D_{10}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{40}^{5}q^{2}-\zeta_{40}^{11}q^{3}+\zeta_{40}^{10}q^{4}+\cdots\)
1500.1.l.b 1500.l 60.l $16$ $0.749$ \(\Q(\zeta_{40})\) $D_{10}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{11}q^{2}+\zeta_{40}^{5}q^{3}-\zeta_{40}^{2}q^{4}+\cdots\)
1575.1.ci.a 1575.ci 35.l $8$ $0.786$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{13}+\cdots\)
1575.1.cn.a 1575.cn 315.bf $8$ $0.786$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{9}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{7}+\cdots\)
1617.1.k.e 1617.k 231.k $16$ $0.807$ \(\Q(\zeta_{48})\) $D_{8}$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+(\zeta_{48}-\zeta_{48}^{7}+\cdots)q^{5}+\cdots\)
1620.1.p.b 1620.p 180.p $4$ $0.808$ \(\Q(\zeta_{12})\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.w.b 1620.w 180.v $8$ $0.808$ \(\Q(\zeta_{24})\) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}q^{5}+\cdots\)
1725.1.l.a 1725.l 345.l $4$ $0.861$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-23}) \) \(\Q(\sqrt{345}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-3\zeta_{8}^{2}q^{4}-2q^{6}+\cdots\)
1725.1.l.b 1725.l 345.l $8$ $0.861$ \(\Q(\zeta_{24})\) $D_{6}$ \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{4}q^{6}-\zeta_{24}^{9}q^{8}+\cdots\)
1725.1.l.c 1725.l 345.l $24$ $0.861$ \(\Q(\zeta_{72})\) $D_{18}$ \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{72}^{5}+\zeta_{72}^{13})q^{2}-\zeta_{72}^{19}q^{3}+\cdots\)
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