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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
103.1.b.a 103.b 103.b $2$ $0.051$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-103}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots\)
104.1.h.a 104.h 104.h $1$ $0.052$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
104.1.h.b 104.h 104.h $1$ $0.052$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(1\) \(-1\) \(-1\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
107.1.b.a 107.b 107.b $1$ $0.053$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-107}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots\)
108.1.c.a 108.c 3.b $1$ $0.054$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots\)
111.1.d.a 111.d 111.d $1$ $0.055$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) \(\Q(\sqrt{37}) \) \(0\) \(1\) \(0\) \(-2\) \(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\)
111.1.d.b 111.d 111.d $2$ $0.055$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-111}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)
111.1.h.a 111.h 111.h $2$ $0.055$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
111.1.i.a 111.i 111.i $2$ $0.055$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
112.1.l.a 112.l 112.l $2$ $0.056$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots\)
116.1.d.a 116.d 116.d $1$ $0.058$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-29}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
116.1.d.b 116.d 116.d $1$ $0.058$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-29}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
116.1.j.a 116.j 116.j $6$ $0.058$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots\)
117.1.j.a 117.j 13.d $2$ $0.058$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots\)
119.1.d.a 119.d 119.d $2$ $0.059$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-119}) \) None \(-1\) \(-1\) \(-1\) \(2\) \(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
119.1.d.b 119.d 119.d $2$ $0.059$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-119}) \) None \(-1\) \(1\) \(1\) \(-2\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
120.1.i.a 120.i 120.i $2$ $0.060$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots\)
124.1.i.a 124.i 124.i $4$ $0.062$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
127.1.b.a 127.b 127.b $2$ $0.063$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-127}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots\)
128.1.d.a 128.d 8.d $1$ $0.064$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots\)
129.1.l.a 129.l 129.l $6$ $0.064$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\)
131.1.b.a 131.b 131.b $2$ $0.065$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-131}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots\)
133.1.m.a 133.m 133.m $4$ $0.066$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots\)
133.1.r.a 133.r 133.r $2$ $0.066$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
135.1.d.a 135.d 15.d $1$ $0.067$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots\)
135.1.d.b 135.d 15.d $1$ $0.067$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots\)
136.1.e.a 136.e 136.e $1$ $0.068$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots\)
136.1.j.a 136.j 136.j $2$ $0.068$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}+(-1-i)q^{3}-q^{4}+(-1+i+\cdots)q^{6}+\cdots\)
136.1.p.a 136.p 136.p $4$ $0.068$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
139.1.b.a 139.b 139.b $1$ $0.069$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-139}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q+q^{4}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
140.1.h.a 140.h 35.c $1$ $0.070$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(1\) \(1\) \(q-q^{3}+q^{5}+q^{7}-q^{11}-q^{13}-q^{15}+\cdots\)
140.1.h.b 140.h 35.c $1$ $0.070$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(-1\) \(-1\) \(q+q^{3}-q^{5}-q^{7}-q^{11}+q^{13}-q^{15}+\cdots\)
140.1.p.a 140.p 140.p $2$ $0.070$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
140.1.p.b 140.p 140.p $2$ $0.070$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(1\) \(-1\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
143.1.d.a 143.d 143.d $2$ $0.071$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-143}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
143.1.d.b 143.d 143.d $2$ $0.071$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-143}) \) None \(1\) \(-1\) \(0\) \(1\) \(q+(1-\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
144.1.g.a 144.g 4.b $1$ $0.072$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots\)
145.1.f.a 145.f 145.f $2$ $0.072$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{4}-iq^{5}+iq^{9}+(-1-i)q^{11}+\cdots\)
145.1.h.a 145.h 145.h $2$ $0.072$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{29}) \) \(0\) \(0\) \(0\) \(-2\) \(q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots\)
147.1.l.a 147.l 147.l $6$ $0.073$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots\)
148.1.f.a 148.f 37.d $2$ $0.074$ \(\Q(\sqrt{-1}) \) $S_{4}$ None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-iq^{11}+(-1-i)q^{17}+\cdots\)
148.1.i.a 148.i 148.i $2$ $0.074$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
148.1.p.a 148.p 148.p $6$ $0.074$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-3\) \(0\) \(q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots\)
151.1.b.a 151.b 151.b $3$ $0.075$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-151}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
152.1.g.a 152.g 152.g $1$ $0.076$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-38}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
152.1.g.b 152.g 152.g $1$ $0.076$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-38}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
152.1.k.a 152.k 152.k $2$ $0.076$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
152.1.u.a 152.u 152.u $6$ $0.076$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-2}) \) None \(0\) \(-3\) \(0\) \(0\) \(q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots\)
155.1.c.a 155.c 155.c $1$ $0.077$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\)
155.1.c.b 155.c 155.c $2$ $0.077$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
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