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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
180.1.m.a 180.m 60.l $4$ $0.090$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots\)
240.1.bm.a 240.bm 240.am $4$ $0.120$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots\)
255.1.i.a 255.i 255.i $4$ $0.127$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\cdots\)
261.1.f.a 261.f 29.c $4$ $0.130$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
300.1.l.a 300.l 60.l $4$ $0.150$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\)
360.1.u.a 360.u 40.i $4$ $0.180$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
368.1.k.b 368.k 368.k $4$ $0.184$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-23}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
408.1.u.a 408.u 51.f $4$ $0.204$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{3}-\zeta_{8}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots\)
432.1.j.a 432.j 48.i $4$ $0.216$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\cdots\)
451.1.f.a 451.f 451.f $4$ $0.225$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
468.1.o.a 468.o 156.l $4$ $0.234$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+q^{13}+\cdots\)
30.2.e.a 30.e 15.e $4$ $0.240$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
496.1.j.b 496.j 496.j $4$ $0.248$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
520.1.bg.a 520.bg 520.ag $4$ $0.260$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{26}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{8}+\cdots\)
520.1.bo.a 520.bo 520.ao $4$ $0.260$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
525.1.k.a 525.k 105.k $4$ $0.262$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{105}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
527.1.f.a 527.f 527.f $4$ $0.263$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}+(-1+\zeta_{8}^{2})q^{5}+\cdots\)
35.2.f.a 35.f 35.f $4$ $0.279$ \(\Q(i, \sqrt{10})\) None None \(-4\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
595.1.u.a 595.u 595.u $4$ $0.297$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
600.1.q.a 600.q 120.q $4$ $0.299$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{30}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots\)
612.1.j.a 612.j 51.f $4$ $0.305$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{11}+q^{13}-\zeta_{8}^{3}q^{17}+\cdots\)
620.1.m.c 620.m 620.m $4$ $0.309$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots\)
620.1.m.d 620.m 620.m $4$ $0.309$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+(\zeta_{12}^{4}+\cdots)q^{7}+\cdots\)
39.2.f.a 39.f 39.f $4$ $0.311$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
660.1.v.a 660.v 165.l $4$ $0.329$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{3}q^{11}+\cdots\)
660.1.v.b 660.v 165.l $4$ $0.329$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{9}+\cdots\)
675.1.g.a 675.g 5.c $4$ $0.337$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}-q^{16}+\cdots\)
675.1.g.b 675.g 5.c $4$ $0.337$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{4}-\beta _{1}q^{7}-q^{16}-\beta _{2}q^{19}+\cdots\)
679.1.j.a 679.j 679.j $4$ $0.339$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{6}+\cdots\)
700.1.j.a 700.j 140.j $4$ $0.349$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{35}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\)
13.3.d.a 13.d 13.d $4$ $0.354$ \(\Q(i, \sqrt{10})\) None None \(-4\) \(-4\) \(8\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
45.2.f.a 45.f 15.e $4$ $0.359$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
720.1.r.a 720.r 80.k $4$ $0.359$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{8}+\cdots\)
720.1.bk.a 720.bk 60.l $4$ $0.359$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+(1-\zeta_{8}^{2})q^{13}-\zeta_{8}^{3}q^{17}+\cdots\)
748.1.i.a 748.i 187.f $4$ $0.373$ \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
765.1.j.a 765.j 255.i $4$ $0.382$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{8}+\cdots\)
765.1.j.b 765.j 255.i $4$ $0.382$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\cdots\)
765.1.m.a 765.m 85.f $4$ $0.382$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
765.1.o.a 765.o 85.g $4$ $0.382$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
765.1.r.a 765.r 85.i $4$ $0.382$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
768.1.i.a 768.i 48.i $4$ $0.383$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
768.1.i.b 768.i 48.i $4$ $0.383$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
780.1.t.a 780.t 195.j $4$ $0.389$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
780.1.bo.a 780.bo 195.u $4$ $0.389$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{3}+\zeta_{8}q^{5}+q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
785.1.h.a 785.h 785.h $4$ $0.392$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
785.1.j.a 785.j 785.j $4$ $0.392$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+\zeta_{8}q^{8}+\cdots\)
812.1.l.c 812.l 812.l $4$ $0.405$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{5}+\cdots\)
812.1.l.d 812.l 812.l $4$ $0.405$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}+\cdots\)
816.1.bc.a 816.bc 51.f $4$ $0.407$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots\)
15.3.f.a 15.f 5.c $4$ $0.409$ \(\Q(i, \sqrt{6})\) None None \(-4\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
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