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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.1.b.a 23.b 23.b $1$ $0.011$ \(\Q\) \(\Q(\sqrt{-23}) \) 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 $1$ $0.015$ \(\Q\) \(\Q(\sqrt{-31}) \) 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 $1$ $0.019$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)
44.1.d.a 44.d 11.b $1$ $0.022$ \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots\)
55.1.d.a 55.d 55.d $1$ $0.027$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\)
56.1.h.a 56.h 56.h $1$ $0.028$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots\)
59.1.b.a 59.b 59.b $1$ $0.029$ \(\Q\) \(\Q(\sqrt{-59}) \) 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 $1$ $0.031$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(-1\) \(q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots\)
68.1.d.a 68.d 68.d $1$ $0.034$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots\)
76.1.c.a 76.c 19.b $1$ $0.038$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
80.1.h.a 80.h 20.d $1$ $0.040$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\)
83.1.b.a 83.b 83.b $1$ $0.041$ \(\Q\) \(\Q(\sqrt{-83}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)
87.1.d.a 87.d 87.d $1$ $0.043$ \(\Q\) \(\Q(\sqrt{-87}) \) 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 $1$ $0.043$ \(\Q\) \(\Q(\sqrt{-87}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)
95.1.d.a 95.d 95.d $1$ $0.047$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\)
104.1.h.a 104.h 104.h $1$ $0.052$ \(\Q\) \(\Q(\sqrt{-26}) \) 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 $1$ $0.052$ \(\Q\) \(\Q(\sqrt{-26}) \) 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 $1$ $0.053$ \(\Q\) \(\Q(\sqrt{-107}) \) 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 $1$ $0.054$ \(\Q\) \(\Q(\sqrt{-3}) \) 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 $1$ $0.055$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) \(\Q(\sqrt{37}) \) \(0\) \(1\) \(0\) \(-2\) \(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\)
116.1.d.a 116.d 116.d $1$ $0.058$ \(\Q\) \(\Q(\sqrt{-29}) \) 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 $1$ $0.058$ \(\Q\) \(\Q(\sqrt{-29}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
128.1.d.a 128.d 8.d $1$ $0.064$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots\)
135.1.d.a 135.d 15.d $1$ $0.067$ \(\Q\) \(\Q(\sqrt{-15}) \) 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 $1$ $0.067$ \(\Q\) \(\Q(\sqrt{-15}) \) 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 $1$ $0.068$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots\)
139.1.b.a 139.b 139.b $1$ $0.069$ \(\Q\) \(\Q(\sqrt{-139}) \) 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 $1$ $0.070$ \(\Q\) \(\Q(\sqrt{-35}) \) 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 $1$ $0.070$ \(\Q\) \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(-1\) \(-1\) \(q+q^{3}-q^{5}-q^{7}-q^{11}+q^{13}-q^{15}+\cdots\)
144.1.g.a 144.g 4.b $1$ $0.072$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots\)
152.1.g.a 152.g 152.g $1$ $0.076$ \(\Q\) \(\Q(\sqrt{-38}) \) 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 $1$ $0.076$ \(\Q\) \(\Q(\sqrt{-38}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
155.1.c.a 155.c 155.c $1$ $0.077$ \(\Q\) \(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\)
164.1.d.a 164.d 164.d $1$ $0.082$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(1\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots\)
171.1.c.a 171.c 19.b $1$ $0.085$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{57}) \) \(0\) \(0\) \(0\) \(-2\) \(q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots\)
172.1.b.a 172.b 43.b $1$ $0.086$ \(\Q\) \(\Q(\sqrt{-43}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{9}-q^{11}-q^{13}-q^{17}-q^{23}+\cdots\)
175.1.d.a 175.d 7.b $1$ $0.087$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\cdots\)
175.1.d.b 175.d 7.b $1$ $0.087$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}-q^{7}-q^{8}+q^{9}-q^{11}-q^{14}+\cdots\)
11.2.a.a 11.a 1.a $1$ $0.088$ \(\Q\) None None \(-2\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
176.1.h.a 176.h 11.b $1$ $0.088$ \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+q^{3}-q^{5}-q^{11}-q^{15}+q^{23}-q^{27}+\cdots\)
183.1.d.a 183.d 183.d $1$ $0.091$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-183}) \) \(\Q(\sqrt{61}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}-q^{4}+q^{9}-q^{12}-2q^{13}+q^{16}+\cdots\)
184.1.e.a 184.e 184.e $1$ $0.092$ \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-46}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\)
196.1.c.a 196.c 4.b $1$ $0.098$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\)
199.1.b.a 199.b 199.b $1$ $0.099$ \(\Q\) \(\Q(\sqrt{-199}) \) None \(-1\) \(0\) \(-1\) \(2\) \(q-q^{2}-q^{5}+2q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
200.1.g.a 200.g 8.d $1$ $0.100$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots\)
200.1.g.b 200.g 8.d $1$ $0.100$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots\)
203.1.c.a 203.c 203.c $1$ $0.101$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-203}) \) \(\Q(\sqrt{29}) \) \(0\) \(0\) \(0\) \(-1\) \(q+q^{4}-q^{7}-q^{9}+q^{16}-2q^{23}+q^{25}+\cdots\)
204.1.g.a 204.g 51.c $1$ $0.102$ \(\Q\) \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(1\) \(0\) \(q-q^{3}+q^{5}+q^{9}+q^{11}-q^{13}-q^{15}+\cdots\)
204.1.g.b 204.g 51.c $1$ $0.102$ \(\Q\) \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+q^{3}-q^{5}+q^{9}-q^{11}-q^{13}-q^{15}+\cdots\)
207.1.d.a 207.d 23.b $1$ $0.103$ \(\Q\) \(\Q(\sqrt{-23}) \) None \(1\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{8}-q^{13}-q^{16}-q^{23}+q^{25}+\cdots\)
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