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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.1.b.a 23.b 23.b $1$ $0.011$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-23}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots\)
31.1.b.a 31.b 31.b $1$ $0.015$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
39.1.d.a 39.d 39.d $1$ $0.019$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)
44.1.d.a 44.d 11.b $1$ $0.022$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots\)
47.1.b.a 47.b 47.b $2$ $0.023$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-47}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
52.1.j.a 52.j 52.j $2$ $0.026$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
55.1.d.a 55.d 55.d $1$ $0.027$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\)
56.1.h.a 56.h 56.h $1$ $0.028$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots\)
57.1.h.a 57.h 57.h $2$ $0.028$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\)
59.1.b.a 59.b 59.b $1$ $0.029$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-59}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots\)
63.1.d.a 63.d 7.b $1$ $0.031$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(-1\) \(q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots\)
68.1.d.a 68.d 68.d $1$ $0.034$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots\)
68.1.f.a 68.f 68.f $2$ $0.034$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)
71.1.b.a 71.b 71.b $3$ $0.035$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-71}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
72.1.p.a 72.p 72.p $2$ $0.036$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
76.1.c.a 76.c 19.b $1$ $0.038$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
77.1.j.a 77.j 77.j $4$ $0.038$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
79.1.b.a 79.b 79.b $2$ $0.039$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-79}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots\)
80.1.h.a 80.h 20.d $1$ $0.040$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\)
83.1.b.a 83.b 83.b $1$ $0.041$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)
84.1.p.a 84.p 21.h $2$ $0.042$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)
87.1.d.a 87.d 87.d $1$ $0.043$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-87}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots\)
87.1.d.b 87.d 87.d $1$ $0.043$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-87}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)
88.1.l.a 88.l 88.l $4$ $0.044$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\)
93.1.l.a 93.l 93.l $4$ $0.046$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
95.1.d.a 95.d 95.d $1$ $0.047$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\)
95.1.d.b 95.d 95.d $2$ $0.047$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
99.1.h.a 99.h 99.h $2$ $0.049$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)
100.1.j.a 100.j 100.j $4$ $0.050$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots\)
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 \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\)
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